rH/5/ Digitized by the Internet Archive in^2007 with funding from IVIicrosoft Corporation http://www.archive.org/details/archbuildhandbookOOkiddrich THE ARCHITECTS' AND BUILDERS' HANDBOOK DATA FOR ARCHITECTS, STRUCTURAL ENGINEERS, CONTRACTORS, AND DRAUGHTS-MEN BY The Late FRANK E. KIDDER, C. E., Ph. D. AUTHOR OF "building CONSTRUCTION AND SUPERINTENDENCE" COMPILED BY A STAFF OF SPECIALISTS AND THOMAS NOLAN, M.S., A.M., Editor-in-Chief FELLOW OF THE AMERICAN INSTITUTE OF ARCHITECTS; PROFESSOR OF ARCHITECTURAL CONSTRUCriON, UNIVERSITY OF PENNSYLVANIA SEVENTEENTH EDITION, ENLARGED TOTAL ISSUE, EIGHTY-FIVE THOUSAND NEW YORK JOHN WILEY & SONS, Inc. London: CHAPMAN & HALL, Limited 1921 The Publishers and the Editor-in-Ch'.ef will be grateful to readers of this volume who will call attention to any errors of omission or commission therein. It is intended to make our publications standard works of study and reference, and, to that end, the greatest accuracy is sought. It rarely happens that the early editions of books are free from errors ; but it is the endeavor of the Publishers to have them removed, and it is therefore desired that the Editor- in-Chief may be aided in his task of revision, from time to time, by the kindly criticism of readers. JOHN WILEY & SONS, Inc. 432 Fourth Avenue, New York Copyright. 1884, 1892. 1897. 1904, BY FRANK E. KIDDER Copyright, 1908, BY KATHERINE E. KIDDER Copyright, 1915, 1921, BY KATHERINE E. KIDDER COMPOSITION, ELECrROrVPfNG, PRINTING AND BINDINr, BRAUNWORTH ft CO., BROOKLYN, N. Y. XTbis 3Booft IS RESPECTFULLY DEDICATED TO THOSE WHOSE KINDNESS HAS ENABLED ME TO PRODUCE IT TO MY PARENTS WHO GAVE ME THE EDUCATION UPON WHICH IT IS BASED TO MY WIFE FOR HER LOVING SYMPATHY, ENCOURAGEMENT AND ASSISTANCE TO ORLANDO W. NORCROSS OF WORCESTER, MASS. WHOSE SUPERIOR PRACTICAL KNOWLEDGE OF ALL THAT PERTAINS TO BUILDING HAS GIVEN ME A MORE INTELLIGENT AND PRACTICAL VIEW OF THE SCIENCE OF CONSTRUCTION THAN I SHOULD OTHERWISE HAVE OBTAINED * * Dedication to First Editicm, Ca^x'v ^:Ci EDITORIAL STAFF EDITOR-IN-CHIEF Thomas Nolan, Professor of Architectural Construction, University of Pennsylvania. ASSOCIATE EDITORS Herman C. Bp:rry, Professor of Materials of Construction, University of Pennsylvania. J. J. CoSGROVE, Consulting Sanitary Engineer. Robins Fleming, of the American Bridge Company, New York, N. Y. L. A. Harding, formerly Professor of Mechanical Engineering, Pennsyl- vania State College. Malverd a. Howe, Professor Emeritus of Civil Engineering, Rose Polytechnic Institute. F. H. KiNDL, Late Consulting Engineer, Pittsburgh, Pa. Rudolph P. Miller, Superintendent of Buildings, Borough of Man- hattan, New York, N. Y. Daniel E. Moran, Consulting Engineer, New York, N. Y. Emile G. Perrot, Member of American Society of Civil Engineers. N. A. Richards, of Purdy & Henderson, Inc., Civil Engineers, New York, N. Y. Edward F. Ries, Consulting Engineer, San Antonio, Texas. Grenvill^ T. Snelling, Formerly Instructor in Architectural Engineer- ing, Columbia University. A. P. Stradling, Manager, Philadelphia Suburban Underwriters' Association. W. H. TiMBiE, Associate Professor of Electrical Engineering, Mass- achusetts Institute of Technology. Charles P. Warren, Late Assistant Professor of Architecture, Columbia University. 46944T NOTE TO SEVENTEENTH EDITION With this edition the name is changed from Pocket-Book to Handbook. The work has been revised, some chapters rewritten, new chapters added, and a new Index made. Many cuts have been reengraved. The twenty-nine chapters of Part II have been revised where necessary to make the data agree with the latest research and practice, and two new chapters have been added, Chapter XXX, on Specifications for the Steelwork of Build- ings, by Robins Fleming, and Chapter XXXI, on Domical and Vaulted Struc- tures, by Edward F. Ries. Chapter XXIII, on Fireproofing of Buildings, and Chapter XXIV, on Reinforced-Concrete Construction, have been rewritten by Rudolph P. Miller. In Part III, the sections on Heating and Ventilation, and Chimney Construction, have been entirely rewritten by Louis A. Harding. The new chapters and sections 'nclude numerous practical exan pies of every- day problems, with solutions worked out in complete detail. In addition to the new chapters numerous new articles have been added to the text and illustrations of Part II, on the fol'owing subjects: New Data on Building Laws Relating to Loads on Masonry; Graphical Method of Determin- ing the Center of Gravity of Plane Figures or Sections; Graphical Method of Determining Moments of Inertia of Plane Figures; Triangular Loading; End Connections of Tension-Members: New Wire-Data; New Matter on Gauges; New Matter on Chains: Graphical Method of Determining the Deflection of Beams; Secondary Stresses; Angles Used as Beams; Data on Girderless Reinforced-Concrete Floors; Data on Tanks, and on Stresses in Cylindrical Tanks, etc. Other revisions and additions have been made, including new sections relating to the Registration of Architects, Standard Documents of the American Institute of Architects, Architectural Education, etc. In its revised, compact, and convenient form, the Editor believes that the work, more than ever before, will maintain its preeminence as the authoritative Handbook of Building-Construction. Philadelphia, July, 192 1. vi PREFACE TO SIXTEENTH EDITION The changes In the fifteenth edition, published in 1908, consisted principally of the rewriting of the two chapters on Fireproofing of Buildings and Reinforced Concrete. In 19 1 2 the undersigned was asked to undertake the revision of the entire book with the cooperation of a corps of Associate Editors, each highly qualified to render the necessary assistance in matters pertaining to his own work. On account of the comprehensive nature of the contents of the Pocket-Book, the many recent changes and rapid developments in different fields of architectural construction, and the consequent effect of such changes on the interrelated subjects treated, the Editor-in-Chief decided to rewrite and reset the entire book. After more than three years of arduous labor, in which the Associate Edi- tors and many other contributors have most ably and generously assisted, the New Kidder is about to be published. It was decided to retain Mr. Kidder's original arrangement of the subject- matter which is divided into three Parts, Part I dealing with practical applica- tions of Arithmetic, Geometry and Trigonometry, Part II with the Materials of Construction and the Strength and Stability of Structures, and Part III with miscellaneous useful information for architects and builders. Each of the twenty-nine chapters of Part II, however, has the name of the Associate Editor who revised or rewrote it printed with the chapter-caption. Part I has been carefully checked and much of the matter rearranged. The twenty-eight chapters of Part II have been rewritten and one new chapter has been added on Reinforced -Concrete Mill and Factory- Construction. Part III has been largely rewritten and all subjects retained have been thoroughly revised. To this part, also, much new matter has been added, such as extended tables of Specific Gravi- ties and Weights of Substances, Architectural Acoustics, Waterproofing for Foundations, the Quantity System of Estimating, the Standard Documents of the American Institute of Architects, Educational Societies of the World and extended lists of Architectural Schools, Books and Periodicals. The Editor-in-Chief has, with very few exceptions, personally checked on every page of manuscript, galley-proof and page-proof the equations, formulas, computations and problems, and has read or examined carefully every word, . figure and illustration, every detail of syntax, paragraphing, punctuation and typography, and every arrangement of tables, captions, classifications, notation, Table of Contents and Index. He is responsible for many changes in the form of presentation of data which it is hoped will add to the Pocket-Book still more of that efficiency and practical helpfulness for which it has been so long noted. Some of these changes may be briefly mentioned. The text has been e tirely reset; the type, while slightly smaller, is clearer and has the lines and paragraphs separated by wide leads; a special type is used for the tables; the paragraphing is revised throughout and every paragraph has a black-face type caption descriptive of the subject-matter; words in italics or with quotation-marks are seldom used, words in small caps taking their place; every chapter is divided into numbered chapter-subdivisions which are briefly descriptive of the classified matter; the number of cross- /lii rreface to Sixteenth Edition references is largely increased and the page-numbers of such references are almost always added; many tables and diagrams which in the former editions read lengthwise of the page have been reset or reengraved to read across the page for greater convenience; the number of illustrations has been largely increased, many old cuts reused have been reengraved, and some diagrams printed with lines of different colors to make the demonstrations clearer; a descriptive caption has been added to every illustration; the abbreviations Chap. I, Chap. II, etc., have been printed with each page-caption of the left-hand pages, thus avoiding the necessity of referring to the Table of Contents to locate any particular chapter. The Editor-in-Chief decided to change some of the unit stresses, especially those for the different woods, and in some cases to recommend more conservative values, and he believes that results based upon such stresses conform to the best engineering practice. This change necessitated the revision of many tables and problems throughout the book which had to be entirely recalculated. Numer- ous practical problems with complete solutions have been added. The deriva- tion of many of the formulas used has been explained, either in the body of the text or in extended foot-notes, for those who wish to understand as well as to use such formulas, and numerous cross-references accompanying them enable the reader to use the Pocket-Book as a textbook for certain parts of the mechanics of materials as well as a handbook for office work. The tables of the properties of structural shapes, of safe loads for columns, beams and girders, etc., have been revised and numerous new tables added. The Editor has found that it is the con- sensus of opinion among architects that the insertion of these tables is a great convenience and for their ordinary office work condenses into one handy vol- ume much of the essential data of several manufacturers' handl)ooks. The difficulty of securing a unity of treatment and of a-voiding repetitions and contradictions in a book of reference the data of which covers so many subjects and is written by so many contributors has been fully realized; but it is believed that in these respects the New Kidder is reasonably successful and will meet with the approval of all who use it. Acknowledgments and thanks are due the Associate Editors for their hearty cooperation and generous contributions of the time and labor taken from their professional work. Acknowledgment is made, also, of the valuable assistance of all others who have furnished new or revised old data, and of many helpful suggestions from Mrs. F. E. Kidder and from the publishers. The Editor-in-Chief expresses the hope that for the architects and builders of this country the new Pocket-Book will continue to be, as Mr. Kidder expressed it in his preface to the first edition in 1884, "a compendium of practical facts, rules and tables presented in a form as convenient for application as possible, and as reliable as our present knowledge will permit;" and also, in its present extension and fuller development, a work which will lead to a still clearer under- standing of the essential principles of sound architectural* construction. THOMAS NOLAN. Philadelphia, September, 1915. PREFACE TO FOURTEENTH EDITION It is now nearly twenty years since the author, then quite a young man, completed the first edition of this work, which, although containing but 586 pages, had required about three years for its preparation. At that time the author thought he had covered all of those practical details relating to the planning and construction of buildings, with which the architect was concerned, tolerably well, and it would appear as though the purchasers of the book thought so too, but as the years have come and gone, so many and such great improve- ments have taken place in the building world, so many articles invented, new methods of construction developed, higher standards established, that the present edition, although containing nearly three times as many pages, is perhaps not more complete, for the times, than was the first edition. When preparing the first edition, it was the aim of the author to give to architects and builders a handbook which should be, in its field, as useful ana reliable as Trautwine's had been to civil engineers; and with that object con- stantly in- view, the book has been revised from time to time to meet the changed conditions in building construction and equipment. About three years ago it was thought, by the publishers and the author, that a thorough and complete revision of the book should be undertaken, and although the re-writing of a work of this character, even with the thirteenth edition to work from, involved many months of close and constant application, the utiliza- tion of those hours which one ordinarily takes for recreation, and at the best' more or less interruption to his regular business, and consequent reduction in income, the writer undertook to prepare a work of a still wider scope, and which should be thoroughly up-to-date in every particular, or at least as far as is practicable, in a work requiring a period of three years in its preparation, and from that time to this he has spared no labor or expense to make the book as useful and complete as he possibly could, without making it too bulky. In this revision the author has had in view: I St. A reference-book which should contain some information on every subject (except design) likely to come before an architect, structural engineer, draughts- man, or master-builder, including data for estimating the approximate cost. 2d. To as thoroughly cover the subject of architectural engineering as is practicable in a handbook. 3d. To present all information in as simple and convenient a form for immedi- ate appHcation as is consistent with accuracy. To this end a great many new tables, arranged and computed by the author, have been inserted. At the time the first edition was written, the term "Architectural Engineering" had not been used in its present apphcation, and the term "Structural Engineer- ing," when used, referred almost exclusively to bridge work. To-day, structural and architectural engineers are concerned almost exclusively with building construction, and their work is more closely allied to that of the architect than to that of the civil engineer; hence the author has had in mind the needs of the structural engineer and draughtsman as well as those of the architect and builder, and the book should be of nearly equal value to both. X Preface to Fourteenth Edition Where it was impossible, for lack of space, to go extensively into any subject, references to other books or sources of information have been given, so that in this way the book may serve as a general index to the many hues of work, materials, and manufactured products entering into the planning, construction, and equipment of buildings. To attain the objects in view, it has been necessary to add considerably to the number of pages, but as experience has shown that the book is used principally at the desk o? draughting-table, and is seldom carried in the r>ocket, it is believed that the convenience of having everything in one book will more than offset any disadvantage resulting from increase in bulk. Nearly the entire book has been re-written, and great pains have been taken to furnish reliable data. A large number of experts in various Hnes have assisted the author, as is manifest by the foot-notes and references. To all of such, and to the many authors of technical works, and to the publishers of technical journals, who have kindly consented to the use of cuts and data, the author takes pleasure in acknowledging his indebtedness, x^lso to Mr. E. S. Hand, of New York, who, for many years, has rendered material assistance in collecting data along the line. of manufactured products. The names and addresses of manufacturers have been given solely for the convenience of the users of the book, and not for any pecuniary considerations; in fact, if money considerations had solely appealed to the writer, this book would never have been re-written, because a technical work of this character can never adequately compensate, in money, for the time, labor, and thought required in its preparation. The many words of appreciation which have come to the author from hundreds of those who have found the book useful have been a great stimulus to further increase its usefulness. As in the former prefaces, the author requests that any one discovering errors in the work or who may have any suggestions looking to the further improve- ment of the book, will communicate the same to him, that the book may be made as complete and reliable as possible. Finally, the author desires to acknowledge his indebtedness to the publishers, who have heartily seconded his efforts in every particular, and who have spared no pains or expense to make a jjerfect handbook. F. E. KIDDER. Denver, Colo., July i8th, 1904. CONTENTS PART I PRACTICAL ARITHMETIC, GEOMETRY, AND TRIGONOMETRY PAGE Arithmetical Signs and Characters 3 Involution ; 3 Evolution, Square Root, Cu^e Root, Rules, and Tables 4 Weights and Measures 25 The Metric System 30 Metric Conversion Tables 32 Scripture and Ancient Measures and Weights 34 Geometry and Mensuration 36 Geometrical Problems 66 Table of Chords 81 Hip and Jack-Rai-ters 90 Trigonometry Formulas and Tables 90 PART II STRENGTH OF MATERIALS AND STABILITY OF STRUCTURES Introduction 121 Explanation of Notation and Symbols . 122 CHAPTER I EXPLANATION OF TERMS USED IN ARCHI- TECTURAL ENGINEERING THOMAS NOLAN professor of architectural construction, university of PENNSYLVANIA 1. Definitions of Some of the Terms Used in Mechanics of Materials . . 124 2. Classifications of the Principal Stresses Caused in Bodies by External Forces 12" CHAPTER II FOUNDATIONS by DANIEL E. MORAN member of AMERICAN SOCIETY OF CIVIL ENGINEERS 1. Definition of the W^ord and Terms Used 129 2. General Requirements 129 3. Geological Considerations 130 xi xii Contents PAGE 4. Composition and Classification of Rocks 130 5. Geology of Earthy Material 132 6. Materials Composing Foundation-Beds 134 7. Characteristics of the Materials of Foundation-Beds 135 8. Allowable Loads on Materials o^ Foundation-Beds 140 9. Unit Loads on Foundation-Beds Allowed by Building Codes .... 142 10. Investigation of th^ Site 142 11. Loading-Tests 145 12. Topographical and Specl\l Conditions 146 13. Loads Comng on the Footings 148 14. Assumed Loads Specifled by Building Codes 151 15. Proportioning Supporting Areas for Equal Settlement 152 16. Determining the Supporting Areas 160 17. Offset Footings 163 18. The Use of Cantilevers in Foundations 165 19. Stresses in Footing Courses 169 20. Methods of Calculating B ending-Stresses in Wall-Footings ... 172 21. Bending Moments in Footings of Columns and Piers 176 22. Design of the Footings 178 23. Steel Grillage in Foundations 181 24. Reinforced Concrete Footings 186 25. Timber Footings for Temporary Buildings ... 186 26. GexNeral Conditions Affecting Foundations and Footings .... 188 27. Wooden-Pile Foundations 188 28. Concrete-Pile Foundations 196 29. Foundation Piers and Foundation Walls 200 30. Methods of Excavating for Foundations 200 31. Protection of Adjoining Structures 214 CHAFfER III MASONRY WALLS. FOOTINGS FOR LIGHT BUILDINGS. CEMENTS AND CONCRETES by THOMAS NOLAN professor of architectural construction, university of pennsylv.^nia ' 1. Footings FOR Light Buildings 223 2. Cellar Walls and Basement Walls 228 3. Walls of the Superstructure 229 4. Natural Cements 235 5. Artificial Cements 236 6. Concrete 240 CHAPTER IV RETAINING-WALLS, BREAST-WALLS, AND VAULT-WALLS BY GRENVILLE TEMPLE SNELLING late member of AMERICAN INSTITUTE OF ARCHITECTS 1. Mechanical Principles Involved 252 2. Retaining-Walls 255 3. Breast-Walls 262 4. Vault-Walls . 263 I Contents xiii CHAPTER V STRENGTH OF BRICK, STONE, MASS-CONCRETE, AND MASONRY BY THOMAS NOLAN PROFESSOR OF ARCHITECTURAL CONSTRUCTION, UNIVERSITY OF PENNSYLVANIA PAGE 1. Crushing Strength of Stonework, Brickwork, Bricks, Etc 265 2. Strength of Terra-Cotta and Terra-Cotta Piers 276 3. Crushing Strength of Building Stones . . . ,. 279 ,4. Compressive Strength of Mortars and Concretes 282 ' 5. Building Laws for Working Loads on Masonry 287 CHAPTER VI FORCES AND MOMENTS BY MALVERD A. HOWE emeritus professor of civil engineering, rose polytechnic institute 1. Composition and Resolution of Forces 288 2. Moments of Forces 289 3. Center of Gravity 291 CHAPTER VII STABILITY OF PIERS AND BUTTRESSES BY GRENVILLE TEMPLE SNELLING late member of american institute of architects 1. Mechanical Principles Involved 297 2. Buttresses with Offsets 298 3. Line of Pressure or Line of Resistance 300 4. Method of Moments 301 5. Graphical Method 303 CHAPTER VIII THE STABILITY OF MASONRY ARCHES BY GRENVILLE TEMPLE SNELLING late MEMBER OF AMERICAN INSTITUTE OF ARCHITECTS 1. Arches. Definitions 305 2. Brick Arches 306 3. Centers for Arches 308 4. Keystones 309 5. Graphical Determination of the Stability of Arches 311 xiv Contents CHAPTER IX REACTIONS AND BENDING MOMENTS FOR BEAMS BY CHARLES P. WARREN LATE ASSISTANT PROFESSOR OF ARCHITECTURE, COLUMBIA UNIVERSITY PAGE 1. Reactions for Beams 322 2. Bending Moments in Beams 324 3. Bending Moments in Beams for Different Kinds of Loading .... 325 4. Graphic Method for Determining Bending Moments in Beams . . 328 5. Reactions and Bending Moments for Beams with Triangular Loading AND for Beams Fixed at Both Ends 331 CHAPTER X PROPERTIES OF STRUCTURAL SHAPES, MOMENT OF INERTIA, MOMENT OF RESISTANCE, SEC- TION-MODULUS, AND RADIUS OF GYRATION BY CHARLES P. WARREN LATE assistant PROFESSOR OF ARCHITECTURE, COLUMBIA UNIVERSITY 1. The Properties of Cross-Sections 332 2. Areas, Moments of Inertia, Section-Moduli, and Radii of Gyration of Elementary Sections , 334 3. Transferring Moments of Inertia to Other Parallel Axes . . , 338 4. Moments of Inertia of Compound Sections 339 5. Radii of Gyration of Compound Sections ... 344 6. Graphical Method of Determining the Moment of Inertia of Plane Figures -"^^S 7. Dimensions^ Moments of Inertia, Radii of Gyration, and Section-Moduli OF Standard Strucpural Shapes 352 CHAPTER XI RESISTANCE TO TENSION, PROPERTIES OF IRON AND STEEL BY HERMAN CLAUDE BERRY professor of materials of construction, university of PENNSYLVANIA 1. Definitions, Working Stresses, and Examples . . -. 375 2. Wrought Iron 377 3. Cast Iron 379 4. Steel 380 5. Standard Specifications for Structural Steel for Buildings . . . 383 6. Tension-Members 385 7. Wire f29 Wire Rope 404 9. Cotton, Hemp, and Manila Rope 406 10. Ch.ains 408 Contents xv CHAPTER XII RESISTANCE TO SHEAR. RIVETED JOINTS. PINS AND BOLTS BY HERMAN CLAUDE BERRY PROFESSOR OF MATERIALS OF CONSTRUCTION, UNIVERSITY OF PENNSYLVANIA PAGE 1. Shear 411 2. Riveted Joints 413 3. Strength of Pins in Trusses 423 4. Strength of Bolts in Wooden Trusses and Girders 429 CHAPTER XIII BEARING-PLATES AND BASES FOR COLUMNS, BEAMS, AND GIRDERS. BRACKETS ON CAST-IRON COLUMNS BY HERMAN CLAUDE BERRY professor of materials of construction, university of PENNSYLVANIA 1. Bearing-Plates and Bases 440 2. Bearing-brackets on Cast-iron Columns 445 CHAPTER XIV STRENGTH OF COLUMNS, POSTS, AND STRUTS BY CHARLES P. WARREN late assistant professor of architecture, COLUMBIA UNIVERSITY 1. General Principles and Definitions 448 2. Strength of Short Wooden Columns 448 3. Strength of Wooden Columns or Struts Over Ten Diameters in Length. Formulas . . . . 449 4. Tables of Safe Loads for Wooden Columns 450 5. Eccentric Loading of Wooden Columns 453 6. Metal Caps and Bolsters for Wooden Columns 454 7. Crushing of Wood Perpendicular to the Grain 454 8. Cast-Iron Columns 455 9. Design of Cast-Iron Columns . 456 10. Strength of Cast-iron Columns. Formulas 459 11. Tables of Safe Loads for Cast-Iron Columns. Examples ..... 461 12. Types, Forms, and Connections of Steel Columns 467 13. Strength of Steel Columns. Formulas 480 14. Design of Steel Columns. Examples. 482 15. Eccentric Loading of Steel Columns 485 16. Tables of Safe Lo.ads for Steel Columns 488 xvi Contents CHAPTER XV STRENGTH OF BEAMS AND BEAM GIRDERS. FRAMING AND CONNECTING STEEL BEAMS BY CHARLES P. WARREN LATE ASSISTANT PROFESSOR OF ARCHITECTURE, COLUMBIA UNIVERSITY PAGE 1. General Principles of tue Flexure of Beams 555 2. Formulas for Safe Loads for Beams for Different Conditions of Load- ing AND Support 558 3. Steel Beams and Girders 564 4. Tables of Safe Loads for Steel Beams and Girders. Examples . . 570 Oblique Loading of I Beams and Channels. Tables 573 Oblique Loading of Angles used as Beams 593 5. Framing and Connecting Steel Beams and Girders 612 CHAPTER XVI STRENGTH OF CAST-IRON LINTELS AND WOODEN BEAMS BY F. H. KINDL late corresponding member AMERICAN INSTITUTE' OF ARCHITECTS 1. Cast-Iron Lintels 620 2. Sections, Stresses, Buckling, AND Deflection of Wooden Beams . . . 627 3. Constants and Coefficients for Beams 628 4. Flexural Strength of Wooden Beams 629 5. Application OF Formulas FOR Flexural. Strengths of Wooden Beams . 631 6. Flexural Strength of Beams 633 7. Tables for Strength and Stiffness of Wooden Beams 635 8. Working Unit Stresses for Woods 647 9. Working Unit Stresses FOR Woods. Taken from Building Laws . . . 647 CHAPTER XVII STRENGTH OF BUILT-UP, FLITCHED, AND TRUSSED WOODEN GIRDERS BY F. H. KINDL late corresponding member AMERICAN INSTITUTE OF ARCHITECTS 1. Built-Up Wooden Girders 652 2. Flitched Beams or Flitch-Plate Girders 655 3. Trussed Beams and Girders 666 Contents xvii CHAPTER XVIII STIFFNESS AND DEFLECTION OF BEAMS BY CHARLES P. WARREN LATE ASSISTANT PROFESSOR OF ARCHITECTURE, COLUMBIA UNIVERSITY PAGE 1. General Principles of the Deflection of Beams 663 2. Formulas for Loads, Based upon the Stiffness of Beams 665 3. Relative Stiffness of Beams 666 4. Cylindrical Beams 667 5. 'Safe Loads for Wooden Beams FOR A Given Deflection 667 6. Nominal and Standard Sizes of Wooden Beams 667 7. Deflection OF Steel Beams . 668- 8. Graphical Determination of Deflection of Beams 670 I CHAl^ER XIX STRENGTH AND STIFFNESS OF CONTINUOUS GIRDERS BY CHARLES P. WARREN LATE assistant PROFESSOR OF ARCHITECTURE, COLUMBIA UNIVERSITY 1. General Considerations 671 2. Supporting Forces or Reactions of Continuous Girders 671 3. Bending Moments of Continuous Girders 673 4. Deflection of Continuous Girders 674 5. Notes on Reactions, Strength, and Stiffness of Continuous Girders . 675 ' 6. Formulas for the Strength and Stiffness of Continuous Girders . . 676 7. Continuous Girders in Grillage Foundations 678 CHAPTER XX RIVETED STEEL PLATE AND BOX GIRDERS BY CHARLES P. WARREN late assistant professor of architecture, COLUMBIA UNIVERSITY 1. General Notes on Plate and Box Girders . . 681 2. Details of (Construction of Plate and Box Girders 682 3. Design of Plate and Box Girders 683 4. Explanation of Tables 688 5. Examples of Plate and Box Girders 688 6. Tables Used in the Design of Plate and Box Girders 702 CHAPTER XXI STRENGTH AND STIFFNESS OF WOODEN FLOORS BY THOMAS NOLAN professor of architectural construction, university of PENNSYLVANIA 1. Loads on Floors and Weights of Floor-Construction 717 2. Tables of Weights of Merchandise 721 3. Determination of Sizes of Joists, Beams, or Girders 724 xviii Contents. PAGE 4. Safe Loads for Plank Flooring 732 5. Tables for Maximum Spans for Floor-Joists 737 6. Determination of Strength of an Existing Floor 746 7. Details of Floor-Framing 749 8. Stirrups and Joist-Hangers 750 9. Comparative Strength of Different Types of Joist-Hangers .... 756 CHAPTER XXII WOODEN MILL AND WAREHOUSE- CONSTRUCTION BY A. P. STRADLING manager, PHILADELPHIA SUBURBAN UNDERWRITERS' ASSOCIATION 1. Mill-Construction 758 2. What Mill-Construction Is 758 3. What Mill-Construction Is Not 759 4. Standard Mill-Construction 760 5. Belts, Stairways and Elevator- Towers 764 6. Standard Storehouse-Construction 765 7. Example of One-Story Workshop 769 8. Saw-Tooth Roof-Construction 772 9. Mill-Construction as Applied to Warehouses 777 10. Steel and Iron Structural Members in Warehouse-Construction . . 780 11. Structural Details of Mill-Construction as Applied to Factories and Warehouses 782 12. Connection of Floor-Beams and Girders 789 13. Wall Supports and Anchors for Joists and Girders 792 14. Weakness of Wrought-Iron Stirrups when Exposed to Fire .... 794 15. Post and Girder-Connections 795 16. Form and Material of Post-Caps 795 17. Roofing-Materials 800 18. Partitions 801 19. Doors and Shutters 801 20 Fire-Protection 801 21 Cost of Mills and Factories Built on the Slow-Burning Principle . 802 22. Cost of Brick Mill-Buildings of Slow-Burning Construction . . 808 CHAPTER XXIII FIREPROOFING OF BUILDINGS by RUDOLPH P. MILLER superintendent of buildings, borough of MANHATTAN, NEW YORK CITY 1. Definitions, Areas, Heights, AND Costs 811 2. Fire-Resistance of Materials 814 3. Column-Protection 822 4. Fire-Proof Floor-Construction 826 5. Fire-Proof Roof-Construction 866 6 Partitions and Wall-Coverings .... 873 7. Fire-Proof Flooring 892 8. Interior Finish and Fittings 893 9. Protection from Outside Hazard 001 10. Extinguishing Devices and Precautionary Measures 9( :-, Contents CHAPTER XXIV REINFORCED-CONCRETE CONSTRUCTION RUDOLPH P. MILLER SUPERINV NDENT OF BUILDINGS, BOROUGH OF MANHATTAN, NEW YORK CITY PAGE 1. Introductory Notes 906 2. Materials Used in Rfinforced-Concrfte Construction 907 3. Design of R fin forced-Concrete Construction 924* 4. Types of Reinforced-Concrete Construction 948 5. Fire- Resistance of Reinforced-Concrete Construction 955 6. Protection Against Corrosion in Reinforced-Concrete Construction 960 7. Erection of Reinforced-Concrete Constructtion 962 CHAPTER XXV REINFORCED-CONCRETE FACTORY AND MILL- CONSTRUCTION BY EMILE G. PERROT MEMBER of AMERICAN SOCIETY OF CIVIL ENGINEERS 1. General Principles and Details 968 2. Design of Floor System 971 3. Design of Spandrel Beams 975 4. Columns and Piers 976 5. Foundations and Footings 978 6. Stair-Design 983 7. Diagrams and Formulas for Beams and Slabs 984 8. Girderless Floors 993 CHAPTER XXVI TYPES OF ROOF-TRUSSES BY MALVERD A. HOWE professor emeritus of civil engineering, rose POLYTECHNIC INSTITUTE 1. Definitions 998 2. Types of Wooden Trusses 998 3. Types of Steel Trusses 1025 4. Arched Trusses 1035 5. Cantilever Trusses 1043 CHAPTER XXVII STRESSES IN ROOF-TRUSSES BY MALVERD A. HOWE professor emeritus of civil engineering, rose polytechnic institute 1. Roof-Loads. Data, Weights Materials, Methods 1046 2. Examples of the Computation of Roof-Loads 1054 3. Determination of Stresses by Computation 1058 XX Contents PAGE 4. Examples Showing Use of Tables in Stress-Computations .... 1065 5. Determination of Stresses in Roof-Trusses by Graphic Methods . . 1065 6. Determination of Wind-Load Stresses 1109 7. Trusses with Knee-Braces 1116 8. Arched Trusses 1118 9. Trussed Arches 1121 10. Arches with Solid Ribs 1132 11. Influence-Lines for Simple Be.ams and Trusses 1134 12. Secondary Stresses IN Truss-Members 1137 CHAKPER XXVIII DESIGN AND CONSTRUCTION OF ROOF- TRUSSES BY MALVERD A. HOWE professor emeritus of CIVIL ENGINEERING, ROSE POLYTECHNIC INSTITUTE 1. Design of Wooden Trusses 1138 2. Design of Steel Trusses 1144 3. Joints of W^ooden Trusses 1149 4. Joints of Steel Trusses 1160 5. Purlins and Purlin-Connections 1169 CHAPTER XXIX WIND-BRACING FOR TALL BUILDINGS BY N. A. RICHARDS OF PURDY & HENDERSON, INC., CIVIL ENGINEERS 1. Data for Wind-Pressure. Building Laws 1171 2. Conditions Determining or Affecting Wind-Bracing 1172 3. General Theory of Wind-Bracing 1173 4. Arrangement of Wind-Bracing 1174 5. Types of Wind-Bracing 1174 6. Computation of Wind-Stresses 1176 7. Illustration of Method of Coatputing Wind-Stresses 1176 8. Analysis of Stresses in Different Types of Wind-Bracing . . . 1179 9. Combination of Dead and Live Loads, with Wind-Load . . , . 1183 10. Wind-Bracing of Water-Towers and Similar Structures .... 1184 11. Recent Examples of Wind-Bracing in Tall Buildings 1187 CHAPTER XXX SPECIFICATIONS FOR THE STRUCTURAL STEELWORK OF BUILDINGS. DATA ON STRUCTURAL STEEL by ROBINS FLEMING OF THE american bridge company, new york, n. y. 1. General 1194 2. M.\terial 1195 3. Loads 1196 Contents xxi PAGE 4. Stresses 1199 5. Design 1201 6. Details 1202 7. Workmanship 1202 8. Painting 1203 9. Inspection 1203 10. Erection 1203 Data on Structural Steel 1204 CHAPTER XXXI DOMICAL AND VAULTED STRUCTURES BY EDWARD F. RIES consulting engineer, SAN ANTONIO, TEXAS 1. Domes • . . 1213 (i) Smooth-Shell Domes 1213 (2) Ribbed Domes . 1222 2. Vaults 1231 (1) Barrel Vaults 1231 (2) Groined Vaults 1235 (3) Ribbed Vaults 1240 PART III USEFUL INFORMATION FOR ARCHITECTS, BUILDERS, AND SUPERINTENDENTS HEATING AND VENTILATION OF BUILDINGS BY LOUIS A. HARDING formerly professor of mechanical engineering, PENNSYLVANIA STATE COLLEGE Physical Units and the Measurement of Heat 1247 Heat 1249 Steam ^_^ 1.251 Properties of Air 7 . 1254 Estimating Heating Requirements of Buildings 1256 Radiation 1264 Fuels and Combustion 1271 Steam-Heating Boilers and Hot-Water Boilers .• . . 1273 Direct Steam Heating 1283 Design of Low-Pressure Steam-Heating Systems 1291 Gravity Indirect Heating 1298 Direct Hot-Water Heating 1202 Furnace Heating 1310 The Design of a Furnace-Heating System 1312 Hot-Blast Heating " 1324 Hot-Blast Heaters 1329 Design of Air-Ducts 1333 Ventilating-Fans 1341 Application of Hot-Blast Heating Data 1342 Ventilation 1348 State Ventilation Laws and Requirements 1364 Specifications for Furnace-work 1357 Specifications for Hot-Water Heating-Apparatus in a Residence . . . 1359 Specifications for a Low-Pressure Steam-Heating Apparatus for Heating BY Direct Radiation 1361 xxiv Contents PAGE Vacuum-Cleaning 1708 Waterproofing for Foundations 1709 Force of the Wind 1717 Copies of Architects' Tr^vcings . 1718 Horse-Power, Pulleys, Gears, Belting, .\nd Shafting 1720 Chain-Blocks, Hoists, and Hooks 1723 Bells 1725 Symbols for the Apostles and Saints 1727 A Circular of Advice on Professional Practice by the American Institute of Architects 1727 Architectural Competitions 1733 Standard Documents of the American Institute of Architects .... 1748 Registration of Architects 1768 Educational Institutions Giving Courses in Architecture 1779 Architectural Societies 1788 Glossary 1 796 Architectural Terms Used in Law 1851 PART I PRACTICAL ARITHMETIC, GEOMETRY AND TRIGONOMETRY RULES, TABLES AND PROBLEMS Involution and Evolutiou 3 1. PRACTICAL ARITHMETIC Mathematical Signs and Characters* The following signs and characters are generally used to denote and abbrevi- ate the several mathematical operations: The sign = means equal to, or equality; — means minus or less, or subtraction; + means plus, or addition; X means multiphed by, or multiplication; -7- or/ means divided by, or division; are indexes or powers, meaning that the number to which they are added is to be squared (2) or cubed {^) ; : is to ) : : so is > are signs of proportion; :to ) \/ is the RADICAL SIGN and means that the square root of the num- ber before which it is placed is to be extracted; \^ means that the cube root of the number before which it is placed is to be extracted; the BAR indicates that all the numbers under it are to be taken together; ( ) the PARENTHESIS means that all the numbers between are to be taken as one quantity; . means decimal parts; thus, 2.5 means 2M0, 0.46 means *Moo. ° means degrees, ' minutes and " seconds; .*. means hence; ' means feet; " means inches. Involution To Square a Number, multiply the number by itself, and the product will be the square; thus, the square of 18 = 18^ = 18 X 18 = 324. The Cube of a Number is the product obtained by multiplying the number by itself, and that product by the number again; thus, the cube of 14 = 14^ = 14 X 14 X 14= 2 744. The Fourth Power of a Number is the product obtained by multiplying the number by itself four times; thus, the fourth power of 10 = 10'* = 10 X 10 X 10 X 10= 10 000. Evolution Square Root. Rule for extracting the square root of a number: (i) Divide the given number into periods of two figures each, commencing at the right if it is a whole number, and at the decimal point if there are decimals; thus, 10236.81 26. (2) Find the largest square in the left-hand period, and place its root in the quotient; subtract the said square from the left-hand period, and to the re- mainder bring down the next period for a new dividend. (3) Double the root already found, and annex one cipher for a trial-divisor; see how many times it will go in the dividend, and put the number in the quotient * See, also, pages 122 and 123, Part 11. 4 Practical Arithmetic Part 1 and also in place of the cipher in the divisor. Multiply this final divisor by the number in the quotient just found, subtract the product from the dividend, and to the rero-ainder bring down the next period for a new dividend and proceed as before. If it should be found that the trial divisor cannot be contained in the dividend, bring doM'n the next period for a new dividend, annex another cipher j to the trial divisor, put a cipher in the quotient and proceed as before. Example. 10236.81 26 (101.17, the square root I 201)0236 201 2021)3581 2021 20227)156026 141589 14437 Cube Root. To extract the cube root of a number, point off the numbel from right to left into periods of three figures each, and, if there is a decimal, commence at the decimal point and point off into periods, going both ways. Ascertain the highest root of the first period, and place it to the right of the number, as in Long division^ cube the root thus found and subtract from the first period; to the remainder annex the next period; square the root already found, multiply by three and annex two ciphers for the trial divisor. Find how many times this trial divisor is contained in the dividend and write the result in the root. Add together the trial divisor, three times the product of the first figure of the root by the second with one cipher annexed, and the square of the second figure in the root; multiply the sum by the last figure in the root, and subtract from the dividend; to the remainder annex the next period and proceed as before. When the trial divisor is greater than the dividend, write a cipher in the root, annex the next period to the dividend and proceed as before. Example. Required, the cube root of 493039 or ■v^493039 493039(79, the cube root 7 X 7 X 7 = 343 7X7X3= 14700 7X9X3= 1890 9X9= 81 1 667 1 150039 150039 Example. Required, the cube root of 403583.419 or -v^403583.4ic 403583-4 1 9 (73 •9» the cube roo* 7X7X7 = 343 7X7X3= 14700 7X3X3= 630 3X3= 9 15339 73 X 73 X 3 = 1598700 73 X 9X3= 19710 9X9 = 81^ 1618491 60583 46017 14566419 14566419 "Evolution Example. Required, tlie cube r6dt of 158252.632929 or ^158252 632929 158252.632929(54.09, the cube root 5X 5X5 = 125 5X5X3= = 7500 5X4X3= 600 4X4 = 16^ 8116 540 X 540 X 3 = 87480000 540 X 9X3= 145800 9X9= 81 87625881 33252 32464 788632929 788632929 TABLES OF SQUARES, CUBES, SQUARE ROOTS, CUBE ROOTS AND RECIPROCALS From I to 1054 The following table, taken from Searle's Field Engineering, will be found of great convenience in finding the square, cube, square root, cube root and reciprocal of any number from i to 1054. The reciprocal of a number is the quotient obtained by dividing i by the number. Thus, the reciprocal of 8 is i -h 8 = 0.125. Practical Arithmetic No. Squares Cubes Square roots Cube roots Reciprocals 1 1 1 1.0000000 1.0000000 1.000000000 2 4 '8 1.4142136 1.2599210 .500000000 3 9 27 1 . 7320508 1.4422496 .333333333 4 16 64 2 . 0000000 1.5874011 .250000000 5 25 125 2.2360680 1.7099759 .200000000 6 36 216 2.4494897 1.8171206 . 166666667 7 49 343 2.6457513 1.9129312 .142857143 8 64 512 2.8284271 2.0000000 .125000000 9 81 729 3.0000000 2.0800837 .111111111 10 100 1000 3.1622VVV 2.1544347 . 100000000 11 121 1331 3.3166248 2.2239801 .090909091 12 144 1728 3.4641016 2.2894286 .083333333 13 169 2197 3.6055513 2.3513347 .076923077 14 196 2744 3.7416574 2.4101422 .071428571 15 225 3375 3.8729833 2.4662121 .066666667 16 256 4096 4.0000000 2.5198421 .062500000 17 289 4913 4.1231056 2.5712816 .058823529 18 324 5832 4.2426407 2.6207414 .055555556 19 361 6859 4.3588989 2.6684016 .052631579 20 400 8000 4.4721360 2.7144177 .050000000 21 441 9261 4.5825757 2 . 7589243 .047619048 22 484 10648 4.6904158 2.8020393 .045454545 23 529 12167 4.7958315 2.8438670 .043478261 24 676 13824 4.8989795 2.8844991 .041666667 25 625 15625 5.0000000 2.9240177 .040000000 26 676 17576 5.0990195 2 . 9624960 .038461538 27 729 19683 5.1961524 3.0000000 .037037037 28 784 21952 5.2915026 3.0365889 .035714286 29 841 24389 6.3851648 3.0723168 .034482759 30 900 27000 6.4772256 3.1072325 .033333333 31 961 29791 6.5677644 3.1413806 .032258065 32 1024 32768 5.6568542 3.1748021 .031250000 33 1089 35937 6.7445626 3.2075343 .030303030 34 1156 39304 5.8309519 3.2396118 .029411765 35 1225 42875 5.9160798 3.2710663 .028571429 36 1296 46656 6.0000000 3.3019272 .027777778 37 1369 50653 6.0827025 3.3322218 .027027027 38 1444 54872 6.1644140 3.3619754 .026315789 39 1521 59319 6.2449980 3.3912114 .025641026 40 1600 64000 6.3245553 3.4199519 .025000000 41 1681 68921 6.4031242 3.4482172 .024390244 42 1764 74088 6.4807407 3.4760266 .023809524 43 1849 79507 6.5574385 3.5033981 .023255814 44 1936 85184 6.6332496 3.5303483 .022727273 45 2025 91125 6.7082039 3.5568933 .022222222 46 2116 97336 6.7823300 3.5830479 .021739130 47 2209 103823 .6.8556546 3.6088261 .021276600 48 2304 110592 6.9282032 3.6342411 .020833333 49 2401 117649 7.0000000 3.6593057 .020408163 50 2500 125000 7.0710678 3.6840314 .020000000 51 2601 132651 7.1414284 3.7084298 .019607843 52 2704 140608 7.2111026 3.7325111 .019230769 53 2809 148877 7.2801099 3 . 7562858 .018867925 54 2916 157464 7.3484692 3.7797631 .018518519 55 3025 166375 7.4161985 3.8029525 .018181818 56 3136 175616 7.4833148 3.8258624 .017857143 57 3249 185193 7.5498344 3.8485011 .017543860 58 3364 195112 7.6157731 3.8708766 .017241379 59 3481 205379 7.6811457 3.8929965 .016949153 60 3600 216000 7.7459667 3.9148676 .016666667 61 3721 226981 7.8102497 3.9364972 .016393443 62 3844 238328 7.8740079 3.9578915 .016129032 Squares, Cubes, Square Roots, Cube Roots and Reciprocals 9 No. Squares Cubes Square roots Cube roots Reciprocals G3 3969 250047 7.9372539 3.9790571 .015873016 64 4096 262144 8.0000000 4.0000000 .015625000 65 4225 274625 8.0622577 4.0207256 .015384615 66 4356 287496 8.1240384 4.0412401 .015151515 67 4489 800763 8.1853528 4.0615480 .014925373 68 4624 314432 8.24G2113 4.0816551 .014705882 69 4761 328509 8.3066239 4.1015661 .014492754 70 4900 343000 8.3666003 4.1212853 .014285714 71 5041 357911 8.4261498 4.1408178 .014084507 72 5184 373248 8.4852814 4.1601676 .013888889 73 5329 389017 8.5440037 4.1793390 .013698630 74 5476 405224 8.6023253 4.1983364 .013513514 75 5625 421875 8.6602540 4.2171633 .013333333 76 5776 438976 8.7177979 4.2358236 .013157895 77 5929 456533 8.7749644 4.2543210 .012987013 78 6084 474552 8.8317609 4 . 2726586 .012820513 79 6241 • 493039 8.8881944 4.2908404 .012658228 80 6400 512000 8.9442719 4.3088695 .012500000 81 6561 531441 9.0000000 4.3267487 .012345679 82 6724 551368 9.0553851 4.3444815 .012195122 83 6889 571787 9.1104336 4.3620707 .012048193 84 7056 592704 9.1651514 4.3795191 .011904762 85 7225 614125 9.2195445 4.3968296 .011764706 86 7396 636056 9.2736185 4.4140049 .011627907 87 75G9 658503 9.3273791 4.4310476 .011494253 88 7744 681472 9.3808315 4.4479602 .011363636 89 7921 704969 9.4339811 4.4647451 .011235955 90 8100 729000 9.4868330 4.4814047 .011111111 91 8281 753571 9.5393920 4.4979414 .010989011 92 8404 778688 9.5916630 4.5143574 .010869565 93 8649 804357 9.6436508 4 . 5306549 .010752688 94 8836 830584 9.6953597 4.5468359 .010638298 95 9025 857375 9.7467943 4.5629026 .010526316 96 9216 884736 9.7979590 4.5788570 .010416667 97 9409 912673 9.8488578 4.5947009 .010309278 98 9604 941192 9.8994949 4.6104363 .010204082 99 9801 970299 ■ 9.9498744 4.6260650 .010101010 100 10000 1000000 10.0000000 4.6415888 .010000000 101 10201 1030301 10.04987^6 4.6570095 .009900990 102 10404 1061208 10.0995049 4.6723287 .009803922 103 10609 1092727 10.1488916 4.6875482 .009708738 104 10816 1124864 10.1980390 4.702GG94 .009615385 105 11025 1157625 10.2469508 4.7176940 .009523810 106 11236 1191016 10.2956301 4.7326235 .009433962 107 11449 1225043 10.3440804 4.7474594 .009345794 108 11664 1259712 10.3923048 4.7622032 .009259259 109 11881 1295029 10.4403065 4.7768562 .009174312 110 12100 1331000 10.4880885 4.7914199 .009090909 111 12321 1367631 10.5356538 4.8058955 .009009009 112. 12544 1404928 10.5830052 4.8202845 .008928571 113 12769 1442897 10.6301458 4.8345881 .008849558 114 12996 1481544 10.6770783 4.8488076 .008771930 115 13225 1520875 10.7238053 4 . 8629442 .008695652 116 13456 1560896 10.7703296 4.8769990 .008620090 117 13689 1601613 10.8166538 4.8909732 .008547009 118 13924 1643032 10.8627805 4.9048681 .008474576 119 14161 1685159 10.9087121 4.9186847 .008403361 120 14400 1728000 10.9544512 4.9324242 .008333333 121 14641 1771561 11.0000000 4.9460874 .008264463 122 14884 1815848 11.0453610 4.9596757 .008196721 123 15129 1860867 11.0905365 4.9731898 .008130081 124 15376 1906624 11.1355287 4.9866310 .008064516 10 Practical Arithmetic Part 1 No. Squares Cubes Square roots Cube roots Reciprocals 125 15625 1953125 11.1803399 5.0000000 .008000000 126 15876 2000376 11.2249722 5.0132979 .007936508 127 16129 2048383 11.2694277 5.0265257 .007874016 128 16384 2097152 11.3137085 5.0390842 .007812500 129 16641 2146689 11.3578167 5.0527743 .007751938 130 16900 2197000 11.4017543 5.0657970 .007692308 131 17161 2248091 11.4455231 5.0787531 .007633588 132 17424 2299968 11.4891253 5.0910434 .007575758 133 17689 2352637 11.5325626 5.1044687 .007518797 134 17956 2406104 11.5758369 5.1172299 .007462687 135 18225 2460375 11.6189500 5.1299278 .007407407 136 18496 2515456 11.6619038 5.1425632 .007352941 137 18769 2571353 11.7046999 5.1551367 .007299270 138 19044 2028072 11.7473401 5.1676493 .007246377 139 19321 2085619 11.7898261 5.1801015 .007194245 140 19600 2744000 11.8321596 5.1924941 .007142857 141 19881 2803221 11.8743421 5.2048279- .007092199 142 20164 28G3288 11.9163753 5.2171034 .007042254 143 20449 2924207 11.9582607 5.2293215 .006993007 144 20736 2985984 12.0000000 5.2414828 .006944444 145 21025 3048625 12.0415946 5.2535879 .006896552 146 21316 3112136 12.0830460 5.2656374 .006849315 147 21609 3176523 12.1^43557 5.2776321 .006802721 148 21904 3241792 12.1655251 5.2895725 .006756757 149 22201 3307949 12.2065556 5.3014592 .006711409 150 22500 3375000 12.2474487 5.3132928 .006666667 151 22801 3442951 12.2882057 5.3250740 .006622517 152 23104 3511808 12.3288280 5.3368033 .006578947 153 23409 3581577 12.3693169 5.3484812 .006535948 154 23716 3652264 12.4096736 5.3601084 .006493506 155 24025 3723875 12.4498996 5.3716854 .006451613 156 24336 3796410 12.4899960 5.3832126 .006410256 157 24649 3869893 12.5299641 5.3946907 .006369427 158 24964 3944312 12.5698051 5.4061202 .006329114 159 25281 4019679 12.6095202 5.4175015 .006289308 160 25600 4096000 12. 649110a 5.4288352 .006250000 161 25921 4173281 12.6885775 5.4401218 .006211180 162 26244 4251528 12.7279221 5.4513618 .006172840 163 26509 4330747 12.7671453 5.4625556 .006134969 164 26896 4410944 12.8062485 5.4737037 .006097561 165 27225 4492125 12.8452326 5.4848066 .006060606 166 27556 4574296 12.8840987 5.4958647 .006024096 167 27889 4657463 12.9228480 5.5068784 .005988024 168 28224 4741632 12.9614814 5.5178484 .005952381 169 28561 4826809 13.0000000 5.5287748 .005917160 170 28900 4913000 13.0384048 5 . 5396583 .005882353 171 29241 5000211 13.0766968 5.5504991 .005847953 172 29584 5088448 13.1148770 5.5612978 .005813953 173 29929 5177717 13.1529464 5.5720546 .005780347 174 30276 5208024 13.1909060 5.5827702 .005747126 175 30625 5359375 13.2287566 5.5934447 .005714286 176 30976 5451776 13.2664992 5.6040787 .005681818 177 31329 5545233 13.3041347 5.6146724 .005649718 178 31684 5639752 13.3416641 5.6252263 .005617978 179 32041 5735339 13.3790882 5.6357408 .005586592 180 32400 5832000 13.4164079 5.6462162 .005555556 181 32761 5929741 13.4536240 5.6566528 .005524862 182 33124 6028568 13.4907376 5.6670511 .005494505 183 33489 6128487 13.5277493 5.6774114 .005464481 184 33856 6229504 13.5646600 5.6877340 .005434783 185 34225 6331625 13.6014705 5.6980192 .005405405 186 34596 6434856 13.6381817 5.7082675 .005376344 Squares, Cubes, Square Roots, Cube Roots and Reciprocals 11 No. Squares Cubes Square roots Cube roots Reciprocals 187 34969 6539203 13.6747943 5.7184791 .005347594 188 35344 6644672 13.7113092 5.7286543 .005319149 189 35721 6751269 13.7477271 5.7387936 .005291005. 190 36100 6859000 13.7840488 5.7488971 .005263158 191 36481 6967871 13.8202750 5.7589652 .005235602 192 36864 7077888 13.8564065 5.7689982 .005208333 193 37249 7189057 13.8924440 5.7789966 .005181347 194 37636 7301384 13.9283883 5.7889604 .005154639 195 38025 7414875 13.9642400 5.7988900 .005128205 196 38416 7529536 14.0000000 5.8087857 .005102041 197 38809 7645373 14.0356688 5.8186479 .005076142 198 39204 7762392 14.0712473 5.8284767 . 005050505 199 39601 7880599 14.1067360 5.8382725 .005025126 200 40000 8000000 14.1421356 5.8480355 .005000000 201 40401 8120601 14.1774469 5.8577660 .004975124 202 40804 8242408 14.2126704 5.8674643 .004950495 203 41209 8365427 14.2478068 5.8771307 .004926108 204 41616 8489664 14.2828569 5.8867653 .004901961 205 42025 8615125 14.3178211 5.8963685 .004878049 20G 42436 8741816 14.3527001 5.9059406 .004854369 207 42849 8869743 14.3874946 5.9154817 .004830918 208 43264 8998912 14.4222051 5.9249921 .004807692 209 43681 9129329 14.4568323 5.9344721 .004784689 210 44100 9261000 14.4913767 5.9439220 .004761905 211 44521 9393931 14.5258390 5.9533418 .004739336 212 44944 9528128 14.5602198 5.9627320 .004716981 213 45369 9663597 14.5945195 5.9720926 .004694836 214 45796 9800344 14.6287388 5.9814240 .004672897 215 46225 9938375 14.6628783 5.9907264 .004651163 216 46656 10077696 14.6969385 6.0000000 .004629630 217 47089 10218313 14.7309199 6.0092450 .004608295 218 47524 10360232 14.7648231 6.0184617 .004587156 219 47961 ^0503459 14.7986486 6.0276502 .004566210 220 48400 10648000 14.8323970 6.0368107 .004545455 221 48841 10793861 14.8660687 6.0459435 .004524887 222 49284 10941048 14.8996644 6.0550489 .004504505 223 49729 11089567 14.9331845 6.0641270 .004484305 224 50176 11239424 14.9666295 6.0731779 .004464286 225 50625 11390625 15.0000000 6.0822020 .004444444 226 51076 11543176 15.0332964 6.0911994 .004424779 227 51529 11697083 15.0665192 6.1001702 .004405286 228 51984 11852352 15.0996689 6.1091147 .004385965 229 52441 12008989 15.1327460 6.1180332 .004366812 230 52900 12167000 15.1857509 6.1269257 .004347826 231 53361 12326391 15.1986842 6.1357924 .004329004 232 53824 12487168 15.2315462 6.1446337 .004310345 233 54289 12649337 15.2643375 6.1534495 .004291845 234 54756 12812904 15.2970585 6.1622401 .004273504 235 55225 12977875 15.3297097 6.1710058 .004255319 236 55696 13144256 15.3622915 6.1797466 .004237288 237 56169 13312053 15.3948043 6 . 1884628 .004219409 238 56644 13481272 .15.4272486 6.1971544 .004201681 239 57121 13651919 15.4596248 6.2058218 .004184100 240 57600 13824000 15.4919334 6.2144650 .004166667 241 58081 13997521 15.5241747 6 . 2230843 : 004149378 242 58564 14172488 15.5563492 6.2316797 .004132231 243 59049 14348907 15.5884573 6.2402515 .004115226 244 59536 14526784 15.6204994 6.2487998 .004098361 245 60025 14706125 15.6524758 6.2573248 .004081633 246 60516 14886936 15.6843871 6.2658266 .004065041 247 61009 15069223 15.7162336 6.2743054 .004048583 248 61504 15252992 15.7480157 6.2827613 .004032258 12 Practical Arithmetic Part 1 No. Squares Cubes Square roots Cube roots Reciprocals 249 62001 15438249 15.7797338 6.2911946 .004016064 250 62500 15625000 15.8113883" 6.2990053 .004000000 251 63001 15813251 15.8429795 6 . 3079935 . 003984064 252 63504 16003008 15. -8745079 6.3163596 .003908254 253 64009 16194277 15.9059737 6.3247035 .003952569 254 64516 16387064 15.9373775 6.3330256 .003937008 255 65025 16581375 15.9687194 6.3413257 .003921569 256 65536 16777216 16.0000000 6.3496042 .003906250 257 6G049 16974593 16.0312195 6.3578611 .003891051 258 63531 17173512 16.0623784 6 . 3600908 .003875909 259 67081 17373979 16.0934769 6.3743111 .003861004 260 67600 17576000 16.1245155 6.3825043 .003846154 20 1 6S121 17779581 16.1554944 6.3900705 .003831418 262 68644 17984728 16.1864141 6.3988279 .003816794 263 69109 18191447 16.2172747 6.4069585 .003802281 264 69696 18399744 16.2480768 6.4150687 .003787879 265 70225 18609625 16.2788206 6.4231583 .003773585 266 70756 18821096 16.3095064 6.4312276 .003759398 267 71239 19034103 16.3401346 6.4392767 .003745318 268 71824 19248832 16.3707055 6.4473057 .003731343 269 72361 19465109 16.4012195 6.4553148 .003717472 270 72900 19683000 16.4316767 6.4633041 .003703704 271 73441 19902511 16.4620776 6.4712736 .003690037 272 73984 20123648 10.4924225 6.4792236 .003676471 273 74529 20346417 16.5227116 6.4871541 .003663004 274 75076 20570824 16.5529454 6.4950653 .003649635 275 75625 20796875 16.5831240 6.5029572 .003636364 276 76176 21024576 16.6132477 6.5108300 .003623188 277 76729 21253933 16.6433170 6.5186839 .003610108 278 77284 21484952 16.6733320 6.5265189 .003597122 279 77841 21717639 16.7032931 6.5343351 .003584229 280 78400 21952000 16.7332005 6.5421326 .003571429 281 78961 22188041 16.7630546 6.5499116 .003558719 282 79524 22425768 16 . 7928556 6.5576722 .003546099 283 80039 22665187 16.8220038 6.5654144 .003533569 284 80656 22906304 16.8522995 6.5731385 .003521127 285 81225 23149125 16.8819430 6.5808443 .003508772 286 81796 23393056 16.9115345 6.5885323 .003496503 287 82369 23639903 16.9410743 6.5962023 .003484321 288 82944 23887872 16.9705627 6.6038545 .003472222 289 83521 24137569 17.0000000 6.6114890 .003460208 290 84100 24389000 17.0293864 6.6191060 .003448276 291 84681 24642171 17.0587221 6.6207054 .003436426 292 85264 24897088 17.0880075 6.6342874 .003424658 293 85849 25153757 17.1172428 6.6418522 .003412909 294 86436 25412184 17.1464282 6.6493998 .003401301 295 87025 25672375 17.1755640 6.6569302 .003389831 296 87616 25934336 17.2046505 6.0644437 .003378378 297 88209 26198073 17.2336879 6.6719403 .003307003 298 88804 26463592 17.2626765 6.6794200 .003355705 299 89401 26730899 17.2916165 6.6868831 .003344482 300 90000 27000000 17.3205081 6.6943295 .003333333 301 90601 27270901 17.3493516 6.7017593 .003322259 302 91204 27543608 17.3781472 6.7091729 .003311258 303 91809 27818127 17.4068952 6.7165700 .003300330 304 92416 28094464 17.4355958 6.7239508 .003289474 305 93025 28372625 17.4642492 6.7313155 .003278089 306 93636 28652016 17.4928557 6.7380041 .003207974 307 94249 28934443 17.5214155 6.7459967 .003257329 .'i08 94864 29218112 17.5499288 6.7533134 .003246753 309 95481 29503029 17.5783958 6.7606143 . 003236246 310 96100 29791000 17.6068169 6.7678995. .003225806 Squares, Cubes, Square Roots, Cube Roots and Reciprocals 13 No. Squares Cubes Square roots Cube roots Reciprocals 311 96721 30080231 17.6351921 6.7751690 .003215434 312 97344 30371328 17.6635217 6.7824229 .003205128 313 97969 30064297 17.6918060 6.7896613 .003194888 314 98596 30959144 17.7200451 6.7908844 .003184713 315 99225 31255875 17.7482393 6.8040921 .003174603 316 99856 31554496 17.7763888 6.8112847 .003164557 317 100489 31855013 17.8044938 6.8184620 .003154574 318 101124 32157432 17.8325545 6.8256242 .003144654 319 101761 32461759 17.8605711 6.8327714 .003134796 320 102400 32768000 17.8885438 6.8399037 .003125000 321 103041 33076161 17.9164729 6.8470213 .003115265 322 103684 33386248 17.9443584 6.8541240 .003105590 323 104329 33698267 17.9722008 6.8612120 .003095975 324 104976 34012224 18.0000000 6.8682855 .003086420 325 105625 34328125 18.0277564 6.8753443 .003076923 320 106276 34645976 18.0554701 6.8823888 .003067485 327 106929 34965783 18.0831413 6.8894188 .003058104 328 107584 35287552 18.1107703 6.8964345 .003048780 329 108241 35611289 18.1383571 6.9034359 .003039514 330 108900 35937000 18.1659021 6.9104232 .003030303 331 109561 36264691 18.1934054 6.9173964 .003021148 332 110224 36594368 18.2208672 6.9243556 .003012048 333 110889 36926037 18.2482876 6.9313008 .003003003 334 111556 37259704 18.2756669 6.9382321 .002994012 335 112225 37595375 18.3030052 6.9451496 .002985075 336 112896 37933056 18.3303028 6.9520533 .002976190 337 113569 38272753 18 . 3575598 6.9589434 . 002967359 338 114244 38614472 18.3847763 6.9658198 .002958580 339 114921 38958219 18.4119526 6.9726826 .002949853 340 115600 39304000 18.4390889 6.9795321 .002941176 341 116281 39651821 18.4661853 6.9863681 .002932551 342 116964 40001688 18.4932420 6.9931906 .002923977 343 117649 40353607 18.5202592 7.0000000 .002915452 344 118336 40707584 18.5472370 7.0067962 .002906977 345 119025 41063625 . 18.5741756 7.0135791 .002898551 346 119716 41421736 18.6010752 7.0203490 .002890173 347 120409 41781923 18.6279360 7.0271058 .002881844 348 121104 42144192 18.6547581 7.0338497 .002873563 349 121801 42508549 18.6815417 7.0405806 .002865330 350 122500 42875000 18.7083869 7.0472987 .002857143 351 123201 43243551 18.7349940 7.0540041 .002849003 352 123904 43614208 18.7616630 7.0606967 .002840909 353 124609 43986977 18.7882942 7.0673767 .002832801 354 125316 44361864 18.8148877 7.0740440 .002824859 355 126025 44738875 18.8414437 7.0806988 .002816901 356 126736 45118016 18.8679623 7.0873411 .002808989 357 127449 45499293 18.8944436 7.0939709 .002801120 358 128104 45882712 18.9208879 7 . 1005885 .002793216 359 128881 46268279 18.9472953 7.1-071937 .002785595 360 129600 46656000 18.9736660 7.1137866 .002777778 361 130321 47045881 19.0000000 7.1203674 .002770083 632 131044 47437928 19.0262976 7.1269360 .002762431 363 131769 47832147 19.0525589 7.1334925 .002754821 364 132496 48228544 19.0787840 7.1400370 .002747263 365 133225 48627125 19.1049732 7.1465695 .002739726 366 133956 49027896 19.1311265 7.1530901 .002732240 367 134689 49430863 19.1572441 7.1595988 .002724796 368 135424 49836032 19.1833261 7.1660957 .002717391 369 136161 50243409 19.2093727 7.1725809 .002710027 370 136900 60653000 19.2353841 7.1790544 .002702708 371 137641 51064811 19.2613603 7.1855162 .002695418 372 138384 51478848 19.2873015 7.1919663 .002688172 14 Practical Arithmetic No. Squares Cubes Square roots Cube roots Reciprocals 373 139129 51895117 19.3132079 7.1984050 .002680965 374 139876 52313624 19.3390796 7.2048322 .002673797 375 140625 52734375 19.3649167 7.2112479 .002666667 376 141376 53157376 19.3907194 7.2176522 .002659574 377 142129 53582633 19.4164878 7.2240450 002652520 378 142884 54010152 19.4422221 7.2304268 .002645503 379 143641 54439939 19.4679223 7.2367972 .002638522 380 144400 54872000 19.4935887 7.2431565 .002631579 381 145161 55306341 19.5192213 7.2495045 .002624672 382 145924 ' 55742968 19.5448203 7.2558415 .002617801 383 146689 56181887 19.5703858 7.2621675 .002610966 384 147456 56623104 19.5959179 7.2684824 .002604167 385 148225 57066625 19.6214169 7.2747864 .002597403 386 148996 57512456 19.6468827 7.2810794 .002590674 387 149769 57960603 19.6723156 7.2873617 .002583979 388 150544 58411072 19.6977156 7.2936330 .002577320 389 151321 58863869 19.7230829 7.2998936 .002570694 390 152100 59319000 19.7484177 7.3061436 .002564103 391 152881 59776471 19.7737199 7.3123828 .002557545 392 153664 60236288 19 . 7989899 7.3186114 .002551020 393 154449 60698457 19.8242276 7.3248295 .002544529 394 155236 61162984 19.8494332 7.3310369 .002538071 395 156025 61629875 19.8746069 7.3372339 .002531646 396 156816 62099136 19.8997487 7.3434205 .002525253 397 157609 62570773 19.9248588 7.3495966 .002518892 398 158404 63044792 19.9499373 7.3557624 .002512563 399 159201 63521199 19.9749844 7.3619178 .002506266 400 160000 64000000 20.0000000 7.3680630 .002500000 401 160801 61481201 20.0249844 7.3741979 .002493766 402 161604 64964808 20.0499377 7.3803227 .002487562 403 162409 65450827 20.0748599 7.3864373 .002481390 404 163216 65939264 20.0997512 7.3925418 .002475248 405 164025 66430125 20.1246118 7.3986363 .002469136 406 164836 66923416 20.1494417 7.4047206 .002463054 407 165649 67419143 20.1742410 7.4107950 .002457002 408 166464 67917312 20.1990099 7.4168595 .002450980 409 167281 68417929 20.2237484 7.4229142 .002444988 410 168100 68921000 20.2484567 7.4289589 .002439024 411 168921 69426531 20.2731349 7.4349938 .002433090 412 169744 69934528 20.2977831 7.4410189 .002427184 413 170569 70444997 20.3224014 7.4470342 .002421308 414 171396 70957944 20.3469899 7.4530399 .002415459 415 172225 71473375 20.3715488 7.4590359 .002409639 416 173056 71991296 20.3960781 7.4650223 .002403846 417 173889 72511713 20.4205779 7.4709991 .002398082 418 174724 73034632 20.4450483 7.4769664 .002392344 419 175561 73560059 20.4694895 7.4829242 .002386635 420 176400 74088000 20.4939015 •7.4888724 .002380952 421 177241 74618461 20.5182845 7.4948113 .002375297 422 178084 75151448 20.5426386 7.5007406 .002369668 423 178929 75686967 20 . 5669638 7 . 5066607 .002364066 424 179776 76225024 20.5912603 7.5125715 .002358491 425 180625 76765625 20.6155281 7.5184730 .002352941 426 181476 77308776 20.6397674 7.5243652 .002347418 427 182329 77854483 20.6639783 7.5302482 .002341920 428 183184 78402752 20.6881609 7.5361221 .002336449 429 184041 78953589 20.7123152 7.5419867 .002331002 430 184900 79507000 20.7364414 7.5478423 .002325581 431 185761 80062991 20.7605395 7.5536888 .002320186 432 186624 80621568 20.7846097 7 . 5595263 .002314815 433 187489 81182737 20.8086520 7.5653548 .002309469 434 188356 81746504 20.8326667 7.5711743 .002304147 Squares, Cubes, Square Roots, Cube Roots and Reciprocals 15 No. Squares Cubes Square roots Cube roots Reciprocals 435 189225 82312875 20.8566536 7.5769849 .002298851 436 190096 82881856 20.8806130 7.5827865 .002293578 437 190969 83453453 20.9045450 7.6885793 .002288330 438 191844 84027672 20.9284495 7.5943633 .002283105 439 192721 84604519 20.9523268 7.6001385 .002277904 440 193600 85184000 20.9761770 7.6059049 .002272727 441 194481 85766121 21.0000000 7.6116626 .002267674 442 195364 86350888 21.0237960 7.6174116 .002262443 443 196249 86938307 21.0475652 7.6231519 .002257336 444 197136 87528384 21.0713075 7.6288837 .002252252 445 198025 88121125 21.0950231 7.6346067 .002247191 446 198916 88716536 21.1187121 7.6403213 .002242152 447 199809 89314623 21.1423745 7.6460272 .002237136 448 200704 89915392 21.1660105 7.6517247 .002232143 449 201001 90518849 21 . 1896201 7.6574138 .002227171 450 202500 91125000 21.2132034 7.6630943 .002222222 451 203401 91733851 21.2367606 7.6687665 .002217295 452 204304 92345408 21.2602916 7.6744303 .002212389 453 205209 92959677 21 . 2837967 7.6800857 .002207506 454 206116 93576664 21.3072758 7.6857328 .002202643 455 207025 94196375 21.3307290 7.6913717 .002197802 456 207936 94818816 21.3541565 7.6970023 .002192982 457 208849 95443993 21.3775583 7.7026246 .002188184 458 209764 96071912 21.4009346 7.7082388 .002183406 459 210681 96702579 21.4242853 7.7138448 .002178649 460 211600 97336000 21.4476106 7.7194426 .002173913 461 212521 97972181 21.4709106 7.7250325 .002169197 462 213444 98611128 21.4941853 7.7306141 .002164502 463 214369 99252847 21.5174348 7.7361877 .002159827 464 215296 99897344 21.5406592 7.7417532 .002155172 465 216225 100544625 21.5638587 7.7473109 .002150538 466 217156 101194696 21.5870331 7.7528606 .002145923 467 218089 101847563 21.6101828 7.7584023 .002141328 468 219024 102503232 21.6333077 7.7639.361 .002136752 469 219961 103161709 21.6564078 7.7694620 .002132196 470 220900 103823000 21.6794834 7.7749801 .002127660 471 221841 104487111 21.7025344 7.7804904 .002123142 472 222784 105154048 21.7255610 7.78.56928 .002118644 473 223729 105823817 21.7485632 7.7914875 .002114165 474 224676 106496424 21.7715411 7.7969745 .002109705 475 225625 107171875 21.7944947 7.8024538 .002105263 476 226576 107850176 21.8174242 7.8079254 .002100840 477 227529 108531333 21.8403297 7.8133892 .002096436 478 228484 109215352 21.8632111 7.8188456 .002092050 479 229441 109902239 21.8860686 7.8242942 .002087683 480 230400 110592000 21.9089023 7.8297353 .002083333 481 231361 111284641 21.9317122 7.8351688 .002079002 482 232324 111980168 21.9544984 7.8405949 .002074689 483 233289 112678587 21.9772610 7.8460134 .002070393 484 234256 113379904 22.0000000 5.8514244 .002066116 485 235225 114084125 22.0227155 7.8568281 .002061856 486 236196 114791256 22.0454077 7.8622242 .002057613 487 237169 115501303 22.0680765 7.8676130 .002053388 488 238144 116214272 22.0907220 7.8729944 .002049180 489 239121 116930169 22.1133444 7.8783684 .002044990 490 240100 117649000 22.1359436 7.8837352 .002040816 491 241081 118370771 22.1585198 7.8890946 .002036660 492 242064 119095488 22.1810730 7.8944468 .002032520 493 243049 119823157 22 . 2036033 7.8997917 .002028398 494 244036 120553784 1^1287375 22.2261108 7.9051294 .002024291 495 245025 22 . 2485955 7.9104599 .002020202 496 246016 122023936 22.2710575 7.9157832 .002016129 Practical Arithmetic Part 1 No. Squares ' Cubes Square roots Cube roots Reciprocals 497 247009 122763473 22.2934968 7.9210994 .002012072 498 248004 123505992 22.3159136 7.9264085 .002008032 499 249001 124251499 22 . 3383079 7.9317104 .002004008 500 250000 125000000 22.3606798 7.9370053 .002000000 501 251001 125751501 22.3830293 7.9422931 .001996008 502 252004 126506008 22.4053565 7.9475739 .001992032 503 253009 127263527 22.4276615 7.9528477 .001988072 504 254016 128024064 22.4499443 7.9581144 .001984127 505 255025 128787625 22.4722051 7.9633743 .001980198 506 256036 129554216 22.4944438 7.9686271 .001976285 507 257049 130323843 22.5166605 7.9738731 .001972387 508 258064 131096512 22.5388553 7.9791122 .001968504 509 259081 131872229 22.5610283 7.9843444 .001964637 510 260100 132651000 22.5831796 7.9895697 .001960784 511 261121 133432831 22.6053091 7.9947883 .001956947 512 262144 134217728 22.6274170 8.0000000 .001953125 513 263109 135005697 22.6495033 8.0052049 .001949318 514 264196 135796744 22.6715681 8.0104032 .001945525 515 265225 136590875 22.6936114 8.0155946 .001941748 516 266256 137388096 22.7156334 8.0207794 .001937984 517 267289 138188413 22.7376340 8.0259574 .001934236 518 268324 138991832 22.7596134 8.0311287 .001930502 519 269361 139798359 22.7815715 8.0362935 .001926782 520 270400 140608000 22.8035085 8.0414515 .001923077 521 271441 141420761 22.8254244 8.0466030 .001919386 522 272484 142236648 22.8473193 8.0517479 .001915709 523 273529 143055667 22.8691933 8.0568862 .001912046 524 274576 143877824 22.8910463 8.0620180 .001908397 525 275625 144703125 22.9128785 8.0671432 .001904762 526 276676 145531576 22.9346899 8.0722620 .001901141 527 277729 146363183 22.9564806 8.0773743 .001897533 528 278784 147197952 22.9782506 8.0824800 .001893939 529 279841 148035889 23.0000000 8.0875794 .001890359 530 280900 148877000 23.0217289 8.0926723 .001886792 531 281961 149721291 23.0434372 8.0977589 .001883239 532 283024 150568768 23.0651252 8 . 1028390 .001879699 533 284089 151419437 23.0867928 8.1079128 .001876173 534 285156 152273304 23.1084400 8.1129803 .001872659 535 286225 153130375 23.1300670 8.1180414 .001869159 536 287296 153990655 23.1516738 8.1230962 .001865672 537 •288369 154854153 23.1732605 8.1281447 .001862197 538 289444 155720872 23 . 1948270 8.1331870 .001858736 539 290521 156590819 23.2163735 8.1382230 .001855288 540 291600 157464000 23.2379001 8.1432529 .001851852 541 292681 158340421 23 . 2594067 8.1482765 .001848429 542 293764 1592200S8 23 . 2808935 8.1532939 .001845018 543 294849 160103007 23 . 3023604 8.1583051 .001841621 544 295936 160989184 23 . 3238076 8.1633102 .001838235 545 297025 161878625 23.3452351 8.1683092 .001834862 546 298116 162771333 23.3666429 8.1733020 .001831502 547 299209 163667323 23.3880311 8.1782888 .001828154 548 300304 164566592 23.4093998 8.1832695 .001824818 549 301401 165469149 23.4307490 8.1882441 .001821494 550 302500 166375000 23.4520788 8.1932127 .001818182 551 303601 167284151. 23 . 4733892 8.1981753 .001814882 552 304704 168196608 23.4946802 8.2031319 .001811594 553 305809 169112377 23.5159520 8.2080825 .001808318 554 306916 170031464 23.53-72046 8.2130271 .001805054 555 308025 170953875 23.5584380 8.2179657 .001801802 556 309136 171879616 23.5796522 8.2228985 .001798561 557 310249 172808693 23 . 6008474 8.2278254 .001795332 558 311364 173741112 23.6220236 8.2327463 .001792115 * Squares, Cubes, Square Roots, Cube Roots and Reciprocals 17 No. Squares Cubes Square roots Cube roots Reciprocals 559 312481 174676879 23.6431808 8.2376614 .001788909 560 313600 175616000 23.6643191 8.2425706 .001785714 561 314721 176553481 23 . 6854386 8.2474740 .001782531 562 315844 177504328 23.7065392 8.252.3715 .001779359 563 316969 178453547 23.7276210 8.2572633 .001776199 564 31S09G 179406144 23 . 7486S42 8.2621492 .001773050 565 319225 180362125 23.7697286 8.2670294 .001769912 566 320356 181321496 23.7907545 8.2719039 .001766784 567 321489 182284263 23.8117618 8.2767726 .001763668 568 322624 183250432 23 . 8327506 8.2816355 .001760563 569 323761 184220000 23.8537209 8.2864928- .001757469 570 324900 185193000 23.8746728 8.2913444 .001754386 571 326041 186169411 23.8956063 8.2961903 .001751313 572 327184 187149248 23.9165215 8.3010304 .001748252 : 673 328329 188132517 23.9374184 8.3058651 .001745201 574 329476 189119224 23.9582971 8.3106941 .001742160 575 330625 190109375 23.9791576 8.3155175 .001739130 576 331776 191102976 24.0000000 8.3203353 .001736111 577 332929 192100033 24.0208243 8.3251475 .001733102 578 334084 193100552 24.0416306 8 . 3299542 .001730104 579 335241 194104539 24.0624188 8.3347553 .001727116 580 336400 195112000 24.0831891 8.3395509 .001724138 581 337561 196122941 24.1039416 8.3443410 .001721170 582 338724 197137368 24.1246702 8.3491256 .001718213 583 339889 198155287 24.1453929 8.3539047 .001715266 584 341056 199176704 24.1660919 8.3-586784 .001712329 585 342225 200201625 24.1867732 8.3634466 .001709402 586 343396 201230053 24.20743C9 ■ 8.3682095 .001706485 i 587 344569 202262003 24.2280829 8.3729668 .001703578 588 345744 203297472 24.2487113 8.3777188 .001700680 589 346921 204336409 24.2693222 8.3824653 .001697793 ■ 590 348100 205379000 24.2899156 8.3872065 .001694915 ! 591 349281 206425071 24.3104916 8.3919423 .001692047 ; 592 350464 207474688 24.3310501 . 8 . 3966729 .001689189 [ 593 351649 208527857 24.3515913 8.4013981 .001686341 < 594 352836 209584584 24.3721152 8.4061180 .001683502 595 354025 210644875 24.3926218 8.4108326 .001680672 , 596 355216 211708736 24.4131112 8.4155419 .001677852 : 597 356409 212776173 24.4335834 8.4202460 .001675042 : 598 357604 213847192 24.4540385 8.4249448 .001672241 i 599 358801 214921799 24.4744765 8.4296383 .001669449 . 600 360000 216000000 24.4948974 8.4343267 .001666667 : 601 361201 217081801 24.5153013 8.4390098 .001663894 ; 602 362404 218167208 24.5356883 8.4436877 .001661130 ' 603 363609 219256227 24.5560583 8.4483605 .-001658375 604 364816 220348864 24.5764115 8.4530281 .001655629 605 366025 221445125 24.5967478 8.4576906 .001652893 606 367236 222545016 24.6170673 8.4623479 .001650165 607 368449 223648543 24.6373700 8.4670001 .001647446 608 369664 224755712 24.6576560 8.4716471 .001644737 609 370881 225866529 24.6779254 8.4762892 .001642036 610 372100 226981000 24.6981781 8.4809261 .001639.344 611 373321 228099131 24.7184142 8.4855579 .001036661 612 374544 229220928 24.7386338 8.4901818 .001C33987 613 375769 230346397 24.7588368 8.4948065 .001631321 614 376996 231475544 24.7790234 8.4994233 .001628664 615 378225 232608375 24.7991935 8.5040350 .001626016 616 379456 233744896 24.8193473 8.5086417 .001623377 ! 617 380689 234885113 24.8394847 8.5132435 .001620746 ! 618 381924 236029032 24.8596058 8.5178403 .001618123 • 619 383161 237176659 24.8797106 8.5224.321 .001615509 ; 620 384400 238328000 24.8997992 8.5270189 .001612903 1 Practical Arithmetic Part 1 No. Squares Cubes Square roots Cube roots Reciprocals 621 385641 239483061 24.9198716 8.5316009 .001610306 622 386884 240641848 24.9399278 8.5361780 .001807717 623 388129 241804367 24.9599679 8.5407501 .001605136 624 389376 242970624 24.9799920 8.5453173 .001602564 625 390625 244140625 25 . 0000000 8.5498797 .001800000 626 391876 245314376 25.0199920 8.5544372 .001597444 627 393129 246491883 25.0399081 8.5589899 .001594898 628 394384 247673152 25.0599282 8.5635.377 .001592357 629 395641 248858189 25.0798724 8.5680807 .001589825 630 396900 250047000 25.0998008 8.5726189 .001587302 631 398161 251239591 25.1197134 8.5771523 .001584788 632 399424 252435968 25.1396102 8.5816809 .001582278 633 400689 253636137 25.1594913 8.5862047 .001579779 634 401958 254840104 25.1793566 8.5907238 .001577287 635 403225 256047875 25 . 1992063 8.5952380 .001574803 636 404495 257259456 25.2190404 8.5997476 .001572327 637 405769 258474853 25 . 2388589 8.6042525 .001589859 638 407044 259394072 25.2586619 8 . 6087526 .001567398 639 408321 250917119 25.2784493 8.6132480 .001564945 640 409600 262144000 25.2982213 8.6177388 .001562500 641 410881 263374721 25.3179778 8.6222248 .001580062 642 412164 254609288 25-. 3377189 8.6267003 .001557632 643 413449 255847707 25.3574447 8.6311830 .001555210 644 414736 267089984 25.3771551 8.6356551 .001552795 645 416025 288336125 25.3968502 8.6401228 .001550388 646 417316 269586136 25.4165301 8.8445855 .001547988 647 418609 270840023 25.4361947 8.6490437 .001545595 648 419904 272097792 25.4558441 8.6534974 .001543210 649 421201 273359449 25.4754784 8.6579465 .001540832 650 422500 274625000 25.4950976 8.6823911 .001538462 651 423801 275894451 25.5147016 8.6668310 .001536098 652 425104 277187808 25.5342907 8.6712665 .001533742 653 426409 278445077 25 . 5538647 8.6756974 .001531394 654 427716 279723264 25 . 5734237 8.6801237 .001529052 655 429025 281011375 25 . 5929678 8.6845456 .001526718 656 430336 282300416 25.6124969 8.8889630 .001524390 657 431649 283593393 25.6320112 8.6933759 .001522070 658 432964 284890312 25.6515107 8.6977843 .001519757 659 434281 286191179 25.6709953 8.7021882 .001517451 660 435600 287496000 25.6904652 8.7065877 .001515152 661 436921 288804781 25 . 7099203 8.7109827 .001512859 662 438244 290117528 25 . 7293807 8.7153734 .001510574 663 439569 291434247 25.7487864 8.7197596 .001508296 664 440896 292754944 25.7681975 8.7241414 .001506024 665 442225 294079525 25.7875939 8.7285187 .001503759 666 443556 295408298 25.8069758 8.7328918 .001501502 667 444889 296740963 25.8263431 8.7372804 .001499250 668 446224 298077632 25.8456960 8.7416246 .001497006 669 447561 299418309 25.8650343 8.7459846 .001494788 670 448900 300763000 25 . 8843582 8.750.3401 .001492537 671 450241 302111711 25.9036677 8.7546913 .001490313 672 451584 303464448 25 . 9229628 8.7590383 .001488095 673 452929 304821217 25.9422435 8.7633809 .001485884 674 454276 306182024 25.9615100 8.7677192 .001483680 675 455625 307546875 25.9807621 8.7720.532 .001481481 676 456976 308915778 26.0000000 8.776.3830 .001479290 677 458329 310288733 26.01922.37 8.7807084 .001477105 678 459684 311685752 26.0384331 8.7850296' .001474926 679 461041 313046839 26.0576284 8.7893468 .004472754 680 462400 314432000 26.0768096 8 . 7936593 .001470588 681 463761 315821241 26.0959767 8.7979679 .001488429 682 465124 317214568 26.1151297 8.8022721 .001466276 Squares, Cubes, Square Roots, Cube Roots and Reciprocals 19 No. Squares Cubes Square roots Cube roots Reciprocals 683 466489 318611987 26.1342687 8.8065722 .001464129 684 467856 320013504 26.1533937 8.8108681 .001461988 685 469225 321419125 26.1725047 8.8151598 .001459854 686 470596 322828856 26.1916017 8.8194474 .001457726 687 471969 324242703 26.2106848 8.8237307 .001455604 688 473344 325660672 26.2297541 8.8280099 .001453488 689 474721 327082709 26.2488095 8.8322S50 .001451379 690 47#100 328509000 26.2078511 8.8365559 .001449275 691 477481 329939371 2G . 2868789 8.8408227 .001447178 692 478864 331373888 26 . 3058929 8.8450854 .001445087 693 480249 332812557 26.3248932 8.8493440 .001443001 694 481636 334255384 26.3438797 8.8535985 .001440922 695 483025 335702375 26.3628527 8.8578489 .001438849 696 484416 337153536 26.3818119 8.8620952 .001436782 697 485809 338608873 26.4007576 8.8663375 .001434720 698 487204 340068392 26. 41968^96 8.8705757 .001432665 699 488601 341532099 26.4386081 8.8748099 .001430615 700 490000 343000000 26.4575131 8.8790400 .001428571 701 491401 344472101 26.4764046 8.88326G1 .001426534 702 492804 345948408 26.4952826 8.8874882 .001424501 703 494209 347428927 26.5141472 8.8917063 .001422475 704 495616 348913664 26.5329983 8.8959204 .001420455 705 497025 350402625 26.5518361 8.9001304 .001418440 706 498436 351895816 26.5706605 8.90433C6 .001416431 707 499849 353393243 26.5894716 8.9085387 .001414427 708 501264 354894912 26.6082694 8.9127369 .001412429 709 502681 356400829 26.6270539 8.9169311 .001410437 710 504100 357911000 26.6458252 8.9211214 .001408451 711 505521 359425431 26.6645833 8.9253078 .001406470 712 506944 360944128 26.6833281 8.9294902 .001404494 713 508369 362467097 26.7020598 8.9336687 .001402525 714 509796 363994344 26.7207784 8.9378433 .001400560 715 511225 365525875 26.7394839 8.9420140 .001398601 716 512656 367061696 26.7581763 8.9461809 .001396648 717 514089 368601813 26.7768557 8.9503438 .001394700 718 515524 370146232 26.7955220 8.9545029 .001392758 719 516961 371694959 26.8141754 8.9586581 .001390821 720 518400 373248000 26.8328157 8.9628095 .001388889 721 519841 374805301 26.8514432 8.9669570 .001386963 722 521284 376367048 26.8700577 8.9711007 .001385042 723 522729 377933067 26 . 8886593 8.9752406 .001383126 724 524176 379503424 26.9072481 8.9793766 .001381215 725 525625 381078125 26.9258240 8.9835089 .001379810 726 527076 382657176 26.9443872 8.9876373 .001377410 727 528529 384240583 26.9629375 8.9917620 .001375516 728 529984 385828352 26.9814751. 8.9958829 .001373626 729 531441 387420489 27.0000000 9.0000000 .001371742 730 532900 389017000 27.0185122 9.0041134 .001369863 731 5343G1 390617891 27.0370117 9.0082229 .001367989 732 535824 392223168 27.0554985 9.0123288 .001366120 733 537289 393832837 27.0739727 9.0164309 .001364256 734 538756 395446904 27.0924344 9.0205293 .001362398 735 540225 397065375 27.1108834 9.0246239 .001360544 736 541696 398688256 27.1293199 9.0287149 .001358696 737 543169 400315553 27.1477439 9.0328021 .001356852 738 544644 401947272 27.1661554 9.0368857 .001355014 739 546121 403583419 27.1845544 9.0409655 .001353180 740 547600 405224000 27.2029410 9.0450419 .001351351 741 549081 406869021 27.2213152 9.0491142 .001349528 742 550564 408518488 27.2396769 9.0531831 001347709 743 552049 410172407 27.2580263 9.0572482 001345895 744 553536 411830784 27.2763634 9.0613098 001344086 Practical Arithmetic Part 1 No. Squares Cubes Square 'roots Cube roots Reciprocals 745 555025 413493625 27.2946881 27.3130006 9.0653677 .001342282 746 556516 415160936 9.0694220 .001340483 747 558009 416832723 27.3313007 9.0734726 .001338688 748 559504 418508992 27 . 3495887 9.0775197 .001336898 749 561001 420189749 27 . 3678644 9.0815631 .001335113 750 562500 421875000 27.3861279 9.0856030 .001333333 751 564001 423564751 27.4043792 9.0896392 .001331558 752 565504 425259008 27.4226184 9.0936719 , .001329787 753 567009 426957777 27.4408455 9.0977010 .001328021 754 568516 428661064 27.4590604 9.1017265 .001326260 755 570025 430368875 27.4772633 9.1057485 .001324503 756 571536 432081216 27.4954542 9.10976G9 .001322751 757 573049 433798093 27.5136330 9.1137818 .001321004 758 574564 435519512 27.5317998 9.1177931 .001319201 759 576081 437245479 27.5499546 9.1218010 .001317523 760 577600 438976000 27.5680975 9.1258053 .001315789 ■ 761 579121 440711081 27.5862284 9.1298061 .001314060 762 580644 442450728 27.6043475 9.1338034 .001312336 763 582169 444194947 27.6224546 9.1377971 .001310616 764 583696 445943744 27.6405499 . 9.1417874 .001308901 765 585225 447697125 27.6586334 9.1457742 .001307190 766 586756 449455096 27.6767050 9.1497576 .001305483 767 588289 451217663 27.6947648 9.1537375 .001303781 768 589824 452984832 27.7128129 9.1577139 .001302083 769 591361 454756609 27.7308492 9.1616869 .001300390 770 592900 456533000 27.7488739 9.1656565 .001298701 771 594441 458314011 27.7668808 9.1696225 .001297017 772 595984 460099648 27.7848880 9.1735852 .001295337 773 597529 461889917 27.8028775 9.1775445 .001293661 774 599076 463684824 27.8208555 9.1815003 .001291990 775 600625 465484375 27.8388218 9.1854527 .001290323 776 602176 467288576 27.8567766 9.1894018 .001288060 777 603729 469097433 27.8747197 9.1933474 .001287001 778 605284 470910952 27.8926514 9.1972897 .001285347 779 60684a 472729139 27.9105715 9.2012286 .001283697 780 608400 474552000 27.9284801 9.2051641 .001282051 781 609961 476379541 27.9463772 9.2090962 .001280410 782 611524 478211768 27.9642629 9.2130250 .001278772 783 613089 480048687 27.9821372 9.2169505 .001277139 784 614656 481890304 28.0000000 9.2208726 .001275510 785 616225 483736625 28.0178515 9.2247914 .001273885 786 617796 485587656 28.0356915 9.2287068 .001272265 787 619369 487443403 28.0535203 9.2320189 .001270648 788 620944 489303872 28.0713377 9.2365277 .001269036 789 622521 491169069 28.0891438 9.2404333 .001267427 790 624100 493039000 28 . 1069386 9.2443355 .001265823 791 625681 494913671 28.1247222 9 . 2482344 .001264223 792 627264 496793088 28.1424946 9.2521300 .001262626 793 628849 498677257 28.1602557 9 . 2560224 .001261034 794 630436 500566184 28.1780056 9.2599114 .001259446 795 632025 502459875 28.1957444 9.2637973 .001257862 796 633616 504358336 28.2134720 9 . 2676798 .001256281 797 635209 506261573 28.2311884 9.2715592 .001254705 798 636804 508169592 28.2488938 9.2754352 .001253133 799 638401 510082399 28.2665881 9.2793081 .001251564 800 640000 512000000 28.2842712 9.2831777 .001250000 801 641601 513922401 28.3019434 9.2870440 .001248439 802 643204 515849608 28.3196045 9.2909072 .001246883 803 644809 517781627 28 . 3372546 9.2947671 .001245330 804 646416 519718464 28.3548938 9.2986239 .001243781 805 648025 521660125 28.3725219 9.3024775 .001242236 806 649636 623606616 28.3901391 9.3063278 .001240685 Squares, Cubes, Square Roots, Cube Roots and Reciprocals 21 No. Squares Cubes Square roots Cube roots Reciprocals 807 651249 525557943 28.4077454 9.3101750 .001239157 808 652864 527514112. 28.4253408 9.3140190 .001237624 809 654481 529475129 28.4429253 9.3178599 .001236094 810 656100 531441000 28.4604989 9.3216975 .001234568 811 657721 533411731 28.4780617 9.3255320 .001233046 812 659344 535387328 28.4956137 9.3293634 .001231527 813 660969 537367797 28.5131549 9.3331916 .001230012 814 662596 539353144 28.5306852 9.3370167 .001228501 815 664225 541343375 28 . 54820 18 9 . 3408386 .001226994 81G 665856 543338496 28.5657137 9.3446575 .001225490 817 667489 545338513 28.5832119 9.3484731 .001223990 818 669124 547343432 28.0006993 9.3522857 .001222494 819 670761 549353259 28.6181760 9.3560952 .001221001 820 672400 551368000 28.6356421 9.3599016 .001219512 821 674041 553387661 28 . 6530976 9.3637049 .001218027 822 675684 555412248 28.6705424 9.3675051 .001216545 823 677329 557441767 28.6879766 9.3713022 .001215067 824 678976 559476224 28.7054002 9.3750963 .001213592 825 680625 561515625 28.7228132 9.3788873 .001212121 826 682276 563559976W. 28.7402157 9.3826752 .001210654 827 683929 565609283 28.7576077 9.3864600 .001209190 828 685584 567663552 28.7749891 9.3902419 .001207729 829 687241 569722789 28.7923601 9.3940206 .001206273 830 688900 571787000 28.8097206 9.3977964 .001204819 831 690561 573856191 28.8270706 9.4015691 .001203369 832 692224 575930368 28.8444102 9.4053387 .001201923 833 693889 578009537 28.8617394 9.4091054 .001200480 834 695556 580093704 28.8790582 9.4128690 .001199041 835 697225 582182875 28.8963666 9.4160297 .001197605 836 698896 584277056 28.9136646 9.4203873 .001196172 837 700569 586376263 28.9309523 9.4241420 .001194743 838 702244 588480472 28.9482297 9.4278936 .001193317 839 703921 590589719 28.9654967 9.4316423 ,001191895 840 705600 592704000 28.9827535 9.4353880 .001190476 841 707281 594823321 29.0000000 9.4291307 .001189001 842 708964 596947688 29.0172363 9.4428704 .001187648 843 710649 599077107 29.0344623 9.4466072 .001186240 844 712336 601211584 29.0516781 9.4503410 .001184834 845 714025 603351125 29.0688837 9.4540719 .001183432 846 715716 605495736 29.0860791 9.4577999 .001182033 847 717409 607645423 29 . 1032644 9.4615249 .001180638 848 719104 609800192 29.1204396 9.4C52470 .001179245 849 720801 611960049 29.1376046 9.4689661 .001177856 850 722500 614125000 29.1547595 9.4726824 .001176471 851 724201 616295051 29.1719043 9.476G957 .001175088 852 725904 618470208 29.1890390 9.4S01061 .001173709 853 727609 620650477 29.2061637 9.4838136 .001172333 854 729316 622835864 29.2232784 9.4875182 .001170960 855 731025 625026375 29.2403830 9.4912200 .001169591 856 732736 627222016 29.2574777 9.4949188 .001168224 857 734449 629422793 29.2745623 9.498G147 .001166861 858 736164 631628712 29.2916370 9 . 5023078 .001105501 859 737881 633839779 29.3087018 9.5059980 .001164144 860 . 739600 636056000 29.3257566 9 . 5096854 .001162791 861 741321 638277381 29.3428015 9.5133699 . .001161440 862 743044 640503928 29.3598365 9.5170515 .001160093 863 744769 642735647 29.3768616 9.5207303 .001158749 864 746496 644972544 29.3938769 9.5244063 .001157407 865 748225 647214625 29.4108823 9 . 5280794 .001156069 866 749956 649461896 29.4278779 9.5317497 .001154734 867 751689 651714363 29.4448637 9.5354172 .001153403 868 753424 653972032 29.4618397 9.5390818 .001152074 22 Practical Arithmetic No. Squares Cubes Square roots Cube roots Reciprocals 869 755161 656234909 29.4788059 9.5427437 .001150748 870 756900 658503000 29.4957624 9.5464027 .001149425 871 758641 660776311 29.5127091 9.5500589 .001148106 872 760384 663054848 29.5296461 9.5537123 .001146789 873 762129 665338617 29.5465734 9 . 5573630 .OG 1145475 874 763876 667627624 29.5634910 9.5310108 .001144165 875 765325 669921875 29 . 5803989 9 . 5340559 .001142857 876 707376 672221376 29.5972972 9.5G829S2 .001141553 877 769129 674526133 29.6141858 9.5719377 .001140251 878 770884 676836152 29.6310648 9.57.55745 .001138952 879 772641 679151439 . 29.6479342 9.5792085 .001137656 880 774400 681472000 29.6647939 9..582S397 .001136364 881 776161 683797841 29.6816442 9.5864682 .001135074 882 777924 686128968 29.6984848 9.5900939 .001133787 883 779689 688465387 29.7153159 9.5937169 .001132503 884 781456 690807104 29.7321375 9.5973373 .001131222 885 783225 693154125 29.7489496 9.6009548 .001129944 886 784996 695506456 29.7657521 9.6045696 .001128668 887 786769 697864103 29.7825452 9.6081817 .001127396 888 788544 700227072 29.7993289 9.6117911 .001126126 889 790321 702595369 29.8161030 9.6153977 .001124859 890 792100 704939000 29.8328678 9.6190017 .001123596 891 793SS1 707347971 29.8496231 9.6226030 .001122334 892 795664 709732288 29.8663690 9.6262016 .001121076 893 797449 712121957 29.8831056 9.6297975 .001119821 894 799236 714516984 29.8998328 9.6333907 .001118568 895 801025 716917375 29.9165506 9.6369812 .001117318 896 802816 719323156 29.9332591 9.6405690 .001116071 897 804609 721734273 29.9499583 9.6441542 .001114827 898 806404 724150792 29.9666481 9.6477367 .001113586 899 808201 726572699 29.9833287 9.6513166 .001112347 900 810000 729000000 30.0000000 9.6548938 .001111111 901 811801 731432701 30.0166620 9 . 6584684 .001109878 902 813604 733870808 30.0333148 9.6620403 .001108647 903 815409 736314327 30.0499584 9.6656096 .001107420 904 817213 738763264 30.0665928 9.6691762 .001106195 905 819025 741217625 30.0832179 9 . 6727403 .001104972 906 820836 743677416 30.0998339 9.6763017 .001103753 907 822649 746142643 30.1164407 9.6798604 .001102536 908 824464 748613312 30.1330383 9.6834166 .001101322 909 826281 751089429 30.1496269 9.6869701 .001100110 910 828100 753571000 30.1662063 9.6905211 .001098901 911 829921 756058031 30.1827765 9.6940694 .001097695 912 831744 758550528 30.1993377 9.6976151 .001096491 913 833569 761048497 30.2158899 9.7011583 .001095290 914 835396 763551944 30.2324329 9.7046989 .001094092 915 837225 766060875 30.2489669 9.7082369 .001092895 916 839056 768575296 30.2654919 9.7117723 .001091703 917 840889 771095213 30.2820079 9.7153051 .001090513 918 842724 773620632 30.2985148 9.7188354 .001089325 919 844561 776151559 30.3150128 9.7223631 .001088139 92J 846400 778688000 30.3315018 9.7258883 .001086957 921 848241 781229961 30.3479818 9.7294109 .001085776 922 850084 783777448 30.3644529 9.7329309 .001084599 923 851929 786330467 30.3809151 9.7364484 .001083423 924 853776 788889024 30.3973683 9.7399634 .001082251 925 855625 791453125 30.4138127 9.7434758 .001081081 926 857476 794022776 30.4302481 9.7469857 .001079914 927 859329 796597983 30.4466747 9.75049.30 .001078749 928 861184 799178752 30.4630924 9.7539979 .001077586 929 863041 801765089 30.4795013 9.757.5002 .001076426 930 864900 804357000 30.4959014 9.7610001 .001075269 Squares, Cubes, Square Roots, Cube Roots and Reciprocals 23 No. Squares Cubes Square roots Cube .roots Reciprocals 931 866761 806954491 30.5122926 9.7644974 .001074114 932 868624 809557568 30.5286750 9.7679922 .001072961 933 870489 812166237 30.5450487 9.7714845 .001071811 934 872356 814780504 30.5614136 9.7749743 .001070664 935 874225 817400375 30.5777697 9.7784616 .001069519 936 876096 820025856 30.5941171 9.7819466 .001068376 937 877969 822656953 30.6104557 9.7854288 .001067236 938 879844 825293672 30.6267857 9.7889087 .001066098 939 881721 827936019 30.6431069 9.7923861 .001064963 940 883600 830584000 30.6594194 9.7958611 .001063830 941 885481 833237621 30.6757233 9.7993336 .001062699 942 887364 835896888 30.6920185 9.8028036 .001061571 943 889249 838561807 30.7083051 9.8062711 .001060445 944 891136 841232384 30.7245830 9.8097302 .001059322 915 893025 843908625 30.7408523 9.8131989 .001058201 946 894916 846590536 30.7571130 9.8166591 .001057082 947 89G309 849278123 30.7733651 9.8201169 .001055966 948 898704 851971392 30.7896086 9.8235723 .001054852 949 900601 854670349 30.8058436 9.8270252 .001053741 950 902500 857375000 30.8220700 9.8304757 .001052632 951 904401 860085351 30.8382879 9.83392S8 .001051525 952 906304 862801408 30.8544972 9.83736G5 .001050420 953 908209 865523177 30.8706981 9.8408127 .001049318 954 910116 868250064 30.8868904 9.8442536 .001048218 955 912025 870983875 30.9030743 9.8476920 .001047120 956 913936 873722816 30.9192497 9.8511280 .001046025 957 915849 876467493 30.9354166 9.8545617 .001044932 958 917764 879217912 30.9515751 9.8579929 .001043841 959 919681 881974079 30.9677251 9.8614218 .001042753 960 921600 884736000 30.9838668 9.8648483 .001041667 961 923521 887503681 31.0CCCOOO 9.8082724 .001040583 962 925444 890277128 31.0161248 9.8716941 .001039501 963 927369 893056347 31.0322413 9.8751135 .001038422 964 929296 895841344 31.0483494 9.8785305 .001037344 965 931225 898632125 31.0644491 9.8819451 .001036269 966 933156 901428696 31.0805405 9.8853574 .001035197 967 935089 904231063 31.0960236 9.8887673 .001034126 968 937024 907039232 31.1126984 9.8921749 .001033058 969 938961 909853209 31.1287648 9.8955801 .001031992 970 940900 912673000 31 . 1448230 9 . 8989830 .001030928 971 942841 915498611 31 . 1608729 9.9023835 .001029866 972 944784 918330048 31.1769145 9.9057817 .001028807 973 946729 921167317 31.1929479 9.9091776 .001027749 974 948676 924010424 31.2089731 9.9125712 .001026694 975 950625 926859375 31.2249900 9.9159624 .001025641 976 952576 929714176 31.2409987 9.9193513 .001024590 977 954529 932574833 31.2569992 9.9227379 .001023541 978 956484 935441352 31.2729915 9.9261222 .001022495 979 958441 938313739 31.2889757 9.9295042 .001021450 980 960400 941192000 31.3049517 9.9328839 .001020408 981 962361 944076141 31.3209195 9.9362013 .001019368 982 964324 940966168 31 . 3368792 9.9396363 .001018330 983 966289 949862087 31.3528308 9.9430092 .001017294 984 968256 952763904 31.3687743 9.9463797 .001016260 985 970225. 955671625 31.3847097 9.9497479 .001015228 986 972196 958585256 31.4006369 9.9531138 .001014199 987 974169 961 504803 31.4165561 9.9564775 .001013171 988 976144 964430272 31.4324673 9.9598389 .001012146 989 978121 967361669 31.4483704 9.9631981 .001011122 990 980100 970299000 31.4642654 9.9665549 .001010101 991 982081 973242271 31.4801.525 9.9699095 .001009082 992 984064 976191488 31.4960315 9.9732619 .001008065 24 Practical Arithmetic No. Squares Cubes Square roots Cube roots Reciprocals DO.i 98()049 979146657 31.5119025 9.9766120 .001007049 9Ji 9:^8036 982107784 31.5277655 9.9799599 .001006036 995 990025 985074875 31.5436206 9.9833055 .001005025 993 99::01G 988047936 31.5594677 9.9866488 .001004016 997 994009 991026973 31.5753068 9.9899900 .001003009 90S 99GC04 994011992 31.5911380 9.9933289 .001002004 9dl 93oo01 997002999 31.6069613 9.9966656 .001001001 lOOU 1000000 1000000000 31.6227766 10.0000000 .001000000 1001 1002001 1003003001 31.6385840 10.0033322 .0009990010 1002 1004004 1006012008 31.6543836 10.0066622 .0009980040 1003 100G009 1009027027 31.6701752 10.0099899 .0009970090 1001 10080 IS 1012048064 31.6859590 10.0133155 .0009960159 lOOo 1010025 1015075125 31.7017349 10.0166389 .0009950249 1006 1012036 1018108216 31.7175030 10.0199601 .0009940358 1007 1014049 1021147343 31.7332633 10.0232791 .0009930487 1008 1016064 1024192512 31.7490157 10.0265958 .0009920635 1009 1018081 1027243729 31.7647603 10.0299104 .0009910803 1010 1020100 1030301000 31.7804972 10.0332228 .0009900990 1011 1022121 1033364331 31.7962262 10.0365330 .0009891197 1012 1024144 1036433728 31.8119474 10.0398410 .0009881423 1013 1026169 1039509197 31.8276609 10.0431469 .0009871668 1014 1028196 1042590744 31.8433666 10.0464506 .0009861933 1015 1030225 1045678375 31.8590646 10.0497521 .0009852217 1016 1032256 1048772096 31.8747549 10.0530514 .0009842520 1017 1034289 1051871913 31.8904374 10.0563485 .0009832842 1018 1036324 1054977832 31.9061123 10.0596435 .0009823183 1019 1038361 1058089859 31.9217794 10.0629364 .0009813543 1020 1040400 1061208000 31.9374388 10.0662271 .0009803922 1021 1042441 1064332261 31.9530906 10.0695156 .0009794319 1022 1044484 1067462648 31.9687347 10.0728020 .0009784736 1023 1046529 1070599167 31.9843712 10.0760863 .0009775171 1024 1048576 1073741824 32.0000000 10.0793684 .0009765625 1025 1050625 1076890625 32.0156212 10.0826484 .0009756098 1026 1052676 1080045576 32.0312348 10.0859262 .0009746589 1027 1054729 1083206683 32.0468407 10.0892019 .0009737098 1028 1056784 1086373952 32.0624391 10.0924755 .0009727626 1029 1058841 1089547389 32.0780298 10.0957469 .0009718173 1030 1060900 1092727000 32.0936131 10.0990163 .0009708738 1031 1062961 1095912791 32.1091887 10.1022835 .0009699321 1032 1065024 1099104768 32.1247568 10.1055487 .0009689922 1033 1067089 1102302937 32.1403173 10.1088117 .0009680542 1034 1069156 1105507304 32.1558704 10.1120726 .0009671180 1035 1071225 1108717875 32.1714159 10.1153314 .0009661836 1036 1073296 1111934656 32.1869539 10.1185882 .0009652510 1037 1075369 1115157653 32.2024844 10.1218428 .0009643202 1038 1077444 1118386872 32.2180074 10 . 1250953 .0009633911 1039 1079521 1121622319 32.2335229 10.1283457 .0009624639 1040 1081600 1124864000 32.2490310 10.1315941 .0009615385 1041 1083681 1128111921 32.2645316 10.1348403 .0009606148 1042 1085764 1131366088 32 . 2800248 10.1380845 .0009596929 1043 1087849 1134626507 32.2955105 10.1413266 .0009587738 1044 1089936 1137893184 32.3109888 10.1445667 .0009578544 1045 1092025 1141166125 32 . 3264598 10.1478047 .0009569378 1046 1094116 1144445336 32.3419233 10.1510406 .0009560229 1047 1096209 1147730823 32 . 3573794 10.1542744 .0009551098 1048 1098304 1151022592 32.3728281 10.15750G2 .0009541985 1049 1100401 1154320649 32.3882695 10.1507359 .0009532888 1050 1102500 1157625000 32.4037035 10.1639636 .0009523810 1051 1104601 1160935651 32.4191301 10.1671893 .0009514748 1052 1106704 1 164252608 32.4345495 10.1704129 .0009505703 1053 1108809 1167575877 32.4499615 10.1736344 .0009496676 1054 1110916 1170905464 32.4653662 10.1768539 .0009487666 Measures of Length 2. WEIGHTS AND MEASURES Measures of Length 12 inches = i foot 3 feet = I yard = 36 inches 5}-i yards = i rod = 198 inches = i6J'^ feet 40 rods = I furlong = 7 920 inches = 660 feet =220 yards 8 furlongs = i mile = 63 360 inches = 5 280 feet = i 760 yards = I yard = 0.0005682 of a mile Gunter's Chain 7.92 inches = i link 100 links = I chain = 4 rods = 66 feet 80 chains = i mile 320 rods Ropes AND Cables 6 feet = I fathom 1 20 fathoms = i cat)le's length Table Showmg Inches Expressed in Decimals of a Foot In 1 2 3 4 5 6 7 8 9 10 11 Foot .0833 .1667 .2500 .3333 .4167 .5000 .5833 .6667 .7500 .8333 .9167 1-32 .0026 .0859 .1693 .2526 .3359 .4193 .5026 .5859 .6693 .7526 .8359 .9193 1-16 .0052 .0885 .1719 .2552 .3385 .4219 .5052 .5885 .6719 .7552 .8385 .9219 3-32 .0078 .0911 .1745 .2578 .3411 .4245 .5078 .5911 .6745 .7578 .8411 .9245 1-8 .0101 .0938 .1771 .2604 3438 .4271 .5104 .5938 .6771 .7604 .8438 .9271 5-32 .0130 .0964 .1797 .2630 .3464 .4297 .5130 .5964 .6797 .7630 .8464 .9207 3-16 .0156 .0990 .1823 .2656 .3490 .4323 .5156 .5990 .6823 .7656 .8490 .9323 7-32 .0182 .1016 .1849 .2682 .3516 .4349 .5182 .6016 .6849 .7682 .8516 .9349 1-4 .0208 .1042 .1875 .2708 .3542 .4375 .5208 .6042 .6875 .7708 .8542 .9375 9-32 .0234 .1068 .1901 .2734 .3568 .4401 .5234 .6068 .6901 .7734 .8568 .9401 5-16 .0260 .1094 .1927 .2760 .3594 .4427 .5260 .6094 .6927 .7700 .8594 .9427 11-32 .0286 .1120 .1953 .2786 .3620 .4453 .5286 .6120 .0953 .7786 .8620 .9453 3-8 .0313 .1146 .1979 .2813 .3646 .4479 .5313 .6146 .6979 .7813 .8646 .9479 13-32 .0339 .1172 .2005 .2839 .3672 .4505 .5339 .6172 .7005 .7839 .8672 .9505 7-16 .0305 .1198 .2031 .2865 .3698 .4531 .5365 .6198 .7031 .7865 .8698 .9531 15-32 .0391 .1224 .2057 .2891 .3724 .4557 .5391 .6224 .7057 .7891 .8724 .9557 1-2 .0417 .1250 .2083 .2917 .3750 .4583 .5417 .6250 .7083 .7917 .8750 .9583 17-32 .0443 .1276 .2109 .2943 .3776 .4609 .5443 .6276 .7109 .7943 .8776 .9609 9-16 .0469 .1302 .2135 .2969 .3802 .4635 .5469 .6302 .7135 .7969 .8802 .9635 19-32 .0495 .1328 .2161 .2995 .3828 .4661 .5495 .6328 .7161 .7995 .8828 .9661 5-8 .0521 .1354 .2188 .3021 .3854 .4688 .5521 .6354 .7188 .8021 .8854 .9688 21-32 .0547 .1380 .2214 .3047 .3880 .4714 .5547 .6380 .7214 .8047 .8880 .9714 11-16 .0573 .1406 .2240 .3073 .3906 .4740 .5573 .6406 .7240 .8073 .8906 .9740 23-32 .0599 .1432 .2266 .3099 .3932 .4766 .5599 .6432 .7266 .8099 .8932 .9766 3-4 .0625 .1458 .2292 .3125 .3958 .4792 .5625 „0458 .7292 .8125 .8958 .9792 25-32 .0651 .1484 .2318 .3151 .3984 .4818 .6651 .6481 .7318 .8151 .8984- .9818 n-16 .0677 .1510 .2344 .3177 .4010 .4844 .5677 .6510 .7344 .8177 .9010 .9844 27-32 .0703 .1536 .2370 .3203 .4036 .4870 .5703 .6536 .7370 .8203 .9036 .9870 7-8 .0729 .1563 .2396 .3229 .4063 .4896 .5729 .6563 .7396 .8229 .9063 .9898 29-32 .0755 .1589 .2422 .3255 .-'<0S9 .4922 .5755 .6589 .7422 .8255 .9089 .9922 15-lP .0781 .1615 .2448 .3281 .4115 .4948 .5781 .6615 .74-48 .8281 .9115 .9948 31-32 .0807 .1641 .2474 .3307 .4141 .4974 .5807 .6641 .7474 .8307 .9141 .9974 1 2 3 4 5 6 7 8 9 10 11 26 Weights and Measures Decimal Equivalents for Fractions of an Inch H2 H4 Decimals Frac- tions H2 H4 Decimals Frac- tions 1 0.015625 33 0.515625 i 2 0.03125 17 34 0.53125 3 0.046875 35 0.546875 2 4 0.0625 Me 18 36 0.5625 Me 5 0.078125 37 0.578125 3 6 0.09375 19 38 0.59375 7 0.109375 39 0.609375 4 8 0.125 H 20 40 0.625 H 9 0.140625 41 0.640625 5 10 0.15625 21 42 0.65625 11 0.171875 43 0.671875 6 12 0.1875 . Me 22 44 0.6875 iMe 13 0.203125 45 0.703125 7 14 0.21875 23 46 0.71875 15 0.234375 47 0.734375 8 16 0.25 H 24 48 0.75 % 17 0.265625 40 0.765625 9 18 0.28125 . .* 25 50 0.78125 19 0.296875 51 0.796875 io 20 0.3125 Me 26 52 0.8125 iMe 21 0.328125 53 0.828125 ii 22 0.34375 27 54 0.84375 23 0.359375 55 0.859375 12 24 0.375 H 28 56 0.875 Ii 25 0.390625 57 0.890625 13 26 0.40625 29 58 0.90625 27 0.421875 59 0.921875 14 28 0.4375 Vie 30 60 0.9375 iMe 29 0.453125 61 0.953125 ii 30 0.46875 31 62 0.96875 31 0.484375 63 0.984375 16 32 0.5 H 32 64 1. i Nautical Measures A nautical or sea-mile is the length of a minute of longitude of the earth at the equator at the level of the sea. It is assumed that 6086.07 f t = 1. 152664 statute or land-miles by the United States Coast Survey. 3 nautical miles = i league Miscellaneous Measures I palm = 3 inches I hai^d = 4 inches I span I meter » 9 inches = 3.2809 feet Surface, Volume and Cubic Measures 2? Measures of Surface 144 square inches = i square foot 9 square feet = i square yard = i 296 square inches 100 square feet = i square (architects' measure) Land MEASubE 30H square yards = i square rod 40 square rods = i square rood = i 210 square yards 4 square roods | = i acre = 4 840 square yards 10 square chains \ =160 square rods (640 acres = i square mile = 3 097 600 square yards = ) 1 102 400 square rods = 2 560 square roods ) 208.71 feet square = i acre = 43S6o square feet A SECTION of land is a square mile, and a quarter-section is 160 acres Measures of Volume 1 gallon, liquid measure = 231 cubic inches, and contains 8.339 avoirdupois pounds of distilled water at 39.8° F., or 58 333 grains I cubic foot contains 7.48 liquid gallons, or 6.428 dry gallons I gallon, dry measure = 268.8 cubic inches I bushel (Winchester) contains 2150.42 cubic inches, or 77.627 pounds dis- tilled water at 39.8° F. A heaped bushel contains 2747.715 cubic inches Dry Measure 2 pints = I quart = 67.2 cubic inches 4 quarts = i gallon = 8 pints = 268.8 cubic inches 2 gallons = I peck =16 pints = 8 quarts = 537.6 cubic inches 4 pecks = I bushel = 64 pints =32 quarts = 8 gallons = 2150.42 cubic inches I cord of wood =128 cubic feet Liquid Measure 4 gills = I pint =16 fluid ounces 2 pints = I quart - 8 gills =32 fluid ounces 4 quarts = i gallon =32 gills = 8 pints =128 fluid ounces In the United States and Great Britain i barrel of wine or brandy = 311^^ gallons, and contains 4.21 1 cubic feet. A hogshead is 63 gallons, but this term is often applied to casks of various capacities. Cubic Measure 1728 cubic inches = i cubic foot 27 cubic feet = i cubic yard In measuring wood, a pile of wood cut 4 feet long, piled 4 feet high, and 8 feet on the ground, making 128 cubic feet, is called a cord. 16 cubic feet make one cord-foot. A perch of stone is nominally i6J'^ feet long, i foot high and iH feet thick, and contains 24^ cubic feet. 2^ Weights and Measures Part 1 A i:>erch of stone is, however, often computed differently in different localities; thus, in most if not all of the States and Territories west of the Mississippi, stone-masons figure rubble by the perch of iQVz cubic feet. In Philadelphia, 2 2 cubic feet are called a perch. In Chicago, stone is measured by the cord of lOo cubic feet. A TON of shipping is 42 cubic feet in Great Britain and 40 cubic feet in the United States. Fluid Measure 60 minims = i fluid drachm 8 fluid drachms = i ounce 16 ounces = i pint 8 pints = I gallon Miscellaneous Measures Butt of Sherry = 108 gallons Puncheon of Brandy = no to 120 gallons Pipe of Port =115 gallons Puncheon of Rum = 100 to no gallons Butt of Malaga = 105 gallons Hogshead of Brandy = 55 to 60 gallons Punckeon of Scotch Whiskey, Hogshead of Claret = 46 gallons = no to 130 gallons Measures of Weight The standard avoirdupois pound is the weight of 27.7015 cubic inches of distilled water weighed in air at 39-^3° F., with the barometer at 30 inches. It contains 7 000 grains. One pound avoirdupois = 1.2 153 pounds troy. Avoirdupois, or Ordinary Commercial Weight I drachm = 27.343 grains 16 drachms = i ounce (oz) 16 ounces = i pound (lb) 100 pounds = I hundredweight (cwt) 20 hundredweight = i ton In collecting duties upon foreign goods at the United States custom-houses, and also in freighting coal and selling it by wholesale, 28 pounds = I quarter 4 quarters, or 112 pounds = i hundredweight 20 hundredweight = i long ton = 2 240 pounds A stone =14 pounds A quintal =100 pounds The following measures are sanctioned by custom or law: i bushel = 1.244 cubic feet or 1J.4 cubic feet, nearly. 32 pounds of oats • = i bushel 45 pounds of Timothy-seed = i bushel 48 pounds of barley = i bushel 56 pounds of rye = i bushel 56 pounds of Indian com = i bushel 50 pounds of Indian meal = i bushel 60 pounds of wheat = i bushel 60 pounds of clover-seed = i bushel 60 pounds of potatoes = i bushel Troy Weight, etc. Weights of Coins 29 56 pounds of butter = i firkin 100 pounds of meal or Hour = i sack 100 pounds of grain or flour = i cental i(X) pounds of dry fish = i quintal 100 pounds of nails = i cask 196 pounds of flour = i barrel 200 pounds of beef or pork = i barrel 80 pounds of lime = i bushel Troy Weight Used in Weighing Gold or Silver 24 grains = i pennyweight (pwt) 20 pennyweights = i ounce (oz) 12 ounces = i pound (lb) A CARAT of the jewelers, for precious stones, is, in the United States, 3.2 grains, but it varies according to different authorities. In London, 3.17 grains, in Paris, 3.18 grains are divided into 4 jewelers' grains. Ihe international carat is 3.168 grains or 200 milligrams. In troy, apothecaries' and avoirdupois- weights, the grain is the same, i pound troy being equal to 0.82286 pound avoirdupois. Apothecaries' Weight Used in Compounding Medicines and in Putting Up Medical Prescriptions 20 grains (gr) = i scruple (Q) 8 drachms = i ounce (oz) 3 scruples = i drachm (3) 12 ounces = i pound (lb) Measures of Value United States Standard 10 mills = I cent 10 dimes = i dollar 10 cents = I dime 10 doUars = i eagle The standard of gold and silver is 900 parts of pure metal and 100 of alloy in I 000 parts of coin. The fineness expresses the quantity of pure metal in i 000 parts. The REMEDY of THE mint is the allowance for deviation from the exact stand- ard fineness and weight of coins. Weights of Coins Double eagle = Si6 troy grains Eagle = 258 troy grains Dollar (gold) = 25.8 troy grains Dollar (silver) = 412.5 troy grains Half-dollar = 192 troy grains 5-cent piece (nickel) = 77.K 5 troy grains 3-cent piece (nickel) = 30 troy grains Cent (bronze) = 48 troy grains 30 Weights and Measures ^art 1 Measures of Time 60 seconds = i minute 365 days = 1 common year 60 minutes = i hour 366 days = i leap-year 24 hours = I day A SOLAR DAY IS measured by the rotation of the earth upon its axis, with respect to the sun. In ASTRONOMICAL COMPUTATIONS and in NAUTICAL TIME the day commences at noon, and in the former it is counted throughout the 24 hours. In CIVIL COMPUTATIONS the day commences at midnight, and is divided into two parts, of 12 hours each. A SOLAR YEAR is the time in which the earth makes one revolution around the sun. Its average time, called the mean solar ye.\r, is 365 days, 5 hours, 48 minutes and 49.7 seconds, or nearly 36534 days. A mean lunar month, or lunation of the moon, is 29 days, 12 hours, 44 min- utes, 2 seconds and 5.24 thirds. It is equal, on the average, to 29.53 days. The Calendar, Old and New Style The Julian Calendar was established by Julius Csesar, 44 B.C., and by it one day was inserted in every fourth year. This was the same thing as assuming that the length of the solar year was 365 days and 6 hours, instead of the .value given above, thus introducing an accumulative error of 11 minutes and 12 sec- onds every year. This calendar was adopted by the church in 325 a. d., at the Council of Nice. In the year 1582 the annual error of 11 minutes and 12 seconds had amounted to 10 daj^s, which, by order of Pope Gregory XIII, was suppressed in the calendar, and the 5th of October reckoned as the 15th. To prevent the repetition of this error, it was decided to leave out three of the inserted days every 400 years, and to make this omission in the years which are not exactly divisible by 400. Thus, of the years 1700, 1800, 1900 and 2000, all of which are leap-years according to the JuHan Calendar, only the last is a leap-year according to the Reformed or Gregorian Calendar. This Reformed Calendar was not adopted by England until 1752, when 11 days were omitted from the calendar. The two calendars are now often called the Old Style and the New Style. The latter style is now adopted in every Christian country except Russia. Circular and Angular Measures Used for Measuring Angles and Arcs, and for Determining Lati- tude AND Longitude 60 seconds (") = i minute (') 60 minutes = i degree (°) 360 degrees = i circumference (C) The second is usually subdivided into tenths and hundredths. A minute of the circumference of the earth is a geographical mile. The DEGREES of the earth's circumference on a meridian average 69.16 com- mon miles. The Metric System The metric system is a system of weights and measures based upon a unit called a meter. The meter was intended to be one ten-millionth part of the distance from the equator to either pole, measured on the earth's surface at the level of the sea. The Metric System 31 The NAMES of derived metric denominations are 'formed by prefixing to the name of the primary unit of measure: Milli, a thousandth Hecto, one hundred Centi, a hundredth Kilo, a thousand Deci, a tenth Myria, ten thousand Deca, ten This system, first adopted by France, has been extensively adopted by other countries, and is much used in the sciences and the arts. It was legalized in 1 866 by Congress to be used in the United States, and is already employed by the Coast Survey, and, to some extent, by the Mint and the General Post- Office. Linear Measures The METER is the primary unit of lengths. lo millimeters (mm) = i centimeter (cm) = 0.3937 inch 10 centimeters = i decimeter (dm) == 3.937 inches 10 decimeters = i meter (m) = 39.37 inches 10 meters = i decameter = 393.37 inches 10 decameters = i hectometer =328 feet i inch 10 hectometers = i kilometer (km) = 0.62137 mile 10 kilometers = i myriameter = 6.2137 miles The meter is used in ordinary measurements; the centimeter, or milli- meter, in reckoning very small distances; and the kilometer, for roads of great distances. A CENTIMETER is about % of an inch; a meter is about 3 feet 3H inches; a kilometer is about 200 rods, or ^i of a mile. (See page $3.) Measures of Surface The square meter is the primary unit of ordinary surfaces. The are, a square, each of whose sides is ten meters, is the unit of landl measures. TOO square millimeters (mm-) =1 square centimeter (cm^) =0.155 square inch 100 square centimeters = i square decimeter = 15.5 square inches 100 square decimeters = i square meter (m^) = i 550 square inches, or 1.196 square yards 100 centiares, or square meters = i are (a) = 119.6 square yards 100 ares = i hectare (ha) = 2.471 acres A square meter, or one centiare, is about 10^ square feet, or iH square yards, and a hectare is about 2}^^ acres. Cubic Measure The CUBIC meter, or stere, is the primary unit of a volume. I 000 cubic millimeters (mm^) = i cubic centimeter (cm') = 0.061 cubic inch I 000 cubic centimeters = i cubic decimeter (dm') = 61.022 cubic inches I 000 cubic decimeters = i cubic meter (m') = 35.314 cubic feet The stere is the name given to the cubic meter in measuring wood and timber. A tenth of a stere is a decistere, and ten steres are a decastere. A CUBIC METEi^, or STERE, is about iH cubic yards, or about 2H cord feet, 32 Weights and Measures Part 1 Liquid and Dry Measures The LITER is the primary unit of measures of capacity, and is a cube, each of whose edges is a tenth of a meter in length. The iiiccTOLiTKR is the unit in measuring large quantities of grain, fruits, roots and hquids. ID milliliters (ml) = i centiliter (cl) = 0.338 fluid ounce 10 centiliters = i deciliter = 0.845 liquid gill 10 deciliters = i liter (1) = 1.0567 liquid quarts 10 liters = I decahter = 2.6417 gallons 10 decaliters = i hectoliter (hi) = 2 bushels, 3.35 pecks 10 hectoliters = i kiloliter =- 28 bushels, i\i pecks A centiliter is about H of a fluid ounce; a liter is about iHs liquid quarts, or 9io of a dry quart; a hectoliter is about 2% bushels; and a kiloliter is one cubic meter, or stere. Weights The GRAM is the primary unit of weights, and is the weight in a vacuum of a cubic centimeter of distilled water at the temperature of 39.2° F. 10 milligrams (mg) = i centigram (eg) = 0.1543 troy grain 10 centigrams = i decigram (dg) = 1.543 troy grains 10 decigrams = i gram (g) = 15.432 troy grains 10 grams = i decagram = 0.3527 avoirdupois ounce 10 decagrams = i hectogram = 3.5274 avoirdupois ounces 10 hectograms = i kilogram (kg) = 2.2046 avoirdupois pounds 10 kilograms = i myriagram = 22.046 avoirdupois pounds 10 myriagrams = i quintal (q) = 220.46 avoirdupois pounds 10 quintals = i tonneau (t) = 2204.6 avoirdupois pounds I kilogram per kilometer = 0.67195 pound per i 000 feet I pound per thousand feet = 1.4882 kilograms per kilometer I kilogram per square milHmeter= 1 423 pounds per .square inch I pound per square inch = 0.000743 kilogram per square millimeter The gram is used in weighing gold, jewels, letters and small quantities of things. The kilogram, or, for brevity, kilo, is used by grocers; and the tonneau, or metric ton, is used in finding the weight of very heavy articles. A GRAM is about 15'/^ grains troy; the kilo about 2H pounds avoirdupois; and the metric ton, about 2 205 pounds. A KILO is the weight of a liter of water at its greatest density; and the metric ton, of a cubic meter of water. Metric numbers are written with the decimal point (.) at the right of the figures denoting the unit; thus the expression, 15 meters 3 centimeters, is written, 15.03 m. When metric numbers are expressed by figures, the part of the expression at the left of the decimal point is read as the number of the unit, and the part at the right, if any, as a number of the lowest denomination indicated, or as a decimal part of the unit; thus, 46.525 m is read 46 meters and 525 millimeters, or 46 and 525 thousandths meters. In writing and reading metric numbers, according as the scale is 10, 100 or I 000, each denomination should be allowed one, two or three orders of figures. Metric Conversion Table The following metric conversion table has been compiled by C. W. Hunt, and is most convenient in dealing with metric weights and measures: Metric Conversion Table Millimeters X 0.03937 Millimeters -^ 25.4 Centimeters X 0.3937 Centimeters 4- 2.54 Meters X 39-37 Meters X 3.281 Meters X 1.094 Kilometers X 0.621 Kilometers -^ 1.6093 Kilometers X 3280.7 Square millimeters X 0.0155 Square millimeters -1- 645.1 Square centimeters X 0.155 Square centimeters 4- 6.451 Square meters X 10.764 Square kilometers X 247.1 Hectares X 2.471 Cubic centimeters 4- 16.383 Cubic centimeters -^ 3.69 Cubic centimeters -f- 29.57 Cubic meters X 35-315 Cubic meters X 1.308 Cubic meters X 264.2 Liters X 61.022 Liters X 33-84 Liters X 0.2642 Liters -^ 3.78 Liters -4- 28.316 Hectoliters X 3-531 Hectoliters X 2.84 Hectoliters X 0.131 Hectoliters X 26.42 ^ Grams X 15-432 Grams X 981 Grams (water) -i- 29.57 Grams -j- 28.35 Grams per cubic centimeter-?- 27.7 Joule X 0.7373 Kilograms X 2.2046 Kilograms X 35-3 Kilograms^ 1102.3 Kilograms per sq cm X 14.223 Kilogrammeters X 7-233 Kilograms per meter X 0.672 Kilograms per cubic meter X 0.062 Kilograms per cheval-vapeur X 2.235 Kilowatts X 1.34 Watts -^ 746 Watts X 0.7373 Calorie X 3.968 Cheval-vapeur X 0.9863 (Centigrade X 1.8) + 32 Francs X 0.193 Gravity, Paris = inches = inches = inches = inches = inches (Act of Congres.s) = feet = yards = miles = miles = feet = square inches = square inches = square inches = square inches = square feet = acres = acres = cubic inches = fluid drachms (U.S. Pharmacopoeia) = fluid ounce. (U.S. Pharmacopoeia) = cubic feet = cubic yards = gallons (231 cubic inches) : cubic inches. (Act of Congress) = fluid ounces. (U. S. Pharmacopoeia) = gallons (231 cubic inches) = gallons (231 cubic inches) = cubic feet = cubic feet = bushels (2 150.42 cubic inches) = cubic yards = gallons (231 cubic inches) = grains. (Act of Congress) = dynes : fluid ounces = ounces avoirdupois = pounds per cubic inch = foot-pounds = pounds = ounces avoirdupois : tons (2 000 pounds) : pounds per square inch = foot-pounds : pounds per square foot = pounds per cubic foot = pounds per horse-pow«r = horse-power = honse-power = foot-pounds per second = British thermal units (B.T.U.) = horse-power = degrees Fahrenheit = dollars = 980.94 centimeter per second 34 Weights and Measures Part 1 Metric Conversion Tables. This and the following table from Moles- worth's Metrical Tables will be found of great convenience in figuring plans to be executed in Mexico and other countries using the metric system. Feet Converted into Meters Feet 1 2 3 4 10 20 30 40 50 60 70 80 90 0.304794 3.35274 6.40068 9.44863 12.4966 15.5445 18.5925 21.6404 24.6884 27.7363 0.600589 3.65753 6.70548 9.75342 12.8014 15.8493 18.8973 21.9452 24.9931 28.0411 0.914383 3.96233 7.01027 10.0582 13.1062 16.1541 19.2020 22 2500 25.2979 28.3459 1.21918 4.26712 7.31507 10.3630 13.4110 16.4589 19.5068 22.5548 25.6027 28.6507 3.047945 6.095890 9.143835 12.19178 15.23972 18.28767 21.33561 24.38356 27.43150 Scripture and Ancient Measures and Weights Scripture Long Measures Inches Feet Inches Digit = 0.912 Cubit = I 9.888 Palm = 3.648 Fathom = 7 3-552 Span = 10.944 Egyptian Long Measures Nahud cubit = I foot 5.71 inches Royal cubit = Grecian Long Measures = I foot 8.66 inches Feet Inches Feet Inches Digit = 0.7554 Stadium = 604 4.5 Pons (foot) = I . 0.0875 Mile = 4835 Cubit = I 1.5984^^ Jewish Long Measures Cubit = 1.824 feet Mile = 7 296 feet Sabbath-day's journey = 3 648 feet Day's journey =33.164 miles Roman Long Measures Inches Feet Inches Digit = 0.72575 Cubit I 5-406 Uncia (inch) = 0.967 Passus = 4 10.02 Pes (foot) = 11.604 Mille (millarium) = 4842 Roman Weight Ancient Hbbra = 0.7094 pound Arabian foot Babylonian foot Egyptian finger Miscellaneous Feet = I -095 = 1. 140 = 0.06145 Hebrew foot Hebrew cubit Hebrew sacred cubit Feet = 1. 212 = 1.817 = 2.002 Metric Conversion Tables 35 Feet Converted into Meters (Continued) Feet 6 6 7 8 9 1.52397 • 1.82877 2.13356 2.43836 2.74315 10 4.57192 4.87671 5.18151 5.48630 5.79110 20 7:61986 7.92466 8.22945 8.53425 8.83904 30 10.6678 10.9726 11.2774 11.5822 11.8870 40 13.7158 14.0205 14.3253 14.6301 14.9349 50 16.7637 17.0685 17.3733 17.6781 17.9829 60 19.8116 20.1164 20.4212 20.7260 21.0308 70 22.8596 23.1644 23.4692 23.7740 24.0788 80 25.9075 26.2123 26.5171 26.8219 27.1267 90 28.9555 29.2603 29.5651 29.8699 30.1747 Example. 44ft = 13-411 meters = 134-11 decimeters = i 341. i centimeters= 13 411 millimeters. The above-mentioned work contains eighty pages of conversion tables similar to the above. Inches and Sixteenths Converted into Millimeters Inches 1 2 3 4 5 25.400 26.987 50.799 52.387 76.199 77.786 101.60 103.19 127.00 128.59 Me 1.5875 H 3.1749 28.574 53.974 79.374 104.77 130.17 3/16 . 4.7624 30.162 55.561 80.961 106.36 131.76 H 6.3499 31.749 57.149 82.549 107.95 133.35 Vi6 7.9374 33.337 58.736 84 . 136 109.54 134.94 H 9.5248 34.924 60.324 85.723 111.12 136.52 7l6 11.112 36.512 61.911 87.311 112.71 138.11 H 12.700 38.099 63.499 88.898 114.30 139.70 Vxis 14.287 39.687 65.086 90.486 115.89 141.28 H 15.875 41.274 66.674 92.073 117.47 142.87 iMe 17.462 42.862 68.261 93.661 119.06 144.46 ■ % 19.050 44.449 69.849 95.248 • 120.65 146.05 13/(6 20.637 46.037 71.436 96.836 122.24 147.63 l^ 22.225 47.624 73.024 98.423 123.82 149.22 1^6 23.812 49.212 74.611 100.01 125.41 150.81 Inches 6 7 8 9 10 11 152.40 153.98 177.80 179.38 203.20 204.78 228.60 230.18 254.00 255.58 279.39 280.98 Mfl H 155.57 180.97* 206.37 231.77 257.17 282.57 3/16 157.16 182.56 207.96 233.36 258.76 284.16 M 158.75 184.15 209.55 234.95 260.35 285.74 M6 160.33 185.73 211.13 236.53 261.93 287.33 % 161.92 187.32 212.72 238.12 263.52 288.92 Me 163.51 188.91 214.31 239.71 265.11 290.51 \i 165.10 190.50 215.90 241.30 266.70 292.09 »/l6 166.68 192.08 217.48 242.88 268.28 293.68 H 168.27 193.67 219.07 244.47 269.87" 295.27 iHe 169.86 195.26 220.66 246.06 271.46 296.86 % 171.45 196.85 222.25 247.65 273.05 298.44 iMe 173.03 198.43 223.83 249.23 274.63 300.03 74 174.62 200.02 225.42 250.82 276.22 301.62 1^6 176.21 201.61 227.01 252.41 277.81 303.21 For meters, move the decimal point three figures forward. Example. SMe inches = 207.96 millimeters = 20.796 centimeters meters = 0.20796 meter. 2.0796 deci- 36 Geometry and Mensuration Part 1 3. GEOMETRY AND MENSURATION Definitions A POINT is that which has only position. A PLANE is a surface in which, any two points being taken, the straight line joining them will be wholly in the surface. A CURVED LINE is a line of which no part is straight (Fig. 1). Fig. 1. Curved Line Fig. 2. Parallel Lines ^ y^ K Oy^ R R y^o R R Fig. 3. Angles Parallel lines are such as are wholly in the same plane, and have the same direction (Fig. 2). A broken line is a line composed of a series of dashes; thus, . An angle is the opening between two lines meeting at a point, and is termed a RIGHT angle when the two lines are perpendicular to each other, an acute ANGLE when it is less or sharper than a right angle, and an obtuse angle when it is greater than a right angle. Thus, in Fig. 3, A A A A SLTe acute angles, 2iTC obtuse ANGLES and R R R R a,re right angles. Polygons A polygon is a portion of a plane bounded by straight lines. A TRIANGLE is a polygon of three sides. A SCALENE TRIANGLE has none of its sides equal; an isosceles triangle has two of its sides equal; an equilateral triangle has all three of its sides equal. Fig. 4. Right-angled Triangle Fig. 6. Isosceles Triangle Fig. 7. Equilateral Triangle A right-angled triangle is one which has a right angle. The side opposite the right angle is called the hypothenuse; the side on which the triangle is supposed to stand is called its base and the other side, its altitude. Polygons 37 A QUADRILATERAL IS a polygon of four sidec. Quadrilaterals are divided into classes, as follows: the trapezium (Fig. 8). which has no two of its sides parallel; the trapezoid (Fig. 9), which has two of its sides parallel; and the parallelogram (Fig. 10), which is bounded by two pairs of parallel sides. Fig. 8. Trapezium Fig. 9. Trapezoid Fig. 10. Parallelogram A' parallelogram whose sides are not equal and whose angles are not right angles is called a rhomboid (Fig. 11); when the sides are all equal, but the angles are not right angles, it is called a rhombus (Fig. 12), and when the angles are right angles, it is called a rectangle (Fig. 13). A rectangle, all of whose sides are equal, is called a square (Fig. 14). Polygons, all of whose sides are equal, are called regular polygons. Fig. 12. Rhombus Fig. 13 Rectangle Fig. 14. Square Besides the square and equilateral triangles, there are: the pentagon (Fig. 15), which has five sides; the hexagon (Fig. 16), which has six sides; the heptagon (Fig. 17), which has seven sides; and the octagon (Fig. 18), which has eight sides. Fig. 15. Pentagon Fig. 16. Hexagon Fig. 17. Heptagon Fig. 18. Octagon The enneagon or nonagon has nine sides; the decagon has ten sides; and the dodecagon has twelve sides. For all polygons, the side upon which it is supposed to stand is called its base; the perpendicular distance from the highest side or angle to the base (prolonged, if necessary) is called the altitude; and a line joining any two angles not adjacent is called a diagonal. A perimeter is the bounding line of a plane figure. A CIRCLE is a portion of a plane bounded by a curve, all the points of which are equidistant from a point within, called the center (Fig. 19). The circumference is the curve which bounds the circle. A radius is any straight line drawn from the center to the circumference. Any straight line drawn through the center to the circumference on each side is called a diameter. 38 Geometry and Mensuration Parti An ARC of a circle is any part of its circumference. A CHORD is any straight line joining two points of the circumference, as bd, Fig. 19. A SEGMENT is a portion of the circle included between the arc and its chord, as A, Fig. 19. A SECTOR is the space included between an arc and two radii drawn to its ex- tremities, as B, Fig. 19. In the figure, ab is a radius, cd a diameter and db a chord SUBTENDING the arc bed. A tangent is a right line which in passing a curve touches Fig. 19. Circle and Parts without cutting it, as fg, Fig. 19. Volumes A PRISM is a volume whose ends are equal and parallel polygons and whose sides are parallelograms. A prism is triangular, rectangular, etc., according as its ends are tri- angles, rectangles, etc. A cube is a rectangular prism all of whose sides are squares. A cylinder is a volume of uniform diameter, bounded by a curved surface and two equal and opposite parallel circles. A PYRAMID is a volume whose base is a polygon and whose sides are triangles meeting in a point called the vertex. A pyramid is triangular, quadrangular, etc., according as its base is a triangle, quadrilateral, etc. A CONE is a volume whose base is a circle, from which the remain- ing surface tapers uniformly to a point or vertex (Fig. 20) . A CONIC SECTION is the plane figure made by a plane cutting a cone. • An ELLIPSE is the section of a cone cut by a plane passing obliquely through both sides, as at ab, Fig. 21. A PARABOLA is a section of a cone cut by a plane parallel to its side, as at cd. > A HYPERBOLA is a section of a cone cut by a plane making a greater angle with the base than that made by the side of the cone, as at eh. In the ellipse, the transverse axis, or long diameter, is the longest line that can be drawn in it The conjugate axis, or short diameter, is a line drawn through the center at right-angles to the long diameter. A frustum of a pyramid or cone is that which remains after cutting oflf the upper imrt of it by a plane parallel to the base. A sphere is a volume bounded by a curved surface, all points of which are equidistant from a point within, called the center. Mensuration treats of the measurement of lines, surfaces and volumes. Rules To compute the area of a square, a rectangle, a rhombus or a rhomboid. Rule. Multiply the length by the breadth or height. Thus, in Figs. 22, 23 or 24, the area = abX be. Fig. 21. Cone with Section-lines Mensuration-Rules 39 Fig. 22. Square Fig. 23. Rectangle Fig. 24. Parallelogram To compute the area of a triangle. Rule. Multiply the base by the altitude and divide by 2. the area of ahc = abx cd Thus, in Fig. 25. To find the length of the hypothenuse of a right-angled triangle when both sides are known. Rule. Square the length of each of the sides making the right angle, add their squares together and take the square root of their sum. Thus (Fig. 26), the length oi ac= 3, and oibc= 4; then ab = V32 4-42 ^ V9 +16 = V^ V25 = 5, or ab= 5 To find the length of the base or altitude of a right-angled triangle when the length of the hypothenuse and one side is known. Rule. From the square of the length of the hypothenuse subtract the square of the length of the other side and take the square root of the remainder. To find the area of a trapezium (Fig. 27). C Fig. 25. Scalene Triangle Fig. 26. Right-angled Triangle Rule. Multiply the diagonal by the sum of the two perpendiculars falling upon it from the opposite angles and divide the product by 2. Thus, ab X (ce + di) To find the area of a trapezoid (Fig. 28). Rule. Multiply the sum of the two parallel sides by the perpendicular dis- tance between them and divide the product by 2. To compute the area of an irregular polygon. Rule. Divide the polygon into triangles by means of diagonal lines and then add together the areas of all the triangles, as 4, -5 and C (Fig. 29), 40 Geometry and Mensuration Part 1 To find the area of a regular polygon. Rule. Multiply the length of a side by the perpendicular distance to the center (as ao. Fig. 30), multiply that product by the number of sides and divide the result by 2. Fig. 28. Trapezoid Fig. 29. Irregular Polygon Fig. 30. Regular Polygon To compute the area of a regular polygon when the length, only, of a side is given. Rule. Multiply the square of the side b3^ the multiplier opposite the name of the polygon in column A of the following table: Table of Factors for Determining the Elements of Polygons Name of polygon Number of sides A Factor fo'r area B Factor for radius of circum- scribing circle C Factor for length of the sides D Factor for radius of inscribed circle Triangle 3 4 5 6 7 8 9 10 11 12 0.433013 1 1.720477 2.598076 3.633912 4.828427 6.181824 7.694209 9.36564 11.196152 0.5773 0.7071 0.8506 1 1.1524 1.3066 1.4619 1.618 1.7747 1.9319 1.732 1.4142 1.1756 1 0.8677 0.7653 0.684 0.618 0.5634 0.5176 0.2887 0.5 0.6882 . 0.866 1.0383 a. 2071 ji.3737 i.5383 1.7028 1.866 Tetragon Pentagon Hexagon Heptagon Nonagon . Decagon Undecagon Dodecagon To compute the radius of a circle circumscribed about a regular polygon when the length, only, of a side is given. Rule. Multiply the length of a side of the polygon by the number in column B of table. Example. What is the radius of a circle that will contain a hexagon, the length of one side being 5 in? Solution. 5 X I = 5 in. To compute the length of a side of a regular polygon inscribed in a given circle, when the radius of the circle is given. Rule. Multiply the radius of the circle by the number opposite the name of the polygon in column C of table. Example. What is the length of the side of a pentagon contained in a circle 8 ft in diameter? Solution. 8 ft diameters- 2 = 4 ft radius; 4 X 1.1756 = 4.7024 ft. Mensuration of Circles 41 To compute the length of a side of a regular polygon, when the radius of the inscribed circle is given. Rule. Divide the radius of the inscribed circle by the number opposite the name of the polygon in column D of table. To compute the radius of a circle that can be inscribed in a given regular polygon, when the length of a side is given. Rule. IMultiply the Icn;^'th of a side of the polygon by the number opposite the name of the polygon in column D. Example. What is the radius of the circle that can be inscribed in an octagon, the length of one side being 6 in ? Solution. Gx 1.2071 = 7.2426 in. Circles To compute the circumference of a circle. Rule. Multiply the diameter by 3.1416. For many purposes, the multiplier ■i,\^ gives suflficiently accurate results. Example. What is the circumference of a circle 7 in in diameter? Solution. 7 X 3.1416 = 21.9912 in, or 7 X sVi = 22 in, the error in this last result being 0.0088 in. To find the diameter of a circle when the circumference is given. Rule. Divide the circumference by 3. 14 16, or for a very close approximate result, multiply by 7 and divide by 22. To find the radius of an arc when the chord and rise or versed sine are given. Rule. Square onk-half the chord and the risk; divide the sum of these squares by twice the rise; the result will be the radius. Example. The length of the chord ac, Fig. 31, is 48 in, and the rise, bo, is 6 in. What is the radius of the arc? Solution. Radius = oc^ + ho^ 242 + 62 = Si in Fig. 31. Circular Arc, Chord and Rise 2 ho 12 To find the rise or versed sine of a circular arc, when the chord and radius are given. Rule. Square the radius; also square one-half the chord; subtract the latter from the former and take the square root of the remainder. Subtract the result from the radius and the remainder will be the rise. Example. A given arc has a radius of 51 in and a chord of 48 in. What is the rise? Solution. Rise = radius — Vradius^ — \^ chord^ =51— V2 601 — 576 = 51 — 45 = 6 in = rise To compute the area of a circle. Rule. Multiply the square of the diameter by 0.7854, or multiply the square of the radius of 3.1416. Example. What is the area of a circle 10 in in diameter? Solution. 10 X 10 X 0.7854 = 78.54 sq in, or 5 X 5 X 3.1416 = 78.54 sq in. Tables of Areas and Circumferences of Circles The following tables will be found very convenient for finding the circum- ferences and areas of circles. 42 Geometry and Mensuration Areas and Circumferences of Circles For diameters from M o to loo, advancing by tenths Dia. Area Circum. Dia. Area Circum. Dia. Area Circum. 0.0 .1 .2 .3 .4 0.007854 0.031416 0.070GS6 0.12560 0.31416 0.62832 0.9424S 1.2566 5.0 .1 .2 .3 .4 19.6350 20.4282 21.2372 22.0018 22.9022 15.7080 16.0221 16.3363 16.6504 16.9640 10.0 .1 .2 .3 .4 78.5398 80.1185 81.7128 83.3229 84.9487 31.4159 31.7301 32.0442 32.3584 32.6726 .5 .6 .7 .8 .9 0.19635 0.28274 0.3S4S5 0.50266 0.63617 1.570S 1.8850 2.1991 2.5133 2.8274 .5 .6 .7 .8 .9 23.7583 24.0301 25.5176 26.4208 27.3397 17.2788 17.5929 17.9071 18.2212 18.5354 .5 .6 T '.8 .9 86.5901 88.2473 89.9202 91.6088 93.3132 32.9867 33.3009 33.0150 33.9292 34.2434 1.0 .1 .2 .3 .4 0.7854 0.9503 1.1310 1.3273 1.5394 3.1416 3.4558 3.7699 4.0841 4.3982 6.0 .1 .2 .3 .4 28.2743 29.2247 30.1907 31.1725 32.1699 18.8496 19.1037 19.4779 19.7920 20.1002 11.0 .1 .2 .3 .4 95.0332 90.7689 98.5203 100.2875 102.0703 34.5575 34.8717 35.1858 35.5000 35.8142 .5 ;6 i .9 1.7671 2.0106 2.2698 2.5447 2.8353 4.7124 5.0265 5.3407 5.6549 5.9690 .5 .6 .7 .8 .9 33.1831 34.2119 35.2565 36.3168 37.3928 20.4204 20.7345 21.0487 21.3028 21.6770 .5 .6 .7 .8 .9 103.8689 105.6832 107.5132 109.3588 111.2202 36.1283 30.4425 30.7566 37.0708 37.3850 2.0 .1 .2 .3 .4 3.1416 3.4636 3.8013 4.1548 4.5239 6.2832 6.5973 6.9115 7.2257 7.5398 7.0 2 .3 .4 38.4845 39.5919 40.7150 41.8539 43.0084 21.9911 22.3053 22.0195 22.9330 23.2473 12.0 .1 .2 .3 .4 113.0973 114.9901 116.8987 1 18.8229 120.7628 37.6991 38.0133 38.3274 38.6416 38.9557 .5 .6 .7 .8 .9 4.9087 5.3093 5.7256 6.1575 6.6052 7.8540 8.1681 8.4823 8.7965 9.1106 .5 .6 .7 .8 .9 44.1786 45.3646 46.5663 47.7836 49.0167 23.5619 23.8701 24.1903 24.5044 24.8180 .5 .6 .7 .8 .9 122.7185 124.0898 120.0709 123.6790 130.0981 39.2699 39.5841 39.8982 40.2124 40.5265 3.0 .1 .2 .3 .4 7.0686 7.5477 8.0425 8.5530 9.0792 9.4248 9.7389 10.0531 10.3673 10.6814 8.0 .1 .2 .3 .4 50.2655 51.5300 52.8102 54.1061 55.4177 25.1327 25.4 1G9 25.7011 20.0752 26.3894 13.0 .1 2 !3 .4 132.7323 134.7822 136.8478 138.9291 141.0261 40.8407 41.1549 41.4690 41.7832 42.0973 .5 .6 .7 .8 .9 9.6211 10.1788 10.7521 11.3411 11.9459 10.9956 11.3097 11.6239 11.9381 12.2522 .5 .6 .7 .8 .9 56.7450 58.0830 59.4403 60.8212 62.2114 26.703.'-^ 27.0177 27.3310 27.6400 27.9002 .5 .6 .7 .8 .9 143.1388 145.2672 147.4114 149.5712 151.7468 42.4115 42.7257 43.0398 43.3540 43.6681 4.0 .1 .2 .3 .4 12.5664 13.2025 13.8544 14.5220 15,2053 12.5664 12.8805 13.1947 13.5088 13.8230 9.0 .1 .2 .3 .4 63.6173 65.0388 60.4761 67.9291 69.3973 28.2743 28.5385 28.9027 29.2108 29.5310 14.0 .1 .2 .3 .4 153.9380 156.1450 153.3677 160.0001 162.8602 43.9823 44.2965 44.6106 44.9248 45.2389 .5 .6 .7 .8 .9 15.9043 16.6190 17.3494 18.0956 18.8574 14.137? 14.4513 14.7655 15.0796 15.3938 .5 .6 .7 .8 .9 70.8822 72.3823 73.8981 75.4296 76.9769 29.8451 30.1593 30.4734 30.7876 31.1018 5 .6 .7 .8 .9 105.1300 167.4155 169.7167 172.0336 174.3602 45.5531 45.8673 46.1814 46.4956 46.8097 . Table of Areas and Circumferences of Circles 43 Areas and Circumferences of Circles (Continued) Advancing by tenths Dia. 15.0 .1 .2 .3 .4 Area CircTim. Dia. Area Circum. Dia. Area Circum. 176.7146 179.0786 181.4584 183.8539 180.2650 47.1239 47.4380 47.7522 48.0604 48.3805 20.0 .1 .2 ,3 .4 314.1593 317.3087 320.4739 323.6547 326.8513 62.8319 63.1460 03.1002 03.7743 04.0885 25.0 .1 .2 .3 !4 490.8739 494.8087 498.7592 502.7255 506.7075 78.5398 78.8540 79.1681 79.4823 79.7965 .5 .0 .7 8 .9 188.6919 191.1345 193.5928 190.0668 198.5565 48.6947 49.0088 49.3230 49.6372 49.9513 .5 .6 .7 .8 .9 330.0636 333.2916 336.5353 339.7947 343.0698 64.4026 64.7108 65.0310 65.3451 65.6593 .5 .0 .7 .8 .9 510.7052 514.7185 518.7476 522.7924 526.8529 80.1106 80.4248 80.7389 81.0531 81.3672 16.0 .1 .2 .3 .4 201.0619 203.5831 206.1109 208.6724 211.2407 50.2655 50.5796 50.8938 51.2080 51.5221 21.0 .1 .2 .3 A 346.3606 349.6671 352.9894 356.3273 359.6809 65.9734 66.2876 66.6018 66.9159 67.2301 26.0 .1 .2 .3 .4 530.9292 535.0211 539.1287 543.2521 547.3911 81.6814 81.9956 82.3097 82.6239 82.9380 .5 .6 .7 .8 .9 213.8246 216.4243 219.0397 221.0708 224.3176 51.8303 52.1504 52.4040 52.7788 53.0929 .5 .6 .7 .8 .9 363.0503 360.4354 309.8361 373.2526 376.6848 67.5442 67.8584 68.1720 68.4867 68.8009 .5 .6 .7 .8 .9 551.5459 555.7163 559.9025 564.1044 568.3220 83.2522 83.5664 83.8805 84.1947 84.5088 17.0 .1 .2 .3 .4 220.9801 220.6533 232.3522 235.0618 237.7871 53.4071 53.7212 54.0354 54.3490 54.6637 22.0 .1 .2 .3 .4 380.1327 383.5963 387.0750 390.5707 394.0814 69.1150 69.4292 69.7434 70.0575 70.3717 27.0 .1 .2 .3 .4 572.5553 576.8043 581.0690 585.3494 589.6455 84.8230 85.1372 85.4513 85.7655 86.0796 .5 .6 .7 .8 .9 240.5282 243.2849 246.0574 248.8456 251.6494 54.9779 55.2920 55.6002 55.9203 50.2345 .5 .6 .7 .8 .9 397.6078 401.1500 404.7078 408.2814 411.8707 70.6858 71.0000 71.3142 71.6283 71.9425 .5 .6 .7 .8 .9 593.9574 598.2849 602.6282 606.9871 611.3618 86.3938 86.7080 87.0221 87.3363 87.6504 18.0 .1 .2 .3 .4 254.4690 257.3043 200.1553 203.0220. 265.9a44 50.5480 50.8028 57.1770 57.4911 57.8053 23.0 .1 . .2 .3 A 415.4756 419.0963 422.7327 426.3848 430.0526 72.2566 72.5708 72.8849 73.1991 73.5133 28.0 .1 .2 .3 .4 615.7522 620.1582 624.5800 629.0175 633.4707 87.9646 88.2788 88.5929 88.9071 89.2212 .5 .6 .7 .8 .9 268.8025 271.7164 274.6459 277.5911 280.5521 58.1195 58.4330 58.7478 59.0019 59.3701 .5 .6 .7 .8 .9 433.7361 437.4354 441.1503 444.8809 448.6273 73.8274 74.1416 74.4557 74.7699 75.0841 .5 .6 .7 .8 .9 637.9397 642.4243 646.9246 651.4407 655.9724 89.5354 89.8495 90.1637 90.4779 90.7920 19.0 .1 .2 .3 .4 283,5287 286.5211 289.5292 292.5530 295.5925 59.6903 60.0044 60.3180 00.0327 60.9409 24.0 .1 .2 .3 .4 452.3893 456.1671 459.9606 463.7698 467.5947 75.3982 75.7124 76.0265 76.3407 76.6549 29.0 .1 ■ .2 .3 .4 660.5199 665.0830 669.6019 674.2505 678.8668 91.1062 91.4203 91.7345 02.0487 92.3628 .5 .6 .7 .8 .9 298.6477 301.7186 304.8052 307.9075 311.0255 61.2611 61.5752 61.8894 62.2035 62.5177 .5 .6 .7 .8 .9 471.4352 475.2916 479.1636 483.0513 486.9547 76.9690 77.2832 77.5973 77.9115 78.2257 .5 .6 .7 .8 .9 683.4928 688.1345 692.7919 697.4050 702.1538 92.6770 92.9911 93.3053 93.6195 93.9336 44 Geometry and Mensuration Areas and Circumferences of Circles (Continued) Advancing by tenths Dia. 30.0 '.2 .3 .4 .0 .7 .8 .9 31.0 .1 .2 .3 .4 .5 .0 .7 .8 .9 32.0 .1 .2 .3 .4 .5 .6 .7 .8 .9 33.0 .1 .2 .3 .4 .5 .6 .7 .8 34.0 .1 .2 .3 .4 .5 .6 .7 8 Area Circum. Dia. Area Circum. Dia. Area Circum 706.8583 711.5786 710.3145 721.0662 725.S336 730.0167 735.4154 710.2299 7J5.0601 749.9000 754.7076 759.6450 704.5380 769.4407 774.3712 779.3113 784.2672 789.23S8 794.2260 799.2290 804.2477 809.2821 814.3322 819.3980 824.4796 829.5768 834.6898 839.8185 844.9628 850.1229 855.2986 860.4902 805.6973 870.9202 876.1588 881.4131 886.6831 891.9688 897.2703 902.5874 907.9203 913.2688 918.6331 924.0131 929.4088 934.8202 940.2473 945.6901 951.1486 956.6228 94.2478 94.5619 94.8761 95.1903 95.5044 95.8186 96.1327 96.4469 96.7611 97.0752 97.3894 97.7035 98.0177 98.3319 98.6460 98.9602 99.2743 99.5885 99.9026 100.2108 100.5310 100.8^51 101.159; 101.4734 101.7876 102.1018 102.1159 102.7301 103.044 103.3584 103.6726 103.9807 104.3009 104.6150 104.9292 105.2434 105.5575 105.8717 106.1858 106.5000 106.8142 107.128; 107.4425 107.7566 108.0708 108.3849 108.6991 109.0133 109.3274 109.6416 35.0 .1 .2 .3 .4 .5 .6 .7 .8 36.0 37.0 .1 .2 .3 .4 .5 .6 .7 .8 .9 38.0 .1 9 !3 .4 .5 .6 .7 39.0 .1 2 !3 .4 .5 .6 .7 .8 .9 962.1128 967.6184 973.1397 978.6768 984.2296 989.7980 995.3822 1000.9821 1006.5977 1012.2290 1017.8760 1023.5387 1029.2172 1034.911 1040.6212 1046.3467 1052.0'iSO 1057.S449 1063.6176 1069.4060 1075.2101 1 OS 1.0299 1086.P3654 1092.7166 1098.5835 1104.4662 1110.3645 1110.2786 1122.2083 1128.1538 1134.1149 1140.0918 1146.0844 1152.0927 1158.1167 1104.1564 1170.2118 1176.2830 1182.3698 1 188.4724 1194.5906 1200.7246 1200.8742 1213.0396 1219.2207 1225.4175 1231.6300 1237.8582 1244.1021 1250.3617 109.9557 110.2699 110.5841 110.8982 111.2124 111.5265 111.840: 112.1549 112.4690 112.7832 113.0973 113.4115 113.7257 114.0398 114.3510 114.66']1 114.9S2C 115.290^ 115.[J]0C 115.9248 116.23! 110.5531 116.8672 117.1814 117.495(1 117.8097 118.1239 118.4380 118.7522 119.0604 119.3805 119.0947 120.0088 120.3230 120.6372 120.9513 121.2655 121.5700 121.8938 122.2080 122.5221 122.8303 123.1504 123.4640 123.7788 124.0929 124.4071 124 7212 125.0351 125.3495 40.0 '.2 .3 .4 .5 .6 .7 .8 .9 41.0 .1 .2 .3 .4 .5 .6 7 .8 .9 42.0 .1 .2 .3 .4 .5 .6 ,7 .8 .9 43.0 .1 .2 .3 .4 .6 .7 .8 .9 44.0 -1 .2 .3 .4 .5 .6 .7 .8 .9 1256.0371 1262.9281 1269.2348 1275.5573 126.0002 1281.8955 126.9203 1288.2493 1294.0189 1301.0042 1307 4052 1313.8219 1320.2543 1326.7024 1333.1003 1339.0458 1346.1110 1352.0520 1359.1780 1305.7210 1372.2791 1378.8529 1385.4424 1392.0470 1398 6685 1405.3051 1411.9574 1418.0254 1125.3092 1432.0086 1 438 7238 1445.4546 1452.2012 1458.9635 1405 74 1472.5352 1479.3446 1480 1697 1493.0105 1499.8070 1500.7393 1513.0272 1520.5308 1527.4502 1534.3853 1541.3360 1548.302i 155 5.247 1562.2826 1569.2962 1576.325' 1583.3706 Table of Areas and Circumferences of Circles 45 Areas and Circumferences of Circles (Continued) Advancing by tenths Dia. 45.0 .1 .2 .3 A .5 .6 .7 .2 .3 .4 .6 .6 .7 .8 .9 47.0 .1 .2 .3 .4 .5 .6 .7 .8 48.0 .1 .2 .3 .4 .5 .6 .7 49.0 .1 .2 .3 Area 1590.4313 1597.5077 1G04.5999 1G11.7077 1G18.8313 1625.9705 1633.1255 1640.2962 1647.4826 1654.6847 1661.9025 1669.1360 1676.3853 1683.6502 1690.9308 1698.2272 1705.5392 1712.8670 1720.2105 1727.5697 1734.9445 1742.3351 1749.7414 1757.1635 1764.6012 1772.0546 1779.5237 1787.0086 1794.5091 1802.0254 1809.5574 1817.1050 1824.0684 1832.2475 1839.8423 1847.4528 1855.0790 1862.7210 1870.3786 1878.0519 1885.7409 1893.4457 1901.1662 1908.9024 1916.6543 1924.4218 1932.2051 1940.0042 1947.8180 1955.0403 Circum. 141.3717 141.6858 142.0000 142.3142 142.6283 142.9425 143.2566 143.5708 143.8849 144.1991 144.5133 144.8274 145.1416 145.4557 145.7699 146.0841 146.3982 146.7124 147.0265 147.3407 147.6550 147.9690 148.2832 148.5973 148.9115 149.2257 149.5398 149.8540 150.1681 150.4823 150.7964 151.1106 151.4248 151.7389 152.0531 152.3672 152.6814 152.9956 153.3097 153.6239 153.9380 154.2522 154.5664 154.8805 155.1947 155.5088 155.8230 156.1372 156.4513 156.7655 Dia. 50.0 .1 .2 .3 .4 .5 .6 .7 51.0 .1 .2 .3 .4 .5 .6 .7 .8 52.0 '.2 .3 .4 .5 .6 .7 53.0 .1 .2 .3 A 54.0 .1 .2 .3 A .5 .6 .7 Area 1963.4954 1971.3572 1979.2348 1987.1280 1995.0370 2002.9617 2010.9020 2018.8581 2026.8299 2034.8174 2042.8206 2050.8395 2058.8742 2066.9245 2074.9905 2083.0723 2091.1697 2099.2829 2107.4118 2115.5563 2123.7166 2131.8926 2140.0843 2148.2917 2156.5149 2164.7537 2173.0082 2181.2785 2189.5644 2197.8661 2206.1834 2214.5165 2222.8653 2231.2298 2239.6100 2248.0059 2256.4175 2264.8448 2273.2879 2281.7466 2290.2210 2298.7112 2307.2171 2315.7386 Circum. 2324.2759 170.9026 2332.8289 2341.3976 2349.9820 2358.5821 2367.1979 157.0796 157.3938 157.7080 158.0221 158.3363 158.6504 158.9646 159.2787 159.5929 159.9071 160.2212 160.5354 160.8495 161.1637 161.4779 161.7920 162.1062 162.4203 162.7345 163.0487 163.3628 163.6770 163.9911 164.3053 164.6195 164.9336 165.2479 165.5619 165.8761 166.1903 166.5044 166.8186 167.1327 167.4469 167.7610 168.0752 168.3894 168.7035 169.0177 169.3318 169.6460 169.9602 170.2743 170.5885 Diu. 171.2168 171.5310 171.8451 172.1593 172.4735 55.0 .1 .2 .3 A .5 .6 .7 .8 .9 56.0 .1 .2 .3 A .5 .6 .7 .8 .9 57.0 .1 .2 .3 .4 .6 .7 .8 .9 58.0 .1 .2 .3 .4 .5 .6 .7 .8 .9 59.0 .1 .2 .3 .4 .5 .6 .7 Area 2375.8294 2384.4767 2393.1396 2401.8183 2410.5126 2419.2227 2427.9485 2436.6899 2445.4471 2454.2200 2463.0086 2471.8130 2480.6330 2489.4687 2498.3201 2507.1873 2516.0701 2524.9687 2533.8830 2542.8129 2551.7586 2560.7200 2569.6971 2578.6899 2587.6985 2596.7227 2605.7626 2614.8183 2623.8890 2632.9767 2642.0794 2651.1979 2660.3321 2669.4820 2678.6476 2687.8289 2697.0259 2706.2386 2715.4670 2724.7112 2733.9710 2743.2466 2752.5378 2761.8448 2771.1675 2780.5058 2789.8599 2799.2297 2808.6152 2818.0165 46 Geometry and Mensuration Part 1 Areas and Circumferences of Circles (Continued) Advancing by tenths Dia. Area Circum Dia. 65.0 '.2 .3 .4 Area Circum Dia 70.0 .1 .2 .3 .4 Area Circum. 60.0 .1 .2 .3 .4 2827.433^ 2836.866C 2846.314^ 2855.778"^ 2865.2582 188.495C 188.8097 189.1239 189.438C 189.7522 3318-.3072 3328.525b 3338.759C 3349.0085 3359.273( 204.2035 204.5171 204.831? 205. 14U 205.4602 3848.451( 3859.454-3 3870.473( 3881.5084 3892.559C ) 219.9115 220.2256 220.5398 220.8540 221.1681 .5 .6. .7 .8 .9 2874.753C 2884.264^ 2893.7917 2903.334S 2912.8926 190.066^ 190.380£ 190.6947 191.008? 191.323C .5 .6 .7 .8 ) .9 3369.554S 3379.S51C 3390.163S 3400.491S 3410.S35C 205.774S 206.0885 206.402C 206.716? 207.031C .5 .6 .7 .8 .9 3903.6252 3914.7072 3925.8049 3936.9182 3948.0472 221.4823 221.7964 222.1106 222.4248 222.7389 61.0 .1 .2 .3 .4 2922.466C 2932.0565 2941.6617 2951.282S 2960.9197 191.637^ 191.95K 192.265^ 192.579( 192.893? 66.0 .1 .2 .3 .4 3421.1944 3431.5695 3441.9G0c 3452.3669 3462.7891 207.3451 207.6595 207.9734 208.2876 208.6017 71.0 .1 .2 .3 .4 3959.1921 3970.352f 3981.5289 3092.720? 4003.9284 223.0531 223.3672 223.6814 223.9956 224.3097 .5 .6 .7 .8 .9 2970.5722 2980.2405 2989.9244 2999.6241 3009.3395 193.207S 193.5221 193.8362 194.1504 194.464C .5 .6 .7 .8 .9 3473.2270 3483.6807 3494.1500 3504.6351 3515.1359 208.9159 209.2301 209.5442 209.8584 210.1725 .5 .6 .7 .8 .9 4015.1518 4026.3908 4037.6456 4048.9160 4060.2022 224.6239 224.9380 225.2522 225.5664 225.3805 62.0 .1 2 ."3 .4 3019.0705 3028.8173 303S.5798 3048.3580 3058.1520 194.7787 195.0929 195.-^071 195.7212 196.0354 67.0 .1 .2 .3 .4 3525.6524 3536.1845 3546.7324 3557.2960 3567.8754 210.4867 210.S009 211.115C 211.4292 211.743c 72.0 .1 2 !3 .4 4071.5041 4082.8217 4094.1550 4105.5040 4110.8687 226.1947 226.5088 226.8230 227.1371 227.4513 .5 .6 .7 .8 .9 3067.9616 3077.7869 3087.6279 3097.4847 3107.3571 196.3495 196.6637 196.9779 197.2920 197.6062 .5 .6 .7 .8 .9 3578.4704 3589.0811 3599.7075 3610.3497 3621.0075 212.0575 212.3717 212.6S5r 213.000C 213.3141 .5 .6 .7 .8 .9 4128.2491 4139.6452 4151.0571 4102.4846 4173.9279 227.7655 228.0796 228.3938 228.7079 229.0221 63.0 '.2 .3 .4 3117.2453 3127.1492 3137.0688 3147.0040 3156.9550 197.9203 198.2345 198.548-7 198.8628 199.1770 68.0 .1 .2 .3 .4 3631.6811 3642.3704 3653.0754 3663.79C0 3674.5324 213.628c 213.9425 214.2560 214.5708 214.8849 73.0 .1 .2 .3 .4 4185.3868 4196.8615 4208.3519 4219.8579 4231.3797 229.3363 229.6504 229.9646 230.2787 230.5929 .5 .6 .7 .8 .9 3166.9217 3176.9043 3186.9023 3196.9161 3206.9456 199.4911 199.8053 200.1195 200.4336 200.7478 .5 .6 .7 .8 .9 3685.2845 3696.0523 3706.8359 3717.6351 3728.4500 215.1991 215.5133 215.8274 216.1416 216.4556 .5 .0 .7 .8 .9 4242.9172 4254.4704 4266.0394 4277.6240 4289.2243 230.9071 231.2212 231.5354 231.8495 232.1637 64.0 .1 .2 .3 .4 3216.9909 3227.0518 3237.1285 3247.2222 3257.3289 201.0620 201.3761 201.6902 202.0044 202.3186 69.0 .1 .2 .3 .4 3739.2807 3750.1270 3760.9891 3771.8668 3782.7603 216.7699 217.0841 217.3982 217.7124 218.0265 74.0 .1 .2 .3 .4 4300.8403 4312.4721 4324.1195 4335.7827 4347.4616 232.4779 232.7920 233.1062 233.4203 233.7345 .5 .6 .7 .8 .9 3267.4527 3277.5922 3287.7474 3297.9183 3308.1049 202.6327 202.9469 203.2610 203.5752 203.8894 .5 .6 .7 .8 .9 3793.6695 3804.5944 3815.5350 3826.4913 3837.4633 218.3407 218.6548 218.9690 219.2832 219.5973 .5 .6 .7 .8 .9 4359.1562 4370.8664 4382.5924 4394.3341 4406.0916 234.0487 234.3628 234.6770 234.9911 235.3058 Table of Areas and Circumferences of Circles 47 Areas and Circumferences of Circles (Continued) Advancing by tenths Dia. Area Circum. Dia. Area Circum. Dia. Area Circum. 75.0 .1 2 !3 .4 4417.8G47 4429.6535 4441.4580 4453.2783 4465.1142 2.35.6104 235.9336 2?.6.2478 236.5019 '236.8761 80.0 .1 .2 .3 .4 5026.5482 5039.1225 5051.7124 5064.3180 5076.0394 251.3274 251.6416 251.9557 252.2609 252.5840 85.0 .1 .2 .3 .4 5674.5017 5687.8614 5701.2367 5714.6277 5728.0345 207.0354 207.3495 207.0637 267.9779 268.2920 .5 .6 .7 .8 .0 4476.9650 44SS.S332 4500.7163 4512.6151 4524.5290 237.1902 237.50i4 237.8186 238.1327 238.^469 .5 .6 .7 .8 .9 5089.5764 5102.2292 5114.8977 5127.5810 5140.2818 252.8982 253.2124 253.5265 253.8407 254.1548 .5 .6 .7 .8 .9 5741.4569 5754.8951 5768.3490 5781.8185 5795.3038 268.6062 268.9203 269.2345 269.54S6 260.8628 76.0 \2 .3 A 4536.4598 4548.4057 4560.3673 4572.3446 4584.3377 238.7610 239.0752 230.3894 239.7035 240.0177 81.0 .1 ;2 .3 .4 5152.0973 5165.7287 5178.4757 5101.2384 5204.0168 254.4600 254.7832 255.0973 255.4115 255.7256 86.0 .1 .2 .3 .4 5808.8048 5822.3215 5835.8539 5849.4020 5862.9659 270 270 270 271 271 1770 4911 8053 1194 4336 .5 .6 .7 .8 .9 4506.3464 4608.3708 4620.4110 4632.4660 4644.5:j84 240.3318 240.6460 240.9602 241.2743 241.5885 .5 .6 .7 .8 .9 5216.8110 5220.6208 5242.4463 5255.2876 5268.1446 256.0398 256.3540 256.6681 256.9823 257.2966 .5 .6 .7 .8 .9 5876.5454 5890.1407 5903.7516 5917.3783 5931.0206 271 272 272 272 273 7478 0619 3761 6902 0044 77.0 '.2 ,3 .4 4656.6257 4668.72S7 46S0.S474 4602.9818 4705.1310 241.9026 242.2168 242.5310 242.8451 243.1592 82.0 .1 .2 .3 .4 5281.0173 5203.0056 5306.8097 5310.7295 5332.6650 257.6106 257.0247 258.2389 258.5531 258.8672 87.0 .1 .2 .3 .4 5944.6787 5958.3525 5972.0420 5985.7472 5999.4081 273.3186 273.6327 273.9469 274.2610 274.5752 .5 .6 .7 .8 .0 4717.2977 4729.4792 4741.6765 4753.8894 4766.1181 243.4734 243.7876 244.1017 244.4159 244.7301 .5 .6 .1 .8 .9 5345.0162 5358.5832 5371.5658 5384.5641 5397.5782 2:^9.1814 250.4956 250.8097 260.1230 200.4380 .5 .6 .7 .8 .9 0013.2047 0020.9570 0040.7250 0054.5088 0068.3082 274.8894 275.2035 275.5177 275.8318 276.1460 7S.0 .1 .2 .3 .4 4778.3624 4790.6225 4802.8083 4815.1897 4827.4909 245.0442 245.3584 245.6725 245.9867 246.3009 83.0 .1 .2 .3 .4 5410.6079 5423.6534 5436.7146 5449.7915 5462.8840 260.752? 261.0063 261.3805 261.6947 202.0088 88.0 .1 .2 .3 .4 6082.1234 0095.9542 0109.8008 0123.0031 0137.5411 276.4602 276.7743 277.0885 277.4026 277.7168 .5 .7 .8 .9 4839.8198 4852.1584 4864.5128 4876.8828 4889.2685 246.0150 246.9292 247.2433 247.5575 247.8717 .5 .6 .7 .8 .9 5475.9923 5489.1168 5502.2561 5515.4115 5528.5826 262.3230 202.0371 202.9513 263.2655 263.5790 .5 .6 .7 .8 .9 0151.4348 6165.3442 6179.2693 6193.2101 6207.1606 278.0309 278.3451 278.6593 278.9740 279.2870 79.0 .1 2 [3 .4 4901.0690 4914.0871 4026.5199 4038.9685 4951.4328 248.1858 248,5000 2^8.8141 249.1283 249.4425 84.0 .1 .2 .3 .4 5541.7604 5554.9720 5568.1902 5581.4242 5594.6739 203.8938 204.2079 204.5221 264.8303 205.1514 89.0 .1 .2 .3 .4 6221.1389 6235.1268 6249.1304 6263.1498 6277.1849 279.6017 279.9159 280.2301 280.5442 280.8584 .0 .7 .8 .9 4063.9127 4976.4084 4988.9108 5001.4460 5013.9897 249.7566 250.0708 250.3850 250.6991 251.0133 .5 .0 .7 .8 .9 5607.9302 5621.2203 5634.5171 5647.8206 5661.1578 265.4646 265.7787 266.0929 266.4071 266.7212 .5 .0 .7 .8 .9 6291.2350 0305.3021 6319.3843 0333.4822 0347.5958 281.1725 281.4867 281.8009 282.1150 282.4292 48 Geometry and Mensuration Areas and Circumferences of Circles (Continued) Advancing by tenths Dia. Area Circum. Dia. Area Circum. Dia. Area Circum. 90.0 63G1.7251 282.7433 293.7389 97.0 7389.8113 304.7345 93.5 6866.1471 .1 6375.8701 283.0575 .0 6880.8419 294.0531 .1 7405.0559 305.0486 .2 6390.0309 283..7717 .7 6895.5524 294.3072 .2 7420.3102 305.3028 .3 6404.2073 283.6858 .8 0910.2780 294.6814 .3 7435.5922 305.6770 .4 6418.3995 284.0000 .9 6925.0205 294.995^ .4 7450.8839 305.9911 .5 6432.6073 284.3141 94.0 0939.7782 295.3097 .5 7406.1913 306.3053 .6 6446.8309 284.6283 .1 6954.5515 295.6239 .0 7481.5144 306.6194 .7 6461.0701 284.9425 .2 6909.3100 295.9380 .7 7496.8532 306.9336 .8 0475.3251 285.2500 .3 0934.1453 290.2522 .8 7512.2078 307.2478 .9 6489.5958 285.5708 .4 0998.9058 296.5063 .9 7527.5780 307.5619 91.0 6503.8822 285.8849 .5 7013.8019 296.8805 98.0 7542.9040 307.8761 .1 6518.1843 286.1991 .6 7028.0538 297.1947 .1 7558.3050 308.1902 .2 6532.5021 286.5133 .7 7043.5214 297.5088 .2 7573.7830 308.5044 .3 r.546.835H 286.8274 .8 7058.4047 297.8230 .3 7589.2101 308.8186 A 6561.1848 287.1416 .9 7073.3033 298.1371 .4 7604.0048 309.1327 .5 0575.5498 287.4557 95.0 7088.2184 298.4513 .5 7020.1293 309.4409 .6 6589.9304 287.7099 .1 7103.1488 298.7655 .0 7035.0095 309.7010 .7 6604.3268 288.0840 .2 7118.1950 299.0790 .7 7651.1054 310.0752 .8 6618.7388 288.3982 .3 7133.0508 299.3938 .8 7606.0170 310.3894 .9 6633.1666 288.7124 .4 7148.0343 299.7079 .9 7682.1444 310.7035 92.0 6647.6101 289.0265 .5 7103.0276 300.0221 99.0 7697.6893 311.0177 J 6062.0692 289.3407 .6 7178.0366 300.3303 .1 7713.2461 311.3318 .2 6676.5441 289.0548 .7 7193.0012 300.0504 .2 77^8.8200 311.0400 .3 6691.0347 289.9690 .8 7208.1016 300.9040 .3 7744.4107 311.9002 .4 6705.5410 290.2832 .9 7223.1577 301.2787 .4 7760.0166 312.2743 .5 6720.0030 200.5973 90.0 7238.2295 301.5929 .5 7775.6382 312.5885 .6 6734.6008 299 9115 .1 7253.3170 301.9071 .0 7791.2754 312.9020 • .7 6749.1542 291.2256 .2 726S.4202 302.2212 .7 7800.9284 313.2108 .8 6763.7233 291.5398 .3 7283 5391 302.5354 .8 7822.5971 313.5309 .9 6778.3082 291.8540 .4 7298.6737 302.8405 .9 7838.2815 313.8451 93.0 6792.9087 292.1681 .5 7313.8240 303.1037 100.0 7853.9816 314.1593 .1 6807.5250 292.4823 .6 7328.9901 303.4779 .2 6822.1569 292.7904 .7 7344.1718 303.7920 .3 68?6.8046 293.1100 .8 7359.3093 304.1002 .4 6851.4680 293.4248 .9 7374.5824 304.4203 Table of Areas and Circumferences of Circles 49 Areas of Circles Advancing by eighths Areas Dia. 0.0 O.J o.i O.f 0.1104 O.J 0.1903 O.f o.i 0, 0.0 0.0122 0.0490 0.3068 0.4417 0.0013 1 0.7854 9940 1.227 1.484 1.707 2.073 2.405 2.701 2 3.1416 3 546 3.976 4.430 4.908 5.411 5.939 6.491 3 7.0GS 7.669 8.295 8.946 9.021 10.32 11.04 11.79 4 12.50 13.36 14.18 15.03 15.90 16.80 17.72 18.66 5 19.63 20.02 21.64 22.69 23.75 24.85 25.96 27.10 28.27 29.46 30.07 31.91 S3.18 34.47 35.78 37.12 7 38.48 39.87 41.28 42.71 44.17 45.66 47.17 48.70 8 50.20 5 1.84 53.45 55.08 50.74 58.42 60.13 61.86 9 03.61 65.39 67.20 69.02 70.88 72.75 74.66 70.58 10 78.54 80.51 82.51 84.54 86.59 88.60 90.76 92.88 11 95.03 97.20 99.40 101.0 103.8 100.1 108.4 110.7 12 113.0 115.4 117.8 120.2 122.7 125.1 127.6 130.1 13 132.7 1S5.2 137.8 140.5 148.1 145.8 148.4 151.2 11 153.9 150.6 159.4 1C2.2 105.1 167.9 170.8 173.7 If) 176.7 179.6 182.6 185.6 188.6 191.7 194.8 197.9 10 201.0 204.2 207.3 210.5 213.8 217.0 220.3 223.6 17 226.9 230.3 233.7 2C7.1 240.5 248.9 247.4 250.9 IS 254.4 258.0 261.5 265.1 2G8.8 272.4 276.1 279.8 19 283.5 287.2 291.0 294.8 298.0 302.4 306.3 310.2 : 20 314.1 318.1 322.0 326.0 330.0 334.1 338.1 342.2 21 316.3 350.4 354.6 358.8 203.0 CG7.2 371.5 375.8 22 380.1 384.4 388.8 393.2 397.0 402.0 406.4 410.9 23 415.4 420.0 424.5 429.1 433.7 438.3 443.0 447.6 24 452.3 457.1 401.8 46G.6 471.4 470.2 481.1 4S5.9 2.^^ 490.8 405.7 500.7 505.7 510.7 515.7 520.7 525.8 20 530.9 536.0 541.1 546.3 551.5 556.7 502.0 507.2 27 572.5 577.8 583.2 5S8.5 593.9 5C9.3 004.8 610.2 2R 615.7 621.2 020.7 632.3 r37.9 643.5 649.1 054.8 29 060.5 660.2 071.9 677.7 083.4 689.2 695.1 700.9 30 706.3 712.7 7ia.(? 724.6 730.0 736.6 742.0 748.0 31 754.8 700.9 767.0 773.1 779.3 785.5 791.7 798.0 32 804.3 810.6 810.9 823.2 829.6 836.0 842.4 848.8 33 855.3 801.8 808.3 874.9 881.4 888.0 894.6 901.3 34 907.9 914.7 921.3 928.1 934.8 941.6 948.4 95'^.3 35 962.1 969.0 975.9 982.8 989.8 996.8 1003.8 1010.8 36 1017.9 1025.0 1032.1 1039.2 1046.3 1053.5 1060.7 1008.0 37 1075.2 1082.5 1089.8 1097.1 1104.5 1111.8 1119.2 U20.7 38 1134.1 1141.6 1149.1 1156.6 1164.2 1171.7 1179.3 1180.9 39 1194.6 1202.3 1210.0 1217.7 1225.4 1233.2 1241.0 1248.8 40 1256.6 1264.5 1272.4 1280.3 1288.2 1296.2 1304.2 1312.2 41 1320.3 1328.3 1336.4 1344.5 1352.7 1360.8 1369.0 1377.2 42 1385.4 1393.7 1402.0 1410.3 1418.6 1427.0 1435.4 1443.8 43 1452.2 1460.7 1469.1 1477.6 1486.2 1494.7 1503.3 1511.9 44 1520.5 1529.2 1537.9 1546.6 1555.3 1564.0 1572.8 1581.6 45 1590.4 1599.3 1608.2 1617.0 1626.0 1634.9 1643.9 1652.9 50 Geometry and Mensuration Circumferences of Circles Advancing by eighths Circumferences Dia. 0.0 O.i 0.1 o.f o.i O.f O.i O.J 0.0 0.3927 0.7854 1.178 1.570 1.963 2.356 2.748 3.141 3.534 3.927 4.319 4.712 5.105 5.497 5.890 2 6.283 6.675 7.068 7.461 7.854 8.246 8.639 9.032 3 9.424 9.817 10.21 10.60 10.99 11.38 11.78 12.17 4 12.56 12.95 13.35 13.74 14.13 14..52 14.92 15.31 5 15.70 16.10 16.49 16.88 17.27 17.67 18.06 18.45 (i 18.84 19.24 19.03 20.02 20.42 20.81 21.20 21.59 7 21.99 22.38 22.77 23.10 23.50 23.95 24.34 24.74 8 25.13 25.52 25.91 26.31 26.70 27.09 27.48 27.88 9 28.27 28.66 29.05 29.45 29.84 30.23 30.63 31.02 10 31.41 31.80 32.20 32.59 32.98 33.37 33.77 34.16 11 34.55 3d .95 35.34 35.73 36.12 36.52 36.91 37.30 12 37.69 38.09 38.48 38.87 39.27 39.00 40.05 40.44 13 40.84 41.23 41.62 42.01 42.41 42.S0 43.19 43.58 14 43.98 44.37 44.76 45.16 45.55 45.94 46.33 46.73 15 47.12 47.51 47.90 48.30 48.69 49.08 49.48 49.87 16 50.26 50.65 51.05 51.44 51.83 52.22 52.62 53.01 17 53.40 53.79 51.19 54.5S 54.97 55.37 55.76 5G.15 18 56.54 56.94 57.33 57.72 58.11 58.51 58.90 59.29 19 59.69 60.08 00.47 60.80 61.26 01.05 02.04 02.43 20 .62.83 63.22 63.61 64.01 64.40 04.79 05.18 65.58 21 65.97 66.30 66.75 67.15 67.54 07.93 08.32 68.72 22 69.11 69.50 69.90 70.29 70.08 71.07 71.47 71 .86 23 72.25 72.64 73.04 73.43 73.82 74.22 74.61 75.00 24 75.39 75.79 76.18 76.57 76.96 77.36 77.75 78.14 25 78.54 78.93 79.32 79.71 80.10 80.50 80.89 81.28 26 81.68 82.07 82.40 82.85 83.25 83.04 84.03 84.43 27 84.82 85.21 85.60 86.00 86..39 80.78 87.17 87.57 28- 87.96 88.35 88.75 89.14 89.53 89.92 90.32 90.71 29 91.10 91.49 91.89 92.28 92.67 93.00 93.46 93.85 30 94.24 94.64 95.03 95.42 95.&1 96.21 96.60 96.99 31 97.39 97.78 c 8.17 98. .57 93.96 99.35 99.75 100.14 32 100.53 100.92 IC 11.32 101.71 102.10 102.49 102.89 103.29 33 103.67 104.07 1( )4.46 104.85 105.24 105.64 100.03 106.42 34 106.81 107.21 1( )7.60 107.99 10S.39 108.78 109.17 109..''>6 35 109.96 110.35 11 0.74 111.13 111.53 111.92 112.31 112.71 36 113.10 113.49 1 3.88 114.28 114.67 115.06 115.45 115.85 37 110.24 110.63 1 17.02 117.42 117.81 118.20 118.00 118.99 38 119.38 119.77 \i >0.17 120.56 120.95 121.34 121.74 122.13 39 122.52 122.92 V. >3.31 123.70 124.09 124.49 124.88 125.27 40 125.66 126.06 V. ^6.45 126.84 127.24 127.63 128.02 128.41 41 128.81 129.20 129.59 129.98 130.38 130.77 131.16 131.55 12 131.95 132.34 132.73 133.13 133.52 133.91 134.30 134.70 43 135.09 135.48 135.87 136.27 130.66 137.05 137.45 137.84 44 " 138.23 138.62 139.02 139.41 139.80 140.19 140.59 140.98 45 141.37 141.70 142.16 142.55 142 94 143.34 143.73 144.12 Table of Areas and Circumferences of Circles 51 Areas and Circumferences of Circles From 1 to 50 Feet Advancing by one inch Diam., Area, Circum., Diam., Area, Circum., Diam., Area, Circum., ft in sqft ft in ft in sqft ft in ft in sqft ft in 1 0.7854 3 m 5 1^.635 15 8H 9 63.6174 28 -^H 1 0.9217 3 m 1 20.2947 15 IIH 1 64.8006 28 63/ 2 1.069 3 8 2 20.9656 16 234 2 65.9051 28 9/2 3 1.2271 3 11 3 21.6475 16 5H 3 67.2007 29 /8 4 1.3962 4 21/8 4 22.34 16 9 4 68.4166 29 33/1 1.5761 4 5% 5 23.0437 17 Vs 5 69.644 29 7 6 1.7671 4 SV2 6 23.7583 17 31/ 6 70.8823 29 101/ 7 1.9689 4 im 7 24.4835 17 6/8 7 72.1309 30 VA 8 2.1816 5 2% 8 25.2199 17 m 8 73.391 30 43/ 9 2.4052 5 5'A 9- 25.9672 18 H 9 74.662 30 7/. 10 2.6398 5 9 10 26.7251 18 '6'A 10 75.9433 30 11/A 11 2.8852 6 H 11 27.4943 18 7A 11 77.2362 31 iM 2 3.1416 6 3-% 6 28.2744 18 lOH 10 78.54 31 5 1 3.4087 6 m 1 29.0649 19 m 1 79.854 31 8H 2 3.6869 6 m 2 29.8668 19 43/8 2 81.1795 31 111/ 3 3.976 7 H 3 30.6796 19 ly^ 3 82.516 32 23/^ 4 4.276 7 VA 4 31.5029 19 lOH 4 83.8627 32 5I/2 5 4.5869 7 7 5 32.3376 20 VA 5 85.2211 32 8% 6 4.9087 7 101/4 1 6 33.1831 20 4% 6 86.5903 32 ll/i 7 5.2413 8 13/8 7 34.0391 20 81.^ 7 87.9697 33 2/8 8 5.585 8 41/2 8 34.9065 20 11/2 8 89.3638 33 61/ 9 5.9335 8 7/8 9 35.7847 21 2% 9 90.7627 33 91/i 10 6.3349 8 103/4 10 36.6735 21 5/2 10 92.1749 34 34 11 6.6813 9 1/8 11 37.5736 21 8% 11 93.5986 34 3>12 3 7.0686 9 5 7 38.4846 21 11^^ 11 95.0334 34 65/ 1 7.4666 9 m 1 39.406 22 3 1 96.4783 34 93/ 2 7.8757 9 113/s 2 40.3388 22 61/^ 2 97.9347 35 % 3 8.2957 10 2/2 3 41.2825 22 m 3 99.4021 35 41/8 4 8.7265 10 5'H 4 42.2367 23 Ys 4 100.8797 35 71/4 5 9.1683 10 83/ 5 43.2022 23 2H 5 102.3689 35 105/8 6 9.6211 10 im 1 6 44.1787 23 634 6 103.8691 36 1/2 7 10.0846 11 3 7 45.1656 23 9U 7 105.3794 36 4/2 8 10.5591 11 m ,8 46.1638 24 m 8 106.9013 36 734 9 11.0446 11 ^% 9 47.173 24 m 9 108.4342 36 107/ 10 11.5409 12 /2 10 48.1962 24 7/4 10 109.9772 37 23/ 11 12.0481 12 Z^A 11 49.2236 24 10->i 11 111.5319 37 51/ 4 12.5664 12 63/ 8 50.2656 25 VA 12 113.0976 37 8% 1 13.0952 12 97^6 1 51.3178 25 m 1 114.6732 37 111/ 2 13.6353 13 1 2 52.3816 25 7% 2 116.2607 38 2Vs 3 14.1862 13 f/f 3 53.4562 25 11 3 117.859 38 53,4 4 14.7479 13 73'4 4 54.5412 26 2M 4 119.4674 38 8^i 5 15.3206 13 10/2 5 55.6377 26 51/ 5 121.0876 39 6 15.9043 14 \% 6 56.7451 26 83^ 6 122.7187 39 31^4 7 16.4986 14 m 7 57.8628 26 11/2 7 124.3598 39 63/^ 8 17.1041 14 ■7% 8 58.992 27 234 8 126.0127 39 91/2 9 17.7205 14 11 9 60.1321 27 53/ 9 127.6765 40 % 10 18.3476 15 2H 10 61.2826 27 9 10 129.3504 40 33/ 11 18.9858 15 5H 11 62.4445 28 H 11 131.036 40 m 62 Geometry and Mensuration Areas and Circumferences of Circles (Continued) Part Diam., ft in Area, sq ft Circum. ft in 13 1 2 3 4 5 6 7 9 10 11 15 1 2 3 4 5 9 10 11 1 2 3 4 5 6 7 8 9 10 11 J 1 2 3 4 5 6 7 8 9 10 11 132.7326 134.4391 136.1574 137.886; 139.626 141.3771 143.1391 144.9111 146.6949 148.4896 150.2943 152.1109 153.9384 155.7758 157.625 159.4852 161.3553 163.2373 165.1303 167.0331 168.9479 170.8735 172.8091 174.7565 176.715 178.6832 180.6634 1^2.6545 184.6555 186.6684 188.6923 190.726 192.7716 194.8282 196.8946 198.973 201.0624 203.1615 205.2726 207.3946 209.5264 211.6703 213.8251 215.9896 218.1662 220.3537 222.551 224.7608 226.9806 229.2105 231.4525 233.7055 235.9682 238.243 240.5287 242.8241 245.1316 247.45 249.7781 252.1184 10 IH m 71/2 lOH IH m 8 2H 5^2 Diam. ft in 43 113/4 44 27/i 44 6 44 9H 45 1/4 45 3^2 45 6H 45 m 46 '^A 46 4 46 7\i 46 im 47 11/2 47 m 47 7^4 47 103^^ 48 2^2 48 51/8 48 81/4 48 im 49 2H 49 5-)4 49 S% 50 50 'ZH 50 61/4 50 m 51 1/2 51 33/4 51 61/2 51 10 52 IH 52 41/4 52 7% 52 WA 53 m 53 47/i 53 8 53 im 54 2H 54 53/8 54 81/2 54 IIH 55 2% 55 6 55 9H 56 1/4 56 3^2 Area, sq ft 9 10 11 20 1 2 3 4 5 6 7 • 8 9 10 11 21 1 2 3 4 5 6 7 Circum., ft in 254.4606 256.8303 259.2033 261.5872 263.9807 266.3864 268.8031 271.2293 273.6678 276.1171 278.5761 281.0472 283.5294 286.021 288.5249 291.0397 293.5641 296.1107 298.6483 301.2054 303.774: 306.355 308.9448 311.5469 314.16 316.7824 319.4173 322.063 324.7182 327.3858 330.0643 332.7522 335.4525 338.1637 340.8844 343.6174 346.3614 349.1147 351.8804 354.6571 357.4432 360.2417 363.0511 365.8608 368.7011 371.5432 374.3947 377.2587 380.1336 383.0177 385.9144 388.822 391.7389 394.6683 397.6087 400.5583 403.5204 406.4935 409.4759 412.4707 56 m 56 9H 57 li 57 4 57 71/^ 57 101/4 58 m 58 41/^2 58 75/8 58 mi 59 2 59 5H 59 81/4 59 nvz 6D 2H2 60 5H 60 83/4 60 im 31/8 Diam. ft in 91/^2 62 m 63 m 63 41/4 63 7% 63 IV/z 64 m 64 43/4 64 71^ 64 11 65 21/4 65 5-^8 65 8M 65 mi 2% Z% 7 lOH 1^8 4^2 7-^8 1034 m 5 81/4 im 2M2 5-H 8^4 23 Area, sq ft 9 10 11 24 1 2 3 4 6 7 8 9 10 11 I 1 2 3 4 5 6 7 8 9 10 11 1 2 3 4 5 6 7 26 Circum., ft in 10 11 27 ' 1 2 3 4 5 6 7 8 9 10 11 415.4766 418.4915 421.5192 424.5577 427.6055 430.6658 433.7371 436.8175 439.9106 443.0146 446.1278 449.2536 452.3904 455.5362 458.6948 461.8642 465.0428 468.2341 471.4363 474.6476 477.8716 481.1065 484.3506 487.6073 490.875 494.1516 407.4411 500.7415 504.051 507.3732 510.7063 514.0484 517.4034 520.7692 524.1441 527.5318 530.9304 534.3379 537.7583 541.1896 .541.6299 548.083 551.5471 555.0201 558.5059 562.0027 565.5084 569.027 572.5566 576.0949 579.6463 583.2085 586.7796 590.3637 593.9587 597.5625 601.1793 604.807 608.4436 612.0931 72 3 72 m 72 m 73 1/^ 73 3H 73 6^4 73 97/i 74 1 74 m 74 7!.4 Table of Areas and Circumferences of Circles 53 W: Areas and Circumferences of Circles (Continued) Diam., Area, Circum., Diam., Area, Circum., Diam., Area, Circum.. 1 ft in sqft ft in ft in sqft ft in ft in sqft ft in 28 615.7536 87 111/2 33 855.301 103 8 38 1134.118 119 4/2 619.4228 88 2?/8 1 859.624 103 11/8 1 1139.095 119 7% 2 623.105 88 5H 2 863.961 104 2/1 2 1144.087 119 10:>4 3 626.7982 88 9 3 868.309 104 53/6 3 1149.089 120 2 4 630.5002 89 Vs 4 872.665 104 8% 4 1154.110 120 5% 5 634.2152 89 ZH 5 877.035 104 11>4 5 1159.124 120 8% 6 637.9411 89 m 6 881.415 105 2% 6 1164.159 120 11% 7 641.6758 89 dy> -7 885.804 105 6 7 1169.202 121 21/2 8 645.4235 90 Ys 8 890.206 105 9/8 8 1174.259 121 5% 9 649.1821 90 Wi 9 894.619 100 H 9 1179.327 121 SH 10 652.9495 90 m 10 899.041 106 3/8 10 1184.403 121 11/8 11 656.73 90 11 H 11. 903.476 106 6% 11 1189.493 122 3/8 29 660.5214 91 m 34 907.922 106 m 39 1194.593 122 61/4 1 604.3214 91 m 1 912.377 107 % 1 1199.719 122 9/2 2 668.1346 91 7^2 2 910.844 107 4 2 1204.824 123 /2 3 671.9587 91 lOVs 3 921.323 107 71/i 3 1209.958 123 3% 4 675.7915 92 vn 4 925.810 107 10/ 4 1215.099 123 644 5 679.6375 92 4'/8 5 930. 3 n 108 1/8 5 1220.254 123 9% 6 683.4943 92 S\i 6 934.822 108 4% 6 1225.420 124 1% 7 687.3598 92 1114 7 939.342 108 7U 7 1230.594 124 4/ 8 691.2385 93 2% 8 943.875 108 lO/s 8 1235.782 124 7% 9 695.1028 93 5/2 9 948.419 109 2 9 1240.981 124 10/2 10 699.0263 93 8>^ 10 952.972 109 oH 10 1246.188 125 1% 11 702.9377 93 11^^ 11 957.538 109 834 11 1251.408 125 43/4 30 706.86 94 2% 35 962.115 109 11% 40 1256.64 125 7% 1 710.791 94 6 1 966.770 110 2/8 1 12G1.879 125 11 2 714.735 94 m 2 971.299 110 534 2 1267.133 126 2/ 3 718.69 95 % 3 975.908 110 8% 3 1272. 39Z 126 53 6 4 722.654 95 3/2 4 980.526 111 4 1277.669 126 8J-2 5 726.631 95 (j-}i 5 985.158 111 3V8 5 1282.955 126 11% 6 730.618 95 m 6 989.803 111 m 6 1288.252 127 2-)4 7 734.615 96 % 7 994.451 111 9% 7 1293.557 127 5-^8 8 738.624 96 4 8 999.115 112 1,.', 8 1298.876 127 9 9 742.645 96 7/i 9 1003.79 112 SVi 9 1304.206 128 H 10 746.674 96 10% 10 1008.473 112 6J/S 10 1309.543 128 3% 11 750.716 97 V/2 11 1013.170 112 10 11 1314.895 128 6/2 31 754.769 97 m 36 1017.878 113 1/s 41 1320.257 128 9% 1 758.831 97 7H . 1 1022.594 113 4/ 1 1325.628 129 H 2 762.906 97 10/8 2 1027.324 113 7/8 2 1331.012 129 3% 3 766.992 98 2 3 1032.004 113 10/8 1 3 1336.407 129 7 4 771.086 98 514 4 1036.813 114 m 4 1341.810 129 10% 1 5 775.191 98 8->8 5 1041.570 114 4/8 5 1347.227 130 m 6 779.313 98 11/2 6 1040.349 114 8 6 1352.655 130 ^Vi 7 783.440 99 2H 7 1051.130 114 ll/sl 7 1358.091 130 7% 8 787.581 99 5% 8 1055.920 115 2H 8 1303.541 130 10^4 I 9 791.732 99 8/8 9 1060.731 115 5% 9 1369.031 131 1% 10 795.892 100 10 1065.546 115 9/1 10 1374.47 131 5 11 800.065 100 3H 11 1070.374 115 11% 11 1379.952 131 8% 32 804.25 100 6M 37 1075.2126 116 2% 42 1385.446 131 11% 1 808.442 100 • 9/2 1 1080.059 116 6 1 1390.247 132 2/2 2 812.648 101 H 2 1084.920 116 9/8 2 1336.462 132 6% 3 816.865 101 3% 3 1089.791 117 M 3 1401.988 132 83/4 4 821.090 101 6/8 4 1094.671 117 3/2 4 1407.522 132 11% 5 825.329 101 10 5 1099.504 117 6/2 5 1413.07 133 3 6 829.579 102 IH 6 1104.409 117 9/8 6 1418.629 133 6% 7 833.837 102 4% 7 1109.381 118 % 7 1424.195 133 9H 8 838.108 102 7/2 8 1114.307 118 4 8 1429.776 134 /2 9 842.391 102 lOH 9 1119.244 118 7\i 9 1435.367 134 3% 10 846.681 103 m 10 1124.189 118 lOWl 10 i440.967 134 63/4 11 850.985 103 4^^ 11 1129.148 119 1% 11 1446.580 134 9% 54 Geometry and Mensuration Areas and Circumferences of Circles (Continued) Diam., ft in Area, sqft Circum., ft in Diam., ft in . Area, sq ft Circum., ft in Diam., ft in Area, sqft Circum., ft in 43 1 2 3 4 5 6 7 8 9 10 11 1452.205 1457.836 1463.483 1469.14 1474.804 1480.483 1486.173 1491.870 1497.582 1503.305 1509.035 1514.779 135 1 135 4H 135 IM 135 lOi--^ 136 15/8 136 4}4 136 7% 136 11 137 2% 137 5H 137 8M 137 11^ 46 1 2 3 4 5 6 7 8 9 10 11 1661.906 1667.931 1673.97 1680.02 1686.077 1692.148 1698.231 1704.321 1710.425 1716.541 1722.663 1728.801 144 m 144 9H 145 % 145 3 1/2 145 65^ 145 97.^ 146 11/^ 146 41/i 146 71/ 146 10)i 147 ly-z 147 4^i 49 1 2 3 4 7 8 9 10 11 1885.745 1892.172 1898.504 1905.037 1911.497 1917.961 1924.426 1930.919 1937.316 1943.914 1950.439 1956.969 153 IIH 154 2H 154 51/2 154 8H 154 1174 155 2^8 155 6 155 914 156 i/i 156 31/i 156 6H 156 9M 44 45 1 2 3 4 5 6 7 8 9 10 11 1 2 3 4 5 6 7 8 9 10 11 1520.534 1526.297 1532.074 1537.862 1543.558 1549.478 1555.288 1561.116 1566.959 1572.812 1578.673 1584.549 1590.435 1596 32j 1602.237 X608.155 1614.082 1020.023 1625.974 1G31.933 1G37.907 1G43.801 1649.883 1655.889 138 2-K 138 5^ 138 9 139 \i 139 314 139 6H 139 9^ 140 % 140 VA 140 iy2 140 10 ^ 141 IH 141 m 141 IM 141 1024 142 VA 142 5 142 • m 142 n\i 143 2'>i 143 51/2 143 8% 143 11^^ 144 3 47 1 2 3 4 5 6 7 8 9 10 11 48 1 2 3 4 5 6 7 8 9 10 11 1734.947 1741.104 1747.274 1753.455 1759.643 1785.845 1772.059 1778.28 1784.515 1700.761 1797.015 1803.283 1809.562 1815.848 1822.149 1828.460 1834.779 1841.173 1847.457 1853.809 1860.175 1866.552 1872.937 1879.335 147 147 148 148 148 148 149 149 149 loOfe 150 150 150 151 151 151 151 152 152 152 152 153 153 153 m 11 21/^ 5H 83^ 111/2 2% m 31/1 % lOi/i m m IVi lOH p/ 81/i 50 1963.5 157 ''A Circular Arcs To find, by the following table, the length of a circular arc when its chord and height, or versed sine is given. Rule. Divide the height by the chord; find in the column of heights the number equal to this quotient; take out the corresponding number from the cokimn of lengths; and multiply this number by the given chord. Example. The chord of an arc is 80 and its versed sine is 30. What is the length of the arc? Solution. 30H- 80= 0.375. The length of an arc for a height of 0.375 i^i from table, 1.34063. 80 X 1.34063 = 107.2504= length o'f arc. Table of Circular Arcs Table of Circular Arcs Hts .001 .00? .003 .004 .005 .000 .007 .008 .009 .010 .011 .012 .013 .014 .015 .016 .017 .018 .019 .020 .021 .022 .023 .024 .025 .026 .027 .028 .029 .030 .031 .032 .033 .034 .035 .036 .037 .038 .039 .040 .041 .042 .043 .044 .045 .046 .047 .048 .049 .050 .051 .052 .053 .054 .055 .056 .057 .058 .059 .060 .061 Lengths 1.00001 1.00001 1.00002 1.00004 1.00007 1.00010 1.00013 1.00017 1.00022 1.00027 1.00032 1.00038 1.00015 1.00053 1.00061 1.00069 1.00078 1.000S7 1.00097 1.00107 1.00117 1.00128 1.00140 1.00153 1.00167 1.001S2 1.00196 1.00210 ] .00225 1.00240 1.00256 1.00272 1.00289 1.00307 1.00327 1.00345 1.00304 1.00384 1.00405 1.00426 1.00447 1.00469 1.00492 1.00515 1.00539 1.00563 1.00587 1.00612 1.00638 1.00665 1.00692 1/ 3720 1.00748 1.00776 1.00805 1.00834 1.00864 1.00S95 1.00026 1.00957 1.00989 Hts I-engths Hts Length,' .002 .063 .064 .065 .066 .067 .068 .009 .070 .071 .072 .073 .074 .075 .076 .077 .078 .079 .080 .081 .082 .083 .084 .085 .086 .087 .088 .089 .000 .091 .092 .093 .09^ .095 .096 .097 .098 .099 .100 .101 .102 .103 .104 .105 .106 .107 .108 .109 .110 .111 .112 .113 .114 .115 .116 .117 .118 .119 .120 .121 .122 1.01021 1.01054 1.01088 1.01123 1.01158 1.01193 1.01228 1.01264 1.01.301 1.01338 1.01376 1.01414 1.01453 1.01493 1.01533 1.01573 1.01614 1.01656 1.0169S 1.01741 1.01784 1.01828 1.01872 1.01916 1.01961 1.02006 1.02052 1.02098 1.02145 1.02192 1.02240 1.02289 1.02339 1.02389 1.02440 1.02491 1.02542 1.02593 1.02645 1.02698 1.02752 1.02806 1.02860 1.02914 1.02970 1.03026 1.03082 1.03139 1.03196 1.03254 1.03312 1.03371 1.03430 1.03490 1.03551 1.03611 1.03672 1.03734 1.03797 1.03860 1.03923 .123 .124 .125 .126 .127 .128 .129 .130 .131 .132 .133 .134 .135 .136 .137 .138 .139 .140 .141 .142 .143 .144 .145 .146 .147 .148 .149 .150 .151 .152 .153 ./54 .155 .156 .157 .158 .159 .160 .161 .162 .163 .164 .165 .166 .167 .168 .169 .170 .171 .172 .173 .174 .175 .176 .177 .178 .179 .180 .181 .182 .183 1.039S7 1.04051 l.Ollir 1.041S1 1.04247 1.04313 1.04.380 1.04447 1.04515 1.04584 1.04652 1.04722 1.04792 1.04802 1.04932 1.05003 1.05075 1.05147 1.05220 1.05293 1.05367 1.05441 1.05516 1.05591 1.05667 1.05743 1.05819 1.05896 1.05073 1.00051 1.06 ISO 1.00200 1 .06288 1.06368 1.06449 1.06530 1.06611 1.06693 1.06775 1.068-58 1.06941 1.07025 1.07109 1.07194 1.07279 1.07365 1.07451 1.07537 1.07624 1.07711 1.07799 1.07888 1.07977 1.08066 1.08156 1.08246 1.08337 1.08428 1.08519 1.08611 1.08704 Hts Lengths Hts Lengths .184 .185 .186 .187 .188 .189 .100 .191 .192 !i93 .194 .195 .196 .197 .198 .199 .200 .201 .202 .203 .204 .205 .206 .207 .208 .209 .210 .211 .212 .213 .214 .215 .216 .217 .218 .219 .220 .221 .222 .223 .224 .225 .226 .227 .228 .229 .230 .231 .232 .233 .234 .235 .236 .237 .238 .239 .240 .241 .242 .243 .244 1.08797 1.08890 1.08984 1 .09079 1.09174 1 .09269 1.09365 1.09461 1.09557 1.09654 1.09752 1.098.50 1.09949 1.10048 1.10147 1.10247 1.10347 1.10447 1.10548 1.10650 1.10752 1.10S55 1.10958 1.11062 1.11165 1.11269 1.11374 1.11479 1.11584 1.11690 1.11796 1.11904 1.12011 1.12118 1.12225 1.12334 1.12444 1.12554 1.12664 1.12774 1.12885 1.12997 1.13108 1.13219 1.133S1 1.13444 1.13557 1.13671 1.13785 1.13900 1.14015 1.14131 1.14247 1.14363 1.14480 1.14.597 1.14714 1.14832 1.14951 1.15070 1.15189 .245 .246 .247 .248 .249 .250 .251 .252 .253 .254 .255 .256 .257 .258 .259 .260 .261 .262 .263 .204 .265 .266 .267 .268 .269 .270 .271 .272 .273 .274 .275 .'>76 .277 .278 .279 .280 .281 .282 .283 .284 .285 .286 .287 .288 .289 .290 .291 .292 .293 .291 .295 .296 .297 .298 .299 .200 .301 .302 .303 .304 .305 1.15308 1.15428 1.15549 1.15670 1.15791 1.15912 1.16034 1.16156 1.16279 1.16402 1.16526 1.16650 1.16774 1.16899 1.17024 1.17150 1.17276 1.17403 , 1.17530 I 1.17657 1.17784 1.17912 1.18040 1.18169 1.18299 1.18429 1.18559 1.18689 1.18820 1.18951 1.19082 1.19214 1.19346 1.19479 1.19612 1.19746 1.19880 1.20014 1.20149 1.20284 1.20419 1.205.55 1.20691 1.20827 1.20964 1.21102 1.21239 1.21377 1.2;515 1.2/654 1.21794 1.21933 1.22073 1.22213 1.22354 1.22495 1.22636 1.22778 1.22920 1.23063 1.23206 56 Geometry and Mensuration Part 1 Table of Circular Arcs (Continued) His Lengths [its Lengths 1.29209 1.29366 Hts [(Cngths Hts Lengi-hs Hts [icngths .30fi .307 1.23349 1 23492 .345 .346 384 1.35575 .423 .424 1.42402 1.425S3 .462 .463 1.49051 1.49842 .385 1.35744 !308 1.23036 .347 1.29523 .386 1.35914 .425 1.42704 .464 1.50033 !309 1.23781 .348 1.29681 .387 1.36084 .426 1.42945 .465 1.50224 .310 1.23926 .349 1 .29839 .388 1.36254 .427 1.43127 .460 1.50416 !311 1.24070 .350 1.29997 .389 1.36425 .428 1.43309 .4()7 1.501)08 .312 1.24216 .351 1.30156 .390 1.36596 .429 1.43491 .468 1.50,i00 !313 1.24301 .35-^ 1.30315 .391 1.36767 .430 1.43673 .409 1.50992 !314 1 .24507 .353 1.30474 .392 1.36939 .431 1.43850 .470 1.51185 !315 1.24654 .354 1.30634 .393 1.37111 .432 1 .44039 .471 1.51378 .316 1.24801 .355 1.30794 .394 1.37283 .433 1.44222 .472 1.51571 !317 1.2494S .356 1.30954 .395 1.37455 .434 1.44405 .473 1.51764 318 1.25095 .357 1.31115 .396 1.37628 .435 1.44589 .474 1.51958 .319 1.25243 .358 1.31276 .397 1.87801 .436 1.44773 .475 1.52152 320 1.25391 .359 1.31437 .398 1.37974 .437 1.44957 .476 1.52340 .321 1 25540 .360 1.31599 .399 1.38148 .438 1.45142 .477 1.52541 322 1.25689 .301 1.31701 .400 1.38322 .439 1.45327 .478 1.52736 .323 1 '->5838 .362 1.31923 .401 1.38496 .440 1.15512 .479 1.52931 !324 1.25988 .363 l.?2086 .402 1.38671 .441 1.45697 .480 1.53126 325 1.26138 .364 1.32249 .403 1.38846 .442 1.45883 .481 1.53322 .320 1 .26288 .365 1.32413 .404 1.39021 .443 1.46069 .482 1.53518 327 1 .26437 .366 1.32577 .405 1.39196 .444 1 . t6255 .483 1.53714 .328 1.26588 .307 1.32741 .406 1.39372 .445 1.46441 .484 1.53010 329 1.26740 .368 1.32905 .407 1.39548 .446 1.46621 .485 1.54106 .330 1.26892 .369 1.33069 .408 1.30724 .447 1.46815 .486 1.54302 .331 1 .27044 .370 1.33234 .409 1.39900 .448 1.47002 .487 1.54499 332 1.27196 .371 1.33309 .410 1.40077 .449 1.471S9 .488 1 .54696 .333 1.27349 .372 1.33564 .411 1.40254 .450 1.4737V .489 1.54893 .334 1.27502 .373 1.33730 .412 1.40432 .451 1.47565 .490 1.55091 .335 1.27656 .374 1.33S96 .413 1.40G10 .452 1.47753 .491 1.55289 .336 1.2:^810 .375 1.34063 .414 1.40788 .453 1.47942 .492 1.554S7 .337 1.27964 .376 1.34229 .415 1.40900 .454 1.48131 .493 1.55685 .338 1.2811S .377 1.34396 .416 1.41145 .455 1.48320 .491 1.55884 .339 1.28273 .378 1.34563 .417 1.41324 .456 1.48509 .495 1.56083 .340 1.28428 .379 1.34731 .418 1.41503 .457 1.48699 .490 1 .56282 341 1.28583 .380 1 .34899 .419 1.41682 .458 1.48880 .407 1.56481 .342 1.28739 .381 1.35068 .420 1.41861 .459 1 .4.9070 .498 1.56681 343 1 .28895 .382 1.35237 .421 1.42041 .460 1 .49269 .409 1 .56881 .344 1.29052 .383 1.35400 .422 1.42221 .461 1.49460 .500 1 .57080 Table of Lengths of Circular Arcs whose Radius is i Rule. Knowing the measure of the circle and the measure of the arc in degrees minutes and seconds; take from the table the lengths opposite the number o degrees,. minutes and seconds in the arc, and muUiply their sum by the radius o the circle. Example. AVhat is the length of an arc subtending an angle of 13° 27' 8> with a radius of 8 ft. Solution. Length for 13° = 0.2268928 27' = 0.0078540 8" = 0.0000388 13° 27' 8"= 0.2347856 Length of arc = i .8782848 ft Table of Circular Arcs 57 Lengths of Circular Arcs. Radius = E Sec 1 Length n. 0000048 Min Length, Deg Length Deg Length 1 0.0002909 1 0.0174533 61 1.0646508 2 0.0000097 2 0.0005818 2 0.0349066 62 1.0821011 3 0.0000145 3 0.0008727 3 0.0523599 63 1.0095574 4 0.0000194 4 0.0011636 4 0.069S132 64 1.1170107 5 0.0000242 5 0.0014544 5 0.0872665 65 1.1314640 6 0.0000291 6 0.0017453 6 0.1047198 66 1.1519173 7 0.0000339 7 0.0020362 7 0.1221730 67 1.1693706 8 0.0000388 8 0.0023271 8 0.1396263 68 1.1868239 9 0.0000436 9 0.0026180 9 0.1570796 69 1.2042772 10 0.0000485 10 0.0029089 10 0.1745329 70 1.2217305 11 . 0000533 11 0.0031998 11 0.1919862 71 1.2391838 12 0.0000582 12 0.0034907 12 0.2094395 72 1.2566371 13 . 0000030 13 0.0037815 13 0.2268928 73 1.2740904 14 0.0000G79 14 0.0040724 14 0.2443461 74 1.2915436 15 0.0000727 15 0.0043633 15 0.2617994 75 1 . 3089969 IG 0.0000776 16 0.0046542 16 0.2792527 76- 1 . 3264502 17 0.0000^24 17 0.0049451 17 0.2967060 77 1 . 3439035 18 0.0000873 IS 0.0052360 18 0.3141503 78 1.3613568 19 0.0000921 19 0.0055269 19 0.3310126 79 1.3788101 20 0.0000970 20 0.0058178 20 0.3490659 80 1.3962634 21 O.OOOIOIS 21 0.0061087 21 0.3665191 81 1.4137167 22 0.0001067 22 0.0063995 22 0.3839724 82 1.4311700 23 0.0001115 23 0.0006904 23 0.4014257 83 1.4486233 24 0.0001164 24 0.00G0813 24 0.4188790 84 1 . 4660766 25 0.0001212 25 0.0072722 25 0.4303323 85 1.4835299 20 0.0001261 26 0.0075631 26 0.4537856 86 •1.5009S32 27 0.0001300 27 0.0078540 27 0.4712389 87 1.5184364 28 0.0001357 28 0.0081449 28 0.4886922 88 1.5358897 29 0.0001406 29 0.00S4358 29 0.50614 '5 89 1.5533430 30 0.0001454 30 0.0087266 30 0.5235988 90 1.5707963 31 0.0001503 31 0.0090175 31 5410521 91 1.5882496 32 0.0001551 32 . 00930S4 32 0.5585054 92 1 . 6057029 33 0.0001600 33 0.0095993 33 0.5750587 93 1.6231562 31 0.0001648 34 0.0098902 34 0.5934119 94 1 . 6406095 35 0.0001097 35 0.0101811 35 0.6108652 95 1.6580628 36 0.0001745 36 0.0101720 36 0.6283185 96 1.6755161 37 0.0001794 37 0.0107629 37 0.6457718 97 1.6929094 S8 0.0001842 38 0.0110538 38 0.6632251 98 1.7104227 39 0.0001891 39 0.0113446 39 0.0806784 99 1.7278760 40 0.0001939 40 0.0116355 40 0.0981317 100 1.7453293 41 0.0001988 41 0.0119264 41 0.7155850 101 1.7627825 42 . 0002036 42 0.0122173 42 0.7330383 102 1.7802358 43 0.0002085 43 0.0125082 43 0.7504916 103 1 . 7976891 44 0.0002133 44 0.0127991 44 0.7679449 104 1.8151424 45 0.0002182 45 0.0130900 45 0.7853982 105 1 8325957 46 0.0002230 46 0.0133809 40 0.8028515 106 1.8500490 47 0.0002279 47 0.0136717 47 0.8203047 107 1.8675023 48 0.0002827 48 0.0139626 48 0.83775f:0 108 1 . 8849556 49 0.0002376 49 0.0142535 49 0.8552113 109 1.9024089 50 0.0002124 50 0.0145444 50 0.8726646 110 1.9198622 51 0.0002473 51 0.0148353 51 0.8901179 111 1.9373155 52 0.0002521 52 0.0151262 52 0.9075712 112 1.9547688 53 0.0002570 53 0.0154171 53 0.9250245 113 1.9722221 54 0.0002618 54 0.0157080 54 0.9424778 114 1.9896753 55 0.0002666 55 0.0159989 55 0.9599311 115 2.0071286 56 0.0002715 56 0.0162897 56 0.9773844 116 2.0245819 57 0.0002763 57 0.0165806 57 0.9948377 117 2.0420352 58 0.0002812 58 0.0168715 58 1.0122910 118 2. 0.^^91885 59 0.0002860 59 0.0171624 59 1 0297443 119 2.0769418 60 0.0002909 60 0.0174533 60 :' .0471976 120 2.0943951 Fig. 32. Circular Arc, 58 Geometry and Mensuration Part 1 To compute the chord of an arc when the chord of half the arc and the versed sine are given. (The versed sine is the perpendicular ho, Fig. 32.) Rule. From the square of the chord of half the arc subtract the square of the versed sine, and take twice the square root of the remainder. Example. The chord of half the arc is 6o, and the Chord and Rise ^^^' versed sine 36. What is the length of the chord of the arc? Solution. 6o2 — 36- = 2 304; V 2 304 = 48; and 48 X 2 = 96, the chord. To compute the chord of an arc when the diameter and versed sine are given. Multiply the versed sine by 2 and subtract the product from the diameter; then subtract the square of the remainder from the square of the diameter and take the square root of that remainder. Example. The diameter of a circle is 100 and the versed sine of an arc 36. What is the chord of the arc? Solution. 36X2=72; 100—72=28; 1002—282=9216; ^9216=96, the chord of the arc. To compute the chord of half an aic when the chord of the arc and the versed sine are given. Rule. Take the square root of the sum of the squares of the versed sine and of half the chord of the arc. Example. The chord of an arc is 96 and the versed sine 36. What is the chord of half the arc? Solution. V362 4- 482 = 60. To compute the chord of half an arc when the diameter and versed sine are given. Rule. Multiply the diameter by the versed sine and take the square root of their product. To compute a diameter. Rule I. Divide the square of the chord of half the arc by the versed sine. Rule 2. Add the square of half the chord of the arc to the square of the versed sine and divide this sum by the versed sine. Example. What is the radius of an arc whose chord is 96 and whose versed sine is 36? Solution. 48^+ 362 = 3 600; 3 600 ^ 36 = 100, the diameter; and the radius = 50. To compute the versed sine. Rule. Divide the square of the chord of half the arc by the diameter. To^ compute the versed sine when the chord of the arc and the diameter are given. Rule. From the square of the diameter subtract the square of the chord j and extract the square root of the remainder; subtract this root from the diam- eter and halve the remainder. To compute the length of an arc of a circle when the number of degrees and ! the radius are given. Rule I. Multiply the number of degrees in the arc by 3.1416 multiplied by ■ the radius and divide by 180. The result will be the length of the arc in the) same unit as the radius. Circles and Spheres 6^ Rule 2. Multiply the radius of the circle by 0.01745 and the product by the degrees in the arc. Example. The number of degrees in an arc is 60 and the radius is 10 in. What is the length of the arc in inches? Solution. 10X3-1416x60=1884.96; and 1884.96-7-180=10.47 in. Or, 10 X 0.01745 X 60 = 10.47 in. To compute the length of the arc of a circle when the length is given in de- grees, minutes and seconds. Rule, (i) Multiply the number of degrees by 0.01745329 and the product by the radius. (2) Multiply the number of minutes by 0.00029 and that prod- uct by. the radius. (3) Multiply the number of seconds by 0.0000048 times the radius. (4) Add together these three results for the length of the arc. (See also, table, page 57.) Example. What is the length of an arc of 60° 10' 5", the radius being 4 ft? Solution, (i) 60° X 0.01745329 X 4 = 4.188789 ft (2) 10' X 0.00029 X 4=0.0116 ft (3) s" X 0.0000048 X 4 = 0.000096 ft (4) The length of the arc = 4.200485 ft To compute the area of a sector of a circle when the degrees of the arc and the radius are given (Fig. 33). (The degrees of the arc are the same as the angle aob.) Rule. Multiply the number of degrees in the arc by the area of the whole circle and divide by 360. Example. What is the area of a sector of a circle whose radius is 5 and length of arc 60°? Solution. Area of circle = 10 X 10 X 0.7854 = 78.54 Hence, area of sector = — '■ = 13.09 360 Note. If the length of the arc is given in degrees and minutes, reduce it to minutes, multiply by the area of the whole circle and divide by 21 600. To compute the area of a sector of a circle when the length of the arc and radius are given. Rule. Multiply the length of the arc by half the length of the radius. The product is the area. To compute the area of a segment of a circle when the chord and versed sine of the arc and the radius or diameter of the circle are given. (The versed sine is the distance cd, Fig. 33.) Rule I. When the segment is less than a semicircle, (i) Find the area of the sector having the same arc as the segment. (2) Find the area of a triangle formed by the chord of the segment and the radii of the sector. (3) Take the difference of these areas. Rule 2. When the segment is greater than a semicircle. Find, by the pre- ceding rule, the area of the lesser portion of the circle and subtract it from the area of the whole circle. The remainder will be the area. To compute the area of the surface of a sphere. Rule. Multiply the diameter by the circumference. The product will be the area of the surface. 60 Geometry and Mensuration Part 1 ^m Example. What is the area of the surface of a sphere lo in in diameter? Solution. Circumference of sphere = ic X 3.1416 = 31.416 in; 10X31.416 = 314.16 sq in, the area of surface of sphere. To compute the total area of the surface of a segment of a sphere. Rule. Multiply the height {be, Fig. 34) by the circumference of the sphere and add the product to the area of the base. ^^^ """^s^ To find the area of the /^ ^\ base, having the diameter of the sphere and the length of the versed sine of the arc abd, find the length of the chord ad by the rule on page 58. Hav- ing, then, the length of the chord ad for the diameter of the base, find the area of the base. Example. The height, be, of a segment abd, is 36 in, and the diameter of the sphere is 100 in (Fig. 34). What is the area of the convex surface and the area of the whole surface? • Solution. 100X3.1416 = 314. 16 in, the circumference of sphere 36 X 314-16 = 11309.76 sq in, the area of the convex surface 10 0- (36 X 2) = 28 Vioo^ — 282 = 96, the chord ad 962 X 0.7854 = 7238.2464 sq in, the area of the base 11309.76 + 7238.2464= 18548.0064 sq in, the total area To compute the total area of the surface of a spherical zone. Rule. Multiply the height, cd (Fig. 35), by the circumference of the sphere (or the convex surface and add to it the area of the two ends for the total area. Fig. 34. Segment of Sphere d Fig. 35. Zone of Sphere Spheroids, or Ellipsoids of Revolution Definition. Spheroids, or ellipsoids, are figures generated by the revolution of a semiellipse about one of its diameters. When the revolution is about the long diameter, they are prolate; and when it is about the short diameter, they are oblate. A PROLATE SPHEROID is approximately cigar-shaped and an oblate spheroid is, in form, somewhat like a watch. To compute the area of the surface of a spheroid. Let a = H the long axis; let 6 = H the short axis; let v^ 2-62 a2 t a' Then, the area of the surface of the oblate spheroid : 2 7ra2 + '-f'»=(:-^) and the area of the surface of the prolate spheroid = 2 7ro2 -f 2 irao • Surfaces and Solids 61 in the first formula, natural logarithms must be used. The natural loga- rithm may be obtained by multiplying the common logarithm by 2.302. The value of the expression sin~^ e may be determined by finding the angle whose natural sine is equal to e and dividing this angle by 57.3. Note. Although the above formulas are compli- cated, no simpler rules that give correct results can be given. To compute the area of the surface of a cylinder. Rule. Multiply the length of the cylinder by the circumference of one of the ends and add to the product the areas of the two ends. To compute the area of a circular ring (Fig. 36). ^'^^' ^^' Circular Ring Rule. Find the area of both circles and subtract the area of the smaller from the area of the larger; the remainder will be the area of the ring. To compute the area of the surface of a cone. Rule. Multiply the circumference of the base by one-half the slant-height or side of the cone, for the convex area. Add to this the area of the base, for the whole area. Example. The diameter of the base of a cone is 3 in and the slant-height 15 in. What is the area of the surface of the cone? Solution. 3X3. 1416 = 9.4248 = circumference of base 9.4248 X 7}'4 = 70.686 sq in = area of convex surface 2>y^2>y\ 07854 = 7.068 sq in = area of base Area of entire surface of cone = 77.754 sq in To compute the area of the surface of the frustum of a cone (Fig. 37). Rule. Multiply the sum of the circumferences of the two ends by the slant-height of the frustum and divide by 2, for the area of the convex surface. Add the areas of the two ends. To compute the area of the surface of a pyramid. Rule. Multiply the perimeter of the base by one- half the slant-height and add to the product the area of the base. To compute the area of the surface of the frustum of a pyramid. Rule. Multiply the sum of the perimeters of the two ends by the slant-height of the frustum, halve the product, and add to the result the areas of the two ends. Fig. 37. Frustum of Cone Mensuration of Solids To compute the volume of a prism. (See page 38 for definition of a prism.) Rule. Multiply the area of the base or end by the altitude or perpendicular height. This rule applies to prisms with bases or ends of any shape, as long as these bases or ends are parallel. 62 Geometry and Mensuration Part 1 To compute the volume of a prismoid. Definition. A prismoid is a soUd with parallel but unequal ends or bases and with quadrilateral sides. Rule To the sum of the areas of the two ends or bases add four times the area of the middle section parallel to them, and multiply this sum by one-sixth of the altitude or perpendicular height. Fig. 38. Quadrangular Prismoid Fig. 39. Prism Truncated Obliquely Example. What is the volume of a quadrangular prismoid, as Fig. 38, in which ab=6 in, cd=4 in, ac = he = lo in, ce = 8 in, e/ = 8 in and ih = 6 in? Solution. Area of top Area of bottom 6 + 4 8 + 6 X lo = 50 sq in X 10 = 70 sq in 6 + 6 Area of middle section = X 10 = 60 sq in 2 [50 + 70 + (4 X 60)] X% = 480 cu in Note. The length of the end of the middle section (as at inn, in Fig. 38) = cd-\-ef 2 To find the volume of a prism truncated obliquely. (I Rule. Multiply the area of the base by the average height of the edges. Example. What is the volume of a truncated prism (Fig. 39) in which ef = 6 mjh = 10 in, ea = 10 in, ci= 12 in, dh = 10 in and/& = 8 in? Fig. 40. Wedge or Right Triangular Solution. Area of base = 6 X 10 =60 Prism sq in Average height of edges 10+12 + 8+10 60 X 10 = 6cx5 cu in Regular Polyhedrons 63 To compute the volume of a wedge or right triangular prism when the ends are parallel and equal. Rule. Multiply the area of one end by the length of the wedge. To compute the volume of a wedge when the ends are not parallel. Rule. Add together the lengths of the three edges, ab, cd and ef (Fig. 40); multiply their sum by the altitude or perpendicular height of the wedge, and then by the breadth of the back, and divide the product by 6. Regular Polyhedrons Definition. A regular polyhedron is a soHd contained within a certain num- ber of similar and equal plane faces, all of which are equal regular polygons. The following is a list of all the regular polyhedrons: (i) The TETRAHEDRON, or pyramid. (2) The HEXAHEDRON, or cube, which has six square faces. (3) The OCTAHEDRON, which has eight triangular faces. (4) The DODECAHEDRON, which has twelve pentagonal faces. (5) The ICOSAHEDRON, which has twenty triangular faces. To compute the volume of a regular polyhedron. Rule I. When the radius of the circumscribing sphere is given. Multiply the cube of the radius of the sphere by the multiplier opposite to the polyhedron in column 2 of the following table. Rule 2. When the radius of the inscribed sphere is given. Multiply the cube of the radius of the inscribed sphere by the multiplier opposite to the polyhedron in column 3 of the table. Rule 3. When the area of the surface of the polyhedron is given. Cube the surface given, extract the square root, and multiply the root by the multipliel opposite to the polyhedron in column 4 of the table. Table of Factors for Determining the Volumes of Regular Polyhedrons Figure 1 Number of sides 2 Factor for volume by radius of circumscribing sphere 3 Factor for volume by radius of inscribed circle 4 Factor for volume by surface Tetrahedron Hexahedron 4 6 8 12 20 0.5132 1.5396 1.33333 2.78517 2.53615 13.85641 8.0000 6.9282 5.55029 5.05406 0.0517 0.06804 0.07311 0.08169 0.0856 Octahedron Dodecahedron Icosahedron To compute the volume of a cylinder. Rule. Multiply the area of the base by the altitude or length. To compute the volume of a cone. Rule. Multiply the area of the base by one-third the altitude. To compute the volume of the frustum of a cone (Fig. 41) . Rule. Add together the squares of the diameters of the two ends or bases and the product of the two diameters; multiply this sum by 0.7854, and this product by the altitude, and then divide this last product by 3. 64 Geometry and Mensuration Part 1 Example. What is the volume of a frustum of a cone 9 in in height, 5 in in diameter at the base and 3 in in diameter at the top? Solution. 5' + 32 = 34. 3x5=15. 15 -It 34 = 49, the sum of the squares of the two diameters added to the product of tlie diameters of the ends. 49 X 0.7854 = 38.4846. 38.48 46 X 9 ^ . = 115.4538 cu m 3 To compute the volume of a pyramid. Rule. Multiply the area of the base by the altitude or perpendicular height, and take one-third of the product. To compute the volume of the frustum of a pyramid. Rule. Find the height that the pyramid would be if Fig. 41. Frustum of Cone the top were put on, and then compute the volume of the completed pyramid and the volume of the part added; subtract the latter from the former, and the remainder will be the volume of the frustum. To compute the volume of a sphere. Rule. Multiply the cube of the diameter by 0.5236. To compute the volume of a segment of a sphere. Rule I. To three times the square of the radius of its base add the square ot its height; multiply this sum by the height and the product by 0.5236. Rule 2. From three times the diameter of the sphere subtract twice the height of the segment; multiply this remainder by the square of the height and the product by 0.5236. Example. The segment of a sphere has a radius, ac (Fig. 42), of 7 in for its base, and a height, ch, of 4 in: what is its volume? Solution. (By Rule i .) 3X7'= i47, and 147 + 42 = 163, or three times the square of the radius of the base plus the square of the height. 163 X 4 X 0.5236=341.3872 cu segment. Second Solution. By the rule for finding the diameter of a circle when a chord and its versed sine are given, we find that the diameter of the sphere in this case is 16.25 in; then, by Rule 2, (3 X 16.25)- (2X4) = 40-75; and 40.75 X 4^ X 05236=341.3872 cu in, the volume of the segment. To compute the volume of a spherical zone Definition. The part of a sphere included be- tween two parallel planes (Fig. 43). Rule. To the sum of the squares of the radii of the two ends add one-third of the square of the height of the zone; multiply this sum by the height and that product by 1.5708. Fig. 42. in = the Segment of Sphere volume of the Fig. 43. Zone of Sphere Figures of Revolution and Irregular Figures 65 To compute the volume of a prolate spheroid. (See page 60.) Rule. Multiply the square of the short axis by the long axis and this product by 0.5236. To compute the volume of an oblate spheroid. Rule. Multiply the square of the long axis by the short axis and this product by 0.5236. To compute the volume of a paraboloid of revolution (Fig. 44). Rule. Multiply the area of the base by half the altitude. To compute the volume of a hyperbo- loid of revolution (Fig. 45). Rule. To the square of the radius of the base add the square of the middle diameter; multiply this sum by the height and the product by 0.5236. To compute the volume of any figure of revolution. Rule. Multiply the area of the generating surface by the circumference described by us center of gravity. To compute the volume of an excavation, where the ground is irregular and the bottom of the excavation is level (Fig. 46). Rule. Divide the surface of the ground to be excavated unto equal squares of about 10 ft on a side, and ascertain by means of a level the height of each corner, a, a, a, b, h, h, etc., above the level to which the ground is to be excavated. Then add together the heights of all the corners that come in one square only. Next take twice the sum of the Fig. 44. Parabo- loid of Revolution 45. Hyperboloid of Revolution a a heights of all the corners that come in two squares, as b, b, b; next three times the sum of the heights of all the corners that come in three squares, as c, c, c; and then four times the sum of the heights of all the corners that belong to four squares, as d, d, d, etc. Add together all these quantities, and multiply their sum by one-fourth the area of one of the squares. The result will be the volume of the excavation. Example. Let the plan of an excavation for a cellar be as shown in Fig. 46, and the heights of each corner above the proposed bottom of the cellar be as given by the numbers in the figure. Then the volume of the cellar will b^tf^ .02 Tiatdoi^i 6 3 4 C d e h 3 4 'Z 3 U 4' d d d 1 - 1 3 a 2 c 2 3 i 1 1 b 'J b a r ig. 46. Plan of I ixcavatio n follows, the area of each square being 10 X 10 = 100 sq ft: Volume = H of 100 (a 's + 2 6 '5 + 3 c 's + 4 ^ 's) The a's in this case =4 + 6 + 3 + 2 + 1 + 7 + 4 2 X the sum of the 6's = 2 X (3 + 6 + i + 4 + 3 + 4) 3 X the sum of the c's = 3 X (i + 3 + 4) 4 X the sum of the J's = 4 X (2 + 3 + 6 + 2) = 27 = 42 = 24 = 52 145 Volume = 25 X 145 = 3 625 cu ft, the quantity of earth to be excavated* 66 Geometrical Problems Part 1 4. GEOMETRICAL PROBLEMS Problem i. To bisect, or divide into equal parts, a given line, ab (Fig. 47). From a and h, with any radius greater than half of ah, describe arcs inter- secting in c and d. The line cd, connecting these intersections, will bisect ah and be perpendicular to it. r '^■ (d Fig. 47. Line Bisected Fig. 48. Perpendicular from Point to Given Line Fig. 49. Perpendicular from Point to Given Line Problem 2. To draw a perpendicular to a giv«n straight line from a point with- out it. First Method (Fig. 48). From the point a describe an arc cutting the line be in two places, as e and /. From e and / describe two arcs, with the same radius, intersecting in g\ then a line drawn from a to g is perpendicular to the line he. Second Method (Fig. 49). From any two points, d and c, at some distance apart in the given line, and with radii da and ea respectively, describe arc d -¥. b Fig. 50. \^ /d Perpendicular from Point in Given Line Fig. 51. Perpendicular from Extremity of Given Line cutting at a and e. Draw ae, which is the perpendicular reequired. This method is useful where the given point is opposite the end of the line, or nearly so. Problem 3. To draw a perpendicular to a straight line from a given point, a, in that line. First Method (Fig. 50). With any radius, from the given point a in the line, describe arcs cutting the line in the points b and c. Then with h and c as centers, and with any radius greater than ab or ac, describe arcs cutting each other at d. The line da is the perpendicular required. Geometrical Problems 67 Second Method (Fig. 51), when the given point is at the end of the line. From any point, b, outside of the line, and with a radius ba, describe a semi- circle passing through a and cutting the given Hne at d. Through b and d draw a straight line inter- secting the semicircle at e. The line ea will then be perpendicular to the Hne ac at the point a. Third Method (Fig. 52), or the 3, 4 and 5 Method. From the point a on the given line measure off 4 in, or 4 ft, or 4 of any other unit and with the same unit of measure describe an arc, with a as a center and 3 units as a radius. Then from b describe an arc with a radius of 5 units, cutting the first arc in c. Then ca is the perpendicular required. This method is particularly useful in laying out a right angle on the ground, or framing a house where the foot is used as the unit and the lines are laid off by the straight-edge. In laying out a right angle on the ground, the proportions of the triangle may be 30, 40 and 50, or any other multiple of 3, 4 and 5; and it can best be laid out with the tape. Thus, first measure off, say 40 feet from a (Fig. 52) on the given Hne; then let one person hold the end of the tape at b, another hold the Fig. 52. Perpendicular from Extremity of Given Line d Fig. 53. Straight Line Parallel to Given Line tape at the 80-ft mark at a, and a third person take hold of the tape at the 50-ft mark, with his thumb and finger, and pull the tape taut. The 50-ft mark will then be at the point c in the line of the perpendicular. Problem 4. To draw a straight line parallel to a given line at a given distance away (Fig. 53). From any two points near the ends of the given line describe two arcs about opposite the given line. Draw the line cd tangent to these arcs and it will be parallel to ab. Problem 5. To construct an angle equal to a given angle (Fig. 54). With the point A , at the apex of the given angle, as a center, and any radius, describe the arc BC. With the point a, at the vertex of the new angle, as a J5/. \ A B a Fig. 54. Angle Equal to Given Angle Fig. 55. Angle of 60** center, and with the same radius as before, describe an arc, as BC. With BC as a radius and 6 as a center, describe an arc cutting the other arc at c. Then will cab be equal to the given angle CAB. Problem 6. From a point on a given line to draw a line making an angle of 60° with the given line (Fig. 55). Take any distance, as ab, as a radius, and with a as a center, describe the arc be. With 6 as a center and with the same radius, describe an arc cutting the 68 Geometrical Problems Part 1 Fig. 56. Angle of 45° first one at c. Draw from a a line through c, and it will make with ab an angle of 60". ' Problem 7. From a given point, A, on a given line, AE, to draw a line making an angle 45° with the given line (Fig. 56). Measure off from Ay on AE, any distance, Ab, and at b draw a line perpendicular to AE. Measure off on this perpendicular be equal to Ab and draw a Une from A through c. This line Ac will make an. angle of 45° with AE. Problem 8. From any point. A, on a given line, to draw a line which will make any desired angle with the given line (Fig. 57). To solve this problem the tables of chords on pages 81 to 89 are used. Find in the table the length of chord to a radius i, for the given angle. Then take any radius, as large as convenient and describe an arc of a circle be, with ^ as a center. Multiply the chord of the angle, found in the table, by the length of the radius Ab, and with the product as a new radius and with 6 as a center, describe a short arc cutting be in d. Draw a hne from A through d and it will make the required angle with DE. Example. Draw a line from A on DE, making an angle of 44° 40' with DE (Fig. 57). Solution. The largest convenient radius for the arc is 8 in. With ^ as a center and 8 in as a radius, describe the arc be. In the table of chords, the chord for an angle or arc of 44° 40' to a radius i is 0.76. Multiplying this by 8 in, the length of the new radius is 6.08 in; and with this as radius and with 6 as a center, describe an arc cutting be in d. Ad will be the line required. Problem 8a. two-foot rule. A 5 ' Fig. 57. Line Making Any Angle with Given Line To lay off a given angle approximately, by means of an ordinary Tables of Angles Corresponding to openings of a Two-Foot Rule* In. Deg. Min. In. Deg. Min. In. Deg. Min. In. Deg. Min. In. Deg. Min. M 1 12 11 22 m 21 37 32 3 8')4 42 46 1 48 2H 11 58 22 13 63/4 32 40 43 24 \^ 2 24 12 34 "h 22 50 33 17 9 44 3 3 00 'h 13 10 23 27 7' 33 54 44 42 H 3 36 13 46 5 24 3 34 33 "\i 45 21 4 11 3 14 22 24 39 "h 35 10 45 59 1 4 47 5 23 H 14 58 "h 25 16 35 47 "h 46 38 15 34 25 53 Vi 36 25 47 17 H 5 58 16 10 "Vi 26 30 37 3 H 47 56 6 34 "h 16 46 27 7 "% 37 41 48 35 H 7 10 17 22 ^i 27 44 38 19 16 49 15 7 46 "h 17 59 28 21 '%" 38 57 49 54 % 8 22 18 35 6 28 58 39 35 "h 50 34 8 58 4" 19 12 29 35 H 40 13 51 13 2 9 34 19 48 H 30 11 40 51 H 51 53 10 10 H 20 24 30 49 'ii 41 29 52 33 H 10 46 21 OG "h 31 26 42 7 * Trau twine. Fig. 58. Angle Bisected Geometrical Problems 69 Lay one leg of the rule on the paper or board with its inner edge coinciding with the given line. Open the rule until the distance between the inner edges at the ends correspond with that given for the angle in the following table; then draw a line by marking along the inner edge of the other leg, and it will give the desired angle within a very close approxi- mation. Problem 9. To bisect a given angle, as BAG (Fig. 68). With ^ as a center and any radius, describe an arc, as cb. With c and b as centers, and any radius greater than one- half of cb, describe two arcs, intersecting in d. Draw from A a line through d and it will bisect the angle BAC. Problem 10. To bisect the angle included between two lines, as AB and CD, when the vertex of the angle is not on the drawing (Fig. 69). Draw/e parallel to AB and cd parallel to CD, so that the two hues intersect, as at i. Bisect the angle eid, as in the preceding problem, and draw a line through i and which will bisect the angle between the two given lines. Problem 11. Through two given points, B and C, to describe an arc of a circle with a given radius (Fig. 60). With B and C as centers and with a radius equal to the given radius, describe two arcs intersecting at A . With ^ as a center and the same radius, describe the arc be, which will pass through the given points, B and C. Problem 12. To find the center of a given circle (Fig. 61). Draw any chord in the circle, as ab, and bisect this chord by the per- pendicular cd. This Hne will pass through the center of the circle and ef will be a diameter of the circle. Bisect ef, and the center will be the center of the circle. Fig. 59. Angle Bisected. Angle not on Drawing Fig. 60. Circular Arc Through Two Given Points Fig. 61. Center of Given Circle Problem 13. To draw a circular arc through three given points, as A, B and C (Fig. 62). Draw lines from yl to ^ and from B to C. Bisect AB and BC by the lines aa and ec and prolong these lines until they intersect at 0, which will be the center for the arc sought. With as a center, and with a radius equal to C, describe at E an arc of indefinite length. With ^ as a center and with J5 as a radius, describe an arc cutting the first at E. Join E with A and D. ADE is the required triangle. Problem 19. To describe a circle about a triangle (Fig 69). Bisect two of the sides, as ^ C and CB, of the triangle, and at their centers, erect perpendicular lines, as ae and he, intersecting at c. With c as a center, and eC as a radius, describe a drcle. It will pass through A and B. Problem 20. To inscribe a circle in a triangle (Fig. 70). Bisect two of the angles, A and B, of the triangle by lines cutting each other at 0. With o as a center, and with oe as a radius, describe a circle. It will be tangent to the other two sides. Fig. 67. Equilateral Tri- ;ingle on Given Base Fig. 68. Scalene Triangle on Given Base ] ig. 69. Triangle and Cir- cumscribed Circle Triangle and Inscribed Circle 72 Geometrical Problems Part 1 Problem 21. To inscribe a square in a circle and to describe a circle about a square (Fig. 71). To inscribe the square. Draw two diameters, AB and CD, at right-angles to each other. Join the points A, D, B and C. ADBC is the inscribed square. To describe the ckcle. Draw the diagonals as before, intersecting at E, and with E as a center and ^£ as a radius, describe the circle. Fig. 71. Inscribed Square and Circumscribed Circle Fig. 72. Inscribed Circle and Circumscribed Square Problem 22. To inscribe a circle in a square and to describe a square about a circle (Fig. 72). To inscribe the circle. Draw the diagonals AB and CD, intersecting at E. Draw the perpendicular EG to one of the sides. Then with £ as a center, and EG as a radius, describe a circle. It will be tangent to all four sides of the square. To describe the square. Draw two diameters, AB and CD, at right-angles to each other, and prolonged beyond the circumference. Draw the diameter OF, bisecting the angle CEA or BED. Draw lines through G and F perpen- dicular to GF, and terminating in the diagonals. Draw AD and CB to com- plete the square. Problem 23. To inscribe a pentagon in a circle (Fig. 73). Fig. 73. Circle and Inscribed * Pentagon Circle and Inscribed Hexagon Draw two diameters, AB and CD, at right-angles to each other. Bisect AO at E. With jE as a center and EC as a radius, cut OB at F. With C as a center and CF as a radius, cut the circle at G and H. With these points as centers and the same radius, cut the circle at / and /. Join /, J, G, C and H. IJGCIII is the inscribed regular pentagon. i J I!, Geometrical Problems 73 Problem 24. To inscribe a regular hexagon in a circle (Fig. 74). Lay off on the circumference the radius of the circle six times, and connect the points. Problem 25. To construct a regular hexagon upon a given straight line, AB (Fig. 75). From A and B, with a radius equal to AB, describe arcs intersecting at 0. With O as a center and a radius equal to AB, describe a circle, and from A or B lay off the lengths BC, CD, DE, EF and FA on the circumference of the circle. ABCDEFA is the required regular hexagon. Fig. 75. Regular Hexagon on Given Line Fig. 76. Regular Octagon on Given Line Problem 26. To construct a regular octagon upon a given straight line, AB (Fig. 76). Produce the line AB both ways and draw the perpendiculars A a and Bb, of indefinite length. Bisect the external angles at A and B and make the length of the bisecting lines equal to AB. From // and C draw lines parallel to ^ a or Bb and equal in length to AB. From G and D as centers describe arcs, with a radius AB, cutting the perpendiculars A a and Bb in F and E. Draw GF, FE and ED. ABCDEFGIIA is the required octagon. Fig. 77. Square and Inscribed Regular Octagon Fig. 78. Circle and Inscribed Regular Octagon Problem 27. To construct a regular octagon in a square (Fig. 77). Draw the diagonals AD and BC and from yl, B, C and D, with a radius equa^ to AO, describe arcs cutting the sides of the square in a, b, c, d^>»j /pA and i Draw at, hf. ed and cb» aihfedcba is the required octagon. <\ ^n.-^l' <. . 74 Geometrical Problems Part 1 Problem 28. To inscribe a regular octagon in a circle (Fig. 78). Draw two diameters, AB and CD, at right-angles to each other. Bisect the angles AOD and AOC by the diameters EF and GIL A~EDHBFCGA is the required octagon. Problem 29. , To inscribe a circle within a regular polygon. First. When the polygon has an even number of sides, as in Fig. 79. Bisect two opposite sides at A and B, draw AB and bisect it at C by a diagonal, DEy connecting two opposite angles, as D and E. The circle drawn with a radius CA and with C as a center is the inscribed circle required. Fig. 79. Regular Polygon, Even Number of Sides, with Inscribed and Circumscribed Circles Fig. 80. Regular Polygon, Odd Number of Sides, with In- scribed and Circumscribed Circles Second. When the number of sides is odd, as in Fig. 80. Bisect two of the adjacent sides as at A and B, and draw lines, AE and BD, to the opposite angles, and intersecting at C. The circle drawn with C as a center and CA as a radius is the inscribed circle required. Problem 30. To draw a circumscribing circle around a regular polygon. First. When the number of sides is even, as in Fig. 79. Draw two diagonals from opposite angles, as E.D and Gil, intersecting at C. The circle drawn with C as a center and with CD as a radius is the circumscribing circle required. Second. When the number of sides is odd, as in Fig. 80. Determine the center, C, as in the last problem. The circle drawn with C as a center and CD as a radius, is the circumscribing circle required. Problems on the Ellipse, the Parabola, the Hyperbola and the Cycloid The Ellipse Problem 31. To describe an ellipse, the length and breadth, or the two axes, being given. First Method (Fig. 81), the two axes, AB and CD, being given. On AB and CD as diameters and from the same center, O, describe the circles AGBII and CLDK. Take any convenient number of points on the circumference of the outer circle, as h, b', h", etc., and from them draw lines to the center, O, cutting the inner circle at the points a, a', a", etc., respectively. From the points ht b', etc., draw lines parallel to the shorter axis CD] and from the points a, The Ellipse 75 a', etc., draw lines parallel to the longer axis AB, and intersecting the first set of lines at c, c' , c", etc. These last points will be points in the ellipse, and by determining a sufficient number of them, the ellipse can be drawn. Fig. 81. Ellipse Described on Given Axes. Second Method (Fig. 82) . Take the straight-edge, made of a stiff piece of paper, cardboard or wood, and from some point as a, mark off ah equal to half the shorter diameter CD, and *ac equal to half the longer diameter AB. Place the straight-edge so that the point h is on the longer and the point c on the shorter diameter. Then will the point a be over a point in the ellipse. Make on the paper a dot at a and move the straight-edge around, always keeping the points h and c over the major and minor axes respectively. In this way any number of points in the ellipse may be determined and the ellipse drawn. Third Method (Fig. 83). Given, the two axes, AB and CD. From the point Z> as a center, and a radius AO, equal to one-half of AB, describe an arc cutting AB at F and F' . These two points are called the foci of the ellipse. Note. One property of the ellipse is, that the sums of the distances of any two points on the circumference from the foci are the same. Tl^us F'D -V DF «• F'E^EPoiF'G-^GF, Fig. 82. Ellipse Described with Straight-Edge 76 Geometrical Problems Part 1 Fix two pins in the axis AB set F and F' and loop upon them a thread, of cord equal in length, when fastened to the pins, to AB, so as, when stretched as per dotted Hne FDF\ it will just reach to the extremity D of the short axis. Place a pencil-point inside the chord, as at E, and move the pencil along, keeping the cord stretched tight. The pencil- point will trace the ellipse required. Problem 32. To draw a tan- gent to an ellipse at a given point on the curve (Fig. 84). Let it be required to draw a tangent at the point E on the ellipse shown. First de- termine the foci F and F' as in the third method for describing an ellipse, and from E draw Hues EF and EF'. Prolong EF' to a, so that Ea equals EF. Bisect the angle aEF by describing arcs from a and F as centers, as shown at b, and through b draw a line through E. This line is the tangent required. If it is required to draw a line normal to the curve at E, as, for instance, the joint of an elliptical Fig. 83. Ellipse Described with String and Pencil Fig. 84. Tangent Drawn to Point on Ellipse arch, bisect the angle FEE', and draw the bisecting line through E, and it will be the normal to the curve and the proper Hne at that point for the joint of an elliptical arch. Problem 33. To draw a tangent to an ellipse from a given point outside of the curve (Fig. 86). From the given point T as a center, and with a radius equal to the distance to the nearer focus F, describe an arc of a circle. From F' as a center, and with a radius equal to the length of the longer axis of the ellipse, describe arcs cutting the circle just described at a and b. Draw lines from F' to a and b, cutting the ellipse at E and G. Draw lines from T through E and G and they will be the tangents required. The Ellipse 77 Fig. 85. Tangent Drawn to Ellipse from Point Outside Problem 34. To describe an ellipse approximately, by means of circular arcs. First. With arcs of two radii (Fig. 86). Take half the difference of the two axes AB and CD, and set it off from the center O to a and c on OA and OC; draw ac and onAB set off half ac from a tod; draw di parallel to ac; set off Oe equal to Od; join ei and draw em and dm parallel respectively to id and ie. With c / \.4' i \ \ \2 y\ ^ / '^<^ \ / m X Fig. { Ellipse Described with Circular Arcs of Two Radii m as a center and with a radius mC, describe an arc through C, terminating in the points 1 and 2 on tnd and me produced. With » as a center^ and with iD as a radius, describe an arc through D, terminating in points 3 and 4 on ie and id produced. With d and e as centers, describe arcs through A and B, connecting the points i and 4 and 2 and 3. The four arcs thus described form approximately an ellipse. This method is not satisfactory when the conjugate or minor axis is less than two-thirds the transverse or major axis. 78 Geometrical Problems Part 1 i ^ Another method of approximating an ellipse by means of arcs of two radii, i is shown in Fig. 87, the axis major AB and the semiminor axis OC being given. Draw the rec- j tangle AabBA, and the diagonal CB. Lay off Cc equal to the differ- ence between OB and OC. Bisect cB at M and erect the perpendicular YD, intersecting CO pro- duced at Y and 05, at X. Make Qx' = Ox. Then will x, x', and Y be the three centers re- quired, the curves be- coming tangent at D and at the corresponding point on the left-hand side of the ellipse. This method results in a curve which is slightly fuller at the haunches than the curve drawn by the preceding method. Second. With arcs of three radii (Fig. 88). On the transverse or major axis Fig. 87. Ellipse Described with Circular Arcs of Two Radii '^\ / / / / / . //-- i"> ¥ Fig. 88. Ellipse Described with Circular Arcs of Three Radii ABl draw the ;ectang]e AGEBA, equal in height to OC, half the conjugate or minor axis. Draw AC and draw GD perpendiculai- to AC. Set off OK equal to The Parabola and Hyperbola i79 JC, and on AK as a diameter describe the semicircle ANK. Extend OC to L and to D. Set off OM equal to CL, and with Z) as a center and with a radius DM, describe an arc. With A and B as centers and with a radius OL, cut AB It P and P. From // as a center, and with a radius HF, cut the arc ah at a. W and 6 are determined in like manner. The points //, a, D, b and W, are the centers of the arcs required. Produce the lines all, Da, Dh, and hlV, and thus determine the lengths of the arcs. This method is practicable for all ellipses. It is often employed [or vaults, stone arches and bridges. The Parabola Problem 35. To describe a parabola when the vertex A, the axis AB and a point, M, of the curve are given (Fig. 89). Construct the rectangle ABMCA. Divide MC into any number of equal parts, four for instance. Divide AC in like manner. Connect Ai, A2 and As. Through i', 2', 3', draw parallels to the axis AB. The intersections I, II and III, of these lines, are points in the required curve. Fig. 89. Parabola and Tangent to Point on Parabola Problem 36. To draw a tangent to a given point, II, of the parabola (Fig. 89). From the given point II let fall a perpendicular on the axis ^iJ at b. Produce the axis to the left of ^1. Make yl a equal to ^&. A line drawn through a and II is the tangent required. The lines perpendicular to the tangent are called NORMALS. To draw a normal to any point, as I, the tangent to any other point, 11 being given. Draw the normal He. From I, let fall a perpendicular Id, on the axis AB. Lay off de equal to be. The line le is the normal required. The tangent may be drawn at I by laying off a perpendicular to the normal le at I. The Hyperbola If from any point, P, of an hyperbola, two straight lines are drawn to two fixed points, as F and F', the foci of the hyperbola, their difference is alwayS the same. ,:, Problem 37. To describe an hyperbola when a vertex, a, the given diflferenc© ab and one of the foci, F are given (Fig. 90). ; ' Draw the axis AB oi the hyperbola, with the given distance ab and the focua 80 F marked on it. Geometrical Problems Part 1 From b lay off bFx equal to aF to determine the other focus Fu Take any point, as i on. AB, and with ai as a radius and F as a center, describe two short arcs above and below the axis. With 6 1 as a radius, and F' as a center, describe arcs cutting those just described, at P and P'. Take several points, as 2, 3 and 4, and determine the cor- responding points Pi, Pi and P4 in the same way. The curve passing through these points is an hyperbola. To draw a tangent to any point of an hyperbola, draw lines from the given point to each of the foci and bisect the angle thus formed. The bisecting hne is the tangent required. Fig. 90. Hyperbola Described The Cycloid The CYCLOtD is the curve described by a point on the circumference of a circle rolling in a straight line. Problem 38. To describe a cycloid (Fig. 91). Draw the straight hne AB. Describe the generating circle tangent to this Ime at its middle point D, and through the center C, of the circle, draw the line Fig. 91. Cycloid Described EE parallel to A B. Let fall a perpendicular from C upon A B. Divide the semi- circumference into any number of equal parts, for example, six. Lay oH on AB and CE distances Ci', i'2', etc., equal to the divisions of the circumference. Draw the chords Di, D2, etc. From the points i', 2', 3', etc., on the Hne CE, with radii equal to the generating circle, describe arcs as shown. From the points i', 2', 3', 4', 5', etc., on the line BA, and with radii equal respectively to the chords 2)r, 2>2, Dz, D4, D5, describe arcs cutting the preceding arcs. Tlie intersections are points of the required cyt:loid. tSfJo) t)ii' Table of Chords SI Table of Chords. Radius = i.oooo 0" 0.0000 0.0003 0.0006 0.0009 0.0012 0.0015 0.0017 0.0020 0.0023 0.0026 0.0029 0.0032 0.0035 0.0038 O.OOil 0.0044 0.0017 0.0049 0.0052 0.0055 0.0058 0.0061 0.0084 0.0067 0.0070 0.0073 0.0076 0.0079 0.0081 0.0084 0.0087 0.0090 0.00:)3 0.0096 0.0099 0.0102 0.0105 0.0108 0.0111 0.0113 0.0116 0.0119 0.0122 0.0125 0.0128 0.0131 0.0134 0.0137 0.0140 0.0143 0.0145 0.0148 0.0151 0.0154 0.0157 0.0160 0.0163 0.0166 0.0169 0.0172 0.0175 0175 0177 0180 .0183 0186 .0189 0192 .0195 0198 0201 0204 0207 0209 0212 0215 0218 0221 0224 0227 0230 0233 0236 0239 0241 0244 0247 0250 0253 .0256 0259 0262 0265 0268 0271 0273 0276 0279 0282 0285 0288 ,0291 ,0294 0297 ,0300 0303 0305 0308 0311 0314 0317 .0320 0323 0326 0329 0332 0335 0337 0340 0343 0346 0349 0352 0355 0358 0361 0364 0368 0369 0372 0375 0378 0381 .0384 0387 .0390 0393 03^6 0398 0401 0404 0407 0410 0413 0416 0419 0422 0425 0428 0430 0433 0436 0439 0442 0445 0448 0451 0454 0457 0460 ,0462 ,0465 ,0468 ,0471 ,0474 0477 0489 .0483 0486 .0489 0492 0494 0497 0500 0503 0506 0509 0512 0515 0518 0521 !0 0524 0524 0526 0529 0532 0535 0538 0541 0544 0547 0550 0553 0556 0558 0561 0564 0567 0570 0573 0576 0579 0582 0585 0588 0590 0593 0596 0599 0602 0605 0608 0611 0614 0617 0619 0622 0625 0628 0631 0634 0637 0640 0643 0646 0649 0651 0654 0657 0669 0663 0666 ,0669 0672 0675 0678 .0681 0683 0686 .0689 0692 0695 0698 0701 0704 0707 0710 0713 0715 0718 0721 0724 0727 0730 0733 0736 0739 0742 0745 0747 0750 0753 0756 0759 0762 0765 0768 0771 0774 0776 0779 0782 0785 0788 0791 0794 0797 0800 0803 0806 ,0808 ,0811 .0814 ,0817 .0820 .0823 .0826 .0829 .0832 .0835 .0838 .0840 .0843 0, 0. 0, 0. 0. 0, 0. 0. 0. 0. 0. 0. 0, 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0, 0. 0. 0, 0.0872 0849 0852 0855 0858 0861 0864 0867 0872 0875 0881 0884 0887,0 0890 0893 0896 0899 0901 0904 0907 0910 0913 .0916 0919 .0922 0925 0928 .0931 0933 0. 0936 0. 0939 0. 0942 0. 0945,0. 0948 0. 0951 0, .095410. 0957J0. 0960 0. 1047 1050 1053 1055 1058 1061 1064 1067 1070 1073 1076 1079 1082 1084 108' 1090 1093 1006 1099 1102 1105 1108 1111 1114 V 1221 1224 1227 1230 1233 1235 1238 1241 1244 1247 1250 1253 1256 1259 1262 126; 1267 1270 1273 1276 1279 0962 0965 0968 0971 0974 0977 0980 0983 0986 0989 0992 0994 0997 . 1000 1003 .1006 1009 1012 1015 1018 1021 1023 1026 1029 1032 1035 1038 1041 1044 1047 11160, 11190 11220. 11250. 11280. 11310. 11340. 11370. 1140 0. 1143|0. 1145J0. 1480. H" 1282 1285 1288 1291 1294 12960 1299 1302 1305 1308 1151 1154 1157 1160 1163 1166 1169 1172 1175 1177 1180 1183 1186 1189 1192 1195 1198 1201 1204 1206 .1209 12120. 12150. 12180. 1221 0. 1311 1314 1317 1320 1323 1325 1328 1331 1334 1337 1340 1343 1346 1349 1352 1355 1357 1360 1363 1366 1369 1372 1375 1378 1381 1384 1386 0. 1389 13920 13950 1395 1398 1401 1404 1407 1410 1413 1415 1418 1421 1424 1427 1430 1433 1436 1439 1442 1444 1447 1450 1453 1456 1459 1462 1465 1468 1471 1473 .1476 1479 1482 1485 1488 1491 1494 1497 1500 1502 150i 1508 1511 1514 1517 1520 1523 1526 1529 1531 .1534 1537 1540 1543 1546 1549 1552 1555 1558 1560 1563 1566 1569 1569 1572 1575 1578 1581 1584 1587 1589 1592 1595 1598 1601 .1604 1607 1610 1613 .1616 1618 1621 1624 .1627 1630 1633 1636 1639 1642 1645 1647 1650 1653 1656 1659 1662 1665 1668 1671 1674 1676 1679 1682 1685 1688 1691 1694 1697 1700 1703 1705 1708 1711 1714 1717 1720 1723 1726 1729 1732 1734 1737 1740 1743 10° 1743 1746 1749 1752 1755 1758 1761 1763 1766 .1769 1772 1775 1778 1781 1784 1787 1789 1792 1795 1798 1801 1804 1807 1810 1813 1816 1818 1821 1824 1827 1830 1833 1836 1839 1842 .1845 1847 .1850 1853 .1856 1859 1862 1865 1868 1871 1873 1876 1879 1882 1885 1888 1891 1894 1897 1900 1902 1905 1908 1911 1914 1917 82 Geometrical Problems Part 1 Table of Chords (Continued). Radius = i.oooo M. U° 12° 13° 14° 15° 16° 17° 18° 19° 30° 31° 0.1917 0.1920 0. 0.1923 0. 0.1926 0. 0. 1928)0. 0.1931iO. 0.1934|0. 0. 193710. 0.19400. 0.1943iO. 0.1946jO. 0.19190. 0.1952,0. 0.1955 0. 0.19570. 0.19600. 0.1963 0. 0.1966 0. 0.1969'0. 0.1972 0. 0.1975 0. 1978 0.1981 0.1983 0.1986 0.1989 0.1992 0.1995 0.1998 0.2001 0.2004 0.2007 0.2010 0.2012 0.201 0.2018 0.2021 0.2024 0.2027 0.2030 0.2033 0.2036 0.2038 0.2041 0.2044 0.2047 0.2050 0.2053 0.2056 0.2059 0.2062 0.2065 0.2067 0.2070 0.2073 0.2076 0.2079 0.2082 0.2085 0.2088 0.2091 2091 2093 2096 2099 2102 2105 2108 2111 2114 2117 2119 2122 2125 2128 2131 2134 2137 2140 2143 2146 2148 2151 2154 2157 2160 2163 2166 2169 2172 2174 2177 2264 2267 2270 2273 2276 2279 2281 2284 2287 2290 2293 2296 2299 2302 2305 2307 2310 2313 2316 2319lO 2322 2325'0 2328 2331 2333 2336 2339 2342 2345 2348 2351 2180 2183 2186 2189 2192 2195 2198 2200 2203 2206 2209 2212 2215 2218 2221 2224 2226 2229 2232 2235 2238 2241 2244 2247 .2250 2253 2255 2258 2261 .2264 2354 2357 2359 2362 2365 2368 2371 2374 2377 2380 2383 2385 2388 2391 2394 2397 2400 2403 2406 2409 2411 2414 2417 2420 2423 2426 2429 2432 2434 2437 2437 2440 2443 2446 2449 2452 2455 2458 2460 2463 2466 2469 2472 2475 2478 2481 2484 2486 2489 2492 2495 2498 2501 2504 2507 2510 2512 2515 2518 2521 2524 2527 2530 2533 2536 2538 2541 2544 2547 2550 2553 2556 2559 2561 2564 2567 2570 2573 2576 2579 2582 2585 2587 2590 2593 2596 2599 2602 2605 2608 2611 2611 2613 2616 2619 2622 2625 2628 2631 2634 2636 2639 2642 2645 2648 2651 2654 2657 2660 2662 2665 2668 2671 2674 2677 2680 2683 2685 2688 2691 2694 2697 2700 2703 2706 2709 2711 2714 2717 2720 2723 2726 2729 2732 2734 2737 2740 2743 2746 2749 2752 2755 2758 2760 2763 2766 2769 2772 2775 2778 2781 2783 2783 2786 2789 2792 2795 2798 2801 2804 2807 2809 2812 2815 2818 2821 2824 2827 2830 2832 2835 2838 2841 2844 2847 2850 2853 2855 2858 2861 2864 2867 2870 2873 2876 2878 2881 2884 2887 2890 2893 2896 2899 2902 2904 2907 2910 2913 2916 2919 2922 2925 2927 2930 2933 2936 2939 2942 2945 2948 2950 2953 2956 2956 2959 2962 2965 2968 2971 2973 2976 2979 2982 2985 2988 2991 2994 0. 0. 0. 0. 0, 0. 0. 0. 0, 2996 2999 3002 3005 3008 3011 3014 3017 3019 3022 3025 3028 3031 3034 3037 3040 3042 3045 3051 3054 3057 3060 3063 3065 3068 3071 3074 3077 3080 3083 3086 3088 3091 3094 3097 3100 3103 3106 3109 3111 3114 3117 3120 3123 3126 3129 .3129 3132 3134 3137 3140 .3143 3146 3149 3152 .3155 3157 3160 3163 3166 3169 3172 .3175 .3178 .3180 .3183 3186 3189 3192 3195 3198 3200 3203 3206 3209 3212 3215 3218 3221 3223 3226 3229 3232 3235 3238 3241 3244 3246 3249 3252 3255 3258 3261 3264 3267 3269 3272 3275 3278 3281 3284 3287 3289 3292 3295 3298 3301 3301 3304 3307 3310 3312 3315 3318 3321 3324 ,3327 .3330 3333 3335 3338 3341 3344 3347 3350 3353 3355 3358 3361 3364 3367 3370 3373 3376 3378 3381 3384 3387 3390 3393 3396 3398 3401 3404 3407 3410 3413 3416 3419 3421 3424 3427 3430 3433 3436 3439 3441 3444 3447 3450 3453 3456 3459 3462 3464 3467 3470 3473 3473 3476 3479 3482 3484 3487 3490 3493 3496 3499 3502 3504 3507 3510 3513 3516 3519 3522 3525 3527 3530 3533 3536 3539 3542 3545 3547 3550 3553 3556 3559 3562 .3565 3567 3570 3573 3576 3579 3582 3585 3587 3590 .3593 3596 3599 3602 3605 3608 3610 3613 3616 3619 .3522 3625 3628 3630 3633 3636 3639 .3642 3645 3645 3648 .3650 3653 3656 3659 3662 3665 3668 3670 3673 3676 3679 3682 3685 .3688 3690 3693 3696 .3699 3702 3705 3708 3710 3713 3716 3719 3722 3725 3728 3730 0.3733 0.3736 0.3739 0.3742 0.3745 0.3 0.3750 0.3753 0.3756 0.3759 0.3762 0.3765 0.3768 0.3770 0.3773 0.3776 0.3779 0.3782 0.3785 0.3788 0.3790 0.3793 0.3796 0.3799 0.3802 0.3805 0.3808 0.3810 0.3813 0.3816 Table of Chords m Table of Chords (Continued). Radius = i.oooo M. 22° 33° 24° 35° 36° 37° 38° 39° 30° 31° 33° 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 0.3816 0.3819 0.3822 0.3825 0.3828 0.3830 0.3833 0.3836 0.3839 0.3842 0.3845 0.3848 0.3850 0.3853 0.3856 0.3859 0.3862 0.3865 0.3868 0.3870 0.3873 0.3876 0.3879 0.3882 0.3885 0.3888 0.3890 0.3893 0.3896 0.3899 0.3902 0.3905 0.3908 0.3910 0.3913 0.3916 0.3919 0.3922 0.3925 0.3927 0.3930 0.3933 0.3936 0.3939 0.3942 0.3945 0.3947 0.3950 0.3953 0.3956 0.3959 0.3962 0.3965 0.3967 0.3970 0.3973 0.3976 0.3979 0.3982 0.3985 0.3987 3987 3990 3993 3996 3999 4002 4004 4007 4010 4013 4016 4019 4022 4024 4027 4030 4033 4036 4039 4042 4044 4047 4050 4053 4056 4059 4061 4064 4067 4070 4073 4076 4079 4081 4084 4087 4090 4093 4096 4098 4101 4104 4107 4110 4113 4116 4118 4121 4124 4127 ,4130 ,4133 ,4135 ,4138 .4141 .4144 .4147 .4150 .4153 .4155 ,4158 4158 4161 4164 4167 4170 4172 4175 ,4178 ,4181 ,4184 ,4187 4190 4192 4195 4198 4201 4204 4207 4209 4212 4215 4218 4221 4224 4226 4229 4232 4235 4238 4241 4244 4246 4249 4252 4255 4258 4261 4263 4266 4269 .4272 4275 4278 .4280 4283 4286 4289 .4292 4295 .4298 4300 4303 4306 4309 4312 4315 4317 4320 4323 4326 4329 .4329 .4332 .4334 .4337 .4340 .4343 .4346 .4349 .4352 .4354 :4357 4360 4363 4366 4369 4371 4374 4377 4380 4383 4386 4388 0. 4391 0. 4394 0. 4397 4400 4403 4405 4408 4411 4414 4417 4420 4422 4425 4428 4431 ,4434 ,4437 .4439 .4442 444, 4448 4451 4454 4456 4459 4462 4465 4468 4471 4474 4476 4479 4482 4485 ,4488 4491 4493 4496 4499 4499 4502 4505 4508 4510 4513 4516 4519 4522 4525 4527 4530 4533 4536 4539 4542 4544 4547 4550 4553 4556 4559 4561 4564 4567 4570 4573 4570 4578 4581 4584 4587 4590 4593 4595 4598 4601 4604 4607 4609 4612 4615 4618 4621 4624 4626 4629 4632 4635 4638 4641 4643 4646 4649 4652 4655 4658 4660 4663 4666 4669 4669 4672 4675 ,4677 ,4680 ,4083 ,4686 .4689 .4692 .4694 4697 4700 4703 4706 4708 4711 4714 4717 4720 4723 4725 4728 4731 4734 4737 4740 4742 474, 4748 4751 4754 .4757 4759 4762 4765 4768 .4771 4773 4776 4779 .4782 4785 4788 4790 4793 4796 4799 4802 4805 ,4807 ,4810 ,4813 ,4816 ,4819 .4822 .4824 .4827 .4830 .4833 .4836 .4838 4838 4841 4844 4847 4850 4853 4855 4858 .4861 4864 4867 4869 4872 4875 4878 4881 4884 4886 4889 4892 4895 4901 4903 4906 4909 4912 4915 4917 4920 4923 4926 4929 4932 4934 4937 4940 4943 4946 4948 4951 4954 4957 4960 4963 4965 ,4968 .4971 4974 4977 .4979 4982 4985 4988 4991 4994 4996 4999 .5002 5005 .5008 -U 5008 5010 5013 5016 5019 5022 5024 5027 5030 5033 5036 5039 5041 5044 5047 5050 5053 5055 5058 5001 5064 5067 5070 5072 5075 5078 5081 5084 5086 5089 5092 5095 5098 5100 5103 5106 5109 5112 5115 5117 5120 5123 5126 ,5129 5131 5134 ,5137 .5140 .5143 5145 .5148 5151 5154 5157 5160 5162 5165 5168 5171 5174 5176 5176 5179 5182 5185 5188 5190 5193 5196 5199 5202 5204 5207 5210 5213 5216 5219 5221 5224 5227 5230 5233 5235 5238 5241 5244 5247 5249 5252 5255 5258 5261 5263 ,5266 5269 5272 5275 5277 ,5280 ,5283 5286 .5289 5291 5294 5297 5300 5303 5306 5308 5311 5314 5317 5320 5322 5325 5328 5331 5334 5336 5339 5342 5345 5345 5348 5350 5353 5356 5359 5362 5364 5367 5370 5373 5376 5378 5381 5384 5387 5390 5392 5395 5398 5401 5404 5406 5409 5412 5415 5418 5420 5423 5426 5429 5432 5434 5437 5440 5443 5446 5448 5451 5454 5457 5460 5462 5465 5468 5471 5474 4576 5479 5482 ,5485 ,5488 ,5490 .5493 .5496 .5499 .5502 .5504 .5507 .5510 .6513 5513 5516 5518 5521 5524 5527 5530 5532 5535 5538 5541 5543 5546 5549 5552 5555 5557 5560 5563 5566 5569 5571 5574 5577 5580 5583 5585 5588 5591 5594 5597 5599 .5602 5605 5608 5611 5613 5616 5619 5622 5625 5627 5630 5633 5636 5638 5641 5644 5647 5650 5652 5655 5658 5661 5664 5666 5669 5672 5675 .5678 .5680 84 Geometrical Problems Part 1 [Table of Chords (Continued). Radius = i.oooo M. 0.5680 0.5683 0.5686 0.5689 0.5691 0.5694 0.5697 0.5700 0.5703 0.5705 0.5708 0.571 0.5714 0.5717 0.5719 0.5722 0.5725 0.5728 0.5730 0.5733 0.5736 0.5739 0.5742 0.5744 0.5747 0.5750 0.5753 0.5756 0.5758 0.5761 0.5764 0.5767 0.5769 0.5772 0.5775 0.5778 0.5781 0.5783 0.5786 0.5789 0.5792 0.5795 0.5797 0.5800 0.5803 0.5806 0.5808 0.5811 0.5814 0.5817 0.5820 0.5822 0.5825 0.5828 0.5831 0.5834 0.5836 0.5839 0.5842 0.5845 0.5847 W 5847 5850 5853 5856 5859 5861 5864 5867 5870 5872 5875 5878 5881 5884 5886 5889 5892 5895 5897 5900 5903 5906 5909 5911 5914 5917 5920 5922 5925 5928 5931 5934 5936 5939 5942 5945 5947 5950 5953 5956 5959 5961 5964 5967 5970 5972 5975 5978 5981 5984 5989 5992 5995 5997 6000 6003 6006 6009 6011 6014 35° 6014 6017 .6020 6022 6025 6028 6031 6034 6036 6039 6042 6045 6047 6050 6053 6056 6058 6061 6064 6067 6070 .6072 6075 6078 6081 ,6083 6086 6089 6092 6095 ,6097 6100 6103 6106 6108 6111 6114 6117 6119 6122 6125 6128 6130 6133 6136 6139 6142 6144 6147 6150 6153 6155 6158 6161 6164 6166 6169 6172 6175 6178 6180 36° 6180 6183 6186 6189 6191 6194 6197 6200 6201 6205 6211 6214 6216 6219 6222 6225 6227 ,6230 6233 6236 6238 6241 6244 6247 6249 6252 6255 6258 6260 6263 6266 6269 6272 6274 62 6280 6283 6285 6288 6291 6294 6296 6299 6302 6305 6307 6310 6313 6316 6318 6321 6324 6327 6330 6332 6335 6338 6341 6343 37° 6346 6349 6352 6354 6357 6360 6363 6365 6368 6371 6374 6376 .6379 6382 6385 6387 6390 6393 6396 6398 6401 .6404 6407 6410 6412 6415 6418 6421 6423 6426 6429 .6432 6434 643' 6440 6443 6445 6448 6451 6454 6456 6459 6462 6465 6467 6470 6473 6476 6478 6481 6484 6487 6489 6492 6495 6498 6500 6503 6506 6509 6511 6511 6514 6517 6520 6522 6525 6528 6531 6533 6536 6539 6542 6544 6547 6550 6553 6555 6558 6561 6564 6566 6569 6572 6575 6577 6580 6583 6586 6588 6591 6594 6597 6599 6602 6605 6608 6610 6613 6616 6619 6621 6624 662' 6630 6632 6635 6638 6640 6643 6646 6649 6651 6654 6657 6660 6662 6665 6668 6671 6673 6676 39° 6676 6679 6682 6684 6687 6690 6693 6695 6698 6701 6704 6706 6709 6712 0fl5 6717 6720 6723 6725 6728 6731 6734 6736 39 6742 6745 747 6750 6753 6756 6758 6761 6764 676' 6769 6772 6775 6777 6780 6783 6786 6791 6794 6797 6799 6802 6805 6808 6810 6813 6816 6819 6821 6824 6827 6829 6832 6835 6838 6840 40° 6840 6843 6846 6849 6851 6854 6857 6860 6862 6865 41° 6870 0, 6873 0, 6876 0, 6887 6890 6892 6895 6901 6903 6906 6909 6911 6914 6917 6920 6922 6925 6928 6931 6933 6936 6939 6941 6944 6947 6950 6952 6955 6958 6961 6963 6966 6969 6971 6974 6977 6982 6985 6988 6991 6993 6996 6999 7001 7004 7004 7007 7010 7012 7015 7018 7020 7023 7026 7029 7031 7034 7037 7040 7042 7045 7048 7050 7053 7056 7059 7061 7064 7067 7069 '072 7075 7078 7080 7083 7086 7089 7091 7094 7097 7099 7102 7105 7108 7110 7113 7116 7118 7121 7124 7127 7129 7132 7135 7137 7140 43° 7143 0. 7146 0. 7148 7151 7154 7156 7159 7162 7165 167 7167 7170 7173 7176 7178 7181 7184 7186 7189 7192 7195 7197 7200 7203 7205 7208 7211 7214 7216 7219 7222 7224 7227 7230 7232 7235 7238 7241 7243 7246 7249 7251 7254 7257 7260 7262 7265 7268 7270 7273 7276 7279 7281 7284 7287 7289 7292 7295 7298 7300 7303 7306 7308 7311 7314 7316 7319 7322 7325 7327 7330 43° 7330 7333 7335 7338 7341 7344 7346 7349 7352 7354 7357 7360 7362 7365 7368 7371 7373 7376 7379 7381 7384 7387 .7390 7392 .7395 7398 7400 7403 7406 7408 741 7414 7417 7419 7422 .7425 7427 .7430 7433 7435 7438 7441 7443 7446 7449 7452 7454 7457 7460 7462 7465 7468 '471 7473 7476 7479 7481 7484 7487 7489 7492 Table of Chords M Table of Chords (Continued). Radius = i.oooo 44° 45° 46° 47° 48° 49° 60° 51° 53° 63 64° 0.7492 0. 0.7495 0. 0.7498'0. 0.7500 0.7503 0.7506 0.7508 0.7511 0.7514 0.7516 0.7519 0.7522 0.7524 0.7527 0.7530 0.7533 0.7535 0.7538 0.7541 0.7543 0.7546 7549 7551 7554 7557 7569 7562 7565 7568 7570 7o73 0.7576 0.7578 0.7581 0.7581 0.7586 0.7589 0.7592 0.7595 0.7597 0.7600 0.7603 0.7605 0.7608 0.7611 0.7613 0.7616 0.7619 0.7621 0.7624 0.7627 0.7629 0.7632 0.7635 0.7638 0.7640 0.7643 0.7646 0.7648 0.7651 0.7654 7654 7656 7659 7662 7664 7667 7670 7672 7675 7678 7681 ,7815 ,7817 ,7820 78230 78250 7828,0 7831 7833 7836,0 7839 7841 7683 76S6 7691 7694 7697 7699 7702 7705 7707 7710 7713 7715 7718 7721 7723 7726 7729 7731 7734 7737 7740 7742 7745 7748 7750 7975 0. 7978,0. 7980 lo, 7983'0. 7986 0. .7988,0. 7991 0. 79941 0. 7996,0. 7999 0. 8002 0. 7844 0. 7847 0. 7849 0, 7852,0. 785510. 785710. 7863 0. 7863 7865 7868 78710 7873 0. 7876 7879 7882 0. 78810 7887 0. 7890 7892 7895 7753 7756 7758 7761 7764 0. 766 7769 7772 7774 7777 7780 7782 7785 7788 7791 7793 7796 7799 7801 7804 7807 7809 7812 7815 7898 7900 7903 7906 7908 7911 7914 7916 7919 7922 7924 7927 7930 7932 7935 7938 7940 7943 7946 7948 7951 7954 7956 7959 7962 7964 7967 7970 7972 7975 8004 8007 8010 8012 8015 8018 8020 8023 8026 8028 8031 8034 8036 8039 8042 8044 8047 8050 8052 8055 8058 8060 8063 8066 8068 8071 8074 8076 8079 8082 8084 808: 8090 8092 8095 8098 8100 8103 8105 8108 8111 8113 8116 8119 8121 8124 8127 8129 8132 8135 8135 8137 8140 8143 8145 8148 8151 8153 8156 8159 8161 .8164 8167 8169 8172 8175 8177 8180 8183 8185 8188 .8294 0. 8297 !o, 8299 jo, 8302 0. 8304 8307 .8310 .8312 8315 8318 8320 8323 8326 8328 8331 8334 8336 8339 8341 8344 8347 8190 8193 8196 8198 8201 8204 8206 8209 8212 8214 8452 8455 0. 8458 8460 jo 846310 8466 8468,0 8471'0 8349 0. 8352 0. 8217 8220 8222 8225 8228 8230 8233 8236 8238 8241 8244 8246 8249 8251 8254 8257 8259 8262 8265 8267 8270 8273 8275 8278 8281 8283 8286 8289 8291 8294 0.8376 8355 8357 8360 8363 8365 8368 8371 8373 .8378 .8381 .8384 8389 8392 8394 8397 8400 8402 8405 8408 8410 8413 8415 8418 8421 8423 8426 8429 8431 8434 8437 8439 8442 8444 8447 8450 8452 8473 8476 8479 8481 8484 8487 8489 8492 8495 8497 8500 8502 8505 8508 8510 8513 8516 8518 8521 8523 8526 8529 8531 8534 8537 8539 8542 8545 8547- 8550 8552 8555 8558 8560 8563 8566 8568 8571 8573 8576 8579 8581 8584 8587 8589 8592 8594 8597 8600 8602 8605 8608 8610 8610 8613,0 86150 8618'0 86210 8623,0 8626 8629:0 8631 8634 lO 0. 8767 0. 8770 0. 8639 8642 8644 8647 8650 8652 8655 8657 8660 0.8665 0. 0, 0. 0, 0. 0. 0. 0. 0. .8668 .86/1 .8673 .8676 .8678 .8681 .8684 .8686 8692 8694 8697 8699 8702 8705 8707 8710 8712 8715 8718 8720 8723 8726 8728 8731 8734 8736 8739 8741 8744 8747 8749 8752 8754 8757 8760 8762 8765 8767 8773 8775 8778 8780 8783 8786 8788 8791 8794 8796 8799 8801 8804 8807 8809 8812 8814 8817 8820 8822 8825 8828 8830 8833 8835 8838 8841 8843 8846 8851 8854 8856 8859 8861 8864 8867 8869 8872 8874 8877 8880 8882 8885 8887 8890 8893 8895 0.8898 8900 8903 8906 8924 8927 8929 8932 8934 8937 8940 8942 8945 8947 8950 8953 8955 8958 8960 8963 8971 8973 8976 8979 8981 8984 8911 8914 89160 89190 8921,0 8924 8992 8994 8997 8999 9002 9005 9007 9010 9012 9015 9018 9020 .9023 9025 .9028 9031 9033 9036 9038 9041 9044 9046 9049 9051 9054 9056 9059 9062 9064 9067 9069 9072 9075 9077 9080 9082 9085 9088 .9090 9093 .9095 9098 9101 9103 9106 9108 9111 9113 9116 9119 9121 .9124 9126 .9129 9132 9134 9137 9139 9142 9145 9147 9150 9152 9155 9157 9160 9163 9165 .9168 9170 9173 9176 9178 9181 9183 9186 9188 9191 9194 9196 9199 .9201 9204 9207 .9209 9212 9214 9217 9219 9222 9225 9227 9230 9232 9235 86 Geometrical Problems Table of Chords (Continued). Radius = i.oooo M. 66° 66° 67° 68° 59° 60° 61° 62° 63° 64° M. 0' 0' 0.9235 0.9389 0.9543 0.9696 0.9848 1.0000 1.0151 1.0301 1.0450 1.0598 1 0.9238 0.9392 0.9546 0.9699 0.9851 1.0003 1.0153 1.0303 1.0452 1.0601 1 2 0.9240 0.9395 0.9548 0.9701 0.9854 1.0005 1.0156 1.0306 1.0455 1.0603 2 3 0.9243 0.9397 0.9551 0.9704 0.9S56 1.0008 1.0158 1.0308 1.0457 1.0606 3 4 0.9245 0.9400 0.9553 0.9706 0.9859 1.0010 1.0161 1.0311 1.0460 1.0608 4 5 0.9248 0.9402 0.9556 0.9709 0.9861 1.0013 1.0163 1.0313 1.0462 1.0611 5 6 0.9250 0.9405 0.9559 0.9711 0.9864 1.0015 1.0106 1.0316 1.0465 1.0613 6 7 0.9253 0.9407 0.9561 0.9714 0.9866 1.0018 1.0168 1.0318 1.0467 1.0616 7 8 0.9256 0.9410 0.9564 0.9717 0.9869 1.0020 1.0171 1.0321 1.0470 1.0618 8 9 0.9258 0.9413 0.9566 0.9719 0.9871 1.0023 1.0173 1.0323 1.0472 1.0621 9 10 0.9261 0.9415 0.9569 0.9722 0.9874 1.0025 1.0176 1.0326 1.0475 1.0623 10 11 0.9263 0.9418 0.9571 0.9724 0.9876 1.0028 1.0178 1.0328 1 .0477 1.0626 11 12 0.9266 0.9420 0.9574 0.9727 0.9879 1.0030 1.0181 1.0331 1.0480 1.0628 12 13 0.9268 0.9423 0.9576 0.9729 0.9881 1.0033 1.0183 1.0333 1.0482 1.0630 13 14 0.9271 0.9425 0.9579 0.9732 0.9884 1.0035 1.0186 1.0336 1.0485 1.0633 14 15 0.9274 0.9428 0.9581 0.9734 0.9886 1.0038 1.0188 1.0338 1.0487 1.0635 15 16 0.9276 0.9430 0.9584 0.9737 0.9889 1.0040 1.0191 1.0341 1.0490 1.0638 16 17 0.9279 0.9433 0.9587 0.9739 0.9891 1.0043 1.0193 1.0343 1.0492 1.0640 17 18 0.9281 0.9436 0.9589 0.9742 0.9894 1.0045 1.0196 1.0346 1.0495 1.0643 18 19 0.9284 0.9438 0.9592 0.9744 0.9897 1.0048 1.0198 1.0348 1.0497 1.0645 19 20 0.9287 0.9441 0.9594 0.9747 0.9899 1.0050 1.0201 1.0351 1.0500 1.0648 20 21 0.9289 0.9443 0.9597 0.9750 0.9902 1.0053 1.0203 1.0353 1.0502 1.0650 21 22 0.9292 0.9446 0.9599 0.9752 0.9904 1.0055 1.0206 1.0356 1.0504 1.0653 22 23 0.9294 0.9448 0.9602 0.9755 0.9907 1.0058 1.0208 1.0358 1.0507 1.0655 23 24 0.9297 0.9451 0.9604 0.9757 0.9909 1.0060 1.0211 1.0361 1.0509 1.0658 24 25 0.9299 0.9454 0.9607 0.9760 0.9912 1.0063 1.0213 1.0363 1.0512 1.0660 25 26 0.9302 0.9456 0.9610 0.9762 0.9914 1.0065 1.0216 1.0366 1.0514 1.0662 26 27 0.9305 0.9459 0.9612 0.9765 0.9917 1.0068 1.0218 1.0368 1.0517 1.0665 27 28 0.9307 0.9461 0.9615 0.9767 0.9919 1.0070 1.0221 1.0370 1.0519 1.0667 28 29 0.9310 0.9464 0.9617 0.9770 0.9922 1.0073 1.0223 1.0373 1.0522 1.0670 29 30 0.9312 0.9466 0.9620 0.9772 0.9924 1.0075 1.0226 1.0375 1.0524 1.0672 30 31 0.9315 0.9469 0.9622 0.9775 0.9927 1.0078 1.0228 1.0378 1.0527 1.0675 31 32 0.9317 0.9472 0.9625 0.9778 0.9929 1.0080 1.0231 1.0380 1.0529 1.0677 32 33 0.9320 0.9474 0.9627 0.9780 0.9932 1.0083 1.0233 1.0383 1.0532 1.0680 33 34 0.9323 0.9477 0.9630 9.9783 0.9934 1.0086 1.0236 1.0385 1.0534 1.0682 34 35 0.9325 0.9479 0.9633 0.9785 0.9937 1.0088 1.0238 1.0388 1.0537 1.0685 35 36 0.9328 0.9482 0.9635 0.9788 0.9939 1.0091 1.0241 1.0390 1.0539 1.0687 36 37 0.9330 0.9484 0.9638 0.9790 0.9942 1.0093 1.0243 1.0393 1.0542 1.0690 37 38 0.9333 0.9487 0.9640 0.9793 0.9945 1.0096 1.0246 1.0395 1.0544 1.0692 38 39 0.9335 0.9489 0.9643 0.9795 0.9947 1.0098 1.0248 1.0398 1.0547 1.0694 39 40 0.9338 0.9492 0.9645 0.9798 0.9950 1.0101 1.0251 1.0400 1.0549 1.0697 40 41 0.9341 0.9495 0.9648 0.9800 0.9952 1.0103 1.0253 1.0403 1.0551 1.0699 41 42 0.9343 0.9497 0.9650 0.9803 0.9955 1.0106 1.0256 1.0405 1.0554 1.0702 42 43 0.9346 0.9500 0.9653 0.9805 0.9957 1.0108 1.0258 1.0408 1.0556 1.0704 43 44 0.9348 0.9502 0.9655 0.9808 0.9960 1.0111 1.0261 1.0410 1.0559 1.070V 44 45 0.9351 0.9505 0.9658 0.9810 0.9962 1.0113 1.0263 1.0413 1.0.^,61 1.0709 45 46 0.9353 0.9507 0.9661 0.9813 0.9965 1.0116 1.0266 1.0415 1 .0564 1.0712 46 47 0.9356 0.9510 0.9663 0.9816 0.9967 1.0118 1.0268 1.0418 1.0566 1.0714 47 48 0.9359 0.9512 0.9666 0.9818 0.9970 1.0121 1.0271 1.0420 1.0.569 1.0717 48 49 0.9361 0.9515 0.9668 0.9821 0.9972 1.0123 1.0273 1.0423 1.0571 1.0719 49 50 0.9364 0.9518 0.9671 0.9823 0.9975 1.0126 1.0276 1.0425 1.0574 1.0721 50 51 0.9366 0.9520 0.9673 0.9826 0.9977 1.0128 1.0278 1.0428 1.0576 1.0724 51 52 0.9369 0.9523 0.9676 0.9828 0.9980 1.0131 1.0281 1.0430 1.0579 1.0726 52 53 0.9371 0.9525 0.9678 0.9831 0.9982 1.0133 1.0283 1.0433 1.0581 1.0729 53 54 0.9374 0.9528 0.9681 0.9833 0.9985 1.0136 1.0286 1.0435 1.0584 1.0731 54 55 0.9377 0.9530 0.9683 0.9836 0.9987 1.0138 1.0288 1.0438 1.0586 1.0734 55 56 0.9379 0.9533 0.9686 0.9838 0.9990 1.0141 1.0291 1.0440 1.0589 1.0736 56 57 0.9382 0.9536 0.9689 0.9841 0.9992 1.0143 1.0293 1.0443 1.0591 1.0739 57 58 0.9384 0.9538 0.9691 0.9843 0.9995 1.0146 1.0296 1.0445 1.0593 1.0741 58 59 0.9387 0.9541 0.9694 0.9846 0.9998 1.0148 1.0298 1.0447 1.0596 1.0744 59 60 0.9389 0.9543 0.9696 0.9848 1.0000 1.0151 1.0301 1.0460 1.0598 1.0746 60 Table of Chords 87 Table of Chords (Continued). Radius = i.oooo / M. 65° 66° 67° 68° 69° 70° 71° 73° 78° M. 0' 1.0746 1.0893 1 . 1039 1.1184 1 . 1328 1 . 1472 1.1614 1.1756 1.1896 0' 1 1.0748 1.0895 1.1041 1.1186 1.1331 1 . 1474 1.1616 1.1758 1 . 1899 1 ■ 2 1.0751 1.0898 1.1044 1.1189 1 . 1333 1.1476 1.1619 1.1760 1.1901 2 3 1.0753 1.0900 1 . 1046 1.1191 1.1335 1.1479 1.1621 1.1763 1 . 1903 3 4 1.0756 1.0903 1.1048 1.1194 1.1338 1.1481 1.1624 1.1765 1.1906 4 5 1.0758 1.0005 1.1051 1.11% 1.1340 1 . 1483 1.1626 1.1707 1.1908 5 6 1.0761 1.0907 1.1053 1.1198 1.1342 1 . 1486 1.1628 1.1770 1.1910 6 7 1.0763 1.0910 1 . 1056 1.1201 1 . 1345 1 . 1488 1.1631 1.1772 1.1913 7 8 1.0766 1.0912 1.1058 1 . 1203 1.1347 1.1491 1.1633 1.1775 1.1915 8 : 9 1.0768 1.0915 1.1016 1.1206 1.1350 1.1493 1.1635 1.1777 1.1917 9 1 10 1.0771 1.0917 1.1063 1.1208 1 . 1352 1.1495 1.1638 1.1779 1.1920 10 11 1.0773 1.0920 1.1065 1.1210 1 . 1354 1 . 1498 1.1640 1.1782 1.1922 11 12 1.0775 1.0922 1.1068 1.1213 1.1357 1.1500 1.1 042 1.1784 1.1924 12 13 1.0778 1.0924 1.1070 1.1215 1 . 1359 1 . 1502 1.1015 1.1780 1.1927 13 14 1.0780 1.0927 1.1073 1.1218 1.1362 1.1505 1.1047 1.1789 1.1929 14 15 1.0783 1.0929 1 . 1075 1.1220 1 . 1364 1 . 1507 1.1050 1.1791 1.1931 15 16 1.0785 1.0932 1.1078 1.1222 1 . 1366 1.1510 1.1052 1.1793 1.1934 16 17 1.0788 1.0934 1.1080 1.1225 1 . 1369 1.1512 1.1654 1.1790 1 . 1936 17 18 1.0790 1.0937 1 . 1082 1.1227 1.1371 1.1514 1.1657 1.1798 1.1938 18 : ; 19 1.0793 1.0939 1 . 1085 1 . 1230 1 . 1374 1.1517 1.1650 1.1800 1.1941 19 20 1.0795 1.0942 1.1087 1 . 1232 1.1376 1.1519 1.1661 1.1803 1.1943 20 21 1.0797 1.0944 1.1090 1.1234 1 . 1378 1.1522 1.1664 1.1805 1 . 1946 21 22 1.0800 1.0946 1.1092 1.1237 1.1381 1.1524 1.1606 1 . 1807 1.1948 22 23 1.0802 1.0949 1 . 1094 1.1239 1 . 13S3 1.1526 1.1068 1.1810 1 . 1950 23 24 1.0805 1.0951 1 . 1097 1.1242 1.1386 1.1529 1.1071 1.1812 1 . 1952 24 25 1.0807 1.0954 1.1099 1.1244 1 . 1388 1.1531 1.1073 1.1814 1 . 1955 25 26 1.0810 1.0956 1.1102 1.1246 1.1390 1.1533 1.1076 1.1817 1.1957 20 27 1.0812 1.0959 1.1104 1.1249 1 . 1393 1.1536 1.1078 1 . 1819 1 . 1959 27 ■ 28 1.0815 1.0961 1.1107 1.1251 1.1395 1.1538 1.1080 1.1S21 1.1962 28 29 1.0817 1.0903 1.1109 1 . 1254 1 . 1398 1.1541 1.1083 1.1824 1 . 1964 29 30 1.0820 1.0966 1.1111 1.1256 1.1400 1.1543 1.1685 1.1826 1.1966 30 31 1.0822 1.0968 1.1114 1.1258 1.1402 1,1545 1.1687 1.1829 1.1969 31 32 1.0824 1.0971 1.1116 1.1261 1 . 1405 1.1548 1.1690 1.1831 1.1971 32 33 1.0827 1.0973 1.1119 1.1263 1.1407 1 . 1550 1.1692 1.1833 1.1973 33 34 1.0829 1.0976 1.1121 1.1266 1 . 1409 1.1552 1.1094 1 . 1836 1.1976 34 35 1.0832 1.0978 1.1123 1.1268 1.1412 1.1555 1.1697 1 . 1838 1.1978 35 36 1.0834 1.0980 1.1126 1.1271 1.1414 1.1557 1.1099 1.1840 1.1980 36 37 1.0837 1.0983 1.1128 1.1273 1.1417 1.1560 1.1702 1.1843 1.1983 37 38 1.0839 1.0985 1.1131 1 . 1275 1.1419 1.1562 1.1704 1 . 1845 1 . 1985 38 39 1.0841 1.0988 1.1133 1.1278 1.1421 1.1564 1.1706 1.1847 1.1987 39 40 1.0844 1.0990 1.1136 1.1280 1.1424 1.1567 1.1709 1.1850 1.1990 40 41 1.0846 1.0993 1.1138 1.1283 1.1426 1.1569 1.1711 1.1852 1.1992 41 42 1.0849 1.0995 1.1140 1.1285 1.1429 1.1571 1.1713 1.1854 1.1994 42 43 1.0851 1.0997 1.1143 1.1287 1.1431 1.1574 1.1716 1.1857 1.1997 43 44 1.0854 1 . 1000 1.1145 1.1290 1 . 1433 1.1576 1.1718 1.1859 1 . 1999 44 45 1.0856 1 . 1002 1.1148 1.1292 1.1436 1.1579 1.1720 1.1861 1.2001 45 46 1.0859 1 . 1005 1.1150 1.1295 1.1438 1.15S1 1.1723 1.1864 1.2004 46 47 1.0861 1 . 1007 1.1152 1.1297 1.1441 1.15S3 1.1725 1.1806 1.2000 47 48 1.0863 1.1010 1.1155 1.1299 1.1443 1.1586 1.1727 1.1868 1.2008 48 49 1.0866 1.1012 1.1157 1.1302 1.1445 1.1588 1.1730 1.1871 1.2011 49 50 1.0868 1.1014 1.1160 1.1304 1.1448 1.1590 1.1732 1.1873 1.2013 50 51 1.0871 1.1017 1.1162 1.1307 1.1450 1.1593 1.1735 1.1875 1.2015 51 52 1.0873 1.1019 1.1165 1.1309 1.1452 1 . 1595 1.1737 1.1878 1.2018 52 53 1.0876 1.1022 1.1167. 1.1311 1.1455 1 . 1598 1.1739 1 . 1880 1.2020 53 54 1.0878 1 . 1024 1.1169 1.1314 1.1457 1.1600 1 . 1742 1 . 1882 1.2022 54 55 1.0881 1.1027 1.1172 1.1316 1.1460 1.1602 1.1744 1 . 1885 1.2025 55 56 1.0883 1 . 1029 1.1174 1.1319 1.1462 1.1605 1 . 1746 1.1887 1.2027 56 57 1.0885 1.1031 1.1177 1.1321 1 . 1464 1.1607 1.1749 1.1889 1.2029 57 58 1.0888 1 . 1034 1.1179 1.1323 1.1467 1.1609 1 . 1751 1 . 1892 1.2032 58 59 1.0890 1.1036 1.1181 1.1326 1.1469 1.1612 1.1753 1.1894 1.2034 59 60 1.0893 1 . 1039 1.1184 1.1328 1.1472 1.1614 1.1756 1 . 1896 1.2036 60 88 Geometrical Problems Table of Chords (Continued). Radius = i.oooo M. 74° 75° 76° 77° 78° 79° 80° 81° 858° M. 0' 1.2036 1.2175 1.2313 1.2450 1.2586 1.2722 1.2856 1.2989 1.3121 0' 1 1.2039 1.2178 1.2316 1.2453 1.2589 1.2724 1.2858 1.2991 1.3123 1 2 1.2041 1.2180 1.2318 1.2455 1.2591 1.2726 1.2860 1.2993 1.3126 2' 3 1.2043 1.2182 1.2320 1.2457 1.2593 1.2728 1.2862 1.2996 1.3128 3 4 1.2046 1.2184 1.2322 1.2459 1.2595 1.2731 1.2865 1.2998 1.3130 4 5 1.2048 1.2187 1.2325 1.2462 1.2598 1.2733 1.2867 1.3000 1.3132 5 , 6 1.2050 1.2189 1.2327 1.2464 1.2G00 1.2735 1.2869 1.3002 1.3134 6 ! 7 1.2053 1.2191 1.2329 1.2466 1.2602 1.2737 1.2871 1.3004 1.3137 7 \ 8 1.2055 1.2194 1.2332 1.2468 1.2604 1.2740 1.2874 1.3007 1.3139 8 9 1.2057 1.2196 1.2334 1.2471 1.2607 1.2742 1.2876 1.3009 1.3141 9 10 1.2060 1.2198 1.2336 1.2473 1.2609 1.2744 1.2878 1.3011 1.3143 10 11 1.2063 1.2201 1.2338 1.2475 1.2611 1.2746 1.2880 1.3013 1.3145 11 12 1.2064 1.2203 1.2341 1.2478 1.2614 1.2748 1.2882 1.3015 1.3147 12 13 1.2066 1.2205 1.2343 1.2480 1.2616 1.2751 1.2885 1.3018 1.3150 13 , 14 1.2069 1.2208 1.2345 1.2482 1.2618 1.2753 1.2887 1.3020 1.3152 14 15 1.2071 1.2210 1.2348 1.2484 1.2620 1.2755 1.2889 1.3022 1.3154 15 ' 16 1.2073 1.2212 1.2350 1.2487 1.2623 1.2757 1.2891 1.3024 1.315G 16 17 1.2076 1.2214 1.2352 1.2489 1.2625 1.2760 1.2894 1.3027 1.3158 17 18 1.2078 1.2217 1.2354 1.2491 1.2627 1.2762 1.2896 1.3029 1.3161 18 19 1.2080 1.2219 1.2357 1.2493 1.2629 1.2764 1.2898 1.3031 1.3163 19 20 1.2083 1.2221 1.2359 1.2496 1.2632 1.2766 1.2900 1.3033 1.3165 20 21 1.2085 1.2224 1.2361 1.2498 '1.2634 1.2769 1.2903 1.3035 1.3167 21 22 1.2087 1.2226 1.2364 1.2500 1.2636 1.2771 1.2905 1.3038 1.3160 22 23 1.2090 1.2228 1.2366 1.2503 1.2638 1.2773 1.2907 1.3040 1.3172 23 24 1.2092 1.2231 1.2368 1.2505 1.2641 1.2775 1.2909 1.3042 1.3174 24 25 1.2094 1.2233 1.2370 1.2507 1.2643 1.2778 1.2911 1.3044 1.3170 25 26 1.2097 1.2235 1.2373 1.2509 1.2645 1.2780 1.2914 1.3046 1.3178 26 27 1.2099 1.2237 1.2375 1.2512 1.2648 1.2782 1.2916 1.3049 1.3180 27 28 1.2101 1.2240 1.2377 1.2514 1.2650 1.2784 1.2918 1.3051 1.3183 28 29 1.2104 1.2242 1.2380 1.2516 1.2652 1.2787 1.2920 1.3053 1.3185 29 30 1.2106 1.2244 1.2382 1.2518 1.2654 1.2789 1.2922 1.3055 1.3187 30 31 1.2108 1.2247 1.2384 1.2521 1.2656 1.2791 1.2925 1.3057 1.3189 31 32 1.2111 1.2249 1.2386 1.2523 1.2659 1.2793 1.2927 1.3060 1.3191 32 33 1.2113 1.2251 1.2389 1.2525 1.2661 1.2795 1.2929 1.3062 1.3193 33 34 1.2115 1.2254 1.2391 1.2528 1.2663 1.2798 1.2931 1.3064 1.3196 34 35 1.2117 1.2256 1.2393 1.2530 1.2665 1.2800 1.2934 1.3066 1.3198 35 36 1.2120 1.2258 1.2396 1.2532 1.2668 1.2802 1.2936 1.3068 1.3200 36 37 1.2122 1.2260 1.2398 1.2534 1.2670 1.2804 1.2938 1.3071 1.3202 37 38 1.2124 1.2263 1.2400 1.2537 1.2672 1.2807 1.2940 1.3073 1.3204 38 39 1.2127 1.2265 1.2402 1.2539 1.2674 1.2809 1.2942 1.3075 1.3207 39 40 1.2129 1.2267 1.2405 1.2541 1.2677 1.2811 1.2945 1.3077 1.3209 40 41 1.2131 1.2270 1.2407 1.2543 1.2679 1.2813 1.2947 1.3079 1.3211 41 42 1.2134 1.2272 1.2409 1.2546 1.2681 1.2816 1.2949 1.3082 1.3213 42 43 1.2136 1.2274 1.2412 1.2548 1.2683 1.2818 1.2951 1.3084 1.3215 43 44 1.2138 1.2277 1.2414 1.2550 1.2686 1.2820 1.2954 1.3086 1.3218 44 45 1.2141 1.2279 1.2416 1.2552 1.2688 1.2822 1.2956 1.3088 1.3220 45 46 1.2143 1.2281 1.2418 1.2555 1.2690 1.2825 1.2958 1.3090 1.3222 46 47 1.2145 1.2283 1.2421 1.2557 1.2692 1.2827 1.2960 1.3093 1.3224 47 48 1.2148 1.2286 1.2123 1.2559 1.2695 1.2829 1.2962 1.3095 1.3220 48 49 1.2150 1.2288 1.2425 1.2562 1.2697 1.2831 1.2965 1.3097 1.322S 49 50 1.2152 1.2290 1.2428 1.2564 1.2699 1.2833 1.2967 I.Z09Q 1.3231 50 51 1.2154 1.2293 1.2430 1.2566 1.2701 1.2836 1.2969 1.3101 1.3233 51 52 1.2157 1.2295 1.2432 1.2568 1.2704 1.2838 1.2971 1.3104 1.3235 52 53 1.2159 1.2297 1.2134 1.2571 1.2706 1.2840 1.2973 1.3106 1.3237 53 54 1.2161 1.2299 1.2437 1.2573 1.2708 1.2842 1.2976 1.3108 1.3239 54 55 1.2164 1.2302 1.2439 1.2575 1.2710 1.2845 1.2978 1.3110 1.3242 55 56 1.2166 1.2304 1.2441 1.2577 1.2713 1.2847 1.2980 1.3112 1.3244 56 57 1.2168 1.2306 1.2443 1.2580 1.2715 1.2849 1.2982 1.3115 1.3246 57 58 1.2171 1.2309 1.2446 1.2582 1.2717 1.2851 1.2985 1.3117 1.3248 58 59 1.2173 1.2311 1.2448 1.2584 1.2719 1.2854 1.2987 1.3119 1.3250 59 60 1.2175 1.2313 1.2450 1.2586 1.2722 1.2856 1.2989 1.3121 1.3252 60 Table of Chords $» Table of Chords (Concluded) . Radius = 1. 0000 M. 83° 84° 85" 86° 87° 88° 89° M. 1 0' 1.3252 1.3383, 1.3512 1.3640 1.3767 1.3893 1.4018 0' 1 1.3255 1.3385 1.3514 1.3642 1.3769 1.3895 1.4020 1 2 1.3257 1.3387 1.3516 1.3644 1.3771 1.3897 1.4022 2 3 1.3259 1.3389 1.3518 1.3616 1.3773 1.3899 1.4024 3 4 l.a261 1.3391 1.3520 1.3618 1.3776 1.3902 1.4026 4 5 1.3263 1.3393 1.3523 1.3651 1.3778 1.3904 1.4029 5 6 1.3265 1.3396 1.3525 1.3653 1.3780 1.3906 1.4031 6 7 1.3268 1.3398 1.3527 1.3655 1.3782 1.3008 1.4033 7 8 1.3270 1.3400 1.3529 1.3657 1.3784 1.3910 1.4035 8 9 1.3272 1.3402 1.3531 1.3659 1.3786 1.3912 1.4037 9 10 1.3274 1.3404 1.3533 1.3661 1.3788 1.3914 1.4039 10 11 1.3276 1.3406 1.3535 1.3663 1.3790 T.3916 1.4041 11 12 1.3279 1.3409 1.3538 1.3665 1.3792 1.3918 1.4043 12 13 1.3281 1.3111 1.3540 1.3668 1.3794 1.39.20 1.4045 13 14 1.3283 1.3413 1.3542 1.3670 1.3797 1.3922 1.4047 14 15 1.3285 1.3415 1 3544 1.3672 1.3799 1.3925 1.4049 15 16 1.3287 1.3417 1.3546 1.3674 1.3801 1.3927 1.4051 16 17 1.3289 1.3119 1.3548 1.3676 1.3S03 1.8929' 1.4053 17 18 1.3292 1 3421 1.3550 1.3678 1.3805 1.3931 1.4055 18 19 1.3294 1.3424 1.3552 1.3680 1.3807 1.3033 1.4058 19 20 1.3296 1.3426 1.3555 1.3682 1.8809 1.3935 1.4060 20 21 22 1.3298 1.3300 1.3428 1.3557 1 3685 1.3811 1.3813 1.3937 1.3939 1.4062 1.4064 21 22 1.3430 1.3559 1.3687 23 1.3302 1.3432 1.3561 1.3680 1.3816 1.3941 1.4066 23 24 1.3305 1.3434 1.3563 1.3091 1.3818 1.3043 1.4068 24 25 1.3307 1.3437 1.3565 1.3693 1.3820 1.3945 1.4070 25 26 1.3309 1.3439 1.3567 1.3695 1.3822 1.3947 1.4072 26 27 1.3311 1.3441 1.3570 1.3697 1.3824 1.3950 1.4074 27 28 1.3313 1.3443 I 3572 1.3639 1.3826 1.3952 1.4076 28 29 1.3315 1.3445 1.3574 1.3702 1.3828 1.3954 1.4078 29 30 1.3318 1.3447 1.3576 1.3704 1.3830 1.3956 1.4080 30 31 1.3320 1.3449 1.3578 1.3706 1.3832 1.3958 1.4082 31 32 33 1.3322 1.3324 1.3452 1.3580 1.3708 1.3710 1.3834 1.3837 1.3960 1.3962 1.4084 1.4086 32 33 1.3454 1.3582 34 1.3326 1.3456 1.3585 1.3712 1.3839 1.3964 1.4089 34 35 1.3328 1.3458 1.3587 1.3714 1.3841 1.3966 1.4091 35 36 1.3331 1.3460 1.3589 1.3716 1.3843 1.3968 1.4093 36 37 1.3333 1.3462 1.3591 1.3718 1.3845 1.3970 1.4095 37 38 1.3335 1.3465 1.3503 1.3721 1.3847 1.3972 1.4097 38 3!) 1.3337 1.3467 1.3595 1.3723 1.3849 1.3975 1.4099 39 40 1.3339 1.3469 1.3597 1.3725 1.3851 1.3977 1.4101 40 41 1.3341 1.3471 1.3599 1.3727 1.3853 1.3979 1.4103 41 42 1.3344 1.3473 1.3602 1.3729 1.3855 1.3981 1.4105 42 43 1.3346 1.3475 1.3604 1.3731 1.3858 1.3983 1.4107 43 44 1.3348 1.3477 1.3606 1.3733 1.3860 1.3985 1.4109 44 45 1.3350 1.3480 1 . 3008 1.3735 1.3862 1.3987 1.4111 45 46 1.3352 1.3482 1.3610 1.3738 1.3864 1.3989 1.4113 46 47 1.3354 1.3484 1.3612 1.3740 1.3866 1.3991 1.4115 47 48 1.3357 1.3486 1.3614 1.3742 1.3868 1.3993 1.4117 48 49 1.3359 1.3488 1.3617 1.3744 1.3870 1.3995 1.4119 49 50 1.3361 1.3490 1.3619 1.3746 1.3872 1.3997 1.4122 50 51 1.3363 1.3492 1.3621 1.3748 1.3874 1.3999 1.4124 51 52 1.3365 1.3495 1.3623 1.3750 1.3876 1.4002 1.4126 52 53 1.3367 1.3497 1.3625 1.3752 1.3879 1.4004 1..4128 63 54 1.3370 1.3499 1.3627 1.3754 1.3881 1.4006 1.4130 54 55 1.3372 1.3501 1.3629 1.3757 1.3883 1.4008 1.4132 55 56 1.3374 1.3503 1 3631 1.3759 1,3885 1.4010 1.4134 56 57 1 3376 1.3505 1.3634 1.3761 1.3887 1.4012 1.4136 67 58 1.3378 1.3508 1.3636 1.3763 1.3889 1.4014 1.4138 58 59 1.3380 1.3510 1.3638 1.3765 1.3891 1.4016 1.4140 59 60 1.3383 1.3512 1.3640 1.3767 1.3893 1.4018 1.4142 60 90 Trigonometry Part 1 Lengths and Bevels of Hip-Rafters and Jack-Rafters Method of Determining the Lengths and Bevels. The lines ab and be (Fig. 92) represent the outside of the walls at the angle of a building; be is the seat of the hip-rafter and gf of a jack-rafter. Draw eh at right-angles to be and make it equal to the rise of the roof'; join b and // and hb will be the length of the hip-rafter. Through e draw di at right-angles to be. With t as a center h a h Fig. 92. m g d c Lengths and Bevels of Hip-rafters and Jack-rafters and with the radius bh, describe the arc hi, cutting di in i. Join b and i and extend gf to meet bi in j; then gj is the length of the jack-rafter. The length of each jack-rafter is found in the same manner, by extending its seat to cut the line 6/. From / draw /y^ at right-angles to /g; also// at right-angles to ie. Make fk equal to// by the arc Ik, or make gk equal to gj by the arci^; then the angle at J is the top bevel of the jack-rafters, and the angle at k the down bevel. Backing of the Hip-Rafter. At any convenient point in be (Fig. 92), as o, draw mn at right-angles to be. From o describe a circle, tangent to bh, cutting be in s. Join m and s and n and s. The lines jns and ns form at s the proper angle for beveling the top of the hip-rafter. 5. TRIGONOMETRY It is not. the purpose of the author to teach the principles or uses of trigonom- etry; but for the benefit of those readers who have already acquired a knowledge of this science, the following convenient formulas and tables of natural sines, cosines, tangents and cotangents have been inserted. To those who know how to apply these trigonometric functions, they will often be found of great con- venience and utility. These tables are taken, by permission, from Searle's Field Engineering, John Wiley & Sons, Inc., publishers. Trigonometrical Functions Trigonometric Functions 91 Let A (Fig. 93) = angle BAC = arc BF and let the radius AF = AB = AH = i Then sin A = BC cos A = AC tan A = DF cot A= HG sec A = AD cosec A = AG versin A = CF =- BE covers A = BK = HL exsec A = BD coexsec A = BG chord A = BF chord 2 A= BI = 2BC Fig. 93. Functions of Right-angled Triangle In the right-angled triangle ABC (Fig. 93) let AB -= c, AC = b and BC = a Then (I) (2) (3) (4) (5) sin A ■■ = cosB cos A = - = sin B tan A = -r = cot J5 cot A = - = tan J5 sec A = r = cosec B (6) cosec A = - — sec B (7) vers A = = covers B (8) exsec A = — ^ — = coexsec B (9) covers A = = versin B (11) a = csin A = 6tan A (12) b = c cos A = a cot A , . c b (13) c = -^ — - = — -j- sin A cos A (14) a = c cos B = b cot B (15) 6 = csin J5 = ctanS (17) fl = V(c + fe)(c-6) (21) area = (18) 6 = V (c + o) (c - a) (19) c = Va2 + 62 (20) C = 90° = A + 5 0^ Trigonometry Solution of Oblique Triangles Part 1 ■A V / \a / \ 1 h o 1 Fig. 94. Oblique-angled .Triangle Given Required Formulas (22) A.B,a C,b,c C = i8o° - (A 4- 5) ^"^i^*^^^^ c = -A-^ sin (A -f B) sin A (23) A.a,b B,C,c sin B = ^^^ 'b C == i8o° - (A + J3) a c = -^ — - • sin C sin A (24) C,a,b \^{A-^B) Vz (A + B) = 90° - H C (25) mA-B) tan '/^ (A - J5) = ^ tan 3^^ (A + B) a + b (26) A,B A=WiA+B) + H{A-B) B = V2U+B)-H(A-B) (27) c , , ^, cos 1/^ (A + B) . , , sin H (A -f B) ^~ ^" + ^^ cos^i(A -^B) "^'^ ^^ sin^HA -5) (28) (29) (30) a, b, c Area A Let cos Yz ab siA C s-Hia + b+c); smHA-\/^'-^l^'-'^ /,,1=.iA(^-«>.tnnU.i-V/^^-?^(^-^> cos,.- ^ ^^ , - -_- ^ ^(5-0) (31) (32) -in " .2^5(5-0) (5-6) (5-c) Area K = 6c 6c = V5 (5 - C) (5 - b) {S - C) (33) A.B,C,a Area „ a2 sin B sin C K — . . 2 Sin A Trigonometrical Functions Oblique Triangles. General Formulas (34) sin A = r = Vi — cos'^ A = tan A cos A cosec A (35) sin A = 2 sin J/i A cos \i A == vers A cot }'i A (36) sin A = Vi7^ vers 2 A = Vi,^ (i — cos 2 A) (37) cos A = 7 = v^i — sin2 A = cot A sin A sec A (38) cos A = I — vers A = 2 cos^ >ia A — i = i — 2 sin^ \^ A (39) cos A = cos2 \iA— sin2 Yi A = ^Yi + Yi cos 2 A (40) tan A tan A = ' - "''' 1 - ^sec^ A I cot A cos A , / I v^i — cos'-^ A sin 2 A (41; ▼ cos'-^ A cos A I + cos 2 A (42) tan A cot A I — cos 2 A vers 2 A , ^ , , . = — : — = —. 7- = exsec A cot Y2 A ^^ sin 2 A sin 2 A (43) - \ -^°'^,^ -- Vcosec^A-i tan A sin A (44) cot A sin 2 A sin 2 A i + cos 2 A ~ I — cos 2 A ^ rers 2 A sin 2 A (45) cot A tan 1/2 A (46) vers A = I — cos A = sin A tan Yz A = 2 sin2 J.^ A (47) vers A = exsec A cos A (48) exsec A = sec A — I = tan A tan J^^ A = -r- — 4/ 1 ~ cos A _ w vers A (49) sin3'iA (50) sin 2 A = 2 sin A cos A ^ X 1/ ^ 4/1 + cos A (si) cos YA=y (52) cos 2 A = 2 cos2 A — I = cos2 A — sin2 A = i — 2 sin^ A [ — cos A -cos A , . ^ ,, . tan A . , . I -cos A 4/ f -c (53) tani/^A = ^-^^^^ = cosec A - cot A = -^^^^^ == V fT^ . . ^ . 2 tan A (54) tan 2 A == (55) cot3'iA = (56) cot 2 A = I - tan2 A sin A _ ij4- cos A _ i vers A sin A cosec A — cot A cot 2 A — I 2 cot A 94 Trigonometry Part 1 Oblique Triangles. General Formulas (Continued) j (57) H vers A i — cos A versAA ^^Vi-y^versA 2+^2(1 + 003^) (58) vers 2 A = 2 sin^ A (59) I — cos A ' exsec^^A = , , ... ^/—, — ; 7-- (i + cos A) + V2 (I + cos A) (6o) . 2tan2A exsec 2 A = :^ — — -r I — tan2 A (6i) sin (A ± B) = sin A cos B zksinB cos A (62) cos (A dz B) — cos A cos B =F sin A sin B (63) sin A + sin 5 = 2 sin H (A + B) cos H (A - B) (64) sin A - sin B = 2 cos H (A + B) sin H (A - i3) (65) cos A + cos ij = 2 cos I/-2 (A + B) cos i/l2 (A - B) (66) cosB-cosA = 2smy2U+B)smy2{A-B) (67) sin2 A - sin2 B = cos2 B- cos2 A = sin (A + jB) sin (A - B) (68) cos2 A - sin2 B = cos (A + B) cos (A - B) (69) tanl I tan^-^^^^^^+^^ xan j-i -\- lan i? — . „ cos A cos 5 (70) . ^ „ sin (A - B) tan A — tan B = ^^; rr cos A cos B Tabic of Natural Sines and Cosines 95 0° 1° ■ 2^^ 3^^ 1 4° ' Sine .00000 Cosin One. Sine .01745 Cosin .99985 Sine Cobin Sine Cosin Sine Cosin .03490 .99939 .05234 .99803 .06976 .99756 60 1 .00029 One. .01774 .99984 .03519 .99938 .05263 .99861 .07005 .99754 59 2 .00058 One. .01803 .99984 .03548 .99937 .05292 .99860 .07034 .99752 58 3 .00087 One. .01832 .99983 .03577 .99936 .05321 .9985S .07063 .99750 57 4 .00116 One. .01862 .99983 .03606 .99935 .05350 .99857 .07092 .99748 56 5 .00145 One. .01891 .99982 .03635 .99934 .05379 .99855 .07121 .99746 55 6 .00175 One. .01920 .99982 .03664 .99933 .05408 .99854 .07150 .99744 54 7 .00204 One. .01949 .99981 .0369? .99932 .05437 .99852 .07179 .99742 53 8 .00233 One. .01978 .99980 .03723 .99931 .05466 .99851 .07208 .99740 52 9 .00262 One. .02007 .99989 .03752 .99930 .05495 .99849 .07237 .99738 51 10 .00291 One. .02030 .99979 .03781 .99929 .05524 .99847 .07266 .99736 50 11 .00320 .99909 .02065 .99979 .0381C .99927 .05553 .99846 .07295 .99734 49 12 .00349 .99999 .02094 .99978 .02839 .99926 .05582 .99844 .07324 .99731 48 13 .00378 .99999 .02123 .99977 .03808 .99925 .05611 .99842 .07353 .99729 47 14 .00407 .99999 .02152 .99977 .03897 .99924 .05640 .99841 .07382 .99727 40 15 .00436 .99999 .02181 .99976 .0392C .99923 .05669 .99839 .07411 .99725 45 16 .00465 09990 .02211 .99976 .03955 .99922 .05698 .99838 .07440 .99723 44 17 .00495 !99999 .02240 .99975 .03984 .99921 .05727 .99836 .07469 .99721 43 18 .00524 .99999 .02269 .99974 .04013 .99919 .05756 .99834 .07498 .99719 42 19 .00553 .99998 .02298 .99974 .04042 .99918 .05785 .99833 .07527 .99716 41 20 .00582 .99998 .02327 .99973 .04071 .99917 .05814 .99831 .07556 .99714 40 21 .00611 .99998 .02356 .99972 .04100 .99916 .05844 .99829 .07585 .99712 39 22 .00640 .99998 .02385 .99972 .04129 .99915 .05873 .99827 .07614 .99710 38 23 .00669 .99998 .02414 .99971 .04159 .99913 .05902 .99826 .07643 .99708 37 24 .00698 .99998 .02443 .99970 .04188 .99912 .05931 .99824 .07672 .99705 36 25 .00727 .99997 .02472 .99969 .04217 .99911 .05960 .99822 .07701 .99703 35 26 .00756 .90997 .02501 .99960 .04246 .99910 .05989 .99821 .07730 .99701 34 27 .00785 .99997 .02530 .99968 .04275 .09909 .06018 .99819 .07759 .99699 33 28 .00814 .99997 .02560 .99967 .04304 .99907 .06047 .99817 .07788 .99696 32 29 .00844 .99996 .02589 .99966 .04333 .99900 .00076 .99815 .07817 .99694 31 30 .00873 .99996 .02618 .99966 .04362 .99905 .06105 .99813 .07846 .99692 30 31 .00902 .99996 .02647 .99905 .04391 .99004 .06134 .99812 .07875 .99689 29 32 .00931 .99996 .02676 .99964 .04420 .99902 .06163 .99810 .07904 .99687 28 33 .00960 .99995 .02705 .99963 .04449 .99901 .06192 .99808 .07933 .99685 27 34 .00989 .99995 .02734 .99963 .04478 .99900 .06221 .99806 .07962 .99683 26 35 .01018 .99995 .02703 .99962 .04507 .99898 .062.50 .99804 .07991 .99680 25 36 .01047 .99995 .02792 .99961 .04536 .99897 .06279 .99803 .08020 .99678 24 37 .01076 .99994 .02821 .99960 .04565 .99896 .06308 .99801 ,08049 .99676 23 38 .01105 .99994 .02850 .99959 .04594 .99894 .06337 .99799 .08078 .99673 22 39 .01134 .99994 .02879 .99959 .04623 .99893 .06366 .99797 .08107 .99671 21 40 .01164 .99993 .02908 .99958 .04653 .99892 .06395 .99795 .08136 .99668 20 41 .01193 .99993 .02938 .99957 .04682 .99890 .06424 .99793 .08165 .99666 19 42 .01222 .09993 .02907 .99956 .04711 .99889 .06453 .99792 .08194 .99664 18 43 .01251 .99992 .02996 .99955 .04740 .99888 .06482 .99790 .08223 .99661 17 44 .01280 .99992 .03025 .99954 .04769 .99886 .06511 .99788 .08252 .99659 16 45 .01309 .99991 .03054 .99953 .04798 .99885 .06540 .99786 .08281 .99657 15 46 .01338 .99991 .03083 .90952 .04827 .99883 .06569 .99784 .08310 .99654 14 47 .01367 .99991 .03112 .99952 .04856 .99882 .06598 .99782 .08339 .99652 13 48 .01396 .99900 .03141 .99951 .04885 .99881 .06627 .99780 .08368 .99649 12 49 .01425 .99990 .03170 .99950 .04914 .99879 .06656 .99778 .08397 .99647 11 50 .01454 .99989 .03199 .99949 .04943 .99878 .06685 .99776 .0M26 .99644 10 51 .01483 .99989 .03228 .99948 .04972 .99876 .06714 .99774 .08455 .99642 9 52 .01513 .99989 .03257 .09947 .05001 .99875 .06743 .99772 .08484 .99639 8 53 .01542 .99988 .03286 .99946 .05030 .99873 .06773 .99770 .08513 .99637 7 54 .01571 .99988 .03316 .99945 .05059 .99872 .06802 .99768 .08542 .99635 6 55 .01600 .99987 .03345 .99944 .05088 .99870 .06831 .99766 .08571 .99632 5 56 .01629 .99987 .03374 .99943 .05117 .99869 .06860 .99764 .08600 .99630 4 57 .01658 .99986 .03403 .99942 .05146 .99867 .06889 .99762 .08629 .99627 3 58 .01687 .99986 .03432 .99941 .05175 .99866 .06918 .99760 .08658 .99625 2 59 .01716 .99985 .03461 .99940 .05205 .99864 .06947 .99758 .08687 .99622 1 60 .01745 .99985 .03490 .99939 .05234 .99863 .06976 .99756 .08716 .99619 ' Oosin Sine Cosin Sine Cosin Sine | Cosin Sine Cosin Sine ' 8< )° 88° 1 8' 7^ 1 86° 85° 96 Trigonometry Part 1 ' 5° G*" r • 8° 9° / Sine (/osin Sine Cosin Sine Coyiu Sine Cosin .99027 Sine Cosin .08716 .99619 .10453 .99452 .12187 .99255 .13917 .15643 .98769 ~m 1 .08745 .99617 .10482 .99449 .12216 .99251 .13946 .99023 .15672 .98764 59 2 .08774 .99614 .10511 .99440 .12245 .99248 .13975 .99019 .15701 .98700 58 3 .08803 .99612 .10510 .99443 .12274 .99244 .14004 .99015 .15730 .98755 57 4 .08831 .99600 .10509 .99440 .1230i .99240 .14033 .99011 .15758 .98751 56 5 .08860 .99607 .10597 .99437 .12331 .99237 .14001 .99000 .15787 .98746 55 6 .08889 .99604 .10620 .99434 .12300 .99233 .14090 .99002 .15816 .98741 54 7 .08918 .99002 .10655 .99431 .12389 .99230 .14119 .98998 .15845 .98737 53 8 .08947 .99599 .10684 .9942S .12418 .99220 .1414S .98994 .15873 .98732 52 9 .08976 .99596 .10713 .99424 .12447 .99222 .14177 .98990 .15902 .98728 51 10 .09005 .99594 .10742 .99421 .12476 .99219 .14205 .98986 .15931 .98723 50 11 .09034 .99591 .10771 .99418 .12504 .99215 .14234 .98982 .15959 .98718 49 12 .09063 .99588 .10800 .99415 .12533 .99211 .14263 .98978 .15988 .98714 48 13 .09092 .99586 .10S29 .99412 .12502 .99208 .14292 .98973 .16017 .98709 47 14 .09121 .99583 .10858 .99409 .12591 .99204 .14320 .98909 .16046 .98704 46 15 .09150 .99580 .10887 .99400 .12020 .99200 .14349 .98905 .16074 .98700 45 16 .09179 .99578 .10916 .99402 .12049 .99197 .14378 .98961 .16103 .98695 44 17 .09208 .99575 .10945 .99399 .12078 .99193 .14407 .98957 .10132 .98690 43 18 .09237 .99572 .10973 .99306 .12700 .99189 .14436 .98953 .16160 .98686 42 19 .09266 .99570 .11002 .09393 .12735 .99180 .14464 .98948 .16189 .98681 41 20 .09295 .99567 .11031 .99390 .12704 .99182 .14493 .98944 .16218 .98676 40 21 .09324 .99564 .11060 .99386 .12793 .99178 .14522 .98940 .16246 .98671 39 22 .09353 .99582 .11039 .99383 .12822 .99175 .14551 .98930 .16275 .98667 38 23 .09382 .99559 .11118 .99380 .12851 .99171 .14580 .98931 .16304 .98662 37 24 .09411 .99556 .11147 .99377 .12880 .99107 .14608 .98927 .16333 .98057 36 25 .09440 .99553 .11176 .99374 .12908 .99103 .14637 .98923 .16361 .98652 35 26 .09469 .99551 .11205 .99370 .12937 .99100 .14660 .98919 .16390 .98648 34 27 .09498 .99548 .11234 .99307 .12960 .99156 .14095 .98914 .16419 .98643 33 28 .09527 .99545 .11203 .99304 .12995 .99152 .14723 .98910 .16447 .98638 32 29 .09556 .99542 .11291 .99300 .13024 .99148 .14752 .98900 .16476 .98633 31 30 .09585 .99549 .11320 .99357 .13053 .99144 .14781 .98902 .16505 .98629 30 31 .09614 .99537 .11349 .99351 .13081 .99141 .14810 .98897 .16533 .98624 29 32 .09642 .99534 .11378 .99351 .13110 .99137 .14838 .98893 .16562 .98619 28 33 .09671 .99531 .11407 .99347 .13139 .09133 .14807 .98889 .16591 .98614 27 34 .09700 .99528 .11431 .99344 .13108 .99129 .14890 .98884 .16620 .98609 26 35 .09729 .99526 .11405 .99341 .13197 .99125 .14925 .98880 .16648 .98604 25 36 .09758 .99523 .11494 .99337 .13220 .99122 .14954 ,98876 .16677 .9S600 24 37 .09787 .99520 .11523 .99334 .13254 .99118 .14982 .98871 .10700 .98595 23 38 .09816 .99517 .11552 .99331 .13233 .99114 .15011 .98867 .10734 .98590 22 39 .09845 .99514 .11530 .99327 .13312 .99110 .15040 .98863 .16763 .98585 21 40 .09874 .99511 .11609 .99324 .13341 .99106 .15009 .98858 .16792 .98580 20 41 .09903 .99508 .11638 .99320 .13370 .99102 .15097 .98854 .16820 .98575 19 42 .09932 .9950e .11667 .99317 .13399 .99098 .15126 .98849 .10849 .98570 18 43 .09961 .99503 .11696 .99314 .13427 .99094 .15155 .98845 .10878 .98565 17 44 .09990 .99500 .11725 .99310 .13450 .99091 .15184 .98841 .10906 .98561 16 45 .10019 .99497 .11754 .99307 .13485 .99087 .15212 .98836 .16935 .98556 15 46 .10018 .99494 .11783 .99303 .13514 .99083 .15241 .98832 .16964 .98551 14 47 .10077 .99491 .11812 .99300 .13543 .99079 .15270 .98827 .16992 .98546 13 48 .10106 .99488 .11840 .99297 .13572 .99075 .15290 .98823 .17021 .98541 12 49 .10135 .99485 .11869 .99293 .13600 .99071 .15327 .98818 .17050 .98536 11 50 .10164 .99482 .11898 .99290 .13629 .99067 .15350 .98814 .17078 .98531 10 51 .10192 .99479 .11927 .99286 .13658 .99063 .15385 .98809 .17107 .98526 9 52 .10221 .99476 .11956 .99283 .13687 .99059 .15414 .98805 .17136 .98521 8 53 .10250 .99473 .11985 .99279 .13716 .99055 .15442 .98800 .17164 .98516 7 54 .10279 .99470 .12014 .99276 .13744 .99051 .15471 .98796 .17193 .98511 6 55 .10308 .99467 .12043 .99272 .13773 .99047 .15500 .98791 .17222 .98506 5 56 .10337 .99464 .12071 .99269 .13802 .99043 .15529 .98787 .17250 .98501 4 57 .10366 .99401 .12100 .99265 .13831 .99039 .15557 .98782 .17279 .98496 3 58 .10395 .99458 .12129 .99262 .13860 .99035 .15586 .98778 .17308 .98491 2 59 .10424 .99455 .12158 .99258 .13889 .99031 .15615 .98773 .17336 .98486 1 60 .10453 .99452 .12187 .99255 .13917 .99027 .15643 .98769 .17365 .98481 t Cosin Sine Cosin Sine Cosin Sine Cosin Sine Cosin Sine / 84° 1 83° 1 82° 1 81» 1 80° 1 Table of Natural Sines and Cosines 9r .' 10^ _ 11° ___J lti° 1 13° 1 14° 1 / Sine* ('osin Sine Cosin Sine .20791 Cosin Sine Cosin Sine Cosin .17305 .98481 .19081 .98103 .97815 .22495 .97437 .24192 .97030 60 1 .17393 .98470 .19109 .98157 .20820 .97809 .22523 .97430 .24220 .97023 59 2 .17422 .98471 .19138 .98152 .20848 .97803 .22552 .97424 .24249 .97015 58 3 .17451 .98406 .19107 .98140 .20877 .97797 .22580 .97417 .24277 .97008 67 4 .17479 .98401 .19195 .98140 .20905 .97791 .22008 .97411 .24305 .97001 50 5 .17508 .98455 .19224 .98135 .20933 .97784 .22037 .97404 .24333 .90994 55 6 .17537 .98450 .19252 .98129 .20902 .97778 .22005 .97398 .24302 .90987 64 7 .17505 .98445 .19281 .98124 .20990 .97772 .22093 .97391 .24390 .90980 53 8 .17594 .98440 .10309 .98118 .21019 .97700 .22722 .97384 .24418 .96973 52 9 .17023 .98435 .19338 .98112 .21047 .97700 .22750 .97378 .24440 .90900 51 10 .17051 .98430 .19300 .98107 .21070 .97754 .22778 .97371 .24474 .96959 50 11 .17080 .98425 .19395 .98101 .21104 .97748 .22807 .97305 .24503 .90952 49 12 .17708 .98420 .19423 .98090 .21132 .97742 .22835 .97358 .24531 .90945 48 13 .17737 .98414 .19452 .98090 .21101 .97735 .22803 .97351 .24559 .90937 47 14 ,17700 .98409 .19481 .98084 .21189 .97729 .22892 .97345 .24587 .90930 40 15 .17794 .98404 .19509 .98079 .21218 .97723 .22920 .97338 .24015 .90923 45 IG .17823 .98399 .19538 .98073 .21240 .97717 .22948 .97331 .24044 .90910 44 17 .17852 .98394 .19500 .98007 .21275 .97711 .22977 .97325 .24072 .90909 43 18 .17880 .98389 .19595 .98001 .21303 .97705 .23005 .97318 .24700 .90902 42 10 .17909 .98383 .19C23 .98050 .21331 .97098 .23033 .97311 .24728 .90894 41 20 .17937 .98378 .19652 .98050 .21300 .97092 .23002 .97304 .24750 .90887 40 21 .17900 .98373 .19080 .98044 .21388 .97080 .23090 .97298 .24784 .96880 39 22 .17995 .98308 .19709 .98039 .21417 .97080 .23118 .97291 .24813 .96873 38 23 .18023 .98302 .19737 .98033 .21445 .97073 .23140 .97284 .24841 .90860 37 24 .18052 .98357 .19700 .98027 .21474 .97007 .23175 .97278 .24809 .96858 36' 25 .18081 .98352 .19794 .98021 .21502 .97001 .23203 .97271 .24897 .96851 35 20 .18109 .98347 .19823 .98010 ,21530 .97055 .23231 .97204 .24925 .96844 34 27 .18138 .98341 .19851 .98010 .21559 .97048 .23200 .97257 .24954 .96837 33 28 .18100 .98330 .19880 .98004 .21587 .97042 .23288 .97251 .24982 .96829 32 29 .18195 .98331 .1990S .97998 .21010 .97030 .23310 .97244 .25010 .96822 31 30 .18224 .98325 .19937 .97992 .21044 .07030 .23345 .97237 .25038 .90815 30 31 .18252 .18281 .98320 .19905 .97987 .21072 .97023 .23373 .97-230 .25000 .90807 29 32 .98315 .19994 .97981 .21701 .97017 .23401 .97223 .25094 .90800 28 33 .18309 .98310 .20022 .97975 .21729 .97011 .23429 .97217 .25122 .96793 27 34 .18338 .98304 .20051 .97909 .21758 .97004 .23458 .97210 .25151 .96786 26 35 .18307 .98299 .20079 .97903 .21780 .97598 .23480 .97203 .25179 .96778 25 36 .18395 .98294 .20108 .97958 .21814 .97592 .23514 .97190 .25207 .96771 24 37 .18424 .98288 .20130 .97952 .21843 .97585 .23542 .97189 .25235 .96704 23 38 .18452 .98283 .20105 .97940 .21871 .97579 .23571 .97182 .25203 .90750 22 39 .18481 .98277 .20193 .97940 .21899 .97573 .23599 .97170 .25291 .96749 21 40 .18509 .98272 .20222 .97934 .21928 .97500 .23027 .97109 .25320 .96742 20 41 .18538 .98207 .20250 .97928 .21950 .97500 .22050 .97102 .25348 .96734 19 42 .18507 .98201 .20279 .97922 .21985 .97553 .23084 .97155 .25370 .96727 18 43 .18595 .98250 .20307 .97910 .22013 .975!7 .23712 .97148 .25404 .96719 17 44 .18024 .98250 .20330 .97910 .22041 .97541 .23740 .97141 .25432 .96712 16 45 .18052 .98245 .20304 .97905 .22070 .97534 .23709 .97134 .25400 .90705 15 40 .18081 .98240 .20393 .97899 .22098 .97528 .23797 .97127 .25488 .90097 14 47 .18710 .98234 .20421 .97893 .22120 .97521 .23825 .97120 .25516 .96690 13 48 .18738 .98229 .20450 .97887 .22155 .97515 .23853 .97113 .25545 .96682 12 49 .18707 .98223 .20478 .97881 .22183 .97508 .23882 .97100 .25573 .96675 11 50 .18795 .98218 .20507 .97875 .22212 .97502 .23910 .97100 .25001 .96667 10 51 .18824 .98212 .20535 .97809 .22240 .97490 .23938 .97093 .25629 .90060 9 52 .18852 .98207 .20503 .97803 .22208 .97489 .23900 .97080 .25057 .96653 8 53 .18881 .98201 .20592 .97857 .22297 .97483 .23995 .97079 .25085 .96645 7 54 .18910 .98190 .20020 .97851 .22325 .97470 .24023 .97072 .25713 .90038 6 55 .18938 .98190 .20049 .97845 .22353 .97470 .24051 .97005 .25741 .90030 5 50 .18907 .98185 .20077 .97839 .22382 .97403 .24079 .97058 .25709 .90023 4 57 .18995 .98179 .20700 .97833 .22410 .97457 .24108 .97051 .25798 .90015 3 58 .19024 .98174 .20734 .97827 .22438 .97450 .24130 .97044 .25820 .96608 2 59 .19052 .98108 .20703 .97821 .22407 .97444 .24104 .97037 .25854 .96600 1 00 .19081 .98103 .20791 .97815 .22495 .97437 .24192 .97030 .25882 Cosin .96593 T Cosin Sine Cosin Sine Cosin Sine Cosin Sine Sine ■ 79° 78° 77° 7r.'> 1 75° Trigonometry ' Part ' 15° 1 1«° 1 17° 1 18° 1 19° 1 t 60 Sine Cosin Sine Cosin Sine 4 .31151 .95024 .32804 .94466 51 10 .26163 .96517 .27843 .90046 .29515 .95545 .31178 .95015 .32832 .94457 50 11 .26191 .96500 .27871 .96037 .20543 .95536 .31206 .95006 .32850 .94447 40 12 .26219 .96502 .27890 .96029 .20571 .95528 .31233 .94097 .32SS7 .94438 4.N 13 .26247 .03494 .27927 .96021 .20599 .9.5519 .31261 .94088 .32914 .94428 47 14 .2627a .96486 .27955 .96013 .29626 .9.3511 .31289 .94079 .32942 .94418 4". 15 .26303 .96479 .27983 .96005 .20654 .95502 .31316 .94970 .32900 .94409 45 16 .26331 .96471 .28011 .95097 .20632 .95493 .31344 .94961 .32007 .94399 44 17 .26359 .96163 .28030 .95959 .20710 .95485 .31372 .94952 .33024 .94390 43 18 .26387 .96456 .2:3067 .95981 .20737 .95476 .31399 .94043 .33051 .94380 42 19 .26415 .96448 .23095 .95972 .20765 .9.3467 .31427 .94933 .33070 .94370 41 20 .26443 .96440 .28123 .95904 .29703 .95459 .31454 .94924 .33106 .94361 40 21 .26471 .96433 .28150 .95956 .20821 .95450 .31482 .94915 .33134 .94351 30 22 .26500 .96125 .28178 .95948 .20349 .95441 .31510 .94906 .33161 .94342 38 23 .26528 .96417 .2S206 .95940 .20370 .95433 .31537 .94397 .33180 .94332 37 24 .26556 .96410 .28234 .95031 .20001 .95424 .31.305 .94888 .33216 .94322 Oii 25 .26584 .96402 .28262 .95923 .20032 .95115 .31503 .94878 .33244 .94313 35 26 .26612 .96394 .28200 .95915 .20960 .95107 .31620 .94869 .33271 .94303 3t 27 .26640 .96386 .2S318 .95907 .20037 .95398 .31648 .94860 .33298 .94293 33 28 .26668 .96379 .28346 .95898 .30015 .95389 .31675 .94851 ..3332(5 .94284 32 29 .26696 .96371 .23374 .95890 .30043 .95380 .31703 .94842 .33353 .94274 3i 30 .26724 .96363 .28402 .9.5882 .30071 .95372 .31730 .94832 .3.3381 .94264 30 31 .26752 .96355 .28-^29 .95874 .30008 .95363 .31758 .94823 .33408 .94254 .94245 20 32 .26780 .96347 .28457 .95865 .30126 .95354 .31786 .94814 .3.34u(i 28 33 .26808 .96310 .28485 .05857 .30154 .95345 .31813 .94805 .33463 .94235 27 34 .26836 .96332 .28513 .95840 .30182 .95337 .31841 .94795 .33400 .94225 26 35 .26864 .96324 .28541 .9.5841 .30200 .95328 .31868 .94786 .33518 .94215 25 36 .26892 .963 IC .28560 .95832 .30237 .95319 .31896 .94777 .33545 .94206 24 37 .26920 .96308 .28597 .95824 .30205 .95310 .31923 .94768 .33573 .94196 23 38 .269tS .06301 .28n_5 .95816 .30292 .95301 .31051 .047.58 .33600 .94186 22 39 .26071) .96293 .28652 .95807 .30320 .95293 .31979 .94749 .33627 .94176 21 40 .2700J .96285 .28680 .95799 .30348 .95284 .32006 .94740 .33655 .94167 20 41 .27032 .96277 .2870^ .95791 .30376 .95275 .32034 .94730 .33682 .94157 19 42 .27060 .96269 .28736 .95782 .30103 .95266 .32061 .94721 .33710 .94147 18 43 .27088 .96261 .28764 .95774 .30431 .95257 .32080 .94712 .23737 .94137 17 44 .27116 .96253 .28792 .95766 .30450 .95248 .32116 .94702 .33764 .94127 16 15 .27144 .96246 .28820 .95757 .30436 .95240 ..32144 .94693 .33792 .94118 15 46 .27172 .96238 .28847 .05710 .30514 .9.3231 .32171 .94684 .33819 .94108 14 47 .27200 .96230 .28875 .95740 .30542 .95222' .32190 .94674 .33846 .94098 13 48 .27228 .96222 .28903 .95732 .30570 .95213 ..32227 .94665 .33874 .94088 12 49 .27256 .96214 .28931 .95724 .30597 .95204 .32254 .946.56 .33901 .94078 11 50 .27284 .96206 .28959 .95715 .30625 .95195 .32282 .94646 .33929 .94068 10 51 .27312 .96198 .28987 .95707 .30653 .95186 .32309 .94637 .33956 .94058 9 52 .27340 .96190 .29015 .95698 .30680 .95177 .32337 .94627 .33983 .94049 8 53 .27368 .961S2 .29042 .95690 .3070S .95168 .32364 .94618 .34011 .94039 7 54 .27396 .96171 .29070 .95681 .30736 .05150 .32392 .94609 .34038 .94029 6 55 .27424 .96166 ! .29098 .05673 .30763 .95150 .32419 .94509 .34065 .94019 5 56 .27452 .96158 1.29126 .95664 ..30791 .95142 .32447 .94590 .34093 .94009 4 57 .27480 .96150 .29154 .95656 .30810 .95133 .32474 .93580 .34120 .93999 3 58 .27508 .96142 •;. 29182 .95647 .30846 .95124 .32502 .94571 .34147 .93989 2 59 .27536 .96134 1 .29209 .95630 .30874 .95115 .32529 .94561 .34175 .93979 1 GO .27564 .96126 1.29237 .95630 j .30902 .95106 .32557 .94552 .34202 .93969 ' Cosin Sine Cosin Sine ICosin Sine Cosin 1 Sine Cosin Sine f 74° 1 73° 1 72° 71° 70° Table of Natural Sines and Cosines 99 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56- 57 68 59 60 20^ Sine Cosin .34202 .34229 ,34257 ,34284 ,34311 .34339 3436G .34393 ,31421 .34448 .34475 34503 34530 .34557 .34584 .34012 .34639 ,3400(j ,3409-i ,34721 ,34748 ,34775 ,34803 ,34830 .34857 .31884 .34912 .34939 .3496() .34993 .35021 .35048 3507i .3510; .35130 .35157 .35184 .35211 .35239 .35266 .35293 35320 35347 35375 35402 ,35429 .35456 .35484 .35511 35538 ,35565 ,35592 .35619 .35647 .35674 .35701 .35728 .35755 .35782 ..35810 .35837 ,93969 .93959 .93949 .93939 .93929 .93919 ,93909 .93899 ,93889 .93879 .93869 .93859 .9334! .93839 .93829 .93819 .93809 .93799 .93789 93779 .93769 ,93759 ,9374', ,9373,': ,93728 .93718 ,93708 ,93698 .93688 .93677 .93667 .93657 .93647 .93637 .93626 .93016 .9360G .93596 .93585 .93575 .93565 .93555 .93544 .93534 .93524 .93514 93503 ,93493 ,93483 ,93472 .93462 .93452 .03441 .93431 .93420 .93410 .93400 .93389 .93379 .93368 .93358 2\° Sine Cosin Cosin Sine 69° ~~ ,35837 ,35864 35891 35918 35945 35973 ,36000 ,36027 ,36054 ,36081 ,36108 ,36135 ,36162 ,30190 .36217 .36244 .30271 .30298 .36325 .36352 .36379 .36406 .36434 .36401 .304SJ: .365 U .3654:; .30509 .36596 .36623 .36650 .36677 .3670' .36731 .3675,'^ .3678.^ .3681:; .36839 .30867 .3689- .36921 .36948 .36975 .37002 .37029 .37056 .370: .37110 .37137 .37104 .37191 .37218 .3724, .37272 .37299 .37326 .37353 .37380 .37407 .37434 37401 93358 .93348 .93337 .93327 .93316 ,93306 .93295 .9328.': ,93274 ,93264 ,9325: .93243 .93232 .93222 .93211 .93201 .93190 .93180 .93169 .93159 .93148 ,93137 .93127 ,93110 .93100 .9309i .93084 .93074 .93063 .93052 .93042 .93031 .93020 .93010 .92999 .9298. .92978 .92967 .92956 .92945 .92935 .92924 .92913 .92902 92892 .92831 ,92870 ,92859 ,92849 ,92838 .92827 928 10 ,92805 .92794 .92784 .92773 .92762 .92751 .92740 .92729 .92718 33" Sine Cosin ,37461 ,37488 ,37515 ,37542 ,37569 ,37595 ,37622 ,37649 ,37676 ,37703 .37730 .37757 .37784 .37811 .37838 .37865 .3789: .37919 .37946 .37973 .37999 .38026 .38053 .38080 .38107 .38134 .38161 .38188 .38215 .38241 .38268 .38295 .38322 .38349 .38376 .38403 .38430 .38456 .38483 .3851C .3853' .38564 .38591 .38617 .38644 .38671 .3869S .38725 38752 38778 38805 38832 ,38859 .38886 .3891 .38939 .38966 .38993 .39020 .39046 .3907; Cosin I Sine Cosin 92718 .92707 .92()97 .92686 .92675 92664 .92653 .92642 .92031 .92620 .92609 .92598 .92587 .92570 .92505 ,92554 .92543 .92532 .92521 .92510 .92499 .92488 .92477 .92400 .92455 .92444 .92432 .92421 .92410 .92399 .92388 .92377 .92300 .92355 .92343 9''332 .92321 .92310 .92299 .9228' .92276 .92205 .92254 .92243 .92231 .92220 .92209 .92198 .92180 .92175 .92164 .92152 .92141 ,92130 ,92119 .9210' .92096 .92085 .92073 ,92062 .92050 23° Sine Cosin .Sin fi8° 67° ,39073 ,39100 ,39127 .39153 .39180 .39207 .39234 .39260 .39287 .39314 .39341 .39367 .39394 .39421 ,39448 ,39474 .39501 .39528 .39555 .395S1 .39608 .39635 .39661 .39688 .39715 .39741 .39768 .39795 .39822 .39848 .39875 .39902 .39928 .39955 .39982 .40008 .40035 .40062 .40088 .40115 .40141 .40168 .40195 .40221 .40248 .40275 .40301 .40328 .40355 .40381 .40408 .404; .40461 .40488 .40514 .40541 .40567 .40594 .40621 .40047 .40674 .92050 .92039 ,92028 .92016 .92005 .91994 ,91982 .91971 ,91959 .91948 .91930 ,91925 ,91914 .91902 .91891 .91879 .91808 .91850 .91845 .91833 .91822 .91810 .91799 .91787 .91775 .91764 .91752 .91741 .91729 .91718 .91706 .91694 .91683 .91671 .91660 .91648 .91636 .91625 .91613 .91601 .91590 .91578 .9150b .91555 .91543 .91531 .91519 .01508 .91496 .91484 .91472 .91461 .91449 .91437 .91425 .91414 .91402 .91390 .91378 .91366 .91355 Sine Cosin Cosin Sine 40674 40700 ,40727 ,40753 ,40780 ,40806 ,40833 .40860 .40886 .40913 .40939 .40966 .40992 .41019 .410-15 .41072 .41098 .41125 .41 .41178 .41204 .41231 .4125" .41284 .41310 .41337 .41363 .41390 .41416 .41443 .41409 41496 ,41522 .41549 .41575 .41602 .41628 .41655 .41681 .41707 .41734 41760 ,41787 ,41813 ,41«40 ,41866 .41892 .41919 .41945 .41972 .41998 .42024 .42051 .42077 .42104 .42130 .42156 .42183 .42209 .42235 .42262 91355 .91343 ,91331 ,91319 ,91307 .91295 .91283 .91272 .91200 .91248 .91236 .91224 .9121 .91200 .91188 .91176 .91164 .91152 .91140 .91128 .91116 Cosin .91104 .91092 .91080 .91068 .91056 .91044 .91032 .91020 .91008 .90996 .90984 .90972 90960 ,90948 .90936 .90924 .90911 .90899 .9088" .90875 .90863 .90851 .90839 ,90820 ,90814 .90802 .90790 .9077^ .9070(; .9C753 .90741 .90729 .90717 .90704 .90692 .90680 .90668 .90055 .90643 .90631 Sine 00 59 58 57 56 55 54 53 52 51 50 49 48 47 40 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 2G 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 100 Trigonometry Part 1 / 25° '^6° 27° . 28° 29° f Sine .42262 C'osin .90631 Sine .43837 Cosin .89879 Sine Cosin Sine Cosin Sine Cosin .45399 .89101 .46947 .88295 .48481 .87462 60 1 .42288 .90618 .43863 .89867 .45425 .89087 .40973 .88281 .48506 .87448 59 2 .42315 .90606 .43889 .89854 .45451 .89074 .46999 .88267 .48532 .87434 58 3 .42341 .90594 .43916 .89841 .45477 .89001 .47024 .88254 .48557 .87420 57 4 .42367 .90582 .43942 .89828 .45503 .89048 .47050 .88240 .48583 .87400 56 5 .42394 .90569 .43968 .89816 .45529 .89035 .47076 .88226 .48608 .87391 55 6 .42420 .90557 .43994 .89803 .45554 .89021 .47101 .88213 .48634 .87377 54 7 .42416 .90545 .44020 .89790 .45580 .89008 .47127 .88199 .48659 .87363 53 8 .42473 .90532 .41046 .89777 .45000 .88995 .47153 .88185 .48684 .87349 52 9 .42499 .90520 .44072 .89764 .45632 .88981 .47178 .88172 .48710 .87335 51 10 .42525 .90507 .44098 .89752 .45658 .88968 .47204 .88158 .48735 .87321 50 11 .42552 .90495 .44124 .39739 .45684 .88955 .47229 .88144 .48761 .87306 49 12 .42578 .90483 .44151 .89720 .45710 .88942 .47255 .88130 .48786 .87292 48 13 .42604 .90470 .44177 .89713 .45736 .88928 .47281 .88117 .48811 .87278 47 U .42631 .90458 .44203 .89700 .45762 .88915 .47306 .88103 .48837 .87264 40 15 .42657 .90446 .44229 .89087 .45787 .88902 .47332 .88089 .48862 .87250 45 16 .42683 .90133 .44255 .89674 .45813 .88888 .47358 .88075 .48888 .87235 44 17 .42709 .90421 .44281 .89662 .45839 .88875 .47383 .88062 .48913 .87221 43 18 .42736 .90408 .44307 .89649 .45865 .88862 .47409 .88048 .48938 .87207 42 19 .42762 .90396 .44333 .89636 .45891 .88848 .47434 .88034 .48964 .87193 41 20 .42788 .90383 .44359 .89623 .45917 .88835 .47460 .88020 .48989 .87178 40 21 .42815 .90371 .44385 .89610 .45942 .88822 .47486 .88006 .49014 .87164 39 22 .42841 .90358 .44411 .89597 .45908 .88808 .47511 .87993 .49040 .87150 38 23 .42867 .90340 .44437 .89584 .45994 .88795 .47537 .87979 .49065 .87136 37 24 .42S94 .90334 .44464 .89571 .40020 .88782 .47562 .87965 .49090 .87121 30 25 .42920 .90321 .44490 .89558 .46046 .88768 .47588 .87951 .49116 .87107 35 26 .42946 .90309 .44516 .89545 :46072 .88755 747614 .87937 .49141 .87093 34 27 .42972 .90296 .44542 .89532 .46097 ,88741 .47039 .87923 .49166 .87079 33 28 .42999 .90284 .44508 .89519 .46123 .88728 .47605 .87909 .49192 .87064 32 29 .43025 .90271 .44594 .89506 .46149 .88715 .47090 .87896 .49217 .87050 31 30 43051 .90259 .44620 .89493 .46175 88701 .47710 .87882 .4924? 87036 30 31 .43077 .90246 .44646 .89480 .46201 .88688 .47741 .87868 .49268 .87021 29 32 .43104 .90233 .44672 .89467 .46220 .88674 .47707 .87854 .49293 .87007 28 33 .43130 .90221 .44698 .89454 .46252 .88661 .47793 .87840 .49318 .86993 27 34 .43156 .90208 .44724 .89441 .46278 .88647 .47818 .87826 .49344 .86978 20 35 .13182 .90196 .44750 .89428 .46304 .88634 .47844 .87812 .49369 .86964 25 36 .43209 .90183 .44776 .89415 .46330 .88620 .47869 .87798 .49394 .86949 24 37 .43235 .90171 .44802 .89402 .46355 .88607 .47895 .87784 .49419 .86935 23 38 .43261 .90158 .44828 .89389 .46381 .88593 .47920 .87770 .49445 .86921 22 39 .43287 .90146 .44854 .89376 .46407 .88580 .47946 .87756 .40470 .86906 21 40 .43313 .90133 .44880 .89363 .46433 .88566 .47971 .87743 .49495 .86S92 20 41 .43310 .90120 .44906 .89350 .46458 .88553 .47997 .87729 .49521 .80878 19 42 .43366 .9010S .44932 .89337 .46484 .88539 .48022 .87715 .49546 .86863 18 43 .43392 .90095 .44958 .89324 .46510 .88526 .48048 .87701 .49571 .86849 17 44 .43418 .90082 .44984 .89311 .16536 .88512 .48073 .87687 .49596 .86834 16 45 .43445 .90070 .45010 .89298 .46561 .88499 .48099 .87673 .49622 .86820 15 46 .43471 .90057 .45036 .89285 .46587 .88485 .48124 .87659 .49647 .86805 14 47 .43497 .90045 .45062 .89272 .46613 .88472 .48150 .87645 .49672 .86791 13 48 .43523 .90032 .45088 .89259 .46639 .88458 .48175 .87631 .49697 .86777 12 49 .43549 .90019 .45114 .89245 .46664 .88445 .48201 .87617 .49723 .86762 11 50 .43575 .90007 .45140 .89232 .46690 .88431 .48226 .87603 .49748 .86748 10 61 .43602 .89994 .45166 .89219 .46716 .88417 .48252 .87589 .49773 .86733 9 52 .43628 .89981 .45192 .89206 .46742 .88404 .48277 .87575 .49798 .86719 8 53 .43654 .89968 .45218 .89193 .46767 .88390 .48303 .87561 .49824 .86704 7 54 .43680 .89956 .45243 .89180 .46793 .88377 .48328 .87546 .49849 .86690 6 55 .43706 .89943 .45269 .89167 .46819 .88363 .48354 .87532 .49874 .86675 5 56 .43733 .89930 .45295 .89153 .46844 .88349 .48379 .87518 .49899 .86601 •4 57 .43759 .89918 .45321 .89140 .46870 .88336 .48405 .87504 .49924 .86646 3 58 .43785 .89905 .45347 .89127 .46896 .88322 .48430 .87490 .49950 .86632 2 59 .43811 .89892 .45373 .89114 .46921 .88308 .48456 .87476 .49975 .86617 1 60 .43837 .89879 .45399 Cosin .89101 Sine .46947 .88295 .48481 .87462 .50000 .80603 ' Cosin Sine Cosin Sine Cosin Sine Cosin Sine / 64° 1 63° 1 62° 1 61° 1 60° 1 Table of Natural Sines and Co'shies 101 ' 30° 31" 1 33° 33° 34° 60 Sine Cosin Sine Cosin .85717 Sine Cosin Sine .54404 Cosin .83867 Sine .55919 Cosin .82904 .50000 .86603 .51504 .52902 .84805 1 .50025 .80588 .51529 .85702 .53017 .84789 .54488 .83851 .55943 .82S87 59 2 .50050 .86573 .51554 .85087 .53041 .84774 .54513 .83835 .55968 .82871 68 3 .50076 .86559 .51579 .85672 .53006 .84759 .54537 .83819 .55992 .82855 57 4 .50101 .86544 .51604 .85657 .53091 .84743 .54561 .83804 .56010 .82839 56 5 .50126 .86530 .51628 .85642 .53115 .84728 .54586 .83788 .50040 .82822 56 6 .50151 .86515 .51653 .85027 .53140 .84712 .54610 .83772 .56004 .82800) 54 7 .50176 .86501 .51678 ,85612 .53164 .84697 .54035 .83750 .56088 .82790 63 8 .50201 .86486 .51703 .85597 .53189 .84681 .54659 .83740 .50112 .82773 52 9 .50227 .86471 .51728 .85582 .53214 .84606 .54083 .83724 .50136 .82757 51 10 .50252 .86457 .51753 .85567 .53238 .84650 .54708 .83708 .56100 .82741 50 11 .50277 .86442 .51778 .85551 .53263 .84035 .54732 .83092 .56184 .82724 49 12 .50302 .86427 .51803 .85536 .53288 .84619 .54756 .83076 .56208 .82708 48 13 .50327 .86413 .51828 .85521 .53312 .84604 .54781 .83660 .56232 .82692 47 14 .50352 .86398 .51852 .85506 .53337 .84588 .54805 .83645 .56256 .82675 46 15 .50377 .86384 .51877 .85491 .53361 .84573 .54829 .83029 .56280 .82669 45 16 .50403 .86369 .51902 .85476 .53386 .84557 .54854 .83013 .56305 .82643 44 17 .5042^? .86354 .51927 .85401 .53411 .84542 .54878 .83597 .50329 .82626 43 18 .50453 .86340 .51952 .85446 .53435 .84520 .54902 .83581 .50353 .82610 42 19 .50478 .86325 .51977 .85431 .53400 .84511 .54927 .83505 .50377 .82593 41 20 .50503 .86310 .52002 .85416 .53484 .84495 .54951 .83549 .56401 .82577 40 21 .50528 .86295 .52020 .85401 .53509 .84480 .54975 .83533 .50425 .82501 39 22 .50553 .86281 .52051 .85385 .53534 .84404 .51999 .83517 .50449 .82544 38 23 .50578 .86266 .52076 .85370 .53558 .84448 .55024 .83501 .56473 .82528 37 24 .50603 .86251 .52101 .85355 .53583 .84433 .55048 .83485 .56497 .82511 36 25 .50628 .86237 .52126 .85340 .53607 .84417 .55072 .83409 .56521 .82496 35 26 .5065} .86222 .52151 .85325 .53032 .84402 .55097 .83453 .56545 .82478 34 27 .50079 .86207 .52175 .85310 .53056 .84380 .55121 .83437 .56569 .82462 33 28 .50704 .86192 .52200 .85294 .53081 .84370 .55145 .83421 .56593 .82446 32 29 .50729 .86178 .62225 .85279 .53705 .84355 .55109 .83405 .56617 .82429 31 30 .50751 .80103 .52250 .85264 .53730 .84339 .55194 .83389 .56641 .82413 30 31 .50770 .80148 .52275 .85249 .53754 .84324 .55218 .83373 .56005 .82390 29 32 .50804 .86133 .52299 .85234- .53779 .84308 .55242 .83350 .56689 .82380 28 33 .50829 .86119 .52324 .85218 .53804 .84292 .55206 .83340 .56713 .82303 27 34 .50854 .86104 .52349 .85203 .53828 .84277 .55291 .83324 .56730 .82347 26 35 .50.^79 .86089 .52874 .85188 .53853 .84201 .55315 .83308 .50700 .82330 25 36 .50904 .86074 .52399 .85173 .53877 .84245 .55339 .83292 .56784 .82314 24 37 .50929 .86059 .52423 .85157 .53902 .84230 .55363 .83270 .56808 .82297 23 38 .50954 .86045 .52448 .85142 .53920 .84214 .55388 .83200 .66832 .82281 22 39 .50979 .80030 .52473 .85127 .53951 .84198 .55412 .83244 .56850 .82264 21 40 .51004 .86015 .52498 .85112 .53975 .84182 .55430 .83228 .56880 .82248 20 41 .51029 .8G000 .52522 .85090 .54000 .84107 .55400 .83212 .56904 .82231 19 42 .51054 .85985 .52547 .85081 .54024 .84151 .55484 .83195 .56928 .82214 18 43 .51079 .85970 .52572 .85066 .54049 .84135 .55509 .83179 .60952 .82198 17 44 .51104 .85956 .52597 .85051 .54073 .84120 .55533 .83103 .56976 .82181 16 45 .51129 .85941 .52021 .85035 .54097 .84104 .55557 .83147 .57000 .82165 15 46 .51154 .85926 .52646 .85020 .54122 .840SS .55581 .83131 .57024 .82148 14 47 .51179 .85911 .52671 .85005 .54146 .84072 .55005 .83115 .57047 .82132 13 48 .51204 .85896 .52096 .84989 .54171 .84057 .55630 .83098 .57071 .82116 12 49 .51229 .85881 .52720 .84974 .54195 .84041 .55654 .83082 .67095 .82098 11 50 .51254 .85866 .52745 .84959 .54220 .84025 .55078 .83000 .57119 .82082 10 51 .51279 .85851 .52770 .84943 .54244 .84009 .55702 .83050 .57143 .82005 9 52 .51304 .85836 .52794 .84928 .54209 .83994 .55726 .83034 .67167 .82048 8 53 .51329 .85821 .52819 .84913 .54293 .83978 .55750 .83017 .57191 .82032 7 54 .51354 .85806 .52844 .84897 .54317 .83962 .55775 .83001 .57215 .82016 fi 55 .51379 .85792 .52800 .84882 .54342 .83940 .55799 .82985 .67238 .81999 5 56 .51404 .85777 .52893 .84866 .54306 .83930 .55823 .82969 .57202 .81982 4 57 .51429 .85762 .52918 .84851 .54391 .83915 .55847 .82953 .57286 .81965 3 58 .51454 .85747 .52943 .84836 .54415 .83899 .55871 .82930 .57310 .81949 2 59 .51479 .85732 .52967 .84«20 .54440 .83883 .55895 .82920 .57334 .81932 1 00 .51504 .85717 .52992 .84805 .54404 .83807 .55919 Cosin .82904 .67358 .81915 ' Cosin Sine Cosin Sine Cosin Sine Sine Cosin Sine / 59° 1 58" 1 57° 1 56° 1 55° 2 Trigonometry Part / 35° 30° 37° Sine jCosin • 38° 39° ' Sine Cosin Sine Cosin Sine Cosin Sine C'Osin ~o .57358 .81915 :58779 .80902 .00182 .79304 .01500 .78801 .02932 .77715 00 1 .57381 .81899 .58802 .80885 .00205 .79840 .01589 .78783 .02955 .77090 59 .57405 .81882 .58820 .80807 .00228 .79829 .01012 .78705 .02977 .77078 58 3 .57429 .81805 .58849 .80850 ^10251 .79811 .01035 .78747 .03000 .77000 57 4 .57453 .81848 .58873 .80833 .00274 .79703 .^51058 .78729 .03022 .77041 50 5 .57477 .81832 .58800 .80810 .00298 .79770 .01081 .78711 .03045 .77023 55 .57501 .81815 .58920 .80799 .00321 .70758 .01704 .78094 .030(58 .77005 54 7 .57324 .81798 .58943 .80782 .00344 .79741 .0172{; .78(i7t) .t)30*)0 .77580 53 8 .57548 .81782 .58907 .80705 .00307 .79723 .01749 .78058 .03113 .77508 52 9 .57572 .81705 .58990 .80748 .00390 .79700 .01772 .78040 .03135 .77550 51 10 .57590 .81748 .59014 .80730 .00414 .79088 .01795 .78022 .03158 .77531 50 11 .57019 .81731 .59037 .80713 .00437 .79071 .01818 .78004 .03180 .77513 40 12 .57043 .81714 .5901)1 .8000i; .00400 .79()53 .01841 .785S0 .03203 .77404 48 13 .57007 .81098 .59084 .80079 .()0J83 .79035 .01804 .78508 .03225 .77470 47 14 .57091 .81081 .59108 .^00^)2 .00500 .79018 .01887 .78550 .03248 .77458 40 15 .57715 .81004 .59131 .80044 .00529 .79000 .01909 .785.32 .03271 .77439 45 10 .57738 .81047 .59154 .80027 .00553 .79583 .01932 .78514 .03293 .77421 44 17 .57702 .81031 .59178 .80')10 .00570 .79505 .01955 .78490 .03310 .77402 43 IS .57780 .81014 .59201 .80503 .00599 .79547 .01978 .78478 .03338 .77384 42 19 .57810 .81597 .59225 .8057() .00''22 .79530 .02001 .78400 .03301 .77300 41 20 .57833 .81580 .592 48 .805.58 .00015 .79512 .02024 .784 42 .03383 .77347 40 21 .57857 .81503 .59272 .80541 .00008 .79494 .02040 .78424 .03400 .77329 39 22 .57881 .81540 .50295 .80524 .00091 .79477 .02009 .78 405 .03428 .77310 38 23 .57901 .81530 .59318 .80507 .00714 .79 459 .02092 .783S7 .03451 .77202 37 24 .57928 .81513 .59342 .80480 .00738 .79441 .02115 .78309 .03473 .77273 36 25 .57952 .81490 .59305 .80472 .00701 .79424 .0213S .78351 .03490 .77255 35 20 .57970 .81479 .59389 .80455 .00784 .79400 .02100 .78333 .0.3518 .77230 34 27 .57999 .81402 .59412 .80438 .00807 .70388 .02183 .78315 .03540 .77218 •33 28 .58023 .81445 .59431) .80420 .00330 .70371 .02200 .78297 .03503 .77199 32 29 .rt^'Oil .8142S .59459 .80403 .00853 .70353 .02220 .78270 .03585 .77181 31 30 .58070 .81412 .59482 .80380 .00870 .79335 .02251 .78201 .03008 .77102 30 31 .58094 .81395 .59500 .80308 .00899 .79318 .02274 .78243 .G3030 .77144 29 32 .58118 .81378 .59529 .80351 .()0922 .79300 •.02297 .78225 .03053 .77125 28 33 .58141 .81301 .59552 .80334 .00945 .79282 .02320 .78200 .03075 .77107 27 34 .58105 .81344 .59570 .80310 .<)0908 .79204 .02342 .78188 .03098 .77088 26 35 .58189 .81327 .59599 .80290 .00001 .79247 .02305 .78170 .03720 .77070 25 6Cy .58212 .81310 .59022 .80282 .01015 .79220 .02388 .78152 .03742 .77051 24 37 .58230 .81293 .59040 .80204 .01038 .79211 .02411 .78134 .03705 .77033 23 38 .58200 .81270 .59009 .80247 .01001 .79193 .02433 .78110 .03787 .77014 22 39 .58283 .81259 .59093 .80230 .01084 .70170 .02450 .78098 .03810 .70996 21 to .58307 .81242 .59710 -.80212 .01107 .79158 .02479 .78079 .03832 .70977 20 41 .58330 .81225 .59739 .80195 .01130 .79140 .02502 .78001 .03854 .70959 19 42 .58354 .81208 .59703 .80178 .01153 .79122 .02524 .78043 .03877 .70940 18 43 .58378 .81191 .59780 .801 (K) .01170 .79105 .02547 .78025 .03899 .70921 17 44 .58401 .81174 .59809 .80143 .01199 .79087 .02570 .78007 .()3922 .70903 16 45 .58425 .81157 .59832 .80125 .01222 .79009 .02592 .77988 .03944 .70884 15 40 .58449 .81140 .59850 .80108 .01245 .79051 .02015 .77970 .03900 .70800 14 ; 47 .58472 .81123 .59879 .80091 .01208 .79033 .02038 .77952 .03989 .70847 13 i 48 .58490 .8110<) .59902 .80073 .01291 .79010 .02000 .77934 .04011 .76828 12 49 .58519 .81089 .59920 .8005() .01314 .78998 .02083 .77910 .64033 .70810 11 50 .58543 .81072 .59949 .80038 .01337 .78980 .02700 .77897 .64050 .70791 10 51 .58507 .81055 .59972 .80021 .01300 .78902 .02728 .77879 .64078 .70772 9 52 .5S590 .81038 .59995 .80003 .01383 .78944 .02751 .77801 .64100 .7'>754 8 53 .58014 .81021 .00019 .7998() .01400 .78920 .0':>774 .77843 .64123 .70735 7 54 .58037 .81004 .00042 .79908 .01429 .78908 .02790 .77824 .61145 .70717 6 55 .58001 .80987 .00005 .79951 .01451 .78S()1 .02819 .77800 .64107 .7t>098 5 50 .5S0S4 .80070 .00089 .79934 .01474 .78-^^73 .02842 .77788 .04190 .70079 4 57 .5^708 .80953 .00112 .79910 .01497 .788.55 .02804 .77709 .64212 .70001 3 58 .5^731 .80930 .00135 .79899 .01520 .78837 .02887 .v;/5i .64234 .7604? 2 59 .58755 .80019 .00158 .79881 .01543 .78819 .02909 .77733 .04250 .76623 1 60 .58779 .80902 .00182 .79804 .01500 .78801 .02932 .77715 .64279 .76604 r Cosin Sine Cosin Sine Cosin Sine Cosin Sine Cosin Sine f 54° 1 53° 52° 51° 1 50° Table of Natural Sines and Cosines 103 / 40° 1 _ 41" 1 42° 1 43° 1 44° ' Sine .04279 Cosin .7()004 Sine Cosin Sine .00913 Cosin Sine Cosin Sine Cosin .05(500 .75471 .74314 .68200 .73135 .(5940(5 .71934 60 1 .04301 .7058(> .(55028 .75452 .00935 .74295 .08221 .73110 .09487 .71914 59 2 .04323 .70507 .(55(550 .75433 .()()950 .74270 .68242 .73090 .(59508 .71894 68 3 .04340 .7()548 .(55(572 .75414 .(5(5978 .7425(5 .08204 .7307(5 .09529 .71873 57 4 .043(;8 .70530 .(55(594 .75395 .0(5999 .74237 .08285 .73050 .(59549 .71853 50 5 .04390 .70511 .(55710 .75375 .(57021 .74217 .08300 .73030 .09570 .71833 55 .04412 .70492 .(55738 .75350 .07043 .74198 .08327 .73010 .(59591 .71813 54 7 .04435 .70473 .(55759 .75337 .070(54 .74178 .08349 .72990 .09012 .71792 53 8 .()4457 .70455 .(55781 .75318 .0708(5 .74159 .08370 .72970 .09033 .71772 52 9 .04479 .7() 13(1 .(55803 .75299 .07107 .74139 .08391 .72957 .09054 .71752 61 10 .04501 .70417 .(55825 .752S0 .07129 .74120 .08412 .72937 .09075 .71732 50 11 .04521 .70398 .05847 .75201 .07151 .74100 .68434 .72917 .09090 .71711 49 12 .04540 .70380 .(558(59 .75241 .07172 .74080 .08455 .72897 .09717 .71091 48 13 .04508 .70301 .(55891 .75222 .07194 .74001 .08476 .72877 .09737 .71(571 47 14 .64590 .7()342 .(55913 .75203 .07215 .74041 .68497 .72857 .09758 .71(>50 40 1.5 .04012 .70323 .(55935 .75184 .67237 .74022 .68518 .72837 .(59779 .71630 45 10 .04635 .70304 .05950 .75105 .07258 .74002 .68539 .72817 .09800 .71610 44 17 .64057 .7028(-: .(55978 .75140 .67280 .73983 .08501 .72797 .09821 .71590 43 18 .04079 .70207 .(50000 .75120 .07301 .73903 .08582 .72777 .(59842 .71569 42 19 .04701 .70248 .00022 .75107 .07323 .73044 .0800? .72757 .(59802 .71549 41 20 .04723 .70229 .0(5044 .75088 .07344 .73924 .08024 .72737 .09883 ,71529 40 21 .04740 .70210 .00000 .75009 .07300 .73004 .08045 .72717 .09904 .71508 39 22 .04708 .70192 .(50088 .75050 .07387 .73885 .08000 .72097 .(59925 .71488 38 23 .04790 .70173 .0(5109 .75030 .07409 .73805 .08088 .72077 .(5994(5 .71408 37 24 .04812 .70154 .0(5131 .75011 .07430 .73840 .08709 .72657 .(599(50 .71447 30 25 .(i48.i4 .70135 .0(5153 .74992 .07452 .73820 .08730 .72037 .09J)87 .71427 35 20 .6485() .70110 .00175 .74973 .07473 .73800 .(58751 .72017 .70008 .71407 34 27 .64878 .70097 .'1(5197 .74953 .07495 .73787 .08772 .72597 .70029 .7138(5 33 28 .04901 .7()078 .00218 .74934 .07510 .73707 .08793 .72577 .7(M)49 .713(5(5 32 29 .04923 .70059 .0(5240 .74915 .(57538 .73747 .(58814 .72557 .70070 .71345 31 30 .()4945 .70041 .(5(5202 .74890 .07559 .73728 .08835 .72537 .70091 .71325 30 31 .04907 .700*22 .00284 .74870 .07580 .73708 .08857 .72517 .70112 .71305 29 32 .()4989 .70003 .6030(5 .74857 .(• 7(502 .73(588 .08878 .72497 .70132 .71284 28 33 .05011 .75984 .00327 .74838 .07(523 .73009 .(58899 .72477 .70153 .71264 27 34 .05033 .75905 .0(5349 .74818 .07(545 .73049 .08920 .72457 .70174 .71243 20 35 .05055 .7594(5 .00371 .74799 .07(50(5 .73029 .(58941 .72437 .70195 .71223 25 30 .(>5077 .75927 .0(5393 .74780 .(5708S .73010 .0S902 .72417 .70215 .71203 24 37 .05100 .75908 .«)()414 .747(50 .07709 .73590 .08983 .72397 .7023(5 .71182 23 3S .05122 .75889 .0(543(5 .74741 .07730 .73570 .(50004 .72377 .70257 .711(52 22 39 .05144 .75870 .0(5458 .74722 .07752 .73551 .(59025 .72357 .70277 .71141 21 40 .0510() .7585 1 .0(5480 .74703 .07773 .73531 .(5904(5 .72337 .70298 .71121 20 41 .05188 .75832 .00501 .74083 .07705 .73511 .69007 .72317 .70319 .71100 19 42 .05210 .75813 .0(5523 .74001 .(;7810 .73491 .09088 .72297 .70339 .71080 18 43 .05232 .75794 .00545 .74044 .07837 .73472 .(59109 .72277 .703(50 .71059 17 44 .05254 .75775 .005(50 .74025 .07859 .73452 .09130 .72257 .70381 .71039 10 45 .05270 .75750 .0(5588 .74000 .(57880 .73132 .(59151 .7223(5 .70401 .71019 15 40 .()5298 .75738 .(5(5010 .7458(5 .07901 .73413 .(59172 .72210 .70422 .70998 14 47 .05320 .75719 .0(5032 .745(57 .(57923 .73393 .(59193 .72190 .70443 .70978 13 4S .05342 .75700 .0(5(553 .74548 .07941 .73373 .t 592 14 .72170 .70403 .70957 12 ,49 .05304 .75080 ,(50075 .74528 .079(55 .73353 .09235 .72150 .70484 .70937 11 50 .05380 .75()01 .(5(5(597 .74509 .07987 .73333 .0025(5 .72130 .70505 .70916 10 51 .05408 .7504^2 .0()718 .74489 .08008 .73314 .09277 .72110 .70525 .7089(5 9 52 .05430 .75023 .0(5740 .74470 .08029 .73294 .(59298 .72095 .70540 .70875 8 53 .05452 .75004 .00702 .74451 .(58051 .73274 .09319 .72075 .70507 .70855 7 54 .05474 .75585 .00783 .74431 .08072 .73254 .(59340 .72055 .70587 .70834 6 55 .05490 .75501) .00805 .74412 .68093 .73234 .()9301 .72035 .70008 .70813 5 50 .05518 .75547 .0(5827 .7't392 .08115 .73215 .09382 .72015 .70028 .70793 4 57 .05540 .75528 .00848 .74373 .08130 .73195 .09403 .71995 .70049 .70772 3 5S .05502 .75509 .00)870 .74353 .08157 .73175 .(59424 .71974 .70070 .70752 2 59 .05584 .75490 .0(5891 .74334 .68179 .73155 .69445 .71954 .70090 .70731 1 60 .05000 .75471 .0(5913 74314 .08200 Cosin .73135 .69466 .71934 .70711 .70711 / Cosin Sine Cosin Sine Sine Cosin Sine Cosin Sine ' _ 4?)° 48° 47° 46° 45° 104 Trigonometry ' 0^ 1° 1 2° 1 3° 1 Tang Cotang Tang Cotang Tang Cotang Tang Cotang .00000 Infinite. .01746 57.2900 .03492 28.6363 .05241 19.0811 60 1 .00029 3437.75 .01775 56.3506 .03521 28.3994 .05270 18.9755 59 2 .00058 1718.87 .01804 55.4415 .03550 28.1664 .05299 18.8711 58 3 .00087 1145.92 .01833 54.5613 .03579 27.0372 .05328 18.7678 57 4 .00116 859.436 .01862 53.7086 .03600 27.7117 .05357 18.6656 56 5 .00M5 687.549 .01801 52.8S21 .03638 27.4899 .05387 18.5615 55 .00175 572.957 .01920 52.0807 .03667 27.2715 .05416 18.4645 54 7 .00204 401.106 .01940 51.3032 .03096 27.0566 .05145 18.3655 53 8 .00233 429.718 .01978 50.5485 .03725 26.8450 .05474 18.2677 52 9 .00262 381.971 .02007 49.8157 .03754 26.6367 .05503 18.1708 51 10 .00291 343.774 .02036 40.1039 .03783 26.4316 .05533 18.0750 50 11 .00320 312.521 .02066 48.4121 .03812 26.2296 .05502 17.9802 49 12 .00349 286.478 .02005 47.7305 .03842 26.0307 .05591 17.8863 48 13 .00378 264.441 .02124 47.0853 .03871 25.8348 .05620 17.7934 47 14 .00407 245.552 .02153 46.4489 .03900 25.6418 .05649 17.7015 46 15 .00436 229.182 .02182 45.8294 .03929 25.4517 .05678 17.6100 45 13 .00465 214.858 .02211 45.2261 .03958 25.2644 .05708 17.5205 44 17 .00495 202.219 .02240 44.6386 .03987 25.0798 .05737 17.4314 43 18 .00524 190.984 .022C9 44.0661 .04016 24.8078 .05766 17.3182 42 19 .00553 180.932 .02298 43.5081 .04046 24.7185 .05795 17.2558 41 20 .00582 171.885 .02328 42.9641 .04075 24.5418 .05824 17.1603 40 21 .00611 163.700 .02357 42.4335 .04104 24.367^ .05854 17.0837 39 22 .oor>io 156.259 .02386 41.9158 .04183 24.1957 .05883 16.9990 38 23 .00669 149.465 .02415 41.4106 .04162 24.0263 .05912 16.9150 37 24 .00698 143.237 .02444 40.9174 .04191 23.8593 .05041 16.8319 36 25 .00727 137.507 .02473 40.4358 .04220 23.6945 .05970 16.7496 35 26 .00756 132.219 .02502 39.9055 .04250 23.5321 .05999 16.6681 84 27 .00785 127.321 .02531 39.5059 .04270 23.3718 .06029 16.5874 33 28 .00815 122.774 .02560 39.0568 .01308 23.2137 .06058 16.5075 32 29 .00844 118.540 .02589 38.6177 .04837 23.0577 .06037 16.4283 31 30 .00873 114.589 .02619 38.1885 .04366 22.0038 .06116 16.3499 30 31 .00902 110.892 .02648 37.7686 .04305 22.7519 .06145 16.2722' 29 32 .00031 107.426 .02677 37.3579 .04424 22.6020 .06175 16.1952 28 33 .00060 104.171 .02706 36.9560 .04454 22.4541 .00204 16.1190 27 34 .00989 101.107 .02735 36.5627 .04483 22.3081 .06233 16.0435 26 35 .01018 98.2179 .02764 36.1776 .04512 22.1640 .06262 15.9687 25 36 .01047 95.4895 .02703 35.8006 .04541 22.0217 .06291 15.8945 24 37 .01076 92.9085 .02822 35.4313 .04570 21.8813 .06321 15.8211 23 38 .01105 90.4633 .02851 35.0695 .04599 21.7426 .06850 15.7483 22 39 .01135 88.1436 .02881 34.7151 .04628 21.6056 .06379 15.6762 21 40 .01164 85.9398 .02010 34.3678 .04658 21.4704 .06408 15.6048 20 41 .01193 83.8435 .02939 34.0273 .04687 21.3369 .06437 15.5340 19 42 .01222 81.8470 .02968 33.6935 .04710 21.2049 .06467 15.4638 18 43 .01251 79.9434 .02997 33.3662 .04745 21.0747 .06496 15.3943 17 44 .01280 78.1263 .03026 33.0452 .04774 20.9460 .06525 15.3254 16 45 .01309 76.3900 .03055 32,7303 .01803 20.8188 .06554 15.2571 15 46 .01333 74.7292 .03084 82.4213 .04833 20.6932 .06584 15.1893 14 47 .01367 73.1300 .03114 32.1181 .04862 20.5691 .06613 15.1222 13 48 .01396 71.6151 .03143 31.8205 .04891 20.4465 .06612 15.0557 12 49 .01425 70.1533 .03172 31.5284 .04920 20.3253 .06671 14.9898 11 50 .01455 68.7501 .03201 31.2410 .04949 20.2056 .06700 14.9244 10 51 .01484 67.4019 .03230 30.9599 .04978 20.0872 .06730 14.8596 9 52 .01513 06.1055 .03259 30.6833 .05007 19.9702 .06759 14.7954 8 53 .01542 64.8580 .03288 30.4116 .05037 19.8546 .06788 14.7317 7 54 .01571 63.6567 .03317 30.1446 .05066 19.7403 .06817 14.6685 6 55 .01600 62.4992 .03346 29.8823 .05005 19.6273 .06847 .06876 14.6059 5 56 .01629 61.3829 .03376 29.6245 .05124 19.5156 14.5438 4 57 .01658 60.3058 .03405 29.3711 .05153 19.4051 .06905 14.4823 3 58 .01687 59.2659 .03434 29.1220 .05182 19.2959 .06934 14.4212 2 59 .01716 58.2612 .03463 28.8771 .05212 19.1879 .06963 14.3607 1 GO .01746 57.2900 .03492 28.6363 .05241 19.0811 .06993 14.3007 / Cotang Tang Cotang Tang Cotang Tang Cotang Tang ' 89° 1 88° 1 87° 1 86° Table of Natural Tangents and Cotangents 105 ' 4° 5' n» 1 T / Tang CJotang Tang .08749 CV>tang Tang Cotang Tang Cotang .06993 14.3007 11.4301 .10510 9.51436 .12278 8.14435 60 1 .07022 14.2411 .08778 11.3919 .10540 9.48781 .12308 8.12481 59 2 .07051 14.1821 .08807 11.3540 .10509 9.46141 .12338 8.10536 58 3 .07080 14.1235 .08837 11.3163 .10599 9.43515 .12367 8.08600 57 4 .07110 14.0655 .08866 11.2789 .10628 9.40904 .12397 8.06674 56 5 .07139 14.0079 .08895 11.2417 .10657 9.38307 .12426 8.04756 55 6 .07168 13.9507 .08925 11.2048 .10087 9.35724 .12456 8.02848 54 7 .07197 13.8940 .08954 11.1681 .10710 9.33155 .12485 8.00948 53 8 .07227 13.8378 .08983 11.1316 .10740 9.30599 .12515 7.99058 52 9 .0725G 13.7821 .09013 11.0954 .10775 9.28058 .12544 7.97176 51 10 .07285 13.7267 .09042 11.0594 .10805 9.25530 .12574 7.95302 50 11 .07314 13.6719 .09071 11.0237 .10834 9.23016 .12603 7.93438 49 12 .07344 13.6174 .09101 10.9832 .10803 9.20518 .12633 7.91582 48 13 .07373 13.5634 .09130 10.9529 .10893 9.18028 .12662 7.89734 47 14 .07402 13.5008 .aU59 10.9178 .10922 9.15554 .12692 7.87895 46 15 .07431 13.4566 .09189 10.8829 .10952 9.13093 .12722 7.86064 45 10 .07461 13.4039 .09218 10.8483 .10981 9.10646 .12751 7.84242 44 17 .07490 13.3515 .09247 10.8139 .11011 9.08211 .12781 7.82428 43 18 .07519 13.2996 .09277 10.7797 .11040 9.05789 .12810 7.80622 42 19 .07548 13.2480 .09306 10.7457 .11070 9.03379 .12840 7.78825 41 20 .07578 13.1969 .09335 10.7119 .11099 9.00983 .12869 7.77035 40 21 .07607 13.1461 .09365 10.6783 .11128 8.98598 .12899 7.75254 39 22 .07036 13.0958 .09394 10.6450 .11158 8.96227 .12929 7.73480 38 23 .07665 13.0458 .09423 10.6118 .11187 8.93867 .12958 7.71715 37 24 .07695 12.9962 .09453 10.5789 .11217 8.91520 .12988 7.69957 36 25 .07724 12.9469 .09482 10.5462 .11240 8.89185 .13017 7.68208 35 2G .07753 12.8981 .09511 10.5136 .11270 8.86862 .13047 7.66466 34 27 .07782 12.8496 .09541 10.4813 .11305 8.84551 .13076 7.64732 33 28 .07812 12.8014 .09570 10.4491 .11335 8.82252 .13106 7.63005 32 29 .07841 12.7536 .09600 10.4172 .11304 8.79964 .13136 7.61287 31 30 .07870 12.7002 .09629 10.3854 .11394 8.77689 .13165 7.59575 30 31 .07899 12.6591 .09658 10.3538 .11423 8.75425 .13195 7.57872 29 32 .07929 12.6124 .09688 10.3224 .11452 8.73172 .13224 7.56176 23 33 .07958 12.5660 .09717 10.2913 .11482 8.70931 .13254 7.54487 27 34 .07087 12.5199 .09746 10.2602 .11511 8.08701 .13284 7.52806 26 35 .08017 12.4742 .09776 10.2294 .11541 8.06482 .13313 7.51132 25 3G .08046 12.4288 .09805 10.1988 .11570 8.04275 .13343 7.49465 24 37 .08075 12.3838 .09834 10.1083 .11000 8.02078 .13372 7.47806 23 38 .08104 12.3390 .09864 10.1381 .11029 8.59893 .13402 7.46154 22 39 .08134 12.2946 .09893 10.1080 .11659 8.57718 .13432 7.44509 21 40 .08163 12.2505 .09923 10.0780 .11688 8.55555 .13461 7.42871 20 41 .08192 12.2067 .09952 10.0483 .11718 8.53402 .13491 7.41240 19 42 .08221 12.1632 .09981 10.0187 .11747 8.51259 .13521 7.39616 18 43 .08251 12.1201 .10011 9.98931 .11777 8.49128 .13550 7.37999 17 44 .08280 12.0772 .10040 9.96007 .11806 8.47007 .13580 7.36389 16 45 .08309 12.0346 .10069 9.93101 .11836 8.44890 .13609 7.34786 15 40 .08339 11.9923 .10099 9.90211 .11865 8.42795 .13639 7.33190 14 47 .08368 11.9504 .10128 9.87338 .11895 8.40705 .13669 7.31600 13 48 .08397 11.9087 .10158 9.84482 .11924 8.38025 .13698 7.30018 12 49 .08427 11.8673 .10187 9.81641 .11954 8.36555 .13728 7.28442 11 60 .08456 11.8262 .10216 9.78817 .11983 8.34496 .13758 7.26873 10 51 .08485 11.7853 .10246 9.76009 .12013 8.32446 .13787 7.25310 9 52 .08514 11.7448 .10275 9.73217 .12042 8.30406 .13817 7.23754 8 53 .08544 11.7045 .10305 9.70441 .12072 8.28376 .13846 7.22204 7 54 .08573 11.6645 .10334 9.67680 .12101 8.26355 .13876 7.20561 6 55 .08602 11.6248 .10363 9.64935 .12131 8.24345 .13906 7.19125 5 56 .08632 11.5853 .10393 9.62205 .12160 8.22344 .13935 7.17594 4 57 .08661 11.5461 .10422 9.59490 .12190 8.20352 .13965 7.16071 3 58 .08690 11.5072 .10452 9.56791 .12219 8.18370 .13995 7.14553 2 59 .08720 11.4685 .10481 9.54106 .12249 8:i6308 .14024 7.13042 1 60 .08749 11.4301 .10510 9.51436 .12278 "8.14435 .14054 7.11537 1 Cotang Tang Cotang Tang Cotang Tang Cotang Tang t 85° 84° 1 83*^ 1 82° 106 Trigonometry t 8° i 9» 1 lO'^ 1 11° t Tang Cotaiig Tang (Jotang Tang Cotang Tang .19438 Cotang .14054 7.11537 .15838 6.31375 .17033 5.07128 5.14455 60 1 .14084 7.10038 .15808 6.30189 .17003 5.00105 .19408 5.13058 69 2 .14113 7.0S546 .15898 0.29007 .17093 5.05205 .19498 5.12802 5S 3 .14143 7.07059 .15928 6.27829 .17723 5.04248 .19529 5.12009 57 4 .14173 7.05579 .15958 6.26055 .17753 5.03295 .19559 5.11279 50 5 .14202 7.04105 .15988 6.254S0 .17783 5.02344 .19589 5.10490 55 6 .14232 7.02637 .10017 0.24321 .17813 5.01397 .19019 5.09704 54 7 .14202 6.91174 .10047 6.23100 .17843 5.0U52 .19049 5.08921 53 8 .14291 6.99718 .10077 0.22003 .17873 5.50511 .19080 5.08139 52 9 .14321 6.9S268 .16107 0.20851 .17903 5.58573 .19710 5.07300 51 10 .14351 6.96823 .16137 0.19703 .17933 5.57038 .19740 5.00584 50 11 .14381 6.95385 .16167 6.18559 .17903 5.50706 .19770 5.05809 49 12 .14110 6.93952 .16190 0.17419 .17903 5.55777 .19801 5.05037 48 13 .14440 6.92525 .16220 6.10283 .18023 5.54851 .19831 5.04207 47 14 .14170 6.91104 .10250 G.15151 .18053 5.53927 .19801 5.03499 4(j 15 .14499 6.89688 .10280 0.14023 .18083 5.53007 .19891 5.02731 16 .14529 6.88278 .10310 6.12899 .18113 5.52090 .19921 5.01971 4-! 17 .14559 6.86874 .10340 0.11779 .18143 5.51176 .19952 5.01210 43 18 .14588 6.85475 .10370 6.10004 .18173 5.50204 .19982 5.00451 42 19 .14618 6.84082 .10405 6.09552 .18203 5.49356 .20012 4.99095 41 20 .14648 6.82694 .10435 6.0^444 .18233 5.48451 .20042 4.98940 40 21 .14678 6.S1312 .16465 6.07340 .18203 5.47548 .20073 4.98188 30 22 .14707 0.79936 .16405 6.00240 .18293 5.40048 .20103 4.97433 3 23 .14737 6.78564 .10525 0.05143 .18323 5.45751 .20133 4.90090 37 24 .14707 6.77199 .10555 6.04051 .18353 5.44857 .20104 4.95945 30 25 .14790 6.75838 .10585 0.02902 .18384 5.43006 .20194 4.95201 35 20 .14826 0.74483 .10015 0.01878 .18414 5.43077 .20224 4.94400 34 27 .14856 0.73133 .10045 0.00707 .18444 5.42192 .20254 4.93721 33 28 .14886 6.71789 .10074 5.99720 .18474 5.41309 .20285 4.92984 32 29 .14915 6.70450 .10701 5.98040 .18504 5.40429 .20315 4.92249 31 30 .14945 C.69116 .10734 5.97570 .18534 5.39552 .20345 4.91510 SO 31 .14975 6.67787 .10704 5.90510 .18504 5.38077 .20376 4.907S5 20 32 .15005 6.06403 .10794 5.95448 .18594 5.37805 .20406 4.90050 2'; 33 .15034 6.65144 .10824 5.94390 .18024 5.30930 .20430 4.89330 27 3i .15004 6.63S31 .10854 5.93335 .18054 5.30070 .20406 4.88005 2(1 35 .15094 6.02523 .10884 5.922Sa .18034 5.35200 .20497 4.87882 '^5 8() .15124 6.61219 .10914 5.91230 .18714 5.34345 .20527 4.87162 21 37 ,15153 6.59921 .10944 5.90191 .18745 5.33437 .20557 4.80444 23 38 .15183 6.58027 .16974 5.S9151 .18775 5.32031 .20588 4.85727 22 39 .15213 0.57339 .17004 5.88114 .18805 5.31778 .20018 4.85013 21 40 .15243 0.50055 .17033 5.87080 .18835 5.30928 .20048 4.84300 20 41 .15272 G.54777 .17003 5.80051 .18865 5.30080 .20079 4.83590 19 42 .15302 0.53503 .17033 5.85024 .18895 5.29235 .20709 4.82882 18 43 .15332 6.52234 .17123 5.84001 .18925 5.2S393 .20739 4.82175 17 44 .15362 6.50970 .17153 5.829C2 .18955 5.27553 .20770 4.81471 10 45 .15391 6.49710 .17183 5.81900 .18980 5.20715 .20800 4.80769 15 46 .15421 6.48456 .17213 5.80953 .19010 5.25880 .20830 4.S0O0S 14 47 .15451 6.47200 .17243 5.79944 .19046 5.25048 .20801 4.79370 13 48 .15481 6.45901 .17273 5.78938 .19076 5.24218 .20891 4.78073 12 49 .15511 6.44720 .17303 5.77930 .19106 5.23391 .20921 4.77978 11 50 .15540 6.43484 .17333 5.70937 .19136 5.22539 .20952 4.77280 10 51 .15570 6.42253 .17303 5.75941 .19106 5.21744 .20982 4.70595 9 52 .15600 6.41020 .17393 5.74949 .19197 5.20925 .21013 4.75900 Q 53 .15030 0.39804 .17423 5.73900 .19227 5.20107 .21043 4.75219 7 54 .15060 0.3S587 .17453 5.72974 .19257 5.19293 .21073 4.74534 55 .15689 0.37374 .17483 5.71992 .19287 5.18480 .21104 4.73851 5 56 .15719 6.36165 .17513 5.71013 .19317 5.17071 .21134 4.73170 4 57 .15749 6.34901 .17543 5.70037 .19347 5.10803 .21104 4.72490 3 5S .15779 6.33701 .17573 5.09004 .19378 5.10058 .21195 4.71813 2 59 .15809 6.32506 .17003 5.08094 .19408 5.15250 .21225 4.71137 1 60 .15838 0.31375 .17033 5.07128 .19438 5.14455 .21250 4.70463 ■* Cotan? Tang Cotang Tang Cotang Tang Cotang Tang » 81° i 80° 1 79° 1 78° Table of Natural Tangents and Cotangents 107 / 1." 1 13° _ 11 T4° II 15° 1 / Tang Cotang Tang Cotang Tang Cotang Tang Jot.ang .21256 4.70463 .23087 4.33148 .24933 4.01078 .20795 3.73205 60 1 .21286 4.69791 .23117 4.32573 .24904 4.00582 .26826 3.72771 59 2 .21316 4.69121 .23148 4.32001 .24995 4.000S0 .26857 3.72338 58 3 .21347 4.68452 .23179 4.31430 .25026 3.99592 .26888 3.71907 57 4 .21377 4.67786 .23209 4.30800 .25050 3.99099 .26920 3.71476 56 5 .21408 4.67121 .23240 4.30291 .25087 3.98007 .26951 3.71046 55 G .21438 4.66458 .23271 4.29724 .25118 3.98117 .20982 3.70616 54 7 .214G9 4.65797 .23301 4.29159 .25149 3.97627 .27013 3.70188 53 8 .21490 4.65138 .23332 4.28595 .25180 3.97139 .27044 3.69761 52 9 .21520 4.64480 .23303 4.28032 .25211 3.90051 .2707G 3.69335 51 10 .215G0 4.63825 .23393 4.27471 .25242 3.96165 .27107 3.88909 50 11 .21590 4.63171 .23424 4.20911 .25273 3.95080 .27138 3.08485 49 12 .21021 4.02518 .23455 4.20352 .25304 3.95190 .27169 3.08001 48 13 .21051 4.61808 .23485 4.25795 .25335 3.94713 .27201 3.07038 47 11 .210^>2 4.01219 .23510 4.25239 .25300 3.94232 .27232 3.07217 46 15 .21712 4.60572 .23547 4.24085 .25397 3.93751 .27263 3.0()79G 45 IG .21743 4.59927 .23578 4.24132 .25428 3.93271 .27294 3.06376 44 17 .21773 4.59283 .23608 4.235S0 .25459 3.92793 .27326 3.65957 43 IS .21804 4.58041 .23639 4.23030 .25400 3.92310 .27357 3.65538 42 19 .21834 4.58001 .23070 4.22481 .25521 3.91839 .27388 3.65121 41 20 .21864 4.57363 .23700 4.21933 .25552 3.91304 .27419 3.64705 40 21 .21895 4.56720 .23731 4.213S7 .25583 3.90890 .27451 3.64289 39 22 .21925 4.50091 .23702 4.20842 .25014 3.90417 .27482 3.63874 38 23 .21956 4.55458 .23703 4.20208 .25045 3.89945 .27513 3.63461 37 24 .21986 4.54826 .23823 4.19750 .2507G 3.89474 .27545 3.63048 36 25 .22017 4.54106 .23854 4.19215 .25707 3.89004 .27576 3.62636 35 20 .22047 4.53508 .23885 4.18075 .25738 3.88530 .27007 3.62224 34 27 .22078 4.52941 .23910 4.18137 .25709 3.88008 .27638 3.61814 33 28 .22108 4.52310 .23046 4.17000 .25800 3.87001 .27070 3.61405 32 29 .22139 4.51093 .23977 4.17004 .25831 3.87130 .27701 3.60996 31 30 .22109 4.51071 .24008 4.1G530 .25862 3.86671 .27732 3.60588 30 31 .22200 4.50451 .24039 4.15997 .25893 3.80208 .27704 3.60181 29 32 .22231 4.49S32 .24009 4.15405 .25924 3.85745 .27795 3.59775 28 33 .22201 4.49215 .24100 4.14934 .25955 3.85284 .27826 3.59370 27 34 .22292 4.48000 .24131 4.14405 .25986 3.84824 .27858 3.58966 26 35 .22322 4.47986 .24162 4.13877 .20017 3.84304 .278S9 3.58562 25 3G .22353 4.47374 .24193 4.13350 .20048 3.83906 .27921 3.58160 24 37 .22383 4.40704 .24223 4.12825 .20079 3.83449 .27952 3.57758 23 38 .22414 4.46155 .24254 4.12301 .20110 3.82992 .27983 3.57357 22 39 .22444 4.45548 .24285 4.11778 .20141 3.82537 .28015 3.56957 21 40 .22475 4.44942 .24310 4.1125G .26172 3.82083 .28040 3.56557 20 41 .22505 4,44338 .24347 4.10730 .26203 3.81630 .28077 3.56159 19 42 .22536 4.43735 .24377 4.10216 .26235 3.81177 .28109 3.55761 18 43 .22567 4.43134 .24408 4.09699 .20206 3.80720 .28140 3.55364 17 44 .22597 4.42534 .24439 4.09182 .20297 3.80276 .28172 3.54968 16 45 .22628 4.41936 .24470 4.08666 .20328 3.79827 .28203 3.54573 15 40 .22658 4.41340 .24501 4.08152 .26359 3.79378 .28234 3.54179 14 47 .22689 4.40745 .24532 4.07039 .20390 3.78931 .28266 3.53785 13 48 .22719 4.40152 .24562 4.07127 .20421 3.78485 .28297 3.53393 12 49 .22750 4.39500 .24503 4.00016 .26452 3.78040 .28329 3.53001 11 50 .22781 4.38909 .24024 4.06107 .26483 3.77595 .28360 3.52609 10 51 .22811 4.38381 .24055 4.05599 .26515 3.77152 .28391 3.52219 9 52 .22842 4.37793 .24686 4.05092 .20546 3.76709 .28423 3.51829 8 53 .22872 4.37207 .24717 4.045S6 .26577 3.70268 .28454 3.51441 7 54 .22903 4.36023 .24747 4.04081 .26008 3.75828 .28486 3.51053 f) 55 .22934 4.36040 .24778 4.03578 .20039 3.75388 .28517 3.50666 5 50 .22964 4.35459 .24809 4.03076 .20070 3.74950 .28549 3.50279 4 57 .22995 4.34879 .24840 4.02574 .20701 3.74512 .28580 3.49894 3 58 .23026 4.34300 .24871 4.02074 .20733 3.74075 .28612 3.49509 2 59 .23056 4.33723 .24902 4.01576 .20704 3.73640 .28643 3.49125 1 60 .23087 4.33148 .24933 4.01078 .20795 3.73205 .28675 3.48741 Cotanp Tang Cotang Tang Cot an p r Tang ' » Cotang d Tang 77° 76° 75° 1 74° 108 Trigonometry Part / 10" 1 17»__ 1 18° II 19° 1 60 Tang Uotang Tang Uotang Tang Cotang Tang Cotang .28675 3.48741 .30573 3.27085 .32492 3.07768 .34433 2.90421 1 .28706 3.48359 .30005 3.26745 .32524 3.07464 .34465 2.90147 59 2 .28738 3.47977 .30037 3.26406 .32556 3.07160 .34498 2.89873 58 3 .28709 3.47596 .30009 3.26067 .32588 3.06857 .34530 2.89600 57 4 .28800 3.47210 .30700 3.25729 .32021 3.06554 .34563 2.89327 56 5 .28832 3.4f^837 .30732 3.25392 .32653 3.06252 .34596 2.89055 55 6 .288C4 3.40458 .30704 3.25055 .32685 3.05950 .34628 2.88783 54 7 .288P5 3.46080 .30796 3.24719 .32717 3.05649 .34661 2.88511 53 8 .28927 3.45703 .30828 3.24383 .32749 3.05349 .34693 2.8S240 52 9 .28958 3.45327 .30800 3.24049 .32782 3.05049 .34720 2.87970 51 10 .28990 3.44951 .30891 3.23714 .32814 3.04749 .34758 2.87700 50 11 .29021 3.44576 .30923 3.23381 .32846 3.04450 .34791 2.87430 49 12 .29053 3.44202 .30955 3.23048 .32878 3.04152 .34824 2.87161 48 13 .29084 3.43829 .30987 3.22715 .32911 3.03854 .34850 2.86892 47 14 .29110 3.43450 .31019 3.22384 .32943 3.03556 .34889 2.86624 46 15 .29147 3.43084 .31051 3.22053 .32975 3.03260 .34922 2.86356 45 16 .29179 3.42713 .31083 3.21722 .33007 3.02963 .34954 2.86089 44 17 .29210 3.42343 .31115 3.21392 .33040 3.02667 .34987 2.85822 43 18 .29242 3.41973 .31117 3.21003 .33072 3.02372 .35020 2.85555 42 19 .29274 3.41004 .31178 3.20734 .33104 3.02077 .35052 2.85289 41 20 .29305 3.41230 .31210 3.20406 .33136 3.01783 .35085 2.85023 40 21 .29337 3.40869 .31242 3.20079 .33109 3.01489 .35118 2.84758 39 22 .29368 3.40502 .31274 3.19752 .33201 3.01196 .35150 2.84494 38 23 .29409 3.40136 .31300 3.19426 .33233 3.00903 .35183 2.84229 37 24 .29432 3.39771 .31338 3.19100 .33200 3.00611 .35216 2.83965 36 25 .29403 3.39406 .31370 3.18775 .33298 3.00319 .35248 2.83702 35 26 .29495 3.39042 .31402 3.18451 .33330 3.00028 .35281 2.83439 34 27 .29520 3.38679 .31434 3.18127 .33303 2.99738 .35314 2.83176 33 28 .29558 3.38317 .31406 •3.17804 .33395 2.99447 .35340 2.82914 32 29 .29590 3.37955 .31498 3.17481 .33427 2.99158 .35379 2.82653 31 30 .29021 3.37594 .31530 3.17159 .33400 2.98868 .35412 2.82391 30 31 .29053 3.37234 .31562 3.1683S .33492 2.98580 .35445 2.82130 29 32 .29085 3.30875 .31594 3.10517 .33524 2.98292 .35477 2.81870 28 33 .29716 3.36510 .31626 3.16197 .33557 2.98004 .35510 2.81010 27 34 .29748 3.3615S .31058 3.15877 .33589 2.97717 .355! 3 2.81350 20 35 .29780 3.35800 .31690 3.15558 .33021 2.97430 .35570 2.81091 25 36 .29811 3.35443 .31722 3.15240 .38054 2.97144 .35608 2.80833 24 37 .29St3 3.35087 .31754 3.14922 .33086 2.96858 .3.5641 2.80574 23 38 .29875 3.34732 .31780 3.14G05 .33718 2.90573 .35674 2.80310 22 39 .29900 3.34377 .31818 3.14288 .33751 2.96288 .35707 2.80059 21 40 .29938 3.34023 .31850 3.13972 .33783 2.96004 .35740 2.79802 20 41 .29970 3.33670 .31882 3.13656 .33816 2.95721 .35772 2.79545 19 42 .30001 3.33317 .31914 3.13341 .33848 2.05437 .35805 2.79289 18 43 .30033 3.32965 .31940 3.13027 .33881 2.95155 .35838 2.79033 17 44 .30005 3.32614 .31978 3.12713 .33913 2.94872 .35871 2.78778 10 45 .30097 3.32264 .32010 3.12400 .33945 2.94591 .35904 2.78523 15 46 .30128 3.31914 .32042 3.12087 .33978 2.94309 .35937 2.78209 14 47 .30100 3.31565 .32074 3.11775 .34010 2.94028 .35009 2.78014 13 48 .30192 3.31216 .32106 3.11464 .34043 2.93748 .30002 2.77701 12 49 .30224 3.30868 .32139 3.11153 .34075 2.934G8 .30035 2.77507 11 50 .30255 3.30521 .32171 3.10842 .34108 2.93189 .30068 2.77254 10 51 .30287 3.30174 .32203 3.10532 .34140 2.92010 .36101 2.77002 9 52 .30319 3.29829 .32235 3.10223 .34173 2.92032 .36134 2.70750 8 53 .30351 3.29483 .32207 3.09914 .34205 2.92354 .36167 2.70498 7 54 .30382 3.29139 .32299 3.09600 .34238 2.92070 .36199 2.70247 6 55 .30414 3.28795 .32331 3.09298 .34270 2.91799 .30232 2.75996 5 56 .30140 3.28452 .32303 3.0899] .34303 2.91523 ^6265 2.75746 4 57 .30478 3.28109 .32390 3.08685 .34335 2.91240 .36298 2.75496 3 58 .30509 3.27767 .32428 3.08379 .34368 2.90971 .30331 2.75246 1 59 .30541 3.27426 .32400 3.08073 .34400 2.90696 .30364 2.74997 60 .30573 3.27085 .32492 3.07768 .34433 2.90421 .36397 2.74748 2 t Cotang Tang Cotang Tang C-otang Tang Cotang Tang 73° 72° 71° 70° Table of Natural Tangents and Cotangents 109 r 20° 1 21° 1 22° 1 23° / Tang .36397 Cotang 2.74748 Tang .38386 (Jotang 2.00509 Tang Cotang Tang Cotang .40403 2.47509 .42447 2.35585 60 1 .36430 2.74499 .38420 2.00283 .40436 2.47302 .42482 2.35395 69 2 .36463 2.74251 .38453 2.60057 .40470 2.47095 .42516 2.35205 58 3 .36496 2.74004 .38487 2.59831 .40504 2.46888 .42551 2.35015 57 4 .36529 2.73756 .38520 2.59606 .40538 2.46682 .42585 2.34825 56 5 ,36562 2.73509 .38553 2.59381 .40572 2.46476 .42619 2.34636 55 6 .36595 2.73263 .38587 2.59156 .40606 2.46270 .42654 2.34447 64 7 .36628 2.73017 .38620 2.58932 .40640 2.46065 .42688 2.34258 53 8 .36661 2.72771 .38654 2.58708 .40674 2.45860 .42722 2.34069 52 9 .36694 2.72526 .38687 2.58484 .40707 2.45055 .42757 2.33881 51 10 .36727 2.72281 .38721 2.58261 .40741 2.45451 .42791 2.33693 60 11 .36760 2.72036 .38754 2.58038 .40775 2.45246 .42826 2.33505 49 12 .36793 2.71792 .38787 2.57815 .40809 2.45043 .42860 2.33317 48 13 .36826 2.71548 .38821 2.57593 .40843 2.44839 .42894 2.33130 47 14 .36859 2.71305 .38854 2.57371 .40877 2.44636 .42929 2.32943 46 15 .36892 2.71062 .388S8 2.57150 .40911 2.44433 .42963 2.32756 45 16 .36925 2.70819 .38921 2.56928 .40945 2.44230 .42998 2.32570 44 17 .36958 2.70577 .38955 2.56707 .40979 2.44027 .43032 2.32383 43 IS .36991 2.70335 .38988 2.66487 .41013 2.43825 .43067 2.32197 42 19 .37024 2.70094 .39022 2.56266 .41047 2.43623 .43101 2.32012 41 20 .37057 2.69853 .39055 2.56046 .41081 2.43422 .43136 2.31826 40 21 .37090 2.69612 .39089 2.55827 .41115 2.43220 .43170 2.31641 39 22 .37123 2.69371 .39122 2.55608 .41149 2.43019 .43205 2.31456 38 23 .37157 2.69131 .39156 2.55389 .41183 2.42819 .43239 2.31271 37 24 .37190 2.68892 .39190 2.55170 .41217 2.42618 .43274 2.31086 36 25 .37223 2.68653 .39223 2.54952 .41251 2.42418 .43308 2.30902 35 26 .37256 2.68414 .39257 2.54734 .41285 2.42218 .43343 2.30718 34 27 .37289 2.68175 .39290 2.54516 .41319 2.42019 .4.3378 2.30534 33 28 .37322 2.67987 .39324 2.54299 .41353 2.41819 .43412 2.30351 32 29 .37355 2.67700 .39357 2.54082 .41387 2.41620 .43447 2.30167 31 30 .37388 2.67462 .39391 2.53865 .41421 2.41421 .43481 2.29984 30 31 .37422 2.67225 .39425 2.53648 .41455 2.41223 .43516 2.29801 29 32 .37455 2.66989 .39458 2.53432 .41490 2.41025 .43550 2.29619 28 33 .37188 2.66752 • .39492 2.53217 .41524 2.40827 .43585 2.29437 27 34 .37521 2.66516 .39526 2.53001 .41558 2.40629 .43620 2.29254 26 35 .37554 2.66281 .39559 2.52786 .41592 2.40432 .43654 2.29073 25 36 .37588 2.66046 .39593 2.52571 .41626 2.40235 .43689 2.28891 24 37 .37621 2.65811 .39626 2.52357 .41660 2.40038 .43724 2.28710 23 38 .37654 2.65576 .39660 2.52142 .41094 2.39841 .43758 2.28528 22 39 .37687 2.65342 .39694 2.51929 .41728 2.39645 .43793 2.28348 21 40 .37720 2.65109 .39727 2.51715 .41763 2.39449 .43828 2.28167 20 41 .37754 2.64875 .39761 2.51502 .41797 2.39253 .43862 2.27987 19 42 .37787 2.64642 .39795 2.51289 .41831 2.39058 .43897 2.27806 18 43 .37820 2.64410 .39829 2.51076 .41865 2.38863 .43932 2.27626 17 44 .37853 2.64177 .39862 2.50864 .41899 2.38668 .43966 2.27447 16 45 .37887 2.63945 .39896 2.50652 .41933 2.38473 .44001 2.27267 15 40 .37920 2.63714 .39930 2.50440 .41968 2.38279 .44036 2.27088 14 47 .37953 2.634S3 .39963 2.50229 .42002 2.38084 .44071 2.26909 13 43 .37986 2.63252 .39997 2.50018 .42030 2.37891 .44105 2.26730 12 49 .38020 2.63021 .40031 2.49S07 .42070 2.37697 .44140 2.26552 11 50 .38053 2.62791 .40065 2.49597 .42105 2.37504 .44175 2.26374 10 51 .38086 2.62561 .40098 2.49386 .42139 2.37311 .44210 2.26196 9 52 .38120 2.62332 .40132 2.49177 .42173 2.37118 .44244 2.26018 8 53 .38153 2.62103 .40166 2.48967 .42207 2.36925 .44279 2.25840 7 54 .38186 2.61874- .40200 2.48758 .42242 2.36733 .44314 2.25663 6 55 .38220 2.01646 .40234 2.48549 .42276 2.36541 .44349 2.25486 5 56 .38253 2.61418 .40267 2.48340 .42310 2.36349 .44384 2.25309 4 57 .38286 2.61190 .40301 2.48132 .42345 2.36158 .44418 2.25132 3 58 .38320 2.60963 .40335 2.47924 .42379 2.35967 .44453 2,24956 2 59 .38353 2.60736 .40369 2.47716 .42413 2.35776 .44488 2.24780 1 60 .38386 2.60509 .40403 2.47509 .42447 2.355S5 Tang .44523 2.24604 ' Cotarig Tang Cotang Tang Cotang Cotang Tang > 60° 68° 1 67° 1 66° 1 110 Trigonometry ' 24** 25° 26° 1 27° / Tang Cotang Tang Cotang Tang .48773 Cotang Tang Cotang .44523 2.24604 .46631 2.14451 2.05030 .50053 1.96261 60 1 .44558 2.24428 .46666 2.14288 .48809 2.04S79 .50089 1.96120 59 2 .44593 2.24252 .46702 2.14125 .48845 2.04728 .51026 1.95979 58 3 .44627 2.24077 .46737 2.13903 .48881 2.04577 .51063 1.95838 57 4 .44662 2.23902 .46772 2.13801 .48917 2.04420 .51009 1.9569S 50 5 .44697 2.23727 .46S08 2.13639 .48953 2.04270 .51136 1.95557 55 6 .44732 2.23553 .46843 2.13177 .48989 2.04125 .51173 1.95417 54 7 .44767 2.23378 .40879 2.13316 .49020 2.03975 .51209 1.95277 53 8 .44802 2.23204 .46914 2.13154 .49062 2.03825 .51246 1.95137 52 9 .44837 2.23030 .46950 2.12993 .49098 2.03075 .51283 1.94997 51 10 .44872 2.22857 .46985 2.12832 .49134 2.03520 .51319 1.94858 50 11 .44907 2.22683 .47021 2.12671 .49170 2.03370 .51356 1.94718 49 12 .44942 2.22510 .47056 2.12511 .49200 2.03227 .51393 1.94579 48 13 .44977 2.22337 .47092 2.12350 .49242 2.03078 .51430 1.94440 47 14 .45012 2.22164 .47128 2.12190 .49278 2.02929 .51407 1.94301 46 15 .45047 2.21992 .47163 2.12030 .49315 2.02780 .51503 1.94162 45 16 .45082 2.21819 .47109 2.11871 .49351 2.02031 .51540 1.94023 44 17 .45117 2.21647 .47234 2.11711 .49387 2.02483 .51577 1.93885 43 18 .45152 2.21475 .47270 2.11552 .49423 2.02335 .51014 1.93746 42 19 .45187 2.21304 .47305 2.11392 .49459 2.02187 .51051 1.9360S 41 20 .45222 2.21132 .47341 2.11233 .49495 2.02039 51088 1.93470 40 21 .45257 2.20961 .47377 2.11075 .49532 2.01891 .51724 1.93332 39 22 .45292 2.20790 .47412 2.10916 .49508 2.01743 .51701 1.93195 38 23 .45327 2.20619 .47448 2.10758 .40004 2.01590 .51798 1.93057 37 24 .45362 2.20149 .47483 2.10000 .49040 2.01449 .51835 1.92920 36 25 .45397 2.20278 .47519 2.10442 .49077 2.01302 .51872 1.92782 35 20 .45432 2.20108 .47555 2.10284 .49713 2.01155 .51909 1.92645 34 27 .45467 2.19938 .47590 2.10126 .49749 2.01008 .51946 1.92508 33 28 .45502 2.10769 .47626 2.09909 .49780 2.00802 .51983 1.92371 32 29 .45538 2.19599 .47662 2.09811 .49822 2.00715 .52020 1.92235 31 30 .45573 2.19430 .47698 2.09654 .49858 2.00509 .52057 1.92098 30 31 .45608 2.19261 .47733 2.09498 .49894 2.00423 .52094 1.91962 29 32 .45643 2.19092 .47769 2.09341 .40031 2.00277 .52131 1.91826 28 33 .45678 2.18923 .47805 2,09184 .40007 2.00131 • .52108 1.91690 27 34 .45713 2.18755 .47840 2.09028 .50004 1.99980 .52205 1.91552 26 35 .45748 2.18587 .47876 2.08872 .50040 1.99841 .52242 1.91414 25 36 .45784 2.18419 .47912 2.08716 .50076 1.99095 .52279 1.91288 24 37 .45819 2.18251 .47948 2.08500 .50113 1.99550 .52316 1.91142 23 38 .45854 2.18084 .47984 2.08405 .50149 1.99400 .52353 1.91017 22 39 .45889 2.17916 .48019 2.08250 .50185 1.09201 .52390 1.90870 21 40 .45924 2.17749 .48055 2.08094 .50222 1.99110 .52427 1.90741 20 41 .45960 2.17582 .48091 2^07939 .50258 1.98972 .52464 1.90607 19 42 .45995 2.17416 .48127 2.07785 .50395 1.98828 .52501 1.90472 18 43 .46030 2.17249 .48163 2.07630 .50331 1.98084 .52538 1.90337 17 44 .46065 2.17083 .48198 2.07476 .50368 1.98540 .52575 1.90203 16 45 .46101 2.16917 .48234 2.07321 .50404 1.98390 .52613 1.90069 15 46 .46136 2.16751 .48270 2.07167 .50441 1.98253 .52650 1.89935 14 47 .46171 2.165S5 .48306 2.07014 .50477 1.98110 .52687 1.89801 13 48 .46206 2.16420 .48342 2.06860 .50514 1.97060 .52724 1.89667 12 49 .46242 2.16255 .48378 2.06700 .50550 1.97823 .52701 1.80533 11 50 .46277 2.16090 .48414 2.00553 .50587 1.97681 .52798 1.89400 10 51 .46312 2.15925 .48450 2.06-100 .50623 1.97538 .52836 1.89266 9 52 .46348 2.15760 .48486 2.06247 .50060 1.97395 .52873 1.89133 8 53 .46383 2.15596 .48521 2.06094 .50696 1.97253 .52910 1.89000 7 54 .46418 2.15432 .48557 2.05942 .50733 1.97111 .52947 1.88867 6 55 .46454 2.15268 .48593 2.05790 .50769 1.90909 .52985 1.S8734 5 56 .46489 2.1510i .48620 2.05637 .50806 1.96827 .53022 1.88602 4 57 .46525 2.14940 .48665 2.05485 .50843 1.96085 .53059 1.88469 3 58 .46560 2.14777 .48701 2.05333 .50879 1.96544 .53090 1.88337 2 59 .46595 2.14614 .48/37 2.05182 .50916 1 .96402 .53134 1.88205 1 60 .46631 2.14451 .48773 2.05030 .50953 1.96261 .53171 1.88073 / Cotang Tang Cotang Tang Cotang Tang Cotang Tarig # 65° 1 64° 1 63° 1 62° 1 Table of Natural Tangents and Cotangents 111 ' 28° 1 29° 1 30° 1 31° 1 60 Tang Cotang Tang Cotang Tang Cotang Tang Cotang .53171 1.88073 .55431 1.80405 .57735 1.73205 .60086 1.66428 1 .53208 1.87941 .55469 1.80281 .57774 1.72089 ,60126 1.66318 59 2 .53246 1.87809 .55507 1.80158 .57813 1.72973 .60165 1.66209 58 3 .53283 1.87677 .55545 1.80034 .57851 1 .72857 .60205 1.66099 57 4 .53320 1.87546 .55583 1.79911 .57890 1.72741 .60245 1.65990 56 5 .5335S 1.87415 .55621 1.79788 .57929 1.72625 .60284 1.65881 55 .53395 1.87283 .55659 ] .79605 .57968 1.72509 .60324 1.65772 54 7 .53132 1.87152 .55697 1.79542 ■ .58007 1.72393 .60364 1.65663 53 8 .53470 1.87021 .55736 1.79419 .58046 1.72278 .60403 1.65554 52 9 .53507 1.86891 .55774 1.79296 .58085 1.72163 .60443 1.65445 51 10 .53545 1.86760 .55812 1.79174 .58124 1.72047 .60483 1.65337 50 11 .53582 1.86630 .55850 1.79051 .58162 1.71932 .60522 1.65228 49 12 .53620 1.86499 .55888 1.78929 .58201 1.71817 .60562 1.65120 48 13 .53657 1.86369 .55926 1.78807 .58240 1.71702 .60602 1.65011 47 14 .53694 1.86239 .55964 1.78685 .58279 1.71588 .60042 1.64903 46 15 .53732 1.S6109 .56003 1.78563 .58318 1.71473 .60681 1.64795 45 16 .53769 1.S5979 .56041 1.78441 .58357 1.71358 .60721 1.64687 44 17 .53807 1.85850 .56079 1.78319 .58396 1.71244 .60761 1.64579 43 18 .53844 1.S5720 .56117 1.78198 .58435 1.71129 .60801 1.64471 42 19 .53882 1.85591 .56156 1.78077 .58474 1.71015 .60841 1.64363 41 20 .53920 1.85462 .56194 1.77955 .58513 1.70901 .60881 1.64256 40 21 .53957 1.85333 .56232 1.77834 .58552 1.70787 .00921 1.64148 39 22 .53995 1.85204 .56270 1.77713 .58591 1.70673 .60960 1.04041 38 23 .54032 1.85075 .56309 1.77592 .58631 1.70560 .61000 1.63934 37 24 .54070 1.84946 .56347 1.77471 .58670 1.70446 .61040 1.63826 36 25 .54107 1.84818 .56385 1.77351 .58709 1.70332 .01080 1.63719 35 20 .54145 1 .84689 .56424 1.77230 .58748 1.70219 .61120 1.63612 34 27 .54183 1.84561 .56462 1.77110 .58787 1.70106 .61160 1.63505 33 28 .54220 1.84433 .56501 1.76990 .58826 1.69992 .61200 1.63398 32 29 .54258 1.84305 .56539 1.76869 .58865 1.69879 .61240 1.63292 31 30 .54296 1.84177 .56577 1.76749 .58905 1.69766 .61280 1.63185 30 31 .54333 1.84049 .56616 1.76629 .58944 1.69653 .61320 1.63079 29 32 .54371 1.83922 .56654 1.76510 .58983 1.69541 .61300 1.62972 28 33 .54409 1.83794 .56693 1.76390 .59022 1.69428 .61400 1.62866 27 34 .54446 1.83667 .56731 1.7C271 .59061 1.69316 .61440 1.62760 26 35i .54484 1.83540 .56769 1.76151 .59101 1.69203 .61480 1.62654 25 36 .54522 1.83413 .56808 1.76032 .59140 1.69091 .61520 1.62548 24 37 .54560 1.83286 .56846 1.75913 .59179 1.68979 .61561 1.62442 23 38 .54597 1.83159 .56885 1.75794. .59218 1.68866 .61601 1.62336 22 39 .54635 1.83033 .56923 1.75675 .59258 1.68754 .61641 1.62230 21 40 .54673 1.82906 .56962 1.75556 .59297 1.68643 .61681 1.62125 20 41 .54711 1.82780 .57000 1.75437 .59336 1.08531 .61721 1.62019 19 42 .54748 1.82654 .57039 1.75319 .59376 1.68419 .61761 1.61914 18 43 .54786 1.82528 .57078 1.75200 .59415 1.68308 .61801 1.61808 17 44 .54824 1.82402 .57116 1.75082 .59454 1.68196 .61842 1.61703 16 45 .54862 1.8227C .57155 1.74964 .59494 1.68085 .61882 1.61598 15 46 .54900 1.82150 .57193 1.74846 .59533 1.67974 .61922 1.61493 14 47 .54938 1.82025 .57232 1.74728 .50573 1.67863 .61962 1.61388 13 48 .54975 1.81899 .57271 1.74610 .59612 1.67752 .62003 1.612«^3 12 49 .55013 1.81774 .57309 1.74492 .59651 1.67641 .62043 1.61179 11 50 .55051 1.81649 .57348 1.74375 .59691 1.07530 .62083 1.61074 10 51 .55089 1.81524 .57386 1.74257 .59730 1.67419 .62124 1.60970 9 52 .55127 1.81399 .57425 1.71140 .59770 1 .67309 .62164 1.60865 8 53 55165 1.81274 .57464 1.74022 .59809 1.67198 .62204 1.60761 7 54 .55203 1.81150 .57503 1.73905 .59849 1.67088 .62245 1.60657 6 55 .55241 1.81025 .57541 1.73788 .59888 1.66978 .62285 1.60553 5 56 .55279 1.80901 .57580 1.73671 .59928 1.66867 .62325 1.60449 4 57 .55317 1.80777 .57619 1.73555 .59967 1.66757 .62366 1.60345 3 58 .55355 1.80653 .57657 1.73438 .60007 1.66647 .62406 1.60241 2 59 55393 1.80529 .57696 1.73321 .60046 1.66538 .62446 1.60137 1 ()0 .55431 1.80405 .57735 1.73205 .60086 1.66428 .62187 1.60033 ~ Cotang Tang Cotang Tang Cotang Tang Cotang Tanff / 61° 60° 59° 1 58° 112 Trigonometry fjgo 33° 34° 1 35° / Tung .62487 Cotang Tang Cotang Tang Cotang Tang Colang 1.00033 .64941 1.53986 .07451 1.48256 .70021 1.42815 60 1 .62527 1.59930 .64982 1.53888 .07493 1.48163 .70001 1.42726 59 2 .62568 1.59820 .65024 1.53791 .67536 1.48070 .70170 1.42038 58 3 .62008 1.59723 .65005 1.53093 .07578 1.47977 .70151 1.42550 57 4 .62649 1.59620 .65106 1.53505 .67620 1.47885 .70194 1.42402 50 5 .626S9 1.59517 .05148 1.53497 .67663 1.47792 .70238 1.42374 55 6 .62730 1.59414 .65189 1.53400 .07705 1.47699 .70281 1.42280 54 7 .62770 1.59311 .65231 1.53302 .07748 1.47607 .70325 1.42198 53 8 .62811 1.59208 .05272 1.53205 .07790 1.47514 .70308 1.42110 52 9 .02852 1.59105 .05314 1.53107 .67832 1.47422 .70412 1.42022 51 10 .62892 1.59002 .65355 1.53010 .67875 1.47330 .70455 1.41934 50 It .62933 1.58900 .65397 1.52913 .67917 1.47238 .70499 1.41847 49 12 .62973 1.58797 .C543S 1.52810 .67900 1.47140 .70542 1.41759 48 13 .63014 1.5S695 .65480 1.52719 .68002 1.47053 .70580 1.41072 47 14 .63055 1.58593 .65521 1.52022 .68045 1.4690? .70029 1.41584 40 15 .63095 1.58490 .65503 1.52525 .68088 1.40870 .70073 1.41497 45 10 .63136 1.58388 .65004 1.52429 .08130 1.40778 .70717 1.41409 44 17 .03177 1.58286 .05040 1.52332 .08173 1.40080 .70700 1.41322 43 18 .63217 1.58184 .05088 1.52235 .08215 1.40595 .70804 1.41235 42 10 .63258 1.58083 .65729 1.52139 .08258 1.40503 .70848 1.41148 41 20 .63299 1.57981 .65771 1.52043 .08301 1.40411 .70891 1.41061 40 21 .03340 1.57879 .65813 1.51940 .68343 1.40320 .70935 1.40974 39 22 .63380 1.57778 .65.^54 1.51850. .68386 1.40220 .70979 1.40887 38 23 .63421 1.57070 .65390 1.51751 .68429 1.40137 .71023 1.40800 37 24 .03462 1.57575 .65938 1.51053 .68471 1.40040 .71000 1.40714 36 25 .03503 1.57474 .65980 1.51502 .68514 1.45955 .71110 1.40027 35 20 .63544 1.57372 .66021 1.51400 .68557 1.4 5804 .71154 1.40540 34 27 .03584 1.57271 .66003 1.51370 .68000 1.45773 .71198 1.40454 33 28 .63625 1.57170 .60105 1.51275 .68642 1.45682 .71242 1.40307 32 29 .63000 1.57009 .60147 1.51179 .68685 1.45592 .71285 1.40281 31 30 .63707 1.50909 .00189 1.51084 .68728 1.45501 .71329 1.40105 30 31 .63748 1.50808 .00230 1.50988 .08771 1.45410 .71373 1.40109 29 32 .03789 1.56707 .00272 1.5C893 .68814 1.45320 .71417 1.40022 28 33 .63830 1.56007 .03314 1.50797 .68357 1.45229 .71401 1.39930 27 31 .03871 1 .505^0 .00350 1.50703 .08900 1.45139 .71505 1.39850 26 35 .63912 1.50406 .00398 1.50007 .08942 1.45049 .71549 1 .39704 25 30 .63953 1. 503^^0 .00440 1.50512 .08985 1.44958 .71593 1 .39679 24 37 .63994 1.50205 .00482 1.50417 .09023 1.44808 .71037 1.39593 23 3S .04035 1.561C5 .00524 1.50322 .09071 1.44778 .71081 1.39507 22 39 .04070 1.5G0G5 .60500 1.50228 .09114 1.44688 .71725 1.39421 21 40 .04117 1.55966 .00608 1.50133 .09157 1.44598 .71709 1.39330 20 41 .04158 1.55866 .00050 1.50038 .09200 1.44508 .71813 1.39250 19 42 .04199 1.55700 .66692 1.49944 .09243 1.44418 .71857 1.39105 18 43 .04240 1.55000 .60734 1.49849 .09280 1.44329 .71901 1.39079 17 44 .64231 1.55507 .60770 1.49755 .69:^29 1.44239 .71940 1.38994 16 45 .04322 1.55407 .00818 1.49001 .09372 1.44149 .71990 1.3S909 15 46 .64303 1.55308 .00800 1.49506 .69416 1.44000 .72034 1.38824 14 47 .64404 1.55209 .66902 1.49472 .69459 1.43970 .72078 1 .38738 13 48 .64446 1.55170 .66944 1.49378 .69502 1.43881 .72122 1.38053 12 49 .64487 1.55071 .06986 1.49284 .69545 1 .43792 .72107 1.38508 11 50 .64528 1.54972 .67028 1.49190 .69588 1.43703 .72211 1.38484 10 51 .64569 1.54873 .67071 1.49097 .69631 1.43614 .72255 1.38399 9 "12 .64610 1.54774 .67113 1.49003 .69675 1.43525 .72299 1.38314 8 53 .64652 1.54075 .67155 1.48909 .69718 1.43436 .72344 1.38229 7 54 .64693 1.54576 .67197 1.48810 .69761 1.43347 .72388 1.38145 6 55 .64734 1.54478 .67239 1.48722 .69804 1 .43258 .72432 1.38000 5 56 .64775 1.54379 .67282 1.48029 .69847 1.43109 .72477 1.37976 4 57 .64817 1.542S1 .67324 1.48536 .69301 1 .43080 .72521 1.37891 3 58 .64858 1.54183 .67300 1.48442 .69934 1.42992 .72505 1 .37807 2 59 .64899 1.54085 .67409 1.48349 .69977 1.42903 .72010 1.37722 1 GO .64941 1.53986 .67451 1.48256 Tang .70021 1.42815 .72054 Cotang 1 .37038 Cotang Tang Cotang Cotang Tang Tang ' rr-'yo 1 cco 1 KK^ 1 C^o • 1 i •T \3 »>o ' a >* 1 Table of Natural Tangents and Cotangents 113 ' 36° 1 37° 1 38° 1 31>° 1 ' Tang Cotang Tang Cotnng Tang Cotang Tang Cotang .72654 1.37638 .75355 1.32704 .78120 1.27994 .80978 1.23490 60 1 .72699 1.37554 .75401 1.32624 .78175 1.27917 .81027 1.23410 59 2 .72743 1.37470 .75447 1.32544 .78222 1.27841 .81075 1.23343 58 3 .72788 1.37386 .75492 1.32464 .78269 1.27764 .81123 1.23270 57 4 .72832 1.37302 .75538 1.32384 .78316 1.27688 .81171 1.2319G 50 5 .72877 1.37218 .75584 1.32304 .78363 1.27611 .81220 1.23123 65 r> .72921 1.37134 .75029 1.32224 .78410 1.27535 .81208 1 .23050 54 7 .72966 1.37050 .75675 1.32144 .78457 1.27458 .81310 1.22977 53 8 .73010 1.36967 .75721 1.32064 .78504 1.27382 .81364 1.22904 52 9 .73055 1.36883 .75767 1.31984 .78551 1.27306 .81413 1.22831 51 10 .73100 1.36800 .75812 1.31904 .78598 1.27230 .81461 1.22758 50 11 .73144 1.36716 .75858 1.31825 .78645 1.27153 .81510 1.22685 49 12 .73189 1.36633 .75904 1.31745 .78692 1.27077 .81558 1.22012 48 13 .73234 1.36549 .75950 1.31606 .78739 1.27001 .81006 1.22539 47 14 .73278 1.36466 .75996 1.31586 .78786 1.20925 .81655 1.22107 46 15 .73323 1.36383 .76042 1.31507 .78834 1.26849 .81703 1.22394 45 11] .73368 1.36300 .76088 1.31427 .78881 1.26774 .81752 1.22321 44 17 .73413 1.36217 .76134 1.31348 .78928 1.26698 .81800 1.22249 43 18 .73457 1.36134 .76180 1.31209 .78975 1.20622 .81849 1.22176 42 19 .73502 1.36051 .76226 1.31190 .79022 1.26546 .81898 1.22104 41 20 .73547 1.35968 .76272 1.31110 .79070 1.26471 .81946 1.22031 40 21 .73592 1.35885 .76318 1.31031 .79117 1.26395 .81995 1.21959 39 22 .73637 1.35802 .76304 1.30952 .79164 1.26319 .82044 1.21886 38 23 .73681 1.35719 .70410 1.30873 .79212 1.26244 .82092 1.21814 37 24 .73726 1.35637 .70450 1.30795 .79259 1.26169 .82141 1.21742 30 25 .73771 1.35554 .76502 1.30710 .79306 1.26093 .82190 1.21670 35 26 .73816 1.35472 .76548 1.30637 .79354 1.26018 .82238 1.21598 34 27 .73861 1.35389 .76594 1.30558 .79401 1.25943 .82287 1.21526 33 28 .73906 1.35307 .76640 1.30480 .79449 1.25867 .82336 1.21454 32 29 .73951 1.35224 .76680 1.30401 .79496 1.25792 .82385 1.21382 31 30 .73996 1.35142 .76733 1.30323 .79544 1.25717 .82434 1.21310 30 31 .74041 1.35060 .76779 1.30244 .79591 1.25642 .82483 1.21238 29 32 .74086 1.34978 .76825 1.30106 .79639 1.25567 .82531 1.21166 28 33 .74131 1.34890 .76871 1.30087 .79686 1.25492 .82580 1.21094 27 34 .74176 1.34814 .76918 1.30009 .79734 1.25417 .82629 1.21023 26 35 .74221 1.34732 .76964 1.29931 .79781 1.25343 .82678 1.20951 25 30 .74267 1.34G50 .77010 1.29853 .79829 1.25268 .82727 1.20879 24 37 .74312 1 .34508 .77057 1.29775 .79877 1.25193 .82776 1.20808 23 38 .74357 1.34487 .77103 1.29606 .79924 1.25118 .82825 1.20736 22 39 .74402 1.34^05 .77149 1.29618 .79972 1.25044 .82874 1.20665 21 40 .74447 1.34323 .77196 1.29541 .80020 1.24969 .82923 1.20503 20 41 .74492 1.34242 .77242 1.29403 .80067 1.24895 .82972 1.20522 19 42 .74538 1.34100 .77289 1.29385 .80115 1.24820 .83022 1.20451 18 43 .74583 1.34079 .77335 1.29307 .80163 1.24740 .83071 1.20379 17 44 .74628 1.33908 .77382 1.29229 .80211 1.24672 .83120 1.20308 16 45 .74674 1.33010 .77428 1.29152 .80258 1.24597 .83169 1.20237 15 40 .74719 1.33825 .77475 1.29074 .80300 1.24523 .83218 1.20166 14 47 .7470^ 1.33754 .77521 1.28997 .80354 1.24449 .83268 1.20095 13 48 .74810 1.33073 .77568 1.28910 .80402 1.24375 .83317 1.20024 12 49 .74855 1 .33592 .77615 1.28842 .80450 1.24301 .83366 1.19953 11 50 .74900 1.33511 .77661 1.28764 .80498 1.24227 .83415 1.19882 10 51 .74946 1.33430 .77708 1 .28687 .80546 1.2415?. .83405 1.19811 9 52 .74991 1.33349 .77754 1.2S610 .80594 1.24079 .83514 1.19740 8 53 .75037 1.33208 .77801 1.28533 .80642 1.24005 .83564 1.10669 7 54 .75082 1.33187 .77848 1.28456 .80090 1.23931 .83613 1.19599 55 .75128 1.33107 .77895 1.28379 .80738 1.23858 .83062 1.19528 5 5G .75173 1 .33026 .77941 1.28302 .80786 1.23784 ^.83712 1.19457 4 57 .75219 1.32946 .77988 1.28225 .80834 1.23710 .83761 1.19387 3 58 .75264 1.32865 .78035 1.28148 .80882 1.23037 .83811 1.19316 2 59 .75310 1.32785 .78082 1.28071 .80930 1.23503 .83860 1.19246 1 60 .75355 1.32704 .78129 1.27994 .80978 1.23490 .83910 1.19175 / Cotang Tang Cotang Tang Cotang Tang Cotang Tang ' -^o 1 ~" ^";;o " 1 --0 1 5 »j ' 52 1 5 1 1 5'^" U' 114 Trigonometry / 40° 41° 42° 1 43° ' Tang Cotang Tang Cotang Tang Cotang Tang Cotang .83910 1.19175 .86929 1.15037 .90040 1.11061 .93252 1.07237 60 1 .83960 1.19105 .86980 1.14969 .90093 1.10996 .93306 1.07174 59 2 .84009 1.19035 .87031 1.14902 .90146 1.10931 .93360 1.07112 58 3 .84059 1.18964 .87082 1.14S34 .90199 1.10867 .93415 1.07049 57 4 .84108 1.18894 .87133 1.14767 .90251 1.10802 .93409 1.00987 56 5 .84158 1.18824 .87184 1.14699 .90304 1.10737 .93524 1.06925 55 G .84208 1.18754 .87236 1.14632 .90357 1.10672 .93578 1 .00802 54 7 .84258 1.18684 .87287 1.14565 .90410 1.10607 .93633 1.00800 53 8 .84307 1.18614 .87338 1.14498 .90463 1.10543 .93688 1.06738 52 9 .84357 1.18544 .87389 1.14430 .90516 1.10478 .93742 1.06076 51 10 .84407 1.18474 .87441 1.14363 .90569 1.10414 .93797 1.06613 50 11 .84457 1.18404 .87492 1.14296 .90621 1.10349 .93852 1.06551 49 12 .84507 1.18334 .87543 1.14229 .90074 1.10285 .93906 1.06489 48 13 .84556 1.18264 .87595 1.14162 .90727 1.10220 .93961 1.06427 47 14 .84606 1.18194 .87646 1.14095 .90781 1.10156 .94016 ] .06365 46 15 .84656 1.18125 .87698 1.14028 .90834 1.10091 .94071 1 .06303 45 16 .84706 1.18055 .87749 1.13961 .90887 1.10027 .94125 1.06241 44 17 .84756 1.17986 .87801 1.13894 .90940 1.09963 .94180 1.06179 43 18 .84806 1.17916 .87852 1.13828 .90993 1.09899 .94235 1.06117 42 19 .84856 1.17846 .87904 1.13761 .91046 1.09834 .94290 1.00056 41 20 .84906 1.17777 .87955 1.13694 .91099 1.09770 .94345 1.05994 40 21 .84956 1.17708 .88007 1.13627 .91153 1.09706 .94400 1 .05932 39 22 .85006 1.17638 .88059 1.13561 .91206 1.09642 .94455 1.05870 38 23 .85057 1.1 7509 .88110 1.13494 .91259 1.09578 .94510 1.05809 37 24 .85107 1.17500 .88162 1.13428 .91313 1.09514 .94565 1.05747 36 25 .85157 1.17430 .88214 1.13361 .91366 1.09450 .94620 1.05685 35 20 .85207 1.17361 .88265 1.13295 .91419 1.09386 .94676 1.05624 34 27 .85257 1.17292 .88317 1.13228 .91473 1.09322 .94731 1.05562 33 28 .85308 1.17223 .88369 1.13162 .91526 1.09258 .94786 1.05501 32 29 .85358 1.17154 .88421 1.13096 .91580 1.09195 .94841 1.05439 31 30 .85408 1.17085 .88473 1.13029 .91633 1.09131 .94896 1.05378 30 31 .85458 1.17016 .88524 1.12963 .91687 1.09067 .94952 1.05317 29 32 .85509 1.16947 .88576 1.12897 .91740 1.09003 .95007 1.05255 28 33 .85559 1.16878 .88628 1.12S31 .91794 1.08940 .95062 1.05104 27 34 .85609 1.16309 .886S0 1.12765 .91847 1.08876 .95118 1.05133 26 35 .85660 1.16741 .88732 1.12699 .01901 1.08813 .95173 1.05072 25 36 .85710 1.16672 .88784 1.12633 .91955 1.08749 .95229 1.05010 24 37 .85761 1.16603 .88836 1.12657 .92008 1.08086 .95284 1.04949 23 38 .85811 1.16535 .88888 1.12501 .92002 1.08622 .95340 1.04888 22 39 .85862 1.10466 .88940 1.12435 .92116 1.03559 .95395 1.04827 21 40 .85912 1.16398 .88992 1.12369 .92170 1.08490 .95451 1.04766 20 41 .85963 1.16329 .89045 1.12303 .92224 1.08432 .95506 1.04705 10 42 .86014 1.16261 .89097 1.12238 .92277 1 .0S309 .95502 1.04644 18 43 .86064 1.16192 .89140 1.12172 .92331 1.08300 .95618 1.01583 17 44 .86115 1.16124 .89201 1.12106 .92385 1.08243 .95673 1.04522 16 45 .86166 1.10056 .89253 1.12041 .92439 1.08170 .95729 1.04461 15 46 .86216 1.15987 .89306 1.11975 .92493 1.0811« .95785 1.04401 14 47 .86267 1.15919 .89358 1.11909 .92547 1.08053 .95841 1.04340 13 48 .86318 1.15851 .89410 1.11844 .92601 1.07990 .95897 1.04279 12 49 .86368 1.15783 .89463 1.11778 .92655 1.07927 .95952 1.04218 11 50 .86419 1.15715 .89515 1.11713 .92709 1.07864 .96008 1.04158 10 51 .86470 1.15047 .89567 1.11G48 .92763 1.07801 .96004 1.04097 9 52 .86521 1.15579 .89620 1.11582 .02817 1.07738 .96120 1.04036 8 53 .86572 1.15511 .89672 1.11517 .92872 1.07676 .00170 1.03976 7 54 .86623 1.15443 .89725 1.11452 .92926 1.07613 .96232 1.03915 6 55 .80674 1.15375 .89777 1.11387 .92980 1.07550 .96288 1.03855 5 56 .86725 1.1530^ .89830 1.11321 .93034 1.07487 .96344 1.03794 4 57 .86770 1.15240 .89883 1.11256 .93088 1.07425 .96400 1.03734 3 58 .80827 1.15172 .89935 1.11191 .93143 1.07362 .90457 1.03674 2 59 .86878 1.15104 .89988 1.11126 .93197 1.07299 .96513 1.03613 1 60 .86929 1.15037 .90040 Cotang 1.11061 Tang .93252 1.07237 .90509 Cotang 1.03553 Tang / Cotang Tang Cotang Tang 4»» 48° ' 47° 1 46° Table of Natural Tangents and Cotangents 115 ^ A ' 14° , , 44° 44° Tang Cotang Tang Cotang Tang Cotang 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 .96509 .96625 .96681 .96738 .96791 .968.50 .96907 .96963 .97020 .97076 .97133 .97189 .97246 .97302 .97359 .97416 .97472 .97529 .97586 .97643 .97700 1.03553 1.03493 1.03433 1.03372 1.03312 1.03252 1.03192 1.03132 1.03072 1.03012 1.02952 1.02892 1.02832 1.02772 1.02713 1.02653 1.02593 1.02533 1.02474 1.02414 1.02355 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 .97700 .97756 .97813 .97870 .97927 .97984 .98041 .98098 .98155 .98213 .98270 .98327 .98384 .98441 .98499 .98556 .98613 .98671 .98728 .98786 .98843 1.02355 1.02295 1.02236 1.02176 1.02117 1.02057 1.01998 1.01939 1.01879 1.01820 1.01761 1.01702 1.01642 1.01583 1.01524 1.01465 1.01406 1.01347 1.01288 1.01229 1.01170 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 92 21 20 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 .98843 .98901 .98958 .99016 .99073 .99131 .99189 .99247 .99304 .99362 .99420 .99478 .99536 .99594 .99652 .99710 .99768 .99826 .99884 .99942 1.00000 1.01170 1.01112 1.01053 1.00994 1.00935 1.00876 1.00818 1.00759 1.00701 1.00642 1.00583 1.00525 1.00467 1.00408 1.00350 1.00291 1.00233 1.00175 1.00116 1 .00058 1.00000 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 ' Cotang Tang t ' Cotang Tang ' / Cotang Tang / 45° 45^ 45° _ il« Trigonometry N. itural Se :ants and Cosecan ts De gre< j_ Secants * ,0' 10' 20' 30' 40' 50' 60' ( ) 1.00000 1.00001 1.00002 1.00004 1.00007 1.00011 1.00015 89 I 1.00015 1.00021 1.00027 1.00034 1.00042 1.00051 1.00061 88 2 1.00061 1.00072 1.00083 1.00095 1.00108 1.00122 1.00137 87 J 1.00137 1.00153 1.00169 1.00187 1.00205 1.00224 1.00244 86 I 1.00244 1.00265 1.00287 1.00309 1.00333 1.00357 1.00382 85 5 1.00382 1.00408 1.00435 1.00463 1.00491 1.00521 1.00551 84 5 1.00551 1.00582 1.00614 1.00647 1.00681 1.00715 1.00751 83 r 1.00751 1.00787 1.00825 1.00863 1.00902 1.00942 1.00983 82 S 1.00983 1.01024 1.01067 1.01111 1.01155 1.01200 1.01247 81 1 J 1.01247 1.01294 1.01342 1.01391 1.01440 1.01491 1.01543 80 li 3 1.01543 1.01595 1.01 649 1.01703 1.01758 1.01815 1.01872 79 1 I 1.01872 1.01930 1.01 989 1.02049 1.02110 1.02171 1.02234 78 IJ I 1.02234 1.02298 1.02 362 1.02428 1.02494 1.02562 1.02630 77 i: J 1.02630 1.02700 1.02 770 1.02842 1.02914 1.02987 1.03061 76 1' I 1.03061 1.03137 1.03 213 1.03290 1.03368 1.03447 1.03528 75 1 ) 1.03528 1.03609 1.03 691 1.03774 1.03858 1.03944 1.04030 74 1 3 1,04030 , .1.04117 1.04 206 1.04295 1.04385 1.04477 1.04569 73 1 J 1.04569 1.04663 1.04 757 1.04853 1.04950 1.05047 1.05146 72 1 I 1.05146 1.05246 1.05 347 1.05449 1.05552 1.05657 1.05762 71 i< ) 1.05762 1.05869 1.05 976 1.06085 1.06195 1.06306 1.06418 70 2( 3 1.06418 1.06531 1.06645 1.06761 1.07479 1.06878 1.07602 1.06995 1.07727 1.07115 1.07853 69 2 I 1.07115 1.07235 1.07356 68 2. I 1.07853 1.07981 1.08109 1.08239 1.08370 1.08503 1.08636 67 2 J 1.08636 1.08771 1.08907 1.09044 1.09183 1.09323 1.09464 66 2^ 1 1.09464 1.09606 1.09750 1.09895 1.10041 1.10189 1 . 1033S 65 2. > 1.10338 1.10488 1.10640 1.10793 1.10947 1.11103 1.11260 64 2 3 1 11260 1.11419 1.11579 1.11740 1.11903 1.12067 1 . 12233 63 2 7 1.12233 1 . 12400 1.12568 1.12738 1.12910 1 . 13083 1 . 13257 62 2 ? 1.13257 1 . 13433 1.13610 1.13789 1.13970 1.14152 1 . 14335 61 2 3 1.14335 1.14521 1.14707 1.14896 1.15085 1.15277 1.15470 60 3 3 1.15470 1.15665 1.15861 1.16059 1.16259 1 . 16460 1.16663 59 3 I 1.16663 1.16868 1.17075 1.17283 1.17493 1.17704 1.17918 58 3 2 1.17918 1.18133 1.18350 1 . 18569 1.18790 1.19012 1.19236 57 3. J 1.19236 1 . 19463 1.19691 1 . 19920 1.20152 1.20386 1.20622 56 3^ I 1.20622 1.20859 1.21099 1.21341 1.21584 1.21830 1.22077 55 3. 5 1.22077 1.22327 1.22579 1.22833 1.23089 1.23347 1.23607 54 3 3 1.23607 1.23869 1.24134 1.24400 1.24669 1.24940 1.25214 53 3 J 1.25214 1.25489 1.25767 1.26047 1.26330 1.26615 1.26902 52 3^ ? 1.26902 1.27191 1.27483 1.27778 1.28075 1.28374 1.28676 51 3< 3 1.28676 1.28980 1.29287 1.29597 1.29909 1.30223 1.30541 30 4( 3 1.30541 1.30861 1.31183 1.31509 1.31837 1.32168 1.32501 49 4 I 1.32501 1.32838 1.33177 1.33519 1.33864 1.34212 1.34563 48 4 I 1.34563 1.34917 1.35274 1.35634 1.35997 1.36363 1.36733 47 4. J 1.36733 1.37105 1.37481 1.37860 1.38242 1.38628 1.39016 46 4^ 1 1.39016 1.39409 1.39804 1.40203 1.40606 1.41012 1.41421 45 60' 50' 40' 30' 20' 10' 0' De- Cosecants grees Table of Natural Secants and Cosecants 117 Natural Secants and Cosecants (Continued) De- Cosecants grees C 10' 20' 30' 40' 50' 60' oo 343.77516 171.88831 114.59301 85.94561 68.75736 57.29869 89 1 57.29869 49.11406 42.97571 38.20155 34.38232 31.25758 28.65371 88 2. 28.65371 26.45051 24.56212 22.92559 21.49368 20.23028 19.10732 87 3 19.10732 18.10262 17.19843 16.38041 15.63679 14.95788 14.33559 86 4 14.33559 13.76312 13.23472 12.74550 12.29125 11.86837 11.47371 85 5 11.47371 11.10455 10.75849 10.43343 10.12752 9.83912 9.56677 84 6 9.56677 9.30917 9.06515 8.83367 8.61379 8.40466 8.20551 83 7 8.20551 8.01565 7.83443 7.66130 7.49571 7.33719 7.18530 82 8 7.18530 7.03962 6.89979 [6.76547 6.63633 6.51208 6.39245 81 9 6.39245 6.27719 6.16607 6.05886 5.95536 5.85539 5.75877 80 10 5.75877 5.66533 5.57493 5.48740 5.40263 5.32049 5.24084 79 11 5.24084 5.16359 5.08863 5.01585 4.94517 4.87649 4.80973 78 12 4.80973 4.74482 4.68167 4.62023 4.56041 4.50216 4.44541 77 13 4.44541 4.39012 4.33622 4.28366 4.23239 4.18238 4.13357 76 14 4.13357 4.08591 4.03938 3.99393 3.94952 3.90613 3.86370 75 15 3.86370 3.82223 3.78166 3.74198 3.70315 3.66515 3.62796 74 16 3.62796 3.59154 3.55587 3.52094 3.48671 3.45317 3.42030 73 17 3.42030 3.38808 3.35649 3.32551 3.29512 3.26531 3.23607 72 18 3.23607 3.20737 3.17920 3.15155 3.12440 3.09774 3.07155 71 . 19 3.07155 3.04584 3.02057 2.99574 2^7135 2.94737 2.92380 70 20 ' 2.92380 2.90063 2.87785 2.85545 2.83342 2.81175 2.79043 69 21 2.79043 2.76945 2.74881 2.72850 2.70851 2.68884 2.66947 68 22 2.66947 2.65040 2.63162 2.61313 2.59491 2.57698 2.55930 67 23 2.55930 2.54190 2.52474 2.50784 2.49119 2.47477 2.45859 66 24 2.45859 2.44264 2.42692 2.41142 2.39614 2.38107 2.36620 65 25 2.36620 2.35154 2.33708 2.32282 2.30875 2.29487 2.28117 64 ' 26 2.28117 2.26766 2.25432 2.24116 2.22817 2.21535 2.20269 63 27 2.20269 2.19019 2.17786 2.16568 2.15366 2.14178 2.13005 62 28 2.13005 2.11847 •2.10704 2.09574 2.08458 2.07356 2.06267 61 29 2.06267 2.05191 2.04128 2.03077 2.02039 2.01014 2.00000 60 30 2.00000 1.98998 1.98008 1.97029 1.96062 1.95106 1.94160 59 31 1.94160 1.93226 1.92302 1.91388 1.90485 1.89591 1.88708 58 32 1.88708 1.87834 1.86990 1.86116 1.85271 1.84435 1.83608 57 33 1.83608 1.82790 1.81981 1.81180 1.80388 1.79604 1.78829 56 34 1.78829 1.78062 1.77303 1.76552 1.75808 1.75073 1.74345 55 35 1.74345 1.73624 1.72911 1.72205 1.71506 1.70815 1.70130 54 36 1.70130 1.69452 1.68782 1.68117 1.67460 1.66809 1.66164 53 37 1.66164 1 . 65526 1.64894 1.64268 1.63648 1.63035 1.62427 52 38 1.62427 1.61825 1.61229 1.60639 1.60054 1.59475 1.58902 51 39 1.58902 1.58333 1.57771 1.57213 1.56661 1.56114 1.55572 50 40 1.55572 1.55036 1.54504 1.53977 1.53455 1.52938 1.52425 49 41 1.52425 1.51918 1.51415 1.50916 1.50422 1.49933 1.49448 48 42 1.49448 1.48967 1.48491 1.48019 1.47551 1.47087 1.46628 47 43 1.46628 1.46173 1.45721 1.45274 1.44831 1.44391 1.43956 46 44 1.43956 1.43524 1.43096 1.42672 1 42251 1.41835 1.41421 45 60' 50' 40' 30' 20' 10' 0' De- grees Secants «f t^'- liA^biJuA :3;;>p-"i r PART II STRENGTH OF MATERIALS AND STABILITY OF STRUCTURES JI THAS Introduction 121 INTRODUCTION EXPLANATION OF SUBJECT-MATTER AND NOTATION 1. Introduction to Part II Subject-Matter of Part II. In the twenty-nine chapters of Part II are given the necessary rules, formulas and data for computing the strength and stability of all ordinary forms of building-construction, whether of wood, steel, concrete or masonry, and in fact of all but the more intricate problems of steel construction, with which few architects care to cope, and which, indeed, are more especially within the province of the engineer. The Rules and Formulas have been reduced to their simplest forms, and, in general, require only an elementary knowledge of mathematics to understand them. The appUcation of the formulas is explained and in most cases their derivation, and it is believed that the formulas, constants and working stresses are representative of conservative and approved contemporary practice. Constants and "Working Stresses. In the use of constants for the strength of materials, the authors and editors have been guided by tlie practice of leading structural engineers, by the available records of tests and by their own expe- rience of many years as practicing and consulting architects and engineers. The varying conditions of building-construction have been taken into account and an attempt made to adapt the values to the practical conditions usually governing such construction. Every possible precaution has been taken to prevent the misapplication of rules and formulas and to insure absolute safety without undue waste of materials. Tables. Much thought and labor have been expended on the preparation of the numerous tables, to insure their accuracy and to arrange them in the most convenient form for use by architects and builders. Many of these tables were computed by the authors and editors, all have been carefully verified, and it is believed that they may be used with perfect confidence. In all cases, un- less otherwise noted, they give the same values that would be obtained by using the formulas specially referred to, while they afford a great saving of time and labor and reduce to a minimum the danger of errors in making the necessary computations. Treatment of the Subject. Owing to the nature of the subjects treated and the large number of pages required to include them all in one book of refer- ence, some forms of construction, such as foundations, masonry and fire-proof construction, roof-trusses, etc., are treated rather briefly. The intention is to give the data needed for immediate use rather than a complete discussion of all the principles involved. Those who wish a more complete treatise on masons* work in general are referred to the ninth edition of Kidder's Building-Con- struction and Superintendence, Part I, Masons' Work.* References are made in the different chapters to various other books and periodicals containing more complete information on some of the subjects. * This has been recently completely rewritten, by Professor Thomfts Nolan, and the data in it supplements the matter of Kidder's Pocket-Book. .ri«»}imi It.' 122 Explanation of Subject-Matter and Notation Part 2 2. Explanation of the Notation or Symbols used in Part II * Besides the usual mathematical signs and characters in general use, the fol- lowing abbreviations and symbols are frequently used: A area of cross-section; also, a constant used in Chapter XVI and equal to Ms the safe unit fiber-stress; a, b, c, . . . m, etc., known or given distances; b breadth, as of beams; C coefficient of strength; c normal distance from neutral axis of cross-section of beam to most distant fiber in same; d diameter, as of rivets; exterior diameter; depth, as of beams; di interior diameter; E modulus of elasticity; Ea, Ec modulus of elasticity for steel and concrete respectively (as in re- inforced concrete); e total deformation or change in length, as in a bar; F shearing-modulus of elasticity; f maximum deflection for a beam; h distance between parallel axes for moments of inertia; / moment of inertia about a line; I/c section-modulus or section-factor; / polar moment of inertia; J' polar moment of inertia of bolts about shaft-axis; K total elastic resistance of a bar; resilience, work; also, a factor or con- stant used in formulas for reinforced concrete; / length; span of a beam; M bending moment; Afmax maximum bending moment; Ml, Mi, etc., bending moments at supports of beams; Mr or SI /c moment of resistance; n number of loads, spans, etc.; P external force; concentrated load; Pi, Pi, Pi, etc., concentrated loads on beams; P pitch of rivets; eccentricity of load on .column; ratio of cross-section of .steel to cross-section of beam (reinforced concrete); r radius of curvature; radius; radius of gyration; ratio of Ea for steel to Ec for concrete (reinforced concrete); R\, Rf, Rz, etc., reactions at the supports of a beam; S unit stress, with subscripts /, c and s for unit stress in tension, com- pression and .shear, respectively; Sh buckling resistance in webs of steel beams; Sh horizontal unit shearing-stress in beams; Se elastic limit; Sf modulus of rupture, or computed flexural strength; /i, h, etc., thicknesses; V vertical shear; W weight of a bar or beam; total uniform load on beam (may include weight of beam) ; wl total uniform load on a beam (may include weight of beam); w weight of a cubic unit of material; uniform load on beam, per lineal unit of length; * See, also, page 3 of Part I. Explanation of the Notation or Symbols 128 X, y, 2, variable distances; a, /3, etc., material constants; constant depending upon material; 6 an angle. Greek letters are used generally for signs of operation, for abstract numbers and for angles. 2 is employed as a symbol of summation. The following are the Greek letters most in use: a Alpha, /S Beta, e Epsilon, rj Eta, Theta, k Kappa, X Lambda, jj, Mu, V Nu, IT Pi, p Rho, cr Sigma, T Tau, Phi, xj/ Psi, w Omega. Note. In a few places in the book it has been considered necessary or advis- able by some of the associate editors to give a different meaning to one or more of the above symbols or to introduce different symbols for the meanings given in the list, but in all such cases the new symbols or meanings have been very clearly indicated. The term breadth is used to denote the horizontal thickness of a beam or the smaller dimension of the cross-section of a rectangular column, post or strut, and is always measured in inches unless expressly stated otherwise. The term depth denotes the vertical height of a beam or girder, and is always measured in inches unless expressly stated otherwise. The term length denotes the distance between supports and is always meas- ured in feet unless expressly stated otherwise. Abbreviations. In order to shorten the formulas, the tabulations of computa- tions, etc., and throughout the text generally, to economize space, the units of measurement are generally abbreviated. For example, foot and feet are abbre- viated, ft; inch and inches, in; pound and pounds, lb; square, sq; cubic, cu; linear, lin; inch-pound or inch-pounds, in-lb; foot-pound or foot-pounds, ft-lb; ounces, oz; horse-power, h.p.; gallons, gal; etc.; and no periods are placed after these abbreviations, except at the ends of sentences. Where the word ton is used in this volume, it always means the net ton of 2 ooo lb. 124 Terms Used in Arcbitectural Engineering Chap. 1 CHAPTER I EXPLANATION OF TERMS USED IN AECHITECTURAL ENGINEERING By THOMAS NOLAN PROFESSOR OF ARCHITECTURAL CONSTRUCTION, UNIVERSITY OF PENNSYLVANIA 1. De^nitions of Some of the Terms Used in the Mechanics of Materials * Terms Used in Architectural Engineering. The following terms fre- quently occur in discussions of the principles of architectural engineering and an understanding of their meaning is essential. Mechanics is the branch of physics that treats of the phenomena caused by the action of forces on material bodies. Applied Mechanics treats of thp law3 of mechanics as applied to construc- tion in the useful arts, as in beams, trusses, arches, etc. Mechanics of Materials treats of, the jefTects of forces in causing changes in the size and shape of bodies. , . Rest is the relation that exists between two points when the straight line joining them does not change in length or direction. A body is at rest relatively to a point when any point in the body is at rest relatively to the first-mentioned point. Motion is the relation that exists between two points when the straight line joining them changes in length or direction, or in both. A body moves rela- tively to a point when any point in the body moves relatively to the first-men- tioned point. Force is that which changes, or tends to change, the state of rest or motion of the body acted upon. It is a cause regarding the essential nature of which • we are ignorant. In the mechanics of materials we do not deal with the nature of forces, but only with the laws of their action. Equilibrium is that condition of a body in which the forces acting upon it balance or neutralize each other; or, it is that condition of a force-system in which the resultant of the force-system is zero. Statics is the branch of Mechanics that treats of the conditions of equilibrium. It is divided into: • (i) Statics of rigid bodies. (2) Statics of practically incompressible fluids. In building-construction we have to deal only with the former. Structures are artificial constructions In which all the parts are intended to be in equilibrium and at rest relatively to each other, as in the case of a bridge- truss or roof-truss. They consist of two or more solid bodies, generally called PIECES or MEMBERS, which are connected at different parts of their surfaces called JOINTS. * In addition to the terms defined here, many others are defined in the chapters of OJart II, and especially in Chapters VI, IX, X, XIV, XV, XVI, XX and XXIV. Definitions of Terms 125 In general there are three conditions of equilibrium in a structure. (i) The external forces acting upon the whole structure must balance each other. These forces are: (a) The weight of the structure; {b) The loads it carries; (c) The upward supporting forces, reactions or resistances under or around the foundations. (2) The forces acting upon each piece of the structure must balance each other. These forces are, for each piece: (a) The weight of the piece; (b) The loads it carries; (c) The resistances or reactions at its joints. (3) The forces acting upon each of the parts into which any piece may be supposed to be divided must balance each other. The Stability of a Structure requires the fulfilment of conditions (i) and (2), that is, the abihty of the structure to resist the displacement of any of its parts. The Strength of a Piece or Member consists in the fulfilment of condi- tion (3), that is, the ability of a piece to resist breaking. The Stiffness of a Piece or Member consists in the ability of a piece to resist bending. The Theory of Structures is divided into two parts: / , (i) That which treats of strength and stiffness, dealing only with single pieces and generally known as the strength of materials or the mechanics OF materials, before defined. (2) That which treats of stability, dealing with the structures themselves. Stress is an internal force that resists a change in shape or size caused by external forces. When the applied external forces reach certain intensities the internal stresses hold them in equilibrium. The Intensity of a Stress is measured by the unit stress, (See Unit Stress.) The intensity of the stress per square inch on any normal surface of a solid is the total stress divided by the area of the section in square inches. Thus, if a bar 10 ft long and 2 in square has a load of 8 000 lb pulling in the direction of its length, the stress on any normal section of the bar is 8 000 lb; and the intensity of the stress per square inch is 8 000 lb/4 sq in = 2 000 lb per sq in. Deformation.* When a solid body is acted upon by an external force an alteration takes place in the volume and shape of the body, and this alteration is called the deformation. In the case of the bar given above, the deformation is the amount that the bar stretches under its load. The Ultimate Strength is the highest unit stress a piece of material can sustain and it is the unit stress at or just before rupture. The Working Unit Stress is the ultimate stress divided by the factor of safety . The Safe Load is the load that a piece can support without exceeding the working unit stresses. * In mechanics the term strain is now synonymous with the term deformation. On account of the tendency to confuse the terms strain and stress the term deformation, is used to denote change in shape and the term strain is omitted in all discussions in the Pocket-Book. 126 Terms used in Architectural Engineering Chap. 1 The Factor of Safety * of a piece of material under stress is the ratio of the ultimate strength of the material to the actual unit stress on the section- area; or it is the number by which the ultimate unit stress must be divided to give the working unit stress. In designing a piece of material to sustain a cer- tain load, it is required that it shall be perfectly safe under all circumstances; and hence it is necessaj*y to make an allowance for any defects in the material, workmanship, etc. It is obvious, that, for materials of different composition, different factors of safety are required. Thus, steel being more homogeneous than wood and less Hable to defects, does not require as high a factor of safety. Again, different kinds of stresses require different factors of safety. Thus, a long wooden column or strut requires a higher factor of safety than a wooden beam. As the factors of safety thus vary for different kinds of stresses and materials, the proper factors for the different kinds of stresses and conditions are given in considering the resistance of the various materials to those stresses under varying conditions. The Unit Stress is the stress on a unit of section-area, and is usually expressed in pounds per square inch. (See Intensity of Stress.) Dead Loads and Live Loads. The term dead load means a load that is applied and increased gradually and that finally remains constant, such as the weight of a structure itself. The term live load means a load that is applied suddenly and causes vibra- tions, such as a train traveling over a railway bridge. It has been found by experience that the effect of a live load on a beam or other piece of material has twice the destructive tendency of a dead load of the same magnitude or intensity. Hence a piece of material designed to carry a live load should have a factor of safety twice as large as one designed to carry a dead load. The load due to a crowd of people walking on a floor is usually considered to produce an effect which is a mean between that of a dead load and a live load, and a suitable factor of safety is adopted accordingly. In municipal -ordinances and laws relating to the allowable loads for floors, the loads to be supported by the floors, exclusive of their inherent construction and stationary fixtures, are gen- erally referred to as the live loads no matter of what they may consist; but the term does not have the exact significance given to it by many engineers and as explained in the paragraph above. The Modulus of Rupture or Computed Flexural Strength is the value of the UNIT fiber-stress S, computed from the flexure-formula M = Sl/c, when a beam is ruptured under a transverse load. Its value is intermediate between the ultimate tensile and compressive strengths of a material. The Elastic Limit is that unit stress at which the deformation of a piece of material begins to increase in a faster ratio than the applied loads. It is sometimes called the elastic strength. The Modulus of Elasticity or Coefficient of Elasticity. In treatises on physics this is often called Young's modulus. It we take a bar of any elastic, material, say one inch square, of any length, and secured at one end, and to the other apply a force, say a certain number of pounds P, pulling in the direction * The ELASTIC LIMITS of materials must be considered in deciding upon working unit stresses and in forming a judgment of the security of materials under stress. When the elastic limit is considered the actual allowable unit stress is made a certain percentage of 'it, as 35 or 50%, according to varying conditions. Both ultimate strengths and elas- tic limits must be taken into account in practice. But the use of the factor of safkty, as determined by the old method, is still a great help in the study and application of the principles of the mechanics of materials, and is used frequently in the Pocket-Book. Classification of the Principal Stresses 127 )l" ii s length, we shall find by careful measurement that the bar has been stretched 1 elongated by the action of the force. If we divide the total elongation e, 1 inches, by the original length / of the bar, in inches, we shall have cjl, the ; .n ELONGATION €, or the elongation of the bar per unit of length; and if ,we J i vide the unit stress S, developed (that is, in this case, the external force P, divided by the area of the cross-section A, or P I A) by this ratio we shall have what is known as the modulus of elasticity, E. Expressed in symbols and rj A by equations, E = Sle = — r—. Hence, we may define the modulus of elas- ejl ticity as the ratio of the unit stress to the unit deformation. Another definition is, the force which would elongate a bar of i sq in in cross-section to double its original length, if that could be done without exceeding the elastic limit of the material. This is evident from the above equation; for if ^ = i and e= I, E will equal P. These formulas apply only when the unit stress S or P/A is less than the elastic limit of the material, e is an abstract number, because e and / are both linear quantities, and hence E is expressed in the same unit as S, that is, in pounds per square inch. As an example of one method of determining the modulus of elasticity of any material the following illustration is given: ^ Suppose we have a bar of wrought iron, 2 in square and lo ft long, securely fastened at one end, and to the other end we apply a tensile force of 40 000 lb. This force causes the bar to stretch, and by careful measurement we find the elongation to be 0.0414 in. As the bar is 10 ft, or 120 in long, if we divide 0.0414 by 120, we shall have the elongation of the bar per unit of length. Per- forming this operation, we have as the result, 0.00034 in. As the bar is 2 in square, the area of cross-section is 4 sq in, and hence the stress per square inch is TO 000 lb. Dividing 10 000 by 0.00034, we have, as the modulus of elas- ticity of the bar, 29 400 000 lb per sq in. This is the method generally employed to determine the modulus of elasticity of iron ties; but E can also be deter- mined from the deflection of beams, and it is in that way that its values for most woods have been found. The modulus of elasticity is used in the deter- mination of the stiffness of beams. The Moment of a Force with respect to an axis is the product obtained by multiplying the magnitude of the force by the shortest distance from the axis to its line of action. The shortest distance is called the lever-arm of the force. The moment of the force is the measure of the tendency of the force to cause rotation about the axis. (See Chapter VI and IX.) The Center of Gravity of a body is the point in the body through which the resultant of the forces exerted by gravity upon all the particles of the body passes. A body may be balanced upon a point placed above or below the center of gravity, because the resultant of any number of forces may be held in equilibrium by an equal and opposite force. Another definition of the center of gravity of a body or bodies is: a point such that there is no tend- ency TO rotation about any axis drawn through it. (For center of gravity of surfaces, lines and solids, see Chapter VI.) 2. Classification of the Principal Stresses Caused in Bodies by External Forces Tension is the stress that resists the tendencj^of two forces acting away from each other to pull apart two adjoining planes of a body. Compression is the stress that resists the tendency of two forces acting toward each other to push together two adjoining planes of a body. 128 Terms Used in Architectural Engineering Chap. 1 Shear is the stress that resists the tendency of two equal parallel forces act- ing in opposite directions to cause two adjoining planes of a body to slide one on the other. Torsion is the stress that resists the tendency of forces to twist a body. Combined Stresses. Parts of structures are often acted upon by several external forces which develop stresses of different character, such as combined flexure and compression, flexure and tension, flexure and torsion, shear and axial compression or tension, torsion and compression, etc. General Requirements 129 CHAPTER II FOUNDATIONS By DANIEL E. MORAN MEMBER 0F_ AMERICAN SOCIETY OF CIVIL ENGINEERS 1. Definition of the Word and Terms Used Definitions. The word Foundation is derived from the Latin verb fundare meaning to establish or lay the base, bottom, keel or foundation of anything. The English word is used in the broadest possible way to describe the base, physical or otherwise, on which anything is supported, and in technical language it may be used to describe any part of a structure on which a subsequent oper- ation or construction is superimposed. Thus a plaster wall may be called the foundation for a fabric to be stretched thereon and the fabric in turn becomes the foundation for various coats of paint or other decorations. More specifi- cally and in relation to a building or other complete structure the word founda- tion is unfortunately applied indiscriminately (i) to construction below grade, such as footing courses, cellar walls, etc., forming the lower section of the struc- ture; (2) to the natural material, the particular part of the earth's surface on which the construction rests; and (3) to special construction such as piling or piers used to transmit the loads of the building to firm substrata. In view of the indefinite meaning of the word it is advisable to use it either to distinguish work below grade, or below the tier of beams nearest to grade, from work above grade. In even a still more restricted sense, it might include only the work below the cellar or basement-floor to rock or other solid foundation-bed. (See Chapter II, Subdivision 29, Chapter III, Subdivision 2, and Water- proofing for Foundations, Part III.) The Foundation-Bed. The natural material on which the construction rests is called the foundation-bed. Walls, piers and columns below grade are called, in general, foundation walls, piers and columns to distinguish them from similar construction above grade and occasionally those only below the basement-floor are so called; the lower portions of walls, piers or columns which are spread to provide a safe base will be called footing courses. 2. General Requirements The Object of Foundations. The object to be borne in mind in designing any foundation is to provide a safe and permanent base for the superstructure such that the movement of the base and of the superimposed structure shall be the least possible and shall result in the least possible damage to the structure. To fully meet the above requireiAents the design and construction should ful- fill the following conditions: (i) The Materials of Construction should be proof against all deteriorating influences, or, if any of the materials arc liable to deterioration they should be permanently protected. (2) Stresses and Future Changes. No part of the foundation-structure should, under any combination of loadings, be stressed beyond safe limit*, and the possibility of future additions or changes in the superstructure, or of a change in the use of the building, should be kept in mind. 130 Foundations Chap. 2 (3) The Load on the Natural Bed should be kept within the safe limit for such *naterial, under the worst conditions to which it may be exposed. In fixing this limit the amount of settlement allowable will in many cases determine the limit rather than the safe ultimate bearing capacity. (4) Adjoining Excavations. The possible danger to the structure or to the stability of the foundation-bed from adjoining excavations or other disturbing causes should be guarded against as far as possible. Physical Conditions of the Site. In order to meet the above requirements, the design should be suited to the physical conditions existing at the location. The architect or engineer should personally examine the site. He should secure all available information relative thereto and, if necessary, should make borings and tests so as to secure reliable information on which to base his design for the foundation. The first step is, therefore, a detailed and exhaustive study of the «ite to determine the characteristics of the foundation-bed on which the struc- ture is to rest. 3. Geological Considerations Character of the Foundation-Bed. A knowledge of geology is of material assistance in many cases in making a proper estimate of the character of the foundation-bed. While it is not proposed in the hmits of this chapter to go into any general geological discussion the following notes may be of value in assisting the architect to determine whether any given deposits can be rehed upon as affording a stable foundation-bed. Broadly speaking, as the location of the building may be in any part of the world, so the materials encountered may belong to any one of the many geological formations forming the surface of the earth. For practical purposes, however, the materials met with are roughly divided into rock, or materials other than rock, roughly defined as earth. 4. Composition and Classification of Rocks Composition of Rocks. Rocks, and the earthy deposits derived from rocks, >ire composed of various minerals of which many hundred kinds are known, each varying from the others in some particular of chemical composition, form of crystallization or other characteristic. A rock or an earthy deposit may con- sist almost entirely of a single mineral, but it is usually composed of several distinct minerals or of mixtures of minerals. The principal classes of rock- forming minerals are: (i) The Silica Minerals, composed of silica (Si02) in different forms; (2) Silicates or combinations of silica, with various metallic bases; • (3). Calcareous Minerals composed of calcite or carbonate of lime (CaCOs) and its combinations. (i) Silica Minerals are different forms of the oxide of silicon, Igiown as Silica. In the crystalline state silica is known as Quartz. This is the most abundant of all Vninerals. Owing to its hardness and insolubihty it resists decomposition and abrasion better than the minerals with which it is associated and grains of it form the principal constituent of sandy deposits. In finely comminuted particles it forms a part of most of the clays. Flint, Chert, Agate, etc., are non-crystalline varieties of silica. Silica also forms the cementing material in many sandstones and other rocks. (2) Silicates or combinations of silica with various bases are second in im- portance only to quartz. Composition and Classification of Rocks 131 Feldspar, an important constituent of granite and other igneous rocks, is a silicate of alumina with potash, soda or lime. When exposed to the action of water it slowly decomposes, forming silicate of alumina, the base of clay. The decomposition of granite results in the formation of clay and crystals of quartz and mica. The mica is very slowly affected and the quartz is practically un- changed. Mica. The various mica minerals are silicates of alumina, with potash and other constituents. All varieties are soft and spUt into thin elastic plates. Small particles of mica are frequently found in sand. Hornblende and Augite are sihcates of lime, magnesia, iron and alumina and are of frequent occurrence. Chlorite, Talc and Soapstone Travertine are hydrated silicates formed from other silicates by a chemical change in which a certain amount of water is absorbed. These minerals are soft and have a soapy feel. Special care should be taken in building foundations on rock of this character to guard against any sliding on the foundation-bed or between parts of the foundation-bed. (3) Calcareous Minerals. The following are the principal calcareous miner- als: Calcite (CaCOs), carbonate of lime, when pure and crystallized, is known as Iceland Spar. It is soluble in water containing CO2. Calcite in varying de- grees of purity forms limestone and marbles. As a result of its solubihty caverns and voids are frequently found in limestone. Dolomite is a carbonate of lime and magnesia. It forms the so-called Dolo- MiTic Limestones, which are less soluble than the calcite hmestone. Selenite, Gypsum, Alabaster, Anhydrite, Aragonite and Apatite are other and less important lime-minerals. Classification of Rocks. Rocks are classified not only according to the minerals of which they are composed, but also according to the way in which they have been formed, as: (i) Igneous Rocks, which have soHdified from a molten condition; (2) Sedimentary Rocks, which have been formed under water by mechani- cal pressure or by cementation due to chemical or organic proceesses; (3) Metamorphic or Plutonic Rocks, which have changed from their original character as igneous or sedimentary rocks. (i) Igneous or Plutonic Rocks are not truly stratified. They may be granular, crystalline or glassy in texture. Granite, syenite, basalt, trap, etc., are examples. Lava, pumice and obsidian are volcanic products, as are also certain deposits of mud and ash. With the exception of volcanic ash and mud, the igneous rocks are enduring and are not liable to present any unforeseen weak- ness as foundation-beds. (2) Sedimentary Rocks are composed of sand, clay and other materials resulting from the breaking down of the original igneous rocks. These materials were deposited in horizontal beds generally by settling from water, and the con- solidation into rock was generally affected under water by chemical, mechanical or organic action. The resultant rock-masses are stratified as a result of their constituent materials having been deposited in layers. As sand and clay are the most abundant products of rock-decomposition, so the sedimentary rocks are most frequently siliceous (sandy) or argillaceous (clayey). Sandstone is composed of grains of sand cemented together by silica, oxides of iron, or carbonate of lime. The durability of sandstone depends on the solu!» 132 Foundations Chap. 2 bility of the cementing material. Carbonate of lime being soluble, sandstones containing it as cementing material yield to the weather and are not as reliable as sandstones having silica or iron oxide as cementing material. Argillaceous Rocks contain clay with fine sand, mud, etc., and while shale and some other varieties are compact and hard when first uncovered, they are liable to deterioration when exposed to frost, water and other disintegrating agencies. Limestone is composed more or less of carbonate of lime derived from the calcareous skeletons of marine animal and vegetable organisms. The char- acter of limestone varies greatly. In so-called fossiliferous limestones, fossils of shells or corals indicate clearly its origin, but in other Hmestones there are no fossils or other indications of the organic origin of the calcareous material. Admixtures of sand, clay, or other impurities may make it difficult to distinguish certain limestones from sandstones or shales. Dolomite is a limestone containing a high percentage of magnesia. Hydraulic Limestone is a limestone containing clay. Chalk is a soft limestone composed of the fine shells of minute marine organ- isms. In general, the purer the limestone the more soluble it is and the greater the danger from fissures or caverns due to the action of water. (3) Metamorphic or Plutonic Rocks are rocks which have been formed from sedimentary or igneous rocks by heat, compression, or moisture, acting alone or in combination. Thus by heat from a nearby intrusion of molten rock, limestone is changed into a crystalline marble. The general effect of meta- MORPHISM is to produce a hard or durable rock. Quartzite, a metamorphosed sandstone, is a crystalline rock of great hardness and durability. Slate is a hard dense rock, sometimes with a well-defined tendency to split into thin plates. It has been formed by metamorphic action from clayey shales and is generally durable, but liable to slide along planes which are sometimes par- allel to the cleavage, or along seams which are not parallel to the cleavage. Gneiss is a "laminated metamorphic rock that usually corresponds mlner- alogically to some one of the plutonic types." * There are many varieties, best classified in accordance with the igneous rocks to which they most nearly corre- spond in composition. Some varieties resemble granite, but the laminated or striped aspect is generally characteristic. They are generally compact and durable. Schists are similar to gneiss but are more finely foliated or striped. In mica- schist there are layers or foliations composed of fine grains or plates of mica. Mica-schists are liable to decomposition and it frequently happens that excava- tions have to be carried to great depths through decomposed rock of this char- acter before solid rock is encountered. The material resulting from the decom- position of this rock contains fine grains of mica and other fine material and, when wet, acts as quicksand. Rock as a Foundation. All rock, if sound and not liable to slippage, is proverbially a solid foundation and capable of supporting any weight which a building is likely to impose on it. Care should be taken that rock liable to disintegration is protected from the weather, water-action, or other disintegrat- ing influences. 5. Geology of Earthy Material Earth and Soil. Materials other than rock, resulting from the disintegra- tion of rock-masses, are broadly classed as earth. The word soil, when used * Kemp. Geology of Earthy Matenal 133 to designate any earthy material not rock, is a misnomer, in that the idea oi FERTILITY, or the lack of it, is conveyed when the word soil is used. The agencies producing the disintegration of the rock masses which form or underlie the entire surface of the earth, are various, but for the purpose of this chapter they may be defmed as (i) chemical and (2) mechanical. (i) Chemical Agencies. By chemical action or decomposition, a rock- mass of great strength and hardness and of complicated mineralogical structure may disintegrate into a noncoherent mass of elementary minerals. Thus a f eldspathic granite under the combined action of water and varying temperature disintegrates, the crystals of feldspar changing chemically and forming the hydrated silicate of aluminum known as clay, while the crystals of quartz, mica or hornblende, being more resistant to chemical action, retain their chem- ipal identity but become detached particles of sand. (2) Mechanical Agencies. By the mechanical agencies, such as the action of frost, moving water or ice, fragments of rock are detached from the ledge of which they originally formed part and are subsequently transported, by the action of glaciers or streams, or by the wave-action in bodies of water. The attrition between the materials thus roughly thrown about breaks up the rock- masses into smaller and smaller pieces without altering the composition of the rock-material. Flowing Water, As flowing water more readily transports small particles than large ones, the larger pieces of rock move intermittently during periods of storm or flood and are deposited as soon as the velocity of the water falls; while the smaller particles are held in suspension longer and, as the velocity of the stream falls, are deposited in the order of their size, the largest first. The rapid upper courses of streams and rivers in mountainous regions constantly roll and grind together the materials in their rocky beds, the heavy masses being moved slowly. The attrition between the fragments forms gravel and sand which are washed down stream to be deposited, as the current slackens, first as BEDS of gravel, then as sand-bars, and finally, in the slow-moving lower levels, as beds of silt and alluvium. Glaciers and Glacial Deposits. The action of glaciers is similar to the ac- tion of streams. Glacial deposits, the so-called glacial drifts, are composed of sand, clay, gravel and boulders but, in general, there is a noticeable differ- ence between glacial deposits and deposits made by rivers or streams. In glacial deposits the boulders frequently exhibit groovings or scratches on their faces and the edges and surfaces of the boulders are generally sharp, so that a boulder may appear as if it had been recently fractured. They rarely exhibit the smooth, water-worn and rounded surfaces found on boulders formed by water-action. Moreover, the glacial boulders may be found singly, or unas- sociated with other boulders in a deposit of sand or gravel. The deposit differs from a river-deposit in that there is no classification as to size; the boulders may occur on the surface or may be disseminated as if by accident through the sand and gravel forming the body of the deposit. Such glacial deposits partake of the character of a rough artificial fill without the stratification or classification as to size which is characteristic of river-deposits. In glacial moraines or dump- ing grounds it not infrequently happens that the surface-water finds underground passages forming so-called sink-holes. A line of glacial deposits extends across the continent of North America from Long Island westward. The southern limits can be determined by reference to geological maps. Glacial and River-Deposits Distinguished. It is important to distinguish between glacial and river-deposits, because, while the occurrence of glacial boulders gives, in general, little or no information as to the character and value 134 Foundations Chap. 2 of the surrounding deposits, the occurrence of boulders, on the other hand, in river-deposits is generally an indication that the bed of which they form a part has been thoroughly consohdated as a result of the river-action which formed it; and, also, because such deposits generally extend down to rock or to some com- pact material which at the time the deposit was made was capable of resisting the action of rapidly flowing water. Wave-Action on Lakes and Along Coast-Lines is constantly working on the materials composing the beach. Rock-masses are broken away from cliffs and ground together, producing boulders, gravel and sand. The sand, being carried more readily by the tidal currents, is deposited in the more sheltered loca- tions and forms beaches, while the larger rock-masses remain near the point of origin in bars and reefs. Beds of Sand, Gravel and Boulders deposited by the action of waves oh the shores of seas or lakes are not necessarily constant in character and tests should be made to determine the character of the material underlying such BEACH-FORM^VTiONS. In large river-valleys where the general formation is composed of silt or other fine material little reliance should be placed on the occurrence of beds of gravel, even if such beds extend over large areas. Tests should be made to determine that such beds are not underlain by less trust- worthy materials. Where tributary streams discharge into large valleys they may deposit bars of sand, gravel and boulders on top of the silt, peat, or other materials formerly deposited by the main river. (See page 136.) The general topographical conditions should serve as an indication of danger in such cases. Results of Chemical and Mechanical Action. As a result of the fore- going brief description of the agencies at work it may be seen that ice, wave and stream-action ahke tend to disrupt rock-masses and to produce boulders, gravel, sand and finer materials. The ultimate result of the combination of chemical action and mechanical action is to reduce the hardest rocks to the finest sand, the most impalpable clays, silts and muds; and the action of wind, wave and moving water is to classify such materials in deposits of grains of uniform size. 6, Materials Composing Foundation-Beds Classification and Definitions. The following list includes the materials which are most frequently encountered, with their definitions. Rock (solid rock, bed-rock, or ledge). Undisturbed rock-masses forming an undisturbed part of the original rock-formation. Decayed Rock (rotten rock). Sand, clays and other materials resulting from the disintegration of rock-masses, lacking the coherent qualities but occupying the space formerly occupied by the original rock. Loose Rock. Rock-masses detached from the ledge of which they originally formed a part. Boulders. Detached rock-masses larger than gravel, generally rounded and worn as a result of having been transported by water or ice a considerable dis- tance from the ledges of which they originally formed a part. Gravel. Detached rock-particles, generally water-worn, romided and inter- mediate in size between sand-particles and boulders. Sand. Non-coherent rock-particles smaller than H in in maximum dimen- sion. Characteristics of the Materials of Foundation-Beds 135 Clay. The material resulting from the decomposition and hydration of feld- spathic rocks, being hydrated silicate of alumina, generally mixed with powdered feldspar, quartz and other materals. Hard-Pan, Any strongly coherent mixture of clay or other cementing material with sand, gravel, or boulders. Silt. A finely divided earthy material deposited from running water. Mud. Finely divided earthy material generally containing vegetable matter and deposited from still or slowly moving water. Dirt. Loosely used to describe any earthy material. Soil. Earthy material capable of supporting vegetable life and generally limited to material containing decayed vegetable or animal matter. Mould. Earthy material containing a large proportion of humus or vegetable matter. Loam. Earthy material containing a proportion of vegetable matter- Peat. Compressed and partially carbonized vegetable matter. 7. Characteristics of the Materials of Foundation-Beds Solid Rock, or, as it is locally known, bed-rock, or ledge, is proverbially a solid foundation. The harder rocks, such as granite, trap, slate, sandstone, limestone, etc., are all capable of carrying the load of any ordinary structure. The softer rocks, among which may be classed the shales, shaley slates and certain marley Hmestones and clay stones, should not be loaded with more than IS tons per sq ft unless they are tested for greater loads. In all cases where foundations are to be placed on what is supposed to be solid rock, care should be taken to determine whether or not the supposed solid consists of a detached portion and, also, in case the bedding-planes of the rock are inclined, if there is danger from a slip of the layer forming the foundation-bed. (See pages 139 and 146 as to side-slope locations.) Decayed Rock. Certain igneous or metamorphic rocks such as granites, gneisses, etc., frequently disintegrate, forming so-called rotten rock or decayed ROCK. The decayed rock is generally found in conformity with the ledge of which it originally formed a part. It may retain the stratification, color and markings of the solid rock, but as a result of the disintegrating effect of water or other agents, it has lost the solid character of the original rock. When struck with a hammer it does not give the characteristic ringing sound of sohd rock. It may be fairly compact and hard, or so^soft as to be readily excavated with pick and shovel. The amount of such disintegrated rock overlying the solid rock varies greatly; in some cases the removal of a few inches will disclose the solid rock, in other cases the layer of decayed rock may be many feet in thick- ness. Test-borings in rotten rock give samples similar to the samples from solid rock; so that it frequently happens that while the foundations are planned for solid rock the excavations disclose a thick layer of rotten rock. In such cases, if it is impracticable to carry the footings down to solid rock, it may be necessary to increase the size of the footings or to adopt some other expedient. Loose Rock. Where a rock-mass detached from the ledge of which it orig- inally formed a part is encountered it must not be loaded in excess of the safe capacity of the material by which it is surrounded. If the voids between ad- joining pieces of loose rock are completely filled in with hard-pan, compact gravel, sand, or clay, the loading may be the same as for the filling-in material but care should be taken to determine that no voids exist. In natural rock* 136 Foundations Chap. 2 fills, as in artificial rock-fills, it may happen that large voids exist between the rock-masses, forming passageways for streams of water, in which case there is extreme danger of settlements. Boulders, Gravel and Sand. Boulders are rock-masses which have been transported by water or ice-action. Boulders are sometimes found dissemin- ated through sand and clay and in such cases the load should be limited by the safe load of the material in which they are found. At other times boulders are found in beds, packed closely together, with the interstices filled in with gravel, sand, or clay. In such cases it is usually safe to assume that no further con- solidation of the mass is likely to take place. If the bed of boulders extends to rock, they will safely sustain any load wliich will not crush them. Gravel. The name gravel is given to rock-particles larger than sand and smaller than the rock-masses known as boulders. If compact, and if no underlying bed of poorer material exists, gravel forms a most desirable founda- tion-bed, equal to sand or boulders in supporting power and not as Hable to be disturbed by adjoining excavations or pumping operations. If cemented it may partake of the quality of hard-pan or rock. Care, however, should be taken to determine whether or not the bed of gravel has been deposited over a layer of silt or ciuicksand. It is possible for this dangerous condition to exist. (See page 134.) Sand. Sand is composed of comminuted rock-material. As quartz is the most abundant rock-mineral and as its hardness and insolubility make it highly resistant to disintegrating action, it will be found to be the principal constituent of most deposits of sand or sandy material. Grains of mica, feldspar, garnet and other minerals are frequently found. Sand is described as being fine, MEDIUM, or coarse, according to the size of the grains of which it is composed. Coarse Sand may contain particles of gravel, but after eliminating all particles which will not pass a screen with 4 meshes to the inch it will be found that a large proportion of the remaining material is too coarse to pass a 40-mesh sieve. Fine Sand, on the other hand, may contain no particles which will not pass A 20-mesh sieve, and a considerable proportion which will pass a loo-mesh sieve. Very Fine Sand is frequently mistaken for clay and, indeed, generally does contain some clay, as clay generally contains fine sand. Uniform Sand is sand in which there is relatively a small variation in the size of the particles. Balanced Sand is sand in which the size of the particles varies from large to small and in which there is no great difference in the numbers of particles of each size. Clean Sand contains no clay or loam, but a pure sand containing a large per- centage of fine particles is often considered to be not clean. Sharp Sand is clean sand containing coarse, angular grains. When firmly grasped in the hand it gives a note, due to the particles slipping over each other. Sharp sand is generally esteemed for use in mortar, although it requires more cement to fill the voids and, in the writer's opinion, is not as desirable as a clean, rounded sand. Rounded or Buckshot Sand is composed of rounded grains not cemented together. Quicksand. This term is popularly used to describe any fine sand, or mix- ture of fine sand and clay, which, when wet, forms a soft, unstable material. Characteristics of the Materials of Foundation-Beds 13^ In the popular mind quicksand is supposed to have some mysterious and peculiar qualities which result in a tendency to flow like water and to suck in animate and inanimate objects. These manifestations are connected with various theories as to the composition of quicksand, some persons insisting that quick- sand must contain Hakes of mica or some slippery mineral, others that the particles must be extremely fine or spherical in shape, while others contend that there must be a certain proportion of fine clay with the sand. The fact is that any uncemented sand, when subjected to the action of moving water, will move and that any sand moving as the result of the action of water becomes a quicksand. The finer the sand the more readily it is affected by a current of water, so that fine sands are more trouljlcsome than coarse sands. A coarse sand, having large voids, permits the flow of a certain amount of water through them; if this flow has not sufficient velocity to disturb the particles of the sand, the sand can be drained without moving it. In a fine sand, having very small voids, a similar flow of water will cause the whole mass to move and there is great difficulty in draining it without producing a current sufficient to cause it to move or flow. Excavations in Quicksand are made difficult by the tendency of the sand forming the sides of the excavation to flow into the excavation; and even if the sides of the excavation are protected, it not infrequently happens that the bottom of the excavation will lift, that is, there will be a movement of material from points outside of the line into the excavation, the movement in general following a curved line, and carrying the sand, under the protected side walls of the excavation. In such cases some advantage may be gained by surround- ing the excavation with driven wells and draining the soil by continued pumping through sand; in other cases, wooden or steel sheeting may be driven to a point below the depth to which the excavation is to be carried, or to some underlying layer of impervious material, in which case the sheeting will act as a coffer-dam to cut off the flow of material. Such sheeting, however, must be practically watertight, as extremely fine sand, when in the condition of quicksand, will flow through very small apertures. Quicksand as a Foundation-Bed is objectionable on account of the danger of its moving or flowing, in case it finds any outlet such as would be afforded by an adjoining excavation. Cases are known where excavations have permitted the escape of quicksand and resulted in the settlement of buildings at a very considerable distance. Such settlements have occurred not only when the footings themselves rested on quicksand, but also when they were on a stratum of coarse sand, gravel or clay of good quality which rested on an underlying stratum of quicksand. Pockets of Quicksand. It frequently happens that pockets of fine sand are found in deposits of mixed character. Where such pockets are small in extent the fine sand may be removed and the spaces filled with concrete. Where the pockets are larger it may be necessary to carry piers through them to a better foundation-bed, to drive piles, or to resort to other expedients. Fine Dry Sand is readily converted into quicksand by the addition of water, which fact should be carefully borne in mind in considering the load on fine sand, as a material which in dry weather is apparently safe, may be, in wet weather, an extremely dangerous one. It is frequently stated that confined quicksand is a perfectly reliable material on which to found a building. While this, as a theory, cannot be controverted, it is a dangerous assumption to act on because of the impossibility of providing that the fine sand shall be always confined. Variation in the Size of Grains of Sand. The accompanying diagram (Fig. 1) shows graphically the results of sieve- tests on characteristic ^sands. 138 Foundations Chap. 2 The dash-line curve (i) is an average, giving the results of sieve-tests on several so-called quicksands; the full-line curve (2) gives the result of sieve-tests on a natural sand which would be classed as a good building sand; the dot-and-dash curve (3) gives the result of sieve-tests on a fine beach sand remarkable for the / 1 iBX^^^f^'^^ — ->^. \ \ 10 Mesh 20 30 50 80100200 Fig. 1. Graphical Illustration of Results of Sieve-tests on Sands uniformity of the size of its grains. For purposes of comparison and in order to show the variation in sands which appear to be substantially the same, the dotted curve (4) has been added. This shows the result of tests on a bank sand apparently as coarse as sand (2), but containing a much larger percentage of fine particles between 0.015 and 0.0055 in in diameter. Fine sand frequently contains a considerable proportion of clay. A chemical analysis of a so-called QUICKSAND from the down-town section of New York City, reported on to the writer by Dr. C. F. McKenna, is as follows: Mark: "Commercial Cable" Silica 73 . 76% Alumina and oxide of iron 18 . 52% Lime i . 60% Magnesia i . 48% Loss on ignition 2 . 26% A rational analysis shows the following composition: Quartz, as given 39 .38% Clay and mica, as given 23 . 94% Feldspathic detritus 36 . 68% On the other hand, a sample of extremely fine sand from Michigan, of which 75% passed a 200-mesh sieve, appears to be absolutely pure quartz. Clay. When pure, clay consists of hydrated silica of alumina, the product of decomposition of feldspar. Ordinarily, various impurities are mixed with the clay, so that, in general, clay may be considered a mixture of hydrated silica of alumina with other finely divided minerals. Mixtures of clay and sand are found, varying from beds of nearly pure clay to beds of nearly pure sand, and no definite classification can be made. The Effect of Moisture on Clay. Clay as generally found in excavations is in a plastic condition due to the presence of moisture, the amount of water present varying greatly. On drying, the clay shrinks in volume and loses its plasticity, becoming a firm and coherent mass resembling in consistency a sun- drie4 brick. Large masses of clay are liable to crack into a number of sma^U, Characteristics of the Materials of Foundation-Beds 139 fragments during the process of drying, as the result of the shrinkage in volume. When these lumps are crushed or ground the clay becomes an extremely fine or impalpable powder. The loss in volume due to the change in the condition of the clay from a moist, plastic state to a thoroughly air-dried condition may amount to from io% to 20% of the original volume. Compact, moist clay is impervious to water in the sense that water cannot pass through it as it would through porous sand; but when clay is exposed to water the clay gradually absorbs the water, so that eventually the entire mass becomes saturated and softened by the water. Clay as a Foundation-Bed. Clay is not a reliable material on which to found a building; first, because of the plasticity of the clay when wet, and secondly, because of its tendency to shrink on losing its contained moisture. The plasticity of clay increases with the percentage of contained water, so that a firm, hard clay may be converted into a Hquid puddle by being agitated in the presence of a sufiicient amount of water. The plasticity is also increased by pressure, as is shown by the action of clay in a brick-machine. Clay, in a founda- tion-bed under moderate pressure imposed on it by the footings of a structure, frequently develops this quality of plasticity, the clay moving out from be- neath the footing and causing serious settlements and displacements of the footings. This movement of the clay may be a local movement, as referred to each footing, in which case the clay flows from beneath the footing laterally toward the side and then upward, causing the surface of the adjacent ma- terial to rise and to form so-called bulges or waves. If this motion is uniform from the center toward the sides, the footing may settle vertically, but more frequently the movement will not be symmetrical and the footing will settle more on one side than on the other. Such movements of the clay may be re- duced or prevented in some cases by the simple device of loading the surround- ing soil, as, for example, by a concrete floor. Movements of Clay Foundation-Beds. The movement of the clay may be on a larger scale, amounting to a general flow of the clay underlying the entire building toward some point where the pressure on the clay is less than the pressure resulting from the load of the building. Such general movements are more likely to happen if the building is located on the side of a hill, so that the clay finds some outlet at a point below the level of the footings. It fre- quently happens that adjoining excavations cause settlements to buildings at a considerable distance, by affording an outlet to a bed of clay. As noted else- where (pages 135 and 146), beds of clay resting on inclined strata of rock or other material are liable to move downward, sometimes with a slow, almost imperceptible movement, and at other times forming landslides of greater ol less magnitude. Protection of Clay Foundation-Beds. Where the foundation-bed is clay, or sand with a considerable amount of clay, it is advisable to protect it from water-action, so far as is possible, by a system of drains surrounding the site of the building and by diverting the surface-water from the building: Care should be taken in back-filling around exterior walls to prevent any accumula- tion of water which might affect the material under the footing. The neglect of such precaution has frequently resulted in serious settlements during, or inmiediately after, construction. Mud, Silt, Peat and Other Unstable Materials. When the site of a structure is in a marsh or on materials which are not capable of affording a safe foundation, the only alternative is to resort to the use of wooden piles, concrete piles, or piers sunk to an underlying and firmer strata. Such special 140 Foundations Chap. 2 constructions will be described under Subdivisions 27, 28 and 29, which consider wooden piles, concrete piles and piers sunk by the coffer-dam or caisson methods. Filled Ground. All artificial fills and some natural fills are liable to a more or less uniform but continuous settlement or shrinkage due to the gradual con- solidation of the material of which the fill is composed. Where the fill is of solid rock this consohdation may amount to little, but where the fill is of earth, and especially where it is of mixed materials, the shrinkage will not only be large in amount but will continue for a very long period. For example, where dirt has been thrown on top of a rock-fill each rain-storm will wash some of the dirt into the voids in the rock-fill, and this action will be continuous until all of the voids are filled in. Any vegetable matter, or other matter liable to decay and shrinkage in volume, will increase the total shrinkage of the mass. Cer- tain natural deposits, such as beds of peat or soils containing vegetable matter, are apt to shrink in volume from the same causes. When it is necessary to found a building on such material it is inevitable that the footings will settle with the mass, notwithstanding that the unit load on the foundation-bed is so small as to be negligible. In such cases the settlements may be vertical and uniform; but if the depth of the fill under one part of the building is greater than the depth under another part, the settlements will not be uniform, as the shrinkage in the fill will, in general, be in proportion to the depth of the fill. No important building should be founded on such material and, wherever possible, the footings should be carried down through the filled-in material to some more reliable underlying stratum. 8. Allowable Loads on Materials of Foundation-Beds General Considerations. Owing to the infinite number of variations in the. materials encountered and the conditions affecting the reliability of such mate- rials, no general or definite rule can be given, and every case should be carefully investigated before determining the allowable unit load on the foundation-bed. If the material and conditions are uniform over the entire site of the building a uniform unit load may be used, but in practice it is frequently found that entirely different conditions exist under different portions of the same building and in such cases great care must be exercised in determining the unit loads. For instance, one section of a building may rest on rock and another section on a light compressible soil or on a clay of doubtful stability. In such cases the unit load on the compressible soil or on the clay must be reduced as much as possible so as to reduce the differences in settlements between the two sections of the building to a minimum. If the entire building were on a compressible soil a very considerable settlement might be allowable, provided it was uniform; but in this particular case it is known beforehand that the part of the building on rock will not settle at all and that any settlements of other parts of the building must be considered as unequal settlements, and, as such, liable to pro- duce cracks and distortions in the building. It is also important to remember that a certain unit load on compressible soil may be safe, in that the soil will ultimately safely support that load; but the use of that load would nevertheless be inadvisable on account of the excessive settlements. In this connection it may be said that a considerable settlement, if uniform, in a detached building may be a matter of no importance; but that where a building is to be con- structed in contact with adjoining buildings or where additions are to be made to an existing building, the total amount of settlement becomes a matter of prime importance. These and other considerations, such as the character of Allowable Loads on Materials of Foundation-Beds 141 the proposed building and of the material composing it, should be borne in mind in selecting the unit load for any given foundation-bed, irrespective of the allowed pressure as given by building codes or by examples quoted in this chapter. Safe Loads on Rock. The safe unit load on rock may often amount to more than the crushing strength of brickwork or stone masonry, and in nearly all cases any material worthy of the name of rock is capable of supporting from 15 to 30 tons per sq ft. Safe Loads on Sand, Gravel and Boulders. When compact and con- fined laterally these materials are capable of supporting 10 tons per sq ft with- out appreciable settlement. It rarely happens, however, that it is advisable to load such materials with more than 5 tons per square foot. . Safe Loads on Loose Sand. By loose sand is meant sand which has not been thoroughly compacted and which may settle by its own weight inde- pendently of a superimposed load. All such materials should be tested and the unit load reduced in accordance with the result of such tests. Loads on Fine Sand or Quicksand. It is probable that fine sand, if absolutely confined, will sustain as heavy a load as coarse sand, but in view of the fact that if afforded the slightest opportunity it is liable to lateral displace- ment, it is inadvisable to found any structure on such material. When it is imperative to place the footings on such material the unit load should be reduced as much as possible and preferably to less than 2 tons per sq ft, and great care should be taken to connect all footings with a continuous layer of concrete so as to prevent any flow of material into the cellar-excavation.. Care should be taken, also, that any sumps, pump-pits, drainage-arrangements and sewerr connections for the building do not permit the escape of any quicksand- Safe Loads on Hard-pan and certain cemented sands partaking of the nature of hard-pan may approximate rock in hardness and reliability. Such materials, however, are liable to soften if exposed to water. If these materials, when uncovered, are dry, experiments should be made to determine how they behave when wet, and if the level of the water in the ground is liable to change so as to reach the layer of hard-pan, the load should be correspondingly reduced. Cemented hard-pan containing gravel has been frequently loaded with more than 10 tons per sq ft. ' Care should be taken, however, to determine that the layer of hard-pan is continuous to a solid substratum, as it frequently happens that layers of hard-pan and fine sand or clay are deposited alternately. • Safe Loads on Clay. Ordinary clay should not be loaded with more than 2 tons per sq ft. If soft and plastic, a load of 2 tons per sq ft may produce inadmissible settlements. Clay containing so large a percentage of sand as to lose its plasticity has been loaded with from 4 to 6 tons per sq ft without undue settlements, and sand or gravel containing sufficient clay to act as a cementing material will partake of the qualities of hard-pan. In general, however, clay is the most dangerous of all the materials on which structures are founded and the unit load should be reduced to a minimum and every precaution taken to prevent the flow of material. Undue reliance should not be placed upon load- ing-tests of clayey soils. It is probable that a loading on a large area which will produce a movement of the clay will on a small area have no effect, so that it is unsafe to rely upon the results of a test-load applied to an area smaller than the actual supporting areas to be used. From the experience gained in the construction of large buildings in Chicago which were floated on clay, the allowable unit load has been generally reduced to 2 tons per sq ft and, in the writer's experience, a load of less than 2 tons per sq ft on clay has pro- duced settlements varying from nothing to J2 in._ 142 Foundations Chap. 2 9. Unit Loads on Foundation-Beds Allowed by Building Codes Variations in Building Codes. Table I gives an outline of the requirements of dififerent cities as to the allowable unit loads on different materials, as contained in their respective building codes or regulations. While the allowed loads given may in some cases be based upon actual experience in the respective localities, it is more Ukely that they are based upon the individual experience of the authors of the codes, or are copied from other codes. The architect should, therefore, not place too much reUance on the unit loads allowed by the codes, but should investigate each case and determine for himself the proper allowance to be made. • Special Requireijients of Some Building Codes. * The Boston code pro- vides that "the footing shall not overload the material on which it* rests." The New Orleans code limits the maximum load to i 400 lb per sq ft, the entire city being on an alluvial-delta formation. The Buffalo code limits the load on soil to 3H tons per sq ft; if the soil is other than hard clay or gravel the supporting areas "shall be extended as directed." The Cincinnati code limits the load on soils inferior to those listed, to i ton per sq ft. 10. Investigation of the Site General Considerations. To determine the character of the materials which will be encountered at the level of a foundation-bed, the architect should first get as definite information as possible from others as to their experience in mak- ing excavations and erecting buildings in that vicinity. In some localities the subsoil conditions are uniform over large areas, while in other localities impor- tant variations may occur within the limits of a city lot. Abrupt changes in surface-topography, changes in the character of the surface-soil or in the native vegetation, proximity to old or existing water-courses are suggestive of sub- surface irregularities. In such cases, and in all cases where there is any doubt as to subsurface conditions, a sufficient number of exploratory borings or test- pits should be made to determine the facts. This exploratory v/ork should go below the level of the proposed footings, should determine the ground-water level and insure that no unsuspected layer of quicksand or other unsuitable material underlies the foundation-bed. The methods in use for such explora- tions are as follows: Testing in an Open Pit. For shallow work an open pit is the most sat- isfactory method as it allows actual inspection of the undisturbed material over a considerable area. If the excavation is in firm material, no sheet-piling or other protection may be required; but if in flowing material, or if carried deeper than adjoining footings, timber sheeting or steel sheeting should be employed. If the excavation is carried no deeper than the proposed footing-level, the under- lying material should be tested by one of the methods hereinafter described. Testing with Steel Bars. A steel bar with a pointed end or a steel pipe provided with a steel point is driven to the required depth by a maul or by a falling weight. While no samples can be obtained by this crude method, it may determine the ground-water level, and a little practice will enable one to distinguish sandy from clayey soils by the sound given out when the bar is twisted. The difficulty of driving is a rough index of the degree of the com- pressibility of the soil. It should be remembered, however, that any dry material will afford considerable resistance to the bar and that a small boulder will stop it; so that not much reliance can be placed on a report that the BAR DROVE HARD Or that it REACHED ROCK. • As codes change, quotations must be verified. Investigation of tiie Site 143 Table I. Loads in Tons per Square Foot on Foundation-Beds Allowed by Building Codes* Character of foundation-bed 4 s .2 s -t-J O "> 'B -b ^ ^ g ^ d d a c c 6 03 d a 1 6 1 J5 Alluvial soils Vz >^ 3 I Firm dry loam 3 I 2-3 I 21/2 3 I Soft clay I 2 Ordinary clay 2 Good solid natural clay Clay in thick beds, always dry 4 2 Clay in thick beds, moderately dry Dry clay 3 3 4 3 4 { 3h 2-3 t8 3-4 \ 4 iK' 21/2 4 3 4 3 4 Hard clay 4 Dry hard clay 4 Soft wet clay and sand 2 2 Ordinary clay and sand together in layers; wet and springy Moderately dry clay and sand 2 2 2 3 2 Stratified clay and stone 4 V2 3'i I Soft wet sand Wet sand I Fine sand firm and dry 3 3 2-3 4 2^ 3 3 2 Fine sand, compact and well ce- mented 4 3 Coarse compact sand 4 4 Very firm coarse sand 4 4 3-4 4 4 4 2 Stiff gravel 4 4 6 3-4 t8 4 4 3H 5 8 Compact sand and gravel, well ce- 6 Gravel and coarse sand, well ce- mented 8 8 Hard-pan ' o-iS Hard shale, unexposed 8 8 10 20 Rock ti5 8 * Some values may change with the changes in building codes, t In caissons. 144 Foundations Chap. 2 Testing with Post-Hole Diggers. For shallow explorations in easily ex- cavated material, the ordinary post-hole digger used for fence-posts, or the longer and larger ones used for telegraph-poles, can be used to depths of from 6 to 8 ft. Testing with Augers. In clay or similar material a single or double-twist carpenter's auger welded to a long rod, or the so-called pod-auger may give satisfactory samples. In gravel or loose and sandy material, the sides of the hole fall in, clogging the operation and destroying the samples. Testing by Dry-Pipe Borings. A pod-auger or the above-described carpenter's auger can be used inside a casing-pipe. The pipe should be driven so as to keep close to the bottom of the hole made by the auger. The pipe prevents the material falling from the sides of the hole and the auger ex- cavates and loosens the material ahead of the pipe and facilitates driving. The above methods are not generally successful for deep holes or where gravel, boulders or compact material interferes with driving the pipe. Testing with Wash-Pipes. For test-borings over lo ft in depth the method in most frequent use is the wash-pipe method. In this method a wrought-iron or steel pipe known as the casing-pipe or drive-pipe is driven .into the earth in much the same way as in the dry-pipe method, but the driving of the pipe is facilitated by the use of a jet of water. The lower end of the casing-pipe is provided with a hollow shoe or reinforcement, slightl}^ larger in outside diameter than the casing. This serves to protect the pipe from injury in driving through gravel or hard-pan, and forms a hole slightly larger than the diameter of the casing. The upi^er end of the drive-pipe is protected from injury by an annular drive-head which has a threaded part fitting the thread on the casing-pii>e and a central hole to admit the jet-pipe. The jet-pipe is small enough to permit It to freely enter the casing-pipe. The lower end is contracted so as to produce a jet-action. The upper end is connected with a water-supply which must be under considerable pressure. The driving-mechanism consists of a cast-iron weight with a central vertical hole large enough to admit the wash-pipe, and stationary verticals supix>rting a block-and-fall and an arrangement which releases the weight when it has reached a predetermined height. With this arrangement, water is continuously pumped through the jet-pipe, the length of which is regulated so that the jet-action loosens the material immedFately below or AHEAD of the casing. Some of the jetting water returns to the surface out- side of the casing and thus lubricates the surface in contact with the outside material. Another part of the water returns to the surface in the annular space between the wash-pipe and the casing, carrying with it particles of the material loosened by the jet. As the jet loosens and washes away the material immediately below the casing, the latter is driven deeper by repeated blows of the ram, the driving and washing being carried on at the same time. The operation is thus continuous until the top of the casing comes close to the sur- face of the ground, when the hammer drive-head and hose-connection are re- moved to permit additional lengths of pipe to be added to the casing and wash- pipes, after which the hose-connection, drive-head and hammer are replaced and the operation is resumed. Borings can be made by this method to great depths in sand, clay or other suitable material. Samples of the material encountered are obtained by settle- ment from the water returning between the jet-pipe and wash-pipe. These samples are not accurate samples as the water separates the materials. The finer particles do not settle readily and the large and heavy particles may not be brought up at all. It is evident that such samples do not give any index as to the solidity of the original deposits. If large gravel, hard-pan or boulders Loading-Tests 145 are encountered there will be great difBculty in forcing the casing past such obstructions. In such cases a drill-rod is sometimes substituted for the jet and the obstruction broken up into small pieces or pushed to one side; but in either case it is difficult to get any sample or real indication of the character of the obstruction. If solid rock or large boulders are encountered, no further progress can be made with the casing and no sample can be obtained by this method. Resort must then be had to one of the core-boring methods described hereafter, to determine the character of the obstruction encountered. Testing by Core-Borings. These borings can be made through rock or boulders and accurate samples obtained. In all core-boring methods the hole is made by rotating a pipe-like tool which makes an annular cut in the rock and leaves a cylindrical core which is afterwards detached and brought to the surface by a gripping-tool called the core-lifter. The cutting is done in different ways. Diamond Bits are annular rings fitted on the lower end of the hollow pipe used as the rotating drill-rod and furnished with a number of small diamonds arranged so as to form cutting-edges, which, when rotated in contact with the rock, gradually wear away the required annular space. The diamonds employed are known as bort, black diamonds, or carbons, and their only resemblance to the stones used by jewelers is the necessary hardness. The carbons ara skillfully secured in a soft metal bed, in sockets drilled in the bit, and they pro- ject below the bit and also sufficiently inside and outside to insure the cutting of a groove large enough to provide clearance for the bit and the attached drill- rod or pipe. Shot-Drills. The same result is arrived at by the shot-drill method, by wliich particles of chilled cast iron called shot are used as the abrasive or cutting- agent. The shot is poured loose into the hole and forced against the rock by the rotating bit. Efficiency of Drill-Methods. Both of the drill-methods mentioned are ex- pensive, but as they are the only methods which will give an accurate sample in rock, one or the other must be employed where the accurate determination of rock is necessary. If the core corresponds to the known underlying rock- formation and the rock is continuous for a length of from 8 to 20 ft, it is safe to assume that solid rock has been reached. If, however, the core is of differ- ent rock from the known underlying formation, the probability is that a boulder has been encountered. If the core is not continuous it may indicate that there are seams in the rock or that there are detached rock-masses. The above- described methods are used after the overlying earth has been penetrated by one of the pipe-sinking methods previously described. The Results of Pipe-Borings are frequently misleading and misinterpreted, and great care should be taken to compare the samples with samples obtained from other borings where the exact character of the materials tested is known. 11. Loading-Tests General Considerations. Loading-tests of the materials forming the foun- dation-bed are made to assist in determining its safe bearing capacity. It is not known to what extent the supporting power of a given soil varies with the area subjected to the unit load, and tests on small areas are not a safe guide for the safe load on large areas. On account of the expense involved, tests on large areas are rarely made, the usual test being on an area of about i sq ft. The test should be made on an undisturbed portion of the foundation-bed, leveled to receive the test-load, and for a space around the area tested, so that the 146 Foundations Chap. 2 adjoining material is not reinforced or surcharged by a bank of unexcavated material. The load should be applied with the least possible jar or movement of the surface in contact with the material of the foundation-bed. Explanation of Methods. A convenient arrangement for this purpose consists of a vertical timber or post carrying a platform to receive the test-load, and having four horizontal guys at the top to keep the post in a vertical position. The bottom of the post, forming the loading-area should be approximately 12 by 12 in and its exact area should be known. The platform, sufficiently strong to support the load to be applied, should be concentric with the post and as close to the bottom of the post as practicable. The load may be pig iron, cement or sand in bags, or any other convenient material. The guys should be not less than four in number, should be attached to the top of the post and should lead horizontally so as not to pull up or down on it. Levels should be read to a point on the post above or below the load, as may be most convenient. The load should be applied gradually and with the least possible jar, care being taken, also, to keep the loading uniform on opposite sides of the post, which should be always vertical. Levels should be taken at frequent intervals during the applica- tion of the load. The level observed when the platform is first in position may be taken as zero and successive settlements referred to it. When the proposed unit load has been reached, no additional load should be added until no further settlement is observed. After this, first 50 and later 100% overload may be added and the total and periodic settlements observed. If the settlement under a test-load of twice the proposed load is not excessive, the test is considered satis- factory. 12. Topographical and Special Conditions Excavations over Inclined Strata. In case the site of a proposed building is on a slope, and especially if the slope is steep, there may be danger from a slip of the material forming the foundation-bed. (See, also, page 135.) This may occur if there is an inclined plane of separation between layers of the under- lying rock, or between the rock-surface and the material overlying the rock, or if inclined strata or beds of clay occur below the foundation-bed. Slips in such locations are the more likely to occur if water is present, as the water increases the weight of the soil and also reduces the coefficient of friction against sliding. Such conditions are frequently indicated by the appearance of springs or springy ground below the site. Where the base of the slope reaches a stream or river there may be danger from the washing away of banks which have been supporting the side slopes of the valley. In the case of deep valleys with steep clay banks, or in any location where landslides have been known to occur, great care should be taken to extend the footings to a bed that will not be affected by any landslide. It sometimes happens that there is a slow, con- tinuous and general movement of the material forming the side slope of a valley toward the center of the valley; but such conditions are rare, fortunately, as, in general, no adequate protection is possible. In certain limestone formations there is danger from natural caves formed in the limestone by the action of water. Excavations Near Navigable Waters. When buildings are located near navigable waters, it not infrequently happens that dredging-operations at a considerable distance induce a flow of fine sand or clay from strata underlying the adjoining banks. This has occurred where the existence of such strata was not suspected. This danger is especially to be guarded against in marshy localities adjoining waters which are, or may be, used as navigable streams, or in locations near the water-front where it is Ukely that docks will be constructed, Topographical and Special Conditions 147 Damage from Adjoining Excavations. Common and statute laws make general provision for the protection of property-owners against damage result- ing from' the acts of others in making such excavations; but an owner has usu- ally no control over such operations, whether on adjoining properties or streets, and in general will prefer the assurance of safety to the possibility of damage to his building and the expense and uncertainty of a lawsuit. While it is not always possible to guard fully against the effects of adjoining excavations, and while the expense of so doing is not always justifiable, due consideration should be given to the matter. The following suggestions, therefore, may be of value. Depth of Adjoining Excavations. Footings adjacent to property-lines or situated where there is a probability of future additions to a building, or footings of a building which adjoins property liable to become the site of building- operations, should go down at least as deep as the maximum probable depth of the adjacent work. In estimating these probabilities, the character of the loca- tion should be taken into account. In medium-priced residential sections footings are rarely carried much deeper than lo ft, a sufficient depth for a cellar of medium height below grade. In high-priced residential sections it is not un- usual to have both a basement and a cellar, in which case a depth of cellar below grade up to 20 ft may be expected. Cellars for residences are rarely carried below 10 ft, if in reaching that depth the excavation goes below the water-level. In fact, a high water-level discourages deep excavation, not only on account of the increased difficulty and expense of excavation but also on account of the expense of waterproofing. In business sections, especially in sections of high ground-rents, there is an increasing tendency toward deep cellars, especially in boiler-rooms, where clear heights of 20 ft and over are de- sirable for modern water-tube boilers. The basements are frequently rentable at high figures for restaurants, vaults, stores, etc., so that in many instances the entire mechanical equipment of the building is housed below the basement in a subbasement and boiler-pit, the excavation for which extends down at least 30 ft and in special cases 60 ft below the curb; and this notwithstanding the fact that the water-level may be only from 10 to 20 ft below the curb. Sewers and Trenches as Affecting Foundations. In cities and towns consideration should be given to the possibility of the construction of trenches in the streets. For the majority of localities it will be sufficient to consider the probable depth of a sewer of the proper depth to serve the street. In other localities it will be necessary to consider the broader question as to the proba- bility of deeper excavations for trunk sewers, subways, etc. As such construc- tions are controlled by broad topographical considerations, no general rules can be given and the local city engineer should be consulted. Foundations Near Mines, Shafts, Wells, Etc. In mining-districts local authorities should be consulted as to danger from the caving of old mine- workings. No adequate provision can be made in the foundation against such widespread caving or subsidence as may result from mining-operations. In some cases, successive falls of rock-fragments from the roof may gradually fill the voids left by the mining-operations, as the loosely piled fragments of the roof will occupy more space as fill than they did as part of the solid roof-mass. It sometimes happens that where the original working is deep, progressive falling of the roof fills all voids, and no surface-settlements result. In other cases the overburden may settle as a solid mass, causing a settlement at the surface equal to the thickness of the old working. Precautionary measures may involve the filling in of the workings, a subject outside the limits of this chapter. In the case of an important building a local mining engineer should be consulted or, if pessibbi the location of the building changed to a safer site. Mining* 148 Foundations Chap. 2 SHAFTS, DEEP WELLS, SHAFTS FOR TUNNELS, etc., may causc disturbances of the soil, but in such cases the settlement is generally concentrated around the shaft or well, and buildings at a reasonable distance are slightly affected, if at all. Foundations Near Tunnels and Trenches for Railroads and Subways. In large cities the necessities of transportation are increasingly calling for con- struction of underground railroads, tunnels and subways. Such constructions are generally planned to follow streets. Railroad tunnels for trunk lines can be expected to follow direct lines to centrally located stations or terminals along routes which avoid, as far as possible, difficulties of construction, condemnation of real estate and damage to high-priced properties. The depth of excavation will generally be as shallow as practicable. Where the tunnel has to dip to pass underneath some obstruction, the approach-grades will probably be at the max- imum or limiting grade of the particular section. Relation of Subways to Foundations of the Most Important Build- ings. In subway-construction for rapid-transit passenger service, the lines can be operated on sharper curves and with steeper grades than would be used in the case of a trunk-line railroad. This permits the lines to follow closely the lines of the city streets. For traffic-considerations the locations will, in general, follow the principal arteries of surface traffic, and stations will, in gen- eral, be located at intersections of important streets, where there is the greatest congestion of population. As such conditions are caused by the existence of trade-centers, and call for the construction of high buildings, it may readily be seen that the heaviest and most important buildings are most likely to have their foundations affected by the construction of a subway in their immediate vicinity. Where there is reason to apprehend the construction of such sub- ways or TUNNELS, information should be sought as to the probable depth of the excavation, the depth at which water is encountered, the character of the material, the probable width of the construction as affecting the use of sidewalk vaults, and the method to be employed in making excavations. Where the excavations for such tunnels and subways have been carried below the levels of the footings of adjoining buildings, as in Baltimore, Boston, Brooklyn, Chicago and New York City, buildings along the routes have been seriously affected. Such results have not been limited to any particular methods used in the con- struction of the tunnels, as even where the excavations were wholly, or partly, in rock, serious damage has been done. 13. Loads Coming on the Footings The Loads to be Considered in the design of the footings of a structure are: (i) The Dead Loads, or the loads due to the actual weight of the completed structure, ready for occupancy. (2) The Live Loads, or the loads due to the occupancy of the building and also to the weight of snow on the roof. (3) The Wind-Loads, or the vertical components of stresses in the structure, produced by wind-pressure. (i) The Dead Load. The dead load of any structure can be accurately calculated. If the structure is properly designed the part of the dead load supported by each element of the foundation can be definitely stated. The total dead load becomes effective as soon as the building is completed, and remains constant thereafter unless additions or alterations are made to or in the struc- ture. Loads Coming on the Footings 1^9 (2) The Live Load. The live load of any structure is the sum of the roof- loads and floor-loads. In designing the roof and floors the calculations for strength are based on an assumed unit load which should be the maximum load, consistent with the probable use of the structure, to which any portion of the roof or floor may ever be subjected. The assumed live load is, therefore, prob- ably greater than the average load for the entire area of a floor or the entire area of the roof. Moreover, as it is improbable that conditions of maximum loading will ever occur simultaneously on the roof and on all of the several floors, it is probable that the maximum load on the footings will be less than the sum of maximum loads on the roof and on the several floors. " The Minimum Live Load for an unloaded building is zero. The Actual Live Load will vary from zero to a maximum, which maximum will generally be less than the total assumed Hve load. The Ratio of the Probable Maximum Live Load to the Assumed Live Load varies in different buildings, so that no table or general rule can be given. The Probable Maximum Live Load. As it is important to know, approxi- mately at least, the maximum live loads to which the footings will be subjected, and as this maximum may be only a fraction of the assumed live loads, the architect should make a careful study of the conditions of loading to which the building will probably be subjected and estimate the probable maximum live load for the entire building. Data for Estimating Live Loads. (See, also, Chapter XXI, pages 718 to 721.) In estimating the probable maximum live loads for different uses, the following notes may be of value. In certain buildings the assumed unit load- ing on the roof and on parts of each floor may be reached at various times, but it is unlikely that the maximum loading of all parts of the building will occur at the same time. In buildings cf many stories the probability of having maximum loads on all of the floors at the same time decreases with the number of stories. Ordinary Household and Office-Furniture weighs from 5 to 10 lb per sq ft of space occupied. While safes, bookcases or filing-cases may produce local load- ings of from 10 to 100 lb per sq ft, the average load on office-floors rarely reaches 10 lb per sq ft. Residences, Apartments and Parts of Hotels not used for public assembhes are rarely loaded with more than 5 lb per sq ft of floor-area. Retail and Wholesale Stores require a large percentage of the floor-area for the use of salespeople and customers, and not over 50% of the floor-area is used for the storage of stock. In estimating the weight of miscellaneous stocks, an average between the lightest and heaviest classes should be taken for the weight per cubic foot, and also, in figuring the total space occupied by stock, an average should be taken between the maximum and minimum amount of stock carried. In RETAIL DRY-GOODS STORES the floor-load for the entire building may amount to not more than 25 lb per sq ft, but in wholesale stores, and especially in grocery and hardware stores, the average load may greatly exceed this figure. In Workshops, Loft-Buildings and Buildings for Manufacturing, the actual live loads will, of course, vary with the class of material handled and the weight of the machinery used, and no general estimate can be made. Where the char- acter of the occupancy to be expected is known it is possible to make a close approximation of the weights of machinery, fixtures and average stock on each floor. Storehouses. In buildings used, in whole or in part, for storage purposes a floor may be used for light, bulky materials which, when stowed so as to leav« 150 Foundations Chap. 2 gangways and working-spaces, will give a resultant load much below the as- sumed load. On the other hand, the heaviest materials may be compactly piled from floor to ceiling in defiance of building regulations, posted notices and common sense. Raw materials or crated or baled materials can be packed closer than miscellaneous articles, and are therefore liable to increase the loads. The 'Ratio of the Total Probable Maximum Live Load to the Total Assumed Live Load having been determined for the entire building, the probable maximum live load for any element of the footing may be readily obtained by multiplying the assumed or calculated live load for that element by this ratio. (3) The Wind-Load is generally calculated on the assumption that the wind may exert a uniform pressure, frequently taken at 30 lb per sq ft, on the entire external area of any side of the building. This assumption makes no deduction for the protecting influences of adjoining buildings. In a building of any size it is improbable that the maximum pressure will be reached over the entire exposed area at the same instant of time, and consequently, if the assumed pressure represents the maximum pressure, the average, at any time, will be less than the calculated total. General Efifect of Wind-Pressure. The horizontal pressure of the wind tends to increase the load on footings on the leaward side of the building and to de- crease the load on footings on the windward side. In many buildings diagonal bracing, called wind-bracing, or other special construction, is used to prevent the building from being deformed by the wind-pressure and to convert the hori- zontal stresses due to the wind-pressure into vertical components, acting along defined lines of support, that is, into either uplifts or loads on certain walls, piers or columns. Where the uplift on any element of the structure is less than the dead load on the same element, the upHft is ignored. Where the vertical component increases the compression in any element it is called the wind-load in THAT ELEMENT of Construction and on the corresponding footing. The design is generally based upon concentrating all of the wind-load on certain external footings. If, on account of the general rigidity of the building, or on account of any other reason, the wind- stresses reach footings not designed to receive wind- loads, the amounts figured on the external footings will be reduced correspond- ingly. It is probable that the maximum effect of the wind results from a series of impulses of short duration and that the effect of such pulsations may be partially overcome by the inertia and elasticity of the buildings; so that the resultant load reaching the footing may be only a part of the theoretical load for the instant during which the maximum pressure is exerted. (See, also. Chapter XXIX, Wind-Bracing of Tall Buildings.) The Probable Maximum Wind-Load acting on the footing is, therefore, less than the theoretical load due to the maximum wind-pressure. If the assumed wind-load represents approximately the maximum wind-pressure, as recorded by a wind-gauge, it would appear safe to assume that only 50% of the assumed wind-load would act to produce a settlement in the footings of a building. Some authors recommend that in proportioning footings all wind-loads be ignored; but this, especially in the case of high and narrow buildings, is mani- festly improper. The minimum wind-load is negative, being actually an uplift from which the load may vary to the maximum, but the maximum will be reached only at rare intervals and will endure for a short period only. The Combined Wind-Load and Live Load. It is improbable that the maxi- mum wind-load and the maximum live load will occur at the same time, which consideration should be borne in mind when the estimate is being made as to the effective wind-load. Assumed Loads Specified by Building Codes 151 14. Assumed Loads Specified by Building Codes^ Table II. Requirements of Building Codes for Assumed Loads for OflBce- Buildings City Requirements Atlanta, Ga., Boston, Mass. , Buffalo. N.Y.... Minneapolis, Minn., Richmond, Va.*. . . St. Louis, Mo.*. . . . St. Paul, Minn.. Cincinnati, O.. Chicago, 111. . New York City*., Cleveland, O Live load, 75 lb per sq ft above ist floor; 150 lb per sq ft on ist floor Footings designed for dead load and 60% of live load and wind-load Live load, 100 lb per sq ft. Wind-load, 30 lb per sq ft where erected in open spaces; in built-up districts, 25 lb at the loth story, 2^1j lb more for each succeeding upper story,, up to a maximum of 35 lb to the 14th story and above Live load, 70 lb per sq ft. Wind-load, 30 lb per sq ft. Foun- dations designed for the acting average loads in the com- pleted and occupied building and not the theoretical or occasional loads Live load, 75 lb per sq ft above the first floor; 100 lb for first floor. Wind-load, 30 lb per sq ft. Roof and top floor, full live load. For each succeeding lower floor, a reduction of 5% until 50% is reached, such reduction being used for the remaining floors Foundations designed for 60% of the live load Live load, 70 lb per sq ft; first floor, 150 lb. Loads carried by the soil, total dead load and 10 lb per sq ft of all the floor-area. Wind-load, 30 lb per sq ft Live load, 60 lb per sq ft above the first floor. First floor, 125 lb. Wind-load, 30 lb. Roof and top floor, full load; for each lower floor, a reduction of 5% until 50% of the full live load is reached, when such reduced load shall be used • for the remaining floors. Footings designed for dead load and live load Live load, 50 lb per sq ft above first floor; 100 lb for first floor. Live load reduced by 5% for each floor below the top until 20% is reached, when such reduced loads shall be used for remaining floors. Wind-load, 20 lb per sq ft above surrounding buildings Live load, 50 lb per sq ft. 50% of the live load used for piles. Piers designed for 85% of live load on top floor and reduced by 5% for each lower floor until 50% is reached, when such reduced loads shall be used for the remaining floors. Wind-load 20_lb per sq ft Footings designed for 60% of the live load Live load 60 lb per sq ft in offices proper. 100 lb per sq ft in halls, lobbies, etc. Footings for walls designed for 50% of live load. Free-standing columns designed for 80% of loo-lb load and 75% of 60-lb load. Wind-load 30 lb per sq ft for free-standing structures in built-up districts; 25 lb per sq ft at the loth story and 2y2 lb less for each lower story, and 2\^ lb more for each higher story, until 35 lb is reached ____________^ * Codes are constantly changing. Richmond's new code gives floor-loads; St. Louis has changed some values; New York City's new code gives floor-load values different from those of the former code. 152 Foundations Chap. 2 Reduction in Assumed Loads. The building codes of various cities con- tain rules governing the assumptions to be made as to live loads and wind-loads, and these rules generally provide for some reduction in the assumed loads. Generally, it will be found possible to meet these requirements and at the same time arrange for the proper proportioning of the supporting areas. Table II, page 151, gives briefly the requirements of the building codes of several cities, as to assumed loads for office-buildings. 15. Proportioning the Supporting Areas for Equal Settlement The Minimum Areas of Support. The actual dead loads and the assumed live loads and wind-loads for each linear foot of wall and for each column, pier, or other supporting element of the building down to the level of the footings having been calculated, a foundation-plan should be prepared giving the amount and center of action of all loads. For safety under the worst possible combina- tion of loads,, each footing should be ample to support the total of the dead loads, live loads and wind-loads coming on it. The minimum areas of support for any footing are obtained by dividing the total of the dead loads, live loads and wind-loads by the safe supporting power of the foundation-bed. If the foundation-bed is rock, or can be considered as incompressible under the unit load, the minimum areas so obtained may be used for the footings. On com- pressible materials, or generally on all materials other than rock, the use of these minimum areas will not result in uniform settlements owing to the fact that the actual live loads and wind-loads are not consistent with the assumed live loads and wind-loads. The Actual Loads on the Footings. In.accordance with what has been previously said, let us assume that the dead load is constant, and that for a building under consideration the probable maximum live load is 50% of the assumed hvc load, that the probable maximum wind-load is 40% .of the assumed wind-load, and that on the completion of the building, for a short period, the live loads and wind-loads reduce to zero. The actual loads on the footings would then be: (i) Upon completion of the building, the dead load only; (2) Under the maximum load due to occupancy and to snow on the roof, the dead load plus 50% of the assumed live load; ,(3) When loaded as in (2) and subject, in addition, to the maximum prob- able wind-action, (a) The footings on the leaward side of the building will sustain the total dead load, plus 50% of the assumed live load, plus 40% of the as- sumed wind-load; (b) The footings on the windward side of a building will sustain the total dead load, plus 50% of the assumed Uve load, minus 40% of the as- sumed uplift; (c) Other footings will support the total dead load, plus 50% of the as- sumed live load, plus zero wind-load; (4) Intermediate conditions as to live loads and wind-loads will produce loadi/igs intermediate between (i) and (3). Variations in Unit Loads on Foundation-Beds. With such known varia- tions it is, therefore, impossible to proportion the supporting areas so that the unit load on the foundation-bed shall be uniform at all times. If the support- ing areas are proportioned in the ratio of the dead load only, the building, on completion, and before occupancy, will uniformly load the supporting areas, and at that time all of the footings should show, equal settlements; but subse- Proportioning the Supporting Areas for Equal Settlement 153 quently, when the supporting areas have been subjected to the full effects of the live loads and wind-loads, certain supporting areas, having a high percentage of live loads, or of live loads and wind-loads, will be subject to a higher unit load, and the corresponding footings will consequently settle more than other footings supporting a low percentage of live loads, or Hve loads and wind- loads. Non-Uniformity in Footing-Settlements. If, on the other hand, the sup- porting areas are proportioned on the basis of the dead loads, plus the maximum live loads, plus the maximum wind-loads, even if the maximum loads are the PROBABLE ACTUAL MAXIMUM LOADS, and not the FICTITIOUS ASSUMED LOADS, it is inevitable that upon the completion of the building and before occupancy, the supporting areas having a lower percentage of Uve loads and wind-loads will have a higher unit load, and the corresponding footings will have settled more than other footings supporting a high percentage of hve loads and wind-loads. On this basis, the footings will not come to a uniform settlement until they have been subjected to the maximum live loads and wind-loads. I Arbitrary Rules for Proportioning Supporting Areas. Various arbi- trary RULES have been recommended for the proportioning of the supporting areas to secure equal settlements. These rules generally provide for a reduc- tion in the assumed live loads and wind-loads, but do not take into consideration the fact that a large proportion of the total settlement of certain footings may take place subsequently to the completion of the building and after other foot- ings may have reached practically their full settlement. Rational Rule for Proportioning Supporting Areas. The rule herein- after recommended provides not only for a reduction of the assumed loads on a more rational basis, but also fof^the proportioning of the footings for the mean load, instead of for the ultimate load, and it is believed that the resulting settle^ ments will be as nearly uniform as possible. The rule is based on the propor- tioning of the footings in accordance with the loads which will act on the footings at the time when all of the dead loads and one-half of the probable maximum live loads and wind-loads exist. The reason for taking one-half of the probable maximum wind-loads and live loads is that these loads vary from zero to a maximum, the average being one-half of the maximum. Provision for Variations in Loads. On the completion of the building and before the live loads or wind-loads have gone on the footings, the settle- ments will not be uniform, because areas designed for a high percentage of live loads and wind-loads will have much less than their average load and will there- fore have settled less than footings having a low percentage of live loads and wind- loads. When these same footings have been subjected to the maximum probable live loads and wind-loads, the settlements will again be unequal, because .the areas have been proportioned for only one-half of the probable maximum live loads and wind-loads; but the footings which originally were the highest will now be the lowest. The inevitable movement due to the variation in the live loads and wind-loads will be equally divided, one-half of the settlement being required to bring the footing to the level of a footing having the dead loads only, and the other half of the settlement carrying it an equal distance below the same footing. In other words, the method provides for the least possible variation between footings having different proportions of live loads and wind-loads. The Mean Load. For lack of a better name, the loads taken for the pro- portioning ot the footings, consisting of the total dead loads, one-half of the probable maximum live loads and one-half of the probable wind-loads coming on each footing, will be called the mean load. 154 Foundations Chap. 2 The Mean Unit Load. The areas will be made such that the load on the foundation-bed due to the mean loads will be uniform, and this uniform load which, in general, will be considerably less than the allowable unit load on the foundation-bed will be called the mean unit load. I'he Minimum Unit Load. The necessity for providing for the worst possible condition of loading is satisfied if the supporting area for all footings is sufficiently large to support the total of the dead loads and the assumed live loads and wind-loads at the allowable unit pressure. The resulting areas of support are the minimum areas, and any change in these areas necessary to make them proportionate to the mean loads must be effected by increasing some areas rather than by diminishing any. Any mean unit load which would give, when divided into the mean loads, areas, aU of which would be larger than the minimum areas, would serve as the mean unit load, but it is more economical to determine the lowest possible mean unit load which, when applied to the mean loads, will give the least possible increase of the areas. This can be done by determining which one of the minimum areas carries the least mean LOAD PER SQUARE FOOT. This area may be selected by calculating the mean load on each of the minimum areas, or more simply, by comparing the table of assumed loads and a table giving the mean loads, and noting which footing has the largest percentage of reduction between the assumed load and the mean load. The resulting mean load on this footing will be the minimum unit LO/\D which can be used as a mean unit load. The Method Reduced to Rule. The method can be reduced to rule as follows: (i) Prepare a table giving in vertical columns or table-divisions for each footing, the dead loads, the assumed live loads, the assumed wind-loads and the total of these three loads. This table is called the table of assumed loads. (2) Prepare a similar table giving the dead loads, one-half of the maximum probable live loads, one-half the maximum probable wind-loads and the total of these three loads. This table will be called the table of mean loads. (3) By a comparison of the two tables, find the supporting area which has suffered the greatest percentage of reduction between the total assumed loads and the total mean loads and find the unit load resulting from the mean load on this area. This unit load will be called the mean unit load. (4) Divide the total mean load as given in the table of mean loads for each footing by the mean unit load. The result will be the required area of sup- port. Short Method for Determining the Mean Unit Load. From the fore- going it follows that the mean unit load can be obtained more directly by tlie fol- lowing rule. Find the supporting area which has suffered the largest percentage of reduction between the total assumed load and the total mean load and multi- ply the allowable unit load on the foundation-bed by the ratio obtained by dividing the total mean load by the total assumed load. Illustrative Example. The following example is figured out more fully than is necessary in practice in order to fully explain the method and also to compare the method with other methods frequently used and recommended. Ordinarily the wind-loads on a building of the size and type assumed in the example would be ignored, but they have been considered here to make the example complete. A factory-building (Fig. 2) is to have four floors above the basement, each capable of supporting an assumed unit load of 200 lb per sq ft. The load on the flat roof is assumed at 50 lb per sq ft. The horizontal wind-pressure is as- sumed as a uniform pressure of 40 lb per sq ft, on the sides A B and CD only. Proportioning the Supporting Areas for Equal Settlement 155 The vertical component of the wind-pressure is to be taken care of by the foot- ings of the side walls. There is also an inteiior self-supporting chimney and ventilating shaft which is protected from the wind and which carries no floor- loads. The foundation-bed is a uniform, sandy material which is expected to compress uniformly and at the rate of ^i in per ton of load per sq ft of supporting area. D Ghini ey C JOl..i D D Col.5 D Xgstnned Load. PLAN SECTION Fig. 2. Foundation-plan and Section of Factory-building The MAXIMUM UNIT LOAD on the foundation-bed is taken at 4 tons, correspond- ing to a settlement of 2 in for the assumed load. The calculated dead loads of the building, including all construction down to the level of the footings, the summation of the assumed live loads and the vertical components of the assumed wind-loads are given in Table III. Table in. Dead Loads and Assumed Live, and Wind-Loads Element of footing Division i, dead loads only, lb Division 2, assumed live loads, lb Division 3, assumed wind-loads, lb Division 4, total dead, live and wind-loads, lb Side walls per lin ft Columns i and 5 Columns 2, 3 and 4 Chimney 14000 137 500 90 000 320 000 8 400 160 000 340 000 2 000 24 400 297 500 430000 320 000 Table-columns are called divisions to avoid confusion with building-columns. 156 Foundations Chap. 2 A careful study of the probable loading of the building shows that the maximum live loads at any one time will not exceed 60% of the total assumed live loads, and that the maximum wind-loads will be less than 50% of the assumed wind- loads, for the reason that the assumed wind-pressure is based upon the highest recorded pressure on a Umited area in an exposed situation, whereas the pro- posed building will be in a sheltered situation. Having, therefore, determined the probable maximum live loads and wind-loads at 60% and 50% respectively of the assumed loads, the so-called mean loads, corresponding to loads half-way *)etwe».n the minirnum and maximum loads, will be one-half of the probable maximum loads, or 60% X]^i= 30% 'of the assumed Hve loads and 50% X I'i = 25% of the assumed wind-loads. Table IV gives the dead loads and the mean live loads and wind-loads separately, and the total of the dead loads and mean loads, which total is to be used in proportioning the areas for least varia- tion in settlement. This is known as the total mean load. Table IV. Dead Loads, Mean Live and Wind-Loads and Total Dead and Mean Loads Element of footing Division 5, dead loads, unchanged, Division 6, one-half of 60% of as- sumed live loads, lb Division 7, one-half of 50% of as- sumed wind- loads, lb Division 8, total mean loads, lb - lb Side walls per lin ft — Columns i and 5 Columns 2, 3 and 4 Chimney 14000 137500 90 000 320 000 2520 48 000 102 000 500 17 020 185 500 192 000 320 000 Table-columns are called divisions to avoid confusion with building-columns. Comparing the two tables it will be seen that the interior columns of the building, columns 2, 3 and 4, had originally the largest percentage of live loads (no wind-loads) , and have consequently suffered the greatest reduction in the amount of total load. The minimum areas of support for columns 2, 3 and 4, and also for the other elements of the footings, are obtained by dividing the total assumed loads given in division 4, Table III, by 8000, the allowable unit load in pounds on the foundation-bed. The resulting areas are given in division 9, Table V. No reduction can be made in these areas without exceed- ing the limitation that the most disadvantageous combinations of loading, how- ever improbable, shall not exceed the safe unit load. The adjustment of the areas to the probable mean loading, as given in Table IV, the table of mean loads, must be accomplished solely by increasing the sizes of certain footings. If we divide the total mean loads in division 8, Table IV, by the minimum areas given in division 9, Table V, we will get the mean load per sqQare foot on the minimum areas for each element of the footing. The results given in division 10, Table V, show that the meiin load for columns 2, 3 and 4 is only 3 568 lb per sq ft, while under the chimney the load is 8 000 lb per sq ft. As no reduction in area is permissible it is necessary to increase the footings under the chimney, side walls and columns i and 5 until the mean unit load corre- sponds to the mean unit load for columns 2, 3 and 5. This is done by dividing the mean loads given in division 8, Table IV, by 3 568, the mean unit load as Proportioning the Supporting Areas for Equal Settlement 157 determined for columns 2, 3 and 4. The resulting areas are given in division II, Table V, and are the areas which should be used. The n^ethod of calculation can be shortened and reduced to a rule as followsi. Compare Table IV, the table of mean loads, with Table III, the table of assumed loads, and find the element of support which has suffered the highest percentage of reduction between the total assumed load and the total mean load, and note the corresponding minimum area of support at the allowable unit load on the foundation-bed. Divide the mean load for the same element of support by the number of square feet in the minimum area of support. The result will be the unit load for mean settlement. Then divide the mean loads for each ele- ment of support by the mean unit load. The results will be the required areas as given in Table V. Table V. Mean Loads on Minimum Areas and Areas for Mean Loads Element of footing Side walls per lin ft Columns i and 5 . . , Columns 2, 3 and 4 Chimney , Division 9, minimum areas, sq ft 3.0s 37-2 53.8 40.0 Division 10, mean loads on minimum areas, lb per sq ft 5580 4986 3 568 Division 11, areas for mean loads, sq ft 4-7 51-9 53.8 89.7 Table-columns are called divisions to avoid confusion with building-columns. Or the mean unit load may be determined by multiplying the allowable unit load by the ratio obtained by dividing the mean load for the element of sup- port having suffered the highest percentage of reduction by the assumed load for the same element. Resulting Settlements. The following Tables VI, VII and VIII show the comparative settlements which may be expected if the supporting areas are proportioned in accordance with different assumptions as to load. In all the tables it is assumed that the foundation-bed will settle H in per ton of load, and that the total assumed load will never load the foundation-bed in excess of 4 tons per sq ft. In Table VI the footings are proportioned in the ratio of the dead loads only. In Table VII the footings are proportioned in the ratio of the total assumed LOADS. In Table VIII the footings are proportioned in the ratio of the mean loads. In each table, division i gives the dead load coming on the footings on the completion of the building. Division 2 gives the load coming on the footings when the building is subjected to the maximum probable live loads and wind- loads. Division 3 gives the supporting areas in accordance with the assumed loading. Division 4 gives the settlements for the unloaded building. Divi- sion 5 gives the settlement after the addition of the maximum probable live loads and wind-loads. Explanation of Table VI. The method of proportioning the areas in the ratio of dead loads only, as recommended by C. C. Schneider* may, in the form of a rule, be stated as follows: * See article on the Structural Design of Buildings, Trans. Am. Soc. C. E., vol. 54, June 1905. 158 Foundations Chap. 2 Compare the table-division of dead loads, Table VI, with the division of assumed live loads, find the element of support which has the highest percentage of live loads to dead Ipads, and note the corresponding minimum area of support at the allowable unit load on the foundation-bed. Divide the dead load for the same element of support by the number of square feet in this minimum area of support, and the result will be the unit load due to the dead load only. Then divide the dead loads for all other elements of support by this unit load, and the results will be the areas required. Thus, in Table VI, it is seen by referring to Table III that columns 2, 3 and 4 have the greatest percentage of Hve load to dead load, and their minimum area of support, as in Table V, is 53.8 sq ft. Then, 90 000 -r- 53.8 = i 675 lb, the unit load due to the dead load only. The area for columns i and 5 is 137 500 -^ i 675 =82.1 sq ft. The process is simi- lar for the other elements. Table VI. Footings Proportioned in the Ratio of the Dead Loads Only Probable settlement where supper deaa tin? areas are proportioned in the ratio of loads only Element of footing Division i Division 2 Division 3 Division 4 Division 5 Dead loads only, lb Maximum probable loads, lb Areas, sq ft Settlements Empty, in Loaded , in Side walls per lin ft Columns i and 5 Columns 2, 3 and 4 Chimney 14 000 137 Soo 90 000 320 000 20 040 233500 294 000 320 000 8.3 82.1 53.8 191. 0.42 0.42 0.42 0.42 0.60 0.71 1.36 0.42 Maximum variation, em pty 0.00 0.94 Maximum variation, loa ded Table-columns are called divisions to avoid confusion with building-columns. The calculations for settlements are readily made, when the amount of com- pressibility of the foundation-bed is known, by multiplying the unit load on the foundation-bed of each element of support by the amount of compressibility of the foundation-bed per unit of load. Thus, in the above example the amount of compressibility is given as V2 in per ton. In Table VI the unit loads, due to dead loads for each element of support, are the same, or i 675 lb = 0.838 tons per sq ft, which, multiplied by }^ = 0.42 in. Similarly, the unit loads due to maximum probable loads for each element of support are determined, and these loads, in tons, multiplied by one-half, give the settlements in inches as given in division 5 of Table VI. Explanation of Table VII. The areas given in Table VII are obtained by dividing the total maximum dead loads, live loads and wind-loads (Table III) by the allowed unit, 8 000 lb per sq ft, and are the minimum areas given in Table V. The settlements for the loaded building are based on the maximum probable loads as given in division 2 of Table VII. Proportioning the Supporting Areas for Equal Settlement 15^ Table VII. Footings Proportioned in the Ratio of the Total Assumed Loads Probable settlement where supporting areas are proportioned in the ratio of total assumed loads Element of footing Division i Division 2 Division 3 Division 4 Divisions Dead loads only, lb Maximum probable loads, lb Areas, sq ft Settlements Empty, in Loaded, in Side walls per lin ft Columns i and 5 Columns 2, 3 and 4. . . . . Chimney . . 14000 137 500 90 000 320 000 20 040 233 500 294 000 320 000 3.0s 37.2 53.8 40.0 I. IS 0.92 0.42 2.00 1.64 1.57 1.36 2.00 pty 1.58 0.64 Maximum variation, loa ded Table-columns are called divisions to avoid confusion with building-columns. Table VIII. Footings Proportioned in the Ratio of the Mean Loads Probable settlement where supporting areas are total mean loads proportioned in the ratio of Element of footing Division i Division 2 Division 3 Division 4 Division s Dead loads only, lb Maximum probable loads, lb Areas, sqft Settlements Empty, in Loaded, in Side walls per lin ft Columns i and 5 14 000 137 soo 90 000 320 000 20040 233 soo 294 000 320 000 4-7 SI. 9 S3. 8 89.7 0.74 0.66 0.42 0.89 1.06 1. 12 1.36 0.89 Columns 2, 3 and 4 Chimney Maximum variation, Maximum variation. em loa pty 0.47 0.47 ded Table-columns are called divisions to avoid confusion with building-columns. Explanation of Table VIII. The areas in Table VIII are obtained as already explained and as given in division 11, Table V, and the methods used in determining the settlements are similar to those used for the preceding tables. In Table VIII it will be noted that columns 2, 3 and 4 have a settle- ment of 1.36 — 0.42 = 0.94 in, as a result of the addition of the live loads and wind-loads. Half of this settlement is required to bring these footings down to the level of the chimney-footing, and the other half of the settlement brings 160 Foundations Chap. 2 them below the chimney-footing. There is no way to prevent this settlement of 0.94 in, but its effect on the building is reduced to a minimum by having the settlement of the footings of columns 2, 3 and 4 start above the chimney-footing and finish below it. The chimney-footing does not change its elevation after the completion of the building, and compared with it, the variation in level of the other footings is the minimum. In their mean position, half-way in their movement, these other footings will be at the same level as the chimney-footing. 16. Determining the Supporting Areas General Requirements. In laying out the areas of support for any struc- ture it should be borne in mind, as previousl}' explained, that (i) the total of the dead loads, assumed live loads and assumed wind-loads should not load the foundation-bed in excess of the allowable load on it; (2) when the foundation- bed is compressible the areas of support should be calculat^^d by the method of mean loads; and (3) the center of gravity of the supporting area should coincide with the center of action of the load to be supported. To these may be added a further condition that (4) economy will be furthered by keeping the support- ing areas simple in outline and by arranging each area as compactly as possible around the center of the load to be supported. (i) The first condition is necessary in order to provide that no possible con- dition of loading will exceed the allowable pressure on the foundation-bed. (2) The second condition provides for making the settlements of different footings as nearly equal as possible. (3) The third condition provides that the settlements of each footing shall be uniform, that is, that the footing shall not settle out of level. (4) The fourth condition provides for economy in design in the footing itself and for economy in making the excavation for the footing, especially in the case of deep excavations requiring sheathing for the protection of their sides. In the case of a free-standing structure, the total load of which is not in excess of the supporting capacity of the entire area of the building at the safe unit load on the foundation-bed, it will generally be possible to arrange simple sup- IX)rting areas whose centers will correspond with the centers of the loads. The disposition of such areas is considered in succeeding paragraphs in the discus- sions of Concentric Loading. In buildings having restricted sites, where walls or columns are placed close to adjoining property-lines, it will frequently be impossible to arrange for simple concentric loadings and necessary to use offset footings, cantilevers or other devices to transfer the loads to supporting areas located on the property. Such supporting areas are discussed in succeed- ing paragraphs relating to Eccentric Footings. Footings with a Concentric Load. In order to have the load on the foundation-bed uniform under a looting it is necessary that the cenier of grav- ity of the supporting area should coincide with the center of gravity of the load, otherwise the area is said to be eccentrically loaded and the resulting load on the foundation-bed will not be uniform. Any variation in the loading of a compressible foundation-bed under a footing will result in an unequal settlement of the footing and this in turn will result in unequal stresses in the wall, pier, or column supported by the area. Wall-Footings with Concentric Load. In the case of a wall, the footing should project an equal distance on each side so that the center of gravity of the supporting area will coincide with the center of gravity of the wall and of the loads transmitted by the wall. The width of the supporting area should vary with the load on the wall, irrespectively of any change in the thickness of the wall OT^ Determining the Supporting Areas 161 Footing for a Concentric Isolated Load. In the case of a simple con- centrated LOAD, as, for example, a load from a column or pier, the footing maj' be circular, square, rectangular, or irregular in outline, but the center of gravity of the area mu5t coincide with the center of gravity of the load. Theoretically the circular shape gives the most economical footing, as the supporting areas extend radially the least possible distance from the center or axis of the load. Where deep excavation is necessary the circular form may lend itself to an economical method of excavation, as, for example, when cylin- drical piers are sunk by the pneumatic method or by dredging. In general, however, for ordinary footings the rectangular form is preferable, in that it lends itself to an economical arrangement of grillage- beams. The square is the most economical rectangle as the sum of the bending movements in the grillage and A Property-Line S bolsters is reduced to a minimum. I w Elongated Supporting Areas. When the J supporting area for an isolated load cannot be -^G ^^ ^ i made a circle or a square, for example, when ^ l* l T ' the square or the circle would overlap an ad- ^ig. 3. Elongated Supporting joining property-line or interfere with an ad- Area. Concentric Load joining supporting area, the necessary area may frequently be made rectangular in form, as ABDC (Fig. 3), having a width Wj twice the distance a between the center of the load O and the limiting line yl 5. The required length / equals the required area divided by w and the area should be centered on O, that is, h must equal h. Combinations of Simple Areas. Two Adjacent Isolated Areas. W' hen adjoining supporting areas overlap or when, for other reasons, it is desirable to combine adjacent footings, the best arrangement may be obtained as follows: Knowing the supporting area required for each of two adjacent concentrated loads and the distance between the centers of the loads, the sum of the two areas should be divided by twice the distance between the load-centers. The quotient will be the width or the dimension of the required rectangle of sup- port taken at right-angles to the line connecting the load-centers; and the other dimension of the rectangle will be twice the distance between the load- centers. The center of the area should be placed so as to coincide with the center of gravity of the two loads, when it will be found that each load will be concentric 'with its own area of support. Where a row of columns requires areas which nearly overlap, the combination of the areas frequently results in economy in excavation and form-work. Supporting Area for a Concentrated Load in the Line of a Wall. If one or more concentrated loads are carried in the line of a wall the additional supporting areas reciuired for such concentrated load may be provided in either of two ways. (i) If the concentrated loads rest on the wall, as, for example, when the wall supports the ends of girders and when the conditions are such that the con- centrated loads are distributed along given lengths of it, then, all that is neces- sary is to increase the width of the footing for the given lengths sufficiently to provide for the total of the uniformly distributed and concentrated loads. (2) If a concentrated load is on the center line of the wall but cannot be dis- tributed by the wall, as when a considerable load is carried by a pier or column to the level of the footings, then one-half the additional area for the concentrated load should be placed on either side of the wall-footing, so that a line connecting the centers of the two areas will pass through the center of the load. In general, fe2 Foundations Chap. 2 T , X. ,i 1 1 J 1 Fig. 4. Square Supporting Area. Wall and Concentric Isolated Load k is desirable that the additional areas, together with the area for the wall lying between them, should approximate a square. Knowing the width of the footing required to support the wall and the additional area required to support the concentrated load, the length of the side of the required square can be determined by the following formula (Fig. 4): Let w = the width of the footing; A = the area required to support the concen- trated load; /= the side of the square which will support a length of wall equal to /, and also provide an additional area equal to ^4. Then Supporting Area for Concentrated Load not in the Center Line of a WalL The same additional supporting area is required for this as for a con- centrated load on the center line of a .wall, but the total area must be divided unequally between the two sides of the wall-footing, the larger portion being placed on the side of the eccentric load. The simplest way to determine the location of the supporting areas for this combination is to determine the size of the required square as if the concentrated load were concentric with the center line of the wall. The next step is to calculate the load due to the wall for the length of this square and determine the location of the center of gravity of the \:ombined loads, that is, the center of gravity of this tvall-load and the concentrated load. The center of the supporting area is then placed concentrically with the center of gravity of the combined loads. In Fig. 5 let w = the required width of the wall-footing; 0= the concentrated load; A = the area required for the support of the concentrated load. Then, as before, the length of the side of the required square will be The center of gravity of the wall-load contained between the* lines AD and BC is at g, and the amount of the load is evidently the load per foot multiplied by the distance AB=f. Knowing the position and amount of the loads at and g, the center of gravity of the combined loads is determined, say at G. This fixes the center for the square. Supporting Area for a Concentrated Load on the End of a Wall. A somewhat different treatment is required for this, but the supporting area may be best determined as follows (Fig. 6): Knowing the width w of the footing required for the support of the wall, the additional area required for the concentrated load and the distance p from the center of the concen- trated load from the end of the wall, proceed in this way. Determine the square whose area corresponds to the sum of the areas required for the support of the concentrated load and for a length of wall equal to twice the projection of the wall beyond the center of the concentrated load. Plot this square A BCD en tne Fig. 5. Square Supporting Area. Wall and Eccen- tric Isolated Load L p ■M J A K E B s i 1 < H. « R H C D 3 C '^ O L -•n Fig. 6. Square Support- ing Area. Isolated Load on End of Wall Offset Footings 163 foundation-plan and also the total area required for the support of the wall. The square A BCD includes an area sufficient for the support of the concentrated load and for a section of the wall EFGH corresponding to a length of wall equal to twice the projection p, multiplied by the width of the footing. It is evident that the area KEHR is loaded both by the wall and the concentrated load; in other words, that the square A BCD is too small by the amount of the rectangle KEHR. The required square LMNO will be approximately the square which will contain the original area A BCD plus the area KEHR, plus twice the area JKRQ. The length of the side LM = MN will be approximately the length of the original square plus one-half of the area KEHR divided by the length of the original square. The resulting square should be moved from the posi- tion shown on the drawing so that its center coincides with the center of gravity of the combined concentrated load and the wall-load back as far as the square goes on the wall. A further approximation may be necessary where accuracy is required. The fmal result should be that the area of the square LMNO should be sufficient to support the concentrated load and that portion of the wall-load JEGQ resting on the square, and that the center of gravity of the square should coincide with the center of gravity of the combined loads. 17. Offset Footings Supporting Areas for Non-Concentric Loads. When walls, columns, or piers are placed close to property-lines the required supporting areas cannot be placed concentrically with the loads without overlapping the property-lines. In such cases recourse must be had to some method which will transfer the loads to supporting areas not con- centric with the loads. An attempt to accomphsh this result, the method known as offsetting the FOOTING has been largely used, especially for side walls adjoining property-lines. While theoreti- cally faulty, if not useless, it is indisputable that OFFSET FOOTINGS have generally served the pur- pose for which they were designed. In the typical construction a cellar wall rests on a course of con- crete or of flat stones forming a footing course considerably wider than the wall, the projection being entirely on one side of the wall. The load acting on one side of the center of the footing loads the supporting area unequally. The vary- ing LOAD on the supporting area can be calculated as follows: In Fig. 7 let W = the total load per unit of length coming on the supporting area; U = the eccentricity of load, that is, the distance between the center of the load and the center of the supporting area; L = the width of the footing = the width of the supporting area = AB; Ki= the unit load, or pressure on the foundation-bed at A, the edge of the footing nearest the load; ' K2 = the unit load, or pressure on the foundation-bed at B, the edge of the footing farthest from the load; y = any ordinate, from A to B. Then the average pressure on the foundation-bed will evidently be W/L. The pressure at A, the edge nearest to the point of application of the load, wiU Fig. 7. Offset Footing. Vary- ing Pressure on Foundation- bed 164 Foundations Chap. 2 be Ki = W/L (i + 6 U/L), or the maximum lo.\d will equal the average load plus six times the average load multiplied by the ratio of the eccentricity divided by the width of the footing. Similarly, the pressure at B, the edge farthest from the point of application of the load, will be A'2 = W/L (1 — 6 U/L), or the minimum load equals the average load minus six times the average load multiplied by the ratio of the eccentricity divided by the width of the footing. When the eccentricity equals H the width, the pressure at B becomes zero. If the eccentricity exceeds H the width there will be an uplift at B, or the foot- ing will have a tendency to overturn. This relation is generally expressed by saying that to avoid an upward reaction the center line of the load must fall within the . middle third of the base. Load-Diagrams for Offset Footings. If in the diagram (Fig. 8) the figure A DEC represents the load-diagram on the foundation-bed for a width of footing AD and the load ^C is the maximum per- missible load, then the area A DEC represents the maximum support afforded by the footing AD. If the width is increased until the load falls on the limit of the middle third or to the width AB, then the load at B is zero and the support is represented by the triangle ABC, the area of which is less than the area A DEC. Moreover, if the width of the footing is reduced until its center is concentric with the load-center, then the load-diagram becomes AFGC, the area of which is greater than either ABC or A DEC. From the foregoing it is evident that any advantage gained by offsetting the footing must be obtained at the cost of concentrating the support given to the wall away from the center line of the wall. I Q ^B Fig. 8. Pressure-diagrams for Footings ^ c 1 B ! c D 1 :5 G Fig. 9 Fig. 10 Fig. 11 Fig. 12 Figs. 9, 10 and 11. Eccentric Loading and Tendencies to Failure Due to Offset Footings; Fig. 12. Improved Type of Construction Eccentric Loading Due to Offset Footings. In Fig. 9, representing a simple case of eccentric loading due to offset footings, the load on the foundation-bed at E is perhaps twice the average load and at F about zero. Tender these conditions the projecting portion of the footing may shear, as iadi- The Use of Cantilevers in Foundations 165 cated, along the line DG. If it does not shear and if there is any settlement due to the load, the settlement will be unequal and the footing course will tend to rotate into the position shown in Fig. 10. The entire load will then be trans- mitted through the inner lower corner D of the cellar wall, rendering the wall unstable and developing a tendenc}^ to move in the direction //, The cellar wall may successfully resist this tendency by its own rigidity assisted by the first-floor beams acting as ties or by the external resistance afforded by an abutting wall or bank of earth, or it may partially or completely fail, developing a horizontal crack as indicated in Fig. 11 at 7. .In this figure it will be noted that the base of the wall itself is offset. This is done to prevent the separate rotation o/ the footing course; but this con- struction docs not diminish- the tendency to rotation of the entire base of the wall and to the formation of a crack at /. An improved type of construction is illustrated in Fig. 12, in which the floor- beams are anchored into the wall and the cellar wall has a continuous stepped batter from the level of the footing up to the level of the beams. The beams should evidently be arranged as tension-members, should run across the build- ing and should be anchored in the opposite wall. While this method may have some effect it is of doubtful efficacy and should never be used for piers. 18. The Use of Cantilevers in Foundations* Application of the Principle of the Lever. The use of the cantilever, in transferring a load to a supporting area not concentric with the load, is based upon the principle of the lever and involves a girder or cantilever connecting the two loads, and a supporting area or areas the center, of action of which lies between the two loads. Part or all of the load on one side counterbalances the load on the other side of the center of the supporting area. Illustrative Example. If an exterior column A (Fig. 13) carrying a load of 400 tons and requiring 100 sq ft of supporting area, at 4 tons per sq ft, the column- center being 18 in from a property-line PP which forms the limit of the building plot, it is evidently impractical to employ a concentric footing 3 by 2>2)\^ ft for its support. If, however, a sufficient counterweight can be found in the shape of an adjacent interior column-load, as at B, the exterior load can be trans- ferred by a girder or cantilever construction CDEF to a supporting area MN •< lying between the two loads, and entirely within the limits of the property. In Fig. 13 let PP represent the property-line, A the center of the load on column A, and B the center of the load on column B. Let the load on A be 400 tons, on B, 200 tons and the distance AB between centers, 20 ft. Assume that a rigid girder CDEF supports and connects the two columns. If now a FULCRUM or point of support G is provided for the girder at some point between A and B, the load on that point can be readily determined from the principle OF THE LEVER by multiplying the load on A, 400 tons, by the distance AB^ 20 ft, and dividing the product by the distance BG, 19 ft; or, the load ori G= 400 X 20/19 = 421 tons-f. The area required for the support of this load, at 4 tons per sq ft, is 421/4 = 105H sq ft. The uplift at B, or the part of the load B required to counterbalance the overhanging load A is, from the principle of the lever, the product of the load A by the lever-arm AG divided by the lever- arm BG. The load on the footing for B is the difference between the original load and the uplift; but in view of the possibility of a reduction in the load A, which would decrease the uplift at B, it is well to provide for a possible increase in the load B. * See, also. Chapter XIX, pages 678 to 680, for an example of a Continuous Girder io Grillage Foundation. 166 Foundations Chap. 2 Determination of the Area of Support. In determining the area of SUPPORT for A, having assumed one dimension of the supporting area to be twice the distance GP, or say 5 ft, the other dimension will be 105 H sq ft/s = 21 ft H in. If the length 21 ft H in, as determined, is found to be excessive, then 2^ Fig. 13. Cantilever Foundation-construction the point G must be moved to the left and the corresponding length of the sup- porting area must be determined as before. When the length of the supporting area for the fulcrum of the cantilever is limited, so that the length parallel to the prop)erty-line is fixed, the width of the area can be determined experimentally or by the use of the formula X= (L+u) - V(L + m)2- 2 WL/IS in which L = the distance between centers of the two loads; W = the load nearest to the property-line; ! / = the length of the supporting area; 5 = the unit load on the supporting area; and u = the distance between the center of action of the load to be cantilevered and the edge of the supporting area nearest to the property-line. If the position of the center of gravity of the load A combined with that part of the load on B which is borne by the cantilever is determined, it will be found to coincide with the fulcrum or point of support G of the cantilever, thus demonstrating that the use of the cantilever provides a means of combining two loads so that their center of gravity falls on the center of a supporting area not concentric with either load. The Grillage Fulcrum. Of course in practice the knife-edge fulcrum shown in the diagram is not used. The bottom flange of the girder forming the cantilever rests on the distributing grillage directly, as is shown in Fig. 14, which may be considered a typical arrangement. The Girdering-Method for Two Equal Loads. When it is desirable to support two or more adjacent concentrated loads on a single supporting area The Use of Cantilevers in Foundations 167 the method called girdering is employed. In the case of two concentrated loads, let A and B (Fig. 15) represent two columns. Let Wi represent the load on A and W2 represent the load on B. Let D represent the distance between the centers of the two loads. Let G represent the center of gravity of the com- bined loads. Let r represent the allowable unit load on the foundation-bed. The required area of support will be {Wi + W2)/r. This area may be of any ^ ^ + ^ i > 1 11 I -I I ' + Fig. 14. Cantilever Foundation. Grillage Fulcrum desired shape, provided that its center of gravity coincides with the center of gravity of the combined loads at G. In general, however, the most economical arrangement will result when each load is as nearly as possible over the center of gravity of its own required area. If, however, this is impracticable, as for example, when either column is near a property-line or an adjoining footing, it will be necessary to distribute the loads of both columns over the area lying be- tween the two columns. In the case of two columns equally loaded, as in Fig. 15, the distance u, from the center of column A to the property-line PP, determines the maximum allowable extension beyond column A. The dimen- sions of the area are obtained by making the length L of the footing equal to 168 Foundations Chap. 2 the distance D between the columns plus twice the extension u. Knowing the length of the required area the width w is determined by simple division. The Girdering-Method for Two Unequal Loads. In the case of columns not equally loaded, the supporting area may be a trapezoid, as in Fig. 16, the center of gravity of which must coincide with the center of gravity of the loads. Knowing the sum and distance apart of the loads and the area for their + V A I' .'.j l . 'i I . 'J f J r, ' J I .1 1 i VM G "\ \":\ I ' " I i"N I ' i \ \ '\ t;' ^ I,. "I I \ \: .i \ .'j jn 'r^U-^ -u—>\? Fig. 15. Girdering-method of Foundations. Two Equal Loads support, and fixing the total length L of the footing in accordance with the requirements tLi.:,t the footing shall not project beyond the line PP, the widths of the footing at tiie small and large end, a and b respectively, can be determined as follows: Let B represent the distance from the small end of the trapezoid to the center of gravity of the two loads and let A represent the area of the trapezoid. Then h =2A/L{sB/L-i) a = 2A/L{2 -sB/L) A = {a -^ b)L/2 and a + b = 2A/L For practical reasons the distance d should be made as small as possible. Stresses in Footing Courses 169 Cantilevering an Exterior Wall. In the case of a wall the same principles apply, but the cantilevering etlect must be distributed along the length of the wall. This can be accomplished by placing a girder under the wall, the girder in turn resting on the cantilever, or by using a number of cantilevers arranged ITTr^TTTTITTP Fig. 16. Girdering-method of Foundations. Two Unequal Loads in fan shape and radiating from the interior load-center. In narrow building^ the cantilevers may run from wall to wall. Double Cantilevering. The considerations controlling the design of the supporting areas required are the same as outhned in the preceding paragraphs. 19. Stresses in Footing Courses Size and Form of Footing Courses. The footing courses of all walls and piers should be larger than the superimposed construction in order to secure STABILITY AGAINST OVERTURNING and to reduce the UNIT LOAD on the founda^j tion-bed. When the change in size is accomplished abruptly as when a wall rests on a grillage or a slab of plain or reinforced concrete the footing is called a SPREAD FOOTING. When the base of the wall is thickened by meaiis of o£fset 170 Foundations Chap. 2 courses so that its bottom course is substantially as large as the footing course the construction is known as a stepped footing. It is evident that no hard and fast Hne can be drawn between the two classes. Whatever the form of the footing is it must be strong enough to distribute the more or less concentrated load coming on it, into a uniform pressure or load on the foundation-bed. The Unit Loads of Footing Courses. If the load on the upper surface of a footing course is uniformly distributed the intensity of the load, or in other words the unit load on the sooting, is obtained by dividing the total load by the area of the base of the wall, pier, or other construction at that level. The load on the foundation-bed should be uniformly distributed and in fact, if the foundation-bed is compressible and the load concentric with the supporting area, it may safely be assumed as uniform, since a compressible material will adjust itself until the loading at different points is substantially uniform. The unit load on the foundation-bed is evidently the total load divided by the sup- porting area. If the area of the footing course varies between the top and bot- tom of the footing the intensity of the load will vary, and if uniformly distributed, the unit load at any level is obtained by dividing the total load by the area of the footing at that level. The Weight of the Footing Itself. This is generally so small when com- pared with the superimposed loads that it may be ignored without serious error. The Transmitting of Loads by Footings. If we neglect the weight of the footing we can consider the footing course as transmitting the imposed load to the foundation-bed or as being subject to two equal loads; one, the super- imposed LOAD, more or less concentrated on the center line of the footing and acting downward; the other, the reaction due to the loading of the foundation- bed, uniformly distributed over the supporting area and acting upward. These loads or forces being equal and opposite in direction, the stresses developed in the footings are due to the differences in the distribution of these loads, and the footing courses simply act to convert concentrated into distributed loads. Manner of Failure of Footings. A footing rriay fail in several ways: (i) by shearing; (2) by direct crushing; (3) by spreading; and (4) by bending or rupture. _B (i) Failure of Footings by Shearing. This is illustrated in Fig. 17, showing a wall the weight of which has caused it to shear along the lines EG and FH. Fig. 17. Failure of Footing ^^^ ^^^^^ tending to cause SHEAR is the weight due by Shearing ^^ ^^^^ ^^^^ ^^^^ ^^^ reaction of the foundation-bed act- ing on the under side of the section EFGII. Since the load is supposed to be uniformly distributed this is equivalent to the product of the area corresponding to the width CD minus the width Gil times the length of the wall considered, by the unit loading on the foundation-bed. For a I -ft length of wall the force causing shear, S, is S=Wil--w)/l in which W = the load due to wall per foot of length in pounds; / = the width of footing; w = the width of base of wall. Or, since W/l = C/ = the unit load on the foundation-bed in pounds per square foot, ZL E5 HI G Stresses in Footing Courses 171 Since U is in terms of feet, / and w also must be in feet. The resistance to shear, R, under the conditions illustrated in Fig. 17, taken for a i-ft length b of the wall, is determined by the equation R=2XdXbXf in which /= the safe resistance of the material to shear, in pounds per square inch; d = the depth of the footing in inches; and b = the length of wall considered = 12 in. Placing S = R, we have 2dbf=^Uil-w)0 Or, since (/ — iv)/2 = the projection of the footing ^ UP = 12 dj The depth of the footing, therefore, must net be less than d=UP/l2f in which P is in feet. Shear in Footings of Piers and Columns. Failure by shear is most likely to occur in footings for piers and columns. The force tending to cause SHEAR is the total load on the column or pier less the reaction of the foundation- bed on the area immediately under the column-base. The resistance offered is determined by multiplying the perimeter of the column-base by the depth of the footing and by the allowable unit shear. When the area of the column-base is small, the entire load may be taken as producing shear. When reinforced concrete is used for the footing, there must be a sufficient number of stirrups to take care of the shear. (See Chapters XXIV and XXV.) Where steel beams are employ d the cross-section of the beams must be sufficient to take care of the shear, otherwise additional web-plates should be added, as is explained in Chapters XV and XX. (2) Failure of Footings by Direct Crushing. The failure of footings by DIRECT CRUSHING of the materials composing the footings rarely, if ever, occurs. Where, however, the concentrated load, due to a pier or column, is distributed by beams or girders which have thin webs, the webs may fail by BUCKLING. Such beams or gird- ers should have their webs re- inforced by vertical stiffeners or by additional web-plates, and the spaces between the beams or girders should be filled with concrete or grout. Where the load transmitted by the column- base exceeds the safe unit load on the material of the footing the area of the column-base may be increased, or a block of granite may be interposed between the concrete or masonrj^ footing and the base of the columns. In this case, however, such granite blocks should be considered as a footing course and designed to resist bend- ing, by formulas hereinafter given. (3) Failure of Footings by Spreading. Failure of the footings by spread- ing may occur under walls or piers, as shown in Fig. 18, especially when the Fig. 18. Failure of Footing by Spreading 172 Foundations Chap. 2 foundation-bed is of clay or other yielding material, which has, under the load of the footing, a tendency to flow along the lines indicated by arrows in the figure. This tendency should be provided against by making the bottom layer continuous and adequate to resist the tension. Vertical joints, such as are made in footings composed of masonry, are sources of weakness, and should be avoided. The tendency to spread is greatest in footings having a spread which is wide compared with the width of the superimposed wall or other construction. The writer knows of at least one important footing which has failed in tliis way, the cracks in general following the joints of the masonry substantially as shown in Fig. 18. (4) Failure of Footings by Bending or Rupture. A footing may fail by bending or RUPTURi;^as a beam or girder. In the case of a wall, if the foot- ing bends, as shown in Fig. 19, the concentration of the load on the lower edges E F B A 1 1 1 I F B rt E ^s ^^W c D Fig. 19 Fig. 20 Fig. 21 Figs. 19, 20 and 21. Failures of Footings by Bending of the wall, as at E and F may cause the base of the wall to fail. This possibility should be borne in mind in designing footings where the load on the wall ap- proaches the allowable unit load for the material composing it, and especially where the width of the footing is much greater than its own width. If the footing fails by rupture the rupture may occur either under the center line of the wall, as in Fig. 20, or at points close to the outer edge of the wall as in Fig. 21. Fig. 20 illustrates the objection to using a footing course composed of. masonry o- stones which do not extend the full width of the footing. The joints in such construction prevent the footing course from acting in tension and the footing as a whole from acting as a beam. H <-ii;f 20. Methods of Calculating Bending-Stresses in Wall-Footings Assumptions Made in Determining Bending-Stresses in Footings. Two methods for the calculation of the bending- stresses in footing courses are in general use. Both are based upon the assumption that the REACTION of the foundation-bed is uniform; but the methods differ in the assumption made as to how the footing course and the base of the super- A E| 4 pt If B structure act. Neither assumption can be held to L- W > be wholly correct. The First Method of Determining Bending- Stresses in Footings. This method is based upon the assumption that the pressure of the wall on the footing is uniform over the area and remains so at all times. If, in Fig. 22, ABCI^ represents a footing course supporting a centrally located waU EFGH, and U O I I -t- H Fig. 22. Bending-Stresses in Footings. First Method Methods of Calculating Bending-Stresses in Wall-Footings 173 W = the load of the wall in pounds per linear foot; w = the width of the wall in feet; and / = the width of the footing in feet; then Yz {I —w) = the projection AE or FB, and W/l = [/ = the unit load per square foot on the foundation-bed. Considering the forces acting on the right of the center line of the wall for a i-ft length of wall, it is evident that the uplift on the half-footing OD will equal ^A W and that its center of action will lie half-way between O and D, or at a distance H / from the center line 00; and, similarly, that the load due to one- half the wall will be H W and that its center of action will be at a distance H w from the center line 00. The resulting moments will be Mi = HWXHl= H Wl and Mz = H WXHw = H Ww and as these two moments act in opposite directions, the resultant moment tending to produce bending in the footing will be the difference between the two, or the bending moment at the center line OO is Mq = Ml - Ml or 3f = H W {l-w) Or, since W/l = U and H {l—w) = P, the projection. Equation (i) may be written in either of the forms • Mq = \^U {l-w)l ) or Ma^MWP ) ^'^ The Error Involved in this first method ir, due to the assumption that the pressure on the upper surface of the footing remains uniformly distributed, as if the base of the wall acted as a fluid, in which case the distribution of the load would remain constant and the formula would be correct. But the base of the wall is not a fluid, but a solid which will resist deformation. If, as in Fig. 19, the footing course A BCD deflects and the base of the wall is assumed to be incompressible, the entire load of the wall will be communicated to the footing through the edges E and F. While such a concentration is, of course, impossible (as the edges E and F will crush or com- press until a considerable area of the base of the ] wall is in contact with the footing) the result is that the weight of the wall is concentrated near the outer edges of its base. Equation (i) gives results which are too large; but as it errs on the side of safety, it is recommended for general use. The Second Method of Determining Bending I I <-^/^| — * I I I -Z- -H Stresses in Footings, also in common use, takes J j^^J into consideration only the projecting portion of the footing as follows: ^ Fig. 23. Bending-stresses in If in Fig. 23 ACBD represents a footmg course Footings. Second Method supporting a centrally located wall EFGH, and if we use the notation of the preceding method, then, if we assume that the footing acts as a fixed beam and the projections AE and FB as cantilevers rigidly supported by the wall, and denote the projection of the footing on either 174 Foundations Chap. 2 side of the wall by P, the reaction of the foundation-bed on this projecting portion P, per unit length of wall, will be PU. The center of action of this force will be at a distance H P from E or F and its moment at E or F will be M = PUxHP = ]^iUP^ or, since P = Vi (/ - w) the value of M may be given in the form Af = HU{l-wy (2) The Error Involved in this second method is due to the assumption that the uplift on the projection P can be resisted by the extreme outer edge of the base of the wall. If the uplift on the projecting part is concentrated on the edge, then the edge must either compress or fail by crushing, which, in either case, would throw the center of support for the cantilever back from the edge of the wall; and this is contrary to the assumption used in calculating the moment. This method takes into consideration only the intensity of the reaction or uplift and the length of the projection, and is known as the projection -method. Comparison of Results. Comparing the results of the two methods, it will be seen that the load cannot act at the two edges E and F as assumed in Equa- tion (2), nor ordinarily can it be uniformly distributed as assumed in Equation (i), but that the intensity of the load per unit of area will vary, being a MINIMUM at the center and a maximum near the edges of the base of the wall. The exact positions of the centers of action are affected by various consider- ations which cannot be fully discussed in this chapter. New Formula for Determining Bending Moments in Footings. The writer has devised a formula which gives values for the bending moment M half-way between the values given by Equations (i) and (2), and which closely corresponds to the assumption that, considering the forces on either side of the center of the wall, the center of action of the half-load of the wall is at the center of the half-wall, when the projection equals zero, and, as the projection increases, moves toward a position which is two-thirds of the distance from the center of the wall to its edge. This formula may be expressed as follows: M^HU{l-w){l-H'w) (3) Or, substituting the value of U in terms of W, M = HW{l-w)ij-w/2l) Weight and Pressure-Units. In practice IF, the weight due to the wall, is generally given in pounds per linear foot of wall, and the allowable pressure on the foundation-bed, while frequently given in tons per square foot, should be reduced to pounds per square foot. The Required Width of the Footing in feet is obtained by dividing the weight of the wall in pounds per linear foot of wall by the allowable unit load on the foundation-bed expressed in pounds per square foot. Moment -Units. The moment tending to produce rupture may be calculatec in foot-pounds or inch-pounds. If in Equations (i), (2) and (3) the dimensions /, w and P are in feet and U is in pounds per square foot, the resulting bending moment will be in foot-pounds per linear foot of wall. As the moment of resist- ance is generally stated in inch-pounds it is more convenient to have the max- imum bending moment or moment of rupture* in inch-pounds. Thus, for Equation (i) • In the flexure-formula the moment of resistance is m»de equal to the bending moment at any cross-section of the footing, and the maximum bending moment 19 sometimes called the moment of rupture* Methods of Calculating Bending-Stresses in Wall-Footings 175 M (in inch-pounds per foot of wall) = 12 M in foot-pounds, or M (in inch-pounds) = yzU {l — w)l (i)' Equation (2) in the same way becomes M (in inch- pounds) = y^ U {I- w)^ (2)' Or, using the more convenient form, M = H UP^ if we express the projection P in inches, instead of in feet, we will have M (in inch-pounds per foot of wall) = 1^4 UP^ Similarly, Equation (3) becomes M (in inch-pounds per foot of wall) = y2U {l — w) (l — H w). (3)' Until Equations (3) or (3)' are more generally accepted, an engineer or designer will avoid criticism and be perfectly safe in using Equation (i), and in the follow- ing pages the writer will use Equations (i) or (i)' unless the contrary is stated. (l.)(3)(2) 6000 5000- pjSOOO- 1000- -. r- - - - ■"1 ~ ' // ^T /^ I / / / / r ^ / i / // n c / / y / ' A' / / / ^^ . /.<\ >' / ^ // ' / // A N> / / ^ \r // l/~ ->? \/ V. / ^ n^. /'/ / >v' /. ^ ^ i > _ Sir fi ' 1 I J i \ 5 6 J 8 9 I in terra of to Fig. 24. Graphical Comparison of Bending Moments in Footings Example. The following is an example illustrating the application of the foregoing formulas: A 24-in wall transmits to the footing 42 000 lb per linear foot of wall. The allowable unit load on the foundation-bed is 3 600 lb per sq ft. What is the width and required moment of resistance * of the footing? 42 000/3 600 = iiYz ft * In the flexure-formula the moment of resistance is made equal to the bending moment at any cross-section of the footing, and the maximum bending ,n3^0JBe;^t,JB sometip^es called the moment of rupture. noisaaJjs 176 Foundations Chap. 2 Then, by Equation (i), we have If = H X 3 600 (iiH - 2) 11^^ - 50 750 ft-lb If Equation (2) is used, we have Jlf = ^^ X 3 600 (11^^ - 2)2 = 42 050 ft-lb and by Equation (3) M =1^X3600(11^^-2) (ii^i-i) = 46 400 ft-lb Comparing the results we see that the moment by Equation (3) is the average of the moments by Equations (i) and (2). Graphical Comparison of Bending Moments in Footings. Fig. 24 is a graphical comparison of the moments for varying ratios of / to w calculated by Equations (i), (2) and (3) on the assumption that w = the width of wall = i ft; U = the unit load on the foundation-bed = i 000 lb per sq ft; and r = l/w. The load on the wall, in pounds, for any value of /, is i 000 /. Comparing the curves of Equations (i) and (2) it will be seen that the results are widely apart, the percentage of variation being highest in the case of small projections. When / is less than twice w, or in other words, when the projection is less than one-half the width of the wall, Equation (2) gives moments less than half the moments given by Equation (i). Equation (2) may be used for small projections. Equation (i) gives results which are too large, especially where the projections are sm ill. Equation (3), giving results half-way between those of Equations (i) and (2) and in accordance with a reasonable hypothesis, would appear to be preferable, but is not in accordance with present practice. 21. Bending Moments in Footings of Columns and Piers ; ' General Statement of the Problem. Fig. 25 represents in plan a pier or column resting on a footing which projects on four sides. The base of the c n n rr column or pier is represented by A BCD, and the footing and its area of support by EFGH. That part of the footing included in the areas MNOF and QRST can be considered as acting in the same way as projecting footings under a wall, but the uplift on the four corners EQMA, etc., on which no superim- posed wall-load is imposed, also causes bending moments. [ , ^ 1 ij: f^ Different Theories. There are several theories, . t c \ more or less complicated and unsatisfactory, as to '■footing with Four^qTal I'"^*'' ^^"" ON THE FOUR CORNER-AREAS should Projections "^ determmed. The discussion 01 these theories would be out of place in this chapter. In a square footing, the projection is not over one-half the width of the superimposed base, the four corner-areas will not aggregate over 25% of the total area of the footing, and it may then be assumed that the bending moment is the same as if the base of the column or pier extended like a wall across the entire footing, as is shown in Fig. 26. To insure these conditions, when the projection of the footing exceeds \i w, and in all cases when the footing is not homogeneous, as when a grillage of steel is used, the load of the column must be distributed over the width of the footing by a girder or bolster or by an extension of the column-base. In case the footing is in several layers, each A, B C . 0-— , Bending Moments in Footings of Columns and Piers 177 B 1 1 1 1 1 1 1 1 1 1 D D B layer must extend the full width of the underlying layer. With such construc- tion it is evident that the bending moment will be the same as if the girder or BOLSTER were a wall and Equation Ci) will be applicable. Bending Moments in Column-Footings. For column-footings Equation (i) can be used, taking the total load in place of the load per foot, and the result will then be the total bending . moment. — Example. A column carrying 96 tons is to be supported on a square concrete slab. The cast- iron column-base is 2 ft square. The allowable pressure on the foundation-bed is 6 tons per sq ft. What is the maximum BENDING MOMENT in the slab? The area of support = 96/6 = p^g^ 26. Column-footing Treated Like Wall-footing 16 sq ft = 4 by 4 ft. The pro- jection is H (4 — 2) =1 ft, or one-half the width of the base, and by the fore- going rule we can calculate the bending moment as if the base of the column extended in one direction across the footing. Applying a convenient form of Equation (i) 1/ = H X 192 000 lb (4 - 2) = 48 000 ft-lb, or 576 000 in-lb The footing must therefore be of sufficient depth to resist this bending moment. ' If in this example the allowable unit pressure on the foundation-bed is 2 tons instead of 6 tons per. sq ft the supporting area and the area of the bottom con- crete footing course will be 96/2 = 48 sq ft. If the footing course can be a square its dimensions will be, with sufficient exactness, 7 by 7 ft. By the rule given, since the projection exceeds one-half the width of the base, there should be a BOLSTER extending across the footing. The bolster will be, therefore, 7 ft long and may properly be composed of two or more steel beams. The cast-iron base may be dispensed with, in which case the base of the column will be pro- vided with a steel base or with flange-angles. Let us assume that the column- base is I ft 6 in square and the width of the bolster 2 ft. i-si The bending moment in the bolster is determined, then, by Equation (i)^ using iH ft, the width of the column-base, for w, and 7 ft, the length of the bolster, for /. M = HX 192 oco (7 — ij'^) = 132 000 ft-lb = I 584 000 in-lb The bendfng moment in the slab is determined in the same way by Equation (i), using 2 ft, the width of the bolster, for w, and 7 ft, the length of the slab, for /. M = li x"i92 00c (7 — 2) = 120 000 ft-lb = I 440 000 in-lb. Footings Other Than Square in Plan. In case it is necessary to use some other shape than a square for the supporting area the resulting moments in the slab and bolster will vary from those calculated above. If in the foregoing example the supporting area, for any reason, is necessarily made 6 by 8 ft, giving 48 sq ft as the required area, and if the bolster is parallel with the 6-ft side, the moment in the bolster will be M = HX 192 000 (6 - iM) = 108 000 ft-lb = I 296 000 in-lb and the moment in the slab will be M = %x 192 000 (8 - 2) = 144 000 ft-lb = I 728 000 in-lb 178 Foundations Cliap. 2 or, the moment in the bolster is less and the moment in the slab is greater than in the case of the 7 by 7-ft supix>rting area. If the bolster runs parallel with the long side, the moments will be, for the bolster, M = HX 192 000 (8 - iH) = 156 000 ft-lb and for the slab, M = Hx 192 000 (6 — 2) = 96 000 ft-lb In footings having more than two layers, each layer must be investigated separately, using./ for the length of the layer which is being determined and w for the width of the superimposed layer. Compound Footings. In compound footings where, for example, a wall and a column or two or more columns are supported by a single footing, or where loads are cantilevered, the loads will in general be distributed to the sup- porting area by girders or cantilevers. The shears and bending moments of such girders or cantilevers must be determined for each case by the methods used in the calculations of beams and girders in Chapters XV and XX. 22, Design of the Footings Materials used for Footings. To possess the required strength the safe MOMENT OF RESISTANCE of the footing must be at least equal to the moment OF rupture, calculated as explained in the preceding paragraphs. Masonry, whether of brickwork or stone, is not generally suitable for any but the light- est buildings, as its tensional strength is low. Concrete, plain or reinforced, or grillages of steel embedded in concrete, are generally employed. (See Chap- ter III for footings for light buildings.) Footings of Homogeneous Slabs. If the footing is composed of a slab OF homogeneous material, as a block of granite or other reliable building stone, or a single layer of concrete, the moment of resistance is, by the well-known flexure-formula for rectangular cross-sections, Mr = H bd^ S (see Chapters X, XV and XVI) in which d = the depth or thickness of the footing, in inches; b = the breadth of the footing, in inches; S = the allowable unit tensile stress of the material, in pounds per square inch; Mr = the moment of resistance. Placing M, the moment of the forces tending to cause rupture, equal to Mr, for a length of wall equal to i foot we have , fc= 12 in and d-' = Vz M/S (4) Substituting in Equation (4) the value for M in inch-pounds as determined by formulas (i), (2) and (3) and a value for S as given in the followmg paragraph, the required depth d can be determined. Safe Tensional Strength for Materials in Footings. The values of 5, the allowable unit tensile stress, for concrete or stone must include a high factor of safety, as experiments show wide variations in the tensional strength and in the modulus of rupture or flexural strength of such materials. The following values for S in pounds per square inch include a factor of safety of from 8 to 10 and should not be exceeded. (See, alsO; Table III, page 628, Chapter XVI.) Design of the Footings 179 r - . 5 in lbs per sq in For brickwork or masonry in lime mortar from o to lo For brickwork or masonry in cement mortar. ...*.. from lo to 40 For concrete, 1:3:6 from 15 to 25 For concrete, i : 2y2. : 5 from 20 to 40 For concrete, 1:2:4 from 30 to 50 For sandstone or limestone in monolithic blocks. . . . from 75 to 150 For granite in monolithic blocks from 100 to 250 Example of Concrete-Footing Design. Concrete Cast as a Unit. A concrete tooting course 4 ft wide supports a wall 2 ft thick. The load on the foundation* bed is 28 000 lb per lin ft of wall, or 7 oco lb per sq ft. Assuming a value for 5 a 35 lb per sq in, what is the required depth for the concrete footing course? The moment of rupture from one form of Equation (i)' is ' M = Vi W (/ - w), or % X i8 coo (4 - 2) = 84 000 in-lb Substituting in Equation (4) d> = Vi X 84 000/35 = I 200, or J = 35 in By Equation (2)' the moment of rupture is M = 1/^4 f/P^ = 1.^4 X 7 000 X 12 X 12 = 42 oco in-lb ind aving of material may be effected by forming steps, is shown in Fig. 27. If the steps are of equal leight the total projection should be equally divided Detween the steps. If the footing is cast in several ayers, or if a granite slab is superimposed on a bed )f concrete, then each layer must be figured separately md the width of the superimposed layer used in place )f w, the width of the wall. Caution in Design of Footings of Several Layers. Equation (2) should not be used where :he footing consists of several layers, as the error iue to the erroneous assumption is cumulative and vould result in a serious concentration on the outer idges of the upper layers. -, ,,_^. ,„ ,^ ^ . Fig. 27. Concrete Steppe«^ Example of Footmgs of Several Layers. In the Wall-footing :ase of footings cast in separate layers the calculations ihould be made as follows: Let h = the length of the footing having a noment, M. From Equation (i), reduced to inch- pounds, , 2M 3W Having d^ded on the depth of each layer, say 15 in, and a value of S, say JS lb, for concrete, then, from the flexure-formula, M = Mr=HXi2XiS* 180 Foundations Chap. 2 X 35 = 15 750 in-lb, which, substituted in the above equation, will give the value of /i, or the length of the top course. Having determined /i, the length of the second course, k, is found in the same way, using h for w, and so on until the required width of the footing is reached. The dimensions / and w are to be taken in feet. Comparison of Unit and Separate-Layer Footings. Footings made in separate layers are very uneconomical in the amount of material required, when compared with those cast in one operation. If the footing in the previous example is designed on the separate-layer basis and the courses assumed to be 15 in thick, their lengths are as follows: 2 M ^1 - ~^ + '^ = 1(2 X IS 750)/ (3 X 28 000)] + 2 = 2.375 ft 3 yV Also /2= 2.75 ft, h = 3.125 it, /4 = 3.50 ft and /s = 3-^75 ft As h is nearly 4 ft, the required length, it may be made so by increasing the thickness of the bottom course to 16 in. The total thickness of the footing is therefore (4 X 15 in) + 16 in = 76 in instead of 35 in, as previously determined by Equation (i) for the footing cast as a imit. 3.0 2.6 a.4 2.2 2.0 ^1.8 ^1.6 2 1.4 1.0 „_ 1 \ \ \ \ V \ \ ^ y \ \ \ y \ \ \ \ \ s. ^ \ V Sy s \ Vy X \ >y s X si' y V \ ^^^0 y \^ N, \ \ ^ ^ -^..^ *l s N \ ""'V) ^ ■*■ ■ — J ^'.. "•^-^ J«^ ^"" — - "~ 4000 6000 8000 lOOOO 12 000 14 000 IGOOO 18 000 20000 Bearing per square foot Fig. 28. Diagram Showing Ratio of Projection to Depth of Footings Rule-of-Thumb Methods for Projections and Steps in Footings. Various arbitrary rules are in use which purport to give for different materials of construction so-called safe projections for given depths of footing or to give the safe ratio between the projection and the depth of a footing. These rules ignore the fact that the uplift varies and they are entirely unreliable, al- though such rules-of-thumb- are often incorporated in the building codes of cities. (See Chapter III, page 224.) Example. The safe projection for offsets in brickwork is frequently given in building codes and in text-books as 3 in jfor a double course of bricks or foc Steel Grillages in Foundations 181 a depth of about 5 inches, the corresponding ratio being 0.6. If we assume the value of S for brickwork at 20 lb per sq in, this offset will be safe when the up- lift is less than 2 666 lb per sq ft, but not safe when the uplift is over 2 666 lb per sq ft. Ratio of Projection to Depth of Footing. For footings of homogeneous material, however, having a small projection and where Formula (2) can be used safely, it is possible to calculate a so-called safe ratio of projection for a given unit load. From Equation (2)' and Equation (4), derived from the formula for the moment of resistance for beams of homogeneous -material and rectangular cross-section, the following formula may be derived: p/d^V^ss/u (5) in which all dimensions are in inches, S in pounds per square inch, and U in pounds per square foot. The quantity p/d is the ratio of the projection to the depth of the beam or footing. For a given value of 5 the ratio will vary in- versely as the square root of U. The diagram (Fig. 28) shows curves for different values of S and U from which the ratio of projection to depth of footing may be taken. Thus, for a concrete footing for which the allowable unit stress, S, in tension is, say 30 lb per sq in, if the load, U, on the foundation-bed is 3 000 lb per sq ft, the allowable pro- jection will be 0.69 times the depth of the footing course. If the concrete is 12 in thick, the allowable offset will be 8.3 in. Conversely, for a given offset, say 12 in, when the unit load is 3 000 lb and 5 = 30 lb as before, the required depth will be 1.45 times the offset. 23. Steel Grillages in Foundations* Advantages in the Use of Steel-Beam Grillages. When it is desirable to avoid the deep excavation required for concrete or masonry footings, and when the load of a wall has to be distributed over a wide area of support, steel rails or steel beams are frequently advantageously used to give the required moment of resistance with a minimum of depth. Steel beams are generally cheaper and preferable to rails, although second-hand rails have frequently been used as an expedient. Preparing the Bed and Setting the Beams. The foundation-bed should be first covered with a layer of concrete not less than 6 in in thickness and so mixed and compacted as to be as nearly impervious to moisture as possible. The beams should be placed on this layer, the upper surfaces brought to a line and the lower flanges carefully grouted so as to secure an even bearing. Sub- sequently, concrete should be placed between and around the beams so as to permanently protect them. Requirements for Steel Grillages. In determining the number and size of the beams for any given footing the following points should be considered: (i) The beams must resist the maximum bending moment, and this without undue deflection. (2) The beams must resist the shearing-stresses, the meeting of which requirement ordinarily provides against crushing. (3) The beams must not be spaced so far apart that there is danger of the concrete filling between the beams failing to distribute the load. (4) The beams must not be spaced so near together as to prevent the placing of concrete between them. The clear space between the flanges of the top layer should preferably be not less than 2 in and should be somewhat more for the lower layers. • See pages 678 to 680 for an example of a continuous girder in grillage foundation. 182 Foundations Chap. 2 (5) Where the bending moment is the governing feature, of two beams of equal weight, the deeper beam should be used. Thus, if the required section- modulus is 147, a 20-in 80-lb beam might be used; but a 24-in 80-lb beam is stiff er and stronger in bending. (6) Where the shear is the governing feature, of two beams of equal weights, the smaller beam is the stronger. Thus, the she.vring value of a 20-in 80-lb beam is greater than that of a 24-in 80-lb beam and is nearly equivalent to that of a 24-in 90-lb beam. However, on account of the greater stiffness of the deeper beam it is sometimes advisable to use it even though the cost is increased. Spacing of Beams in Grillage. Table IX gives the limiting spacing for steel beams, based upon the safe capacity of the concrete filling acting as a beam, for loads of from i to 6 tons per sq ft. Since, however, in such small spans there is considerable arching effect, the concrete will safely distribute the load on larger spans than those given in the table, provided a sufficient number of tic-rods of proper size are used to take up the thrust of the arches. Table IX. The Limiting Spacing for Steel Beams Used With Concrete Filling Depths of beams Spa. ling of beams for the following pressures per square foot I ton 2 tons 3 tons 4 tons 5 tons 6 tons in ft in ft in ft in ft in ft in ft in 6 I 3 II 10 9 8 o 7 7 8 I I 6 8 I I I 3 II 1 I 10 II 9 10 8 9 9 10 I 2 II I I 5 I 6 I 2 I 4 I I 2 II 1 I 10 1 12 IS 18 2 3 3 S 8 1 10 2 3 2 8 I 6 1 10 2 3 I 4 I 8 I II I 3 I 6 I 9 I 2 I 5 I 8 20 4 2 II 2 s 2 2 I II I JO 24 4 9 3 6 2 II 2 7 2 4 2 2 The Design of a Wall-Footing of steel beams is illustrated by the follow- ing example: A 24-in wall carries 42 000 lb per lin ft. What should be the size and spacing of steel beams to distribute the load over the foundation-bed at 3 600 lb per sq ft? The required width of the footing is 42 000/3 600 = 11 f t 8 in and the bending moment by Equation (3) is 556 800 in-lb per lin ft of wall. The amount of shear, by the formula given on page 170, isS =W (I — 'w)/l, or 34 800 lb. As the beams are in double shear the single shear per linear foot of wall is 17 400 lb. The required section-modulus per linear foot of wall is ob- tained by dividing the bending moment by the allowed fiber-stress in the steel, or 556 800/16 000 (assumed fiber-stress) = 34.8. By referring to Table IV, page 355, giving the section-moduli of steel beams we find that a 12-in 3ii'^-lb beam has a section-modulus of 36. To satisfy the condition of bending, the beams must not be spaced more than 36/34.8= 1.03 ft, center to center. To satisfy the condition of web-crippling due to direct compression, the unit com- pressive stress must not exceed the value of Sh, Table II, page 575, which, for a i2-in 3iV^-lb beam, is 13 060 lb per sq in. The area of the beam resisting compression is the length over which the load is distributed, times the web* thickness. Some authorities consider that the load is distributed over a length Steel Grillages in Foundations 183 equal to the loaded portion of the beam plus one-half the depth of the beam, but in this and the following example the length of only the loaded portion is taken. In this case the area is therefore 24 x 0.35 = 8.4 sq in. If the beams are spaced 1.03 ft on centers the unit direct compression is 42 000 x 1.03/8.4 = 5 150 lb, which is well within the allowed stress given by Table II, page 575. To satisfy the condition of web-crippling due to shear, the ' shearing-stress must ' not exceed the value as derived from the formula for allowable shear. (See, in Chapter XV, paragraphs and foot-notes relating to Buckling of Beam- Webs and to the illustrative Example 15 in that chapter.) The approximate, allowed, unit shearing value may be obtained by dividing the value of Sb (Table II, page 575) by the factor F, the values of which are given in Table TX A, following. For example, for a 12-in 3iH-lb beam this shearing value = 13 060/, 165 = 7915 lb per sq in. The shearing capacity of the beam is obtained by multiplying this unit stress by the depth of beam times the web-thickness, or 7915X I2X 0.35 = $$ 240 lb, or much more than required. Only one of the conditions of web-crippling need be considered by applying the following rule: If the shear divided by the depth of the beam is greater than the total load divided by the product of the distance (over which the load is distributed) by the factor F, investigate for shear; if otherwise, investigate for direct compres- sion. This rule may also be expressed as follows: According as {I — 'w)/l is greater or less than 2 D/w'F, investigate for shear or for compression. Here / = length of beam, lu = loaded portion of beam, D = depth of beam, w' = length of beam, over which the load is assumed to be distributed (often taken = w + HD) and F = the factor for the given beam obtained from Table IX A. All dimensions must be taken in the same unit. If, instead of the 12-in beams, 15-in 42-lb beams, having a section-modulus of 58.9 are used, the spacing will be 58.9/34.8 = 1.7 ft nearly, say i ft 8 in. By referring to Table IX, page 182, it is seen that the spacing of the beams is well within the safe limit of the concicte and no tie-rods are theoretically necessary. It is preferable, however, to use at least one row of tie-rods. Table IX A. Values of Factor F* for Shearing Values for Various Beams r Beams For standard- weight beams For heavy- weight beams 12-in beam 15-in beam 1 8- in beam 20-in bearrt 24-in beam 1.65 1. 71 1.76 1.77 1. 91 1. 52 1.50 1.58 1.62 1.67 * The factors, F, which have been deduced to be used in connection with Sb, Table II, pages 574-5, to give the safe unit shearing value based on web-crippling, will help greatly in investigations of shears in case tables of safe shears are not obtainable. It is to be noted, however, that the values derived from the use of F are approximate only, as this factor is a little different for every beam; and to give its value for every beam would require as much space as complete tables of safe shears. The values of F are not given for the new sections of light beams as they are not usually good sections for grillages. It may be mentioned that the standard weight for each size of beam for which F is given is always the next weight higher than the minimum weight given in Table II, j)ages 574-5, except for the 20-in beams, for which the minimum weight, 65 lb, is also the standard weight. The rule given above for detefmining whether web-crippling based on shear or on direct compression is the determining condition eliminates one of the calculations to be made in investigatiug grillages. 184 Foundations Chap. 2 The Design of a Column-Footing of steel beams is illustrated by the following example: A column carries 576 tons. The allowable pressure on the foundation-bed is 3 tons per sq ft. What should be the arrangement, number and size of the steel beams composing the grillage? The required area of sup- port = 576/3 = 192 sq ft. In order to make the problem as general as possible let it be supposed that practical considerations limit the width of the footing to 12 ft. The dimensions of the concrete mat on which the lower layer of beams rests will be 12 by 16 ft. By referring to the diagram (Fig. 28) we find that if the mat is made 12 in thick an offset of 6 in is permissible. The dimensions of the lower layer of beams will therefore be 11 by 15 ft. A suitable grillage for the given conditions may be designed of two or of three layers. If two layers are used the length of the top beams will be 11 ft. Assuming the column-base = 30 in, the loaded portion = qVz ft, and by Formula (i), the bending moment * = H X I 152 000 lb X (11 — 2^) X 12 X H = 14 688 000 in-lb, from which the required section-modulus (at 16 000-lb maximum fiber-stress) = 918. By re- ferring to Table IV, Chapter X, five 24-in 90-lb beams have a section-modulus of 932.5 and consequently satisfy the condition of bending. By applying the rule given in the preceding paragraph for the design of a wall-footing, to see if web-crippling due to shear or to compression is to be investigated, {I — w)/l = 0.773 and 2 D/w'F = 0.958, which, being greater than 0.773, shows that the beams should be investigated for web-crippling due to compression, by the method explained in the previous example. It will be found that the five 24-in 90-lb beams also satisfy this condition and will therefore be used. Their flange- width is about 7H in, so they should be spaced about 9'/^ in on centers, requir- ing the length of the column-base to be about 3 ft 9 in. The calculation for the lower layer is similar, the length of the beams being 15 ft and the loaded portion, 3 ft 9'in. It is rarely necessary to investigate the lower layer for web- crippling, the condition of bending, except for the top layer, being usually the governing feature. If, owing to conditions of bending, it is not practicable to make the beams of the top layer sufficiently long to extend across the required width of the concrete mat, it is then necessary to make the grillage of three layers. The calculation for a three-layer grillage for the same problem as the preceding is as follows: Calculation of the Top Layer. For web-crippling due to compression, I 152 000 \h = Sb X w' X t X n, where Sb = the allowable unit stress, w' = the length of beam over which the load is assumed to be distributed, / = the web- thickness and n = the number of beams. Referring to Table II, Chapter XV, and assuming a 20-in 75-lb beam to be used, Sb = 13 660 lb per sq in and / = 0.649 in. Taking w' = 30 in (the width of the column-base), 13 660 x 30 X 0.649 = 265 960 lb and the value for five beams is i 329 800 lb, which is more than enough. But it is found that five 20-in 70-lb beams would not be suffi- cient. It will be economical to make these beams of the greatest length for which they will resist bending. The section-modulus of one beam is 126.9; ^.nd the total Mr = 5 X 126.9 X 16 000 (assumed fiber-stress). This may be determined, also, by Formula (i) in which M = H WP. From these equations the projec- tion P = 35H in, and the length of the beams is therefore (2 X 35H) + 30 (the width of the base) = 100V2 in, or approximately 8 ft 4 in. By applying the foregoing rule to see if web-crippling due to shc^r must be considered, (100— 3o)/ioo= 0.7 which is less than 40/(30 x 1.62) = 0.82, and the shear need not be investigated. * It is to be noted that the bending moment is the same as for a beam uniformly loaded with 576 tons on a span of Sy-i ft, (/ — w), and that the number and size of the required beams, as far as bending is concerned, may be taken from the tables giving the safe loads of beams. See Table IV, Chapter XV. Steel Grillages in Foundations 185 ililiiiilLli The width of the flanges of these beams is nearly 6H in, so that they should be spaced from 8V^ to 9 in, thus making the required length of column- base about 3 ft 6 in. Calculation of the Second Layer. Since the length of the top layer is limited to 8 ft 4 in and the width of the lowest layer is 11 ft, it will be necessary to have an intermediate layer. This will cover the area given by the length of beams of the top layer and the width of the lower layer, or 8 ft 4 in by 11 ft. The beams will of course be at right-angles to those of the top layer, so their length will be II ft, and they are to be so spaced as not to exceed 8 ft 4 in. Since the width of the top course is 3H ft, their projection is (ii ft— 3]^ it)/ 2 = 3% ft, the amount of single shear is i 152 000 X 3.75/1 1 = 392 720 lb and the bending moment is H X i 152 000 X 45 in= 12 960 000 in-lb. Using 16 000 lb as the fiber-stress the required section-modulus is 810. By referring to Table IV, Chapter X, for section- moduli and determining the maximum shear as above ex- plained, we find that ten 15-in 60-lb beams will have a total section-modulus of 812, and they will also be ample for shear. Furthermore, ten beams spaced to cover a width of 8 ft 4 in will give a spacing, center to center of beams, of about 10 in, which is sufficient. It would be better, however, to use ten 18-in 55-lb beams. Calculation of the Bottom Layer. Taking the effective width of the middle layer as 8 ft, the projection of the beams is (15 ft — 8 ft)/2 = sVz ft. Then similarly to the above, the shear = 268 800 lb. M = 12 096 000 in-lb, from qr Ml f • iLlliill ' ' n' 1 1 f \ t \ I [ "i (' ] \ \ [ "1 )f'\ 1 J L 1 . 1 1 I 1 L J t — — J 1/ J 1" 1 1^ j 1 i t i i t J • L\ iM 1.1 r ^ J 1 l^. J I 1 " . ' 1 Fig. 29. Steel-beam Grillage Column-footing which the section-modulus = 756, and thirteen 15-in 42-lb beams, spaced loH in on centers, will be required, or two 15-in 60-lb beams and ten 15-in 42-lb beams may be used, increasing the spacing between the beams. In this case the heavy beams should be placed nearest to the center of the footing. This grillage is illustrated in Fig. 29. t86 Foundations Chap. 2 24. Reinforced-Concrete Footings Advantages and Disadvantages. Reinforced concrete has in recent years been largely used for footings. The arguments in favor of its use are: (i) Low cost of the footing-construction; (2) Reduction in the amount of excavation required; (3) Convenience, as compared with the use of steel-beam grillages, in that the reinforcing-steel is readily obtainable, can be cut to length on the work and handled without derricks. The objections urged are: (i) Danger of defective workmanship, as the strength of the footing depends upon the proper mixing and placing of the concrete, the proper placing of the reinforcement and the complete union of the concrete with the reinforcement. The danger of defective workmanship is increased by reason of the usual difficul- ties of foundation- work, in that water and mud are generally present and the difficulty of careful work and inspection is greater. (2) Danger of the deterioration of the steel reinforcement either by rusting or by electrolysis. This danger is increased by the presence of moisture and by the relatively small cross-section of the reinforcing-bars. In this connection it is well to remember that in reinforced-concrete girders as usually designed the concrete on the tension side is stressed beyond its elastic limit, as a result of which, numerous fine cracks are developed under the figured load. Use of Reinforced Concrete for Foundations. From the foregoing it is apparent that great care should be used in connection with reinforced concrete in foundations, especially as any defect is difficult to detect or repair. Rein- forced concrete is used not only for so-called mats or slabs but is frequently used for distributing-girders, bolsters and even for cantilevers. The author's preference is against reinforced concrete for foundations for important structures. The Methods Used in Calculating the Strength of Reinforced-Con- crete Slabs, Girders, etc., are explained in Chapters XXIV and XXV, The stresses coming on the reinforced-concrete construction are to be determined in the same way as explained for footings of other materials. 25. Timber Footings for Temporary Buildings Timber Footings. For buildings of moderate height timber may be used to give the necessary spread to the footings, provided water is always present. The footings should be built by covering the bottom of the trenches, which should be perfectly level, with 2-in planks laid close together and longitudinally with the wall. Across these planks heavy timbers should be laid, spaced about 12 in on centers, the size of the timbers being proportioned to the transverse stress. On top of these timbers again should be spiked a floor of 3-in planks of the same width as the masonry footings which are laid upon it. A section of such a footing is shown in Fig. 30. All of the timber-work must be kept below low-water mark, and the space between the transverse timbers should be filled with sand, broken stone, or concrete. The best, woods for such founda- tions are oak, long-leaf yellow pine and Norway pine. Many of the old build- ings in Chicago rest on timber footings. Calculations for the Sizes of the Cross-Timbers. The sizes of the trans- verse timbers should be computed by the following formula: Breadth m mches = ~ -. » Timber Footings for Temporary Buildings 187 w representing the bearing resistance of the foundation-bed in pounds per square foot, p the projection of the transverse timbers beyond the 3-in planks, in feet, 5 the distance on centers of the timbers in feet, and d the assumed depth of the beam in inches. A is the constant for strength.* The values recommended for it are 67 for long-leaf yellow pine and white oak, 44 for Norway pine, and 39 for common white pine or spruce, all increased from 30 to 40% for temporary build- ings. (See Table II, page 628.) Fig. 30. Spread Footing of Timber Example. The side walls of a given building impose on the foundation a pressure of 20 000 lb per lin ft; the soil will only support, without excessive settlement, 2 000 lb per sq ft. It is decided for economy to build the footings as shown in Fig. 30, using long-leaf yellow-pine timber. What should be the size of the transverse timbers? Solution. Dividing the total pressure per linear foot by 2 000 lb, we have 10 ft for the width of the footings. The masonry footing we will make of granite or other hard stone, 4 ft wide, and solidly bedded on the planks in Portland, cement mortar. The projection p of the transverse beams will then be 3 ft. We will space the beams 12 in on centers, so that ^=1, and will assume 10 in for the depth of the beams. Then, by the formula. the breadth in inches = 2 X 2000 X 9 X I 100 X 90 and we should use 4- by lo-in timbers, spaced 12 in on centers. If spruce timber were used we should substitute 55 for 90, and the result would be 6H in. (See note, page 628, for ^4 increased from 30 to 40%.) Foundations for Temporary Buildings. W^en temporary buildings are to be built on a compressible soil, the foundations may, in some parts of the country, be constructed more cheaply of timber than of any other material, and in such cases the durability of the timber need not be considered, as when it is sound it will last two or three years in almost any place, if thorough ventilation is provided. The World's Fair buildings at Chicago (1893) were, as a rule, supported on timber platforms, proportioned so that the maximum load on the soil would not exceed i}4 tons per sq ft. Only in a few places over mud-holes were pile foundations used. * The values given to the term A of the formula vary In different building codes. 188 Foundations Chap. 2 26. General Conditions Affecting Foundations and Footings General Considerations. Where the footings of a building rest on wet sand, or on clay, it is important that any movement of the material forming the foundation-bed be prevented if possible. In many cases it is advisable to con- nect all footings with a concrete floor to prevent any uplift of the foundation- bed between the footings. Where unequal settlement is apprehended it is inadvisable to have long columns firmly attached to the footings, as any unequal settlement of the footings develops a bending-stress in the column; such bending-stresses, in the case of long columns, may become extremely serious, resulting possibly in the rupture or distortion of the columns. In such cases it has even been proposed to design the bases of the columns with ball-and-socket joints which would allow unequal settlement of the footings without distortion or bending of the columns. Such connections, however, could not be generally used because of the necessity of bracing the structure against the horizontal pressure of the wind, but they would be entirely practicable in the case of long interior columns. The Minimum Depth of Footings is limited by the depth of the cellar, by the requirements of the cellar as to whether part of the footings can project above the cellar-floor level, and by the depth of the footing itself. The minimum depth will be advantageously exceeded if, by a slight increase in depth, a material capable of sustaining a higher unit load is found on which to rest the footings; or if, as explained in previous articles of th's chapter, greater security is afforded by locating the footing at a greater depth. These considerations will influence the design of a footing and in all cases should be taken into consideration. In some cases it may be cheaper to abandon the use of a spread footing of any type and resort to piles or masonry construction going to rock or to some other solid substratum. Where there is any question on this point, careful comparison should be made of the advantages and costs of the two methods. In general, however, it will be cheaper to spread footings immediately below the cellar- excavation level than to employ any of the various deep-foundation methods. Deep Foundations are necessary when the material at the level at which SPREAD footings would Ordinarily be constructed is not suitable, or in case it is desirable for any reason to carry the foundations of the building down to an underlying stratum of greater supporting power. Recourse must then be had to one or more of the following expedients: (i) Wooden piles; (2) Concrete piles; (3) Piers or walls constructed in pits or trenches, or by other methods, and going down to the required depth to reach a solid stratum. 27. Wooden-Pile Foundations The Use of Wooden Piles. When it is required to build upon a compres- sible soil that is constantly saturated with water and of considerable depth, the most practicable method of obtaining a solid and enduring foundation for buildings of moderate height is by driving wooden piles. Many buildings in the city of Boston, Mass., and several tall oflice-buildings of New York City and Chicago, rest on wooden piles, and they are extensively used for supporting buildings, grain-elevators, etc., erected along the water-front of coast and lake cities. The durability of wooden piles in ground constantly saturated with water is beyond question, as they have been found in a perfectly sound condir tion after the lapse of from six to seventeen centuries. Wooden-Pile Foundations 189 Municipal Requirements. The laws of Boston require that wooden piles ihall be capped with block-granite levelers or with Portland-cement concrete, ind that the spacing shall not exceed 3 ft between centers. The laws of Chicago equirc that wooden piles shall be driven to rock or hard-pan and capped with ,Tillage of timber, concrete, or steel, or a combination of these. The laws of ^ew York specify a minimum diameter of 5 inches and a maximum spacing of J feet between centers. The Maximum Loads Allowed on "Wooden Piles in various cities are as follows: Atlanta, 20 tons; Philadelphia, 20 tons; Buffalo, 25 tons; Minneapolis, 20 tout; Richmond, 25 tons; St. Louis, as many tons as the piles will safely iupport; Chicago, 25 tons; Louisville, 20 tons; St. Paul, 25 tons; New York, 20 tons; Portland, Ore., 25 tons; Cleveland, 25 tons. Most of the above cities ilso limit the allowed load by Wellington's formula which is hereinafter given m page 193, under the heading, Bearing-Power of Piles. Kinds of Wood Used for Piles. Wooden piles are made from the trunks ol trees and should be as straight as possible and not less than 5 in in diameter a,t the small end for light buildings, or 8 in for heavy buildings. The woods generally used for piles are spruce, hemlock, white pine, Norway pine, long-leaf and short-leaf yellow pine, pitch-pine, cypress, Douglas fir, and occasionally oak, hickory, elm, black gum and basswood. There does not appear to be much difference in the woods as to durability under water, but the tougher and stronger woods are to be preferred, especially where the piles are to be driven to hard-pan and heavily loaded. Preparing Wooden Piles for Driving. The piles should be PREPARED FOR DRIVING by cutting off all limbs close to the trunk and sawing the ends square. It is probably better to remove the bark, although piles are more often driven with the bark on, and it is doubtful if the bark makes much difference one way or the other. For driving in soft and silty soils, experience has shown that the piles drive better with a square point. When the penetration is less than 6 in at each blow the top of the pile should be pro- tected from BROOMING by put- ting on an iron ring, about i in less in diameter than the head of the pile, and from 2H to 3 in wide by % in thick. The head should be chamfered to iit the ring. When driven into compact soil, such as sand, gravel, or stiff clay, the point of the pile should be shod with iron or steel. The method shown at A, Fig. 31, answers very well for all but very hard soils, and for these a cast conical point about 5 in in diameter, secured by a long dowel, with a ring around the end of the pile, as shown at B, makes the best shoe. Piles that are to be driven in or ri ''B Points of Wooden Piles Prepared Driving for 190 Foundations Chap. 2 j exposed to salt water should be thoroughly impregnated with creosote, dead oil, i or coal-tar, or some mineral poison to protect them from the teredo or ship- | WORM, which will completely honeycomb an ordinary pile in three or four years. | Driving Wooden Piles with the Drop-Hammer. The piles should alwa5rs i be driven to an even bearing, which is determined by the penetration under ! the last four or five blows of the hammer. The usual method of driving piles ] for the support of buildings js by a succession of blows given with a block of cast iron or steel, called the hammer, which slides up and down between the t uprights of a machine called a pile-driver. The machine is placed over the ! pile, so that the hammer descends fairly on its head, the piles always being driven with the small end dowru The hammer is generally raised by steam-power i and is dropped either automatically or by hand. The usual weight of the hammers used for driving piles for building foundations is from i 500 to 2 500 lb, and the fall varies from 5 to 20 ft, the last blows being given with a short fall. , Occasionally, hammers weighing up to 4 000 pounds and over are used. Driving Wooden Piles with the Steam-Hammer. Steam-hammers* are to a considerable extent taking the place of the ordinary drop-hammers in large cities, as they will drive many more piles in a day, and with less damage to the piles. The steam-hammer delivers short, quick blows, from sixty to seventy to the minute, and seems to jar the piles down, the short interval be- tween the blows not giving time for the soil to settle around them.f In driv- ing piles care should be taken to keep them plumb, and when the penetration becomes small, the fall should be reduced to about 5 ft, the blows being given in rapid succession. Whenever a pile refuses to sink under several blows, before reaching the average depth, it should be cut off and another pile driven beside it. When several piles have been driven to a depth of 20 ft or more and refuse to sink more than H in under five blows of a i 200-pound hammer falling 15 ft, it is useless to try them further, as the additional blows only result in brooming and crushing the heads and points of the piles, and splitting and crushing the intermediate portions to an unknown extent. Spacing Wooden Piles. Piles should be spaced not less than 2 ft nor more than 3 ft, on centers, unless iron, wooden, or reinforced-concrete grillage is used. When long piles are driven closer than 2 ft on centers there is danger that they may force each other up from their solid bed on the bearing stratum. Driving the piles close together also breaks up the ground and diminishes the bearing power. When three rows of piles are used the most satisfactory spac- ing is 2 ft 6 in on centers across the trench and 3 ft on centers longitudinally, provided this number of piles will carry the weight of the building. If they will not, then the piles must be spaced closer together longitudinally, or another row of piles driven; but in no case should the piles be less than 2 ft apart on centers, unless driven by means of a water-jet. The number of piles under the different portions of the building should be proportioned to the weight which they are to support, so that each pile will receive very nearly the same load. Capping Wooden Piles. The tops of the piles should invariably be cut off at or a little below low water-mark, otherwise they will soon commence to decay. They should then be capped, either with large stone blocks, or concrete, or with timber or steel grillage. Granite Capping. Wooden piles are sometimes capped with block-granite LEVELERS which rest directly on the tops of the piles. If the stone does not fit * See Table XI, page 204. t The 5 000 piles, averaging 48 ft in net length, under the Chicago Post Office were driven with a steam-hammer weighing 4 400 lb and delivering 60 blows per minute. W ooden-Pile Foundations 191 r ;he surface of the pile, or a pile is a little low, it is wedged up with oak or stone //edges. In capping with stone a section of the foundation should be laid out m the drawings showing the arrangement of the capping stones. A single ^tone may rest on one, two, or three, but not oii four piles, nor on three piles in 1 straight line, as in the two last-mentioned , ::ases it is practically impossible to make the stones bear evenly. Fig. 32 shows the best arrangement of the capping for three rows of piles. Under dwellings and light buildings the piles are often driven in two rows, staggered, in which case each stone should rest on three piles. After the piles are capped, large footing stones, extending in single pieces across the wall, shouW be laid in cement mortar on the capping. Fig. 33 shows a partial piling-plan, with the arrange- ment . of the capping stones, of the Boston Chamber of Commerce Building. It may be seen that most of the stones rest on three piles, and a very few on two piles. '^^yj r ^-^-2 3^^<-2 3^V> Fig. 32. Stone Capping for Three Rows of Wooden Piles Concrete Capping. In many buildings a very ;ommon method of capping is to excavate to a depth of I ft below the tops of the piles and i ft Dutside of them and to fill the space thus excavated solid with Portland-cement concrete, deposited in layers and well rammed. After the concrete is brought level with the tops of the piles additional layers are deposited over the whole width of the foundation until the concrete attains a depth of i8 in above the piles. On this foundation brick or stone footings are laid as on solid earth. If long bars of twisted steel, about % in square in cross-section are embedded in the concrete about 3 in above the tops of the piles, the construction makes, in the opinion of the author, the best form of capping, the twisted bars giving great transverse strength to the concrete. Timber-Grillage Capping. The pile foundations of many buildings have heavy timber grillages bolted to the tops of the piles and stone or concrete foot- ings laid on top of the grillages. The tirnbers for the grillages should be at least 10 by 10 in in cross-section, and should have sufficient transverse strength to sustain the load from center to center of piles, using a low fiber-stress. They should be laid longitudinally on top of the piles and fastened to them by means of DRIFT-BOLTS, which are plain bars of iron, either round or square in section, and driven into holes about 20% smaller in section than the bolts themselves. Round or square bars i in in section are generally used, the holes being bored by a -M-in auger for the round bolts and by a %-in auger for the square bolts. The bolts should enter the piles at least i ft. It heavy stone or concrete footings are used and the space between the piles and timbers is filled with concrete level with the tops of the timbers, no more timbering is required; but if the lootings are made of small stones and no concrete is used, a solid floor of cross-timbers, at least 6 in thick for heavy buildings, should be laid on top of the longitudinal capping and drift-bolted to them. Where timber grillage is used it should, of course, be kept entirely below the lowest recorded water-line, as otherwise it will rot and allowjthe building to settle. It has been proved conclusively, however, that any kind of sound timber will last practically forever if completely immersed in water. 192 Foundations The Advantages of Timber Grillage are that it is easily laid and effectually) holds the tops of the piles in place. It also tends to distribute the pressure 3venly over the piles, as the transverse strength of the timber will help to caYry o oro b |o Fig. 33. Piling-plan, Chamber of Commerce Building, Boston, Mass. the load over a single pile, which for some reason may not have the same bearing capacity as the others. Steel beams, embedded in concrete, are sometimes used to distribute the weight over piles, but some other form of construction can generally be employed at less expense and with equally good results.* * For a description of the pile foundations and capping of the Chicago Post Office, see Freitag's Architectural Engineering, pages 350 to 352. Wooden- Pile Foundations 193 Specifications for Wooden-Pile Foundations. This contractor is to firr- nish and drive the piles indicated on sheet No. i. The piles are to be of sound spruce (hemlock, long-leaf yellow pine) perfectly- straight from end to end, trimmed close, and cut off square to the axis at both ends. They are to be not less than 6 in in diameter at the small, end, lo in at the large end, when cut off, and of sufficient length to reach solid bottom, the neces- sary length of piles to be determined by driving test-piles in different parts of the foundation. All piles are to be driven vertically, in the exact positions shown by the plan, until they do not move more than 5 in under the last five blows of a hammer weighing 2 000 lb and falling 20 ft. All split or shattered piles are to be re- moved if possible and a good one driven in place of each imperfect one. In cases where such piles cannot be removed an additional pile is to be driven for each imperfect one. If the piles show a tendency to broom, they are to be bound with wrought-iron rings, 2\^ in wide and y2 in thick. All piles, when driven to the required depth, are to be sawed off square for a horizontal bearing at the grade indicated on the drawings. The Bearing Power of Piles. In regard to their use for supporting build- ings, piles may be divided into two classes: (i) Those which are driven to ROCK or HARD-PAN, that is, firm gravel or clay and (2) those which do not reach hard-pan. (i) A pile belonging to this class when driven through a soil that is sufficiently firm to brace the pile at every point, may be computed to sustain a load equal to the safe resistance to crushing on the least cross-section. If the surrounding soil is plastic the bearing power of the pile will be its safe load computed as a column, having a length equal to the length of the pile when capped. Test- piles driven on the site of the Chicago Public Library Building, through 27 ft of soft, plastic clay, 23 ft of tough, compact clay and 2 ft into hard-pan, sus- tained a load of 50.7 tons per pile for two weeks without apparent settlement. There are many instances where piles driven to the depth of 20 ft in hard clay sustain from 20 to 40 tons, and a few instances where they sustain up to 80 tons per pile. (2) A pile belonging to this class depends for its bearing power upon the FRICTION, COHESION and buoyancy of the soil into which it is driven. The safe load for such piles is usually determined by the average penetration of the pile under the last four or five blows of the hammer. Several engineers have formulated rules for determining the safe loads for piles of this class, but there are so many conditions that modify the amount of the penetration, and its exact determination, and so many varying conditions of driving and of soil, that it is considered impossible to formulate any rule that can be considered entirely satisfactory for all the conditions under which such piles are driven. The Engineering News Formula. The formula generally used by engineers was derived by M. A. WelHngton, and is often referred to as the Engineering News formula: The safe load in tons = 2 wh/ {S + 1) in which w = the weight of the hammer in tons; h = the height of fall of the hammer in feet; 6* = the penetration in inches under the last blow or the average under the last five blows. When loads are based on this formula the piles should be driven until the pene- tration does not exceed the limit assumed, or if this is found to be impracticably 194 Foundations Chap. 2 new calculations must be made based on the smallest average penetration that can be obtained, and a greater number of piles used. In localities where piling is commonly used for foundations, the least penetration that can be obtained within practical limits of length of pile can generally be ascertained by observa- tion, or by consulting somebody who is experienced in driving piles. The longer the pile the less, as a rule, will be the final set or penetration. Where there is no experience to guide one it will be necessary to drive a few piles to determine the length of pile required, or the least set for a given length of pile. Some piles will have to be driven further than others to bring them to bearings of equal resistance. When the piles are to be loaded to more than 50% of the assumed safe load, the final set of each pile should be carefully measured by an inspector, the broom and splintees being removed from the head of the pile for the last blow. Safe Loads for Piles. Table X, computed by the above forniula, gives the safe loads for different penetrations, under different falls of a hammer weighing I ton. For a hammer of different weight multiply the safe load in the table by the actual weight of the hammer in tons. Thus, for a hammer weighing I 000 lb, the values in the table should be multiplied by 3'^ and for a i 500-lb hammer, by %. Table X. Safe Loads in Tons for Piles For hammer weighing i ton Penetration of pile in inches Height of the fall of the hammer in feet 3 4 5 6 8 10 12 19.4 16.1 13.8 12.0 10.7 9.6 8.8 8.0 6.9 6.0 5-3 4.8 4.0 3.4 14 16 18 -9.1 24.0 20.7 18.0 16.1 14.4 13.1 12.0 10.3 9.0 8.0 7.2 6.0 5.1 20 25 30 0.25 0.50 0.75 1. 00 1.25 1.50 1. 75 2.00 2.50 3.00 3.50 4.00 5. 00 6.00 4.8 4.0 3.4 3.0 6.4 5.3 4.6 4.0 3.6 3.2 8.1 6.7 5.7 S.o 4.5 4.0 3.6 3.3 1:1 6.9 6.0 5.4 4.8 4.4 4.0 3.4 3.0 12.9 10.7 9.2 8.0 7.1 6.4 5.8 5.3 4.6 4.0 3.6 3.2 16. 1 13.3 11.5 lO.O 8.9 8 7.3 6.7 5.7 5.0 4.4 4.0 3.3 22.5 18.7 16. 1 14.0 12.5 11. 2 10.2 9-3 8.0 7.0 6.2 5.6 4.7 4.0 25.8 21.3 18.4 16.0 14.3 12.8 II. 7 10.7 91 8.0 7.1 6.4 5.3 4.6 32.3 26.6 23.0 20.0 17.9 16.0 14.6 13.3 II. 4 10. 8.9 8.0 6.7 5.7 33.3 28.8 25.0 22.3 20.0 18.2 16.7 14.3 12. 5 II. I 10.0 8.3 7.1 34. 5 30 26.7 24.0 21.9 20.0 17. 1 15-0 13.3 12.0 lO.O 8.6 Example of Computations for Pile Foundation. Suppose that from the observations of the pile-driving for an adjacent building it is found that piles driven from 20 to 30 ft take a set of i in under a i 200-lb hammer falling 20 ft, and that additional blows result in about the same set. From Table X we find that the safe load for a fall of 20 ft and a penetj tion of I in is 20 tons. Multiplying by the weight of the hammer in tons, we have 12 tons as the safe load per pile. Suppose that the total load oil lin ft of footing is 13 tons. As we must have at least two rows of piles, and' each two piles will support 24 tons, it follows that the spacing of the piles longitudinally should be 24/13 = i ft 10 in. As this is too close, we should use three rows of piles, spaced 2 ft apart laterally, and the longitudinal spacing 'ofl Wooden-Pile Foundations 195 wouid then be 36/13 = 2 ft 9 in. The width of the capping would be about 5 ft. If the load on the piles under the interior columns, for example, is 105.8 tons, this, divided by 12, the safe load for one pile, gives nine piles, or three rows of three piles each, which should be spaced 2 ft 6 in apart, each way. Some Actual Loads on Wooden Piles. The following examples of the actual loads supported by piles, under well-known buildings, and of loads which piles have borne for a short time without settlement, should be of value when designing pile foundations. Boston. At the Southern Railroad Station three piles were loaded with about 60 tons of pig iron, 20 tons per pile, without settlement. The allowed load was 10 tons per pile. Piles 12 in in diameter at the butt and 6 in at the point, driven 31 ft into hard, blue clay near Haymarket Square, failed to show movement under 30 tons, the ultimate load being probably 60 tons.* Other piles driven 17.9 ft sustained a load of 31 tons each. The average penetration under the last ten blows of a I 710-lb hammer faUing from 9 to 12 ft varied from 0.4 to 0.95 in per blow for fifteen piles. Piles 25 ft long under the Chamber of Commerce Building penetrated about 3 in under the last blow of a 2 000-lb hammer falUng about 15 ft. Chicago. In the Public Library Building the piles were proportioned to 30 tons each and were tested to 50.7 tons without settlement. In the Schiller Building the estimated load was 55 tons per pile; the building settled from iH to 2H in. In the Passenger Station of the Northern Pacific Railroad, at Harrison Street, piles 50 ft long were designed to carry 25 tons each and did so without per- ceptible settlement. The Art Institute Building, parts of the Stock Exchange Building and also a large number of warehouses and other buildings on the banks of the river rest on piles. New York City. The Ivins (Park Row) Building is supported by about 3 500 14-in spruce piles, arranged in clusters of fifty or sixty, for single columns, and a corresponding number under piers supporting two or more columns. The piles were driven to refusal of i in under a 20-ft fall of a 2 000-lb hammer. The material is fine, dense sand to a depth of over 90 ft. But few piles could be driven more than 15 or 20 ft. The average maximum load per pile is 9 tons.f The American Tract Society's Building is supported on piles. Brooklyn. Piles under the Government Graving Dock, driven" 32 ft, on the average, into fine sand mixed with fine mica and a Httle vegetable loam, are supposed to sustain from 10 to 15 tons each. New Orleans. Piles driven from 25 to 40 ft into a soft alluvial soil carry safely from 15 to 25 tons, with a factor of safety of from 6 to 8. J The Cost of Driving Wooden Piles. § The cost of driving piles naturally varies with the character of the soil, and the conditions under which they are driven. New York City. A 2 500-lb drop-hammer drove 4 piles per day of 10 hours, with a steam-hammer, 13 piles per day were driven, for the same foundation. The piles were 70 ft long, 8 in in diam at the point and 15 in at the head. The average cost of driving 800 piles with the steam-hammer was $2 each. In New York Harbor i 800 piles were driven by a steam-hammer, from 24 to 26 ft into gravel and hard-pan, at a cost of 80 cts each. * Horace J. Howe, American Architect, June ii, 1898. t For a description of this foundation, see the Engineering Record of July 23, 1898. t W. M. Patton. § These prices are now (1920) considerably higher. 196 Foundations Chap. 2 Chicago. Forty Norway-pine piles were driven by a firm of contractors IS ft deep every ten hours at a cost, for driving, of 55 cts each. Another firm drove from 60 to 65 piles, each 45 ft long and 15 ft deep, into hard sand each day at a cost of about 30 cts each. In both cases steam-hammers were used.* Boston. Spruce piles from 30 to 45 ft long cost from $3 to $5, in place. Long-leaf yellow pine piles, as long as 70 ft, cost about $15 apiece for the piles themselves, and $2 or more each for the driving. Oak piles from 40 to 50 ft long cost from $8 to $10 each, in place. f Some Other References to Wooden Piles and Pile-Driving. A very valuable paper on "Some Instances of Piles and Pile-Driving, New and Old," by Horace J. Howe, was published in the American Architect and Biulding News, commencing June 11, 1898. The paper records a great many tests and gives several formulas and many experiences of distinguished engineers. Part I of Building Construction and Superintendence, by F. E. Kidder, gives additional information in regard to pile foundations and experiments on the bearing power of piles. Much valuable information on piles is given in "A Practical Treatise on Foundations, " by W. M. Patton. The recent Engineers' Handbooks, also, should be consulted for additional data. 28. Concrete-Pile Foundations Durability of Wooden and Concrete Piles, Concrete piles, either plain or reinforced, possess many advantages over wooden piles and, in general, can be'used in all places where wooden piles can be driven. Concrete piles, com- pared with wooden piles, have primarily the advantage of greater permanence. Timber piles, kept constantly wet and protected from the action of the torredo or other destructive influences, may be practically everlasting, but cannot be counted upon above water level; whereas concrete piles should be proof against all deteriorating actions, whether wet or dry, except the action of freezing on wet concrete. Strength of Wooden and Concrete Piles. Concrete piles without rein- forcement, if made of good concrete, should have nearly the same crushing STRENGTH per squarc inch as ordinary yellow-pine piles, and with properly placed reinforcement concrete piles should ha,ve a much higher crushing strength per square inch than timber piles. Moreover, timber piles do not have uni- form CROSS-SECTIONS. For instance, a slender timber pile 40 ft in length and 12 in in diameter at the butt, is probably not over 6 in in diameter at the point. In direct compression the load on a point-bearing pile of the above dimensions is limited to the safe load on the point of the pile, where it is 6 in in diameter; and a cylindrical concrete pile, 12 in in diameter and under similar conditions, will have a cross-section of 113 sq in at all points, compared with the cross- section of 28 sq in at the point of the timber pile. Moreover, if we consider both piles as long columns, it must be borne in mind that a timber pile may not be straight and that it may, therefore, be subject to stresses and deformations due to eccentric loading, which are avoided in a straight, concrete pile. Reinforced-Concrete Piles. In practice concrete piles are generally rein- forced, and if a pile is to be considered as a long column the reinforcement may be increased at the center, so as to provide for stresses due to handling and to its acting as a long column. The concrete piles may be formed complete, above ground, in which case they may be straight or tapered, with square, cir- •ular or other cross-sections. The reinforcement may consist of a number of * American Architect, June 4, 1898, page 78. t George B. Francis, in American Architect, July 23, 1898. Concrete-Pile Foundations 197 Vertical rods generally disposed symmetrically around the axis of the pile. The vertical rods should be connected by horizontal wiring or by spiral reinforcement. As before stated, the reinforcement may be increased at the central section so as to provide against stresses due to the use of the pile as a long column, in which case the additional reinforcement should be placed near the periphery of the cross-section. Types of Concrete-Pile Reinforcement. There arc many types of rein- forcement, one method even employing a woven-wire fabric which is laid out flat on a table and covered with a thin layer of concrete, the entire mat comprising the wire fabric and the concrete being then rolled into a solid cylindrical form which, when set, forms the finished pile. The concrete piles may be formed in PLACE by any one of several different methods. The Raymond System of Concrete Piling. In this system of concrete piling a permanent form is provided for each pile. The Raymond system consists of a collapsible steel mandrel or core, tapering from 8 in in diameter at the point at the rate of 0.4 in per foot in length, until in a length of 37 ft> the cUameter equals 23.2 in. Upon this expanded mandrel or core is placed a spirally reinforced sheet-metal shell, the reinforcement of which is grooved into the metal on 3-in centers the entire length of the core or pile. This rein- forcement imparts rigidity and stiffness to the shell, renders it capable of with- standing very severe soil-pressure and prevents admixture of foreign substances into the green concrete. The combined mandrel and shell is driven into the ground to a proper refusal; the mandrel is then collapsed and withdrawn from the shell, leaving the shell permanently in the ground; and the interior of the shell or form is then inspected, and when perfect from tip to top, is tilled with green concrete. Thus the pile is completed. The extreme taper of the shell, combined with the friction between the shell and the surrounding soil, increases the carrying capacity of the pile. The safe load on a Raymond pile varies from 25 to 30 tons. The Simplex Method of Forming Concrete Piles in Place. The Simplex Method differs from the Raymond method and may be briefly described as follows: A steel pipe, generally cylindrical in form, of the required- size and length and fitted with a detachable cast-iron conical driving-point, is driven into the ground to the required depth; the pipe is then partially filled with concrete. A piston-like plunger, smaller in diameter than the inside diameter of the pipe, is then placed on the concrete and the pipe is partially withdrawn, leaving the driving-point and part of the superimposed concrete in the ground. This operation is repeated until the pile is built up to the required height. In cer- tain materials, instead of using a detachable driving-point, the driving-point consists of two jaws hinged to the lower end of the pipe, so arranged that while during the driving they form a driving-point, when the pipe is withdrawn they open and form an extension of the cylindrical pipe. In other words, the jaws are formed of steel plates previously bent to the same radius as the radius of the pipe and so hinged that when they are in their open-position the plates forming the jaws constitute an extension of the cylindrical surface of the pipe. It is evident that plain reinforcing-bars can be placed in position before concrete is put into the pipe. Caution for Concrete Piles Built in Place. Care should be taken in design- ing and placing the reinforcing for all concrete piles built in place, that the subsequent placing of the concrete does not throw the reinforcement out of position and that all voids between the reinforcement and the shell are com- pletely filled. 198 Foundations Chap. 2 The Pedestal Pile is designed to give an enlarged cross-section at the base of the pile. The method is similar to that of the Raymond method, the increase in diameter being obtained as follows: After the pipe has been driven, the driving-core is withdrawn and the pipe partially filled with concrete. Then the concrete in the pipe is rammed, forcing the concrete out of the pipe and com- pressing the material below the pipe, so that the concrete is forced into the soil. A repetition of this operation results in forming a base or mushroom below the pipe larger in diameter than the diameter of the pipe. Finally the pipe is with- drawn, the filling and ramming-operations continuing meanwliile, until the pile is carried up to the required height. Composite Piles. Protected piles, for use in localities where the torredo affects the life of timber piles under water, are composed of timber piles with concrete coatings held in position by steel reinforcements in the shape of expanded metal or wire netting. Such piles are to be considered as timber piles rather than as concrete piles. Timber Piles with Concrete Caps. In some localities where the permanent water-level is considerably below the level of the required excavation, timber piles have been driven with a follower, the follower consisting of a steel pipe or cylindrical shell. When the head of the pile is driven to a safe distance below low water the pipe-follower is filled with concrete and withdrawn, leaving the concrete pier resting on a timber pile. This composite pile would appear to possess the advantage of combining the cheapness of a timber pile below the water-level with the permanency of a concrete pile above the water- level. Great care, however, should be used in adopting this method on account of the difficulty of securing proper connection between the concrete and the wooden pile. The Methods used in Driving Built-up Piles are practically the same as are used in driving wooden piles, except that a cushion of wood, rope, or other material is placed on the head of the pile to be driven to cushion the blow of the hammer. Steam-driven or air-driven reciprocating hammers are pref- erable to the ordinary drop-hammers. In stiff materials the use of a water- jet is advisable and, in fact, in many cases indispensable. In lifting concrete piles use is made of a special sling which is attached to a pile at two points, each point one-quarter of the length of the pile from the end. The sling should have a spreader so that the stress due to the oblique pull of the chain-sling is takea up by the spreader rather than by the pile. The Casting of Concrete Piles. Concrete piles should be cast in one piece by a continuous operation so that there will be no plane of weakness formed between partially set concrete and fresh concrete. They may be cast either in a vertical position, in forms, or in a horizontal position. Square-sec- tion concrete piles have been cast in a horizontal position and side-forms, only, used, the previously cast concrete pile, protected by paper, forming the bottom form. In some cases, where it is intended to use a water-jet in sinking a pile, the latter is cast around an iron pipe which is afterwards used for the water- jet. In general, however, this is dispensed with and an external detachable pipe used for the water-jet. Incidental Advantages of Concrete Piles. In many cases, where concrete piles are more expensive than timber piles, the saving in excavation and foot- ings more than offsets the increased cost. For example, if the excavation for the cellar of a building does not go down to water-level, the use of timber piles will necessitate excavating down to a point below water-level in order that the piles may be cut off low enough to keep their heads always wet. Concrete Concrete-Pile Foundations 199 piles, however, can be driven from the level of the bottom of the cellar-excava- tion, and this additional excavation and the necessary construction between the excavation-level and the level of the cut-off for the timber piles thus avoided. Moreover, as one concrete pile may have a supporting power equal to the supporting power of four wooden piles, the size of the footings will be much smaller with concrete piles than with wooden piles. Comparison of Wooden and Concrete Piles under Piers. The footings for a column or pier 24 in sq in section, requiring for its support, say, sixteen wooden piles, spaced 2 ft 6 in from center to center, will be, allowing for sUght [inequalities in driving, approximately 10 ft square, the projections being 4 ft beyond the size of the base. Such a footing will ordinarily require a steel grillage or reinforced-concrete base, or, if made of ordinary concrete, will be of very considerable depth; whereas, if four concrete piles, placed 3 ft from center to center, are used, instead of wooden piles, the area of the base will be a little Dver 4 ft square and the projection will be only i ft. A suitable footing would consist of a reinforced-concrete cap not over 2 ft in thickness. The saving in cost of excavation, concrete and steel in the footing is all in favor of the use 3f concrete piles. Concrete Piles under Walls. In the case of a continuous wall, where the load per linear foot of wall is not great, a single row of concrete piles is often mfficient to support the weight of the wall. In such cases, the piles should not be placed in straight hues but should be staggered, and a sufficient footing ihould be constructed connecting the heads of the piles, so as to afford stability to the wall. The Method Employed in Calculating Reinforcement for Concrete Piles is the same as that employed in calculating ordinary reinforced-concrete :olumns, the only difference being that where a pile is not point-bearing, but is dependent on the surrounding material for its support, it need not be considered I LONG COLUMN. PoiNT-BEARiNG PILES deriving their support from some solid material on which their lower extremity rests, must be considered as long rOLUMNS, on the assumption that the material surrounding the piles may fail to support them. In the case of friction-piles, depending for their support .ipon the surrounding material, this assumption cannot be made, as any failure Df the material will involve a settlement of the pile. It should be borne in mind that any structure supported on piles supported by skin-friction is dependent "or its stability upon the continued supporting power of the material surround- ng the piles. In many cases buildings resting on piles driven into soft ground lave settled as the result of the consolidation and settlement of the material surrounding the piles, notwithstanding the fact that the piles when driven were imply able to support the loads for which they were designed. Iron-Pipe Piles with Concrete or Reinforced-Concrete Filling have been I in place of wooden or concrete piles, especially in underpinning- work. The objection to the use of such piles is that the iron pipe forming the external hell may rust, in which case the strength of the pile is reduced to the strength )f the concrete filling and the reinforcement contained therein. The writer Delieves that they should not be used for permanent work. Loads Allowed on Concrete Piles. The building laws of most cities illow on concrete piles from 350 to 500 lb per sq in on the concrete plus from 3 000 to 7 500 lb per sq in on the vertical reinforcement. On this statement t would appear possible to design a short concrete pile 12 in square, on which the allowed load would be 100 tons, and it is possible that such a pile, tested IS a SHORT column, would develop in a testing-machine a strength justifying 200 Foundations ' Chap^ the use of such construction; but, bearing in mind that the character of tn support for the base of such a column is underground and cannot be inspected, and bearing in mind also the uncertainties attending the manufacture of the pile, it is evident that it would be improper to load a pile to this extent in practice. It would, however, be considered good practice to load concrete piles up to one- third of a test-load applied to not less than 3% of the piles used. In ordinary practice, reinforced-concrete piles are loaded up to 500 lb per sq in of cross-sec-_ tion. 29. Foundation Piers and Foundation Walls •i^ff Foundation Piers and Walls as distinguished from ordinary cellar pie and WALLS, extend from the level of the underside of the cellar-floor to rock or other solid foundation-bed. (See page 129, Subdivision i, and also Chapter III, pages 228-9.) In general, such piers and walls are composed of concrete and are of such dimensions that the safe unit loads on the concrete forming them are not exceeded. If the foundation-bed is rock, compact hard-pan, or gravel, there need be little or no enlargement of the base of the pier or wall, as the safe unit loads on such natural foundation-beds are generally equal to the safe unit loads on the concrete forming the body of the pier or wall. The design of such piers and walls is therefore an entirely simple matter governed by the principles already outlined, and by certain considerations mentioned hereafter. The Methods used in the Construction of Foundation Piers and Walls are, however, necessarily varied to suit different materials and to meet different conditions encountered, and the design of a pier necessarily differs with different methods- of construction. For example, if the construction is to be executed by means of the ordinary sheet-piling method, piers and walls will have in general rectangular outlines. But if the Chicago method or the pneu- matic CAISSON is employed, it will generally be cheaper to use piers having a circular cross-section and the support for walls may be a succession of cylinders rather than continuous walls. The detailing of the concrete structure consti- tuting the piers or walls is simple after a determination is made of the methods by which the construction is to be put in place. This subject is discussed in the following chapter-subdivision, Methods of Excavating for Foundations. ^^_ 30. Methods of Excavating for Foundations ^" Simple and Complex Excavations. Excavations in earth for footings of walls and piers may vary from simple trenches and pits of the required sizes and depths to accommodate the footings, up to deep subaqueous excavations requiring all the resources of engineering skill. The Sides of Excavations. If the earth is firm and the depth not excessive the sides of the excavation may be self-supporting, in which case the excavation may be made the neat size of the footing and the sides of the excavation may take the place of forms for the concrete deposited to form the footing. Where the excavation is deep, and especially where the earth is not firm, the sides of the excavation must be sloped or, if made vertical, must be supported by bracing or by some form of sheet-piling. Where the excavation is over 8 ft in depth it will generally be cheaper to support the sides of the excavation than to slope them. Where the excavation adjoins a property-line it will generally be inad- visable to slope the excavation on account of damage to the adjoining property, and in such cases it will be necessary to use sheeting, even if sloping the earth would be cheaper. -m- Ill*l? iipppii y Methods of Excavating for Foundations 201 Bracing in many cases will serve to support the sides of the excavation with- out the necessity of close sheeting. The bracing may consist simply of short pieces of plank placed against opposite sides of the excavation and held in position by horizontal timber struts secured by wedges; or, especially in narrow trenches, some form of an EXTENSIBLE SEWER-BRACE may be used. Fig. 34 repre- sents a usual form of ex- tensible BRACE. Generally, however, the sides of an ex- cavation will not stand with a vertical face, even if braced in this manner, for any length of Fig. 34. Extensible Brace for Narrow Excavations time, and if the material is loose sand or soft clay, such bracing is entirely inadequate. In such cases, and in fact generally, some form of continuous sheet-piling must be employed. Ordinary Wooden Sheet-Piling consists of a continuous line of vertical planks held against the sides of the excavation by horizontal timbers known as WALES, WALING or BREAST-TIMBERS, these wales, or breast-timbers being in turn supported either by cross-braces extending across the excavation to an oppo- site wall or side of the excavation, or by inclined struts known as shores or ; pushers, extending to the bottom of the excavation where heels or inclined platforms are sunk in the undisturbed material to afford points of support. Earth-Pressure on Sheet-Piling. The load on the sheeting due to the sarth-pressure may be calculated on the assumptions made for the design of iETAiNiNG-WALLS, but the thickness of the sheeting planks, the sizes and spacing Df the breast-pieces and braces, if figured on this basis, will in general exceed the dzes constantly used with success and safety in such work. The probable reason "or this is that an earth bank, when steadied and in part supported by the sheet- ng, does not, for a considerable time, lose the cohesion between its particles latural to most earth banks in their original and undisturbed state. Or, in )ther words, under these conditions no real angle of friction is developed in he earth-mass. Local experience and practice should be consulted and will 'cnerally serve as a guide. Earth banks apparently similar will, however, act cry differently and no general rule can be given. It should be borne in mind hat the earth composing a bank should be, as far as possible, protected from ar, from the action of water and from alternating freezing and thawing; and hat permanent work should be completed as rapidly as possible so as to \ oid the deteriorating effects of time and exposure on the structure of the >ank. The Thickness of the Sheeting Planks required may be calculated on the ssumption that the earth bank is composed of loose material having a definite ngle of slope and coefficient of friction; but practically, under favorable onditions, 2-in planks may be used for a depth of drive of i6 ft, 3-in planks up 24 ft and 4-in planks up to 32 ft; and timbers, 8 by 12 in, have been driven 1 favorable material to a depth of over 40 ft. Depths and Numbers of Drives. Ordinarily the depth to which a plank an be driven is limited by its ability to resist the shock due to driving, and in nfavorable material a plank may become shattered before it is driven to the bove-quoted depths. If the required depth cannot be reached by the first planks r drive, a second, and sometimes a third and fourth set of planks are employed, ^s the breast-pieces supporting the first line of planks must remain in place. 302 Foundations Chap.fl he breasF the planks in the second set or drive have to be placed inside of the breast^ pieces, thus reducing the size of the excavation by the amount of the necessary offset.' Where more than one drive is required the first drive should be started at a sufficient distance outside to allow the planks forming the second or the second and third drives to be placed outside of the required area for the bot- tom of the excavation. Cutting and Fitting Sheeting Planks. The sheeting planks may be SQUARE-EDGED where there is no water or fine loose sand, but where water or running sand is to be excluded the planks should be tongued and GROOVED, or SPLiNED. The use of tongued and grooved planks has the additional advantage that the planks are more readily kept in Hne. It is O) Fig. 35. Small Power-hammer for Driving Sheeting Planks Fig. 36. Large-size Power-ham- mer and Sheeting Planks usual to cut the bottom edge of each plank on a shght angle, so that m driv it is WEDGED against the preceding plank. The top of each plank may be fitted to receive an iron driving-cap; or, if this is not used, the upper corners of the plank should be cut off so that the effect of the blows will be coiij:entrated along its vertical axis, and the tendency of the plank to split, due to a blow on one corner, thus diminished. The Means Employed for Driving the Sheeting vary with the depth and the size of the sheeting. For small jobs and for moderate depths of drive, the primitive method of driving by hand with ringed wooden mauls still prevails. For work involving a considerable amount of driving, and in all cases for long drives, power-hammers driven either by steam or compressed air are preferably employed. A small-sized power-hammer (Fig. 35) resembles a STEAM-DRILL and may be handled by two or three men without any special lif tmg- Methods of Excavating for Foundations 203 appliances. The larger sizes of power-hammers (Figs. 36 and 37) are practically small, power, pile-driving hammers arranged with a special driving-head to fit the sheeting employed. Such hammers are handled by derricks or are carried in a frame similar to .a pile-driver frame. Ordinary drop-hammers are sometimes used, but are not as advantageous as the reciprocating power- hammilRS, as the blow struck by the drop-hammer shatters the plank, while the frequent light blows of the power-hammer tend to keep the planks and the adjacent material in motion and accomplish the required work with less damage to the sheet-piling. The weights and dimensions of several types of pile- driving hammers are given in Table XI, page 204. Manner of Driving Sheeting Piles. In prac- tice, a shallow excavation is first made to the proper line for the outside of the sheeting planks. The top breast-timber is temporarily secured in place and the lower end of the planks placed be- tween this timber and the bank. If the planks are long, temporary top guides or stay-braces are arranged so as to keep the planks vertical until they have been driven well into the ground and guided by the permanent breast-pieces. The planks are then driven as the excavation pro- gresses, each plank being driven a few inches in turn. As the driving goes on the material under the lower edge of the planks is loosened with a shovel or with a crowbar, the operation being so conducted that the planks are held true to line. The horizontal breast-timbers and their braces are placed in position as the excavation progresses. If inclined braces are to be used the excavation 'in the center is taken out first, leaving a sloping bank against the sides of the excavation. This permits of the placing of the inclined braces and of the \ heels for their points of support before there is any danger to the bank. After the first breast-piece and its inclined brace are set in place, the second and subsequent breast-pieces and braces are put in as the excavation proceeds, Sheet-Piling for Excavations Below Water- Level. These excavations may be made by the sheet-piling method if there is not too much water and if water can be drained out of the material without inducing a flow of sand or clay below the bottom of the sheet-piling. In some cases, where unfavorable conditions exist, but where there is an underlying stratum of impervious material, it is possible to drive the sheeting in advance of the excavation, so that the bottom of the sheeting makes a tight joint with the impervious stratum, cutting off the flaw of water and material. Where a considerable amount of water finds its way into the excavation, the water must be led to a sump or depression from which it is ejected by means of a pump or a steam-syphon. Where the founda- tion-bed is below water-level and the material is sand, clay, or other material which would be softened by the action of the»water, it should be protected by having the sump at a considerable distance from the area to be used for the sup- Fig. 37. Large-size Power- hammer for Driving Sheet- ing Planks 204 Foundations Chap. 2 Table XI. Weights and Dimensions of Pile-Driving Hammeis 6 Dimensions over all Cylinder tes 11 § i^ 1 ^ « o 1 1 ^ 3 ? Q B o CO 3.6 c/2 ^ o 3 'o 'in o rt en lb lb m in in in in cult m in m Duty, size of piles or piling ham- mer will drive Warrington Steam Pile-Hammers Manufactured by Vulcan Iron Works, Chicago, 111. i6 coo 9850 6500 3800 1350 800 1 •16K2 13K2 loH 8 4 4 II vy concrete piles 18" sq or rd piles 14" sq or rd piles 10" sq or rd piles 4"Xi2" sheeting 3''Xi2'' sheeting Cram Steam Pile-Hammers Manufactured by A. F. Bartlett & Co., Saginaw, Mich. 8 400 5500 4 200 I 000 2^ 27 2 20 iH 20 m 12 8H|i8'' sq or rd piles 8H 14" sq or rd piles 8H 10" sq or rd piles 5HI 4"X 12" sheeting U Manufactured by nion Pile-Hammers Union Iron Works, Hoboken, N. J. 12 100 I 8000 2 5S0O 3 4500 4 2500 5 I 400 6 850 7 365 1550 548 890 663 363 214 129 70 100 so 750 2 28 8H no 30 600 iVz 28 8K2 130 18 300 ili 25 6V2 135 15 200 iH 23 sV^ 150 10 150 I 20 aVi 200 8 100 I 17 4'/2 250. 5 60 H 14 3^/^ 300 3 40 H 10 3H ! Hvy concrete piles ! 18'' sq or rd piles ! ia" sq or rd piles ! 10" sq or rd piles 6"Xi2" sheeting 4"Xi2" sheeting "X 12" sheeting "X6" sheeting Goubert Steel-Pile Driving- Hammer Manufactured by A. A. Goubert, New York, N. Y. 5 000 3400 950 I 500 800 200 17 14 8 14 ISO SO 6H 10 160 2S 4 8 200 ID 24 81/4 \^. 22 6H \i .... 18" sq or rd piles 12" sq or rd piles 4" sheeting New Monarch Steam Pile-Hammer Manufactured by Henry J. McCoy Co., New York, N. Y. 18" sq or rd piles 14" sq or rd piles 6"Xi2" sheeting 3"Xi2" sheeting I 7 000 I Soo 90 24 24 9 I2K> I2S 35 600 2 24 814 2 4600 850 72 20 20 7H II ISO 20 300 iy> 20 SH 3 2800 450 S4 18 18 4H 7 17s IS 150 I 18 8H 4 800 I2S 48 14 14 3H 6 250 10 6S 'H McKiernan-Terry Pile-Hammers Manufactured by McKiernan-Terry Drill Co., New York, N. Y. 9 7 SOO I 500 77 21 27H IS 12 200 60 600 2 21 6K2 7 S 000 800 67 21 22H 1 2 1/2 10 22s 35 350 1H2 21 6^A 5 I soo 200 S6 II 14^4 7 8H 300 20 200 iH II A'A 3 640 68 54 9 9K> 3M 5^4 300 IS ISO I 9 3H I I4S 21 42 8 6^ 2H m 500 ID 100 H 8 2H 18'' sq or rd piles 14" sq or rd piles 4"Xi2" sheeting 3"Xi2" sheeting 2"Xio" sheeting Ingersoll-Rand Sheet Pile-Driver Manufactured by Ir^gersoU-Rand Co., New York, N. Y. Gi| I 20o| 20o| SoIiiHlii I 4 I 7HI300 I 10 |iio |iM|....|...| 4''Xi2'' sheeting Methods of Excavating for Foundations 205 port of the footing. This may be accomplished by making the area to be sheeted and excavated large enough to accommodate the sump outside of the support- ing area, or by sinking a separate excavation to be used exclusively as a sump; or the same result may in some cases be accomplished by the use of drive- wells, driven to a point below the level of the footing in which continued pumping may reduce the level of the water to a point below the footing. Care also should be taken, when the level for the footing is reached, to prevent the foundation-bed from being disturbed and softened by unnecessary tramping of workmen over the surface of the excavation. The foundation-bed should be left as nearly as possible in its original or natural condition. Steel Sheeting has been largely employed recently in place of wooden sheet- ing. It has the advantage that it can be driven in advance of the excavation, thereby reducing the likelihood of any flow of material under the sheeting. It also has the advantages of affording greater strength for a given thickness of sheeting, of being driven to a greater depth, and in many cases of being with- drawn and used over again. As generally manufactured, it has the further advantage of being interlocking, so that there is less danger of its getting out of line and leaving openings between adjacent pieces. All of these advantages have been considered by engineers in using steel instead of wooden sheeting. The Use of Steel Sheeting. The fundamental idea of steel sheeting is not new, as cast-iron sheet-piling was used in England as far back as 1822 and various combinations of steel plates have been used in coffer-dams. The general use of steel sheeting started in this country in 1899 when Luther P. Friestedt drove experimental interlocking channel-bar sections. Since that time it has come into general use, and with its aid many excavations have been made with steel sheet-piling which would have been impracticable with timber sheeting. Earth-Pressure on Steel Sheeting. In using steel sheeting, it should be borne in mind that the earth-pressure coming on the steel sheeting is the same as the earth-pressure coming on timber sheeting, and the breast-pieces and braces should be as strong as in the case of timber sheeting. Certain forms or sections of steel sheeting offer considerable resistance to bending due to the lateral earth-pressure. With such forms the horizontal breast-pieces may be spaced farther apart than with ordinary timber sheeting or steel sheeting not having this property; but the strength of the breast-pieces and of their braces must be sufficient to take up the entire load coming on the sheeting, irrespective of the spacing between such breast-pieces, for in case there is a failure in these the entire sheeting will fail. Different Forms of Steel Sheeting. Various types of steel sheeting are on the market. In making a selection between different forms of sheeting, the character of the material to be encountered should be borne in mind, as the simpler, more compact sections will penetrate hard or gravelly soils with less danger of deformation than the more complicated sections made up of thin plates and shapes. The various companies manufacturing different forms of sheet-piling publish catalogues containing data as to the weight and also giving the properties of the different sections. These catalogues may be obtained from the manufacturers, but for convenience illustrations of some of the principal sections, with their dimensions and weights and other details, are given in the following pages. There are other types of steel sheeting than those shown m Figs. 38 to 44* 206 Foundations Chap. 2 S^^^"'^ Fig. 38. Lackawanna Steel Sheet-piling Lackawanna Steel Sheet-Piling* Composition and Dimensions of Sections Sections Per linear foot, lb Per sqiiare foot, lb Straight-web, H in thick 12.54 37.187 42.5 40.83 60 21. s 35 40 35 48 Straight-web, % in thick Straight-web, Yi in thick Arched-web, 14 in long Arched-web, 15 in long This piling is adapted to straight or circular work. ._ • Manufactured by the Lackawanna Steel Company. Methods of Excavating for Foundations h 1 Fig. 39. United States Steel Sheet-piling 207 United States Steel Sheet-Piling * Composition and Dimensions of Sections Size Web in b in h/2 in 12H in, 38 lb 9 13H 9H 9 in, 16 lb This piling is adapted to straight or circular work. * Manufactured by the Carnegie Steel Company. .h.T^ii. m^^rJ Fig. 40. Friestedt Interlocking Channel-bar Piling Friestedt Interlocking Channel-Bar Piling • Composition and Dimensions of Sections Channels Zees h/2, in No. Description In Lbs per ft In Lbs per ft I 10 in, 28 lb 10 IS zMXM 4.8 9 2 10 in, 34 lb 10 20 MXM 4.8 9 3 12 in, 34 lb 12 20.5 3-)iX% 8.6 10^^ 4 12 in, 39 lb 12 2S 3HX?i 8.6 10^^ 5 15 in, 39 lb 15 33 A\^X% 9.2 13H 6 15 in, 45 lb IS 40 A%X% 9.2 13H Manufactured by the Carnegie Steel Company. 208 Foundations Chap. 2 ,,^>;v^^^^^?^^^^^^^/M^/^/^M, Fig. 41. Standard Sheet-piling Standard Sheet-Piling * Composition and Dimensions of Sections Size, Weight per No. square foot, A B C D in lb I 12X5 35. o 12 3.94 5 0.34 2 I2XS 36.25 12 3.97 5 0.37 3 ISX6 37.20 15 4.75 6 0.37 4 15X6 39.75 15 4.81 6 0.44 5 15X6 42.25 15 4-87 6 0.50 An interlocking bar is wedged to each beam at the mill and the two pieces are driven kS a unit. * Manufactured by the Jones & Laughlin Steel Company. Fig. 42. Spring-lock Sheet-piling Spring-Lock Sheet-Piling * Composition and Dimensions of Sections Distance, A 15 U in 19U in 2zy\ in ^6-in plate.weight per square foot, in pounds . H-in plate, weight per square foot, in pounds. . 17 20 14^2 17 13H 16 Plates may be obtained curved to any radius for circular work. * Manufactured by the Mitchell-Tappen Company. — A- Fig. 43. Slip-joint Sheet-piling Slip- Joint Steel Sheet-Piling * Composition and Dimensions of Sections Distance, A 6 in gin 12 in IS in No. 14-gauge, weight per square foot, in pounds. No. 16-gauge, weight per square foot, in pounds. 5.4 4.3 5.8 4.0 5.7 3.9 5.6 Manufactured by the Mitchell-Tappen Company. Methods of Excavating for Foundations 209 Fig. 44. Wemlinger Steel Sheet-piling Wemlinger Steel Sheet-Piling* Composition and Dimensions of Sections No I 2 3 4 5 6 7 8 9 10 Depth of corrugation 2 Me 12 5 2 12 7-5 2 H 12 8.5 2V2 12 8 2K2 H 12 9-5 2I/2 12 11-5 2K> Me 12 13.5 4 3/1 6 18 15 4 H 18 19 4 Mo 18 23. 5 1 Thickness Width, center to center of lap. .... . Weight per square foot in pounds . . The dimensions given are in inches. * Manufactured by the Wemlinger Steel Piling Company. The Poling-Board or Chicago Method is a special method of excavation in general use in Chicago and in occasional use elsewhere for excavations which go to a great depth in clay or in other suitable material. It has the advan- tage over the ordinary sheet-piling method that the lining of the excavation is not driven. The method is not generally used for trenches or for square ex- cavations as a circular excavation is more readily handled. The success of the method depends entirely upon the character of the material to be encountered, as the excavation is first made and the sides of the excavation afterwards supported. The method in detail for a circular excavation for a pier-foun- dation may be described as follows: (i) A circular excavation slightly in excess of the size required for the pier is carried down to a depth of 5 ft, great care being taken to have the sides of the excavation vertical and true to the circle. (2) Vertical planks called lagging-pieces, 5 ft in length and slightly beveled on their edges so that each piece may be considered as a stave with radial joints corresponding to the size of the required circle, are set in place against the walls of the excavation. These planks are held in place by two or more steel rings, generally made in quadrants, so that they may be conveniently handled and bolted together. The planks are wedged firmly against the walls of the excava- tion by means of wooden wedges driven between the planks and the iron rings. (3) As soon as the first set of lagging is compFete, the excavation is carried down for another section, 5 ft in depth, and another section of lagging is put in place and secured in the same manner. Depth and Character of Excavations in the Poling-Board Method. In the manner described above the excavation may be carried down for an indefinite distance, a depth of 100 ft having frequently been attained. In many cases the bottom of the excavation is belled out to a larger diameter than the ex- cavation for the main shaft of the pier with the object of reducing the load of the foundation-bed to a unit load less than the safe unit load on the main shaft of the pier. This method is not adapted for running sand nor for clay that is not solid enough to stand with vertical sides during the necessary interval between making the excavation and placing the lagging. In some cases where a stratum of quicksand has been encountered, the excavation has been carried past it 210 Foundations Chap. 2 by the use of a cylindrical shell of steel, forced by jacks through it to an under- lying impervious layer of clay; but in general this method is dependent for its success upon a continuous body of impervious material. The Open-Caisson Method or Well-Curb Method is used for piers to be carried to a considerable depth, and has advantages over the sheet-piling method in certain materials. It is a development of the old method used in sinking masonry wells and, in its modern form, consists of a structure which eventually forms part of the pier itself and which is arranged with an open chamber at its base in which men may excavate the material under the structure and allow it to settle as the excavation proceeds. It is evident that a central opening or shaft must be left in the structure to permit of the passage of men and material. Details of the Open-Caisson Method. In detail, the method may be described as follows: First a curb or cutting-edge of timber or steel, following the out- line of the pier, is constructed on the surface of the ground. The outer face of this curb is generally vertical and is protected with a steel plate which ex- tends below the main section of the curb, so as to form a cutting-edge or sharp downward projection serving to penetrate the soil slightly in advance of the excavation. On this curb a wall of timber, concrete, or masonry is constructed, inside of which the so-called working-chamber affords room for the workmen to be employed in excavating. Above the working-chamber the walls may con- tinue to a height corresponding to the required height of the pier, leaving the central space to be filled in after the required depth is reached; or a roof may be built over the working-chamber and the entire cross-section of the pier filled with concrete or masonry excepting only a small central opening large enough to accommodate a hoisting-tub or bucket and to permit of the ingress and egress of the men employed in sinking the construction. In practice, the excavation is started before the pier-structure is carried up to its final height, after which the excavation and the building up of the pier progresses simultaneously, the constantly increasing weight of the structure aiding the sinking of the pier. When the excavation has reached rock or a firm substratum, further excava- tion is stopp)ed and the working-chamber and the central opening are packed full of concrete, leaving finally a complete pier-structure extending from the rock to the proper level to receive the steel grillage or other construction com- ing on the pier. Advantages of the Open-Caisson Method. This method of construction has the advantages that the workmen at all times are protected, that obstructions, such as boulders or logs, may be removed from under the cutting-edge, and that when rock is encountered, ample opportunity is afforded for the proper preparation of the rock-surface to receive the final concrete filling. If a moderate amount of water is encountered, not accompanied by a flow of material, it can generally be taken care of by means of pumps. Dredged Wells are similar to the open caissons described in the previous paragraphs and are used v/here large quantities of water are encountered. The construction of the piers is similar to that of the piers used in the open-caisson method; but the central shaft and working-chamber are designed to permit of the use of a clam-shell dredge or other form of dredge, and the water is allowed to rise to its natural level in the working-chamber and shaft. This method can be used to advantage when a considerable amount of water-bearing sand or other material is found overlying level rock or other firm foundation- bed. When the dredging and the sinking of the pier-structure have been carried down to the hard underlying strata it is sometimes possible to pump out the water. If this is not practicable the bottom may be prepared by divers for the reception of the concrete filling, and the concrete may be deposited through water, Methods of Excavating for Foundations 211 care being taken to use some special arrangement to protect the concrete from being injured by loss of its cement-content, in the process of deposition. The Well-Digger's Method is also occasionally used in making pit-excava- tions under walls or in cramped locations. By this method the sides of the excavation are supported by planks placed horizontally. The method of plac- ing the planks is as follows: A shallow excavation, the depth of a plank, is made by ordinary methods, and a set, consisting of four planks fitting the four sides of the excavation, is secured in place. Before proceeding with the general excavation of the pit a trench is dug directly alongside and underneath one of the side planks of the first set. As soon as this trench is deep enough to accommodate the planks for the second set, the side of the trench under the plank already in place is cut to a vertical face, the plank placed in position and the loose earth temporarily back-filled against it. As soon as the four planks forming the second set have been put in place by this method, the two side planks are wedged against the bank, the end-planks being used as struts. The end-planks are wedged into position and nailed or cleated to the side planks forming a pressure-resisting frame supporting the side of the excavation. A continuation of this method enables the excavation to be carried on indefi- nitely, provided there is no flow of water or run of material causing an inflow of material into the excavation. The Pneumatic-Caisson Method. Where piers or foundation walls have to be carried to a considerable depth through water-bearing materials, and espe- cially where large bodies of quicksand are encountered, the pneumatic-caisson METHOD must be resorted to. This method is based upon the principle of a DIVING-BELL and may be briefly described as follows: The construction of the pier is similar to the piers previously described as used in the open-caisson and dredged-well construction, except that the working-chamber and shaft are made air-tight and connected with a device called an air-lock, so that compressed air may be introduced into the working-chamber. The object of the compressed air is to prevent water entering into the working-chamber. This is accomplished in accordance with the well-known principle of the diving-bell by having the compressed air constantly kept at a pressure which will counterbalance the water-pressure at the level of the cutting-edge of the working-chamber. The pressure of the air evidently must vary with the depth of the cutting-edge below water-level. A column of water i in square in cross-section weighs .43 H lb per vertical ft, and it will therefore be counterbalanced by an air-pressure of .43H lb per sq in over the normal air-pressure. If the column of water is 30 ft in height, it will weigh thirty times .43 H lb, or will be counterbalanced by an air- pressure of 13 lb per sq in above the atmospheric pressure. The Maximum Air-Pressure in the Pneumatic Caisson in which men can work for short periods is about 43 lb per sq in above atmospheric pressure, correspond- ing to a depth below water-level of about 100 ft. At this depth the work is carried on in shifts of from two to three hours duration, and great care must be exercised in coming out of the air-pressure. The physiological effects of compressed air are often serious; pains in the joints, damage to the ear-drums resulting in deafness, and the so-called caisson-disease render work at high pressure extremely hazardous. The Air-Lock Used in Connection with the Pneumatic Caisson is a device for the purpose of retaining the air in the caisson and at the same time permitting the passage of men and material in and out. It consists essentially of a metallic AIR-TIGHT chamber or SHELL connected to the working-chamber either directly or to an air-tight lining or extension of the central shaft-opening. This air- chamber has two doors, oae at the bottom, opening downward into the shaft 212 Foundations Chap. 2 and the other in the upper head of the air-lock chamber, also opening down- ward and afifording a direct connection to the open air. In the operation of an air-lock one of these two doors must at all times be closed so as to prevent the free escape of air through the air-lock. If the bottom door is closed, it will be held firmly to its seat by the uplift of the compressed air in the shaft, which is at all times in direct communication with the working-chamber. If, under these conditions, the upper door is open, the interior of the air-lock will be in direct communication with the open air and the air contained in the lock will evidently be at atmospheric pressure. Workmen and materials may then enter the air- lock. In order to pass into the shaft and working-chamber, it is necessary, first, to close the upper door, and secondly, to shift the so-called equalizing VALVE and admit compressed air into the space between the two doors, until the air-pressure is brought up to the air-pressure in the working-chamber and shaft. Pressure on the upper side of the lower door will then equal the pressure on the lower side and the lower door may be opened, the upper door being firmly held against its seat by the compressed air in the air-lock. As soon as the lower door opens, the men and material may be passed into the shaft and working- chamber. In coming out the operations are reversed; men and material enter the air-lock through the open lower door, the lower door is closed and held tightly against its seat, and the equalizing valve is shifted, affording a connection be- tween the interior of the air-lock and the external air. The compressed air escapes through the equalizing valve, reducing the pressure in the air-lock to atmospheric pressure, and the upper door has atmospheric pressure on both sides of it. It may then be opened, giving free connection with the outside air. The Design of Pneumatic Caissons. The first consideration is, of course, to have the final structure a permanent and sufficient pier to carry the load to be imposed upon it. To this end the cross-section of the pier at all points from top to bottom should be capable of carrying safely the maximum load. As the cross-section of the pier is generally, in the finished pier, composed of solid con- crete, the cross-section will be determined by the allowable load on the concrete. For piers the cross-section will generally be square or circular; for walls the caisson will generally be not less than 6 ft in width, as it is difficult to sink caissons having a width less than 6 ft. If the caisson is to be carried to solid rock, the bearing on the rock need be no larger than the cross-section of the concrete pier; but if the excavation does not go to rock, it is frequently desir- able to BELL OUT the base of the pier so as to reduce the loading on the founda- tion bed to a unit load less than that allowable on concrete. The operation of BELLING OUT is difficult in some materials; in a compact material it can be gen- erally accomplished without serious difficulty. Piers Sunk by the Pneumatic-Caisson* Method may be constructed of various combinations of materials. The side walls and roof of the working-chamber were formerly frequently constructed of timber. In many cases they are now formed of steel; but in recent designs the working-chamber is generally formed of reinforced concrete, the only structural steel used being an angle or a plate and angle composing the cutting-edge. The outside of the caisson is preferably made vertical. The superimposed pier is generally of the same size as the work- ing-chamber, at least it is generally so in piers sunk for buildings. A Typical Design for a Caisson Built of Reinforced Concrete is given in Fig. 45, in which AB h the angle-iron and plate forming the so-called cutting-edge and C is the working-chamber formed by the side walls DE and DE and by the roof £E. The concrete side walls are reinforced with steel rods attached to the cutting-edge, and extending upward into the body of the pier, and the roof and body of the pier are reinforced to take care of stresses due to construe- Methods of Excavating for Foundations 213 tion and sinking. In building up the working-chamber, the interior forms are arranged so as to support the concrete which makes the roof. These are sub- sequently removed. The exterior forms may constitute a permanent part of the structure, in which case they are called a coffer-dam, or they may be removed as soon as the concrete has sufficiently set. At the center of the pier an open- ing is left to serve as the SHAFT or opening connecting the working-chamber with the AIR-LOCK. The sides of this opening or of the upper part of it, only, are lined with an AIR-TIGHT STEEL SHELL. To the upper end of the steel shell the air-lock is connected. If the height of the pier does not exceed 40 ft the construc- tion of it may be completed before the excavation is com- menced. Generally, however, the construction of the pier is stopped as soon as the work- ing-chamber and from 5 to 10 ft of the superimposed pier has been constructed; then sufficient excavation is done, without the use of compressed air, to carry the cutting-edge down to water-level. This is called DITCHING the caisson and is done so that the caisson will have some slight latepal support from the soil before the construction is carried up high enough to make it top- heavy. When the entire pier or the first section is finished, excavation is resumed and the whole structure is sunk as the excavation progresses, care be- ing taken to remove any obstruction from beneath the cutting-edge. During the progress of sinking compressed air is conducted to the working-chamber through the supply-pipe G, the excavated material being hoisted through the shaft F. The shaft F is fitted with a ladder for the use of the workmen. Details of Caisson-Sinking and Filling. In sinking the caisson and super- imposed pier, care must be taken to maintain it in a vertical position. This end may be accomplished in large caissons by means of the excavation itself. In case one side of the caisson is high the excavation on that side will be carried somewhat in advance of the excavation on the low side, and the material under the cutting-edge of the high side will be removed while a bank of material is kept under the cutting-edge of the low side. These methods, however, are of little avail when the caisson is narrow. In such cases that part of the caisson which is above ground is held in position by guides or other devices; but it Reinforced-concrete 214 Foundations Chap. 2 frequently happens that the caisson in its final condition is considerably out of its correct location and considerably out of plumb. In general, therefore, the size of the caisson should be made larger than the minimum size necessary, in order to allow for errors in its final location. When the caisson has reached the required depth the foundation-bed is prepared for the reception of the concrete filling and the working-chamber filled with it, care being taken that it completely fills all voids and is in perfect contact with the roof. Finally, the air-lock and the steel Uning of the shaft are removed and the shaft-opening filled with con- crete to the proper level to receive the grillage or other construction forming the base of the column which is to rest on the caisson. The Height of Caisson-Piers. The height of a pier cannot be exactly fixed until it is known to what depth the caisson must sink in order to reach the foundation-bed. If the rock is found at a greater depth than anticipated, additional height is added to the top of the pier after the caisson is in its final position; but if, on the other hand, the rock is found unexpectedly high, the top of the pier will have to be cut off. If the finished elevation of the pier is to be below the level of -the general excavation, it is usual to extend the exterior surface of the pier to the required height by means of a tem.porary chamber- structure called a coffer-dam, the height of which corresponds to the depth of the finished surface below the level of the general excavation. Inside of this COFFER-DAM some STEEL GRILLAGES may conveniently be set. The Freezing Process for Excavations. This method has sometimes been employed in making excavations. In this country its use has been limited to one or two mining-shafts, but in Germany it has been resorted to in making excavations for building-foundations. The method consists in driving steel pipes into the ground. These pipes are closed at the bottom and at the top are connected to smaller pipes through which brine, at an extremely low tem- jxjrature, is made to circulate. The refrigerating effect results in freezing the water contained in the soil, converting quicksand to a frozen mass resembhng soft sandstone. When: the freezing has progressed sufficiently to form a solid wall or coflfer-dam around the excavation, the material inside the frozen wall may be excavated. This method has the advantage, theoretically, of being applicable to excavations of any depth. There are many precautions necessary, and for the present, at any rate, it should only be considered as a possibility. 31. Protection of Adjoining Structures General Considerations. The common law provides that any person mak- ing an excavation is responsible for resulting damage to adjoining property. Statute laws as embodied in the building codes of different cities may modify or limit this responsibility, but in general, excavations should be made in such a manner as to cause the least possible damage to surrounding property. Where there are no adjoining structures it is generally sufficient to slope the sides of the excavation so as to prevent the sliding of material into the excavation, or, at least, to sheet-pile and brace the sides of the excavation; but where the excava- tion is to be made alongside of an existing structure, and carried below the footings of such structure, it is necessary to take special measures for its protec- tion. Such work is described as shoring, underpinning and protecting ad- joining STRUCTURES, and may involve the carrying of the weight of part or all of the buildings on temporary supports, the removal of the old footings and the construction of new footings at lower elevations. Shoring. When the excavation for the new building does not go much below the adjoining footings and when the material is fairly solid, it may suflBce to transfer a portigu of the load of the wall to temporary footings. This may be Protection of Adjoining Structures 215 accomplished by means of heavy inclined posts called shores, arranged to act as INCLINED COLUMNS OF STRUTS. Each Shore consists of a post, the lower end of which rests on a platform, generally consisting of planks and timbers arranged so as to form a temporary spread footing. This platform should be placed at a depth which will insure that subsequent operations will not under- mine it. The upper end of the post fits into a hole or niche cut into the wall to be supported. The post itself may be a timber with a square cross-section, usually 12 by 12 in, and of the required length. Provision is made, between the platform and the lower end of the post, for wedges or jacks, so that when operated their lifting effect transfers part of the weight of the wall from its footing to the temporary foundation or platform. During this operation all parts of the temix)rary structure are in compression and brought into bearing, and the material under the platform is compressed and solidified as much as possible. Kinds of Shores. If the shore is to act preferably for lifting only, it is kept as nearly vertical as possible and is known as a lifting shore. If it is to act preferably to combine a horizontal pushing action with the lifting action, it is placed at a considerable angle from the vertical and is then known as a pushing shore or steadying shore. In arranging such shores care should be taken to have the niche cut close to a floor-level of the building to be shored, as otherwise the horizontal component of the thrust of the shores might buckle the wall. Numbers and Sizes of Shores. Where a wall is light, a number of smaller shores should be used in preference to a few large ones. Where a wall is high, two or more shores of varying lengths may be used, and these may conveniently be placed in the same vertical plane and rest on the same O^ ^ platform. Wedges and Screw-jacks. In transferring the load of a wall from its own footing to the temporary platform, use is made of wooden Fig. 46. Standard orsteel wedges, lype 01 bteel screw- TACKS Screw-jack hydraulic ^^^' ^^' ^^^^'^^^^ Type of Steel Screw-jack jacks; or, wedges and jacks may be used in combination. Wooden wedges should be made of hard wood and are generally arranged in pairs, both wedges being driven at the same time. The lifting effect of such wooden wedges is powerful, but where a considerable settlement of the temporary foundation is anticipated, it is more convenient to use screw-jacks, as they can take up a considerably settlement. Materials and Types of Screw-jacks. The screw-jacks usually manu- factured for this purpose are made of cast iron and have rough threads, with too coarse a pitch to have much lifting effect. Screw-jacks of a better kind are made of steel and have a machine-thread of small pitch. Such jacks can be obtained capable of hfting weights up to 100 tons. Figs. 46 and 47 represent 216 Foundations Chap. 2 standard forms of screw-jacks. When a single screw-jack i.s used in connec- tion with a post or shore, a hole to receive the threaded portion of the jack is bored in the end of the timber used for the shore, the end being squared to receive the nut. Such an arrangement is called a pump and is illustrated in Fig. 48. When a lifting effect greater than that exerted by a single jack is re- quired, the jacks are arranged in pairs in connection with a short timber or cross- Fig. 48. Pump, or Screw-jack let into End of Shore Shore, Screw-jacks and head Timber Crosa- HEAD. Such an arrangement is illustrated in Fig. 49. It has the advantage that after operating the jacks, blocking and wedges can be placed between the platform-timbers and the cross-head so that the post resting on the cross-head has a direct and solid bearing on the platform. By this method the load of the wall can be thrown on the platform by the jacks and after the blocking and wedg- ing is in position the jacks can be removed. Hydraulic Jacks. Where excessively heavy loads are to be lifted, hydraulic JACKS may be used in place of screw-jacks but an objection to them is that they are liable to slack back under the load. While the load, therefore, should not be permanently supported on hydraulic jacks, they may be used to take the load temporarily while the blocking and wedging are being placed between the cross-head and the temporary footing. In this way an indefinite number of shores may be set and taken care of with a single pair of hydraulic jacks. Example of Shoring. Fig. 50 shows the method jised in shoring the orna- mental front wall of a heavy building, advantage having been taken of the nu- merous deep margin-drafts shown in the section. In order to avoid the necessity of cutting niches for the tops of the shores, nine hardwood blocks, a, a, etc., were fitted to the margin-draft grooves in the masonry. Nine similar blocks, bt b, etc., were gained into and bolted to the vertical timber VV, space being Protection of Adjoining Structures 217 L Wl ± tvc^ J T 6 3= 3= ^ Fig. 50. Shoring an. Ornamented Wall left between the a blocks and the b blocks for adjusting wedges w, w, etc. Three headpieces, Ti, T2 and Ts were keyed and bolted to VV and transmitted to it the uplift of the three shores, Si, S2 and Ss. Each shore had a 60- ton screw-jack at its base. Each shore is shown fitted with a pump or detached extension- piece arranged for the screw-jack. 218 Foundations Chap. 2 Needling. Needles or girders are employed when part or all of the weight of the wall has to be carried, as when the old footing is to be removed and the wall UNDERPINNED or Carried down to a new footing at a greater depth. Example of Needling and Underpinning. Fig. 51 represents a typical case of UNDERPINNING, the Several operations being as follows: (i) The General Excavation is carried down to within a few inches of the bottom of the footing BB under the wall W. (2) The Pit DDDD, properly braced and protected by sheet piling, is sunk to approximately the level of the proposed excavation, this pit being placed at a safe distance from the existing wall. In good material it may be safe to Fig. 51. Wall-needling and Underpinning have this pit approach to within a few feet of the footing course of the wall, but in material which is liable to run it should not approach the wall closer than its depth. No hard and fast rule can be given, and in every case great care should be taken to prevent any movement of the material from under the ad- joining footing. (3) The Platforms. On the bottom of this pit-excavation, a platform FF is placed, generally composed of heavy timbers resting on a base of heavy planks^ and acting as a support for the outer end of the needle. During the construction of this pit a similar pit may be dug on the inside of the wall to pro- vide for the support of the inside end of the needle; but as this involves the destruction of the cellar-floor the method of procedure inside the building is generally different from this. If the material is solid it is sometimes sufficient to place the platform for the support of the inside end of the needle directly on the cellar-floor and at such a distance from the wall that the necessary excavation for the new footing will not disturb it; or the platform may be placed on the cellar-floor and a line of sheeting LL, properly braced, so placed that the excavation can be made for the new footing. This is generally sufficient to prevent any serious settlement of the temporary platform for the inside end of the needle. Protection of Adjoining Structures 219 (4) The Insertion of the Needles. Having provided a support for each end of the NEEDLE it only remains to cut a hole through the wall, as at ^, insert the needle GG, put the post and blocking MN under the outside end of the needle, and the blocking and jacks under the inside end. The post MN may be fitted with wedges as shown at K, or with one or more screw-jacks. The needle GG may consist of one or more heavy timbers or one or more steel I beams. In any case, the load to come on this needle should be figured and its strength made ample to safely support such load. As soon as the weight of the wall W is transferred to the needles and to the temporary platforms prepared to receive the load, that part of the wall which is below the needles and all of the foot- ing may be removed and all of the excavation for the new footing made. 1 1 1 1 1 1 1 1 ' 1 1 1 1 ' 1 1 A 1 1 II 1 II 1 1 1 1 1 1 1 1 1 1 1 i 1 1 1 1 1 i 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1,1 1 A 1 1 ' 1 ' 1 ' 1 ' 1 ' 1 ' 1 1 II 1 II J .' 1 1 1 1 1 1 1 '11 -r^ 1 1 1 1 1 1 1 ^ 1 1 1 1 1 1 II f^ ) 1 1 1 1,1 1 1 1.1 1 < < ■ 1 1 1 1 ^ 1 1 1 ^ ^^ 1 1 1 1 1 ^. ' 1 1 1 1 1 1 1 1 ^ 1 1 1 1 1 ' X ' r 'I'l'-lMI 1 1 1 1 1 1 l«l 1 1 h--^ p====s=n Wedffinff Nee TT ' 1 ' 1 Nee( le-B !am8 1 1 1 1 1 , 1 1 1 1 1 1 1 1 Stones 1 J--L 1 1 . 1 1 1 1 1 1 1 1 1 1 1 II 1 1 1 1 1 1 1 1 1 1 1 1 ' 1 ' 1 1 1 1 1 1 1 1 1 1 1 1 1 1 i 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 III 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 II II 1 1 1 1 1 1 1 1 1 i 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 i 1 1 1 1 1 J I'll 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 II 1 II III 1 ' 1 ' 1 ' 1 ■ 1 ' 1 ' 1 1 1 ' 1 1 1 ' 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 a 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 . 1 1 1 1 1 1 1 1 1 1 1 1 ' 1 ' 1 ' 1 ' 1 ' 1 ' 1 ' 1 ' 1 ' 1 ' 1 1 ' 1 1 1 .1 1 1 1 1 1 1 1 1 1 1 1 1 i TJ 1 1 1 1 1 III 1 1 1 g 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ' 1 ' 1 ' 1 ' 1 ' 1 ' 1 ' 1 1 ' 1 1 ' 1 1 1 1 1 1 1 1 II III 1 1 1 1 1 rJ III 1 1 1 1 1 II 1 1 1 1 1 ^ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 II 1 ^ ' 1 ' 1 ' 1 ' 1 ' 1 ' 1 ' 1 ' 1 ' 1 ' 1 ' 1 ' 1 ' 1 ' 1 ' ^^. Fig. 1. Stone Footing. Openings be carefully considered whatever the ma- at Joints terial of the footmgs. If the projection of the footing or offset of the courses is too great for the strength of the stone, brick, or concrete, the footing will crack, as shown in Fig. 2. The proper offset for each course depends upon the vertical load, the transverse strength of the material, the resisting power of the foundation-bed and the thickness of the course. t Tables for Offsets for Masonry Footing Courses.! As stated in Chapter II, in the discus- sion of the design of stepped footings, there are V-* — i rule-of-thumb methods giving so-called safe projec- . X 1 — . tions for given depths of footings or giving the ratios V 1 — . between the projections and the depths of the courses. ,^, ^_..^ ,X>- ->^^'x"^*^ Tables of offsets for footing courses of different ma- p. Z^r^^ k *' F t* terials have been computed from the flexure-formula (^^^ Excessive Offsets apphed to the projecting footing courses considered as CANTILEVER BEAMS uniformly loaded by the upward pressures on the under side. Although these tables, so computed, are incorporated in some building codes, they cannot be safely used without numerous restrictions, exceptions and modi- fications, and hence they are, in general, unreliable and of use only as approxi- mations. As these tables are still inserted in engineers' and architects' hand- books, the table of offsets for masonry footing courses, in a revised form, is re- tained in this chapter with the recommendation that for footings of several offsets it be used with caution and that for such footings the methods explained in Chapter II be used when greater accuracy of results is required. Notes Regarding Use o f Tab le I. The values in Table I are computed from the formula l=Md VSf/wJ which is derived from the flexure-formula for a uniformly loaded cantilever beam, and slightly changed to make the numerical coefficient of the second member of the equation the value shown. § In this equation, / = the maximum allowed offset of the footing course in inches, d =i the thickness of the footing course in inches, S^ = the modulus of rupture * See Offset Footings, Chapter II, especially Subdivisions 17 and 22. t See Chapter II, Subdivision 22, for a complete discussion of the principles involved in the design of projecting footings, ratio of projection to depth of footing, etc., for homo- geneous slabs, separate-layer footings, etc. X See Chapter II, Subdivision 22, page 180. § See, also, formula in Chapter II, Subdivision 22. Foe tings for Light Buildings 225 Table I. Approximate Values of Offsets for Masonry Footing Courses in Terms of the Thickness of the Course The values are computed with a factor of safety of lo. Material of the footings 5y in pounds per square inch w in tons per square foot North River Bluestone (ordinary run) Granite (average) Limestone (average) ^ Sandstone (average) Brickwork (good bricks in natural-cement mortar, I : 2, 60 daj'^s old) Brickwork (hard-burned bricks in Portland-cement mortar, i : 3, 60 days old) Concrete (Portland cement, i : 2 : 4, i month old) . Concrete (Portland cement, i : 2 : 4, 6 months old) 3000 1850 I 375 I 375 125 400 300 400 4.1 32 2.8 1.6 1-3 1.5 2.9 2.2 2.0 2.0 o."5 I.I 0.9 I.I 2.0 1.6 1-4 1.4 0.7 0.6 0.7 of the materials in pounds per square inch, w = the determined or assumed pressure on the bottom surface of the footing course considered, in tons of 2 000 lb per sq ft, and / = the factor of safety used. The table gives the values of l/d for three unit pressures w. For example, if w is taken at 2 tons per sq ft, then for Umestone or sandstone footings l/d = 1 .4, and if d, the thickness of the footing course, is 12 in, the offset or projection should be 16 or 17 in. The values given in the tal)le for Sf, the modulus of rupture for the materials, differ very slightly from those given in Subdivision 22 of Chapter II, in Table I of Chapter XV and in Table III of Chapter XVI. If results are required based upon different fiber-stresses, upon a different factor of safety, or upon different pressures per square foot, the formula may be used instead of the table. It should always be borne in mind that as each footing course transmits the entire weight of the wall and its load, the pressure will be greater per square foot on the upper courses, and that the offsets should be made proportionately less; and that the values in Table I, when applied to stone-masonry footings, are really valid for the lower offset only, and then only when the footing is built of stones the thickness of which is equal to the thickness of the course, which have a projection of less than half their length, and which are well bedded in cement mortar. Concrete Footings.* For buildings of great weight, except the very heaviest, and especially for those built on a clay soil, concrete generally makes the best footing, and it is even preferable to and generally cheaper than large slabs of stone. When the concrete is properly made and used, it attains a strength equal to that of most stones, and under walls, being devoid of joints, it is like a CONTINUOUS BEAM, having sufficient strength to span any soft spots that happen to be in the foundation-bed. When deposited in thin layers and well rammed, concrete becomes firmly bedded on the bottom of the trenches, so that there is no possible chance for settlement except that due to the compression of the soil. * For an example of concrete-footing design, see Chapter II, Subdivision 22. For reinforced -concrete-footing design, see C^hapter II, Subdivision 24. See, also, Chapter XXV, paragraphs relating to footings, pages 978 to 982. 226 Masonry Walls. Cements and Concretes Chap. 3 Preparing the Trenches. For footings, concrete made with Portland cement is preferable, and it should have a thickness of at least 8 in, even under light buildings; and for buildings of more than two stories, a thickness of at least 12 in. On firm soils, such as hard clay, the trenches should be accurately dug and trimmed to the exact width of the footings, so that the concrete will fill them. When the foundation-bed is of loose gravel or sand it is generally necessary to set up planks to confine the concrete and form the sides of the footings. These planks may be held in place by stakes; they should be left in place until the concrete has become hard, which generally requires from two to four days, after which they may be pulled up and dirt filled in against the concrete. The proportions and manner of mixing concrete are described in the latter part of this chapter. Depositing the Concrete. Concrete should be used as soon 'as mixed and should always be deposited in layers, which as a rule should not exceed 6 in in thickness, especially for the first layer. On small jobs where the work is done by hand' the concrete is usually carried to the trenches in wheel-barrows and dumped into the trenches. The height from which the concrete is dumped, however, should not exceed 4 ft above the bottom of the trench, because when it falls from a greater height the heavy particles are apt to separate from the lighter ones. As soon as the concrete has been deposited in the trenches, it should be leveled off and then tamped with a wooden rammer weighing about 20 lb, until the water in the concrete is brought to the surface. Concrete should not be permitted to dry too quickly, and if twenty-four hours elapse between the deposits of the successive layers, the top of each layer should be sprinkled before the next is put in place. For buildings over five stories high, it Is a good idea to place a stone footing course above the concrete footing, if suitable stones for the purpose can be obtained. Brick Footings. Where the foundation walls are of brick, the footings are usually brick or concrete. For interior walls on dry ground, and in many 1 BRICK 1I-BRICKS WmM Mi Fig. 3. Brick Footing. Wall One Brick Thick Fig. 4. Brick Footing. Wall One and One-half Bricks Thick localities for outside walls, brick footings are fully as good as stone footings, provided good, hard bricks are used and the footings are properly built. Brick footings should always start with a double course on the foundation-bed and then be laid in single course for ordinary footings, the outside ot the work being laid all headers, as in the accompanying illustrations, and no course projecting more than one-fourth the length of a brick beyond the one above it, except in the case of an 8-in or 9-in wall. For brick footings under high or heavily loaded walls, each projecting course should be made double, the header-course above and the stretcher-course below. Figs. 3, 4, 5 and 6 show footings for walls Footings for Light Buildings 227 2 BRICKS varying from one brick to three bricks in thickness. The bricks used for foot- ings should be the hardest and soundest that can be obtained, should be laid in cement mortar and should be either grouted or thoroughly slushed up, so that every joint shall be entirely filled with mortar. The writer favors grouting for brick footings, that is, the using of a thin mortar to fill the inside joints, as he has always found that it gives very satisfac- tory results. The bottom course of the footing should always be laid in a bed of mortar spread on the bottom of the trench after the latter has been care- fully leveled. All bricks laid in warm or dry weather should be thoroughly wet before laying, for, if laid dry, they rob the mortar of a large percentage of the mois- ture it contains, greatly weakenin; hi^rSM M^ MB ...^ ^ J , Fig Brick Footing. Wall Two Bricks Thick the adhesion and strength of the mortar. Careful attention should be given to the laying of the footing courses of buildings, as upon them the stability of the work largely depends. If the bottom courses are not solidly bedded, if any rents or voids are left in the beds of the masonry, or if the materials themselves are unsound or badly 3 BRICKS ^m. ^^^^^^^^^^ %g&i Fig. 6. Brick Footing. Wall Three Bricks Thick put together, defects in the superstructure are almost sure to show them- selves sooner or later, and almost always at a period when remedial efforts are difficult and expensive. Inverted Arches.* In a few buildings in which the external walls are divided into piers with wide openings between them, and in which the support- ing power of the soil is not more than 2 or 3 tons per sq ft, it was thought desir- able to connect the bases of the piers by means of inverted arches, for the pur- pose of distributing the weight of the piers over the whole length of the footings. Examples of inverted-arch footings are shown in Figs. 7 f and 8,t which represent respectively the construction employed in the Drexel Building in Philadelphia * For an example worked out in full, showing the method of proportioning inverted arches, see Chapter III, Building Construction and Superintendence, Part I, Masons* Work, by F. E. Kidder. t From the Engineering Record, May, 1899, and Nov., 1890. $2$ Masonry Walls. Cements and Concretes Chap. 3 and the World Building in New York City. Unless the piers are about equally loaded, however, it is generally impossible to distribute the weight evenly, and if the arches extend to an angle of the building, the end-arch must be provided with ties of sufficient strength to resist the thrust of the arch, as otherwise it may push out the corner-pier. It is usually better to build the piers with sepa- rate footings, projecting equally on all sides of the pier, and each proportioned Fig. 7. Inverted-arch Footing. Drexel Fig. 8. Inverted-arch Footing. World Building, Philadelphia Building, New York to the load supported. The intermediate wall may be supported by steel beams or by arches. About the only advantage over ordinary masonry footings possessed by inverted arches is in the resulting shallower foundations. The following, relating to inverted arches, is taken from the New York build- ing law: "If, in place of a continuous foundation wall, isolated piers are to be built to support the superstructure, where the nature of the ground and the character of the building make it necessary, in the opinion of the Commissioner of Buildings having jurisdiction, inverted arches resting on a proper bed of concrete, both designed to transmit with safety the superimposed loads, shall be turned between the piers. The thrust of the outer piers shall be taken up by suitable wrought-iron or steel rods and plates." (Law of 1906.) 3. Cellar Walls and Basement Walls Definitions. These terms are generally applied to walls which are below the surface of the ground or below the water-table or first-floor beams, which support the superstructure and which go down to the foundation walls, properly so called. (See Chapter II, Divisions i and 29.) Walls whose chief office is to withhold a bank of earth, such as the walls around areas, are called RETAINING- WALLS. (For retaining-walls, see Chapter IV.) Materials for Cellar and Basement Walls. These walls may be built of brick, stone or concrete. Brick is suitable only in very dry soils or for a party wall with a cellar or basement on each side of it. Portland-cement concrete is an excellent material for foundation walls, and is being more extensively used in their construction every year. The concrete may be filled in between wooden forms, which hold it in place until it has set, or concrete blocks molded so as to form a solid wall may be used. If poured concrete is used the forms Walls of the Superstructure 229 should be removed as soon as the concrete has set and the walls should be sprinkled once or twice a day, if the weather is dry, so that the concrete will not dry too quickly Good hard ledge-stone, especially if it comes from the quarry with flat beds, makes not only a strong wall but, if well built, one that will stand the effects of moisture and the pressure of the earth much better than a brick wall. Between a good stone wall and a wall of Portland-cement concrete, there is probably not much choice, except perhaps in the matter of expense, the relative cost of stonework and concrete varying in different localities. A wall built of soft stones, or stones that are very irregular in shape, with no flat surfaces, is greatly inferior to a concrete wall, or even to a wall of good hard bricks, and should be used only for dwellings or light buildings. Stone walls should never be less than i8 in thick, and should be well bonded, with full and three-quarter headers, and all spaces between the stones should be filled solid with mortar and broken stones or spalls. The mortar for stonework should be made of cement and sharp and rather coarse sand. The outside walls of cellars and basements should be plastered. smooth on the outside with i : 2, or i : iH cement mortar, from Vi to % in thick. In heavy-clay soils it is a good idea to batter the walls on the outside, making them from 6 in to i ft thicker at the bottom than at the top. Thickness of Cellar and Basement Walls. This is usually governed by that of the walls above, and also by the depth of the wall. Nearly all building regulations require that the thickness of the cellar and basement wall, to the depth of 12 ft below the grade-line, shall be 4 in greater than the thickness of the wall above for brick, and 8 in greater for stone, and that for every additional 10 ft or part thereof in depth, the thickness shall be increased 4 in. In all large cities the thickness of the walls of buildings is controlled by law. For buildings in which the thickness of the walls is not so governed, the following table will serve as a guide: Table II. Thickness of Cellar and Basement Walls Height of building Dwellings, hotels, etc. Warehouses Brick, in Stone, in Brick, in Stone, in Two stories 12 or 16 16 20 24 28 20 20 24 28 32 16 20 24 24 28 20 24 28 28 32 Three stories Four stories Six stories . . 3. Walls of the Superstructure Brick and Stone Walls, Very little is known regarding the stability of walls of buildings beyond what has been gained by practical experience. The only stresses in any horizontal sections of such walls, which can be determined with any accuracy, are the direct weight of the walls above and the pressure due to the floors and roof. In most walls, however, there is a tendency to buckle, to overcome which it is necessary to make them thicker than would be required to resist the direct crushing stress. The resistance to fire should also be taken into account in deciding upon the thickness of any given wall. 230 Masonry Walls. Cements and Concretes Chap. 3 The strength of a wall depends also very much upon the quality of the materials used and upon the way in which the wall is built. A wall bonded every 12 in in height, and with every joint slushed full with good rich mortar, is as strong as a poorly built wall 4 in thicker. Walls laid with cement mortar are also much stronger than those laid with lime mortar, and a brick wall built with bricks that have been well wet just before laying is very much stronger than one built with dry bricks. Thickness of External Walls. In nearly all the larger cities oC the country the minimum thickness of the walls is prescribed by law or ordinan':e, and as these requirements are generally ample they arc commonly adhered to by archi- tects when designing brick buildings. Table III * gives the thickness of brick walls required for mercantile buildings in representative cities of different sections of the United States, and allords about as good a guide as one can have, because the values given, as a rule, represent the judgment of well- qualified and experienced persons. Walls for dwellings arc generally per- mitted to be 4 in less in thickness than: for warehouses, although in some cities little or no distinction is made between business blocks and dwellings. Table IV gives the thickness required for the brick walls of dwellings, tene- ments, hotels and office-buildings t in Chicago. The thickness given is the mini- mum that should be allowed for the walls of such buildings, unless certain special conditions exist. For modifications for different classes of buildings see the building code. In St. Louis the two upper stories of dwellings are required to be 13 in, the next two below, 18 in, the next two 22 in, and the next two 26 in thick. In compiling Table III the top of the second floor was taken at 19 ft above the sidewalk, and the height of the other stories at 13 ft 4 in, including the thickness of the floor, as the New York and Boston laws and the laws of some other cities give the height of the walls in feet instead of in stories. W'hen the height of stories exceeds these measurements the thickness of the walls in some cases will have' to be increased. The Chicago ordinance (1916) specifies that "where 12-in walls are used, the story-heights shall not exceed 18 ft, where i6-in walls are used, the story-heights shall not exceed 24 ft, and where 20-in walls are used, the story-heights shall not exceed 30 ft." General Rule for Thickness of Walls. Although there are great dilTer- ences in the thickness given in Table III, more indeed than there should be, a general rule might be formulated from it, for mercantile buildings over four stories in height, which would be somewhat as follows: For bricks equal to those used in Boston or Chicago, make the thickness of the three upper stories 16 in, of the next three below 20 in, the next three 24 in and the next three 28 in. For a poorer quafity of material make only the two upper stories 16 in thick, the next three 20 in, and so on down. In buildings less than five stories in height the top story may be 12 in thick. In determining the thickness of walls the following general principles should be recognized: (i) That walls of warehouses and mercantile buildings should be heavier than those used for living or oflBce purposes. • Since this table was compiled, some provisions of some laws have been changed, but the requirements relating to the thicknesses of walls vary but little from those given. As building laws of different cities are amended from time to time, architects and builders must be guided by the code in force in the city in which a building is to be erected. The table represents the average requirements and is useful for comparative purposes and as a guide for those building outside of cities, or where no special building laws are in force. t For other than steel skeleton construction. Walls of the Superstructure 2 Table III.* Thickness in Inches of Walls for Mercantile Buildings and. Except in Chicago, for All Buildings Over. Five Stories in Height Height and location of building Stories ISt 2d 3d 4th 5th 6th 7th 8th Two stories Three stories Four stories Five stories Six stories Seven stories Eight stories f Boston i6 12 12 12 I8 13 17 13 20 i6 i6 i6 i8 17 17 13 2C i6 20 i6 22 21 17 I8 20 20 20 20 22 21 21 I8 2-1 24 20 20 26 26 21 22 24 28 20 20 26 26 22 28 32 24 24 30 30 22 12 12 12 12 13 13 13 13 i6 i6 12 T2 I8 17 17 13 i6 i6 i6 i6 i8 17 17 i8 20 i6 20 i6 22 21 17 I8 20 20 20 20 22 21 21 I8 20 24 20 20 26 21 22 24 28 24 20 26 26 22 ' New York Chicago Minneapolis St. Louis Denver San Francisco New Orleans ( Boston i6 12 12 12 13 13 13 13 i6 i6 i6 12 18 17 17 13 20 i6 i6 i6 i8 17 17 i8 20 20 20 i6 22 21 17 i8 20 24 20 20 22 21 I8 20 24 20 20 26 21 22 New York. Chicago Minneapolis St. Louis Denver San Francisco New Orleans f Boston i6 12 12 12 13 13 13 13 20 i6 i6 12 i8 17 17 13 20 20 i6 i6 i8 17 17 i8 20 20 20 i6 22 21 l8 20 24 20 20 22 21 i8 New York Chicago Mirneaoolis St. Louis Denver , San Francisco New Orleans f Boston i6 i6 i6 12 13 13 13 13 20 i6 i6 i6 I8 17 17 13 20 20 l6 i6 i8 17 i8 20 20 20 l6 22 21 18 New York Chicago St. Louis San Francisco New Orleans f Boston i6 i6 i6 12 13 13 13 13 20 i6 i6 i6 i8 17 13 20 20 i6 i6 i8 17 i8 New York Chicago Minneapolis .... Denver New Orleans Boston i6 i6 i6 12 13 17 13 20 i6 i6 i6 i8 17 13 i6 i6 i6 12 13 T.7 x3 New York Chicap:o. St. Louis New Orleans Boston New York Chicago Minneapolis Denver New Orleans * See paragraphs and foot-note on page 230. 232 Masonry Walls. Cements and Concretes Chap. 3 Table III (Continued).* Thickness in Inches of Walls for Mercantile Buildings and, Except in Chicago, for all Buildings Over Five Stories in Height Height and location of building Nine stories Ten stories Eleven stories Twelve stories Boston .. New York. . Chicago Minneapolis. St. Louis Denver Boston New York. . Chicago Minneapolis^ St, Louis Denver Boston New York. Chicago St. Louis.. . Denver . . . . Boston New York. Chicago. . . . St. Louis. . . Denver. . . . Stories ist 2d 3d 4th 5th 6th 7th 8th 9th loth nth 12th 26 26 * See footnote on page 230. Table IV.f Thickness of Enclosing Walls for Residences, Tenements, Hotels and Office-Buildings, t Chicago Building Ordinance (1916) Number of stories Base- ment Stories 1st 2d 3d 4th Sth 6th 7th 8th 9th lOth iithi2th Basement and . . . One-story Two-story Three-story Four-story Five-story Six-story Seven-story Eight-story Nine-story Ten -story Eleven-story. . . . Twelve-story. . . 12 16 16 20 24 24 24 24 28 28 28 32 12 12 16 20 20 20 20 24 24 28 28 28 12 12 16 20 20 20 24 24 28 28 28 12 16 16 20 20 20 24 24 24 28 12 16 16 20 20 20 24 24 24 16 16 16 20 20 24 24 24 16 16 16 20 20 20 24 16 16 16 20 20 20 16 16 16 20 20 16 16 16 20 16 16 16 16 16 16 t These thicknesses are allowed when certain requirements are fulfilled in regard to lengths of walls, heights of stories, etc. For these, modifying restrictions and for the classifications of buildings in regard to their uses the building laws must be consulted. The table is inserted in this form as a useful general guide and as an illustration of the average contemporary practice. For modifications for different classes of buildings, see code. 1 For other than steel skeleton construction. Walls of the Superstructure 233 (2) That high stories and clear spans exceeding 25 ft require thicker walls. (3) That the length of a wall is a source of weakness, and that the thickness should be increased 4 in for every 25 ft over 100 or 125 ft in length. In New York the thicknesses given in the table must be increased for buildings exceed- ing 105 ft in depth on the lot. In Western cities the tables are compiled for warehouses 125 ft in depth, as that is the usual depth of lots in those cities. (4) That walls with over 33% of openings should be increased in thickness, (s) That partition walls may be 4 in less in thickness than the outside walls if not over 60 ft long, but that no partition should be less than 8 in thick. Walls Faced with Ashlar. "Bearing walls faced with ashlar shall be at least 16 in thick. Ashlar shall not be included in reckoning the thickness of walls unless it is either at least 8 in thick or alternately 4 in and 8 in to allow at least a 4-in bond. Ashlar not having at least a 4-in bond in alternate courses must be tied to the backing by metal anchors, one to each block, 3 ft or less long and two to each block over 3 ft long." * Stone Walls should generally be 4 in thicker than required for brick walls. Hollow Walls. Hollow walls are undoubtedly desirable for dwellings, and might well be used for other buildings not more than four or five stories in height, on account of the security afforded from the weather. Owing to the fact that they are usually more expensive than solid walls and occupy more space, they are not very extensively used in this country. The Boston building law requires that vaulted walls shall contain, exclusive of withes, the same amount of material as is required for solid walls, and the masonry on the inside of the air-space in walls over two stories in height shall be not less than 8 in thick, and the parts on either side shall be securely tied together with ties not more than 2 ft apart in each direction. Walls of Concrete Blocks. Blocks made of Portland-cement concrete, and formed in molds, are frequently used for building walls and partitions that are comparatively thin and bear light loads. Patents have been taken out on different forms of blocks and on machines or processes for making the same, and many buildings have been erected with walls built of these blocks. Most of the blocks are molded so as to form hollow walls. Block construction of this kind has an advantage over poured walls, in that the blocks are thoroughly seasoned before they are set and hence no provision is required for expansion or contraction. For the thin, light walls above mentioned the concrete-block construction is better adapted than solid concrete. The expense of forms is avoided and also the tendency to crack and to leave an unsatisfactory surface- finish. Concrete blocks may be substituted for any ordinary stone or brick masonry. Building laws usually require the thickness of walls of hollow con- crete blocks to be not less than that required for brick walls. They should not be used in party walls. (See, also. Chapter XXIII, Subdivision 2.) Walls of Hollow Tiles. Hollow tiles are used for the external walls of dwellings and sometimes for factories in some locations and under certain restrictions. For example, the building laws (19 13) of the District of Columbia allow approved hollow tiles, not less than 12 in in thickness, to be used for the • Boston Building Law, in force in 1915. 234 Masonry Walls. Cejnents and Concretes Chap. 3 external walls of dwellings located not less than 3 ft from the side or party line of the lot. The Philadelphia laws do not allow the use of hollow tiles for any external wall or heavy bearing partition. As far as fire-resistance is concerned, construction of hollow tiles is, of course, superior to wooden construction, and its use is increasing, the outside walls being usually covered with cement or stucco, although occasionally left with the finished texture of the tile surface. The reason hollow tiles are prohibited by building ordinances for certain uses is because when. heated and then suddenly cooled by water they are apt to crack, from the sudden contraction. Recent conflagrations have shown that hard- burned terra-cotta will crack and fall to pieces under severe heat alone. (See, also, Chapter XXllI, Subdivision 2.) Party Walls. There is much diversity in building regulations regarding the thickness of party walls, although thty all agree in that such walls should never be less than 12 in thick. About one-half of the laws require that party walls shall be of the same thickness as external walls; the remainder are about equally divided between making the party walls 4 in thicker or thinner than for independent side walls. When the walls are proportioned by the rule pieviously given the author believes that the thickness of the party walls should be increased 4 in in each story. The floor-load on party walls is obviously twice that on side walls, and the necessity for thorough fire-protection is greater in the case of party walls than in other walls. Enclosing Walls for Steel, Skeleton Construction. In buildings of the skeleton type the outer masonry walls are usually supported either in every story or every other story by the steel framework, and carry nothing but their own weight. Such walls may, therefore, be considered as only one or two stories high, and are usually made only 12 in thick for the whole height of a twelve-story or fifteen-story building. For skeleton construction, the Chicago ordinance allows enclosing walls of i2-in thickness for all stories. The former New York City code* required the use of 12-in enclosing walls for 75 ft of the uppermost height thereof, or to the nearest tier of beams to that measure- ment, and 4 in additional thickness for every lower 60-ft section or to the near- est tier of beams to such vertical measurement, down to the tier of beams near- est to the curb-level. But, on account of the severity of some of the require- ments as applied to very high buildings of skeleton construction, permission was frequently given by the Commissioners of Buildings, who were empowered to modify the building laws within certain Hmits, to reduce the thicknesses of certain walls for very high buildings, according to the peculiar circumstances of each case, without endangering the strength and safety of the building. A few of the earlier tall buildings were built with self-sustaining walls, starting from the foundation, while columns were introduced merely to support the floors and to give additional stiffness. ''The World Building, New York City, erected in 1890, is an extreme example of high-building construction, with self-sustaining walls. The main roof is 191 ft above the street-level, making thirteen main stories, above which is a dome containing six stories, in all, a height of 275 ft above the street. The self-sustaining walls are built of sandstone, brick and terra-cotta, the thickness increasing from 2 ft at the top to as much as 1 1 ft 4 in near the bottom, where the walls are ofTset to a concrete footing IS ft wide. The walls are vertical on the outside faces, the thickness being varied by inside offsets, so that the columns are recessed into the walls at the bottom, but emerge and are some distance clear of the walls at the top."t • The revised Code, 1916-17, allows 12-in curtain walls in skeleton buildings the entire height of building, when supported on girders in each story. This practice is followed by about fifty other cities. t From Architectural Engineering, by J, K, Freitag. Natural Cements 235 4. Natural Cements and Mortars* Properties and Uses of Natural Cements. The first hydraulic cements used in this country were natural cements, manufactured by the calcination of argillaceous limestone containing sufficient silica, alumina and iron oxide to confer hydraulic properties when the burned rock was pulverized and gauged with water. These natural cements were very widely manufactured and used until recent years, when they have been practically completely replaced by Portland cement. Natural cements vary in color from light yellow to dark brown according to the content of oxide of iron, and in distinction to Portland cements they are not uniform in their composition or behavior. The chemical composition and physical characteristics of various natural cements vary within wide limits, not only between cements manufactured in different mills, but be- tween the products of the same mill at different times. Natural cements set more rapidly than Portland cements and are slower in developing strength. The production of natural cement in the United States for 1913 was 800000 barrels, while during the same year the production of Portland cement was 82 000 000 barrels; from which it is seen that the natural-cement industry is relatively almost extinct. Natural cement may be used in massive masonry where weight rather than strength is the essential feature. It is used, also, for certain special purposes, such as in the manufacture of safes and in certain industries where a quick-setting cement is necessary. Where economy is the governing factor, a comparison m2Ly be made between the use of natural cement and a leaner mixture of Portland cement that will develop the same strength. Weight. The specifications of the American Society for Testing Materials require that a bag of natural cement shall contain 94 lb, net, of cement, and that each barrel of natural cement shall contain three bags of this net weight. Strength. A natural-cement mortar, in order to comply with the require- ments of the standard specifications of the American Society for Testing Ma- terials, must show a tensile strength, for the neat cement, of at least 150 lb per sq in, when one week old, and 250 lb at the end of 28 days; or, when mixed with three parts of standard Ottawa sand, 50 lb at the end of one week, and 125 lb at the end of 28 days. The strength of i : 2 natural-cement mortar is about equal to that of i : 4 Portland-cement mortar. Proportions of Natural Cement and Sand for Mortar and Concrete. For mortar for rubble-stone masonwork and ordinary brickwork, one part of natural cement may be mixed with three parts of sand, by measure. Hydraulic Lime. A product closely related to natural cement is hydraulic LIME. This is manufactured in the same way as natural cement, but the rock used contains sufficient Hme to permit it to slake like quicklime. When the resulting product is pulverized, it sets and hardens as an hydraulic cement. Hydraulic limes arc largely manufactured in Europe, and especially in France, and Belgium, but in the United States they have been manufactured only in a few localities. This is due to the fact that while rock of suitable composition is widely found, the impurities are not uniformly distributed through it, but are found in layers or seams which prevent the material from being uniformly burned. The portion of the rock immediately adjacent to and including the. seam of impurities overburns, frequently melting like a slag, while the purer portions consist simply of quicklime; and while the resulting mass slakes partly,, the product when pulverized is unreliable as a cement. * Practical data relating to Cements, Limes and Plasters were furnished the Editor by the Charles Warner Company of Wilmington, Del. For Limes and Plasters, see Part III, pages 1548 to 1558. 236 Masonry Walls. Cements and Concretes Chap. 3 Grappier Cement is a by-product produced during the calcination of hy- draulic \AllE. La Farge Cement is an imported non-staining grappier cement. It develops nearly the same strength as the Portland cements. 5. Artificial Cements and Mortars The Artificial Cements used in the United States include Portland tement and Puzzolan or slag cement. Portland Cement. The principal artificial cement in this country to-day is Portland cement. It is manufactured from two raw materials which are ground to extreme fineness to secure an intimate mix before burning, aiid it is from this fact that it derives its name, artificial cement. These ma- terials must be so proportioned that in the finished cement, silica, alumina, iron oxide and lime will be present in a certain ratio which must be maintained within close limits. In the Lehigh Valley region of Pennsylvania, in which are located some of the leading Portland-cement mills of the United Stales, the raw materials used are limestone and cement-rock. The cement-rock is an im- pure hmestone carrying argillaceous or clay-matter. In order to bring the lime- content up to the required percentage, it is usually found necessary in this region to add limestone. In other districts the raw materials used are lime- stone and clay, limestone and shale, marl and clay and also blast-furnace slag and Hmestone. The product from the last-mentioned mixture should not be confused with the common slag cement or Puzzolan cement, as the slag is simply used as a raw material supplying silica, alumina, iron oxide and lime; and with the exception of the use of slag to furnish these ingredients, the process of manu- facture and the properties are substantially the same as for the other Portland cements. The raw mix in a Portland cement mill is analyzed at most mills several times each hour to keep the composition of the cement within the proper Umits. The raw material, which is pulverized as fine as the finished cement, is burned in rotary kilns, the fuel used in most instances being powdered coaL From the kiln it issues in the form of clinker, the name given to the semivit- rified product. After cooling, calcium sulphate in the form of gypsum is added to control the set and the product is pulverized and packed for shipment. The manufacture and properties of Portland cement have been made the subject of careful study by the American Society for Testing Materials and by the American Society of Civil Engineers. The result of this study is embodied in the standard specifications of the American Society for Testing Materi^ds, ex- tracts from which are given in the paragraphs following. These si>ecilications furnish a reliable guide for the acceptance or rejection of any shipment of ce- ment and have been very widely adopted by the leading architects and engineers of this country. These specifications do not stipulate that l^ortland cement shall consist of any one particular composition, but in this respect confine themselves to the Hmitation of the magnesia (MgO) and anhydrous sulphuric acid (SO3) con- tent. The reason for this is that with different raw materials it is found neces- sary to vary the composition of the cement to obtain the correct physical properties in the finished material. Different cements which satisfy the require- ments of these standard specifications are generally considered satisfactory ce- ments for use, although the composition of one may vary in some particulars from that of another. The chemical composition of a good brand of Port- land cement is about as follows: Lime, 62; silica, 23; alumina, 8; and impurities, such as iron oxide, magnesia, und sulphuric acid, 7. Standard Specifications for Portland Cement.* The following extracts give the most important requirements for Portland cement: • From the Standard Specifications and Tests for Portland Cement, revised, 1916 (ef- fective, January i, 1917), by the American Society for Testing Materials. Artificial Cements 237 (i) Definition. Portland cement is the product obtained by finely pulveriz- ing clinker produced by calcining to incipient fusion an intimate and properly pro- portioned mixture of argillaceous and calcareous materials, with no additions sub- sequent to calcination excepting water and calcined or uncalcined gypsum. (2) Chemical Limits. The foUqwing limits shall not be exceeded: Loss on ignition, per cent 4 . 00 Insoluble residue, per cent 0.85 Sulphuric anhydride (SO3), per cent 2 .00 Magnesia (MgO), per cent .*. 5 .00 (3) Specific Gravity. The specific gravity of cement shall be not less than 3.10 (3.07 for white Portland cement). Should the test of cement as received fall below this requirement a second test may be made upon an ignited sample. The specific-gravity test will not be made unless specifically ordered. (4) Fineness. The residue on a standard No. 200 sieve shall not exceed 22 per cent by weight. (5) Soundness. A pat of neat cement shall remain firm and hard, and show no signs of distortion, cracking, checking, or disintegration in the steam test for soundness. (6) Time of Setting. The cement shall not develop initial set in less than 45 minutes when the Vicat needle is used, or 60 minutes when the Gilmore needle is used. Final set shall be attained within 10 hours. (7) Tensile Strength. The average tensile strength in pounds per square inch of not less than three standard mortar briquettes composed of i part cement and 3 parts standard sand, by weight, shall be equal to or higher than the following: Age at test, days Storage of briquettes Tensile strength, lb per sq in 7 28 I day in moist air, 6 days in water I day in moist air, 27- days in water 200 300 (8) The average tensile strength of standard mortar at 28 days shall be higher than the strength at 7 days. (9) Packages and Marking. The cement shall be delivered in suitable bags or barrels with the brand and name of the manu- facturer plainly marked thereon, unless shipped in bulk. A bag shall contain 94 lb net. A barrel shall contain 376 lb net. (10) Storage. The cement shall be stored in such a manner as to permit easy access for proper inspection and identification of each shipment, and in a suitable weather-tight building which will protect the cement from dampness. (11) Inspection. Every facility shall be provided the purchaser for careful sampling and inspection at either the mill or at the site of the work, as may be specified by the purchaser. At least 10 days from the time of sampling shall be allowed for the completion of the 7-diay test, and at least 31 days shall be allowed for the completion of the 28-day test. The cement shall be tested in accordance with the methods hereinafter prescribed. The 28-day test shall be waived only when specifically so ordered. (12) Rejec- tion. The cement may be rejected if it fails to meet any of the requirements of these specifications. Sections (13) to (15), also, relate to Rejection. (See complete Specification.) Puzzolan or Slag Cements are not used extensively and never in important work. Their manufacture and properties may be briefiy described as follows: Blast-furnace basic slag is granulated by running it in a molten condition into water. This accomplishes two objects. The slag is broken up into fine particles and the sudden chilling enhances its hydraulic properties. These particles are dried and ground with hydrated lime, in the proportion of from 15 to 25% of hydrated lime and from 75 to 85% of granulated slag. Such cement, known as slag cement, is slow-setting and slow-hardening, and does not develop as 238 Masonry Walls. Cements and Concretes Chap. 3 much strength as natural or Portland cement. Slag cements are characterized by their light Hlac color, their extreme fineness and their low specific gravity. They are considered unreliable for use except for foundation- work under ground where they are not exposed to air or running water. Stainless Cements. Any ordinary Portland or natural cement will stain limestones, some porous marbles, some granites and some other light-colored stones. The best non-staining material is hme, that is, lime free from excess of iron oxide. There are some Portland cements, however, which are called non- staining CEMENT^, and where care is used in their manufacture and they are free or comparatively free from iron oxide, they cause no trouble. Among the non-staining cements which have been extensively used for masonry on which staining would be objectionable, is La Farge Cement, before mentioned. It is made at Teil, France, is light-colored and contains a small percentage of iron and soluble salts. There are other non-staining cements on the market. For setting stones, and in order to retard the setting of the cement until the stones are well bedded, i part by volume of lime-paste is usually mixed with 4 parts of the cement. Cost of Portland Cement.* Portland cement can now (1915) be purchased in this country at prices ranging from 90 cents to $2.50 per barrel, free on board cars at the mills. The cost of the sacks and the freight are extra. The retail price for single barrels varies from about $2.00 to $2.50 per barrel. As a rule, the cost of cement in carload lots is about 85 cts per bbl at the mills. An extra charge of 10 cts per bbl for bags is made when the cement is delivered in paper bags. The extra charge is 40 cts, if dehvered in cloth, but the mills refund this 40 cts when the bags are returned in good condition. There is a charge of 40 cts when the cement is furnished in wooden barrels and no allowance is made for barrels returned. It is generally cheaper in the end to buy the cement in cloth bags and return the empty bags. For about 500 miles, the freight- charges are about 40 cts per bbl of cement, making the total cost per bbl for this distance $1.25, when purchased in cloth bags and when the 40 cts per bag are refunded. Testing costs from 3 to 5 cts per bbl, or from $5 to $6 per carload. Unloading and storing near the station cost about 3 cts per -bbl, and about 2 cts per bbl are usually added to the costs to allow for handling and returning empty sacks, and freight-charges for and damage to same. Teaming costs about 5 cts per bbl per mile. The total cost, therefore, according to these average costs, is about $1.38 per bbl for the cement ready for use for mortar or concrete. (For Cost of Concrete, see page 249; also foot-note for same.) Water Required in Mixing Cement Mortar. Good Portland cement requires relatively little water to make a good mortar. Neat cement will take from 20 to 22% (by weight) of water to produce the normal consistency, a quick-setting cement requiring more water than one that is slow-setting. If a greater quantity of water is required, it indicates the presence of an excess of free hme. When sand is mixed with cement, in the proportion of 3 to i, not more than from 9 to 12^% (by weight) of water will be required. Natural cements and slag cements require more water than do Portland cements. Too much water drowns the cement, retards the setting and weakens the mortar. Cements can also be weakened or even spoiled by a deficiency of water. Portland-Cement Mortar. For first-class mortar not more than 3 bbl of sand should be added to i bbl of cement. For rubble stonework under ordinary conditions a mortar composed of 4 parts of sand to i of cement will answer every purpose, and be much stronger than lime mortar. For the top surface of floors ♦ See foot-note, page 249. Cement Mortars 239 and walks, from i to i H parts of sand may be mixed with i part of cement. I to 3 Portland-cement mortar has about the same strength at the end of one year as r to i natural-cement mortar. Mortar made with fine sand requires a much larger quantity of cement to obtain a given strength than mortar made with coarse sand. (See page 276 for ideal mortar with hydrated lime for brickwork.) Effects of Low Temperatures and Freezing on Cement Mortars. The rate of setting and hardening of cement mortar is greatly affected by the temper- ature, and the exposure and loading of new work often depends upon the pre- vailing temperature. The freezing of natural-cement mortars should be en- tirely avoided as it seriously injures them. Although freezing greatly retards the hardening of Portland-cement mortars and concretes, it does not appear to injure them. Thin coats of mortar, such as plaster, and troweled surfaces or those on which free moisture is formed should not be applied in freezing weather as they are apt to scale. In general, it is undesirable to work with mortar or concrete in freezing weather, as the difficulties of properly mixing and placing the materials are then increased; it must be admitted, however, that successful work with Portland-cement mortar and concrete has been done in temperatures considerably below freezing. The Effect of Salt in Mortar. When salt is added to the water of mix- ture, the freezing-point is lowered, and, within certain limits, the freezing of the mortar or concrete is prevented. 1 he ultimate strength of mortar does not appear to be reduced when the amount of salt does not exceed 10%. Tetmajer gives the amount of salt required to lower the freezing-temperature as equal to 1% of the weight of the water per degree F. below 32''. The rule for the pro- portion of salt used in the works at Woolwich Arsenal, is said to have been as follows: ''Dissolve i lb of rock-salt in 18 gal of water when the temperature is at :i>2° ¥., and add 3 oz of salt for every three degrees of lower temperature." Effect of Hot Water and of Soda. Hot water hastens the setting of Portland-cement mortar, and 2 lb of carbonate of soda in i gal of water, boiled and mixed in mortar, hastens the setting and lessens the danger of freezing. Quantity of Mortar required for Masonry and Plastering,* "One bbl of Portland cement and 3 bbl of sand, thoroughly and properly mixed, will make 3H bbl, or 12 cu ft of good strong mortar. This will be sufficient to lay up lYz cu yd of rough stone, or about 750 bricks, with from \i to 5^-in joints, or cover 125 sq ft of surface, i in thick, or 250 sq ft, Yi in thick." "One bbl of natural cement and 2 bbl of lime, mixed with about Yi bbl of water, will make 8 cu ft of mortar, sufficient to lay 522 common bricks, with from Y^ to %-m joints, or about i cu yd of rough rubble. " For the top coat of walks or floors, i bbl of Portland cement and i of sand will cover from 75 to 80 sq ft, Yi in thick, or from 50 to 56 sq ft; % in thick. One bbl of Portland cement and lYi bbl of sand will cover from no to 120 sq ft of floor, Y in thick, or from 75 to 80 sq ft, % in thick. The Mixing of Mortar. Mortar may be mixed by hand or by mechanical mixers, the latter being preferable for the mixing of large quantities. When the mixing is by hand, it should be done on platforms made water-tight to pre- vent the loss of cement. The cement and sand should be mixed dry in small batches and in the proportions required, the platform being clean. W'ater is added and the whole mass remixed until it is homogeneous and leaves the mixing hoe clean when drawn out. Mortar should never be retempered after it has begun to set. * These figures can be considered as approximate only, as the amount of mortar will vary on different jobs. 240 Masonry Walls. Cements and Concretes Chap. 3 Adhesive Strength of Portland Cement, Sulphur and Lead for Anchor- ing Bolts.* "Fourteen holes were drilled in a ledge of solid limestone, seven of them being i% and seven iH in in diameter, and all being 3^2 ft deep. Seven % and seven i-in bolts were prepared with thread and nut on one end and with the other end plain but ragged for a length of sVi ft. *'Four were anchored with sulphur, four with lead and six with cement, mixed neat. Half the number of the %-m and i-in bolts being thus anchored with each of the three materials, all stood until the cement was two weeks old. Then a lever was rigged and the bolts pulled, with the following results. "Sulphur: Three bolts out of four developed their full strength 16000 and 31 000 lb. One I-in bolt failed by drawing out, under 12 000 lb. Lead: Three bolts out of four developed their full strength, as above. One r-in bolt pulled out, under 13 000 lb. Cement: Five of the bolts out of six broke with- out pulling out. One i-in bolt began to yield in the cement at 26 000 lb, but sustained the load a few seconds before it broke. "While this experiment demonstrated the superiority of cement, both as to strength and ease of application, it did not give the strength per square inch of area. To determine this, four specimens of limestone were prepared, each 10 in wide, 18 in long and 12 in thick, two of them having 1^4-in holes, and two of them 2>4-in holes drilled in them. Into the small holes .i-in bolts were cemented, one of them being perfectly plain round iron, and the other having a thread cut on the portion which was embedded in the cement. Into the 2%-in holes were cemented 2-in bolts similarly treated, and the four sp^^cimens were allowed to stand 13 days before completing the experiment. At the end of this time they were put into a standard testing-machine and pulled. The plain i-in bolt began to yield at 20000 lb and the threaded one at 21 000 lb. The 2-in plain bolt began to yield at 34 000 lb and the threaded one at 32 000 lb, the force in all cases being very slowly applied. The pump was then run at a greater speed, and the stones holding the 2-in bolts split at 67 000 lb in the case of the smooth one and at 50 000 lb in the case of the threaded one. "It is thus seen that for anchoring bolts in stone, cement is more reliable, stronger and easier of application than either lead or sulphur, and that its re- sistance is from 400 to 500 lb per sq in of surface expensed. It is also a well- ascertained fact that it preserves iron rather than corrodes it. The cement used throughout the experiment was an English Portland cement. " 6. Concrete t « Properties and Uses of Concrete.^ There is probably no material that is so enduring or better adapted for foundations, walks and basement floors, etc., than cement concrete, and for certain classes of buildings it is used with ad- vantage for the walls, floors and interior supports. There are now thousands of buildings in this and other countries in which all of the structural portions are formed of reinforced concrete, and the use of Portland-cement concrete for a * The test of these materials is reported in the American Architect, page 105, vol. xxiv. t The subject of concrete in general, including plain or mass-concrete and reinforced concrete, is to-day so important, and the available data so vast in amount that only those brief statements of general principles and of the best engineering practice that are the most important for the architect and builder to know can be included in a handbook of this kind. For full treatments of the subject, the readers are referred to the numerous recent treatises, tests, proceedings of engineering societies, etc. X For reinforced Concrete, see Chapter XXIV; for Concrete Foundations, Chapter II; ior Reinforced-Concrete Factory Construction, Chapter XXV; and for Strength of Con- crete, Chapter V. See, also. Chapter XXIII, pages 817 and 843. Concrete 241 great variety of purposes is rapidly extending, due to the reduced price of Portland cement, and to a better appreciation and understanding of its proper- ties and merits. Concrete may be defined as an artificial stone, made by uniting cement, water and what is called an aggregate, consisting of small and large particles of sand or screenings and gravel or broken stone; and when made with good Portland cement, in proper proportions, it becomes so hard and strong that when pieces of it are broken, the line of fracture often passes through the particles of stone, showing that the adhesion of the cement to the stone is greater than the cohesive strength of the stone itself. The Aggregates.* "Extreme care should be exercised in selecting the aggre- gates for mortar and concrete, and careful tests made of the materials for the purpose of determining their qualities and the grading necessary to secure maximum density or a minimum percentage of voids. A convenient coefficient of density is the ratio of the sum of the volumes of materials contained in a unit volume to the total unit volume. (See, also, pages 908 and 909.) " (i) Fine Aggregates should consist of sand, crushed stone, or gravel screen- ings, graded from fine to coarse and passing when dry a screen having ^-in diam holes; it preferably should be of siliceous material, and should be clean, coarse, free from dust, soft particles, vegetable loam or other deleterious matter, and not more than 6% should pass a sieve having 100 meshes per hn in. Fine aggre- gates should always be tested. Pine aggregates should be of such quality that mortar composed of one part Portland cement and three parts fine aggre- gate by weight when made into briquettes will show a tensile strength at least equal to the strength of i 13 mortar of the same consistency made with the same cement and standard Ottawa sand. This is a natural sand obtained at Ottawa, 111., passing a screen having 20 meshes and retained on a screen having 30 meshes per lin in. It is prepared and furnished by the Ottawa Silica Com- pany, for 2 cts per lb, free on board cars, at Ottawa, 111., under the direction of the Special Committee on Uniform Tests of Cement of the American Society of Civil Engineers. If the aggregate be of poorer quality the proportion of cement should be increased in the mortar to secure the desired strength. If the strength developed by the aggregate in the i : 3 mortar is less than 70% of the strength of the Ottawa-sand mortar, the material should be rejected. To avoid the removal of any coating on the grains, which may affect the strength, bank sands should not be dried before being made into mortar, but should con- tain natural moisture. The percentage of moisture may be determined upon a separate sample for correcting weight. From 10 to 40% more water may be required in mixing bank or artificial sands than for standard Ottawa sand to produce the same consistency. ** (2) Coarse Aggregates should consist of crushed stone or gravel which is retained on a screen having yi-in diam holes and graded from the smallest to the largest particles; they should be clean, hard, durable and free from all deleterious matter. Aggregates containing dust and soft, flat or elongated particles should be excluded from important structures." Any kind of stone is suitable for the coarse aggregate which has such strength that the strength of the concrete is not limited by the strength of the stone. Great strength is of little advantage beyond this minimum. The stones gener- ally employed are granites, traps and limestones. Shales and sandstones of * Most of the matter of this paragraph, and of following paragraphs relating to concrete, consists of data and conclusions formulated by the joint committees of the Am. 5oc. C. E., Am. Soc. for Test. Mats., Am. Ry. Eng. and Maint. of Way Asso., and Asso. of Am. Portland Cement Manfrs. In regard to Aggregates, etc., see, also, the same subjects in Chapter XXIV, pages 908 and 909, and foot-notes on page 908 in that chapter. 242 Masonry Walls. Cements and Concretes Chap. 3 deficient strength should be tested before use. Screened gravel generally makes a good coarse aggregate. " The maximum size of the coarse aggregate is governed by the character of the construction. For reinforced concrete and for small masses of unreinforced concrete, the aggregate must be small enough to produce with the mortar a homogeneous concrete of viscous consistency which will pass readily between and easily surround the reinforcement and fill all parts of the forms. For concrete in large masses the size of the coarse aggregate may be increased, as a large aggregate produces a. stronger concrete than a fine one, although it should be noted that the danger of separation from the mortar becomes greater as the size of the coarse aggregate increases." The use to be made of the concrete determines the maximum size of the coarse aggregate. When used in mass-concrete construction, such as heavy walls, the maximum size may run up to 2^^ and 3 in with good results. For reinforced work and thin walls, however, it is necessary to reduce the maximum size to i in or less. It has been found that the following are the maximum sizes for the coarse aggregate of plain or mass-concrete in the best practice: for foundations, 2y2 in; for abutments, 2 in; for arch-rings, iH in; and for copings, thin walls, etc., I in. "Cinder concrete should not be used foi' reinforced-concrete structures. It may be allowable in mass for very light loads or for fire-protection purposes. The cinders used should be composed of hard, clean, vitreous clinkers, free from sulphides, unburned coal, or ashes. (See, also, page 909.) " Water for Mixing Concrete. The water used in mixing concrete should be free from oil, acid, alkalies, or organic matter. " Preparing and Placing Mortar and Concrete. " (i) Proportions.* The materials to be used in concrete should be carefully selected, of uniform quality, and proportioned with a view to securing as nearly as possible a maximum density. "(a) Unit of Measure. The unit of measure should be the cubic foot. A bag of cement, containing 94 lb, net, should be considered the equivalent of i cu ft. The measurement of the fine and coarse aggregates should be by loose volume. "(b) Relation of Fine and Coarse Aggregates. The fine and coarse aggre- gates should be used in such relative proportions as will insure maximum den- sity. In unimportant work it is sufficient to do this by individual judgment, using correspondingly higher proportions of cement; for important work these proportions should be carefully determined by density-experiments and the sizing of the fine and coarse aggregates should be uniformly maintained or the proportions changed to meet the var>dng sizes. " (c) Relation of Cement and Aggregates. For reinforced-concrete con- struction, one part of cement to a total of six parts of fine and coarse aggre- gates, rheasured separately, should generally be used. For columns, richer mixtures are generally preferable, and in massive masonry or rubble concrete a mixture of i : 9 or even 1:12 may be used. These proportions should be determined by the strength or the wearing-qualities required in the construc- tion at the critical period of its use. Experienced judgment based on individual observation and tests of similar conditions in similar localities is an excellent guide as to the proper proportions for any particular case. For. all important construction, advance tests should be made of concrete, of the materials, pro- portions and consistency to be used in the work. These tests should be made under laboratory conditions to obtain uniformity in mixing, proportioning and * See, also, in Chapter XXIV, paragraphs relating to these subjects on page 910, and ,foa«,-note relating to the same, on page 908 of that chapter. Concrete 243 storage, and in case the results do not conform to the requirements of the work, aggregates of a better quality should be chosen or richer proportions used to obtain the desired results." Professor Turneaure of the University of Wisconsin gives the following as the proportions of cement, sand and coarse aggregate generally used for various classes of work: For reinforced columns and structural parts requiring extra strength from i : i : 2 to i : i J-^ : 3 For buildings, thin walls, reinforced concrete, tanks and impervious construction from i : 2 : 4 to i : 2H : 4H For structures requiring great strength rather than mass from i : 2^-^ : 5 to i : 3 : 6 For structures requiring mass rather than strength, foundations, etc from i : 3 : 6 to i : 4 : 8 ' " (2) Mixing Concrete. The ingredients of concrete should be thoroughly mixed and the mixing should continue until the cement is uniformly distributed and the mass is uniform in color and homogeneous. As the maximum density and greatest strength of a given mixture depend largely on thorough and com- plete mixing, it is essential that the work of mixing should receive special atten- tion* and care. Inasmuch as it is difhcult to determine, by visual inspection, whether the concrete is uniformly mixed, especially where limestone or aggre- gates having the color of cement are used, it is essential that the mixing should occupy a dcfuiite period of time. The minimum time will depend on whethef the mixing is done by machine or hand. * "(a) Measuring Ingredients. Methods of measurement of the proportions of the various ingredients should be used \#hich will secure separate and uni- form measurements of cement, fine aggregate, coarse aggregate and water at all times. "(b) Machine-Mixing. When the conditions will permit, a machine-mixer of a type which insures the uniform proportioning of the materials throughout the mass should be used, as a more uniform consistency can be thus obtained. The mixing should continue for a minimum time of at least one minute after all the ingredients are assembled in the mixer. " (c) Hand-Mixing. When it is necessary to mix by hand, the mixing should be on a water-tight platform and especial preca'utions should be taken to turn all the ingredients together at least six times and until they are homogeneous in appearance and color." "The most satisfactory method * of mixing concrete by hand is to first prepare for the mixing of the materials, a tight floor of planks, or, better still, of sheet iron with the edges turned up about 2 in. Upon this platform should first be spread the sand, and upon this the cement. The two should then be thoroughly and immediately mixed by means of shovels or hoes until of an even color. Enough water should be added to make a thin mortar wliich is then spread again. The gravel, if used, should then be added, 'and then the broken stone. Gravel and stone should be first thoroughly wet, if originally dry. The mass should be turned until all the ingredients are thoroughly incorporated and all the stone and gravel covered with mortar, this requiring from four to six turn- ings." " (d) Consistency. The materials should be mixed wet enough to result in a concrete of such a consistency that it will flow into the forms and about the metal reinforcement when used, and which, at the same time, can be conveyed from • This paragraph is condensed from several recent specifications. 244 Masonry Walls. Cements and Concretes Chap. 3 the mixer to the forms without separation of the coarse aggregate from the mortar. "(e) Retempering. Mortar or concrete should not be remixed with water after it has partly set." (3) Placing Concrete, "(a) Methods. Concrete after the completion of the mixing should be handled rapidly, and in as small masses as is practicable, from the place of mixing to the place of final deposit, and under no circum- stances should concrete be used that has partly set. A slow-setting cement should be used when a long time is likely to occur between mixing and placing. Concrete should be deposited in such a manner as will permit the most thorough compacting, such as can be obtained by working with a straight shovel or shcing tool kept moving up and down until all the ingredients have settled in their proper places by gravity and the surplus water has been forced to the surface. Special care should be exercised to prevent the formation of laitance,* which hardens very slowly and forms a poor surface on which to deposit fresh concrete. All LAITANCE should be removed. When suspended work is resumed, con- crete previously placed should be roughened, thoroughly cleansed of foreign material and laitance, thoroughly wetted and then slushed with a mortar con- sisting of one part Portland cement and not more than two parts fine aggregate. The faces of concrete exposed to premature drying should be kept wet for a period of at least seven days." "(b) Mixing and Depositing Concrete in Freezing Weather. Concrete should not be mixed or deposited at a freezing temperature, unless special pre- cautions are taken to avoid the use of materials covered with ice-crystals or containing frost, and to provide means to prevent the concrete from freezing after being placed in position and until it has thoroughly hardened. As the coarse aggregate forms the greater^ portion of the concrete, it is particularly important that this material be heated to well above the freezing-point. "(c) Rubble Concrete. Where the concrete is to be deposited in massive work, its value may be improved and its cost materially reduced by the use of clean stones thoroughly embedded in the concrete and as near together as is possible while still entirely surrounded by concrete. " (d) Depositing Concrete Under Water. In placing concrete under water it is essential to maintain still water at the place of deposit. The use of TREMiES,t properly designed and operated, is a satisfactory method of placing concrete through water. The concrete should be mixed very wet (more so than is or- dinarily permissible) so that it will flow readily through the tremies and into the places with practically a level surface. The coarse aggregate should be smaller than ordinarily used, and never more than i in in diameter. The use of gravel facilitates mixing and assists the flow of concrete through the tremies. The mouth of the tremie should be buried in the concrete so that it is at all times entirely sealed and the surrounding water prevented from forcing itself into the tremie; the concrete will then discharge without coming in contact with the water. The tremie should be suspended so that it can be lowered quickly when it is necessary either to choke off or prevent a too rapid flow; the * Laitance is a whitish, gelatinous substance of about the same composition as cement but with little tendency to harden. It accompanies a disintegration of some of the cement from the surface of concrete which is exposed to the action of water in which it is deposited. The con6rete is thus weakened and the laitance, also, weakens the bond between old and new material and should be removed before fresh concrete is placed. t A tremie is a round or square box or tube of wood or plate iron open at the top and bottom. The diameter varies from 12 to 24 in. The tremie rests in the deposited con- crete, extends above the water-level and is kept full of concrete, which escapes at the bottom as the tube is shifted over the surface. Concrete 245 lateral flow should preferably be not over 15 ft. The flow should be continuous in order to produce a monolithic mass and to prevent the formation of laitance in the interior. In large structures it may be necessary to divide the mass of concrete into several small compartments or units, filling one at a time. With proper care it is possible in this manner to obtain as good results under water as in the air. " Forms for Concrete. "Forms should be substantial and unyielding, so that the concrete will conform to the designed dimensions and contours, and should be tight in order to prevent the leakage of mortar. The time for removal of forms is one of the most important considerations in the erection of a structure of con- crete or reinforced concrete. Care should be taken to inspect the concrete and ascertain its hardness before removing the forms. So many conditions affect the hardening of concrete, that the proper time for the removal of the forms should be decided by some competent and responsible person, especially where the atmospheric conditions are unfavorable. It may be -stated, in a general way, that forms should remain in place longer for reinforced concrete than for plain or massive concrete, and that the forms for floors, beams and similar hori- zontal structures should remain in place much longei than for vertical walls. When the concrete gives a distinctive ring under the blow of a hammer, it is generally an indication that it has hardened sufficiently to permit the removal of the forms with safety. If, however, the temperature is such that there is any possibility that the concrete is frozen, this test is not a safe rehance, as frozen concrete may appear to be very hard." Shrinkage of Concrete and Temperature-Changes. "Shrinkage of con- crete, due to hardening and contraction from temperature-changes, causes cracks, the size of which depends on the extent of the mass. The resulting stresses are important in monolithic construction and should be considered care- fully by the designer; they cannot be counteracted successfully, but the effects can be minimized. Large cracks produced by quick hardening or wide ranges of temperature can be broken up to some extent into small cracks by placing reinforcement in the concrete; in long continuous lengths of concrete, it is better to provide shrinkage-joints at points in the structure where they will do little or no harm. Reinforcement is of assistance and permits longer distances between shrinkage-joints than when no reinforcement is used. Small masses or thin bodies of concrete should not be joined to larger or thicker masses without providing for shrinkage at such points. Fillets similar to those used in metal castings, but of larger dimensions, for gradually reducing from the thicker to the thinner body, are of advantage. Shrinkage-cracks are likely to occur at points where fresh concrete is joined to that which is set, and hence in placing the concrete, construction-joints should be made on horizontal and vertical lines, and, if possible, at points where joints would naturally occur in dimen- sion-stone masonry." Effect of Heat on Concrete Fireproofing.* "The actual fire-tests of concrete and reinforced concrete have been limited, but experience, together with the results of tests thus far made, indicates that concrete, on account of its low rate of heat-conductivity and the fact that it is incombustible, may be used safely for fireproofing purposes. The dehydration of concrete probably begins at about 500° F. and is completed at about 900° F.; but experience indi- cates that the volatilization of the water absorbs heat from the surrounding mass, which, together with the resistance of the air-cells, tends to increase the heat- resistance of the concrete, so that the process of dehydration is very much re- * See, also, Chapter XXITI, page 817. 246 Masonry Walls. Cenlents and Concretes Chap. 3 tarded. The concrete that is actually affected by fire remains in position and affords protection to the concrete beneath it. The thickness of the protective coating required depends on the probable duration of a fire which is Hkely to occur in the structure and should be based on the rate of heat-conductivity. The question of the conductivity of concrete is one which requires further study and investigation before a definite rate for different classes of concrete can be fully established. However, for ordinary conditions it is recommended that the metal in girders and columns be protected by a minimum of 2 in of con- crete; that the metal in beams be protected by a minimum of iVi in of concrete, and the metal in floor-slabs be protected by a minimum of i in of concrete. It is recommended that in monolithic concrete columns, the concrete to a depth of iVi in be considered as protective covering and not included in the effective section. It is recommended that the corners of columns, girders and beams be beveled or rounded, as a sharp corner is more seriously affected by fire than a round one. " Waterproofing Concrete. "Many expedients have been used to render concrete impervious to water under normal conditions, and also under pressure- conditions that exist in reservoirs, dams and conduits of various kinds. Expe- rience shows, however, that where mortar or concrete is proportioned to obtain the greatest practicable density and is mixed to a rather wet consistency, t^e resulting mortar or concrete is impervious under moderate pressure. A con- crete of dry consistency is more or less pervious to water, and compounds of various kinds have been mixed with the concrete, or applied as a wash to the surface for the purpose of making it water-tight. Many of these compounds are of but temporary value, and in time lose their power of imparting imperme- ability to the concrete. In the case of subways, long retaining-walls and reser- voirs, provided the concrete itself is impervious, cracks may be so reduced by horizontal and vertical reinforcement properly proportioned and located, that they are too minute to permit leakage or are soon closed by infiltration of silt. Coal-tar preparations applied either as a mastic or as a coating on felt or cloth- fabric are used for waterproofing, and should be proof against injury by liquids or gases. For retaining-walls and similar walls in direct contact with the earth, the application of one or two coatings of hot coal-tar pitch to the thor- oughly dried surface of concrete is an efficient method of preventing the pene- tration of moisture from the earth. " (See, also, Waterproofing for Founda- tions, Part III. Surface-Finish of Concrete. "Concrete is a material of an individual type and should not be used in imitation of other structural materials. One of the important problems connected with its use is the character of the finish of exposed surfaces. The finish of the surface should be determined before the concrete is placed, and the work conducted so as to make possible the finish desired. For many forms of construction the natural surface of the concrete is unobjectionable; but frequently the marks of the boards and the flat, dead surface are displeasing, thus making some special treatment desirable. A treatment of the surface either by scrubbing it while green or by tooling it after it is hard, which removes the film of mortar and brings the aggregates of the concrete into relief, is frequently used to remove the form-markings, break the monotonous appearance of the surface, and make it more pleasing. The plaster- ing of surfaces should be avoided, for even if carefully done, the plaster is likely to peel off under the action of frost or temperature-changes. " Design of Massive Concrete. "In the design of massive or plain concrete, no account should be taken of the tensile strength of the material, and sections Should usuaUy be proportioned, so as to avoid tensile stresses, except in slight Concrete 247 amounts, to resist indirect stresses. This will generally be accomplished, in the case of rectangular shapes, if the line of pressure is kept within the middle third of the section, but in very large structures, such as high masonry dams, a more exact analysis may be required. Structures of massive concrete are able to resist unbalanced lateral forces by reason of their weight; hence the element of weight rather than strength often determines the design. A relatively cheap and weak concrete, therefore, will often be suitable for massive concrete struc- tures. It is desirable generally to provide joints at intervals to localize the effect of contraction. Massive concrete is suitable for dams, retaining-walls, and piers and short columns in which the ratio of length to least width is rela- tively small. Under ordinary conditions this ratio should not exceed six. It is also suitable for arches of moderate span, where the conditions as to founda- tions are favorable." Quantities of Materials Required per Cubic Yard of Concrete.* The following tables give the quantities of Portland cement required to make i cu yd of mortar and the quantities of cement, sand and stone required to make i cu yd of concrete. They are based upon formulas deduced by Halbert P. Gillette. Barrels of Portland Cement per Cubic Yard of Mortar Voids in sand, 35%, i bbl of cement yielding 3.65 cu ft of cement paste Proportion of cement to sand I to I I to l]-2 I to 2 I to 21-2 I to 3 I to 4 Barrel specified to be 3.5 cu ft Barrel specified to be 3.8 cu ft Barrel specified to be 4.0 cu ft Barrel specified to be 4.4 cu ft bbl 4.22 4.09 4.00 3.81 bbl 3-49 3.33 3.24 3-07 bbl 2.97 2.81 2.73 2.57 bbl 2.57 2.45 2.36 2.27 bbl. 2.28 2.16 2.08 2.00 bbl 1.76 1.62 1.54 1.40 Cubic yard of sand per cu yd of mortar 0.6 0.7 0.8 0.9 I.O 1.0 Barrels of Portland Cement per Cubic Yard of Mortar Voids in sand, 45%, i bbl of cement yielding 3.4 cu ft of cement paste Proportion of cement to sand Barrel specified to be 3-5 cu ft Barrel specified to be 3.8 cu ft Barrel specified to be 4.0 cu ft Barrel specified to be 4.4 cu ft Cubic yard of sand per cu yd of mortar I to I I to iK' I to 2 I to 2y> I to 3 I to 4 bbl bbl bbl bbl bbl bbl 4.62 3.80 3.25 2.84 2.35 1.76 432 3.61 3.10 2.72 2.16 1.62 4.19 346 3-00 2.64 2.05 1.54 3.94 3.34 2.90 2.57 1.86 1.40 0.6 0.8 09 1.0 1.0 1.0 "In using these tables remember that the proportion of cement to sand is by volume and not by weight. If the specifications state that a barrel of cement shall be considered to hold 4 cu ft, for example, and that the mortar shall be * Quoted, by permission, from the Handbook of Cost Data for Contractors and En- gineers, by Halbert P. Gillette, published by The Myron C. Clark Publishing Company, Chicago.Ill. See 1914 revised edition, pages 538 to 540. This handbook contains com- plete and voluminous data on quantities, costs, etc., of building materials and operations. 248 Masonry Walls. Cements and Concretes Chap. 3 I part cement to 2 parts sand, then i bbl of cement is mixed with 8 cu ft of sand, regardless of what is the actual size of the barrel, and regardless of how much cement paste can be made with a barrel of cement. If the specifications fail to state what the size of a barrel will be, then the contractor is left to guess. "If the specifications call for proportions by weight, assume a Portland ce- ment barrel to contain 380 lb of cement, and test the actual weight of a cubic foot of the sand to be used. Sand varies extremely in weight, due both to the variation in the per cent of voids, and to the variation in the kind of minerals of which the sand is composed. A quartz sand having 35% voids weighs 107 lb per cu ft; but a quartz sand having 45% voids weighs only 91 lb per cu ft. If the weight of the sand must be guessed at, assume 100 lb per cu ft. If the specifications require a mixture of i part of cement to 2 parts of sand, by weight, we will have 380 lb (or i bbl) of cement mixed with 2 times 380, or 760 lb of sand; and if the sand weighs 90 lb per cu ft, we shall have 760 divided by 90, or 8.44 cu ft of sand to every barrel of cement. In order to use the tables above given, we may specify our own size of barrel; let us say 4 cu ft; then, 8.44 divided by 4 gives 2.n parts of sand by volume to i part of cement. Without material error we may call this a i to 2 mortar, and use the tables, remembering that our barrel is now * specified to be' 4 cu ft. If we have a brand of cement that yields 3.4 cu ft of paste per bbl and sand having 45% voids, we find that approximately 3 bbl of cement per cu yd of mortar will be required. "It should "be evident from the foregoing discussions that no table can be made, and no rule can be formulated that will yield accurate results unless the brand of cement is tested and the percentage of voids in the sand determined. This being so, the sensible plan is to use the tables merely as a rough guide, and, where the quantity of cement to be used is very large, to make a few batches of mortar, using the available brands of cement and sand in the proportions specified. Ten dollars spent in this way may save a thousand, even on a com- paratively small job, by showing what cement and sand to select." Ingredients in One Cubic Yard of Concrete * Sand-voids, 40%; stone-voids, 45%; Portland-cement barrel yielding 3.65 cu ft paste. Barrel specified to be 3.8 cu ft Proportions by volume I :2:4 I :2:s 1:2:6 i:2i/^:5 1:21/2:6 I :3:4 Barrels cement per cu yd concrete 1.46 0.41 0.82 1.30 0.36 0.90 1. 18 0.33 1. 00 113 0.40 0.80 1. 00 0.3s 0.84 I-25 0.53 0.71 Cubic yard sand per cu yd concrete Cubic yard stone per cu yd concrete Proportions by volume I :3:5 1:3:6 1:3:7 1:4:7 1:4:8 I :4:9 Barrels cement per cu yd concrete 1. 13 0.48 0.80 1.05 0.44 0.88 0.96 0.40 0.93 0.82 0.46 0.80 0.77 0.43 0.86 0.73 0.41 0.92 Cubic yard sand per cu yd concrete Cubic yard stone per cu yd concrete * This table is to be used where cement is measured packed in the barrel, for thft ordinary barrel holds 3.8 cu ft. Concrete 249 "It will be seen that the above table can be condensed into the following: "Rule. Add together the number of parts and divide this sum into ten, the quotient will be, approximately, the number of barrels of cement per cubic yard. "Thus for a I 12:5 concrete, the sum of the parts is i plus 2 plus 5, which is 8; then 10 divided by 8 is 1.25 bbl, which is approximately equal to the 1.30 bbl given in the table. Neither this rule nor this table is applicable if a different size of cement-barrel is specified, or if the voids in the sand or stone differ mate- rially from 40% and 45% respectively. There are such innumerable com- binations of varying voids, and varying sizes of barrels, that the author does not deem it worth while to give other tables. " Ingredients in One Cubic Yard of Concrete * Sand-voids, 40%; stone-voids, 45%; Portland-cement barrel yielding 3.65 cu ft of paste. Barrel specified to be 4.4 cu ft Proportions by volume I : 2 ; 4 1:2:5 I :2:6 I •.2Y2. '.$ 1:21/2:6 1:3:4 Barrels cement per cu yd concrete Cubic yard sand per cu yd concrete Cubic yard stone per cu yd concrete 1.30 0.42 0.84 1. 16 0.38 0.9s 1. 00 0.33 1. 00 1.07 0.44 0.88 0.96 0.40 0.9s 1.08 0.53 0.71 Proportions by volume 1:3:5 1:3:6 1:3:7 1:4:7 1:4:8 I :4:9 Barrels cement per cu yd concrete 0.96 0.47 0.78 0.90 0.44 0.88 0.82 0.40 0.93 0.75 0.49 0.86 0.68 0.44 0.88 0.64 0.42 0.95 Cubic yard sand per cu yd concrete Cubic yard stone per cu yd concrete Cost of Concrete. t (For Cost of Cement, see page 238.) The average cost of sand may be taken at 30 cts per cu yd to cover digging and loading, but when washed or screened the cost averages between 40 and 55 cts per cu yd. Hauling and freight-charges generally raise the cost of sand, ready to unload at the site, to from 90 cts to $1.10 per cu yd, and about 15 cts per yd additional must be added, if unloaded from cars. Gravel costs from $1.20 to $1.40 per cu yd, unloaded at the job, and crushed stone from $1.45 to $1.60. These prices are, of course, average prices only, and include moderate-haul teaming and un- loading. For hand-mixing and placing of soft concrete, and spreading without any ramming, the labor-cost varies from 90 cts to $1.30 per cu yd. This is for handling in barrows materials that are conveniently at hand. This cost will be much higher for dry concrete, and hand-mixing costs may reach $2 or $3 per cu yd. For machine-mixing alone and with machines taking four bags to the batch, the cost of mixing may be even as low as 50 or 60 cts per cu yd. For placing alone, the cost is about 75 cts per cu yd; this includes wheeling the concrete, dumping it in place and spreading and spading it into forms. This cost could be almost doubled where unusual care had to be exercised to obtain a good surface and where there was an extra amount of spading. The costs * This table is to be used when the cement is measured loose, after dumping it into a box, for under such conditions a barrel of cement yields 4.4 cu ft of loose cement. t War-conditions changed many costs. Values given are retained temporarily for pur- poses of comparison. 250 Masonry Walls. Cements and Concretes Chap. 3 are reduced for heavy mass-concrete, and have been as low as 50 or 60 cts per cu yd for machine-mixing and placing together, by mixer and derrick or by tracks and cars. The following approximate schedule * of labor-costs for mix- ing and placing concrete is given by L. li. Allen of the Aberthaw Construc- tion Company, in Professor Hool's excellent treatise: For footings $1 . 50 per cu yd For floor-slabs not exceeding 4H in in thickness $1 .60 per cu yd For floor-slabs exceeding 5 in in thickness $1 .00 per cu yd For columns and thin walls $i . 50 per cu yd For walls exceeding 18 in in thickness $1 .00 per cu yd For dams and thick retaining-walls $0.70 per cu yd For the unit cost due to the cost of the tools, plant and supplies, $1 may be taken as an average for jobs requiring from 4 000 to 10 000 cu yd of concrete. It varies, of course, with the character and magnitude of the work. The cost for this item is reduced in larger jobs, falling to 80 or even 70 cts per cu yd; and it is increased in operations of less magnitude to from $1 to $1.50 per cu yd, for, say, 3 000 cu yd of concrete. When the amount of concrete required is as small as 600 or 7cx) cu yd, hand-mixing is generally more economical than machine-mixing. Mr, Allen summarizes * the cost of i cu yd of concrete for a building requiring 5 000 cu yd of reinforced-concrete work in floors and columns as follows, the cost of forms and steel and finishing of the surface not being included: Cement, t% bbl, at $1.38 per bbl $2 .30 Sand, 3'^ cu yd, at $1 per cu yd 0.50 Stone, 1.35 tons, at $1.40 per ton 1.89 Labor, per cu yd 1.35 Plant, per cu yd i . 00 Total, per cu yd $7 . 04 In this summary the exact theoretical proportions or quantities of cement, sand and stone required for i cu yd of concrete, and deduced from formulas, are not adhered to, the author stating that the exact theoretical proportions are the net quantities of the materials determined by careful experiment, that "conditions on actual construction work do not approach those of laboratory work and that there is always a considerable waste of cement, sand and stone." In view of these facts, he states that, "when estimating quantities, it is not safe to allow less than the following amounts of cement for different proportions of mix: I : il'i : S niix 2 . 00 bbl per cu yd 1:2 14 mix 1 . 66 bbl per cu yd I : 21^^ : 5 mix i . 40 bbl per cu yd 1:3 : 6 mix i . 20 bbl per cu yd " It is customary to allow H cu yd of sand and i cu yd of crushed stone, to I cu yd of concrete, and to estimate the weight of crushed stone at 100 lb per cu ft. The Weight of Concrete varies from no to 155 lb per cu ft, according to the material used. Concrete of the usual proportions weighs from 140 to 150 lb per cu ft. Trap-rock concrete weighs from 148 to 155; limestone or gravel concrete, from 142 to 148; and cinder concrete from 80 to 115 lb per cu ft. * Reinforced Concrete Construction, by George A. Hool, McGraw-Hill Book Companyt New York. Concrete 251 The Strength of Concrete. See Chapter V. Earlier Examples of Portland-Cement Concrete. From the foregoing it is seen that for foundation- work to-day, mass-concrete varies in proportions from ai:3:6toai:4:8 mix. Some of the earher examples are added for comparison. Foundations of the United States Naval Observatory, Georgetown, D. C.r I part cement, 2i/i sand, 3 gravel, 5 broken stone, (i bbl of cement, 380 lb, made 1.18 yd of concrete.) Foundations of the Cathedral of St. John the Divine, New York: i part Portland cement, 2 parts sand, 3 parts quartz gravel of pieces from ij^i to 2 in in diameter. (17 cx)o bbl of cement made 11 000 yd of concrete.) Manhattan Life Insurance Building, New York, filling of caissons: i part Alsen Portland cement, 2 parts sand, 4 parts broken stone. Johnston Building (15 stories), New York, filling of caissons: i part Portland cement, 3 parts sand, 7 parts stone, finished on top for brickwork with i part cement and 3 parts gravel. Professor Baker states that the concrete foundations under the Washington Monument were made of i part Portland cement, 2 parts sand, 3 parts gravel and 4 parts broken stone, and that this mixture stood, when six months old, a load of 2 000 lb per sq in, or 144 tons per sq ft. 25? Retaining-Walls, Breast-Walls and Vault- Walls Chap. 4 CHAPTER IV KETAINING-WALLS, BREAST-WALLS AND VAULT-WALLS By GRENVILLE TEMPLE SNELLING MEMBER OF AMERICAN INSTITUTE OF ARCHITECTS 1. Mechanical Principles Involved General Principles. Before discussing more in detail the problems relating to masonry structures, in which, if improperly constructed, a tendency to slide or overturn on their bases may be developed, a familiarity with what are known as the THEOREM OF FRICTION and the theorem of the middle third will be of assistance in comprehending the methods indicated for rendering such struc- tures stable. Theorem of Friction. If a body rests on an inclined plane it will remain stationary until the angle , that the plane makes 'with the horizontal, Body on Inclined Plane. Fig. 4 Graphical Representation of Forces becomes so great that the friction developed between the surfaces of the body and the plane is no longer sufficient to prevent the body from sliding down the plane (Fig. 1). Assume the body //// resting on the plane EF. The weight, W, of this body is shown graphically by the line AB, applied at its center of gravity A (Fig. 2). Mechanical Principles Involved 263 This weight can be resolved into two component forces, one, AC, normal to the inclined plane and the other, AD, parallel to it. It is the parallel or tangential force which tends to pull the body down the plane and which is resisted by the friction developed between the two surfaces. The friction developed between any two surfaces in contact depends upon the nature of the materials of which they are composed and the intensity of the forces pressing them together; and it resists the tendency to slide only up to a certain point. As the angle , which the inclined plane makes with the horizontal, increases, the tangential component T, of the weight W, increases, until it becomes greater than the frictional resistance, and the body moves down the plane (Fig. 3). From trigonometry, T=Wsm(l> N = Wcos, or, r = i\^tan0 There is evidently a position of the plane, intermediate between the positions shown in Figs. 1 and 3, in which the component force T is just balanced by the friction and in which the body remains at rest although just on the point of sHding (Fig. 4). If the angle which the inclined plane makes with the hori- zontal, at the moment when the body is just about to slide, be designated by , the friction developed between the two surfaces will be equal to N tan 0, since, when the angle of inclination of the plane to the horizontal is (f>, the tangential component of the weight just balances the friction. From the equation T = N tan it is evident that the friction is directly proportional to N and to tan . Tan (f) is then known as the coefficient of friction and as the angle of REPOSE, or, in the case of stone s\irfaces, it is often known as the angle of friction. The following Table I gives the average values of these constants as deter- mined by experiment. Table I. Coefficients and Angles of Friction Kind of surface Coefficient of friction, tan Angle of friction, Granite, limestone and marble: Soft dressed upon soft dressed 0.70 0.55 0.65 65 0.60 0.50 0.50 0.33 0.40 0.60 0.40 0.30 35° 00' 28 50 33 00 33 00 31 00 26 46 26 40 18 20 21 50 31 00 21 50 16 40 Hard dressed upon hard dressed Hard dressed upon soft dressed Stone, brick or concrete i Masonry upon masonry Masonry upon wood (with the grain) Masonry upon wood (across the grain) Masonry upon dry clay Masonry upon wet or moist clay Masonry upon sand Masonry upon gravel Soft stone upon steel or iron Hard stone upon steel or iron In this discussion only the weight AB (Figs. 2, 3 and 4), of the body has been considered; but the body might be subjected to the action of other forces be- sides the force of gravity, in which case these other forces would be combined with the weight in order to find the resultant, this resultant being again resolved into a tangential and a normal component. Since the angle BAC is equal to the 254 Retaining-Walls, Breast-Walls and Vault-Walls Chap. 4 angle PEG (Figs. 2, 3 and 4), given a certain normal pressure exerted by the body on the plane, the amount of the tangential pressure T depends upon the angle PEG. The problem in actual practice reduces itself to so arranging the conditions that no matter what the position of the plane may be, the angle , which the resultant W, makes with the normal N, to the plane, will not be greater than the angle of friction or repose. ;" Theorem of the Middle Third. When any surface is subjected to pres- sure from the action of any force or forces, this total pressure may be con- sidered as a SYSTEM OF AN INFINITE NUMBER OF PARALLEL FORCES, equal or unequal in intensity. These forces will have a resultant, whose magnitude, DIRECTION and point of APPLICATION can be determined, either graphically, or by moments, as explained in Chapter VI. The determination of these three elements of this resultant force may at times become of the utmost importance to the engineer. Pressure of this nature is technically known as the stress to which the sur- face in question is subjected. (See Chapter I.) When the intensity of a stress is not the same at different points of a surface, it is called a varying stress, while if, on the contrary, its intensity remains the same at every point of the surface, it is called a uniform stress. When a stress varies it may do so in one or two ways. It ma}^ vary uni- formly, that is to say, in a uniform manner, following some definite law of variation, so that, knowing this law, its intensity may be determined for any given point of the surface; or non-uniformly, following no law. When a stress varies in the former manner it is called a uniformly varying stress This is the case most frequently met with in engineering problems. Resultant of the stresses Fig. 5. Resultant within Middle Third Fig. 6. Resultant at Middle' Third In dealing with isolated forces, such as concentrated loads on a beam, we are usually interested in determining the magnitude and point of application of the resultant of these forces. When, however, the question is one of stress, or of an unlimited number of forces, the problem that usually presents istelf is one in which the resultant is known, in magnitude, direction and point of application, and in which it is required to determine the distribution of the stress to which the surface is subjected. Or, in actual practice, it is required to so arrange the parts of the structure that this resultant shall have such a mag- nitude, direction and point of application that the stress to which the surface under consideration is subjected shall not exceed certain limits of safety, determined beforehand by experience. For example, when the resultant of a known amount of pressure or stress acts at the center of gravity of the sur- face subjected to the stress, this stress is uniformly distributed over the surface. Retaining- Walls 255 Resultant of the stresses When the resultant acts at a distance of two-thirds the total width of the surface from one edge or boundary line of the surface, and at one-third the width from the other edge, the stress is uniformly varying; and its in- tensity at the edge farthest from the point of application of the resultant is zero and at the other edge a maximum or twice the average stress. When, however, the total amount of the stress remaining the same, the point of application of the resultant is at a greater distance from one edge than two-thirds the total width of the surface, a certain part of the surface adjacent to the edge furthest from the resultant is subjected to a stress of a contrary NATURE to that distributed over the rest of the area; that is to say, if the stress to which the major part of the surface is subject is a compressive stress, the stress acting on the remainder of the surface is a tensile stress. The stresses in a surface resulting from three different positions of the resultant force may be illustrated graphically, as shown in Figs. 5, 6 and 7. (See, also. Chapter XXXI, pages 1225 and 1234.) 2. Retaining-Walls Definitions. A Retaining-Wall is a wall built to resist the pressure of earth, sand, or other filling or backing deposited behind it after it is built, as distinguished from a breast-wall or face-wall, which is a similar structure built to prevent the fall of earth which is in its undisturbed, natural position, but from which part has been excavated, leaving a vertical or inclined face. Fig 8 is an illustration of the two kinds of wall. Fig. 7. Resultant beyond Middle Third Retaining-wall and Breast-wall Theories of Retaining-Walls. A great deal has been written on the theory . OF retaining-walls, and many theories, involving elaborate calculations for determining the conjugate pressures in the earth-backing behind the wall, have been developed for computing the thrust which a bank of earth exerts against such a wall, and for determining the form of wall which offers the great- est resistance with the least amount of material. There are so many condi- tions, however, upon which the thrust exerted by the backing depends, such as the cohesion of the earth, the dryness of the material, the mode of backing up the wall, etc., that in practice it is impossible to determine the exact thrust which will be exerted against a wall of a given height. It is necessary, therefore, in designing retaining-walls, to be guided by experience rather than by theory. As the theories of retaining-walls are so vague and unsatisfactory, we shall not 256 Retaining-Walls, Breast- Walls and Vault-Walls Chap. 4 include any in this work, but offer, rather, such suggestions, rules and cautions as have been established by practice and experience. A construction sug- gested from empirical data, which has been found to work well in practice, for determining the thrust of the earth-backing and the dimensions of the WALL to properly resist this thrust, is given on page 257. In designing a retaining-wall the backing as well as the wall itself must be carefully considered. The tendency of the backing to slip is very much less when the material is in a dry state than when it is saturated with water, and hence every precaution should be taken to secure good drainage. Besides surface-drainage, there should be openings left in the wall for the water which may accumulate behind it to escape. The manner in which the material is filled against the wall, also, affects the stability of the backing. If the ground is made irregular, with steppings, as shown in Pig. 8, and the earth well rammed in layers inclined down from the wall, the pressure will be very trifling, provided that attention is paid to drainage. If, on the other hand, the earth is tipped in the usual manner, in layers sloping down towards the wall, almost the full pressure of the earth will be exerted against it, and it must be made strong enough to withstand such pressure. Slopes of Repose and Angles of Repose. Cases may occur in practice in which the conditions are not such as are shown in Fig. 8, which shows only a limited amount of fill or new material put in behind the wall on top of the original slope of the grade; cases in which, on the contrary, the wall has been built on the natural surface of the ground with a view to creating an entirely new terrace or embankment and where all the material back of the wall is new. All of this material does not beat upon the wall and tend to overturn it, for sand or loose earth taken from an excavation and deposited on the surface of the ground does not spread itself out like a liquid but piles up in a mound. This PILING UP is due to the friction developed between the separate particles as they slide one over the other while being dumped. This phenomenon is observed in the action of any solid material broken up into separate particles; and although the SLOPE OF THE SIDES of such a mound varies with different materials, it is, in general, the same for the same material. The angle of this slope is known as the ANGLE OF NATURAL SLOPE of the material. This angle for the materials gen- erally used for fill is given in the following Table II. Table 11. Slopes of Repose, Angles of Repose and Weights of Loose Materials Kind of earth Slope of repose* Angle of repose Weight in lb per cu ft Sand, clean Sand and clay Clay, dry Clay, damp, plastic Gravel, clean Gravel and clay Gravel, sand and clay . Soil Soft rotten rock Hard rotten rock Bituminous cinders. . . Anthracite ashes 1.5 to I 1.33 to I 1.33 to I 2 to I 1.33 to I 1.33 to I 1.33 to I 1.33 to I 1.33 to I I to I I to I I to I 33" 41' 36 53 36 53 26 34 36 53 36 53 36 53 36 53 36 53 45 00 45 00 90 100 100 100 100 100 100 100 no 100 65 30 * The slope is that of horizontal to vertical projection. Retaining-Walls 257 Pressures on Retaining-Walls. Even under the conditions shown in Fig. 8, Dnly a part of the fiUed-in material will exert a pressure on the wall. It would be natural to suppose that the part of the fill exerting pressure on the wall would be determined by the angle of natural slope, all material from a natural horizontal grade up to this angle being able to take care of itself, and all the material above the angle needing the wall to hold it in place. Experi- ment shows that this is not strictly true, for as the earth settles into place certain forces of internal elasticity and tendencies toward a state of equilibrium come into play creating internal stresses which produce the conjugate pressures already referred to. The exact determination of these internal STRESSES demands relatively complicated calculations which would be out oi place in a book of this character. The construction given in the following paragraphs for determining the slope of the cleavage-plane, between that part of the backing which sustains itself and the triangular fill which actually bears on the wall, is sufficiently accurate, however, for all practical purposes. The Slope of the Cleavage-Plane. The following construction (Figs. 9 and 10), based upon empirical data, for determining first, the prism of earth Fig. 9. Method of Determining the Prism of Earth which exerts pressure on the back of the wall and secondly, the proper dimen- sions for the wall, has been found to work well in practice, when certain neces- sary precautions are taken. These include proper drainage behind the wall, proper ramming of the fill and eflScient bracing of the wall during its construc- tion. In the calculations to determine the pressure of the earth and the weight of the wall, a shce i ft thick is first considered. Then the area of the triangle ABE is proportional to the volume and weight of the slice of earth causing pressure on the wall, and as the area "of the cross-section of the wall is propor- tional to the volume and weight of the shce of the wall itself. To determine the prism of earth which exerts pressure against the back of the wall, decide first upon the batter to be given to the back of the wall. In this case it made 8o° with the horizontal, an angle slightly greater than that advised by Trautwine. Draw BH (Fig. 9), making an angle ABH, equal to 2 0, with the back of the wall; continue this Une until it meets at H the slope of the surface of the earth back of the wall, prolonged. From A, the top of the wall, draw A J parallel to BF the natural slope of the fill. This has been taken at 35°, as a fair average value. Erect a perpendicular from the middle of JB, ?.nd with any point, 0, as a center, on this perpendicular, describe an arc passing 258 Retaining-Walls, Breast-Walls and Vault- Walls Chap. 4 through J and B. Draw HO and bisect it, and with 0' as a center and 00' as a radius, describe the arc cutting the arc J KB at K. Again, with a radius HK and with H as center, describe the arc KL, and finally, from L, draw LE parallel CO J A . The intersection of this line with the surface of the ground locates the Fig. 10. Method of Determining Dimensions of Retaining-wall point E. The line EB is the line of the cleavage-plane which separates the part of the backing which bears against the wall from the part which exerts no lateral pressure. Having found the dimensions of the volume of earth, the thrust of which must be resisted by the wall, the next step is to determine what the dimensions OF the wall should be to. properly resist this thrust. Usually one or two trials are necessary before the proper solution of the problem is found. In the ex- ample given, a preliminary trial was made with a thickness at the base of 4 ft. This construction is shown with the green lines (Fig. 10). After drawing the triangle representing the base of the prism of earth, find its center of gravity, G (Chap. VI). From this point draw two normals, one to the back of the wall and the other to the line of the cleavage-plane. Draw the two lines, GM and GN, making angles with these normals. Lay off ver- tically from the center of gravity, at any convenient scale of so many square Retaining-Walls 259 inches to the linear inch, the area of the triangle of the base of the prism, the area, as already explained, being proportional to the volume of the prism and its weight. Resolve this weight-line along the two hnes GM and GN (Chap. . VI). This will give the magnitude and direction of the thrust or pressure of the earth against the wall. Apply this pressure at a point on the back of the wall one-third of the distance from the bottom, as shown by the arrow. This is the force which may tend to overturn the wall and which tends to make it SLIDE along the base. (See Fig. 6.) To resist these overturning and sliding-tendenctes, the weight of the wall combined with the pressure of the earth behind it should produce a resultant which satisfies the following conditions. First, its magnitude should not be great enough to cause a unit pressure on the foundation-bed greater than it can safely bear; secondly, it should pass within the middle third of the base so that the stress over the entire area of the base will be a compressive stress; and thirdly, it should make an angle with a normal to the plane of the founda- tion-bed not greater than the angle of friction between the stone, brickwork, concrete, or other masonry of the footings and the sand, clay, or rock of the foun- dation-bed. In order to determine these conditions, the center of gravity of the cross- section of the wall must be detcr.nined and a vertical line drawn through this point until it intersects the line of the earth-thrust produced. It is at this intersection of the lines of action of the two forces that their resultant acts. To find the center of gravity of the cross-section of the wall, the method of dividing the trapezoid into two triangles has been followed, the center of gravity of each triangle being found and these two points being joined by a line. The intersection of this line with the median line drawn between the base and the top of the wall is the center of gravity of the trapezoid. In this example, for convenience, the scale used for the composition of the forces of the pressure of the earth and the v/cight of the wall is one-half the scale used for the resolution of the forces representing the weight of the earth-prism. In the first trial, shown by the green lines, the first and third conditions neces- sary to insure stability are fulfilled; but the second is not, the resultant pass- ing outside the middle third of the base. This indicates, theoretically, a sUght tensile stress or a tendency for the joints at the back of the wall to open. Another trial, therefore, is shown with the red Hnes, the thickness of the wall being increased as shown by the rectangle CC'D'D. In this second trial the weight of the wall is necessarily increased while the earth-thrust remains the same. As in this case the resultant passes within the middle third, it is concluded that a wall of these dimensions, 5 ft base by 10 ft height and with an 80° batter, will be safe and will properly resist the thrust of the earth- backing. Details of Construction. Retaining-walls are generally built with a batter- ing, that is, a sloping face, as walls of this form are the strongest for a given amount of material; and if the courses are inclined down towards the back, the tendency to slide on each other will be resisted, and it will not be necessary to depend upon the adhesion of the mortar. The importance of making the resist- ance independent of the adhesion of the mortar is obviously very great, as it wou)d otherwise be necessary to delay the backing up of the wall until the mortar had thoroughly set, which might require several months. In brickwork it is advisable to let every third or fourth course below the frost- line project an inch or two. This increases the friction of the earth against the back and causes the resultant of the forces acting behind the wall to become more nearly vertical, and to fall farther within the base, increasing the stabiUtyc, 260 Retaining-Walls, Breast-Walls and Vaiilt-Walls Chap. 4 It also conduces to strength to make the courses of varying heights throughout the thickness of the wall, and to have some of the stones, especially those near the back, sufficiently high to extend through two or three courses. By this means the whole masonry becomes more effectually interlocked or bonded together as one mass and is less liable to bulge. The courses of masonry are often laid with their beds sloping in, as in Fig. 15, to overcome the tendency of the courses to slide on each other. Where the ground freezes to a great depth, the back of the wall should be SLOPED FORWARD for three or four feet below its top surface, as at OC (Fig. 11), Fig. 11. Retaining-wall for Deep- freezing Earth Fig. 12. Retaining-wall with Rectangular Cross- section -8-0 ^ Fig. 13. Retaining- wall with Triangular Cross-section and this slope should be quite smooth, so as to lessen the hold of the frost and prevent displacement. Figs. 12, 13, 14 and 15 show the approximate relative vertical sectional AREAS of walls of different shapes that would be required to resist the pressure of a bank of earth 12 ft high. The first three examples are calculated to --^sist the maximum thrust of wet earth, while the last shows the modified form usually adopted in practice. Notes on the Thickness of Retaining- Walls. As has been stated, about the only practical rules for retaining-walls are the empirical rules based upon ex- perience and tests. Trautwine* gives the following Table III for the thickness at the base of vertical retaining-walls with a sand backing deposited in the usual manner. The first column contains the vertical height CD (Fig. 16) of the earth as compared with the vertical height of the wall, AB. The latter is assumed to be i, so that the table begins with a backing of the same height as the wall. These vertical walls may be battered to any extent not exceeding iH in to i ft, or i in 8, without affecting their stability and without increasing the base. If the wall is built as in Fig. 17, with the ground practically level with the top, the top of the wall should be not less than 18 in thick, and the thicknesses at a, a, etc., just above each step, should be from one-third to two-fifths of the * The Civil Engineer's Pocket-Book, John C. Trautwine. k~ 70---^ Fig. 14. Retaining-wall with Triangular Cross- section Fig. 15. Retaining- wall with Stepped Back Retaining-Walls Table III. Proportions of Retaining-Walls (Thickness of wall at the base in parts of the height, AB, Fig. 16) 261 Total height of the earth Wall of cut Wall of rubble or Wall of good. compared with the height of the wall above ground stone in mortar brick, good mortar dry rubble I 0.35 0.40 0.50 I.I 0.42 0.47 0.57 1.2 0.46 0.51 0.61 1.3 0.49 0.54 0.64 1.4 o.si 0.56 0.66 1.5 0.52 0.57 0.67 1.6 0.54 0.59 0.69 1.7 0.55 0.60 0.70 1.8 0.56 0.61 0.71 2 0.58 0.63 0.73 2.5 0.60 0.65 0.7s 3 0.62 0.67 0.77 4 0.63 0.68 0.78 6 0.64 0.69 0.79 14 0.65 0.70 0.80 25 0.66 0.71 0.81 or more 0.68 0.73 0.83 height from the top of the wall to each of these levels. If the earth is banked above the top of the wall, the thicknesses should be increased as indicated by the table given above. If built upon ground that is aflected by frost or sur- face-water, the footings should be carried sufficiently below the surface of the ground at the base to insure against heaving or settling. Fig. 16. Retaining-wall with Raised Sand Backing Fig. 17. Retaining-wall with Stepped Back Rainforced-Concrete Retaining-Walls. With the constantly increasing use of REINFORCED CONCRETE for various purposes, there has come, also, the construction of retaining-walls in this material. Figs. 18,* 19 * and 20 * show three designs by A. L. Johnson for retaining-walls to satisfy the * Plain and Reinforced Concrete, Taylor and Thompson. 262 Retaining-Walls, Breast-Walls and Vault-Walls Chap. 4 requirements of banks 5, 10 and 20 ft high. The wall shown in Fig. 20 is reinforced at intervals with counterforts. The walls themselves in Figs. 18 and 19 act as caniilever beams. The footings, in all three cases, are ,subjected to two principal external forces, the resultant of the resisting /I "anchor-bolts Fig. 18. Reinforced-concrete Retaining-wall, 5 ft High Fig. 19. Reinforced-concrete Retaining-wall, 10 ft High upward pressure of the foundation-bed and the resultant of the down- ward pressures of the fill. In Fig. 20 the coping acts as a beam fixed at BOTH ENDS, with a span equal to the distance between the counterforts, and loaded with the proper proportion of the load due to the pressure of the fill behind the wall and transmitted to the coping by the wall. The wall itself in this case acts as a ^'loor-slab supported on all four sides and subjected to an approximately evenly distributed load. The counterforts arc in tension. The MAXIMUM BENDING MOMENTS for thcsc various cases can be determined (Chapter IX) and the necessary dimensions and reinforcement to be pro- vided decided by the rules given in Chapter XXIV. 3. Breast-Walls Breast-Walls. Where the ground to be supported is firm, and the strata are horizontal, the ofBce of a breast- wall (Fig. 8) is more to protect than to sustain the earth. It should be borne in mind that a trifling force skilfully applied to un- broken ground will keep in its place a mass of material, which, if once allowed to move, would crush a heavy wall. Great care, therefore, should be taken not to Vault-WaUs 263 eipose the newly opened ground to the influe^xe of air and water longer than is requisite for sound work, and to avoid leaving the smallest space for motion between the back of the wall and the ground. The strength of a l3reast-wall must be proportionately increased when the strata to be supported incline down Fig. 20. Reinforced-concrete Retaining-wall with Counterforts and Apron towards the wall; where they incline down from it, the wall need be httle more than a thin facing to protect the ground from disintegration. The preserva- tion of the NATURAL DRAINAGE is One of the most important points to be attended to in the erection of breast-walls, as upon this their stabihty in a great measure depends. No rule can be given for the best way to do this; it is a matter for attentive consideration in each particular case. 4. Vault- WaUs Vault- Walls. In large cities it is customary to utilize the space under the sidewalk for storage or other purposes. This necessitates a wall at the curb- line to hold back the earth and the street-pressures and also the weight of the sidewalk. Where practicable the space should be divided by partition-walls about every lo ft, and when this is done the outer wall may be advantageously built of hard bricks in the form of arches, as shown in Fig. 21. The thickness 264 Retaining-Walls, Breast- Walls and Vault-Walls Chap. 4 of the arch should be at least i6 in for a depth of 9 ft and the rise of the arch from one-eighth to one-sixth of the span. If partitions are not practi- cable, each sidewalk-beam may be supported by a heavy I-beam column, with either flat or seg- mental arches between, of either brick or concrete. Fig. 22 * shows a detail of the outer walls of the vault under the sidewalk around the Singer building, New York City. These walls consist of a core formed by two-ring brick arches with vertical axes, built between the flanges of 8-in vertical steel I beams spaced about 5 ft apart and bedded at the bottom in a con- crete footing. Their tops are joined by 6-in horizontal I beams and braced laterally by the sidewalk-beams, 5 ft apart. The arches themselves are segmental, with a rise of about 6. in. Vault-wall with Partitions Fig. 22. Vault-walls of Singer Building, New York City and are built up solid against an 8-in outside face-wall. A 4-in plain curtain wall is built inside against the flanges of the vertical beams, inclosing seg- mental air-chambers in front of each arch. * From The Engineering Record, Feb. 26, 1898. ' Crushing Strength of Stonework, Brickwork, Bricks 265 CHAPTER V STRENGTH OF BRICK, STONE, MASS-CONCRETE AND MASONRY By THOMAS NOLAN PROFESSOR OF ARCHITECTURAL CONSTRUCTIOI«f, UNIVERSITY OF PENNSYLVANIA 1. Crushing Strength of Stonework, Brickwork, Bricks, etc. Stresses in Masonry. By the term strength of masonry is generally meant its resistance to a direct compressive force or load, and this is the only direct stress to which masonry should be subjected. Stone lintels and footings may be subjected to a transverse or bending stress, but they can hardly be included in the term masonry, as they consist of single pieces. There are also tendencies to bend and to split apart in brick walls and piers, as they are usually high in proportion to their lateral dimensions, but the stresses thus developed cannot be accurately determined and should be avoided as much as possible. It is impossible to fix values for the strength of brickwork or stonework with anything like the exactness possible for wooden or steel hiembers, for the reason that there is not only a great variation in the strength of different kinds of brick and stone, even when taken from the same kiln or quarry, but the strength of walls and piers is also greatly affected by the kind and quality of the mortar used, the way in which the work is built and bonded, and the amount of moisture in the materials when they are laid. All that can be done, therefore, is to give values which will be safe for the different kinds of masonry built in the usual manner. Working Compressive Strength of Masonry. The building laws of most of the larger cities of this country specify the maximum loads per square foot allowed to be placed upon different kinds of masonry, and these laws must govern the architects in such cities. When there is no restriction of this kind. Table I gives a pretty good idea of the maximum loads which it is safe to put upon the different kinds of work mentioned. Table II gives the maximum safe loads specified in the building laws of several cities, and the remaining tables of the chapter give records of numerous tests made to determine the ultimate com- pressive strengths of various kinds of bricks, building stones, mortars and con- cretes, and are of value in determining the safe loads for special cases. In determining the safe compressive resistance of masonry from tests on the ulti- mate compressive strength of work of the same kind, a factor of safety of at least lo should be allowed for piers and 20 for arches. Table I. Safe Working Loads for Masonry Brickwork IN Walls or Piers Tons per square foot Eastern Western Red brick in lime mortar 7 5 Red brick in hydraulic-lime mortar ... 6 Red brick in natural-cement mortar, 1:3 10 8 Arch or pressed bricks in lime mortar 8 6 Arch or pressed bricks in natural-cement mortar 12 9 Arch or pressed bricks in Portland-cement mortar. .. , 15 12H 266 Strength of Brick, Stone, Mass-Concrete and Masonry Chap. 5 Piers exceeding in height six times their least lateral dimensions should be increased 4 in in lateral dimensions for each additional 6 ft. Stonework Tons per square foot Rubble walls, irregular stones 3 Rubble walls, coursed, soft stone 2\-2 Rubble walls, coursed, hard stone 5 to 16 Dimension-stone, squared, in cement mortar: Sandstone and limestone 10 to 20 Granite 20 to 40 Dressed stone, with ?4-in dressed Joints, in Portland-cement mortar: Granite 60 Marble or limestone, best 40 Sandstone 30 The height of columns should not exceed eight times the least diameter, unless the least diameter is sutficiently greater than necessary for the strength of the material used. Concrete * Portland-cement mortar, i : 8, 6 months, 10 tons; i year, 15 to 20 tons Natural-cement mortar, i : 6, 6 months, 3 tons; i year, 5 to 8 tons Hollow tile Safe loads per square inch of effective bearing parts Hard fire-clay tiles 80 lb Hard ordinary clay tiles 60 lb Porous terra-cotta tiles 40 lb Mortar In K'-in joints, 3 months old Tons per square foot Portland-cement mortar, 1:4 40 Natural-cement mortar, 1:3 13 Lime mortar, best 8 to 10 Best Px>rt land-cement mortar, i : 2, in H-ln. joints for bedding iron plates 70 The values given above are generally very conservative The leading archi- tects and engineers of Chicago recommended for that city in 1908 the follow- ing SAFE WORKING PRESSURES for brick and stone masonry and concrete: Common brick of crushing strength equal to i 800 lb Lb per Tons per per sq in: sq in sq ft In lime mortar 100 7H In lime-and-cement mortar 125 9 In natural-cement mortar 150 loVr^ In Portland-cement mortar 175 l2^ * See pages 283 to 287. Crushing Strength of Stonework, Brickwork, Bricks 267 Select, hard, common brick, of crushing strength equal Lb per Tons per to 2 500 lb per sq in: sq in sq ft In I part Portland cement, i lime-paste and 3 sand. 175 12Y5 In I : 3 Portland-cement mortar ... 200 14^^ Pressed and sewer-brick, of crushing strength equal to 5 000 lb per sq in: In I : 3 Portland-cement mortar. 250 18 Paving brick, in i : 3 Portland-cement mortar 350 251,^ Concrete, natural cement, 1:2:5 :.... 150 10% Concrete, Portland cement, 1:3:6, machine-mixed. . 300 21% Concrete, Portland cement, 1:3:6, hand-mixed 250 18 Concrete, Portland cement, 1:2:4, machine-mixed. . 400 28H Concrete, Portland cement, 1:2 : 4, hand-mixed 350 25 H Rubble, uncoursed, in lime mortar 60 4H Rubble, uncoursed, in Portland-cement mortar 100 yVi Rubble, coursed, in lime mortar 120 8% Rubble, coursed, in Portland-cement mortar. 200 14H Ashlar, Hmestone, in Portland-cement mortar 400 28H Ashlar, granite, in Portland-cement mortar 600 43 V^ Table II. Comparison of Building Laws* Materials Granite, cut • Marble and limestone, cut Sandstone, hard cut Hard-burned brick in Portland- cement mortar Hard-burned brick in natural- cement mortar Hard-burnsd brick in cement-and- lime mortar Hard-burned brick in lime mortar Pressed brick in Portland-cement mortar Pressed brick in natural-cement mortar Rubble stone in natural-cement mortar Portland-cement concrete in foun- dations, I : 2 14 Natural-cement concrete in foun- dations, I : 2 : 4 Bos- Buf- New- Chi- St. Phil- adel- phia, ton, falo, York, cago, Louis, 191S 1909 1917 1916 1907 1914 Den ver. 1898 Allowable pressures in tons per sq ft 60-72 40 30 43-5C 29 18 IS II K2 8t 36 15 43 29 29 18-28! loM!! * See important notes on page 287 relating to various building laws and working loads for masonry, etc. t In Portland-cement mortar. t In Portland-cement mortar, lo; in lime-cement mortar, 7. § According to mixture. IJ I : 2 : 5 mixture. Brick Piers. As a rule brickwork is subject to its full safe resistance only when used in piers, and in small sections of walls, under bearing-plates. In the 268 Strength of Brick, Stone, Mass-Concrete and Masonry Chap. 5 latter case but a few courses receive the full load, and hence a greater unit stress may be allowed than for piers. Values for computing the area of bearing- plates are given in Chapter XIII. Aside from the quaUty of the work and materials the two elements which most influence the strength of brick piers are the ratio of height to least lateral dimension and the method of bonding. When the height of a brick pier exceeds six times its least lateral dimension the load per square foot should be reduced from the values given in Table I. Formulas for the Safe Strength of Brick Piers exceeding six diameters in height. From the records of numerous tests on the strength of brick piers, from some formulas published* by Ira O. Baker, and also from personal obser- vation, Mr. Kidder deduced the following formulas for the maximum working loads for first-class brickwork in piers whose height exceeds six times the least lateral dimension. For piers laid with rich lime mortar: Safe load per square inch = i lo — 5 11 1 D (i) For piers laid with i : 2 natural-cement mortar: Safe load per square inch = 140 — 5H B.ll> (2) For piers laid with i : 3 Portland-cement mortar: Safe load per square inch = 200 — 6 EJD (3) H representing the height in feet, and D the least lateral dimension in feet.f For a pier 20 ft high and 2 ft square these formulas will reduce the safe load to 4.3 tons per sq ft for lime mortar, 6.1 tons for natural-cement mortar and 10 tons for Portland-cement mortar. No pier over 8 ft high should be less than 1 2 by 1 2 in in cross-section and when from 6 to 8 ft high piers should be at least 8 by 12 in in cross-section. The following is the Chicago law (1914): "Isolated piers of concrete, brick or masonry shall not be higher than six times their smallest dimensions unless the above unit stresses | are reduced according to the following formula: P = C(i.25-///2oZ)) (4) in which P is the reduced allowed unit load, C the unit stress above referred to, E the height of the pier in feet and D the least dimension of the pier in feet. No pier shall exceed in height twelve times the least dimension. The weight of the pier shall be added to other loads in computing the load on the pier. " Brick piers intended to carry more than 50% of the safe loads given above should not be built in freezing weather nor with dry bricks. Lime mortar should not be used for building piers that are to receive their full load within three months. Effect of Bond on the Strength of Brickwork. Brick piers, loaded to the point of destruction, always fail by the splitting and bulging out of the * In the Brickbuilder, April, 1898. t For piers faced with pressed bricks, laid with joints \i in or less in thickness, and backed with common bricks in lime mortar, only the dimensions of the backing should be considered in figuring their strength. If the backing is laid in cement mortar and the face-bricks are well tied to the backing, the full section of the pier may be considered. For piers veneered with stone or terra-cotta, 4 in thick, only the strength of the backing should be considered. \ These are in general the "safe working pressures" for brickwork previously mentioned as recommended by the Chicago architects and engineers in 1908. Crushing Strength of Stonework, Brickwork, Bricks 269 piers themselves, and not by direct crushing of the bricks or mortar, showing that piers are weakest in their bond and in the tensile or transverse strengths of the bricks. It is very important, therefore, to have the brickwork well bonded, and all joints filled with mortar or grouted. The strength of a brick pier in- tended to carry an extreme load would probably be increased by bonding fre- quently with hoop-iron in addition to the regular brick-bond.* Bond-Stones in Brick Piers. Many competent architects and builders consider that the strength of a brick pier is increased by inserting bond-stones, from 5 to 8 in in thickness and the full size of the pier in cross-section, every 3 or 4 ft in height. For example, the Building Laws for the City of New York (1906) require bond-stones every 30 in in height, and at least 4 in in thickness, to be built into brick piers which contain less than 9 superficial feet of section, and which sup- port any beam, girder, arch, or column on which a wall rests, or lintel spanning an opening over 10 ft and supporting a wall. The New York laws allow per- forated steel or cast-iron plates of the full cross-section of the pier to be used instead of the bond-stones. On the other hand, there are many first-class builders who consider that bond-stones in a brick pier do more harm than good, and the author is of the opinion that this is generally the case. The Boston Building Laws do not require intermediate bond-stones. If bond-stones are used, they should be bedded so as to bear rather more heavily on the inner portion of the pier than on the outer 4 in, for unless this is done the outer shell will take most of the load, and will be likely to bulge away from the core. A pier which supports a girder or column should have a cap-stone or iron plate of suflScient strength to distribute the pressure over the entire cross-section of the pier. Walls Faced with Stone, Terra-Cotta, or Cement Blocks. Brick walls faced with blocks or ashlar of any material should always have the backing laid in cement mortar or in cement-and-Hme mortar, unless the backing is very thick, that is, 30 in or more. The aggregate thickness of the mortar joints in the backing is so much greater than in the facing, that any shrinkage or com- pression of the mortar tends to throw undue weight on the facing and to sepa- rate it from the backing. Veneering of any kind should be tied to the backing at least every 18 in in height. The Building Ordinances of several large cities require that all bearing walls faced with bricks laid in running bond, and all walls faced with stone ashlar less than 8 in thick, shall be of such thickness as to make the wall independent of the facing conform to that required for unfaced walls. Ashlar 8 in thick and bonded into the backing may be counted as part of the thickness of the wall. Grouting.f It is contended by persons having large experience in building that masonry carefully grouted, when the temperature is not lower than 40° F., will give the most efficient result. Many of the largest buildings in New York City have grouted walls. The Mersey docks and warehouses at Liverpool, England, one of the greatest pieces of masonry in the world, were grouted throughout. It should be stated, however, that there are many engineers and others who do not believe in grouting, claiming that the materials tend to separate and form layers. Crushing Height of Brick and Stone. If we assume that the weight of brickwork is 120 lb per cu ft, and that it would commence to crush under 700 lb • The manner in which brick piers fail is excellently shown by illustratioos on page 79 of the Brickbuilder for May, 1896. t See American Architect, July 2J, 1887, page 11. 270 Strength of Brick, Stone, Mass-Concrete and Masonry Chap. 5 per sq in, then a wall of uniform thickness would have to be 840 ft high before the bottom courses would commence to crush from the weight of the brickwork above. Average sandstones, at 145 lb per cu ft, would require a column 5 950 ft high to crush the bottom stones, and an average granite, at 165 lb per cu ft, would require a column 10 470 ft high. The Merchants' shot-tower at Balti- more is 246 ft high, and its base sustains a pressure of 6y2 tons per sq ft, the tons being long tons of 2 240 lb. The base of the granite pier of Saltash Bridge (by Brunei), of solid masonry to the height of 96 ft, and supporting the ends of two iron spans of 455 ft each, sustains ^y2 tons per sq ft. Stone Piers. Piers of good strong building stone laid in courses the full cross-sections of the piers, with the top and bottom courses bedded true and even, may be built to support very heavy loads. The height of such piers, however, should not exceed ten times the least lateral dimension, and when it exceeds eight times the thickness, the load should be reduced. The joints should not exceed % in in thickness and should be spread with i : 2 Portland- cement mortar, kept back i in from the face of the pier to prevent spalling of the edges. A test of the strength of a limestone pier 12 in square is described under Marbles and Limestones, in this chapter. Rubble-work should not be used for piers whose height exceeds five times the least dimension, or in which the latter is less than 20 in. Records of Tests on the Crushing Resistance of Bricks. Table III gives the results of some tests on bricks, made under the direction of Mr. Kidder in behalf of the Massachusetts Charitable Mechanics' Association. Table III. Ultimate and Cracking Strengths of Bricks Kind of brick Size of test- specimen Area of face. Com- menced to crack under lb per sq in Net strength, lb per sq in Philadelphia face-brick . Philadelphia face-brick. Philadelphia face-brick. Average Cambridge brick (Eastern) . Cambridge brick (Eastern) . Cambridge brick (Eastern) . Cambridge brick (Eastern) . Average Boston Terra-Cotta Co.'s brick. Boston Terra-Cotta Co.'s brick. Boston Terra-Cotta Co.'s brick. Average New England pressed brick. New England pressed brick. New England pressed brick. New England pressed brick. Average Whole brick Whole brick Whole brick Half brick Whole brick Half brick Half brick Half brick Whole brick Whole brick Half brick Half brick Half brick Half brick 33.7 32.2 34.03 10.89 25.77 12.67 13.43 11.46 25.60 28.88 12.9s 13.2 13.30 13 45 4303 3400 2879 3527 3670 7760 3 393 3 797 46SS II 518 8593 3530 7880 3862 8 180 2 480 4 535 4764 6 062 5831 5862 5918 982s 12 941 11 681 14 296 12 186 13 839 II 406 9 766 11 670 10 270 13530 13 082 13 08s 12 490 Crushing Strength of Stonework, Brickwork, Bricks 271 The specimens were tested in the government testing-machine at Watertown, Mass., and great care was exercised to make the tests as perfect as possible. As the parallel plates between which the bricks are crushed are fixed in one posi- tion, it is necessary that each specimen tested should have perfectly parallel faces. The bricks which were tested were rubbed on a revolving bed until the top and bottom faces were perfectly true and parallel. The preparation of the bricks in this way required a great deal of time and expense; and it was so difficult to prepare some of the harder bricks that they had to be broken and only one-half of the brick prepared at a time. The Philadelphia bricks used in these tests were obtained from a Boston dealer, and were fair samples of what is known in Boston as Philadelphia Face- Bricks. They were very soft bricks. The Cambridge bricks were the common bricks, such as are made around Boston. They are about the same as the Eastern bricks. The Boston Terra-Cotta Company's bricks were manufactured of a rather fine clay, and were such as are often used for face-bricks. The New England pressed bricks were hydraulic-pressed bricks, and were almost as hard as iron. From tests made on the same machine by the United States Government in 1884, the average strength of three (M. W. Sands) Cambridge, Mass., face- bricks was 13 925 lb, and of his common bricks, 18 337 lb per sq in, one brick developing the enormous strength of 22 351 lb per sq in. This was a very hard- burned brick. Three bricks of the Bay State (Mass.) manufacture showed an average strength of 11 400 lb per sq in. The New England bricks are among the hardest and strongest in the country, those in many parts of the West not having one-fourth the strength given above; so that in heavy buildings, where the strength of the bricks to be used is not known by actual tests, it is advisable to have the bricks tested. Ira O. Baker reported some tests on Illinois bricks, made on the 100 000-pound testing-machine at the University of Illinois in 1888 and 1889, which give for the crushing strength of soft bricks, 674 lb per sq in, for the average of three face-bricks, 3 070 lb per sq in, and for four paving- bricks, 9 775 lb per sq in. In nearly all makes of bricks it will be found that the face-bricks are not as strong as the common bricks. Tests of the Strength of Brick Piers Laid with Various Mortars.* These tests were made for the purpose of testing the strength of brick piers laid up with different cement mortars, as compared with those laid up with ordinary mortar. The bricks used in the piers were procured at M. W. Sands's brickyard, Cambridge, Mass., and were good ordinary bricks. They were- from the same lot as the samples of common bricks described above. The piers were 8 by 12 in in cross-section, and nine courses, or about 22yz in high, except- ing the first, which was but eight courses high. They were built Nov. 29, 1881, in one of the storehouses at the United States Arsenal in Watertown, Mass. In order to have the two ends of the piers perfectly parallel surfaces, a coat of pure Portland cement, about V* in thick, was put on the top of each pier and the foot was grouted in the same cement. On March 3, 1882, three months and five days later, the tops of the piers were dressed to plane surfaces at right-angles to the sides of the piers. On attempting to dress the lower ends of the piers, the cement grout peeled off, and it was necessary to remove it entirely and put on a layer of cement similar to that on the tops of the piers. This was allowed to harden for one month and sixteen days, when the piers were tested. At that time the piers were four months and twenty-six days old. As the piers were built in cold weather, the bricks were not wet. They were built by a skilled * Made under the direction of F. E. Kidder. 272 Strength of Brick, Stone, Mass-Concrete and Masonry Chap. 5 bricklayer and the mortars were mixed under his superintendence. The tests were made with the government testing-machine at the Arsenal. The follow- ing table is arranged so as to show the result of these tests, and to afford a ready means of comparison of the strength of brickwork with different mortars. The piers generally failed by cracking longitudinally, and some of the bricks were crushed. The Portland cement used in these tests was made by Brooks, Shoo- bridge & Company, of England. Roman cement is a European natural cement, usually, although not always, containing a low percentage of magnesia. It sets rapidly, has about one-third the strength of true Portland cement and is much weakened by the addition of sand. Table IV. Tests of Piers of Common Bricks Laid in Different Mortars Piers 8 by 12 in in section, built of common bricks in common mortar Lime mortar Lime mortar, 3 parts; Portland cement, i part Lime mortar, 3 parts; Newark and Rosen- dale cements, i part Lime mortar, 3 parts; Roman cement, i part Portland cement, i part; sand, 2 parts. . . . Newark and Rosendale cements, i part; sand, 2 parts Roman cement, i part; sand, 2 parts Ultimate strength of pier. lb ISO 000 290 000 24s 000 195000 240 000 205 000 185 000 Pressure per sq in under which pier commenced to crack, lb 833 187s I 354 I 041 I 302 708 I 770 Ultimate strength, lb per sq in 1 562 3 020 2552 2 030 2 500 2 135 I 927 As the actual strength of brick piers is a very important consideration in building-construction, some tests, made by the United States Government at Watertown, Mass., and contained in the report of the tests made on the Govern- ment testing-machine for the year 1884, are given as being of much value. Three kinds of bricks were represented in the construction of the piers, and mortars of different composition, ranging in strength from lime mortar to neat Portland-cement mortar. The piers ranged in cross-section dimensions from 8 by 8 to 16 by 16 in, and in height from 16 in to 10 ft. They were tested at the age of from 18 to 24 months. Table V gives the results obtained and memoranda regarding the size and character of the piers. Table VI gives the results obtained from tests of the strength of brick piers made at the McGill University, Montreal, laboratories, in March, 1897. Recent Tests of Brick Piers.* Elaborate tests of brick piers, with valuable results,! were made in 1908 by A. N. Talbot and D. A. Abrams at the Uni- versity of Illinois Experiment Station. Table VII is a summary of these results. The tests were made on sixteen brick piers, the lengths of which varied from * See, also, results of important tests made in 19 14 and 1915 at Columbia University, New York, by J. S. Maqgregor. t Bulletin 27, University of Illinois Engineering E.xpcriment Station, Sept. 29, 1908 Crushing Strength of Stonework, Brickwork, Bricks 275 ^Z^ a ^ M IT) M (N a» r<) a> o rr pq 00 ro r^ vo ro ■«i- o fOvO VO "* M 00 a» t- ro 00 ^ p, C^ UO m CO ^ o (N 00 fO r^o fo r0»O O o Ot-OO^OOwt~OrO looo r-N a>a.ir)oo M M CO *OiOOiOO O O <0 VO \n o o M VO M O O O 'O'd'd'dT^'d c p c CTJrtrtoSrtaJ-tf+J+J «^" b »--'" »-'" b l^" £ S S a a a a a a||| a a a a a a o s s OOOOINMPJNNVOVO 0000Nrtrl-OPO 'ON rOHOiroc^MO^Oit^ <00» OvOt^CTiOO'Oroo^l- rOOO ~ CS O 1 O^ C^ CO O 00 (^ 00 M O ir> ^ 00 «o vo t ex. c r- M M o o o t^ o o ro t^VO O^OO 00 § 00 f^ 00 o ro o a.vo ^ M -^ o M ■ ^ ^ " " ^ ^ ^ ^ S Vj »-<»-.(-- o VhVhI-.V-.V-.I-.J-iW.I-.'' OOOOOOOOO^ : Ti OJ s . (N (N : fe : E fi r! -M a; C y (D o i V • rt T) • eeessegeg (i>io«^ Mfo Q'+Q ooocoocyiC?>c^NrofO ocy» oc^ct> -1 M > -. M<^ OlMNNNMCVIP^O (N C» N (N i 204 1985 3 weeks H in thick mortar, 3 sand on one side Table VII. Tests of Brick Piers, Made at the University of Illinois The amounts given are average values Characteristics of piers Average unit load lb per sq in Ratio of strength of pier to strength of brick Ratio of strength of pier to strength of first of series Crushing strength of 6-in mortar- cubes lb per sq in Ratio o^ strength of pier to strength of cubes Shale building bricks Well laid, i : 3 Portland- ) cement mortar, 67 days ) 3363 0.31 (Stand-) 1 ri \ 2870* 1. 17 Well laid, i : 3 Portland- ^ cement mortar, 6 months. 3950 0.37 1. 18 Well laid, i 13 Portland- cement mortar, eccentri- cally loaded, 68 days 2800 0.26 0.83 Poorly laid, i : 3 Portland- cement mortar, 67 days. . . 2 920 0.27 0.87 2870* 1.05 Well laid, I : 5 Portland- cement mortar, 65 days. . . 2225 0.21 0.66 1 710 1.30 Well laid, i : 3 natural- cement mortar, 67 days. . . I 750 0.16 0.52 305 5. 75 Well laid, I : 2 lime mortar. 66 days I 450 0.14 0.43 Underburned clay bricks Well laid, i : 3 Portland- cement mortar, 63 days. . . I 060 o 27 0.31 2870* 0.37 old. Average value based on thirteen tests of i : 3 Portland-cement mortar-cubes, 60 days 276 Strength of Brick, Stone, Mass-Concrete and Masonry Chap. 5 lo to io>2 ft. The lateral dimensions were i2>^ by i2>^ in. Two grades of bricks were used, an excellent class of building bricks and a soft grade seler:ted as representative of inferior bricks. Different qualities of mortar and different grades of workmanship were employed. Compression-tests of single bricks gave these average results. For hard, shale building bricks, bedded in plaster, crushing strength, flatwise, lo 700 lb per sq in; modulus of rupture, edgewise, 6-in span, i 670 lb per sq in. For soft or underburned clay bricks, crushing strength, flatwise, 3 900 lb per sq in; modulus of rupture, 480 lb per sq in. The Macgregor tests showed that maximum strength with minimum expense for brickwork is obtained with mortar made of yi cu ft of Portland cement, ^ cu ft of hydrated Hme and 3 cu ft of sand, or a i : i : 6 mixture. Tensional Strength of Brickwork. See Chapter II, page 179. 2. Strength of Terra-Cotta and Terra-Cotta Piers General Properties of Terra-Cotta. The lightness of terra-cotta, combined with its great compressive strength, together with its durability and indestructi- bility by fire, water, frost, etc., renders it an especially valuable building material. Terra-cotta for building purposes, whether plain or ornamental, is generally made of hollow blocks formed with webs to give extra strength and keep the work true while drying. This is necessary because good, well-burned terra- cotta cannot safely be made more than about \Vi in thick, whereas, when re- quired to bond with brickwork, it must be at least 4 in thick. When extra strength is needed, these hollow spaces are filled with concrete or brickwork, which greatly increases the crushing strength of the terra-cotta, although alone it is able to bear a very heavy weight. "A solid cubical block of terra-cotta has borne a crushing-stress of more than 500 tons." Crushing Strength of Terra-Cotta Blocks. Some exhaustive experiments made by the Royal Institute of British Architects give the following results as the crushing strengths of terra-cotta blocks: Crushing weight per cu ft Solid block of terra-cotta 523 tons Hollow block of terra-cotta, unfilled 186 tons Hollow block of terra-cotta, lightly made and unfilled 80 tons Tests of terra-cotta manufactured by a New York Company, which were made at the Stevens Institute of Technology in April, 1888 gave these results: Crushing weight Crushing weight per cu in per cu ft Terra-cotta block, 2-in square, red 6 840 lb or 492 tons Terra-cotta block, 2-in square, buff 6 236 lb or 449 tons Terra-cotta block, 2-in square, gray 5 126 lb or 369 tons In tests for the New York Building Department, made at Columbia University, dense terra-cotta blocks developed a net crushing strength of 4 721 lb per sq in or 340 tons per sq ft, and semiporous, 2 168 lb per sq in or 156 tons per sq ft, these results being in each case the averages of a series of tests. (See page 815.) From these results, the writer would place the safe working strength of terra- cotta blocks in the wall at 5 tons per sq ft when unfilled, and 10 tons per sq ft when filled sohd with brickwork or concrete. Strength of Terra-Cotta and Terra-Cotta Piers 277 Tests of Terra-Cotta Piers. Tests * of terra-cotta block piers were made about the same time (January, 1907, and January, 1908) that the brick piers referred to in Table Vll were made. The tests were made on terra-cotta piers, the lengths of which varied from 9 ft 9 in to 12 ft 7% in. The lateral dimensions varied from SVz by S^i in to 17V2 by ly^i in. "The piers were built and tested in two lots, an interval of about one year separating the times of making the tests. The two lots of piers were built of blocks which came in different ship- ments. The cement used was the same brand in both years, although the lots Table VIII. Tests of Terra-Cotta Piers, Made at -the University of Illinois The amounts given are average values. The table gives results of tests of piers of second shipment, except for the concave-end blocks. The piers recorded in this table were all 12 H by i2yi in by 9H ft. Characteristics of piers Well laid, i : 3 Portland-1 cement mortar , concentr i- > cally loaded 1 Well laid, i : 3 Portland- cement mortar, eccentri- cally loaded Poorly laid, 1 : 3 Portland- cement mortar, concen- trically loaded Poorly laid, i :3 Portland- cement mortar, eccentri- cally loaded Well laid, I : 3 Portland- cement mortar, concen- trically loaded Well laid 1 : 5 Portland- cement mortar, concen- trically loaded, inferior unburned blocks t Blocks with concave ends, I : 2 Portland-cement mortar Average unit load lb per sq in 4300* 2 970 Ratio of strength of pier to strength of block, gross area 0.83* 0.65 0,64 0.60 0.6s 0.86 Ratio of strength of pier to strength of first of series Stand- "j ard [ I . 00* J 0.81* o 76 0.75 0.71 0.78 0.69 Crushing strength of 6-in mortar- cubes lb per sq in Ratio of strength of pier to strength of cubes 1.26* 1.05 1.06 0.88 Estimated. t Blocks of good quality, but undcrbumcd. were different. The terra-cotta block piers were generally made in sets of two. Each set was constructed and loaded similarly. Three of the piers were laid up hurriedly (poorly laid); the remainder were built with the usual care given to such work. The load was applied to the piers in different ways, although gen- erally apphed continuously to failure." Some piers were loaded eccentrically to failure and one was loaded both concentrically and eccentrically, but the additional eccentric load was not sufficient to cause failure. * See Bulletin No. 27, University of Illinois Engineering Experiment Station, Sept. 29, 1908. 278 Strength of Brick, Stone, Mass-Concrete and Masonry Chap. 5 Comparison of Results of Tests of Brick and Terra-Cotta Piers. In the tests summarized in Tables VII and VIII, ''both the brick piers and the terra-cotta block piers gave high strengths in all cases where strong mortar and care in building were used. The eftect of the strength of the mortar was appar- ent in the carrying capacity developed in the piers, smaller loads being indi- cated for piers built with i : 5 Portland-cement mortar than for those with i : 3 Portland-cement mortar, and still smaller loads for those with i : 2 lime mortar. The effect of the quality of the bricks is shown in the piers made with inferior bricks, these piers carrying- only 31% as much as piers built with the better grade of bricks. In the ease of the terra-cotta piers, the blocks which were culled out as somewhat inferior gave a pier-strength which was perhaps 30% less than the piers built with superior blocks. The effect of the attempt to represent hurried or careless workmanship in two brick piers and in three terra- cotta block piers was a loss in strength of about 15% and 25% respectively. "In the well-built brick piers, concentrically loaded, the- ratio of strength of pier to compressive strength of individual brick ranged from 31 to 37%, and in the underburned clay-brick pier the ratio was 27%. In the terra-cotta block piers, concentrically loaded, the ratio of strength of pier to that of individ- ual block was 74% (an incompleted test) and 83, 85 and 89% for the others. The higher ratio found for the terra-cotta block piers than for brick piers sug- gests that the ability of individual pieces to resist transverse forces is an ele- ment in the strength of the completed pier; and this suggestion may have an important bearing on the advantageous size of the component blocks which may be used in a compression-piece where great strength is required. " The strength of the pier is greater than that of the mortar-cubes in both brick and terra-cotta block piers, except the soft-brick piers, which had bricks of low compressive strength. Both the strength of the individual bricks or blocks and the strength of the mortar affect the resistance of the pier, and the relative effect of the two depends upon the character of the materials. It is evident, however, that the better the individual piece the more important it is to have a mortar of high resisting strength. "The results obtained in applying the loads eccentrically were found to agree very well with those obtained from ordinary analysis. "The quality of workmanship in laying up such columns has an important bearing upon the resisting strength. The work of building piers, however, is not difficult and requires only ordinary care. Full joints and an even bearing are important, and the ordinary workman ought to be able to construct piers of great strength. In the tests made on piers intended to re;present poor or careless workmanship, the decrease in strength was not as much as anticipated. However, it must be understood that careful and trustworthy work is essential and that a few poor joints will materially reduce the strength of the structure. Wherever good material and good workmanship are insured the strength of masonry of this kind may be utilized with advantage. " Strength of Terra-Cotta Brackets or Consoles. A cornice-modillion made by the Northwestern Terra-Cotta Company, iiK' in high at the wall-line, 8 in wide on the face, and with a projection of 2 ft, was built into a wall and the upper surface loaded with 2 tons of pig iron without any effect upon the modilHon. Another bracket, 53^2 in high, 6 in wide and with a 14-in projection, made in the East, broke at the wall-line under 2 650 lb, while a duplicate of it sustained 2 400 lb for one month without breaking.* The Weight of Terra-Cotta. The weight of terra-cotta in solid blocks is 120 or 122 lb per cu ft. When made in hollow blocks iVz in thick the weight * See The Brickbuilder, Vol. 7, page 142. Crushing Strength of Building Stones 279 varies from 65 to 85 lb per cu ft, the smaller pieces weighing the most. For pieces 12 by 18 in or larger on the face, 70 lb per cu ft will probably be a fair average. The tables in the manufacturers' catalogues give the various bearing- areas, weights per square foot, thicknesses of parts, sizes of blocks, etc., for por- ous and semiporous blocks for all purposes. 3. Crushing Strength of Building Stones (i) Sandstones Longmeadow, Mass., Stone.* Reddish-brown sandstone, two blocks about 4 by 4 in in cross-section and 8 in in height. Block No. I commenced to crack at 10 S33 lb per sq in, and flew from the machine in fragments at 13 596 lb per sq in. Block No. 2 commenced to crack at 3 012 lb per sq in and failed completely at 9 121 lb per sq in. Sandstone from Norcross Brothers' Quarries, East Longmeadow, Mass., Soft Saulsbury Stone.* Block No. i, 4 by 4 by 8 in high, commenced to crack at 8 250 lb and failed at 8 812 lb per sq in. Block No. 2, 4 by 4 by 8 in high, commenced to crack at 6 500 lb and failed at 8 092 lb per sq in. Hard Saulsbury Stone.*' Block No. i, 4 by 4 by 8 in high (about), commenced to crack at 12 716 lb and failed at 13 520 lb per sq in. Block No. 2, same size as No. i, commenced to crack at 13 953 lb and failed at 14 650 lb per sq in. Kibbe Stone.* Block No. i, 6 by 6 by 6 in, commenced to crack at 12 590 lb and failed at 12 619 lb per sq in. Block No. 2, same size as No. i, commenced to crack at 12 185 lb and failed at 12 874 lb persqin. Brown Stone from the Shaler & Hall Quarry Company, Portland, Conn.f The results of the tests are as follows: Table IX. Crushing Strength of Brown Sandstone Dimensions Sectional area sq in First crack lb Ultimate strength lb per sq in Classification Height in Compressed, surface in 2.50 2.50 2.98 2.95 2.51 2.48 2.50 2.48 3.00 2.98 2.55 2.48 2.45 2.47 2.9s 2.97 2.53 2.52 6.13 6.13 8.85 8.85 6.45 6.25 84800 81 700 123 200 122 000 63850 58 340 13980 13330 13920 15 020 9900 9330 ist quality I St quality 2d quality 3d quality Bridge Bridge Brown Stone from the Middlesex Quarry Company, Portland, Conn.f Four nearly cubical blocks, about iM in square. Pressure per square inch at time of failure: No. i, 10 928 lb; No. 2, 10 322 lb; No. 3, 8 252 lb and No. 4, 6 322 lb. * These tests were made with the United States testing-machines at Watertown Arsenal, Mass. t From tests made by Colt's Patent Fire-arms Manufacturing Company. t These tests were made with the United States testing-machines at Watertown Arsenal, Mass. 280 Strength of Brick, Stone, Mass-Concrete and Masonry Chap. 5 Red Sandstone * from Greenlee & Son's Quarries at Manitou, Col. One specimen failed at ii ooo lb per sq in; weight, 140 lb per cu ft. Light-Red Laminated Sandstone,! from St. Vrain Canon, Col., a very hard stone, excellent for walks and foundations. Crushing strength on bed, 11 505 lb per sq in; weight, 150 lb per cu ft. Gray Sandstone f (free-working) from Trinidad, Col. Crushing strength, 10 000 lb per sq in; weight, 145 lb per cu ft. Gray Sandstone f from Fort Collins, Col. (laminated and similar in quality to the St. Vrain stone). Crushing strength on bed, 11 700 lb per sq in; weight, 140 lb per cu ft. One ton of this stone measures just a perch in the wall. (2) Granite Red Granite -t from Platte Canon, Col. Crushing strength per square inch, 14 600 lb; weight per cubic foot, 164 lb. (3) Lava Stones Lava Stone from the Kerr Quarries, near Salida, Col. Four cubical blocks. J The results of the tests are as follows: Table X. Crushing Strength of Lava Stone Dimensions Sectional area sq in First crack lb Ultimate strength Height in Compressed surface in lb lb per sq in 4.00 4.00 2.00 1-99 4.00 4.00 2.00 1.99 4.00 4.00 1-99 1.99 16.00 16.00 3.93 3.96 1 65 900 174 100 36400 38 200 165 000 174 100 37 100 38200 10369 10 881 9322 9 646 Lava Stone,t Curry's Quarry, Douglas County, Col. Crushing strength, 10675 lb per sq in; weight, 119 lb per cu ft. Experience has shown that this stone i? not suitable for piers, or where any great strength is required, as it cracks v ary easily. (4) Marble and Limestone White marble quarried at Sutherland Falls, Vt. Two cubical blocks about 6 in square. § Block No. I commenced to crack at 9 750 lb per sq in and failed suddenly at II 250 lb per sq in. Block No. 2 did not crack until it suddenly gave way at 10 243 lb per sq in. Test of a Limestone Pier. A pier of Lemont limestone, i sq ft in cross-section and 9 ft in height, composed of seven stones with bearing surfaces planed per- fectly true and parallel to the natural bed and the joints washed with a thin grout of the best English Portland cement, was tested at the Watertown Arsenal for William Sooy Smith, and only commenced to crack when the full power of the machine, 400 tons, was exerted. • These tests were made with the United States testing-machines at Watertown Arsenal, Mass. .t From tests made for the Board of Capitol Managers of Colorado by State Engineer E. S. Nettleton, in 1885, on 2-in cubes. t From tests made by the Denver Society of Civil Engineers, in 1884, also on 2-in cubes. § Tested at the United States Arsenal, Watertown, Mass. Crushing Strength of Building Stones 281 (S) Bricks and Various Stones Table XI gives the crushing strength of various kinds of bricks and building stones, the pressure being normal to the plane of the bed. Table XI. Crushing Strength of Brick and Stone * Pressure at right-angles to bed Kind of brick or stone Bricks: Common, Massachusetts Common, St. Louis, Mo Common, Washington, D. C Paving, Illinois ; Granites; Blue, Fox Island, Me Gray, Vinal Haven, Me Westerly, R. I Rockport and Quincy, Mass Milford, Conn Staten Island, N. Y East St. Cloud, Mmn Gunnison, Col Red, Platte Canon, Col. Limestones: Glens Falls, N. Y Joliet, 111..,.,.. Bedford, Ind Salem, Ind. , Red Wing, Minn Stillwater, Minn Sandstones: Dorchester, N. B. (brown) Mary's Point, N. B. (fine grain, dark brown) Connecticut brown stone, f (on bed) Longmeadow, Mass. (reddish brown) Longmeadow, Mass. (average, for good quality) . Little Falls, N . Y Medina, N. Y Potsdam, N. Y. (red) Cleveland, Ohio North Amherst, Ohio Berea, Ohio Hummelstown, Pa Fond du Lac, Minn Fond du Lac, Wis Manitou, Col. (light red) St. Vrain, Col. (hard laminated) Marbles: Lee, Mass Rutland, Vt Montgomery Co., Pa Colton, Cal. ; Italy Flagging: North River, N. Y Crushing strength, lb per sq in 10 GOO 6417 7370 5 000 to 13 000 1487s } 000 to 18 000 15 000 17 750 22 600 22 250 28 000 13 000 14 600 11 475 12775 5 000 to 10 000 862s 23 000 10750 9 ISO 7700 J 000 to 13 000 J 000 to 14 000 12 000 98SO 17 000 5 000 to 42 000 6800 6 212 \ 000 to 10 000 12 810 8750 6237 ) 000 to II 000 II 505 22900 10 746 10 000 17783 12 is6 1342s * For more complete tables of the strength, weight and composition of building stones, see new data, tables, etc. by Professor Thomas Nolan in Kidder's Building Construction and Suoerintendence, Part I, Masons' Work. \ This stone should not be set on edge. 282 Strength of Brick, Stone, Mass-Concrete and Masonry Chap. 5 (6) Additional Data on the Strength of Building G tones Average Data for Building Stones of Good Quality. The following average relative values* are given by R. P. Miller.f Sandstone: weight, 150 lb per cu ft; specific gravity, 2.40; crushing strength, 8 000 lb per sq in; shearing strength, i 500 lb per sq in; modulus of rupture, i 200 lb per sq in; modulus of elasticity, 3000000 lb per sq in. Granite: weight, 170; specific gravity, 2.72; crushing strength, 15 000; shearing strength, 2 000; modulus of rupture, 1500; modulus of elasticity, 7000000. Limestone: weight, 170; specific gravity, 2.72; crushing strength, 6000; shearing strength, 1000; modulus of rupture, i 200; modulus of elasticity, 7000000. Marble: weight, 170; spe- cific gravity, 2.72; crushing strength, 10 000; shearing strength, 1400; mod- ulus of rupture, i 400; modulus of elasticity, 8000000. Slate: weight, 175; specific gravity, 2.80; crushing strength, 15 000; modulus of rupture, 8 500; modulus of elasticity, 14 000 000. Trap-Rock: weight, 185; specific gravity, 2.96; crushing strength, 20 000. The following average relative values are given by A. I. Frye.t They are the results of tests made on small cubes of the materials. Sandstone: crush- ing strength, 9 000 lb per sq in; Granite and Gneiss: crushing strength, 17 733 lb per sq in. Limestones and Marbles: crushing strength, 14 445 lb sper sq in. Slate: crushing strength, 10 000; ultimate tensional strength, 3 000; modulus of rupture, 5 000 lb per sq in. When stones are not tested, Frye recommends the following average values for ultimate strengths to be used in determining the safe stresses. Sandstone: crushing strength, 5 000; ultimate tensional strength, 150; modulus of rupture, I 200 lb per sq in. Granite and Gneiss: crushing strength, 12000; mod- ulus of rupture, i 600 lb per sq in. Limestones and Marbles: crushing strength, 8 000; ultimate tensional strength, 800; modulus of rupture, i 500 lb per sq in. The following working unit stresses in pounds per square inch for stone slabs or single blocks of stone are recommended by W. J. Douglass. § Sandstone: compression, 700; tension (direct and flexural), 75; shear, 150. Granite, Syenite and Gneiss: compression for hard, i 500; for medium, i 200; for soft, I 000; tension (direct and flexural), 150; shear, 200. Limestone: com- pression for hard, i 000; for medium, 800; for soft, 700; tension (direct and flexural), 125; shear, 150. Marble: compression for hard, 900; for soft, 700; tension (direct and flexural), 125; shear, 150. Bluestone Flagging: compres- sion, I 500; tension (direct and flexural), 200. 4. Compressive Strength of Mortars and Concretes The Compressive Strength of Lime Mortar. The crushing strength of common lime mortar, six months old and composed of i part lime to 6 parts sand by measure, varies from 150 to 300 lb per sq in or from 10.8 to 21.6 tons per sq ft. Lime mortar alone should never be used wher« any but moderate loads are to bear upon the work, nor where the full loading is to be applied before the mortar has had time to harden. * The values in all cases are as follows: weight, in lb per cu ft; strength, modulus of rupture and modulus of elasticity, in lb per sq in. t American Civil Engineers' Pocket Book (1912), page 357. t Civil Engineers' Pocket-Book (19 13), page 511. § American Civil Engineers' Pocket Book (1912), page 575. Compressive Strength of Mortars and Concretes 283 The Compressive Strength of Natural-Cement Mortar. The crushing strength * of natural-cement mortar, neat, averaged, for 7 days, 2 010; for 28 days, 2 689; for 3 months, 3 646; and for ^months, 5 052 lb per sq in. When mixed with 2 parts of standard quartz sand, the mortar averaged in crushing strength, for 7 days, 940; for 28 days, i 390; for 3 months, i 730; and for 6 months, 2 012 lb per sq in. For 2 years, an additional increase of 18% and 6% may be assumed for the neat and sanded mortars, respectively, of natural cement. The Compressive Strength of Portland-Cement Mortar. The crushing strength* of Portland-cement mortar, neat, averaged, for 7 days, 5915; for 28 days, 7 041; for 3 months, 7 347; and for 6 months, 9 760 lb per sq in. When mixed with 3 parts of standard quartz sand, the mortar averaged, in crushing strength, for 7 days, 941; for 28 days, i 290; for 3 months, i 490; and for 6 months, i 529 lb per sq in. When mixed with 3 parts of Ottawa sand, the mortar averaged, in crushing strength, for 7 days, i 199; for 28 days, i 796; for 3 months, i 887; and for 6 months, 2 181 lb per sq in. For 2 years, an . additional increase of about 16% and' 18% may be assumed for the neat and sanded mortars, respectively, of Portland cement. Relation of Compressive to Tensile Strength of Mortars. While it may be stated as a very general guide that the compressive strength of hy- draulic-cement mortars is from six to ten times the tensile strength, these ratios are variable and cannot be used as a reliable basis for calculations. The tensile, strength of Portland-cement mortars, under normal conditions, increase^, rapidly during the first few days, the rate of change gradually, falling off. In- / 7 days the tensile strength is generally from one-half to two-thirds of the ulti- mate strength, which is practically reached in 2 or 3 months. The compressive strength, however, continues to increase with age and the rate of increase varies according to a somewhat different law. The Compressive Strength of Concrete. There are many reasons for the variations in the values of the compressive strength of concrete and the principal factors are (i) the quality of the cement, (2) the size and character of the aggregates, (3) the quantity of the cement to a unit volume of the con- crete, (4) the manner of mixing, (5) the density of the mixture, (6) the condi- tions under which it seasons, and (7) its age; and of these various conditions affecting the determination of the compressive strength the most important are generally the proportions of the different ingredients of the mixture and its age. Although tables of average values of ultimate crushing strengths of con- crete are published and are of general value, they may be misleading unless considered with caution. In important operations it is advisable to have the concrete tested and to adjust by trial the character and proportions of the in- gredients until the required strength is obtained. Form of Specimen for Compression-Tests. For compression-tests of concrete in general, 4 to 12-in cubes of the mixture have been the standard forms of test-specimens; but since the advent of reinforced-concrete construc- tion and the growth of the importance of determining the elastic properties of concrete, it has been found that a cylindrical test-specimen gives more definite results than a cube. A common shape of such cylinder is one in which the height is about three times the diameter, and the cylinders are not less than 6 by 18 in. It is found that the compressive strengths of these cylinders of concrete are from 10 to 15% less than those of the cubes, but for cylinders of * From compression-tests made by W. P. Taylor on cylindrical specimens i in in height, about iH in in diameter and i sq in in cross-section. 284 Strength of Brick, Stone, Mass-Concrete and Masonry Chap. 5 still greater slenderness the compressive strengths remain about constant for heights up to about seven diameters. Compression-Tests on Concrete Cubes. From some tests made in 1899 for the Boston Elevated Railway Company at the Watertown Arsenal, on T2-in cubes of concrete made with five brands of Portland cement, coarse, sharp sand and broken stone up to 2j'2-in size, having 49.5% voids, the following average values of the compressive strengths were obtained: Table XII. Compression-Tests on Concrete Cubes Mixtures 7 days lb per sq in I month lb per sq in 3 months lb per sq in 6 months lb per sq in 1:2:4 1:3:6 I 560 I 310 2400 2 160 2900 2520 3820 3090 Compression-Tests on Concrete-Cylinders. For cylindrical test-speci- mens of concrete, made under reasonably good conditions as to character of materials and care in mixing, an average compressive strength of about 2 000 lb per sq in is usually developed in a i : 2 : 4 Portland-cement concrete in from I to 2 months; and of about i 600 lb per sq in in a i : 3 : 6 mixture. When the conditions are unusually favorable somewhat higher values than these are obtained, but when the materials and workmanship are poor the ultimate com- pressive stresses are lower. Increase in Compressive Strength of Portland-Cement Concrete. In regard to the increase of compressive strength of Portland-cement concrete with age, tests show that the ultimate compressive strength is nearly reached in 60 days, at which time the strength varies from 80 to 90% of its value in i year's time. Ultimate Strengths of Natural-Cement Concrete. For natural-cement concrete, the ultimate compressive, tensile and shearing strengths and the mod- ulus of rupture may be taken at about one-half the corresponding values for Portland-cement concrete, unless natural cements of known and tested values are employed. Strength of Unreinforced Concrete Columns. Short concrete columns, of lengths up to 10 or 15 diameters, develop a crushing strength of from 10 to Table XIII. Compression-Tests on Unreinforced Concrete Columns Average ulti- Kind of Average age mate compres- concrete sive stress days lb per sq in 1:1:2 60 3600* i:iV^:3 60 2 270 1:2:4 60 I 600 I : 21^^ : 5 60 I 200 1:3:6 60 935 I : 3H : 7 60 745 1:4:8 60 600 • This value was estimated as it was beyond the range of the tests. Compressive Strength of Concretes 285 20% less than that for short prismatic or cylindrical specimens. In Table XIII are the results obtained by A. N. Talbot * on short, round, unreinforced stone- concrete columns, 12 in in diameter and 10 ft in length. A wet-mixture concrete was used, of the different proportions shown, the forms were removed after 10 days and the columns were tested through 60 days. The values given in the table were deduced from the straight-line formula 12 CXX) Ultimate compressive strength, lb per sq in = — — 400 in which formula Sa = the ratio of sand to cement St = the ratio of stone to cement For example, in the 1:3:6 mixture, Sa = 3 and St = 6 Crushing Strength of Concrete Affected by Area of Bearing Surface. Professor Hool states f that if a load is applied over the central part, only, of the bearing surface of a concrete test-specimen in compression, the. unit load will be greater than if it is applied over the entire surface; and this is due to the fact that the outer parts tend to assist the inner part to resist the stress. This was shown by tests made on some of the 12-in concrete cubes used in the tests made for the Boston Elevated Railway Company and referred to in the preced- ing paragraphs. Thirty-six of these concrete cubes were crushed by applying the load over the entire upper bearing-surface of 144 sq in and an equal number of similar concrete cubes were then crushed by applying the stress over a smallei area, 10 by 10 in, or 100 sq in. After this, the cubes of a third set were crushed by the application of the stress over the still smaller area, 8 by SH in, or 66 sq in. The tests of the second set gave unit crushing strengths 12% higher than the first, and those of the third set unit crushing strengths 28% higher than the first. Working Stress for Bearing on Concrete. "When compression is applied to a surface of concrete of at least twice the loaded area, a stress of 32.5% of the compressive strength may be allowed, "t Working Stress for Axial Compression on Concrete. "For concentric compression on a plain concrete column or pier, the length of which does not exceed 12 diameters, 22.5 % of the compressive strength may be allowed." * (For the strength of reinforced-concrete columns, see Chapter XXIV, page 945.) Recommended Ultimate Compressive Strengths of Portland-Cement Concrete. I Table XIV, of ultimate compressive strengths of concrete of different mixtures gives the values recommended by the American Society for Testing Materials, even though occasional tests show higher results. The values given are recommended as the maximum ultimate unit compressive strengths that should be used in design and on which the permissible working stresses should be based as a proper percentage of the same. The report referred to states, also, that "in selecting the permissible working stresses to be allowed on concrete, we should be guided by the working stresses usually allowed for other materials of construction, so that all structures of the same class, but composed of different materials, may have approximately the same degree of safety. " (For working stresses for concretes, masonry, etc., see this chapter, pages 265 to 276.) * See University of Illinois Bulletin, No. 20, 1907, and Engineering News, Sept. 26, 1907. t See Reinforced Concrete Construction, Vol I., page i8, by George A. Hool. t Report of Committee on Concrete and Reinforced Concrete, of the American Society for Testing Materials, Nov, 20, 1912, 280 Strength of Brick, Stone, Mass-Concrete and Masonry Chap. 5 Table XIV. Ultimate Compressive Strengths of Different Mixtures of Portland-Cement Concretes Aggregates Mixtures 1:1:2 lb per sq in 1 :iK' :3 lb per sq in 1:2:4 lb per sq in I : 2H : 5 lb per sq in 1:3:6 lb per sq in 3300 3000 2 200 800 2800 2 500 I 800 700 2 200 2 000 I 500 600 1800 I 600 I 200 500 I 400 I 300 1 boo 400 Gravel, hard limestone and hard sandstone Soft limestone and sand- stone Cinders Effect of Consistency on the Crushing Strength of Concrete. Concrete that is mixed fairly dry and tamped until the moisture is brought to the surface, develops a somewhat greater compressive strength than concrete mixed with more water. From a large number of tests * average compressive strengths of wet, plastic and dry concretes were determined. The age of the concrete was 1 year and 8 months, and five brands of cements were used. The mean com- pressive strengths were, for the wet concrete, 2 130; for the plastic^ 2 200; and for the dry, 2 350 lb per sq in. In another series of tests f greater differences appeared. At the age of i month the mean compressive strengths in ix)unds per square inch were, for the wet concrete: granite, 3 155; gravel, 2 300; limestone, 4 195. For the medium concrete: granite, 4090; gravel, 3 545; limestone, 2 975. For the damp con- crete: granite, 4 520; gravel, 4 610; limestone, 4 365. At the end of 3 months the values for the granite aggregates were, for the wet concrete, 4 755; for the medium, 4 990; and for the damp, 5 445. Effect of Size of Stone on the Compressive Strength of Concretes. It may be stated, generally, that the use of stones of a maximum size consistent with convenience generally results in a maximum compressive strength in the concrete. Stones of the larger sizes are generally more uniformly graded than the smaller stones, and consequently grade better with the sand and give greater strength. From tests t made by W. B. Fuller, the average compressive strengths, at 140 days, of i : 9 concrete, were, for maximum size of stone J-i in, i 000 lb per sq in; for i-in stone, i 150 lb per sq in; and for 2^-in stone, i 400 lb per sq in. Comparison of Compressive Strengths of Gravel and Stone Concretes. Concretes made with broken stone have, gcnerall}'-, a somewhat greater com- pressive strength than those made with gravel. From tests made by E. Candlot, the average compressive strength at 30 and 180 days, of concrete made with iH-in. maximum-size broken stone, was 20% greater than that of concrete made of gravel of about the same size, the percentage of voids being nearly the same, 40% voids for the gravel and 47.4% voids for the broken stone. The average difference at 12 months, however, was reduced to 9%. * Made for G. W. Rafter. See "Tests of Metals," 1898. t Made in 1908. See Bulletin No. 344, United States Geological Survey. t See Trans. Am. Soc. C. E., Vol. 59, 1907. Building Laws for Working Loads on Masonry 287 Effect of the Strength of the Aggregate on the Compressive Strength of Concrete. The compressive strength of , trap-rocks, granites and most limestones is relatively so great that it cannot reduce the strength of the con- crete itself. Some sandstones, however, have a much lower average compressive strength, and if they are friable and soft may lower relatively the final strength of the concrete. A concrete of low strength results from using cinders for the aggregate. Building Laws for Working Loads on Masonry.* As previously mentioned (page 265) the building codes of most cities specify working loads to be used for masonry and as shown in Table II (page 267) these loads vary greatly. It is important, therefore, that the architect should be acquainted with the municipal code by which the construction of his building is governed. As building laws and regulations are constantly changing this information should be obtained from the code itself, care being taken that the latest edition and all supplements are consulted. A few requirements, pecuHar to the codes in which they are found, will be cited. The Chicago code (1916) gives for eight classes of brickwork bearing values ranging from 100 lb per sq in for common brick with good lime mortar to 350 lb per sq in for paving brick with i to 3 Portland-cement mortar. This code discriminates between concrete mixed by hand and by machine, values of from to 250 to 350 lb per sq in being given for hand-mixed concrete and from 300 to 400 lb per sq in for the same mixture if mixed by machine. The values in the Buffalo code are exceptionally low, common brick laid in lime mortar being allowed but 3 tons and concrete in foundations but 4 tons per sq ft. The Louisville code introduces values for "Louisville-cement mortar." The practice of stating values of local material is to be commended. The Denver code gives a value of 3 tons per sq ft on common brick with coal-dust in lime mortar, 3 tons for hollow tile in cement mortar and 8 tons for terra-cotta, solid, in cements The Seattle code gives for the allowable compressive stress of mass concrete 20% of its compressive strength in twenty-eight days. The building code rec- ommended by the National Board of Fire Underwriters is followed by a number of cities. This code includes in its list of allowable compression values, 1000 lb per sq in for Portland-cement grout, neat, and 1500 lb per sq in for Portland- cement grout, neat, not over yi in thick, between steel members in foundations. For natural-cement concrete values are given of 125 lb per sq in for a i : 2 : 4 mixture and 80 lb per sq in for a i : 2 : 5 mixture. The average ultimate com- pressive strength for terra-cotta blocks designed to be normally laid with the cells vertical, and which are tested with the cells in that position, must not be less than 1200 lb per sq in. The allowable working stress on such blocks must not exceed 120 lb per sq in. The average ultimate compressive strength for terra-cotta blocks designed to be normally laid with the cells horizontal, and which are tested with the cells in that position, must not be less than 800 lb per sq in. The allowable working stress on such blocks must not exceed 80 lb per sq in. Hollow building blocks may be filled solidly with Portland-cement concrete or cement mortar to increase the stability and to aid in distributing the load, but the allowable working stress on such blocks must not be greatet than that permitted for unfilled blocks. * Condensed from valuable data from Robins Fleming. See, also, pages 265 to 267 and Table II, page 267. 288 Forces and Moments Chap. 6 CHAPTER VI FORCES AND MOMENTS By MALVERD A. HOWE PROFESSOR OF CIVIL ENGINEERING, ROSE POLYTECHNIC INSTITUTE 1. Composition and Resolution of Forces Composition and Resolution of Forces. Imagine a round ball placed on a plane, frictionless surface at A (Fig. 1), the surface being perfectly level, so that the ball has no tendency to move until some force is applied to it. If, now, the force, F, is applied to the ball in the direction indicated by the arrow, the ball will move in that direction. If, instead of one force only, two forces, P ajid Pi, are apphed to the ball, it will not move in the direction of either of the forces, but will move in the direction of the RESULTANT of thcse forces, or in the direction Ab. If the magnitudes of the forces P and Pi are indicated by the lengths of the lines, then, if we complete the parallelogram ABDC, the diagonal DA represents the direction and magnitude of a single force which has the same effect on the ball as that resulting from the two forces P and Pi. If, in addition to the two forces P and Pi, the third force, P2, is applied, the ball will move in the direction of the resultant of all three forces, and this resultant is obtained by completing the parallelogram ADEF, of which the resultant DA and the third force Pi are two adjacent sides. The diagonal R of this second parallelogram is the resultant of all three forces, and the ball will move in the direction Ae. In the same way the resultant of any number of forces may be found. Again, suppose a ball, whose weight is indicated by the length of the line W (Fig. 2), is suspended by two inclined cords. What are the magnitudes of the pulls or stresses which are developed in the cords and which keep the ball suspended at the point A? This is the converse of the last case. Instead of finding the diagonal or the resultant, the diagonal, which is the line W, is given, and the sides of the parallelogram are to be found. To find these the lines representing the directions of P and Pi are prolonged and from B lines parallel to them are drawn to complete the parallelogram. Then CA is the required mag- nitude of the stress in cord P, and BC of that in cord Pi. Thus one force may have the same effect as many, or many the same effect as one. Forces Represented by Straight Lines. In considering the action of forces, it is convenient to represent them graphically by straight lines with arrow- heads, as in Fig. 3. The length of the hne, if drawn to a scale of pounds, repre- sents the MAGNITUDE OF THE FORCE in pouuds; the position of the line indicates Fig. 1 . Composition of Forces B Fig. 2. Resolu- tion of Forces Moments of Forces 289 Fig. 3. Force Represented by a Straight Line Parallelogram of Forces its LINE OF action; the arrow-head indicates its sense or the direction in which it acts; and the point A its point of application. Thus the magnitude, direction and point of appli- cation are indicated and the force is completely repre- sented. Parallelogram of Forces. If two forces applied at one point are represented in mag- nitude and direction by two straight lines inclined to each other, their resultant is the diagonal of the PARALLELOGRAM formed on those lines. Thus, if the lines AB and AC (Fig. 4) represent two forces acting at a point A, to find the force which will have the same effect as the two forces, the parallelogram ABDC is completed and the diagonal AD drawn. This line represents the resultant of the two forces. When the two given forces act at right- angles to each other, the magnitude of the resultant is equal to the square root of the sum of the squares of the magnitudes of the other two forces. Triangle of Forces. If three forces acting at a point are represented in magnitude and direction by the sides of a triangle taken in order, they arc in equilibrium. Let P, Q and R (Fig. 5) represent three forces acting at the point 0. If a triangle can be drav/n, like that shown at the right in Fig. 6, having sides respectively parallel to the direc- tions of the forces and taken in the same order, the forces are in equilibrium. If such a triangle cannot be drawn, the forces are not in equilibrium. The Polygon of Forces. If any number of forces acting at a point can be represented in magnitude and direction by the sides of a polygon taken Triangle of Forces in order, they are in equihbrium. theorem. This follows directly from the preceding 2. Moments of Forces Moments. In considering the stability of structures and the strength of materials, we are often obliged to take into consideration the moments of the forces acting on a structure or on some part of a structure; and a knowledge of the general principles of moments is essential to the proper understanding of these subjects. When we speak of the MOMENT OF A FORCE, we must have in mind some fixed point or line with respect to which the moment is taken. The moment of a force with respect to any given point, or CENTER OF MOMENTS, is the product of the magnitude of the force and the perpendicular distance from the point to the LINE OF ACTION of the force; or, in other words, the mo- ment of a force is the product of the magnitude of the force by the ARM with which it acts. Thus if we have the force F (Fig. 6). and wish to determine its moment with respect to the point F, we determine the per- pendicular distance Pa, between th? point and the line of action of the force, and multiply it by the magnitude of the force. For example, if the magnitude 290 Forces and Moments Chap. 6 Fig. 7. Pi Algebraic Sum of Unlike Parallel Forces -B -h-^ — >: 3- Fig. 8. Algebraic Sum of Mo- ments of Unlike Parallel Forces B of the force F is 500 lb and the distance Pa is 2 in, the moment of the force with respect to the point P is 500 lb X 2 in = i cx50 in-lb.* Parallel Forces. If any body is in a state of rest or equilibrium under the action of parallel forces, the sum of the forces acting in one direction equals the sum of the forces acting in the opposite direction. Thus if we have the parallel forces Pi, P^ P^ and P^ acting on the rod AB (Fig. 7), in a direction opposite to that of the forces Pi, Pi and Pa, then, if the rod is in equilibrium, the sum of the forces P^, P2, P3 and P** must equal the sum of the forces Pi, P2 and P3. Parallel Forces Opposite in Character. If any number of parallel forces, not all acting in the same direction, act on a body, if the body is in equilibrium, the sum of the moments of the forces tending to turn the body in one direction about any given point is equal to the sum of the moments of the forces tending to turn it in the opposite direction. Let Pi, P2 and Fz (Fig. 8) represent three parallel forces acting on the rod AB. If the rod is in equilibrium, the sum of the forces F2 and P3 is equal to Pi. Also, if we lake the end of the rod, A, for the center of moments, the moment of Pi is equal to the sum of the moments of P2 and P3 about that point, because the moment of Pi measures the tend- ency to turn the rod clockwise, and the sum of the moments of P2 and P3 measure the tend- ency to turn the rod contra-clockwise, and there is no more tendency to turn the rod one way than the other. For example, let the mag- nitude of forces P2, P3 each be represented by 5 force-units, the distance Aa by 2 length-anits and the distance AB hy 4 length-units. The magnitude of the force Pi must equal the sum of the magnitudes of the forces P2 and P3, or 10 force-units, and its moment with* respect to any point in the plane of the forces must equal the sum of the moments of P2 and Fz with respect to the same point. If we take A as the center of moments, the moment of Pi = 5 x 2 = 10, and of P2 = 5 X 4 = 20. Their sum equals 30; hence the moment of Pi must be 30. Dividing .the mo- ment 30 by the force Pi = 10 force-units, we have for the arm, 3 length-units; or the force Pi must act at a distance of 3 units from A to keep the rod in equilib- rium. If we take h as the center of moments, the force Pi has no moment, as the length of its lever-arm is zero; and, for equilibrium, the moment of P2 about h must equal the moment of P3 about the same point; or, as in this case the magnitudes of the forces P2 and Fz are equal, they must both be applied at the same distance from b, showing that b must be half-way between a and B, as was demonstrated before. Three Parallel Forces, the principle op the lever. This principle is based upon the two preceding propositions and is of great importance and con- * The expressions pound-feet and pound-inches are often given to these products ♦o distinguish them from foot-pounds and inch-pounds, by which work and energy are measured. Center of Gravity 291 venience. If a body is in equilibrium under the action of three parallel forces acting in the same plane, each force is proportional to the normal distance be- tween the other two. Thus, if, as in Figs. 9, 10 and 1 1, three forces, Pi, Pt and i \ ? 16 A>' C , 6 12 Q ( > 5 Pa p« Pi Fig. 9. Principle of the Lever Fig. 10. Principle of the Lever 6 Pa, act on the rod AB, in order that it may be in equilibrium, the following relations must obtain between the magnitudes of the forces and the distances between their points of application; Pi_ Pi^ Pi^ CB ' AB ' AC or Pi:P2:Pz::CB:AB:AC This is the case of the common lever and shows the method of determining what weight a given lever will raise. The proportion is also true for any ar- rangement of the forces (as shown in Figs. 9, 10 and 11), provided, of course, the forces are lettered in the order shown in the figures. For example, let the distance ^C be 6 in and the distance CB,bc 12 in. If a weight of 500 lb is applied at the point B, how much will it raise at the other end and what support will be required at C (Fig. 10)? Applying the rule just given, we have the pro- portion; Pa-.Pi-.iACiCB or 500: Pi:: 6: 12 Hence Pi = i 000 lb; or 500 lb applied at B will Fig. 11. Principle of the Lever lift I 000 lb resting on or suspended at A. The supporting force at C must, by the principles of parallel forces im EQUILIBRIUM, be cqual to the sum of the forces Pi and Ps, or i 500 lb in this case. 3. Center of Gravity General Principles. The lines of action of the force of gravity converge towards the center of the earth; but the distance of the center of the earth from the bodies which we have occasion to consider, compared with the size of those bodies, is so great, that we may consider the lines of action of the forces as parallel. The number of the forces of gravity acting upon a body may be con- sidered as equal to the number of particles composing the body. The center of GRAVITY of a body may be defined as the point through which the resultant of the parallel forces of gravity, acting upon the body, passes for every position 01 ine body. If a body is supported at its center of gravity and turned about Px 292 Forces and Moments Chap. 6 that point, it will remain in equilibrium in all px)sitions. The resultant of the parallel forces of gravity acting upon a body is obviously equal to the weight OF THE body; and if a force, equal in magnitude to the resultant, is applied, acting in a line passing through the center of gravity of the body, and in a direction opposite to that of the resultant, the body will be in equilibrium. Center of Gravity of a Straight Line. The word line here means a material line whose transverse section is very small, such as a very fine wire. The center of gravity of a straight line or rod of uniform size and material is at its middle point. This proposition is too evident to require demonstration. The Center of Gravity of the Perimeter of a Triangle is at the center of the circle inscribed in the triangle formed by the lines joining the middle points of the sides of the given triangle. Thus, let ABC (Fig. 12) be the given triangle. To find the center of gravity of its perimeter, find the middle points, D, E and F, and connect them by straight lines. The center of the circle inscribed in the triangle formed by these lines will be the center of gravity sought. ° F Center of Gravity of Symmetrical Lines. Fig. 12. Center of Gravity of The center of gravity of a line which is sym- Perimeter of Triangle metrical with reference to a point is at that point. Thus 'the center of gravity of the cir- cumference of a circle or of an ellipse is at the geometrical center of the figures. The center of gravity of the perimeter of an equilateral triangle, or of a regular polygon, is at the center of the inscribed circle. The center of gravity of the perimeter of a square, rectangle, or parallelogram is at the intersection of the diagonals of those figures. Center of Gravity of a Surface. A surface here means a very thin plate or shell. If a surface can be divided by a line into two symmetrical halves, the center of gravity will be on that line; if it can thus be divided by two lines, the center of gravity will be at their intersection. Center of Gravity of Regular Figures. The center of gravity of the sur- face of a circle or an ellipse is at the geometrical center of the. figure; of an equilateral triangle or regular polygon, at the center of the inscribed circle; of a parallelogram, at the intersection of the diagonals; of the surface of a sphere, or of an eUipsoid of revolution, at the geometrical center of the body; and of the convex surface of a right cylinder, at the middle point of the axis of the cylinder. Center of Gravity of Irregular Figures. Any figure bounded by straight lines may be divided into rectangles and triangles, and, the center of gravity of each part being found, the center of gravity of the whole figure may be deter- mined by treating the centers of gravity of the separate parts as particles whose • weights are proportional to the areas of the parts they represent. (See page 296.) Center of Gravity of Triangles. To find the center of gravity of a tri- angle, draw a line from each of two angles to the middle of the opix)site side. The intersection of the two lines is the center of gravity. Center of Gravity of Quadrilaterals. To find the center of gravity of any quadrilateral, draw the diagonals, and from that end of each diagonal which is farthest from the intersection, lay off, toward the intersection, the length of its shorter segment. The two points thus formed, together with the point ol Center of Gravity 293 intersection, will form a triangle whose center of gravity is that of the quad- rilateral. Thus, let Fig. 13 be a quadri- lateral whose center of gravity is to be found. Draw the diagonals AD and BC, and from A lay oQ AF = DE, and from B lay off BH = CE. From E draw a line to the middle of FH, and from F a line to the middle of EH. The point of intersection of these two lines is the center of gravity of the quadrilateral. This is a method commonly used for finding the centers of gravity of the voussoirs of an arch. Table of Centers of Gravity. Let a be a line drawn from the vertex of a figure to the middle point of the base, and D the distance from the vertex to the center of gravity of the figure. Then (Fig. 14) : Center of Gravity Quadrilateral In an isosceles triangle ^ = % In a segment of a circle, vertex at center of circle D = chord^ In a sector of a circle, vertex at center of circle D ■■ In a semicircle, vertex at center of circle D 12 X area 2 X chord : R X '■ 4R 3Xarc : = 0.4244!? In a quadrant of a circle D = %R In a semieliipse, vertex at center of circle D = 0.4244 a In a parabola, vertex at intersection of axis with curve D = %a In a cone or pyramid D = %a IsoBcxjles Triangle Segment of Circle Sector of Circle Fig. 14. Center of Gravity of Triangle, Segment and Sector In a frustum of a cone or pyramid, let h = the height of the complete cone or pyramid, hi = the height of the frustum, and let P*W the vertex be at the apex of the complete cone or pyramid; then, e- B -e w D = 4 (A3 - hi^) Fig. 15. Center of Gravity of Two Heavy Particles Center of Gravity of Two Heavy Particles. Let F be the weight of a particle at A (Fig. 15), and W that of a particle at C. The center of gravity is at some point, B, on the line joining A and C. The point B must be so situated that if the two particles were held together by a stiff wire and supported at B by a force equal in magnitude to the sum of P and W they would be in equilibrium. The problem then is 294 Forces and Moments Chap. 6 W2 Fig. 16. Center f»f Gravity of Several Heavy Particles solved by the principle of the lever, and we have the proportion (see Three Parallel Forces. The Principle of the Lever), P+W: P:: AC: BC If W = P, then BC= AB, or the center of gravity will be half- way between the two particles. This problem is of great importance and has many practical appUcations. Center of Gravity of Several Heavy Particles. Let W\, Wi, Wz, Wa and \W (Fig. 16) be the weights of the particles. Join W\ and Wi by a straight line and find their center of gravity A, as in the preceding problem. Join A with Wz and find the center of gravity B, which will be the center of gravity of the three weights Wi, W2, W3. Proceed in the same way with each weight. The last center of gravity found will be the center of gravity of all the particles. In both of these cases the lines joining the particles are supposed to be horizontal lines, or else the horizontal projections of the straight lines which join the points. Center of Gravity of Compound Sections Found by Moments. To determine the strength of a beam having an unsymmetrical cross-section, it is first necessary to determine the distance of the center of gravity of this section from the upper or lower surface of the beam. Various other computations, also, involve finding the center of gravity of an irregular figure, so that the problem is one of practical importance. If the figure of which the center of gravit}^ is to be found can be divided into parts which are themselves regular figures, the readiest and simplest method of finding the distance of the center of gravity from one edge of the section is by means of moments. To explain this method assume a T-shaped section of uniform thick- nes?, hinged on a wire XX, as in Fig. 17. The T section is made up of two rectangles, one forming the flange, the other the web. The center of gravity of each rectangle is at its own center of figure and may be readily found. If the T section is placed horizon- tally, as in the figure, the axis XX being fixed, it will immediately, by the force of gravity, revolve about the axis until it be- ' -^ comes vertical, and the sum of the moments fig. 17. Center of Gravity of of the forces causing the revolution is Compound Sections by Moments A' Xd' -^ A" X d", A ' representing the weight of the web and A" the weight of the flange. To hold the T section in a horizontal position, there must be a moment of some force acting in an opposite, or upward, vertical direction and just equal to the sum of the two moments causing revolution downwards. If the force A, of this moment, tending to cause revolution upward, is equal to the weight of the entire T sec- tion, it must be applied at the center of gravity of the entire figure to make its moment just equal to the sum of the moments of the two downward forces. Center of Gravity 295 But the moment oi AhAxd, therefore d is the distance from the end of the web, or from the axis XX, to the center of gravity of the entire figure. Therefore, since Axd = A' X d' -{- A" X d", J = A'xd'-^A"xd" (i) d As the weight of any homogeneous material of uniform thickness is proportional to the area, A, A' and A" may be used to represent areas as well as weights. Expressing formula (i) as a rule, we have: Center of Gravity of Compound Figures. The distance of the center of gravity of a compound figure from any line of reference is equal to the sum of the products, obtained by multiplying the area of each of the simple parts into which the compound figure is divided by the distances of its center of gravity from the line of reference, divided by the area of the entire figure. This rule ap- plies to any compound figure. Example I. Assume that the T section shown in Fig. 17 has the dimensions in- dicated. Then A' equals 6, A" equals 8, and A equals 14 sqin; and - .,.M- .! M \'i M H M H Ho ft ft ft ft ft ft ft ft 2 0.55 56 0.58 0.60 0.61 0.64 0.68 4 0.70 0.72 0.74 0.76 79 0.83 0.88 6 81 0.83 0.86 0.89 0.92 0.97 I 03 8 91 0.93 0.96 1.00 1.03 1.09 1. 16 10 0.99 I 01 1.04 . 1.07 I. II 1. 18 1.26 15 1. 17 1. 19 1.22 1.26 1.30 1.40 I 50 20 1.32 I 35 • 1.38 1.43 1.48 1.59 1.70 25 1.45 1.48 1.53 1.58 1.64 I 76 1.88 30 1.57 1.60 1.65 1. 71 1.78 I 91 2 04 35 1.68 1.70 1.76 1.83 1.90 2 04 2.19 40 1.78 1. 81 1.88 i.<^^ 2.03 2.18 2.33 50 1-97 2.00 2.08 2.16 2.25 2.41 2.58 6o 2:14 2.18 2.26 2. 35 2.44 2.62 2.80 8o 2.44 2.49 2.58 2.68 2.78 2.98 3.18 100 2.70 2.75 2.86 2.97 3.09 3.32 3.55 120 2.94 2.99 3.10 3.22 3.61 3.88 140 3.16 3.21 3-33 3.46 3.60 3.87 4.15 160 3.36 3.44 3.58 3.72 3.87 4.17 180 3.56 3.63 3.75 3.90 4.06 4.38 200 3.74 3.81 3.95 4.12 4-29 220 3-91 4 • 00 , 4.13 4.30 4.48 240 4.07 4.15 4.30 4.48 260 4.23 4-31 4.47 4.66 280 4.38 4.46 4.63 300 4.53 4.62 4.80 Example 2. Having decided what the thickness of the arch-ring will be it remains to determine whether such an arch would be stable if built. The following example will illustrate the method of determining this. Consider an unloaded semicircular arch of 20-ft span. First, to find the depth of tlie keystone, we will use Rankine's Formula. Depth of key =» V 0.12 X 10 = V1.2 = i.i ft Trautwine's Formula gives nearly the same result, T^ , , , V lo-H 10 Depth of key « h 0.2 f t = 1.3 ft <1 But if we should compute the stability of a 20-ft semicircular arch with a keystone 1.3 ft deep, we should find that the arch is very unstable; hence, ir this case, we cannot use the formula and mv-st act upon our own judgment In the opinion of the author, the arch-ring of such an arch should be at leas 2\(i ft deep and the stability of the arch should be tested for that thickness In all calculations on the arch, it is- customary to consider it i ft thick a * Taken from The Civil Engineer's Pocket-Book, John C. Trautwine. Arches 311 right-angles to its face. This allows the areas of the faces to be substituted for the ACTUAL weights of the voussoirs and their loads. This method was used in the discussion of Retaining- Walls, Chapter IV, and Piers and But- tresses, Chapter VII. Furthermore, it is evident that if an arch i ft thick is stable, any number of arches of the same dimensions built alongside of it would be stable. In determining the stability of masonry arches it is also customary to neglect any increase in the strength of the arch from the mortar in the joints, or in other words, to consider the arch as laid up dry. Graphic Determination of the Stability of Arches. An arch has already been defined as a particular arrangement of blocks of stone or other material, these blocks being .called the vous- soirs. For the sake of simplicity consider an unloaded arch. In such an arch each voussoir is sub- jected to the action of three forces, (i) the thrust that it receives from the voussoir next above it in the arch-ring, (2) the force of gravitation, or its own weight and (3) the reaction to the resultant thrust. The first two forces combine into one and form the thrust that this voussoir exerts on the one next below it in the arch-ring (Fig. 7). The points in which these various thrusts cut the joints are called the centers of pressure of the joints, while the line joining these centers of pres- sure is called the line of pressure or line of resistance.* In order that an arch may be absolutely stable, this line of resistance must fall within the middle third of the arch-ring. (See Theorem of the Middle Third, Chapter IV.) If the arch is stable the centers of pressure on the various joint-Hnes are within the middle third of the voussoir-depths and the angles made by the different thrusts with the normals to the joints are less than the angle of friction of the material of which the arch is constructed. If these conditions are not ful- Thrust from voussoir. next above Center of pressure Resultant thrust on voussoir next below •♦—Thrust of voussoir Fig. 7.« Equilibrium of Forces on Voussoir Failure of Semicircular Arch. Haunches Sliding Down Fig. 9. Failure of Semicircular Arch. Haunches Sliding Up filled the criteria of safety, explained in Chapter VII in the discussion of the Stability of a Buttress, will not be satisfied; and at any joint where these conditions do not obtain, the voussoir above the joint will tend to slide along the joint-plane if the angle made by the thrust with a normal to the joint is greater than the angle of friction. If the center of pressure Ues out.side the middle third, there will be a tendency for the voussoir to overturn. When these tendencies reach extreme limits actual failure may occur. Figures 8, 9, 10 and 11 illustrate some of the ways in which an arch may fail, Figs. 8 and 9, * This line is called, interchangealily, the line of pressure, the line of resistance, tlie RESIST.ANCE-LINE, etc. (See, also, Chapter XXXI, pages 1225 and 1234.) 312 The Stability of Masonry Arches Chap. 8 showing different parts of the masonry sliding on the joints and Figs. 10 and 1 1 the failures caused by the passing of the Une of pressure near the intrados or extrados. Before passing to the actual discussion of the graphic method for determining the stability of arches, a consideration of the action of the stresses developed in a construction of this kind will assist in a clearer understanding of the subject. Fig. 8 shows how, if the line of resistance along the haunches of the arch «\hould turn sharply downward and in so doing make with a normal to one of the joints an angle greater than the angle of friction, the voussoirs at this point Fig. 10. Failure of Semicircular Arch. Fig. 11. Failure of Poinled Arch. Opening of Arch-ring Opening of Arch-ring would tend to slide inward on their joint-planes, forcing outward the voussoirs at the spring and crown of the arch. Fig. 9 shows how failure of the arch would occur under similar conditions, but with the line of resistance turning sharply upward instead of downward. In these two cases it is conceivable that, al- though the RESISTANT THRUST at the joint where failure takes place makes an angle with the normal greater than the angle of friction, its point of application is still within the middle third of the joint. Figs. 10 and 11, on the contrary, illustrate methods of failure in which, al- though the angle made by the thrust may be such as to cause no slipping of one joint on another, its point of application is suflSciently outside the middle third of the arch- ring itself at the crown to cause overturning. In Fig. 10 the line of resistance passes high up, or perhaps entirely outside of the arch-ring, in the voussoirs at the crown of the arch and low down along the haunches. In Fig. 11 exactly contrary conditions exist. The ten ways in which a masonry arch may fail have been classified as follows: * " (i) By crushing of the masonry; (2) By sliding of one voussoir upon another; (3) By one voussoir or section of masonry overturning about an adjacent voussoir or section; (4) By shearing in a horizontal or vertical plane, this applying to solid concrete arches and not to voussoirs; (5) As a column when the ratio of the unsupported length of an arch to its least width is greater than twelve; (6) From striking the centering before the mortar is hard or when the arch, although stable under the full load, is not stable under its weight alone; (7) By striking the centering or loading the arch during construc- tion unsymmetrically; (8) By settlement of the foundations; (9) By sliding upon the foundations; (10) By overturning about any point in the pier or abutment. Methods (8) and (9) are the most common ways of failure. All methods of failure, however, must be guarded against in design." While some of these ways of failure may seem other than those illustrated in the foregoing figures, they may be perhaps more properly considered causes * W. J. Douglas in American Civil Engineering Pocket-Book, nage 625. Arches 313 OF FAILURE than WAYS OF FAILURE; and all, with the exception of the first, bring about a position of the line of resistance in the arch-ring which causes failure in one of the ways noted. In regard to the method of failure (i), the conditions may be such that the loading, although symmetrical, is so«excessive that although the line of resistance remains within the middle third, the total pressure on a joint is sufficient to CRUSH THE MATERIAL of which the arch is constructed. Such conditions, how- ever, are not common. From the foregoing discussion it is evident that in order to determine whether or not a given arch is stable, it is necessary to find the true line of resistance corresponding to the conditions of loading, form and dimensions of that par- ticular arch. It is always possible, in every arch-ring, to pass one maximum and one minimum line of resistance. The true line of resistance will lie somewhere between these two. The method of procedure, therefore, is to pass tentatively, a line of resistance, either a maximum or a minimum one, and see if it remains within the middle third. If it does not, as it may not be the true line of resistance, it does not mean necessarily that the arch is not stable. The next step then, is to note where it departs farthest from the middle third, and to pass a second line of resistance through the same point on the crown-joint and the point on the line of the middle third where the original line departs farthest from the middle third. If this second line of resistance remains within the middle third it is reasonable to assume that the arch is stable. In these various operations it is only necessary to consider half the arch when the loading is symmetrical, and this is usually the case in architectural problems. The number of voussoirs, also, into which we divide the half-arch, is immaterial and the joints need not coincide with those of the actual arch. In order to pass a line of resistance through an arch-ring, the thrust exerted by the other half at the crown-joint on the half-arch is first determined. This thrust is then combined with the resultant of the weight of the first voussoir and its load to determine the thrust exerted by this voussoir on the one next below it, and this thrust, in turn, is combined in the same way with the resultant of the weight and the load of the second voussoir, and so on down to the spring- ing-joint, for each succeeding voussoir. The points in which the various lines representing the thrusts cut the joints are known as the centers of pressure, and the fine joining them is the line of pressure or line of resistance. In performing this operation, the center of gravity of each voussoir as well as the fine passing through the center of gravity of the whole half-arch must be located. The face of each voussoir may be considered a trapezoid, and any one of the methods for finding the center of gravity of this figure may be used for finding the center of gravity of each voussoir. The method of dividing the trapezoid into triangles is here employed and is shown at the side of the arch in Fig, 12. (See, also, in Chapters VI and VII.) As the determination of the position of the line passing through the center of gravity of the half-arch is the problem of finding the resultant of a system of parallel forces, the method involving the drawing of the equilibrium-polygon may be used. The most convenient way to determine the stability of an arch is to use the GRAPHIC method. The steps in this method are outlined in the preceding para- graphs. Each of the operations will now be considered in detail. First Step. Draw one-half the arch to as large a scale as convenient, and divide it into voussoirs of equal size. In the example shown in Fig. 12, the arch-ring is- divided into ten voussoirs of equal face-areas. As already pointed out, it is not necessary that these should represent the actual voussoirs of which the arch is built. Next, the face-area of each of these voussoirs is to be foimd. 314 The Stability of Masonry Arches Chap. 8 Method of finding oentar gravity of vousaolr Where the arch-ring is divided into voussoirs of equal size, this is most easily done by computing the total area of the arch-ring and dividing this total area by the number of voussoirs. The formula for finding the area of one-half the arch-ring is as follows: Area in square feet = ©7854 (''^ — 1^) In this formula r is the outside radius and n the inside radius in feet. In this problem, for example, if the Area of the arch-ring = o 7854 (12.52 — lo^) = 44.2 sq ft as there are ten equal voussoirs, the area of each voussoir is 4.42 sq ft. Hav- ing drawn out one-half of the arch-ring, divide the crown-joint into three equal parts, and with radii of O'E and O'F describe the arcs dividing the arch-ring into thirds. Second Step. Choose the points E and H through which to pass a MINIMUM LINE OP RE- SISTANCE. The points F and G, through which a MAXIMUM LINE OF RE- SISTANCE can be passed, could equally well have been chosen. It should be noted that an un- loaded semicircular arch is more apt to fail by opening at the in- trados at the crown and at the extrados at the haunch, and there- C G H Fig. 12 Line of Pressure in Unloaded Semicircular Arch-ring fore, in this case, the line of resistance prob- ably passes nearer the outer third at the crown and nearer the inner third at the HAUNCH. To determine this minimum line of resistance the minimum thrust, applied at the point E of the crown-joint, must first be determined. The half-arch is in equilibrium under the action of three forces: (i) the thrust at the crown, acting horizontally, applied at the point E and preventing the half-arch from overturning inward; (2) the weight of the half-arch considered as a vertical force, acting through its center of gravity and tending to overturn it inwards about the point D; and (3) A force equal and oppo- site TO THE RESULTANT of these two forces and passing from // to /. / is the intersection of the weight-line through the center of gravity of the half-arch, with the line of action of the thrust at the crown, prolonged. It is thus possible to construct the triangle of these three forces and determine the magnitudes of the thrusts, when the position of the weight-line of the half-arch is deter- mined. It is first necessary to draw a vertical line through the center of gravity of each voussoir. The center of gravity of one of the voussoirs may be found by the method of triangles, as shown in the supplementary figure at the side of the arch-ring. Having determined the positions of the centers of gravity of the voussoirs. Arches 315 locate them on the voussoirs as shown. From the point E (Fig. 12) lay off verti- cally, to a scale of so many square units to a linear unit, the area of each voussoir, one below the other, commencing with the top voussoir. The length of the hne EK will then equal the total area of the arch-ring. From E and K (Fig. 12) draw 45° hnes intersecting at O. Draw Ow i, Ow 2, Ow 2>, etc. Then where OE intersects the first vertical line through the center of gravity of the first voussoir at a, draw a line parallel to Ow i, intersecting the second vertical at h. Draw he parallel to Chv 2, cd parallel to Ow 3 and so on to k. Draw kL parallel to Ow 10 and prolong it downward until it intersects EO pro- longed, at L. A vertical line drawn through L will pass through the center of gravity of the half arch-ring. This is an application to a practical problem of the method of finding, by the equilibrium-polygon, the line of action of the resultant of a system of parallel forces. The weights of the individual voussoirs act along parallel vertical lines and the weight of the half-arch is their resultant in magnitude. Third Step. To determine the thrust at the crown and the reaction AT the spring, draw a horizontal hne through E, the upper part of the middle third, and a vertical line through L, the two lines intersecting at / (Fig. 12). For the arch to be stable, it is, in general, considered necessary for the line OF resistance to pass within the middle third. First, assume that the line of pressure or resistance starts at E and comes out at H. Draw a line /// the direction of the hne of action of the resultant of the thrust at the crowr^ and the weight of the half-arch, and draw, also, a horizontal line opposite the point w ID, between N and M. This horizontal line MN represents the magni- tude of the horizontal thrust at the crown, for INM is the triangle of the three forces in equilibrium, the thrust at the crown, the weight of the half-arch and the reaction at the spring. Draw 7£^ 10 0^ parallel to ///, and the lines O^w 1, O^w 2, O^w 3, etc. O^E, equal to NM, is the thrust at the crown, and w 10 0^, equal to MI, the reaction at the spring. INM and EKO^' are similar triangles. Fourth Step. It is required next, to determine the line of resistance through the arch-ring. The thrust at E is combined with the weight of the first voussoir; their resultant is found and in turn combined with the weight ot the second voussoir; and so on for all the voussoirs. The intersections of these resultants with the joint-lines are the centers of pressure; the line joining these centers of pressure is the line of resistance. These resultants could be determined by drawing a series of parallelo- grams .OF FORCES over each voussoir. This would complicate the figure and involve unnecessary labor. It is found more convenient to draw the triangles OF FORCES one after the other, at the right-hand side of the figure and then transfer the results thus obtained by means of parallel lines to the figure Itself, especially as the weights of the voussoirs have already been laid off along the line F.K, at Ew 1, w 2,ws,w4,w 5, etc. Then from the point where O^E prolonged intersects the first vertical in voussoir number i, draw a (green) line to the second vertical, parallel to O^wi; from this point, a (green) line to the third vertical, parallel to O^^w 2 and so on. The last line should pass through //. Join the various points, where these (green) lines cut the joints at the centers of pressure, by the broken (red) line. This last line drawn is the line of .resistance. If this line lies entirely within the middle third of the arch-ring, the arch may be considered to be stable. But suppose that the line of resistance passes not only outside of the middle third but also outside of the arch-ring itself; it is still possible that the arch is not unstable. This is the case in Fig. 12 and we will next determine if a 316 The Stability of Masonry Arches Chap. 8 line of resistance can be drawn which will remain within the limits of the middle third of the arch-ring. Fifth Step. The Second Trial. Reproducing the condition of Fig. 12 in Fig. 13, without the construction Unes, it is seen that the line of resistance leaves the arch-ring at R and j;^ enters it again at S, while it is 1^ furthest -from it at U. If, at U, " a perpendicular is erected to a straight Une joining the two points R and 5, this perpen- dicular line VW, called the line OF FRACTURE, will be approxi- mately the trace of the plane along which, with the line of resistance under consideration, the arch will tend to fail, pre- sumedly by TURNING OVER tO the right about the point V. This shows that the thrust at THE CROWN, assumed to be applied at the point E, while of sufficient intensity to maintain equilibrium about //, is not of sufficient intensity to maintain equilibrium about V. If now a SECOND THRUST, of Sufficient intensity to maintain equilibrium about V, or better, about X, can be applied at E without being so great in magnitude that it will overturn the arch outward about G, or some other point on the outer Hne of the middle third, it C Fig. G H D 13. Line of Fracture in Unloaded circular Arch-ring Spring-line C G H D Fig. 14. Second Line of Pressure in Unloaded Semicircular Arch-ring is reasonable to conclude that the line of resistance resulting from this thrust is very nearly the true line of resistance in the arch-ring and that the arch is stable. In order to determine this new lini? of resistance the new thrust at thf Arches 317 CROWN must be found (Fig. 14). The preliminary steps required for this are the same as before until the seventh voussoir is reached. This is divided into two voussoirs by the line VW (Fig, 14), one being w6 w6"^ and the other the remainder of this seventh voussoir, and this division must be allowed for along the load-line EK, at wd w6^. The line w6 w6"' represents the area of vous- soir 6**, and the Hne w6" wy the area of the remainder of the seventh voussoir. The vertical line IL, passing through the center of gravity of that part of the half-arch above the line VW, is found by prolonging backwards the line hg, parallel to wG ^, until it intersects OE at L. To find the new thrust at the CROWN by completing the triangle of forces for this thrust and the force equal and opposite to their resultant, the inclined (blue) line must be drawn through the point X and the horizontal (blue) line through w6°'. The new thrust then is as before NM, equal to O^E. This thrust is laid off at O^E, the (green) lines O^w i, O^w 2, O^^w 3, etc., being drawn as before and the new line of re- sistance being drawn through the points where the parallels to these (green) C G H D O' Fig. 15. Line of Pressure in Loaded Semicircular Arch-ring lines cut the joints. This new line of resistance, if drawn correctly, should pass through X. It Hes within the middle third, except for a short distance at the springing, and hence it is justifiable to consider the arch stable. If it had passed outside the middle third to any great extent, in this second trial, this presumption would not have been justified. This discussion explains the method of determining the stability of an un- loaded semicircular arch. Such cases very seldom occur in practice, but they serve to illustrate the methods which apply generally to all other cases. With LOADED arch-rings there is slight difference in the method of determining the position of the center of gravity. Example 3. A loaded or surcharged semicircular arch (Fig. 15) will be considered next. Assume the same arch shown in Figs. 12, 13 and 14, and sup- pose it to be loaded with a wall of masonry of the same thickness and weight per square foot as that of the arch-ring, the upper surface of the wall being an inclined plane, i ft above the arch-ring at the crown, and 8 ft above it at the spring. The assumption of the particular load in this case is a purely arbitrary 318 The Stability of Masonry Arches Chap. 8 one for the purpose of illustrating the method of solution. The determination of the ACTUAL LOAD that comes upon an arch in any given case is by no means easy, so numerous are the uncertain elements that affect the transmission of this load to the arch- ring. The customary procedure i.i to assume that the load is itself transmitted to the arch-ring vertically downward. Each voussoir thus receives that portion of the load which is included .between two vertical lines drawn to the points of intersection of the joints on either side of that voussoir with the extrados. Hav- ing made this assumption it is necessary next to determine how much of the total superimposed masonry bears upon the arch-ring. It is a matter of common observation that if an opening is made in a wall, especially in a wall that has stood for some time, the major portion of the masonry above this opening is self-supporting, limited portions only, bounded by a some- what irregular line, falling down into the opening, as shown in Fig. 16. The profile of this bounds; ry-line depends upon the nature of the material of which the wall is constructed, the size of the stones, bricks, etc., the character of the bond and the quality of the mortar. This being the case, all the masonry above an arch should not be considered as the load on it. Some authorities recommend considering as the proper load, for brick- work, a trlangular part of the wall, the sides of which triangle have an in- clination to the horizontal of 45°; others assume an inclination of 60° (Fig. 16). (See, also, Chapter XV, page 612.) The exact determination of this load by mechanical laws is difficult if not impossible. It is better to consider each case separately and by a careful study of the conditions to determine as closely as possible just what portion of the weight of the superimposed masonry is transmitted to the arch. Having assumed a load for this particular arch-ring (Fig. 15), the procedure is as follows: First Step of Example 3. This involves the finding of the center of gravity of the ARCH-RING AND LOAD COMBINED. Divide the arch-ring into five voussoirs of equal size. In this case the area of each voussoir is equal to 44.2 sq ft h- 5, or 8.8 sq ft. (See under First Step, Fig. 12, preceding example.) The surcharge or load, also, is divided into five parts, not necessarily equal, by drawing ver- tical lines to the points of intersection of the joints and the extrados. The ap- proximate area of each one of these surcharges is found by multiplying half the sum of the lengths of the two parallel vertical sides by the length of the horizontal distance between them. The positions of the center of gravity of each voussoir and of the center of gravity of each voussoir-surcharge are determined as in the preceding example. The CENTERS OF GRAVITY of these SURCHARGES can be found by dividing each TRAPEZOIDAL FIGURE into TRIANGLES as shown, remembering that the medial line in this case joins the middle points of the two parallel faces. As, the latter are vertical, the medial lines approach a horizontal direction. This construc- tion is shown on surcharge i", Fig. 15. Having drawn the lines of action of the weights of the various voussoirs and of their loads through their respective centers of gravity, the lines of action of the combined weight of each voussoir and its load must be found. The construction for this operation is shown at 16. Triangle of Loading Opening Arches 319 the left of Fig. 15. The method used, that of the equilibrium-polygon, is the same as that employed in the previous example to find the line passing through the center of gravity of the half-arch, only in this case the forces are reduced to two. Furthermore, as the areas of the various voussoirs are equal it is possible to superimpose the different force-diagrams, one over the other, and so save considerable labor. Begin, therefore, by laying off along the line RS at the left of the loaded arch, and at any convenient scale, fw, the area (weight) of a voussoir; then from w, in turn, the distances zy i^, w 2", iv 3", etc., , representing the areas of the successive surcharges, i*^, 2", 3^, etc., always at the same scale. The scale to be employed later for laying off the combined weights of the voussoirs and their loads along the line AK is the best one to choose, but the difference in scales is not important. In this particular instance the two points i" and 5" coincide because the two areas i'^ and 5"^, although of different shapes, are each equal to 6.7 sq ft. This is a mere coincidence. Next draw /O" and 4" O" at 45° to RS, and in turn, 0"w, 0"i", 0"2«, etc. As the problem which presents itself is to combine the weight of each voussoir with its individual surcharge, and as the weights of all the voussoirs are equal, and, furthermore, as the forces which are to be combined to find their resultant are only two, the two POLE-LINES or RAYS 0"f and 0"w in the force-diagram serve in each case, and the funicular polygon is reduced to a triangle. Draw gh, ik, Im, np and rs parallel to 0"w, and ///, kii, mv, px and sy parallel to 0"f; and draw gt, iu, Iv, nx andry parallel respectively to 0"i", 0"2°, 0"^'^, O'V' and 0"s^. The points /, w, V, X and y are the points through which to draw the heavy (red) lines of action of the combined weights of the voussoirs and their surcharges. Having found and drawn these lines, the procedure for finding the line IN is the same as in the previous example, except that the distances Ewi 1°', wi i", wi 2", etc., instead of being equal to the weights of the voussoirs alone, are equal to the combined weights of each voussoir and its surcharge, Ewi i^, being equal to/i", wi i/^ to wi 2" being equal to/ 2", etc. The line EO is drawn at 45° to AO' , but as the position of the pole-point, 0, is entirely arbitrary, the line Ow 5 s" has been drawn in this case in such a way that falls well over toward the left of the figure, thus avoiding a certain amount of confusion in the drawing which would have resulted if Oiv 5 5* had made an angle of 45° with ^0'. The lines ah, he, A and de are drawn respec- tively parallel to tvi i"0, wi 2^0, etc., and eL is produced backward parallel to Ow 5 5" until it intersects EO at L, which is the point through which the heavy (red) line IN, passing through the center of gravity of the whole half-arch and its surcharge, should be drawn. A vertical line drawn through L will pass through the center of gravity of the arch-ring and its load. If this were an arch designed for a building and if the only abutments possible were of such size and form that it was essential for the thrust exerted by the last or fifth voussoir on these abutments to approach more nearly the vertical, the architectural expedient of increasing slightly the weight of the surcharge, 5*^, on this voussoir by adding some piece of ornament, such as a cartouche, could be resorted to. A case of this kind in actual practice is the archway over the entrance to the service-court- yard of the Grand Opera House in Paris, where the pyramidal stone ornaments which surmount the cornice on either side of the central motive were added after the original design was made, with this end in view. In the example illustrated in Fig. 15 {he areas of the faces of the surcharges are shown by the figures on these faces. For the second surcharge from the crown, for example, the area is 8.1 sq ft. Second Step of Example 3. This involves the determination of the thrust AT THE CROWN and the line of resistance. The method of finding this thrust 320 The Stability of Masonry Arches Chap. 8 Arches 321 at the crown is similar to that employed in the previous example. In that example, however, it was found that this thrust, appUed at E and determined by assuming // as the point of application of the reaction at the spring, produced a line of resistance which fell considerably below the middle third. But instead of performing the operations required by a second trial, as in the previous exam- ple, the expedient is tried of slightly increasing the inclination to the vertical of the (blue) line IM, and so assuming a somewhat greater thrust at the CROWN. As the line of resistance, as shown in Fig. 15, passed with this thrust departs but slightly from the middle third near the springing, we are justified in assuming that this arch is stable under the given conditions. The method used for this example may be used, also, for a semielliptical arch. Example 4. This example (Fig. 17) illustrates the application of the preced- ing methods, with some variations, to the determination of the position of the center of gravity of a loaded segmental arch, the thrusts at the crown and spring and the line of pressure or resistance through the arch-ring. In this case, instead of dividing the arch-ring into a certain number of voussoirs with joints radiating from a center and considering the surcharge on each individual voussoir, the method of dividing the arch-ring and its load into vertical slices, in this case two feet wide, and computing the areas of the entire slices has been adopted. Having computed the areas of the slices, including in each case the combined areas of the sliced part of the arch-ring and its surcharge, we lay them off in order from E, to a convenient scale, and then proceed as in the previous examples. The remaining steps required to determine the thrusts at the crown and at the spring and the line of resistance are also the same as explained in the foregoing paragraphs. In a flat segmental arch there is practically no need of dividing the arch-ring into voussoirs by joints radiating from a center, in order to determine its stability. Of course, when built, they must be made to radiate. Fig. 17 shows the graphical analysis of an arch of 40-ft span and carrying a load i^Vz ft high at the crown. The depth of the arch-ring is 2 ft 6 in. It is seen that the line of resistance lies entirely within the middle third, and that the arch is therefore stable. It is to be noted that the hne of resistance in a segmental arch should be drawn through the lower or inner edge of the middle third at the springing. It is to be noted, also, that the horizontal thrust at the crown and the thrust T against the supports are very great when com- pared with those in a semicircular arch; and hence, although the segmental arch is the stronger of the two, it requires much heavier abutments. The fore- going examples serve to show the various methods of determining the stability and thrusts of any arch used in buildings. 322 Reactions and Bending Moments for Beams Chap. 9 CHAPTER IX EEACTIONS AND BENDING MOMENTS FOR BEAMS By CHARLES P. WARREN LATE ASSISTANT PROFESSOR OF ARCHITECTURE, COLUMBIA UNIVERSITY 1. Reactions for Simple Beams Definition of Reaction. One of the fundamental principles of static equilib- rium is that the sum of all the forces acting upon a body in one direction must be balanced by the sum of another set of forces acting in the opposite direction. Therefore, in the case of a beam or girder, the loads acting downward must be balanced by an equal set of forces at the supports, acting upward. These up- ward forces are called thrusts, or reactions and in computing the strength of beams one of the first steps is to determine them, since the loads are usually given in intensity and position. The Principle of Moments. The reactions may be determined by the application of another fundamental principle of static equilibrium for forces acting in the same plane. The algebraic sum of the moments of all the forces Fig. 1. Simple Beam. One Concentrated Load taken about any point in the plane in which they act must be zero. The moment of a force about a point is the product of the magnitude or intensity of the force by the perpendicular distance between the line of action of the force and the point. The perpendicular distance is called the lever-arm, and the point the center of moments. Forces acting upward are considered positive and those acting downward are considered negative. The center of moments may be taken at any point in the plane of action of the forces, but it is more convenient to take it at one of the reactions. For example, the beam in Fig. 1 supports a concentrated load P at the distance m from the left support. To find the left reaction take the center of moments at the right reaction. Then the equation of moments is Rd - Pn = o. from which Ri = Pn/l (i) Reactions for Beams 323 In like manner, to find ^2 the center of moments is taken at Ri and the equation of moments is R2I - Pm ■■= o, from which Rt = Rmjl (i)' From the first principle of statics mentioned, R\-V Ri. must equal P; hence, as a check, Pn/l + Prnjl = P. Example i. Let a beam 15 ft in span support a concentrated load of 700 lb» 6 ft from the left end; or, P = 700, w = 6 and w = 9. Then, from Formula (i), ^1 = 700 X 9/15 = 420 lb. Ri = 700 X 6/15 = 280 lb and 420 + 280 = 700 lb. For a concentrated load at the middle, or for a uniform load over a simple beam, it is evic ^nt without applying the conditions of equilibrium, that each reaction is one-naif the load, for, in Formulas (i) and (i)', m and n each equal 1/2 and Ri ana R2 = y2 P. For any number of concentrated loads (Fig. 2) the reactions may be found by adding together the reactions found by Formula (i) due to each load separately, or they may be computed in one operation by the following formula: I -7l-„ Fig. 2. Simple Beam. Three Concentrated Loads To find the right reaction, the center of moments is taken at the left support, and the equation of moments is hence. RJ' — PlMi — PiMi — P3W3 = o P\m\ -\- P-imi -f Pzrm R2 = / (2) In like manner, to find Ri the center of moments is taken at R2 and the equa^ tion of moments is Ril — Piui — P2W2 — P3W3 = o from which Pim -\- P2W2 4- Psm , , i?, = ^ (3) Example 2. Suppose the beam in Fig. 2 is 20 ft in length. Let there be three concentrated loads of 500, 800 and 600 lb placed 5, 9 and 12 ft respectively from the left support. Then / = 20, m\ = 5, m2 = 9, W3 = 12, Pi = 500, Pa = 800 and Pz= 600. Substituting in Formulas (2) and (3), 500X5-1-800X9 + 600X12 „ ,, Rx= = 845 lb 20 „ 500X15 + 800X11 + 600X8 ,, R^ = = I 055 lb and 500 -f 800 -(- 600 = 845 -f- 1 OSS = I 900 lb 324 Reactions and Bending Moments for Beams Chap. 9 To find the reactions for a combination of uniformly distributed and con- centrated loads, to each of the reactions obtained by Formulas (i) or (2) for the concentrated loads, add one-half the distributed load. Thus, suppose the 20-ft beam in this example weighs 40 lb per linear ft. This is considered as a uniformly distributed load and for the entire beam it is 40 lb X 20 = 800 lb. By the rule, one-half of this is added to each reaction, so that the total reactions are,i?2 = 845 + 400 = i 245 lb andi?i= i 055 + 400 = i 455 lb. Example 3. For a distributed load applied over only a part of the span, as in Fig. 3, assume the load to be concentrated at the middle of the part over m=4.5-' ^T* m=5.5- I __.-^__J 43i_ _,_ _3.. 10 = 50 lbs. per ft. f?i Z = 10 Fig. 3. Simple Beam. Distributed Load over Part of Span which it acts and use Formulas (1) and (i)'. For example, let w (Fig. 3) equal $0 lb per linear ft, applied for a distance of 5 ft over the beam. Then W, the total load, is 50 lb X 5 = 250 lb. This may be assumed to be concentrated at its center, 4.5 ft from the left support. Then P = 250, m = 4.5 and m = 5.5; and from Formulas (i) and (i)', 250X5.5 ,, and 250X4-5 ,, A2= = T12.5 lb Therefore, for any combination of concentrated and uniform loads distributed over the entire beam, or over only part of it, find the reactions due to the con- centrated loads by Formulas (i) or (2), and to them add the reactions due to the uniformly distributed loads. 2. Bending Moments in Cantilever and Simple Beams Definitions. The bending moment is a measure of the tendencies of forces to break a beam by bending or flexure. Fig. 4 shows the manner in which a simple bearn, supported at the ends, breaks when subjected to a load greater than it can bear. The effect of a load upon a beam is to cause it to sag, or bend. The bending of the beam shortens, or compresses, the upper fibers and Stretches, or elongates, the lower fibers. So long as the resistance of the fibers * See, also. Chapter XV, pages 555 to 563. Bending Moments in Beams for Different Kinds of Loading 325 to shortening, or compression, and to stretching, or tension, is greater than the tendency of the load to disrupt them, the beam carries the load; but, when the load causes a greater tension, or compression, on the fibers than they are capable of resisting, the beam breaks. The stretching of the fibers before breaking allows the beam to bend; hence, the name bending moment has been given to the forces causing a beam to bend and perhaps ultimately to break. Fig. 4. Manner of Rupture of Simple Beam In order to calculate the flexural strength of a beam, it is necessary to ascertain the nature and extent, first, of the external forces acting to break the beam, and secondly of the internal forces or stresses tending to resist rupture.* The external forces tending to break the beam by flexure are the downward loads and the upward reactions. Each acts with a leverage equal to the perpendicular distance from its line of action to the section at which the beam tends to break. The algebraic sum of the moments of these external forces on the left, or right, of any section is called the bending moment for that section, since it is the momei^t of the resultant of the forces which tends to bend the beam at that section. It is generally designated by M. Then, from the definition, the bending moment for any section of a beam resting on two supports and in a state of flexure under a load or loads is If = the moment of either reaction minus the sum of the moments of the loads between that reac- tion and the section. The moment of the reaction is upward, or positive, and the moment of any load downward, or negative, if the part of the beam on the left of the section is considered. 3. Bending Moments in Beams for Dif- ferent Kinds of Loading Case I Beam Fixed at One End and Loaded with a Concentrated Load P, Near the Free End Fig. 5. Cantilever Beam. Con- Maximum bending moment, at wall = Pxl centrated Load near Free End Bending moment at any other section x = Fx Note. If / is in feet, the bending moment will be in foot-pounds; if / is in hiches, the bending moment will be in inch-pounds. Case II Beam Fixed at One End and Loaded with a Uniformly Distributed Load W, (Fig. 6.) Maximum bending moment, at wall = W X I/2 At any other section x, M = ■wxXx/2 = WX-/2 Note. W = wl and w = the load per unit of length. * See Chapter X for a discussion of these internal stresses and of the resisting moment. 326 Reactions and Bending Moments for Beams Chap. 9 Case III Beam Fixed at One End and Loaded with Both a Concentrated and a Unifonnly Distributed Load (Fig. 7). Maximum bending moment, at wall = Pxh+WX I1/2 ^^^ ^^ r*--aj--->i Fig. 6. Cantilever Beam. Uni- formly Distributed Load Fig. 7. Cantilever Beam. Distrib- uted Load and Load at Free End Case IV Beam Supported at Both Ends and Loaded with a Concentrated Load at the Middle (Fig. 8). Maximum bending moment, under the load = FI/4 P Fig. 8. Simple Beam. Concentrated Load at the Middle Case V ' Beam Supported at Both Ends and Loaded with a Uniformly Distributed Load W (Fig. 9). Maximum bending moment, at the middle = Wl/S Fig. 9. Simple Beam. Uniformly Distributed Load Bending Moments in Beams for Different Kinds of Loading 327 Case VI Beam Supported at Both Ends and Loaded with a Concentrated Load not at tho Middle (Fig. 10). Maximum bending moment, mider the load = Pmn/l r ^-m-^ n- »P Fig. 10. Simple Beam. Concentrated Load not at the Middle Case VII Beam Supported at Both Ends and Loaded Symmetrically with Two Equal Concentrated Loads (Fig. 11). Maximum bending moment = Pm and is the same for any section of the beam between the two loads. Fig. 11. Simple Beam. Two Concentrated Loads Symmetrically Placed From these examples it will be seen that all the quantities which enter into the computation of the bending moment are the load, the span and the distance of the point of application of the load from the center of moments. Case Vin Beam Supported at Both Ends and Loaded with a Distributed Load Over Part of the Span (Fig. 12). -n- Fig. 12. Simple Beam. Distributed Load over Part of Span If assumed under the center of the load, M*max = Wmn/l — TT/i/S When m and n are equal the bending moment =WXI/a, —W X /i/8 * This is only approximately correct when m and n are unequal. For the exact value, find the section of zero shear; the maximum bending moment will be at that section. (See, also, Example 5, page 561.) 328 Reactions and Bending Moments for Beams Chap. 9 Example 4. In Fig. 12 let W = 800 lb, w =» 8 ft, « = 1 2 ft, / = 20 ft and /i - 8 ft. Then the bending moment 800 X8XI2 800X8 A Q . ,u = = 3 840 — 800 = 3 040 ft-lb, or 36 480 m-lb 20 8 Example 5. In Fig. 12 let w = n = 10 ft, / = 20 ft. h= 4 it and IF = 600 lb. Then the bending moment 600 X 20 600 X 4 ., ,, . ,, = — - — ■= 3 000 — 300 = 2 700 it-lb, or 32 400 m-lb 4 8 The Bending Moment for any Case Other Than the Above may easily be obtained by the graphic method, which will now be explained. 4. Graphic Method of Determining Bending Moments in Beams Beam with One Concentrated Load (Fig. 13). The BENDING MOMENT of a beam supported at both ends and loaded with one concentrated load may be determined graphically, as follows: 1 Let P be the load, I ^~!F ^^ i appHed as shown. Then, by the rule under Case VI, the MAXIMUM BENDING MOMENT is under the load and = Pmn/l Draw the beam, with the given span, accurately to scale, and measure down the Hne AB, io 3. scale of FOOT-POUNDS to the LINEAR INCH, a distance equal to the bending moment. Connect B with each end "^ig. 13. Bending-moment Diagram. Load One Concentrated of the beam. To find the bending moment at any other point of the beam, as at 0, draw the vertical line y to BC. Its length, measured to the same scale to which AB \% drawn, will give the bending moment at 0. The figure DBCAD is called the bending-moment diagram and the hnes BD and BC are called influence lines for the bending moments. 'I wyO h«. Fig. 14. Bending-moment Diagram. Two Concentrated Loads Beam with Two Concentrated Loads (Fig. 14). To draw the bending-moment diagram for a beam with two concentrated loads, draw the doited lines ADD and ACD, giving the bending-moment dia- Graphic Method of Determining Bending Moments in Beams 329 GRAMS for each load separately. EB is laid out to scale, equal to Ptnn/l and FC equal to Pirs/l The bending moment at the point E is equal to EB (from the load P) + Eb (from the load Pi), or Af = EB -{• Eb = EBi; and at F the bending moment is equal to FC -\- Fc= FCu The bentding-moment diagram: for both loads is ABiCiD and the maximum bending moment is, in this particular case, the hne FCi measured to scale. Beam with Any Number of Concentrated Loads (Fig. 16.) Proceed as in the last case, and draw the bending-moment diagram for each load separately. Make AD = Ai + A2-\- A3, BE = Bi -{■ B2 + B3 and Fig. 15. Bending-raoment Diagram. Three Concentrated Loads CF=Ci + C2-f C3. The figure IIDEFIFI will then be the bending-mo- ment diagram corresponding to all the loads. The bending-moment diagram for a beam with any number of concentrated loads may be drawn in the same way. Beam with a Uniformly Distributed Load (Fig. 16). Draw the beam with the given span, accurately to a scale as before, and at the middle of the beam draw the vertical line A B, to a scale of a certain number of foot-pounds to the linear inch, equal to Wl/S, from Case V, W represent- ing the whole distrib- uted load. Connect the points C, B, Dhy a PARABOLA to obtain the bending-moment DIAGRAM. To find the bending moment at any point a, draw the vertical line ab, measure it to the same scale to which AB h drawn, and it will be the bending moment desired. Methods for drawing the parabola will be found in Part I, page 79. Beam Loaded with Both Distributed and Concentrated Loads (Fig. 17). To determine the bending moments in this case, combine the bending-moment DIAGRAMS for the concentrated loads and for the distributed load, as shown in Fig. 16. Bending-moment Diagram. Whole Beam Distributed Load ovcif 330 Reactions and Bending Moments for Beams Chap. 9 Bending-moment Diagram. Concentrated Loads Distributed and Fig. 17. The bending moment at any section of the beam will then be limited by the line ABC on top and by the line CDEFA on the bottom; and the max- imum BENDING MOMENT Will be the longest vertical line that can be drawn n between these two bounding Hnes. For example, the bending moment at X is BE. The point of MAXIMUM BENDING MO- MENT depends upon the position of the concen- trated loads and the relative magnitude of the distributed load; it may or may not occur at the middle of the beam or under one of the concentrated loads. Example 6. What is the greatest bending moment in a beam of 2o ft span (Fig. 18), loaded with a distributed load of 8oo lb, a concentrated load of 500 lb 6 ft from one end, and a concentrated load of 600 lb 7 ft from the other end? Solution, (i) The maximum bending moment due to the distributed load, from Case V, is If //8, or 800 X 20/8 = 2 000 ft-lb. Lay off vertically over the middle of the beam, and at any convenient -^ o ■'^^•p^jT]^' B~ scale, say 4 000 ft-lb to the inch, 5i = 2 000 ft-lb, and draw a parab- ola through the points yl, 5 and C. (See page 79-) (2) The maximum bending moment for the concentrated load of 500 lb, from Case VI, is 500 X 6 X 14/20, or 2 100 ft-lb. Draw £2 = 2 100 ft-lb to the same scale as 5i, and then draw the lines ylEandCE. (3) The maximum bending moment for the concentrated load of 600 lb, In like manner, is 600 X 7 X 13/20, or 2 730 ft-lb. Draw Z)3 = 2 730 ft-lb and connect D with A and C. (4) Make EH equal to the distance from 2 to 4, and DG to the distance from 3 to 5, and draw AHGC. The MAXIMUM BENDING MOMENT Will be represented by the longest vertical Hue which can be drawn between the parabola ABC and the broken line AHGC. In this example the longest vertical line which can be drawn is Xy, and it ihould scale 5 645 ft-lb. Bending-moment Diagram. Concentrated Loads Distributed Beams with Triangular Loading and with Fixed Ends 331 The position of the line Xy is determined by drawing the line TT\ parallel to II G and tangent to ABC. Draw Xy vertically through point of tangency. 5. Reactions and Bending Moments for Beams with Triangular Loading and for Beams Fixed at Both Ends.* Beams with Triangular Loading have reactions and bending moments as follows: Beam Supported at Both Ends, Fig. 19 (a) End-reactions: Ri = R2 = 14 W Bending moment at any px)int =Wxi }4—2x'^/sl^) Maximum bending moment, at center = 1^7/6 Beam Supported at Both Ends, Fig. 19 (b) End-reactions: i?i =H W, R2= %W Bending moment at any point ={Wx/s){i —x^/l) Maximum bending moment (at x = 0.58 /) = .128 Wl Cantilever Beam, Fig. 19 (c) Reaction: Ri = W Bending moment at any point = Wx^/3 l^ Maximum bending moment (at i?i) = Wl/s Beams of Cases IV, V, and VI, with Fixed Ends, ^ig. 19. Triangular Load- have reactions and bending moments as follows: '"^ ^'^ Beams Case IV A. Beam Fixed at Both Ends, with a Concentrated Load P at the Middle (Fig. 8) End-reactions: 7?i = /?., = H Z' Maximum positive bending moment, under the load = Pl/8 Maximum negative bending moment, at ends = Pl/S Case V A. Beam Fixed at Both Ends, with a Uniformly Distributed Load W (Fig. 9) End-reactions: Ri = R^ = i/^w Maximum negative bending moment, at ends = Wl/ 12 Maximum positive bending moment, at center = Wl/24 Case VI A. Beam Fixed at Both Ends, with a Concentrated Load P at Distance m from Left End and Distance // from Right End (Fig IQ) End-reactions: Ri = Pn^^ m -f n)/P; R2 = PmHs n + m)/P Maximum bending moment, negative , at left end, M\ = Pmn'^/l^ at right end, M2 = Pm ^n/l 2 Bending moment under load, positive = R^m — Mi * From notes by Robins Fleming. 332 Properties of Structural Shapes, etc. Chap. 10 CHAPTER X PROPERTIES OF STRUCTURAL SHAPES. MOMENT OF INERTIA, MOMENT OF RESISTANCE, SECTION- MODULUS AND RADIUS OF GYRATION By CHARLES P. WARREN LATE ASSISTANT PROFESSOR OF ARCHITECTURE.. COLUMBIA UNIVERSITY 1. The Properties of Cross-Sections The Moment of Inertia. The strength of a cross-section to resist stresses, in either a beam or a column, depends not only upon the area but also upon the form of the cross-section. The parts of the cross-section farthest from the neutral axis, which always passes through the center of gravity of the cross- section, are much more efficient in resisting bending stresses than those parts adjacent to the axis; so that some mathematical expression must be obtained that will represent the efficiency of the entire cross-section to resist bending stresses when compared with that of any other cross-section. This expression is called the Moment of Inertia and is usually designated by the letter I. The Moment of Inertia of any cross-section may be defined as the sum of the products obtained by multiplying each of the elementary areas of which the section is composed by the square of its normal distance from the neutral axis of the section. By an elementary area is meant an area smaller than any dealt with in simple mathematics, and it is, therefore, impossible to find an exact expression for the moment of inertia of a cross-section by such methods. By means of the calculus, however, exact formulas have been deduced from which the moments of inertia of simple geometrical forms, such as rectangles, triangles, circles, etc., may be found, with respect to different axes. The NEUTRAL AXIS of the cross-section of a beam, girder, column, etc., which is in a state of flexure, is the line on which there is neither tension nor compres- sion in the fibers, and when the unit stresses do not exceed the elastic limit of the material, it can be shown that this neutral axis passes through the center of GRAVITY of the cross-section. The normal distance of the extreme fibers from the neutral axis is usually designated by the letter c or the letter y. The former is used in the notation of this book. Since for all sections except squares and cirdes, there are, in general, two neu- tral axes corresponding to the more common positions cf the sections, it follows that there are also two moments of inertia commonly used; for a rectangle, for example, a greatest moment of inertia about an axis perpendicular to the long side and a least moment of inertia about an axis perpendicular to the short side. The moments of inertia of the cross-sections of all rolled shapes have been calculated and are tabulated in the manufacturers' handbooks. Thus, for example, the moments of inertia of the cross-section of a i2-in, 31.5-lb I beam, with respect to axes perpendicular to the web and parallel to the web, are, from Table IV, equal to 215.8 and 9.5 biquadratic inches respectively. Formulas for calculating the moments of inertia of other simple sections are given on the following pages. Properties of Structural Shapes, etc. 333 The Moment of Resistance. In Chapter IX, under the chapter-subdivi- sion treating of the bending moments in beams, page 325, it was stated that in order to calculate the flexural strength of a beam it is necessary to ascertain the nature and extent, first, of the external forces tending to break the beam by flexure, and, secondly, of the internal forces or stresses tending to resist rupture. The external forces cause the bending moments,* and the internal stresses the moments of resistance, at the various cross-sections of a beam. The moment of resistance or the resisting moment at any cross-section of a beam is the algebraic sum of all the moments of the internal horizontal stresses in that section with reference to a point in that section. It is usually represented by the expression Sljc, in which S is the horizontal unit stress, tensile or compressive, as the case may be, upon the fiber most remote from the neutral axis of the section, and called the fiber-stress; / is the moment of inertia of the area of the section with reference to the neutral axis; and c is the shortest distance from the most remote fiber to that axis. Since, for equilibrium of forces and stresses at any cross-section of a beam, the bending moment equals the resisting moment for that section, if M represents the bend- ing moment we have the equation M = Sl/c (i) This is known as the flexure formula and is universally used for investi- gating the flexural strength of beams. The Section-Modulus or Section-Factor. That expression l/c in the above formula is generally known as the section-modulus or section-factor. This quantity for the principal rolled sections is given in Tables IV, V, VI, VII, VIII, XI, XII, XIII and XIV. Corresponding to the two moments of inertia generally used for all sections (except for squares and circles) there are two section-moduH also, one for each axis. Thus, the section-modulus of the 12-ii^ 31.5-lb I beam, with respect to a neutral axis perpendicular to the web, is l/c = 215.8/6 = 36; and for the axis parallel to the web, it is l/c = 9.5/2.5 = 3.8. For other shapes the section-modulus may be found by dividing the moment of inertia by the normal distance of the extreme fiber from the neutral axis. The Radius of Gyration. The efifect of the form of the cross-section of a column on its strength is determined by a quantity called the Raehus of Gyra- tion, which is as necessary in the determination of the strength of a column as the moment of inertia is in the determination of the strength of a beam. It is denoted by the letter r. The value of the radius of gyration for any section is determined by the formula r=Vl/A (2) in which / is the moment of inertia of the section and A the section-area. The radius of gyration is the normal distance from the neutral axis to the center of gyration, and the center of gyration of a section is the point where the entire area might be concentrated and have the same moment of inertia as the actual distributed area. The radius of gyration of a section is a distance and it is always less than the distance, c, from the neutral axis to the remotest fiber. For the two moments of inertia above referred to, and commonly used, there are two corresponding radii of gyration. The least of these is the one to be used in the investigation of the strength of a column as it is referred to the axis about which the column is most likely to fail The radii of gyration of the rolled * See Chapter IX, page 325, for definition of "bending moment," 334 Properties of Structural Shapes, etc. Chap. 10 shapes are given in the tables of the properties of sections, mentioned above. For the 12-in 31.5-lb I beam, r = 4.83 in and r' = i.oi in. The radius of gyration of any other section may be found by Formula (2). Formulas for the moments of inertia, radii of gyration and section-moduli of the principal elementary sections are given on the following pages. In the case of a hollow section or a section with a reentering hollow part, the moment of inertia of the hollow part is to be subtracted from that of the enclosing area. JMoments of inertia when referred to the same axis can be added or subtracted like any other quantities which are of the same kind. 2. Areas, Moments of Inertia, Section-Moduli and Radii of Gyration of Elementary Sections J = the moment of inertia Ijc — the section-modulus r = the radius of gyration A = the area of the section c — the normal distance of most remote fiber from neutral axis The position of axis referred to in each case is represented by the broken line SQUARE Axis of moments through center l._. "1 -4 u..—d----^ 1 = d c = - ' 2 12 / _^ c ~ 6 r = — ;= = 0.288675 d V12 SQUARE Axis of moments on base f"l \'l 4 i«— -d-— : A = d^ c=d 3 {_? c 3 A r= — ^ = 0.577350 i Properties of Structural Shapes, etc.', RECTANGLE Axis of moments through center 4-1 _i —b---^ d b^ I _bd^ c ~ 6 r= — ^ =o. 288675 i V12 RECTANGLE Axis of moments on base t T 1 4 1 lJ___ --ii c= d b^ 3 c 3 r=~— = 0.577350 1 7 = A = — 2 c = d bd^ 12 I _bj^ c 12 = 0.408248 (/ TRAPEZOID Axis of moments through center of gravity 't <- — 6- .4 = d{b + h) d{b+2by) " Sib+bi) ^^_ d{bl^2b) Sib + bi) dHb^-}-4hbi + br' ) ' 3(^{b + bi) C 12 (61 -f- 26) r = ^ V ^&' -{-4bbiTb7) 6 (6 + 6i) * To find c and Ci, see Chapter VI, page 295. Properties of Structural Shapes, etc. 337 TRAPEZOID Axis of moments on base U 5 A-- c- I-- I 2 = d d'(b-\-3bi) 12 dUb^shi) c 12 ' tA+- iii T SECTION AND CHANNEL Axis of moments through center of gravity A = id + ti{b-l) t <- ^^---b >| |.4 J?^,^ * tdxy2d-{-ti{b-t){d-\iti) ' ^ = A / = /c3+kl3-(6-/)(ci-/l)5 ■=v/| k — b- CIRCLE Axis of moments through center ird^ A = — = 0.785398^/2 4 d c= - 2 I = -— = 0.049087 d* 64 I ^^' - = — = 0.09817s a' c 32 HOLLOW CIRCLE Axis of moments tlirough center IT (d^ - di"^) A = -^^ ^ = 0.785398 id'-di') 4 c= - 2 i = :: — — = 0.049087 (a* — rfi'*) 64 c 32 d = 0.098175 {d*-di^) Vd^ + di^ * To find the values of c and Ci, see Chapter VI, page 295. 338 Properties of Slructural Shapes, etc. Chap. 10 CHANNEL Axis of moments through center of gravity xM^zk ::^- CROSS-SECTION Axis of moments through center of gravity IRREGULAR I SHAPE Axis of moments through center of gravity "} — v\ — ~ I T i.i.J f cL -b— i- A =■ tib -]-2i{d- k) ^ 2dH-^dxh^ 2 A Ac- -W: A=td-^ti{h-t) d c= - 2 td^ + h^ {b - t) 12 I Id^+hHb-t) c 6d UP - /l3 {b - t) V 12{td-\-tl{b-l)) A = bh-\-d4^b,h r* td^^- h'^ibi -0 + h(b-t)(2d- h) td'i+ti^ib- 2A -/) -^n{bi-l)(2d- -h) / 6,C3-(6i- 2.4 /)X (C-/l)3 k,3 + 3 -(b-t)x(ci-ti) a * To find c and ci, see Chapter VI, page 295. 3. Transferring Moments of Inertia to Other Parallel Axes Explanation of Formula. It is often necessary to determine the moment of inertia with respect to some other axis than the one passing through the center of gravity of the section, such, for example, as one passing through the base and parallel to the other. Suppose it is desired to find the moment of in- ertia of a rectangle about an axis passing through the lower base, as in the second figure on page 335. It may be demonstrated by the principles of mechanics that the moment of inertia of any section with respect to any axis is equal to the moment of inertia of the section with respect to a parallel axis through the center of gravity, plus the product of the area of the section multi- plied by the square of the normal distance between the axes. This rule may be expressed by the formula /i = / + ^A« (3) Properties of Structural Shapes, etc. 839 in which /i is the required moment of inertia, / the moment of inertia of the section with respect to the axis through its center of gravity and parallel to the given axis, A the area of the section and h the normal distance between the axes. From this it is seen that the moment of inertia of any section-are^, is less for an axis through its center of gravity than for any other parallel axis. For example, consider the rectangle shown on page 335, of breadth b and depth d, the / of which is known to be bd^/ 12 for an axis passing through the center of gravity and parallel to the base. Then, for a parallel axis through the base, the above formula \ gives: bd^ ., d ■■— -{-bdxl 12 V- — I ~ 12 4 3 XI idn Fig. 1 -N Moment of Inertia of Cross-section of Steel Angle Thus the moment of inertia of the cross-section of the steel angle shown in Fig. 1, about the axis MN, is equal to the moment of inertia about the axis XX plus the product of its area multiplied by h^. The moments of inertia for the sections of the standard rolled shapes of structural steel may be found from the tables given -in this chapter. The distance ci, also, may be found from the same tables; and this distance subtracted from d will give the distance h of Formula (3). Suppose, for example, that it is desired to find the moment of inertia of the cross-section of a 4 by 3 by Vz-'m angle, placed, with the long leg horizontal, about an axis MN, 12 in from the back (Fig. 1). Turning to Table XI, the area of the angle-section = 3.25 sq in. /, the moment of inertia of the angle- section about an axis 2-2, or A^A^ of Fig. 1, parallel to the long leg = 2.4, a, the distance of this axis from the back of the long leg = 0.S3 in and h, the distance between the axes = {d— ci) = 12 — 0.83 in = 11. 17 in. Substituting these values in Formula (3) /i= 2.4 4- 3-25 X 11.17^= 2.4 + 405-50 = 407-9 4. Moments of Inertia of Compound Sections The Moment of Inertia of a Compound Section made up of a number of smaller sections may be found by the same formula, Ii = I -\- Ah^. Denote the SUM OF THE MOMENTS OF INERTIA of the separate sections making up the com- pound section, with respect to an axis through the center of gravity of that section, by S/i. Formula (3) then becomes XIi = ^{I + Ah') (4) That is, to find the moment of inertia of any compound section made up of a number of smaller sections: (i) Find the moment of inertia of each of the smaller sections about an axis passing through its own center of gravity and parallel to the neutral axis of the compound section; (2) Multiply the area of each of the smaller sections by the square of the dis- tance between its center of gra\nty and the center of gravity of the whole figure; (3) Add the results found by (i) and (2) for the moment of inertia of the whole figure. For example, consider the cast-iron beam or lintel shown in section in Fig. 2; 340 Properties of Structural Shapes, etc. Chap. 10 (i) /of upper ilange-section / of web-section / of lower flange-section Total (2) Ah"^ for the upper flange Ah"^ for the web Ah^ for the lower flange Total = 4XiVi2 = M2 = 1X183/12 = 5832/12 = 16X1^12 = 1^2 = 5852/12 = 487.6 = 4X (12.5)== 625 = 18X32= 162 = 16 X (6.5)2 =676 = 1463 (3) Total of (r) and (2) = 487.6 + i 463 = /i of compound section = i 950.6 The moment of inertia of the cross-section of any compound beam, therefore, can generally be readily found by using the tables of properties of sections which ^-i?-A \ ¥^ -4-L II t -16- c ^L ) Zl___JL- Fig. 2. Moment of Inertia of Cross-section of Cast- iron Lintel give the numerical values of / for the various rolled shapes of which the beam is composed, with respect to the axis through the center of gravity. The Moment of Inertia of a Single-Web Girder-Section. Consider, for example, the single- web girder shown in section in Fig. 3, and made up of one \^ by 24-in web and four 4 hy 3 by H-in flange-angles with the long legs placed horizontally. Turn- ing to Table XI, the moment of inertia of the cross-section of one of these angles about an axis XX (2-2 "in the table) parallel to the long leg= 2.4, a:nd the distance of this axis from the back of the long leg {y in the table) = 0.83 in; hence A, the distance between the axis of the- angle-section and the axis of the girder-section = 12 — 0.83= 11. 17 in. A, from the table = 3,25 sq in. The moment of inertia of the cross-section of each angle about the axis of the girder, therefore, from Formula (3), is 7i = 2.4 -H 3.25 X (11.17)2 =» 407.9, and for the four angles = 1631.6. Since the axis of the cross-section of Fig. 3. Moment of Inertia of Cross-section of Plate Girder. No Flange-plates Properties of Structural Shapes, etc. 341 the web-plate is coincident with the axis of the section of the girder, its moment of inertia = hd?l\2 = HX (24)3/12 = 576. This may be found directly from Table I. page 346, Moments of Inertia of Rectangles. The moment of inertia, therefore, of the section of the compound girder = 163 1.6 4- 576 = 2207.6. The Moment of Inertia of a Section of a Compound Girder with Flange-Plates is found in the same way, except that the moments of inertia of the sections of the flange-plates with respect to the axis of the girder-section must be added to the moments of inertia of the cross-sections of the other members. The girder in Fig. 4 is com- posed of one 30 by %-m web-plate, four 5 by 4 by ^le-in angles, with the longer legs horizontal, and two 12 by V^-in flange-plates. /( = /]) for cross-section of web (from Table I, page 346) = 843.75 h for each angle-section = I i- Ah"^ (Formula 3) From Table XI, for each flange-angle, /= 6.6, A = 4.75 and the perpendicular distance from center of gravity to back of long leg= 1..10 in. Hence A= 15 — 1.10= 1390 in. /i = 6.6 + 4-75 X (13.90)2=924.35; and for four angles = 3 697.4. / for the cross-section of each flange-plate = 12 X i}AYl\2 = 0.125, ^ = 3'^ X 12 = 6 s(i in and /r = 15 -f- \i = 15.25 in. For each flange-plate, then, /i = 0.125 -f 6 X (15-25)^ = 1395-125; and for the two plates, 2 790.25. The moment of inertia for the cross-section of the whole girder, therefore, with reference to the horizontal axis passing through the center of gravity of the section = 843.75 + 3 697.4+ 2 790-25 = 7331.4- It will be noticed that the moments of inertia of the cross-sections of the flange-plates and angles about their own neutral axes is .so small, compared with their moments of inertia about the neutral axis of the girder-section, that they might be omitted without any appreciable error. Therefore, in calculating the moments of [^inertia for riveted girders, it is the custom of many engineers to let /i = Ah"^ for flange-plate and angle-sections. In that case, for the girder-section in Fig. 4, Fig. 4. Moment of Inertia of Cross- section of Plate Girder with Flange- plates / for web /i for angles = Ah"^ I\ for flange-plates = Ah^ = 843.75 = 3671.00 = 2 790.00 Moment of inertia of entire girder-section = 7 304.75 The Moment of Inertia of a Section of a Box Girder. Let the box girder shown in I'ig. 5 be composed of two % by 30-in webs, two 16 by H-in flange-plates and four 4 by 3 by Yi-ivi. angles with the long legs horizontal. 342 Properties of Structural Shapes, etc. Chap. 10 i— Fig. 5. Moment of Inertia of Cross-section of Plate-and-angle Box Girder / for each Dange-plate = hd^/12 = 16 X i}AYl\2 = 0.16; A = Yz X 16 in = 8 sq in and A = 15 + H = 15-25 in. /i = / + vlA^ = 0.16 + 8 X (15-25)' = 1 860.64; and for the two flange-plates, 3 721.28. / for each angle = 2.4, A = 3.25 and the distance from the back of the long leg to an axis through the center of gravity of the angle, parallel to the long leg = 0.83 in; so that h= 15 — 0.83 = 14.17 in. /i for the four angles is (4 X 2.4) -f (4 X 3.25) X (14-17)' = 2 619. / for each web (Table I, page 346) = 843.75 and for the two webs = I 687.5. The mo- ment of inertia, there- fore, for the entire girder-section = 3 721.28 -f 2 619 + 1687.5 = 8027.78. The Moment of Inertia of the Sec- tion of a Channel Box Column. Fig. 6 shows the cross- section of a column made up of two lo-in 15-lb channels, set 6.33 in apart, back to back, and two \^ by 12-in side plates. Let it be required to find the moment of inertia of the section about the two axes AB and CD. (i) Find the moment of inertia about the axis AB. /, for one of the side plates with respect to an axis through its own center of gravity and parallel to AB=i2X{}Ay/i2 = o.i2Sy .^_ A = y-iXi 2-in = 6 sq in and the distance of its center of gravity from ^5 is 5.25 in. Therefore, with respect to ^5,/i = 0.125 4-6 X (5.25)' = 165.5. The moment of inertia of a lo-in 15-lb channel with respect to an axis through its center of gravity and perpendicular to the web (Table VIII, page 359) = 66.9. Hence the moment of inertia of the whole column-section with respect to the axis AB = (2X165.5) +(2X66.9) = 464.8. (2) Find the moment of inertia about the axis CD. 7, for one of the side plates (Table I, page 346) = 72. 7, for one of the channels with respect to an axis parallel to the web = 2.30, A = 4.46 and the distance of the center of gravity from the back of the web = 0.64 in, approximately. Hence A = 3.165 -f 0.64 = 3.8 in. 7i =2.30-1- 4.46 X (38)2 = 66.7 and the moment of inertia of the whole column- section with respect to the axis CD= (2 X 72) + (2 X 66.7) = 277.4. -^:j- -}- r4 Fig. 6. Moment of Inertia of Cross-section of Plate- and-channel Box Column 45. jr IL. IT "C +2 ifi" Fig. 7. Moment of Inertia of Cross-section of Three- web Plate-and-angle Box Column Properties of Structural Shapes, etc. 343 The Moment of Inertia of the Section of a Heavy Plate-and-Angle Column. Fig. 7 shows the cross-section of one of the basement-columns in the Bankers' Trust Company Building, New York City. It is made up of six flange-plates, each 27 by H in section; two flange-plates, each 27 by iHe in; four flange-angles, each 6 by 6 by ^Me in; eight outer web-plates, each 18 by iHein; four web-angles, each 6 by 3^2 by i-Me in; and two middle web-plates each 18 by Yie in. What is its moment of inertia of the entire column-section with respect to the axis AB? I for each 27 by ^4-in flange-plate (Table I) = i 230.19 / for six 27 by -^-in flange-plates = i 230.19 X 6 = 7 381.14 / for each 27 by 1 lie-in flange-plate (Table T) = i 127.67 / for two 27 by iHs-in flange-plates =1 127.67 X 2 = 2 255.34 / for both flanges 9 G36.48 For the flange-angles (Table XIT, page 366) the area of a 6 by 6 by i^e-in angle = 10.37, its / with respect to an axis parallel to AB (Fig. 7) and passing through its center of gravity = 33.7 and the distance of this axis from the back of the leg = 1.84 in. Its Ii with respect to the axis ^J5 is found by Formula (3), page 338, /i = I -\- Ah^. h = 13.5 — (0.12 -h 4.16) = the distance from the axis AB to the parallel axis through the center of gravity of the angle = 9.22 in. Hence, substituting in Formula (3), /i = 33.7 + 10.37 X (9.22)2 = 915.15 I\ for the four flange-angles =915.15X4= 3 660.6c Each outer web is 4 x ^Me in = 2% in thick. Hence the I for each outer web about the horizontal axis through its center of gravity = 18 X (2.75)3/12 = 31.2. A = 18 by 2.75 in = 49.5 sq in. The distance from its center of gravity to the axis AB is 13.5 — (1.38 + 1.84 -\- 4.16 -f 0.12) = 6.01 or, say 6 in. From Formula (3), therefore, I\ = 31.2 -}- 49.5 X 6^ = i 813.2 and for both outer webs /i = i 813.2 X 2 = 3 626.4 For the four web-angles, from Table XI, page 363, the area of a 6 by ^M by ^Ms-in angle = 8.03, its / with respect to an axis through its center of gravity and parallel to the long leg = 6.9 and the dis- tance of this axis from the back of the long leg = 0.99 in. h, the horizontal distance between the two axes = ^e in, or 0.5625 in • (the thickness of one of the middle web-plates) -f- 0.99= T.55 in, approximately. Therefore, for one web-angle, from Formula (3), /i = 6.9 -I- 8.03 X (1.55)' =26.17 and for the four angles, /i = 26.17 X 4 = 104.68 The middle web-plates are together Me in X 2 = THin= 1.125 inthick. The/ ( = /i) for the two plates is 18 X (1.125)^12 = 2.14 The moment of inertia of the entire column-section for the axis A B is, therefore, the sum of these moments of inertia for the differ- ent parts: 7i for the eight flange-plates 9 636.48 I\ for the four flange-angles 3 660.60 1^1^. I\ for the eight outer web-plates 3 626.40 B| /i for the four web-plates 104 68 ^ptt /i for the middle web-plates 2.14 K The moment of inertia for the entire section 17 030.3? 344 Properties of Structural Shapes, etc. Chap. 10 5. Radii of Gyration of Compound Sections The Radius of Gyration of any Compound Section may be found from Formula (2), page 333, by dividing the moment of inertia of the section by the total area of the section and taking the square root of the quotient. Thus, the radii of gyration of the channel-column section shown in Fig. 6, about the axes A B and CD, are found as follows: xi = (the sum of the areas of two \^ by i2-in plates, or 12 sq in) -f (the sum of the areas of the two channels, or 8.92 sq in) = 20.92 sq in. / about AB = 464.8 and about CD = 277.4. Therefore, f , with respect to the axis A B = and n, with respect to the axis CD = = 4.71 = 3.68 Since n is the smaller, iL is the value to be used in the column-formula. It is to be noted that this value of r agrees with the r of the lo-in channel-column in Table XXV, on page 533. The value of n does not, however, agree exactly with the n in the same table, the variation being caused by a difference in the spacing of the channels, back to back. The Least Radius of Gyration of a Section of a Plate-and-Angle Column. As another example, let it be required to find the least radius of gyration of the cross-section of the plate-and- angle column shown in Fig. 8, made up of one ^/i by i2-in web-plate, two ^i by 12-in side plates and four 4 by 4 by l^i-'m angles. (i) Find the moment of inertia about the axis AB. For the axis AB, I for each one of the side plates with respect to an axis through its own center of gravity and parallel to the axis A B = 12 X (^i)Vi2 = C.05. A = %X 12 = 4.5 sqinand h = 6^6 in. /i = 0.05 -I- 4.5 X (6fl6)2 = 172.33. / for each one of the angles with respect to an axis through its center of gravity and parallel with the flange-leg is 5.6, A = 3.75 and the dis- tance of the center of gravity from the back of. the flange of the angle = 1.18. Hence, A = 6 in — 1. 18 in = 4.82 in and h for each angle = 5.6 + 3-75 X (4-82)2= 92.71. / for the web-plate =« 54. The moment of inertia of the whole column-section, therefore, about the axis AB = (2 X 172.33) + (4 X 92.71) + 54 = 769.5c. (2) Find the moment of inertia about the axis CD. I for each side plate = 54. / for each angle =5.6 and A for each angle = 3.75. The -distance of the center of gravity of each angle from the back of the flange of the angle = 1. 18 in and hence, h = 1.18 in-f y\& in = 1.36 in, approximately, h for each angle = 5.6 +3.75 X (1.36)2=12.54. / for each web-plate = 0.05. Themoment of inertia of the whole column-section, therefore, about the axis CD = (2 X 54) + (4X 12.5.1) -h 0.05 = 158.21. Since this is the least moment of inertia the least radius of gyration will like- wise be about the axis CD. The area of the cross-section of the column = (4 X 3.75, the area of the angles)-}- (3 X 45, the area of each plate) = 28.5. f'=3 158.21/28.S = 5.55 and r, the least radius of gyration =2.35. Fig. 8. Least Radius of Gyra- tion of Cross-section of Plate- and -angle Column Moment of Inertia Determined Graphically 345 The Radius of Gyration of the Cross-Section of a Hollow Rectangular Column. As another example, let it be required to find the radius of gyration of the cross-section of a hollow rectangular cast iron column with outside dimen- sions 6 by 6 in and with a shell H in thick. (See figures and formulas for hol- low squares and rectangles, page ^35.) A = 6"^ - (5.5)2 = 36 - 30 25 = 5.75 sq in. / = (b'P-bibi^)/j2 = [64- (5.5)Vi2 = (i 296- 9io)/i2 = 386/12 = 32.2. f2== 32.2/5.75 = 5.6 and r = 2.37 in. The radii of gyration of round-section columns and square-section columns, varying from 2 to 20 in in diameter and of metal varying from H to 2 in thick, are given in Tables II and III, see pages 348 to 351. For example: the radius of gyration of a 6 by 6-in square-section cast-iron column with a shell J-i in thick, is, from Table III, 2.35 in. 6. Graphical Method of Determining the Moment of Inertia of Plane Figures * The Moment of Inertia may be Determined Graphically as follows: Divide the shape in question, Fig. 9,t into strips parallel to BC. Through the centers of gravity of the strips draw indef- inite hues /i, Jo, etc. Along a line ab lay off lengths/;, /2, etc., pro- portional respectively to areas /i, fz, etc. When the strips are narrow and of equal width, each strip may be assumed propor- tional to the length of the strip measured through its center of gravity. Through a and b draw lines at 45° with ab to deter- mine the pole 0, from which the rays Od, Oe, etc. are drawn. Con- Fig- ^' Graphical Determination of Moments of Inertia t struct the equilibrium-polygon ^'.?/. (See page 296.) A line sS parallel to BC will be a gravity- axis. The moment of inertia about this axis is equal to the area of the given figure ABC multiplied by the area of the polygon gsf. The square root of this area gsf is the radius of gyration of the figure ABC with regard to the axis sS. A graphic method especially adopted to irregular figures is given in detail in Goodman's Mechanics Applied to Engineering. See, also, Merriman's American Civil Engineers' Handbook. * From notes by Robins Fleming. t Figure from Ott's Graphic Statics (Clark's Translation, London, 1876). Church's Notes and Examples in Mechanics. See, also, 346 Properlies of Structural Shapes, etc. Table I.* Moments of Inertia of Rectangles i ^ Neutral axis through center and normal to depth Depth in inches Widths of rectangles in inches H Me H Me Vz Me % 2 O.I7 0.21 0.25 0.29 0.33 0.38 0.42 3 0.56 0.70 0.84 0.98 1. 13 1.27 1. 41 4 1-33 1.67 2.00 2.33 2.67 3.00 3.33 5 2.60 3.26 3.91 4.56 5.21 5.86 6.51 6 4. SO 5.63 6.75 7.88 9.00 10.13 11.25 7 7. IS 8.93 10.72 12.51 14.29 16.08 17.86 8 10.67 13.33 16.00 18.67 21.33 24.00 26.67 9 IS. 19 18.98 22.78 26.58 30.38 34.17 37.97 lO 20.83 26.04 31.25 36.46 41.67 46.87 52.08 II 27 -73 34.66 41.59 48.53 55.46 62.39 69.32 12 36.00 4500 54.00 • 63 00 72.00 81.00 90.00 13 45-77 57.21 68.66 80.10 91.54 102.98 114.43 14 57.17 71.46 85.7s 100.04 114.33 128.63 142.92 IS 70.31 87.89 105.47 123.05 140.63 158.20 175.78 i6 85.33 106 . 67 128.00 149.33 170.67 102.00 213 33 17 102.35 127.94 153 53 179.12 204.71 . 230.30 255.89 18 121.50 151.88 182.25 212.63 243.00 273.38 303.7s 19 20 142.90 178.62 214.34 250.00 250.07 291.67 285.79 333.33 321.52 375.00 357-24 416.67 166.67 208.33 21 192.94 241.17 289.41 337.64 385.88 434.11 482.34 22 221.83 277.29 332.75 38S.21 443.67 499.13 554.58 23 253.48 316.8s 380.22 443.59 506.96 570.33 633.70 24 288.00 360.00 432.00 504.00 576.00 648.00 720.00 25 325.52 406 . 90 488.28 569.66 651.04 732.42 813.80 26 366.17 457.71 549.2s 640.79 732.33 823.88 915.42 27 410.06 512. 58 615.09 717.61 820.13 922.64 1025.16 28 457.33 571.67 686.00 800.33 914.67 1029 . 00 1143.33 29 508.10 635.13 762.16 889.18 1016.21 1143.23 1270.26 30 562.50 703.13 843.7s 984.38 1125.00 1265.63 1406 25 32 682.67 853 .33 1024 . 00 1194.67 1365.33 1536.00 1706.67 ^ 818.83 1023.54 1228.25 1432.96 1637.67 1842.38 2047.08 36 972.00 1215.00 1458.00 1701.00 1944.00 2187.00 2430 . 00 38 I143.17 1428.96 1714.75 2000.54 2286.33 2572.13 2857 92 40 1333.33 1666.67 2000.00 2333.33 2666.67 3000.00 3333.33 42 1543.50 1929 38 2315.25 2701.13 3087.00 3472.88 3858.75 44 1774.67 2218.33 2662 . 00 3105.67 3549.33 3993.00 4436.67 46 2027.83 2534. 79 3041.7s 3548.71 4055.67 4562.63 S069.58 48 2304.00 2880.00 3456.00 4032.00 4608 . 00 5184.00 5760.00 SO 2604.17 3255.21 3906.25 4557.29 5208.33 5859.38 6510.42 S2 2929.33 3661.67 4394.00 5126.33 5858.67 6591 00 7323.33 54 32B0.50 4100.63 4920.75 5740.88 6561.00 7381 . 13 8201 . 25 S6 3658.67 4573.33 5488.00 6402.67 7317.33 8232 . 00 9146.67 58 4064.83 50S1.04 6097.25 7113.46 8129.67 9145.87 10162.08 6o 4500.00 5625.00 6750.00 7875.00 9000 . 00 10125.00 11250.00 * This table may be used in computing the moments of inertia of plate girders, columns and other compound sections in which plates are used. See pages 341 and 342. Properties of Structural Shapes, etc. §47 Table I* (Continued). Moments of Inertia of Rectangles Neutral axis through center and normal to depth Depth Widths of rectangles in inches inches iHe .... 1 ,..> H 1^6 li iMe 2 3 4 0.46 1. 55 3.67 0.50 1.69 4.00 0.54 1.83 4-33 0.58 1.97 4.67 0.6: , a. I] S-oc J 0.67 C 2.25 ) 5:33 5 6 7 8 9 7.16 12.38 19.65 29.33 41.77 7.81 13.50 21.44 32.00 45. 56 8.46 14.63 23.22 34.67 49.36 9. II 15.75 25.01 37.33 53.16 97' 16. 8i 26.8c 40. a 56.9! r 10.42 i 18.00 ) 28.58 ) 42.67 > 60.75 10 II 12 13 14 57.29 76.26 99.00 125.87 157.21 62.50 83.19 108.00 137.31 171.50 67.71 96.12 117.00 148.75 185.79 72.92 97.0s , 126.00 160.20 200.08 78.1: 103.9^ 135.0c 171.6^ 214. 3i \ 83.33 \ 110.92 ) 144. CX3 [ 183.08 5 228.67 17 i8 19 193.36 234.67 281.47 334-13 392.96 210.94 256.00 307.06 364.50 428.69 228.52 277.33 332.65 394.88 464.41 246.09 298.67 358.24 425.2s 500.14 263.6' 320. a 383.8: 455.6: 535. 8( r 281.2s > 341.33 \ 409.42 J 486.00 ) 571.58 20 21 22 23 24 458.33 530.58 610.04 697.07 792.00 500.00 578.81 665.30 760.44 864.00 541.67 627.05 720.96 823.81 936.00 583.33 675.28 776.42 887.18 1008.00 62s. oc 723.52 831.8' 950.55 1080. oc ) 666.67 771.75 r 887.33 1013.92 ) 1152.00 25 26 27 28 29 895.18 1006.96 1127.67 1257.67 1397.29 976.56 1098.50 1230.19 1372.00 1524 31 1057. 94 1190.04 1332.70 1486.33 1651.34 1139. 32 1281.58 14.35. 22 1600.67 1778.36 1220.7c 1373 i: 1537.7: 171S.0C 1905.35 } 1302.08 \ 1464.67 5 1640.25 ) 1829.33 } 2032.42 30 32 34 36 38 1546.88 1877.33 2251.79 2673.00 3143.71 1687.50 2048 . 60 2456.50 2916 00 3429-. 50 1828.13 2218.67 2661.21 3159.00 3715.29 1968.75 2389.33 2865.92 3402 . 00 4001.08 2109. 3J 2560. oc 3070.6: 3645.0c 4286. 8i 5 2250.00 ) 2730.67 5 3275.33 ) 3888.00 i 4572.67 40 42 44 46 48 3666.67 4244.63 4880.33 5576.54 6336.00 4000 . 00 4630.50 5324 00 6083.50 6912.00 4333.33 5016.38 5767.67 6590 . 46 7488.00 4666.67 5402 . 25 6211.33 7097.42 8064.00 5000.0c 5788. i: 6655. oc 7604. 3^ 8640.0c > 5333.33 J 6174.00 5 7098.67 5 8111.33 ) 9216.00 50 52 54 56 58 6o 7161.46 8055.67 9021.38 10061.33 11178.29 12375.00 7812.50 8788.00 9841 . 50 10976.00 12194.50 13500.00 8463.54 9520.33 10661.63 11890.67 13210.71 14625.00 9114.58 10252.67 11481.75 12805.33 14226.92 15750.00 9765.6. 10985 . oc I230I.8J 13720. oc 15243.12 16875. oc J 10416.67 ) 11717.33 I 13122.00 ) 14634.67 I 16250.33 ) 18000.00 * This table may be used in cor npiiting tl le moments of inertia of plate girders. columns and other compound sections in which plates are used- See pages 341 and 342. 348 Properties of Structural Shapes, etc. Chap. 10 Table II.* Areas and Radii of Gyration of Hollow-Round Sections ""^ ^ Area = ~ — - — - = 0.7854 {D^ - rf*) Bq in Radius of gyration V£)2 + 2 - 2 _ rf2) sq In Diam. D, inches A and r Thickness ( in inches ^% iH iH \\h. iH i3/4 1^/i 2 2 A r 3 A Y 4 A r 5 A r . k 6 A r 7 A r 20.76 . 2.12 22.58 2.08 8 A r 24.30 2.46 26.51 2.43 28.62 2.39 30.63 2.36 9 A r 27.83 . 2.81 50.43 2.78 32.94 2.74 35.34 2.70 37.65 2.67 39.86 2.64 10 A ' r 31.37 . 3.16 J4.36 3.13 37.26 3.09 40.06 3.0s 42.76 3.02 45.36 2.98 47.86 2.9s 50.27 2.92 II A r 34.90 . 3.51 58.29 3.48 41.58 3.44 44.77 3.40 47.86 3.36 50.8s 3.33 S3. 75 3.29 56.5s 3.26 12 A r 38.44 ^ 3.87 ti.22 3.83 45.90 3.79 49.48 3.75 52.97 3.71 56.3s 59.64 3.64 62.83 3.61 13 A r 41.97 ^ 4.22 ^6.14 4.18 50.22 4.14 54.19 4.10 58.07 4.06 61.85 4.03 65.53 5.99 69.12 3.95 14 A r 45.50 . 4.57 50.07 4.53 54.54 4.49 58.91 4.45 63.18 4.41 67.35 4.38 71.42 4.34 75.40 4.30 IS A . r 49-04 . 4.92 54.00 4.88 58.86 4.84 63.62 4.80 68.28 4.76 72.8s 4.73 77.31 4.69 81.68 4.65 16 A r 52.57 . 5.27 57.92 5.23 63.18 5. 19 68.33 5.15 73.39 5. II 78.34 5.08 83.20 S.04 87.97 5.00 17 A r 56.11 ( 5.63 51.85 5.59 67.50 5-55 73.04 5.51 78.49 5.47 83.84 5.43 89.09 539 94.25 535 18 A r 59.64 < 5.98 35.78 5.94 71.82 5.90 77.75 5.86 83.60 5.82 89.34 5.78 94.98 S.74 100.53 5. 70 19 A r '63.18 ( 6.33 59.70 6.29 76.13 6.25 82.47 6.21 88.70 6.17 94.84 6.13 100.87 6.09 106.82 6.0s 20 A r 66.71 ' 6.69 ^3.63 6.64 80.45 6.60 87.18 6.56 93.81 6.52 100.33 6.48 . 106.77 6.44 113. 10 6.40 * From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. 360 Properties of Structural Shapes, etc; Chap. 10 T^ible m.* Areas and Radii of Gyration of Hollow-Square Sections Area = {D^ - d^) sq, in Radius of gyration = V/- /Z)2 + fiP. Side inches A and r Thickness in inches H Me H \^ % H H 1 2 A 1.75 2. II r 0.72 0.70 3 A r 2.75 1. 13 3.36 1. 10 .... 4 A r 3.75 1.53 4.61 1.51 5-44 1.49 7.00 1.44 5 A r 4.7s i.94 5.86 1.92 6.94 9.00 1.85 10.94 1.80 12.75 1.76 6 A r 5. 75 2.35 7. II 2.33 8.44 2.30 11.00 2.25 13.44 2.21 15-75 2.17 17 2 .94 .12 20.00 2.08 7 • A r 6.75 2.76 8.36 2.73 9-94 2.71 13-00 2.66 IS. 94 2.62 18.75 2.57 21 2 .44 ■ 53 24.00 2.48 8 A r 7.75 3.17 9.61 3.14 11.44 3.12 15.00 3.07 18.44 3.02 21.7s 2.98 24 2 -94 .93 28. ©0 2.89 9 A r 8.75 3.57 10.86 355 12.94 3. S3 17.00 3.48 20.94 3.43 24.7s 3.38 28 3 -44 .34 32.00 3.29 10 A r 9.75 3.98 12. II 3.96 14.44 3.93 19.00 3.88 2344 3.84 27.7s 3.79 31 3 .94 .74 36.00 3.70 II A r 10.75 4.39 13.36 4.37 IS. 94 4.34 21.00 4-29 25. 94 4-24 30.75 4.20 35 4 44 15 40.00 4.10 12 A ■ r 11.75 4.80 14.61 4.77 17.44 4. 75 23-00 4.70 28.44 4- 65 33.75 4.60 38 4 '^ 44.00 4. SI 13 A r 12.75 5.21 15.86 5. 18 V.l 25.00 5. 11 30.94 5.06 36.7s 5. 01 42 4 U 48.00 4.92 14 A r 13.75 5.61 17. II 5.59 20.44 5.56 27.00 5.51 33.44 5. 47 39.75 5.42 1 94 37 52.00 5-32 IS A r 14.75 6.02 18.36 6.00 21.94 5-97 29-00 . 5.92 35-94 5-87 42.7s 5. 83 49 5 44 78 56.00 5. 73 i6 A r 15.75 6.43 19.61 6.41 23.44 6.38 31.00 6.33 38.44 6.28 45.75 6.23 52 6 94 19 60.00 6.14 17 A r 16.75 6.84 20.36 6.81 24-94 6.79 33.00 6.74 40.94 6.69 48.75 6.64 56 6 44 59 64.00 6.54 i8 A r 17.75 7.25 22.11 7.22 26.44 7.20 35.00 7.15 43.44 7.10 51.75 7.05 59 7 94 00 68.00 6.95 19 A r 18.7s 7.66 23.36 7.63 27.94 7.61 37.00 7.56 45-94 7. SI 54.75 7.46 63 7 44 41 72.00 7.36 20 A r 19.7s 8.06 24.61 8.04 29.44 8.01 3900 7.96 48.44 7.91 57.75 7.87 66 7 94 82 76.00 7.77 * From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. Properties of Structural Shapes, etc. 351 Table ni * (Continued). Areas and Radii of Gyration of Hollow-Square Sections 'mmm::"\ Area - (D« - rf2) sq in Radius of gyration = 1/ • — in V 12 Side inches X Thickness i in inches 1 Y iH iH 1% i'/^ 1% m iH 2 2 A Y 3 A r 4 A Y •• 5 A Y 6 A Y 7 A '. j6.44 28.75 Y 2.44 2.40 8 A Y JO. 94 2.84 33.75 2.80 36.44 2.76 39.00 2.72 9 A Y J5.44 3.2s 38.75 3.20 41.94 3.16 45.00 3.12 47.94 3.08 50.75 3.0s 10 A Y 1;i^ 43-75 3-61 47.44 3.57 51.00 3.52 54.44 3.48 57.7s 3-44 60.94 3.40 64.00 3.37 II A Y U.44 4.06 48.75 4.01 52.94 3.97 57.00 3.93 60.94 3.88 64.75 3.84 68.44 3.80 72.00 3-76 12 A Y 18.94 4.46 53.75 4-42 58.44 4-37 63.00 4-33 6744 4.29 71-75 4-25 75.94 4.20 80.00 4.16 13 A Y 53.44 4.87 58 75 4.82 63.94 4.78 69.00 73.94 4.69 78.7s 4.65 83.44 4.61 88.00 4.56 4.74 14 A Y 57-94 5-28 63-75 5-23 69.44 5. 18 75.00 5-14 80.44 5.10 85.75 5.05 90.94 5.01 96.00 4-97 15 A Y 52.44 5.68 68.75 5.64 74.94 5.59 81.00 5.55 86.94 5.50 92.75 S.46 98-44 5.41 104.00 5.37 i6 A Y 66.94 6.09 73 75 6.04 80.44 6.00 . 87.00 5,95 93.44 5.91 lii 105.94 5.82 112.00 5.77 17 A Y 71.44 6.50 78.75 6.45 85.94 6.40 93. CO 6.36 99-94 6.31 106.75 6.27 113.44 6.23 120.00 6.18 i8 A Y 75-94 6.90 83.75 6.86 91-44 6.81 1:?? 106.44 6.72 113.75 6.67 '1;il 128.00 6.58 19 A Y 80.44 7-31 88.75 7.26 96.94 7.22 105.00 7.17 112.94 7.12 120.75 7.08 128.44 7.03 136.00 6.99 20 A Y 84-94 7-72 '\l 102 . 44 7 62 III. 00 7.58 119-44 7.53 127.75 7.49 135.94 7.44 144-00 7.39 * From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. 352 Properties of Structural Shapes, etc. Chap. 10 7. Dimensions, Moments of Inertia, Radii of Gyration and Section- Moduli of Standard Structural Shapes Explanation of Tables. As in using structural -steel shapes the choice is practically confined to such shapes as are rolled by the mills, it is essential to have at hand the dimensions and properties of those shapes in order to calcu- late the necessary sizes to meet special requirements for strength and practical conditions of economy and framing. Since 1890 great changes have been made both in the materials and in the shapes of the standard sections. The roUing- mills which manufacture the most complete assortment of structural shapes are those of the Carnegie Steel Company, the Cambria Steel Company, the Jones & Laughlin Steel Company and the Bethlehem Steel Company. In general, the products of these mills, especially beams and channels, are respectively similar in shape. This is particularly true of the shapes rolled by the first three of the companies named. The standard steel beams and channels considered in the following pages are rolled by all of these mills, with the exception of those of the Bethlehem Steel Company. With a few exceptions the following tables of properties of stand- ard structural shapes have been adopted by permission from the Pocket Companion of the Carnegie Steel Company. It may be well to state that the tables of properties for the various structural shapes, published by the companies named above, do not agree exactly, even for the same weights, but the differences are not of practical importance. The tables of the Cambria Steel Company and of the Carnegie Steel Company for beams and channels agree more closely. As angles are very extensively used foi a great many purposes, the properties are given for all sizes rolled and also a table showing from which mills the different sizes may be obtained. Natur- ally it will generally be advantageous to use a size that is rolled by several mills. Tables XV, XVI and XVII will be found very convenient when computing the strength of struts formed of pairs of angles, and Table XVIII when com- puting the same for pairs of channels. Standard Steel Beams and Channels.* Common Dimensions STRUCTURAL BEAMS A.A.S.M. STANDARD SECTIONS ^t n = minimum web » t ~~ R = minimum web -\- o.io" r = Vio minimum web h = distance between flange- fillets Slope of flange, 1:6= i6%% = 9° 27' 42" • From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. Properties of Structural Shapes, etc. 353 STRUCTURAL CHANNELS A.A.S.M. STANDARD SECTIONS T n = minimum web = / R = minimum web +0.10" r = Mo minimum web Slope of flange, 1:6= 16%% = 9° 27' 42'' Dimensions for Structural Beams are those adopted by the Association of American Steel Manufacturers and apply to all Structural Beams, except American Standard Sections B i, B 2 and B 3, also Sections B 24 and B 81. The dimensions of the Supplementary Beams, B 61 to B 68, inclusive, cannot be readily reduced to formulas. Slope of flange is i : 11 = 5° 11' 40". Dimensions for Structural Channels are those adopted by the Association of American Steel Manufacturers and apply to all Structural Channels, except Section C 20, the 13-in sizes, which are Car Building Channels. 354 Properties of Structural Shapes, etc. Table IV.* Properties of I-Beam Sections |2^ Chap. 10 Sec- tion- index Depth of beam Weight iK>t Area of sec- tion Width of flange Thick- ness of web Axis I -I Axis 2-2 / r I-/C / r I/c in lb sq in in in in* in in3 in* in in3 B6i 27 90.0 26.33 9.000 0.524 2958.3 10.60 219. 1 75.3 1.69 16.7 B.4 24 1150 IIO.O 105.0 33.98 32.48 30.98 8.000 7.938 7.87s 0.750 0.688 0.625 2955. 5 2883.5 2811.5 9.33 9-42 9.53 246.3 240.3 234.3 83.2 81.0 78.9 1.57 1.58 1.60 20.8 20.4 20.0 B I 24 100. 950 90.0 85.0 80.0 29.41 27.94 26.47 25.00 23.32 7.254 7.193 7.131 7.070 7.000 0.754 0.693 0.631 0.570 0.500 2379.6 2309 2238.4 2167.8 2087 . 2 9.00 9.09 9.20 9-31 9.46 198.3 192.4 186.5 180.7 173.9 48.6 47.1 45.7 44-4 42.9 1.28 1.30 1.31 1-33 1-36 13-4 13.1 12.8 12.6 12.3 B62 24 740 21.70 9.000 0.476 1950. I 9.48 162.5 61.2 1.68 13.6 B63 21 60.5 17.68 8.250 0.428 1235.5 8.36 117. 7 43.5 1-57 10.6 B 2 20 100. 9S.O 9.00 85.0 80.0 29.^^1 27.94 26.47 25.00 23.73 7.284 7.210 7.137 7.063 7.000 0.884 0.810 0.737 0.663 0.600 1655.6 1606.6 1557.6 1508.5 1466.3 7.50 7.58 7.67 7-77 7.86 165.6 160.7 155-8 150.9 146.6 52.7 50.8 49 -o 47.3 45.8 1-34 1.35 1.3© 1.37 1.39 14.5 14.1 13.7 13.4 13.1 B 3 20 7S.O 70.0 65.0 22.06 20.59 19.08 6.399 6.325 6.250 0.649 0.575 0.500 1268.8 1219.8 1169.5 7.58 7.70 7.83 126.9 122.0 117. 30.3 29.0 27.9 1.17 1. 19 I. 21 9.5 9. 2 8.9 B8r 18 90.0 85.0 80.0 7S.O 26.47 25.00 23.53 22.05 7 . 245 7.163 7.082 7.000 0.807 0.725 0.644 0.562 1 260 . 4 1220.7 1181 .0 1141.3 6.90 6.99 7.09 7.19 T40.0 135-6 131. 2 126.8 52. 50.0 48.1 46.2 1.40 1.42 1.43 1.45 14.4 14.0 13.6 13.2 B80 18 70.0 65.0 60.0 SS.o 20.59 19.12 17.65 15.93 6.259 6.177 6.095 6.000 0.719 0.637 0.555 0.460 921.2 881.5 841.8 795-6 6.60 6.79 6.91 7.07 102.4 97-9 93-5 88.4 24.6 23.5 22.4 21.2 1.09 I. II 1. 13 1. 15 1:1 7.3 7.1 B64 18 48.0 14.08 7.500 0.380 737.1 7.23 81.9 30.0 1.46 8.0 B S IS 7S.O 70.0 65.0 60.0 22.06 20.59 19.12 17.67 6.292 6.194 6.096 6.000 0.882 0.784 0.686 0.590 691.2 663 . 7 636.1 609.0 5.60 5.68 5-77 5.87 92.2 88.5 84.8 8l.2 30.7 29.0 27.4 26.0 1. 18 1. 19 1.20 I. 21 9.8 9.4 1° B 7 IS SS-O So.o 450 42.0 16.18 14.71 13.24 12.48 5. 746 S.648 5.555 S.soo 0.656 0.558 0.460 0.410 511. 483.4 455-9 441.8 5.62 5.73 5.87 5. 95 68.1 64.5 60.8 58.9 17. I 16.0 151 14.6 1.02 1.04 1.07 1.08 5.9 5.7 5.4 5.3 B65 15 37.5 10.91 6.7SO 0.332 405.5 6.10 54. 1 19.9 1.35 5.9 Note. The [exponential figures used with / and I/c denote the mathematical " dimen- sions" of these qualities, that is, the number of times the linear unit appears as a factor in the quantities. • From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. Properties of Structural Shapes, etc. 355 Table IV* (Continued). Properties of I-Beaiu Section -1 Sec- tion- index Depth of beam Weight foot Area of section Width of flange Thick- ness of web Axis I- [ Axis 2-2 / r I/c in3 / r in3 in lb sq in in in in« m in< in 1.04 III, 1.08 B 8 12 55-0 50.0 45-0 40.0 16.18 14/1 13 M 11.84 5. 611 5.489 5.366 5.250 0.821 0.699 0.576 0.460 321.0 303.4 285.7 269.0 4.45 4.54 4.65 4.77 53.5 50.6 47-6 44.8 17.5 16. 1 14-9 13.8 6.2 .5-9 ; 5-6 ; S.3 ' B 9 B66 12 12 35.0 31.5 28.0 10.29 9.26 8.15 5.086 5.000 0.436 0.350 228.3 215.8 4.71 4.83 4.95 38.0 36.0 33.2 10. 1 9.5 12.6. ; 0.99 I.OI 1.24 4-0 1 3.8 ! , 4.2 6.000 0.284 199.4 Bii 10 40.0 350 30.0 25.0 11 .76 10.39 8.82 7.37 5.099 4.952 4.805 4.660 0.749 c . 602 0.455 0.310 158 7 146.4 134-2 122.1 3.67 3-77 3.90 4.07 31.7 29.3 26.8 24.4 Vs 7.7 6.9 0.90 91 0.93 0.97 3 7 3 4 3.2 3.0 B67 10 22.25 6.54 5.500 0.252 113 6 4.17 22.7 9.0 1.17 3.3 B13 9 35.0 30.0 25.0 21.0 10. 29 8.82 7.35 6.31 4.772 4.609 4.446 4.330 0.732 0.569 0.406 0.290 III. 8 101. q 91.9 84.9 3.29 3.40 3.54 3.67 24.8 22.6 20.4 18.9 1:1 5.7 5.2 0.84 0.85 0.88 90 i.l 2.5 2.4 B15 8 25-5 23.0 20.5 18.0 7.50 6.76 6.03 5.33 4.271 4.179 4.087 4.000 0.541 0.449 0.357 0.270 68.4 64.5 60.6 56.9 3.02 3.09 3.17 3.27 17 I 16.1 15.2 14.2 4.8 4.4 4.1 3.8 0.80 0.81 0.82 0.84 2.2 2.1 2 o- 1-9 B68 8 17.5 5.12 5.000 0.220 58 4 3.38 14.6 6.2 1. 10 2-5 B17 7 20.0 17.5 15.0 5.88 5. 15 4.42 3.868 3.763 3.660 0.458 0.353 0.250 42.2 39.2 36. ~ 2.68 2.76 2.86 12. 1 11 .2 10.4 3.2 2.9 2.7 0.74 0.76 0.78 1-7 1.6 1.5 B 19 6 17.25 14.75 12.25 5.07 4-34 3.61 3.575 3.452 3.330 0.475 0.352 0.230 26.2 24.0 21.8 2.27 2.35 2.46 8.7 8.0 7.3 2.4 2.1 1.9 0.68 0.69 0.72 1.3 1.2 1 .1 B21 5 14.75 12.25 9.75 4.34 2:87 3.294 3.147 3.000 0.504 0.357 0.210 15.2 13.6 12. 1 1.87 1.94 2.05 6.1 1-7 1.5 1.2 0.63 0.63 0.65 i.o 0.92 0.82 B23 4 10.5 9.5 8.5 7.5 3.09 2.79 2.50 2.21 2.880 2.807 2 . 733 2.660 0.410 0.337 0.263 0.190 7.1 6.8 6.4 6.0 1.52 1.55 1.59 1.64 3.6 3-4 3.2 3.0 1 .0 0.93 0.85 0.77 0.57 0.58 0.58 0.59 0.70 0.66 0.63 0.58 B77 3 7.5 6.5 5-5 2. 21 1.63 2.521 2.423 2.330 0.361 0.263 0.170 2.9 2.7 2.5 I. IS 1.19 1.23 1.9 1.8 1.7 0.60 O.S3 0.46 0.52 O.S2 O.S3 0.48 0.44 0.40 See "Note" with table on preceding page. • From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. 356 Properties of Structural Shapes, etc. Table V.* Properties of H-Beam Sections Chap. 10 These may be employed as. columns, using the axis 2-^ Sec- Depth of Weight Area of Width of Thick- Axis i-i Axis 2-2 per ness tion- beam foot seclrion flange of web T r T/r. T r I/c index in* in 1.87 in3 8.8 in lb sqin in in in* in in3 H4 8 34.0 10.00 8.0 0.375 IIS. 4 3.40 28.9 3S.I H3 6 23.8 7.00 6.0 0.313 4S.I 2.S4 ISO 14.7 1.45 4.9 H 2 5 18.7 5-50 SO 0.313 23.8 2.08 9-5 7.9 1.20 31 Hi 4 13.6 4.00 4.0 0.313 10.7 1.63 5.3 3.b 0.95 1.8 See " Note " with Table IV, page 354. ♦ From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. Properties of Structural Shapes, etc. 357 Table VI.* Properties of Bethlehem I-Beam Sections Depth of beam Weight per . foot Area of section Thick- ness of web Width of flange Increase of web and flange for each lb increase of weight Neutral axis perpendicular to web at center Neutral axis coin- cident with center line of web / r I/c / r in lb sq in in in in in< in in3 in* in 30 120.0 35-30 0.540 10.500 o.oio 5239 .6 12.18 349-3 165.0 2.16 28 105.0 30.88 0.500 10.000 O.OII 4014. I 11.40 286.7 131 -5 2.06 26 90.0 26.49 0.460 9500 O.OII 2977.2 10.60 229.0 101.2 1.9s 24 84.0 24.80 0.460 9-250 0.012 2381.9 9.80 198. 5 91. 1 1.92 24 83.0 24 59 0.520 9-130 0.012 2240 . 9 9.S5 186.7 78.0 1.78 24 73.0 21.47 0.390 9.000 0.012 2091.0 987 174.3 74.4 1.86 20 82.0 24.17 0.570 8.890 0.015 1559-8 8.03 156.0 79.9 1.82 20 72.0 21.37 0.430 8.750 0.015 1466.5 8.28 146.7 75.9 1.88 20 69.0 20.26 0.520 8.145 0.015 1268.9 7-91 126.9 51.2 1.59 20 64.0 18.86 0.450 8.075 0.015 1222. I 8.05 122.2 49.8 1.62 20 S90 17.36 0.375 8.000 0.015 1172.2 8.22 117. 2 48.3 1.66 18 S90 17.40 0.49s 7.675 0,016 883.3 7.12 98.1 39.1 I. SO 18 S4.0 IS. 87 0.410 7.S90 0.016 842.0 7.28 93.6 37.7 1.54 18 52.0 IS. 24 0.375 7 -555 0.016 825.0 7-36 917 37.1 1.56 18 48. 5 14.2s 0.320 7-500 0.016 798.3 7.48 88.7 36.2 1. 59 IS 71.0 20.95 0.520 7.500 0.020 796.2 6.16 106.2 61.3 1.71 IS 64.0 18.81 0.605 7.195 0.020 664.9 S.9S 88.6 41.9 1.49 IS S40 15.88 0.410 7.000 0.020 610.0 6.20 81.3 38.3 1. 55 15 46.0 13.52 0.440 6.810 0.020 484.8 S.99 64.6 25.2 1.36 IS 41.0 12.02 0.340 6.710 0.020 456.7 6.16 60.9 24.0 1. 41 IS 38.0 11.27 0.290 6.660 0.020 442.6 6.27 59.0 23.4 1.44 12 36.0 10.61 9.44 0.310 0.335 6.300 6.205 0.025 0.025 269.2 228.5 5. 04 4.92 44.9 38.1 21.3 16.0 1.42 1.30 12 32.0 12 28. 5 8.42 0.250 6.120 0.025 216.2 5.07 36.0 15.3 1.35 10 28.5 8.34 0.390 S.990 0.029 134.6 4.02 26.9 12. 1 1. 21 10 23. S 6.94 0.250 5. 850 0.029 122.9 4.21 24.6 II. 2 1.27 9 24.0 7.04 0.365 5-555 0.033 92.1 3.62 20. 5 8.8 1. 12 9 20.0 6.01 0.250 5.440 0.033 85.1 3.76 18.9 8.2 1. 17 8 19s 5. 78 0.325 5.325 0.037 60.6 3.24 IS. I 6.7 1.08 8 17. 5 5.18 0.250 5.250 0.037 57.4 3.33 14.3 6.4 I. II See " Note " with Table IV, page 354. • Adapted from Catalogue of Structural Shapes, 1909 Edition. Bethlehem St^ Company, Bethlehem, Pa. 858 Properties of Structural Shapes, etc. Chap. 10 Table Vn.* Properties of Bethlehem Girder-Beam Sections Depth of beam Weight per foot Area of section Thick- ness of web Width of flange Increase of web and flange for each pound increase of weight Neutral axis perpendicular to web at center Neutral axis coin- cident with center line of web I r I/c / r in lb sq in in in in in* in in» in* in 30 30 300.0 iSo.o 58.71 53- 00 0.750 0.690 15.00 13.00 o.oio o.oio 9150.6 8194.5 12.48 12.43 610.0 546.3 630.2 433-3 3.28 3.86 28 38 180.0 165 52.86 48.47 0.690 0.660 14:35 12.50 O.OII Q.OII 7264.7 6562.7 11.72 11.64 518.9 468.8 533.3 371 9 3.18 3.77 36 36 i6o.o ISQO 46.91 43.94 0.630 0.630 13.60 12.00 O.OII O.OII 5620.8 S153.9 10.95 10.83 432.4 396.5 435.7 314-6 3.05 2.68 34 24 I4P.0 130.0 4116 3S.38 Q.600 Q.530 13.00 12. QO 0.013 0.012 4201.4 3607.3 10.10 10.10 350. 1 300.6 346.9 249-4 a. 90 3.66 30 20 140.0 113. 41.19 33.81 Q.640 0.550 13.50 13.00 o.ois o.ois 3934.7 3343.1 8.44 8.4S 393. 5 334.3 348.9 339.3 291 2.70 l8 92.0 37-12 0.480 II. SO 0.016 IS9I.4 7.66 176.8 183.6 3.59 IS 15 IS 140.0 104.0 73- 41.27 30.50 21.49 0.800 0,600 0.430 11.75 11.25 10.50 0.020 0.030 0.020 1593-7 1320. I 883.4 6.31 6.33 6.41 312.4 162.7 117. 8 331.0 313.0 123.2 3.83 3.64 3.39 13 13 70.0 SS.o 20.58 16.18 0.460 0.370 10.00 9-75 0.02s 0.035 S38.8 433.0 5.13 5.17 89.8 73.0 114. 7 81. 1 3.36 3.34 10 9 8 44.0 38.0 32. s 12.95 11.33 9-54 0.310 0.300 0.390 9.00 8.50 8.00 0.030 0.033 Q.G37 344.3 170.9 114. 4 4.34 3.90 346 48.8 38.0 28.6 57.3 44.1 32.9 3.10 1.98 1.86 8ee'« N6te ♦• ^ ^th Tal )le IV. page 354- •Ada Compan pted fro y, Beth m Cata lehejn, logue df Pa. '-^ gtructu ral Shape s. 1909 Editic m. Bel hleher a Steel Properties of Structural Shapes, etc. Table VIII.* Properties of Channel-Sections 359 ,___^ r^ 7 [7= =» ' -J d^ 1 — 1—1 j •^ D t-» ^ I Depth chan- Weight per Area of Width of Thick- ness of Axis i-i Axis 2-2 X " - nel foot tion flange web / r I/c / r I/c in df Df in lb sq in in in in* in in3 in* in in8 55-0 16.18 3.818 0.818 430.2 S^ 57.4 12.2 0.87 4.1 0.82 '8.53 II. 9 > 50.0 14.71 3.720 0.720 402.7 S.23 S3. 7 n.2 0.87 3.8 0.80 «-7i I2.O0 IS 450 13.24 3.622 0.622 375.1 5.32 So.o 10.3 0.88 3.6 0.79 0.78 -8.92 ;9.i5 12.23 40. 11.76 3-524 0.524 347.5 5.43 46.3 Vs 0.89 3.4 12.42 35.0 10.29 3.426 0.426 319.9 5.58 42.7 0.91 3.2 0.79 ;9.43 12.73 33 9-90 a. 400 0.400 312.6 5.62 41.7 8.2 Q.91 3.2 o.n 9-50 !6.6o 12.82 40.0 11.76 3.418 Q.758 196.9 4.09 32.8 6.6 0.7S 2.5 o.n 9.6i2 35.0 10.29 3.296 0.636 179-3 4.17 59 0.76 2.3 I'M 6.81 9.73 12 30.0 8.82 3.173 O.S13 l6l.7 4.28 26:9 5.3 0.77 2.1 7.07 9.911 25.0 7.35 3.050 0.390 Q.280 144.0 4.43 24.0 4.5 0.79 1.9 0.68 7.36 10.21 20.5 6.03 3.940 128. 1 4.61 21.4 3.9 0.81 1.7 0.70 7.67 10.^ 35. 10.29 3.183 0.823 iiS.S 3.35 23.1 4.7 0.67 1.9 0.70 5.17 8.00 30.0 8.82 3.036 Q.676 103.2 3.42 20.7 4.0 0.67 1.7 0.65 5.40 S.67 8.14 10 25-0 7.35 3.889 0.529 91.0 3.52 18.2 3.4 0.68 1.5 0.62 S.28 20.0 5.88 3.742 0.382 78.7 3.66 15.7 2.9 0.70 1.3 0.61 S.97 8.54 ISO 4.46 2.600 0.240 66.9 3.87 13.4 2.3 0.72 1.2 0.64 fe.33 9.P2 25.0 7 35 2.815 0.615 70.7 3.10 15.7 3.0 0.64 1.4 0.62 '4.84 7.43 9 20.0 5.88 2.652 0.452 60.8 3.21 13.5 2.5 0.65 1.2 o.ss :S.i2 7 .8^9 15.0 4.41 2.488 0.288 SO. 9 3.40 II. 3 2.0 0.67 I.O 0.S9 S.49 7.98 13.25 3.89 2.430 0.230 47.3 3.49 10.5 1.8 0.67 0.97 0.61 5. 63 8.19 21.25 6.25 2.622 0.582 47.8 2.77 II. 9 2.3 0.60 I.I 0.59 4.23 6,71 18.75 5.51 2.530 0.490 43.8 2.82 no 2.0 0.60 1.0 0.S7 4-38 6.77 8 16.25 4.78 2.439 0.399 39.9 2.89 10. 1.8 0.61 0.95 0.56 4.54 6.89 13.75 4.04 2.347 0.307 36.0 2.98 9.0 1.6 0.62 0.87I0.56I4.72 7.07 11.25 3.35 2.260 0.220 32.3 3. II 8.1 1.3 0.63 o.79,o.58J4.94 7-37 19 75 S.81 2.513 0.633 33.2 2.39 9-5 1.9 0.56 0.96 0.583.48 5.94 17 25 507 2.408 0.528 30.2 2.44 8.6 1.6 0.57 0.87 0.563.64 5.99 7 14.75 4.34 2.303 0.423 27.2 2.50 7.8 1.4 0.57 0.79 o.54'3-8o 6.07 12.25 3.60 2.198 0.318 24.2 2.59 6.9 1.2 0.58 0.71 0-53;3.99 6.21 9 75 2.85 2.090 0.210 21. 1 2.72 6.0 0.98 0.59 0.63 0.55 4.22 6.53 15 5 4 56 2.283 0.563 19.5 2.07 6.5 1.3 0.53 0.74 0.55 2.91 5-23 6 13 382 2.160 0.440 17.3 2.13 58 I.I 53 0.65 0.52 3.09 5-29 10 5 3.09 2.038 0.318 15. 1 2.21 5.0 0.88 53 0.57I0.50 3.28 5-42 8.0 2.38 1.920 0.200 13.0 2.34 4.3 0.70 0.54 0.500.52 352 5-71 II. 5 338 2.037 0.477 10.4 1.75 4.2 0.82 49 o.54'o.5i 2.34 4.51 5 9.0 2 6s 1.890 0.330 8.9 1.83 3.6 64 0.49 0.45,0.48 2.56 4.62 6.5 I 95 1.750 0.190 7-4 1.95 3.0 0.48 0.50 0.38,0.49 2.79 4.87 7-25 2 13 1.725 0.325 4.6 1.46 2.3 0.44 0.46 0.35I0.46 1.85 3.84 4 6.25 1.84 1.652 0.252 4.2 1.51 2.1 0.38 0.45 0.32 0.46 1.96 3.93 5. 25 1.55 I 580 0.180 3.8 1.56 1-9 0.32 0.45 0.29 0.46 2.06 4.04 6.0 1.76 1.602 0.362 2.1 1.08 1.4 0.31 0.42 0.27 0.46 1,07 3.07 3 5-0 1.47 1.504 0.264 1.8 1. 12 1.2 0.25 0.42 0.24 0.44 1. 19 3-12 4.0 1. 19 1. 410 0.170 1.6 1. 17 I.I 0.20 0.41 0.21 0.44 1. 31 3.22 * Rearranged from Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. See "Note" with Table IV, pge 354. t These values make r the same for both axes. 360 Properties of ^Structural Shapes, etc. Chap. 10 Tftble IX.* Dimensions of Sections and Weights of Small Grooved Steel Channels Section- Si?eof Width of Thickness of Weight per -'■• index section, flange. web. foot. in in in lb C-i«4 2% me M 2. 55 C-165 2H H Me 2.09 C-166 2% iHe H 1.63 C-183 2 H H 2.11 C-184 2 Me Me 1.68 :' '^^" C-18S 2 H H 1.26 C-190 1% iHe Me 1. 71 iT' C-191 iH H H 1.33 S C-193 iM 'H2 ^^2 1.33 C-I9S m H \^ 0.96 C-197 m H Me 1-47 ' ' ■■', C-199 iH H ^^ 0.93 C-200 iH Yie Me 1. 12 }{-' C-203 I H ^ 0.83 A C-207 I ^U H 0.71 C-213 H Me H 0.66 ■ i C-217 H H H 0.58 C-219 H H H 0.54 C-2JH H ^2 H2 0.40 C-aa3 H Me H 0.43 • IloUed by the Jones & Laughlin Steel Company, Pittsburgh, Pa. Properties of Structural Shapes, etc. M Table X. Sizes and Makes of Rolled Steel Angles The following table has been compiled to show angles of various sizes rolled by different companies. The word "all" indicates that angles of the sizes mentioned are rolled by all the companies included in the list. The abbreviations refer to the following companies: Cam., Cambria Steel Company; Car., Carnegie Steel Com- pany; J. & L., Jones & Laughlin Steel Company. Angles with unequal legs Angles with equal legs Sizes in inches Companies Sizes in inches Companies 8 X6 Cam. and Car. 8 X8 All 8 X3H Car. 6 X6 All 7 XsVi All 5 XS All : '] •ii 6 X4 All 4\iX4l i Cam. , -J jF 6 X3K2 All 4 X4 AU ftvl 5 X4 All 3l'^X3^/ i AU ;;.s / 5 Xal'i All 3HX3^ i . J.&L. 5 X3 All 3 X3 AU 4^/^X3 Car. and J. & L. 2%X25 i Cam. and J. & L. !: 4 X3J'i All 2'/^X2^ i All 4 X3 All 2^X2^ i Cam. and J. & L. 33^^X3 All 2 X2 All 3^/2X2!^^ All iHXi^, i AU l 3^X2 J.&L. iJ'^Xi^/ i All {^ 3HXi^^ J.&L. 1%XI3/ i J.&L. i' 3 X2K2 All iMXi'/ i AU i 3 X2 All 1^6 Xl? U J.&L. \ 2>.^X2 All I Xi AU 2l/^Xl% J.&L. HX ? i J. & L. 2Hxiy2 Car. and J. & L. 2i/iXiH Cam. ■ % 2MXIH J.&L. V 2HX1H Car. and J. & L. t 2 XlH Car. and J. & L. t 2 XiH J.&L. s 2 XiH Car. 2 Xl J.&L. iHXiH J.&L. iHXi'A Car. iMXiH J.&L. ii'^XiH Car. iJ'^Xi J.&L. mx n J.&L. I X^He J.&L. I X H J.&L. 362 Properties of Structural Shapes, etc. Chap. 10 Table XI.* Properties of Angle-Sections. Unequal Legs. r-3 ;...jpo i> .?iv/ r; >i;4f)/, Jl N ■-'■ A li.j;}>;>ji>' Axis i-i Axis 2-2 Axis Weight Area 3-3 Size per of foot section I r I/c X I r I/c y ^'inin in lb" sqin in* in in3 in in* in in3 in in 8X6 Xi 44.2 ; 13.00 80.8 2.49 15. 1 2.65 38.8 1.73 8.9 1.65 1.28 8X6 X.^Me 41.7 12.25 76.6 2.50 14.3 2.63 36.8 1.73 8.4 1.63 1.28 8X6 XH 39. i 11.48. 72.3 .2.51 13.4 2.61 34.9 1.74 7.9 1. 61 1.28 8X6 XI 3/16 36.5 •10.72 67.9 2.52 12.5 2.59 32.8 1.75 7.4 1-59 i.29 8X6 XM • 33.8 9-94 63.4 2.53 II. 7 2.56 30.7 1.76 6.9 1.56 1.29 8X6 . X"/i6 31.2 9-15 58.8 2.54 10.8 2.54 28.6 1.77 6.4 1.54 1.29 8X6 XH , 28. 5 8.36 54.1 2.54 9-9 2.52 26.3 1.77 5.9 1.52 r.30 8X6 X?i6 25.7 7.56 49-3 '2.55 8.9 2.50 24.0 1.78 5.3 1.50 .r.30 8X6 X\^ 23.0 6.75 44.3 2.56 8.0 2.47 21.7 1.79 4.8 1.47 1.30 8X6 XMe 20.2 ' S-93 39.2 2.57 7.1 2.45 19-3 1.80 4.2 1. 45 1.30 8X3>^Xi 35.7 10.50 66.2 '2. SI 13.7 3.17 7.8 0.86 3.0 0.0? 0.89 0.73 i8>«3HX-'-M6 33.7 990 62.9 2.52 12.9 3.14 7-4 0.87 2.9 C).73 31 ..7 ; Q-30 59.4 2.53 12.2 3.12 7-1 0.87 2.7 0.87 0.73 SXs^/^X^Me 29.6 8.68 ■55.9 2.54 II. 4 3.10 6.7 0.88 2.5 0.8s 0.73 ' 8X3^X3/4 27.5 8.06 52.3 ^2.55 10.6 3.07 6.3 0.88 2.3 0.82 0.73 i 8X3ViXiM6 2SJ3 7.43 48. 5 2.56 9-8 3.05 5.9 0.89 2.2 0.80 0.73 ; 8X3HXH 23.2 0.80 44.7 2.57 9.0 3.03 S.4 0.90 2.0 0.78 0.74 8X3HXri6 21.0 ^•15 40.8 2.57 8.2 3.00 5.0 0.90 1.8 0.75 0.74 , 8X3^/^XH 18.7 ^.50 36.7 2.58 7.3 2.98 4.5 o'.gi 1.6 0.73 0.74 1 8X31-^X^6 16.5 4.84 32.5 2.59 6.4 2.95 4,1 0.92 1.5 0.70 0.74 7X3HXI 32.3 Q.SO $•97 45.4 2.19 10.6 2v7^ ■b'-3 0.89 •3.0 0.96 0.74 7X3HXIM6 30.5 43.1 2.19 10. 2.69 7.2 b.89 ' 2.8 0.94 0.74 7X3^/^X7/^ 28.7 $.42 40.8 2.20 9.4 2.66 6.8 0.90 2.6 0.91 Q.74 1 iXz^AX^U 26.8 7.87 38.4 2.21 8.8 2.64 6.5 0.91 - 2.5 0.89 D.74 \ iXzViXH 24.9 7.31 §•75 36.0 2.22 8.2 2.62 6.1 0.91 i 2.3 Q.87 0.74 1 7X31^^X11/16 23.0 33.5 2.23 7.6 2.60 5.7 0.92 2.1 0.85 0.74 ■ 7X3HX)^ 21.0 fi7 30.9 2.24 7.0 2.57 5-3 0.93 2.0 0.82 6.75 ; ixz\^xy\% 191 3-59 28.2 2.25 6.3 2.55 4.9 0.^3 1.8 0.80 0.75 : 7X3^^X1^^ 17.0 5.00 25.4 2.25 5.7 2.53 4.4 0.94 1.6 oi.78 0.75 ' 7X3V^XM6 iS.o 4.40 22.6 2.26 5.0 2.50 4.0 0.9s 0.§0 ' 1.4 0.7s 0.76 7X3HXH 13.0 4.80 19.6 2.27 4.3 2.48 3.5 ! ^-3 ,Q.73 p. 76 6X4 Xi 30.6 i.oo S.50 30.8 1.85 8.0 2.17 10.8 ':l:<>9 '3.8 i^-X7 b.85 • 6X4 XI Me 28.9 293 1.86 7.6 2.14 10.3 i.io • 3.6 -i.i^ b.85 L6X4 Xli. 27-2 ...JZ..8S.-. 27.7 1.86 7^2 2-12 9..& ^ I . u 3-A~ 1.12 _o,afi« 6X4 XI Me 25.4 7.47 26.1 1.87 6.7 2.10 9.2 I. II 3.2 I.IO 0.86 6X4 XH 23.6 6.94 245 1.88 6.2 2.08 8.7 1. 12 3.0 1.08 0.86 6X4 XI He 21.8 6.40 22.8 1.89 5.8 2.06 8.1 1. 13 2.8 1.06 0.86 6X4 X^/i 20.0 5.86 21. 1 1.90 5.3 2.03 7.5 1. 13 2.5 1.03 0.86 6X4 XMe 18. 1 5.31 19-3 1.90 4.8 2.01 6.9 1. 14 2.3 1. 01 0.87 6X4 XH 16.2 4.75 17.4 1. 91 4.3 1-99 6.3 1. 15 2.1 0.99 0.87 6X4 XMe 14.3 4.18 15.5 1.92 3.8 1.96 5.6 1. 16 1.8 0.96 0.87 6X4 XH 12.3 3.61 13. 5| 1.93 3.3 1.94 4.9 1. 17 1.6 0.94 0.88 See " Note " with Table IV, page 354. • From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. Properties of Structural Shapes, etc. m Table XI * (Continued). Properties of Angle-Sections. Uaequal Le^g ,1 H! 2^ i. tfc -r-3 11 ^3 Size 6X3M2X1 6X3'/2XiM6 6X3V^X7/6 6X3HXIM6 6X3K2X% 6X3'/2XiM6 6X3HXH 6X3V2Xri6 6X3V2XK2 6X3V'2XM6 6X3V2X34 6X3}'2X5/i6 5X4 Xli 5X4 X'Vis 5X4 X3/i 5X4 XI He 5X4 XH 5X4 XMe 5X4 XH 5X4 XMo 5X4 X3/^ 5X3^/^X^4 5X3V^XJM6 5X3^/^X^4 5X3l'^XiH6 5X3M2XH 5X3M2XM6 5X3^/2X1/2 5X3^2X^1 6 5X3/2 X"H 5X3HXM6 5X3 X^Mo SX3 XH 5X3 X^Vie 5X3 X5^ 5X3 X^ifl 5X3 XH 5X3 XMe 5X3 X% 5X3 XMa Weight per foot lb 28.9 27.3 '25.7 24.0 22.4 20.6 18.9 17. 1 15.3 13.5 II. 7 9.8 24.2 22.7 21. 1 19-5 17.8 16.2 14.5 12.8 11. 22.7 21.3 19-8 18.3 16.8 15.2 13.6 12.0 10.4 8.7 19.9 18.5 17. 1 15.7 14.3 12.8 II. 3 9.8 8.2 Area of section 8.50 8.03 7.55 7.06 6.56 6.06 5.55 5.03 4.50 3.97 3.42 2.87 711 6.65 6.19 5-72 5.23 4.75 4.25 3.75 3.23 6.67 6.25 5.81 5-37 4.92 4.47 4.00 3.53 3.05 2.56 5:84 5.44 5.03 4.61 4.18 3.75 3-31 2.86 2.40 Axis i-i 29.2 ,27.8 26.4 24.9 23.3 21.7 20.1 18.4 16.6 14.8 12.9 10, Q 16.4 15.5 14.0 13.6 12.6 II. 6 10.5 9-3 8.1 15.7 14.8 13.9 13.0 12.0 II. o lO.O 8.9 7.8 6.6 14.0 13.2 12.3 II. 4 10.4 9-5 8.4 7.4 6.3 I/c 1.89 7.8 7-4 7.0 6.6 6.1 5.6 .90 5.2 .91 4.7 .92 4.2 1.93! 3.7 1.94 3-3 1.95 2.7 1.52 50 1.53 4.7 1.54 1.54 1.55 1.55 1.57 1.58 1. 59 1.53 1.54 1.5 1.56 1.56 1.57 1.58 1-59 1.60 1. 61 1.55 1.55 1.56 1.57 1.58 1.59 1.60 1. 61 1. 61 4.4 4.1 3-7 3-4 3-1 2.7 2.3 4-9 4.6 4-3 4.0 3.7 3 3 3.0 2.6 2.3 19 45 4.2 3-9 3-5 3-2 2.9 2.6 2.2 1-9 2.26 2.24 2.22 2.20 2.18 2.15 2.13 2 2.aS 2.06 2.04 2.01 1. 71 1.6 1.66 1.64 1.62 1.60 1.57 1.55 1.53 1.79 1.77 1.75 1.72 1.70 1.63 1.66 1.63 1. 61 1.59 1.8 1.8 1.82 1.80 1.77 1.75 1.73 1.70 1.68 Axis 2-2 I/c 0.92 0.93 0.93 0.94 0.94 0.95 0.96' 0.96I 0.971 0.981 0.99: 1. 00 1. 14 1. 15 1.15 1. 16 1. 17 1. 18 1. 18 119 1.20 0.9') 0.97 0.9S 0.98 0.99 1. 00 1.02 1.03 0.80 0.80 0.81 0.81 0.82 0.83 0.84 0.84 0.85 2.9 1. 01 2.7 0.99 2.6 0.97 2.4 0.95 2.3 0.93 2.1 0.90 1.9 0.88 1.8 0.86 1.6 0.83 1.4 0.81 1.2 0.79 I.O 0.76 3.3 1. 21 3.1 1. 18 2.9 1. 16 2.7 1.14 2.5 1. 12 2.3 I. 10 2.0 1.07 1.8 1.05 i.b 1.03 2.5 1.04 2.4 1.02 2.2 1. 00 2.1 0.97 19 0.95 1.7 0.93 1.6 0.91 1.4 0.88 1.2 0.86 1.0 0.84 1.7 0.86 1.6 0.84 1.5 0.82 1.4 0.80 1.3 0.77 I.I 0.75 1.0 0.73 0.8Q 0.70 0.75 0.68 See " Note " with Table IV, page 354. * From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. 364 Properties of Structural Shapes, etc. Chap. Table XI* (Continued). Properties of Angle-Sections. Unequal Legs K 1 I :x: ii ^3 y I Weight Area Axis i-i [ Axis 2-2 Axis 3-3 Size foot of section I r I/c X I r 1/c y fwm in lb sq in in* in in3 in in* in in3 in in 4^12X3 X^Me 18.5 5.43 10.3 1.38 3.6 1.65 3.6 0.81 1-7 0.90 0.64 4K2X3 XH 17.3 5. 06 9-7 1.39 3.4 1.63 3.4 0.82 1.6 0.88 0.64 4K2X3 XI He 16.0 4.68 91 1.39 3.1 1.60 3.2 0.83 1.5 0.85 0.64 a\^X3 XH 14.7 4.30 8.4 1.40 2.9 1.58 3.0 0.83 1.4 0.83 0.64 4K2X3 XYie 13.3 3.90 7.8 1. 41 2.6 1.56 2.8 0.85 1.3 0.81 0.64 4K2X3 XH II. 9 3.50 7.0 1.42 2.4 1. 54 2.5 0.85 i-.i 0.79 0.65 4}^iX3 XVie 10.6 3.09 6.3 1.43 2.1 1. 51 2.3 0.85 1.0 0.76 0.65 4K2X3 X% 9.1 2.67 55 1.44 1.8 1.49 2.0 0.86 0.88 0.74 0.66 4K2X3 XMc 7.7 2.25 4.7 1.44 1.5 1.47 1.7 0.87 0.75 0.72 0.66 4 X3'/^XiM6 18.5 5.43 7.8 1. 19 2.9 1.36 5-5 1. 01 2.3 1. 11 0.72 4 X3HX-)4 17.3 5.06 7.3 1.20 2.8 1.34 5.2 1. 01 2.1 1.09 0.72 4 X3K2XIH6 16.0 4.68 6.9 1. 21 2.6 1.32 4.9 1.02 2.0 1.07 0.72 4 X3HXH 14.7 4.30 6.4 1.22, 2.4 1.29 4.5 1.03 1.8 1.04 0.72 4 X3K2XM6 13.3 3.90 5-9 1.23, 2.1 1.27 4.2 1.03 1.7 1.02 0.72 4 X3HX3'^ II. 9 3.50 53 I. 231 1.9 1.25 3.8 1.04 1.5 1. 00 0.72 4 X3HX716 10.6 3.09 4.8 1.24 1.7 1.23 3.4 1.05 1.3 0.98 0.72 4 X3HXH 9.1 2.67 4.2 1.25 1.5 1. 21 3.0 1.06 1.2 0.96 0.73 4 X3}'^XM6 7.7 2.25 3.6 1.26 1.3 1. 18 2.6 1.07 1.0 0.93 0.73 4 X3 XI Me 17. 1 5.03 7.3 1. 21 2.9 1.44 3.5 0.83 1.7 0.94 0.64 4 X3 XM 16.0 4.69 6.9 1.22 2.7 1.42 3.3 0.84 1.6 0.92 C.64 4 X3 X^Me 14.8 4.34 6.5 1.22 2.5 1.39 3.1 0.84 1.5 0.89 0.64 4 X3 X% 13.6 3.98 6.0 1.23 2.3 1.37 2.9 0.8s 1.4 0.87 0.64 4 X3 XMe 12.4 3.62 5.6 1.24 2.1 1.35 2.7 0.86 1.2 0.85 0.64 4 X3 XH II. I 3.25 5.0 1.25 1.9 1.33 2.4 0.86 I.I 0.83 0.64 4 X3 XMe 9.8 2.87 4.5 1. 25 1.7 1.30 2,2 0.87 1.0 0.80 0.64 4 X3 XH 8.5 2.48 4.0 1.26 1.5 1.28 1-9 0.88 0.87 0.78 0.64 4 X3 XMe 7.2 2.09 3.4 1.27 1.2 1.26 1.7 0.89 0.74 0.76 0.65 4 X3 XH 5.8 1.69 2.8 1.28 I.O 1.24 1.4 0.89 0.60 0.74 0.65 3HX3 XiMe 15.8 4.62 5.0 1.04 2.2 1.23 3.3 0.85 1.7 0.98 0.62 3HX3 X)4 14.7 4.31 4.7 1.04 2.1 1. 21 3.1 0.85 1.5 0.96 0.62 3HX3 XI He 13.6 4.00 4.4 1.05 1-9 I.I9 .3.0 0.86 1.4 0.94 0.62 3HX3 XH 12.5 3.67 4.1 1.06 1.8 1. 17 2.8 0.87 1.3 0.92 0.62 3HX3 XMe II. 4 3.34 3.8 1.07 1.6 1. 15 2.5 0.87 1.2 0.90 0.62 3HX3 XH2 10.2 3.00 3.5 1.07 1.5 1. 13 2.3 0.88 I.I 0.88 0.62 3HX3 XHe 9.1 2.65 3.1 1.08 1.3 1. 10 2.1 0.89 0.98 0.85 0.62 3^/^X3 XH 7.9 2.30 2.7 1.09 I.I 1.08 1.8 0.90 0.85 0.83 0.62 3V^X3 XMe 6.6 1.93 2.3 1. 10 0.96 1.06 1.6 0.90 0.72 0.81 0.63 3ViX3 XH 5.4 1.56 1-9 I. II 0.78 1.04 1.3 0.91 0.58 0.79 0.63 3^/^X21/4X1 Me 12.5 3.6s 4.1 1.06 1-9 1.27 1.7 0.69 0.99 0.77 0.53 3HX2H2XH II. 5 3.36 3.8 1.07 1.7 1.25 1.6 0.69 0.92 0.75 0.53 3HX2HXM6 ''10.4 3.06 3.6 1.08 1.6 1.23 1.5 0.70 0.84 0.73 0.53 3l^X2HXH 9-4 2.75 3.2 1.09 1.4 1.20 1.4 0.70 0.76 0.70 0.53 3V4X2HXH6 8.3 2.43 2.9 1.09 1.3 1. 18 1.2 0.71 0.68 0.68 0.54 3l'4X2HXH 7.2 2. II 2.6 1. 10 I.I 1. 16 I.I 0.72 0.59 0.66 0.54 3HX2HXM6 6.1 1.78 2.2 I. II 0.93 1. 14 0.94 0.73 0.50 0.64 0.54 3HX2HXV4. 4.9 1.44 1.8 1. 12 0.75 I. II 0.78 0.74 0.41 0.61 0.54 See " Note " with Table IV, page 354. * From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. Properties of Structural Shapes, etc. 365 Table XI* (Continued). Properties of Angle-Sections. Unequal Legs ->t Weight Area Axis i-i Axis 2-2 Axis 3-3 Size foot of section / r I/c X I r I/c y in ^-min in lb sq in in4 in in» in in\ in in3 in 3 X2HXM6 9.5 2.78 2.3 0.91 1.2 1.02 1.4 0.72 0.82 0.77 0.52 3 X2i/2Xi/i 8.5 2.50 2.1 0.91 i.o 1. 00 1.3 0.72 0.74 0.75 0.52 3 X2K2XM6 7.6 2.21 1.9 0.92 0.93 0.98 1.2 0.73 0.66 0.73 0.52 3 X2K2X3/^ 6.6 1.92 1.7 0.93 0.81 0.96 1.0 0.74 0.58 0.71 0.52 3 X2I/2XM6 5.6 1.62 1.4 0.94 0.69 0.93 0.90 0.74 0.49 0.68 0.53 3 X2i^iXH 4-5 1. 31 1.2 0.95 0.56 0.91 0.74 0.75 0.40 0.66 0.53 3 X2 XH 7.7 2.25 1-9 0.92 I.O 1.08 0.67 0.55 0.47 0.58 0.43 3 X2 XIU 6.8 2.00 1-7 0.93 0.89 1.06 0.61 0.55 0.42 0.56 0.43 3 X2 XVs 5.9 1.73 1.5 0.94 0.78 1.04 0.54 0.56 0.37 0.54 0.43 3 X2 XMo 5.0 1.47 1.3 0.95 0.66 1.02 0.47 0.57 0.32 0.52 0.43 3 X2 XK 4.1 1. 19 I.I 0.95 0.54 0.99 0.39 0.57 0.2s 0.49 0.43 21/2X2 XH 6.8 2.00 I.I 0.75 0.70 0.88 0.64 0.56 0.46 0.63 0.42 25.^X2 XVia 6.1 1.78 I.O 0.76 0.62 0.85 0.58 0.57 0.41 0.60 0.42 2l/^X2 X% 5.3 1.55 0.91 0.77 0.55 0.83 0.51 0.58 0.36 0.58 0.42 21/2X2 XM6 4.5 1. 31 0.79 0.78 0.47 0.81 0.45 0.58 0.31 0.56 0.42 2I/2X2 XH 3.62 1.06 0.65 0.78 0.38 0.79 0.37 0.59 0.25 0.54 0.42 2I/2X2 XVm 2.7s 0.81 0.51 0.79 0.29 0.76 0.29 0.60 0.20 0.51 0.43 2M2X2 XH 1.86 0.55 0.35 0.80 0.20 0.74 0.20 0.61 0.13 0.49 0.43 2l/4Xl3'^2XM6 3.92 1. 15 0.71 0.79 0.44 0.90 0.19 0.41 0.17 0.40 0.32 2l.^Xl'/2XH 3.19 0.94 0.59 0.79 0.36 0.88 0.16 0.41 0.14 0.38 0.32 2Hxiy2xyi6 2.44 0.72 0.46 0.80 0.28 0.85 0.13 0.42 O.II 0.35 0.33 2HXiy2XH 5.6 1.63 0.7s 0.68 0.54 0.86 0.26 0.40 0.26 0.48 0.32 2Hxiy2XVi6 5.0 1.45 0.68 0.69 0.48 0.83 0.24 0.41 0.23 0.46 0.32 2Hxiy2x% 4.4 1.27 0.61 0.69 0.42 0.81 0.21 0.41 0.20 0.44 0.32 2HXiViX^i6 3.66 1.07 0.53 0.70 0.36 0.79 0.19 0.42 0.17 0.42 0.32 2MXIK2XH 2.98 0.88 0.44 0.71 0.30 0.77 0.16 0.42 0.14 0.39 0.32 2HXIHXM6 2.28 0.67 0.34 0.72 0.23 0.75 0.12 0.43 O.II 0.37 0.33 2 Xl3'^2XH 3.99 1. 17 0.43 0.61 0.34 0.71 0.21 0.42 0.20 0.46 0.32 2 X1K2XM6 3.39 1. 00 0.38 0.62 0.29 0.69 0.18 0.42 0.17 0.44 0.32 2 XiHXH 2.77 o.8r 0.32 0.62 0.24 0.66 0.15 0.43 O.I< 0.41 0.32 2 X1K2XM6 2.12 0.62 0.25 0.63 0.18 0.64 0.12 0.44 O.II 0.39 0.32 2 XlK2Xj'i 1.44 0.42 0.17 0.64 0.13 0.62 0.09 0.45 0.08 0.37 0.33 2 XiHXH 2.55 0.75 0.30 0.63 0.23 0.71 0.09 0.34 O.IO 0.33 0.27 2 X1K4XM6 1.96 0.57 0.23 0.64 0.18 0.69 0.07 0.35 0.08 0.31 0.27 i3/4XiHXH 2.34 0.69 0.20 0.54 0.18 0.60 0.09 0.35 O.IO 0.35 0.27 i3/4XiV4XM6 1.80 0.53 0.16 0.55 0.14 0.58 0.07 0.36 0.08 0.33 0.27 i^4XiHXi/^ 1.23 0.36 O.II 0.56 0.09 0.56 0.05 0.37 0.05 0.31 0.27 1HXIHXM6 2.59 0.76 0.16 0.45 0.16 0.52 O.IO 0.35 O.II 0.40 0.26 IM2XIMXM 2.13 0.63 0.13 0.46 0.13 0.50 o.c8 0.36 0.09 0.38 0.26 iHXiHXMe 1.64 0.48 O.IO 0.46 O.IO 0.48 0.07 0.37 0.07 0.35 0.26 See " Note " with Table IV, page 354. * From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. 366 Properties of Structural Shapes, etc. Chap. 10 Table Xn.* Properties of Angle-Sections. Equal Legs \ :~^'" Weight Area A xis i-i and Axis 2 -2 Axis 3-3 Size of - section • per foot I r J/c X rmin in lb sq in in^ in inS in in 8X8X1H 56.9 16.73 98.0 2.42 17-5 2.41 1. 55 8X8X1M6 54.0 15,87 9i 5 2.43 16.7 2.39 1.56 8X8X1 51.0 15,00 89 2.44 IS. 8 2.37 1.56 8X8X»M6 48.1 14,12 84 3 2.44 14.9 2.34 1.56 8X8X7/^ 45.0 13.23 79 6 2.45 14.0 2.32 1.56 8X8X^1 a 42.0 12.34 74 7 2.46 13. 1 2.30 1-57 8X8X^4 38.9 11.44 69 7 2.47 12.2 2.28 1.57 8X8X^18 3S.8 10.53 64 6 2.48 JI.3 2. 23 1.5a 8X8XH 32.7 9.61 59 4 2.49 10.3 a. 23 1.58 8X8X^6 29.6 8.68 54 I 2.50 11 a. 21 i-sa 8X8XH 26.4 7.73 48 6 2.51 2.19 1.5a 6X6X1 37.4 11.00 35.5 1.80 8.6 1.86 I.l6 6X6X^^6 3S.3 10.37 33.7 1.80 8.1 1.84 1. 16 6X6X^/6 • 33.1 9-73 31.9 I.8i 7.6 1.82 1. 17 6X6X^^6 31.0 9.09 30.1 1.83 7. a 1. 80 1. 17 6X6X^4 28.7 8.44 28.3 1.83 6.7 1.78 I 17 6X6X1 H6 26.S 7.78 26.2 1.83 6.3 1.7S 1. 17 6X6XH 24.2 7.11 24.2 1.84 5-7 1.73 1. 17 6X6X916 21.9 6.43 22.1 1. 85 S.I 1. 71 1. 18 6X6x1/2 19.6 5-75 19.9 1.86 4.6 1.68 1. 18 6X6X^16 17.2 S.06 17.7 • 1.87 4.1 1.66 1. 19 6X6XH 14.9 4.36 15.4 1.88 3.5 1.64 1. 19 SXSXI 30.6 900 19.6 1.48 5.8 1. 61 0.96 5X5X1^6 28.9 8.50 18.7 1.48 5.5 1.59 0.96 5XSX^^ 27.2 7.93 17.8 1.49 5.2 1.57 0.96 SXsXme 25. 4 7.47 16.8 1.50 4.9 1.55 0.97 SXSXH 23.6 6.94 15.7 1.50 4.5 1.52 0.97 SXSX^VU 21.8 6.40 14.7 1. 51 4.2 1.50 0.97 SXSXH 20.0 5.86 13.6 1.52 3.9 1.43 0.97 SXsXVia 18. 1 5.31 12.4 1.53 35 1.46 0.98 SXSXH 16.2 4.7s II. 3 1.54 32 1.43 0.98 5X5X^6 14.3 4.18 10. 1.55 2.8 1. 41 0.98 5X5XH 12.3 3.61 8.7 1.56 2.4 1.39 0.99 4X4XIM6 19-9 S.84 8.1 1. 18 3.0 1.29 0.77 4X4XM 18.5 5.44 7.7 1. 19 2.8 1.27 0.77 4X4X1 He 17. 1 5.03 7.2 1. 19 2.6 1.25 0.77 4X4XH 15.7 4.61 6.7 1.20 2.4 1.23 0.77 4X4X9i6 14.3 4.18 6.1 1. 21 2.2 1. 21 0.78 4X4X1/^ 12.8 3.7s 5.6 1.22 2.0 1. 18 0.78 4X4XM6 II. 3 3.31 S.o 1.23 1.8 1. 16 0.78 . 4X4XH 9.8 2.86 4.4 1.23 1. 5 1. 14 0.79 4X4XM6 8.2 2.40 3.7 1.24 1.3 1. 12 0.79 4X4XH 6.6 1.94 3.0 1.25 i.o 1.09 0.79 See ' Note " with Table IV, page 354. * From Pocket Companion, Carnegie Steel Company, Pittsbergh, Pa, Properties of Structural Shapes, etc. 367 Table XII* (Continued). Properties of Angle-Sections. Equal Legs ^ Weight Area Axis i-i and Axis 2 -2 Axis 3-3 Size per of foot section I r I/c X ymin in lb sq in in< in inS in in 33'^X3K2X1^'16 17. 1 5.03 5.3 1.02 2.3 1. 17 0.67 3y2xmxH l6.o 4.69 S.o 1.03 2.1 1.15 0.67 aHXaHx^Me 14.8 4.34 4-7 1.04 2.0 1. 12 0.67 aViXaJ'^xH 13.6 3.98 4-3 1.04 1.8 1. 10 0.68 3HX3K2X»/^6 12.4 3.62 4.0 I. OS 1.6 1.08 0.68 3y2Xiy2xy2 II. I 3.2s 3.6 1.06 l.S 1.06 0.68 3}'^X3K2XM6 ti 3.87 3 3 1.07 1.3 1.04 0.68 3VtX3'/2XH 2.48 a. 9 1.07 1.2 1. 01 0.69 3VtX3K3XMQ 7.3 a. 09 a. 5 1.08 0.98 0.99 0.69 3'/2X3}'^XH 5.8 l:% a.o 1.09 0.79 0.97 0.69 3 X3 XH J1.3 a. 6 0.88 1.3 0.98 0.57 3 X3 XMe 10.4 3.06 2.4 0.89 1.3 0.95 0.58 3 X3 X^^ It a. 75 a. a 0.90 I.I 0.93 0.58 3 X3 XMa 3.43 3.0 0.91 0.9s 0.91 o.s8 3 X3 XH 72 2. II 1.8 0.91 0.83 0.89 0.S8 3 X3 XMa 6.1 1.78 1. 5 0.92 0.71 0.87 0.59 3 X3 XH 4.9 1.44 J. 2 0.93 0.58 0.84 0.59 2\^X2MX\'i 7-7 2.25 1.2 0-74 0.73 0.81 0.47 2MX2\iXlU 6.8 2.00 i.i 0.75 o.6s 0.78 0.48 2y2X2\^XH S.9 1.73 0.98 0.75 0.57 0.76 0.48 2\hX2yixV\^ S.o 1.47 0.85 0.76 0.48 0.74 0.49 2l/iX2>/^XH 4. J 1. 19 0.70 0.77 0.39 0.72 0.49 2HX2HXM6 3.07 0.90 o.SS 0.78 0.30 0.69 0.49 21/^X2^2X1/^ 2.08 0.61 0.38 0.79 0.20 0.67 0.50 2 X2 XTIe 53 1.56 0.54 0.59 0.40 0.66 0.39 2 X2 X3/i 4.7 1.36 0.48 0.59 0.35 0.64 0.39 2 X2 X5l6 3.92 I. IS 0.42 0.60 0.30 0.61 0.39 2 X2 XM 3.19 0.94 0.35 0.61 0.2s 0.59 0.39 2 X2 XMs 2.44 0.71 0.28 0.62 0.19 0.57 0.40 2 X2 XH 1.6s 0.48 0.19 0.63 0.13 0.55 0.40 i^XiMXMo 4.6 1.34 0.35 0.51 0.30 0.59 0.33 i3/4Xi3/4X^i 3.99 1. 17 0.31 0.51 26 0.57 0.34 i^XiMXMe 3-39 1. 00 0.27 0.52 0.23 0.55 0.34 iMXi%XH 2.77 0.81 0.23 0.53 0.19 0.53 0.34 lMXl3/4X3/i6 2.12 0.62 0.18 0.54 0.14 o.Si 0.35 i%Xi3/4XH 1.44 0.42 0.13 55 O.IO 0.48 0.35 ll/^XlK2X3/i 3 35 0.98 0.19 0.44 0.19 O.SI 0.29 iV^XiHXMe 2.86 0.84 0.16 0.44 ,0.16 0.49 0.29 iHXiy2XH 2.34 0.69 0.14 0.45 0.13 0.47 0.29 iHXiHXria 1.80 0.53 O.II 0.46 O.IO 0.44 0.29 iHXii/^XH 1.23 0.36 0.08 0.46 0.07 0.42 0.30 iMXiHXMe 2.33 0.68 0.09 0.36 O.II 0.42 0.24 i^XiHXH 1.92 0.56 0.08 0.37 0.09 0.40 0.24 iMXiHX-Me 1.48 0.43 0.06 0.38 0.07 0.38 0.24 iHXiViXH 1. 01 0.30 0.04 0.38 0.05 0.3S 0.25 I XI XK 1.49 0.44 0.04 0.29 0.06 0.34 0.19 I XI XM6 1. 16 0.34 0.03 0.30 0.04 0.32 0.19 I Xi XH 0.80 0.23 0.02 0.31 0.03 0.30 0.19 See " Note " with Table IV, page 354. ? From Pocltet Companionj Carnegie Steel Company, Pittsburgh, Pa. 368 Properties of Structural Shapes, etc. Chap. 10 Table Xin.* Properties of T Sections. Flange and Stem Equal iJ — 1 Size Tir •_i,+ Area Axis Flange Stem Minimum thickness per foot of sec- tion I r I/c X / r I/c Flange Stem in in in in lb sqin in^ in in3 in in< in in3 6H 6K2 0.40 0.4s 19.8 5. 80 23-5 2.01 5.0 1.76 10. 1 1.32 3.1 4 4 4 4 V2 13.5 10. 5 II. 7 3-97 3.09 3.44 5.7 4.5 3.7 1.20 1. 21 1.04 2.0 1.6 i.S 1. 18 1. 13 1.05 2.8 2.1 1.9 0.84 0.83 0.74 1.4 I.I I.I 3 3 3V^2 3 3 1.U 3/i Me 9.2 9.9 8.9 2.68 2.91 2.59 3.0 2.3 2.1 1.05 0.88 0.89 1.2 I.I 0.98 1. 01 0.93 0.91 1.4 1.2 1.0 0.73 0.64 0.63 0.81 0.80 0.70 3 3 2\^ 3 3 2\^ Me Me 7.8 6.7 6.4 2.27 1-95 i.87 1.8 1.6 I.O 0.90 0.90 0.74 0.86 0.74 0.59 0.88 0.86 0.76 0.90 0.75 0.52 0.63 0.62 0.53 0.60 0.50 0.42 2M 2% 2\h 2M Me Vie H Me Me 5.5 4.9 4.1 1.60 1.43 1. 19 0.88 0.65 0.52 0.74 0.67 0.66 0.50 0.41 0.32 0.74 0.68 0.65 0.44 0.33 0.25 0.52 0.48 0.46 0.35 0.29 0.22 2 2 1% 2 2 Me H Me 4.3 3.56 3.09 1.26 1.05 0.91 0.44 0.37 0.23 0.59 0.59 0.51 0.31 0.26 0.19 0.61 0.59 0.54 0.23 0.18 0.12 0.43 0.42 0.37 0.23 0.18 0.14 1^4 H Me H Vie 2.47 1.94 2.02 0.73 0.57 0.59 0.15 O.II 0.08 0.45 0.45 0.37 0.14 O.II O.IO 0.47 0.44 0.40 0.08 0.06 0.05 0.32 0.32 0.28 O.IO 0.08 0.07 Z I I I Me Me Me Me 1. 59 1.25 0.89 0.47 0.37 0.26 0.06 0.03 0.02 0.37 0.29 0.30 0.07 COS 0.03 0.38 0.32 0.29 0.03 0.02 O.OI 0.27 0.22 0.21 0.05 0.04 0.02 See "Note" with Table IV, paf!;e 354. * From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. Properties of Structural Shapes, etc. 369 Table XIV.* Properties of T Sections. Flange and Stem Unequal r ^ Axis i-i Size Axis 2-2 Weight Area of Minimum per " thickness foot sec- Flange Stem tion / r I/c X in / r I/c Flange Stem in in in in lb sq in in* in in3 in* in in' 5 3 H 1«%2 II. 5 3.37 2.4 0.84 I.I 0.76 I3.9 1. 10 I..6 5 2^ Me 10.9 3.18 1.5 0.68 0.78 0.63 4.1 1. 14 1.6 A\^ 3H Me iMe 15.7 4.60 5.1 1.05 2.1 I. II 3.7 0.90 1.7 4H . 3 % 3/^ 9.8 2.88 2.1 0.84 0.91 0.74 3.0 I 02 1.3 4H 3 Me Me 8.4 2.46 1.8 0.85 0.78 0.71 2.5 1. 01 I.I 4H iH % % 9.2 2.68 12 0.67 0.63 0.59 3.0 1.05 1.3 43^^ 2H Me Me 7.8 2.29 i.b 0.68 0.54 0.57 2.5 1.05 I.I 4 5 3'^ 1/^ 15.3 4.50 10.8 1-55 3.1 1.56 2.8 0.79 1.4 4 5 34 3/i II.9 3.49 8.5 1.56 2.4 1. 51 2.1 0.78 I.I 4 4H ^^ H 14.4 4.23 7.9 1.37 2.5 1.37 2.8 0.81 1.4 4 4H % % II. 2 3.29 6.3 1.39 2.0 1. 31 2.1 0.80 I.I 4 3 % H 9.2 2.68 2.0 0.86 0.9c 0.78 2.1 0.89 I.I 4 3 Me Me 7.8 2.29 1.7 0.87 0.77 0.75 1.8 0.88 0.88 4 2l/i 3/^ 3/i 8.5 2.48 1.2 0.69 0.62 0.62 2.1 0.92 i.o 4 2}.^2 Me Me 7.2 2.12 I.O 0.69 0.53 0.60 1.8 0.91 0.88 4 2 % % 1-^ 2.27 0.60 0.52 0.40 0.48 2.1 0.96 I.I 4 2 Me Me 6.7 1.95 0.53 0.52 0.34 0.46 1.8 0.95 0.88 3V^ 4 Ki i/i 12.6 3.70 5.5 1. 21 2.0 1.24 1-9 0.72 I.I 3H 4 H ^/^ 9.8 2.88 4.3 1.23 1.5 1 .19 1.4 0.70 0.81 3H 3 1/^ H 10.8 3.17 2.4 0.87 I.I 0.88 1-9 0.77 I.I . 3H 3 % H 8.5 2.48 1.9 0.88 0.89 0.83 1.4 0.75 0.81 3}'^ 3 Me H 7.5 2.20 1.8 0.91 0.85 0.85 1.2 0.74 0.68 3 4 ^/^ Vie II. 7 3.44 3.06 5.2 1.23 1-9 1.32 1.2 0.59 0.81 3 4 Me 10.5 4-7 1.23 1.7 1.29 I.I 0.59 0.70 3 4 34 %■ 9-2 2.68 4.1 1.24 1.5 1.27 0.90 0.58 0.60 3 3H ¥2 H 10.8 3.17 3.5 1.06 1.5 1. 12 1.2 0.62 0.80 3 SH Me Me 9.7 2.83 3.2 1.06 1.3 1. 10 1.0 0.60 0.69 3 3H H H 8.5 2.48 2.8 1.07 1.2 1.07 0.93 0.61 0.62 3 2H ^■^ H 7.1 2.07 I.I 0.72 0.60 0.71 0.89 0.66 0.59 3 , 2K2 Me Me 6.1 1.77 0.94 0.73 0.52 0.68 0.75 0.65 0.50 2\i 3 H H 7.1 2.07 1.7 0.91 0.84 0.95 0.53 0.51 0.42 2K2 3 Me Via 6.1 1.77 1.5 0.92 0.72 0.92 0.44 0.50 0.35 2l/i iH Me Me 2.87 0.84 0.08 0.31 0.09 0.32 0.29 0.58 0.23 2 iVz H M 3.09 0.91 0.16 0.42 0.15 •0.42 0.18 0.45 0.18 IH 2 Me Me 2.45 0.72 0.27 0.61 0.19 0.63 0.06 0.92 0.08 IH iH H H 1. 25 0.37 0.05 0.37 0.05 0.33 0.04 0.32 0.05 iH % No. 9 H 0.88 0.26 O.OI 0.16 O.OI 0.16 0.02 0.31 0.04 See "Note" with Table IV, page 354. • From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. ^^^ Properties of Structural Shapes, etc. Chap. 10 Table XV.* Properties of Double-Angle Sections. Equal Legs ANGLES PLACED BACK TO BACK ^ 3! ■y'^^ Single angle Two angles Radii of gyration, r, in inches Size, in Weight Area, Axis i-i Axis 2-2 per foot, sq in In H-in 3,i-in i/^-in 54-in lb contact apart apart apart apart 8 X8 XiH 56.9 33.46 2.42 3.42 3.51 3.55 3.60 3.69 1^6 42.0 24.68 2.46 3.37 3.46 3.50 3.55 3.64 \^ 26.4 15.51 2.51 3 33 3.41 3.45 3.50 3.59 6 X6 Xi 37.4 22.00 1.80 2.59 2.68 2.72 d.77 2.87 iMfi 26.5 15.56 •1.83 2.54 2.63 2.67 2.71 2.8? i 5 XS Xi 14.9 30.6 8.72 18.00 1.88 1.48 2.49 2.19 2.58 2.62 2.66 ^.38 2.75 2.47 2.28 2.33 iHs 21.8 12.80 1. 51 2.13 2.22 2.26 2.31 2.4a ^A 12.3 7.22 1.56 2.09 2.17 2.21 2.26 2.35 4 X4 X^Me 19-9 11.68 1. 18 1.75 1.85 1.89 1.94 2.04 Vx 6.6 3.88 1. 25 1.66 1.75 1.79 1.84 1.93 3V^X3HX»3/i6 17. 1 10.06 1.02 1.55 1.65 1.70 1.75 1.85 1 H 5.8 3.38 1.09 1.46 1.55 1.59 I 64 1.73 , 3 X3 XH 11.5 6.72 0.88 1.32 1. 41 1.46 i-Sr i.6i \ H 4.9 2.88 0.93 I. 25 . 1.34 1.38 1.43 1.53 i 2l/^X2HXH 7-7 4.50 .0.74 1.09 1. 19 1.24 1.29 1.39 ; H 4.1 2.38 0.77 1.05 1. 14 1. 19 1.24 1.34 i 2 X2 YJA^ 5.3 3.12 0.59 0.88 0.98 1.03 1.08 1. 19 i M 3.19 »,i.88 0.61 0.85 0.94 0.99 1.04 1. 14 This table and the two following are employed in computing the safe resistance to compressive stress of two angles, back to back, used as struts or as the compression- chords of roof-trusses, etc., by the following rule: Obtain from the compression-formula in use the allowed stress per square inch corresponding to the ratio of slenderness of the section, and multiply that value by the area. The result will be the allowable compressive stress. . Example i. Section given. Required the safe load in compression, as per formula S = 19 000 — 100 //r, on a strut composed of two angles, 4 by 4 by \i in, back to back, with an unsupported length of 9 ft. Area of section, A = 3. 88 sq in; least radius of gyration, r = 1.25 in. Ratio of slenderness, //r = 9 X 12 -^ 1.25 = 86.4. Allowed unit stress, 5 = 19 000 — 100 X 86.4 = 10 360 lb per sq in. Safe load, AS — 3.88 X 10 360 =» 40 200 lb. Example 2. Stress given. Required a section for a member in compression, 12 ft 3 in long, made of two angles separated by ^^-in gusset-plates, to resist a total stress of 35 odo lb; ratio of slenderness not to exceed 120. Assume two angles, 5 by 3 by Me in, long legs back to back. Area of section, A = 4.80 sq in; least radius of gyration, r = 1.26 in. Ratio of slenderness, //r = 12.25 X 12 -^ 1.26 = 116. 7. Allowed unit stress, 5 = 19 000 — loo X 116.7 = 7 330 lb per sq in. Safe load, AS = 480 X 7 330 = 35 200 lb. In the first case the least radius of gyration is that about the axis r-i; in the second case, about the axis 2-2; in all cases the least radius of gyration determines the ratio of slenderness and therewith the allowed safe compressive stress. In all cases, also, the two angles are to be secured together by stay-rivets, so spaced as to insure that the section acts as a unit. The ratio of slenderness of any single angle between ri vets must always be less than that of the strut or compression-chord. •From Pocket Companion, Carnegie Stee^ Company, Pittsburgh, Pa» Properties of Structural Shapes, etc. 371 Table XVI.^ Properties of Double-Angle Sections. Long Legs Vertical ANGLES PLACED BACK TO BACK hIkm^^4'' y- Single angle Two angles Radii of gyration, r, in inches Size, in Weight per foot, lb Area, sq in Axis i-i Axis 2-2 In - contact H-in apart ^6-in apart i/^-in apart M-in apart 8 X6 Xi 7/16 44.2 33.8 20.2 26.00 19.88 11.86 2.49 2.53 2.57 2.39 2.35 2.31 2 2 2 48 44 39 2.52 2.48 2.43 2.57 2.52 2.48 2.66 2.61 2.56 8 XsHXi H 35.7 27.5 16.5 21.00 16.12 9.68 2.51 2.55 2.59 1.26 1.20 I. IS 35 29 23 1.40 1.34 1.28 1. 45 1.39 1.32 1.55 1.49 1. 41 7 Xal'ixi 3/8 32.3 23.0 13.0 19.00 13 50 7.60 2 19 2.23 2.27 1. 31 1.25 1.20 40 34 28 1.45 1.39 1.33 1.50 1.44 1.37 1.60 1.53 1.46 6 X4 Xi 30.6 21.8 12.3 18.00 12.80 7.22 1. 85 1.89 1.93 1.60 1.55 1.50 69 63 58 1.74 1.68 1.62 1.79 1.73 1.67 1.89 1.82 1.76 6 X3y2xi Mo 28.9 20.6 9.8 17.00 12.12 5.74 1.85 1.89 1.9s 1.37 1. 31 I. 25 47 41 33 1. 51 1.45 1.37 1.56 1.49 1.42 1.66 1.60 1.50 5 X4 XVs 24.2 II. 14.22 6.46 1.52 1.59 1.66 1.58 76 66 1.80 1.70 1.85 1.75 \% 5 XaViX^/i M6 22.7 8.7 13.34 5.12 1.53 1. 61 1.42 1.33 51 41 1.56 1. 45 1. 61 1.50 1. 71 1.59 5 X3 X^Vie 19-9 8,2 11.68 4.80 1. 55 i.6i 1. 18 1.09 27 17 1.32 1.22 1.37 1.26 1.47 1.35 aVixz xm^XMe 95 4.5 5.56 2.64 0.72 0.75 1.37 1. 31 1.46 1.40 I-Si 1.45 I.S6 1.50 1.66 1.59 3 X2 XH 7-7 4.1 4-50 2.38 0.5s 0.57 1.42 1.38 1.52 1.47 1. 57 1.52 1.62 1.57 1.72 1.67 2HX2 X\i ■ H 6.8 3.62 4.00 2.12 0.56 O.S9 I. IS I. II I.2S 1.20 1.30 I.2S 1.35 1.30 1.46 1.40 • From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa, Properties of Structural Shapes, etc. 373 Table XVIII. Properties of Double-Channel Sections STAND^UlD CHANNELS PLACED BACK TO BACl^ 3 ^ ^^ rrTTTy/ y7777n\ The radii of gyration given correspond to directions indicated by the arrow-heads Radii of gyration, r, in inches Depth, Thick- ness of Weight per foot of one channel, lb Area of two Axis 2-2 in web, in channels, sq in A.xis i-i Vx-\v\. %-in i-in apart apart apart 0.40 3300 19.80 5.62 1.38 1.48 1.58 0.43 35.00 20.58 5.58 1.38 1.47 1.57 0.52 40.00 23.52 5.43 1.37 1.46 1.56 15 0.62 45.00 26.48 5.32 1.37 1. 45 1.56 0.72 50.00 29.42 • 5.23 1.37 1.46 I 56 0.82 55-00 32.36 5.16 1.38 1.47 I 58 0.28 20.50 12. o5 4.61 1.24 1.34 1.44 0.39 25.00 14.70 4.43 1. 21 1. 31 1. 41 12 0.51 30.00 17.64 4.28 1.20 1.30 1.40 0.64 35.00 20.58 4.17 1. 21 1. 31 1. 41 1.76 40.00 23.52 0.09 1.23 1.32 1 = 43 0.24 15.00 8.92 3.87 1. 14 1,24 1.34 0.38 20.00 11.76 3.66 1. 10 1.20 1. 31 10 0.53 25.00 14.70 3.52 1. 10 1.20 1. 31 0.68 30.00 17.64 3.42 1. 12 1.22 1.33 0.82 35.00 20.58 3. 35 1. 16 1.26 1.37. 0.23 13.25 7.78 3.49 1.09 1. 19 1.29 9 0.29 15.00 8.82 3.40 1.07 1. 17 I 28 0.45 20.00 11.76 3.21 I. OS 1. 15 1.26 0.62 25.00 14.70 3.10 1.07 1. 17 1.28 374 Properties of Structural Shapes, etc. Chap. 10 Table XVIII (Continued). Properties of Double-Channel Sections STANDARD CHANNELS PLACED BACK TO BACK ^~1 1-4- <-— 4rs-> 1 The radii of gyration given correspond to directions indicated by the arrow-heads Radii of gyration, r, in inches Depth, Thick- ness of Weight per foot of one channel, lb Area of two Axis 2-2 in web, in channels, sq in Axis i-i YAn ^^in i-in apart apart apart 8 0.22 II. 25^ 6.70 3.11 1.04 1. 14 1. 25 8 0.31 13-75 8.08 2.98 1.04 1. 14 1.25 8 0.40 16.2s 9-56 2.89 1.03 1. 14 1.24 8 0.49 18.7s 11.02 2.82 1.03 ■I. 14 1.24 8 0.58 21.25 12.50 2.77 1.03 1. 14 1.24 7 0.21 975 5.70 2.72 0.99 1.09 1.20 7 0.32 12.25 7.20 2.59 0.99 1.09 1.20 7 0.42 14.7s 8.68 2.50 0.99 1. 10 1. 21 7 0.53 17.25 10.14 2.44 1. 00 1. 10 1. 21 7 0.63 19.7s 11.62 2.39 1. 00 1. 10 1.22 6 0.20 8,00 4.76 2.34 0.94 1.05 I. IS 6 0.32 10.50 6.18 2.21 0.94 I. OS 1. 16 6 0.44 1300 7.64 2.13 0.9s 1.06 1. 16 6 0.56 IS. 50 9.12 2.07 0.9s 1.06 1. 17 5 0.19 6.50 3.90 1.95 0.89 1. 00 1. 10 5 0.33 9.00 5.30 1.83 0.90 1. 00 I. II S 0.48 II. SO 6.76 1.7s 0.91 1. 01 1. 12 4 0.18 5.25 3-10 1.56 0.84 0.9s 1.06 4 0.25 6.25 3.68 I. SI 0.84 0.95 1.06 4 0.32 7-25 4.26 1.46 0.84 0.9s 1.06 3 0.17 4.00 2.38 1. 17 0.80 0.91 1.02 3 0.26 5.00 2.94 1. 12 0.81 0.92 1.03 3 0.36 6.00 352 1.08 0.83 0.93 I. OS Definitions, Working Stresses and Examples 375 CHAPTER XI RESISTANCE TO TENSION. PROPERTIES OF IRON AND STEEL By HERMAN CLAUDE BERRY PROFESSOR OF MATERIALS OF CONSTRUCTION, UNIVERSITY OF PENNSYLVANIA 1. Definitions, Working Stresses and Examples The Ultimate Tensile Strength of a material is the amount of internal stress which a section one square inch in area is capable of exerting against an external axial force. It is the unit stress or intensity of stress, expressed in pounds per square inch, which the material can withstand. It is often called the ultimate strength or ultimate stress of the material. Its value for any material depends on the tenacity of the fibers or the cohesion of the particles of which the material is composed. An Axial Force is one which acts uniformly over the section of a prismatic body so that the resultant of the distributed forces coincides with the axis of the body. Hence the total axial force which any cross-section of a body will resist is the product of the ultimate strength of the material and the area of the cross-section, in square inches. Safe Working Stress. The ultimate strength of different building materials has been found by pulling apart bars of known dimensions and dividing the maximum load each sustained by the area of the bar before testing. This ulti- mate strength, however, must not be used to proportion the size of members of structures, because of variations in material, hidden defects and imperfect workmanship; and, especially, because of indefiniteness as to the maximum load that may be imposed on the structure. To provide safety against the rupture of a member and the consequent failure of the structure from any of these causes, the proportions of the members must be based on safe working stresses which are usually some fractional part of the ultimate strength found by experiment to provide proper security against failure. The Factor of Safety is the ratio of the ultimate strength to this safe working stress for that material. Its value ranges generally from 2 to 10, depending upon the nature of the material and the service to which it is^applied. Safe Working Stress in Tension. Table I gives these values for various building materials. The total safe load that may be applied to a piece of material of uniform section is found by multiplying the cross-section of the piece, in square inches, by the safe working stress opposite the name of the material of which the piece is composed. Then if P = the safe load in lb, St = the allowable safe working stress in tension, b = the width of a rectangular bar, h = the depth of a rectangular bar, d = the diameter of a round bar, there results, for a rectangular bar, P=bhSt ^ (i) and for a round bar, P = o.7S54 d^St {2) 376 Resistance to Tension. Properties of Iron and Steel Chap. 11 The area of cross-section to support a load P is, for a rectangular bar, P A = St and for a round bar .=v^ 0.7854 5« Table I. Safe Working Stress in Tension for Building Materials * (3) (4) Material Cast iron Wrought iron Steel, medium Chestnut Douglas fir Hemlock Pine, long-leaf yellow . Pine, short-leaf yellow. Pine, Norway Pine, white Redwood Spruce. White oak Safe stress lb per sq in (St) 3 000 12 000 16 000 850 800 600 I 200 900 800 700 700 800 I 200 * Note. For woods these values may be increased up to 30% for selected, perfectly protected, commercially dry timber, not subject to impact, that is, for ideal conditions. (See, also, pages 637 and 647.) Example i. What size of medium-steel angle should be used to sustain a tensile force of 64 000 lb? Answer. By formula (3), 64000 the net sectional area = 16000 = 4.00 sq m From the Table of the Properties of Angles (Chapter X) we find that a 4 by 4 by ^-in angle has an area of 4.61 sq in, which is to be reduced by a H-in hole for a H-'m rivet, leaving 4.61 — {J4XH) = 4.06 sq in, net area. This is slightly in excess of the required amount. The SAFE LOAD for angles commonly used in roof-trusses is given in Table X; and the reduction in sectional area caused by rivet-holes, in Tj^ble XI, this chapter, and in Table I, Chapter XX. See also, Chapter XII, page 414, paragraph on Punching Rivet-Holes. Example 2. What size of white-pine tie-beam should be used to sustain a tensile force of 60 000 lb? Answer. By formula (3), 60000 = = 85.7 sq m the net sectional area = If the depth is taken at 1 2 in, the net width must be 85.7 = 7.2 in. Allowance must be made for the increase in tension on the lower side of the beam, due to its own weight, and also for any cutting that may be necessary in making the connections or holes for truss-rods. If there is a 2-in hole through the beam, a Wrought Iron 377 lo by 1 2 -in timber must be used. This makes allowance for the weight of the beam itself. If the unsupported length of the beam is great, the allowance for the weight must be made according to the methods explained in Chapter XV, page 572, for the calculation of tie-beams subjected to transverse loading. 2. Wrought Iron Manufacture. Wrought iron is a mixture of pure iron and slag, about 96% iron and 3% slag, together with from V2 to %% of other elements including carbon, phosphorus, sulphur and manganese. It is made from pig iron and iron oxide, or mill-scale, in a reverberatory furnace consisting of a firebox, a hearth or working-chamber, and the necessary dampers and flues. The impur- ities are removed from the iron at different stages in the process, silicon and manganese during the melting-down stage, part of the phosphorus and sulphur during the clearing-stage and the carbon and remainder of the phosphorus and sulphur during the boiling-stage. The iron is then in a pasty condition ready for a thorough stirring by the workman, who collects it into balls of about 80 lb weight and takes it to a squeezer or forge where the greater part of the slag is removed. It is then rolled out into muck-bars. These bars are cut into pieces which are piled into bundles suited to the size of the finished bar. The piles are heated and rolled again. The rolling reduces the amount of slag and makes the material denser. The process of reroUing may be repeated a number of times to produce double or triple-refined merchant-bar iron. The Appearance of Wrought Iron is very much like that of steel. It may be distinguished from steel by nicking one side of the bar and bending it away from the nick. Iron will split along the slag-laminations and show the coarsely fibrous nature of the material; while steel will bend or rupture at the nick without splitting, any fracture being finely fibrous or crystalline. When ruptured in a tension-test wrought iron shows a dark fibrous fracture. If the specimen is grooved before testing or broken in impact the fracture will be coarsely crystalline. Welds, Wrought iron is more easily welded than steel because the work may be accomplished through a wider range of temperature than with steel. A weld may develop the full strength of the bar, but tests on hand-forged welds on rough tie-bars reported by Kirkaldy gave average values of about 60% of the strength of the bar. Use. Wrought iron is no longer used for the manufacture of structural shapes, such as angles, channels and beams, its use for structural work being practically limited to bars, rods and bolts. It can be worked more easily than steel in threading-machines; and on this account, unless steel is specified, some companies will furnish truss-rods, bolts, etc., in wrought iron. Specifications * for Wrought Iron. Wrought iron may be purchased under the Specifications of the American Society for Testing Materials. Material Covered, i . These specifications cover two classes of wrought-iron plates, as determined by the kind of material used in their manufacture, namely: Class A, as defined in Section 2 (6); Class B, as defined in Section 2 (c); ♦These Specifications for Wrought-Iron Plates are issued by the Society under the fixed designation A 42. They were adopted in 1913 and revised in 19 18. There are also A. S. T. M. Standard Specifications for Staybolt Iton, Refined Wrought-Iron Bars, Iron and Steel Chain, etc. 37S Resistance to Tension. Properties of Iron and Steel Chap. 11 I. Manufacture Process. 2. (a) All plates shall be rolled from piles entirely free from any admixture of steel. (b) Piles for Class A plates shall be made from puddle-bars made wholly from pig iron and such scrap as emanates from rolling the plates. (c) Piles for Class B plates shall be made from puddle-bars made wholly from pig iron or frorrva mixture of pig iron and cast-iron scrap, together with wrought- iron scrap. II. Physical Properties and Tests Tension-tests. 3. (a) The plates shall conform to the following minimum reciuirements as to tensile properties: Properties considered Class A Class B 6 in to 24 in incl, in width Over 24 in to 90 in incl, in width 6 in to 24 in incl, in width Over 24 in to 90 in incl, in width Tensile strength, lb per sq in Yield-point, lb per sq in Elongation in 8 in, per cent 49 000 26 000 16 . 48 000 26 000 12 48 000 26 000 14 47000 26000 10 (h) The yield-point shall be determined by the drop of the beam of the testing- machine. The speed of the cross-head of the machine shall not exceed ^4 in per minute. Modifications in Elongation. 4. For plates under V\& in in thickness, a deduction of 1 from the percentages of elongation specified in Section 3 shall be made for each decrease of Vm in in thickness below He in. Bend Tests. 5. (a) Colu-Bend Tests. The test-specimen shall bend cold through 90° without fracture on the outside of the bent portion, as follows: For Class A plates, around a pin the diameter of which is equal to il^i times the thickness of the specimen; and for Class B plates, around a pin the diameter of which is equal to three times the thickness of the specimen. (b) Nick-Bend Tests. The test-specimen, when nicked on one side and broken, shall show for Class A plates, a wholly fibrous fracture, and for Class B plates, not more than 10% of the fractured surface to be crystalHne. Test-specimens. 6. Tension and bend-test specimens shall be taken from the finished plates and shall be of the full thickness of plates as rolled. The longitudinal axis of the specimen shall be parallel to the direction in which the plates are rolled. Number of Tests. 7. (a) One tension, one cold-bend and one nick-bend test shall be made for each variation in thickness of Ys in and not less than one test for every ten plates as rolled. (b) If any test-specimen fails to conform to the requirements specified by reason of an apparent local defect, a retest shall be made. If the retest also fails, the plates represented by such test will be rejected. III. Finish Finish. 8. The plates shall be straight, smooth, and free from cinder-spots und holes, injurious flaws, buckles, blisters, seams, and laminations. ^^ Cast Iron 379 IV. Marking Marking. 9. The plates shall be stamped or otherwise marked as designated by the purchaser. V. Inspection and Rejection Inspection. 10. (a) The inspector representing the purchaser shall have free entry, at all times while work on the contract of the purchaser is being per- formed, to all parts of the manufacturer's works which concern the manufacture of the plates ordered. (See complete Specifications for Sections 10, 11 and 12.) 3. Cast Iron Cast Iron has been defined as a saturated solution of carbon in iron, the carbon-content varying from i^/^ to 4% according to the other impurities con- tained. It is hard, brittle, non-malleable and very fluid when melted, so that it is well adapted for casting into complex forms. Manufacture. It is produced in the blast-furnace, which is essentially a closed refractory-lined stack, with a valve-charging device at the top, tuyeres or openings in the lower part for the introduction of the air-blast, and a hearth at the bottom with a tap-hole for the periodic withdrawal of the iron and slag. The FURNACE-IRON is cast into pigs about 3 ft long and weighing about icxd lb each. Foundry-castings are made from pig iron and scrap melted in a cupola and poured into green-sand molds. The charge is made up of different quanti- ties of the different grades of pig so as to control the physical properties of the castings, principally through control of the silicon-content. . Appearance. Castings have a gray or white fracture according to the condi- tion of the contained carbon, the gray fracture indicating graphitic or separated carbon and the white the combined carbon. Gray iron is softer and tougher and is specified for ordinary castings. Strength. Cast iron does not have a definite elastic limit. A relatively small stress will produce some permanent deformation. Its ultimate tensile strength varies from 15 000 to 20 000 lb per sq in; and in some iron is as high'' as 30 000 lb per sq in. Its compressive strength varies over a wide range, 80 000 lb per sq in being a fair average value. Defects. Castings are liable to several common defects the chief of which are blow-holes due to the formation of steam from the damp molds, sand-holes due to misplaced sand, rough surfaces, cold shuts due to chilling of the iron and failure to fill the parts of the mold, shrinkage-cracks due to uneven cooling of the castings in parts of different thickness. In cored castings, also, the walls are frequently of variable thickness because of the shifting of the cores. This is especially frequent in case of hollow columns cast in a horizontal position. Because of these defects and on account of the low ultimate strength, cast iron should never be used where it is subjected to any great tensile stress. Specifications* for Cast Iron. The specifications of the American Society for Testing Materials, for gray-iron castings, include the following require- ments: 1. Unless furnace -IRON is specified, all gray castings are understood to be made by the cupola-process. 2. The sulphur-contents are to be: For light castings, not over o.io per cent. For medium castings, not over o.io per cent. For heavy castings, not over 0.12 per cent. * These specifications are issued under the fixed designation A 48. They were adopted in 1905 and revised in 1918. The complete specification can be obtained from the Society. 380 Resistance to Tension. Properties of Iron and Steel Chap. 11 3. In dividing castings into light, medium and heavy classes, the following standards have been adopted: Castings having any section less than V2 in thick shall be known as light CASTINGS. Castings in which no section is less than 2 inches thick shall be known as HEAVY CASTINGS. Medium castings are those not included in the above classification. 4. Transverse Test. The minimum breaking strength of the arbi- tration-bar under transverse load shall be: For light castings, not under 2 500 lb. For medium castings, not under 2 900 lb. For heavy castings, not under 3 300 lb. In no case shall the deflection be under o.io in. Tension-Test. Where specified this shall be: For light castings, not less than 18 000 lb per sq in. For medium castings, not less than 21 000 lb per sq in. For heavy castings, not less than 24 000 lb per sq in. The specifications give explicit directions for casting the arbitration-bar, which is iV4 in in diameter and 15 in long. Two of these are cast for each twenty tons of castings. One of each pair must fulfill the requirements to per- mit acceptance of the castings. The bar is loaded at the middle at a rate that will cause a o.io-in deflection in from twenty to forty seconds. The tension- test is not recommended. II. Castings shall be true to pattern, free from cracks, flaws and excessive shrinkage. In other respects they shall conform to whatever points shall be specially agreed upon. 4. Steel Steel is a mixture of compounds of iron and carbon with small quantities of other elements, including manganese, phosphorus, sulphur, silicon, etc. The carbon-content controls the hardness and strength of the steel. Less than 0.10% of carbon is present in the soft steels, which have most of the charac- teristics of wrought iron; while steel with more than 0.40% carbon is capable of being tempered, cannot be welded and is very much stronger. Manganese acts as a cleanser during the process of manufacture, and increases the forge- ab lity of the steel. Phosphorus and sulphur are harmful in their effects, phos- phorus making steel brittle under sudden loading and sulphur making it hot -short or brittle when heated. Manufacture. Structural steel is manufactured by the Bessemer and the open-hearth processes. In the first, molten cast iron is charged into a Bessemer converter, an air-blast is driven through the charge from i^erforations in the false bottom of the converter and the silicon, sulphur and carbon burned out. Carbon in the form of.fcrro-manganese is then added to deoxidize the charge and give the proper content of carbon in the finished steel, which is quickly drawn off and poured into ingots. Phosphorus is not removed ordi- narily by the Bessemer process; but if the lining of the converter is made of basic material, such as dolomite limestone, and if lime is added with the charge, the phosphorus will unite with it and be poured off with the slag. The Open-Hearth Process. In this process scrap-steel, pig-iron or molten furnace-iron and limestone flux are charged on the hearth of a Siemens furnace, a reducing gas-flame is directed onto the charge and the carbon and other impurities are gradually removed. When the reduction is about completed sam- Steel 381 pies are taken and carbon determined so that the charge may be withdrawn at the proper time. The process thus permits of much more accurate control of the product. The material is more uniform and consequently more dependable in service than Bessemer steel. Open-hearth steel is used for most struc- tural work. Phosphorus may be removed by the basic process as in case of Bessemer steel. Ores running low in phosphorus are generally used in America so that the basic process is httlc employed here. The Effect of Carbon and Phosphorus on the static strength of steel for the limits of carbon included in structural steel is an increase in strength of about I ooo lb per sq in for each o.oi% increase in either element. Cunning- ham's formula St = 40 000 + 100 000 (C + P) gives the approximate relation between the strength and the chemical composi- tion. C and P are respectively the amounts of carbon and phosphorus ex- pressed in percentage. For example, the ultimate strength of a steel having 0.15% carbon and 0.07% phosphorus is, approximately, St = 40 000 + 100 000 (0.15 + 0.07) = 62 000 lb per sq in The Percentage of Elongation decreases as the carbon-content and ulti- mate strength increase. An approximate relation being , , . I 400 000 percentage of elongation = • St Since the total elongation of a ruptured specimen is due to the local stretch- ing at the point of rupture and the uniform elongation over the whole gauge- length, it is necessary to report the gauge-length when reporting this result. Since the local elongation is the same for a 2 or an 8-in length, the percent- age OF elongation for the same material, tested on a 2-in gauge-length, is greater than if measured on an 8-in length. The Elastic Behavior of a specimen of steel loaded to rupture is best shown by a stress-strain diagram on which the stresses are plotted as vertical ordi- nates and the elongations or strains as abscissas, as in Fig. 1. Five significant results are shown: (i) The Modulus of Elasticity (E). The relation between the stress and the strain or elongation is called the modulus of elasticity. It is equal to the unit stress divided by the unit strain or deformation and is represented graph- ically by the tangent of the angle of the initial line with the horizontal. Its value for steel for tension is about 30 000 000 lb per sq in. (2) The Elastic Limit (E.L.) is that unit stress beyond which the ratio of stress to strain ceases to be constant, or beyond which the curve ceases to be a straight line. (3) The Yield-Point (F.P.), slightly above or beyond the elastic limit, is that unit stress at which the specimen begins to stretch without increase in the load. This stress may be determined from a test without the use of deli- cate measuring -apparatus by the drop of the beam or halt in the gauge of the testing-machine. (4) The Ultimate Strength {U.S.) is the greatest unit stress the specimen can sustain. (5) The Rupture-Stress (R) is the unit stress at the time of failure. This is the unit stress at the point of failure after the area of the cross-section of the 382 Resistance to Tension. Properties of Iron and Steel Chap. 11 specimen has been reduced; and because of the rapid dropping off of the load it is difficult to determine. It is not regularly observed in testing, attention being called to it merely to emphasize the fact that the ultimate strength of steel is not the stress at the time of failure of the specimen. This is true, alio, for wrought iron and ductile materials in general. 60000 60000 2 40000 ^_ U.S. \ -^ \ V.P. \ E.L ^^ \ E = tan a = 30000 000 0.0025 0.05 0.10 0.15 0.20 0.25 0. 6 Unit elongation The horizontal scale for the distance a & is ten times greater than for the remaining distance Fig. 1. Stress-strain Diagram of Test on Steel Specimens. 0.35 Effect of Punching and Shearing. Structural steel is hardened by the action of the punch and shear in the process of manufacture in the shop. On the die-side the metal is forced to flow from the tool and this cold working hardens and injures it as may be shown by a cold-bend test. The effect may be removed by annealing; but in the best work it is usually specified that rivet-holes shall be reamed during the assembling of the parts. This removes ^e injured metal and brings the parts into better alinement for the insertion of the rivets. The injury from shearing may be removed by milling the sheared edges. The Coefficient of Expansion of steel is o.ooo oo6 s per degree Fahrenheit. The ELONGATION in a length /, due to a change in temperature of / degrees, is then e = o.ooo oo6 5 U in which / is expressed in inches and / in degrees Fahrenheit. The Weight of Steel is taken at 489.6 lb per cu ft. The sectional area of a member in square inches multiplied by 3.4 equals the weight in pounds per linear foot. The Working Stress for structural steel in tension in buildings and bridges is Standard Specifications for Structural Steel for Buildings 383 i6 ooo lb per sq in in most specifications and building laws. For members subject to constant load some designers use a working stress of 20 000 lb per sq in. 5. Standard Specifications for Structural Steel for Buildings Specifications. These specifications are issued by the American Society for Testing Materials under the fixed designation A 9. They were adopted in 1901 and revised in 1909, 1913, 1914 and 1916. Extracts from these specifications follow: I. Manufacture Process, i. (a) Structural steel, except as noted in Paragraph (6), maybe made by the Bessemer or the open-hearth process. (b) Rivet steel, and steel for plates or angles over % in in thickness which are to be punched, shall be made by the open-hearth process. II. Chemical Properties and Tests Chemical Composition. 2. The steel shall conform to the following re* quirements as to chemical composition: Chemical content Phosphorus Sulphur f Bessemer. ... \ open-hearth. . Structural steel not over o. lo per cent not over o . 06 per cent Rivet steel not over 0.06 per cent not over 0.045 per cent Ladle Analyses. 3. An analysis of each melt of steel shall be made by the manufacturer to determine the percentages of carbon, manganese, phosphorus and sulphur. This analysis shall be made from a test-ingot taken during the pouring of the melt. The chemical composition thus determined shall be re- ported to the purchaser or his representative, and shall conform to the require- ments specified in Section 2. Check Analyses. 4. Analyses may be made by the purchaser from finished material representing each melt. The phosphorus and sulphur-content thus determined shall not exceed that specified in Section 2 by more than 25 per cent. III. Physical Properties and Test s e following require- Tension-Tests. 5. (a) The material shallr conform to th ments as to tensile properties: Properties considered Structural steel Rivet steel 55 000-65 000 0.5 tens, strength I 400 000* Tens, strength 22 46 000-56 000 . 5 tens, strength I 400000 VielH-noint min lb Der so in Elongation in 8 in, min, per cent Tens, strength * See Section 6. (ft) The yield-point shall be determined by the drop of the beam of the testing- machine. 384 Resistance to Tension. Properties of Iron and Steel Chap. 11 Modifications in Elongation. 6. (a) For structural steel over % in in thick- ness, a deduction of i from the percentage of elongation in 8 in, specified in Section 5 (a), shall be made for each increase of }i in in thickness above % in, to a minimum of i8 per cent. {h) For structural steel under Mo in in thickness, a deduction of 2.5 from the percentage of elongation in 8 in, specified in Section 5 (a), shall be made for each decrease of He in in thickness below Me in. Bend Tests. 7. (a) The test-specimen for plates, shapes and bars, except as specified in Paragraphs {h) and (c), shall bend cold through 180° without cracking on the outside of the bent portion, as follows: For material H in or under in thickness, flat on itself; for material over % in, to and including i M in in thick- ness, around a pin the diameter of which is equal to the thickness of the specimen; and for material over 1 34 in in thickness, around a pin the diameter of which is equal to twice the thickness of the specimen. {h) The test-specimen for pins, rollers, and other bars, when prepared as specified in Section 8 {c), shall bend cold through 180° around a i-in pin without cracking on the outside of the bent portion. (c) The test-specimen for rivet steel shall bend cold through 180° flat on itself without cracking on the outside of the bent portion. Test-Specimens. 8. (a) Tension and bend-specimens shall be taken from rolled steel in the condition in Parallel Section not less Ci I which it comes from the rolls, except as specified in Para- graph {h). {b) Tension and bend-test specimens for pins and rollers shall be taken from the fin- ished bars after annealing, when anneaUng is specified. (c) Tension and bend-test specimens for plates, shapes r... -n re- r cx i x ^ ^nd bars, except as specified Fig. 1a. Form of Specimen for Steel-test . -^ 1 / j\ a \ j in Paragraphs (a), (e), and CO. shall be of the full thickness of the material as rolled; and may be machined to the form and dimensions shown in Fig. 1a, or with both edges parallel. (d) Tension and bend-test specimens for plates over i ^ in in thickness may be ma- chined to a tliickness or diam- eter of at least % in for a length of at least 9 in. {e) Tension-test specimens \^e) Jiension-iest specimens 1"^ ; for pins, rollers and bars over ^ote> ^e.GageI:engfh,,Earailel Portions and jniTets shall be as shown, but the ends may be of any Form -which will fil the Holders of "the Testing Machine^ Fig. 2. Form of Specimen for Pins, Rollers, Bars, , etc., Over 1}/^ Inches Thick I H in in thickness or diameter may conform to the dimen- sions shown in Fig. 2. In this case, the ends shall be of a form to fit the holders of the testing-machine in such a way that the load shall be the axial. Bend-test speci- mens may be i by H in in section. The axis of the specimen shall be located at anj' pcint midway between the center and surface and shall be parallel to the axis of the bar. Tension-Members 385 (/) Tension and bend-test specimens for rivet steel shall be of the full-size section of bars as rolled. Number of Tests. 9. (a) One tension and one bend-test shall be made from each melt; except that if material from one melt differs ^ in or more in thickness, one tension and one bend-test shall be made for both the thickest and the thinnest material rolled. (6) If any test-specimen shows defective machining or develops flaws, it may be discarded and another specimen substituted. (c) If the percentage of elongation of any tension-test specimen is less than that specified in Section 5 (a) and any part of the fracture is more than % in from the center of the gauge-length of a 2-in specimen or is outside the middle third of the gauge-length of an 8-in specimen, as indicated by scribe-scratches marked on the specimen before testing, a retest shall be allowed. IV. Permissible Variations in Weight and Thickness Permissible Variations. 10. The cross-section or weight of each piece of steel shall not vary more than 2.5 per cent from that specified; except in case of sheared plates, which shall be covered by the following permissible variations. One cubic inch of rolled steel is assumed to weigh 0.2833 lb. (a) When Ordered to Weight per Square Foot: The weight of each lot in each shipment shall not vary from the weight ordered more than the amount given in Table I.* (b) When Ordered to Thickness: The thickness of each plate shall not . vary more than o.oi in under that order. The overweight of each lot in each shipment shall not exceed the amount given in Table II.* V. Finish Finish, i t . The finished material shall be free from injurious defects and shall have a workmanlike finish. VI. Marking Marking. 12. The name or brand of the manufacturer and the melt-number shall be legibly stamped or rolled on all finished material, except that rivet and lattice-bars and other small sections shall, when loaded for shipment, be properly separated and marked for identification. The identification-marks shall be legibly stamped on the end of each pin and roller. The melt-number shall be legibly marked, by stamping if practical, on each test-specimen. VII. Inspection and Rejection '' ^'^ '^ \^/ " ' Inspection. 13. (See complete Specifications for Sections 13, 14 and 15.) 6. Tension-Members Angles. The best section for tension-members of relatively small size depends greatly on the kind of end-connections used. Angles or channels are generally used for riveted connections. For very small members rectangular bars, such as lacing-bars, may be used. The strength of such members is computed on the net area through the rivet-holes. Angles used in tension should have lugs riveted to the outstanding legs and the tie-plate for the better distribution of the stress over the section. Tests on angles with riveted connections reported by F. P. McKibbenf gave from 77 to 86% of the strength of the material as shown by * Tables I and II are omitted here for lack of space. The complete specifications C3B be obtained from the Society. t Proceedings of the American Society for Testing Materials, Vol. VI, 1906. , 386 Resistance to Tension. Properties of Iron and Steel Chap. 11 tension-tests on standard specimens cut from these angles. Lugs increased the strength from 4.7 to 8.7%. It was also shown that a connection giving the center of the pull on the center of gravity of the section gave considerably higher strengths than when the center of pull was in line with the gauge-line of the rivets. In computing the net sectional area as reduced by rivet and bolt- holes Table XI will be found very convenient. Eye-Bars are used for the main tension-members of pin-connected trusses. They are rectangular in section with a forged head upset in dies and of the same thickness as the bar. The eye is accurately drilled in position in the axis of the bar, true to diameter and exact central distance. Because of its advantages for forging, soft steel is used in making eye-bars. They are also carefully an- nealed before drilling. Table VI gives the dimensions of standard eye -bars manufactured by the mills of the American Bridge Company. These bars are of practically the same dimensions as the standard bars of other com- panies. There is from 34 to 42% excess material in the section through the eye to insure in the forged part the development of the full strength of the body of the bar. Standard bars should be used in design to avoid the expense of making special dies in which to form the heads. Bars of less than the given minimum thickness are liable to fail, when loaded, by buckling in the head. Thick bars increase the bending-stresses in the pins and thus, indirectly, the necessary size of the eye. Except for very large structures they are limited to about 2 in. Tests of FuU-Size Eye-Bars are generally required when a great number of them are to be used in a structure, one in every fifty bars being usually tested. The specifications for carbon-steel bars require that an [ultimate tensile strength of 56 000 lb per sq in shall be developed, that the elongation in the whole length shall be 10% and that failure shall occur in the body of the bar. Nickel steel has been used for tension-members on a few long-span bridges. The working stress on the eye-bars was increased about one-half over that used for O J^Qnii iHiQCr O Fig. 3. Eye-bar with Screw-ends for Sleeve-nut or Turn-buckle carbon steel, and the requirements of the test-bars made correspondingly severe. The eye is made Vso in greater than the diameter of the pin. Bars packed on the same pins are drilled at the same setting so as to be of exactly the same length. Bars must be true to length within %2 in. Small eye-bars are some- times made with upset screw-ends and sleeve-nuts or turnbuckles in the middle for adjustment, as shown in Fig. 3 and Table VI, page 395. 1^2 D-^. Loop-eyes and Sleeve-nuts Loop-Rods (Fig. 4, and Table VII) of round or square section with welded loop-ends are used for counterties and bracing. Because of the weld they are not so dependable as other types of tension-members, but, because of the adjustment, are well adapted for this service as secondary members. Tension-Members 387 Fig. 5. Forked Loop A Forked-Loop Rod, Fig. 5, may be used for one of two tension-rods so as to avoid eccentricity where two rod^ balance each other on a pin. A clevis at each end of one of the rods accompUshes the same object. Turnbuckles and Sleeve-Nuts. The dimensions of these for adjust- ing the lengths and initial stress in ties are given in Table VIII, page 397. The open turnbuckle has the advantage of being easily inspected to note that the thread has sufficient bearing and that the ends of the rods do not butt together. Upset Screw-Ends are threaded enlargements on the ends of rods or bolts designed to give to the threaded portions a strength as great as that of the body of the bar. Because of effects of forging it is necessary to make the area of the cross-section of the upset end at the root of the thread a little larger than that of the rod itself. A standard upset rod will fail in the body of the bar with- out damaging the threaded portion enough to prevent the turning of the nuts^ The dimensions given are nearly the same with all manufacturers. If upset rods can not be obtained the section-area at the root of the thread must be used in computing the safe load. Clevises. Table IX, page 398, gives the dimensions and other details fot clevises according to the latest standards of the American Bridge Company. Tables. The following tables will be found useful in designing tension* members, or for drawing turnbuckles, sleeve-nuts, clevises, etc. The strength of plain rods in Table II is based on the area at the root of tlie thread. For lengths and weights of tie-rods and anchors for steel beams, see Table XIX, Chapter XV. Resistance to Tension. Properties of Iron and Steel Chap. 11 Table II. Safe Loads in Pounds on Round Rods Plain rods Upset rods 1 Load in pounds based on area Load in pounds based on full | at root of thread area of rod Diameter inches Stress in lb per sq in Stress in lb per sq in 10 000 12000 16000 10 000- 12000 16000 ^i 270 324 432 491 590 785 ^/ie 450 540 720 767 920 I 230 % 680 816 1088 I 104 I 320 1770 Vio 930 I 116 1488 1503 I 800 2 400 % I 260 I 513 2 016 1963 2360 3140 «A6 I 620 1944 2592 2485 2970 3960 % 2020 2424 3232 3068 3680 4910 % 3020 3624 4832 4418 5300 7070 % 4 200 5040 6 720 6013 7 210 9620 I 5500 6600 8800 7854 9420 12570 ' iVs 6 940 8328 II 104 9940 II 930 15900 IH 8930 10 716 14288 12 270 14720 19630 1% 10570 12680 16 910 14 840 17 810 23750 IV2 12950 15 540 20 720 17670 21 200 28 270 1% 15 150 18 180 24240 20730 24 880 33170 18/4 17440 20030 27900 24 050 28860 38480 iVs 20 480 24580 32760 27 610 33 130 44180 2 23020 27620 36830 31 420 37 700 50270 2V8 26340 31 610 42150 35 460 42550 56640 2H 30230 36280 48370 39760 47710 63600 2% 33000 39600 52800 44300 53160 70 880 2y2 37 ISO 44630 59440 49 080 58900 78 530 2% 46190 55430 73900 59390 71 270 95 020 3 54280 65 140 86 850 70680 84820 113 090 3V4 65 100 78 120 lot 160 82950 99 540 132 720 31/2 75480 90570 120 770 96 210 115 450 153 840 3% 86410 103 690 138 250 ITO 450 132 540 176690 4 99930 119 920 159 «*^9o 125 660 tso 790 201 050 4H 113 290 135900 181 300 141 800 170 160 226880 4V2 127 430 152900 203900 159000 190800 254400 4% 142 200 170 600 227500 177 200 212 640 283 520 5 157 630 189 100 252 200 196300 235 560 314 080 5V4 175 720 210 800 '281 100 216 400 259 680 346200 5V2 192 670 231 200 308300 237500 285000 380000 5% 212 620 255 100 340 200 259600 311 000 414700 6 230 980 277200 369600 282 700 339 200 452 300 Tension-Members 389 Table III. Safe Loads in Pounds for Flat Rolled Bars Computed for a stress of i6 coo pounds per square inch Thick- ness in inches Width in inches 1 I lU ■ iy2 1% 2 2V4 2V2 2«/4 3 3Vi Vifl 1 000 I 250 2 000 2 250 2 500 2750 3 000 3250 I 500 1750 Vs 2 000 2500 3000 3500 4 000 4500 5000 5500 6000 6500 yio 3 000 3750 4500 5250 6 000 6750 7500 8250 9 000 9750 Vt 4 000 5 000 6000 7 000 8000 9 000 10 000 II 000 12000 13000 •yi6 5 000 6 250 7 500 8750 10 000 II 250 12500 13 750 15000 16250 % 6 000 7500 9000 10 500 12 000 13500 15 000 16500 18 000 19500 Tifl 7000 8750 10500 12 250 14000 15 750 17500 19 250 21 000 22750 V2 8000 10 000 12 000 14 000 16 000 18 000 20 000 22 000 24 ooc 26000 rio 9000 II 250 13500 15750 18 000 20250 22500 24750 27 000 29250 ^^M ID 000 12 500 15 000 17500 20 000 22 500 25 000 27500 30 000 32500 Hio II 000 13 750 16 500 19250 22 000 24750 27500 30250 33000 36750 % 12 000 15 000 18 000 21 000 24 000 27 000 30 000 33000 36 000 39000 i%o 13000 16 250 19500 22750 26000 29250 32500 35 750 39000 42250 Vh 14 000 17500 21 000 24500 28000 31500 35000 38500 42000 '45500 1^/la 15000 18750 22 500 26 250 30000 33750 37500 41 250 45000 48750 I 16 000 20 000 24 000 28 000 32 000 36000 46 000 44000 48000 52000 iVio 17 000 21 250 25500 29750 34000 38250 42500 46750 SI 000 55250 iVs 18 000 22 500 27 000 31500 36000 40500 45000 49500 54000 58500 rYio 19 000 23750 28500 33250 38000 42750 47500 52250 57000 61750 iM 20 000 25000 30 000 35000 40 000 45000 50000 55000 60000 65000 1% 22 000 27500 33000 3850c 44000 49500 55 000 60 500 66000 71500 iy2 24000 30000 36000 42000 48 000 54 000 60 000 66 000 72 000 78 000 i-ys • 26 000 325CO 39000 45500 52000 58500 65 000 71500 78 000 84500 1% 28000 35000 42000 49000 56000 63000 70 000 77000 84 000 91 000 1% 30000 37500 45 000 53500 60 000 67500 75000 83500 90 00c 97500 2 32000 40 000 48 000 56 000 64000 72000 80000 88000 96000 104 000 ' , ' ' _ _ - - . -. 390 Resistance to Tension. Properties of Iron and Steel Chap. 11 Table HI (Continued). Safe Loads in Pounds for Flat Rolled Bars Computed for a stress of i6 ooo pounds per square inch Thick- Width in inches ness in inches 3V2 3% 4 4U 4V2 4«/4 5 5V2 6 6V2 He 3500 3 750 4 000 4250 450a 4750 5 000 5500 6 000 6500 Vs 7 000 7500 8000 8500 9000 9500 10 000 II 000 12 coo 13000 8/16 10500 II 250 12 000 12750 13500 14250 15 000 16 500 18 000 19500 H 14 000 15000 16000 17000 18000 19000 20000 22 000 24000 26000 "/io 17500 18750 20 000 21 250 22 500 23750 25 000 27500 30 000 32500 % 21000 22 500 24000 25500 27000 28 500 30000 33000 360c XD 39000 '^/io 24500 26 250 23 000 29750 31500 33250 35000 38 500 42 oc X) 45500 ¥2 28000 30000 32000 34000 36000 38000 40000 44000 480c 50 52 000 »/l6 31500 33750 36000 38250 40500 42750 45 000 49 500 54 o< )0 58500 % 35 000 37500 40 000 42500 45000 47 500 50 000 55 000 60 oc XD 65000 Hie 38 500 41 250 44 000 46750 49500 52 250 55000 60 500 66 a :o 71500 % 42000 45000 48000 51 000 54000 57000 60000 66 000 720c )0 78000 13/iQ 45 500 48750 52000 55 250 58500 61750 65 000 71 500 78 0< )0 84500 Vs 49000 52500 56000 59 500 63000 66 500 70000 77 000 84 o< X) 91 000 "/!'« 52 500 56250 60 000 63750 67 500 71 250 75000 82 500 900c )0 97 500 I 56000 60000 64 000 68000 72000 76000 80 000 88 000 96 o< X) 104 000 iVia 59 500 63750 68000 72250 76500 80750 85 000 93500 102 a 50 no 500 i^^ 63000 67500 72000 76500 8i 000 85500 90000 99000 108 0< X) 117 000 I%0 66500 71 250 76000 80750 85500 90250 95000 104 500 114 o< X) 123 500 lU 70000 75 000 80000 85000 90000 95000 100 000 no 000 120 0( X) 130 000 1% 77000 82 500 88000 93500 99000 104 500 no 000 121 000 132 o< DO 143 000 1^2 84000 90 000 96000 102 000 108000 114 000 120000 132 000 144 o< X) 156000 1% 91 000 97500 104000 no 500 117 000 123500 130000 143000 156 X) 169 000 1% 98000 105 000 1X2 000 119 000 126000 133000 140 000 154000 168 a DO 182 oco 1% 10$ 000 112 500 120 000 127500 135 OQO 142 500 150 OQO 165000 i8qo( DO 195000 2 112 000 120 000 128 000 136000 144000 152000 160000 176000 192 0( DO 208000 1 Tension-Members Table IV. Safe Loads in Pounds for Flat Rolled Bars Computed for a stress of lo coo lb per square inch* Thick- ness in inches iVi 1V2 1% 1% Width in inches 630 I 250 1880 2500 3 130 3750 4380 Sooo 5630 6 250 6880 7 500 8 130 8 750 9380 10 poo 10600 n 300 XI 900 12 500 13 800 IS 000 16300 17500 18800 20 000 iV* 1V2 i3/i 780 I 560 2340 3130 3910 4630 5 470 6250 7030 7810 8590 9380 10 200 10 900 11 700 12 500 13300 14 100 14 800 15 600 17 200 18800 20 300 21 900 23400 25 000 940 1880 2810 3750 4 690 5630 6 560 7500 8 440 9380 10 300 11 300 12 200 13 100 14 100 15 000 15900 16 900 17 800 18800 20600 22 500 24 400 26 300 28 100 30 000 1 090 2 190 3280 4380 5470 6560 7660 8750 9840 10 900 12 000 13 100 14 200 15300 16 400 17 soo 18600 19 700 20800 21 900 24 100 26 300 28 400 30 600 32800 35 000 1 250 2 500 3750 5 000 6250 7500 8750 10 000 11 300 12 500 13 800 15 000 163PO 17500 18800 20000 21 300 22 500 23800 2S 000 27500 30 000 32 500 35 000 37500 40 00c 2l/4 2V3 2% 1 410 2 810 4 220 5630 7030 8440 9840 11 300 12 700 14 100 15 500 16 900 18 300 19 7»o 21 100 22 500 23900 25 300 26 700 28 100 30900 33800 36 600 39400 49 200 45000 I 560 3130 4690 6250 7810 9380 10900 12 500 14 100 15600 17 200 18800 20300 21 900 23 400 25 000 26600 28 100 29 700 31300 34400 37 500 40600 43800 46900 50 000 I 720 3440 5 160 6880 8590 10300 12 000 13800 IS 500 17 200 18 900 20600 22300 24 100 25 800 27 500 39300 30900 32 700 34400 37800 41300 44700 48 100 51 600 55 000 I 880 3750 5630 7500 9380 II 300 13 100 IS 000 16900 18800 20 600 22 500 24 400 26300 28 100 30000 31900 33800 35600 37500 41300 45000 48800 52500 56300 60000 3V4 2030 4 060 6 090 8130 JO 200 12 200 14200 16300 18300 20300 22300 24 400 126400 28400 30500 32 SOO 34 soo 36600 38600 40600 44700 48800 S2 800 56900 60900 65000 • For unit stresses of 12 000, 12 500, and 15 000 lb increase by ^o, Vi, and V2 respec- tively. For working strength of wrought iron and steel, see pages 376 and 382. 392 Resistance to Tension. Properties of Iron and Steel Chap. 11 Table IV (Continued). Safe Loads in Pounds for Flat Rolled Bars Computed for a stress of lo ooo lb p)er square inch Thick- Width in inches ness in inches 3V2 3% , 4 4V4 * aV2 4?i 5 5^/^ 6 6V2 Vl6 2 190 2340 2810 2970 3130 3440 3750 4 060 2500 2660 Vs 4380 4690 5 000 5310 5630 5 940 6 250 6880 7500 8 130 %6 6560 7030 7500 7970 8440 8910 9380 10300 II 300 12 200 ■ . i ■ 8750 9380 10 000 10 600 II 300 II 900 12 500 13800 15 000 16300 %e 10 900 II 700 12 500 13300 14 100 14800 15600 17 200 18 800 20 300 - % 13 100 14 100 15 000 15900 16 900 17800 18800 20 600 22 500 24400 Vio IS 300 16 400 17500 18600 19700 20 800 21 900 24 100 26 300 28 400 V2 17500 18800 20 000 21 300 22500 23800 25 000 27500 30000 32500 »/l6 19700 21 100 22500 23900 25300 26 700 28 100 30900 33800 36600 % 21 900 23400 25 000 26 600 28 100 29700 31 300 34400 37 SCO 40 600 Hio 24 100 25 800 27500 29 200 30900 32 700 34400 37800 41 300 44700 8/4 26300 28 100 30000 31 900 33800 35600 37500 41 300 45 000 48800 1«/16 28 400 30500 32500 34500 36600 38600 40 600 44700 48800 528C0 % 30600 32800 35000 37200 39400 41 600 43800 48 100 52 500 56 900 1-yio 32800 35 200 37500 39800 42 200 44500 46 900 SI 600 56 300 60900 I 35000 37500 40 000 42500 45000 47500 SO coo 55000 60 000 6s 000 iVio 37200 39800 42500 45200 47800 SO 500 53100 58400 63800 69 100 iVs 39400 42 200 45000 47800 50600 53400 56300 61 900 67500 73 TOO 18A6 41 600 44500 47500 50500 53400 56400 59400 65300 71 300 77200 IV4 43800 46 900 SO 000 53100 56300 59400 62500 68800 75000 81 300 1% 48 100 SI 600 55000 58 400 61 900 65 300 68800 75 < XX) 82500 89400 11/2 52500 56300 60 000 63800 67500 71300 75000 82. >oo 90 000 97S0O 1% 56900 60 900 6s 000 69100 73100 77200 81 300 89. too 97500 105 600 iVi 61 300 65 600 70 000 74400 78800 83 100 87500 96. JOO 105 000 113 800 1% 65 600 70300 75 000 79700 84 400 89 100 93800 103 00 112500 121 900 2 70000 75000 80 000 8s 000 90 000 95000 100 000 no c XX3 120000 130 000 :.-. r? fO ,,.>-;i 1 _ * See foot-note, preceding table. xx> ? I nn;> ,oc)? c i Tension-Members 393 Table V. Standard Proportions of Upset Screw-Ends for Round and Square Bars Round bars Square bars Diam. of round or Excess Excess side of Diam. Diam. of Number of effec- Diam. Diam. of Number of effec- square of upset screw at of tive area of upset screw at of tive area bar screw- root of threads of screw- screw- root of threads of screw- in end thread per end over end thread per end over in in inch bar % in in inch bar % V2 8/4 0.620 10 54 % 0.620 10 21 «/l« 3/4 0.620 10 21 Vh 0.731 9 33 % % 0.731 9 37 I 0.8.37 8 41 Hio I 0.837 8 48 I 0.837 8 17 % I 0.837 8 25 iVs 0.940 7 23 ^u 1% 0.940 7 34 iM 1.065 7 35 % iVi 1.065 7 48 1% 1. 160 6 38 i-yi« 1V4 1.065 7 29 1% 1. 160 6 20 I 1% 1 . 160 6 35 1V2 1.284 6 29 iVio 1% 1. 160 6 19 1% 1.389 51/2 34 iVs 1 1/2 1.284 6 30 1% 1.389 5V2 20 i-Tio 11/2 1.284 6 17 1% 1.490 5 24 iM 1% 1.389 sVi- 23 1% 1. 615 5 31 iV\ti 1% 1.490 5 29 1% 1. 615 5 • 19 1% 1% 1.490 5 18 2 1. 712 4V2 • 22 iVio 1% 1. 615 5 26 21.^8 1.837 4^2 28 IV2 2 1. 712 4V2 30 2V8 1.837 4V2 18 irio 2 1. 712 4V2 20 2l/4 1.962 4V2 24 1% 2V8 1.8.37 4V2 28 2% 2.087 4V2 30 1% 2V8 2U 1.837 1.962 4V:i 4VI. 18 26 2% 2.087 4V2 20 2V2 2.175 4 21 i^'^/ui 2U 1 . 962 4VI. 17 2% 2.300 4 26 iVs 2% 2.087 4^2 24 2% 2.300 4 18 i^yio 2I/2 2.175 4 26 2% 2.425 4 23 2 2V2 2.175 4 18 2V8 2.550 4 28 2M« 2% 2.300 4 24 2% 2.550 4 20 21/8 2-''/8 2.300 4 17 3 2.629 31/2 20 23/lC 2% 2.425 4 23 3V8 2.754 31/2 24 394 Resistance to Tension. Properties of Iron and Steel Chap. 11 Table V (Continued). Standard Proportions of Upset Screw-Ends for Round and Square Bars Round bars Square bars Diam. of round or Excess Excess side of Diam. Diam. of Number of efTec- Diam. Diam. of Number of efifec- square of upset screw at of tive area of upset screw at of tive area bar screw- root of threads of screw- screw- root of threads of screw- in end thread per end over end thread per end over in in inch bar % in in inch bar % 2V4. 2V8 2.S50 4 28 3V8 2.754 3V2 18 2^/i6 2^/8 2.550 4 22 3V4 2.879 3y2 22 23/^8 3 2.629 3V2 23 3% 3.004 3^1- 26 aVie 3V8 2.754 3V2 28 3% 3 004 3V2 19 2V2 3V8 2.754 3V2 21 3V2 3.100 3V4 21 2»/l6 3V* 2.879 3V2 26 3% 3.225 3y4 24 2% 3H 2.879 3V2 20 3% 3.225 3H 19 2Hi6 3% 3.004 3V2 . 25 3^/4 3.317 3 20 2% 3% 3.004 zV^ 19 3% 3.442 3 23 . 2l8/i6 3V2 3- 100 3V4 22 3'/8 3-442 3 18 2V8 3% 3.225 3H 26 4 3.567 3 21 2i-ri6 3% 3.225 3V4 21 4V8 3.692 3 24 3 3^i 3.317 3 22 4V8 3.692 3 19 3V8 . 3% 3.442 3 21 4% 3.923 2% 24 3V4 4 3.567 3 20 4V2 4.028 2% 21 3^/^8 4V8 3.692 3 20 4% 4.153 2% 19 3V2 4U 3.798 2'V8 18 3% 4V2 4.028 2% 23 3% 4% 4.IS3 2% 23 3% 4% 4.255 •2% 21 Remarks. As upsetting reduces the strength of iron, bars having the same diameter at the root of the thread as that of the bar invariably break in the screw-end when tested to destruction, without developing the full strength of the bar. It is therefore necessary to make up for this loss in strength by an excess of Tnetal in the upset screw- ends over that in the bar. Table V is the result of numerous tests on finished bars made at the Keystone Bridge Company's Works in Pittsburgh, Pa., and gives proportions that will cause the bar to break in the body rather than in the upset end. The screw-threads in the above table are the Franklin Institute standards. To make one upset end for a 5-in length of thread, allow 6 in in length of rod, addi- tional. Tension-Members 395 Table VI .* Steel Eye-Bars (AMERICAN BRIDGE COMPANY standard) \ Ordinary Eye-Bar 5 Adjustable Eye-Bar Minimum length of short end from center of pin to end of screw, 6 ft, pref- erably 7 ft. Thread on short end to be left hand Pitch and shape of thread A. B. Co standard ii=::±g)--H j^ -t-> 2 3 4 5 6 7 8 9 lO 12 14 B Thicl ar Head cness Dia. Maximum pin Additional material, c, ft and in Max, in I I Min, in Bar Screw-end | Ex- cess head over bar, % 37.5 40.0 41.7 2 2yi 3 4 5 6 7 8 t H ^8 Dia. in Ex- cess up- set over bar, % 33.6 36.6 31.4 41.2 38.1 36J 34.3 41.6 23.9 23.9 32.0 35.7 44.6 36.2 24.1 30.2 34.2 38.3 L'th m, in Additional material, 6, ft an(J in For or- der- ing bar I- I- 4 I- C) For figur- ing w't 0- 7 O-II 1- 4 in 4K' t6H Dia. in 2% 3-M 2K2 33'-2 4V2 3H 4H 5H 4'/2 5K2 6 1/2 8H 6K2 ly 7 8 9 7 8 9 7H 9K2 9 loi.^ 11^2 10 IIK2 13 12 14 15 For or- der- ing bar For fig- ur- ing w't 6 7 t 8 7^/i 8K2 t 9V^2 I- 3 1- 7 2- O-IO I- 2 I- 7 I- I I- 5 I-IO 1- 6 I-IO 2- 2 1-8 2- 2 2-9 I-IO 2- I 2- 8 2- 2 2- 6 2-1 1 2- 3 2- 6 2-1 1 2-6 3- r i-M 2 4 5 5 5 I- I- O-IT 8 1-6 i-ii 2- 4 t«/4 'A I 2% 2H 2% I- I- I- I- I- I I- I I- I O-II I- I I- 2 I- O-II I- I- I I- 2 I- I- I- I I- 2 I- r- I I- 2 I- 2 I- I- I I- I I- 2 I- 3 8 8 7H 9H 8H iH 'A I 10 II tl2 37.5 35.0 I-ll 2- 3 2- 8 2- I 2- 8 3- 3 t =)4 I t y^ I , t ^4 I 2\\ 2\b. 2\h 2 I I 12 I3K2 ti5 2H 2% 3 3H 274 3 zM z\^ 3^/4 5\^ 6 6J,^ 6 6 7 7 7 7 iVi 8 7J'^ 8H 8K2 8 81/^ 8K2 9 9V^ 8i^^2 ^\^ 8 1 8 8^A 9 7'A 8 8H 9H 2 2 2 2 2 I I — I 1 5^^ l'/8 14 14M 17K2 fiSH 375 2- 4 2- 6 3- 2 2- 7 2-1 1 3^ 2- 8 3- 3- 4 2-II 3- 7 3- 5 3-9 4- I 3-8 4- 2 4-8 4- 3 4-10 5- 5 35.7 37.5 38.9 35.0 ti i»/i i}4 iH I3/^ 1 1/2 \iA i\i iH i\^ 1% 3J'^ 3^4 4 4'/4 4 4H \Vi 4^/4 4K 4^^ 4^/4 5 5H 25.8 28.0 33.2 37.3 I 1 1/8 18 19 t20_ 20 22 26.9 2(9.5 32.4 35.4 25.9 27.4 29.3 31.4 35.2 8 SH 9 9H 8 8H 81/i 9 10 22I./2 24 t25 26 1/2 28 t29H 2-10 3- 3 3- 7 2 2 lK4 37.5 3-3 3-8 4- I 3- 9 4- 4: 4-8 31 33 t34 35.7 Bars marked f should be used onHy when absolutely unavoidable i6 2 36 t37K2 14 16 37.5 34.4 4-1 1 5- 5 4-5 4-10 Deduct pin-hole when figuring weight * From Pocket ComDanion. Carneeie Steel Comoanv. Pittsbureh. Pa. 396 Resistance to Tension. Properties of Iron and Steel Chap. 11 Table YH.* Loop-Rods AMERICAN BRIDGE COMPANY STANDARD „ [• -Left thread ^T^nTTTLengthJ:., I .fr %|;~-'^g~P"'^ Min.lengthiV^ | 5"->; For Turnbnckle *-^ I p-S-'sJ For sleeve-nut Pitch and shape of thread A. B. Co standard Additional length A, in feet and inches, for one loop. A=4.i7/>+5.8y Diam. of pin, 2^4 •t3y4 t4H t5^4 t6K t6% Diameter or side r of rod in inches 4 ^^ I i^ iW I'M 1^12 i^i 1% o- 9^2 O-IC O-II I- 3 4 -6 I- 73'^ I- 8H •9^/i o-io o-ioH i-oH I- ll'^ I- 3 I- 4 5 I- 6 I- 7 1- 8 1-9 i-io i-ii 2- O 2- I O-II 0-IlH - I Mi - 2H I- 3K2 I- 4^'^ :-5H - Wi ■- 7K> I- 8H I-IO 2- 4 2- 5 2-6 0-113^^ I- o I- I I- 2 I- 3 I- 4H 1- 6K2 ■ 7K2 • 8i^^2 ■9^i I-IOJ'^ 2- O^^ 2- 1K2 2M2 2- 3K2 2- 5 2-6 2- 7 2- 9 2-10 2-1 1 I- 9 2- oYl ■ iH ■23'2 ' 3H ■ 5I/2 ■6j.^2 2-m -io3'^ 3- o 3- I I- 23/2 I- zVi I- 4^2 I-SJ'^ I- 7 1- 9 -10 I-II 2- o 2—2 2- 3 2- 4 2- 5 2- 6 2-. 73'^2 2- 9H 2 103-^ 2-1 1 3'^ 3- o}'^ 3- l'/^ 1-43^^ I- 63/2 I- 7K2 1- 93-^2 i-ioH 2- 03'^ 2- 2 2- 3 2- 4 2- 5 2- 6 2- 7 2- 8 2- 9 2-10 2-II 3- O 3- I 3-23^ I- 5 I- 6 I- 7 1- 9 1-9J-I i-io3'^ 1-113^^2 2- ©3^^ 2- VA '.- 2y2 2- 3'/^2 2- 4».^ 2- 53^^ I- 6 1- 8 9 I-IO I-II 2- O 2- I 2- 2 2- 3 2- ^^^ 2- S\^ 2- 63.-a 2- 63.^1 2- 73-^ 2- 7'/^ 2- 8'/ 2- 9 2-10 • 3- o 3- I 3- 2 3- 3 2- 9H 2-103^ 3- 1K2 3-33'i 3- 3'/^ I- 75-^ 1-8^^ I- gVi i-i 2- I 2- 2 2- 3 2- 4 2- s 2-6 2- 7 2- 8 2- 9 2-10 2-11 \i 3- o^^ 3- 1K2 3-23. -103^13 -Il3'l2 2- 03^^ ■ l3'^2 ■ 21/2 3K2 2-4^i ■ 6 ■ 7 - 8 2- 9 3- AVi Pins marked f • From Pocket are special. Maximum shipping length of Z = 35 ft. Companion, Carnegie Steel Company, Pittsburgh, Pa. Tension-Members 397 Table VIII.* Turnbuckles and Sleeve-Nuts AMERICAN BRIDGE COMPANY STANDARD All s dimensions in inch es T URNBUCKLE Sleeve- Nuts Or-^ c?-^ m ±=^ ^ "^ ® \%m^ \ tut |-*^ '! • r nl~ Tt 319^ O-M 1^^ ^r-^ <^ r 1^ — ; ^ — l-—-^ ^ 6 ->i K6-^ U— z!— >} a=e" ; a=g" for turnbuckles marked f Pitch and shape of thread, A. B. Co Pitch and shape of thread, A. B. Co standard standard Dia. of Standard dimensions Dia. Standard dimensions screw W't, of W't, u d / c / g 6 lb screw 11 d / a b c t lb % Vie 7K8 91 6 3/i6 Vi iMe T Me 21/^2 vMe ^8 H H I3//8 I H H iM 5/i M H 13/^8 I Me 2%o 1^16 7IH6 7?^ 1^6 Me M I Ma 1 1/2 IK2 % 1^6 Me 3/i iMe % iH 8H iHe n^2 >6 2 2 Vs 1V16 8H IH H I 2M 3 "% iK> 7 I'H 1% 1% H 3 I iH 9 iMg Vl6 iM 2Mc 4 I 1M2 7 1^6 m 1% H 3 1% iiMe 9% iMc Yi iH 2^6 S i.y% i-}4 7M2 2 2M6 1% Me 4 iM iH m iMc Vz 1^2 234 6 1% I'K 7M2 2 2^6 1% Me 4 i-ys 2M6 io\i iiMo Vi I^^ 3M6 7 m 2 8 23/i 23/4 iMs % 5 iH 2^ 10V2 1% % l3/4 3M6 8 iVz 2 8 2% 2% i^i % 6 1% 2V16 I078 2 % I^^ 3^2 10 iMs 2M m 2% 3-Ke m lie 8 ly^ 2% II Ki 2>^ % 2 3% II 1^4 214 m 23/4 3^6 m Me 9 i~/k 21^6 11^4 2^6 iHo 2^^ 3^/^ 12 1% 2H 9 3% 3% 2H K> 10 2 3 12 2^/^ iHe 2H 4H 14 2 2\^ 9 3\i 3% 2H 'A II 2\i 3^6 I23/i 2).^ 23/^,, 2K2 4^/^ 17 2\i 2% 9H 3V2 4He 2% Me 14 2^-4 ?>% 123/4 2IM6 1^6 2M2 4% 20 2% 23/4 9K2 3^2 4He 2% Me 15 2^A iVi^ iM 23/4 1-Me 2% 43^6 22 2% 3 10 3'A 4K2 2% % 18 21/2 3% I3K2 3H6 2 ^^2 3 59^ 25 2H 3 10 3% 4K2 2% % 19 2>4 4H I4K4 3H 'Mc 3H 5% 33 2% 3\i 10M2 A% 4^ Me 2li iMe 23 2% 4M6 I4H 3M6 I ^^2 3H 6Hc 36 2li 3V2 II A% sH 3% H 27 3 \H IS 3^^ ^2 3M2 6% 40 3 3y2 II A% S% 3% H 28 3H A% 15% 3^/i I Me 4 6)4 50 3H 3% II H 5 51 Me 3% »Me 35 zYz 5K1 16K' 4K I%2 4 7M 65 3H 4 12 S% 6M 3% % 40 sH 55^ 17H 4^6 iMe S 8M 95 3% 4H 12M2 s% 61 He 3% iMe 47 4 6 18 4-H iMe 5 8-M 108 4 4M2 13 m 7He AM I 55 t4K 6H 2m 4«/^ 1% 5%2 9H 140 4H A% 13K' m 7K2 A% I Me 65 U'A 6% 22^/^ 5'/^ 1% 6H io->4 19s 4M2 5 14 6% 71 Me 4% I Me 75 UH 7H 23^/^ 5'H 2 63^^ II M 205 ts 7'/2 24 6 2\i 6K2 11^^ 250 * From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. 398 Resistance to Tension. Properties of Iron and Steel Chap. 11 Table IX * Clevises AMERICAN BRIDGE COMPANY STANDARD All dimensions in inches Grip I H t^ *i rClearance-lina ■\<-n-^--\-- a — Grip=thickness of plate+H in, but must not exceed dimension/ Clevis- No. Head Max Min Nut 2H 4H 3 S Max Min u 3Ha 4H 6^6 Pork W't. lb CLEVIS-NUMBERS FOR VARIOUS RODS AND PINS Rods Pins Round Square Upset I iH 2 2H 2^ I iH m 2 2H I iH m m 2 2\i 2H 2% 2\i 2H 2% 2li 3 iH iH 1% 2H 2H 2% 3H 3H Clevises above and to right of zigzag line may be used with forks straight, tho^ below and to left of this line should have forks closed so as not to overstress the pin. L ? From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. Tehsion-Members 399 Table X. Safe Loads in Tension for Common Sizes of Angles with On^s %-Inch Rivet-Hole for a %-Incli Rivet Load in pounds for a stress of i6 coo lb per sq in Size of angle Load Size of angle Load 6X4X% 100 SCO 3V2X2HX% 45000 % 85 000 Vw 41 100 Va 68900 V2 % 37 000 28500 5X3^2 X% 82 500 M 19500 % 70 100 V2 57000 3X3X% V2 45000 37000 5X3X% 76500 % 28500 % 64900 % 19500 V2 53000 % 40 500 3X2V2XV2 % 33000 25 600 4X-lX«4 76500 f/i« 21 800 % 40 500 V4 17 600 4X3V3X% 60000 % 37600 3X2X7x0* 25900 25600 4X3X% 53 000 «/io* 21 8oo Va 45 000 H* 17 600 % 34600 272X2^15X710 25900 3V2X3V2XH 64500 % 22600 % 55 000 ^Aq 19200 V2 45 000 Vi 15500 % 34600 2^X2X'^Aq 22400 3V2X3X% SO 100 % 19500 V2 41 000 S/io 16600 % 31 500 Vi 12800 • These are special angles, risk of delay in delivery. It is better not to use them in ordinary work because of The End-Connections often determine the strength of angle tension- members. Some specifications for structural work require angles subject to direct tension to be connected by both legs if the section of both legs is con- sidered; and if connected by one leg, the section of one leg only is considered effective. Reliable tests (page 385) show this requirement to be needlessly severe. For single angles connected by one leg, the Specifications for the Structural Steelwork of Buildings, Chapter XXX, allow the net area of the connected leg and one-half that of the outstanding leg to be considered effective. (See Waterbury, Stresses in Structural Steel Angles, John Wiley & Sons, Inc., New York, 1917.) 400 Resistance to Tension. Properties of Iron and Steel Chap. 11 Table XI. Sectional Area to be Deducted from Plates and Angles for One Round Hole Note. Bolt-holes should be Via in larger than the diameter of the bolt; rivet-holes are usually Vs in larger than the diameter of the rivet.* II Diameter of hole in fractions of an inch and inches i H Ho % Ho V2 »/l6 % Hie % 1%G Vs i-Tio I iHc l3/l6 ivic I»/i6 %6 V4 0.05 0.06 0.07 0.08 0.09 O.II C.12 0.13 O.I-i 0.15 0.16 0.18 0.19 0.20 0.23 0.27 0.30 0.06 0.08 0.09 O.II 0.13 0,14 0.16 0.17 0.19 0.20 0.22 0.23 0.25 0.27 0.30 0.36 0.39 •ri6 0.08 O.IO 0.12 0.14 0.16 0.18 0.20 0.21 0.23 0.25 0.27 0.29 0.31 0.33 0.37 0.45 0.49 % 0.09 0.12 0.14 0.16 0,19 0.21 0.23 0:26 0.28 0.30 0.33 0.35 0.38 0.40 0.45 0.54 0-59 Via Q.II 0.14 0.16 0.19 0.22 0.25 0.27 0.30 0.33 0.36 0.38 0.41 0.44 0.46 0.52 0.63 0.69 1/2 0.13 0.1() 0.19 0.22 0.25 0.28 0.31 0.34 0.38 0.41 0.44 0.47 0.50 0.53 0.59 0.72 0.78 ric 0.14 0.18 0.21 0.25 0.28 0.32 0.3.5 0.39 0.42 0.46 0.49 0.53 0.56 0.60 0.67 0.81 0.88 % 0.16 0.20 0.23 0.27 0.31 0.35 0.39 0.43 0.47 0.51 0.55 0.59 0.63 0.66 0.74 0.90 0.98 Hie 0.17 0.21 0.26 0.30 0.34 0.39 0.43 0.47 0.52 0.56 0.60 0.6/. 0.69 0.73 0.82 0.99 1.08 3/4 0.19 0.23 0.28 0.33 0..S8 0.42 0.47 0.52 0.56 0.61 0.66 0.70 0.75 0.80 0.89 1.08 1. 17 i%c 0.20 0.25 0.30 0.36 0.41 0.46 0.51 0.56 0.61 0.66 0.71 0.76 0.81 0.86 0.97 1. 17 1.27 % 0.22 0.27 0.33 0.38 C.44 0.49 0.55 0.60 0.66 0.71 G.77 0.82 0.88 0.93 1.04 1.26 1.37 1%6 0.23 0.29 0.35 0.41 0.47 0.53 0.59 0.64 0.70 0.76 0.82 0.88 0.94 1. 00 I. II 1.35 1.47 I 0.25 0.31 0.38 0,44 0.5c 0.56 0.63 0.69 0.75 0.81 0.88 0.94 1. 00 *■" I -19 1.44 1.56 * See also Table I, Chapter XX and paragraph, Punching Rivet-Holes, page 414. 7. Wire Manufacture. Iron and steel wires are made from billets a])out 4 in square. These are rolled into long rods which are dipped in acid to remove the scale And furnish lubrication for the drawing process. This consists in pulling the rods while cold through steel dies haying a series of holes of gradually decreasing diameters. The cold working of the metal hardens it and makes it brittle so that it is necessary to anneal it at intervals during the process. The drawing increases the strength of the material, so that wires of different sizes, although made of the same material, differ greatly in ultimate strength. Finish. The common grades of iron and steel wire are furnished in several different finishes: plain black, bright tinned, copper-coated, japanned and with single and double coats of zinc galvanizing. The last is applied by passing the wire through the melted zinc which is deposited as a coating and forms one of the best-known protections against corrosion. Wire-Gauges. Table XIII gives, according to several gauges, the diameters of the different numbers of wire that have come into use for different purposes and have been brought out by different manufacturers. In ordering wire by number it is best to specify which gauge is meant. Strength. Table XIV gives the sizes according to the J. A. Roebling's Sons Company gauge, with the weight and length and the strength on an assumed basis of 100 000 lb per sci in. The different kinds of wire vary so widely in ulti- mate strength, on account of both the difference in quality of the material and the effect of the drawing, that in order to obtain the approximate strength of ^ Wire 401 wire, reference must be made to Table XII in connection with the foot-note to Table XIV. The following table is arranged from values which were published in the Catalogue of the J. A. Roebling's Sons Company: Table XII. Approximate Ultimate Strength of Different Sizes of Iron and Steel Wire Kind of wire Soft iron Telegraph and telephone (steel) Special aviator Piano wire Plough steel wire Hard-drawn copper trolley wire Hard-drawn telegraph and telephone copper Ultimate strength Large size Small size lb per sq in lb per sq in 45 000 60 000 60 000 80 000 247000 28s 000 307 000 340000 200 000 345 000 50 000 not used 56 000 66 oco The Uses of Wire are so many and varied that a bulky treatise would be required to adequately cover the subject. The catalogues of the American Steel and Wire Company mention electrical wires and cables of many kinds, telephone and telegraph wires, ignition-wires and cables for automobiles, motor- boats and aeroplanes, wire rope, wire tacks, wire fences, piano-wire, barbed wire, flat wire and so on, through a long list. The magnitude of the wire-output in the United States is seen from the fact that of the total production of 32 000 000 tons of all kinds of finished rolled iron and steel for the year 19 16, 3 500 000 tons were wire rods. For electrical purposes copper wire is mostly used. See Electric Work for Buildings, Part III, for information regarding wires and wire- calculations. The Brown & Sharpe Gauge is followed in the United States as the standard for copper wire> though there is a growing tendency to distinguish different electrical wires by their diameters, expressed in mils. (One mil = o.ooi in. A circular mil is the area of a circle o.ooi in in diameter.) The American Steel and Wire Company's Gauge is almost universally followed throughout the United States for steel wire. The Birmingham gauge, an English gauge, is the only wire-gauge recognized in successive Acts of Congress establishing tariffs, and for many years has been used as the basis for duties assessed on imported wire. Aside from these purposes its use is not extensive. The American Steel and Wire Company's Music-Wire-Gauge, now known as the Music- Wire-Gauge, upon recommendation of the United States Bureau of Standards, has been adopted as the standard for piano-wire. * See, also, pages 402, 403, 1469, 1473, 1509, 1510, 1512, and 1600. 402 Resistance to Tension. Properties of Iron and Steel Chap. Table XIII. Comparison of Standard Gauges for Wire and Sheet Metal * Diameter or thickness in decimals of an inch Washburn Birm- ingham or Stubs iron- United & Moen, Ameri- British Number of American or Brown States standard Roebling, American Stubs steel - can Screw Imperial or English gauge & Sharpe gauge for Steel & Co. legal wire- gauge wire- gauge sheet and plate iron and steel Wire Co., stccl- wire-gauge wlre- gauge wire- gauge standard wire- gauge ooooooo 0.5 . 4900 0.500 oooooo 0.580000 0.4687s 0.461S 0.464 ooooo 0.500 0.516500 0.4375 0.4305 0.432 oooo 0.454 . a6dooo 0.4062s 0.3938 0.400 ooo 0.42s 0.409642 0.37s 0.362s 0.0315 0.372 CX) 0.380 0.364796 0.34375 0.3310 0.0447 0.348 o 340 0.324861 0.312s 0.3065 0.0578 0.324 I 0.300 0.289297 0.28125 0.2830 0.227 0.0710 0.300 2 0.284 0.257627 0.265625 0.2625 0.219 0.0842 0.276 3 0.259 0.229423 0.2s 0.2437 0.212 0.0973 0.252 4 0.238 0.204307 0.23437s 0.22S3 0. 207 0.1105 0.232 5 0.220 0.181940 0.21875 0.2070 0.204 0.1236 0.212 6 . 203 0.162023 0.20312s 0.1920 0.201 0.1368 0.192 7 0.180 114285 0.1875 0.1770 0.199 0.1500 0.176 8 165 0. 128490 17187s 0.1620 0.197 0.1631 0.160 9 0.148 0.114423 0.15625 0.1843 0.194 0.1763 0.144 lO 0.134 0.101897 0.140625 0.1350 0.191 0.1894 0.128 ir 0.120 0.090742 0.125 0.1205 0.188 0.2026 0.116 12 0.109 0.080808 0.10937s 0.1055 0.185 0.2158 0.104 13 0.095 0.071962 0.09375 0.0915 0.182 0.2289 0.092 14 0.083 0.064084 0.078125 . 0800 0.180 0.2421 0.080 15 0.072 0.057068 0.070312s 0.0720 0.178 0.2552 0.072 i6 0.065 0.050821 0.0625 0.0625 0.175 0.2684 0.064 17 0.058 0.045257 0.05625 0.0540 0.172 0.2816 0.056 i8 0.049 0.040303 0.05 0.047s 0.168 0.2947 0.048 19 0.042 0.035890 0.04375 0.0410 0.164 0.3079 0.040 20 0.035 0.031961 0.037s 0.0348 0.161 0.3210 0.036 21 0.032 0.028462 0.03437s 0.0317 0.157 0.3342 0.032 22 0.028 0.025346 0.03125 0.0286 0.155 0.3474 0.028 23 0.025 0.022572 0.028125 0.0258 O.IS3 0.3605 0.024 24 0.022 0.020101 0.025 0.0230 0.151 0.3737 0.022 25 .0.020 0.017900 0.021875 0.0204 0.148 0.3868 0.020 26 0.018 0.015941 0.01875 0.0181 0.146 0.4C00 0.018 27 0.016 0.014195 0.0171875 0.0173 0.143 0.4132 0.0164 28 0.014 0.012641 0.015625 0.0162 0.139 0.4263 0.0148 29 0.013 011257 0.0140625 0.0150 0.134 0.4395 0.0136 30 0.012 0.010025 0.0125 0.0140 0.127 0.4526 0.0124 31 O.OIO 0.008928 0.0109375 0.0132 0. 120 0.4658 0.0116 32 0.009 0.007950 0.01015625 0.0128 6.115 0.4790 0.0108 ' 33 0.008 0.007080 0.009375 0.0118 0.112 0.4921 0.0100 34 0.007 . 006305 0.0085937s 0.0104 O.IIO 0.5053 0.0092 35 0.005 0.005615 0.0078125 0.009s 0.108 0.5184 0.0084 36 0.004 0.005000 0.00703125 . 0090 0.106 0.5316 0.0076 37 0.004453 0.006640625 0.0085 0.103 0.5448 0.0068 38 0.003965 0.00625 0.0080 0. lor 0.5579 0.0060 39 40 0.003531 003144 0.0075 0.0070 0.099 0.5711 1 0.097 0.1:842 1 0.0052 0.0048 The United States Standard Gauge was legalized by Act of Congress, March 3, as a standard gauge for sheet and plate iron and steel, and is used by the Custom I Department and by sheet-plate and tin-plate manufacturers. • See also, pages 401, 403, 1469, 1473, 1509, 1510, 1512, and 1600. Wire 403 Table XIV. Weight, Length and Strength of Steel Wire * Gauge of J. A. Roebling's Sons Company j Breaking- Number of Diameter Area load in pounds at Weight in pounds Number of feet in gauge in sq in rate of 100 000 lb Per I 000 ft Per mile 2 000 pounds persq in oooooo 0.460 0.166191 16 619 558.4 29-18 3582 ooooo 0.430 0.145221 14 522 487.9 2576 4099 0000 0.394 0.121304 12 130 407.6 2 152 4907 000 0.362 0.102922 10 292 345.8 1826 5783 oo 0.331 . 0S6049 8605 289.1 I 527 6917 0.307 0.074023 7402 248.7 I 313 8041 I 0.283 0.062902 6 290 211. 4 I 116 9463 2 0.263 0.054325 5 433 182.5 964 10 957 3 0.244 . 046760 4676 157. 1 830 12 730 4 0.225 0.039761 3976 133.6 705 14970 s 0.207 0.033654 3365 113. 1 597 17687 6 0.192 0.028953 2895 97.3 514 20 559 7 0.177 . 024606 2 461 82.7 437 24 191 8 0.162 0.020612 2061 69.3 366 28878 9 0.148 0.017203 I 720 57.8 305 34600 lo 0.135 0.014314 I 431 48.1 254 41584 II 0.120 0.0113T0 I 131 38.0 201 52 631 12 0.105 0.008659 866 29.1 154 68 752 13 0.092 . 006648 665 22.3 118 89525 14 0.080 0.005027 503 16.9 89.2 118 413 15 0.072 0.004071 407 13.7 72.2 146 198 i6 0.063 0.0031 17 312 10. 5 55.3 191 022 17 0.054 0.002290 229 7.70 40.6 259 909 i8 0.047 0.001735 174 5. 83 30.8 343 112 19 0.041 0.001320 132 4.44 23.4 450 856 20 0.035 . 000962 96 3.23 17. 1 6x8 620 This table was calculated on a basis of 483.84 lb per cu ft for steel wire. Iron wire is a trifle lighter. The breaking strengths were calculated for 100 000 lb per sq in throughout, simply for convenience, so that the breaking strengths per square inch of wires of any strength may be quickly determined by multiplying the values given in the table by the ratio between the strength per square inch and 100 000. Thus, a No. 15 wire, with a strength per square inch of 150 000 pounds, has a breaking strength of 150000 - „ 407 X = 610.5 lb. 100 000 It must not be inferred from this table that steel wire invariably has a strength of 100 000 lb per sq in. As a matter of fact its strength ranges from 45 000 lb per sq in for soft, annealed wire to over 400 000 lb per sq in for hard wire. * See, also, pages 401, 402, 1469, 1473, 1509, iSio, 1S12, and i6oa t Also American Steel & Wire Company, etc. 404 Resistance to Tension. Properties of Iron and Steel Chap. 11 8. Wire Rope Kinds of Wire Rope. There are several kinds of wire rope in common use. In each there are three or more qualities depending on the kind of wire used and the kind of core about which the strands are laid. The Trenton Iron Company Hsts the following: (i) Hatilage or Transmission-Rope, composed of six strands of seven wires each, laid about a hemp core. It is used for haulage, transmission of power, in places where surface-wear is of chief consideration and where sheaves of suflScient diameter may be used. (2) Hoisting-Rope, composed of six strands of nineteen wires each. It is used for elevator service, shafts and derricks, and in places where it is not sub- ject to abrasion and where flexibility is of chief consideration. (3) Scale Rope, composed of six strands of nineteen wires each, the inner coils of the strands being of fmer wire. It is intermediate in flexibihty between the first and second kinds of rope. (4) Non-Spinning Hoisting-Rope, having eighteen strands of seven wires each. Twelve of the strands are laid in reverse direction to the inner six, making it well adapted for hoisting in free suspension without untwisting and turning the load. (5) Extra-Flexible Hoisting-Rope, having eight strands of nineteen wires each. (6) Special Flexible Hoisting-Rope, having six strands of thirty-seven wires each. (7) Hawser-Rope and Flexible Running-Rope, having six strands of twelve galvanized wires each, laid about a hemp core. (8) Tiller-Rope, composed of six small seven-strand ropes laid about a hemp core. It is the most flexible of wire ropes and is used to operate tillers and for hand-ropes in elevators. The Lay of Wire Rope is the twist of the wires in the strands relatively to the strands in the rope. In the ordinary lay the twist of the strands is the reverse of that of the wires, while in the Lang lay the strands are laid in the same direction as the twist of the wires. This latter gives a greater distribution of the wearing-surface and a somewhat greater flexibility; but it has the dis- advantage of a tendency to untwist and for this reason should not be used for hoisting weights in free suspension. Wire rope is also made up in flat or rib- bon FORM. For large sizes it is more flexible than standard rope and may be run over smaller drums. Materials for Rope. Nearly all of the above kinds of rope are made up in the following materials: (i) Best Grade of Wrought Iron. This is used in high-speed passenger- elevator SERVICE as it seems to suffer less from the .effects of the stresses due to the starting and stopping of the cars. (2) Cast-Steel Wire, with an ultimate strength of from 160 000 to 210 000 lb per 5q in, according to the size used. (3) Extra-Strong Cast-Steel Wire, with an ultimate strength of from 190 000 to 230 000 lb per sq in. (4) Plow-Steel Wire with an ultimate strength of from 200 000 to 230 000 lb per sq in. Ordinary galvanized-wire rope should not be used for other than standing rope. A short service running through sheaves will break the coating and permit Wire Rope 405 Table XV. Strength of Wire Rope Arranged from the 191 2 list of John A. Roebling's Sons Company Approximate breaking- Minimum diameter of Weight load in pounds drum or sheave Trade Diameter per foot, in feet j number inches hemp core Iron Cast steel Iron Cast steel IIOISTING-ROPE Six str xnds of nint iteen wires each, about a hemp core I 2\i 8.00 144 000 266 000 14 9 2 2 C.30 110 000 212 000 12 8 21/1. 1% 5.55 100 000 192 000 12 8 3 1% 4.85 88000 170 000 11 7 4 1% 4.15 76000 144000 10 6.5 5 iVi' 3.55 66 000 128 000 9 6 5¥2 r'/8 3 56000 112 000 8.5 5.5 6 •iVi 2.45 45 600 94000 7.5 5 7 1% 2 37200 76 000 7 4.5 8 9 I 1.58 29 000 60 000 6 4 Vh ] .20 23600 46 000 5-5 3.5 ID % C .89 17000 35000 4.5 3 10^/4 % c .62 12 000 25 000 4 2.5 lO^/l' ^1(5 c .50 9400 20 000 3-5 2.25 io=)4 1/ij c •39 7800 16800 3 2 loa VlO 0.30 5800 13 000 2 75 1.75 lob % 0.22 4800 9600 2.25 1.5 STANDING ROPE Six str ands of seven wires each II IV2 3 55 64 000 126 000 16 II 12 1% 3 56000 106 000 15 10 13 lu 2.45 46 000 92 000 13 9 14 iVs 2 38000 74000 12 8 15 I I 58 30 000 24 000 62 000 48 000 10.5 9 7 6 16 Vs 1.20 17 % 0.89 17 600 37200 7.5 5 18 11/10 0.75 14 600 30800 7-25 4.75 19 f>:s 62 12000 26 000 7 . 4.50 20 »/i« 0.50 9600 20 000 6 4 21 1/2 0.39 7400 15 400 5.5 3.5 22 VlO 0.30 5 200 II 000 4 5 3 23 % 0.22 4400 9 200 4 2.75 ' 24 ^/i« 0.15 3400 7 000 3 5 2.25 25 9/1j2 0.125 2 400 5000 3 1.75 The working load is to be taken at one-fifth the breaking-load. This is assumed i calculating the diameter of the sheaves. 406 Resistance to Tension. Properties of Iron and Steel Chap. 11 rapid corrosion of the rope. Because of the many kinds and qualities of rope it is well to consult the manufacturers as to which kind will best suit the condi- tions for any particular service. The John A. Roebling's Sons Company, Tren- ton, N. J., the Trenton Iron Company, Trenton, N. J., and A. Leschen & Sons Rope Company, St. Louis, Mo., are among the largest manufacturers of full lines of ropes. I Coils. Wire rope should not be coiled like hemp rope, and in order to avoid kinking, should be taken from the reels without twisting. If it is not shipped on a reel, to avoid injury it must be rolled over the ground like a wheel. ^ Lubrication. It is very important that running ropes be properly lubri- cated, since, if proper care is not taken, the wear on the interior parts, between the wires, may be almost as great as the outside abrasion. The oil should pene- trate to the core of the rope and yet not drip ofif a few days after application. Information as to the care of rope may be obtained of the Wire Rope Lubrica- ting Company, Newark, N. J. Sheaves. The size of sheaves recommended in the tables are calculated for a working-load of one-fifth the given breaking-load. If smaller sheaves are used the life of the rope will be greatly shortened, because of the excessive bending of the outer wires. Table XVI. Galvanized, Steel- Wire Strands For guys, signal-cords, trolley-line span wire, etc. Taken from the American Steel & Iron Company's list Diameter in inches List price per 100 feet* Weight per loo feet Approximate breaking-load in pounds % $7.25 80 14000 %o 5.75 65 II 000 V2 4.50 S2 8500 Via 3.7s 41 6 soo % 2.75 30 5000 %6 2.2s 22 3800 V4 1.75 13 2300 ?32 I. SO 9^/2 I 800 «/!• 1. 25 7V2 I 400 %2 I. IS 5V2 900 Vs 1. 00 3V4 600 %2 .80 2 400 9. Cotton, Hemp and Manila Rope Rope is made of cotton, hemp, and Manila fiber. Cotton is used for small iJizes, only, and for such purposes as sash-cord, etc. Manufacture. In the manufacture of rope the fiber is first spun into yarn. J'rom twenty to eighty threads are twisted together into strands and the Strands, three or four, are laid together, opposite in direction to the twist in \he strands, but in the same direction as the threads. This causes the fibers »;o be twisted as the rope untwists and produces a balancing of forces that tends to keep the rope in shape. Cables and Hawsers, are made up of strands of rope. * These pre-war prices must be increased as per current price-lists. Cotton, Hemp and Manila Rope 407 Rope used forHoisting wears rapidly from the action of the pulleys and also from the bending which causes a slight internal motion between the fibers and a chafing and grinding away of the interior. Stevedore-Rope, of the C. W. Hunt Company, is filled with a tallow and plumbago lubricant which decreases the internal friction, lubricates the outside of the rope and thus greatly prolongs its life. Strength. The values of the strength of new rope, given in Table XVII, are taken from the Specifications of the United States Navy Department, issued in June, 1910, at the Boston Navy- Yard. Manufactu .'ers generally adopt these sizes and weights and claim a strength equal to or a little greater than the values given. The unit strength for the different sizes varies, being about 14 000 lb per sq in for the smaller and about 10 000 for the largest size. The approx- imate formula, offered by C. W. Hunt, of 720 times the square of the circum- ference in inches, is equivalent to about 9 000 lb per sq in. American hemp, tarred, has about 5% greater strength than Manila rope of the same size. The navy specifications give for two-strand American-hemp rope, 85% of the strength of the three-strand rope of the same material. Table XVII. Strength and Weight of Rope Specifications of the United States Navy, June, 1910 Circum- ferences in Diameters in Manila hemp, plain-laid American hemp, tarred, plain-laid, three strands Weights lb per ft Breaking- loads lb Weights lb per ft Breaking- loads lb I iH 1V2 l8/4 2 2Vi 2«/4 3 3V4 3V2 3% 4 4V2 5 5V2 6 7 8 9 10 0.24 0.32 0.40 0.48 0.56 0,64 0.72 0.80 0.87 0.95 1.03 1. 16 1. 19 1.27 1.43 1. 59 1. 75 1.90 2.22 2.54 2.87 3.14 0.02 0.033 0.05 0.083 O.IO 0.14 0.17 0.21 0.26 0.30s 0.36 0.42 0.47 0.54 0.67 0.83 1. 00 1. 21 1.63 2.17 2.70 3.33 700 I 000 I 800 2500 3 000 4 000 5 000 5500 6600 7800 9 200 IC500 12 200 13700 17400 21 800 27700 31 000 36 200 47300 60 000 74200 0.051 0.06 0.067 0.083 0.105 o.i6 0.21 0.26 0.32 0.37 0.44 o.Si 0.59 0.67 750 I 060 1 670 2340 3325 3 955 4720 5770 7 000 8400 9800 II 200 13000 14550 1 Manila-hemp rope is made in three strands and in sizes up to 3 in in circumference; four strands are used for s'zes larger than 3 in in circumference. 408 Resistance to Tension. Properties of Iron and Steel Chap. 11 Working Load. The working load for slow-speed derrick and hoisting- service is usually taken at one-seventh the breaking-load. This makes some allowance for the loss of strength at splices and connections. The deterioration of rope exposed to the weather is very rapid. For Manila rope from i to i% in in diameter, running over sheaves of the diameters given, C. W. Hunt in Trans. Am. Soc. M. E., Vol. XXIII, gives a table embodying approximately the fol- lowing results of experience: Table XVIII. Working Loads for Manila Rope Working load = C X breaking-load of new rope D = minimum diameter of sheave in inches Speed Feef per minute Kind of work Value of C D for rope of diameter of I in 1% in Slow Medium . . . Rapid so to 100 150 to 300 400 to 800 Derrick, crane, quarry, etc. Wharf, cargo, etc. 0.014 0.056 0.028 8 12 40 14 18 70 The wear in such service is very rapid, a ii/^-in rope wearing out in lifting from 7000 to 10 000 tons of coal. On the other hand, a i^/^-in transmission-rope running at 5 000 ft per min and carrying i 000 horse-power over sheaves 5 ft and 17 ft in diameter, lasts for years, the difference being due to the smaller stress and larger sheaves. 10. Chains Manufacture. Large chains are made by hand- welding from best wrought- iron bar, and small chains up to H in are best made of mild open-hearth steel, electric-welded. The bending and welding reduce the strength so that the chain is not twice but only from 1.55 to 1.70 times as strong as the original bar from which it was made. Stud chain having a bar welded across each link to stiffen it and prevent fouling in handling, is not as strong as open-link CHAIN, but has a higher elastic limit and working strength. G. A. Goodenough, in a Bulletin from the IlHnois Engineering Experiment-Station, finds the maxi- mum stresses at the elastic hmit of the material to be as follows: If F is the load, d the diameter of the bar, and S the stress, the formulas are: P = 0.5 d^S for stud-link, and P = 0.4 d^S for open link. Proof-Tests. A proof-test is applied to chains by the manufacturers. The load applied is one-half the average breaking-loaix It serves to detect bad welds and gives a chain a slight permanent sot, so that for working loads there- after there will be Uttle stretching of the chain. Care of Chains. Chains in constant use require lubrication and frequent annealing. They harden in service and are liable to unexpected failure if not annealed. It is recommended that hoisting chains and sUng chains be annealed at least once a year. Chains 409 Table XIX. Sizes, Weights, Proof-Tests and Average Breaking-Loads for Chains Bradlee and Company, Philadelphia D.B.G. special crane Crane Size of Approxi- mate chains weight per foot Average Average in Proof-test breaking- Proof-test breaking- lb load lb load lb lb Vt % I 932 3864 1680 3360 % 1% 4186 8372 3640 7280. V2 2.5 7728 15456 6 720 13 440 % 4.1 II 914 23828 10360 20720 «/4 6.2 17388 34 776 15 120 30 240 Vs 8.4 22 484 44968 20440 40880 I 10.5 29 S68 59 136 26880 53 760 iVs 13.6 37576 75 152 34 160 68 320 ' lU 16 46 200 92400 42 000 84 000 1% 19.2 55 748 III 496 50680 loi 360 IV2 23 66528 133 056 60480 120 960 1% 28 74 382 148 764 1% 31 82 320 164 640 1%' 35 94360 188 720 2 40 107 520 215 040 2% 46. 5 121 240 242 480 The speciQcatious of the United States Navy Department require the same proof-test as is given above for crane-chain and a breaking-strength .10% greater than that given for special crane-chain. Table XX. Proof-Tests and Average Breaking-Loads for Studded Chain- Cables Specifications of the United States Navy Department Size of cable in Proof-test lb Average breaking- load lb Size of cable in Proof-test lb Average breaking- load lb I iVh iH i-yio 1% iVio iVl> iri6 1% 1% 1% 34 607 43812 54 194 59784 65 574 71 672 78041 84678 91588 106 222 121 937 67 526 82 686 100 630 109 771 119 355 129 38s 139 861 150 783 162 152 186 228 212 188 2 2V10 21/8 2H 2V2 2% 2% 2% 3 3Vs 130 202 138 739 147 544 156 622 175 591 216 779 238 995 262 302 286 692 312 i6s • 339 102 225 687 239 732 254 223 269 160 300373 368 153 404 719 443 069 483 203 52s 121 567 823 410 Resistance to Tension. Properties of Iron and Steel Chap. 11 Factors of Safety. For dead loads the factor of safety may be as low as four provided the breaking of the chain would not imperil life. This is the factor generally quoted in catalogues, but is too low for most purposes as the MAXIMUM fiber-stress is then well above the elastic limit of chain-iron. Where loads are to be raised repeatedly with machinery which can be operated without jerks or sudden change of speed, the use of a factor of six is good" practice. If a chain must be used where shocks occur, the instantaneous LOAD should be calculated, and a high factor of safety employed. Grades of Chain. Chains up to i}4 in are usually made in three grades, called PROOF, bb, and bbb. The proof is the cheapest grade, and is made in longer links than the others. This is not ordinarily proof-tested, bb is the next grade, somewhat shorter linked, and is proof-tested, bbb is of still shorter link and more carefully made. Crane Chair is finished in such a way as to be without twist when hanging with one end free, so that hooks and fittings are always facing their proper direction. Dredge Chain is straightened as is Crane Chain, and made with uniform links to run over a wheel. Steel Loading Chain is made mostly in small sizes for use where the weight compared to the strength is to be a maximum. It is the highest-grade hand-made chain. Block Chain is fitted to the pocket-wheel in which it is to run. In small sizes it is usually electric-welded. Electric- Welded Chain is made in small sizes and is rapidly replacing the hand-made below H in. It is stronger and more uniform. Sizes of Chain. Chain is ordinarily made of wire or rod, H2 in larger than the NOMINAL diameter, by which it is called. If chain is desired made of wire of the size by which it is called, it must be specified as exact size. Steel Loading Chain, Block Chain, and frequently Dredge Chain, are made exact. Stud- Link Anchor Chain is made of wirC; Vti^ in above its nominal diameter. Shear 411 CHAPTER XII RESISTANCE TO SHEAR. RIVETED JOINTS. PINS AND BOLTS By HERMAN CLAUDE BERRY PROFESSOR OF MATERIALS OF CONSTRUCTION, UNIVERSITY OF PENNSYLVANIA 1. Shear Shear is the internal stress in a body which resists the tendency of two adja- cent parts to sUde on each other, due to the action of two equal and parallel external forces, called shearing- FORCES, acting on opposite sides of the plane of shear. If the piece abed of Fig. 1 repre- sents a short simple beam of brittle material on which a suffi- cient load is applied, it will fail in VERTICAL shear at / and g, as shown, by a sliding on the sections of the beam at these points, be- cause the upward force of the reaction at 5 and the downward force of the load adjacent to S, against which it acts across the section at 5, is greater than the total shearing resistance of the section. Shear is present over the entire length of the beam, and at any section is equal to the reaction at S minus the weight of the load between the reaction and the section in question. In general, the vertical shear at any section of a beam subjected to vertical loads is equal to the algebraic sum of all the vertical forces acting on the beam on either side of the section. Single and Double Shear. A rivet connecting two bars under tension (Fig. 2) is subjected to a shearing-stress. If one section of Shearing-failure of Beam Fig. 2. Example of Single Shear the rivet transmits the force the rivet is said to be in single shear; if two sections, it is in double shear. Distribution of Shear. Shear is considered to be uniformly distributed over the section except in cases of torsion and of complex stresses. For the ordinary cases of shear in rivets, etc., if 5s == the allowable unit stress in shear, A = the area under stress, and P = the safe shearing-load; then P = ASs (i) The Ultimate Strength in Shear has been determined for building materials by testing suitably prepared specimens and dividing the maximum load ob- 412 Resistance to Shear. Riveted Joints. Pins and Bolts Chap. 12 served by the area tinder stress. For material like wood, in which there are planes of weakness, tests must be made which take these into account. The direction of the force with respect to these planes must be considered in choos- ing the SAFE WORKING STRESS from the tables. Safe Working Stresses in Shear. Table I gives safe working stresses. in SHEAR for those building materials usually subjected to such stresses. Table I. Safe Working Stress in Shear for Building Materials* Material Safe stress in lb per sq in 3000 7SOO 10 coo (average) With the Across the grain gram 200 I 000 lOO - 500 ISO I 250 130 I 000 100 900 ICX> 600 100 750 Cast iron (New York). Wrought iron Steel, bolts, rivets White oak White pine Long-leaf yellow pine. . Short-leaf yellow pine. Douglas fir Hemlock Spruce * Note. For woods, these values may he increased up to 30% for selected, perfectly protected, commercially dry timber, not subject to impact, that is, for ideal conditions. (See, also, pages 637 and 647.) Shear in Wooden Tie-Beams. There are a few cases in architectural con- struction in which the weakness of wood in shear must be provided for. The one most frequently arising is the framing of the end of the tie- ' beams in wooden trusses. i) oi \nvi Y'lg. 3 was made from a photograph of a shearing- failure of a tie-beam from the thrust of the rafter. Horizontal Shear in Wooden Beams. Failure Hke that shown in Fig. 1 rarely occurs in wood; but rectangular Fig. 3. Shearing-failure m Wood wooden beams, the length of which is less than about twenty times the depth, are liable to fail by HORIZONTAL SHEAR along the middle, under about the same loads that cause the allowable working stresses in bending. Shear at the End of a Tie-Beam. In the case of the truss- joint (Fig. 4), the thrust S of the rafter tends to shear off the part A BCD along the pkmc of which CD is the trace. This area under stress must offer a shearing resist- ance equal to the horizontal component H of the thrust S. The width of the beam b, being fixed, formula (i) gives ^,, n={CDx b) Ss or CD = n/hs., The shear being in the same direction as the grain of the wood, the lower value r„ 'T'„U1„ T 4. U« ,-.^ — 1 Riveted Joints 413 Example i (Fig. 4). The horizontal component of the thrust of a rafter is 20 GOO lb. The long-leaf yellow pine tie-beam is 10 in wide. How far should the beam extend beyond the point D? Solution. In this case H = 20 000 lb. From Tabfe I, Ss= 150 lb per 20 000 sq m. Then CD = ^ = 13.3 10 X 150 in and should be made at least Truss-joint As actually constructed a large part of the thrust is generally taken up by a bolt or strap at the foot of the rafter to hold it in place. As the bolt and shoulder seldom act together, either the length CD on the tie-beam should be made long enough to resist the entire thrust, or the bolt or strap designed to do so without relying on the shearing resistance in the plane of CD. The design of such joints is more fully considered under Subdivision 4, pages 429 to 439 of this chapter. 2. Riveted Joints Use of Rivets. Rivets almost exclusively are used in connecting the plates and shapes which make up the members of framed steel construction. ' Rivet-Definitions. A rivet is a piece of cylindrical rod with a head forged on one end and usually with a slight taper at the other end of the shank. The grip (Table IV) of the rivet is the length betweeen the under sides of the heads after driving, or the thickness of the parts joined. The length (Table IV) of the rivet is equal to the grip plus enough of the stock to form a head, and is measured from the end of the shank to the under surface of the head. The DIAMETER OF THE SHANK of a rivct is made equal to its nominal diameter, but rivets are driven into holes /^'"^ y^ Vh in larger in diameter and upset by the driving so as to completely fill the holes. The shearing values and bearing values are based upon the nominal area and not upon the area of the hole. Riveting consists in heating the rivet to a welding-heat, passing it through holes in the parts to be joined and forging another head out of the pro- jecting shank. This may be done by hand-hammering; but \^7 1 — ^ / / - \ *- Fig. 5. Forms of Rivet-heads shops use compressed-air-operated hand-hammers or large riveting-machines which form the head and cause the shank to completely fill the hole by heavy pressure on a die. Material of Rivets. Rivets are made of soft steel and of wrought iron. Rivet-steel is generally used. The head may have any of the forms shown in Fig. 5, although the first, called the rutton-head, is the standard for structural work. The fourth or countersunk head is used where it is necessary to have a flat surface, as over a bearing-plate. 1^4 Resistance to Shear, Riveted Joints. Pins and Bolts Chap. 12 The Sizes of Rivet-Heads differ slightly at different mills, The Standards of the American Bridge Company give for the diameter of the head, one and one-half times the diameter of the shank plus Vs in, and for the height of the head, 0.425 times the diameter of the head. Countersunk heads have a SLOPE of 30° and a depth equal to one-half the diameter of the shank. The Pitch of Rivets. By this is meant the center-to-center distance between them in a line of riveting. The distance between lines of rivets, or from the back of an angle or channel to a rivet-line. is called the gauge-dis- tance. By staggered pitch is meant the arrangement of rivets midway between others on successive rivet-lines in order to decrease the section less than when they are arranged in rectangular rows, and at the same time to place a greater number of rivets in a definite area. The pitch should not be made less than three diameters of the rivet and the distance from the edge of the plate not less than one and one-half diameters, although it may be necessary to make the distance less when small angles are used. The pitch of counter- sunk rivets must be greater than that of button-head rivets because of the greater amount of material removed. Punching Rivet-Holes. Rivet-holes are made with power-punches. The spacing is marked on the different parts to be fastened together by means of wooden templates with holes drilled to locate the position of the rivets. When the different parts are assembled, the holes are laid out by the same template- register, so that the rivets may be inserted without difficulty. Punching makes a ragged hole. The flow of the metal under the great pressure hardens it and causes a loss in strength of from 11 to 33% as reported by W. C. Unwia for soft steel. The injury may be removed by annealing or by reaming away the injured part of the metal. Enlarging a %-in. hole by reaming to iVs in has been found to remove all the injurious effects of punching. One method practiced in the best work is to punch the holes Via in less in diameter than the diameter of the rivets, and to ream them to a diameter Via in greater, after the parts are assembled and bolted together. This removes the greater part of the injury from punching and corrects the alinement of the holes. (See Table XI, page 400, and Table I, page 702.) Drift-Pins. When the alinement of a hole is such as to prevent the insertion of the rivet, it is the practice in some shops to drive in a tapered drift-pin and distort the holes in some of the plates sufficiently to set the rivet. This causes local stresses and injury to the plates and should not be permitted. Shop-Riveting is done with powerful air or hydraulic riveting-machines which may exert a pressure of from 30 to 50 tons, sufficient to upset a perfect head on the projecting end of the shank and to completely fill the hole even though the alinement is imperfect. Contraction on cooling causes great pres- sure between the parts, so that it is probable that in good work the rivet is under little or no shearing-stress, the force being transmitted through the frictional resistance of the plates. Clearance. It is important that the designer place the rivets so they may be inserted from one side and pounded on the other for hand-work, or so that the machine may reach them for machine-riveted work. For example, the minimum distance from the inside face of the leg of one angle to a line of rivets in the other leg must not be less than i^s in for %-in rivets, i in for %-in rivets, etc. In general, a distance % in greater than the diameter of the head should be allowed for clearance. Inspection. The common imperfections in riveting are loose rivets and ECCENTRIC HEADS. Loose rivets may be detected by holding the hand against Riveted Joints 415 one side of the rivet-head and tapping the other side with a light hammer. If loose, a slight slip may be felt. The loose rivets should be marked to be cut out and replaced. The inspector should also carefully check open holes left for field-connections, and see that flattened and countersunk rivets are as called for, because such work may be done at less expense in the shop than in the field, where it may cause delay. The Failure of Riveted Joints may occur (i) In TENSION, by the tearing of the plate through the line of rivets (Fig. 8). (2) In SHEAR, by the cutting of the rivets (Fig. 7). (3) In BEARING, by the crushing of the plate in front of the rivets, the split- ting of the plate, or, in some cases, by the shearing out of the sections in front of the rivets. In a careful design of a joint the strength against failure by eaph^ of these methods must be investigated (Fig. 6 and Fig. 9). ', Fig. 6 Fig. 7 . Fig. 8 Figs. 6 to 9. Methods of Failure in Riveted Joints "X Fig. 9 The Steps in the Design of any type of riveted joint are, (i) the selec- tion of the size of the rivet to be used, (2) the determination of its shearing and bearing strength and the use of the smaller value of the two to divide into the total load to be transmitted and thus determine the number of rivets, (3) the arrangement of the rivets in the plate and the investigation of its strength in tension at the dangerous section. The Size of Rivets is determined in part by shop-practice. Holes can- not be punched in plates which are thicker than the diameter of the punch. The following table gives the size of rivets used with plates of different thickness. Some specifications for structural work require all rivets to be % in, except where thick plates require larger ones. tiickness of plates Size of rivets V4to7/iy in % in ^2 to % in %in iVi6toi8/i6in % in % to I in I in Tables II and III give the shearing and bearing values for different sizes of rivets in plates of different thickness for two values of working stresses each; shear at 7 500 and 10 000 lb per sq in and bearing at 15 000 and 18 000 lb per sq in. Values for higher stresses can be figured by proportion from these tables. The lower stresses should be used with wrought iron or in parts subjected to live loads; the higher stresses where only constant or dead loads are present. 416 Resistance to Shear. Riveted Joints. Pins and Bolts Chap. 12 The SHEARING VALUE is cqual to the area of the rivet multiplied by the working stress; the bearing value is equal to the area of the projected surface under pressure multiplied by the working stress in bearing, or, if /= the thickness of the plate; d = the diameter of the rivet ; and Sb = the working stress in bearing; then the bearing value P = dtSb (2) The Shearing and Bearing Values may be taken directly from the tables, and if a rivet is in double shear, twice the quantity in the table is to be used for its shearing value. Quantities above the heavy broken lines are bearing VALUES greater than the values in single shear, so that for these conditions, the number of rivets necessary in a joint required to transmit a certain load is determined by dividing the load by the value in single shear. If rivets are in, double shear, the number of rivets required is found by dividing the load by the BEARING VALUE. Rivet-Proportions.* The following diagrams show various rivet-proportions, including the dimensions of shanks and of finished and countersunk heads: COUNTERSUNK HEADS FINISHED HEADS Diam head = V/2 diani of 3baQk+ J^'dept^ of head = ^^u)«diamof.head -' These proportions vary slightly at different mills and in different handbooks. Depth of head = V2 diara of shank. Bevel of head = 60° Riveted Joints 417 Conventional Signs for Riveting. The following diagrams show some conventional signs for riveting: Shop Field Two Full Heads Countersunk Inside (Farside) and Chipped Countersunk Outside (Nearside) and Chipped Countersunk both Sides and Chipped o iNsroE Outside (Farside) (Nearside) Both Smfea Flattened to y^ in high or Counter- sunk and not Chipped Flattened to vi in high Flattened 3/^ in high This system, designed by F. C. Osborn, has for its foundation a diagonal cross to represent a countersink, a blackened circle for a field-rivet and a diagonal stroke for a flattened head. The position of the cross with respect to the circle, inside, outside, or on both sides, indicates the location of the countersink; and similarly, the number and position of the diagonal strokes indicate the height and position of the flattened heads. Any combination of field, countersunk and flattened-head rivets liable to be used may be readily indicated by the proper combination of the above signs. Resistance to Shear. Riveted Joints. Pins and Bolts Chap. 12 o o r-? d M M • o o o - C . «- : J5 • (N ,. fO "^t 1^ S% s^ n • o> o o M N M M M M O. M *o X <» . . n 8 R o o o o Itf^ S; : b'iqO" rfO: btii . /,: 00 oo cy> ^ cs w !^ -* o 35 C a^ o VO t^ t^ 00 00 a» o i V5 rid -3 '•§ ! *J -^:.^ ^ o .8 ^ 8 ^ ^2 VO lo o in o» -^f a> Xi X X ^ • io ITi VO VO l> t^ t- 00 00 bC o S > u ^ ^ o o ■■§ « a 1 § o o ■* lO lo a> u 'd • ro ■* -* -I- lO ICVO VO vO t^ t> -o S3 ^1 11 o o o o o o o o H o o 4 ;3 .iS :r?5 5,.<^ (N lO a» IN ^% f^S 1? N PO fO fO ■* '^ rt lo lO lO VO VO o . -n 0) cr o o to o o ^ ^ ^ o 8 R il. RR ;?J •>* VO 00 M 00 CS lO / :^ / ^ '"' f-l M M (N M fO fO ■* lo VO O l> 00 o o o o o o O O o o o o O M V, ■i »A 15 J? iO "^ ^ .aK2 X? to 15 r . ■ § s? ^ in lO ^ s c» 00 o> 0^8 rj^ 'I: ■ A o o o o o o o o o o M M M M O A p V)^ ^•' c e « «0 e o « «D .=. ;j^ v-rt vj-l V.0O •v'* ^00 kj^ d 1 oS^ I--- r^Ci-^ «S^ H 95^ t-^H Riveted Joints 8 § l§ o t- 00 •^ • t ■ M M M M ' o o o o o o o V. s ;^^ 00 lO ;r s ^ Pi II «*- rt • o> o^ o ro C (U •^ •^ ■^ . . a» o o •u • 1^ ; o 2 8 ^^ o o 00 t- 00 ro .8 ■8 Pn o ^^ • rj- a> rf 00 ro ro 00 ro rt « 1'^ • -^ Tt lO lOVO 8 g> ss 2v8 2.8 8 o 8 o O J3 00 M N lO a> (N vo a. ro to •^1 • c^ 0» lO roo a. (N lO I- (O fe^-^ H M CS CJ « ro PO ro ro ■* rj- rt V5 ^ D C ? a* 8 8 "S. °^ la ^^ 2 8 O O O R .^s. M in o» '+ o o» 00 O o r^^ 2& M M H N ro ro Tt lO iO o l> 00 O^ M JU y "O 4 "* ro fO IT) S "^ 00 to ro ro ■<+ Jo o to *J ^ '^.^ M 00 s& c3 . ) O t^ 00 o PO fO Tt lO t^ Cr» 3 u.- k'' o o o o o o o o o o o o O ^ 1^ w ^--ric 1 a to \r> »o to to to to }Cp; ^'^ M 00 toS t^ ro g 1 J^ 00 ■§*- f . m in t- 00 00 Ok o o o o o o o o o o M •^ « ^ feg .s&- g 6-9 Q o o • o o » It 1 ;?J^^ »0^ rH S!H^ v,0(3 l^ M M ^ ^ ♦ S' c] \< — Grip,5-?i [<— Grip, 6- J< ^Length- -^: k Length- — >i !<— Length- — > ^ — Length- >i Diameter Diameter Grip _ Grip 6 a V2 ^ % % Vs I y2 % 3/4 78 I V2 l\^ I«/4 iVs 2 2y8 V2 iVs iy4 iTt 1% 1% % 1% iVs 2 2y8 2y4 % iy4 1% l3/^8 l72 IVI' % 1% 2 2y8 2y4 2% 3/4 l3/^8 11^2 iy2 1% 1% Vs iVs 2y8. 2y4 2% 2y2 Vs iy2 1% 1% l3/4 l3/4 I 2 2H 2% 2y2 26/8 I 1% l3/4 l3/4 l78 l78 Vs 2y8 2% 2V2 2% 2% Vs ■ l3/4 I78 l78 2 2 u 2H 2V2 2% 23/4 278 y4 iVs 2 2 278 278 % 2% 2% 2% 278 3 3/8 2 278 278 274 2y4 % 2y8 2% 3 3ys 3y4 y2 2y8 2y4 23/^8 2% 2y2 % 2% 3 3y8 3U 3% % 2y4 23/^8 2y2 2y2 2% % 3 3V4 3% 3y2 3% 3/4 2l/l>. 25/^8 23/4 2^4 278 % 3Vs 3% 3y2 3% 33/4 % 2% 23/4 278 278 3 2 3V4 3V2 3% 3% sVs 2 23/4 278 3 3 378 Vh 3% 3% 3% 3y8 4 , ys 278 3 378 37s 3y4 3V. 3'r4 3V8 4 4^8 4V4 y4 % k 3V8 3y4 3y4 33/8 374 3% 33/8 3y^: 3% 3V8 4 4y8 V2 3V4 4 4ys 4y4 43/8 y2 3V4 33/^8 3y2 372 3% - % 3% 4ys 4y4 4% 4y2 ^/^S 3% 3y2 3% 3% 3% . §4 4 4y4 4% 4^2 4% 3/4 3y2 3% 33/4 3% 378- -i.'5& 4V8 4% 4y2 4% 43/4 Vs 3% 3% 378 378 4 -'. 3 4% 4% 4«/4 4% 5 3 378 4 4 4% 4Vi' Vs 4^1' 4% 4y8 5 sVs . Vs ■ 4 4y8 478 4y4 4%'r Vi 4% 4y8 5 sVs sU y4 478 4y4 4V4 43/8 472^ % 4% 5^, 'Yf 5y4 5% 8/^8 4y4 43/8 43/^8 4y2 4%^: V2 4Vs 5^^ sVf 5% sVs y2 43/^8 4y2 472 4%. 4%- % 5 5V4 5% 5y2 5% % 4y2 4^5/^8 4^8 43/4 4%^ % sVs 5% 5}^ 5% 53/4 3/4 4% 43/4 ,43/4 478 5- ■^. Vs 5V4 sV. 5% 5^4 sVs % 43/4 478 478 5 sVs- 4 5% 5% 5% 5% 6 4 478 S 5 5V8 SV4 Vs 5% sVs 6 eVs 6y4 ys sVs sH sV^ 5% sy2 Vi 5% 6 eVs 6y4 6% y4 .5% 5% 53/8 572 5^8 % 6 6y4 6% 6% 6% % 5V2 5% 5% 5% 53/4 V2 6V8 6% eVs 6% 63/4 H' 5% 5% 53/4 5% 578 % 6V4 6\^ 6% 63/4 6% % 5^4 578 578 578 6 3/1 6% 6% 6% eVs 7 3/4 578 6 6 6 678 % 6V2 6% eVs 7 7y8 Vs 6 678 678 678 674 5 6-'>8 eVs 7 7ys 7yi 5 6y8 6y4 674 674 6% Vs TVs 7y4 7% ys 6% 6% 672 V4 7V4 73/8 7y2 y4 672 672 6% % 7% 7y2 7% 3/^8 6% 6% 63/4 Va 7% 734 778 V2 678 678 7 % . 7% 7% 8 % 7 7 7y8 % 7ys 8 SVs .. 3/4 778 778 7y4 Vs 8 sys 8V4 • ^8 7y4 774 7% For weight of rivets, see page 1443. Riveted Joints 421 Use of Riveted Joints. Riveted joints are used in building-construction (i) in tie-bar splices, (2) in floor-beam connections, (3) in the joints of trusses, (4) in riveted girders, and (5) in column-connections. r^ TIT- Fig. 10. Lap-joint Fig. 11. Butt-joint with Single Cover-plate o o splicing of Tie-Bars. Tie-bars may be spliced by a lap-joint (Fig. 10); by a BUTT-JOINT with a single cover-plate (Fig. 11); or by a butt-joint with two cover-plates (Fig. 12). The Butt-joint is symmet- rical and more efficient than the others because of the absence of any tendency to bend when under a load. The net area of the cover-plates at the section through the rivets at the end of the main plate must be equal to Fig. 12. Butt-joint with Two Cover-plates O 010 O O O I O O O O OjO o 0000 O OiO o Joint I the net area of the main plate through the rivets at the end of the cover-plate. Fig. 14 shows a better arrangement of rivets than that in Fig. 13, because less area is removed at the critical section of the cover-plates. In some cases it may be necessary to make the aggregate thickness of the cover- plates greater than the thickness of the main plates. A joint with one line of rivets is said to be single-riveted, one with two lines double- Fig.13. Cover-plate. Six Rivets at Critical Section riveted, and one with more than two unes, chain-riveted. Example 2. It is required to determine the number of rivets in the splice of a 12 by V2-in tie-bar which is subject to a tensile force of 65 000 lb. Solution. Assuming that the load is constant, the stresses in Table III may be used. Assuming, also, a lap-joint like that in Fig. 15, and %-in rivets, the value in shear of one rivet is found to . be 4 420 lb and the bearing value V ^^ o o O 0^\. 1 against a V2-in plate, 6 740 lb. The number of rivets is determined by the shear to be equal to 65 000 divided by 4 420, or fifteen. Since sixteen rivets are required to complete a figure smaller but similar in arrangement to that shown in Fig. 15, this number is used. There is some latitude possible in the spacing of the rivets, but with a width of 12 in, the horizontal gauge-lines are placed 1^2 in apart for symmetry. If the pitch P, as shown in Fig. 15, is required to be three times the diameter of the rivet, this diagonal pitch across the rivet-spacing n^ust be 2.23 in, qr o o I o o o! o o 00 00 o I O CO o 00 00 Joint I Fig. 14. Cover-plate. Four Rivets at Criti- cal Section 422 Resistance to Shear. Riveted Joints. Pins and Bolts Chap. 12 greater. The length of the horizontal or third side of the right-angled triangle, having an hypotenuse of 2.25 in and a vertical altitude of 1.5 in, is 1.68 in, which requires that this distance ED, etc., be 1.75 in, if measured in multiples of ^ in. Floor-Beam Connections. The two following examples il- lustrate common types of floor- beam connections. Example 3. It is required to determine the number of %-in rivets to connect a lo-in 25-lb Fig. 15. Rivet-spacing in Cover-plate ' beam supporting 24 000 lb to a 15-in 42-lb I beam, using a shearing-stress of 10 000 lb per sq in and a bearing-stress of 18 000 lb per sq in. Solution. From the table of properties of standard I beams, pages 354-5. the thickness of the web of the lo-in 25-lb beam is found to be 0.31 in, say ^lo in, and of the 15-in 42-lb beam, 0.41 in, say Vie in. Referring to Table III, page 419, the bearing values for a %-in rivet for these tliicknesses of webs are re- spectively 4 210 lb and 5 890 lb. The shearing value of the rivet is 4 420 lb. The rivets in the lo-in beam are in double shear; hence the bearing value gov- erns. The number of rivets, then, is 12 000, the end-reaction, divided by 4 210, or 3. For the 15-in beam the shearing value is less, and the number of rivets required is 12 000 divided by 4 420, or 3. Hence two standard connection- anglesi 6 by 4 by % in and 5 in long, may be used. Each has three holes in one leg and two in the other. The leg with three holes is placed on the lo-in beam with the rivets in double shear, and the leg with two holes is connected to the 15-in beam; thus, in the latter case there are four rivets where only three are required for strength. They are driven in the field during the erection of the structure and the working stress is accordingly made less in most specifications because of the better work possible with the heavy machines used in shop-work, than with the tools available in the field. Example 4. It is required to determine the number of %-in rivets in a 4 by 4 by H-in angle-bracket attached to an i8-in 5 5 -lb beam and support- ing a 10 by i2-in wooden beam on which there is a load of 18 000 lb. Solution. The rivets are in single shear with a shearing-resistance of 4 420 lb, taken from Table III. ' The thickness Of the web of the I beam is Vio in, giving a bearing value of 5 890 lb. Dividing 9 000 lb, the end-reaction, by 4 420 lb, the controlling value, we find that two rivets are insufficient. The bracket may be fastened with three 'li-in rivets with a spacing of 4 in. Two Vs-in rivets are sufficient to hold the bracket. Rivets in Plate Girders. The methods of determining the rivets in plate and box girders are given in Chapter XX. Bending Stress in Rivets. While the bending strength of rtNS at the joints of articulated trusses is always investigated, this is never done in the case of RIVETS. A hot rivet properly driven is, when cold, under a tensile stress which is nearly equal to the elastic limit of the material. This causes great pressure between the plates and a consequent frictional resistance to movement, which, under the usual conditions, equals the allowed shearing-force on the rivet; and so, until an initial slip occurs, there can be no bending STRESSES in the rivet. In the case of very long rivets driven in holes where Strength of Fins in Trusses 423 there is an imperfect alinement of the plates and a consequent difficulty in making the rivets fill the holes completely, it is not probable that any large bending stresses can occur in the rivets of a structure. This has been avoided in a few structures for which long taper rivets were specified to be used in holes REAMED with TAPERED REAMERS, thus insuring a perfect filling of the holes. Working Stresses. Tables II and III are based on stresses which approx- imate those used in the best practice. Table II is used for the few structures made of wrought iron and for those places in steel structures that are subject to severe conditions of service, as in the floor-systems of bridges. Table III is used for ordinary structural work made under the conditions governing in modern shop-practice. For comparison, the following stresses taken from the specifications of Theodore Cooper for Steel Railroad Bridges and Steel Highway Bridges are given: Specification for Steel railroad bridges Steel highway bridges Allowable stresses on rivets, lb per sq in Bearing IS 000 (i2 ooo on floors) 22 500 for laterals 18 000 (14 400 on floor- beams) 27 000 for laterals Shear 9 000 (7 200 on floors) 13 500 for laterals 10 000 (8 000 on floor- beams) 14 000 for laterals Rivets driven in the field are allowed two-thirds the value of shop-driven rivets. 3. Strength of Pins in Trusses* Truss-Pins. In the design of the pins at the joints of trusses the stresses in SHEAR, BEARING FLEXURE or BENDING must be investigated. The Shearing-Force at any section of the pin is the algebraic sum of all the forces acting on the pin on either side of the section. The stress is considered to be uniformly distributed over the cross-section of the pin. When the forces do not act in the same plane they must be resolved into vertical and horizontal components and the resultant of these components taken as the shear at any desired section. This may be done by the principles of graphic statics, or by TRIGONOMETRICAL and ALGEBRAICAL METHODS, the graphic method being, for some, the more rapid. The Bearing Area on the pin is taken as the projection of the area of CONTACT, the area of this projection being equal to the diameter of the pin multiplied by the thickness of the plate. The bearing is assumed to be uni- formly distributed; hence for any load the intensity of the pressure may be decreased by increasing the thickness of the plate or the diameter of the pin. The Bending Moments on the pin may be found by the principle of MOMENTS or by methods involving the principles of graphic statics explained in Chapter IX in finding the bending moments of beams. The forces are con- sidered to be concentrated at the middle of the bearing-plates. If they do not lie in a plane with the pin they must be resolved into their vertical and hori- * Since the introduction of rolled-steel shapes and riveted joints, pin-joints for trusses of moderate span in buildings have fallen into disuse. The general principles of theijt design, however, are given here. 424 Resistance to Shear. Riveted. Joints. Pins and Bolts Chap. 12 zontal components and these component forces in the two planes treated sepa- rately. The resultants in both planes at any section may be combined and a single resultant force acting on the section obtained, and also the consequent stresses due to it. Table V. Shearing and Bearing Values of Pins for One-Inch Thickness of Plate , in Pounds per Square Inch Diam- eter of pin, in Area of pin, sq in Bearing value at 12 000 lb per sq in, lb Single shear 7 Soo lb per sq in, lb Diam- eter of pin, in Area of pin, sq in Bearing value at 12 000 lb per sq in, lb Single shear 7 500 lb per sq in, tons I 0.78s 12 000 5 890 ' 4 4V8 12.57 13.36 48000 49500 47.0 50.1 iVs 0.994 13 500 7 455 1V4 1.227 IS 000 9 202 a\\ 14.19 51 000 53.2 1% 1. 48s 16500 II 132 4% 15.03 52500 56.3 1V2 1.767 18 000 13252 4y2 IS. 90 54000 59- 6" 1% 2.074 19500 15555 4% 16.80 55 500 63.0 1% 2.405 21 000 18037 4% 17.72 57000 66.3 1% 2.760 22500 20707 4% 18.67 58500 70.0 2 3.142 24 000 23565 5 19 64 60 000 73.6 2V8 3.547 25500 26 Goo sVs 20.63 61 500 .77.3 2V4 3.976 27 000 29820 sU 21.65 63000 81.2 » 2% 4.430 28 500 33225 5% 22.69 64500 85.1 2V2 4.909 30000 36817 5^1' 23.76 66 000 89.1 2% 5.412 31 500 40590 5% 24.8s 67500 93.2 2% 5.940 33000 44550 5% 25.97 69 000 97.3 2% 6.492 34500 48690 tons 5% 27.11 70500 lOI.I 3 7.069 36000 26. 5 6 28.27 72 000 106 3V8 7.670 37500 28.7 6% 29.46 73500 no 3V4 8.296 39000 31.0 GM 30.63 75000 115 3% 8.946 40500 33.5 63/8 31.92 76 500 119 3y2 9.621 42000 36.0 6V2 33.18 78 000 124 3% 10.32 43500 38.7 6% 34.47 79 500 129 3% II. OS 45 000 41.4 6% 35.79 81 000 134 3% 11.79 46500 44.2 6% 37.12 82 500 139 ^ L I ^wwwva'^ Dg~ 1 X 4-40,000 I? In the Method of Moments a section is taken at each force in succession and the moment of the forces about a point in the section found, due consider- ation being given to the direc- tion of turning. This is done at each force on one side of the pin, if the bars are arranged symmetrically, and in both the vertical and horizontal planes. Inspection of the results will usually indicate which section the horizontal and vertical E IT Fig. 16. Pin- joint has the greatest resultant moment when components, H and F, are combined. This is done by using the formula B?^ W-\- 7* since; graphically, the resultant R is the diagonal of the rectangle Strength of Pins in Trusses 425 Table VI. Maximum Bending Moments in Inch-Poimds to be Allowed on Pins for Maximum Fiber-Stresses of is ooo, 20 000 and 22 500 Pounds per Square Inch Diam- Moment Moment Moment Diam- Moment Moment Moment eter of for S = for 5 - for 5 = eter of for S = for 5 = for 5 = pin, IS 000 20 000 22 500 pin, IS 000 20 000 22 500 in in-lb in-lb in-lb in in-lb in-lb in-lb I 1470 i960 2 210 4 94200 125700 141 400 iVs 2 100 2800 3140 4V8 103 400 137800 155 000 M 2880 3830 4310 aM 113 000 150700 169 600 1% 3830 5 100 5740 4% 123300 164 400 185000 iVs 4970 6630 7460 4V2- 134200 178 900 201 300 1% 6 320 8430 9480 4% 145 700 194300 218500 1% 7890 10500 II 800 4% 157800- 210 400 236 700 iVh 9710 12 900 14 600 4% 170 600 227 500 255900 2 II 800 15700 17700 5 184 100 245400 276 100 2V8 14 100 18800 21 200 5V8 198200 264300 297300 2Va 16800 22 400 25 200 sM 213 100 284 100 319600 xYs 19700 26300 29 600 5% 228 700 304900 343000 2V2 23000 30700 34500 SV2 24s 000 326700 367500 2% 26 600 35 500 40 000 5% 262 100 349500 393 100 2% 30600 40800 45900 5«/4 280 000 373300 419 900 2% 35000 46 700 52500 5% 298 600 398200 447900 3 39800 53000 59600 6 318 100 424 100 477100 3V8 44900 59900 67 400 61/s 338 400 451 200 507600 3H 50600 67400 75800 6Vi 359500 479400 539 300 3% 56600 75500 84 900 6^^8 381500 508 700 572300 3^/1' 63 100 84 200 94700 6y, 404400 539200 606600 f/n 70 100 93500 105 200 6% 428 200 570900 642300 3% 77700 103 500 116 500 6% 452900 603900 679400 3% 85700 114 200 128500 6% 478 500 638 000 717800 Remarks. The following is the formula for flexure, If =5"/ /c, with the reductions made to adapt it to a beam of circular section: M = S7rd^/2,2 = SAd/?, M = the moment of forces for any section through the pin; : .;fj'{; S = the stress per sq in in extreme fibers of pin at that section; A = the area of the section; d = the diameter; TT = 3-14159. The forces are assumed to act in a plane passing through the axis of the pin. The above table gives the values of M for different diameters of pin, and for three values of S. If the maximum value of M is known, an inspection of the table will show what the diameter of the pin must be so that S will hot exceed 15 000, 20 000, or 22 500 lb, as the requirements of the case may be. i i on // and V. Example 6 illustrates the method for the condition of inclined FORCES acting on the pin. In Example 5 the same method is employed to deter- mine the size of the pin in a simple joint. 426 Resistance to Shear. Riveted Joints. Pins and Bolts Chap. 12 Example 5. It is required to determine the size of the pin for the joint shown in Fig. 16 in the lower chord of a steel truss. The middle bar is a vertical sus- pension-rod to hold the chord in place. Solution. Beginning at the section between the outer bars, the algebraic sum of the forces on either side of the section is 40000 lb, hence this is the shear. At the section next to the suspender the sum is zero; therefore there is no shear at the middle of the pin. The bearing pressure is 40 000 lb. Its intensity depends on the diameter of the pin and the thickness of the bars. To find the bending moment on the pin the forces are considered concentrated at the middle of the bars and moments taken about sections through the forces. The moment at the section through the second bar is 40 000 lb X i in, equal to 40 000 in-lb. If moments are taken about a point between the inner forces the same result is obtained. From Table VI it is found that a 2%-in pin at 20 000 lb per sq in is sufficient. From Table V the bearing value of a 2%-in pin' is found to be only 33 000 lb at a stress of 1 2 000 lb per sq in, which makes it necessary to increase the size of the pin to 3% in. The shearing value of this pin is 67 000 lb. In this case the diameter of the pin is determined by the bearing-stress, but it is necessary to investigate the oth6r stresses to be sure of the correct size, especially in case of heavy bearing-plates. Bending Moments on Pins. The finding of the bending moment due to the forces acting on a pin is usually the most difficult part of the work of deter- mining its proper size. In the case of a simple pin, properly packed and lying in the plane of the forces acting on it, the greatest moment is usually the prod- uct obtained by multiplying the outer force by the central distance between the outer bars; but when the forces act in several planes the work is more complicated. The graphical method illustrated in the solution of the two following examples has some advantages; but the method of moments applied at the end of the solution of the first example is equally rapid in practiced hands and capable of greater refinement in the results. Example 6. It is required to find the bending moment on tne pin of the joint, one-half of which is shown in Fig. 17. The bars are each i in thick, the channel of the vertical member V^ in thick and the center of the hanger is % in from the center of- the channel. Solution. Since the joint is symmetrical it is necessary to construct but one- half of the force-diagram and equilibrium-polygon which really apply to the joint. From the conditions of equiUbrium of forces, the vertical com- ponent of the inclined force is upward, and equal to the sum of the downward forces, 34 000 lb; and its horizontal component acts with the 60 000-lb force, to the amount of 17000 lb, a sufficient amount to close the force-diagram. The following construction is special, in that but one-half of the entire graphical diagram is shown. This is made possible because of the symmetry of the joint, the bending moment being constant over the middle of the pin. In the diagram (Fig. 18) ^1J5 is drawn at an angle of 45° with the horizontal, and commencing at c, the distances are laid off to scale between the bars, and the lines 1-2, 2-3, etc., drawn parallel to the forces they represent at the joint. The oblique force is resolved into its components 1-4 and 1-5. The stress-diagram (Fig. 19) is drawn as follows: On a horizontal fine the forces are laid off to scale in the order they occur on the pin, 1-2, 2-3, 3-4 and 4-1, the closing of the diagram being a check on the correctness of the value of the forces. Beginning at i, 1-5, 5-6 and 6-1 are laid off to scale, parallel to the forces in the vertical plane. From i the line r-o is drawn at an angle of 45**, for convenience in making good intersections, and equal to a convenient number, say 20 000 lb, in the same sgale to which the loads are drawn. The StrengUi of Pins in Trusses 427 point O is the pole of the stress-diagram, the pole-distance being 20 000 lb. From the principles of graphics the bending moment at any point on the pin is equal to the intercept between the proper ray of the equilibrium-polygon and the closing Une, multipUed by the pole-distance. To complete the figures, a-2, 0-3 and 0-4 are drawn from O, and from c cd is drawn parallel to 0-2, c^ parallel to 0-3, ef parallel to 0-4 and fk parallel to o-i. In the same way rs is drawn parallel to 0-5, st to 0-6 and tv to o-i. Then according to the above principles, the moment at any section due to the forces in the horizontal plane is proportional to the ordinate at that section drawn from the line AB to the line cdefk bounding the equilibrium-polygon; and the moments due to the vertical forces are proportional to the ordinates drawn to the line rstv, the numerical value being the length of the ordinate times 20 000, the pole-distance. Fig. 19 Fig. 20 Figs. 17 to 20. Pin-joint and Moment-diagrams Where both moments are present, the resultant or true rrioment is proportional to the hypotenuse of the right-angled triangle having for its sides the ordinates in the two planes at the point in question. At X this is shown by the line mn. This measures 2,42 in, and being the longest diagonal or hypotenuse that can be drawn in the figure, it follows that the maximum bending moment. on the pin is 2.42 X 20 000 = 48 400 in-lb. To find the effect of changing the arrangement of the members on the pin, it may be assumed that the inclined bar is placed outside the inner chord-bar. The horizontal stress-diagram then becomes 1-2, 2-3, 3-4', 4-1. The equilib- rium-polygons become cdefk' and r's't'w, as shown in Fig. 20. In these polygons the longest diagonal measures 3% in, which gives a bending moment of 3% in X 20 000 lb = 75 000 in-lb, showing that the arrangement of the eye-bars in Fig. 17 is better. As a rule the bending moment is less when those forces that 428 Resistance to Shear. Riveted Joints. Pins and Bolts Chap. 12 oppose each other are placed together. It may be further reduced by making the outside bar one-half the thickness of the main horizontal bars. To check by the method of moments the value of the maximum bending moment obtained by the graphic method for the first arrangement, the mo- ments of the forces in the horizontal plane are taken about r. This gives Mh = 38 500 lb X 3.0 in + 38 500 lb X I. o in — 60 000 lb X 2.0 in = 34 000 in-lb, which is the value of the moment in the horizontal plane across the middle of the pin. In the vertical plane moments are taken about a point /, giving Mv = 34 000 lb X 1.5 in — 22 000 lb X 0.75 in = 34 500 in-lb From these component moments the resultant maximum bending moment is M = V 34 ooo2 + 34 5002 = 48 400 in-lb Example 7. Another illustration of the graphical method of finding the bending moment on a pin is given for the joint A of the truss-diagram shown in Fig. 23 Fig. 24 Figs. 21 to 24. Force-polygons and Equilibrium-polygons for Bending Moments a Pin 4 Fig. 21.-^ Fig. 22 shows the arrangement and size of the members. The stresses given in Fig. 21 are for one-half the number of members at the joint. As in Example 6, the symmetrical arrangement makes it unnecessary to draw more Strength of Bolts in Wooden Trusses and Girders 429 than one-half of the force-polygon and equilibrium-polygon. The web of the , channel is reinforced to make it % in thick. Solution. The line AB (Fig. 24) is drawn at an angle of 45° and ah, etc., are laid off to scale, equal to the distances between the members. At each point of application of a force a line is drawn parallel and to scale, to represent that force. The inclined forces are then resolved into their horizontal and vertical components. The force-diagram (Fig. 23) is then drawn, the horizontal forces being laid off to scale in the order in which they occur, 1-2, 2-3, 3-4 and 4-1. The pole-distance is then laid off at an angle of 45° and equal to 20 000 lb to the same scale of forces. The pole o is then joined with 2, 3, 4 and i. Then in Fig. 24, ab is drawn parallel to 0-2, be to 0-3, cd to 0-4 and de to o-i. In the same way the line hjkB is drawn. From inspection it is seen that hb is'the longest intercept, even longer than any diagonal that may be drawn from the extremities of the horizontal and vertical intercepts at any point along AB. To the same scale that makes o-i represent 20 000 lb, hb represents 31 800 in- lb; therefore the bending moment on the pin is 31 800 in-lb. In Table VI a pin 2% in in diameter, at a fiber-stress of 20 000 lb per sq in, has an allowable moment of 35 500 in-lb, and in Table V a bearing value on i in of 31 500 lb. A force of 31 800 lb on % in is equal to 42 400 for a i-in bar; so it is necessary to use a larger pin to accommodate the bearing requirement. From Table V a pin 3V2 in in diameter is found to be necessary. The shearing value of this pin is 72 000 lb more than twice the load, so, again, it is the bearing that con- trols the size of the pin. If the thickness of the bars is increased the diameter of the pin may be reduced to 3 in. 4. Strength of Bolts in Wooden Trusses and Girders The Working Stresses for Bolts on which Table VII and Table VIII are computed are based on a factor of safety of five applied to the average of many tests on dry timber. In some specifications it is permitted to increase the BEARING PRESSURE between timber and bolts as much as 50% above that per- mitted for short struts. The values in the tables are somewhat less than the tests on large trusses made at the Massachusetts Institute of Technology, in 1897, would indicate as safe values. These were reported in the Engineering Record, November 17, 1900. Table IX gives the allowable maximum tension, shear and bending moments for wrought-iron and steel bolts. Kinds of Stress in Bolts. Bolts in wooden trusses are subject to the same kinds of stress as the rivets and pins in steel structures. When the pieces joined are less than 2 in thick and the bolts are tightly drawn up so as to develop considerable frictional resistance between the pieces, the bolts are proportioned to resist the total force in shear and in bearing. When the pieces are more than 2 in thick the bending is taken into account and the bolts must be investigated for stresses in shear, in bearing and in bending. The SHEAR is assumed to be uniformly distributed over the cross-section of the bolt, and the bearing area is the area of the projection of the bolt on the timber, which area is equal to the diameter of the bolt multiplied by the length in con- tact. The BEARING STRENGTH is given as a property of the bolt although its value depends upon the crushing strength of the tim,b.er. The bending mo- ment on the bolt is found in the same manner as for pins in steel trusses, although the cases are usually less complicated. Illustrations of the Use of Bolts. The principles involved in the use of bolts in wooden trusses and girders and in the use of the tables may be best illustrated by the solution of examples in each of the following cases: 430 Resistance to Shear. Riveted Joints. Pins and Bolts Chap. 12 (i) Bolts in tie-beams, thin pieces. (2) Bolts in girders to support brackets. (3) Bolts as pins in the joints of trusses. (4) Bolt-and-strap joints in trusses. (5) Bolts under tension to hold the foot of a rafter. (See, also, " Joints in Wooden Trusses," Chapter XXVIII, pages 1149 to 11 60. Case I. Bolts in Tie-Beams, Thin Pieces. Tie-beams of wooden trusses, when longer than 30 ft, are usually made up of a number of pieces. This con- struction is cheaper than the use of a single stick. Two-inch planks bolted together are generally used. The location of the joints in the courses of planks and the number and size of the bolts are the special considerations in the design of such a joint. In general, the joints in adjacent courses are placed as far apart as possible and not more than two joints are placed opposite each other in the same section. The simplest case is that of a plain fish-plate joint like a common butt-joint with two cover-plates as shown in Fig. 12. The number of BOLTS for such a joint is found in the same way as the number of rivets in steel tie-bars. The bolts must be spaced as required in the second column under each timber in Table VII, to provide against shearing in front of the bolt. Table VU.* Safe Bearing Value of Bolts per Inch of Length Parallel to the Grain in Timber and Distance from Center to Center of Bolts or to End of Timber Diam- eter of bolt, Long-leaf yellow pine White pine and short-leaf yellow pine Doug as fir White oak Bearing Bearing Bearing Bearing 1 in at I 400 Dis- at I 100 Dis- at I 200 Dis- at I 400 Dis- lb per tance, lb per tance, lb per tance, lb per tance, sq in, in sq in, in sqin, in sqin, in lb lb lb lb % I 050 4V2 82s 5V4 900 4V4 I 050 3y2 Vs 1225 5 960 s«/4 I 050 5 1225 4 I I 400 5% I 100 6V2 I 200 . 5V2 I 400 4H iVs I 575 6V2 1237 7^1' 1350 6y4 1575 5 IV4 I7SO 1 1375 8 I 500 7 1 750 5y2 1% 1925 7% I 512 9 , I 650 78/4 1925 6^i 1V2 2 100 8V2 I 650 9% 1800 8y2 2 100 6% 1^4 2450 10 1925 iiy2 1950 9V4 2450 7% 2 2800 11V2 2200 13 2400 11V4 2800 9 2V4 3150 12% 2475 14% 2 700 i2y2 3 150 10 2V2 3 500 14V4 2750 i6Vt 3000 14 3500 iiy4 2% 3850 15V4 302s 18 3300 i5y2 3850 i2y4 3 4 200 17 3300 19 3600 17 4 200 i3y2 The distance from the end is equal to the diameter of the bolt plus the length on which twice the shear is equal to the bearing value of the bolt against the end-fibers. See Notes with Table XVI, Chapter XVI, for increase in allowed stresses. • When the effect of the inclined surfaces upon the unit stresses is taken into account, the formula for the normal intensity of stress for cylindrical pins or bolts, given in Chapter XXVIII, page 11^8, may be used. This formula will give lawef Values than those of Table VII. Strength of Bolts in Wooden Trusses and Girders 431 Table VIII.* Safe Bearing Value of Bolts per Inch of Length Across the Grain in Timber Long-leaf yellow pine, lb Short-leaf yellow, pine and Douglas fir, lb White pine, lb White oak, lb 262 306 3SO 394 437 482 52s 612 700 187 218 250 281 312 343 375 437 500 150 175 200 225 250 275 300 350 400 375 437 500 562 625 687 750 875 1000 Table IX. Maximum Allowable Tension, Shear and Bending Moment for Wrought-Iron and Steel Bolts Diam- eter of bolt, in Net area, sq in Wrought iron Steel Tension at 12 000 lb per Shear at 7500 lb per Bending moment at 15000 lb per Tension at 16 000 lb per Shear at 10 000 lb per Bending moment at 20000 lb per sq in, in-lb sq m, sq in, lb sq m, sq m. lb in-lb lb lb % 0.302 3620 3310 620 4830 4420 830 % 0.420 5040 4510 980 6 720 6 010 I 3i(i I iVs 0.550 0.694 6600 8328 5 890 I 470 8800 7 850 I 960 7460 2 100 II 100 9940 2800 iM 0.893 10 716 9200 2880 14290 12 270 3830 1% 1.057 12680 II 140 3830 16 910 14850 5 100 1V2 1.295 15 540 13250 4970 20 720 17670 6630 i«/4 1 . 746 20 930 18 040 7890 27910 24050 10500 2 2.302 27 620 23560 II 800 36830 31420 15700 2V4 3.023 36280 29820 16800 48370 39760 22 400 2V2 3.719 44 630 36820 23000 59510 49090 30700 2% 4.620 55430 44550 30 600 73910 59400 40800 3 5.428 65 140 53010 39800 86850 70690 53000 3V1 6.510 78 120 62 220 SO 600 104 160 82960 67400 Example 8. A typical tie-beam used as a lower chord of a Howe truss is shown in Fig. 25. It is 50 ft long, of Douglas fir and subject to the tension in the different panels shown in the figure. Solution. The thickness of the plank Is drawn out of scale in the figure to show the joints more clearly. The black circles show the vertical tension-rods, which so nearly cut the middle plank in two that it is not considered a part of the tensile member. The arrangement of the planks and the lengths to be used must be determined for each case. In the one shown there is but one splice in the middle panels where there is the greatest tension. The distance 432 Resistance to Shear. Riveted Joints. Pins and Bolts Chap. 12 XY is 12 ft, which is about as small as will serve for the transfer of the tension from A' X.Q B. In this beam the two outer planks, A and A', must be large enough to resist the whole tensile stress in the middle panels because of the joints in B and C. At the inner end of the second panel there is 58 000 lb tension which must be carried to the end of the first panel. Because of the -50 0- 6- ^ bolts -11-1 bolts Y^*^—' *-^ -H Y' -^-^ I ! I ■ 36000 Ibs.T— >|<-58000 Ibs. T > i < 66000 lbs.Tj>|< 8 0^^ >^ 8'0- Fig. 25. Plan of Built-up Tie-beam joints in A and A' this must be transmitted to B and C in order to pass the point X. . Assuming that 29 000 lb, one-half the tension, is carried on plank A to be transmitted to C by the shear and bearing on the bolts, and dividing this by 7 850 lb, the allowable shear on a i-in bolt, four bolts are found to be necessary. But the bearing value of a i-in bolt in Douglas fir 2 in thick, is only 2 400 lb, which makes twelve bolts necessary. These are required in the distance XV, 12 ft. From the distances in Table VII, it is found that the end-bolts must be 5^^^ in from the ends of the planks, say 6 in; this leaves ii ft, in which distance eight bolts are to be arranged. If four bolts are placed in pairs, two at each end, as -c->h- ^14?^''- -14%"- Fig. 26. Elevation of Beam Opposite X of Fig. 25 shown in Fig. 26, the intermediate spaces are 14?^ in. The bolts bind the beam together better if they are staggered, as indicated in Fig. 26, and not placed on the middle line. The number of bolts mentioned is sufficient to make the splice, but there should be bolts in the distance YV, and between the ends and X and X\ to bind the planks together. These need not be as large or as close together as the others; %-m bolts spaced 2 ft are sufficient. There should be two bolts at the end of the beam. Each bolt should be driven through a hole of the same size as the bolt and the nuts should be screwed up tight. Case II. Bolts in Girders to Support Brackets. The construction shown in Figs. 27 and 28 is commonly used in cases in which the requirements do not allow the girder to project its full depth below the joists. The bolts shown in Fig. 27 must be investigated for bearing and shear, and those shown in Fig. 28 for BEARING, SHEAR and BENDING. In either case the shearing value of the bol^ in single shear must equal or be greater than the greater of the forces S or S', The BEARING per inch on the wood of the girder, when B is in inches, is Strength of Bolts in Wooden Trusses and Girders 433 This must be kept within the values given in Table VII for the timber used. For the case shown in Fig. 28 the bending moment in pound-inches is M^SLh or u^s'Lh i;;: yd. I whichever is the larger. B and L are measured in inches and S in pounds. ■• > ■■•■> Fig. 28 J^igs. 27 and 28. Bolts Supporting Brackets on Girders Example 9. For the construction shown in Fig. 27 it is required to determine the number and size of bolts, the Douglas fir girder being 8 by 14 in, with a span of 14 ft, and the Douglas fir joists 3 by 12 in, with a span of 20 ft, center to center of girders. The floor-load, including the floor, is 60 lb per sq ft. The angles are 4 by 3^2 by %\\x. * Solution. The floor-area supported by the girder is 14 by 20 ft. At 60 lb per sq ft, the load is 14 X 20 X 60 = 16 800 lb. The load 5, on one side, is 8 400 lb. • A 34-in bolt has a shearing-value of 4 420 lb. Hence two bolts are necessary to satisfy the shearing condition. The bearing value of the bolt in the wood, across the grain, is, from Table VIII, 1S7 lb per inch of length, or i 496 lb for the width of the girder. The number of bolts required, then, is 16 800 divided by I 496 or approximately ii, which gives a spacing of about 15 in. Example 10. In the construction shown in Fig. 28, the girder is 6 by 14 in, of Douglas fir and has a span of 12 ft. The joists are 2 by 12 in and have an i8-ft span, center to center of girders. The floor-load is 65 lb per sq ft. There are 3 by 4-in strips on the sides of the girder. The distance L is 3 in. It is ji;Qqjaifj?4 to find the number and size of bolts to be used. * -, ^j •\'i\\i\-\ Solution. The total load on the girder is ■' ' ■"■' 12 X 18 X 65 = 14 040 lb 5=7 020 lb The bearing load per inch of thickness of the girder is 14 040 = 2 340 lb The bending moment on one side of the girder is 7020X3 . ,, • = 10 530 m-lb .XX5 o^ 10 jrri'jn<«{ - n. since the force S acts at the center of pressure on the bracket-strip, iVi in from the edge of the girder. The shear is 7 020 lb, which requires two %-m steel bolts at 4 420 lb for oii^ as given in Table IX. '^'' ^ The bearing (Table VIII) on a ^i-in bolt is 187 lb per inch of length; thei'efore it requires thirteen bolts for bearing. 434 Resistance to Shear. Riveted Joints. Pins and Bolts Chap. 12 The allowable bending moment on a %-in steel bolt is 830 in-lb, from Table IX. To take care of the lo 530 in-lb requires thirteen bolts. A Vs-in steel bolt has an allowable bending moment of i 3 10 Ib-in, making eight of them sufficient. The 3 by 4-in pieces may be held in place by thirteen •ji-'m bolts spaced 11 in on centers, if two of them are placed 6 in from the ends. Case III. Bolts as Pins in the Joints of Trusses. For ties or STRUTS joined by bolts in the manner indicated in Figs. 29, 30 and 31 and having the thickness B exceeding 2 in, the diameter of the bolt or the number of bolts must be computed for shearing, bear- ing and FLEXURE. For any of these joints the forces are as follows: The single shear = S/2 On the sections between B and B' (Fig. 30) The bearing on the pin per inch of length = S/B or S'/B' The greater is to be used. The bending moment = SL/iz on the assumption of a contin- uous BEAM, uniformly loaded. If there are more bolts than one, the quantities obtained ELEVATION B' _a^ B' V2S- 1/2 S- PLAN Fig. 29. Bolt through Rafter and Tie-beam a -Vo S - 3 by the above formulas are to be divided by the number of bolts to find the part to be taken care of by one bolt. In Fig. 29, S is the horizontal component of the thrust T, Example 11. It is required to determine the diameter of a bolt for a joint like that shown in Fig. 29. The rafter is 6 by 10 in, of Douglas fir, the tie-beams 3 by 10 in, of the same material, the thrust in the rafter 30 000 lb, and its inch- nation 30°. Solution. The horizontal com- ponent of 30 000 lb at 30° is prac- tically 26 000 lb. Then 5=2$ 000 lb and the shear =13 000 lb. .B = 6 in and L = 9 in. Bearing per inch of length on the bolt = 26 000/6 Bending moment = 26 000 X 9/12 = 1.9 500 in-lb In Table IX, a i%-in steel bolt is found to be necessary to resist a shear of 13 000 lb, and a 2M-in bolt for a bending moment of 19 500 in-lb. To resist 4 333 lb end-bearing pressure on i in a larger bolt is required than is given in Table VII. Dividing 4 333 by i 200, the allowable bearing on Douglas fir, a 3%-in bolt is found to be necessary. This is larger than it is desirable to use, so the joint must be redesigned with a view to reduce the bearing pressure on Fig. 30. Bolt in Wooden Tie-beam . ■ 4 333 lb -f-l I %SM==^B', ' I I B iL! ! S- I Strength of Bolts in Wooden Trusses and Girders 435 the bolt. If an 8 by 8-in strut and 4 by 8-in tie-beams are used, B becomes 8 in and L 12 in. This gives • Bearing pressure = 26 000/8 = 3 250 lb per inch of length of the bolt (: Bending moment = 26 000 X 12/12 = 26 000 in-lb The total shear at the section on one side of the strut is the same as before. From Table VII it is found that a 2%-in bolt is large enough to provide for the bearing and that a 2Mj-in bolt is sufficient for the bending as given in Table IX. Hence if an 8 by 8-in strut is used, there must be a 2%-in bolt and the distance D must be 15H' in (Table n VII). 2^ s^- B-T7^ J^ I Example 12. For the same construc- tion as in Fig. 29 and the same con- ditions as in the first part of Example II, it is required to determine the size , , . of the bolts when it is necessary to '5/s<- | 1 B'i | " -A use three. j * "^ /^ Solution. The shear, beanng, and ' bending moment are the same as in Fig. 31. Bolts in Wooden Tie-beam Example 11, but because there are • j u three bolts each quantity is divided by 3 to determine the force resisted by each. Shear = 13 000/3 = 4 333 lb and requires a %-m steel bolt (Table IX) Bearing = 4 333/3 = i 444 lb and requires a iV+in bolt (Table VII) Bending moment = 19 500/3 = 6 500 in-lb, and requires a iMi-in steel bolt (Table IX). In this case the bending moment determines the size of the bolts, which may be arranged as shown by the dotted circles in Fig. 29. Example 13. It is required to determine the diameter of the bolt for the construction shown in Fig. 30, in which the inner beam is of Douglas fir and 6 by 8 in in section, and the outer beams 3 by 8 in, the tension being 24 000 lb. Soludon. S= 24 000; B=6m; X = 9 in. Single shear on the bolt = 24 000/2 = 12 000 lb r Bearing-pressure per inch of length of bolt =24 000/6 = 4 000 lb Bending moment =24000X9/12=18000 in-lb From Table IX a lU-in steel bolt is found sufficient to resist the shear, and a 2V4-in bolt large enough to resist the bending. In Table VII the largest bolt considered, 3 in, is too small in bearing value. Dividing the load to be resisted by I 200 gives sVs in, as the diameter necessary to resist the bearing. The distance D must be 4 000/(2 X 130) + 3^ in or i834 in. Example 14. If two bolts are used, one behind the other, it is required to determine the diameter of the bolt that should be used, the conditions and loading being the same as in Example 13. Solution. Dividing the quantities obtained in Example 13 by 2, Single shear = 6 000 lb and requires a %-in steel bolt Bearing = 2 000 lb and requires a 2-in bolt Bending moment = 9 000 in-lb and requires a i%=-in steel bolt The allowable bearing on a i^/i-in bolt is (2y2 %) less than the required amount, so that in general, since the other requirements are more than satisfied, the smaller bolt would be used. For the 18/4-in bolt, the distance D is 9H in. The space between the bolts may be increased somewhat beyond the value given m 436 Resistance to Shear. Riveted Joints. Pins and Bolts Chap. 12 Fig. 32. Strap and Bolt at Foot of Rafter Table VII, and they may be located out of the same line as a further precau- tion against splitting. Case IV. Bolt-and-Strap Joints in Trusses. The construction shown in Fig. 32 is sometimes used to connect the foot of the rafter of a wooden truss to the tie-beam. When the distance D is sufficient to resist the shear due to the thrust of the rafter, the strap is of value only in holding the rafter in place, and there are no greater pressures brought upon the bolt. When it is impos- sible to make D the necessary length, the bolt and strap must be designed to resist the full force in the direction of the strap. As the STRAP is usually not more than from V-^ to % in thick, its width is such that the bearing between it and the rafter is small compared ^ with that between the bolt and rafter. The forces acting on the bolt are the only ones that need con- sideration. These are: /u Single shear = 5/2 = the ten-* sion in the strap on one side Bearing pressure per inch of length = S/B, where B is the width of the tie-beam in inches Bearing pressure per inch of length between strap and bolt = S/2 t To fmd the value of 5, the force- polygon is drawn as shown at the right in Fig. 32. T is drawn parallel to the rafter and with a length, to a con- venient scale, equal to the thrust. From the end a an indefinite line is drawn parallel to the axis of the strap, and from b another line perpendicular to the seat of the rafter. These intersect at c, so that ac, measured by the same scale used in laying off T, is the magnitude of the force S in the strap. If the rafter rests on top of the beam, be is vertical, but if the tie-beam is dapped, as shown by the dotted line, the line from b is drawn perpendicular to the bottom of the notch, making the intersection at c'. It is seen that notching the tie- beam in this way increases the stress in the strap. Example 15. It is required to determine the size of a strap and pin-bolt to hold the rafter without notching into the tie-beam of a long-leaf yellow-pine king-post truss. • The rafter is 6 by 6 in, is inclined at an angle of 45° and is under a compressive stress of 18 000 lb. The tie-beam is 6 by 8 in in section. Solution. Since the inclination is 45°, a consideration of the force-polygon in Fig. 32 shows ab equal to ac, so that The force 5 = the thrust T = 18 000 lb Single shear on bolt =18 000/2 = 9 000 lb Tension in strap on one side = 9 000 lb Bearing pressure per inch of bolt against wood =18 000/6 = 3 000 lb Bearing pressure in pounds per inch between strap and bolt = 9 000// in which / equals the thickness of the strap. The allowable pressure between the strap and the top of the rafter is 350 lb per sq in (Table VII), which, on the 6-in rafter, gives Allowable load per inch of width of strap = 6 X 350 = 2 100 lb The strap then must be 18 000/2 100 or 8.6 in wide. At 10 000 per sq in in tension the necessary section of the strap is 0.9 sq in, requiring a thickness of Strength of Bolts in Wooden Trusses and Girders 437 about O.I in, a sufficient thickness if the strap were strong enough to develop a uniform pressure over the rafter. It is not good practice, however, to use such thin material, because of the danger of loss of strength due to corrosion. No metal less than % in thick should be used in such places. The bearing-pressure per inch, between the strap and the bolt, for a %-in strap = 9 ooo/% = 24 000 lb The bolt, then, must take a single shear of 9 000 lb, a bearing pressure of 3 000 lb against the wood for each inch of length, and a bearing of 24 000 lb per inch of length against the strap. From Table IX a i^^-in steel bolt is sufficient to resist the shear, from Table V a 2-in bolt is large enough to resist the bearing from the strap, and from Table VII a 2^4 -in bolt is found necessary to resist the 3 000-lb bearing from the wood per inch of length of bolt. This makes the 2^4-in bolt satisfactory for the joint. The pressure from the bolt to the wood, however, is not parallel with the grain but inclined at 45°. The allowable pressure against wood across the grain is about one-fourth of that with the grain. According to the formula given in Chapter XXVIII, page 1138, the allowable pressure per square inch for this case is 612 lb instead of the 1 400 per sq in allowed for direct compression with the grain. The reduced allowable pressure makes it necessary to use a 4.9-in bolt, say a 5-in bolt, which would be impracticable, for it would almost cut the tie-beam in two. It thus appears that this form of joint is not good design for a truss of this span. For shorter spans the joint may be made in accordance with the requirements given. It has the advantage of not presenting any projections below the tie-beam. Case V. Bolts in Tension to Hold the Foot of a Rafter. In the joint shown in Fig. 33 the bolt is subject to DIRECT TENSION Only. The amount of the tension 5 is found by the construction explained in Case IV. The rafter may be let into the tie-beam or rest on top of it, the tensioa in the bolt being less in the latter case; but it is easier to erect the truss if the rafter is notched into THE BEAM from iM to 1V2 in for ordinary spans and loads, to hold it while the pieces are fitted. After this is done, the holes may be bored exactly where required. Whenever S exceeds about 10 000 lb for trusses made of timber for which the highest bearing stresses are allowed, a cast plate, as shown in Fig. 34 and made to fit the inclination of the bolt, should be let Fig. 34. Special Washer into the tie-beam at the head of the bolt to distribute the pressure. The diameter of the hole for the bolt should be Vs in larger than the diameter of the bolt. The distance D must be made sufficient to provide for the horizontal component of S, at the allowed working stress of the material for shear with the grain. The horizontal component is found by drawing a vertical line from c and a horizontal line from a and measuring ad to the scale of the diagram. For safety, this force must be less than the product of the distance D, the width of the beam and the allowed shearing-stress given in Table I, page 41?;.^ ^^^^^^^ ,, Fig. 33. Bolt in Tension at Foot of Rafter 438 Resistance to Shear. Riveted Joints. Pins and Bolts Chap. 12 Example i6. For the same conditions as in Example 15, for the size of the members and the thrust in the rafter, it is required to determine the diameter of the bolt and the distance D for a joint of the type shown in Fig. 33. Solution. To find S, draw T equal to i8 000 lb, at a convenient scale, and parallel to the rafter. At a, draw an indefinite line perpendicular to the rafters and at 6 a fine perpendicular to the seat of the rafter. This makes .S" greater than in Example 15, as ac now scales 27 000 lb. From Table IX, a i%-in steel bolt is sufficient to take this in direct tension. The horizontal component found as directed above, scales 19 000 lb. The width of the tie-beam is 6 in, which at the allowed shearing-stress, 150 lb per sq in, gives 900 lb as the stress that must be cared for by each inch oi D. 19 000 lb divided by 900 gives 21 in, the required distance D. (See, also, Chapter XXVIII, Joints in Wooden Trusses.) The compression against the grain on the end of the cast-iron washer must also be investigated. 19 000 lb divided by the width, 6 in, gives 3 166 lb that must be resisted per inch of width of beam. At i 400 lb per sq in, as an allow- able working stress, this makes it necessary to set the casting 2V4 in into the lower side of the beam, which exceeds the depth usual in ordinary practice. Some tests made at the Massachusetts Institute of Technology on large trusses, and reported in 1897, indicated that for a test carried to rupture the stresses prescribed for usual designs might safely be more than doubled. Tests on timber under long-continued loading indicate that rupture finally occurs for stresses approximating one-half of those developed in tests carried to immediate failure. This, and the fact that decay may affect the strength of the members, emphasizes the wisdom of using conservative working-stresses in this material. 8x8' Cast Washers Fig. 35. Joint with Two Bolts in Direct Tension Example 17. It is required to determine the size of bolts for the joint shown in Fig. 35, the thrust being 65 500 lb and the truss-members being made of long-leaf yellow pine. Solution. The tension in the bolts is found first by drawing the force-polygon as shown at the right in the figure. To the same scale that ab represents 65 500, ac represents 96 500 lb. If the load is equally divided between the bolts, each has a tension of 48 250 lb. From Table IX this force requires a 2\i-\n steel bolt. The horizontal component ad is 68 350 lb, which must be resisted by the shear- ing strength of the wood between the end of the cast-iron washer on the under Strength of Bolts in Wooden Trusses and Girders i39 side of the tie-beam and the end of the beam resting on the wall. At 150 lb per sq in, this requires 68 350/150, or 455 sq in. If the beam is 8 in wide, this requires a length of 57 in along the beam from the washer to the end. The bearing of the cast-iron washer against the end-fibers of the tie-beam is also 68 250 lb. At an allowable pressure of i 400 lb per sq in the depth of the washer should be 68 350/(8 X i 400) = 6.1 in. This would almost cut the beam in two. The ultimate strength of the wood in compression is about five times the working stress, and since a considerable part of the horizontal force may be resisted by the body of the bolt as well as by the friction of the washer, it is probable that with washers % in thick there would be little sign of weak- ness at the joint even when the truss is fully loaded. Theoretically the washers on the top surface of the rafter should be deter- mined by the allowable working stress in compression across the fi.bers. This for long-leaf pine is taken at 350 lb per sq in (Table VI, page 454). The area, then, is 48 250/350, or 138 sq in. This requires a washer 11% in square. The 8 by 8-in washer used, assumes a pressure of 755 lb per sq in, but as the tests of the Forest Service of the United States Department of Agriculture give 3 480 lb per sq in as the elastic limit for long-leaf yellow pine, it is very likely that there would be no signs of injury at this point, other than a slight indenta- tion, when the truss is fully loaded. ! 440 Bearing-Plates and Bases for Columns, etc. Chap. 13 CHAPTER XIII BEARING-PLATES AND BASES FOR COLUMNS, BEAMS AND GIRDERS. BRACKETS ON CAST-IRON COLUMNS* By HERMAN CLAUDE BERRY PROFESSOR OF MATERIALS OF CONSTRUCTION, UNIVERSITY OF PENNSYLVANIA 1. Bearing-Plates and Bases The Purpose of Bearing-Plates or Bases. When a heavily loaded col- umn, beam or girder is supported on a masonry wall or pier, a bearing-plate or BASE of suitable dimensions must be used to distribute the load so that the pressure will not exceed the safe bearing strength of the masonry (Table I). < UJ CQ <— p— > SECTION Fig. 1. Simple Bearing- plate K n ^ \ V /J xx • • // / -~ i ( ( ' 1 / n s, J. f \ ^ Fig. 2. Beveled Cast- iron Plate with Pin Fig. 3. PLAN Ribbed Cast-iron Plate The bearing-plate is designed to be stiff enough to distribute the pressure under it uniformly, and its area is determined by dividing the load on it by the allowable pressure per unit of area (Table II). Simple Bearing-Plates. Fig. 1 shows a simple bearing-plate under a beam. It may be a steel or cast-iron rectangular plate of sufficient thickness to prevent its bending at the edge of the beam from the pressure of the * See, also, Chapter XIV, Subdivisions 8 to ii. Bearing-Plates and Bases 441 masonry below. For anchors for steel beams on bearing-plates, see Chapter XV, page 619. Cast-iron Plates with Pin. Fig. 2 is a cast-iron plate wixg a dowel-pin to fit inside the shell of a cast-iron column, or into a recess cut in the bottom of a wooden one. The pin holds the base-plate in position. Cast-iron Ribbed Bases. Fig. 3 is a cast-iron ribbed base for a large cylindrical cast-iron column, capable of supporting a load heavy enough toj break a plate similar to the one shown in Fig. 2, at the edges of the columnj unless the plate were made unduly thick. ' Table I. Allowable Bearing Pressure on Different Kinds cf^Masonry Kind of masonry Allowable pressures Lb per sq Tons per sq ft From the building laws of New York, 19 17 Brick, in lime mortar , in lime-and-cement mortar in Portland-cement mortar Rubble masonry, in Portland-cement mortar. . Concrete, Portland cement, 1:2:4 no 160 250 140 500 11^ 18 10 36 From the building laws of Chicago, 191 6 Rubble, in lime mortar in Portland-cement mortar Coursed rubble, in lime mortar in Portland-cement mortar Ashlar, limestone, in Portland-cement mortar granite, in Portland-cement mortar. Concrete, Portland-cement, 1:2:4, hand-mixed . . . . machine-mixed . 60 100 120 200 400 600 350 400 4-32 7-2 8.6 14.4 28.8 43.2 25-4 28.8 The Bases of the Steel Cores of Composite Columns used in reinforced- concrete construction have areas sufficient to distribute the loads of the columns over the concrete in the foofings at the allowable working stress of the concrete. (See, also, page 474, Figs. 14 and 15.) Example i. The basement-columns of a warehouse are designed for a load of 212 000 lb each. It is required to determine the size of the base-plates to rest on the concrete foundations. (Table II used.) Solution. At an allowable pressure of 208 lb per sq in, the required area is 212 006/208 or I 020 sq in, or about 32^2 in square. The plan and section of the base-plate is shown in Fig. 3. Forms of Base-Plates. For small columns and wooden posts with light loads, plain flat plates of cast iron or steel are generally used. The cast-iron plates may have a raised ring or cross to fit inside a hollow metal column, or a dowel, from i>2 to 2 in in height for a wooden one. If the plate is very thick the outer edges may be beveled to save weight, as shown in Fig. 2, but no part of it should be less than about % in thick. \ 442 Bearing- Plates and Bases for Columns, etc. Chap. 13 Table n. Allowable Loads on Standard, Steel Bearing-Plates on Walls Bearing on wall, in Safe bearing value of plate in pounds Size of plate, in Bricks laid in mortar of Lime, 112* lb per sq in Lime and cement, 162* lb per sq in Cement, 208* lb per sq in 6 6X 6 6X 8 4070 5400 5 800 7800 7500 10 000 8 6Xio 8X 8 6 700 7 200 9 000 10700 • II 200 9700 10200 I?, vx> 15500 16 200 12500 13300 16 600 20000 20 800 10 8XIO 8X12 loXio 12 14 I0XI2 10X14 13450 15700 19500 22 700 25 200 27900 I2XI2 12X14 12X16 12x18 14X14 16 150 18800 22 000 24 200 22 TOO f-., 25 000 28 200 23300 27 400 31 200 34500 31 800 36300 40 800 30000 35000 40 100 45 000 40800 46 600 52 400 i6 14X16 14X18 ' 14X20 16x16 16x18 16x20 16x22 31 400 28 700 32300 35800 39500 45400 41500 46 600 SI 900 57000 58 200 53200 59800 66 700 73200 ♦ These valu es are slightly difi erent from those Df the New York Code (1916). Ribbed Bases. If the calculated size of a bearing-plate is so large that its projection beyond the edge of the column would be more than about 6 in, a RIBBED BASE similar to that shown (Fig. 3) for a cylindrical column is used. For such bases it is unnecessary to consider the transverse stresses. When these bases are bolted to the columns they add greatly to the general stability of the supporting members because of the greater width of such bases. Proportions of Ribbed Bases. The height H of this type of base should be approximately equal to the projection P, and the diameter D equal to the diameter of the column. The projection C should be at least 3 in to permit the bolting of the column to the base. The thickness of all parts of the casting should be the same and approximately equal to the thickness of the column- shell. There must be no thin webs as they result in breakage from shrinkage- stresses. Base-Plates for Steel Columns are usually made of steel plates and shapes as shown on the channel-columns in Chapter XIV, Figs. 17, 18 and 19. Cast- iron bases are sometimes used for very heavy columns. If conditions are favorable to the action of corrosion the cast iron is to be preferred. ' Bearing-Plates and Bases 448 The Area of Bearing-Plates under Beams and Girders is found in the same manner as the area of plates under columns. If the load on the beam is uniformly distributed over the beam or concentrated at its middle, the required area of the plate is one-half the total load on the beam divided by the allowable bearing per unit of area on the masonry; but if the load is a moving load, the greatest possible end-reaction must be divided by the allowable bearing. For example, a heavily loaded truck standing near the end of the beam causes a pressure on the bearing-plate much greater than one-half its weight. The true reaction for the actual conditions must be found by the methods explained in Chapter IX. The Thickness of the Bearing-Plate is found by the formula used to determine the flexure of beams. It must be determined in each case. For a typical case the forces acting are shown in Fig. 5, which represents a transverse rt M t< — b — >| \< 1 H [ Fig. 4. Simple Bearing-plate under I'Beara ciifffflmT Fig. 5. Forces Acting on Half of Bearing-plate vertical section through one-half the plate. The vertical section at C, and through and parallel with the web of the I beam, is taken through the center of the plate, which is the dangerous section, or section of maximum bending mo- ment. In Figs. 4 and 5, b' is the bearing depth on the wall; / is the length of the plate, parallel with the wall; b is the width of the flange of the beam; R is the load on the bearing-plate. Replacing the uniform- loads by the equivalent forces at the center of gravity of each, these forces are represented by the longer arrows. The bending mo- ment at the section at c is the same as the moment of the concentrated forces, giving, M={R/2Xl/4)-{R/2Xb/4) or M=R/2X{l-b)U This is equal to the resisting moment at the same section c, or, at stress 5", Sl/c, in which l/c is the section-factor. (See Chapter XV.) This reduces to Sf^b /6. Equating the bending moment and the resisting moment there results St''b'/6 = Ril-b)/S and t= O.S66 Vr {I -b)/Sb' For 5=3 GOO for cast iron, tliis reduces to t = o.oiBSVR{l-b)/b' For 5 = i6 GOO for steel plates, it becomes t = b.oo68s Vr (/ - b)/b' (i) (a) 444 Bearing-Plates and Bases for Columns, etc. Chap. 13 Example 2. It is required to determine the length and thickness of a cast- iron bearing-plate linder a wooden beam which is 10 in wide and supports a load of 24 ocK> lb. The plate is 8 in wide and bears that width on a brick wall laid up in lime mortar. Solution. The load on the plate is 24 000/2 =12 000 lb. From Table II, the area of the plate is 12 000/112 = 108 sq in. Hence, if the width of the plate is 8 in, its length must be 13 V2 in. Then, from Formula (i) / = 0.0158 V 12 000 (13% — io)/8 = 1. 15 in A plate iVi in thick would be used. Example 3. It is required to determine the length and thickness of a steel bearing-plate under the end of a 24-in 8o-lb I beam supported on a 12-in brick wall laid up in lime-and-cement mortar and carrying a load of 60 000 lb. The width of the flange of the beam is 7 in. (See Table I.) Solution. The load on the plate is 60 000/2 = 30 000 lb The area of the plate = 30 000/160 = iSjH sq in The length of the plate is 187. 5/1 2 = 15.6 in Then, from Formula (2) / = 0.00685 "^30 000 (15,5 — 7)/i2 = I in Standard Sizes of Steel, Wall Bearing-Plates. These are given in Table II, and are based upon ALLOWABLE pressures of 112, 162 and 208 lb per sq in. These unit pressures are based upon the allowable pressures of the New York and Philadelphia building laws which are ex- pressed in tons per square foot. Because of the complicated formula on which the thickness depends it is best to compute the thickness for each case. Bearing-Plates under Columns. The general rules already given j^for the proportions of ribbed bases similar to that shown in Fig. 3 are a sufficient guide for detailing such bases; but in case simple FLAT PLATES are used under columns, their thickness must be computed according to the principles govern- ing bending. The stress in a flat plate supported Fig. 6. Flat Bearing-plate at the middle and subjected to a uniform load cannot for Column be determined by the ordinary methods of mechanics. The approximate solution here given is generally used in the design of base-plates and column-footings. It gives values found to be safe in practice. In Fig. 6, let B = the length of the side of the plate as determined by tht allowable pressure on the supporting masonry; D = the side or diameter of the column; P = {B — D)l 2 = the projection of the plate; / = the thickness of the plate; A' = the area of the plate outside the column; w = the allowable bearing pressure on the masonry due to the load on the column. Then in Fig. 6, the pressure on one-fourth of A', shown enclosed by the dotted lines in the figure, causes shearing and bending stresses in the section of the plate along the line ab. Considering the part enclosed and taking moments |^|x)Ut the section ab, the following equation is obtained from the usual bend- g/ilbn^ 7 / a b \ Bearing-Brackets on Cast-iron Columns 445 ing-moment formula. (See Chapter XV, page 557.) That is, the resisting moment equals the bending moment, or t Sl/c^MA'Pw For the rectangular section at ah, this may be written StW/^^VWPw whence / = V^ATw/VsD which becomes for 5 = 3 000 t = 0.022^ V A' Pw/D and for 5 = 16 000 / = 0.0097 VA'Piv/D Example 4, It is required to determine the size and thickness of a cast-iron bearing-plate to be used under a wooden post 12 in square in cross-section and designed for a load of 115 200 lb. The plate is to be set on brickwork laid in cement mortar in New York. (See Table I.) Solution. The required area of the base is 115 200/250 = 461 sq in. V^46i = 21.47 and a 22-in. square plate would be used. Then A' = 461 — 144 = 317 sq in P = (22 — i2)/2 = 5 in D = 12 in w = 250 lb per sq in j^ Hence / = 0.0224 V317 X 5 X 250/12 =^ 4 iii ' This thickness may be beveled to i K in at the edge. The computed thickness is greater than is usual for such plates, some formulas having more practical constants which really assume a stress of about 10 000 lb per sq in in cast iron in bending. If the plate is made of steel / = o.oo97\/3i7 X 5 X 250/12 = i^ in 2. Bearing-Brackets on Cast-iron Columns The Usual Column-Connections for fastening beams and girders to cast- iron columns are shown in Fig. 7.* The end of the beam or girder is set on a SHELF P, under which is a bracket-support C, cast on the side of the column. For a single beam, one bracket is sufficient; for wide beams or girders there should be two ribs. The ends of the beams are fastened to the column by bolting to LUGS L, cast on the column above the bracket. Sometimes a column is fastened by bolts passing through the bottom flange^of the beam and through the shelf-plate. This connection greatly decreases the lateral stabihty of a building and should not be used. The Shelf and Brackets, when loaded, are subject to shearing and bend- ING-STRESSES. The SHEAR at thc outer surface of the column-shell is equal to the end-reaction of the beam it supports. The bending-stress is due to the application of the load on the shelf-plate at some distance from the surface of the column. It causes a tension at the top of the bracket which tends to tear out the shell of the column, and causes, also, a compression at the foot of the rib. The thickness of the rib must be great enough to withstand the com- pression from the load above; and since the stress is variable along a section^ * See also, Figs. 5 and 7, pages 457 and 458. --^^ 446 Bearing-Plates and Bases for Columns, etc. Chap. 13 as along the line X, a rough approximation may be made by assuming the stress at the extreme edge to be twice the average stress, and by further assum- ing that the section in the rib takes care of all the compression. This maj^es it unnecessary to find the center of gravity and the moment of inertia of the section at X, both of which must be known if the flexure-formula is used. This procedure, also, makes unnecessary any assumption as to the true position of the center of pressure on the top surface of the bracket. With the thick- ness of rib given in the tables there is an ample factor of safety for any load Fig. 7. • Cast-iron Columns with Bearing-brackets that may be applied through a beam. The double ribs are required when wide beams are used, not for strength, but to prevent the failure of the shelf from eccentric loading. Tests of Cast-iron Brackets. Brackets of cast-iron columns tested by the New York Building Department gave a shearing strength of 4 200 lb per sq in on the section at the column when the load was applied at the end of the bracket, and an average of 8 000 lb per sq in when the load was distributed over the bracket-shelf. The range of stress in the first case was from 2 450 to 5 600 and in the second from 4 100 to 10 906 lb per sq in. In seventeen out of twenty-two tests the manner of failure was the tearing out of a hole in the body of the column. It appears that when the thickness of the rib and shelf is the same as that of the shell of the column, there is generally ample strength for the support of beams and girders; but that in the case of very heavily loaded beams, the shearing and crushing strength should be investigated. From the results of the tests mentioned, a low working stress for shear must be assumed. The Bevel of Brackets. If the shelf P (Fig. 7), on which the beam rests, 16 cast square with the column, when the beam deflects, the load is brought on. the extreme end of the bracket, causing an increased bending-stress in the Beadng-Brackets on Cast-Iron Columns 447 bracket and connections and tending to tear a hole In the column-shell. To avoid this the bracket-shelf should be sloped downward, away from the column, and should have a bevel of Vh in to the foot. Standard Connections for Cast-iron Columns. Table III, published originally in the Bassiac Rolling Mill Handbook, and widely used by other manufacturers, will be found useful when detailing cast-iron columns. Table IH. Standard Connections for Cast-iron Columns All dimensions are in inches Depth Thick- of A B C D E F G // K ness of beam 2 1 1/2 2 lugs I 20 5 5 6 10^/^ 1V2 lV2 18 4 ■; 6 loi/i. 1V2 1^2 2 1V2 2 I IS 4 .V/2 .SV2 qVa 1V2 iVi 2 1V2 1% I 12 3 3 4y2 7% ■ 1V4 IM 2 iVa 1V2 I Holes cored for %-in bolts \h'd 9dT ! fM:df r»-jt> Depth Thick- of A B C D E F ^ H K ness of ' beam lugs 10 3V4 ^V2 4 7 1V4. I 2 1I/2 1V2 I 9 3 3 4 7 I I 2 1V2 1V2 I 8 2y2 3 4 7 I I 2 1V2 1V2 % 7 2V4 2H' 4 7 I I 2 i^l> iH 8/4 ■ Holes cored for %-in bolts 448 Strength of Columns, Posts and Struts Chap. 14 CHAPTER XIV STRENGTH OF COLUMNS, POSTS AND STRUTS By CHARLES P. WARREN LATE ASSISTANT PROFESSOR OF ARCHITECTURE, COLUMBIA UNIVERSITY 1. General Principles and Definitions Slenderness-Ratio. The manner in which a material fails under compression* or pressure depends not only upon its nature, but also upon its dimensions and form, that is, upon the ratio of its length to its cross-section or diameter. This ratio is denoted by Ijr and is known as the slenderness-ratio. I Three Classes of Columns. The actual compressive strength of a material tnust be determined on very short specimens in which there is no tendency to bend or to buckle. The load required to break the specimen does not change much until the length is increased to about ten times the diameter or LEAST LATERAL DIMENSION. When that ratio is exceeded, the specimen tends to fail by bending or by buckling instead of by direct compression. According to their manner of failure, therefore, columns in general may be divided into three classes: '■ (i) Short Columns, in which the slenderness-ratio does not exceed lo iand which fail by direct compression. I (2) Columns in which the slenderness-ratio varies from 10 to 30 for timber and cast iron and from 10 to 90 for steel. The failure of columns of this class is due partly to direct compression and partly to bending. (3) Long Columns, in which the slenderness-ratio exceeds 30 for timber and cast iron and 90 for steel. These columns fail wholly by bending or buckling, which causes flexural stresses of compression and tension on the concave and convex sides respectively. . 2. Strength of Short Wooden Columns The Safe Load for a Short Wooden Column, the length of which is not more than 10 times the least dimension, may be computed by the formula _ , , , area of cross-section X 5 , . Safe load = '—, — (i) factor of safety ;in which 5 denotes the crushing strength of the given material as stated in ! Table I. ; I The Factor of Safety to be selected depends upon the place where the col- ! umn is used, the load which comes upon it, the quality of the material and, in a large measure, upon the value given to S. For lumber of ordinary quality, con- taining no very bad knots, a factor of safety of five may be used; or, in other words, the safe stress per square inch of section-area may be taken as one-fifth of the values given in Table I. If the column is badly season-checked, cross- grained, or contains bad knots, a larger factor, say six or seven, should be used. The character of the load, also, should be taken into consideration in determining the factor of safety. Thus for a wooden post supporting a brick wall a larger factor should be used than for one supporting a floor, as in the former case the full lo?d is at all times on the post, and the least reduction of its section-area in Strength of Wooden Columns or Struts 449 case of fire might cause it to give way. Wooden posts supporting machinery, or wooden struts in railway bridges, should have a factor of safety of from six to eight, if the values of S given in Table I are used. Table I.* Average Crushing-Loads in Pounds per Square Inch, for Build- ing Materials Materials For stone, brick, concrete and masonry, see Chap- ter V Metals Cast iron Wrought iron Steel, rolled shapes Woods, with the grainf Cedar Chestnut Crushing- loads, lb per sq 80 000 55 000 60 000 3500 4 000 Materials Woods (continued) Cypress Hemlock Oak, white Pine, long-leaf yellow. . . Pine, short-leaf yellow, . Douglas fir Pine, Norway Pine, white Redwood, California. . . Spruce Whitewood Crushing- loads, lb per sq 3500 4 000 Sooo Sooo 4000 4500 3500 4 000 4 000 4500 3000 .b * See, also. Table XVI, pap;e 647, and Table I, page 1138. t These are values for wooden columns under 15 diameters in height and are, of course, average values. For the safe loads, per sq in, on timbers, perpendicular to the grain, see Table VI. Example i. What is the safe load for a long-leaf yellow-pine column, 10 by icv- in in cross-section and 12 ft long, using a factor of safety of 5? Solution. Area of cross-section = 100 sq in; safe load per sq in =5 000/5 I 000 X 100 = 100 000 lb. p Example 2. It is required to support a brick wall weighing 80000 lb by a Douglas-fir column 1 1 f t long. What should be the cross-section of the column? Solution. As previously stated, for these conditions it would be wise to use a factor of safety of 6. Then the safe resistance per square inch of section-area = 4 500/6 = 750; 80000/750 =106 sq in required, about equivalent to a 10 by lo-in cross-section. 3. Strength of Wooden Columns or Struts Over Ten Diameters j in Length. Formulas Formulas for Wooden Columns. When the length of a column exceeds about ten times its least cross-dimension it is liable to bend under the load, and hence to break under a less load than would break it if it were shorter and of the same cross-section. To deduce a formula which will make the proper allow- ance for the length of a column has been the aim of many engineers, but their formulas have not always been exactly verified by actual results. Until recently the formulas of Lewis Gordon and C. Shaler Smith have been used generally by engineers, but the extensive series of tests made by the Govern- ment testing-machine at Watertown, Mass., on full-sized columns, showed that these formulas did not agree with the results there obtained. James H. Stan- wood in the year 1891 plotted the values of all the tests made at the Watertown Arsenal up to that time on full-size columns. From the results thus obtained 450 Strength of Columns, Posts and Struts Chap. 14 he deduced the following straight-line formula for long-leaf yellow-pine and white-oak columns: ^ , , , . , length in inches , ^ Safe load per square inch = i coo — lo X ,— — rT~' — • — ^ — (2) breadth in inches The author has carefully compared this formula with the results of actual tests, and with other formulas,* and believes that for timber without serious defects and with not more than 10 or 12% of moisture, it meets the actual con- ditions as nearly as any other formula. He has therefore prepared Tables II HI, IV and V for the strength of round and square columns of the sizes generally iised in practice. Of course other formulas must be used when required by cer- tain city building laws. For other sizes the loads can easily be computed by the formulas. For columns having bad knots or other defects, or more than io or 12% of moisture, or which are to be exposed to the weather or known to be eccentrically loaded, a deduction of from 10 to 25% should be made from the values given in the tables. The loads for columns of other species of wood were computed by the following formulas of the same form as that of Formula (2) : For Douglas fir and spruce, ^ - , , . , „ „ length in inches , . Safe load per square inch = 850 — 8.5 X , r-z—. — : — - — • (3) breadth in inches For chestnut, hemlock, short-leaf yellow pine and white pine, ^ . . . . . length in inches , . Safe load per square inch = 75° — 7-5 X , rT~' — ; — \ — (4) breadth in inches For cedar, cypress, redwood, Norway pine and whitewood, „ , . . . , ^ ^ length in inches , . Safe load per square inch = 625 — 6 X : 1,^-. — : — ; — • (5) breadth in inches In these formulas the breadth is the least side of a rectangular column, or the diameter of a round column. The round columns were computed for the half- inch, to allow for being turned out of a square column, of the next size larger. The formulas were used only for columns with a diameter or least side exceed- ing 12 diameters for yellow pine and white oak, and exceeding 10 diameters for other woods. 4. Tables of Safe Loads for Wooden Columns Tables II, III, IV and V give the safe loads in pounds for round and square wooden columns of different cross-sections and lengths and of different kinds of wood. They were computed from formulas as explained above and are for favorable conditions of material, seasoning and position in buildings. * There are many formulas for the safe loads per square inch of cross-section of wooden columns. Among those frequently used are the following: American Railway Engineering and Maintenance of Way Association, F/A ^S{i-l/6od) Department of Agriculture, P/A = 5 (700 -f 15 l/d)/{7oo + IS l/d + lydn Winslow Formula (Chicago Law), P/A =5(i-//8od) In these formulas, P is the safe load in pounds, A the area of the cross-section in square inches, P/A the safe load in pounds per square inch, S the safe end-bearing compression per square inch, / the length in inches and d the least side or diameter in inches. These formulas give smaller safe loads than those of Tables II, III, IV and V; but as the loads of these tables are to be decreased for unfavorable conditions and the loads determined from the three formulas mentioned increased for favorable conditions, the results are about the same. Tables of Safe Loads for Wooden Columns 451 Table II. Safe Loads in Pounds for Long-Leaf Yellow-Pine and White- Oak Columns, Round and Square Size of column in inches 4X6 sVi round. 6X6 6X8 6XiO yH round . 8X3 8X10 8Xl2 93^^ round , loXlo I0Xl2 ioXl4 iij-i round I2XI2 12X14 12X16 14X14 16X16 18X18 20X20 Length of column in feet 18 200 19590 30 200 40300 50400 38 540 64 000 80 000 96 000 7090© 100 000 120 000 140 000 103900 144 000 168 000 192 000 196 000 256 000 324 000 400 000 16 80Q 18760 28800 38 400 48 000 37 130 54 400 68 000 8 1 600 61 970 100 000 120 000 140 000 103 900 144 000 168 000 192 000 196 000 256 000 324 000 400 000 15 360 17550 27 400 36 500 45 600 35 710 52 500 65 600 78 700 60 190 85 600 102 700 119 800 90 912 144 000 168 000 192 000 j 196 000 j 256 000 324 000; 400 000 1 16 500 25 900 34600 43200 34300 50 600 63 200 76 800 58350 83 200 99 800 116 500 88730 123 800 144500 [I65 100 j 196 000 256 000 324 000 400 000 I 25 200 33600 42 000 33590 49 600 62 000 74400 57429 82 000 98 400 114 800 87 690 122 400 142 800 163 200 170 900 229 100 324 000 400 000 16 24 500 32 600 40 800 32890 48 600 60 800 73000 56580 80800 97 000 113 100 86550 121 000 141 iooii37 161 300: 157 169 100 1 165 225 300J221 289 400 285 400 000 356 109440 , 127 680 145 920 . 115 5 1344 153 t ._ , 162 400 155 800 217 f 2808 352 c J 600 )8oo 2 000 209900 272 i6o 342400 Table HI. Safe Loads in Pounds for Douglas-Fir and Spruce Columns, Round and Square Size of column in inches 4X6 SVz round. . 6X6 6X8 6X10 7>^ round , . 8X8 8X10 8X12 gVi round. . 10X10 10X12 10X14 II H round. 12X12 12X14 i2Xi6 14X14 i4Xi6 16X16 Length of column in feet 15500 16 650 25704 34272 42 840 32740 47870 59840 71808 54150 85 000 102 000 119 000 88290 122 400 142 800 163 200 166 600 190400 217 600 14 280 15790 24 480 32 640 40 800 31540 46 240 57800 69360 52650 74800 89 760 104 700 79 100 no 160 128 520 146 880 166 600 190 400 217 600 13050 14 900 23 256 31 008 37760 30340 44 600 55 760 66 910 51 150 72 760 87300 loi 860 77 250 107 700 125 660 143 600 149 450 170 800 217 600 14030 22 032 29376 36 720 29 140 42970 53720 64 460 49580 70 720 84860 99 000 75400 105 260 122 800 140 350 146 600 167 500 194700 21 420 28560 35700 28540 42 160 52 700 63 240 48820 69 700 83 640 97580 74470 104 040 j 121 38O1 138 7;?o, 145 i8o| 165 900; 193 000 20808 27744 34'68o 27940 41 340 51680 62 000 48 070 68680 82 400 96 150 73 550 102 800 119 950 137 080 143 760 164300 191 400 26 740 39710 49 640 59560 46570 66 640 80 000 93300 71 700 loo 360 117 100 133800 140900 161 000 188200 64 600 77500 90 400 69850 97 920 114 240 130 560 138 ( 157 800 184900 66 160 , 93 000 ; 108 S20 124030 i 132 400 IS I 3Q0 178 400 452 Strength of Columns, Posts and Struts Chap. 14 Table IV. Safe Loads in Pounds for Chestnut, Hemlock, Short-Leaf Yellow-Pine and White-Pine Columns, Round and Square Size of column in inches 4X6 5'/^ round 6X6 6X8 6Xio jH round 8X8 8Xio 8Xi2 9^^ round loXio 10X12 10X14 II H round. . . 12X12 12X14 12X16 14X14 16X16 18X18 20X20 Length of column in feet 12 600 13900 21 600 28800 36 000 27850 40 768 50960 61 152 46 440 66 000 79 200 92 400 69 820 108 000 000! 126 000 000 144 000 000 147 003 000 ' 192 ODD 000 j 243 000 0001300 000 II 520 13 160 20 520 27360 34 200 26780 39360 49 200 59 040 45 160 64 200 77040 89880 68 160 95040 no 8oo 126 700 147 000 192 000 243 000 300 000 12370 19440 25 920 32 400 25 720 37880 47 360 56830 43740 62 400 74880 87 360 66 490 92880 loS 300 123 800 129 300 192 000] 243 000 [300 000 16 18 900 25 200 31 500 25 190 37 120; 46 400 55 68o| 43 100 61 500- 73 800' 86 100; 65 770: 91 700' 107 000 122 300 128 100 170 500 243 000 300 000 18360 24 480 30 600 24 660 36480 44 600 54720 42 400 60 600 72720 84840 64 833 90 700 105 840 120 900 127 000 168 900 217 000 300 000 35 000 43 760 52500 41 120 58800 70 560 82 320 63 170 88 560 103 300 118 000 124 400 166 100 213 800 267 6001 57 000 68 400 79 800 61 600 86 400 100 802 115 200 121 900 163 000 210 600 264 000 82080 95 760 109 400 116 800 157400 204 100 256 000 Table V. Safe Loads in Pounds for Cedar, Cypress, Redwood, Norway- Pine and Whitewood Columns, Round and Square Size of column in inches 4X6 SH round/. , . 6X6 6X8 6X10 7'/^ round 8X8 8X10 8X12 gH round 10X10 10X12 10X14 II H round. . . 12X12 12X14 12X16 14X14 16X16 18X18 20X20 Length of column in feet II 520 12350 19 080 25440 31 800 24 220 35 450 44320 53180 40 000 62 500 75000 87500 64 930 90 000 105 000 120 oco 122 500 160 000 202 500 250 000 10550 II 730 18 216 24 290 30360 23380 34300 42 480 51 450 39000 55 400 66480 77560 58390 90 000 105 000 120 000 122 500 160 000 202 500 250 000 9 800 II 180 17352 23140 28 920 22540 33 150 41 440 49730 37860 53 960 64 800 75600 57 140 79780 93 170 106 300 no 350 160 000 202 500 250 000 8 700 10 490 16 490 21 980 27 480 21 660 32 000 40 000 48 000 36 800 52 520 63 000 73500 55800 78 000 91 050 104 000 108 350 143 870 202 500 250000 16050 15 21 400 26 760 26 21 260 1 20 31 420J 30 39280J 38 47 1401 46 36 230 35 51 800; 51 62 i6oj 61 72520 71 55 170' 54 77 180; 76 90 050' 89 102 900 lor 107 400 106 142 590 141 183 060 181 250 ooo'25o 620 830 .. 040 . . 820 . . 850 29 560 37 270 44 730 34 080 49 300 59 510 69 550' 53 320 74 000 87 700 99 400 104 570 139 760 179 000 224 i 48 200 57840 67 480 51 950 72 860 85 000 97 150 102 300 136 960 176 580 221 200 69 400 80 900 92500 98 400 132 360 171 400 215 200 . Eccentric Loading of Wooden Columns 453 5. Eccentric Loading of Wooden Columns General Principles. When the load on a short column or post is not axial, that is, when the column supports a girder on one side only, or*when the weight from one girder is much more than that from the others, the load is said to be ECCENTRIC, and the distance from the point of application of the load to the axis of the column, denoted by p, is called the eccentricity of the load. It is evi- dent that the stress in the column will increase with p, and that the total unit stress S, on the side of the column in which the compression is the greatest, will be greater than for an equal axial load. Formula for Eccentric Load. Suppose the eccentric load to be applied as shown in Fig. 1, then the sectional area of the required square or rectangular column may be computed by the fol- lowing formula (See, also, page 486) : The sectional area of the column in square inches is A = {P-VPx)/S^^PiP/Sd (C) in which A = sectional area in square inches P = concentric load on column in pounds Pi = eccentric load in pounds S = safe stress in pounds per square inch p = distance from axis of column to cen- ter of bearing in inches d = side of column parallel with girder, in inches ELEVATION Gfirder A Fig. PLAN 1. Eccentric Load on Wooden Column , In assuming the value of S, the probable ratio of the side to the length of the column should be taken into account. Thus if it is probable that the length will not exceed 12 times the side, both being measured in inches, for oak, long-leaf yellow-pine or Douglas-fir columns, or 10 times the side for other woods, then the value of S for short columns may be taken. If the ratio will probably be greater than this, then the probable ratio should be roughly calculated and S computed for that ratio by the formula given for columns more than 10 or 12 diameters in length, as noted in preceding paragraphs. Example 3. The lower post in Fig. 1 supports a total load on its cap-plate of 60 000 lb, including the reaction of 1 2 000 lb from girder A . What should be the size of the column if made of Douglas fir and if 12 ft in height? Solution. As it is probable that the column will have to be 10 in square S may be taken from Table I. With a factor of safety of 5, this is equal to 4 500/5 =» 900 lb per sq in. Pi= 12 000 \h, d = 10 in and p, the distance from the axis of the column to the center of bearing of the girder = 7 in. Then from Formula (6), the sectional area of the column is A = 60 000 6X12 000 X 7 = 66.6 + 56 = 122.6 sq in. 900 900 X 10 about equivalent to a 12 by 12-in square column. From Table III, it may be seen that an 8 by lo-in column concentrically loaded will carry almost 60 000 lb. 454 Strength of Columns, Posts and Struts Chap. 14 Hence, the eccentric load from the girder increases the dimensions of ttom flanges, (extending around all sides of the coluoin, unless otherwiso detailed,) lugs, seats, brackets and separators, reinforced bj lilleta and webs, all as detailed. Brackets shall be beveled on seats and be provided with ample fillets and webs. CONNECTIONS "All columns shall be bolted together throuph their flanges and top plaice with not less than four, and to the bases with not less than eight, ^4," bolts. ' "Beams, channels and beam-girders shall be bolted to the lugs, or web-separators, of cast-iron columns by two bolts for beams 12"or less in depth and by three bolts for all others. In all cases the webs are to be in close contact with the lugs and separators. Built-up girders shall be bolted to the columns through web angle-Btiffeners-" TESTS "All hollow castings shall have' two, or, more, ^" holes drilled in the shell as directed, to exhibit the thickness of the metal, and those showing a variation of more than 3^' will be rejected.'* \J All holts to be %"m diameter unless lave a projection of S'except where other-w eled on seatt and ample flUeta proy Wed whi 'flanges to be drilled to a template ^g saop piREC . Column flanges Brackeisto bt. bev Open h )les In 00 diameter of bolt Open I oles in bea!m•^agB t^ be ooted ^^'larger than, dhtmetei 3ni[; 4? / oftherwiee marked^ shown. practicable* 1 irger than CH ofjjolK -ir- ^ ¥ ^ Fig. 5. Connections for Cylindrical Cast-iron Columns Typical Connections for a Cylindrical Cast-iron Column. Fig. 5 shows the details of a cylindrical cast-iron column with typical beam and girder-con- nections, dimensions and specification-notes. (See, also, details of connections, brackets, base-plates, etc., for cyUndrical columns in Chapter XIII, Figs. 2, 3 and 7 and Table III of same chapter.) 45S Strength of Columns, Posts and Struts 'Chap. 14 G^st-Iroi Columns M'ith Hollow-Square Cross-Section. The columns • I ' ) next in point of economy of cross-section are those with the HOLLOW-SQUARE cross-section (Fig. 3). They are generally used for wall columns because it is easier to bond them into the masonry than if they had a circular section. Columns of hollow rectangular cross-section of unequal sides are some- times found to be more available than those of square section. The H-Shape Column (Fig. 4) ranks third in regard to economy of material. It is particularly well adapted for wall columns in skeleton construction for the following reasons: Fig.' 6. H-shaped Cross- section of Cast-iron Column * * "VjThBlsa l)olte go ihrough Ijevelea^aEnge^,/" "beveled waehexe to "match shall Ije used, ^o thatrthe lieatkantltiufcof the bolt'^ill be parallel. V- TaPPLA33:H. "Steel top plates, not leas than }i fhicTc, of the size Teqiiined l)y tlie dimensions of tho joint, and. to afford .f ulLbeaTings for the angle-bracketSj shall be placed be- tween Qie ends of all columns cast with one side or \eith one bacJCopen, and whenever, a column of less diameter is placed upon top of anotjier. TJiey shall also-bcruBed — to make up any shortage in length of casWron xsohinms. l?lates for double columns ehaTLbe cast •vdth. top and \>ot- .1 torn flanges. .A^terthe plates have been f1rin <='(l -aifl. tho j - J proper lioles for connections, they shall be truljr fiekti and of uniform thickness.*' Note J These y columns ace particularly welt adapted ton itall. columns in skeleton constr.uction. Only the edges come near the face of the vail and there are no project- ing .rime or flang^ee to be in. the yrsey. Fig. 7. Connections for H-shaped Cast-iron Column (i) Being entirely open, with both the interior and exterior surfaces exposed, any inequalities in thickness can be readily discovered and the thickness itself Strength of Cast-iron Columns. Formulas 459 easily measured, thus obviating any necessity for drilling, and rendering the inspection of the columns much easier. (2) The entire surface of the column may be protected by paint. (3) When built in brick walls the masonry fills all voids, so that no open space is left; and if the column is placed as shown in Fig. 6, only its edges come near the face of the wall. (4) Lugs and brackets can be cast on such columns more readily and effectively than on cylindrical columns, especially for wide and heavy girders, and the. connections do not require projecting flanges, which are often in the way on cylindrical columns. (5) An eccentric load may be applied to the web where its effect is less and where it is more evenly distributed than when it is applied to the outer rim or shell. Details of connections and brackets for H -shaped cast-iron columns are shown in Fig. 7. Details of Connections of Cast-iron Columns. The bearings of a cast- iron column should always be faced true to the axis of the column, and the columns should be bolted together by four ^4-in bolts for columns 10 in in diameter or less, and by six bolts for 12-in and larger columns. Faced plates, as shown in Fig. 5, are inserted between the flanges of columns to make up for any shortage in length and also when a column of smaller diameter is placed" over one of greater diameter. For convenience in erecting columns, the joint is gen- erally placed just above the beams or girders supported by the columns. Projecting Caps and Bases. A column with or- namental cap and base should that is, if it is to support Fig. 9. Cast-iron Column with Cap and Base. Slight Projections Fig. 8. Cast-iron Column with Cap and Base. Wrong Method never be cast as shown in Fig. a load. In every bearing column, the core should extend in a straight line from end to end. Plain molded caps and bases may be cast solid as in Fig. 9; but if more ornamental caps are desired, or heavy projecting bases, they should be cast separately and attached to the straight columns by screws. W, Strength of Cast-iron Columns. Formulas Formulas for Cast-iron Columns. The ultimate resistance of cast iron to crushing is generally taken at 80 000 lb per sq in, and for posts, pintels, etc., where the length is not more than six times the diameter or breadth, it will usually be safe to assume a working strength of six tons per square inch of metal. For longer posts or columns, the strength is affected by the ratio of 460 Strength of Cclumns, Posts and Struts Chap. 14 length to diameter, but to just what extent is not known with absolute certainty; hence all formulas for columns must be more or less theoretical. The conse- quence is that while a great many formulas have been published, there is none that is universally accepted. The two following Formulas * (7) and (8), were for many years more commonly adopted than any others, as they appeared to agree as well as any with actual tests. Formula for Hollow, Cylindrical, Cast-iron Columns with Square Ends Ultimate strength, in pounds. * sq of length in in = metal-area X [80000^(1+- 800 X sq of diam in in )] (7) Ultimate strength, in pounds = 80000 A in which A is the area of the cross-section in square inches. * The tables in the handbook of the Cambria Steel Company (1913) are based on Formulas (7) and (8), and they were adopted in some building laws. They are based upon the form of Gordon's formula, which, in turn, is Rankine's formula with d, the diameter or least lateral dimension, substituted for r, the least radius of gyration of the cross-sec- tion. Rankine's formula is sometimes referred to as Gordon's formula. The values obtained by these formulas will be slightly in excess of those given in the old Chicago building law (see tabulation in this foot-note), and considerably less than those permitted by the former building law of New York City, S = 11 300 — 30 l/r. (Present code, 5 = 9000 - 40 l/r. "■ '■'^■' '''^■. i In 1898 Professor W. H. Burr made an analysis of the results of a number of experi- ments on full-size, hollow, cylindrical cast-iron columns made at the Watertown Arsenal, Mass., and at PhcenLxville, Pa., and by plotting the results found that a straight-line formula having the equation 5 = 30500— 160 l/d, in which S is the ultimate strength of the metal per square inch of column-area, represented the average of the plotted results. With a factor of safety of 4 this would become 5=7 625 — 40 l/d and with a factor of safety of 5, 5 = 6 100 — 32 l/d. According to Professor Burr's analysis the values for S given in the fourth column of Table VII represent a factor of safety of a little over 4 for l/d = 20, and of nearly 7 for l/d = 36. Formulas for finding the value of S according to the former codes of Chicago and Boston. Cylindrical columns Rectangular columns Old Chicago Code Old Boston Code Old Chicago Code Old Boston Code TO 000 10 000 10 000 10 000 ^ '^eoo'd^ 800T2 /2 ^ 800 d^ I 1 ^' 1066 (/2 The former New York City Building Code Formula was S = 11 300 — 30 //r Compared with the results of tests that have been made on full-size cast-iron columns it has been shown that while in Chicago a factor of safety of 8 was allowed, the actual factor of safety was a little over 4, that in Boston it was slightly under 4, while in New York it was a trifle over 6. The formula in the new (1916) Chicago code is 5 = 10 000 — 60 l/r, while the new (1915) Boston code gives the values of S for l/r from 10 to 70. A series of tests on full-size cast-iron columns and brackets was made under the direc- tion of Stevenson Constable, in December, 1897, a report of which, with illustrations, may be found in the Engineering Record for January 8 and 22, 1898. Tables of Safe Loads for Cast-iron Columns. Examples 461 Formula for Hollow, Rectangular, Cast-iron Columns with Square Ends Ultimate strength, in pounds = metal-area X fso ooo ^ ( i + ^Q °f 'ength in in \ "j L \ I 067 X sq of least side in in / J Ultimate strength, in pounds (8) aiiac in 111 y _j 80 000 A i + /Vio67^2 in which A is the area of the cross-section in square inches Formula for Solid, Cylindrical, Cast-Iron Columns Ultimate strength, in pounds = metal-area X fso ooo - . + - L^^fJ^SS^i^il^^^"] ,. L 266 X sq of diam in in J or Ultimate strength, in pounds = I + /V266^2 in which A is the area of the cross-section in square inches. For H -shaped cokimns use formula (7), taking d as the feast side. The safe load is generally taken at one-eighth of the ultimate strength or breaking-load. Eccentric Loading. Cast-iron columns should not be loaded with a heavy, ECCENTRIC LOAD, that is, a load applied on one side of the column without a corresponding load on the other side, as cast iron is unable to resist very great bending stresses. (See, also, eccentric loading of wooden and steel columns, pages 453 and 485.) 11. Tables of Safe Loads for Cast-iron Columns. Examples Explanation of Tables. As the allowable pressure per square inch op METAL depends upon the ratio of length to diameter, without regard to actual dimensions (that is, it would be the same for a column 6 in in diameter and 1 2 ft long, as for one 8 in in diameter and 16 ft long), it is practicable to prepare a table which will give the value of the terms of Formulas (7) and (8) inclosed in brackets for all ratios of diameter to length, and thus simplify very much the computation for any particular column. Table VII has been computed by means of Formulas (7) and (8) for ratios of length to diameter varying from 8 to 36, and the same result will be obtained by using the values given in this table as by using the corresponding formula. To use this table it is only neces- sary to divide the length of the column by the least thickness or diameter, both in inches, and opposite the number in the first column of the table coming nearest to the quotient, find the safe strength per square inch for the column. This load is multiplied by the metal-area in the cross-section of the column and the result is the safe load for the column. Examples (5) and (6) will illus- trate the use of Tables VII to X. Example 5. What is the safe load for a lo-in hollow, cylindrical cast-iron column, 15 ft long, the shell being i in thick? Solution. In this case the ratio l/d, which is the length of the column divided by the diameter, both in inches, is 18, and opposite 18 in Table VII the safe load per square inch for a cyhndrical column is found to be 7 1 17 lb. The metal- area of the column, from the table of areas on pages 42 and 463, is equal to the area of a lo-in circle minus the area of an 8-in circle, or, 78.53 — 50.26 = 28.27 sq in. Multiplying these two together, for the safe load of the column the result is 28.27 sq in X 7 n? lb per sq in = 201 917 lb, or about 100.5 tons. 462 Strength of Columns, Posts and Struts Chap. 14 Tables VIII, IX and X. To still further facilitate computations, Tables VIII, IX and X, have been prepared, which give at a glance the safe loads, based on a factor of safety of 8, for columns of the more common sizes and lengths. For lengths between those given in the tables sufficiently accurate results may be obtained by interpolation. For any other factor of safety, multiply the safe load given in the table by 8, and divide by the new factor of safety. Example 6. What is the safe load for a Q-in hollow, cast-iron column of square cross-section 1 2 ft long, the shell being i in thick? • Solution. From Table IX, the safe load is 129 tons. The same result may be obtained by using Table VII. The ratio Ifd in this case is 144/9 =16 and the corresponding safe load in pounds per square inch is 8 064. The area of the column is 32 sq in. Hence, the safe load is 32 sq in X 8 064 lb per sq in = 258 048 lb, 'or 129 tons, which agrees with the safe load given in Table IX for the same column. Table VII. Breaking-Loads and Safe Loads in Pounds per Square Inch for Hollow, Cylindrical and Hollow, Rectangular, Cast-Iron Columns Calculated by Formulas (7) and (8) Length in Breaking-weight in pounds Safe loads in pounds per inches divided per square inch square inch. Safety- by external factor 8 breadth or diameter Cylindrical Rectangular Cylindrical Rectangular 8 V4 074 75470 9259 ■9433 9 72661 74350 9082 9293 10 71 no 73126 8 888 9140 11 6950s 71870 8 688 8983 12 67800 70487 8 475 8 811 13 66060 69084 8257 8 635 i: 14 64257 67567 8032 8446 IS 62450 66060 7806 8257 16 60606 64516 7576 8064 17 58780 62942 7 347 7867 18 56 940 61 360 7 117 7670 19 SS 134 59 745 6892 7468 20 53 333 S8180 6 666 7272 21 SI S8o 56 610 6447 7 076 22 49 843 55 020 6 230 6877 23 48163 53470 6 020 6684 24 46512 51 950 5814 6494 25 44918 50440 5614 630S 26 43360 48960 5420 6 120 27 41 862 47530 5 233 5940 28 40404 46 no 5 050 5764 29 39000 44742 4 875 5 592 30 37647 43390 4706 5 424 31 36347 42 080 • 4 543 5260 32 35090 40816 4386 5 102 33 33 m 39 580 4 235 4 947 34 32 720 38380 4090 4 797 35 31608 37 244 3 951 465s 36 30 534 36 120 3817 4515 Tables of Safe Loads for Cast-iron Columns. Table VIII. Safe Loads in Tons of 2 000 pounds for Hollow, Cylindrical, Cast-iron Columns with Square Ends Based on Formula (7). Safety-factor 8 Diam- T eter, 1 in hick- aess, in Length of column in feet Area of metal, sq in Weight, linft 6 8 10 12 14 16 18 20 22 24 5 34 38 29 32 24 27 10.0 11.3 11.2 12.7 12.4 14. 1 15 7 14.7 16.8 18.8 31.3 35.3 35.0 39-7 38.7 44.0 490 46.0 52. 6 58.9 53.4 61.2 68.7 H li 39 45 5'A I 46 52 40 16 ■10 30 34 26 29 3! 36 39 43 49 54 6 52 60 47 53 59 41 47 52 36 41 45 48 55 61 27 31 34 24 27 30 34 38 43 .... 7 % I 65 74 8^ 60 68 76 54 62 6S 38 43 18 8 H I 78 89 100 72 83 93 67 76 86 61 70 79 71 50 57 64 45 51 58 40 46 52 36 41 47 33 37 42 17. 1 19.6 22.0 9 I 103 117 129 98 no 122 91 103 114 85 95 105 80 90 99 71 80 89 6S 73 81 67 74 54 61 67 49 55 61 22.3 25.1 27.8 69.8 78. 5 87.0 10 I 118 133 147 161 112 127 141 154 106 120 133 146 100 1X2 12.=; 136 93 105 116 127 86 97 107 118 79 89 99 109 73 82 91 100 67 76 84 92 62 69 77 84 25.1 28.3 31 4 34.4 78 4 88.4 98.0 107.4 II I i^ 1% 149 165 182 197 143 159 175 190 137 152 167 181 129 144 158 171 122 135 148 161 114 126 139 151 106 118 129 140 98 109 120 130 91 lOI III 121 85 94 103 112 31 4 34.9 38.3 41.6 98.2 109. 1 119. 7 129.9 12 1K2 184 202 220 237 178 195 212 229 171 188 204 220 163 179 194 210 154 170 184 199 146 160 174 187 137 150 128 141 153 165 120 132 143 154 112 123 133 144 3«.4 42.2 45.9 49-5 120. 1 131. 9 143.4 154.6 13 202 222 242 261 196 216 235 254 190 209 227 245 182 200 218 235 174 191 208 224 165 181 197 213 156 172 187 201 147 162 176 190 138 152 166 179 130 143 156 168 42.0 46.1 50.2 54.2 131 .2 144.2 156.9 169.4 14 iH 1% 242 264 285 306 236 258 278 298 229 250 270 289 221 241 260 279 212 231 250 268 203 221 238 256 193 210 227 243 183 199 215 231 173 189 204 219 164 178 193 207 50.1 54.5 58.9 63.2 156.5 170.4 184.1 197.4 rS i^^ 1% 1% 268 309 332 354 280 303 325 346 272 295 316 337 264 285 306 327 254 275 295 315 244 264 283 302 234 252 271 288 223 241 259 276 212 229 246 263 203 219 235 251 68.3 72.8 183 9 203.4 213-4 227.6 16 iH 333 358 382 455 327 351 375 446 3T9 343 366 435 310 333 356 423 300 322 344 410 290 3tl 332 395 278 299 319 380 267 286 306 364 255 273 292 347 243 261 279 332 68.3 73.4 78.3 93.2 213. 5 229.3 244.8 291.3 ■ J 464 Strength of Columns, Posts and Struts Chap. 14 Table IX. Safe Loads in Tons of 2 000 Pounds for Hollow, Square and Rectangular, Cast-iron Columns, with Square Ends Based on Formula (8). Safety-factor 8 Size, 4X 6 4X 8 4X 9 4X10 4X12 5X 8 5X 9 5X10 5X12 6X 6 6X 8 6X 9 6X10 6X12 6X15 7X 7 7X 9 7X12 8X 8 8X10 8X12 Thick- ness, Length of column in feet 28 35 39 42 49 48 61 52 67 57 73 65 84 51 65 60 78 65 84 70 91 80 104 95 123 67 85 77 100 93 121 83 107 129 95 122 148 106 138 127 167 154 16 18 Area of metal, sq in 12.75 15.75 17.25 18.75 21.75 17.25 22.00 18.75 24.00 20.25 26.00 23.25 30.00 15.75 20.00 18.75 24.00 20.25 26.00 21.75 28.00 24.75 32.00 29.25 38.00 18.75 24.00 21.75 28.00 26.2s 34.00 21.75 28.00 33-75 24.75 32.00 38.75 27.7s 36.00 43.7s Tables of Safe Loads for Cast-iron Columns. 465 Table IX (Continued). Safe Loads in Tons of 2 000 Pounds for Hollow, Square and Rectangular, Cast-iron Columns, with Square Ends Based on Formula (8). Safety-factor 8 ] Lengt in feet 1 of column Size, Thick- ness, Area of metal, Weight, linft in 8 10 12 14 20 24 sq in 16 18 8X16 I 193 181 168 155 142 130 119 99 44.00 137.5 iVi 236 221 206 190 174 159 145 121 53 75 168.0 9X 9 ¥i III 106 99 93 86 80 74 63 24.75 77.3 t 144 137 129 120 112 103 96 85 32.00 100. 9X12 I 171 162 153 143 133 123 114 97 38.00 118. 8 iH 209 198 186 174 162 149 138 118 46.25 144.5 9X16 I 207 196 185 173 161 149 138 117 46.00 143.8 iH 254 240 226 212 197 182 168 143 56.25 175.8 10X10 I 165 158 150 142 133 125 117 lOI 36.00 112. 5 iH 201 193 183 172 162 152 142 123 43.75 136.7 10X12 I 184 176 167 158 148 139 129 112 40.00 125.0 iKi 224 214 204 192 181 169 158 137 48.75- 152.3 10X15 I 211 202 192 181 170 160 149 129 46.00 143.8 iH 258 247 235 222 209 19s 182 158 56.25 175-8 10X16 I 220 211 200 189 178 167 155 135 48.00 150.0 iH 270 258 245 232 218 204 190 165 58.75 183.6 10X18 I 239 228 217 205 193 181 168 146 52.00 162.5 iH 293 280 266 251 236 221 207 179 63 -75 199 2 10X20 I 257 246 234 221 208 194 181 157 56.00 175.0 iH 316 302 287 271 255 239 223 193 68 75 214-9 10X24 I 294 281 267 252 237 222 207 180 64.00 200.0 iH 362 346 329 311 292 274 255 221 78.75 246.1 12X12 li 183 177 171 164 156 149 141 126 38.90 121. 7 I 207 201 193 185 177 168 159 142 44.00 137.5 iH 253 245 236 223 •216 206 195 174 53.75 168.0 \Vi 296 288 277 26s 253 241 228 204 63.00 196.9 12X1S I 235 228 220 211 201 191 181 162 50.00 156.3 iH 288 280 269. 258 246 234 222 198 61.25 191-4 12X16 I 245 237 228 219 209 199 188 168 52.00 162.5 12X18 I 263 256 246 236 225 214 203 181 56.00 175.0 12X20 I 282 274 264 253 241 229 217 194 60.00 187-5 12X24 I 320 310 299 287 274 260 246 220 68.00 212.5 14X16 I 268 261 254 246 238 229 219 200 56.00 175.0 14X20 I 307 298 290 281 272 261 250 228 64.00 200.0 14X24 I 345 336 326 316 306 294 280 257 72.00 225.0 16X16 I 300 284 278 271 264 256 247 229 60.00 187.5 16X24 I 380 360 352 344 334 324 313 291 76.00 237.5 18X18 I 340 340 320 314 307 299 291 274 68.00 212.5 20X20 I 380 380 361 356 349 342 334 317 76.00 237.5 20X24 I 420 420 399 393 386 378 369 351 84.00 262.5 .._ , |, , , 466 Strength of Columns, Posts and Struts Table X. Safe Loads in Tons of 2 000 Pounds for H-Shaped, Cast-iron Columns Based on Formula (7). Safety-factor 8 Size, in Area of Length of column in feet i X . 1 metal, ?! \^ s-^ ^xx ^^^^^J^;X\-^ a b t in 10 12 13 14 : 1 - f i 6X 6X % I 123/^ 16 41 53 36 46 33 43 31 40 h u' ' ■■ *i 1% 19^^ 64 56 52 48 15 16 ■ 18 20 6X 8X M I 18 46 60 40 52 37 48 34 45 iH 21 ^i 73 63 59 54 7X 7X1 19 69 62 58 55 52 49 43 38 iM 23]^ 84 75 71 67 63 59 53 46 7X 9X1 21 76 68 64 61 57 54 48 42 iH 25H 93 83 79 74 70 66 59 51 8X 8X M 16% 66 60 57 54 51 49 44 39 I 22 86 78 74 70 67 64 57 51 iH 26^i 105 95 91 86 82 78 70 63 8X10X1 24 93 85 81 77 73 69 62 56 iM 293/i 114 104 99 94 90 85 76 69 1K2 34K2 134 122 117 III 105 100 89 81 9X 9X1 25 102 94 91 87 83 79 72 66 iM 30H 125 116 III 106 102 97 89 81 1K2 36 147 136 130 125 120 114 104 95 9X10X1 26 106 98 94 90 86 83 75 69 1% 31^6 130 120 IIS III 106 lOI 92 84 i\^ 37^^ 153 142 136 130 125 119 108 99 loXioXi 28 118 III 107 103 99 95 88. 81 iH 34^/^ 145 136 131 127 122 127 108 100 1 1/2 40H 171 160 155 149 144 138 128 117 1% 46% 196 184 177 171 165 158 146 134 10X12X1 30 127 119 IIS III 106 102 94 87 iM 36^:^ 156 146 141 136 131 126 116 107 1^2 43H 184 172 166 160 154 148 137 126 m 49^^ 211 198 191 184 177 170 157 144 2 56 236 222 214 207 199 191 .176 162 12X12X1 34 151 144 140 136 132 128 121 113 iw 4l7/^ 186 177 172 167 163 158 149 139 ii/^ 49H 220 209 203 198 193 187 177 165 1% 56^ 252 241 234 227 221 216 202 i89 2 64 284 271 263 256 249 242 227 213 12X14X1H 44% 197 188 183 177 173 168 158 148 i\^ 52}^^ 233 222 216 210 204 199 186 174 m 60H 268 255 248 241 235 228 214 201 2 68 302 288 280 272 265 257 241 226 2H 75^/^ 335 319 310 301 292 285 268 251 Types, Forms and Connections of Steel Columns 467 12. Types, Forms and Connections of Steel Columns Use of Steel Columns, Struts, Trusses, etc. Owing to the many ad- vantages of built-up steel columns over cast-iron columns, especially for all buildings, and to the great reduction that has taken place in the cost of steel construction, built-up columns are now very extensively used in buildings of even moderate height; and for skeleton construction, or for buildings exceeding six stories in height, they are certainly much to be preferred to cast-iron columns. Steel trusses, also, are no\y much more commonly used in buildings than in former years, so that the architect must have at hand data for designing them and for computing their strength. In the following pages the author has en- deavored to cover the subject of columns and struts quite completely, to furnish such data as will enable the designer to decide upon the shape of column or strut it is best to use, and also to determine the sizes and sections of such col- umns with the least labor. Types and Forms of Steel Columns. The following are cross-sections of the majority of steel columns in general use, arranged in the order of their sim- plicity of construction, that is, the number of rows of rivets they require: Bethlehem H col No rivets Lally steel-con- crete column No rivets Plate-and-angle j column Two rows of rivets Channel-column with plates or lattice-bars Four rows of rivets Plate-and-angle column with side plates Six rows of rivets Box column Eight rows of rivets Considerations Governing the Selection of Steel Columns. There are considerations other than simplicity of construction which sometimes govern the selection of a column. Some of the most important of these are explained in the following paragraphs: (i) Cost and Availability of Material. I beams, channels, plates and angles are the most common commercial sections. They are easily rolled and are manufactured by all of the large mills. They are reasonable in price and may be obtained promptly in large numbers in any locality where a steel building ia likely to be erected. Patented sections, or the product of one mill, do not, as a rule, fulfill these conditions. 468 Strength of Columns, Posts and Struts Chap. 14 (2) Amount of Labor Required and Facility With Which it can be Performed in Shop and Field. In the shop the complexity of the column-section and the number of pieces of which it is composed greatly affect the cost of labor. If there are numerous small pieces such as lattice-bars, splice-plates, etc., each of which requires cutting and fitting together, with frequent handling, the cost is proportionately great. The cost of a column depends, also, largely upon the number of rivets required and whether they can all be driven by machine so as to avoid the slower and more expensive hand-riveting. The same general remarks apply to labor in the field; the connections should be as simple as possible, the rivets easy of access and as few in number as is consistent with strength. (3) Simplicity of Connections Between Column and Supported Members. This is quite an important consideration in the design of a large building and sometimes governs the choice of the section to be used. Where there are four beams to a column, on opposite sides, and all of the same height, a satisfactory connection can be made with almost any section; but where the beams are spaced irregularly, both in regard to position in plan and to height, and where eccentric loads must be provided for, it is very important that the section of the column itself affords as great an opportunity as possible for the connections of the beams. In this respect, possibly, closed sections are inferior to open sections having a central web. (4) Adaptability to Connections Which Transfer Compressive Stresses Directly to Axis of Column, In this respect, also, sections of an open construc- tion, in which the girders transmit their loads almost directly to the central axis of the column, thus avoiding the disadvantage of eccentric loading, are superior to those of a closed construction. (5) Adaptability to Changes in Thickness of Metal in Members of Columns, to Suit Different Loads in Different Stories. It is not desirable to make the columns carrying the upper floors of a building very small, since the beams and girders supporting the upper floors are usually of the same dimensions as those of the lower floors and consequently require just as heavy and secure connec- tions. It is almost impossible to make such connections with small columns, and consequently, in order to reduce the area of a column in proportion to a lighter load to be carried, it is better to reduce the thickness of the material used and to keep the general dimensions of the section the same. (6) Adaptability to Fire-Proof Covering. Closed sections in general can be more compactly fireproofed than open sections. General Considerations Affecting the Choice of Steel Columns. It is almost impossible to say that any one of the foregoing types of steel columns is superior to the others. Each has its own good points, and the column whose section has theoretically the best distribution of material may not always be the best one to use, because of the eccentric loads to be carried, or because of other conditions. The choice in most cases will depend upon the personal views of the designer, as well as upon the local conditions as to cost and manufacture, promptness of delivery and the details of the problem. Further descriptions of the different columns, and also the special advantages claimed for them, are given in the following pages. Steel-Column Connections. When steel columns were first designed it was customary to use cap-plates to connect the story-lengths, and the beams or girders often rested upon these plates. In modern practice, however, the col- umn-joint is generally placed just above the beams and girders for convenience in erection and the plates are often omitted The columns are closely fitted Types, Forms and Connections of Steel Columns 469 together with milled ends, and spHce-plates are riveted to the sides or flanges as shown in the illustrations of typical steel-column details, Figs. 17 and 18. As it is impossible in these pages to include the subject of column-connections in anything but a general way, the only attempt that has been made in this direction is to illustrate common forms of connections that have been used with different kinds of columns. These will be found in the description of columns in the following pages. Number of Rivets Required. No general rule can be given for the number of rivets and size of the brackets required for column-connections, as the loads to be supported vary in different buildings and in different parts of the same building. The number of rivets required in each connection must therefore be determined by the rules given in Chapter XII for designing riveted joints. Connections for single beams, however, will generally require the same number of rivets as are given for beam-connections (Chapter XV, page 617). The allowable stress for rivets in column-connections is generally taken at 10 000 lb per sq in for single shear and 18 000 or 20 000 lb per sq in for bearing. (See Tables II and III, pages 418 and 419, Chapter XII.) Spacing of Rivets. Steel columns fail either by deflecting bodily out of a straight line or by the buckling of the metal between rivets or other points of support. Both actions may take place at the same time, but if the latter occurs alone, it may be an indication that the rivet-spacing or the thickness of the metal is insufificient. The rule has been deduced from actual experiments upon riveted columns that the distance between centers of rivets should not exceed, in the line of stress, sixteen times the thickness of metal of the parts joined, with a maximum spacing of 6 in, and that the distance between rivets or other points of support, at right-angles to the line of stress, should not exceed thirty-two times the thickness of the metal. The usual practice in designing columns is to space the rivets the minimum distance on centers at both ends, for a length equal to twice the least dimension of the column, with the maximum spacing of 6 in between. Steel-Pipe Columns.* Steel-pipe columns are used for interior construction to carry beams and girders supporting floors, walls and chimneys in all classes of buildings, such as tenements and apartment-houses, factories, garages, churches, warehouses, etc. A particular demand for steel-pipe columns is at the angles of show-windows in mercantile buildings. In buildings of moderate height the floor-joists are usually supported by the side walls and the columns have to support only a relatively light wall above. For such places wrought-steel pipes may be advantageously used for the columns. They may be used, also, for the columns supporting the roof of one-story buildings. In the Borough of Brook- lyn, New York City, pipe-columns were formerly calculated by the formula S = 14 000— 8o//r, in which S, I and r have values as explained below for New York and Chicago formula. If the columns are filled with concrete, the area of the cross-section of the concrete is multiplied by 500 and the product added to the load supported by the pipe. (See, also, page 477 and the Tables on page 516). This formula gave a factor of safety of four. New York and Chicago Codes now use the formula, S= 16000— 7o//r in which S is the permissible unit fiber-stress, / the length in inches and r the radius of gyration of the cross- section of the pipe. This gives a carrying capacity greater than the former formulas gave. In Philadelphia, pipe-columns are allowed to carry * Much valuable data relating to steel-pipe columns was furnished the editor-in-chief by P. C. Patterson and J. A. McCullough of the National Tube Company, Pittsburgh, Pa. 470 Strength of Columns, Posts and Struts Chap. 14 ahout 6% more than is allowed in New York. Where pipe-columns are fdlcd with concrete the cast cap and base are secured to the pipe in each case by con- crete which is reinforced internally by a pipe of smaller diameter. Where Fig. 10. Coanections, Caps and Bases for Steel -pipe Columns these steel-pipe columns filled with concrete are used, care should be taken that the pipes are entirely filled, and that there are no air-spaces in the concrete. These concrete-filled columns, sometimes reinforced with smaller pipes, have Types, Forms and Connections of Steel Columns 471 a large carrying capacity. Pipe-columns may have their supporting power about doubled in many cases by concrete filling. (See, also, paragraph on Lally Columns, page 477). One type of steel post-cap used in connection with pipe. Fig. 11. Connections, Caps and Bases for Steel-pipe Columns columns to carry wooden girders is shown in Figs. 62 and 63 of Chapter XXII. There are many other forms of cast and wrought caps for pipe-columns. The design of proper caps and bases is the most difficult part of adapting tubular columns to practical problems in building-construction. Figs. 10 and 11 show 472 Strength of Columns, Posts and Struts Chap. 14 various forms of steel-pipe column-connections, caps and bases sufficiently sug- gestive to enable a designer to properly develop their details. Advantages of Steel-Pipe Columns. A wrought-steel pipe when used as a column generally has the following advantages: (i) It will support a greater load per square inch of cross-section than any other shapes and styles of mild-steel columns of the same slendeeness-ratio, II r, for most of the columns of different slenderness-ratios recently tested (1908 and 1909) at the Watertown Arsenal. (2) Its section has the greatest possible least radius of gyration, r, for the same outside diameter and section-area. This makes pipe-columns espe- cially advisable when it is desired to obstruct the view as little as possible, as in the corners of show-windows, in balcony-supports, etc. (3) It may be used with greater slendcrness-ratio, //r, than any other section without reducing the load per square inch in order to conform to permissible loading-rules, such as those of the New York City and the Chicago building codes. (4) Its curved walls permit the use of relatively thinner material than may be used with columns with flat surfaces; that is, its thickness, /, divided by the outside diameter, d, may be iji = ^^0 with as great security from wrinkling, called also buckling, bulging or local failure, as the box column, which good practice of competent engineers limits to Ho of the unsupported width of flat surfaces. The ratio ild=\^v> =^/^"/2o" is about the limit of practicable working of the ordinary lap-weld process, and all commercial pipes have a smaller ratio. (5) Manufacturers are now regularly making pipes for sizes up to and includ- ing 16 in outside diameter, in lengths up to 40 ft. Notes on the Use of Steel-Pipe Columns. The following general notes and suggestions should be observed in the use of steel pipe for columns: (i) As in the case of columns of any construction, it is obvious that com- petent designing and detailing as well as proper fabrication of the end-connec- tions for pipe-columns be insisted upon. Otherwise the advantages of the circular section may be nullified. (2) When the loading must be eccentric care must be exercised in the proper selection and size of pipe to be used. The relative economy in the use of the circular section, however, increases with the length and slenderness of the column. (3) A capital or base should never be screwed to a pipe, because cutting the thread reduces the section. Where screw-threads must be used, only the area below the root of the threads should be considered as available for the sup- porting power. (4) The ends of a pipe to be used for a column should always be faced off in a lathe, the facing being normal to the general axis. A pipe should not be turned nor bored in fitting capitals or bases but, if possible, the capital or base should always be forced or shrunk to an even bearing on the faced end of the pipe. Where the capital or base must be inserted, it is hable to start a wrinkle or buckle and the load should be adjusted to the probable lessening of supporting power. The bearing surfaces in capitals and bases should be, of course, always lathe-faced. It may be found that with careful foundry-work it is not neces- sary to bore the castings; but it may, in some cases, be cheaper to use relatively poor foundry-work and bore the castings, as well as face the seats. (5) Pin-ends or ball-and-sockrt ends are generally preferable to flat or fixed ends for a slenderness-ratio l/r, of 100 or less, because tests show that columns so fitted usually carry heavier loads before failure. This is increasingly Types, Forms and Connections of Steel Columns 473 evident as llr decreases. Any form of end-connection of column that may cause a flexure from a falling floor may endanger the whole structure. Fig. 12. Connections for Bethlehem H Columns (6) "All columns should have sufficient stiffness to safely withstand the chance deflecting forces to which they may be exposed. This usually involves considerations of eccentricity as wefl as of flexure due to transverse load. (7) "It is desirable to adhere always to the trade sizes of pipe Icnown as M^flCHANT, STANDARD, EXTRA STRONG, DOUBLE-EXTR4 STRONG, CASING, BOILER* 474 Strength of Columns, Posts and Struts Chap. 14 TUBES, etc., and avoid special production which usually entails delays and special prices, (8) Tables XII and XIII give the safe loads which standard and extra- si rong steel-pipe columns are permitted to carry under the New York and Chicago codes. Philadelphia laws permit slightly greater loads. Supplementary tables of safe loads for double- extra STRONG steel-pipe columns are furnished by the manufacturer and may be useful in cases where a mini- mum diameter is required; but it should be remembered that such pipe always costs more per pound, owing to its greater cost of manufacture. H-Beam and I-Beam Struts and Columns. For struts and columns carrying light loads, H beams and I BEAMS are probably the most economical,* as they require very little riveting except for the splices and connections. Owing, however, to the narrow flanges of even the deepest I beams it is not practicable to rivet very heavy girders to them; nor can they ordinarily be riveted to the web, because the latter is generally so 1 Fig. 13. Section gf Bethlehem H Column Showing Variation in Area I_ ^ z w Fig. 14. Concrete-filled Lally Steel Column Fig. 15. Lally Column. Typical Connections thin that too many rivets will be required for the connection. Tables XVII is a table of safe loads for the Carnegie steel H beams or I beams used as columns. Types, Forms and Connections of Steel Columns 475 Bethlehem Columns. As far as shop-work is concerned the Bethlehem COLUMNS are just as economical as the ordinary H-beam or I beam columns as they, also, are rolled and not built up or assembled. The only fabrication required is that for the si)lic:e-plates and connections. Typical connections are shown in Fig. 12 from which the simpHcity of detail and small amount of fabrication required are apparent. They are, moreover, superior to the I-beam columns because they afford a wider flange for attaching the beams and girders, besides being t L J Fig. 16. Section of Steel ,Plate- and-angle Column TYPICAL ANGLE-COLUMN Bearing on masonry TYPICAL ANGLE-COLUMN Bearing on steel Fig. 17.* Connections for Steel Plate-and-angle Columns * From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. 476 Strength of Columns, Posts and Struts Chap. 14 more economical of cross-section. Bethlehem columns are rolled in four sizes, 8, lo, 12 and 14 in in width, but by spreading the rolls, as shown in Fig. 13, the section-area of each width can be increased considerably. The TYPICAL splice; 4:ngle-coJluma to Channel-col.iamB| TYPICAL SPLICE Angl^-colnmnSj differjeut sizes TYPICAL CHANNEL-COLUMN TYPICAL SPLICE Bearing on steel Channel-columns, different sizes Fig. 18.* Connections for Steel Plate-and-channel Columns section-areas of columns of the largest size may also be increased by riveting side plates to the flanges. Tables of dimensions and properties of Bethlehem rolled steel columns and of the safe loads they will carry are given in Tables XVIII to XXI. Although these columns have been rolled in Germany since * Fronn Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa, Types, Forms and Connections of Steel Columns 477 1902, it was not until the establishment in 1908 of the larger improved mills at Bethlehem, Pa., that these sections became available for use in this country. They are gradually superseding plate-and-angle and box columns, particularly those of the smaller sizes. Lally Columns. Lally columns (see, also, pages 469 to 474 and Tables on page 516) are patented columns made with a circular steel shell, as shown in- Fig. 14, and filled with a concrete composed of sand, cement and blue trap-rock, and thoroughly com- pressad. The larger columns have, in addition, a steel reinforcement, which makes a light, but strong support. They are in many buildings replacing masonry piers for supporting girders because of the saving in space, and are extensively used in mill- construction. Typical connections are shown in Fig. 15. The Lally formula for the safe loads in tons is given with Tables XXII and XXIII, page 516. Plate-and-Angle Columns. Four angles and a plate riveted together as shown in Fig. 16 are now being extensively used in building-construction; particularly for columns having an unsupported length of less than 90 radii; also for the outer columns in steel-mill buildings, and for light columns support- ing the roofs of railway stations, etc. Columns with this form of cross-section are especially con- venient for making beam and girder-connections and for splic- ing, and are also well adapted to resist eccentric loads. The width of the plate is generally such that the least radius of GYRATION is in the direction ^2, and this radiuc may be obtained directly from Tables XVI and XVII, pages 370 and 372. Fig. 19. Steel Channel- column with Lattice-bars Fig. 20. Spacing of Lattice-bars in Channel-columns Pocket Companion, Channel-Columns. Typical column-details for plate- and-angle and channel-columns, taken from the Carnegie 19 1 5 edition, are shown in Figs. 17 and 18 and represent current practice in office-building construction. Lattice-Columns. Two channels, set back to back, at such a distance that the radii of gyration will be equal about both axes, and connected by lattice- bars, as shown in Fig. 19, make a very desirable column for moderate loads, as in the upper stories, or in buildings of three or four stories in height. For greater loads, short cover-plates may be riveted to the flanges in place of the lattice-liars. Such columns are very satisfactory, especially for making con- nections. Rule for Latticing of Channels and Angles. When channels are con- nected by lattice-work, as in Fig. 20, in order that there may not be a tendency 478 Strength of Columns, Posts and Struts Chap. 14 in the channels to bend between the points of bracing, the distance / should be made equal to the total length of the strut multiplied by the least radius of gyra- tion of a single channel, and the product divided by the least radius of gyration for the whole section; or, in which I - length between points of bracing; h = total length of strut; r = least radius of gyration for a single channel; n =« least radius of gyration for the whole section. This same rule will also apply to angles, although with them the lattice-work is generally doubled, as in Fig. 21. L .^ J Total length=i^ ( Fig. 21. Double Lattice-bars on Angle-columns It is generally found desirable to make the distance I less than that obtained by the above formula. The inchnation of the lattice-bars with the axis of the column or strut is usually about 6o° for single and 45° for double bars. The proper distance for d or D, Fig. 20, for a pair of channels, so that the radius of gyration will be the same in both directions, is given in Table VIII, page 359. The following tabulations are taken from the Handbook of the Cambria Steel Company, 1915 edition. Sizes of Lattice-Bars to be Used with Latticed Channel-Columns Dimensions of Center of hole to end of bar, Distance center to Depth of channels lattice-bars Weight of lattice-bars per foot center of rivets, d w Thickness a Maximum Minimum in in in lb in ft in in 6 iH H 1.28 i'/^ iii/^ 6^ 7 m H ■1.49 iH I i\^ 1% 8 2 Me 2.12 iH I 3 81 He 9 2 M6 2.12 iM 1 4H 9H 10 2 % 2.55 iH I ^M iQiHe 12 2H H 2.87 m I \o\^ 13 IS 2H % 3.19 TYi 2 2\(l 15M6 Types, Forms and Connections of Steel Columns 47^ Sizes of Stay-Plates to be Used with Latticed Channel-Columns Minimum size of stay-plates at ends of columns Weight of minimum stay-plates Diameter of rivets oil pi! . |0 19 6 Thickness I Oj 01 u 16 |0 in lb -< M 8H H 1H 4.38 H 9H 'A 10 6.5S H f^. c lOj.^ Me 9 8.37 H itH Ma 13 II. 95 H ub 12H H 13 15.62 H -*4 t§ uVa H IS 22.73 H i6H ^4 IS 25.90 H Plate-and-Angle and Box Columns. Plate-and-angle columns, as showri in Fig. 16, requiring but two rows of rivets are very economical columns for buildings of moderate height, as they afford excellent opportunities for connect- ing the beams and girders. Tables of safe loads are given in Table XXIV of this chapter. When a more compact section is required than that afforded by the larger sizes, the section-area may be increased by riveting plates to the angles as shown in Fig. 22 which is a section of one of the columns in the Munic- Fig. 22. Heavy Plate- and-angle One-web Column Fig. 23. Heavy Plate- and-angle Two-web Column Fig. 24. Heavy Plate-and-angle Three-web Column ipal Building, New York City. This, however, greatly increases the expense of the shop-work, and it is therefore usually more economical to substitute Bethlehem H columns, or channel or box columns. For high buildings or heavy loads, where the required section^ areas of columns are greater than can be obtained by using channel-columns or Bethlehem columns without flange-plates, BOX COLUMNS made of plates and angles, as shown in Fig. 23, which is one of the columns in the Bankers' Trust Company Building, New York City, will prob- ably be found to be more satisfactory. The thickness and number of web-plates . and flange-plates can be varied with the load to be supported. Ordinary con- nections for BOX COLUMNS are the same as those for channel-columns, shown in Fig. 18. For the tallest buildings and heaviest loads box columns with TRIPLE WEBS as showu in Fig. 24 are the best. They are used in the highest buildings erected, such as the Masonic Temple in Chicago, and the Bankers* 480 Strength of Columns, Posts and Struts Chap. l4 Trust Building, the Municipal Building, the Wool worth Building and the Met- ropoUtan Tower in New York City. Fig. 24 is a cross-section of one of the columns in the last-mentioned building. Details of a similar column used in the Bankers' Trust Company Building are shown in Fig. 7 on page 342. It is of course impracticable to give tables of safe loads for plate-and-angle COLUMNS with flange-plates and for box columns, owing to the great variety of combinations that can be used, but Example 10 of this chapter shows how the columns are designed and their strength determined. (See page 485.) Steel Struts in Trusses. These are generally made* of a pair of latticed channels, or of channels aiid plates for heavy trusses with pin-connections, and of either a pair of light channels or a pair of angles with uneven legs for light trusses. For roof-trusses having a span not exceeding 80 ft, a pair of 4 by 6 by ^4-in angles is generally sufficient for any of the compression-members unless they are subjected to transverse stress; and the minor struts are very often made of a pair of 3 H by 2 J' 2 by H-in angles. The angles arc placed from ^ to % in apart to permit the filler-plates used at the joints to go between them. For compression-members subject to transverse stress a pair of channels gen- erally offers the best section. If necessary the channels can be reinforced by plates at the top and bottom. A pair of angles, with a deep web -plate riveted between, is often used for the principles of Fink trusses where they are subject to a slight transverse stress. (See, also, Fig. 6, page 1146.) For very light compressive stresses and for short members a single angle is sometimes used; but this is not considered good practice, as it causes eccentric loading on the gusset- plates at the truss-joints. A pair of small angles, or some other combination with a symmetrical cross-section should always be used for truss-members. Where angles are used in pairs they should be connected by a rivet and small filler-plate or separator every two feet in length, to prevent them from spring- ing apart. In regard to the maximum length of steel struts in trusses it is not considered good practice to use a strut whose unsupported length exceeds ISO times its least radius of gyration, or 50 times its least width, 13. Strength of Steel Columns. Formulas Principles Governing the Resistance of Built-up Steel Columns. Pro- fessor William H. Burr states * that "the general principles which govern the resistance of built-up columns may be summed up as follows: the material should be disposed as far as possible from the neutral axis of the cross-section, thereby increasing the radius of gyration, r; there should be no initial internal stress; the individual portions of the column should be so firmly secured to each other that no relative motion can take place, in order that the column may fail as a whole, thus maintaining the original value of f." The experiments made by Professor Burr indicate that a closed column is stronger than an open one. It should also be remembered that any column such as an I beam, channel, or angle, the cross-section of which has a maximum and a minimum radius of gyration, is not economical for use under a single concentric load, as the mini- mum radius of gyration must be used in the calculation, and part of the mate- rial is to a certain extent wasted when the ideal efficiency of the column is considered. Formulas for Steel Columns. A great many formulas are used for cal- culating the strength of steel columns and struts, of the lengths usually em- ployed in practice, but scarcely any two authorities agree upon the same one. These formulas may all be grouped into two general classes, those founded * Elasticity and Resistance of the Materi'ds of Engineering, by William H. Burr. Strength of Steel Columns. Formulas 481 on Rankine's formula * (ii) and those founded on the straight-line formula (12). (See the following paragraphs.) In the dilTerent formulas different values arc assigned to the arbitrary constants. Previous to 1888 Rankine's or Gordon's formulas were almost universally used for all columns, although with more or less variation in the constants employed. About 1885 Professor Burr, after having conducted a series of tests upon full-size column-sections deduced what is now known as the straight- line formula. As this is easier of applica- tion than Rankine's formula, it has gradually found favor with engineers, espe- cially as the results differ but little from those obtained by the older formula. Formulas Compared. Which one, of all the formulas in use, should be employed in calculating the safe load for columns is an open question, but the author, after careful deliberation, has decided to recommend Rankine's for- mula for the following reasons. In the first place it is safe and conservative and if it errs at all, it is on the side of safety; and in the second place it has a wider application, as the values assigned to the arbitrary constants have been more generally agreed upon, whereas there is a greater variety in the values of the constants employed in the straight-line formula. Of course one is not free to choose when city laws compel the use of certain formulas. No tables of safe loads for columns, satisfying the requirements of all cities, could be com- piled. The author has accordingly thought it best to insert the various tables of SAFE LOADS for different forms of columns as computed in the very latest handbooks although not necessarily based upon Rankine's formula, and to insert Table XI, specially computed and giving the comparative safe loads in POUNDS PER square INCH OF METAL-AREA for columns, as determined by seven different formulas. (See pages 493 to 495.) Formulas Used in Building Codes. Rankine's formula (called Gordon's FORMULA in many codes) is specified in the building codes of the following cities: Philadelphia, Boston, Baltimore, and Milwaukee; and in the Cambria hand- book. The straight-line formula is specified in the building codes of New York City, Chicago, St. Louis, Minneapolis, Washington and many other cities, and is used in the Carnegie and Bethlehem handbooks. Formulas Used in Practice. The following formulas, in the opinion of the author, represent the best current practice. They are formulas for safe loads, S, in pounds per square inch of cross-section, on steel columns and struts. In these formulas / is the length of the column in inches and r the least radius OF GYRATION of the cross-section. (See, also, Chapter X, pages 333, 34^, etc.) The SAFE LOAD, P, for any column is equal to S, obtained by one of the follow- ing formulas, multiplied by the section-area of the calumn in square inches; or P=AS (10) Rankine's formula, used in the Cambria handbook, is 12 500 (11) i + /V36ooor2 The formula recommended by Professor Burr is S = 10 000 — 40 l/r (12) The formula used by the American Bridge Company and Carnegie's Pocket Companion is 5 = 19 000 — 100 l/r (13) with a maximum of 13 000 lb per sq in. * Rankine's formula is sometimes referred to as Gordon's formula, but Gordon used the least lateral dimension or the diameter of the column instead of the least radius o| gyration of the cross-section. 482 Strength of Columns, Posts and Struts Chap. 14 The formula used by the American Raihvay Engineering Association and the New York and Chicago building codes is 5 = i6 ooo — 7o//r (14) with a maximum of 16 000 lb per sq in for New York and 14 000 for the others. The formula used in the New York City building code previous to 19 16 was 5= IS 200- 58 //r (is) The formulas used in the Catalogue of the Bethlehem Steel Company are 5 = 16 000 - SS ^h, for //f over S5 (^6) and 5 = 13 000 lb per sq in, for Ijr under 55 Fowler's shghtly modified formula for steel struts in trusses is 5 = 12 500 — so ^h (17) The value so in Fowler's formula is 41% when / is in inches, and soo when / is in feet. For a comparison of most of these formulas, see Table XI, pages 493 to 495 and the comparative diagram of formulas, page 496. 14. Design of Steel Columns. Examples Practical Use of Column-Formulas. UnUke the beam-formula the column- formulas in general use do not give a direct method of calculating the dimensions of a column that will support a given load, owing to the presence in the column- formula of two unknown quantities, A and r, which are dependent upon one another. Hence in designing columns, the section must be first assumed and then tested for the safe load P, or for the maximum unit fiber-stress S. This is an apparently roundabout method of designing columns, but unfortunately there seems to be no more direct way. When a column, is to be selected or designed, its axial load P is given and also its length and the condition of its ends. A proper allowable unit stress, 5, is assumed, suitable for the given material and for the conditions under which it is to be used, or in accordance with the requirements of the local building code; or the value of S is given in the specification according to which the column is to be designed. A cross- section is then selected in accordance with the principles explained on pages 467 to 469. For this assumed cross-section A and r are determined and then sub- stituted in the formula, which is solved for P. If the assumed dimensions give a value for P that agrees with the actual load, they are correct. If, however, the resulting value of P is smaller than the actual load, the assumed size is too small, and it will be necessary to choose a larger size and solve again. If on the contrary, the actual load is less than the safe calculated load, a column with a smaller element of cross-section is assumed and a new value of P obtained. After a few trials a size that gives a satisfactory result for the required conditions will be found. Examples Illustrating the Use of Column-Formulas and Tables. Since the column-tables in the last half of this chapter give the safe loads of the major- ity of column-sections of current practice, having determined which section it is most advisable to use under any given conditions, it is merely necessary to consult the tables and select the column of the required size to support the actual load. Example 7. The following is an example showing the method of selecting pETULKHEM ROLLED H COLUMNS for buildings. Design of Steel Columns. Examples 483 Example Showing the Method of Selecting Bethlehem Rolled H Columns for Buildings For illustration, the interior columns of an actual sixteen-story building are taken as an example. The story-heights and the loads on the columns are given in the following tabulation: Stories Heights of stories , ft Loads on col- umns, tons Safe loads , tons H column-section required Dimensions Weights of sec- tions, lb per linft Section- numbers D, in in B, in . i6th 15th 14th 13th I2th nth loth 9th 8th 7th 6th 5th 4th 3d 2d ISt Basement 12 13 14 13 13 13 13 13 13 13 13 13 13 13 15 17 12 27 53 79 104 128 151 174 197 219 241 261 281 301 321 341 363 395 55.0 81.5 132.2 174.8 219. 1 263.8 310- 1 341.3 403.5 1% m io-% 12H uM 14')^ 15 15H 1S% Me iHe I'Me iMe i^He 8.00 8.12 10.12 12.08 14.08 14.19 14.31 14.39 14.54 31.5 48.0 71.0- 91. 5 II4-5 138.0 162.0 178.5 211. H8 H8 Hio H12 H14 H14 H14 H14 H14 D is the depth of the column, T the thickness of the flanges and B the breadth of the flanges. Columns for buildings are usually selected in lengths of two stories. By inspection of the tables of safe loads for H columns, it is found that no columns smaller than 14-in H sec- tions have sufficient capacity for the lower stories. Where there is no Umitation as to the size of the column, the column with the largest dimensions and having the required capacity will be the most economical. The unsupported length of a column should not exceed 150 radii of gyration, which is the Hmit of length for which safe loads are given in the tables. In the best practice the unsupported length of a column is frequently required not to exceed 120 or 125 times the least radius of gyration; various Umits for l/r are indicated in the tables by zigzag lines. The safe loads given in the tables are for concentric or symmetric loading. When the loads are not centrally or symmetrically applied, the size of the column should be calculated by Formula (18), page 486. Example 8. Suppose that in a 20-story office-building to be erected in Chicago, the load on each of the first-story columns, which are 16 feet in length, is 700 tons. What columns should be used? Turning to Table XXI, page 515, giving the safe loads for Bethlehem 14-in H columns it is seen that a 14-in 287,5-lb column, the heaviest rolled, will support only 549.3 tons; this type of column, therefore, cannot be used. More- 484 Strength of Columns, Posts and Struts Chap. l4 over a casual inspection of the tables of safe loads for plate-and-angle and channel-columns shows that they are not suitable because of the thick flanges and web-plates required. Consequently the columns in the lower stories will probably have to be of the box type, with double or triple webs, as shown in Figs. 23 and 24. The upper columns, however, may be of the plate-and-angle or channel-type, whichever will be the more economical. The heaviest plate- and-angle column, without flange-plates (Table XXIV, page 522), composed of four 6 by 4 by %-in angles and one 12 by y^-in web, will support, for a length of 14 feet, the height of most of the upper stories, 469 000 lb; and a channel-col- umn (Table XXVI, page 541) composed of two 12-in 30-lb channels and two 14 by yi-'m plates will support 502 000 lb. The former weighs 125 and the latter 13 1. 4 lb per hn ft, so there is not much choice as far as economy of material is concerned. The channel-column, however, requires four rows of rivets while the plate-and-angle column requires only two rows, so this added expense of fabrication would have to be considered. Assuming, however, that the plate- and-angle type is more desirable, the next step is to design the individual columns. The load upon each of the uppermost columns, which are 20 ft in length, is 70000 lb. Turning to Table XXIV, page 518, it will be seen that a column composed of four 4 by 3 by ^-in angles and one 8 by ^-in web will support, for a length of 20 ft, 77 000 lb; but this load is below the lower zigzag line and hence the slenderness-ratio of the column exceeds 120. Assuming, for the pur- pose of illustration, that the limit of l/r is 120, a heavier section must be selected. On page 519 of Table XXIV, continued, it is seen that the lightest 20-ft column, for which l/r does not exceed the required ratio, is one composed of four 5 by 3).^ by %-'m angles and one 10 by %-'m web, and that for a length ' of 20 ft it will support 121 000 lb, or 51 000 lb more than will come upon it. Continuing the design of the columns, suppose that one in the 14th story, 14 ft in length, supports 175 tons, or 350 000 lb. From Table XXIV, page 522, it is found that a column composed of four 6 by 4 by %-'m angles and one 12 by J-i-in web-plate, for a length of 14 ft, will carry 373 000 lb. In the table, the safe load is calculated by Formula (13), whereas the Chicago Building Code specifies Formula (14). Hence, as this building is to be erected in Chicago, the chosen column must be tested by the latter formula. Its A is 29.44 sq in and its least r, 2.65 in. To test it by the formula, / = 14 ft X 12 = 168 in, and l/r = 168 in/2.65 in = 63. Substituting in Formula (14), S = 16000 — (70 X 63) = 16 000— 4 410 =11 590 lb per sq in. From Formula (10), the safe load for the column, P = AS = 29.44 sq inX 11 590 lb per sq in = 341 209 lb, which is less than the actual load. Therefore, the next heavier column, with angles ^He in thick, should be selected. Example 9. In an ofiice-building to be erected in Philadelphia, the use of the Bethlehem rolled-steel H columns has been decided upon. One of these col- umns, 15 ft in length, supports 170 000 lb, or 85 tons. What should be the size of this column? According to Table XIX, page 508, giving the safe loads for Bethlehem col- umns, a lo-in 49-lb column, 15 ft in length, will carry 86.3 tons, an apparently safe load. Bethlehem-column loads, however, are calculated by the straight-line formula, whereas in Philadelphia, Rankine's (called Gordon's) formula is the standard. This formula with the arbitrary constants inserted is S = ■ ^ ^^^ (See Table XI, page 493-) I + • {l/rp Eccentric Loading of Steel Columns 485 From Table XIX, A = 14.37 sq in and the least r = 2.49 in; / is 15 ft or 180 it? l/r= 180 in/2.49 in= 72.3. Substituting in the formula, 16 250 16 250 16 250 I 1 + 5 227/11 000 16 227/11 000 iH (72.3r II 000 16 250X11 000 178750000 — = . == jj 015 lb per sq m 16 227 16 227 and from Formula (10), page 481, P = AS = 14.37 sq in X II 015 lb per sq in = 158 285 lb or 79.1 tons, which is less than the tabular load. Hence the next heavier column, weighing 54 lb per sq ft, would have to be used. Example 10. Figure 7, page 342, shows the cross-section of one of the basement-columns in the Bankers' Trust Company'sBuilding, New York City. It is 20 ft in length and supports 2 230 tons. Is the column safe? The first step is to find its least radius of gyration which is equal to V//.4. The least moment of inertia of this section was found to be 17 030. (See page 343.) The area is made up as follows: Flanges. The flanges are composed of six 27 by %-in plates and two 27 by iMe-in plates. The area of the cross-section of each 27 by %-m plate is 20.25 sq in and of the six plates, 121.50 sq in. The area of the section of each 27 by iHe-in plate is 18.56 sq in and of the two plates, 37.12 sq in. Hence the total sectional flange-area is 121.50+ 37.12 = 158.62 sq in Flange-angles. Each flange-angle is 6 by 6 by ^Vie in. Its section-area is 10.38 sq in. Hence for the four, A = 10.38 X 4 = 41.52 sq in Outer Web. The outer web-plates are each 18 by iMs in. The area of each one is 12.375 sq in and of the eight 99.00 sq in Web. Each web-angle is 6 by 3!/^ by i^e in with a section- area of 8.03 sq in; and for four angles the section-area is 32,12 sq in Web. The web is composed of two 18 by ^le-in plates, each with a section-area of 10.125 sq in. For two the area is 20.25 sq in The area of the entire section, therefore, is 35151 sq in ^2 = 7/^ = 17030/351.5 = 48.5 and r=V48.5 = 7in / = 20 ft = 240 in and l/r = 240 hi/7 in = 34.3 Substituting in the former New York City building code Formula (15), page 482, S --= 1$ 200- 58 X 34-3 = 15 200— 1989 = 13 211 lb per sq in From Formula (10) P = AS = 351.5 sq inX 13 211 lb per sq in = 4643 666 lb, or 2 321 tons. Hence the column is perfectly safe. 15. Eccentric Loading of Steel Columns General Principles. Where columns are used in tiers, one above another, the beams and girders which they support must necessarily rest upDii brackets projecting or extending varying distances beyond the shell or section-areas or axes of the columns. Such connections cause BEisrorNG moments in the columns. When equal loads are applied at equal distances on opposite sides of a column. 486 Strength of Columns, Posts and Struts Chap. 14 the bending moments caused by them in the column balance each other, and the CENTER OF STRESS may be considered as coinciding with the axis of the column. When, however, a load is applied on one side (Fig. 25) without a corresponding load on the opposite side, it is called an eccentric load and the area of the cross-section of the column should be increased correspondingly. There is unfortunately no direct method by which this additional area can be determined. The usual method of procedure is to assume a section in excess of that required to support the total load and then compute the fiber-stress due to the combined balanced and eccentric loads. If this works out too large or too small another trial is made. Formula for Eccentric Loads on Steel Columns. The following formula (compare with Fig. 25) is used to determine the combined fiber-stresses due to the concen- trie and eccentric loads (See, also, page 453): Let P =^ the concentric or balanced load in pounds. Pi = the eccentric load in pounds, M = the bending moment due to the eccentric load in inch-pounds = Pix, X = the eccentricity of the load Fi in inches. (See note below.) I = the moment of inertia of the area of the cross-section of the column about an axis at right-angles to the direction of the bending, c = the distance of the outermost fiber in the cross-section from the same axis, A = the area of column-section in square inches and S = the actual fiber-stress in pounds per square inch Fig. 25. Channel-column with Eccentric Load. Elevation Then S={P-{-PO/A-hMc/I (18) Note. In measuring the eccentricity, the distance, x, is generally measured from the axis of the column to the center line or half-breadth line of the bracket or bearing. Examples of Eccentric Loading of Steel Columns. The following ex- amples illustrate the use of the formula and tables in determining the safe eccentric loads } for steel columns. Example 11. The total load on the top of a column 32 ft in length is 194 000 lb, of which 30 000 lb come from the end of a girder. There is no corresponding load on the opposite side. (See Fig. 26.) It is proposed to use a channel- column. What is the size of the required column? By referring to Table XXVI, page 539, it is seen that a column composed of two 12-in 20.5-lb channels and two 14 by ^i-in plates will support, for a length of 32 ft, 227 000 lb, a somewhat greater load than will come on the column. For the sectioii of this column, /»-2= 41S, A = 22.56 sq in, r = 4.29 in and l/r ** Fig, 26. Channel -column with Eccentric Load. Section Eccentric Loading of Steel Columns 487 384/4.29 = 89. Substituting in Formula (ii), page 481, to find the safe unit fiber-stress 12500 12500 12500 12500 I /// ^9 I +(89)^36 000 I -1-7 921/36 000 ~* 43 921/36 000 36000 12500X36000 450000000 „ =s • = = 10 245 lb per sq in 43921 43921 The actual stress in pounds per square inch of the column-section is found by Formula (18), 5 = (P + Px)lA + Mcjl. P = 164 000 lb, Pi = 30 000 lb, A = 22.56 sq in and M = Pio; in-lb. x= the distance in inches from the axis 2-2 of the column to the outside of the web, plus the distance from the outside of the web to the center of the bracket. The former distance can be found from Table XXVI. It is 4 in. Let the distance from the outsldq of the web of the channel to the center of the bracket riveted to the web of the channel be 2 in, the projection of the bracket being 4 in; then x, the lever-arm of the moment of the load Pi, or the eccentricity, is 4 in 4- 2 in = 6 in. M, therefore, is Pix or 30000 lb X 6 in. c is 7 in, since the plates are 14 in wide. I2-2 = 415. Sub- stituting in Formula (i8) ■ 164000+30000 30000X6X7 oc I c c ciu . ' 5 = 1 = 8 5qq ^ 2 036 = II 636 lb per sq m , 22.56 415 >. 7t)u As this exceeds the safe unit fiber-stress of 10 245 lb per sq in, the column- section is too small. For a second trial, consider a 12-in, 20.5-lb channel-column with 14 by ^^-in plates. For this section, /2— 2 = 473, A = 26.06 sq in, rz— 2 « 4.26 in and l/r ^ 384/4.26 = 90. „ 12 500 " 12 500 1250Q I +(90)2/36 000 1 + 8100/36000 44100/36000 12500X36000 ,, = . — JO 204 lb per sq in. 44 100 ■ The actual stress from Formula (18), as before, is 164OOO+3OOOQ 30000X6X 7 , ^^ ' OIU o = — ■ i ■ = 7 444 + 2 664 = 10 108 lb per sq in 26.06 473 - As this is less than the safe stress of 10 204 lb, the second selection is safe. Example 12. A Bethlehem H column 14 ft long carries 90.56 tons, of which 15.52 tons are eccentric, being apphed to the flange of the column as shown in Fig. 27, the distance from the outside of the flange to the center of the bearing being 2 in. What is the size of the column required? Try a 12-in, 84.5-lb column, which, for a length of 14 ft, or 168 in, will carry 161.4 tons (Table XX). For this column, A = 24.92, ^2— 2 = 3.03, /i— 1 = 676.1, 72-2 = 228.5 and / is 14 ft, or 168 in; hence l/r = 168/3.03 = 55. Substituting in Formula (15), assuming that that formula is specified, 5 = 15 200 — 58 X55 == 12 010 lb per sq in. Since the eccentric load causes bending in a direction at right-angles to the axis i-i. Fig. 27, the bending moment due to the eccentric load is Pi, or 15.52 tons or 31 040 lb, multiplied by its lever arm x, which is the distance from the axis i-i to the outside of the flange plus the distance from this surface to the center of bearing. The former dimension, taken from the! Bethlehem Catalogue, is 6H6 in and the latter is 2 in; hence x = 8H6 in dr fdr convenience, 8 in. The distance, c< also, of the outermost fiber Irom ih^ ^pps 488 f Strength of Columns, Posts and Struts Chap. 14 i-i is 6M« in, which for convenience will be considered 6 in. /i— i about the axis i-i is 676.1. Substituting in Formula (i8-), 5 =(150 080+ 31 040)724.92 + (31 040 X 8 X 6)/676.i = 7 268 + 2 204 = 9 472 lb per sq in. As this is far below the safe stress of 12 010 lb, the column selected is too large, and a smaller one, probably a 12-in 64.5-lb column would prove sufficient. Suppose, on the other hand, the eccentric load were applied to the web and the balanced loads to the flanges. The safe unit fiber- stress, as before, is 12 010 lb per sq in, for no matter how the loads are applied, the safe unit stress determined by reference to the least radius of gyration, ri—i, should not be exceeded. Under the second condition of loading the eccentric load, also, will cause bending about this same axis 2-2; hence in Formula (^) the 1 for this axis, which is Fig. 27. Bethlehem H Column with Eccentric Load 228.5, must be used, a; = 2 in +0.25 in = 2.25 in, 0.25 in being one-half the thickness of the web. (See the Bethlehem Catalogue.) Hence, from Formula (18), the actual unit fiber-stress is 6* = (150080 +31 040)724.92+ (31 040X6X2.25)7228.5 = 7 268+ I 835 = 9 103 lb per sq in. 16. Tables of Safe Loads for Steel Columns Safe Loads per Square Inch of Metal-Area for Steel Columns and Struts. To lessen the labor of calculating the strength of steel columns and struts, of whatever shap3, the author has computed Table XI, which gives safe VALUES of S for ratios of llr varying from 30 to 120. For ratios of Ijr which are not whole numbers, the values can be readily interpolated. The values in this table should correspond exactly with the results obtained by using the corre- sponding formulas. Safe Loads for Steel-Pipe Columns. Tables XII and XIII give the safe LOADS for STEEL-PIPE COLUMNS. These loads are based upon the formula recom- mended by the New York and Chicago Codes, 5 = 16 000—70 llr. (See Steel- Pipe Columns, pages 469 to 474.) Safe Loads for Channel and Angle-Struts. Tables XIV, XV and XVI give the safe loads for standard CHAt^fNELS and angles used as struts. Only those sizes that are most commonly used are given. In Table XIV the safe LOADS for both the minimum and the maximum radius of gyration are given. If the strut is used also as a beam, or is stayed so that it cannot bend sidewise, the larger value may be taken; but if free to bend in either direction, then the smaller value should be taken. If the struts are subjected to a transverse stress they should be computed as explained under the heading Strut-Beams, pages 571 and 572. Safe Loads for Steel-Beam Columns, Bethlehem Columns, Lally Col- umns, Plate-and-Angle and Channel Columns. Tables XVII to XXVII, givinsj the safic loads for these columns, were not computed by the author, but by the different manufacturers; they are, however, believed to be perfectly safe, provided that an increase in area is made for eccentric loads. Use of Table XI for Determining Safe Loads for Steel Columns. This table will be found of great assistance in calculating the strength of col- Tables of Safe Loads for Steel Columns 4SS limns and of struts and also in making calculations for eccentric loads. To use it to find the strength of a column, it is merely necessary to multiply the value corresponding to the slenderness-ratio of the column, by the section-area, the result being the safe load the column can support. As an illustration of this, the column considered in Example 8 has a slenderness-ratio of 63 and a section-area of 29.44 sq in. Its strength is to be calculated by the Chicago Building Code formula, the results of which are tabulated in the sixth column of Table XL From this the value of a slenderness-ratio of 63 is 11 590 lb per sq in. Therefore, by the rule stated above, the safe load is 11 590 lb per sq in X 29.44 sq in = 341 209 lb. In Example 10, the column in the Bankers* Trust Company Building has a slenderness-ratio of 34.3, and an area of 351.5 sq in. The value corresponding to 34, from column 5 of Table XI, is 13 228 and for 35 it is 13 170 lb per sq in; hence for 34.3 it would be about 13 2 1 1 lb per sq in. Accordingly, the safe load is 13 2 1 1 lb per sq in X35 1 .5 sq in = 4 643 666 lb. Column 5 of Table XI gives values for old New York code. Example 13. What is the safe resistance of a strut composed of two s-in 9-lb channels, separated % in aij^ free to bend in either direction, the length of the strut being 7 ft 6 in? Solution. From Table XVIII, page 374, the least radius of gyration for this section is i, hence l/r= 90/1 = 90. From the eighth column of Table XI, the value of S opposite 90 is 8 000 lb per sq in; the safe load, then, is equal to 8 000 lb per sq in, multiplied by the area of the two channels, 5.3 sq in, or 42 400 lb. Example 14. What is the safe stress for a 7-in 15-lb I beam when used as a strut? It is 90 in in length and free to bend in either direction. Solution. From Table IV, page 355, the least radius of gyration of this sec- tion is 0.78, and the area is 4.42 sq in. l/r = 90/0.78 = 115.4. From the eighth column of Table XI, the value opposite 115 is 6 750 and opposite 116 it is 6 700 lb per sq in; so for 115.4 it would be about 6 730 lb per sq in. The safe lead, therefore, is 6 730 lb per sq in X 4.42 sq in = 29 746 lb. By means of the tables and rules given in Chapter X the section-area and LEAST radius OF GYRATION of any Standard section or any combination of sec- tions may be found; and once these arc determined the strength of a strut or column may be readily computed, as in the above examples. Use of Table XI for Eccentric Loads for Steel Struts. A? an illustra- tion of its application to determine eccentric loads, refer again to Example 11. The value of l/r for this column is 89. The safe unit fiber-stre^ was found to be, by Formula (11), 10245 lb per sq in. The practically identical result can be obtained by looking for the value opposite 89 in column 2 of Table XI. It is found to be 10 250 lb. Proportion of Floor-Loads Borne by Columns. (See, also, pages 148 to 152.) In tall buildings it is customary to reduce the column-loads some- what fro.n the loads used in calculating the floor-beami. This is done on the theory that it is quite impossible for the entire floor-area of every story to be loaded to the maximum limit at the same time. For all buildings except ware- houses it would seem, in general, to be good practice to design the columns to carry all the dead load and 75% of the assumed live load. Of course city laws vary in these requirements. Thus, if in an office-building, the dead load, or weight of the floor-construction, is 80, and the live load 80 lb per sq ft, the load on the columns would be 8o-|- 60= 140 lb per sq ft times the floor-area sup- ported by the column. In some cases the reduction might be even greater, depending upon the live load assumed and the position of the column in the building, the reductions being greater in the lower than in the upper stories. 490 Strength of Columns, Posts and Struts Chap. 14 The Building Code of New York City specifies that for buildings exceeding five stories in height the column-loads shall be made up as follows: For the roof and top floor the full Uve loads shall be used; for each succeeding lower floor it shall be permissible to reduce the live load by s% until 50% of the live load is reached, when such reduced loads shall be used for all remaining floors. (For assumed loads for ofiice-buildings, required by the building codes of sev- eral cities, see page 151). Column-Sheets. In a high building the column-loads vary to such an extent and are made up of so many elements, that to avoid omissions and errors it is necessary to make a tabulated list of all the loads transferred through the columns to the footings. In a building of skeleton construction the column- loads include floor and roof-loads, wind-loads, spandrel and pier-loads, the weight of the columns themselves and their fire-proof covering, and in some cases special loads, such as tanks, vaults, safes and elevator-loads. In tabulating the floor-loads it is advisable to separate the dead and live loads for con- venience in proportioning the footings. (See, also, pages 148 to 160.) Formulas for computing the wind-loads on columns are given in Chapter XXIX; these loads, also, are considered as Hve loads. Eccentric loads should always be tabulated separately from the balanced column-loads. On page 491 is shown a form of column-sheet which combines all ordinary requirements. The total load for each story is the sum of all of the loads above. The schedule on page 492 shows a very convenient form for column-lengths and column-parts. Important Notes Regarding Safe Loads on Columns. (See pages 504 and 505, and 517 to 554.) "For ratios of Ih up to 120 and for greater ratios up to 200, use the values given in the following table for the allowable stress in pounds per square inch. For intermediate ratios, use proportional amounts."* Ratio Amount Ratio Amount 60 13000 130 6 500 70 12 000 140 6oo<} 80 II 000 ISO 5 500 90 10 000 160 Sooo 100 9 000 170 4500 no 8000 180 4000 120 7 000 190 3SOO "(s). For bracing and combined stresses due to wind and other loading, the permissible working stresses may be increased 25 per cent, provided the section thus found is not less than that required by the dead and live loads alone.* "(6). General. The effective or unsupported length of main compression members shall not exceed 120 times, and for secondary members 200 times, the least radius of gyration."* The values for ratios of Mr above 120 are computed from the formula 5= 13 000— 50 //r, but the important condition should be observed, that for //r above 120, com- pression-members should never be used for main members but only as secondary members subject to wind-stresses, etc. (See, also, page 495 for minimum ratio of II r for main members and for secondary members, such as bracing struts, etc.) * From the Construction Specifications of the American Bridge Company. Column-Sheets Form of Column-Sheet 491 Story Character of loading Column No. i Column 2 Load on column, concentric Load on column, eccentric 1 i8th top Roof and ceiling, dead load Roof and ceiling, live load Masonry piers Spandrels, cornice, etc Elevators Tanks Column and casing Wind-load Total Sectional area required sq in sq in ; 17th From column above.* Floor, dead load Floor, live load Masonry piers Spandrels Safes, vaults, etc Column and casing Wind-load Total Sectional area required sqin sqin 1 Base- ; ment i From column above.* Floor, dead load Floor, live load Masonry piers Spandrels Sidewalk' Column and casing Wind-load Total Footings Sectional area required sq in sqin Deduct m) live load , Total footing-load Area of footing required • sqft * In bringing down the load from the column above, the eccentric loads may be added to the concentric loads and their sum placed in the first column. 492 Strength of Columns, Posts and Struts Schedule of Column-Lengths and Parts Chap. 14 Column No. i Column No. 2 Roof -line • Top of columns t i 7th story 7th Floor-line 23' x^ Xox 4" >X • 6th Story 6th Floor-line ^ ^0 i >< Sth Story 1 5th Floor-line 13' - \^X c t 4H" i ist Floor-line r T I Basement Top of stool 11' xx Grade 15.0 T Si" 8H- . £S Tables of Safe Loads for Steel Columns 493 Table XT. Safe Loads in Pounds per Square Inch of Metal Area for Steel Columns and Struts / = length in inches r = least radius of gyration in inches Mr Rankine' s (Gor- don's) and Cambria Phila- delphia Boston Code Wash- ington, D. C* Chi- cago t and N. Y. n\ § .^ >^ Am. Bridge Co. and Carnegie Fowler's formula for struts l/r 8 - CO h •0 - - » K K \ 1 KO 8| ^ 8 ^ § -. - 8 8 ^ CO 1 1 M + KO + VO + 8 2" "^ 8 fo 8 1 ►"• M Is^ M M I II III IV V VI VII VIII IX 70 II 000 II 240 12850 II 140 II 100 12 000 9000 70 71 10965 II 140 12780 II 082 II 030 II 900 8950 71 72 10930 II 040 12 710 II 024 10960 II 800 8900 72 73 10890 10940 12640 10966 10890 II 700 8850 73 74 10 850 10845 12565 10-903 10 820 11 600 8800 74 75 10 810 10750 12 490 10850 10750 11 500 8750 75 76 10770 10655 12 420 10792 106S0 II 400 8700 76 77 10735 10560 12345 10734 10 610 II 300 8650 77 78 10695 1046s 13270 10676 10540 II 200 8600 78 79 10655 10 370 13 19s 10 618 10470 II 100 8550 79 8o I06IS 10 275 13 120 10 560 10 400 II 000 8500 80 8i 10 575 10 180 13 045 10502 10330 10900 8450 81 82 10535 10085 II 970 10444 10260 10800 8400 82 83 1049s 9990 II 895 10386 10 190 10700 8350 83 84 10450 9800 1182s 10328 10 120 10 600 8300 84 85 10 410 9810 II 755 10270 10050 10500 8 250 85 86 10370 9720 II 680 10 212 9930 10 400 8 200 86 87 10330 9630 II 605 10 154 9910 10300 8 150 87 88 10290 9 540 IIS30 10096 9840 10200 8 100 88 89 10 250 9450 II 460 10 038 9770 10 100 8050 89 90 10205 9360 II 390 9980 9700 10 000 8000 90 91 10 165 9370 II 315 9922 9630 9900 8950 91 92 10 125 9285 II 240 9864 9560 9800 8900 92 93 10085 9200 II 165 9806 9490 9700 8850 93 94 10040 9 115 II 095 9748 9420 9 600 8800 94 95 9 995 8930 II 025 9690 9350 9500 7750 95 96 9 955 8845 10950 9632 9280 9400 7700 96^ 97 9915 8760 10880 9 574 9 210 9300 7650. 97 98 9875 8675 10 810 9516 9 140 9200 7600 98 99 9830 8590 10740 9458 9070 9 100 7 550 99 lOO 9785 8510 10 670 9400 9000 9000 7500 100 lOI 9740 8430 10595 9 342 8930 8900 7450 lOI 102 9695 8350 1052s 9234 8860 8800 7 400 102 103 9650 8270 10455 9 226 8790 8 700 7350 103 104 9610 8190 1038s 916S 8720 8600 7300 104 105 9570 8 115 10 315 9 no 8650 8500 7250 los io6 9525 8 040 10245 • 9052 8580 8400 7 200 106 107 9480 7965 10 175 8994 8510 8300 7 150 107 io8 9 435 7890 10 105 8936 8440 8200 7 100 108 109 9 395 7815 1003s 8878 8370 8100 7050 109 * Also Atlanta, Ga., Jersey City, N. J., Newark, N. J., Paterson, N. J.. Worcester, Mass., and old New York Code, ^ I Am. R'y Eqgrg. Ass'n th© sarfte upto//r, 100, i(or ^s^kniiftembers.^ Maximum, I4.000. Tables of Safe Loads for Steel Columns Table XI (Continued) . Safe Loads in Pounds per Square Inch of Metal- Area for Steel Columns and Struts / = length in inches • r = least radius of gyration in inches l/r no III 112 113 114 IIS 116 117 118 119 120 Rankine's (Gor- don's) and Cambria II 9 355 9310 9265 9 220 9 180 9 140 9095 9050 9 010 8970 8930 Phila- delphia III 7740 766s 7590 7 520 7450 7380 7310 7240 7 170 7 100 7035 Boston Code IV 9970 9 900 9830 9 760 9695 9630 9560 9 495 9430 9365 9300 Wash- ington, D. C* 8820 8762 8704 8646 8588 8530 8472 8414 8356 8293 8 240 Chi- cago t and N. Y. ^E S VI 8300 8230 8 160 8090 8 020 7950 7880 7810 7740 7 670 7 600 Am. Bridge Co. and Carnegie VII 8 000 7900 7 800 7700 7 600 7 500 7400 7300 7 200 7 100 7 000 Fowler's formula for struts VIII 7000 6950 6 900 6850 6800 6750 6 700 6650 6 600 6550 6500 l/r IX no III 112 113 114 IIS 116 117 118 119 120 In the Comparative Diagram (page 496) of Compression Formulas the names of the formulas and the maximum ratio of l/r for main members and secondary members are as follows: Compression-formulas Maximum ratio of l/r Main members Secondary members American Bridge Company American Railway En:,Mneering Association .... v_ hicago Building Laws Ranltine's (Gordon's) formula New York Building Laws 120 100 120 X20 1 20 140 120 200 120 150 120 140 120 Boston Building Laws *t See foot-notes on pages 493 and 494. 496 Strengths of Columns, Posts and Struts Chap. 14 Comparative Diagram of Compression-Formulas § Allowable Untt Stresses in Pounds per Square Inch g § ^ ^ _ _ I HDUi ajiTnbsTDCl spunoj ui sassoi^s ;!«n «iq^Monv ^ T 7 ^ g ^ t z .0- J- " o f /■ s s 1 - J" g A S g ^ -t it ^. 8 ±1 W- i JS t 7 ^ o 7 t X- s Z- _/ - ^ /' -M s Z IS ^ g ^ ^z § "^ • 7 »^5 ^ g t i#^ ^ T^.jw'l?^ ^ slE Z ZtfeZ^ 3 / ^2/ "^ 8 f/ ^ ^4^/ s * V ^ ^4; " s ife M ^ • s /^^t(4 ^.^^ s jL.^ztr s l^%lAl o5 J- ^At _.. -4^^/% c* 1^/u A /L'T- «d ^/o/LJlA p -At t M £ 't jZ Q t/~M- ^'' ly . 'J " tu\ i t CO o 4 tt-i'l t '^ tfrw r\ r O 5 1^ / ^ ? ( ^%r/- ^-t ^ - A' r -h Tables of Safe Loads for Steel Columns Table XII.- Safe Loads in Tons of 2 000 Pounds for Standard Stc el-Pipe Columns. See National Tube Company's Handbook for Values of r Used Loads in tons of 2 000 pounds. Table based on New York and Chicago laws. For- mula used, 6"= 16 000— 70 l/r, in which S = allowable compressive stress for steel in pounds per square inch, /= length of column in ir.ches. r= least radius of gyration in inches. Loads above or to the left of the zigzag lines correspond to values of l/r greater than 1 20. 1 Lengths 2 1 Nominal sizes of pipe. Inside diameters in inches 2M 1 3 1 3M 1 4 1 4H 1 5 1 6 1 7 ft Thickness in decimal parts of an inch 1 c 3-154 1 0.203 1 0.216 0.226 0.237 0.247 0.258 0.280 0.301 40 36 15.00 33 10.20 18.37 30 24 13.33 16.46 19.60 21-73 25.10 5 7 9 11 96 73 50 26 7.41 92.5 11.09 12.94 8.43 11.32 13.24 15.16 28.47 21.68 30.71 32.96 35.20 37.45 39-69 .-10.81 20 18 16 14 13 12 II 4.96 6.57 7-37 4.60 6.28 7.97 9.65 23.77 25.86 27.9s 30.04 31.08 17.09 19.01 20.93 21.90 14.78 16.62 17.54 3.06 3.81 13 03 10.49 T^ PT 4.57 8.18 11.33 12.18 14 15 79 68 18.46 19.38 22.86 23,82 32.12 33.17 41.94 43.06 2 29 5.32 8.q8 ID 9 2 3 86 44 6.08 9.78 10.59 13.02 13.86 lb 17 5b 44 20.30 21.22 24.78 25.74 34.21 35-26 44.18 45.30 6.83 8 4 01 7-59 8.34 11.39 12.20 14.70 15 -.54 18 19 33 21 22.14 23.06 26.71 27.67 36.30 37.34 46-43 47-55 7 4 S8 6 S 16 9.10 13.00 16.38 20 09 23.98 28.63 38.39 48.48 5 5 73 9 86 13-81 ' 17.23 20 98 24.90 29 -59 39 -07 48.48 Nominal sizes of pipe. Inside diameters in inches. 8 1 9 1 10 1 II 1 12 1 13 1 14 15 Lengths ft Thickness in decimals parts of an inch 0.322 0.342 0.365 0.375 0.375 0.375 0.375 0.37s 40 36 19.16 23.96 28.77 33.87 40.81 51.26 56.85 60.68 66.27 72.45 78.05 81,88 87.47 91.30 96.89 46 26 33 30 27.57 31.17 37-70 50.34 54.43 58.51 61.05 65.24 69.44 70 .•47 74.67 78.86 82.25 91.67 101.09 105 . 29 109.49 41.53 45.35 86.44 90.64 95.87 27 34.77 I 00.06 24 38.37 40.18 62.59 73. 6i 83.06 94.84 104.26 113.68 22 40.78 51.73 65.32 76.43 85.86 97.64 107.06 116.48 20 43.18 54-28 68.04 79.23 88.65 100.43 109 . 86 119.28 18 45.58 56.83 70.76 82.03 91.45 103.23 112.65 122.08 16 47.98 59-38 73.48 84-83 94.25 106.03 115.45 124.88 14 50.38 61.93 76.21 87.62 97.05 108.83 118.25 127.67 13 51-58 63.21 77.57 89.02 98.4s 110.23 119.65 128.85 12 52.78 64.49 78.93 90.42 99.8s 111.62 120.61 12S.85 II 53-99 65.76 80.29 91.82 101,24 112,36 120.61 128.85 10 55-19 67.04 81.65 93-22 102.05 112.36 120.61 128.85 9 56.39 68.31 83.01 93.81 102.05 112.36 120.61 128.85 8 57.59 69.59 83.36 93.81 102.05 112.36 120.61 128.85 7 58.79 69.82 83.36 93.81 102.05 112.36 120.61 128.85 6 58.79 69.82 83.36 93.81 102.05 112.36 120.61 128.85 1 5 58.79 69.82 83.36 93.81 102.05 1 112.36 1 120.61 1 128.85 * Furnished by the National Tube Company, Pittsburgh, Pa. 498 Strength of Columns, Posts and Struts Chap. 14 Table XIII.* Safe Loads in Tons of 2 000 Pounds for Extra-Strong Steel- Pipe Columns. See National Tube Company's Handbook for Values of r Used Loads in tons of 2 000 pounds. Table based on New York and Chicago laws. For- 1 mula used 5 = 16 000 - ^ol/r, in which S= allowable compressive stress for steel in pounds per square inch. /= length of column in inches, r= le 1st radius of gyration in inches. Loads above or to the left of the zigzag lines correspond to values of l/r greater than 120. | Lengths, ft Nominal sizes of pipe. Inside diameters in inches 2 2H 1 3 1 3M 4 4K 1 5 6 1 7 Thickness in decimal parts of an inch 0.218 1 0.276 0.300 0.318 0.337 0.355 0.375 5-432 0.500 36 22.52 33 14.16 28.11 30 27 24 22 18.99 23.81 28.64 33.69 39.28 9.74 12.38 11.21 15.39 18.19 44.86 48.58 7.68 31.86 20 18 16 14 13 5.78 8.14 10.51 10.19 12.69 1=^.20 15.02 17.66 20. q8 35.07 38.29 41.51 44.72 46.33 52.31 56.03 59-75 63.48 65-34 23 -77 26 . 56 29.3s 30.75 6.29 20.31 22.95 24.27 3.69 4-71 8.52 12.87 17.71 9.64 14.06 18.96 12 II 2 91 5-74 6.76 10 75 15.24 16.42 20.22 21.47 25-59 26.91 32.15 33.54 47-94 49-55 67.20 69.06 11.87 10 3 4 72 7.79 12.98 14. 09 17.60 18.79 22.72 23-98 28.23 34.94 36.33 51.16 52.76 70.92 72.78 S3 8.81 7 5 34 9.83 10.86 15-21 16.32 19.97 21.15 25 - 23 26.48 30.88 32.20 37.73 39.12 54.37 55.98 74-64 76.51 6 15 6 b 96 11.88 17.44 22.33 27-74 33.32 40.52 57.79 78.34 S 7 77 12.91 ' 18.55 ' 23.52 28.99 34.84 ' 4192 58.83 78.. 34 Nominal sizes of pipe. Inside diameters in inches 8 9 1 10 1 II 1 12 1 13 1 14 1 15 ft Thiekness in decimal parts of an inch 0.500 . 500 0.500 0.500 0.500 0.500 0.500 0.500 40 36 27.60 40.14 47 - .59 54.25 66.80 74-26 79-36 95.06 102.52 107.62 11508 120. i8 127.64 61.71 67.30 72.89 78.48 84.07 86.82 33 30 27 40.64 S3. 18 79-85 85.45 91.04 96.63 92.41 98.00 103.60 109.19 108. II 113-70 119.30 124.89 120.67 126.27 131.86 138.83 144-42 46 . 23 58.77 64.36 69.95 5i-8i 22 61.13 73.68 87.80 100.36 112 .92 128.62 141.18 153.75 20 64.85 77.40 91.53 104.09 116.65 132.35 144.91 157.48 18 68.58 81.13 95.26 107.82 120.38 136.08 148.64 161. 21 16 72 30 84.86 98.98 111.54 124.11 139-81 152.37 164.94 14 76.03 88.58 102.71 115.27 127.84 143 ■ 54 156.10 168.67 13 77-89 90.45 104.58 117.14 129-70 145.40 157.97 170 43 12 79-75 92.31 106.44 119.00 131.56 147.27 159.44 170-43 II 81.61 - 94.17 108.30 120.87 133.43 148.44 159.44 170.43 10 83.48 96.04 no. 17 122.73 134.70 148.44 159.44 170.43 9 85-34 97-90 112.03 123-70 134.70 148.44 159.44 170.43 8 87.20 99.76 112.70 123-70 134.70 148.44 15944 170.43 7 89.06 100.33 112.70 123-70 134.70 148.44 1.59-44 170.43 6 89.34 100.33 112.70 123.70 134.70 148.44 159-44 170.43 •■? 89.34 ' TOO. 33 112.70 ' 123.70 1 134.70 1 148.44 ' 159-44 ' 170.43 1 * Furnished by the National Tube Company, Pittsburgh, Pa, Tables of Safe Loads for Steel Columns 499 Table XIV. Safe Loads in Tons of 2 000 Pounds for Struts Formed of a Pair of Steel Channels Distance between webs, ^ in If strut is free to bend in either direction, use smaller load given Stresses in pounds per square inch: 12 000 for lengths of 30 radii and under; 13 500 — 50 l/r for lengths over 30 radii n /I -7 ) 32.36] 5.62 1.47 5.53 1.46 5.43 1.45 5.32 1.46 5.23 1.47 5.16 101.57 118.80 105.32 123.48 T20.I3 141. 12 134.91 158.88 150.36 176.52 165.60 194.16 194.16 17.64 20.58- 23.52 8.92 j 11.76 j 14.70 j 17.64 j 20.58 j 7.78; 8.82 j 11.76] 14.70] 1.34 4.61 I 31 4.43 1.30 4.23 1. 31 4.17 1.32 4.09 59.81 72.36 72.32 83.20 86.52 105.84 101.25 123.48 116. 01 141. 12 1.24 3.87 1.20 3.66 1.20 352 1.22 3.42 1.26 3.35 42.94 53.52 55 "" 70.56 69.82 88.20 84.40 105.84 99.76 123.48 1. 19 3.49 1. 17 3.40 1. 15 3.21 1. 17 3.10 36.83 46.68 41.45 52.92 54.85 70.56 69.09 87.83 57. ic 72 / 63.95 83.20 82.46 105.84 96.52 123 110.66 141. 12 40.78 53.52 52.92 70.56 66.15 87.94 80.04 105.13 94.' 122.34 34.87 46.48 39.18 52.52 51.77 69 50 65.31 86.43 54 85 80 118 73 88 48' 123 66.100 12] 141 50 113 88,158 17 126 52,176 78 139 16 194 54.40 72.36 65 . 60 83.20 78.36 105.84 91.78 123.43 105.31 141. 12 SI. 70 72.36 62.21 88.20 74.30I 105.48, 87. TO: 122.65 99.96 139.82 38.64 53.29 49.93 69 -73 62.47 86.69 75.71 103.63 89.93 120.49 36.48 52.62 47.04 68.79 58.80 «5.44 71.35 102.04 85.04 118.64 32.91 45.82 36.93 51.81 48.71 68.38 61.55 85.00 30.94 45.16 34.66 50.98 45.65 67.39 57.77 83.56 49.02 71.99 58.83 87.28 70.25 104 . 25 82.37 121. 16 94.66 138.06 44.50 32.41 50.10 42.57 66.23 54.00 82.17 77.44 IT8.80 80.09 123.00 91 14 140.41 102. oS 1.57.82 114.00 174-75 126.10 192.00 43.62 70.43 52.03 85 . 26 62.09 101.78 72.90 118.33 83.96 134.65 30.01 50.43 38.22 65.85 47.77 81.69 58.34 97.41 70.33 IJ3.I3 25.07 43.15 27.8 48.64 36.42 64.00 46.48 79-30 * 0{ single channel Strength of Columns, Posts and Struts Table XIV (Continued). Safe Loads in Tons of 2000 Pounds for Struts Formed of a Pair of Steel Channels ? A Distance between webs, li in ^^te If strut is free to bend in either direction use smaller load given i Stresses in pounds per square inch: ♦i— 1 -^-i II 000 for lengths of 50 radii and under; 1 13 500 - 50 l/r for lengths over 50 radii ^^ Depth, in Weight per lin foot. Thick- ness of web. Area of two chan- nels, ^2-2 ri-u in Length in feet lb* in sq in 6 7 8 9 10 II II. 25 0.22 6.70 { 1.04 33.63 31.70 29.76 27.83 25.91 23.96 3. II 36.85 36.85 36.85 36.85 36.85 36.85 13.75 0.31 8.o8| 1.04 2. 98 40.56 44-44 38.23 44.44 35.89 44-44 33.57 44-44 31.24 44-44 28.90 44.44 8 16.25 0.40 9.56{ 1.03 2.89 47-82 52.58 45.05 52.58 42.25 52.58 39-48 52-58 36.68 52.58 33-91 52.58 18.75 0.49 11.02 j 1.03 55-12 51.93 48.70 45-51 42.29 3909 2.82 60.61 60.61 60.61 60.61 60.61 6S.6i 0.58 12.50 { 1.03 62.53 58.90 55-25 51.62 47-96 44-34 21 .25 2.77 68.75 68.75 68.75 68.75 68.75 68.75 9-75 0.21 5.7o{ 0.99 2.72 28.11 31.35 26.39 31.35 24.66 31.35 22.94 31.35 21.20 31-35 19-47 31.35 7.20 1 0.99 35. SI 33.33 31-15 28.98 26.78 24-60 12.25 0.32 2.59 39.60 39.60 39-60 39-60 39-60 39 42 7 14.75 0.42 8.68 { 0.99 2.50 42.71 47.74 40.18 47.74 37.56 47.74 34-93 47'- 74 32.28 47.74 29-66 47.13 17.25 0.53 10.14 { 1. 00 2.44 50.19 55.77 47.15 55.77 44.10 55.77 41.06 55-77 38.02 55.77 34.98 54.73 0.63 11.62I 1. 00 57.52 54.03 50.54 47-06 43.57 40.08 19 -75 2.39 63-91 63.91 63.91 63.91 18.46 63.91 62.39 8.00 4.76 { 0.94 23.02 21.50 19.98 16.94 15.42 0.20 2.34 26.18 26.18 26.18 26.18 26.02 25.41 6 10.50 0.32 6.i8{ 0.94 2.21 29.89 33.99 27.91 33.99 25.94 33.99 23-97 33.99 22.00 33.32 20.02 32.48 13.00 0.44 7.64 1 0.95 37.11 34.68 32-27 29.87 27.44 25.04 2.13 42.02 42.02 42.02 41.88 40.81 39-72 0.56 9.12I 0.95 44.30 41.40 38.53 35.66 32.78 29.89 15.50 2.07 50.16 50.16 50.16 49.68 48.33 47-03 6.50 0.19 3.90 { 0.89 18.43 17.13 15.81 14.49 13.18 11.86 1-95 21.45 21.45 21.45 20.92 20.32 19-72 t; ■2ni 0.90 25.17 23.41 21.65 19.87 18. II 16.35 5 9.00 0.33 5 .301 1.83 29-15 29.15 28.83 27.97 27.10 26.22 0.48 6.76J 0.91 32.26 30.03 27.81 25.58 23.35 21.12 11.50 1. 75 37.18 37.18 36.36 35.20 34.03 32.88 0.18 0.84 14.28 13.17 12.07 10.96 9.8s 5.25 3.iO| I.S6 17.05 16.75 16.15 15.55 14.96 14-36 6.25 3.68 { 0.84 16.95 15.64 14.33 13.02 11.70 4 0.25 1. 51 20.24 19.72 18.99 18.26 17.53 ieiso 4.26 0.84 19.62 18.10 16.59 15.07 13.54 7.25 0.32 1.46 23.43 22.63 21.75 20.87 19.98 19.12 * Of single channel, Tables of Safe Loads for Steel Columns 501 Table XV. Safe Loads in Tons of 2 000 Pounds for Single-Steel-Angle Struts 1^ Angles with Unequal Legs Stresses in pounds per square inch: . II 000 for lengths of 50 radii and under;" 13 500 — SO llr for lengths over 50 radii Size, in Thick- ness, in r axis 3-3,* in Area, sq in Length in feet 4 5 6 7 8 9 10 6 X4 0.88 0.86 3.61 7.99 42.78 40.00 37 21 34.44 31.64 28.86 26.07 5 XaVi 0.76 0.7s 3-05 5.81 5 X3 Me 0.66 0.64 2.40 5.44 4HX3 Mo 0.66 0.64 2.25 5.06 24^66 22.29 19 92 17.55 15.18 4 X3K2 Mo •>4 0.73 0.72 2.25 5. 06 11.49 25.73 10.57 23.62 9 21 65 51 8.72 19.40 7.79 17.29 6.86 15.18 4 X3 Me •>4 0.6s 0.64 2.09 4. 09 10.25 22.86 9.28 20.67 8 18 32 47 7.36 16.27 6.39 14.07 3K2X3 Me Ms 0.63 0.62 0.62 1.93 2.30 3-67 9-35 11.07 17.67 8.43 9.9(3 15.90 7 8 14 51 84 12 6.59 7.74 12.35 3I/2X2I/2 Ki H I/I2 0.54 0.54 0.53 1.44 2. II 2.75 6.52 9-55 12.34 5.72 8.38 10.78 4 7 9 92 21 22 3 X2l.^2 Ms K2 0.53 0.52 0.52 1. 31 1.92 2.50 5.88 •8.52 II. 10 5.13 7.42 9.66 4 6 8 39 31 22 3 X2 K2 0.43 0.43 0.43 1. 19 1.73 2.25 4.71 6.85 8.91 3.88 5.64 7.34 2K'X2 % 0.42 0.42 0.42 1.06 1.55 2.00 4.13 6.03 7.79 3.37 4.93 6.36 * This is the least radius of gyration with reference to the diagonal axis 3-3. (See Table XI, pages 362 to 365.) Strength of Columns, Posts and Struts Table XV (Continued). Safe Loads in Tons of 2 000 Pounds for Single- Steel-Angle Struts Angles with Equal Legs Stresses in pounds per square inch: II 000 for lengths of 50 radii and under; 13 SCO — so l/r for lengths over 50 radii Size, in Thick- ness, in r axis 3-3.* in Area, sqin Length in feet . 4 S 6 7 8 9 10 6 X6 3/i 1.19 1. 18 1.17 4.36 7. It 9.74 33.98 39.10 53.57 33.93 38.96 53.37 33.83 37.14 50.77 31.74 35.35 48.28 30.64 33.54 45.77 19.54 31.72 43.36 18.44 29.93 40.78 5 X5 H 0.99 0.97 0.96 3.61 5.86 7.99 19.85 32.23 43.94 18.89 30.50 41.44 17.80 28.68 38.95 16.71 26.86 36.45 15.64 25.06 33 .95 14.53 23.24 31.46 13.42 21.43 28.96 4 X4 0.79 0.78 0.77 0.77 2.86 3.75 4.61 5.44 14.96 19-54 23 -93 28.24 13.88 18.10 22.13 26.12 12.79 16.65 20.33 23.99 II. 71 15-22 18.55 21.89 10.61 13-78 16.75 19.77 9.53 12.33 14.95 17.65 3V2X3H Me K2 % 0.69 0.68 0.67 0.67 2.09 3.25 3.98 4.69 10.47 16.20 19-74 13.26 9.56 14-77 17-95 21.16 8.65 13.34 16.17 19.06 7-74 11.90 14.39 16.96 6.83 10.47 12.61 14-86 3 X3 0.59 0.58 0.58 0.57 1.44 2. II 2.75 3.36 6.79 9.88 12.87 15.60 6.06 8.73 11-45 13.84 5-32 7-69 10.03 12.07 4-59 6.60 8.60 10.30 2^X2'/^ 0.49 0.49 0.48 0.47 0.90 1. 19 1.73 2.2s 3.87 5.10 7-35 9-44 3.32 4.39 6.27 8.01 2.76 3-66 5.19 6.57 2HX2H Mc M % Me 0.44 0.44 0.43 0.43 0.81 1.06 1. 55 1.78 3.26 4.26 6.13 7.14 2.70 3.54 5.05 5.80 2.80 3-95 4.53 2 X2 Me H 0.40 0.39 0.72 0.94 2.70 3.45 2.16 2.72 2.00 * This i i the least radius of gyratic n, with reference to the dia gonal i ixis 3-: . (See Table XII pages 36 6 and 36 7-) Tables of Safe Loads for Steel Coiuiriri^ Table XVI. Safe Loads in Tons of 2 000 Pounds for Double-Steel-Angle Struts Long Legs Parallel AND One-Halt Inch Apart ? Stresses in pounds per square inch: 1-^J IM. -L ) II 00c for lengths of 50 radii and under; r ' 13 50c — so IJr for lengths over 50 radii '^ Si2e, in Thick- ness, in Least in Area. two angles. Length in feet • sqin S 6 7 8 10 II 12 8 X6 H 2.49 13. S3 74.36 74.36 74.36 74.36 74.36 73.34 71.72 1 2,65 26.82 147-51 147.51 147.51 147.51 147.51 147.51 144.62 6 X4 % 1.67 7.22 39.71 39.71 39.65 38.35 35.77 34.47 33.14 1^6 1.74 14.94 82.17 82.17 82.17 80.26 75.07 72.50 69.91 6 X3H 34 1.43 1.46 6.84 3' r.62 >.50 37.57 49.50 36.13 47.81 34 45 .69 31.82 30.38 40.41 29.00 ■ 38.56 9.00 45 •97 42.27 % 1.49 II. 10 61.05 61.05 59 27 57.05 52.51 50.29 48.07 ' ^Me 1-52 14.12 77.66 77.66 75.82 73.03 67.42 64.65 61.88 5 X4 3/^ 1-59 6.46 3« .53 35.53 35.07 33.86 31.41 30.20 28.99 M 1.54 12.38 68.09 68.09 66.69 64.28 59-45 57 04 54.62 5 X3V2 H 1. 51 6.10 33.55 33.55 32.70 31.49 29.05 27.84 26.64 H 1. 55 11.62 63.91 63.91 62.69 6c .45 55.95 53.71 51.44 H 1.27 5-72 31 .46 30.50 29.15 27 .80 25.09 23.75 22.39 5 X3 H 1.30 7.50 41.25 40.23 38.51 36 .78 33.32 31.59 29.85 H 1.33 9.22 5C ).7i 49.76 47.69 45 .59 41.40 39.30 37.29 % 1.36 10.88 .5c .84 58.94 56.63 54 .23 49.42 47.05 44.66 4 XaH % 1.25 5.34 2C >.37 28.35 27.07 25.79 23.23 21.94 20.66 % 1.20 10.12 5= .66 53.13 50.60 48.07 43.01 40.48 39.95 4 X3 % 1.26 4.96 2' .28 26.28 25.12 24.00 21.64 20.49 19.30 M 1.22 9.38 51.59 49.47 47.18 44.85 40.24 37.94 3564 H 1. 12 2.88 I, .58 14.81 14.03 13.26 11.72 10.95 10.18 3K2X3J'i % 1. 10 4.22 22 .73 21.59 20.42 19.28 16.97 15.82 14.67 Vz 1.09 5.50 2S .56 28.05 26.53 25.02 21.98 20.47 18.96 • 3 X2 1.06 0.93 7.30 2.38 3? .92 36.86 11.45 34.78 10.69 32.74 28.58 8.39 26.51 7.62 24.43 12.22 9 .92 H 0.92 4.50 23.04 21.58 20.10 J8 .64 15.70 14.23 2K2X2 3/l6 0.79 1.62 7.86 7.24 6.63 6 .01 2 X2 K2 Me 0.75 0.62 4.00 ic .00 .22 17.40 5.54 15.80 4.82 14 .20 1.44 t 4.13 2 X2 H 0.61 1.88 8.08 7.14 6.20 5.26 Strength of Columns, Posts and Struts Chap. 14 Table XVII.* Safe Loads in Units of i ooo Pounds for Steel-Beam Columns Allowable fiber-stress in pounds per square inch: .13 000 for lengths of 60 radii or under Reduced for lengths between 60 and 120 radii, by Formula (13), 5 = 19 000 — ioo//r Weights do not include details For values for l/r above 120, see notes on page 490 Effective length, ft 13 14 15 16 17 18 23 24 25 26 27 28 29 30 31 8-in 34-lb 130.0 130.0 130.0 130.0 130.0 130.0 130.0 130.0 125.8 119-4 1130 106.6 100.2 93.8 87.3 80.9 74.5 69.0 65.8 62.6 59-4 56.2 53.0 49.8 46.6 43.4 40.2 370 33-7 30.5 Depth and weight of sections H beams 6-in 23.8-lb 91.0 91.0 91.0 91.0 91.0 91.0 86.7 80.9 75.1 693 63.5 57.7 51-9 47-6 44-7 41.8 38.9 36.0 33-1 30.2 27.3 24.4 21.5 5-in 18.7-lb 71.5 71.5 71.5 71.5 71-5 66.0 60.5 55.0 49-5 44.0 38.5 35.8 33.0 30.3 27.5 24.8 22.0 19-3 16.5 4-1 n 13.6-lb I beams 15-in 42-lb 162.2 162.2 162.2 162.2 153-9 140. 1 126.2 112. 3 98.5 86.0 79.0 72.1 65.2 58.2 51.3 44.4 37.4 i2-in 3i3'^-lb 120 120. 120 lo-in 25-lb 95.8 95.8 95.8 94.4 85.3 76.2 67.1 58.0 50.2 45.7 41. 1 36.5 32.0 27.4 22.9 Area, sq in 10.00 7.00 5.50 12.48 7.37 /, i.in*., r\ I, in.., /2 2. in* . ^2 2, in.. 115-4 3.40 35.1 1.87 45.1 2.54 14.7 1.45 23.8 2.08 7.9 1.20 10.7 1.63 3.6 95 441.8 5-95 14.6 215.8 83 9.5 Weight, lb per lin ft 34 23.8 18.7 13.6 42 31H 122.1 4.07 6.9 0.97 Safe load- values above the upper heavy line are for ratios of llr not over 60; between the heavy lines for ratios up to 120 llr\ and those below the lower line are for ratios not over 200 llr 25 those heavy • From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. Tables of Safe Loads for Steel Columns Table XVII * (Continued). Safe Loads in Units of i ooo Pounds for Steel- Beam Columns i' Allowable fiber-stress in pounc s per square inch: ^f l 3 000 for lengtns ot bo raan or under deduced for lengths between 60 and 120 radii, by Formula (13), 5 = 19 000 — lool/r Veierhts do not include details J > ^ 1 For values for l/r above 120, see notes on page 490 Eflfective length, ft Depth and weight of sections I beams 9-in 2i-lb 8-in i8-lb 7-in 15-lb 6-in i2H-lb S-in 9%-lb 4-in 7K2-lb 2 3 4 5 6 7 8 9 10 II 12 13 14 IS i6 17 i8 19 20 21 22 23 24 25 26 27 28 29 3P 82.0 82.0 82.0 69.3 69.3 69.3 57-5 57.5 46.9 46.9 37.3 37.3 28.7 28.5 24.0 19 S 56.8 50.0 43.2 36.4 44-5 38. S 32. s 26.5 33.3 28.0 22.7 77.8 69.4 61.0 52.6 44.2 63.2 55.6 48.0 40.4 IS. 2 13.0 10.8 8.S 18.8 16. 1 13. 5 10.8 30.3 26.9 23.5 20.1 22.9 19-9 16.8 13.8 35.0 40.0 35.8 31.5 27-3 23.1 18.9 31.2 27.4 2^.6 16.7 13.3 10.8 19.8 16.0 31 Area, sq in 6.31 5. 33 4.42 3.61 2.87 2.21 /i-i. in^ ri-i, in h 2. in* ra 2, in.,... 84.9 3.67 5.2 0.90 56.9 3.27 3.8 0.84 36.2 2.86 2.7 0.78 21.8 2.46 1-9 0.72 12. 1 2.0s 1.2 0.6s 6.0 1.64 0.77 0.S9 Weight. lb per lin ft 21 18 IS 12H 9% 7H Safe load- values above between the heavy lines line are for ratios not ove :he upper heavy line are for ratios of l/r not over 60; those for ratios Up to 120 l/r; and those below the lower heavy r 200 l/r * From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa,, 606 Strength of Columns, Posts and Struts Chap. 14 Table XVIH. Safe Loads in Tons of 2 000 Pounds for Bethlehem Rolled- Steel 8-Inch H Columns with Square Ends Unsupported length, ft Allowable stress in pounds per square inch: 13 000 for lengths under 55 radii; 16 000 — 55 IJr for lengths over 55 radii 14 IS 16 17 18 20 24 26 Area, sq in /i-i, in*, J-i 1, in. 72-2. in*, Ti-i, in. Weight of section, lb per lin ft 59-7 59.7 58. 1 56. 5 55.0 S3. 5 52.0 50.4 48.9 47.4 4S.9 42.8 66.1 66.1 64.7 63.0 61.3 59-7 58.0 56.3 54.6 S3.0 SI. 3 48.0 39.7 36.7 44.6 41.3 38.0 9.17 105.7 3.40 35. 8 1.98 121. 5 3.46 41. 1 2.01 34.5 74.8 74-8 73.3 71.4 69.6 67.7 65.8 64.0 62.1 60.2 58.4 54.6 83.4 83.4 81.9 79.8 77.7 75.7 92.2 92.2 90.6 88.3 86.1 83.8 lOI.O lOI.O 99-5 97.0 94. S 92.1 73.6 71.5 69.4 81.5 79-2 76.9 89.6 87.1 84.6 82.2 67.4 65.3 61. 1 74.6 72.4 67.8 79.7 74.7 50.9 47.1 43.4 139-5 3.48 47.2 2.03 39.0 12.83 158.3 3-51 53.4 2,04 14. x8 177.7 3. 54 59-8 2.05 48.0 197 8 3.57 66.3 2.07 53.0 109.9 109.9 108.4 105.7 103.0 100.3 97.7 95.0 92.3 89.6 86.9 81.6 57.0 63.2 69.8 76.2 52.8 58.7 64.8 70.9 48.7 54.1 59.9 65.5 16.90 218 6 3 60 731 2.08 57-5 Loads below the heavy line are for lengths greater than 125 radii Tables of Safe Loads for Steel Columns 507 Table XVIII (Continued). Safe Loads in Tons of 2000 Pounds for Beth- lehem Rolled-Steel 8-Inch H Columns with Square Ends Unsupported length, ft Allowable stress in pounds per square inch: 13 000 for lengths under 55 radii; 16 000 — 55 llr for lengths over 55 radii 14 15 16 17 18 24 26 Area, sq in /i 1, in* ri-i, in. /2-2, in* y%~i, in. Weight of section, lb per lin ft 118. 8 118. 8 117. 3 114-4 iii.S 108 7 102.9 100. o 97.1 94.2 88.5 82.7 76.9 71.2 18.27 240.2 3.63 80.0 2.09 62.0 127.8 127.8 126.5 123-5 120.4 117.3 II4-2 III. 2 108. 1 105 -o 101.9 95.8 136.8 136.8 135-6 132.4 129. 1 125.8 122. 5 119. 2 116. 112. 7 109.4 102.9 9<3.3 146.0 146.0 144-9 141 -4 137-9 134.4 131. o 127-5 124.0 120.5 117. o no. I 83.5 77.3 19.66 262.5 3.65 87.1 67.0 83-2 96.2 154-6 154.6 153-6 149-9 146.2 142.6 138.9 135.2 131.6 127.9 124.2 116. 9 109.6 163.8 163.8 163. 1 159.3 155.4 151. 6 147.7 143.9 140.0 136. 1 132.3 124.6 116. 9 102.2 94.9 109.2 101.5 21.05 285.6 3.68 94.4 2.12 22.46 309.5 3.71 101.9 2.13 76.5 23.78 333. S 3.75 109.2 2.14 81.0 25.20 359.0 3.77 117. 2 2.16 85.5 173.2 173.2 172.6 168.6 164.5 160.5 156.4 152.4 148.3 144.3 140.2 132. 1 124.0 115.9 107.8 26.64 385.3 3.80 125.1 2.17 90.5 Loads below the heavy line are for lengths greater than 125 radii 508 Strength of Columns, Posts and Struts Chap. 14 Table XIX. Safe Loads in Tons of 2 000 Pounds for Bethlehem Rolled- Steel lo-Inch H Columns with Square Ends Unsupported length, ft 2 ' 1 1 r. Allowable stress in pounds 13000 for lengths under 55 per square inch: radii* r_. „r 16 000 - 55 llr for lengths over 55 radii 1 10 II 12 13 14 IS 16 18 20 22 24 26 28 93.5 93.5 92.1 90.2 88.3 86.3 84. 5 80.7 76.9 73.1 69.3 65.4 103.4 103.4 102.2 lOO.I 98.0 95.9 93.8 89.6 85.4 81.3 77.1 72.9 114. 2 114. 2 113. 1 110.8 IC8.S 106.2 103.9 99-3 94.7 90.1 85.6 81.0 125.0 125.0 123.9 121. 4 118. 9 116. 4 113. 9 108.9 103.9 989 93.9 88.9 135.9 135.9 134-9 132.2 129.5 126.9 124.2 118. 8 113. 4 108.0 102.6 97.2 146.8 146.8. 145.9 143.0 140. 1 137.2 134.3 128.5 122.7 116. 9 III. I 105.3 157.9 157.9 157.0 153.9 150.8 147.7 144.6 138.4 132.2 126.0 119. 8 113.5 61.6 68.7 76.4 83.9 91.8 86.4 80.1 99.5 93.7 87.9 107.3 lOI.I 94.9 30 32 57.8 54. 64. 5 60.3 71.8 67.2 78.9 73.9 Area, sq in 14.37 15.91 17.57 19.23 20.91 22.59 24.29 /i-i.in* ^i-i. in /2-2.in< ^-2 2. in 263. 5 4.28 89.1 2.49 296.8 4.32 100.4 2.51 331.9 4-35 112. 2 2.53 368.0 4.37 124.2 2.54 405.2 4.40 136.5 2.56 443.6 4.43 149. 1 2 57 483.0 4.46 162.0 2.58 Weight of section, lb per lin ft 49.0 54.0 59.5 65.5 71.0 77.0 82.5 Loads below the heavy line are for lengths greater than 125 radii Tables of Safe Loads for Steel dolumnS too Tiblie XIX (Continued) . Safe Loads in Tons of 2 000 Pounds for Bethle- hem Rolled-Steel lo-Inch H Columns with Square Ends Unsupported length, ft 2 1 Allowab i^ 000 r. le stress in pounds per square inch: l_ u 16 000 — 55 l/r for lengths over 55 radii 1 10 II 12 13 14 IS 16 18 20 22 24 168.9 168.9 168.3 165.0 161. 7 158.4 155. 1 148.5 142.0 135.4 128.8 180. 1 180. 1 179-6 176. 1 172.6 169.1 165.6 158.6 151.6 144.6 137.6 190-6 190.6 190.2 186.6 182.9 179-2 175.5 168. 1 160.7 153.3 145.9 201.9 201 9 201.9 198.0 194. 1 190.3 186.4 178.6 170.8 163. 1 155.3 213.2 213.2 213.2 209.3 205.2 201.2 197.0 188.9 180.7 172. 5 164.4 224.6 224.6 224.6 220.7 216.4 212. 1 207.8 199-2 190.7 182. 1 173-5 236.1 236.1 236.1 232.2 227.7 223.2 218.7 209.8 200.8 191-8 182.8 173.8 26 28 30 32 122,2 1,^0.6 138.5 147-5 156.2 165 115. 6 109.0 102.4 123.6 116. 6 109.6 131.2 123.8 116. 4 139 8 132.0 124.2 148.0 139-9 131. 7 1.56.4 147-8 139.2 164.9 155.9 146.9 Area, sq in 25.99 27.71 29.32 3^.06 32.80 34-55 36.32 /i-i. in* ^11. in ^2-2. in* ^2- 2. in 523.5 4.49 175.1 2.60 565 2 4.52 188.6 2.61 607.0 . 4.55 201.7 2.62 651.0 4.58 215.6 2.64 696.2 4.61 229.9 2.65 742.7 4.64 244.4 2.66 790.4 4.67 259 3 2.67 Weight of section, lb per lin ft 88.5 94.0 99.5 105. 5 in. 5 117. 5 123.5 Loads below the heavy line are for lengths greater than 125 radii 510 Strength of Columns, Posts and Struts Chap. 14 Table XX. Safe Loads in Tons of 2 000 Pounds for Bethlehem Rolled- Steel z 2-Inch H Columns with Square Ends Unsupported length, r ft 2 1 Allowable stress in pounds per square inch: 13 000 for lengths under 55 radii; 16 000 — 55 //r for lengths over 55 radii 16 18 24 26 28 30 32 34 36 123.5 123.5 122. 5 136.2 136.2 135.4 149-1 149-1 148.3 162.0 162.0 161. 4 118. 3 114. 1 109.9 130.8 126.2 121. 6 143-3 138.3 133.2 155.9 150.5 145. 1 105.7 101. 5 97.3 117. 112.4 107.8 128.2 123.2 118. 1 139.7 134-2 128.8 93.1 88.9 103. 1 98.5 113-1 T08 I 123 4 117 9 175. o 175.0 174.5 168.6 162.8 156.9 151. 1 145 2 139 4 133.5 127.7 84.7 80.5 76.3 89.3 84.7 98.0 93.0 107. 1 101.7 121. 9 116 o 110.2 104 3 188.0 188.0 187.7 181.5 175.2 169.0 162.8 156.5 i50.3 144.0 137 8 201. 1 201.1 201.0 194 3 187-7 181. 174-4 167.7 161.1 154-4 147 8 131 -6 i2.S.3 119 I 112. 8 134.4 127.8 121.1 214.2 214.2 214.2 207.2 200.1 193.1 186.0 178.9 171.9 164.8 157.7 150 7 143.6 136.6 129.5 Area, sq in /i-i,in*. ri-i,in.. /2-2,in*. rj-2. in. . Weight of section, lb per Hn ft 19.00 499.0 5.13 168.6 64.5 20.96 556.6 5. IS 188.2 3.00 22.94 615.6 5.18 208.1 3.01 78.0 676.1 5.21- 228.5 303 84.5 26.92 738.1 5. 24 249.2 304 28.92 801.7 5.27 270.1 306 98.5 30 94 866.8 5.30 291.7 3 07 32.96 933.4 5.33 313.6 3.08 Loads below the heavy line are for lengths greater than 125 radii Tables of Safe Loads for Steel Columns 511 Table XX (Continued). Safe Loads in Tons of 2000 Pounds for Bethl«^ hem Rolled-Steel la-Inch H Columns with Square Ends Unsupported length, ft 2 Allowab "^ le stress in pounds per square inch: jL-i' 16 000 — 55 l/r or lengths over 55 radii 1 10 12 14 16 18 20 22 24 26 28 30 32 34 236.7 226.7 226.7 219.6 212. 1 204.7 197.3 189.9 182.5 175.0 167.6 160.2 239.9 239 -9 239.9 232.6 224.8 217.0 209.1 201.3 193.5 185.6 177.8 170.0 253.3 253.3 253.3 246.0 237.8 229.6 221.4 213.2 204.9 196.7 188. 5 180.3 266.7 266.7 266.7 259.3 250.6 242.0 233.4 224.8 216. 1 207.5 198.9 190.3 28 28 28 25 24 23 22 21 2C 2C 0.3 0.2 o.a 2.6 3.S 4.S 5.5 6.4 7.4 8.4 •0.3 293.7 293.7 293.7 286.0 276.6 267.1 257.7 248.3 238.8 229.4 219.9 210.5 307.3 307.3 307.3 299.7 289.9 280.1 270.3 260.5 250.7 240.9 231.0 221.2 152.8 162. 1 172. 1 181. 6 191. 3 201. 1 211. 4 201.6 191. 8 36 38 145.3 137.9 154.3 146.5 163.9 155.6 173.0 164.4 182.3 173.2 191. 6 182.2 Area, sq in 34.87 36.91 38.97 41.03 43.10 45.19 47.28 A-i. in* ''i-i. in h^2, in* r-i-i,\n I 000.0 5.36 335.0 3.10 I 069.8 5.38 357.7 3. II 1141.3 5.41 380.7 3.13 I 214.5 5-44 404.1 3.14 1289.4 5.47 428.0 3.15 X 366.0 5.50 452.2 3.16 1444.3 5.63 477.0 3.18 . Weight of section, lb per lin ft 118. 5 125.5 132.5 139.5 146. s 153.5 161. Loads below the heavy line are for lengths greater than 125 radii 512 Strength of Columns, Posts and Struts Chap, li Table XXI. Safe Loads in Tons of 2 000 Pounds for Bethlehem Rolled- Steel 14-Inch H Columns with Square Ends Unsupported length, ft Allowable stress in pounds per square inch: 13 000 for lengths under 55 radii; 16 000 — 55 IJY for lengths over 55 radii 16 18 24 26 28 30 32 36 40 44 159 o 159 o 159 o 158.5 153.8 149.2 144 5 139-9 135.2 130. 5 125.9 121. 2 111.9 102.6 Area, sq in 24.46 /i-i. inf ri_i, in. li^i, in< r2-2. in. 884.9 6.01 294. 5 3.47 Weight of section, lb per lin ft 83.5 173.9 173-9 173.9 173.9 168.5 163.4 158.4 153.3 148.2 143.2 138. 1 133. 1 122.9 188.9 204.0 219. 1 234-3 188.9 204.0 219. 1 234.3 188.9 204.0 219. 1 234.3 188.6 204.0 219. 1 234.3 183.2 198. 1 212.9 228.0 177.7 192.2 206.6 221.3 172.2 186.3 200.3 214.6 166.7 180.4 194.0 207.9 161. 2 174.6 187-7 201.2 155.8 168.7 181. 4 194.5 150.3 162.8 175. 1 187.8 144.8 156.9 168.8 181. 1 133.8 145. 1 156.2 167.7 112. 8 26.76 976.8 6.04 325.4 3.49 91.0 122.9 III. 9 29.06 1070.6 6.07 356.9 3.50 99.0 133.4 121. 6 143-6 131.0 31.38 1166.6 6.10 387.8 3.52 106.5 33.70 I 264. 5 6.13 420.3 3.53 114.5 154.3 140.9 36.04 1364.6 6.16 453.4 3.55 122.5 249-5 249-5 249-5 249.5 243-0 235-9 228.8 221.7 214.5 207.4 200.3 193-2 1790 164.7 150. 5 38.38 1466.7 6.18 486.9 3.56 Loads below the heavy line are for lengths greater than 125 radii Tables of Safe Loads for Steel Columns 513 Table XXI (Continued). Safe Loads in Tons of 2 000 Pounds for Beth- lehem Rolled-Steel 14-Inch H Columns with Square Ends 2 Allowable 13 000 foi 16000 — Unsupported length, ft "^ Y 5tress in pounds per squ. lengths under 55 radii; 55 l/r for lengths over 5 ire inch: .\\—=i 5 radii ,. 1 10 12 14 16 18 20 22 24 26 28 30 32 36 263.8 263.8 263.8 263.8 257.4 249 9 242.4 234.9 227.4 220.0 212.5 205.0 190.0 279.2 279.2 279.2 279.2 27*5 264.6 256.7 248.9 241.0 233 I 225.2 217.3 201.5 294.7 294.7 294.7 294.7 288.1 279.8 271.5 263 . 2 254-9 246.6 238.3 230.0 213.5 310. 1 310. 1 310. 1 310.1 303.4 294.7 286.0 277.3 268.6 259-9 251.2 242.5 225.1 325.7 325.7 325.7 325.7 319 309.9 300.8 291.7 282.6 273-5 264.4 255.3 237.1 341.3 341.3 341.3 341.3 334-6 325.1 315-6 306.1 2966 287.1 277.6 268.1 249-1 40 44 175. 1 160. 1 185.7 170.0 196.9 180.3 207.7 190.3 218.9 200.7 230.1 211. 1 Area, sq in 40.59 42.9s 45.33 47.71 50.11 52.51 ^1-1. in* ri_i, in /^2.in* I 568.4 6.21 519-7 3.58 I 674.7 6.24 554.4 3.59 I 783.3 6.27 589. 5 3.6i 1894.0 6.30 626.1 3.^2 2007.0 6.33 662.3 3.64 2122.3 6.36 699.0 3.65 Weight of section, lb per lin ft 138.0 146.0 154.0 162.0 170.5 178.5 Loads below the heavy line are for lengths greater than 125 radii Strength of Columns, Posts and Struts Chap. 14 Table XXI (Continued). Safe Loads in Tons of 2 000 Pounds for Beth- lehem Rolled-Steel x 4-Inch H Columns with Square Ends Unsupported length, ft 2 1 1 r. Allowable 13000 f 16000 - stress in pounds 3r lengths under 55 - 55 l/r for lengths per square inch: radii; r._ 7 I over 55 radii i 10 12 14 16 18 20 22 24 26 28 30 32 36 40 44 357.0 357-0 357.0 357.0 350.3 340.4 330. 5 320.6 3I0.7 300.8 290.9 281.0 261.2 372.8 372.8 372.8 372.8 366.1 355.8 345.5 335.2 324.9 314.6 304.3 294.0 273.4 388.6 388.6 388.6 388.6 381.9. 371.2 360.5 349.8 339.1 328 4 317-7 307.0 285.6 403.5 403.5 403.5 403.5 396 •» 385.8 .374.8 363.7 352.6 341 -6 330-5 319.4 297.3 419-4 419-4 419 4 419-4 412.9 410.5 390.0 378.5 367.1 355.6 344.1 332.6 309.7 435.4 435 4 435.4 435.4 429.0 417.2 405.3 393-4 381.6 369.7 357.8 345. 9 322 . 2 451.4 451.4 451.4 451.4 445-2 433-0 420.7 408.4 396 -2 383.9 371.6 350.4 334 8 241.4 221.6 252.8 232.2 264.2 242.8 275.1 253.0 286.8 263-8 298.5 274.8 310.3 285.8 Area, sq in 54 92 57.35 59.78 62.07 64-52 66.98 69.45 /i-i.in* ruuin lutAn* ^2-8. in 2239.8 6.39 736.3 3.66 2359.7 6.41 744.2 *3.67 2481.9 6.44 812.6 3.69 2603.3 6.48 849.8 3.70 2730.2 $.51 889.3 3.71 2859.6 6:53 9294 3.73 2 991. 5 6.56 970.0 3.74 Weight of section, lb per lin ft 186. 5 19s -0 203.5 211. 219. S 227.5 236.0 Loads below the heavy line are for lengths greater than 125 radii Tables of Safe Loads for Steel Columns 515 Table XXI (Continued). Safe Loads in Tons of 2 000 Pounds for Bethle- hem Rolled-Steel 14-Inch H Columns with Square Ends Unsupported length, ft 1 -1 Allowable stress in pounds per square inch: ' 13 000 for lengths under 55 radii; 16 000 — 55 llr for lengths over 55 radii 10 467.6 12 467.6 14 467.6 16 467.6 18 461.5 20 448.9 24 26 28 30 32 36 40 44 436.2 423.6 410.9 398.2 385.6 372.9 347.6 483.8 483.8 483.8 483.8 477-9 464.8 451.8 438.7 425.7 412.6 399-6 386.5 360.4 322.2 296.9 334.3 308.1 500.0 500.0 500.0 500.0 494.4 480.9 467.4 454.0 440.5 427.1 413.6' 400.2 373.3 516.4 516.4 516.4 516.4 510.9 497.0 483.2 469.3 455.5 441.6 427.8 413.9 386.3 532.8 532.8 532.8 532.8 527.6 513.3 499-1 484.8 470.6 456.3 442.1 427.8 .399-4 346.4 319.5 358.6 330.9 370.9 342.4 549. 3 549.3 549-3 549-3 544-3 529.6 515.0 500.4 485-7 •471 - 1 4.56.4 441.8 412.5 383 -3 354.0 Area, sq in -^1-1. in" n^i, in. ^2-2. in* Weight of section, lb per lin ft 71.94 3125.8 6.59 I 011.3 3.75 244. 5 74.43 3262.7 6.62 1053.2 3.76 76.93 79-44 3402.1 6.65 1095.6 3 77 3544.1 6.68 1 138.7- 3.79 261.5 81.97 3688.8 6.71 1 182.4 3.80 273.5 84.50 3836.1 6.74 I 226.7 3.81 287. 5 Loads below the heavy line are for lengths greater than 125 radii 516 Strength of Columns, Posts and Struts Chap. 14 Table XXII. Safe Loads in Tons of 2 000 Pounds for Light- Weight Lally Columns,* Factor of safety between 4,5 and 5 Calculated by theiormula, P = ^^(13 500 — 140 //J) -\- AAi 000 4- II //J) in which yl 5 and ^c'^''^' t^ie areas of steel pipe and concrete, in square inches, /the length ill inches, and d the outside diameter of pipe, in inclies Outside diam- Weight per Hnear Length of co lumn in feet 13 14 15 16 eter, in foot, in 6 7 8 9 10 II 12 3 3^ 4 5 6 9.64 13.09 17.02 21.05 25 90 36.82 6 9 13 14 20 28 6 9 13 14 20 28 5 8 12 13 19 27 '8" 12 13 19 27 7 n 12 18 26 10 II • 18 26 10 17 . 25 17 24 23 22 16 23 Table XXin. Safe Loads in Tons of 2 000 Pounds for Heavy-Weight Lally Columns* Factor of safety between 4.5 and 5 These loads can be greatly increased by reinforcing the concrete Calculated by in which A^ am the formula, P = Agiis 500 — 140 l/d) Ar are the areas of steel pipe and concret + Ac{i 000 + 11 l/d) e, in square inches, / the length in inches, and d the outside diameter of pipe, in inches Weight 1 Length of columns in feet Outside diameter, per linear in foot, lb 6 8 10 12 14 16 18 20 3H 4 IS 20 12 16 II 15 10 9 12 14 II 4K2 24 20 18 17 16 15 5 29 27 26 31 24 29 22 28 21 26 19 5K 36 32 24 22 6^ 49 45 43 41 40 38 35 34 32 7% 64 58 56 54 52 51 49 46 44 m 81 74 72 69 67 •65 62 60 57 9% 100 93 89 87 85 82 79 77 75 10^ 123 III 109 107 104 lOI 99 96 93 X1V4, 146 131 128 124 122 119 117 113 III I2M 169 150 146 144 141 139 135 133 ■ 130 *For areas of cross-sections of metal and concrete, and for other data used in compu- tations for determining safe loads by formula, see Handbook of the United States Coluj Company, Cambridge, Mass. (See, also, pages 469 to 474, and page 477.) 1 Tables of Safe Loads for Steel Columns 517 Table XXIV.* Safe Loads in Units of i ooo Pounds for Plate-and-Angle Columns Vn 3 Allowable fiber-stress in pounds per square inch. ^K I 1 13 000 for lengths of 60 radii or under Reduced for lengths between 60 and 120 radii, by Formula (13), 5 = 19 000 — 100 l/r Weights do not include rivet-heads or other details For values for l/r above 120, see notes on page 490 13 Web-plate 6" XK" | Web-plate 8''XH'' Effective length, ft SX ^1 5x JX ^X >5 Jx ^X \x. 'bo'^ 'bCNf< 6 7 8 69 ' 63 56 81 88 94 86 79 72 65 57 no lOI lOI 119 119 78 72 82 76 69 63 56 50 103 95 87 78 70 62 96 ?9 83 76 70 63 57 115 \ 107 ' 100 92 85 78 70 9 10 II 12 13 14 15 i6 17 i8 19 20 21 22 23 24 25 26 27 28 29 30 49 43 66 60 54 49 38 35 32 28 25 22 18 50 47 43 39 36 32 28 25 43 40 37 34- 32 11 23 20 45 42 39 35 32 26 22 56 52 48 44 40 36 32 28 52 49 46 43 39 36 33 30 27 23 63 60 56 52 49 45 41 38 34 30 Area, sq in 5.74 6.26 6.74 7.24 8.48 7.76 9.12 /i-i.in* n-i, m ^2, in* ^2-2. in. ... . 34.3 2.45 6.2 1.04 39-1 -2.50 10.3 1.28 42.6 2.51 10.3 1.24 81.2 3.35 10.3 1. 19 96.9 3.38 12.9 1.23 90.1 3.41 16.0 1.44 107 3.43 20.2 1.49 Weight, lb per lin ft . . 1Q.6 21. 5 23.1 24.8 29.2 26.4 31.2 The safe load-values above the upper heavy line are for ratios oil/r not over 6o; those beTweenthrheavy lines are for ratios up to 120 l/r; and those below the lower heavy line are for ratios not over 200 l/r • From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. Strength of Columns, Posts and Struts Chap. 14 TaWe XXIV * (Continued). Safe Loads in Units of i 000 Pounds for Plate^ and-Angle Columns n>, . 2 _ Allowable fiber-stress in oounds oer sauare inch: ^ V 13 000 for lengths of 60 ra Reduced for lengths betw Formula (13), 5 = 19 oo( Weights do not include rive ) For values for l/r above 1 2 dii or under een 60 and 120 radii, by D — TOO l/r t-heads or other details 0, see notes on page 490 12 Effective length, Web-plate S^XMe" Web-plate 8"XW it El It >0 1? IS; g^5 •wX •*X If if 5 ^X 6 7 8 9 10 II 12 13 IS i6 17 i8 19 20 21 22 23 24 25 26 27 28 29 30 ] 1 25 142 141 141 141 161 161 161 168 168 168 188 188 188 208 208 208 25 142 112 104 96 138 130 121 ri2 136 128 121 158 149 140 131 123 114 105 97 88 163 154 145 136 127 1x8 109 100 90 185 175 165 155 14s 135 124 114 104 206 196 185 174 163 152 141 130 120 89 J04 113 105 97 89 81 31 73 ii 77 66 62 58 54 50 47 43 39 35 31 73 68 64 60 55 SI 47 42 38 34 75 71 67 63 59 55 51 48 44 40 36 83 79 74 70 66 61 57 53 48 44 39 86 81 77 11 63 59 54 49 45 40 a I 5 5 4 18 3 »8 3 8 3 3 8 3 8 no 105 100 94 89 83 78 72 67 62 56 51 Area, sc^ in 9.62 IQ.94 10.86 12.42 12.92 .14.48 16. 00 /i-i. in* ''i-i. in /2-2, in*,.... «rj-5, in no 3.38 29.7 1.47 127 I 51 122 3. 35 303 1.67 I4J 3.36 36.3 I 71 143 3.33 37.2 1.70 161 3.34 43.5 1.73 178 3 33 50.2 i 77 • Weight, Ibperlinft.. 32.9 37.3 37.3 42. s 44.2 49.4 54)5 The safe load-values above the upper heavy line are for ratios of l/r not over 6o: those between the heavy lines are for ratios up to i2ol/r; apd tho$,e below the lower heavy line are for ratios not over 200 l/r ? From P.Qpket Copipanipp, Carpegfje Steel Copip^ny, J?k|:sl^ur^h, Pa. Tables of Safe Loads for Steel Columns §1? Table XXIV* (Continued). Safe Loads in Units of i ooo Pounds for Plate- and-Angle Columns .. '5 \ Allowable fiber-stress in pounds per square inch: A \ — ,r ^> + -^- 13 000 for lengths of 60 radii or under 1.- Reduced for lengths between 60 and 120 radii, by Formula (13), ^ t^ S = 19 000 — 100 l/r Weights do not include rivet-heads or other details For values for l/r above 120, see notes on page 490 1 \2 Web-plate io"XH" Web-plate lO^XMe" Web-plate io"X?i" ,^ ^ Effective length, ft jx gX to ^x sx ^i 4^ -# i ,x C-x ^X Cx «5? ^X *ro "^ "po 't %!• ^ V> 6 99 91 82 74 107 125 125 133 133 149 149 149 170 170 170 178 178 178 198 198 198 207 207 207 207 7 8 9 107 100 93 119 III 125 117 142 164 170 192 10 II 12 66 58 86 79 71 103 95 87 108 99 91 133 125 116 154 145 135 160 150 140 181 170 160 207 203 194 52 13 14 15 48 44 40 64 79 71 82 73 108 99 91 126 107 ^,39 121 III 149 138 127 18S 175 166 57 54 65 68 ■ i6 17 36 32 50 47 61 57 64 60 82 98 lOI 116 157 148 77 90 93 106 i8 28 43 53 55 73 85 88 lOI 139 19 24 40 49 51 69 Si u 95 130 20 36 45 47 64 76 90 121 21 22 33 29 41 37 42 38 60 56 71 .67 73 84 79 112 107 23 25 34 34 SI 62 '^} 74 103 24 30 47 57 58 68 98 25 26 43 39 5? 53 48 63 57 93 89 84 , 48 34 43 43 52 28 47 80 1 29 75 30 71 Area, sq in 7.74 8.26 9.62 10.25 If -49 13-05 13., ^7 15.23 15.9s /i-i. in* 134 148 176 181 201 232 237 267 279 ^1-1. in 4.16 4.23 4.28 4.20 4.18 4 22 4.17 4.19 4.18 /2-2.in* 10.3 16.0 20.2 20.7 30.3 36.3 37.2 43.5 70.6 r2_o, m 1. 15 1-39 1.45 1.42 1.62 1.67 .1.65 1.69 2.10 Weight, Iboerlinft .. 26.5 28.1 32.9 35 39-4 44.15 46.8 52.0 54.4 The safe load-valu es above the upper heavy line are for ratios of l/r not over 60; those between the hej ivy lines are for ratios up to 120 l/r; and those below the lower heavy line are for rat los not over 200 l/r •From ?oc]k^t Cpmpa^ipii, Carnegie 5teel Compaqj^, Pittsburgh, Pa. 520 Strength of Columns, Posts and Struts Chap.. Table XXIV* (Continued)* Safe Loads in Units of i ooo Pounds for Plate- and-Angle Columns \^ ^^^_ e inch; dii. by ails 490 + 1 i 1 r I Allowable fiber-stress in pounds per squar 13 000 for lengths of 60 radii or under Reduced for lengths between 60 and 120 ra Formula (13), 5 = 19 000 — 100 l/r Weights do not include rivet-heads or other det 2 For values for l/r above 120, see notes on page Effective length, ft Web-plate io"X^^" Web- plate io"XF2" Web-pl. 10" X H" JX ^X "0 -ax ^x 1 IF s;x :x 6 7 8 9 lO II 13 13 232 232 232 232 232 236 236 236 236 236 236 236 266 266 266 266 266 266 266 266 296 296 296 296 296 296 296 296 312 341 370 370 370 370 370 370 370 370 386 386 386 386 386 386 386 386 312 312 312 312 312 312 312 341 341 341 341 341 341 341 230 220 210 . 200 190 180 235 226 218 200 257 248 238 229 220 210 201 191 182 172 163 IS4 144 288 302 291 280 269 258 247 236 225 214 203 192 181 170 333 321 309 297 28S 274 262 250 238 226 214 203 191 363 350 337 325 312 299 287 274 261 249 236 223 210 378 36s 351 338 32s 312 298 285 272 258 245 232 218 15 i6 278 267 2S7 247 237 226 216 206 19s 18S 175 164 17 i8 19 20 21 170 160 150 140 130 201 192 184 167 158 ISO 141 132 22 23 24 25 26 27 28 29 30 123 118 113 108 103 98 93 88 83 126 121 117 113 109 139 134 130 125 IS7 146 141 164 158 IS3 147 181 164 198 192 186 179 207 200 193 187 Area, sq in 17.87 18.19 20.47 22.75 24.00 26.24 28.44 29.69 500 4.10 213 2.68 /i-i.in* ri-i, in -^2-2. in* »'2-2. in 31S 4.20 82.3 2. IS 319 4.19 ^2 361 4.20 2.61 401 4.20 160 2.6s 412 4.14 i6S 2.62 451 4.15 186 2.66 489 4. IS 206 2.69 Weight, Ibperlinft.. 60.8 62.0 70.0 77.6 81.8 89.4 97.0 101.3 The safe load-values above the upper heavy line are for ratios of l/r not those between the heavy lines are for ratios up to I2Q l/r; and those below t over 60; he lower * From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa, Tables of Safe Loads for Steel Columns 521 I'able XXIV * (Continued) . Safe Loads in Units of i ooo Pounds for Plate- and-Angle Columns 2 All ,^„-oK1„ pound „,..„,„... 1 ^^"^ J f) 13 000 for lengths of 60 rad ii or ui der :^! X /, Reduced for lengths between 60 and 120 radii, by -f| L.. _ 1 Formula (13), >- ^ = 19 GOG — 100 Weights do not include rivet-heads l/r or other details ^— . For values for l/r above 120 , see no tes on page 490 b J Effective Web-plate Web-plate X2"X^l6" Web-plate I2''X^^" k :; ^ ^ "v, jx ^^ Nf> length, ft -SbX ^X |x # Sx c!";^ cX c:: C5 P!^/^ a%^ a^^ CsJM a"*!;' ci^ c3 (^ rt ro rt ro ^0 aO "5 To ^x ri-.N rtT^ -.-• ^X ^X ^X rfX -.^ -J | Effective Web-plate 12'' x%" Wph-nlatp jy VlVcU-pi^" Web-plate i2"X3'^" Effective length, ft rf^ IN ^ ^b 'g^^X «5 II 12 13 14 15 16 383 333 3S3 383 383 428 428 423 428 428 428 458 458 458 45s 458 458 487 487 487 487 487 487 507 507 507 507 507 553 553 553 553 553 553 379 506 491 476 461 447 432 417 • 403 338 373 358 344 329 314 299 285 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 3.'^ 368 357 346 334 323 312 301 289 278 267 256 244 233 222 211 419 407 395 383 370 346 334 322 310 297 28S 273 261 249 237 447 434 421 407 394 381 368 355 342 329 316 303 290 277 264 250 475 461 447 433 419 405 391 377 363 349 335 321 307 293 279 26s 542 526 510 495 479 463 448 432 416 401 385 369 354 338 323 307 203 197 191 186 272 228 221 215 242 235 229 257 250 243 264 257 249 294 287 279 Area, sq in 29-44 32.94 35.22 37.50 39^00 42.50 7i-i.ini ''1-1, in V2. in* ''2-2. m 916 5. 58 291 3.14 1073 5.71 348 3.2s 1 136 5.68 368 3.23 I 197 5.65 388 3.22 I 215 S.58 394 3.18 1377 5.69 451 3.26 Weight, lb per lin ft.. 100.2 112. 1 120. 1 127.7 132.8 144.7 The safe load- values a those between the heav^ heavy line are for ratios bove the upper heavy line are for ratios of l/r not over 60; i lines are for ratios up to 120 l/r] and those below the lower not over 200 //> j , "From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. 524 Strength of Columns, Posts and Struts Table XXIV* (Continued). Safe Loads in Units of i ooo Pounds for Plate- and-Angle Columns y ^ .j^\- • |2 • w Allowable fiber-stress in pounds per square inch: 13 000 for lengths of 6o radii or under Reduced for lengths between 6o and 120 radii, by Formula (13), 5 = 19 000 — 100 l/r Weights do not include rivet-heads or other details For values for l/r above 120, see notes on page 490 Effective length, ft Web-plate i2"X3'i" 13 14 15 17 18 19 23 24 25 26 27 28 29 30 31 32 33 34 35 Area, sq in h-u in* ri-i, in 72-2, in*. . . . ^2-2' ill Weight, lb per lin ft. 582 582 582 S82 582 610 610 610 610 610 610 Web-plate i2"X^A'' K4^ 630 630 630 630 630 630 675 675 675 675 675 675 1.^|x 721 721 721 721 721 569 553 536 520 503 487 470 < 454 437 421 404 388 371 354 338 321 596 579 562 544 527 509 492 475 457 440 422 405 353 336 613 663 594 644 576 625 558 606 540 587 522 568 504 548 486 529 468 510 450 491 431 472 413 453 395 434 377 415 359 396 341 377 309 323 30T 293 315 306 331 322 313 44.74 1437 5.67 472 3 25 152.3 46.94 1495 5.64 492 3.24 159-9 48.44 I 513 5.59 499 3.21 165.0 361 351 342 51.94 1682 5.69 176.9 714 694 674 654 634 614 594 574 554 534 514 494 474 454 434 414 394 381 371 55.44 1856 5.79 613 3.33 188.8 766 766 766 766 766 766 763 742 721 700 679 658 637 616 595 574 553 532 511 490 469 448 427 409 399 58.94 2037 5.88 671 3.37 200.7 The safe load- values above the upper heavy line are for ratios of l/r not over 60; those between the heavy lines are for ratios up to 120 l/r', and those below the lower heavy line are for ratios not over 200 l/r * From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. Tables of Safe Loads for Steel Columns 525 Table XXIV ^= (Continued). Safe Loads in Units of i 000 Pounds for PUte- and-Angle Columns ^A_ f ^ Allowable fiber-stress in pout] 13 000 for lengths of 60 radii or Reduced for lengths between 6 Formula (13), 5 = 19 000 — 10 Weights do not include rivet-head •4^ ds per square inch: under D and 120 radii, by ol/r s or other details Y t^ For values for l/r above 120, see notes on page 490 1 Effective length. Web-plate i2"X^i" to to |x|S ^X {^%t to II 12 13 14 15 812 812 812 812 812 857 857 857 857 857 903 903 903 903 903 948 948 948 948 948 948 948 994 994 994 994 994 994 994 1039 1039 1039 I 039 1039 1039 1039 16 17 18 19 20 21 22 * 23 24 25 26 27 28 29 30 31 812 812 857 857 903 903 791 769 747 725 703 681 659 637 615 593 571 549 527 505 840 817 794 771 748 725 702 679 657 634 611 588 565 542 888 864 840 817 793 769 745 721 697 673 649 62s 601 577 937 912 887 862 837 . 812 787 762 738 713 688 663 638 613 588 563 538 513 986 960 934 908 882 856 830 805 779 753 727 701 675 649 623 • 597 571 545 1034 I 007 980 953 926 899 872 845 818 791 764 737 710 684 657 630 603 576 32 33 34 35 483 461 439 519 496 473 553 •529 505 427 456 484 Area, sq in 62.44 65.94 69.44 72.94 76.44 79.94 Ji-i, in* ri-i, in /2-2. in* r2-2f in 2224 5.97 728 341 2418 6.06 785 3.45 2618 6.14 842 3.48 282s 6.22 899 3.51 3038 6.30 956 3.54 3259 6.38 1014 3.56 Weight, lb per lin ft.. 212.6 224. 5 236.4 248.3 260.2 272.1 The safe lo those betweer heavy line art ad-values i 1 the heav3 i for ratios ibove the upper heavy line are for ratios o(l/r not over 60; / lines are for ratios up to 120 l/r; and those below the lower not over 200 l/r * From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. Strength of Columns, Posts and Struts Chap. Table XXIV =<" (eontinued). Safe Loads in Units of i ooo Pounds for Plater and-Angle Columns 1 ^^ Allpwable fiber-stress in pounds per square inch: 13 000 for lengths of 60 radii or under Reduced for lengths between 60 and 120 radii, by Formula (13), 5=19 000 — 100 l/r Weights do not include rivet-heads or other details For values for l/r above 120, see notes on page 490 1 u 1 1 T 2 Y Effective length, ft Web-plate I2^'XH^' Web-plate 14" X^^'^ to Ixl'^. cv^j3X ttXn ^ to III -fX^^^. n.X«V II 12 13 14 15 i6 17 I 085 I 08s I 085 I 085 1 08s I 08s 1 08s I 130 I 130 I 130 I 130 I 130 I 130 I 130 39? 392 392 392 392 422 422 422 422 422 452 452 452 452 452 4.74 474 474 474 474 497 497 497 497 497 387 375 415 403 444 431 470 456 497 482 468 453 439 425 410 396 381 367 353 338 324 309 295 281 i8 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 1082 1054 I 026 998 970 942 IS 858 830 802 774 746 718 690 662 634 606 I 130 363 352 340 328 317 305 270 ?58 246 235 223 311 390 377 365 352 340 327 314 302 264 251 239 417 404 390 377 363 350 336 323 309 296 282 269 255 442 428 415 401 387 373 359 345 331 317 3P3 289 275 261 I lOI 1072 1043 J 014 985 9S6 927 898 ^69 840 811 782 753 S^ 667 638 227 220 214 208 243 236 229 222 205 200- 194 251 244 237 230 267 260 253 245 188 201 216 Area, sq in 83.44 86.94 30.19 32.47 34.75 36.50 38.25 /i-i, in4 ri-i, in /?-2.in4 ri-2,in 3486 6.46 107 1 3.58 3 721 6.54 1128 3.60 I 261 6.46 291 3.10 I 351 6.45 311 3.09 1436 6.43 331 3.09 1539 6.49 360 3.14 1643 6.55 388 3.T9 Weight, lb per lin ft.. 284.0 295.9 102.8 II0.8 118. 4 124.3 130.3 The safe lo those betwee heavy line ai ad- values £ n heavy li e for ratios ibove the upper heavy line are nes are for ratios up to 120 l/r not over 200 l/r. for ratios of l/r not over 60; and those below the lower * From Pocicet Corapanion, Carnegie Steel Company, Pittsburgh, Pa. Tables of Safe Loads for Steel Columns 527 Table XXIV* (Continued). Safe Loads in Units of i opo Pounds for Plate- and-Angle Columns ■ , A 12 A . 1 . . 1 f ' i Allowable fiber-stress in pounds per square inch: 1 h- 1 13 000 for lengths of 60 radii or under 1 Reduced for lengths between 60 and 120 j-adii, by Formula (13), \X . S = 19 000 — 100 l/r VA\ Weights do not include rivet-heads or other details Y '2 "^ Effective length, Web-plate ia^'XYs" Web-plate I4"XK2'' "" to G- SX f II 12 13 14 IS 16 17 520 520 520 520 520 520 543 543 543 543 543 543 566 566 566 566 566 5^6 595 595 595 595 595 623 623 623 623 623 595 623 507 533 517 502 487 472 456 441 426 410 395 380 364 349 334 318 303 S5r 535 518 502 486 470 454 437 421 405 389 373 356 340 324 308 ■ 578 561 544 527 510 493 476 459 442 424 407 390 373 356 339 322 605 587 569 551 533 51S 497 tl? 443 425 407 390 ^72 ^54 336 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 493 478 463 448 433 418 403 388 374 359 344 329 314 299 284 275 267 260 290 282 275 298 290 282 312 304 295 327 318 309 Area, sq in 40.00 41-75 43.50 45.74 47-94 ii-i.in* ^1-1. m /2-2. in* ^2-2, in 417 3.23 I8S7 6.67 446 3.27 I 885 6.58 451 3.22 1970 6.56 472 3.21 2053 6.54 .492 3.20 Weight, lb per lin ft.. 136.2 142.2 14S.1 155.7 163.3 The safe load-values above the upper heavy line are for ratios of l/r not over 60; those between the heavy lines are for ratias up to 120 l/r; and those below the lower heavy line are for ratios not over 200 l/r ,.., „. • 1 * From Pocket Companion, Carnegie Steel Company, l>ittsburgb» Pa. 528 Strength of Columns, Posts and Struts Chap. 14 Table XXIV* (Continued). Safe Loads in Units of i ooo Pounds for Plate- and-Angle Columns , ^ '-^ ^ i inch: dii, by ails 490 A ? M Allowable fiber-stress m pounds per square 13 000 for lengths of 60 radii or under Reduced for lengths between 60 and 120 ra Formula (13), 5 = 19 000 — 100 l/r Weights do not include rivet-heads or other det For values for l/r above 120, see notes on page ' Y I2 V ■ Effective length, ft Web-plate u"XH" ^r^x rj-XN%t |x|| rtX(N%t II 12 13 14 IS i6 737 737 737 737 737 737 782 782 782 782 782 782 828 828 828 828 828 828 873 873 873 873 873 873 873 919 919 919 919 919 919 919 646 646 646 646 691 691 691 691 691 691 643 17 i8 19 20 21 22 23 24 25 26 27 28 29 30 31 32 624 606 587 568 549 530 511 493 474 455 436 417 399 380 361 6^- 055 635 615 596 576 556 536 517 497 477 457 438 418 398 378 726 705 684 664 643 622 602 581 560 540 519 498 477 457 436 415 776 754 733 711 689 668 646 62s 603 S81 560 516 495 473 452 ' 430 826 803 780 758 735 713 66? 645 622 600 577 554 532 509 487 464 852 829 805 782 758 734 711 687 664 640 617 593 569 546 522 499 [ 475 901 876 851 827 802 778 753 728 704 679 655 630 60s 581 556 532 507 345 33 34 35 336 326 317 365 356 346 396 385 375 415 404 444 432 461 489 Area sq in 49.69 53.19 56.69 60.19 63.69 67.19 70.69 /i-i. ^2-2. in^ n in* n 2081 6.47 499 3.17 2302 6.58 556 3.23 2529 6.68 613 3.29 2"764 6.78 671 3.34 3006 6.87 728 3.38 3255 6.96 785 3.42 3512 7.05 842 3.45 Weight, lb per lin ft.. 169.3 181. 2 193.1 205.0 216.9 228.8 240.7 The safe load-values those between the hea lower heavy line are fo above the upper heavy line are for ratios of l/r not vy lines are for ratios up to 120 l/r; and those b r ratios not over 200 l/r over 60; slow the •Fft m Pocket ( ^mpanion Carnegie Steel Com pany, Pitt sburgh, Pa I, Tables of Safe Loads iot Steel Columns 529 Table XXIV* (Continued). Safe Loads in Units of i ooo Pounds for Plate- and-Angle Columns ^ 1^ ^ ^^ifT" M [tk Y '2 ^ Allowable fiber-stress in pounds per square inch: 13 000 for lengths of 6o radii or under Reduced for lengths between 6o and 120 radii, by Formula (13), 5 = 19 000 — 100 l/r Weights do not include rivet-heads or other details For values for l/r above 120, see notes on page 490 Effective length, ft 13 14 15 16 17 18 19 23 24 25 26 27 28 29 30 31 32 33 34 35 Web-plate u"XW 4J w (U^X 964 964 964 964 964 964 964 949 924 872 847 821 796 770 744 719 693 668 642 617 591 565 540 1 010 I 010 I 010 I 010 I 010 I dio I 010 §v, Weights do not include rivet-heads or other details ^.., f , M^i . For values f( 1 Y "i '^ For values for l/r above 120, see notes on page 490 Effective length, ft 13 14 15 16 17 ' 18 19 23 24 25 26 27 28 29 30 31 32 33 34 35 Web-plate u"XH" o I 250 I 250 I 250 I 250 I 250 I 250 1250 I 250 I 250 I 250 I 229 I 201 I 172 I 144 I 115 1087 1058 I 030 I 001 973 944 916 887 859 830 I 315 I 315 I 315 I 315 I 135 I 315 I 315 I 315 I 315 4J V (u;?; 1367 1367 I 367 I 367 1367 1367 1367 I 367 I 367 1 308 1277 I 246 I 216 1 185 ri54 I 12^ 10^ I 062 I 031 I 000 970 939 908 877 847 1364 I 333 I 301 I 269 I 237 I 206 I 174 I 142 I III 1079 1047 I 015 984 952 920 I 419 I 419 I 419 I 419 I 419 1419 I 419 I 419 I 419 I 419 1388 1356 1323 I 290 I 258 I 225 I 192 I 160 I 127 1094 I 062 1 029 996 964 931 I 471 I 471 I 471 I 471 I 471 I 471 I 471 1471 I 471 I 471 1443 I 409 1375 I 342 1308 1274 I 241 I 207 I 173 I 139 I 106 I 072 I 038 I C05 971 ^?5x I 523 I 523 I 523 I 523 I 523 I 523 I 523 I 523 I 523 1523 I 497 I 463 I 428 I 393 I 359 I 324 1289 I 254 I 220 I 185 I 150 I 115 I 081 I 046 I on Area , sq in /i-i, in*. ri_i, in.. 7^2. in*. r^-h in. Weight, lb per lin ft. , 96.19 5 457 7.53 1579 4-05 327.4 101.19 105.19 109.19 5484 7.36 I 581 3.95 5830 7-44 1666 3.98 6187 7-53 1752 4.01 344.2 357.8 371.4 113.19 6552 7.61 1837 4.03 385.0 117. 19 6928 7.69 I 922 4-05 398.6 The safe load- values above the heavy line are for ratios of l/r not over 60; and those below the heavy line are for ratios not over 120 l/r * From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. Tables of Safe Loads for Steel Columns 531 Table XXIV* (Continued). Safe Loads in Units of i ooo Pounds for Plate- and-Angle Columns A |2 A 1 ^1 — o - Jf - _1 , k Allowable fiber-stress in pounds per square inch: 13 000 for lengths of 60 radii or under Reduced for lengths between 60 and 120 radii, by Formula (13), S = ig 000 — 100 l/r Weights do not include rivet-heads or other details For values for l/r above 120, see notes on page 490 ^ Ir-T" ': ElTcctive length, ft Two web-plates I4''X3'2-" 'Scroti <^ rtX M^b |x|| 00 ^X; 1 Effective length, Two [o-in channels, latticed Two lo-in channels, two 14-in plates J2 a> ^"0 OJ il 4^ n 1' •38 ft 1 » 11 a^' a^ ^.a a^ ^J a 2 47. xi i lO w 6-w 10 w cS'w i ir)f-"^ ly^'^^ ^^ cs ro •^ M N II ii6 153 191 229 252 275 298 312 12 ii6 IS3 191 229 252 275 298 312 13 ii6 153 191 229 252 275 298 312 14 ii6 153 191 229 252 275 298 312 15 ii6 153 191 229 252 275 298 312 i6 ii6 153 191 229 252 275 298 312 17 i8 19 20 ii6 ii6 ii6 153 153 191 229 252 252 252 252 275 275 275 275 298 298 298 298 312 312 312 312 189 184 179 224 2l3 211 150 146 114 21 22 III 109 142 139 174 169 205 199 252 275 298 312 251 273 295 308 23 io6 135 164 193 246 267 289 302 24 103 131 159 187 241 261 282 295 25 100 127 154 iSo 235 256 276 288 26 98 123 149 174 230 250 270 282 27 95 119 144 168 235 244 263 275 28 92 IIS 139 162 219 238 257 268 29 89 112 134 156 214 232 250 261 30 87 108 129 149 209 226 244 255 31 84 104 124 143 203 220 238 248 32 8i 100 119 137 198 214 231 241 33 78 96 114 131 193 209 225 235 34 75 92 109 125 187 203 219 228 35 73 88 104 121 182 197 2212 221 Area, sq in 8.92 11.76 14.70 17.64 19.42 1 21.17 22.92 24.01 h-i, in4 134 158 182 207 416 468 520 491 ^i-i.in 3.87 3.66 3.52 3.42 4.63 4.70 4.76 4-52 h-2.in* 197 241 284 323 369 398 426 442 ^2-2. in 4.70 4.53 4.39 4.23 4.36 4.33 4.31 4.29 Weight, lb per lin ft.. 39.3 49-4 .59.4 69.4 65.7 71.7 77.6 81.7 Safe load-values a1 oove the upper heavy line are for ratios of l/r not over 60; those between the h javy lines are for ratios u p to 120 l/r\ and those below the lower heavy line are or ratios not over 200 l/r Strength of Columns, Posts and Struts Chap. 14 Table XXIV* (Continued). Safe Loads in Units of i ooo Pounds for Plate- and-Angle Columns ^ A |2 A J Allowable fiber-stress in pounds per square inch: 13 000 for lengths of 60 radii or under Reduced for lengths between 60 and 120 radii, by Formula (13), 5 = 19 000 — 100 l/r Weights do not include rivet-heads and other details For values for l/r above 120, see notes on page 490 1^: ' Y 2 ^ Effective length, Two web-plates u"XW 00 (L( ON W^fO 00 00 00 lx?^8 . 00 ^X..o 00 II 12 13 14 15 I6 17 i8 19 20 21 22 23 1949 1949 I 949 1949 1949 1949 I 949 1949 I 949 1949 1949 1949 1949 2 027 2027 2 027 2027 2 027 2 027 2027 2 027 2 027 2027 2027 2 027 2 027 2 092 2092 2 092 2092 2 092 2 092 2092 2 092 2 092 2092 2092 2 092 2 092 2157 2 157 2 157 2 157 2 157 2 157 2 157 2 157 2 157 2157 2 157 2 157 2157 2 157 2157 2 222 2 222 2 222 2 222 2 222 2 222 2 222 2 222 2 222 2 222 2 222 2 222 2 222 2222 2 222 2287 2 287 2287 2 287 2287 2 287 2 287 2287 2287 2287 2 287 2287 2 287 2 287 2 287 24 25 26 27 28 29 30 31 32 33 34 35 I 918 1879 I 841 I 802 I 763 1724 1686 1647 I 608 1569 I 530 1492 2027 2 027 2 092 2 092 2 009 I 972 I 935 I 8Q9 1862 182s 1789 I 752 I 715 1679 2077 2039 2 002 1964 I 926 1889 I 851 I 813 I 775 1738 2 146 2 107 2068 2029 I 991 1952 I 013 1874 1836 I 797 2 214 2 175 2 135 2095 2055 2 016 1976 I 936 1896 1857 2283 2242 2 202 2 161 2 120 2079 2039 1998 1957 I 916 Area, sq in 149.94 155.94 160.94 165.94 170.94 175.94 /i-i.in* ri-i, in /^2.in4 r2-2. in 8 916 7.71 3 222 4.64 9248 7.70 4049 5. 10 9741 7.78 421I6 5.12 10248 7.86 4383 5.14 10767 7.94 4 549 5.16 II 298 8.01 4716 5.18 Weight, lb per lin ft.. 510. 1 S30\S 547.5 564.5 581.5 598.5 Safe load-values abo below the heavy line ai ve the heavy line are for ratios of l/r not ovc •e for ratios not over 120 l/r r 60; those * From Pocket Companion, Carnegie Steel Company. Pittsburgh, Pa, I Tables of Safe Loads for Steel Col umns 533 Table XXV.* Safe Loads in Units of i ooo Pounds for lo-Inch Channel- Columns t-^y-t T-^ \ — T-r Allowable nbcr-strcr.s in pounds per square X 13 000 for lengths of 60 radii or under inch: oyJi--- ? - - Reduced for lengths between 60 and 120 radii, by | — Formula (13), 1 5=19 000 — 100 l/r l^ 1 j^ Weights do not include rivet-heads or other details 1 ^^ T7^, values for l/r above 120, see notes on page 490 : 4^ ,.b ^ 1----12--- ->^ Two lo-in channels latticed Two lo-in channels, two 12-in plates . ^ , ^ Effective length, ,i2 oj d) J2 Is |l 11 art a.5 ll Cj2 ft 3^ . f^ J2 ^J-^ CS Q< rt'ft ri-Q, rt Qh -^o '0 <" •Si; -s.s la ^.B -Sa ^.a la il fl =2.1 10^ 1- '"' 0» cs *-* M : Two lo-in channels, two 14-in plates . w w OT w 4S w Effective length. c c2 c3 Is ft ^■3. ^^ •^? c3 0, M^ •§•? i-s c CJ.5 c 0.5 2 ^ c ^'0 6«N ^ ■' :2 2 4:k 10 f? "r a y-7 <-' fl 0-7 ^ C ai ^'% ^,S £"S ^•2 XI -v 6:;^ -Vcox 62"^ 6-^ '6T 6^ ro ro ro ro rn fO II 480 502 525 548 571 593 12 480 502 525 548 571 593 13 480 502 525 548 571 593 14 480 ■502 525 548 571 593 15 480 502 525 548 571 593 i6 480 502 525 548 571 593 17 480 502 525 548 571 593 i8 480 502 525 548 571 593 19 480 502 525 548 571 593 20 480 502 525 548 571 593 21 477 500 522 544 567 589 22 467 488 510 532 554 575 23 456 477 499 520 541 562 24 446 466 487 508 529 549 25 435 455 475 495 516 536 26 424 444 464 483 503 522 27 414 432 452 471 490 509 28 403 421 440 459 478 496 29 392 410 429 446 465 483 30 382 399 417 434 452 . 469 31 371 388 405 422 440 456 32 360 377 394 410 427 - 443 33 350 36s 382 398 414 430 34 339 354 370 385 401 416 35 328 343 359 373 389 403 Area, sq in 36.89 38.64 40.39 42.14 43.89 45.64 ^1-1. in* 757 ■ 814 873 932 994 I 056 1 ^i-i, in 4.53 4.59 4.65 4.70 4.76 4.81 1 72-2. in* 637 666 695 723 752 780 I »'2-2. in 4.16 4.15 4.15 4.14 4.14 4.13 ; Weight. ( lb per lin ft.. 125.5 131. 4 137.4 143.3 149.3 155.2 ; Safe load- values above the heavy line are for ratios of l/r not over 6o; those be- ' low the heavy line are for ratios not over 120 l/r * prom Pocket Companion, Carnegie Steel Company, J*ittsburgh, Pa, 638 StreBLgth of Columns, Posts and Struts Chap. Table XXV* (Continued). Safe Loads in Units of i ooo Pounds for lo-Inch Channel-Columns „ -H i );-"' ]2" . L. ' 1 "^ Allowable fiber-stress in pounds per square inch: 1 ^ r 0.)' 13 000 for lengths of 60 radii or under i ^ 8>^— ; -L " Reduced for lengths between 60 and 120 radii, by Formula (13), 1 i 5 = 19 000 — 100 l/r t ^ 1 u Weights do not include rivet-heads or other details _ 1 For values for l/r above 120, see notes on page 490 1 ; f V . J2 V .•^---u- ->|_ Effective Two lo-in channels, two 14-in plates 4$ 4s "S^ 'S^ 13 « length, s5 §J3 a p4 §3 ^ « ^ p. ^ a -s.a '^. c O'Y ^ a O'Y o.s ".13 ^s.2 £•7 -^.2 .Q^ ^ « ^\4. '^T "3^*^ •3,5 i^ %t: ^"m fO ro CO fO ro II 609 632 654 677 700 723 12 609 632 654 677 700 723 13 609 632 654 677 700 723 14 609 632 654 677 700 723 15 609 632 654 ■ 677 700 723 16 609 632 654 677 700 723 17 609 632 654 677 700 723 18 609 632 654 677 700 723 19 609 632 654 677 700 723 20 609 632 654 677 700 723 (502 624 647 669 691 714 21 22 588 610 632 654 675 697 23 575 596 617 639 660 681 24 561 582 603 624 644 665 25 547 568 588 608 628 648 26 533 553 573 593 612 632 27 520 539 559 578 596 616 28 506 525 544 563 581 599 29 492 511 529 547 565 583 30 479 496 514 532 549 567 31 465 482 500 517 533 550 32 , 451 • 468 485 502 517 534 33 437 454 470 487 502 S18 34 424 . 440 455 471 486 502 35 410 42s 441 456 470 485 Area, sq in 46.83 48.58 50.33 52.08 53.83 55.58 /i-|.in^ I 018 1080 I 144 1 209 . 1275 I 343 ri-i, in 4.66 4.72 4.77 4.82 4.87 4.92 /2-2. in^ . 788 816 845 874 902 931 ^2-2. in 4.10 4.10 4.10 4.10 4.09 4.09 Weight, lb per Un ft. 159-3 165.2 171. 2 177. 1 183. 1 189.0 Safe load- values abo^ re the heavy line are for ratios of l/r not over 60; those be- low the heavy line are or ratios not over 120 l/r ♦ From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. Tables of Safe Loads for Steel Columns 530 Table XXVI.* Safe Loads in Units of i ooo Pounds for 12-Inch Channel- Columns ;: -11 "|2 " '-i. Allowable fiber-stress in !in cT pounds per square inch: 1 M 13 000 for lengths of 60 radii or under =^^ L J. Reduced for lengths between 60 and 120 radii, by Formula (13), J 1 5 = 19 000 - 100 l/r l^ 1 k Weights do not include rivet-heads or other details i For values for l/r above 120, see notes on page 490 'S^ — ;;:t2 — ^ Two i2-in channels, latticed Two i2-in channels, two Effective length, ft 14-in plates -3 g ^3 1j OS «3 6-3 J2 a; (U •Sii 3.x CO 3i 8"" M ro JJ5 8 8 8 II 157 191 229 268 293 316 339 12 157 191 229 268 293 316 339 13 157 191 229 268 293 316 339 14 157 191 229 268 293 316 339 IS 157 191 229 268 293 316 339 16 157 191 • 229 268 293 316 339 17 157 191 229 268 293 316 339 18 157 191 229 268 293 316 339 19 157 191 229 268 293 316 339 20 157 191 229 268 293 293 316 316 339 339 21 22 23 157 157 191 229 2^5 259 253 190 186 225 220 290 283 312 305 334 326 155 24 152 182 215 248 277 298 319 25 149 178 210 242 271 291 312 26 146 174 205 236 265 284 304 27 142 ^Z^ 200 230 258 277 297 28 139 166 19s 224 252 271 290 29 136 162 190 218 246 264 282 30 133 158 185 212 239 257 275 31 129 154 180 206 233 250 268 32 126 ^50 175 200 227 243 260 33 123 146 170 194 220 2I0 253 34 120 142 165 188 214 246 35 117 138 160 182 208 223 238 Area, sq in 12.06 14.70 17.64 20.58 22.56 24.31 26.06 ^1-1. in4 256 288 323 359 658 730 803 ''1-1. m 4.61 4.43 4.28 4.17 5.40 5.48 5.55 V2. in* 244 279 316 351 415 444 473 ^2-2. m 4.50 4.36 4.23 4.13 4.29 4.27 4.26 Weight. lb per Un ft.. 50.4 59.4 694 79-4 76.7 82.7 88.6 Safe load-values abc /e the heavy line are for ratios of l/r not over 60; those below the heavy line ar e for ratios not over 120 l/r * From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. 540 Strength of Columns, Posts and Struts Chap. Table XXVI* (Continued). Safe Loads in Units of i ooo Pounds for 12-Inch Channel-Columns ^--"',v-i L ■ Allowable fiber-stress in pounds i 13 000 for lengths of 60 radii or unde ^pr Qnii;^r a Jnr^Vr t^ J" -J 1 r 1 ' -4-1 _J, Reduced for lengths between 60 and 120 radii, by | Formula (13). i S = 19 000 — 100 1/ r [^ 1 ^ Weights do not include rivet-heads or other details i — \ For values for l/r above 120, see notes on page 490 hn? 1^ C71 Effective Two i2-in channels, two 14-in plates '3 w Is 4^ 1 ^ II II length, J! P. S3 C 03 ^ a ^ ^ a o-v a o.-< ^ ^ j3 a'S ^5 :aZ ^^ 'S^^ 8 i""^ r^ ^- i(?"~^ i"^ II 362 384 396 419 441 464 487 12 362 384 396 419 441 464 487 13 362 384 396 419 441 464 487 14 362 384 396 419 441 464 487 15 362 384 396 419 441 464 487 16 362 384 396 419 441 464 487 17 362 384 396 419 441 464 487 18 362 384 396 419 441 464 487 19 362 384 396 419 441 464 487 20 21 22 23 362 362 384 384 396 396 419 441 464 487 418 409 400 440 431 463 453 485 474 464 3 3 55 47 377 369 387 378 421 443 24 3 39 360 370 390 411 432 453 25 3 32 352 361 381 401 422 442 26 3 24 344 352 372 392 412 431 27 T 16 335 344 363 382 402 421 28 3 08 327 335 354 372 391 410 29 3 00 318 326 344 362 381 399 30 2 92 310 318 335 353 371 388 31 2 84 302 309 326 343 361 377 32 1 77 293 300 317 333 350 367 33 2 69 285 291 307 323 340 356 34 2 61 277 283 298 314 330 345 35 2 53 268 274 289 304 320 334 Area, sq in 27.81 29.56 30.45 32.20 33.9s 35.70 37.45 I\-u^n* 878 954 910 986 I 063 I 142 I 223 ri-i, in 5.62 5.68 5-47 5-53 5.60 5.66 5.71 -^2-2, in< 501 530 537 565 594 622 651 r2-2. in. 4.24 4.23 4.20 4.19 4.18 4.18 4.17 Weight, lb per lin ft.. 94.6 TOO. 5 103.6 109.5 115. 5 121. 4 127.4 Safe load-values abo ve the heavy line are for ratios of l/r not over 60; those below the heavy line a re for ratios not ovqr 120 l/r • From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. Tables of Safe Loads for Steel .Columns 541 Table XXVI* (Continued). Safe Loads in Units of i ooo Pounds for 12-Inch Channel-Columns X-"'wt >-» J^ —rr Allowable hber-stress in pounds per square inch: J' "u/ 13 000 for lengths of 60 radii or under i -^- — 8j — ^ Reduced for lengths between 60 and 120 radii, by j — Formula (13), , 5=19 000 — 100 l/r 1-J. 1 As Weights do not include rivet-heads or other details 1 [— —X For \ ^alues for l/r above 120, s< je notes Dn page 490 W ,2 t 1 ^-—ii'-- — &i — 7 ■■ Two 12- in channels, two 14-in plates w W Ui w" M 73 w 4b ^ _w to ElTective '^ a3 -^n is -^^ -^^ 2 V IB length, §3 1 u H ^ ^ ^ r! ^ ^ ^ ti ^ p. ^ a ^ 0, ^a d u-v a u-v " d o--^ " d jQ"X ^.2 -^'5 ^.2 ^.5 ^^ jo-S jQ,« ^CON if 6'-^ 6? 6"" %b -^^ io'm CO ro CO CO ro fO J^. ro J II 502 52s 548 571 593 609 632 654 12 502 525 548 571 593 609 632 654 13 502 525 548 571 593 609 632 654 14 502 52s 548 571 593 609 632 654 IS 502 525 548 571 593 609 632 654 16 502 525 548 571 593 609 632 654 17 502 525 548 .571 593 609 632 654 18 502 525 548 571 593 609 632 654 19 502 525 548 571 593 609 632 654 20 21 502 525 548 571 593 609 632 654 498 521 543 565 588 601 623 645 22 487 509 531 . 553 575 587 609 631 23 476 497 518 540 56r 573 594 616 24 465 486 506 527 548 559 580 601 25 453 474 494 514 535 545 566 586 26 442 462 482 502 522 532 552 571 27 431 451 469 489 508 518 537 557 28 420 439 457 476 495 504 523 542 29 409 427 445 463 482 490 509 527 30 397 415 432 450 468 477 494 512 31 386 404 420 438 455 463 480 497 32 375 392 408 425 442 449 466 483 33 364 380 396 412 428 435 452 468 34 352 368 383 399 415 421 437 453 35 341 357 371 386 402 408 423 438 Area, sq in 38.64 40.39 42.14 43.89 45.64 46.83 48.58 50.33 h-u in* I 174 1258 I 340 I 424 I 509 1459 1544 1630 n-i, in 5.52 5.58 5.64 5.70 5.75 5.58 5.64 5.69 I2-2. in* 659 688 717 745 774 779 808 837 ''2-2, in 4.13 4.13 4.12 4.12 4.12 4.08 f.o8 4.08 Weight, lb per lin ft.. 131. 4 137.4 143.3 149.3 155.2 159.3 165.2 171. 2 Safe load- values al 30ve the heavy line are for ratios of l/r no t over 60; those below the heavy line are for ratios not over 120 l/r * From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. 542 "Strength, of Columns, Posts and Struts Chap. 14 Table XXVI* (Continued). Safe Loads in Units of i ooo Pounds for 12-Inch Channel-Columns L ^^ 7 1 e inch: Xi ^2"' Allowable fiber-stress in pounds per squai T% r^ .-i-. 13 000 for lengths of 60 radii or under i-'- J, Reduced for lengths between 60 and 120 radii, by | T Formula (13), 1 5 = 19 000 — 100 l/r 1-^ ' k Weights do not include rivet- heads or other details — — For values for l/r above 120, sec notes on page 490 Tv ,,2 V h"— 14 H Effective Two i2-in channels, two 14-in plates "o QJ |l Is 4'^ -Ss 4s 4^ length, §3 gjs §2 H g3 «l §3 ft rt 0. a ^ a a 05 » rs a rt e^ d^ -s.s 0"H •g.s -g.a -g.s -g.? -5.2 ■ ^s^ -Q.S ■£-^ £n- a± £n2 jOvfS Tp^n "S" »o1^ »o '-' 10 M ro ^ fO ro ro fo ^ ro II 677 700 723 745 768 791 814 12 677 700 723 745 768 791 814 13 677 700 723 745 768 791 814 14 677 700 723 745 768 791 814 IS 677 700 723 745 768 791 814 . 16 677 700 723 745 76S 791 814 17 677 700 723 745 768 791 814 18 677 700 723 745 768 791 814 19 677 700 723 745 768 791 814 20 21 677 700 723 745 768 791 814 668 689 712 734 757 779 802 22 653 674 695 717 739 761 783 23 637 658 679 700 722 743 765 24 622 642 663 684 704 725 746 25 607 626 646 667 687 707 728 26 591 610 630 650 670 689 709 27 576 594 614 633 652 672 691 28 561 578 597 616 635 654 672 29 545 S63 581 599 617 636 654 30 530 547 564 582 600 618 635 31 515 531 548 565 583 600 617 32 515 532 548 565 582 599 33 484 499 515 531 548 564 580 34 469 483 499 515 530 546 562 35 453 467 482 498 513 528 543 Area, sq in 52.08 53.83 SS.58 57.33 5908 60.83 62.58 /i-i, in* I 719 1808 1899 1992 2087 2183 2280 n-i, in 5. 74 5.80 5.85 5.89 5.94 5.99 6.04 /j-o, in* 865 894 922 951 980 I 008 1037 rj_2, in : 4.08 4.07 4.07 4.07 4.07 4.07 4.07 Weight, lb per liii ft.. 177. 1 183. 1 189.0 195.0 200.9 206.9 212.8 Safe load-values abo ve the heavy line are for ratios of l/r not over t K); those below the heavy line a re for ratios not over 120 l/r • From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. Tables of Safe Loads for Steel Columns 54d Table XXVI'* (Continued). Safe Loads m Units of i 000 Pounds for 12-Inch Channel-Columns ,.S"'"r i Ulowable fiber-stress in pounds nch: per square 1 ■ Vi 1 ' 13 1 ^ 1 .lof-^ 000 for lengths of 60 radii or under r^ _l Reduced for lengths between Formula (13), 60 and 120 radii .by 1 U, We S = 19 000 - 100// r 1 r^ i ights do not include rivet-heads or other details values for l/r above 120, see notes on page 490 r ,k -Tp-| Foi U .' _ — ig- ---►! Two i2-in channels. two i6-in plates w" /) w w' ' W ,- OT W cr w m ^ ,n w m jjn ^ Effective '^^ - "^^S 13^ •SS 13 jy 13S -^^ ^^ ■32 (U 7 723 749 762 788 814 840 19 6i 9 645 671 697 723 749 762 788 814 840 20 6i 9 645 671 697 723 749 762 788 814 840 21 6i 9 645 671 697 723 749 762 788 814 840 22 6i 9 645 671 697 723 749 762 788 814 840 23 24 25 6i 6i 9 645 9 645 671 671 697 697 723 723 749 749 762 762 788 814 840 787 772 813 797 838 822 ~6l 635 660 686 711 736 747 26 59 9 623 648 673 697 721 732 756 781 805 27 58 7 611 635 659 683 707 718 741 766 789 28 57 5 599 622 646 669 693 703 726 750 773 29 56 3 586 609 633 655 678 688 711 734 757 30 55 2 574 596 619 642 664 674 696 719 741 31 54 562 583 606 628 649 659 681 703 724 32 52 8 549 571 593 614 635 644 665 687 708 33 51 6 537 558 579 600 621 630 650 672 692 34 50 4 525 545 566 586 606 615 635 656 676 : 35 49 3 512 532 553 572 592 600 620 640 660 Area, sq in 47- 64 49 64 51.64 53.64 55.64 57.64 58.58 60.58 62.58 64.58 /i-i. in^ ~T1 81 I 678 I 777 1878 IQ80 2084 2015 2 IIQ 2225 2333 n-i, in 5. 76 5.81 5.87 5.92 5.97 6.01 5.87 5.91 5.96 6.01 72-2, in* I I 21 I 164 1206 1249 I 292 1334 1349 1392 1434 1477 ^2-2. in 4. 85 4.84 4.83 4.83 4.82 4.81 4.80 4.79 4.79 4.78 Weight, lb per lin ft.. 162 .0 168.8 175.6 182.4 189.2 196.0 199-2 206.0 212.8 219.6 Safe load- value s above the heavy line are for ra tios of llr not over i )o; tho se be- low the heavy lir le are for rt itios not over 120 l/r • From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. 644 Strength of Columns, Posts and Struts Table XXVI "*■ (Continued). Safe Loads in Units of i ooo Potmds for Z2-Inch Channel-Columns " 1 •v-^ '^J-'t D .„ , , /-. . i-r /\iiowaDie noer-stress in pounas per square men: 1 lOj' -^ T _1 13 000 for lengths of 60 radii or under Reduced for lengths between 60 and 120 radii, by -— 1 Formula (13), i 1 S = 19 000 — 100 1/ i A^ j ^ Weights do not include rivet-heads or other details 1 ij For values for l/r above 120, see notes on page 490 ! V ,J2 S^ ^---IQ >; Two i2-in channels, two i6-in pk Effective ites 4s -Ss ll Is -Z^ -^ ^ -^1 'a3 OT length, «t §5 §1 §« §5 §5 C eg CE ft cj f^ cS 0* a ^ rt 0. rt _ d 0, d _ (i p, d _, ciJ^ ^.S ^.S •g.s •s.s "'I oS •Ss ^ 0. ^^« jQ.^ jQ.® ^NPO £x £4 -^■^ £^ £.S -o-r -r ri ,lr 10 '^^ UT^ 10-^ ir; •-< lA5-< ITi m^ f<; ro fy^M re fO •-• fO f<^M ro II 866 892 918 944 970 996 I 022 I 048 1074 I 100 12 866 892 918 944 970 996 I 022 I 048 I 074 I 100 13 866 892 918 944 970 996 I 022 I 048 1074 I 100 14 866 892 918 944 970 996 I 022 I 048 I 074 I 100 15 866 892 918 944 970 996 I 022 1048 1074 I 100 i6 866 892 918 944 970 996 I 022 I 048 1074 I 100 17 866 892 918 944 970 996 I 022 I 048 1074 1 100 • i8 866 892 918 944 970 996 I 022 I 048 I 074 I 100 19 866 892 918 944 970 996 I 022 I 048 I 074 I 100 20 866 . 892 918 944 970 996 I 022 I 048 1074 I 100 21 866 892 918 944 970 996 I 022 I 048 I 074 I TOO 22 866 892 918 944 970 996 I 022 I 048 1 074 I 100 23 24 866 892 918 944 970 996 I 022 I 048 I 074 I 100 864 889 915 940 966 992 I 017 I 042 1068 I 093 25 26 847 830 872 854 897 922 947 972 997 I 022 1047 I 027 I 072 I 050 879 903 928 953 977 I 002 27 814 837 862 885 909 934 957 981 1006 I 029 28 797 820 844 867 891 914 937 961 985 I 007 29 780 803 826 848 872 895 917 941 964 986 30 764 785 808 830 853 876 897 920 943 965 31 747 768 791 812 834 857 878 900 922 943 32 730 751 773 794 81S 837 858 880 901 922 33 713 734 755 775 797 818 838 859 881 900 34 697 716 737 757 778 799 818 839 860 879 35 680 699 720 739 759 779 798 819 839 858 Area, sq in 66.58 68.58 70.58 72.58 74.58 76.58 78.58 80.58 82.58 84.58 h-i.in* 2443 2555 2668 2783 2901 3 020 3 141 3264 T389 3516 ri-u in 6.06 6.10 6.15 6.19 6.24 6.28 6.32 6.36 6.41 6.45 /2-2, in* I 520 1 562 I 60s 1648 1690 I 733 1776 I 818 I 861 I 904 r2-5. in 4.78 4.77 4.77 4.76 4.76 4.76 4.75 4.75 4.75 •4.74 Weight, lb per lin ft.. 226.4 233.2 240.0 246.8 '253.6 260.4 267.2 274.0 280.8 287.9 Safe load- values a bove the heavy line are for ratios of l/r not ov er 60; those below the heavy lin e are for ratios not over 120 / /r • From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. Tables of Safe Loads for Steel Columns 545 Table XXVII.* Safe Loads in Units of i ooo Pounds for 15-Inch Channel- Columns Li » » n , < /-i pounds per square inch: 1 "h TT- /iiiowanie iioer-stress in T 13 000 for lengths of 60 rad 'X- ii or under =i - - Reduced for lengths between 60 and 120 radii, by -^ Formula (13), ; i .S = 19 000 — 100 l/r i /^ 1 1 .A Weights do not include rivet-heads or other details . 1 ' ■ For values for l/r above 120 '^"" — , bcc lUJi-eb uii page 4y" 1 y ,k ^ r '--16 > Two i^in channels, latticed Two 15-in channels, two i6-in plates Effective (U (U i^ i ^iii j' ' ^j J ^ Two 15-in channels , two i6-in plates ^ Effective »2 w 0) OJ '% S P ^ S •SI length, g« C ct3. B^ C d gj3 H ft 03 a. <^7^ f^-o. rt ^ rt V! a ^ ci-^ -S.a ^ ^ M ^ »c a ^ ^ -c c M ^ ti «J d o-^ d o-v fl ^ i, -^'1 ^'1 '^.S Xi"^ -oi '^'1 ^N* ^ NpO "T j^ 'TX 1—1 spO i^^ r fO F\ ^- r^ II 491 517 528 554 580 606 632 12 491 517 528 554 580 606 632 13 491 517 528 554 580 606 632 14 491 S17 528 554 580 606 632 IS 491 517 528 554 580 606 632 16 491 517 528 554 580 606 632 17 491 517 528 554 580 606 632 18 491 517 528 554 580 606 632 19 491 517 . 528 554 580 606 632 20 491 517 528 554 580 606 632 21 491 517 528 554 580 606 632 22 491 517 528 5.54 580 606 632 23 24 491 491 517 517 528 554 580 606 632 527 552 578 604 629 617 :77.2sT * ■ , 482 507 517 542 567 592 26 473 498 507 531 555 580 605 27 464 488 497 520 544 .569 592 28 454 478 486 510 533 557 580 29 445 468 476 499 522 545 568 30 435 458 466 488 SIX 533 556 31 426 448 456 478 499 522 543 32 416 438 446 467 488 510 531 33 407 428 436 456 477 498 519 34 398 418 42s 446 466 487 507 35 388 408 415 435 454 475 494 Area, sq in 37.80 39-80 40.58 42.58 44.58 46.58 48.58 /i-i, in*..... 1 715 1847 I 861 1994 2 129 2 267 2406 n-i.in 6.74 6.81 6.77 6.84 6.91 6 98 7.04 /i-2. in* 875 917 930 973 I 016 I 058 I lOI ra-j.in • 4.81 4.80 4.79 4.78 4.77 4.77 4.76 Weight. lb per Un ft.. 127.2 134. c 138.0 144.8 151. 6 158.4 165 2 Safe load- values above the heavy line are for ratios of l/r not over 60; those below the heavy line are for ratios not over 120 l/r • From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. Tables of Safe Loads for Steel Columns 547 Table XXVII* (Continued). Safe Loads in Units of i ooo Pounds for 15-Inch Channel-Columns r^Q — -^ a^ Allowable fiber-stress in pounds per square inch: \ ^ r :i: 13 000 for lengths of 60 radii or under I Reduced for lengths between 60 and 120 radii, by Formula (13), 1 5 = 19 000 — 100 l/r M\ Weights do not include rivet-heads or other details 1 For values for l/r above 120, see notes on page 490 y ,h y\ 1<---16--- ^. Effective Two 15-in channels, two r6-in plates •SS <^ !^, is w -^1 -SS 4m length, ft it H C5 §1 g5 §5 Crt g- -^ vi XI ^ '^ B x: p< XJ c -s.^ X5 c! u.n <^ c ^ a *-*■?' CJ.w SI !o •^"i X) 2 ^•r ^ =0 U2NCfl j3 « i? 1'-- 1>T 6^ 'si 6- "^r^ "* ^ "^ 'f '* ■9^ 722 748 774 786 16 644 670 6q6 722 748 774 786 17 644 670 696 722 748 774 786 18 644 670 696 722 748 774 786 19 644 670 696 722 748 , 774 .786 20 644 670 696 722 748 774 786 21 644 670 696 722 748 774 786 22 644 670 696 722 748 774 786 23- 24 644 670 696 722 748 774 786 639 665 690 715 741 767 777 25 627 651 677 701 727 752 761 26 614 638 663 687 712 737 746 27 602 625 649 673 697 721 730 28 589 612 636 6S9 683 706 715 29 577 599 622 645 668 691 699 30 564 586 609 631 653 676 684 31 551 573 595 616 639 661 668 32 539 560 581 602 624 646 653 33 526 517 568. 588 609 630 637 34 514 534 554 574. 595 615 622 35 501 520 541 560 580 600 606 Area, sq in 49-52 51.52 53-52 55.52 57.52 59-52 60.48 /i-i,in« 2 322 2 461 2 602 2 746 2891 3039 2946 ''i-i. m 6.85 6.91 6.97 7.03 7.09 7.15 6.98 /2-2.in* I 106 I 149 I 192 I 234 I 277 I 320 1322 r2-2, m 4.73 4.72 4.72 4.71 4.71 4.71 4.68 Weight, lb per lin ft.. 168.4 175.2 182.0 188.8 195-6 202.4 205.6 ' Safe load-values abo ve the heavy line are for ratios of l/r not over 60; those below the heavy line ar e for ratios not over 120 l/r *From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. 648 Strength of Columns, Posts and Struts Chap. 14 Table XXVII* (Continued). Safe Loads in Units of i ooo Pounds for 1 5-Inch Channel-Columns Allowable fiber-stress in pounds per square inch: T>] r ^'T^ 13 000 for lengths of 60 radii or under i -- 1 Reduced for lengths between 60 and 120 radii, by Formula (13), ,i 5 = 19 000 — 100 l/r ♦ r^ ^ Weights do not include rivet-heads or other details i For values for l/r above 120, see notes on page 490 !V J2 v! W 'IQ- -5- Effective Two iS-in channels, two i6-in plates 4 s 4 s Oi -* ^•;ii' "^M ■* Tj- ^ ■^ II 812 838 864 890 916 942 968 12 812 838 864 890 916 942 968 13 812 838 864 890 916 942 968 14 8X2 838 864 890 916 942 968 15 812 838 864 890 916 942 968 16 812 838 864 890 916 942 968 17 812 838 864 890 916 942 968 18 812 838 864 890 916 942 968 19 812 838 864 890 916 942 968 20 812 838 864 890 916 942 968 21 812 838 864 890 916 942 968 22 812 838 864 890 916 942 968 23 24 812 838 864 890 916 942 968 802 827 853 879 904 930 956 25 786 811 836 861 886 912 937 26 770 794 819 844 868 893 918 27 754 778 802 826 850 874 898 28 738 761 785 808 832 856 879 29 722 745 768 791 814 837 860 30 705 728 751 773 796 818 841 31 689 711 734 756 778 800 822 32 673 695 716 738 760 781 803 33 657 678 699 720 741 763 784 34 641 662 682 703 723 744 764 35 625 645 665 685 705 725 745 Area, sq in 62.48 64.48 66.48 68.48 70.48 72.48 74.48 A-i. in* 3094 3244 3396 3550 3707 3865 4026 ^i-j.in 7.04 7.09 7.15 7.20 7.2s 7.30 7.35 I2-2, in* 1365 1 408 I 450 1493 1536 1578 I 621 ^2-2. in 4.67 4.67 4.67 4.67 4.67 4.67 4.67 Weight, lb per lin ft.. 212.4 219.2 226.0 232.8 239-6 246.4 253.2 Safe load-values abo ve the heavy line are for ratios of l/r not over 60; those below the heavy line a re for ratios not over 120 l/r • From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. Tables of Safe Loads for Steel Columns 549 Table XXVII* (Continued). Safe Loads in Units of i ooo Pounds for xs-Inch Channel-Columns T^T-i r^ 1 (^ Allowable fiber-stress in pounds per square inch j :-iii'--^ 13 000 for lengths of 60 radii or under '^ - .J_.. 1 Reduced for lengths between 60 and 120 radii, by — =• Formula (13), 1 i 5 = 19 000 — 100 l/r lA 1 — 1 — ■^ Weights do not include rivet-heads or other detai Is For values for l/r above 120, see notes on page 490 IV J2 V [<— -18- ->i Two i5-in channels, two i8-in plates - ^ « w" > w w w w Effective length, II 11 s| Is C 05 Is ^1 Is ft cj r:; ci 0< '^'^ a Oi f^":^ rt';3 rt O4 d'Ti ^ ^ ■Ss ^ ^ -s.s M ^ ^ ^ -^ d ^ ^ o ti " a ^ rt ^ ti 0.5 c ^"t ^ L ^•v ^ i XI "t rO"? Xi 1 Effective length, Two 15-in channels, two i8-in plates II S4 4b ^1 4'^ a 0, |l u xi a J ^ -g.s ^ ^ -^ a X 0, X! c! -^ a O'Y a ^ fl o.n ^•? O-Y 0.5 " -^xS ^•r J3^2 JD-V JD i> -OS. Xi-fo ^ -4« 65 %T ^-^ It 6-^ 4? 6"" 6'^ fO ro rr ■^ ^ Tt ■«* II 648 677 686 715 745 774 803 832 12 648 677 686 715 745 774 803 832 13 648 677 686 715 745 774 803 832. 14 648 677 686 715 745 774 803 832 15 648 677 686 715 745 774 803 832 i6 648 677 686 715 745 774 803 832 17 648 677 686 715 745 774 803 832 i8 648 677 686 715 745 774 803 832 19 648 677 686 715 745 774 803 832 20 648 677 686 715 745 774 803 832 21 648 677 686 715 745 774 803 832 22 648 677 686 715 745 774 803 832 23 648 677 686 715 745 774 803 832 24 648 677 686 715 745 774 803 832 25 648 677 686 . 715 745 774 803 832 26 648 677 686 715 745 774 803 832 27 28 29 648 677 686 715 745 774 803 832 643 632 671 660 680 668 708 736 764 793 821 807 696 723 751 779 30 621 649 657 684 711 738 766 793 31 610 637 645 672 698 725 752 779 32 599 626 634 660 685 712 738 764 33 589 615 622 648 673 698 725 750 34 578 603 610 636 660 685 711 736 35 S67 592 599 624 648 672 698 722 Area, sq in 49 83 52.08 52.77 55.02 57.27 59-52 61.77 64.02 Ii-i.in* 2470 2627 2525 2682 2841 3002 3166 3332 ri_i, in 7.04 7.10 6.92 6.98 7.04 7.10 7.16 7.21 -^M. in* IS14 1575 1589 I 649 I 710 I 771 1832 1892 r2-8. in Weight. 5. 51 5.50 5.49 5.48 5.46 5.45 5.45 5.44 lb per lin ft.. 169.5 177. 1 179-5 187. 1 194.8 202.4 210. 1 217.7 Safe load- values above the heavy line are for ratios of l/r not over 6o ; those below the heavy line are for ratios not over 120 l/r ^1 * From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. Tables of Safe Loads for Steel Columns Table XXVII* (Continued). Safe Loads in Units of x ooo Pounds for X5-Ineh Channel-Columns J:-"Kr--i r- cr^ ' ^^ Allowable ftber-stress in pounds per square inch: 13 000 for lengths of 60 radii or under 1 ^ r 1 -'Xi Reduced for lengths between 60 and 120 radii, by- ■ 5! 1 M5 ■ — 4 Formula (13), tH 1 5=19 000 — 100 l/r i,^ 1 ^. Weights do not include rivet-heads or othei* details — 1 — For values for l/r above 120 , see notes on page 490 •;^..i8.k...x' Effective Two 15-in channels, two i8-in plates is i'& i^ •s'l -% s •ss length, §1 g^ §:§ §1 gs «l ft d ^ rt ft w ^ rt P* rt ^ rt^ CO ^ ^ a -S.a ^ C! •s.s ^ rt •S.s ^ a o-Y 0-^ o-S o.« ^ *-• 10 'm' in ^ >0 M 10 "^ >0 M ■^ Tf "* -"T II 841 871 900 929 958 988 I 017 12 841 871 900 929 958 988 I 017 13 841 871 900 929 958 988 I 017 14 841 871 900 929 958 938 I 017 15 841 871 900 929 958 988 I 017 16 841 • 871 900 929 958 988 I 017 17 841 871 900 929 958 988 I 017 18 841 871 900 929 958 988 I 017 19 841 871 900 929 958 988 I 017 20 841 871 900 929 958 988 I 017 21 841 871 900 929 958 988 I 017 22 841 871 900 929 958 988 I 017 23 841 871 900 929 958 988 1 017 24 841 871 900 929 958 988 I 017 25 841 871 900 929 958 988 I 017 26 841 871 900 ■929 958 988 I 017 27 28 841 871 900 929 958 987 970 I 015 ^29 857 885 913 942 29 814 843 870 897 926 953 980 30 800 828 855 882 909 936 963 31 786 813 839 866 893 919 945 32 771 798 • 824 850 877 902 928 33 757 783 809 834 860 885 911 34 743 768 793 818 844 868 893 35 728 754 778 802 827 852 876 Area, sq in 64.73 66.98 69.23 71.48 73.73 75.98 78.23 /i-i.in* 3 221 3387 3556 3727 3900 4076 4 255 ri-i, in 7.05 7. II 7.17 7.22 7.27 7.32 7.37 ^5^2. in* 1903 1964 2 025 2086 2 146 2 207 2268 ^8-2. in 5.42 5.42 5. 41 5.40 5.40 5.39 5.38 : Weight. Hb'per lin ft.. 220.1 227.7 235.4 243.0 250.0 258.3 266.0 Safe load-values abo ve the heavy line are for ratios of l/r not over 60; those below the heavy line ai e for ratios not over 120 l/r * From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. Strength of Columns, Posts and Struts Chap. 14 Table XXVU* (Continued). Safe Loads in Units of i ooo Pounds for x 5-Inch Channel-Columns X uW-, 1 1^ ..L. J. J ! \ 18'i-?.., -tl Allowable fiber-stress in pounds per square inch' 13 000 for lengths of 60 radii or under Reduced for lengths between 60 and 120 radii, by Formula (13), 5 = 19 000 — 100 l/r Weights do not include rivet-heads or other details For values for l/r above 120, see notes on page 490 Effective length, ft Two is-in channels, two i8-in plates is 4S 1 J^M '^'m I 105 I 134 I 105 I 134 I 105 I 134 I IDS 1 134 1 105 I 134 1 105 I 134 I 105 I 134 I 105 I 134 I 105 1 134 I 105 I 134 I 105 I 134 I 105 I 134 I 105 I 134 I 105 I 134 I 105 I 134 I 105 I 134 §1 Gi3 0/ to 13 14 IS 16 17 18 19 VI 24 25 26 27 H«.i 28 0-29 i.' 30 uc 31 i^-.V 32 ??;33 3^1 35 I 046 I 046 I 046 I 046 I 046 I 046 I 046 I 046 1 046 I 046 I 046 I 046 I 046 I 046 I 046 I 046 1075 1075 1075 I 075 1075 1075 1075 1075 I 075 1075 1075 1075 I 075 1075 1075 1075 I 163 I 163 I 163 I 163 I 163 I 163 I 163 I 163 I 163 I 163 I 163 I 1^13 I 163 I 163 I 163 I 163 I 222 I 222 I 222 I 222 I 222 I 222 I 222 I 222 1 222 I 222 I 222 I 222 I 222 I 222 I 222 I 222 1044 I 026 I 009 991 973 955 937 919 901 1073 I 102 I 054 I 083 1 036 I 064 I 017 I 045 999 I 026 980 I 007 962 988 943 969 925 950 1 131 I 112 I 092 I 073 I 053 I 034 I 014 995 975 I 159 I 139 I 119 1099 1079 1059 1039 I 019 999 I 195 I 174 I 153 I 132 I III I 090 I 069 I 280 I 280 I 280 I 280 I 280 I 280 I 280 I 280 I 280 I 280 I 280 I 280 I 280 I 280 I 280 I 280 I 253 I 231 I 208 I 186 I 164 I 142 I 120 Weight, 80.48 4436 7.42 2329 5. 38 273.6 82.73 4619 7-47 2389 5.37 281.3 84.98 4805 7.52 2450 5-37 288.9 87.23 89.48 4 994 7.57 2511 5.37 5185 7.61 2572 5.36 296.6 304.2 93.98 5 575 7.70 2693 5.35 319. 5 98. 4S 5 976 7.79 281S 5.35 334.8 - Safe load-values above the heavy line are for ratios of l/r not over 60; those below the heavy line are for ratios not over 120 l/r * From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. Tables of Safe Loads for Steel Columns 553 Table XXVII* (Continued). Safe Loads in Units of i coo Pounds for 15-Inch Channel-Columns ^ f ^ Allowable filler-stress in 13 000 for lengths of 60 rad Reduced for lengths betwe Formula (13), S = 19 000 Weights do not include rivet For values for l/r above 120 e inch: idii, by ails 490 >- < F ..L ii or under en 60 and 120 k — 100 l/r -heads or other det see notes on page > '. ' . . ' ^ I2 ^ Effective length, Two 15-in channels Two 15-in, 45-lb channels 35 lb 45 lb i 1= Ceo SJ%. 1 s. 03 M fe ^ m n5 f^ fe M II 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 I 340 I 340 I 340 I 340 I 340 1340 1340 1340 1340 1340 I 340 I 340 1340 1340 1340 I 340 I 408 1408 I 408 I 408 1408 1408 I 408 I 408 I 408 1408 I 408 I 408 1408 I 408 1408 I 408 I 485 1485 1485 1485 1485 1485 1485 1 485 1 485 1485 1485 1485 1485 1485 1485 1485 1547 I 547 I 547 I 547 I 547 1547 I 547 1547 I 547 1547 1547 I 547 I 547 I 547 I 547 I 547 1547 1547 1547 I 612 I 612 I 612 I 6X2 1 612 I 612 I 612 I 612 I 612 I 612 1 612 I 612 I 612 I 612 I 612 I 612 I 612 I 612 I 612 I 677 1677 1677 I 677 1677 1677 1677 1677 I 677 1677 1677 I 677 1677 1677 1677 1677 1677 I 677 1677 I 742 I 742 I 742 1 742 1742 1.742 1742 1742 1742 1742 I 742 I 742 I 742 I 742 I 742 1742 1742 1742 I 742 I 331 1307 I 284 . 1394 1369 1344 1 465 I 439 I 413 30 31 32 33 34 35 I 261 I 238 I 214 I 191 I 168 I 145 I 320 I 295 I 270 1246 I 221 I 197 1387 I 361 1335 I 309 I 283 I 257 1543 I 519 1495 I 471 I 447 1424 I 607 1582 1557 1532 I 507 I 482 I 670 1644 I 618 I 592 1566 I 540 1735 1708 I 681 1654 I 627 I 600 Area, sq in 103.08 108.33 114.23 118.98 123.98 128.98 133.98 /i-i.in* Ti 1, in 6037 7.65 2919 5.32 6 123 7.52 3 021 5.28 6233 7.39 3148 5.25 6397 7.33 4 240 5.97 404.5 6843 7.43 4407 5.96 7300 7.52 4 573 5-95 7769 7.61 4 740 5.9s /2-2, in* ;'2 2t in Weight, lb per lin ft.. 350. 5 368.4 388.4 421. 5 438.5 4SS.5 Safe load-values above the heavy line are for rati below the heavy line are for ratios not over 120 l/r Ds of l/r not over 6 0; those * From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. 554 Strength of Columns, Posts and Struts Chap. 14 Table XXVU* (Concluded). Safe Loads in Units of i ooo Pounds for is-Inch Channel-Columns 1 |3 are inch: radii, by letails e 490 Allowable nber-stress m pounds per squ 13 000 for lengths of 60 radii or under Reduced for lengths between 60 and 120 Formula (13). S = 19 000 - iQo//r Weights do not include rivet-heads or other c For values for l/r above 120, see notes on pag >- > j F k. < ' r I2 ^ Two 15-in, 45-lb channels Effective length, Is. txfy mi nS P ^ M 1 S II v.- 14 i 15 s^r,..i6i ., '.: 20 '^'.\ ^I >24 25 26 27 28 29 I 807 r I 807 r, I 807 I 807 I 807 1807 p I 807 l\ I 807 :■■ I 807 1807 1807 I 807 \i , I 807 I 807 I 807 I 807 I 807 I 807 I 807 1872 I 872 1872 I 872 1872 1872 I 872 1872 I 872 1872 1872 1872 1872 I 872 1872 I 872 I 872 I 872 I 872 1937 I 937 I 937 I 937 I 937 1937 I 937 I 937 I 937 I 937 I 937 I 937 I 937 I 937 1937 1937 1937 I 937 I 937 2002 2 002 2 002 2 002 2 002 2002 2 002 2002 2 002 2 002 2002 '2 002 2 002 2 002 2 002 2002 2 002 2 002 2 002 2067 2 067 2067 2067 2 067 2 067 2 067 2 067 2067 2 067 2 067 2067 2 067 2067 2 067 2 067 2067 2 067 2067 2 132 2 132 2 132 2132 2132 2 132 2132 2 132 2132 2 132 2 132 2 132 2 132 2132 2 132 2 132 2 132 2 132 2132 30 . 31 32 33 34 35 1798 I 770 I 742 I 714 . 1686 I 658 1863 1834 1805 I 776 I 747 I 718 I 926 1896 1866 1836 1806 1775 1 991 1 960 1929 1897 1866 1 835 2054 2 022 1989 1957 1925 1893 2 118 2085 2 052 2 019 1985 1952 Area, sq in 138.98 143.98 148.98 153.98 158.98 163.98 10846 8.13 5740 5.92 A-i, in* ri_i, in J^2-2, in* ^2-2. in 8251 7.70 4907 5.94 8744 7.79 5073 5.94 9251 7.88 5 240 5.93 506.5 9770 7.97 5 407 5.93 10 301 8.05 5 573 5.92 Weight, lb per lin ft.. 472.5 489. 5 523.5 540.5 557.5 Safe load- values abo\ below the heavy line ar -^e the heavy line are for ratios of l/r not ovei e for ratios not over 120 l/r " 60: those • From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. General Principles of the Flexure of Beams 555 CHAPTER XV .,, ,;, ji,. STRENGTH OF BEAMS AND BEAM GIRDERS. FRAM- ING AND CONNECTING STEEL BEAMS By CHARLES P. WARREN LATE ASSISTANT PROFESSOR OF ARCHITECTURE, COLUMBIA UNIVERSITY 1. General Principles of the Flexure of Beams Definitions. A structural member placed in a generally horizontal position upon two or more supports or projecting from some other construction is called a BEAM. A GIRDER is a beam carrying smaller or secondary beams. A canti- lever BEAM is a beam supported at the middle, or having one end fixed, as in a wall, and the other end free; or it is the part of a beam which overhangs, or projects, beyond a support. A simple beam is one which rests upon two sup- ports, one at each end. A continuous beam rests upon more than two supports. The distance between the supports of a simple beam, or, when so specially desig- nated from center to center of the bearings, is the span. It is usually designated by l. The loads on beams are either uniformly distributed or concen- trated. A uniformly distributed or uniform load includes the weight of the beam itself and any load spread evenly over it, such as the weight of a wall. Uniform loads are estimated by their intensity per unit of length of the beam, in pounds per linear foot. A uniform load per linear foot is represented by w, and the total uniform load by wl or W. A concentrated load is a single applied weight, such as a column and its load, or the load from another hJeam, and iS designated hy P. Stresses and Deformations. A load on a simple beam causes the fibers to bend or deflect, and eventually to break across, or in other words, a load induces transverse or flexural stresses in the fibers. Since it is impossible to bend or deflect a simple beam without causing a shortening of the fibers on the upper or concave side and an elongation of the fibers on the lower or convex side, a load on a beam causes compression in the upper fibers and tension in the lower fibers, while between the two there is a neutral layer or surface of fibers which is unchanged in length and which is called the neutral surface of the beam. In a cantilever beam the reverse is the case, the upper fibers being in tension and the lower ones in compression. Laws Determined by Experiment. From experiments it has been found that the amount of elongation or shortening of any fiber is directly propor- tional to its distance from the neutral surface of a beam; hence, if the elastic limit is not exceeded, the stresses, also, are proportional to their distances from this neutral surface. The trace of the neutral surface on a cross-section of a beam is called the neutral axis of the cross-section. Within the elastic limit of a material the neutral surface passes through the centers of gravity of the cross-sections of a beam for all materials. Bending Moments and Resisting Moments.* To determine the strength of any beam to resist the effects of any load or series of loads, two things must * See, also, Chapter IX, pages 324 and 325. .jjiO oi ^td 556 Strength of Beams and Beam Girders Chap. 15 be determined: first, the moment or moments of the external destructive force or forces tending to bend and break the beam, which is called the maximum BENDING moment; and, secondly, the moments of the combined resistances of all the libers in the dangerous section of the beam to being broken, which, in their summation, are called the moment of resistance or the resisting moment. ' The Methods of Finding the Bending Moments for any load or series of loads are explained in Chapter IX. The moment of resistance is equal to the SECTION-MODULUS or section-factor, denoted by Ijc, multiplied by the unit stress on the outermost fiber of the material, denoted by 5", and it equals the bending moment. Hence M = Sljc (i) This is known as the flexure-formula and it is the fundamental formula for designing beams. Formulas for finding the section-moduli of common shapes are given in Chapter X, and the values of Ijc or the section-moduli of the standard rolled shapes, are given in the tables in the same chapter. The Coefficient of Strength,* sometimes given in tables of steel beams, is the maximum distributed load that a beam of one foot span would support without producing a fiber-stress exceeding the safe limit, generally i6 ooo lb per sq in. As the strength of a beam varies inversely as its span, the safe load for any span may be obtained by dividing this coefiicient by the span in feet. I , Factors of Safety. In order that a beam shall just be able to carry a load and not break, that condition of equilibrium must exist, in which the maxi- mum bending moment in the beam is equal to the section-modulus multiplied by the ultimate strength of the material. In order that a beam may be abundantly safe to carry a given load, the product of the section-modulus by the ultimate strength of the material must be several times greater than the maximum bending moment; and the ratio which this product bears to the maximum bending moment, or which the breaking-load bears to the safe LOAD, is known as the factor of safety, that is, ultimate strength Factor of safety = • — working stress Ultimate Strengths and Safe Fiber-Stresses. By the strength of the MATERIAL is meant a certain constant quantity which is determined by experi- ment, and which is known as the ultimate breaking strength. This value is of course different for each material. Table I gives the values of this constant divided by the factor of safety, or in other words, the working stress, for most of the materials used in building-construction. The section-moduli multiplied by these values will give the safe resisting moments for the beams. The values of S in Table I for steel are about one-fourth those of the breaking- loads; for cast iron, about one-sixth; for average specimens of wood, one-sixth; and for stone and concrete, one-tenth. The safe compressive strength of cast iron for the compression-side of beams is i6 ooo lb per sq in, in the New York Building Code. This is considered too high by some engineers and the author recommends lo ooo lb per sq in. This value has been used in calculating the safe loads for cast-iron columns. (See Chapter XIV, page 461.) The safe loads for the steel shapes given in the tables in this chapter are all computed ♦ The values for coeflficients of strength have been omitted from most of the tables, following the policy of some of the latest handbooks, as the safe loads for beams, for example, can be as readily determined from the data of the tables directly, as by the process of dividing such coefficients by the spans. See, however, pages 586 to 591 and 623 to 628. General Principles of the Flexure of Beams 657 )n the value of i6 ooo lb per sq in for S, but these full loads should be used vith caution, and reduced when necessary to satisfy any unusual conditions. For riveted steel girders 14 000 lb per sq in was the value formerly given to 5, mi the usual value now is 16 000 lb per sq in. Table I. Safe Unit Fiber-Stresses, S, for Flexure of Beams * ft is to be noted that these are average values, especially those for wood. For allowable higher stresses for timber, see also, notes on pages 628, 637 and 647- Materials Wood unseasoned f Cast iron, tension-side. . Cast iron, compression-side Wrought iron (rolled beams) Steel (rolled beams) Steel (riveted girders) both flanges Steel (pins, rivets and bolts) Cedar Chestnut Cypress Douglas fir Elm Hemlock Locust Long-leaf yellow pine Norway pine Values of S, lb per sq in 3000 16 000 12 000 16 000 16 000 24 000 700 800 800 I 000 900 600 I 200 I 200 800 Materials Wood unseasoned f Values of lb per sq in Redwood, California Short-leaf yellow pine Spruce White oak White pine Bluestone flagging (North River) Brick (common) Brickwork (in cement)... Granite (average) Limestone (average) Marble (average) Sandstone (average) Slate (average) Concrete (Portland) 1:2:4 Concrete (Portland) 1:2:5 Concrete (natural) 1:2:4- Concrete (natural) 1:2:5. 750 I 000 700 I 200 700 305 50 30 180 145 125 no 400 30 * For a comparison of values given in different building laws see Table XVII, page 648, Chanter XVI. Compare, also, with Table XVI, page 647, Chapter XVI. For ultimate stresses for woods, see Tables XVIII and XIX, pages 650 and 651, Chapter XVI. For safe loads for unit beams, see Tables II and III, page 628, Chapter XVI. t Add from 30 to 40% for seasoned, protected timber, used without impact. Beams Unsymmetrically Loaded or of Irregular Cross-Section. There are certain loadings and cross-sections of beams that occur most frequently in building-construction, and for which tables have been worked out that give the safe loads directly; but for a beam unsymmetrically loaded, or for a beam of irregular cross-section, it is impossible to compute tables for strength, as in each case the values must be computed by determining either the section-modulus, I/c required to resist the maximum bending moment, or the maximum bend- ing' moment that may be allowed for a given value of the section-modulus. General Formulas for the Flexure of Beams.* The general formula for any beam in a state of flexure under any system of loading is Maximum bending moment in inch-pounds = section-modulus X S or Also . . It maximum bending moment m in-lb Section-modulus = ^ I/c = Mm^/S or (2) (2)' (3) (3)' • See, also, Chapters IX. X and XVI. 558 Strength of Beams and Beam Girders Chap. 15 If the bending moment is computed in foot-pounds, these formulas become section-modulus X S or and Maximum bending moment = Section-modulus Mmax= SI / 12 C 1 2 X maximum bending moment (4) (4)' (5) l/c= 12 i/max/5 (5)' By substituting for the bending moments their values in terms of the loads and the spans, the following formulas which apply to beams of any cross-section are readily deduced. 2. Formulas for Safe Loads for Beams for Dififerent Conditions of Loading and Support I/c =• the section-modulus; S = the safe unit fiber-stress in pounds per square inch; W = the total uniform load in pounds; P = the concentrated load in pounds; / = the span in feet. Values of l/c for the various shapes and sizes of structural-steel shapes are given in the tables of Chapter X. Case I Beam Fixed at One End and Loaded with a Concentrated Load P, Near the Free End (Fig. 1). From Formula (4)', MraAX = SI/ 12 C From Case I, Chapter IX, ^/max = PI Hence PI = SI/12 c and the safe load in pounds is P = SI/12 cl Load and the section-modulus is I/c = 12 Pl/S Example i. A steel T bar is fixed at one end in a brick wall, and loaded at the other end with 600 lb, the distance / being 4 ft. What is the size of the bar required to support the load with safety? (In all examples the weights of the beams are neglected, unless particularly mentioned.) Solution. Allowing 16 000 lb per sq in for the value of S, Formula (6)' gives l/c = (12 X 600 X 4)/i6 000 = 1.8 The next step is to ascertain what T bar has a section-modulus equal to 1.8. In Table XIV, page 369, the nearest section-modulus to this is i .9, correspond- ing to a 3 by 4 by H-in T bar. ^For an I beam, by Table IV, page 355, l/c = 1.8, the same as for the T bar, and calls for a 3-in 6.5-lb I beam. Fig. 1. Cantilever Beam, near Free End (6) (6)' Formulas for Safe Loads for Beams, etc. Case II 650 Beam Fixed at One End and Loaded with a Uniformly Distributed Load W (Fig. 2). From Formula (4)' Mmi.x== SI/12C From Case II, Chapter IX, Mu,ax=lf//2 Hence Wl/ 2== SI /12 c and the safe load in pounds is W=^Sl/^cl (7) and l/c = 6 Wl/S (7)' Fig. 2. Cantilever Beam. Dis- tributed Load over Entire Span Example 2. What is the size of a can- tilever steel I beam required to carry a uniformly distributed load of 150 lb per ft over a length of 6 ft? Solution. W = 150 X 6= 900 lb. Substituting in formula (7)', ^ . 6 X 900 X 6 I c = — = 2.02s 16 000 In Table IV, page 355, the nearest section-modulus to this is 1.9, which is that of a 3-in 7.5-lb beam, the heaviest of that depth. However, as the lightest 4-in beam, also, weighs 7.5 lb per ft it probably would be selected be- cause of its greater stillness, although its section-modulus is 3, still greater than required. Case III Beam Supported at Both Ends and Loaded with a Concentrated Load at the Middle (Fig. 3). From Formula (4)' Afm»x= SI /12 c From Case IV, Chapter IX, l/max = PI/ 4 Hence P//4 = 57/12 c and the safe load in pounds is P = Sl/3cl (8) and l/c = 3Pl/S (8)' P Fig. 3. Simple Beam. Load at Middle of Span Example 3. What steel I beam will safely support a concentrated load of 7 tons applied at the middle of a 15-ft span? Solution. P= 7 tons= 14000 lb. Substituting in formula (8)', 3X 14000X 15 /A = 16000 39-3 Referring again to Table IV, page 355, it is seen that a 12-in 35-lb beam has 560 Strength of Beams and Beam Girders Chap. 15 a section-modulus of 38, while a 12-in 40-lb beam, the next larger size, has a section-modulus of 44.8. The 35-lb beam, however, would undoubtedly be safe. Case IV Beam Supported at Both Ends and Loaded with a Uniformly Distributed Load (Fig. 4). Mm&x= SI /12 c i/max = Wl/S Wl/S = Sl/l2C W = 2 SI/ 3 cl (9) Fig. 4. Simple Beam. Distributed Load over Entire Span From Formula (4)' From Case V, Chapter IX, Hence and the safe load in pounds is ancf l/c = 3Wl/2S (9)' example 4. What steel I beam will safely carry a uniformly distributed load of I 000 lb per ft over a span of 25 ft? Solution. W = wl== I 000 X 25 = 25 000 lb. Substituting in Formula (9)', . 3X25000X25 ^A = Tr~r- = 58.6 2 X 16000 From Table IV, page 354, the nearest section-modulus is 58.9, which is that of a 15-in 42-lb beam. Case V Beam Supported at Both Ends and Loaded with a Distributed Load Over a Part of the Span (Fig. 5). Fig. 6. Simple Beam. Distributed Load over Part of Span In this case the load is generally given, and the problem is to determine the Bize of the required beam. This can be done accurately only by computing Formulas for Safe Loads for Beams, etc. 561 the maximum bending moment as explained for Case VIII, Chapter IX, and substituting the value thus found in Formulas (3)' or (5)'. Example 5. What steel I beam will safely carry a uniformly distributed load of I 200 lb per ft, over part of the span, beginning at a point 5 ft from the left reaction and extending over a distance of G ft, the span of the beam being 18 ft? Solution. The first step is to find the point of maximum bending moment, which is the point ol no shear. Obviously the maximum shear is just at the right of the reaction nearest the load, which in this case is the left reaction. To find the left reaction (see Chapter IX, page 324) the center of moments is taken at the right reaction and the equation of moments is RiXiS it — (i 200 lb X 6 ft) X 10 ft = o. 18 i?i = 72 000 and Ki = 4 000 lb. The shear just at the right of Ri is therefore +4 000 lb which, if the weight of the beam itself is not considered, remains unchanged for every section of the beam between the left reaction and the uniformly distributed load of i 200 lb per ft. From there on in passing to the right, the shear is diminished at the rate of i 200 lb per ft; and it becomes zero, therefore, at a point 4000 Ib/i 200 lb per f t = ss ft to the right of the 5-ft point. Hence the point of no shear and consequently the point of maximum bending moment is at 5 ft + 3-3 ft, or 8.3 ft, from the left end. The equation for the maximum bending moment at this point is, therefore, Mraax = 4 000 lb X 8.3 ft - (i 200 lb X3-3 ft) X 3.3/2 ft = 33 200 ft-lb — 6 534 ft-lb = 26 666 ft-lb, or 319 992 in-lb From Formula (3), I/c = 319 992 in-lb/i6 000 lb per sq in = 20. From Table IV, page 355, the nearest section-modulus corresponding to this is 20.4, that of a 9-in 25-lb beam. A lo-in 25-lb beam, however, being stronger and stiller, would probably be used. The lo-in 2 2. 2 5 -lb beam is what is termed a sup- plementary BEAM. (See Case VIII, Chapter IX, and pages 352 and 353.) Case VI Beam Supported at Both Ends and Loaded with a Concentrated Load, not at the Middle (Fig. 6). iniiflrh'iV rti -s ' Fig. 6. Simple Beam. Concentrated Load at any Point From Formula (4)', From Case VI, Chapter IX, Hence and the safe load in pounds is and m, n and / being in feet. Mm^x= SI /12 c iWinax = Pmn/l Pmn/l = SI/12 c P = SIl/ 12 cmn I/c = 12 Pmn/lS (10) (10)' 562 Strength of Beams and Beam Girders Chap. 15 Example 6. A steel I beam 20 ft in span is to support a concentrated load of 24 000 lb at a distance of 6 ft from the left support. What must be the size and weight of the beam? Solution. In this case P = 24 000 lb, / = 20 ft, w = 6 ft, n = 14 ft and S = 16 000 lb per sq in. Then Formula (10)' gives 12 X 24 000 X 6X 14 I/c 20 X 16 000 = 75-6 Table IV, page 354, the nearest value for the section-modulus l/c for axis i-i is above 75.6, or 81.2 for a 15-in 60-lb beam. An i8-in 55-lb beam having a section-modulus of 88.4 would be used, unless conditions fix the head room, as it weighs 5 lb per ft less, and being deeper is consequently stiffer. Case VII Beam Supported at Both Ends and Loaded Symmetrically with Two Equal Concentrated Loads (Fig. 7). Fig. 7. Simple Beam. Equal Concentrated Loads Symmetrically Placed From Formula (4)' and Case VII, Chapter IX, each of the safe loads in pounds is P = SI/ 12, cm {iV) and I/c= 12 Pm/S (11) Example 7. A 12-in steel channel, 12 ft in span, supports half the loads of two ro-in beams 4 ft from each end. Each beam is designed to carry 16 000 lb. What is the size and the weight of the channel required? Solution. The channel supports only one-half the load on each beam; hence, jP = 8 000 \h;m = 4 ft, 5 = 16 000 lb per sq in, and by Formula (11)', 12 X 8000X4 I/c 16 000 ■ 24, which is the section-modulus of a 12-in 25-lb channel. (See Table VIII, page 359-) Weights of Beams in Flexure-Formulas. It will be noticed that in for- mulas (11) and (11)' the span of the beam is not taken into account, and if the beam itself had no weight there would be no difference in the fiber-stresses no matter how far apart the loads P were placed. In reality, however, steel beams have considerable weight, and to be absolutely correct an example such as the one above should include the weight of the beam, which would, of course, be a uniformly distributed load. The maximum bending moment of the beam can be found graphically as explained on page 329, and the value of I/c com- puted by Formulas (3)' or (5)'. Where, however, the loads are spaced so as to divide the beam into three equal parts, as in the last example, one-third of the weight of the beam may be added to P with sufficient accuracy. Thus, the Formulas for Safe Loads for Beams, etc. 663 weight of the channel in the above example between the supports would be 25 IbX 12, or 300 lb, and F would be 8 100 lb, which would give a value for l/c of 24.1. The factor of safety in the loads allowed is generally large enough to offset the slight effect produced by the weight of the beam; but if the full load assumed is likely to be imposed on the beam, then allowance must be made for the weight of the beam itself. Case VIII Beam Supported at Both Ends and Loaded Symmetrically with Several Con- centrated Loads (Fig. 8). In this case it is necessary to compute the maximum bending moment in the beam and proportion the beam by Formulas (3)' or (5)'. Example 8. A steel-beam girder is to be designed to support a brick wall, 16 in thick and weighing 138 000 lb, over an opening 22 ft wide. The girder must also support the ends of four lo-in floor-beams j< -23 ■ ^ .-»> beam carrying 16 000 lb. — =j TK, Tji^ TT^^ rfg^^ p- What is the size and weight 1 |j { | ||| 1 1 j of the girder required? k-3J^-'-4^ — 5^--^ — 5^-4k- — b^-^-^^ Solution. The first step pjg §. Simple Beam. Several Concentrated Loads is to make an allowance for Symmetrically Placed the weight of the girder. The total load on the girder (neglecting the weight of the girder itself) = 138 000 lb+4X 8000 lb (one-half the load on each beam) = 170000 lb, or 85 tons. As this is much more than the heaviest single rolled beam will carry, it will be necessary to use a pair of beams and the load on each beam, therefore, will be 42.5 tons. Considering for the present the entire load as uniformly distributed, Table IV, page 577, shows that to support 42.5 tons, or 85 000 lb, over a span of 22 ft requires a 24-in 85-lb beam. The girder then will weigh between sup- ports 2X85X22=3 740 lb, or about 4 000 lb." This added to the weight of the wall makes, for the total distributed load, 142 000 lb. The next step is to determine the maximum bending moment. By the formulas given in Chapter IX the maximum bending moments for the various loads may be found as follows: For the wall and girder (Case V, page 326), 22 X 142 000 , „ ITmax = ■ = 390 500 ft-lb For the beam Bi (Case VI, page 327), 8oooX3HXt81/4 . ,, il/imax = ■ = 23 545 ft-lb 22 For the beam B2 (Case VI, page 327), 8 000X81/^X13^2 ... M2m« = = 41 727 ft-lb 22 The beams being spaced symmetrically from the middle of the span, the bend- ing moments for ^3 and Ba will be equal to those of B2 and Bi respectively. Plotting the bending moments to a scale, in the manner explained for Figs. 17 and 18, page 330, the diagram shown in Fig. 9 is obtained. The greatest bend- ing moment is the ordinate Mx, which scales 486 500 ft-lb, or 5 838 000 in-lb. 504 Strength of Beams and Beam Girders Chap. 15 Note. Since the loads arc symmetrically placed, this ordinate is over the middle point of the girder, but it is drawn to one side in the figure in order not to confuse it with the ordinate M, the maximum bending moment for the uni- formly distributed load. Substituting this value of Mx in formula (3)', l/c 5 838000 in-lb 16 000 lb per scj in --3^5 the section-modulus for both beams, or 182.5 for one beam. From Table IV, page 354, it is found that a 24-in 90-lb beam has a section-modulus of 186.5, and two 90-lb beams will just answer. The assumption of a uniform distribution of such a loading over every foot of a girder usually results in the selection of lighter beams than are indicated by the second solution, in which each concen- trated load is considered as really con- centrated at a point. The two beams should be securely bolted together with separators near each connection of beams jBi, B2, Bs, B\, and at each end of the girder. A DOUBLE-BEAM GIRDER, however, is not considered the best kind of girder to use under this condition of loading, as it is r/ ^ Vl ^^^ good construction nor economical of !li4^te^M-r — d^ I J ■M-t::3^/A material. As a general rule beam gir- ders should be used only when the loads can be applied to the upper flanges of both beams. Transferring a load directly to the web of one beam, even though it is connected with the other beam by means of separators, does not insure as equal distribution of the loading. The author, therefore, recommends in this case a riveted beam girder or a riveted plate girder. The method above indicated applies to any method of loading, the only difference in the cal- culation being in the determination of the maximum bending moments. Inclined Beams. The strength of beams inclined to the horizontal may be computed, with sufficient accuracy for most purposes, by using the formulas given for horizontal beams, and taking the horizontal projeciions of the beams as the spans. 3. Steel Beams and Girders* Materials Used for Beams. Practically the only materials used in struc- tural work for beams, at the present day, are wood, steel and reinforced concrete. As wooden beams are always rectangular in cross-section, the general formulas used in this chapter can be much simplified by substituting for l/c its value in terms of the breadth and depth of the beam. Formulas for wooden beams will therefore be found in Chapter XVI. Cast iron, also, is occasionally used for beams or lintels, but as this material is much stronger in resisting compression than tension, the beam must be of a special shape in order to use the material to advantage. The strength of cast-irou beams is therefore considered under ♦ For the deflection of steel bearns, see Chapter XVIII. Bending-moment Diagram for Beam Shown in Fig. 8. Steel Beams and Girders 565 a special heading in Chapter XVI. Formulas for reinforced-concrete beams are given in Chapter XXIV, pages 924 to 939; and Chapter XXV, page 992. Forms of Steel Beams. Since 1893, steel beams have superseded wrought- iron beams, and the latter are now never used. Any shape of rolled steel may be used as a beam, but the I shape is the most economical, as it possesses the greatest resistance for a given weight of metal. Next to the I beam, in economy, is the channel, then the deck beam; angles and tees are the least economical of all shapes. The following values show the safe loads per pound of steel, for the various shapes, for a lo-ft span; the same ratio would hold for other spans. lo-in I beam lo-in channel lo-in deck-beam 4 by 6-in angle 4 by 5 -in tee 104 94.6 83.0 28.7 21.6 The Deepest Beams, the Strongest, Stiffest and Most Economical. The STRENGTH of a wooden or steel beam of rectangular cross-section varies as the SQUARE OF THE DEPTH, directly as the breadth and inversely as the length, and the stiffness varies directly as the cube of the depth, directly as the breadth and inversely as the cube of its length; hence the deeper beam will have the greater strength and stiffness in proportion to its sectional area. With I beams these relations do not hold strictly, because of the variation in the forms of the cross-sections, but they are approximately true. It therefore follows that, for any given span, it is more economical in floors, where other conditions will permit, to use deep beams spaced farther apart or to use one deep beam in place of two shallower beams. Thus if a distributed load of 39 tons is to be supported over a span of 16 ft, one 20-in 65 -lb beam, two 15-in 42-lb beams, or three 12-in 40-lb beams, could be used; but the 20-in beam would weigh only i 105 lb, allowing for 6-in bearings, as compared with i 428 lb for the 15-in beams and 2 040 lb for the 12-in beams, and the bolts and separators would be saved. Light and Heavy Steel Beams. Light beams are more economical than heavy beams of the same diopth, except when the span is so short that the safe load is governed by the resistance of the web to buckling, in which case the heavy beams are the more economical. Maximum Safe Loads for Steel Beams. All loaded beams are, in general. Subject to three kinds of stresses. The most destructive are generally those due to the bending moments, and have already been considered. The second kinds are those which tend to shear a beam, or to make one part slide on the other vertically. (See paragraph on Shearing-Stresses in Steel Beams and Girders, page 567.) These stresses, however, seldom need to be considered except in the case of riveted girders and short beams with very thick webs. The third kind of stress is that which tends to cause the web of a beam to buckle; and in a steel beam over a span very short in proportion to the depth of the beam, the resistance of the web to buckling generally determines the maximum load that the beam, without stiffeners on the web, will support. (See, also, pages 182, 183 and 567.) Safe Loads for Steel Beams.* To save time in calculating, tables of safe loads for structural and supplementary beams and channels used as beams under conditions of transverse loading, have been prepared, which give the uni- formly distributed safe loads in thousands of pounds for spans customary * Part of the matter of the following paragraphs relating to steel I beams has been adapted by permission, from the Pocket Companion, Carnegie Steel Company, Pitts- burgh, Pa. 566 Strength of Beams and Beam Girders Chap. 15 in building-construction. They are based upon an extreme fiber-stress of 1 6 GOO lb i^er sq in on the fibers farthest from the neutral surface of the beam. The Tables of Safe Loads for Angles and Tees, pages 586 to 591, give the values at the same fiber-stress on spans of one foot, from which the safe load for any span-length may be obtained by direct division, and also the values for those spans at which the allowed safe load will produce a deflection of Heo of the span-length. The loads in all cases include the weight of the beam, which should be deducted in order to arrive at the net load which the beam will support. For several concentrated loads or for a combination of distributed and concen- trated loads it will be necessary to use the methods previously explained under Case VIII, page 563. Use of Tables for Concentrated Loads. To use any of the following tables for concentrated loads, find the equivalent distributed load by multi- plying the concentrated load by the factor given in Table IV, page 632, and then use the beam having a safe load equal to the load thus found. In addition to the conversion-factors in that table the following, also, will be found convenient: For two equal loads applied at one-third the span from each end, multiply one load by 2%. For two equal loads applied at one-fourth the span from each end multiply one load by 2. For a beam fixed at one end, and loaded at the other, multiply by 8. Fqr a beam fixed at one end, and uniformly loaded over the entire length, multiply by 4. Unusual Conditions of Loading of Beams.* It is assumed in all cases that the loads are applied normal to the axis i-i as shown in the tables of the properties of sections in Chapter X, and that the beam deflects vertically in the plane of bending only. If the conditions of loading involve the introduc- tion of forces outside this plane of loading, the allowable safe loads must be determined from the general theory of flexure in accordance with the mode of application of the load and its character. This applies particularly to unsym- metrical sections, such as angles, which should be used under those condi- tions of loading where the section can deflect vertically only, being rigidly se- cured against lateral deflection or twisting throughout the entire span. In all such cases of eccentric loading, the actual safe loads would be considerably lower than the tabulated safe loads, which have been based upon the most favorable conditions of loading. Vertical Deflection of Steel Beams.* In the case of beams intended to carry plastered ceilings, experience indicates that the vertical deflection, to avoid cracking the plaster, should be limited to not more than Heo of the span-length. This span-limit for steel beams is approximately, in feet, twice the depth in inches and is indicated in the tables by the lower, broken, hori- zontal lines. Beams intended for such purposes should not be used for greater spans unless the allowable tabular safe load exceeds the actual load to be sup- ported. As the dead load of a floor is supported by the floor-beams before the plaster is applied, only the deflection due to the live load really needs to be considered. The vertical deflection of beams is explained in Chapter XVIII. Lateral Deflection of Steel Beams.* The tabular safe loads are based upon the assumption that the compression-flanges of the various sections are * Part of the matter of this paragraph has been adapted, by permission, from the Poc ket Companion, Carnegie Steel Company, Pittsburgh, Pa. J Steel Beams and Girders 567 secured at proper intervals, against lateral deflection, by the use of tie-rods or by other means. The lateral unbraced length of steel beams and girders should not exceed forty times the width of the compression-flanges. When the unbraced length exceeds ten times the width, the tabular safe loads should be reduced. An explanation of the method of reducing the tabular loads when the unsupported length exceeds ten times the flange-width is given in Chapter XVIII, page 670. (See Bethlehem Handbook for sidewise deflection.) Shearing-Stresses in Steel Beams and Girders.* The safe-load tables for beams and channels arc computed solely with reference to safe unit stresses DUE to flexure, and the safe loads uniformly distril^uted on the spans given will not cause average shearing-stresses in the web greater than the 10 000 lb per sq in, the average safe working strength of steel in shear. When, however, beams are loaded with heavy loads concentrated near the supports, or when beams of short span are loaded with uniformly distributed loads to their full carrying capacity as regards flexure, the bending moments may be small in comparison with the reactions at the supports, and the beams may fail along the neutral surface as a result of longitudinal shearing-stresses, or they may BUCKLE as a result of the combined longitudinal and vertical web-stresses. On such spans the safe shearing or buckling strength of the web rather than the resistance of the flanges to bending-stresses may limit the carrying capacity of the beam. Buckling Values of Beam- Webs.* The vertical shearing-stresses or the vertical compressive components of the web-strcsscs may under some con- ditions exceed the safe resistance of the beam to buckling, and there remains the possibility that a web or web-plate, which is amply secure against the safe allowed shear of 10 000 lb per sq in, will not be of sufficient strength when con- sidered as a column. In such cases provision must be made for security against buckling either by stiffeners or by an increased thickness of the web or web- plate. (For the determining conditions for web-buckling of steel beams in gril- lages, based on direct compression, see page 183.) Conditions of Web-Buckling of Steel Beams. There are two conditions of WEB -buckling (scc, also, foot-note for paragraphs relating to Tables II and III). (i) The part of the beam bearing on the support is subject to direct com- pression, and the web over this part must be capable of resisting it. If this area is too small the end of the beam will fail, as a column, causing the web to buckle. It is therefore necessary to calculate the required length of the bear- ing. (2) The beam throughout its length between the supports, or in case of a cantilever beam, from its end to the support, is subject to shear. It is gen- erally supposed that the shear develops stresses of tension and compression in the web; that these stresses act at right-angles to each other in the plane of the web and at an angle of 45" with the neutral surface of the beam; and that these DIAGONAL STRESSES are equal in magnitude or intensity to the vertical shear at any point. It is the compressive stress that tends to buckle the web. Formulas for Safe Buckling Resistance of Steel Beams.* In regard to the first condition of buckling a series of experiments has been made on beams of various depths and web-thicknesses to arrive at a basis for a simpler method of computation to use in the investigation of the safe buckling resistance of * Part of the matter of this paragraph has been adapted, by permission, from the Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. 568 Strength of Beams and Beam Girders Chap. 15 beams with unsupported webs, and from these experiments the following for- mulas * have been deduced: ilUlinTli . Safe end-reaction R= SbXi Safe interior load F = 2SbXt (-;) (•■n) In these formulas, R is the end-reaction, P the concentrated load, / the web- thickness, d the depth of the beam, ai half the distance over which the concen- trated load is applied and a the whole distance over which the end-reaction is applied; while Sb is the safe resistance of the web to buckling, in fxjunds per square inch, by the straight-line formula Sb = 19 000 — 100 d/2 r d/2 = I in the column-formula f- The first formula is general and applies to any condition of loading. The second formula covers the case of a single load concentrated at the middle of a span; it can be extended to cover a system of concentrated loads provided the sum of the distances ai is not less than a. Tables II t and III J give for beams and channels with unsupported webs: * These formulas, in order to satisfy the first condition, are used in the Pocket Com- panion, 1915 Edition, Carnegie Steel Company, Pittsburgh, Pa. t This is the column-formula used by the American Bridge Company and in Carnegie's Pocket Companion, S being the allowable compressive unit stress in pounds per square inch within the usual hmits of l/r. See Formula (13), page 481. t In regard to the shearing of steel beams, allowable web-shears, etc., the value, for example (see Example 15, this chapter, and on pages 182 and 183 of Chapter II), of 42 000 lb per sq in for a 12-iu, 3iy2-lb I beam, given in Table II, page 575, taken from Carnegie's Pocket Companion, is based on the allowed direct shear without including the condition of web-crippling. That is, the 42 000 lb is determined by taking the area of the web, 0.35 X 12= 4.2 sq in and multiplying it by 10 000 lb per sq in, which is the value there used for the safe unit shearing -stress. The beam is therefore calculated as being good for 42 000 lb shear, but it is necessary to make a further investigation to ascertain whether the stresses due to shear will cause the web of the beam to buckle. As stated in the paragraph on page 567, on the Buckling Values of Beam- Webs there are two conditions of web-buckling or web-crippling. In the case of a plate girder the end-stiffeners provide for the first condition, and the intermediate stiffeners for the second condition. The web itself may then be counted on for its full shearing value. In the case of beams, however, it is not generally economical to use stifiFeners, so that the web alone must meet every condition. The Carnegie Pocket Companion gives a formula, reproduced in the preceding para- graph, and gives the derived lengths of bearings in Tables II and III, to satisfy the first condition. Some of the formulas used in the manufacturers' handbooks, for maximum safe shear based on web-buckling for the second condition, are as follows: Passaic Steel Company, V = .+ " 3000/2 1 2 000 di Cambria Steel Company, V = .j I 500 /2 Bethlehem Steel Company, V= ' 3 000/2 Steel Beams and Girders 569 V ' (i) " The allowed wkb -resistance Sb, in pounds per square inch, computed from this compression-formula. (See, also, page 183.) (2) *' The distance a, or the distance over which the end-reaction must be dis- tributed when the shearing-stress V in the web is the maximum allowal^le stress of 10 000 lb per sq in. (3) " The allowable end-reaction R, when a is taken at sli in, which is the usual length of beam actually resting on the 4-in angles ordinarily used in build- ing-construction for beam-seats. (4) *' The allowable shear V, on the gross area of the cross-section of the beam or channel-webs, at 10 000 lb per sq in." In regard to the second condition of web-buckling, the maximum allow- able SHEAR may be calculated by the formula, 12 000 di in which V = the maximum safe web-shear in pounds; d = the depth of the beam; / = the thickness of the web; and h = the height between the flange- fillets. (See Example 15, this chapter and also example on pages 182 and 183.) " In addition to these data which have to do with the maximum loads on beams and channels as computed from the web-resistance, Tables II and III give, also, the maximum bending moments in foot-pounds, obtained by the multi- plication of the section-modulus of each section by the allowed fiber-stress of 16 000 lb per sq in and the division of the product by 12 in order to reduce to a foot-pound basis. These maximum bending moments may be used on inspection instead of the table of properties to ascertain the proper size of a section to be used in any particular instance." in all of which V = the maximum safe web-shear in pounds; d = the depth of the beam; i = the thickness of web: and A = the distance between the flange-fillets. It is to be noted that the length of the element in compression on the 45° line is h V2, and that the square of this length is 2 h"^. It is this value, 2 h-, that is substituted for /2 in the column-formula used by the Cambria Steel Company in deducing its formula for shear based on web-buckling. The tensile stress, however, tends to keep the compressive stress from buckling the web, and for this reason the Passaic and Bethlehem engineers take the more liberal value of 3 000 P instead of i 500 P. The Passaic Steel Company, however, used the more conservative unit value of 10 000 lb, reduced, instead of the 12 000 lb used by the others. The Passaic and Cambria formulas give about the same results, a 12-in, 3i3'^-lb I beam by the former having a safe shear of 33 352 lb and by the latter, 33 188 lb. The Passaic Steel Company is no longer in existence and their handbook is out of print. The Bethlehem Steel Company's handbook has tables for Bethlehem shapes only. If, in any case, no table of maximum shears of beams, based on web-crippling, is at hand, it is suggested that the values may be determined from the formula, ^. 12 000 dt 1 + I SCO P in which, as before, V = the maximum safe web-shear in pounds; d = the depth of the beam; / = the thickness of the web; and h = the distance between the flange-fillets. For the beam mentioned and used in Example 15, page 571, in this chapter and in the example on pages 182 and 183, d = 12 in, / = 0.35 in. It = 9.762 in, /2 = 0.1225, /{2 = 95.296644 and V = 33 i88 lb. This formula is recommended as being the most conservative, although there is not a great difference in the results, and the formula of the former Passaic Steel Company is i^tained elsewhere in Kidder's Pocket-Book. See, for example, page 686 and Table III of Chapter XX. Editor-in-chief. 670 Strength of Beams and Beam Girders Chap. 15 Table VII is a table computed by Mr. Kidder, giving the strength of small rectangular steel channels or grooved steel. These are often used for supporting metal lath in suspended ceilings, and the table will be found useful in determining the size to use for any given span and spacing. 4. Tables of Safe Loads for Steel Beams and Girders. Examples Example 9. Direct Bending from a Uniformly Distributed Load. As an illustration of the use of these tables let it be required to determine the proper size and weight of an I beam to carry safely a uniformly distributed load of 34 000 lb over a span of 20 ft, the weight of the beam not being included. Solution. From Table IV, page 579, a 15-in 50-lb beam will carry 34400 lb. The weight of this beam is 50 lb X 20 ft = i 000 lb, making a total load to be supported of 35 000 lb. This is so little in excess of the safe load that the excess need not be considered. Had the dilTerence been more, however, the next heavier beam should be used. Example 10. Direct Bending from a Concentrated Load. To illustrate the use of the tables to determine the size and weight of beams required to carry concentrated loads, Examples 10 and 11 are given. What I beam, 15 ft in span, will safely support 8 000 lb, concentrated at a point 5 ft from the left support? Solution. The distance 5 ft is one-third of the span, and the conversion- factor for this (Table IV, page 632) is 1.78. The equivalent uniformly dis- tributed load, therefore, is 8000X 1.78= 14 240 lb, and from Table IV, page 581, a 9-in 25-lb I beam will carry 14 500 lb for a span of 15 ft, and will just answer the purpose. Example 11. Direct Bending from Two Equal Concentrated Loads. What I beam, 15 ft in span will safely support two equal concentrated loads of 6 000 lb each, appUed 5 ft from each end? Solution. The distance 5 ft is one-third the span, but the multiplier in this case is 2^ (page 566)- Hence, the equivalent uniformly distributed load is 6 oooX 2% = 16 000 lb and the beam required (Table IV, page 580) is a lo-in 25-lb, I beam which will carry 17 400 lb. The same result is obtained by using Formula (11)', page 562. This formula is, I/c = 12 P?n/S. Substituting, l/c =12X6 000 X 5/16 000 = 22.5. The nearest section-modulus to this is 24.4, that of a lo-in 25-lb I beam. Example 12. Maximum Bending Moment from a Distributed Load Over Part of the Span. The beam in Example 5, Case V, page 561, has a maximum bend- ing moment of 26 626 ft-lb. What beam is required? Solution. The nearest bending moment to this in the first column of Table II, page 575, is 27 240 ft-lb, which corresponds to a 9-in 25-lb I beam. Example 13. Allowable Web-Shear.* The maximum shear in the beam of Example 12 is just at the right of the left reaction or bearing, and equals 4 000 lb. Is the beam safe for shear? Solution. From Table II, page 575, in the column for V, the allowable web- shear for a 9-in 25-lb beam is 36 540 lb. Hence, the beam is safe if web-buckling is not taken into account. Example 14. Shear.* It is required to determine the maximum load which a 9-in 25-lb I beam can support without exceeding the safe web-resistancy ' the section. * See paragraphs and foot-note relating to buckling of beam-webs, pages 567 to 561 ice^j I Tables of Safe Loads for Steel Beams and Girders. Examples 671 Solution. From Table IV, page 581, the maximum load for this beam, given in small figures above the heavy, horizontal lines, is 73 100 lb. Example 15. Safe Buckling Resistance. See, also, paragraphs and foot-note relating to buckling of beam-webs on pages 567 to 569 and also example oq pages 182 and 183. According to Table II, page 575, the allowable web-shear for a i2-in, 31.5-lb I beam is 42 000 lb. Will this shear cause the web of the beam to buckle? Solution. The web-shear is determined by multiplying the area of the web, that is, 0.35 in X 12 in = 4.2 sq in, by 10 000 lb per sq in, the safe unit shearing- stress. The maximum shear which will not cause the web to fail by buckling may be found by the formula given on page 569 for the second condition of web- buckhng. 12 000 dt i + - I 500 /2 From the dimensions of structural beams (see Carnegie's Pocket Companion, I Beams, Profiles, Weights, etc.) the thickness t of the web of a 12-in, 3i-5-lb I beam is 0.35 in, the depth of the beam isd= 12 in and h, the distance between flange-fillets, is 9.762 in. Substituting these values in the formula, 12 000 X 12X0.35 50400 50 400 ^ 50 400 9-7'32^ " 95.296644 95.296644 279.046644 . 1500X0.352 1 500X0.1225 183.7s 183.75 50400X183.75 9 261 OCO 00 u ^ iu = ^-^ — = — — = ss 188, or about 33 190 lb 279.040644 . 279.046644 As this is less than the allowable web-shear of 42 000 lb given in the tables, if account is to be taken of the web-buckling from the second condition men- tioned in the preceding pages, a larger or heavier beam should be used or the loads reduced, so that the maximum shear will not exceed ss 190 lb. (For de- termining conditions for web-buckling of steel beams in grillages, based on direct compression, see page 183.) Example 16. Safe End-Reactions for Web-Buckling. In Example 8, page 563, the two 24-in 9o-lb I beams carry 170000 Ib-H (4 000 lb, the weight of the* beams) = 174000, lb or 87 000 lb for each beam. Assuming that they rest' upon 4-in brackets riveted to columns at each end of the span, are the end- reactions excessive? Solution. Since the loading is symmetrical, each reaction for each beam is one-half the total load on each beam, or 43 500 lb. From the last column in> Table II, page 574, the maximum end-reaction R, for a 24-in 90-lb beam, is' 74 410 lb. Hence, the beam is safe as far as the compression from the end- reactions is concerned. Strut-Beams. It is not considered good construction to subject a strut to a transverse loading, causing a certain amount of flexure in it and thus adding to the compressive stress. Conditions often exist, however, where practical consider- ations make it desirable to use a strut as a beam, also, as in the top chord or in the principals of a truss. To determine the size of a member in a case of this kind the following method should be used: (i) Find the section-modulus l/c, for the member for the transverse load by Formulas (2)' to (11)', using 12 000 lb per sq in as the value of S, and find the area of the cross-section of a steel shape corresponding to the value of l/c thus found. See note at end of Example 17. f 572 Strength of Beams and Beam Girders Chap. 15 (2) Find the section-area required to resist the compressive stress, by dividing that stress by the vakie opposite //r in column VIII of Table XI, page 493. (3) Add together the two areas and use for the required member a piece or pieces of material having a section-area next larger than the total area found. Example 17. Strut-Beam. Combined Bending and Compression. The principal rafter in a truss, 8 ft 6 in long between joints, supports the end of a purlin at the middle of the span. The weight from the purlin is 2 800 lb and the compressive stress in the rafter 30 000 lb. It is proposed to use a pair of angles for the rafter, set with the long legs vertical and K2 in apart. What are the dimensions of the angles, the strut being braced laterally ? Solution, (i) By Formula (8)', //c =; 3X2 800 X 8.5/12 000= 5.95 for the pair of angles, or 2.98 for each angle. (See note at end of this example.) From Table XI, page 363, the nearest vakie to this with reference to the axis i-i is 3.0, the section-modulus for a 5 by 3V2 by ^i-in angle. The section-area of one angle is 4 sq in and of two angles, 8 sq in. (i) From Table XVI, page 371, the least r for a pair of 5 by 3H by \h-m angles, which would be about the axis i-i, since the strut is braced laterally, is about 1.58 (between 1.55 and 1.61). Then the slenderness-ratio //r = 8 ft 6 in/1.58 in= 102 in/1.58 in= 64.5. From column VIII, Table XI, page 493> -S* = 9 250 lb per sq in. Hence, 30 000 lb/9 250 lb per sq in = 3.24 sq in, approximately. (3) The section-area required, therefore, is 8 -j- 3.24 = 11.24 sq in, which, from Table XI, page 363, is about equivalent to that of two 5 by 4 by iHe-in angles. As the section-area in both calculations exceeds that actually required, no allowance for the weight of the angles need be made. Note. Because of the increase in the tendency of the strut to deflect, caused by the combined stresses of flexure and compression, lower values of S are used than in the cases of simple flexure, or of simple compression. Tie-Beams. Steel beams subject to combined tensile and transverse stresses should be calculated in a way similar to that explained above for strut-beams. The section necessary to resist the transverse stress should be found first, then the section-area necessary to resist the tensile stress, and the two added together. ! Example 18. Tie-Beam. Combined Bending and Tension. One span of a tie-beam, 10 ft between joints, supports a load of 6 000 lb at the middle, and at the same time is under a tensile stress of 84 000 lb. It is proposed to use two steel channels for the tie-beam. What size and weight are required for the channels? Solution. A load of 6 000 lb applied at the middle of a beam has the same effect as a load of 12 000 lb uniformly distributed, or 6 000 lb for each channel. From Table V, page 584, a 7-in, 9.75-lb channel will be required, its section- area (Table VIII, page 359) being 2.85 sq in. The additional area required to resist the tensile stress is 84 000 lb/ 16 000 lb per sq in = 5.25 sq in, or 2.63 for each channel. The total area for each channel, therefore, should be 2.85 -f-2.63 B= 5,48 sq in. A 7-in, 19.75-lb channel has a section-area of 5.81 sq in, and an 8-in, 18.75-lb channel has a section-area of 5.5 sq in. Either one will be sufficient, but the 8-in channel will probably be more economical, as it weighs I lb per ft less. Example 19. Channel, Set Flatwise. W^hat is the size of the channel, set flatwise, required to support a uniformly distributed load of 180 lb per ft over a span of 10 ft, or 1 20 in? Solution. IF = 180 X 10 = I 800 lb. From Case V, page 326, A/max = T^//8 =• I 800 X 1 20/8 = :^ 000 in-lb. From Formula (3)', page 557, I/c= M/S=* Oblique Loading of I Beams and Channels 573 27 000/16 000= 1.7. From Table VIII, page 359, the Ijc about the axis 2-3 corresponding to this is that of a 12-in, 20.5-lb channel. Example 20. Rectangiilar Steel Bar with Long Side Vertical. In a suspended, plastered ceiling it is proposed to use 2 by ^^-in steel bars, 4 ft or 48 in long, to carry the plaster. What is the safe load each bar will support, if set with the long side vertical? Solution. From Table I, page 346, the / for a 2 by ^^-in bar is o 250. c = one-half the depth = i in. Ijc = 0.250/1 = 0.250. Also, from Formula (2)', page 557, M^„^= Sl/c. Substituting, lfni.x = 16 oooX 0.250 = 4 000 in-lb. But, from Case V, page 326, Mn,ax = H^//8, and hence, 4 ooo=PFX48/8 =■ 6 W, and fF = 4 000/6 = 666 lb. Oblique Loading of I Beams and Channels * Oblique Loading of Purlins on Sloping Roofs. (See, also pages 593, 1 169 and 1 170.) In Tables II to V it is assumed that I beams and channels are set with webs vertical and carry vertical loads. This is not the case when used as purlins on SLoriNG roofs. There are then fiber-stresses due to the components of the bending moment both at right-angles and parallel to the plane of the roof. The resultant fiber-stress may be calculated from the equation on page 11 70. This equation is used in determining the values given in Table I A. It may be noted that the second term causes the fiber- stress to increase rapidly with the slope of the roof. If purlins were propor- tioned according to the equation given or from the Table I A, they would often be much larger than those commonly used. For small slopes the second term of the equation may be reduced or eliminated by the stiffness of the roof- covering, and for other slopes by connecting the purlins with sag-rods running up the sloping sides of the roof to an unyielding connection at the peak. Table I A. Ratio of Max mum F.ber-Stress to Bending Moment for I-Beam and Channel Purlins Set of Right-Angles to Rafters and Free to Move in Any Direction. Loading Vert'cal and Oblique to Web Purlin 6-in I beam 12 K lb. 7 -in I beam 15 lb. . . 8-in I beam i8 lb. . . g-in I beam 21 lb. . . lo-in I beam 25 lb. . . 12-in I beam sil^lh. 6-in channel 8 lb . . 7-in channel 9% lb 8-in channel 11 34^ lb gin channel 13H lb to-in channel 15 lb. . 12-in channel 20H lb 0.14 o. 10 0.07 0.05 o 04 0.03 0.23 0.08 0.05 Slope of roof in inches per foot o.is O.II cog 0.07 o 05 0.40 0.30 0.23 0.18 0.15 cog 0.56 0.33 o. 26 0.42 0.31 0.23 0.18 0.15 0.8'; 0.66 0.52 0.42 0.34 0.23 o 47 o 35 o. 27 O. 21 0.17 0.13 0.76 0.60 0.40 o. 26 0.53 0.39 0.30 o. 24 o.ig 0.14 1. 10 0.85 0.68 0.55 0.45 0.30 0.61 0.46 0.3s 0.28 0.22 0.17 1.30 1. 01 0.80 0.6s 0.54 0.36 " From Notes by Robins Fleming. 574 Strength of Beams and Beam Girders Chap. 15 Table n.*t Maximum Beiiding Moments and Web-Resistance of I Beams Mm&x d V t V ^ftt a R Maximum Depth Weight Thickness Allowable Allowable Minimum End- bending of per of web- buckling end- reaction moment ft-lb beam linft web shear resistance bearing a=3Hin in lb in lb lb per sq in in lb 292 130 27 90.0 0.524 141 480 10080 20.0 54140 328 390 115.0 0.750 180000 13460 II. 8 95880" 320390 IIO.O 0.688 165 120 12 960 12.5 84690 312390 105 . 0.625 150000 12350 13.4 73 320 264 400 100. 0.754 180 960 13490 II. 8 96 620 256 560 24 95. 0.693 166 320 13 000 12.5 85610 248 710 90.0 0.631 151 440 12 410 13.3 74 4IO 240 870 85.0 0.570 136 800 II 710 14 5 63410 231 920 80.0 0.500 1 20 000 10 690 16.5 50 780 216670 74.0 0.476 114 240 10 260 17.4 46 400 156 930 21 60. 5 0.428 89880 10500 14.8 39320 220 750 100.0 0.884 176 800 15080 8.3 113 320 214 210 950 o.8io 162 000 14720 •8.6 loi 370 207 680 90.0 0.737 147 400 14300 9.0 89590 201 140 85.0 0.663 132 600 13780 9-5 77630 195 510 20 80.0 0.600 1 20 000 13 230 10. 1 67 460 169 170 750 0.649 129 800 13 660 .<9.« 75380 162 640 70.0 0.575 115 000 12 980 10.4 63420 155 930 65.0 0.500 100 000 12080 II. 6 51320 186 720 90.0 0.807 145 260 15 140 7.4 97 730 85 260 180 840 05.0 0.725 130 500 14 700 7-7 174960 80.0 0.644 115 920 14 160 8.2 72940 169 080 75 0.562 loi 160 13450 8.9 60480 136 480 18 70.0 0.719 129 420 14670 7.8 84350 130 590 65.0 0.637 114 660 14 no 8.3 71890 124710 117 860 60.0 0.555 0.460 99900 13380 9.0 59 420 44980 550 82 800 12 220 10. 2 109 200 48.0- 0.380 68400 10800 12.2 32830 122 890 750 0.882 132 300 16 050 5-6 •102 660 117 980 70.0 0.784 117 600 15690 5-8 89 160 113 080 65.0 0.686 102 900 •15 210 6.1 75650 108 270 60.0 0.590 88500 14600 6.5 6244X) 90850 IS 55 -o 0.656 98 400 15040 6.2 71 530 85940 50.0 0.558 83 700 14340 6.7 58020 81 040 450 0.460 69 000 13350 7-5 44520 78 530 42.0 0.410 61 500 12 670 8.1 37660 72 130 37.5 0.332 49800 II 180 9.? 26910 V is compute d at lo 000 lb per sq i n of gross a irea of web -section. •FromT ocket Com panion, Ca rnegie Stee 1 Company , Pittsburg h, Pa. t See, als 0, foot-note on page 5 68, with pa ragraphs n 'lating to tl lis table ar d to Table III, and pa ragraphs n page 567 , relating to web-buc kling of st< iel beams. See, also, page i8.«- Tables of Safe Loads for Steel Beams and Girders 575 Table H ♦ t (Continued). Maximum Bending Moments and Web-Resistances 01 1 JBeams Mm&x d w t V So^ a R Maximum Depth Weight Thickness Allowable Allowable Minimum End- bending of per of web- buckling end- reaction moment beam linft web shear resistance bearing i lb lb lb lb lb lb lb lb lb lb lb "6 ' 7 8 283.0 36:).o 330.2 300.0 3G1.9 ^32.6 302.9 273.6 231.9 228.S I7Q.8 i 0.60 ' 0.81 1.06 352.5 302.2 264.4 293.2 256.6 284.2 248.7 179.3 156.9 328.4 320.4 240.9 216.7 9 259-3 291.9 284.8 277.7 235.0 228.0 221. 1 214. 1 206.1 192.6 139.5 1.34 10 II 2334 212.2 262.7 238.8 256.3 233-0 249-9 227.2 211. 5 192.3 205.2 186.6 199.0 192.7 185.5 168.7 173.3 157.6 125-5 II4.I 1.66 2.00 180.9 175.2 12 194-5 218.9 213.6 208.3 176.3 171. 165.8 160.6 154.6 144.5 104.6 2.38 13 179-5 202.1 197.2 192.2 162.7 157.9 153- 1 148.2 142.7 133.3 96.5 2.80 14 166.7 187.7 183. 1 178.5 151 -I 146.6 142. 1 137-6 132.5 123.8 89.7 3.24 IS 156.6 175. 1 170.9 166.6 141. 136.8 132.6 128.5 123.7 1156 83-7 3.72 16 145-9 164.2 160.2 156.2 132.2 128.3 124.4 120.4 116. 108.3 78.4 4.24 17 137-3 154. s 150.8 147-0 124-4 120.7 117. 113-4 109. 1 102.0 73.8 4.78 18 129.7 146.0 142.4 138.8 117-5 ;i4.o no. 5 107. 1 103. 1 96.3 69.7 5.36 19 122.8 138.3 134-9 131. 5 111-3 108.0 104.7 101.4 97.6 91.2 66.1 5.98 20 116. 7 131. 4 128.2 125.0 105.8 102.6 99-5 96.3 92.8 86.7 62.8 6.62 21 III. I 125. 1 122. 1 119. 100.7 97-7 94.7 91.8 88.3 82.5 59.8 7.30 22 106.1 119. 4 116. 5 II3-6 96.1 93-3 90.4 87.6 84.3 78.8 571 8.01 23 101.5 114. 2 III. 4 108.7 92.0 89.2 86.5 83.8 80.7 75-4 54-6 8.76 24 97-3 109. S 106.8 104. 1 88.1 85.5 82.9 80.3 77.3 72.2 52.3 9.53 25 93-4 105.1 102.5 100. 84.6 82.1 79-6 77-1 74.2 69.3 50.2 10.35 26 89-8 lOI.O 98.6 96.1 81.4 78.9 76.5 74.1 71.4 66.7 48.3 II. 19 27 86.4 97-3 94-9 92.6 78.3 76.0 73.7 71-4 68.7 64.2 46.5 12.07 28 83.4 93-8 91-5 89-3 75-5 73-3 71 -I 68.8 66.3 61 9 44-8 12.98 29 80.S 90.6 88.4 86.2 72.9 70.8 68.6 66.4 64.0 59.8 433 13.92 30 77.8 87.6 85-4 83-3 70.5 68.4 66.3 64.2 61.8 57.8 41-8 14.90 31 75-3 84-7 82.7 80.6 68.2 66.2 64.2 62.2 59.8 55-9 40-5 15.91 32 72.9 82.1 80.1 78,1 66.1 64.1 62.2 60.2 58.0 542 39-2 16.9s 33 70.7 79-6 77.7 75.7 64.1 62.2 60.3 58.4 56.2 52. 5 38.0 18.03 34 68.6 77-3 75-4 73-5 62.2 60.4 58.5 56.7 54.6 51-0 36.9 19.13 35 66.7 75.1 73-2 71-4 60.4 58.6 56.8 55.1 53.0 495 35.9 20.28 ; 36 64.8 73-0 71.2 69-4 58.8 57.0 55-3 53-5 51.5 48.2 34-9 21.45 ; 37 63.1 71.0 69-3 67-5 57.2 55-5 53-8 52.1 50.1 468 33.9 22.66 38 61.4 69.1 67-5 65.8 55-7 54-0 52.4 50.7 48.8 456 33.0 23.90 39 59-8 67-4 65-7 64.1 54-2 52.6 51.0 49-4 47-6 44.4 32.2 25.18 40 58.4 65-7 64.1 62.5 52.9 51-3 49-7 48.2 46.4 433 31.4 26.48 41 56.9 64.1 62.5 61.0 51.6 50.1 48.5 47.0 45-3 42.3 30.6 27.82 42 55.6 62.6 61.0 59-5 50.4 48.9 47.4 45.9 44.2 41.3 29.9 29.20 43 54.3 61. 1 59-6 58.1 49-2 47.7 46.3 44.8 43.1 40.3 29.2 30.60 44 53-0 59-7 58.3 56.8 48.1 46.6 45.2 43-8 42.2 39.4 28.5 32.04 45 51-9 58.4 57-0 55.5 47-0 45-6 44.2 42.8 41.2 38.5 33.52 46 50.7 57.1 55.7 54-3 46.0 44.6 43.3 41-9 40.3 37.7 35.02 47 49-7 55-9 54.1 53.2 45.0 43-7 42.3 41.0 39.5 36.9 36.56 48 49 48.6 47.6 54-7 53^4 52^1 44-1 42.8 41.5 40.1 _38-7 jA-}. 38.14 39-74 ire" 52.3 51-0 43.2 4I-9 40.6 39.3 37-9 35.4 50 46.7 52.5 51 -3 50.0 42.3 41.0 39-8 38.5 37.1 34.7, 41.38 Loads above the upper heavy lines will cause maximum allowable j >hears in webs. S ee, also, paragraphs in text and foot-note with same, page 567, re iating to web-buc Loads kling in beams below the lower broken lines will cause excessive deflections * From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. Strength of Beams and Beam Girders Chap. 15 Table IV * (Continued). Safe Uniform Loads in Units of i ooo Pounds for Steel I Beams Maximum bending stress 16 000 lb per sq in. Beams secured against yielding sidewise Span, Depth and weight of sections Coeffi- cient of 20-in i8-in ft deflec- tion 100 95 90 85 80 75 70 65 90 85 80 75 lb lb lb lb lb lb lb lb lb lb lb lb 5 35:^-6 0.41 353 2 .-.. 6 7 294 -3 252.3 324.0 294.8 265.2 240.0 259.6 230.0 200.0 290.5 261.0 231.8 202.3 0.60 0.81 285.6 244.8 276.9 237.7 225.6 193.3 216.8 185.9 249.0 213.4 241. 1 206.7 229.9 223.4 178.2 200.0 193.2 8 220.7 214.2 207.7 201. 1 195.5 169.2 162.6 155.9 186.7 180.8 175.0 169. 1 1.06 9 196.2 190.4 184.6 178.8 173.8 150.4 144-6 138.6 166.0 160.7 155.5 150.3 1.34 10 176.6 171. 4 166. 1 160.9 156.4 135.3 130. 1 124.7 149.4 144-7 140.0 135. 3 1.66 II 160.5 155.8 151. 146.3 142.2 123.0 118. 3 113. 4 135.8 131. 5 127.2 123.0 2.00 12 147-2 142.8 138.5 134. 1 130.3 112. 8 108.4 104.0 124.5 120.6 116. 6 112. 7 2.38 13 135.8 131. 8 127.8 123.8 120.3 104. 1 100. 1 96.0 114. 9 III. 3 107.7 104. 1 2.80 14 126. 1 122.4 118. 7 114. 9 III. 7 96.7 92-9 89.1 106.7 103.3 100. 96.6 3.24 15 II7-7 114. 2 no. 8 107.3 104.3 90.2 86.7 83.2 99-6 96.4 93.3 90.2 3.72 i6 no. 4 107. 1 103.8 100.6 97.7 84.6 81.3 78.0 93.4 90.4 87-5 84.5 4.24 17 103.9 100.8 97.7 94.1 92.0 79-6 76.5 73.4 87.9 85.1 82.3 79-6 4.78 i8 98.1 95.2 92.3 89.4 86.9 76.3 72.3 69.3 83.0 80.4 77.8 75.1 5.36 19 92.9 90.2 87.4 84.7 82.3 71.2 68.5 65.7 78.6 76.1 73.7 71.2 5.98 20 88.3 85. 7 83.1 80.5 78.2 67.7 65. 1 62.4 74.7 72.3 70.0 67.6 6.62 21 84.1 81.6 79.1 76.6 74-5 64.4 62.0 59-4 71. 1 68.9 66.7 64.4 7.30 23 80.3 77-9 75.5 73.1 71. 1 61.5 59.1 56.7 67.9 65.8 63.6 61.5 8.01 23 76.8 74.5 72.2 70.0 68.0 58.8 56.6 54.2 64.9 62.9 60.9 58.8 8.76 24 73.6 71.4 69.2 67.0 65.2 56.4 54-2 52.0 62.2 60.3 58.3 56.4 9-53 25 70.6 68.5 66.5 64.4 62.6 54-1 52.0 49.9 59-8 57-9 56.0 54.1 10.35 2« 67.9 65. 9 63.9 61.9 60.2 52.1 50.0 48.0 ♦57-5 55.6 53.8 S2.0 II. 19 27 65.4 63.5 61.5 59 6 57.9 50.1 48.2 46.2 55-3 53-6 51.8 50.1 12.07 28 63.1 61.2 59-3 57.5 55.9 48.3 46. 5 44.6 53.3 51-7 50.0 48.3 12.98 29 60.9 59- 1 57-3 55.5 53.9 46.7 44.9 43-0 51.5 49 9 48.3 46.6 13-92 30 58.9 57.1 55. 4 53.6 52.1 45.1 43.4 41.6 49.8 48.2 46.7 45- 1 14.90 31 57.0 55.3 53.6 51.9 50.5 43.7 42.0 40.2 48.2 46.7 45.2 43.6 15-91 33 55.2 53.6 51-9 50.3 48.9 42.3 40.7 390 46.7 45.2 43.7 42.3 16.95 . 33 53.5 51.9 50.4 48.8 47.4 41.0 39.4 37.8 45-3 43.8 42.4 41.0 18.03 34 51.9 50.4 48.9 47.3 46.0 39-8 38.3 36.7 43-9 42.6 41.2 39-8 19-13 35 50. 5 49.0 47.5 46.0 44.7 38.7 37.2 35.6 42.7 41-3 40.0 38.6 20.28 36 37 49.1 47.7 47.6 46.3 46.2 44.9 44-7 43. 5 43.4 42.3 37.6 36.6 36.1 35.2 34-7 33-7 _4_i-S 40.2 38.9 37.6 21.45 22.66 46.4 39-1 37'8 '36.6 38 46.5 45.1 43.7 42.3 41.2 35.6 34-2 32.8 39-3 38.1 36.8 35.6 23.90 39 45.3 43.9 42.6 41.3 40.1 34.7 33-4 32.0 25.18 40 41 44-1 42.8 41^5 40.2 A^jI 33.8 3_2.5 31.2 26.48 27.82 43.1 41.8 40. 5 39-2 38.1 33.0 31.7 30.4 42 42.0 40.8 39.6 38.3 37.2 32.2 31.0 29.7 29.20 Loads above the upper heavy lines will cause maximum allowable shears in webs. See, also, paragraphs in text and foot-note with same, page 567, relating to web-buckling in beams Loads below the lower broken lines will cause excessive deflections , • From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. Tables of Safe Loads for Steel Beams and Girders Table IV * (Continued). Safe Uniform Loads in Units of i ooo Pounds for Steel I Beams Maximum bending stress, i6ooo lb per sq in. Beams secured against yielding sidewise a Depth and weight of sections 11 •3 ^ — ■ — — i8-in 15-in 8-^ ^ . 70 65 60 55 48 75 70 65 60 55 50 45 42 4 5 6 lb lb lb lb lb lb lb lb lb lb lb lb lb u 258.8 229.^ 199.8 136.8 261.6 235.2 c'o^.'s 177.0 196.8 167.4 i^S.o 12-^.0 0.27 0.41 0.60 245.8 196.6 163-8 181. 7 145.4 121. 1 218.4 182.0 208.9 199-5 166.3 165.6 188.8 157.3 180.9 150.8 173.2 144.4 137.5 129.7 108. 1 114. 6 174. 1 157. 1 104.7 7 8 156.0 149-2 142.5 124.7 134.7 117. 9 124.8 109 . 2 140.4 134-8 118. 129.2 113. 1 123-7 108.3 103.8 90.8 98.2 85.9 92.6 81.0 89.8 78.5 0.81 1.06 136.5 130.6 122.9 9 121. 3 116. 1 no. 9 104.8 97.1 109.2 104.9 100.5 96.2 80.8 76.4 72.0 69.8 1.34 10 109.2 104.5 99.8 94.3 87-4 98.3 94.4 90.5 86.6 72.7 68.8 64.8 62.8 1.66 II 99.3 950 90.7 85.7 79-4 89.4 85.8 82.2 78.7 66.1 62.5 58.9 57.1 2.00 12 91.0 87.1 83.1 78.6 72.8 81.9 78.7 75.4 72.2 60.6 57.3 54.0 52.4 2.38 13 84.0 80.4 76.7 72-5 67.2 75.6 72.6 69-6 66.6 55.9 52.9 49.9 48.3 2.80 14 78.0 74.6 71-3 67-3 62.4 70.2 67.4 64.6 61.9 51.9 49-1 46.3 44.9 3.24 15 72.8 69.6 66.5 62.9 58.2 65.5 62.9 60.3 57.7 48. 5 45.8 43.2 41-9 3.72 i6 68.2 65.3 62.4 58.9 54-6 61.4 590 56.5 54.1 45.4 43.0 40.5 39-3 4.24 17 64.2 61.5 58-7 55-5 SI -4 57-8 55-5 53-2 50.9 42.8 40.4 38.1 37.0 4.78 i8 60.7 58.0 55.4 52.4 48. 5 54.6 52.4 50.3 48.1 40.4 38.2 36.0 34.9 5.36 19 57-5 55.0 52.5 49.6 46.0 SI. 7 49.7 47.6 45.6 38.3 36.2 34.1 33.1 5.98 20 54.6 52.2 49. P 47-1 43.7 49.2 47.2 45.2 43.3 36.3 34.4 32.4 31.4 6.62 21 52.0 49-7 47.5 44.9 4X.6 46.8 44-9 43.1 41.2 34.6 32.7 30.9 29.9 7^0 22 49-6 47.5 45-3 42.9 39-7 44.7 42.9 41 -I 39.4 33.0 31-3 29.5 28.6 8.01 23 47.5 45.4 43.4 41.0 38.0 42.7 41.0 39-3 37.7 31.6 29.9 28.2 27.3 8.76 24 45.5 43.5 41.6 39-3 36.4 41.0 39.3 37.7 36.1 30-3 28.6 27.0 26.2 9-53 25 43.7 41.8 39.9 37.7 34-9 39.3 37.8 36.2 34.6 29.1 27.5 25-9 25.1 10.35 26 42.0 40.2 38.4 36.3 33-6 37.8 36.3 34-8 33.3 28.0 26.4 24.9 24-2 II. 19 27 40.4 38.7 37-0 34.9 3^-4 36.4 35.0 33-5 32.1 26.9 25-S 24.0 23.3 12.07 28 390 37.3 35.6 33.7 31-2 35.1 33-7 32.3 30.9 26.0 24.6 23-2 22.4 12.98 29 37.6 36.0 34.4 32-5 30.1 33.9 32.5 31.2 29.9 25.1 23-7 22.4 21.7 13.92 30 31 36.4 35.2 34.8 33.7 33.3 32.2 31.4 30.4 29.1 28.2 _32_8 31.5 30^2 28.9 24^2 22.9 21.6 20.9 14.90 15.91 31.7 30.4 29.2 27.9 23.4 22.2 20.9 20.3 32 34.1 32.6 31.2 29.5 27.3 30.7 29.5 28.3 27.1 22.7 21.5 20.3 19 6 16.95 33 33.1 31-7 30.2 28.6 26.5 18.03 34 32.1 30.7 29.3 27.7 25-7 19 13 35 31.2 29.8 28.5 26.9 25.0 20.28 36 37 .3?i3 29.0 27.7 26.2 24-3 23.6 21.45 22.66 295 ~28".'2 27.0 25.5 38 28.7 27.5 26.3 24.8 230 23.90 Loads above the upper heavy lines will cause maximum allowable shears in webs. See, also, paragraphs in text and foot-note with same, page 567, relating to web-buckling in beams Loads below the lower broken lines will cause excessive deflections ♦From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. 580 Strength of Beams and Beam Girders Chap. 15 Table IV * (Continued). S^fe Uniform Loads in Units of i ooo Pounds for Steel I Beams Maximum bending stress, i6 ooo lb per sq in. Beams secured against yield ing sidewise Depth and weight of sections h i5-in i2-in lo-i.n CO 8-0 37 Mi 55 50 45 40 35 31 Mi r28 40 35 30 25 22 »4 3 4 5 6 lb lb lb 167.8 lb lb lb lb lb lb lb lb lb lb 90-6 197.0 I'ss's 1C4.6 840 f... 68.2 I4Q.8 120.4 91.0 62.0 so .4 0.15 0.27 0.41 0.60 190.2 142.7 114. 1 95.1 112. 8 84.6 67.7 56.4 104. 1 78.1 62.5 52.1 134.8 107.9 89.9 127.0 110.4 101.5 81.2 67 6 71.6 57.2 47.7 I0I.6 84.7 95.6 79.7 76.7 63.9 52.1 43.4 48.5 40.4 96.1 59 I 7 82.4 81.5 77.0 72.6 68.3 58.0 54.8 50.6 48.4 44.6 40.9 37.2 34.6 0.81 8 72.1 71.3 67.4 63. 5 59-8 50.7 48.0 44-3 42.3 39-0 35.8 32.6 30.3 1.06 9 64.1 634 59-9 56.4 53.1 45.1 42.6 39.4 37.6 34.7 31.8 28.9 26.9 1.34 10 57. 7 57.1 53 50.8 47.8 40.6 38.4 3S.S 33.9 31.2 28.6 26.0 24.2 1.66 II 52.4 51.9 49.0 46.2 43.5 36.9 34.9 32.2 30.8 28.4 26.0 23.7 22.0 2.00 12 48.1 47.6 44.9 42.3 39.8 33.8 32.0 29.5 28.2 26.0 23.9 21.7 20.2 2.38 13 44.4 43.9 41.5 39- 1 36.8 31.2 29s 27.3 26.0 24.0 22.0 20.0 18.6 2.80 14 41.2 40.8 38.5 36.3 34.2 29.0 27.4 25-3 24.2 22.3 20.4 18.6 17-3 3.24 IS 38.4 38.0 36.0 33.9 31.9 27.1 25.6 23.6 22.6 20.8 19. 1 17.4 16.2 3.72 i6 36.0 35.7 33.7 31.7 299 25.4 24.0 22.2 21.2 195 17.9 16.3 15.1 4-24 17 33-9 33.6 31.7 29.9 28.1 23.9 22.6 20.9 19.9 18.4 16.8 IS. 3 14.3 4.78 i8 32.0 31.7 30.0 28.2 26.6 22.5 21.3 19.7 18.8 17.4 15.9 14. 5 13. 5 5.36 19 30.4 30.0 28.4 26.7 25.2 21.4 20.2 18.7 17.8 16.4 15.1 13.7 12.8 5.98 20 21 28.8 27 -S 28.5 27.2 27.0 25.7 25.4 24.2 23.9 22.8 20.3 19.3 19.2 18.3 17.7 16.9 16.9 15.6 14.3 13.0 12. 1 11.5 6.62 " 30 16. 1 14.9 13.6 12.4 22 26.2 25.9 24.5 23.1 21.7 18.4 17.4 16. 1 IS. 4 14.2 13.0 II. 8 II. 8.01 23 25 I 24.8 23.4 22.1 20.8 17.6 16.7 15.4 8.76 24 25 24.0 23.1 23.8 22.5 21.2 19.9 16.9 16.0 14.8 9.53 10.35 22.8 21.6 20.3 19. 1 16.2 15.3 14.2 26 22.2 21.9 20.7 19.5 18.4 IS. 6 14.8 13.6 ... II. 19 27 21 4 12.07 28 20.6 12.98 29 19.9 13.92 30 19-2 14.90 31 18.6 15.91 32 18.0 ... 16.95 Loads above the upper heavy lines will cause maximum allo^ vable shears in webs. See, also, paragraphs in text and foot-note with same, pa Lge 567, relating to web-buckling in beams. Loads below the lower broken lines will cause excessive deflecti ons . j-:r From Pocke t Con ipanio n, Cai negie Steel Comp any, 1 ^ittsbi irgh, ] ^a. Tables of Safe Loads for Steel Beams and Girders 581 Table IV * (Continued). Safe Uniform Loads in Units of i ooo Pounds for Steel I Beams Maximum bending stress 16 000 lb per sq in. Beams secured against yielding sidewise Span, ft Depth and weight of sections Coeffi- cient of deflec- tion 9- n 8-in 7-in 35 lb 30 lb 25 lb 21 lb 25>^ lb 23 lb 2oy2. lb 18 lb I7H lb 20 lb 17^^ lb IS lb 3 4 5 6 7 8 9 10 II 12 13 14 IS 16 17 18 19 20 131.8 102.4 73.1 52.2 86.6 71.8 57.1 64.1 49.4 35.0 o.is 0.27 0.41 0.60 0.81 1.06 1.34 1,66 2.00 2.38 2.80 3.24 372 4.24 4.78 5.36 5.98 6.62 43.2 88.3 66.2 53.0 44.2 37-9 33.1 29.4 26.5 24.1 22.1 20.4 18.9 17.7 16.6 15.6 14.7 80.5 60.4 48.3 40.2 34.5 30.2 26.8 24.1 22.0 20.1 18.6 17.2 16. 1 15.1 14.2 13.4 72.6 54.5 43.6 36.3 31. 1 27.2 24.2 21.8 19.8 18.2 16.8 15.6 14.5 13.6 12.8 12. 1 60.8 45.6 36.5 30.4 26.1 22.8 20.3 18.2 16.6 15.2 14.0 13.0 12.2 II. 4 57.3 43.0 34-4 28.7 24.6 21.5 19. 1 17.2 15.6 14.3 13.2 12.3 II. 5 10.8 S3. 9 40.4 32.3 26.9 23.1 20.2 18.0 16.2 14.7 13.5 12.4 II. 5 10.8 10. 1 3S.2 42. Q 39.8 29.9 23.9 19.9 17. 1 14.9 13.3 11.9 10.9 10. 9.2 8.5 '¥.0 7.S 50.3 40.3 33.6 28.8 25.2 22.4 20.1 18.3 16.8 IS. 5 14.4 13.4 12.6 II. 8 II. 2 37.9 30.3 25.3 21.7 19.0 16.9 15.2 13.8 12.6 11.7 IQ.8 10. 1 9.5 3 2.1 5.7 C.4 J. 4 ).i ^.3 2-9 .7 ).7 ).9 ).2 J.~6 5.0 27.6 22.1 18.4 15.8 13.8 12.3 II. 10. 9.2 8.5 _r9 7.4 6.9 31. 1 25.9 22.2 19-5 17.3 15.6 14.2 13.0 12.0 II. I 10.4 9.7 2, 2 li l( i: I] ic ( t ~'i I 10.7 10. 1 10. 1 9.6 9.5 9.0 8.9 8.4 9.2 8.6 13.9 13.3 12.7 12. 1 II. 5 10.9 10.6 10. 1 Span, ft Depth and weight of sections Coeffi- cient of deflec- tion 6-in 5-in 4-in b 3-in lb 14% lb 12H lb 14% lb I2H lb m lb 10V2 lb 9\^ lb 27.0 18.0 12.0 9.0 7.2 6.0 S.I 4.5 8}/2 lb 21.0 16.9 II. 3 8.5 6.8 5.6 4.8 4.2 7 1 7K2 lb 61/2 lb lb I 2 3 4 5 6 7 8 9 10 II 12 13 14 57.0 42.2 27.6 50.4 35-7 21.0 32.8 15.2 10.6 8.0 6.4 5.3 4.5 4.0 21.7 20.7 10.4 6.9 5.2 4.1 3.5 15*8 9.f 6.-1 4.8 3.8 3.2 8.8 59 4.4 3.5 2.9 0.02 0.07 0.15 0.27 0.41 0.60 0.81 1.06 1.34 1.66 2.00 2.38 2.80 3.24 46.6 31.0 23.3 18.6 iS-5 13.3 II. 6 10.3 9-3 8.5 7.8 32.3 21.5 16.2 12.9 10.8 9.2 8.1 7.2 6.5 29.1 19.4 14.5 II. 6 9-7 8.3 7.3 6.5 5.8 19.0 12.7 95 7.6 6.3 5.4 4.8 28.4 21.3 17. 1 14.2 12.2 10.7 9.5 8.5 7.8 7.1 25.8 19-4 IS. 5 12.9 II. I 9.7 8.6 7.7 17.2 12.9 .10:3 8.6 7.4 6.4 5-7 5.2 3.0 2.6 2.7 2.4 2.5 2.2 4.2 3.8 4.0 3.6 3.8 3.4 35 3.2 5.9 5.4 5.3 4.8 4.7 4.3 7.0 6.5 7.2 6.7 6.6 6.1 6.0 5.5 .. ■ .. Loads at webs. See to web-buc Loads be ove t also, ding lowtl he upper h paragraphs in beams le lower brc eavy in te >ken 1 lines 1 xt an nes vi ;vill cj i foot ill cat luse maximum allowable sh -note with same, page 567, r ise excessive deflections ears in elating ?From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. 582 Strength of Beams and Beam Girders Chap. 15 Table V.* Safe Uniform Loads in Units of i ooo Pounds for Steel Chaniaels Maximum b< mding stress , 16 00 lb per sq in. Beams secured against yielding I sidewise Span, ft pth and weight of Coeffi- cient of deflec- tion sections De 15- in 13- in 55 lb 50 lb 45 lb 40 lb 35 lb 33 lb 50 lb 45 lb 40 lb 37 lb 35 lb 32 lb 3 4 S i ;> ^ 7 8 9 10 II 12 13 14 15 i6 17 i8 19 20 21 22 23 24 25 26 27 28 29 30 31 32 245-4 216.0 186.0 157-2 127.8 120.0 205.7 146.9 129.2 1175 97-5 0.15 0.27 0.41 0.60 0.81 1.06 1.34 1.66 2.00 2.38 > 2.80 3.24 3-72 4.24 4.78 5.36 5.98 6.62 7-30 8.01 8.76 9-53 10.35 II. 19 12.07 12.98 13.92 14.90 15.91 16.95 176.3 204.0 153.0 122.4 102.0 87-4 76.S 68.0 61.2 55.6 510 471 43-7 40.8 38.2 36.0 34.0 32.2 30.0 29.1 27.8 26.6 25.5 24.5 23.5 22.7 21.9 21.1 20.4 19.7 19.1 190.9 143.2 114,5 95.4 81.8 71.6 63.6 57.3 52.1 47-7 44.1 40.9 38.2 35.8 33.7 31.8 30.1 28.6 27.3 26.0 24.9 23.9 22.9 22.0 21.2 20.5 19.7 I9.I 177.8 133-4 106.7 88.9 76.2 66.7 59-3 53.3 48.5 44.5 41.0 38.1 35.6 33-3 31.4 29.6 28.1 26.7 25.4 24.3 23.2 22.2 21.3 20.5 19.8 19. 1 18.4 17.8 171. 6 128.7 103.0 85.8 73.6 64.4 57-2 51.5 46.8 42.9 39-6 35.8 34.3 32.2 30.3 28.6 27.1 25.7 24.5 23.4 22.4 21.5 20.6 19.8 160.3 120.2 9S.2 80.2 68.7 60.1 53.4 48.1 43.7 40.1 37.0 34.4 32.1 30.1 28.3 26.7 25.3 24.0 22.9 21.9 20.9 20.0 19.2 123.6 98.9 82.4 70.6 61.8 54-9 49-4 44-9 41.2 38.0 35-3 33-0 30.9 29.1 27.5 26.0 24.7 23.5 22.5 21.5 20.6 19.8 19.0 18.3 17.7 17.0 16.5 113. 8 91.0 75.8 65.0 56.9 50.6 45.5 41.4 37.9 35-0 32.5 30.3 28.4 26.8 25.3 239 22.8 21.7 20.7 19.8 19.0 18.2 17.5 16.9 16.3 15.7 15.2 III. I 88.9 74-1 63. 5 55.6 49-4 44.5 40.4 37.0 34.2 31.8 29.6 27.8 26.1 24.7 23.4 22.3 21.2 20.2 19-3 18.5 17.8 III. 7 89-4 74.5 63.8 55.9 49-7 44.7 40.6 37.2 34.4 31-9 29.8 27.9 26.3 24.8 23.5 22.3 21.3 20.3 19.4 18.6 17.9 17.2 106.6 85.3 71. 1 60.9 53.3 47-4 42.7 38.8 35.5 32.8 30.5 28.4 26.7 25.1 237 22.4 21.3 20.3 19.4 18.5 17.8 17. 1 16.4 103.2 82.6 68.8 59-0 51-6 45.9 41.3 37-5 34.4 31-8 29.5 27-5 25.8 24.3 22.9 21.7 20.6 19-7 18.8 18.0 17.2 ir».5 15.9 97-5 78.0 65.0 55.7 48.7 43.3 39-0 35.4 32.5 30. <9 27-9 26.0 24.4 22.9 21.7 20.5 19-5 18.6 17.7 17.0 16.2 15.6 IS-O 17. 1 16.5 15.9 15.3 14.8 18.5 19.1 18.4 17.8 17.2 16.6 16.0 .T5.8 15.2 15.3 14.7 14.4 13.9 18.5 17.9 17.2 16.7 15.9 15.4 14.7 14.2 14. J 13.9 Loads at webs. See to web-buc Loads be ove t also kling lowtl he up para in bea le low per h graph ims er bro 2avy 5 in t kenl ines will c 2Xt and foo nes will cai ause maxim t-note with ise excessive um a same jdefle llowable sh , page 567, actions ears in relating •Fi ■omP acket Comp mion, Carnegie St eel Compan y, Pit tsburgh, Pa. i" a'l Tables of Safe Loads for Steel Reams and Girders 583 Table V * (Continued). Safe Uniform Loads in Units of i ooo Pounds for Steel Channels Maxim am bending stress, 16 000 Ifc persq in. Beams secured against yielding sidewise ight of sections Depth and we Span, ft Coeffi- cient of deflec- tion 12-in lo-in 40 25 20t4 35 30 35 30 25 20 IS lb lb lb lb lb lb lb lb lb lb 2 3 4 181.9 152.6 123.1 93-6 67.2 164.6 135.2 105.8 '76.4 4^.0* 0.07 0.15 0.27 175. 1 116.7 87.5 123.2 82.1 61.6 no. I 73.4 55.1 97.0 64.7 48.5 106.2 79-7 95.8 71.8 85. 3 64.0 56.0 42.0 47.6 35.7 56.9 5 70.0 63.7 57.5 51.2 45.5 49-3 44.0 38.8 33.6 28.5 0.41 6 58.4 53.1 47.9 42.7 38.0 41. 1 36.7 32.3 28.0 23.8 0.60 7 50.0 45.5 41. 1 36.6 32.5 35.2 31.5 27.7 24.0 20.4 0.81 8 43.8 39-8 35.9 32.0 28. 5 30.8 27.5 24.3 21.0 17.8 1.06 9 38.9 35.4 31.9 28.4 25.3 27.4 24.5 21.6 18.7 IS. 9 1.34 10 35.0 31.9 28.7 25.6 22.8 24.6 22.0, 19-4 16.8 143 1.66 II 3'i.8 29.0 26.1 23.3 20.7 22.4 20.0 17.6 15.3 13.0 2.00 12 29.2 26.6 23.9 21.3 19.0 20.5 18.4 16.2 14.0 11.9 2.38 13 26.9 24.5 22.1 19.7 17.5 19.0 16.9 14.9 12.9 II. 2.80 14 25.0 22.8 20.5 18.3 16.3 17.6 15.7 13.9 12.0 10.2 3-24 15 23.3 21.2 19.2 17. 1 15.2 16.4 14.7 12.9 II. 2 9.5 3.72 i6 21.9 19.9 18.0 16.0 14.2 15.4 13.8 12. 1 10.5 8.9 4.24 17 20.6 18.7 16.9 15. 1 13.4 14.5 13.0 II. 4 9.9 8.4 4.78 i8 19-5 18.4 17.7 16.8 16.0 14.2 12.7 13.7 12.2 10.8 9-3 8.8 7.9 5. 36 5. 98 19 15. 1 13. 5 12.0 13.0 II. 6 10.2 7.5 20 21 17.5 16.7 15.9 15.2 14.4 13.7 12.8. 1 1. 4 12^3 II. ._?iZ. 8.4 ..111. 6.62 730 12.2 10.8 II. 7 10.5 9.2 8.0 6.8 22 15.9 14. 5 13. 1 II. 6 10.4 II. 2 10. 8.8 7.6 6.5 8.01 23 IS. 2 13.9 12. 5 II. I 9-9 8.76 24 25 _Hl?. 13.3 12.0 10.7 __9A 9.53 10.35 14.0 '12'. 8" II. 5 10.2 9.1 26 13.5 12.3 II. I 9.8 8.8 II. 19 Loa ds abc )ve the upper heavy lines will cause rm ixirnum allowable a lears in webs. See, also, paragrap hs in t ext and foot-note w ith same, page 567, relating to we Loa b-buck dsbel ling in beams DW the lower broken lines will cause exc essive deflections * From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. 584 Strength of Beams and Beam Girders Chap. 15 Table V * (Continued). Safe Uniform Loads in Units of i ooo Pounds for Steel Channels Maximum bending stress, i S 000 lb per sq in. Beams secured against yielding sidewise Span, ft Depth and weight of sections Coeffi- cient of deflec- tion 9-in 8-in 7-in 25 20 IS I3V4 21 H m V 16M 13^^ 11V4 I9?4 nVi 14^4 12H 9H lb lb lb lb lb lb lb lb lb lb lb lb lb lb no. 7 81.4 9^.1 78.4 63.8 49.1 88.6 73.9 59.2 44.S 2 3 83.8 55. 9 72.0 48.0 51.8 41.4 63.7 42.5 58.. 39. < )S3.2 )3S.S 48.0 32.0 35-2 28.7 SO. 6 33.7 46.0 30.7 41.4 27.6 ^6.8 29-4 0.07 0.15 40.2 37.4 24.621.4 4 41.9 36.0 30.1 28.0 31.8 29.5 J26.6 24.0 21.5 25. 3 23.0 20.7 18.4 16. 1 0.27 5 6 33.5 27.9 28.8 24.0 24.1 20.1 22.4 18.7 25. 5 21.2 23.^ I9.i 121.3 17.7 19.2 17.2 20.2 16.9 18.4 15.3 26.6 13.8 14.7 12.3 12.9 10.7 0.41 0.60 16.0 14.4 7 23.9 20.6 17.2 16.0 18.2 16.' IS 2 13.7 12.3 14.4 13.1 II. 8 10.5 9.2 0.81 8 20.9 18.0 IS. I 14.0 15.9 14.^ 13.3 12.0 10.8 12.6 11.5 10.4 9.2 8.0 1.06 9 18.6 16.0 13.4 12.5 14.2 13.C II. 8 10.7 9.6 II. 2 10.2 92 8.2 7.1 I 34 10 16.8 14.4 12. 1 II. 2 12.7 II. 7 10.6 9.6 8.6 10. 1 9.2 83 7.4 6.4 1.66 II IS 2 13 I II. I0.2 II. 6 10.6 9-7 8.7 7.8 9.2 8.4 7.5 6.7 5.8 2.00 12 14.0 12.0 10. 1 9 3 10.6 9.7 8.9 8.0 7.2 8.4 7.7 6.9 6.1 5.4 2.38 13 12.9 II. I 9.3 8.6 9.H 9.C 8.2 7.4 6.6 7.8 7.1 6.4 57 4.9 2.80 14 IS 12.0 II. 2 10.3 9.6 8.6 8.0 8.0 75 9.1 8.5 8..1 7.8 7.6 7.1 6.9 6.4 6.2 57 7.2 6.6 5.9 5.3 4.6 3.24 3.72 6.7 6.1 5.5 4.9 4.3 i6 17 10.5 9-9 9.0 8.5 75 7.1 7.0 6.6 8.0 7.3 6.7 60 54 6.3 5-7 5.2 4.6 4.0 4.24 4.78 7.5 6.9 6.3 5.6 S.I i8 19 9 3 8.0 6.7 6.2 7.1 6.5 59 5 3 4.8 5.36 5.98 8.8 7.6 6.3 5.9 20 8.4 7.2 6.0 5.6 6.62 Span, Depth and weight of sections Coeffi- cient of 6-in S-in 4-in 3-in ft deflec- 15^2 13 ioV{ 8 11!^ 9 6^2 7M 6M S»4 6 5 4 tion lb lb lb lb lb lb lb lb lb lb lb lb lb 47-7 26.0 21.7 158 I 2 67.6 5=8 38.2 24.0 44.4 22.2 33.0 19.0 24.4 12.2 W.2 II. I 144 14 7 7 4 13.1 6.6 10.2 5.8 0.02 0.07 34 7 30.8 26. ? 23.1 18.9 10. 1 3 23.2 20.5 17. ? 15.4 14.8 12.6 10.5 8.1 7.4 6.7 4 9 4 4 3.9 0.15 4 17.4 IS. 4 13. 1 II. 6 II. I 9.5 79 6.1 5.6 5.1 3 7 3.3 2.9 0.27 5 6 7 13 9 II. 6 99 12.3 10.3 8.8 10. J 9.< 7. i 9.2 3 7.7 7 6.6 8.9 7.4 6.3 7.6 6.3 54 6.3 53 4-5 4.9 4.5 4.1 2 9 2.6 2.3 1.9 0.41 0.60 0.81 4.1 3.5 3.7 3.2 3.4 29 2 5 2.2 2 I 1.9 1.7 8 8.7 7.7 6. 1 5.8 55 4.7 4.0 3.0 2.8 2.5 I 8 1.6 1. 5 1.06 9 7.7 6.8 6.< D S.I 4.9 4.2 3.S 2.7 2.5 2.2 1.34 lO II 6.9 6.3 6.2 5.^ \ 4.6 ) 4.2 _4 4 4.0 3.4 3.2 7.9 2.4 2.2 2.0 1.66 2.00 5.6 4.< 12 13 5.8 5.1 4 . > 3 9 3.7 32 2.6 2.38 2.80 5 3 4.7 4- [ 3.6 14 5.0 4.4 3.{ I 3.3 3 24 Loads above the upper heavy lines will cause maximum allowable sli ears in wet>s. See. also, paragraphs in text and foot-note with same, page 567. relating to web-buckling in beams Loads below the lower broken lines will cause excessive deflections • From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa, Tables of Safe Loads for Steel Beams and Girders 585 Table VI.* Safe Uniform Loads in Units of i ooo Pounds for Steel H Beams Maximum bending stress, i6 ooo lb per sq in. Secured against yielding sidewise Depth and weight of sections Coefficients of deflection Span, ft 8-in 34.0-lb 6-in 23.8-lb 5-in 18.7-lb 4-in 13.6-lb 3 4 s 7 8 9 10 II 12 13 14 IS i6 17 i8 25.0 3T.3 19.0 14-3 11.4 o.iS 0.27 0.41 37-6 25-4 20.3 32.1 60.0 51.3 44.0 38s 34.2 30.8 28.0 25.6 23-7 22.0 20.5 19.2 26.7 22.9 20.1 17.8 16.0 14.6 13-4 16.9 14.5 12.7 11.3 10. 1 9-5 8.1 71 0.60 0.81 1.06 1.34 1.66 2.00 2.38 2.80 3.24 3.72 4.24 4.78 5.36 6.3 5.7 9.2 8.5 12.3 11.5 18. 1 171 Table VH. t Safe Uniform Loads in Pounds for SmaU Steel Channels, or Grooved Steel Computed for a fiber-stress of 16 000 lb per sq in Secured against yielding sidewise Depth, in Weight Span in feet Section- number foot, lb 2 2.S 3 3.5 4 4.5 5 6 2H 3.80 378s 3028 2523 2 163 I 892 1682 I 514 I 261 2 2 2.90 2560 2048 I 706 I 463 I 280 1 138 I 024 853 3 4 2 3.60 2880 2304 I 920 1643 1440 I 280 I 152 960 2 3.60 3 120 2496 2080 1783 I 560 138b I 248 I 040 2 2.60 1 2256 1804 IS04 I 289 I 128 I 000 902 752 6 2 2.00 I 418 II34 945 810 709 630 5t>7 472 7 g iH 1. 13 907 726 60s S18 454 403 363 302 256 iH 1.32 768 614 512 439 384 341 307 9 10 iH 1.46 868 694 578 496 434 386 347 289 iM 0.94 47S 380 316 271 237 211 190 II iH 1. 12 469 375 313 268 234 208 188 12 iH 1. 00 437 350 291 250 218 194 175 13 I 0.83 336 268 224 192 168 .... 14 I 0.68 266 212 177 152 133 IS li 0.67 224 180 149 128 112 16 li 0.69 229 183 152 130 .... 17 Va 0.53 133 106 88 • From Pocket Companion, Carnegie Steel t Complied by F. E. Kidder. See note on Company, Pittsburgh, Pa. page 570. Strength of Beams and Beam Girders Chap. 15 Table VIII.* Safe Uniform Loads in Units of i ooo Pounds for Steel Angles with Equal Legs. (See page 566.) Neutral Axis Parallel to Either Leg Maximum bendi ng stress, 16 000 lb per sq in. Secured against yielding side wise Size, \ hick- less, 1-ft span Maximum span, 360 X deflection Size, Thick- i-ft span Maximum span, 360 X deflection in in Length, in in Safe load Safe load Length, ft Safe load Safe load ft 8X8 I H 186.99 8.31 22.5 zHXsVi ^Me 24.00 2.55 9-4 8X8 I Ha 177.81 7.87 22.6 s'AXiVz H 22.51 2.37 ^l 8X8 I 168.53 7.43 22.7 3V^X3F2 ^Hg 20.91 2.18 9.6 8X8 me 159 15 6.98 22.8 35^^X3'/^ 3M2X3K2 Me 19.31 17.60 2.00 1. 81 9-7 9.7 8X8 % 149-55 6.53 22.9 3HX3K2 '/^ 15.89 1.62 9.8 8X8 13/16 139.84 6.08 23.0 3/2X3^/2 Me 14.08 1.42 9-9 8X8 % 130.03 5.63 23.1 sHXsli H 12.27 1.23 10. 8X8 Hie 120.00 5.18 23.2 3K2X3K2 Me 10.45 1.04 10. 1 8X8 H 109.87 4.73 23.2 s'AXsV^ H 8.43 0.83 10.2 8X8 Me 99 63 4.28 23.3 3 X3 % 13.87 1.69 8.2 8X8 H 89.28 3.82 23.4 3 X3 Me 12.69 I 53 8.3 3 X3 Y' 11.41 1-37 8.3 6X6 1 6X6 6X6 91.41 86.51 81.39 5.48 5-16 4.84 16.7 16.8 16.8 3 X3 3 X3 3 X3 3 X3 Me % Me 10.13 8.85 7.57 6.19 1. 21 1.04 0.88 0.71 8.4 8.5 8.6 8.7 6X6 1^6 76.27 4.51 16.9 6X6 % 71.04 4.18 17.0 2HX2V2 Vi 7.79 1.15 6.8 6X6 6X6 6X6 iMo Via 65.81 60.37 54.83 3.85 3-51 3.17 17. 1 17-2 17-3 2l/2X2^1j 2l^^X2»-i 2K2X2K2 2K>X2H Me Me 6.93 6.08 5.12 4.16 1. 01 0.87 0.72 0.58 6.9 7.0 7.1 7.2 6X6 H 49-17 2.83 17.4 21^^X21/2 Me 3.20 0.44 7.3 6X6 Me 43.41 37 65 2.48 2.14 17.5 2}'^X2H H 2.13 0.29 7.4 6X6 % 17.6 2 X2 Me 4.27 0.79 5.4 2 X2 3/i 3.73 0,68 5.5 5X5 1 61.87 4.55 13.6 2 X2 Me 3.20 0.57 5.6 5X5 ^Me 58.56 4.28 13.7 2 X2 M 2.67 0.46 5.7 5X5 H 55.15 4.00 13.8 2 X2 Me 2.03 0.35 5.8 5.8 5X5 me 51.73 3.73 13.9 2 X2 78 1.39 0.24 5X5 y^ 48.32 3.45 14 -O iHXiYi Me 3.20 0.68 4.7 5X5 iMe 44.80 3.18 14. 1 I>tXl3/4 3/i 2.77 0.60 4.7 5X5 H 41.17 2.90 14.2 i%xm Me 2.45 0.51 4.8 5X5 rie 37,44 2.62 14.3 iliXiM U 2.03 0.41 4.9 5X5 M 33-6o 2.34 14.4 mxiH Me 1.49 0.30 5.0 5> :5 Via 29.76 2.06 14.5 1^4X1^4 H 1.07 0.21 5.1 5> :5 % 25.81 1. 78 14.5 iHXi>^ I'/^Xii/^ Me 2.03 1. 71 0.51 0.42 4.0 4.1 4> C4 »M6 32.11 2.95 10.9 I'/^XiH M 1.39 0.33 4.2 4X4 H 29.97 2.73 II. iHXiV^ Me 1.07 0.25 4.3 4X4 »He 27.84 2.51 II. I IHXIK2 H 0.77 0.17 4.4 4X4 . H 25.60 2.29 II. 2 iHXiH Me 1. 17 0.36 3.3 4X4 Me 23.36 2.07 II. 3 iHXiH H 0.97 0.29 3.4 4X4 H 21.01 1.85 II. 4 iHXiH Me 0.76 0.22 3.5 4X4 Me 18.67 1.63 11.4 iHXiH H 0.52 0.14 3.6 4X4 H 16.21 1. 41 II. 5 I Xi M 0.60 0.22 2.6 4X4 Me 13.76 1. 19 II. 6 I XI Me 0.47 0.17 2.7 4X4 H 11.20 0.96 II. 7 I XX H 0.33 0.12 2.8 1 * From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. Tables of Safe Loads for Steel Beams and Girders 587 Table IX.* Safe Uniform Loads in Units of i ooo Pounds of Steel Angles with Unequal Legs. (See page 566.) Neutral Axis Parallel to Shorter Leg Maximum bending stress, i6 000 lb per sq in. Secured against yielding sidewise I-ft Maximum I-ft Maximum Size. Thick- span span, 360 X deflection Size, Thick- Span span, 360 X deflection in ness, in ness, in Safe Safe Length, in Safe Safe Length, load load ft load load ft 8X6 I 161. 17 7.49 21.5 6X3^2 I 83.52 S.S7 iS.o 8X6 1^6 152.21 7.04 21.6 6X3H 15/6 79.04 5. 24 IS. I 8X6 % 143.04 6.59 21.7 6X3H % 74.45 4.90 15.2 8X6 1^6 133.87 6.14 21.8 6X31^^ 1^6 69.87 4.57 IS. 3 8X6 % 124.48 5.68 21.9 6X3I/2 H 65.07 4.23 15.4 8X6 1M6 114.88 5.22 22.0 6X3H 1H6 60.27 3.89 IS. 5 8X6 •>i 105.28 4.76 22.1 6X3^^ ^A 55.36 3.55 IS. 6 8X6 Me 95.47 4.30 22.2 6X3K2 Ha 50.35 3.21 IS. 7 8X6 \^ 85.55 3.84 22.3 6X3Vi H 45.23 2.86 15.8 8X6 ViO 75.41 3.37 22.4 6X3!/^ 7/6 40.00 2.52 15.9 6X3i/i % 34.67 2.17 16.0 8X3'/^ I 146.03 7-53 19-4 ■ 6X3K2 5/6 29.23 1.83 16.0 8X3H ^Me 138.03 7.08 19.5 8X3'/^ % 129.92 6.63 19.6 8X3^^^ 13/16 121.60 6.17 19.7 5X4 I'i 53.23 4.00 13 3 8X3M2 M 113.17 5.72 19.8 5X4 13.i6 50.03 3.73 13.4 8X3^/^ iHe 104.58 5.23 19.9 5X4 % 46.61 3.46 13. 5 8X3H H 95.79 4.78 20.0 5X4 1/6 43.20 3.19 13.5 ^XM 9/16 86.93 4.32 20.1 5X4 % 39-79 2.92 13.6 8X3H H 77.97 3.86 20.2 5X4 Vie 36.16 2.64 13.7 8X3K2 7/16 68.80 3.39 20.3 5X4 H 32.53 2.36 13.8 5X4 Vie 28.80 2.07 13.9 7X3>^ I 112.85 6.52 17.3 5X4 H 24.96 1.78 14.0 7X3I/2 iMe 106.67 6.13 17.4 7X3^/^ H 100.48 5. 75 17.5 7X3H 13/6 94.08 5.36 17.6 5X3H % 52.05 4.04 12.9 7X3K2 3/ 87.68 4.97 17.6 5X3H . 13/6 48.85 3.76 13.0 7X3H .Hie 81.07 4.58 17.7 5X3H % 45.65 3.49 13.1 7X3!'i H 74.35 4.18 17.8 5X3!/^ 11/6 42.35 3.21 13.2 7X3H 9/6 67.52 3.77 17.9 5X3 V^ % 38.93 2.93 13.3 7X3'/^ V2 60.59 3.37 18.0 5X31-^ M6 35.41 2.64 13.4 7X3H 7/6 53.44 2.96 18. 1 5X3!/^ Vl 31.89 2.36 13. 5 7X3^/^ % 46.19 2.54 18.2 5X3I/2 7/6 28.16 2.07 13.6 5X3\^ % 24.43 1.79 13.7 6X4 I 85.55 5.56 15.4 sXsH 5/6 20.69 1. 51 13.7 6X4 15/6 80.96 5.22 15. 5 6X4 7/i 76.27 4.89 15.6 SX3 13/6 47.47 3.77 12.6 6X4 1^6 71.47 4.55 IS. 7 5X3 M 44.37 3.49 .12.7 6X4 3/ 66.67 4.22 15.8 5X3 iHe 41.17 3.22 12.8 6X4 11/6 61.65 3.88 IS. 9 5X3 % 37.87 2.94 12.9 6X4 H 56.64 3.54 16.0 5X3 9/6 34.45 2.65 13.0 6X4 ^6 51.52 3.20 16. 1 5X3 H 31.04 2.37 13.1 6X4 H 46.19 2.85 16.2 5X3 7/6 27.52 2.09 13.2 6)^4 M6 40.85 2.51 16.3 5X3 % 23.89 1.80 13.3 6X4 3/i 35.41 2.16 16.4 5X3 5/6 20.16 1. 51 13.4 * From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa, 588 Strength of Beams and Beam Girders Table IX * (Continued). Safe Uniform Loads in Units of i ooo Pounds for Steel Angles with Unequal Legs. (See page 566.) Neutral Axis Parallel to Shorter Leg Maximum bending stress, 16 000 lb per sq in. Secured against yielding side wise i-ft Maximum i-ft Maximum Size, Thick- span span, 360 X deflection Size, Thick- span span, 360 X deflection ness. in . " ' in in Safe Safe Length, in Safe Safe Length, load load ft load load ft 4HX3 13/16 38.61 3.36 11.5 3 X2I/2 Me 12.27 1.53 8.0 4HX3 H 36. OS 3. II TI.6 3 X2I/2 Vi 11.09 1.37 8.1 4HX3 I'/ie 33-49 2.87 II. 7 3 X2i/i Me 9-92 1.22 8.1 4HX3 H 30.83 2.62 II. 8 3 X2K2 % 8.64 1.06 8.2 4^^X3 Me 28.16 2.38 II. 8 3 X2I/2 Me 7.36 0.89 8.3 4HX3 K2 25.28 2.13 II. 9 3 X2i^^ H 5.97 0.71 8.4 4HX3 Me 22.40 1.87 12.0 4V^X3 H 19.52 1. 61 12. 1 3 X2 1/4 10.67 1.39 7-7 4HX3 Me 16.43 1. 35 12.2 3 X2 Me 9-49 1.22 7.8 4 X3I/2 iMe 31.15 2.94 10.6 3 X2 % 8.32 1.05 7.9 4 X33'^ H 29 23 2.73 10.7 3 X2 Me 7.04 0.88 8.0 4 X3H iMe 27 . 20 2.52 10.8 3 X2 M 5.76 0.71 8.1 4 X3^/^ H 25 . 07 2.3c 10.9 4 X3>^ ^16 22.93 2.08 II. 2M2X2 Vi 7.47 1. 15 6.5 4 X3'/^ 1/^ 20.69 1.86 II. I 2HX2 Me 6.72 1.02 6.6 4 X3H 7/16 18.35 1.64 II. 2 2M2X2 % 5.87 0.88 6.7 4 X3'/^ 3/i 16.00 1. 41 II. 3 2I/2X2 Me 5.01 0.74 6.8 4 X3H 5/16 13.44 1. 18 II. 4 2^/^X2 H 4.05 0.59 6.9 4 X3 13/i6 30.61 2.97 10.3 2K2X2 Me 3.09 0.44 7.0 4 X3 M 28.59 2.75 10.4 21.4X2 \^ 2.13 0.30 7.1 4 X3 me 26.56 2.53 10.5 4 X3 % 24.53 2.31 10.6 2\^X\V2 Me 4.69 0.73 6.4 4 X3 Me 22.40 2.09 10.7 2l/4Xll/2 M 3.84 0.59 6.5 4 X3 I'i 20.16 1.87 10.8 2V2Xll/i Me 2.99 0.45 6.6 4 X3 Me 17.92 1.64 10.9 4 X3 % 15.57 1.42 II. 2KX1I/2 J'i 5.76 1.02 5.6 4 X3 Me 13.12 1. 19 II. 2HX1I/2 Me 512 0.90 5.7 4 X3 H 10.67 0.96 II. I 2HX1H H 4.48 0.77 5.8 3HX3 i^e" 23.47 2.57 9.1 2l/4Xll/2 Me 3.84 0.65 5.9 3l'^X3 % 21.87 2.38 9.2 2i/4Xii/i M 3.20 0.53 6.0 3^X3 iMe 20.37 2.19 9-3 2HXI1/4 Me 2.45 0.40 6.0 3HX3 S/^ 18.77 2.00 9.4 3HX3 9/ie 17.17 1. 81 95 2 Xll/4 H 3.63 0.70 5.2 3^/^X3 ^^ 15.47 1.62 9.5 2 XlH Me 3.09 0.58 5.3 3HX3 Me 13.76 1.43 9.6 2 Xll/i. M 2.56 0.47 5.4 3^X3 % 12.05 1.24 9.7 2 X1K2 Me 1.92 0..35 5-5 33'^X3 Me 10.24 1.05 9.8 2 Xll/i \^ 1.39 0.24 5.6 3l'^X3 H 8.32 0.84 9.9 2 Xll/i K 2.45 0.47 5.2 31/^X21/^ iMe 19- 73 2.19 9.0 2 XiH Me 1.92 0.36 5.3 3»/^X2i/^ 5/i 18.24 2.00 91 3^/^X21.^ Me 16.64 1.82 9.1 I%Xll/4 H 1.92 0.42 4.6 3HX2].i ^ 15.04 1.63 9.2 iMXiH Me 1.49 0.32 4.7 3^^X2H Me 13.44 1.44 9.3 i3/4Xii/i H 1. 00 0.21 4.8 3V4X2i/^ 34 11.73 I 24 9-4 ii/4Xii/4 Me 1. 71 0.44 39 3*/^X2i/^ Me 9.92 1.04 9-5 iHXii/4 M 1.39 0.35 4.0 3^X21/^ M 8.00 0.83 9.6 ii/4XiM Me 1.07 0.26 4.1 ♦ From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. Tables of Safe Loads for Steel Beams and Girders 689 Table X.* Safe Uniform Loads in Units of i ooo Pounds for Steel Angles with Unequal Legs. (See page s66.) Neutral Axis Parallel to Longer Leg Maximum bending stress, i6 ooo lb per sq in. Secured against yielding sidewise I-ft Max imum i-ft Maximum Size, Thick- Span span, 360 X deflection Size, Thick- span span, 360 X deflection in ' in ' in Safe Safe Length, in Safe Safe Length, load load ft load load ft 8X6 I 95.15 5.44 17.5 6X3I/2 I 30.93 3.09 10. 8X6 15/16 89.92 5. II 17.6 6X3H2 15/6 29.23 2.90 10. 1 8X6 H 84.69 4.79 17.7 6X3^^ % 27.63 2.71 10.2 8X6 1M6 79.36 4.45 17.8 6X3H 13/6 25.92 2.52 10.3 8X6 H 73.92 4.13 17.9 6X3H % 24.21 2.33 10.4 8X6 iMo 68.37 3.80 18.0 6X3H 11/6 22.51 2.14 lo.S 8X6 54 62.72 3.48 18.0 6X3H H 20.69 1.95 10.6 8X6 ^6 56.96 3.15 18. 1 6X3H 9/6 18.88 1.76 10.7 8X6 H SI. 09 2.81 18.2 6X3K2 l/i 16.96 1.57 10.8 8X6 Ma 45.12 2.47 18.3 6X3»/^ 7/6 15.04 1.38 10.9 6X3!/^ % 13.12 I 19 II. 8X35'^ I 32.21 3.10 10.4 6X3^^ Ma 11.09 1. 00 II. I 8X3I/2 Me 30.40 2.90 10.5 8X3H H 28.69 2.71 10.6 8X3H me 26.88 2.52 10.7 5X4 % 35.31 3.15 II. 2 8X3H 94 25.07 2.33 10.8 5X4 1^6 33.17 2.93 11.3 8X3K2 11/16 23.15 2.13 10.9 5X4 H 30.93 2.71 II. 4 SXsVi H 21.33 1.94 II. 5X4 1/6 28.69 2.50 II. 5 8X3I/2 ri6 19.41 1.74 II. I 5X4 % 26.45 2.28 II. 6. 8X3V^ H 17.49 1.57 II. 2 5X4 Vie 24.11 2.16 II. 7 8X3K2 Vie 15.57 1.38 II. 3 5X4 H 21.76 1.84 II. 8 5X4 Vie 19.31 1.62 11.9 7X3'/2 I 31.57 3.10 10.2 5X4 % 16.75 1.40 12.0 7X3K2 1^6 29.87 2.90 10.3 7X3K2 % 28.16 2.71 10.4 SX3K2 li 26.88 2.71 9.9 1X3^ 1^6 26.45 2.52 10.5 5X3!/^ i-Me 25.28 2.53 10. 7X3K2 % 24.64 2.33 10.6 5X3'/i % 23.68 2.34 10. r 7X3K2 iMe 22.83 2.14 10.7 5X3I/2 11/6 21.97 2.15 10.2 7X3K2 % 21.01 1.95 10.8 5X3K2 H 20.27 1.97 10.3 7X3'/2 Vie 19.20 1.76 10.9 5X3i/i 9/6 18.45 1.78 10.4 7X3H ¥2 17.28 1.57 II. 5X3I/2 V2 16.64 1.60 10.4 7X3H 7/16 15.36 1.38 II. I 5X3I/2 lU 14.83 1. 41 10.5 iXs'A H 13.44 1. 19 II. 2 5X3K2 H 12.91 1.22 10.6 5X3I/2 5/6 10.88 1.02 10.7 6X4 I 40.43 3.55 II. 4 6X4 15/6 38.29 3.33 II. 5 6X4 'A 36.16 3.12 II. 6 5X3 13/6 18.56. 2.16 8.6 6X4 13/6 33.92 2.90 II. 7 5X3 H 17.39 2.00 8.7 6X4 H 31.68 2.69 II. 8 5X3 11/6 16. II 1.83 8.8 6X4 11/6 29.44 2.47 II. 9 5X3 % 14.83 1.67 8.9 6X4 5/^ 27.09 2.26 12.0 5X3 Vie 13.55 1. 51 9.0 6X4 9/6 24.64 2.05 12.0 5X3 \i 12.27 1.35 9.1 6X4 H 22.19 1.84 12. 1 5X3 Vie 10.88 1. 18 9.2 6X4 7/6 19-73 1.62 12.2 5X3 H 9-49 1.02 9-3 6X4 H 17.07 1.39 12.3 5X3 Vie 8.00 0.8s 9.4 ? From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. 590 Strength of Beams and Beam Girders Chap. Table X * (Continued). Safe Uniform Loads in Units of i ooo Pounds for Steel Angles with Unequal Legs. (See page 566.) Neutral Axis Parallel to Longer Leg Maximum bending stress, 16 000 lb per sq in. Secured against yielding sidewise 4HX3 4y2X3 4HX3 4V^X3 4HX3 4HX3 4K2X3 4HX3 4K2X3 X3H X33'^ X3H X3H X3H X33'^ X3H X33'^ X3 X3 X3 X3 X3 X3 X3 X3 X3 X3 3HX3 3K2X3 3K2X3 3}'iX3 31^^X3 3HX3 3M2X3 3HX3 3'AX3 3V^X3 3HX2y2 3HX2H 3HX2K2 33'^X2H 3V^X2i/i 3MX2y2 3yzX2M 3\^X2\(i Thick- ness, % Vie 'A 1^6 iHe y2 7/16 Ma i-ft span Safe load 18.24 17.07 15.89 14.61 13.33 12.05 10.77 9-39 8.00 24-53 22.93 21.33 19 63 17.92 16.21 14.40 12.59 10.67 17.92 16.7s 15.57 14.40 13.12 11.84 10.56 9.28 7.89 6.40 17.60 16.43 15.36 14.19 12.91 11.73 10.45 9.07 7.68 6.19 10.56 9.81 8.96 8. II 7.25 6.29 5. 33 4.37 Maximum span, 360 X deflection Safe load 2.15 1.99 1.83 1.67 1. 51 1.35 1. 19 1.03 0.87 2.56 2.37 2.18 1.98 1.79 1.60 1.41 1.22 1.03 2.15 1.99 1.83 1.67 1. 51 1. 35 119 1.03 0.87 0.70 2.17 2.01 1.85 1.60 1.52 1.36 1.20 1.04 0.87 0.70 1. 51 1.39 1.26 1. 13 0.99 0.8s 0.71 0.58 Length, ft Size, X2l/i X2I/2 X2^ X2H X2\i X2K2 3 X2 3 X2 3 X2 3 X2 3 X2 2KX2 2M2X2 2l/^X2 2K2X2 2 1/2X2 2I/2X2 2l/^X2 •2i/iXi3'^ 21/2XI/2 2j'iXll/2 2HX1K2 2}4Xl/2 2/4Xll/i 2HX1K2 2MX1/2 2l/Xl}'i 2 X1/2 2 XiH 2 XiH 2 X1/2 2 X1/2 2 XiH 2 XiH 1^4 XiM iMXiH i%XiH iMXiH l/2XlH iHXiH Thick- ness, y2 7/6 Vie Me 3/8 Via H Me I-ft span Safe load 8.75 7.89 7.04 6.19 5.23 4.27 5.01 4.48 3.95 3.41 2.77 4.91 4.37 3.84 3-31 2.67 2.13 1.49 1. 81 1.49 1. 17 2.77 2.4s 2.13 1. 81 1.49 1. 17 2.13 1. 81 1.49 117 0.80 1.04 0.80 .1.01 0.80 0.56 1. 17 0.99 0.78 • From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. Tables of Safe Loads for Steel Beams and Girders 591 i|)l(B XI. * Safe Uniform Loads in Units of i ooo Pounds for Steel Tees with . Neutral Axis Parallel to Flange. (See page 566.) Maximum bending stress, 16 000 lb per sq m. Secured against yielding sidewise EQUAL FLANGE AND STEM • Maximum Maximum i-ft span, 360 i-ft span, 360 Size Weight span X deflec- Size Weight span X deflec- per tion per tion foot, lb foot, lb Flnge Stem Safe Safe L'gth Flnge Stem Safe Safe L'gth in in load load ft in in load load ft 6H 6H 19.8 52.80 2.77 19-1 2^4 2M 4.9 4-37 0.69 6.3 4 4 13. 5 21.55 1.89 II. 4 2M- 21/4 4-1 3.41 0.53 6 4 4 4 10.5 16.85 1.45 II. 6 2 2 4.3 3.31 0.59 5 6 z\^ 3K2 II. 7 16.32 1.65 9.9 2 2 3.56 2.77 0.49 5 7 3K2 ZVi 9.2 12.69 1.27 10. 1% 1% 3.09 2.03 0.41 4 9 3 3 9-9 11.73 1. 41 8.3 iH 1 1/2 2.47 1.49 0.36 4 I 3 3* 8.9 10.45 1.24 8.4 l'/2 l'/^ 1.94 1. 17 0.27 4 3 3 3 7.8 917 1.08 8.S 1 1/4 iM 2.02 I. CI 0.30 3 4 3 3 6.7 7.89 0.92 8.6 iH iH 1. 59 0.78 0.22 3 5 2Y2 2K> 6.4 6.29 0.90 7.0 I I I. 25 0.49 o.i8 2 7 2V1 2V1 5.5 5.33 0.75 7.1 I I 0.89 0.35 0.12 2 9 2H 2V4 4.9 4-37 0.69 6.3 .,::H7/ ^lA^V- UN EQUAL FLA^ fGE AN D Sl^E %A'.AiW. ff y Maximum Maximum Si ze Weight per foot, lb l-ft span span, 360 X deflec- tion Si ze Weight per foot, lb I-ft span span, 360 X deflec- tion Flnge Stem Safe Safe L'gth Flnge Stem Safe Safe L'gth in in load load ft in in load load ft 5 3 13.4 11. 41 1.25 9-1 3^2 3 10.8 12.05 1.42 8.5 5 2V1 10 9 8.96 1.20 7.5 3M2 3 8.5 9-49 1.09 8.7 4M2 3V2 15 7 22.72 2.37 9.6 3'/^ 3 7.5 9.07 1.04 8.7 43^^ 3 9 8 9.71 1.07 9-1 3 4 II. 7 20.69 1.92 10.8 4K2 3 8 4 8.32 0.90 9.2 3 4 10.5 18.35 1.68 10.9 4H 2yi 9 2 6.72 0.87 7.7 3 4 9.2 16. II 1.47 II. ^V^ 2H 7 8 5.76 0.74 7.8 3 3K2 10.8 15.89 1.66 9.6 4 5 IS 3 33.39 2.40 13.9 3 3M2 9.7 14.19 1.46 9-7 4 S II 9 25.92 1.84 14. 1 3 sVz 8.5 12.37 1.26 9.8 4 4 4^^ 4H 14 4 27.09 21.12 2. IS 1.65 12.6 3 3 2^/2 7.1 6.1 6.40 5.55 0.89 0.76 7.2 II 2 12.8 2K2 7.3 4 3 9 2 9.60 1.08 8.9 2K2 3 7.1 8.96 1.08 8.3 4 3 7 8 8.21 0.90 91 2I/2 3 6.1 7.68 0.91 8.4 4 2\^ 8 5 6.61 0.87 7.6 2^/2 iH 2.87 0.93 0.2S 3.7 4 2H 7 2 5.65 0.73 7.7 2 1 1/2 3.09 1.60 0.36 4.4 4 2 7 8 4.27 0.70 6.1 iH 2 2.45 2.03 0.37 5.5 4 2 6 7 3.63 0.59 6.2 l\i iM 1. 25 0.57 0.15 6-1 33^^ 4 12 6 21.12 1.90 II. I iH % 0.88 0.14 0.07 1-9 Z\^ 4 9 8 16. S3 1.46 II. 3 ... * From Pocket Companion, Carnegie Steel Coiripany, Pittsburgh, Pa. 692 Strength of Beams and Beam Girders Chap. 15 Bethlehem I Beams.* Bethlehem I beams from 8 to 24 in in depth, in- clusive, have the same strength, or section-modulus, as Standard beams of the same depth. Bethlehem beams, due to the proportions of the sections, weigh generally 10% less than standard beams of the same depth and strength. For example (Table VI, page 357), a Bethlehem 15-in I beam, weighing 54 lb per ft, has a section-modulus of 81.3. The corresponding standard section (Table IV, page 354) is a 15-in I beam weighing 60 lb per ft, with a section-modulus of 81.2. Therefore, for equal strength, the Bethlehem beam weighs 6 lb per ft less than the standard beam, or a saving of 10% in weight. Similar com- parisons with other sizes of the standard beams previously rolled by the mills of this country show that the Bethlehem I beams afford an equal carrying capacity, but with practically 10% less weight of metal. Thickness of Webs and Flanges. It is claimed that the webs of standard beams are much thicker than required for a scientifically proportioned section. It is impossible to reduce the web-thickness in the ordinary mill, but with the Grey Mill webs of the desired thickness can be produced. By adding to the FLANGES part of the metal thus saved, the strength of the beam is main- tained, thereby affording a lighter section of the same strength. The wide FLANGES give increased lateral stiffness, which commends the use of such beams in many cases, where the narrow flanges and lack of sufficient lateral rigidity prevent the use of ordinary standard beams. Depth and Weight of Bethlehem Beams. Formerly the heaviest beams rolled in this country were 24 in deep, weighed 115 lb per ft, and had a section- modulus of 246.3. Whenever greater strength was required, a riveted girder was necessary. Bethlehem beams are rolled to a maximum depth of 30 in, weigh 200 lb per ft, and have a section-modulus of 610, or two and one-half times the strength of the largest beam previously rolled. The opportunity for using ROLLED BEAMS instead of built-up riveted girders is, therefore, greatly increased. These rolled beams and girders afford a saving in weight of metal and also a large economy in cost of fabrication, as they do not require the punching, assembling and riveting necessary for building a riveted girder. Bethlehem Girder Beams.* Bethlehem girder beams, from 8 to 24 in in depth, inclusive, have a strength, or section-modulus, equal to that of two minimum-weight standard I beams of the same depth. The girder beam, however, weighs generally i2V2% less than the combined weight of the two standard beams, not considering the saving in weight of separators needed for assembling the standard beams into a girder. For example, a Bethlehem 15-in girder beam, weighing 73 lb per ft has a section-modulus of 11 7. 8 (Table VII, page 358). Two standard 15-in I beams, each weighing 42 lb per ft, have together a like section-modulus of 117. 8 (Table IV, page 354). Thus, for equal depth and strength, the girder beam weighs 11 lb per ft less than the two standard beams. This is a saving of 13% in weight, not including separators, which would add at least 2},^ lb per ft more to the weight of the assembled girder. In this case a total saving of 16% in weight is afforded by the Bethle- hem girder beam, besides the saving in the cost of assembling the standard beams into a girder. Safe Uniformly Distributed Loads for^ethlehem I Beams and Girder Beams. Tables XII * and XIII,* pages 594 to 602, give the safe uniformly distributed loads in tons of 2 000 lb, on Bethlehem girder beams and I beams for a maximum fiber-stress of 16 000 lb per sq in. The tabular loads include • Adapted by permission from the Catalogue of Bethlehem Structural Shapes, Bethlc hesn Steel Company, South Bethlehem, Pa. Oblique Loading of Angles Used as Beams 603 the weight of the beam, which must be deducted to obtain the net load a beam will support. Safe loads for intermediate or heavier weights of beams can be obtained from the separate column of corrections, given for each size. This last column of the table states the increase in safe load for each pound of increase in weight per foot of beam. If the load is concentrated at the middle of the span, the safe load is one-half the safe uniformly distributed load for the same span. The safe loads on short spans may be limited by the shearing strength of the web, instead of by the maximum fiber-stress allowed in the flanges. This limit is indicated in the tables by the heavy hori- zontal lines. The loads given above these lines are greater than the safe crip- pling or buckling strength of the web, and must not be used unless the webs are stiffened* In such cases it will generally be advisable to select a heavier beam with a thicker web. To use these tables for other spans, or for other distribution of the loading, see explanation, page 566. To use these tables for beams yielding laterally, see Lateral Deflection, pages 566 and 670. Oblique Loading of Angles Used as Beams f Oblique Loading of Purlins on Sloping Roofs. (See, also, pages 573, 1169 and II 70.) The preceding Tables VIII, IX and X for safe loads on angles are based on the neutral axis being parallel to one of the legs. When this is not the case, as in roof- purlins (Fig. 10), the strength of a given angle may be found by taking its section-modulus from Table XI A and using the fundamental formula for flexure (page 557). It should be noted that purlins set as at (a) are stronger than {b), Fig. 9a. Fig. 9a. Strong and Weak Setting of Angle-Purlins on Sloping Roofs Table XI A. Section-Moduli of Angle-Purlins Set at Right-Angles to Rafters, as in (a) Fig. 9a, and Free to Move in Any Direction. Loading Vertical. Purlin 2 X 2H X 2HX 2HX 3 X 3 X 3HX 2 X 2 X 2HX 2MX 2MX 2H X 2^ X 2^X 3 X 3 X 3HX s'AX 4 X 4 X M angle.. }4 angle.. H angle.. H angle.. 14 angle . . % angle.. H angle.. % angle.. li angle.. % angle.. •)1o angle. ?/8 angle . . Vs angle.. J^^ angle . . Slope of roof in inches per foot 0.18 0.30 0.31 0.42 0.44 0.64 0.56 0.84 0.7S I. II 1.48 1.76 2.50 3 • 30 c. 19 0.31 0.32 0.44 0.46 0.67 O.S9 0.89 0.80 1. 18 1-55 1.86 2.66 3-52 0.22 0.38 0.37 0.52 0.56 D.82 3.76 I. 14 I .02 1.47 1.96 2.34 3.41 ^•52 0.24 0.41 0.39 0.55 0.60 0.89 0.83 1.58 2. 12 2.52 3 70 4.84 0.26 0.44 0.42 0.60 0.65 0.95 0.89 1.29 I. 18 I .70 2.30 2.71 4.00 5.18 0.31 0.49 0.48 0.68 0.74 I .06 0.84 I. 19 1.27 1.76 2.06 2.42 317 4.09 * See pararaphs and foot-note, page 567 t From Notes by Robins Fleming. relating to web-buckling of beams. 594 Strength of Beams and Beam Girders Chap. 15 Table XII. Safe Uniform Loads in Tons of 2 000 Pounds for Bethlehem Girder Beams Beams secured against yielding sidewise 30-in G 28-in G 26-in G Span, ft Add for each lb Add for each lb Add for each lb G3oa G30 increase G28a G28 increase G26a G26 increase in weight in weight in weight 200 lb 180 lb 180 lb 165 lb 160 lb 150 lb 18 180.75 161.87 0.44 153.75 138.89 0.41 128. II 117.47 0.38 19 171.24 153.35 0.41 145.66 131.58 0.39 121.37 III. 29 0.36 20 102.68 145.68 0.39 138.38 125.00 0.37 115.30 105.72 0.34 21 154.93 138.74 0.37 131.79 119. OS 0.35 109.81 100.69 0.32 22 147.89 132.44 0.36 125.80 113.64 0.33 104.82 96.11 0.31 23 141.46 126.68 0.34 120.33 108.70 0.32 100.26 91-93 0.30 24 135.56 121.40 0.33 115. 31 104.17 0.31 96.08 88.10. 0.28 25 130.14 116.55 0.31 110.70 100,00 0.29 92.24 84.58 0.27 26 125.14 112.06 0.30 106.44 96.16 0.28 88.69 81.32 0.26 27 120.50 107.91 0.29 102.50 92.60 0.27 85.41 78.31 0.25 28 116.20 104.06 0.28 9S.84 89.29 0.26 82.36 75.52 0.24 29 112. 19 100.47 0.27 95.43 86.21 0.25 79-52 72.91 0.23 30 108.45 97.12 0.26 92.25 83.34 0.24 76.87 70.48 0.23 31 104.95 93.99 0.2s 89.27 80.65' 0.24 74.39 68.21 0.22 32 101.67 91 05 0.25 86.48 78.13 0.23 72.06 66.08 0.21 33 98-59 88.29 0.24 83.86 75.76 0.22 69.88 64.07 0.21 34 95.69 85.70 0.23 81.40 73-53 0.22 67.82 62.19 0.20 35 92.96 83.25 0.22 79.07 . 71.43 0.21 65.88 60.41 0.19 36 90.38 80.93 0.22 76.88 69.45 0.20 64.05 58.73 0.19 37 87.93 78.75 0.21 74.80 67.57 0.20 62.32 57.15 0.18 38 85.62 76.67 0.21 72.83 65.79 0.19 60.68 55.64 0.18 39 83.42 74.71 0.20 70.96 64.10 0.19 59.13 54.22 0.17 40 81.34 72.84 0.20 69.19 62.50 0.18 57.65 52.86 0.17 41 79-35 71.06 0.19 67.50 60.98 0.18 56.24 51.57 0.17 42 77.47 69.37 0.19 65.89 59.53 0.17 54.90 50.34 0.16 43 75.66 67.76 0.18 64.36 58.14 0.17 53.63 49.17 0.16 44 73.94 66.22 0.18 62.90 56.82 0.17 52.41 48.06 0.15 45 72.30 64.75 0.17 61.50 55.56 0.16 51.24 46.99 0.15 46 70.73 63.34 0.17 60.16 54.35 0.16 50.13 45.97 0.15 47 69.22 61.99 0.17 58.88 53.19 0.16 49.06 44.99 0.14 48 67.78- 60.70 0.16 57.66 52.09 o.is 48.04 44.05 0.14 Safe loads given inc ude weigl it of beam Maximum fiber-stre ss, 16 000 1 b per sq in The section-numbe rs are give m for convenie nee in ide ntificati on and ordering . Tables of Safe Loads for Steel Beams and Girders 595 Table XII (Continued). Safe Uniform Loads in Tons of 2 000 Pounds for Bethlehem Girder Beams Beams secured against yielding sidewise 24-in G 20-in G i8-in G Add for each lb Add for each lb Add for each lb 1 Span, ft G24a G24 increase G2oa G20 increase G18 increase in weight in weight in weight 140 lb 120 lb 140 lb 112 lb 92 lb 12 13 ISS.61 143.64 133.60 123.33 • 0.52 0.48 130.43 104.09 0.44 0.40 78.59 0.39 0.36 120.40 96.09 72.54 14 133.38 114.52 0.45 III. 80 89.23 0.37 67.36 0.34 IS 16 17 124.48 106.88 100.20 0.42 0.39 0.37 104.34 97.82 92.07 83.28 78.07 73.48 0.3S 0.33 0.31 62.87 58.94 55.47 0.31 0.29 0.28 116. 71 109.84 94.31 18 103.74 89.07 0.35 86.95 69.40 0.29 52.39 0.26 19 98.28 84.38 0.33 82.38 65.74 0.28 49.63 0.25 20 93.37 80.16 0.31 78.26 62.46 0.26 47.15 0.24 21 88.92 76.3s 0.30 74.53 59 48 0.25 44.91 0.22 22 84.88 72.88 0.29 71.14 56.78 0.24 42.87 0.21 23 81.19 69.71 0.27 68.05 54.31 0.23 41.00 0.20 24 77.80 66.80 0.26 65.22 52.05 0.22 39 .29 0.20 25 74.69 64. IS 0.25 62.61 49.97 0.21 37.72 0.19 26 71.82 61.66 0.24 60.20 48.04 0.20 36.27 0.18 27 69.16 59-38 0.23 57. 97 46.26 0.19 34.93 0.17 28 66.69 57.26 0.22 55.90 44.61 0.19 33.68 0.17 29 64.39 55.29 0.22 53.97 43.07 0.18 32.52 0.16 30 62.24 53.44 0.21 52.17 41.64 0.17 31.43 0.16 31 60.24 51.72 0.20 50.49 40.30 0.17 30.42 O.IS 32 58.35 50.10 0.20 48.91 39.04 0.16 29 -47 0.15 33 56.58 48.58 0.19 47-43 37.8s 0.16 ' 28.58 0.14 34 54.92 47. IS 0.18 46.04 36.74 0.15 27.74 0.14 35 53.35 45.81 0.18 44.72 35.69 0.15 26.94 0.13 36 51.87 44.54 0.17 43.48 34.70 o.is 26.20 0.13 37 50.47 43.33 0.17 42.30 33.76 0.14 25.49 0.13 38 49.14 42.19 0.17 41.19 32.87 0.14 24.82 0.12 39 47.88 41. II 0.16 40.13 32.03 0.13 24.18 0.12 40 46.68 40.08 0.16 39-13 31.23 0.13 23.58 0.12 Safe loads giv en incluc ie weight of beam . Maxirr um fiber-s tress, 16 000 lb per sq in Loads given a bove the heavy lin es are grc ^ater thai 1 safe loads for web -crippling. See paragraphs and accc )mpanyin{ I foot-no te, page 567, relatin g to web -buckling of beams Safe loads giv en belo\i T the lowe r, broker 1 line cat ise deflecti ons excee ;ding Heo of the span The section-n umbers £ ire given : or conve nience in identifical ion and ordering S96 Strength of Beams and Beam Girders Table XII (Continued). Safe Uniform Loads in Tons of 2 000 Pounds for Bethlehem Girder Beams Beams secured against yielding sidewise 15-in G i2-in G Span, ft Add for each lb Add for each lb Gisb Gisa G15 increase Gi2a G12 increase in weight in weight 140 lb 104 lb 73 lb 70 lb 55 lb 10 II 113.26 102.96 86.76 78.88 62.83 0.39 0.36 47.89 43.54 38.40 34.91 0.31 0.29 57.12 12 94 38 72.30 52.36 0.33 39-91 32.00 0.26 13 87.12 66.74 48.33 0.30 36.84 29.54 0.24 14 15 80.90 75.51 61.97 57.84 44.88 41.89 0.28 0.26 34-21 27-43 0.22 0.21 31.93 25.60 16 70.79 54-23 39-27 0.25 29.93 24.00 0.20 17 66.62 51 04 36.96 0.23 28.17 22.59 0.19 18 62.92 48.20 34.91 0.22 26.61 21.33 0.18 19 59-61 45-67 33 07 0.21 25.21 20.21 0.17 20 56.63 43-38 31.42 0.20 23.95 19.20 o.i6 21 53.93 41-32 29.92 0.19 22.81 18.28 0.15 22 51.48 39-44 28.56 0.18 21.77 17.45 0.14 23 49 24 37-72 27.32 0.17 20.82 16.69 0.14 24 25 47-19 45 30 36.15 34.71 26.18 25.13 0.16 0.16 19.95 16.00 0.13 0.13 19.16 15.36 26 43-56 33.37 24-17 0.15 18.42 14.77 0.12 27 41.95 32.13 23.27 0.15 17.74 14.22 0.12 28 40.45 30.99 22.44 0.14 17.10 13.71 O.II 29 39-05 29.92 21.67 0.14 16.51 13.24 O.II 30 31 37J5 _ 28.92 _20^94_ 0.13 0.13 15.96 15.45 12.80 12.39 O.IO 0.10 36.54 27.99 20.27 32 35.39 27.11 19.63 0.12 14.97 12.00 O.IO 33 34.32 26.29 19 04 0.12 14.51 11.64 O.IO 34 33.31 25.52 18.48 0.12 14.09 11.29 0.09 35 32.36 24.79 17.95 O.II 13.68 10.97 0.09 Safe loads given include w eight of be am. Maxi mum fiber-stress, 16 Doo lb per sq in Load given above the hea vy line is greater tha n a safe load for web- crippling. See paragraphs and accompa nying foot -note, page 567, relating to web -buckling of beams. Safe loads given below the lower, bro ^00 of the span given for c Thes >ection numb 2rs are onveni ence in identifacatio a and c jrdering Tables of Safe Loads for Steel Beams and Girders 601 Table XIII (Continued). Safe Uniform Loads in Tons of 2000 Pounds for Bethlehem I Beams Beams secured against yielc ing sidewise i2-in I lo-in I Span, ft Addfo each It r Add for each lb ■ B120 B12 increas e Bio increase in weight in weight 36 1b 32 lb 28.5 lb 28.S lb 23.5 lb 9 26.59 22.57 21.36 0.35 15.95 14.57 0.29 10 23.93 20.31 19.22 0.31 14.35 13 II 0.26 II 21.76 18.46 17.47 0.29 13.05 11.92 0.24 12 19-94 16.92 16.02 0.26 11.96 10.92 0.22 13 18.41 15.62 14.79 0.24 11.04 10.08 0.20 14 17.09 14.51 13.73 0.22 10.25 9.36 0.19 15 15.95 13.54 12.81 0.21 9.57 8.74 0.17 16 14.96 12.69 12.01 0.20 8.97 8.19 0.16 17 14.08 11.95 II. 31 0.19 8.44 7.71 o.is 18 13.30 11.28 10.68 0.17 7.97 7.28 o.is 19 12.60 10.69 10.12 0.17 7.55 6.90 0.14 20 21 11.97 11.40 10.15 967 9.61 9.15 0.16 0.15 ___7_.i_8__ __.AAS__ 0.13 0.12 6.84 6.24 22 10.88 9.23 8.74 0.14 6.52 S.96 0.12 23 10.41 8.83 8.36 0.14 6.24 5. 70 O.II 24 25 __9.97_ 8.46 8.01 0.13 0.13 5. 98 5.74 5.46 5.24 O.II O.IO ■ 9-57 '""¥.'12" ""'"7."69" 26 9.20 7.81 7.39 0.12 5.52 5.04 O.IO 27 8.86 7.52 7.12 0.12 5.32 4.86 O.IO 28 8.55 7.25 6.86 O.II 5-13 4.68 0.09 29 8.25 7.00 6.63 O.II 4.95 4-52 0.09 30 9.98 6.77 6.41 O.II 4.78 4.37 0.09 31 7.72 6.55 6.20 O.IO 32 7.48 6.35 6.01 O.IO 33 7.25 6.15 5.82 O.IO. 34 7.04 5.97 5.65 0.09 35 6.84 5.80 5.49 0.09 Safe loads giver include weight of beam. M aximum fiber-stress, 16 000 lb per sq in Safe loads giver I below the broken lines cause deflections exceeding I ^60 of the span The section-nur nbers are given for convenien ce in identification and ordering 602' Strength of Beams and Beam Girders Table XIII (Continued). Safe Uniform Loads in Tons of 2 000 Pounds for Bethlehem I Beams Beams secured against yielding sidewise Span, ft 9-in I Add- for each lb increase in weight 8-inI Add for each lb increase in weight B9 B8 24 lb 20 lb 17.S lb 19-5 lb 5 6 7 8 9 10 II 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 21.83 18.19 15 60 13.6s 12.13 10.92 9.92 9.10 8.40 7.80 7.28 6.82 6.42 6.07 20.18 16.81 14-41 12.61 II. 21 10.09 917 8.41 7.76 7.21 6.73 6.31 593 5. 61 0.47 0.39 0.34 0.29 0.26 0.24 0.21 0.20 0.18 0.17 0.16 0.15 0.14 0.13 0.13 0.12 O.II O.II O.IO O.IO O.IO 0.09 0.09 0.09 0.08 o.oS 16.16 13.46 11.54 10.10 8.98 8.08 7 34 6.73 6.21 5.77 5.39 5.05 15.30 12.75 10.93 9-57 8.50 7.65 6.96 6.38 5.89 5. 47 5.10 4.78 0.42 0.35 0.30 0.26 0.23 0.21 0.19 0.17 0.16 15 0.14 0.13 0.12 0.12 II O.II • O.IO O.IO 0.09 0.09 0.08 4.75 4-49 4.25 4.04 3.85 3.67 3.51 3.37 3.23 4.50 4-25 4.03 3.83 3.64 3.48 3.33 3.19 3.06 5.75 5.46 5. 20 4.96 4.75 4.55 4-37 4.20 4.04 3.90 3.76 3.64 5.31 5.04 4.80 4-59 4.39 4.20 4.04 3.88 3-74 3.60 3 48 3.36 1 Safe lo£ sq in Safe lo£ span The sec ids given include weight of beam. Maximum fiber-stress, 16 000 lb per ids given below the broken lines cause deflections exceeding Hso of the tion-numbers are given for cdnvenietKe in identification and ordering Tables of Safe Loads for Steel Beams and Girders 603 Riveted Single-Beam and Double-Beam Girders.* Where a single ROLLED BEAM is insufficient to carry a load, the required capacity may be secured by fabrication in various ways. Two beams can be used, connected by bolts and separators. The total strength of these is twice that of the single beam of the same depth and weight. Care should be taken, however, to see that the loads are apportioned to them equally, and where it is necessary for the beams to act as a unit, the separators should consist of plates and angles and not be made of cast iron. If the loading is not uniformly distributed over the two beams, the strength of each must be computed separately. The use of a single- beam GIRDER with plates at top and bottom to sustain a given load is often more economical in material than the use of two beams connected by bolts and separators. The beam girders in Table XIV, pages 605-6, have about twice the carrying capacity of the single beams of which they are built. Tables XIV and XV give the safe loads for the single and double -beam GIRDERS commonly used. The values given in the tables are founded upon the moments of inertia of the various sections, deductions being made for the rivet-holes in both flanges. In Table XIV, taken by permission from Carnegie's Pocket Companion, the safe loads are based upon a fiber-stress for flange-bend- ing of 16 000 lb per sq in, and in Table XV, retained from the former edition of Kidder's Pocket-Book, upon a fiber-stress of 13 000 lb per sq in. For other fiber- stresses, as 14 000 or 15 000 lb per sq in, the safe loads in Tables XIV or XV may be decreased or increased by proportion as the loads vary as the fiber- stresses. f * For tables of riveted plate girders, see Chapter XX. t The editors decided to retain Table XV for the safe uniformly distributed loads for riveted steel-beam box girders, based upon a bending fiber-stress of 13 000 lb per sq in. To use this table for fiber-stresses of 14 000, 15 000 or 16 000 lb per sq in, divide the tabular loads by 13 and multiply the quotients by 14, 15 or 16, respectively, for the safe load at the required fiber-stress. In regard to Table XV, Mr. Kidder said, in the preceding editions of this pocket-book, "in order to amply compensate for the deteriora- tion of the metal around the rivet-holes from punching, and also because these girders are more often used to support permanent loads, such as brick or stone walls, the maximum fiber-stress [for riveted double-beam girders] was limited to 13 000 lb per sq in, although it is but right to state that most of the latest handbooks of the steel-manufacturers give tables of safe loads for such girders based upon a fiber-stress of 15 000 lb per sq in. The author advises that for loads of masonry, which usually come very close to the estimated loads, and which are constantly applied, the girders be not loaded beyond the values given in the following tables (that is, based upon 13 000 lb per sq in), while for ordinary floor-loads, which seldom reach the estimated loads, an addition of Hth may be added to the values given in the tables." Girders fabricated of single steel I beams and plates riveted to the upper and lower flanges, as shown in Table XIV, are not often used to support masonry walls, because of their relatively narrow flange-width and lack of lateral stiffness. In case they are used to support masonry walls and are not thoroughly braced laterally, it is recommended that the safe loads be reduced as explained, from those given in Table XIV, to agree with a fiber-stress of 13 000 or 14 000 lb per sq in, according to the span, bracing, character of loading, etc. It is recommended, also, that for girders fabricated of two steel I beams and plates riveted to the flanges, as shown in Table XV, and carrying masonry walls, the safe loads, given in this table and computed for a fiber-stress of 13 000 lb per sq in, be used, or, if increased, that the fiber-stress be taken not greater than 14 000 lb per sq in. Recent handbooks have contained tables of safe uniformly distributed loads for fabri- cated steel girders computed from safe unit fiber-stresses, in pounds per square inch, for flange-bending as follows. For riveted single-beam girders: Carnegie Steel Company, 1903 Edition, no tabks; Carnegie, 1915 Edition, 16000, based upon t!he section-modulus of the gross area of the cross-section; Cambria Steel Company, 191 2 Edition, no tables; (former) Passaic Steel Company, 1903 Edition, no tables; Kidder's Pocket-Book, previous editions, no tables. For riveted double-beam girders: Car- 604 Strength of Beams and Beam Girders Chap. 15 Example 21. A 13-in brick wall, 15 ft high, is to be built over an opening of 24 ft. What is the size of the double-beam girder required? Solution. Assuming 25 ft as the distance, center to center of bearings and 121 lb per cu ft as the weight of brickwork, the weight of the wall is25XiSXi2i = 45 375 ib, or about 22.68 tons. From Table XV, page 610, a girder composed of two i2-in steel beams, each weighing 31.5 lb per ft, and two 14 by \^-m flange- plates will carry safely, for a span of 25 ft, a uniformly distributed load of 23.23 tons, including its own weight. Deducting the latter, 1.42 tons, given in the next column, the result is 21.81 tons for the safe net load, which is 0.87 ton less than required. From the following column of the table it is seen that by in- creasing the thickness of the flange-plates He in it is safe to add 1.52 tons to the allowable load. This will more than make up the difference. Hence the re- quired DOUBLE-BEAM GIRDER will be composcd of two i2-in 31.5-lb beams, and two 14 by ^le-in steel flange-plates. A SINGLE-BEAM GIRDER (according to Table XIV, page 606), composed of one 15-in 42-lb I beam and two 8 by J^i-in flange-plates will carry, at 16000 lb per sq ft, 49 000 lb over a span of 25 ft, and as it is lighter, weighing but 69.2 lb per ft to the others 113.6 lb, it would be more economical. The DOUBLE-BEAM GIRDER is, however, more suitable in this particular case, as the 13-in wall should have a wider bearing than 8 in, and, also, the safe load should be decreased from the tabular load to correspond to a fiber-stress of 13 000 or 14 000 lb per sq in because of the nature of the loading, the long span, etc., or, what amounts to the same thing, the strength of the girder should be increased to correspond to the decreased fiber-stress. (See foot-note, page 603.) A 49 000-lb load at 16 000 lb per sq in fiber-stress corresponds to a 49 000 X i^ia = 60307-lb load at 13 000 fiber-stress, as far as selecting a corresponding girder from table is concerned. A single-beam girder (Table XIV) com- posed of one 15-in 60-lb I beam and two 9 by %-m flange-plates will carry 68 000 lb and weighs only 98.3 lb per ft. Therefore, as far as strength is con- cerned, to suit the conditions of loading, this would be the proper single-beam GIRDER to use, and it would also be cheaper than the double-beam girder determined by Table XV; but the width of bearing for the 13-in wall is still only 9 in compared to 14 in with the double-be.\m girder. negie, 1903, 15000, ^Me-in rivet-holes deducted; Carnegie, 191.5, no tables; Cambria, 15 000, i^e-in rivet-holes deducted; Passaic, 15 000, 1 Vie or ^yio-in rivet-holes deducted; Kidder, previous and new editions, 13 000, i^^ie-in rivet-holes deducted. For riveted siNGLE-WEB, PLATE-AND-ANGLE GIRDERS (see Chapter XX): Carnegie, 1903. 15000, i^lfi-in rivet-holes deducted; Carnegie, 191S, 16 000, based upon section-modulus of the gross area of cross-section; Cambria, 15000, i^e or i4,^6-in rivet-holes deducted; Passaic, 15 000, ^Me or ^Yia-in rivet-holes deducted; Kidder, previous editions, 12 000 and 13000 for flanges, ^ie or ^^--le-in rivet-holes deducted (also contained the Passaic tables). For riveted multiple-web, plate-and-angle girders (see Chapter XX): Carnegie, 1903. 15000, ^ Me -in rivet-holes deducted; Carnegie, 1915. 16000, based upon section-modulus of the gross area of cross-section (the elements, only, of these girders, and not the loads, are given): Cambria, no tables; Passaic. 15000, ^Me or '"^'Ifi-in rivet -holes, deducted; Kidder, previous editions, same as for single-web plate-and- girders. The revised edition of Kidder's Handbook uses, by permission, the Carnegie tables for all but the riveted double-beam girders, for which the old Kidder tables are retained. The limiting conditions of use are fully explained in the te.xt and foot notes. Editor- in-chief. Tables of Safe Loads for Steel Beams and Girders 605 Table XIV.* Safe Uniform Loads in Units of i ooo Pounds for Riveted Steel-Beam Girders Maximum bending stress, i6 ooot lb per sq in _.4_4i-— o-J _,^7^^-1 r-fio;:,--; ._J ^ A i^ r \% 'T\ ^ L ^ 1 ':^i.. ^ _.L x^ 1 -.1 %^ 1 _t '± !.._ _t ^ "■" ^ "~ 5J Span , J^ 1 .i-c iJ k .1^ --ti k, Co- efH- cients of 1 ; • • 27-in90-rDbeam 24-in 8o-lb beam 24-in 8o-lb beam 20-in 8o-lb beam ft 12 by %-in 12 by %-in 10 by ^^-in 10 by %-in de- plates plates plates plates flec- tion Increase Increase Increase Increase in safe in safe in safe in safe loads for loads for loads for loads for Safe He-in Safe Me-in Safe He-in Safe He-in loads increase in thick- ness of flange- plates loads increase in thick- ness of flange- plates loads increase in thick- ness of flange- plates loads increase in thick- ness of flange- plates 13 14 370 343 IS. 9 14.8 312 289 14.2 13.2 259 II. 7 10.9 9.7 9-0 2.80 3-24 235 218 240 15 321 13.8 270 12.3 224 10. 1 204 8.4 3.72 16 17 301 130 12.2 253 "5 10.9 210 198 9-5 9.0 191 180 7.9 7.4 4.24 4.78 283 238 18 267 II. 5 225 10.3 187 8.4 170 7.0 5.36 19 253 10.9 213 9-7 177 8.0 161 6.6 5 98 20 240 10.4 203 9.2 168 7.6 153 6.3 6.62 21 229 9-9 193 8.8 160 7.2 146 6.0 7.30 22 219 9-4 184 8.4 153 6.9 139 5-7 8.01 23 209 90 176 8.0 146 6.6 133 5-5 8.76 24 200 8.6 169 7-7 140 6-3 127 5-3 9.53 25 192 8.3 162 7-4 135 6.1 122 S.o 10.35 26 185 8.0 156 7-1 129 5-9 118 4.8 II. 19 27 178 7.7 150 6.8 125 5.6 113 4-7 12.07 28 172 7-4 145 6.6 120 5.4 109 4-5 12.98 29 166 7-1 140 6.4 116 5.2 105 4-3 13.92 30 160 6.9 135 6.2 112 S-i 102 4.2 14.90 31 155 6.7 131 6.0 109 4-9 99 4.1 15.91 32 150 6.5 127 5.8 lOS 4.8 96 3.9 16.95 SZ 146 6.3 123 5.6 102 4.6 93 3.8 18.03 34 T41 6.1 119 • 5-4 99 4-5 90 3-7 19 13 35 137 5.9 116 5-3 96 4-3 87 3.6 20.28 Area 44-33 in^ 41.32 in2 35.82 in2 38.7 3 in^ /Ai-it 450.8 in' 380.0 in' 315-5 in' •286.7 in' Wgt 152.2 lb per ft 141 . 2 lb per ft 122.5 lb per ft 131. lb per ft Saf( I loads above the 1 leavy, horizontal lines exceed the re sistanc e of the we ) and girder s should be provi< led with stiflFeners ; for limiting cor iditions , see expla natory notes on page 567. See Pocket Companio n for 13 and 14-ft spans. We ghts given for girc !ers do not include stiffeners, rivet-h sads or other deta Is * From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. t See paragraph on Riveted Single-Beam and Double-Beam Girders, page 603, and the foot-note for same regarding fiber-stresses. t I/c is the section-modulus or section-factor of the cross-section with reference to the axis i-i. 606 Strength of Beams and Beam Girders Chap. Table XIV* (Continued). Safe Uniform Loads in Units of i ooo Pounds for Riveted Steel-Beam Girders Maximum bending stress, 16 coot lb per sq in i J<-rio'--: r"T'^'"'T"^; U-9"-^ t^ Y" : ^ ^ t ^ r T^ r^ ' L ._i |.„ .1 U i._ _.L Span, ._ix J Vi^ 1 /^ V«k . jsJ w : Co- efB- cients of f 1 tS , ; r-CZ- uJ_, -^-■C 0^ ■ AH^g-C^ 20-in 65-lbbeam, i8-in 55-lb beam, 15-in 6o-lbbeam, 15-in 42-lb beam, ft 10 by %-\n 9 by H-in 9 by ^^-in 8 by Vi2-in de plates plates plates plates flec- tion Increase Increase Increase Increase in safe in safe , in safe in safe loads for loads for loads for loads for Safe He -in Safe He-in Safe Mo-in Safe Htj-in loads increase in thick- ness of flange- plates loads increase in thick- ness of flange- plates loads increase in thick- ness of flange- plates loads increase in thick- ness of ' flange- plates 9 10 279 251 14.2 12.7 218 196 II-5 10.3 189 170 9-4 8.5 137 8.5 7.6 1-34 1.66 123 II 12 13 228 209 II. 6 10.6 9.8 178 9.4 8.6 7.9 155 142 1.31 7.7 7.1 6.5 112 102 95 6.9 6.4 5.9 2.00 2.38 2.80 164 151 193 14 179 91 140 7.4 122 6.1 88 5.5 3.24 IS 167 8.5 131 6.9 113 5.7 82 5.1 3.72 16 157 8.« 123 6.5 106 5.3 77 4.8 4.24 17 148 7.5 IIS 6.1 100 5.0 72 4.5 4.78 18 139 7.1 109 5.7 95 4.7 68 4.2 5.36 19 132 6.7 103 5.4 90 4.5 65 4.0 5. 98 20 125 6.4 98 5.2 85 4.3 61 3.8 6.62 21 119 6.1 93 4.9 81 4.0 59 3.6 7.30 22 114 5.8 «9 4.7 77 3.9 56 3.5 8.01 23 109 55 85 4.5 74 3.7 53 3.3 8.76 24 105 5.3 82 4.3 71 3.5 51 3.2 9.53 25 100 S.I 79 4.1 68 3.4 49 3.1 10.35 26 97 4.9 76 4.0 65 3.3 47 2.9 II. 19 27 93 4.7 73 3.8 63 3.1 46 2.8 12.07 28 90 4.6 70 3-1 61 *. 3.0 44 2.7 12.98 29 87 4.4 68 3.6 59 2.9 42 2.6 13.92 30 84 4.2 65 3.4 •57 2.8 41 2.5 14.90 Area 31.58 in2 27.18 in2 28.92 in2 20.48 in^ Ilc^-xX 235.2 in3 184. 1 in3 159-5 m' 1 15. 3 ni3 Wgt 107. 5 lb per ft 93.3 lb per ft 98.3 lb per ft 69.21b per ft Safe I loads above the 1 leavy, horizontal : ines exceed the res >istance of the wet 3, and girder s should be provi led with stiffenen ,; for limiting con ditions, see explan atory notes on page 567. See Pocket Companu jn, 1915 for 9-ft. SI )an Wei ghts given for gir ders do not incluc ie stifTeners, rivet -heads or other d etails * From Pocket Companion, Carnegie Steel Company, Pitsburgh, Pa. t See paragraph on Riveted Single-Beam and Double-Beam Girders, page 603, and the foot-note for same regarding fiber-stresses. \ I/c is the section-modulus or section-factor of the cross-section with reference to the axis I -I. Tables of Safe Loads for Steel Beams and Girders 60? Table XV. Safe Uniform Loads in Tons of 2 000 Pounds for Riveted Steel-Beam Box Girders Two 20-In steel I beams and two 16 by H-in steel plates Two steel .U-7^^. Two steel" '^lr-"-.r<»'' ^"^P Dis- plates, i6by H in d 20-m beams, 80.0 lb L^^l^ perft plates, i6by H in 4 20-1 n beams, 6s.o lb Increase in weight of girder center to center of bear- ings, ft Safe loads, uniformly distrib- uted (in- Weight of girder (includ- ing rivet- Increase in safe loads for He-in in- Safe loads, uniformly distrib- uted (in- cluding weight of Weight of girder (includ- ing rivet- Increase in safe loads for Mo-in in- for He-in increase in thick- ness of flange- plates cluding weight of heads), in crease in thickness heads), in tons of crease in thickness girder), 2 000 lb of flange- girder), of flange- in tons of plates in tons of plates 2 000 lb 2 000 lb 10 199.67 1.22 1.06 7.34 0.03 7.22 176.72 II 181. 51 1.34 6.56 160.66 1. 16 6.68 0.04 12 166.39 1.46 6.02 147.26 1.27 6.12 0.04 13 153 60 1.58 5.56 135. "^5 1.37 5.65 0.04 14 142.64 1.70 5.16 126.24 1.48 5.2s 0.05 15 133.12 1.83 4.81 117.82 1.58 4.90 0.05 i6 124.80 1.95 4.51 110.45 1.69 4.59 0.05 17 117.47 2.07 4.25 103.96 1.79 4.32 0.06 i8 110.94 2.19 4.01 98.18 1.90 4.08 0.06 .19 105.10 2.31" 3.80 93 01 2.01 3.86 0.06 20 99.83 2.43 3.6i 88.36 2. II 3.67 0.07 21 95.08 2.56 3.44 84.15 2.22 3.50 0.07 22 90.77 2.68 3'. 28 80.33 2.32 3.34 0.07 23 86.82 2.80 3.14 76.84 2.43 3.19 0.08 24 83.20 2.92 3.01 73.64 2.53 3.06 0.08 25 79.87 3.04 2.89 70.69 2.64 2.94 0.08 26 76.80 3.16 2.78 67.97 2.75 2.82 0.09 27 73.96 3.29 2.68 65.46 2.85 2.72 0.09 28 71.32 3.41 2.58 63.12 2.96 2.62 0.09 29 68.86 3.53 2.49 60.94 3.06 2.53 o.io 30 66.56 3.65 2.41 58.91 3.17 2.45 O.IO 31 64.41 3.77 . 2.33 57.01 3.27 2.37 0.10 32 62.41 3.89 2.26 55.22 3.38 2.29 O.II 33 60.51 4.02 2.19 53.56 3.48 2.22 O.II 34 58.73 4.14 2.12 51.98 3.59 2.16 O.H 35 57.05 4.26 2.06 50.50 3.70 2.10 0.12 36 55.46 4.38 2.01 49-09 3.80 2.04 0.12 37 53.96 4.50 1.95 47.77 3.91 1.98 0.12 38 52.54 4.62 1.90 46.51 4.01 1.93 0.13 39 51.20 4.75 1.8s 45.32 4.12 1.88 0.13 The above values are based on a maximum fiber-stress of 13 000 lb per sq in, rivet-holes in both flanges deducted. See paragraph on Riveted Single-Beam and Double-Beam Girders, page 603, and the foot-note for same regarding fiber-stresses. Weights of girders correspond to lengths, center to center of bearings. 608 Strength of Beams and Beam Girders Ckap. 1$ Table XV (Continued). Safe Uniform Loads in Tons of 2 000 Pounds for Riveted Steel-Beam Box Girders Two i8-iri steel I beams and two 16 by 5 t-in iteel plates ■ JK-T-V^ 1 Two i8-iri '. -o//' Two ^ lii^S ^ Two i8-in ^ beams. beams i6by?4-in 70 lb 55 lb steei plates Add to Dis- ^ ^Sr^ per ft per ft /^l :^ ^ weight tance, center to t=^ CT- Two i^by ^4-in steel plates =^ of gird- er for He-in center increase of bear- ings, ft Safe loads in tons, includ- Weight of Add to safe loads for Mo-in Safe loads in tons, includ- Weight of Add to safe loads for Add to safe loads for yi 6-ia in thick- ness of plates ing weight girder, lb increase in thick- ing weight girder, lb 5 pounds increase increase in thick- of girder ness of of girder in weight ness of plates of beam plates 12 132.2 2712 5.43 123.0 2 352 2.81 . 5.43 82 13 122.0 2933 5.01 113. 5 2548 2.61 5.01 88 14 113-3 3 164 4.66 • 105.3 2 744 2.43 4.66 95 15 105.7 3390 4.35 98.3 2 940 2.27 4.35 102 16 99.1 3616 4.07 . 92.2 3136 2.12 4.07 109 17 93.3 3842 3.83 86.8 3332 2.00 3.83 116 18 88.1 4068 3.62 82.0 3528 1.90 3.62 122 19 83.5 4294 3.43 77.6 3724 1.80 3.43 129 20 79-3 4 520 3.26 73.8 3920 I. 70 3.26 136 21 75.5 4746 3.10 70.2 4 116 1.62 3.10 143 22 72.1 4972 2.96 67.0 4312 1.54 2.96 150 23 69.0 5198 2.83 64.1 •4508 1.47 2.83 156 24 66.1 5424 2.72 . 61.5 4 704 1. 41 2.72 163 25 63. 5 5650 2.61 590 4900 1.36 2.61 170 26 61.0 5876 2.51 56.7 ■ 5096 1.30 2.51 177 27 58.8 6 102 2.41 54.6 5292 I. 26 2.41 184 28 56.6 6328 2.33 52.7 5488 1. 21 2.33 190 29 54.7 6554 2.25 50.9 5684 1. 17 2.25 197 30 52.9 6780 2.17 49-2 5880 1. 13 ^ 2.17 204 31 51.8 7006 2.10 47.6 6 076 1. 10 2.10 211 32 49-6 7232 2.04 46.1 6272 1.06 2.04 218 33 48.1 7458 1.98 44-7 6468 1.03 1.98 224 34 46.7 7684 1.92 43-4 6664 1. 00 1.92 231 35 45.3 7910 1.86 42.1 6860 0.97 1.86 238 36 44.1 8 136 1. 81 41.0 7056 0.94 1. 81 245 37 42.9 8362 1.76 39.9 7 252 0.92 1.76 252 38 41.2 8588 1.72 38.8 7448 0.90 1.72 258 The above values are based on a maximum fiber-stress of 13 000 lb per sq in, rivet-holes iti both flanges deducted. See paragraph on Riveted Single-Beam and Double-Beam Girders, page 603, and the foot-note for same regarding fiber-stresses. Weights of girders correspond to lengths, center to center of bearings. ^ i Tables of Safe Loads for Steel Beams and Girders 609 Table XV (Continued . Safe Uniform Loads in Tons ol 2 000 Pounds for Riveted Steel-Beam Box Girders Two 15-in steel I beams and two 14 by ^s -in steel plates Twoi5-inbeams, T-o 15-in benmsj 1* 75.0 lb per ft 60.0 lb per ft r.-^'^- ^l- ^^^-GX^' ^ ^ j^<. r s r'r Dis- r^ ^r^ i^ r^ ^r-'^ A- M Increase in safe load for He-in increase in thick- ness of flange- plates Increase in weight «=^F 0- ^ o-* ^-^ — ^^o=» '^ tance, Steel Plates, Steel Plates, Steel Plates, of gird- center to center of bear- 14 by % in 14 by Vh in 14 by V% in er for He-in increase in thick- Safe loads, uni- Weight Safe loads, Weight Safe loads, Weight ings, formly of gird- formly of gird- formly of gird- ness of ft distrib- er (in- distrib- er (in- distrib- er (in- flange- uted (in- cluding weight of girder). cluding rivet- heads), in tons of 2 000 lb uted (in- cluding weight of girder) , cluding rivet- heads), in tons uted (in- cluding weight of girder). cluding rivet- heads), in tons plates in tons in tons of 2 000 lb in tons of 2 000 lb of 2 000 of 2 000 of 2 000 lb lb lb 10 122.33 1.06 III. 01 0.91 90.29 0.72 4.63 0.03 II III. 21 1.17 100.92 1. 00 82.08 0.79 4.21 0.03 12 101.95 1.27 92.51 1-09 75.24 0.86 3.86 0.03 1.3 94 10 1.38 85.40 1. 18 69.45 0.93 3.57 0.04 14 87.38 1.48 79-30 1.27 64.50 1. 00 3.31 0.04 IS 81.56 1-59 74-01 1.36 60.19 1.08 3.09 0.04 i6 76.46 1.70 69.38 1-45 56.43 1. 15 2.90 0.05 17 71.96 1.80 65-30 1.54 53.11 1.22 2.72 0.05 ^ i8 67.96 1. 91 61.67 1.63 50.16 1.29 2.57 0.05 19 64.39 2.01 58.43 1.72 47.52 1.36 2.43 0.05 20 61.17 2.12 55.50 1. 81 45-14 1.44 2.32 0.06 21 58.25 2.22 52.86 1.90 42.99 1. 51 2.21 0.06 22 55.60 2.33 50.46 2.00 41.04 1.58 2. II 0.06 23 53.19 2.43 48.27 2.09 39-25 1.65 2.02 0.07 24 50.97 2.54 46.25 2.18 37.62 1.72 1.93 0.07 25 48.93 2.65 44.40 2.27 36.12 1.79 1.85 0.07 26 47.05 2.76 42.70 2.36 34.72 1.87 1.78 0.08 27 45-31 2.86 41.12 2.45 33.44 1.94 1. 71 0.08 28 43.69 2.96 39-65 2.54 32.25 2.01 1.66 0.08 29 42.18 3.07 38.28 2.63 31.13 2.08 1.60 0.08 30 40.78 3-17 37-00 2.72 30.09 2.15 1.54 0.09 31 39.46 3.28 35.81 2.81 29.12 2.23 1.49 0.09 32 38.23 3.38 34.69 2.80 28.21 2.30 1.45 0.09 33 37-07 3.46 33.64 2.99 27.36 2.37 1. 41 O.IO 34 35.98 3- 60 32.65 3-08 26.55 2.44 1.37 O.IO 35 34.95 3.70 31.72 3-17 25.80 2.51 1.33 O.IO 36 33-98 3.81 30.84 3.27 25-08 2.58 1.29 O.IO 37 33 -06 3.91 30.00 3.36 24.40 2.66 1.25 O.II 38 32.20 4.02 29.*2I 3.4s 23-76 2.73 1.22 O.II 39 • 31.37 4.13 28.47 3-54 23.15 2.80 1. 19 O.II The above values are based on a maximum fiber-stress of 13 000 lb per sq in, rivet-holes in both flanges deducted. See paragraph on Riveted Single-Beam and Double-Beam Girders, page 603, and the foot-note for same regarding fiber-stresses. Weights of girders correspond to lengths, center to center of bearings. Strength of Beams and Beam Girders Chap. 15 Table XV (Continued). Safe Uniform Loads in Tons of 2 ooo Pounds for Riveted Steel-Beam Box Girders Two i2-in steel I beams and two 14 by H-in steel i)lates ,-^3- K^C'^^^ Fwo i2-in rr'i^ i2-in "^ "r^ " r ' 'CU^]y T. beams, beams, 40.0 lb 31.S lb per ft per ft r^ ^r^ i^ .i^Sr^-^. Increase Dis- '=^ 57^ «-o cr-' in weight tance, [ Two steel plai es, Two steel plates , of girder center to 14 by ]^i in 14 by H in for Me-in center increase of bear- ings, Safe loads, uniformly Weight Increase in safe loads for Safe loads, uniformly Weight ^l icrease in thick- ness of ft distrib- of girder distrib- of girder ^^ ads for flange- uted (in- cluding weight of (includ- ing rivet- heads), in Me-in in- crease in thickness uted (in- cluding weight of (includ- 1/ ing rivet- ^^ heads), in ^^ 6-in in- ease in ickness plates girder), in tons of tons of 2 000 lb of flange- plates girder), in tons of tons of ^f 2 000 lb flange- plates 2 000 lb 2 000 lb 10 64.94 0.65 3.75 58.08 0.57 3.81 0.03 II 12 59.02 54.12 0.71 0.78 3.40 52.80 0.63 0.68 3.45 3.17 0.03 0.03 3.12 48.40 13 49.95 0.84 2.88 44.68 0.74 2.93 0.04 14 46.39 0.91 2.68 41.48 0.80 2.72 0.04 IS 43.29 0.97 2.50 38.72 0.85 2.53 0.04 16 40.59 1.04 2.34 36.30 0.91 2.38 0.05 17 38.20 1. 10 2.21 34.16 0.97 2.24 0.05 18 36.08 1. 17 2.08 32.27 1.03 2. II 0.05 19 34.18 1.23 1.97 30.57 1.08 ~ 2.00 0.05 20 32.47 1.30 1.87 29.04 1.14 1.90 0.06 21 30.93 1.36 1.78 27.66 1.20 1. 81 0.06 22 29 52 1.43 1.70 26.40 1.25 1.73 0.06 23 28.23 1.49 1.63 25.25 1.31 1.65 0.07 24 27.06 1.56 1.56 24.20 1.37 1.58 0.07 25 25.98 1.62 1.50 23.23 1.42 1.52 0.07 26 24.98 1.69 1.44 22.34 1.48 1.46 0.08 27 24.05 1.75 1.38 21.51 1.54 1. 41 0.08 28 23.19 1.82 1.34 20.74 1.60 1.36 0.08 29 22.39 1.88- 1.29 20.03 1.65 1. 31 0.08 30 21.65 1.95 1.25 19.36 1. 71 1.27 0.09 31 20.95 2.01 1. 21 18.73 1.77 1.23 0.09 32 20.29 2.08 1. 17 18.15 1.82 1. 19 0.09 33 19.68 2.14 1. 14 17.60 1.88 1. 15 O.IO 34 19.10 2.21 1. 10 17.08 1.94 1. 12 O.IO 35 18.5s 2.27 1.07 16. 59 1.99 1.09 O.IO 36 18.04 2.34 1:04 16.13 2 '05 1.06 O.IO 37 17. 55 2.40 1. 01 15.70 2. II 1.03 O.II 38 17.09 2.47 0.99 15.28 * 2.17 1. 00 ©.II 1 39 16.65 2.53 0.96 14.89 2.22 0.98 O.II 1 The above values are based on a maximum fiber-stress of 13 000 lb per sq in, rivet-holes in both flanges deducted. See paragraph on Riveted Single-Beam and Double-Beam Girders, page 603, and the foot-note for same regarding fiber-stresses. Weights of girders correspond to lengths, center to center of bearings. Tables of Safe Loads for Steel Beams and Girders 611 Table XV (Continued). Safe Uniform Loads in Tons of 2 000 Pounds for Riveted Steel-Beam Box Girders Two lo-in steel I Beams and two 12 by ^^-in steel plates r-Q MK^ -Q-, Two lo-in r^ Wk^ Two lo-in "^ ^^ r %^ r beams. beams, 35.0 lb 25.0 lb ^ ^r^ 1^ per ft ^U K per ft Increase Dis-, tance, center to center of bear- ings, ft Tw steel plat 12 by ]ri ir es, I Two steel plates, 12 by }ri in in weight of girder for He-in increase in thick- ness of Safe loads, uniformly Weight Increase in safe Safe loads, uniformly Weight Increase in safe distrib- uted (in- cluding weight of of girder (includ- ing rivet- heads), in loads for He-in in- crease in thickness distrib- uted (in- cluding weight of of girder (includ- ing rivet- heads), in loads for M 6-in in- crease in thickness flange- plates girder), in tons^of 2 000 lb tons of 2 000 lb of flange- plates girder) , in tons of 2 000 lb tons of 2 000 lb of flange- plates ID 44.35 0.55 2.59 39-23 0.47 2.64 0.02 II 40.32 0.60 2.36 35.66 0.52 2.40 0.03 12 3(3.96 0.65 2.16 32.69 0.56 2.20 0.03 13 34.12 0.71 1.99 30.18 0.61 2.03 0.03 14 31.68 0.76 1.85 28.02 0.66 1.89 0.03 15 29.57 0.82 1.73 26.15 0.71 1.76 0.04 i6 27.72 0.87 1.62 24.52 0.75 1.65 0.04 17 26.09 0.93 1.52 23.08 0.80 1.55 0.04 i8 24.64 0.98 1.44 ■21.79 0.85 1.47 0.04 19 23.34 1.04 1.36 20.65 0.89 1.39 0.05 20 22.18 1.09 1.30 19.62 0.94 1.32 0.05 21 21.12 i.i5 1.23 18.68 0.99 1.26 0.05 22 20.16 1.20 1. 18 17.83 1.04 1.20 0.05 23 19.28 1.26 1. 13 17.06 1.08 1. 15 0.06 24 18.48 1. 31 1.08 16.3s 1. 13 1. 10 0.06 25 17.74 1.36 1.04 15.69 1. 18 1.06 0.06 26 17.06 1.42 1. 00 15.09 1.22 1.02 0.06 27 16.43 1.47 0.96 14.53 1.27 0.98 0.07 28 15.84 1.53 0.93 14.01 1.32 0.94 0.07 29 15.29 1.58 0.89 13-53 1.37 0.91 0.07 30 14.78 1.64 0.86 13.08 1. 41 0.88 0.07 ' 31 14.31 1.69 0.84 12.65 1.46 0.8s 0.08 32 13.86 1. 75 0.81 12.26 1. 51 0.82 0.08 33 13-44 1.80 0.78 11.89 1. 55 0.80 0.08 34 13.04 1.86 0.76 11.54 1.60 0.78 0.08 35 12.67 1. 91 0.74 II. 21 1.65 0.75 0.09 36 12.32 1.96 0.72 10.90 1.70 0.73 0.09 37 11.99 2.02 0.70 10.60 1.74 0.71 0.09 38 11.67 2.07 0.68 10.32 1.79 0.69 0.09 39 11.37 2.13 0.66 10.06 1.84 0.67 O.IO The above values based on a maximum fiber-stress of 13 000 lb per sq in, rivet-holes in both flanges deducted. See paragraph on Riveted Single-Beam and Double-Beam Girders, page 603, and the foot-note for same regarding fiber-stresses. Weights of girders correspond to lengths, center to center of bearings. 6i2 Strength o( Beams and ISeam Girders Chap. 15 Beams Supporting Brick Walls. In calculating the size of a girder to sup- port a brick wall, the structuie of the wall should be carefully considered. If the wall is without openings and does not support floor-beams, only that part of the wall included within the dotted lines, Fig. 10, need be considered as being supported by the girder. The beams in that case, however, should be made very stiff, so as to have little deflection. If there are several openings above the girder, and especi- ally if there is a pier over the middle part of it, as shown in Fig. 11, then the manner in wliich the loading is distributed should be carefully considered. In a case of this kind, only the dead weight included between the dotted lines A A and BB should be considered Fig. 10. Triangular Loading of Beams under Brick Walls Fig. 11. Loading of Beams under Walls with Openings as coming upon the girder, and proper allowance made for the concentration of the greater part of the load at or near the middle. If, however, the lower windows are two-thirds their total width, or more, above the girder, then it is more reasonable to suppose that the wall included between the lines CC rests upon the girder, and also to consider that this load is uniformly dis- tributed over it. When beams extend under the entire length of a wall which is more than i6 or i8 ft long, the weight of the entire wall rather than the weight of a triangular part of it should be taken as coming upon the beams; for, if they should bend, the wall would settle, and might push out the supports and cause the whole structure to fall. (See, also, page 318.) 5. Framing and Connecting Steel Beams and Girders Standard Separators. When beams are used to support walls, or as girders to carry floor-beams, they are often placed side by sifie; and should in such cases be connected by means of bolts and cast-iron separators fitting closely between the flanges of the beams. The office of these separators is, in a measure, to hold in position the compression-flanges of the beams by preventing SIDE deflection or BUCKLING, and also to unite the beams so as to cause them to act in unison as regards vertical deflection. Separators should be provided at the supports, at points where heavy concentrated loads are imposed, and at regular intervals of from 5 to 6 ft between. TRe illustra- tions, dimensions, etc., given in Table XVI, are for the standard separaxj in common use. ixaii I Framing and Connecting Steel Beams and Girders 613 Table XVI.* Separators for Steel Beams AMERICAN BRIDGE COMPANY STANDARD Beams Separators •>4-in bolts d "A Dimensions -£ 11 .s ^£ 1% Diagrams -: Weight -^ per foot. W 2i S ti -J & lb J w in h in d t in ii 1 1^ G 24 II5-II0-I0S 8^4 16% 8 20 12 •) 631 ^•^ I0>^ 3.4 0.25 100 8 151/2 7H 20 12 ■) ^28 3.6 10 3.2 0.25 24 95 and 90 85 80 .. 100 and 95 8 8 8 8 15I/4 I5M 15 15H 7V4 7/2 7 20 20 20 12 5^ 12 •} 12 -^ i28 <^29 ii 29 3.6 3.6 3.6 10 9VC> 9K2 3.2 3.1 3.1 3.2 0.25 0.25 0.25 1 t 16 12 •) ^ 22 2.9 10 0.25 ^ 20 90 7K2 14% 6% 16 12 •> ^22 2.9 9V1 3.1 0.25 v _.. _ : _ 85 and 80 7Vz 14H 6-); 55 m 1 2 1/4 5% II 7K2 /2 II 1.6 8 2.7 0.25 l^V/«' 15 50 and 45 42 6K2 12^ 12 6 6 II II 7K2 7H /2 12 .^ 12 1.6 1.6 8 8 8 2.7 2.7 0.25 0.2s 5^' cored holes 55 6 11% 5M m 5 /2 9 1.3 2.7 0.25 12 50 6 II 1/2 5I/J m 5 '4 9 1.3 8 2.7 0.25 45 6 iiKi 5V4 SYa 5 /^2 9 1.3 1Y 2.6 0.25 12 40 and 35 31.5 6 6 iiH II 5K2 5Ki 8% 5 5 /2 9 l'^ 9 l^ 6 1.3 1.3 I.I 1V2 7K2 2 6 0.25 216 1.3 0.25 40 sVi 10% 4% 7V2 0.13 10 35 sVi loH 4% 7'/2 '/2 6 I.I 7 1.3 0.13 f^' ^^" 30 sVi I0K2 5 7K2 M2 7 I.I 7 1.3 0.13 25 5H 10 5 7/2 H 7 I.I 7 1.3 0.13 35 5 10 4H 6^2 K2 5 0.9 7 1.3 0.13 1 '' — ■*• 9 30 5 9VC 4Kt 6H ^2 5 0.9 6K2 1.2 0.13 ill" 1 25 5 9K 4K 6K2 H 5 0.9 6K 1.2 0.13 ^i^ I 21 25.5 \v. 9W 9 4K 4 6H /' 5 0.9 0.8 6K 1.2 0.13 ^ 5^^ '/i ^ 6 I.I 0.13 8 23 4'/2 8% 4 5H /2 4 0.8 6 I.I 0.13 — ] . . 20.5 and 18 20 4H 411 8K 8H 4 4 5K 5 K2 4 0.8 \ o.-j 6 6 i.i I.] 0.13 0.13 l.A. \\ i 7 17-5 \\i 8V. 4 5 Vi I \ 0.' 6 I.] 0.13 ^-*'kii"^/ H" — '*^ — ^^ 15 4K 8M 41^^ 5 Vi i \ 0.- 6 I.] 0.13 ^f 17.25 6 14-75 4 4 73/ J3V i aV \ oX ) 5M I.] I I. 0.13 [ 0.13 %''cored' hole 12.25 4 nv r I aV Vi 4| o.( 5 5V I I. [ 0.13 For 5-in, 4-in and 3-in beams.'use i-in gas-pipes, 3H, 3 and 2^^tn long, respectively * From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. 614 Strength of Beams and Beam Girders Chap. 15 Gas-Pipe Separators. Separators formed of pieces of gas-pipe, cut to the desired lengths and slipped over the bolts are often used by contractors. (See bottom of Table XVI.) Such separators permit the beams to act independently of each other, and should not be used in any place where one beam is liable to receive a greater load than the other; and as this condition exists in almost every case where two or more beams are used together, it follows that "cast- iron separators, made to fit the space between the beams," should be specified in almost every instance. As noted in Table XVI, gas-pipe may sometimes be used for 5, 4 and 3-in beams. Separators with two bolts should be used for beams 1 2 in or more in depth. For 1 2-in beams one bolt is sometimes used when the load is light; for beanis under 12 in in depth one bolt is sufficient. FRAMING DETAILS OF FRAMING BETWEEN COLUMNS SHOP-DRAWING OF GIRDER (STANDARD CONNECTIONS FOR 9 BEAMS] .m^ • c < • ( >• ) >• ■■1 -fo o - o SECTION A B }4 Clearance-^ SECTION C D IF PUN OF ABOVE WITH UPPER FLANGES REMOVED ELEVATION SHOWING THE COPING OF BEAMS CONNECTIONS FOR BEAMS AND GIRDERS " Connection-angles shall in no case be less in thickness than the web of the beam or girder to which they are fastened, nor shall the width be less than H the depth of the beam, except that no angle-knee shall be less than 2y/' wide nor required to be more than 6 wide. Web-angles, the full depth of the web, must be used for all girder- connections. " Fig. 12. Framing of Steel I Beams and Girders Beam-Connections. Steel beams and channels are framed together by means of short pieces of angles, which are usually riveted to the floor-beam or tail-beam and bolted to the girder. The angles are always used in pairs, one on each side of the beam. If the floor-beam is framed flush, either with the top or bottom of the girder, or if two beams of the same height are framed together, the end of the beam supported should be coped, or cut to fit the shape of the girder or supporting beam. The maximum clearance-space allowed between the end Framing and Connecting Steel Beams and Girders 615 Fig. 13. Framing to Riveted Plate Girder of the beam and the web varies from Me in in the smaller beams to H in in the larger ones. Figs. 12 and 13 show various details of beams framed together and also to girders. When a floor-beam rests on top of another beam or girder, as in Fig. 15. the beam should be secured by means of a pair of wrought-iron 616 Strength of Beams and Beam Girders Chap. 15 CLIPS, shown in Fig. 14, shaped so as to fit closely the top flange of the girder, and either bolted or riveted to the opposite sides of the lower flange of the floor- beam. Fig. 16 shows one method of framing the ends of wooden floor-joists to steel beams, a 4 by 3 by %-in angle being riveted the whole length of the steel beam, by %-in rivets, about 6 in apart. The joists are usually secured by iron or ^ \\^x S/^ Anchor rig. 14. Clip for Fas- tening Steel Beam on Top of Another Fig. 15. Steel Beams Fastened One on the Other by Clips Fig. 1 6. Framing of Wooden Joists to Steel I Beam •CLAMPS or ANCHORS, and framed about i in above the upper flange of the beam to allow for settlement. If these joists are over 3 ft apart, short lengths of angles may be placed under each one.* Standard Connection-Angles for I Beams and Channels. The size of the angles and the number of rivets used for connecting steel beams, vary somewhat with different shops and with different structural engineers, so that there cannot be said to be a universal standard. The variations in the differ- ent STANDARDS, however, are not very great, and as the connections adopted by the Carnegie Steel Company are perhaps the most used, the author has se- lected them for illustration in Table XVII. The connections have been pro- portioned with a view to covering most cases occurring in ordinary practice, with the usual relations of depth of beam to length of span. In extreme in- stances, however, where beams of short relative span-lengths are loaded to their full capacity, or when beams frame opposite each other into another beam with web-thickness less than %t in, it may be found necessary to make provision for additional strength in the connections. The limiting span-lengths, also, at and above which the standard connection-angles may be used with perfect safety, are also given in Table XVIII. • For details of the framing of floor-beams and girders, see Chapters XXI and XXII and also Professor Nolan's revised Chapters II and VII of Kidder's Building-Construction and Superintendence, Part II, Carpenters' Work, Framing and Connecting Steel Beams and Girders 617 Table XVII.* Connections for Steel Beams AMERICAN BRIDGE COMPANY STANDARD 2Ls4'x4''xi^xl'8i^'' Weight 46 lb 21" 2Ls4"x4"xi^"xl'2i^* Weight 33 lb 12" *5^-* ^H} -& 2Ls4".x4'x>{'^xO'8i4- Weight IT lb r; 6'/ 5" Weight 39 lb 2o;'i8;'i^" 2)^' .2Ls4x4'xy6X0ai^' Weight 23 lb io;'9;'8" ^^ 2H ^ ^ 2H' P Jl 1 ^ H r-'^ 2.Ls6x4"x%"xO'5>^" Weight 13 lb 4'; 3" 2J^fHH2)^' 2 Ls 6"x.4"x % X 0'3' 2 Ls G^x 4"x %"x 0'2* Weight 7 lb Weight 5 lb Rivels andbolts '>^ diameter Weiglits given are for %"shop rivets and angle-connection^; abouf 20 per cent should be added for field-rivets or bolts * From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa, 618 Strength of Beams and Beam Girders Chap. 15 Table XVin.* Limiting Values of Connections for Steel Beams Value of VnliiP*^ of niit^t^tirliTiP' 1pp*XX\^lXX^ JLV^^O KJi. \^\Jl.LXX\^\^\i k\JX,X CLXX^X^Aj nection Field-rivets Field-bolts Shop; •>4-in rivets or turned bolts, single shear, lb Min. allow- ;^4-in rough Min. allow- _ Depth, Weight, rivets in able span, bolts, able span, lb per enclosed uniform t. single uniform I, in in ft bearing, lb load, ft in shear, lb load, ft tT 27 90 82 530 61 900 18.9 ~w 49500 23. b ( 80 67 500 S3 000 17 S ti 42 400 21.9 y% 24 ' 74 64 260 S3 000 16 4 H 42 400 20 4 li 21 60 1^ 48150 44200 14 2 % 35300 17.8 Vs 20 6S 45 000 35300 17 6 % 28300 22 I '6 18 1 55 41 400 35300 13 3 t' 28300 16.7 Ys I 48 34 200 35300 12 8 He 28300 15-4 V^ 15 [ 42 I 37^ 36900 35300 % 9 f5 28300 II. I Ys 29880 35300 "9 7 'A 28300 10.2 91 6 1 31 K2 23 600 26 soo 8 I VlG 21 200 90 Ys 12 i 28 19 170 26 500 9 2 VX6 21 200 9-2 H ( 25 27 900 17 700 7 4 Vs 14 100 9.2 Ys 10 i 221^ 22 680 17 700 6 8 Vs 14 100 8.6 Ys 9 21 26 100 17 700 5 7 Vs 14 100 71 5g g ^17^ 24300 17 700 4 3 'A 14 100 5 4 H 18900 17 700 4 4 y% 14 100 5-5 % 7 15 II 300 8800 6 2 % 7 100 78 Ys 6 12H 10 400 8800 4 4 % 7 100 5 5 Ys 5 9H 9 Soo 8800 2 9 v% 7 100 36 Ys 4 lY^ 8600 8800 2 2 ^6 7 100 2.7 Ys 3 SV2 7 700 8800 I 3 Yi 7 100 1-4 Ys 1 Allowable Unit Stress in Pounds per Square Inch t ( Rivets shop 12 000 Rivets, enclosed.. shop 30000 Single shear Rivets and turned Rivets, one side, .shop 24000 bolts field 10 000 Bearing Rivets and turned Rough bolts field 8 000 bolts...; field 20000 Rough bolts field 16 000 / = Web-thickness, in bearing, to develop maximum allowable reactions, when beams frame opposite Connections are figured for bearing and shear (no moment considered) The above values agree with tests made on beams under ordinary conditions of Where the web is enclosed between connection-angles (enclosed bearing), values are greater because of the increased efficiency due to friction and grip Special connections must be used when any of the limiting conditions given above are exceeded, as when an end-reaction from a loaded beam is greater than the value of the connection of the shorter span with the beam fully loaded; or a less thickness of web when maximum allowable reactions are used *From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. t For slight variations from these values, see Chapter XXVIII. Table I and Chapter XXX, 4, Stresses. Tie-Rods and Anchors for Steel Beams and Girders 619 ' Table XIX.* Lengths and Weights of Tie-Rods and Anchors for Steel Beams AMERICAN BRIDGE COMPANY STANDARD 2K'toiK ^'toiy/ ' [^"""H^~""^c. tocof '^ir/ii • uL^ff^-tni \ Hl^---:^- beams s / — !'• ' %-INCH TIE-RODS i B*i« !<---3'--->j Lengths and Weights tor Various Distances Center to Center of Beams Weights include two nuts CtoC L'th Wgt CtoC L'th Wgt CtoC L'th Wgt CtoC L'th Wgt ft in ft in lb ft in ft in lb ft in ft in lb ft in ft in lb I I 3 2.30 I 3 I 6 2.67 I 6 I 9 3.05 I 9 2 3.42 2 2 3 3.80 2 3 2 6 4.17 2 6 2 9 4.55 2 9 3 4.92 3 3 3 5.30 3 3 3 5.07 3 b 3 9 6.05 3 9 4 6.42 4 4 3 6.80 4 3 4 t 7.17 4 b 4 9 7.55 4950 7.92 5 5 3 8.30 5 3 5 6 8.67 5 b 5 9 9 05 5960 9.42 6 6 3 9.80 6 3 6 6 10.17 6 6 b 9 TO. 55 6 Q 7 10.92 7 7 3 11.30 7 3 7 11.67 7 b 7 9 12.05 7 9 8 12.42 8 8 3 12.80 8 3 8 6 13.17 8 6 8 9 13.55 8 9 9 13.92 For strength of rods, see Table II, page ; Anchors * Swedge-Bolt Weight includes nut Built-In Anchor-Bolts Government Anchor M ^^^^mm^ Diameter Length Weight in . ft In lb VA 9 1 1 1 3 1.3 2.3 3.1 6.1 [-in rod, i ft 9 in long. Wt., 3 lb Angle-Anchor OH When center to center of anchors is less than Two angles, 6 by 4 by Me by 2H in width of washer, use washer with two holes Weight with M-in bolts, 7 lb For bearing-plates, bases, etc., see Chapter XIII. ♦ From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. 620 Strength of Cast-iron Lintels and Wooden Beams Chap. 16 CHAPTER XVI STRENGTH OP CAST-IKON LINTELS AND WOODEN BEAMS By F. H. KINDL LATE CORRESPONDING MEMBER AMERICAN INSTITUTE OF ARCHITECTS 1. Cast-iron Lintels Form of Cross-Section. Owing to the fact that the resistance of cast iron to tension is only about one-fifth of its resistance to compression, the shapes of beams most economical for wrought iron or steel would be wasteful for cast iron. The extreme brittleness of cast iron, and the danger of flaws in castings, render it an undesirable material for resisting transverse stress. About the only form in which cast-iron beams are now used in building-construction in this country is in the shape of lintels for supporting brick or stone walls, in t)M>n??//}% places where a flat soffit is desired, and the walls are ^%^ not to be plastered. Cast-iron lintels are also i - - - - occasionally used over store-fronts, the face of the lintel being paneled and molded for architectural effect. Experiments on Cast-iron Beams. Before wrought-iron I beams were manufactured, cast- i • ^ Tssm BEAMS were frequently used as the only available ones, other than those of wood or stone. Early in the nineteenth century Eaton Hodgkin- ^i^^%M^^^^%%m%%^ son, an English engineer, made a series of experi- Fig.l. Cross-section of Cast- "^^^^s with cast-iron beams, from which he found iron Lintel of Ideal Form ^^^ the form of cross-section of a beam of that material which will resist the greatest transverse stress is that shown in Fig. 1, in which there is six times more metal in the bottom than in the top flange. The relative thicknesses of the three parts, the web, the top flange and the bottom flange, may be, with advantage, as 5, 6 and 8, respectively. Strength of Cast-Iron Beams. If made with these proportions, the width of the top flange will be equal to one-third that of the bottom flange. As the result of his experiments, Hodgkinson gave the following rule for the breaking- weight at the middle for a cast-iron beam of this form: I area of bottom flangeX / depth \ I . -uX'-u X 2.426 _,,.,,. \ m square inches / V in inches/ , ^ Breakmg-load m tons = -^ ^^ — ^ (i) clear span in feet This rule, although largely empirical, agreed very well with the few experi- ments that were made. Structural engineers, however, use the general formu- las for the strength of beams, as given in Chapter XV, except that the section- modulus is found by dividing the moment of inertia by the distance of the neutral axis from the bottom of the beam, and the safe tensile strength is Cast-iron Lintels 621 used in the flexure-formula. Thus the general formula for a beam supported at both ends and with the load uniformly distributed, as given in Chapter XV, page 560, is: Safe load in pounds = 2^^ __ x 5^ As St, the safe tensile strength for cast iron should be taken at 3 000 lb, this formula becomes 2 000 l/c Safe load in pounds = ■ (2) and, for either section given below, I/c = Moment of inertia A h lb ib ib "^ " I ' " ^ I I NPUTRAL AXIS' NEUTRAL AXIS' The MOMENT OF INERTIA is computed by the formula (see page 33s) (3) in which b denotes the combined thickness of the webs, and the distances d, d\, and J2 are measured from the neutral axis, which must pass through the CENTER OF GRAVITY of the Section. The center of gravity may be found by the method explained in Chapter VI. This formula may be used for any of the above sections when the depth does not exceed the width, and the thickness of each web is at least equal to the thickness of the flange. In lintels with a singlf web it is well to make the thickness r 1 _L.. r _^ -6=2 1 Fig. 2. Cross-section of Cast-iron Lintel with Three Webs of the web V4, or Vs in greater than the thickness of the flange. For a beam with a cross-section like that shown in Fig. 1, Formula (2) agrees very closely with Formula (i), when a factor of safety of six is used. Example. The following example illustrates the application of Formula (2) : It is required to compute the safe load for a cast-iron lintel having the section shown in Fig; 2 and a clear span of 10 ft. The load is uniformly dis- tributed, and the thickness of the metal i in. Solution. The first step is the finding of distance d, that the center of gravity, through which the neutral axis of the cross-section passes, is below the top- surface of the beam. This is found by taking the^moments of the areas of the cross-sections of webs and flange about the line XY, and dividing their sum by the area of the entire section. (See page 294.) Each web-section is 11 in deep and i in thick; hence the area of each is 11 sq in. The moments of the THREE WEBS about XY will then be 3X11X5^/^= 181. 5 The moment of the flange about XY = 28 X iiV^ = 322 503.5 622 Strength of Cast-iron Lintels and Wooden Beams Chap. 16 The area of the entire cross-section = 6i sq in 503.54-61 = 8.25 = i in Then d = 8.25 in d^ = 561.5 ^i = 3-75ii^ ^1^= 52.7 di = 2.75 in d'>} = 20.8 The MOMENT OF INERTIA is next found by Formula (3) : r 3X561.5+28X52.7-25X20.8 & = 3 in h' = 28 in l/c = 880/3.75. From Formula (2) the safe load = (2 000 X 234.6)/io = 46 920 lb, or 23.4 tons. Ends and Brackets of Cast-iron Lintels. When a lintel, the cross-sec- tion of which has the shape of an inverted T (-L), is used over a single opening, the Fig. 3. Cast-iron Lintel with Tapering Web web may be tapered towards the ends, as in Fig. 3, without affecting the strength. If the flange is more than 8 in wide, brackets should be cast in the middle, as at A, Fig. 3. When CONTINUOUS lintels are used over store- fronts or similar places, ends should be cast on the lintels, as in Fig. 4, and the ends of abutting lintels Fig. 4. Cast-iron Lintel with Ends for Bolting bolted together. All lintels with two or three webs should haveCsolid ends con- necting the webs. Tables of Strength of Cast-iron Lintels. The tables on the following pages have been computed in accordantce with Formula (2)^ ^The weight of the Cast-Iron Lintels 623 lintel itself should be deducted from the safe load. In using these tables it should be remembered that the values are for loads uniformly distributed. If the load is concentrated at the middle, it should be multiplied by 2. If at some other point than the middle, the load should be multiplied by the value given on pages 566 and 632, which most nearly corresponds with the position of the load. For other spans than those given, the distributed load should be multipHed by the span, and the lintel used which has acoEmciENT of strength C (Table I) just above the product thus obtained. (For explanation of coeffi- cient of strength, see Chapter XV, page 556.) Example. It is required to support a 12-in brick wall, 10 ft high, over an opening 5 ft 6 in wide, with a cast-iron lintel. At a distance of 22 in from one support, a girder, which may bring a load of 9 600 lb on the lintel, enters the wall. What should be the dimensions of the lintel? Solution. At no lb per cu ft, the wall above the lintel weighs 10 X 5^/^ X no = 6050 lb. As 22 in is one-third of the span, the concentrated load is multi- plied by 1.78 (page 632), making the load 17 088 lb. The total equivalent dis- tributed load is then 23 138 lb. Multiplying this by the span there results 127 259 lb, or 63.6 tons, as the least value for the coefficient of strength C. From the table, it is found that a 12 by lo-in lintel, i in thick, with one web, has a coefficient of strength of 72.2; and that a 12 by 8 by ii4-in lintel with two webs, has a coefficient of strength of 69.9. A lintel with two webs is best for a 12-in wall, and interpolating between the values of C for the i-in and 2-in thicknesses of the 12 by 8-in lintel, 65.4 is found to be the value of C for a thickness of iVs in. This exceeds the required value by enough to more than compensate for the weight of the hntel itself; hence a 12 by 8 by iV^-in lintel with two webs is used. Flaws in Castings. Owing to the Hability of flaws in the castings, cast-iror beams should always be carefully inspected before being accepted. 624 Strength of Cast-iron Lintels and Wooden Beams Chap. 16 Table I. Safe Distributed Loads in Tons for Cast-iron Lintels Lintels of 1-^-4=^ Shapes K- WIDTH ->j U_wiOTH->l J » • » Loads include weights of lintels. Maximum tensile stress 3 ooo lb per sq in. See remarks, pages 622 and 623. Size, width by depth, in Thick- ness of metal. Weight per foot. c, tons Span in feet in lb 5 6 7 8 9 10 II 12 H 26.3 15.9 3.18 2.65 2.27 1.98 1.76 1.59 1.44 1.32 6x 6 I 34.4 19.0 3.80 3.16 2.71 2.37 2. II 1.90 1.72 1.58 iH 42.0 21.5 4-30 3.58 3.07 2.68 2.39 2. IS 1.95 1.79 % 28.6 17.8 3.56 2.96 2.54 2.22 1.98 1.78 1. 61 1.48 7X 6 I 37. 5 21.3 4.26 3.55 3.04 2.66 2.36 2.13 1.93 1.77 iH 45-9 24.0 4.80 4.00 3.43 3.00 2.66 2.40 2.18 2.00 % 31.0 22.6 4-52 3.76 3.23 2.82 2.51 2.26 2.0s 1.88 7X 7 I 40.6 27.5 5. SO 4.58 3.93 3.43 3.05 2.75 2.50 2.29 iM" 49-8 31.4 6.28 5.23 4.49 3.92 3.49 3.14 2.85 2.62 H 31.0 19.6 3.92 3.26 2.80 2.45 2.18 1.96 1.78 1.63 8X 6 I 40.6 23.4 4.68 3.90 3.34 2.92 2.60 2.34 2.12 1.9s iH 49-8 26.4 5.28 4.40 3.77 3.30 2.93 2.64 2.40 2.20 ' H 33.3 25.0 5.00 4.16 3.57 3.12 2.77 2.50 2.27 2.08 8X 7 I 43.7 30.3 6.06 5.05 4.33 3.79 3.36 3.03 2.75 2.52 iH 53.7 34.8 6.96 5.80 4.97 4.35 3.86 3.48 3.16 2.90 ?4 35. 6 30.6 6.12 5.10 4.37 3.82 3.40 3.06 2.78 2.55 8X 8 I 46.8 37.6 7.52 6.26 5.37 4.70 4.18 3.76 3.41 3.13 iH 57.6 43.4 8.68 7.23 6.20 5. 42 4.82 4.34 3.94 3.61 H 38.0 36.5 7.30 6.08 5.21 4.56 4.05 3.65 3.31 3.04 8X 9 I 50.0 45.2 9.04 7.53 6.45 5.65 5.02 4.52 4. II 3.76 iH 61. 5 52.6 10.52 8.76 7.51 6.57 5.84 5.26 4.78 4.38 H 40.4 26.S 5.30 4.41 3.78 3.31 2.94 2.65 2.41 2.21 I2X 6 I 53.1 31.6 6.32 5. 26 4.51 3.95 3.51 3.16 2.87 2.63 iH 65.4 34.8 6.96 5.80 4.97 4.35 3.86 3.48 3.16 2.90 H 45.0 41.7 8.34 6.95 5.95 5.21 4.63 4.17 3.79 3.48 I2X 8 I 59-4 51.2 10.24 8.53 7.31 6.40 5.69 5.12 4.6s 4.26 iH 73.2 58.5 11.70 9.75 8.35 7.31 6.50 5.85 5. 32 4.87 % 49-8 58.0 11.60 9.66 8.28 7.25 6.44 5.80 5.27 4.83 12X10 1 65.6 72.2 14.44 12.03 10.31 9.02 8.02 7.22 6.56 6.01 iH 81.0 83.8 16.76 13.96 11.97 10.47 9.31 8..^8 7.62 6.98 H 54.4 75.2 15.04 12.53 10.74 9.40 8.35 7.52 6.83 6.26 12x12 I 71.9 94.8 18.96 15.80 13.54 11.85 10.53 9.48 8.62 7.90 iH 88.9 III. 5 22.30 18.58 15.92 13.93 12.39 II. IS 10.12 9.29 Cast-iron Lintels 625 Table I (Continued). Safe Distributed Loads in Tons for Cast-Iron Lintels 1" Lintels of 1 1 '1 .Shapes Loads include weights of lintels. Maximum tensile stress 3 ooo lb per sq in. See remarks, pages 622 and 623. Size, width by depth., in Thick' ness of metal, in Weight per foot, lb c, tons Span in feet 5 6 7 8 9 10 11 12 I2X 6 2/4 I 52. 7 68.8 84.0 31.7 37.6 43.0 6.34 7.52 8.60 5.28 6.26 7.16 4.53 5.37 6.14 3.96 4.70 5.37 3. 52 4.18 4.77 3.17 3.76 4.30 2.88 3.42 3.91 2.64 3.13 3.58 I2X 8 I 62.1 81.3 99.6 49-5 60.9 699 990 12.18 13.98 8.25 10.15 11.65 7.07 8.70 9.98 6.19 7.61 8.73 5.50 6.76 7.76 4.95 6.09 6.99 4.50 5.53 6.35 4.12 5.07 5.82 14X 6 I 57.4 75:0 91.8 35.5 42.0 48.0 7.10 8.40 9.60 5-91 7.00 8.00 5.07 6.00 6.85 4.43 5.25 6.00 3.94 4.66 5.33 3.55 4.20 4.80 .3.22 3.82 4.36 2.96 3.50 4.00 I4X 8 I 66.8 87.5 107.4 55.4 68.1 78.8 11.08 13-62 15.76 9.23 11.35 13.13 7.91 9.73 11.25 6.92 8.$i 9.85 6.15 7.56 8.75 5.54 6.81 7.88 5. 03 6.19 7.16 4.61 5.67 6.56 i6x 6 I 62.1 81.3 99-6 39- 1 46.8 52.9 7.82 9.36 10.58 6.51 7.80 8.81 5. 58 6.68 7.55 4.88 5.85 6.61 4.34 5.20 5.88 3.91 4.68 5.29 3.55 4.25 4.81 3.25 3.90 4.40 i6x 8 I 1K4 71.5 93.8 115. 2 61.4 74.6 86.8 12.28 14.92 17.36 10.23 12.43 14.46 8.77 10.65 12.40 7.67 9-32 10.85 6.82 8.29 9.64 6.14 7.46 8.68 5.58 6.78 7.89 5. II 6.21 7.23 20X 6 I 71. 5 93.8 115. 2 47-2 55.1 62.0 9.44 11.02 12.40 7.86 9.18 10.33 6.74 7.87 8.85 5.90 6.88 7.75 5.24 6.12 6.88 4.72 5.51 6.20 4.29 5. 01 5. 63 3.93 4.59 5.16 20X 8 I 80.8 106.2 130.8 72.6 89.5 102. s 14.52 17.90 20.50 12.10 14.91 17.08 10.37 12.78 14.64 9.07 11.18 12.81 8.06 9.94 11.39 7.26 8.95 10.25 6.60 8.13 9.31 6.05 7.45 8.54 20X10 I 90.2 118. 8 146.5 100.5 125.4 146.8 20.10 25.08 29.36 16.75 20.90 24.46 14.35 17.91 20.97 12.56 15.67 18.35 11.16 13.93 16.31 10.05 12.54 14.68 9-13 11.40 13.34 8.37 10.45 12.23 20X12 I 99.6 131. 3 162. 1 122.6 158.0 189.5 24.52 31.60 37.90 20.43 26.33 31.58 17.51 22.57 27.07 15.32 19.75 23.68 13.62 17.55 21.05 12.26 15.80 18.95 11.14 14.36 17.22 10.21 13.16 15.79 24X 8 I 90.2 118. 8 146.5 83.4 102.4 117. 16.68 20.48 23.40 13.90 17.06 19.50 11.91 14.63 16.71 10.42 12.80 14.62 9.26 11.37 13.00 8.34 10.24 11.70 7.58 9-31 10.63 6.95 8.53 9.75 626 Strength of Cast-iron Lintels and Wooden Beams Chap. 16 Table I (Continued). Safe Distributed Loads in Tons for Cast-Iron Lintels Lintels at "T' Shapes ->j r^ ^- Loads include weights of lintels. Maximum tensile stress 3 ooo lb per sq in. See remarks, pages 622 and 623. Size, width by depth, in Thick- ness of metal, in Weight per foot, lb c, tons Span in feet 5 6 7 8 9 10 II 12 24X10 I 99.6 131. 3 162. 1 116. 144. 167. 23.20 4 28.88 6 33.52 19-33 24.06 27-93 16.5 20.6 23.9 7 14-50 3 18.05 4 20.95 12.88 16.04 18.62 11.60 14-44 16.76 10.54 13.12 15.23 9.66 12.03 13.96 24X12 1 109.0 143.8 177.7 150. 189. 223. 4 30.08 6 37.92 44.60 25.06 31.60 37.16 21.4 27.0 31.8 8 18.80 6 23.70 5 27.87 16.71 21.06 24.77 15 -04 18.96 22.30 13-67 17.23 20.27 12.53 15.80 18.58 28X 8 I 99-6 131. 3 162. 1 95. 115. 130. 5 19.10 23.00 5 26.10 15-91 19.16 21.75 13-6 16.4 18.6 4 11.93 3 14.37 4 16.31 10.61 12.77 14.50 9.55 11.50 13.05 8.68 10.45 11.86 7.98 9-58 10.87 28X10 I 109.0 143.8 177.7 130. 164. 188. 26.00 8 32.96 5 37.70 21.67 27.46 31.41 18.5 23-S 26.9 7 16.25 4 20.60 3 23.56 14.44 18.31 20.94 13.00 16.48 18.85 11.82 14.98 17.14 10.83 13-73 15.70 28X12 H I 118. 3 156.3 193.3 162. 211. 252. 5 32.50 8 42.36 50.40 27.68 35.30 42.00 23.2 30.2 36. c 1 20.31 6 26.48 31.50 18.06 23.53 28.00 16.25 21.18 25.20 14.77 19 25 22.91 13.54 17.6s 21.00 I .INTELS OF Shape s t DEPTH i fe WIDTH -M 16X 6 H I 74.4 96.9 118. 1 43. 52. 59. 3 8.66 4 10.48 3 11.86 7.21 8.73 9.88 6.1 7.4 8.4 8 5.41 8 6.55 7 7.41 4.81 5-82 6.59 4-33 5.24 5.93 3.93 4.76 5.39 3.60 4.36 4.94 i6x 8 I 88.5 115. 6 141. 6 68. 83. 97. 1 13.62 9 16.75 19.40 11.35 13.98 16.16 9-7 11.9 13.8 3 8.51 8 10.48 5 12.12 7.56 9.32 10.77 6.81 8.39 9.70 6.19 7.62 8.81 5.67 6.99 8.08 20X 8 I 97.8 128. 1 157.2 80. 98. 113. 2 16 . 04 7 19.74 9 22.78 13.36 16.45 18.98 II. 4 14.1 16.2 5 10.02 12.33 7 14.23 8.91 10.96 12.65 8.02 9-87 11.39 7.29 8.97 10.35 6.68 8.22 9-49 Sections, Stresses, Buckling and Deflection of Wooden Beams 627 Table I (Continued). Safe Distributed Loads in Tons for Cast-iron Lintels Lintels or Loads include weights of lintels. Maximum tensile stress 3 000 lb per sq in. See remarks, pages 622 and 623. Size, width by depth, Thick- ness of metal, Weight per foot lb C, tons Span in feet 24 X 8 iH I iH III. 9 146.9 180.7 126.0 165.6 204.1 107.2 140.6 172.6 121. 3 159-4 196.3 135.3 178. 1 219-7 130.7 171-9 211. 9 144-7 190.6 235-3 112. o 139-7 163. 5 146.7 184.8 218.8 91 9 112. 8 130.2 127.8 159.5 183.6 166.6 209.3 247-7 141. 4 177.4 207.8 186.0 234.6 277.9 22.40 27.94 32.70 29.34 36.96 43.76 18.38 22. SC 26.04 25.56 31.90 36.72 ,33.32 41.86 49.54 28.28 35.48 41.56 37.20 46.92 55.58 18.66 23. 27.25 24.45 30.80 36.46 15.31 18.80 21.70 21.30 26.58 30.60 27.76 34.88 41.28 23.57 29.57 34.63 31.00 39-10 46.31 16.00 19.95 23.35 20.95 26.40 31.25 13.12 16. II 18.57 18.25 22.78 26.23 23.80 29.90 35.39 20.20 25.34 29.68 26.57 33.51 39.70 14.00 17.46 20.43 18.33 23.10 27.35 11.49 14.10 16.27 15.97 19.94 22.95 20.82 26.16 30.96 17.67 22.17 25-97 23.25 29.32 34.74 12.44 15.52 18.16 16.30 20.53 24.31 10.21 12.53 14.47 14.20 17. 72 20.40 18.51 23.2s 27.52 15.71 19.71 23.09 20.66 26.06 30.88 13.97 16. 35 14.67 18.48 21.88 9-19 11.28 13.02 12.78 15.95 18.36 16.66 20.93 24.77 14.14 17.74 20.78 18.60 23.46 27.79 10.18 12.70 14.86 13.33 16.80 19-89 8.35 10.25 11.83 II. 61 14.50 16.69 15.14 19.02 22.51 12.85 16.12 18.89 16.91 21.32 25.26 9.33 11.64 13.62 12.22 15.40 18.24 7.66 9-40 10.85 10.65 13.29 15.30 13.88 17.44 20.64 11.78 14.78 17.31 15. SO 19. 55 23.16 2. Sections, Stresses, Buckling and Deflection of Wooden Beams and Girders Sections and Fiber-Stresses. The cross-sections of wooden beams are almost invariably square or rectangular, and those shapes only are con- sidered in the following rules and formulas. Beams should have such a cross- section, that the maximum fiber-stress due to transverse bending, the maximum horizontal shear and the compression across the grain at the end-bearings do not exceed the average allowable unit stresses as set forth in Table XVI. Buckling. Wooden girders should be braced laterally to prevent buckling when the ratio of length to breadth exceeds twenty, or designed with a reduced fiber-stress from that allowable, where this ratio is exceeded. Tables VII to XV assume such bracing. Joists should have bridging not over 8 ft on centers. The percentage of reduction of fiber-stress for girders should be as follows: 628 Strength of Cast-iron Lintels and Wooden Beams Chap. 16 Ratio of length to width 20 to 30 Percentage of reduction 25 30 to 40 40 to 50 50 to 60 34 42 50 Deflection. It is also important that beams carry the loads without deflect- ing beyond a limit fixed by the use to which the structure is applied; this limit is generally taken at Vso of an inch per foot of span for plastered ceilings. 3. Constants and CoeflSicients for Beams Value of the Constant, A. The letter A in the following formulas (4) to (16), denotes the safe load for a unit beam, i in square in section and i ft in span, loaded at the middle of the span. This is also one-eighteenth of the ALLOWABLE FIBER-STRESS in pounds per square inch. (See Table I, on page 557.) The following are the values of A, obtained by dividing by eighteen the RECOMMENDED UNIT STRESSES for TRANSVERSE BENDING, and those given in the building laws of New Ybrk, Chicago, Baltimore and Boston. Table II.* Coefficients for Iron, Steel and Wooden Beams. Formulas Values for A in Materials New York Chicago Baltimore Boston Recom- mended t Cast iron 167 667 889 90 67 67 44 167 667 889 72 44 44 33 167 667 889 100 56 75 167 667 889 83 56 56 167 667 889 67 39 39 33 44 67 S6 Wrought iron .... Steel Yellow pine White pine Spruce Hemlock Chestnut * Oak . . . 67 67 67 72 83 56 Douglas fir • For safe allowable working unit stresses for other 'woods, see Table XVI, page 647. From these values, A may be determined by dividing them by eighteen. See Table XVII, page 648, for other stresses for woods, taken from various building laws. See Tables XVIII and XIX, pages 650 and 651, for the ultimate strength of woods. t The values of A for wo(*den beams may be increased from 30 to 40% for temporary structures, and for commercially dry and protected timber, not subject to impact, or for ideal conditions. Table III. Coefficients Recommended for Stone J and Concrete Beams. Values of A Materials Values of A Materials Values of A Granite 10 8 7 6 Bluestone 17 22 1-7 I.I Limestone Slate. Marble Sandstone Concrete 1:2:4 Concrete 1:2:5 t Values of A for stone beams were taken from former Building Laws of New York ancl from the rec^uirements of the Board of Fire Underwriter^. FlexUral Strength of Wooden Beams m 4. Flexural Strength of Wooden Beams Section-Modulus. For beams with a rectangular cross-section, the formulas for strength can be simplified by substituting for the section-modulus its Value Va bd-, where b is the breadth and d the depth of the section. Substituting this value in the general formulas for beams with rectangular cross-sections arid of any material, the following formulas result: Beams Fixed at One End and Loaded at the Other (Fig. 5). ^ , , , . , breadth X square of depth X^* , , bate load, m pounds = 7—. — 7 — ^ (4) or Breadth, in inches 4 X length in feet 4 X load X length in feet square of depth XA* (5) -Z— w Fig. 5. Cantilever Beam. Load near Free End Fig. 6. Cantilever Beam. Distrib- uted Load over Entire Span Beams Fixed at One End and Loaded with a Uniformly Distributed Load (Fig. 6). breadth X square of depth X A* Safe load, in pounds =. Breadth, in inches 2 X length in feet 2 X load X length in feet square of depth X ^* P (6> (7) -Z- Fig. 7. Simple Beam. Load at Aliddle of Span Beams Supported at Both Ends and Loaded at the Middle (Fig. 7). ^ - , , , , breadth X square of depth Xyl* bare load, m pounds = Breadth, in inches span in feet span in feet X load square of depth X ^ * * For values of A, see Tables II and III. (8) (9) 630 Strength of Cast-iron Lintels and Wooden Beams Chap. 16 Beams Supported at Both Ends and Loaded with a Uniformly Distributed Load Over Entire Span (Fig. 8). Fig. 8. Simple Beam. Distributed over Entire Span 2 X breadth X square of depth XA* Safe load, in pounds = Breadth, in inches span in feet span in feet X load (lo) (ii) 2 X square of depth X ^ * Beams Supported at Both Ends and Loaded with a Uniformly Distributed Load Over Only a Portion of the Span (Fig. 9). -m- Fig. 9. Simple Beam. Distributed Load over Part of Span In this case the dimensions of the beam required to carry the load can be accurately determined only by computing the maximum bending moment, as explained in Chapter IX, and substituting the value thus found in Formula (i6), following. If, however, the length /i is very short in comparison with /, and near the middle, then the load may be considered as concentrated at the middle of the span and the breadth of the beam may be found by Formula (9). For- mula (13) is used if the load is at one side of the middle. The error will be on the safe side. Beams Supported at Both Ends and Loaded with Concentrated Load, not at the Middle of the Span (Fig. 10). Fig. 10. Simple Beam. Concentrated Load at Any Point breadth X square of depth X span X ^ * Safe load, in pounds = Breadth, in inches = • 4XfnXn 4 X load XmXn square of depth X span XA* ' For values of .4, see Tables II and III. (12) (13) Application of Formulas for Flexural Strength of Wooden Beams 631 Beams Supported at Both Ends and Loaded with P Pounds at a Distance m, from each End (Fig. 11). ^^ Pa ^P Fig. 11. Simple Beam. Two Equal Concentrated Loads Symmetrically Placed Safe load, P, in pounds ) breadth X square of depth X A* at each point Breadth, in inches 4X w 4 X load at one point X m (14) (15) square of depth XA* Note. In the last two cases the lengths denoted by m and n should be in feet, as the spans are in feet. 5. Application of Formulas for Flexural Strength of Wooden Beams Example i. What load, 6 ft out from the wall, will an 8 by 14-in long-leaf yellow pine beam, securely fastened at one end into a brick wall> sustain with safety? Solution. The safe load in pounds (Formula 4) = ■ = 4377 lb 4X6 Example 2. It is desired to suspend tw.o loads of 10 000 lb each, 4 ft from each end of an oak beam, 20 ft long. What should be the size of the beam? Solution. Let the depth of the beam be assumed to be 16 in. Then (For- mula 15) 4 X 10 000 X 4 The breadth = ■ = 9.3 in, nearly 256 X 67 The beam, therefore, should be 10 by 16 in in cross-section. Beam with Several Loads. It is required, next, to determine the size of a beam which is supported at both ends, and which will safely support several concentrated loads, or a distributed load and one or more concentrated loads. The correct method of finding the least size of a beam that will safely support a combination of loads, is to first find the maximum bending moment, as ex- plained in Chapter IX, page 329, and then substitute the value thus found for this BENDING MOMENT in the following formula: 4 X maximum bending moment in f t-lb Breadth, in inches = ■ (16) square of depth X A A shorter and easier method is to find the equivalent distributed load for each concentrated load, and then find the size of a beam required to support the total equivalent distributed load thus found. The equivalent distributed loads for concentrated loads applied at different proportions of the span from either end, may be obtained by multiplying the concentrated loads by the follow- ing factors: * For values of A, see Tables II and III. 632 Strength of Cast-iron Lintels and Wooden Beams Chap. 16 Table IV. Factors for Equivalent Distributed Loads Factor Position of load For a concentrated load For a concentrated load For a concentrated load For a concentrated load For a concentrated load For a concentrated load For a concentrated load For a concentrated load For a concentrated load Applied at middle of span Applied at one-third the span Applied at one-fourth the span Applied at one-fifth the span Applied at one-sixth the span Applied at one-seventh the span AppHed at one-eighth the span Applied at one-ninth the span Applied at one-tenth the span Multiply by 2. Multiply by 1.78 Multiply by 1.5 Multiply by 1.28 Multiply by 1^6 Multiply by 0.98 Multiply by % Multiply by 0.79 Multiply by 0.72 * (See, also, Chapter XV, Safe Loads for Steel Beams, page 566.) Thus, a concentrated load of 900 lb, applied at one-sixth the span from one support, will result in the same maximum bending moment as a distributed load of 900 X 1%, or i 000 lb. The above method for finding the size of a beam for a combination of several loads gives a larger beam than the correct method, by Formula (16), for the reason that the maximum bending moment will not be equal to the sum of the in- dividual bending moments. Hence, when there are several heavy loads to be sup- ported, it is economical to compute the maximum bending moment by the graphic METHOD explained in Chapter IX, page 3 k n I I 1 I 1 h- 4t— 329. ^-4- ^^5- k-y^^ \ tH • . . Example 3. The girder G, Fig. 12, sup- r \ ports the rafters of a flat roof, and also Fig. 12. Girder with Three Concen- three heavy beams, A, B and C, blocked up trated Loads above the roof and supporting a large tank filled with water. The timber is to be long-leaf yellow pine. The weight of the roof and allowance for snow is 7 500 lb. Each of the beams A, B and C, impose a load on the girder, due to the weight of the tank and its contents, of 3 000 lb. What should be the size of the girder? Solution. The roof-load may be considered to be uniformly distributed. The load from beam, A, is applied at one-third the span from one end; the load from B, five-twelfths the span from the other end; and the load from C, one- sixth the span. The fraction five-twelfths is the mean of one-half and one-third; hence the load from B should be multiplied by 1.89. Multiplying the con- centrated loads by their proper factors, the equivalent distributed load is found to be as follows: Roof-load, distributed. Load from A, 3 000 X 1.78 Load from By 3 000 X 1-89 Load from C, 3 ocjo X iV^ figuivalent distributed load =21 843 lb Relative Strengths of Beams 635 Assuming i6 in as the depth of the beam, and using Formula (ii), The breadth = ''"""l^^! = 7-6 in 2X256X67 ' Assuming 14 in for the depth, 10 in is obtained for the breadth; hence, the girder must be 10 by 14 in, or 8 by 16 in in cross-section. Strut-Beams and Tie-Beams. A strut-beam is a beam that is subject to[both a transverse and a compressive stress. A tie-beam is one that is subject to direct tension in addition to the transverse stress. To find the strength of either, first find the size of a beam required to resist the transverse stress, and then the size of* a timber, of the same depth as the beam, to resist the direct tension or compression, and add the two breadths together. Example 4. A spruce tie-beam, 10 ft long between joints, sustains a ceiling- load of 2 000 lb and a direct tensile stress of 40 000 lb. What should be th^ dimensions of the beam? Solution. As a ceiling-load is uniformly distributed, the size of the beam is determined by Formula (11), page 630. Assuming the depth to be 10 in 10 X 2 000 The breadth = , or 2 1/^ in, nearly 2 X 100 X 39 The resistance of spruce to tension (see Table XVI, page 647) is 800 lb per sq in. 40 000/800 = 50 sq in, which is equivalent to a 5 by lo-in section. It will require, therefore, a beam 7^/^ by 10 in in cross-section to resist both the trans- verse stress and the direct tension. If the tie-beam is cut in any way so as to reduce the section, except over a support, the dimensions must be increased accordingly. Example 5. A strut-beam of white pine, 10 ft long, supports a distributed roof-load of 6 000 lb, and is also subject to a direct compression of 64 000 lb. What should be the size of the beam? Solution. Assuming 14 in for the depth, the breadth for the transverse load is found by Formula (11), page 630 rr^, 1 11 10 X 6 000 . , The breadth = • =3.9 m, nearly 2X196X39 Using Formula (4), page 450, from which is computed Table IV, page 452, giving the safe loads for white-pine posts, it is found that a ^V2 by 14-in post, 10 ft long will safely carry the compressive stress, 64 000 lb. Hence it will re- quire a 7V2 by 14-in beam to resist the compressive stress, and a 4 by 14-in beam to resist the transverse load. The beam, therefore, should be 12 by 14 in in cross-section to resist them both. 6. Relative Strengths of Beams Relative Strengths of Rectangular Beams. From an inspection of the foregoing formulas it is found that the relative strengths of beams of rec- tangular cross-sections, for the different cases is as shown in Table V. Strengths of Beams of Any Constant Cross-Section. The strength- ratios given in Table V are true for beams of any constant cross-section ol whatever form. Beam on Edge. When a beam of square cross-section is supported on its edge, that is, when one of its diagonals is vertical, it will bear about seven-tenths as great a breaking-load as it will when it is supported on one side. 634 Strength of Cast-iron Lintels and Wooden Beams Chap. 16 Table V. Relative Strengths of Rectangular Beams Kind of load Position of load Strength ratios Beam supported at both ends Uniformly distributed Concentrated Concentrated Concentrated Concentrated Concentrated Concentrated Concentrated Concentrated Concentrated Over entire span At middle of span At one-third the span At one-fourth the span At one-fifth the span At one-sixth the span At one-seventh the span At one-eighth the span At one-ninth the span At one-tenth the span I Yxfs . 25^2 81/64 2^8 Beam fixed at one end, or cantilever beams Uniformly distributed Concentrated Over entire span At the free end Beam supported at one end and fixed at the other end Uniformly distributed Concentrated Over entire span Near the middle of span I mo Beam fixed at both ends Uniformly distributed Concentrated Over entire span At middle of span I The Strongest Beam Cut From a Cylindrical Log is one in which the breadth is to the depth as 5 is to 7, very nearly, and the dimensions of such a beam can be found graphically, as shown in Fig. 13. Any diagonal, as ab, is drawn and divided into three equal parts by the points c and d; from these points- lines perpendicular to ab are drawn, and the points e and / connected with a and b, as shown. Cylindrical Beams. A cylindrical beam is only ten-seventeenths as strong as a beam with a square cross-section, the side of the square being equal to the diameter of the circular section of the cylindrical beam. Hence, to find the safe load for a cylindrical beam, first find the proper load for the corresponding square- section beam, and divide this load by 1.7. The Bearing of the Ends of a Beam on a wall beyond a certain distance does not strengthen the beam. In general, a beam should have a bearing of 4 in, or if it is very long, 6 in. The Weight of the Beam Itself. The formulas given for the strength of beams do not take into account the weight of the beams themselves, and hence the safe loads of the formulas include both the external loads and the weights of the material in the beams. In small wooden beams, the weight of Fig. 13. Strongest Beam of Rectangular Section Cut from Log Tables for Strength and Stiffness of Wooden Beams 635 ^ each beam is generally so small, compared with the external load, that it need not be taken into account. But for larger wooden beams, and for metal and stone beams, the weight of the beam should be subtracted from the safe load if the load is distributed; and if the load is applied at the middle, one-half the weight of the beam should be subtracted. The Weight of Timber. The weight per cubic foot for different kinds of timber may be found in the table in Part III, pages 1501 to 1508, giving the Weights of Various Substances. 7. Tables for Strength and Stiffness of Wooden Beams Tables VII to XV for the Strength and Stiffness of Wooden Beams are given on pages 638 to 646, for beams one inch in breadth. To find the strength for any other breadth, multiply the proper tabular value by the breadth of the beam in inches. To obtain the required breadth for any load, divide the given load in pounds by the proper tabular value. In heading the tables, prom- inence has been given to the values used for S, and the corresponding values of ^, so that those who prefer to use for any wood a value different from that recommended, need only to look up the table based on the value they desire to employ. For certain cases and in some cities, the building laws specify i 300, I 500 and I 800 pounds as values of S to be used for long-leaf yellow pine; hence Tables XIII, XIV and XV, based on these -values, are added. Since timber is weak Li horizontal shear compared with its strength in tension and compression, the safe load a beam of short span can carry is governed, not by its resistance to cross-breaking, but by its resistance to shearing along the neutral surface. Wooden beams and joists, therefore, should be dimensioned to safely withstand this shearing action. The ratio of the shearing to the flexural strength is not exactly the same for different kinds of wood, but for practical use and in the tables it has been assumed to be one-twelfth of the working unit fiber-stre'ss. As it can be shown * that the ratio of the span to the depth of a rectangular beam, uniformly loaded, is directly proportional to its cross-breaking stress and shearing working stress, the tabular loads are figured for the permissible unit fiber-stress, where the length of the span is twelve or more times the depth of the beam; while for shorter lengths, the tabular loads are governed by the shear. To determine the safe load on beams for a deflection not exceeding Vaeo of the span, tabular values have been placed directly underneath the safe loads for strength. These values are based on the modulus of elasticity, E, given in the tables. The formula for flexure used in determining the safe uniformly distributed loads in the tables is (see Formulas (i), page S33 ^i^d (2)', page 557) ,, SI Shd^ Wl Hence W , in which / is the span in inches ' 3I .r. The formula for shear is ■^' ' * Materials of Construction, J. B. Johnson, page 55. 636 Strength of Cast-iron Lintels and Wooden Beams Chap. 16 The FORMULA FOR DEFLECTION is (sec, also, Formulas (i) to (17) and Table I, Chapter XVIII) Ed? W = in which / is the span in feet; 8100/2 M = maximum bending moment in inch-pounds; / = moment of inertia of the cross-section of the beam in biquadratic inches; c = d/2 = one-half the depth of the beam in inches; SI/c = resisting moment of the cross-section in inch-pounds; W = total safe load in pounds, uniformly distributed; h = breadth of the beam in inches; * d = depth of the beam in inches; / = span, in feet or inches, as noted for the dififerent formulas; S = unit flexural fiber-stress in pounds per square inch; S3 =S/i2 = horizontal unit shearing-stress, in pounds per square inch, along the neutral surface; E = modulus of elasticity in pounds per square inch. Example 6. What is the safe, uniformly distributed load, corresponding to a fiber-stress of i 500 lb per sq in, for an S by 14-in long-leaf yellow-pine beam supported at both ends, and having a 24-ft clear span? Solution. From Table XIV, the load for a i-in thickness is 1362 lb. Hence, I 362 X 8 = 10896 lb, the total load for the beam. If the deflection of this beam should not be more than J-^co of the span, the safe load for i -in thickness should not exceed 882 lb. Hence, 882 X 8 => 7 056 lb, is the maximum load to be used in this case. It is assumed that i 500 lb per sq in is allowed for S. Example 7. What should be the size of a Norway-pine beam required to carry a distributed load of 6 400 lb over a clear span of 18 ft? Solution. From Table X, it is found that a beam 12 in deep and i in thick and with an i8-ft span, will support 711 lb. Dividing the load, 6400 lb, by 711, the result is 9 for the breadth of the beam in inches. Hence the beam should be 9 by 12 in, to carry a distributed load of 6 400 lb over a span of 18 ft. As the deflection-load of 593 lb can be increased 20% for Norway pine, the beam is safe for deflection; if, however, cypress is used, 593 must be taken in place of 711, to determine the breadth of the beam. This would result in a beam 11 by 12 in. Different Positions of Loads. To find the safe load, concentrated at the middle of the span of a given beam, find the safe distributed load, as in Example 6, and divide this load by 2. To find the safe load concentrated at some point other than the middle of the span, find the safe distributed load for the given span, and divide this load by the proper factor taken from Table IV, page 632. To find the size of a beam to support a given concentrated load, multiply the given load by the factor corresponding to the position of the load, as given in Table IV, and then proceed as in Example 7. Use of Formulas. If in doubt as to the application of the tables, in special cases, use one of the formulas, from (4) to (16), applying to the case. The formulas and tables should always give the same result. Nominal and Actual Sizes of Beams. The tables may be used for beams the dimensions of which are less than the nominal dimensions. Dressed beams, and, in many localities, floor-joists carried in stock, are more or less scant of the nominal dimensions, and for such beams and joists a reduction in the safe load must be made to correspond with the reduction in size. The Tables for Strength and Stiffness of Wooden Beams 63T DRESSED SIZES are generally i/4 in scant, up to 4 in in breadth, above which they are V2 in scant; while in depth they are all generally V2 in less than the nominal size. The safe loads may be obtained by multiplying the safe loads for the corresponding nominal sizes, as given in Tables VII to XV, by the factors given in the following table. Table VI. Conversion Factors for Actual Sizes of Wooden Beams Cross-sections of beams in inches Factors Cross-sections of beams in inches Factors 1% X5'/2 2'>;i X5V2 1% x6H 2% xey^ m xiYz 2%X7K2 1% X9V2 2) i X9K2 1.47 2.31 1. 51 2.51 1.54 2.42 1.58 2.48 1^4X11^2 2MX11V2 ly^xizVi 2y^xizVi • i^4Xi5K2 2^4X15^2 i^4xi7H 2MX17K2 1. 61 2.53 1.63 2.56 1.65 2.58 1.65 2.60 Example 8. What is the safe load for a 2% by 13^/^-in spruce beam, with an i8-ft span? Solution. From Table VIII, the safe load for a i by 14-in beam is 847 lb. Multiplying this by 2.56, we have 2 178 lb as the safe distributed load for a beam 2% by 13!/^ in in cross-section. For a full 3 by 14-in cross-section, the safe load would be 2 541 lb. Stone Beams. The above formulas may be used for rectangular stone beams when the proper coefficients, recommended in Table III, page 628, are inserted. Sandstone beams should never be subjected to any heavy loads and sandstone lintels should be relieved by steel beams or by brick arches over them or back of them. Concrete Beams are generally reinforced with steel rods, but when used without reinforcement, the coefficient, A, given in Table III, is recommended. Use of Tables VII to XV. The safe loads given in Tables VII to XV are correct for the fiber-stresses indicated; but for greater convenience in using the tables, each figure in the units-place of each value may be made a cipher, and each figure in the tens-place may be increased by one when the unit-figure is six or greater. Thus, 505 would be 500, 506 would be 510, etc. Important Notes on Stresses and Loads for Wooden Beams. In compiling and using the tables of safe loads for wooden beams, the following important considerations must be kept in mind: (i) Unseasoned timber is very much weaker than commercially dry timber, that is, timber containing from 10 to 15% of moisture. (2) Timber containing large or loose knots is much weakened. (3) When impact has to be considered, the stresses should be reduced. (4) For continuous, heavy loading, relatively low stresses should be used. (5) Commercial dimensions are smaller than nominal dimensions. (6) Timbers deteriorate and the factors of safety for strength grow smaller with time. (7) The modulus of elasticity, E, for unseasoned timber, should be reduced 50% from its value given for thoroughly seasoned timber. (8) It is better engineering practice to compute tables of safe loads based on conserva- tive stresses for average or poor conditions, increasing the values given when conditions are ideal, than to recommend values for ideal conditions which usually do not exist. (See notes, pages 628 and 647, regarding increase in the table-values.) Editor-in-Chief. 638 Strength of Cast-iron Lintels and Wooden Beams Table VII. Safe Distributed Loads * in Pounds for Rectangular Wooden Beams For Average Hemlock. Maximum Fiber-Stress, S = 600 lb per sq in. E = 900 000 lb per sq in. il » 33 Span in feet The first horizontal line gives the depth of the beam in inches ' The loads are for beams one inch wide and supported at both ends 6 7 6 8 10 12 14 16 18 400 533 ■ 533 666 666 800 800 933 933 1066 1066 I 200 I 200 343 8 9 300 266 533 666 666 800 800 933 933 I 066 1066 I 200 I 200 474 10 II I 240 j 427 388 666 800 800 933 933 1066 1066 I 200 I 200 60S 12 13 { 7e\ \ 143 ) 356 328 555 513 800 933 933 1066 1066 I 200 I 200 738 14 15 1 171 I 122 ( t6o 305 } 291 j 285 j 477 445 686 640 933 106Q 1066 I 200 I 200 871 \ 107 253 1 16 17 ( 150 \ 94 267 ) 222 ) j 251 I 197 417 392 ) 384 ) 600 565 817 762 1066 I 200 I 200 I 003 18 19 1 237 I 175 f 225 ( 157 371 j 343 i 351 } 308 j 534 505 726 688 948 898 I 200 I 137 20 { 213 I 142 333 480 ) 480 ) 653 854 I 080 277 21 I 317 1 252 462 ) 435 ) 623 813 I 029 22 j 303 \ 229 436 ( 594 776 982 397 ) 23 ( 290 1 211 417 \ 363 ) 568 742 939 24 j 278 \ 193 400 545 ) 529 ) 712 900 334 25 1 384 1 308 523 j 488 j 683 864 26 1 369 1 284 503 ( 452 j 657 831 27 ( 356 1 264 482 633 ) 625 j 800 418 28 { 343 1 245 467 609 ) 582 ( 772 389 29 { 451 353 589 ) 542 j 745 30 1 436 569 720 ) 720 ) 339 50s Loads above zigzag lines calculated for horizontal shear, the upper is calculated for strength, the lower for deflection Where two loads are given, not to exceed ^eo the span. * Add 30 to 40% to strength-values for ideal conditions. See notes, pages 6^8, 637- 647. Tables for Strength and Stiffness of Wooden Beams 639 Table VIII. Safe Distributed Loads * in Pounds for Rectangular Wooden Beams For Average White Pine, Spruce and Eastern Fir. Maximum Fiber- Stress, iS = 700 lb per sq in. £ f = 1 000 000 lb per sq in. A " 39 Span in feet 13 14 IS 16 17 18 23 24 25 26 27 28 29 30 The first horizontal line gives the depth of the beam in inches The loads are for beams one inch wide and supported at both ends 467 400 350 311 f 280 I 267 ( 255 1 221 ( 233 I 185 ( 216 ( 158 ( 200 1 136 f 187 \ 119 { 175 I 104 622 622 552 497 383 374 356 323 332 281 311 247 293 219 276 195 262 175 777 777 777 777 707 648 598 556 518 486 482 458 427 433 381' 410 342 389 308 370 280 354 255 338 234 324 215 933 933 933 933 933 933 933 861 800 747 700 660 623 560 534 534 484 509 441 487 403 468 371 448 342 430 316 415 293 400 272 089 089 089 952 897 847 802 762 726 692 662 641 635 588 610 542 586 502 565 465 544 432 526 403 508 377 I 244 I 244 I 244 1244 I 244 I 244 I 244 I 244 I 244 I 244 I 172 I 107 I 048 996 948 906 866 830 796 766 750 738 695 711 646 687 602 664 562 * Add 30 to 40% to strength- values for ideal conditions. See notes, pages 628, 637, 6V7. t For first-class, dry spruce and Eastern fir, £ = i 200 00 could safely be used, making the safe deflection-loads those given in Table XI. See, also, foot-note with Table VII. 640 Strength of Cast-iron Lintels and Wooden Beams Chap. Table IX. Safe Distributed Loads * in Pounds for Rectangular Wooden Beams For Average California Red Wood and Cedar. Maximum Fiber-Stress, iS = 750 lb per sq in. E = 700000 lb per sq in. A = 41.7 Span in feet 13 14 15 16' 17 18 23 24 25 26 % 28 29 30 The first horizontal line gives the depth of the beam in inches The loads are for beams one inch wide and supported at both ends ( 292 j 428 382 375 292 333 231 300 187 274 155 250 130 231 no 214 95 667 667 667 592 547 533 443 485 366 445 307 410 262 382 226 356 197 333 173 833 833 833 833 833 757 714 641 600 641 512 595 441 556 384 521 337 491 299 463 267 439 240 I 000 I 000 923 ) 885 I 857 1 763 I 800 665 750 584 706 518 667 462 632 414 {600 374 ( 572 \ 339 ( 547 1 309 ( 522 ( 282 i 500 1 260 I 480 I 239 I 463 \ 221 ( 444 I 205 I 428 . I 190 14 I 167 I 167 I 167 I 167 I 167 I 167 I 167 I 167 I 167 I 060 I 020 929 961 822 908 733 860 658 816 594 778 526 742 491 710 448 681 412 653 380 628 351 605 326 583 203 563 282 544 264 1333 I 333 1333 1333 1333 1333 1333 1333 1333 I 333 1333 1254 I 223 I 184 I 090 I 122 982 I 066 886 I oi6 803 970 732 928 670 890 616 854 567 821 525- 791 487 762 452 736 421 712 393 * Add 30 to 40% to strength -values fpr ideal conditions. See notes, pages 628, 637, 647. See, also, foot-note with Table VlL Tables for Strength and Stiffness of Wooden Beams Table X. Safe Distributed Loads * in Pounds for Rectangular Wooden Beams For Average Norway Pine, Cypress and Chestnut. Maximum Fiber-Stress, S = 800 lb per sq in. £ f = 900 000 lb per sq in, A = 44 Span in feet The first horizontal line gives the depth of the beam in inches \ The loads are for beams one inch wide and supported at both ends 6 8 10 12 14 16 18 6 7 8 9 10 II 12 13 14 15 16 17 18 19 20 21 22 23 , 24 1 ^-^ .26 27 28 29 30 533 711 711 711 889 889 889 889 889 1066 1066 1066 1066 1066 1066 I 244 1244 I 244 I 244 I 244 1244 1244 1 244 1244 I 422 I 422 I 422 1422 I 422 I 422 1422. I 422 1422 I 422 I 422 I 600 I 600 I 600 1600 I 600 I 600 I 600 1 600 : I 600 I 600 I 600 I 600 I 600 { 457 400 ) 375 ) 356 ) 296 i 320 240 291 199 267 166 246 142 229 122 214 107 200 94 632 569 ) 569 ) 517 1 470 j 474 } 395 i 438 337 407 291 800 742 684 ) 658 j 635 I 567 ( 593 494 556 432 524 384 494 343 468 308 445 277 1 423 \ 252 ( 404 \ 229 { 387 ( 211 { 371 1 193 985 914 854 \ 854 ) 800 ) 750 j 754 1 66s ) 7it 593 674 532 640 4«o 609 435 5;«2 397 557 363 534 334 f 512 ( 308 1 492 \ 284 ( 474 » 264 ( 457 I 245 379 253 356 222 ( 335 1 197 I 316 I 175 1 300 \ 157 ( 284 1 142 I 161 I 089 I 02s 968 1 914 ) 917 1 846 i 871 752 830 692 792 630 758 577 726 529 697 488 670 452 646 418 622 389 i 601 I 353 1 581 i 339 1339 I 264 I 198 I 138 1 I 138 1 1084 ) 1032 j 1035 ) 941 i 990 860 949 790 9" 728 876 675 843 625 813 582 785 542 759 506 1 441 1372 1309 I 253 ) 1225 } I 200 ] II26 } 1 152 i 1037 ( I 108 1 960 } 1068 i 890 } 1029 1 827 { 993 ) 770 I 960 1 720 } . ^ , . . . 1 * Add 30 to 40% to strength- values for ideal conditions. See notes, pages 628, 637, 647. See, also, foot-note with Table VII. t For safe deflection-loads, for Norway pine, add 20% to the above values. I : 642 Strength of Cast-iron Lintels and Wooden Beams Chap. 16 Table XI. Safe Distributed Loads * in Pounds for Rectangular Wooden Beams For Average Douglas Fir and Short-Leaf Yellow Pine. Fiber-Stress, S = i ooo lb per sq in. E i = i 200 000 lb per sq in. A = 55-6 Span in feet The first horizontal line gives the depth of the beam in inches The loads are for beams one inch wide and supported at both ends 6 8 10 12 14 16 18 6 7 8 9 10 II 1 " 13 14 15 16 17 18 yg 21 22 1 ^^ \ ^' I 26 { 27 ' 28 29 30 667 889 889 889 I III I III I III I III I III I 333 1333 1333 1333 1333 1556 1556 1556 1556 1556 1778 1778 1778 1778 1778 1778 1778 1778 1778 1778 1778 2 000 2 000 2000 2 000 2 000 2 000 2 000 2 000 2 000 2 000 2000 2 000 2 000 ( I 1 { { { { { { 1 ..) ;•'• i.. 571 500 ) 500 ) 444 ) 395 J 400 j 320 j 364 265 333 222 308 190 286 163 267 143 250 125 790 711 647 ) 628 f 593 ) 527 j 547 ) 449 i 508 388 474 337 445 296 f 419 1 263 ( 395 I 234 f 374 1 210 1 356 I 190 1 I 010 926 1333 1333 1556 1556 1556 I 556 855 794 ) 757 3 741 1 659 3 695 578 654 512 618 457 585 410 556 370 ( 528 i 336 1 50s ( 306 ( 483 \ 281 r 463 \ 258 I 231 II43 I 067 I 000 ) I 000 j 942 1 886 f 890 ) 790 j 843 710 800 641 762 581 727 529 696 484* 667 445 1 640 \ 410 ( 61S \ 386 f 593 \ 352 ( 572 1 327 1452 I 361 I 281 I 210 I 146 ) I 126 1 I 088 ) I 016 ) I 037 ) 922 j 990 841 947 770 908 706 871 650 838 602 807 558 778 518 { 751 \ 484 ( 726 1 452 1674 I 581 1498 1423 1355 1293 ) I 254 i 1237 ) I 147 ) I 186 1053 I 138 972 1094 900 1054 834 I 016 776 982 725 949 674 1895 I 800 I 714 1636 1565 1500 1 1500 } I 440 ) 1384 } 1385 1 1286 ] 1334 ) I 186 ( 1286 J I 103 } I 241 ) I 027 { I 200 1 960 1 •iw* JH> ■ ♦Add tFor 30 to 40% to strength -values for ideal conditions, deflection-loads for Douglas fir, add 25%. See, See notes, pages 628, 637, 647. also, foot-note with Table VIL Tables for Strength and Stiffness of Wooden Beams 643 Table XII. Safe Distributed Loads * in Pounds for Rectangular Wooden Beams For Average White Oak and Long-Leaf Yellow Pinef. Maximum Fiber- Stress, S = i2od lb per sq in. E = i 500 000 lb per sq in. A « 66.7 Span in feet 9 10 13 14 15 16 17 18 19 23 24 25 26 27 28 29 30 The first horizontal line gives the depth of the beam in inches The loads are for beams one inch wide and supported at both ends 686 600 ( 533 \ 495 i 480 I 400 f 437 ( 332 ( 400 \ 278 ( 369 I 247 I 343 I 204 f 320 ( 179 J 300 \ 156 I 067 I 067 I 067 854 776 711 658 656 561 610 485 569 422 533 371 502 329 474 293 449 263 10 1333 1333 1333 1333 1333 I 212 I III I 026 953 946 890 824 834 724 785 642 741 572 702 513 666 462 634 420 606 383 579 351 556 322 I 600 I 600 I 600 I 600 I 600 I 600 I 600 1477 I 371 1280 I 200 I 130 I 108 I 067 990 I 010 886 960 802 914 726 872 662 835 605 800 557 768 513 738 473 711 440 636 410 14 1867 1867 1867 1867 1867 1867 1867 1867 1867 I 741 1633 1537 1452 1375 1306 I 272 1245 I 154 I 188 I 051 I 136 962 I 090 882 1045 813 I 006 753 969 698 933 648 902 605 871 566 16 2 133 2 133 2 133 2 133 2133 2 133 2 133 2133 2133 2133 2133 2 009 1898 179s 1708 I 626 1552 1484 I 435 1423 I 318 1366 I 215 I 313 I 125 1265 1043 I 218 970 I 178 903 I 138 843 • ideal conditions. See notes, pages 628, 637, , 1500 and 1800 lb per sq in, see Tables XIII, 644 Strength of Cast-iron Lintels and Wooden Beams Chap. 16 Table XIII. Safe Distributed Loads in Pounds for Rectangular Wooden Beams Maximum Fiber-Stress, S= i 300 lb per sq in. A = 72.2 Span feet 13 14 15 16 17 18 -19 (20 21 22 23 24 25 26 27 28 29 30 The first horizontal line gives the depth of the beam in inches The loads are for beams one inch wide and supported at both ends 867 743 650 567 520 473 433 400 371 347 325 I 155 I 155 I 155 I 027 924 840 770 711 660 616 578 544 514 487 462 1444 1444 1444 1444 I 444 I 311 I 200 I III I 032 963 903 849 802 760 722 688 6S7 628 602 1733 1733 1733 1733 1733 1733 I 733 I 600 i486 1387 1300 I 224 I 156 1095 I 040 990 945 904 867 832 800 770 743 2 022 2 022 2 022 2 022 2 022 2 022 2 022 2 022 2 022 1887 1770 I 664 1572 1490 I 415 1348 1286 I 230 I 179 I 132 1088 I 048 I on - 976 943 2 311 2 311 2 311 2 311 2 311 2 311 23H 2 311 2 311 2 311 2 311 2 175 2054 1946 1849 I 761 I 681 1608 I 541 1479 I 422 1369 I 321 I 275 I 232 2600 2 600 2 600 2 600 2 600 2 600 2 600 2 600 2 600 2 600 2 600 2 600 2 600 2463 2340 2 229 2 127 2035 1950 1872 I 800 I 733 I 671 I 614 I 560 Loads above the heavy, black zigzag lines are calculated for resistance to shear. For safe deflection-loads, see values in Tables VII to XII, according to the value of E lused, and determined by the deflection-formula, page 636. \ 8if. I Tables for Strength and Stiffness of Wooden Beams 645 Table XIV. Safe Distributed Loads in Pounds for Rectangular Wooden Beams Maximum Fiber-Stress, S= i 500 lb per sq in. A= 83.3 Span in feet The first horizontal line gives the depth of the beam in inches The loads are for beams one inch wide and supported at both ends 6. 8 10 12 14 16 18 6 7 8 9 10 II 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 I 000 1333 1333 1333 1667 1667 1667 1667 1667 2 000 2 000 2 000 2 000 2 000 2 000 • 2 000 2333 2333 2333 2667 2667 2667 3000 3000 3 000 3 000 3000 3000 3000 3000 3 000 3 000 3000 3000 3 000 857 750 667 600 548 500 462 428 I 18S I 067 970 890 820 764 712 667 2333 2333 2333 2333 2333 2333 2667 2667 2667 2667 2667 2667 2667 2667 I 515 1390 I 282 I 190 I 112 I 042 982 926 878 1846 I 714 I 600 isoo I 412 1334 I 264 I 200 I 144 1094 I 044 I 000 960 926 888 856 2178 2 042 1974 I 815 I 720 1632 1556 1484 I 420 1362 I 306 I 256 I 210 I 166 I 126 1088 2 510 2370 2246 2133 2 032 I 940 1856 I 780 I 708 1642 I 582 1524 1472 I 422 2842 2 700 2 571 2 455 2348 2250 2 lOo 2 076 2.000 1930 1862 1800 Loads above the heavy, black ziezac liness are calculated for resistance to shear. For safe deflection-loads, see values in Tables VII to XII, according to the value of i used, and determined by the deflection-formula, page 636. 646 Strength of Cast-iron Lintels and Wooden Beams Chap. 16 Table XV, Safe Distributed Loads in Pounds for Rectangular Wooden Beams Maximum Fiber-Stress, S = i 800 lb per sq in. A = 100 Span in feet The first horizontal line gives the depth of the beam in inches The loads are for beams one inch wide and supported at both ends 6 8 10 12 14 16 18 6 7 8 9 10 II 12 13 14 15 16 17 19 20 ! 21 22 23 24 25 26 27 • 28 29 30 I 200 I 600 1600 I 600 2 000 2 000 2 000 2 000 2 000 2 400 2 400 2 400 2 400 2400 2 400 2 400 2800 2800 2800 2800 2800 28CO 2800 2800 2800 3 200 3 200 3200 3200 3 200 3200 3200 3 200 3200 3200 3 200 3600 3600 3600 3600 3 600 3600 3600 3600 3600 3600 3600 3600 3600 I 030 900 800 720 655 600 554 514 480 450 I 422 I 280 I 164 I 067 98s 914 I 818 1667 1539 1428 2215 2057 1920 1800 1694 I 600 I 516 1440 I 371 1309 1252 I 200 I 152 IIO8 I 067 I 029 853 800 1333 I 250 I 176 I in 1053 I 000 2613 2450 2306 2 178 2063 i960 1867 I 782 1704 1633 1568 I 508 1452 I 400 1352 1307 753 711 674 640 3 012 2844 269s 2 560 2438 2327 2 226 2 133 2 048 1969 1896 I 829 1766 1707 3 411 3240 3086 2945 2817 2 700 2592 2492 2 400 2314 2235 2 160 Loads above the heavy, black zigzag lines are calculated for resistance to shear. . For safe deflection-loads, see values in Tables VII to XII, according to the value of E used, and determined by the deflection-formula, page 636. • Working Unit Stresses for Woods. Taken from Building Laws 647 8. Working Unit Stresses for Average, Unseasoned Woods Safe Working Unit Stresses for unseasoned woods (except for E) are given in Table XVI. They are compiled and adapted largely from recommended UNIT STRESSES adopted by the Association of Railway Superintendents of Bridges and Buildings and by the American Railway Engineering Association. (See, also, page 449.) Table XVI. Safe Working * Unit Stresses for Unseasoned Woods, in Pounds per Square Inch Kind of wood Factor of safety Ten Tension Compression With the grain § Across the grain Ten With the grain End- bear- ing Five Col umnst under IS diams Five Across the grain Four Bending f Shearing Ex- treme fiber- stress § Six Modu- lus ol "elasti- city,! I £/i 000 One With the grain Four Across the grain Four White oak White pine Long-leaf yellow pine Douglas fir Short-leaf yellow pine Red pine and Norway pine . . Spruce and east- ern fir Hemlock Cypress Cedar Chestnut Cal. red wood . . . Cal. spruce T 200 7t)o I 200 800 900 800 800 600 600 TOO 850 700 200 50 60 SO SO I 400 I 100 I 400 I 200 12 00 I 100 I 000 I I 100 900 I 000 800 I 000 900 800 750 900 800 75c 750 800 800 800 SCO 200 3SO 200 250 200 200 150 200 200 250 ISO I 200 700II I 200 8001 I 000 800 7oolf 600 800 700 800 7SO 800 I SCO I 000 I Soo 1 SCO z 200 I 100 z 200 900 900 700 z 000 700 z 200 2CO ZOO ISO Z30 zoo zoo zoo 150 zoo z coo soo I 250 900 z 000 7SO 7SO 600 400 soo * The stresses given, except for E, may be increased 30% for protected, commercially dry timber, not subject to impact, as in most buildings. t See also, Table I, page 557, Table XVII, page 648, and Table I, page ZZ38. i The larger end-bearing stresses are frequently used for short columns and for column- formulas. (See tables, pages 449, 1138.) Lower factors of safety give higher stresses. § Some of these values are considered too low, relatively, by some building codes. II These values of E are for seasoned timber. For unseasoned timber, reduce E 50%. H The New York Building Code (i^tV) stresses ifcr these are z 200 lb per sq in. 9. Working Unit Stresses for Woods. Taking from Building Lawtf. '• The Allowable Working Unit Stresses for different woods, taken from the building laws of four cities, are given in Table XVII. The UNIT STRESSES are for tension, compression, bending and shear. , ^ . . ^ _ ^ 648 Strength of Cast-iron Lintels and Wooden Beams Chap. 16 Table XVII. Working Unit Stresses for Woods, in Pounds rer Square Inch Kind of stress Kind of wood New York * Chicago Baltimore § Boston H Tension Yellow pinet . • White pine. . . . SpruceJ Hemlock Douglas fir. . . . Oak. . . . AmV. -} Locust /'V I 200 700 8oo 6oo 8oo 1300 800 800 800 I 300 ll'i ■ I oooSLYP 1 800LLYP I 000 I 200 800 oV/ I 500 I 200VP Compression with the grain Yellow pinet • • White pine. . . . SpruceJ Hemlock Douglas fir. . . . Oak I 6oo I 000 I 200 8oo I 200 I 400 I 200 I 100 700 700 500 I 100 900 800SLYPI! I oooLLYP 800 800 600 I 600 1 000 1 OGO I 500 1400 I 000 I 200 800NC or YP Locust Compression across the grain Yellow pinet • • White pine. . . . SpruceJ Hemlock Douglas fir. . . . Oak 350 250 200 150 200 500 250 200 200 150 600LLYP 400 400 500 500 250 250 400 600 I 600 1 000 1000 I 500 I 400 500 600 I 000 40oNCorVP Locust 250SLYP!! Transverse bending Yellow pinet • • White pine. . . . SpruceJ Hemlock Douglas fir. . . . Oak Locust J 6oo I 200 I 200 8oo I 200 I 200 I 300 800 800 600 I 300 I 200 I 800LLYP I 000 I 350 I 000 I 500 I oooSLYPit Shear with the grain Yellow pinet • • W^hite pine. . . . Sprucet Hemlock Douglas fir. . . . Oak 150 lOO 100 100 100 200 130 80 80 60 130 200 looLLYP 85 90 75 150 100 100 120 ISO 100 Locust i2oSLYPi| 90VP Shear across the grain Yellow pinet. • White pine. . . . Spruce J Hemlock Douglas fir. . . . Oak I ooo 500 500 600 1000 I 000 500LYP 350 350 350 I 200 800 800 I 000 I 200 720 Locust 400VP • Stresses named by N. Y. are given in the 191 7 Building Code of the Borough of Manhattan. Exception: Dist. of Columbia omits hemlock, omits chestnut in shear across, grain and puts spruce and Virginia pine under one caption; Cincinnati makes caption of white pine and spruce, with N. Y. white-pine values, and gives 270 for hemlock, for shear across grain, t Chicago, "Douglas fir and long-leaf yellow pine." tChicago, no values for spruce; spruce-values apply to Norway pine. |I Chicago, values given for short-leaf yellow pine, SLYP. § Baltimore, LLYP is long-leaf yellow pine; NC or VP, N. Carolina or Virginia pine. If Boston, yellow pine is "yellow pine (long-leaf).'* Ultimate Unit Stresses for Woods 649 10. Ultimate Unit Stresses for Woods The Average Ultimate Unit Stresses for the coniferous or softwoods and for the broad-leaved or hardwoods, together with the average weights of the woods per cubic foot arc given in Tables XVIII and XIX. The values given are compiled from many tests on numerous species of timber. In regard to the range of vahies for the same kind of wood, it may be stated that the higher values are for specimens which contained a percentage of water varying from 15 to 20%; and that tests on laboratory specimens showed greater strength than the actual pieces used in construction. The weights per cubic foot are averages of the weights of many specimens tested and agree generally with average values given in other tables of weights of materials. 650 Strength of Cast-iron Lintels and Wooden Beams Chap. 16 Table XVm.* Average Ultimate Unit Stresses for the Coniferous or Softwoods, in Pounds per Square Inch Kind of wood Cedar (white) Cedar (red) Cypress Hemlock Pine (white) Pine (red), (Norway pine) Pine (yellow), (long- leaf) Pine (yellow), (short- leaf) Douglas fir (Oregon pine) Redwood (California) Spruce (black) Spruce (white) Weight in lb per cu ft, dry Tension Compression Bend- ing (mod- ulus of rup- ture) With the grain Across the grain 19.72 8 000 4 000 700 5 000 to to to 20.70 II 400 6 000 23.66 8 000 4 000 to 7 000 700 5 000 29.80 4 000 4 000 700 5 000 to to to to 6000 8 000 800 II 700 26.42 6 000 4 000 600 3500 to to to to 32.29 8 700 7420 700 25.55 3000 3000 700 4 000 to to to to 12 000 6 650 I 000 10 000 30.25 5 000 6 000 800 5 000 to to to to 13 000 8000 I 000 12 300 43.62 6000 5 000 I 000 7 000 to to to to 13 000 9500 I 400 14 200 38.40 5 000 4 000 900 6 000 to to to to 10 000 9000 I 000 12 400 32.14 9 000 4880 800 6500 to to to to 14000 9800 I 200 12 100 26.23 7 000 to 10853 3000 to 4 000 800 4500 28.57 5 000 4 000 700 4 000 to to to 19500 7850 12 000 25.25 5 000 4 000 700 4 000 to to to 19500 7850 12 000 Shear With the grain 400 225 to 423 300 to 700 400 to 700 500 to 600 400 250 to 400 250 to 400 * The higher values of tensile and compressive strengths are for " dry " or " sea- soned " timber containing from 10 to 15% of water. For safe fiber-stresses for flexure, .see Table I, page 557. Ultimate Unit Stresses for Woods 6 Table XIX.* Average Ultimate Unit Stresses for the Broad-Leaved or Hardwoods, in Pounds per Square Inch Kinds of wood Weight in lb per cu ft, dry Tension Compression With the grain Across the grain Bend- ing (mod- ulus of rup- ture) Shear With the grain Ash (white). Ash (red) . . . Ash (green). Chestnut Elm (white) . Gum , Hickory Locust Lignum-vitae . Maple (hard). Maple (white) . Mahogany (Central America) Oak (white). Oak (chestnut) Oak (live) Oak (red and black) Poplar (whitewood) Walnut (white) (but- ternut) Walnut (black). 38.96 44.35 41.00 45-26 36.83 46.16 to 52.17 45.70 77.12 43.08 32.84 46.35 53 63 59-21 40.75 30.00 25.46 38.11 II 000 to 17 000 9 000 to 13 000 8 000 to 13 000 15 000 to 18 000 12 800 to 18 000 10 500 to 24 800 11 000 8 000 to 10 000 8 000 to 10 000 2300 to 17 900 10 000 to 19500 10 000 13 000 10 000 4 000 to 9 000 6800 8 000 to 9 800 5 000 6 000 to 10 000 5 600 to 8500 7 000 to 10 000 7 000 to 11 700 8800 7 000 to 9940 6 000 to 7500 6 000 4500 to II 300 7500 9 000 4 000 to 8500 4 000 to 5700 5 000 to 6800 7 .500 I 900 900 2 700 to 3200 I 700 to I 900 6300 to 14 200 5 100 to 16 000 5 000 7300 to 13 600 6 000 to 12 700 5400 to 24300 6 000 9 100 to 15 400 450 to I 100 I 000 to. I 200 399 to 537 750 to I 000 * The higher values of the tensile and compressive strengths are for " dry " or " seasoned " timber containing from lo to is% of water. For safe fiber-stresses for flexure, see Table I, page 557. 652 Built-Up, riitched and Trussed Wooden Girders Chap. 17 CHAPTER XVII STRENGTH OF BUILT-UP, FLITCHED AND TRUSSED WOODEN GIRDERS By F. H. KINDL LATE CORRESPONDING MEMBER AMERICAN INSTITUTE OF ARCHITECTS 1. Built-Up Wooden Girders Built-Up Wooden Beams. Wooden beams or girders built up of planks, spiked or bolted together side by side, will generally be somewhat stronger •than solid girders of the same dimensions, because the planks will be better seasoned and freer from check-cracks and other defects. For beams or girders ID in or less in depth, spikes will usually be sufficient to bind the planks together; but for deeper beams, bolts should be used in addition to the spikes, to prevent the planks from separating and the outer planks from warping or curling away Ifrom the others. Bolts. Two bolts should be placed at each end of the beam and every four feet of its length. Lengths of Planks. When a beam is built up in this way each plank _ should extend the full length of the beam. In a continuous bbam, the planks should break joints over the supports. The planks of built-up beams should ■ always be set on edge, never flatwise. Compound Wooden Beams. It is sometimes necessary to use a wooden beam for a longer span or greater load than is safe for the deepest single beam that can be obtained, or for a beam built up of planks. In such cases compound WOODEN BEAMS may be used. Definition. By a compound wooden beam or girder is meant a beam built up by placing two or more single beams over another one, with the view of having them act as a single BEAM having the depth of the combined beams. Strength of Com- pound Beams. If two Fig. 1. Two Simple Wooden Beams, One Over the Other, lo by lo-in beams were Loaded in Middle placed one on top of the other, and the upper one loaded at the middle, the beams would act as two separate beams (Fig. 1) and their combined strength would be no greater than if the two Ueams were placed side by side. If, however, the two beams can be joined so that the libers of the lower beam will be extended as much as would be the case in a single beam of the same depth, or, in other words so that the two beams will not slip on each other, the compound beam will have four times the strength of the SINGLE BEAM. Tests of Compound Beams. Various attempts have been made to join beams thus placed so as to prevent the two parts slipping on each other, and Bullt-Up Wooden Girders 653> during the years 1896-7, Edgar Kid well, of the Michigan College of Mines, made an extended series of tests of the efficiency of compound beams of differ- ent patterns. From these tests much valuable data was obtained. A full description of the tests, accompanied by the conclusions of the author, and the rules and data for proportioning the bolts and keys, of keyed beams, is pub- lished in the Trans. Am. Soc. M. E., vol. 27. Simple Form of Compound Beam. A form of compound beam, some-; times used in American building-construction, is shown in Fig. 2, diagonal .boards in opposite directions being nailed to each side of the two timbers to prevent their slipping on each other. T. M. Clark, in his Building Superin- tendence, advocates this as one of the best forms of compound beams, and Fig. 2. Simple Form of Compound Wooden Beam places its efficiency at about 95% of that of a solid beam of the same depth. Professor Kidwell made nine tests of this type of beam. In six of the beams the ratio of span to depth was as 12 to i, and in three of the beams, as 24 to i. The shorter beams gave an average efficiency, without much variation, of 71.4%, and the longer beams an efficiency of 80.7%. It was found that the beams failed by the splitting of the diagonal pieces or the drawing of the nails; "in every case, long before the beam broke, the struts split open or the nails were partly drawn out or bent over in the wood, thereby permitting the component beams to slide on each other." When built with diagonal boards, iM in thick, nailed with tenpenny nails, as in Fig. 2, the working strength of such a beam may be taken at 65% of the strength of -Spruee-Beam-28-fti-Span- Fig. 3. Compound Keyed and Bolted Wooden Beams a solid beam of the same depth and of a breadth equal toijthe breadth of. the timbers. The deflection of the beam, however, will be about double that of a solid beam of the same size, and on that account this type of beam is not to be recommended for supporting floors with plastered ceilings or for carrying plastered partitions. Keyed Beams. Professor Kidwell tested, also, several types of keyed BEAMS, and found that a compound beam keyed and bolted together, as shown in Fig. 3, is the most efficient form that it is practical to build. ■ - 654 BuUt-Up, Flitched and Trussed Wooden Girders Chap. 17 It was found that with oak keys it was possible to obtain an efficiency for spruce beams of 95%, while the deflection varied from 20 to 25% more than would be expected in a soUd beam. Cast-iron Keys. By using cast-iron keys the deflection was found to be but little, if any, greater than for a solid beam. Shape of Keys. The keys must be wedge-shaped, as shown in Fig. 4, so that they can be driven tightly against the end-wood. Efficiency of Keyed Beams. Professor Kidwell recommends that for ordinary purposes an efficiency of 75% be allowed when oak keys are used and of 80% when the keys are of cast iron. The width of an oak key should be twice its height. Numerous small keys closely spaced gave better results than fewer large keys. In his report, Professor Kidwell gives formulas, also, for the number and spacing of the keys. Keys, Bolts and Washers for Compound Beams. As compound beams, when used, are generally built up of 8, 10, 12 or 14-in timbers, Mr. Kidder, some years ago, prepared a table giving the sizes of keys, the number required on each side of the middle of the span, their minimum spacing and the sizes of the bolts and washers to be used for such beams of from 20 to 36-ft spans. He noted that the maximum safe loads for such beams should be 75% of the loads computed by Formula (10), page 630, for a beam supported at both ends, and loaded with a uniformly distributed load. Table I. Keys, Bolts and Washers for Compound, Keyed Wooden Beams Size of beams Size of keys JBolts Washers Number of keys each side of center line White pine Spruce Doug- las fir Long- leaf yellow pine i6-in beams 20-in beams 24-in beams 28-in beams iH by 3 -in oak keys i^^ by 3 -in oak keys 2 by 4 -in oak keys 2H by 4^^-in oak keys %-in H-in ?i-in 7:i-in 3 -in 3 -in 35'^-in 3H-in 7 9 8 9 8 II 9 10 II 13 12 12 12 15 14 14 Size of keys Bolts Washers Minimum spacing of'keys ii/^by3 -i 2 by 4 -i 2H by 4H-i n oak keys ^-in li-in 3-in 3-in 3-in 1 1 H-in IS -in 17 -in iiKi-in 15 -in 17 -in 9 -in ii^^-in 13 -in 9 -in iij'^-in 13 -in ti oak keys n pak keys .... The Breadth or Thickness of Compound Beams should be not less than two-fifths of the depth. The Number of Keys required is not affected by the length or breadth of the beam, if the beam is figured for the full safe load. In Spacing the Keys (Figs. 3 and 4) they should not be closer than the minimum spacing given in Table I. For beams loaded at the mid lie, the spac- ing of the keys should be uniform from X to Y, Fig. 3, V being one-eighth the span from the center lia&. ^jlt Jj^j^^i^tj^ Rcg. Jbpty^ai the keys, center to cea- Flitched Beams or Flitch-Plate Girders 655 ter, works out less than the minimum spacing, the safe load should be cor- respondingly reduced or the thickness of the beam increased. For Beams Uniformly Loaded, the first four or five keys from the end should be spaced for minimum spacing, and the spacing of the remaining keys increased toward the point Y. When the ratio of depth to span is greater than I to 1 6, the inner key may be a Httle more than one-eighth the span from the center line, for distributed loads. Fig. 3 shows the proper spacing for a 20-in spruce beam of 28-ft span and for a long-leaf yellow pine beam of 30-ft span; and the tabulation below gives the proper spacing of keys for spruce beams of B PLAN OF 14" X 24" SPRUCE BEAIVI-36' SPAN Fig. 4. Details of Keyed and Bolted Wooden Beam longer spans, figured from the end of the beam in each case. For other woods and spans the spacing should be made as near like these as the fixed condi- tions will permit. Four examples of spacing are given below. The sizes of bolts and washers to be used are given in Table I. If the beam is not over 10 in wide, the bolts may be arranged as for the spruce beam (Fig. 3); if 12 in wide or over, the bolts should be staggered as shown for the hard-pine beam. In a very wide beam the bolts might be spaced as in detail B, Fig. 4. Spacing of keys in inches for spruce beams, commencing at end, for uniformly distributed loads: 16 Au-in spruce beam, 32-ft span, 10, 12, 12, 16, 19, 24, 32 20-in spruce beam, 32-ft span, 10, ii^^, iiV^, 11^, 12, 12, 12, 13, 15, 18, 24 24-in spruce beam, 36-ft span, 13, 15, 15, 15, 15, 16, : " 28-in spruce beam, 36-ft span, 15, 17, 17, 17, IS, 16, 18, 20, 30 17,17,17,17,17,17 3. Flitched Beams or Flitch-Plate Girders Flitch-Plate Beams (Fig. 5) were at one time much used, but with the present prices of steel it is cheaper and better to use steel beams. The following explanation and formulas are given, however, for the benefit of those who might have occasion to use a beam of this kind. It has been found in practice that the thickness of the wood should be sixteen times the thickness of the steel As the steel is so much suffer than the wood, we must 656 Built-Up, Flitched and Trussed Wooden Girders Chap. 17 proportion the load on the wood so that the latter will bend as much as the steel plate bends: otherwise the whole load might be thrown on the steel plate. The MODULUS OF ELASTICITY of Steel is about twenty times that of long-leaf yellow pine; so that a beam of this wood, i in wide, will bend twenty times as much as a plate of steel of the same ^T^^^ P ^^"*"^ ^^ _ size and under the same load. Plence, :® ^ --'-^-^^^y^^^^f^f^ if we want this beam to bend just as {rO _ : : o - - - - ^' - ' } much as the steel plate, we must put Fig. 5. Flitch-plate Girder ^^^y one-twentieth the load on it. If the wooden beam is sixteen times as thick as the steel plate, we should put sixteen-twentieths of its safe load on it, or, what amounts to the same thing, use a constant only four-fifths of the strength of the wood. Formulas for Flitch-Plate Girders. On this basis the following formulas have been derived for the strength of flitch-plate girders, in which the thick- ness of the wood is sixteen times the breadth of the steel, approximately: Let d = depth of beam in inches b = total thickness of wood in inches / = clear span in feet / = thickness of steel plate in inches ( 53.6 for long-leaf yellow pine ^' * = \ 4S for Douglas fir (31 for spruce P = total load at middle in pounds W = distributed load in pounds Then, for beams supported at both ends, Safe load at middle in pounds = -~ (A'b -{- 889 /) (i) Safe distributed load in pounds = -— (A'b + 889 /) (2) (3) 4 / wi For distributed load, ^ = V — ; • For load at middle, d=\/-—' (4) V^'^, -1^889/ ^ The bolts should be % in in diameter, and spaced 2 ft on centers. Each end should have two bolts, as in Fig. 5. Example. What is the safe load, uniformly distributed, for a girder composed of three 4 by 14-in Douglas-fir timbers and two % by 14-in flitch-plates, with a span of 25 ft? Solution. By Formula (2), Safe load = ^(45 X 12 -f 889 X 3/4) =18 922 lb 25 3. Trussed Beams and Girders Use of Trussed Beams and Girders. Whenever we wish to support a floor upon girders having a span of more than 30 ft, we must use a trussed GIRDER, a riveted steel-plate girder, or two or more steel beams. Under * For commercially spasoned timber and for ideal conditions these values may increase about 30%. Trussed Beams and Girders 657 some circumstances and in some parts of the country it may be cheaper or more convenient to use a large wooden girder, and truss it, as in Figs. 6, 7, 8 or 9. Depth of Trussed Girder. For all these forms it is desirable to give the girders as much depth as the conditions allow; as, the deeper the girder, the smaller the stresses in the pieces. In the Single-Strut Trussed Girder, we either have two beams, and one rod which runs up between them at the ends, or three beams, and two rods running up between the beams in the same way. The beams should be in one continuous length for the whole span, if they can be obtained in that length. The requisite dimensions of the tie-rod, struts and beams, in any given case, must be determined by first finding the stresses developed in these pieces, and then the areas of cross-sections required to resist these stresses. For a Single-Strut Truss (Fig. 6), the stresses in the pieces may be deter- mined by the following formulas: For a Distributed Load W Over the Whole Girder (Fig. 6) Fig, 6. Trussed Wooden Girder, One Vertical Strut Tension in T Compression in C _ W length of T 2 length of C iW. W Compression in B= — ,X (See Note.) length of B (5) (6) (7) length of C Note. When the beam B is in one piece, the full length of span. If B is jointed over the strut then compression in C or tension in R = V2 W. For a Concentrated Load P Over C (Fig. 6) Tension in T P length of r = -X: 2 length of C (8) Compression in C = P P Compression in B = length of B 2 length of C (9) For a Girder Trussed as in (Fig. 7), Under a Distributed Load W Over the Whole Girder Compression in 5 = Tension in R Tension in B W length of S 2 length of R = % W. (See Note.) W length of B 2 length of R bTJO dIodV- (10) (11) Note. When the beam B is in one piece, the full length of span. If B is jointed over the strut then compression in C or tension in R = V2W. 658 • Built-Up, Flitched and Trussed Wooden Girders Chap. 17 For a Concentrated Load, P at the Middle (Fig. 7) Fig. 7. Trussed Wooden Girder. One Vertical Tie ^ ■ . e ^^ length of 5 Compression in 6 = — X ; 2 length of R Tension in R Tension in B = P P length of B 2 length of R (I2) (i3) For a Double-Strut Trussed Beam (Fig. 8) with a Distributed Load W Over the Whole Girder (Beam B Divided into Three Equal Spans) Fig. 8. Trussed Wooden Girder. Two Vertical Struts Tension in T Compression in C = — W^ length of T 3 length of C ^ ' ' T, , ■ . y^ W length of 5 Compression in B or tension in D = — X ,: — 3 length of C For a Concentrated Load P Over Each of the Struts C (Fig. 8) . length of T Tension in T = PX length of C Compression in C = P Compression in B or tension in Z> = P X length of B length of C (14) (^5) (16) (17) For a Girder Trussed as in Fig. 9, and Under a Distributed Load W Over the Whole Girder (Beam B Divided into Three Equal Spans) . . ^ W length of S Compression in 5 = — X , — 7-=: 3 length of R (18) Tension in R W 3 ,,,..„ . . ^ W length of 5 , , Tension m B or compression in D =— X , ; — ;-;: (19) 3 length of R Trussed Beams and Girders 65^ For Concentrated Loads P Applied at Joints 2 and 3 (Fig. 9) 2 3 Fig. 9. Trussed Wooden Girder. Two Vertical Ties Compression in 6" = P X length of S length of R Tension m R = P Tension in B or compression in D = PX length of B length of R (20) (21) Trusses constructed as shown in Figs. 8 and 9 should be divided so that the rods R, or the struts C, will divide the lengths of the girder into three equal or nearly equal parts. The lengths of the pieces T, C, B, R, S, etc. should be measured on the axial lines of the pieces. Thus, the length of R should be measured from the center line or axis of the tie-beam B to the center line OR AXIS of the strut D; and the length of C should be measured from the axis of the rod to the axis of the strut-beam B. After determining the stresses in the pieces by these formulas, we may com- pute the areas of the cross-sections by the following rules: compression in strut (22) Area of cross-section of a short strut = in which Sc for cast iron may be taken at from 13 000 or 14 000 lb per sq in, and for wood as given in Table XVI, page 647. The size of the long strut D (Fig. 9) should be determined by means of Tables 451 and 452 for wooden columns, Chapter XIV. The diameters' of the tie-rods may be obtained from Table II, page 388. For the beam B (Figs. 8 and 9) when the load is distributed, we must compute its necessary area of cross-section as a strut (Fig. 8) or a tie (Fig. 9), and also the area of its cross-section, as a beam, required to support its load, and use a beam with a section equal to the sum of the two sections thus obtained. Area of cross-section of B to resist ) tension compression > = or (23) tension or compression ) St Sc v^' In the trusses shown in Figs. 6 and 7, with distributed loads, Wxl 4Xd^XA In the trusses shown in Figs. 8 and 9, with distributed loads, Wxl Breadth of B (as a beam) = - — — — - (25) (Compare Equation (24) and (25) with Equation (11), page 630.) W denotes the total distributed load in pounds on the girder, and / the length in feet of one section of the beam. When the loads are concentrated over the struts C (Fig. 8) or at the joints R (Fig. 9) then there will be no transverse Breadth of B (as a beam) = - (24) 660 Built-Up, Flitched and Trussed Wooden Girders Chap. 17 STRESS on the beams B, and they need be proportioned for the compressiv^e or TENSILE STRESS, Only, as the case may be. In Formulas (23), (24) and (25), for Sc and St, substitute the values for safe unit stresses for compression, Table XVI, page 647, and for tension, Table II, page 388, and for A substitute the values recommended in Tables II and XVI, pages 628 and 647. Illustrative Examples. To illustrate the method of computing the dimen- sions of the different parts of girders of this kind, two examples are given. Example 1. It is required to design a trussed girder of the form shown in Fig. 6, for a span of 30 ft. The girders are to be 12 ft on centers, and are to carry a floor loaded with 100 lb per sq ft. The girder consists of three strut- beams B, side by side, and two rods. We can allow the rod T to come two feet below the beams B, and we will assume that the depth of the beams B will be 12 in; then the length of C, measured from the center line of the beam, will be 30 in. The length of iJ is 15 ft, and by computation, or by scaling, we find the length of T to be 15 ft 2M in. Solution. The total load on the girder equals 100 lb multiplied by the span multiplied by the distance of the girders on centers, or, 100 X 30 X 12 = 36 000 lb. From Formula (5), „ . . ^ 36000 1821/2 in Tension m T = X : — - = 109 500 lb 2 30 m . or 54 750 lb on each of the two rods. For such a large stress it is best to upset the ends of the rods, and allowing 16 000 lb per sq in for steel rods, we find from Table II, Chapter XI, that we must use two 2li-\n steel rods. The strut-beam we will make of long-leaf yellow pine. From Formula (7) we find the compressive stress in ^ = (36 000/2) X (180/30) = 108 000 lb. As we are to use three beams side by side, there will be 36 000 lb compression in each beam. To resist the compression there is required an area of 36 ooo/i 000 or 36 sq in, which is equal to 3 by 12 in. From Formula (24) we find the total breadth required to resist the transverse 36 000 X IS . , , , , ... stress = : = 14 m; or each beam must be 4^^ by 12 m in section to 4X144X67 resist the transverse stress, and 3 by 12 in to resist the compressive stress. Consequently each beam must be 7^^ by 12 in in cross-section. [ As this would make the girder very wide, 27 14 in, we will use beams 14 in deep, increasing the depth of the girder i in, so that the height on centers will still be 30 in. The area required to resist the compressive stress will be the same as before, 36 in, but as the beam is 14 in deep the breadth will be only 2.57 in. 36 000 X I") The total breadth to resist the transverse stress will be -^ ~ = 10.28 in, 4X196X67 or 3.43 in for each beam. The total breadth for each beam will therefore be 6 in. A beam with a cross-section of 6 by 14 in will meet the requirements. The total width of the girder will then be 22H in. The load on C= % IF = 22 500 lb, or II 250 lb over each rod. The theoretical sectional area in square inches necessary to resist this load =11 250/13 000 for cast iron and 1 1 250/1 000 for oak. As the struts must be the full width of the girder, however, it will be necessary to make the sectional area much greater than the theoretical re- quirements. If made of cast iron the strut should be of the shape shown in Fig. 10, and if of oak, of the shape shown in Fig. 11. The cast-iron strut will be the best, but an oak strut will answer. Trussed Beams and Girders 661 Example 2. It is required to support a floor over a lecture-room 40 ft wide, by means of trussed girders; and as the room above is to be used for electrical purposes, it is desired to have a truss with very httle iron in it. It is decided^ therefore, to use a truss such as is shown in Fig. 9. Solution. Where the girders rest on the wall, there will be brick pilasters having a projection of 6 in, which will make the span of the truss 39 ft, and the rods RR will be placed so as to divide the tie- beam into three equal spans of 13 ft each. The tie- beam B will consist of two long-loaf yellow pine beams, with the struts S coming between them. There are two rods, instead of one, at RR, coming down on each side of the struts S, and passing through iron castings below the beams B, and forming supports for them. The height of the truss from center to center of timbers must be limited to 18 in. The trusses arc 8 ft on centers. The total floor-area supported by one girder is 8 by 39 ft, or 312 sq ft. The heaviest load to which the floor will be subjected is the weight of the people in the room, for which 75 lb per sq ft is an ample allowance; and the weight of the floor itself is about 100 lb per sq ft. This makes the total weight ^liable to come on one girder 31 200 lb. M '-y^^uM W . 157 m Fig. 10. Cast-iron Strut for Two Tie -rods Fig. 11. Wooden Strut for Two Tie-rods Compression in S, from Formula (18) = — X - 3 : 90 7oo'lb>''>^l'l' Tension in one pair of rods W ■■ — = 10 400 lb 3 rr . . „ . . ^ PF 156 in lension m B or compression m D = — X = 90 130 lb 3 18 m As the unsupported length of D is greater than that of S, a beam that will resist the compression in D will be ample for S. We find from Table II, Chap- ter XIV, that it will require a post 10 by 12 in in cross-section to resist the com- pression in D, which is 13 ft in length. The tension in each rod is only 5 200 lb; but as the rods must support a larger washer at the bottom, they are made I in in diameter, not upset. The tension in each of the beams B is 45 065 lb. This divided by i 200, the safe unit tensional stress for long-leaf yellow pine = 37-6 sq in, or about 2% by 14 in. The total breadth of the tie-beam to resist the transverse load is found from Formula (25). Assuming 14 in for the depth of B Breadth oi B = 31 200 X 13 = 5.15 in, or about 2H in for each beam 6 X 196 X 67 The breadth of each tie-beam must therefore be 2% 'm+ 2\i in = 5H in. Hence the tie-beams must be 5 by 14 in in section. The girder, therefore, must be built with 10 by i4-in strut-beams and two 5 by 14-in tie-beams, each 42 ft Jong. The i-in rods may be cut H in into the strut->beams, and I'i in into the tie- 662 Built-Up, Fiitched and Trussed Wooden Girders Chap. 17 beams, so that the latter will come close against the struts S. The thrust of the strut S is equal to its compressive stress, and a connection between the tie- beams and the struts must be designed that will resist this thrust, which in this case is 90 700 lb. As the inclination of the strut is very slight, there is ample room for bolts. It is best to use bolts which are at least iH in in diameter. As they are in double shear, the resistance to shearing of one bolt is 35 340 lb. (See Table IX, page 431.) Steel bolts are used. The bearing area of a iH-in bolt in a timber 10 in wide is 15 in. For the bearing resistance of long-leaf yellow pine, we may allow i 400 lb per sq in (Table XVI, page 647), which will give 21 000 lb as the bearing resistance of one i^^-in steel bolt. As the force to be resisted is 90 700 lb, it will require five ii'i-in steel bolts to sustain this bearing pressure, the resistance to shearing being greater than this stress. The number of bolts required to resist the bending moment must now be determined. The total bending moment to be resisted (see page 434, Chap- ter XII) = 90 700 times the distance, in inches, between the centers of the tie- beams divided by 12, or 90 700 X ^%2 = 113 375 in-lb. From Table IX, page 431, we find that the maximum bending moment, at a fiber-stress of 20000 lb per sq in, for a iH-in steel bolt is 6 630 in-lb. Hence it will require seventeen iH-in bolts to resist the thrust in 5 without bending the bolts. As it is impracticable to put in so many bolts, larger ones must be used. For a 2H-in steel bolt, the maximum bending moment is 30700 in-lb (Table IX, page 431), and four times this is 122800 in-lb; hence four 2H-in steel bolts will be suflacient to resist the bending stress, and also the shearing and bearing-stresses. It will be seen from this example that it is much more difficult and expensive to make satisfactory end-joints for girders trussed as in Figs. 7 and 9 than it is for the single and double-strut trusses like those shown in Figs. 6 and 8. The latter forms are to be preferred when the conditions will admit of their use. These four cases of trussed girders are but special examples of trusses. The stresses in them may also be determined by the methods explained in Chapter XXVII; and where the divisions of the girder cannot be made uni- form, the stresses should be computed by the general methods there explained. General Principles of the Deflection of Beama 663 CHAPTER XVIII STIFFNESS AND DEFLECTION OF BEAMS By CHARLES P. WARREN LATE ASSISTANT PROFESSOR OF ARCHITECTURE, COLUMBIA UNIVERSITY 1. General Principles of the Deflection of Beams* Strength and Stiffness. In many structures it is necessary that beams and girders shall be not only strong enough but stiff enough; that is, not only must RUPTURE be prevented, but the beams must not bend so much as to ap- pear unsightly, or to crack the ceiling. Therefore, in many cases, deflection, rather than absolute strength, may become the governing consideration in determining the size of a beam. Unfortunately, there is no method at present of combining the two calculations for strength and for stiffness in one. A beam properly proportioned for strength will not bend enough to stress the fibers beyond the elastic limit, but it may in some cases bend more than a due regard for appearances will justify. The distance that a beam bends under a given load is called its deflection, and its resistance to deflection is called its stiffness. A General Formula for the Maximum Deflection of any beam under a concentrated or uniformly distributed load not stressed beyond the elastic LIMIT is: ^ ^ . . . , load in pounds X cube of span in inches X c . Deflection m mches = — 7—,^ — 7-. tz : — U} modulus of elasticity X moment 01 inertia The values of c are as follows: For beam supported at both ends, loaded at the middle 0.021 For beam supported at both ends, uniformly loaded 0.013 For cantilever beam, loaded at free end 0.333 ' For cantilever beam, uniformly loaded o. 125 Deflection of Beam with Rectangular Section. By making the proper substitutions in Formula (i), the following formula for a rectangular beain supported at both ends and loaded at the middle may be derived: ^ ^ . . . , load in pounds X cube of span in feetX i 728 Deflection in inches = — r 7- — . ^^ ^ (2) 4 X breadth X cube of depth X E Modulus of Elasticity. From this formula the value of the modulus of ELASTICITY, £, for different materials, has been calculated by accurately measur- ing the actual deflection of known beams under given loads applied at the middle and then substituting these known quantities in Formula (2). Simple Formula for Deflection. Formula (2) may be simplified some- what by representing i 728 /4E by i/F, which gives the formula Deflection in inches = ^ — — ; (3) bXd^XF'] For a DISTRIBUTED LOAD the deflection will be five-eighths of this. * See, also, in Chapter XVI, formula on page 636 and Table XVI, page 647. t Tke constant F corresponds to Hatfield's F, in his treatise on "Transverse Strains." 664 Stiffness and Deflection of Beams Chap. 18 To Find the Load at ' the Middle that will cause a given deflection, transpose Formula (2) so that the load becomes the left-hand r^ember of the equation. Thus: 1 > . Load at middle 4 X breadth X cube of depth X defl ection in in X E in pounds (4) ^ culpe o^ span X i 728 / j ;; ? , ^ Limit of Deflection. In order that this formula may be of use in deter- mining the maximum load which may be placed upon a beam, the limit of the DEFLECTION must in some way be tixed. This is generally done by making it a certain proportion of the span. Allowable Deflection of Floor-Beams. Trcdgold and other authorities state that if a floor-beam detiects more than one-fortieth of m inch for EVERY FOOT OF SPAN, it is liable to crack the ceiling on the under. side; and hence this is the limit which is often set for the deflection of beartis in fiirst-class buildings. Formulas for Deflection of Floor-Beams. If the length in feet divided by 40 ;^ substituted for the deflection in inches, Formula (4) becomes breadth X cube of depth X & Load at the middle = - square of span in feet (5) in which e— — 17 2S0 Most engineers and architects, however, think that one-thirtieth of an inch per foot of span, that is, Hoo of the span, is not too much to allow for the deflection of floor-beams, as a floor is seldom subjected to its full estimated load, and then only for a short time. Table I. Values of Constants for Stiffness or Deflection on Beams* Material Cast iron Wrought iron Steel Ash......... Calif orilia redwood. .......... Cedar.. Chestnut Cypress Douglas fir. :iXt A /ll liW ViX^ Hemlock .-\.v '^-m »"020'wl^/EI Hence the deflection of the continuous girder is only about % that of a non- continuous girder. The greatest deflection of a continuous girder of two spans is not at the middle of either span, but between the middle point of a span and one of the abutments. The greatest deflection of a continuous girder of two equal spans, loaded at the middle of one span with a load of P lb, and at the middle of the other with Pi lb, is, for the span with the load, P (2sP-9Pi)/3 Maximum deflection = -^—- 1 (17) for the span with load Pi (23 P\ — 9 P) P Maximum deflection = • (iia) I 536 EI When both spans have the same load Maximum deflection = J^es Pl^/EI {17b) * In this continuous beam the maximum bending moment is the minus bending mo- ment over the middle support and in each of the two simple beams the maximum bend- ing moment is a plus bending moment and is between two supports. Notes on Reactions, Strength and Stillness of Continuous Girders 675 The greatest deflection of a simple beam supported at both ends and loaded at the middle with P lb is Maximum deflection = P/V48 EI or the deflection of the continuous girder is only ^r, that of a non-continuous one. Continuous Girder of Three Equal Spans. Uniformly Distributed Load Over Each Span. The load per unit of length is w lb. Greatest deflection at the middle of middle span = 0.00052 wl^/EI (t8) Greatest deflection in the end-spans = 0.006884 zf/^/£/ (19) Hence the maximum deflection of the continuous girder is only about \^ that of a non-continuous girder. Continuous Girder of Three Equal Spans. Concentrated Load P at the Middle of Each Span. Greatest deflection at the middle span = Hso PPlEI (20) Greatest deflection at the middle of end-spans = ^Heo PP/EI . (21) Hence the maximum deflection of the continuous girder is only I'/^o of that of the non-continuous girder. 5. Notes on Reactions, Strength and Stiffness of Continuous Girders Supports and Reactions of Continuous and Non-Continuous Girders. From the foregoing, some conclusions can be drawn which will be of use in deciding whether it is best in any case to use a continuous or a non-continuous GIRDER. From the formulas given for the reactions of the supporting forces in the different cases of continuous girders it is seen that the end-supports do not bear as much of the load as they do when the girders are non-continuous. The difference is added to the reactions of the other supports. This might be of advantage in a building in which the girders run across the building, and have their outside ends supported by the side walls and their inside ends by piers or columns. In this case, by using continuous girders, part of the load could be taken from the walls and transferred to the piers or columns. But in cases of this kind, the vibration may have to be considered. .If the building is a miU or factory in which the girders support machines, any vibration in the middle span of the girder is carried to the side walls if the girder is continuous; while if non-continuous girders are used, with their ends an inch or so apart, little or no vibration is carried to the side walls from the middle span. In all cases of important construction the supporting forces should be carefully considered. Relative Strength of Continuous and Non-Continuous Girders. As the . RELATIVE STRENGTH of contiuuous and non-continuous girders of the same cross-section, material and spans, and loaded in the same way, is proportional to their maximum bending moments, the strength of a continuous girder can be calculated, from the formula for its maximum bending moment. From the values given for these bending moments for the various cases considered, it is seen that the parts of the girder most stressed are those which come over the middle supports. It is seen, also, that, except in the single case of a girder of two spans uniformly loaded, the strength of a continuous girder is greater than that of a non-continuous girder. But the gain in strength in some in- stances is not very great, although it is generally enough to pay for making the girder continuous. 676 Strength and Stiffness of Continuous Girders Chap. 19 Relative Stiffness of Continuous and Non-Continuous Girders. The stiff- ness of a girder varies inversely as its deflection; that is, the less the deflec- tion under a given load the stiffer the girder. From the values given for the MAXIMUM DEFLECTION of continuous girders, it is evident that the stiffness of a girder is increased by making it continuous; and this is usually the principal advantage in the use of continuous girders. It sometimes happens in building- construction that it is necessary to use beams and girders of much greater strength than is required to carry the superimposed load, because the deflections of smaller beams or girders would be too great. But if continuous girders are used they may be made of just the size required for strength, because their deflections are less. Where great stiffness is required, therefore, continuous beams or girders should be used if possible, as in the case of grillage-girders. (See Example 3, page 679.) 6. Formulas for the Strength and Stiffness of ContinuottS' Gitders Girders of Rectangular Cross-Section. For convenience, the proper formulas for Calculating the strength and stiffness of continuous girders of rectangular cross-section are given. The formulas for strength are deduced from the flexure- formula M = 67/ c, modified for the rectangular section of breadth b and depth d. Bendmg moment =» (22) 6 in which S is the safe unit fiber-stress. This is eighteen times the coefficient A*oi Table II, page 628. Strength. Continuous Girder of Two Equal Spans. Uniformly Distributed Load Over Each Span. Breaking-load f = -. (23) where b denotes the breadth and d the depth of the girder in inches, and / the length of one span, in feet. The values of the constant A are three times the values given in Table II, page 628. For long-leaf yellow pine, 201 ; for Douglas fir, 168; chestnut, 132; and for spruce and white pine, 117 lb per sq in, are rec- ommended for the values of A in these formulas. Continuous Girder of Two Equal Spans. Concentrated Load at the Middle of Each Span. Breaking-load = % X ^-^^^i-^ (24) Continuous Girder of Three Equal Spans. Uniformly Distributed Load Over Each Span. Breaking-load = % X ^^"^^'^^ (25) Continuous Girder of Three Equal Spans. Concentrated Load at the Middle of Each Span. Breakmg-load = % x (26) * See, ilso. Table I, page 557, and Tabie XVI, page 647, for safe fiber-stresses, t Breaking-load in pounds in all cases. Formulas for the Strength and Stiffness of Continuous Girders 677 Stiffness. Continuous Girder of Two Equal Spans. Uniformly Distributed Load Over Each Span. The following formulas give the loads which the beams will support without deflecting more than one-thirtieth of an inch per foot of span. r . bXd^Xei Load on one span = (27) ^ 0.26 X/2 ^ '^ Continuous Girder of Two Equal Spans. Concentrated Load at the Middle of Each Span. b "X. d^ X €1 Load on one span = 1% x -, (28) Continuous Girder of Three Equal Spans. Uniformly Distributed Load Over Each Span. Load on one span = • (20) 0.33 Xl^ ^^^ Continuous Girder of Three Equal Spans. Concentrated Load at the Middle of Each Span. T J ,^, bXd^Xei Load on one span = 2%i x (30) The value of the constant ei is obtained by dividing the modulus of elas- ticity by 12 960; and, for the three woods most commonly used as beams, the following values may be taken: Long-leaf yellow pine, 116; white pine, 77; spruce, 92; Douglas fir, 116. (For other woods, see Table I, page 664.) For Continuous Steel Beams the requisite size may be found by first com- puting the MAXIMUM BENDING MOMENT, by mcaus of Formulas (12) to (15), and then selecting a beam that has a 3 X maximum bending moment in ft-lb , ^ section-modulus = ■ — (31) 4000 Values for the section-moduli for the different shapes of rolled steel used as beams are given in the tables in Chapter X, Example i. What steel beam should be used to support two loads of 16 000 lb each, concentrated at the middle of two spans of 10 ft each, the beam being continuous? Solution. Formula (13(1) gives the maximum bending moment as Me PI, or 30000 ft-lb. Therefore, from Equation (31), a beam having a section-modulus equal to 3 X 30 000/4 000 or 22.5 should be used. From the Table IV, page 355, it is found that a 9-in 30-lb beam has a section modulus of 22.6, and a lo-in 25-lb beam a section modulus of 24.4. Either of these beams will there- fore answer, the lo-in beam being the cheaper, however, and also the stiffer. Example 2. A steel beam continuous over three spans is required to support a uniformly distributed load of i 000 lb per lin ft. The two end-spans are 12 ft each, and the middle span 10 ft. What should be the size and the weight of the beam used? Solutio^, The maximum bending moment is found by Formula (14), and is 1000X1000-1-1000X1728 ' ; . « ;2 630 4(30+24) 678 Strength and Stiffness of Continuous Girders Chap. 19 The section-modulus, by Equation (31), must equal 3 X 12 630/4 000- 9.47, which requires a 7-in 15-lb beam (Table IV, page 355). If the beam were not continuous an 8-in i8-lb beam would be required for the i2-ft spans, and a 7-in 15-lb beam for the lo-ft span. For a beam of two equal spans, loaded uniformly, the strength is the same as though it were not continuous. The formulas given for the reactions at the supports, and for the deflections of continuous girders with concentrated loads, were verified by Mr. Kidder by means of careful experiments on small steel bars. The remaining formulas were verified by comparing them with the formulas of other authorities where it was possible to do so. In regard to some of the cases given the author has never seen any discussion of them in any work on the subject. 7. Continuous Girders in Grillage-Foundations ,„ GrlUage-Beams Considered as Inverted Continuous Girders. As stated in the beginning of this chapter, continuous girders, as such, are seldom used in building-construction, although their employment in grillage-beam footings is fre- ^^^M\ R uiiiiiiiiiiiiiiiiiiiiiiiiiiniijl Fig. 3. Continuous Girder in Grillage-foundation Fig. 4. Shear-diagram and Bending-moment Diagram quent. Fig. 3 represents a footing consisting of two layers of beams, which dis- tribute the load of the three columns above, uniformly over the foundation-bed. By inverting the footing the three columns become the supports or reactions, and the upper layer of beams, a continuous girder, loaded with a uniformly distrib- uted load which is the pressure of the lower layer. As in practice the column- Continuous Girders in Grillage-Foundations 679 loads are never equal, and the distance between the columns seldom equal, it is necessary to project the continuous girder beyond the most heavily loaded column in order to insure a uniform pressure upon the lower layer. Because of these limitations none of the formulas previously deduced can be applied, although the principles upon which they are based hold good. Maximum Bending Moment. Since the reactions in this case are the given column-loads it is required first to find the maximum bending moment. From what has already been said about continuous girders, it is evident that the point of maximum bending moment may be under columns i or 2, or between the columns. Since the maximum bending moments are the points of no SHEAR, construct the shear-diagram, find where the shear passes through zero, and calculate the bending moments at. these points. The maximum bend- ing moment is determined, as in examples i and 2, in order to determine the section-modulus of the girder. Example 3. The continuous girder under columns i, 2 and 3 (Fig. 3) is S3 ft long; the overhang, to the left of column i, 6.25 ft; the distance between columns i and 2, 13.12 ft; between columns 2 and 3, 12.88 ft; and from column 3 to the right edge of the girder, .75 ft. The column-loads are as follows: on column I, 565 tons; on column 2, 600 tons; and on column 3, 255 tons. The column-loads may be considered uniformly distributed over parts of the girder by the bases, which are 3 ft wide under columns i and 2 and 18 in wide under column 3. The unit pressure under column i, therefore, is 565/3 = 188.3 tons; under column 2, 600/3 = 200 tons; and under column 3, 255/1.5 = 170 tons. The unit pressure under the continuous girder is (565 + 600 -[- 255)/33 = 43 tons : ; , , The first step in the calculation of the girder is the determination of the POINTS OF no shear and the plotting of the shear-diAgrAm in Fig. 4. It is obvious from the shear-diagram that there are four points of no shear and con- sequently four points of possible maximum bending moment. The first of these is under column i, the second between columns i and 2, the third under column 3 and the fourth between columns 2 and 3. The bending-moment diagram is shown by the solid curved line in Fig. 4. The points of contra- flexure or no bending moment are the intersections of this line with the hori- zontal line of reference. The shear-diagram,* shown by the broken line in Fig. 4, may be constructed as follows: Fit = -h 43 tons per ft X (6.25 - 1.5 = 4.75 ft) = -f 204.25 tons F2 = ( 4- 43 tons per ft X 6.25 ft) - 565/2 tons = -f 268.75 - 282.5 = -13.75 tons This shows that xi, the point of no shear, lies between points i and 2. To find this point let y be its distance beyond or to the right of point i. Then, the equation for no shear is 43 tons X (4-75 ft + y ft) = 188.3 X y, or 204.25 _^43-y= 188.33/, from whjch 145.33/= 204.25 and y- 1.4 ft: hence xi, the first point of no shear, is 4.75 ft -I- 1.4 ft, or 6.1 ft from the left end.| The SECOND POINT OF no .shear, Xi, is such a distance from the left end that the DOWNWARD SHEARING-FORCE of 565 tons from column I is neutrahzed by • The upward forces are here called plus or positive and the downward forces minus or negative. • t Fi is taken at point i, the left edge of base of Column i, F2 at point 2, at the axis of Column 2, etc. X The following computations are carried oiit to one decimal-place, only, the nearest approximate values being used. 680 Strength and Stiffness of Continuous Girders Chap. 19 an equal upward shearing-force of 43 tons per ft. on xt ft. Hence xz = 565/43 = 13.1 ft. Fe = + 43 tons per ft X [(6.25 -f- 13.12 - 1.5) = 17 9 ft] - 565 tons = 7697 - 565 = +204.7 tons ^7 = +43 tons per ft X (6.25 -f 13.12 = 19.4 ft) - (565 + 600/2 tons) = + 834.2 — 865 tons = — 30.8 tons This shows that the third point of no shear, xs, lies between 6 and 7. Let y be its distance to the right of point 6. The equation for no shear at this point is 43 tonsX (17.9 ft + >> ft) = 565 tons-|- (200 tonsXy ft), or 769.7 + 43 y — 565 + 200 y. from which 157 y = 204.7 and y = 1.3 ft. Hence X3, the third point of no shear, is 17.9 ft+ 1.3 ft = 19.2 ft from the left end. The FOURTH POINT OF NO SHEAR, ^4, is such distance from the left end that the DOWNWARD SHEARING-FORCE of columns I and 2, amounting to 565 + 600 or 1165 tons, is neutralized by an equal upward shearing-force of 43 tons per ft on .^4 ft. Hence ^4=1 165/43 = 27.1 ft. Having found the points of no shear, the bending moment at these points may now be determined. , M at :¥i = 43 tons X 6.1 ft X 6.1/2 ft - 188.3 tons X 1.4 ft X 1.4/2 ft = + 615.5 ft-tons M 2XXi = 43 tons X 13. 1 ft X 13. 1/2 ft — 565 tons X 6.8 ft = — 152.4 ft-tons Af at :^3 = 43 tons X 19.2 ft X 19.2/2 ft - 565 tons X 12.9 ft- 200 Tx 1.3 ft X 1.3/2 = + 467 ft-tons M ditx\ = 43 tons X 27.1 ft X 27.1/2 ft — 565 tons X 20.8 ft — 600 tons X 7.7 ft = ~ 582.2 ft-tons The maximum bending moment therefore is at xi and equals 615.5 ft-tons* or I 231 000 ft-lb. Substituting in Formula (31), the section-modulus is found 3X1 231 000 to be = 923.2. The following beams could be used, as far as 4000 flexure is concerned. For investigations of the resistance of the girders to web- buckling or crippling, see Chapter II, pages 182 to 184, and Chapter XV, pages 567 to 569. Four standard 24-in iio-lb I beams, section-modulus of each, 240.3 (page 354) Three Bethlehem 30-in 120-lb I beams, section-modulus of each, 349.3 (page 357) Three Bethlehem 24-in 140-lb girder-beams, section-modulus of each, 350.1 (page 358) Two Bethlehem 28-in i8o-lb girder-beams, section-modulus of each, 518.9 (page 358) . The 28-in and 30-in beams are stiff er than the 24-in beams, have a smaller total amount of steel and cost less than the others for the number of beams required. * The bending moments at Xi and x^ have very nearly the same numerical values, and in the computations the retaining or dropping of figures in the second decimal-place ma.y change the result and make the value at x^ slightly greater than at Xi, General Notes on Plate and Box Girders 681 CHAPTER XX RIVETED STEEL PLATE AND BOX GIRDERS By CHARLES P. WARREN LATE ASSISTANT PROFESSOR OF ARCHITECTURE, COLUMBIA UNIVERSITY 1. General Notes on Plate and Box Girders Types of Riveted Girders. Girders built up of plates and angles, as shown in section in Figs. 1 to 4, are extensively used. This is undoubtedly owing to the simplicity of their construction, to the comparatively low cost of the shapes of which they are fabricated and to their adaptability to any arrangement of loads or to any span for which girders are usually required. Riveted girders, however, are seldom made for spans greater than 6o ft and are seldom more than 6 ft in depth. The most common forms of these girders are shown in Figs. 2 and 4. -r JL. Fig. 1 Fig. 2 Fig. 3 Types of Riveted Girders Fig. 4 The girders with a single vertical plate called the web are usually called PLATE GIRDERS, and thosc with double or triple webs, box girders. Plate girders are more economical than box girders, and more accessible for painting and inspection; but box girders are stiff er laterally and should always be used where great length of span requires wide flanges. In general, it may be said that plate girders should be used to support floor-beams and floor-arches and walls not over 12 in thick, and that box girders should be used where a flange- width greater than 12 in is required. The girder shown in section in Fig. 1 has no flange-plates and should be used only for comparatively light loads and short spans, and never to support masonry. Flange and Web. The term flange, as applied to riveted girders, includes all the metal in the top or bottom parts of the girder, exclusive of the web-plates.* The DEPTH of a riveted girder is the distance between the centers of gravity of the flanges; but in practice this is usually taken as the depth of the web- plate, and the word will be so used in this chapter. The top and bottom of the flange-angles extend H in beyond the top and bottom of the web-plate. (See the figure in Table IV, page 706.) Stiffeners are short pieces of angles * This may be modified, however, as some engineers include one-sixth of the web-area in the effective flange-area. See, also, Flange-Area in the examples of this chapter. 682 Riveted Steel Plate and Box Girders Chap. 20 riveted to the web at intervals, to keep it from buckling. They should fit closely against the horizontal legs of the llange-angles, and should always be used at the supports and under concentrated loads. Economic Depths of Girders. The depth of a riveted girder may vary from one-tenth to one-fifteenth or, in exceptional cases, one-sixteenth the span. The greatest economy of material is said to be obtained when the depth is one- twelfth the span. Thus for a 36-ft span a 3-ft girder should be used if the conditions will permit; but the least depth should be He of 36, or about 2 ft 5 in or, in exceptional cases, He of 36, or 2 ft 3 in. A girder is said to have its ECONOMIC DEPTH when the amount of material in the flanges is equal to that in the web, and there are no cover-plates. The rule holds approximately when there are cover-plates. The Width of the Top Flange should not be less than one-twentieth the distance between lateral supports; or if there are no lateral supports, then not less than one-twentieth the span. Arches Between Girders, or floor-beams riveted to the sides of girders, may be considered as lateral supports. 2. Details of Construction of Plate and Box Girders* General Requirements for Plate and Box Girders. The following re- quirements are those which must be generally satisfied in the design of riveted girders. (i) All the connections and details of the several parts shall be of such strength that, upon testing, rupture shall occur in the body of the members rather than in any of their details or connections. (2) In members subject to tensile stress full allowance shall be made for the reduction of the section by the rivet-holes. (3) The webs of plate girders, when they cannot be obtained in one length, must be spUced at all joints by a plate on each side of the web. (4) Tees must not be used for splices. (5) Stiff eners shall be used at the ends of all girders, wherever there are con- centrated loads, and elsewhere when the shearing-stress is greater than the resistance to buckling. (6) The pitch, that is, the distance between centers of rivets, shall not ex- ceed 6 in, nor 16 times the thickness of the thinnest outside plate, and it shall not be less than 2H in for H-in rivets, or 2^/i in for Ji-in rivets, in a straight hne. (7) The rivets used should be H in in diameter for plates from % to H-in thick, and % in in diameter for plates of greater thickness. (8) The distance between the edge of any piece and the center of a rivet- hole must never be less than iH in. (9) In punching plates or other members, the diameter of the die shall in no case exceed the diameter of the punch by more than He in. (10) All RIVET-HOLES must be so accurately punched that when the several parts forming one member are assembled, a rivet, He in less in diameter than the hole, can be inserted, hot, into any hole without reaming or stressing the metal by the use of drift-pins. (ti) The rivets when driven must completely fill the holes. (12) The rivet-heads must be hemispherical, except where flush surfaces are required, and of uniform size throughout for rivets of the same size. They must be full and neatly made, and be concentric with the rivet-holes. • These requirements are taken largely from Biricmire's " Compound Riveted Girders.'* Design of Plate and Box Girders 683 (13) Whenever possible, all rivets must be machine-driven, (14) The several pieces forming one built member must fit closely together, and, when riveted, must be free from twists, bends or open joints. (15) Girders 60 ft and less in length seldom require splicing, as the plates and angles can readily be obtained in such lengths. In spUcing the top flange, when of two or more thicknesses, no additional cover-plate will be required over the joint, but the ends should be planed true and butt closely. The rivets should be spaced closer near the joint. (16) The plate covering the bottom flange must be of the same area as the plates joined, and of sufficient length to take a number of rivets equal tOb the' strength of the cover-plate. 3. Design of Plate and Box Girders The Principal Steps in the Design of Riveted Girders. In designing a riveted girder to sustain safely a given load, the following steps are necessary: (i) The determination of the required flange-area. (2) The determination of the thickness of the web to resist (a) Shearing. (b) Buckling. This step also determines if stiffeners are necessary. (3) The determination of the number and pitch of the rivets. (4) The approximate weight of the girder. (5) The determination of the length of the flange-plates when more than one is required for each flange. (i) The Flange- Area. In determining the flange-area of riveted girders, it is customary to assume that the bending moments are entirely resisted by the upper and lower flanges, the web being assumed to resist the shear only. Just what should be included in the flange-area is a question on which engineers differ. Some include the flange-plates and angles and one-sixth of the web-area, others the flange-plates and angles only, while others include the flange-plates and only the horizontal legs of the angles, the vertical legs being considered as belonging to the web. In compression-flanges, usually the upper ones, the gross section- area may be taken, provided the rivets are machine-driven and fill completely the holes; but in tension-flanges, usually the lower ones, the net area is taken, that is, the gross area minus the area of the greatest number of rivet-holes in any cross-section,, since the stresses of tension are not transmitted through the rivets as are those of compression. A general formula* for determining the flange-area, which applies to all conditions of loading is Area of one flange __ maximum bending moment in foot-tons in square inches depth of web in feet X safe unit fiber-stress in tons or A^Mm^^/dS (l) * This may be derived from what is sometimes called the p'tATE-GiRDER formula, Afmax = SAd, in which S is the safe unit bending-stress in the flange at the section of maximum bending moment, A is the area of the cross-section of either flange and d is ap- proximately the depth of the girder. Of course the units must be the same in both mem- bers of the equation. If the center of moments is taken at the center of gravity of the cross-section of either flange-area and if the area of metal resisting bending is considered to be concentrated in the flanges, the depth of each being very small compared to that of the girder-depth, then 5^1 is the total horizontal stress in either flange, d its lever- erm and SAd the resisting moment of the cross-section, equal to Af mai. Hence A = Mmtix/dS. Another method uses the section-modulus, I/c = M/S, in determining the flange-areas and proportioning the girder. (See pages 706 to 716.) 684 Riveted Steel Plate and Box Girders Chap. 20 Rules for finding the maximum bending moment for different conditions of loading are given in Chapter IX. S, the SAFE UNIT FIBER-STRESS FOR FLANciE-BENDiNC, was formerly taken at from 13 000 to 16 000 lb per sq in, the tallies in the manufacturers' handbooks giving the safe loads, etc., for riveted girders, varying in regard to this stress.* If it is required to compute the safe uniformly distributed load for a girder already constructed or designed, the following formula f may be used. The safe load in pounds, uniformly distributed is 8 X net area of bottom flange X depth in itxS W = ■ f ^ • span m feet or W=^SAdS/l (2) From the result the weight of the girder itself should be subtracted. For the safe concentrated load at the middle of the span take one-half the result obtained by formula (2) and subtract the weight of girder. (See Case IV, page 326.) (2) The Thickness of the Web. The thickness of the web is determined by its resistance to vertical shearing. Whether or not stiff eners shall be used is determined by the resistance of the web to buckling. (a) Shearing. To resist the vertical shear the net sectional area of the WEB in square inches must be the maximum vertical shear A = Fmax/5 (3) V and S being both in tons, 5 is taken at 10 000 J lb or 5 tons per sq in. (See Table II, page 703.) The maximum vertical shear in any beam or girder is at the greater reaction and is equal to it. For a girder supported at both ends and uniformly loaded with a load W, the maximum vertical shear is ''^ F,nax=Tr/2 For a girder supported at both ends and loaded at the middle with a load P, Fmax = P/2 For a girder supported at both ends and loaded as in Fig. 7, Fmax = Pm/l = Ri For a girder supported at both ends and loaded with two equal concentrated loads P, P, equally distant from the middle, as in Fig. 8, Fmax = P = Ri = R2 For combinations of loads the maximum vertical shear will equal the greater reaction. The method of determining the reactions at the supports of a beam or girder is given in Chapter IX, Subdivision i. The vertical sUearing- * See Chapter XV, paragraphs relating to riveted single and double-beam girders and foot-note with same, pages 603 and 604; also page 704. The value in most city codes is now 16 000 lb per sq in. t From Formula (i) just explained, and from Case V, page 326, If max = SAd and A/max = Wl/S. Hence Wl/S = SAd and TF = 8 AdS/l. t This is a conservative value. The Carnegie Pocket Companion and the building laws of most cities permit 10 000 lb per sq in for steel. Design of Plate and Box Girders 666 FORCE at any given vertical section of a beam or girder between the supports is the algebraic sum of all the vertical external forces acting on the beam to the 'IT a\ \ R Xi Yx rig.5 [R2 |r7 _a . Fig.6 |R2 ue — .n >'< hUI -a. Fig.7 T Ri Eig.8 IR2 ■nL k=p 50 80 100 60 R|=140 Figs. 5 to 9. Diagrams for Vertical Shears for Different Loadings left of that section, forces acting upwards being considered as plus, and those acting downwards being considered as minus. Thus, in the case of the beam shown in Fig. 9, the reaction Ri will be found, by the method explained in Example 2, page 323, and by Formulas (2) 686 Riveted Steel Plate and Box Girders Chap. 20 and (3), page 323, to be 150 lb, and that at R2 to be 140 lb. The shear at vari- ous sections may be found by applying the foregoing definition of vertical SHEAR, thus: Shear at X = + 150 — 50 = -f 100 lb Shear at F = + 150 — 50 — 80 = + 20 lb Shear at Z = + 150 — 50 — 80 — 100 = — 80 lb Shear at O = + 150 — 50 - 80 — 100 — 60 = - 140 lb The manner in which the vertical shear varies between the supports, under different dispositions of the loads, is shown graphically by the hatched areas in Figs. 5 to 9; in the first three cases W and F are assumed to have the same value. When the load is uniformly distributed the vertical shear can be found graphically by laying off vertically Ri and R2 to a scale of pounds, and drawing the line ab, Fig. 5. The shear at X will then be represented by the ordinate Xi and the shear at Y by Fi, and they can readily be scaled. (b) Buckling.* The safe resistance of the web to buckling, in pounds per square inch, may be determined by the formula 10 000 Sb = ■ i + - d^ (4) 3 000/2 in which Sb is the safe buckling value in pounds per square inch, d is the depth of the web in the clear between flange-plates in inches and / is the thickness of the web in inches. When this resistance is less than the unit stress for VERTICAL shear at any section, stiffeners must be used. Stiff eners. These should be made of angles, not less than sH by sH by % in in size. They should always be tightly fitted between the flange-angles, so as to support the horizontal flanges. In order to bring the stiffeners in contact with the web and the vertical leg of the angles, fillers, of the same thickness as the flange-angles, are generally used, as shown in Fig. 10. Where there are several girders exactly alike, something may be saved by omitting the flllers and bending the stif- feners, as shown in Fig. 11. This bend- ing, however, can be done properly, only by the use of special dies, and costs more than the fillers unless there are many stiffeners. The spacing of stiffeners is more a matter of judgment and experience than of exact calculation. Shear-diagrams, shown in Figs. 5 to 9, are of great assistance in visualizing shearing-stresses. The general rule is to place the stiffeners not farther apart than the depth of the full web-plate on girders over 3 ft in depth, with a maximum spacing of 5 ft. On girders under 3 ft in depth they are placed 3 ft apart. Girders 2 ft and lesa in depth require no stiffeners. On girders supporting distributed loads they are generally placed nearer together at the ends than towards the middle. * See Table III, page 705, and also in Chapter XV, the paragraphs and foot-note, pages 567 to 569, relating to the web-buckling of beams and girders. The formula used for web-buckling in Table III, page 705, is the formula that was used in the Pa.ssaic Steel Company's Manual, and as the values computed by it vary but little from those deduced by the Cambria formula (see page 568), Table III is retained| ^ U is« Fig. 10. Stiffeners with Fillers Design of Plate and Box Girders 687 Stiffeners should always be placed at the ends of girders and directly over the edge of each support, as shown in Fig. 18, and wherever there are concentrated loads. On plate girders the stiffeners are always placed on each side of the web; on box girders on the outside only. The Bearing of Girders. This depends somewhat upon the character of the loading, but a safe general rule is to make the bearing of the girder beyond the edge of the support equal to one-half the depth of the girder. (3) The Number and Pitch of the Rivets, (a) Rivets m Web-Legs of Angles. It will readily be seen that when a plate or a box girder is loaded, the tendency of the bending moments is to cause the flange-plates and angles to SLIDE horizontally past the web; this tendency is resisted by the rivets which connect the angles with the web. The total amount of this tendency TO slide, called the horizontal flange-stress, between any section of the flange and the nearer end of the girder, is equal to the bending moment at that point divided by the depth oi the web.* The total number of rivets between that section and the nearer end must be such that their combined resistance to shearing or bearing, whichever has the lower value, shall equal this horizontal flange-stress at the section; or - . horizontal flange-stress , ^ number of rivets = :; ^ : ;^ — (5) bearmg or shearing of one rivet and the total number of rivets in the web-angle from end to end is twice this, or , , r . 2 X maximum bending momentf in foot-pounds , ^ total number of nvets = , — ■; — : — ;: : ;: : — (6) depth of web in feet X least resistance of one nvet If the number or rivets determined by formula (6) is such that they would be more than 6 in apart, then the number must be increased, as in ho case should they have a greater pitch than 6 in. (b) Rivets in Flange-Legs of Angles. With a single cover-plate. For girders with a single cover-plate, it is customary to put the same number of rivets in the flange-leg as in the web-leg for a distance'of 3 ft from the ends of the girder, staggering the rivets as in Fig. 15. Beyond that point to the middle of the girder one-half the number of rivets will be sufficient, provided this will not give them a greater pitch than 6 in. With two or more cover-plates. When two or more cover-plates are used, each plate must have sufficient rivets between the end of the plate and the point where its resistance is required, that is, for example, between a and b, Fig. 13, to transfer to the angle and flange-plates between, an amount equal TO the safe strength of the plate. From this point to the middle point of the girder, the rivets can be spaced according to the rule for the greatest pitch. (c) Rivets in Stiffeners. The spacing of rivets in the stiffeners is generally determined by the rules given for the pitch of rivets. Further explanation of the method of determining the spacing of rivets will be found in the following • examples. ' (4) The Approximate Weight of the Girder. In determining the size of a riveted girder to support a given load, it is desirable to be able to add to the * See Formula (i), page 683, and foot-note relating to it. M = SAd, and hence SA = M/d, SA being the total amount, in pounds, of the tendency to slide, and 5 being the horizontal unit, flange, fiber-stress in pounds per square in, due to flexure. A is the area in square inches of the cross-section of the flange and J" is the approximate depth of the girder. t Because the maximum horizontal flange-stress is equal to the maximum bending moment divided by the girder -depth, or SuxazA — Mma.x/d. 688 Riveted Steel Plate and Box Girders Chap. 20 superimposed load the weight of the girder itself, as this often forms a con- siderable part of the load to be supported. The following empirical rule* is often used to determine the approximate weight of a plate or box girder: Weight of girder between supports, in tons = Wl/ ^oo (7) in which W equals the load to be supported, in tons, and / equals the span, in feet. The constant 700 was determined for girders of from 35 to 50 ft long, but may be used without much excess for girders of shorter spans. (5) The Determination of the Lengths of the Flange-Plates. For the methods used to determine these, see the following examples. 4. Explanation of Tables The Calculations for the Design of Riveted Girders may be greatly facilitated by the use of Tables I, II, III and IV at the end of this chapter. Table I gives the sectional area that should be deducted for rivet-holes in plates of different thicknesses. In computing this table % in was added to the diameter of the rivet to allow for the injury to the metal caused by punching and also to allow for the expansion of the heated rivet. Table II gives the safe shearing value for web-plates for various depths and thicknesses, and the deduction to be made for each %-in or J^-in rivet. Table III gives the safe resistance to buckling per square inch of net section, and also the total safe resistance in pounds for the more common sizes of web- plates, with two rivet-holes deducted. It is very seldom that any vertical sec- tion between the stiffeners contains more than two rivet-holes. Tables giving the dimensions and properties of angles will be found in Tables XI and XII, pages 362 to 367, and the shearing value and bearing values of rivets are given in Tables II and III, pages 418 and 419. Table IV gives the elements of riveted plate girders of various depths, from which it is possible to select economical sections for almost any ordinary condi- jjipn of loading. 5. Examples of Plate and Box Girders Example i. It is required to support the floor over a room 50 by 64 it, by means of riveted steel plate girders, placed across the room, 16 ft on centers. The room above is to be used for general assembly purposes. The floor-joists are of wood and there is a plaster ceiling on the under side of them. The design of the girder is required. First Step. The Load. The first step is to determine the load to be supported by each girder. The floor-area supported by each girder is 50 by 16 ft, or Soo sq ft. The weight of the floor-construction between the girders will not be over 25 lb per sq ft, and an allowance of 100 lb per sq ft for the live load will be ample. The unit load, 125 lb X 800= 100 000 lb, or 50 tons, the load to be carried by the girder. To this should be added the weight of the girder itself. Substituting in Formula (7), the approximate weight of the girder = -: — = 3.57 tons, or about 7000 lb, 700 and the total load, in round numbers, is 107 000 lb. This, of course, is uni- formly distributed. • From "Compound Riveted Girders," by W. H. Birkmirc. Examples of Plate and Box Girders 689 Second Step. The Flange- Area. The next step is to determine the flange- area. Before this can be done, however, the width and depth of the girder must be decided. As it is desirable to keep the girder as shallow as possible, consistent with good engineering, the case will be considered an exceptional one and the depth of the wcb-plate will be made 36 in, which is about one- sixteenth the span and a little less than the usual hrait. As the girders arc braced sidewise by the floor-joists, it will not be necessary to make the width of the flange-plates one-twentieth the span of the girder, and it may be made 12 in width. The flange-area may be determined by Formula (i), page 683, and is A = Mru^^/dS a / . X maximum bending moment (ft-tons) or nange-area (sq m) = — — depth of web (ft) X ^ (tons per sq in) The maximum bending moment for a uniformly distributed load on a simple beam is Mm-Ax = Wl/S (Case V, page 326), or in this particular case, 53.57 tons X 50 ft/8 = 334-8 ft-tons. The value of 5 * has varied in the handbooks from 6 to 8 tons, depending upon varying conditions and upon the judgment of engineers. A value of 5 of 8 tons or 16 ooq lb per sq in is the requirement of the new New York Building Code, and of the codes of most cities. In this example 14 cxx) lb per sq in is assumed for S. Substituting this value in the formula gives for the net area of either flange, 334-8/(3 X7) = 16 sq in. The upper flange may now be designed. For a girder of this size and loaded in this way, it will be advisable to try two 5 by 3H by Mo-in angles, with the long legs horizontal. t The sectional area of these angles (Table XI, page 363) is 7.06 sq in which leaves 9 sq in for the area of the flange-plates. Dividing this by i2-in, the width of the flange, gives % in for the total thickness of" the plates, which may be made up of two %-m thick plates. Of course, any other combina- tion of plates and angles having an area of cross-section of 16 sq in will fulfill the conditions of the problem, the selection in all cases depending upon the judgment and experience of the designer. Note, also, that no part of the web has been included in the flange-area although it would be safe to include one- sixth of it. This also is a matter of individual opinion. As the lower flange is in tension, the rivet-holes should be deducted in order to obtain the net area. Assuming that ^4-in diameter rivets are used, it will be noted that the greatest loss of section is by two rivet-holes opposite each other, connecting the angles with the plates of the bottom flange. From Table I, page 702, the area of two %-in rivets in a %-in plate is 1.31 sq in, and in a Me-in plate, the same thickness as that of the angles, it is 0.76 sq in. The sum of these thicknesses is 2.07 sq in, which must be added to the net area of the upper flange-plates, 16 sq in, making 18.07 sq in for the gross area of the lower * See, in Chapter XV, paragraphs and foot-notes, page 603, relating to fiber-stresses for bending for riveted beam girders, etc. t For the flange-angles of plate girders the S by 33'i-in size is most commonly used, when the flange-plate is 12 in wide, and 6 by 4-in angles when the flange-plate is over 12 in wide. For box girders 5 by 4, 5 by 3^, 4^y 3V2 and 3H by 3H-in are common sizes;, while for very heavily 'loaded girders, requiring two rows of rivets in the web-leg, 6 by 6-in angles are often used. For most riveted girders, in which only one row of rivets is required, the short leg is riveted to the web, so as to bring most of the material as far from the neutral axis of the girder as possible. The minimum thickness of flangCrangles should be ^i in, and the maximum thickness for ordinary loads is H in. 690 Riveted Steel Plate and Box Girders Chap- 20 flange-plates. This additional area may be obtained by increasing the thick- ness of the plates to H in. The flanges will then be made up as follows: Upper flange: Two angles, 5 by 3^ by Me-in = 7.06 sq in, gross area Two plates, 12 by ^-in = 9.00 sq in. gross area Total 16.06 sq in. gross area Lower flange: Two angles,. 5 by sVz by Me-in = 7.06 sq in, gross area Two plates, 12 by J^^-in = 12.00 sq in, gross area Total = 19.06 sq in, gross area Third Step. The Length of the Flange-Plates. To determine this it is necessary to plot the bending-moment diagram shown in Fig. 12. The bending- Fig. 12. Diagrams for Bending Moments and Vertical Shears. n[t^ment diagram for a girder under a uniformly distributed load is bounded by a parabola having a height over the middle of the girder equal to the maximum bending moment. From the middle point C, of a horizontal line AB, at any convenient scale, lay off a vertical line CD, equal to the maximum bending moment, 334-8 ft-tons. Construct the parabola ADB (see page 79); then the bending moment at any other point, as E, is equal to the ordinate EF above that point, measured to the same scale. Examples of Plate and Box Girders 691 To find the theoretical length of the flange-plates of the lower flange, inclose the bending-momen} diagram in a rectangle and from any convenient point, such as C, lay off any line CG, equal to the total flange-area, 19 units in length, and at such an angle that the upper end G will lie on a horizontal line drawn through D. Divide the line CG into three parts. CH representing the sectional area of the angles, equal to 7 units, and /// and IG representing the sectional area of the two plates, equal to 6 units each. Draw horizontal lines through // and /; then the line J J will represent the theoretical required length of the second or upjx^r flange-plate and the line KK the length of the first or lower flange-plate. In practice, however, the plates are usually extended beyond the points / and K on each side as an additional factor of safety, a distance suffi- cient to take enough rivets to transmit at least one-third the resistance of the plate. It is also customary to make the first or lower flange-plate the full length of the girder as it greatly stiffens the angles and adds but a small amount to the cost. Theoretically the length of the flange-plates of the top flange would be less than the length of the plates of the lower flange, because the flange-area of the top flange is less than that of the lower flange; but they are usually made the same length. Fourth Step. The Web. Webs are proportioned to resist the shear. The maximum shearing-stress in a girder uniformly loaded is equal to either reaction, which in this case is one-half the total load, or 53 500 lb. As the girder is 3 ft deep, this small shear would require a very thin section, thinner than the min- imum thickness for webs, which is % in. From Table II, page 703, it is seen that the shearing resistance of a -H by 36-in web-plate is 135 000 lb, which is greatly in excess of the actual shear. Fifth Step. The Stiflfeners. As before explained, stiffeners will be required whenever the vertical shear exceeds the safe resistance of the web to buckling. The vertical shear is 53 500 lb and the resistance to buckling may be found from Table III, page 705. This, for a % by 36-in web with two %-iu. rivets is found to be 31 560 lb; hence stiffeners will have to be used. As stated under Buckling of Web, page 686, the spacing of stiffeners is more a matter of judgment and experience than of exact calculation, and for this a shear-diagram, also shown in Fig. 12, is of great assistance. It may be constructed as follows: On a horizontal line LM, lay off to any convenient scale vertical lines LN and MP, each representing 53 500 lb. Connect the points N and P; then the vertical shear at any point is equal to the ordinate at that point, measured to the same scale. Thus, at Xi, 3 ft from the left end, the shear is 47 500 lb, at X2, 6 ft from L, it is 40 500 lb, at X3, 9 ft from L, it is 34 000 lb and at Xi, 12 it from L, it is 27 500 lb. As the vertical shear at X3 is greater than the safe resist- ance to buckling and at A"4 less, it might be safe to stop the stiffeners at X4; but as the floor-joists are framed flush, or nearly so, with the top of the girder, and rest upon angles riveted to its web, it will be advisable to put about 3 stiffeners between A'4 and the corresponding point on the right-hand half of the girder. Additional stiffeners should be placed directly over each support, making 15 stiffeners on each side of the girder. These will be made of 4 by 4 by %-in angles. Sixth Step. The Number and Pitch of the Rivets. First, the number of rivets in the web will be considered. As a rivet is required at the end of each stiffener, it will be necessary to determine the number and spacing of the rivets between each pair of adjacent stiffeners. In the web, the rivets are in double, shear. In Tables II and III, pages 418 and 419, values are given based uponj unit shearing values of 7 500 and 10 000 and bearing values of 15000 and 18 Qoo lb per sq in. (See foot-notes with these tables.) The shearing resistance 692 Riveted Steel Plate and Box Girders Chap. 20 of a %-in rivet at lo ooo* lb per sq in is 4 420 X 2 = S 840 lb for double shear, and the bearing value of the same rivet in a ^^-in plate, at 20 000* lb per sq in, is 5 630 lb. As the bearing value is the smaller, it will determine the number of rivets required. The number of rivets from either end of the girder to any point depends upon the horizontal flange-stress at that point, and it has been shown that the flange- stress is equal to the bending moment divided by the depth of the web. (See foot-notes with Equations (5) and (6).) Scaling off the bending moment above the point Xi gives 75 ft-tons; hence the horizontal flange-stress is equal to 75/3 = 25 tons = 50 000 lb. The number of rivets required between this point and the left reaction is, from Formula (5), equal to 50 000/5 630 = 10 rivets, which are to be spaced in a distance of 36 in, making the spacing 3.6 in. Above X2 the bending moment scales 141.24 ft-tons, the flange-stress is 141. 24/3 = 47.08 tons, or 94 160 lb, and the number of rivets required between X2 and A is 94 160/5 630 = 17; but 10 of these are required between -Yi and A, leaving 7 to be placed between A'l and A'2 in a distance of 36 in making the spacing 5.1 in. At A's, the bending moment scales 197.4 ft-tons, and the flange-stress is 197.4/3 = 65.3 tons, or 130 600 lb. The number of rivets required is 130 600/5 630= 24, but 17 of these are required between X2 and A, leaving 7 to be placed between X2 and A3, making the spacing the same as in the second panel. At A'4 the bending moment scales 243.96 ft-tons, and the flange-stress is 243.96/3 =81.32 tons or 162 640 lb. The number of rivets required is 162 640/5 630= 30, but 24 of these are required between A3 and A , leaving 6 to be placed between A'3 and A'4 in a distance of 36 in, making the spacing 6 in. As this is the maximum spacing allowed, it will be used from Xa to the corresponding point on the opposite right-hand half of the girder. The same number of rivets will be used in the flange-legs of the angles as in the web-legs, but they will be spaced so that they will come between those in the web. The outer flange-plate scales 28 ft 6 in in length in the bending-moment dia- gram, but this length, as before stated, should be increased sufficiently to take enough rivets to transmit at least one-third of the resistance. The area of the plate is y2 in X 12 in = 6 sq in, minus the area of two %-in rivet-holes, 0.87 sq in (Table I, page 702), leaving a net area of 5.13 sq in. The resistance of the plate is therefore equal to 5.13 sq in X 14 000 lb per sq in = 71 820 lb. One- third of this, or 23 940 lb, must be transferred by rivets placed beyond the points //. As the rivets in the flange are in single shear, the shearing value of one rivet in single shear, 4 420 lb, will govern. The number of rivets re- quired, then, is 23 940/4 420 = 6, or 3 in each angle. The spacing of the rivets in this panel is 6 in. The plates will therefore be extended 18 in on either side of//. * The shearing value of rivets is taken at from 7 000 to 12 000 lb per sq in and the bearing value at from 12 000 to 24 000 lb per sq in. The usual values are 10 000 lb for shear and 20000 or 24 000 lb for bearing. Values of 12 000 lb for shear and 24 000 lb for bearing are the requirements of the New York Building Code A bearing value other than those of Tables 11 and III, pages 418 and 419, is purposely used in this example, as it is frequently necessary to use different unit stresses than those from which some particular table has been computed. If no other table is at hand for the values based upon some particular rivet bearing-stress. Tables II and III, pages 418 and 419, can be used and the new value found by proportion; or the bearing-stress can be found by multiplying the product of the diameter of the rivet and the thick - Bess of the web by the new unit stress. In this example, Table III, page 419, gives, for 18000 unit stress, 5060 lb for bearing; ^% of this gives 5622 lb for a 20000 unit stress. Also, H in by ^ in by 20000 lb persqin =5625 lb. Examples of Plate and Box Girders 693 splices. As the total length of the girder is but 53 ft, it will not be necessary to splice the webs or the flanges, because the extreme length of a H by 36-in plate is no ft and of a 12 by H-in plate, 90 ft.* It is never necessary to splice angles as they are rolled in lengths up to 90 ft. In very long, deep girders, however, it is sometimes necessary to splice the web, and the joint is sometimes made at the middle, as theoretically there is no vertical shearing-stress in the web 0,00. 00 0,0, 0,0 0,0 0.0,0 0,0 b ' ' ' ' ' L- ' ' • d Fig. 13. Splicing of Inner Plate of Bottom Flange of Plate Girder. Example i at that point when the load is uniformly distributed. Gerterally, however, the web is spliced in two places, equidistant from the middle of the girder. The splice is calculated for vertical shear only, the rule being to divide the shear at the splice by the safe shearing value or bearing value of one rivet. This gives the number of rivets required on each side of the splice-plate, unless the maximum pitch is exceeded, when more are added. oooooiooooo 00 Ooo|00000 00000 00000 00 ooooo 00 Fig. 14. Plan of Splice-plate. Example i Whenever a splice is required in a flange-plate, it should be, if possible, at a point just beyond the end of the plate above it. The joint must be made by riveting to the spliced plate, a plate of the same thickness and of sufficient length to receive a number of rivets on each side of the joint equal to the strength of the plate that is spliced. When the flange is made up of two plates of the same thickness, the simplest method of splicing the inner plate is as shown in Fig. 13. IB Fig. 15. Elevation of Part of Plate Girder. Example i Let e denote the theoretical position of the end of the outer plate, as determined by the bending-moment diagram, and a the point to which the plate must be extended to receive rivets of a resistance equal to one-third the strength of the plate. Then let the joint in the inner plate be just over a and extend the outer plate to b, or such a distance that it can receive a number of rivets equal in resistance to the strength of one plate. * Tables of extreme lengths are published in the various handbooks. The above dimensions, for example, are taken from the table en page iii of Carnegie's Pocket com- panion. 694 Riveted Steel Plate and Box Girders Chap. 20 Fig. 16 shows one end of the girder, drawn according to the foregoing calcu- lations. The Bill of Quantities for the Girder. A B CD r /^^ K-5'3- f<3'0- Pi rr^ rt\ '6->|^104<-4: 1?« r^ 4'2'l(>H-4' Giitler r\ - 4'll"->i f?4 -2410- Fig. 16. Box Girder Supporting Example 2 Brick Wall. The following is a bill of quantities ^ for the construction of this girder. Load: 100 000 lb, uniformly distributed. Span 50 ft. Depth 3 ft Upper flange: Two angles, 5 by 3H by Me in, 53 ft long One plate 12 by ^ in, 53 ft o in long One plate, 12 by H in, 31 ft 6 in long Lower flange: Two angles, 5 by 3^^ by Ms in, 53 ft long One plate, 12 by H in, 53 ft o in long One plate, 12 by H in, 31 ft 6 in long Web: One plate, 36 by % in, 53 ft o in long 30 stiffeners, 4 by 4 by %-in angles, 2 ft 11 in long 30 filler-plates, 4 by \^ in, 29 in long 92 ft 8 in of 4 by 4 by Vz-in angles for sup- porting floor-joists Rivets: Yi in in diameter Example 2. The wall shown in Fig. 16 is to be supported by a riveted-steel box girder at the height indicated. It is re- quired to design the girder. First Step. The Load. The first step towards designing the girder is the de- termination of the load. The space under the lower windows is too small to dis- tribute the weight from the piers uniformly over the girder, so that the only safe assumption is that the weight of the wall between the lines A and B is concen- trated at Pi, the weight of wall between lines B and C at P2 and so on. The floor-joists run across the building, so that only the weight of the wall will be supported by the girder. Allowing 200 lb per square foot of face for the 21-in wall, and 165 lb for the 17-in wall, both walls being plastered on the inside: Load at Pi ils' 3" X 10' - 7' X 2' 3'1 X 200 = Is' 3" X 40' - (2' 3" X 14' + 3' 2" X 7')1 X 165 = . 7350 . . . 25 795 I = 33 145 lb Examples of Plate and Box Girders 695 Load at P2 [7'4"Xio'-4'6"X7'o"]X20o= ^ 366 ( _ [7'4"X 4o'-(4'6"X 14'+ 4' 9"X 7')] X 165 = 32 354 } ~ 4072om Load at Pz = that at Pa = 40 720 lb Load at P4 i"X 10'- 2'3"X7']X200 = ^ ^^^ I =^0 27R lb i"X4o'- (2'3"X i4'+3'2"X7')]X 165= ....23595 ) ______ Total load on girder = 144 863 lb or 72.4 tons From Equation (7) approximate weight of girder = = !' _ H4' 1 Wxl 72.4X24)^ ., ^ = 2.5 tons, or 5 000 lb 700 700 About one-third of this, or say i 600 lb, should be added to P2 and Pz, and 900 lb to P\ and P4. This will give, approximately, the following loads, applied as in Fig. 17: P\ = 34 000 lb P2 = 42 300 lb Pz = 42 300 lb P4 = 31 200 lb P3 m — ^'^'' T ^ ''^' — ^ Li ML .--^y /\ I Fig. 17. Diagram for Bending Moments. Example 2 Second Step. The Determination of the Maximum Bending Moment. By means of the formula under Case VT, page 327, the maximum bending moment in foot-pounds for the loads are found to be as follows: 17 D ir 34000X i'6"X23'4" o ,, ,, For Pi, Af max = T~~T, = 47 980 ft-lb For P2, Mmax For P3, ilf max For P4, If max 24' 10" 42 300X8^ 11^^X15' 11'' 24' 10" 42 300 X 16^ 3'' X 8^ 7^^ 24' 10" 3i200Xi'4''X23'6^^ 24' 10" = 242 000 ft-lb = 237 900 ft-lb = 39 420 ft-lb Plotting these moments to a scale, as explained for Fig. 15, page 329, the bending-moment diagram shown in Fig. 17 * is obtained. The maximum bend- * The bending moments in this diagram are drawn to a scale of about 400 000 ft-lb to one inch. 696 Riveted Steel Plate and Box Girders Chap. 20 ing moment is at P2, over the longest ordinate bb and where the vertical shear is zero, and is equal to the length of the ordinate bb, which scales 418 000 ft-lb, or 209 ft-tons. Third Step. The Determination of the Flange- Area and the Length of the Cover-Plates. Before these can be determined, the depth of the web-plate must be decided. As there is nothing to limit the depth of the girder, it will be made about one-tenth of the span, or 30 in. Then by Formula (i), page 683, A = Mma.\/dS, and using 14 000 lb or 7 tons per sq in for S, the gross area of upper flange = 209/2.5 X 7 = 12 sq in As the thickness of the wall to be supported is 21 in, the flange-plate must be at least 20 in wide and not less than 9i in thick. The sectional area of a % by 20-in plate is 7'/^ sq in, leaving ^Vi sq in to be made up by the angles. The sectional area of two 5 by sH by Me-in angles is 7.06 sq in (Table IX, page 363), which leaves a small excess for the lower flange. For rivets % in in diameter, the loss in area due to two rivet-holes in a -^i-in plate is (Table I, page 702) 0.65 sq in and in a Mo-in plate, the thickness of each angle, 0.76 sq'in, making 1.41 sq in in all, for which the excess in the angles is more than suffi- cient. The width of the flange being more than one-twentieth the span makes lateral support unnecessary. Fourth Step. The Webs and Stiffeners. The maximum shear is equal to the maximum reaction which in this case is obviously equal to the left reaction. Taking the center of moments at the right reaction, the equation of moments is, RiX 24.83'= (17 tonsX 23.33') + (21.15 tonsX i5-9i') + (21.15 tonsX 8.58') + (15.6 tons X 1.33') whence 24.83 xRi= 935-3215 ft-tons and Ri = 37-669 tons, or 75 ssS lb. Note that the bads have" been changed from pounds to tons, for convenience in mak- ing the calculations. As this box girder has two webs, the maximum shear in each web will be 37 669 lb. The thinnest web permissible is ^i in thick. From Table IT, page 703, the resistance of a % by 30-in web-plate to shearing is I T 2 500 lb, so that the webs are amply safe in resisting vertical shear. From Table III, page 705, the safe resistance to buckling, deducting for two %-in rivets, is S3 830 lb. As this is less than the maximum shear, stiffeners will be used, placed 2 ft 4 in from each support, with Ave between them, making the spacing about 3 ft 4 in on centers. Two others will be placed over each support. 4 by 4 by ^-in angles. will be sufficient for the stiffeners. Note. If the loads were really concentrated at the points Pi, Pi, etc., as from columns or girders, it would be necessary to place stiffeners at each one of these points and two in each of the intermediate spaces, but as the pier- loads are partly distributed it will be better to space them as first planned. Fifth Step. The Number and Pitch of the Rivets. The rivets in the web- legs and flange-legs of the angles are in single shear. From Table III, page 419, the shearing value of a %-'m rivet in single shear at 10 000 lb per sq in is 4 420 lb, and the bearing value in a ^i-in plate at 18 000 lb per sq in is 5 060 lb. Hence the shearing value will govern. The number of rivets required depends upon the flange-stress, which is equal to the maximum bending moment divided by the depth of the girder. (See Formula (i), page 683.) The bending moment at Pi, found by moments or graphically by scaling off the ordinate aa, Fig 17. is 56.5 ft-tons.* This, divided by the depth 2.5 ft, gives 22.6 tons, * This may be found, also, by taking Pi as the center of moments and multiplying -^1 = 37-669 tons by the lever-arm 1V2 ft. The result is 56.5 ft-tons. The bending moments at the other loads may be determined by taking, in each case, the algebraic sum of the moments of the external vertical forces on either side of each point considered. Examples of Plate and Box Girders 697 or 45 200 lb, for the flange-stress, or 22 600 lb for each web. The number of rivets, therefore (Formula (5), page 687) is 22600/4420=6. The distance from Pi to the left reaction is 18 in, which makes the spacing 3 in. The flange-stress at P2 is 209.88 ft-tons/2.5 ft = 83.95 tons, or 167 900 lb, and oiTe- half of this is 83 950 lb. The number of rivets therefore is 83 950/4 420 = 19. But 6 of these are required between Pi and the left reaction, leaving 13 to go between Pi and P2, a distance of 89 in, making the [)itch about 6.9 in. As this exceeds the maximum allowable pitch, the rivets will be spaced 6 in on centers between Pi and Pi, and between Pi and Ps. The spacing on the right- hand end of the girder will be made the same as that on the left. Some details of the girder are shown in Fig. 18. 0^ 'o'^o^o^ol t)^o'"o'"o"o'-o ["cT-Tr 0000 5_/a Q C\ 4 ^nOn°r.Or.O.^° 0^o|Po']opD' O O o C o o o o o o 000 Fig. 18. Elevations and Section of Box Girder. Example 2 The Details and Bill of Quantities for the Girder. The loads, dimensioiw, size, number of pieces, etc., for the girder are given in the following summary: Loads: 34 000 lb, i ft 6 in from left support. Span: 24 ft 10 in 42 300 lb, 8 ft II in from left support. Depth: 30 in 42 300 lb, 8 ft 7 in from right support 31 200 lb, I ft 4 in from right support Both flanges: Four angles, 5 by z\^ by Yxa in, 27 ft 6 in long One plate, 20 by % in, 27 ft 6 in long Two webs: % by 30 in, 27 ft 6 in long Twenty-two stiffeners: 4 by 4 by % in, 29H in long Twenty- two filler-plates: 4 by Me in, 23 in long Rivets: % in in diameter Example 3. What are the dimensions of a box girder, 40 ft in span, required to support the following loads? 90 tons from a column, 8 ft from the left support; 75 tons from a column, 12 ft from the right support; and a masonry pier, 10 ft in length, beginning 10 ft from the left support and weighing 4 tons per running ft. (See Fig. 19.) First Step. The Determination of the Reactions, Shears and Bending Mo- ments. To find either reaction, the center of moments is taken at the other reaction. The equation of moments for the left reaction is, therefore, taking the center of moments at the right reaction, 40 Ri = (90 tons X 32 ft) -f- (40 tons X 25 ft*) -\- (75 tons X 12 ft) from which 4o7?i = 4 780 ft-tons and R\= 119.5 tons ♦ In considering the moments of forces, distributed loads are treated as if they were concentrated at their centers of gravity. Riveted Steel Plate and Box Girders Chap. 20 In like manner, the equation of moments for the right reaction is 40 R2={75 tons X 28 ft) + (40 tons X 15 ft) + (90 tons X 8 ft) from which 40 i?2 = 3 420 ft-tons, and Rz = 85.5 tons The greatest vertical shear Vi is equal to the greater reaction, which is 119.5 tons. The shear-diagram (Fig. 19) may be constructed by laying off at Fig. 19. Elevation of Box Girder and Diagrams for Bending Moments and Vertical Shears. Example 3 any convenient scale an ordinate equal in length to 119.5 tons. Immediately at the right of point i, under the left column, the shear is equal to 119.5 — 90 = 29.5 tons. It is the same at point 2, the left end of the wall. At point 3, the right end of the wall, the shear is 1 19.5 - 90 - 40 = - 10.5 tons, showing that the shear passes through zero somewhere between 2 and 3, which is the point of maximum bending moment. This point, X, is by scaling the shear-diagram, 17.4 ft from Ri. It is over the point of intersection of the slanting line ia Examples of Plate and Box Girders 699 the shear-diagram, with the horizontal line of reference. This slanting line is drawn from the top of the shear-ordinate for point 2 to the bottom of the shcar-ordinate for point 3. Just at the right of point 4, the shear is 119.5 — 90— 40— 75 = — 85.5 tons, the same as the right reaction. The point X, of no shear and maximum bending moment, may be found, also, as follows: At the left of point 2 the shear is 29.5 tons. One foot to the right of 2 it is 29.5 tons— 4 tons= 25.5 tons. Two feet to the right of 2 it is 29.5— 8 tons = 21.5 tons, etc. Therefore, since the shear decreases at the rate of 4 tons per . foot, it will be zero at 29.5/4 or 7,4 ft at the right of 2, or 17.4 ft from Ri. The maximum bending moment is at A^, the point of no shear. The equation of moments, considering the forces to the left of X, is 1/max = (119-5 tons X 17-4 ft) - (90 tons X 94 ft) - (4 tons X 74 ft X 74 ft/2) 7.4 ft/2 is the distance from X to the center of gravity of the wall-load to the left of X, and is the lever-arm of that load, considered as a vertical downward force concentrated in a single line of action. Hence if max = 2 079.3 - 846 - 109.5 = I 123.8 ft-tons The bending-moment diagram may be constructed by laying off at X, at any convenient scale, an ordinate XC equal to i 123.8 ft-tons in length. It is neces- sary to find the bending moment at other points, since the bending-moment diagram cannot be plotted,, as in the previous examples, because the uniform load is not distributed over the entire girder. The other critical points are i, 2, 3 and 4. Ml = (119.5 tons X 8 ft) = 956 ft-tons 3/2= (119.5 tonsX 10 ft) — (90 tonsX 2 ft) = i 015 ft-tons Ms = (119.5 tons X 20 ft) — (90 tons X 12 ft) — (40 tons X 5 ft) = i no ft-tons Mi = (119.5 tons X 28 ft) — (90 tons X 20 ft) — (40 tons X 13 ft) = i 026 ft-tons By laying off ordinates at these points equal by scale to the respective bending moments; drawing straight lines from R to A, the extremity of the ordinate through I, and from A to B; drawing curved lines from B through the points C and D; and connecting D and E and E and R2 by straight lines; the bending- moment diagram R1ABCDER2 may be constructed. Second Step. The Webs. As stated on page 683, it is considered safe by many engineers to include one-sixth of the web-area in the flange-area, and this will be done in this example. The web, therefore, must be designed first. As there is nothing to limit the depth of the girder, it will be made 3 ft deep, about one-twelfth the span. The greatest vertical shear is equal to the greater or left reaction, 119.5 tons. Since the girder carries a brick wall, it must be of the box type, and hence the vertical shear on each web is 59.75 tons. A ]r^ by 36-in web will be tried first. Its area is 18 sq in, from which must be deducted the loss in area due to the rivet-holes for the rivets through the stiff eners. The rivets will be placed the maximum distance on centers, making six in each stiffener. Because of the concentrated loads near the reactions more rivets will be required, and in order to avoid a close spacing, %-in rivets will be used. From Table I, page 702, the sectional area to be deducted for a ^^-in rivet in a ^^-in plate is 0.50 sq in; hence the net area of the web is 18 — (6 X 0.50) =15 sq in, and its shearing resistance, at 10 006 lb or 5 tons per sq in (Table II, page 703), is 15 X 5 tons= 75 tons, which is 15.25 tons in excess of the 59.75 tons required. Third Step. The Flange-Area. From Formula (i), page 683, the flange area, A = Mmtix/dS =• ^-^ = 53.5 sq in 3X7 700 Riveted Steel Plate and Box Girders Chap. 20 As the girder ha? no lateral support, the flange-width should be not less than one- twentieth the span, which will make it 2 ft. The upper flange may be proportioned as follows: One-sixth of net section-area of two webs = 5 . 00 sq in Two 5 by 5 by ^ie-in angles,* with section-area = 10.62 sq in Three %& by 24-in plates, with section-area of 13.50 sq in each = 40. 50 sq in Total section-area of upper flange = 56 . 1 2 sq in To proportion the lower flange, allowance must be made for the loss in area due to two rivet-holes. From Table I, page 702, the area of two %-in rivet-holes in a yia-in plate (thickness of angles) = i . 12 sq in Areat of two rivet-holes in three -^i-in flange-plates =. . . 3 . 75 sq in Total rivet-area = 4 . 87 sq in Hence the gross section-area of the lower flange must be 53.5 + 4-87= 58 sqin. This may be made up of One-sixth of net section-area of two webs = 5.0 sq in Two 5 by 5 by YiQ-in angles, with section-area = 10.62 sq in Three H by 24-in plates, with section-area of 15 sq in each = 45 . 00 sq in Total section-area of lower flange J = 60.62 sq in The length of the flange-plates is determined from the bending-moment diagram. Draw a horizontal line through C (Fig. 19) and at any point, as 3, lay off to any convenient scale and angle, a line 3 // = 60.62 units in length, with its upper extremity on the horizontal line FG drawn through C. Divide this line into five parts: 3 /, containing 5 units for the web-area; //, 10.62 units for the angles; and JK, KL and Z,// of 15 units each, for the three plates. Draw horizontal lines through the points 7, /, K and L as shown. The horizontal intercepts of these horizontals in the bending-moment diagram will give the theoretical lengths of the flange-plates. For practical considerations, the inner plate is always carried the full length of the girder and the other plates are ex- tended beyond the intersection-points on either side, a distance sufficient to take enough rivets to transmit at least one-third of the resistance of the plate. The resistance yl 5, of the outer plate is 15 sq inXT4ooolb per sq in =2 10 000 lb. One-third of this, or 70000 lb, must be resisted by rivets placed beyond the points A A. From Table III, page 419, at 10 000 lb per sq in, the shearing value of a J^-in steel rivet in single shear is 6 010 lb and in a ^-in plate its bearing value at 18 000 lb per sq in is 9 820 lb. Hence the number of rivets required is 70 000/6 010 = 12, or 6 on each side. With a 2-in pitch this would lengthen the plate 12 in at each end. The' outside plates in this particular girder would be extended far enough to pass beyond the bise of the column on the left side of the girder. * Angles with equal legs are selected because the same number of rivets will be re- quifecl in both legs, as they are all in single shear, and large angles are selected because the rivets will have to be staggered, owing to the concentrated loads being placed so near the ends of the girder. t Since ^le-in plates are selected for the upper flange, it is reasonable to suppose that ^i-in plates will be necessary for the lower flange. X Both flange-areas are made slightly in excess of the requirements, because in this example one-sixth of the web-area is included. Examples of Plate and Box Girders 701 Fourth Step. The Stiffeners. From Table III, page 705, the safe buckling value of a ^^ by 36-in plate with two ^6-in rivets is 62 320 lb, and as this is much less than the shearing value, stiffeners must be used. The stiffeners under the concentrated loads may be considered as short struts in direct com- pression. Assuming that 4 by 4 by H-in angles are used for the stiffeners, the safe load from Table XV, page 502, is over 20 tons. The greatest concen- trated load is 90 tons, and hence four stiffeners will be placed under each column. Four more will be placed at each bearing, as shown in Fig. 19, four on each side, between the columns, about 4 ft on centers; and two on each side, between the columns and the bearings, making 15 on each side, or 30 in all. Fifth Step. The Number and Pitch of the Rivets. In a box girder, the rivets are in single shear. The shearing value of a ^i-in rivet at 10 000 lb per sq in is, from Table III, page 419, 6 010 lb, and its bearing value at 18 000 lb per sq in, in a Yie-in plate, the thinnest outside plate, is 6 880 lb; hence the shearing value will govern. The number of rivets depends upon the horizontal flange-stress, which is equal to the maximum bending moment divided by the depth of the girder (Formula (i), page 683). 3/ at i = 956 ft-tons, and the horizontal flange-stress = 956/3 = 319 tons, or 638 000 lb. From Formula (5), page 687, the number of rivets required = 638 000/6 010 = 106, or 53 on each side. These are to be spaced in a distance of 8 ft, or 96 in, which makes the pitch about i .8 in. As this is less than the minimum pitch, 2^i in, or three diameters, the rivets will have to be staggered. Hence the justification for selecting large angles with, equal legs for this paricular girder. _ At X the horizontal flange-stress =j I 123.8/3 = 374.6 tons, or 749 200 lb, and the number of rivets is 749 200/6 oio; = 124, or 62 on each side; 53 of these, however, are required between Ri and i, leaving 9 to be placed between i and X, a distance of about 9 ft. As the re- sulting pitch will exceed the maximum pitch, they will be placed 6 in on centers between i and X. At 4 the horizontal flange-stress = i 026/3 = 342 tons, or 684 000 lb. The number of rivets is 684 000/6 010 = 112, or 56 on each side, to be spaced in a distance of 12 ft, or 144 in, making the spacing 2.5 in. Be- tween 4 and X the maximum pitch will be determined as before. Sixth Step. The Weight of the Girder. So far, no account has been taken of the weight of the girder. The practice is to neglect this weight when the max- imum bending moment due to it alone is less than 10% of the maximum bend- ing moment due to the loads. From Formula (7), page 688, the weight of the girder = 205 X 40/700 =12 tons. From Case V, page 326, the maximum bend- ing moment due to it = 12 X 40/8 = 60 ft-tons. As this is much less than 10% of I 123.8 ft-tons, the maximum bending moment due to the loads, it may be neglected. Had it been otherwise, the weight would have to be considered as an additional uniformly distributed load over the entire girder and a new bend- ing-moment diagram drawn. Other Data on Riveted Girders. By applying the principles illustrated in the preceding examples it is possible to compute the necessary dimensions and details for riveted girders under any conditions of loading. If further examples are desired, the reader is referred to " Compound Riveted Girders," by WilHam H. Birkmire, in which different examples of loading are fully worked and ex- plained, and also to other recent treatises on this subject. Detail Drawings and Stress-Diagrams of one of the earlier heavy plate girders used in building-construction are published in the Engijieering Record of Dec. 28, 1895. This girder is one of six plate girders used in the construc- tion of Tremont Temple, Boston, Mass., Blackall & Newton, architects. The girder is 75 ft long between centers of columns, 6 ft i in deep, with flanges 28 in 702 Riveted Steel Plate and Box Girders Chap. 20 wide, and is calculated to support distributed and concentrated loads aggre- gating 497.5 tons. The single web-plate is 64% in deep, and "A in thick at the ends; the flanges are 4y2 in thick at the middle of the girder; and the flange- angles are 6 by 8 by i in. Since that time there have been erected for many of the large buildings a number of riveted girders of very great size and strength, and details of their construction may be found in the engineering and architec- tural periodicals. 6. Tables Used in the Design of Plate and Box Girders Tables T, II, III and IV contain data usually reciuired for the design of plate and box girders to satisfy all but the most unusual conditions. Table I.*t Sectional Area in Square Inches to be Deducted from Plates and Angles for Rivet-Holes Taken % inch in excess of diameter of rivet J Number of rivets, i in Number of rivets, li in Thickness diameter diameter of plate, in I 2 3 4 1 2 3 4 I 1. 12 2.25 3.37 4.50 1. 00 2.00 3.00 4.00 1^6 1,05 2.10 3.16 4.21 0.94 1.87 2.81 3.75 % 0.98 1.97 2.9s .3.93 0.87 I.7S 2.62 350 m6 0.91 1.83 2.74 3.65 0.81 1.62 2.44 3.25 H 0.84 1.69 2.53 3.37 0.7s I. SO 2.25 3.00 • iHe 0.77 1.55 2.32 3.09 0.69 1.37 2.06 2.75 % 0.70 1. 41 2. II 2.81 0.62 1.25 1.87 2.50 916 0.63 1.26 1.90 2.53 0.56 1. 12 1.69 2.25 H 0.56 I. II 1.69 2.25 0.50 I. 00 1.50 2. CO Me 0.49 0.98 1.47 1.97 0.44 0.87 1. 31 I 75 % 0.42 0.84 1.26 1.69 0.37 0.75 1. 12 1.50 Ni mber of rivets, ?l in Nur nber of rivets, % in Thickness diameter diameter of plate, in I 2 3 4 ' 2 3 4 I 0.87 1.75 2.62 3. SO 0.75 1.50 2.25 3.00 15/16 0.82 1.64 2.46 3.28 0.70 1.40 2. II 2.81 % 0.77 I. S3 2.30 3.06 0.65 1.31 1.96 2.62 1^0 0.71 1.42 2.13 2.84 0.61 1.22 1.83 2.44 H 0.66 1. 31 1.96 2.62 o.s6 1.12 1.69 2.25 1M6 0.60 1.20 1.80 2.40 0.51 1.03 1.54 2.06 H 0.5s 1.09 1.64. 2.19 0.47 0.94 1. 41 1.88 Yie 0.49 0.98 1.48 1.96 0.42 0.84 1.26 1.69 H 0.43 0.87 1. 31 I.7S 0.37 0.75 1. 12 1.50 Me 0.38 0.76 1. 15 I. S3 0.33 0.66 0.98 1. 31 % 0.32 0.6s 0.98 1. 31 0.28 0.56 0.84 1. 12 Me 0.27 0.55 0.82 1.09 0.23 0.47 0.70 0.94 K 0.22 0.44 0.66 0.87 0.18 0.37 0.56 0.75 * For explanation of tables, see Subdivision 4, page 688. t This table is taken from "Comiwund Riveted Girders," by W. H. Birkmire. I See paragraph, Punching Rivet-Holes, page 414, and Table XI, page 400. Tables Used in the Design of Plate and Box Girders 703 Table II.* Safe Shearing Value of Web-Plates in Pounds Mild steel. Gross area. Safe unit stress, lo ooo lb per sq in Depth, in Thickness in inches % Me H ViO % H ^ 28 30 32 36 40 42 46 48 105 000 112 500 120000 135000 150000 157500 172500 180 000 122 500 131 300 140000 157 500 175000 183800 201 300 210 000 140 000 150 000 160000 180 000 200 000 210 000 230 000 240 000 157500 168800 180 000 202 500 225 000 236 300 258800 270 000 175000 187500 200 000 225 000 250000 262 500 287 500 300 000 210 ooo 225 000 240000 270 000 300 000 315000 345000 360 000 245000 262 500 280 000 315000 350 000 367500 402 500 420 000 Deductions in pounds for one %-in rivet f 3200 3800 4300 4900 5500 6600 7700 Ded actions in ] X)unds for one }i-in rivet t 3700 4400 5000 5600 6 200 7500 8700 * For explanation of tables, see Subdivision 4, page 688. t The area of the hole is taken ^i in in excess of the diameter of the rivet to allow for injury of the metal sustained by punching. Example 4. What is the safe shearing value of a 36 by H-'m wel>-piaie with seven H-in rivets in the stifleners? Solution. The gross shearing value = 135 000 lb The deduction for seven rivets =7X3 200 = 22 400 lb The safe shearing value =112 600 lb To use this table for any other unit stress, divide the shearing value by 10 000 and multiply by the given unit stress. For example, what is the safe shearing- value of a 40 by %-in web-plate at 12 000 lb per sq in? (250 ocx)/io) X 12 = 300 000 lb. Tables of Riveted Steel Plate Girders.t It is not practicable to give TABLES OF SAFE LOADS for riveted steel plate girders because of the great variety of combinations of plates and angles that can be selected for any given condition of loading. Moreover, any variation in the loading would make the tables use- less. In place of the safe loads, therefore, the properties or elements of RIVETED STEEL PLATE GIRDERS are given in Table IV, pages 706 to 716, which will aid in determining the size of the girder and the approximate thickness of the plates and angles for any special case. To determine the dimensions and other details of a girder suitable to carry any specified loading, determine the MAXIMUM END-REACTION in pounds and the maximum bending moment in inch- pounds. Select from Table IV the different parts for a girder of the required DEPTH, a THICKNESS OF WEB as determined by the maximum end-reaction and a suitable section-modulus as determined by dividing the maximum bending t For tables of riveted single-beam girders and double-beam girders, see Tables XIV and XV, pages 605 to 611. 704 Riveted Steel Plate and Box Girders Chap. 20 moment by the permissible unit stress for flexure in pounds per square inch. The spacing of the rivets, the number and position of the stiffeners, the LENGTH OF THE FLANGE-PLATES, if more than one are needed, and the loss IN FLANGE-AREA and WEB-AREA due to the punching of the rivet-holes, must be determined in each case by the rules already given. The weights of the rivets and stiffeners are not included. As an illustration of the use of these elements or properties, in Example (i) the total losui on the girder is 107 000 lb, making each end-reaction 5,5 500 lb. The maximum bending moment is 334.8 ft-tons, or 8 035 000 in-lb. The section- modulus //c = MAS' = 8035000/14 000= 574. The depth of the girder is limited to 36 in. Looking up the properties of 36-in girders in Table IV, page 709, it is seen that a %-in web is more than sufficient to resist the end- reaction. The nearest section-modulus to 574 is 567.2, that of a girder com- posed of a 36 by Me-in web, 5 by sV^i by ^'2-in angles, and 12 by H-in flange- plates. In working out the problem in detail it was found that the girder required 5 by sV^ by ^e-in angles and two 12 by yz-'m flange-plates to com- pensate for the loss of area due to the punching of the rivet-holes. (See pages 219 and 710.) Table IV is based upon an extreme fiber-stress for flexure of 16 000 lb per sq in, and gross sections are used in determining the values given. The attention of readers is called to the two methods of plate and box-girder design: (i) the oni^ using the plate-girder formula (page 683), and (2) the one using the section- modulus (pages 703 and 704, and 706 to 716). It is customary, also, to take into account the tendency of the compressing-flange of the girder, if long between lateral bracings, to buckle or fail as a column; and the permissible reduced flange- stregs is determined by column-formulas. Tables Used in the Design of Plate and Box Girders 705 Table III.* Safe Buckling Values of Web-Plates SAFE UNIT BUCKLING VALUE IN POUNDS PER SQUARE INCH Calculated by formula f Sb = ■ I +- 3000/2 ' Sb = safe buckling resistance in pounds per square inch; d = depth of web between flatige-plates in inches; / = thickness of web in inches in the clear Depth, in Thickness in inches ■K ha 'A Vie % % H 28 30 32 36 40 42 48 3498 3192 2889 2456 2087 1930 1548 4 228 3896 3624 3069 2696 2 455 1994 4890 4546 4228 3666 3 191 2983 2543 5476 5 133 4787 4229 3724 3498 2918 5932 5656 5 339 4748 4 228 3992 3371 6522 6226 5656 5 133 4889 4228 6 920 6392 5882 5649 4992 TOTAL SAFE RESISTANCE IN POUNDS FOR PLATES WITH TWO %-IN RIVETS Depth, in Thickness in inches H Me K> 80880 81 560 81 500 79190 75 920 % . % % 28 30 36 42 48 34 450 33830 31560 29 140 26860 48 580 48 150 46 000 43 230 40360 64 200 64 230 62800 60 040 58820 97340 99880 loi 750 100 440 97450 138 200 145 300 147 600 146 670 191 570 198960 202 000 TOTAL SAFE RESISTANCE IN POUNDS FOR PLATES WITH TWO ^^-IN RIVETS Depth, in Thickness in inches Vs Vi6 ¥2 9^6 % % % 28 30 36 42 48 34 TOO 33510 31 310 28 950 26 700 48 I TO 47720 45660 42960 40 140 (>3 570 63 640 62 320 59660 58490 80 100 80840 80900 78700 75520 96 390 98980 ICO 690 99 800 96910 136960 144 230 146 690 145 860 190 170 197 710 200930 * For explanation of tables, see Subdivision 4, page 688. t See in Chapter XV the paragraphs and foot-notes, pages 568 and 569, relating to the web-buckling of I-beams. The formula for the above table is the formula that was used in the Passaic Steel Company's Manual, and as the values computed by it vary but little from those deduced by the Cambria formula, Table III is retained as it is. See, also, page 686. paragraph relating to Safe Resistance of Web to Buckling. Riveted Steel Plate and 'Box Girders Table IV.* Elements of Riveted Plate Girders ^ ^ W "T" To determine the details of construction of a girder suit- able to carry any specified loading, determine the maxi- mum end-reactions in pounds and the maximum bending moment in inch-pounds Select from the table a girder having the desired depth, St thickness of web as determined by the maximum end- reaction and a suitable section-modulus, determined by dividing the maximum bending moment by the permissi- ble unit bending fiber-stress in pounds per square inch For limiting conditions, see the pages 702 to 705 and the first three subdivisions of this chapter Weights given do not include stiffeners, rivet-heads, or other details Section- modulus, axis, i-i, in3 242.0 270.9 306.1 343.6 378. 5 414. 1 151. 5 176.8 186.6 201.2 219.6 252 . o 260.7 341 5 354.4 377.4 386.1 415.2 435.1 454-5 479.3 526.1 569-9 613.9 200.4 233.4 233. 5 265.8 274-5 314.8 Web- plate, 24X% 26XM« 26X5s 26XIU Sizes Flange- angles, SX3>^XH 5X3^X5^ 5X31/^X1/2 5X3K2XH 4X3 XH 5X31/^X^6 4X3 XH 6X4 X% 5X3I/2XM2 6X4 XV2 SXsJ'^X^i 6X4 XH 6X4 X3/i 5X3y2XH 6X4 XH 5X3i^iXV2 6X4 XI/2 5X3I/I2XH 6X4 XK2 6X4 XH 6X4 XH 6X4 XVi 4X3 XV2 4X3 XH 5X3^/^X^2 6X4 XH 5X3HXH 6X4 XH Flange- plates, 12X3/8 12XH 12X/2 12X58 I2XH UXH i2XK> 14 XH 12XH 14 XH I2XH uXH 14XH I4XM I4XK Weight per foot Web- plate and flange- angles, lb 97.8 72.2 72.2 85.0 85.0 97.8 61.6 69.2 72.0 76.8 82.0 92.4 94.8 82.4 127.6 87.6 82.4 87.6 98.0 100.4 98.0 113. 2 113. 2 127.6 83.1 93.1 93.1 103.5 105.9 118. 7 Flange- plates, lb 30.6 40.8 40.8 51.0 51.0 a5-7 40.8 47.6 51.0 47.6 51.0 59-5 59-5 71-4 71.4 Maximum end- reaction in thousands of pounds 60.8 60.8 60.8 60.8 60.8 60.8 56.3 56.3 563 S6.3 56.3 56.3 56.3 67.5 67.5 67.5 67.5 67.5 67. 5 67.5 67.5 67.5 67. 5 67.5 78.8 78 8 78.8 78.8 78.8 78.8 * From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. tional values are given in the Pocket Companion. Tables Used in the Design of Plate and Box Girders 707 Table IV *t (Continued). Elements of Riveted Plate Gifders Sizes Weight per foot Maximum end- Section- Web- modulus, axis i-r, Web- Flange- Flange- plate and flange- angles, Flange- reaction in thousands in3 plate, in angles, in plates, in plates, lb of pounds lb 361.3 6X4 X% 133. 1 78.8 384.0 SXz^AXYz 12XK2 93.1 40.8 78.8 421.8 5X3K2XK2 12 x% 93.1. 51.0 78.8 441.7 6X4 XVi 14XK2 103.5 47.6 78.8 461. 1 26XM6 SXzYzX^A 12 X- ■i 105.9 51.0 78.8 485.9 6X4 XVi I4X^ ■i 103.5 59.5 78.8 532.7 6X4 X^^ I4X- ^ 118. 7 59.5 78.8 576.5 6X4 XH I4X-] i "118.7 71.4 78.8 620.5 6X4 X% 14X5 i 133. 1 71.4 78.8 185.6 5X3HX% 70.3 56.3 211. 6X4 Xf^ 77.9 56.3 1 230.3 5X3^2X1'^ 83.1 56.3 264.1 27XM0 6X4 XH 93.5 56.3 273.2 5X3^2X5/^ 95.9 S6.3 304. 5 5X3K2XH I2X?i 70.3 30.6 56.3 315.3 6X4 X% 108.7 56.3 344.2 SXz\iX% 12X3 ^ 70.3 40.8 56.3 337.7 6X4 X^i 115.7 67.5 366.7 SX2,¥2X% 12XK2 77.3 40.8 67. 5 i 372.8 6X4 XH 14XH 84.9 35.7 67.5 i 388.5 6X4 xy\ 130. 1 67.5 1 411. 7 5X3'/^XH 12X? '2 90.1 40.8 67.5 420.8 6X4 x% 14XJ 12 84.9 47.6 67.5 1 437.0 28X% 6X4 X% 144.5 67. 5 i 452.5 5X3K2XK2 I2Xv i 90.1 51.0 67.5 1 474.3 6X4 XH 14X3 '2 100.5 47.6 67.5 1 49.5.3 5X3^X^6 12 X-^ i 102.9 51.0 67.5 1 521.9 6X4 XH I4X^ i 100.5 595 67.5 I 573-1 6X4 XM I4X^ 4 IIS. 7 59.5 67.S 1 620.4 6X4 X^)s 14X2 4 115. 7 71.4 67.5 i 668.6 6X4 X% 14X5 4 130. 1 71.4 67.5 257.1 SXzViXH 96.1 78.8 i 292.4 6X4 XH 106.5 78.8 301.8 5X3K'X5/^ 108.9 78.8 ' 345.8 6X4 X% 121. 7 78.8 ! 396.5 6X4 XVa. 136. 1 78.8 1 419.5 28X7l6 5X3M2XI/2 12X .^ 96.1 40.8 78.8 445.1 6X4 Xli 150.5 78.8 460.2 5X3HXi/i 12X Vs 96.1 51.0 78.8 1 482 . 6X4 XK2 14X Yt 106.5 47.6 78.8 503. 5X3^2X5/^ 12X H 108.9 51.0 78.8 529.6 6X4 XVi. 14X 54 106. 5 59. 5 78.8 580.8 6X4 XH 14X % 121. 7 59-5 78.8 * From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa, t For explanation of table, see page 706. 708 Riveted Steel Plate and Box Girders Chap. 20 Table IV *t (Continued). Elements of Riveted Plate Girders Sizes Weight 1 3er foot Maximum end- Section- ■ Web- modulus, plate and flange- angles. reaction in axis I- 1, Web- Flange*- Flange- Flange- thousands in3 plate, in angles, in plates, in plates, lb of pounds lb 628.0 28X^6 6X4 XH 14X^4 121. 7 71.4 78.8 676.2 6X4 X^4 14X^1 136. 1 71.4 78.8 221.8 5X3^2X5^ 79 9 74.3 250.5 6X4 X3/6 87.5 74-3 272.1 5X3l"2X»/2 92.7 74.3 310.3 6X4 XVz 103. 1 74.3 320.5 5X3'/iXH 105.5 74.3 353.8 5X3HX->6 I2X?8 79 9 30.6 74-3 366.2 5X3'/''X3/i 117. 5 74.3 368.1 6X4 X^A 118. 3 74.3 397.8 5X3HXH 12XH 799 40.8 74.3 404.7 6X4 X% I4XH 87.5 35.7 74.3 423.1 30XH 6X4 XH 132.7 74.3 446.6 SXsViXH 12XH 92.7 40.8 74.3 456.1 6X4 X% 14XH 87. 5 47.6 74.3 475.8 6X4 Xli 147. 1 74.3 490.3 5X3V2Xyz I2X% 92.7 51.0 74.3 514.0 6X4 XH I4XH 103. 1 47.6 74.3 536.7 5X3HX->i I2XH 105. 5 510 74.3 565.1 6X4 XH 14X5/^ 103. 1 59 5 74.3 620.6 6X4 X'>i I4X:H 118. 3 59 5 74.3 671.3 6X4 X% 14X94 118. 3 71.4 74.3 723.8 6X4 XH 14X94 132.7 71.4 74.3 281.4 5X3HXH 99-0 86.6 319 5 6X4 XK> 109.4 86.6 329.7 sX3HX-5^ III. 8 86.6 375.5 5X3HX^/4 123.8 86.6 377.3 6X4 X% 124.6 86.6 432.3 6X4 X% 139 86.6 455.5 5X3'AXVz 12XH 99 40.8 86.6 485.0 30X^10 6X4 x% I. S3. 4 86.6 499 2 5X3HXV2 12X% 99-0 51.0 86.6 523 6X4 XH I4XH 109.4 47.6 86.6 545.6 SXsViXH I2XH III. 8 51. 86.6 574.0 6X4 XH I4XH 109.4 59 5 86.6 629. 5 6X4 XH 14x9^ 124.6 59-5 86.6 680.1 6X4 XH I4XK 124.6 71.4 86.6 732.6 6X4 XH 14x94 139.0 71.4 86.6 290.6 5X3HXH 105-4 99-0 328.8 6X4 XH IIS. 8 99.0 338.9 30XH 5X3HX5^ 118. 2 99-0 384.7 5X3HXH 130.2 99.0 386.5 6X4 X5^ 131. 99-0 * From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. t For explanation of table, see page 706. Tables Used in the Design of Plate and Box Girders 709 Table IV *t (Continued). Elements of Riveted Plate Girders Sizes Weight per foot Maximum end- Section- Web- modulus, axis i-i. Web- Flange- Flange- plate and flange- angles. Flange- reaction in thousands in3 plate, in angles, in plates, in plates, lb of pounds lb 441.5 145.4 99.0 6X4 X% 464.4 5X3^/^X1/^ I2X^^ 105.4 40.8 99.0 494.2 6X4 X% 159.8 99.0 508.0 5X3^/^XJ^ 12X5^ 105.4 51.0 99.0 531.9 2PX\^ 6X4 XK2 14X1/2 115. 8 47.6 99.0 554. 5 SXzyiX% 12XH 118. 2 51.0 99.0 582.8 6X4 xy2 I4X^^ 115. 8 59.5 99.0 638.3 6X4 X^^ 14XH 131. 59.5 99.0 688.9 6X4 X% 14 X% 131. 71.4 99.0 741.3 6X4 X% 14X3/1 145.4 71.4 990 351.7 5X3^2X3/^ 83.7 81.0 283.7 6X4 X?6 91.3 81.0 307.7 33X^% 5X3i/2X'/^ 96.5 81.0 308.4 6X6 XH 101.7 121. 5 350.3 6X4 X\i 106.9 81.0 430.3 6X6 X\^ 124.3 135.0 460.0 5X3'/2X?4 125. 1 87.8 462.4 6X4 X% 125.9 87.8 503.3 6X4 X^^ 14X5^ 95.1 35.7 87.8 510.5 6X6 XH 142.7 135.0 530.2 6X4 X% 140.3 87.8 531.6 6X6 X% I4X^^ 105. 5 35.7 135.0 554.3 5X3K2XK2 12X1/^ 100.3 40.8 87.8 565.1 6X4 X% 14 XH 95.1 47.6 87.8 593.2 6X6 X?4 I4X^^ 105. 5 47.6 135.0 595.3 6X4 X% 154.7 87.8 606.8 36X3/8 5X3HXK2 I2X5i 100.3 51.0 87.8 636.5 6X4 XK2 14X/2 no. 7 47.6 87.8 654.9 6X6 X% I4X-H 105.5 59.5 135.0 664.2 5X3HX-5i 12XH 113. 1 51.0 87.8 674.4 6X6 XV^ 14X/2 124.3 47'. 6 135.0 698.0 6X4 XK' 14X^4 110.7 59.5 87.8 735.5 6X6 XH i4X^/i 124.3 59.5 135.0 766.6 6X4 XH iaX% 125.9 59-5 87.8 796.8 6X6 XI/2 i4xyi 124.3 71.4 135.0 813. 1 6X6 XM I4XH 142.7 59. 5 135.0 827.6 6X4 XH 14X3/ 125.9 71.4 87.8 873.8 6X6 XYi 14x54 142.7 71.4 135.0 892.8 6X4 XYi i4X^i 140.3 71.4 87.8 357.7 5X3'/2XH 108.0 102.4 404.7 36X^6 6X4 XH 118. 4 102.4 417.0 sxmx% 120.8 102.4 443.6 6X6 X\^ 132.0 157.5 * From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa, t For explauation of table, see page 706, 710 Riveted Steel Plate and Box Girders Chap. 20 *" Table IV *t (Continued). Elements of Riveted Plate Girders Sizes Weight per foot Maximum end- Section- Web- modulus, plate reaction in axis i-i. Web- Flange- Flange- Flange- thousands in3 plate, angles, plates, flange- plates, of in in in angles, lb lb pounds 473. 3 5X3HXM 132.8 102.4 475-7 6X4 XVs 133.6 102.4 523.8 6X6 XH 150.4 157.5 543.5 6X4 XH 148.0 102. 4 567.2 5X3yixy2 12XK2 108.0 40.8 102.4 608.6 6X4 x% 162.4 102.4 619.7 5X3HXH 12X54 108.0 51-0 102.4 649 5 6X4 XH I4XK^ 118.4 47.6 102.4 677.1 36X^6 5X3HXH 12XH 120.8 51.0 102. 4 687.3 6X6 XH 14XH 132.0 47.6 157-5 710.8 6X4 XH uXH 118. 4 59.5 102.4 748.4 6X6 XH uXH 132.0 59.5 157.5 779 5 6X4 X^^ 14XH 133.6 59-5 102.4 809.5 6X6 X]^ I4X% 132.0 71.4 157.5 825.9 6X6 XH 14X5^ 150.4 59.5 157-5 840.4 6X4 XH 14X34 133.6 71.4 102.4 886.6 6X6 XH UXH 150.4 71.4 157-5 905.5 6X4 XH 14XH 148.0 71.4 102.4 418.0 6X4 XH 126.0 117.0 456.9 6X6 XH 139.6 180.0 489.0 6X4 X% 141.2 117. 537.1 6X6 XH 158.0 180.0 556.9 6X4 XU • 155.6 117.0 614.5 6X6 XH 176.© 180.0 621.9 6X4 Xli 170.0 117. 662.5 6X4 XH 14XH 126.0 47-6 117.0 689.2 6X6 Xli 193.6 180.0 700.3 6X6 XH I4X^ 139.6 47.6 180.0 723.7 36X}'^ 6X4 XH 14 X -^'6 126.0 59-5 117.0 761.3 6X6 XH I4XH 139-6 59-5 180.0 792.3 6X4 X^^ 14X5/^ 141.2 59-5 117.0 822.3 6X6 XH UXH 139.6 71.4 180.0 838.8 6X6 XH uXH 158.0 59-5 180.0 853.2 6X4 XH 14x34 141. 2 71.4 117. 899.4 6X6 XH 14X^4 158.0 71.4 i8o.o 918.3 6X4 XH 14X3/4 155.6 71.4 117.0 973.7 6X6 XM uXH 176.0 71.4 180.0 I 039.4 6X4 XH 14X1 155.6 95.2 117. 0. I 094.1 6X6 X3/4 14X1 176.0 95.2 180.0 I lOI.I 6X4 X^ 14X1 170.0 95.2 117. I 164.9 6X6 Xli 14X1 193.6 95.2 180.0 444.7 36XH 6X4 Xi/i 141. 3 146.3 483.5 6X6 XH 154.9 225.0 * From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. t For explanation of table, .see page 706- Tables Used in the Design of Plate and Box Girders 711 Table IV *t (Continued). Elements of Riveted Plate Girders Sizes Weight per foot Maximum end- Section- Web- modulus, plate and flange- angles. reaction in axis i-i, Web- Flange- Flange- Flange- thousands in3 plate, angles, plates, plates, of in in in lb pounds lb SIS. 7 6X4XH 156. 5 146.3 S63.7 6X6X5/^ 173.3 225.0 S83.S ex4XH 170.9 146.3 641.2 6X6XH 191.3 225.0 648. s 6X4XH 18S.3 146.3 688.4 6X4XH 14XH 141. 3 47.6 146.3 715.8 6X6X^^ 208.9 225.0 726.2 6X6XH I4X>^ 154.9 47.6 749-4 6X4X1/^ I4XH 141. 3 59-5 146.3 787.0 6X6XK2 14 XH 154-9 59 5 225.0 818. 1 36X^8 6X4X5^ 14XH 156.5 59-5 146.3 847.9 6X6XK2 14X% 154.9 71.4 225.0 864.6 6X6X5/^ 14X% 173.3 59-5 225.0 878.8 6X4X5/^ 14XM 156.5 71.4 146.3 924.9 6X6X5/^ 14X^4 173.3 71.4 225.0 943.9 6X4X% I4X% 170.9 71-4 146.3 999-3 6X6X% I4X% 191-3 71.4 225.0 1045.9 6X6XH i4Xi 173.3 95.2 225.0 1064.7 6X4XM 14X1 170.9 95.2 146.3 I 119. 3 6X6X3/4 I4XI 191. 3 95.2 225.0 I 126.3 6X4X^ 14X1 185.3 95.2 146.3 I 190. 1 6X6XT^ 14X1 208.9 95.2 225.0 390.2 ^X4X3/^ 102.8 101.3 427. 5 6X6X34 113. 2 157.5 477.2 6X4XH 118. 4 IOI.3 527.2 6X6XH 132.0 157. 5 561.4 6X4X^/6 133.6 101.3 606.6 . 6X4X% 14X34 102.8 35.7 101.3 623.5 6X6X5i ISO. 4 157 5 638.3 6X4X5^ i6X^i 102.8 40.8 101.3 642.1 6X4XM 148.0 101.3 643.2 6X6X34 14X34 113. 2 35.7 157. 5 675.1 42XH 6X6X3/i i6X% 113. 2 40.8 157. 5 678.6 6X4X'^^ 14XK2 102.8 47.6 101.3 715.2 6X6XH 14X^4 113. 2 47.6 157.5 716.5 6X6X94 168.4 157.5 719.5 6X4X% 162.4 101.3 757.7 6X6X% i6X^^ 113.2 54.4 157.5 763.7 6X4X^4 I4XV^ 118. 4 47.6 101.3 787.2 6X6XH 14X^4 113. 2 59-5 157.5 806.2 6X4X5'^ 16XH 118. 4 54.4 101.3 806.4 6X6X^^ 186.0 157.5 812.7 6X6XK2 UXH 132.0 47.6 157.5 * From Pocket Companion, Carnegie Steel Company Pittsburgh, Pa. t For explanation of table, see page 706. Riveted Steel Plate and Box Girders Chap. 20 Table IV *t (Continued). Elements of Riveted Plate Girders Sizes Weight E)er foot Maximum end- Section- Web- modulus, plate and flange- angles, reaction in axis i-i. Web- Flange- Flange- Flange- thousands in' plate, in angles, in plates, in plates, lb of pounds lb 835. 5 6X4X'/^ 14X9^ 118. 4 59-5 101.3 855.2 6X6XK2 16XK2 132.0 54.4 157.5 884.2 6X6X1^^2 14X9^ 132.0 59-5 157.5 917.3 6X4X)i 14X9^ 133.6 59-5 101.3 937.3 6X6XK2 i6X9i 132.0 68.0 157.5 955.7 6X6XH 14X94 132.0 71-4 157.5 970.4 6X4XH i6X9i 133.6 68.0 101.3 977.6 exexH i4X9i 150.4 59.5 157.5 988.7 6X4X^A 14X94 133.6 71-4 101.3 I 030.8 42X^4 6X6XH 16X9^ 150.4 68.0 157.5 1048.6 6X6X'}i 14X94 150.4 71.4 157.5 1066.6 6X4X^4 14X94 148.0 71.4 101.3 I 112. 4 6X6X5^ 16X94 150.4 81.6 157.5 I 130.4 6X4X94 16X94 148.0 81.6 101.3 1138.S 6X6X% 14X94 168.4 71-4 157.5 I 194. I 6X6XH i6X7/^ 150.4 95.2 157.5 I 202.3 6X6X94 16X94 168.4 81.6 157.5 I 283.5 6X6X)4 16X74 168.4 95.2 157-5 I 286.4 6X4Xli i6X^i 162.4 95.2 101.3 1369.9 6X6XH i6X^i 186.0 95.2 157.5 495.3 6X4XH 127.3 118. 1 545.4 6X6XK2 140.9 183.8 579.5 6X4X9^ 142.^ 118. 1 641.6 6X6XH 159.3 183.8 660.2 6X4X94 156.9 118. 1 734.7 6X6X)4 *77.3 183.8 737.6 6X4X^^ 171. 3 1x8. 1 781.5 6X4XK2 14XK' 127.3 47.6 118. 1 824.0 6X4XK2 i6X3'2 127.3 54 4 118. 1 824.6 6X6X^s 194.9 183.8 830.4 6X6XK2 14X^2 140.9 47 6 183.8 853.1 42XM6 6X4X1/2 i4X9i 127.3 59 5 118. 1 872.9 6X6XK2 16XK2 140.9 54 4 183.8 901.8 6X6X1/^ i4X9i 140.9 59 S 183.8 934.9 6X4X9i 14X96 142.5 59 5 118. 1 954.9 6X6X1/^ 16X98 140.9 G3 183.8 973.2 6X6X1/^ 14X94 140.9 71 4 183.8 988.1 6X4XH 16X96 142.5 68 118. 1 995.3 6X6XH 14X98 159-3 59 5 183.8 I 006.2 6X4X9^ 14X94 142.5 71 4 118. 1 I 048.4 6X6XH 16X96 159-3 68 183.8 1066.2 6X6X9i 14X94 159-3 71 4 183.8 I 084.1 6X4X94 14X94 156.9 71 4 118.1 • From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa, t For explanation of table, see pago 706. Tables Used in the Design of Plate and Box Girders 713 Table IV *t (Continued). Elements of Riveted Plate Girders Sizes Weight per foot Maximum end- Section- Web- modulus, plate and flange- angles, reaction in axis i-i. Web- Flange- Flange- Flange- thousands in3 plate, angles, plates, plates, of in in in lb pounds i6X% lb I 129.9 6X6XH 159-3 81.6 183.8 I 147.9 6X4X>4 16X^/4 156.9 81.6 118. 1 I 156.0 6X6XM I4X% 177.3 71-4 183.8 I 211. 6 42X7/6 6X6XH 16X7/6 159-3 95-2 183-8 I 219.8 6X6X)4 i6X% 177.3 81.6 183.8 1300.9 6X6X% i6X% 177-3 95-2 183.8 1387.3 6X6Xj^6 i6Xi^6 194.9 95.2 183-8 513 5 6X4XH 136.2 135.0 563.5 6X6XK2 149-8 210.0 597.7 6X4X-H 151. 4 135-0 659.8 6X6XH 168.2 210.0 678.4 6X4X=^4 165.8 135 752.8 6X6X% 186.2 210.0 755.8 6X4X^i 180.2 I3S-0 799.2 6X4X5^^ 14X1/^2 136.2 47-6 135.0 841.7 6X4XK2 16XM2 136.2 54-4 135.0 842.7 6X6X7/i 203.8 210.0 848.1 6X6X'/2 14XK2 149-8 47-6 210.0 870.8 6X4XH 14XH 136.2 59-5 135.0 890.6 6X6XH 16XH 149-8 54-4 210.0 919-4 6X6X3'^ , 14X^6 149-8 59-5 210.0 952.6 6X4X^/6 14XH 151-4 59-5 135.0 972.6 42XK2 6X6XH 16XH 149-8 68.0 210.0 990.8 6X6X3^^ I4X% 149-8 71-4 2I0,0 1005.7 6X4XH 16X^/6 151. 4 68.0 135.0 I 012.9 '6X6X)6 14XH 168.2 59-5 210.0 1023.7 6X4X>i 14XM 151-4 71.4 135. I 066.0 6X6XH 16X-H 168.2 68.0 210.0 1083.7 6X6XH 14X3/4 168.2 71.4 2IO.O I 101.7 6X4XM I4X'% 165.8 71.4 135.0 I 147.5 6X6XH 16XM 168.2 81.6 210.0 I 165.4 6X4X=H i6X% 165.8 81.6 135.0 I 173.6 6X6X% i4X% 186.2 71.4 210.0 I 229.0 6X6X)i 16X^6 168.2 95-2 210.0 I 237.4 6X6X-)4 i6X% 186.2 81.6 210.0 I 318.4 6X6 XK 16X7/6 186.2 95.2 210.0 I 321.2 6X4X^6 16X3^6 180.2 95.2 135.0 I 4047 6X6X^i 16X^6 203.8 95.2 210.0 466.9 6X4X3/i no. 4 121. 5 512.7 6X6X3/6 120.8 180.0 567.4 4^X% 6X4X^^ 126.0 121. 5 628.9 6X6XH 139-6 180.0 664.9 6X4XH 141. 2 121. 5 * From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. t For explanation of table, see page 706. 714 Riveted Steel Plate and Box Girders Chap. 20 Table IV *t (Continued). Elements of Riveted Plate Girders Sizes Weight per foot Maximum end- Section- Web- modulus, plate and flange- angles. reaction in axis i-i, Web- Flange- Flange- Flange- thousands in3 plate, in angles, in plates, in plates, lb of pounds lb 714.4 6X4XK I4X?^ no. 4' 35.7 121. 5 741-3 6X6X5^ 158.0 180.0 750.8 cxaxh i6X3/^ no. 4 40.8 121. 5 758. 5 6XAXH 155-6 121. 5 759-5 6X6X% UXH 120.8 35.7 180.0 795-9 6X6XH i6X% 120.8 40.8 180.0 797.0 6X4XH 14XM2 no. 4 47.6 121. 5 841.9 6X6X% 14XK2 120.8 47.6 180.0 848.3 6X4X% 170.0 121. 5 850.1 6X6X% 176.0 180.0 890.4 6X6XH i6XJ/^ 120.8 54.4 180.0 895.5 ex^xH UXH 126.0 47-6 121. 5 924.3 0X6XH 14XH 120.8 59-5 180.0 944-0 6XaX^ 16X1/2 126.0 54-4 121.5 955-2 6xex% 193-6 180.0 955 -8 6X6X3'^ 14X1/^ 139-6 47-6 180.0 977.7 6X4X1/^ UX% 126.0 59-5 121.5 1004.3 48X-K 6X6XV2 lexvz 139-6 54-4 180.0 1037-6 6X6XV2 ux% 139.6 59.5 180.0 1072.7 6X4XH 14XH 141.2 59.5 121. 5 1098.2 6X6XH 16XH 139.6 68.0 180.0 I 119-5 6X6X1^ UXH 139.6 71.4 180.0 I 133-3 6X4X^i lexH 141.2 68.0 121. 5 I 147- I 6X6XH uX^A 158.0 59.5 180.0 I 154.4 6X4XH 14XM 141. 2 71.4 121. 5 I 207.8 6X6X5;^ 16XH 158.0 68.0 180.0 I 228.4 6X6XH I4X% 158.0 71.4 180.0 I 245.2 6X4X% 14X3/4 155. 6 71.4 121.5 I 301.2 6X6XH i6X% 158.0 81.6 180.0 I 317.9 6X4X% i6XH 155.6 81.6 121. 5 1334.0 6X6X% 14X^1 176.0 71.4 180.0 1394.7 6X6XH i6X^i 158.0 95.2 180.0 I 406.7 6X6X% 16XM 176.0 81.6 180.0 1498.1 6X4X^6 i6X7/i 170.0 95-2 121.5 1499-7 6X6X3/i 16X^6 176.0 95-2 180.0 I 601.3 6X6X^6 i6X^i 193.6 95-2 180.0 591 -2 6X4XH 136.2 141. 8 652.7 6X6X1/^ 149 -8 210.0 688.7 6X4XH 151. 4 141.8 765 -0 48XM6 6X6X5/^ 168.2 210.0 782.3 6X4X3/1 165.8 141. 8 872.1 6X4X7/6 180.2 141.8 873-8 6X6X% 186.2 210.0 • From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. t For explanation of table, see page 706. Tables Used in the Design of Plate and Box Girders 715 Table IV *t (Continued). Elements of Riveted Plate Girders Sizes Weight per foot Maximum Section- Web- end- modulus, plate and flange- angles. reaction in axis I -I, Web- Flange- Flange- Flange- thousands in3 plate, angles, plates, plates, of in in in lb pounds lb 918.8 6X4X^2 14 X'/ 136.2 47-6 141. 8 967.3 6X4X^/^ 16XH 136.2 54-4 141. 8 979.0 6X6X^4 203.8 210.0 979 -o 6X6XK2 14X/2 149.8 47.6 210.0 I 000.8 6X4X1/2 i4X)6 136.2 59. 5 141. 8 I 027 ■ 6 6X6XK2 16X1/ 149.8 54.4 210.0 1060.8 6X6X'/2 I4X-H 149-8 59.5 210.0 1095.8 6X4XH 14XH 151. 4 59.5 141 -8 I 121. 4 6X6X^^ 16X5/6 149-8 68.0 210.0 I 142.5 6X6XH 14X^4 149-8 71.4 210.0 I 156.5 6X4XS/i 16X5/6 15I-4 68.0 141. 8 I 170.3 48XM6 6X6XH 14XH 168.2 59.5 210.0 I 177.4 6X4XH 14XM 151-4 71.4 141 -8 I 230.9 6X6X% i6X-)6 168.2 68.0 210.0 1251.5 6X6XM 14XK 168.2 71.4 210.0 1268.2 6X4XU i4X)4 165.8 71.4 141. 8 1324 3 6X6XH i6X-)4 168.2 81.6 210.0 I 341.0 6X4X% i6X% 165.8 81.6 141. 8 1357.0 6X6X-M I4X-M 186.2 71.4 210.0 I 417.7 6X6X5/6 16X7/ 168.2 95.2 210.0 I 429.8 6X6XM 16XM 186.2 81.6 210.0 I 521.0 6X4X7/6 16X7/ 180.2 95.2 141. 8 1522.7 6X6X3/4 16X7/6 186.2 95.2 210.0 I 624 . 2 6X6X3^6 16X7/ 203.8 95-2 210.0 615.0 6X4XH 146.4 162.0 676.4 6X6XK2 160.0 240.0 712.4 6X4X% 161. 6 162.0 788.8 6X6X^6 178.4 240.0 806.0 6X4X% 176.0 162.0 ■ 895.8 6X4X7/6 190.4 162.0 897.6 6X6X% 196.4 240.0 942.1 6X4XK2 14X1/ 146.4 47-6 162.0 990.6 6X4X1/2 16XH 146.4 54.4 162.0 I 002.3 48X'/2 6X6X/2 14X1/2 160.0 47.6 240.0 I 002.7 6X6X7/6 214.0 240.0 I 024.0 6X4X/2 14X5/6 146.4 59-5 162.0 I 050 . 8 6X6XH 16x1/2 160.0 54-4 240.0 1083.9 6X6X1/ 14X5/6 160.0 59-5 240.0 I 119. 6X4X% 14XH 161. 6 59.5 162.0 I 144.5 6X6X/2 16X5/ . 160.0 68.0 240.0 I 165.6 6X6X1/ 14X3/4 160.0 71.4 240.0 I 179.6 6X4X5/6 16X5/6 161. 6 68.0 162.0 I 193.4 6X6X5/ UXH 178.4 59.5 240.0 * From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa. t For explanation of table, see page 706. 716 Riveted Steel Plate and Box Girders Chap. 20 Table IV *t (Continued). Elements of Riveted Plate Girders Sizes Weight per foot Maximum end- Section- Web- modulus, plate and flange- angles. reaction in axis i-i. Web- Flange- Flange- Flange- thousands ins plate, in angles, in plates, in plates, lb of pounds lb I 200.5 • 161. 6 71.4 162.0 6X4X-H 14XK 1254. 1 6X6XH 16XH 178.4 68.0 240.0 I 274.5 6X6XH 14 XK 178.4 71^4 240.0 I 291 . 2 6X4X->4 14XK 176.0 71.4 162.0 I 347.3 6X6XH i6X>4 178.4 81.6 240.0 1 364.0 48XI/2 6X4 X}4 16X3/1 176.0 81.6 162.0 I 380.0 6X6X% 14X^/4 196.4 71.4 240.0 I 440.6 6X6XH i6X^/i 178.4 95.2 240.0 1452.8 6X6X^1 i6X)i 196.4 81.6 240.0 1543.9 6X4Xj^^ i6Xli 190.4 95.2 162.0 I 545.6 6X6X% i6X% 196.4 95.2 240.0 I 647.1 6X6X^4 i6X% 214.0 95.2 240.0 * From Pocket Companion, Carnegie Steel Company, Pittsburgh, Pa, t For explanation of table, see page 706. Layout of Floor-Framing 717 CHAPTER XXI STRENGTH AND STIFFNESS OF WOODEN FLOORS By THOMAS NOLAN PROFESSOR OF ARCHITECTURAL CONSTRUCTION, UNIVERSITY OF PENNSYLVANIA The Problems Stated. The problems which are presented in this part of building-construction are, in general, (i) the designing of the joists and girders forming the framework of the floor to safely support the greatest load likely to come upon it, and (2) the determination of the maximum safe load for a floor already built. The first of these problems is the one with which architects and builders more commonly have to deal, and is, therefore, considered first. Layout of the Floor-Framing. Before any calculations can be made for the sizes of the timbers it is necessary to know the spans of the joists, and, if there are openings in the floor, or the floor-joists have to support longitudinal partitions, a framing-plan should be made, showing the floor-area that will be supported by each joist, and also the position of partitions or special loads. If the floor is to be supported by posts and girders the position of these should also be accurately indicated on the framing-plan. Where the joists are sup- ported entirely by walls or partitions, the spans of the joists will of course be fixed by the plan of the building. When the distance between a wall and a partition is too great for a single span, there may be a question as to the best locations for the posts and girders. When planning a building in which wooden joists are to be used, it is important to keep in mind the general scheme of the floor-framing and particularly the spans. Whenever practicable the spans of wooden joists should not exceed 24 ft. When the distance between the sup- porting waUs exceeds 30 ft, girders should be placed so that the maximum span of the joists will not exceed 24 ft for light buildings nor from 16 to 18 ft for warehouses. In School Buildings it is desirable to have the rooms at least 27 ft wide, and hence in this class of buildings the joists usuaUy have spans of from 27 to 30 ft. For a span of 30 ft, however, 16- in joists should be used, and as these are expen^ sive, and often diflicult to obtain, it is much better and more economical to make the schoolrooms 27 by 32 or 34 ft, than to make them 30 ft square. A schoolroom 27 ft wide by from 32 to 34 ft long, with windows on the long side, only, is economical and satisfactory, as it permits of using 3 by 14-in joists, 28 ft long, and also results in the most satisfactory lighting. Continuous Joists. When joists are supported by a girder placed so that a 24-ft or 26-ft joist extends over the two spans, it is always better to have the joists continuous over the girder, as by that construction they make a much stiffer floor. (See Chapter XIX.) Floor-Loads. Having decided on the arrangement of the joists, and drawn a framing-plan showing the spaa and the locations of all special timbers, the 718 Strength and Stiffness of Wooden Floors Chap. 21 next step involves the determination of the loads for which the joists and girders are to be proportioned. Floor-loads are made up of two parts, the weight of materials composing the floor itself, and the ceiling below, if there is one; and the load liable to be put on the floor. The first is called the dead load, and the second the live load. When the safe load for a floor is spoken of the ^live load is generally meant. Weight of "Wooden Floor-Construction. Wooden floors usually consist of (i) beams, commonly called joists,* or floor- joists, (2) one or two thcknesses of flooring-boards, and, in a finished building, (3) a ceiling underneath the joists. In figuring the weight of %-in flooring-boards it will be sufliciently accurate to estimate the weight of a single thickness at 3 lb per sq ft. The joists may also be figured at 3 lb per ft, board-measure, with the exception of hard-pine and oak joists, which should be figured at 4 lb per ft, board-measure. The weight of the joists must also be reduced to their equivalent weight per square foot of floor. Thus, the weight of a 2 by 12-in joist is about 6 lb per lin ft. If the joists are spaced 12 in on centers, this will be equal to 6 lb per sq ft; but if the joists are 16 in on centers there will be but one lineal foot of joist to every iH sq ft, which will be equivalent to 4li lb per sq ft; and if they are 20 in on centers, the weight will be equal to 3H lb per sq ft; spaced 24 in on centers, the weight wiU be 3 lb per sq ft. The weight of a lath-and-plaster ceiling should be taken at 10 lb per sq ft, and of a ^4 -in wooden ceiling at 2I/2 lb per sq ft. A corrugated-iron ceiling weighs about i lb per sq ft. For stamped- steel ceilings, 2 lb per sq ft will cover the weight of the metal and furring. The following table, giving the weight of joists, wiU be found convenient in figuring the weight of floors: Table I. Weight of Floor- Joists per Square Foot of Floor Sizes of joists Spruce, hemlock, white pine Spacing in inches, center to center Hard pine or oak Spacing in inches, center to center 16 2X 6. 2X 8. 3X 8. 2X10. 3X10. 2X12. 3X12. 2X14. 3X14. lb lb 3 4 6 5 7H 6 9 7 2H 3 4H 3H sH 6H 4 6% m 14 3 4 6 S 7H 6 9 7 lOl/^ Weight of Crowds. I J. Johnson reports f results of some tests to ascer- tain the weight of crowds ot men, in which he obtained weights of 154.2, 143.9, * Some building laws use the term floor -beam; in.ste?Ld[ of the word joist. \ See Engineering News, April 14, 1904. Loads on Floors 719 148.1 and 156.9 lb per sq ft. The last-mentioned weight was obtained by pack- ing 67 men in a room about 6 by 11 ft in size. Professor Johnson also found that with 50 men in the room, making a load of 122 lb per sq ft, the crowd was compacted "so that a man could elbow his way through it only with persever- ance and determined effort." Superimposed Loads. There is much difference of opinion as to what. allowance should be made for the live load. Table II shows the minimum allowance for live loads for different classes of buildings, as fixed by the build- ing laws of the cities mentioned. (See, also, page 149.) Table 11. Minimum Safe Superimposed Loads for Floors, Required by Various Building Laws Classes of buildings Dwellings Hotels, tenements and lodg- ing-houses Office-buildings Buildings for public assembly Stores, warehouses and mfg. bldgs Minimum live load per square foot of floor Buffalo, Boston, 1905 191S 70 70 100 I20t SO 80 100 I25t lOOj Phila- delphia, 914 70 100 120 I20t New York, 1917 40 60 60* 100 I20t St. Louis, 1910 60 60 70* loot isot ■* First floor, 150 lb. f Also sch6olhouses. J And upwards. It was the opinion of Mr. Kidder that the following allowances for floor-loads, taken in connection with the values given for the safe strength of joists or beams, provide absolute safety with proper allowance for economy. Lb per sq ft For dwellings, sleeping-rooms and lodging-rooms 40 For schoolrooms 50 For office-buildings, upper stories 60 For office-buildings, first story 80 For stables and carriage-houses 65 For banking-rooms, churches and theaters 80 For assembly-halls, dancing-halls and the corridors of all public buildings, including hotels 120 For drill-rooms 150 Live Loads for Stores and Buildings for Light Manufacturing. Floors for ordinary stores, light manufacturing and light storage should be computed for not less than 120 lb per sq ft, and for a concentrated load at any point of 4 000 lb. Live Loads for Dwellings, etc. Floors of dwellings, tenements, lodging-houses and rooms in hotels, are seldom loaded with more than 20 lb per sq ft for the entire area, and a minimum load of 40 lb per sq ft should provide for all possible contingencies. 720 Strength and Stiffness of Wooden Floors Chap. 21 Live Loads for Office-BuUdings. The floors of offices are, as a rule, not more heavily loaded than the floors of dwellings, but the possibilities for increased loads from safes and heavy furniture, and possibly from a more compact crowd of people, are greater, so that the minimum floor-load for offices should be some- what increased. Some years ago the firm of Blackall & Everett, in Boston, found that the average live load in 210 offices, in three prominent office-buildings in that city, was between 16 and 17 lb per sq ft, while the average load for the 10 heaviest office-buildings was 33.3 lb per sq ft. As such loads, however, are as a rule unevenly distributed, some portions of the floor being generally much more heavily loaded than others, it would not appear to be safe to use this average to determine the strength of floor-beams and floor-arches, although it would probably answer for the columns. There seems to be a considerable differ- ence of opinion among the leading architects and structural engineers as to just what allowance should be made for office-floors. Among some of the earlier fire-proof office-buildings, for example, may be mentioned the former Mills Building in San Francisco in which the five loads were assumed at 40 lb per sq ft for all floors above the first. In the Venetian Building, Chicago, the second, third and fourth floors were calculated for 60, and the upper floors for 35 lb per sq ft of live load, while in the Old Colony and Fort Dearborn Buildings in Chicago, the five loads on the floor-beams were assumed at 70' lb per sq ft. At the present time (1915), 50, 60, 70, 75, 100 and 150 lb per sq ft are the minimum live loads for the design of floors of office-buildings required by the building laws of six different cities. C. C. Schneider recommends* for the design of floors of office-buildings above the first floor, for the uniform load of the floor-area, 50; for concentrated loads applied at any point of the floor, 5 000; and for the uniform load for girders, i 000; the 50 being in pounds per sq ft, the 5 000 in pounds and the i 000 in pounds per linear foot. Live Loads for Churches, Theaters and School-Houses. ''An allowance of 120 lb per sq ft for the live load in churches, theaters and school-houses is much greater than the actual conditions reciuire. The average size of a schoolroom is about 28 by 32 ft, and such a room usually contains seats for fifty-six scholars and the teacher. Assuming the average weight of each scholar at 120 lb, the average live load, including ten visiting adults and the desks and furniture, is 13 lb per sq ft. Even supposing that the scholars of two rooms were united for some special occasion, there would be only 22 lb per sq ft; and this is as great a load as it is possible to imagine in such a room, as the fixed desks prevent the crowding together of the scholars except at the sides of the room. From this reasoning, therefore, 50 lb per sq ft would appear ample for schoolrooms. As a matter of fact, 3 by 14-in long-leaf yellow-pine joists, 16 in on centers and with a 28-ft span, have been used for school-room floors for years; but such beams, if calculated by the formula for stiffness, would support a live load of only 43 lb per sq ft. (Table XII, page 643 and Table I, page 718.) The minimum floor-space allotted to a single seat in theaters is 4 sq ft, while the average is about 5 sq ft. Assuming the weight of an opera-chair at 35 lb and of the average adult at 140 lb, a liberal allowance, there results an average of 44 lb per sq ft of floor. A minimum of 80 lb per sq ft would therefore seem to provide for any possible crowding during a panic, except in corridors. On the other hand, it has been shown (see Weight of Crowds, page 718) that a crowd of able-bodied men may result in a load of about 120 lb per sq ft, and this should be the minimum for assembly-halls without fixed desks and also for the corridors of all public buildings. For armories, the minimum load should be increased on account of the vibration. " f * "General Specifications for Structural Work of Buildings," 19 10, page 57. t F. E. Kidder. Weights of Merchandise 721 The Average Floor-Loads for Stores has also been greatly over-estimated. W. L. B. Jenney found that the average load on the floors of the wholesale ware- house of Marshall Field & Company, in Chicago, was but 50 lb per sq ft, and very few retail stores will average over 80 lb per sq ft. An allowance of 1 20 lb per sq ft is suflicient for ordinary retail stores, with the possible exception of hardware stores. Live Loads for Warehouses. Warehouses, on the other hand, may be very heavily loaded, and the floors in buildings intended for the storage of merchan- dise should be prorx)rtioned to the especial class of goods which they are de- signed to support. Table III, originally compiled by C. J. H. Woodbury,* and to which some additions have been made by the Insurance Engineering Experiment Station and by Mr. Kidder, will be found of assistance in deciding upon the live load to be assumed for warehouse-floors. The weights per square foot are for single packages. If the goods are piled two or more cases high, the weight per square foot of floor will of course be increased accordingly. In fact, the height to which the goods are liable to be piled is a very important con- sideration in fixing upon the floor-load. In Table III "the measurements were always taken to the outside of case or package, and gross weights of such pack- ages are given. " Methods of Determining the Sizes of Joists, Beams or Girders Re- quired for Any Building. As already explained, the first step is the making of a framing-plan of the floors or enough of it to show any special framing and also the span and floor-area supported by the different joists, beams or girders. Table III. Weights of Merchandise Materials Measurements Floor- space, sq ft Con- tents, cu ft Weights Total, lb Per sq ft Per cuft Wool Bale, East India Bale, Australia Bale, South America. . Bale, Oregon Bale, California Bag, wool Stack of scoured wool . 30 5.8 7.0 6.9 7.5 5.0 12.0 26.0 340 33 o 330 30.0 340 385 I 000 482 550 200 113 66 143 70 73 40 IS 29 15 17 7 5 Woollen Goods Case, flannels Case, flannels, heavy., Case, dress goods Case, cashmeres Case, underwear Case, blankets Case, horse-blankets. . S-S 12.7 220 40 46 71 IS. 2 330 5.5 22.0 460 84 10.5 28.0 5S0 52 7-3 21.0 350 48 10.3 3S..0 450 44 4.0 14.0 250 63 16 13 18 ' The Fire Protection of Mills, page 118. 722 Strength and Stiffness of Wooden Floors Chap. 21 Table III (Continued). Weights of Merchandise Materials Measurements Floor- space, sq ft Con- tents, cuft Weights Total, lb Per sqft Cotton, Etc Bale Bale, compressed Bale, American Cotton Co Bale, Planters' Compressed Co, Bale, jute Bale, jute lashings Bale, manila Bale, hemp Bale, sisal 8.1 44.2 515 64 41 21.6 550 134 4.0 II. 263 66 2.3 7.2 254 no 2.4 9-9 300 1 25 2.6 I0.5 450 172 3-2 10.9 280 88 8.7 34.7 700 81 53 17.0 400 75 Cotton Goods Bale, unbleached jeans. . . Piece duck Bale, brown sheetings. . . . Case, bleached sheetings . Case, quilts Bale, print cloth Case, prints Bale, tickings Skeins, cotton yarn Burlaps Jute bagging 3.6 4.8 7.2 4.0 4.5 3.3 300 75 235 330 295 175 420 325 130 100 72 68 65 69 41 44 93 99 Rags in Bales White linen .... White cotton . . . Brown cotton . . Paper shavings. Sacking Woollen Jute butts 8.5 39-5 910 107 9-2 40.0 715 78 7.6 30.0 442 59 7-5 340 507 68 16.0 65.0 450 28 7.5 30.0 600 80 2.8 II. I 40c 143 Paper Calendered book Supercalendered book . Newspaper Strawboard . . . Leather-board. .^ Writing Wrapping Manila Weights of Merchandise Table III (Continued). Weights of Merchandise Materials Measurements Floor- space, sq ft Con- tents, cu ft Weights Total, lb Per sq ft Grain ' Wheat, in bags Wheat, in bulk Wheat, in bulk Wheat, in bulk mean Barrels, flour, on side Barrels, flour, on end Corn, in bags Cornmeal, in barrels Oats, in bags Bale of hay Hay, Dederick, compressed Straw, Dederick, compressed. . . . Tow, Dederick, compressed Excelsior, Dederick, compressed. Hay, loo.se 4.1 3.1 3.6 3-7 3-3 5.0 1.75 1-75 1.75 1,75 5.4 7-1 3.6 5.9 3.6 20.0 5.25 5.25 5.25 5.25 2i8 2i8 112 2l8 96 284 125 100 150 100 39 53 70 31 59 29 57 72 57 86 57 Dyestuffs, Etc Hogshead, bleaching powder. Hogshead, soda-ash Box, indigo Box, cutch Box, sumac Caustic soda in iron drum Barrel, starch Barrel, pearl-alum Box, extract logwood Barrel, lime Barrel, cement, American. . . . Barrel, cement, English Barrel, plaster Barrel, rosin Barrel, lard-oil , Rope 11.8 39-2 I 200 102 10.8 29.2 T^T 128 3.0 9.0 385 4.0 3.3 150 38 1.6 4-1 160 100 4.3 6.8 600 140 3.0 3.0 10.5 250 83 10.5 350 117 1.06 0.8 55 52 3.6 4-5 225 63 3.8 5.5 325 86 3.8 5.5 400 105 3.7 6.1 325 88 3-0 9.0 430 143 4-3 12.3 422 98 MlSCELL.^NEOUS Box, tin Box, glass Crate, crockery Cask, crockery Bale, leather Bale, goatskins Bale, raw hides Bale, raw hides, compressed. Bale, sole-leather Pile, sole-leather Barrel, granulated sugar Barrel, brown sugar Cheese 2.7 9-9 13-4 7-3 II. 2 6.0 6.0 12.6 3.0 3-0 5 39 6 42 5 12 2 16 7 30 30 8 9 7 5 7 5 139 99 I 600 162" 600 52 190 26 300 27 400 67 700 117 200 22 317 106 340 113 * For pressure of grain in deep bins, see Engineering News, March 10, 1904, pages 224 and 336, and Dec. 15., 1904. 724 Strength and Stiffness of Wooden Floors Chap. 21 The second step is to determine approximately the weight of the floor and ceil- ing, and decide what superimposed load per square foot the floor is to be designed to carry. Having done this, the next step is the computing of the required dimensions of the common floor-joists. For most buildings the size of floor- joists required can be readily determined by reference to Tables XIII to XVII, inclusive, and XXII to XX \T, inclusive, of this chapter. For other floor-loads the sizes of the common joists may be determined by computing the' load to be supported by a single joist and then, l^y the formulas or tables in Chapter XVI or the formulas in Chapter XVIII, determining the dimensions of tHe joists to support that load. (See Example i.) P'or the floors of all buildings except stores and warehouses it is recommended that the sizes of the common joists be determined by the formulas for stiffness in Chapter XVIII or the stiffness- values in the tables in Chapter XVI, unless one value, only, is given in tables for safe loads, in which case that value may be used. For stores and ware- houses the sizes of the joists may be proportioned by the formulas or strength- values of the tables in Chapter XVI. The Dimensions of Special Beams, such as headers, trimmers and beams sup- porting partitions, and also of the girders, should be determined in the same way, that is, by comput- W;^ ing the maximimi load ___^p the beam may have to Wm support, and then the ^^--^^ dimensions of a beam ym /- that will support that ^p load with safety. The Zm manner of making the ^p computations is ex- ^p plained in the following ~^^M. examples. :==:^P Example i. The sim- .-^^. plest type of floor-fram- ^^ ing is that shown in Fig. 1, in which all of the joists are of the same span and support equal floor-areas. In such a floor, the floor-area sup- ported by each joist is equal to the span, L, multiplied by the spacing, 5, in feet. The load on each joist is equal to the floor-area multiplied by the sum of the dead-loads and superimposed or live loads. To show the applica- tion of the above-mentioned formulas and tables we will assume that Fig. I represents the framing of a floor in a dwelling-house or lodging-house, that L = i8 ft, 5 = 1 6 in or I H ft, and that the timber is common white pine. The joists are to support a plastered ceiling and a double floor of ^i-in boards. What should be the size of the joists; average quality, conditions not ideal? Solution. The floor-area supported by each joist is iH by i8, or 24 sq ft. From Table XIII or XXII, pages 737 and 742, for a span of 18 ft, the joists will probably have to be at least 2 by 12 in, and their weight will be about \Vi. lb per sq ft (see Table I, page 718). The plastered ceiling weighs about 10 lb and the flooring 6 lb per sq ft, making the total weight of the floor 20V2 lb per sq ft. For the superimposed load we should allow at least 40 lb per sq ft (see page 719). This might be greater, if exacted by any particular building law. The load on a single joist will, therefore, be, with these assumed unit loads, ^oVi lb by 24 sq ft, or i 452 lb. From Table VIII, page 639, we find that the maximum load for a i by * ^ Fig. 1. Plan of Floor-joists Computations for Wooden Beams and Girders 725 i2-in white-pine joist of i8 ft span is 623 lb; hence to support i 452 lb will require a breadth equal to 1452/623 = 2^''^ in. Therefore, to comply with the requirements for both strength and stiffness, the joists should be 2H by 12 in. This is not a stock size. Joists 2 by 12 in, 12 in on centers, may next be tried. Each joist must support i 116 lb, requiring, by Table VIII, page 639, a 1.8 by i2-in joist, determined by the quotient i 116/623. So that, in this example, white-pine joists of a nominal size of 2 by 12 in and spaced 12 in on centers might be used, although they are slightly under the required depth, as the dressed size is about 1% by 113-^ in. From Table VI, page 637, the conversion-factor is 1.61, and 623 lb X 1.61 = i 003 lb which is less than i 116 lb, the load to be supported. From Tables XIII and XXII, pages 737 and 742, the maximum spans for 2 by 12 in white-pine joists, 12 in on centers, are 19 ft and 18 ft 8 in respectively, according to the assumed value of the modulus of elasticity for white pine. For 3 by 12-in joists, 16 in on centers, the load is I 506 lb, and i 506/623 = 2% in. The dressed size is almost 2^4 by iiH in, the conversion-factor, 2.53, and 623 X 2.53 == i 576 lb, an amount greater than I 506 lb. Tables XIII and XXII, again, give 19 ft 8 in and 19 ft 4 in for the maximum spans. Joists 3 by 12, 16 in on centers, are stronger than neces- sary. If, in this ex- ample, the span is made 20 ft, by Table VIII, page 639, for 12-in joists two values for the safe loads are found, and the smaller, stiff- ness-value, should be used, unless the deflec- tion need not be con- sidered. Example 2. Fig. 2 shows a partial section of a dwelling, in which the second-floor joists support a plastered partition which also supports the attic joists. What should be the size of the second-floor joists to meet the re- quirements of STRENGTH, the timber being fair-quality Eastern spruce with a safe fiber-stress assumed to be 700 lb per sq in for flexure? As the effect of a concentrated load, compared with a distributed load, in producing deflection, is not as great as the comparative effect in producing rupture, whenever a beam has a considerable concentrated load it may be calculated by the formula or tables FOR strength only. The timber is assumed to be poorly seasoned. Solution. The first step will be to determine the load on a single floor-joist. We will assume, as a trial, that the joists are to be 2 by 10 in, 12 in on centers, that both the first-story and second-story ceiUngs are to be plastered, and that Section Through Floors and Partitions 72G Strength and Stiffness of Wooden Floors Chap. 21 only single flooring will be used in the second story and attic. We will assume that the attic-joists are to be 2 by 8 in, 16 in on centers, and that the width of floor supported by the partition is 10 ft. The second-floor area supix)rted by a single joist is 12 in by 15 ft, or 15 sq ft. The weight of the floor- joists per sq ft is 5 lb, of the plastered ceiling 10 lb and of the flooring 3 lb, making the dead load per sq ft 18 lb. For the live or super- imposed load we should allow 40 lb and hence the load per square foot on each second-floor joist due to the second floor and its load is 58 lb. As the floor- area for a single joist is 15 sq ft the load from tiue second floor is 15 sq ft by 58 lb per sq ft or 870 lb on each joist. We must now find what will be the load from the partition and attic-floor. The attic-floor and ceiling weigh about 16 lb per sq ft, and 24 lb is a sufiicient allowance for the live load. The weight per linear foot on the partition will therefore be 400 lb. A partition of 2 by 4-in studs, lathed and plastered on both sides, weighs about 20 lb per sq ft of face; hence tlie partition itself weighs iSo lb per lin ft. The partition and attic-floor, therefore, bring a load of 580 lb on each second-floor joist, con- centrated at a point one-fourth of the span from the inner end of the joist. To combine this concentrated load with the load from the second floor, we must multiply the concentrated load by 1.5 (Table IV, page 632), which gives an equivalent distributed load of 870 lb. Adding this to the second-floor load we have i 740 lb as the total load for which each joist should be proportioned. From Table VIII, page 639, we find that the safe load for a i by lo-in spruce joist of 15-ft span is 5r8 lb; hence the breadth of each joist should be equal to I 740/518= 3.36 or about 33^ in. Deeper joists, therefore, must be used. If we try 2 by 12-in joists, 12 in on centers, the safe load for a i by lo-in spruce joist of 15-ft span is 747 lb. Hence the breadth is i 755/747 = 2.35 or about 2\i in, indicating 2H by 12-in joists, 12 in on centers. If the fiber-stress is assumed at 800 lb per sq in, the values of Table X, page 641, may be used. This will give, for 2 by 12-in joists, 12 in on centers and 15-ft span, 850 lb for the safe load for a i by 12-in joist; and i 755/850 = about 2 in. The load per sq ft on each of these joists is i 755/15 = 117 lb; and Tables XVI and XXV, pages 739 and 744, give 16 ft 6 in and 16 ft i in for the maximum safe spans. Example 3. It is required to determine the sizes of the girders and joists in the floor shown in Fig. 3, all of the timbers being of long-leaf yellow pine, and the floor above being supported by posts and girders in the same way. The building is intended for lodging purposes, and the height of the story is 10 ft. There is to be a double floor and the ceilings and partitions are to be plastered. The floor-joists are to be spaced 16 in on centers. Average timber, poorly seasoned. Solution. We will first determine the size of the common joists at A , calling the span 24 ft. The floor-area supported by a single joist is 24 by iH ft, or 32 sq ft. From Table XIII or XXII, pages 737 and 742, for a 24-ft span, 2H by 14-in joists are probably required. We will allow 8% lb per sq ft for the weight of joists and bridging (Table I, page 718), 10 for the ceiling and 6 for the flooring, making 24% lb per sq ft for the dead load. For the live load we will allow 40 lb per sq ft. The load for which the joists should be proportioned is, there- fore, 32 by 64^4 or 2 072 lb. We may use Table XII, page 643, to find the maximum load for a i by 14-in joist of 24-ft span. The deflection-load given in the table is 882 lb; hence the thickness of the joists must equal 2 072/882 == 2.35 or about 2H in. Therefore 2H by 14-in long-leaf yellow-pine joists, 16 in on centers, may be used, but they should run -full 2I/I2 iji thick. The joists at B (Fig. 3) have to support a partition, but as the span is much less, and the Computations for Wooden Beams and Girders 727 partition is quite near the end of the joists, it will be safe to make them of the same size as at ^ . The joists at C (Fig. 3) have the same floor-load to support as at ^, and in addition the weight of the partition, which is concentrated at one-third of the span from one support. As the partition is lo ft high, 13 H sq ft of partition will be supported by each joist, the joists being i6 in on centers. Assuming 20 lb Fig. 3. Plan of Floor-framing Showing Partitions Above per sq ft of face as the weight of the partition, we have 267 lb as the weight from the partition to be borne by each joist. To reduce this to an equivalent distributed load, we should multiply by 1.78 (Table IV, page 632), which gives 468 lb. The joists at C, therefore, should be proportioned to a uniformly distributed load of 2 o72-f 468= 2 540 lb, which requires 14-in joists, 2,88 in thick, or, say, 3 .by 14-in joists. 728 Strength and Stiffness of Wooden Floors Chap. 21 The Header. We will next determine the required breadth for the header, H (Fig. 3), the depth being necessarily 14 in, the same as for the joists. The header is 14 ft long and must support the floor half-way to the wall, or a floor-area of 14 by 9 ft, or 126 sq ft. Multiplying this area by 64% lb, the weight per square foot, we have 8 159 lb, the total floor-lead to be supported, to which must be added a certain percentage of the partition. The portion of the partition supported by the header is (14 f t — i ft 4 in) = 12 ft 8 in long and 10 ft high, and v/ill weigh about 20 lb per sq ft of face, or a total of 2 532 lb. As the partition is one-ninth of the span from the header, eight-ninths of its weight will be supported by the header and on-^-ninth by the wall. Eight-ninths of 2 532 is 2 251 lb, which, added to the floor-load, makes a total load for the header of 10 410 lb. From Table XII, page 643, we find that the safe load for a i by 14-in beam of long-leaf yellow pine, 14-ft span, is i 867 lb; hence it will require a breadth of 10 410/1 867 = 5.58 in. If the tail-beams are framed into the header, it should be thicker to allow for the weakening effects of the framing; so that, in this case, the header should be at least 6 by 14 in in actual cross-section, before any framing is done. The Trimmers. We will next consider the trimmer, T (Fig. 3). This beam has four loads: (i) a distributed floor-load; (2) a distributed load from the partition above; (3) one-half the load on the header //; (4) and a small direct load from the longitudinal partition. (i) The strip of floor supported by the trimmer will be about 12 in wide and 24 ft long, and wiU weigh 64% lb per sq ft X 24 sq ft = i 554 lb. (2) The partition above wiU weigh 10 X 24 ft X 20 lb per sq f t = 4 800 lb. (3) One-half of the load on // is 10 410/2 = 5 205 lb. As this is concentrated at one-fourth the span from the support, we must multiply it by 1.5 (Table IV, page 632) to obtain the equivalent distributed load, which then becomes 5 205 X 1.5 = 7 808 lb. (4) About 8 in of the longitudinal partition must be supported by the trimmer, and this will weigh 10 x ^^ ft x 20 lb per sq ft = 133 lb. As it is concentrated at one-third the span from the support, we must multiply by 1.78 (Table IV, page 632) to obtain the equivalent distributed load, which then becomes 133 X 1.78= 237 lb. The total load for which the trimmer must be computed will be, therefore: ; (i) From the floor i 554 ih (2) From the partition above 4 800 lb (3) From the header 7 808 lb (4) From the longitudinal partition 237 lb Total : 14 399 ih The trimmer should be of the same depth as the joists, 14 in. From Table XII, page 643, we find that a i by 14-in long-leaf yellow-pine beam of 24-ft span will safely support 882 lb and not cause a deflection of more than Heo of the span. Hence, the breadth of the trimmer would be 14 399/882 = 16.34 in, which is greater than the depth. This would suggest the substitution of a steel I beam of proper size or the use of a deeper wooden beam, such as an 11 by 16 or a 12 by i6-in beam. If the. deflection of the wooden beam is not taken into account, the strength-value, i 090 lb of Table XII, page 643, may be used, giving 14 399/1 090= 13.21 in as the width of the beam. This would agree with the former New York Code for strength. If the flexure fiber-stress is taken at i 300 lb per sq in, permitted by the Chicago code, Table XIII, page 644, may be used, giving 14 399/1 179 = 12.21 in for the widttj of the trimmer. Computations for Wooden Beams and Girders 729 If I 800 lb per sq in is taken for S, Table XV, page 646, is used, giving 14 399/. I 63.3 = 8.81 in for the width. Hence, the architect will be governed by laws in cities, or by engineering judgment or experience elsewhere, and this applies to the joists as well as to the girders. If wooden trimmers are used, they should be hung in beam-hangers (see last part of this chapter). The load on the trim- mer, R, will be the same as on the trimmer, T, except for the cross-partition. Deducting the weight of this partition, we have 14 399 — 4 8cx3 = 9 599 lb for the equivalent distributed load on R, wkich, from Table XII, page 643, gives, for the required breadth 10.88 in or 8.8 in, depending upon whether the deflection is or is not considered. Other variations in the required width of a 14-ia wooden girder will result from the use of other fiber-stresses. The Girders. The floor-area supported by the girder, G (Fig. 3), is equal to 12 by 24 ft, or 288 sq ft. As a general rule, it will be safe in estimating the live load on girders to take only 85% of the load assumed for the floor-beams, be- cause there will always be some portion of the floor supported by the girder that is not loaded, and pro])ably other portions that will not be loaded up to the assumed load. Hence, the live load would be 85% of 40 lb, or 34 lb. The dead load of the floor and ceiling will be about 25 lb, and the girder itself will weigh between i and 2 lb per sq ft, say* 2 lb per sq ft of floor, more, so that we will use 61 lb per sq ft for the total floor-load on this girder. As girder G sup- ports 288 sq ft, this will be equivalent to 17 568 lb. The girder supports, also, a partition, 9 ft high, above, which will weigh 12x9x20 = 2 160 lb. The total load for which the girder should be proportioned is, therefore, 19 728 lb. As- suming 14 in for the depth of the girder, we find from Table XII, page 643, that the safe load for a i by 14-in long-leaf yellow-pine beam of 12-ft span is I 867 lb; hence the breadth of girder, G, should be 19 728/1 867 = 10.56 in and an II by 14-in girder could be used. The girder, G' (Fig. 3), supports a floor-area at the left of 12 x 12 = 144 sq ft, which represents a distributed load of 8 784 lb. On the right side of the girder, there is a strip of floor 40 in wide by 12 ft long (8 in of the floor being included in the load on T) which will weigh 2 440 lb. This may be considered as a con- centrated load applied 20 in, or one-seventh the span, from the end of the girder, in which case the effect of the load is practically the same as if the load were distributed. The load coming upon girder G' from T will equal one-half the actual distributed load on T, plus three-eighths (H of %) of the load on //. The load on // we found to be 104101b, and three-eighths of this is about 3900 lb. The actual distributed load on T we found to be i 5544-4800 = 6354 ib, and one-half of this is 3 177 lb. Hence the trimmer, T, transmits a load of 3 900 -1- 3 177 = 7 077 lb to the girder, which must be considered as a concentrated load applied at one third the span from the support, and hence we must multiply it by 1.78 (Table IV, page 632) to obtain the equivalent dis- tributed load, which gives 12 597 lb. The load for which the girder, G' (Fig. 3), should be computed will be From the floor at the left 8 784 lb From the floor at the right 2 440 lb From the trimmer, T .* 12 597 lb From the partition above. 2 160 lb '$ ^.,.1 , Total 25 981 lb From Table XIT, page 643, we find that this load will require a (13.9 by 14-in) 14 by 14-in girder. For this floor, therefore, the requirements, if long-leaf yellow pine is used, and if the maximum flexure fiber-stress, S, is 730 Strength and Stiffness of Wooden Floors Chap. 21 taken at i 200 lb per sq in (a conservative vaUie for non-ideal conditions, for example) and the modulus of elasticity, E, at i 500 000 lb per sq in, are as follows: an II by 14-in girder at G; a 14 by 14-in girder at G' ; an 11 by 16, or 12 by i6-in wooden beam or a steel I beam for the trimmer, J"; an 11 by 14-in beam for the trimmer, R; a 6 by 14-in beam for the header, //; 23^ by 14-in joists at A and B; and 3 by 14-in joists at C. For these stress-requirements the architect might decide to use steel I beams for girders G, G', etc., and for the trimmers, T and R. For 5, 1300, Q'able XIII, page 644, may be used for long-leaf yellow pine; for S, 1500 lb per sq in. Table XIV, page 645; for a fiber- stress, S, of 1800 lb per sq in, Table XV, page 646; and for S equal to 1600 lb per sq in. Table XII, page 643, with the strength-values increased one-third. Of course, the sizes of the timbers are diminished as the assumed safe fiber- stre.sses are increased. This example illustrates nearly all of the computations that are required to determine the sizes of the joists and special beams or girders in any ordinary floor-construction. The method of computation is the same for any floor- load, the only difference being that the greater the live load assumed the greater will be the loads for which the beams must be proportioned. As will be seen, the most laborious computations are those for beams which receive loads from different sources, and it will generally be found that the weakest portions of any particular floor arc the headers, trimmers and girders, and the beams which support partitions. The Strength of Mill-Floors. The beams and girders for mill-floors should be computed by the same general method illustrated in the foregoing examples, involving, (i) the determination of the loads on the beams and girders and, (2) the sizes of the beams and girders required to support such loads. Required Thickness of Plank Flooring. The thickness of the plank floor- •ing in mill construction may be determined by formulas (i) and (2): k in in ) 4 /weig nigth ) " V Thickness of plank in in ) 4 /weight per sq ft x l"^ required for strength ) » 24 x .4 Thickness of plank in in ) * /weight per sq ft x l^ required for stiffness ) V 19.2 X <^i (i) (2) In these formulas, / is the span in feet, from center to center of beams, A the constants for strength (page 628), and ei the constant for stiffness (page 664), When the planks are connected by ^4-in splines, and extend over two spans. Formula (i) may be used. If the planks arc in single lengths from beam to beam, or are not splined, then Formula (2) should be used. Tables IV to XI,* inclusive, show the safe loads for plank flooring of different woods, thicknesses and spans, derived from the formulas for strength and stiffness, the values in the first horizontal line in the case of each thickness of plank * Tables VIII to XI, inclusive, were calculated by Mr. F. E. Kidder and are retained from the preceding edition of the Pocket-Book. Tables IV to VII, inclusive, are added to conform to the most conservative fiber-stresses of the building codes and of the other chapters of the new edition. In the judgment of many constructors the higher values of Tables VIII to XI are safe when more favorable conditions of quality and dryness of materials prevail. In using any of the tables, care must be taken to notice whether or not the safe loads given include the weight of the flooring itself. In the revision of this chapter the author is indebted to Professor F. H. Safford, of the University of Penn- sylvania, for the computations required for the new Tables IV to VII and for the checking 9f Tables VII! to XI. • Explanation of Tables 731 denoting the loads given by the formula for strength and the figures iri the second line those given by the formula for stiffness. The span is supposed to be measured from center to center of beams. The values given by the formula for strength should be considered safe only for spHned floors and where the planks are continuous over at least two spans. If the thickness of the planks falls short H or even H in from the dimensions given, the safe loads must be mate- rially reduced. In Table IV, the modulus of elasticity, E, on which ci in the stiffness-formula depends, is i 500 000 lb per sq in, and the safe fiber-stress, S, on which the constant for strength. A, depends, is i 200 lb per sq in, A being 67. The safe loads given are within the requirements of all cities for strength and stiffness foi; long-leaf yellow pine, and of all cities for Douglas fir. In Table V, £ is i 200 000 lb per sq in, S, i 000 lb per sq in, and A is 56, The loads given satisfy the requirements of Chicago and of most other citie^ for strength for short-leaf yellow pine. The values given for stiffness, also, are recommended for this wood. ! In Table \T, E is i 200 000 lb per sq in, S, 800 lb per sq in, and A is 44^ The loads given satisfy the requirements of all cities for strength, for spruce,' Norway pine and white pine, and the values given for stiffness, also, are recommended for spruce. For Norway pine, E = i 100 ocx) lb per sq in may be used. In Table VII, E is i 000 000 lb per sq in, S, 'joo lb per sq in, and A is 39. The loads given for strength can be used for any woods of that safe fiber- stress, and the loads for stiffness are recommended for white pine. In Tables VIII, IX, X and XI, the safe loads are calculated from still other values oi S, A, E and ei, indicated with each table, and may be used by those who wish to assume larger safe values for the strength and stiffness-factors in cases where there are no restrictions from building laws. For any other values of A or ei required, such values must be inserted in Formula (i) or (2) and the thicknesses of the planks determined or the safe load determined for any given thickness of planks. Note. It is to be noted that for ideal conditions and commercially dry lum- ber, protected from moisture, and when there is no impact, the given fiber-stresses for flexure may be increased from 30 to 40%. (See, also, important notes on pages 628, 637 and 647 regarding stresses in and loads on wooden beams.) 732 Strength and Stiffness of Wooden Floors Chap. 21 Table IV. Safe Live Loads* in Pounds per Square Foot for Plank Flooring See explanation on pages 730-1 • The loads are based on the following values. Strength: S= 1 200 lb per sq in, A= 67; stiffness: £= i 500 000 lb per sq in, ei= 116 LONG-LEAF YELLOW PINE AND DOUGLAS FIR f Thickness of planks, in Distance between centers of floor-beams, in feet 4 5 6 7 8 9 10 II 12 iH 353 229 226 117 157 68 115 43 88 29 70 20 2H 567 466 363 239 252 138 185 87 142 58 112 41 91 30 75 22 63 17 2% 760 724 486 371 338 214 248 135 190 90 150 64 122 46 100 35 84 27 3H 788 764 547 442 402 278 308 187 243 131 197 95 163 72 137 55 4 715 660 525 416 402 278 318 196 257 143 213 107 179 82 5 820 812 628 544 496 382 402 278 332 209 279 161 6 904 940 715 660 579 481 478 361 402 278 * Weight of ceiling, if any, and also of the flooring itself is to be deducted from these values, t If S for Douglas fir is taken at 1000 lb per sq in, use Table V. Table V. Safe Live Loads "i" in Pounds per Square Foot for Plank Flooring See explanation on pages 730-1. The loads are based on the following values. Strength: S = 1 000 lb per sq in, ^ = 56; stiffness: E = 1 200 000 lb per sq in, Cx = 92 SHORT-LEAF YELLOW PINE Thickness of planks, in Distance between centers of floor-beams, in feet 4 5 6 7 8 9 10 II 1 12 .li 295 182 189 93 131 54 96 34 74 23 2% 474 370 303 189 211 no 155 69 118 46 94 32 76 24 23/4 635 574 406 294 282 170 207 107 159 72 125 50 102 37 84 28 71 21 3V2 I 029 659 606 457 351 336 221 257 148 203 104 165 76 136 57 114 44 4 860 597 523 439 330 336 221 26s 155 215 113 178 85 149 65 S 933 686 644 525 431 415 303 336 221 278 166 233 128 6 987 756 745 597 523 484 382 400 .87 336 221 ♦ Weight of ceiling, if any, an4 also of the flooring itself is to be deducte4 from these values. Tables of Safe Loads for I*lank Flooring 733 Table Vt. Safe Live Loads* in Pounds per Square Foot for Plank Flooring See explanation on pages 730-1 • The loads are based on the following values. Strength: S= 800 lb per sq in, A = 44; stiffness: £= i 200 000 lb per sq in, Ci= 92 SPRUCE, NORWAY PINE AND WHITE PINE Thickness of planks, in Distance between centers of floor-beams, in feet 4 5 6 7 8 9 ID n 12 1% 232 182 148 93 103 54 76 34 58 23 2% 372 370 238 189 i6s no 122 69 93 46 74 32 60 24 2% 499 319 294 222 170 163 107 125 72 99 50 80 37 66 28 zV^ 809 517 359 351 264 221 202 148 160 104 129 76 107 57 89 44 4 676 469 345 330 264 ^221 209 155 169 113 140 85 117 65 S 733 539 412 326 303 264 221 218 166 183 128 6 776 594 469 380 314 287 264 221 * Weight of ceiling, if any, and also of the flooring itself is to be deducted from these values. Table VII. Safe Live Loads* in Pounds per Square Foot for Plank Flooring See explanation on pages 730-1 • The Iq^ds are based on the following values. Strength: S = 700 lb per sq in, A = 39; stiffness: £ = i 000 000 lb per sq in, Ci = 77 FOR HEMLOCK AND WOODS OF SIMILAR STRENGTH AND STIFFNESS Thickness of planks, in 1 Distance between centers of floor-beams, in feet 4 206 152 8 9 10 II 12 5 6 7 l7/^ 132 78 91 45 67 28 2% 330 309 212 158 147 92 lOJi 58 82 39 65 27 .,... 2% 442 480 283 246 197 142 146 90 III 60 87 42 71 31 zVi 717 459 319 293 234 185 179 124 142 87. 115 63 95 48 80 37 4 936 599 416 306 276 234 185 185 130 ISO 95 124 71 104 55 5 936 650 478 366 361 289 253 234 185 193 139 163 107 6 936 688 526 416 337 319 278 240 234 18S * Weight of ceiling, if any, and also of the flooring itself is to be deducted from these valu«s. 734 Strength and Stiffness of Wooden Floors Chap, 21 Table VIII. Safe Live Loads* in Pounds per Square Foot for Plank Flooring See explanation on pages 730-1. The loads are based on the following values. Strength: -5** i 800 lb per sq in, A = 100; stiffness: E=« 1 780 000 lb per sq in, Ci« 137 Recommended by Mr. Kidder for LONG-LEAF YELLOW PINE Thickness of planks, in Distance between centers of floor-beams, in feet 4 5 6 7 8 9 10 11 12 iH 515 258 325 126 222 68 160 38 120 21 92 II 72 5 2H 831 536 527 268 362 149 262 88 197 . 54 153 34 121 24 97 12 80 6 2U 1 118 838 710 421 488 237 354 144 267 91 208 59 165 38 134 25 no 15 zYi 1 158 884 798 504 582 310 442 202 345 136 276 94 225 67 186 47 4 1046 759 763 470 580 308 454 210 364 148 296 106 246 77 5 1200 934 913 618 716 427 576 304 471 223 392 166 6 1322 I 081 1038 751 836 540 686 398 572 300 * Weight of ceiling, if any, to be deducted. The weight of the flooring has been deducted from values derived from formulas. Deduction about 72 lb per cu ft floor-material. Table IX. Safe Live Loads * in Pounds per Square Foot for Plank Flooring See explanation on pages 730-1. The loads are based on the following values. Strength: 5 = i 620 lb per sq in, A = 90; stiffness: E= 1 425 000 lb per sq in, fi= 110 Recommended by Mr. Kidder for DOUGLAS FIR AND SHORT-LEAF YELLOW PINE 1 1 Thickness : of planks, ■ in Distance center to center of floor-beams, in feet 4 5 6 7 8 9 10 II 12 1% 462 205 291 99 199 52 143 28 106 15 81 7 64 2% 747 428 473 212 324 117 234 68 176 41 136 25 107 14 ■ 2% 1005 670 637 335 438 187 317 112 239 69 185 44 147 23 119 17 . 97 9 ' zVi I 040 7c6 717 401 522 246 395 159 308 106 246 72 200 50 165 34 4 1362 I 061 940 606 685 374 520 244 406 165 325 115 265 81 220 58 • 5 1476 1 198 1078 745 819 491 642 338 516 240 . 422 174 351 128 6 1560 1302 1 187 863 932 597 749 428 614 314 512 236 * Weight of ceiling, rf any, to be deducted. The weight of the flooring has been deducted from values derived from formulas. Deduction about 72 lb per cu ft floor-material. Tables of Safe Loads for Plank Flooring 73S fable X. Safe Live Loads * in Pounds per Square Foot for Plank Flooring See explanation on pages 730-1 • The loads are based on the following values. Strength: 5= 1 260 lb per sq in, A =» 70; stiffness: £= i 294 000 lb per sq in, ej « 100. Recommended by Mr. Kidder for SPRUCE Thickness of planks, in Distance between centers of floor-beams, in feet 4 5 6 7 8 9 10 II 12 1% 360 188 227 92 155 49 III 28 83 15 64 8 50 2% 581 391 368 194 252 108 182 64 137 39 105 24 83 15 67 54 23/4 782 612 496 307 341 173 247 104 186 66 144 42 115 28 - 93 18 76 2>yi 1228 1274 781 644 548 367 391 225 296 146 231 98 184 68 150 47 124 33 4 1060 968 731 554 533 343 405 225 317 153 253 108 207 77 171 56 5 1 148 1093 839 682 638 450 500 311 402 212 329 162 273 120 6 I 213 I 188 924 789 725 548 583 394 478 290 400 220 * Weight of ceiling, if any, to be deducted. The weight of the flooring has been deducted from values derived from formulas. Deduction about 72 lb per cu ft floor-material. Table XI. Safe Live Loads * in Pounds per Square Foot for Plank Flooring See explanation on pages 730-1. The loads are based on the following values. Strength: S = x 080 lb per sq in, A = 60; stiffness: E= 1 073 000 lb per sq in, ei = 83 Recommended by Mr. Kidder for WHITE PINE Thickness of planks, in Distance between centers of floor-beams, in feet 4 5 6 7 8 9 10 II 12 iH 307 •153 193 74 131 39 94 21 70 II 53 5 41 2% 496 318 314 157 214 85 154 50 116 40 89 18 70 10 56 2% 668 499 424 249 290 139 210 83 158 52 122 33 97 20 78 12 63 z\^ 1088 I 041 691 526 476 298 346 183 261 119 203 78 162 53 131 36 108 25 4 906 791 625 451 455 278 345 181 269 123 215 85 175 60 145 43 5 982 893 716 555 544 366 426 251 342 178 281 129 232 95 6 I 419 1553 1037 970 789 643 619 445 497 319 407 234 339 175 * Weight of ceiling, if any, to be deducted. The weight of the flooring has been deducted from values derived from formulas. Deduction about 72 lb per cu ft floor- material. 736 Strength and Stiffness of Wooden Floors Chap. 21 Tables for the Maximum Span of Floor- Joists. As the timbers commonly used for floor-joists are sawed to regular sizes and are usually spaced either 1 2 or 16 in on centers, it is practicable to show by means of tables the sizes of joists required to support given loads with given spans and spacings. Tables giving the MAXIMUM SAFE SPANS are the most convenient for general use, and the follow- ing tables have accordingly been prepared. They show at a glance the max- imum spans for which different sizes of floor-joists and ceihng-joists should be used for different loads and spacings, and it is believed that they will be found applicable to most buildings in which wooden floor-joists are used. By knowing the size of a room and the purpose for which it is to be used, the sizes of the floor-joists required can be determined at a glance. Incidentally the tables show, also, the kind of wood most economical to use. If, owing to the room being irregular in shape, the joists must be of different lengths, the spacing or thickness of the joists may be varied, so that the same depth may be used throughout. Precautions Required in Using Tables. The precautions necessary in using these tables are in regard to the superimposed loads and the actual sizi:s of the timbers. The total loads for which the maximum spans have been com- puted are given at the head of each table. The actual weight of the floor (joists, flooring, plastering and deafening, if any) subtracted from the total load will give the superimposed load, that is, the load which the floor is expected to carry. If the actual sizes of the joists are less than the nominal dimensions, the spans or spacings must be reduced from those given in the tables, and as the stock sizes of joists generafly run from li in to % in scant of the nominal dimensions, this fact should always be taken into account when determining upon the sizes of joists. In this connection it will be convenient to remember that 2-in joists, spaced 16 in on centers, have the same strength as I'/ii-in joists, 12 in on centers. A reduction should also be made for any cutting of the JOISTS that may be required. No allowance has been made for partitions, and when they are to be supported by the floor-joists, additional joists should be used or the span reduced according to the relative direction or position of the partitions and joists. , ■ I Tables XH to XX. Tables XII to XVI, inclusive, were computed by the formula for stiffness (Chapter XVI, page 636 and Chapter XVIII, page 665), on the assumption that the deflection should not exceed Ho in per foot of span. They are based on the values of E (the modulus of elasticity) recommended by F. E. Kidder. Tables XVII to XX, inclusive, were computed by the formula for strength (Chapter XVI, page 635), and values for S (the safe fiber-stress) recommended by Mr. Kidder. The spans given in Tables Xlt to XX; inclu- sive, come within the requirements of the Buffalo and Denver building laws, and Tables XII, XIV, XV, XVI and XVII comply with the Chicago law and very nearly with the New York law; but to comply with the Boston law a reduction of about one-sixth must be made from th« spans given (1914).* Tables XXI to XXIX f inclusive, were computed for reduced values of E (the modulus of elasticity,) S (the flber-stress for flexure) and A (the constant for flexural strength) in the formulas used, these values agreeing generally with the stresses throughout the revised handbook. Of these neW~-tables, also, Tables XXI to XXV, inclusive, were computed by the fo"rmula for stiffness, and Tables XXVI to XXIX, inclusive, by the formula for strength. * Building Codes arc frequently revised and must be consulted. t In the revision of this chapter the author is indebted to Mr. A. T. North. M. Am. Soc. C. E., for valuable assistance in the computations required for the new Tables XXI to XXIX. "^ Tables for Maximum Span of Ceiling and Floor-Joists 737 Table XII. Maximum Span for Ceiling- Joists See explanatory notes on page 736 d, 20 pounds 1 ^ . Total loa per square foot Sizes of Distance on Hemlock, *E = White pine, £ = I 073 000 Norwav pine or spruce. Douglas fir or Texas pine, Long-|eaf yellow pine. joists centers I 045 000 R = i 294000 E = i 425000 £ = i 780000 in in ft in ft in ft in ft in ft in 2X4 12 9 3 9 5 10 I 10 5 II 2 2X4 16 8 5 8 6 9 I 9 5 10 I 2X6 12 14 14 I 15 I 15 7 16 8 2X6 16 12 8 .12 10 13 8 14 ' 2 15 2 2X8 12 18 8 18 10 20 I 20 9 22 4 2X8 16 17 17 2 18 4 18 II 20 5 2X8 20 15 9 IS 10 17 17 6 18 10 ' Total load, 24 pounds per square foot | 2X10 12 22 22 2 23 8 24 5 26 4 2X10 16 20 20 2 21 7 22 3 23 10 2X10 20 18 6 18 8 20 20 7 22 2 2X1 V 12 26 s 26 8 28 5 29 4 31 7 2X12 16 24 24 2 25 10 26 8 28 8 2X12 20 22 3 22 5 24 24 8 26 8 * E is the modulus of elasticity and is in pounds per square inch. Table XIII. Maximum Span for Floor- Joists for Dwellings, Tenements ar id Grammar -School Roo ms with Fix ed Desks See explanatory notes on page 736 Total load, 60 pounds per square foot Sizes of Distance Hemlock, White pine, Norway pine or Douglas firot Long-leaf yellow R = i 073000 spruce. Texas pine. pine. joists centers I 045 000 E = I 294 000 E = i 425 000 E = i 780000, in ^ in ft in ft in ft in ft in ft in 2X6 12 9 9 9 10 10 5 10 10 II 7 2X6 16 8 9 8 10 9 6 9 10 10 6 3X6 12 II I II 2 12 12 5 13 4 3X6 16 10 I 10 2 10 10 II 2 12 I 2X8 12 12 II 13 I 13 II 14 S IS 6 2X8 16 II 9 II 10 12 8 13 I 14 I 3X8 12 14 9 14 II 16 16 6 17 8 3X8 16 13 6 13 7 14 6 IS 16 2 2X10 12 16 2 16 4 17 5 18 19 4 2X10 16 14 9 14 10 15 9 16 4- 17 7 Total loa d, 66 pounds per square fc )Ot 3 Xio 12 18 18 I 19 3 20 21 6 3 Xio 16 16 3 16 5 17 7 18 2 19 6 2 X12 12 18 10 19 20 3 20 10 22 * 6 2 X12 16 17 2 17 3 18 4 19 20 6 3 X12 12 21 6 21 8 23 2 24 2S 9 3 X12 16 19 7 19 8 21 I 21 9 23 5 2 X14 12 22 22 2 23 8 24 4 26 3 2 X14 16 20 ■• 20 I 21 6 22 2 23 10 2^/^2X14 12 23 8 23 10 25 6 26 3 28 3 2' 2X14 16 21 6 21 8 23 2 23 10 25 8 3 X14 12 25 4 25 4 27 I 28 30 I 3 X14 16 23 23 24 7 2S 4 27 4 E is the modulus of elasticity and is in pounds per square inch. 738 Strength and Stiffness of Wooden Floors Chap. 21 Table XIV. Maximum Span for Floor- Joists for Office-Buildings See explanatory notes on page 736 Total load, 93 pounds per square foot Sizes Distance White pine, * E = i 073000 Norway pine Douglas fir Long-leaf of on or spruce, or Texas pine, yellow pine, joists centers E = i 294 000 E = i 425 000 £ = i 780000 in in ft in ft in ft in ft in 3X8 12 12 10 13 9 14 2 15 4 3X8 16 II 8 12 6 12 10 13 10 2X10 12 14 I IS I 15 6 16 7 2X10 16 12 9 13 8 14 I 15 2 3X10 12 16 I 17 3 17 9 19 2 3X10 16 14 8 15 8 16 2 17 5 2X12 12 16 10 18 I 18 8 20 I 2X12 16 15 4 16 5 17 18 3 Total load, 96 pounds per square foot 3 X12 12 19 ? 20 6 21 2 22 9 3 X12 16 17 S 18 7 19 3 20 8 2 X14 12 19 6 20 10 21 7 23 2 2 X14 16 17 9 19 19 7 21 2 2^2X14 12 21 I 22 6 23 2 25 2i/^Xi4 16 19 2 20 4 21 2 22 8 3 X14 12 22 4 23 10 24 8 27 7 3 X14 16 20 4 21 8 22 S 24 I E is the modulus of elasticity and is in pounds per square inch. Table XV. Maximum Span for Floor- Joists for Churches and Theaters with Fixed Seats See explanatory notes on page 736 Total load, 102 pounds per square foot Sizes Distance White pine, * E = i 073000 Norway pine ■ Douglas fir Long-leaf of joists on centers or spruce, £ = I 294 000 or Texas pine, E = i 42s 000 yellow pine, E = i 780000 in in ft in ft in ft in ft in 3X8 12 12 6 13 4 13 9 14 10 3X8 16 II 4 12 2 12 6 13 6 2X10 12 13 7 14 7 IS I 16 a 2X10 16 12 4 13 3 13 8 14 9 3X10 12 15 8 16 9 17 3 18 7 3X10 16 14 2 IS 2 IS 8 16 10 2X12 12 16 5 17 7 18 I 19 6 2X12 16 14 10 IS II 16 5 17 8 Total load, ic )5 pounds per sq uare foot 3 X12 12 18 7 19 II 20 6 22 I 3 X12 16 16 10 18 I 18 7 20 I 2 X14 12 19 20 3 20 10 22 6 2 X14 16 17 3 18 s - 19 20 6 2K2X 14 12 20 4 21 9 22 6 24 3 21^^X14 16 18 7 19 10 20 6 22 I 3 X14 12 21 8 23 2 23 10 2S 9 3 X14 16 19 8 21 I 21 9 23 4 ■ E is the modulus of elasticity and is in pounds per square ioQh. Tables for Maximum Span of Floor-Joists 739 Table XVI. Maximum Span for Floor- Joists for Assembly-Halls and Corridors See explanatory notes on page 736 Total load, 123 pounds per square foot Sizes of joists in 3X8 3X8 2X10 2X10 3X10 3X10 2X12 2X12 Distance on centers in 16 12 16 Whit s pine, E = i 073 000 ft in II 7 10 8 12 10 II 7 14 8 13 4 IS 4 14 Norway pine or spruce, £ = I 294 000 ft in IS 14 16 15 Douglas fir or Texas pine, E = i 425 000 ft in 13 16 14 17 15 Long-leaf yellow pine, £ = I 780 000 ft in 14 12 15 13 17 15 18 16 8 Total load, 126 pounds per square foot 3 X12 3 X12 2 X14 2 X14 2K2X14 2HX14 3 X14 3 X14 17 IS 17 16 19 17 18 17 19 17 19 17 19 17 19 * E is the modulus of elasticitv and is in nounds ner snuare inch. Table XVII. Maximum Span for Floor- Joists for Retail Stores See explanatory notes on page 736 Total load, 174 pounds per square foot White pine, 5 = 1080 lb per sq in * A=6o Norway pine Douglas fir Long-leaf Sizes of Distance on or spruce, 5 = 1 260 or Texas pine, 5 = 1620 yellow 5=1 pine, 800 joists centers lb per sq in A =70 lb per sq in A=go lb per sq in A=ioo in m ft in ft in ft in ft in 3X8 12 II 6 12 5 14 I 14 9 3X8 16 9 II 10 2 12 2 12 9 2X10 12 II 8 12 8 14 S 15 I 2X10 16 10 2 10 II 12 5 13 I 3X10 12 14 4 IS 6 17 7 18 7 3X10 16 12 5 13 5 IS 2 16 2X12 12 14 I IS 2 17 2 18 2 2X12 16 12 2 13 I 14 II IS 8 Total load, 177 pounds per square foot | 3 X12 12 17 2 18 5 20 II 22 I 3 X12 16 14 10 16 3 16 17 7 18 2 19 n 19 21 I I 2 X14 16 14 2 IS 2 17 3 18 2 2i/^Xi4 12 18 2 19 7 22 3 23 6 23.2X14 16 IS 9 17 19 3 20 4 3 X14 12 19 II 21 6 24 S 2S 8 3 X14 16 17 3 18 7 •21 2 22 3 * A in the tables is assumed flexural fiber the coefficient in formulas for beams and is one-eighteenth of the stress, S. T40 Strength and Stiffness of Wooden Floors Chap. 21 Table XVIII.* Maximum Span for Rafters. Shingled Roofs not Plastered See explanatory notes on page 736 Total load, 48 pounds per square foot Norway Douglas Long-leaf Hemlock, White pine» pine or fir or Sizes of Distance 5=990 5 = 1080 spruce. Texas pine, yellow pine, 5=1800 on lb per sq in lb per sq in 5=1 260 5 = 1620 joists centers t^=55 A=6q lb per sq in A = 7o lb per sq in A=9o lb per sq in A = 100 in in ft in h in ft in ft in ft in 2X4 16 7 4 7 9 8 4 9 6 10 10 2X4 20 6 7 6 10 7 6 8 6 8 10 2X6 16 II I II 7 12 6 14 2 15 2X6 20 9 II ID 4 II 2 12 8 13 4 3X6 16 13 7 14 2 15 3 17 5 18 3 3X6 20 12 2 12 8 13 8 15 7 16 4 2X8 16 14 9 15 6 16 8 18 II 20 2X8 20 13 3 13 10 14 II 16 II 17 10 2X8 24 12 I 12 . 7 13 7 15 6 16 3 2X10 16 18 6 19 3 20 10 23 8 25 2X10 20 16 7 17 3 18 8 21 2 22 3 2X10 24 IS I 15 9 17 19 3 20 4 Table XIX.* Maximum Span for Rafters. Slate Roofs not Plastered, or Shingle Roofs Plastered See explanatory notes on page 736 Total load, 57 pounds per square foot Norway Douglas Long-leaf ellow pine, 5 = 1800 Sizes of Distance on Hemlock, White pine, 5 = 1 080 lb per sq in pine or spruce, 5=1260 fir or Texas pine, 5 = 1620 J 5=990 lb per sq in joists centers tA-SS A =60 lb per sq in A=yo lb per sq in A =90 b per sq in A = 100 in in ft in ft in ft in ft in ft in 2X4 16 6 9 7 I 7 7 8 8 9 2 2X4 20 6 6 4 6 9 7 9 8 2 2X6 16 10 2 10 7 II 6 13 13 8 2X6 20 9 I 9 6 10 2 II 7 12 3 3X6 16 12 6 13 14 I IS II 16 9 3X6 20 II I II 8 12 7 14 3 IS 2X8 16 13 7 14 2 IS 3 17 4 18 3 2X8 20 12 2 12 8 13 8 IS 6 16 4 2X8 24 II I II 7 12 6 14 2 14 II 3X8 16 16 7 17 4 18 9 21 3 22 5 3X8 3X8 20 24 14 ID 15 6 16 9 19 20 I 13 7 14 2 15 3 17 4 18 4 2X10 16 17 17 8 19 2 21 7 22 10 2X10 20 15 2 15 10 17 I 19 4 20 6 2X10 24 13 10 14 6 IS 7 17 8 18 8 ♦Tables XVIII, XIX and XX are intended fr r climates where a 2-ft snow- fall may be (expected. In the Southern States, where there is very little snow, the spa IS in Table XVIII will be safe for slate or gravel roofs if th 2 joists arc sawed to the full dimensions. Variations in " Safe spans" in different tables, 1 or the same kind of wood, d spend upon the assume d safe flex ural fiber-stre 3S or moduhis of elasticity or both. t A in the tables is the coefhcient in formulas for beams and is one-eighteenth of the assumed flexural fiber-stress, S. Table for Maximum Span of Rafters 741 Table XX.* Maximum Span for Rafters. Slate Roofs Plastered, or Gravel Roofs not Plastered See explanatory notes on page 736 Total load, 66 pounds per square foot Sizes of joists Distance on centers Hemlock, 5 = 990 lb per sq in White pine, 5 = 1 080 lb. per sq in A =60 Norway pine or spruce, 5=1260 lb per sq in A =70 Douglas fir or Texas pine, 5 = 1620 lb per sq in A =90 Long-leaf yellow pine, 5=1800 lb per sq in A = 100 in in ft in ft in ft in ft in ft in 2X6 16 9 5 9 10 10 8 12 I 12 9 2X6 20 8 6 8 10 9 6 10 9 II 5 3X6 16 II 7 12 I 13 I 14 10 15 7 3X6 20 10 4 10 10 II 8 13 3 14 2X8 16 12 7 13 2 14 2 16 2 17 2X8 20 II 3 II 9 12 9 14 5 IS 2 2X8 24 10 3 10 9 II 7 13 2 13 10 3X8 16 15 5 16 I 17 5 19 9 20 10 3X8 20 13 9 14 5 IS 3 17 8 18 8 3X8 24 12 7 13 2 14 2 16 2 17 2X10 16 15 9 16 6 17 9 20 2 21 3 2X10 20 14 I 14 8 15 II 18 19 2X10 24 12 10 13 5 14 6 16 6 17 5 2X12 16 18 10 19 9 21 4 24 2 2S 6 2X12 2X12 20 16 10 17 8 19 I 21 8 22 10 24 15 5 16 I 17 5 19 9 20 10 * Tables XVIII, XIX and XX are intended for climates where a 2-ft snow-fall may be expected. In the Southern States, where there is very little snow, the spans in Table XVIII will be safe for slate or gravel roofs if the joists are sawed to the full dimensions. Variations in "Safe spans" in different tables, for the same kind of wood, depend upon the assumed safe flexural fiber-stress or modulus of elasticity or both. t A in the tables is the coefficient in formulas for beams and is one-eighteenth of the assumed flexural fiber-stress, 5. 742 Strength and Stiffness of Wooden Floors Chap. 21 Table XXI. Maximum Span for Ceiling- Joists See explanatory notes on page 736 Total load, 20 pounds per square foot Sizes of joists Distance Hemlock, White pine, Norway Short-leaf yellow pine Long-leaf yellow pine, centers * £ = 900 000 E = i 000 000 pine, £ = i 100 000 spruce, Douglas fir, £ = I 200 ooc £ = i sooooo in in ft in ft in ft in ft in ft in 2X4 12 8 II 9 3 9 6 9 10 10 7 2X4 16 8 I 8 5 8 8 8 II 9 7 2X6 12 13 5 13 10 14 4 14 9 IS 10 2X6 16 12 2 12 7 13 13 - 5 14 s 2X8 12 17 10 18 6 19 I 19 8 21 2 2X8 16 16 3 16 10 17 4 17 10 19 3 2X8 20 15 I IS 7 16 I 16 7 17 10 Total load, 24 pounds per square foot | 2X10 12 21 21 9 22 5 23 I 24 II 2X10 16 19 I 19 8 20 5 21 22 2 2X10 20 17 8 18 4 18 II 19 6 21 2X12 12 25 2 26 26 II 27 9 29 II 2X12 i6 22 II 23 9 24 6 2S 2 27 2 2X12 20 21 3 22 22 9 23 S 25 2 * £ is the modulus of elasticity and is in pounds per square inch. Table XXn. Maximum Span for Floor- Joists for Dwellings, Tenements an d Grammar-School Rooms with Fixed Desks See explanatory notes on page 736 Total load, 60 pounds per square foot j Sizes of joists Distance Hemlock, White pine, Norway Short-leaf yellow pine. Long-leaf yellow pine. on centers *£:=9ooooo £ = i 000000 pine, £ = i 100 000 spruce, £ = i 200 000 Douglas fir, £ = I 500 000 in in ft in ft in ft in ft in ft in 2X 6 12 9 3 9 7 9 II 10 3 II 2X 6 16 8 5 8 9 9 9 3 10 3X 6 12 10 8 II II 4 II 8 12 7 3X 6 16 9 8 10 10 4 10 8 II S 2X 8 12 12 4 12 10 12 3 13 8 14 8 2X 8 16 II 3 II 8 12 12 4 13 4 3X 8 12 14 2 14 8 IS 2 IS 7 16 10 3X 8 16 12 II 13 4 13 9 14 2 15 3 2X10 12 IS 6 16 16 7 17 18 3 2X10 16 14 I 14 7 IS 15 6 16 8 Total load, 66 pounds per square foot [ 3 Xio 12 17 2 17 9 18 4 18 II 20 4 3 Xio 16 IS 7 16 2 16 8 17 2 18 6 2 X12 12 18 18 8 19 3 19 8 21 4 2 X12 16 16 4 16 II 17 8 18 19 S 3 X12 12 20 7 21 4 22 22 8 24 S 3 X12 16 18 8 19 4 20 20 7 22 2 2 X14 12 21 21 II 22 5 23 I 24 10 2 X14 16 19 I 19 9 20 5 21 22 7 2HX14 12 22 7 23 S 24 2 24 II 26 10 2M2X14 16 20 6 21 3 21 II 22 7 24 4 3 X14 12 24 24 10 2S 8 26 5 28 6 3 X14 16 21 10 22 7 23 4 24 2S 10 ' E is the modulus of elasticity and is in pounds per square inch. Tables for Maximum Span of Floor- Joists 743 Table XXUI . Maximum Span for Floor- Joists for Office-Buildings See explanatory notes on page 736 Total load, 93 pounds per square foot j Sizes of joists Distance Hemlock, White pine, Norway Short-leaf yellow pine, Long-leaf yellow pine, centers * £ = 900 000 E — i 000 000 £ = I 100 000 spruce, E = i 200 000 Douglas fir, E = i 500 000 m m ft in ft in ft in ft in ft in 3X 8 12 12 3 12 8 13 I 13 6 14 6 3X 8 16 ■ II I II 6 II II 12 3 ,13 2 2X10 12 13 4 13 10 14 3 14 8 IS 10 2X10 16 12 2 12 7 13 13 4 14 5 3X10 12 15 4 IS 10 16 4 16 10 18 2 ; 3X10 16 13 II 14 5 14 10 IS 4 16 7 ' 2X12 12 16 16 7 17 2 17 8 19 2X12 ;« 14 7 15 I 15 7 16 17 3 Total load, 96 pounds per square fo •ot 3 X12 12 18 2 18 10 19 5 20 21 6 3 X12 16 16 6 17 I 17 8 18 2 19 7 2 X14 12 18 6 19 2 19 10 20 s 21 II 2 X14 16 16 10 17 5 18 18 6 19 II 2I/2X14 12 19 II 20 8 21 4 22 23 8 2 1/2X14 16 18 2 18 9 19 5 19 II 21 6 3 X14 12 21 2 21 11 22 8 23 4 25 a 3 X14 16 19 3 19 II 20 7 21 3 22 10 * £ is the modulus of elasticity and is in pounds per square .inch. ,. Table XXIV. Maximum Span for Floor- Joists for Churches and Theaters with Fixed Seats See explanatory notes on page 736 Total load, 102 pounds per square foot Sizes of joists Distance Hemlock, White pine. Norway pine, £ = i 100 000 Short-leaf yellow pine, Long-leaf yellow pine, on centers ♦£=900000 £ = i 000000 spruce, £ = i 200000 Douglas fir, £ = i 500000 in in ft in ft in ft in ft in ft in 3X 8 12 II 10 12 3 12 8 13 I 14 I 3X 8 16 10 9 II 2 II 6 II II 12 9 ' 2X10 12 12 II 13 5 13 10 14 3 15 4 2X10 16 II 9 12 2 12 7 13 13 II , 3X10 12 14 10 IS 4 IS 10 16 4 17 7 '■■ 3X10 16 13 6 13 II 14 S 14 10 16 2X12 12 IS 7 16 I 16 8 17 I 18 5 2X12 16 14 2 14 8 IS I IS 7 16 9 Total loa i, 105 pounds per square f 30t 3 X12 12 17 8 i8 3 18 10 19 S 20 II 3 X12 16 16 16 7 17 I 17 8 19 2 X14 12 18 18 7 19 3 19 8 21 4 2 X14 16 16 4 16 II 17 5 18 19 4 2I/2X14 12 19 4 20 I 20 8 21 4 23 2I/2X14 16 17 7 18 3 18 10 19 4 20 11 3 X14 12 20 7 21 4 22 22 8 24 5 3 X14 16 18 8 19 4 20 26 7 22 2 E is the modulus of elasticity and is in pounds per square inch. 744 Strength and Stiffness of Wooden Floors Chap. 21 Table XXY. Maximum Span for Floor- Joists for Assembly-Halls and Corridors See explanatory notes on page 736 Total load , 12a pounds per square foot Sizes D of joists c istance Hemlock, White pine. Norway Short-leaf yellow pine. Long-leaf yellow pine. enters * £=900 000 E = i 000000 R = i 100 000 spruce, £ = I 200 000 Douglas fir, £ = I 500 000 in in ft in ft in ft in ft in ft in 3X 8 12 II 2 II 7 II II 12 3 13 3 3X 8 16 II 10 6 10 10 II 2 12 2X10 12 12 2 12 7 13 13 S 14 5 2X10 16 II I II S II 10 12 2 13 I 3X10 12 13 II 14 5 14 II 15 4 16 6 3X10 16 12 8 13 I 13 7 13 II IS 2X12 12 14 7 IS 2 IS 8 16 I 17 4 2X12 16 13 3 13 9 14 2 14 8 IS 9 Total loac [,126 pounds per square foot 3 X12 12 16 7 17 2 17 9 18 3 19 8 3 X12 16 IS I IS 7 16 I 16 7 17 10 2 X14 12 16 II 17 6 18 I 18 7 20 I 2 X14 16 IS 4 15 II 16 s 16 II 18 3 21^^X14 12 18 2 18 10 19 6 20 I 21 7 2i/iXi4 16 16 8 17 3 17 10 18 4 19 9 3 X14 12 19 4 20 I 20 8 21 4 22 II 3 X14 16 17 7 18 3 18 10 19 4 20 10 • £ is the modulus of elasticity and is in pounds per square inch. Table XXVI. Maximum Span for Floor- Joists for Retail Stores See explanatory notes on page 736 Total load, 174 pounds per square foot Sizes of Distance Hemlock, 5 = 600 lb White pine, spruce, 5=700 lb Norway pine, 5=800 lb Douglas fir short-leaf yellow pine 5 = 1 000 lb Southern long-leaf yellow pine, 5 = 1 200 lb on per sq in *A=33H joists centers per sq in A =38.88 per sq in per sq in per sq in A =44.44 A=5S.SS A =66^^ in in ft in ft in ft in ft in ft in 3X 8 12 8 7 9 3 9 II II I 12 2 3X 8 16 7 S 8 8 7 9 7 10 6 2X10 12 8 9 9 S 10 I II 4 12 5 2X10 16 7 7 8 2 8 9 9 10 10 9 3X10 12 10 9 II 7 12 s 13 10 IS 2 3X10 16 9 3 10 10 9 12 13 2 2X12 12 10 6 II 4 12 2 13 7 14 10 2X12 16 9 I 9 10 10 6 II 9 12 10 Total loac [, 177 pounds per square fc X)t 3 X12 12 12 6 13 6 14 6 16 2 17 9 3 X12 16 10 10 II 9 12 6 14 IS 4 2 X14 12 12 2 13 I 14 15 8 17 2 2 X14 16 10 6 II 4 12 2 13 7 14 II 2\iXi4 12 13 7 14 8 IS 8 17 6 19 2 2HX14 16 II 9 12 8 13 7 15 2 16 8 3 X14 12 16 8 18 19 3 21 6 23 7 3 X14 16 14 5 l^ 7 16 8 18 8 20 5 ♦ A in the tables is the coefficient in formulas allowable flexural fiber-stress S. For values of 62S. for beams and is one-eighteenth of the A for other woods, see Table II, page Tables for Maximum Span of Rafters 746, Table XXVII.'<' Maximum Span for Rafters. Shingled Roofs, not Plastered See explanatory notes on page 736 Total load, 48 pounds per square foot Sizes of Distance on Hemlock, 5=600 lb per sq in tA=33H White pine, spruce, 5 = 700 lb Norway pine. 5=800 lb ' Douglas fir, short-leaf yellow pine, 5 = 1 000 lb Southern long-leaf yellow pine, 5=1 200 lb joists centers per sq in yl =38.88 per sq in A =44-44 per sq in A =55.55 per sq in A=66% in in ft in ft in ft in ft in ft in 2X 4 16 5 9 6 3 6 8 7 5 8 2 2X 4 20 5 2 S 7 5 II 6 8 7 4 2X 6 16 8 8 9 4 10 II 2 12 3 2X 6 20 7 9 8 4 8 11 10 10 II 3X 6 16 10 7 II S 12 3 13 8 IS 3X 6 20 9 6 10 3 10 II 12 3 13 S 2X 8 16 11 6 12 6 13 4 14 II 16 4 2X 8 20 10 4 II 2 II II 13 4 14 7 2X 8 24 9 5 10 2 10 II 12 2 13 4 2X10 16 14 5 15 7 16 8 18 8 20 5 2X10 20 12 II 13 II 14 II 16 8 18 3 2X10 24 II 9 12 9 13 7 15 2 16 8 Table X xvin.* Maximum Span for Rai ters. Slate Roofs, not Plastered, or Shingled Roofs , Plastered J See explanatory note 3 on page 736 IXS Total load, 57 pounds per square foot -■■'. Sizes of Distance Hemlock, 5=600 lb White pine, spruce, 5=700 lb Norway pine, Douglas fir, short leaf yellow pine. Southern long-leaf yellow pine. on per sq in 5=800 lb 5=1 000 lb 5=1 200 lb joists centers tA=33H per sq in A =38.88 per vsq in per sq in per sq in A =44.44 A =55.55 A=66H in in ft in ft in ft in ft in ft in 2X 4 16 5 3 5 9 6 I 6 10 7 6 2X 4 20 4 9 5 I 5 6 6 I 6 8 2X 6 16 7 II 8 7 9 2 10 3 II 3 2X 6 20 7 I 7 8 8 2 9 2 10 I 3X 6 16 9 9 10 6 II 3 12 7 13 9 3X 6 20 8 8 9 5 10 I II 3 13 4 2X 8 16 10 7 II 5 12 3 13 8 IS 2X 8 20 9 6 10 3 10 II 12 3 13 5 2X 8 24 8 8 9 4 10 II 2 12 3 3X 8 16 13 14 IS 16 9 18 4 3X 8 20 II 7 12 6 13 5 15 16 4 3X 8 24 10 7 II 5 12 3 13 8 IS 2X10 16 13 3 14 4 15 3 17 I 18 9 2X10 20 II 10 12 9 13 8 IS 3 16 9 2X10 24 10 10 II 8 12 6 13 II IS 3 * Tables XXVII, XXVIII and XXIX are intended for climates where a 2-ft snow-fall may be expected. In the Southern States, where there is very little snow, the spans in Table XXVII will be safe for slate or gravel roofs if the joists are sawed to the full dimen- sions. Variations in "Safe spans" in different tables, for the same kind of wood, depend upon the assumed safe fliexural fiber-stress or modulus of elasticity or both. t See foot-note with Table XXVI. 746 Strength and Stiitness of Wooden Floors Chap. 21 Table XXIX.'*' Maximum Span for Rafters. Slate Roofs, Plastered, or Gravel Roofs, not Plastered See explanatory notes on page 736 Total load, 66 pounds per square foot Sizes of joists Distance on centers Hemlock, 6' =600 lb per sq in tA=33H White pine, spruce, 5=700 lb per sq in yl =38.88 Norway pine, 5=800 lb per sq in ^=44.44 Douglas fir, short-leaf yellow pine, 5 = 1 000 lb per sq in /I =55-55 Southern long-leaf yellow pine, 5 = 1 200 lb per sq in A=66^yi in in. ft in ft in ft in ft in ft in 2X 6 16 7 S 8 8 6 9 6 10 5 2X 6 20 6 7 7 2 7 7 8 6 9 4 3X 6 16 9 9 9 10 5 II 8 12 10 3X 6 20 8 I 8 9 9 4 10 5 II 5 2X 8 16 9 10 10 8 II 4 12 8 13 11 2X 8 20 8 10 9 6 10 2 II 4 12 5 2X 8 24 8 8 8 9 3 10 5 II 4 3X 8 16 12 I 13 13 II IS 7 17 I 3X 8 20 10 9 n 8 12 5 13 II IS 3 3X 8 2X10 24 16 9 10 10 8 II 4 12 8 13 II 17 5 12 4 13 3 14 2 IS ii 2X10 20 II II II 12 9 14 2 IS 7 2X10 24 10 I 10 tb i II 10 13 14 a 2X12 16 14 9 ti If 17 I 19 I 20 II 2X12 20 13 2 14 3 15 3 17 I 18 8 2X12 24 12 I 13 13 II IS 7 17 '1 • Tables XXVII, XXVIII and XXIX are intended for climates where a 2-ft snow-fall may be expected. In the Southern States, where there is very little snow, the spans in Table XXVII will be safe for slate or gravel roofs if the joists are sawed to the full dimen- sions. Variations in "Safe spans" in different tables, for the same kind of wood, depend upon the assumed safe flexural fiber-stress or modulus of elasticity or both. t See foot-note with Table XXVI. To Determine the Strength of an Existing Floor. When a building i$ leased for mercantile or manufacturing purix)ses the tenant will generally desire to know the greatest load w!\ich it will be safe to put upon the floors, and some building laws require that the safe load for the floors in certain classes of buildings shall be computed and posted in a conspicuous place in each story. It is therefore important that every architect should know how to compute the; safe strength of any existing floor. The problem is practically the reverse of' that of proportioning a floor to a given load. In speaking of the strength of a floor a distinction should be made between the safe strength and the safe load. The SAFE STRENGTH should mean the maximum safe load for the beams, includ- ing the weight of the construction, flooring and ceiling, while the safe load refers to the maximum load which may safely be placed uix)n the floor. The safe load is found by first computing the safe strength and then subtracting the weight of tl\e materials forming the floor, including the ceiling below, if there is one. The most convenient measurement for either the safe strength or the SAFE LOAD of a floor is in pounds per square foot. The following examples will serve to show the method of determining the safe load for an ordinary ware- house-floor. Example 4. It is required to determine the safe load per square foot for a floor framed as shown in Fig. 4, the building being in a city the laws of which Determination of Strength of an Existing Floor 747 allow I 200 lb per sq in for the safe flexure fiber-stress for the wood of which the joists and girders are made. The joists are covered with two thicknesses of %-in flooring and the ceihng below is corrugated iron. Solution. The first step will be to find the s'afe strength of the 22-ft joists. As this is a warehouse-floor we will use the tables for strength throughout. From Table XII, page 643, for S = 1 200 lb i)er sq in, we find the safe strength of a i by 14-in joist of 22-ft span to be i 188 lb; hence the strength of a 2Vz by 14-in joist will be i 188 x 2^^ = 2 970 lb. As the joists are 16 in on centers, each joist supports a floor-area of V/ix 22 ft= 29!^ sq ft. The SAPE STRENGTH PER SQUARE TOOT of this portion of the floor will therefore Load from Staii- 1800 Ibg. Stin-up Fig. 4. Plan of a War^lipuse-floor be 2 970/29.3 = loi lb.- Suppose the estimated weight of the floor per square foot is 8 lb for the joists, 6 lb for the flooring and i lb for the corrugated-iron ceiling, or, say, 15 lb in all. Then the SAtE load per square rooT for the 22-ft joists will be loi — 15 =^ 86 lb. The Headers. We will next find the safe load for the 4 by 14-in headers at each side of the stair-well. As the tail-beams are framed into the headers, we should deduct one inch from the thickness of each header for the loss of strength in framing, leaving 3 by 14 in for the effective dimension of each. From Table. XII, page 643, we find the safe strength of a i by 14-in beam of i2-ft span to l>e i 867 lb. Hence the strength of the 3 by 14 will be i 867 x 3 = 5 601 lb. The floor-area supported by each header is 4H x 12 ft = 54 sq ft; hence the safe strength of the header per square foot of floor is 5 601/54 == 104 lb. Deducting the weight of the floor per square foot, we have 104 ■- 15 = 89 lb for the safe load. i -'■ ■ Trimmer A. Trimmer A (Fig. 4) supports about the same amount of floor- ing as one of the common joists, and supports, also, the ends of the headers. Deducting 2H in, the thickness of the common joists, we have a 5 by 14-in beam 748 Strength and Sti^ness of Wooden Floors Chap. 21 left to support the headers. As the headers are supported in iron stirrups, or beam- hangers, no deduction in strength need be made for framing. To find the safe strength of a beam loaded with two concentrated loads, equidistant from the supports, we must use Formula (14), Fig. 11, page 631. In tliis case m = 8 ft 10 in, or 8% ft and A = 1 200/18 = 66.7 (Table XII, page 643). Applying the formula, the safe load at each joint = 5 X 14 X 14 X 66.7/4 X 8-^6 = I 848 lb. The floor-area supported by one stirrup is equal to one-half of the area sup- ported by the header, or 27 sq ft; hence the safe strength per square foot of the 5 by 14-in header is i 848/27 = 68 lb, and deducting 15 lb per sq ft for the weight of the floor, we have 53 lb per sq ft as the safe load that the trimmer will support on the floor at each side of the stairs. Considering, as found above, that the safe load for the 2^/^ in, which we deducted to take the place of a common joist, is 86 lb per sq ft, we might consider the safe load for the trimmer as the average of 86 and 53, or about 70 lb per sq ft. Trimmer B. This 10 by 14-in timber (Fig. 4) has to support the same floor- loads as trirtimer A, and also the lower end of a flight of stairs for which an allow- ance of at least i 800 lb should be made. This stair-load being practically concentrated at the middle of the trimmer is equivalent to a distributed load of 3 600 lb. As the safe load for a i by 14-in joist of 22-ft span is i 188 lb (Table XII, page 643), it win require a thickness of 3 600/1 188= 3 in to support the stairs, leaving 7 in to support the floor-loads. As this is I'i in less than the thickness of trimmer A, it is evident that the strength of the floor at B will be a little less than at A ; but as it is improbable that the entire floor-space will be loaded at any given* time, it would be safe to rate the strength of the floor at each side of the stairway at 70 lb per sq ft, live load, and beyond the stair- way at 86 lb. Partitions. When the floor supports partitions, the weight of the latter and any load resting upon them must be taken into account in determining the safe load for the floor. If a partition runs the same way as the joists, then only the joist directly under the partition, and the joists at each side will be affected; but if a partition runs across the joists, then it affects the safe load of the entire floor. Example 5. Suppose that the 22-ft joists in the floor shown in Fig. 4 have to support a plastered partition 12 ft high, running across the joists half-way be- tween the walls. What will be the safe load for the floor? Solution. A plastered partition with 2 by 4 or 2 by 6-in studs, set 16 in on centers, weighs about 20 lb per sq ft of partition-face; hence a partition 12 ft high will weigh 240 lb per lin ft of partition. As the joists are 16 in on cen- ters, each joist supports iH hn ft of partition, weighing 320 lb. As this load is concentrated at the middle span of the joists it is equivalent to a distributed load of 640 lb. In Example 4, we found the safe distributed load for the 2y2 by 14-in joists of 22-ft span to be 2 970 lb. Subtracting 640 lb from this we have 2 330 lb, which may be used for the floor. As the floor-area supported by one joist is 29H sq ft, the safe strength of the floor per square foot is 2 330/29 H = 79 lb, and the safe load is 79 — 15 = 64 lb per sq ft. Hence the partition decreases the safe load by 86 — 64 = 22 lb per sq ft. Whenever the ui:)per-floor joists are supported b}'' a partition carried by a floor below, the effect of the partition and its load upon the strength of the lower floor should be very carefully com- puted. Bridging of Floor- Joists. By BRrociNrG is meant a system of bracing for floor- joists, either by means of small struts, as in Fig. 5, or by means of single Bridging and Framing of Wooden Floors 749 Fig. 5. Floor-joists with Bridging pieces of boards set at right-angles to the joists and fitting in between them. The effect of this bracing is of decided advantage in sustaining any concen- trated LOAD upon a tloor; but it does not materially strengthen a floor to resist a UNIFORMLY DISTRIBUTED LOAD. The bridging also stiffens the joists, and pre- vents them from turning sidewise. It is customary to insert rows of cross-bridging from 5 to 8 ft apart; and to be effective the rows of bridging should be in straight lines along the floor, so that each bridging- strut may abut directly opposite those adjacent to it. The method of bridging shown in Fig. 5, and known as cross- bridging, is considered to be by far the best, as it allows the thrust to act parallel to the axis of the strut, and not across the grain, as must be the case where single pieces of boards are used. The bridging should be of iH by 3-in stock, for 2 by lo-in and smafler joists, and of 2 by 3-in stock for 12- and 14-in joists. Framing of Wooden Floor-Beams. In dwellings, tenements and lodging- houses it is frequently necessary to frame the timbers so- that they are fluslf with one another. The old methods of framing the tail-beams and headers or headers and trimmers by mortise-and-tenon joints are now generally superseded by hanging the timbers in stirrups or malleable-iron joist -hangers. In this con- struction the entire strength of the timbers is retained, whib the cost of the hangers is often less than the labor-cost in pre- paring the mortise-and-tenoi\ joints. All headers 6 ft oi more in length should be carried in joist-hangers ot stirrups and this is usually required in the building codes, of the large cities. In ware^ houses and all first-class build-' ings the • framing should be done by means of joist-hangers. For light floors, with moderate spans, it is generally safe to frame the tail-beams into a header, provided the latter is strong enough to carry the load and allow i in in thickness for the mortising. Headers, also, carrying not more than two tail-beams are often framed into the trimmers. In case the old methods of framing are used instead of the superior methods with joist-hangers, the best shape and proportions for the tenons and ends of the tail-beams or headers are those shown in Fig. 6. This form of framing Fig. 6. Framing of Joists into Header 750 Strength and Stiffness of Wooden Floors Chap. 21 probably offers as large a proportion of the strength of the timbers as it is possible to utilize, although for tail-beams it was the opinion of Mr. Kidder that a single tenon like that shown in Fig. 7 is fully as strong, especially when the header is built up of 2-in planks spiked together. In either case, if the floor Fig. 7. Alternate Method of Framing Joists into Header Fig. 8. Framed Joist Split by Load is loaded to its full strength, the tail-beam will split at the bottom of the tenon, as shown in Fig. 8, which illustrates the weakening effect of the mortise-and-tenon framing. Stirrups and Joist-Hangers. The first device used for framing headers to trimmers without mortising was the wrought-iron stirrup shown in Fig. 9. These are made either single or double, depending upon whether one or two beams are to be supported. To prevent the floor from spreading and thus per- DOUBLE STIRRUP Fig. 9. Framing with Wrought-iron Stirrups mitting the header to slip out of the stirrup, a joint-bolt may be inserted, as shown in the two right-hand illustrations of Fig. 9. To determine the strength of a stirrup, multiply the sectional area of the iron, in square inches, by 12 000 lb per sq in. (Table i, page 376.) The following sizes of iroa should, in general, be used for the different sizes of joists to be supported: Joist and Beam-Hangers 751 Sizes of joists or timbers to be Sections of stirrup- supported, in inches • iron in inches 2 by 8 to 3 by lo H by 2H 4 by 10 to 4 by 12 ^6 by 2}^^ 6 by 1 2 to 3 by 14 %hy s 8 by 12 to 4 by 14 H by 3H 6 by 14 H by 4 8 by 14 to 10 by 14 H by 4 Joist-Hangers. Aside from the matter of strength there are objections to the use of stirrups. If the timber on which they rest is not perfectly dry, the stirrups will settle by an amount equal to the shrinkage of the beam on which they rest, and let down the header with them, and the projection of the iron above the top of the timbers will necessitate cutting out the flooring. If the stirrups are exposed in this way their appearance is objectionable. While they may be designed to resist any tensional stress the resistance of steel to bending is comparatively small, and the resulting crushing of the timber where they go over the edge is the chief objection to the use of stirrups of this type for heavily loaded floors. The small bearing of a timber on a stirrup is y///){///////j\ Cracka Developed >^ ^^^ X — / ^'' rj^^^^z^ i* / '"'/^^^m 5- / %|%gw Iv 1 ^M^m^ p" -,_,,. Timber Crushed Cracka Developed Fig. 10. Failure of Steel Stirrup Wall-hanger not sufficient to distribute the load on the wood over the required area. This increases the bearing per square inch, allows the hanger to crush into the edge and tends to straighten out the stirrup as shown in Fig. 29, page 757. The same serious objection applies to the use of steel stirrup-hangers in brick walls to carry beams free of the walls. As previously explained, all the load is brought to the extreme edge, causing a much greater load per square inch on the masonry than is allowable. Fig. 10 * shows the effect of crushing, in a warehouse-building in Minneapolis, Minn. Wall-hangers made of steel stirrups should not be used. Patented steel hangers riveted to bearing-plates are likewise very undesirable as the crushing effect is greatest at the outer edge, due to the straightening-out tendency of the hanger at this point. Figs. 11 and 12 illustrate the Duplex and Goetz joist-hangers, which are patented and are claimed to be superior to the old-style stirrups. The Duplex hanger is used not only for ordinary building-construction, but for the most heavily loaded mill-construction in factories and warehouses. As these hangers are made of malleable iron they will not straighten out when heated, in case of fire, and drop the beams. That is what happens to wrought-steel stirrups * Taken from a paper on "Joist and Wall-Hangers," read by Mr. F. E. Kidder at a meeting of the Colorado Chapter of the American Institute of Architects, February 27, X903. 752 Strength and Stiffness of Wooden Floors Chap. 2 when the twist becomes heated. This hanger has proven perfectly satisf actor and is extensively used. Both are made in sizes to fit all regular sizes of joist oi girders, and have ample strength for the purpose for which they are intended Fig. 11. Duplex J»ist-hanger Fig. 12. Goetz Joist-hanger As shown by the illustrations, they are made to be inserted in round holes bore( in the side of the carrying timbers, at or a little above the center line. Witl these hangers the effect of shrinkage is reduced one-half, and the other two ob Fig. 14. Duplex I-beam Shelf-hanger. Joists Raised Less than Four Inches jections to the stirrup, previously mentioned, are overcome. The Duple: hanger has ridges on the inside of the side brackets to hold the beam. For timbers of larger size and for the heaviest construction, the Duplex hangers Joist and Beam-Hangers 753 By this shown in Fig. 32, page 789, ate used and are bolted to the beams, construction the entire building is tied together laterally. Fig. 13 shows the Duplex I-beam hanger for framing floor-joists to I beams' This hanger is made to exactly lit into the flange of the I beam. It has a rib 15. Duplex I-beam Box Hanger. Joists Raised More than Four Inches Fig. 16. Duplex Wall-hanger for Joists on the bottom, Ys in high, which serves as a tie when the joist is placed in the hanger, and it provides a bearing of at least 4'/2 in for the joist. It is made to carry any joist of regular size, and offers one of the best devices for framing wooden joists to I beams of the same depth. The hangers arc looked to the web of the I beam. Fig. 14 shows the Duplex I-beam shelf-hanger which is used when the construction requires the joists to be raised above the lower flange of the I beam less than 4 in. Fig. 15 illustrates the Duplex I-beam box-hanger and is recommended where the joists are raised more than 4 in above the lower flange of the I beam. In both these construc- tions the hangers arc bolted singly or opposite, as required, on the I beam and the loads are carried on the lower flanges of the beams. Fig. 16 shows a similar hanger made to support the wall-end of a floor- joist. This form of construction is considered much superior to the method of building the Fig. 17. Duplex Steel Wall-hanger for Large Beams Fig. 18. Duplex Extra-heavy Wall-hanger for Mill-construction joists into a wall, as it absolutely prevents dry-rot, and permits the joists to fall, in case of fire, without throwing the wall. It also gives the load a good bearing on the wall. Fig. 17 illustrates the Duplex steel wall-hanger for larger timbers, and Fig. 18 shows the Duplex extra-heavy wall-hanger for the heaviest 754 Strength and Stifitness of Wooden Floors Chap. 21 mill-constmction. These hangers bear the label of approval of the National Board of Fire Underwriters and are generally considered the best-designed wall- hangers now on the market. This hanger gives an extra bearing on the masonry* and is so constructed that it reacts as a unit and distribute > the load equally over the entire surface of the masonry. There is no tendency for a hanger of this Fig. 19. Duplex Wall-hanger for Concrete Blocks Fig. 20. "Ideal" Wrouglit-steel Beam-hanger type to crush in at the edge of the masonry and straighten out, as is the case with some other types of wall-hangers. Fig. 19 shows the Duplex wall-hanger used in connection with walls constructed of concrete blocks. These hangers are often used in repair-work in party walls, as they avoid the cutting of large holes in the walls, and also provide an easy and simple method of carrying the joists clear of the walls. The Ideal hanger illustrated in Fig. 20 is made of wrought Fig. 21. "Ideal" Wrought- steel Beam-hanger Fig. 22. "Ideal" Wrought-steel Wall-hanger steel and corrugated at the points where it is beiit over. This reinforces it and tends to prevent bending at these points. Fig. 21 illustrates another form of the Ideal hanger with holes for spiking to a timber. This hanger, also, is corrugated. In these hangers the full strength of the steel is retained as the 6bers of the metal are not cut in forming them. They are made of wrought- steel bars folded to the required shape. Fig. 22 shows the Ideal hanger riveted Joist and Beam-Hangers 755 to a steel plate and in position to be built into a brick wall. Other illustrations of wall-hangers are given in Chapter XXII. The Van Dorn hanger, illustrated in Fig. 23, is essentially a stirrup forged from high-grade steel. The few tests that have been made would seem to indicate that it developes a greater re- sistance to bending than the ordinary stirrup, while it gives a wider bearing Fig. 23. Van Dorn Beam-hanger Fig. 24. Van Dorn Wall-hanger for the joist and presents a much neater appearance. Fig. 24 shows the same hanger riveted to a bent iron plate, to build into brick walls. When the hanger is to be used over a steel beam the upper ends are bent to fit over the flange of the beam, as in Fig. 25. "Although I know of no test of the strength of a Van Dorn I-beam hanger, it would seem as though it must be much stronger than Fig. 25. Van Dorn I-beam Hanger Fig. 26. National Joist or Beam-hangCT the pattern made for wooden beams, on account of the clinch over the flange of the I beam. The Van Dorn hangers have been used in many important build- ings. " * Figs. 26 and 27 show the general form of two other patented joist-hangers,, v^hich are forged from plate steel. Both of these hangers, also, are made to be *F. E. Kidaer. 756 Strength and Stiffness of Wooden Floors Chap. 21 built into brick walls and to go over steel beams. The National hanger (Fig. 26) has a flange on top, which helps materially in distributing the load over the top of the beam as shown in figure. The larger hangers of this style have holes in the top for large spikes. This hanger and the Lane hanger (Fig. 27) have been much used. Comparative Strengths of Different Types of Joist- Hangers. Although the tests that have been made to deter- mine the strength of different hangers are few in number, a sufficient nmnber have been made to show that any one of the hangers described, including the common stirrup, is abun- dantly strong for any single rLOOR-BEAM not exceeding 4 by Fig. 27. Lane Joist or Beam-hanger ^4 in in cross-section It is only m the case of a header or trimmer which supports a load over a considerable floor-area that the strength need be considered at all. From tests made at various times on joist-hangers and on girder-hangers, it would appear that, under extreme loads, two-part hangers usually develop great strength. A two-part hanger, carrying a le by i47in girder, sustained a load of 38 000 lb without injury to the hanger itself. A similar hanger held until loaded up to 39 550 lb, when one side broke off short under the nipple projecting into the timber, the condition of the hanger after failure being shown in Fig. 28. A common stirrup made from % by 2V2-in wrought iron failed under a load of 13 750 lb by bending and pulling over the header, as shown in Fig. 29. A 6 by 12-in steel hanger " began to straighten out under a load of 13 300 lb, and failed to hold under a load of 18 750 lb."* Single hangers of the stirrup-type do not break, but fail by the bending up of the parts which lie over the top of the header as shown in Fig. 29. They also appear to crush the wood under them par- ticularly at the edges, to a very much greater extent than does the spool of the Duplex hanger. With a double stirrup the ultimate strength is measured by the strength of the iron. Thus, a double stirrup, made of % by 2]4-\n wrought iron, was loaded up to 57 650 lb (28 825 lb on each side), when it broke at one of the lower corners. A single stirrup would of course be just as strong if it could be kept from bending. In actual construction the flooring over the beams to some extent prevents the top of a stirrup from springing up. The tests that * From data compiled by Mr. K-idcJer from a series of tests on beam-hangers au4 joist-hangers, Fig. 28. Result of Test of a Two-part Beam-hanger Comparative Strengths of Joist-Hangers 757 have been made of two-part hangers show conclusively that where only a single hanger is used the holes which are bored in the header do not seriously affect its strength when the load is within the safe limit, and a test made at Balti- more, Md., August 24, 1904, with 2 by i2-in joists, spaced 12 in on centers and suspended by these hangers let into a header formed of three 3 by 12-in joists, spiked together, would seem to prove that even when the holes are 1 2 in apart they do not seriously weaken it. '' The only record of the fail- ure of any form of hanger when in actual use in a building, of which I am aware, is that of a failure in Minneapohs, where a portion of six floors of a ware- house fell, on Nov. 7, 1902, through the failure of a wall-hanger made from a 4 by 2 by %.-in structural- steel angle, which was sheared and bent, and riveted to an 8 by 16 by %-in bearing-plate. The failure was due to the crushing of the outer edge of the brickwork under the hanger, and the consequent bending up of the top portioc-. The actual load on the hanger was about 15 000 lb." * *F E. Kidder. See, also, Engineering News, Nov. 20, 1.902. Fig. 29. Result of Test of Wrought-iron Stirrup- hanger 758^ Wooden Mill and Warehouse-Construction Chap. 22 CHAPTER XXII WOODEN MILL AND WABEHOUSE-CONSTEUCTION By A. P. STRADLING SUPERINTENDENT OF SURVEYS, PHIL.^DELPHIA FIRE UNDERWRITERS* ASSOCIATION 1. Mill-Construction Definition. The term mill-construction is commonly used to designate a method of construction brought about largely through the influence of the Boston Manufacturers' Mutual Fire Insurance Company of Boston, Mass., and especially through the efforts of Mr. Wm. B. Whiting, whose judgment in mechanical matters, and experience and skill as a manufacturer were for many years devoted to the interests of insurance companies, and to the improvement of factories of all kinds. The extended use of this system and the improvements that have been made in it during recent years are probably due more to the influence of Mr. Edward Atkinson, President of the Boston Manufacturers' Mutual Insurance Company and Director of the Insurance Engineering Experi- ment Station at Boston, than to that of any other individual. Cost. The purpose of mill-construction is to reduce the fire-risk to its low- est point without going to the expense of fire-proof construction. The increasing cost of heavy timber, however, and in fact of all lumber, together with the lessened cost of the erection of the so-called fire-proof types, constructed entirely of reinforced concrete, or built with protected steel frames and incom- bustible floors, and the recognition, also, of the obvious advantages of more fire-resisting CONSTRUCTION, especially in the congested sections of cities, are bringing these types into more general use. The cost of these latter types of construction is, in many instances, no more than the cost of various types of mill-construction. The Slow-burning or Mill-Construction Type. The experience of years has entirely justified the use of this type. It renders possible a somewhat less costly, and at the same time, what is of great importance, a more effective system of fire-protection than can be installed in buildings of light construction, with the so-called joisted floors and with the roofs made of boards supported on 2-in, 3-in, or 4-in joists. The entire subject of slow-burning or mill-con- struction as applied to factories is most admirably described and illustrated in Report No. 5 of the Insurance Engineering Station of the Boston Manu- facturers' Insurance Company, No. 31 Milk Street, Boston, Mass., from which the author has, by permission, taken and adapted many of the following illus- trations and descriptions. 2. What Mill-Construction Is* (i) Heavy Timbers. Mill-construction consists in so disposing the timbers and planks in heavy, solid masses as to expose the least number of corners or ignitable projections to fire; and to the end, also, that when fire occurs it may be most readily reached by water from sprinklers or hose. ' * From Report No. 5 of the Insurance Engineering Station of the Boston Manufac tmers' Insurance Company, No. 31 Milk Street, Boston, Mass. What Mill-Construction is Not 769 (2) Flr6-Stops. It consists in sepai'ating every floor from every other floor by incombustible stops, by installing automatically closing hatchways and by encasing stairways either in brick or other incombustible partitions, so that a fire will be retarded in passing from floor to floor to the utmost consistent with the use of wood or any material not absolutely fire-proof. (3) Fire*Retardatits. It consists in guarding the ceilings over all specially hazardous stock or processes with fire-retardant materials, such as plaster- ing laid over wire lath or expanded metal, or over wooden dovetailed lath, following the lines of the ceilings and of the timbers and leaving no interspaces between the plastering and the wood; or else in protecting the ceilings over hazardous places with asbestos, air-cell boards, sheet metal, Sackett Plaster Board, or other fire-retardant. (4) Fire-Safeguards. It consists not only in so constructing the mill, work- shop, or warehouse that fire will pass as slowly as possible from one part of the building to another, but also in providing all suitable safeguards against fire. 3. What Mill-Construction Is Not (i) Concealed Spaces. Mill-construction does not consist in so disposing a given quantity of materials that the whole interior of a building becomes a series OF WOODEN cells, or concealed spaces, connected with each other directly or by cracks through which fire may freely pass where it cannot be reached by water. ^' (2) Size of Timbers, Fire-Stops, etc. It does not consist of an open-timber construction of floors and roofs which resembles mill-construction, but which is built with light timber of insufficient size and with thin planks, without fire- stops or fire-guards from floor to floor. (3) Stairways. It does not consist in connecting floor with floor by com- bustible wooden stairways encased in wood less than two inches thick. (4) Partitions. It does not consist in putting in very numerous light, wooden divisions or partitions. (5) Sheathing and Furring. It does not consist in sheathing brick walls with wood, especially when the wood is set off from the walls by furring, and even if there are stops behind the furring. (6) Varnish. It does not consist in permitting the use of varnish on wood- work over which a fire will pass rapidly. (7) Glass, Fire-Shutters and Wire-Glass. It does not consist in leaving windows exposed to adjacent buildings and unguarded by fire-shutters or wire-glass. (8) Painting and Dry-Rot. It does not consist in painting, varnishing, filling or encasing heavy timbers and thick planks, as they are customarily delivered, and thus making possible what is called dry-rot, caused by a lack of ventilation or opportunity to season. (9) Sprinklers, Pumps, Pipes, Hydrants, etc. It does not consist in leaving even the best-constructed building in which dangerous occupations are followed without automatic sprinklers, and without a complete and adequate equipment of pumps, pipes and hydrants. (10) Finishing in Wood and Other Materials. It does not consist in using more wood in finishing a building after the floors and roof are laid than is absolutely necessary, since there are now many safe methods available at low cost for fi^nishing walls and constructing partitions with slow-burning or in- 760 Wooden Mill and Warehouse-Construction Chap. 22 combustible materials. Accordingly if plaster is to be put on a ceiling and is to follow the line of the underside of the flooring and the flooring-timbers, it should be plain lime-mortar plaster, which is suflSciently porous to permit seasoning. The addition of a skim-coat of lime-putty is hazardous, especially if the overflooring is laid over rosin-sized or asphalt paper. This rule applies to almost all timber as now delivered. Examples of all of the faulty methods of construction above mentioned have been found in various buildings pur- porting to be of mill-construction, and they all form parts of what has some- times been called combustible construction. 4. Standard Mill-Construction Example of Standard Mill-Construction. Fig. 1 shows a cross-section through a mill of the customary or standard type recommended by the Boston Manufacturers' Mutual Insurance Company, the details of construction being revised to May, 1908. "Walls. If additional stories are required, the walls may be increased in thickness according to the number of stories added, after a computation has been made of the loads which a standard factory may be called upon to sus- tain. Walls should be of brick and at least 13 in thick in the upper story, and their thickness should be increased in the lower stories to support additional loads. Plastered walls are often to be preferred to unplastered walls. Window- arches and door-arches should be of brick, and window-sills, outside door-sills and under-pinning of granite or concrete. Roofs and Floors. The roofs should be of 3-in pine planks spiked directly to the heavy roof-timbers, and covered with five-ply tar-and-gravel roofing. Roofs should incline from V2 to % in per ft, and incombustible cornices are recommended when there is exposure from neighboring buildings. Floors should be of spruce planks, 4 in or more in thickness according to the floor- loads, spiked directly to the floor-timbers, and kept at least V2 in away from the face of the brick walls. In order to obviate the danger of cracking the walls, which sometimes results from the swelling of planks laid close against them, these spaces left between walls and floor-planks must be covered by strips or battens both above and below. In floors and roofs, the bays should be from 8 to loVu ft wide, and all planks two bays in length should be laid to break joints every 4 ft, and grooved -for hard-wood splines. Usually an overfloor of birch or maple is laid at right-angles to the planking, but the best mills have a double overfloor, a lower one of soft wood, laid diagonally upon the planks and an upper on^e laid lengthwise. This latter method allows boards in alleys or passageways to be easily replaced when worn, while the diagonal boards brace the floors, reduce the vibration, and distribute the floor-loads more uniformly than the former method. Between the planking and the overfloor should be two or three layers of heavy, hard paper, laid to break joints, and each mopped with hot tar or similar material to make a reasonably water-tight as well as dust-tight floor. The usually rapid decay of the basement or lower floors of mills makes it desirable, whenever wood is not absolutely necessary, to make such floors of cement. If wooden floors are required, crushed stone, cinders, or furnace slag should be spread evenly over the surface, and covered with a thick layer of hot-tar concrete. On this tarred felt is often laid, well mopped with hot-tar asphalt, and over it a flooring of 2-in seasoned planks, well pressed down and nailed on edge without perforating the water-proofing under it. The hard- wood boards of the overfloor are then nailed across the planks. Cement concretes promote decay of wood in contact with them. If extra supports are required for heavy machinery, independent foundations of masonry should be Standard Mill-Construction 762 Wooden Mill and Warehouse-Construction Chap. 22 provided. In view of the difficulties frequently met with in preserving base- ment floors of the ordinary timber construction, because of the lack of suitable ventilation underneath, and also in view of the rapid decay of timber and plank floors in bleacheries, dye-works, print-works, and the like, in which the floors quickly become saturated with moisture, artificial-stone floors are being laid in many of the modern plants. Sizes and Kinds of Timbers. All woodwork, not standard construc- tion, in order to be slow-burning, must be in large masses which present the least surface possible to a fire. No pieces less than 6 in in width should be used for the lightest roofs, and for substantial roofs and floors much wider ones are needed. Timbers should be of sound, long-leaf, yellow pine, and for sizes up to 14 by 16 in, single pieces are preferred; or, timbers 7 to 8 by 16 in, are often used in pairs bolted together, without air-spaces between. They should not be painted, varnished or filled for three years because of the danger of dry rot, and for the same reason, an air-space should be left in the masonry around the ends. Beam-Boxes, Column-Caps, etc. Timbers should rest on cast-iron PLATES or beam-boxes in the walls and on cast-iron caps on the columns. Beam- boxes are of value as they strengthen the walls when the floor loads are heavy and the distance between windows small; they facilitate the laying of the bricks and the handling of the beams; and there is less danger of breaking the bricks in putting the beams in place. They also insure proper air-spaces around Flashing Rooflngv Fig. 2. Floor-timber on Wall-plate Fig. 3. Roof -timber on Wall-plate the ends of the beams. Fig. 2 shows a floor-timber resting on a cast-iron wall- plate with a lug for anchoring the timber to the wall. Fig. 3 shows a roof- timber resting on a cast-iron wall-plate, an overhanging, open, wooden cornice and a wrought-iron joist-anchor. Fig. 4 shows a cast-iron cap and PINTLE for columns, and dogs for holding the floor-timbers together. Fig. 5 shows a roof-timber resting on a column-cap cast to fit the slope of the roof; the timbers are held together by i-in wrought-iron dogs. These diagrams are Intended only as general illustrations of slow-burning or mill-construction. The details should always be adapted to the special conditions of the site and to the purposes for which the buildings are used. Columns of yellow pine should be bored through the axis, making a i^^-in- diameter hole, and should have y2-in lateral vent-holes near the top and bottom. The ends should be carefully squared. To prevent dry-rot, wooden columns Standard Mill-Construction 763 should not be painted until they are thoroughly seasoned. They should be set on PINTLES which may be cast in one piece with the cap, or separately. Cast- iron COLUMNS are preferred by some engineers, and when a building is equipped with automatic sprinklers, such columns have proved satisfactory; but they ToplFioorinff Tarred Paper Roof Planking, Fig. 4. Post-cap and Pintle for Floor-timber and Columns Roof, Timber Fig. 5. Roof -timbers on Column- cap are not as fire-resisting as wooden columns. Wrougiit-iron or steel columns should not be used unless encased with at least 3 in of fireproofing. Windows should be placed as high and made as wide as possible to obtain the greatest amount of light, and the use of ribbed glass is recommended for the upper sashes. Weight, Deflection and Vibration. In computing the size of the timbers as a ratio to the working-load, consideration must be given not only to the weights which are to be carried, but also to the character of the machinery which is to be operated on the floors. Beams of sufficient strength to support the weights may vibrate or deflect under the weight and action of the machinery; and there are, therefore, three factors, weight, deflection and vibration, which must be considered in determining the width and depth of the beams that are to be used in the structure. Objectionable Types of Construction. "We do not approve what has been sometimes miscalled mill-construction, that is, longitudinal girders resting upon posts and supporting floor-beams spaced 4 ft, more or less, on centers. This mode of construction not only adds to the quantity of wood used, but the disposal of the timbers obstructs the action of the sprinklers, pre- vents the sweeping of a hose-stream from one side of the mill to the other, and the girders also obstruct the most important light, that from the top of the windows." Timber, Ventilation, Painting, etc. Timbers, unless known to be thor- oughly seasoned, should not be encased in any kind of air-proof plastering nor painted with oil-paints; white-wash, calcimine and water-paints may be used, as they are porous. As a rule, timbers should be left unprotected, since a fire which will seriously impair and destroy heavy timbers will already have done its work upon other parts of the structure. Single and Compound Beams. While, in general, single beams should be used, in some instances it may be desirable to substitute compound beams, made by fastening two or more beams or thick planks side by side. It is often easier to obtain well -seasoned lumber in small dimensions. Such compound beams should be tightly bolted together without air-spaces, and owing to the danger of dry-rot, should not be painted or varnished for three years. 764 Wooden Mill and Warehouse-Construction Chap. 22 Steam-Pipes. If a mill is to be heated by conveying steam through pipes, such pipes should be hung overhead. Cornices. Wherever buildings are exposed or are liable fo be exposed to fire in the near future, the cornices should be of non-combustible construction or, preferably, the walls should extend above the roof-timbers. Glass, Frames and Shutters. All openings in walls should be protected either by approved wire-glass in approved, metal frames or by standard fire- shutters. . 5. Belts, Stairways and Elevator-Towers Continuous Floors. One of the most important features of slow-burning <;:0NSTRUCTi0N is to make each and every floor continuous from wall to wall, 1 s 3 " ■ J 1 1 i ' 1 ' e i J.-' -t^: pq avoiding, as far as possible, holes for belts, stairways, or elevators so that a fire may be confined to the story in which it starts. No well-informed mill- owner, engineer or builder will, therefore, fail to locate elevators, stairs, and main belts, in brick towers or in sections of the building cut off from all rooms Standard Storehouse-Construction 765 by incombustible walls. All openings in these walls should be protected by STANDARD FIRE-DOORS, preferably self-closing. In modern practice all belts and ropes which may be used for the transmission of power to the various rooms, are placed in incombustible vertical belt-chambers, from which the power is transmitted by shafts through the walls into the several rooms of the factory. There should be no unprotected openings in the inner walls of this belt- chamber. Shafts above Roof. Skylights. All shafts for stairs, elevators, BELTS, etc., should extend at least 36 in above the roof, and all such shafts should be, if possible, on the outside of the building. Elevator and belt-shafts should be covered with thin glass skylights in metal frames, protected under- neath with wire netting. Figs. 6 and 7 illustrate a section and plan of a cotton- mill, showing elevator, stair and belt-shafts arranged on the above principle. Closets should be in a separate tower rather than in manufacturing rooms. The Boiler-Plant should be in a separate building cut off from the engine- room by a brick wall, and the openings in this wall should bp protected by auto- matic, sliding, standard fire-doors. 6. Standard Storehouse-Construction Example of Storehouse-Construction. Fig. 8 shows a cross-section through the fire-tower and Fig. 9 the first-story plan, including the elevator and stair- tower of a four-story storehouse. Area. Buildings for this purpose should not, in gen- eral, exceed 5 000 sq ft in AREA. When used, however, for storage of non-haz- ardous goods, the area may be in- creased to 10 000 sq ft. Height of Stories. In storehouses, the stories should be made low enough (Fig. 10) to prevent overloading, and when designed for case-goods, the height of stories should be sufficient to take two cases, with a 12-in, clear space under the beams to allow for the distribution of water from the sprinklers. Fire-Walls. For convenience, as well as to separate the different hazards of raw materials and finished goods, the building should be divided into sections by fire-walls extending at least 36 in above the roof. One-Story Storehouses. A one-story storehouse is recommended in preference to the design just described, whenever there is a sufficient quantity of level land at disposal for this purpose. The one-story building is cheaper, more convenient, and, when separated into small divisions by fire- walls, repre- sents the safest method of storehouse-construction. Timbers and Framing. The floor-timbers and roof-timbers should be of long-leaf yellow pine, in single pieces, if possible. If necessary to use double beams, they should be bolted together without air-spaces between them. Tim- CR0S5 SECTION THROUGH TOWER Fig. 8. Four-story Storehouse. Section through Fire-tower 766 Wooden Mill and Warehouse-Construction Chap. 22 bers should rest on cast-iron plates or beam-boxes in the walls, and on cast-iron caps on the columns. At least V2-in air-spaces should be left around all beams built into the masonry, allowing free ventilation and preventing dry rot. Col- Fig. 9. Four-story Storehouse. First-story Plan UMNS of yellow pine should have their end-surfaces cut square with the column- axis. . . Floors. The floors of such buildings should be continuous, without open- ings, and of the standard slow-burning construction, described under Standard Isometric view Fig. 10. Four-story Storehouse. Isometric View MiLL-CoNSTRUCTiON. The flooring should be constructed as called for under Standard Mill-Construction. In order that the floors may be as nearly water-proof as possible, tarred paper, mopped with tar, should be applied, as previously suggested. The floors in each story of the tower should be at least I in lower than the floor in the adjoining compartment, and the sills of the door- openings to the tower should be inclined to make up the difference in levels. The sill, also, of the^ outside door of the tower should be lower than the tower- floor. Standard Storehouse-Construction 76? Scuppers. Water on the floors of the tower will ordinarily flow down the tower-stairs, and the arrangement of the floor-levels indicated above will ordi- narily prevent water from an upper story from flowing into one of the lower compartments, if it is escaping through the tower. Cast-iron scuppers are advised, and they should be set in the brickwork at frequent intervals, and so designed that they will carry away rapidly a maximum quantity of water from the floors of each compartment. To further the drainage of water, the floors should be inclined from the middle of the compartments to the scuppers. Fig. 11 shows the wind-shield scupper* which embodies the latest improvements. ^xVERTICAL SECTION FRONT ELEVATION Fig. 11. Detail of Wind-shield Scupper In the old-style scupper only one flap is provided on the outside of the building. During winter and windy weather, this flap blows open and sometimes freezes open. This results in a continuous draft through the scupper and over the working floor of the factory or warehouse and necessitates an increase in the amount of heat furnished. The scupper shown in Fig. 11 corrects this condi- tion by providing the light wind-shield on the floor-level of the scupper. When the outer flap blows open the wind-shield shuts off the draft from the outside. This scupper, in addition, acts as a fire-retardant when an adjoining building is burning, and when there is a tendency for the flames to communicate through an open scupper and ignite merchandise on the floor. The wind-shield, by shutting off the drafts and fire, acts as a retardant or shield to keep out the llames. * Manufactured by the Wind-Shield Scupper Company, i Madison Avenue, New York City. 768 Wooden Mill and Warehouse-Construction Chap. ^2 Tower for Stairways, Elevators, etc. Access to the various stories is obtained by means of a brick tower outside the main building, extending 36 in above the roof, and containing stairways, elevators, etc., .access to which is Storage oLRaw Material Y/ //////^////////////// i storage of Goods Fig. 12. Stairway-tower and Galleries at Side of Storehouse obtained by open galleries at each floor-level. (See Fig. 12.) A doorway from the upper story of the tower affords a ready means of reaching the roof. Automatic hatches are not necessary for the elevator, as guard-gates serve every purpose. If it is necessary to construct the tower for the elevator and stairs inside of the building, access to it should be as shown in Fig. 13. This Fig. 13. Stairway-tower Inside of Storehouse ' construction serves, also, as a fire-tower, part of the outside wall being omitted. Roof Walls and Parapets. The walls should extend 36 in above the roof and the parapet should be laid in cement, because the moisture readily ab- sorbed by the bricks would otherwise pass downward and make the walls of the top story damp. In some instances a course of bricks dipped in coal-tar is laid above the roof-level. Sprinklers, Standpipes and Hose. Mills and storehouses should ibe pro- tected throughout by automatic sprinklers and by inside standpipe and hose-equipments. Dry-pipe sprinklers should never be used unless it is im- practicable to heat the building. These systems should be planned and super- vised by a thoroughly reliable fire-protection engineer. (See, also, Chapter XXIII, pages 903 to 905.) .^ Example of One-Story Work-Shop 769 7. Example of One-Story Work-Shop Economy. For work-shops on cheap, level land, and especially for buildings in which the stock is heavy, one-story buildings have proved to be more economical than higher buildings, in cost of floor-area, supervision, moving stock in process of manufacture and repairs to machinery, much of which can be run at greater speeds than when it is in high buildings. Warming and Ventilating. Window-Area. Such buildings are readily warmed and ventilated, and heavy-plank roofs are free from condensation in cold weather. Window-areas should be as large as practicable, as a large window- area reduces the hours of artificial illumination. If the building is exposed to fire from another building or buildings of hazardous occupancy, the windows should be of the Fenestra, Lupton or other equally good, steel construction, glazed with wire-glass. The forced circulation of heated air is a very desirable method of heating mills, and should be used in connection with overhead steam- pipes. Floors. As wooden floors are subject to rot, the general floor-construction, if possible, should be of concrete or earth or some other non-combustible mate- rial. But as the dust rising from floors of such materials injures machinery, and as the dripping of oils weakens such floors and seems to make a wooden flooring-surface necessary, the following construction is recommended. Broken slag or stone, several inches in thickness and thoroughly rolled, is first put down, and over this a 4-in layer of tar-concrete. On this is laid a i-in thickness of asphalt, evenly rolled. Over this, 2 or 3-in hemlock planks, bedded in hot pitch, are laid and over them a % or iVs-in maple floor, at right-angles to the planks. Column and Beam-Construction. Figs. 14 and 15 show clearly the mode of column and beam-construction. No beams or other structural timbers should be painted or varnished until thoroughly seasoned. The Roofs should be as called for under Standard Mill-Construction. Trusses in roofs are ordinarily from 8 to 20 ft on centers, the 3-in planks span- ning the distance between the trusses as shown in Fig. 14, or resting on purlins not less than 8 ft on centers, and running longitudinally, as in Fig. 15. Cornices and Gutters. In Fig. 14, the overhanging open cornice is shown, with a drip to the outside and without gutters. Roofs sloping back to inside gutters, as shown in Fig. 15, are preferable. Projecting brick cornices, which protect the woodwork from outside fires, are shown in Fig. 15. If the building is exposed to other buildings of hazardous construction and occupancy, parapetted brick walls and cornices are needed. Roof-Construction. The roof-planks should be at least two bays in length, breaking joints every 3 ft; or, if purlins are used, the planks should cover at least two spaces between the purlins, and break joints as above. Roof-timbers should be well anchored to walls in a safe and suitable manner. While the saw-tooth form of roof may be used with this type of building, it may not be always necessary or advisable; and the types shown in Figs. 14 and 15 are types common for machine-shops, foundries, and similar buildings, in which increased head-room is required for traveling cranes. The middle sec- tion over the crane is often provided with saw-tooth skylights with excellent results, and the side bays and others are made higher for galleries. Steel Structural Members. In ordinary one-story machine-shops, or in buildings of similar nature, where wide spans or trusses are necessary, the use of steel structural members is not objectionable. 770 Wooden Mill and Warehouse-Construction Chap. 22 ^ b S ^ Example of One-Story Work-Shop m Lp^H 772 Wooden Mill and Warehouse-Construction Chap. 8. Saw-Tooth Roof-Construction* The Great Advantages and the increasing use of saw-tooth roof-construc- tion, and the lack of familiarity with it at many factories, make it desirable to outUne important features. Two Typical Designs are illustrated, Fig. 16, a textile weave-shed with a good basement for the shafting for driving the looms on the main floor above, thus dispensing with the overhead shafting and belting in the weave-room; and Fig. 17, a design for a light machine-shop or foundry. Other designs, using light wooden trusses or reinforced-concrete walls, are applicable. Roof-Types. It may be well to state here that while light roofs with 2-in and 3-in joists and with light boards should never be used, and while the prin- ciples of SLOW-BURNING or MILL-CONSTRUCTION, with its heavy timbers, are preferred, the increasing difficulty of promptly obtaining yellow-pine lumber of good dimensions, and its increasing cost, often necessitate the use of trusses and rather light timbers; but in no case should these timbers be less than 6 in in width nor of insufficient depth to carry the load. This, also, is in order that they may be slow-burning. The roofs in all cases should be constructed of planks and have wide bays. Steel Roof-Trusses. The adaptability of the light forms of steel for FRAMING TRUSSES, especially when wide spans are needed, often compels their use; and in plants having a safe occupancy, such as that of metal-workers, steel trusses are not objectionable, providing adequate sprinkler-protection with a good water-supply is available to prevent quick failure of the steel work, due to heat from the combustion of the contents of the building or from the burning of the roof. Similar protection is, of course, needed in shops with wooden TRUSSES, if disastrous fires are to be prevented; but experience has shown that the STEEL-TRUSSEu ROOF will fail much more rapidly than one of wood under similar conditions. Wooden versus Steel Columns. Wooden posts are nearly always avail- able and should be given preference; but if light steel columns are necessary they should be well protected by insulating materials if they are in roorns con- taining combustibles, as the column is the vital part of the roof-support. Advantages of Saw-Tooth Roofs may be outlined as follows: (i) Uniform Diffusion of Light throughout the room, thus making all space in it available. With all interior surfaces painted white and with ribbed glass in the sashes, the diffusion of light is almost perfect. (2) Better and Cheaper Lighting. Greater adaptability for lighting large floor-areas in wide buildings with low head-room when compared with what is necessary in wide buildings with the ordinary form of monitor-skylights. Saw-tooth roofs furnish the true solution of the problem of excluding the direct . riys of the sun and obtaining the very desirable north light. They result in greater econOxMY in lighting, as they lower the fixed charges due to the smaller number of hours per day during which artificial light is necessary. (3) Better Working-Conditions, especially in textile-mills, thereby increas- ing production and encouraging permanency of employees. (4) Special Adaptability to many Industries. The saw-tooth form is especially adapted to weaving and similar processes in textile-factories, to ma- chine-shops, foimdries doing hght work, and similar processes, such as assem- * Taken and adapted by permission from the Boston Manufacturers' Mutual Insur- ance Company's specifications for the construction of saw-tooth roofs. Saw-Tooth Roof-Construction 773 774 Wooden Mill and Warehouse-Construction Chap. 22 Saw-Tooth Roof-Construction 776 bling and drafting, and to some dye-houses where careful matching of colors is necessary. Disadvantages of Saw-Tooth Roofs. While the testimony of those who have had experience with saw-tooth roofs is almost uniformly favorable, some difficulties have been experienced, practically all of which may be summed up as due to either faulty design or poor workmanship. The difficulties ia general are caused by (i) Leaks, due to severe conditions during winter in our northern cUmates. (2) Poor Ventilation. (3) Excessive Heat when roofs are thin. (4) Excessive Condensation on the underside of roof and glass when the temperature outside is low and there is considerable moisture in the rooms. Approved Methods of Construction. The following suggestions show how the difficulties mentioned may be obviated if the approved methods are applied to special cases by competent engineers or architects. What is good engineer- ing from the view-point of the manufacturer can also be good fire-protection ENGINEERING, and any design should be adapted to both if the best interests of the manufacturer are to be served: (i) Diffused Indirect Sunlight. As it is desirable to avoid direct sun- light and at the same time obtain an abundance of light, perfectly diffused, the saw-teeth should face approximately north and the glass should be inclined to the vertical to take advantage of the brighter light in the upper sky and to prevent cutting off the light by the saw-tooth immediately in front; and, above all, to assure the diffusion of the light over the floor rather than on the under side of the roof-planking. (2) Angle of Glass. For the glass an angle of from 20° to 25** from the vertical and an angle of approximately 90° at the top of the saw-tooth will be about right, the variations depending upon the amount of light required and the latitude. A sharper angle at the top is not needed, as it increases the cost, and makes more roof to be covered and larger spans; more glass, also, is required in proportion, and the light is not as good, as more light from the sky is lost and too much light is thrown on the under side of the roof. (3) Glazing-Details. Double glazing with a space left between the lights of glass is preferred on account of its conducting qualities; but it is not always necessary, except in the more northerly countries. The inside glazing should be done with factory-ribbed glass, set with the ribs vertical and facing in. Shadows cast by trusses are then almost unnoticeable. (4) Gutters and Conductors. Condensation-gutters are needed inside, at the bottom of the sashes, and they should be drained through inside con- ductors and not to the outside under the bottom of the sashes, as these latter admit cold air and are liable to freeze. (5) Valleys between the saw-teeth should be flat, from 14 in to 2 ft in width and pitched V2 in per ft towards the conductors, which should be of ample size, and not much over 50 ft apart, and prefciably less. The necessary pitch may be obtained by cross-pieces of varying heights set on top of the trusses, and thus avoiding hollow spaces. (6) Prevention of Leaks. Leaks, which are common faults, may ordi- narily be prevented by a careful design of the gutters, valleys and sashes, and by insisting on good workmanship and materials. The roof-covering of asphalt or pitch should be continuous through the valleys and extend up to the glas^ 776 Wooden Mill and Warehouse-Construction Chap. 22 ^Galv. Iron Plashing ,5 Ply Roofing: plus extra layer of Felt '^No24 Gal V.Iron Asbestos -Summit One form of construction understood to have been very satisfactory is shbwn in Fig. 18 and in connection with it, reference should be made to the papers and discussion on Saw-Tooth Roofs in Trans. Am. Soc. M. E., 1907, vol. 2S, which contain much of value. (7) Warming and Ventilation. Experience, has demonstrated the advan- tage of a combination of direct radiation with a fan sufficient only for ven- tilation and TEMPERING the heat of the room. Heating-pipes, should usually be placed overhead and directly under the front of the saw-teeth, and run the entire length, and in this position assist in preventing condensa- tion. Where there is no moving shafting, some forced circula- tion is necessary, and it is best obtained by a fan, which drives the air from either a dry basement or from outside as may be required, and dis- charges it over heat- ing-coils to the story above. In weaving and similar rooms this is especially necessary and advan- tageous in promoting the health and com- fort of the employees, and in making their w o r k i n g-efficiency greater. Ventilation and cooling of these large areas with comparatively low stories must not be neglected. Ample vents are needed at the top in the form of large metal ventilators with double walls and tight dampers. They are recommended in place of pivoted or swinging sash, which are apt to leak in driving storms, and when open, allow dirt to blow in from the roof. Good windows are advised in side walls and experience has shown their value. (8) Details of Framing and Construction. The framing of the saw- teeth may be of timber, steel or reinforced concrete. The design should be such as will obstruct the light as little as possible, strong enough to hold wet snow without sagging, and stiff enough to carry shafting motors, etc., when they are to be overhead. When wood or steel is used the roof-planking should be 3 in or more in thickness spanning bays from 8 to 10 ft in width. Hollow spaces in roofs should not be permitted. They are very undesir- able from a fire-standix)int, and any condensation which may take place in them during cold weather soon rots both planks and sheathing. Sheathing, even without spaces behind it, is a more or less objectionable feature, as it is readily combustible; but if it is used it should be applied directly to the under side of the roof-planks, with only a layer of some insulating material between, so that there will be no concealed spaces. If 3-in planks are sufficient for a flat roof, they should be, also, for a saw-tooth roof; and with a good circulation of air there should be no trouble, except in wet rooms. In such rooms there i3 Fig. 18. Detail of Valley of Saw-tooth Roof Mill-Construction as Applied to Warehouses 777 bound to be tondcnsalion, whether they are under a roof or under the floor of a room above, unless large quantities of dry air are discharged into them. (9) Cost. Saw-tooth roofs necessarily cost more than flat roofs, as there is practically the same amount of roofing as in flat roofs and, in addition, the cost of windows, glazing, flashing, conductors, condensation-gutters for skylights, and a somewhat larger cost for heating. The additional cost of these items does not, however, fairly represent the comparative cost, as there should be considered the total cost of the building compared with that of an ordinary one with sufficiently high stories and with a width narrow enough to give the required light. When this is done the slight additional cost is far outweighed by the advantages gained for work requiring very good light. 9. Mill-Construction as Applied to Warehouses Cost. Owing to the increasing cost of heavy timbers for wooden construc- tion, to the lower cost of the so-called fire-proof construction, and also to the better fire-resisting qualities of the latter, owners, architects and builders should carefully compare the cost of construction, and also the cost of insur- ance of the two types, before deciding on the one to be used. The difference in the cost of construction between these two types is so small, that in many local- ities the lower cost will be in favor of the reinforced concrete or other type of FIRE-PROOF construction. The cost of construction is al3o in favor of the fire-proof type, where both long spans and strength are required. Timber-Spacing for Sprinklers. Warehouses of mill-construction should be built so as to allow the best possible distribution of water from auto- matic SPRINKLERS, with the least possible obstructions, and floor-timbers, therefore, should be as few as the floor-loads will allow. There should be no concealed spaces of any kind in the building. To insure the greatest efficiency for sprinkler-systems, it is better to adapt the timber-spacing to suit the sprink^ lers, rather than to arrange the sprinklers to suit the timber-spacing. Mill-Construction Adapted to Warehouses. The features of bad con-r struction mentioned under What Mill-Construction is Not are as objec- tionable in warehouses as in factories, while the construction advocated fot mills may be used with almost equal advantage in the erection of warehouses. But as the latter are usually erected in the more thickly settled portions of a city, they are more subject to the dangers of a conflagration; and it should be understood that even the best slow-burning construction will stand but a short time after a Are has obtained a good headway, the main object of mill- construction being to retard the spreading of fire by the use of heavy timbers and the absence of concealed spaces. In applying the principles of mill- construction to warehouses, therefore, the general principle of using large timbers placed as far apart as the loads will permit, and of avoiding aU concealed spaces, should be constantly kept in mind. Warehouse-Floors, however, are generally required to sustain heavier loads than are found in woolen and cotton-mills, and hence require heavier con- struction. While WAREHOUSE -FLOORS are quite often built with transverse girders, 8 orio ft apart, the spaces being spanned by flooring from 4 to 6 in thick, the more common method of construction is to use one or more lines of longitu- dinal girders supporting floor-beams spaced as far apart as possible, preferably not less than 8 ft on centers. Area and Height. The area of buildings of this type should be, preferably, not over 7 500 sq ft, and in no case should it exceed 15 000 sq ft between fire-walls. If buildings of large area are required, it is advisable to divide them into 778 Wooden Mill and Warehouse-Construction Chap. 22 separate sections by fire-walls, thus reducing the liability to one fire, and afford- ing an opportunity of storing hazardous goods in one or more sections, and non-hazardous or less hazardous goods in the remaining sections. Where ground is available, it is better to have a building of large area and lower HEIGHT divided into fire-sections, than to have a building of lesser area and greater height, as the former construction affords a more economical handling of goods, and less concentration of values. Buildings of this type should be limited to 65 ft in height, and to six stories, thus discouraging the overloading of floors. Piled goods should be kept at least 18 in away from beams, thus allowing for the distribution of water from the sprinklers. Walls should be of brick, and not less than 13 in thick in the upper story, and they should be increased in thickness on the lower floors to take care of additional loads. Party walls should be increased at least 4 in in thickness, and all walls should be laid in cement mortar, should extend above the roof at least 36 in and be coped with stone, salt-glazed terra-eotta, or similar non- combustible materials. Openings in division walls should be limited to as few as possible, not over three in each story, they should not exceed 80 sq ft each in area, and should be protected by double, automatic, sliding fire-doors, as specified elsewhere. (See Chapter XXIII, page 907.) ELEVATION Balcony Floor-supports and rails Fire-proof. Note: Walls of brick or other approved material, built solidly from foundations to at least 36 inches above I'oof. Stair-treads, etc., of fire-proof material. Fig. 19. Tower Fire-escape. Outside-balcony Entrance Openings in "Walls. As a protection against fires from surrounding prop- erties, openings in outer walls should be small, limited to as few as possible, and protected by standard fire-shutters and doors, or standard wire-glass windows. If the surrounding buildings are of hazardous occupancy or inferior construction, and the distance between the warehouse and the latter but a few feet, shutters are preferable, as wire-glass windows are recommended only where the exposures are moderate. Even though the building is not exposed Mill- Construction as Applied to Warehouses 779 to fire from other buildings, the protection of window-openings may prevent the spread of fire from story to story through the windows. Girders and Beams which support the floors and roof should be single PIECES, not less than 6 in in least dimension, and with a sectional area of not less than 72 sq in; while columns should be not less than 8 by 8 in in cross- section in the upper story, and should be increased in size in the other stories to take care of any additional loads. The beams and girders should be self- releasing (Fig. 2), and the floors should be built as outlined under standard mill-construction, page 760, inclined at least i in in 20 ft, made as nearly water-proof as possible, and scuppered to the outside of the building. These scuppers should be set in brick-work at frequent intervals, of sufficient size to carry off the maximum amount of water from each floor, and so constructed that they will prevent the admission of cold air to the building. (See Fig. 11.) Towers. The floors should be continuous from wall to wall, avoiding holes for belts, stairways, elevators, etc. All such openings should be enclosed in a brick tower or in towers extending not less than 36 in above the roof, coped as above, and accessible from each story by means of an outside balcony (Fig. 19). Openings in face-wall extend from floor to ceiling, Vestibule-floor of fire-proof construction. Railing at opening. Fig. 20. Tower Fire-escape for Adjoining Buildings Where it is impossible, owing to the location or otherwise, to have these open- ings on the outside, they should be placed in brick towers constructed inside the building and connecting with an entrance to a fire-proof vestibule, open to the weather. There should be openings from each story to the vestibule, each protected by standard fire-doors (Fig. 20). Gravity-Tanks for Automatic Sprinklers are usually placed on extension^ of such towers, and they should be built to carry the additional load iniposed. Easy access to the roof of the building may be had from a window or windows placed in the tower, and such opening or openings should be protected by fire- shutters, especially where the tower is elevated a sufficient distance to allow the tank to be placed inside of the tower, thus preventing flames from gaining access to the tower and destroying the tank and tank-supports. ^ 780 Wooden Mill and Warehouse-GortstrUctioil Chap. 22 Boilers should be, preferablyy in a separate building, cut off by standard fire-doors from the warehouse; or, if in the main building, should be located in a room of fire-proof construction, access to which should be from outside the building only. Structural Steel Members should never be used in this type o^ coiistriiction, as they will not resist even a moderate fire. If used, they should be protected with fire-proof material. The lintels should be brick arches and not sleel sections. 10. Steel and Iron Structural Members in Warehouse-Construction Metal versus Wooden Standard Members. Owing to the fact that a beam or column of steel or wrought iron when heated will fail by buckling or bending very much sooner than an equivalent beam or post of wood, it is important that such members be of wood, provided that the wooden beams have a sectional area of at least 72 sq in, and are not less than 6 in in least dimen- sion, and that wooden columns have a sectional area of not less than 8 by 8 in. Cast-iron columns, also, will generally fail in fire and water sooner than wooden columns. Fireproofing Steel Beams and Girders. When steel beams and col- umns are used, fireproofing is necessary to make them as fire-resisting as ____^____^__^ __^ the floors. Such beams ' ^—p ( and girders may be fire- -i •B$«. r— ^^ ---- v:^ ^ PROOFED as shown in Fig. 21. Metal- wire mesh should be placed as shown, and tied to the beams and girders with metal clips; and to insure rigidity during the pouring of the concrete and to keep the mesh in alignment, forms should be used. The concrete should be poured before the floors are laid, and after the wooden beams are in position. After completion, the insulation should be at least i in at the edges of the flanges, 2 in under the lower flange of the beam and 3 in under the lower flange of the girder. The webs should be filled solid. Where there is little storage of a combustible nature in the building, the beams may be protected as shown in Fig. 22. (See, also, pages 863 to 866.) Fireproofing Metal Columns. Columns, either steel, wrought-iron, or cast-iron, should be protected even to a greater extent than girders and beams, and should have at least 3 in of concrete at the flanges, at least iVu in at the edges, and be filled solidly against the webs. Fig. 23 shows two columns protected by concrete held by wire mesh on %-in rods, and all securely held to the column by metal clips. Forms should be used and the concrete should be poured as the girders and beams are protected. Steel beams, girders and columns are difficult to protect, especially at the intersections of steel and wood, and this insulating material can best be applied before the floors are laid. The fire- proofing of these members wUJ bgjptit^e^avail, unless the materials are good. ^Mesh -Clip Fig. 21. Fireproofing of Steel Beam with Concrete and Plaster Steel and Iron Structural Members in Warehouse-Construction 781 well tied to the metal members, and applied by workmen who understand such work. Alternate Metliod Rods if used may bo Bharpeued and driven and fastened with heavy staple. At least % in of plaster outside of lath, 2 coat work. Between rods or cJiannels wrap lower flange with piece of metal latli to provide ample thiclgjess of plaster over flange. Channel punchecl^ for 2 in wire nails. Metal lath to be well stapled on to the wood, H in. rod or H in channel spaced every" 18 in. where beam la more than 10 in deep. Metal lath to be wired to channel or rod.. Can be cut away for hauyers and pointed up after hangers are in place. Fig. 22. Fireproofing of Steel Beam with Metal-lath and Plaster ^"Rods - Pat. Clamp "^Wire Mesl/ l"Plaster''^ Fig. 23. Fireproofing of Steel Columns with Concrete and Plaster Fig. 24 illustrates the protection of a round column by reinforced concrete. Here the concrete is held in position by wire mesh on metal furring, held in position by metal clips or ties. The fireproofing should be at least 4 in thick, and forms should be used in surrounding the columns. In addition to the above reinforcements for these columns, lateral reinforcement should be added by means of iron rods wound spirally around mesh, and placed 12 in on centers. After the forms are re- moved, and the wooden floors are laid, the columns and girders should be finished with a i-in thickness of hard plaster, filUng all interstices between the woodwork and the insulation. 1 riastei 3 Concrete Fig. 24. Fireproofing of Cast-iron Column with Concrete and Plaster Tile, 782 Wooden Mill and Warehouse-Construction Chap. 22 owing to the difficulty of properly bonding it, is not as effective as concrete; but if securely bonded by means of metal, it is quite satisfactory. Fig. 25 illustrates the protection of a girder and a column by means of tile. There are other equally efficient methods of beam and column-protection, described in Chapter XXIII. In buildings of warehouse-construction, heavy goods are 7jWf;?f/^/f/f/fw?wmfjfjff/)f//f///>f//nf;/////N/f/f/fnf^ ttttl IflffW 'M% 'Hnllow Til Ywu(u<{({onry but is not as elTectlve in preventing dry-rot as the wall- box or wall-hanger. Steel and Malleable-Iron Post-Caps and Bases. Fig. 27 illustrates other details of construction which may be used. The bottom post rests on a steel POST-BASE. The post-cap shown on the bottom post is a Duplex four-way Structural Details of Mill-Construction 783 STEEL POST-CAP, while the POST-CAP above it is one of the malleable-iron type, approved by the National Board of Fire Underwriters. The post-cap shown at the top, also, is of malleable iron and intended for lighter construction or for girders which run across the post as shown. The girders in every case are carried clear of the wall by means of approved wall-hangers and the beams are carried by the girders in malleable-iron joist-hangers. Fig. 26. Mill-construction. Column, Girder and Joist-framing Cast-iron Post-Caps and Bases. Fig. 28 illustrates other details of con^ struction. The lowest post rests on a heavy, cast-iron, ribbed post-base. The first-story floor-girders are carried at the post by means of heavy, cast-iron post-caps and are built into the wall in cast-iron wall-boxes. When cast iron is used for post-caps it is essential that it be made extra-heavy, as cast iron is very uncertain on account of the uneven shrinkage when cooling, which often causes internal stresses and weakens the caps. Flaws, also, may develop 784 Wooden Mill and Warehouse-Construction Chap. 22 during the manufacuure which weaken the caps and greatly impair the safety of the building. An objection to cast iron is its tendency to crack and break during a lire when cold water is thrown on it. The post-caps shown in Fig. 28 are of cast iron for the first and second floors, Duplex steel for the third floor, and malleable iron on the top post. '/r/AV/Z/A-'/^ Fig. 27. Mill-construction. Malleable-iron Post-caps and Bases Duplex, Combination Post-Cap. Fig. 29 illustrates the use of the Duplex COMBINATION POST-CAP on the bottom post. This cap is made with a malleable- iron lower part and a steel upper part. The post-cap shown on the second post is called the Ideal post-cap and consists of a steel upper part with steel angles riveted underneath to fit the post. The cap shown on the top post Structural Details of Mill-Construction 785 is the old-style, cast-iron cap. The wall-hanger, wall-box, wall-plate and JOTST-HANGER shown are used in standard construction. Fig. 28. Mill-construction. Cast-iron Post-caps and Bases Steel Post-Caps. Fig. 30 illustrates various forms of steel post-caps. The Ideal post-cap is shown on the bottom post and the Van Dorn post-cap on the post next above. On the top post the Star post-c.ai' is shown. This hrva a fin for wliich the top of the post must be slotted to receive it. Steel joist- 786 Wooden Mill and Warehouse-Construction Chap. 22 HANGERS aic shown for the two lower floors. The Ideal joist-hanger is illustrated in the lower floor. Tt is spiked to the sides and top of the girder. The Van Dorn joist-hanger is shown in the second floor, while the old-style STIRRUP is shown in the top floor. The wall-hangers illustrated are of the approved type. Fig. 29. Mill-construction. Combination Post-caps, etc. Framing Steel Beams and Girders. Fig. 31 iUustrates the use of I-beam girders in place of wooden girders and their connections with wooden beams. In this kind of construction it is necessary to fireproof the steel beams, as they are more readily afi"ected by heat in case of fire than large wooden timbers. Intense heat often causes them to collapse and ruin a building. The hanger Structural Details of Mill-Construction 787 shown in the first floor is used where the I beams and wooden beams are of the same height. This hanger provides an extra bearing for the timber and has proved very satisfactory. The hanger shown in the second floor is used when it is necessary to raise the wooden beam above the lower flange of the ^teel beam. This hanger brings all the load on the lower flange of the I beam and Fig. 30, Mill-construction. Steel Post-caps, etc. provides an anchorage for the wooden beam. It is used singly or in pairs on the I beam as required, and is bolted through the web of the I beam. This has been found to be a very economical and efficient construction. In the third floor the wooden beam is shown framed to the I beam by means of a shelf- ANGLE. With this form of construction it is necessary to rivet the shelf- 788 Wooden Mill and Warehouse-Construction Chap. 22 '■////////x y////////////////////////y/////////////////7^ Fig. 31. Mill-construction. Framing Steel Beams and Girders ANGLE to the web of the I beam. The upper detail shows the old-fashioned STIRRUP passing over the top flange of the I beam and carrying the wooden beam. The post-caps shown are the Duplex steel post-caps which are approved by the National Board of Fire Underwriters. Connections of Floor-Beams and Girders 789 12. Connections of Floor-Beams and Girders Girder-Hangers and Joist-Hangers. To render the construction, and particularly the girders, slow-burning, it is important to have no hollow spaces between the top of the girders and the flooring, that is, to have the top surface of the floor-beams flush with that of the girders. This, of course, neces- sitates framing the floor-beams into the girders. For heavy CONSTRUCTION the only kind of framing that is permissible is one in Fig. 32. Duplex Hanger for Heavy Floor-beams Fig. 33. Framing I Beam and Wooden Beam of Same Depth which some kind of joist-hanger is used. The various kinds of joist-hangers now in the market have been illustrated and commented on in the last part of Chapter XXI^ When the floor-beams are 6 by 12 in or larger in cross-section, and the girders! are of wood, the author would give the preference to the Duplex hanger' shown in Fig. 32. (See, also, pages 752 and 753.) If steel-beam girders are used in place of wooden girders, there are several methods in use for framing the wooden beams. Fig. 33 shows a steel I beam, and a wooden beam of the same depth framed into it and resting on its lower flange. In most cases, however, this does not afford a sufficient bearing for the wooden beam. Fig. 34 shows a shelf-angle riveted to the web of the I beam. Whenever this method of supporting the beams is used, enough bolts or rivets should be used to support the load carried by the shelf- angles. Each %-m bolt may be considered to support 3 000 Fig. 34. Wooden Beam Framed to I Beam with lb on each side of the girder, Shelf-angle and each %-in bolt, 4 000 lb. The methods shown in Figs. 35 and 36 are sometimes used, but are open to objection on account of the weakening of the wooden beams when loaded. Fig. 37 shows a stirrup-type of hanger. This construction permits the 790 Wooden Mill and Warehouse-Construction Chap. 22 Fig. 35. Wooden Beam Framed to I Fig. : Beam with Wooden Cleat Wooden Beam Framed to I Beam with Shelf-angle Fig. 37. Wooden Beam Framed to I Fig. 38. Wooden Beam Framed to I Beam Beam with Stirrup-hanger with Duplex Hanger Fig. 39. Wooden Beam Framed to I Beam with Duplex Shelf-hanger L=ri] Fig. 40. Wooden Beam Framed to I Beam with Duplex Box-hanger Connections ot Floor-Beams and Girders 791 framing of the wooden beam at any desired height, and has proved satisfactory. These hangers can be used with any depth of beam or girder, and are furnished by all manufacturers of steel joist-hangers of the various types, as well as by blacksmiths who can make wrought-iron stirrups. Fig. 38 shows the Du- plex-type OF HANGER for framing a wooden beam flush with the lower flange of the I beam. This hanger is attached by means of bolts. Fig. 39 shows Fig. 41. Floor-framing with Van Dorn Hangers and Post-caps the same design of hanger, with the shelf-construction used to carry the wooden beams up to 4 in above the lower flange of the I beam. Fig. 40 shows a hanger for carrying the wooden beams 4 in or more above the lower flange of the I beam. The hangers described in Figs. 38, 39 and 40 are all of the Duplex type, and arc so constructed that all the load is carried on the lower flange of the Fig. 42. Floor-framing with Duplex Hangers and Post-caps I beam, which is a very satisfactory and ideal construction whenever it is necessary to frame wooden beams into and not rest them on the I beams. The design is a very economical one for framing wooden beams to I beams, as the holes for attaching these hangers can be punched while thS steel is being fabri- 792 Wooden Mill and Warehouse-Construction Chap. 2^ cated, and the hangers are attached to the steel beams by means of boUs when the wooden beams are put in place. These hangers are provided with lugs or lag-screws for anchoring the wooden beams securely to the steel girder. Fig. 41 shows a floor-framing with the Van Dorm steel hangers. Fig. 42 shows the floor framed with the Duplex type of hanger and post-cap. The same principle of construction is applicable to larger wooden beams spaced farther apart. 13. Wall-Supports and Anchors for Joists and Girders Box Anchors, Wall-Hangers, etc. Anchoring. In a warehouse intended to be constructed on the slow-burning principle, the floor-beams and girders should be anchored to, and supported by the walls in such a way that in case the beams are burned through, the ends may fall without injuring the walls; and where large timbers are used, provision should be made against the possibility of drv rot. Box Anchors. The method of supporting the beams in mill-construc- tion as originally de- veloped in the New Eng- land mills is shown in Fig. 43. Early Form of Beam-support in Mill-construction Fig. 43. This fulfilled the requirements above mentioned, but it weakened the walls to some extent. The Goetz cast-iron Fig. 44. Goetz Box Anchor for Wooden Beams Fig. 4.5. Goetz Box An- chor for Wooden Beams BOX anchors shown in Figs. 44, 45 and 46 and the Duplex wall-box shown in Fig. 47 are decided improvements on the anchor shown in Fig. 43, as they Wall-Supports and Anchors for Joists and Girders 793 Fig. 46. Goetz Box Anchor for Wooden Girders afford all the advantages of the latter without weakening the walls, unless the floor-beams are very wide. The wall-box as shown in Fig. 47 is rnade with a malleable-iron bottom plate and a steel box above. It has a rib on the plate at the back, which extends up and down, and acts as a secure anchorage in the brickwork. These wall-boxes are made wedge-shape, and it is therefore impossible to pull them out of the wall. The more weight there is on the beam, the stronger will be the bond that holds the beam to the box and the box to the wall. In case of fire or accident, the joists can burn through or break; and in falling they can free them- selves from the an- chorage and leave the wall standing. The wall is not even weakened by the space left in it, because the box remains, and the crushing strength of this cast-iron box is much greater than that of the wall. No break or breach is made in the wall, and the box that remains, securely held, forms a space for the easy replacement of the wooden beam. The box provides a perfect and secure foundation for each beam. Fire from a defective flue cannot ignite a beam-end, because it is protected by a ventilated, CASx-moN box. The WALL-BOXES have air-spaces, also, in the sides, Yj in wide, which permit a circulation of air around the ends of the beams, effectually preventing dry , rot. If timber is wet or unseasoned these wall-boxes allow it to dry out after it is put in the building. The average weight of a box like that shown in Fig. 45, for 2 by 12-in joists, is 10 lb. Wall-Hangers. Another device [y^ for obtaining the same results in a different way is the wall-hanger. Figs. 48 and 49 show Duplex wall- hangers for large timbers. The hanger shown in Fig. 49 is made of open-hearth steel and is extra-heavy. Each of these hangers is provided with a plate which has an 8-in bearing on the wall, and the bearing of the timbers on the hanger is also 8 in. For beams not exceeding 10 in in breadth there is probably little choice between the box anchor, Fig. 46, and the wall-hangers, Figs. 48 and 49, except perhaps in the price and appearance. When the wall-hanger is used, no hole is left in the wall, and a saving of 6 in in the length of the beams is effected, which in some cases would be a consideration. For girders 12 by 14 in 9,^4 upw£|.rds in cross-section, the author believes that the hanger shown itt Fig. 47. Duplex Wall-box with Ribbed Plate 794 Wooden Mill and Warehouse-Construction Chap. 22 Fig. 49 is preferable to the box anchor. Wall-hangers made from stirrups should not be used for heavy beams. The use of any one of the hangers or Fig. 48. Duplex Wall-hanger for Large Wooden Girder Fig. 49. Duplex Extra-heavy Wall- hanger for Large Wooden Girder boxes is obviously greatly superior to the ordinary method of anchoring beams or girders to walls, and the use of such hangers will undoubtedly save much loss which would be caused by the falling of the walls. These are almost invariably Fig. 50. Application of Wall-hanger to Brick Wall pulled down by the ordinary iron anchors when the beams fall. Fig. 50 shows the application of a wall-hanger. 14. W.eakness of Wrought-Iron Stirrups when Exposed to Fire Stirrups and Fire-Tests. Referring to this subject, Professor J. B. Johnson, of Washington University, said: " The recent fire-tests of steel stirrups and brick walls which were made under my supervision in this city (St. Louis), show very conclusively that unprotected stirrups are extremely dangerous. These stirrups become red-hot in a few minutes and then rapidly char and burn away the ends of the beams; and they also bend down, so that in from twenty to thirty minutes after the fire reaches the stirrups, the beam is dropped right out of the twisted steel by the straightening out of this bend or twist." The Duplex Hangers possess an advantage over steel stirrups because, being of malleable iron, they are not as quickly afifected by heat, there are no twists or bends to straighten, and the bearing in the trimmer or header is to a great degree protected by the form of construction. During the severe fire at Paterson, N. J., February 9, 1902, some Duplex wall-hangers were sub- jected to a most severe test without apparent injury. It is undoubtedly desir- able that all structural iron should be protected from fire, but it is almost im- practicable to. effectively protect the stirrups used in connection with woodtn beams without going to a greater expense than the character of the construction Varrants. Form and Materical of Post-Caps 795 15. Post and Girder-Connections Iron Cap-Plates, Wooden Bolsters, etc. Whenever a building is con- structed with wooden posts extending through several stories, each upper post should rest on an iron cap-plate, fitted over the post below, and never on a girder or even on a wooden bolster. A bolster would not be objectionable were it not for the fact that the pressure under the post is generally sufficient to crush the fibers of any kind of wood. Then, too, there is always some settle- raent due from shrinkage. As posts are used expressly for the support of beams or girders, the iron caps must, of course, extend sufficiently beyond the upper post to afford ample bearing for the end of the girder. This bearing in square inches should be equal to at least one-half the load on the girder divided bj^ the safe resistance of the wood to crushing across the grain, as given in Table IV, page 454. Example. A i^ by 14-in yellow pine girder is designated to support a possible load of 38 000 lb. What bearing should it have* at the ends.^ Solution. The safe resistance given for long-leaf yellow pine to crushing across the grain, is 350 lb per sq. in. One-half the load on the girder is 19000 lb, and hence the bearing area should be 19 000 divided by 350 or about 54 sq in. As the breadth of the beam is 12 in this would require a bearing lengthwise of the girder of 4V2 in. In no case should the bearing be less than that required by the above rule. 16. Form and Material of Post-Caps Cast-iron versus Steel Post-Caps. Formerly cast-iron post-caps were used for the framing of the girders at the columns and posts. But the uncer- tainty attached to the use of cast iron, and the necessity of extremely heavy caps to assure safe construction have led most engineers to specify steel post- caps, as they are unquestionably the strongest form of construction for fram- ing posts and girders. The use of steel post-caps is to be recommended, there being no uncertainty regarding the strength of steel as there is concerning the strength of cast iron used for post-cap construction. Internal stresses due to uneven cooling may seriously affect the strength of a cast-iron cap, while a honeycombed casting may be used, undetected, and affect the safe carrying capacity; so that failure of the cap may occur even from the vibration due to the machinery in the building. Cast-iron Post-Caps are still used in some localities and a few of the com- mon forms as well as those of steel post-caps are shown. Fig. 51 shows a form which is frequently used for light construction. Fig. 52 shows a similar cap for a cylindrical post. These caps permit the use of girders wider than the post. When the girders and floor-beams are in place, and especially when the building is occupied, there is no danger of the girders or posts slipping on the plate; in fact it would require a greater force to move them. The girders should be tied together longitudinally by iron straps spiked to their sides. Many persons, however, consider it important in a building of slow-burning construction, to have the posts tied together in vertical lines, and the girders secured in such a way that they will be self-releasing without pulling dowii the posts. Figs. 5.3 and 54 show two post-caps which fulfill these requirements. With these caps the ends of the girders are not fastened by bolts or spikes, but are held in place and tied longitudinally by means of the lug L on the Goetz cap, and by pins on the Duvinage cap; so that in case the girder is burned to the breaking point, it can fall without pulling on the post. Provision is also made for bolting the cap to the upper post. The author doubts very much. 796 Wooden Mill and Warehouse-Construction Chap. 22 Fig. 51. Cast-iron Post-cap for Fig. 52. Cast-iron Post-cap for Cylindrical Wooden Square-section Wooden Post , Post Fig. 53. Cast-iron Duvinage Post-cap with Beam-pins Fig. 54. Cast-iron Goetz Post-cap with Beam-lugs Fig. 55. Cast-iron Post-cap with High Sides Form and Material of Post-Caps 797 however, if posts bolted together in this way will stand after the girders have fallen, as the planking will be likely to pull the posts over, even if they* do not burn as quickly as the beams. Fig. 55 shows another form of cast cap with high sides, allowing lag-screws to be driven in the holes to tie the girders. Fig. 57. Steel Post-caps for Posts Varying in Section. Second Figure Shows Four- way Beam-construction A Steel Post-Cap, v/hich is approved by the National Board of Fire* Under- writers and bears their label, is shown in Fig. 56. This post-cap is made up of steel side-plates and heavy steel brackets, all held rigidly together by means of four heavy bolts. The posts and girders are fastened to the cap by means of 798 Wooden Mill and Warehouse-Construction Chap. 22 Fig. 58. Steel Post-cap. One-way Beam-construe- Fig. 59. Malleable-iron Post- tion caps Fig. 60. Steel Post-cap for Continuous Post Fig. 61. Malleable-iron Post-cap with Steel Top-plate Z^ IT # ""^^ ."iri%^ Fig. 62. Steel Post-cap for Cylindrical Wooden Post. Perspective Form and Material of Post-Caps 790 lag-screws, permitting the girders to. release themselves in case of fire. By this method the entire construction is tied together vertically and longitudinally. This cap, on account of its simple design, lends itself readily to every form of construction desired. Various Types of Post-Caps. Fig. 57 illustrates one post-cap in which the width of the girder is less than that of the post below, and also another post- o o o U) o 1 t 1 1, 5 l) SIDE ( ) • ,x'==-->^ — 1' l-^ — ^^^^^.r^'" PLAN Fig. 63. Steel Post-cap for Cylindrical Wooden Post. Elevations and Plan CAP in which the width of the girder is greater than that of the post below. In the latter four-way brackets are riveted to the side-plates to provide for the FOUR- WAY CONSTRUCTION. Fig. 58 sllOWS a ONE-WAY CONSTRUCTION. Fig. 60 shows a POST-CAP which is used when it is required to run a post through two stories. This is what is known as a con- tinuous POST-CAP. The bracket instead of being made clear across l^e cap is made short on both sides and fitted into shoulders notched into the post, so as to make a more rigid construction. Fig. 59 shows two POST-CAPS made of malleable iron which are preferable to cast-iron caps as they will not break off in case of a fire when cold water comes in contact with them. This danger is present when cast- iron POST-CAPS are used. The cap shown is made in two parts so that it will fit posts and girders of different sizes. This cap, also, is approved by the Board of Fire Underwriters. Fig. 61 shows a com- bination POST-CAP, the upper part of which is made of steel plate, and the lower part of malleable iron. Figs. 62 and 63 show steel post-caps for round posts. They are also frequently used for pipe-columns and concrete- filled columns. (See, also, Steel-Pipe Columns, page 469 and Lally Columns, pages 474 and 477.) F,ig. 64 shows a steel post-cap intended for lighter Fig. 64. Steel Post-cap for Light Con- struction 800 Wooden Mill and Warehouse-Construction Chap. 22 construction. Fig. 65 shows Van Dorn post-caps. Fig. 66 illustrates the Star post-cap which is made of a bent steel plate with a fin projecting below into a slot in the post. Both are approved by the Underwriters. It is necessary I J Fig. 65. Van Dorn Steel Post-caps to slot out the post in order to insert this fin. Post-caps which completely encircle the top of the post in a socket, to a great measure tend to pre- vent the twisting effect of the post, which is so noticeable when the posts are of wood. There is an objection to the use of the four-way post-cap when the girders are of wood, because the floor-beams that are hung from a girder drop a distance equal to the shrinkage in the girder, if the beams are hung in stirrups, or by one-half this amount if they arc hung in Duplex hangers. The beams sup- ported on the post-cap cannot drop at all, and consequently the floor will be higher over the beam supported by the posts, than over the inter- mediate beams. In one building where deep beams were used, the unevenness in the floor amounted to nearly an inch and was very notice- able. Wherever wooden girders are used it is, therefore, a much better construction to support all of the floor- beams from the girders, in which case the shrinkage will be uniform. With steel girders there is no shrinkage, and a beam may be placed opposite the posts with advantage. 17. Roofing-Materials Warehouse-Roofs are almost always flat and, like floors, should be continu- ous from wall to wall, without openings. The occupancy of such buildings calls for little light, and hence skylights and other roof-structures are not re- quired. Dampness and Leaks. Stored goods may l)e very easily damaged by water, and roofs, therefore, should be of such construction that they will prevent damp- ness, either through leakage or condensation. While roofs are usually built as flat as possible, the incline should be sufficient to dr;^in readily, and the out- Fig. 66. Star Steel Post-cap with Fin Fire-Protection 801 lets should be of sufficient capacity to quickly drain the roof of a maximum amount of water. Slag or Tin are almost exclusively used on buildings of this type, although asphalt or other mastics are sometimes used with good results. Slag Roofs should be constructed generally as described on pages 1595 to 1599 and should be not less than S-ply, with the maximum amount of coating. The flashings and counterflashings should be of copper or heavily-coated best terne- plates. Tin Roofs should be laid with the best open-hearth, palm-oil-process terne- plates, laid on felt or other suitable material which will avoid condensation and act as a fire-retardant. Canvas Roofing will stand hard usage, as is shown by its continued use on decks of vessels and steamers; but it is not adapted to large buildings. Provisions for Flooding Roofs. When warehouses are located in congested districts, surrounded by higher buildings, or by buildings of light construction or hazardous occupancy, their roofs should be so constructed that they may be flooded during severe fires in such surrounding buildings. ' This can be accom- plished by using good roofing-materials, making high flashings, waterproofing the walls above the roof-line, and providing roof-outlets of types that will allow the placing of stoppers at the scuppers. (See Fig. 11.) 18. Partitions Non-bearing Partitions. This refers only to those light walls or enclosures which separate rooms, etc., and not to those walls which divide the building into sections. Partitions, as here defined, bear no floor-loads. Buildings of the SLOW-EURNING TYPE, for occupancies described above, need but few partitions, and these should be built of non-inflammable materials, preferably metal lath and plaster on light, metal studding. All cupboards, closets, lockers, etc., in a building of this type should be of metal, or other equally non-inflammable material. 19. Doors and Shutters Fire-Underwriters' Specifications. Doors and shutters should be built as outlined in the Rules and Requirements of the National Board of Fire Under- writers for the construction and installation of fire-doors and fire-shutters, as these specifications are accepted by architects and builders as the standard. Door-Openings should be limited to 80 sq ft, or less, each, and all communica- tions between buildings or sections of a building protected with double, auto- matic, sliding doors. 20. Fire-Protection Automatic Sprinklers, supplied with an ample quantity of water at a good pressure, are needed in mills, storehouses, factories, warehouses, etc., where combustible goods are made or stored, or where large values are at stake. They may, in fact, be installed in buildings of any type of construction and occupancy, but are most effective in buildings of fire-proof or mill-construction. Inside Standpipes, with outlets in each story, in the basement and on the roof, should be installed at points readily accessible in case of fire, and should have a sufficient quantity of good hose attached at each outlet. Roof Nozzles. If a building is badly exposed to other buildings of inferior construction or hazardous occupancy, a Monitor-nozzle of large size, located on the roof, is advisable. 802 Wooden Mill and Warehouse-Construction Chap. 22 Public Water-Supplies. If these are not available, a private fire-service may be advisable. Competent Supervision. All of the above fire-protection equipments should be installed by men familiar with their operation, and supervised by competent fire-protection engineers, under plans approved by underwriters having jurisdiction. 21. Cost* of Mills and Factories Built on the Slow-Burning Principle Difficulty of Estimating Costs from Tables. The cost of a building of this type of construction depends upon the cost of material plus the cost of labor, and as the cost of either varies greatly in different localities the cost of similarly constructed buildings must also vary. Even if the cost of labor and materials does not vary, the cost of buildings of the same area will depend much upon the height, floor-loads, distance between bearing-points, design, etc., and it is dilhcult to deduce a table accurate enough for use in computing even the approximate cost of buildings per square foot of floor-areas. One firm of architects t states: ''Experience has taught us that estimating the cost of a building either by the square-foot 'method or the cubic-foot method has proved dangerous and misleading, and it was al^andoned by us many years ago except to obtain a general idea of the cost of a building. We have found that the only relia1)le way to approximate the cost of a building is to block it out and to figure the approximate quantities, which at the market prices prevailing at the time the building is to be erected, will give the approxi- mate cost of said building." Owing to the high cost of lumber, a fire-proof building will cost but little, if any, more than a building of mill-constriktion; and owing to this fact it is always advisable to determine the cost of buildings of both types before deciding upon the t3^pe to be used. Buildings of mill- construction are becoming obsolete in some .localities, and owing to the lower rate of insurance on buildings of fire-proof construction, those of the latter type are much preferred, as in the end they cost less. It is not always safe to compare the total cost of labor with the cost of the labor per diem, as the cheaper labor is often the more expensive in the end, this depending largely upon the locality and the conditions imposed. Tables showing the approximate cost of buildings of the mill-construction type are computed from the cost of mill-buildings of light construction (cotton-mills with lateral beams only) and are not adapted to computing the cost of heavy warehouses or similar factory-construction. The figuring of the cost of such buildings from the COST PER square foot gives, at the very best, only approximate results; and as a discrepancy of but i ct per sq ft will sometimes amount to thousands of dollars, the method is hardly accurate enough to estimate even the approximate cost. The Cost of Buildings of Mill-Construction in New England. The following eight buildings were designed by Lockwood, Greene and Company of Boston, Mass., who submit data and descriptions of ])uildings of mill-con- struction with their cost per square foot. These buildings are, with a single exception, situated within a limited area where cost of labor and materials vary but little. The floor-loads vary from 75 to 150 lb per sq ft, and the cost runs from $0,715 to $1.56 per sq ft. Considering the textile-mills only, the average cost is $1,038 per sq ft, while the average cost of all these buildings is $1,113 per sq ft. * These are pre-war prices, but the data are retained for purposes of comparison of rela- tive costs of different types of buildings, or of buildings in different sections of the country. For the cost of reinforced-concrete mills, warehouses, etc., see pages 1613 and 1618, t Farrot & Livaudais, Ltd.. New Orleans. La. Cost of Mills and Factories Built on the Slow-Burning Principle 803 A Cotton Spinning-Mill. This mill has an attached picker-house, office and dye-house wings, and was built in Rhode Island in 191 1. The following are the details of construction: main mill, four stories; size, 263.17 by 131.67 ft; two-story picker-house, 42,67 by 131.67 ft; one-story dye-house 55 by 85.67 ft; brick stair- tank, and other towers; walls of hard brick; plank and wearing- lloors on transverse I-beam framing, supported by cast-iron columns, except in five bays, where both transverse and longitudinal framing is used; slag roof- ing on plank on wooden transverse rafters; floors Ijuilt for a live-load of 75 lb per sq ft. The cost of the buildings was $0,965 per sq ft. A Four-Story Cotton-Mill. This mill is without basement. It was built, together with the fan-room and repair-shop additions in Georgia, in 19 10. The following are the details of construction: mill, four stories; size, 272 by 128 ft; office and repair-shop, one story in height and 122.67 by 36 ft in plan; regular mill-construction, that is, brick walls, hard-pine transverse floor-framing, wooden columns and plank floors, except for six bays of the fourth floor which .have steel I-beam longitudinals in addition to the hard-pine transverse timbers, and for sixteen bays of the roof-framing which have both longitudinal and transverse hard-pine timbers, these having been found necessary in both cases because of the omission of the alternate columns. These buildings have extensive monitors, saw-tooth skylights, stair-towers, etc. The floors are designed to carry a live load of 75 lb per sq ft. The cost of the building was $0,715 per sq ft. A Cotton-Mill of Irregular Shape. This mill is considerably wider at one end than at the other and has a basement at one end. It was built in Massachusetts in 191 1. The following are the details of its construction: mill, five stories; length, 311.67 ft and average width, 75.42 ft; five-story wing, 65.26 by 40.01 ft, with extensive pent-houses; stair and elevator-towers and skylights; brick walls, transverse wooden floor-framing, supported by cast-iron columns and brick walls; conditions at site demanded extensive foundations; windows in fourth and fifth stories of one wall protected by wire-glass in metal frames; and floors built for a live load of 75 lb per sq ft. The cost of the buildings was $1,172 per sq ft. A One-Story Machine-Shop. This was built near Boston, Mass., in 19 10. The main building is 200 by 136.375 ft with a connecting wing, 50 by 39.33 ft. It has brick walls; longitudinal, steel, I-beam framing; transverse, steel, saw- tooth skylight framing; plank roof covered with tar and gravel; 20-ft longitu- dinal and i6-ft transverse bays; steel I-beam columns; 4¥2-'m cement floors except for three bays which have a i-in maple overflooring, a i-in North Caro- lina pine, intermediate layer, a 3-in kyanized spruce-plank layer, and 4V2 in of tar-concrete; and extensive saw-tooth sky fights. The cost of the buildings was $1,288 per sq ft. A Building for Manufacturing Automobiles. This building has forge- shop extensions and was built in Connecticut in 19 10. The main building has four stories and a basement and is 54 by 151 ft in plan with a one-story extension, 50 by 149 ft, with extensive pent-houses and monitors. The factory- building has brick walls, transverse yellow-pine framing on heavy wooden col- umns and on walls, floors of i-in maple overflooring over 4-in yellow-pine planks, a roof of 3-in yellow-pine planks covered with tar and gravel, and a 4^^-in cement, basement-floor. The extension has brick walls; a brick-on-edge floor laid on a 4-in course of cement concrete on earth; steel roof-trusses, of 47-ft, 4-in span placed 10 ft on centers; tar-and-gravel roof; and extensive monitors. The floors are built to carry a five load of 125 lb per sq ft. The cost of the building was $1,075 P^r sq ft. 804 Wooden Mill and Warehouse-Construction Chap. 22 A Two-Story Wooden Box-Factory. This factory has no basement. It was built near Boston, Mass., in 1909. In plan it is 155 by 305 ft and its aver- age height is 32.5 ft. It has brick shafts; transverse wooden framing for the first floor; transverse beams supported by longitudinals for the second floor and roof; wooden columns and plank floors; and wooden monitors. The floors are designed to carry a live load of 150 lb per sq ft. The cost of this building was $0.84 per sq ft. A One-Story-and-Basement Weave-Shed. This was built near Boston Mass., in 1909. It is 213 by 244.17 ft in plan, with extensive entrances, towers and saw-tooth skylights. It has brick waUs; longitudinal I-beam girders sup- porting transverse I-beam girders in the first story, resting on brick piers; transverse hard-pine girders supporting longitudinal girders for the saw-tooth skylight-framing; heavy, wooden floors and roof; wooden columns; an earth basement-floor; and foundations on concrete piles. The floors are designed to carry a five load of 100 lb per sq ft. The cost of the buildings, on the one- story basisj was $1.56 per sq ft. A Two-and-One-half Story Picker-House. There is, also, a two-story house and a one-story connecting passage between the two buildings mentioned above for the cotton mill of irregular shape, which were built in Massachusetts in 191 1. The picker-house is 64 by 95 ft in plan; the waste-house 21 by 49 ft; the covered bridge 10 by 40 ft; and the average height of the building 42.58 ft. The wafls are of brick. The picker-house has transverse wooden framing sup- ported by wooden columns and has plank floors. The waste-house wing has transverse, steel I-beam framing and no columns, and concrete-slab floors. The floors are designed to carry a live load of 75 lb per sq ft. The cost of the building, including plumbing, was $1.29 per sq ft. The Cost of Buildings of Mill-Construction in Philadelphia, Pa., and Vicinity. The following five buildings were designed by Stearns & Castor, Philadelphia, Pa., who submit data and descriptions, with the cost per square FOOT. These buildings are within a very limited area, being in or within a few miles of l^hiladelphia, and are of somewhat heavier construction than those described above, the floor-loads varying from 120 to 150 lb per sq ft and the cost ranging from $0.86 to $1.23 per sq ft. The average floor-load is 132 lb and the average cost $1.02 per sq ft. The two spinnirig-mifls mentioned are de- signed for avera,ge floor- loads of 120 lb and their average cost was $1.00 per sq ft. A Chocolate-Factory. This was built in Philadelphia, Pa., on open ground. It has an ornamental exterior; walls of Sayer and Fisher brick with terra-cotta trimmings, and a main building, 83 by 303 ft in plan and two stories in height. One section of the building, 60 ft in length, is three stories high. The story- heights are 14 ft from top to top of floors. The floors are designed to carry a Hve load of 150 lb per sq ft. It has foundations of concrete; heavy mill- floors on heavy timber-framing; a slag roof; all stairways and elevators in brick towers; and openings in division walls equipped with fire-doors. The cost of the building, excluding plumbing, heating, electric work, elevators, fire- protection and mechimical equipment, was $0.86. A Four-Story-and-Basement Chocolate-Factory. This building was erected in Philadelphia, Pa. It is 44 by 130 ft in plan, with average story- heights of 13 ft. It was built in a congested part of the city, between other build- ings. The cost of underpinning and shoring the adjacent buildings is included in the cost given. It has plain brick walls; slow-burning floor-construction on heavy, wooden timbers, with finished flooring of maple; stairways and elevators Cost of Mills and Factories Built on the Slow-Burning Principle 805 in brick enclosures; and a slag roof. The floors are designed to carry a live load of 150 lb per sq ft. The cost of the buildings including plumbing, but excluding heating, electric work, elevators, fire-protection and mechanical equipment, was $1.23 per sq ft. A Spinning-Mill. This building was erected in Philadelphia, Pa., on ground open and easy of access. Its exterior is of brick, without ornamentation. It is 64 by 268 ft in plan, three stories in height, the stories throughout being 15 ft 6 in from top to top of floors. The floors throughout are calculated to carry a live load of 120 lb per sq ft. It has walls of brick; a slow-burning floor-con- struction with finished flooring of maple; a slag roof; and stairways and ele- vators in brick enclosures. The cost of the building, excluding plumbing, heating, electric work, elevators, fire-protection and mechanical equipment was $0.93 per sq ft. A Spinning-Mill. This building was erected in Philadelphia, Pa., on ground open and easy of access. Its exterior is a plain brick design. It is 69 by 269 ft in plan and three stories in height, the story-heights throughout being 15 ft' 6 in from top to top of floors. The floors throughout are calculated for a live load of 120 lb per sq ft. It has brick walls with concrete foundations; a slow- burning floor-construction with a finished flooring of maple; ' a slag roof; all stairways and elevators in brick enclosures; and aU openings in division walls equipped with fire-doors. The cost of the building excluding the plumbing, heating, electrical work, elevators, fire-protection and mechanical equipment, was $1.07; and the cost of the building including the plumbing, heating, elec- trical work, elevators and fire-protection, but excluding the mechanical equip- ment, was I1.34. A Clothing-Factory. This building was erected in Woodbine, N. J., on ground open and easy of access. Its exterior is of brick, without ornamentation. It is 45 by 179 ft in plan and three stories in height. The basement is 10 ft in height, and the other stories 12 ft in height from top to top of floors. The floors are calculated throughout for a live load of 1 20 lb per sq ft. It has walls of brick; slow-burning floors with yellow-pine finished flooring; a slag roof; and aU stairways and elevators in brick towers. The cost of the building, exclud- iilfe heating, electrical work, fire-protection and mechanical equipment, but in- cluding freight-elevators and plumbing, was $1.01 per sq ft. The Cost of Buildings of Mill-Construction in the Middle West. The following six buildings were designed by F. C}. Mueller, Hamilton, Ohio, who submits data and descriptions with the costs of buildings of heavier con- struction. The floor-loads vary from 200 to 300 lb and the cost from $0.62 to $0.96 per sq ft. The paper-mill at Taylorsville, III., is partly of concrete construction, and was built at a cost of $1.30 per sq ft. Exclusive of the last- named building, the average floor-load is 230 lb and the average cost $0,805 per sq ft. An Addition to a Paper-Mill. This was built in Dayton, Ohio.. It is a two-story brick building, 116 by 79 ft in plan. The first story is used for paper- storage and the second story as a finishing-room. The first floor is of cement on a Qnder fill; and the second floor of 2%-in yellow- pine planks with an over- flooring of %-in maple, supported by 8 by 14-in beams, 14 by ifi-in girders and 10 by lo-in wooden posts. The floors are figured for a live load of 200 lb per sq ft. The roof is supported by six steel trusses and 4 by lo-in wooden purlins, and covered with i%-in sheathing and composition roofing. The foundations are of concrete. The cost of the building, exclusive of the plumbing and heat* ing, was $0.75 per sq ft. 806 Wooden Mill and Warehouse-Construction Chap. 22 An Addition to a Foundry. This one-stor>', brick, foundry-building was erected in Hamilton, Ohio, is 432 by 63 ft in plan, and has a one-story wing, 86 by 46 ft in plan, and a one-story cupola-house, 28y2 by 26y2 ft in plan. It has a wooden floor in the wing only and dirt floors elsewhere. It has concrete foundations; a composition roof on 2V4-in sheathing, supported by 12 by 14-in girders, 6 by 12-in beams and 6-in cast-iron columns; an elevator in the cupola- house; and all doors of tin-clad construction. The cost of the building was $0,836 per sq ft. A Paper-Mill. This was built in Monroe, Mich., and is a one-story-and- basement brick building, 185 by 87 ft in plan, with an end-wing 234 by 35 ft. It has heavy beam and girder floor-construction, designed to carry a live load of 300 lb per sq ft; concrete foundations and a basement- part, 130 by 87 ft. It is designed for one paper-making machine and four beaters, has a composition roofing and one skylight over the boiler-room. The cost was $0.88 per sq ft. A Paper-Mill. This is an irregular-shaped brick building erected in Kennil- worth. La., and is 356 by 168 ft in plan. About one-third of it is two stories and the remainder one story in height. It has a heavy wooden, beam, girder and post-construction; a stone foundation on cypress-grillage footings; and floors designed to carry heavy paper-making machinery with a live load of 250 lb per sq ft. The cost of the building was $0.96 per sq ft. A Warehouse. This is a one-story-and-basement brick building, erected in Hamilton, Ohio, and is 38 by 50 ft and designed for a live load of 200 lb per sq ft. It has a cement floor in the basement; 10 by 14-in girders, 8 by 12-in beams and ID by lo-in posts supporting 3%-in flooring; 10 by 14-in girders and lo-in round, wooden posts carrying 2H-in sheathing and composition roofing. The cost of the building was $0.62 per sq ft. A Paper-Mill. This was built in Taylorsville, 111., and has a main building, two stories in height and 49 by 130 ft in plan; a one-story part, 138 by 81 ft in plan; and a one-story wing, 42 by 144 ft in plan. There is a basement under almost the entire building. The foundations are of concrete and there are . cement floors in the basement. The first floor is of reinforced-beam, girder and slab-construction, designed for a live load of 250 lb per sq ft; the second floor of mill-construction, supported by cast-iron columns, 14 by i8-in wooden girders and 12 bj^ i6-in wooden beams; and most of the roof is supported by steel trusses and wooden purlins. The second floor was designed for a live load of 150 lb per sq ft. There arc extensive skylights, pent-houses, etc. The cost of the building was $1.30 per sq ft. The Cost of Buildings of Mill-Construction in Toronto^ Canada. The building described in the following paragraph was designed by Sproatt & Rolph, of Toronto, Canada, who submit data of a warehouse-building with all floor-openings and windows and other outer wall-openings protected in an approved manner, and erected at a cost of $1.12 per sq ft. A Five-Story-and-Basement Seed-Warehouse. This was built in Toronto, Canada, and is 1 11 by 14c ft 3^2 in in plan. The floor-heights are 13 ft 1 in, and the total height is 66 ft. The floors are built of 2 by 6-in pieces of pine on edge and the bays measure 1 2 ft 5 in by 13 ft. The beams are of loijg-leaf yellow pine, 14 by 18 in in section; the posts of similar material, varying from 8 by 8 in to 16 by 16 in; the walls are of hard, red brick with gray stone fac- ings; and the sashes and frames are of steel throughout. The building has three elevators in a brick-enclosed shaft and one staircase in a separate brick shaft. The floors are designed to carry a live load of 250 lb per sq ft. The cost o! the building, exclusive of the heating and lighting, was $1.12 per sq ft. Cost of Mills and Factories Built on the Slow-Burning Principle 807 The Cost of Buildings of Mill-Construction in Northwestern Canada. The following four buildings were designed by J. H. G. Russell, Winnipeg, Canada, and are ' warehouses of very superior, heavy construction, widely separated in location, yet varying little in cost. The floor-loads used vary from 300 to 350 lb, hve load, per sq ft and the cost varied from $1.41 to $1.54 per sq ft. The average cost was $1.46 per sq ft. A Seven-Story-and-Basement Warehouse. This was built in Winnipeg, Canada, and is 50 ft 6 in by 1 19 ft 9 hi in plan. The floors are of 6-in spruce with %-in maple overflooring. All floors are on heavy girders and columns; the elevators are in brick shafts; and the walls are of brick, except the first story front wall, which is of cut stone. The floors are designed to carry 300 lb per sq ft, live load. The cost of the building, exclusive of the heating, elevators, etc., was $1.46 per sq ft. A Three-Story-and-Basement Warehouse. This was built in Winnipeg, Canada, and is 62 ft 6 in by 86 ft 6 in in plan. Heavy fir timbers were used for framing. It has a 6-in fir-plank solid floor with Vn-in maple overflooring; stairs and elevators in brick towers; brick walls with the openings in the rear and sides of the building protected. The floors were designed to carry a live load of 350 lb per sq ft, and the cost of the building, excluding the heating, etc., was $1.41 per sqft. A Warehouse. This is a six-story-and-basement building, erected in Saska- toon, Canada, and is 50 by 112 ft in plan. The floors are of 6-in fir, with%-in maple overflooring, and are supported by heavy fir timbers. The building has brick walls with a front of pressed brick and cut-stone trimmings; some of the openings are protected by wire-glass windows; and the stairs and elevators are in brick shafts. The floors were built to carry 35^ lb yier sq ft, Hve load, and the building cost, exclusive of the heating, elevators, etc., $1.44 per sq ft. A Five-Story-and-Basement Warehouse. This was built in Edmonton, Canada, and is 50 by 137 ft in plan. The floors are of 6-in fir with %-in maple overflooring. The building has brick walls and the front and one side wall are faced with pressed bricks with stone trimmin/^s. It has the openings in the rear wall protected and the stairs and elevators are in brick shafts. The walls are strong enough for two additional stories and the floors are designed to carry 350 lb, live load, per sq ft. The cost of the building, exclusive of heating, elevators, etc. was $1.54 per sq ft. The Cost of Buildings of Mill-Construction in Vancouver, Canada. The building described in the following paragraph was designed by Dalton & Eveleigh, Vancouver, Canada, who give data of a warehouse with floors designed to carry an average load of 500 lb per sq ft and costing $1.09 per sq ft. Although the heaviest timbers and the heaviest wall-hangers and beam-hangers were used, and the floors built of the maximum thickness, the cost was extremely low. This no doubt was partly due to the proximity of the timber and the facilities for transporting it by water. A Warehouse for the Storage of Heavy Hardware. This was erected in Vancouver, Canada. The main building has four stories and a basement, and is 85 ft 6 in by 115 ft 6 in in plan. The oflace-wing has four stories and a basement and is 60 by 40 ft. There is, also, a four-story and half-length-base- ment building, 38 by 120 ft, connecting with the two upper stories of the main building by means of a steel bridge 40 ft long. The walls above the basement are of hard-burned brick and the concrete basement walls and floors are treated with hydrolite. The main girders are set 23 ft on centers and vary in section from 12 by 16 in to 18 by 24 in and are all one-piece sticks. The posts, set 11 ft 808 Wooden Mill and Warehouse-Construction Chap. 22 lo in on centers, vary from 12 by 12 in in one piece, to 20 by 38 in, in three pieces. The joists, set 4 ft on centers, vary from 8 by 16 in to 16 by 24 in in one piece. The floors are made of 4 by 6-in and 4 by 4-in pieces, laid soUd, with top flooring made of 2 by 6-in, edge-grain, tongued and grooved pieces, with two layers of asbestos between, weighing lo^^-i ounces per sq ft. All the tim- bers are of fir. There are three brick-enclosed elevators with fire-doors, and one elevator in a wooden shaft, built ''solid" of 3 -in thick pieces. The office- front is of pressed brick, and has plate glass, marble steps and copper trim. The windows are glazed with wire-glass in metal frames, and there are fire- doors on the outer door-openings. The roof is made of a 6-ply composition with a gravel coating. The live load used for the floors varied from i 000 lb per sq ft on the ground floor to 250 lb on the top floor, the average five load being 500 lb per sq ft. The walls and posts were designed to carry two additional stories, with a five load of 225 lb per sq ft. The cost of the building, exclusive of the heating and office and warehouse-fixtures, was $1.09 per sq ft. 22. Cost* of Brick Mill-Buildings of Slow-Burning Construction Approximate Cost of Brick Mill-Buildings. Mr. C. T. Mainf has made a series of diagrams showing the cost in New England, in 19 10, per square foot OF FLOOR SPACE, of BRICK MILL-BUILDINGS of different sizes, from one to six stories in height, and of the type known as slow-burning. The calculations are made for total floor-loads of about 75 lb per sq ft. The figures taken from the diagrams are given on the following page. The costs include ordinary foundations and plumbing, but no heating, sprinklers or lighting. Modifications of the Costs given in Table I: (i) If the soil is poor or the conditions of the site are such as to require more than ordinary foundations, the cost win be increased. (2) If the building is to be used for ordinary storage-purposes with low stories and no overflooring, the cost will be decreased from about 10% for large, low buildings to 25% for small, high ones, about 20% being usuaUy a fair allowance. (3) If the building is to be used for manufacturing and is substantially built of wood, the cost will be decreased from about 6% for large, one-story building^ to 33% for ^mall, high buildings; 15% would usually be a fair allowance. (4) If the building is to be used for storage and built with low stories and sub- stantially of wood, the cost wiU be decreased from 13% for large, one-story buildings to 50% for small, high buildings; 30% would usually be a fair allow- ance. (5) If the total floor-loads are more than 75 lb per sq ft the cost is increased. (6) For oflSce-buildings, the cost must be increased to cover the exterior architectural treatment and the interior finish. (7) Reinforced-concrete buildings, designed to carry floor-loads of 100 lb or less per sq ft will cost about 25% more than those of the slow-burning type of mill-construction. * These are pre-war prices, but the data are retained for purposes of comparison of relative costs in the analysis made. For the cost of reinforced-concrete mills, warehouses, etc., see pages 4613 and 1618, I f Engineering News, January 27, 1910. Cost of Brick Mill-Buildings of Slow-Burning Construction 809 Table I. Cost of Brick Mill-BuUdings per Square Foot of Floor-Area Length in ft 50 100 150 200 250 300 350 400 500 Width in ft One story 25 $1.90 $1.66 $1.58 $1.54 $1.51 $1.49 $1.48 $1.47 $1.46 50 1.52 1.29 1. 21 1. 18 1. 16 1. 15 1. 14 1. 13 1.13 75 1. 41 1. 21 1. 12 1.08 1.06 1.04 1.03 1.02 1.02 125 1.32 1.09 1.02 0.98 0.90 0.94 0.94 0.93 C.92 Two stories 25 2.00 1.62 1.52 1.47 1.44 1. 41 1.39 1.38 1.36 50 1.50 1.21 1. 13 1.09 1.06 1.05 1.04 1.03 1.02 75 1.34 1.08 1. 01 0.97 0.94 0.92 0.92 0.91 0.90 125 1.22 0.97 0.90 0.86 0.84 0.82 0.81 0.80 0.86 Three stories | 25 1.98 1.57 1.47 1.42 1.39 1.38 1.36 1.35 1.34 50 1.47 1. 17 1.07 1.03 1. 01 1. 00 0.98 0.98 0.98 75 1.30 1.05 0.98 0.94 0.91 0.89 0.88 0.87 0.86 125 1. 18 0.93 0.86 0.82 0.80 0.78 0.77 0.76 0.76 Four stories | 25 - 2.00 1. 61 1.50 1.45 1.42 , 1.40 1.38 1.37 1.36 50 1.38 1. 17 1. 10 1.05 1.02 1. 00 1. 00 0.99 0.98 75 1.32 1.08 0.97 0.93 0.90 0.88 0.88 0.87 0.87 125 1.20 0.93 0.85 0.81 0.78 0.77 0.76 0.75 0.74 Six stories | 25 2.10 1.72 1.57 1.51 1.48 1.46 1.44 1.43 1.42 50 I. S3 1. 21 1. 12 1.08 1.05 M.04 1.03 1.02 1.02 75 1.35 1.08 0.98 0.94 0.92 0.90 0.89 0.88 0.86 125 1.22 0.96 0.86 0.82 0.79 0.78 0.77 0.76 0.76 The COST PER SQUARE FOOT of a building 100 ft wide is about midway between that of one 75 ft wide and one 125 ft wide; and the cost of a five-story building about mid- way between the costs of a four-story and a six-story building. Additional Data for estimating costs of foundation-walls and other walls are given in the following table: Table 11. Cost of Walls in Brick Mill-Buildings of Slow-Burning Construction Number of stories I 2 3 4 5 6 Foundations, including excavations Cost per lin ft: Outside walls $2. 00 1.75 0.40 0.40 $2.90 2.25 0.44 0.40 $3.80 2.80 0.47 0.40 $4.70 3.40 0.50 0.43 $5.60 3.90 0.53 0.45 $6.50 4.50 0.57 0.47 Inside walls Brick walls Cost per sq ft of surface: Outside walls Inside walls 810 Wooden Mill and Warehouse-Construction Chap. 22 Columns, including piers and castings, cost about $15 each. Assumed Height of Stories: From ground to first floor, 3 ft. Buildings 25 ft wide, stories 13 ft high; 50 ft wide, 14 ft high; 75 ft wide, 15 ft high; 100 ft and 125 ft wide, 16 ft high. Cost of Floors: 32 cts per sq ft of gross floor-space, not including columns; 38 cts, including columns. Cost of Roof: 25 cts per sq ft, not including columns; 30 cts, including columns. Roof to project 18 in on all sides of buildings. Stairways, including partitions, $100 each flight. Include two stairways and one elevator-tower for buildings up to 150 ft long; two stairways and two eleva- tor-towers for buildings up to 300 ft long. In buildings over two stories in height, three stairways and three elevator-towers for buildings over 300 ft long. Plumbing Fixtures. In buildings of more than two stories figure $75 for each fixture, including the piping and partitions. Allow for two fixtures on each floor up to 5 poo sq ft of floor-space, and one fixture for each additional 5 000 sq ft, or fraction thereof, of floor-space. Definitions SIX CHAPTER XXIII FIREPROOFING OF BUILDINGS By RUDOLPH P. MILLER SUPERINTENDENT OF BUILDINGS, NEW YORK CITY 1. Definitions, Areas, Heights, and Costs Definitions. The term fire-proof, while now quite well understood by architects, is still used in a very broad sense by the public. To be strictly fire-proof, a building must be constructed and finished entirely with incom- bustible materials, and any of these materials, such as steel or iron, which are injuriously affected by heat or streams of water must be efficiently protected by other materials which are not so affected. This precludes the use of wood, whether exposed or not exposed, also all exposed steel or iron, common glass^ and most building stones. It is safe to say that there are very few buildings in this country that are absolutely riRii-PROOF. There are many, however, that could not be destroyed by fire, and in which the salvage would probably amount to from 60 to 80%; and it is the latter class which is generally meant when the term fire-proof is used. Incombustible buildings, and buildings of wooden construction protected to a greater or less degree from the flames, are sometimes advertised as fire-proof; but such buildings should be considered merely as slow-burning. It is undoubtedly the duty of every architect to be well informed concerning the fire-proof qualities of all materials that enter into the construction and finishing of buildings, and to know how to use these materials to the best advantage. His choice and use of materials is then limited only by the character of the building and the interests of his clients. It is intended to furnish this information in a concise manner in this chapter. The National Fire Protection Association recommends the discontinuance of the term fire-proof, and the use of the term fire -resistive in its stead. The former term is the one used in the building laws of all the larger cities. Municipal Definitions, Municipal definitions as to what constitutes fire- proof construction have a great bearing on the construction of buildings within their jurisdiction. None is entirely comprehensive and the detailed requirements must be consulted in each case. The Chicago definition is typical of most of them. Chicago Definition.* "The term fire-proof construction shall apply to all buildings in which all parts that carry weights or resist strains,! a-nd also all exterior walls and all interior walls and all interior partitions and all stairways and all elevator enclosures are made entirely of incombustible materials, and in which all metallic structural members are protected against the effects of fire by coverings of a material which shall be entirely incombustible, and a slow heat conductor, and hereinafter termed fire-proof material. Reinforced concrete * Quoted matter is left in its original form. The editor-in-chief is not responsible for its syntax, punctuation, etc. t Stresses are meant. 812 Fireproofing of Buildings Chap. 23 as defined in this ordinance shall be considered fire-proof construction, when built as required by Section 550." When Fire-proof Construction Should be Employed. A building should be designed, built, and finished to conform to the purpose for which it is to be used. A building containing but Uttle inflammable material, and that not of great value, need not be as thoroughly fire-proof as one designed for the storage of valuable goods, or for the protection of life in case of fire. The height of a building is an important factor in determining whether it should be fire-proof or not. The rate of increase in the difficulty of coping with fire in a building is greater than that of the increase in the height. The area covered by a building, also, is important, although in most instances interior division-walls may be provided which practically cut up a building into a series of smaller buildings. Some of the limitations placed upon non-fire-proof buildings by various municipal laws will be found in the following classification and in Table I, page 813. Limiting Areas for Non-Fire-proof Buildings. New York City, 7 500 sq ft on an interior lot. 12 000 sq ft on a corner. 15 000 sq ft when facing three streets. Chicago, 111., 9 000 sq ft if of ordinary joisted construction. 1 2 000 sq ft if of slow-burning construction. St. Louis, Mo., 7 500 sq ft. Boston, Mass., 10 000 sq ft. Cleveland, Ohio, Mill-Construction: 20 000 sq ft when facing streets on four sides. 15 000 sq ft when facing streets on three sides. 12 000 sq ft when facing streets on two sides. 9 000 sq ft when facing streets on one side. 5 000 sq ft on any lot when of hazardous occupancy. Cleveland, Ohio, Ordinary Construction: 1 2 500 sq ft when facing streets on four sides. 10 000 sq ft when facing streets on three sides. 7 500 sq ft when facing streets on two sides. 5 000 sq ft when facing streets on one side. 2 000 sq ft on any lot when of hazardous occupancy. Cost of Fire-proof Construction. F. VV. Fitzpatrick, found, previous to 1903, that fire-proof construction for office-buildings, hotels, etc., adds from 9 to 13% to the cost of ordinary construction with wooden joists. For stores and warehouses the difference will often be less than 5%.* Walter F. Ballinger stated (1909) that reinforced-concrete construction cost from 10 to 15% more per square foot of floor-surface than mill-construction and about 25% less than steel-frame and terra-cotta fire-proof construction, f Figures given by J. P. H. Perry (191 1) indicated that reinforced-concrete construction added from 2 to 20% to the cost of mill-construction for commercial buildings, with an average of 6.7% for various localities and all classes of buildings in the United States. The increase in cost of structural-steel fire-proof construction over reinforced- concrete construction averaged 6.4% for fourteen buildings of all classes in various localities, t More recent comparisons are not available, but it can be safely asserted that the increased cost of fire-proof construction over mill- * Fireproof, for Marcii, June, and July, 1903. t Proc. Nat. Fire Prot. Asso., 1909. tProc. Nat. Asso. Cement Users, 191 1. Heights for Non-Fire-proof Buildings 813 § b s S ^ Ph oPh to W (U o tii m to (U (U -l-> 4-S a> o +^ rt- lO O O "^ cr» 00 vO <£> ^ t-. lO O 3 Ph O '- 2; o bo ^ 9 o '5 BrQ o 1 S PQ CO O • ^ 0) fel4 Fireproofing of Buildings Chap. 22 construction and ordinary joisted construction is less than indicated by thes( figures. Divisions of the Subject. In constructing fire-proof buildings it is neces sary to consider: (i) Materials to be used. (2) Form of construction. (3) Protecting devices. (4) Extinguishing appliances. This general order is followed in the discussion of the subject in this chapter. 2. Fire-Resistance of Materials Effect of Heat on Building Materials. All materials of construction an more or less injuriously afifected by high temperatures. Furthermore, an incom BUSTIBLE material is not necessarily fire-resisting, as, for instance, steel The value of various materials in fire-proof construction is indicated in th( following paragraphs. Brickwork. Common brickwork, when of a good quality, will stand exposun to severe fire for a considerable length of time. Experience has shown thai thick walls are less afi"ected by heat than thin walls, and that hard-burnec bricks stand' better than soft or underburned bricks. In the Baltimore anc San Francisco fires, it was demonstrated that for outside v/alls brick is superioi as a fire-proof material to any other material used in wall-construction. Stone in General. Very few stones successfully stand the action of seven heat, and consequently stone in general should l)e used very sparingly in fire proof buildings, and certain kinds of stone not at all. Granite will explode and fly to pieces or disintegrate into sand when exposec to flames. Limestone and Marble are usually ruined if not totally destroyed by ar ordinary fire. They are the least desirable of all stones for use in a fire-prooi building, and the granites come next. Sandstone when fine-grained and compact sometimes stands fire without serious injury, but in the case of a severe conflagration it is generally so badly affected that it has to be replaced. Terra-Cotta is made from clay by mixing it with water into a plastic mass, shaping the same into the form desired and baking it at a high temperature in kilns. For the usual structural form the shaping is generally done by forcing the plastic mass through a special die by means of machinery. Ornamental terra-cotta must generally be shaped by hand. Ornamental Terra-Cotta. This material, and especially that which has a glazed surface, is well adapted for the trimmings of a building that is intended to be fire-proof. It should, however, be made heavy enough to carry both its own weight and its share of the wall-load.* Structural Terra-Cotta. Terra-cotta, as used for floor-arches, column and girder-protection, and for building light, hollow walls, is made of three differ- ent compositions, the material being known as Dense, Porous, and Semi- porous, according to the method of manufacture. Dense Tiling is made from a variety of clays. Some manufacturers use • Fire Prevention and Fire Protection, J. K. Freitag. Fire-Resistance of Materials 815 more or less fire-clay, and combine it with potter's clay, plastic clays, or tough brick-clay. It is very dense and possesses high crushing strength. In outer walls exposed to the weather and required to be light, it is very desirable. Some manufacturers furnish it with a semiglazed surface for the outer walls of build- ings. For such use it has great durability, and effottually stops moisture. In using dense tilHng for fireproof filling, care should be taken that the tiles are: free from cracks, sound, and hard-burned. Porous and Semiporous Terra-Cotta is made by mixing sawdust with the clay, the sawdust being destroyed by the action of the heat, leaving the material light and porous. A small proportion of fire-clay mixed with the plastic clay is desirable but not essential. The proportion of sawdust should be from" 25 to 35%, according to the toughness of the clay used. Care is required in the process of manufacture to have the work of mixing, drying, and burning thoroughly done. The burning should be done in down-draught kilns, by a quick process. The product should be compact, tough, and hard, and should ring when struck with metal. Poorly-mixed, pressed, or burned tiles, or tiles from short or sandy clays, present a ragged, soft, and crumbly appearance, and are not desirable. When properly made, porous terra-cotta will not crack or break from unequal heating, or from being suddenly cooled with water when in a heated condition. It can be cut with a saw or edge-tools, and nails or screws can be easily driven into it to secure interior finish, slates, tiles, etc. As a successful heat-resistant and non-conductor for the protection of other materials, it must be ranked very high. Semiporous Tiling. This material was introduced by those factories which use pure fire-clay in the manufacture of tile, to enable them to compete with the standard porous material. During the process of grinding the clay, about 2o% of ground coal is mixed with it. This coal aids in the burning of the material and also makes it lighter and more or less porous. Tiling made by this process is admitted to be a much better fire-resistant than the solid or. dense material. E. V. Johnson says: "personally, I believe that good semi- porous fire-clay tile is fully as efficient as a fire-resisting material as the standard makes of porous terra-cotta." Strength of Terra-Cotta. (Sec, also, page 276.) In tests made at Columbia University for the building authorities of New York City on terra-cotta blocks taken from material delivered in the open market, the following crushing STRENGTH was developed: Table II. Crushing Strength of Terra-Cotta Description of material Position of cells in test Compressive strength, lb per sq in Gross area Net area Dense tile ( Vertical 1 Horizontal I Vertical ( Horizontal 1864 S8S I 027 257 4721 2613 2168 I 008 Semiporous tile The inequality in strength of the two materials can be overcome by using thicker webs and shells for the semiporous or porous material. In the matter 816 Fireproofing of Buildings Chap. 23 of WEIGHT, porous and semiporous terra-cotta have the advantage over dense tile. Dense tiling, when heated and cooled by water, is liable to crack from the sudden contraction; "blocks with two or more air-spaces are very liable to have the outer webs destroyed under this action. . Even if not cooled with water, other fires have shown that hard-burned terra-cotta will crack and fall to pieces under severe heat alone." * The experience of the recent conflagra- tions in Baltimore and San Francisco fully bears out this statement. The collapse of the floors of one of the buildings in Baltimore was largely due to the weakening of the terra-cotta arches by reason of the breaking off of the outer shells. Porous terra-cotta is non-heat-conducting in itself, and the best qualities will usually resist fire and water successfully; but if the product "is not burned at a sufficiently high temperature to consume all of the sawdust, the throwing of cold water upon the heated surfaces will cause an expansion or disintegration due to the absorption of the water and its conversion into steam." Porous terra-cotta absorbs water freely, and if allowed to freeze when wet is more or less injured. If the process is permitted to continue, the blocks become so weakened that they are unsafe for use. Concrete Blocks and Concrete Tiles. f Numerous forms of building blocks and tiles are manufactured of I^ortl.md-cement mortar or concrete for use as substitutes for brick, stone, and terra-cotta. Concrete blocks are made by the DRY PROCESS I)y tamping a dry-concrete mix into shape in forms, or by the WET PROCESS which consists of pouring a semiliquid or slusii-mix into molds and curing the product by air or steam. A third method, known as the PRESSURE-PROCESS, is similar to the first, mechanical or hydraulic pressure being substituted for the tamping. Concrete hollow tile is being made for the same uses as terra-cotta tiling, for partitions and floors in general, and for enclosure-walls as well as for partitions in residences. For wall-bearing purposes, the tiles are usually filled solid for a layer or two where the beams rest upon them. In hollow-block construction, distinction should always be made between the strength -of the jjbcks when laid with the core-holes vertical and when laid with the core-holes horizontal, as the strength, in the latter position, approximates only one half ot what it is in the former. The specifica- tions of the American Concrete Institute, 1917, are generally accepted as the best practice in the manufacture of concrete blocks. (See, also, Chapter III, page 233.) Concrete Tile. Concrete building tiles have been used for residences in Chicago, III., Rochester, N. Y., and the suburbs of New York City. The shape and size of the blocks vary with the make of the product. In size and shape they resemble terra-cotta tile, though the walls and webs are thicker. A WET-PROCESS tile was tested by the Bureau of Buildings, New York City, in 191 1, and showed a compressive strength in pounds per square in as shown in Table III, page 817. The Trout Concrete Tile Corporation of Flushing, N..Y., has developed a method of making hollow tile whereby lightness is combined with strength. The Trout tile is made in a hydraulic machine, with a pressure of 1200 lb to each sq in of net area of the tile. While this pressure is being applied, the particles of concrete are automatically moved about until the voids are filled, find the result is a dense, hard product of even quality. This process permits the making of tile with thm walls, thereby reducing the weight to a minimum, A tile 8 in high, 8 in wide, and 15M in long, with two cells, and with walls • Fife Prevention and Fire Protection, J. K. Freitag. t The subject is fully treated in Concrete Engineers' Handbook, by Hool and Johnson, Fire-Resistance of Materials Table III. Compressive Strength of Concrete Tile 817 Dimensions and use Cells vertical Cells horizontal Height, in Kind of tile Number of cells Gross area, lb per sq in Net area, lb per sq in Gross area, lb per sq in Net area, lb per sq in 8 ID lo 12 8 Wall-tile Wall-tile Corner-tile Wall-tile Wall-tile (Trout^O 2 2 2 4 2 528* 633 5IO I oi6 I 510 I 580 1 050 2 588 320 351 ■360' 746 I 228 I 066 - *r rrout Tile tes ted by Bare au of Buildi ngs, New York, in 1914 and webs i in thick, weighed 91.7 lb. Its compressive strength is given in the last line of Table III. Concrete. Stone concrete, under the action of heat, is affected much the same way as brickwork The heated surface expands, and as the concrete is a very poor conductor, the other surface remains cool and either cracks or causes warping. The heat also affects the strength and texture of the concrete, causing a disintegration of the concrete to a depth of about i in. Often the surface spalls off with a report. If water is applied after the heat, the surface is washed away to the depth of the affected part. These effects vary somewhat with the stone used in the aggregate. SiUceous gravel has been found by tests and in actual fires to be very destructive to concrete. Granite, on account of the difference between its coefficient of expansion and that of the concrete, is likely to spall. Limestone calcines under the action of heat and is liable to destruction for some depth by the water. Trap-rock is a satisfactory material to use, from the standpoint of fire-resistance as well as that of strength. If there is no application of water after the fire and the surface is allowed to cool off gradually, the concrete may set again and become hard. It is not well however, to rely on this. (See, also, Chapter III, page 245, for the effect of heat on concrete fireproofing.) Slag Concrete. Blast-furnace slag has been used as the aggregate in con- crete, with satisfactory results as to both fire-resistance and strength.* Care must be exercised in the selection of the slag. R. L. Humphrey says that only acid slag should be used and that it must be "dense, tough, and free from sulphur." Sanford Thompson states that the slag must be "air-cooled, crushed, screened from dust, and free from foreign material," and that "excep- tional care must be used in proportioning, mixing, and placing." f Cinder Concrete. Cinder concrete, because of its porous character and the nature of its aggregate, makes an excellent fireproofing material. Tests and the experience of conflagrations would indicate that it is the best. Care must, however, be taken in the selection of the cinders. They must be clean furnace- cinders, free from unburnt coal. When properly selected and proportioned, * For a series of tests and description of materials, see pamphlet issued by the Camegi* Steel Company, 1911, Furnace Slags in Concrete. See, also, Proc. Am. Soc. for Test. Mat., 1914. A full discussion of slag concrete is published in the Iron and Coal Trade Review (London), for Nov. 22 and 29, 1918. , . t Engineering Record, March, 1917. 818 Fircproofing of Buildings Chap. 23 cinders produce good concrete, but generally a very non-homog6neous material is obtained, so that its strength is variable and doubtful. If ground by machinery before mixing, a better and more reliable concrete is produced. In using cinder concrete in floor-construction the working loads are generally determined from load-tests and a high factor of safety is used. The former practice in New York City was to take oue tenth of the breaking-load as the WORKING LOAD. The building code now prescribes a formula for com- puting the strength of cinder-concrete floors, within certain Umitations. Corrosive Action of Cinders. When cinder concrete is used to encase steel, either as a protective covering or as a part of a concrete construction, the corrosive effect of cinders must be guarded against. A. discussion of thi? subject will be found in Chapter XXIV, pages 960 and 961. Mortars, Plasters, and Plaster of Paris. Mortar and plaster must neces- sarily enter into the composition of all masonry buildings, whether built of brick, stone, or terra-cotta. That ordinary lime mortar, when weU made, v^ill endure for unlimited periods of time, in dry situations, has been proved by actual use. Hydraulic-cement mortars are equally durable in wet or damp places. For laying brickwork or tile work in first-class buildings, cement-and- sand mortar is preferable to any other; and cement mixed with lime mortar gives greater strength than lime and sand alone. Regarding the fire-proof qualities of mortars and plaster compositions there has been much controversy; the truth of the matter seems to be that all such compositions will withstand the action of heat up to a certain degree, when they are affected in one way or another, depending not only upon the composition but in large measure upon their body, and upon the way in which they are used. Lime mortar for walls was formerly considered as the most satisfactory, so far as fire-resistance is concerned; but since the improvements in cement-manufacture, cement mortar is generally preferred. Lime plaster, applied on wire lath, will withstand a high degree of heat without injury, but is liable to be washed away in places by streams of water. Gypsum plasters, usually termed hard wall-plasters, or patent plasters, when applied to brickwork or metal lath, are superior in heat- resistance to common lime, and the patent plasters will stand the combined effects of fire and water longer than the common mortars. Plaster of Paris. Compositions of plaster of Paris (gypsum) and broken bricks, wood chips, or sawdust are non-conductors of heat and possess fire- resisting properties of considerable importance; and on account of their light- ness and cheapness, are often used in fire-proof or semi-fire-proof buildings. In France such compositions have been used for generations to form ceilings between beams, and their durability and fircproofing qualities are unquestioned in that country. Plaster of Paris compositions when subjected to severe heat are softened on the surface, and when water is thrown upon them they wash away to some extent. Asbestic Plaster. A plaster made by mixing Asbestic with freshly slacked lime-putty has been used to some extent in New York City. Asbestic is made from a serpentine rock, mined near Montreal, Canada, and contains a large proportion of asbestos. "Claims of great fire-resisting properties are made for this material, as well as resistance to the effects of water during fire; cracking and discoloration due to the percolation of water or acids are also claimed to be avoided. The plaster is tough and elastic, and it will receive Aails without chipping or cracking. The weight is siiid to about half that, of ordinary cement mortar." Asbestic was subjected to a severe fire-and- water test in the presence of the oflicials of the Supervising Architect's office at Washington, D. C, "and the plaster did not crack or drop, but remained intact. All of Fire-Resistance of Materials 819 the walls, ceilings, and columns of the appraiser's warehouse in New York City were covered with a coat of Ashestic, from J^ to ^ in thick, applied on the concrete or terra-cotta surfaces. The great objection to the use of this materi;il lies in its slow drying, the time required for a thorough drying out being usually very long." * Asbestos-Products. Asbestos fiber combined with cement is manufactured in the form of steam-packings, corrugated sheathings, roof-coatings and shingles, wall-boards and building-lumber, insulating sheathing and blocks, asbestos theater-curtains, various forms of preservative and fire-resisting compounds, and substitutes for v/all-plaster and stucco. The value of these products lies in their low heat-conductivity and incombustibility. Asbestos Building Lumber is made in standard sheets, 42 by 48, and 42 by 96 in in size, and varying in thickness from % i« (about iH lb per sq ft in weight) to I in (about 10% lb per sq ft in weight). When seasoned it is harder than ordinary wood, stakes nails and screws, and it can be manipulated with heavy tools and machinery such as are used for working iron. It is too hard for ordinary wood- working tools. It is sufficiently elastic to withstand ordinary vibration, expansion, and contraction of surrounding parts, wind-pressure, and blows; and in large pieces, it can be bent around slight curves without splitting. Asbestos Corrugated Sheathing is corrugated asbestos building-lumber, reinforced with sheet steel of from No. 24 to No. 27 United States gauge, or with woven-wire netting. It is applied in the same way that corrugated iron is applied, either nailed to wooden strips bolted to the purlins, or clipped directly to the purlins by clips of hoop-iron or wire. It comes in standard sheets, 27H in wide and in lengths of 4, 5, 6, 7, 8, and 10 ft. Asbestos Roofing-Shingles, suitable for wooden-roof construction, possess fire-resisting qualities far superior to wooden shingles. The ad\'antages claimed are their fire-proof qualities, toughness, elasticity, and hghtness in weight; ease of manipidation, cutting, sawing, and shaping to fit dormer windows, chimneys, etc.; and their immunity from the corrosive action of salt air. The principal companies manufacturing asbestos building-products are the Johns-Manville Company, New York City; the Keasljcy & Mattison Company, Ambler, Pa.; and the Asbestos Manufacturing Company, Lachine, Canada. Asbestos-protected Metal consists of steel sheets of from No. 28 to No. 20 United States gauge, coated on both sides with asphaltum-compoimds contain- ing heavy natural oils, and covered with layers of asbestos-felt put together under great pressure. The sheets are made flat, corrugated, or beaded. It forms an incombustible roofing, siding, sheathing, and interior-finish material. The manufacture of this product is controlled by the Aspromet Company, ot ritt.sburgh, Pa. Steel and Wrought Iron. Wrouglit iron and steel will expand, bend, and twist under a moderate degree of heat. Inasmuch as a temperature of i 700" F. is not unusual in fires, these materials should not be used in fire-proof con- struction without proper protection. Fire tests at the Continental Iron Works in 1896 showed that unprotected steel columns under load began to fail when the temperature reached about i 100° F.f In the Baltimore and San Francisco fires there were many instances of failure in steel columns due to lack of or to insulRcient protection. Cast Iron. "As the result of tests and actual experience in conflagrations it may be stated that unprotected cast iron can stand practically unharmed up * Freitap;. t See Engineecring News, Aug. 6, 1896. 820 Fireproofing of Buildings Chap. 23 to temperatures of 1 3cx> or i 500° F. while carrying very heavy loads, even with frequent applications of cold water while the metal is at a red heat."* In the tests at the Continental Iron Works, referred to in the preceding paragraph, a temperature of nearly 1 300° F. was reached before the cast-iron columns began to fail. The contents of most mercantile buildings, when burning freely, would probably generate a heat exceeding at times 2000° F. Consequently, cast-iron columns, when unprotected, are almost sure to fail in such a fire either bj'' bend- ing or breaking. No building in which unprotected iron or steel columns are used can be considered fire-proof; but in many classes of buildings unprotected cast-iron columns might safely withstand any heat to which they would probably be exposed. From a fire-resisting point of view, when there is no protective covering, cast-iron columns are unquestionably preferable to steel columns. Fire-proof Wood. To meet the requirements of certain provisions of the New York City Building Code, an attempt has been made to produce fire-proof wood. The processes for rendering wood fire-proof, in general, consist in im- pregnating its fibers with certain chemicals. After the fireproofing-process, the lumber should be thoroughly kiln-dried before it is used. The softwoods are more easily thoroughly treated than the hardwoods, the resinous woods bdng particularly difficult to handle. "The treatment of the wood to render it fire-proof slightly raises the igniting- point of the wood. The treated wood is harder to light than the untreated wood, taking two to three times as long to ignite. The amount of wood destroyed when exposed to the action of a flame is from 5 to 12 per cent greater in the case of an untreated wood than in the case of a treated wood. The untreated wood furnished more flame than the treated wood. The untreated wood will sustain flame longer than the treated wood after the source of heat has been removed. From this it can be seen that the fire-proofed wood is less Hkely to ignite and less likely to cause the spread of fire than the imtreated wood."t Among the disadvantages of fire-proof wood should be mentioned an increased difficulty in working the wood, and a tendency to dull woodworking-tools more rapidly than with untreated wood. Hence an increased cost in the use of fire- proof wood. The salts used in the process of fireproofing being hygroscopic, tend to keep the woodwork damp. Hardware or other metalwork in contact with fire-proofed wood is liable to corrode. The strength of the wood is often affected, and in some cases the wood becomes quite brittle. These two last- mentioned faults can be largely overcome by neutralizing the fireproofing- solution by a proper mixture of acid and alkaline salts. The test, known as the timber- test, applied to fire-proof wood in New York City, consists in placing a stick of the treated wood, % by 1 1^ in in cross-section and 8 in in length, for two minutes over a crucible gas-furnace in which a con- stant temperature of 1 700° F. is maintained; then removing the test-piece, noting the time it continues to flame and glow; and then scraping away the charred wood and determining the percentage of unburned wood. The con- ditions of acceptance are that, "the flame and glow should disappear within ten to twenty seconds after the removal of the test-piece from the furnace, and the unburned and uncharred section at the center of the specimen should be not less than 50 to 70 per cent of the original cross-section, depending on the variety of wood under test." If the wood has been thoroughly treated, a splinter of it after having been exposed to flame and withdrawn, wiU show * Freitag. t See Insurance Engineering, Vol. IV, page 551; also Professor Norton's Report No. I to t\\"; Boston Manufacturers' Mutual Fire Insurance Company. Fire-Resistance of Materials 821 no glow or flame. Other tests have been suggested and used but need not be described here. Wire-Glass. The introduction of this material has made it possible to secure fire-protection in many cases, without the necessity of disfigurement due to fire-shutters. Wire-glass is either ribbed, rough, maze, cobweb, or polished PLATE, with wire embedded in its center during the process of manufacture. \ "The temperature at which the wire is embedded in the glass insures ad- hesion between the metalhc netting and the glass, and the two materials become one and inseparable, so that if the glass is broken by shock, by intense heat, or from other cause, it remains intact." It is this property of remaining intact that gives it its fire-retarding qualities. Although fire and water may cause cracks to spread throughout the glass, the wire holds the pieces so firmly that flames cannot pass through it. Many severe tests during actual fires have positively demonstrated the truth of the above claim. For warehouses and factories the ribbed or maze glass is generally preferable; but for oflices, or wherever clear transparent glass is desired, the polished plate is nearly if not quite as acceptable as the same glass without the wire, the effect being the same as that obtained by looking through a window with a screen on the out- side. Where fire -resistance is the desired feature, the following requirements should be satisfied. The thickness of the plate at the thinnest part should be not less than }i in, and the plane of the wire mesh should be midway between the two surfaces of the glass. No wire should be smaller than No. 24 Brown & Sharpe gauge. The unsupported surface of the glass should not exceed 720 sq in in any case and should be contained in a metal frame not larger than 5 by 9 ft between supports. The chief manufacturers of wire-glass in this coun- try are the Pennsylvania Wire Glass Company, Philadelphia, Pa; the Mis- sissippi Wire Glass Company, New York; the Western Glass Company, Streator, 111.; and the Highland Glass Company, W^ashington, Pa. As now manufactured by the continuous process, it is rolled in lengths up to about 10 ft and in thick- nesses up to Yi in. Prism Glass. Prisms installed for the purposes of increased* light are usu- ally not contained in frames which are designed to withstand severe heat. The dimensions of the unsupported electro-glazed panel should not exceed 50 in in either direction. The polished plate in prism-glass units should not exceed 4 in in either direction, with a minimum thickness of Me in. In Report No. II of the Insurance Engineering Experiment Station, C. L. Norton describes a scries of comparative fire-tests on electro-glazed Luxfer prisms, 0.35 in thick and 4 in square; electro-glazed plate, }4 in thick and 4 in square; and J^-in wire- glass. The results of these tests indicate that the three materials, in sheets up to 24 by 30 in, are of equal value in fire-resistant properties and remain in effective operation up to the time when the temperature of melting glass is reached. (See, also, page 1578.) Fire-proof Paint. Numerous so-called fire-proof paints have been in- troduced in recent years. When applied to woodwork they provide a more or less effective protection against fire and may, for this reason, prevent the spread of fire. The following regulations regarding fire-proof paint were given in the annual report of the Manhattan Bureau of Buildings, New York, for 1904. "(i) The term fire -proof paint shall be understood to mean any prepara- tion used to cover the surfaces of wood or other materials for the purpose of protecting the same against ignition. " (2) No fire-proof paint will be considered satisfactory unless it so protects the wood or other material to which it is apphed that the same will not flame 822 Fireproofing of Buildings Chap. 23 or glow after having been subjected to the flame of a gasoHne torch for two minutes. " (3) Before applying fire-proof paint to any material the surfaces must be cleaned. " (4) Application of fireproof paint must be repeated whenever it is found that the material to which it is applied is no longer protected to fulfill Specifi- cation No. 2." 3. Column -Protection Girder and Column-Protection. As the columns and girders of a building form the back-bonf- of the structure, it is of vital importance that they he very thoroughly protected from heat. As a rule, the manner of protecting these structural elements depends quite largely upon the floor-system adopted. Where concrete is used for the floor-construction it is generally also employed for incasing the columns and girders; where hollow tile is used in the floors, the same material is almost invariably employed for protecting the steel frame. The methods used for protecting girde.s are described in Subdivision 4 of this chapter. (.See, alsj, piges 780 to 782.) Necessity for Column-Protection. It is now gcnerafly recognized that iron and steel columns should he incased with some material that will thoroughly pro- tect the metal against fire. In 1896 a committee of the American Society of Mechanical Engineers, in conjunction with representatives from other organiza- tions, made a scries of fire-tests on full-sized unprotected cast-iron columns and steel columns, loaded to their figured safe capacities. These tests showed that the steel columns failed at an average temperature of i 150° F., and the cast- iron columns at an average temperature of i 300° F., the failure setting in after an exposure to the fire of from 23 minutes to i hour and 20 minutes, or an average duration of about 50 minutes. In order to determine the vdlue of several materials as satisfactory protective coverings, the Bureau of Buildings Table IV. Tests of Protective Coverings Materials under test Temp, on face of pro- tective material, degrees Fahr. Temperature of plate at back of protective material, degrees Fahr. Before heating After heating for 2 hr Heat- trans- mission Terra-cotta: dense, hollow, 2 in thick.. Terra-cotta: semiporous, solid, 2 in thick 1700 I 700 I 700 I 700 I 700 I 700 I 700 I 700 75 73 69 70 72 73 66 76 223 244 159 163 167 363 248 296 148 171 90 93 95 290 182 218 Piaster of Paris and shavings, 2 in thick .-. Plaster of Paris and asbestos, 2 in thick . Plaster of Paris, wood fibers, and in- fusorial earth, 2 in thick Concrete of ground cinders, iMo in thick Cinder concrete, on metal lath, 2 in thick Metal lath and patent plaster, about ^2 in thick over i in air-space Column-Protection mz of New York City made a series of tests on the iiEAT-coNinTCTrvrTY of these materials. A cast-iron plate covered with tlie material under test was subjected to a temperature of i 700° F. for two hours over a crucible furnace, and the heat of the plate noted at regular intervals of time. The results of the tests are shown in Table I.V on page 822. Fig. 2. Hollow-tile Protection. Cylindrical Column Blocks set in cement mortar, occasionally, in addition, bound witli copper wire at inter- vals of I'o" Fig. 1. Hollow-tile Protection. Plate-and-anglc Column Fig. 3. Ribbed-tile Protection. Cylindrical Column Terra-Cotta Column-Protection. Fig. 1 shows the manner in which built- up columns are protected in the best class of fire-proof buildings when tile fire- proofing is used. Figs. 2, 3, and 4 show common methods of protecting cylin- drical columns, and Figs, o and 6 columns of rectangular cross-section. The steel guard, shown in Fig. 1, is often employed in mercantile and manufacturing buildings, and put on to a height of 4 or 5 ft above the floor. The efficiency of this construction is greatly increased by wrapping the columns with wire lat\> before plastering, although it is not a common practice. To insure the protec- tion of the metal under the most trying conditions, it is imperative that the Fig. 4. Solid-tile Pro- tection. Cylindrical Column Fig. 5. Hollow-tile Protec- tion. Built-up Box Column Fig. C. Hollow-tile Pro- tection. Square Column section 824 Fireproofing of Buildings Chap. 23 protective coverirtg shall not be detached by the streams from the firemen's hose, and thus expose the steel. This can be positively guarded against only by using two layers of tiling or concrete and wrapping the inner layer with metal lathing. Fig. 7 shows a column protected in this way, the construction being essentially that adopted in the Fair Building in Chicago, 111. The inner layer of tiles is wrapped with wire lath embedded in the mortar, and all spaces between the tiles and metal are filled solid with cement mor- tar. Concrete Column- Protection. Where concrete is to be used for column-protection, the way to obtain the most efficient construc- tion is undoubtedly to surround the metal with cinder concrete, poured inside of a plank form set around the column, a coat of liquid cement being first applied with a brush to the metal. The plank form should be set at least 2 in out- ade of the metal. It is generally conceded that this forms one of the most efficient fire-casings for columns, and, in addition, lends added stiffness to the steel members embedded in it. It is advisable to reinforce the concrete or anchor it by Fig. 7. Double-tile and Metal-lath Column-protection i:rz: #10 Galv. Steel Wire Loops B,^ Wood Form, Full Column Fig. 8. Concrete Column-protection and Wooden Form yH Bolt -^ SS^SSS^^^^^" J^fBoIt'' Fig. 9. Concrete Column-protection and Wooden Form Column-Protection 825 means of metal lath to the steel column. There are two general methods in use in applying the concrete. Fig. 8 illustrates a column which is first wrapped spirally with No. lo gauge galvanized wire, 12 in on centers, to afford a key for the concrete. The wood forms are placed the full length of the column, and the concrete poured from a hole in the ceiling above. A slush -mixture of either cinder or stone concrete of i : 2 : 5 mix may be used. Fig. 9 shows a form of rough boards, made in- sections from 4 to 6 ft in length and provided with yokes at each end. The concrete may be thoroughly tamped about the column as each section is placed and filled. Fig. 10 shows a method of furring the column with stiffened wire lath, which serves as a substitute for the wooden forms and at the same time anchors the concrete to the steel. A similar ^Plas':;er ^" thick Space Steel rurring Strips Fig. 10. Concrete Column-protection. Wire-lath Furring Fig. 11. Metal-lath and Plaster Column-pr<^ tection method may be employed to obtain an air-space by placing immediately around the column an envelope of metal lath with a 2-in layer of concrete. In many buildings with reinforced concrete floors, the columns are protected simply by plaster on metal lath. When only a single covering is provided, the protection cannot properly be considered fire-proof; but when two cover- ings are provided, as in Fig. 11, they are probably all that is necessary for cast- iron columns. The greatest defect in lath and plaster for fireproofing is that the plaster is hable to be dislodged by the force of the water from the firemen's hose. When there are two coverings, however, thfs danger is reduced to a mini- mum. (See, also, Chapter XXII, Figs. 23, 24, and 25.) Plaster Column-Covering. Plaster-blocks have been used in buildings as a column-covering, but their use is not to be recommended. While it is true that their non-conductivity is in their favor, it is difficult to secure them firmly. Tlicy are easily washed away by hose-streams and subject to greater damage than other materials. In unimportant work their cheapness may, at times, justify their use. Protection of Connections between Columns and Girders. The most defective parts of the coverings of columns, whatever the materials used, are probably those about the connections with the beams and girders. Concrete undoubtedly is better adapted for covering these parts of the column than any other material, because, being elastic, it can be made to fit into any space and around any form of connection. 826 Fircproofing of Buildings Chap. 23 The Cement-Gun. During recent years, a new method of protecting structural steel by means of the cement-gun has been introduced. This gun consists essentially of two superimposed tanks, forming two compartments, from the bottom of which a dry mixture of sand and cement is ejected by com- pressed air through a hose-hne with a nozzle at the end. To this nozzle a smaller hose delivers a supply. of water under pressure, which is applied to the dry con- stituents just before they emerge from the nozzle. The mortar issuing in the form of a spray shoots out from the nozzle with considerable force and im- pinges on the surface of the steelwork. The columns of the fifty-five-story Woolworth Building in New York City are provided with a ij^-in coating of cement mortar applied in this way, and coated on the outside with a 2-in thickness of terra-cotta. The steelwork, also, of the new Grand Central Ter- minal Buildings in New York City are protected with a 2-in coat of cement mortar or Gunnite. By this means, inaccessible corners are readily protected without the use of forms. Tests have shown that Gunnite is superior in tensile and compressive strength, permeability, absorption, porosity, and adhesion to good hand-made products of the same kind.* Recesses for Pipes. "As a matter of economy, both in original cost and in the matter of space, it has been the common practice to rim water-pipes, waste-pipes, and vent-pipes immediately alongside the steel columns and inside the fire-resisting covering." f This is undoubtedly "bad construction, as Freitag 1 Space for Pipes and Wires«^ Concretev Pipe-space Fig. 12. Tile Column-protection with Pipe- space Fig. 13. Concrete Column-protec- tion with Pipe-space illustrates by explaining its disastrous results in recent conflagrations; and in the better types of fire-proof "buildings, the pipe-space is now separated from the columns by the fircproofing. Fig. 12 shows a method of running the pipes in some fire-proof buildings, and it is probably as satisfactory as any arrange- ment in which the pipes are to be run beside the columns. Fig. 13 shows a somewhat similar method in which concrete, metal lath, and plaster are em- ployed for the fircproofing. 4. Fire-proof Floor-Construction Fire-proof Floors. In the study of fireproofing-materials by far the great- est attention has been given to floor-construction; and of the very large number of types which have been developed, the characteristic and leading ones are here. considered. * Engineering News, 191 2, Vol. 67, page 26; and Vol. 68, page 1086. t Fire Prevention and Fire Protection. J. K. Freitag, page 374' I Fire-proof Floor-Construction 827 Requirements for a Fire-proof Floor. It goes without saying that a fire- proof floor must l)e made of incombustible materials. It seems unnecessary, also, to mention that it must resist as much as possible the transmission of heat, so as to afford thorough protection to the metal incased by it or forming an essential part of it. The materials used should not disintegrate or otherwise fail when exposed to heat or flame. They should also resist the action of water that may be used to extinguish a fire. The lloor-construction should be essen- tially water-tight, so as to prevent damage by water in stories below. It should be designed to safely carry its load at all times. The New York City Building Code describes certain acceptable forms of fire-proof floors, but also provides for the acceptance of other forms which successfully meet the prescribed fire and strength tests. Fully eighty tests have been made under the auspices of the New York City authorities and these, together with a few made by the authorities of other cities, comprise practically all that have been made in this country. The British Fire-Prevention Committee of London has also made a number of such tests.* Fire Tests for Floors. The standard fire test of the American Society for Testing Materials! is essentially the same as that required by the New York City Building Code and as the one used by the British Fire Prevention Committee. Briefly, the New York test consists in subjecting the floor in ques- tion, carrying a load of 150 lb per sq ft, to a fire maintained at 1 700° F. for four hours; and then in applying a stream of water, at 60-lb nozzle-pressure, for ten minutes, the floor being considered satisfactory if there has been no appreciable deterioration due to the test and if it has resisted the passage of flames during the test. Types of Floor-Constructions. In considering the several systems of floor- construction, they are for convenience divided into the following types or groups: (i) Brick arches, (2) Terra-cotta or tile floors: a. Segmental, b. Flat side-construction, c. Flat end-construction, d. Reinforced-tile arches, e. Guastavino, (3) Concrete floors: a. Segmental, b. Flat reinforced floors, c. Sectional systems, (4) Gypsum floors, (5) Metal-lumber-construction. Brick Floor-Arches. The first attempt at fire-proof floor-construction between wrought-iron beams was made by using brick arches sprung between the beams and resting on the bottom flanges, as iUustrated by Fig. 14. When this form of construction is used the bricks should be hard, well-burned bricks, or hoflow bricks of jgood shape, laid to a line on centers without mortar, with their lower edges touching; and all the joints should be filled in with cement grout. The bricks of one line should break joints with those of the next adjoining, and in case there is more than one row, the joints of one row should also break * For a list of these tests made in the United States and in London, see Proc. Am Soc. for Test. Mats., Vol. VI, page 128. t See Year Book, Am. Soc. Test. Mats. 828 Fireproofing of Buildings Chap. 23 joints with those of the row above or below. The arches need not be over 4 in thick for spans between 6 and 8 ft, provided the haunches are filled with a good cement and gravel concrete, put in rather wet. The rise of the arch should be about one-eighth the span, or i^ in to the foot; and the most desirable span Fig. 14. Brick Floor-arch is between 4 and 6 ft. The building laws of many cities provide that when the spans exceed 5 ft the arches must be increased in thickness, generally to 8 in. The HAUNCHES should be filled with concrete, level with the top of the arch. In first-class fire-proof construction the bottom flanges of the beams should be protected by terra-cotta skewbacks, as in Fig. 15 which shows the construction Finished Floor^ Fig. 15. Brick Floor-arch. Government Printing Office, Washington, D. C. used for the floors of the principal stories of the Government Printing Office at Washington, D. C* A 4-in brick arch of 6-ft span, well grouted and leveled off with Portlant-cement concrete, should safely carry 300 or 400 lb to the square foot. Experiments have shown that brick arches will stand very severe pound- ing and a great amount of deflection without failure. The weight of a floor, such as is shown in Fig. 14, is about 40 lb per sq ft, without the concrete fill or finish. Tie -RODS, as described on page 865, should always be provided. The brick arch is the strongest type of arch for the span it occupies, with the excep- tion, perhaps, of the stone-concrete arch. It is perhaps, also, the most expensive. Its weight necessitates a heavier framework than is required for other types; and, on account of its appearance, it is adapted only to buildings of the warehouse type. Terra-Cotta or Tile Floor-Arches. Terra-cotta or tile as a fire-proof material, and the relative merit of dense, porous, and scmip(3rous tile have been discussed on page 815. For floor-construction the scmiporous tile is probably the best as it is a compromise between the advantages and disadvantages of the dense and porous tile, particularly as to strength and fire-resisfance. As indi- * A description of the structural features of this building may be found in the Engineer- ing Record for Dec. 6, 1902, Fire-proof Floor-Construction 829 cated on page 827, five different types of terra-cotta floor-construction, including a larger number of systems, will be discussed. For these a great variety of shapes and sizes of blocks, of the dense, porous, and semiporous material, are manufactured in this country. The largest company devoted to the manu- facture and erection of hollow-tile fireproofing-material is the National Fire Proofing Company, New York and Chicago. Another large company is Henry Maurer & Son, New York. Any one of the large companies can make any form of blocks desired, except such as are covered by letters-patent, and, as a rule, they can make them in dense, porous, and semiporous material. Advantages of Tile Floor-Arches. Many architects prefer the use of TERRA-COTTA ARCHES in buildings because the setting of them causes less dis- turbance to the mechanics of other branches of the construction. During the placing of concrete arches the continual dripping of water and bits of con- crete interferes seriously with other work. The work of installing tile arches is generally more rapid than for other types and it is not necessary to wait for them to dry out. The quality of terra-cotta can be readily judged from its appearance, not only before it is put in place but also after it is set. Thus it does not require the constant supervision necessary for materials that are mixed as they are put in place. Disadvantages of Tile Floor-Arches. The principal disadvantage of TILE ARCHES for floor-construction is the difficulty of adapting any system to the filling of irregular-shaped spaces. The arches must be set between I beams or channels, and to get the best effect the supporting beams must be parallel or nearly so. Tile arches, especially of the end-constructions, are weakened more by holes for pipes than are the monolithic floors. As there is no bond between the rows of tiles in the end-construction arch, if a single tile in a row is cut out or omitted, there is nothing to hold up the remaining tiles in the row except the adhesion of the mortar in the side joints. In this respect side- method arches have an advantage over the end-construction. Where it is necessary to use considerable concrete filling over the arch the weight of the floor-construction will usually greatly exceed that of the concrete systems, and this additional weight means, also, additional expense. The floor-blocks are liable to breakage and chipped blocks in the floor are not unusual. Inspection of Floor- Arches. Flat arches of hollow tile require close inspec- tion during erection to see that broken or imperfect tiles are not used; that the ribs in end-construction tiles abut opposite each other; that all joints are properly mortared and that all of the steelwork is properly protected. Much poor workmanship has been allowed to pass in order to avoid delay, and also because it cannot be discovered until the centering is removed. A tile arch generally looks better on the top surface than it does on the bottom.* Setting of Tile Floor-Arches. Tile arches are always set on wooden centers suspended by 1)olts hooked over the tops of the I beams. For all spans of 5 ft and over, the centers should be sHghtly cambered. Before any floor- arches are set, all girders projecting below floor-beams should be completely covered on the bottom and sides, independently of the floor-construction. To protect the steel from rust it should have a good coat of Portland-cement mortar before the tiles are applied. After the centers are in place the beam-tiles should be placed under the bottom of the beams and mortar slushed on the sides. The entire sides of the skew backs which rest against the floor-beams should then be covered with just enough mortar to give them a perfect bearing, and shoved * The careless workmanship possibk^ in the setting of tile arches was clearly set forth in an article in Engineering News, April 14, 1898. 830 Fireproofing of Buildings Chap. 23 up against the beams. After this, the intermediate blocks, with their ribg on one end and one side covered with a full bed of mortar, should be shoved into place. The keys should have mortar on both sides and one end, if side- method KEYS are used, and they should tit snugly, but not tight. " Under no con- ditions should a key be rammed in place. It is better to use a smaller key and fill out the space left with either a solid slab of tile, or, if the opening is too small, with a piece of slate."* "In setting tile arches it is very common to build the arches in string-courses, first fitting all the skews, then all the intermediates, and finally all the keys. This is bad practice, as it loads the center, both planks and stringers, to excess, causing too great a deflection. In the end-construc- tion the arches should be built one by one, each being complete before the next is started. In side-construction, where joints are broken longitudi- nally, the arches should be keyed up or completed at the first point wheie the intermediates meet the hues of the key, thus completing the successive arches as rapidly as possible."! All joints in the arches should be filled with mortar, especially at the top. Wetting the Floor- Tiles. In warm weather all hollow tiles, whether dense or porous, should be well wet or water-soaked before laying. In freezing weather they must be kept dry. Mortar for Setting Floor-Tiles. "Mortar for setting porous hollow tile should never be made of cement and sand alone, as such mortar is too short, rolls off the tile, and does not insure a full joint."* A good mortar is made by mixing the cement and sand in the proportion of 1:3, and adding cold lime putty or hydrated lim.e to the extent of 10% of the cement-content. The mortar should be thoroughly worked. Hot lime mortar should never be used. In dry weather the centers can be removed in 36 hours after the tiles are in place, but it is much better to allow 48 hours and even longer in cold or wet weather. Filling above Tile Floor-Arches. The strength of all tile arches is greatly increased by wetting their top surface and covering it with a rich cinder con- crete, mixed with Portland cement, well tamped and brought level with the t jps of the steel beams. If the floors are to be finished in wood, nailing-strips are required to secure the flooring. These naihng-strips are usually dovetail- shape in cross-section, about 2K' in wide at the top, sH in at the bottom and from 1% to 2 in thick. It is preferable to lay them at right-angles to the steel beams, so that they may be secured to the top flanges by metal chps, as in Fig. 16. /""[TZ-^y'y^ Fig. 16. Segmental Tile Floor-arch Before the nailing-strips are laid, all piping and wiring which must go above or through the tile arches should be put in place. After the nailing-strips are in place the tops of the steel beams should be covered with a thin coat of Port- * E. A. Hoeppner. t I'rcitiig Fire-proof Floor-Construction 831 land-cement-and-sand grout, applied with a brush. The spaces between the nailing-strips should be filled with a i : 8 or i : lo cinder concrete, finished about yi in below the tops of the strips. Some architects claim better results with strips of rectangular section, with nails driven horizontally into the ver- tical sides to form the grip in the concrete. This method avoids the loosening of the strips and flooring from any shrinkage of the strips. Tile Filling-Blocks. In cases where the tops of the tile arches are 2 in or more below the tops of the steel beams, hollow tile blocks are sometimes used for fiUing to the top of the beams, as in Fig. 23. These blocks are lighter than good concrete, but they do not strengthen the arches. Cement Floors. If the floors are to be finished with cement, the cement and concrete should be at least 2V2 in and preferably 3 in thick above the steel beams, and should be blocked out in sections of not over 6 ft square, with joints extend- ing through the concrete. When practicable the joints in one direction should be over the beams. Weather-Protection. Terra-cotta arches should always be protected against rain or snow, especially in freezing weather, as both the blocks and the mortar in the joints are injured by freezing. Porous terra-cotta, especially, may be utterly ruined by freezing when soaked with water. Protection of Ceilings from Stains. "If plastered ceilings are to be used, the terra-cotta work should be protected against the smoke or soot from the hoisting-engines. Stains are also quite hable to occur from the effects of iron in the clay, or from the cinders in the concrete over the arches, if the floor is allowed to become wet."* To prevent these stains several kinds of hydraulic paints have been used, some of which have proved very effective. Segmental Tile Floor- Arches. "This form of arch is the strongest and cheapest. It is particularly adapted to warehouses, lofts, factories, sidewalks, or wherever great strength is required and a flat ceiling is not necessary. When a light, strong arch is required in deep beams and a flat ceiHng is also demanded, this result can be obtained by using a metal-lath ceiHng suspended below the beams." f These arches are usually formed by either 6 or 8-in hollow tiles, set on the side-coNstruction principle and bonded endwise like a brick vault. ^oUcLBeam TUe Fig. 17. Segmental Tile Floor-arch. Deep Skew They can be used for spans up to 20 ft, but it is better to limit the span to about 16 ft. "End-construction blocks may be used, but they are unsatisfac- tory, unless the arches are of uniform span and rise throughout. The rise of the side-construction arch can be varied by increasing the thickness of the upper or lower part of the mortar joint, but this cannot be done with the end- construction method." t * P>eitag. t Bevicr, National Fire Proofinj; Company, New York City. 832 Fireproofing of Buildings Chap. 23 Figs. 17 and 18 show typical forms of segmental arches. The weighi of the arch-tiles will run about 26 lb per sq ft for 6-in tile and 32 lb for 8-in Span, c. to c of beams, 19 1}4 Fig. 18. Segmental Tile Floor-arch. Deep Beam. Dropped Skew tile. To these weights should be added the weight of concrete filling, flooring, plaster, etc. Thickness of Webs. "For general use the webs of segment-tile should be ^ in thick for semiporous tile and H in for porous tile. The skewback should be at least H in thick for the first-named material and i in for the second. For printing-establishments or any other building where a large amount of vibra- tion occurs the webs of all tiles must be designed in proportionate thickness to the load they are required to carry."* These thicknesses apply to Chicago practice more particularly, where a stronger tile is produced than in the East. In New York City webs are generally % in thick for semiporous and i in for porous tiles. Rise of Segmental Floor-Arches. The rise of the soffit of the arch above the springing-line should be from one tenth to one eighth the span. The greater the rise the less will be the thrust of the arch. No single-cell tiles should ever be used in any form of terra-cotta arch-construction. Filling the Haunches. The haunches of segmental arches should be filled with good cement concrete-leveled up to a point not less than i in above the CROWN of the arch. For short spans cinder-concrete filling may be used, but for wide spans it is better to use gravel concrete, as the concrete filling contributes to the strength of the arch at the haunches. Tie-Rods. The thrust of segmental arches is very considerable, so that it is important to provide tie-rods between the beams. A formula for determin- ing the stress in the tie-rods and their diameter is given on page 865. To be most eft'cctive the tie-rods should be placed at the center of the skew. Placing the tie-rods in this manner, however, may cause them to project below the soffit of the arch, giving an unsightly appearance to the ceiling. It is also more difficult to protect them when in this position. Strength of the Segmental Semiporous- Tile Floor-Arches. The safe .LOADS per square foot on 6 and S-in segmental arches, with side-construction, scmiparous tile, a rise of one-eighth the sp m, webs and shells % in thick, and with a factor of safety of 7, as obtained from the tables of the National Fire Proofmg Company are given in Table V. Side-Construction Tile Floor-Arches. By this term is understood the llat-tile arches in which the voids in the blocks run parallel with the beams, as shown in Fig. 19. One advantage of this arch over the end-construction is * E. A. Hocppner. Fire-proof Floor-Construction 833 Table V. Safe Loads for Segmental Semiporous-Tile Floor-Arches Span, 6-inch arch, 8-inch arch, Span, 6-inch arch, 8-inch arch, ft lb lb- ft lb lb 4 I 103 I 318 II 402 480 5 878 1049 12 370 442 6 735 883 13 340 407 7 630 735 14 317 379 8 554 662 15 296 353 9 490 585 16 278 331 10 443 529 These loads include the weight of construction; so that to get the safe live load, all the dead load of arch-blocks, concrete fill, plastering, flooring, etc., must be deducted. the BREAKING OF JOINTS that is effected in the setting of the blocks, by means of which the failure of a single block does not impair the strength of the arch beyond that block. The webs should not be less than ^ in thick. "Radial JOINTS are sometimes specified but should be avoided, as they incur needless expense in manufacture and endless confusion and delay in setting, without any Fig. 19. Flat Tile Floor-arch. . Side-construction compensating advantage. " * In the skew^acks a web should always be pro- vided across the block at the lower flange of the beam, as at this point comes the greatest pressure in this block. Arches have collapsed because of failure to provide this web. The depth of the arch must be proportioned to the span between the beams and to the load to be carried. For ordinary loads, a safe rule is to make the depth of the block iH in for each foot of span, plus the amount necessary for protection below the beams. Safe loads for semiporous- tile arches, side-construction, with webs % in thick and a factor of safety of 7, as given by the National Fire Proofing Company, are shown in Table VI. End-Constniction Flat Floor-Arches. In this construction the sides and voids of the individual blocks run at right-angles to the beams, so that the pres- sure on the blocks is endwise of the tile. It has been conclusively demonstrated that hollow tiles are much stronger in end-compression than transversely. "The objection urged against this construction is that it is wasteful of mortar and difficult to get the edges of the blocks properly bedded. They do require slightly more mortar, but the second objection is not serious, for, if the blocks are cut to a proper bevel, the tighter they are set the stronger the arch."* The individual blocks in the end-construction are commonly made rectangular in shape, advancing by i in from 6 to 15 in in depth. The length and width, also, of the blocks may be varied, but the standard size is 12 in for both dimen- sions. The number of partitions or webs in the blocks varies with the size of * Bevier, National Fire Proofing Company, New York City. 831 Fireproofing of Buildings Chap. : Table VI. Safe Loads for Semiporous, Side-Construction, Tile Floor-Arches Depth of arch 6 in 7 in Sin 9 in ID in 12 in Weight of arch per sq ft 24 lb 261b 27 lb 29 lb 34 lb 37 lb Span of arch, ft in Strength of arch in pounds per square foot 4 4 6 5 5 6 6 6 6 7 197 156 230 182 148 263 208 168 296 233 189 156 131 438 346 281 232 195 166 525 415 336 278 234 199 172 These loads represent the gross loads; so that for the safe live loads the weight of the construction, including the arch-blocks, fill, flooring, plastering, etc., must be deducted. For blocks with thicker webs the loads may be increased proportionately. Where no loads are given in the table, the spans are considered excessive for the depth of block specified. The weights of arch given in the table are for the lightest blocks. If thicker webs are used, the weight of block must be taken proportionately greater. '» the blocks and also with the strength desired. The 6-in, 7-in, and 8-in blocks usually have two vertical partitions and one horizontal partition, or one vertical and one horizontal, for blocks 8 in wide. The lo-in and 12-in arches may have either one or two horizontal partitions. Arch-blocks over 12 in deep should always have at least two horizontal partitions. In the strongest blocks the voids are about 3 in square. "The arch-blocks must be set end to end in straight courses from beam to beam, and cannot be set breaking joints, as in the side- construction method."* Thickness of Web. This should be at least % in for porous and ^ in for semiporous tiling. The thicker the webs the greater will be the strength and fire- resistance of the arch. The end-joints are always beveled, as in Fig. 20, the ends being parallel; thus all the intermediate blocks are made with the same die. Form of Skewback. An end-construction arch may have skewbacks formed of the same blocks, with notches in the ends of the blocks to fit over the Fig. 20. Flat Tile Floor-arch. End-construction bottom flanges ol" the beams, as in -Fig. 20. It is generally considered that the end-construction skewback is much stronger than the side-construction skew- Fire-proof Floor-Construction 835 back but on account of the large amount of mortar lost in the voids and the difficulty of obtaining an even bearing with end-construction skewbacks, and, also, because of the greater facility with which the side-construction skew- backs can be used, contractors generally prefer to use the latter; and this has given rise to the form of arch shown in Fig. 21. But a more important reason for using side-construction skewbacks with end-construction arches is the better protection against fire that they afford to the beam or girder. To develop the necessary strength, side-construction skewbacks should have a large sectional area and a suffi( ient number of partitions, following, approximately, the lines of thrust. With any form of skewback the recess for the beam-flange should be of ample width, so that when the tiles are set the protecting flanges on the skew- backs will not touch the bottom of the beams, but will be at least 34 in below them. Many varieties of side-construction skewbacks are made to meet all possible conditions. Keys. Both end-construction and side-construction keys are used with end-construction arches, the choice of the key depending principally upon its Fig. 21. Flat Tile Floor-arch. Combination End-construction and Side-construction length. If the span of the arch is such that the standard intermediate blocks require a key 6 in or more in width, the end-method key is used, as in Fig. 20; but if the space for the key is small, a side-method key, such as shown in Fig. 21, is used. As the key is almost entirely in compression, a side-construction key 6 in or less in width will usually give all the strength required, provided that the horizontal webs are in the same line with those in the intermediate blocks. E. V. Johnson, western manager of the National Fire Proofing Company, says: "We prefer the use of an end-construction key in all cases where possible. Our cus- tom is to use side-construction keys for spaces of 6 in and under, and end- construction keys for larger spaces. When using the latter keys we inserts J^-in fire-clay slab between the ends of the tile." \ Raised Skewbacks. Where flat arches are sprung between i8-in, 20-in, or\ 24-in beams it is necessary either to use a raised skewback or else to have a largf space above the top of the tile arches which must be filled in some way. Rdv'o^ skewbacks are preferable to a hollow space above the tiles and cheaper thai concrete filling. They are often used for roof-arches, because for that pur- pose it is seldom necessary to make the arches as deep as the beams, while the top must be about on a level with the beams. Raised skewbacks are almost always made on the side-construction principle. Fig. 22 shows a typical form of raised skewback for end-construction arches. Flat Versus Paneled Ceilings. In connection with the raising of the arches above the bottom of the beams or girders, J. K. Freitag calls attention to the advantages of flat ceilings, as follows: "Flat, unbroken ceilings are always to be preferred to any type of terra-cotta arch which may require a paneled efi:ect due to the projection of the girders or beams below the main 836 Fircproofing of Buildings Chap. 23 ■ ceiling-line." A perfectly flat ceiling reflects more li^ht, makes a better-lighted room, and deflects the heat. Paneling forms pockets for the retention of heat and flame and greatly increases the exposed area. Fig. 22. Raised Skews for End-constmction Arches Floor-Arches and Beams of the Same Depth. A deep block makes a much stronger floor than a shallower one, and for tho same depth of beams a lighter and cheaper floor. A 12-in arch weighs less per sciuare foot than a 10-in arch with 2 in of concrete flUing; and it costs less. Depth, Span, and Weight. The maximi^m spans for different depths and the AVERAGE WEIGHTS per square foot of this type of arch, set in place, are as follows: Table VII. Maximum Spans for Flat Tile Floor-Arches of Different Depths and Weights Depth of arch , Maximum span, Weight per sq ft, m ft in lb 6 4 6 29 8 5 6 31 9 6 32 10 6 6 33 12 8 39 IS 9 46 16 10 50 The weights per square foot, as given by different manufacturers vary greatly, V no doubt, to the character of the material used and to the thickness of the we"bs. The DEPTH OF ARCH most frequently used i? 10 in, the girders being spaced to use lo-in I beams for joists spaced from 5 to 6 ft apart. As a rule the depth of the arch should be about equal to the depth of the beam, as it is just about as cheap and much better construction to use deeper tiles and less concrete filling. Safe Loads for End-Construction Tile Floor-Arches. The strength: of flat arches of hollow tile depends upon the crushing resistance of the mate- rial, the sectional area per linear foot of arch, the depth, and the span. For these reasons it is impossible to give a table for strength which applies to all arches. The values given in Table VIII for end -construction arches are based upon arch-blocks of the cross-sectional areas, per foot, given in the second horizontal. Fire-proof Floor-Construction 837 line of the table, and arc intended to have a factor of safety of 7, with the weight of the tile only, deducted. Mr. Hinton says: "The safe loads a,s they stand in the table afford a safe general statement of safe loads for all section i since they represent specifically a Ught section in the case of each arch." Table VIII. Safe Loads for End-Construction Tile Floor-Arches * Semiporous material of sectional area per linear foot, as given in the second line The loads are in pounds per square foot of floor Depth of arch in inches 6 ' 8 9 10 12 15 Areas, sq in 310 340 370 400 430 490 580 Spans, ft in lb lb lb lb lb lb lb 4 6 5 5 6 6 6 6 7 7 6 8 196 155 254 202 1^)3 319 254 206 170 141 391 312 254 209 175 147 470 376 306 253 212 179 153 648 519 424 352 29s 251 215 185 968 777 636 529 446 380 326 282 * This table is condensed from two tables prepared by H. L. Hinton. Patented End-Construction Tile Floor-Arches. Figs. 23 and 24 show two variations of a type of arch invented and patented Ijy E. V. Johnson when Fig. 23. Excelsior End -construction Tile Floor-arch. Side-skew manager of the Pioneer Company, Chicago, III. The right to manufacture and use this arch, in certain territory, has been granted to the National Fire Proofing Company, and to Henry Maurer & Son, New York City. The original shape of the arch-tile is illustrated in Fig. 24. Henry Maurer & Son have modified the shape to that shown in Fig. 23, as they consider that this shape gives a stronger and slightly heavier atch than one of the original shape. The advantages of this arch are the reduction in weight for an equal strength, and the clear space of 5 in between the tiles, which avoids the cutting of the blocks for the tie-rods. This arch can be adapted to any span up to lo ft by using blocks of suitable depth 838 Fireproofing of Buildings Chap. 23 Fig. 24. Johnson End-construction Tile Floor-arch. Original Form The LIMIT OF SPAN, WEIGHT PER SQUARE FOOT, and SAFE LOAD of the ExcelsiOF' arch (Fig. 23) is given by Maurer & Son as follows: Table IX. Maximum Spans for Excelsior Tile Floor-Arches Depth of arch, in Limit of span, ft Weight per sq ft, lb Safe load per sq ft, lb 8 9 ID 12 Sto^ 6 to 7 7 to 8 8 to 9 27 29 33 38 300 350 300 350 The National Fire Proofing Company has made arch-blocks as deep as 20 in and as h^avy as 56 lb per sq ft. This company and Henry Maurer & Son use semiporous material for the arch-blocks. It should be noticed that the arch made by the former has an end-construction skewback, while the latter uses a SIDE-CONSTRUCTION SKEWBACK. The National Fire Proofing Company for- merly used the side-construction skewback, but found that when arches of this tyi)e were tested to destruction the skewbacks were almost invariably the parts which failed; hence their adoption of the end-construction skewback. Henry Maurer & Son, however, have tested, without failure. Excelsior arches of 8 ft and lo-ft spans, and with skewbacks as shown by them, with loads of over i 000 lb per sq ft. These arches have been extensively used in l)oth eastern and western cities Reinforced-Tile Floor-Arches. In order to obtain a wide-span flat arch or to obtain a reduced depth of arch-block for the shorter spans, the manufacturers of terra-cotta have applied to their floor-construction the principle of rein- forcement WITH METAL, wliich is the basis of reinfori ed-concrcte construction. Compared with reinforced concrete, even when cinders nre used for the aggre- gate, the greater depth and hollow construction of these reinforced-tile ARCHES secure for them greater strength per square foot for the same weight of construction. On the other hand, however, they are undoubtedly more ex- pensive than cinder-concrete floor-construction, because of the material used and the increased height of the building due to thicker floors. The Herculean Arch.* These floor-arches are built of semiporous terra- cotta blocks, 12 by 12 in on top and var^^ing from 6 to 12 in in depth, according * Patented and manufactured by Henry Muurer &; Son, 1898 and 1900. Fire-proof Floor-Construction 839 to the span and load. In the sides of the blocks are grooves to receive iH by iH by yiG-'m T bars. The blocks are laid end to end the entire length of the span, with a bearing of from 4 to 6 in on the walls or girders, presenting two continuous grooves, which are filled with cement mortar, and into which the T bars are then inserted. The T bars must, of course, extend the full length of the span. The grooves in the next course are then filled with cement mortar and the blocks pushed into place, thus thoroughly covering the steel with mortar. All joints between the blocks are filled with cement mortar and the blocks are laid to break joint endwise, as in Fig. 25. This iloor has been used for spans Fig. 25. Herculean Reinforced, Tile Floor-arch varying from 19 to 23 ft. The weight per square foot given for the terra- cotta blocks and steel T bars is 26 lb for blocks 6 in deep, 33 lb for 8-in blocks, 42 lb for lo-in blocks and 51 lb for 12-in blocks. The manufacturers estimate the s^\rE LOADS for this construction as follows: For a i2-in arch with a 20-ft span, 400 lb per sq ft. For a lo-in arch with a i6-ft span, 400 lb per sq ft. For a 8-in arch with a 12-ft span, 150 lb per sq ft. The CHIEF ADVANTAGE of this Construction is said to be its low cost as com- pared with the cost of systems equally fire-proof and requiring steel beams every 6 or 8 ft. It is particularly well adapted to buildings with masonry walls and partitions, as in such buildings little or no structural steel is required. The floor-construction affords, also, an unusually smooth undersurface, thereby reducing the cost of plastering. No tie-rods are required for this floor. The Johnson Long-Span Flat Floor-Construction. This reinforced- TiLE FLOOR was iuvcntcd by E. V. Johnson, and is now controlled and erected by the National Fire Proofing Company. Its general construction is as follows: A temporary flat centering is first erected, and over this is spread a layer of rich Portland-cement mortar about % in thick. On top of this mortar is laid a woven fabric containing steel rods varying from ^ to H in in diameter, according to the span, and spaced from 2 to 8 in, center to center. Another layer of the same mortar is then spread on top and hollow tiles, from 3 to 1 2 in in depth, according to the span, are then set in the mortar and laid so as to break 310 Fireproofing of Buildings Chap. 23 JOINT and to form continuous rows from one support to the ofher. A layer of concrete, also, about 2 in thick, is usually spread on top of the tiles. Fig. 26 Fig. 26. Johnson Reinforced, Tile Floor-arch shows the general method of construction of this system, but without the rods, which are inserted in place as the fabric is used. For short spans the fabric can be used without the rods. This system differs from the flat concrete system- only in the substitution of hollow tiles for the concrete in the upper portion of the slabs, the strength of the floor depending upon the reinforcement and the ADHESION of the cement mortar to the steel and tiles. As the tiles are covered both on the bottom and top with concrete, the fireproofing prop- erty, also, is measured by the resistance of the concrete and not by that of the tiles. Tests have shown that the adhesion of the mortar is perfect and that it will stand a high temperature without injury. This construction can be used for any span up to 25 ft, the most advantageous span being about 16 ft. The WEIGHT per square foot, including the fabric and the cement on the bottom and in the joints, but not on top of the tile, is as follows: Depth of tile, inches 12 10 9 8 7 6 5 4 Weight per square foot, in pounds 60 55 45 42 37 34 26 24 Tha concrete above the tile should l:>e figured at 12 lb per sq ft for each inch in thickness. The strength of the floor, with i in of 1:3 Portland-cement mortar on top of the tiles, is given in Table X. The New York Reinforced-Tile Floor-Arch. This arch (Fig. 27) was designed by P. H. Bevier, of the New York City branch of tlie Nation^il Fire Proofing Company, for use ''when a Hght and cheap but strong floor construc- tion with a flat ceiling is required, and is particularly adapted to wide spans in shallow beams. When light flcKjr-const ruction with deep !>eams is necessary it can be secured by setting the blocks level with the tops of the beams and using a flat metal lath ceiling, or by omitting the ceiling a panel effect is obtained. When shallow beams arc used the blocks are set level and 1 in below the bottom of the beams. Light cinder concrete or dry cinders are used to level up to the top of the beams. A wire-truss reinporckmp.nt, similar to that shown in Fig. 28, used in this system, is shipped to the building in reels, and is cut to proper Fire-proof Floor-Construction 841 Table X. Ultimate Strength of the Johnson Floor-Construction Span in feet Thicknes 3 of tiles in inches 12 10 9 8 7 6 s 4 3 Ultimate strength n poun Is per square foot 10 3 375 2 5f^o 2 140 I 8,^0 I 525 T 265 I 000 775 560 II 2 8oo 2 340 1 780 I 53'i 1 264 I 0-^2 832 640 464 12 2 350 I wer of any existing masonry construction, and one third the absorbing power of the best-known felt."* Concrete Floors. Concrete used in fire-proof floors may be either plain or reinforced. Without reinforcement its use is generally practicable for very short spans only, on account of its weight. In this chapter it is considered only as a floor-filling between steel beams. Chapter XXIV is devoted to a dis- cussion of the principles governing the design and use of reinforced concrete. Advantages of Reinforced Concrete for Floor-Construction. Although many advantages are claimed for reinforced concrete over the tile systems the principal advantage is that of economy, taking into account the cost of both the steel framework and the filling between. The other important ad- vantages are less weight per square foot of floor (usually but not always the case), adaptabihty to irregular framing, and rapidity of construction. Except in the immediate locality of the tile-factories, fire-proof floors of concrete can * The Brickbuilder, January, 1914. Fire-proof Floor- Construction 843 usually be placed at less expense than is incurred in setting floors of hollow tile; and when the spans permit the use of cinder concrete, the concrete floors are lighter than those of the tile, when both floors have the same strength. Some of the long-span tile-systems, on the other hand, are much lighter than many of the concrete floors that are now being built. The materials entering into the construction of reinforced-concrete floors are readily obtained in almost any locality, no specially prepared material is required, except perhaps in a few special forms of reinforcement, and the work can be done almost entirely by unskilled labor. Less capital is required for concrete work than for the tile- constnictions, and no material need be carried in stock during an idle period, except tools, mixing-machines, old centering, etc. That the above advantages are real is sufliciently proved by the immense amount of reinforced concrete now under construction throughout the world. Wherever a floor is to have a finished, cement surface, reinforced-concrete constructions are considerably cheaper than any tile system, because in the former, the entire concrete is used to give strength, while with the flat-tile arches it merely increases the dead weight. Disdavantages of Reinforced Concrete for Floor-Construction. One decided disadvantage connected with concrete floor-construction is the inter- ference in a large measure with the progress of other parts of the work. During its installation, there is a constant dripping from the 'floor, making it some- times impossible to continue other lines of work. After the completion of the floors a long time is required, depending upon the weather, for the drying out, before interior fmishing can proceed. Composition of the Concrete. The materials used for concrete are dis- cussed on pages 240 to 241 and on page 817. Portland cement, only, should be used in any floor-construction. For most reinforced-concrete floors, having a span between the steel beams of 8 ft or less, cinder concrete is generally used for the reason that concrete mixed with cinders is much lighter than that mixed with broken stone or gravel. The usual proportions of cinder con- crete are one of cement, to two of sand, and five or six of cinders. For a first- class concrete the cinders must be screened through a mesh not larger than ^/i in, and only hard-coal cinders should be used. Good cinders may some- times be obtained from power-plants using soft coal, but they must be well screened and free from* ash. Concrete mixed with common ashes, a mixture oc- casionally used, has little strength and is totally unrehable. For all spans ex- ceeding 8 ft, either gravel or broken rock should be used, and these should be mixed with one part cement, to two of clean sharp sand, and four of stone or gravel. The weight of cinder concrete will vary from 80 to no lb per sq ft, depending upon the coarseness of the material, the quantity of sand, and the amount of tamping. For ordinary purposes a 1:2:5 cinder concrete should be used, weighing 96 lb per cu ft, or 8 lb per sq ft per inch of thickness. Forms of Reinforcement. While steel in small sections is used almost entirely for the reinforcement, there is a great variety in the shape and char- acter of the rnetal employed. Different forms of reinforcement are described and discussed in Chapter XXIV. AH of them may be used, and most of them are now being used in floor-construction. In addition to those forms discussed there, others that are not readily adapted to beam-construction are used in floor-construction. Such are the mi<:tal fabrics described farther on under the different types of construction. The proper position for the reinforcement in a floor-construction is that in which it wiH take the tensionai, stresses, that is, in floor-slabs, near the lower surface. The most logical form is that of a rod or bar. a greater number of smafl rods or bars is preferable to a smaller number of larger ones, because the proportion of the area of adhesion between 844 Fireproofing of Buildings Chap. 23 steel and concrete to the sectional area of steel is greater in the former case. This result is apparently attained in systems in which wire fabrics are used. But the disadvantage in the use of the smaller reinforcement is the greater pos- sibility of CORROSION and consequent failure of the construction. There is a further disadvantage in the use of wire fabrics; they are easily displaced in the process of placing of concrete, either getting too low and becoming exposed to fire or corrosion, or getting too high with a corresponding weakening of the floor. Another detail that must be remembered when using metal fabric is that the mesh must be large enough to allow a good bond to be formed between the concrete above and below it. Reinforcements in the form of bars set ver- tically in the concrete have a tendency to shear through slabs which are under heavy loads. The best and most logical reinforcement for fire-proof floors consists of from ^ to ;>i-in round or square rods, either plain or deformed, spaced at varying distances to suit the spans and loads. Necessity for Cross-Bars. Where wire strands or bars are used for rein- forcement it is essential to have cross-bars as well as transverse tension- bars, because, when the loads are heavy and concentrated, or when a heavy body falls upon a slab the concrete will crack between the carrying bars. This can be readily demonstrated by testing with a drop-test a floor-slab that has no cross-bars. When the load is uniformly distributed the cross-bars are not brought into play; floor-loads, however, are more often concentrated than uniformly distributed Segmental Concrete Floor-Arches. For heavy warehouse-floors the ARCH systems are preferable to the flat systems, because in the former the concrete is used in its strongest form, and less reinforcement is required. In warehouses, also, a ceihng formed of a series of arches is not objectionable. For spans between floor-beams of 5 ft or less, a i : 6 gravel-concrete arch, 3 in thick at crown and without any reinforcement, should sustain, without crack- ing, a distributed load of i 500 lb per sq ft. For spans exceeding 5 ft, the cele- brated Austrian experiments (i 891-189 2) see"m to show that the reinforcing of concrete with small I beams adds greatly to the strength of the arch; but that small rods or netting are not of sufiicient advantage to warrant the additional expense.* Tests made on arches of 8-ft span gave the foUowing results: A concrete arch, s% in thick, 91^ in rise, broke at 1 130 lb per sq ft. A Monier arch (wire netting), ii^o in thick, 101.4 in rise, or about one half the thickness of the concrete arch, failed at i 217 lb per sq ft. A brick arch, 51,^ in thick, 9.85 in rise, failed at 885 lb per sq ft. A hoUow-brick arch, s^Yie in thick, 51^6 in rise, failed at 401 lb per sq ft. A concrete arch, 13-ft span, 31^6 in thick, 15^ in rise, failed at 812 lb per sq ft. A Melan arch, 3^ in thick, 11.4 in rise, broke at 3360 lb per sq ft. The Melan arch had I beams s],i in deep, spaced 40 in apart. The structure was one year old when tested. The concrete arch, considered as a monolithic construction, if built of stone concrete, is superior to the brick arch. The cinder-concrete arch is inferior only in point of strength. Such an arch should be at least 4 in deep at the crown, and the rise should be not less than one eighth the span. ' Cinder con- crete should not be used for spans exceeding 8 ft. The strength of such an arch for ordinary cinder concrete is about the same as that of a 6-in segmental-tile arch of the same span, a s gi ven in Table V. All arch systems, whether of concrete or tile, require tie-rods between the beams to take up the thrust of the arches. (See page 865.) Weight of Segmental Concrete Arches. The weight of soHd segmental Q-y, * See Architecture and Building, Jan. 4, 1896. Fire-proof Floor-Construction 845 arches may be found by the following formula which gives results approximately correct when the rise of the arch is not more than one sixth of the span: W=(w/i2){c+4S/p) in which W =weight of arch, in pounds per square foot; w = weight of material, in pounds per cubic foot; c = thickness of arch at crown, ^n inches; 5 =span of arch, in feet; p = ratio of span to rise of arch. Table XI gives the weight per square foot of arches having a thickness of 4 in at the crown and constructed of stone or gravel concrete, taken at 144 pounds per cubic foot, for various spans and ratios of span* to rise. For greater thicknesses at the crown these weights should be increased by 1 2 lb for each inch of additional thickness. For other materials the weights are directly proportional to the weights of the materials. Thus, if cinder concrete weighing 102 lb per cu ft is used, the weight of the arch for any particular span and ratio of span to rise is 102/144, or 17/24, of the weight given in the table for the same span, ratio, and thickness at the crown. Cinder concrete of good quality weighs, according to density, from 96 to 108 lb per cu ft. Table XI. Weight per Square Foot of Segmental Concrete Arches Concrete taken at 144 lb per cu ft Ratio of span to rise Thickness of arch at crown, in Span in feet 5 6 7 8 9 ID 6 7 7 V' 8 ." 4 4 4 4 4 88 85 82 80 78 96 93 89 86 84 104 100 96 93 90 112 107 102 99 96 120 114 109 106 102 128 122 116 112 108 Flat Reinforced Floors. These floors consist of slabs of concrete, varying in thickness according to the span and load, constructed between the steel floor-beams and reinforced near the lower surface with steel in one of the shapes referred to on page 843, and further described under their respective names. For ordinary loads the thickness of the slab should be at least 5^8 in for each foot of span, with a minimum thickness of sH in. Thinner slabs have been used, but the thickness should be carefully considered for each particular case. The floor- slabs are not usually of the same depth as the beams supporting them. The position of the slabs, therefore, determines the character of the ceiling. When the bottom of the slabs is placed at or below the lower flanges, a flat ceiling results, and the space over the slabs must be flUed to the underside of the flooring with some incombustible material, thus often increasing the weight. When the slabs are set at the top flanges, there is a paneled ceiling, unless a hung ceiling is pro- vided. Strength of Flat Floor-Construction. The following empirical formula, representing the practise established by the New York Building Code, is based on an investigation of cinder concrete floor-construction made by Harold Perrine 846 Fircproofing of Buildings Chap. 23 and Oeor^e E. Strehan,* undc.T the joint auspices of Columbia University and the Bureau of Buildings, Manhattan, New York. w = Kda/S'^ in wlii( li w =safe load, in pounds pf:r sfjuare foot, including the weight of slab; d = distance, in inches, from toj) of slab to center of reinforcement; a = cross-sectional area, in square /inches, of the reinforcement, for each foot of width of slab; S =span, in feet, of slab; K =a coefficient with values as follows: when cinder concrete is used, 26000 if the reinforcement consists of steel fabric continuous over supports; 18000 if the reinforcement consists of steel rods or other shapes securely hooked over or attached to the supports; and 14 000 if the reinforcement is not continuous over the supports; and when stone or gravel concrete is used, 30000, 20000, and 16000, respect- ively, for the corresponding conditions. The material contemplated by this formula is a concrete consisting of one part of J'ortland cement, and not more than two [)arts of sand, and five parts of stone, gravel, or cinders. The reinforcement consists either of steel rods or other suitable shaixis, or steel fabric. In case cold-drawn steel fabric is used, the ten- sional reinforcement should not be less than ^Moo%, and in case other forms of reinforcement are us(;d, not l(;ss than 2>^oo%, the percentage being based on the sectional area of the slal) al)ove the center of the reinforcement. For proper Iprotection against fire and corrosion the center of the rciiifoncment should be at least I in al)ove the lK)ttom of the slab, l)Ut there should always be at least % in of concrete outside of any part of the reinforcement. The formula should not be applied to spans exceeding 8 ft. Cinder-concrete floors should be limit(;d to that span in any case. Expanded Metal. This mat(;rial is now so well known that it requires only a brief descrii)tion. The diamond mesh shown in Fig. 29 is used in floor-con- FiG. 29. Expanded Metal, Diamond Mesh struction. For this purpose; the 3-in juesh is used, the size of the mesh being designated by the width of the diamond shaped spaces. It comes in sheets 8, 10, 12, and j6 ft long, and from 3 to 8 ft wide, according to the width of the mesh. It is made from a soft, tough .steel of fine texture, varying in thickness from No. 13 to No. r, Stubbs gauge. The standard sizes offered by the Cq • Trans. Am. Soc. C. E., Vol. LXXIX, 191S. pagc .-523. the Uoiia, J Fire-proof Floor-Construction 847 soHdated Expanded Metal Companies and the Northwestern Expanded Metal Company are in accordance with a decimal variation in cross-section, thus: 0.25, 0.30, 0.35, 0.40, etc., sq in per ft of width. The designations of the sizes indicate the cross-sectional areas per foot of width, thus: 3-9-20 denotes a 3-in mesh, No. 9-gauge plate, and a cross-sectional area of 0.20 sq in per ft of width. The Youngstown Iron & Steel Company and the General Fire Proofing Company offer from eight to ten sizes of expanded metal with a range sufficient to take care of the needs of concrete-floor designs. Concrete and Expanded-Metal Floor-Construction. Of the numerous styles of floor-construction possible with expanded-metal reinforcement, the type shown in Fig. 30 is generally used and recommended. At the right hand Fig. 30. Concrete Flodr-construction. Expanded-metal Reinforcement of the figure is shown the construction when there are steel beams, and at the left hand when there are reinforced-concrete beams. The advantages claimed for expanded metal as a reinforcement are La better arrangement in the con- crete than is possible with an equal amount of material in any other form; great efficiency in the carrying of concentrated loads, due to the obliquity of the strands; a uniform distribution of small sections at frequent intervals, pref- erable to larger sections at greater intervals; an increased ultimate strength and high elastic limit, due to the method of manufacture, thus combining the advantages of a low-carbon steel with a high ultimate strength; and a mechanical bond with the surrounding concrete. When used between I beams, without other reinforcement, the spans usually vary from 6 to 8 ft, although panels 12 ft wide between beams have been constiucted. In placing expanded metal in the concrete, it is necessary to lap the sheets on the ends up to and including 3-9-20, one diamond (8 in); from 3-9-25 to 3-6-60, one and a half diamonds (12 in); and heavier than 3-6-60, two diamonds (16 in). Table XII. Properties of Rib-Metal Size- Width of sheet, Area of metal per foot of number width, sq m 2 I") 0.540 3 24 0.360 4 32 0.270 5 40 0.216 6 48 0. 180 7 56 O.IS4 8 64 0.13s Rib-Metal. The Trussed Concrete Steel Company of Detroit, Mich., is manufacturing a steel reinforcement for concrete floors consisting of a series of straight ribs or main tension-members rigidly connected by light cross-ties expanded from the same sheet of metal in the form of a mesh (Fig. 31). It is manufactured from medium open-hearth steel in seven sizes of mesh, 2, 3, 4, 848 Fireproofing of Buildings Chap. 23 5, 6, 7, and 8 in, and in lengths up to i8 ft. It is supplied in either flat or curved sheets, and longer lengths and special sizes of mesh can be provided. The width Area of rib 0.09 sq in Ribs spaced 2, 3, 4, 5, 6, 7, and 8 in Fig. 31. Rib-metal Reinforcement for Concrete Floors of sheet is governed by the size of mesh, there being nine bars or ribs in each sheet. Welded-Metal Fabric. The CHnton Wire Cloth Company manufactures a welded fabric or mesh which has been extensively used in the United States as a reinforce- ment for concrete construction of all kinds. Fig. 32 shows the general style of the fabric, the meshes and wires of which can be varied indefmitely, upwards from a i-in mesh. The advantage claimed for this fabric as a reinforcement for slab-construction is that the carrying wires may be varied, both in size and spacing, to give the necessary area for any given weight and span, and the distriliuting or cross-wires, also, may be varied in the same way. The direction of the wires coincides with the line of stress, so that there is no tendency to distort the rectangle of the mesh. The cross- wires, being welded to the carrying wires, are rigidly held in place and prevent the latter from shpping in the concrete. The claim is made that the elongation that takes place in the carrying wire under the stress of heavy loading, is divided along the carrying wire as often as the cross-wires occur, instead of being concentrated at one point as is the case with loose rods or wires. In the meshes Fig. 32. Welded-metal Fabric. Clii • ton Wire Cloth Fire-proof Floor-Construction 849 Commonly used the carrying wires vary from No. lo to No. 3 in size (Washburn & Moen gauge), and are spaced from 1 lo 4 in on center?; while the distribut- ing wires vary from No. 11 to No. 6 in size, and are spaced from 3 to 12 in on centers. Welded metal is manufactured in long rolls, and l>y its use all joints and laps are avoided. A floor can be made with a continuous metallic bond from wall to wall, that is, when the mesh is laid over the tops of the steel beams. The width of the rolls varies from 48 to 86 in. Lock-woven Steel Fabric. This fabric* is made up in a rectangular mesh, the usual spacing of the longitudinal wires being 3 in on centers and that of the •transverse wires 12 in on centers. These spacings can be easily varied to meet Longitudinal Wire Transverse Wire DETAIL OF LOCK Fig. 33. Lock-woven Fabric special conditions. The fabric is usually made 54 in wide and comes in rolls containing from 150 to 600 hn ft, the 150-ft length being commonly used. While the usual width of the fabric is 54 in, it can be varied in multiples of i3^ in from 18 in up to a maximum of 54 in. The longitudinals or carrying wires of the fabric are held in place by the transverse wires as shown in Fig. 33. The longi- Stonc or Cinder Concrete. ^ Lock-voven Steel Fabric. \^^- wm^$i^ Beam Wrap/ Fig. 34. Concrete Ceiling-slab Reinforced with Lock-woven Fabric tudinal wires can be furnished in sizes \-arying from No. 14 to No. 7 gauge, the sectional area of the fabric ranging from 0.0201 sq in to 0.1968 sq in per ft of width. Heavier fabric can be furnished to meet special conditions. The trans- verse wires are usually No. 14 or No. 12. The longitudinal wires are made by a special process which gives them an ultimate tensii-e strength of from 150 000 to 180 000 lb per sq in, with a correspondingly high elastic limit. The fabric can be furnished either black or galvanized. This fabric has the general advan- tages common to any continuous, rectangular-mesh material, as it provides a continuous bond from end to end of a structure, and the wires are so placed that they lie parallel to the lines of stresses which they are called upon to carry. The standard type of construction for floor-slabs and roof-slabs is similar to that shown in Fig. 30 for expanded metal. Where a flat ceihng is desired the type of construction shown in Fig. 34 is very useful. Both of these types have been tested by the Bureau of Buildings of the City of New York on spans up to ana * Controlled by W. N. Wight & Company, New York City. 850 Fireprooling of Buildings Chap. 23 including 6 ft, for live loads running from 130 to 3,30 lb per sq ft; and on spans of 7 ft, approvals have been given up to 175 lb per sq ft, and on spans of 8 ft, up to 150 lb per sq ft. The arches were constructed of cinder concrete and the figures given are based on a factor of safety of 10. In addition to its use for the con- struction, of floor-slabs and roof-slabs, the fabric is suitable for use in panel- walls, sewers, penstocks, and tanks, and in all other places where a sheet-reinforcement can be used to advantage. Triangle-Mesh Wire-Fabric Reinforcement. Under this name the Ameri- can Steel and Wire Company is manufacturing a wire fabric of cold-drawn steel wire for the reinforcement of fire-proof floors. A detail of the standard material is shown in Fig. 35. The triangular mesh is built up of either single or stranded longitudinals with the cross-wires or bond-wires running diagonally across the width of^ the fabric. It is claimed that the triangular mesh affords an even distribution of the steel, reinforcing in every possible direction, and that the Fig. 35. Wire-fabric Reinforcement, Triangular Mesh Strength is increased by reason of the truss-construction. For floor-reinforce- ment, this fabric is used the same way that any of the other fabrics previously described are used, and as indicated in Figs. 26, 30, and 34. The longitudinal wires in Triangle Mesh are invariably spaced 4 in on centers, but the diagonal wires may be spaced either 4 or 8 in apart. The manufacturers can furnish different styles, giving variations in the cross-sectional area from about 0.032 sq in to about 0.395 sq in per ft in width of the fabric, or a variation in weight per square foot of from 0.2 to 1.6 lb. The material is furnished either galvanized or plain. The longitudinal wires are made of either a single wire or of two or three wires stranded. The cross-wires or bond-wires are of either No. 14 or No. i2>^ gauge. Special sizes of additional area can be furnished upon applica- tion>to the company. This fabric is said to have an ultimate strength of not less than 85 000 lb per sq in. Dovetailed Corrugated Sheets. Ferroinclave. Sheets of thin steel corru- gated so as to form dovetailed grooves have been used as a reinforcement and cen- tering for concrete-steel, the dovetailing serving to unite the sheets to the con- crete. The Brown Hoisting Machinery Company of Cleveland, Ohio, has Fire-proof Floor-Construction 851 patented, under the name Ferroinclave, a tapered corrugation which is small enough to hold hard mortar, and hence can ])e plastered on the under side. Fig. 36 shows a partial section of the Ferroinclave corrugated sheets, the depth of the corrugations being 3^ in, the distance from center to center of corrugations 2 in, and the corrugations, with the opening between the edges, K in. The tapering of the corrugations is of especial advantage for roofs, as it allows the sheets io be lapped at the end-joints, making a roof absolutely tight, even if water should penetrate the cement coating. The principal advantage in the use of corru- gated sheets for floor-construction is that they sustain the concrete, when the spans are of moderate width, before it has set, thus saving the cost of centering and the time required to put it in place. This advantage, however, appears to be offset by the high cost of the sheets when they have to be shipped. For roofs, however, this construction is light and relatively cheap, as the total thickness need not exceed iK in for spans of 4 ft 10 in. To make the roof water-tight some water-proof covering is required. With a good coat of hard plaster or gauged mortar on the under-side, the iron will not be affected by heat in case of fire until a considerable time has elapsed; and even if the mortar on the under- side should be more or less dislodged by the streams of water, it can be replaced, Fig. 36. Ferroinclave Reinforcement for Concrete Floors at a very slight expense. Another advantage in the use of Ferroinclave for roofs is that a building can be covered and made water-tight in the mo.st severe winter weather and the cement appHed during the following spring. Ferroinclave is made in sheets 20 in wide and up to 10 ft long, and it is usu- ally of No. 24 gauge. For roofs it is attached to purlins in the same way that iron roofmg is attached, the most economical spacing of the purlins being 4 ft loj^^ in center to center, which accommodates sheets 10 ft long and leaves an end- lap of 3 in. For the cement top coat on roofs, a mixture of one part Portland cement to two parts sand, applied to a thickness of % in above the top of the sheets, is sufficient. For floors a rich gravel or crushed-stone concrete should be used, the thickness being governed by the span and the loads to be supported. The following table shows the ultimate strength of No. 24 Ferroinclave with different thicknesses of concrete, as determined by actual tests with sheets 20 in wide over a 4-ft 10 ^-in span: Thickness in inches of i : 2 mortar above the metal ii^ 2 21,^ 3 31.^ 4 Ultimate strength in lb per sq ft for a span 4 ft loH in 615 915 1220 1560 i860 2120 A factor of safety of 6 should be ample for ordinary loads. Ferroinclave is especially adapted for the roofs and floors of large manufac- turing plants, and may be used to advantage for partitions, stair-treads, vats, water-closet partitions, and fire-proof doors. 852 Fireproofing of Buildings Chap. 23 Berger's Multiplex Steel Plate. Fig. 37 shows a section of a corrugated steel plate manufactured by the Berger Manufacturing Company, Canton, Ohio, for floor and roof -construction, the plate being an invention of G. Fugman. As shown in the illustration, it consists of a series of vertical corrugations of sheet steel, painted or galvanized, ending at the top and bottom in three half- circle arches, separating the vertical sides of the corrugations from each other and giving stiffness to the top and bottom of the plate. The plate is made with depths, D, of 2, 23.4, 3, 31.^, and 4 in, and in corresponding widths of 131,^, 14, 14H, and 15 in. The maximum length of plate is 10 ft. It can be made of any gauge of steel, from No. 24 to No. 16, but No. 18 is as heavy a weight as is generally required. For floors and roofs, the corrugated plate is laid on top of the beams and the top portion filled with concrete and leveled off about i in above the plate. For wooden floors the nailing-strips may be embedded in the concrete and the bottom of the strips raised only about yi in above the top of the plate. The construction is very hght and strong and requires no centering. It cannot be plastered, however, on the under side, and where a Fig. 37. Berger's Multiplex Steel Plate plaster ceiUng is required it must be constructed independently of the plate by means of furring-strips and metal lath. The weight of the 4-in plate, with a 1:2:5 furnace-slag concrete leveled i in above the top of the plate, is about 40 lb per sq ft, and the safe load for a io-ft span is given at 270 lb per sq ft. While this floor has several practical advantages, it cannot be considered thoroughly lire-proof, because the metal is exposed on the bottom. But with a plastered cdiling on the under side, the iron would probably not be affected by any ordinary fire before the latter could be controlled. Permanent Centering. Numerous forms of sheet-metal fabrics have been developed in recent years for use as floor-reinforcements. They consist, gen- erally, of steel plates pressed into series of solid ribs, variously spaced, between which the metal is stamped or perforated, or deployed into an open mesh- work. The characteristic form is shown in Fig. 3S. The mesh is kept small enough to prevent ordinary concrete from passing through. For use as a reinforcement the sheets are furnished either in flat or segmental form. A i : 21,-2 : 5 stone or cinder concrete may be used, the thickness depending upon the span and the load to be provided for. For spans exceeding from 3 to 5 ft, according to the gauge of metal, the sheets must be temporarily supported until the concrete has set. The difficulty of providing efficient fire-protection on the underside of reinforce- ments of this type, and around the lower flanges of the supporting steel beams, is a serious disadvantage. Besides, the bond between the metal and the floor- concrete is on one side of the sheet only. Some of the forms now on the market. Fire-proof Floor-Construction 853 with their special characteristics, are briefly described in the following para- graphs. Fig. 38. Permanent Centering. Characteristic Form Rib-Truss. These plates, manufactured by the Berger Manufacturing Com- pany, Canton, Ohio, are designed with five longitudinal ribs, 6 in on centers, and 1/2, %, I, and ly, in high. The metal between the ribs is slit into truss- loops which are further reinforced with beads at right-angles to the main ribs. The standard sheets are 24 in in width and are carried in stock in lengths up to 12 ft, and made of No. 24, 26, 27, and 28-gauge metal. Self-Sentering. In this form, manufactured by the General Fireproofing Company, Youngstown, Ohio, the ribs are lyie in in height, 3% in on centers, and connected by expanded metal. The sheets are 29 in in width and come in lengths from 4 to 12 ft, varying by units of i ft. Self-Sentering is made of Nos. 24, 26, and 28-gauge metal. (Sec, also, page 885.) Hy-Rib. Ily-rib, controlled by the Trussed Concrete Steel Company Detroit, Mich., is made in sheets measuring 10^/2 in from center to center of outside ribs and having four ribs i>i6 in in height; and also in sheets 14 in in width having three ribs. There is also a type known as the Deep Rib. The lengths are 6, 8, 10, and 12 ft. The sheets are of No. 24, 26, or 28 United States gauge, and are furnished either flat or in various types of curves. (See, also, page 886.) Corr-Mesh. Corr-Mesh is manufactured by the Corrugated Bar Company, Inc., Buffalo, N. Y., which supplies, also, special clips for splicing and fastening the mesh to the supporting members. It is made in two types. One has ribs % in high, spaced 3% in on centers; the other type has ribs Yiq in high, spaced 3 in on centers. For the ^.i-in-rib Corr-Mesh the sheets are 13 in wide, and for the -^ie-in-rib Corr-Mesh they are 18 in wide. The mesh is furnished in United States standard gauges, Nos. 24, 26, and 28. Standard sheets are 6, 8, 10, and 12 ft in length. No allowance need be made for side laps, but at least 2 in should be allowed for end-laps. Duplex Self-Centering. The Youngstown Iron Steel Company, Youngs- town, Ohio, manufactures the Duplex Self-Centering It is 23 in in width, is furnished in lengths of from 4 to 12 ft, and in Nos. 24, 26, and 28 metal, United States gauge. It weighs 1.37 lb per sq ft for the No. 24 gauge, 1.03 lb for the No. 26 gauge, and 0.86 lb for the No*. 28 gauge; and it has a corresponding cross sectional area per foot of width, of 0.411, 0.308, and 0.257 sq in. Sectional Systems. During recent j'ears, the unit system or separately MOLDED SYSTEM, cousisting of sliop-madc reinforced-concretc members, such as 854 Fireproofing of Buildings Chap. 23 girders, lintels, floor-slabs, and wall-panels, made at a factory and shipped to the sites of building operations, has been^ receiving considerable attention in this country. This system is more completely discussed in Chapter XXiV, page 953, under the title Separately Molded Construction. Separately molded members have been used between the steel beams of fire-proof floor-construction as a substitute floor-filling for the usual terra-cotta or concrete floor-arches. The advantages of such systems, where they are practicable, are obvious. Such members are usually made as large as can be conveniently handled and of com- paratively long span. Disadvantages of Sectional Systems. The reason that the sectional SYSTEMS have not found favor is because they necessitate a fairly uniform spacing of beams throughout a structure, and this is generally impracticable. The casting of the parts has hitherto not been commercially successful, as the forms, although used repeatedly, have been more expensive than the usual centering at the building; and it is also generally necessary to use a concrete that is richer and more carefully prepared in order that it may stand the additional handling. Even with all possible care, the breakages in transportation are considerable. As the methods of manufacture of factory-made members are constantly being perfected, chiefly in mechanical contrivances for cheapening the forms and reduc- ing the handling during the process of manufacture, the economy of this system is being substantiated, and particularly when it is used in combination with a light structural-steel fire-proofed frame. Waite's Concrete Beam. In Fig. 39 is shown a type of sectional floor- CONSTKUCTION that has been used in a number of buildings by the Standard Jlod Relnforceownt Cliaanel Reinforcement Fig. 39. Waite's Concrete I Beams Concrete Steel Company of New York City. The floor-construction consists of a series of concrete I beams lo or 12 in in depth, supported on the lower flanges of the steel beams, which are spaced from 5 to 7 ft apart. The concrete beams are set about 18 in apart and the spaces between the lower flanges are filled in with a cinder concrete of the same composition as the I beams. On the tops of the concrete beams is placed a metal fabric of small mesh on which a lean-concrete slab is laid. This makes a comparatively light floor-construction, because of the large spaces between the concrete beams. The concrete I beams are cast at the shop and allowed to harden before they are sent to the building. In the lower flange is inserted, as shown, a steel reinforcement, of small circular or other cross-section, to furnish the necessary tensile strength. The beams are cast with the proper lengths, in accordance with the drawings; and any slight variations at the building are made up by filling the spaces between the ends of the concrete beams and the webs of the steel beams, and covering the webs of the latter with concrete. A similar construction, consisting of a series Fire-proof Floor-Construction 855 of T beams, with lower flanges 11,^2 i" thick and 12 in wide and stems 2 In thick and 12 in deep, of i : 4 cinder concrete, reinforced with Mo-in rods near the flanges, and without floor-finish of any kind, successfufly withstood the fire, water, and load tests of the New York City Bureau of Buiklings after having been constructed 28 days. This system has proved to he practical in cases in which a flat or level ceiling is required and the steel floor-beams are 10 in or more in depth. The cost of construction compares favorably with that of other flush-ceiling types. The Siegwart Floor System. This system (Fig. 40), designed by Hans Siegwart, of Lucerne, Switzerland, is in extensive use in that country. The ^ 1 X 2^4 wood sleepers 2 • yi° rods at supports i ii r- r i ^ i ^ iiii ir ii I I I . r r . iiiiii - iiiii i ii - i r i - 2 - 3C ° rodb at supports TYPICAL FLOOR BLOCK 6^0 Vide IsVlonu. Total Weight 48G7^or G2.3^ sq.ft. llein f orcement 1 -f ^"x %' Havemeycr Bar in eacti Web Mixture(l -2»4-3i4)top inch 1-5 Mortar Fig. 40. Siegwart Reinforced-concrete Floor-construction sectional units are usually made 10 in in width, the height and reinforcement varying with the span and load. In a test on a beam of this type, designed to carry a Uve load of 150 lb per superficial ft over a i6-ft span, the construction withstood a satisfactory four-hour fire test with a load of 150 lb per sq ft, followed after the fire by a test with a load of 600 llj per sq ft. It is claimed for this system, that using the same working units for the strength of the material, the dead weight of the construction is only one half that of a monolithic reinforced- concrete floor designed to carry the same load with the same percentage of reinforcement. "The Siegwart Company claim their method to be much cheaper than monolithic floors. From quotations furnished by their Canadian Company, the price in Montreal is quite a little less than the author's expe- rience for monolithic floors in the same city, ranging from 17 to 26 cts per sq ft, erected for various spans and loads."* A modification of the Siegwart system has been developed by Gros\'enor Atterbury, and has been employed in two-story and three-story residence-buildings for the Sage Foundation Homes Company at Forest HiUs (Long Island), N. Y. SECTION Fig. 41. ^^ Climax Reinforced-concrete Floor-construction The Climax Floor System. This system (Fig. 41) was designed by S. M. Randolph. The design is similar to that of the Siegwart floor system. * Chas. D. Watson, Concrete Construction with Separately Moulded Members and Costs, Proc. Nat. Asso. Cement Users, Vol. VI, 1910. 856 Fireproofing of Buildings Chap. 23 The Vaughan Floor System. The Vaughan Company of Detroit, Mich., is manufacturing a shop-made unit which is employed considerably throughout the Middle West. The general form of this unit is like that of Waite's concrete beam, shown in Pig. 39. The Watson Floor System. Two typ^s of sectional floor systems foi fire- proof floor-fillings between steel beams are shown in Figs. 42 and 43. Foi long Factory made Unit Concrete Floor Beam TYPE A Suspended Ceiling? Fig. 42. Watson Reinforced-concrete Floor-construction. Without Slabs spans and heavy loads, the T sections are used, laid side by side; and for spans less than 20 ft and loads of 200 lb per sq ft or less, the beams are spaced 5 ft on centers with flat slabs between. This system is controlled and installed by the Unit Construction Company of St. Louis, Mo. Beams and girders are Field Concrete]['«V Fireproofing Fig. 43. Watson Reinforced-concrete Floor-construction. With Skibs cast with unit frames in horizontal molds, and slabs are made on edge in steel forms. In the American School Board Journal for August, 1912, Theodore II. Skinner describes the construction and erection of a story-and-basement school- house with a structural-steel frame and shop-made reinfc5tced-concrete joists, with unit-ril)lK'd reinforced-concrete slabs. Gypsum Floors. Gypsum has been extensively used for floors and roofs in fire-proof buildings. It furnishes a light construction which, with the additional Fire-proof Floor-Construction 857 advantage of the rapidity with which it can be put in place, is economical not only with respect to the floor itself but also on account of a saving in the amount of the structural steel supporting it. Another favorable feature is the great heat-insulating property of gypsum, resulting in absence of condensation and a reduction in the cost of heating the building. The Metropolitan System. This construction consists of a series of steel cables suspended from the supporting steel beams and encased in a slab of pure calcined gypsum containing about 15% of wooden chips. The cables are generally composed of two No. 12 galvanized-steel wires, twisted. They are made contin- uous over the supports, being securely fastened over the flanges of the end-beams or channels by heavy S hooks or other suital)le means. The cables are spaced from I to 3 in apart, depending on the carrying capacity desired. They are held taut by a ^i-m round steel rod, laid at the middle of the span at right-angles to their direction. The mixture of gypsum and chips is sent to the work in bags and placed on wooden centers, as in the case of concrete floors, wet, and allowed to set. The sides and flanges of the supporting steel beams are^'ncased in the same material, all as shown in Fig. 44. The minimum thickness of floor-slabs is 4 in; Cables Composed of Two No. 12 ,^ Galvanised -Steel Wires Twisted ,X' F4=^ ' Metropolitan Com.po6ition / ^^"Steel DeflecU. Under Steel Deflection - Hod FiG. 44. MetropoHtan Fire-proof Floor the usual thicknesses for roofs are 3 and 3H in. The finished slabs weigh about 4 lb per sq ft per in in thickness. Spans of from 6 ft 6 in to 7 ft are said to make the most economical arrangement, all things considered. Spans should not exceed 10 ft. The safe gross strength of the construction may be determined by the formula, 24.Td in which w =the safe gross load per sq ft of floor or roof-surface, in pounds; r=the safe tensile strength of the twisted cables, in pounds, which for the ordinary case of two No. 12 cold-drawn steel wires, may be taken at 365 lb; d =the deflection of the cable, in inches, and equals the slab-thickness less the sum of the protection of the cables at the center of the slab and over the supports, that is, ordinarily, the slab-thickness less i in; h =the spacing of the cables, in inches; L =the span, or distance, between centers of supports of the slab, in feet. No tie-rods are necessary in this floor-construction; but in the end-bays, when the lateral stiffness of the beams together with the compressive strength of the floor-slab is not sufficient, struts must be provided of such size and spacing as are necessary to resist the pull of the cables. This floor-construction is con- trolled and installed by the Keystone Gypsum Fireproofing Corporation, New York. 858 Fireproofing of Buildings Chap. 23 Metal Lumber. A system of prcssed-steel I joists, channel- joists, corner- joists, wall- ribbons, etc., has been developed as a substitute for ordinary wooden framing in the construction of walls, floors, roofs, and partitions. In the floor- construction, the I joists and channel-joists, of from No. i6 to 12 United States gauge sheet metal, are braced by metal bridging, to give additional rigidity.. A typical floor-construction is shown in Fig. 45. The steel floor-joists are covered above with a concrete slab reinforced with expanded-metal lath, and the lower flanges are protected by a ceiling of metal lath and cement plaster attached to the joists by means of the prongs. The metal-lumber joists frame into ordinary steel girders, resting on a shelf-angle as shown in the drawing. The joists are cut to length at the factory, properly marked and tagged and, with the erection- diagrams, are shipped to the site. All joints and splices are riveted in the fleld. The steel girders should be properly incased in some flre-proof covering. The Fig. 45. Berber's Metal Lumber and Concrete Floor-construction materials for this floor-construction are manufactured l)y the Berger Manufac- turing Company, Canton, Ohio; the General Fireproofing Company, Youngs- town, Ohio; the Truscon Steel Company, Youngstown, Ohio; and the National* Pressed Steel Company, Massiflon, Ohio. They publish safe-load tables for ipetal-lumber I joists and channel-studs for spans of from 4 to 20 ft. This sys- tem, contemplating the use of steel joists and girders, not thoroughly incased with fire-proof materials, cannot ordinarily be considered thoroughly fire- resistant, although a specially constructed floor with all the steel covered and' protected with fire-proofing-material has passed the fire test prescribed by the New York Building Code. (See page S27.) It has been extensively used to replace combustible building-construction, especiaUy in residence-buildings. Protection of Girders and Beams. No form of floor-construction can he considered thoroughly fire-proof unless it includes a protection of the lower flanges of all steel beams and girders, or provides for the protection of all steel used in its construction or support. The material used for the protective cover- ing is generally the same as that used in the floor-construction itself. The Fire-proof Floor- Construction 859 principal materials are tile, either dense, porous, or semiporous; gypsum; and concrete, either of cinders, stone, or slag. Beam-protection, where the floor- construction incases the side of the beams, as in Fig?. 17, 19, or 34, should never he less than i in thick. Where paneled ceihngs are used, that is, where the lower part of the beams is below the lower side of the floor-construction, as in Figs. 18 or 30, the protection should be increased to at least iy2 in at all points. Tile Beam-Protection. When tile is used, there are two types of protec- tion. In one case the blocks incasing the bottom flanges of the steel beams meet Fig. 46. Tile Protection for Box Girder at the middle of the lower side of the flanges; in the other, they simply turn under the edges of the bottom flanges and hold flat tiles with beveled edges Fig. 47. Tile Protection for Single-beam Girder against the lower side of those flanges. The latter is considered the better method, although in this method the danger of breakage of the part extending 860 Fireproofing of Buildings Chap. 23 under the flange is supplemented by the possibility of an omission of the flat protection-tiles. The blocks incasing the lower flanges may be the skewbacks of the arch, or they may be separate blocks. Different forms and conditions are illustrated in Figs. 15 to 24. Fig. 26 shows the entire beam protected by blocks on both sides. Girders, which often project below the ceiHng-line, are much more exposed to the effects of fire and water than the floor-beams, and they should have, therefore, the most eflacient protection. As a rule, such girders should be provided with not less than 4 in of terra-cotta protection at the sides, and iy2 in of solid tile on the lower side, with a space of H in between the terra- cotta tiles and the girder. Fig. 46 is a typical method of protecting girders by means of hollow tiles. The bottoms of the skewbacks are prevented from spreading by wire ties placed in the end-joints between the soffit-tiles and hooked into the round holes in the skewbacks. Single-beam girders are usually pro- tected as shown in Figs. 22 and 47, the latter figure showing more particularly the protection of a beam at the side of an opening in the floor. Concrete Beam-Protection. A more thorough incasing of the webs and lower flanges of beams and girders can be accomphshed by the use of concrete. The superior fire-proof character of cinder concrete makes it the best material for this purpose. If of sufficient thickness and properly applied, it will hold securely, without reinforcement, around the flanges of beams and girders. But where it is less than 2 in thick, wire or metal lath, wrapped around the flanges, should be embedded in it. A common form of concrete-protection is shown on right hand side of Fig. 30. Sometimes the soffit of the beam is pro- tected by a concrete slab with an insulating air-space. This method is one that may be advantageously used for the protection of girders. A fire test of this form of girder-protection made in the Butterick Building, New York City, thoroughly estabhshed its efficiency. Hung ceilings are sometimes used as the protection for the steel beams. This is very bad practice, as these ceilings are more than likely to collapse in a severe fire. The experience in the Bal- timore fire confirms this belief. (See, also, pages 780 to 782.) The Fireproofing of Trusses. When steel trusses are used to support the roof or several stories of a building it is very important that they be protected, not only from heat sufficient to warp them, but also from expansion sufficient to affect the vertical position of the columns on which they are supported. The following description of the covering of the trusses in the Tremont Temple, Boston, Mass., furnishes a good illustration of the way in which this should be accomphshed: "The steel girders were first placed in terra-cotta blocks on all sides and below, these blocks being then strapped with iron all around the girders, and upon this was stretched expanded-metal lathing, covered with a heavy coating of Windsor cement; over this comes iron furring, which receives a second layer of expanded-metal lath, the latter, in turn, receiving the finished plaster. There is, consequently, in this arrangement for fire-protection, first, a dead-air space, then a layer of terra-cotta, a Windsor cement covering, another dead-air space, and finally, the external Windsor cement." Numerous shapes of terra-cotta tiles are made for incasing the structural shapes commonly used in steel trusses. Some of these are shown in Fig. 48. The tiles should always be secured in place by metal clamps passing entirely around the envelope, or better stiff, by wrapping with wire lath. The tiling should then be plastered with hard wall-plaster. Trusses, also, may be fire-proofed by completely in- casing the several members in cinder concrete, either with or without metal reinforcement. The method of incasing steel columns by means of the cement- gun (page 826) is also applicable t9 the protection of steel trusses, and if of suf- ficient thickness would probably serve as a suitable fire-protection; but no Fire-proof Floor-Construction 861 definite data on this latter point are as yet available. When trusses are to be fireproofed, the additional weight must be provided for in the strength of the trusses themselves. SECTION OF BRACING SECTION OF STRUT Fig. 48. Tile Protection for Members of Steel Trusses Steel Framing for Fire-proof Floors. Before the framing-plans of a build- ing can be made, it is necessary to decide, in a general way, upon the system OF FLOOR-CONSTRUCTION or fireproofing that will be employed Thus, if any one of the LONG-SPAN SYSTEMS, such as the Herculean, Johnson, and many of the concrete systems, is to be adopted, the girders should be spaced so that the floor-construction will span between them, without floor-beams, as shown in Fig. 49, while if an ordinary flat-tile arch is to be used, floor-beams will Jj^r^l^ V fr Fig. 49. Steel Floor-framing for Long-span Construction 862 Fireproofing o{ Buildings Chap. 23 be required, spaced from 5H to 9 ft apart, and these beams must be supported by girders, as indicated in Fig. 50. When there are no floor-beams, a strut- beam should be riveted between the columns, as in Fig. 49, to hold the latter in place during erection and to stiffen the building. It should be remembered that with floor-beams spaced not more than 7 ft on centers, almost any system ■iDf ^^^o^^"^^ /^ ^ H XL »E1 h 6 C - CI rl- 4- 66 — - 3^ □ q Fig. 50. Steel Floor-framing for Short-span Construction ^ of floor-construction may be employed; while if the floor-beams are omitted, there are few systems to select from. With any form of filling between beams or girders, less steel is required for moderate than for excessive spans of beams or girders. Computations for the Steel Framing. The computations for the steel beams and girders of a fire-proof floor are very much the same as for a wooden floor. The load or loads which any given beam is required to support are first estimated and then the beam of the necessary size to support the load is selected.. The DEAD LOAD for any fire-proof floor may be estimated with sufficient accuracy by means of the data given in this chapter in connection with the different systems of floor-construction. The dead load should include the weight of the beams, the fireproofing, including all concrete filling, the plastering, furring, lathing, nailing-strips, and flooring. The live loads may be estimated by means of the data given in Chapter XXI, pages 718 to 721. Example. The best arrangement for the columns in a retail store is to set them 18 ft on centers in one direction and 19 ft 6 in in the other. It is decided to run the girders as shown by Fig. 50, and to put a beam opposite each column Fire-proof Floor-Construction 863 and two beams between the columns. It Is required to determine the proper sizes of the beams and girders, using an ordinary end-arch construction between the beams Solution. From Table VII, page 836, we find that the least depth of arch which it is advisable to use is 10 in, but as we will probably have to use 12-in beams it will be better to figure on a 12-in arch, as this will give less filling on top. The weight of the 12-in arch will be about 39 lb per sq ft. We shall probably require 2 in of concrete filling on top, which will weigh 16 lb, and I H in of hght fiUing between naiUng- strips, weighing, say, 9 lb per sq ft. The flooring and nailing-strips will weigh about 4 lb, the plastering on the ceiling 5 lb, and we must allow at least 6 lb per sq ft for the weight of the beams them- selves. These make a total dead weight of 79 lb per sq ft. The live load for a retail store should be taken at 150 lb per sq ft, making a total load per square foot on the beams of 229 lb. The total load that each beam must be capable of supporting will be 6H ft by 18 ft by 229 lb, or 26 793 lb, or 134 tons, which is assumed to be uniformly distributed. From Table IV, page 580, we find that this load, with a span of i^ ft, will require either a 12-in, 4S-lb beam, or a is-in, 42-lb beam. The latter will be both stronger and cheaper, but will increase the thickness of the floor by 3 in and require additional filling. The girder must support two concentrated loads of 26 793 lb or 13.4 tons each. On page 566 it is stated that when a beam supports two equal loads applied at points one third the length of the span from each end, the equivalent uni- formly distributed load may be found by multiplying one load by 2^. Multi- plying 26 793 lb by 2% we have 71 448 lb as the equivalent distributed load on the girder, to which should be added the weight of the girder. This requires a standard 24-in 80-lb beam (Table IV, page 577). If instead of using tile arches between beams 6J4 ft apart, we conclude to use the Herculean or Johnson construction spanning from girder to girder, we should frame our floor as in Fig. 49. For this span we should require lo-in tiles, weighing 55 lb per sq. ft. Allowing 8 lb for i /n of concrete, 9 lb for filling, 4 lb for flooring and strips, and 5 lb for pkstering, we have 81 lb as the dead load per square foot. We have added nothing for the weight of the girder, as this will be fully offset by the portions of the floor not loaded. The live load per square foot will be 150 lb as before, and the total load to be supported by the girder, 18 ft by 19 ft 6 in by 231 lb, or 81 081 lb, or 40.54 tons, which will require a 24-in 80-lb beam (Table IV, page 577). Hence by this arrangement we save the weight of the floor-beams; but a 6-in strut-beam should be pierced between the columns, as in Fig. 49. The calculations for any other floor-construction are similar to the calculations for this example, the only variations being in the figuring of the dead weights of the construction. Tables for Floor-Beams. It is a difficult matter to prepare tables that may be generally used, showing the size of steel beams required for fire-proof floors, because such beams are often irregularly spaced, and there is a wide variation in the dead loads. The following tables, however, may be used in making approx- imate estimates and in checking the computations for any particular floor. The sizes of I beams given may be safely used where the total live and dead loads do not exceed the values given in the headings. The total loads should include sufficient allowance for the weights of any partitions that the floor-beams may be called upon to support. Table XIII gives the sizes and weights of I beams for floors of offices, hotels, and apartment houses; Table XIV, for floors of retail stores and as- sembly-rooms; and Table XV, for floors of warehouses. The total loads used in the computations are, respectively, 120, 200, and 270 lb per sq ft. 864 Fireproofmg of Buildings Chap. 23 Table XIII. Sizes and Weights of I Beams for Floors of Ofl&ces, Hotels, and Apartment-Houses Total load, 120 pounds per square foot Span of Distance between centers of beams in feet ' ' beams 4 ^/^ 5 S'A 6 7 in feet in lb in lb in lb in lb in lb 10 6 121/4 6 12I.I 6 12^ 6 12H 7 IS II 6 12M 6 12M 7 IS 7 IS 7 IS 12 6 12 M 7 IS 7 IS 7 IS 8 18 13 7 15 7 IS 7 IS 8 18 8 18 14 7 IS 8 18 8 18 8 18 9 21 15 8 18 8 18 8 18 ' 9 21 9 21 16 8 18 9 21 9 21 9 21 10 25 17 9 21 9 21 9 21 10 25 10 25 18 9 21 9 21 10 25 10 25 12 31 ^'i 19 9 21 10 25 10 25 10 25 12 Zi\^ 20 10 25 10 25 12 31 H 12 31 H 12 3l¥i 21 10 25 12 31 H 12 31 H 12 31H 12 Zi\^ 22 10 25 12 31 H 12 31 H 12 31 H 15 42 23 12 31 5^^ 12 31H 12 31 H 12 31 V^ 15 42 24 12 31^/^ 12 31^/^ 12 zi\i IS 42 15 42 25 12 31^/^ 12 31^/^ IS 42 IS 42 15 42 Table XIV. Sizes and Weights of I Beams for Floors of Retail Stores and Assembly-Rooms Total load, 200 pounds per square foot Span of Distance between centers of beams in feet beams . 4)'^ 5 5K2 6 7 in feet in lb in lb in lb in lb in lb 10 7 IS 7 IS 7 IS 8 18 8 18 II 7 15 8 18 8 18 8 18 9 21 12 8 18 8 18 9 21 9 21 9 21 13 8 18 9 21 9 21 10 25 10 25 14 9 21 9 21 10 25 10 25 12 31 1/^ IS 9 21 10 25 10 25 12 31 H 12 31 H 16 10 25 10 25 12 311/^ 12 31 H .12 31 H 17 10 25 12 z^Vi 12 31^/^ 12 ziYi 12 40 18 12 31 H 12 J1M2 12 313-^ 12 40 12 40 19 12 31 H 12 31 3'^ 12 40 12 40 15 42 20 I? 31 H 12 40 12 40 IS 42 15 42 Fire-proof Floor-Construction 865 Table XV. Sizes and Weights of I Beams for Floors of Warehouses Total load, 270 pounds per square foot Distance between centers of beams in feet Span of beams 4K2 5 s'A ■ 6 6V2 •" (ppf in lb in lb in lb in lb in lb 10 8 18 8 18 8 18 9 21 9 21 II 8 18 9 21 9 21 9 21 10 25 12 9 21 9 21 10 25 10 25 10 25 13 10 25 10 25 10 25 12 31 3-^ 12 31 H 14 10 25 12 31 H 12 31 V^ 12 s^Vz 12 3iV^ 15 12 31^2 12 31 H 12 31^2 12 31 Vi 12 40 16 12 31 H 12 31 3^^ 12 31 3'^ 12 40 12 40 17 12 31 '/i 12 40 12 40 12 40 15 42 18 12 40 12 40 IS 42 IS 42 15 42 19 12 40 IS 42 IS 42 IS 42 15 42 20 IS 42 IS 42 IS 42 IS 45 IS 55 Tie-Rods. In all segmental arches and other types in which a thrust is exerted against the beams, tie -rods must be provided to prevent the beams from being pushed apart, and especially to prevent the outer bays from spread- ing. They should run from beam to beam from one end of the floor to the other. If the outer arches spring from an angle, as in Fig. 14, the tie-rods in this bay should be anchored into the walls with large plate-washers. The tie-rods should be located in the lines of thrust of the arches, which are ordinarily below the half -depth of the beams, and in some cases near the bottom flanges. If their appearance is objectionable, they should be hidden by a hung ceiUng. For constructional purposes they are desirable in all types of floor- construction, even though the floors do not exert a thrust on the beams. As a rule tie-rods are proportioned and spaced according to some rule of THUMB rather than by actual calculations of the thrust. For the interior arches this practice is probably safe enough, but for outside spans, and particularly for segmental arches, the thrusts of the arches should be computed and the rods proportioned accordingly. The spacing of the rods is generally eight times the depth of the supporting beams, but never more than 8 ft. For interior flat-tile arches, the following rule can usually be safely followed: for spans of 6 ft or less, use %-in rods spaced about 5 ft apart; for 7 -ft spans, ^-in rods, 5 ft apart; and for g-ft spans, K-in rods, 4 ft apart. The horizontal thrust of an arch may be found by the following formula: r = in which T = pressure or thrust in pounds per linear foot of arch; w = load on arch in pounds per square foot, uniformly distributed; L = span of arch, in feet; K = rise of segmental arch, or effective rise of flat arch, in inches. 866 Fireproofing of Buildings Chap. 23 The RISE of a segmental arch is measured from the springing-line to the soffit of the arch at the middle. For flat hollow-tile arches, the effective rise may be figured from the top of the beam-flange to the top of the tiles. As the tiles usually project from i\^ to 2 in below the bottom of the beams, the effective rise will be from 2 to 2]^i in less than the thickness of the arch. For the interior arches of a floor, w may be taken for the live load only, but for the exterior arches, w should include both the full dead and live loads. Having found the thrust of the arch, the spacing of the rods of any particular size may be readily determined by dividing the safe load given for that size of rod in the table on page 388, allowing 16 000 lb unit stress, by the thrust. The result •will be the spacing in feet. Example. What size of tie-rods and what spacing should be used for the floor-construction described on page 863, in the preceding example? Solution. The depth of a tile arch is 12 in, the dead load 79 lb and the assumed live load 150 lb. The span between the beams is 6\i ft. Then, for the interior arches, w = 150 lb, R = 12 — 2}'i == g\i in, L = 6H ft and T = (3 X 150 X 42.25)7(2 X 9H) = I 000 lb. The tensile strength of a M-in rod, not upset, at 16 000 lb per sq in, is, from Table II, page 388, 4 832 lb. Divid- ing this by I 000 we have a little less than 4 ft 10 in as the spacing. The tensile strength of a %-in rod is given as 6 720 lb, which would admit of a spac- ing of a little more than 6 ft 8 in. For the outer spans, w should be taken at 150+79=229 lb. Then 7"= (3 X 229 X 42.2S)/(2 X 9^^) = i 526 lb.. For this thrust we should use %-m rods spaced about 4 ft 5 in apart. Load-Tests. It may be desirable at times to test fire-proof floors after they have been installed. The same precautions should be taken as for tests on rein- forced-concrete construction, described on page 967. If it is desired to determine from such tests the ultimate strength, a section of the floor of a width equal to the span should be cut loose from the rest and loaded to destruction, the supporting steel beams being shored up during the test. The safe working load is found by dividing the breaking-load by the proper factor of safety. 5. Fire-proof Roof-Construction Flat Roofs. Flat roofs are constructed in the same way as the floors, except that the beams and girders are set so as to give a slight pitch to the roof to drain the water. As the roof-loads are usually less than the floor-loads and as there are no partitions to be supported, the arches or roof-panels are usually considerably lighter than the floor-panels, but the general construction is prac- tically the same for both. When the roof is formed of reinforced concrete, the beams may be set so that the concrete will give the desired inclination to the roof and will have a nearly uniform thickness, as this reduces the amount of concrete required, and also the weight. In cases where level ceilings are de- sired, however, it would be cheaper to set the roof-beams level and to grade the roof with dry cinders, as the cost of the hung ceiling would more than offset the cost of the extra construction necessary to take the added weight of cinder fill. Jf the roof is to be covered with tin or copper, nailing-strips should be em- bedded in the concrete, as for wooden floors, and the entire roof sheathed, as it is claimed that tin or copper laid over terra-cotta or concrete will rust out in a few years.* Gravel or tile roofs may be built without woodwork of any kind. Whether terra-cotta, gypsum tile, or concrete is used for the roof-panels, the sides and bottoms of the steel beams and girders should be efficiently protected, ♦ Freitag. Firc-proof Roof-Construction 867 as well as all columns and all other structural metal in the roof-space. In an ordinary building, in which there are stair-wells or elevator-wells, the roof and upper ceiling are likely to be more severely tested by heat, in case of fire, than any of the floors below, and experience has shown that this part of the build- ing often has the poorest protection. Pitched Roofs. Pitched roofs may be constructed in various ways, accord- ing to the material that is to be used and the kind of roofing that is to be em- ployed. When terra-cotta or gypsum tile is to be used for the fireproofing, the most common method of construction is that which involves the framing of the roof with I-beam rafters and T-iron purhns, set horizontally and spaced i in farther apart than the lengths of the tile. Between the tees, book tiles, or roofing- tiles are placed as in Fig. 51, and the roofing is appUed directly to the surface of Fig. 51. Tile Fireproofing for Roof -construction the tiles. If the roofing is to be of slate or of clay tiles, solid, porous terra-cotta blocks should be used between the tees, as nails are held better by solid blocks than by hollow tiles; gypsum roof tile is also suitable for this purpose. The same construction may be used for flat roofs; but on account of the expense of the tees it will usually be more expensive than the construction above described, and not as strong or desirable. With the construction shown in Fig. 51, it is impossible, by any economical method, to efliciently protect the bottom of the T irons from the efi"ects of heat. Rcinforced-ciruier concrete, or reinforced porous terra-cotta tile, Johnson System, affords an excellent and also an economical construction for fire-proof pitched roofs. Either of these construc- tions may be filled between or on top of the rafters without the use of purlins, except about once in from 6 to lo ft, to prevent sliding and to stiffen the roof. "Three-inch plates of concrete, with expanded metal embedded, have been successfully used in spans of from 6 to 7 ft and in some cases even in 8-ft spans. The concrete is deposited on wooden centerings, as in the floor-construction, and the upper side is smoothed off during the setting and floated smooth and straight to receive the roof-covering."* The roof-covering, usually slate, or * Freitag. 868 Fireproofing of Buildings Chap. 23 clay tiles, may be nailed directly to the concrete, as nails are held nearly as well by cinder concrete as by wood. This applies only to cinder concrete, as it is quite impossible to nail into rock concrete or gravel concrete. In concrete roofs the rafters, also, should be surrounded with concrete held in place by BOOK TILE GOVE:RNMENr ROOFING THE Fig. 52. Hollow Book Tile and Solid Tile for Roofs metal lath. With tcrra-cotta roofs, the beams should be incased with terra- cotta blocks. Fig. 52 shows the standard shapes of book tiles and solid roofing- tiles. These are made 2, 21,4, and 3 in thick, and from 16 to 24 in long. Three- inch book tiles weigh about 13 lb per sq ft, and 21,^-in solid tiles about 16 lb Fig. 53. Bonanza Reinforced-cement Tiles for Pitched Roofs per sq ft. Tiles of both of these shapes are also used for ceilings and where a light, fire-proof filHng is required. Reinforced-Cement Tiles. Cement tiles of interlocking types, made in the factory and reinforced with metal fabric or mesh, may be laid without sheathing directly on steel purlins. This type of construction, however, is suitable only as a semi fire-resisting roof -covering, as it is usually made with plates of insuffi- cient thickness and does not contemplate the thorough incasing of the steel understructure with concrete or other fire-resisting materials. Bonanza Cement Tile roofing is a type of this shop-made tile and is manufactured and controlled by the American Cement Tile Manufacturing Company, Pittsburgh, Pa. Two types of tiles are made, one for pitched-roof and the other for flat-roof construction (Figs. 53 and 54). The properties of the tiles are given in the fol- lowing tabulation: Fire-proof Roof- Construction Standard, Pitched-Roof Tiles Thickness of tiles about i in Over-all dimensions of tiles 26 by 52 in Tile-surface exposed to weather 24 by 48 in Number of tiles per 100 sq ft of roof i2j.^ Weight of tiles per 100 sq ft of roof 1450 lb Standard, Flat-Roof Tiles Width of tiles 24 in Length of tiles 60 in or less Thickness of tiles iy2 In Weight of tile-construction 16 lb per sq ft 869 Fig, 54. Bonanza Reinforced-cement Tiles for Flat Roofs The flat-roof tiles are designed for and have been used in connection with buildings for manufacturing-plants on spans of 5 ft between purlins. On these spans they have l^een tested up to an ultimate live load of 250 lb per sq ft. The top surfaces of these tiles are finished in a weather-proof and water-proof material of a dark, terra-cotta-red color. . Steel Fabric r=f; "^ Eeinf orcjlng - Steel THROUGH TYPE Reinforcing - Steel Reinforcing - Steel "H" TYPE Fig. 55. Structolite Roof-tile 870 Fireproofing of Buildings Chap. 23 Structolite Roof-Tile. Shop-made roof-tiles made of a dense quick-setting gypsum cement, called structolite by the manufacturers, are put on the market by the United States Gypsum Company of Chicago, III. The material used is said to have an average ultimate crushing strength of 2 000 lb per sq in. As the material weighs only 77 lb per cu ft, a very light roof-construction results. The tiles are reinforced with steel in much the same manner as reinforced concrete, and their strengths are figured by the same formulas, using working stresses appropriate to the materials. For spans from 4 to 6 ft, a trough-like tile is used, as shown in Fig. 55. For greater spans, up to 10 ft, the T type and H type of tile are used, the latter when a continuous flat ceiling is desired. The tiles are placed directly on channel or I-beam purlins, but when the flanges of the purlins are less than 21,^ in wide, bearing-plates should be inserted between the tiles and purlins. The weights of the roof-tiles in lb per sq ft are as follows, the tiles themselves being generally designed for safe superimposed loads of 50 lb per sq ft. Span, ft Depth, in Trough type, lb T type, lb H type, lb 4 5 6 7 8 9 10 5 5 5 6 6 7 14 14 IS 13!/^ • 14H 16 16 21 21 22 22 Robertson Process. Under the name of Robertson Process Floor, the H. H. Robertson Company, Pittsburgh, Pa., make and install gypsum floor- construction of the same general character and design as the Metropolitan Floors (page 857). They also manufacture pre-cast roof- tiles designed on the same suspension-principle. The cables protrude about 2 in at the ends of the slabs, near the top surface. When set in place on the roof-purlins with their ends abutting, the projecting ends of the cables of adjoining slabs are tied together by a device that draws them taut, thus effecting continuity. The tiles are rab- betted at the ends where the cables emerge, and these rabbets are filled with gypsum, covering over and protecting the cable-connections. The following are the standard sizes of roof -tiles: 3 in thick, 24 in wide, varying in length by 3 in, from 4 ft o in to 6 ft o in 3 in thick, 21 in wide, varying in length by 3 in, from 6 ft o in to 6 ft 9 in 3 in thick, 18 in wide, varying in length by 3 in, from 6 ft 9 in to 7 ft o in 3^ in thick, 15 in wide, varying in length by 3 in, from 7 ft o in to 8 ft o in sy2 in thick, 12 in wide, varying in length by 3 in, from 8 ft o in to 8 ft 6 in The weight per sq ft is 14 lb for the 3-in tiles and 16 lb for the s^^-in tiles. Mansard Roofs are usually framed with rafters, riveted or bolted to wall- plates. The space between the rafters may be filled with cinder concrete, hollow partition-tiles, or blocks extending from rafter to rafter, as in Fig. 56. Slates or tiles may be nailed directly to cinder concrete or to porous terra-cotta. Prob- vibly the best way to attach slates or tiles is to nail 11,4 by 2-in wooden strips to \he outer face of the concrete or terra-cotta, set them at the proper distances Hpart to receive the slates or tiles, and then plaster between the strips with Fire-proof Roof-Construction 871 icement mortar. This gives a better nailing for the roofing, and the wooden L Strips are not affected by fire until the slate is practically destroyed. Roof-Coverings. The materials ordi- narily used for the roof -covering of fire- pro©? buildings are: (i) tar and gravel; (2) asphalt and gravel or sand; (3) vitrified tiies, bricks, or slate tiles over tarred felt. Tar and gravel, or asphalt felting and gravel or sand, offer the cheapest roof suitable for a fire-proof building; and when a good quality of felt and distilled pitch or the best grades of asphalt are used, make a very satisfactory covering. Such roofs, however, require to be renewed about every ten years. The roofing is put on in the same manner as over wooden construction, the felt being laid directly on. the concrete. Probably the best flat roof that can be put on a building is one of vitrified or slate tiles, laid over five plys of tarred felt. The felt is laid and mopped as for a gravel roof, and the tiles are bedded on the felt in cement mortar. Vitrified tiles, about 8 in square and 1 3^ in thick, are made for this purpose, and slate tiles, 1 2 in square by i in ithick, have been used. Flat, vitrified-brick tiles, also, are used. Gravel roofing ,'should not be used on roofs which have an indination exceeding f4 in in i ft. For pitched or inclined roofs, slates, clay tiles, or metal tiles may be used. Clay tiles are superior to slate when exposed to fire and are generally to be preferred to slate; this is especially true of some of the patent interlocking tiles. v(See, also, pages 1582 to 1587, and 1595 to 1599.) Suspended Ceilings. Office-buildings, apartment-houses, etc., having flat roofs, require ceilings below the roofs in order to make a proper finish in the Fig. 56. Tiles for Mansard Roof IH X 5fa Haflgera, Geiliag Constmction HZ3 (i]^ "channel Bars ^Metal Lath : Laced to Channel Bars Tig, 57. Suspended-ceiling Construdioil rooms, and also for heat-in»ulation. In office-buildings the ceilings of the top story are often framed and constructed like the floors, but with a lighter con- struction. More often the ceilings are suspended from the roof; as this requires much less steel and is consequently much cheaper. It answers the purpose fully as well, that is, if the roof-b6ams are efficiently protected: Fig. 57 shows 872 Fireproofing of Buildings Chap. 23 a common construction for such ceiUngs. Wrought-iron hangers, about 1 16 by YiQ in or I by i<^ in, split at one end to hook over the lower flanges of the roof-beams, are used to support Me by %-in flat steel bars, spaced about 4 ft on centers; and to the under-side of these are laced %-in, ^-in, or 11,4 -in channels, 12 or 16 in on centers, to receive the metal lathing. The bottom of each hanger is bent at right-angles to form a seat for the bar, and the bar is laced to the hangers. No bolting or riveting is required, all con- nections being made by lacing wire, or by bending the iron. Where stiffened wire lath is used, the chan- nels may be spaced 16 in on centers; but if the or- Fig. 58. Suspended Ceiling. Details of Two-bar System dinary expanded laths are used, it is better to place the channels 12 in on centers. If ordinary lime mortar is used for plastering a 1 2-in spacing is really necessary. Another system is one which uses only one set of horizontal bars, which are spaced close enough to receive the lathing, and Which are supported by hangers. With stiffened wire lath- ing, roof-beams spaced not over 5 ft apart, and short hangerp, this may be the cheaper system; but without the stiffened lathing, there is no stiff- ness to the ceiling at right-angles to the bars. Where the hangers are 3, 4, or 5 ft long, and the spans between the beams Roof beams 5 ets. J— -12^=-^ Fig. 59. Suspended Ceiling Details of Two-bar System wider than 5 ft, the two-bar system, shown in Fig. 57, requires less steel, for the reason that the channels, having spans of only 4 ft, may be made very light, and only one third or one fourth the number of hangers are required. In place of the small channels, small T bars or flat bars may be used, but when the bars are held by lacing, channels are preferable. iMgs. 58* and 59* show very satisfactory details for the construction of the two-bar system. Instead of the hook shown in Fig. 58, the hanger may be spHt at the top, one half bending around one side of the beam-flange and the other half around the other side. Where the ceiling is suspended below terra- cotta arches, toggle-bolts are used for the support of the hangers. The ends of the small bars supporting the lathing are usually spliced by means of sheet- iron clamps, about 6 in long, wrapped closely around the bars and hammered tight. For suspended ceilings under segmental or paneled floor-construction, the same methods are employed, except that the hangers are replaced by clips holding the ceiUng-bars close to the soffits of the beams. " From Fire Prevention and Fire Protection, J. K. Freitag, pages 687 and 688. Partitions and Wall-Coverings 873 6. Partitions and Wall-Coverings Requirement of Fire-proof Partitions. As a rule the partitions in fire- proof buildings are not required to support any weight, but merely to serve the purpose of dividing the spaces into rooms, and to confine a fire to the compart- ment in which it originates. No greater strength, therefore, is required in a partition than is necessary to carry its own weight. Rigidity, however, is re- quired, and a rigidity in proportion to its height and unsupported length. When partitions separate apartments or sections of a story, that is, when they are practically without window-openings or door-openings, they should be rigid enough to prevent the passage of water from a hose-stream as well as the pass- age of flame. In other cases this may be unnecessary; in fact, at times it may seem desirable to construct partitions which can be easily removed to get at a fire spreading through doors or windows. The materials of partitions should be incombustible. They should be poor conductors of heat. It is desirable, also, to have them unaffected by water. Lightness is a good property, as any increase in the dead weight of the construction adds to the cost of the structure. Partitions should be as sound-proof as possible. Window-openings should be avoided, when possible, in fire-proof partitions, and even door-openings should be reduced in number to a minimum. In many buildings, however, in which halls have no openings into streets or courts, such windows are necessary for lighting the halls. When this is the case the frames should be made fire-proof, wire-glass should be used, and, if possible, the sash made stationary. Fire Tests on Partitions. In New York City no materials or types of con- struction are permitted for interior permanent partitions in fire-proof buildings that have not met the required fire tests. The standard test of the American Society for Testing Materials is based on the New York test.* Briefly, these tests require that the partition shall resist for one hour the destructive action of a wood fire, the heat of which has been gradually increased to 1 700° F. during the first half-hour and maintained at that temperature for the balance of the time; and that it shall resist, also, for two and a half minutes at the conclusion of the fire test, the application of a hose-stream at 30 lb pressure. Types of Partitions. Fire-proof partitions that are in common use may be grouped, according to the materials or the method of construction used, as follows: (i) Brick; (2) Hollow tile or terra-cotta; (3) Concrete (stone or cinder) ; (4) Gypsum block; (5) Plaster or concrete, with metal. The choice of the materials and the type of construction are largely influenced by the character of the building and the purposes for which it is used. Partition- Walls. For bearing-partitions, that is, those which support floor- beams, there are probably no materials more satisfactory than brick and con- crete. The latter may be used either in the form of blocks, or may be poured into forms. Dense tile, also, is being used with satisfactory results for bearing- walls. Tests show a crushing strength, on net sections, equal to that of brick. Hollow-Tile or Terra-Cotta Partitions. These are usually built of blocks, either square or brick-shaped, according to the particular product used. The square blocks are usually 12 by 12 in on the face, and the brick-shaped blocks are usually 12 in long iDut vary in height. Both shapes are made in thick- * See latest Year Book, Am. Soc. for Test. Mats. 874 Fircprooiing of Buildings Chap. 23 nesscs varying from 2 to 12 in. The 3-in, 4-in, and 6-in blocks are commonly used, the 4-in blocks being the most popular for ordinary work. For the more important partitions, such as stair and elevator-enclosures, nothing narrower than the 6-in blocks with the double row of cells should be used. The blocks are commonly set with the voids vertical. Fig. 60 shows typical Fig. 60. Hollow-tile or Terra-cotta Partition-blocks shapes of both the square and brick-shaped blocks. Fig. 61 shows round- cornered and angle-cornered partition-blocks, which must be set vertically. "Terra-cotta partitions of a 2-in thickness have been placed on the market, but have not been extensively used. A 2-in terra-cotta partition of any strength or efficiency is quite impracticable, and where floor-area is so valuable that more space cannot be occupied, terra-cotta is not the material to be employed."* • Freitag. Partitions and Wall- Coverings 875 Through the addition, however, of band-iron laid between the courses and patented under the name Phoenix,* the strength of a 2-in tile partition is greatly- increased. The New York partition, Bevier Patent, consists of 2-in tiles, rein- . forced with truss-metal, such as is used in the New York floor-arch. (See Fig. 28.) Fig. 61. Hollow-tile Round-comer and Angle Partition-blocks Porous Versus Dense Materials. For inside partitions the porous mate- rials are preferable to the dense, while for outside walls the dense materials should be used. With dense tiling it is necessary to insert either wooden nailing-strips, which are very objectionable, or blocks of porous tile to take their place. It is becoming daily more difficult to get the sawdust necessary to make the porous material. Mortar. Tile partition-blocks should be set in mortar made of one part lime-putty, two parts cement, and from two to three parts sand. The blocks should be well wet before setting and the partition wet down before the plaster- ing is appHed. Heights and Lengths of Terra-Cotta Partitions. "The safe height of terra-cotta partitions in inches may be approximated by multiplying the thickness in inches by 40. Common practice allows a safe height of 12 ft for 3-in, 16 ft for 4-in, and 20 ft for 6-in partitions. For partitions without side- Supports the LENGTH should not materially exceed the safe height. Doors and . high windows may be considered as side supports, provided the studs run from floor to ceiHng."t Weights. The weights of either porous or dense terra-cotta partitions should not be taken at less than the following, adopted by the Hollow Building Tile Association, as proper average weights: 2-in partition, 14 lb per sq ft; 3-in partition, 16 lb per sq ft; 4-in partition, 18 lb per sq ft; 5-in partition, 20 lb per sq ft; * Made by Henry Maurer & Son, New York, t Freitag. 876 FIreproofing of Buildings Chap. 23 6-in partition, 22 lb per sq ft for one-cell blocks; 6-in partition, 24 lb per sq ft for two-cell blocks; 8-in partition, 30 lb per sq ft; not including plastering, which adds about 10 lb per sq ft for both sides. Concrete Partitions. Partitions of stone concrete are seldom used because of the forms necessary for their erection, which make them comparatively expensive. Unless reinforced they take up too much room. Furthermore they are the heaviest of all partitions. Even in buildings that are entirely of reinforced concrete they are not always used. Cinder-concrete partitions are somewhat lighter and considerably cheaper than those of stone concrete. Yet even these are too heavy and too troublesome to construct to be satisfactory. Among the partitions tested and approved by the New York City Building Bureau is one that consists of cinder-concrete blocks, 2 1.4 and 3 in thick, the thicker ones being hollow, 12 in high, and 18 in long. They have their edges cast with tongues and grooves that furnish more or less of a bond between the blocks when they are set. Hollow, concrete building-blocks make fairly good partitions, but are objectionable on account of their thickness and weight. Gypsum-Blocks. The term gypsum-blocks is now -more generally em- ployed than the term plaster-blocks, as it is more accurately descriptive. The principal makes on the market are the acme, made by the Acme Cement Plaster Com- pany, St. Louis, Mo.; the ANCHOR, made by the Ameri- can Gypsum Company, Port Clinton, O.; the pyrobar, made by the United States Gypsum Company, Chicago, 111.; the BELL, made by the Rock Plaster Manufacturing Company; the blocks of the Niagara Gypsum Company and the M. A. Reeb Corpora- tion, both of Buffalo, N. Y.; and the blocks of the Plymouth Gypsum Company, Fort Dodge, Iowa. The usual size of these blocks is 12 in by 30 in, although some are made ISH in by 32 in. The thickness is generally 2, 3, 4, 5, 6, and 8 in, for the hol- low blocks, and 2 and 3 in for the solid blocks. Gypsum-Block Partitions. Blocks made of gypsum (plaster of Paris) combined with various substances, such as cinders, wood chips, cocoanut fiber, asbestos, etc., have been largely used for partitions in fire-proof buildings. The principal advantages claimed for these partitions are their great lightness and reduced cost compared with other forms of partitions. Gypsum blocks can be readily cut with a saw, and have a considerable holding power for nails. In the fire tests, made for the Bureau of Buildings, New York City, they have generally shown considerable resistance to the flame and have transmitted less heat than partitions of any other form. They did not, however, always stand the hose- stream, some of them being easily pierced, and all of them being more or less washed away by the water. An objectionable characteristic of these blocks is ^G. 62. Plaster-blocks. Doweled Construction. Partitions and Wall-Coverings 877 their tendency to absorb moisture while being stored and to draw water from the plastering when it is applied. This moisture works down to the bottom of the partition where it is hkely to injure the wooden base. These par- titions are made in thicknesses varying from 2 to 4 in, those less than 3 in in thickness generally being solid; and their height should not exceed from 50 to 60 times the thickness of the blocks, unplastered. Hollow blocks should always be set with the ceils horizontal. The edges of the blocks are generally grooved or otherwise arranged so that the mortar joint forms a key between them. In some forms of these partitions the blocks are bonded together by means of metal dowels,* running across the horizontal and vertical joints from one block into the adjoining one, as shown in Fig. 62. The cut illustrates the use of the block in the construction of dumb-waiter shafts and shows how the blocks are anchored at the corners by iron dowel-angles. Gypsum plaster is used in laying plaster-blocks, and occasionally fibered-gypsum plaster, tempered with Fand, may be employed. All of the partitions in the newer portions of the Monadnock Block, Chicago, and in many other prominent buildings of Chicago and New York City, are of Gypsum blocks. Gypsum blocks make the lightest practical partition known. The weight of these partitions per square foot may be taken as follows; Thicknessof block, inches. . 23 4 5 6 8 Weight in lb per sq ft 10 121,^ 141,^ 171,^ 19 26 About 8 lb per sq ft should be added to obtain the weight of the partition when plastered on both sides. Mackolite. A plaster-block extensively used is the Mackolite Hollow Block, made by the A. B. Fireproofmg Company, Chicago, III. Mackolite partition tiles are generally made in the form shown in Fig. 63. The 3-in, 31,4-in, and 4-in tiles are made 48 and the others 30 in long, all the tiles being 12 in high. The blocks are laid in regular courses, breaking joint as in cut-stone work. Lime mortar is used for setting. In fitting around openings or at angle? the blocks are cut with a saw, and this effects a material saving in time and material. It is claimed that the blocks make very strong par- titions. The composition of the blocks is plaster of Paris mixed with certain chemicals, reeds, and fiber. Reeds of the same length as the blocks are placed in the molds and the plaster of Paris and fiber are then mixed with water, to which the chemical has been added, and poured around the reeds so that they are nowhere exposed. The reeds give longitudinal strength to the blocks while the fiber makes them tough and elastic. The material sets in about half an hour, after which the blocks are kiln-dried for four days. Gypsinite Partitions. The main feature of these partitions is the gypsinite STUD which is handled and erected in the same manner as a wooden stud in the ordinary non-fire-proof partitions. The stud is composed of wooden naihng- strips completely protected and embedded in a plaster-composition known as * Patented by the Sanitary Fircproofing and Contracting Co., New York City. Fig. 63. Mackolite Partition-blocks 878 Fireproofing of Buildings Chap. 23 GYPSiNiTE CONCRETE. The studs arc carefully made and are plumb and true. Metal lath or plaster-boards are secured to the studs and plastered, completing the partition, which is about 4I/S in thick. (Fig. 64.) This partition is slightly heavier than the ordinary partition of wooden construction. It is quite as stiff and as strong as a good tile or other partition, and the nailing-strip feature of the studding facilitates the application of a wooden trim. It is said to be particularly sound-proof, and the spaces between the studs afford an opportunity to conceal pipes, wires, etc. Gypsinite studs are 3 by 3 by 12 in, and weigh 3 lb to the foot. They can be made any size required. Fig. 64. Gypsinite Studs, Metal Lath, and Plaster in the partitions the studs are usually placed 16 in on centers and bridged as iriay be required. They are fastened to the floor or ceihng by the use of sills and plates of the same material, or by light channel-irons, which are spiked to the fireproofing. The manufacturers believe that in large quantities these studs can be furnished as cheaply as wooden studs and that the partitions can be erected as cheaply as ordinary lath-and-plaster partitions. Gypsinite studs are manufactured by the United States Gypsum Company, Chicago, 111. Solid, Plaster-and-Metal Partitions. Thin partitions of plaster appHed to metal lath and metal studs, made solid, and finished about 2 in thick, have been extensively used in fire-proof buildings. They are remarkably stiff, owing to the adhesion of the plaster to the steel, and they are lighter and occupy less ^pace than any other practical fire-proof partition of equal strength. In the ^re tests these partitions act very much like the plaster-block partitions, resist- ing thoroughly the passage of the flames. But the plaster always washes off Vhen the hose is applied and the lath becomes exposedr The rigidity of the Partitions and Wall-Coverings 879 metal fabric on the metal studding has been considered by firemen a disad- vantage, as it is very difficult to cut through it when necessary to get at a fire. The construction of these partitions is practically the same for the different fabrics used, which are described on pages 846 to 850. This lath or fabric ap- pears to be subject to the corrosive effects of the plaster. In the demolition of the Pabst Building, Ne^ York City, the metal lath used throughout in the partitions was found to be considerably corroded, after about four years, even though the lath had been painted. On the other hand other cases are cited by %' Nailing / Strip Fig. 65. Two-inch Solid Plaster Partition. Elevation the manufacturers, such as the Chess residence at Pittsburgh, Pa., the Sturtevant residence at Springfield, Mass., and the West End Trust Building at Philadelphia, Pa., in which after twenty years no corrosion of the metal lath in plaster par- titions was observed. The investigations of the United States Bureau of Standards of various forms of stucco-construction seem to bear out the manu- facturers' contention. The lath should in all cases be protected against initial or incipient corrosion by painting or galvanizing before being embedded in the cementitious material. Weights of Plaster-and- Metal Partitions. The weight of a 2-in solid partition, when dry, is about 20 lb per sq ft. The weight of partitions of greater Fireproofing of Buildings Chap. 23 thickness may be estimated on a basis of 1 20 lb per cu ft for plaster, and 96 lb for cinder concrete, slightly tamped. Construction of Solid Two-Inch Partitions. Figs. 65 and 66 show the usual method of constructing 2-in partitions. The studs, usually J^-in or i-in %* Channel- Furring for Base' 3^ Steel Rod- FlG. ( R'juLrli Frame Staple/ No. 18 Gai. Wire Lacing.^ Two-inch Solid Plaster Partition. Horizontal Section channels, are bent and punched at the ends, and at the bottom are nailed to wooden strips, which are first secured to the floor-panels, or to the top of the steel beams where the partitions come over them. These wooden strips have been found necessary as a sort of cushion to allow the studding to expand in case of fire. At the top, the studs are nailed to the underside of the floor-panels, or, if there is a suspended ceiling, they are wired to the bars supporting the ceiHng. At the openings, i by i by sig-in angles are used, and these are bored every 16 in for No. 12 screws, used in attaching the rough wooden frames to the angles. After the studding is in position, the metal lathing is laced to one side of it with No. 18 galvanized wire. After the lathing is in place the car- penter should attach wooden grounds to secure the base, and pegs or spot-grounds for chair-rail, picture-molding, etc. These grounds are secured by staples, and when the partition is plastered, become very rigid. In plastering these partitions, five coats of plaster are required to make a good job; a scratch -coat on one side, a brown coat on each side, and the usual white coat on each side for finishing. It is essential for all thin partitions that a hard-setting mortar be used, such as Acme Cement, King's Windsor Cement, Adamant, or Rock Wall Plaster.* The partitions acquire their stiffness largely from the solidity of the plastering, hence the firmer and harder the plastering the more substantial the walls. Double Partitions. Electric wires and yAn gas-pipes can be run in the 2-in SOLED partitions; but if it is desired to run larger pipes, double partitions, X Steel Rod' IS^Y ':^'Concret^;:>,^-.o. ^1,^ Rough Frame ^o..l8 Gal. Wire Lacing '' ^2 "x 2"^ >^" L Fig. 67. Four-inch Solid Plaster and Concrete Partition. Horizontal Section that is, partitions with lathing on each side of the studding, must be used. For these partitions, 2-in, 3-in, or 4-in channels, or fiat bars set edgewise, may be used, sheet-steel channels being probably the most economical. When the space between the studs is not filled with mortar or concrete, the double partition * Made respectively by the Acme Cement Plaster Company, St. Louis, Mo.; T. B King & Company, New York; the United States Gypsum Company, Chicago, 111.; ftnd the Rock Plaster Manufacturing Company, New York. Partitions and Wall-Coverings 881 i 1 i t i L will not stand fire and water as well as the solid partition, while it is much more expensive. Construction of Solid Four-Inch Partitions. Fig. 67 shows a partial sec- tion through a solid partition finishing 4 in thick when plastered. It has great strength and resistance to fire and water, and afi'ords convenient spaces for pipes and thicker jambs for door-frames. These partitions have cores of cinder concrete, with metal lath on both sides, and are plas- tered in the usual way. As the concrete will receive nails, no wooden furring is required to fasten the base- boards, chair-rails, and picture-moldings in place. Berger's Economy Studding and Furring. Fig. 68 illustrates a patent stud manufactured by the Berger Manufacturing Company, Canton, Ohio. It is made of No. 18 or No. 20 sheet steel, and in five sizes, varying from % to 11,4 in. The peculiar ad- vantage of this stud is the provision for attaching the lath. For this purpose prongs are punched from both sides of the flange, which are left standing at right-angles to the face of the flange. The lath is placed against the stud, the prongs pressed through the meshes and then turned up over the lath with a hammer. This fastens the lath more firmly and securely than by any other method. The ends of the studs are secured by sockets which are fastened to the floor and ceiling, a clear space being left above the top of the studs for expansion. Where partitions intersect or where there are angles, angle-irons with prongs are used in place of the T irons. By using these studs and expanded-metal lathing, a saving in cost can be effected over the construction shown in Fig. 66. These T's are used, also, for supporting suspended ceilings under I beams, the T's being secured to the flanges of the beams by specially de- signed clips. Furring-strips and channels, also, are made on the same principle. Spacing of Studs in Two-Inch Solid Partitions. For 2-in solid partitions with ys-in roUed channels or I -in Economy Studs, the studs should be placed 12 in on centers when the height of the story exceeds 10 ft. When the height of the story is less than 10 ft, a spacing of 16 in will answer. For hollow partitions with 2-in studs, the -studs can be spaced 16 in on centers for story-heights of 61 ft and less. For greater heights they should be placed 1 2 in on centers. Rib Stud. In Fig. 69 is shown the Rib Stud made by the Truscon Steel Company, Detroit, Mich. It is made in widths of 214, sH, 4\i, 63,4, and 814 in; and in lengths up to 18 ft. The studs are made of open-hearth steel, the two-rib studs weighing 0.55 lb per ft and the three-rib studs, 0.85 lb per ft. P'or 2-in solid partitions with % or i-in channels or studs, the studs should be spaced from 12 to 16 in on centers, depending upon the stiffness and rigidity of the lath. A 1 2-in spacing should never be exceeded when the height of story is more than 12 ft. For hollow partitions with 2-in studs, the studs can be spaced 16 in on centers for story-heights of 16 ft or less, when No, 24 (United States gauge) expanded metal or No. 18 (United States gauge) wire lath, 2},^ by i Fig. 68. Berger Studding or Furring and Stud- sockets 882 Fireproofmg of Buildings Chap. 23 2}i mesh, are employed. For greater heights the spacing should never exceed 12 in. No. 2 2 (United States gauge) expanded metal, weighing at least 4^4 lb per yard, and No. 20-gauge V-stiffened wire lath or wire lath with rods or stifl- eners spaced 7i,<> to 8 in on centers, give satisfactory rigidity for both partitions " jf J ff jr f f f f f jr /' 2J4 Inches and 3% Indies Wide. k u r* jd y y 9 4M Inches Wide. » el &? &! Bf! a? b! a . 6^ Inches and 8J4 Inches Wide. Fig. 69. Rib Stud for Plaster Partitions and ceilfngs when the studs or furring-strips are set 16 in on centers. Lath should be wired to the metal studding with No. i8-gauge annealed galvanized wire. Metal Lath. Numerous styles of metal lath have been put on the market in recent years to provide for a cheap, light, and thin partition-construction. For fire-proof buildings metal STUDDING should always be used. Metal lath is supplied either plain, painted, or gal- vanized. It is recommended that metal lath be always at least painted, to prevent initial corrosion until the lath can be covered by the mortar. Gal- vanizing is necessary where there is danger of moisture reaching the lath while it is without a protective coat of lime or cement. Where a par- ticular type of lath is not mentioned in a specification, it should be generally described as follows: " Painted or galvanized No. 24-gauge expanded-metal lath, weighing not less than 3H lb per sq yd, or painted or galvanized woven- wire cloth. No. 19 Fig. 70. Expanded-metal Lath with Diamond- shaped Mesh Partitions and Wall-Coverings 883 gauge, 2i/^ meshes to the inch, with stiffeners placed 8 in on centers and weigh- ing not less than s}i lb per sq yd." Metal lath should be so made that it will take plaster freely, key it thoroughly, and wholly embed itself in it. These are characteristics of expanded-metal and woven-wire laths which make them superior to sheet lath. Sheet laths are economical in the use of mortar, which merely covers one side of the lath and latches through the perforations without thoroughly embedding the metal. The difficulty of stretching plain wire lath tight enough to make a firm foundation for plaster and the resulting necessity for a close spacing of the studs to secure the required bearing, has led to the introduction of stiffened wire cloth and ribbed or corrugated expanded metal in order to obtain the necessary rigidity. To overcome the necessity for separate bearing-studs, expanded-metal and sheet-metal laths are manufactured also in a one-piece steel lath-and-stud. Expanded metals differ in the process of manufacture. One type is made by simply slitting the sheet and deploying it into the diamond shape; the^ther type is made from thin strips of soft, tough steel, by a mechanical process which pushes out and expands the metal into the mesh and at the same time reverses the direction of the edge, so that the flat surface of the cut strand is nearly at right-angles to the .general surface of the sheet. It is claimed Fig. 71. Expanded-metal Lath with Rectangular Mesh that the cold work- ing of this low-carbon steel increases the elastic limit and ultimate STRENGTH. In Specifying expanded metal, it is necessary to give the weight of the finished product per square yard as well as the gauge of metal, as the strands may be of various widths. Expanded metal is made either with diamond- shaped (Fig. 70) or rectangular (Fig. 71) meshes. When laid with the long strands per- pendicular to the studs, the lath with the rectangular mesh is the stronger of the two. Rigidity is also obtained by corrugating and expanding the metal in various forms, which make the so-called ribbed, corrugated, and integral laths. Wire cloth is stiffened by clipping corrugated-steel furring-strips to the lath or by weaving or welding rods or V-shaped stiffeners at regular intervals. Types of Metat Lath. Metal lath may be classified as follows: (i) Expanded-metal lath; (a) Diamond and rectangular mesh, (b) Ribbed or corrugated, (c) Integral, combining functions of both lath and studding, (2) Sheet lath; (a) Flat perforated, (b) Integral, combining functions of both lath and studding, (3) Woven-wire lath; (a) Plain, (b) Stiffened. Some of the laths and their characteristics are given in the following para- graphs. 884 Fireproofing of Buildings Chap. 23 (1) Expanded-Metal Lath Rotary Diamond-Mesh Lath. This lath is made by the Berger Manu- facturing Company, Canton, Ohio. It is furnished in sheets i8 by 96 in, of Nos. 27, 26, 25, and 24 gauge, weighing respectively 2^ lb, 2i,<> lb, 3 lb, and 3.4 lb per sq yd. It is made of Toncan Metal, for which greater homogeneity is claimed than for charcoal-iron and steel, and less liability to corrosion or PITTING. Bostwick Lath. Bostwick lath is made by the Bostwick Steel Lath Com- pany, Niles, Ohio. It is furnished in sheets 14 by 96 in, approximately i sq yd, and is made in Nos. 24 and 27 gauge. Steelcrete Lath. This material is manufactured by the Consolidated Expanded Metal Companies, Braddock, Pa., and is furnished in two styles, known as steelcrete A lath and steelcrete B lath, for exterior stucco-work; and in the standard-form diamond lath, extensively used for exterior and in-- terior plastering- work. Steelcrete diamond lath is divided into three desig- nations, P lath, F lath, and H lath. The P lath meets the specifications of the United States Post Office Department, weighs 4.37 lb per sq yd, and is manu- factured from 22-gauge material in sheets 24 by 97 in. The F lath is manufac- tured in sheets 24 by 97 in from the gauges 24, 25, 26, and 27, respectively weighing 3.40, 3.00, 2.55, and 2.33 lb per sq yd. The H lath has a size of sheet 28 by 97 in and is manufactured from the gauges 24 and 26, weighing respect- ively 2.90 and 2.20 lb per sq yd. Steelcrete lath can be obtained manufac- tured from open-hearth black sheets or galvanized sheets, or in copper-bearing sheets (acid-resisting) . A Diamond-Mesh Lath is made by the Penn Metal Company, Boston, Mass., in sheets 24 by 96 in in size and of the following gauges: No. 22, weighing 4 lb per sq yd; No. 24, weighing 3.4 and 3 lb per sq yd; No. 26, weighing 23^ lb per sqyd; and No. 27, weighing 2.3 lb per sq yd. For such extraordinary, conditions as are found in gas-plants, dye-works or places where excessive moisture or salt-air action exists, Hampton Rust-Resisting Lath is made. Key Expanded-Metal Lath, made by the General Fireproofing Company, Youngstown, Ohio, is furnished in sheets 24 by 96 in, in Nos. 27, 26, 25, and 24 gauge, weighing respectively 2.34, 2.50, 3.00, and 3.40 lb per sq yd. Kno-Burn Lath, made by the North Western Expanded Metal Company, Chicago, 111., is .furnished in sheets 18 by 96 in, in Nos, 27, 26, 25, and 24 gauge, weighing respectively 2},^, 2\'2, 3, and 3.4 lb per sq yd. When made from a special acid-resisting sheet steel, this lath is sold under the name XX Century Expanded Metal Lath. Herringbone Expanded Metal Lath (Fig. 72), made by The General Fire- proofing Company, Youngstown, Ohio, is furnished in three styles. A, AAA, and BB. Style A is made in sheets 13^^ by 96 in (i sq yd), of No. 28-gauge metal, weighing 3 lb per sq yd. Style AAA is made in sheets 18 by 96 in, and from 27, 26, and 24-gauge metal, weighing 2.53, 2.81, and 3.79 lb per yd, respectively. Style BB is made in sheets 2014 by 96 in {i^i sq yd), of Nos. 27, 26, and 24-gauge metal, weighing respectively 21^, 2},^, and 3-% lb per sq yd. It is made of steel, American ingot-iron, or galvanized sheets. Ribs are set across studs and slope down towards them. Sykes Expanded Cup-LatK, made by the Sykes Metal Lath and Roofing Company, Niles, Ohio, is furnished in sheets 18 by 96 in, with an antirust coating, or painted black, or galvanized. It is made of Nos. 27, 26, and 24- ^auge metal, weighing respectively 2.8^ 3, and 3.7 lb per sq yd, Expanded-Metal Lath 885 Standard Rib Lath, made by the Truscon Steel , Company, Detroit, Mich., is furnished in sheets 20H by 96 in, in grades i, 2, and 3, weighing respectively 2.74, 3.42, and 4.10 lb per sq yd. This company makes also the Beaded Plate Fig. 72. Expanded-metal Lath, Herringbone Mesh Rib-Lath, which is about 35% heavier and more rigid, permitting wider spacing of the studs. Netmesh Diamond Expanded-Metal Lath is manufactured by the Mil- waukee Corrugating Company, Milwaukee, Wis. This lath is furnished in sheets, 24 by 96; in 27, 26, 25, and 24 gauges, painted; and in 26 and 24 gauges only, hot-galvanized after cutting. This Company, also, makes corrugated OR SELF-FURRING LATH, in sheets 21 1.^ by 96 in, same gauges, except No. 25, as for NETMESH. Kno-Fur Lath, made by the North Western Expanded Metal Company, Chicago, 111., is furnished in sheets 22 by 96 in, of Nos. 24, 25, 26, and 27-gauge metal, weighing respectively 3.80, 3.36, 2.82, and 2.62 lb per sq yd. This lath has ribs running obliquely across the sheets at the same angle as the strands of the mesh. This corrugation is said to give the lath greater rigidity so that it can be used on 32-in centers for walls and on 24-in centers for ceilings. The corrugations act as furring-strips. It is made from a special acid-resisting STEEL and is always supplied painted. Integral Expanded-Metal Lath. Truss-metal lath, Fig. 73, made by the American Rolling Mill Company, Middletown, Ohio, is furnished in sheets Fig. 73. Truss Metal Lath 28 by 90 in, of Nos. 26 and 28-gauge metal, weighing respectively 80 and 66.7 lb per 100 sq ft. A partition constructed of this lath in one of the test-structures at Columbia University, New York City, passed through and withstood, with- out any sign of distress, the fire and hose-streams of five successive tests. Self-Sentering, made by the General Fireproofing Company, Youngstown, Ohio, is furnished in sheets 29 in wide and in lengths varying by i ft, from 4 to 886 Fireproofing of Buildings Chap. 23 12 ft, of Nos. 28, 26, and 24-gauge metal, weighing respectively 0.58, 0.70, and 0.93 lb per sq ft. The width of 29 in is the covering capacity, as laps are pro- vided for by outside ribs. (See, also, page 853.) Hy-Rib, made by the Truscon Steel Company, Detroit, Mich., is furnished in three types known as 4-Rib, 3-Rib, and Deep Rib. The first is in sheets loj,^ in wide, and the others in sheets 14 in wide. (See, also, page 853.) All styles are furnished in Nos. 24, 26, and 28-gauge metal. The standard lengths are 6, 8, 10, and 12 ft. Other lengths below 12 ft are cut, but the waste is at the cost of the purchaser. Hy-Rib sheets interlock at the sides and ends. In ordering, no allowance need be made for side laps, but for end-laps 2 in should be allowed for laps over supports, or 8 in between supports. Trussit is manufactured by The General Fireproofing Company, Youngs- town, Ohio, in sheets 19 in in width, and in lengths of 8, 10, and 12 ft, from 27, 26i and 24 gauge, weighing 0.57, 0.62, and 0.83 lb per sq ft, respectively. (2) Sheet Lath Clinched Lath, made by the American Rolling Mill Company, Middle- town, Ohio, is furnished in sheets 13 ^ by 96 in (1 sq yd), of No. 30-gauge metal, weighing 43,4 lb per sq yd. Truss-Loop Lath, Fig. 74, made by the Bostwick Steel Lath Company, Niles, Ohio, is furnished in sheets 13],^ by 96, 161,4 by 80, and 24 by 96 in, weighing 434 lb per sq yd. This lath is furnished painted unless otherwise specified. Genfire Sheet-Steel Lath, made by the General Fireproofing Company, Youngstown, Ohio, is furnished in sheets 24 by 96 in, weighing 4.6 lb per sq yd, painted unless otherwise specified. Sykes Trough Sheet Lath, made by the Sykes Metal Lath and Roofing Company, Niles, Ohio, is furnished in sheets 131,2 by 96 in (i sq yd), 151,^ by 96, i8l^ by 96, and 231.^ by 96 in, weighing 5 lb per sq yd, and made with an antirust coating, or painted or galvanized. Integral Sheet Lath. Rib-Truss, made by the Berger Manufacturing Company, Canton, Ohio, is furnished in widths of 24 in, and in stock lengths of 4, 5, 6, 8, 10, and 12 ft, as follows: Fig. 74. Bostwick Truss-loop Lath Gauge Weight per square yard in pounds 1 3-2-10 rib H -in rib 73 78 81 86 88 94 117 125 27 28 26 24 83 92 100 133 Woven-Wire Lath 887 (3) Woven-Wire Lath Woven-Wire Lath is furnished with or without stiffeners, which are either rods or V-shaped ribs running through the wire mesh to reinforce and stiffen it. It is suppHed painted or unpainted, or it is galvanized after weaving. It can be furnished to order in any required width up to lo ft. In widths less than i8 in, there is a small charge for stripping. Before ordering, it is very important to ascertain the proper width, especially of stiffened lath, as it is desirable to have the edges of the lath lap at the supports where it is laced to iron furring. When the lath is not of the proper width the results are not so good and there is hable to be a waste of material. The standard width of plain and of V-rib stiffened LATH is 36 in. When beams or studs are spaced 16 in from center to center, the lath should be 32 or 48 in wide. The Clinton Stiffened Lath has corrugated-steel furring-strips attached every 8 in, crosswise of the fabric, by means of metal clips. These strips con- stitute the FURRING, and the lath is applied directly to the underside of the floor- joists, or to planking, furring, brick walls, etc. This lath is made in 36-in widths, with 2)4 meshes to the inch, and comes in 100-ft rolls. The manufacturers of this lath make, also, a lath stiffened with round rods, H to i in in diameter, spaced from 8 to 12 in apart. It can be had either galvanized or japanned, and in thicknesses from 18 to 21 gauge. Clinton plain wire lath is furnished in roUd 200 ft long. The Roebling Standard Wire Lath (controlled by the New jersey Wire Cloth Company, New York), is made of plain wire CLOTH, in which, at intervals of 73^ in, stiffening ribs are woven. These ribs have a V-shaped section and are made of No. 24 sheet steel, H and i in in depth. The ^-in rib is the standard size for lathing on Woodwork. This lathing requires no furring, and is applied directly to woodwork or to walls, with steel nails driven through the bot- tom of the V, as shown in Fig. 75. The No. 20 V-rib stiffened lathing affords a satisfac- tory surface for plastering, when attached to Studs or beams spaced 16 in apart. The i-in V-rib lathing is used for furring exterior walls. It provides an air-space between the wall and plaster. Where this lath is to be applied to light iron furring, a Mo or ^-in solid steel rod is substituted for the V-rib, and the lathing is attached to light iron furring with lacing wire. This lath is distinguished from the others by the term Solid-Rib Stiffened Wire Lath. The Roebling lath, whether plain or stiffened, is made with 2 by 2, 2^^ by '2H, and 2H by 4-in mesh, the last named being known as close warp. The 2M by 2% mesh is adapted to all plasters contain- ing the usual proportion of hair or fiber. The 2H hy 4-in mesh should be used for hard plasters and thin partitions. The lath can be furnished in widths up to 10 ft, the rolls averaging 50 yd in length. Wall-Boards. There are various forms of wall-boards of an incombustible nature, most of them made of gypsum in combination with felts. They can be used as suljstitutes for laths. They are very light and require but little plaster- ing material When this saving is taken into account, wall-boards cost less than metal lath and but little more than wooden lath with three coats of plaster. The Fig. 75. Roebling V-rib Stiffened Wire Lath 888 Fireproofing of Buildings Chap. 23 boards are generally 32 by 36 in in size, and }4, Me, y^, or l^ in in thickness. The thinnest boards {\i in) weigh i V2 lb per sq ft, and the thickest (3^ in) 2 J^ lb. Wall-boards of asbestos are described on page 819. The best known is transite, made by the H. W. Johns-Manville Company, New York. Sackett's Wall-Board. This is a composite board of three layers of pure gypsum and four thin layers of wool-felt. The boards can be nailed to wooden studding or set flat against solid beams or planks, and can be cut with a saw. For plastering, the best results are obtained by applying first a brown coat of hard wall-plaster, 34 to y^ in thick, and when this is thoroughly set, finishing it with a thin coat of regular hard finish of lime-putty and plaster. Tests and investigations at the Underwriters' Laboratories "have shown Sackett Board, Perfection Brand, to be suitable as abase for fibered-gypsum plasters; and when attached to walls, ceilings, and partitions and coated with V2 in of plaster, possess fire-retarding properties considerably higher than those of wooden lath with gypsum or lime-and-cement plaster." The Perfection Brand, Sackett's Wall- Board, is H in thick, and is attached with No. 10^2, 3^-in, flat-headed, ^-barbed wire nails, i M in long, and spaced not more than 6 in at each support. Sackett's Board is made by the United States Gypsum Company, Chicago, 111., and the Grand Rapids Pluster Company, Grand Rapids, Mich. Other makers of gypsum wall-boards are the J. B. King Company, New York (Diamond Brand), the Southern Gypsum Company, North Holston, Va. (Economy Brand), and the American Gypsum Company, Port Clinton, Ohio (Monarch Brand), Metal-Rib Plaster-Board is composed of alternate layers of strong absorbent paper reinforced with fine annealed wire about 2 in on centers, and stiffened transversely with 3'2-in iron bands. No. 32 gauge, placed 8 in on centers. The material is made up to a total thickness of about \\& in, impregnated with- a coal-tar product, and provided every 2 in with Me-in circular holes to key the plaster. This is added to the adhesive effect of the absorbent paper. It is furnished in rolls 85 ft long and 34 in wide, nailed directly to the studs or beams set 12 or 16 in on centers, and lapped 2 in at all joints. This board is recom- mended for use with hard -plaster mortars only, and forms a satisfactory basis for three-coat work, in which the lap-joint obviates the cracking frequently associated with ordinary plaster-board construction. Bestwall. Bestwall is primarily intended for use as an interior finish on side walls and ceilings in buildings of all classes. It may be used in all situations where finishes of lath and plaster may be used, and in many situations where the latter finish is not adaptable. It consists of a single layer of fiber calcined gypsum, surfaced on each side with specially prepared water-proofed paper se- curely bonded to the surface. Bestwall is ^ in in thickness, and is furnished in ' stock sizes 47% in wide, and in lengths of 5, 6, 7, 8, 9, and 10 ft. The finished product presents a smooth, true surface, which is light cream in color on the face-side and gray on the reverse side. The edges are sHghtly beveled to pro- vide for the filling of the joints, and are doubly reinforced. Its weight is ap- proximately 1850 lb per 1,000 sq ft. Interior finish composed of Bestwall is applied by nailing the Bestwall directly to the joists, studs, and furring, and filling the joints between the pieces of Bestwall with a specially prepared filler of the same composition as the core of the board. For the nailing, threepenny fine wire nails, spaced from 2 to 3 in at the edges and from 8 to 1 2 in at the inter- , mediate supports, are used. The filling consists of two operations; first, rough- ing IN and then, troweling out, to a smooth, true finish, flush with the surface. Bestwall is cut and fitted either with a saw or by scoring and breaking over a straight-edge. The completed finish presents a smooth, true, continuous surface, Deadening Properties of Partitions 889 without showing joints or nail-heads, and ready to receive, if desired, a decoration • of paint, paper, tint, etc. Shaft-Construction. The most important partitions in a building are those inclosing interior shafts. Vertical openings through buildings form flues and cause up-drafts. In all buildings, fire-proof as well as non-fire-proof, therefore, they should be inclosed for two reasons: first, to prevent a fire that would find a natural outlet in such openings from spreading to other floors; and secondly, to prevent, as far as possible, a fire from getting into these openings where the draft would greatly increase its fury. To be thoroughly effective the inclosed walls should be constructed of the same materials as the outside walls of the buildings, namely, brick, stone, or concrete. While they need not be of the same thickness as the outside walls, 12 in is recommended as a minimum thick- ness. In less important structures terra-cotta partitions are sometimes used for such inclosing walls. In the walls inclosing elevator-shafts no openings except those necessary for entrance-doors should be permitted. The doors should be of fire-proof construction, pages 901-2, and made solid. Glass lights are sometimes provided in such doors, although this is not good practice; if they are used, wire-glass, only, should be used, in accordance with the limita- tions noted on pages 90^-3. Open grille-work for passenger-elevator enclosures is being rapidly superseded by construction which is more fire-resisting. The architectural features of open grilles may still be retained for the fronts and doors of such elevators by using them in conjunction with approved wire-glass con- struction. In interior light-shafts and vent-shafts, openings must necessarily be provided, but here again the construction of the window- frames, sashes, and glazing should be as far as possible as described on pages 901 to 903. When- ever the occupancy of a building admits, the stairs, also, should be inclosed in masonry walls, with fire-proof doors at the openings. Unless so inclosed the stairways form flues for the flames, and the stairs themselves, consequently, are exposed to intense heat. In such situations, even absolutely fire-proof stairs could not be used during a fire, and possibly it is for this reason that greater pains have not been taken to make them fire-proof. Shaft-walls should in all cases be carried 3 ft or more above the roof. Deadening Properties of Partitions. The resistance to the passage of sound thrcaigh fire-proof partitions is an important consideration in buildings used for living-apartments; and where the rooms are to be used as music-studios, it becomes a matter of still greater importance. In January, 1895, some tests were made to determine the relative deadening properties of the different partitions shown in Fig. 76, the object being to decide upon the construction that should be used in Steinway Hall, Chicago, 111. The rank of the different partitions tested, in sound-proof i:fficiency, is shown by the numbers at the right of the partition-diagrams. The 4-in porous partition was used, but was not a success. In the Fine Arts Building, in the same city, double partitions, similar to No. i, were used, and it is said that they were a great success. It is surprising to note that in the tests above mentioned, the 2-in-solid~plaster par- tition. No. 3, plastered with common mortar, ranlced higher in sound-deadening properties than those with double studs. In 1892 C. L. Norton tested the sound-deadening properties of partitions of several forms, for the purpose of selecting a construction which was the most fire -resisting and sound-proof for the dormitories of the New England Conservatory of Music, in which prac- tically every room is a music-studio.* The various partitions were rated by Professor Norton as shown in the following table: * The results of these tests, with a description of the partitions, were published ii^ Insurance Engineering for August, 1902. 890 Fireproofing of Buildings Chap. Air Space ^Plaster Plabter-^ ^»W' c Angle Iron'^ f ^^ ^^'^'^ ^^*^ Filled in solid 12 "Centers \ with EUistei; ^Wire Cloth Laced to Rod. SOLID PLASTER PARTITION K -2 Studs 16 Centers 'Wire Cloth. Laced to Rods »^" Rod 12" Centers'^ ""y^^^^nu^mnU) ' Centers X .vNt.,Fijlinj^. _ Expanded-Metal/ * ^%" yK"l^od 12 "Centers 5 2 "iron Studs 16* Centers ^Wire Cloth Laced to Rod \Plaster /Iron 16" Centers J^xpanded.Metal- Expanded Metal- Mron IG" Centers Fig. 76. Relative Deadening Properties of Partitions Furring for Outside Walls 89J Table XVI. Sound-Deadening Properties of Partitions No. Room Side Scale I E Left lOO 2 E Right .95 3 E Rear 95 4 C Rear 85 5 C Left 85 6 C Right 8o 7 D Rear 75 8 D Right 75 9 B Right 6o lO A Rear 50 II - B Rear 50 12 A Right 45 13 B Left 40 14 A Left 40 IS D Left 30 Composition Cabot's quilt, 3 thick and metal lath Cabot's quilt, 2 thick and metal lath Cabot's quilt, 2 thick and metal lath Sackctt board, 2 felt on channels Sackett board, 2 felt on channels Sackett board, 2 felt Metal lath and paper Metal lath, paper, and felt Two 2-in Keystone blocks with 2-in air-space 4-in National tcrra-cotta blocks 3-in Keystone blocks 3-in National terra-cotta blocks 2-in Keystone blocks 2-in National terra-cotta blocks 2-in metal lath, solid plaster "Nothing more is to be inferred from the numerical efficiencies, under 'scale,* than that the first partition is about three times as good as the last, and that the numerical interval between any two partitions on the list merely indicates the order of the magnitude of the difference between the partitions." Professor Norton recommended a partition of Sackett Board and plaster with two thick- nesses of Cabot's ciuilt between the plaster-boards, and this construction was adopted. The studding was put up the same as for the 2-in solid partition, the quilt secured to each side of the studs, and the plaster-board wired on to the studs through the quilt. This makes as light a partition, also, as it is possible to construct. The investigations by Professor F. R. Watson of the University of Illinois showed that 2-in solid, metal-lath partitions are more sound-deadening than 3-in hollow, gypsum-block partitions. Gypsum tile has been found to be more satisfactory than, terra-cotta tile of the same thickness. Furring for Outside Walls. The outside walls of fire-proof buildings are generally finished on the inside by plastering applied directly to the masonry. When the walls are of brick, it is often desirable to fur them so that there will be an air-space between the plaster and the masonry to prevent the passage of moisture. This furring should be either of terra-cotta or metal, and never of wood. For this purpose furring-bricks may be used. They are made of brick- clay and of the same size as common bricks; but they are hollow. They are built up with the rest of the wall, on the inside face, and bonded into the wall by the usual header-courses. Split furring-tiles, also, are often used on the inner side of brick walls, as shown in Fig. 77. The tiles are either i Y^ or 2 in thick and 12 by 12 in on the face. The face is grooved to give proper bond for the plastering. At recesses in the walls partition-blocks are substituted across the openings, making a continuous wall-surface. When using furring-tiles, the mason should be careful not to drop mortar into the hollow spaces. When walls are furred or lined with tile, solid porous terra-cotta blocks should be built in wherever nailings are required for bases, picture-moldings, etc. Wire lathing, also, with i-in V ribs woven in every 7H in, makes a good furring for brick walls, as it is easily applied and leaves air-spaces between the wall and plaster. All of these devices also protect the walls from being warped by heat during a fire, and prevent the passage of heat through the walls in summer and winter. 892 Fireproofing of Buildings Chap. 23 Metal Furring. To produce architectural forms in the interior decoration of fire-proof buildings, metal furring and metal lath are now almost uni- versally used. The furring is always of a sham nature, and never employed Fig. 77. Hollow-Tile Wall-furring to carry loads of any magnitude; so that the only requirement is that it shall be incombustible and furnish a satisfactory ground for attaching the metal lath. For coves, cornices, false beams, etc., the furring-members are made of light bars, angles, tees, or channels, attached to the walls by means of nails, staples, or toggle-bolts, and to the steel beams by means of bolts, hangers, chps, etc. The furring-pieces are bent or shaped to the approximate outlines of the finished plaster-work, so that when the lathing is applied it will require not more than I ]i or 2 in of plaster to give the desired outline. For plane surfaces, the furring should be brought to within % in of the plaster-line. Deep beams, etc., should be braced by diagonal rods, to prevent distortion. All structural-steel members should always be fire-proofed back of the furring. The lathing is secured to the furring by means of No. i8 galvanized lacing-wire. The spacing of the furring should be either 12 or 1 6 in, according to the kind of lath that is to be used. When chases in walls are covered over, the covering should be done with metal furring and lath. The casings for vertical pipe-lines, also, should be of this construction and the space about the pipes at the floor-level should be filled solidly with fire-proof material, to cut off all connection between stories. 7. Fire-proof Flooring Fire-proof Flooring. The floor-surfaces of most fire-proof buildings consist of hard-wood flooring secured in the usual manner to nailing-strips embedded in the concrete or in the filling above it. It is sometimes advisable to use in- combustible flooring. The New York City Building Code requires that in all buildings over 150 ft in height, the floor-surfaces shall be of stone, cement, tiling, or similar incombustible material, or of wood treated by some process which renders it fire-proof. For warehouses and factories, floors finished with Portland-cement mortar are about as satisfactory as floors with any other over- floor finish; and cement floors have been much used for the guest-rooms of Fire-proof Flooring 893 hotels. In the latter rooms, the floors are covered with carpets, which are secured to wooden strips embedded in the cement around the borders of the rooms. This makes a very sanitary floor, and one as easy for the feet as a car- peted wooden floor. For pubHc corridors, banks, lobbies, toilet-rooms, etc., the encaustic, vitreous, ceramic, or marble tilings are generally used. In France and Germany large quantities of cement tiles are used. Cement tiles have been in- troduced into this country, also, but have not yet been able to compete with the encaustic tiles. In most buildings, however, the use of stone, cement, or tile flooring is inadvisable. These materials are cold and trying to the feet. As a rule, cement floor-surfaces do not wear well. Asphaltic flooring is sometimes used, but it is not pleasing in appearance. This material and different floor- tiles are discussed on pages 1604 to 1609. The characteristics of fire-proofed wood and its availability for this purpose are considered in the discussion of that material on page 820. Composition Flooring. Several attempts have been made to obtain a flooring-material which could be spread, without joints, over an entire floor, and at the same time be elastic, wear well, withstand water, acids, etc., and not be too expensive. Various mixtures of magnesite, asbestos, fine sand, sawdust mixed with linseed-oil, and some binder hke chloride of magnesium, have been put on the market under different names, all more or less meeting the require- ments above stated and being, also, fire-proof. These materials are shipped in the form of a dry powder to the place where they are to be used, and are there mixed with a speciafly prepared liquid. The resultant is a plastic material which is laid upon the surface to be covered in much the same way that ordi- nary cement or plaster is put on. The materials harden in from 12 to 24 hours in moderately dry weather, when the floor is ready for use. When properly laid the floor presents a smooth, fine-grained, and continuous surface, resem- bling linoleum. These materials are made in various colors, such as red, white, yellow, brown, gray, black, blue, and green, and can be laid on wood, stone, concrete, asphalt, cement, or metals. Another advantage is that they can be carried up on the walls so as to form a covered base, without cracks or joints. Among the manufacturers furnishing such floorings may be mentioned: General Kompolite Company, Long Island City, N. Y.; Marbleoid Company, New York City; Franklyn R. Muller Company, Chicago, 111.; and Ronald Taylor Company, New York City. Asphalt Mastic Flooring. This flooring is in the nature of an asphaltic CONCRETE consisting of natural asphalt and a well-graded mineral aggregate of sand, gravel, and crushed stone, ranging in size from that which passes a 200- mesh screen to ^ in. The material is sent to the building-site in blocks and is there broken up, reheated, and mixed with the coarser aggregate, the softened mass being laid down in one or two courses, depending upon the thickness desired, and smoothed down by rubbing with wooden floats. It is laid without construction-joints, the usual thickness being ij^ in, weighing 18 lb per sq ft. The finished flooring is tough, ductile, water-proof, resistant to acids, alkaU and brine, fire-proof, noiseless, and easy on the feet. It is especially suitable for factories and warehouses. It is manufactured by the H. W. Johns-Manville Company, New York 8. Interior Finish and Fittings Interior Finish. In buildings in New York City in which the flooring must be of incombustible material, the interior finish, also, including the doors, door- jambs, window-frames, sashes, bases, and trims, must be made of incombustible 894 Fireproofing of Buildings Chap. 23 materials. The same materials that are accepted for flooring can be used for this interior finish also. Several of the largest buildings in New York City, including the Fuller Building, have all the trim constructed of fire-proof WOOD. In the Hotel Gotham, all the doors and interior finish are made of Alignum. Metal Doors, Sashes, Frames, and Trim.* The effort to make the interior of buildings fire-proof has resulted in metal-covered wood, and in doors, sashes, frames, trim, and moldings of hollow steel or other metal. Many very large buildings have in recent years been equipped wholly or in part with these products, and the products themselves have reached a stage of great perfec- tion of workmanship and efficiency. Several cities in the United States compel the use of these products for certain parts of buildings which are over a certain height; and it is probably only a question of time when other cities will pass ordinances compelling their use. At the present time cost enters largely into the question of substituting them for wood. Among the first attempts in the United States to fire-proof the interior trim of buildings were those made in New York City, about the year 1880, in the form of metal-covered woodwork, by the firm of Campbell & Bantossell of that city. About this time, also, there were introduced along with various processes of fire-proofing woodwork, FIRE-PROOF PAINTS. Later, fire-proof wood was introduced, that is, wood which has the resin and other inflammable components extracted from it, and the fiber left. In the course of a few years the metal-covered- wood industry developed to such a stage that it was possible to trim with its products the interior of a building and keep a good appearance. Notable examples are the Manhattan Life Insurance Company's Building and the Barclay Building, and, of more recent date, the Metropolitan Tower, f the Fifth Avenue Office-Building, the Germania Life Insurance Company's Building, and the Var.derbilt Hotel, all in New York City; the Hoge Building, Seattle, Wash.; the Hall of Records, Los Angeles, Cal.; the Rockefeller Annex, Cleveland, Ohio, etc. The rough, unfinished appearance of the standard tin-clad door set men to seeking a product for use in interior finish which would lend itself to rnore decorative effects. The Xalamein iron and other metal-covered work resulted. In the meantime improvements were constantly being made in hollow sheet-metal doors and trim, and from about the year 1903 hollow steel construction for this work came into use. Owing to its generally superior workmanship and to the splendid enamel surfaces which can be given it by Various baking-processes, this type of interior finish has found favor in the eyes of the architects and owners of modern offices, and mercantile and public buildings. Kalamein Iron. J Kalamein Iron is the trade name given to one of the open-hearth sheet-steel products which is covered with a thin alloy of tin and lead in much the same way that galvanized iron by galvanic immersion is coated with zinc. "The name Calamine (with Galmci of the Germans) is commonly supposed to be a corruption of Cadmia. Agricola says it is from * For a brief outline of this subject, illustrated with numerous detail drawings, see article on Metal Doors, Sashes, Frames, and Trim, by Professor Thomas Nolan, in Kidder's Building Constructon and Superintendence, Part II, Carpenters' Work. t The Metropolitan Tower has a metal-covered trim which is a special bronze-pl^te construction over a wooden core. This was developed by The John W. Rapp Company, afterwards consolidated with The J. F. Blanchard Company into the United States Meta? Products Company, New York City. t Among the better known manufacturers of metal-covered work, whose doors are inspected and labeled by the Underwriters' Laboratories, Inc., are the United States Metal Products Company, New York. City and the Thorp Fireproof Door Company, Minneapolis, Minn. Interiot Finish and Fitting^ 895 Calamus, a reed, in allusion to the slender forms (stalactic) common in the Cadmia formation."* The term Kalamein is often used incorrectly, by archi- tects and others, for any form of metal-covered woodwork, whether the metal is steel, copper, or bronze, to distinguish metal-covered from hollow metal con- struction; but the term is obviously misleading and causes much confusion. In several instances architects have specified Kalamein material expecting bronze METAL to be used in the covering, whereas the manufacturer's interpretation of the specification was that Kalamein iron was intended. Metal-Covered Doors, Frames, and Trim. The cores of metal-covered doors and frames are built up of oak or white-pine strips dovetailed together lengthwise to the grain. In gluing up the strips into stiles and rails the grain of each strip is reversed, in order to resist the tendency of the core to twist. The stiles and rails are mortised, tenoned, and box-wedged, and the cores are covered with asbestos paper or board and enclosed with sheet metal, either steel (which may be painted to match a wooden trim, or electroplated with copper, brass, or bronze), or soHd sheet copper, brass, or bronze. For doors up to 3 ft 4 in in width and 8 ft in height, both sides are often made of continuous sheets of metal, which have the panels pressed into them by hydraulic pressure and are without seam or joint. The metal sheets of the two sides, in one make of door,t are made to overlap in a depression on the edges of the door and are secured in place by screws which pass through both face-sheets. The standard thickness of this door is 2j^ in. When these doors are more than 3 ft 4 in in width, each face is generally made of two sheets which meet over a middle stile and lock together with a flush double-lock joint. This makes a double row of vertical panels. Metal-Covered Window-Frames and Sashes. Window-frames and sashes, as well as door-frames and doors, are made of metal-covered wood. Bronze is the metal usually recommended and preferred although Kalamein iron may- be substituted when a much cheaper construction is necessary. This cheaper metal may be painted and will give fair service but it is not recommended. Galvanized iron and copper, also, are used. " Window-frames and sashes of Kalamine or of sheet-metal over wooden cores are principally used for windows or skylights where the only danger of fire-contact is through flying sparks. They are non-combustible rather than fire-resisting. The lights are usually of plate glass, especially if Kalamine trim is used simply to comply with the law in those cities where non-combustible windows and doors, etc., are required in buildings of a certain class or of a height a^ove fixed Hmits. Previous mention has been made of their efficiency as demonstrated in the burning of the Kohl building in San Francisco, and their value, even as a substandard protection, has been pointed out; but for efficient fire-resistance, Kalamine windows, especially, are an unknown quantity, as the resistance offered by the lighter members, such as sash-rails, is questionable. The better examples of the work present pleasing workmanship and finish. If some composition could be used.for the body instead of wood, without producing chemical action harmful to the metal, a superior type of Kalamine work would result which would be of great value." | Hollow Metal Finish in General. § The transition from metal-covered * Dana's Dictionary of Mineralogy. t The Richardson seamless door, made by the Thorp Fireproof Door Company, Minne- apolis, Minn. X Fire Prevention and Fire Protection, by J. K. Freitag. § Among the better-known manufacturers of hollow, sheet-metal doors, trim, etc., are the Dahlstrom Metallie Door Company, Jamestown, N. Y.; the National Automatic 896 Fireproofing of Buildings Chap. 23 wood to HOLLOW SHEET METAL for doors, sashes, frames, trim, moldings, etc., was naturally and easily made and to-day the latter type of construction, when expertly carried out, results in details for interior work which are very efficient to resist fire and handsome in appearance. It would be difficult to devise con- structional details which would be more satisfactory and at the same time present greater possibilities in the way of elaborate design and high finish; and it is on account of all these advantages that this type of construction is used in the interior equipment of many of the best examples of fire-resisting build- ings, especially for the doors, frames, sashes, and trim of corridors, hallways, stair and elevator-enclosures, and even for entire office-partitions. Because of the non-absorbent character of the baked-enamel finish this material is partic- ularly sanitary; and hollow metal doors are more easily cleaned than any others, especially if all moldings are omitted and panels made simply as smooth depres- sions. The thickness of standard hollow metal doors approved by under- writers, varies from iK to 23^ in. Hollow Metal Doors. The Dahlstrom patent sheet-metal door* is made from two No. 20-gauge-steel plates, one stile and one panel-face being formed from each of the sheets, which are connected by interlocking seams on opposite sides of the panels and make practically a double door. In construct- ing the panels they are first lined with a sheet of asbestos next to the steel on each side, and the space between is filled with a layer of hair-felt paper, which makes a resilient filling that is a non-conductor of heat. The stiles are left hollow, but strips of cork are laid perpendicularly across the center of each to deaden the metallic ring. The panels are then attached to each other to form the door by planting on and welding in place properly formed cross-rails, at the top and bottom, and wherever else they may be desired; the moldings are coped over the molded stiles at the sides. The top and bottom edges of the door are then reinforced with channels and bars, and the doors made perfectly straight and rigid. The fire-resistance of this construction is increased by letting no rivets or screws pass through from one side of the door to the other in the exposed parts. The transmission of heat is thus avoided. While the door is being put together, provision is made for attaching the hardware. After the doors have been put together, they are sent to the finishing department where the steel is thoroughly cleaned from all rust, grease, or other impurities. They are then given six or eight coatings of enamel, being baked after the application of each coat in large ovens which are heated to 300° F. After the final coat of varnish is put on, they are usually rubbed to an egg-shell, gloss-finish, equal in quahty to any hardwood-finish, and more durable because baked on. The surfaces can be grained to imitate with wonderful exactness any wood, such as quartered oak, mahogany, Circassian walnut, etc. If the doors are to receive glass panels they are provided with detachable moldings to hold the glass in place. Doors of the Dahlstrom, hollow metal type are installed in the corridors and partitions of the Singer Building and towerf, and the United States Express Building, New York City; the Bell Telephone Ex- change Building, Philadelphia, Pa.; the Seventh Regiment Armory, Chicago, 111.; the Pontchartrain Hotel, Detroit, Mich.; the Bank of Commerce Building, St. Louis, Mo.; the First National Bank Building, Denver, Col.; and the Royal Insurance Building, San Francisco, Cal. In some of the buildings men- Door Company, Chicago, 111.; the Solar Metal Products Company, Columbus, Ohio; and the Central Metallic Door Company, Gary, Ind. * Made by the Dahlstrom Metallic Door Company, Jamestown, N. Y. t A severe fire in the twenty-sixth story of this tower was effectually confined to the room in which it originated by the doors of this type of construction. Interior Finish and Fittings 897 tioned in the preceding articles, hollow metal doors, trim, and moldings are accompanied by bronze or other metal-covered wood window-frames, sashes, etc. Hollow Metal Door-Frames, Trim, and Moldings. After the hollow metal door reached an advanced stage of construction the manufacturers turned their attention to the problems involved in making metal frames and moldings. It was found that moldings made by the ordinary hot-rolled PROCESS were too rough and heavy and required too much labor to smooth and finish their surfaces; and that those pressed from light-gauge steel by the common methods were not clear-cut and definite in their outhnes, and were limited in length and in variety of shapes. Accordingly, what is known as the cold-drawn METHOD of making frames, trim, and moldings, was developed and perfected, and moldings made by this process are now used for many kinds of interior work. The cold metal is drawn through special dies to give it the required shape and the bright finish is retained. The corners and angles come out sharp and true and the pieces possess much greater strength and rigidity than those hot-rolled and several times thicker. There are dies for over a thousand shapes. Moldings can now be made in lengths up to 40 or even 50 ft, but extra-freight rates and other drawbacks make it inadvisable to ship it in lengths of over 20 ft. Besides the cold-rolled special high-grade steel, brass, bronze, and copper are used in their manufacture. The rolled shapes include angles, channels, and Z bars; moldings for bases, cornices, wire-conduits, door-jambs, sash-bars, panels, and glass; picture-frames, door and window- casings, and trims of all kinds; wainscoting and chair-rails; and numerous miscel- laneous sorts. Wrought-iron welded one-piece door-frames are made for use in fire-proof partitions. These frames are constructed scientifically of specially rolled wrought iron in. several different shapes. The mitered corners are welded together making the frame one solid piece. They are made for any thickness or type of door or partition, require no bracing, and can be fitted with invisible hinges if required. Hollow Metal Window-Frames and Sashes. (See, also, Sheet-Metal for Fire-Resisting Window-Frames and Sashes, page 902). Hollow metal window- frames and sashes, as well as those which are made of metal-covered wood and of cast iron, wrought iron, drawn bronze, cast bronze, etc., and glazed with wire-glass, prism glass, electroplated glass, etc., are used in those parts of build- ings in which the exposure to fire is not great enough to require the use of hinged or rolling shutters, or where a more pleasing appearance is demanded than that resulting from the use of hinged or rolling fire-shutters. Owing to many im- provements made in recent years, both in design and details of manufacture, hollow, sheet-metal window-frames and sashes are now ranked among the best types of those of moderate cost for general use. The National Fire Pro- tective Association, by its recommendations and standardizations, and the tests and labeling systems of the underwriters' laboratories, have been largely instrumental in bringing about these improvements and results. About the only disadvantage connected with the use of sheet-metal windows is a relatively rapid deterioration when neglected. The materials used for making hollow metal window-frames and sashes are galvanized iron or steel; copper; sheet metal, copper-plated; and sheet metal, bronze-plated. The sashes are glazed with plate or maze wire-glass where good appearance is an essential requirement, or with RIBBED OR ROUGH wire-glass where a translucent material only is desired. Of course, clear glass, unwired, may be used when additional fire-resistance is not the object. The National Board of Fire Underwriters fix, within certain limits, the various constructional details, the maximum permissible sizes of openings for 898 Fireproofing of Buildings Chap. 23 glass, etc. The principal regulations have been very conveniently condensed by Mr. J. K. Freitag.* Solid Steel Windows. Where large window-surfaces giving maximum light are desired, as in factories, the so-called solid steel windows are frequently used. They have been given this name because the frames and muntins are made of solid, rolled-steel sections, jointed at their junctions or intersections by special methods, in some cases oxy-acetylene welded, so as to make strong and stiff frames. The manufacturers generally carry stock sizes varying in approxi- mate widths from 3 to 6 ft, and approximate lengths from 3 to 9 ft. The glass panes are about 12 by 18 in. The movaJDle sections, or ventilators, are pivoted on horizontal axes, though a counterbalance type, also, is made for use in hospitals and public buildings. Ventilators should not exceed 5 ft in either direction, nor more than 18 sq ft in area. Among the principal makers are the Detroit Steel Products Company (Fenestra), Detroit, Mich.; David Lupton's Sons Company, Philadelphia, Pa.; American Steel Window Company, Chicago, 111.; and Truscon Steel Company, Youngstown, Ohio. Electroplated Trim. This product is made by a process which consists in electrically depositing a layer of copper on the outer surface of wooden moldings or doors. The metallic deposit preserves the markings of the grain of the wood and makes a very presentable door. A good sample of this work has been in- stalled in the United Engineering Building, New York City, by the New York Central Metal Company of the same city. Some very fine work of this kind has been done by the Hecla Iron Works of New York City, by electroplating on a fire-proof material known as Lignolith. Cement Trim. Keene's cement has been used for many years for running base-moldings, door and window-trim, etc., and in many European buildings practically all of the interior finish is of this material. Any molding can be run in it with good sharp angles, and it is suf- ficiently hard to stand ordinary usage. Fig. 78 shows a door-opening with a trim of Keene's cement. This detail can be further improved by covering the wooden frame and door with thin metal. The metal and cement can be painted as de- sired. Molded Hollow Tiles for Inside Finish. These are also being substituted for the ordinary wooden finish. The Fig. 78. Door-jamb with Cement Trim Amelia Apartments, erected by H. B. Camp at Akron, Ohio, in 1901,! is built almost entirely of hollow tile. "The bases, the picture-moldings, and the architraves around the doors were made of specially formed tiles, as shown in Fig. 79. These tiles were afterward painted to harmonize with the scheme of color-decoration. All of the floors throughout the building are covered with a cement composition composed of Sandusky cement and ground wood, troweled down smooth and level." Metallic Furniture and Fittings. In offices, banks, libraries, and public buildings, the furniture and fixtures are about the only articles on which a * For the principal regulations, conveniently condensed, see Fire Prevention anrl Fire Protection, by J. K. Freitag. t Described in the journal, Fireproof, July, 1903. Interior Finish and Fittings 899 fire can feed, if the building itself is fire-proof, and if these are made of incom- bustible materials there is no chance for a fire to gain headway or to do much Fig. 79. Hollow-tile Door-trim, Picture-molding and Base '^zzzzzz^zkz^ ^jzmm^^mzz^: ■^zzzzzz^zzzzz^ damage. Almost anything in the way of furniture and fittings, including even roll- top desks and highly ornamental cabinets, may now be obtained in metal; and many Ubraries, banks, and court-houses have been fitted up and furnished entirely with incombustible cabinet-work. Catalogues can be obtained from the leading companies engaged in the manufacture of metal fur- f« 1^— NiTURE, such for example as the Art Metal Construction Company, Jamestown, N. Y., the Berger Manufacturing Company. Canton, Ohio, the Van Dorn Iron Works, Cleveland, Ohio, and the Library Bureau, New York City and Bos- ton, Mass. Stairs. In a majority of fire- proof buildings the architects have contented themselves with putting in INCOMBUSTIBLE STAIRS of iron, with perhaps slate or marble treads. As pointed out in the first pages of this chapter, unprotected iron cannot be considered fire-proof, but it is difficult to protect the ironwork of a stairway, as it is usually built, and at the same time preserve an ornamental effect. If exposed metal construction is to be used, cast iron is much to be preferred to steel, as the cast metal will retain its shape under severe heat far better than thin facings or frameworks of steel. Slate and marble treads and platforms, unless supported underneath, should never be used in staircase-construction. When subjected to heat, marble and slate crack and fall away, leaving the stairs impassable. A fire-department captain in New York City lost his fife through the collapse of a marble platform. If these materials are to be used, therefore, there should be a subtread of iron or concrete beneath them. A really fire -proof staircase should be constructed with as little Fig. 80. Hollow-tile Steps for Staircase 000 Fireproofing of Buildings Chap. 23 ironwork as possible, and what ironwork there is, incased in Tire-resisting materials. It is possible and practicable to build stairs of clay tiles, bricks, or reinforced concrete, that are absolutely fire-proof. The stairs in the Pension Building at Washington, D. C, are built of brick, with the exception of the treads, which are slate; and in many of the earlier government buildings the stairs are of stone. Stones suitable for stairs, however, are not as resistant as cast iron to heat. Part I of Building Construction and Superintendence* contains descriptions and illustrations of ' brick stairs. The Guas- tavino Company has built several stair- cases according to its system of construction, using flat clay tile em- bedded in cement. No iron-work whatever is used ' in this con- struction; hence it is eminently fire-proof. Fig. 80 shows a par- tial section of a tile staircase such as was used in the Amelia Apartment Building, Akron, Ohio. The blocks were of hard-burned material, glazed, and 4 ft long. They were supported upon the partition-walls and were used by the mechanics for carrying up material during the erection of the build- ^■jSar 13'onCentei Fig. 81. Reinforced-concrete Stairs, Government Printing Office, Washington, D. C. Fig. 82. Ferroinclave Foundation for Stair-treads and Risers ing. Reinforced concrete, with slate or marble treads, is a good material for the construction of stairs, and permits of very elaborate and complicated construc- tion. Fig. 81 1 shows the construction of the stairs in the Government Printing * By Frank E. Kidder, rewritten by Thomas Nolan, t From the Engineering Record, of Dec. 6, 1902. Protection from Outside Hazard 901 Office at Washington, D. C. These stairs have steel girders and strings enclosed in the solid concrete, which is molded to form the steps and risers, as shown in the detail. The steel strings, however, are hardly necessary, as the reinforcing-bars give sufficient strength. Some excellent details for ornamental iron stairs were pubUshed in Fireproof, March, 1903, in an article by J. K. Freitag. The cor- rugated sheet metal, known as Ferroinclave (page 851), offers a very conven- ient foundation for cement stairs. When built between walls or partitions or with an open string. Fig. 82 shows one way in which the material has been used, the stairs being finished with about 2 in of cement over the metal and plastered underneath. The Ferroinclave is bolted to lugs or brackets screwed to or cast on the strings. Slate or marble treads and risers may be embedded in the mortar if desired. (See, also, pages 947 and 983.) 9. Protection from Outside Hazard Window-Protection. To be thoroughly protected against the outside hazard, buildings must have the openings in the outside walls provided with some means of effectively closing those openings against flame. The same provision should be made for openings in the partition-walls of large buildings. Four GENERAL TYPES of dcviccs are in use for this purpose: (i) tin-covered wooden shutters; (2) steel shutters or doors; (3) metal frames and sash, glazed with wire-glass; and (4) v/ater-cur tains. Types of Window-Protection Compared. When properly constructed, the TIN-COVERED WOODEN SHUTTER is Still the most effective window-protection. "In a very severe fire in Lynn, Mass., in which the heat was intense enough to melt most of the tin from the outside of the tinned plates covering the shutters, it was found afterward that the wood was charred to a depth of only about % in. The shutters were warped slightly, but afforded sufficient protection against the heat to allow men to remain behind them to put out such fire as occasionally crept through. This would not have been possible behind iron shutters under similar conditions."* Steel shutters, under the action of heat, warp very readily and transmit considerable heat. They belong to the cheapest type of window-protection. "There is one objection to the use of shutters on window-openings, and that is that they depend on fallible human agency to be effective. They must necessarily be open while the building is in use. When the need for them comes they are apt to be overlooked and are not closed. Certain it is that on many buildings they are not closed at night."* The METAL-FRAME-AND-wiRE-GLASs WINDOWS are not as unsightly as shutters of almost any kind are apt to be. They are more likely to be closed at night and more readily closed when necessary. They do not hide a fire and are more easily opened when it is necessary to reach a fire. The one serious objec- tion to them is the intense radiation of heat from the wire-glass, f Tin-covered Wooden Fire-Shutters and Doors. The effectiveness of this device depends on its construction. "Only well-seasoned non-resinous wood, dressed, tongued and grooved in narrow boards, should be used. Wood containing moisture or resin may generate, under heat, sufficient ^steam or gas to force off the tin covering and expose the wood to the flame. The body of the door should consist of two or three layers of such boards laid at right-angles with each other and fastened together by clinch-nails. The best grade of tin should be used. No solder must be used, and the tin plates should be lock- • Insurance Engineering, Dec, 1902. t For a consideration of water-curtains, see page 903. 902 Flreproofing of Buildings Chap. 23 jointed, with the nails in the seams. The nails must be long enough, at least iH in, to secure a good hold beyond the depth to which the wood is likely to char, which is about % in. Under intense heat the wood is certain to char, but if the nails are long enough to hold the tin up against the wood, and the tin is properly put on so as to keep the air out to prevent burning, the shutter will stand under severe strains."* The hinges, fastenings, or hangers must be bolted to the door, not nailed or screwed, as nails or screws would pull out during a fire. If hung on hinges, the hinge-hook should be built into the wall. This door was designed for use in mills, but it has worked so satisfactorily that it is generally adopted wherever a fire-proof door is wanted and its ap- pearance is not olDJectionable. Fire-proof shutters, also, are made in this way. The National Board of Fire Underwriters issues complete specificationsf for this type of door and shutter, and these specifications should be closely fol- lowed for satisfactory results. Doors of this type, provided for the openings in interior partition-walls, are often, and wherever possible should be, hung on inclined tracks so that they will close automatically. Where it is desirable to keep them open most of the time, an automatic release operated by a fusible link is provided. (See, also, page 778.) Metal-coyer^d Wooden Doors as Fire-Doors. Wooden doors covered by the Kalamein or other process (page 894) are sometimes used as fire-doors yrhere apf)earance is a consideration. They are not considered equal, however, to the STANDARD TIN-COVERED WOODEN DOORS. Steel Fire-Doors and Shutters. For a satisfactory steel fire-door g, yi-'m sheet of steel should be used, and it should be reinforced on the back with^ frame of angle-irons, not less than iH by iH by M in, and increasing in size with the door or shutter. These doors or shutters may operate in one of l^hree ways: (i) swing on hinges, (2) slide on tracks, or (3) roll vertically. The SWINGING DOORS or shutters are the most rehable as there are no com- plicatpd parts to get out of order. They should be hung on eyes built into the piiasonry walls. Sliding doors or shutters must have the rails on which they pperate protected by metal shields to prevent obstruction. For larger openings the rolling shutters are generally preferred. They are made in horizontal jointed sectional strips, which wind up on a roller placed in a pocket above the opening, the ends nioving in metal grooves to hold them in place. They gen- erally operate vertically, although some are made to operate horizontally, the rollers being set vertically in pockets at the sides of the openings. These latter are more apt to get out of order. The vertically operated doors or shutters are balanced by springs or weights to make them move easily up or down. Where they are intended to be closed in case of necessity only, they are slightly weighed and held open by means of fusible links, so that in case of fire they will close automatically. Sheet-Metal for Fire-resisting Window-Frames and Sashes. J These are now made weather-tight and perfectly practicable in all respects, and should be used wherever fire-resisting windows are desired. The sashes are made especially for holding wire-glass. These sheet-metal windows are made in a great variety of forms to meet all purposes and the sashes may be stationary, pivoted eith^ horizontally or vertically, hinged, or double-hung with weighty, like ordinary windows. For factories, warehouses, stairways, and elevator? shafts, a stationary lower and a pivoted upper sash are commonly used, as thi? is the cheapest type of window. The double-hung windows are now made * Insurance Engineering, Dec, 1902. t To be had for the asking. X S^, also, Hollow Metal Window-Frames and Sashes, page 897. Extinguishing Devices and Precautionary Measures 903 to work as smoothly as wooden sashes in ordinary box frames. For offices, hotels, etc., a window having two sashes, glazed with wire-glass, and closing and locking automatically in case of fire, and a third inner sash glazed with clear glass, has all of the advantages of an ordinary window with the additional advantages of fire-protection and better diffusion of light. Metal fly-screens, also, can be used with these windows. All movable sashes, glazed with wire- glass, should be provided with a device by which the sashes will close and lock automatically in case of fire. Two thicknesses of wire-glass are sometimes used with a ventilated air-space of at least i in between the lights. 10. Extinguishing Devices and Precautionary Measures Water-Curtains. "The vulnerable portion of buildings generally is the front, where great window-openings are desired for purposes of light, and where it is considered objectionable on account of appearance to have shutters or even wire-glass windows. These large window-openings afford great oppor- tunities for the spread of fire across streets. The danger of damage is much increased where the fronts, as is very common, are made of unprotected metal- work. A notable example, illustrating such danger, was the building of the Manhattan Savings Institution, New York City, which was severely damaged and almost destroyed by a fire in a six-story non-fire-proof building across the street. Such conditions might be overcome to some extent perhaps, by the introduction of some system such as the water-curtains that were placed on the Chicago Public Library. This is practically a sprinkler system set along the edge of the cornice of the building, and so arranged as to furnish a thin sheet of water in front of the building. Such a sheet will, however,- not extend far before it is turned into spray and thus becomes practically useless. A similar arrangement placed at each window-opening might be more useful, though it is doubtful whether it would be of much value in any severe conflagration."* The rules of the National Board of Fire Underwriters for open sprinklers or water-curtains determine the sizes of piping and feed-mains, and the general arrangement of the system. Precautionary Measures in General. f No matter how thoroughly a build- ing is fireproofed, if it is filled with combustible goods, as a warehouse, store, or factory, there is always the possibility of a fire, which, if unchecked when first started, must necessarily entail a great loss and more or less damage to the building. If a fire is discovered and checked in its incipient stage this loss is avoided. There are now many valuable devices for detecting and checking fires, which should be installed in every warehouse, and which often may be placed with advantage in buildings used for other purposes. The more imxx)rtant of these are automatic alarms, automatic sprinklers, and standpipes. Automatic Alarms. The prompt discovery of fire generally brings about prompt extinguishment, but as it is not practicable to have someone on duty in all parts of a property at all times, fires may gain serious headway before being discovered, unless some system of automatic notification is used. Next to auto- matic sprinklers, approved automatic fire-alarm systems, thermostats, are per- haps the most important of the fire-protection devices. There are two general classes of thermostats: one which operates at a fixed or predetermined temperature, and the compensating-type. The latter requires a certain rise in temperature within a given time. This latter type is common in Europe, while in this country the fixed-temperature-type has been preferred. The compen- * Insurance Engineering, Dec, 1902. ' t ^§§, al§9, CJi^J?t#F :5Qai, page 7fi§, 904 Fireproofing of Buildings Chap. 23 sating-types seem to have been used with some success in certain sections, but have not proved altogether satisfactory. For general use it would appear that the SOLDER-TYPE OF THERMOSTAT has many advantages when used in connection with a simple closed-circuit system. The most common type of thermostat system is the electric system, in which the thermostats are designed to open or close the electric circuit and cause bells to be rung at designated points. The thermostats, or circuit-closers, may be of the fixed-temperature type or adjusted to operate at any desired temperature. The former are chiefly of the solder- type, while the most common variety of the latter type consists of a spring of two dissimilar metals, which expand unequally. The Aero System. The best-known system of the compensating-type is the aero system installed by the Aero Fire Alarm Company, New York City.* This consists of a small copper tube attached to the ceiling. A quick rise in temperature, as in the case of fire, expands the air in the tube and acts on a sensi- tive diaphragm, which latter makes an electrical connection, causing a trans- mitter to operate and send in an alarm. The Reichel System is installed by the Pacific Fire Extinguisher Company, San Francisco, Cal. This system is of the compensating-type, the Reichel thermostats* consisting of a thermopyle of special design which is connected in series with an electric circuit. Any rapid increase in heat generates sufficient current to actuate a transmitter. Slow changes in temperature do not operate the system. The Derby Automatic Fire- Alarm System is installed by the American Fire Prevention Bureau, New York City. This system consists of a tv/o-wire closed circuit, and uses the Derby fire-sentinels,* in multiple, across the line. Any derangement of the circuit gives a local or central station trouble- alarm. Upon the operation of a sentinel thermostat, resistance is auto- matically cut out of the circuit, thereby causing the operation of fire-gongs and transmitters. The Derby Fire Sentinel can be used on wiring systems utilizing primary, storage, or public-service energy up to no volts. The Sentinels are made for attaching to open wiring and also for use in connection with concealed work. The Watkins Thermostat is installed by the Automatic Fire Alarm Com- pany, New York City. It consists of a perforated metal case, enclosing a flat SPRING OF TWO DISSIMILAR METALS. The Spring is fastened at one end, and the heat causes a movement, due to the unequal expansion of the two metals. Watkins thermostats are wired in multiple, the wiring system being part open and part closed. The thermostats are adjusted by hand. They are likely to be affected by corrosive influences, moisture, and rough handling. This system, however, has been more largely installed than any other, being the principal type of thermostat used in Boston, New York, and l^hiladelphia, where, with good supervision, its record has been satisfactory. Automatic Sprinklers. "An automatic sprinkler is a device for distribut- ing water by means of a valve which is arranged to open under the action of heat, as from a fire which it is intended to extinguish. The distribution of water which results from properly located sprinklers occurs in the form of a rain of jets or drops, and is sufficient to drench almost any inflammable stock beyond the point of ignition. The distribution is also economical, as the water is more evenly appHed than from a nozzle attached to a fire-hose, and the source is directly above the fire. Whenever combustible merchandise constitutes the contents of a building, automatic sprinklers are of great value, and in "Approved by the Underwriters' Laboratories. Extinguishing Devices and Precautionary Measures 905 buildings of a height so great as to make the upper stories difficult of access, especially if containing large areas and very combustible contents, sprinklers constitute the best protection obtainable." * Sprinkler-systems may be divided into two general types: (i) the wet-pipe system, or automatic sprinklers, just described; (2) the dry-pipe system. Where the water cannot be kept from freezing in the ordinary wet-pipe system, recourse is had to the dry-pipe system. The sprinkler-pipes are filled with air under pressure, which is automatically released by the opening of a head-valve under heat. This release of pressure opens the dry valve in the main supply-pipe, allowing water to flow through the sprinkler-pipes and the open heads. Automatic sprinkler-heads are made to open at various temperatures: ordinary, 155° to 165°; intermediate, 212°; hard, 286°; and extra hard, 360° F. The higher-temperature sprinklers are put in locations where the heat is above normal, such as boiler-rooms and dry-rooms. Various types, made by the following manufacturers, have been approved by the National Board of Fire Underwriters :t International Sprinkler Company, New York City; General Fire Extinguisher Company, Providence, R. I.; Automatic Sprinkler Company of America, New York City; Crowdar Brothers, St. Louis, Mo.; Esty Sprinkler Company (H. G. Vogel Company, New York, sole agents); Globe Automatic Sprinkler Company, Philadelphia, Pa.; Independent Sprinkler Company, Philadelphia, Pa.; Ohio Automatic Sprinkler Company, Youngstown, Ohio; and Rockwood Sprinkler Company, Worcester, Mass. Sprinkler Supervisory Devices. These devices consist of apparatus for "transmitting signals when gate- valves are closed or open; when water in tanks falls below or is restored to a predetermined level; when pressure in air-tanks falls below or is restored to a predetermined amount; when water in tanks falls below or rises above predetermined temperatures; also to transmit water-flow signals and to withold signals from water-surges or variable pres- sures." They are used in connection with central-station signalling systems for supervising the operation and maintenance of sprinkler-equip- ments. The devices of the American District Telegraph Company of New York City, are approved by the National Board of Fire Underwriters, f Stand-Pipes and Hose-Reels. In office-buildings, hotels, and apartment- houses, where sprinkler-systems are hardly suitable, stand-pipes with hose- reels in each story and on the roof, ready for instant use, constitute the best means of quickly controlling a fire. All buildings over certain heights should be so equipped, the height being fixed by the ability of the local fire department to reach effectively the upper parts of the building with its hose-streams. The stand-pipe should be from 23^2 to 6 in in diameter, according to the size and height of the building, and should be connected with the water-supply of the building and provided with Siamese connections at the street-level for the fire department. Check-valves should be provided, so that when the fire-depart- ment engines are attached, their force will be added to the force due to the head of water from the fire-tanks, or to the fire-pumps, or to the force of the city water system. Stand-pipes should be placed within the stair-enclosures. In some cities the practise is to attach them to the outside fire-escapes of the building. The number and location of stand-pipes should be such that all parts of the -building can be reached by at least one stream supplied by hose not exceeding 100 ft in length. * J. K. Freitag. t List of Fire Appliances, National Board of Fire Underwriters, 906 Reinforced-Concrete Construction Chap. 24 CHAPTER XXIV REINFORCED-CONCRETE CONSTRUCTION * By RUDOLPH P. MILLER SUPERINTENDENT OF BUILDINGS, BOROUGH OF MANHATTAN, NEW YORK CITY I. Introductory Notes Definition. The term reinforced concrete is defined in the proposed standard regulations of the American Concrete Institute as "an approved mix- ture of Portland cement, with water and aggregates in which metal (generally steel) has been embedded in proportionately small sections, in such a manner that the metal and the concrete assist each other in taking stress."! Historical Notes. The great value of concrete as a structural material when subjected to compression only has been recognized for centuries. The use of reinforced concrete, however, as a practicable and commercial form of construc- tion is comparatively recent. It is true that as far back as 1869, Frangois Coignet of Paris took out letters patent on a combination of iron and concrete, and that even before this, in 1867, the principle of reinforcing concrete with iron had been apphed by P. A. J. Monier, a gardener of Paris, to the making of large flower-pots; still, the general application to building-construction did not occur till about the middle of the last decade of the nineteenth century. In its develop- ment it was first appUed to bridge-construction. The discussion of the subject in this chapter is confined to its use in the construction of buildings. The earliest example of a building of reinforced concrete in this country, and probably in the world, is that erected in 1875 bj^ W. E. Ward, near Port Chester, N. Y., in which "not only all the external and internal walls, cornices, and towers were constructed of concrete, but all of the beams and roofs were exclusively made of concrete reinforced by Ught iron beams and rods." $ The Erection of Reinforced-Concrete Work. In general outline, a build- ing operation in reinforced concrete consists in the usual preparations of the site by excavation or otherwise, the provision of suitable foundations for walls, columns, or other supports, the erection of a series of wooden molds or forms, the placing of the necessary steel reinforcement, the pouring of the concrete, and the removal of the forms after the concrete has set sufficiently to sustain itself and the load that may come on it during construction. From the beginning of the erection of the forms the successive steps are progressive, that is, the placing of the steel and pouring of the concrete are going on in the lower sec- tions or stories while the forms are being erected for the upper sections or stories. So that in a large operation the carpenters, the steel-setters, and the concreters may all be working at the same time, one set shghtly in advance of the others, without interference one with the others. These several steps in the operation * For Concrete in general and Mass-Concrete, see Chapter III, pages 240 to 251; for Strength of Concrete without Reinforcement, Chapter V, pages 283 to 287; and for Reinforced-Concrete Factory-Construction, Chapter XXV. See, also. Chapter XXllI pages 817 and 842. t Proc. Am. Concrete Inst., Vol. XV, 1919. t For a further and more extended history the reader is referred to the larger treatises on this subject and to Edwin Thacher's article in Engineering News, March 26, 1903. Materials Used in Reinforced-Concrete Construction 907 are considered in greater detail in Chapter-Subdivision 7, page 962, Erection of Reinforced-Concrete Construction. 2. Materials Used in Reinforced-Concrete Construction The Materials used in reinforced concrete are concrete and steel. The concrete forms the mass of the construction. Its proper use is to resist com- pression. While it has some tensile strength the amount is so small and so variable that it should always be neglected. Steel is used for the reinforcing material as it furnishes the greatest amount of strength at the least expense. Wrought iron could be used, but it is practically unobtainable under present conditions, and, as already intimated, its use is not economical. Concrete. The concrete consists of a mixture of cement and some aggre- gate, in definite proportions, with the necessary water to cause the setting of the cement. Cement. Portland cement should always be used in reinforced concrete, and it should always be tested before being used. Even in small jobs it is im- portant to know that the cement is strong and sound. In purchasing the cement, the certificate of some reliable testing-laboratory should be made one of the conditions of acceptance. Under all circumstances, it is always best to have the testing done at some well-estabhshed and properly equipped cement-testing laboratory. The results of tests in temporary laboratories are often abnormal and may lead to unnecessary controversies with the manufacturers. To be acceptable, a cement should meet the following requirements as called for in standard specifications. * Specific Gravity. The specific gravity of the cement should be not less than 3.10. Fineness. It should leave by weight a residue of not more than 22% on a No. 200 sieve. Time of Setting. It should develop initial set in not less than 45 or 60 min- utes, according as the Vicat or Gillmore needle is used, but must develop final set within 10 hours. Tensile Strength. The minimum requirements for tensile strength for briquettes of i -in-square section should be as follows, and should show no retro- gression in strength within the periods specified: Neat cement 28 days (i day in moist air, 27 days in water) 600 lb per sq in One part cement, three parts standard Ottawa sand 7 days (i day in moist air, 6 days in water) ; 200 lb per sq in 28 days (i day in moist air, 27 days in water) 300 lb per sq in Constancy of Volume. Pats of neat cement about 3 in in diameter, y^ in thick at the center, and tapering to a thin edge, should be kept in moist air for a period of 24 hours. The pat is then exposed in an atmosphere of steam, i in above boiling water, in a loosely closed vessel, for 5 hours. These pats, to satisfactorily pass the requirements, should remain firm and hard and show no signs of distortion, checking, cracking, or disintegration. * For the complete standard specifications see the latest Year Book of the Am. Soc. for Test. Mats. See, also. Chapter III, page 237, for the principal clauses of the last Standard Specifications for Portland Cement, adopted in 1916, and effective January I, 1917, by the Am. Soc. for Test. Mats. The tensile strengths for neat cement are now omitted. ^S Reinforced-Concrete Construction Chap. 24 Sulphuric Acid and Magnesia. The cement should not contain more than 2% of anhydrous sulphuric acid (SO3) nor more than 5% of magnesia (MgO). The test for constancy of volume or soundness is of particular importance for reinforced-concrete work. When used in large masses an occasional batch of concrete made with unsound cement may not seriously affect the final result, but in reinforced-concrete building operations, where the different members of the structures are comparatively small, the safety of the entire building may be jeopardized by the use of a small amount of unsound cement in some impor- tant part, such as a column. Aggregate.* By the term aggregate is understood the materials, including the sand, mixed with the cement to make the concrete. In practically all cases, the sand is a necessary element. Sand. "The sand should be clean. One may obtain some idea of its cleanli- ness by placing it in the palm of one hand and rubbing it with the fingers of the other. If the sand is dirty, it will discolor the palm. Unless from a bank of known quahty, a sand should be tested for tensile strength of mortar, before using. Preference should be given to sand containing a mixture of coarse and fine grains. Extremely fine sand even if clean makes a weak mortar and should never be used unless with a large excess of cement." f Mortars composed of one part Portland cement and three parts fine aggregate or sand, by weight, should show a tensile strength of at least 70% of the strength of i 13 mortar of the same consistency and of the same cement mixed with standard Ottawa sand. The New York Regulations specify that fine aggregate shall consist of sand, crushed stone, or gravel screenings, passing when dry, a screen having J^-in- diameter holes, and passing not more than 6% through a sieve having 100 meshes per Hnear inch. The Chicago Regulations specify that not less than 45% shall be retained on a screen of 400 meshes to the square inch. (See, also, page 241.) Coarse Aggregate. For the coarser material of the aggregate many materials are used and many others have been suggested. Its selection is gen- erally dependent upon local conditions. If possible, gravel or crushed stone should be used. Whatever is used should be a clean, hard substance that will secure to the concrete the necessary strength; that is, the crushing strength of this material should be equal to or greater than that of the mortar used, at least at the age of 28 days. In any case, where no reliable information is to be had on the strength of a concrete made from a given aggregate, careful investi- gation should be made before such material is used. (See, also, page 241,) Gravel. Gravel, like sand, should be clean. If dirty it should be washed before being used. To get the most satisfactory or uniform results, gravel should be screened and graded and then mixed in definite proportions, as the RUN OF the bank will generally not give uniform results. (See, also, page 241.) Stone. The most satisfactory stone that can be used is trap-rock (under which term are included most of the rocks of igneous origin), because of its toughness and great compressive strength. The granites, as they are com- mercially known, are considered by some equal in quality to trap-rock for the making of concrete. The presence of mica in considerable proportion in some of the so-called granites would seem to make them unsuitable. Limestones, * See, also, Chapter III, pages 240 to 251. The data there on Aggregates, Propor- tioning Materials, etc., relate more particularly to mass-concrete, while the data of Chapter XXIV is intended to cover, more in detail, reinforced concrete. t Treatise on Concrete, Plain and Reinforced, Taylor and Thompson, third edition, T916, page 12, . Materials Used in Reinforced-Goncrete Construction 909 if the soft varieties are excepted, make excellent concrete as far as strength is concerned. They would, however, seem to affect the fire-proof character of the concrete. (See Tables «n page 956.) The harder and more compact SANDSTONES, also, may be used successfully, but great care must be exercised in their selection. Conglomerate, which is in reality a hard, coarse sandstone, should give very satisfactory results. On account of their low crushing strength, SLATE or SHALE should not be used in concrete. Besides the stones thus far mentioned, broken brick, terra-cotta, furnace-clinker and furnace-slag have been suggested. In the selection of broken brick or terra-cotta, care must be taken to get hard-burned material. The crushing strength of such material when well selected, is a little more than that of acceptable concrete, 28 days old. But ordinarily, commercial brick or terra-cotta will not meet the require- ments for a good aggregate, and these materials should be used only as a last resort and then only after careful investigation. (See, also, page 241.) Cinders. Furnace-clinkers should be clean and entirely free from com- bustible matter. Cinders are often used where fireproofing is the primary consideration, and no doubt good constructions may be obtained, with extreme care, by the use of clinker or cinder concrete, especially if the material is ground, screened and graded as suggested for gravel. But in general practice the con- crete is not uniform in quality and is unreliable in strength. It is therefore not considered in this chapter. In Chapter XXIII, Fireproofing of Buildings, its usj is disjcussed on pages 817 and 818. (See, also, page 242.) Size of Aggregate. The size of the aggregate may vary from ^ to 23^ in in largest diametrical dimension, depending on the particular purpose for which it is to be used. Where the mass of concrete is comparatively large the aggregate may run as high as 3 in in size. This may sometimes be the case in foundations and in large piers and thick walls. In columns, girders, beams and slabs, very unsatisfactory results would be obtained if so large a stone were used. For such work no stone or other aggregate should be used larger than would pass a i-in screen. In important girders and columns, especially when the reinforcing-bars are closely spaced, the size should be made even smaller so that a concrete of viscous consistency is produced "which will pass readily be- tween and easily surround the reinforcement and fill all parts of the forms. " * The maximum sizes allowed for the aggregate in reinforced concrete in the dif- ferent cities are as follows: St. Louis and Bufi"alo, stone that will pass a K-in ring, that is, "three-quarter-inch stone"; New York, Cleveland and Philadelphia, stone that will pass a i-in ring; Chicago, stone passing i -in-square mesh; San Francisco, for floors and fireproofing, i-in stone, for foundations, 2-in stone. (See, also, page 241.) Water. "The water used in mixing concrete should be free from oil, acid, alkalies, or organic matter. " * Proportions of the Materials. The proper proportion of the materials entering into the concrete is dependent upon the size and character of the mate- • rials. In cities in which there are regulations governing reinforced-concrete con- struction, the mixture to be used is generally specified. In the absence of other considerations the most satisfactory and reliable mixture is, one part of Portland cement, two parts of sand and four parts of stone or gravel. It is the mixture that has been used in most of the experimental work on reinforced concrete, and there is therefore much trustworthy information to be had concerning it. In the case of large or important operations, however, great economy can often * Trans, Am. Soc. C. E., 1917, Vol. 81, page 1115- 910 Reinforced-Concrete Construction Chap. 24 he effected by a preliminary study of the materials to be used and of their proper proportions. In general, for given materials, the most economical mix- ture is also the strongest. The old method of determining the proportions of concrete by measuring the voids in the coarser particles by means of water poured into a box containing i cu ft of the material and then providing that quantity of finer material, assuming the cement the same as sand, is not to be recommended. It does not give accurate or satisfactory results. A better method is to take the materials to be used and make trial-mixtures by varying the proportions, always using, however, the same amount of cement and water. These trial-mixtures are placed successively in a measuring vessel of fixed size and tamped, and the height to which the vessel is filled for each mixture is noted. The proportions that give the lowest height, or result in the smallest volume, will give the most satisfactory concrete. (See, also, page 242 and fol- lowing pages.) The best and most scientific method, howe-'/'^r, is that known as the IvDECHAN- ICAL ANALYSIS, devised by W. B. Fuller. In this method the available materials, including the cement, are separated into the various sizes by means of a series of sieves; curves are plotted which indicate the p)ercentages of the whole mass, which pass the several sieves; and from a study of these curves the proportions of the different aggregates are determined. For a detailed description of this method the reader is referred to the chapter on Proportioning Concrete in the 191 2 edition of the Treatise on Concrete, Plain and Reinforced, by Taylor and Thompson. As an example of the saving possible, the following case, given in the work just referred to, will be of interest. "The ordinary mixture for water-tight concrete is about 1:2:4, which re- quires 1.57 barrels of cement per cubic yard of concrete. By carefully grading the materials by methods of mechanical analysis the writer has obtained water- tight work with a mixture of about 1:3:7, thus using only i.oi barrels of cement per cubic yard of concrete. This saving of 0.56 barrel is equivalent, with Portland cement at $1.60 per barrel, to $0.89 per cu yd of concrete. The added cost of labor for proportioning and mixing the concrete, because of the use of five grades of aggregate instead of two, was about $0.15 per cu yd, thus effecting a net saving $0.74 per cu yd. On a piece of work involving, say, 20000 cu yd of concrete, such a saving would amount to Si 4 800, an amount well worth considerable study and effort on the part of those in respon- sible charge." In the ordinances or regulations governing reinforced concrete of various cities the proportions to be used are generally prescribed. In New York, "the concrete for reinforced-concrete structures shall consist of a wet mixture of one part of Portland cement to not more than six parts of aggregate, fine and coarse, either in the proportion of one part of cement, two parts of fme aggregate and four parts of coarse aggregate, or in such proportion that the resistance of the concrete to crushing shall not be jess than 2 000 lb per sq in after hardening for 28 days." In Chicago, various grades of concrete arc specified with the ulti- rnate compressive resistance, to be developed, from a mixture of i : i : 2 and an ultimate strength of 2 900 lb per sq in, to a t : 3 : 7 mixture with a strength pf I SCO lb per sq in. In Buffalo and San Francisco the proportion is given as one of cement to six of aggregate; in Boston it is one of cement to five of aggregate. Compressive Strength of Reinforced Concrete. For reinforced-concrete work no mixture should be used that docs not develop a compressive STRENGTH of at least 2 000 lb per sq in at the age of 28 days. The crushing strength of various concretes is shown in the following table: Materials Used in Reinforced-Concrete Construction 911 Table I . Compressive Strength of Portland-Cement Concrete of Different Proportions Proportions Com- Age, months pressive strength Authority- Cement Sand Stone persq in I 4 4 370 2 4 •2 506 3 4 I 812 4 4 830 5 o 4 532 6 o 4 169 7 4 118 2 4 4 2 178 3 4 6 8 4 4 I 815 I 135 James E. Howard, Tests, Watertown Arsenal 5 10 4 707 6 12 4 738 2 2 4 I 768 2 3 4 I 911 2 4 4 2147 2 5 4 2 452 2 6 4 2 124 2 7 4 I 650 2 8 4 1295 J 1 2 4 I 2399 G. A. Kimball, Tests of Metals, U. S. A. ( Taylor and Thompson, Tests, Water- ( town Arsenal 2H S I 3255 I Watertown Arsenal, Tests of Metals, ( U. S. A. 3 5 T 2042 Working Stresses for Reinforced Concrete. Some formulas for the strength of reinforced-concrcte construction provide for the use of the ultimate STRENGTH of the concretc and the application of a factor of safety. This practice is not to be recommended as it necessitates either the test of the con- crete or the assumption of an ultimate strength. While it is undoubtedly de- sirable that the concrete should be tested, this is generally impracticable when the building is being designed. It should be done during construction and is done on the best work, to make sure that the concrete is up to the require- ments. Various factors of safety from two and one half to ten have been pro- posed. Different factors of safety are used for different members of a structure or for different conditions. This is another reason why it would be better to use WORKING stresses than ultimate stresses. The following working stresses are recommended for reinforced concrete that will develop a crushing strength ©f 2 000 lb per sq in in 28 days: Extreme fiber-stress in compression 650 lb per sq in Shearing-stress 40 lb per sq in Vertical shearing-stress when all diagonal tension is re- sisted by the steel, and the steel-resistance to both negative and positive moments is fully developed 150 lb per sq in Direct compression Soo lb per sq in Bond-stress between concrete and plain reinforcing-bars. . 80 lb per sq in Bond-stress between concrete and suitable deformed bars. 100 lb per sq in Table II gives the stresses allowed by various building ordinances. 912 Reinforced-Concrete Construction 03 " ^'o'o "rt «^ 03 'w O Ifl c o ^>,-^ ^ fc e o fe 6 C3 -O '^ - g c 'a3 to ° .i: o o ?l ^3 o CiO o •Q 03 ^ 03 X5 M ^ ^ u-» O lo »o tn lO (N n u M M o x- u «\ 2 B ^ fU •- +j o* bfl •S ^ 2^ "^ d ^ o u O o o o o o C 10 d Tt ^ VD ■* u- rl- ■^ t- 1 Qi U C ^ CO '^ o^ ^ ^ »>H o ''^ ^ * Jj) O O '^•£8 8 o ii b ^ ^ ^ o '3 o m m 3 2 Q^8a lO ^ t-, >o -^ ^ cd v(0 >* v::^ H 8.S£ r*i w,_- wage ., w "^ O •-• 1 JJ in l~~ ir <£5 KD V\* (N 00 cr> »o pi oc oc >-* >. o^ r^ cd to C-. Oi 6 1 < CTi _t/: t-l o M 6 bD as 4^ 1 c la O 1; .H 'o 6^ '0 o IS 8 1^ it c ^ o a. PQ om Q en m Materials Used in Reinforced-Concrete Construction 913 Steel Reinforcement. The function of the steel reinforcement is to take up the longitudinal and diagonal tensile stresses and in some cases, as in columns and in beams reinforced at the top, to give additional compressive strength. Mild or High Steel. Two grades of steel are used for the reinforcement, MILD STEEL and HIGH-CARBON STEEL. MiLD or MEDIUM STEEL is USed for all structural shapes and is the ordinary merchant-steel. It has an ultimate tensile strength of from 60 000 to 70 000 lb per sq in, and its elastic hmit is about one half the ultimate strength. High-carbon steel has a greater percentage of carbon and is therefore more brittle. Its ultimate strength is about 105 000 and its elastic limit about 55 000 lb per sq in. The use of high-carbon steel would permit greater stresses in the reinforcement, and consequently a less amount of steel and a greater economy in construction. On account of its greater brittleness, however, it is Hable to sudden failures under stress. It is also often found to be cracked or broken when sent to the work, and unless it is very care- fully inspected there is great Uability of defective material getting into the structure. Furthermore, much of the so-called high-carbon steel has been found in practice, after testing, to fall far short of the specifications. Its use is therefore to be avoided, unless special care is taken to secure an absolutely re- liable article and to. have it inspected and tested. For large, important work this would be desirable. Ordinarily, however, mild steel should be used, as com- mercially it is manufactured and sold under such standard conditions that it is reliable. As-the modulus of elasticity of high-carbon steel is practically the same as that of medium steel, the deformation under any given loading is the same and there is no special advantage in the use of one over the other. Steel meeting the specifications of the American Society for testing materials* for reinforcing- bars is recommended. See Table HI. The phosphorus in the steel should not exceed 0.10% for Bessemer steel nor 0.05% for open-hearth steel. For slab and small beam-reinforcement where wire or small rods are suitable, steel manu- factured from Bessemer billets may be used with a tensile strength of 105 000, and a yield-point of not less than 52 500 lb per sq in. Working Stresses for Steel. The generally accepted working stress for medium steel is 16 000 lb per sq in in tension. Tests have shown that in cases where the failure of reinforced-concrete beams is due to the failure of the rein- forcement, the stress in the metal had not more than reached the yield-point. This point is somewhat lower than the elastic limit. The working stress in the steel, therefore, should be a fixed proportion of the yield-point or the elastic hmit. It is held by some that this ratio should not be as high as one to two, but more nearly one to three, reducing the working stress in mild steel as given above to 10 000 or 12 000 lb per sq in. In using high-carbon steel they would advocate a similar ratio of the elastic limit, whatever that may be, according to test. Ordinarily 20 000 lb per sq in is taken as the working stress for high-car- bon steel. Allowable working stresses in steel reinforcement in various cities are given in Table II, page 912. Tension-Members. Reinforcement is used in a variety of shapes and com- binations, nearly all of them patented and some of them forming the basis for so-called systems. Where the reinforcement is employed to take up tension, as in a beam or girder, the bond between the concrete and the steel is relied upon to develop the tensional stresses in the steel. The plain bars depend entirely upon the adhesion of the steel and the concrete for the action of the two mate- rials in combination, or the full tensile strength of the rod is developed by anchor- ing the rods into the concrete at the ends, in which case the beam becomes more * American Society for Testing Materials Standards, 1918. 914 Reinforced-Concrete Construction 2^ (0 +J Ti3 O w o o o.^ w o •« o o a 00 " O CO ♦H-^ *^ c H 6.S w 0113 as O 00 bo^.S Materials Used in Reinforced-Concrete Construction 915 analogous to a trussed beam with the rod as the tension-member. In cross- section, plain bars are usually round or square, though sometimes flat bars, angles, tees, or other shapes are used. In regard to the use of square bars and some other shapes, it is contended that the edges start initial cracks in the con- crete as it shrinks in setting. Twisted flat bars, when placed too near the sur- face of the concrete, cause a spaUing or breaking out of the concrete from between the convolutions, when the steel is under stress. Commercial Sizes. As a result of the shortage of steel during and since the world-war, the larger producers of reinforcing-bars have agreed to eliminate many of the commercial sizes of bars formerly in use and are now Hmiting their stocks of bars to the following sizes: Area Equivalent to Area Equivalent to o. no sq in o. 196 sq in 0. 250 sq in 0.307 sq in . 442 sq in ^-in round K-in round }4-in square ^-in round H-in round 0.601 sq in 0. 785 sq in 1 . 000 sq in 1 . 266 sq in 1 .563 sq in J^-in round I -in round i-in square I i^-in square I M-in square Difhculty in obtaining reinforcement will be avoided to a great extent by the use of these sizes in designing reinforced concrete. Deformed Bars. With the deformed bars the adhesion of the concrete to the steel is supplemented by a mechanical bond due to the shape of the bar. The following deformed bars have been and are at present widely used. The Ransome Bar. The Ransome Twisted Bars (Fig. 1) are made of square bars. Bars should be "twisted cold with one complete twist in a length of not Fig. 1. The Ransome Twisted Bar over twelve times the thickness of the bar."* The work on the bars in the twist- ing process increases the elastic limit and the tensile strength; but the amount of the increase is not fixed, as variations in the grade of rolled steel may result, aftei* twisting, in still wider variations. The users of this bar generally assume a working stress of 20 000 lb per sq in. The patent on this bar has expired and it may now be used by anyone. Strictly speaking, this is not a deformed bar. These bars can be obtained in all sizes, varying by K in from 5^ to i M in. Larger sizes, also, can be obtained on special order. Fig. 2. The Buffalo Deformed Bar The Buffalo Deformed Bar. The Buffalo Steel Company of Tonawanda, N. Y., makes a square bar with rounded edges, thus eliminating the sharp cor- * American Society for Testing Materials Standards, 1918, pages 149 and 152. 916 Reinforced-Concrete Construction Chap. 24 ners. The deformations consist of raised stars along the sides of the bar, as shown in Fig. 2. It is made in sizes of from Vg to i3^-in diameter, and the cross-sectional areas are equal to the areas of equivalent squares. The bars are rolled from old railroad rails and comply with the Standard Speciftcations of the American Society for Testing Materiyls, for reinforcing-steel of that kind. The steel is a high carbon steel with a tensile strength of 8o ooo lb per sq in. Corrugated Bars. Cor- rugated bars (Fig. 3), both square and round in cross- section, are made by the Cor- rugated Bar Company, Inc., Buffalo, N. Y., of both medium and high-elastic-limit steel with a yield-point of about 50 000 lb per sq in. Corr-Bars are furnished either straight and cut to length, or bent ready for the forms. The standard sizes are as follows: Fig. 3. Corrugated Bars. Round and Square Corrugated Rounds Size in inches H K2 He H H li I iH iH Net area in square inches Weight per foot in pounds O.II 38 19 0.66 0.25 0.86 0.30 I. OS 0.44 1.52 0.60 2.06 0.78 2.69 0.99 3.41 1.22 4.21 Corrugated Squares Size in inches H % H H H % I iH iH Net area in square inches 0.06 0.22 0.14 0.49 0.25 0.86 0.39 1.35 0.56 1.94 0.76 2.64 1. 00 3.43 1.26 4.34 1.55 5.35' Weight per foot in pounds Fig. 4. The Havermeyer Bar, Square s^nd Round Materials Used in Reinforced-Concrete Construction m The Havermeyer Bar. The Havermeyer Bar (Fig. 4), controlled by the Concrete Steel Company, Youngstown, Ohio, consists of square and round bars rolled with a series of gradual projections and depressions on all sides, the defor- mations being so designed that there is a constant cross-sectional area. They are furnished in the following sizes and weights: Size in inches Square bars Round bars Area in square Weight per Area in square Weight per inches foot in pounds inches foot in pounds H 0.0625 0.212 0.0491 0.167 % 0.1406 0.478 0.1104 0.375 H 0.2500 0.850 0.1963 0.667 % 0.3906 1.328 0.3068 1.043 % . 0.5625 1. 913 0.4418 1.502 % 0.7656 2.603 0.6013 2.044 I I. 0000 3.400 0.7854 2.670 iH 1.2656 4.303 0.9940 3.379 t3^ I 5625 T 8006 5.312 6.428 7.650 1.2272 4.173 iH 2.2500 A variation of 5% under and 2H% over the above weights is required for rolling. This company also rolls a flat bar with similar deformations on the wide faces. This form is recommended where bars must be bent in curves, as in silos, sewers, etc. In running them through a tire-machine to bend them, the edges of the flats prevent the lugs from being damaged. The Diamond Bar. The Diamond Bar (Fig. 5), put on the market by the Concrete Steel Engineering Company, New York, is a bar of absolutely uniform Fig. 5. The Diamond Bar section. There is consequently no waste of metal due to the deformations. This bar is practically a round bar, and as sudden transitions from one section to Fig. 6. The Rib-bar another are avoided, all tendency to cause initial cracks in the concrete is over- come. The weights and areas of Diamond bars are equal to those of plain square bars of Hke denominations. Bars from }4 to i M in in diameter naay be ob- tained. 918 Reinforced-Concrete Construction Chap. 24 The Rib-Bar. The Rib-Bar (Fig. 6) manufactured by the Truscon Steel Company, Youngstown, Ohio, is a rolled bar with a series of cross-ribs. These bars are made with rectangular or round section and are furnished in sizes of from y^to 1% in, the areas of the cross-sections being equivalent to squares of equal denominations; but the weights are sHghtly greater, and are as follows: Sqi lare bars Round bars Size, in Area, Weight per Area, Weight per sq in linear foot, ib sq m linear foot, lb Vs 0.1406 0.48 0.1 104 0.379 M 0.2500 0.86 0. 1963 0.674 H 0.3906 1.35 0.3068 I 054 M 0.562s 1.9s 0.4418 I. 517 % 0.7656 2.6s 0.6013 2.065 I I . 0000 3.46 0.7854 2.697 iH 1.2656 4.38 0.9940 3.414 i^ 1.5625 5. 41 Kalman Grip-Bars. These bars are similar in general design to the Rib- Bars, differing from them by having the ribs running entirely around the bars, instead of half-way. They are kept in stock in both round and square sections of standard sizes and weights, by the Paul J. Kalman Company, St. Paul, Minn. Fig. 7. The Ovoid Bar The Ovoid Bar. The Gabriel Concrete Reinforcement Company of Detroit, Mich., furnishes the Ovoid Bar (Fig. 7), in sizes and areas as follows: Size in inches Vs ^ ^ ¥4. % I iH Area in square inches . . . Weight ill pounds 0. 1406 0.4940 0.250 0.873 0.3906 1.3560 0.5625 1.9470 0.7656 2 . 6430 I .000 3.446 1.2656 4.3540 The Monotype Bar. These bars are cruciform in section, and have, at intiervals, ribs connecting the stems. (Fig. 8.) The cross-sectional areas are Fig. 8. The Monotype Bar equivalent to those of standard round and square bars. They can be secured trom the Edward A. Tucker Company, Boston, Mass. Materials Used in Reinforced-Concrete Construction 919 Rivet Grip-Bars. These bars are rolled in sections equivalent to standard square bars. The cross-section is especially designed so that shear-members Fig. 9. The Rivet Grip-bar may be rigidly attached, as shown in Fig. 9, thus securing such advantages as are claimed for them. They are handled by the Concrete Reinforcing and Engineer- ing Company, Cleveland, Ohio. Rivet grip- bars, size Area, sq in Perimeter, in Weight, per foot, lb 3^ in ^in Hin 14 in I m iH in iH in o. 1406 0.3906 0.562s 0.7656 • 1 . 0000 1.2656 1.562s 1.63 4.00 4-25 4.75 5. 19 5.75 6.50 0.478 1.328 1.913 2.603 3.400 4.303 5.313 Wire Mesh and Expanded Metal. Other types of tension-reinforcement, such as WIRE -MESH FABRIC and EXPANDED METAL in various forms, have beeil discussed in Chapter XXIII, Fireproofing of Buildings. Wire fabric has come into very general use as a slab-reinforcement, as it resists temperature-cracks and the cracking of the concrete from impact or shock. It is made in various gauges with heavy longitudinal or carrying wires and lighter transverse dis- tributing, or tie-wires. Expanded metal is similar to wire mesh in providing reinforcement in both directions, rigidly spaced and attached or fastened to- gether. This additional advantage is claimed for it; it provides reinforcement in all directions, thus taking care of concentrated loads. Anchoring. Different methods have been used for anchoring the tension- bars in reinforced concrete. In the Hennebique system of construction (Fig. 10) where plain bars are used, the ends of the rods are split and flared out. In other constructions the ends of the bars are simply turned at right-angles in such direction as is most suitable. In some instances nuts and washers have been placed at the ends of reinforcing-rods. Where reinforced-concrete floors are used in connection with steel columns the rods are run through the web-plates or through angle-brackets and secured with nuts. Adhesion. The strengths of the bond between concrete and steel for various forms of bars and differing conditions are shown in Table IV. After the bond has failed, the reinforcement still acts in conjunction with the concrete, due to a moving or frictional resistance. Numerous tests nave shown this fric- S20 Reinforced-Concrete Construction Chap. 24 tional resistance to be about two thirds of the initial bond-strength. The BOND-STRENGTH for ordinary round or square-section bars may be taken at 200 Fig. 10. The Hennebique System to 300 lb per sq in, depending upon the character of the concrete and the degree of roughness of the steel. Mechanical bond depends upon the shape of the bar and the compressive and shearing strength of the concrete. Table IV. Results of Tests on Adhesion Between Concrete and Steel Kind of bar Size tested in fraction of inch Concrete Age Ultimate strength developed in lb per sq in of sur- face in contact Round % •% % % li Vs ■ % % % ■ % % % % % H H 'A 1:2:4 1:3:6 60 days 30 days 30 days 90 days 90 days 30 days 31 days 25 days 7 mos. 7 mos. 7 m.os. 7 mos. 7 mos. 7 mos. 7 mos. 7 mos. 7 mos. 7 mos. 31 days 30 days 412 (a) 274 ib) 437 ic) 642 (c) 431 (c) 294 (c) 648 id) 500 (c) I 290 (e) I 318 (e) I 199 (e) 701 (e) 796 ie) 962 ie) 977 (e) 934 ie) 735 ie) 564 ie) 640 id) 646 ic) Square Square (rusted) Square (rusted) Square Square Twisted (Ransome). Twisted 1:2:4 Twisted Neat cement I : I 1 : 2 1:3 I :4 Neat cement I : I I :2 I :3 1:4 1:2:4 Twisted . . . Twisted Twisted Twisted Corrugated Corrugated Corrugated Corrugated Corrugated Corrugated Thatcher (/) The following are the authorities for the above tests: (a) A.N.Talbot. (b) C. M. Spofford. (c) New York City Rapid Transit Co. (d) T. L. Condron. (e) Testsof 'Metals, Watertown Arsenal, 1904. if) No longer manufactured. Materials Used in Reinforced-Concrete Construction 921 Shear-Members. In many of the tests on full-sized concrete beams, failure occurs by the development of diagonal breaks near the supports. The first diagonal crack in a beam, with nothing but horizontal tension-steel at the bottom, is apt to occur when the maximum vertical shear is from loo to 200 lb per sq in. Since the vertical shear is accompanied by a horizontal shear of equal intensity in all parts of the beam, it was formerly thought that this diag- onal failure was due to these shearing- forces at the end of the beam and vertical stirrups or bent-up rods were provided to resist the horizontal shear. More recent tests have shown that the shearing strength of concrete is from 60 to 80% of the compressive strength, and that these cracks are diagonal and in the direction which could be expected from the theory of diagonal tension, which attributes them to a combination of the shearing-stress with the hori- zontal tensile stress. The inclined cracks which first appear are due to a rupture of the concrete in tension. The most effective way to prevent this rupture is to provide reinforcement in the direction of the stress that is inclined upwards toward the supports, as nearly as possible normal to the line of the diagonal crack. Vertical reinforcement could be used, but it would not act until def- ormation or downward displacement of the concrete occurred on the side of the crack away from the support. If vertical stirrups are used for this reinforce- ment, they must be spaced a less distance apart than the effective depth of the beam, and they must l)e looped around, though not necessarily attached to, the horizontal bars. When inclined reinforcement is used, it must be rigidly at- tached to the longitudinal members and spaced a less distance apart than the effective depth of the beam. The reason for this is that the magnitude and in- clination of the diagonal tension increases from the middle toward the end of the beam, being inclined 45° where the horizontal tension becomes zero. The Kahn Bar. In the Kahn Trussed Bar (Fig. 11) the attachment of the stirrups to the tension-member is positively secured. The, bars are square op Fig. 11. The Kahn Bar pentagonal in cross-section with webs rolled on them at two diagonally opposite edges. The stirrups are formed by shearing these webs through a part of their length and turning up parts, as shown in the cut. These stirrups may be placed so as to turn up in pairs or so as to alternate on opposite sides of the bar, making the spacing- of the stirrups closer than when turned up in pairs. Another advan- tage incidental to the use of this bar is that the greater effective cross-section in the steel is at the middle, the point of greatest bending moment with the usual loading. Two disadvantages, however, are the separation of the concrete by the wings above and below the bar, and the Hmitation as to the effective stirrup- length in deep beams. This bar is controlled by the Truscon Steel Company, Youngstown, Ohio. The Kahn Trussed Bar can be oljtained in the sizes shown in table on page 922. Steel in Compression. The steel reinforcement in reinforced concrete is used in certain cases to assist in developing compressive strength when the concrete is not sufficient for the purpose, as. in the case of beams and girders with 922 Reinforced-Concrete Construction Chap. 24 ' Size, in Weight per linear foot, lb Area, sq in Standard length of diagonals, in HXiH HX2H6 ^ 1HX2M 1HX2H 1 2 X3K 1.4 2.7 4.8 6.8 10. 2 0.41 0.79 1. 41 2.00 3>oo 12 12-24 12-24-36 36 36 rods placed above the neutral axis, and columns with rods placed vertically. The use of the steel reinforcement in resisting compression will be treated more at length in Subdivision 3 of this chapter, in the paragraph Compression Rods in Beams and Girders, page 941. On account of the uncertainty, however, of the steel and concrete each receiving its proportionate share of the load, the use of steel in compression should be avoided as much as possible. The Position of the Reinforcement. The importance of the exact posi- tion OF THE REINFORCEMENT in the concrete will become more apparent in the discussion of the design of beams. A slight displacement of the steel will ma- terially affect the strength. If the steel shifts upward the beam is weakened, if it shifts downward the protection of the steel against rust or fire is reduced. In the so-called unit systems the reinforcements, including the tension-rods and stirrups, are so tied and framed together that after being placed in the forms the possibility of shifting their positions with respect to the other surfaces of the beam or to one another is practically entirely removed. The Unit System. The. particular advantages in the use of a unit system of reinforcement isj as already indicated, the assurance that each and every part Fig. 12. The Unit System of the reinforcement is in its exact relative position, and maintains that position during the placing of the concrete. The reinforcement for each beam or girder is as carefully laid out as the location of cover-plates, stiffeners, connection-angles, and rivets in a built-up steel girder. It can consequently be thoroughly in- spected and checked before being placed in position. Being marked, its exact location is easily determined by the foreman on the job, from the erection- plan. After it is put in place a quick inspection will show at once whether it is correctly placed or not, as it must fit and extend the full length of the mold. Being fabricated off the job there is less interference between workmen. The Materials Used in Reinforced-Concrete Construction 923 fabrication can proceed while the molds are being made, and consequently greater speed in erection is possible. The frames are readily transported and less liable to get mixed than loose rods sent to the job. The Unit System (Fig. 12) is the pioneer of this type of construction and is manufactured by the American System of Reinforcing, Chicago, 111. Its par- ticular features are the bending up of some of the longitudinal reinforcements near the supports and the use of round U-shaped stirrups, wound around the bars while hot and allowed to shrink into place. The Cummings System (Fig. 13) is manufactured by the Electric Welding Company, Pittsburgh, Pa. The particular feature of this system is the forming As fumiehed and shipped Fig. 13. The Cummings System of the top layer cf small rods into rectangular frames which, after being fastened to the lower layer at suitable points, permit the bending up of the ends to act as shear-members or stirrups, thus utilizing for shear the steel that is not required for bending moments. The Luten Truss. The Luten Truss (Fig. 14) consists of longitudinal rods with alternate members bent diagonally upwards across the beam and con- Fig. 14. The Luten Truss tinning along the upper surface to the end of the beam. Diagonal members are provided through all the region of diagonal tension in both ends of the beam. This frame is provided with a clamp and wedge that locks the members together. It is controlled by the National Concrete Company, Indianapolis, Ind. The Corr-Bar Unit. The Corr-Bar Unit, Fig. 15, made by the Corrugated Bar Company, Inc., Buffalo, N. Y., is provided with a continuous stirrup of both Fig. 15. The Corr-bar Unit vertical and inclined web-members with a rigid anchorage at both top and bot- tom. In tests by Professor Talbot on this type of reinforced beam, considerably higher values than ordinary were obtained in vertical shear. 924 Reinforccd-Concrete Construction Chap. 24 3. Design of Reinforced-Concrete Construction Girders, Beams, and Slabs. DifTerent formulas for the design of reinforccd- concrete girders, beams, slabs, etc., based on various theoretical considerations, have been devised by different investigators. The formulas here given have been widely accepted and are offered because they are simple in form and give satisfac- tory results. If anything, they err on the side of safety; and furthermore, they have been found to give results closely in accord with actual tests. They are used by the New York City Building Bureau, and are accepted by other authorities. Assumptions in the Formulas. The formulas are based on the following assumptions: (i) The BOND between the concrete and steel is sufficient to make the two materials act together. (2) A PLANE CROSS-SECTION of a beam before bending remains a plane section after bending, and the stress and strain* in any fiber of either material are directly proportional to the distance of that fiber from the neutral axis of the cross-section. (3) The MODULUS OF ELASTICITY of the concrete in compression remains con- stant within the assumed working stresses. (4) The TENSION AL STRESS is taken entirely by the steel; that is, the tensile strength of the concrete is not considered. Fig. IG represents a longitudinal section and a cross-section of a reinforced- ^ncrete beam in a state of flexure or bending under a load. The fibers above ks-l Trace of Neutral Surface „ d Fig. 16. Sections of Reinforced-concretc Beam the NEUTRAL SURFACE of the beam or above the neutral axis of the cross-sec- tion are in compression and according to the assumptions the stresses vary in direct proportion to their distances from the neutral surface or axis, so that the total area of compression in the concrete, representing the total compressive STRESS, may be graphically indicated by the shaded triangle. The total ten- SIONAL STRESS may be assumed to be concentrated at the center of gravity of the cross-section of the steel reinforcement. One of the conditions of static equi- librium for the beam is that the algebraic sum of all the horizontal stresses in the cross-section shall be zero; that is, that the sum of all the compressive stresses, or the resultant compressive stress in the concrete, must equal the total or resultant tensional stress in the steel. Formulas for Reinforced-Concrete Beams. From these assumptions, based upon theot^etic and experimental laws, the following formulas are derived, in which St = the allowable unit tension or working stress in the steel in pounds per square inch; * Deformation. Design of Reiiiforced-Concrete Construction 925 Sc = the allowable unit compression or working stress in the extreme fibers of the concrete in pounds per square inch; r = the ratio of the modulus of elasticity of the steel to the modulus of elasticity of the concrete; d = the effective depth of the beam, in inches, that is the distance from the center of gravity of the steel reinforcement to the extreme fibers in compression; X = the ratio of the depth of the neutral axis from the extreme fibers in compression, to the effective depth of the beam, so that xd = the distance of the neutral axis, in inches, from the extreme fibers in compression; b = the width of the beam; p = the ratio of the cross-section of the steel to the cross-section of the beam, considering the beam all of that part of the concrete above the center of gravity of the steel; M = the maximum bending moment at the dangerous section of th6 beam; Mr = the moment of resistance at the dangerous sectiori of the beam, and must of course be equal to or potentially greater than the maximum bending moment;* K = a. factor used for simplification of the formulas. This factor is con- stant for any given steel and concrete; As= sectional area of the steel in square inches. For beams of rectangular cross-section M==Mr = Kbd2 (i) the value of K being determined by the formula K = St imPwiit'i'-d (2) which formula can be deduced from the laws of flexure of beams and the assumptions noted above. In the use of this formula for the value of K it must be remembered that the ratio of St to Sc for any given ratio of steel to concrete, p, is a constant, so that corresponding values of St and Sc must be used. This ratio, p, often spoken of as the PERCENTAGE OF REINFORCEMENT, is the expression in the first parenthesis of the second member of Formula (2) P=- (l)0-^£) (3) * The "moment of resistance" or the "resisting moment" referred to any cross-section of a beam in a horizontal position and in a state of flexure under a load or loads is the algebraic sum of the moments of the internal horizontal stresses with reference to a point in that section; and the "bending moment" for that section is the algebraic sum of the moments of all the external vertical forces on either side of the section with reference to the same point (the forces on the left side being usually taken). The resisting moments increase with the bending moments and in the flexure formula, M^Sl/c (see Chapters IX and X), they are made equal to each other, M being the bending moment and SI /c the resisting moment. In the following formulas, M and the expression "bending moment" generally, denote the maximum bending moment, Mmax is often used to denote the latter. 926 Reinforced-Concrete Construction The value of x is derived from the expression x = rp\ •(s/^,-) Values for K and x for corresponding values of p, for different conditions fixed by the building authorities of different cities, are given in Tables V, VI, VII and VIII. Table V. Values for Formulas for Reinforced Concrete r = 12 p X K 5, St K Sc St K Sc St 0.004S 0.279 ...... 65.4 516 16 000 0.0050 0.291 72.2 550 '* o.ooss 0.303 69.3 507 14 000 79.2 580 " 0.0058 0.310 73.0 525 " 83.4 600 " 0.0060 0.314 75.2 535 " 86.0 612 " 0.0065 0.325 81.2 560 " 92.8 640 0.0070 0.334 74.7 503 12 000 87.2 587 " 96.5 650 15 510 0.0075 0.344 79-5 523 " 93.0 610 " 99.0 14900 0.0080 0.353 84.7 544 " 98.8 635 101.2 14350 0.00S5 0.361 89.9 565 " 103.3 650 13800 103.3 13800 0.0090 0.369 94.7 584 " 105.1 13350 105.1 13350 0.0095 0.377 99-6 60s 107.0 ^^ 12900 107.0 12 900 O.OIOO 0.384 104.5 625 " 108.8 12500 108.8 12500 0.0105 0.392 109.5 643 " no. 9 12 130 no. 9 12 130 O.OIIO 0.399 112. 4 650 II 790 112. 4 II 7QO 112. 4 11 790 il l\fU O.OII5 0.405 114. II 450 114. 11450 114. 11450 0.0120 0.412 115-7 '* II 160 115. 7 II 160 115. 7 II 160 0.0125 0.418 117. 2 " 10900 117. 2 10900 117. 2 10860 0.0130 0.424 118. 2 " 10600 118. 2 10 600 118. 2 10 600 0.0135 0.430 119. 8 " 10350 119.8 10350 119. 8 10350 0.0140 0.436 121. 2 " 10 120 121.2 10 100 121. 2 10 100 0.0145 0.441 122.2 " 9890 122.2 9870 122.2 9870 0.0150 0.446 123.2 *' 9660 123.2 9660 123.2 9660 0.0155 0.452 124.8 9460 124.8 9460 124.8 9460 0.0160 0.457 126.0 9270 126.0 9270 126.0 9270 0.0165 0.462 127.0 9 100 127.0 9 100 127.0 9 100 0.0170 0.467 128.0 " 8930 128.0 8930 128.0 8930 0.0175 0.0180 0.471 0.475 129. 1 130. 1 " 8740 129. 1 8740 8580 129. 1 130. I. 8 740 8580 8580 130. 1 0.0185 0.480 131 '\ 8 440 131. 8440 131. 8440 0.0190 0.485 132. 1 " 8300 132.1 8300 132. 1 8300 0.0195 0.489 133 " 8 150 133.0 8 150 133.0 8 150 o.oaoo 0.493 134.0 8010 134.0 8010 134.0 8 010 Design of Reinforced-Concrete Construction Table VI. Values for Formulas for Reinforced Concrete 927 p X K Sr. St K ^"^c St K Sc St 0.0025 0.217 51.0 506 22 000 0.0030 0.235 55.3 511 20 000 60.8 S62 0.0035 0.251 57.7 503 18 000 64.2 558 70.6 614 " 0.0040 0.266 65.7 542 " 72.9 602 " 78.7 650 21 610 0.0045 0.279 73.5 581 " 81.6 645 " 82.3 " 20 150 0.0050 0.291 81.3 618 85.4 650 18 910 85.4 " 18910 0.0055 0.303 88.5 650 17900 88.5 17 900 88.5 " 17900 0.0060 0.314 91-5 " 17 000 91.5 17000 91. S 17 000 0.0065 0.325 94.2 " 16250 94.2 16250 94.2 " 16250 0.0070 0.334 96.5 " 15 510 96.5 15510 96. 5 " 15510 0.0075 0.344 99-0 " 14900 99.0 14900 99.0 14900 0.0080 0.353 101.2 " 14 350 101.2 14350 101.2 " 14350 0.0085 0.361 103.3 " 13800 103.3 13800 103.3 " 13800 0.0090 0.369 105. 1 " 13325 105. 1 13325 105.1 " 13325 0.0095 0.377 107.0 " 12900 107.0 12 900 107.0 " 12900 O.OIOO 0.384 108.8 " 12 480 108.8 12480 108.8 12 480 0.0105 0.392 no. 9 •• 12 130 110.9 12 130 110.9 " 12 130 O.OIIO 0.399 112. A II 790 112.4 II 790 112.4 11 790 0.0II5 0.405 113. 9 " II 450 113. 9 II 450 113. 9 " 11 450 0.0120 0.412 II5-6 " II 160 115.6 II 160 115. 6 11 160 0.0125 0.418 117. 2 " 10900 117.2 10900 117.2 " 10900 0.0130 0.424 118. 4 " 10 600 118. 4 10 600 118. 4 " 10 600 0.0135 0.430 120.0 " 10350 120.0 10350 120.0 " 10350 0.0140 0.436 121. 2 " 10 100 121. 2 10 100 121. 2 '* 10 100 0.0145 0.441 122.2 " 9870 122.2 9870 122.2 " 9870 0.0150 0.446 123.2 " 9660 123.2 9660 123.2 " 9660 0.0155 0.452 124.8 " 9460 124.8 9460 124.8 " 9460 0.0160 0.457 126.0 9270 126.0 9270 126.0 " 9270 0.0165 0.462 127.0 " 9 100 127.0 9 100 127.0 " 9 100 0.0170 0.467 128.0 " 8930 128.0 8930 128.0 " 8930 0.0175 0.471 129. 1 " 8740 129.1 8 740 129. 1 " 8740 0.0180 0.475 130. 1 " 8580 130. 1 " 8580 130. 1 " 8580 0.0185 0.480 131. " 8440 131 8 440 131 " 8440 0.0190 0.485 132. 1 " 8300 132. 1 " 8300 132. 1 " 8300 0.0195 0.489 133.0 " 8150 133.0 " 8 150 133.0 " 8150 0.0200 0.493 134.0 8 010 134.0 8010 134.0 8010 928 Reinforced-Concrete Construction Chap. 24 Table Vn. Values for Formulas for Reinforced Concrete r = IS p X K S, St K 5, St K S„ St 0.0050 0.320 71.6 Soo 16 000 0.0055 0.332 78.3 530 *' 0.0060 0.344 85.1 558 " 0.0065 0.35s 80.2 513 14 000 91-6 586 ** 0.0070 0.36s 86.1 537 " 98.3 614 0.0075 0.375 92.0 560 " 105. 1 640 *' 0.0080 0.384 "8^.6 5 00 12 000 97.6 583 " 108.9 650 15600 0.0085 0.393 88.6 5 19 103.3 606 III.O 15040 0.0090 0.402 93.5 5 37 " 109.0 627 " 113. 2 14520 0.0095 0.410 98.4 5 56 " 114. 8 648 " 115. 1 14 020 O.OIOO 0.418 103.3 5 73 " 117. 1 650 13600 117. 1 13600 0.0105 0.425 108.2 5 93 " 118. 6 " 13 ISO 118. 6 13 ISO O.OIIO 0.433 113. I 6 II " 120.5 12760 120.5 12760 0.0II5 0.440 117. 9 6 27 << 122.0 12420 122.0 12420 0.0120 0.446 122.7 6 47 " 123-4 12080 123-4 12080 O.OI2S 0.453 125.0 6 50 II 780 125.0 II 780 125.0 11-780 0.0130 0.459 126.8 II 480 126.8 II 480 126.8 II 480 0.0135 0.46s 127.7 II 200 127.7 II 200 127-7 II 200 0.0140 0.471 128.9 10 920 128.9 10920 128.9 10920 0.0145 0.477 130.4 10690 130.4 10 690 130.4 10690 0.0150 0.483 131. 7 10465 131. 7 •' 10465 131. 7 10465 0.0155 0.488 133.0 10 240 133.0 10 240 133 -0 10240 0.0160 0.493 133.9 10 010 133.9 10 010 133 9 10 010 0.0165 0.498 135.2 9810 135 2 9810 135.2 9810 0.0170 0.503 136 ■ 9 620 136.0 9 620 136.0 9620 0.0175 0.508 1372 9 435 137 2 9 435 137.2 9 435 0.0180 0.513 138.2 9 260 138 2 9260 138.2 9260 0.0185 0.518 139-4 9 100 139-4 9 100 139 4 9 100 0.0190 0.522 140.3 8940 140.3 8940 140.3 8940 0.0195 0.527 141. 1 8790 141. 1 8790 141. 1 8790 0.0200 0.531 142.0 ' 8630 142.0 8630 142.0 8630 Design of Reinforced-Concrete Construction Table VIII. Values for Formulas for Reinforced Concrete r =■- 15 p X K .S', •5, K S^ Se K ^c St 0.0030 0.258 60.3 512 22 000 0.0035 0.276 '63.5 507 20 000 69.9 557 " 0.0040 0.292 72.3 548 79-5 604 " 0.004s 0.306 72.7 528 18 000 80.7 587 88.8 646 " 0.0050 0.320 80.5 563 89.4 626 " 92.9 650 20 800 0.0055 0.332 88.1 596 " 96.0 650 19 610 96.0 19 610 0.0060 0.344 95.6 628 •* 99.1 18620 99.1 18620 0.0065 0.355 101.8 650 17760 101.8 17 760 101.8 17760 0.0070 0.365 104. 1 16950 104. 1 16950 104. 1 16950 0.0075 0.375 106.7 16 250 106.7 16 250 106.7 16 250 0.0080 0.384 108.9 15600 108.9 15600. 108.9 15600 0.0085 0.393 III.O 15 040 III.O 15040 III.O 15040 0.0090 0.402 113. 2 14520 113. 2 14520 113. 2 14520 0.0095 0.410 115. 1 14 020 115. 1 14020 115. 1 14 020 O.OIOO 0.418 117. I 13600 117. 1 13600 117. 1 13600 0.0105 0.425 118. 6 13 150 118. 6 13 150 118. 6 13 150 O.OIIO 0.433 120.5 12 760 120.5 12760 120. s 12 760 0.0II5 0.440 122.0 12 420 122.0 12420 122.0 12 420 0.0120 0.446 123 4 12080 123.4 12 080 123.4 12 080 0.0125 0.453 125.0 II 780 125.0 II 780 125.0 II 780 0.0130 0.459 126.4 II 480 126.4 II 480 126.4 II 480 0.0135 0.465 127.7 II 200 127.7 II 200 127.7 II 200 0.0140 0.471 128.9 10 920 128.9 10920 128.9 10 920 0.0145 0.477 130.4 10 690 130.4 ( 10690 130 4 10690 0.0150 0.483 •131. 7 10 465 131. 7 10465 131 7 10 465 0.0155 0.488 133.0 10240 133.0 10 240 133 10 240 0.0160 0.493 133 9 10 010 133 9 TO 010 133 9 10 010 0.0165 0.498 135 9810 135 9810 135 9810 0.0170 0.503 136.0 9 620 136.0 9620 136.0 9620 0.0175 0.508 137.2 9 435 137.2 9 435 137.2 9 435 0.0180 0.513 138.2 9 260 138.2 9 260 138.2 9260 0.0185 0.518 139 4 9 100 139 4 9 100 139 4 9 100 . 0190 0.522 140. 1 8940 140. 1 8940 140. 1 8940 0.0195 0.527 141. 1 8790 141. 1 8790 141. 1 8790 0.0200 0.531 142 8630 142.0 8630 142.0 8630 930 Reinforced-Concrete Construction Cinder Concrete. Values of K for cinder concrete are gix^en in Tables IX and X, which are, however, recommended to be used only for slabs. Cinder concrete, though an excellent fireproofing material, lacks strength and should be used as a structural material for the slabs, only, between the beams. Table IX. Values for Formulas for Reinforced Cinder Concrete . r = 35 p X K 5o St K Sc St 0.0005 0.170 7.5 94 16000 7.5 94 16000 o.ooio 0.232 14.8 138 " 14.8 • 138 16 000 0.0015 0.276 21.8 174 " 18.8 150 13800 0.0020 0.3II 28.7 206 20.9 II 633 0.0025 0.340 33.9 225 15300 22.6 10 200 0.0030 0.365 36.1 13688 24.0 9125 0.0035 0.387 37.9 " 12439 25.3 8293 0.0040 0.407 39-6 " II 447 26.4 7631 0.0045 0.425 41.0 10625 27.4 7083 0.0050 0.442 42.4 " 9 945 28.3 6630 0.0055 0.457 43.6 " 9348 29.1 6232 0.0060 0.471 44.7 " 8831 29.8 5 888 0.0065 0.484 45.7 " 8377 30.4 5585 0.0070 0.497 46.7 " 7988 31. 1 5325 0.0075 0.508 47. 5 " 7620 31.6 5080 0.0080 0.519 48.3 '* 7298 32.2 4866 0.0085 0.529 49-0 " 7 001 32.7 4668 0.0090 0.539 49-7 " 6738 33 2 4492 0.009s 0.548 50.4 " 6489 33.6 4326 O.OIOO 0.557 51.0 " 6266 340 4178 o.oios 0.56s 51.6 6054 34-4 4036 O.OIIO 0.573 52.1 " 5860 34.8 3907 0.0II5 0.581 52.7 " 5 684 35.1 ^^ 3789 0.0120 0.588 53.2 5513 35.5 3675 O.OI2S 0.59s 53.7 " 5 355 35.8 3 570 0.0130 0.602 54.1 " 5 210 36.1 3 473 0.0135 0.608 54.5 " S067 36.4 3378 0.0140 0.6IS 55.0 " 4942 36.7 3295 0.014s 0.621 55-4 " 4818 36.9 " 3212 0.0150 0.0IS5 0.626 0.632 55.7 56.1 " 4695 37.1 3130 " 4587 37.4 3058 0.0160 0.637 56.4. " 4 479 37.6 2986 0.016s 0.643 56.8 " 4384 37.9 2923 0.0170 0.648 57.2 " 4288 38.1 2859 0.0175 0.652 57-4 4 191 38.3 2794 0.0180 0.657 57.7 4 106 38.S 2738 0.0185 0.662 58.1 " 4026 38.7 2684 0.0190 0.666 58.3 3 943 38.9 2629 0.019s 0.671 58.6 3871 39.1 2 581 0.0200 0.67s 58.9 3 797 39.2 2531 Design of Reinrorced-Concrete Construction Table X. Values for Formulas for Reinforced Cinder Concrete r = 30 p X K So. 6^ K s. s K 6.62 s. St 0.0005 0.159 7.6 100.6 16 000 7.6 100.6 16 000 88 14000 O.OOIO 0.216 14.9 148 " 14.9 148 13.0 129.5 o.oois 0.259 22.0 185 " 22.0 185 " 19.2 162 " 0.0020 0.292 28.8 219 " 28.8 219 " 25.2 192 " 0.0025 0.319 35 8 251 " 35.6 250 15950 28.5 200 12750 0.0030 0.344 42.6 279 " 38.1 14300 30.4 '* II 480 0.0035 0.365 48 .'i 300 15620 40.1 13030 32.0 10 420 0.0040 0.386 50.4 14480 42.1 12 060 33.6 9650 0.0045 0.402 52.2 " 13400 43.4 II 170 34.8 8930 0.0050 0.418 54.0 " 12540 45.0 10450 36.0 8360 0.0055 0.433 55.6 " II 810 46.3 9860 370 7870 0.0060 0.447 57.0 II 180 47.5 9320 38.0 7450 0.0065 0.460 58.5 " 10 620 48.7 8850 38.9 7080 0.0070 0.472 59-7 " 10 120 49-7 8440 39-8 6750 0.0075 0.483 60.7 9660 50.6 8 050 40.5 6 440 0.0080 0.494 61.9 " 9270 51.6 7730 41.3 6 170 0.0085 0.504 63.0 " 8900 52.5 7420 42.0 5 930 0.0090 0.514 63.9 ". 8560 53.3 7130 42.6 5710 0.0095 0.523 64.9 " 8250 54.1 6870 43.2 5500 O.OIOO 0.532 65.7 7980 54-7 6650 43.7 5320 0.0105 0.540 66.4 " 7710 55.4 6420 44.3 5 140 O.OIIO 0.547 67.2 7460 55.9 6 220 44.7 4970 O.OII5 0.555 67.8 " 7240 56.5 6 040 45-2 4820 0.0120 0.562 68.5 7020 57.1 5850 45.7 4680 0.0125 0.569 69.3 6830 57.7 5680 46.2 4550 0.0130 0.576 69.8 " 6650 58.2 5540 46.5 4430 0.0135 0.582 70.4 6460 58.6 5380 46.8 4310 0.0140 0.588 71.0 " 6310 59-2 5 260 47.3 4 210 0.0145 0.594 71.5 " 6 140 59-5 5 120 47-6 4090 0.0150 0.600 72.0 " 6 000 60.0 5000 48.0 4 000 0.0155 0.606 72.6 *• 5860 60.5 4880 48.4 3910 0.0160 0.612 73.1 " 5730 60.9 4780 48.7 3820 0.0165 0.617 73.6 '• 5610 61.3 4670 490 3740 0.0170 0.622 74.0 " 5480 61.7 4570 49-4 3660 0.0175 0.627 74.5 " 5370 62.0 4470 49.6 3580 0.0180 0.632 74.9 " 5270 62.4 4390 49-9 3SIO 0.0185 0.636 75.3 " 5 160 62.7 4300 50.2 3440 0.0190 0.641 75.7 " 5 060 63.1 4 220 50.4 3370 O.OT95 0.645 76.0 " 4960 63.3 4 130 50.7 3300 0.020c 0.649 76.4 4870 63.6 4060 50.8 3240 Reinforced-Concrete Beams of Rectangular Cross-Section. In determin- ing the SIZE OF BEAM required for any given case, r and the limiting values of Sc and St are generally given, and K can be determined for any ratio, p, of con- crete to steel. The value of M, the maximum bending moment, that is, the bending moment at the dangerous section of the beam, is determined from the conditions of loading, the span and the spacing; and the width and depth of the beams are to be found. Formula (i) may then be put in the more con- venient form. d = M_ Kb (5) 932 Reinforced-Concrete Construction Chap. 24 A value for b is assumed and the equation solved for d. Architectural or structural reasons will often limit the width or depth and several trials may hav^ to be made. Reinforced-Concrete Slabs. For the strength of slabs the same formulas apply. A slab may be treated (i) as a rectangular beam of unusual width; (2) as a series of beams set one alongside the other, the width of each beam being equal to the spacing of the reinforcing-rods, and one rod being used for each beam; or (3) as a series of beams of unit width, the area of steel for each beam being the area of reinforcement per unit of width. Check-Formulas. It may sometimes happen that it is advisable to check a given or existing beam-construction as to strength or compliance with speci- fications for working stresses. In that case the following formulas will be convenient (see, also, page 992): (6) (7) If the strength of the beam for the assumed working stresses is to be deter- mined, these values of St and Sc are inserted in Formulas (6) and (7), and the least value of M is used. If the values of M resulting from these equations are not equal, the full benefit of one of the materials is not being obtained. If the stresses in the steel or concrete due to a given loading are to be determined the formulas are put in the following forms: St = M (8) (9) These formulas apply to rectangular beams only. M in Formulas (8) and (9) is the maximum moment due to the external forces, or the maximum bend- ing moment. The value of x can be determined from Tables V to X. In For- mula (8) it will be noted that the denominator of the fraction is an expression for the area of the steel multipUed by the lever-arm of the resisting moment, that is, the distance from the center of gravity of the steel to the center of com- pression in the concrete. Similarly, in Formula (9), the denominator of the fraction is an expression for the area of the concrete in compression multiplied by the lever-arm, x again being determined by Formula (4) and M being the maximum bending moment due to the external forces. Reinforced-Concrete T Beams. Where beams or girders are used in rein- forced-concrete building-construction there are usually accompanying floor-slabs. If these slabs are cast with the beams or girders they add very much to the strength of the latter, and when adequate bond and shearing-resistance are pro- vided between the slab and the stem or beam, economical design requires that the slab shall be considered in determining the strength of the beam. The width of slab that may be taken as part of the beam should not exceed one sixth the span-length of the beam, and the overhanging part on either side of the web or stem should njt exceed six times the thickness of the slab. In any case. Design of Reinforced-Concrete Construction 933 the flange must not be considered wider than the distance between the beams. In ordinary floor- const ruction the spacing of beams, girders, and columns is gen- erally an architectural or commercial consideration. Generally, the simplest pro- cedure, therefore, is to first determine the thickness of slab required for the given spacing of beams, and this determines the thickness of the flange of the T beam. In the calculation of the girder, it is not objectionable to use the same slab, or as much of it as may be permissible, that has been used in the consideration of the beam framing into that girder, as the compression-stresses, in the two cases, act at right-angles to, and practically assist, one another. When, however, the principal slab-reinforcement is parallel to the girder, in the case of a combined slag, beam, and girder-construction, the slab-action produces compression in the same direction as the girder-compression with a resulting overstress in the con- crete. In this case, transverse reinforcement should be provided at right-angles to the girder and extending well into the slab. Formulas for Reinforced-Concrete T Beams. Fig. 17 shows a cross^sec- tion of a T beam resulting from the use of the slab as part of the beam, and I xl Fig. 17, Cross-section of Reinforced-concrete T Beam shows clearly, also, the notation used in the formulas. In a construction of this kind three cases may be considered: Case I. The neutral axis may fall below the flange, in which case M^StA M-- ?"('-f) (lo) (II) In these formulas the small area of concrete in compression below the flange is neglected and the center of compression is assumed to be at the center of the flange. This is done to simplify the formulas. The result is not materially afl"ected and errs on the side of safety. The position of the neutral axis is given by Formula (12) 2r dAs+yt^ ^~ 2d{rAs-^b't) and the most economical percentage of steel by Formula (13) _ Scb'i ^ ~ 2 Stbd (12) (13) M'^^StAsid--] (14) and 934 Reinforced-Concrete Construction Chap. 24 Case 2. The neutral axis may coincide with the under side of the flange, in which case The economical value of p in this case is the same as in Case i, Formula (13). Cas^ 3. The neutral axis may fall above the lower edge of the flange. This case is the same as Case 2, since for purposes of calculation all the concrete in the flange below the neutral axis is neglected and / becomes xd in this case as in the last. Alternate Solution for Cases 2 and 3. In Cases 2 and 3 the section may also be considered as rectangular, with a depth d and a width b', and the for- mulas for rectangular beams, (i) to (9), may be used. Tables V, VI, VII, and VIII are also applicable in these two cases. When the slab is considered an integral part of the beam, adequate bond and shearing resistance between the slab and the web of the beam must be pro- vided. The concrete is ordinarily adequate to take the vertical shear through the flanges next to the stem, and is further strengthened by placing horizontal steel reinforcements across the top of the beam or girder, as described above. Whether or not the resistance to shear is adequate can be determined by the formula 2tb' in which Ss is the unit vertical shear at AB, and Sh is the unit horizontal shear at BC (Fig. 17). This should not exceed the safe unit shear for concrete unless Steel reinforcement is provided. The .value of Sh in the formula is b{d- HI) which, it will be noted, is the total vertical shear divided by the effective area of the stem. Moduli of Elasticity. In the derivation of all these formulas and in the determination of the values of K, the ratio of the modulus of elasticity of the steel to that of the concrete plays an important part. It is necessary then to know what values to use. The generally accepted modulus of elasticity of steel is 30 000 000 lb per sq in. The modulus of elasticity of concrete varies with many conditions. Even in the same mixture, the character of the materials, as well as the manner of mixing and placing, affect it. The modulus increases with the age of the concrete. It also increases with the richness of the mix- ture. It seems to decrease with an increase in the load on the concrete. It should also be noted that the modulus of elasticity as determined from a beam in flexure is greater than that determined from compression- cylinders. More- over the modulus of elasticity as determined from compression varies with the point selected on the stress-strain cuive. The different values for the ratio of THE MODULUS OF ELASTICITY of the stcel to the modulus of elasticity of the con- crete to be used in the design of reinforced-concrete construction, as fixed by the building regulations of various cities and by other authorities, is given in Table II, page 912. Values for the modulus of elasticity of concrete under different Design of Reinforced-Concrete Construction 935 loads and for different mixtures determined by actual tests at the Watertown Arsenal are given in Table XL Table XI. Elastic Properties of Broken-Stone Concrete Twelve-Inch Cubes Composition Cement Sand Broken stone 4 4 4 4 6 6 6 6 12 Age 7 days I mo 3 mos 6 mos 7 days I mo 3 mos 6 mos I mo 3 mos 6 mos Modulus of elasticity in pounds per square inch between loads of 100 and 6oo lb per sq in 2 593 ooo 2 662 000 3 671 000 3 646 000 1 869 000 2 438 000 2 976 000 3 608 000 I 376 000 I 642 000 I 820 000 600 and I 000 lb per sq in 2 054 000 2 445 000 3 170 000 3567000 1 530000 2 135 000 2 656 000 3503000 I 364 000 I 522000 000 and 2 000 lb per sq in : 351 000 : 462 000 ! 158 000 i 582 000 : 219 000 : 805 000 [ 868000 Tests made by * Geo. A. Kimball. * Tests of metals, U. S. A., 1899, page 741. Working Stresses. The working stresses for concrete and steel allowed by various cities are given in Table II on page 912. In the determination of K the values of Sc, St, and r as taken from Table II are substituted in Formula (2), or, the value of K may be taken directly from Tables V to VIII, pages 926 to 929 and substituted in Formula (5). For M in that formula, the maximum BENDING MOMENT duc to the external forces is used. Bending Moments in Beams. Beams and girders are usually considered as SIMPLE BEAMS, that is, as beams supported at both ends, but not built in. Fig. 18. Reinforcement for Uniformly Distributed or Symmetrically Placed Load Fig. 19. Reinforcement for Unsymmetrically Placed Concentrated Load restrained, or continuous, although in many instances they are actually carried, a^ CONTINUOUS BEAMS, over the supports. If continued over a support, there 936 Reinforced-Concrete Construction Chap. 24 is a NEGATIVE BENDING MOMENT at that support, and this negative bending mo- ment should be taken care of ])y reinforcements in the upper part of the beam. This bending moment is one half that at the middle of a simple supported beam loaded at the middle, and two thirds that at the middle of a simple supported beam, uniformly loaded. In the case of simple supported beams loaded either at the middle or with a uniformly distributed load, the bending moments de- crease toward the supports. For these reasons it is advisable in arranging the steel to be used for the tensional reinforcement, to select the bars or rods in pairs, so that, as the supports are approached, a part of the reinforcement may be turned up toward the top and carried across the supports near the top as in- dicated in Figs. 18 and 19. For continuous beams and slabs with um'formly distributed loads, the following are recommended for maximum positive and MAXIMUM NEGATIVE BENDING MOMENTS I "For beams, the bending moment at middle and at support for interior spans, should be taken equal to wl'/ii, and for end spans it should be taken equal to wl^/io for middle and interior support, for both dead and live loads. "In the case of beams and slabs continuous for two spans only, with their ends restrained, the bending moment both at the middle support and over the middle of the span should be taken equal to ie;/Vio-"* Beams simply supported at the ends must be considered as simple beams with maximum positive bending moments equal to wl^/Z. In all the above values, w is the load per linear unit and / the span in the same unit. Bending Moments in Slabs. As floor-slabs are usually carried continuously across the supports, the maximum bending moment due to a uniformly distrib- uted load is assumed to be less than in beams simply supported at the ends. The New York City Regulations provide that "the bending moments at the center and at intermediate supports of floor-slabs continuous over two or more supports shall be taken as T'F//i2." The same regulations provide that "the bend- ing moments of slabs that are reinforced in both directions and supported on four sides and fully reinforced over the supports (the reinforcement passing into the adjoining slabs) may be taken as Wl/F for loads in each direction, in which F=8 when the slab is not continuous or when continuous over one support, and F = i2 at both- center and supports when the slab is continuous over both supports." In these expressions W is the total distributed load and / the span. In square slabs with two-way reinforcement it is usually assumed that the load- ing is uniformly distributed and that half the load is carried by each system. In rectangular slabs the amount of load carried by each system of reinforcement is given by the formula r= (i8) 2 n in which r is the proportion of load carried by the transverse reinforcement, W the total load on the slab, and n the ratio of its longer to its shorter side. Using this proportion of load, each set of reinforcements is calculated as a slab with supports on two sides only, and the total number of rods required is de- termined on the assumption of equal spacing. The rods may then be spaced uniformly at the usual spacing for the central half of the slab and gradually re- duced in number per foot of width to the edge of the slab, using one half as many rods for the remaining two quarters. In this way, the amount of reinforce- ment is reduced 25%. When the length of the slab exceeds the breadth by 50%, the stresses in the longitudinal steel become so low that the construction is * Trans. Am. Soc. C. E., 1917, page 1127. Design of Reinforccd-Concrete Construction 937 uneconomical. The slab should then be treated as one with a one-way reinforce- ment. Shrinkage-Stresses and Temperature-Stresses. In slabs resting on or carried over two support's some reinforcement should be provided at right- angles to the tension-rods to provide against shrinkage-stresses and tem- perature-stresses. Incidentally, this reinforcement may also serve to keep the tension-rods properly spaced. In general it should not be less than one third of one per cent in amount and well distributed. It is common practice to use from J^ to ^-in rods, spaced about 2 ft apart. Deformed bars with irregu- lar surfaces and reinforcements of small diameters, placed as close as practi- cable to the surface, are most effective. The Disposition of the Steel. In designing the reinforcement for any form of loading, the full sectional area required must be provided at the point of MAXIMUM bending MOMENT. As the supports are approached, part of the reinforcement, as already indicated, is turned up, but care must be taken to keep it so distributed that at any point there is still sufficient reinforcement below the neutral axis to furnish the necessary tensional resistance. The arrangement of reinforcement for a uniformly distributed or symmetrically disposed load is shown in Fig. 18, and for^an unsymmetrically placed concentrated load, in Fig. 19. In the first instance the maximum bending moment is at the middle of the beam, the reinforcement is symmetrical about that point, and as much as one half the amount of reinforcement may be turned up. In the second instance the maximum bending moment is at some other point than the middle, the rein- forcement must be so disposed that the full amount required will be under the load or at the point of maximum bending moment, and the turning up must be done between that point and the support. Other conditions might require less than half the reinforcement to be turned up. There is another reason for turning up the reinforcements toward the ends. In addition to the resistance to the NEGATIVE BENDING MOMENT, there is a resistance to the shear offered by the metal running through the concrete at the points where the diagonal TENSION occurs. The Percentage of Reinforcement. The amount of the reinforcement in any case is determined by Formulas (3) and (13) for rectangular and T beams respectively. The values obtained by these formulas give the most econom- ical amount. This may vary from 1,4% to iH% of the cross-section area of concrete, but will usually run about ^io%- The nearest stock size of rods giving this amount or a slightly greater amount can be selected from the table given on page 15 14, or from the catalogues of the manufacturers of the various deformed bars.* The number of rods used to make up the necessary sectional area must be determined by considerations mentioned in the follow- ing paragraphs. The Number of Reinforcing-Rods. As already suggested, an even number adapts itself better to a symmetrical or balanced arrangement both in cross-sec- tion and horizontal section. One rod does not permit of the turning up toward the support. Two rods may be made either to continue along the lower edge of the beam, or one may start at one support, run along the lower part and turn up be- yond the middle as it approaches the second support; and the second rod run similarly along the bottom from the second support and turn up after passing the middle as it approaches the first support. Three rods may be arranged so that two continue along the bottom and the third, the middle one, turns up as it ap- proaches the supports. The arrangement for 4, 5, or 6 rods will naturally suggest * See, also, paragraph on Commercial Sizes, page 915. 938 Reinforced-Concrete Construction Chap. 24 itself from what "has been ah-eady said. Too large a number of rods is not de- sirable, as a large number of them together acts more or less as a screen for the coarser particles of the concrete and prevents a close contact between it and the steel. This matter of complicated reinforcement is one of considerable practical importance. If, however, the steel is satisfactorily incased with concrete, a larger number of small rods is preferable to a small number of larger ones. The AREA OF CONTACT of a rod of smaller size is proportionately greater than that of a rod of larger size, as the perimeter varies directly as the diameter, and the sectional area as the square of diameter of the cross-section. In order that a rod may not slip, the adhesion of the steel to the concrete must be equal to or greater than the tension in the steel. The Adhesion Required. The tension in a reinforcing-rod at any point having been determined from the given formulas, it must next be determined if, in either direction from that point, the area of contact of the steel is large enough tc make the total adhesion equal to or greater than the tension. If there is a deficiency in this respect it must be made up either by a mechani- cal bond or by anchoring the reinforcements at the ends. Safe values for adhesion of concrete and steel are given in Table II, page 912. A safe rule to apply, without calculation, to the case of beams with a maximum bending moment at the middle, is to make the diameter of the rods not more than one two-hundredth of the span. Under ordinary conditions, generally speaking, the length of rod on either side of the point of maximum bending moment should be at least eighty diameters for plain rods, and not less than fifty diameters for deformed bars. Under unusual conditions the adhesion should be carefully studied. The apparent discrepancy between the first and second statements of this paragraph is explained by an allowance made and based upon the fact that the tension in the steel does not decrease uniformly with the decrease in dis- tance from the supports. The allowance is purely arbitrary but is considered safe. For cases of unsymmetrically loaded beams it is best to examine care- fully into the conditions. The Separation of the Rods. It has not been unusual in tests on beams to have the concrete split off from the under side along the line of the reinforce- ment. This is due in part, if not entirely, to an insufficiency of concrete between and around the reinforcement. To avoid this the spacing or separation of the reinforcing-rods in the cross-sections of the beams must be such that the resistance of the concrete to shear at the level of the rods is at least equal to the ADHESION of the concrete to the steel. As a general rule the rods should be spaced not less than two-and-one-half diameters on centers and about two di- ameters from the sides of beams. The clear distance between rods and the space between rods and edges of beams should in no case be less than iH in. De- formed bars, if stressed to their full tensional value, should be spaced farther apart, than plain bars. At the middle of a beam, the bond-stress is low, but at the top of a continuous beam, over the supports, where the negative moment de- creases rapidly, the bond-stress is apt to be excessive and frequently limits the diameter of the reinforcement. Provisions against Shear or Diagonal Tension. Numerous tests of beams reinforced with horizontal rods without stirrups or inchned reinforcement have shown that diagonal cracks occur when the maximum shear over the cross- section is from 100 to 200 lb per sq in. Tests conducted on concrete with the purpose of eliminating all other stresses but direct shear have given a shearing strength of concrete of from 800 to i 600 lb per sq in. The ordinary concrete beam has, therefore, a cross-section of sufficient area to withstand a shearing- STRESS of 200 lb per sq in. The cracks always occur at points where a large Design of Reinforccd-Concretc Construction 939 SHEARING -STRESS exists in combination with moment-stresses. Under con- centrated loads, diagonal-tension failure occurs under the concentration, and in a simple beam under a uniformly distributed load, the cracks appear near the supports. The inclination of the diagonal tension in the concrete being a resultant of two-forces, changes, therefore, with the variations of shear and TENSION. For beams with horizontal rods only, that is, beams in which the wer-stresses are resisted by the concrete, the safe shearing values to be used under various building regulations are given in Table II, page 912. The shearing-stress in this case is determined by dividing the total vertical shear by the product of the effective depth, that is, the distance from the center of compression to the center of the steel, by the width of the beam. The maximum shearing-stress shouid, in this case, not exceed 2% of the compressive strength of the concrete. When the resistance of the concrete to shear is not sufficient, web- reinforcement must be provided by one of the following methods or by a com- bination of them: (i) By attaching to or looping around the horizontal members, stirrups or vertical members; (2) By securely attaching inclined rods to the horizontals in such manner as to prevent slipping; • (3) By bending of a part of the longitudinal reinforcement at certain points, thus providing against the diagonal tension and allowing a sufficient amount of horizontal steel to remain to resist the direct tension. It is customary to use the calculated vertical shearing-stress as a measure of the diagonal tensile or web-stresses. In all cases, the concrete may be assumed to carry its safe load, and it is ordinarily assumed that two thirds of the external vertical shear is resisted by the web-reinforcement. For beams reinforced with web-members, the total vertical external shear over the ef- fective section should not exceed 6% of the compressive strength of the con- crete. The Building Code of New York City specifies that the shearing-stress in concrete, when all the diagonal tension is resisted by steel, shall not exceed 150 lb per sq in. For beams in which part of the longitudinal reinforcement is in the form of bent-up rods, the maximum vertical shearing-stress should not exceed 3% of the compressive strength of the concrete. The stresses in web-reinforcements may be determined by the following formulas: for stirrups P = Vs/l (i^) for members inclined 45°, not bent-up bars, P = 0.7 Vs/l (20) in which s is the horizontal spacing of the web-members, V the total external vertical shear, / the eflective depth from center of compression to center of steel and P the stress in a single reinforcing-member. Fixing the allowable tensile stress at 16 000 lb per sq in, the spacing of web-members is expressed by the following formulas, when A is the cross-section of a web-member: s =16 000 Al/V (^^) and s = i6ooo AI/0.7V (22) In determining the length of horizontals necessary to pr(^rly care for the bending stresses, the same method may be employed as for plate girders, the 940 Reinforccd-Concrcte Construction Chap. 24 remainder of the bar being carried up as an incHned member and carried over the top of the supports in continuous beams. The rods remaining at any ix)int at the bottom or top must be of sufficient sectional area to carry the direct tension beyond this point. There must also be a sufficient length beyond this point to prevent slipping. Web-members must be so spaced that therfe will be a reinforce- ment intersecting every 45° line of rupture below the neutral axis. The New York City Code prescribes that the spacing of the web-members should not exceed three fourths of the depth of the beam in that portion where the web- stresses exceed the allowable value for shear in concrete. Sufficient bond- strength of web-reinforcement should always be provided in the coivrPRESSiON- siDE of the beam. In simple beams, that is, beams resting on two supports, the ends of the bars should preferably be bent into hooks. Where bent up through large angles, web-members should extend horizontally along the upper part of a beam for some distance. Attached Shear-Members. Stirrups need not be firmly attached to the ten- sional reinforcement; but the allowable bond-stresses and shearing-stresses in the concrete must not be exceeded in transmitting the stresses between stirrups and longitudinal rods. The stirrups and inclined members must also develop sufficient bond-stresses to transmit the entire stresses for which they are de- signed, and they must sometifiies be supplemented with anchorages in the com- pression-side of the beam. It is, perhaps, better to have them attached, as they will certainly assist in anchoring the tensional reinforcement. Different forms of stirrups and methods of attachment are used. In the Kahn system (Fig. 11) the stirrups form a part of the tensional reinforcement. The U form, either upright or inverted, is a very common form of stirrup, and may be a rod of either round or square cross-section, or a flat strap as shown in Figs. 10 and 13. The Hennebique system employs both inclined rods and vertical stirrups. In some cases, when the slabs and beams are constructed together, the slab-rein- forcement is carried through the upper ends of the stirrups. The Bond between Steel and Concrete. The bond between the steel in tension and the concrete must not exceed the safe working value. If the bond is not sufficient, the rod will slip. Tension-rods must, therefore, never be too large to develop sufficient bond-strength to transmit the stresses. Where bent-up bars are employed, the bond-stresses in places, in both the straight and bent bars, will be higher than if all bars are straight. In cantilever beams, the ends of the bars at the supports are fully stressed and the bars must be carried into the supports and anchored to develop this stress. In anchoring bars, an additional length must always be provided above that required, on the Assumption of uniform bond-stresses. Wherever possible, adequate bond- strength should be provided throughout the length of the bar in preference to end-anchorage. Between plain bars and concrete the bond-strength may be assumed to be 4% of the compressive strength of the concrete. The Breadth of a Reinforced-Concrete Beam of Rectangular Cross- Section. The breadth of a rectangular beam, and of the stem of a T beam, as already indicated, is generally dependent upon the amount of reinforcement necessary, and it is equal to the sum of the diameters of the tension-rods, the required spaces between them, and the amount of concrete outside of the rods needed to resist the shearing-stresses and to protect the steel. When no stirrups are used in a beam it is necessary, also, to make the width of the concrete suffi- cient to resist the horizontal shearing-stresses. This width should be at least equal to the sum of the perimeters of the tensional reinforcing-rods. The amount of concrete to be provided below the steel is fixed by the requirements for proper protection of the steel against fire and corrosion. (Pages 955-962.) Design of Reinforced-Concrete Construction 941 Compression-Rods in Beams and Girders. Steel reinforcement in the form of rods is sometimes provided above the neutral axis in beams and girders for the purpose of providing additional compressive strength where there is not sufficient concrete above the neutral axis to resist the total com- pression. If steel reinforcement is to be used for this purpose, the steel should be placed as high as possible, and the allowable unit compression in the steel limited to the actual compression in the concrete at that point multiplied by the ratio of the modulus of elasticity of the steel to that of the concrete, as in the case of columns with vertical reinforcement. The use of steel in com- pression in beams and girders, however, is not recommended, since at best it is very uneconomical and the steel has a tendency to buckle and disrupt the concrete. Reinforced-Concrete Columns. Reinforced-concrete columns are of three general types: (i) concrete with vertical reinforcement near the outer surfaces; (2) concrete wrapped with spirally-wound wire or with metal bands; (3) concrete with a metal core. Lengths of Columns. The lengths of reinforced-concrete columns are vari- ously Hmited by different authorities as follows, the figures being in each case the ratio of the length to the least lateral dimension: New York 15 Chicago 12 Philadelphia 15 St. Louis IS Cleveland 15 Baltimore 16 San Francisco 15 Buffalo 15 Detroit 15 New York limits, also, the least side or diameter to 12 in, and San Francisco to 10 in. , Vertically-Reinforced Columns. In determining the strength of columns with vertical reinforcement, the steel is assumed to carry a load per square inch equal to the working load per square inch on the concrete times the ratio of the moduli of elasticity of the steel and concrete. The allowable stresses, ratio of moduH, etc., are given in Table II, page 912. For example, in New York a load of 500 lb per sq in is allowed on the concrete, and 15 times 500, or 7500 lb per sq in on the steel, 15 being the ratio of the moduli, as fixed by the regulations, for 1:2:4 concrete and steel. Not less than K% nor more than 4% of vertical reinforcement should be used in reinforced-concrete columns. The reinforcing- rods should be tied together horizontally at intervals of not more than the least side or diameter of the column. This prevents, to a great extent, the buckhng of the reinforcement under load and the consequent splitting of the concrete. The vertical reinforcement, in order to serve its purpose of taking up the bending in the column, should be placed as near the outer surfaces of the column as possible, consistent with proper protection of the steel. (See page 958.) If tension is possible in the longitudinal steel, due to bending, the bars must be spliced to resist the stress. In the disposition of the steel- the same pre- cautions are necessary as in the case of beams, in order to avoid a too close spacing of the reinforcing-pieces or an excess of reinforcing-material. (See page 937.) As the concrete in columns is generally poured into the molds at the extreme top, it is particularly important to keep the interior^ free from interlacing steel across the column. In columns in which the steel is assumed 942 Reinforced-Concrete Construction Chap. 24 to furnish part of the compressive strength, it should be made continuous from the columns of one story into those of the stories below. The rods extending from one column may be connected with those above or below by means of pipe-sleeves. Laterally-Reinforced Columns. Tests made on hooped concrete columns at the University of lUinois in 1907, at the Watertown Arsenal in 1906, and at the University of Wisconsin in 1906 and 1907, show that the ultimate compressive strength of such columns is increased from 500 to i 000 lb per sq in for each percentage of hooping employed. The increase of strength is due to the lateral COMPRESSIVE STRESSES developed by the restraining action of the hoops or bands at right-angles to the direct compressive stresses. Below the limit of elasticity, however, very Httle stress is developed in the lateral steel, and the tests show that at an early stage, the deformation or shortening of the column is equal to that of plain concrete. With further loading, the laterals begin to work and prevent failure, thus increasing the so-called toughness of the column and the ultimate compressive or breaking strength. This efifect has been va- riously allowed for by considering the hooping-metal equivalent to and replaced by imaginary longitudinals. Considere and other investigators have shown that the hooping is equivalent to 2.4 times as much longitudinal steel. It is gener- ally conceded that hooping permits of a somewhat higher unit stress in the con- crete. The New York City Building Code permits an axial compression in such columns, having not less than H% nor more than 2% of hoops or spirals spaced not farther apart than one sixth the diameter of the enclosed column nor more than 3 in, and having not less than 1% nor more than 4% of vertical reinforce- ment, not to exceed 500 lb per sq in on the concrete within the hoops or spirals, nor 7 500 lb per sq in on the vertical reinforcement, plus a load per square inch on the effective area of the concrete equal to twice the percentage of lateral reinforcement multipHed by the permissible tensile stress in the lateral reinforce- ment. St. Louis and Cleveland permit 2.4 times the volume of hooping to be considered as longitudinal reinforcement; Chicago 2.5 times; and Cincinnati 2.2 times. ^ New York Requirements Expressed by Formulas. The safe loads for reinforced-concrete columns according to the requirements of the New York Building Code may be determined by the following formulas, in which W= total safe load, in pounds; Ae = the effective cross- sectional area of concrete, in square inches, which, in the case of columns with longitudinal reinforcement only, may be taken as the entire area, and in the case of hooped columns is limited to the area within the hoops; As— the cross-sectional area of' the longitudinal steel, in square inches; p = percentage of lateral reinforcement (hooping), that is, the volume of the hooping divided by the volume of the concrete enclosed within the hooping, for each unit length of column; Sc= allowable compressive stress in the concrete, in pounds per square inch, which is taken at 500 for i : 2 14 concrete, and at 600 for i : i^ : 3 concrete; 5s = allowabte compressive stress in the steel, in pounds per square inch, which is taken at 7500 when 1:2:4 concrete is used, and at 7200 when I : i}4 : 3 concrete is used; Sh= allowable tensile stress in the hooping steel, in pounds per square inch, which may be taken at 35% of the elastic limit, but not more than 20 000. Design of Reinforced-Concrete Construction 943 For columns with longitudinal reinforcement only, W = AcSc + AsSs but the area of the steel must not be less than i^%, nor more than 4% of the area of the concrete, and the reinforcement must be secured against displacement by 34-in steel ties spaced not farther apart than 15 diameters of the vertical rods, nor more than 12 in. Example. What is the safe carrying capacity of a 12-in square column of 1:2:4 concrete, reinforced in each corner with %-m square bars? Solution. The area of the concrete may be taken at 12X12 =.144 sq in. A K-iu square bar has a sectional area of 0.7656 sq in. The area of the steel is 4 X 0.7656 = 3.06 sq in, a little over 2% reinforcement. The allowable stresses for concrete and steel are 500 and 7500 lb per sq in, respectively. Hence W = 144 X 500 +3-o6 X 7 500 = 94 950 lb = 473^ tons For hooped columns, W = AcSc + AsSs-^2pAcSfi with longitudinal reinforcement not less than 1%, nor more than 4%, and hooping not less than }4%, nor more than 2%, the hooping being spaced not farther apart than one sixth of the diameter of the enclosed column, and at most, 3 in. Example. Determine the maximum load that should be placed on a 24-in round column of i : i}4 -^ concrete, with spiral hooping of Mo-in cold-drawn wire, having a 3-in pitch, and reinforced longitudinally with six i-in round bars, equally spaced just inside the hooping, and fastened to it, the concrete being 2 in thick outside the hooping. Solution. The effective sectional area of the concrete has a diameter of 20 in, and is therefore 20 X2o>:o. 7854 =314.16 sq in. For an inch in height, the cubic contents of the concrete is 314.16 cu in. The area of a i-in round bar is 0.7854 sq in. The area of longitudinal steel is 6X0.7854=4.71 sq in, about i}4%. The cross-sectional area of yie-in wire is 0.0767 sq in. The length of one turn of wiqe is 62.75 iu, and as the turn is made in a height of 3 in, the cubic contents for an inch of height of the column is K X 62.75 X 0.0767 = 1.60 cu in, about H%. The working stress per square inch for the con- crete is 600 lb, for the longitudinal steel 7 200 lb, and for the hooping 20 000 lb. Hence W = (314-16 X 600) + (4.71 X 7 200),+ (2 X o.oos X 314-16 X 20 000) = 285 240 lb, or 142.6 tons Details of Lateral Reinforcement. At the top or base of the columns in each story, the wrapping should be made to continue through the floor-con- struction. Under certain conditions, when the floor-construction is practically silid about the columns, thus affording good lateral support, equal to the wrapping, it may be better to omit the wrapping and avoid the possible com- plication of steel reinforcement from column, girder, and floor-construction and the consequent breaking of the bond of the concrete. The materials used for the wrapping are either steel wire or steel bands. When wire is used it is spirally, wound and continuous through the full length of the column. The ends of the wire are turned into the column and turned down to such an extent that when the concrete has been poured and set, there will be sufficient anchorage to resist 944 Reinforced-Concretc Construction Chap. 24 the tension in the wrapping due to the outward pressure of the concrete. When metal bands are used, as in the Cummings system, care must be taken to make the riveted joints in the bands as strong as the bands themselves. A form of wrapping that has the merits of rapidity and ease of erection is shown in the columns used in the Bush Terminal Warehouse, Borough of Brooklyn, New York City, described on page 958. 'ilh. Fig. 20. Concrete Column with Steel Core Metal-Core Columns. The object of this type of column is to provide a construction for tall or heavily loaded buildings that will have the necessary strength and yet not encroach too seriously on the floor-space. For this form of column some engineers advocate placing a steel core through the axis of the concrete, the steel taking the bulk of, if not all of, the load.* "A rational basis of design is to determine the strength of the steel column by the use of the column- formula for the proper l/r of the column and to consider the concrete of the core- • Trans. Am. Soc. C. E.. Vol. XIV, Part E, page 556. Design of Reinforced-Concrete Construction 945 section to have a stress-value proportional to the strength of plain con- crete." * William H. Burr designed a column (Fig. 20) for the McGraw Building, New York City. The steel core has sufficient strength as a column, independent of any concrete, to carry the entire dead load coming upon it, the stresses in the steel being in no case greater than those allowed on steel columns under the New York Building Code, consideiing the ratio of length to radius of gyration. Furthermore, those stresses were not allowed to exceed 9 000 lb per sq in in any case. The Uve loads were provided for by placing enough concrete within the steel framework to prevent the stress on the concrete from exceeding 750 lb per sq in. This is one twelfth of the maximum allowable load on the steel. The concrete outside of the steel was considered only as a protection against fire and corrosion. Columns of this type should be designed with caution. The concrete should not be rehed upon to tie the steel units together or to* transmit stresses from one unit to another. The units should be tied together by tie- plates or lattice-bars in conformity with the standard practice for structural steelwork. For high percentages of steel, the concrete will develop low unit stresses, and caution should, therefore, be used in placing dependence upon the concrete, t Rich Mixtures of Concrete. Increasing the proportion of cement in a mixture increases the ultimate strength of the concrete projx)rtionally and is effective in designing columns with smaller cross-sectional area. The increased compressive strength is also accompanied by a higher modulus of elasticity. Furthermore, the employment of a rich mixture also permits of higher propor- tional stresses in the steel and consequently a more economical design. The internal stresses in a monoHthic member, however, may be considerably com- plicated by the excessive shrinkage of rich mixtures, which have a tendency to crack. The New York Building Code provides that "in concrete columns the compression on the concrete may be increased twenty per cent when the fine and coarse aggregates are carefully selected and the proportion of cement to total aggregate is increased to one part of cement to not more than four and one-half parts of aggregate, fine and coarse, either in the proportion of one part of cement, one and..one-half parts of fine aggregate, and three parts of coarse aggregate, or in such proportion as will secure the maximum density. In such cases, how- ever, the compressive stress in the vertical steel shall not exceed seven thousand two hundred pounds per square inch." Cummings Lateral Reinforcement. Robert A. Cummings of Pittsburgh, Pa. (Electric Welding Company), following a European practice, has applied a method of reinforcing compression-members by placing horizontal wire spirals in planes at right-angles to the main compressive stresses. This practice is based on the theory that the failure of a concrete prism will take place along Hues parallel to the direction of the applied load. The method has been very success- ful in reinforcing the heads of precast concrete piles, driven by hammer. Cast-Iron Columns. When a building for any reason need not be treated as a fire-proof structure, space and time may be saved by using cast-iron or STEEL COLUMNS. In such cases the column-connections must be designed with suitable bearings for the concrete construction and so that there will be a con- tinuity in that construction; for the great advantage in reinforced-concrete construction lies in its monolithic character. When cast-iron columns are used, the heads of the columns may be cast with openings through which the * tlniversity of Illinois Bulletin, No. 56, 1912. t Proc. Am. Soc. C. E., Feb., 1913, page 153. 946 Reinforced-Concrete Construction Chap. 24 reinforcement may pass from one side to the other. Fig. 21 nhows how this has been done in a building at Gay and Christopher Streets, New York City with- out impairing the strength of the columns at the connections. Granolithic ^Finish Cinder Concrete ^—^ -:^ .1st Story/ Column W Pintles P to have a combined Area equal to the Area of the Column they have to Support, to be cast on at top of Support-, ^ Basoraent ing Column. Column Fig. 21, Connections for Cast-iron Columns and Reinforced-concrete Construction Steel Columns. In steel columns it is simpler to provide connections between the reinforcing-rods and the steel shapes of the columns. When the reinforcement does not go through the columns, some rods should be placed outside of them to tie as much as possible the concrete on one side to that on the other. Eccentric Loads. Bending stresses due to lateral and eccentric loads must be computed so that- the combined direct and bending stress does not exceed the allowable maximum stress for axial compression. Formulas for eccentric loading on columns are given in Chapter XIV, pages 453 and 486. Concrete Walls. If not reinforced, concrete walls are generally required to be of the same thickness, for given conditions, as brick walls. Under such cir- cumstances they are not as economical as brick walls. If reinforced and used as bearing-walls, they can be reduced to about two thirds the thickness of brick walls, provided, however, that the bad on the concrete does not exceed the safe load per square inch permitted on reinforced columns. The ratio of unsupported height to thickness should not exceed that fixed for columns. For spandrel- walls, supported entirely on girders, the minimum thickness should be 4 in. Such walls should be reinforced with not less than % lb of steel per square foot of wall, in the form of rods placed vertically and, less frequently, horizontally. Reinforced-Concrete Footings. (See, also, pages 186, 225, and 226.) The principles underlying the design and construction of reinforced-concrete footings are the same as those applied to other types of footings. In wall, pier, or column- footings, the overhang or off-set must be considered as an inverted cantileveK loaded uniformly with a load per square foot equal to the load per square foot imposed on the underlying soil. The reinforcing-rods will then necessarily be placed near the lower surface of the footing and the size and number determined by formulas given on page 925. A detail often overlooked in reinforced-con- Design of Rein forced -Concrete Construcdon 947 Crete footings is the tendency to shear at the edge of the wall, pier, or column supported. When footings would otherwise become very eccentric, cantilevers should be resorted to, the same as for steel construction. (See pages 165 to 169, and 978 to 982). The maximum bending moment on the cantilever is deter- mined and the concrete girders designed as described on page 925. Steel in footings should be protected by at least 3 in of concrete. Economy of Reinforced-Concrete Footings. Great economy over steel- grillage or other types of footings may often be effected by the use of rein- FORCED-coNCRETE FOOTINGS. The cost of the latter type will vary from 20 to 40% of the cost of a corresponding steel-grillage footing. This difference is easily accounted for. The amount of excavation for the reinforced footing is generally much less than for the steel grillage. A smaller amount of concrete is used, and this concrete is considered in the calculations for strength; whereas in the steel grillage, the concrete is chiefly provided for incasing and protecting the steel. The amount of steel is much less, being used only to supply the ten- sional resistance of the construction, .the compressive strength ])eing supplied by the much cheaper material, concrete. Incidentally, the protection of the steel in the reinforced footing is generally more certain than in the steel -grillage footing. Concrete Piles. Concrete piles are discussed in Chapter IT, pages 196 to 200, and some of the types are there described. Connections in Reinforced-Concrete Construction. Much good Judgment can be displayed and must be 'exercised in the design of the details in these connections. The great value of reinforced-concrete construction over other types is the possiinlity of securing great rigidity. This can only be attained when the result is as nearly monolithic as possible. We than have mass to take up vibration and this advantage, in the case of workshops or factories in which there is machinery, is readily seen. The reinforced-concrete buildings that came through the severe San Francisco earthquake in May, 1906, in good condition, were those in which attention had been given to the details and con- nections. ITo secure a monolithic character requires continuity not only in the concrete, but also in the reinforcement. This often means that there is a net- work of steel at the connections. If this is carried to excess, the bond and con- tinuity of the concrete is apt to be broken, even when the spaces between the steel units are thoroughly filled. But when there is such a network of steel it also acts like a sieve and the spaces are not readily filled. For this reason it is well to use a richer mixture at the columns and to keep the aggregate as small as possible. The connections of floor system to columns are particularly trouble- some in this respect, and partly for this reason and partly to insure rigidity, brackets should be provided under the girders at the columns, with metal rein- forcement near the inclined surfaces of these brackets. Reinforced-Concrete Stairs.* Some of the most interesting work that has been done in reinforced concrete has been the construction of stairs. The rein- forcement, being in the form of comparatively small, hmber bars, can be adapted to almost any shape for which molds can be constructed, and when a wet, rich concrete with small aggregate is used, little or no difficulty need be experienced in casting. As an example of such work, the stairs in the residence of G. W. Vanderbilt, in New York City, may be cited. When these stairs were five weeks old a test of their strength was made, without distress, by dropping a bundle of four bags of cement, weighing about 380 lb, from the floor aliove to * See, also, pages 9cx> and 983. 948 ' Reinforced-Concrete Construction Chap. 24 the intermediate platform, a distance of ii ft. No injurious effects were no- ticed.* 4. Types of Reinforced-Concrete Construction f Mill-Construction. In locaHties where the cost of labor is high and where the conditions cause more or less congestion, it is probably more economical to use brick instead of concrete for the walls. In such cases the type of construc- tion is similar to ordinary mill-construction. Provision must be made to an- chor the beams and girders, and this can be done by bending the ends of the reinforcing-rods so that they will extend horizontally into the walls on each .side. Skeleton Construction. The skeleton type of construction seems to be the form best adapted to reinforced concrete. A framework of columns, girders, beams, and flooring is built, as in steel construction, the wall-girders and columns, of course, being designed to carry the weights of the outside walls as well as that part of the floor-loads and live loads which comes on them. The work, in this type of construction, can generally progress more steadily than in the mill- construction since the concrete work need not be stopped at any time to wait for the brickwork to be carried up, if brick is used for the walls. In the skele- ton construction any type of outside wall may be used; brick, concrete, tile, etc. In some cases the panels are simply filled in with brickwork, 8 or 12 in* thick, leaving the concrete columns and girders showing between the brick panels. For walls situated on property -lines where adjoining buildings are likely to be erected, this is not objectionable. If the wall remains exposed and a good appearance is a consideration, the columns and girders can be treated architec- turally to set off the brickwork; or the brickwork may be continued as a facing over the outside of the columns and girders. This was done in some of the Bush Terminal Warehouses, Borough of Brooklyn, New York City. J To thoroughly secure this brick facing, galvanized anchors were placed in the concrete columns and girders as they were erected, projecting sufficiently to bond into the brick- joints. In using concrete for the panels the sides of the columns are cast with pockets, grooves, or recesses to receive the panels, which, as in the case of brick- work, are most satisfactorily and most economically built after the removal of the molds from the skeleton frame. In the Marlborough-Blenheim Hotel, at Atlantic City, N. J., the panels are filled in with hard-burned terra-cotta tiles and a stucco applied on the outside. This makes a comparatively light con- struction and affords good insulation. The particular advantage in the skele- ton TYPE of construction, especially for workshops and factories, is the possibihty of large window-areas affording light and ventilation. System M. A type of construction known as System M has been developed by the Standard Concrete Steel Company of New York City (Fig. 22). It con- sists of a light steel skeleton frame designed to carry the dead load of the entire structure, except that the columns are designed to carry the gross loads. The structure is incased in concrete, making ultimatelya reinforced-concrete construc- tion. § Its advantage consists in its adaptation to the erection and inspection of the steel reinforcement before even the centers or molds are placed in position. Under congested conditions, such as prevail in large cities, it is a rapid form of * For a detailed description, see Cement, Jan., 1904, and Engineering Record, Dec. 12, 1903. P'or other examples of stair-construction, see Engineering News, June 30, 1904. t See, also, Chapter XXV. i For a description of this building, see Engineering Record, March 3, 1906. § For fuller description, see Engineering News, April 25, 1907, and Engineering Record, June 22, 1907. Types of Reinforced-Concrete Construction 949 construction. The use of the steel in this type is, however, not economical. In order to get the necessary strength in the steel framework, shapes must be used which do not offer the amount of adhesion that should result from the Fig. 22. System M Type of Jleiuforced -concrete Construction j amount of metal used. Furtliermore such shapes must necessarily be subjected to some bending, which tends to break the bond between concrete and steel. Flat-Slab Construction.* In this form of construction beams and girders are eliminated almost completely, if not entirely, and the slab is made to rest directly on the columns; the tops of the columns are enlarged into extended caps. This system of construction employs a shallower floor-construction than is ordi- narily attainable. The floor-centering, too, for purposes of erection, is somewhat simpler, especially in those forms of slabs in which the lower surface is all in one plane. The slab may be of uniform thickness between the edges of the column- capitols, or a portion of it, symmetrical about the columns, may be thickened to form a column-drop, or the slab may be thickened to form a band or shallow beam between columns, with a paneled ceiling at the center of the panel. Based on the method of reinforcing the slab and columns, a number of systems have been developed which may be divided into four general classes: (i) the TWO-WAY system; (2) the four-way system; (3) the three-way system; and (4) the circumferential system. In the tw^o-way system, the reinforcement is placed in direct bands between thf^ columns in both directions, with an interior system of two-way rectangular bands on the remaining panel-area at the center. In the four-way system, the reinforcement is placed in two direct bands in the two rectangular directions, and in two diagonal bands which cross the panel diagonally between columns. In the three-way system the reinforcement is placed in bands directly connecting the columns and passing over the column- heads. In the circumferential system, circumferential reinforcement is placed around the columns, with bars radiating from the column-centers. Con- centric rings of reinforcement are also placed at the center of the sides joining column-centers, which overlap the circumferential reinforcement at the columns, and the center of the panel is reinforced in a similar manner. Some of the systems developed are modifications of the above or a combination of two or more of the general types described. The principles of design are based on empirical analyses determined by extensometer tests made on completed buildings. Akme System. This is a two-way system developed by the Condron Company, Chicago, III. It is constructed either with a slab of uniform thick- ness, with a drop-panel, or with a paneled ceiling. Each panel of the slab is * See, also, Girderless Floors, Chapter XXV, page 993. 950 Reinforced-Concrete Construction Chap. 24 divided into two sets of strips, called the main-slab strips and the mid-slab STRIPS, which are designed as flat, shallow beams. Corr-Plate System. This type of construction has been developed and in- stalled by the Corrugated Bar Company, Buffalo, N. Y. The construction is similar to other two-way systems and is installed either with or without drops. The reinforcement is distributed across the entire slab, with varying spacing to resist the stresses determined experimentally. Mushroom System. The mushroom system, invented by C. A. P. Turner, MinneapoUs, Minn., is one of the earliest of the flat-slab constructions. The striking and essential feature which gives this system its name is the gradual spreading out of the column at the top to form a cap, the diameter of which is seven sixteenths of the sum of the distances between columns in the direction of the sides of the slab. The longitudinal column-reinforcement is bent to follow the curved outer surface of the cap, and the cap is reinforced both radially and circumferentially. The slab-reinforcement is placed at the top of the slab over the columns and allowed to sag to a catenary curve with the low point near the bottom of the slab at the middle of the span. The thickness of the slab varies from \ii5 to y20 of the shorter distance between the column-centering. This is essentially a four-way systJ'.m with the added features described above. The Cantilever Flat Slab, designed by the Concrete Products Company, Chicago, 111., is another type of four-way system. It differs from the one de- scribed in the preceding paragraph mainly in the construction of the column-cap. The column-bars are not bent to the shape of the cap but continue up straight. The horizontal cap-reinforcement is provided by a shop-made frame of radial bars, held together by a Diamond Bar which is intended to resist the circum- ferential stresses. The diameter of the cap is about yio the span and the thick- ness of the slab about Hs the span. Whenever necessary to provide for large shearing-stresses and bending-stresses around the column, the slab is increased in thickness at that point, forming, in appearance, an extended cap at the column-head, l.ater extensometer tests have proved the use of radial rods with rings around the column-heads to be inefficient, and they therefore have been abandoned. Three-Way System. This system was invented and patented by David W. Morrow, Cleveland, Ohio. The columns are located at the apexes of equilateral triangles, making equal the bands of steel between the columns. The reinforce- ment over the columns is placed in three instead of the four layers of the four- way systems. Flaring circular caps, with hexagonal or circular drops, are pro- vided over the columns. S. M. I. System. This systeni was Invented and patented by Edward Smulski, and is controlled by the S. M. I. Engineering Company, Boston, Mass. Circumferential and radial reinforcement is placed in both the top and bottom of the slab, with trussed bars extending both rectangularly and diagonally be- tween the columns (Fig. 23). The radial bars are provided with a semicircular hook to transfer the stresses into the concrete by loond, and to engage the ring of reinforcement in the center of the panel. To prevent cracking on the top of the slab between columns, additional short, straight bars are sometimes used. Patents for Flat-Slab Construction. In 1901 and 1902 patents were granted to O. W. Norcross, covering girderlcss floor-construction reinforced with bands of wire netting extending from column to column. AppH cation for the original C: A. P. Turner patents was made in 1905. In 1915 the United States Courts held that the Norcross patents covering girderless floors were funda- mental, and that bands of bars were, to all intents and purposes, the same as Types of Reinforced-Concrete Construction] mx Fig. 23. S. M. I. Flat-slab System hands of wire netting. It would seem, therefore, that any system of floor-con- struction depending upon bands of bars running either diagonally or crosswise from column to column constitutes an infringement of the Norcross patents. The leading promoters of flat-slab construction in the United States are now licensed under the Norcross patents; but several other United States patents have been granted covering special methods of construction and reinforcement. * Combination Hollow-Tile and Reinforced-Concrete Construction. In seeking to minimize the cost of centering, the floor-construction shown in Fig. 24 has been devised. It consists of a series of rein forced-concrete beams with clear spaces between them of the width of the holiow-tile blocks. In erection, a 952 Reinforced-Concrete Construction Chap: 24 flat centering is used, which, however, need not even be continuous. Planks, a few inches wider than the concrete beams, are placed under the spaces to be filled by the beams, and the tiles are laid in rows and supported along their edges by the planks, thus forming the sides of the molds for the beams. The reinforce- ment is placed and the concrete poured, with or without floor-phtes, as the neces- sities of the case may require. Care must be taken in pouring the concrete Fig. 24. The Combination Tile and Reinforced-concrete System that the tiles are not displaced sidewise. The tiles should fit closely at their joints, otherwise the finer particles of the concrete are liable to flow into them, either making the concrete porous or requiring more cement and sand than is necessary. This form of construction, besides being economical in centering, offers the advantages of a flat ceiling without the application of lath and, in roof- construction partic\flarly, of freedom from condensation. The Floretyle Systems. A floor-construction similar to the hoflow-tile construction just described has been devised by the Truscon Steel Company, Youngstown, Ohio, in which forms of corrugated sheet steel, called floeetyles, replace the hollow tiles. The Floretyles are furnished in lengths of 283^ and 45 in, and in depths of 6, 8, 10, and 12 in. The width at the base is 20V2 in, with the sides tapering at an angle of 7° 30'. They are furnished in two types, either with serrated edges for use with the company's Hy-rib lath for ceilings, or with straight edges for use where paneled ceilings are required. Other makes of metal forms used in the construction of reinforced-concrete floors are the g f steel tiles of the General Fireproofing Company, Youngstown, Ohio, and the wiscoforms of the Witherow Steel Company, Pittsburgh, Pa. Besides a reduction in weight of finished floors, the additional advantages in the use of these steel tiles or forms over the terra-cotta fillers are: Greater economy in centering, larger covering capacity, less bulk in shipment because the forms can be nested, and less danger 6 in 8 in 10 in 12 in 14 in Average weight, in pounds 40.100 0.278 58.300 46.000 0.319 61 .700 S3-SOO 0.371 63 . 000 61 .000 0.423 63.800 72.600 0.50s. 62 . 200 Cubic feet of concrets per . square foot of floor Core-area, percentage of sec- Types of Reinforced-Concrete Construction 953 of absorption of water from the concrete and of the flooring-out of the cement at the joints. A concrete floor of G F steel tiles, spaced so as to make 4-in con- crete beams, 24 in on centers, and liaving 2 in of concrete above the tiles, with- out ceiling, is said to have the properties shown in the table on page 952, according to the depth of tiles used. Two- Way Tile Systems. Similar in general principle but using reinforce- ment in two directions, at right-angles with one another, is the combined hol- LOW-TiLE-AND-coNCRETE FLOOR, Controlled by the Republic Fireproofing Com- pany, Inc., New York City, under the Burchartz patents (Fig. 25). This system employs terra-cotta blocks, channels, and soffits, providing uniform flat ceilings to which plaster can be applied without the use of metal lath. - In this case the floor is calculated as a slab supported on four sides. (See page 936.) The con- crete is prevented from running into the hollow spaces of the tile by the use of the terra-cotta channels as shown. Floredomes. In the floredome -construction, put on the market by the Truscon Steel Company, Youngstown, Ohio, the tile spacing-blocks of the two- way tile SYSTiSM are replaced by rectangular dome- shaped steel forms with the under side open. Lightness in floor-weight, ease and rapidity of installation, and no breakages are the advantages claimed. The ceiling-treatment in this con- struction is similar to that in the Floretyle system. The base of the domes is uniformly 21.5 in square; the depth varies, being 6, 8, 10, or 12 in. Strength of Combination Systems. While the tiles may under favorable conditions add to the strength of the combined floor-construction, the chances of unsatisfactory workmanship are too great to consider them in the calculations for strength. In the floors reinforced in one direction, the construction should be treated as a series of either rectangular beams, or T beams, as the concrete extends either to or above the top face of the tiles. The two-way reinforced construction should be treated as if it consisted of a slab supported on four sides, or as a series of intersecting rectangular beams, or T beams. If the con- struction is to be treated as a series of T beams or as a slab, the concrete should extend at least 2V^ in above the top surface of the slab and the tiles or fillers should not exceed 60% of the volume of the construction. Separately-molded Construction. The unit or separately-molded con- struction consists of precast reinforced-concrete members, columns, girders, beams, or slabs, either molded at the site of the building, or made at the factory and shipped to the site ready for use. The various members are swung into place in much the same manner as steel is erected, and fitted together in the structure by interlocking reinforcement and poured grouting. Great economy is claimed for this method of erection on account of the saving of forms. Maxi- mum economy, however, cannot be obtained on a building operation of less than 80 000 sq ft, as economy is obtained by the greater use of the forms and the familiarity of the erecting-crews with the particular type of building. But under good conditions, economy can also be shown on an operation involving as Httle as 50 000 sq ft. The advantages of this construction are said to be: The great number of uses possible of one set of forms, especially on a large opera- tion; the small number of men required, due to the extensive use of locomotive- cranes, motor trucks, derricks, etc.; the ease with which the units may be in- spected while being poured and before entering the building; and the fact that all shrinkage takes place before the units enter the structure, thus eliminating shrinkage-cracks in the building. The disadvantage of such a system, however, appears to lie in the lack of sufficient rigidity in tall, separately-molded unit " structures. All floor-members must be designed and cast as simple, non-con- tinuous units, with the reinforcement left projecting at both ends to serve for Reinforccd-Concrete Construction Chap. 24 Fire-Resistance of Rcinforced-Concrete Construction 955 tying the structure together. These junctures are made after the units are hoisted into place, and supported by a pouring of rich concrete. For tall struc- tures it is more feasible to erect a light structural-steel frame and employ the precast floor-units only. (See Chapter XXITI, page 854.) The saving in cost is noted particularly in low buildings, and more especially in one-story struc- tures,* such buildings having been erected at a saving of from 10 to 20% over MONOLITHIC construction. Methods of interlocking the units and providing satisfactorj'' details are constantly being improved and a series of tests of the efficiency of such connections is being carried on by the Unit Construction Company of St. Louis, Mo. There are under construction, or already completed, many buildings of this type installed by the above company, including five-story buildings for the National Lead Company, at St. Louis, Mo., Kansas City, Mo., and Pittsburgh, Pa.; a three-story l^uilding for the Ohio Cultivator Com- pany, at Belleville, Ohio; five acres of car-barns at Philadelphia, Pa.; and approx- imately thirteen-and-a-half acres of cotton-warehouses at Memphis, Tenn. The Ransome Engineering Company cvf New York City has erected five-story and six-story buildings with its Unit system, in Boston, Mass, 5. Fire-Resistance of Reinforced-Concrete Construction Non-Conductivity of Reinforced Concrete. Concrete is a poor conductor of heat, and in this fact lies whatever virtue it has as a fire-proof material.! A series of tests made by Professor Woolson of Columbia University, New York City, and reported at the 1907 meeting of the American Society for Testing Mate- rials, shows the following results: — | (i) "That all concrete mixtures when heated throughout to a temperature? of I 000° to I 500° F. will lose a large proportion of their strength and elasticity, and that this fact must be well remembered in designing." (2) "That all concretes have a very low thermal conductivity, and therein lies their well known heat resisting properties." (3) "That as a result of this low thermal conductivity, two to two and one- half inches of concrete covering will protect reinforcing metal from injurious heat for the period of any ordinary conflagration (provided, of course, that the concrete stays in place during the fire)." (4) "That reinforcing metal exposed to the fire will not convey by conduc- tivity an injurious amount of heat to the embedded portion." (5) "That the gravel concrete was not a reliable or safe fire-resisting aggre- gate." t Loss of Strength of Reinforced Concrete. If its non-conductivity were all that is involved in the fire-proof character of concrete, the minimum thick- ness required for the protection of the steel could be easily determined. But the STRENGTH of the concrete is more or less affected when exposed to extreme heat. An effort has been made to determine this effect and a summary § of the results as reported by Professor Woolson of Columbia University, New York City, is given in Tables XII and XIII. * Engineering Record, Vol. 60, page 643; Engineering News, Vol. 58, page 5; Pro- ceedings National Association of Cement Users, 1910, page 391. t It must be remembered that in this and succeeding paragraphs on the fire-resisting properties of concrete, only such material as is used in reinforced concrete, is considered. The value of cinder concrete as a fire-proof material is discussed in Chapter XXIII, page 817. X Engineering News, Aug. 15, iQo?, page 168. § Proc. Am. Soc. for Test. Mats., Vol. IV, page 433- 956 Reinforced-Concrete Construction Chap. 24 Fire Tests on Reinforced Concrete. The effect of fire on reinforced concrete has l)een studied in a number of tests made by the building authorities of New York City and Philadelphia, and in some of the conflagrations in this country, notably at San Francisco. The tests to which the sample full-size constructions have been subjected are similar to the test described in Chapter XXIII, page 827.* Table XII. Tests of Concrete Blocks Heated on All Sides f Specimens, 6 by 6 by 14-in prisms; proportions 1:2:4 Age 2 months; temperature 1500* F. Treatment Aggregate Limestone Trap-rock Cinder Gravel Modulus of elasticity, At 200 lb per sq in: Unheated 6 000 000 200 000 3 430 000 150 000 129 000 4 355 000 222 CXX) 188000 4 355 000 348000 3140 I 400 997 I 090 000 49500 571000 960 000 8000000 Heated 3 hours Heated 5 hours At 400 lb per sq in: Unheated 6000 000 285 000 6 887 000 Heated 2 hours Heated 5 hours At 800 lb per sq in: Unheated 5 647 000 425 000 2740 I 345 870 915 000 6 000 000 Heated 3 hours . . Breaking-load in lb per sq in: Unheated Heated 3 hours I 400 547 504 2 780 Heated 5 hours Table XIII. Concrete Blocks Heated on One Face Only t Specimens, 6 by 6 by 14-in prisms; proportions 1:2:4 Age 2 Months; temperature i 500" F. Treatment Aggregate Limestone Trap-rock Modulus of elasticity. (Blocks heated 5 hrs.) At 200 lb per sq in 293 400 521 700 730 700 I 840 200000 268000 379000 I 705 At 400 lb per sq in At 800 lb per sq in . Breaking-load in lb per sq in • For a partial list of thef.e tests, see Table in Proc. Am. Soc. for Test. Mats., Vol. VI, page 128. Several tests have been made since that report was submitted, t Proc. Am. Soc. for Test. Mats., Vol. VI, page 446. I Proc. Am. Soc. for Test. Mats., Vol. VI? page 448. Fire-Resistance of Reinforced- Concrete Construction 057 The conclusion, from a study of the tests in detail,* shows that to a depth averaging about i in, the concrete is seriously impaired and easily \yashed off by a hose-stream applied to the surface. Any stone containing an appreciable per- centage of carbonate of lime will calcine and may cause failure. Where the con- struction is poorly designed, allowing an excessive deflection, the fine cracks in the concrete below the steel will open to such an extent as to permit the heat to reach the metal reinforcements. When the reinforcement is such as to pro- duce a plane of weakness in the concrete there is Hable to be a flaking off of the concrete and a consequent exposure of the metal. Actual Fire Tests of Reinforced Concrete. The earliest test of a re- inforced-concrete building in an actual fire occurred in 1902, in the four-story factory of the Pacific Coast Borax Company, at Bayonne, N. J. The roof of this building was of wood, and with the contents of the building, was destroyed by the fire. The only damage suffered was a break in the top floor caused by the fall of a heavy tank that had been supported by the roof. At the same time an adjoining building constructed with unprotected steel posts and beams was twisted into a tangled mass of metal. Tests in the Baltimore Fire. In the Baltimore fire there was but one reinforced -concrete building of the three exposed to the fire, from which any fair conclusion can be drawn. In one of the buildings, the concrete construction was entirely destroyed, but this was probabl^^ due to the falling walls and the failure of other non-fire-proof parts. In a second building, the heavy rein- forced-concrete floor of a banking-room came out practically unharmed; but it was not exposed to severe fire. The third structure was, however, exposed to severe fire. The contents of the building were destroyed and a large part of the outside brick walls fell. The floors, five in number, were all of reinforced con- crete supported on concrete columns, having replaced an old wooden-joist con- struction. A test made after the fire showed that the floors were still strong enough to sustain the loads for which they were designed, although the floor- slabs were cracked. The girders were cracked longitudinally near the lines of the reinforcement, and the columns were spalled to such an extent as to expose most of the reinforcement. It would have been difficult to restore the building so that it would resist another such attack, f Tests in the San Francisco Firfe. The effects of the fire on concrete construction in the conflagration immediate^'' following the San Francisco earth- quake in 1906 are summed up in the following paragraph from the report of a committee of engineers that investigated the subject. " Concrete floors generally had hung ceilings, and, where thus protected, were uninjured. Where exposed, the concrete is in most cases destroyed, for instance, in the Sloan, Rialto, and the Aronson Buildings, and the Crocker Warehouse. The concrete is dry, and while in many cases hard, yet all the water has been burned out and it may be said to be destroj^ed, even if able to support weights. Floor-coverings of wood invariably burned, adding to the destruction. Sleepers were generally burned. Surfaces of cement mortar fared much better, the lino- leum covering remaining practically intact." t In discussing the report, Mr. A. L. A. Himmelwright, who made a personal inspection of the ruins, concludes that reinforced concrete is inferior as a fire- resisting construction to any form of steel construction with concrete floors and * The detailed reports are on file in the Bureau of Buildings, Borough of Manhattan, New York. t Captain Sewell in his report on this building draws a different conclusion. See Engineering News, March 24, 1904, page 276. t Proc. Am. Soc. C. E;, March, 1907, page 330. 958 Relnforced-Concrete Construction Chap. 24 concrete column and girder-protection, but superior to steel construction with terra-cotta floor and terra-cotta column and girder-protectiort. "Where this method was used, a very slight attack of fire was generally sufficient to cause the rupi:ure of the concrete underneath the reinforcing-metal, so that it fell away, exposing the metal. There were comparatively few l)uildings, however, in which this method of construction was used."* Thickness of Concrete Required. From a study of the tests and fires just referred to, the fair conclusions as to the amount of protection against fire would seem to be as follows: (i) In all columns and in large and iniix)rtant girders, trusses, or other supports, at least 2 in of concrete outside of all reinforce- ments; (2) in girders and beams and in slal)s of long spans, about 1^ in of con- crete outside of all reinforcements; (3) in stair-work, floor-slabs of short span, and walls and partitions, from 54 to i in of concrete outside of all reinforcement. The provisions recommended in the Building Code of the National Board of Fire Underwriters are : " Steel reinforcement shall have a minimum pro- tection of concrete on all sides as follows: In columns and girders, 2 mches; in beams and walls, iH in; and in floor slabs, i inch. The steel in footings for walls and columns shall have a minimum protection of 4 inches of concrete. "The minimum thickness of concrete surrounding and reinforcing members one-quarter inch or less in diameter shall be one inch; and for members heavier than one-quarter ineh the minimum thickness of protecting concrete shall be four diameters taking that diameter, in the event of bars of other than circular cross-section, wliich lies in the direction in which the thickness of the concrete i3 measured; but no protecting concrete need be more than fcur inches thick for bars of any size; and provided, further, that all columns and girders of rein- forced concrete shall have at least one inch of material on all exposed surfaces over and above that required for structural purposes; and all beams and floor slabs shall have at least three-quarters inch of such surplus material for fire-re- sisting purposes." Other Forms of Protection for Reinforced Concrete. Because of the effects produced by fire on reinforced concrete, as above described, and the difficulty of restoring the construction where so affected, various suggestions have been made to protect the concrete construction with other materials. On account of its excellent fire-resisting quahties (see page 817), cinder concrete naturally suggests itself. This material is out of the question where strength is required. But its use may be combined with that of stone concrete, by placing a sufficient thickness for protective purposes on the outside of the rein- forcements in columns, below the neutral axis in l)eams and girders, f and on the under surface of floor-.slabs. Difficulties are likely to be encountered; however, in placing two kinds of concrete in the same mold, but these difficulties are not insurmountable. Careful inspection is required to see that the poorer material is not put in place of the stronger. One kind of concrete should follow the other immediately in order to secure a bond between the two. This sug- gestion, serving at the same time another purpose, was satisfactorily applied to the column-protection in the Bush Terminal Warehouses in the Borough of Brooklyn, New York. The steel-wire wrapping for the columns was prepared in sections 2 ft in height. Metal lath with about a J^-in mesh was placed outside the wrapping and secured to it. This was then placed in a cylindrical wooden mold 2 ft in height and with a diameter 4 in larger than the wrapping, thus forming an inner side of the mold. The space between the wrapping and the wooden mold was then filled with cinder concrete. When set and the mold * Trans. Am. Soc. C. E., 1907, Vol. LTX, page 305. t Trans. Am. Soc. C. E., Vol. LVI, page 284. Fire-Resistance of Reinforccd-Concrctc Construction 959 removed, the result was a hollow cylinder of cinder concrete, 2 in thick and 2 ft high, with the column-wrapping attached to the inside. These cylinders were set one over the other in the building till the proper column-height was reached, such vertical rods as were wanted were put in, and the interior filled with concrete. Thus was produced a fire-proof, wrapped column, without expense and inconvenience of any column-molds in the building. A form of fire-protection, advocated by the National Fire Proofing Company of Pittsburgh, Pa., is shown in Fig. 26. Here columns, beams, and girders are Fig. 2G. Tile Protection for Reinforced Concrete completely incased with hollow-tile blocks. Being either laid in the molds or forming them, their rough and furrowed porous surfaces cause them to adhere firmly to the concrete. They afford as efficient protection here as they do for steel columns, and if destroyed the blocks can be replaced. Effect of Aggregate on Fire-Resistance. Fire tests on full-size reinforced- concrete columns, conducted by Walter A. Hull at the Pittsburgh laboratories of the Bureau of Standards, show that the nature of the aggregate plays an impor- tant part in resistance to fire. Silicious gravels appear to make unsatisfactory concrete from the standpoint of fire-resistance. Limestone concretes are superior to other materials tested, including trap-rock and blast-furnace slags. Coatings of cement plaster, i in thick, and secured by a light, metal lath, protected the columns so effectively that the strength, after a four-hour fire test, was as much as four times that of the unplastered columns after the test, and about 90% of that of the column which had not been subjected to fire. Other forms of pro- tective coverings investigated and proved effective, were a roofing-material of Portland cement, sand, and asbestos, and cylindrical forms of cast gypsum, 3 in thick, made and applied in a manner similar to those of cinder concrete described on page 958. The unsuitability of gravel concrete as fire-proof construction, was pointed out • by Ira H. Woolson as early as 1907* and appears to have been later confirmed * Proc. Am. Soc. for Test. Mats., 1907. 960 Reinforced-Concrete Construction Chap. 24 by an actual fire in a reinforced-concrete warehouse at Far Rockaway, N. Y., in 1916. From this the conclusion was drawn that "all concrete specifications should contain a definite warning against the use of quartz gravel in concrete liable to be exposed to high heat."* 6. Protection Against Corrosion in Reinforced-Concrete Construction. Thickness of Reinforced Concrete. The thickni:ss of concrete required for protection against fire has been found to be also ample for protection against CORROSION. It is well established that steel embedded in neat cement will not corrode. C. L. Norton of the Massachusetts Institute of Technology, Boston, Mass., draws the following conclusions from a series of experiments made in 1902 and 1903.1 (i) Steel embedded in neat cement is secure against corrosion; (2) Steel embedded in a dense concrete mixture is safe against corrosion; (3) To assure a thorough coating of the steel the concrete should be mixed wet; (4) Porous concrete allows the admission of moisture and will not protect the steel thoroughly; (5) A coating of rust is not a protection against further corrosion, as has been sometimes claimed. In these experiments the steel was incased in concrete i?/^ in thick on all sides. From this it would appear that (6) The steel of reinforced concrete is secure against corrosion, provided it is thoroughly embedded in concrete, and (7) A slight coating of rust on the steel, where embedded, does no harm, as the cement is strongly alkaline and will counteract the acidity of the iron oxide and prevent further corrosion. "In practical deygn the most important question which arises is how far a concrete may be cracked (due to bending of beams) without exposing the steel to corrosive influences. In this respect it seems to the writer that the minute cracks which appear in the early states of the tests can have very little in- fluence." t This means that within the safe working limits, there is no danger from corrosion on account of the fine cracks due to tension in beams and girders. Corrosion of Steel in Cinder Concrete. Cases are on record of serious CORROSION OF STEEL embedded in cint)er concrete. In a report to the Struc- tural Association of San Francisco, Cal.,§ the committee investigating the sub- ject states that in cinder concrete "the extent of the corrosion is great enough to seriously endanger the safety of the floors, and it is not probable that the floors would have supported their loads more than one to three years longer." The committee recommended "that the Structural Association try to amend the present building law so as to exclude the use of cinder concrete in floor- slabs or for fireproofing." Mr. William H. Fox in his investigations |I on this same subject finds that '* after about forty days' treatment, the specimens were broken, and the steel carefully examined for corrosion. With but one exception, one or more of the three steel pieces in each specimen showed unmistakable signs of corrosion. * Report to National Board of Fire Underwriters, on the fire in question, t Reports Nos. 4 and 9, Insurance Experiment Station of the Boston Manufacturers Mutual Tire Insurance Company. X Professor Turneaure in Trans. Am. Soc. for Test. Mats., Vol. IV, page 505. § Engineering News, Nov. i, 1906, page 458. !i Engineering News, May 23, 1907, page 569. Protection Against Coirosion in Rein forced-Concrete Construction 961 Apparently it made no difTerence how the concrete was mixed, wet or dry, tamped or imlamped, whether the steam or water treatment was used, the result was the same, rust streaks and spots were found; the difference in the amount of corrosion being imperceptible." He concludes that "to secure a dense homo- geneous cinder concrete, a thorough tamping is necessary. A rich mixture, either 1:1:3 or one in which the proportion of cement to aggregate is larger, should be used in all cases. The greatest of care should be taken in mixing the materials, and it may be necessary to resort to the seemingly imj^ractical method of coating the reinforcement with grout before placing in the concrete." In a series of chemical and physical tests,* made by George Borrowman of the University of Nebraska, it was found that disintegration of cinder concrete was caused by the oxidation of iron and sulphur producing internal stresses and consequent cracking with occasional efflorescence of ferrous sulphate on the surface. From these tests, it was concluded that cinders with much sulphide and sulphate sulphur are likely to give unsatisfactory results, especially if there is much coke or porous material present; also that such material (cinders) may be improved if allowed to weather with occasional washing, until the ferrous iron and sulphur have been washed and leached out of the cinders. The cinders used in these tests were from carefully screened steam coal and slack. The analysis showed considerable ferrous iron and sulphur as sulphide and sul- phate. On the question of the corrosion of steel in cinder concrete Professor Norton concludes: "There is one limitation to the whole question, that is, the possibility of getting the steel properly incased in concrete. Many engineers will have nothing to do with concrete because of the difficulty in getting 'sound' work. This is especially true of cinder concrete, where the porous nature of the cinders has led to much dry concrete and manj^ voids, and much corrosion. I feel that nothing in this whole subject has been more misunderstood than the action of cinder concrete. We usially hear that it contains much sulphur and this causes corrosion. Sulphur might, if present, were it not for the presence of the strongly alkahne cement; but with that present the corrosion of steel by the sulphur of cinders in a sound Portland concrete is the veriest myth, and as a matter of fact the ordinary cinders, classed as steam cinders, contain only a very small amount of sulphur. There can be no question that cinder concrete has rusted great quantities of steel, but not because of its sulphur, but because it was mixed too dry, through the action of the cinders in absorbing moisture, and that it contained, therefore, voids; and secondly, because in addition the cinders often contain oxide of iron which, when not coated over with the cement by thorough wet mixing, causes the rusting of any steel which it touches. There is one cure and only one, mix wet and mix well. With this precaution I would trust cinder concrete quite as quickly as stone concrete in the matter of cor- rosion."! In 1902 the Pabst Building in New York City, an eight-story steel skeleton construclioi, was taken down after standing for about four yeirs. The floor- filling betwji n the steel I beams in this case consisted of cinder concrete on metal lath, built in segmental form.t The steelwork generally was found to be free from rust, though it should be remembered that all the steel had been painted. § Taking all things into consideration it is probably safe to use cinder ♦Journal of Industrial and Enpineerinp; Chemistry, June, 1912. t Report No. 9, Insurance Experiment Station, Boston Manufacturers Mutual Firo Insurance Company. J Roeblinc; system, now obsolete. § Trans. Am. Soc. C E., Vol, L. page 297. 962 Reinforced-Concretc Construction Chap. 24 concrete, if care is taken to provide a proper mixture and careful and thorough workmanship. 7. Erection of Reinforced-Concrete Construction Forms for Reinforced Concrete. For the erection of reinforced concrete, it is generally necessary, first, to construct molds or centerings for the col- umns, floors, etc. Wood is the material used for this purpose. Sheet-metal centering has been used with questionable success and economy. In the selec- tion of the wood for the molds a clean grade of dressed pine should be used. It should be thick enough to resist warping and to resist deflection between sup- ports. It must be coated on its surface with soap or some other satisfactory Fig. 27. Wooden Form for Reinforced-concrete Column substance to prevent it from sticking to the concrete. The forms or molds must be erected carefully, the exact size of the proposed parts, and must be true in position and direction. For floor-molds, sufficient supports must be provided, not only to carry safely the heavy wet concrete, but also such materials as are liable to be placed on the floors up to the time when the concrete has set suflEi- ciently to carry such loads. The supports must have sufficient rigidity to prevent deflection in the molds. The molds should be so constructed that they can ])e easily removed when the concrete has set. Sharp corners should be avoided as much as possible, as the wood is Hable to stick in them. Where there are reentrant angles in the finished concrete-work, the molds should have beveled edges, and at salient edges of the finished concrete-work, triangular strips should be nailed in the corners of the molds to produce a beveled edge in the concrete. Erection of Reinforced-Concrete Construction 963 To prevent the spreading of the sides of the molds, cleats must be provided at sufficient intervals. In the case of beams and girders, these are gen- erally secured by nailing. In the case of columns and piers and often in walls, the cleats are so notched at the ends that long bolts * with washers may be used to hold them in place, as shown m Fig. 27. In removing the form the bolts are loosened and the cleats and the rest of the form are ready to use again. In some cases, particularly in the construction of walls, the cleats are held in place by wires running through the mold. These wires become embedded in the concrete and in removing the molds they are cut and the portions iji the con- crete are allowed to remain. The items of molds and centerings needed in the erection of reinforced-concrete buildings form a considerable part of the cost of construction. Economy in this respect can l^e affected in designing and planning by making the floor-panels throughout a building uniform in size and by repeat- ing, as far as possible, such parts as piers, walls, etc. Successful attempts have been made to dispense with the erection of timber molds and centering by casting the various members of the construction on the ground and assembling and erecting them in the same way that wood or steel columns, beams, and floors are assembled and erected. (See page 953.) Concrete Mixing. In all reinforced-concrete work the concrete should be MIXED MPXHANICALLY. Satisfactory^ hand-mixing can be obtained and might be resorted to in, very small jobs, where it would be uneconomical to set up a MACHINE-MIXER. But a much more uniform product will result from machine- mixing, and most types of mixers are mounted on wheels so as to be easily moved to a job. IVIechanical mixers are either continuous mixers or batch-mixers. In the continuous mixers the materials are fed sometimes by hand and sometimes mechanically, and the concrete issues continuously. The product, however, is not Ukely to be as uniform as that from the batch-mixer; for when the latter is used it is under constant supervision, whereas when the continuous mixer is used the machine is relied upon. Of the batch-mixers the rotary type is the one giving most general satisfaction. Among the efficient examples of this type may be mentioned the mixers made by the Ransome Concrete Machinery Company, New York City, and the T. L. Smith Company, Chicago, III. They are made in different sizes and with capacities varying from about 10 to 60 cu yd per hour. Charging Concrete-Mixers. In charging a concrete-mixer the materials for each batch, carefully measured, are dumped into the mixer and the machinery started. After completing a definite number of revolutions, sufficient to thor- oughly mix the ingredients, the concrete is discharged into wheelbarrows or other implements for carrying it to the molds. Each batch should be completed before another is started. To obtain uniform results the number of revolutions in each operation should be the same. It is not well to trust to the judgment of the man in charge of the machine, as to when the mixing has been thorough. He should be instructed to count the revolutions each time. A good plan is to attach a gong which rings when the fixed number of revolutions has been com- pleted. The Code of the National Board of Fire Underwriters cafls for "at least 20 revolutions," and the "speed of the mixer shah not exceed 20 revolutions per mmute." Wet Concrete Mixture. The water is introduced during the process of mixing. The amount, also measured, should be such as to produce what is known as a wet mixture, that is, a mixture that has the consistency of molasses and that will readily flow around and thoroughly incase all steel to be embedded. It may be necessary to vary the amount of water somewhat in placing a large mass of concrete, as in walls, since the water generally works itself upward 064 Reinforced-Coiicrete Construction Chap. 24 through the successive layers. For transporting the concrete from the mixer to the mold, steel wheelbarrows, each holding about 2 cu ft, are generally employed. A larger vehicle, holding about 6 cu ft, is made by the Ransome Concrete Machinery Company, Dunellen, N. J., and is found very economical in larger work. When the conditions will permit, concrete may also be distrib- uted by means of chutes, but care must be exercised to secure a consistency, that will prevent the separation of the coarse aggregate from the mortar. The transporting through the chutes may be done either by gravity or by com- pressed air. Tests have shown that an excess of water tends to decrease the strength of concrete, so that care must be taken not to use more water than is necessary to place the concrete properly. Pouring the Concrete. Ideal conditions would obtain if the process of PLACING CONCRETE could be CONTINUOUS. This is not generally practicable; so it is important that the point at which work is stopped each day shall be so selected and predetermined that the strength of the construction shall suffer least. In smaller buildings, with floor-areas not exceeding about 3 000 sq ft, it should be possible to so arrange the progress of the work that each entire floor- construction may be placed in one day. In larger work it is necessary to lay off a certain area to be completed within the time of concreting for the day. Work should not leave off across important beams or girders, and the tempo- rary stopping should be arranged for when the work is at the middle of slabs or minor floor-beams. If any parts of floor-slabs are considered in the calcula- tions for the strength of the beams or girders, such parts must be concreted at the same time and must be considered parts of such beams or girders. Joints in columns should be made perpendicular to the axes of the columns, and, as far as possible, at the lower side of girders. Columns should be .allowed to set for at least two hours before girders are cast on them, in order to provide for settlement and shrinkage. Ramming the Concrete. As soon as the concrete has been poured into the molds, and during the process of pouring, it should be continually rammed to secure complete filling of the molds, density in the finished product, and thor- ough adhesion to the reinforcement. In wet concrete, such as is used for build- ings, this ramming should be done with a flat steel spatula at the end of a handle long enough for comfortable manipulation. For column-work the handle is lengthened out so as to reach to the bottom of the forms. Ordinary spades are sometimes employed, and where no special tools are provided, rammers are sometimes made of 2 by 3-in scanthngs, rounded off at the top end to make a handle. Where a smooth surface is de.sired the spatula rammer should be used, particularly at the sides of the molds. The honeycombed appearance that results from improper ramming is difficult to remedy afterward without a surface of patches. After having been placed, the concrete should be kept damp by sprinkling it with a hose until it has thoroughly hardened. The tap- ping of the forms with a hammer while the concrete is still plastic and before it has begun to set will cause it to flow more freely into place in intricate forms and around reinforcing-bars, especially when a dryer concrete, recommended by recent investigators, is used. Tapping after it has started to set, however, tends to weaken the concrete.* Removing the Forms from Reinforced Concrete. No fixed rule can be given for the remoxal of the forms, as the time required for the setting of concrete varies with the consistency of the mixture, and the climatic and other y:-^SiBe "Effect of Vibrations, etc.," by Duff A. Abrams, Proc. Am. Concrete Inst. Vol. XV, 1919- Erection of Reinforced-Concrete Construction 965 conditions. Numerous failures of reinforced concrete have been attributed to the too early removal of forms. In warm weather concrete will set more quickly than in cold. The setting process may be somewhat accelerated after a day or two, by removing the boards forming the sides of beams or girders and leaving in the planks on the underside and the props supporting them. ' In cold weather it is advisable to warm the building during the setting process by means of salamanders. The Finish of Concrete Surfaces. The faposed surfaces of concrete walls are variously treated in attempts to produce a satisfactory appearance. Where no special provision is made, the marks of the lumber used in the forms are almost certain to show, and the lines of demarcation between successive layers are clearly defined. To eliminate these lines, grooves are sometimes purposely formed, by tacking on the sides of the molds triangular or trapezoidal strips that produce sunk joints in the wall, and give it an ap])earance resembling dressed stone. The successive layers of concrete arc in such cases stopped at these hues so that the junction of the two layers is hidden. In some cases the surface is purposely left rough and scratched like the scratch-coat in plaster- ing, and then stuccoed with a neat cement or a rich cement mortar. In this form of finish there is always some danger that the stucco will flake off. The surface, as it comes from the mold, is sometimes hammer-dressed, or rather picked with a special hammer. This hammer has an edge at right-angles to the handle, and the edge is indented and made a series of points. A roughened face is thus produced which in time shows a uniform texture. Another method is to remove the forms as soon as the concrete is sufficiently hard and to rub the surface with a plasterer's float or a block of carborundum, concrete, or stone, using a thin grout or fine sand with plenty of water between the float and the wall-surface. Brushing, also, may be resorted to, consisting in scrubbing the surface, while still green, with a wire brush, and a mixture of one part of hydro- chloric acid to six parts of water. A similar finish may be obtained by sand- blasting after the concrete has thoroughly hardened. The Finish of Reinforced-Concrete Floors. If the floor-stirfaces are not to be covered with a wooden flooring, a satisfactory finish may be obtained by placing over the surface, before the concrete has had time to set thoroughly, a mortar finish from i to iH in thick, and troweling to make it smooth and level. If the finish is attempted after the concrete has set, the new and the old work will probably not bond; and there is always danger of flaking off unless the finish itself is of considerable thickness. Bonding Old and New Concrete. Various fluids and special cementitious materials have been put on the market for the purpose of bonding new and old CONCRETE SURFACES. Whether or not these materials have any special merits, it is now generally accepted that a good rich cement mortar will form sufficient bond between two concrete surfaces, providing the surfaces are clean. If the stress is compressive, the old surface of the concrete should be cleaned and wet, and the surface may be roughened. Joints y^hich are subject to tension should be coated with a i : i3^^ or a i : 2 cement mortar before the new concrete is cast. In building walls which must be water-tight, the structure should be made monolithic And if it cannot, all dirt and laitance should be removed, and a thin layer of very rich mortar placed. Inspection of Reinforced-Concrete Work. In all reinforced-concrete work it is of extreme importance to have competent and thorough inspection or SUPERINTENDENCE. The iuspcctor should be familiar with the nature and qual- ities of the different materials entering into the construction. He should have 9G6 Reinforced-Concrete Construction Chap. 24 a knowledge of the underlying principles of the design of reinforced-concrete structures, so that he may reaUze the importance of carrjdng out all the details, and particularly of placing the reinforcement exactly as planned. He must be sufficiently alert and active to see that the work of the contractor is progressing properly; so that, for instance, work shall not have to be rebuilt because of error in the forms. The materials used in the construction, particularly the cement, should be tested as the work progresses. Cubes of the concrete as used should be made up each day and at the end of seven days should be tested for com- pression, and if necessary again at the age of twenty eight days. This record will serve as a guide in the acceptance of the work, or in deciding on the neces- sity for a load test of the finished structure. Under no circumstances, however, should it replace or serve as an excuse to omit the testing of the cement upon delivery or before acceptance. In addition to the details discussed in this chapter, details which require the attention of the inspector on the work, a few others may be especially mentioned here: (i) In JOINING NEW WORK with that which is already in, and wliich has begun to set, the surface must be thoroughly cleaned and wet. In stopping off work, it is good practice where possible, to cast a groove in a surface that is to be joined with another, so that when the work is afterward continued, a tongue-and- groove junction is effected. (2) All FORMS or MOLDS must be carefully cleaned out just before the concrete is poured. The bottoms of the column-molds must be especially watched for this, as shavings, sawdust, and even blocks of wood are liable to fall into them unobserved. It is well to leave off a small piece of one side of the column-mold at the bottom, for purposes of observation and cleaning, and to close it up just before pouring the concrete. (3) Great care should be excerised in pouring and ramming concrete in deep molds, such as for columns, walls, etc., in order to get the molds thoroughly filled at the bottom. In careless work it is not unusual to find in such places very porous concrete, if not large pockets. This is particularly liable to occur when there is considerable rcinforcing-stecl in the construction. (4) It should be remembered that concrete shrinks in setting. Hollow spaces at the tops of columns are sometimes found to be due to this cause. As these are not always observable from the outside after the forms are removed, great care should be exercised to guard against them. In pouring, therefore, the molds should be filled to overflowing to the top of deep molds. (5) The exact position of the rein forcing-steel in the concrete is of such vital importance that particular mention is again made of it here. In loose-bar con- struction the greatest care must be exercised, in the first place, to have the rein- forcement carefully placed, and then to avoid its being shifted out of position by the pouring and the ramming of the concrete. (6) The REiNFORCiNG-STEEL of thosc systems in which the advantage of at- tached stirrups is claimed, is often, for convenience in shipping, sent with the stirrups laid flat or close to the main bar. It Is intended that in placing them on the job the stirrups shall be turned up to their proper positions. Unless carefully inspected, this is liable to be neglected. (7) The use of a unit type of construction (see page 922) practically obviates these two last-mentioned dangers, as the enlire reinforcement comes framed to- gether, so that the relative positions of reinforcing-rods or bars cannot be changed; and a glance will show whether the fkame is complete or has been damaged, and, when placed in the molds, whether it fits or not. In this type of construction the parts are all assembled in the shop from details carefully drawn and checked, in much the same wcty that steel beams, girders, columns, etc., are fabricated from Erection of Reinforced-Concrete Construction 907 detailed shop drawings. The work of the inspector or superintendent on the job is very much simplified, and hence the liability of error reduced to a minimum. Load Tests on Reinforced-Concrete Construction. Load tests on the finished structure should only be resorted to when, all reasonable care having been exercised to obtain good results, some doubt still exists as to the results. Such tests, however, should not be accepted in place of a strict compliance with the specifications. The architect should know beforehand that his building is correctly designed and safe, and should empk>y, if necessary, an engineer. The contractor should understand at the outset that the structure has been designed for certain definite purposes and loads, and that the materials and details of construction specified are not to be changed. If the contractor furnishes the design, as he sometimes does, a practice thoroughly condemned, the architect should prescribe in his specifications that such design shall be checked and approved by an engineer appointed by him. A fair load to be applied in a test is one half the weight of the construction plus one-and-one-half times the working live load. The stresses in the construction are then equal to one-and-one-half times the working stresses assumed in designing. Under these conditions there should not be any evidences of distress, and the deflections should not exceed Hfio the span. The material used for the load test should he so selected and placed that, when uniformly distributed, as required, it will not arch and assist the compressive strength of the beam or floor. Pig iron is a very good material to use. Bricks are more generally available, but must often be piled very high to get the required load, consuming much time and labor in making the test. When bricks are used they should be set in vertical piles with spaces of 2 or 3 in between them, thus avoiding all arching of the load. 968 Reinforced-Concrete Factory and Mill-Construction Chap. 25 CHAPTER XXV REINFORCED-CONCRETE FACTORY AND MILL- CONSTRUCTION * I Bv - -/ EMILE G. PERROT MEMBER OF AMERICAN SOCIETY OF CIVIL ENGINEERS General Principles. The problem involved in the proper design of a rein- forced-concrete factory or mill is a far more difficult one than might appear from a superficial examination of the finished structure. This applies to build- ings constructed wholly or in part of reinforced concrete, and is due to the fact that maximum economy and efficiency in production can only be obtained when the building is thoroughly adapted to a given occupancy and use. Laymen, and even some architects, look upon the factory as a mere workshop, consisting of four walls with floors and roof. To them it seems an easy matter to locate the structure with reference to the lot or site and then supply it with stairways, elevators and kindred features. This, however, is not the case. Each industry uses processes pecuHar to itself. The ease with which these processes can be employed renders the profit-making more or less successful; hence it is neces- sary to design the building to suit them. However, as the purpose here is to explain what constitutes proper design, as appHed to the reinforced-concrete construction of a factory or mill-building, a typical case will serve to make clear the principles involved. This chapter, therefore, deals with such general types as would seem to meet the needs of the greatest number of persons. Walls, Floors and Roofs. Reinforced-concrete construction may be used for walls and floors, or for floors and roofs only, in the latter case substituting for reinforced-concrete walls some masonry construction such as brick or stone. It is not always advisable to use reinforced concrete for walls. Circumstances very frequently arise in which it is more suitable and economical to use brick walls or piers. Types of Floor-Construction. The floor-construction may be divided into two general types, the beam-and-slab type and the girderless type. The beam-and-slab type may in turn be divided into varieties. For example, it may consist of beams supported by columns, with slabs spanning from beam to beam. This arrangement corresponds to simple mill-construction in wood, where the heavy timbers run across the building every 8 or lo ft. The timbers rest on the wall at one end and on a post at the other, with 3 or 4-in splined planks spanning from beam to beam. The earlier types of reinforced-concrete floors were patterned after this system. The next method was the introduction of girders running from column to column, and the placing of the columns farther apart, say twice the distance common to the former system. The beams are gpaced as formerly. This may be called the beam-and-girder system. Still another variation of the beam-and-slab type is the square-panel system, in * For Concrete in general and Mass-Co^erete, see Chapter III, pages 240 to 251; for Strength of Concrete without Reinforcement, Chapter V, pages 283 to 287; and for Reinforced-Concrete Construction in General, see Chapte? XXIV, the paragraphs of which, corresponding to the same det^s 4iscuss^4 Uere, shQuW ?^l3Q t>? Te^4. See, alse; Chapter XXUI, p£«es 8;; ^nd 844. Number and Arrangement of Columns 969 which the beams are arranged along four sides of a square, a column being placed at each of the four corners. The simplest type of reinforced- concrete construction for factories is some form of the beam-and-slab type with walls and piers of reinforced concrete. The girderless type consists of a heavy flat slab supported on columns without the use of beams or girders. The column-head is enlarged to form a large bearing-surface and the columns are spaced so as to form square bays as near as possible. A typical example is worked out at the end of this chapter. Columns. In general, as few columns as possible should be used to support a floor, in order that they may not interfere with the placing of machinery, and to insure the most economical use of the floor-space. From the standpoint of i^-n— r IT i r I I r ^ T 1 ' I III ■T 1 r T I n I I T I n Jr Fig. 1. Cross-section of Building economy of construction, however, the use of one column to not more than 400 sq ft of floor-space has been found to meet average requirements. This, of course, does not include construction of a special class. Adopting this, then, as the standard, and bearing in mind the fact that the nearer a building comes to being square in plan the less is the total length of exterior wall required to enclose a given area, it can be assumed that a four-story building 75 ft wide with tv/o rows of columns, making three spans across the building, is a suitable one for many purposes. (See Fig. 1.) The Lighting of a Building of this width, with story-heights of 14 ft, top to top, will be ample for most purposes. There are always some parts of the floor-space for which a strong light is not absolutely essential and which can be devoted to aisles and to the storing of material in process of manufacture. The central part of the floor-space is generally used for this purpose, while the 970 Reinforced-Concrete Factory and Mill-Construction Chap. 25 machinery is placed nearer the windows where the hght is best and where the work is done. It is usually better, therefore, not to have a row of columns along the central axis of the building, unless it is definitely known that such an arrangement will not interfere with the proper use of the lloor-space. In a building 75 ft wide, two rows of columns, with spans of 25 ft crosswise of the structure, leave the central part of the floor-space free. Dividing 25 into 400 sq ft, the floor- space allowed for each column, gives 16 ft as the distance between columns, measuring lengthwise of the building. Bays. The reason in this instance for making the bays rectangular instead of square is that there would be another row of columns if a square bay with a maximum of 20 ft in either direction were assumed. This would be likely to End of Building s W Fig. 2. Part Floor-plan of Building interfere with the judicious placing of machinery and would result in a row of columns along the central axis of the building. This is not considered good practice r*nd should be avoided, except when there is to be only one row of columns in the building. Example of a Typical Bay, The design of a typical bay of the size men- tioned above, 25 by 16 ft, will now be considered. Referring to the illustrations (Figs. 1 and 2), it is seen that the windows occupy the major portion of the wall- area, the sill being set much lower than is usual in brick buildings. This is done to avoid the necessity of the construction of an extra-high spandrel beam, as the lintel over the windows below performs the double function of supporting the floor and forming a curtain wall. The head of the window is carried up to the under side of the floor-slab to simplify the construction of tlie bottom Design of a Typical Floor-System 971 of the lintel and at the same time permit the window to extend to the ceiling, thereby introducing the light at the highest possible point and allowing the rays to project far into the room. The first beam should be set as far back as possible from the outside wall and windows, so that the angle of the direct rays of light will be as nearly horizontal as practical^le. It will be found best to have the main girders run across the building, bearing on the walls and interior columns. These girders may be made as deep as economy of design suggests, as they run parallel with the light-rays and do not interfere with the lighting-scheme. Again, a deep girder is relatively very economical. It also acts as a stiffener across the narrower dimension of the building, thus increasing the resistance to vibration caused by moving machinery. Design of Floor-System. The various elements of the floor-system consist of columns, girders, beams and slabs. Each cf these will be considered sepa- rately. A live load of 1 20 lb per sq ft is ample for light manufacturing purposes. This is the load prescribed by the Building Regulations of the City of Phila- delphia. The Slabs. The spacing of the beams should be governed both by economy of the form-construction and the maximum distance a slab will span while carrying the load safely. It is impractical to make a slab less than 3 in thick. Its dead weight, with concrete weighing 150 lb per cu ft, is s7H lb per sq ft. Allowing for a i-in cement finishing-coat, weighing 12^/12 lb per sq ft, to be laid on the concrete, the total live and dead load which the slab must carry, if it is 3 in thick, is 120 lb + 50 lb = 170 lb per sq ft. Referring to the diagram of the strength of reinforced-concrcte slabs (Fig. 18), calculated on a basis of the bending moment equaling Wl/ 10, no curve is found in the 3-in diagram for a span of 6 ft to carry a load of 1 70 lb per sq ft. Some other slab must be used, therefore, to carry the load. The Slab-Reinforcement. Referring to the diagram of the 4-in slab in Fig. 18 and following the 6-ft line until it intersects the horizontal line opposite 187 ^i lb per sq ft, it is found that a 4-in slab, reinforced with 0.195 sq in per lin ft, or two Me-in square bars per foot, will carry slightly more than is required for the slab in question. The total load, if the slab is 4 instead of 3 in thick, is 182 i/i lb per sq ft, and as the i87H-lb Ime is the nearest to this load, the 4-in slab, reinforced as above, is adopted. The reinforcing-rods are placed i in from the bottom of the slab and are of sufficient length to extend over two spans and lap 18 in at each end; the joints are made over the beams and not in the space between them (Fig. 3). The Beams. The beams running from girder to girder are considered next (Fig. 2). The span, center to center of girders, is 16 ft, and the distance apart 6 ft 3 in, making an area of 100 sq ft carried by each beam. To the load per square foot of 1821^ lb must be added the weight of the beam itself, which is assumed to be 15 lb per sq ft of floor-area, rnaking a total of 19 7 1/^ lb per sq ft to be carried by the beam. This multipHed by the area, 100, equals 19 750 lb. The bending moment caused by this load on the beam, based on the formula M = Wl/10, which for partially restrained beams is the one generally used, is 379 200 in-lb. The slab acts with the stem or beam to form a T beam and hence is as- sumed to be the compression-flange of the girder; and as the slab is 4 in thick, the depth of the beam and the amount of reiniforcement can readily be found by refer- ring to Fig. 21, which is the diagram of the strength of T beams having a 4-in slab. The beam-depth in the diagram is the depth of the stem below the slab. In the diagram opposite the center of the space between 350 000 and 400 000 on the left-hand side, the depth of beam that best suits the conditions can be selected, and at the bottom of the diagram is given the total area of steel to 072 Rclnforced-Goncrete Factory and Mill-Construction Chap. 25 be used in the reinforcing-rods. As the depth of a beam from the standpoint of economical use of material should be about one-twelfth the span, a beam 14 or 16 in deep is found to comply with this rule. Below the space where the line representing the 14-in depth of beam intersects the line representing the bend- ing moment, it is seen that the area of steel necessary is 1.8 sq in. Distributing Fig. 3. Plan of One Bay, Showing Reinforcing this over four bars, each bar should contain 0.45 sq in. The area of one ^Vie-in square bar is 0.47 sq in, and hence a beam 14 in deep, reinforced with four ^Vic-in square bars, is used. The width of the beam should be 6 in. A safe rule to determine the width of the beam-stem is to allow Il^ in of concrete iireproofmg on the sides of the bars and arrange the bars in two rows, if the beams have three or more bars. The distance in a horizontal direction, center to center of bars, should be 2V^ times the diameter, but in any case there should be a i in space between the bars horizontally, to permit the concrete to thoroughly incase them. Arrangement of the Bars. Assuming the bars to be twisted, the distance, center to center, of the two bars is 1% in. Addnig to this the diameter of the bars on their diagonal, which is about iVs in, and 3 in for the fireproofmg, the sum is 6 in as the width of the beam required in this case (Fig. 6). It would be perfectly practicable to arrange the four bars in one row across the bottom of the beam; but the width would have to be 9% in, which is wider than safety requires. An additional objection to the latter arrangement is that it requires more concrete, thus adding to the dead weight of the construction. There should be 2 in of concrete under the bottom of the rods for hreproofing. Width of Beam. Of course, the width of the beam must be sufficient to permit easy pouring of the concrete. Where wooden-box forms are used, it is not good practice to make beams narrower Ihan 6 in. If the beam is very deep, say 36 in, 6 in would be too narrow a width in which to place the steel and clean out the beam-forms. Practical considerations very frequently govern the width of beams. Stirrups and Reinforcing-Bars 973 Stirrups. There should be in each beam and girder a sufi&cient number of stirrups, made of at least %6-in round bars, bent U-shaped, run under the bottom rods and extended up into the slab with an angle-bend 6 in long. If the beam or girder is short and excessively deep, %-in round or heavier stirrups should be used. The function of stirrups is to unite mechanically the slab to the beam, so that perfect T-beam action will result, and also to assist in the resistance to diagonal tension or shear as it is commonly called. The num- ber of stirrups in a beam should be approximately^ one for each foot of the span, center to center, but the spacing should be as stated below. Thus, a i6-ft beam should have not less than sixteen stirrups, that is, eight on each side of the center line. Stirrup Spacing for Distributed Loads. For beams with distributed loads, the stirrups are to be spaced so that the minimum distance between them will be 6 in in ordinary cases, and the maximum distance not more than 36 in at the middle of the beam. Each half of the beam should be divided into three parts. The division nearest the sup- port should contain ap- proximately one-half the number of stirrups allotted to one-half the beam, or one-fourth the total num- ber. The middle division should contain one- sixth the total number, and the division next to the cen- ter line one-twelfth the total number, as shown in Fig. 4. If the distribution does not work out evenly the spacing which comes the nearest to this should be used. Stirrup-Spacing for Concentrated Loads. When there are concentrated loads the stirrups should be designed to suit the loading, but in any case, for a distance equal to about one-fifth the span from each end, the stirrups should be spaced at least from 4 to 6 in on centers. A good rule to follow is to err on the side of safety and to put in plenty of stirrups, if the determination of the exact number is in doubt, as there should be a sufficient number of them to resist that part of the diagonal tension not safely resisted by the concrete. The Arrangement of the Bars in the Beam is shown in Fig. 4. The two upper bars are bent upwards near the supports to resist the negative bending moment, which causes tension at the top of the beam near the supports. These bars should extend into the next span at least 30 in to form a tie. As rein- forced concrete is of a monolithic character, it is necessary to introduce metal bars wherever the concrete is subjected to tensile stresses. While it is not necessary to provide as much steel at the top of the beam over the supports as the formula, for restrained beams gives, if 50% of the area in the beam is carried F'vj. 4. Section Showing Elevation of Beam 974 Reinforced-Concrete Factory and MiU-Construction Chap. 25 to the top and over the supports, as shown in the illustration, the beam will be perfectly safe when calculated on a basis of M equaling Wl/io. In some cities, beams must be calculated on the basis o( M = Wl/S. Then it is only neces- sary to have about one-fourth the number of the bars bent up near the supports. These bars, however, should extend at least 30 in beyond the center of the girder or column to tie the building together. For Simple Beams with Uniformly Distributed Loads, all rods for 60% of the span should be straight and the truss-rods should bend up from the points so determined. For Beams or Girders with Concentrated Loads, all bars are run straight as far as the concentrated loads extend. Beyond these loads, towards the sup- ports, one-half the number of bars may be bent up as above. - Plan of Wall Qplumn Footings. Plan of Interior Column Footings. Fig. 5. Elevation of Girder and Plans of Column-Footings The Girders. The girders running across the building arc calculated on the basis of carrying their own weight as a uniformly distributed load and con- centrated loads at the points where the beams frame into them. Referring to the illustrations. Figs. 2 and 5, it will be noticed that there are three beams on each side supported by the girder, the fourth beam being carried by the column. Each concentrated load equals the total load on the beams, or 19 750 lb. The weight of the girder can be assumed as 20 lb per sq ft of area carried, 20 X 400 = 8 000 lb. This acts as a distributed load. Oac-haU the span oi 25 ft, or 12 ft Girders and Lintels 975 6 in, is ISO in. The bending moment at the middle of the girder from the con- centrated and distributed loads is M = (29 625 X 150) - ( 19 750 X 75) + 8 000 X 300 3 262 500 in-lb Reinforcing-Bars and Width of Girder. Referring again to Fig. 21, in the center of the space opposite 3 300 000 and 3 250 000, the line of a 26-in deep beam is shown to intersect the vertical line representing 8 sq in of steel. Hence eight I -in square bars arranged in two horizontal rows are used. The width of girder must be 12 in in order to have the proper distance between the bars and at the same time have 1I/2 in of concrete fireproofing on the sides (Fig. 7). Cemeut Top, )/^aSq-i mmm Cement Top Kg Sq. Bars jjjj " Stirrups Fig. 0. Cross-section of Beam ,L -%° Stirrups iH' 8- 1 Sq. Cars J. -12''—^. Fig. 7. Cross-section of Girder The Width of the Concrete Slab over the Girder is found by multiplying the area of the steel liy the number on the hne of the 26-in beam, which is 8.7. This constant is used for any area of steel when the beam is 26 in deep; the constants on the other beams are to l)e hkewise used for their respective beams. In the case of this girder, the width of the T beam is 8.7 X 8 = 69.6 in, or 34.8 in on each side of the middle of the girder. The portion of the slab used at the T flange of the girder or beam should not exceed on each side of the beam ten times the slab- thickness, nor one- third the span. In the case now being considered, the Umit is not exceeded. Similarly the width of the slab acting as the compression-flange of the 14-in beam is 1.8 X 12 = 21.6 in, twelve being the constant for 14-in beams. The Lintels. The next member to design is the lintel, or spandrel beam over the window (Figs. 2, 5, and 8). This should be, for practical considerations, 6 in thick. As the bottom of the lintel is flush with the bottom of the slab, the slab- rods must run into the hntel over the top of the hntel-rods. In addition to the stirrups in the Hntel there should be bars of the same size as the stirrup-bars, spaced about 12 in apart and bent at right-angles, one leg extending up 12 in into the lintel and the other 18 in out into the slab; or else the slab-bars should be bent up, extending into the lintel 12 in. These make a perfect tie between the slab and lintel. The bottom of the lintel should be made with a rebate to receive the head of the window-frame. The load carried by the Hntel is the load from the slab, the weight of the window and the dead weight of the Hntel. The load from the floor-slab is 13 H ft (the clear span of the lintel) X 3 f t = 40 3^ sq ft X 182 1/^ lb, the load ix^r square foot on the floor-slab, or a total load from the floor-slab of 7 371 lb. The total height of the Hntel to the top of siH is 3 ft. As it is 6 in thick this makes the weight per Hn ft 75 X 3 ='225 lb, the total weight of the Hntel being 225 X 13 M = 3 038 lb. For the window 10 lb per sq ft is allowed. The area being X3H X n ft, the height of the window, or in even 076 Reinforced-Concrete Factory and Mill-Construction Chap. 25 figures 149 sq ft, the weight is 149 X 10 lb = i 490 lb. The total load on the lintel, then, is 7 371 + 3 038-}- i 490= 11 899 lb. The Lintels Figured as Rectangular Beams. By referring to the paragraph Explanation of Diagrams and Formulas, page 992, for the strength of rectangular beams, it is seen that when reinforced with 0.5% of steel the safe load carried by the beam is W = wl ■■ = 48—. Hence, a 6 by (36 —6) -in beam will carry 48- 6X27- 13-5 =» 15 552 lb. The depth 27 is used, as it is taken to the center of action of the steel. This is more than the load upon the lintel and hence the lintel is safe. A reinforcement of 0.5% equals 0.005 of 162 sq in, the area of the concrete, or 0.81 sq in; and if two bars are used, each must be of 0.4-sq-in sectional area. Two %-in square bars, each having an area of 0.39 sq in, will be used.' These should be located 2 in from the bottom, and run straight. There should be two %-in square bars near the top of the lintel, running the full length, and fourteen %6-in stirrups, as shown in the illustra- tion (Fig. 8). The top bars take the place of bent bars and also prevent vertical cracks which are liable to occur from shrinkage near the middle of the lintel. Sq. Bars Stin-ups Bend up Ends of Slab-Bars Cement Top m The Columns. Having established the design of the lloor-system, the dimen- sions of the wall piers, interior columns and footings are next determined. A Fig. 8. Vertical Section, Showing Lintel schedule of the loads on the interior cohmins will now be made. The Load from the Roof. Assuming a live roof load of 30 lb per sq ft and 10 lb additional for accidental load from overhead shafting, the total Hve load is 40 lb per sq ft. The weight of the slab, if 3 in thick, which is as thick as is usually required, is 37^^ lb per sq ft. The beams and girders weigh another 30 lb per sq ft (12 plus 18), making a total dead load of 70 lb, including the covering. Adding the live load of 40 lb to this gives 1 10 lb per sq ft as the total dead and live load. The Load on the Fourth-Story Column, then, is 400 times no lb or 44 000 lb, not counting the weight of the column itself. For practical reasons no column should be made less than 10 by 10 in in cross-section. Allowing, therefore, 500 lb per sq in unit stress on the concrete for columns, which is the unit stress allowed by the Philadelphia Building Bureau in reinforced-concrete columns with vertical reinforcement, the carrying capacity of a 10 by lo-in column is 100 times 500, or 50 000 lb, which is in excess of the load to be carried. (See Table I.) The Load on the Third-Story Column is the load from the one above of 44 000 lb plus the load of one bay of the fourth floor, which is 217 lb X 400 = 86 800 lb, being the total dead and live load; or 86 800 -+- 44 000 =130 800 lb, to which mu§t be added the weight of the column, which is assumed to be 300 lb per lin ft. As it is about 1 1 ft long in the clear, the weight of the column is 3 300 lb, which, added to 130 800 lb, equals 134 100 lb. The area of the cross-section of a 16 by i6-in column is 256 sq in, which, at 500 lb per sq in, gives 128 000 lb as Columns and PierS 977 the safe carrying capacity. While this is 6 loo lb less than the load to be carried, it is within 4y2% of the required strength. It is customary to make a reduc- tion of the load to be cariied on the columns in proportion to the amount of floor-area carried, the reduction being greater as the floor-area increaseSi Usu^ ally a 5% reduction of the live load per floor, with a maximum not exceeding 50% on the bottom columns for high buildings, is considered good practice. Table I. Strength of Reinforced-Concrete Columns. Length, Fifteen Diameters Columns' with vertical bars. Safe working stress on concrete 500 lb per sq in, the strength of the rods being neglected in figuring the columns Size Area Total safe loads in lb. Size Area Total safe loads in lb 8X 8 64 32 000 18X18 324 162 000 9X 9 81 40 500 ■19X19 361 180 500 10X10 100 50000 20X20 400 ■ 200 000 iiXii 121 60 500 21X21 441 220 500 12X12 144 72 000 22X22 484 242000 13X13 169 84500 23X23 529 264 500 14X14 196 98 000 24X24 576 288000 iSXiS 225 112 500 25X25 625 312500 16X16 256 128 000 26X26 676 338 000 17X17 289 144 500 27X27 729 364 500 The Load on the Second-Story Column is 134 100 lb plus the load from the third floor and the weight of the columns, all of which is assumed as being equal to the fourth-floor load and weight of column, or 90 100 lb, making tht load 224,200 lb. A 21 by 21-in column will carry 441 times 500 lb per sq in, or 220 500 lb. The Load on the First-Story Column is 224 200 lb plus the second-floor load of 86 800 lb and the weight of the column, which, at 600 lb per lin ft, is 6 600 lb, or a total of 317 600 lb. A 25 by 25-in column will carry 625 times 500 lb per sq in, or 312 500 lb, which is almost the required strength. The column-schedule then becomes For the first story 25 x 25 in in cross-section. For the second story 21 x 21 in in cross-section. For the third story 16 x 16 in in cross-section. For the fourth story 10 x 10 in in cross-section. '' The Reinforcement in the Columns should consist of eight %-in round rods in the two lower and four in the two upper stories, with ties of i^-in round wire every 12 in, as shown in Fig. 9. It is the custom to use the same unit stress on reinforced-concrete columns up to 15 diameters, and not to use columns whose length exceeds 15 diameters. The Wall Piers. The schedule of all the wall piers is made by the method used for the interior columns. The details of the calculations are not gone into here, results only being given. The size of the wall piers is deter- mined by the architectural effect desired and by practical considerations. Assuming 30 in as the smallest face-dimension of the piers, this size should be carried up the full height of the building (Fig. 10). The reveal of the piers to the spandrels is 6 in, and the spandrels should line up flush with the inside sf the piers if by so doing they are not made extremely thick. Reinforced- 978 Relnforced-Concrete Factory and Mill-Construction Chap. 25 concrete spandrels may be 6 in thick and give good results. It is not wise to make them thinner than this, on account of the difficulty of constructing them. It is to be noticed, also, that the hntels or spandrel beams act as ties from one wall pier to another. They should be of sufficient strength not only to carry the vertical loads coming upon them, but also to act as braces to take up any vibra- \i Wire Ties, spaced 12 apart ; Rciuf. G--r? Kods '■ i 1 ■ ■ ■ o '. *■../ * --'^ .' 1 Keiuf. 8-%'''Kods ^ Wire Ties, spaced 12 apart) Fig. 9. Interior Column Fig. 10. First-story Wall Pier tion in the direction of the length of the buildin^?; just as the deep cross-girders resist the vibration in the direction of the width of the building. Very fre- quently the main girders are run lengthwise of the building, that is, spanning the shortest distance, while the beams run across the building. Sometimes this will make the construction more economical; but the reduced height of the windows in the side walls due to the necessity of lowering the window-heads to permit the beams to be carried by a lintel running over them,, is objectionable, as the light from the windows in this position is not as effective as when they are run up to the under side of the floor-slab or ceiling. The wall-pier schedule, figured on the assumption above, becomes For the first story 30 x 16 in in cross-section. For the second story 30 X 12 in in cross- section. For the third story 30 x 12 in in cross-section. For the fourth story 30 x 12 in in cross-section. It will be noticed that the piers in the three upper stories are of the same dimensions. This is due to practical requirements, the reveal of the pier to the spandrel being 6 in and the minimum spandrel-thickness 6 in. The pier must be 1 2 in in order to be flush on the inside of the building. Spread Foundations. The use of reinforced concrete for the footings of a building results in economical construction when it is necessary to project the base or footing more than is customary or permissible without reinforcement of some kind. In order to give sufficient information for the design of the founda- tions for the building under discussion in this chapter, as well as for other types of construction met with in practice, several examples are worked out in the following pages. The simplest form of reinforced concrete spread footing is shown in Fig. 5 and consists in considering the overhanging portions of the footings as cantilever beams. The footings of the interior columns are de- signed as explained in the following paragraphs. The Load on the Footing. The load on the footing is assumed to be 317 000 lb and the safe bearing value of the soil 7 000 lb per sq ft. This requires a spread footing of 317 coo lb divided by 7 000, or 45 sq ft. The side of the square which comes the nearest to this area is 6 ft 9 in and its area is 45.5 sq ft. The Design of the Footing. The footing is designed as follows: As each square foot of footing sustains an upward pressure of 7 000 lb, the overhanging portion is treated as a cantilever beam uniformly loaded. The load directly Footings and Foundations 979 under the column proper causes no bending, and this load is neglected in finding the bending moment. The rods should be run as shown in Fig. 5, some diago- nally and some at right-angles to the sides, the first layer located 3 in from the bottom of the footing. The size of the rods on the diagonal is now to be de- termined and the others are to be made the same size. The longest length of the i-ft-wide diagonal cantilever is 4 ft, measured from the center of the column to the intersection of the i-ft-wide strip with the side of the square. The bend- ing moment on this strip is equal to the load on an area, outside of the column, 3 ft long and i ft wide, or (3 X 7 000 =21 000 lb) X 30 in = 630 000 in-lb, 30 in being the distance from the axis of the column to the center of gravity of the area. Assuming the footing to be 24 in thick over-all, the center of action of the steel will be about 5 in up from the bottom, making an epfective depth of 19 in. As the lever-arm for the steel is nine-tenths of the depth when the stress in the concrete is 600 lb per square inch, the resulting stress per square inch in the steel (maximum stress 16 000), is 16000 X 0.9 =14 400. As the bending moment is 630 000 in-lb, the number of square inches of steel necessary per foot 630 000 in width is '-= 2.34 sq in. This formula is for rectangular beams 14 400 X 19 when the bending moment is given. (See Formula (i), page 992.) Spacing the rods 4 in on centers requires three rods per foot, each requiring a cross-section area of 0.78 sq in. As a %-in square bar has a section-area of 0.76 sq in, this size will be used. The bars in the layers at right-angles to the side are made the same size and spaced as above, so as to avoid complications in the construction of the footing. It would be possible to space these farther apart, but this re- finement is unnecessary, (See Fig. 5.) When the load on a column is such as to require a footing more than 2 ft thick, it is customary to slope the top of the footing, thus saving in the quantity of concrete, or else to provide a concrete plinth or. block at the bottom of the column on top of the footing so as to reduce the projection of the footing and thereby make a more economical design. If steel column-cores or hooped columns with vertical reinforcements are used, a metal base-plate is necessary on top of the footing of sufficient size to limit the direct stress on the footing to 500 lb per sq in. The Foundations for the Outside Walls may be designed in either of two ways: first, as continuous footings such as are usual in ordinary construc- tion, and secondly, as isolated piers under the wall columns. In the first case it is necessary to reinforce the footings and foundation-walls, as these act as continuous beams loaded at each column, and must be made strong enough to distribute the loads from the columns uniformly over the entire length. of the footings. The foundation-walls and footings can be treated as inverted con- tinuous beams (Fig. 11), the upward reaction of the earth being considered a uniformly distributed load on the beams, and the wall piers being considered a* columns supporting tlie beams, with the load on each pier as equal to the load on such supports. Fig. 12 shows the arrangement of the reinforcing-rods. Their size is determined as explained in the following paragraph. Since the load per running foot of the foundation is equal to the load from a pier divided by the distance apart of the piers, omitting the weight of the spandrel below the first-story windows, this load per running foot =191 140 lb, the load from the pier -^ 16 ft = 11 946 lb. As great refinements in calculations are not required in footing-work of this kind, because of the advisability of large factors of safety for this part of the building and the small reduction in cost due to any such refinement, the strength of this continuous beam is calculated by the formula 980 Reinforced-Concrete Factory and Mill-Construction Chap. 25 M =. ir//8, assuming / to be the clear distance between the piers, or, in this case, 13 ft 6 in (Fig. 12). Therefore, W = 13HX 11 946 = 161 271 lb and the bend- ing moment M = (161 271 X i62)/8 = 3 265 737 in lb. As the size of the beam is determined by the tliickness of the wall and its depth, all that is necessary is to !otal, 191140 lb. Total, 191U0 Ib^ Total, 191U0 lb: T T IT T T t T T T T T T T T T T ? t T- T T 11 n n T 1 1 IT T T T T T n I r Load per Running Foot 119i6 lb. Fig. 11. Foundation-wall an Inverted Continuous Beam find the area of the steel by referring to Formula (i), page 992, which gives M 3 265 737 A = -, ov A = ■ = 4.3 sq in, distributed in eight %-in square 14400 a 14400X52 bars with a total area of cross-section of 4.48 in. These are in two layers, four running straight and four bent as shown in Fig. 12. The top layer is placed 2 in Center Line of Column. Center Line of Column- '-r EourHi'^ I ^•2-9^1 "VT¥-y^; . I i'*'"'" Bars, I ;^2'9^~1 j / I ^^^A^Two liars'^ / V-WTwoBars^ ' 5^^=^^=^ -V-V-y iy- : SECTION A-A ^--M^ Fig. 12 Arrangement of Rods in Foundation-wall from the top of the concrete. The footing is made wider than the wall to keep the load on the soil within the safe limit of 7 000 lb per sq ft. The width is determined as follows. As the column-spacing is 16 ft, center to center, 7 000 X 16 = 112 000 lb, the load the foundation i ft wide and 16 ft long will carry; hence to carry 212 120 lb (the load from the pier, plus 20980 lb, the weight of the spandrel and footing), 212 120 is divided by 112 000, giving 1.9 ft for the width of the footing, or i ft 11 in, nearly. Isolated Piers. In the second case, a spread footing is provided under each wall column in the same manner as under the interior columns, but designed for the lighter load. The foundation or spandrel wall is not made as heavy as in the first case, as it carries no load except its own weight and the wall or window above it. (See Fig. 5.) Where the soil is bad and of low carrying capacity, the pier-method is found to make an economical foundation, especially where it is necessary to use piling under the building, as the piles can be grouped under the piers and columns, and capped with reinforced concrete. The foundation or spandrel walls, properly reinforced, can be carried from pile-cap to pile-cap, as they do not depend on the soil directly under them to sustain the load. Combined Column-Footings. It very frequently happens that a build- ing is to be built adjacent to and abutting on a property-line, and as the foundations must not encroach upon the adjacent property the columns must be Combined Column-Footings 981 built on the edge of the footings. In order to secure uniform soil-pressure it is often necessary to combine an interior with an exterior column-footing so as to distribute the load uniformly from the two columns to the soil below. Some- times it is necessary to combine the footings of more than two columns. Fig. 13 shows the details of an actual construction and may be regarded as typical. The loads from the columns in this case are almost identical, one being 700 000 lb fk jC: C0IN0.2 700,0001b. r==^T ^<-4 4S. Present Stoue Wall- Col No. 1 700,000 IbT' Col. 5a*x25!__^ >oint o£ Maximum IJending Moment Five Bars bent up — -sJI I Five Bars bent up — Jin! I Five Bars bent down. Fifteeli 1 '. 4 ""tw^Bar8 L ^'Stirrupsl ' \, I f M It f t t M t -r t ^ t t M t SIDE ELEVATION Party Line- 'H ;fc:-13' Fig. 13. PLAN Combined Column-footing and the other 790 000 lb, so that the shape of the combined footing in plan can be RECTANGULAR, as the center of gravity of the two loads is practically at the middle of the span. When one column is more heavily loaded than the other, the center of gravity of the loads is no longer at the middle of the span, but nearer one column; hence it is necessary to make the combined footing trape- zoidal in plan so that the center of gravity of the trapezoid will coincide with the line of action of the resultant of the loads from the columns. The following calculations for the design of this footing are the actual ones made, and serve as a good example of the necessity of assuming certain sizes at the start which the final calculations may change. The width of the founda- tion being determined by the load-limit on the soil, which in this case is not to exceed 7 000 lb per sq ft, and the size of the column-base being known, we may proceed to determine the bending moment in the footing. We assume an area of 7 X 32 ft = 224 sq ft, giving a soil-pressure of i 490 000 lb -h 224 sq ft = 6 650 lb per sq ft, or 6 650 X 7 = 46 550 lb per running foot. The point of maximum bending moment is where the vertical shear is zero and is determined by the equation 700 000/46 550 = 15 ft. Also, 15 ft — 1.05 ft = 13.95 ft. Hence Minax = [(700 000 X 13-95) = 9 765 000 ft lb] - [(46 550 X 15 X 7H) = 5 236 875 ft lb] = (4 528 125 X 12) = 54 337 500 in lb 982 Reinforced-Concrete Factory and Mill-Construction Chap. 25 The I. OS ft is one-half the column- width, 2 ft i in. We may determine the depth of the foundation by assuming a cross- sectional area of the reinforcing-steel and solving in Formula (i), page 992, for the depth. For practical considerations square bars larger than iJ4 in square bhould not be used; hence by trial we hnd that thirty iH-in square bars with a ocction-area of 46.8 sq in, placed in two rows in the top part of the foundation, will space out just right for a width of beam of 64 in, which is 6 in wider than the 58-in dimension of Column No. i. The depth then by this formula is M 54 337 500 o . , or d= — = 80 m, 14 400 A 14 400 X 46.8 the depth from the center of the steel to the bottom of the concrete. Therefore, 80 + 4 = 84 in, the total depth of the foundation. The WIDTH of the footing at the base must be increased to keep the unit |1 Cenienl Fig. 14. Section through Flight of Reinforced-concrete Stairs stress on the concrete in compression within the allowable stress, 600 lb per sq in. As the total horizontal compression in the beam must equal the total tensioii in order to satisfy the requirements for equilibrium, we have total tension =16 000 lb per sq in X 46.8 sq in = 748 800 lb. From Table V, page 930, Chapter XXIV, the depth of the area of the concrete in compression is equal to 0.31 X 80 = 24.8 in. The width is found by dividing 748 800 by (300 X 24.8 = 8 440) the resistance of the concrete per inch in width of the beam, which gives 89 in for the width of the concrete at the bottom of the footing, 300 lb being the average unit stress on the area of the concrete in compression, since the stress actually Reinforced-Concrete Stairs 983 varies from 600 lb on the outside upper surface of the concrete to zero at the neutral axis. The Stairs. The ease with which stairs can be built of reinforced concrete has led to its general adoption for this purpose in reinforced-concrete buildings. As stairs are generally enclosed in stair-towers or shafts, their construction usually takes the form of the double run or half-pace type (Fig. 14). This reduces the length of the run so that the construction does not become too heavy. Each run of stairs is considered as an inclined beam and is so figured, being supported at the top and bottom on the stair-landing header-beam. The rods are placed near the bottom of the slab and run continuously from top to bottom.. The depth of the beam is considered to be equal to the distance from the sofht of the stairs to the corner formed by the tread and rise, as shown by the letter D in Fig. 14. The landings are figured the same as floor-slabs. Their supporting beams are calculated to carry the load coming upon them from the landing and from the upper stair-run, which starts from' the landing-beam. The lower stair- run, coming up under the landing-beam, acts as an inclined strut and supports one-half of this beam. Hence the span of the landing-beam is equal to the dis- tance from the wall of the stair- tower or shaft to the inside edge of the stair-run from below, and is a Httle more than one-half the width of the stair-shaft. This makes the design of reinforced-concrete stairs very economical. (See page 905.) Example in Stair-Design. It is assumed that each of the runs is 4 ft wide, and that the maximum live load that can come upon the stairs in a crush is one person, weighing 150 lb, for each 2 ft of step, or 75 lb per lin ft of step. With steps 4 ft wide the live load is 300 lb per step or, for ten steps, 10 times 300 or 3 000 lb per run for the live load. The dfead load is approximately 400 lb per step, or 4 000 lb for the run. This makes a total load on the inclined beam of 7 000 lb. The span in calculating inclined beams is taken at the horizontal distance between supports; hence in our example the span is 8 ft 9 in. The " Wood Form ^" .I'CemcutTop Fig. 15. Detail of Reinforced-concrete Steps maximum bending moment, therefore, is 7 000 X 105 = 73 SCO in-lb, figuring the run as partially restrained. Assuming the thickness of the slab to be 5 in, the effective depth is 4 in, and the area of steel per foot of width for this depth and bending moment as above is ■ ■ = 1.3 sq in, approximately. If %-in 4 X 14 400 square bars are used having a section area of 0.56 sq in, they should be spaced S^k in apart. It is customary, also, to run 14-in square bars, spaced 2 ft on centers, at right-angles to the main rods, as shrinkage-bars. It is also customary to run the rods which reinforce the run of the stairs, from the wall-edge of plat- form at the top to the wall-edge at the bottom, bending the rods to make them come in the bottom of the landing-slabs and act as their reinforcement. This makes a very rigid and economical construction. The treads should be finished with a I -in top surface of cement and grits; and the risers can be brushed smooth 984 Reinforced-Concrete Factory and Mill-Construction Chap. 25 500 —*■ ~~" "~" — — -~" -*- — — ■ — — 1 — 450 ?^ ^ V 1 1 400 P3 D f "S ^ t (^{ .s c! M d o oKf| □ V § to ;^' I A '-'5 ^ Je 11. -r, 1 1 a 43 ^ 1- a foot. ." ^ i 53 i _a ■i \ ^ ^ V l\ 2 — -1- r. ft. a = \\ 1^ n ifl ^ Y Z 250 i 7] g? "1 <^ ^\ \ a \ A ft — 3. □_i \ \\ ^3 =5 [ ,^ L A Poui 3 V \ \ \ \ \ — V v> V \ \ Vy 150 \ y s^ V V \ \ \ \\ V \,^ •^ V \ V s> \ 100 \ s \ S s> ^s \, \^ \ S ^ ^ s — — — — — s ^ \ N <: N. ^ N N x^ \ 60 \ "V ' ^ V - ' 5. 6 3 Slab 7„ 8 4 Slab 10 M = ^i ' Span of feet Fig. 16. Diagram for Strength of Rcinforced-concrete Slabs when their forms are removed. The riser-forms should be removed as soon as the concrete has set sufficiently to hold its shape, so that the top of each step or tread can be incorporated into the concrete. Top-surfacing applied after the concrete has set hard is very likely to become loose and break off. A very good form of step is shown in the detail^ Fig. 15. When the stair-runs arp Strength of Rcinforced-Concrete Slabs 985. very long and cannot be carried, at bottom and top where the steps start and stop, on header beams, a reinforced-concrete beam, forming an outside string, should be used and the stair-reinforcement run parallel with the risers from the string to the v/all. The lieam forming the string can be made any convenient height and width, and reinforced to suit the load. m a a (JQQ . „ ^ — p ^ 600 „ « -t a £ L ° a « r »*l5_ ^ °h\l ■*' oT ° T '^' "^^ . '. . f^!^ ^u-rg"=' £ y^rt :.^ "^ !. "^ I S ^ a i: W ^ <:? -^ " M^*^ S -a * \a - « f'nn •S' fe V ■ a "^ \ W ° " ^ '^ \ 1— fa <£ ^e \\\ ^^ "S n 1 H '^^ Si ^Ti 450 d ^ MIV'^- " " ■ :« '?^ — 'Va \ 1 / ^ • S|\ ArvV ►, vtW o v\\\ o Ann LA —P — \ \\\ Ann V I f-< \\\\~ --1 1\ ^ \y\ rr \ U 'l^ft C/J 350 ^ jV_ __ ._ '""^ t-l lA ' C Uu a TTx r ~\\\ m \r\ u \a$' qm T^ 300 \n VSt - - ^^ \\\ US :_ ^_. b \ Y Y ^\ ^ ^V^ 250 aiyj r" T _ - - >\Mr \ V \ > V V V V^i oon 200 - V \^ ^ ir^ N>S^^ ' ~ 150 ^vTC^ ^ - ^^^ I -^^\^.' ^s^^i^ ^V-v- mn \. S. ^ inn KA - - • ._.__._ 5 6 .7 „ 8 9 10 11 () 5 Slab . j_W? Span in feet ^ 0„ 10 11 1-3 13 G Slab Fig. 17. Diagram for Strength of Reinforced-concrete Slahs Explanation of Diagrams and Formulas. Figs. 16, 17, 18 and 19 are to be used in designing reinforced-concrete slabs. These diagrams are plotted from calculations made in accordance with the 1907 Regulations of the Phila- delphia Bureau of Building Inspection, which permit a unit compressive stress of 600 lb per sq in in the concrete and a tension of 16 000 lb per sq in in the ?teel, with a ratio of the moduli of elasticity of steel to concrete equal to 12, 986 Reinforced-Concrete Factory and Mill-Construction Chap. 25 These unit stresses give a factor of safety of 4, based on the ultimate strengths of the materials and have been found to give results in practice which are con- sistent with safety and economical construction, the concrete being a i : 2 : 4 JU 1 irt £ « = 10 a i: - 2 Si ^ i <^ .a n -2- «^ ° i!: I. CQ =°.'^i ^ ui a ^c;~g~E. i-^^ N II. £ "^' s ° ** T'5"§"T l^^il 3"T"V a M — 1^^^°., \ ?Tl YT^iV 1^ ^H ^ J.1I f- V s ^ uU f ^. $ ^ >=V\ tS .-^ ?§ 4tt ^ iSt 4\^ ~ f-\ --^A^ ?. Ky ^ CUv 1 ^- & tAG + ^ -^-5\^ H^ \i V-UC \-^ VaVs 3 ti -A-^A^ 4^ \-vX V>t Xav_ X5^ ^^^s 1 3-S^ ScASv- V5^ ^^ S^v 5 N^ ^^^^ VS "^ vs: 1 ^2s S^s^ V '^^ s^^ ^^. "^ ^^ v^ , ^ it 3 i 5, 6 6 7// . 8 iSlab au Span in feet Fig. 18. Diagram for Strength of Reinforced-concrete Slabs 9 10 ^=10 mixture and the aggregate a good hard stone. The building laws of various cities usually specify the allowable unit stresses to be used in designing reinforced- concrete structures, and when they differ from those used in the calculations. Strength of Relnforced-Concrete Slabs 987 corrections will have to be made in the results obtained when using the diagrams. However, when one has the option of choosing his own method of calculating, the diagrams may be used with absolute safety. Figs. 20, 21, 22 and 23 are diagrams of the strength of T beams. The cal- culations in these diagrams are based on the same unit stresses as above; but - t □ ? s: _:■; 7.50' _ 4 .. '^ -1 ^a siJ, _t4l" -J 1 r .:. ^ ^ »,^ 1 '. "-IS, i ST^iT z-S ^ '?V* ii a--^' ' - •i-o" t-^i-- -- " coo ij- " -W ^ — \\^^- f 1- ' A-s - ^ l^^^iU^ ^< ^ si^il^S; — ^ ^- ^'■"^ s IS ^U\ " iw ^ • 4- iiv \ ^ □ H -\V 'n ViO •" '" W \ \ O 500 /; H I u \ U o V vlV iA\ - !j <'ai \ \A\ w\ XV \ ' W ~ C7 \ R ? V t- "^ 4m TftlV \j^t i A\X ^ \v V\^ " r2 qp;n i \\\ u xit ^VA \V • o ^-\^ \ ^c A^A m ouv Y rr 5Vr- ' 4AV^ v\\v t^s - JiVQ OKA X ^ ^ J5^ • I '^^ ^5S Sxo ' ^& V^5, 5ax^ ^\5^ 9(00 it-VJ^ \v\ . . '^" ^ ^^>$^ ^^\S ' wv^ S^N^^ ^^Sk ^$SS!v ^\(\ \^^^ vi^ 1 IjO ^^S^ s^ vS ^^ inn J [ . . .._L -|800 I :Too -650 -jm -I -550 :5oo \m -40O :350 :30o :250 ^200 5153 -lOO so 6 7 8 M _W7 9, 10 11 13 13 6 'Slab 5 6 7„ 8 9 10 11 ,5 Slab Span in feet Fig. 19. Diagram for Strength of Reinforced-concrete Slabs the effective depth of the beam is taken as the distance from the center of action of the steel to the center of the concrete slab and not to a point one-third the thickness of the slab from the top. The beam-depths in the diagrams are the depths of the stems below the slab. The width of the slab in compression is found by multiplying the area of the steel by the constant given in the dia- grams for the corresponding depth of beams. Reinforced-Concrete Factory and Mill-Construction Chap. 25 2.500,000 DIAGRAM OF STRENGTH OF T BEAMS j 2.400.000 / / 1 2,300.000 / ' y 2.200.000 / / / / / 1 2.100,000 / // 1 // / / 2.000.000 y / / / / / / , 1 1.900.000 / // / / /y 7 / / 1.800.000 500,000 m '// / / v . ^y '//// //. / y / ^^ / 400.000 '//// // / / / / // / / 300,000 // y m/ /. / 3-] nch Slab 200.000 M V / M/// y 100.000 m y// 12 3 4 5 Area, A, of steel, square inches. pi|. 20. Diagram for Strength of T Beam§ Strength of Reinforced-Concrete T Beams 989 iooooo DIAGRAM OF STRENGTH OF T BEAMS 3,400.000 1 "7 ■~j r 7 ~*~ / / / 3.300.000 / / / r / / 3,200,000 / / 3,100,000 / / i / / i 3,000.000 / 1 ' 1 2,900.000 / 1 1 / i 1 2,800.000 / / 1 i / 1 2.700.000 ./ f / / f 2,600.000 00 /"i / , f >-/ / / 1 2.500.000 / ao/ / f / / i y 1 2,400.000 / 1 -/ / / r ' a> 1 / y 2,300.000 ) 1 CjJ 1 / / / 1 ?u L 2,200,000 / / 1 / ° 7 f / 1 4 2.100.000 r , 1 1 n / / 1 1 / 2,000.000 / 1 1 ^ f / k/ 1,900,000 1 1 J 1 1.800.000 1 1 1 ^ / / 1 1 '^' 1 1,700,000 / 1 / / .^ y / 1 / / 1,000,000 / f y 1 / / J / 1,500,000 1 / ^ / i "^ / 1 ' / f / q V 1,400.000 rh / y f W-^ rr 1 / J / 1,300,000 / If . / / / ' 1 / / 1.200,000 11 1 i r "v/ / / II ' 1 ^ / ^ 1.100,000 , II / i ^/ / S- / / f 1 I /, \^ y 1.000,000 11 II 1 1 / / / 11 ' 1 ' 1 / J ^ / 900,000 It 1 1 J / ^/ II 1 i 1 / / 800.000 II If 1 / / 1 1 1 \ J / / 700,000 If. 1 / / / If 1 . f r 600.000 If / / / / 1 / . 500.000 I // / / /// f ^ / 400.000 / / rIK h- Jla |g V 300.000 / 200,000 I iW. 7 100,000 m 133456789 10 Area, A, of steel, square inches. Fig. 21. Diagram for Strength of T Beams 990 Reinforced-Concrete Factory and Mill-Construction Chap, DIAGRAM OF STRENGTH OF T BEAMS . 25 2 3 i 5 6 7 8 9 10 11 12 13 li 15 Area, A , of steel, square inches. Fig. 22. Diagram for Strength of T Bearos Strength of Reinforced-Concrete T Beams DIAGRAM OF STRENGTH OF T BEAMS 991 3 1 5 f) T 8 9 10 H 12 13 14. Area, A, of steel, square inches. Fig. 23. Diagram for Strength of T Beams ^92 Reinforced-Concrete Factory and Mill-Construction Chap. 25 The following formulas are for the strength of rectangular beams or slabs, based on various percentages of steel, the beams being considered to be as simply- supported at the ends. They are calculated in accordance with the Philadelphia requirements, and can be used in investigating the strength of rectangular beanis and slabs without obtaining the bending moment. They are very con- venient in checking up a design already made, or in establishing the area of the steel reinforcement when the size of the concrete beam or slab is fixed, aS shown by the example given. 7V = load in pounds per runnmg foot; b = breadth of beam in inches; d = depth to center of action of steel in inches; / = span in feet; p = percentage of steel to area of concrete above center of steel to top of beam. When P = o.5% then w = 4S-—- bd^ p = 0.6% w^ = 56 — rr. bd^ p = 0.8% W = 62 P = o-9% w^ = 64.5 /2 bd^ bd^ /2 /,= !% ^^67_ Example. Find the total load per square foot that can be carried by a 4-in slab, with a 5-ft clear span, reinforced with 0.8% of steel per running foot. Solution. 12x32 - 108 ^^^,, w = 62 X = 62 X — = 266.6 lb 5=^ 25 From this must be deducted the weight of slab and floor-finish to obtain the live load. If finished with i-in cement top coat laid directly on the concrete the total dead weight is 621^ lb, which, deducted from 266.6 lb, leaves 204.1 lb. Note. If the total load carried by the beam is desired, iise / instead of /^ in the formula. These formulas are based upon the stress in the concrete not exceeding 600 lb per sq in and a tension in the steel of 16 000 lb per sq in, with a ratio of the moduli of elasticity of the concrete and steel equal to 12. Formula for the Resisting Moment of Rectangular or T Beams. This is Formula (6), page 932, Chapter XXIV, only in a different form, and is to be used when the percentage of steel is not greater than 0.58 of 1%. M = the maximum bending moment in inch-pounds; d = the depth from the top of the beam to the center of action of the steel in inches; A = the area of the sum of the cross-sections of the steel bars in square inches. M M = Ax 16 000 X o.g d ov A = 14400 a or d=' — 7 (i) 14 400 A Girderless Floors 993 Example. Given a bending moment of 217 728 in-lb and a depth (over all) of beam of 16 in, to find the sectional area of steel necessary to make the resisting moment equal to the bending moment. Solution. M , 217 728 A = or ^ = = 1. 12 sq m. 14 400 d i4 400Xi33'i Using two round bars of -Xt-in diameter we have 0,56 sq in X 2, or 1.12 sq in. Allowing 2 in for fireproofing and y2 in to the center of the bars, the effective depth of the beam is reduced to 13}^^ in. For the width of the beam we can use Formula (5), page 931, Chapter XXIV, substituting for K the value correspond- ing to the unit stresses and the ratio of the moduli of elasticity for the con- crete and steel we have been using, namely, 600 and 16 000 lb per sq in for the unit stresses and 12 for the ratio. This value of K, from Table V, page 926, Chapter XXIV, is 83.4 and M = 83.4 bd^. Transposing, we have M , 217 728 . 217 728 = , or = = = 1A..7, m 83.4 d'' 83.4 X (i3K>)2 83.4 X 182.2 The beam therefore will be i43'i in X 16 in in cross-section, reinforced with two %-m round rods placed so that there will be 2H in from the bottom of the beam to their center. As the width of this beam is excessive for the number of rods used, it is uneconomical. It would be better to design the beam with a T section reducing the width to 6 in for the stem and making the top flange 143^^ in wide and 13.5 X 0.31 = 4.18 in thick. The ratio of the distance of the neutral surface below the top of the beam to the effective depth of the beam, for the values we have been using is 0.31 (see Table V, page 926, Chapter XXIV), and in order to have sufficient concrete in compression at the top of the beam to balance the tensile stress in the steel, the head or flange of the T must extend from the top to the line of the neutral surface. Girderless Floors.* In order to familiarize the student with the design of GIRDERLESS FLOORS, an example is worked out, in which the area of a panel or bay is assumed to be 400 sq ft, the same as that of a typical bay in the factory -build- ing already considered in this chapter. The column-spacing is made the same in both directions, so that the panels are square, with a length of side of 20 ft. Without discussing the various methods of computing the strength of flat, re- inforced-concrete plates, we will use one under consideration by the Bureau of Building Inspection of Philadelphia. f This is a conservative jnethod. . It has been carefully worked out in all its details and applications and gives results consistent with safety and economical design. The following paragraphs set forth the notation and equations of this method as published by the Philadelphia Bureau which calls it the drop-construction. L = the length, center to center of columns, of the longest of straight bands in inches. Li = the distance or width, edge to edge, between capital-heads in inches. w = the total dead and live load per square foot. d — the distance from the center of action of the concrete in compression to the center of the steel at the drop in inches. di = the distance from the center of action of the concrete in compression to the center of the steel at the center of the slab in inches. * See, also, Chapter XXIV, pages 949 to 951. Flat-Slab Construction, t To Edwin Clark, Chief of the Bureau of Building Inspection, Philadelphia, Pa., is due the credit for working out and perfecting the practical applications of this method. 994 Reinforced -Concrete Factory and Mill-Construction Chap. 25 If the drop-construction is not used, d = di. Sufficient depth of slab is to be provided for shearing-stresses as well as for bending-stresses. Width of capital-head = not less than ^io L. Width of drop = WiooL. Width of bands = ^Moo L. X = the area of section of steel over the capital-head. xi = the area of section of steel in center of bay. — M = the bending moment at the edge of the capital-head. + M = the bending moment at the center of the span. ^, , , ... . . . w, , total bay — capital-head The load carried by the straight band = X iv 2 total bay — capital -head wLi -M = X 2 12 total bay — capital-head wLi + M= X 2 24 Width of concrete to resist compression at edge of capital-head = width of drop. WLi Width of concrete to resist compression when negative moment = 24 = width of band, in which T = the thickness of slab. Width of concrete to resist compression at middle of span = width of band. dX 16 000 Place 66% of x in straight bands , . , , 1 ™ ^ , . ,. , , , f over capital-head. Place 43% of X in diagonal bands j di X 16 000 Place 66% of xi in straight bands . . , „ . T^, -...-. ,, , > at middle of span. ' Place 43% of xi in diagonal bands ] M The drop equals the abacus outside of the capital-head, or the increased thickness of the concrete to obtain the necessary compression in the concrete. TMs is not *?encrally necessary when the live load of the floor is light, say 120 lb per sq ft and the span is not excessive. To determine d and di deduct from the total thickness of the slab i in to the center of the steel when the rods are H in or less in diameter; if over % in deduct iy2 in; and multiply the result by 0.9. The result will be the distance from the center of the steel to the center of action of the compressive stresses in the concrete. The depth h is the distance from the top of the slab to the center of the steel and is used in finding the thickness of the slab. Applying the above formulas to the example considered, using a floor-load of 120 lb per sq ft as in the previous example, and assuming an average slab-thickness of 8 in with a i-in top finish- coat of cement, the dead load is 100 lb 4- 13 lb = 113 lb, which added to the hve load = 233 lb, total. The arrangement of the bands is shown in plan, Fig. 24, the width being Mo L, or H the span of 20 ft, which is to ft. The diameter of the column-head is Via L, or 4 ft. The width of the drop is 3^00 L, or 7 ft 7 in. 995 A N Fig. 24. Arrangement of Bands in Girderless Floor The total area of the bay = 20^ = 400 sq ft. The area of the capital-head = 42 = 16 sq ft. Then, by the formula, the load carried by the straight bands = 44 736 X U 400— 16 X 233 = 44 736 lb -M^- 44 736 X 16 X 12 + ilf : 44 736 X L\ 44736X16X12 = 715 776 in-lb 357 ^8 in-lb 24 24 The bending-moment diagram is shown in Fig. 25. It is necessary next to find the thickness of the concrete at the drop. The formula used to find the depth of a beam when the bending moment, the width of the beam and the allowable stresses are given, is as follows, in which h equals the total depth of the slab from the center of the steel to the top of the concrete: V 0.27 X hSa V 0.27 X 91 5776 _,/-— = V 100 = 10 in X 600 In this formula h = the width of the drop and Sr. = 600 lb per sq in. The depth of the drop over all, therefore, is 10+ i = 11 in (Fig. 26). M The steel over the column at the drop = x = — in which d= o.g h or 0.9 X lo = 9. 715776 9X 16000 dX 16 000 = 4.9 in, or about 5 in 996 Reinforced-Concrete Factory and Mill-Construction Chap. 25 The straight band will have 66% of 5 or s-S sq in of steel. A H round rod has a cross-sectional area of o.ii sq in. Therefore, there will be -^— = 30 bars over 0.1 1 the capital-head in the straight band. As the bars from the adjoining span over- lap the column-head, extending into the next span as far as the edge of the drop, each straight band over the column will have 3^^ or fifteen bars. The diagonal ■ Center, line of Column Top Surface Fig. 25. Bending-moment Diagram for Girder- less Floor Fig. 26. Capital-head and Slab in Girderless Floor bands will have 43% of 5 or 2.15 sq in, which will require twenty 5i-in round rods over the column, or ten on each side, lapped as above. The thickness of the slab at the middle of the span is found by the formula given above, substi- tuting the proper values for the letters. The formula becomes T 0,27 X357^ X 138 X 600 : V32= 5.6 in The total depth is 5.6 -f i in = 6.6 in, or about 7 in. The width of the band = 10 ft-f- (3 X 6 = 18) = 138 in. For the steel at the center of the span M . , . , , , ^ . ic = + m which di = 0.9 A or 0.9 X 7 = 6.3 in di X 16 000 357 888 " c V. ^ ^ =3.5 sqm 6.3 X 16 ocx> The straight bands will have 66% of 3.5 or 2.31 sq In of steel which will re- quire — ^^ — = twenty-one %-in round bars or six bars more for the middle of the o.n span than for the band set over the column. In practice the rods are made the full length of the span, from column to column, plus the width of the drop, or in this example 20 ft-}- 7 ft 7 in = 27 ft 7 in for the fifteen rods. Six additional rods, 13 ft long or about the distance from the edge of one drop to the edge of the next one, must be used with the fifteen to make the twenty-one required for the middle of the span. The diagonal bands will have in the center 43% of 3.5 sq in = 1.5 sq in which require fourteen ^^-in round rods or four more than one set of rods over the column These four, how- ever, are to be added at the middle of the span between the drops. The rods are bent up over the column-head so as to be near the top of the slab to take care of the negative bending moment, the bars extending horizontally near the top of the slab the full width of the drop. It is necessary to provide bent radial rods extending down into the column and outwards as far as the outer ring with two Girderless Floors 997 or more rings as reinforcements of the column-head. The size and number of these varies with the span and load; but for the floor under consideration there should be eight i-in radial rods as near the top of the slab as practicable, the diameter of the outer one being equal to the width of the band and that of the inner one being equal to the capital-head. It will be noticed in the above analysis that before any calculations could be made certain assumptions were necessary, such as the thickness of the slab, which was assumed as 8 in, in order to obtain the dead load; whereas in the finished design the thickness of the slab is 7 in and the drop 1 1 in, which, however, does not affect the practical results materially. It is for this reason that the design of flat slabs should be intrusted only to those who have wide experience in the design of reinforced concrete, as good judgment enters into the making up of a successful design; and one who is inexperienced should consult a specialist in this particular system of construction, if a design is to be put into execution. Among the best methods of determining, girdless floors is that embodied in the Chicago Rulings Governing the Design and Construction of Concrete Flat Slabs, which went into effect March 1,1918. The following are some of these rulings: The least dimensions of concrete columns shall be not less than |'l2 the panel-length, nor less than K12 the clear height of the column. The minimum total thickness of the slab, in inches, shall be deter- mined by the formula, t = -y/w/Ai, in which / is the total thickness of the slab in inches, and W the total live and dead load, in pounds, on the panel, measured center to center of columns; but in no case shall the thickness be less than L/32 (L is the panel length, center to center of columns) for floors, nor less than L/40 for roofs, nor shall a less thickness than 6 in be used. The allowable unit punching shear on the perimeter of the column-capital shall be Ho of the ultimate compressive strength of the concrete. The allowable unit shear on the perimeter of the drop-panel shall be Moo of the ultimate compressive strength of the concrete. "For the purpose of establishing the bending moments and the resisting moments of a square panel, the panel shall be divided into strips known as strip A and strip B. Strip A shall include the reinforcement and slab in a width extending from the center hne of the columns for a distance each side of this center Hne equal to one-quarter of the panel-length. Strip B shall include the reinforcement and slab in the half width remaining in the center of the panel. At right angles to these strips, the panel shall be divided into similar strips A and B, having the same widths and relations to the center line of the columns as the above strips. These strips shall be for designing purposes only, and are not intended as the boundary lines of any bands of steel used." Bending-Moment Coefficients for interior panels for two-way and four- way systems, wall panels and panels without drops or capitals, are given in detail. When the length of panel does not exceed the breadth by more than 5 per cent, all computations shall be based on a square panel whose side equals the mean of the length and breadth. In no rectangular panel shall the length exceed the breadth by more than one-third of the latter. Wall columns in skeleton construction shall be designed to resist a bending-moment of PFZ/6g at the floor and WL/so at the roof. Interior columns must be analyzed for the worst condition of unbalanced loading. The Point of Inflection; Tensile Stress in Steel and Compressive Stress in Concrete; Rectangular Panels, Four-way System; Rectangular Panels, Two-way System; Placing of Steel; are considered under their respective headings. 998 Types of Roof-Trusses Chap. 26 CHAPTER XXVI TYPES OF ROOF-TRUSSES By MALVERD A. HOWE PROFESSOR EMERITUS OF CIVIL ENGINEERING, ROSE POLYTECHNIC INSTITUTE 1. Definitions Use of Trusses. Whenever the distance between the side walls of a build- ing exceeds about thirty feet, and there are no intermediate walls or columns, it is usually necessary to support the roof on trusses. The ceilings of large rooms, assembly-halls, etc., also, require trusses for their support. In many cases the roof and a ceiling are carried by the same trusses. ^ Truss is a framework, composed of straight, or sometimes curved, mem- bers or pieces so arranged that the structure as a whole acts as a beam. Since a triangle is the only figure which cannot be changed in shape without changing the length of one or more of its sides, it follows that the pieces forming a truss must be arranged so as to form triangles. The members of a truss are usually subjected to longitudinal stresses only, either compressive or tensile. Curved members and members which act as beams supporting loads are subjected to additional bending stresses. Each member of a truss is either a tie or a strut. A Tie is a member which has developed in it a longitudinal tensile stress. A Strut is a member which has developed in it a longitudinal compressive stress. When vertical, struts are sometimes called posts or columns. The Top Chord of a truss is composed of the upper outside members. In some forms of roof -trusses top chords are called rafters (Fig. 2). The Bottom Chord of a truss is composed of the lower outside members (Fig. 2). In roof-trusses the bottom chord is commonly called the tie-beam. The Web-Members are those connecting the chords (Fig. 2). A Joint is the point of intersection of two or more members of a truss (Fig. 2). A Panel is the distance between two adjacent joints in either the upper or lower chords (Fig. 2). Purlins. Whenever possible all roof -loads and ceiling-loads should be^ trans- ferred to trusses at the joints. This usually requires beams spanning the space between trusses at corresponding joints. These beams, when supporting the roof, are called purlins (Fig. 2). 2. Types of Wooden Trusses The Simplest Truss that can be built is that shown in Fig. 1. It consists of three members forming a triangle. As the unsupported length of a strut, for economical reasons, should not exceed 12 feet, such a truss is not suitable for spans exceeding from 20 to 24 ft; and even for a span of 20 ft there should be a center rod, as shown by the dotted line R, to support the tie-beam. To utilize this truss for spans greater than 24 ft, it is necessary to brace the rafters from the foot of the center rod, as shown in Fig. 2. This gives us the king-rod truss, the modern type of the old-fashioned king-post truss which is shown Types of Wooden Trusses 999 in Fig. 3 and which was built wholly of wood except for the iron straps at S and P. Rods and Braces. When the tie-beam supports a ceiling or attic-floor, rods should be inserted at RR, Figs. 2 and 4, to support the load on the tie-beam. By increasing the number of rods and braces, as in Figs. 4 and 5, this type of truss may be used for spans up to 64 ft, and even for greater spans; but on account of the increased length of the center struts and rods it • is not an economical type when the span exceeds 60 ft. When there is no load on the tie-beam the rods RR, Figs. 4 and 5, merely sup- port the tie-bc£nn and are often omitted. Triangular Howe Trusses. The trusses shown in Figs. 4 and 5 are sometimes called Howe Simplest Three-piece Truss, j Spans up to Twenty-four Feet TRUSSES as the character of the stresses in the web-members corresponds with that of the stresses in the web in the standard form of Howe truss. They are also called triangular Howe trusses to distinguish them from the standard Howe truss with parallel chords. Principal oi ^ Rafter Fig. 2. King-rod Truss. Spans up to Thirty-six Feet Queen-Rod Truss. The rise of the rafter in any of the trusses, Figs. 1 to 5, should never be less than 6 in in 12 in or 261.^°; a Vs pitch, or a rise of 8 in in 12 in, is generally the most economical. When the span exceeds 36 ft, it is more economical to cut off the top of the truss as in Fig. 6, which shows the modern type of the ancient queen-post truss. This truss is frequently used for the support of deck roofs, although it may also be used for a pitched roof with a ridge. When the top chord is more than 12 ft long, the size of the member may be considerably reduced by using a center rod and a pair of struts as shown in Fig. 7. The center rod will be especially needed if the bottom chord or tie-beam is subject to a bending stress. The center rod should never be used, however, without the braces. 1000 Types of Roof-Trusses Chap. 26 Counters. The truss shown in Fig. 6 differs from those shown in Figs. 1 to 5, in not being composed entirely of triangles and in having a rectangle in the middle. Assuming the joints to be pin-connected and without friction, it FOR SPANS FROM 25 TO 35 FT. Fig. 3. Modem King-post Truss Fig. 4. Six-panel Triangular Howe Truss. Spans from Thirty-six to Fifty Feet Eight-panel Triangular Howe Truss. Spans from Forty-eight to Sixty Feet is evident^hat a very small inequality in the position or magnitude of the load- ing will cause the failure of the truss since the rectangle will not retain its shape. This is easily verified by means of a cardboard model fastened at the joints Types of Wooden Trusses 1001 with ordinary eyelets. When the joints at the corners of the rectangle are not perfectly free to turn they have a tendency to prevent distortion. When the Fig. 6. Queen-rod Truss. Spans from Thirty to Forty-five Feet loading is entirely upon the left of the center the truss itself tends to assume a form similar to that shown in Fig. 8. The distortion of the rectangle may be prevented by the introduction of a diagonal member as shown in Fig. 9. For ^-Top Chord Fig. 7. Queen-rod Truss. Spans from Forty to Fifty-two Feet the loading shown, the diagonal is in compression and is usually called a COUNTERBRACE. If the piece were in tension it would be called a countertie. Unsymmetrical Loads. Although roof-trusses of the type shown in Fig. 9, supporting symmetrical loads, do not theoretically require counters, it is never- Fig. 8. Distorted Queen-rod Truss theless advisable to brace the rectangle along both diagonals to insure stability under accidental, unsymmetrical loading and to relieve the joints from any stresses due to the latter, which is usually caused by wind, snow and floor-loads.' 1002 Types of Roof-Trusses Chap. 26 Reversal of Stresses. In some trusses subjected to different loadings at different times, the diagonal web-members near the center may be subjected to tension for one loading and compression for another loading. In such cases it Fig. 9. Counterbraced Queen-rod Truss is advisable to introduce a member following the other diagonal of the quadri- lateral containing the member subjected to the two kinds of stress, to assist the main member. This piece, also, is called a counterbrace br countertie according to the kind of stress it has to resist. If this is not done, the member Iron Strap Span 45 4, Pitch of Rafter 9H in 1 foot Fig. 10.. Queen-post Truss. Massachusetts Charitable Mechanics' Association Build- ing, Boston, Mass. which is subjected to two kinds of stress must be designed for both tension and compression and the. ends connected at the joints to meet the same conditions. An Ornamental Queen-Post Truss, supporting a portion of the roof of the Massachusetts Charitable Mechanics' Association building in Boston, Mass., and Types of Wooden Trusses 1008 designed by Mr. William G. Preston, is shown in Fig. 10. The truss-members, which are of long-leaf yellow pine, were worked from limbers of the dimensions given. In this truss wooden members instead of rods are used for the vertical ties, and are bolted and tenoned to the tie-beam and secured to the rafters by iron straps. The curved ribs take the place of counterbraces. -2>^"Rod |[<-lXEod [J«-2XRod Fig. 11. Queen-rod Truss. Museum of Fine Arts, St. Louis, Mo. A Queen-Rod Truss from the Museum of Fine Arts, St. Louis, Mo., designed by Peabody & Stearns, is shown in Fig. 11. It supports the floor below by means of three rods. The truss-rods have nuts and washers below the tie-beam, and the threads on the rods are long enough to receive turnbuckles which connect the suspension-rods with the truss. This is generally the best method of suspending a floor from a truss. Fig. 11a shows a detail of joint A of the truss in Fig. II. Counters Omitted for Special Reasons. Fig. 12 shows a truss, sometimes used when it is desired to keep the middle part of an attic free from .obstructions. In building this truss it is advisable to construct the lower part of the rafters of two timbers, thoroughly bolted together, as shown. What has been said in regard to counterbraces in queen-rod trusses applies also to this truss, although in the latter the continuous rafter aids very materially in resisting distortion from wind- pressure; so that for ordinary construction and for spans not exceeding 40 ft it is safe to omit counterbraces. Manner of Supporting Common Rafters. Before describing other types of trusses, it may be well to consider the manner of supporting the common rafters by the trusses. Occasionally it is desirable to span the common rafters from truss to truss, but as a general rule it is better construction to support them by means of large beams or purlins which themselves span from truss to truss, as shown in Fig. 13. Purlins. The trusses can be designed so that the purlins need not be more than 10 ft apart, and very often not more than 6 or 8 ft apart; so that the common rafters need not be more than 2 by 4 or 2 by 6 in in cross-section, while the trusses may be spaced 12, 14, or i6 ft on centers. As a rule a spacing of Fig. 1 1 A. Detail of Joint A , Fig. 1 1 . 1004 Types of Roof-Trusses Chap. 26 about 14 ft for the trusses and of 9 ft 6 in for the purlins is found to be the most economical arrangement. Another advantage in the use of purlins is that where they are placed at the truss-joints no bending stresses are developed in the truss-rafters or chords; and hence the latter may be made Ughter than if ;Ilafter8 Fig. 12. Queen-rod Truss with Middle Part Clear. Spans up to Forty-two Feet they supported the common rafters. For wooden trusses of 60 ft or greater span, purUns should always be used. Supports for Purlins. Purhns may be placed with their sides either vertical or at right-angles to the plane of the roof, as shown in Figs. 2 and 13. The ends of the purUns may be supported by means of beam-hangers, des- cribed in Chapter XXI; by double stirrups; by 3-in planks bolted and spiked to the sides of the trusses; or they may rest on the top chords themselves. The ceiling- joists or floor- joists are usually sup- ported at the sides of the tie-beams, as at ^ , Fig. 13, or simply rest Fig. 13. Manner of Supporting Common Rafters and Purlins on them, as at J?. When they support an attic floor it is better to use the latter construction. In the case of scissors trusses it is sometimes more economical to support the ceiling- joists by purlins; but when the tie-beams are horizontal it is more economical to use them for the direct support of the ceiling-joists or floor-joists. All chords which support rafters, ceihng-joists or floor-joists must be designed for bending stresses as well as for longitudinal stresses. Trusses with Horizontal Chords. For the support of flat roofs, with or without a ceiling below, and for conditions such that horizontal trusses are Types of Wooden Trusses 1005 practicable, the types shown in Figs. 14 to 17 are undoubtedly the most satis- factory for wooden construction, when the span does not exceed 8o ft; and except in localities where the cost of iron rods is relatively great, it is as econom- ical as any. In this work the name Howe truss is given to this type, as it is an adaptation of the Howe bridge- truss to building-construction; and the term horizontal truss is also sometimes used. Trusses of this type can be Bottom Chord Fig. 14. Five-panel Howe Truss , Counter Braces ^^ Fig. 15. Six-panel Howe Truss A_ B Top Chords C Fig. 16. Ten-panel Howe Truss Fig. 17. Six-panel Howe Truss with Top Chord Inclined made strong enough for spans up to 150 ft; but when the span exceeds 100 ft it is generally cheaper to use a steel truss of the Pratt type in which the verti- cals are in compression and the diagonals in tension. When a Howe truss is placed in the longitudinal direction of a flat roof, the top chord may be given the inclination of the roof itself, so as to support the rafters without the blocking as shown in Fig. 17. For deck roofs the top chord may be inclined upwards toward the center or deck-ridge, to conform to the shape of the roof, as shown in 1006 Types of Roof-Trusses Chap. 26 Fig. 18. For deck roofs and mansard roofs the middle panels should have counterbraces, as shown in Fig. 18, to resist the wind-pressure against the sides of the roof and any unequal distribution of snow. Height of a Howe Truss. The height of the truss, measured from center to center of the chords, should never be less than one-ninth the span for spans up to 36 ft, nor less than one-tenth the span for spans from 36 to 80 ft. Fig. 18. Howe Truss for Deck Roofs As a general rule a height of from one-seventh to one-sixth the span will be most economical. When the top chord is inclined, as in Fig. 17, the height at X, that is, at the shortest rod, should not be less than the limit given above. Number of Panels in a Howe Truss. In this type of truss a panel is the space between two adjacent rods or between an outer rod and the end- joint (Fig. 14). As a rule, the number of panels should be such that the diag- onals will have an inclination of from 36° to 60°, an incHnation of about 45** being the most economical. It is not material whether there is an even or an odd number of panels. If the position of one or more of the purhns is fixed by some special requirement, then the panels should be so arranged that the upper joints come under the purhns, and the inclination of none of the diagonals is less than 36°. Although it is generally better to have the truss symmetrical about the center, it is not absolutely necessary; nor is it necessary to make the panels of uniform width. When the truss is not symmetrically loaded, however, it may be necessary to reverse the brace in one of the center panels. This point is considered in Chapter XXVII, page 1 102, under the subject of unsymmetri- CALLY LOADED TRUSSES. Counterbraces in a Howe Truss. If there is any chance of the truss being more heavily loaded on one side of the center than on the other, counter- braces, that is, braces inchned in the opposite direction from that of the regular braces, should be placed in the center panels, as shown by the dotted Imes in Fig. 15. If the truss is deep and the diagonals long it is economical to counter- bi'ace each panel as shown in Fig. 18. If the number of panels is odd, as shown in Fig. 14, no diagonals are required in the middle panel when the braces and the loading are symmetrical; but it is good practice to cross-brace this panel to provide for any accidental unsymmetrical loading. Spacing of Trusses. The most economical spacing, center to center, of the trusses, all things considered, is usually from 12 to 16 ft for spans up to 60 ft, and from 14 to 20 ft for greater spans. Spacing of Purlins. Purlins should always be placed as near the truss- joints as possible; they should also be spaced so as to effect the greatest economy in rafter-construction. Their spacing, therefore, determines, to a large extent, the number of panels. When the height of the truss is not more than one-ninth or one-tenth the span, it is often more economical to place a purlin over every other joint, as in Fig. 16. Types of Wooden Trusses mi Table I. Dimensions for Six-Panel Howe Trusses, Symmetrically Loaded Timber, Norway pine, Douglas fir, or eastern spruce. (See Fig. 15) TJnds 1 Dis- Braces not upset Span tance apart Total height Top chord Bottom chord ctoc A B C D E F ft ft ft in in in in in in in in in 12 j 6 7 6X 6 6X 8 6X 6 6X4 6X3 }lV8 % % S 2 GX 8 6X 8 6X 6 GX6 6X4 36 15 I 6 8 6X 8 GX 8 GX 6 6X4 6X3 }iVi 74 54 S 2 8X 8 8X 8 8X 6 6X6 6X4 '/8 78 18 { 6 8 6X 8 GX 8 6XS 6X6 6X4 jiVi Va f'4 5 2 8X 8 8X 8 8X 8 6X6 6X4 /8 /8 12 1 7 7 8X 6 8X 8 8X6 8X4 6X4 }lu % R/« 5 II 8X 8 8X 8 8X 6 8X5 8X4 /» 42- 7 8 8X 8 8X 8 8X 6 8X5 6X4- } 1% Va »'i 15 j S II 8X 8 8X 8 8X 8 8X6 8X4 78 /■i 18 1 7 8 8X 8 8X 8 8X 8 8X6 8X4 }lV2 «Vi 6 I 8X10 8X10 8X 8 8X6 8X4 I /■i 8 8 8X 8 8X 8 8X 8 8X6 8X4 }l% 1 1% 12 ] 6 8 8X 8 8X 8 8X 8 8X 8 8X6 8X6 8X4 8X4 % % 48. 8 8 8X 8 8X 8 %^ IS j 6 10 8X10 8X10 8X 8 8X6 8X4 I 18 { 8 8 8X 8 8X 8 8X 8 8X6 8X4 } iVa % 6 10 8X10 8X10 8X10 8X6 8X4 I 9 8 8X 8 8X 8 8X 8 8X6 8X4 } 1% -/ «/i 12 1 7 6 8X 8 8X10 8X 8 8X6 8X4 /8 /Jr 9 8 8X 8 8X 8 8X 8 8X6 8X4 } 1% 8/." 54" 15 1 7 7 8X10 8X10 8X 8 8X6 8X4 I 74 18 { 9 10 8X10 8X10 8X10 8X8 8X6 1 1% 1V8 % 7 7 10X10 10X10 10X8 8X8 8X4 10 9 8X 8 8X10 8X 8 8X6 6X6 1 1% I % ■' 12 \ 8 4 8X10 8X10 8X10 8X6 8X4 GO- ID 10 8X10 8X10 8X10 8X6 6X6 } 1V2 1V8 ^i 15 i 8 4 10X10 10X10 loX 8 10X6 8X4 18 { 10 10. 10X10 10X10 loX 8 10X6 8X6 [ IVi jT,^ 0/ 8 4 10X10 10X10 10X10 10X6 8X6 12 G 8X10 8X10 8X10 8X6 6X6 ]iVj % 12 j 9 7 10X10 10X10 loX 8 10X6 8X6 ^ TO' 15 1 12 9 6 9 10X10 10X12 10X10 10X12 loX 8 10X10 10X6 10X8 8X6 10X6 } 1% I^^ % 18 { 12 6 10X10 10X10 10X10 10X6 8X6 ] iVs iV-L % 9 9 10X12 10X12 10X12 10X8 10X6 14 2 10X10 10X10 10X10 10X6 8X6 } T% iy8 % 12 j ID 10 10X10 10X10 10X10 10X6 8X6 8o- IS { 14 II 2 10X10 10X12 10X10 10X12 10X10 10X10 10X8 10X8 8X6 10X6 } 1% 1V4. Vs 18 { 14 4 10X12 10X12 10X12 10X8 8X6 [2 1% II I 10X12 10X14 10X12 10X8 10X6 1008 Types of Roof-Trusses Chap. 26 Bearing on "Wall or Post. The point where the axial lines of the end brace and of the tie-beam intersect should always come over the support, and if possible over the axis of the supporting wall or post. Stresses in a Howe Truss. The stresses in the chords are always greatest at the middle of a truss, diminishing towards the supports, while the stresses in the rods and diagonals are greatest at the ends of a truss. Table of Dimensions for a Howe Truss. In symmetrical trusses having panels of uniform width and uniformly loaded, the stresses in the differ- ent members are proportional to the span, number of panels, height of truss, spacing of trusses and load per square foot. It is therefore possible to prepare tables giving the proper dimensions of the members of such trusses. Table I gives the dimensions for six-panel trusses for heights of one-sixth and one-eighth the span and for three different spacings. These dimensions are for a flat roof covered with tin, sheet iron, or composition; a snow-load of 1 6 lb per sq ft, equivalent to about 24 in of light, dry snow; also for a lath-and-plaster ceiling supported by the bottom chord. The chords and braces are of Norway pine and the rods of wrought iron. These dimensions apply only when the rafters , A -^s^ /\^ y^<^ /V\_/^^ XV ; V 000 H F i v^ vv W w 4.Pins Bolt -Spaa Fig. 19. Lattice Truss are supported on purlins placed at the upper joints, as in Figs. 15 and 16. When the rafters rest on the top chord, as in Fig. 17, the dimensions of the latter must be increased and special calculations made for it. The dimen- sions given in the table may be used for trusses of greater height than that given, but not for trusses of less height, as the less the height the greater the stresses in the chords and braces. When the conditions of load, span, height and spacing are not exactly as given above and in the table, the stresses should be determined and the members of the truss proportioned accordingly; but even in such cases the table will serve somewhat as a check on the com- putations. Lattice Trusses. In localities where timber is not expensive the lattice TRUSS (Fig. 19) is often fomid economical for supporting flat roofs. This type of truss was invented for bridges by Ithiel Towne in 1820 and a large number of Types of Wooden Trusses 1009 railroad bridges have been constructed with trusses of this type, some of which are in service now (19 15) in New England. The principal objections to the truss are its tendency to twist sidewise, hke a thin board on edge, its flexibility in a vertical plane and the difficulty of getting sufficient bearing material at the supports. As indicated in Fig. 19, the truss is composed of top and bottom chords, usually parallel, connected by lattice bracing. The chords are com- posed of four planks, two being on one side and two on the opposite side of the web. For the bottom chord the planks should be as long as can be obtained and arranged so that no two splices are near the same point. The available area of the bottom chord to resist tension is the area of three planks less the area cut out at the joints by the connecting pins or bolts. Each member of the web consists of a single plank arranged as shown in Fig. 19. The braces are inclined at an angle of about 45° and usually three sets are sufficient, as shown in the figure. The connections are best made with American-locust pins, which give large bearing areas without much extra weight. Modern construction employs bolts, which are expensive and add considerable weight, There should be at Bottom Chor^ Fig. 20. Vertical Section of Truss Shown in Fig. 19 Fig. 21. Lower Joint 5 of Truss Shown in Fig. 19 least two pins at each connection, if the planks are wide enough to permit, and three, at least, at the chord-joints. Since about one-half the web planks resist tensile stresses, the web projects beyond the chord at least 4 in to provide sufficient longitudinal shearing area. The ends are reinforced by vertical tim- bers cut in between the chords and each set of diagonals is thoroughly fastened to these timbers. In some cases it is necessary to add timbers on the outside of this and extend them down to the lower face of the bottom chords to relieve them of excessive bearing-stresses where they rest on the supports. The methods of determining the stresses in this truss are considered in Chapter XXVII, pages 1089 to 1091. Figs. 20 and 21 show details of this lattice truss. Wooden Trusses with Raised Bottom Chords. All of the trusses thus far described have horizontal bottom chords; and this construction is the most desirable as well as the most economical and should be used whenever condi- tions do not necessitate a greater height of ceiling. In roofing churches, public halls, etc., raised ceilings are often desirable as they increase the general height of a room without increasing the height of its side walls. lOlU Types of Roof-Trusses Chap. 26 Table 11. Dimensions for Lattice Trusses, Uniformly Loaded Timber, Norway pine, Douglas fir, and yellow pine. (Fig. 19) Span Spacing of trusses Height out to out of chords No. of spaces No. and size of pes of bottom chord No. and size of pes of top chord Size of braces No. and diameter of treenails or bolts, joints 1-5. Fig. 19 ft ft ft in in in in in in in in 5 6 i6 4 2X 6 4 2X 6 2X 6 4 I 12 7 2 12 4 2X 6 4 2X 6 2X6 4 I 5 7 i6 4 2X 6 4 2X 8 2X 6 4 I 40' 14 7 3 12 4 2X 6 4 2X8 2X 6 4 I i6 5 8 i6 4 2X 8 4 2X 8 2X 8 4 iH . 7 4 12 4 2X 8 4 2X 8 2X 8 4 lV4: c 6 8 i6 4 2X 8 4 2X 8 2X10 4 iM 12 8 8 12 4 2X 8 4 2X 8 2X10 4 1V4 __, J 6 8 i6 4 2X 8 4 2X 8 2X10 4 iH 50^ 14 8 8 12 4 2X 8 4 2X 8 2X10 4 iVi i6 6 9 i6 4 2X 8 4 2X10 2X10 4 i^ 8 8 12 4 2X 8 4 2X 8 2X10 4 iH 12 8 4 i6 4 2X10 4 2X10 2X10 4 1% 10 10 12 4 2X10 4 2X10 2X10 4 1% 6o- 8 4 i6 4 2X10 4 2X10 2X10 4 1% 14 10 10 12 4 2X10 4 2X10 2X10 4 1% i6 8 4 i6 4 2X10 4 2X10 2X10 4 1% 10 10 12 4 2X10 4 2X10 2X10 4 1% 9 5 i6 4 2X10 4 2X12 2X10 4 1% 14 12 4 12 4 2X10 4 2X10 2X10 4 1% 70- i6 9 5 12 4 i6 12 4 2X10 4 2X10 4 2X12 4 2X10 2X10 2X10 4 1% 4 1% i8 9 6 i6 4 2X12 4 2X12 2X10 4 2 r 12 6 12 i6 4 2X1*2 4 2X12 4 2X12 4 2X12 2X10 2X12 4 2 4 2 14 II 14 12 4 2X12 4 2X12 2X12 4 2 80- i6 II 2 i6 4 2X14 4 2X14 2X12 4 2 14 12 4 2X12 4 2X12 2X12 4 2 18 II 2 i6 4 2X14 4 2X14 2X12 4 2 14 1 12 4 2X12 4 2X14 2X12 4 2 Note. All joints should be thoroughly spiked and packing blocks used where neces- sary. When treenails are used each chord-joint should have in addition one %-in bolt as shown in Fig. 21. Scissors Trusses. For the roofs described in the preceding paragraph some form of the scissors truss, so named from its resemblance to a pair of scis- sors, is most often used. When correctly designed, with members of the proper size, and with joints carefully proportioned to the stresses, it is a very good truss for supporting roofs over halls and churches, up to a span of 48 ft; but for greater spans it should be used with caution, as the stresses become very great and the joints difficult to make. Figs. 22 to 27 show different forms of this truss and modifications of it adapted to different spans and roof-pitches. None of these trusses exerts a large horizontal thrust if the members are of ample size and the joints properly made. The members having a plus sign on Types of Wooden Trusses 1011 Fig. 22. Simple Scissors Truss. Spans up to Thirty Feet Fig. 23. Scissors Truss. Spans Exceeding Thirty Feet Fig. 24. Scissors Truss. For Steep Roofs. (See Chapter XXVIII, Figs. 18 and 19) 1012 Types of Roof-Trusses Chap. 26 or close to them are in compression, while those having a minus sign are in TENSION. The determination of the actual horizontal thrust is considered on pages 1085-1087. The members indicated by a single line should be rods, Fig. 25. Modified Scissors Truss. For Medium Pitch. (See, also, Chapter XXVIII, Figs. 18 and 19) except in the case of bottom chords. Fig. 22 shows the simplest form of the SCISSORS truss, which is suitable for spans up to 30 ft. When the span exceeds 30 ft, it is more economical to use two purlins on each side to support the com- -32 Span. laApait Fig. 26. Finished Cambered Truss. (See, also. Chapter XXVIII, Figs. 18 and 19) mon rafters; and additional supports from the bottom chords are generally required, calling for additional rods and braces, as shown in Fig. 23. For a gt^ep roof the arrangement shown in Fig 24 is generally the best, and for 9 Types of Wooden Trusses 1013 flatter roof that shown in Fig 25, in which the scissors pieces do not cross nor run through; Fig. 26 shows a finished truss, built on somewhat the same lines as the one shown in Fig. 25 but with only one purhn. This truss can hardly be classified as a scissors truss but is shown here for convenience. It is really the same type as that of the truss shown in Fig. 33. The truss shown in Fig; 27 is similar to that shown in Fig. 24, with the peak cut off> but for spans Fig. 27. Modified Scissors Truss. Spans Exceeding Thirty-six Feet. (See, also, Chapter XXVIII, Figs. 18, 19 and 20) exceeding 36 ft, is more economical. It can also be used where the roof is hipped. With this form it is better to use ceiling-purlins to support the ceiling- joists than to span the latter from truss to truss. Hammer-Beam Trusses. Two of the principal characteristics of the Gothic style of architecture are the relatively elaborate ornamentation of structural parts and the exposure to view of the construction of a building as a whole. As the pointed arch and steep roof were developed the roof-truss became an important feature in the ornamentation as well as in the construction of Gothic halls and churches. The trusses of this period were built almost entirely of wood and generally of very heavy timbers, to give the appearance of great strength. One of the most common types of these Gothic trusses, and also the most ornamental, was the hammer-beam truss, still often used in churches designed in the Gothic style. Figs. 28 and 29 show early English forms of this truss, which takes its name from the horizontal beam H, called the hammer- beam, at the foot of the principal rafter. In the more ornamental trusses this hammer-beam was usually carved to represent royal personages or angels. These trusses differ in principle from those thus far described, in having no bottom chord and no substitute for one. In fact the trusses shown in Figs. 28 and 29 do not come within the scope of the definition of a truss given at the beginning of this chapter. Although the rafters or principals are connected near the top of the truss by a short collar-beam, this offers but httle resistance to the tendency of the rafters to spread at their lower ends; and hence the truss depends either upon the transverse strength of the rafters or upon the resistance of the walls to keep it intact and, generally, upon both. This form of truss is actually that of an arch, as vertical loads produce inclined reactions at the . supports. In the halls and churches of the Gothic period the walls were generally 1014 Types of Roof-Trusses Chap. 26 very thick' and usually reinforced on the outside by buttresses built against them and directly opposite the roof-trusses. In most cases such a wall possesses sufficient stability to withstand the thrust of the truss, and hence the bottom chord may be dispensed with; but in a wooden building the walls, unless tied at the top, offer no resistance whate^>er to being thrust out and hence, in such buildings, no truss which exerts an outward thrust on the walls should be used. =i=it=!t=jt=iyb^- m ^SECTION OF SECTION OF ^PRINCIPAL RAFTER COLLAR BEAM r ROOF OVER NAVE CHAPEL. SUFFOLK, ENG. Span \ 8 ft. Fig. 28. Hammer-beam Truss. Early English Form It is therefore generally impracticable to use a hammer-beam truss in a wooden building. Where these trusses are used, the ceiling is generally formed of matched sheathing, nailed to the under side of the jack-rafters between the purhns, thus allowing the latter to be seen. The purlins are generally decorated, and f alse ribs are often placed vertically between them, to divide the ceihng into PANELS. The main rafters should be made very large to prevent them from breaking at the point A, Figs. 28 and 29. Types of Wooden Trusses 1015 Truss for First Church, Boston, Mass. An excellent example of a hammer-beam truss adapted to modern conditions is shown in Fig. 30, which represents one-half of one of the trusses designed by Ware & Van Brunt, for Fig. 29. Hammer-beam Truss. Early English Form the First Church, Boston, Mass. The truss is finished in black walnut and has the effect of being very strong and heavy. Fig. 31 shows the framing of the same truss without the casing and falsework. It should be noticed that inside the turned column in the upper part of the truss. Fig. 30, there is an iron Typfes df Roof-Trusses Fig. 30. Hammer-beam Truss. First Church, Boston, Mass. Types of Wooden Trusses 1017 rod, Fig. 31, which resists the tensile stress. In this form of truss the line of outward thrust of the arch enters the wall just above the corbel, K; and, as. its direction is inclined only about 30° from the vertical, its tendency to over- throw the wall is not very great, and may be resisted, in this particular case^^ FRAMING OF HAMMER BEAM TRUSS Span 61 feet DISTANCE BETWEEN TRUSSES ABOUT 15 feet Fig. 31. Framing of Truss Shown in Fig. 30 by a wall 20 in or 2 ft thick, thoroughly reinforced by a buttress of proper dimensions built on the outside. In trusses of this kind, the various members should be securely fastened together wherever they cross or touch each other, and the structure as a whole made as rigid as possible. No dependence should be placed upon the casings and panel-work for any extra strength. 1018 Types of Roof-Trusses Chap. 26 Truss for Emmanuel Church, Shelburne Falls, Mass. Fig. 32 shows another form of truss designed by Van Brunt & Howe, for Emmanuel Church, *>helbume Falls, Mass. It is probably a variation of the hammer-beam Fig. 32. Truss for Emmanuel Church, Shelburne Falls, Mass. .'Casting Fig. 33. Wooden Truss with Iron Ties. Spans up to Thirty-six Feet form and when securely bolted together at all the joints can be designed so as to exert very little thrust on the walls. The rafters and cross-tie are each formed of two pieces of timber, separated but bolted together, the small •upright members passing between these pieces. The hammer-beams are carved Types of Wooden Trusses 1019 to represent angels. The action of the stresses in hammer-beam trusses i^ explained in Chapter XXVII, pages 1087 to 1089. Wooden Trusses with Iron Ties. Where there is no ceiling beneath the roof and it is desirable to make the trusses as light in appearance as possible, Near Rod C Fig. 33a. Detail of Joint B, Fig. 33 Fig. 33b. Alternate Detail of Joint at Ridge, Fig. 33 wrought-iron or steel rods may be used for the ties, and the wooden * rafter- pieces and struts retained. For moderate spans such trusses are cheaper than steel trusses; and where the rafters and puriins are of wood they are about as good. Figs. 33 and 34 show forms of trusses well adapted to many roofs. The dimensions given in Fig. 34 are for yellow-pine or Douglas-fir timber and wrought- DETAILi CASTINGS ON STRUTS ir^ ^Z-1%"' 2K Pin -24 0- 10 ti&tteT9-..,^^^^S)r ^ \ m^^Mvin -■-■/ \j I-1JK'° 2«-Pto C "^ ^Hook Fig. 34. Wooden Truss with Iron Ties iron rods, and are ample for a slate roof, the trusses being spaced from 12 to 14 ft on centers. Trusses of the form shown in Fig. 33 are sometimes made with the rods C and D continuous. They should not be made in this way, however, unless the entire rod is proportioned for the stress in C, as this stress is greater than that in D. The best construction for the joint B is illustrated 1020 Types of Roof-Trusses Chap. 26 Fig. 35. Hammer-beam Truss for Grace Chap)el, New York City in Fig. 33a, which shows a cast-iron shoe fitted to the end of the strut to receive the pin. For the truss shown in Fig. 34, a shoe made as shown in the detail drawing makes a better connection for the rods, two of the latter being placed outside of the brackets and three between them. For a truss with a single strut, a turnbuckle on the rod E serves to tighten the rods. When there are three struts, there should be five turnbuckles, as in Fig. 34. A cast-iron shoe should be made to receive the foot of the rafter and the rods secured to a pin passed through shoe and rafter. At the apex, also, of the truss shown in Fig. 34, there should be castings to receive the ends of the rafters, and pins for the tie-bars. The apex-joint of the truss (Fig. 33) may be made either by crossing the rods through a CAST WASHER, or as shown in Fig. 33b. The pins at the joints should be computed for shear, bearing and flexure. More modern construction re- places the cast iron shown with steel plates and pins. When a hammer- beam truss is to be supported on a clerestory-wall which is not very thick nor braced from the outside, a truss of the form shown in Fig. 35 may be used to advantage. It has the appearance of a hammer-beam truss and when placed over a high nave the effect of the rods is not objectionable. These tie-rods should extend through the hammer- beams to their outer ends. Truss for Grace Chapel, New York City. The curved ribs a, a, Fig. 35, have a ten- dency to bend at their smallest section and braces under the ham- mer-beams are necessary to prevent vertical deflec- tion in the latter. A truss similar to this was used in Grace Chapel, New York City. Truss for Metropolitan Concert-Hall, New York City. Fig. 36 shows a form of truss used to support the roof of the Metropolitan Concert-Hall, New York City, George B. Post, architect. The span is about 54 ft and the propor- tions are about as shown. The arch between rafters and raised rib is orna- mented with sawed work and the truss has a very light and airy appearance. The tie-rod is kept from sagging by a vertical rod from the crown of the arch, Fig. 36. Truss for Metropolitan Concert Hall, New York City Types of Wooden Trusses 1021 Wooden Arched Ribs with Iron or Steel Ties. For roofing large halls or rooms a segmental timber arch, with an iron or steel tie to take up the horizontal thrust, is about the cheapest construction, especially where there is no ceiling to be supported. Figs. 37 and 38 are good examples of this form of j-xloVerTr^i!! Fig. 37. Segmental Timber Arch truss, the arched ribs supporting all the load and the tie-rods preventing tha ends of the arch from the spreading which would result without them. Truss for M. C. M. A. Building, Boston, Mass. This truss is shown in Fig. 37 and the framework shown above the arch is simply to support the pur^ lins and rafters and carry the load directly to the arch. It does not assist the truss in any way in carrying the load. Fig. 38. Segmental Timber Arch Trusses for the Fifth Avenue Riding-School, New York City. The method of supporting the roof of the Fifth Avenue Riding-School,* New York City, was rather unusual and very ingenious; and as it is an excellent example of the advantage of the arched form of truss, a brief description is added. The plan of the riding-room, which is io6 ft 6 in long by 73 ft wide, is shown in Fig. 39. This space is kept free from columns, the entire roof being supported by two large trusses, one of which is shown in Fig. 38. The entire roofing is supported by smaller trusses resting on these two large ones, each of the latter, however, ♦ Remodeled in 1905. The old trusses were used in the altered structure. 10'22 Types of koof-Trusses Chap. 26 Fig. 39. Plan of Truss-framing of Fifth Avenue Riding-school, New York City .} IRON TIE TO OPPOSITE COLUMN 106 6 DISTANT FSj 40. Detail of Iron Skewback and Post of Truss Shown in Fig. 3£ Types of Wooden Trusses iD2S eventually carrying a roof -area, equal to about 2 930 sq ft, and a great amount of extra framework. The method employed to resist the thrust of these large arches without the use of rods showing in the room is very ingenious. Opposite the upper ends of the iron posts which receive the arched ribs are oak struts Fig. 41. Arched Wooden Truss. City Armory, Cleveland, Ohio. Span 79 feet held in place by. iron tie-bars and heavy iron beams and together forming a horizontal truss at each end. These two trusses are prevented from being pushed out by two 3 by i-in iron tie-bars in each side wall, as shown in the plan (Fig. 39). The lower ends of the two iron posts are tied together by iron rods running under Fig. 42. Arched Wooden Truss, Sanger Hall, Philadelphia, Pa. the floor the whole length of the room. Altogether this gives for the tie-rods of each truss two 3 by i-in iron bars and one ii/^-in-diam iron rod, equivalent to two 3% by I-in tie-bars. Enlarged sections of the ribs, uprights and braces are shown in Fig. 38. It should be noticed that the uprights have iron rods through their axes, holding the two ribs together. Fig. 40 shows a detail, or 1024 Types of Roof-Trusses Chap. 26 enlarged view, of the iron skewback and post at each end of the truss shown in Fig. 38. Truss for City Armory, Cleveland, Ohio.* Fig. 41 shows the method adopted for supporting the roof and gallery, the arch being of wood. Truss for Sanger Hall, Philadelphia.! Fig. 42 shows one-half of an ARCHED WOODEN TRUSS which, with seventeen others, was designed to support the roof over the central bay of Sanger Hall, Philadelphia, Hazelhurst & Huckel, Line ,;2-3 X 6 126 C-C Pins 2-ljS^ ® 2^4 Rollers ' Stone 2'6"x4'0" Fig. 43. Three-centered Curved Wooden Truss. O. N. G. Armory, Cincinnati, Ohio architects. This building was erected in 1897 for the use of the Eighteenth National Siingerfest, and was intended only for temporary vise. With the dimensions slightly increased, however,, these trusses would be suitable for permanent use. They were spaced 20 ft center to center. A description of the building. and trusses was published in the Engineering Record of January 9, 1897. Truss for the O. N. G. Armory, Cincinnati, Ohio. Fig. 43 shows a truss used in this building. The curve of the axial line of the arch-truss is a three- centered ellipse. Hannaford & Sons were the architects of the building and G. Bouscaren was the designer of the trusses. (See the Engineering and Build- ing Record, December 7, 1889.) * The building has been remodeled and is now used for commercial purposes, t This building was torn down immediately after the meeting. Types of Steel Trusses 1025 3. Types of Steel Trusses Trusses for Pitched Roofs. For ordinary conditions and for spans under lOO ft, some one of the types shown in Figs. 44 to 55 will generally meet the requirements of strength and economy. Trusses of these types are composed of rolled plates and angles and have riveted joints. This is not only a cheaper con- struction than a combination of shapes and rods with pin- joints but is also much more rigid. Where one dimension of the trusses does not exceed about 10 ft they can be completely riveted up in the shops. In case they are large a little judgment will divide them into parts which can be shipped by rail, leaving but few joints to be riveted at the building; but entire trusses having spans even of loo ft can be raised from the ground and put in place. Occasionally a struc- ture is of such magnitude that this is not feasible, in which case the trusses must be raised in parts and riveted afterwards. For a narrow shed or shop a Fig. 44. Truss for a Narrow Shed or Shop Fig. 45. Simple Fink Truss. Spans from Twenty to Thirty-six Feet truss of the shape shown in Fig. 44 is the most economical, the truss proper being that portion enclosed within the points A, B, C. This truss is practically the same as that shown in Fig. 45. For spans of from 24 to 48 ft, and inclina- tions not exceeding 6 in to the foot, the types shown in Figs. 46 and 47 are the most suitable. Trusses of the types represented by these two figures are called Fig. 46. Fan Truss. Spans from Thirty-six to Fifty Feet FAN TRUSSES. The truss shown in Fig. 45 is known as a simple Fink truss. The truss shown in Fig. 47 is supported on columns, the knee-braces B and the pieces A being stressed only when the building is subjected to wind-pressure. A sag-tie, shown by the middle dotted line, Fig. 46, is generally inserted. "When the roof-construction demands three purlins on each side of the truss, 1026 Types of Roof-Trusses Chap. 26 one of the fonns shown in Figs. 48, 49, 50, or 51 should be used. The term French appears to be generally given to those trusses in which the tie-beam is raised or cambered in the middle. The truss shown in Fig. 51 may be called Fig. 47. Fan Truss with Knee-braces. Spans from Forty to Sixty Feet a TRIANGULAR Pratt TRUSS as the web is composed of verticals in compression and diagonals in tension. This truss is not as economical as the Fink truss, except when the inclination of the rafter is less than ^^4. pitch. This is on account of the great length of the web-members in compression. In designing Fig. 48. Fink Truss. Spans from Forty to Eighty Feet steel trusses it is desirable to have as many members, and especially as many long members, in tension as possible, as a given weight of steel resists a much greater stress when in tension than when in compression. The great economy of Fink trusses and fan trusses lies in the fact that most of the members Fig. 49. French Truss. Spans from Forty to Eighty Feet ] are in tension and the struts are short. By comparing Figs. 50 and 51, it is seen that the inner strut in Fig. 50 is only one-half as long as the strut in Fig. 61. If the roof is hipped it is desirable to have vertical members in the hip- trusses to receive the short trusses or trussed purlins. Types of Steel Trusses im Fig. 50. Fink Truss with Vertical Struts Depth of Fink and Fan Trusses. The depth of these trusses at the middle is usually determined by the roofing-material. Thus slate should not be used on a roof in which the rise is not equal to one-third the span. For wooden shingles the rise should be not less than one-fourth and for corrugated iron not less than one-fifth the span. Steel-roll roofing may be used where the rise is but one- twelfth the span. There are many kinds of so-called ready roofing put up in rolls which may be used for any slope ex- ceeding 34 in to the foot. Tar-and-gravel roofing should never be used on a slope exceeding % in to the foot. Considering the con- struction of the roof and the weight of the trusses, the most economical pitch for a roof is about one- fourth the span, or what is commonly called a quarter-pitch, the rise of the rafters being 6 in for each 12 in of run, or 26° 34'. When the rise is less than one-sixth the span some other type of truss is generally required. When the inclination of the roof is determined almost entirely by the question of economy the rise is generally made from 6 to 7 in in 12 in. With Fink TRUSSES or FAN TRUSSES having inclinations for the rafters not exceeding 30°, it is more economical to employ a horizontal chord or tie. A truss whose bottom chord has a rise of 2 or 3 ft, as in Fig. 49, presents a better appearance, however, than one with a horizontal chord. Raising the bottom chord also materially increases the stresses in the truss-members and hence increases the cost. For steep roofs, however, it is generally as economical to raise the bottom chord, because of the shortening of the members. Number of Panels. The number of panels that should be used in each half of the truss is determined in great measure by the construction of the roof. Fig. 51. Triangular Pratt Truss Fig. 52. Fink Truss with Knee-braces. Span Sixty-eight Feet If jack-rafters and purlins are used the length of a panel may be as great as 12 ft; if there are no jack-rafters and the planking of the roof is nailed directly to the purlins, the latter are placed not more than 8 ft apart; and if the roof is covered with corrugated iron secured to the purlins, the purlins should be not more than 5 ft on centers. Whenever the purhns are more than 4 ft apart they should be placed at the truss-joints to prevent large bending-stresses in the top chord. 1028 Types of Roof-Trusses Chap. 26 The spacing of the purlins, therefore, generally determines the number of panels in each half of the truss. For this reason also, the same form of truss may be required for spans of 40 and 80 ft; but of course the members will not be as heavy in the 40-ft truss as in the one with greater span. Most of the trusses shown in Figs. 45 to 55 are drawn from executed designs and give a good idea of the most economical division for different spans. Truss over Car-Barn, Newark, N. J. When stresses due to flexure are developed in the truss-rafters, that is, when they are loaded between the joints Fig. 53. Fink Truss. Span Fifty-one Feet Six Inches the distance between the latter should not exceed 9 ft, and preferably 7 or 8 ft depending somewhat upon the distance between the trusses themselves. The diagram shown in Fig. 55 represents one-half of one of the steel trusses used in roofing a car-barn for the North Jersey Railway Company, Newark, N. J. There are 13 of these trusses spaced 19 ft 2^4 in on centers, each having a span of 9814 ft between the centers of the supporting columns, to which they are riveted by splice-plates engaging the end connection-plates and the webs of the columns. The dimensions of the principal members of these trusses are indicated in con- Fig. 54. Fink Truss with Vertical Struts, for Drill-hall. Span Eighty Feet nection with Fig. 55. There is a more complete description in the Engineering Record of June 22, 1901. These trusses were shipped in four sections, which were assembled on the ground in a horizontal plane and riveted up complete. The bottom chord was stiffened by rails lashed on each side of its entire length, and a sling being attached to the apex of the top chord, the truss was hfted and set on top of the columns by a gin-pole, 50 ft in length. The roofing consists of corrugated iron supported by 5-in I-beam purlins, weighing 10 lb to the foot, spanning from truss to truss and bolted to the rafters with Types of Steel Trusses 1029 two bolts at each end. The general spacing of the purlins is 4 ft 9% in. This is a good example of an extremely hght roof, the weight of each truss being about 4 200 lb and the entire weight of truss, purlins, bracing of lower chord and corrugated-iron roofing being only 8 lb for each horizontal foot of surface cov- ered. Table III. List of Descriptions of Different Types of Roof-Trusses Engineering Record Date March 19, 1892 July 20, 1901 January 4, 1902 February 22, 1902.. August 12, 1905 September 2, 1905 . September 16, 1905 November 2, 1907 . September 16, 1911 October 7, 191 1 Type Howe Fink Fan Fink Pratt Fan Fan Fink Truss Truss Fink Number of panels 16 12 16 Truss over Drill-hall. The truss shown in Fig. 54 was designed for the roof of a drill-hall having a span of 80 ft and a spacing between trusses of 20 ft. The roof was to be constructed with 2 by 8-in rafters supported by purlins at the Main Tie l-4i 2 5"x 3J^ X % L's „ \ t i> b " " " 4-5. 2-3^ x2H"xVi6"L's a^-^ \ sb i_ Rafter, 1-2. 2-5 "x 3M"x Vie L's T b \ " 2-3. 2-5" X 8} \ rA c, 2-3"x 2yi\y^' L's J <^'x 5/16 L's 2 ^ €> 1) \ y b >-yf a / v-'r \ / / 4 / b /:; \ .y^ ^ <*Cfcl* \ / \ / 25 5% J 4 49'lK- Jl.. J8K Fig. 55. Truss over Car-bam, Newark, N. J. Span Ninety-eight Feet, Three Inches. (See, also, Chapter XXVIII, Fig. 25) points A, B, C, D, E and F. Sashes were to be placed in the rise CD, to light the interior of the building. The joint at X was located with reference to the position of the gallery-rod; but if there had been no gallery it would have been more economical to space the vertical struts uniformly, as in Fig. 50. In all the trusses illustrated the plus sign adjacent to a member denotes that the member is in compression, while the minus sign denotes that it is in tension. The members above the main rafter, as CD, DE and EF, in Fig. 54, and a and b in Fig. 55, do not form a part of the truss proper, but are merely a framework to 1030 Types of Roof-Trusses Chap. 26 support the elevated roof, and in drawing the stress-diagram for the vertical Ipads they would be omitted. In the issues of the Engineering Record given in Table III may be found de- scriptions and illustrations of several types of roof-trusses, including the forms described above. Fink Trusses with Pin- Joints. The use of pin-joints in ordinary roof- trusses has practically been abandoned, even for long-span heavy trusses. In the Engineering Record of March 12, 1892, there is a description of a Fink truss, with pin-joints. The truss is heavy and is built entirely of rolled metal. The tension-members are 5, 6 and 7-in eye-bars. The span is about 105 ft. Trusses for Flat Roofs. For supporting flat roofs or roofs having a fall not exceeding i in to the foot, one of the types shown in Figs. 5G to 60 will gen- Fig. 5G. Warren Truss with Verticals. Span Fifty-six Feet erally be found economical, the choice of the particular type depending somewhat on the span and on whether the truss is supported by columns or by brick or stone walls. For spans up to about 50 ft, either of the forms shown in Figs. 56 or 57 answer all practical requirements. The truss shown in Fig. 56 is intended to be used where the slope of the roof is at right-angles to the truss. It can be built, however, with the top chord incHned as in Fig. 57. The end-diagonals in Fig. 56 are in tension, while in Fig. 57 they are in compression. The portions of the lower chord between the end-joints and the walls (Fig. 56) have no stress Fig. 57. Warren Truss with Verticals and Knee-braces. Spans from Thirty to Fifty Feet from the roof -load, but are put in to add rigidity to the construction as a whole. In trusses supported by brick walls this type is preferable to that shown in Fig. 57, while the latter is more suitable when the roof is supported by columns. The vertical A, Fig. 57, is inserted to receive the tension or compression from brace B, and has no stress from the roof-loads. Double Warren Truss. The truss shown in Fig. 58 is known as a double Warren truss, and is desirable where it is important to make the trusses as .^^llpw as practicable. It can be built )yith light members, anc} i^ a ypry s^fi Types of Steel Trussps im truss, being especially suitable for roofs supported by steel columns. Fig. 58 is drawn from a truss in actual use. The member in the middle indicated by the dotted line should never be omitted, although examples may be found where it has not been included. Fig. 59^ also, represents a roof-truss which was con- structed with a span of 57 ft and supported by steel columns. The entire lo^d on the truss is transmitted to the columns at the intersection of the diagonals Rafterss. Fig. 58. Double Warren Truss BB and the top chord. Fig. 60 shows a truss of 96-ft span over a pier-shed. New York City, the trusses being spaced 20 ft apart. They are about 10 ft high and weigh i 300 lb each. They were delivered from the shops completely assembled and riveted, and were raised and set in position by falls suspended from two masts. The dimensions of these trusses are given in the Engineering Record of January 18, 1896. Fig. 59. Pratt-truss Type. Span Fifty-seven Feet The Plus and Minus Signs in these illustrations, as has been mentioned before, indicate compression and tension, respectively, under a uniformly dis- tributed dead load. The plus and minus signs used together indicate that the member may be subject to either tension or compression according to the direction of the wind or to the manner of distribution of the snow. In most of these trusses unsymmetrical loads may change the stresses in the Fig. 60. Warrep-truss Type. Pier-shed, New York City. Span Ninety-six Feet diagonals near the middle of the truss. This changing of stresses due to unequal loading is considered on pages 1096 to 1104. The trusses shown in Figs. 56 to 60 are almost invariably built with riveted connections and with angle or channel -shapes for all members. The Pratt Truss, shown in Figs. 61 and 62, is the form of steel truss best adapted to support floor-loads, the members indicated by double lines being in compression and those indicated by single lines in tension* When 1032 Types of Roof-Trusses Chap. 26 supporting floors are subject to moving loads, counterties should be inserted where indicated by dotted lines. For trusses of this type piN-connections are generally employed and are preferable to riveted connections. . The Quadrangular Truss. The truss shown in Fig. 63 is known as a quad- ^iiANGULAR TRUSS, and has the proportions of the truss over the amphitheater /\ \ \ / \/ / / \ / \ \ /\ /\ / / \ ..: Fig. 61. Pratt Truss of the Madison Square Garden, New York. Figs. 64 and 66, also, show variations of this type, differing, however, from the latter in having all the diagonals in each half-truss inclined in the same direction. In the typical truss their direction is usually reversed at about the middle of each half-span in order to keep them in tension. The plus and minus signs indicate the kind of stress produced in Fig. 62. Suspended Pratt Truss a member by a uniformly distributed dead load. It should be noticed that the middle diagonals of trusses 64 and 66 are in compression. These trusses are well adapted to steel construction and to spans up to 180 ft. When the span exceeds 100 ft one end of the truss should be supported on rollers to allow for the EX^^^^j pr^fiONTRACTiON in the steel. In these trusses the load is trans- Fig. G3. Quadrangular Truss. Amphitlieater, Madison Square Garden, New York City %rtt:eidfo'tl^'tbp of the column-support, the truss proper being included within •the points^, jB, C, D and E, Figs. 64 and 65. The continuation of the bottom chord to the columns is for the purpose of bracing the roof from the latter, there being no stresses in these end-chord members due to vertical loads. This mem- ber B, Fig. 63, and the corresponding member in Figs. 64 and 65 should be con- structed to resist both tension and compression. For short spans the lower Types of Steel Trusses 1033 Fig. 65. Ouadrangular Truss rj7 V + \ 1 H 1871 [7 ^ V V •^^i-«-13'8^| t-..i ^ .i_.._ "f--^ ^16^^ ^12 ^^- > ^16^' • DIAGRAM OF TRUSS Fig. 66. Diagrams of Trusses in Auditorium, Kansas City, Mo. Plan of Two Trusses Showing Lateral Bracing 1034 Types of Koof-Trusses Chap. 26 chord may be made in the shape of a semicircle or half-ellipse so as to give more of an arch-eflfect. There are numerous examples in this country of quad- lladius -113'2»/ie SPanels 9'9=78'0 =Spaa Fig. 67. Riveted Truss with Broken Top Chord. Power-house, Interborougli Rapid Transit Company, New York City 3«J.4 n 3%" - ? Radiu3^3l2 } Fig. 68. Pin-connected Truss Over Drill-hall, 71st Regiment Armory, New York City rangiilar trusses having spans of from loo to i8o ft. For the wider spans it is customary to build the trusses with pin-connections, eye-bars being used for the ties. When this is done it is usually necessary to insert counterbraces Arched Trusses m^ in two panels of each half of the truss as shown by the dotted lines, Fig. 63, as under an unsymmetrical or wind-load the stresses in the diagonals arc gener- ally reversed. For spans less than loo ft, the trusses may be built with riveted CONNECTIONS. In this case the diagonals are generally made of angles capable of resisting both tension and compression, the counterbraces, therefore, not being required. For this type of truss the stresses due to wind and snow should be computed independently of the dead load and the membefs computed for the maximum stresses produced by every possible combination of loading. Trusses for the Auditorium, Kansas City, Mo. A description, with illustrations, of the truss shown in Fig. 66, which is a diagram of one of the trusses over the Kansas City Auditorium, may be found in the Engineering Record for July 22, 1899, and in the Engineering News of November 2, 1899. Riveted Truss with Broken Top Chord. A description is given in the Engineering Record of October 15, 1904. The span is 78 ft between centers of the supporting columns (Fig. 67). Truss for Drill-Hall, New York City. A pin-connected truss, over the drill-hall of the 71st Regiment Armory, New York City, has a span of 190 li 4 in and full descriptions of it are given in the Engineering News of June 16, 1904, and in the Engineering Record of July 2, 1904 (Fig. 68). i. Arched Trusses Difference Between an Arched Truss and a Trussed Arch. For sup- porting the roof of very large spaces such as drill-halls, riding-halls, railway train-sheds, etc., trusses in the form of arches or arches composed of trussea members are often employed . The essential difference between an arched truss and a trussed arch is that under vertical loads the supporting forces of an ardied truss are vertical, while for a trussed arch they are incHned. Bowstring Trusses. Pre- vious to the year 1880 most of the wrought-iron trusses of wide span were built in the form of a bow, from which the term bowstring was derived. Trusses of this type were built with spans of from 88 to 211 ft and with a rise at the middle of from Vs to V4, the span. At that time this type was considered the most economical for spans exceed- ing 120 ft, but in recent years they have been com- paratively Httle used. Fig. 69 is the diagram of a bow- string truss with a span o^ 153 ft 6 in. The trusses iri this particular case ares spaced 21 ft 6 in apart. Fig. 69. Bowstring Truss Fig. 70. Bowstring Truss The arched top chord consists of a wrought-iron deck-beam 9 in deep, with a 10 by ii4-in plate, riveted to its upper flange. Towards the springing this rib is strengthened with 7 by Vs-in plates riveted on each side of the deck-beam. The struts are wrought-iron I beams 7 in deep. The bottom chord has a sectional area of 6^^ sq in and each diagonal tension-rod Jl 1036 Types of Roof-Trusses Chap. 26 diameter of iV4 in. Each truss is fixed at one end and rests on rollers at the other, allowing free expansion and contraction due to changes of tem- perature in the metal. Fig. 70 shows a similar truss having a span of 212 ft. It consists of BOWSTRING PRINCIPALS Spaced 24 ft apart. The rise is one-fifth the span, the middle of the bottom chord rising 17 ft, and of the top chord 4oy2 ft above the springing. The top chord is a 15-in wrought-iron I beam and the bottom chord a round rod in short lengths, 4 in in diameter and thickened at the joints. The ties of the bracing are of plate iron from 5 to 3 in in width, and % in thick. The struts are formed of bars having the form of a cross. During the last ten or twelve years a number of roofs have been supported on trusses which can hardly be classed as simple trusses; and yet it is questionable if they are true arches. Probably the frames act partially as simple trusses and partially as arches. Trusses for the Conservatory Building, Garfield Park, Chicago, 111. Engineering News, August 27, 1908. The roof is supported by pointed trusses spaced 12 ft 6 in on centers. The truss-span is 80 ft 6 in, center to center of end-supports. The chords of the trusses are parallel and connected by Warren BRACING. Both ends of the trusses are bolted to the supports and consequently there must be some horizontal thrust under certain conditions. The trusses are riveted at all joints and have no hinges or pins. Trusses for the Chicago and North Western Railway Station, Chicago, 111. Engineering Record, June 18, 19 10. The roof over the main waiting-room is carried by trusses each having a span of 90 ft 4 in and a rise of 31 ft and being riveted to columns about 27 ft 6 in apart. All connections are riveted. The clear height of the bottom chords at the middle is 84 ft. Trusses for the Peoria and Pekin Union Railway Trains-Shed, Peoria, 111. Engineering Record, December 8, 1900. The trusses are riveted to columns about 30 ft above the floor and spaced 20 ft apart. The truss-span is 109 ft 4 in, center to center of end-supports, with a clear rise of about 10 ft. The depth at the middle is 18 ft and at the end 6 ft. All connections are riveted. Trusses for the New Union Station, Washington, D. C. Engineering Record, February 6, 1904. The concourse-roof is supported by crescent trusses, each having a span of 132 ft 514 in and a clear rise of 22 ft SV2 in. They are spaced about 39 ft 4 in apart. One end of each truss rests upon masonry and the other is riveted to a heavy plate girder. All connections are riveted. The bottom chord at the middle is 45 ft above the floor. The trusses over the waiting-room of the same station have a span of 137 ft 8 in and a rise of 45 ft 5 in. The chords are parallel and the ends are anchored with bolts to the masonry. Trusses for the Riding-Hall, Armory for Squadron C, National Guard, Brooklyn, N. Y. Engineering News, August 29, 1907. The main trusses have a span of 179 ft 2 in and a rise of about 66 ft in the clear. The total depth of the truss at the middle is 14 ft, while at the ends, where the chords approach each other and finally become vertical, it is 3 ft 3 in. One end is anchored to the masonry and the other is on rollers. The trusses are in pairs 10 ft ii^/^ in on centers and the pairs are spaced 38 ft 8^/^ in on centers. All connections are riveted. Trusses for the New Rock Island Terminal Station Train-Shed, Chicago, 111. Engineering Record, September 12, 1903. Engineering News, August 6, 1903. The trusses over the tracks have a span of 221 ft i in center to center of the end-pins, a rise of 28 ft and a depth at the middle of 25 ft 6 in. They are Arched Trusses 10^/ supported bjT columns and are spaced from lo ft 3 In to 19 ft 6 in apart. All principal connections are made with pins. Curved Trusses with Horizontal Ties. Curved or arched trusses are often constructed with a horizontal member connecting the ends at the supports. This makes the structure as a whole, including the horizontal member, usually called the tie-rod, a simple truss requiring only vertical supporting forces for vertical loads, provided one end is free to move, as it is when placed on rollers. When the trusses are supported by long columns it may be assumed that the ends have freedom. A few examples are given, some of which are commonly classed as true arches. Trusses for the Sullivan Square Station, Elevated Railway, Boston, Mass. Engineering Record, June 15, 1901. Fig. 71. These arches spring K— 4_.^1.,,. _. // Fig. 71. Arched Truss for Sullivan Square Station, Elevated Railway, Boston, Mass. from steel columns and are provided with tension-rods which take up the thrust. The arch proper rests on two 4iA-in pins at each end, as indicated in the diagram, the tie-rods being connected to them. The bracing below each pin is riveted to the column and the arch itself is built of angles and plates with riveted con- nections. Fig. 71a shows the joint at A where the tie-rods are connected and held up by a i-in suspension-rod from the crown of the arch. This construc- tion is the same in principle as that of the wooden arch shown by Fig. 42. United States Express Company's Receiving Station, New York City. Engineering Record, October 22, 1904. The roof -trusses in this building are supported on 24-in brick walls at the level of the second-story floor and have their ends connected by I beams which form a part of the floor-framing of the second story. Each truss has a span of 74 ft 4 in and a clear rise of 27 ft. They are spaced about 24 ft 5 in apart and have all connections riveted. Since the 1038 Types of Roof-Trusses Chap. 26 tjes are very heavy one might be led to classify these trusses with true arches, fixed at the ends; but as the condition of fixed ends rarely obtains in practice, it is better to consider this type of structure as an arched truss with a tic-rod, or possibly as similar to the type shown in Fig. 75. Table IV. General Dimensions of a Few Three-Hinged Arches Location Span ft in Rise ft in Tie Syracuse University lOI 4 106 121 10 134 149 9 163 6 172 178 6 181 184 189 8 190 4 191 4 215 227 230 252 8 259 300 8 363 "56 2i4 96 3 32 6 66 6 73 5% 69 9V2 80 90 2V2 94 (about) 103 aV^ 88 oj 84 73 94 89' 9% 88 3V2 100 4 206 4 Floor-b^ms No tie tTwo 1% X iVs t2V2X2y2 tTwo 2% round rods 9-in I beam No tie No tie No tie tTwo 1%-in round rods Two channels tTwo 4 X %-m plates t9 X Via-in plate Two i2-in I beams Lawson Riding-Academy Machinery Hall, Chicago Exp ; . 22nd Reg. Armory, New York Coliseum Chicago (new) . . Newark, N. J., Armory Government Bldg., St. Louis Exp.. Coliseum, St. Louis Hartford, Conn., Armory Frankfort, Germany, Train-Shed... 69th Reg. Drill- Hall, New York. . . 5th Reg. Armory, Baltimore, Md.. . 47th ^eg. Armory, Brooklyn, N. Y. Coliseum, Chicago (old) 74th Reg. Arpiory, Buffalo, N. Y. . Coal-Shed, Wende, N.J Jersey City Train-Shed. Philadelphia Train-Shed Broad Streef; Station, Phila Manufacture^ and Liberal Arts Bldg., Chicago Exp Location Distan c ce, center to enter* Reference Syracuse University 17 ft 32 ft 50 ft II an 22V2 31 an 35 ft 36 ft 6 an 33 ft 6%£ iiK' in in Sin d52ft .0 25 ft d 26V2 ft in 8 in d 52% ft 6 in ind 38^/4 ft R. Aug. 22, 1908 R. Dec. 31. 1904 R. Dec. 24, 1892 N. May 5, 1910 N. Sept. 14^ 1899 R. May 26, 1900 N. Sept. 29, 1904 N. Aug. 10, 1899 R. Sept. 12, 1908 R. Mar. 5, 1892 R. June 3, 1905 R. May 14, 1904 R. Dec. 23, 1899 N. Nov. 12, 1896 R. June 9, 1900 R. Oct. 3. 1908 N. Sept. 25, 1899 R. July 16, 1892 R. June 10, 1893 N. Sept. I, 1892 Lawson Riding-Academy Machinery ii^l\, Chicago Exp 22nd Reg. Armory, New York Coliseum, Chicago (new) Newark, N. J., Armory Government Bldg., St. Louis Exp.. Poliseum. St. Louis Hartford, Conn., Armory Frankfort, Germany, Train-Shed... 69th Reg. DriU-Hall, New York . . 5th Reg. Armory, Baltimore, Md.. 47th Reg. Armory, Brooklyn, N. Y. Coliseum, Chicago (old) 34 ft 46 ft 4 in 5 in 74th Reg. Armory, BufTalo, N. Y.. Coal-Shed, Wende, N. J Jersey City Train-Shed 22 ft 14^2 £ loU in md 43^1' ft Philadelphia Train-Shed. Broad Street Station, Phila Manufactures and Liberal Arts Bldg., Chicago Exp * Center to center of end-supports. X To lower chord. N. Engineering News. t Dimensions in inches. R. Engineering Record. Arched Trusses Sj^Pin '2-l>g Plates Fig. 71a. Detail at A, Fig. 71. Trusses for Drill-Hall, 13th Regiment Armory, Scranton, Pa. Engi- neering Record, August 24, 1901. These roof-trusses are about 5 ft deep and are spaced about 12 ft on centers. The truss-span is 156 ft, over all, with a rise of 47 ft in the clear. The ends rest on flat plates and are connected by a tie consisting of two i%-in round rods. Freedom of motion is provided at one end by slotting the holes for the anchor- bolts. Trusses for Armory Drill-Hall, Providence, R. I. Engineering Record, April 13, 1907. The type of roof-truss used in this building is com- monly called a three-hinged arch, there being a pin at each support and one at the crown; but the two end-pins are connected by a tie and one end-shoe is provided with rollers and hence the structure is a simple truss composed of three members, two of which are trusses in themselves. The truss-span is 166 ft 8 in and the rise about 61 ft. The trusses are riveted and spaced about 26 ft i in on centers. Trusses for the Pennsylvania Railway Train-Shed, Pittsburgh, Pa. Engineering Record, August 23, 1902. The trusses have three hinges and a TIE and a roller-bearing at one end. The truss-span is 255 ft % in between end-pin centers, the rise 93 ft between pin-centers and the depth at the cente^- 7 ft. The trusses are riveted and stand in pairs 9 ft on centers and the pairs are spaced 49 ft 6 in on centers. The Three-hinged Arch as employed for supporting the roofs over large rooms, train-sheds, drill-halls, etc., is composed of two curved trusses, usually of the same form and dimensions, resting upon pins at the supports and con- nected by a pin over the middle of the span. The supports are assumed to be fixed in position and are often connected by a tie to insure stability and take up the horizontal thrust of the arch. While a metal tie between masonry sup- ports does not make these supports fixed in position imder all or any conditions of loading, yet for all practical purposes they may be so considered; and these three-hinged structures which have ties, provided there is no arrangement for horizontal end-movement due to roller-bearings, etc., may be classified with those whose supports must resist all horizontal as well as all verticq,! forces. The bottom pins are usually placed below the floor-level so that the tie-rods, when used, may be concealed by the floor or even made a part of its framing. Under certain conditions the arches can be so designed that the horizontal thrust will be quite small and the supports designed without the use of the hofizontal tie. The special advantages of the three-hinged arch for the class of build- ings above mentioned are economy and a maximum amount of clear space beneath the truss. Much of the economy results from the omission of support- ing columns. The base of the arch being very near the ground-level, it is also well designed to resist wind-pressure. Another advantage of this type is the free movement allowed under temperature-changes without causing additional stresses in the members of the structure, the middle part rising or falling freely with a slight rotation of the half-trusses about the pivots. In the case of the arches of the buildings of the Paris Exposition, it was estimated that a range of temperature of 100° F. would produce a change in level of 2% in at the center pivot. The arched ribs are usually built of plates, angles, or channels, yti^ 1040 Types of Roof-Trusses Chap. 26 riveted connections and frequently with a solid-plate web at the bottom. The determining of the stresses and detailing of the members and joints require the services of a. competent structural engineer; but the illustrations given will enable the architect to decide on the general shape of the trusses for the purpose of making preUminary drawings and the computations and detail drawings can be made later. -2 Square bars Three-hinged Arch. Manufactures and Liberal Arts Building, Chicago Exposition Fig. 72. Half Truss. Trusses for Railway Station, Frankfort-on-the-Main, Germany. The first suggestion for hinging the ribs at the crown was made by M. Manton, a French engineer. The writer believes that the first application of this principle to roof-trusses, at least on a large scale, was made in the train-sheds of the Union Railway Station completed in the year i888at Frankfort-on-the-Main, Germany. These trusses have a span 'of about 184 ft. Engineering Record of September 12, 1891, and March 5, 1892. Trusses for Machinery Hall, Paris Exposition. The large roof of the Machinery Hall of the Paris Exposition of 1899 was supported by trusses of Arched Trusses mi this type, the span being 368 ft and exceeding anything hitherto attempted in roof-trusses. Since then trusses of this kind have been frequently used for roofing large exhibition-halls, train-sheds, armories, and similar buildings. Trusses for Manufactures and Liberal Arts Building, Chicago Exposi- tion. Fig. 72 shows the half-truss of one of the three-hinged arches sup- porting the roof of the Manufactures and Liberal Arts Building of the Chicago Exposition. Engineering News, September i, 1892. Trusses for Drill-Hall, Brooklyn, N. Y. Fig. 73, in a similar manner, shows the half-truss of one of the three-hinged arches over the drill-hall of ^2 Bars 4 X % Fig. 73. Half Truss, Three-hinged Arch, Drill-hall, Brooklyn, N. Y. the 47th Regiment Armory, Brooklyn, N. Y. Engineering Record, December 23, 1899. A description of the arch shown in Fig. 74 is given in the Engineering Record of November 19 and December 24, 1892. The horizontal thrust due to the dead load is small. Two-hinged Arches. When there are only two pins, usually at the sup- ports, the trusses become two-hinged arches. As in the case of three-hinged erches, there may be a tie or the supports may be entirely depended upon to resist the horizontal thrust. Trusses for Live-Stock Pavilion, Chicago, 111. In the Engineering News of June 28, 1906, there is a description of the two-hinged arches supporting the roof of this building. The arch span is 198 ft, the rise 54 ft and the truss- spacing 42 ft. Each truss has a tie consisting of one 2^l6-in round rod. Trusses for Railway Station, Cologne, Germany. This station, owned by the Prussian Railways, has two-hinged arches supporting the roof of the train-shed. The arch-span is 209 ft 6 in and the rise 79 ft. There is a brief mention of it in the Engineering News, October 6, 1892. A number of roofs 1042 Types of koof-Trusses Chap. 26 -121-10- *| JH'«g. 74. Three-hinged Arch, Machinery Hall, Chicago Exposition Fig. 75. Two-hinged Arch, Exposition Hall, Providence, R. I. Cantilever Trusses 1043 are supported by structures similar to that shown in Fig. 75. While such a frame is not strictly a two-hinged arch, owing to the lack of freedom at the supports, it may, however, for all practical purposes, be so considered. Table V. List of Buildings with Trusses of the Two-Hinged-Arch Type Name Span Spacing Armory, Pawtticket, R. I ft 82 92 96 100 104 ii8 120 122 176 196 ft 24 25 24 24 25 24.5 23 to 25 30 24.5 35 Armory, Portland, Me Phoenix Hall, Brockton, Mass Armory, Northampton, Mass. Palace Rink, Hartford, Conn Exposition Hall, Providence, R. I Armory, Cleveland, Ohio Armory, Boston, Mass. . . Armory, 22d Reg., New York City Armory, Brooklyn, N. Y These structures are described in Building Construction and Superintendence, Part HI, by F. E. Kidder and are similar to the type shown in Fig. 75. Fixed Arches, or arches without hinges, are seldom employed in buildings. In a number of examples cited above the structures have the appearance of being fixed at the ends, but a closer inspection indicates that they are not sufficiently anchored to warrant their being classed as fixed arches. -.^ 5. Cantilever Trusses General Principles. A cantilever beam or cantilever truss is that portion of a larger beam or truss which extends beyond one of the supports, as B in Figs. 76 to 79 and A in Fig. 80. The overhanging portion B is called the cantilever-arm and the portion C the anchor-span. The cantilever-arm may support at its end another beam or truss. The term cantilever was originally used to designate a projecting beam which served as a bracket; in engineering it is used to denote a beam or girder fixed at one end, by being either built into a wall, or, as is more commonly the case, extended a sufficient distance beyond its support to form an anchorage. Thus in Fig. 76, which shows a beam resting on two supports, B is the cantilever or cantilever-arm and C the anchor-span or anchorage. It is obvious that if this entire beam were uniformly loaded the support P would carry the greater part of the total load; and also, that an additional load W, at the end of the cantilever, might cause a negative reaction or upward pull at the support D, in which case the reaction at P would exceed the load on the beam, unless the negative reaction at D is considered as an additional load. Although both conditions of loading occur in practice, the cantilever end of the truss usually requires an anchorage rather than a support at the inner end. As apphed to roof-construction some such arrangement as is shown in Fig. 77 is generally required to make this method of support prac- ticable; that is, a wide middle span, with shorter spans or aisles on each side of it. Each cantilever-arm is usually made from V4 to V& the middle span and a simple middle truss, represented by S, supported by the arms of the canti- levers, is used to support the rest of the roof. In all such cases, therefore, can- tilever trusses must be used in pairs, one on each side of the building; and there must be room or passages outside of the principal span to permit the use of the 1044 Types of Roof-Trusses Chap. 26 outer or anchor-spans. This arrangement is generally found in auditoriums, armories, exhibition-halls and similar buildings, and is sometimes conveniently adapted also to other classes of structures. Of course, in a large building a beam consisting of a single member such as is shown in Fig. 77 could not be used; Fig. 79 Figs. 76 to 80. Fig. 80 Cantilevers and Cantilever Trusses but the principle of construction is the same whether the cantilever is a single member or a large truss. Fig. 78 is the diagram of a truss which takes the place of the beam CB in Fig. 77, the single lines representing the tension-members and the double lines the compression-members. Fig. 81 shows the complete arrangement of two of these trusses with the accompanying middle truss, for an Fig. 81. Suggestion for Wooden Cantilever Truss entire roof. The truss-principle shown in these figures may be developed to almost any extent. The lower chord may be curved, but the general outline of the truss is best adapted to those, roofs in which a wide middle part is to be supported by cantilevers. For bridge-trusses or floors the form shown in Fig. 79 may be used; whik for shed and platform-roofs, open on one side, trusses Cantilever Trusses 1045 of the form shown in Fig. 80 are about the only ones practicable. In this latter truss the proportions of the arms are such that only a slight support is required at W, and a consequent compressive stress developed in the lower portion of the rafter. Advantages and Disadvantages of the Cantilever Truss. The cantilever truss possesses some special advantages. The clear height in the middle is greater than can be obtained with any other type excepting the three-hinged arch; its appearance is light and graceful, and there is no horizontal thrust and conse- quently no necessity for tic-rods. The particular advantage of this truss for very great spans is that it can be erected without scaffolding under the middle part, and in bridge-work this is considered as its only advantage. It is claimed by some prominent engineers that the cantilever type of truss is not an economi- cal one and not as desiral^le for spans of 150 ft or more as the three-hinged ARCH. It does not as readily lend itself to methods of allowing for expansion and contraction as the three-hinged arch, the bowstring truss, or the quad- rangular TRUSS. For certain classes of buildings, however, and especially where the middle span does not exceed 150 ft, it can perhaps be used with better architectural effect than is possible with other types, the cost remaining about the same. For roofing platforms, grand-stands, etc., where an outer support is not desired, it is the only type available. Truss for Grand-Stand, Monmouth Park, N. J. Fig. 82 is a diagram of one of the cantilever trusses supporting the roof of the grand-stand at this Fig. 82. Cantilever Truss, Grand-staud, Monmouth Park, N. J. racing-track, the details of which were published in Architecture and Building, in February, 1890. This is an instance in which the cantilever was the only type of truss that could be used and the form adopted is both simple and economi- cal. As will be seen from the drawing, the main supporting column extends to the top of the truss, as is usually the case with cantilever trusses, and the truss is' riveted to each side of it. The upper and lower chords are made of two angles and a web-platc. The bracing consists of angle-bars used in pairs and varying from 3 by 2 by i/4 in to 3 by 3 by %6 in, the whole frame being connected by rivets. Trusses for the Fore River Ship-building Shed, Quincy, Mass. In the Engineering Record, July 26, 1902, there is a description of the roof of this building, in which the cantilever trusses have an overhang of 60 ft. Roof-Trusses for Grand-Stand, Empire City Trotting Association, Yonkers, N. Y. These trusses have cantilever-arms at each end, 25 ft 6 in on one end and 15 ft 6 in on the other. The intermediate truss has a span of 50 ft. This structure is described in the Engineering Record, February 10, 1900. Other examples of cantilever roofs are given in Building Construction and Superintendence, Part III, by F. E. Kidder. 1046 Stresses in Roof-Trusses Chap. 27 CHAPTER XXVII STRESSES IN ROOF-TRUSSES By MALVERD A. HOWE PROFESSOR EMERITUS OF CIVIL ENGINEERING, ROSE POLYTECHNIC INSTITUTE 1. Roof-Loads. Data, Weights, Materials, Methods Data for Roof-Trusses. Before the stresses in a roof-truss can be deter- . inined it is necessary to decide upon the character of the roof-covering, the method of supporting it between the trusses, the geometrical shape and span of the trusses and the spacing of the trusses. Roofing Materials for Pitched Roofs. The materials suitable for covering pitched roofs are slate, burnt-clay tiles, metal tiles or shingles, wooden shingles, corrugated iron, tin with standing seams, standing-seam steel roofing and various kinds of ready roofing. The least slope to which these materials may be laid without danger of leaks, the weight per square foot of roof and the com- parative cost are indicated in Table I. The cost, however, can only be considered as approximate, as it varies for different materials, locahties and the scales of wages. Table I. Covering Materials for Pitched Roofs Material Slates, black Slates, green Slates, red Burnt-clay tiles, interlocking pattam Tin shingles, painted dalvanized-iron tile, painted Cedar shingles, stained or painted. . . Corrugated iron, painted Standing-seam steel roofing, painted. Ready roofing Least rise Comparative of rafter cost per m 12 m square 8 $7.00 to $12.00 8 7.00 to 10.00 8 12.00 to 17.00 7 15.00 to 25.00 6 8.00 to 10.00 6 13.00 to IS. 00 6 3.80 to 7.20 3 4.00 to 4-50 2 4.00 to 4-50 I 3.50 to 4.50 Roofing Materials for Flat Roofs. Flat roofs or roofs having a fall of Irom 1^ to % in to the foot are usually covered with tar and gravel, asphalt, ready roofing, or tin with lock-and-solder joints. A good tin roof costs about $8.00 a square, not including the painting. The other kinds vary from $3.50 to $4.50 a square. Manner of Supporting the Roof from the Trusses. Wooden roofs, sup- ported by wooden trusses, require common or jack-rafters to support the sheath- ing or slate, and generally purlins to support the rafters, although in some cases it may be more economical to span the rafters from truss to truss (Fig. 17, Chapter XXVI). When slates or burnt-clay tiles are used on steel roofs, they are usually secured to steel angles, running parallel with the walls and spaced from 8 to ioy2 in apart, as may be necessary to accommodate the size of the slates or koof-Loads. Data, Weights, Materials, Methods 1047 tiles. If the span is not more than 6 or 7 ft, the angles may be fastened to thd ' truss-rafters. As a rule, however, when slates or tiles are to be used, it is cheaper to space the trusses from 16 to 20 ft apart, and to use purlins and jack-rafters to support the smaller angles. Quite often, wooden rafters and sheathing are used with steel trusses. This is more economical, but of course increases the fire-risk. Unprotected steel is little if any better than wood. If corrugated iron is to be used for roofing, the most economical construction for steel roofs is to space the trusses from 16 to 20 ft apart, and to use light I beams for purlins, spaced about 4% ft on centers, as in Fig. 52, Chapter XXVI, the corrugated iron being secured to the purlins by straps. If warm air comes in contact with the underside of a corrugated roof, either the roofing should be laid on boards, or some kind of anticondensation lining should be provided, as otherwise the moisture in the air will condense and fall on the floor or objects below. Flat roofs always require rafters and sheathing, or fire-proof filling between the rafters. Spacing of Trusses. From the above it is seen that the economical spacing of the trusses depends to a great extent upon the kind of roofing that is used, and also upon the span. As a general rule, however, the most economical spacing is about as follows: For WOODEN TRUSSES under 80-ft span, from 12 to 16 ft on centers. For WOODEN TRUSSES over 80-ft span, from 16 to. 24 ft on centers. For STEEL TRUSSES Under 80-ft span, from 16 to 20 ft on centers. For STEEL TRUSSES over 80-ft span, from 20 to 40 ft on centers. The SPACING of a number of steel trusses of wide span is given in Chap- ter XXVI. When the distance between the trusses exceeds 16 ft for wooden roofs or 20 ft for steel roofs, it is generally necessary to use trussed purlins. Having decided upon the kind of truss to be used, the spacing of the trusses and the roof-construction, a section-drawing of the roof should be made, showing an elevation of the truss, the points at which the purlins are to be supported, the manner of supporting the ceiling, if there is one, and any other loads that are to be supported by the trusses. The section and truss-drawing, with the tables of the weights of roofing-materials, will furnish the necessary data for computing the loads at each joint. Until the stresses have been determined, the sizes of the members computed, and the joints detailed, an exact drawing of the truss cannot, of course, be made; but in order to compute the loads and stresses, it is necessary to know the positions of the joints, and these can be indicated with sufiicient accuracy before the exact sizes of the members are determined. Chapter XXVI gives suflSicient information regarding the various types of trusses to enable one to decide upon the height and the number and arrangement of the struts and ties; and the sizes of the members can be approx- imated for the preliminary drawings. Roof and Ceiling-Area Supported at Any Joint. Calculations for the stresses in a truss are always based on the assumption that the loads are trans- ferred to the joints, and that the members are free to move at the joints as if hinged, although the actual joints may be made with riveted or other connec- tions. The loads at the joints are, of course, equal to the reactions of the pur- lins, or of the tie-beams or principals, if these receive the ceiling-joists or rafters. When the load on the roof or ceiling is uniformly distributed, as is usually the case, the simplest method of computing the joint-loads is to determine the roof or ceiling-area contributory to the joint, and to multiply this area by the weight or load per square foot. The area contributory to any joint is equal to the product of the distance measured half-way to the next joint, on each side, by the dis- tance measured half-way to the next truss or wall on each side. Thus if Fig. 1 104a Stresses in Roof-Trusses Chap. 27 * represents truss i, of Fig. 2, the roof-area contributory to joint 2 is, in square feet, 8+14 -r, , , , , ... 14+ 12 • X a. For truss 2, the area supported by the same joint is ' X fl; or, if we let D represent the length in feet of roof or ceiling supported at each joint, the area in square feet supported by joint 2 is aXD, and the area sup- Fig. 1. Rafters and Ceiling Joi8tS-2 x 8" 16*on centers. King-rod Truss . vy/-x- -,v/.' '//w^^^^wjawajm;/ www//mww/.'m.w' ,< -y— -f- r ported by joint 3 is 2 ^ X Z). In the same way, the ceiling-area supported at joint 6 is c X -D, the arrow-heads being half-way between the joints. It makes no material difference in the joint-loads whether the common rafters are sup- ported on purlins or whether they rest on the top chord of the truss, provided the purlins come at or close to the joints and the load is uniformly distributed. Thus the width of the ceiling contrib- utory to joint 7 (Fig. 3) is equal to c, just the same as in Fig. 1. The arrange- ment in Fig. 1 produces cross-bending stresses in the tie-beam, while that in Fig. 3 does not. When the trusses are spaced a uniform distance apart, D, Fig. 2, is, of course, equal to the distance between centers of trusses. When the trusses are not spaced uniformly, D is equal to one-half the distance from the center of the truss on the left to the center of the truss on the right. When a purlin is more than 12 in from a joint, or the roof-area is not symmetrical, as is often the case at hips and valleys, the joiiit-load is determined by the principle of- the REACTION OF BEAMS, as explained in Chapter IX. Examples showing the computation of joint-loads are given a little farther on. Roof-Load per Square Foot. By the term roof-load is meant the weight of the materials composing the roof, trusses and purlins, an ample allowance for 4- -r- — [ Truss 1 ^ A.. ^4 %/^//////UAA/^/M////mw/m/MMm^^^^ Fig. 2. Plan of Wall and Trusses Roof-Loads. Data, Weights, Materials, Methods 1049 snow and also an allowance for wind-pressure. The weight of the materials is called the dead load. Snow is generally considered a live load, acting vertically. The pressure due to the wind is always assumed to act normal to, or at right-angles to, the surface of the roof; but for trusses of less than loo-ft 2'x 6*Raftera 16"0.C. ^ H^ e=i2 2- A ye X 12" ^ -12'2^^ ^H 12 2''-—, -+ — J QiJ 6--^ .,.-^-4 -36 6--. -^ Fig. 3. Queen Truss. (See, also, Figs. 12, 53 and 54 and Chapter XXVIII, Fig. 1)— span it is usually combined with the dead load, wind-load and snow-load and treated as one vertical load. This does not apply to the Fink and fan types. (See page 1109.) Data for Computing Dead Loads. The dead load of any roof may be estimated with sufl5cient accuracy from the following data: Table n. Weights per Square Foot of Roof-Surface Shingles, common, 2V2 lb; 18 in, 3 lb Slates, %6 in thick, 7V* lb; -"/i in thick, 9.6 lb (the common thickness is %e in for sizes up to 10 by 20 in) Plain tiles or clay shingles, 11 to 14 lb Roman tiles, old style, two parts, 12 lb; new style, one part, 8 lb Spanish tiles, old style, two parts, 19 lb; new style, one part, 8 lb Improved Oriental tilesr 11 lb Ludowici tiles, 8 lb For tiles laid in mortar add 10 lb per sq ft Copper roofing, sheets, i^i> lb; tiles, 1% lb Tin roofing, sheets or shingles, including one thickness of felt, i lb Corrugated iron, painted or galvanized. No. 26, i lb; No. 24, 1.3 lb; No. 22, 1.6 lb; No. 20, 1.9 lb; No. 18, 2.6 lb; and No. 16, 3-3 lb Standing-seam steel roofing, i lb Five-ply felt and gravel roof, 6 lb ; Four-ply felt and gravel roof, 5^1j lb Three-ply ready roofing (elaterite.ruberoid, asphalt, etc.). from 0.6 to i lb Skylights with galvanized-iron frame, i/4-in glass, ^¥2 lb; %6-in, 5 lb; %-in, 6 lb Sheathing, i in thick. 3 lb per sq ft for white pine, spruce, or hemlock; 4 lb for yel- low or pitch pine 1050 Stresses in Roof-Trusses Chap. 27 Table HI. Weights of Rafters per Square Foot of Roof-Surface Size of rafter in inches Spruce, hemlock, white pine. Spacing in inches, center to center Hard pine. Spacing in inches, center to center i6 20 24 16 20 24 2X 4 2X 6 2X 7 2X 8 2Xio lb 1V2 2V4 2^/8 3 38/4 lb 1,2 1.8 2,1 2.4 3 lb I 1V2 1% 2 2V2 lb 2 3 3V2 4 5 lb 1.6 2.4 2.8 3.2 4 lb iVs 2 2% 3V3 Wooden purlins weigh about 2 lb per sq ft of roof-surface when the span is between 12 and 16 ft. For steel roofs the sizes and weights of the purlins and rafters should be computed for each particular case. Weight of Truss. To the weight of the roof-construction proper should be added an allowance for the weight of the truss. If trusses could be built in exact accordance with the theoretical requirements their weight would be directly proportional to the roof-load and span; but as there is always some extra material, it is impossible to determine the weight of the truss exactly until it is completely designed. Several tables for the weights of wooden trusses and formulas for steel trusses have been published, but hardly any two of them are alike. The following are some of the formulas in use: For Wooden Trusses W = 0.04 L -\- 0.000167 L^ W = 0.50 -I- o.o7sL ( N. C. Ricker, for trusses like Figs. 4 ( and and 5, Chapter XXVI. H. S. Jacoby. For Steel Trusses fF= 0.75 4-0.075 L Mansfield Merriman and Jacoby. PT = 0.6 4- 0.06 L, for heavy loads { ^ ^ ^ , r ' t- 1 ^ Tjr , r f 1- w 1 J ( ^' E. Fowler, for Fmk trusses. py - 0.4 + 0.04 L, for light loads ) ' ^^ P / L \ ( M. S. Ketchum, for steel mill-build- 45 \ SVJ/ ( ing trusses. W = 0.05 L-\-i2/A H. G. TyrreU. In the above formulas, W — weight of truss in pounds per square foot of hori- zontal projection of the roof supported, L = span in feet, A = distance between trusses, and P = capacity of truss in pounds per square foot of horizontal pro- jection. Tables IV and V, compiled from a comparison of other tables and formulas, and from the weights of actual trusses, are sufficiently accurate for the purpose of determining stresses. The weights given are probably slightly in excess of the actual weights of average trusses, as it is preferable to have the error, if any, on the safe side. It should be noted that the weights are for each square foot of roof-surface, and not for the horizontal area. Table VI gives the actual weights of a number of large steel roofs. Roof-Loads. Data, Weights, Materials, Methods 1051 Table IV. Weights of Wooden Trusses per Square Foot of Roof-Surface* Span ft Up to 36 36 to 50 so to 60 Goto 70 veto 80 Soto 90 90 to 100 100 to no no to 120 V'j. pitch V'i pitch H pitch Flat lb 3 3V4 3% 5 5% lb ^^ 3% 4 4V2 5 6 6% 7V3 8K' lb 3«/4 4 4% 5V2 7 lb 4 4^^ 4% 5V1 6 7 Table V. Weights of Steel Trusses per Square Foot of Roof-Surface Span ft Up to 40 40 to 50 so to 60 60 to 70 70 to 80 80 to 100 100 to 120 120 to 140 y% pitch lb lb 5.25 6.3 5 75 6.6 6 75 8.0 7 25 8.5 7 75 9.0 8 5 10. 9 5 II. 10 II. 6 Vz pitch ^/4 pitch lb 6.8 7.2 8.6 9-2 9-7 10.8 12.0 12.6 Flat lb 7.6 8.0 9.6 10.2 10.8 12.0 13.2 14.0 Table VI. Weights and Spacing of Some Steel Roofs of Wide Span, Including Trusses, Purlins and Braces, but not Roof-Covering or Rafters Name of building Type of truss Span ft Spacing, center to center of trusses, ft Weight per sq ft sloping surface, lb Weight of one truss, tons Armory, Pawtucket, R. L. . Armory, Portland, Me Phoenix Hall, Brockton, Mass Fig.7St 82 92 96 100 104 118 120 122 24 25 24 24 25 241/3 23-25 30 241/2 35 8.7 9-7 8.6 8.0 II. 8 9-5 12.4 6.7 9 10 8.5 II. 5 12. s 21 Armory, Northampton , Mass Palace Rink, Hartford, Conn . . • Ex. Hall, Providence, R. I.. Cleveland, Ohio, Armory.. Armory, Boston, Mass Armory, 22d Regt., N. Y. .. Armory, Brooklyn, N. Y.... '• 176 196 * For scissors trusses, increase one-third, t Chapter XXVI. 1052 Stresses in Roof-Trusses Chap. 27 The data for the first seven buildings in Table VI were compiled by H. G. Tyrrell, who states that all of the seven roofs were proportioned for slate and plank roofing resting on wide rafters 2 ft apart, supported by st^4 purlins about 10 ft apart. The spans given are measured from center to center of side bearings. Stresses were computed for a dead load of 25 lb per sq ft, a snow-load of 10 lb per sq ft of sloping surface, and a horizontal wind-load of 40 lb per sq ft or a 28-lb-per-sq-ft normal pressure. Data for computing the weights of floors and floor-loads supported by trusses, and for fire-proof construction, may be found in Chapters XXI and XXIII. Snow-Loads. As a basis for making an allowance for snow, Table VII is perhaps as good a guide as any that can be given. When snow-guards are placed on a roof, the same allowance is made for a half-pitch as for a one-third pitch. Table VII. Allowance for Snow in Pounds per Square Foot of Roof-Surface Location Southern states and Pacific slope Central states Rocky Mountain states New England states Northwest states Pitch of roof V2 * t a- o o- 5 0-10 o-io 0-12 V3 * t o- 5 7-10 10-15 lo-is 12-18 * t o- 5 IS-20 20-25 20-25 25-30 % Vq or less 5 30 35 40 45 Columns headed by an asterisk (*) are for slate, tile, or metal; those headed by a dagger (f) are for shingles. Wind-Pressure.* For roofs having a pitch of 5 in or more to the foot, an allowance must be made for wind-pressure. For trusses of the Fink, fan, king, or QUEEN TYPES, the usual practice is to include the wind-pressure with the vertical loads, and to make a single allowance for both wind and snow, as during a gale snow is not likely to stay on a steep roof. When the wind-pressure is added to the vertical loads, the allowance for wind and snow combined should not be less than indicated in Table VIII. Table VIII. Allowance for Wind and Snow Combined in Pt)unds per Square Foot of Roof-Surface Location Northwest states New England states Rocky Mountain states Central states Southern and Pacific states . Pitch of roof 60° 30 30 30 30 30 30 30 30 30 30 Vs 25 25 25 25 25 30 25 25 25 25 37 35 27 V^ 45 40 35 30 No roof -truss should be proportioned for a total load of less than 40 lb per sq ft of roof-surface except flat roofs in warm climates. For trusses having spans exceeding 100 ft (except trusses for flat roofs) and for trusses in which a partial f (See, also, Chapter XXX, page 1199, and pages 1394 and 1717-) Roof-Loads. Data, Weights, Materials, Methods 1053 load may produce maximum stresses, or call for counterbracing, as is the case in QUADRILATERAL TRUSSES, and trusses with CURVED CHORDS, the stresses for all the different loadings should be found separately and each member of the truss proportioned for the maximum stress to which it may be subject under any possible combination of loads. For determining the stresses due to wind-pres- sure alone the force of the wind is usually assumed to act in a direction normal, that is, at right-angles, to the slope of the roof. This force is commonly based on a horizontal wind, producing a pressure of 30 lb against a vertical surface. This corresponds to a wind-velocity of nearly 100 miles per hour. According to Marvin's formula, P = 0.0032 F2 where P = the pressure in lb per sq ft against a surface normal to the direction of the wind and V = the velocity in miles per hour. For P = 30 lb, V = 96.3 miles. The normal pressure per square foot of roof-surface corresponding to pressures of 20 and 30 lb per sq ft against a vertical surface is given in Table IX. Table IX. Wind-Loads in Pounds per Square Foot of Roof-Surface* Inclination of roof 5 10° 15° 21° 48' = i,^-pitch 26° 34'=i4-pitch 30° 33° 4i'=V3-pitch 40° 45° 0'= 1/2 pitch. 60° and above. . , Normal pressure P„, pounds per square foot P=30 lb S.I 10. 1 14.6 19.8 22.4 24.0 25. 5 26.7 28.3 30.0 P = 20lb 35 6.8 9-6 13 I 14.0 16.0 17.0 18.2 18.9 20.0 The values in Table IX are based on Duchemin's formula, ^'^"^H-sin^^ in which P is the pressure per square foot on a vertical surface, Pn the normal component of pressure and the angle of inchnation of the roof wfth the hori- zontal. The wind not only produces a pressure upon the windward side of the roof but a suction upon the leeward side; therefore all roof-covering should be securely fastened, all joints in the trusses so constructed that they will resist tension and compression, and the trusses themselves securely anchored to the supports. Variations in Loading for which Stresses should be Found. To deter- mine the maximum stresses under any possible condition of loading, stresses should be found for the following cases: (i) Stresses due to permanent dead loads, (2) Snow covering only one side of roof, (3) Snow covering entire roof, ». (4) Wind on side of truss nearer the expansion-end, (5) Wind on side of truss nearer the fixed end. ♦ (See, also, Chapter XXX, page 1199, and pages 1394 and 171 7.) 1054 Stresses in Roof-Trusses Chap. 27 \t is generally assumed that the maximum wind-pressure and the snow-load cannot act on the same half of the truss at the same time; hence the combina- tions for maximum stress will be either cases i and 3 or cases i, 2, and 4 or 5. If the trusses are supported on iron columns instead of on walls the wind-force is transferred to the foundations through the columns, producing a bending moment in the columns. The stresses in the columns, trusses and knee-braces sliould therefore be determined for the wind-pressures against the side of the building and roof. These pressures are obtained by multiplying the area of the vertical surfaces by the full pressure per square foot and the area of the roof by the normal component, given in Tabic IX. Kansas City Auditorium. For the trusses supporting the roof of the Kan- sas City Auditorium (Fig. 66, Chapter XXVI) stresses were computed for the following conditions: First, full dead and live load on both galleries and the roof-garden, and wind-pressure due to a velocity of 45 miles an hour; second, full dead load, snow-load, and gallery live load, wind-pressure 10 lb and no load on roof -garden floor; third, full dead load and 50 lb wind-pressure; fourth, full dead load and wind-pressure at 45 miles an hour, and full live loads on gallery and roof -garden on one side only. Snow-loads throughout were taken at one- third of the dead load. Examples showing manner of combining the stresses due to different conditions of loading are given on pages 1114 and 11 23-8. 2. Examples of the Computation of Roof-Loads* King-Rod Truss. Example i. The first example considers the roof and truss shown in Fig. 1, page 1048, which it is assumed represents truss 2 of Fig. 2. It is assumed that the timber is to be common white pine and that the roof is to be covered with %6-in slate of medium size on %-in sheathing. The ceiling is to consist of lath and plaster. The dead load of roof and truss per square foot of roof -surf ace is made up as follows: lb per sq ft For slate 7^/4 For sheathing. •. 3 For rafters 3 For purlins .• 2 For truss 3 Total 18V4. For wind and snow-load combined there should be allowed about 28 lb (the pitch being about 40°), which makes a total roof-k)ad of 46^/4 lb. To avoid fractions, however, the load is assumed to be 48 lb per sq ft. As the distance to truss I, Fig. 2, is 14 ft and to truss 3, 12 ft, the length of roof supported by the truss is 13 ft. The roof-area supported by the purlins at joint 2 is equal to the distance a multiplied by 13 ft; and a is one-half the distance from the wall- plate to the ridge-purlin, or 22 ft 8 in divided by 2, or 11 ft 4 in, or nV^ ft. Hence the roof-area supported at joint 2 is 11 V^ by 13 ft, or i47V^ sq ft. The roof-area supported by the purlins at joint 3 is 2 6 by 13 ft, or 12% by 13 ft, or i6oi.^ sq ft. Multiplying the roof-areas by the load per square foot, 48 lb, there results 7 072 lb for the load at joint 2; and 7 696 lb for the load at joint 3. The load at joint 4 is equal to that at 2, as the truss is symmetrical. The ceiling- loads at joints 6 and 7 are computed next. The ceiling-area supported at joint 6 is c X 13 ft, o* 8^ by 13 ft, or 107^4 sq ft. The area supported at joint 7 is 8% by 13 ft, or 114% sq ft. The actual weight of the ceiling i>er square foot is * In the following five examples all loads are considered as acting vertically. "J Examples o£ the Computation of Roof-Loads 1055 3 lb for the joists and lo lb for the lath and plaster; but where there is a large attic-space liable to be used for storage it is well to make a small allowance, say 5 lb per sq ft, for any extra attic-load. Therefore, i8 lb per sq ft is allowed for the weight of the ceiling, which makes the weight at joints 6 and 8, 107^4 sq ft by 18 lb per sq ft, or i 930 lb; and the weight at joint 7, 114% sq ft by 18 lb per sq ft, or 2 067 lb. As soon as computed, the roof and ceiling- loads should be marked on a truss-diagram, as in Fig. 10. The roof and ceiling- loads at joint I are transmitted directly to the wall and need not be taken into account in determining the stresses in the truss. Queen Truss. Example 2. It is required to compute the joint-loads for the truss shown in Fig. 3, page 1049. ^'l timber is to be of spruce and the roof is to be covered with shingles on i-in sheathing. The ceiling is to be of lath and plaster. The dead load is: lb per sq ft Weight of shingles 2 V^ Weight of sheathing 3 Weight of rafters. 2^4 Weight of purlins 2 Weight of truss 3 Total dead load per sq ft 1 2% Allowance for wind and snow. * 30 Total roof-load in pounds per square foot 42% For the weight of the ceiHng it is well, for a truss of this kind, to allow at least 20 lb per sq ft. It will be assumed that the trusses are to be spaced uniformly 15 ft on centers. Then the roof-area supported at joint 2 is 9% by 15 ft, or 147^2 sq ft, and the load at this joint is 6 306 lb. The purlin at joint 3 supports the roof, from a point midway to joint 2, to the ridge, or 6 = 4 ft 1 1 in -|- 8 ft 5 in, or 13 ft 4 in. The roof-area supported at this joint is isVs by 15 ft, or 200 sq ft, and the load is 8 550 lb. The loads at joints 4 and 5 are equal respectively to those at 3 and 2. For the ceiling-loads at joints 7 and 8 there is an area to be supported equal to 12% by 15 ft, or 182 V2 sq ft, which, multiplied by 20, gives 3 650 lb. Scissors Truss. Example 3. For this example the church-roof shown in section in Fig. 4 is considered. In this roof the trusses take the place of the rafters and ceiling-beams, the sheathing spanning from truss to truss and the laths for the ceiling being nailed to iV4 by 2V^-in furring strips, spaced 12 or 16 in on centers. Assuming that the parts of the trusses have the dimensions indi- cated in the figure, and that the wood is white pine, the actual weight of one truss is about i 200 lb. The roof-area supported by one truss is 170 sq ft, and hence the weight of the trusses is about 7 lb per sq ft of roof-surface. This weight is more than twice that given in Table IV, owing principally to the close spacing of the trusses and also to the small dimensions of their members. The weight of the sheathing and shingles is about 5^^ lb and 30 lb is allowed for wind- pressure. The roof is too steep for snow to lodge on it. This gives a total roof- load of 421.^ lb per sq ft of sloping surface. For the weight of the ceiling 12 lb per sq ft is ample, as no load other than its own weight is likely to come upon it. The roof-area supported at joint 2 is 10% by 2V2 ft, or 27 sq ft. The area sup- ported at joints 4 and 5 is equal to 12^3 by 2^^ ft, or 31 sq ft for each. The ceiling-area supported at joint 3 is 14^^ by 2I/2 ft, or 35V2 sq ft. Multiplying each joint-area by the corresponding loads per square foot, there results i 148 lb 1056 Stresses in Roof-Trusses Chap. 27 * for the load at joint 2, i 318 lb for each load at joints 4 and 5, and 426 lb for the load at joint 3. Truss over Car-Barn. Example 4. In this example the roof is of corru- gated iron, supported by a steel truss of the shape shown in Fig. 55, Chapter XXVI. This truss supports nothing but the corrugated iron, the purlins and the pressure due to wind and snow, the use of the building not requiring the suspending of any load from the trusses. In figuring the dead loads for such a roof, the sizes of the purhns and the gauge of the iron should first be definitely Fig. 4. Scissors Truss. (See, also, Fig. 24 and Chapter XXVIII, Fig. 2) fixed, so that the weight per square foot of roof may be accurately determined. In this instance the purlins are 5-in I beams spaced 4 ft 9 in on centers, and weighing 10 lb per linear foot. The weight of the purlins per square foot of roof is therefore equal to 10 lb divided by 4%, or 2.1 lb. For a span of 4 ft 9 in the corrugated iron should be No. 18 gauge (see Corrugated Iron, Part III, page i6ot) weighing 2 lb per sq ft. For the weight of the truss and bracing the weight taken is that given in Table V for a span of 100 ft and V4-pitch, 10.8 lb.* This gives a total dead load of 14.9 lb per sq ft of sloping surface. For wind and snow we should allow 22 lb per sq ft if the building is situated in the Central states, making the totiil roof-load 36.9 lb per sq ft. It is quite generally recommended, however, that no roof should be designed for a load less, all told, than 40 lb per sq ft; the joint-loads, therefore, should be computed on that basis. The only loaded joints in this truss are those under the purlins. The trusses are spaced 19 ft 2^4 in and the purlins 4 ft 9 in on centers, the roof- area supported at each upper joint being 91 sq ft. The joint-loads, therefore, should be figured at 3 640 lb. Even for the locality in which it was built, this ♦ The actual weight of this truss and bracing was 4 lb per sq ft of sloping surface, which is remarkably small. Examples of the Computation of Roof-Loads 1057 is a very light roof; and it would hardly be considered safe for states further north or west. Truss for Flat Roof. Example 5. This truss is for a flat roof (Fig. 5). The timber is of spruce and there is a five-ply gravel roof and a plastered ceiling. For the dead load we have, lb per sq ft Weight of roofing 6 Weight of sheathing 3 Weight of rafters 2^4 Weight of purlins 2 Weight of truss, about , 4^4 Total dead load in pounds per square foot 17^/^ No allowance is required for wind-pressure, but the snow-load is a large per^ centage of the total load in any of the Northern states, as indicated in Table VII. ■^ g'l^ ^ ^g". ^1 o'x e'Rafters Fig. 5. Howe Truss Assuming that the building is located in one of the Central states, 30 lb per sq ft should be allowed for snow, making the total roof-load 47!/^ lb. The plaster ceiling and the ceiling- joists weigh about 12^/4 lb and as the roof-space is not likely to be used for storage, 13 lb per sq ft is a sufficient allowance for the ceil- ing. Assuming that the trusses are to be uniformly spaced, 14 ft on centers, the roof-area supported at joint 2 is 9V^ by 14 ft, or 133 sq ft, and the area sup- ported at joint 4, 9% by 14 ft, or 135^/^ sq ft. The ceiling-area supported at joint 3 is 91^^ by 14 ft, or 130% sq ft and at joint 5, 9 by 14 ft, or 126 sq ft. Mul- tiplying each of these areas by the corresponding load per square foot, we have 6 317 lb for the load at joint 2, 6 428 lb at joint 4, i 699 lb at joint 3, and i 638 lb at joint 5. In practice it is hardly worth while to compute the stresses closer than 100 lb, so that the loads may as well be put down at an even 50 or 100 lb above the loads obtained by computation. When the roof is supported by purlins, there are often some joints of the truss which have no load. Thus for the truss shown in Fig. 16, Chapter XXVI, there are no loads on joints 2, 6 and 10. The roof-area supported at joint 4 (Fig. 16) is equal to one-half the distance OB multiplied by the distance halfway to the truss on each side. If the lower chord supports ceihng-joists, there is a load at each of the joints 3, 5, 7, 9, etc. Stress-diagrams can be drawn for any arrangement of loads, the important point being to compute the loads exactly as they are placed on the truss. These five examples illustrate fairly well the method of computing the loads on different types of trusses. Other special cases of loading should be com- puted on the same principles. 1058 Stresses in Roof-Trusses Chap. 27 3. Determination of Stresses by Computation Stresses. To determine the stresses, a diagram of the truss, composed of single lines representing the central axial or median lines of the truss-members, should first be carefully drawn to a scale and the loads at the different joints indicated by arrows and numbers as in Figs. 10 and 12. If the center lines of the members, as they are actually placed, do not intersect at common points, they must be made to do so in the diagram, as the stresses can be computed only on the assumption that the center lines of all members meeting at any joint intersect at a common point. In wooden trusses it is not always practicable to place the members so that their center hues meet in a common point at each joint; but this condition should obtain as nearly as practicable, and in steel trusses the joint-connections should be made so that the hnes passing through the centers of gravity of the cross-sections of the members meeting at a joint intersect in the same point. Table X. Coefficients for Determining the Stresses in Simple Fink and Fan Trusses , WHEN PANEL-LOADS ARE ALL EQUAL ^\ < 1 = span R^=^1.5 P i^span |R^=2.5P Simple Fink Truss Simple Fan Truss To find the stress in any member, multiply its factor by the panel-load, P SIMPLE FINK TRUSS Member A B D F. G. K A B. C. D E. F. G. K Kind of stress .Compression Tension //A=3 2.70 2.15 0.83 2.25 1.50 0.75 //A =3. 464 = 30° 300 2.50 0.87 2.60 1.73 0.87 //A=4 3 35 2.91 0.89 3 00 2.00 I 00 l/h=S 4.04 3.67 0.93 3.7s 2.50 1. 25 SIMPLE FAN TRUSS Compression 451 5.00 5. 59 6.73 3.54 4.00 4-55 5.59 " 3.40 4.00 4.70 5.99 0.93 I. CO 1.08 1. 21 " 0.93 1. 00 1.08 1. 21 Tension 3. 75 4.33 5.00 6.25 " 2.25 2.60 3.00 3.75 1.50 1.73 2.00 2.50 Determination of Stresses by Computation 1059 Computation of Stresses. As a general rule^ the stresses in a roof-truss can be determined much more readily by the graphic method than by mathemati- cal COMPUTATIONS and with as close a degree of accuracy as is necessary. Inhere are a few forms of trusses, however, for which the stresses can be more easily determined by computation. Such trusses must be symmetrical in shape and the joint-loads all alike, as is quite frequently the case with simple steel roofs having no ceiling-load. Tables X to XIII give constants by which the stresses in Fink and fan trusses may be readily computed simply by multiplying the constant by the panel or joint-load. These tables apply, however, only when the rafter is divided by the struts into equal spaces, giving equal panel -loads. For any other conditions the stresses should be determined by the graphic method. Table XI. Coefficients for Determining the Stresses in an Eight-Panel Fink Truss WHEN PANEL-LOADS ARE ALL EQUAL C^AZ -^ = span Ri=3.5P Eight-panel Fink Truss To find the stress in any member, multiply its factor by the panel-load, P Member Kind of stress //A=3 ^^=3.464 =30° //A=4 l/h = 5 A. B. C. D. E. F. G. I.. K. L. M. N. O. P. Compression Tension I tt/ij no bjioi 6.31 5.76 5-20 4-6s 0.83 I 66 0.83 0.-7S 0.7s I. SO 2.25 5. 25 7.00 6.50 6.00 5.50 0.87 1.73 0.87 0.87 0.87 1.73 2.60 6.06 >\ h 7.83 7.38 6.93 6.48 0.89 1.79 0.89 1. 00 1. 00 2.00 300 7.00 942 9 OS 8.68 8.31 0.93 1.86 0.93 1. 25 1.25 2.50 3-75 %.n 1060 Stresses in Roof-Trusses Chap. 27 Table XII. Coefficients for Determining the Stresses in Cambered Fink and Fan Trusses WHEN PANEL-LOADS ARE ALL EQUAL AND THE CAMBER EQUALS ONE- SIXTH THE RISE Fig.E To find the stress in any member, multiply its factor by the panel-load, P TRUSS LIKE FIG. A Member Kind of stress l/h-- ///i=3 464 = 30° l/h=4 l/h = 5 A B. D F. G. K Compression Tension 3.64 3-09 0.83 3.07 1.80 1.43 4.13 3.63 0.87 362 2.08 1.69 4.70 4.25 0.89 4.24 2.40 1.98 5. 78 5-41 0.93 5.40 3 00 2.52 TRUSS LIKE FIG. B A. B. C. D. E. F. G. K. Compression 6.09 6.88 7.83 9.64 •• 4.89 5. 63 6.48 8.10 •• 4.96 5.88 6.93 8.89 " 1.04 1. 15 1.26 1.49 " 1.04 LIS 1.26 1.49 Tension 5.12 6.03 7.07 9.01 2.70 3.12 3.60 4.50 2.66 3.13 3.67 4.69 Table XIV gives coefficients which are general for any span and depth for eight-panel roof-trusses with the Howe and Pratt types of bracing. Tables XV and XVI give .formulas for computing the stresses in symmetrical Howe and Pratt trusses which are symmetrically loaded. The coefficients are given for trusses having an odd number of panels. For the Howe truss with an even number of panels the coefficients for the center load on the top chord are each d'iv5ued by two. For the center load on the bottom chord the coefficients are also divided by two, except that for the center vertical, which remains unity. Determination of Stresses by Computation 1061 For the Pratt truss with an even number of panels the coefficients are divided by two for the center loads for all pieces, except that for the center vertical for loads on the top chord, the coefficient remains unity. For the young architect or engineer these tables will be found useful in furnishing a check upon stresses determined by graphic methods. Table Xin. Coefficients for Determining the Stresses in an Eight-Panel Cambered Fink Truss Sc- WHEN PANEL-LOADS ARE ALL EQUAL AND CAMBER EQUALS ONE-SIXTH THE TOTAL RISE 1« i Rf 3.5 P To find the stress in any member, multiply its factor by the panel-load, P Member A, B. C. D E. F. G. I. K L. M N. O. P. Kind of stress Compression Tension l/h=3 8.49 7-94 7-39 6.83 0.83 1.66 0.83 1.02 1.02 2.87 3.89 7.17 6.15 3.60 ^/A= 3.464 =30° 9 63 9.13 8.63 8.13 0.87 1.73 0.87 1,21 1. 21 3.37 4.58 8.44 7-23 4.16 l/h=4 10.96 10. SI 10.06 9.61 0.89 1.79 0.89 1. 41 1. 41 3.96 5.37 9.90 8.48 4.80 //A=5 13.49 13. II 12.74 12.37 0.93 1.86 0.93 1.80 1.80 5.04 6.8s 12.61 10.81 6,00 1002 Stresses in Roof-Trusses Chap. 27 Table XIV. Coefficients for Eight-Panel Roof-Tnisses Sec g^^L^^w^-HlT Triangular Howe Trues Triangular Pratt Trusfl Spa.n-nh=l- Ceiling- loads, Length of member .75V«-+4 o.i25AVw2-t-4 .SoV«2+4 " .25Vw2+4 .OoV«-4-4 •♦ 1.75 « 0.125 nh 1.75 n " 1.50 n " o.i25A's/«2-f64 Stress = coeflBcient X P or p. For a half-truss supported at A and B, reduce all top chord coefficients by \^n^-{- 4 and all bottom-chord coefficients by n. The coefficients for the web-m«mbers used remain unchanged. Determination of Stresses by Computation 1063 Table XV. Coefficients for Howe Trusses which are Symmetrical About the Center of the Span and Symmetrically Loaded Member L] and U^ Li and C/3 L3 and f/4 U D^ D^ Dz r>i Fi F2 F3 Fx Vi. F3 7 panels Pi P2 i.o • 1.0 1.0 1.0 1.0 1.0 1.0 5 panels Pi 1.0 1.0 3 panels Px a^h For loads Pi, P2, etc., the coefficients for the chords and diagonals are the same as given for the loads Pi, Po, etc. The coefficients for the verticals for loads Pi, P2, etc.. are given in the supplementary table below the general table. Tension is indicated in the truss diagram by light lines. 1064 Stresses in Roof-Trusses Chap. 27 Table XVI. Coefficients for Pratt Trusses which are Symmetrical About the Center of the Span and Symmetrically Loaded P, p,- p, p, p, p. Member Li and L2 Lz and Ui L4 and Uz u,=u... Di D2 Dz D, Vi V2 F3 V2. Vz. 7 panels Pi {a+b+c)^h y/b^+h^^h i.o i.o 5 panels Pi {a-\-b)^h 3 panels Pi a-^A For loads Pi, p^, etc., the coefficients for the chords and diagonals are the same as given for the loads Pi, P^, etc. The coefficients for the verticals for loads pi. Pi, etc., are given in the supplementary table below the general table. Tension is indicated in the truss-diagram by light lines. Determination of Stresses in Roof-Trusses by Graphic Methods 1065 4. Examples Showing Use of tables in Stress-Computations Simple Fan Truss. Example i. In this example a simple fan truss of 36-ft span is considered. The distance on centers of trusses is 12 ft. The height of truss is 9 ft, or l/h = 4. The total load per square foot of roof is 40 lb. The length of rafter is 20 ft, nearly. The panel-load, P=2%xi2X40 = 3 200 lb. Then from Table X, Stress in lower end of rafter ^ = 3 200 x 5.59 = 17 888 lb Stress in ends of main tic Z*" = 3 200 x 5.00 = 16 000 lb Stress in center of main tie G = 3 200 x 3.00 = 9 600 lb Stress in braces D and £ = 3 200 X 1.08 = 3 456 lb Stress in tie K = s 200 x 2 = 6 400 lb Five-Panel Howe Truss. Example 2. (Table XV.) A five-panel Howe truss is considered, for which ^ = 6 ft, a = 9 ft, 6 = 10 ft and c = 12 ft. Let the trusses be spaced 10 ft on centers, the roof-load be 40 lb per sq ft and the ceiling- load 15 lb per sq ft. The panel-loads become: Pi= V2( 9+10) (ioX4o) = 3 8oolb ) _ ,, /'I =¥2(9+10) (10X15) = 1400 lb j -5 200 ID P2 = ¥2(10+12) (10X40) = 4 40olb (^ _ „ p2=V2 (10+ 12) (loX 15) = I 700 lb S -^ '°^^^ Li and i/2 = % X 5 200 + % \ 6 100 =17 000 lb Z2 and f/3 = % X 5 200 + ^% X 6 100 = 27 100 lb Di = 10.82/6 (5 200 -f- 6 100) = 20 400 lb D2 == 1 1.66/6 X 6 100 =11 90b lb Fi = 4 400 -f- I 400 + I 700 = 7 500 lb F2 = I 700 lb In the above results all values between 50 and 100 have been considered 100. 5. Determination of Stresses in Roof-Trusses by Graphic Methods The Graphic Method is the simplest and in most cases the quickest method of determining the stresses in a roof-truss; and it has, besides, the additional advantage of being applicable to any true truss-form or any arrangement of loads. There is also less chance of making a mistake in the graphic method than in the method of numerical computation, as an error in the graphical analysis almost always becomes manifest. When the principles are under- stood, STRESS-DIAGRAMS cau be very quickly drawn, without the aid of books or tables. For the forms of trusses in common use, the method of drawing the stress-diagrams is quite simple; and a careful study of the following examples, supplemented by a little practice in drawing the diagrams, should enable any architect, draughtsman, or builder to understand the principles involved in the GRAPHICAL ANALYSIS OF ROOF-TRUSSES. Principles Upon Which the Graphic Method is Based. To thoroughly understand this method, a knowledge of the composition and resolution of FORCES, as explained in Chapter VI, is essential; and before studying this subject the student should read carefully pages 288 and 289. . The theorems stated and explained on these pages form the basis of graphic statics. In the graphic method all forces, including the loads, are represented by straight lines, and the directions of the forces must be constantly kept in mind. Often it is of assistance to indicate the direction of a force by an arrow- head, as explained on page 289. The direction in which a force acts with refer- ence to a body indicates, also, whether it is a pushing or a pulling force, or whether the member on which the force or in which the stress acts is in compres- sion or TENSION. This is more fully explained in the following pages, and also in connection with several of the stress-diagrams. 1066 StFesses in Roof-Trusses Chap. 2T Forces and Stresses which Act On and In a Truss. Every stress-dia- gram represents three sets of forces, viz., the external loads, the supporting forces or reactions, and the stresses in the truss-members. Supporting Forces or Reactions. For a truss to remain in place, two ot the conditions for equilibrium are that the algebraic sums of the vertical and horizontal components of all the forces acting upon the truss must respectively equal 2sero. Then the horizontal and vertical components of the supporting forces or reactions, taken together, must respectively equal the horizontal and vertical components of the loads. The lo.vds and reactions are considered as the external forces acting on the truss and form part of the stress-diagram. Symmetrical Loads. When the loads or vertical forces are symmetrical on each side of the middle of the span, the supporting forces are equal, and each is equal to one-half the total load on the truss. Unsymmetrical Loads. When the loads are not symmetrical about the middle, either in regard to point of application or to magnitude, the supporting forces are unequal and in most cases must be determined before the stress-dia- gram can be drawn. The supporting forces for unsymmetrically loaded trusses may be computed by the method of the moments of forces, explained on pages 322 to 324. Stress-Diagrams for Vertical Loads. Before the stress-diagram for a truss can be drawn, it is necessary to make a skeleton drawing of the truss, representing the central or median lines of the members as explained on page 1058. This diagram, called the truss-diagram, should be drawn on the same sheet of paper as the stress-diagram, for convenience in drawing the latter. The truss-diagram should also have all of the loads which come on the truss indicated by arrows and figures, as in the following examples. Supporting Forces. The supporting forces, also, should be indicated on ithe truss-diagram as in Fig. 10. These forces are determined as explained on pages 322 to 324. Lettering the Truss-Diagram. After the truss-diagram is drawn, it is con- venient to letter it according to the method known as Bow's Notation, which allows a ready comparison of the truss-diagram and the stress-diagram, and also enables the student to readily draw the stress-diagram and to immedi- ately determine the ch.vracter as well as the magnitude of the stresses. The essential principle of this method is the lettering of each space on each side of every external force and of every member of the truss, so that on the truss- diagram a truss-member or external force is denoted by the letters on each side of it. When the stress-diagram is drawn, it will be found that the same letters come at the ends of the lines representing the external forces and the stresses in the truss-members. The Simple Triangular Frame is much used in building construction, and most forms of roof-trusses are combinations of such triangles. It is, therefore, worth while to. show how easily the above principles may be used to determine the stresses in such a frame. Diagram i, Fig. 6, represents the truss-diagram of a triangular frame properly lettered. A load of 100 lb is applied at the apex. The weight of the frame is disregarded. In diagram 2, a vertical line ab is drawn, 1 in long (say to a scale of 100 lb to the inch), representing the force AB. From b, bd is drawn equal to R2 and from d, da equal to Ri. These three lines represent the external forces acting on the truss, and the polygon abda, called the force-polygon, is always a closed figure if the forces are in equilibrium. Since the force AB is vertical and Ri and R2 are parallel to AB, the figure abda is a straight Une, bd and da coinciding with ab. If the external forces form a closeo Determination of Stresses in Roof-Trusses by Graphic Methods 1067 I'OLYGON when laid ofif to scale, usually in order, the frame or truss upon which they act will not be moved either vertically or horizontally by the forces. The FORCE-POLYGON should always be drawn and closed before any attempt is made to determine the stresses in the members of the truss. The stresses in the members of the truss will now be found, beginning with those meeting at joint r. Pieces A C and CD meet at this joint. The stresses in these two pieces and Ri are in EQUILIBRIUM and, consequently, if laid off in order will form a closed pigure as shown in Chapter VI. In diagram 2, da represents Ri in magnitude and direction. From a draw a line parallel to ^C and from d a line parallel to CD O 1. Tt-uss-diagratn Fig. 6. Triangular Frame 2. Stress-diagram and prolong them until they intersect at c. ac is the stress in AC, and cd that in CD. ac, cd and da, or Ri, are in equilibrium since they form a closed fig- ure. Taking the forces in order, da, or Ri, is known to act towards the joint. The direction ac is also towards the joint and hence the stress is of the same character as the force Ri and the piece ^C is in compression. AC pushes against the joint as Ri does. Continuing around the stress-polygon dac, in the same direction, cd acts away from the joint and the stress in CD is opposite in character to the force R\, or CD is in tension. CD pulls away from joint i*. At joint 2, the stresses in the pieces BC and CA and the force AB are in equi- librium. The sides of the stress-polygon are ah, he and ca (diagram 2). The force ah which represents the load of 100 lb acts down and towards the joint, he and ca also act towards this joint, showing that the stresses in BC and CA are of the same character as the force AB, or that the pieces push against the joint and that each is in compression. At joint 3, the two pieces meeting are DC and CB. The stress-polygon is hdc. Here hd acts towards the joint, dc away from the joint, and ch towards the joint. As found before, the stress in DC is tension and that in CB, compression. Diagram 2 is made up of three stress-polygons, one for each of the joints shown in diagram i. Each of these polygons is considered independently when determining the magnitude and character of the stresses or forces. This is important to remember when the stress-polygons are combined as in diagram 2. In determining the character of the stress in AC, for example, from the stress-polygon dac for joint i, the force ac acts towards joint i, while from the stress-polygon ahc for joint 2, ca acts towards joint 2. In both cases the piece ^C is pushing against the joints at its ends and is in compression. If arrow-heads are used in indicating the di- rections of the forces in the stress-polygons, they should be erased as soon as the characters of the stresses for the joint being considered have been found; otherwise, where polygons are combined as in diagram 2, each line will have two arrow-heads pointing in opposite directions, leading to confusion. . Arrow-heads may be placed upon the truss-diagram. Each piece will have two arrow-heads, one at each end, referring to the joint at the end. When the arrow-heads point 1068 Stresses in Roof-Trusses Chap. 2\ Piece in Tension away from each other the piece is in compression, and when they poin towards each other the piece is in tension. It is important to keep in mind the direction in which the forces and stresse are considered in order, in going around the truss or around a joint. In Figs 6 and 8 the curved arrows, show that a clockwise direction has been chosen This makes the stress-Hnes of the stress-diagram come on the left of the load line. This direction has been taken for all the trusses in this chapter, excep for a few diagrams for wind-loads. The stresse could have been deterrnined just as well b] taking a contra-clockwise direction. If two men pull on the two ends of a rope exerting pulling forces of equal intensity, thi TENSiONAL STRESS in every cross-section of th rope is equal to the force with which one mai pulls; and each end of the rope pulls away fron the man holding it, with a force equal in magnitude to that which he exerts Thus if each man exerts a force of loo lb the stress in the rope is loo lb an( each end of the rope pulls away with a force of loo lb. If the men push agains the two ends of a piece of timber with a force of loo lb, the timber pushe against each man with a force of loo lb, although the entire compressivj stress in every cross-section of the timber is but loo lb. Consequentl: stress-lines are sometimes drawn with arrow-heads pointing towards eacl other, as at A, Fig. 7, denoting tension; or with arrow-heads pointin] b +58 d D^ Fig. 7. Piece in Compression Indication of Character of Stress D 1 +58 p=ioo C 2 -1-58 3 ^^\ B 1 4- 1/ 2=66^ o 1. Truss-diagram c 1 +58 2 3 \,^^ B A / \ P=100 ' R2=6 3. Truss-diagram Fig. 8. Trussed Beam 4. Stress-diagram in opposite directions, as at B, denoting compression. It is better, however to omit arrow-heads on stress-lines, putting them . on lines representing external forces only. The stress in any member of a truss acts ir opposite directions at the two ends of the piece. This is an important trutl to remember jn drawing stress-diagrams. The Trussed Beam. Fig. 8 shows a load supported by a beam, post or strut and two ties instead of by two struts and a tie. The effect on the rod forming Determination of Stresses in Roof-Trusses by Graphic Methods 1069 the two ties is the same whether the load is applied as shown in diagram i, or as shown in diagram 3. Considering the case shown in diagram i: The force- polygon is dcod (diagram 2); the sides of the stress-polygon for joint 1 are od, db and ho, the stress in DB being compression, and that in BO, tension. For joint 2 the sides of the stress-polygon are dc, ca, ah and hd, the stress in CA be- ing compression; that in AB, compression; and that in BD, compression. For joint 3 the sides of the stress-polygon are ac, co and oa. The stress in ylC is com- pression; and that in OA, tension. The condition shown in diagram 3, where 1. Truss-diagram Fig. 9. Crane Truss 2. Stress-diagram 7700 H— -SlO- -- 'rr; -^ r-T — Tt: r^'ir^Vfi \ the load is suspended from joint 4, leads to a different form of stress-diagram, but the method of construction remains the same. The stresses in the pieces are the same with the exception that the 'stress in the piece A Bis zero for the case shown in diagram 3. The Crane Truss. Fig. 9, diagram i, shows the truss-diagram of a crane carrying a vertical load at joint 2. The external forces acting on the frame are, the load at joint 2, the supporting force at joint 3, and the stress in the guy CA . Since the frame is in equilibrium under the action of these three forces, they meet in a point. This provides a ready method for determining the direction and magni- tude of the supporting force at joint 3 . Prolong the line CA and draw a vertical line through joint 2 until it intersects the line CA, prolonged, at O; then, since the sup- porting force must pass through jofnt 3, sO is the direction of this force. The force -poly- gon is now drawn. The sides of this polygon are he, ca and ah. ca is the stress in the guy CA which is in tension. The stress-polygons for each joint can now be readily drawn and the stresses in the members of the frame determined (diagram 2). The following examples, worked out in detail and with considerable repeti- tion, will enable the student to grasp the principles of the graphic method for determining stresses in framed structures. King-Rod Truss. Example i. Fig. 10 shows the truss-diagram of tho truss represented in Fig. 1, properly drawn, lettered and figured, ready for R2=U785 Fig. 10. King-rod Truss. Truss-diagram 1070 Stresses in Roof-Trusses Chap. 27 drawing the stress-diagram. The supporting force at the left is SM, the load at joint I is MA, the bottom of the rafter isAE, the left portion of the tie-beam or bottom chord is ES, etc. The loads acting at joints i, 2, 3, 4 and 5 are designated as MA, AB, BC, CD and DN respectively, and those at joints 8, 7 and 6 as OP, PQ and QS respectively. It makes no difference what letters are used, except that it is better to first letter the outside spaces consecutively and then the inside spaces. Force-Polygon. The force-polygon is now constructed by laying off to scale (Fig. 10a) the external forces in order, beginning with the force MA, and ..^ following with AB, BC, CD, DN laid off downward, NO laid off upward, OP, PQ, QS laid off downward, and SM laid off upward. If the work is correct, these forces form a closed figure. Stress-Diagrams. The stress-dia- gram is drawn by taking the forces acting on the joints in consecutive order, com- mencing at one of the supports. It is convenient to start with the support at the left, or at joint i. In actual com- putations it is not necessary to number the joints, but in order to refer to them in the description it is necessary to num- ber them in the illustrations. Commenc- ing at joint I, the first step in drawing the STRESS-DIAGR.4M js to draw a vertical line to a scale of pounds-to-tiie-inch to Stress- represent the supporting force SM. This hne is the line sm already drawn in con- structing the force-polygon (Fig. 10a) which might be drawn to the scale of 16 000 lb to the inch. It is best to use a scale as large as convenient in order to have a relatively small stress- diagram. An engineer's scale, one divided to loths, 2oths, 30ths, etc., of an inch, is found most convenient for these drawings. The small letter s is placed at the bottom of the line sm, and the letter m at the top. From m is laid off ma representing the load MA . A line is then drawn from a, parallel to the rafter AE, and a line from s parallel to the tie-beam ES. The two lines meet at e, and ae represents the stress in AE and es the stress in ES. The supporting force, represented by sm, acts upward, and the others follow in rotation, showing that ae acts towards joint i and that the member ^£ is in compression, and show- ing that es acts from joint i and that the member ES is in tension. Consider next the stresses at joint 6. Commencing at the bottom of the joint and going around to the left, the first force that is known is the load QS, or i 930 lb, which is measured to the scale used from g to s, downward, as the loads act downward. The point ^ was located in drawing the stress-polygon for joint i, and q and s in constructing the force-polygon for the external forces. The next stress that is known is the stress se which has just been determined. As this stress acts to the right from joint i, it will act to the left from joint 6, as the stresses in the two ends of a strut or a tie act in opposite directions, as explained on page 1068. The stresses in EE' and E'Q are not known, so from e a line is drawn parallel to EE' and extended so that a line drawn from its extremity e' and parallel to E'Q closes on q. The lines ee' and e'q are thus found, which repre- sent the stresses in EE' and E'Q respectively. Starting with $e, tl>e stress i^ Fig. .;JOiU>jTfiing-rod Truss. .,,;. ,,|j diagram Determination of Stresses in Roof-Trusses Dy Graphic Methods 1071 SE, known to be tension and acting from joint 6, and going around the diagram in rotation, EE' and E'Q are found to be in tension. At joint 2 the stresses in E'E and EA and the force or load AB are known, leaving the stresses in BF and FE' to be detennined. From a lay oflf downward ab equal to the force or load AB. From b draw a line parallel to BF, and from e' a line parallel to FE'. Prolong these lines until they intersect at /; then bf is the stress in BF and fe' that in FE'. Both members are in compression. At joint 3, the un- known forces or stresses are the stresses in CG and . GF. From c draw a Una parallel to CG, and from / a line parallel to GF. The two lines intersect at g, and eg is the stress in CG and gf that in GF. CG is in compression and GF in tension. Since the truss is sym- metrical and symmetri- cally loaded, the stresses in the members on the right of the middle are the same as in those on the left. The stresses in the members on the left of the middle have been determined so that it is Roof Load iS lb. per Bq.ft. Ceiling Load 181b. per sq.ft. R,= 11785 1930 2070 1930 Fig. 11. King-rod Truss. Stresses not necessary to draw the stress-polygons for joints 4, 5, 8 and 7 R2= H785 It is good -practice to complete the stress-diagr.\m including the stresses for every joint in the truss. A closed symmetrical figure will result, unless some error is made in the construction, thus checking the work. The scale is now applied to the different lines of the stress-diagram and the magnitudes of the stresses obtained as indicated on the corresponding lines of the truss-dia- GR/\M (Fig. 11), In practice the diagrams of Figs. 10 and 11 are combined in ■ 'n\j lo T C Queen Truss. Truss-diagram. (See, also, Figs. 3, 53 and 54 and Chapter XXVIII, Fig. 1) one drawing. They are shown separately here merely to indicate the succes- sive steps in the drawing of the diagrams and in the determination of the stresses. The Queen Truss. Example 2. The diagram in Fig. 12 represents the center lines of the members of the queen truss shown in Fig. 3; and the loads indicated are those found in example 2, page 1055. The middle braces in the middle panel are indicated by dotted lines in the truss-diagram, because imder a symmetrical load there are no stresses in these members, and they are therefore not represented by lines in the stress-diagram. As the truss is sym- 1072 Stresses in Roof-Trusses Chap. 27 ii\iUi J I metrically loaded, each supporting force or reaction is equal to one-half the total load, or 1 8 500 lb. There are no purlins at joints i and 6 to carry rafters and ceiling-joists, which are supported by the walls of the building, so there are no external loads at these joints as in the previous example. The very small dead load due to the truss itself is neglected. To draw the force-polygon, first draw the vertical line qa (Fig. 12a) equal in leiigth, to some scale, to the magnitude of the left supporting force; then in rotation and at the same scale lay off the distances ab, be, cd and dg, downward; go, equal t6 the right supporting force, upward; and op and Pq downward, closing the figure at q. To construct the combined stress-diagram using the force-polygon just drawn, as a foundation, first consider joint i. From a draw a line parallel to AE and from q a line parallel to EQ. The triangle qae represents the three forces in equilibrium, meeting in a point and acting at joint i. As the supporting forces act upward, the arrow-head on qa points upward. Fol- lowing the sides of the stress-polygon qae in rotation, ae acts towards the joint and eq from the joint, showing that ae is in compression and eq in tension. Next determine the stresses acting at joint 2. The stress in EA is now known and represented by the line ea, and as the stress at joint 2 acts in a direction opposite to that at joint i, it now acts upward towards joint 2. The next force is the load, 6 300 lb, which acts downward. The point b has already been found by measuring from a a distance equal to 6 300 lb at the same scale as used in drawing qa. There now remain two stresses to be found for joint 2, those in BF and FE. Draw bf parallel to BF, and fe parallel to FE, the two lines intersecting at /. Then the sides of the polygon abfe represent respectively the magnitudes of the four forces acting at joint 2; and the character of the stresses is determined by the directions in which the stress-lines are drawn, in order, in going around the joint. In this case they all act toward the joint, and EA, BF and FE are in compression. The stresses acting at joint 3 or 7 may be determined next, as only two of them are unknown at either joint. Considering the external force and the three stresses acting at joint 3, the stress in FB has been determined and is represented by the line fb, which is drawn up- ward for this joint. The load or force BC, 8 550 lb, is known and is represented by be. ch is drawn parallel to CH, and hf parallel to IIF, closing the polygon. The length of ch determines the magnitude of the stress in CH and hf the stress in HF. The stresses in all the truss-members but HP are now determined. This stress is found by considering the force and stresses acting at joint 7. At this joint the force PQ, or 3 650 lb, and the stresses in QE, EF and FH, represented respectively by pq, qe, ef and fk, have been determined. The line hp, represent- ing the stress in HP, completes the polygon for j/ftint 7. Hence hp determines the stress in HP, and as ho is drawn from left to right, from the joint, HP is m tension. With reference to joint 3, the line ch is drawn towards joint 3 and hence CH is in compression. Scaling the lines in the stress-diagram (Fig. 12a) the figures shown by the side of the lines are obtained. They indicate the mag- nitude of each stress in pounds, the -f sign denoting compression, and the — sign, tension. The two foregoing examples illustrate the method of drawing the stress-diagrams for simple symmetrical trusses, symmetrically loaded. The truss-diagrams should be diavfxx in accordance with the measurements give^, Fig. 1!2a'. ' Qu6fen Truss. Stress-diagram Determination of Stresses in Roof-Trusses by Graphic Methods 1073 but to a scale of not less than Vs in to the foot; and the stress-diagram should be drawn, line by line, in accordance with the foregoing directions and the results obtained and compared with those given in the figures. A variation of loo or 200 lb for small stresses and less than 1% for large stresses may be ex- pected, but a greater variation indicates either that sufficient care has not been exercised in drawing the stress-Unes exactly parallel to the corresponding lines of the truss-diagram, or that an error has been made in drawing the truss-dia- gram, or in scaling the lines of the stress-diagram. After these two examples have been worked, a number of the following examples, also, should be solved, until the principles are fully understood. Truss for Museum of Fine Arts, St. Louis, Mo. Example 3. Fig. 13 represents the truss-diagram of the truss shown in Fig. 11, Chapter XXVI, f S^ O ie'o'l - Ro^4iai;o Fig. 13. Truss-diagram. Museum of Fine Arts, St. Louis, Mo. Fig. 13a. Stress-diagram the loads indicated being approximately those due to the roof and suspended floor below. The loads being symmetrically disposed, each supporting force is equal to one-half the total load, or 41 040 lb. The counterb races CC, shown in Chapter XXVI, are omitted from the truss because they have no stress when the truss is uniformly loaded. To draw the stress-diagram (Fig. 13a), first draw to scale the vertical line sa, equal to 41 040 lb, equal to Ri; and then ab and bs parallel respectively to AB and BS and representing the stresses acting at joint I. At joint 2, the line ba represents the stress in BA ; ac, equal to 7 200 lb, the load AC; cd, the stress in CD; and db the stress in DB. The polygon bacdb represents the forces in equilibrium acting at joint 2. At joint 3 there are three unknown forces; and as three unknown forces out of five in one polygon cannot be determined, joint 4, where dc and the load CF are known, is considered next. Measuring oQ the load cf, equal to 12 240 lb,' the stresses in FE and ED only are to be determined. These are found by drawing /g parallel to FE, and ed parallel to ED, the two lines intersecting at e. At joint 3, sb, bd, de and the force, qs are known, and eg and gq are drawn to close the polygon sbdegs. At 1074 Stresses in Roof-Trusses Chap. 27 joint lo the force pq, equal to 12 000 lb, and qg are known; and gg' and g'p are drawn to close the polygon. At joint 5, g'g, ge and ef are known and ih and hg' are drawn to close the polygon. Since there is no load at joint 5, / and i fall at the same point in the stress-diagram. The stresses in pounds, in the various members of the truss, are given in numbers on the corresponding lines in the stress-diagram (Fig. 13a). Triangular Howe Truss. Example 4. Consider the skeleton triangular Howe truss represented in Fig. 14 loaded as shown by the weight of the roof 10320 10320 M £ ^^'ioS20 [L 10320 ^^ 10.320' ^. Q «ooa P 3000 o 3000 N* 3000 1^ 3000 C> sooo ^ Fig. 14. Triangular Howe Truss. Truss -diagram ^sooo IX Fig. 14a. Triangular Howe Truss. above and a ceiling t>elow. To draw the stress-diagram, first draw to scale the supporting force qj, equal to 46 620 lb. Then lay off jk equal to 10 320 lb, kl equal to 10 320 lb, etc. Then draw the lines Ja and aq, and the three forces Bt the left support are known. At joint 0, pq and qa are known and ab and bp are drawn to close the polygon. At joint i, ba, aj and jk are known and kc and cb are drawn to close the polygon. At joint 2, op, pb and be are known and cd and do are drawn to close the polygon. At joint 3, dc, ck and kl are known and le and ed are drawn. At joint 4, no, od and de are known and ef and /« are Determination of Stresses in Roof-Trusses by Graphic Methods 1075 drawn to close the polygon. At joint ^, /e, el an.d Im are known and mg and gj are drawn. Joint 7 is considered next, for at joint 6 there are three unknown stresses; and by the graphic method three out of five forces, meetiiig in a point and in equilibrium, must be known in order to determine the other two. At joint 7, gm and mm' are known and mg' and g'g are drawn to close the polygon. This completes the determination ot the stresses in all the pieces for one-half of the truss and of course the stresses for each half are the same as the loading is symmetrical. Eight-Panel Howe Truss. Example s- For the next example a Howe TRUSS is considered, whose center lines give the diagram shown in Fig. 15. Fig. 15. Howe Truss. Truss-diagram This truss is used for a span of 64 ft, and it supports, in addition to a flat roof, a plaster ceiling below the bottom chord and a gallery on each side. The loads at the different joints are about as indicated in Fig. 15. To draw the stress- diagram (Fig. 15a), first construct the force-polygon by laying off to scale in rotation the external forces, commencing with the left reaction 34 200 lb. Next, commencing at joint o, the supporting force sa is known, the stress in the rafter is ap, and the stress in the tie ps, closing the polygon. At joint i, pa and ab +500U i Fig. 15a. Howe Truss. Stress-diagram are known and hn and np are drawn, closing the polygon. At joint 2, gs, sp and pn are known and nm and mg are drawn. At joint 3, w«, nh and be are known and d and Im are drawn. The stresses at the remaining joints are found in the same way as those at 3 and 4. The stresses in pounds in the various members of the truss are noted in figures in the stress-diagram (Fig. 15a). Howe Truss Loaded at Alternate Joints. Example 6. (Fig. 16.) This example of a Howe truss is selected to show how to proceed when there is no 1076 Stresses in Roof-Trusses Chap. 27 load at one or more of the joints. F[g< 16 represents the center lines of a truss 50 ft in span and only 5 ft in height. In order to give the braces an inclination approximating 45°, the truss is divided into ten panels; but purlins are placed over every other joint, as in Fig. 16, Chapter XXVI. The loads from these purlins are about 5 000 lb. The stresses at joint i are found in the same manner as in the previous example, always starting with the supporting force. At joint 2 the stress-line da is already drawn; and as there is no load at this joint, 5000 Ri=aoooo Fig. 16. Howe Truss. Truss-diagram a line is drawn from a parallel to AE (A covers the entire space from joint i to joint 4), and a line from d parallel to ED, the two lines intersecting at e. The force-lines and stress-lines are as follows: At joint 3: od, de, ef a.ndfo; At joint 4: fe, ea, ab, bg and gf; At joint 5: of, fg, gh and ho] At joint 6: hg, gb, bi and ih; At joint 7: oh, hi, ij Siudjo; At joint 8: ji, ib, be and ck; the latter line extending to the point of beginning, j, showing that there is no stress in kj: At joint 9 the only stresses are oj and lo, for as there is no stress e -fioooo Fig. 16a. Howe Truss. Stress-diagram in JK, for equilibrium there can be none in KL. There is, also, no stress in the middle rod. Although these members have no stress, it is advisable to insert them in the truss in order to stiffen the top and bottom chords. They may be made very light, say ^4 in in diameter for the rods and 3 by 6 in in cross- gection for the braces, Determination of Stresses in Roof -Trusses by Graphic Methods 1077 Howe Truss with Slanting Top Chord. Example 7. In order to give a slope to the roof it is often desirable to incline the top chord of a Howe truss as in Fig. 17, Chapter XXVI. Fig. 17 shows the truss-diagram for such a truss, and Fig. 17a the stress-diagram. The latter is drawn in the same way as the stress-diagram in Example 5, but because the top chord is not level, the stress- diagram is not symmetrical. When the stress-diagram is not symmetrical it is necessary to complete the entire diagram, so as to show the stress in every mem- ber of the truss. The stress-lines for joint 9 are om, nin, nr and ro. This leaves R2 = 10000 Fig. 17. Howe Truss with Slanting Top Chord. Truss-diagram Fig. 17a. Howe Truss with Slanting Top Chord. Stress-diagram only the line rj to complete the diagram; and if the diagram has been correctly drawn, a Hne joining r and / will be exactly parallel to RF. There is no stress in the rod //. Pratt Truss. Inclined Ties. Example 8. (Fig. 18.) This truss has the same dimensions as the truss shown in Fig. 14, but the diagonals incline in the opposite direction and are in tension, while the verticals, except the middle one, LL', are in compression. This form of truss is sometimes used in wooden con- struction to avoid the long middle braces shown in Fig. 14. Long ties are, as a 1078 Stresses in Roof-Trusses Chap. 27 rule, more economical thail long struts. The construction of the stress-diagram requires no additional explanation after that given for the stress-diagram in Fig. 14a. The student should compare the magnitude of the stresses scaled and marked in Fig. 18a with those in Fig. 14a, and note the eflect of the change in the direction of the braces. The truss represented by Fig. 14 requires a very much larger rod in the middle than is required for KL and K'L' in the truss of Fig. 18. The middle rod for the truss shown in Fig. 18 may be made very light. Fig. I 8a. Pratt Truss. Inclined Ties. Stress-diagram. This truss, however, requires, for good construction, special cast-iron washers for the rods. Simple Fan Truss. Example 9. (Fig. 19.) This figure shows the skeleton of a simple fan truss with rafters inclined 30° and divided into three equal panels, making the loads AB, BC, CC, etc., equal. The stress-diagram is drawn according to the principle already explained and requires no special treatment. As the loads are equal, the stresses in this truss may be readily figured by means of Table X, and the student should compare the stresses thus determined with those obtained by scaling the stress-diagram. Determination of Stresses in Roof-Trusses by Graphic Methods 1079 Cambered Fink Truss. Example lo. (Fig. 20.) The inclmation of the rafters is 30° and the distance between the trusses 20 ft. The loads are cal- culated for a slate roof on boards or on angle-iron purlins. Commence the stress-diagram by drawing a vertical line equal to the supr)orting force Ri, ot 56 350 lb, and lettering the lower end of the line and the upper end c, as these R,=5000 Fig. 19. Fan Truss. Truss-diagram are the letters on each side of the supporting force at joint o. an and no are drawn parallel to AN and NO. For joint i, na is drawn upward; ab is laid oflf equal to 16 100 lb and bm and mn are drawn parallel to BM and MN. At joint 2 on and mm are known, and ?nl is drawn parallel to ML, the sides of the stress- polygon being on, nm, ml and lo. not found in any of the preced- At joint 3 a new condition is met, which is. T ing examples and which is peculiar to this form of truss, viz., three apparently unknown forces. From a study of the truss-diagram, however, it is seen that LM and IK act as parts of BELLY-RODS, taking up the thrust from the lower ends of the struts at joints 2 and 5; and as the loads at joints i and 6 are equal and NM and IH are the same length, the stress in IK is the same as the stress in LM, which is already known. This reduces the number of unknown forces at joint 3 to two. The first force known at this joint is Im, the next mb and the next be, equal to 16 100 lb. From c a line is drawn parallel to CI and from /, the initial point, a line parallel to KL. Between these two lines there must be a line, ik, parallel to IK and equal in length to ml; and this Hne is determined by means of the dividers and a parallel ruler and straight-edge. If correctly drawn, the joint i will fall in line with nm. The sides of the stress-polygon for joint 3 are, then, hn, mb, be, ci, ik and kl. Fig. 19a. Fan Truss. Stress-diagram 1080 Stresses in Roof-Trusses Chap. 27 At joint 4 the stress-lines are ol, Ik, kg and go. At joint 5 the stress-lines are gk, ki, ih and hg. At joint 6 the stress-lines are hi, ic, cd and dh. If the stress-diagram is accurately drawn, a line from d parallel to the rafter will pass through the point h. The vertical tie GG' (Fig. 20) has no stress and its only purpose is to prevent the horizontal tie from sagging. Fig. 20. Cambered Fink Truss. Truss-diagram 1' Fig. 20a. Cambered Fink Truss. Stress-diagram Cambered Fink Truss. Example ii. (Fig. 21.) This is the truss shown in Fig. 20, with two additional loads. Steel trusses of this shape are often required to support loads from below. In Fig. 21 there are two loads of 4 tons each, supported at joints s and 9, in addition to the roof-loads. The stress- diagram is drawn in exactly the same way as in Fig. 20a, except that at joint s the first-known force ro, parallel to RO, 4 tons, is laid ofif, locating r. At this joint, then, ro, ol and Ik are known and kg and gr are drawn to close the polygon. It should be noticed that the stresses in NM, IH, ML, KI and LK are not affected by the ceihng-load. This is evident by comparing Fig. 21a with Fig. 20a. All of the other stresses, however, are increased because of the increase in the supporting forces, the greatest increase being in KG and HG. Detennination of Stresses in Roof-Trusses by Graphic Methods 1081 8 8 B 4^ (H ^ ''H/^ <^!x^V ^ L rA/ -38. c' >3— ^^9^f — ^^oeJ^I Span =So'o" Ti" O \ R A' o' Pj= 32 • Fig. 21. Cambered Fink Truss. Truss-diagram R|=32 Fig. 21a. Cambered Fink Truss. Stress-diagram 5200 ^'V, Fig. 22. Scissors Truss. Truss-diagrara Fig. 22a. Scissors Truss. Stress-^ diagram 1082 Stresses in Roof-Trusses Chap. 27 Simple Scissors Truss. Example 12. (Fig. 22.) This is the truss- diagram of the truss shown in Fig. 22, Chapter XXVI, which is the simplest form of the SCISSORS TRUSS. The truss-dia^ram is drawn by commencing with the line oa equal to the supporting force, 9 600 lb, and then in order the forces ah, bb', b'a', a'r and ro, forming the polygon of the external forces. At joint i, oa is known and ad and do are drawn, closing the polygon. At joint 2, da and ab are known and be and ed are drawn, closing the polygon. At joint 3, eb and bb' are known and b'e' and e'e are drawn. This determines the stresses in one-half the truss. Those for the other half are, of course, of the same magnitude and character, but the stress-diagram should be continued for the second half of the truss as a check. Scissors Truss. Example 13. Fig. 23 is the truss-diagram of the truss shown in Fig. 23, Chapter XXVI, with the loads figured about as they would Ri = 1*600 B' 6400 .j*°i V*' ~' o'^ ^"i. T J R2= U600 -^ '<:^ Fig. 23. Scissors Truss. Truss-diagfam Fig. 23a. Scissors Truss. Stress- diagram be for a slate roof and wooden ceiling and for a spacing of 1 2 ft on centers. The stress-diagram is begun by drawing the line oa equal to the supporting force at joint I C14 600 lb). The sides of the stress-polygons for the different joints are as follows: At joint i: oa, ae and eo; At joint 2: ea, ab, bf and fe; At joint 3: oe, ef, Jh and ho; At joint 4: hfyjb, bk and kh\ At joint 5: TO {1 100 lb), oh, hk, Id and Ir; At joint 6: Ik, kb, be (5 400 lb), cm and ml', At joint 7 : mc, cc' (5 \oq lb), c'm' and m'm. The student should notice how much the stresses in the principal members of this truss exceed the supporting forces or loads, and particularly the great stress in the middle rod. For these reasons this is not an economical type of trugs for spans exceeding 36 ft. ■Determination of Stresses in Roof-Trusses by Graphic Methods 1083 Scissors Truss. Example 14. Fig. 24 is the truss-diagram of the truss shown ill Fig. 4, page 1056, arid for which the roof and ceiling-loads are computed in Example 3, page 1055. The truss shown in Fig. 4 is built of planks spiked and bolted together, but the stresses are found in precisely the same way if the truss is made of heavy timbers and supports a greater roof-area. It should be remembered that only the shape of the truss and the loads, including their point of application, affect the stress-diagram. The stresses at joints i and 2 are readily found, commencing with oq, equal to R\. At each of joints 3 and 4, however, there are three unknown forces. We cannot obtain the stresses at joint 4 until those acting at joint 3 have been determined. The known forces at 3 are the load RO, equal to 430 lb, and the stresses acting in OE and EF\ and the unknown forces, those acting in FU, HK and KR. UK and KR are in ten- sion and serve to hold joint 3 from falling down and outwards. Either one, but not both, may be omitted, and the greater the stress is in one the less it is in the other. The only way to complete the stress-polygon for joint 3 is to fix the Ri=3fi00 Ror=3600 +'J^ Fig. 24. Scissors Truss. Truss-diagram. (See, also, Fig. 24a. Scissors Truss. Fig. 4 and Chapter XXVIII , Fig. 2) Stress-diagram amount of 6ne of the unknown stresses arbitrarily. The most satisfactory analysis seems to be to make the stress in HK equal to that in KR. This is done as follows: The first known force at joint 3 is the load represented by ro, the point r being obtained by measuring upwards from 0, 430 lb; next, the Hues oe and ef are known. From / a line is drawn parallel to FH and from r, a line parallel to KR. These two lines must be connected by a third line parallel to HK. This fine should be drawn so that its length is equal to ^r, which can be done by means of dividers. Lettering the ends of this line h and k the sides of the completed stress-polygon for joint 3 are ro, oe, ef, Jh, hk and kr. Knowing the stress in UF, there are but two unknown forces at joint 4, and these are readily found. The sides of the stress-polygon for joint 5 are Ic, cc'^ c'V and VI. Cona- paring this stress-diagram with that of Fig. 23a, it is seen that the stress in the middle rod is much less in proportion to the loads for the truss shown in Fig. 24 than for the one shown in Fig. 23, this reduction being due to the horizontal tie RK. For light trusses built of planks, spiked or bolted together, the. form of truss shown in Fig. 24 is preferable to that shown in Fig. 23. Scissors Truss. Example 15. Fig. 25 is the truss-diagram of the scissors TRUSS shown in Fig. 27 of Chapter XXVI. The line EF in Fig. 25 does not 1084 Stresses in Roof-Trusses 7800 7spo < -K'g Chap. 27 ■w ;iS= -26500 c;i=. +26500 .../], l^ i^ "t •?! O' -s-\c 1 4-t 6 ! (*i'_i aT^ a +6500 / pig. 25a. Scissors Truss. Stress-diagram Determination of Stresses in Roof-Trusses by Graphic Methods 1085 correspond with the center line of the strut in Fig. 27, because the inner end of this strut is dropped slightly on account of the detail of the joint; but in truss- diagrams all lines must go from joint to joint, otherwise the stress-diagram can not be drawn. There are no stresses in the middle diagonals under a symmetrical vertical load; hence they are shown by dotted lines in Fig. 25. As no complica- tions arise in drawing the stress-diagram of this truss, a detailed description is unnecessary. The sides of the stress-polygons for the different joints are as follows: For joint I : oa, ad, do; For joint 2: ro, od, de, er; For joint 3: ed, da, ah, bf,fe; For joint 4: fb, be, ch, hf; For joint 5 : sr, re, ej, fh, hs. ch and hs coincide, showing that the compression in CH is equal to the tension in US. The plus and minus signs in Fig. 26, as in all the other diagrams, denote compression and tension respectively. Truss without Tie- Stress-diagram Truss Without Tie-Beam. Example 16. Fig. 26 shows a truss which is neither a scissors truss nor a hammer-beam truss, yet this form can be made to appear similar to the hammer-beam truss by inserting a curved brace below joint 3, and replacing the pieces OH and OH' by curved members. There is no difficulty in drawing the stress-diagram shown in Fig. 26a. The Horizontal Thrust of Scissors Trusses. In the examples just given it has been assumed that the reactions are vertical and consequently that there is no HORIZONTAL THRUST. Tliis would be true if the materials composing the frames were absolutely rigid. This is not the case, however, and all trusses built along the geometrical lines of their shape change in shape after the full load is applied. In the scissors truss this changes the length of the span, making it longer and permitting the rafters to sag. If the trusses are con- structed with a camber in the rafters and the span made a little short, the thrust against the supports can be practically eliminated by fastening one end of the truss and providing for a movement at the other, so that when the full roof and ceiling-loads have been placed on the truss the span will have its correct length. In order to do this we must know how much the span will change in length under the full load. This can be determined in the manner shown in the follow- 1086 Stresses in Roof-Trusses Chap. 27 ing example and by referring to Fig. 26b. Let Diagram i represent a simple SCISSORS TRUSS loaded as shown with i ooo pounds at each top-chord joint, and let the left end be assumed to rest u[3on. rollers. Then both reactions will be vertical and the stresses in each member can be foimd from the usual stress- diagram shown in Diagram 2. Let S be the stress in any member as found from Diagram 2; u, the stress in any member produced by one pound acting horizontally at K and from L as found from Diagram 3; A, the area of any 1000, ^=1500 Fig. 26b., Simple Scissors Truss and Stress-diagrams member, in square inches;' /, the length of any member, in inches; E, Young's modulus of elasticity of the material Composing any member and D, the total CHANGE IN LENGTH OF SPAN when the truss is subjected to its full load. Then, If H is the HORIZONTAL FORCE applied at K, which is necessary to make the value ol D = o • Theory and Practice of Modern Framed Structures, Johnson, Bryan and Turneaure (John Wiley & Sons); Roofs and "Bridges, Merriraaa and Jacoby (John Wiley & Sons). Determination of Stresses in Roof-Trusses by Graphic Methods 1087 The detailed calculations for Fig. 26b are given in Table XVII, assuming that all members, excepting FG, are composed of 6 by 6-in white pine timbers with £ at I ooo coo lb per sq in, and that FG is an upset round steel rod having an area of 0.785 sq in with E equal to 30 000 000 * lb per sq in for steel. Table XVII. Computations for D and H for a Particular Scissors Truss (I) Member (2) s, Dia- gram 2 (3) A /4) S-^A (5) M, Diagram 3 (6) (7) Sul AE (8) uH AE AE BF CG DH....... EM HM EF FG GH +3160 +2100 +2100 +3160 — 2360 -2360 + 800 — 1980 + 800 36 36 36 36 36 36 36 0.785 36 87.8 58.3 58.3 87.8 65.5 65.5 22.2 25.22 22.2 +0.71 +0.71 +0.71 +0.71 -1.58 -1.58 — 1. 00 84.8 84.8 84.8 84.8 126. 5 126.5 63.2 80.0 63.2 0.00528 0.00351 0.00351 0.00528 0.01316 0.01316 0.0 0.00672' 0.0 0.00000118 0.00000118 0.00000118 0.00000118 . 00000875 0.00000875 0.0 0.00000340 0.0 0.05062 0.00002562 D = 0.05062 in and // = 0.05062 ~ 0.00002562 = 1975, or, approximately, 2 000 lb. This shows that the span would lengthen about ^0 in, if allowed free movement at one end; or, if fixed, there would be a horizontal force of 2 000 lb tending to push the supports out. In column 4 it is seen that the stresses per square inch are only about one- tenth of those permissible. Assum- ing that the loads become 10 000 lb at each apex-joint, the horizontal deflec- tion becomes about V^ in, and the horizontal thrust becomes 20000 lb. This shows conclusively that a large excess of material must be employed in the scissors truss, particularly in the members em and hm which contribute over one-half the value of D as shown in column 7, if the horizontal deflection is to be made so small that its effect may be neglected. As stated before, if the truss is permitted to deflect horizontally until fully* loaded, the walls or supports will have sensibly no horizontal thrust to resist. The Hammer-Beam Truss. As usually constructed the hammer-beam TRUSS is expected to exert more or less horizontal pressure at the supports; and this is provided for by heavy walls and buttresses. The diagram of such a truss is shown in Fig. 27, in which the curved braces usually built in the middle part of the truss are not shown, as they are considered to be purely orna- mental and for vertical loading have no stresses. The brace OM is drawn as though it were straight; but a curved brace may be used instead, without alter- ing the diagram. The stress in the curved piece is that found from the stress- diagram, increased by the bending stress due to its curvature. To determine stresses in the members of this truss it is necessary to first find the horizontal thrust of the truss against the wall. To do this all the truss-members from joint o to joint 4 are considered to form a framed brace, or assemblage of pieces supporting the upper portion of the truss at joint 4, or a single brace, shown by the broken line 04, Fig. 27, is assumed to have the same effect on the wall as all the pieces put together in the framed strut; that is, the truss is * If 29000000 lb per sq in is used for the value of E for steel the. values of D and B will be slightly changed. See Table I, page 664. 1088 Stresses in Roof-Trusses Chap. 27 considered to have the same horizontal thrust as the truss shown in Fig. 27a. The load at joint 4 is evidently: 12 000 lb, plus the load at joint 5, plus hali the load at joint 6, plus half the load at joint 2; making in all, 36 000 lb. To find the horizon- ^^^^. TAL THRUST and the stresses the proce- dure is as follows: ab (Fig. 27b) is laid off equal to the load at joint 2, be equal to the load at joint 4, cd equal to the load at joint 5, and dd' equal to the load at joint 6. Then the load at joint 4 (Fig. 27a) = V2ab + bc-\- cd+y2 dd'; and if a horizontal Une is drawn from x to the left, and from the center of ab a line parallel to the Una 4-0 (Fig. 27a) these two lines will intersect at m, and mx is the magnitude of the horizontal THRUST exerted on the wall at the joint o. Having obtained this thrust, it is easy to determine the stresses in the pieces. At joint o the four forces in R 1=42000 Fig. 27. Hammer-beam Truss. Truss-diagram H =18000 R.f42000 n' " 18000 Fig. 27a. Hammer-beam Truss. Truss-diagram Fig. 27b. Hammer-beam Truss. Stress-diagram equilibrium are the resistance to the thrust, mx, the vertical supporting force mn and the stresses ao and om, closing the polygon. At joint i, oa, af and fo are the stresses in OA, AF and FO. At joint 3 the stresses are mo, of, fg and gm; at joint 2 they d,Tefa, ab, bg and gf; at joint 4 the stresses are mg, gb, be a.nd ci. Determination of Stresses in Roof-Trusses by Graphic Methods 1089 closing the polygon. It will be noticed that the polygon closes without allow- ing any line to be drawn parallel to IM; hence there is no stress in IM, with vertical loading. When there are wind-loads there is some compression in /i/, and this member is a necessary part of the truss. At joint 5 there are the stresses ic, cd, dk and ki, and at joint 6. kd, dd',d'k' and k'k, which complete the stresses for one-half the truss, which are all that are needed. Comparing, now, the diagram 10 tons Span =-48'0" Fig. 28. Suspended Pratt Truss. Truss-diagram \ "'/ + 12.8 / \ A \ / \/V'=-8 / / a'' \- UA / / \ / s' X / V* •1- .|<--8'-^--8'- Rl- -19,250 - -8- - "4^ - 8- - >|<- - -8 — >[<— -8- - >| R2 = 64,259 Fig. 48. Cantilever Truss. Truss-diagram to 19 250 lb equal to Ry. The next force is the load of 2 500 lb, which also acts down, and which locates the point b. From b a line parallel to BI is drawn and from a line parallel to 70, locating the point i. bi acts from joint i and to towards it, showing that BI is in tension and 10 in compression. The remainder of the stress- diagram is drawn by the same methods employed for the diagrams of Figs. 46a and 47a. At joint 6 the force- polygon is begun with the force R2 or o'o, which acts upward, and the upper end of which must be at o. Con- sequently 0' is located by measuring downward from 0, 64 250 lb. The sides of the stress-polygon for this joint are o'o, o?n, mn and no'. After gh, the load at joint 13 is laid off, the remaining dis- tance ho' should be just equal to the load at joint 14, or 12500 lb. If Ri and Rz have been correctly computed and the stress-diagram accurately drawn, the points ^, u and TV will fall in the line no'. l^^i Fig. 48a. Cantilever Truss. Stress-diagram Determination of Wind-Load Stresses 1109 6. Determination of^ind-Load Stresses Wind-Loads. Thus far the stresses due to vertical loads only have been considered, the pressure of the wind being combined with the dead load and considered as acting vertically. For triangular and Fink trusses this method is sufficiently accurate, as the wind-pressure never causes a maximum stress in excess of that obtained by the method explained in connection with the foregoing examples. For trusses with curved chords and in fact for almost all forms of steel trusses except those of the Fink and fan types, it is not safe to consider wind-pressure as acting vertically, because the wind acts gen- erally in a direction at right-angles to the roof-surface, and upon but one side of the roof at a given time, thus loading the truss unsymmetrically and often caus^ ing stresses of an opposite kind from those produced by a vertical loading. Braces which are inactive under a vertical load may therefore be necessary to resist the force of the wind, or the total stress due to wind and vertical load combined may be greater than it would be if the wind-pressure were considered as a vertical load. To design a roof-truss correctly, therefore, it is necessary to determine the stresses due to vertical loads and wind-loads separately and then combine them so as to get the greatest stress that may be produced under any probable conditions. (See statement on page 1049.) Curved Chords. In the calculation of trusses with curved chords it is the usual practice to find the stresses for the following different loadings and then combine them to obtain the maximum stress: Stresses due to the wind on the side of the truss nearer the expansion-end; stresses due to the wind on the side of the truss nearer the fixed end; stresses due to the permanent dead loads; stresses due to snow covering the entire roof or only one-half of the roof; and, in special cases, stresses due to snow covering only a small area of the roof on one side. Wind and Snow. It is generally assumed that the maximum wind-pressure and the snow-load can not act on the same half of the truss at the same time. For trusses with straight rafters it will generally be sufficient to find the stresses due to the permanent dead load, and to the wind from both directions, disregard- ing the snow-load when the pitch of the roof is 45° or greater. For the Northern states, when the pitch is less than 30°, it is well to consider that a heavy sleet may be on both sides of the roof at the time of a heavy wind and to add about 10 lb per sq ft of roof-surface to the dead load to allow for it. In localities where heavy snowfalls may be expected, the stresses due to the full snow-load should also be found, as these combined with the permanent dead load may exceed those due to dead load, sleet and wind-pressure. Wind Stress-Diagrams. These are affected by the manner in which the truss is supported. If both ends of the truss are fixed, the wind-reactions are paral- lel to the resultant wind-load; if one end is free to move horizontally, that is, on rollers or supported on a rocker, the reaction at the roller-end is vertical and that at the fixed end inclined. ''If one end be fixed and the other merely supported upon a smooth iron plate, the reaction at the free end may have a horizontal component equal to the vertical component multiplied by the coeffi- cient OF friction, which is about one-third." Fixed and Free Ends of Trusses. Wooden trusses may be considered as fixed at the ends. Steel trusses, when supported on masonry walls, should have one end fixed and the other free to move; and when the span exceeds 70 ft the free end should be supported on rollers to permit of expansion or contraction. When steel trusses are supported by steel columns, as in steel mill- buildings, the trusses are rigidly attached to the columns and no provision 1110 Stresses in Roof-Trusses Chap. 27 is made for expansion. In such buildings the wind-pressure causes a bending STRESS in the columns, which must be provided for. Truss with Fixed Ends. Example 31. Wind -pressure is usually assumed to be applied uniformly over one side of the roof and to act at right-angles to the surface of the roof. The joint-loads or panel-loads, therefore, are proportional to the roof-areas supported. When the joints divide the ra fter into panels of equal length, the joint-loads are uniform, except for the joints at the edges of the roof. The actual wind-pressure is obtained by multiplying the roof surface by the values given in Table IX, page 1053. For this example the triangular truss shown in outline by Fig. 49 is considered and it is assumed that the span and spacing of the truss are such as will give a load of i ocx) lb at joints 2 and 4. The loads at joints i and 5 are only one-half of those at 2 or 4. To find the supporting forces or reactions, draw a line representing the resultant of the loads, cutting the bottom chord at A''. As the loads aVe symmetrical the resultant acts at the middle of the rafter and at right-angles to it. The reactions Ri and Rt are inversely proportional to the two segments into which a horizontal line joining the points of support is divided by the resultant, or iii this case to X-7 and i-X, 3000 \R 1000 Fig. 49. Triangular Truss. Truss-diagram Fig. 49a. Triangular Truss. Stress-diagram the greater reaction being at joint i. The sum of the reactions are equal to the sum of the loads. To find the reactions graphically, draw a line from joint i, at any angle, say from 30° to 45°, and measure off a distance equal to the total load. In Fig. 49 the line 1-8 represents 3 000 lb. Join 7 and 8, and from X draw a line parallel to 7-8, intersecting 1-8 at X'. Then S-X' is the reaction at joint I and X'-i the reaction at joint 7. To draw the stress-diagram, Fig. 49a, first draw the load-line ae equal to the sum of the loads, in this case 3 000 lb, and perpendicular to the rafter 1-5, and divide it so that ao is equal to A''-8. Then, at joint I, oa is the supporting force, ab is 500 lb and hf and fo are drawn parallel respectively to BF and FO, intersecting at /. The external forces and stresses act in the direction oa, ab, bf and fo, showing that BF is in compression and FO in tension. At joint 2 the stress-lines lire fh, be equal to i 000 lb, eg and gf. The stress-lines at joint 3 are of, fg, f^h and ho; at joint 4, hg, gc, ed, di and ih; and at joint 5, id, de, ck and ki. If the load-line has been correctly divided at 0, and the stress-lines have been drawn exactly parallel to the lines of the truss, the point k will fall vertically above the point i. At joint 6 the stress-lines are oh, hi, ik and ko. As the figure must close by a horizontal line through o, it is evident that the Determination of Wind-Load Stresses nil line KIC of the truss-diagram cannot be represented, and therefore there can be no stress in this member when the wind is from the left. At joint 7 the reaction eo is known, acting up, and ok and ke must close the figure, showing that the line he represents the stress in the entire length of the right rafter, and that there is no stress in the bracing on that side of the truss when the wind is from the left. When, however, either the lower chord or the rafter is not straight, some of the braces on that side come into action. By noting the character of the stresses in Fig. 49a, it is seen that the different members of the truss have the same kind of stress as is produced by vertical loads. As the wind may blow from either direction, it is evident that both sides of the truss must be made alike. This example illustrates the method of drawing the stress-diagram for any truss with a straight rafter when both ends of the truss are fixed. Truss on Rollers. Example 32. When one end of the truss is free to MOVE, the reaction at that end must always be practically vertical, and this condition gives a considerable variation of stress when the wind is on different sides of the roof; so that it is necessary to draw two wind-stress diagrams, one Fig. 50. Triangular Truss. Truss-diagram and Stress-diagram, Wind Left tor WIND FROM THE LEFT, marked W.L, and one for wind from the right, marked W.R. It is customary with authors when writing on this subject to consider that the rollers are always under the right-hand support, and this custom is followed here. In practice the rollers may be placed under either end, as both sides of the truss are usually proportioned to the maximum stresses. For this example we will take the same truss-diagram that was used in Fig. 49, illustrating it again in Fig. 50, which is drawn to show wind from the left. Lay off the load-line 1-8 and divide it at X', as in example 31. Draw a hne ae, perpendicular to the rafter and equal to 1-8 in length, and divide it into two segments of the same proportions. Through x' on ae draw a horizontal line, and through e a vertical line, the two intersecting at 0. Then eo represents the vertical reaction at joint 7 and oa the reaction at joint i. The stress-lines at joint I are: oa, ab equal to 500 lb, hj and/(?. At joint 2: Jh, he, eg and gf. The remainder of the diagram W.L. is completed exactly as described for Fig. 49a, the only difference between the two being the location of point 0, which givei increased stresses in the bottom chord for the truss of Fig. 50. Fig. 51 represents the same truss with wind from the right. To draw the stress-diagram W.R. start with id, perpendicular to the rafter and equal to the total load, 3 000 lb. Divide the line at x' into two segments of the same proportions as the segments 1112 Stresses in Roof -Trusses Chap. 27 of the line 1-8, Fig. 50, the.longer segment being at the top. To find the reac- tions draw a horizontal Hne through x' and a vertical Hne through t, the two lines intersecting at 0. Then do is the reaction at joint i, and ol the reaction at joint 10. For this diagram it is better to start with joint 10 and take the forces in the reverse order from that in which they were taken before. The stress-lines at joint 10 are ot, is equal to 500 lb, sn and no\ at joint 9, ns, sr, rm and mn; at joint 8: on, nm, ml and lo; at joint 7, Im, mr, re, ek and kl; and at joint 5, Fig. 51. Triangular Truss. Truss-diagram and Stress-diagram, Wind Right ke, ed, di and ik. If the diagrams have been correctly drawn the point i will fall vertically above the point k. On comparing the two diagrams for W.L. and W.R. it is seen that the stress-lines for the rafters and braces are of the same length and that the stresses are of the same character in both, but that the stress in the bottom chord is considerably less when the wind is from the right. This condition does not apply to all trusses, however, so that it is best to draw the two stress-diagrams for wind from both directions. Queen Truss. Example 33. Fig. 52 represents the outline of a queen-rod TRUSS for a roof having a rise of 14^^ in in 12 in. As the truss is of wood the supports are considered fixed. Joint 2 divides the rafter into two equal parts, consequently the wind-load at this joint is twice that at joint i or 4. For convenience it is assumed that the wind-load at joint 2 is i 000 lb and at joints i and 4, 500 lb. The resultant is 2 000 lb acting through joint 2 and intersects the tie-beam at X. To find the supporting forces, draw the line 1-8 equal to 2 000 lb and connect 7 and 8. From X draw a line parallel to 7-8 intersecting 1-8 at X'. Then 8-X' is Ri or the supporting force at joint i and X'-i or R2 the supporting force at joint 7. Begin the stress-diagram (Fig. 52a) by drawing the line ad at right-angles to the rafter 1-4, and equal in length to 1-8 or 2 000 lb. By means of dividers locate the point so that oa equals S-X'. Then the stress- lines for joint i arc oa, ab, be and eo; at joint 2, eb, be, cf a.ndfe; at joint 3, oe^ ef,fh and ho; and at joint 4, hf, fc, cd, dk and kh. It is seen that the force-poly- gon at joint 4 will not close without the brace KH, because the initial point in drawing the polygon is at h, and a horizontal line through d does not pass Determination of Wind-Load Stresses in3 trirough h. A queen-rod truss, therefore, requires braces in the middle panel lo resist the wind-stress. With the wind from the fight, a brace is required from ioint .3 to joint 6. At joint 5 the stress lines are oh, hk, kl and lo. It should be noticed that lo acts towards the joint, showing that LO is in compression. At Fig. 52. Queen Truss. Truss-diagram Fig. 52a. Queen Truss. Stress* diagram, Wind Left first it would seem as though this could not be true, but if we glance at joint 7 we see that Ri is thrusting in on the joint, and that a strut is required to keep the joint in position. This condition is true only when the inclination of the rafter is greater than 45°. When the inclination of the rafter is exactly 45% Fig. 53. Queen Truss. Truss-diagram. (See. also, Figs. 3, 12 and 54 and Chapter XXVIII, Fig. 1) there is no stress in LO, and when the inclination is less than 45°, LO is in ten- sion. The stress-lines for jomt 6 are Ik, kd and dL If no errors are made, a line through d parallel to DL passes through the point /, previously obtained. A very slight inaccuracy vr^ io'-ating the point X', or in drawing the stress-diagram, 1114 Stresses in Roof-Trusses Chap. 27 however, causes the line through d to pass to one side or the other of point /; and if this happens, it shows that there has been some inaccuracy somewhere. In practice, a slight divergence does not materially affect the stress. At joint 7 the sides' of the stress-polygon are ol, Id and do = Ri, the lines being already drawn. Combination of Stresses. Example 34. For the purpose of showing how the stresses due to wind and vertical loads are combined, the truss-diagrams in Figs. 53 and 54 are shown, being the same as in Fig. 12, and representing the Fig. 53a. Queen Truss. Stress- diagram Fig. 54. Queen Truss. Truss-diagram. (See, also, Figs. 3, 12 and 53 and Chapter XXVIII, Fig. 1) truss shown in Fig. 3. The stresses first determined are those due to the weight of the roof and ceiling and to an allowance of 10 lb per sq ft for sleet. On page 1055 the roof-area supported at joint 2 was found to be 147^^ sq ft and at joint 3, 200 sq ft. On page 1055 the weight of the roof was estimated at 12% lb per sq ft, and allowing 10 lb for sleet, there results 22% lb as the greatest dead load under a heavy wind. This gives 3 360 lb for the lead at joint 2 and 4 550 lb for the load at joint 3. The ceiling-loads will, of course, be the same as in Fig. 12. Fig. 53 shows the loads due to weight of materials and sleet, as computed above, and the ceiling-loads. Fig. 63a is the stress-diagram for these loads, with the stresses indicated by figures. This diagram is drawn exactly in the same way as the stress-diagram in Fig. 12, page 107 1. Wind-Stresses. The inclination of the roof is very close to 45°, and from Table IX, page 1053, the normal wind-pressure for that angle is found to be 28 lb. Multi- plying^ the roof-area at joints 2 and 3 by 28, the wind-loads indicated in Fig. 54 are obtained. The wind-load at joint i, also, must be found. The rcof-arca suppvMled at this joint, allowing 17 in for eave-projection (Fig. 3) is 6M1 by 15 ft, or 95 sq ft, which makes the wind-load 2 660 lb. The next step is to find the point at which the resultant of these loads cuts the rafter. As the. loads are I not symmetrical or uniform on the rafter, the point through which the resultant acts must be determined by means of moments about joint i. The arms of the loads at joints 2 and 4 are figured on the truss-diagram (Fig. 54). The moments are 4 140 lb X 9^/12 ft = 38 9<^S ft-lb 5 600 lb X i8iA ft = 102 200 ft-lb The sum of the moments = 141 185 ft-lb Determination of Wind-Load Stresses im The resultant is the sum of all the loads, or 12 400 lb, and the distance of its point of application from i is found by dividing the sum of the moments by the result- ant force, or 141 185 ft-lb divided by 12 400 lb = ii.4- ft. Measuring off 11.4 ft on the rafter from joint i and drawing a line at right-angles to it intersecting the tie-beam, the point X is determined. From i the line 1-8 is drawn at any angle and equal in length to the sum of the loads, 12 400 lb, and 7-8 is drawn. From X a line is drawn parallel to 7-8, intersecting 1-8 at X'. Then 8-X' is Ri or the supporting force at joint i and ^ -r is R2 or the supporting force at joint 7. Supporting Forces Computed by Moments. The supporting forces ipay also be computed by moments. The moments of the loads about joint i tend to rotate the truss from left to right. To prevent this rotation there is the moment of the supporting force R2 acting vX joint 7 to rotate the truss from right to left. To maintain equihbrium, the moment of i^2 about joint i must just equal the sum of the moments of the loads about the same point. This sum was found above to be 141 185 ft-lb. The arm of R2 is the perpendicular distance between its hne of action and joint i. Continue i?2 to meet the dotted line at P. The dis- tance from force i?/l to P scales, say 26.5 ft. (By trigonometry, 26 ft.) Knowing the arm, the value of R2 is obtained by dividing the sum of the moments of the loads, 141 185, by the arm, or 26.5 ft. This gives 5 344 lb. As the sum of Ri and R2 must equal the total load, Ri equals 12 400 less 5 344 lb, or 7 056 lb. The distance S-X' and X'-i should scale reasonably close to these figures. Knowing the supporting forces, the stress- diagram, Fig. 54a, is drawn exactly as described for Fig. 52a. As the inclination of the rafters is a little greater than 45°, 0£' is in compression, but the stress is very small. The figures on Fig. 54a indicate the stresses in pounds. The stresses may now be tabulated and should be arranged as in the following table. In tabulating the wind-stresses, it should be remembered that the wind may blow against either side of the truss, and the greatest stress liable to occur should be put in the table. .cbW ;^/ ^-3600 Fig. 64a. Queen Truss. Stress-diagram, Wind Left Table XVra. Stresses for the Trusses Shown in Figs. 12, 53 and 54 Members Dead weights and sleet (Fig. 53.4) Wind-stresses (Fig. 54) Totals Stresses (Fig. 12) AEor A'E' BF or B'F' c//'or cn EF ////' + 16 150 + 13 800 + 9600 + 2350 — 5 400 — IT 200 — 9 600 +5 100 +5 100 +3 600 +4100 +5 100 -3 700 -5 950 -3 150 +21 250 +18900 + 13 200 + 6450 + 5 100 — 9 100 -1/ 150 -12 750 + 25 600 + 21 300 + 14 700 + 4400 — 6900 — 17 60c -147CJ FH or F'H' EO . . HP The truss-members are lettered as in Fig. 54. Thus the stress in the rafter F'B' is greater than in the rafter on the other side, and this stress acts through the entire length of the rafter; hence the stress for AE and BF should be entered as 5 100 lb, the stress in F'B'. In the same way the stress in the rod H'F' is 1116 Stresses in Roof-Trusses Chap. 27 greater than in F/7; hence the stress in H'F' should be tabulated. The stress in OE' slightly reduces the tension due to the dead load, but as the stress in EQ increases it, the stresses in EQ and HP should be tabulated. Both sides of the truss should of course be made alike,, and two l)races should be inserted in the middle panel. In the fifth column of the table are given the stresses due to the ceiling-load and a vertical load on the roof of 42% II) per sq ft, as obtained from the stress-diagram. Fig. 12. Comparing the stresses in the fourth and fifth columns, it is seen that except for the brace EF, and for the two rods, the stresses obtained by combining snow and wind and adding to the dead weight are greater than thQ totals due to wind, dead weight and sleet. Vertical loads, of course, cause no stresses in the braces of the middle panel, and unless the wind-stresses are drawn, it is necessary to estimate the sizes of these braces. The stresses in these braces, however, are so small that large pieces of timber are not required. The stresses given in the fourth column are unquestionably nearer what the real stresses are likely to be than those in the fifth column. If the roof is erected in a warm climate where there is no sleet, these stresses may be further reduced by omitting the 10 lb per sq ft added for sleet. If, on the other hand, the in- clination of the roof is less than 30°, the stresses produced by a heavy fall of snow without wind generally exceed the sum of those due to dead weight, sleet and wind; and for such roofs the stresses due to the maximum snow-load should always be computed. Reactions. The reactions, or supporting forces of the truss shown in Fig. 54, are very much inclined from the vertical. As the dead load, however, is always acting on the truss, the inclination of the real reaction is never so great, but more nearly vertical; and when there is no wind the reactions are exactly ver- tical. The theoretical reaction, due to both wind-load and dead load, is the diagonal of a parallelogram, the two adjacent sides of which are the reactions for the dead load and wind-load drawn to the same scale. Thus if a-7, Fig. 54, represents the reaction due to the wind and h-^ the vertical reaction, due to the dead load and drawn to the same scale, then R'^ is the resultant reaction, modified somewhat, however, by friction. Examples 31, 32 and s^ serve to show the general method of drawing wind stress-diagrams, and are sufficient to enable the student to draw those diagrams for most trusses v/ith straight rafters. For trusses with curved rafters the diagrams become more complicated, and the reader is referred to Graphical Analysis of Roof Trusses, by Charles E. Greene and to other standard handbooks on the subject. 7. Trusses with Knee-Braces Knee-Braces are generally used to give greater stability to the structure as a whole when roof-trusses are supported by columns. Under the action of vertical loads the stresses in these members are usually assumed as zero, which would be true if the materials composing the truss, knee-kraces and columns were rigid. This discussion will deal, however, with the effect of wind blowing against one side of the building and roof. The actual stresses in the knee- braces, columns and truss-members will probably never be known exactly, as there are so many variable factors entering into the problem. In the usual construction, in which columns are bolted to masonry pedestals at the bottom, either riveted or bolted to the trusses at the top, and in which the knee-braces are riveted at both ends, the degree to which these connections may l)e considered fixed is a question leading to many arguments and differences of opinion. This will not be discussed at all; but it will be shown how the stresses in all members of the framework can be found under given assumptions. Assume, for example, that the bottoms of the columns are sufficiently fixed, so that a powt of no* Trusses with Knee-Braces 1117 MOMENT is midway between the bottom of the knee-brace and the masonn^ pedestal (equivalent to assuming a pin at this point), and so that the top attach- ments and those of the knee-braces may be considered as pin-connections. Taking the truss and loading shown in Fig. 55, it is clear that the outside forces must be in equilibrium, and, unless the points M and N are unlike in some l5oa. Fig. 55. Truss with Kn^-braces. Truss-diagram particular, the reactions at these points will be parallel to the direction of the resultant of the wind-forces. Lay off to any convenient scale the wind-forces in order, as shown in Fig. 55a. Then XY is the direction and magnitude of the resultant wind- pressure and also the direction of Ri and Ri. The magnitudes of i?i and Ri are found by meansof the equilibrium polygon explained on page 1097. Rx is equal to SX and R2 to YS. These reactions are correct in direction and mag- nitude unless some condition is imposed to change them. If there are no moments at M and N and these points are restrained from moving vertically, the vertical com- ponents of R\ and R2 must remain constant, even in the extreme case where M may be assumed as a pin-connection and N as resting on rollers. Any assumption may be made as to the magnitudes of the horizontal components at these points as long as the sum of the two equals the sum of the horizontal components of Rx and R^. It is customary to assume these as equal. In this case the reactions at M and N are TX and YT, respectively. The next step is to find the effect of these reactions at the points O, Q, P and R. The vertical components Vi and Vz act as vertical forces at O and P. The horizontal com- ponents produce bending moments at O and P, and, in effect, horizontal forces at O, P, Q and R. Taking the left column, the 8 100 lb acting towards the left would move the column to the left if not prevented by the joints at O and Q. 55a. Truss with Knee-braces. Force-polygon Ills Stresses in Roof-Trusses Chap. 27 If the member MQ is considered to act as a lever with a fulcrum at O, a hori- zontal force of 8 loo lb acting towards the left at M will produce a pressure, or a force acting from left to right at Q which equals, by the method of moments, the center of moments being at O, 8 loolbX 7.5 ft -t- 5 ft = 12 150 lb. At 0, in like manner, taking the center of moments at Q, 8 100 lb X 12.5 ft -h 5 ft = 20 250 lb A\ v# 121 50 ^^150o\^^^ Fig. 56. Truss with Knee-braces. Truss-diagram / Fig. 57. Truss with Knee-braces. Stress-diagram is produced, acting from right to left . These forces are shown in Fig. 56. When combined with those shown in Fig. 55 they give the forces acting at O, Q, R and P which are used in constructing the stress-diagram shown in Fig. 57. 8. Arched Trusses An Archied Truss is one which has the form of an arch and which is so supported at the ends that the reactions produced by vertical forces are vertical. This is usually accomplished by placing pin-connections at the supports and providing rollers at one end to permit horizontal movement. Stresses in an Arched Truss. The determination of the stresses in the members of an arched truss is readily accomplished by following the methods given in the previous examples. Arched Truss with Roller-Support. Example 35. In Fig. 58 is shown the left half of an arched truss and the roller-support. This truss has the ' shape and dimensions of a truss in the Live Stock PaviUon, Union Stock- Yard Arched Trusses 1119 and Transit Company, Chicago, III. It is discussed in the Engineering News of June 28, 1906. The loading shown is symmetrical about the middle of the span and hence each reaction equals one-half the total load. Fig. 58a shows Ri=195 0(X) Fig. 58. Live Stock Pavilion, Chicago, 111. Truss-diagram 24 +535000 110-11-12 18-19 Fig. 58a. Live Stock Pavilion, Chicago, 111, Stress-diagram for Truss the stress-diagram for one-half of the truss. The stresses upon the right of the middle are the same as those upon the left. The HORIZONTAL DEFLECTION of this truss is measured by the movement of the ROLLER-END. This movement is computed in the manner explained for the SCISSORS TRUSS, pages 1085-7, by the formula D =i:{Sul ^AE). ' Where D is the 1120 Stresses in Roof-Trusses Chap. 27 HORIZONTAL MOVEMENT, 5 the stress in any member as given by the stressKliagram shown in Fig. 58a, m the stress in any member produced by the unit load applied at the roller end of the truss and acting in a horizontal direction (Fig. 58b), I the length of any member, A the area of any member, E Young's modulus of elasticity for the material composing any member and S the sign of summation, and when limits are not designated, the formula indicates that S(5w/ -i- AE)is to be taken for each member of the truss. For the loads and areas indicated in Fig. 58, the rollers will move about lo in when i(vi i-i2 yj v £ is 30 000 000 lb per sq in. In order that a given span may obtain under a given load, each tension-member must be constructed shorter than its geometrical length by an amount which it is lengthened by the stress which it resists, and each compression-member must be lengthened in a hke manner. Any Fig. 58b. Live Stock Pavilion, ^^her loading will produce a change in the Chicago, 111. Stress-diagram length of the span. To reduce the horizontal DEFLECTION without changing the lengths of the members they would have to be made excessively heavy. A truss of the form shown in Fig. 58 is not economical as an arched truss on rollers but may be satisfactorily used by connecting the two end -pins by a tie- rod. Arched Truss with Tie-Rod. When a tie-rod is employed the members become much lighter and can be built according to their geometrical lengths. The stress in the tie-rod may be found from the formula in which St is the stress in the tie- rod. A' the area of the tie-rod, I' the length of the tie-rod and E'. Young's modulus of elasticity for the material composing the tie-rod. The other symbols have the significance given above for the expression for D. Since the stress and area of the tie-rod appear in the above equation it is necessary to assume an area and then compute the value of St. If this produces a unit stress in the tie-rod differing greatly from the allowable value, a new trial must be made. Having found the stress in the tie-rod, the resulting stresses in the truss-members can be found graphically from a stress- diagram which will be of the form shown in Fig. 58b, which was constructed for a horizontal force of i 000 lb. The stresses can be found, also, by multiplying the stresses produced by one pound b^' the value of St. The stresses produced by St combined algebraically with those obtained from Fig. 58a give the final stresses. These stresses differ but little from those which obtain for a two- hinged arch of the form shown in Fig. 58, and such structures with the tie- rod are often classed as two-hinged arches. Assumption of Areas. Since the deflection of the truss shown in Fig. 58 depends upon the areas of the members, it is evident that they must be either known or assumed before the formulas for D or St can be applied. For a new structure the areas are of course unknown and the problem of determining the stresses becomes one which is sometimes classed as cut-and-try. For the first trial, the areas may be assumed as unity and the corresponding value of St found and then the combined stresses. The members may now be designed as to area and a new trial made with these areas. Usually the second trial is sufficient, as a slight change in areas does not materially affect the values of St. Trussed Arches 1121 9. Trussed Arches Symmetrical Trussed Arches. The three-hinged arch is the simplest form of TRUSSED ARCH, and, as used in buildings, it is usually symmetrical in form, consisting of two trusses connected by a pin over the middle of the span and resting on a pin at each support. The stresses in the truss-members are found by the ordinary graphical methods after the reactions have been determined. ^ 82-3^^ >| 1^— ll-O " >K 1 -1-0-^ — ^11-C— >|^— 1-1-0^UJ< — l-l-o' >k . 1 -1-0^ — ^l-l'ol^>|-5'3'^ 1 ! ! J i! i| « I h±1l44 Fig. 59. Three-hinged Arch. Truss-diagram Fig. 59a. Stress-diagram The SUPPORTING FORCES are inchned and may be resolved into two components, one vertical and the other horizontal. For symmetrical loading the two reac- tions are equal in magnitude. The vertical components are each equal to one- half the vertical loading. The horizontal components are equal in magnitude and opposite in character. The following examples illustrate the methods to be followed in the determination of the stresses. 1122 Stresses in Roof-Trusses Chap. 27 Trussed Three-hinged Arch. Example 36. Fig. 59 shows one-half of a TRUSSED THREE-HINGED ARCH with a Vertical load of I 000 lb per top-chord joint. Fig. 59a shows the stress-diagram for this loading; but before it can be drawn, the vertical and horizontal reactions at the left support must~be deter- mined. The vertical reaction is (7 X i 000) -|- 500 = 7 500 lb or one-half the ver- tical load. The horizontal component or the horizontal thrust of the arch may be found by moments. The center of moments will be taken at the middle H,«| O Vi= 457,750 Fig. 60. Liberal Arts Building, Chicago, 111. Truss-diagram Fig. 60a. Stress-diagram pin at the crown as at this point the moment is zero. The equation of moments is III X 72.5 + I 000 (5.25 -\- 16.25 -H 27.25 -\- 38.25 -H 49.25 4- 60.25 + 71.25) -f 500 X 82.25 - 7 500 X 78.75 = o, or III = 281 750 ^ 72.5 = 3 886 lb Having determined Vi and Hi, the stress-diagram shown in Fig. 59a can be readily constructed. Since the arch is symmetrical, it is necessary to draw but one-half the stress-diagram. If the right half of the arch is removed and in its place a horizontal force applied at the middle pin, the magnitude of this force i& Trussed Arches 1123 equal to the horizontal thrust Ih, since, for equilibrium, the algebraic sum ot the horizontal forces is zero. Trussed Three-hinged Arch. Example 37. Fig. 60 represents one-half of a TRUSSED THREE-HINGED ARCH used in the Liberal Arts Building of the Colum- bian Exposition, Chicago, 111., 1893. (See Engineering Record, July 9, 1892.) Fig. 60a is the stress-diagram for the loading shown in Fig. 60. Combination of Stresses. In Examples 35 and 36 only the efifect of vertical loads has been considered. Where three-hinged arches are employed they must be designed to carry dead, snow and wind-loads. The dead and snow- .g <0 its ^'^^.M ''""m "32000^ FD.ft 43.48- : — ^Z: ■:<^S: .65.66- g.(2^< T5.54 84.43- — — i"lt 11 /22 ^ ll \^21 20 JS > ^y^j 18 yf All JT / 1 t W^' sp 3 8H -'■ Fig, Fig. 61. 5th Regiment Armory, Baltimore, Md. Truss-diagram Fig. 61a. Stress-diagram I loads are vertical loads but the snow-load is not symmetrical in all cases. The wind-load is usually considered as acting normal to the roof. In order to be sure that the maximum stresses are obtained, the stresses for the following con- ditions of loading must be found and combined, (a) For dead load only, (6) For snow-load covering left half of roof, (c) For snow-load covering right half of roof, {d) For wind-load acting normal to roof on left of center, (e) For wind-load acting normal to roof on right of center. 1124 Stresses in Roof-Trusses Chap. 27 ^21 .22 o. Fig. 61b. 5th Regiment Armory, Baltimore, Md. Stress-diagram Snow on Bight ofCrowi^ Fig. 61c. 6th Regiment Armory, Baltimore, Md. Stress-diagram J^- \ S^^,^.-3u_,. S.o S„ J3^ 13 ■pj^- \ \ i\ ^kJ^^C^) i 3^^^/ >^ r\" ^ 9/ J<:;;^\3T^ A \r"29 ^ / %«/28 vV / K 6/\ 27 y^ coi % y 26 \ y / -/ / / C/ ''X 25 / 24 X/' / / / 7 / •^ i/\ 23 / / / / / \i>/h =13200 1% 1 Fig. 61d. 5th Regiment Armory, Baltimore. Md. Truss-diagram Trussed Arches 1125 The stresses for the above conditions of loading are to be found for one-half of the arch. In combining the stresses those which occur at the same time are to be used in determining maximums. Many engineers do not consider snow and wind-loads acting on the same portion of the roof simultaneously. Trussed Three-hinged Arch. Example 38. Fig. 61 shows one-half of a TRUSSED THREE-HINGED ARCH with the dead, snow and wind-loads indicated at each of the upper-chord joints. This form of truss supports the roof of the 5th Regiment Armory, Baltimore, Md., described in the Engineering Record of May 14, 1904. The stresses for the loadings specified above will be deter- mined and it will be shown how these are to be combined. Dead-Load Stresses. The reactions are obtained by the method used in Example 35. Vi is 77 900 lb and Hi 32 000 lb. -Fig. 61a is the stress-diagram for the members shown in Fig. 61. Snow on Left Half of Span. Assuming that the snow covers the portion of the arch shown in Fig. 61 and taking the center of moments at the middle pin, it is found by moments that Vi is equal to 26 700 lb and H^ is equal to 15 000 lb. Beginning at the support the stress-diagram shown in Fig. 61b is readily drawn. Snow on Right Half of Span. With the snow on the right of the crown, the portion of the span shown in Fig. 61 is unloaded. The total snow-load is 41 200 lb and it has just been found that the vertical reaction at the support adjacent to the loading is 26 700 lb; hence the vertical reaction at the other support is 41 200 less 26 700 lb or 14 500 lb or Vi for the case considered. Since the moment at the middle pin is zero, Vi (half the span) less Hi (rise of the arch) equals zero, or 14 500 X 95 -16 — ^1 X 92.0 = o; and Hi = (14 500 X 95-i6) -^ 92 =15 000 lb which is the same as found above. As before, beginning at the left support, the stress-diagram is constructed as shown in Fig. 61c. | |j Snow Covering Entire Span. The algebraic sum d ]! , of the stresses found from the two cases above for > 1 1 snow-loads will give the stresses produced by a j.1 snow-load covering the entire span. I pj^"^ Wind-Load on Left of Crown. Here no two of | the loads are parallel. This condition increases the I _ labor in finding the reactions. These may be com- | ~'*"~^"j — — ^ puted by moments, but a graphical method is ' '*"'hVi8^^^^'^^ found more convenient. The direction and mag- KthH ' t A ■> nitude of the resultant of the wind-forces are first ^^ory, Baltimore^MT Force' found by graphics. As shown in Fig. 61e, the wind- polygon loads are laid off in order. Then 3-13 is the direc- tion and magnitude of the resultant. Next, from any point O draw the strings Si, S2, S3, etc., and construct the equilibrium polygon shown in Fig. 6 Id, begin- ning by drawing string Si from A, and so on until string Sn cuts the line BC passing through the middle pm and the pin at the right support. This is the direction of the reaction at the right support. In Fig. 61 e, from 13 draw a line parallel to BC and from a line parallel to So in Fig. 6 Id, and prolong them until they meet at i. Then 1-3 is the reaction at A and 13-1 that at the right support. Resolving these into vertical and horizontal components, Vi equals 23 400 lb, Hi equals 13 200 lb, F2 equals 18 000 lb and H2 equals 18 600 lb. Fig. 61f shows the stress-diagram from the left support up to the crown. Wind-Load on Right of Crown. Since the reaction at A, Fig. 61d, produced by this load, must pass through the hinges, or pins A and C, th^ stress-diagram 1126 Stresses in Roof-Trusses Chap. 27 will be exactly similar in shape to that shown in Fig. 61c; but the values of Fa and Hi will be i8 ooo lb and i8 6oo lb respectively. The stresses will bear a direct proportion to the stresses found from Fig. 61c, and hence a new diagram is not necessary. ;. 61p. 5tb Regiment Armory, Baltimore, Md. Stress-diagram %. Combination of Stresses. The maximum stresses may now be determined, To illustrat^-^e m<^tho(|, consider ihe lower chord 1-37. . >*'' ■' ' /^ ' ''■ ,."■, -^ .., ^ '., ..Vt Jb (a) Dead-load stress, +22 100 (h) Snow on left of crown, — 14 300 (c) Snow on right of crown, + 37 800 ((/) Wind-load on left of crown, — 31 6oq {e) Wind-loAd on- right of crown, -f 46 900 (/) Snow over all, + 23 500 Total stress without wind, +59 900 (a) + (e), + 69 000 (a) + W, - 9500 The maximum stresses are 69 000 lb compression and 9 500 lb tension, assum- ing that the wind and snow-loads are not considered to act on the same side of the crown. If no such restriction is made, the maximum stresses are 106 800 lb compression and 23 800 lb tension. In a like manner the maximum stress in each member of the truss is determined. Tables XIX and XX give the max- imum STRESS for the members shown in Fig. 61. Stress-Diagrams for Three-hinged Arches. The stress-diagrams in the above cases are very difhcult to construct owing to the great number of lines and the difficulty in drawing them exactly parallel to the Hnes of the truss- diagram. One or more members should be computed as a check on the graph- ical work. Three-hinged Arch with Tie-Rod. The introduction of a tie-rod connect- ing the end-pins of a three-hinged arch and placing rollers under one end Trussed Arches 1127 practically changes the arch into a simple truss composed of three members, two trussed rafters and a horizontal tie. Under vertical loading, the support- ing forces are vertical, but for wind-loads the supporting force at the end with- out rollers is inclined. The stresses in the truss-members are the same as found above for the three-hinged arch. Th*e stress in the tie-rod equals the hori- zontal thrust found above at the roller-end for the given loading. The support at the roller-end is designed for vertical forces only, while the support at the other end must resist the vertical reaction and the total horizontal component of the forces acting on the structure, or for roofs the horizontal component of the wind- forces. This is very much smaller than the horizontal force which must be resisted when the structure is without a tie-rod or a true three-hinged arch. Table XIX. Three-hinged Arch. Chord-Stresses Thousand pounds Snow on Snow on Wind Wind Max. stresses | Member, Dead load, left of right of Snow over all on left of on right of Fig. 61 Fig. 61a crown, Fig. 6lB crown, Fig. 61c the roof crown. Fig. 6lF crown,* Fig. 61c Ten sioi Com- i pression 3-14 + 25.2 + 6.1 -2.1 + 4.0 +25.6 - 2.6 50.8 3-16 - 6.3 - 7.0 — 14.0 — 21.0 +32.8 -17.4 30. 7 26.5 3-18 - 18.7 -13.2 -21.4 - 34.6 +42.6 -26.5 58. i 23.9 3-20 — 190 -13.9 -22.8 - 36.7 +45.8 -28.3 61. 2 26.8 4-22 - 22.4 -15. 5 -28.0 - 43.5 +58.7 -34.7 72. ( 3 36.3 5-24 - 26.8 -15.8 -35.1 - 50.9 +73.8 -43.5 86. [ 47-0 6-26 - 26.6 — II. 2 -41.0 — 42.2 +85.3 -50.8 88. ( i 58. 7 7-28 — 22.0 -3.9 -44.6 - 48.5 +90.7 -55.3 81. 2 68.7 8-30 - 13.3 + 7.8 -44.8 - 37.0 +89.6 -55.6 68. c ) 76.3 9-32 - 3.7 -1-20.2 -41.7 - 21. 5 +81.9 -51.7 55.^ i 78.2 10-34 + 6.4 +30.0 -33.5 - 3.5 +67.2 -41.5 35. [ 73.6 11-36 + 14.3 +30.0 —20.6 + 9.4 +47.2 -25.5 II.- 2 61. 5 12-38 + 18.7 +19.3 - 2.8 + 16. 5 +23.3 - 3.5 42.0 13-39 -f 21.8 H-22.6 - 3.3 + 19-3 +27.8 - 4.1 49.6 1-39 + 18.8 - 5.4 +21.9 + 16.5 - 6.7 +27.2 46.0 1-37 -1- 22.1 -14.3 +37.8 + 23.5 -31.6 +46.9 9.. ) 69.0 I-3S + 33.3 -II. 3 +51 .9 + 40.6 -53.2 +66.0 19-^ ) 99.3 1-33 + 47.7 + 2.1 +61.0 + 63.1 -69.5 +75.6 21. { i 125.4 1-31 + 63.0 -I-18.1 +64.8 + 82.9 -78.3 +80.4 15.. I 161. 5 1-29 + 18.4 +31. 5 +65.1 + 96.6 -80.1 +80.7 61.' 1 130.6 1-27 + 90.3 +41 I +61.8 +102.9 -75.0 +76.6 208.0 I-2S + 98.7 +45.7 +55.8 +101. 5 -62.8 +69.2 213.6 x-23 '-^-102. 6 -^46.0 +48.5 + 94.5 -46.3 +60.1 208.7 1-2 1 -I-101.8 +42.9 . +40.0 + 82.9 —26.0 +49.6 194.3 I-I9 +102.3 +42.3 +37.9 + 80.2 -20.3 +47.0 191. 6 1-17 + 86.7 +34.8 +29.3 + 67.7 - 9.6 +36.3 157.8 l-IS + 59-5 -t-22.4 +16.2 + 38.6 + 3.9 +20.1 102.0 I-I4 + 77-4 +29,2 +21.0 + 50.2 + 5.2 +26.0 132.6 By proportion, 18 600 : 15 000. Tie-Rod and no Rollers. If the rollers are omitted and a tie-rod is used, the stress in the tie-rod and the reactions are indeterminate. They depend upon the relative rigidities of the tie-rod and the material composing the supports. If the tie-rod is made very heavy so that its stretch will be very small whea 1128 Stresses in Roof-Trusses Chap. 27 stre.ssed, the stresses in all members of the structure may be taken the same as found for the condition where rollers are used, and the horizontal component of the wind-load equally divided between the supports. iM.M .i., . Table XX. Three-hinged Arch. Web-Stresses 5io<-iqj.»« v'f!i' Thousand pounds Snow on Snow on Wind Wind Max. stresses Member, Fig. 61 Dead load, Fig.GlA . left of crown, Fig.eiB right of crown. Fig. 61C Snow over all the roof on left of crown. Fig. 61f on right of crown,* Fig. 61c Ten-, sibii Com- pression 39-38 - 4.9 - 3.8 + 2.1 - 1.7 -13-7 + 2.6 16. 5 36-37 +10.4 + 0.3 +14.5 +14.8 -18. 5 +18.0 8.1 28^7 34-35 +14.5 + 8.3 +13.0 +21.3 -18.6" +16. 1 4.1 38.9 32-33 +17.8 +12.7 +10.6 +23.3 -15.4 +13. 1 43.6 30-31 +19-7 +13.8 + 7.6 +21.4 -10.7 + 9.4 42.9 28-29 +20.3 +12.3 + 4.7 +17.0 - 4-9 + 5.8 38.4 26-27 +18.7 + 9.3 + 1.2 +10.5 + 3.4 + 1.5 29.5 24-25 +15.3 + 5.4 - 1.8 + 3.6 +10.8 — 2.2 26.1 22-23 +10.2 + 1.5 - S-i - 3.6 +19.0 - 6.3 29.2 20-21 + 9-9 + 3.5 + 2.0 + 5.5 + 2.4 + 2.5 15.9 18-19 - 0.7 - 9-3 - 2.7 — 12.0 + 6.6 - 3.3 13.3 5.9 16-17 -13.6 - 6.8 - 8.1 -14.9 +10.9 -10. 30.4 14-IS -42.3 -15.9 -II. 4 -27.3 + 2.8 -14. 1 72.3 37-38 - 7.1 +11. 2 —22.0 — 10.8 +29.8 -27.3 23.2 22.7 35-36 -12.9 - 3-5 -16.3 -198 +24.9 —20.2 36.6 12.0 33-34 -16.8 -IS. 8 -10.4 -26.2 +18.8 -12.9 45. 5 2.0 31-32 -17 9 -19.2 - 4.2 -23.4 +10.0 - 5.2 42.3 29-30 -17.9 -17.0 + 0.6 — 16.4 + 1.4 + 0.7 34.9 27-28 -14. 1 -11.6 + 5.0 - 6.6 - 7.4 + 6.2 25.7 25-26 - 9-4 - 5.3 + 8.7 + 3.4 -17.0 +10.8 26.4 1.4 23-24 - 4.7 + 0.4 +11. +11. 4 -23.3 +13.6 28.0 9-3 21-22 + 3.0 + 5.2 +13. 1. +18.3 -29.5 +16.2 26.5 24.4 19-20 + 0.8 + 1.6 + 3.1 + 4.7 — 7.4 + 3.8 6.6 6.2 17-18 +18. 5 + 9.2 +10 9 +20.1 -14.8 +13.5 41.2 15-16 +36.3 +16.8 +17.8 +34.6 -19-1 +22.1 75.2 j * By proportion, 18 600 : 15 000. i j Changes in Temperature do not seriously affect the stresses in the members' of a TRUE THREE-HINGED ARCH, or one with a tie-rod and rollers at one end,j as the change in geometrical shape is quite small. For the arch with a tie-rod i and no rollers, the effect of changes in temperature may affect the supporting' forces if the tie-rod is not so protected that it will change but little from its average temperature. In most structures this is the case as the tie-rod is iii or under the floor of the building. The Two-hinged Arch differs essentially in construction from the three- Hinged ARCH in having only two pins or hinges which are placed at the supports.; Fig. 62 shows the form of truss which will be used in explaining the method for- finding the stresses in the members of the truss. Supporting Forces. The supporting forces are inclined but can be re- solved into vertical and horizontal components. The vertical components are readily found as they are the same as for a simple truss on two supports. The horizontal components depend upon the areas of the members and their modul^ OF elasticity when the dimensions of the truss and the loading are known. ' •• Trussed Arches 1129 Horizontal Thrust for Vertical Loads. -■=XS-2 This can be found from the formula AE where the symbols have the significance given on page 1086. But this contains the unknown area A for each piece. For a preliminary trial the procedure is as follows: In the truss shown in Fig. 62, divide the span into twenty equal parts and at the centers of the divisions erect verticals. Through the points on these verticals, midway between the chords of the truss, draw a smooth curve as shown. This line will be designated the axis of the arch. Number the points desig- Mi. %s ^£ 'c?"!^ 13 /> ''^ v-^SS k--9.9- ^^ _^ tfl -^JlI. _^^ _5_&i-^ _ 1^ 24 25 -r'TF 1 I Fig. 62. Two-hinged Arch. Truss-diagram L_^-. nated above, i, 2, 3, etc., as shown in Fig. 62, and let x and y be their coordi- nates with the left support as the origin. Scale the length of the curve between the centers of the divisions so that y is practically the ordinate of the center of the short length of curve, and call this length of the curve 5^. On a radial line at each point numbered i, 2, 3, etc., scale the distances between the upper and lower chords, calling the distance h and compute V2 h^= I, which expresses, approximately, the moment of inertia of the section when the chord-areas are unity and the web-members are neglected. Let M represent the bending MOMENT at any point having the abscissa x, of the loads, considering the truss as a simple beam on two supports; or, for a single load P, M = Rx— P (x— a), X being greater than a, where a is the distance of the load P from the left sup- port. Then if 5.9 -^ EI is represented by <}> the horizontal thrust can be found from the formula, 1130 Stresses in Roof-Trusses Chap. 27 For the vertical loading shown in Fig. 62, the value of Hi is io8 ooo lb, and Vu being one-half the total load, is 195 000 lb. The stresses in the members of the truss can now be found by the usual graphical method. The snow-load, if any, must be treated in a Hke manner. The computations are considerably shorter, since 2y20 remains unchanged, regardless of the loading. Wind-Loads. For wind-loads the process is not changed very much. The value of M is the moment of the wind-loads, assuming the truss as hinged at the right support and on rollers at the left support. The value of Vi, which is vertical, is found by taking the sum of the moments of the wind-loads about the hinge at the right support and dividing this by the length of the span. The value of Hi is found from the formula given above, and then the stresses are found by the ordinary stress-diagram. The maximum stresses are now found and the proper areas of the members determined. The True Horizontal Thrust. The method just given is a close approxi- mation to determine the areas of the pieces so that the correct formula for Hi can be applied. This formula is SSid ^ uH AE^'MAE where the symbols have the meaning already given. Applying this formula for the dead load shown in Fig. 62 and areas shown in Fig. 58, the value of //j is no 600 lb, which is but httle different from the value found by the approximate method. Dead-Load Stresses. The stress-diagram for the dead LOAD is shown in Fig. 62a. Considerable care must be exercised in drawing the stress- diagrams, and their correct- ness should be checked by computing the stresses in one or more pieces. Compare Fig. 62a with Fig. 58a. Changes in Temperature. Unlike the three-hinged arch the TWO-HINGED ARCH is Fig. 62a. Two-hinged Arch. Stress-diagram affected by changes in temperature an4 the stresses which are produced by such changes must be provided for. Vi= O and ^1 is determined from the formula where e is the coefficient of expansion for the material composing the truss, t° the number of degrees change in temperature and L the span of the truss. The other symbols have the significance already given. The above formula assumes that the truss-members are of the same kind of material. After Hi has been found, the stresses can be determined by constructing the stress-dia- gram which will be of the shape shown in Fig 58b. Tie-Rod. If a tie-rod connects the two supports of a two-hinged arch the remarks made concerning such an arrangement for the three-hinged arch apply here. Trussed Arches 1131 The Fixed Arch has no hinges and is a type which is seldom employed by architects in the truss-form. The rigid analysis of a trussed fixed arch is very long and tedious, so a few formulas will be given, necessary for the solution of ARCHES WITH SOLID WEBS, sucli as PLATE-GIRDER ARCHES. These formulas may be applied to truss-forms, where the chords are approximately parallel, without serious error. Midway between the top and bottom chords draw a smooth curve, called the arch-axis, and designate the distance between its ends as L or the span of the axis. Divide the span into n equal parts and at the centers of these divisions draw perpendiculars until they cut the arch-axis. C.L. Fig. 63. Fixed Arch. Truss-diagram Number the points i, 2, 3, etc., as shown by Fig. 63, which also indicates the nomenclature employed. Determination of Hu Vi and Hiifi. The equilibrium-polygon for a single inchned load is shown in Fig. 63, in its true position with reference to the arch- axis. This locates the point of application of Ih. The following formulas are very close approximations for arches having a rise greater than one-eighth the span. Hi = ZmxyA" ^ XyA" ' XK j XyK ( "EniryK l^mxyK{z — n) ..{: E%yi Hi XK Vi = Hiy2 — //2J/2 ZK + ri S/i Hi yi is measured down from A when Hiyi is negative. S is the sum of quantities lit governs for each point on the arch-axis numbered i, 2, 3, . . . «. For 'example -(i),-(i).-(i), -hetc. 1132 Stresses in Roof-Trusses Chap. 27 / is the moment of inertia of the chords about an axis midway between them. The sections of the chords are to be taken on radial lines passing through points i, 2, 3, etc. X and y are the coordinates of the points i, 2, 3, etc, in Fig. 63 dx L x = z— = z — 2 2n mxy is the moment at the point on the arch-axis having the coordinates xy assum- ing that the given loading is supported by the axis hinged at the right end and on rollers at the left end. n is the reaction at the left support under the conditions specified for mxy. In the above formulas the only terms which depend upon the loading are those containing mxy and ri, the others being constant for any given arch. While but one load has been used, any number may be used by considering mxy and r\ as the sum of the respective quantities for each load. Stresses. The stresses in the truss- members can be found by the ordinary graphical methods when //i, Fi and Hyi are known. For example, assume the numerical values shown in Fig. 64. The resultant of Vi and Hi is resolved into two components parallel and perpendic- ular to the bottom-chord member at the support. Then T must act at the upper-chord joint as shown. The two reactions parallel to the bottom chord are found by moments. The stress-diagram can now be drawn beginning with these forces and proceeding until the right support is reached. Symmetrical Loading. When the loading is symmetrical, Hiyi = hence Fi =fi. Also Fig. 64. Fixed Arch. Reactions =n2i/t and -Hi XK XK Changes of Temperattire. For temperature-changes, Ht = e/°L -^ XyA" Hxyi = Hiyi = Ht -^^ yi = HyK F, =0 10. Arches with Solid Ribs ■ \\ Arches with Solid Ribs. While this chapter considers trusses only, ifc may not be out of place to briefly consider arches having solid ribs. The computations for Vi, Hi and Hiyi remain unchanged, excepting that / now is the moment of mertia of the radial section of the rib at points i, 2, 3, etc. Arches with Solid Ribs 1133 Fiber-Stresses. If x and y are the coordinates of any point on the gravity- axis of the rib, which should coincide with the arch-axis, the bending moment at this point is, for each load, Mx = Ihyx + Vxx - Thy -P{pc-a)-Q{y - b) Ihyi is negative when y\ is measured below A in Fig. 64. Mxyc , Nxy ^ -~I~ '^ A where c is the distance from the gravity-axis to the outermost fiber. For the TWO and three-hinged arches, Hiyi =o. Radial Shear. Let Hx be the algebraic sum of all the horizontal components on the left of the section, Vx the algebraic sum of all the vertical components on the left of the section and 6 the angle which the radial section, upon which the shear is wanted, makes with the vertical. Then Tx = Vx cos 6 — Hx sin 0. Two-hinged Parabolic Arch. If the center line of the solid rib is a par- abola, when EI cos is a constant, the following simple formulas give the values of Vi and Hi'. o '. V 11 F. = P(i-i)-Q^*(i-A) .o,uinor,ri, and Hx = %-P[k{i-2k^ + k')]-Q 1 1 -^[5(1 -^-2^ + 4^3) -8H in which k = a^ L (Fig. 63), / is the rise of the axis, P is the vertical load acting down, Q is the horizontal load acting from left to right and h is the moment of inertia of the section of the rib at the crown. Fixed Parabolic Arch. In like manner the following formulas apply for the arch without hinges: V=P{l-kY{^-\-2k)-^Q{k- ^2)2 Hi = — ^ P)^2 (l - i^)' - Q { I + ^U - 15 + 50 ^ - 60 ^2 + 24 ^3) I Hiyx ==- Pk {i - k)H5k- 2) -fQ\ 2 k {1 - k)H2 - 7 k^Sk^)] 2 Ht=^.EI,et'' Htyx= —.El^ef AJ 27 The values of the factors containing k in the above formulas are given in tabular form in A Treatise on Arches.* Circular Arches, with solid ribs of constant cross-section and the center line an arc of a circle, may be considered by using formulas somewhat similar to those given for parabolic arches but very much longer and more complex. Formulas and tables for their solution are given in the treatise on arches referred to above. ♦ A Treatise on Arches, by Malverd A. Howe, John Wiley & Sons, Inc., New York. 1134 Stresses in Roof-Trusses Chap. 27 11. Influence-Lines for Simple Beams and Trusses An Influence-Line is a line showing the variation in any function at anj section of a beam or for any member of a truss, caused by a single load moving across the span. For convenience the load is usually considered as unity. A P Q B Ri' H X — >: a • \d CL 1^ -^^ t uior! ^^^„,„— . Fig. 65. Influence-lines. Reactions for Beams Reaction for a Single Load. If the load P, Fig. 65, moves from A towards B, the left reaction, when P is distant x from B, is expressed algebraically b> Ri= Px-7- L, which is an equation of a straight Hne. If x = o, Ri= o, and ii X = L, Ri = P. If we make ac = P and draw the two straight lines ab and cb the ordinate de immediately below P is the value of Ri for this position of P 11 ac= unity, then Ri = P {de). R R, P^ A Q Q 4 Fig. 66. Influence-lines. Reactions for Beams |< a '->H- -^^-' — . S^ —>-»->] Fig. 67. Influence-lines. Moments for Beams : Reaction for More than One Load. The reaction for any number ol ^ncentrated loads can be found as shown in Fig. 66. The moment at C, Fig. 67, when F . (a) jb] L Bending Moment for a Single Load. Pxa \< -6, -»J Fig. 68. Influence-lines. Moments for Beams + Pads + P^idi. This gives the moment at C for a given position of the loads, but this is not necessarily the greatest moment which these loads may cause, as some other position may cause a greater moment. The greatest moment at C will obtain when some concentration is at C. Let P be this concentration and ^ a -^ — b Fig. 69. Influence-lines. Moments for Trusses assume it to be divided into two parts, nP and mP so that n-\-,m= i, and n is greater than zero and less than i. The maximum moment at C will occur when Pi + P2 + P3-fP4 Px + nPi ■ The point in the beam where any given moving load causes the greatest POSSIBLE MOMENT is SO situated that the middle of the span is half-way between it and the center of gravity of the load.. Since a concentration will always be at the point, a few trials will determine the proper concentration to use. For example, two equal concentrated loads should be placed on the beam so that 1136 Stresses in Roof-Trusses Chap. 27 the middle of the span is at the quarter-point between the concentrations. The MAXIMUM MOMENT falls Under the concentration nearer the middle of the span. Chord- Member in Truss with One Set of Web-Members Vertical. In Fig. 69 the top chord member UiUz has its center of moments at L2 and the bottom chord member X1L2 at Ui. The influence-diagram for the moments at L2 and U2 is precisely the same as shown in Fig. 67. The moment produced by any load P is P {de). As long as one set of web-members is vertical the INFLUENCE-DIAGRAM wifl be identical with that shown in Fig. 69, regardless of the inclination of the diagonals or the chord-members. Chord-Members in Truss with Inclined Web-Members. The moments at points in the loaded chord, Fig. 70, have influence-diagrams identical with C Uo ^ 5 ^ Fig, 70. Influence-lineg. Moments for Trusses 2 Us I Va Ui Ur. Ill > Fig. 71. Influence-lines. Shear for Trusses that shown by Fig. 69. For the unloaded chord a slight modification must be made. For example let U2 be a center of moments, then if the loads were on a beam, mgn would be the influence-diagram (Fig. 70). For all loads on the left of Li and on the right of Li the diagram is correct and the moments at f/2 = Pi^i and Piaz. For loads between Li and Li draw the line rs. The moment at /72 is P2a2. Web-Members of Trusses with Parallel Chords. Fig. 71. The stress in UiLz equals the shear in the panel LiLz multiplied by the secant of Q» The Secondary Stresses in Truss-Members 1137 INFLUENCE -DIAGRAM will be drawn for the shear. For any load between L3 and B, the shear in this panel equals R2', hence, with ah as a reference-line, ha' is the INFLUENCE-LINE for i?2 and the shear is Pia.u Psas, etc., until the point L3 is reached. In Hke manner af is the influence-line for Ri and the shear for loads on the left of Z2 is Pia\. The shear for the loads P2 between L2 and L3 is Rx less the amount of P2 which is transferred to L2. The influence-diagram for the reactions of P2 on a span L2L3 is ff'e. The shear in this panel due to P2 is P2{dd') less P2 (d'c) or ^2^2- A load at k produces no shear in the panel. 12. Secondary Stresses in Truss-Members * Secondary Stresses. In the determination of stresses in a truss it is usually assumed that they act along the gravity-axis of each member; that the gravity-axes of all members at any joint meet at a common point; that the members are free to turn around this point, the joints being considered frictionless; and that all loads, including the weights of the members, are applied at the joints only. The stresses determined with these assumptions are axial or direct stresses, sometimes called primary stresses or main stresses. The assumptions made are not realized in practice and other stresses, called secondary stresses, are induced. An eccentricity causing bending moment occurs in the common case of the rivet-line not coinciding with the gravity- axis where angles connected with one leg only are used to resist direct stress. If the gravity-axes of members about a joint do not intersect at the same point bending moments are induced. The resistance of a joint to free angular move- ment as the truss deflects also induces bending moments. The weights of horizontal and inclined members add slight bending-stresses to the direct stresses in these members. At the supports there will be a resistance to hori- zontal deformation from temperature-changes and the deflection of the truss. The degree of this resistance depends upon the coefiicient of friction between the truss and the support, the vertical loads and the length of span. Members not straight and imperfect workmanship are other causes of secondary stresses. :With care in the design and fabrication secondary stresses in ordinary roof-trusses from the above causes^ need not be considered seriously. The main causes, 'however, of secondary stresses are faulty details. The actual shearing- stress sometimes found in details is much more than the direct shearing-stress, because of eccentricity in the lines of stress-action. Eccentric riveted connections may not be wholly avoided but they should be reduced to a mini- mum. The history of bridge and building-failures is mostly a story of faulty details. A structure has seldom given way for lack of strength in the main members. But if the strength of a structure is measured by the strength of its weakest part, it can be only as strong as the weakest detail. Because of this, connections that induce large secondary stresses, insufficient lacing of compression-members and careless grouping of rivets, have all invited disaster. The importance of the detailer's work is often underrated. What is usually considered the designing of a structure may be comparatively easy while the detailing may be difficult. A well-designed structure may be spoiled by poor detaiUng. The detailer should be a designer, that is, a designer of details, and at the same time the designer should be thoroughly familiar with detaihng. ♦ From Notes by Robins Fleming. 1138 Design and Construction of Roof-Trusses Chap. 28 CHAPTER XXVIII DESIGN AND CONSTRUCTION OF ROOF-TRUSSES By MALVERD A. HOWE PROFESSOR EMERITUS OF CIVIL ENGINEERING, ROSE POLYTECHNIC INSTITUTE 1. Design of Wooden Trusses Proportioning the Members. In Chapter XXVII it has been shown how the STRESSES in the members of a truss, supporting known loads, may be found. The next step is to proportion the members for the stresses which they have to resist. The methods employed and the allowable unit stresses are given in detail in Chapters XI to XVI, inclusive. For example, tension-members are considered on pages 385 to 400; steel strut-beams and tie-beams on pages 571 and 572; and wooden strut-beams and tie-beams on page 633. As a matter of convenience the unit stresses used in this chapter are given in the following table in a condensed form. White pine is here used for the wooden trusses. Table I. Allowable Unit Stresses Used in Truss-Design * Material Kind of stress Safe unit stress lb per sq in White pine Tension with the grain 700 50 I 100 200 200 I 100 100 500 700 J 12 000 7SOO 15 000 15 000 16 000 10 000 20 000 ?4 000 16 000 10 000 Tension across the grain Compression on end-fibers . Compression across the grain Compression across the grain, round pins. . Columnsf under 15 diam long Shear with the .grain Shear across the grain Transverse, fiber-stress Wrought iron Rolled steel Bolts in bearing Rods in tension Bolts in shear Bolts in bearing Bolts in bending, fiber-stress Beams in bending, fiber-stress Beams in shear ♦ See also, the tables on pages 376, 412, 449, 454, 557. 647 and 1200. These must be modified, when necessary, to comply with building laws. White pine is used for the examples in this chapter because of the difficulties in making the joints owing to the rel- ative softness of the wood. If one can design a truss in white pine he will have no trouble with the design of trusses constructed with other kinds of wood. t See, also, Table I, page 449, and Table XVI, page 647- tThe Borough of Manhattan, New York, Building Code (1917), gives i 200 for this value. Other values are about the same as in the table. Inclined Surfaces of Wood. The normal intensity of the stress on inclined surfaces may be found from the empirical formula r =q+{P - q){0/^oy Design of Wooden Trusses 1139 where r equals the permissible normal unit stress on this inclined surface, q that across the fibers, p that on the end of the fibers and Q the angle the inclined surface makes with the direction of the grain. For white pine this gives r = 200 4- ^^9 Round Pins on End-Fibers.* For all practical purposes the permissible unit stress may be taken as the mean of p and 5; or, for white pine \^ {p-\- q) = 650 lb per sq in Wooden Columns over Fifteen Diameters Long. The formula f used in this chapter and considered amply conservative by many engineers is the formula approved by the American Railway Engineering and Maintenance of Way Association in 1907. For white pine this formula is '^ Si = S (i — 1/60 d) = 1 100 (i — 1/60 d) where 5, = the permissible unit stress, 5 = the permissible compression on the end-fibers, I = the length of the column in inches and d the least dimension of the cross-section of the column in inches. Steel Columns. For the shapes used in roof-trusses, the formula advocated by C. E. Fowler in bk specifications for roof-trusses is used in this chapter: Si = 12 500— 500 l/r where Si = the permissible unit stress, / = the length of the column in feet, and r = the least radius of gyration of the cross-section of the column. Example i. The truss shown in Fig. 1, which is the queen truss shown in Figs. 3, 12, 53 and 54 in Chapter XXVII, is considered for this example. The stresses given in tlie following table are used. The members RR are wrought- iron round rods, not upset at the ends;, and all other members are of white pine. None of the members in this truss is subject to transverse stress, so direct tension and compression onlj'^, have to be considered: Table II. Stresses and Dimensions for the Truss Shown in Figure t Member A B. C. D. E. N, M R. ^ Stress in pounds +21 250 -|-i8 900 -f 13 200 + 6450 + 5 100 -17 150 -12 750 Dimensions 6 by 6-in white pine 6 by 6-in white pine 6 by 6-in white pine 4 by 6-in white pine 4 by 6-in white pine i6 by 8-in white pine or Three 2 by 8-in pieces with %-in bolts, 2 ft on centers One iH-in round rod Vertical Rods, Fig. 1. The tension in each rod is 9 100 lb. If the permis- sible stress is 12 000 lb, the section-area of each rod is 9 100 -m 2 000 = 0.76 sq in. The net area of a iH-'u\ rod is 0.694 sq in; and of a itl-in rod, 0.893 sq in. The iH-in rod would answer but the iH-in rod is preferred. * When the same unit stresses are used for flat and curved surfaces, Tables VII and VlII, pages 430 to 431, of Chapter XII may be used. I For other formulas and Tables based upon them, sec Chapter XIV, pages 449 to 452. 1140 Design and Construction of Roof-Trusses Chap. 28 Rafters, Fig. 1. The stress in the rafter at A is 21 250 lb and at B 18 900 lb; but as it will be made of one piece, the size is governed by the greater stress. The unsupported length is about 9 ft, and assuming the least dimension of the (9 X I2\ I — - I = 770 lb per sq in. 21 250/770 = 60 X 6/ 27.6 sq in =the area of cross-section required, which is less than that of a 6 by 6-in piece. A 6 by 6-in timber is actually sV^ by s'/^-in, with a cross-sectional area of 30.25 sq in, a little in excess of the area required. In general the nominal and STANDARD sizcs of timbers differ by about one-half an inch in each cross-dimension. Fig. 1. Queen Truss. (See, also, Figs. 4a, 10, 13 and 16 and Chapter XXVII, Figs. 3, 12, 53 and 54) Member C, Fig. 1. The stress in this member is 13 200 lb and its unsupported length, 12 ft. In this case l/d = 24, wheni = 6 in; Si = 660 lb per sq in. The required section-area is 13 200/660 = 20 sq in, and hence' a 6 by 6-in timber is used. The top-chord should have one dimension constant in order to facilitate the making of good connections at the joints. Braces, Fig. 1. The stress in the brace Z) is 6 450 lb and its unsupported length about 9 ft. A 4 by 6-in timber is first tried. Here l/d = 27 and Si = 605 lb per sq in. The required area, therefore, is 10.7 sq in and a 4 by 4-in timber answers the purpose; but for additional stifTness and convenience in making con- nections, a 4 by 6-in piece is used. Each brace, E, has a stress of 5 100 lb and a total length of 17 ft. If the braces are bolted where they cross the unsupported length may be taken as 8'/^ ft. It is evident that a 4 by 6-in piece is ample for each brace. Bottom Chord, or Tie-Beam, Fig. 1. The maximum tension in the bottom- chord is 17 150 lb in N. The permissible unit stress is 700 lb per sq in; hence the net section-area required is 17 150/700= 24.5 sq in. A 2 by 12-in plank, if continuous from end to end of the truss and without holes and notches, will take care of the stress alone but will not permit of proper connections. A 6 by 6-in piece is selected, but it may be necessary to substitute for it a 6 by 8-in piece when the connections are made and it is spliced in the middle. If the member is built up of planks, three 2 by 8-in pieces are required; and they must be Design of Wooden Trusses 1141 thoroughly bolted together by a pair of bolts every 2 ft of their length. If 24- ft and 14-ft lengths are used, the joints of the strands will be about 10 ft apart. Example 2. For this example the truss illustrated in Fig. 2, which is the scissors truss shown in Figs. 4 and 24, Chapter XXVII, is considered. The direct stresses for dead load, wind and snow were found in Chapter XXVII and are given in the following table. The rafters and the bottom chord support Fig. 2. Scissors Truss. (See, also, Chapter XXVII, Figs. 4 and 24) loads between the joints and consequently must resist cross-bending stresses as well as direct stresses. The load on each piece is given in the table under the word transverse. Table III. Stresses and Dimensions for the Truss Shown in Figure 2 Member Stress, lb Transverse load. lb Dimensions, white pine A B D -1-8 000 -h6 6oo +1890 + 750 -4350 -2 530 -1875 . -5400 -1875 I 000 I 320 Two 2 by 8-in planks Two 2 by 8-in planks One 2 by lo-in plank One 2 by lo-in plank Two I by 8-in planks Two I by 8-in planks One 2 by lo-in plank One 2 by lo-in plank One 2 by lo-in plank E F H 5 470 384 T Ti Rafter B, Fig. 2. The piece B rather than the piece A is considered, as it is considerably longer. The total vertical load on the piece acting as a beam is I 320 lb and the horizontal span is about 8 ft. The bending moment at the center 1142 Design and Construction of Roof-Trusses Chap. 28 is li (i 320 X 8X 12) = 15 840 in-lb. If the depth of the piece is assumed to be 8 in, the proper thickness is found from the equation, 15 840= H Sbd^ = M (700 X 8X 8X fc), or h= 2.12 in. This neglects the component of the ver- tical load parallel to the rafter. Considering now the direct compression of 6 600 lb and remembering that the sheathing is nailed to the rafter, the least dimension d of the piece is it» depth, which may be taken the same as that used for the piece resisting the transverse stress. The unsupported length of the piece is about 12 ft. Then l/d = 18, ^i = 770 lb per sq in and the required area of cross-section is 6 600/770 = 8.6 sq in. As the depth is 8 in, the thickness is about I.I in. Combining the two pieces, the total thickness is 2.12 +1.1 = 3.22 in, and a piece having the nominal size of 4 by 8 in is required. Since the sheathing is nailed to the rafters, two 2 by 8-in planks may be used without de- creasing the stiffness of the member. While the above method of designing a piece subject to two kinds of stress is not correct for all conditions which occur in practice, the results are on the safe side, and the method has the ad- vantage of being easily applied. Member S, Fig. 2. Considering the transverse load first, the bending moment at the middle is found to be % (470 X 15. 5 X 12) = 10 930 in-lb. If the depth is assumed to be 10 in, the required thickness, found from the equation 10 930 = % (700 X 10 X 10 X &), is 0.94 in; or, a board i by 10 in in cross-sectional area will carry the transverse load if prevented from twisting sidewise, which it has a tendency to do in this case where the ceiling is attached directly to the member. The side-stiffness will be further increased when the additional material for resisting the tension is in place. The net area for the direct tension of i 875 lb is 2.68 sq in, which requires a board 10 in wide and only a trifle over \i in thick. The total thickness becomes 0.94 -|- 0.27 = 1.21 in, and it will therefore be nec- essary to use a 2 by lo-in plank. Member B, Fig. 2. This is in compression, but the stress is quite small, being only 750 lb. The possible extension of the 2 by lo-in piece used for S is next considered, to find if it can be extended and used here. The unsupported length *s about 6 ft, and the least dimension 2 in; hence l/d = 36, Sx = 440 lb per sq in and the required area of the cross-section becomes less than 2 sq in. The 2 by lo-in piece is therefore ample. Members T and Ti, Fig. 2. Inspection shows that a 2 by lo-in plank is quite sufficient for these pieces. Member D, Fig. 2. The unsupported length is about 7 ft. Then, f or ^in legs, back to back, the least value of r = 0.78 in (Table XVI, page 371). 5i = 12 500- 500 X 12/0.78 = 4810 lb per sq in 5 000 ^ 4 810 = 1.04 sq in, required. The area of the two angles used is 2 X 1.06 = 2.12 sq in (Table XVI, page 371). Member CD, Fig. 5. The stress in this member is very small and one angle will probably fulfill the requirements. For one angle, 2 H by 2 by U in, the least r = 0.42 in (Table XI, page 365) and ^i = 5 300 lb per sq in, indicating that this angle gives a large excess of strength. As pointed out above, it is better to use two angles. Sienderness-Ratio. The best specifications Hmit the ratio of the least dimen- sion to the unsupported length of a compression-member to 50, unless the allow- able unit stress as given by the column-formula is decreased. The member EF is 2y2 in deep and about 144 in long, so that its length is 57.6 times its least dimension. As there is a great excess of area, the actual unit stress is much below that given by the formula. Stay-Rivets. The compression-members made up of two angles and designed as described in the preceding paragraphs, have been considered as if acting as solid pieces. It is clear that the various parts must be so fastened together that no individual piece will buckle. If / is the unsupported length of the member 1148 Design and Construction of Roof-Trusses Chap. 28 as a whole, r the corresponding least radius of gyration, r' the least radius of gyration for any part and /' the unsupported length of the part, or the distance between stay-rivets, there is the following relation: I'/r' = l/r or /' = Ir'/r For the member EF I' = 144 x 0.42/0.78 =- 78 in. Practice reduces this to 2 or 3 ft. Tension-Members, also, should be riveted together in a similar manner to make the parts pull together. Example 5. The next truss considered is the Fink truss shown in Fig. 7, in which two angles are used for ail members and ■>:i-in rivets at the connec- tions. Member AC, Fig. 7. For a unit stress of 16000 lb per sq in, the net area required is 21 800/16 000 = 1.36 sq in. Two 2H by 2M by H-in angles have a section-area of 2.38 sq in (Tab/e XII, page 367). Deducting 2 {VsX H) = 0.41 sq in, the net sectio»< becomes 1.94 sq in, while the required area is 1.36 sq in. a H u •■^1 -21800 C -18700 E - 12500 I I V SlV : H ' I Fig. 7. Fink Truss. (See, also, Figs. 22, 22a, 22b, 22c, and 22d) Members CB and £//, Fig. 7, are composed of angles of the same size. Members CD^ DP^ EF and PO, Fig. 7, are made of two 2^/^ by 2 by H-in angles with a net area of 2.12 sq in. This greatly exceeds the required area. Members BC, BP and DB, Fig. 7. From the preceding example it is evident that a pair of minimum-size angles will be quite sufficient. Two 2H by 2 by H-in angles, having a section-area of 2.12 sq in, are used. Member AB, Fig. 7. For this member in which there is a direct compres- sion of 23 500 lb and a transverse stress due to a load of 2 500 lb, a preliminary trial is made with two 5 by 3!/^ by %-m angles, with the 5 -in legs back to back and separated by a H-in gusset-plate. The moment of inertia about an axis passing through the center of gravity of the two angles and parallel to the shorter legs is (Table XI, page 363) 7.78* and the corresponding radius of gyration is 1.6 in. About a vertical axis the radius of gyration is (Table XVI, page "371) 1.42 in, which is the least radius to be used in the column-formula. The * It will be noticed that the values given for the properties or elements of the angles used in this example differ slightly from those given in the tables referred to, as the section-area, I, r, X, etc. This changes the result very slightly and is due to variations in the decimal figures of values in different editions of manufactures' handbooks. Editor-in-chief. Joints of Wooden Trusses 1149 moment produced by the 2 500-lb load at the center of the member is H (2 500 X 9.2 X 12) = 34 500 in lb. The section-area of the two angles is (page 363) 6.1 sq in. 5 = 23 500/6.10+ (34 500 X 1.61)77.78= 10990 lb per sq in Si = 12 500— (sooX 9.2)/i.42 = 9 260 lb per sq in Since ^i is less than S, it is seen that the angles selected are a little too light. Instead of using angles of greater thickness it will be better to select a larger size. If two 6 by 3]- 2 by %-m angles are used (page 363) 5 = 23 500/6.86 -1- (34 500 X 2. 04)/ 1 2.86 = 8 890 lb per sq in Si = 12 500 - (500 X 9.2)/i.34 = 9 070 lb per sq in This shows that there is ample strength and stiffness and that the area is in- creased by 0.76 sq in. If two 5 by sl^ by ^le-in angles had been used, the area would have been increased 0.96 sq in (page 363). The least radius of gyration used in the expression for Si assumes that the angles will be separated by H-in gusset-plates. If thicker gusset-plates are used^ the value of r will increase. Practical Details. The use of uniform sizes for members in the same straight line is economical and adds rigidity to the truss. The angles can be furnished up to lengths of 60 ft and over, thereby reducing the labor of cutting them and decreasing the number of rivets and the size of the gusset-plates. The portion of the truss AEG shown by Fig. 7 would be completely riveted up in the shops, leaving only three joints to be riveted at the building. In general, any truss which has one outside dimension not exceeding 10 ft, can be shipped by rail. This governs the location of the splices. 3. Joints of Wooden Trusses The Joints of any truss should be proportioned with as much care as is used in determining the sizes of the members, so that the truss will be equally strong in all its parts. The general principles and methods for designing joints are explained in Chapter XII and illustrated by examples. To further explain the subject, the methods of design of some of the joints for the trusses shown in Figs. 1 and 3 are added in this chapter. Joint I, Fig. 1. This is the most important joint in the .truss. There are many forms for this joint, but only a few of them are illustrated. Fig. 8 shows a SIMPLE BOLTED JOINT. The rafter rests in a notch in the bottom chord and is held in place by one or more rolled-steel bolts. These bolts are perpendicular to the axis of the rafter, and the stresses in them are found graphically by the diagram abc (Fig. 8) in which ac is perpendicular to the scarf-cut or seat of the rafter. The tension in the bolts is found to be 31 550 lb, and with a permis- sible stress of 16000 lb per sq in, the net section-area required is 1.97 sq in, which corresponds to one ijg-in bolt (Tabic II, page 388). The washer, bear- ing across the grain of the rafter, will have an area of 31 550/200= 158 sq in (page 1 1 38). Since the top-chord is actually but sH in wide, the length of the plate is about 28 in. Such a plate would look out of proportion with one bolt, so five %-in bolts are substituted, having a net section-area of 2.10 sq in (Table II, page 388). Two bolts are placed near each end of the plate and one bolt is placed in the middle. The bolts are spaced about 9^/^ in apart. The thick- ness of the plate may be taken as one-fifth the distance from the end of the plate to the nuts of the first pair of bolts. This distance is about 3.4 in; hence the thickness is 0.67 in. A %-in plate is used. The lower end of each pair of bolts is provided with a plate-washer bearing upon the inclined surface of the white-oak bolster as shown. The angle of inclination approximates 45** 1150 Design and Construction of Roof-Trusses Chap. 28 and hence the allowable pressure on the wood is 500 -f (i 400— 500) H = 725 lb per sq in. (Sec Table VI, page 454, Table XVI, page 647, and the equation on page 1138.) The pair of bolts carry a tension of 31 550 X % = 12 620 lb, and this stress requires a plate having an area of 12 620/725= 17.4 sq in, which will be provided by a plate 5H by 4 by ^ in. For the single bolt, a 4 by 4-in CAST-IRON BEVELED WASHER is used, having a 3,4-in lug let into the bolster to take the horizontal component of the pull in the bolt. To prevent the bolster slipping on the bottom chord, two oak keys are employed. (See Table VI, page 454, and Table I, page 113S, for permissible unit stresses.) The horizontal component of the pull in the bolts is about 22 300 lb, and for one key, 11 150 ^^^f^ [{-20^-— H 4 X 5^x X" C.I. Washer ^1 x 5>^ (27 350/10 000) = 1.37 sq in, requiring two i-in steel bolts (Table III, page 419). The thickness of the steel plaj^ necessary to give sufficient bearing against the bolts is V'i (13 675) -^ 20 000 X I, or ^ = .34 in. A y2-[n plate is there- fore ample. Joint I, Fig. 3. An ordinary CAST-IRON ANGLE-BLOCK can be used in this particular case as shown in Fig. 9b. Other Details for Joint i. Fig. 3. Another design for this joint, but for another truss, is shown in Fig. 9c. The rafter and bottom chord are of long-leaf yellow pine and the metal parts of steel. The stresses are transmitted through 3 by %-in plates in bearing against the end-fibers of the v/ood, and from these plates to the side plat] through the bolts in bending. The side plates should be drawn up agaii the wood by lag-screws, as shown, to prevent buckling when in compressioi Fig. 9d. Truss with Cast-iron Angle-block Joints of Wooden Trusses 1153 Fig. 9d shows a good application of the cast-iron angle-block used in the trusses of a blacksmith-shop of the Boston & Maine Railroad Company. The bearing and shearing values are provided for principally by a tenon on the back let into the bottom chord as indicated by the dotted lines. Joint 2, Fig. 1. Where a brace abuts against a rafter, as in this joint, one cut on the end of the brace should bisect the angle made between the brace and the rafter, and the second cut should be at right angles to this, as shown iri Fig. 10. The end is then set in a notch or mortise to keep the brace in place and to trans- mit the pressure to the rafter. The purhn may be supported by a 3 -in plank, as Fig. 10a. Purlin-connection. Purlins on Top of Truss-chord Fig. 10. Detail of Joint 2, Fig. 1, with Rod Added Fig. 10b. Purlin-con nection with Steel- Angles Fig. 10c. Purlin-connec- tion with Wooden Bear- ing-block Fig. IOd. Purlin-connection with Beam-h-anger shown in Fig. 10. Some form of metal hanger, of the Duplex type is often preferred. In the truss shown in Fig. 1, there is no vertical rod at this joint; but many trusses have a rod there, and one is therefore shown in Fig. 10. The washer on top of the rafter must have sufficient area to transmit the stress ih the rod to the rafter. Other forms of purlin-connections are shown in Figs. 10a to IOd. Apex of King-Rod Truss. Fig. 11 shows the joint at the top of a king- rod TRUSS with a Duplex hanger to support the purlin. The wrought-iron or steel plate for large trusses should extend along the top of each rafter a sufficient distance to permit its being fastened by lag-screws or bolts. Fig 12 ghows a castjng in place of the ROLi-PP plat^. 1154 Design and Ccnstruction of Roof-Trusses Chap. 28 Joint 3, Fig. 1. This should be made as shown in Fig. 13. The inclined cuts bisect the angle made between the two 6 by 6-in pieces. In place of the CAST-IRON WASHER a WROUGHT-IRON OF STEEL PLATE may be USCd. ^ Thick Fig. 11. Detail of Apex of King-rod Truss Fig. 12. Alternate Detail for Apex of King-rod Truss pO^'SixOx 5^'* Washer Fig. 13. Detail of Joint 3, Fig. 1 Fig. 14. Detail of Joint 2, Fig. 3 Joint 2, Fig. 3. One method of making the connections at this joint is shown in Fig. 14. The end-cut of the main brace is made as shown, the distance d pJi^L^ Sx g'x X Pla^te Fig. 15. Alternate Detail of Joint 2, Fig. 3 being determined by the necessary area of the inclined cut in the top chord. The permissible unit pressure is about 525 lb per sq in. Then 33 450 lb requires 64 sq in, or the distance d is sl little greater than the depth of the brace. This Joints of Wooden Trusses 1155 form of detail can only be used for the end-brace by making two notches as shown by the dotted Hnes. A much better method is shown in Fig. 15, where an ANGLE-BLOCK is used. The angle-block is made of very hard wood so that the bearing of the brace is provided for, and it is notched into the chord a suffi- cient amount to transfer the horizontal component of the stress in the brace to the chord. A notch i in deep carries i loo X 9H = lo 450 lb (Table I, page 1 138); hence for a horizontal component of 27350 lb (Fig. 4), the notch is made 2% in deep. This clearly shows that braces should be inclined at least 45° with the horizontal, unless awkward or weak details are ^ to be tolerated. The vertical rod here has a stress of 13 492 lb. The WASHER on top of the chord transfers this stress in bearing across the grain. At a unit stress of 200 lb (Table I, page 1 138), the area is 67.4 sq in, requiring an 8 by 9 by %-in plate. 6 X 8 X ^ Washer Fig. 16. Detail of Joint 7, Fig 1 Joint 7, Fig. 1. This is shown in Fig. 16, and the above discussions cover all details of its design. Splices. Since it is not economical and often impossible to procure timbers exceeding 25 or 30 ft in length, it is necessary to make one or more splices in the chords. The top-chord of a Howe truss is spliced by placing the tim- bers end to end, and by spiking or bolting on side planks to keep them in place. The bottom chord cannot be treated in this manner, as it is in tension. Hook-Splice or Tabled Fish-Plate of Wood. It is assumed that the bottom chord of the truss shown in Fig. 3 is to be spliced at the middle of the span. Fig. 17a shows this splice. It is as- sumed that the side pieces are of white pine. The total depth of the notches is 48 5604- (iiooXiiH)=(/=3.84 in (Table I, page 11 38). Each notch, then, is about 2 in deep. The length of the table is /= H [48560-^(100 X 1 1 '/^)] = 2 1 in. The net thickness of each side # g round x2^-^12x -idl k -42^ li I ■^ zEhL. ^F- Fig. 17. Splice of Bottom Chord of Truss piece is Vz (48 560)/ (700 X nH) = 3 in, without deducting anything for the two bolt-holes. The chord-pieces have less than the required area because of the deep notches required; hence a 12X 12-in timber is required if this form of splice is used. The proper dimensions are shown in Fig. 17a. Metal Splice. Fig. 17 shows an old 'and very efficient form of splice, pro- portioned to replace the form shown in Fig. 17a. Splices for Built-up Chord. The top chord, when built lt of 2-in planks, requires thorough spiking with two H-'m bolts at the ends of each plank. The bottom chord, which is in tension, should be so arranged that the ends of the planks in one strand are well removed from the ends in other strands. Thd 1156 Design and Construction of Roof-TrusSes Chap. 28 middle strand of a built-up chord is completely cut away to permit the passage of the vertical rods. The strands should be thoroughly spiked, and bolted every 2 ft, care being taken to see that the bolts do not come nearer than 5 in from the end of any plank. While built-up members are in favor with build- -21- r .Table 12x12: -*- —21 -H< 21-— ^^t^ -21- X bolts Fig. 17a-. Alternate Detail for Splice of Bottom Chord ers because the materials are readily obtained, yet for important structures the writer believes it is worth while to use a little more effort and pay a little more to get SOLID STICKS for truss-members. Wall- Joint of Scissors Trusses. In scissors trusses the joint over the wall formed by the rafter and tie-beam should always be carefully proportioned owi adJ 1- -13" Wall- ed. Elate 14* long J3, 8^" X 4K' Lag Screjya Dotted lines show screws on, other side. Fig. 18. Wall-Joints for Scissors Trusses, Figs. 24 to 27, Chapter XXVI to the stresses; otherwise the joint is liable to open and the wall to be pushed out. Much greater strength is required in this joint than in the wall-joint of a KING-ROD truss of thc same span, because the stresses in a scissors truss are usually at least twice and sometimes three or four times as great as in a truss with a horizontal tie-beam. For a scissors truss built of planks, as in Fig. 2, Joints of Wooden Trusses 1157 a i-in bolt through the center of each joint, with as many spikes as can be driven, will ordinarily give sufficient strength. For trusses like those shown in Figs. 24 to 27 of Chapter XXVI, one of the best methods of making the wall- joint, unless the roof is quite flat, is that shown in Fig. 18, which is the detail of an actual joint where the stress in the tie-beam was 25 000 lb. It should be noticed that the wrought-iron strap is secured to the tie by lag-screws in- stead of BOLTS. It is practically impossible to bolt a strap to each side of a beam so as to get a good bearing for all of the bolts, owing to the difficulty in boring the holes straight; and if the holes are bored a little large, some bolts may bear on the wood and some may not. With lag-screws each screw is bound to get a good bearing in the wood. The holes in the two sides of the strap must, of course, be staggered, so that they will not come opposite each other. The net sectional area of the strap should at least be eqiml to the stress in the tie-beam divided by 2 X 12 000 (Table I, page 1138). The number of lag-screws, 4or both sides, is found by dividing the stress in the tie-beam by the resistance of one screw. For the safe resistance of lag-screws used in this way, the values given in Table V are recommended. In the joint shown in Fig. 18, the stress in the tie-beam is 25 000 lb, and the wood is Douglas fir. The above rules, therefore, require a sectional area in the strap of H (25 ooo)/i2 000 = 1.05 sq in and twenty-three ^-in lag-screws. Only thirteen are shown in Fig. 18- Table V.* Safe Resistance of Mild-Steel Lag-Screws When Used as in Fig. 18 Size of screw in Safe resistance in pounds Minimum inches thickness of strap in Oak White Douglas Long-leaf diam. length pine fir pine inches Vs iV2 288 255 267 288 M Vi 4 512 454 474 512 V4. % 4 800 709 741 800 Ka % AM I 153 I 022 I 067 I 153 Me % 5 1 569 I 391 I 453 I 569 H * Based upon experiments made (1915-1916) by Professor H. A. Thomas. With a thickness of % in, the width of the strap necessary to give a sectional area of 1.05 sq in is 1.05/. 375, or about 3 in. To this should be added the diam- eter of one lag-screw to obtain the working width. Thus 3 -f- M = 3^4 in. The strap used is 4 by Y^ in in cross-section, as some additional strength is obtained by the bolt at X, which it is necessary to insert to hold the timbers together while the truss is being raised into position, and also to bring them tightly together before fitting the strap. Fig. 19 shows another method of making this joint which may be used with advantage -when the inclination of the rafter is less than 45°. One advantage in using this truss is that if it is erected one piece AT A TIME, the tie-beams may be put up first, thus providing a seat to receive the rafters. The strap prevents the end of the rafter from springing up. The diameter of the bolt should be proportioned to the horizontal component; of the stress in the rafter. Fig. 20 shows a good form of joint to use at joint 5 of Fig. 27, Chapter XXVI, when it is desired to substitute a wooden tie for the rods shown in Fig. 27. The sectional area of the strap and the number of lag-screws should be proportioned by the rules given for Fig. 18. Washers. Where iron or steel rods are used in wooden trusses, wasTiers are necessary under the heads and nuts to properly distribute the loads on the wood. The dimensions of the washers are determined by the allowable bear- 1158 Design and Construction of Roof-Trusses Chap. 28 ing pressure on the wood and the magnitudes of the loads. Table VI gives the allowable loads which can be transmitted by standard round cast washers and rectangular washers bearing across the wood fibers. Table VII gives the di- mension of standard round cast washers. The bearing areas of these washers Casting Fig. 19. Alternate Detail for Fig. 18 are too small for use on the softer woods and, therefore, except when the rods are small, it is better to use rectangular washers of iron or steel plate. Very- large washers should be cast, and should have the form shown in Fig. 20a. The use of the ribs gives the required strength and saves considerable material. Fig. 20. Detail of Joint 5, Fig. 27, Chapter XXVI Fig. 20a. Cast-iron Washer with Brackets Thickness of Rectangular Steel-Plate Washers. The thickness of rec- tangular steel-plate washers can be found from the following formulas in which / is the distance from the edge of the plate to the nut and / the thickness of the plate. When used On white oak / = 3.4 / On white pine ^=5.2/ On long-leaf yellow pine / = 3-9 ^ On short-leaf yellow pine / «* 4.6 4 Joints of Wooden Trusses 1^ Table VI. Safe Bearing Resistance of Cast-iron Washers, in Pounds Round wa'ihers Size, Area,* White pine. Short-leaf Long-leaf White oak, in yellow pine, lb yellow pine, lb lb sq in lb Vi 5.16 I 030 I 290 I 810 2580 % 6.69 I 340 I 670 2340 3350 % 7.78 I 560 I 950 2720 3890 % 10.4 2080 2 600 3640 5 200 I II. 7 2340 2930 4 100 5850 \% 16.6 3320 4150 5810 8300 iM 26.9 5380 6730 9420 13500 28.6 5 720 7 ISO 9630 10 000 14 300 38.5 7 700 13500 19300 2 49-9 9980 12500 17500 25 000 2Vi 62.8 12 600 15700 • 22 000 31 400 2K2 77.1 IS 400 19300 27 000 38600 2% 92.9 18600 23 200 32500 46500 3 no. 2 22 000 27 600 38600 55 100 Rectangular washers 4X 6 24 4800 6000 8 400 12 000 8 32 6 400 8000 II 200 16 000 6X 6 36 7 200 9000 12 600 18 000 7 42 8 400 losoo 14700 21 OGO 8 48 9600 12 000 16800 24 000 9 54 10 800 13500 18 900 27 000 10 60 12 00b 15 000 21 000 30000 8X 8 64 12800 16000 22400 32000 9 72 14 400 18 000 25 200 36 000 10 80 16 000 20 000 28 000 40 000 12 96 19 200 24 000 33600 48 000 loXio 100 20 000 25 000 35 000 50000 II no 22 000 27500 38500 55 000 12 120 24 000 30000 42 000 60 000 14 140 28 000 35 000 49000 70 000 12x12 144 28800 36 000 SO 400 72 000 14 168 33600 42 000 58 800 84 000 16 192 38400 48 000 67 200 96 000 14X14 196 39200 49000 68600 98 000 16 224 44800 56000 78 400 112 000 Unit values, lb per sq in 200 250 350 500 * The actual areas bearing on the wood are given for round washers, washers the total area is given, no allowance being made for holes. Details. Many other forms of connections are in use and their proper design simply demands that the methods explained in Chapter XII and in this chapter be consistently followed. All details are not suitable for all cases and the de- signer must use common sense in the selection of the particular type to b6 used and in its design. Wood is very variable in its properties and consequently large factors of safety are used for certain kinds of stress and smaller factors 1160 Design and Construction of Roof-Trusses Chap. 28 for others. Heavy trusses, in which the sizes of the members are selected ac- cording to the magnitudes of the stresses, should be very carefully worked out in every detail, while small trusses with large excess of material do not demand as much care. Table VII. Proportions of Standard Cast-iron Washers / \ (Q)f}'^- ^ ;\ \ y 1 'VMm 7. u vV_^.J. ^ -r .1 i*^ D V, - • '1 Diam of bolt, d D d" d' T Weight, Bearing area, in in in in lb in sq in H 2^ ^^i ^9/^6 % 1/^ S.i6 % 3 m 11/16 H % 6.69 H 3H 2% 13/6 H 11/ 7.78 Ti 3H 2% 15/6 % ii/ 10.40 I 4 2% 1 1/6 iM 21/ 11.70 iH 4% 2% 1^6 m 3 16.60 iH 6 3 l5/6 1% 5% 26.90 iH 6K 3H 1% m 6 28.60 iH 7H 3% 1% 1% 9H 38. SO 2 8H 4H 2H 2 I7H 49 90 2H m 4% 2% 21/ 20 62.80 2^ loH sH 2H ■ 2H 27 H 77.10 2V4 iiH S% 2-^A 2% 36 92.90 3 12^4 6M 3H 3 46 110.20 Fc r sizes not given, D = 4^ + M" d"= 2d-{- H d' = rf + H T '- = d 4. Joints of Steel Trusses Trusses with Riveted Joints are usually made with angles for the web- members and generally for the chords, although the latter are sometimes made of a pair of channels or of two angles and a web-plate. The members are connected at the joints by means of gusset-plates, to which all of the members are riveted. Typical examples of riveted joints in roof-trusses are shown in Figs. 22 to 24e. When the rafter or chord has a web-plate, as in Fig. 23a, the web-members are riveted to this plate and a gusset-plate is not required except at the end-joint and apex, as shown in Figs. 23a and 23e. In order that there shall be no twisting, it is necessary to make the principal members of the truss double, so that the gusset-plates can be riveted between them. Where single angles are used for web-members and two such members come at one joint they should be riveted to opposite sides of the gusset-plates. For equal strength the thickness of the gusset-plate should be such that the bearing on the rivets equals the strength of the rivets in double shear, the thickness, how- ever, not exceeding the combined thickness of the two angles. Practical con- siderations seldom make the gusset Qver H u^ thick for ordinary construction. Joints of Steel Trusses 1161 In laying out the joints, which should be done to a scale of not less than i in to the foot, the members should be arranged, when practicable, so that the lines passing through their centers of gravity will coincide with the lines of the truss- diagram, and thus meet at a single point, as in Fig. 21. This is not always praC' ticable, but the prin- ciple should be followed --Su„^^ , 0_,_0 _^^ O O r. as closely as possible. For small angles the RIVET-LINES of the members may be con- sidered, without serious error, to pass through the centers of gravity of the sections. The number of rivets re- quired for each mem- Fig. 21. Riveted Truss-joint with Truss-diagram Lines ber must be determined according to the stress in that member, the resistance of the rivets being considered for both shearing and bearing. The method of determining the number of rivets in a joint is explained in Chapter XII, but to show more clearly the application to truss-joints, the joints for the truss shov/n in Fig. 7 will be designed. General Considerations, Truss of Fig. 7. It is assumed that the truss will be shipped in three parts, making all the joints shop-riveted except those at G and the splices at each end of the piece EH. All gusset-plates are to be ^^-in thick and all rivets %-'m, except in the 2-in legs of angles, where ^i-in rivets are to be used. Since the bearing of a %-'m plate on a ^4-in rivet at 20 000 lb per sq in (Table I, page 1138) is 5 630 lb, or at 18 000 lb per sq in (Table III, page 419) is 5 060 lb, and the resistance of the rivet in double shear, 2X4 420 = 8 840 lb (Table III, page 419), the number of rivets in all the joints is governed by the bearing value. Only one leg of the angles will be connected 10} [ynh) oT o-L— ■ 1 «-> 1 ^^ Fig. 22. Detail of Jo'int A, Fink Truss, Fig. 7 Fig. 22a. Detail of Joint D, Fink Truss, Fig. 7 to the gusset-plate as about 80% of the full strength of the angle is thereby developed if not less than three rivets are used. The use of hitch-angles for the outstanding leg has but little influence in increasing the efficiency of the connection. Two rivets may be considered the minimum number in any con- nection, regardless of the unimportance of the member. Joint A, Fig. 7. The top-chord stress is 23 500 lb, and if one rivet carries 5 630 lb into the gusset-plate, five rivets will be required to carry this total 1162 Design and Construction of Roof-Trusses Chap. 28 stress. In like manner four rivets are required for the bottom chord. The supporting force or the reaction is transferred to the gusset through the bottom chord prolonged. In this case the reaction is about 8 8oo lb which reqdires two rivets. Fig. 22 shows the arrangement of this joint at the e.xpansion-end. Joint D, Fig. 7. The web-members each require less than one rivet, but two or three should be used. Since the top-chord angle is continuous, the number of rivets in it is determined by the difference between the two adjacent stresses and the load of the purlin if it rests on the chord. Here again the number of rivets required falls below the minimum number. Fig. 22a shows this joint. Joint E, Fig. 7. The piece CE requires four rivets and the web-members the mioimum number permissible. The piece EU requires, at 20 000 lb per sq in M ^'pC I lO ^ i^r^Q?!!* • • •■ u o-i — .' ' ' Fig. 22b. Detail of Joint E, Fink Truss, Fig. 7 Fig. 22c. Detail of Joint E and Splice in Ell, Fink Truss, Fig. 7 bearing vajue, 12 500/5 630= 2.22 rivets; but as this connection is one to be made in the field, it is customary to increase the number 25%. This makes the required number three. Sometimes the outstanding legs are spliced to the member CE by a plate. Without doubt this increases the strength of the joint, but it is doubtful if the increase in strength is enough to offset the extra cost. Fowler's specifications do not permit the piece EH to be connected to the gusset-plate. They specify that the connection shall be made upon the right of E. This arrangement allows the use of a smaller gusset-plate at E which may be counterbalanced by the ad- ditional metal required for the splice beyond E. (Figs. 22b and 22c.) Joint G, Fig. 7. The pieces BG and EG are shop-riveted to the gusset on one side and FIELD-RIVETED on the Other. In order to make the joint sym- metrical, the number of shop- RiVETS is made the same as required for the field-connection. In this case the top chord requires five rivets and the web-member three. Two rivets may be used in the sag-tie. (Fig. 22d.) Field-Connections. Bolts are often used instead of rivets for making field- connections. If the bolts fit the holes snugly, there is no serious objection to their use. In fact a good bolt is better than a poor rivet. For important work, however, bolts should not be used unless turned true to size and driven into true holes. Open holes or holes for field-rivets are indicated by black circles. Shop-Drawings. It is not advisable for the architect to make complete drawings for the steelwork. He should make what are usually designated as general drawings. These are made to scale and give the general dimensions Fig. 22d. Detail of Joint G, Fink Truss, Fig. 7 Joints of Steel Trusses G 1163 C E Span 70' Rise 14'5' Fig. 23. Fink-truss Diagram. (See, also, Figs. 23a to 23e) , v^ o o O O O O O 1 o^o o o o O O Oi 6 X 4 X yl Lb. 'O' , • • • • • • 1 ,•/ For kneebrac6 Fig. 23a. Detail of Joints .4, 5 and C of Fig. 23 ^^ Fig. 23b. Detail of Joint D, Fig 23. ?5^ l9Jq£xl3 X ^ ^^£^ '^y.n.\ . 6i4iJ«L«. tO o o o • L.!.-.-i»---.. E ^8x%"Pl. Fig. 23c. Detail of Joint £, Fig. 23 1164 l)esign and Construction of Roof-Trusses Chap. 28 and sizes of the various members, and show each rivet approximately in its proper position. The manufacturer who fabricates the structure prefers to make his own shop-drawings to conform with his standards and methods. Examples from Practice. Figs. 23 to 23e show the details of a modern shop-truss. These details were taken from the shop-drawings but with the rivet-spacing omitted. No metal under Me in thickness, or rivets under % in Fig. 23d. Detail of Joint F, Fig. 23 Fig. 23e. Detail of Joint G, Fig. 23 in diartieter, are used. Another point may be mentioned in connection with this truss; very few bevel-cuts are made. The contrary appears to be the case for the details of the very light truss shown in Figs. 24 to 24e, in which BEVEL-cuTS are made on the angles and more cuts than necessary on the gusset- plates. These two trusses were designed by manufacturers widely separated 2-4'x 3"x ^i'' ;C 2-3h\2H''xX,i' jE I I 2-2K'^ 2>i"x X"i.» Fig. 24. Fink-truss Diagram. (See, also, Figs. 24a to 24f) and are quite different in their details; and the variations emphasize the fact that the architect should not attempt to make shop-drawings. Trusses with Knee-Braces. Fig. 25 represents joint i of Fig. 55, Chapter XXVI, and was engraved from the working drawing made by the New Jersey Steel and Iron Company, Trenton, N. J. Another detail of a truss-connection to a column is shown in Fig. 26. This was used in the template-shop roof-truss, Ambridge plant of the American Bridge Company, Ambridge, Pa. Fig. 27 Joints of Steel Trusses 1165 Fig. 24a. Detail of Joint A, Fig. 24 Fig. 24b. Detail of Joint B, Fig. 24, 1166 Design and Construction of Roof-Trusses Chap. 28 li rivets U this memboi Fig. 24c. Detail of Joint D, Fig. 24 Fig. 24d. Detail of Joint F, Fig. 24 Joints of Steel Trusses 1167 1 /r % i-Jveta ia out leg X/"^^^!?^ r l-2"x Ji" I. ^ Fig. 24e. Detail of Joint C, Fig. 24 21*x ^" plate sVv 4-2J^x2"ii4''LnO* lug"Z"2x J-^'l 9Jf^ 17VboUs2Ji'' 8-%"bolt8 2"i '-7'9X Kivef8.b See Column DetiUU' Fitr. 1^. Detail of Toint 1. Fie. 55. Chapter XXVI 1168 Design and Construction of Roof-Trusses Chap. 28 shows the wall-end of a small truss supported by brick walls. The intersection of the STRESS-LINES is approximately in a point above the center of the support. Fig. 26. Connection of Steel Truss with Steel Columns Bed PI. 12 X 12 X J^ Anchor Bolts l"Diani. 13 long Anchor PI. 5"xl0"x%" G©) ^O^O^O^O^ on\ ^^o'^d^d^ ^ i &> TOP VIEW OF SHOE PLATE SHOWING ANCHOR BOLTS IN SLOTTED HOLES [ Fig. 27. Wall-end of Steel Truss. Support and Anchoring-details This condition is seldom considered by architects. Usually it is possible without any extra expense to satisfy tliis requirement and thereby to a great extent pre- vent unknown bending-stresses. Purlins and Purlin-Connections 5 1 Purlins and Purlin- Connections 1169 Purlins. Where the roofing is supported directly on the purlins, as is gen- erally the case in light steel roofs, the purlins and trusses are usually spaced so close together that simple rolled shapes may be used for the purlins. For Fig. 28. Puriin-connections. Steel Clips, Angles and Z Bars . Fig. 29. Purlin-connections. Steel Sections with Wooden Nailing-strips spans between trusses of from 8 to lo ft, angles are commonly used, and for greater spans, Z bars, channels and I beams. Wooden Purlins are often used with steel trusses. If steel purlins support wooden rafters or plank roofing, a nailing-strip of wood is bolted to the purlin, as shown in Fig. 29, When the distance between purlins is 15 ft or more, a line of ^^-in rods should run from the ridge through the purlins, to prevent them from sagging in the plane of the roof. The purlin at the ridge must be designed to take the vertical com- ponent of the stress in these rods. Purlin-Connections. Figs. 28, 29 and 30 show a few of the various methods of fastening the purUns to the trusses. Design of Purlins. Fig. 31 shows the cross- sections of a rectangular wooden purlin and of the usual rolled steel shapes employed for purUns. As stated on page 11 70, when using wooden purlins the formula for the stress in the outer fiber is true only when used with reference to the principal axes of the section. Then, if one principal axis does not lie in the plane of the loading, the loading must be resolved into two components, respectively parallel to the two principal axes. (See, also, pages 573 and 593.) Fig. 30. Purlin-connection, Braced Channel 1170 Design and Construction of Roof-Trusses Chap. 28 Let S'= the fiber-stress with reference to the principal axis, A A, for the rec- tangle, i-i for the I beam and channel, and 4-4 for the angle and Z bar. M' =» the bending moment of the component of the load which lies in the plane per- pendicular to the above axis. /' = the moment of inertia of the section with Fig. 31. Sections of Wooden and Steel Purlins reference to the above axis, c' = the distance of any selected fiber from the above axis. For the other principal axis use S", M", I" and C"; then if »S is the resultant fiber-stress, S ^S' ^S" = We'll' + M"c"ll" For the rectangle, 5 = y -f- 5" = 6 M'lhd 2 -f 6 W'lhH For the channel and I beam, 5=^+5"= M'dll /i-i -f M"hl2 72-2 For the angle and Z bar, S =S' ^S" = M'c'/h^^-\-M"c"h-z The application of these formulas offers no difficulties except in the cases of ANGLES and Z bars. For the other forms, the values of / and c are given in the tables of properties of the sections (Chapter X). The locations of the prin- cipal axes for the Z bars and angles are also given in the tables, but the values of c are not given for any of the fibers. The easiest way to get the value of c in any particular case is to draw the section of the angle or Z bar full size, locate Uie principaJ axes and then measure the actual distances, c. Data for Wind-Pressure. Building Laws 1171 CHAPTER XXIX WIND-BRACING OF TALL BUILDINGS By N. A. RICHARDS OF PURDY & HENDERSON, INC., CIVIL ENGINEERS 1. Data for Wind-Pressure. Building Laws Tall Buildings of Modern Construction, that is, buildings with skeleton frames and light curtain walls or (iller walls, require that resistance to wind- pressure be considered with care. The proportions of a building and the arrange- ment and strength of the walls determine to what extent special bracing must be provided. Building ordinances in the larger cities usually require consider- ation of a stated wind-pressure. Where such ordinances do not definitely fix the assumed pressure, a unit force of 30 lb per sq ft of surface is generally considered proper and adequate. (See, also, page 150.) Building Laws. The following are extracts * from the building ordinances of New York City, Chicago, Philadelphia and Baltimore with reference to wind- pressure: New York (ipi7) "When Considered. All buildings over 150 ft in height and all buildings or parts of buildings in which the height is more than four times the minimum horizontal dimension, shall be designed to resist a horizontal wind pressure of 30 lb for every square foot of exposed surface measured from the ground to the top of the structure, including roof, allowing for wind in any direction. "Stability. The overturning moment due to wind pressure shall not exceed 75 per cent of the moment of stability of the structure, unless the structure is securely anchored to the foundation. Anchors shall be of sufficient strength to safely carry the excess overturning moment, without exceeding the working stress prescribed. "Allowable Stresses. When the stress in any member due to wind does not exceed 50 per cent of the stress due to live and dead loads, it may be neg- lected. When such stress exceeds 50 per cent of the stress due to live and dead loads, the working stresses prescribed may be increased by 50 per cent in design- ing such members to resist the combined stresses." Chicago (191 5) "All buildings and structures shall be designed to resist a horizontal wind pressure of twenty pounds per square foot for every square foot of exposed sur- face. In no case shall the overturning moment due to wind pressure exceed seventy-five per cent of the amount of stability of the structure due to the dead load only. "For stress produced by wind forces combined with those from live and dead load, the unit stress may be increased fifty per cent over those given above; but the section shall not be less than required if wind forces be neglected." * Quoted literally. Form in general not edited or changed. Some paragraph-captions added by associate editor. 1172 Wind-Bracing of Tall Buildings Chap. 29 Philadelphia (191 5) Wind Pressure. "In all buildings allowances shall be made for wind pres- sure, which shall not be figured at less than thirty pounds per square foot of elevation where erected in open spaces or upon wharves. In high buildings, erected in built-up districts, the wind pressure shall not be figured for less than twenty-five pounds at tenth story, two and one-half pounds less on each succeed- ing lower story, and two and one-half pounds additional on each succeeding upper story, to a maximum of thirty-five pounds at fourteenth story and above. Wind Bracing. "Wind bracing may be provided by making the connection joint between girders and columns sufficient for the vertical load as well as the bending due to side pressure; or brackets may be placed at this joint, propor- tioned for the side pressure; or diagonal bracing may be placed between columns, proportioned to transfer the shear of the side pressure to the footings. Base of Column must be Anchored. Where buildings are narrow and tall, so that the overturning due to wind is more than the down pressure of the unloaded building, the base of column must be anchored down to a sufficient foundation to counteract this upward strain. " * Baltimore (1914) Wind Pressure. "AH new buildings exposed to wind shall be made strong enough to resist a horizontal wind pressure in any direction of thirty pounds per square foot of exposed surface, measuring the entire height of the building. Calculation of. "The additional loads caused by the wind pressure upon beams, girders, walls and columns must be determined by calculation and added to other loads for such members, as provided for in Section 19 of this Article.f Special Bracing. "Special bracing shall be employed wherever necessary to resist the distorting effect of the wind pressure. Overturning Moment. "In no case shall the overturning moment due to the wind pressure exceed fifty per cent of the moment of the stability of the structure. " Magnitude of Unit Stresses Used for Wind-Pressure. As the above extracts indicate, it is generally considered proper to use high unit stresses when allowing for wind-pressure. The practice is based on the assumption that the highest unit wind-pressure will occur very infrequently and that its duration usually will be limited to a very few moments. It should be noted that the combined stresses due to wind-loads and dead and live loads should not exceed ordinary stresses by more than 50%. If stresses developed by the wind alone do not exceed 50% of those due to dead and live loads, they may be neglected. 2. Conditions Determining or Affecting Wind-Bracing Construction which Resists Wind-Pressure. The dead weight of a build- ing, the exterior walls, the interior partitions and the ordinary connections of beams to columns, all aid in resisting wind-pressure, but to a degree which is not determinable in any exact way; and these factors vary greatly, also, in different buildings. Any allowance for these factors must be largely a question of pure guesswork, or it may be judgment, based on the resistance which other buildings have offered when no special bracing was provided. It is therefore best to make special bracing take care of all, or very nearly all, of an assumed MAXIMUM pressure, when the building under consideration is unusually light in construction, or when its proportions are such as to make resistance to wind- pressure a prime consideration. * Stress is meant, t This refers to a section of the Baltiniore building law#. Conditions Determining Wind-Bracing 1173 Height and Width as Affecting Wind-Pressure. It is generally safe to neglect wind-pressure in structural designs for buildings ten stories or less in height, where the average width Hoot is not less than one-third the height. It is also usual to omit special provision for wind-brac- ing in higher buildings where the width is two-thirds the height, or more. The writer believes the above approximations repre- sent conservative practice, so far as general rules are possible. Dead Load as Affecting Wind-Pressure. A building should not be so proportioned that the overturning moment of a wind-pressure of 30 lb per sq ft exceeds 75% of the avail- able RESISTING MOMENT of the dead load. If necessary, the col- umns should be anchored to the foundations. 3. General Theory of Wind-Bracing Buildings Considered as Cantilevers. Buildings are usu- ally considered to resist wind as C 1 Top of nei ghborin g Building -^ SECTION l'6" -4-7'0^ I'e'' -5G'0- PLAN, Fig. 1. Section and Plan of Wind-braced Building CANTILEVER GIRDERS or trusses, planted in the earth. Assuming a building of the general dimensions shown in section and plan in Fig. 1. with a wind-^ 1174 Wind-Bracing of Tall Buildings Chap. 29 pressure against side yl, the walls A and B, together with the cokimns, beams, etc., in these walls, arc tV't flanges of the girders. Walls C and Z>, with their framing, together with other intermediate lines of vertical framing, form the web of the cantilever and transmjt the vertical shears. Steel brac- ing in horizontal planes is seldom necessary, as ordinary floor-constructions are generally sufficient to transmit wind-loads to the vertical bracing. In some cases, however, it is necessary to add steel bracing in the floors. Such a case is found in the tower of the new Custom-House, in Boston, Mass. The ele- vators and stairs are next to the west wall throughout the typical stories. Under this arrangement there is no adequate provision in the ordinary floor-construc- tion for a wind-pressure on the north or south face to reach the resisting bracing in the west face, as the various open wells cut off nearly all direct connection between the floors and this wall. Flat plates were therefore added on top of the floor-beams at each floor-level, running out from the wall girders behind the wells into the main floor-construction, and attached at each end with connec- tions sufficient to transmit the horizontal increment of the wind-ptessure at each floor to the bracing which resists it. 4. Arrangement of Wind-Bracing Sf Usual Position of the Bracing. As wind-pressure is assumed to be uni- formly distributed over the face of a building, it is best to arrange systems of bracing, as nearly as may be, symmetrically about the axis of each face. It is generally easier to conceal in the exterior walls the required knees, gussets, or other braces, and bracing is usually placed there. When the lines of bracing have been selected, the areas of wall-surfaces which bring wind-pressure to each are readily determined. Bracing of Buildings of Irregular Plan. Some buildings are of such shape that it is impossible to provide bracing of equal stiffness in lines symmetrical about the center of wind-pressure. This is notably true when the plan is TRIANGULAR, as in the so-called Flatiron Building or in the Times Building, New York City. The result is a tendency in such buildings to twist about a VERTICAL AXIS. The analysis of the resistance offered by a building to a twist of this sort is unsatisfactory and complicated. The stresses produced in any usual case, however, are small, if not negligible. In the examples mentioned above, provision against twist is made by the use of deep spandrel girders all around the building at each floor-level. 5. Types of Wind-Bracing Ordinary Beam and Girder Column-Connections. Wind-bracipg should be so proportioned that the joints between horizontal and vertical members are sufficient to prevent the distortion of the frame, and the main horizontal and vertical members sufficient to resist any bending moments produced throughout the joints, as well as any direct loads coming on them. The ordinary connec- tions of steel beams to steel columns (Fig. 2) provide considerable resistance to a distortion from side thrust. This is also true, of course, of connections between beams and columns made of cast iron or concrete; but as these types are not well adapted to construction where wind-bracing is required, they will not be con- sidered. A usual connection for beams or girders to columns consists of clip- angles above and below the beam, and perhaps a stiffener below, if the beam is large. Usually, in high buildings, four rivets are used to connect either flange to the clip-angles above and below, and four to connect each clip to the column. The value of four rivets, in single shear, multiplied by the depth of the beam. Types of Wind-Bracing 1175 gives the resisting value of such a connection against a moment due to side thrust. In lower buildings it is usual to specify two rivets instead of four in each flange, and in the case of very high or narrow buildings, six rivets are some- times used. Resistance of Beam and Girder-Connections to Wind-Pressure. It is sometimes assumed that the connections of all beams or girders (running in the r~~T — ' « ) Oj ( ) o "ol( |> o .. «^:^ O o .^^-^ — —A < > Ml' ( > 'V ^ Fig. 2. Ordinary Girder and Column-connections Fig. 3. Heavy Girder and Column -connection same direction as the wind) to columns act at their full value to resist the wind. This is undoubtedly wrong, because the many connections could probably not be made to work at the same time, and also because building-frames are seldom arranged so that such a result could be possible, under any rational assumption, in regard to the distribution of the vertical shears. Side clips are sometimes added to the column-connections to furnish additional stiffness. They are not of great value, however, as on most beams they are not deep enough to help much. Heavy Column-Connections in Wind-Resistance. Column-connections are sometimes made very heavy, as shown in Fig. 3. A connection of this kind can be arranged to resist a large twist. The resisting value is, of course, measured by the resisting moment of the rivets connecting the beam to the cHp- angles, or by the connection of the angles to the column. This type is used wher«» the resistance to wind is provided for in a very large number of connections, perhaps in all the column-connections, throughout the building. Such an 1176 Wind-Bracing of Tall Buildings Chap. 29 arrangement was used in the Hudson Terminal Buildings, New York City. There are several objections to this type of connection. Double beams or girders are required, and the resulting finish is awkward in appearance; tne cost, also, of double, compared with single, beams and girders, is high. The additional fireproofing, also, increases the expense, and on the whole, it docs not generally prove a satisfactory method of stiffening a building. The Gusset-Plate Type of Wind-Bracing. In addition to ordinary beam and girder-connections, as described in the preceding paragraphs, there are several distinct types of special wind-bracing commonly employed. Perhaps the most common form is the gusset-plate, shown in Fig. 4. This is not usually an economical type, ^ (Si^ -{-fl'i) multiplied by xi, or the stress in Fig. 8. Portal Type of Wind-bracing Combination of Dead and Live Loads with Wind-Loads 1183 the flange t equals ^ (EH + Hi) multiplied by i^i/ji, and this is a maximum when xi/yi. has its greatest value. There is approximation in this treatment, but it is on the side of safety. If the flange t has a section proportioned to these maximum stresses the requirements will be fulfilled. The stress in, and section-area required for, the flange r can be obtained in a similar manner. The connection of the portal above this flange to the portal and column above must be such that it will safely resist the stress H 2// at each leg. 9. Combination of Dead and Live Loads with Wind-Loads General Principles. It usually happens that the same girders that are used as wind-bracing serve also to carry floors or walls. The dead and live loads should be considered with the wind, and the resultant combined stresses Fig. 9. Types of Columns Arranged for Wind-bracing. ascertained. It should be borne in mind that the maximum bending moment caused by the wind is often at a point on the girder more or less removed from the point of maximum bending moment for dead and live loads. When result- ant shears and moments are considered, in which the forces are the wind-load and the live and dead loads, it is generally deemed proper to use unit stresses 50% in excess of those of common practice under usual loading. The columns should be investigated for direct live, dead and wind-loads and for the bending due to wind. The resultant stress, again, should not exceed 150% of the stresses generally used for live and dead loads only. It is often best to design columns with a special view to proper connections for bracing. This aids in 1184 Wind-Bracing of Tall Buildings Chap. 29 both design and detail. In Fig. 9 are shown a few typical arrangements of column-material illustrating this point. 10. Wind-Bracing of Water-Towers and Similar Structures The Principles Involved in Water-Tower Bracing. In the case of a TOWER WITHOUT MASONRY WALLS, a problem IS presented much simpler than that of a building, as the indeterminate factors of resistance are largely I ' " J eliminated. The bracing should coJncction^oidBuiiing be designed to resist the full wind-pressure. It should be borne in mind that in water- towers the condition of minimum stability obtains when the tank is empty. The most common form for tower-bracing is the sway-rod. The analysis of stresses is the same as described on page ii8i. The application of the thrust is largely at the top where the tank stands, but this does not in any way alter the an- alysis. The legs of water-towers are frequently sloped to give a greater spread at the bottom. In this case the stresses are more readily determined by graphic methods than by algebraic or trigonometrical computation. (See Chapter XXVII.) The Assumed Unit Pres- sures should be somewhat greater for towers than for build- ings. Towers are small in com- parison with buildings, and the probability of the full wind-pres- sure being developed over the entire surface is greater. Prob- ably 40 lb per sq ft is ample. Pressure against a cylindrical body, such as a tank, may be taken at about two-thirds of the full pressure against the projec- tion on the diametrical plane. The stresses under this assumed pressure should be kept within usual bounds for ordinary dead or live loads. The anchorage of Fig. 10. Whitehall Building. Lines of Bracing Plan and each post should exceed, by a safe margin, the full uplift due to the assumed pressure. The weight of water in the tank should not be considered as resisting the uplift. A Good Example of a Steel Water-Tower is described and illustrated in the Engineering Record of June 20, 1903, the stress-diagrams and details of con- struction being given. Examples of Wind-Bracing in Tall Buildings 1185 Fig. 11. Whitehall Building. Wind-bracing on Line I, Fig. IQ 1186 Wind-Bracing of Tall Buildings Chap. 29 ==tr ^2-1.') 11 3.{ /^2^0"][ 15*\ '2-10"][ I"-'^^ ^ "][15*>\^ ^2-f]t.8' 22nd Floor «-%"riv8.- 21 8t A^-10"l[ 15*-^ ^ "][ 15^^ ^-^ 218 ][ 8 =1^ / .2-10 ][ 15* ^ X^ 10"][ 15 i^ #2.p[ji)^': plate I ^ /^-10''][ 15*N /^2.\d^1l 15^ 19th ^^'loor J,3th_ Floor r^^ W--'/ - 2-12 ][20,V. X2-I iLi=>' f^t^niH, s 9.19 Tf Wl.*^ ^ »"][ >5^\ ^-pTfiiM'i B M^>i^ ^ZIX ^2^ioj[r^^^ '^l0t.]l^li'_J 2 >2-IlO ][.15 } 2-12 ][ 20 U' 32-%" • ^2^i0][jr, p ^ .15"l[ SSt^^ 2^lsrFx l^x^ 'Z 2-I5"][ SS^ ^ ^ ^ K'-2.15"][ 33 1 '^2.15"j[ 33*A\ ^ 'Vt. ;-ij]t20\^-j l TT i^ i^- ' 2.15 ][ 3i^ -%. K 15'JL 33*>\ floor 2nd r^.l5"][33^ V21-%"rlv-^^ "^ X2.I "K3^^ ^-{12"] [ 2U,4V i: I ?^^ /^2.15"]L33t^\\ Fig. 12. Whitehall Building. Wind-bracing on Line II, Fig. 10 Examples of Wind-Bracing in Tall Buildings 1187 11. Recent Examples of Wind-Bracing in Tall Buildings The Whitehall Building f (Figs. 10 to 17), 2 to 14 West Street, New \ork City, consists of a thirty-one story addi- tion to the earlier Battery Place Building. It joins the older twenty-story building which is on the south. As the plan, Fig. 10, indicates, the building is very long and nar- row when compared with its height and it represents a type in which wind-bracing must be considered an essential feature. The six lines of bracing indicated on the plan (Fig. 10) by the Roman numerals and the letters W.B. were chosen so as to interfere as httle as possible with the requirements of the plan. Knee-braces were used as far as practi- cable, but in several instances it was neces- sary to use GUSSETS because of the limited space available. It was assumed that the ordinary connections of girders to columns, and the walls, furnished sufficient stiffness down to the twenty-fourth floor-level. Be- low that level the bracing was proportioned as described on pages 1179-80; that is, al- lowance was made for the indeterminate FACTORS or RESISTANCE equal to the wind- moment at the twenty-fourth floor. The United States Realty Building t (Fig. 18), IIS Broadway, New York City, is another example of a building in which SPECIAL BRACING is quite essential. It is twenty-one stories high, and its width is small when compared with its length and height. Bracing was used, as indicated, in the end-walls, but it was not feasible to put enough in these hnes to do all the work. Additional lines were therefore added be- tween some of the elevator-shafts and in other places as shown on the plan. No special bracing was used above the fifteenth floor. The Morton Building § (Fig. 19), 681 Fifth Avenue, New York City, is but twelve stories high, but is rather narrow. The building is on 'an interior lot, and it was necessary to keep the openings in the ex- terior walls as large as possible, in order to properly light the interior. This, of course, made the exterior walls of but little value Fig. 13. Whitehall Building, bracing on Line III, Fig. * Purdy & Henderson acted as designing engineers for these buildings. t Clinton & Russell, architects. X Francis H. Kimball, architect. § McKim, Mead & White, architects. 1188 Wind-Bracing of Tall Buildings Chap. 29 IV Fig. 14. Whitehall Building. Wind- bracing on Line IV, Fig. 10 Floor '19th Floor 18th Floor =^1 3rd^-j Floor iBt Floor ^2-:io' y^-iojC-ii 'lL15* .18 1,55 2--10Ji^5* 2-10"y[ I5i* :^ 2-15 ][ ••53' 15.%"rh %^i^ 4 Pis. 8"x 1^" 2-15"] [ 33* _ IS-J^Tivs. 7 y 4 Pis. 8"x. 3^' 15"lL 33' ^ 1 Pis. 8". 9/- rs Jt 33' 15.J^'rriv8.' ^2-15] '^ 20-3xf" QHbI 1 Web 33':x >^- /y\ VPeb45';r5^" /::^2.i5''jc^'^ 20-%"ri»8? y^2-15"3[ 33' - I ^ 2-12-1 [,201^ *A N I ^ \ rs SA^ ^ ■k^: ^^ k^. ^ ^ r^ ■111. 05 J=;'T' 32 i 2> 4 ^ aiid VI '4 1?1 Fig. 15. Whitehall Building. Wind- bracing on Line V and VI, Fig. 10 Examples of Wind-Bracing in Tall Buildings 1189 Wind-Bracing of Tall Buildings sChap. 29 Pig!. 16 Fig. 17 Fig. 17. Whitehall Building. Wind-bracing Details Examples of Wind-Bracing in Tall Buildings 1191 . u'q'/u J --■rr.— — :r - • — — nr-- --J — j— W.B.«i IH I fll wraT^r' h ' W.B. -irt^^r _L Fig. 18. United States Realty Building. Plan and Lines of Braciiig -42'0^ W.B. t "SY.B. t W,.B, ffl W.B. W.B. W.B. i ^ 1 5" bk W.B Elevator Fig. 19. Morton Building. Plan and Lines of Bracing 1192 Wind-Bracing of Tall Buildings -43'6'^ I Stairs W.B. I Elevjiitors | ' f^-24'6'^ Coniieotion to OU Old Building I S ! 3 Ele|*tor i £leV|itors Fig. 20. Masonic Building. Plan and Lines of Bracing ^n'o" lEleratJor }EleTat)3r ] \ ! ', > > oa 4 . . . > , H- . iq h 11" Sr--- 1 ' . L J 1 'I li ' 1 ;; lb per sq in Tension, net sociion, rolled steel i6 coo Oiroct compression, rolled steel and steel castings 16 000 Rending on extreme fibers of rolled shapes, built sections, tHr.lers, and steel castings, net section 16 000 Bemliivg, on extreme tibers of pins 24 000 Shear, on shop-rivets and pins 12 000 Shear, on field-rivets 10 000 Shear, on bolts 9 000 Shear, average, on webs of plate girders and rolled beams, gross section . 10 000 Bearing pressure, on shop-rivets and pins 24 000 Bearing, on field-rivets 20 000 Bearii\g, on Ixilts 1 S 000 Tension, in rivets 7 000 Tension, in field-bolts (not anchor-holts) 9 000 \\>al compression, on gross section of columns and struts 16 000 —7c where / is the effective length of the member, in inches, and r is the least radius of gyration of section, in inches, with a maxi- mum of 13 000 (47) For aiMiuNKi) stresses due to wind and other loads the unit stresses in Paragraph (46) may be increased 50%, except for Paragraph (44), provided tiie section thus obtained is not less than that required if wind-forces are neglected. (48) When the laterally unsupported length, /, of the compression-flange of beams and girders exceetis 12 times its width, b, the unit stress in the cou- PRESsiON-FLANGE, shall not cxcccd 19 000 -250//6. (49) CorNTERSi*NK Ri\TTS in platcs of thickness equal to or greater than one half the diameter of rivet shiUl be assumed to have three fourths the value of rivets with full heads. In plates of thickness less thim one half the diameter of rivet their values shall be tiiken as three eighths that of full-headed rivets. Rivets with fl.\ttened Ht:ADS of height not less than Hin, or one half the diam- eter of the rivet for *i;-in rivets and less, may be assumeti to have the value of a>rresix>nding rivets with full heads. Rivets with heads flattened to less than these heights shall have countersunk holes and be regarded as countersunk rivets. (50^ The allowable pressure of column-b.\ses and be.\ring-plates on masonry shall not exceed, in pounds per square inch, the following. (See, also, pages 205 to ^6;^, and 441.) lb per sq in On brickwork, cement mortar. .50 On brickwork, hme mc^rtar ... 1 50 On Portland-cement concrete, 1:2:4 mixture 500 On Portland-cement ci^ncrete, 1:3:5 mixture S50 On rubble m;is^>nry, cement mortar :oo On rubble masc^iry, lime mortar \ :o On first-class dimension sandstone 400 On first-class limestone 500 On first-class granite 600 Design 1201 5. Design (51) General Design-Requirements. Trusses shall be riveted structures. Tension-members as well as compkession-members shall he composecl of rolled shapes or built-up sections. Flat bars with riveted ends shall not be used. (52) In calculating tension-members, net sections shall be used. The diam- eters of rivet-holes shall be assumed to be y^ in larger than the nominal size of the rivet. In single angles connected by one leg, the net area of the connected leg and one half that of the outstanding leg shall be considered eflcctive. (53) The nominal sizes of rivets shall be used in calculations of their values. (54) In proportioning columns provision shall be made for eccentric loading. (55) Columns AND struts with direct loads of 40000 lb or less, when spliced, shall have the entire load transmitted through splice-plates. (56) Column-splices shall be designed to resist the bending-stresses, and to make the columns practically continuous for their whole length. (57) Members subject to reversal of stress from moving loads shall be proportioned for the stress requiring the larger section, but their connections shall be proportioned for the larger stress plus one half the smaller. (58) The effective length of main compression-members shall not exceed 120 times th(;ir least radius of gyration, and for secondary members and lateral bracing, 160 times their least radius of gyration. Any portion of the cross- section of a compression-member may be neglected in computing the radius of gyration, provided that portion is neglected in the design of the member. (59) Wheel-loads of cranes shall be assumed to be distributed on the top flanges of runway girders over a distance equal to the depth of the girder, with a maximum of 30 in. (60) Plate girders shall be proportioned either by the moment of inertia of their net section, or upon the assumption that the bending-stresses are resisted by the flanges concentrated at their centers of gravity, and that the shear is resisted by the web. When the second method is used one eighth of the gross section of the web, if properly spliced, may be used as flange-section. (61) Web-plates of girders shall have a thickness of not less than Meo of the unsupported distance between flange-angles. (62) Flange-plates of girders shall be limited in width, so as to extend not more than 6 in beyond the outer line of rivets connecting them to the angles. (63) Web-stiffeners, in pairs, shall be placed over bearings, at points of concentrated loadings and at intermediate points, usually not farther apart than the full depth of the girder, when the thickness of the web is less than Ho of the unsupported distance between flange-angles. (64) Stiffeners under concentrated loads and over bearings shall be designed as columns, with a length equal to one-half the depth of the girder, and shall have enough rivets to properly transmit the shear. When loads are transmitted through the bearing of stiffeners, the bearing value may be assumed at 24 000 lb per sq in of section, excluding the area of the chamfered portion over fillets of flange-angles. (65) The DEPTH OF GIRDERS AND ROLLED BEAMS in floors shall be not less than H4 of the span, and if used as roof-purlins shaU be not less than ^2 of the span. In case of floors subject to shocks and vibrations the depth shall be limited to Mo of the span. (66) Steel purlins shall be single rolled shapes, plate girders or lattice girders. 1202 Specifications for Structural Steelwork of Buildings Chap, 30 (67) Lateral, longitudinal, and transverse bracing in all structures shall preferably be composed of rigid members, and shall be designed to withstand wind and other lateral forces when building is in process of erection as well as after erection. (68) Wind-bracing shall be provided for tall buildings by making the con- nection-joint between girders and columns sufficient for the bending due to side pressure as well as for the vertical load; or diagonal bracing shall be placed between columns, proportioned to transfer the shear of the side pressure to the footings. (69) No steel in any structural member subject to stress shall be less than ]4, in thick, except the webs of rolled beams and channels. Steel subject to the action of hamiful gases or severe atmospheric conditions shall be not less than Mo in thick. 6. Details (70) General Detail Requirements. Details throughout shall conform to first-class standard practice. (71) No connection except lattice-bars shall have less than two rivets, prefer- ably three, for better handling in fabrication. (72) In cases where it is necessary to carry loads subject to shock by bolts in tension, check-nuts shall be used. When bolts go through beveled flanges, BEVELED WASHERS to match shall be used so that head and nut are parallel. In general, rivets and bolts in tension shall be avoided as far as practicable. (73) Abutting Joints in compression-members faced for bearing shall be spUced sufficiently to hold the connecting members accurately in place. (74) When two or more rolled beams are used to form a girder, they shall be connected by bolts and separators at intervals of not more than 6 ft. All beams having a depth of 12 in and more shall have at least two bolts to each separator. (75) The minimum distance between centers of rivet-holes shall be three diameters of the rivet, and the maximum distance in the line of stress eight diam- eters. (76) The minimum distance from the center of any rivet-hole to a sheared edge shall be iH in for ;^8-in rivets, iM in for ^-in rivets, iK in for 5^-in rivets, and i in for H-in rivets; and to a rolled edge, 1%, ij4, i, and % in, respectively. (77) The maximum distance from the center of any rivet-hole to any edge shall be eight times the thickness of the plate. (78) The pitch of rivets at the ends of built compression-members shall not exceed four diameters of the rivets for a length equal to one-and-one-half times the maximum width of the member. (79) The latticing of compression-members shall be proportioned to resist a shearing-stress equal to 2% of the direct stress. Tie-plates shall be provided at each end and at intermediate points where latticing is interrupted. In main members carrying calculated stresses, the end tie-plates shall have a length not less than the distance between the Hnes of rivets connecting them to the flanges, and intermediate ones not less than half this distance. Their thickness shall be not less than Voo of the same distance. 7. Workmanship (80) General Requirements. All workmanship shall be first-class in every respect. Workmanship, etc. 1203 (8i) Material shall be thoroughly straightened before being worked, by methods that will not injure it. (82) Shearing shall be done accurately, and all portions of the work exposed to view neatly finished. (83) Abutting surfaces of compression-members, except where joints are fully spliced, shall be planed to an even bearing so as to give close contact throughout. (84) Punching shall be done accurately, but occasional inaccuracies in match- ing of holes may be corrected with a reamer. The diameter of the punch shall be not more than Vie in larger, i^or that of the die 3^ in larger than the diameter of the rivet. Rivets shall be driven by pressure-tools wherever possible. (85) Holes in material of same thickness as diameter of punch may be punched full size. (86) Web-stiffeners of plate girders under concentrated loads shall have the ends milled. 8. Painting (87) General Painting Requirements. Cast iron need not be painted at the shop. Steelwork for foundations to be entirely embedded in concrete shall not be painted, but must be free of dirt, grease, or other matter which would impair the bond of the concrete. . Other steelwork shall be thoroughly cleaned and given one coat of paint before shipment. One coat shall be given to surfaces that are inaccessible after being riveted together. (88) Machine-fmished surfaces shall be coated with white lead and tallow before shipment. (89) After erection all structural metalwork shall be cleaned of dirt and rust and given one coat of paint of a color or shade different from that of the shop-coat. (90) All painting at the shop and site shall be done by hand when the surface of the metal is perfectly dry. Painting shall not be done in freezing weather. (91) Paint shall be a good quality of red lead or graphite, ground in pure Un- seed oil or their equivalent. 9. Inspection (92) General Requirements. All inspection and tests shall be made at the option and expense of the purchaser. (93) If material is tested at the mills, the necessary number of test-pieces and the use of a testing-machine shall be furnished free of charge by the steel-con- tractor. (94) The purchaser or his representative shall have free access at all times to the mills where material is rolled and to the shops where it is fabricated. In ample time for his needs he shall be given dates of mill and shop-operations and furnished with complete working drawings. 10. Erection (95) General Requirements. The structural steel and iron, except anchor- bolts, loose hntels, and material not connected with the main frame of the struc- ture, shall be erected by the steel-contractor on foundations furnished by the purchaser. (96) Care shall be taken that all steelwork is level and plumb before bolting or riveting 1204 Data on Structural Steel Chap. 30 (97) Proper provision shall be made for resisting stresses due to erection opera- tions. (98) In general, field-connections shall be riveted, but connections of the follow- ing classes may be bolted: (a) Light subordinate framing, such as purlins, monitor and skylight-framing, girts, platforms, stair-framing,' partitions, ceilings, and penthouses; {b) Ordinary framing of beams to beams, and beams to girders; (c) Connections not subject to direct shearing-stress. All connections, however, affected by loads that cause undue vibration, shall be riveted. One-story buildings, not subjected to excessive wind-pressure or not supporting heavy concentrated loads, shafting, or moving loads, may be bolted throughout. The threaded part of a bolt shall not be so long that the bearing value of the unthreaded portion is reduced to less than the shearing value of the bolt. Washers shall be used under nuts wherever needed. (99) Drift-pins shall be used only to bring parts together. Unfair holes shall be made to match by reaming. (100) After finishing the work the erector shall remove his equipment and all rubbish resulting from his operations. DATA ON STRUCTURAL STEEL* Estimating the Cost of Structural Steel for Buildings Structural steel for buildings is commonly made up of I beams, channels, angles, Z bars and plates, which may be used as single beams or braces, or built into riveted girders, columns, or trusses. The Z bars are now seldom used for columns or other structural work in buildings. The cost of the completed steel- work is made up of the following items: (i) Cost of the plain steel at the mill, plus freight and dealers' profits. (2) Extras for cutting, punching, fitting and assembling into girders, columns, or trusses. (3) Cost of the fittings, such as connection-angles, gusset-plates, etc. (4) Shop-painting. (5) Cost of erection at the building. (6) Painting after. erection. Base-Price of Steel. For orders of any considerable size, the cost of plain steel is based on the price at the mills plus the freight to the point of delivery. The BASE-PRICE, free on board cars at Pittsburgh, Pa. (1920), is about $2.45 per 100 lb for I beams and channels 15 in and less, and for angles and zees from 3 to 6 in. I beams over 15 in, cost 10 cts per 100 lb extra, and tees over 3 in, 5 cts extra. For angles, channels and zees under 3 in, the base is $2.45 at Pittsburgh. For angles, over 6 in, $2.45 -f So.io.f For H beams, $2.45-!- $0.10. For deck beams and bulb angles, $2.45 -{- $0.30. t For corrugated and checkered plates, $2.65-!- 5i.7S.§ For plates, structural, the base is $2.65. * Valuable data v/as contributed for this section by Associate Editor, Robins Fleming. t $2.45-|-$o.io means a base-price of $2.45 and an extra $0.10. t $2.45-|-$o.3o means a base-price of $2.45 and an extra of $0.30. § 2.6s-|-$i.75 means a base-price of $2.65 and an extra of $1.75; the same with $2.65 -|-$o.i5, etc. Corrugated steel, painted, is usually quoted at a base-price plus an extra for painting. At present (1920) it is $4.25-!- $0.25. Data on Structural Steel 1205 For plates, flange, the base is $2.65 + $0.15.* For corrugated steel, painted, No. 22, $4. 25 -|- $0.25.* For corrugated steel, galvanized. No, 22, $5.30. For steel sheets, black, Nos. 10 and 11, $4.00. For steel sheets, galvanized, Nos. 10 and 11, $4.70. For steel sheets, black. No. 22, $4.20. For steel sheets, galvanized. No. 22, $5.25. For bar-iron, the base is $4.50. For rivets, $4.50. For steel bars, I2.35. Freight-Rates (March, 1920) in car-load lots are: Pittsburgh to Albany, N. Y 27 .0 cts to Baltimore 23 , o cts to Boston 29 . 5 cts to Buffalo, N. Y 21.0 cts to Chicago 27.0 cts to Cincinnati 23 . 5 cts to Cleveland 17.0 cts to Columbus, O , 20.0 cts to Denver 99 . o cts Pittsburgh to Louisville 26.5 cts to New York 27.0 cts to Norfolk, Va 31.5 cts to Philadelphia 25.0 cts to Richmond, Va 30 . o cts to Rochester, N. Y 21.0 cts to St. Louis 34.0 cts to Washington, D. C 24.0 cts On account of the expense of carrying beams in stock, local dealers usually charge from 3/2 to i3/^ ct a pound, extra, on orders supplied from stock. f Standard Classification of Extras. These lists are for steel bars and SMALL SHAPES, and the extras are added to the base-prices for each 100 pounds. This standard classification was adopted June 15, 19 19, by the Carnegie Steel Company. Specification and Inspection Hull-material, subject to United States Navy Department specifications for medium or soft steel ,$0.10 High- tensile hull-steel (except rivet-rods) subject to United States Navy Department specifications i.oo Charges for other than mill-inspection, such as Lloyd's or American Bureau of Shipping, for buyer's account. Quantity-Differentials All specifications for less than 2 000 lb of a size will be subject to the fol- lowing extras, the total weight of a size ordered to determine the extra, regard- less of length and regardless of exact quantity actually shipped: * $2.65-1- $1.75 means a base-price of $2.65 and an extra of $1.75; the same with $4.25 -|-$o.25, etc. Corrugated steel, painted, is usually quoted at a base-price plus an extra for painting. At present (1920) it is $4.25 -[-$0.25. t At present (1920) a war tax of 3% is to be added to the rates given. 1206 Bata on Structural Steel Chap. 30 Quantities less than 2 000 lb, but not less than i 000 lb $0.15 Quantities less than i 000 lb 0.35 Straightening Machine-straightening $0.10 Machine-Cutting to Specified Lengths, Rounds and Squares, i^ Inches and Larger Machine-cutting to lengths over 48 in $0.15 Machine-cutting to lengths over 24 in to 48 in, inclusive 0.25 Machine-cutting to lengths over 12 in to 24 in, inclusive 0.35 Machine-cutting to lengths of 12 in and less, extra will be furnished on application, but will not be less than 0.45 The above extras apply only to .50 per cent carbon and under. Extras for machine-cutting over .50 per cent carbon will be furnished on application. Extras for machine-cutting Rounds and Squares under iH in, Flats, etc., will be furnished on application. Cutting to Specified Lengths, Other than Machine-Cuttiag Cutting to lengths of 60 in and over No charge Cutting to lengths over 48 in to 59 in, inclusive ^0.05 Cutting to lengths over 24 in to 48 in, inclusive o.io Cutting to lengths over 12 in to 24 in, inclusive 0.20 Cutting to lengths of 12 in and less, extra will be furnished on application, but will not be less than 0.30 Cost of Erecting. For erecting ordinary beams and columns in buildings having masonry walls the cost of erection should not exceed $20 per ton when there are bolted connections, and it will sometimes be as low as $13 per ton. For erecting the steelwork of skeleton buildings having riveted connections it is customary to allow $18 per ton. Cost of Painting. The usual charge for shop-painting is about $3 per ton, but if done in accordance with the specification on page 1203 it would exceed this amount. For painting one additional coat after erection, allow about $3.50 per ton. Roof-Trusses. In lots of at least six, the shop-cost of ordinary roof-trusses in which the ends of the members are cut off at right-angles is about as follows:* Trusses weighing i 000 lb each, from $2.00 to $3.50 per 100 lb; trusses weighing I 500 lb each, from $2.00 to $2.50 per 100 lb; trusses weighing 2 500 lb each, from Si. so to S2.50 per 100 lb; and trusses weighing from 3 500 to 7 500 lb, from S1.25 to $2.00 per 100 lb. Pin-connected trusses cost from 10 to 30 cts per 100 lb more than riveted trusses.* Steel Mill-Buildings. The average shop-cost for the frames of steel mill- buildings, including draughting, is about $40 per ton, and the cost of erection from $20 to $35 per ton.* Cost of Drafting. Details for church and court-house roofs having hips and valleys cost from $10 to $20 per ton; details for ordinary mill-buildings cost from $6 to $12 per ton. The cost of making shop-drawings varies greatly with the character of the construction of the buildings, and with the accuracy of the * If there is little duplication or parts of if manual labor enters into the fabrication to any great extent the costs given will be increased. Data on Structural Steel 1207 architect's drawings. The average costs per ton of steel, for making shop- drawings are about as follows: For entire skeleton construction, in which the loads are all carried to the foundations by the steel columns, $4.00. For the interior parts which are supported on steel columns, when the outside walls carry the floor-loads and their own weight, $3.50. For the interior parts which are supported on cast-iron columns, when the outside walls carry the floor-loads and their own weight, $2.50. For construction without columns, and in which the floor-beams rest on ma- sonry walls, $2.50. For buildings in which roof-trusses supported by columns comprise the greater part of the construction, $7.00. For buildings in which roof-trusses on masonry walls comprise the greater part of the construction, $4.00. For mill-buildings, average, $9.00. For manufacturing or shop-buildings, with flat roofs, and one story in height, $3.00. For alterations, additions, remodeling, which require measurements before details and shop-drawings can be made, $12.00.* Approximate Estimates of the Weight of Steel in Buildings. Accord- ing to H. G. Tyrell,t the weight of steel in any proposed new building may be roughly estimated from the following data, which is a fair average for buildings not over eleven stories high, designed according to the Building Laws of the City of Boston: Per sq ft of floor Apartment-houses and hotels, with outside frame 14 lb Apartment-houses, without outside frame 9 lb Office-JDuildings, with outside frame 23 lb Office-buildings, without outside frame 15 lb Warehouses, with outside frame 28 lb Warehouses, without outside frame 18 lb For buildings higher than eleven stories, the weight of floors will increase in direct proportion to the number of stories, while the weight of columns will increase more rapidly. For the approximate weight of roof-trusses, see Chapter XXVII, pages 1050 to 1052*. Weights of Steel in Buildings | Factors Affecting the Weights of Steel Structures are many and varied. The weight per square foot of area or per cubic foot of volume of a structure already built should not be assumed as the weight of a proposed structure unless all the conditions which govern the one are found in the other. Munici- pal building codes specify floor-loads and these vary greatly. The prescribed wind-pressure, working stresses and column-loads, affect the weight. The architectural features to be followed also play an important part. In mill- buildings the weight is affected by the kind of roofing and siding used, capacity * This cost of $12.00 includes the cost of taking measurements. This generally has to be done by the contractor. t Estimating Structural Steel, in Architects & Builders' Magazine, Jan., 1903. t From Notes by Robins Fleming. 1208 Data on Structural Steel Chap. 30 of cranes, spacing of trusses and columns, shafting, special loadings and the allowable minimum thickness of metal. Weights of Steel in a Number of Structures are given in the following table and notes. The caution regarding such weights being taken as prece- dents should be emphasized. The office-building heading the list is the Equitable building, the largest office-building in the world. Average dimensions in feet Weight in Weight in Tiers pounds per pounds per of square foot cubic foot Width Length Height beams of framed area of volume Office-buildings 159 308 542 41 37-00 2.55 43 79 217 17 26.10 2.20 90 90 258 22 28.92 2.41 81 139 225 19 21.90 1.83 43 104 149 13 33.40 2.99 48 III 115 9 17.34 1.51 Hotels 97 119 244 20 26.02 1.92 84 143 270 24 26.95 2.39 96 lOI 232 18 25.40 2.02 108 120 "S 9 14.00 1. 01 Department-stores 133 219 150 II 23.87 1.77 62 211 130 8 29-44 1.83 103 132 89 7 18.30 1.45 Warehouses 100 los 131 10 22.83 1.76 88 121 121 9 20.60 1.85 145 357 102 7 30.80 2.13 58 72 52 3 31.3s 1.87 Among prominent New York buildings the 55-story Wool worth Building with a ground-area of 31 000 sq ft weighs 3.0 lb per cu ft.; the 39-story Bankers' Trust Building with an area of 9 000 sq ft, 3.1 lb.; the 2S-story Municipal Building with an area of 42 700 sq ft, 3.6 lb; the 25-story Hotel McAlpin with an area of 31 000 sq ft, 2.0 lb. The lo-story Curtis Building oi Phila- delphia with an area of 94000 sq ft weighs 3.0 lb. The structural steel in four buildings of Pittsburgh, the Arrott, the Farmers' Bank, the Empire and the Oliver, is quoted as weighing respectively 2.8, 2.3, 2.1 and 1.8 lb per cu ft. For buildings of from 8 to 12 stories in which the exterior walls are carried by steel framing the weight per cubic foot of volume may be assumed at 1.9 lb for office-buildings and 1.5 for hotels. Armories. The three-hinged arches with roof-framing of an armory in Brooklyn, 191 by 300 ft in area, weighs 15.5 lb per sq ft of ground area. An armory in BufTalo, 233 by 335. ft, weighs 18.3 lb. The steelwork of the Kings- bridge Armory, New York City, 289 by 590 ft, said to cover the largest drill- hall in the world, weighs about 90 lb per sq ft, of which one half is roof and one half floor and miscellaneous framing. Boiler-Shops. Sizes and weights per square foot of a few boiler-shops are as follows: 167 by 336 ft, three aisles, floor in center and cranes in outer aisles, concrete roof and sides, steel purlins and girts, 23.9 lb; 124 by 300 ft, three Data on Structural Steel 1209 aisles with 15, 25 and 50- ton cranes respectively, steel purlins and brick walls between columns, 36 lb; 74 by 160 ft, lo-ton crane in center aisle, single beams over side aisles to carry roof, galvanized corrugated-steel covering and siding, 16,15 lb; 85 by 140 ft, two aisles, one with crane, 20.8 lb; 94 by 97 ft, two aisles, one with crane, 26.3 lb. Car-Barns. The steel roof-trusses and bracing of a car-barn 100 by 154 ft, wood purHns, brick walls, weighs 6.2 lb per sq ft. Another car-barn, 44 by 270 ft, corrugated-steel roof, and sides on steel purlins and girts, 9.15 lb. Another, 100 by 154 ft, four aisles, concrete roof on steel purlins, 11.8 lb. Cement-Plants. Four cement-plants with ground-areas of 58 000, 73 000, 83000 and 128000 sq ft respectively, weigh respectively, 23.6, 22.0, 23.5, and 17.5 lb. These weights are the averages of the buildings that usually form a cement-plant. The individual buildings vary from 10 lb for an engine-room to 36.7 lb for a clinker-grinding room. Coal-Bunkers. The weights of six coal-bunkers of the suspended type and with capacities of from 350 to i 000 tons, range from 128 to 234 lb per ton of capacity, the average being 204 lb. A system of rectangular pockets to store 7 500 tons (10 ft 6 in from ground to valves) weighs 158.3 lb per ton of capacity. In all cases the weights of supports but not of roofs are included. A 35 by 70-ft coal-bin supported on plate girders with a capacity of i 000 tons weighs 240 lb per ton of capacity, including the roof-trusses that carried the conveyor. Forge-Shops. The steel framing for the roof of a forge-shop 83 by 126 ft, with no columns and no cranes, covered with corrugated steel on steel purlins, weighs I I.I lb per sq ft of ground-area. A forge-shop 220 by 240 ft, four aisles, each with crane-runways, composition roofing, concrete sides, steel purlins and girts, weighs 24.6 lb. A forge-shop no by 425 ft for heavy work, 47 ft 6 in to bottom chord, two aisles each with a 50-ton crane, tile roof, glass and brick sides, weighs 40 lb. Foundries. A pipe-foundry, 50 by 150 ft, slate covering, wooden purlins, brick walls, 15-ton crane, weighs 11.35 lb per sq ft. A similar one for the same company, 45 by 82 ft, with a 30-ton crane, weighs 17.23 lb. A foundry, 71 by 180 ft, one center aisle, with light crane, lean-to each side, corrugated- steel roof and sides, weighs 14.8 lb. A foundry, 150 by 290 ft, for a pump- company, four aisles with 20-ton crane in one aisle, wooden purHns, two 40 by 50-ft charging-floors of concrete on steel beams, weighs 13.9 lb. A foundry, 116 by 252 ft, equipped for heavy work, 60-ft center aisle, two side aisles, 28-ft charging-floor, storage-platform, weighs 38.9 lb. Machine-Shops. A machine-shop, 90 by 328 ft, for heavy work, one center aisle 40 ft wide with 25-ton crane, each side aisle 25 ft wide with gallery- floor and 5-ton crane underneath, tile roof on steel purHns, brick and glass sides, weighs 43 lb per sq ft of ground-area. A two-story machine-shop, 69 by 422 ft, three aisles, light cranes in lower story, composition roof, steel purHns, concrete sides, weighs 35.15 lb. A one-story building, 75 by 300 ft, 20 ft to bottom chord, shafting, corrugated-steel roofing and siding, weighs 13.0 lb. Another one-story building, 70 by 100 ft, 18 ft to bottom chord, shafting, concrete roof on trusses 10 ft apart, no purHns, weighs 13.88 lb. In addition, the steel framing for the Hy-rib sides of this building weighs 3.44 lb per sq ft of vertical surface. A machine-shop, 116 by 252 ft, 60 ft center aisle, with upper lo-ton-crane runway and lower 25-ton-crane runway, two side aisles 28 ft wide with traveling jib-cranes, weighs ss lb. RoUing-Mills. A rolHng-miU, 93 by 186 ft, corrugated-steel roof and sides, weighs 17.6 lb per sq ft. Another, 170 by 384 ft, two aisles each with 1210 Data on Structural Steel Chap. 30 5-ton cranes, saw-tooth roof-trusses on longitudinal girders, concrete slabs on steel purlins, brick walls between columns, weighs 17-5 Ih. A similar building for shop-purposes weighs 18.62 lb. Paper-Mills. The entire structural steel for three paper-mills weighs respectively 18.4, 20.6 and 21.4 lb per sq ft of area. All roof-trusses are of the flat type, spaced 8 ft apart in the first and third, and i6 ft in the second. Power-Houses. A power-house, 44 hy 186 ft, 49 ^ to Iwttom chord, 60- ton crane tile roof on steel purlins, brick walls between columns, weighs 50 lb per sq ft. Another, 53 by 270 ft, 33 ft to bottom chord, 20-ton crane, tile roof on steel purlins, brick walls and sash between columns, weighs 39-6 lb. Another, 120 by 96 ft, one aisle for boiler-room and one with lo-ton crane for engine- room, steel purlins for concrete roof-covering, brick walls between columns, weighs 17.8 lb. Train-Sheds. The train-shed of the Pennsylvania Raihoad in Phila- delpliia, 598 ft long and with arches 300 ft 8 in from center to center of pins, weighs 39.1 Vb per sq ft of ground-area; the train-shed of the same , railroad at Jersey City, 777 ft long and with arches 252 ft 8 in, weighs 27.9 lb; and that of the Philadelphia & Reading Railroad in Philadelphia, 506 ft 8 in long and with arches 259 ft 8 in, weighs 31.5 Ih. The train-shed, 390 by 8x5 ft, of the Central Railroad of New Jersey in Jersey City, is a series of concrete and steel umljrellas, of the Bush-type. The structural steel weighs 17 lb per sq ft of area. Three Industrial Plants. In one of the plants of a great industrial cor- poration a two-story shop, 51 by 380 ft, weighs 28 lb per sq ft of ground-area; a three-story shop, 80 by 420 ft, 37-9 Ih I a three-story shop, 80 by 300 ft, 46.3 lb; a three-story shop, 80 by 630 ft, 67.5 Ih; a four-story shop, 77 by 140 ft, 66.6 lb; a foundry, 121 by 150 ft, 40.5 lb. In another plant of the same cor- poration, a three-story machine-shop, 80 by 51c ft, weighs 84.3 lb; a five-story office-building, 49 by 243 ft, 70.3 lb; a power-house, 55 by 120 ft, 37-5 lb; a bkicksraith-shop, 81 by 200 ft, 15.6 lb. In a plant of another corporation, a boiler-house, 50 by 94 ft, weighs 23.3 lb; a furnace-building, 60 by 160 ft, 25.1 lb; a roUing-mill, 80 by 80 ft, 24.4 ft; a rod-mill, 243 by 220 ft, 28.1 lb. Cost of Merchant Steel. The cost of merchant iron and steel of all kinds is based on a certain size of each particular shape, which is taken as the base, and the price of all other sizes is figured at a certain extra rate above the base according to a standard card of mill-extras. The base-price may fluc- tuate and be changed without notice, but the extras remain constant, and arc the same in all localities. The following tables include the standard classification of extras on iron and steel bars. Data on Structural Steel mi standard Classification* of Extras oh Iron and Steel Bars Adopted July 15, igig. Rounds and squares Sizes % to 3Hg in ^to ii'io irt 3^ to ^le in Ms in % in H2 in Mo in Yzz in Va, in. 564 in, Extra per 100 lb Base $0.05 o.io 0.20 0.25 0.30 0.3s 0.40 0.50 0.75 Sizes Vii in M 6 in 3H tos^e in iYi t0 4M6 in 4!/^ to 49^0 in 4/^ to 5 Ho in SH to 5^6 in 5^ to 6H6 in 6)^ to 6H6 in SY^ to 7^^ in Flats Sizes to 6 mX r% to I in to 6 inX M to Me in 1 J-i 6 to 1 •)! 8 inX y. to % in iMf to 1^6 inX % to Me in 9l6 toH inX % to 1^ in 91 G to 5^ inX H to Me in 3^ inX % to Me m K2 inX M to Me in Me inX y^ in Me inX H to Me m % inX Vx to Me m K to 6 inX tHe to iMe in K to 6 inX c^ toiH m M to 6 inX [5/8 to 2^ in H to 6 inX3 to 4 in Standard Classification t of Angles, Channels and Tees Angles Sizes t}/2 X I li in and wider, but under 3 in X M e in and over . I H X 1 3^ in and wider, but under 3 in X 3^ in I X I to 1 3'i X I H in X ^1 e in and over I X I to 13/4 X i3i in X 3^ in VsXVs ■ in X Mo in KXVs ■ in X 3^ in HXH in X Me in HXK in X 3^ in YsXYs inX3^in YgXYs inXHain 3^X3^ inX3^in H XH in X less than 3/^ in 3 in on one or both legs X less than 34 in , Unequal-leg angles are subject to special prices, which will be furnished on application * Intermediate sizes take the next higher extra. It is not customary to enforce more than one half the "standard-card extras" for round and square bars, t Intermediate sizes take the next higher extra. 1212 Data on Structural Steel Chap. 30 Standard Classification * of Angles, Channels and Tees (Concluded) Channels I ^2 in and wider, but under 3 in X M 6 in and over 1 3^^ in and wider, but under 3 in X H in I to 1 34 in X M 6 in and over I to iM in X H in I to 1 34 in X %4 in % and K in X Me in and over 3^ and 3^^ in X 3^ in 3^ and ^^ in X %4 in ^ in X 3^ in and over s^g in X ^^2 in 3/^ in X ^^4 in and over ". 3^ in X ^64 in Extra per 100 lb $0 15 25 25 35 50 30 40 55 1 20 I 40 I 80 Tees I H X 1 3^ in and wider, but under 3 in X M 6 in and over I X I to iJ4 X i34 in X Me in and over I X I to i>^ X 1^4 in X K in 3^ X>8 inXMe in K X ^ in X 3^ in M X M in X ^i 6 in MX^inX3^in ^X^in X^in H X )i in X 3-8 in Unequal- leg tees are subject to special prices, which will be fur- nished on application. Extra per IOC lb $0 20 40 50 50 60 60 70 z 30 I 80 * Intermediate sizes take the next higher extra. The base for car-load lots for any city may be obtained by adding the freight- rates given on page 1524 to the base prevailing at the mills. Domes 1213 1 CHAPTER XXXI DOMICAL AND VAULTED STRUCTURES* J I By I ■ : I EDWARD F. RIES • CONSULTING ENGINEER, SAN ANTONIO, TEXAS 1. Domes * Classification: Domical structures may be considered under two main divisions: (i) Smooth-shell domes, and (2) ribbed domes. The first division may again be divided into (a) domes with shells of uniform thickness, and (b) domes with shells of uniformly varying thickness. The materials of con- struction of division (i) are brick, stone, concrete, and tile; and of division (2), steel, concrete, and wood. A dome may be constructed with or without a LANTERN, or with or without an occulus or eye; and in the case of ribbed domes, they may have either circular or polygonal bases. (i) Smooth-Shell Domes Mechanical Principles. Under this heading are considered both (a) domes with shells of uniform thickness, and (b) domes with shells of uniformly vary- ing thickness, and also domes with or without lanterns and eyes. A dome whose shell tapers toward the top is the more stable dome. It is evident that the upper part, or crown, tends to fall in and thereby push out the lower por- tion; hence the lighter the upp)er part is in relation to the lower part, the more stable the dome. The exact actions of the internal stresses in a dome are difficult to determine, but a very practical solution can, however, be developed after assuming that the stresses are parallel to a surface midway between the outer and inner surfaces of the dome. General Analysin. A dome may be imagined to consist of a number of horizontal rings of decreasing diameter, each one laid on top of another. Since the upper part tends to fall in and push out the lower part, there must be a tendency to contract each ring in the upper part and to expand each ring in the lower part. That is, there must be end-compression on all stones (imaginary divisions in concrete) of the upper part, and end-tension on all stones of the lower part. The dividing line or horizontal joint between these upper and lower parts of the dome is called the joint of rupture. The angle made by the joint of rupture with the vertical (center of dome as apex of angle) is known as the critical angle. It is evident, then, that the determination of the joint of rupture and the critical angle determines also the points below which there is tension in the rings. By reinforcing the lower part with steel bands or rods to resist this tension, the dome can be made secure. If the dome is a FLAT DOME, that is, one in which the angle the base makes with the vertical is less than the critical angle, the tension-steel must be placed at the base of the dome to resist the outward push or thrust, * See, also, Chapters VII and VIII. 1214 Domical and Vaulted Structures Chap. 31 Notation and Theory (See Fig. 1): r = mean radius of dome; a = thickness of shell at crown; / = thickness of shell or of ring at any point; a = angle made with the ver- tical by radius to lan- tern-ring. Center of dome is the apex of angle. In a dome without lantern, a =o; 0= angle made with the ver- tical by radius passing through any point in shell (in equations angles are in radians); c = constant of variation of / with respect to arc 6; cr — =» a constant (based on a above notation) for any dome; 0= critical angle, that is, the angle made with the vertical by the joint of rupture; w = weight of cubic unit of masonry; V = volume of shell of com- plete dome above any ring; Wd='U^V = total weight of complete shell above any ring (including the part removed for eye) ; Wi-o = weight of lantern minus weight of shell removed for occulus or eye {Wi-o may be either positive or negative); W^Wa-\-Wi-o; n = — — - , a constant for any dome; 2 T war 2 P — total tangential pressure for any ring, due to lantern and shell above that ring; U = tangential pressure per unit-length of ring; H = total radial horizontal pressure on any ring, due to outward push or thrust of shell above that ring; T = hoop-tension or hoop-compression in ring, due to 77; Using this analysis and notation, the following equations are developed: Equation (i) t = a ■\- crO Equation (2) F= 27rf2[a(i — cos 0) -\- cr (sin 0— d cos 0)] Fig. 1. Smooth-shell Concrete Dome. Analysis Equation (3) Wa = wV =^ 2'k war [- cos 6) 4- — (sin O—dcosd) =war'^z. ].. Domes 1215 in which Equation (5) U = war = war (Si + S), in which Si = -T-y^ and 27r (i — cos e)+~ (sin d— 6 cos 6) "[(wc [cr -t cosec 6— cotan 0-\ — (i — d cotan ^) -^+ ^^ sin2^ sin^ J Equation (4) P = 2ir war- \ (n cosec d -\- cosec 0— cotan ^) + — (i —^ cotan 0) cosec — cotan -| — (i — cotan 0) a sin Equation (6) T= — = war^ n cotan + (i — cos ^) cotan 6 27r L 4- — (sin 0— ^ cos 0) cotan = war'^ (Fi+ F), in which Y\= n cotan and [,.-. F = I (i — cos 0) cotan 0+- (sin 0— cos 0) cotan I „ . , ^ cr „^ COS0— sin^^ Equation (7) —= n cosec^ ^-- a I + cos Design and Investigation of Smooth-Shell Circular Domes. By the use of the foregoing equations any circular dome can be designed or investigated. The computations, however, connected with some of these equations are long and tedious, and are simpHfied by using curves plotted from the solutions found, after giving different values to some of their elements or factors. (See Plates I, II, III, and IV.) Equation (7) is represented by the curves in*Plate I. By the use of these curves the position of the joint of rupture for any dome is found by inspection when the values of — and n are known. The value of — is easily determined, as c a a can be found by using Equation (i) after determining or assuming a, the thick- ness at the crown, and t, the thickness at the base; and the value of n is found from the ratio n = ;. 2Trwar^ Equation (3) is represented by the curves in Plate II. From these curves the weight of any shell is determined. Equation (5) is represented by the curves in Plate III. Knowing the values of n and — , the values of Si and S are found by inspection, and hence U is easily a computed. 1216 Domical and Vaulted Structures Ciiap. 31 Values of -^ Plate I. Curves for Determination of Joint of Rupture of Domes. Based on Equation (7) Equation (6) is represented by the curves in Plate IV. Knowing the values oi When n and — , the values of Yx and Y are found, and T computed for any ring. n equals zero, Fi equals zero, and the value of T depends upon Y as given in the lower curves. It will be noticed that F increases as Q increases until the crit- ^ ICAL ANGLE for a dome without lantern, or eye (w = o), is reached; that is, each successive ring increases the outward thrust, and at the critical angle there is a maximum value of F, and hence a maximum hoop-tension T. After the CRITICAL angle is passcd the rings are in tension, and therefore T and F are reduced by the tension required of the ring or masonry. The curves also indicate that the stability of a dome with a shell of imiform Domes Values of z Plate. II. Curves for Determination of \yeight of Shell of Domes. Based on Equation (3) thickness and with no lantern is not affected by the thickness of the shell, since c = o, and therefore — = o, regardless of the value of a. a Example. It is required to design a smooth-shell reinforced concrete DOME of 45-ft radius, and with a lantern of lo-ft radius, weighing 50 000 lb. The shell within the lantern is to be removed, forming an eye. (Fig. 2.) Solution. Assume a crown-thickness, a, of 5 in, and a thickness, /, at the base of 8 in. From Equation (i) cr t—a t^ a+ crd, or - = — — 1218 Domical and Vaulted Stnictures Chap. 31 +0.5 \ \.A y s._|...s ^A- - - ; s,..4r:^. t t... . \ xj'^s.. m __ . .- -:|^^. -J --.==-----^-=---;:::;;;:--^^^^= - o ilo ' ■ + .-t-:"": ■ : : ^ -0.6 j 'd im+ntTnTlt |Jji4l4+llllllll liiliitro \\m ;> .%'-' '-'' ,.'"' 7 "w" 'y'" -'" " ": ::::::::: : -1.0 ^ /' /' S''" 1 i y'<^'' / t' \ i 1 ^ ' u.iL \\4u ;-a-r.)(S +<;'» 2.0 r^>' ? IJol^ . t 1&- * : : : : ;iF ' 'WV ' .... " " " " ' ■ '"'" ±"";l/ .' " """ X""' Y'A ' 1 ., '',^1? '\ . /^/ Aa^ - , /.X ' i y. , 1.0 t .' .'K ' t4f . cn : .: :'^'^'' :' > '^ «M o ,'' /'','' '' ''' 'dSi'' «> f'' ,'' i^' ^' ,'' ,'T \' , ' n ^,,>^>'f>'f A'xL'^ ■< \ ^"^ '.^ -._ u '" > ' ^P^SJ-^ -^^'Li>^^^ ' ' ' i - ' ' ' 1 j> •" ' T r^ r '<*;^ ""Jk^^-^^ ■'^'^^^^-^^ --f -(!-i*T^ ::t::::;: i|^^^^ -^^ ;^1<^"Tj1— -^ "^ !j_--r|^ -H''^ "',--'" g:::±;h::;;:::;;;:;:::::::::::: ::::: ! ffllffr ^--.-.- r-^ L_ — riiiiiiiiiiiiiiiiiiiiiiii 1 ::::::::: 1 1 ^ 1|0 20 30 4|0 50 60 70 80 Angle d Plate III. Curves for Determination of Tangential Stress per Unit-length of Dome- ring. Based on Equation (s) For the dome without wind-loads or snow-loads Cr 12 12 a ©'-«■ • = o.^i lO The angle a = sin~^ — = i2~ so'. 45 From Plate II the weight of the shell removed for the eye is •fe) 150 -- ) (45)'(o.i6s) = 20 883 lb Domes 1219 +0.5 ¥ 1 T -\1 X i .^- : " ..T..\.!s.^_ !_..__ : :: __ 1 LA.-'s- v.-l - ..lA \ '-, \t \^\ \\-^.<:lt I ^ '!;•,:+:. ^^. : ' *>^ 1 '"■-... " ! - ; . :■ , : , . ' . .._^— . mtiiiiiiiiii 1 o 1 ^ = 1rT...t:::+-ff+fr:^ ^&i..i.... i -0.5 - ;;:::^- ::"-----"::::=-:^^=''''^^^ ^" rf I .'''' fit'"" .-■■'"---'•'"" Till > t '' ^' .--'''.--■''' T / /TT/'' T''-'' -1.0 'Ti:':'""m''' 4i J ^' ¥ t'../_/ % \._i _ sr^-- 4'.:.!|:::T (wj-a* r^)(Y,+ yilillli^iB > J5 .6 .5 .4 .3 4j-r±f^!^-— hi |; i i 1 i P i 4i| .2 .1 1 , 10 20 3 40 50 rtT±FFF 60 70 1 80 1 Plate IV. Angled Curves for Determination of Hoop-tension or Hoop-compression in Dome- ring. Based on Equation (6) Therefore PFi-o = 50 cx)o— 20 883 = 29 117 lb For wind bads and snow-loads a simple and safe method of procedure is tx> allow a uiiif jrm load over the surface of the dome, since this load can be trans- lated int > its equivalent in inches of masonry and hence the same equations and curves used. A wind l)ad, for example, of 25 lb per sq ft, is equivalent to 2 in of concrete weighing 150 lb per cu ft Hence the new a and / equal 7 and 10 in, respectively. Hence from Equation (i) 10 7 cr 12 12 = 0.307 fe)- 396 1220 Domical and Vaulted Structures Chap. 31 and Wi- 29 117 27rwaf2 27r(iso) (a • 0.026 ^ (45)2 Weight of Lantern, 60,000 lb From Plate I, with — = 0.307, a and n =0.026, the critical angle is found to be 52° 35'. From Plate IV, at the critical ANGLE for the dome with snow- load and wind- load '& T= i5o\ — ) (45)'(o.o20-|- 0.352) = 65 914 lb tens' 3n This must be resisted by steel reinforcing rods. Allowing a unit tensional stress of 16 ceo lb per sq in in the steel, a total of 6s9M • . , -^ = 4.12 sq in sectional area . 16 000 of steel is required. At the base ({?=8c°) T = 150 (~\ (45)^(0.005 + 0.186) = 33 843 lb The total cross-sectional area of steel in tension at the base is 33843 . . , r — = 2.12 sq in, given by five 16 000 round rods, each % in in diameter. 'The remaining required sectional area of steel, 4.12— 2.12 = 2 sq in, must be spaced in the lower part of the dome over an angular distance of (80°— 52° 35') = 27° 25' = 0.4785 radian, or 0.4785X45= 21.53 ft up the surface of the dome. The assumed thickness of shell at the base was 8 in, and the thickness at the lantern-ring will be, from Equation (i), cr ^ t =a-^ crd = a-\-a — d Fig. 2. Smooth-shell Concrete Dome Lantern and Eye. See Example 5+5 (0.43) (0.2 239) = 5.48 in Allowing 0.2 per cent of steel cross-section, horizontally and meridionally, for secondary stresses caused by temperature-changes and possible unequal snow-loads and wind-loads, there should be 8 X12 X 0.002 = 0.19 sq in of steel cross-section per running foot at the base, and 5.48 X 12 X0.002 = 0.13 sq in per running foot at the lantern-ring. The spacing of the horizontal reinforcing * The snow-load on the top of the lantern is taken care of because snow-loads and wind- loads over the entire dome were included, and only the actual masonry of the eye was subtracted. Domes 1221 is best found as indicated in Fig. 3. Curve A gives the total amount of steel necessary for secondary stresses above any point in the cross-section of the shell. Curve B gives the necessary tensional resistance, using Curve .4 as a 10 15 20 25 30 35 10 Distance in Feet Jleasured up the Sliell Fig. 3. Diagram for Determination of Amount of Horizontal Steel Reinforcing in Concrete Domes starting-point for the ordinates. Various points on the curve are easily deter- mined. For example, for 6 = 70° ^ = 5 + 5(o.43)(i-22i7) =7.63 in The cross-section of temperature-steel per foot at 70** is 7.63 X 12 X 0.002 = 0.18 sq in The total cross-section of temperature-steel above 70° is then 0.18 -+- 0.13 X (1.2217 — 0.2239)45 = 6.96 sq in The tension-steel cross-section (Plate IV) above 70° is (150) (7/12) (45)2(0,298^-0.009) 4.12 — - : 0.72 sq in 16 000 With points determined in this manner the curves are developed. The total cross-section of horizontal steel in the entire cross-section of the shell is 8.45 -f 2.00 = 10.45 sq in with an additional 2.12 sq in of tension-steel at the base. If ^-in round rods are used, there will be — '—— = 54, required in the shell. By dividing the area 0.1963 1222 Domical and Vaulted Structures Chap. 31 below the curve (Fig. 3) into 54 parts, the distance up from the base, where each rod should be placed, is determined. The meridional steel should be such that there will be 0.19 sq in of cross-section per foot of circumference at the base, and 0.13 sqin per foot of circumference at the lantern-ring; that is, if 3^-in round rods are used, they should be spaced — — — = i .03 ft at the base, and — — — = 0.19 0.13 1.51 ft at the lantern-ring. The punching-shear at the lantern-ring is equal to = 12. 1 lb per sq in .(5.48) (27rioX 12) This is well within the limit of 40 lb per sq in. (2) Ribbed Domes General Principles. The following discussion applies to domes of either circular or polygonal horizontal cross- sections. All steel doiiies are ribbed domes, and usually have from six to twenty-four ribs resting against a lantern- ring or SPIDER at the top. The ribs may have solid webs, perforated v.el f, or latticed webs, with angle or channel-flanges. The latticed angle-ribs are prefer- able because of their Ughtness. The tension-rings and compression-rings may be built similar to the main ribs, and should brace the latter throigh rigid gusset-connections. The diagonals are usually rods with turnbuckles fcr adjust- ment. Concrete-ribbed domes or wooden-ribbed domes may be designed according to the same general principles followed for steel domes, but the diag- onals are omitted and dependence for rigidity is, placed on the slab-f.llings between the ribs. The Schwed.er Method for the Design of Steel Domes. W. Schv^edler has by simple resolution of the forces derived equations for domes, based on the forms of SURFACES OF revolution. These equations are easily checked vhen the forces acting through a rib (the rib acting as a strut between the joints) and through a ring at a joint are considered. The following laws may be stated: (i) The ribs are in maximum stress when the whole dome is loaded; (2) A ring is in maximum tension when all of the dome above the ring is fully loaded, and in maximum compression when all of the dome below the ring and the ring itself is fully loaded; (3) The diagonals are not stressed when the dome is symmetrically loaded. The diagonals in a panel are in maximum stress when the dome on one side of a meridional plane passed through the center of that panel is fully loaded and the other side unloaded. In Fig. 4 let ai, a.1, ca, etc. = angles made by rib-sections with the horizontal; /3i, ^2, ^3, etc. = angles made by diagonals with the ribs; Pi, Pa, Pz, etc. = dead loads at ends of rib-sections; Li, L2, L3, etc. = live loads at ends of rib-sections; Di, D2, D3 etc. = stresses in rib-sections; T\, Ti, Ti, etc. = stresses in rings; A""!, iV?, N-i, etc. = stresses in diagonals; n — number of ribs. Domes 1223 \ X Tr. ELEVATION SECTION Fig. 4. Schwedler Ribbed Dome L/2 = — sin ai sin az sin as (Pi + 7.1 ) cot ai Dicosai , etc. 2 sin - 2 sin - n w (when the result is negative the stress is compressive). 1224 Domical and Vaulted Structures Maximum J. = (^■ + ^O c ot «i- (P. + /.. + />,) cot g. Chap. 31 Minimum T, = ^- ^"t «, - (A + P. + £,) cot a, . TT z Sin - n Maximum T> = (-P' + ^- + A + Z.,) cot «,- (f . + £. + ^8+ £, + f .) cot g, Minimum T, = (^■ + -P') '^"ta^- (f ■ + Pa + Pa + i.3) cot a^ etc. i\ri. 2 sin ai cos /3i i\r2= ■ X1 + 1. 2 2 sin oro cos / ,- Z,i + Z2 4- jl3 ^3 = — : -, etc. 2 sin as cos ^3 Fig, 4a. Graphical Determination of Stresses in Ribbed Domes For the stresses in the diagonals the factor 2 is introduced because Muller- Breslau found, by exact analysis, stresses only one half as large as those determined by the simple resolution of forces. The diagonals are stressed under a wind-load, and this is resisted by assuming a vertical live load equal to from 20 to 30 lb per sq ft of horizontal PROJECTION. A GRAPHICAL METHOD, developed by E. Schmidt, for determining the stresses A, A, A, Ti. Ta, n, etc., is shown in Fig. 4a. Weights of Steei Domes. It was found by Scharowsky, from calculations made for a large number of Schwedler FLAT DOMES Varying in span from 60 to 180 ft, that the weight of the lantern and steel skeleton per sq ft of projected (covered) area is w= 0.01565+4 where w = pounds per square foot of projected area, and S = the span, in feet. For preliminary calculations on full HEMISPHERICAL DOMES, the weight found by this equation should be in- creased from two and a half to three times. Domes 1225 Steel Dome of the Horticulture Palace, San Francisdd, Cal.* This is a SCHWEDLER HEMISPHERICAL DOME of iS2-ft Span, with twenty-fouF latticed ribs, 36 in deep, carrying a lantern-ring or spider at the top, and connected by eleven horizontal rings. The lantern-ring is 6 ft in diameter, 36 in deep, with a solid web, and braced twice diametrically. The ribs are constructed of two 4 by 4 by Me-in angles at the top, two 3 by 3 by Me-in angles at the bottom, and a 2 3^ by 23^ by J^-in angle single-lattice web. The dome-steel weighs about 17 lb per sq ft of projected area. Concrete Ribbed Domes. In a reinforced-concrete ribbed dome the number of ribs, varying from eight upward, is determined by the substruc- ture and the size of the dome. The different steps in designing a ribbed rein- forced- concrete dome are: (i) the determination of the number of ribs and rings; (2) the determination of the loading, per rib, using the required shell-thickness and the assumed rib-sizes and ring-sizes for preliminary calculations; (3) the finding of the forces acting on the ribs by the use of Schwedler's formulas; (4) the drawing of the elastic curve for the ribs; (5) the determination of the stresses and necessary reinforcement in the ribs, rings, and slabs; (6) the adjust- ment of sizes and loads, so as to be on the side of safety; and (7) the reworking of the preliminary computations for the final design. The elastic curve should always remain in the middle half f of the rib, and should never be so far away from the center of gravity of the rib-section that the maximum com- pressive stress of 500 lb per sq in in the outer fiber of the rib is exceeded. The reinforcement in the ribs should be sulhcient to resist the flexural stresses due to the eccentricity of the elastic curve. The reinforcement in the rings should be sufficient to resist the tensile stresses, and should be as straight as possible in order to avoid a sidewise stress or movement. The rings must be reinforced to resist their flexure, as beams. The panel-slabs, if domical (see Smooth-Shell Domes), should be reinforced for shrinkage -stresses and tem-^ perature-stresses, in addition to the reinforcement for tension below the critical angle. If the slabs are straight they should be designed as floor-slabs, and by similar methods. Example. J It is required to build a dome (Fig. 5) with a span of 132 ft and a rise of 31 ft 6 in. This makes the radius 85 ft. The eye is to be 12 ft in diam- eter. The outer surface of the dome is to be a domical slab on ribs, carrying a suspended plastered ceihng forming the inner surface. Solution. § To obviate the necessity of building a complete domical form, supported from the floor below, the decision is to build a ribbed dome as follows: It is decided to build a central tower to temporarily carry the upper ends of the ribs, to precast these ribs, raise them into position, cast the ring of the eye, sus- pend the ring-forms from the ribs, pour the rings in place, and then fill in the slab-panels on forms supported from the rings and ribs. Since the span of the dome is 132 ft, the circumference at the base is 41 4-7 ft. Because of the suspension of the panel-forms, it is well to keep the panel- * A. W. Earl and T. F. Chase, Engineering Record, Oct. 24, 1914. t The usual practice has been to keep the resistance-line within the middle third in arches generally. In reinforced-concrete arches and domes it may depart a small dis- tance outside the middle third, but there should be sufficient steel to resist any tension developed. The ribs of domes differ from ordinary arches as they are rigidly braced by the rings and the slab-panels. t The dome of this example is similar to the dome over the Hippodrome at Copen- hagen, Denmark, by Christiani and Nielsen. See the periodical, Concrete, for December, 1917. § In the solution of this example all calculations have been made with the slide-rule. 1226 Domical and Vaulted Structures Chap. 31 \ \ \ \ \ \ ^ \, \ \ \ \ \ \ \ .,\ \\ \ \ 1 , - -^ \- -66 ':=^'85 sin 5^56^ \ V \ \- \ '0 \ \ DIAGRA.M A^ D.I4GRAM CROSS-SECTION OF EYE-RINQ Fig. 5. Segmental Concrete Ribbed Dome Domes 1227 WIDTHS within about a 20-ft limit. Hence twenty ribs are necessary. With three intermediate rings, the lower panels are approximately square. The rings are not to show below the cciUng, and hence a narrower spacing toward the top is unnecessary for appearance. For preliminary calculations, allowing 1 1 00 lb per lin ft for the eye-ring and the load due to a glass covering over the eye, 250 lb per ft for the weight of the ribs, and 150 lb per ft for the weight of the intermediate rings; and assuming a slab-thickness of 3H in, a suspended plaster ceiling ^i in thick, and 25 lb per sq ft of surface for snow-loads and wind- loads (or an equivalent of a 2-in thickness of concrete), the loading on the ribs is as shown in Diagram A of Fig. 5. To illustrate the method of determining THE LOADS, the Calculations for the loading at the lower intermediate ring are given. The weight of the rib is 250X17.39 = 4347 lb. The weight of" 2X7rX8sXsin39° 14' ,, ^, the ring is 150 =2534 lb. The weight of the 20 shell and ceiling between 6 = 33° 21' and 0= 45° 5' is, from the curves in Plate II, with - =0, a (85)2(1.84)- 150 (^'■^^':^-^) (85)^(1.03) = 15 570 lb The total dead load is 4 347+ 2534 -f- 15 570= 22 451 lb The total live load is 15 570 X 2 sH-^ ■■ 7 330 lb The stress D4 (see method in Fig. 4a), in the lower section of the rib is the largest, and according to Schwedler's formulas, page 1223, is 6 6cxD+ 15 301 + 22 908-I- 29 781 ■ :; a — ; = io5 4°° lb sin 45 5 The eccentricity of the stress Di is 85— (85 cos 5° 51') = 0.445 ft The* moment due to the eccentricity of Dt is 105 400 lb X 0.445 ft = 46 903 ft-lb, or 562 836 in-lb To resist the column-like compression of Di there is required a cross-sec- tional area of rib of 105 400 ' e ^ ■ = 211 sq m of concrete 500 To resist the effect of the eccentricity of the stress A, it is necessary to insert enough steel so that the total stress in it, multiplied by the distance between the top and bottom steel reinforcements, is equal to the moment, 562 836 in-lb, already found. Since the eccentricity of Z>4 is 0.445 ft, and the line of action of the thrust is to be kept within the middle half of the rib,* the rib will be 4 X 0.445 = 1.78 ft = 21 H in in depth * See foot-note on page 1225. i22S Domical and Vaulted Structures Chap. 31 Allowing iH in of concrete for steel-protection at the top and bottom of the rib, the distance between the inner and outer reinforcements is 2iK — 3 = 183^ in Therefore a stress of 562 836 • -^^ = 30 424 lb is to be resisted by the steel at the top and bottom. Since there is steel in both COMPRESSION and tension, the allowable unit stress in it is /65oXi8H\, ^ Q ,u I — I (15— i) = 7 83olbper sqi \ 2ii^ / This is because the allowable compressive unit stress in the outer fibers of con- crete beams is 650 lb per sq in; the ratio of the modulus of elasticity of the steel and of concrete, 15; and the distance between the inner and outer steel 'reinforcements, and the distance of the rib-depth, 18K and 21K in respectively. The I in the expression (15 — 1) is to take care of the stress carried by the concrete replaced by the steel. The TOTAL cross-section of steel necessary at both the top and bottom of the rib is, therefore, 30424 Q — -— = 3.89 sq m 7830 furnished by four i^-in round rods. The best arrangement of the 211 sq in of concrete, and the steel, results in a cross-sectional shape shown in Diagram B of Fig. 5. The stirrups should be spaced not more than three fourths of the distance between lines of longitudinal steel, or 54 X 18H = 12 in (approximately), and they should be made from ^-in round rods. Because of the ties in the flanges, it is advisable to use small J^-in rods as stiffeners at the inter- sections of the ties and stirrups. Projecting loops should be left for fastening the panel-slabs. The actual weight per linear foot of the ribs is 211 — X 150 = 220 lb 144 for the concrete, plus (4 + 3.38)+ II = 25 lb for the steel, equal to a total of 245 lb, as against 250 lb per lin ft previously allowed in the calculations. As the ribs are to be precast and raised into place, it is necessary to determine whether they are of sufficient strength for this, and whether they will stand, un- supported by the rings, without breaking under their own weight. By consider- ing the ribs to be simple arches, and testing them by determining the line of thrust, it is found that they are amply safe. In order to resist the thrusts or stresses developed by raising the ribs into place, it is necessary to tie the ends together with bow-string rods. The stresses in all of the rings, except the footing-ring, are compressive. This is because they are all above the critical angle. (See Smooth-Shell Domes.) Therefore, in determining the stresses by Schwedler's formulas, only the equations for the minimum values of Ti, Ti, Ti, and Ti need be used. The stress in the eye-ring is (5750+850) cot 9° 55' - 1 20 600 Jb 2 sm — 20 Domes 1229 The stress in the first intermediate ring is (S 750 cot 9° 55O— (5 750+ 12 146+3 155) cot 21° 38' = — 65 000 lb ■T 2 sin — 20 The stress in the second intermediate ring is (5 750+ 12 146) cot 2i°38'— (s 750+ 12 146+ 17 573 + 5 335) cot 33" 21' = — 53 900 lb The stress in the third intermediate ring is (5 750+12 146 + 17 573) cot 33° 21^ -(5 750+12 146+17 573+22 451 + 7330) cot 45° 5^ ^ — 35 600 lb The stress in the footing-ring is tensile, and hence the equation for the max- imum VALUE of Ts gives (5 750+850 +12 146+ 3 155+ 17 573 + 5 335+ 22451 + 7330) cot 45° 5^ 2 sin — 20 = 238 000 lb 1 20 600 The EYE -ring should have = 242 sq in of concrete, but for appearance it should be as wide as or wider than the ribs; hence it is made 21H in high and 16 in wide. This size allows, also, a firm anchorage for the rib-reinforcing. With 1% of reinforcing it requires four iH-in round rods. (See Diagram C, Fig. 5.) The first intermediate ring should be 65 000 = 130 sq m 500 in cross-section, requiring a 7-in width and a 18 J^-in height, to resist the load, as a column. As the ring must also act as a beam, carrying its own weight, the weight of half the slab, and the live load (the forms taking the place of the live load during construction), steel must be added to resist the bending moment 2x85 sin 15° 47'^ /130 ^ \ / 27r85 sin 15° 47^ ^ / 6710+3 i55 \ /^ = 3 570 ft-lb = 42 840 in-lb SuflScient steel, in tension and compression, must be added to keep the addi- tional stress in the concrete, due to this moment, down to 150 lb per sq in, since 500+ 150 = 650 lb per sq in is the maximum allowable compressive stress in the concrete of the beam. From Formula (i) page 925, or Formula (5) page 931. 42 840 7X(i7)' From .Formulas (2), (3) and (4), (pages 925-6), when K = 21.2 and St = 16000 lb per sq in; Sc = 245 lb per sq in, p = 0.0014, and x = 0.185. Since Sc must 1230 Domical and Vaulted Structures Chap. 31 not exceed 150 lb per sq in, it is necessary to add comfression-steel to resist a stress of /24S_2S^\ ^7)(q J85 X 17) = I 040 lb The allowable stress in the compression-steel (page 1228), less the stress already allowed for the concrete which lA replaced by the steel, if placed i H in from the outside, is (— ^^ — I ( (0.185 X 17) — 1.5) (15- i) = 4 770 lb per sq in \0.185 X 17/ \ / The amount of compression-steel is, therefore, I 040 = 0.22 sq in, cross-section 4770 The tensile-steel necessary is 0.0014 X 7 X 17 = 0.16 sq in but because of the negative moment at the ribs, the same cross-sectional area is used as for compression, that is, 0.22 sq in, furnished by two 3^-in round rods. The unit-shear is / 130 \ / 27r85 sin 15° 47 '\ / 6710+3 i55 \ 18.6 lb per sq in 7 X 17 X I I ^^1 X 2 No stirrups are necessary to resist shear, but stirrups made from K-in round rods should be spaced about 18 in on centers, to tie the panel-slabs securely to the ring. The second intermediate ring, if made the same size as the first, will have a stress of 53900 7X.8H '4i61bpersqin The moment will be /130 \ ( 2lr85 sin 27° 31^ , / n 375 + 5 335 \ / ^TrSs sin 27° 31^ \i44 ^ '^7 \ 20 / \ 2 / \ 20 / 12 = 10 300 ft-lb =123 600 in-lb From Formulas (i), u), (3), and (4), (pages 925-6), A' = 6i.2,5f = 455 lb per sq in, p = 0.0043, and X = 0.3. Since Sc cannot exceed 650— 416 = 234 lb per sq in, the compression-steel must resist (^'^-^')(r)(o.3Xi7)^-^3 930 lb The section-area of the compression -steel is, therefore, 3930 = 0.62 sq in furnished by two %-in round rods at top and bottom. The unit shear is Vaults 1231 /130 ^ \ /27r8 5 sin27°3i Y / ii375+5 335 \ 7 X17 X (-t) = 46.9 in per sq in X 2 It is therefore necessary to resist 46.9 — 40 = 6.9 lb per sq in of shear, with STIRRUPS, that is, with two ^-in round-rod stirrups, spaced 12 in apart at the ends, and the others 18 in apart through the remaining distances. The THIRD INTERMEDIATE RING is 7 by 1 83^ in in section, with two J4-m round rods at top and bottom, and with two 3/^-in round-rod stirrups, spaced 9 in apart at the ends, two more, spaced 12 in, and the rest spaced 18 in. The MOMENT due to the eccentricity of the column-like thrust, that is, the longitudinal horizontal compressive stress, in the rings is resisted by the slabs. A more exact analysis may be made by considering only the normal components OF THE LOADS on the rings in determining these moments. The FOOTING-RING must have enough tensile-steel to resist the outward push or THRUST of the ribs, that is 238000 = 14.9 sq in of steel cross- section. In 16 000 addition to this, if the ring acts as a beam, there must be sufficient steel to resist the moment due to the combined weights of the dome and the ring itself. The PANEL-SLABS being domical and above the critical angle, are in com- pression, and should be designed as illustrated in the discussion of Smooth- Shell Domes. 2. Vaults * Classification. Vaults may be conveniently considered under the following divisions: (i) Barrel vaults, (2) Groined vaults, and (3) Ribbed vaults (Masonry, Tile, or Framed). General Considerations. A knowledge of the elastic theory of arches and the stability of buttresses is necessary in a rigid investigation of vaults, since their design involves the application of the principles of that theory. (See, also, Chapters VII and VIII.) In any vault, lines of action of the stresses or thrusts must pass through the material between certain limiting lines; otherwise the vault may fail. These thrusts are brought to the grade-line, or to foundations, by walls, often buttressed in the case of barrel vaults, and by piers and but- tresses in the case of groined and ribbed vaults. By building vaults of light materials, such as hollow bricks or hollow tiles, the magnitude of the thrusts are decreased, and lighter walls, piers, or buttresses can be used. (a) «-) <*> Fig. 1. Three Methods of Building Barrel Vaults Barrel Vaults. Fig. 1, (a), (b), and (c), illustrates three methods of building barrel vaults. In {c) the longitudinal ribs are merely for appearance, as • • A full treatment of this subject may be found in the Handbuch der Architektur, .and Breyman's Baukonstructious Lehre. 1232 Domical and Vaulted Structures Chap. 31 (a) Fig. 2, (c) (d) (6) Methods of Joining Barrel Vaults to Walls they do not strengthen the vault. The diagrams (a) and (b), Fig. 2, illustrate two methods of disengaging the masonry of barrel .vaults from the walls. Diagram (6) is the better method, and improves the appear- ance of the vault on the inside. Diagrams (c) and (d) illustrate the use of stone skewbacks for seg- mental vaults. Strength of Barrel Vau'ts. Barrel vaults may be considered as a series OF ARCHES set next to each other; and hence if a sec- tion one unit long is found safe when investigated as an arch, the vault itself is considered safe. By build- ing the wall and the vault together as a unit, to a point on the arc 6o° from the vertical or crown, that is, to a point on the in- trados one third of the distance from the horizontal spring-hne, the actual span is materially decreased. With the spring-line at 6o°, the line of thrust in an unloaded arch or barrel vault of an equal thickness throughout, will remain within a strip whose radial thickness or width is about one forty-second of the radius. If the line of thrust is to remain within the middle third of the arch-ring or vault-ring, / should be (f/42) X 3 = r/14. If it is to remain within the middle half, / should be (r/42) X 2 = f/21. In the following example, the theory of the middle half will be fol- lowed, in which / = r/2i. If it were assumed that / = r/14, the line of thrust being kept within the middle third, the span of the vault In the example would have to be changed from 21 to 14 ft. If built, then, as described (Fig. 3), the minimum thickness of the unloaded vault-shell is about one twenty-first of the vault-radius, that is, t=r/2i The VE-RTICAL COMPONENT Pv of the thrust P is equal to the weight of half the free vault, that is, of the section A BCD. It can be shown that the horizontal Ftg. 3. Analysis of Barrel Vault Vaults 1233 COMPONENT Ph of the thrust is 0.79 of the vertical component, and that the thrust is not at right-angles with the spring-line AB; that is, P/i=o.79^ Example. It is required to construct a barrel vault over a corridor 21 ft wide. The vault-radius is loVz ft, and the minimum thickness of the shell is 10.5/2 1 = 0.5 f t = 6 in. If built of brick it is cheaper to build a ribbed vault, as . the unit-dimensions of bricks are approximately 4 in, 8 in, 12 in, etc. Referring to Fig. 4, it is found that a 4-in vault with ribs 4 by 8 in every 3 ft 3 in, is equiva- 10 jr it \ % -- - - \ - - - - --- \ Q " S 8 __ _ _ A _ _ __ ___ ^ ^ OJ S ta : -- : --- -- c \ ^ St r ^ _ - 4 ^ ~K -- \-- - -^^ |J 2 i " . ?K'^ ^ - ^ ""^iM - ------ ,S J^WfArP 5 ^ ' \. \Mh\ ' ^ * ' \ ^ijh \ \// M ^ " k. ^-^ Xsiti^ - -I - - \ J^^.- - s^ _ - 5 ^^" ^^ Q -S ^V. _ -^S 2- it \ ^v - \ ^^ s \ s :^ ^s. \ s _ ^v _ _ _ 5i Ny, 4 6 8 10 12 14 Equivalent Thickness in Inches Fig. 4. Barrel Vaults, Ribbed and Non-ribbed. Equivalent Thicknesses lent to a 6-in vault, and hence would be used. The brick masonry weighs 125 lb per cu ft. The VERTICAL COMPONENT Po of the thrust is I4/12X3MX i/37rXio.5X 125] -f [4/12 X 8/12 X i/37r(io.5 + 0-33) X 125I = 5 595 lb per lin ft The HORIZONTAL COMPONENT Ph of the thrust is 0.79 X 5 595 = 4 420 lb per lin ft. The supporting wall must be thick enough, buttressed enough, or loaded suf- ficiently from above, to take care of this horizontal component of the thrust. Fig. 5 is a graphical analysis of the stresses in this vault. It will be noticed in Fig. 5 that the line of pressure remains in the middle half of the vault- thick- ness. Scheffler, after numerous tests of vaults, stated * that if one fourth the * Theorie der Gewolbe. 1234 Domical and Vaulted Structures Chap. 31 vault-thickness is deducted at the extrados, and one fourth at the intrados, and that if the line of pressure found according to the elastic theory of arches is Fig. 5. Graphical Determination of Stresses in a Barrel Vault confined to the remaining portion, that is, the middle half, then the vault may be considered safe. Fig. 6 shows the resistance-line passing slightly outside the Fig. 6. Line of Pressure through Vault-thickness middle third.* It illustrates tho hss conservative theory that the resistance- Hne might in some cases pass near the outside of the middle half. The arch or vault in Diagram (6) of Fig. (3 would have a greater tendency to fail according to the middle-third theory, because the line of pressure or resist ance-Une passes outside of the middle third. Diagram (a) of Fig. 6 shows the same arch or vault with the shell cut so that the line of pressure passes down the exact center of the uncut portion. This results in a sort of theoretical or ideal arch-form. * See foot-note relating to Concrete Ribbetl Domes, page 1225. Vaults 1235 Of course the thickness of part c must be sufficient to develop a safe compres- sive resistance in the material, and it is advisable to add sufficient steel to take care of any tension in the parts farthest from the resistance-line. Vaulted con- struction is often relatively protected and free from the live loads and moving loads to which arches are generally subjected; and for such construction Scheffler's conclusions are considered valid. Groined Vaults. A groined vault is formed by the intersection of two BARREL VAULTS. (Scc (a), Fig. 7.) By using groined, vaults it is possible to Perspective, Showing Penetrations and Intersections Intersecting Vaults of Different Widths Fig. 7. Groined Vault bring the tops of windows and doors above the spring-lines of the vaults, and to concentrate the pressures or thrusts on piers or columns. Groins. The intersections of two vaults, called groins, are straight lines in horizontal projection, only when they are of the same curvature and height. If the vaults are of different widths, it is best to make one semicircular, draw the horizontal projections of the groins as straight Hues, and then determine the contour of the other vault. This is illustrated in Fig. 7 {h). Vault A is semi- circular and has a span ^. Vault B has a span B. CC are the groins, and D is the circular contour of the narrow vault. Any points, a, b, c, etc., are chosen at random, and lines a-az, h-hi, c-oi, etc., and a-ai, b-bi, c-a, etc., drawn parallel to the axes of the respective vaults. The line as-ai is laid off equal to ai-a^; br-btf equal to 61-&2, etc. The smooth curve connecting ai, bi, a, etc., is the contour E of the vault B. In like manner the contour F of the groins is found by similarly laying off a-,-a^, b^-b^, etc., equal to ai-as, bx-bi, etc. The VAULT-SHELLS, at the intersections or groins, should never have what might be called miter- joints. The vaults should be monohthic or there should be concealed ribs to carry the vault-shells and transmit the thrusts to the piers. If the intersecting vaults are of stone, and of the same diameter, the groins may be built as shown in Fig. 8 (a) for small vaults, or as in Fig. 8 {b) for larger vaults. In Fig. 8 (a) the groin-stones are L-shaped and are cut so as to carry the stone courses of one vault around to the other vault. The stone shown in Diagram {a) of Fig. 8 is shown in plan at b, with two views at c and d. A better method is shown in Fig. 8 {b). Here the groin-stones are cut so that the joints 1236 Domical and Vaulted Structures Chap, 31 are normal to the groins, thus forming concealed ribs. This bearing-surface is obtained as follows. Point a, the intersection of an extended vault-joint and the groin-edge, is projected down to a' and h\ the intersections of the projecting line and the assumed side and center hnes of the rib. Point b' is projected- up to Fig. 8. Groiri'details for Stone Vaults of the Same Diameter 6", a point on the center line or edge of the rib. From 6" a horizontal line interr sects with a Hne projected up from a' to give c" a point on the joint, which is drawn normal to the groin. The intersection d'' of this joint with the groin- e4ge is projected down to d' on the center line of the rib. By connecting Vaults 1237 a' and d' , and d' and e" (the point opposite a' on the other side of the rib) with a curved line, the lower edge of the bearing-surface is determined. Points d' and e' projected up determine d and e, the same points in elevation. Fig. 9. Groin-details for Stone Vaults of Different Diameters Other points on these curved lines can be found by choosing points between a and d and projecting them in the same way as in the method used to find the projections of /. The procedure is as follows. The point / is projected down 1238 Domical and Vaulted Structures Chap. 31 to the center line of the rib, locating g' . Then g' is projected up to g" , the inter- section with the line representing the joining of the upper surfaces of the vaults. A horizontal Une is projected over from g" to/", the point of intersection with the normal joint. The point i" is projected down to/', on the projecting Une from/. By connecting/' and h' {h! is opposite/' and equidistant from the center Hne of the rib) with a straight line, the upper edge of the bearing-surface is determined. The point h is found by projecting up from h' . By connecting a! and /', and e' and h'\ also a and /, and e and h, the side edges of the bearing-joint are located. The lower bearing- surface of a stone, or the upper bearing-surface of the next lower stone, is found in a similar manner. If the vaults are not of the same diameter, either of two methods may be used. The number of stone courses in both vaults may be made the same, thus making the courses in the wide vault wider than those in the narrow vault, and the method of finding the shape of the groin-stones is similar to that shown in Fig. 8(6) ; or the stones may be the same width, thus making a greater number of courses in the wide vault than in the narrow vault. In the latter case the groin-stones are de- termined as in Fig. 9. To take care' of the different number of courses in the two vaults, one course in the narro^y vault is sometimes made to receive two courses in the wide vault, as shown by stone A in Fig. 9. Because the joint a is higher than the joint h, there results a peak toward the side of the groin-Hne. This is cut ofif at right-angles to the groin, thus making the bearing-surface c. This surface is determined as follows. The intersection of the joint-planes d and e is at/. The vertical projection /i, of/, is drawn through h\, found by projecting up h and g, and a horizontal line from g\. The intersection of /i and a line through gi, normal to the groin-curve gives ii, which, projected to i, gives the intersection of the sides of the bearing-surface c. The point / is found . by projecting up k, the intersection of a and the diagonal, to ^1; then projecting k\ to j\, the intersection with the normal Hne; and then projecting j\ to /. By connecting g and / with a curved line (other points of which are determined by drawing lines parallel to a and proceeding by the method used in finding/); and g and i, and/ and /, with straight lines; the sides of c are determined. If the vaults are built of brick, it is better to run the courses at right-angles to the groins, thus giving a chance for the bricks to overlap, as shown in Fig. 10. If the brick courses are to run parallel to the center line of the vaults, it is necessary to use stone ribs to carry the shell. Determination of the Stresses in Groined Vaults. The problem of a groined vault span- , (ci) ning a rectangular area which is not square, Fig. 10. Groins of Brick Vaults ^^ ^^^^ considered, as a vault spanning a SQUARE AREA ofTcrs fewer difficulties and can be worked out on the same principles. The problem is to span an area, whose half-length of the short diameter is a, and whose half-length of the long diameter is h. Fig. 11 (a). In order to obtain a more stable construction, the point of inter- section of the crowns of the vault is raised a distance cd = c'd, thus giving the crown of the long-span vault a slope cc and the crown of the short-span vault a slope c'J. The vault is divided into strips ^, B, C, etc., and A', B' , C, etc., from the rib R, as shown in the projected area in Fig. 11 {a). The rib R is Vaults 1239 Fig. 11. Determination of Stresses in Groined Vaults 1240 Domical and Vaulted Structures Chap. 31 given a width equal to the assumed width of the supporting diagonal concealed arch, and the widths A, B, C, etc., and A', B', C, etc., are obtained by dividing the two vaults into the same number of equal parts. These strips are considered as adjacent arches resting on the rib R. For simphfication the hne of pressure or resistance-line of each strip is placed in the center of that strip as gk in A and g'k' in A'. The error in this is on the side of safety. Even though the projected areas of the two intersecting vaults are the same, the actual surface-area of the smaller-span vault is slightly larger than that of the longer-span vault. Therefore, if the vaults are of the same thickness, the shorter-span vault is slightly heavier than the larger- span vault. In order to have the resultants of the horizontal components of the thrusts from strip A and strip A\ strip B and strip B\ etc., parallel to the direction of the rib R, the procedure is as follows. The thrusts of the strips on the heavier side, that is of strips A, B, C, D, E, and F, are determined as. shown in Fig. 1 1 (6) and (c) . The curvature of the strips being the same, the work can be considerably lessened by dividing the arch into sections of unequal lengths for weight-determinations. The dividing line for the sections is found, by projecting up the point of intersection of the line of pressure of each strip and the side of the rib R, as g to g', h to h\ etc. The weights w\, W2, wz, etc., of each section are then determined and the composite load-Une drawn as in Fig. 11 (c). The positions of W a, Wb, Wc, etc., in Diagram (b) are determined by the usual stress-polygon. H is then drawn so as to be at the upper limit, and the dififerent thrusts so as to act near the lower limit of the middle half of the vault-thickness. * Lines drawn in Fig. 1 1 (c) parallel to these thrusts, determine their values, and the values of the hori- zontal components Ha, Hb, He, etc. The weights w'l, w'i, w'z, etc., in Diagram {d), are found in the same way, the load-line in Diagram (/) drawn, and the positions of W \', Wb', Wc\ etc., found as before. H' in Fig. 11 {d) is drawn, at the upper limit of the middle half in this demonstration.* Ha\ Hb\ He', etc., however, must have such values that the resultants of Ha, and Ha', Hb and Hb', etc., are parallel to R. The required values of Ha', Hb', He', etc., are found as in Fig. 11 (e), by laying off Ha, Hb, He, etc., and drawing Ti, Ti, Ts, etc., parallel to R. The resulting values of Ha', Hb', He', etc., are then laid ofif in Fig. 1 1 (/) and the thrusts drawn. When drawing the thrusts in Fig. 11 (d) through the intersection, of H'. and Wa', H' and Wb', etc., parallel to their directions in Fig. 11 CO, it is found that they act very slightly above the lower edge of the middle half. The rib R is then drawn as in Fig. 1 1 [h) and the points of application of the loads located. The load-polygon is drawn as in Fig. 11 {g). The resultants R\, R-i, etc., are drawn in both Diagrams {h) and {g) of Fig.ll, the position of X in Diagram {h) found by the usual stress-polygon, and the thrusts Z and Y determined. The point through which Z, Diagram (A), passes at the spring of the rib, should be so chosen that the line of pressure remains at least within the middle half of the rib; or the more usual and conservative limits of the middle third may be used. In the case of brick vaults the strips A, B, C, etc., are taken at right-angles to the groin, resulting in vertical loads, only, on the assumed rib. Ribbed Vaults. In ribbed vaults the ribs are designed to be built first, to be free-standing, and of sufficient strength to support the shell when it is placed over them. To simplify the construction, all the rib-arcs are ordinarily • made with the same radius, thus making all the ribs disengage each other at the * The theory of the middle third is the one usually followed, as it is the most conserva- tive and results in a larger factor of safety. See, also, foot-note on page 1225. Vaults 1241 same height. This makes the narrower rib-arches pointed, and the diagonal rib-arches semicircular, but they are all constructed of similar stones with cross- sections of the same shape. To determine the points A and B (Fig. 12), at which the ribs become independent of each other and of the wall, the proceeding is as follows. In plan the clustered ribs are shown just above the column- capitals, with the diagonal ribs extending into the wall a distance ab. To find the height at A , draw an arc through a with the same curvature as that of the diagonal rib, and draw at right-angles to the ribs, in plan, a line from h, until it cuts this arc at c. The height ch is the height at A . The height at B, equal tofe, is found in the same way. The webs, or parts of the vault-shell supported by t'le ribs, are Fig. 12. Vault-rib Construction usually shallow arches in cross-section, and are spherical triangles, that is, they are domical. In order to use to the fullest advantage the finished lower portions of the vault as supports for the upper courses as laid, the courses of the vault-shell, or web are laid in planes normal to the wall and the transverse ribs. This is shown in horizontal projection in Fig. 13 I. The web being arched in both directions, the thrusts act in two directions, as in domes. From the study of the theory of domes it is found that the thickness of the shell in a dome has no effect on ITS stability. The web in ribbed vaults being domical, can be made relatively thin, but for stone or brick vaults it should not be less than about 4 in thick for spans up to 35 ft. ■ The ribs are designed as arches, loaded with the thrusts of the web supported. These thrusts are determined as illustrated in Fig. 13 II. The vaulting resting on the half -wall, or transverse rib A, and the half-diagonal rib B, is divided into any number of equal lunes, or figures bounded by the two inter- secting arcs, and radiating from the axis of the dome of which that part of the vaulting is a spherical triangle. This axis is found by projecting, at right- angles from the rib§ A and B, lines starting at the center of curvature of the ril?§ tm Domical and Vaulted Structures Chap. 31 and intersecting at the point e, which is the projection of the axis of the dome. The RADIUS OF THE DOME is then Ri in Fig. 13 II, equal to the distance from e to Fig. 13. Determination of Stresses in Vault-ribs the spring of the diagonal rib B. The thrust of each lune on the ribs is then found as shown for lune L. Example. Let the radius -Ri, Fig. 13 II, be 25 fee:, and let the shell be 4 in ihick, constructed of stone, and weighing 125 lb per cu ft. The angle (by meas- urement) is 54° 30', and the angle a is 18° 30'. These are found by projecting up from the point of intersection / of the center line of the lune L and the center of the rib B, and the intersection g of the center line of the lune L and the crown- line of the vault, to /x and gi, respectively, on the vertical projection £1 of the lune L. Using the same notation, equations, and curves as were derived for smooth- shell domes (page 1214), it is found from Plate II, with - = o and a = 18° 30', a that Wi-o= -125(4/12) (25)2(0.33)= -85941b and that -8594 27r(i25)(4/i2)(25)' = —0.0525 From Plate I it is found that the critical angle, for values of — = o and a Vaults 1243 n = —0.0525, is 55° 30', and the vaulting should be back-filled as high as this, as shown. From Plate III, with — = o. and w = — 0.0525, it is found that at = 54° 30' U = (125 X 4/12 X 25)(-^.o79 + 0.63) = 573 lb By measurement, the width of lune L at / is 2 ft; hence the total tangential PRESSURE C (Fig. 13), is 2 X 573 = i 146 lb. The horizontal component D of this is 6 655 lb, and the component F (along the rib B) of Z) is 5 750 lb. The vertical component E of C is 9 339 lb. The value of T is found from Plate IV to be 125 X 4/1 2 X (25) ^ x (—0.004 + 0.295) = 7 570 lb, and the component // (along the rib B) of T is 3 630 lb. The THRUSTS acting on the rib B of the other lunes above L are found in the same way, and the portion of rib above the back fill investigated as an arch. In Fig. 13 that portion of the rib below the web is not indicated. For vaults with semicircular diagonals of about 33-ft span, the ribs should be from 7 to 10 in wide and from "ro to 14 in in total height, and the minimum dimensions of the projecting portions of the ribs below the webs, for smaller vaults, should be 3 3^ in width and 6 in in height.* Tile Vaults. Tile vaults, as built by the R. Guastavino Company, are constructed of tiles, from 6 by 12 to 24 in in plan, and i in in thickness, and laid in several layers so as to make a solid, thin shell that is both light and strong. Because of the overlapping of the tiles, the shell has considerable tensile resistance, and the vaults are practically monolithic. It is due to this and to the lightness of the construction that the thrusts and the weight of the entire structure are materially reduced. Ordinarily a finished acoustic tile, backed by rough constructional tile, is used for the exposed surfaces. Framed Vaults. Vaulting in buildings of moderate cost is frequently constructed by suspending from the roof-trusses steel or wooden frames carrying lath and plaster. The roof-trusses must in this case be designed to carry the direct loads of the framed vaulting, which must be of the required strength and shape to carry and fit the plastered surfaces. * Handbuch der Architektur. PART III USEFUL INFORMATION ARCHITECTS, DRAUGHTSMEN, BUILDERS, AND SUPERINTENDENTS AND ALL WHO HAVE TO DO WITH THE BUILDING TRADES Note. The editor has arranged the information in Part III in the following order : Heating and Ventilation. Chimneys. Hydraulics, Plumbing and Drainage, Gas and Gas-Piping. Lighting and Illumination of Buildings. Electric Work for Buildings. Architectural Acoustics. Weights, Quantities, and Miscellaneous Data on Building Materials. Dimensions and Data Useful in the Preparation of Drawings and Specifica- tions. Miscellaneous Information for Architects and Builders, Glossary of Architectural and Technical Terms. Legal Definitions of Architectural Terms. Ill THA4 Heating and Ventilation of Buildings 1247 HEATING AND VENTILATTON OF BUILDINGS* By LOUIS A. HARDING ©'FORMERLY PROFESSOR OF MECHANICAL ENGINEERING, PENNSYLVANIA STATE COLLEGE Physical Units and the Measurement of Heat System of Units. In this country the system of units in general use by engineers is known as the foot-pound-second system, and the following defini- tions and examples will show the significance of each. Defiinition of Units Employed. The unit of time is the second, which is equal to — part of the mean solar day. / = time. Time is also expressed in 86 400 minutes and hours. L = length. The unit of length is the foot = 0.3048 meter. W = weight. The unit of weight is the pound = 0.4532 kilogram. A = area. The unit of area is the square foot. The unit often used is the square inch. V = volume. The unit of volume is the cubic foot. Volume = area X length = A XL. In calculations involving the quantity of air required Q is often used for cubic foot. Example. The volume displaced per stroke by the plunger of a pump, if the diameter is 6 in and the stroke is 12 in, is J^i X 6^ X 12 = 339.29 cu in, or 0.196 cu ft. If the plunger makes 30 working strokes (not revolutions) per minute, then the plunger-DisPLACEMENT per minute is 0.196 X 30 - 5.88 cu ft. One United States gallon =231 cu in = 0.1336 cu ft. This pump will therefore theoret- ically dehver 5.88/0.1336, or 44 gal per minute. The actual delivery of the pump will be 10 to 15% less, owing to the slip, which is the leakajge back through the pump-valves, around the plunger, and that due to imperfect fiUing of the pump-cylinder on the suction-stroke. Density. D = density. The weight of a unit volume (i cu ft) of a sub- stance is called its density. The density of water at 70° F. is 62.3 lb per cubic foot. The density of air at 70° is .075 lb per cubic foot. The pump in the pre- ceding example would, therefore, handle 5.88 X 62.3 or 366 lb of water per minute. If the water-end of the pump is operated by a steam-cylinder- having a dis- placement of 0.349 cu ft per stroke, and takes steam at the same pressure for the full stroke as in the direct-acting type and if we assume that the steam- pressure is loo-lb gauge, we find from the steam-table (Table I), that the density of steam at this pressure is 0.2565 lb. The steam-consumptjon of the pump, therefore, would be 0.2565 X 0.349 X 30 X 60 = 161. 6 lb per hour, theoretically. A fan handling 10 000 cu ft per minute of air at 70° F, delivers 10 000 X .075 = 100 lb per minute. Velocity, v = velocity. The rate of motion of a body is measured by the distance passed over in a unit time. Velocity is expressed in feet per second. * Much of the data of this section has been condensed from Vol. I of Mechanical Eailinmenf of Til1llfHnP' Heat of Evaporation a p necebsary to oy.excome Molecular attrasfiaft Fig:. 7 Figs. 4 to 8. Diagrams Explaining the Generation of Steam P is the pressure of the atmosphere in pounds per square feet (barometric pressure). It is evident then that the latent heat r = p -\- APu, or p -r — APu The term APu is the heat-equivalent of the work performed for the change in volume from water to steam. The heat added from the starting-point (32° F.), is known as total heat (//), or q -i-r = H. If more heat is added, the pressure remaining constant, the temperature of the steam rises and the steam becomes what is known as superheated steam. The heat added is equal to the meaij specific heat {Cp) of the steam, times the change in temperature (ts — 212). The specific heat of steam is the Btu, or heat, required to raise the temperature of i lb of the steam 1° F. Since the specific heat of steam is less than that of water, the slope of this line becomes greater than that of the water-line The point is now located at h (Fig. 8), and the steam has increased in volume in the cylinder (Fig. 5), until the piston occupies the dotted position B'. If instead of the above condition of pressure, additional pressure is added, Steam m Table I. Properties of Saturated Steam. ' G. A. Goodenough Absolute pressure Inches of mercury Lb per sq in Tem- pera- ture, deg. F. Vol- ume, cu ft per lb Weight, lb per cuft Heat-content in Btu of liquid of vapor Latent heat in Btu of vapor- ization t H 4.072 8.144 12. 216 16. 29 20.36 24-43 30 14.74 16 18 24 26 28 30 32 34 36 38 40 50 54 60 64 70 74 80 84 90 94 100 104 no 114 120 124 130 134 140 144 ISO 154 160 164 170 174 180 190 200 126.10 152.99 170.07 182.87 193-21 201 .96 212.13 216.3 222.4 228.0 233 -I 237.8 242.2 246.4 250.3 254-0 257.6 260.9 264.2 267.2 281.0 285 292 296 302 306 312 31S 320 323 327.8 330.7 334.8 337.4 341.3 343.7 347.4 349.7 353.1 355.3 358.5 360.5 363.6 365.6 368.5 370.4 373.1 377.6 381.9 173.6 90.6 62.0 47.35 38.43 32.41 26.7s 24.76 22.18 20. 10 18.38 16.9s 15.73 14-67 13.76 12.95 12.24 11.60 11.03 10.51 8.53 7.93 7.18 6.76 6.22 5 5 5 4 4 4 4 4 3 3 3 3 3 3 3 3 2 90 48 23 905 709 442 279 057 921 735 620 461 363 226 140 020 945 2.839 2.773 2.679 2.620 2.536 2.4o8|o 2 . 292I0 00576 01104 01614 02112 02602 03086 03739 04038 04508 04976 0544 0590 0636 0681 0727 0772 0818 0862 .0907 09SI .1173 . 1261 .1392 . 1479 . 1609 .1695 .1824 . 1910 ,2039 . 2124 . 2251 ■ 2337 .2465 .2550 .2678 .2762 .2889 .2973 .3100 .3184 .3311 .3396 .3522 .3606 .3733 .3817 3943 .4154 .4364 94.02 120.9 137.9 150.8 161 . 1 169.9 180. 1 184.3 190. 5 196.0 201.2 206.0 210.4 214.6 218.6 222.4 225.9 229.4 232.6 235.8 249.8 254-7 261 .7 266.1 272.2 276. 1 281.6 285.1 290.1 293.3 297.9 300.9 305. 1 307.9 311. 9 314.4 318.2 320,. 6 324.2 326. 5 329.8 332.0 335.2 337-3 340.3 342.3 345.2 350. 354-5 116. 2 127.9 135.0 140.3 144.4 147.9 151. 8 153.4 155.7 157-7 159.6 161. 3 162.8 164-3 165.7 166.9 168. 1 169.2 170.3 171. 3 175. 6 177. 1 179-I 180.3 182.0 183.0 184.4 185.3 186.5 187.3 188.4 189.0 190.0 190.6 191.4 191-9 192.6 193. 1 193-7 194. 1 194-7 195-I 195-7 196.0 196.5 196.8 197.2 197.9 198. 5 I 022.2 I 007.0 997.1 989.5 983.3 978.0 971.7 969.1 965 961 958 955 952 949 947 944 942 939-9 937-7 935-5 925.9 922.4 917-4 914-3 909.8 906.9 902.8 900. 2 986.4 894.0 890.5 888.2 884.8 882.7 879-5 877.5 874-4 872 869 867 864 863 860 858 856 854 852 847 844 * Condensed from original tables published by John Wiley & Sons, Inc, 1254 Heating and Ventilation of Buildings Part 3 as shown by the weight W in Fig. 6, the temperature of the boiling-point will be raised from the temperature of 212° F. to some other point, as ti (Fig. 8). As may be seen by this figure, the sensible heat g has been increased to qi. When more heat is added the water is evaporated at the temperature h, and if heat again be added the saturated steam will become superheated steam. Quality of Steam. The proportion of the dry steam, per pound of steam delivered by the boiler, is known as the quality of the steam and is repre- sented by the symbol x, and the heat (Hx) contained in the steam above 32° F. is g + xr; the state-point is located at E (Fig. 8). Specific Volume and Density. The volume of a pound of steam is known as the SPECIFIC volume v, and as may be seen by comparing Figs. 5 and 6, de- creases as the pressure increases. The reciprocal of this, or the weight of steam per cubic foot, is known as the density, and is denoted by d or i/v. Entropy. Another quantity known as entropy is made use of in calcula- tions relating to steam-engines and turbines, and is defined as the ratio obtained by dividing the quantity of heat added to a substance by the absolute tempera- ture at which it is added. The Total Heat, //, of a dry, saturated vapor for any pressure and tem- perature is the sum of the heats required to raise the temperature of one pound of the liquid from the freezing-point to the given temperature and corresponding pressure and entirely vaporize it at this pressure. For this case x = i, and consequently II ^{p + APu) + g = y -f g The total heat {Hx) of wet vapor at any pressure and temperature is II X = xr + q It is manifestly incorrect to say that this is the heat in the vapor, as the APu is not the heat in the vapor, but the external work performed by the vapor while evaporating. Superheated Steam or Vapor. Superheated steam is defined as water- vapor which has been heated out of contact with its hquid, until its temperature is higher than that of saturated vapor at the same pressure. The heat-content of superheated steam or vapor may be expressed by the equation Hs =q -^f -{■ Cp{ts -t) =11 +Cp its - /) where ts is the temperature of superheated vapor, / the temperature of saturated vapor at the corresptmding pressure, q the heat of the hquid at /, and r the heat of vajxirization at temperature /. Cp is the mean specific heat of superheated vapor (approximately 0.50), // the total heat of i lb of dry sat- urated steam, and lis the total heat of i lb of superheated steam. Properties of Air Charles* Law. Charles' Law refers to the relation between pressure, volume and temperature of a gas, and may be stated as follows. The volume of a given weight of gas varies directly as the absolute temperature at constant pressure, and the pressure varies directly as the absolute temperature at constant volume. Hence, when heat is added at constant volume Vc* this equation results: P2 Ts Pi ~ Tx Properties of Air 1255 or for the same temperature-range, at constant pressure Pc, the relation is Tx In general, for any weight of gas M, since volume is proportional to weight at any given volume and temperature, PV = MRT JBmitaa which is the characteristic equation for a perfect gas. In this formula P = the absolute pressure of the gas in pounds per square foot « 21 16.8 (atmospheric pressure) ; V 5= the volume of the weight M in cubic feet; M == the weight in pounds of the gas taken; R = a constant depending on the nature of the gas = 53.37 for air; T = the absolute temperature in degrees Fahrenheit (/ -f- 459.6). Table II. Properties of Dry Air Barometric pressure, 29.921 in. Specific heat, 0.24 Btu absorbed Cubic feet Temperature Weight per Per cent of by one cubic of dry air in degrees cubic foot volume at foot dry air warmed one Fahrenheit in pounds 70° Fahrenheit per degree Fahrenheit degree per Btu 0.08636 0.8680 0.02080 48.08 10 0.08453 0.8867 0.02039 49-05 20 0.08276 0.9057 0.01998 50.05 30 0.08107 0.9246 0.0I9S7 5J.JQ 40 0.07945 0.9434 0.01919 52.11 50 0.07788 0.9624 0.01881 53.17 60 0.07640 0.9811 0.01846 54.18 70 0.07495 I .0000 0.01812 55.19 80 0.07356 I .0190 0.P1779 56.21 90 0.07222 1.0380 0.01747 57.25 100 0.07093 1.0570 0.01716 58.28 no 0.06968 1.0756 0.01687 59-28 120 0.06848 1-0945 0.01659 60.28 130 0.06732 I.1133 0.01631 61.32 140 0.06620 I. 1320 0.01605 62.31 150 0.06510 1.1512 0.01578 63-37 160 0.06406 I. 1700 0.0ISS4 64.35 170 0.06304 I. 1890 0.01530 65.36 180 0.06205 I .2080 0,01506 66.40 190 0.06110 1.2270 I -2455 0.01484 0.01462 67.40 68.41 200 . OdOI 240 0.05673 I. 3212 0.01380 72.46 300 0.05225 1.4345 0.01274 78.50 350 0.04903 1.5288 0.01197 83.5s 400 0.04618 1.6230 0.01130 88.50 450 0.04364 1. 7177 0.01070 93.46 500 0.04138 I.8113 0.01018 98.24 5S0 0.03934 I . 9060 0.00967 103.42 600 0.03746 2.0010 0.00923 108.35 700 0.03423 2.1900 0.00847 118.07 1256 Heating and Ventilation of Buildings Parts A PERFECT GAS conforms exactly to the above equation, and while no gases are PERFECT in this sense, they conform so nearly that the above equation applies to most engineering-computations. The volume of i lb of air, known as the SPECIFIC VOLUME, at any temperature and pressure, can be found at once by the equation V = (53-37 X T)/P Estimating Heating Requirements of Buildings Heat Required and Supplied. The amount of heat, measured in Btu to be SuppUed by the heating-apparatus to a building to maintain the inside tempera- ture above that of the outside, commonly termed heat-losses, is: (a) The heat required to offset the heat- transmission of the walls, ceiling or roof, and floor. This loss of heat depends upon the type and materials of con- struction used and the temperature-difference to be maintained between the inside and the outside of the building. (b) The heat required to warm the air entering the building from the outside, either by infiltration or purposely introduced for ventilation. (c) The heat supplied by {persons, lights, machinery and motors, which may be deducted from the sum of items (a) and (b) to obtain the net amount of heat to be supplied by the heating-apparatus. (Item (c) is usually not considered.) It is customary in all calculations connected with the design of heating- installations to base the estimate on the amount of heat per hour to be supplied by the apparatus. The total heat to be supplied per hour is // = [(item a) -|- (item b) — (item c)] Btu. The method in use for the calculation of the various items above mentioned will now be taken up and discussed in the order given. Temperatures. The inside temperature to be maintained and the air re- quired for ventilation for various classes of work are discussed under Ventilation, to which the reader is referred. The outside temperature for which the heating- installation should be designed is fixed by the lowest outside temperature that is liable to continue for several days during the heating-season. Usual Inside Temperature Specified Kind of buildings Public buildings. . Factories Machine-shops. Foundries, boiler-shops, etc Residences Bath-rooms Schools Hospitals Paint-shops V'.V'i .1 . . 0-S.S . T Degrees P. 68-72 65 6o-6s 50-60 70 85 70 72-75 80 In designing the heating-system a temperature of from 10*' to 15° F. higher than the lowest recorded temperature is recommended to be used for the out- side temperature. Heat-Transmission of Walls, Ceilings, Roofs, Floors, etc. (a) The heat- loss through building-construction is dependent upon the character of the material, thickness and character of the surfaces, and the velocity of the air over the surfaces. Numerous tests have been conducted by various experi- menters to determine accurately the heat-transmission of various types of Estimating Heating Requirements of Buildings Table HI. Outside Temperatures Lowest and Average Temperatures in the United States. All stated in Fahrenheit degrees and compiled from United States Weather Bureau Records State Ala . . Ariz. . Ark.. Cal. . Col. . Conn. D. C. Fla... Ga... Idaho 111.. . Ind.. la.... Kan.. Ky... La... Me... Md. . Mass. Mich. Minn. Miss . Mo. . Mont, City Mobile Montgomery . . Flagstaff Phoenix Fort Smith Little Rock . . . San Diego .... Independence.. Denver Grand Junction Southington. . . Washington. . . Jupiter Jacksonville. . . Savannah Atlanta Boise Lewiston Chicago Springfield .... Indianapolis. . . Evans ville .... Sioux City .... Keokuk Dodge City . . . Wichita Louisville New Orleans . . Shreveport. . . . Eastport Portland Baltimore Boston Alpena Detroit Duluth Minneapolis. . . Meridian Vicksburg Springfield .... Hannibal Havre Helena Lowest -25 -15 -31 -26 -26 7 - 5 -21 -17 - 7 -13 -27 -24 -41 -33 - 6 - I -29 -20 -55 -42 Aver- age.* 57-7 56.1 34.8 58.9 49. 5 52.0 57.2 48.7 38.4 39-2 36.3 42.9 69.8 60.9 57.2 51.4 39.6 42.5 35.9 39.0 40.4 44.1 32.1 37.6 42.9 45.0 60.5 55.7 31. 1 33.5 43.3 37.2 29.1 35. 3 25.5 28.4 53-9 56.0 43.0 39.7 27.7 30.9 State Neb. . Nev. . N. H N. J.. N. Y. N. M. N. C. N. D. Ohio . Okla . Ore. . Pa... R. I. . S. C. . S. D.. Tenn. Tex. . Utah. Vt. .. Va... Wash. W.Va. Wis. . Wyo . City North Platte.. Lincoln Carson City. . . Winnemucca. . Concord Atlantic City. . Saranac Lake.. New York City Roswell Santa Fe Hatteras Charlotte Devil's Lake. . Bismarck Toledo Columbus Oklahoma Baker City. . . . Portland Pittsburgh .... Philadelphia. . . Providence. . . . Rock Island. . . Charleston .... Columbia Huron Yankton Knoxville Memphis Corpus Christi. Fort Worth . . . Salt Lake City. Northfield Cape Henry. . . Lynchburg. . . . Seattle Spokane Parkersburg. . . Elkins La Crosse Milwaukee .... Cheyenne Lander Lowest -35 -29 - 22 -28 -35 - 7 -38 - 6 -14 -13 8 - S -51 -44 ~i6 —20 -17 —20 - 2 —20 - 6 - 9 - 4 7 2 -43 -32 -16 - 9 II - 8 20 -32 5 - 5 3 -30 -27 - 21 -43 -25 -38 -36 * Average is taken from October i to May i. construction. The following table represents the results of the experiments (1914-15) by Harding and Willard in this connection, based on an average outside wind-movement of approximately 15 miles per hour; 1258 Heating and Ventilation of Buildings Table IV. Heat-Tiransmission of Building-Construction Parts Construction Thick- ness, Btu transmitted per square foot per hour Temperature-difference 20 40" 6o° 70° 8o° Blain bilckr-nU 9 13 I8 24 .363 .281 .220 .174 7.3 5.6 4.4 3.5 14-5 II. 2 8.8 7.0 21.8 16.9 13.2 10.4 25.4 19.7 IS. 4 12.2 29.0 22.5 17.6 13.9 .217 .185 .156 .132 4-3 3.7 . 3.1 2.6 8.7 7.4 6.2 5.3 13.0 II. I 9.4 7.9 IS. 2 13.0 10.9 9.2 17.4 14.8 12.4 10.6 .20 4.0 8.0 12.0 14.0 16.0 i^m$^wm^ • 547 .370 .279 10.9 7.4 5.6 21 .9 14.8 II. 2 32.8 22.2 16.7 38.3 25.9 19-5 43.8 29.6 22.3 .409 .325 .281 8.2 6.5 5.6 16.4 13-0 II. 2 24.5 19-5 16.9 28.6 22.8 19.7 32.7 26.0 22. S .784 .714 .655 .563 IS. 7 14.3 13.1 II. 3 31.4 24.6 26. 2 22.5 47.0 42.8 39-3 33.8 54-9 So.o 45-9 39-4 62.7 57.0 52.4 45.0 For 3-in concrete covered with slag roofing, de- duct approximately iO% from values stated. Single Double Triple 1. 126 22.5 45-0 67.6 78.8 .450 9-0 18.0 27.0 31.5 .281 5.6 II. 2 16.9 197 .018 .360 .720 1.08 1.26 90.0 36.0 22.5 One air-change per hr cu ft 1.44 Btu loss per foot of sash perimeter per hour Wooden sash Wooden sash, metal strip. . . . Hollow metal sash Hollow metal sash, stripped. . 2.05 41.0 82.0 123 144 0.43 8.6 17.2 26 30 4.5 90 180 270 315 1.6 32 64 96 112 164 34 360 128 • For lath-and-plaster ceiling with no floor above, double the values given for wooden floor with plaster ceiling. Estimating Heating Requirements of Buildings 1259 The following data on the heat-transmission of various types of roofs were taken from the test-results of C. L. Norton: Table V. Heat-Transmission through Roofs Construction Btu per sq ft per hour per i ° difference in temperature of still air inside and outside APM gypsum slab roof 4 in thick with S-ply tar and felts. . APM gypsum slab roof 3 /^ in thick with 5-ply tar and felts APM gypsum slab roof 3 in thick with 5-ply tar and felts. Spruce planks 3 in thick with 5-ply tar and felts 0.134 0.149 0.170 0.192 0.282 0.348 0.488 0.508 0.575 0.633 Hard-pine plank 3 in thick with 5-ply tar and felts Hollow terra-cotta tile 3 in thick with 5-ply tar and felts. . . Stone concrete 6 in thick with 5-ply tar and felts Cinder concrete 4 in thick with 5-ply tar and felts Stone concrete 4 in thick with 5-ply tar and felts Stone concrete 3 in thick with 5-ply tar and felts The heat-transmission of stone walls is approximately 50% greater than that of brick of equal thickness. The Btu-loss per foot of sash-perimeter is based on the leakage-determinations by Voorhees and Meyer, Trans. Am. Soc. H. and V. E., 1916. Heat-Transmission of Roofs and Floors. The temperature of the air in contact with the under side of a ceiling or roof is found to be higher than the temperature maintained at the breathing-line, at which point the temperature is usually measured; and this is due to the natural tendency of the warmer or less dense air to rise. It is recommended that an increase of approximately 15% be made to the specified inside temperature for the temperature at the ceiUng for ceiling or wall-heights not exceeding 15 ft, and 30% for ceiling-heights of 20 ft or more, in estimating the heat-loss of roofs. Thus, if 65° F. is the spe- cified inside temperature to be maintained in a room the height of which is 20 ft, the temperature of the air in contact with the under side of the roof may be assumed to be 65° -|- 30%, or 85° F. The loss of heat through the ceiling of a room over which a large air-space exists, through partitions between a heated and a cold room, or through the first floor to the cellar, may be estimated on the assumption that the warmed rooms give off sufficient heat tc maintain the temperature of these colder spaces according to the following schedule: Closed attics under metal or slate roofs 14° F. Closed attics under tile, cement, tar, or gravel roofs 23 '^ F. Cellars and rooms kept closed 35° F. The heat-transmission of floors that are laid directly upon the ground may be estimated on the assumption that the ground in contact with the under side of the floor has an approximate temperature of 50° F. Thus the estimated heat- loss through a 6-in concrete floor laid directly upon the ground, assuming an inside temperature of 65° F., is 0-563 (65 — 50) or 8.4 Btu per square foot per hour Heat-Loss by Infiltration, (b) The heat required to warm the outside air 1260 Heating and Ventilation of Buildings Parts which may enter by leakage through the cracks or clearances around windows and doors is that required to raise the temperature of the weight of incoming air per hour from the outside to the inside temperature. Let b =Btu required per hour to heat the incoming air; / =inside room-temperature in degrees Fahrenheit; to = outside temperature; Cp = specific heat of air at constant pressure =0.24; d = density of the air at temperature /; =0.075 for 70° inside temperature; =0.076 for 60° inside temperature; Q = cubic feet of air per hour entering building by infiltration, measured at temperature /; W = weight of air per hour entering building by infiltration = d XQ; Then b =Cp (t - k) Q X d = 0.24 XW X{t - /o); = 1.26 Q for 70° inside temperature; = 1.08 Q for 60° inside temperature. There are two assumptions made by engineers in practice for obtaining the value of Q. The common method in vogue is to assume a certain number of air-changes n, per hour in the cubical contents C, of the room in accordance with the following table: Table VI. Number of Air-Changes per Hour Halls Rooms on ist floor Rooms on 2nd floor Offices and stores, ist floor Offices and stores, 2nd floor Churches and public assembly-rooms, Large rooms with small exposure . , . . Factory -buildings n = 2 to 3 n — I H to 2 n = ^ to 2 n = H to I n = M to I Example. Required the heat-loss, by infiltration, from a room containing 20 000 cu ft, the temperature of which is maintained at 70° F. in zero weather, the estimated number of air-changes n, being two per hoiu:. Solution. Q = 2 X 20 000 = 40 000 cu ft of air entering per hour measured at 70.° F. b = 0.018 X40 000 X (70 — o) =50 400 Btu per hour. The other method is to use the estimated amount of air-leaking in the build- ing through the cracks around the sash-perimeter and meeting-rail. The fol- lowing data may be used in this connection and is based on a wind-movement of approximately 20 miles per hour (Voorhees and Meyer Tests). Plain wooden sash Plain wooden sash, weather- stripped Hollow metal sash Hollow metal sash, weather- stripped Copper-covered sash 24 216 to 268 72 to 150 132 cu ft air per hour per foot perimeter cu ft air per hour per foot perimeter cu ft air per hour per foot perimeter cu ft air per hour per foot perimeter cu ft air per hour per foot perimeter For a room with more than one outside wall use only the sum of the per- imeters of the windows, in the side having the greater number. Estimating Heating Requirements of Buildings 1261 Example. An office 14 by 16 by lo-ft-high ceiling, has two 3 by 7-ft wooden- sash windows. The maintained inside temperature is 70°, and the outside temperature 0° F. Required the heat-loss by infiltration. Solution. By the first method, assuming two air-changes per hour, the loss is b = 1.26 X 2 X (14 X 16 X 10) = 5 645 Btu per hr By the second method this loss is: ry b = 1.26 X2(3 +3 +3+7 +7 perimeter) X 114 =6 607 Btu per hir Increase in Heat-Losses for Tall Buildings. It is advisable to increase the calculated heat-losses above the tenth floor by approximately 15% for walls that are exposed to the prevailing winds. Heat Supplied by Persons, Lights, Motors, Machinery, etc. (c) The quantity of heat emitted by persons is ordinarily not of sufficient importance to be taken into account, except in cases of assembly-halls and theaters. The following allowances may be made when required: (i) Persons: Man at rest 400 Btu per hour Man at work 500 Btu per hour The heat introduced by lights is as follows: ■ ;r t • ,(2) Lights: Electric lamps: Btu per hour equals watts per lamp X number of lamps X 3415 Gas-lighting: I cu ft producer gas 150 Btu I cu ft illuminating gas 700 Btu I cu ft natural gas i 000 Btu 'A Welsbach burner averages 3 cu ft of gas per hour and a fish-tail burner cu ft per hour. (3) Motors. Motors and the machinery which they drive, if both are located in the room, convert all of the electrical energy supplied into heat, which is retained in the room if the product being manufactured is not removed until its temperature is the same as the room-temperature. (4) Machinery. If power is transmitted to the machinery from the outside, then only the heat-equivalent of the brake horse-power, d.h.p., supplied is used. In the first case the ^ ,. , , motor horse-power ^ Btu supplied per liour = --, . . X 2 546 elnciency of motor and in the second case Btu per hour = d.h.p. X 2 546 in which 2 546 is the Btu equivalent of i horse-power hour. In high-powered mills this is the chief source of heating and is sometimes sufficient to overheat the building even in zero weather, thus requiring cooling by ventilation the year round. Short Rules for Estimating the Heat-Loss of Buildings. There is a great variety of ruli:-of-thumb methods for estimating the heat-loss // for proportioning the heating-surface required when direct radiation is to be 1262 Heating and Ventilation of Buildings Parts used. These so-called practical rules are intended to be based on average building-construction and on the ratio of wall and glass-surface to the cubical contents as found in buildings of the class to which they refer. These rules when modified for unusual conditions and appHed by engineers of long experi- ence in the proportioning and design of heating systems produce satisfactory results. They are, however, rapidly being discarded except as rough checks on the more refined methods of calculation. Carpenter's Rule. The following formula, or rule, which has been widely used for many years in this country, was proposed by R. C. Carpenter. It is SECOND FLOOR Fig. 9. Floor-plans and Section of Building Explained in Table VII. (See, also, Fig. 34) not intended to be applied to buildings covered with corrugated sheet steel or metal lath and plaster walls, unless the wall-constant is changed to suit the con- dition. By reference to Table IV, it will be noted that a fair average value for the heat-transmission of the usual well-constructed building-wall is approximately Estimating Heating Requirements of Buildings 1263 Table VII. Tabulation of Heat-Losses for Building Shown in Fig. 9. Room- designation Net volume, cu ft Net wall-area, sq ft Floor or ceiling, sq ft Glass-area, sq ft I 2 3 4 5 First floor: Sample-room. Hall Laboratory. . Office Toilet Second floor: Mgr's office. . Hall Gen'l office . . Sup't's office.. 10 o8o 2 595 4 320 2 520 900 4320 2 595 10 080 4320 852 99 378 288 90 393 119 852 393 864 216 360 210 75 360 216 864 360 180 ' 45 "' 90 60 30 75 25 150 75 : jii 1 • Totals 41 730 3464 730 Room- designation Transmission-loss, Btu per hour Infiltration loss, Btu per hour Total heat- loss, Btu per hour a Wall-loss 19.7 X col. 3 Floor or ceiling- loss, 13. X col. 4 18.8 X col. 4 Glass- loss, 78.8 X col. 5 Assumed no. air- changes per hour Infiltra- tion-loss, 1.26 Xcol. 2 Xcol. 9 I 6 7 8 9 10 II First floor: Sample-room. Hall Laboratory. . Office Toilet Second floor: Mgr's office. . Hall Genl. office. . Sup't's office. 16 784 I 950 7 446 5 674 1 773 7 742 2 344 16 784 7 742 II 232 2 808 4 680 2 730 975 6768 4 061 16 243 6 768 14 184 3 556 7 112 4728 2 364 5 910 I 970 II 820 5 910 I 3 2 2 2 2 3 • 2 12 700 10 809 10 886 6350 2 268 10 886 10 809 25 400 10 886 54900 19 123 27358 19 482 7380 31 306 19 224 70 247 31 306 Totals 100 OQA 280 326 0.25 Btu and for glass i.o Btu per degree difference between the inside and out- side temperature per hour. Professor Carpenter states that usually we may, with sufficient accuracy, neglect all inside walls, floors and ceilings and consider only the outside walls. The estimated number of air-changes per hour, by infiltration, has already I been given in Table VI. 1264 Heating and Ventilation of Buildings Part 3 Let C = cubical contents of room in cubic feet; n = number of air-changes per hour (see Table VI) ; 0.02 = Btu to raise i cu ft of entering air i° F.; W = net wall-surface in square feet; G = glass-surface in square feet; (/ — h) = temperature-difference between inside and outside; H = total heat to be supplied per hour in Btu; 11 = (o.o2«C +G -\- }iW) it - /o). Calculating the Heat-Loss of a Building. The following example (Table VII) will serve to illustrate the method employed in calculating and tabulating the heat-loss of a typical building, the floor-plans and section being shown in Fig. 9. (See, also, Fig. 34.) The heating requirements are for a temp)erature of 70° F. in zero weather. The heat-transmission for the outside walls per square foot is taken from Table IV for a temperature-dilTerence of 70°. The heat-loss through the first floor is based on a temperature-difference of 70—35 or 35°. The heat-transmission per square foot per 1° difference in temperature per hour for i^^-in wood is 0.37; hence for 35° it is 0.37 X 35 = 13 Btu per hour. The heat-loss through the ceihng of the second floor is based on a temperature- difference of 70 — 23 = 47°, 23° being the assumed temperature of the attic in zero weather. The heat-transmission per square foot per hour is therefore 47 X 0.40 = 18.8 Btu. The infiltration-loss is, in this example, based on an estimated number of air-changes per hour as indicated in Table VII. By Carpenter's rule the heat-loss of this building based on two air-changes per hour, is [0.02 X 2 X 41 730 + (3 464/4) + 730] X 70 = 228 564 Btu per hour Radiation Direct Radiation. Steam or hot-water radiators placed in the room to be heated are termed direct radiators or direct radiation. Common types of direct radiators are shown in Figs. 10, 11, 12 and 13. Indirect Radiation. Radiators used to warm the air passed over them, the heating of the building being accomplished by hot air, are termed indirect radiators or indirect radiation. (See Figs. 45 and 46.) This type of radiation is frequently used for installations in which provision must be made for ventilation as well as heating, as in the case of schools, public buildings, etc. Indirect radiation is also used to some extent in high-grade residence-heating where direct radiation may be thought unsightly, particularly for the first floor. Direct radiation is ordinarily employed for the floors above the first floor. The principal use of indirect radiators is in connection with the hot-blast system of heating, described later, in which a fan is used to circulate the air over the radiator and through the duct system. Direct-Indirect Radiation. Direct-indirect radiators (Fig. 14) arc radiators placed in the rooms to be heated and furnished with a cold-air con- nection through the outside wall. It serves the purpose of providing tem- pcred-air ventilation. Materials and Connections of Radiators. Radiators are constructed of cast iron, pressed steel or pipe-coils. The sections for one-pipe steam systems are connected only at the bottom. The sections for hot-water radiators and two-pipe steam systems are connected at both top and bottom. The latter is known to the trade as hot- water radiation. Radiation 12G5 Pressure in Radiation. Cast-iron radiators should not be operated above 15 Ib-per-sq-in pressure. Standard pipe-coil direct radiation may be operated up to a 125-lb pressure. Rating of Radiators. Radiators are rated according to the square-foot area of external heating-surface. Cast-iron and prcsscd-steel direct radiators are built up of sections. The amount of heating-surface per section of cast-iron radiators for the various standard heights manufactured is given in Table VIII. r*^^ r^ 1 ' hi ^ 1 riM 3) ^. Fig. 10. Rococo Three-column Radiator Fig. 1 1. Peerless Three-column Radiator New Type of Direct Cast-iron Radiator. The American Radiator Com- pany has recently placed on the market a new type of direct cast-iron radiator termed Corto. Approximately 30% more heating-surface for a given floor-area is obtainable with this than with other types of direct radiation. The length of each section is 2 in and the width 8 in for all heights. The heating-surface per section is as follows: 42-in, 5 sq ft 2 7 -in, 3 sq ft 38-in, 4H sq ft 23-in, 2M sq ft 34H-in, 4 sq ft 193^-in, 2 sq ft 31-in, 33^ sq ft Wall-radiation (Fig. 12) is largely used in bath-rooms, and also for factory- heating where the width of column-type radiation is objectionable. (See Table IX for rating and dimensions.) Pressed-Metal Radiators. These radiators have been developed in recent years, and are most ingeniously fabricated of No. 20 United States standard- gauge soft-iron sheets made into shapes, widths and heights which correspond almost exactly with the cast-iron column-radiators. Each section is made up of two pressed sheets joined by a double-lapped seam and the separate sections are connected by single-lapped seams. The pipe-connection is made into a threaded malleable-iron ring secured to the end-section by rolling the sheet 1266 Heating and Ventilation- of Buildings Table VIII. American Direct Radiators Heights, widths, lengths and heating-surfaces Parts Height in inches 45 38 26 23 Peerless, single-column, steam and water. . Rococo, single-column, steam and water. . Peerless, two-column, steam and water. . . Rococo, two column, steam and water. . . . Verona, steam and water Peerless, three-column, steam and water. . Rococo, three-column, steam and water. . . Peerless, four-column, steam or water. . . . Rococo, four-column, steam or water Aetna flue, steam or water Italian flue, steam or water Rococo window, steam or water sH 4H 3 3 Height in inches 16 Length per section in inches Width of section in inches Peerless, single-column, steam and water. . Rococo, single-column, steam and water. . Peerless, two-column, steam and water. . . Rococo, two-column, steam and water. . . , Verona, steam and water , Peerless, three-column, steam and water. . Rococo, three-column, steam and water. . , Peerless, four-column, steam or water. . . . Rococo, four-column, steam or water Aetna flue, steam or water Italian flue, steam or water. . . . » Rococo window, steam or water iH^ 4M 3M 2H 2^ 2K 3 3 3 3 3 4V2 4K2 TVs 7H 8 9 9 loH 10 H 12H 8H * Peerless 15-in in steam only. The location of the figures in the above columns in line with the names of patterns of radiators indicates the heights in which the various patterns are made. The figures themselves represent the amount ;of heating-surface contained in each section. To obtain the total length of the radiator, multiply the length per section by the num- ber of sections. Table IX. American Rococo Wall-Radiators Ratings and measurements of sections Section-numbers Length, in Width, in Thickness, in Thickness (with bracket), in Heating- surface. sq ft S-A 16^ 213^ 20 Mg 13 Me 13 Mo 13 -yia 2^ 2Vs 3^ 3H 5 7 9 7-A and 7-B .... 9-A and 9-B .... Radiation 1267 metal snugly over a suitable flange on the inner face of the ring. Air-valve connections are made in a similar manner. See Fig. 13 and Table X. These Fig. 12. Typical Installation of Rococo Wall-radiators in Single Tier on Adjustable Brackets radiators are light in weight and therefore easy to handle and install, and cost less for freight and shipping charges. For the same height, width and area of Fig. 13. Presto Single-column Pressed Metal Radiator heating-surface these radiators are shorter than cast-iron radiators, being spaced iH instead of 2H in, center to center of sections. Direct Pipe-Coil Radiation is largely used in manufacturing establishments and is usually made up of iM or i^-in pipe screwed into cast-iron manifolds as shown in Fig. 15. Heat-Emission of Direct Radiation. The unit heat-transmission K, or the Btu transmitted by one square foot of direct radiation per hour per degree dif- 1268 Heating and Ventilation of Buildings Pari 3 Table X. Presto Single-Column Floor or Wall-Radiators for Steam or Water Each section is 4 H in wide. Legs spread sH in Number of sections Length * iy2 in per section j-surface i Heating n square feet 32 in high 26 in high 23 in high 20 in high 17 in high 14 in high 2 sq ft per section I 5 sq f t per section l.3sqft per section I.I sqft per section 0.9 sq ft per section 0.7 sq ft per section 4 5 6 7 8 9 10 6 7H 9 10 H 12 13 H 15 8 10 12 14 16 18 20 6.0 7.5 9.0 10.5 12.0 13. 5 ISO 5.2 6.5 7.8 9.1 10.4 II. 7 13.0 4.4 5. 5 6.6 7.7 8.8 9.9 II .0 3.6 4.5 5-4 6.3 7.2 8.1 9.0 2 3 4 4 5 6 7 8 5 2 9 6 3 * Length of radiator over all, including malleable-iron hubs. Add % in for each bushing. Legs are detachable and can be applied to any section. These radiators are tapped i H in and bushed as specified. ference between the heating-medium and the temperature of the air in the room, varies somewhat with the type of radiator, height, temperature, etc. Fig. 14. Direct-indirect Radiator-installation Coefficients of Transmission for Direct Steam-Radiators. Tatle XI is based on the average performance of direct steam-radiators standing exposed in still air at 70° F. with steam at 220° F., or 2 -lb pressure, with a standard Radiation 1269 temperature-difference of 150°. In order to apply the coertidents given in Table XI to conditions other than standard, it is only necessary to know the Pipe-Coil Radiators and Connections Air-Valve CSteam) [jBushinff Air-Vial ye for Watei \ Branch-Tee A.V.CAlter- native^ Union Check-Valve ^^iC - Expansion-Bolts - Steel or W.I. Pipes — Hook-Platea ~ fastened to Walls R. *n(] I ^ Jb ■/ I I I Reducing- I I Elbow R. ? I Union^- Dirt-Pocket (Capped) Radiator for Two-Pipe Low-Pressure Steam-System. Air-Valve her© I Plug yfo*- Water Radiator for Two-Pipe Vacuum Steam-System, Divided Surface. Table / Branch-Tees (Crane Co.) Run Open Inlet Open Run Open N0.2 For Circulation I Closea,' Outlet Open Closed \ \ No. r. fo r Bos_Colls_Jl Cloned Inlet Open f.^ Order bj Size and Numbet Linear Feet oflPipe perP'KS. 2.9' of 1 -^ Pipe=l=^'n.S. 2.3' of. Vj" " = 1°'II.S. 2.0' of iV/ " ■= i°'n.s. 1.6' of 2" " ^ 1^'H.S. 1" Branch-Tees 1J4" Branch-Tecs, 3"c-c IH" Branch-Tees, 3H"c-c 2" Branch-Tees, VA" c-c RUDB Runs Runs Runs \"-vA"\m" 2" i 1K"-1M"| 2" 2J^" VA"-2" 2H" 3" 2" 2H"-3" VA" No. of Branches No. of Branches No. of Branches No. of Branches 2 to 9 2to 2to 16 16 3 to 16 3 to 16 3to 16 3to 12 3to 12 3to 12 3 to 10 3to 10 3to 10 Inside Diama. Inside Diams. Inside Diams. Inside Diams. m' 2%" 2y," 2H'"' 2H" 2y/' 2Ji"- |2>/i" 2%" m" 3J4" 3H" Notes. Ail openings in Branch-Tees for circulation are tupped right hand. Branch-Tees for Box Coils are always tapped left hand in branches and right hand in back inlet. The run and back opouiuKa of Branch-Tees are tapped the same siie as branches, imless otherwise ordered. Fig. 15. Pipe-coil Radiation-data Variation in K for a given increase or decrease in the temperature-range above or below 150°, the standard range. An examination of test-data so far avail- 1270 Heating and Ventilation of Buildings Parts able seems to indicate, that this variation Is nearly 0.2% per degree above or below the standard range of 150°. Thus, if a three-column, 38-in high, direct radiator is to be used in a room kept at 60° F., with steam at 230°, we would have a temperature-range of 170° or 20° above standard, and the value of K would become K = (1.55 + 0.002 X 20 X 1.5s) = i-6i and each square foot of radiation would give off 1.61 X 170 = 274 Btu per hr. Table XI. Values of K for Direct Radiators Type of radiator Height of radiator 32 in 38 in 20 and 22 in 26 in 1.9s 1.80 1.70 1 .60 1.85 1.9s 1.90 2.00 1.90 I. 75 1.65 . I. 55 1. 85 1.70 1.60 1.50 1.80 1.6s 1.55 1.4s 1.57* Two columns Four columns . . Flue, 42 sq ft Window . . . Wall (horizontal) Wall (vertical) Pipe-coils • Air entering flues at 70° F. and leaving same at 152° F. Allen, /([■increases (i) as height of radiator is reduced and (2) as number of columns or width of radiator decreases. Coefficients of Transmission for Direct Hot- Water Radiators. Table XI may be used for values of K for hot-water radiators of the same type as there listed, but allowance should be made for the lower temperature-range in hot- water heating. Thus, with a room usually at 70° F., and water at 180° entering and at 160° leaving the radiator, the temperature-range is only 100°, or 50° less than the standard range. Then for a two-column 26-in high direct radiator,! the value of K becomes K = (1.75 - 0-002 X 50 X 1.75) = 1-58 and each square foot of this radiation gives off, 1.58 X 100 = 158 Btu per hr. Concealed Radiators. The effect of placing a grill in front of a direct radiator, with a cover over the top, reduces the heat-emission by approximately 20%. A clear space between the radiator, wall and enclosure should not be less than 2H in. Concealed radiators are not looked upon with favor from a strictly sanitary point of view. The Usual Assumptions Made for the He?.t-Transmission of Direct Radiation is 250 Btu per sq ft per hr for low-pressure steam (2 lb) cast-iron tadi- ators, and 150 Btu per sq ft per hr for cast-iron hot-water radiators with the water at 180°. The square-foot rating of heating-boilers is based on the above figures. For more exact values use the data given in Table XI. Accordingly, a hot- water installation requires 66%% more radiation than a low pressure steam system. Example. It is required to determine the amount (R) of direct cast-iron radiation, low-pressure steam and hot water, to supply a heat-loss of // = 10 000 Btu per hr I Fuels and Combustion 1271 Solution. For the direct steam system R - 11/250 = 40 sq ft and for a direct hot-water system R = n/150 = 66M sq ft If a three-column cast-iron radiator, 38 in high, is to be. used, the heating-surface of which is 5 sq ft per section, it will require 40/5 = 8 sections for the steam-job, making the length of radiator equal to 8 X 2 3^^ = 20 in. Fuels and Combustion Classification of Fuels. Fuels are generally classified as solid, liquid, and gaseous. Solid fuels are coal, wood, and wastes. Liquid fuels are petroleum and its products. Gaseous fuels are natural and artificial gas. Coal-Fields in the United States. Most of the anthracite is found in beds of less than 500 sq miles in area located in eastern Pennsylvania. The prin- cipal deposit of semibituminous coal is about 300 miles long by 20 miles wide and lies along the eastern edge of the Northern Appalachian field. The bitumi- nous coals extend from this deposit westward. A little graphitic coal is found in Rhode Island. Composition of Coal. The uncombined carbon in coal is known as fixed CARBON. Some of the carbon-constituent is combined with hydrogen, and this, together with other gaseous substances driven off by the application of heat, form that portion of the coal known as the volatile matter. The fixed carbon and the volatile matter constitute the combustible. The oxygen and nitrogen contained in the volatile matter are not combustible, but custom has applied this term to that portion of the coal which is dry and free from ash, thus includ- ing the oxygen and nitrogen in the combustible. Classification of Coals. Coals may be classified according to the percentages of fixed carbon and volatile matter contained in the combustible. Table XII. Classification of Coals (Kent) Name of coal Percentages of combustible Btu per pound of combustible Fixed carbon Volatile matter Anthracite 97.0 to 92.5 92.5 to 87. 5 87. 5 to 75.0 75.0 to 60.0 65.0 to 50.0 50.0 and under 3.0 to 7.5 7.5 to 12. s 12. 5 to 25.0 25.0 to 40.0 350 to 50.0 So.o and over 14 600 to 14 800 14 700 to IS 500 15 500 to 16 000 14 800 to 15 300 13 500 to 14 800 II 000 to 13 500 Semianthracite .... Semibituminous . . . Bituminous, East. . . Bituminous West. . . Lignite. Calorimetric Determinations. The only accurate and reliable way to deter- mine the heating- value of a fuel is to do so experimentally with a calorimeter. For soUd fuels, the bomb-calorimeter is the most practical. The various types On the market include the Mahler, the Hempel, the Atwater and the Emerson. These consist essentially of a tight vessel containing a weighed sample and oxygen Under pressure. This receptacle is placed within another vessel containing a known weight of water and surrounded by heat-insulating material to minimize 1272 Heating and Ventilation of Buildings Parts radiation The sample is exploded electrically, and the heat absorbed by the surrounding water is determined by means of a very accurate thermometer reading hundredths of a degree. Correction has to be made for the heat ab- sorbed by the instrument itself, and for radiation. For a complete description of calorimeters and their use, see Carpenter and Diederichs' Experimental Engineering. Calorific Value by Formula. The following expression, known as Du Long's FORMALA for hcating-value per pound of coal, can be used if the ultimate chemical analysis of the fuel is known: F = 14 600 C + 62 GOO (5 - VsO) + 4 000 5 where C, H, 0, and S represent the proportionate parts of each element per i lb of fuel, and F denotes the heat- value in Btu per pound due to combustion. This formula does not apply when the fuel contains carbon monoxide, CO, but can be made to apply by adding a term, 10 150 C, in which C is the proportionate part of carbon burned to the monoxide. Example. The application of the formula to a coal of ultimate analysis as here given follows: Analysis (based on fuel as received) c 74-79% H 4.98 6.42 N 1.20 S 3-24 H2O 1.55 Ash 7.82 100.00% Then by Du Long's formula, 14 600 X 0.7479 + 62 000 (0.0498 — 0.0642/8) H- 4 000 X 0.0324 = 13 650 Btu per i lb of coal. A bomb-calorimeter test showed 13 480 Btu for this coal. The formula fails to allow for evaporating and superheating the moisture present in the fuel. Combustion of Fuel. Combustion, as used in steam-engineering, signifies a rapid chemical combination between oxygen, and the carbon, hydrogen, and sulphur composing the various fuels. This combination takes place usually at Table XIII. Theoretical Amount of Air Required for Combustion Fuel Composition by weight Lb of air per lb of fuel %c %H %o Wood-charcoal 93.0 80. 94-0 91.5 87.0 70.0 58.0 So.o 85.0 3.5 so SO 6.0 6.0 13.0 2!6"' 4.0 20.0 31.0 43-5 i.o II. 16 9.6 10.8 II. 7 II. 6 8.9 7.68 6.00 14.30 Peat-char oal Coke Anthracite coal. Bituminous coal, dry.. ..... Lignite. Peat, dry Wood, dry Mineral oil Steam-Heating Boilers and Hot- Water Heaters 1273 high temperature with the evolution of light and heat. The substance com- bining with the oxygen is known as the combustible, and if it is completely burned or oxidized the combustion is perfect, that is, no more oxygen can be taken up by the products of the reaction. The combustion is imperfect or incomplete when carbon burns to form carbon monoxide, CO, instead of the dioxide, CO2, since the former may be further burned to form carbon dioxide if the necessary oxygen is supplied. It is necessary to provide for an excess of air when burning coal under either natural or forced draft, amounting to approxi- mately 50 to 100% of the net calculated amount, or about 18 to 24 lb per lb of coal. Less air results in imperfect combustion and smoke, while an excess cools the fire and setting and carries away a large percentage of the heat in the flue- gases. Table XIV. Weight and Calorific Value of Various Gases at 32 Degrees Fahren- heit and Atmospheric Pressure, with Theoretical Amount of Air Required for Combustion Gas Symbol Cubic feet of gas per pound Btu Cubic feet of air required per cubic foot of gas Per pound Per cubic foot Hydrogen Carbon monoxide. . . Methane Ethane Ethylene . , . . H CO CH4 C2H6 C2H4 C2H2 178.0 12.81 22.4 12.0 12.8 13.79 62 000 4380 23 842 22 400 21 430 21 430 348 342 I 065 I 86s I 67s I 555 2 . 408 2.388 9. 57 16.74 14.33 11.93 Acetylene Fuel-Storage. Space for fuel-storage must be based on fuel -consumption per season as estimated under Fuel-Consumption, page 1278, and in government buildings it is customary to proportion the storage-space on the basis of 8 sq ft of floor-area per ton, the storage-space being made ample to hold an entire season's supply. The following volumes per ton of 2240 lb of coal are given for proportioning storage-space: bituminous coal, 41 to 45 cu ft, and may run as high as 49 cu ft; anthracite coal, 34 to 41 cu ft; charcoal, 123 cu ft; coke, 70.9 cu ft. This is based on fuel broken down ready for market. Also i bushel hard coal = 86 lb and i bushel soft coal = 76 lb. Steam-Heating Boilers and Hot- Water Heaters Pressures, Attention, and Materials. Heating-boilers usually operate under much lower pressure than do power-boilers, and in most cases receive far less attention. The steam-boilers are usually designed to operate on from 2 to 5 LB steam-pressure, and the water-boilers or hot-water heaters are seldom sub- jected to a hydrostatic head in excess of 100 ft when in operation. The atten- tion given these boilers is of such an intermittent characti^.r that they must carry the heating-load for comparatively long periods without firing. These periods may range from 6 to 10 hrs and in consequence the combustion-rate is low, and relatively large grates and fire-pots are necessary. The materials employed for constructing heating-boilers are cast iron, especially for the smaller sizes, although boilers of nearly 100 equivalent steam-boiler horse- power (see Rating of Heating-Boilers) are made of this same material; and 1274 Heating and Ventilation of Buildings Part 3 STEEL or WROUGHT IRON, which are more generally used in the larger sizes. The government departments usually specify steel heating-boilers, and they are used extensively in oflSce and loft-buildings as well. Boiler Heating-Surface. The capacity of any boiler or water-heater depends on the amount of, and the temperatures on the opposite sides of, the heat- transmitting surfaces in contact with the water in the boiier on one side, and the fire or hot gases on the other. It is most important that a rapid circulation of water and the hot gases shall take place over these surfaces, and preferably in opposite directions. Two kinds of surface are distinguished in boiler-practice, and known as direct and indirect surface. Direct surface is that on which the fire shines, and indirect that in contact with the flue-gases only. All such surface must have water on the opposite side. In some boilers the hot gases are allowed to come in contact with the boiler-surface above the water-line so that there is only steam in contact with this surface on the inner side. Such surface is known as superheating-surface in order to distinguish it from ordinary heating-surface. Direct surface is the more valuable of the two, per square foot, as it is usually subjected to a higher temperature, and furthermore because the intensity of radiation from an incandescent surface appears to vary as some power of the temperature of that surface, either the third or fourth. Equivalent Evaporation. The equivalent evaporation of a boiler is the pounds of water the boiler would evaporate per pound of coal burned if it received the feed-water at 212°, and evaporated it into steam at this same tem- perature and pressure, so that the evaporation would take place from and at 212° F. In practice the feed- water is usually below this temperature and evaporation actually takes place at some higher temperatrue than 212°. Hence, to find the equivalent evaporation it is always necessary to make use of the following relation: (X2r2 -\- Qi — q\) .971-7 X P where the fractional part of the expression is known as the factor of evap- oration; so that E = factor of evaporation X P E = equivalent evaporation from and at 212 ** F., in pounds; X2 = quality of steam as actually evaporated; r2 = latent heat of steam as actually evaporated; 52 = heat of the liquid as actually evaporated; ^1 = heat of the Hquid as actually fed to boiler; P = actual evaporation in pounds per pound of fuel burned; 971 . 7 = latent heat of steam at 212° F. Boiler Horse-Power. A boiler horse-power is the energy required to evap- orate 34.5 lb of water at 212° F. into dry steam of 212° F., or 971-7 X 34-5 = 33 S24 Btu The horse-power rating of a boiler is always measured in terms of the equivar I lent evaporation. Thus, if we divide the equivlaent evaporation of a boiler I by 34-5 we get the boiler horse-power developed. Boiler-Efficiencies. Heating-boilers, operate i at their rated capacity, will | show an efficiency of from 55 to 65%. This efficiency is the ratio of heat I absorl^ed per pound of dry coal by the water and SLcam in the boiler to the actuaJ heat-value of one pound of the coal, and is the combined efficiency of the boiler and furnace. Steam-Heating Boilers and Hot-Water Heaters 1275 Rates of Combustion for Heating-Boilers. Combustion-rates for varying sizes of grates are given in Table XV: Table XV. Combustion-Rates Grate-areas Coal per square foot per hour, in pounds Remarks 6 sq ft or less (small), 6-10 sq ft (medium), 10 sq ft or larger (large), 5 6.6 A variation of io% up or down from these rates is perfectly safe. The higher values are for full-sized chimneys with lined flues and the lower for unlined flues or long breeching-connections. 4 to 8 sq ft 10 to i8 sq ft 20 to 30 sq ft 4 6 10 (Am. Soc. H. and V. E. Com. 1909.) Rates of combustion reported for anthracite coal, as fired in inter- nally fired heating-boilers. See Transactions for further details. Rating of Heating-Boilers. Standard Conditions. It is the general cus- tom of American manufacturers of heating-boilers to rate their boilers in terms of the number of square feet of standard direct cast-iron radiating-surface which the boiler is capable of supplying under the following conditions: (i) Steam boilers; steam-pressure 2-lb gauge at boiler. (2) Hot- water boilers; water- temperatures: 180° F. leaving, and i6o** F, entering boiler. (3) Fuel; anthracite coal of stove-size. The RATE OF COMBUSTION, or amount of coal necessary per hour for the boiler to develop its rating has, until recently, seldom been given; and the method of determining the rating has varied with different makers and is seldom stated. Moreover, it is possible for a boiler to be placed on the market and assigned a certain rating although such rating has never been actually checked by test. It therefore becomes most important to not only establish standard conditions FOR rating-tests, but to require the manufacturer to be in a position to pro- duce certified test-sheets of such tests for his line of boilers. The standard conditions under which a boiler should be tested to develop its rating are gen- erally understood by the manufacturers at the present time to be as follows: (i) Pressure, temperature and fuel as stated above. (2) Fuel-capacity to be sufficient to carry the boiler from 6 to 8 hr on one charge and leave 20% reserve for igniting fresh charge. (3) Draft of sufficient intensity to burn the fuel at the required rate. A chimney n^t less than 40 ft in height is recommended. (4) Each square foot of direct cast-iron radiation has a transmission-value of 250 Btu, and 150 Btu per hour for steam and water-radiators respectively. (5) The condensation from steam-radiators returns to the boiler at the same temperature as the steam, or without loss of heat, so that the boiler simply sup- plies the latent heat of evaporation at 2 lb pressure, or 967 Btu per lb evaporated. (6) The water from hot-water radiators returns to the boiler at 160°, allowing a 20° drop in the radiators, so that there is no loss in temperature allowed in the return-main. (7) Suitable heat-allowance must be made for all connecting piping and boiler- surface, and such surface must be figured as radiating-surface or its equivalent. 1276 Heating and Ventilation of Buildings Part 3 A general rule is to add, for an ordinary installation, about 50% of the sq ft of radiation installed, in calculating the total load on the boiler, with anthracite fuel and 65% with l)ituminous fuel, to allow for radiation-loss of piping and boiler and the additional tax on the boiler due to starting up with cold radiation. Equivalent Boiler Horse-Power Rating of Heating-Boilers. The capacities of heating-boilers may be stated in boiler horse-power, and the equiva- lent of same in square feet of standard radiation may be easily determined as follows: Since i boiler horse-power is equal to 34.5 lb of water evaporated per hour, from and at 212° F., the boiler must dehver 34-5 X 971.7 (latent heat at 212° F.) = 33 524 Btu per hr Now since i sq ft of standard cast-iron steam-radiation transmits 250 Btu per hour, I boiler horse-power = 33 524/250 = 134. i sq ft of this radiation, or I sq ft of direct cast-iron steam-radiation = 0.00756 boiler horse-power It also follows that the equivalent boiler horse-power rating of a hot-water heater is 33 524/150 = 223.5 sq ft of direct cast-iron hot-water radiation, or I sq ft of direct cast-iron hot-water radiation = 0.00447 boiler horse-power Grate-Surface. It is always advisable to check the grate-area required /or heating-boilers, especially if the total heat-loss to be suppHed by the boiler Is known. This total heat-loss must include not only the calculated loss, due to transmission through walls and glass, for which the radiation is proportioned, but also about 50% additional for heat-losses from the piping system, boiler, etc. So that, if ^ is the building-loss in Btu, 1.5 // = total Btu-loss. Then G = 1.5/// (C XF XE) where C = rate of combustion in pounds of dry coal per square foot of grate- area per hour, F = calorific value of fuel in Btu per pound of dry coal (12 000 is the usual assumption for anthracite coal), and E = the combined efficiency of boiler and grate (60% is the usual assumption). G is in sq ft and the boiler selected should have not less than this grate-area. Special attention is called to the distinction between grate-area and fire-box or fuel-pot area as explained below under Depth of Fuel-Pot. Depth of Fuel-Pot. The average of the fire-box area is usually somewhat larger than the grate-area in sectional boilers, while it may be less than the grate-area in certain types of round boilers. In any event the capacity of the fire-box or fuel-pot from grate to middle of fire-door should alwtiys be suf- ficient to hold all the coal required for an 8-hr firing-period, plus at least 20% reserve to be used for igniting a fresh charge. The following method is used to determine the depth of pot or the firing-period as the case may be. Let G = grate-area in sq ft, C = rate of coml)Ustion, A average area of fire-pot, h = firing-period in hours, W = weight of fuel per cu ft (50 lb for anthracite and 40 lb for bituminous), D = depth of fuel -bed in ft. Then (GC Jt} -f 20% (allowance to ignite fresh charge) = total weight of one charge; also, AWD = total weight of one charge. Hence D = i.2GCh/AW, or A = AWD/1.2GC Steam-Heating Boilers and Hot- Water Heaters 1277 As noted above D is measured from grate to center of fire-door, which varies from 8 X 14 in in small, to 11 X 19 in in large boilers. This formula allows for the greater bulk of soft coal. Example. Given a boiler with grate-area of 8 sq ft, average area fire-pot 9 sq ft, height to center of fire-door = 18 in, rate of combustion = 6 lb per sq ft of grate for anthracite coal. Required the number of hours this boiler will carry its load on one charging. Solution. ^ = (9 X 50 X i.s)/(i-2 X 8 X 6) = II. 7 hours Effects of Fuels on Ratings. All ratings are based on anthracite coal of STOVE-SIZE unless otherwise stated. In case bituminous coal is used and the boiler is selected by catalogue-rating, a boiler with fire-pot having at least 25% greater capacity should be selected, for the same weight of coal occupies 25% more space. With soft coal additional heating-surface is also required as the accumulation of soot from such coal renders the heating-surfaces less effective than when hard coal is used. Boilers for pea-coal should also have a larger fire-pot than those for stove or furnace-coal. The small sizes of anthracite contain far more ash than the larger sizes, and hence have a greater bulk for the same heating effect; so that larger fuel-pots for the same capacity are required. Firing-periods, differing from the one on which the boiler is rated, will also affect the fuel-holding capacity. For example, if it is required to operate a certain line of boilers designed for an 8-hr period on a 12-hr basis, at least 50% greater fuel- holding capacity will be necessary and a larger boiler must be selected, as shown by the formula already given for the depth of the fuel-pot. Equivalent Rating for Conditions Other than Standard. If often happens that the load connected to a steam- or hot-water boiler may not be operated under the standard conditions previously assumed as a basis of rating. In this case tables of ratings cannot be used until the equivalent value of this load in terms of square feet of standard cast-iron radiation has been determined. The following relations show a method for finding such equivalent values: Let i? = sq ft standard cast-iron radiation = 250 Btu per sq ft for steam, and 150 Btu per sq ft for water. Also let r = actual sq ft of radiation to be supplied; K = coefficient of transmission for this radiation; ts or tw = temperature of steam or average temperature of hot water in the radiator; ta = temperature of air surrounding radiator; K{ts — ta) = radiation-factor or Btu given off per sq ft per hr; Then Rs = ri X Ki{ts — ta) /2S0, and Rw = rz X K^itw — /a)/i5o Example. (Steam-heating.) Required the size of boiler (rating in sq ft of standard cast-iron radiation) to supply i 000 sq ft of direct pipe-coil radiation. Steam-pressure = 5-lb gauge. Air = 65° F. K (by test) = 2.42 Btu. From steam-tables, ts = 227.14, R = 1000 X 2.42(227.14 — 65)7250 = 1000 X (2.42 X 162.14)7250 = I 570 sq ft. To this add 50% for pipe and boiler- radiation and the additional tax for starting up with cold radiation, or, 1.5 X I 570 = 2 355 sq ft, or practically a 2 400-sq-ft-capacity boiler will be required. The grate should be checked by calculation previously given to ascertain minimum size. G =i.5H/{C XF XE) 1278 Heating and Ventilation of Buildings Part 3 Example. (Water-heating.) Let Q = total number of gal of water to be heated in h hours. W = (SH XQ)/h = weight of water to be heated per hour ^1 = initial temperature of water, k = final temperature of water Then Wih - ti) = Btu to be supplied per hour. Hence Wik - /i)/iSo =hot- water-heater rating required. W{k - h)/2So = steam-boiler rating required. Example. A swimming pool contains 50 000 gal of water, and this water is heated by being passed through a hot-water heater in four hours. Entering- temperature = 50° F. and final temperature =75° F. Hot-water radiation reduced to equivalent standard value =[(50000 X 8H)/(4 X 150)] X (75 — 50) =17 350 sq ft = rating of hot- water heater, to which must be added 50% for losses from piping, etc. Fuel-Consumption. The estimated fuel-consumption for heating- boilers per heating-season may be based on grate-areas, square feet of radiation installed, or culjic contents of building to be heated. The United States Treasury Department allows 5 tons of coal per sq ft of grate-area per season of 240 days, or I lb of coal per cu ft of contents of building for the same period. This applies to government buildings. The district steam-heating companies estimate 500 lb of steam per sq ft of direct steam-radiation per season, which is practically the same as 70 lb of coal of good quality. This is approximately equivalent to assuming that one-third of the radiation installed is in operation continuously for 240 days. In other words, the coal required for a heating-season is about one- third the quantity that would be used if all the radiation were in constant use every hour of the day and night. The amount of coal for maximum conditions is determined as follows: Since each foot of direct steam-radiation or its equivalent will give ofif 250 Btu per hour under conditions of 2 lb (220°) pressure at boiler, and 70° air sur- rounding the direct radiators (the piping on the average job may be roughly taken as 25% of the direct radiation); and since for approximation we may assume 8 000 Btu per pound of anthracite coal burned; we can readily estimate the amount of coal per hour li R — amount of direct radiation iii square feet: (1.25 xR X 2.5o)/8ocx3 = C = coal per hour in pounds In a heating-season of 7 months or 210 days of 24 hours each, there would be burned under maximum conditions during the entire period (1.25 XR X 250 X 210 X 24)/(8 000 X 2 000) = 0.0984^ tons of coal the actual consumption being. about one-third of the maximum possible, or 0.0328 R tons of coal for the heating-season. For hot- water heating the fuel- consumption for the entire season is approximately 0.0197 R tons. ' Types of Heating-Boilers. Cast-iron steam-heating boilers are designed to be operated at a maximum pressure of 15 lb per sq in, and the sections are tested by the manufacturer to about 100 lb per sq in, hydrostatic pressure. Cast-iron boilers are constructed of sections, which are connected by means of nipples of either the push or screw-type. The sections are held in place by means of long bolts. Round -type boilers have horizontal sections surrounding the fire-pot, and in the sectional type the sections are placed vertically. (See Figs. 16, 17, and 18.) The maximum size of round-type boilers manufactured is rated at about I 400 ft. Sectional boilers are ol)tainable up to a 10 000-sq-ft-rating. See manufacturers' catalogues for capacities, dimensions, etc.) Steam-Heating Boilers and Hot- Water Heaters 1279 Smokeless or Down-Draft Cast-iron Boilers. Boilers having a water-grate are now being made for use with free-burning soft coal, where local smoke- ordinances would not permit the use of such fuel on ordinary gratesu ft Fig. 16. Sectional Type of Cast-iron Boiler Drain to Seweo Fig. 1 7. Tfiinniings and Connections for Sectional Steam-heating-boiler 1280 Heating and Ventilation of Buildings Pait3 Selection of Cast-iron Boilers. The selection of cast-iron boilers should not be influenced too largely by considerations of price, and the ease with which they may be carried into a building where structural conditions interfere with the introduction of a steel boiler. In many cases the character of the service or attendance, or both, especially in govern- ment and other pubHc building work, may be such that steel equipment, which is cap- able of withstanding more abuse, should be used. This is particularly true when the returns are handled by a pump. If cast- iron boilers are to be installed, the grate- area necessary should be carefully computed as already indicated, using an average rate of combustion, and a fuel-pot depth based on the firing-period required. The United States Treasurj' Department selects cast- iron boilers by proportioning them to carry 25% more radiation than actually installed if anthracite coal is used, and 35% more if bituminous coal is used. In addition to this, suitable allowance must be made for mains and other piping, and in most cases two boilers are installed, each capable of supplying two-thirds of the radiation in order to provide for units which can be operated with a high-load factor, and also ^. ^„ _ . , _, ,^ ^ ., act as a reserve for each other in case of a Fig. 18. Section of Round-type Boiler breakdown. Steel Heating-Boilers. There are two general types of all-steel boilers used for heating work, the fire-box type and the return tubular type. In the fire-box type the grate and combustion-chamber are surrounded by an extension of the steel shell which is water-jacketted. The products of com- bustion pass directly through the tubes to the smoke-flue located in the rear. In the return tubular type, the boiler consists of a shell with tubes set in a brick setting, the grate and combustion-chamber being directly under the front portion of the shell. The products of combustion in this case pass under and around the shell to the rear of the boiler, and then through the tubes to the front into the smoke-box. Fire-box type boilers may be obtained in capacities ranging from 500 to 13 000 sq ft of direct radiation. The most common of these boilers are the Dunning, Gorton, and Kewanee. Detailed information as to capacities, dimensions, etc., may be obtained from the makers' catalogues. As usually constructed, these boilers are designed for a working pressure of 60 lb per sq in and are so insured by the boiler-insurance companies. This type may be obtained with or without (portable type) brick-setting. The return tubular boiler is erected with a brick setting and as ordinarily constructed, is designed for a working pressure of 100 lb per sq in, but may be obtained for a working pressure of 150 lb per sq in if desired. It is primarily a power-typ)e boiler, but is commonly used in con- junction with large heating systems having 10 000 sq ft or more of direct radia- tion. These boilers are rated on a basis of 10 sq ft of boiler heating-surface per boiler horse-power. A special design of setting is required for smokeless com- bustion when bituminous coal is to be used as fuel. The so-called standard setting should not be used in this connection. (See Boilers and Rules for Con- Chimneys for Heating-Boilers 1281 structlon in Mechanical Equipment of Buildings, Vol. II, by Harding and Willard.) Chimneys for Heating-Boilers. (See also, under Chimneys, page 1364.) In order to produce an intensity of draft sufficient to properly operate low- pressure heating-boilers, hot-water boilers, and hot-air furnaces up to their rated capacity, the chimney should not be less than 40 ft in height, measured from the grate. No flue should be less than 8 X 8 in. The failure of many heating-installations may be traced to insufficient draft to burn the fuel at the rate required to run the boiler or furnace to rated capacity. The tempera- ture of flue-gases leaving the boiler should range between 400° and 500° F. when the apparatus is worked at its rated capacity. The chimney should be so located with reference to any higher buildings nearby that wind-currents will not form eddies and force the air downward in the shaft, as shown in Fig. 19. The flue should run as nearly straight as possible from the base to the top outlet. The outlet must not be capped so that its area is less than the area of the flue. The flue should have no opening into it other than the boiler smoke-pipe. Sharp bends and ofl^sets in the flue often reduce the area and choke the draft, and the flue must be free of any Fig. 19.Relation of Height of Chimney to Draft feature which prevents the full area for the passage of smoke. If the flue is made of tile, the joints must be well cemented, or all space between the tile and brickwork fiUed in tightly. There must be no open crevices into the flue where the tile sections meet, other- wise the draft will be checked. If the flue is made of brick, the stack should have outside walls at least 8 in thick to insure safety. The inside joints should be well struck, and each course should be well bedded and free from surplus mortar at the joints. The exposed bricks at the top of a brick chimney should Table XVI. Fire-Clay Flue-Linings Robinson Clay Product Co., Akron, Ohio Rectangular Round Nominal Actual size Actual size Inside Outside size, outside. inside, diameter, diameter, m m m m m 4HX 81^ 4HX SVs 3M X 7 6 7M 4HX13 4HX13H 3M6X11M 7 sy2 4KX18 4HX17 3^^^ XIS}^ 8 9 6 X12 6 X12 4H XioM 9 loH 7 X 7 7MX 7H 55^ X 5^ 10 12 8HX SH 8HX 8M , 7H X 7H 12 14 8HX13 8V2X13 6% Xii^ IS 17 K 8HX18 8HX18 eVi X16 18 20 K 13 X13 13 X13 iiH XiiM 20 23 13 X18 13 X18 10 M X15M 24 27 18 X18 18 X18 isH XisH 30 35 1282 Heating and Ventilation of Buildings Parts be laid in cement mortar to prevent the acid fumes and rain from cutting out the joints. This will happen if lime mortar is used. The most desirable loca- tion for a chimney is near the center of the building, as all walls are then kept warm. If there is a soot-pocket in the Hue below the smoke-pipe opening, the clean-out door should always be tightly closed. If this soot-pocket has other openings into it from fireplaces or other connections, these openings check the draft and prevent the best results. The smoke-pipe should not extend into the flue beyond the inside surface of the latter. If it does extend beyond, its end cuts down the area of the flue. The joints, where the smoke-pipe fits the smoke-hood of the boiler, or where the pipe enters the chimney, should be made tight with boiler-putty or asbestos cement. Fire-clay flue-linings are used in the best practice for small and medium-sized flues. Rectangular flue-hnings are rated by outside dimensions^ and round Hiiings by inside dimensions. Flues for Elitchen Ranges and Fireplaces. (See also, under Chimneys, page 1364.) For a kitchen range an 8H by 8H-in tile flue is ordinarily sufficient, but an 8H by 13-in is better. For fireplaces the sectional area of the flue for burning wood or bituminous coal should be from Mo to 14 the area of the fire- place-opening for a rectangular flue, and H2 for a circular flue. For burning anthracite coal the areas may be reduced to H2 and Me respectively. Selection of Chimney-Flues. (See also, under Chimneys, page 1364.) The selection of chimney-flues for heating-boilers must depend upon the judgment of the heating-engineer, but it is believed that Table XVII, by R. C. Carpenter, will very much assist the engineer in selecting flues. It is necessary that area and HEIGHT, THICKNESS OF WALLS, GENERAL STRUCTURE, and the POSITION OF THE TOP OUTLET with reference to the building and other buildings near by should be carefully noted and observed in the selecting or building of a flue. The figures given under the varying heights of chimneys are diameter-measurements in inches, or, the side of a square, the theory being that the spirally ascending column of smoke and gases will make a 12 by 12 -in flue no more "eff"ective in practical working-area than a twelve-inch round flue. Rectangular shapes may be used if the area is equal and the difference in width and breadth is not extreme. • A maximum ratio of 2 : i for the internal dimensions should not be. exceeded. Table XVII. Chimneys for Steam and Hot- Water Boilers Direct radiation Height of chimney-flue Steam, sqft Water, sq ft 30 ft 40 ft 50 ft 60 ft Soft 250 375 7.0 6.7 6.4 6.2 6.0 500 750 9-2 8.8 8.2 8.0 7.6 750 I 150 10.8 10.2 9.6 9.3 8.8 I 000 I 500 12.0 II. 4 10.8 10. s 10. I 500 2 250 14.4 13.4 12.8 12.4 II. S 2 000 3 000 16.3 15.2 14. 5 14.0 13.2 3 000 4 500 18.5 18.2 17.2 16.6 15.8 4 000 6000 22.2 20.8 19.6 19 17.8 5 000 7 500 24.6 23.0 21.6 21.0 19.4 6 000 9 000 .26.8 25.0 23-4 22.8 21 .2 7 000 10 500 28.8 27.0 25 5 24.4 23 8 000 12 000 3®. 6 28.6 26.8 26.0 2.; 2 9 000 13 500 32.4 30.4 28.4 27.4 r- 6 10 000 IS 000 34 32.0 30.0 28.6 27.0 Direct Steam-Heating 1283 Rules for Grate-Areas and Stack-Dimensions. For return tubular type of boilers N. S. Thompson gives tlie following rules for grate-areas and stack-dimen sions : R = total direct radiation in building; B. II. S. = heating-surface in boiler; G = area of grate; (all in sq ft) B. H. S. = R ^ 7 for steam; R -=- ii for water. G = B. II. S. -r- 25 (anthra- cite, pea, or rice coal); G = B. H. S. -j- 30 to B. H. S. -;- 35 (bituminous coal, plain grate); G = B. H. S. -^ 45 (lower grate of down-draft furnace). H = height of^stack, ft. A = area of grate, sq ft. S = area of stack, sq ft. S = A -j- V H (anthracite coal, lump coal, oil, and gas). S = (A X 1.25) -~ V H (bituminous and small anthracite). For anthracite, pea, or rice coal, tube-area must be not less than }4 grate, and always larger than stack. For boilers with down-draft furnace, tube-area must be not less than }4 of lower grate, and always larger than stack. Maximum length of tube must not exceed 48 diameters. Maximum length of boilers, 54-in diameter and under, must not exceed 3 diameters; over S4-in, 2V2 diameters. Tubes, an odd number of feet in length, are not used. Stacks for Tall Buildings are special cases and may be designed by methods used in the design of chimneys for power-boilers. (See Power Plants and Refrigeration, by Harding and Willard. See also. List of Tall Brick Chimneys, page I379-) Direct Steam Heating Systems of Direct Steam Heating in Use. Systems for heating with direct steam radiators are broadly divided into two general classes, known as: (i) GRAVITY CIRCULATING SYSTEMS, and (2) MECHANICAL CIRCULATING SYSTEMS. The distinguishing characteristic is the manner in which the water of condensa- tion from the radiators is returned to the boiler. In the first type the condensate enters the boiler by gravity, due entirely to the static head existing in the returns, and the sytem is a closed circuit. The steam-pressure existing in the boiler, mains, and radiators is the same, except for friction-pressure losses due to the flow of steam to the heating-surfaces. In the second type the condensate is allowed to return to a receiver or feed-water heater and is then forced into the boiler by a pump, or return-traps, or both. This is not a closed system, and the pressure in the boiler may be much higher than that in the mains and radi- ators. The receiver is usually vented to the atmosphere, and in the case of vacuum systems an additional pump is attached directly to the returns and arranged to discharge the condensation into the receiver or heater. Gravity cir- culating systems are further divided into the one -pipe system and the two-pipe system with basement-mains supplying risers to the various floors above (Figs. 20, 21 and 22), or with overhead mains supplying drop-risers to the floors below. In the latter system the steam and water of condensation in the risers flow in the same direction; so that less friction is produced as countercurrents do not occur and smaller pipe-sizes may be used. The overhead system is very com- monly spoken of as the mill's system. One-Pipe Gravity Systems. The one -pipe circuit system (Fig. 20) with basement-mains is probably the simplest, and most common gravity system in use. The steam-main rises close to the basement-ceiling, just above the boiler, and then grades down uniformly from this high point with a fall of i or ^ in in 10 ft. When the last radiator has been ?'jrved the main drops below the boiler 1284 Heating and Ventilation of Buildings Parts water-line and its size is reduced, as on the run back to the boiler it carries only condensation and is known as a wet return. This return may be run above the boiler water-line if necessary, and is then called a dry return. Return-mains are graded i in in 30 ft in gravity work. In either case an automatic air-valve Note ; Separate branched to all first-lloor radiators Not less t 18 "above boiler water-line / DETAIL OF FIRST-FLOOJl RADIATOR- CONNECTIO.NS DETAIL AT END OF MAIN Fig. 20. Low-pressure Gravity System. One-pipe Basement-main must be installed on the end of the main at the drop, as shown, to vent the same when air collects in the piping. The elevation of the end of the steam-main with respect to the boiler water-line must be carefully determined, in order that water may not back up from the boiler and flood the main, including the air-valve and K aJiator Braneh-ruus at cleiling below- PLAN OF 2ND FLOOR CONNECTIONS Riser Fig. 21. One-pipe Relief Easement-main branches. It is customary to maintain at least 18 in between the under side of main at the drop and the normal water-line of the boiler to provide for contin- gencies. In operation it will be noted that steam and water flow in the same direction through the one-pipe steam-main, and in opposite directions through the basement-branches, risers, and radiator-branches. This necessitates larger piping and valves than in any other steam system, and especially is this true of the main, which must be run fuU size from boiler to drop, unless dripped as shown under piping -details. Direct Steam-Heating 1285 The ONE -PIPE RELIEF SYSTEM (Fig. 21) is Very similar to the one-pipe circuit system except that the risers are dripped individually into the return, and the steam-main carries no radiator-condensation, and is itself dripped at intervals into the return-main, which may run dry or wet. This makes it possible (i) to reduce the size of main as radiation is taken off, (2) to use smaller branches, and (3) to run the main much closer to the basement-ceiling, a very important .consideration where basement-space is valuable. A combination or the one- pipe relief and the two-pipe system is frequently used in large installations, the latter being used for the first and second floors, and the former for the upper floors of high buildings. In this way the amount of condensation flowing down the one-pipe risers against the steam is much reduced and smaller risers may be used. The application of the one-pipe sj^stem, with gravity-circulation and basement-mains to tall buildings, is not at all unusual, and if the piping is properly designed for the circulation of steam and the return of the water of condensation it will be found satisfactory. In the case of long narrow buildings heated by a gravity system it may be necessary to provide a deep boiler-pit so that the elevation of water in the return-connections will not flood the far end of the steam-mains. Two-Pipe Gravity Systems. The two-pipe system with basement-mains (Fig. 22) is often used in large buildings, and in all work where indirect Fig. 22. Two-pipe Basement-main fa|se wat^r-une J radiation is installed. This system can be readily adapted to mechanical vacuum systems, and is very extensively used in this connection. It will be noted, however, that when apphed to a gravity system the return from each radiator is separately sealed, either by dropping below the water-line to a wet return or else by using drip-loops, as shown at the left, before connecting to a dry return. Even in one-pipe work all drips or reliefs are sealed as shown in Fig. 22. If this precaution is not taken steam may enter a drip or return from the outlet-end and cause knocking in the system due to countercurrents of steam and water of condensation. Any drip, relief, return-riser, or connection from the steam to the return-side of the system must be sealed. This may be done by connecting below the water-line, or efse by using a running trap or a return-trap somewhere on this connecting line. Neglect of this precaution will cause an unsatisfactory operation of the System. Automatic Radiator Air-Valves for Gravity Systems. The automatic REMOVAL OF AIR from steam-radiators must be provided for if the highest effi- ciency of the radiating-surfaces is to be realized in gravity circulating systems. 1286 Heating and Ventilation of Buildings Parts Manually controlled air-valves or cocks are usually neglected, and are seldom used for steam-radiators although their use is quite general for hot-water radi- ators. Fig. 23 shows a float-type of automatic air- valve. Thermostatic air- valves are finding favor in this field. The proper location of the air-valve on a steam-radiator is at the end of the radiator opposite the steam-inlet, and as near the bottom of the radiator as possible, since air is heavier than steam at the same temperature. In practice, however, the manufacturer of radiators VALVE CLOSED VALVE OPEiS Fig. 2^. Norwall Automatic Air-valve usually places the air-valve tapping about two-thirds the height of the radiator from the floor in order to prevent possible flooding of the valve. Special Gravity Systems. In addition to the low-pressure gravity systems already described there are many special steam heating systems known as air- Steam 25 ^ or above HIGH-PRESSURE EXHAUSTER-STEAM Fig. 24. The Paul Air-line System TWO-PIPE SYSTEM LINE, VAPOR, and vacuttm systems, also operating with gravity-return of the water of condensation. The air-ltne .system may be attached to any one or two-pipe gravity system, and is applied by connecting the automatic air- valve of each radiator with small-size piping to 'an exhauster which maintains a slight vacuum in the air-piping and effectually removes the accumulation of air in the radiators. As this scheme is a positive means of air-removal its application to the ordinary one or two-pipe gravity system will improve its operation. The original air-line system is known as the Paul systkm (Fig. 24). The ex- haustion used for less t|ipji j^gp^f|^is, a water-driven vacuum-pump^,}vitjia^^ Direct Steam-Heating 1287 sure of at least 20 lb per sq in. Larger systems use a high-pressui-e steam-jet (see above), or if steam is not available, a motor-driven vacuum pump of about H horse-power, i in air-mains in basement, and a gate valve on each air-riser are used. The steam used varies from i to 5% of the total condensation. All radiator-connections are made as shown. The Bishop-Babcock-Becker Com-j "^ ^"Air-Liue Main Automatic Electric Switch ^5 o and Vacuum- Controller Foundation' Fig. 25. The Bishop-Babcock-Becker Air-Iinc System pany manufacture the following line of air-pumps that are used for exhausters in air-line systems (Fig. 25) : Table XVIII. Hydraulic Exhausters Diam Diam . City Max. Number City Max. Length Number motor- suction- of stroke, of pump water- cap. of pump water- cap. cylin- dep-, in cylin- der, in pres- sure, lb direct rad., sq ft pres- direct rad., sq ft in Ib 2 2y2 4 lOI 20 700 104 40 4 000 2 2Y, 4 lOI 40 8oo io6 20 6 600 2^ 4 6 102 20 900 io6 40 9 600 2% S^-Mg 10 102 40 I 100 2-106 20 14000 104 20 2 500 2-106 40 20 000 Mechanical Vacuum Systems. The so-called mechanical Vacuum Systems are of the two-pipe type, and have a vacuum-pump attached directly to the returns. This pump may be steam or motor-driven, but must be capable of handling both air and water, as no air-valves can be used on the radiators in the vacuum system. The return-end of each radiator is equipped with a radiator- 12S8 Heating and Ventilation of Buildings Table XIX, Motor-Driven Exhausters Parts Number of pump Max. capacity, direct radiation, sqft Cylinder-sizes Size of connection Strokes per minute Horse- power Bore, in Stroke, Disch'e- pipe. Suction- pipe, in m I 279 112 113 114 115 4 ooo 10 ooo i8 ooo 28 ooo 35 000 2}i 3 4 4 5 3 3H S 5 I I 2 I I 2 150 70 70 68 60 I 2 ^ 1 trap, usually of the thermostatic type and commonly termed a vacuum-valve, such as the Dunham (Table XX), Webster, lUinois, Monash, etc. A volatile liquid is employed in the thermostatic element or bellows. This liquid is vapor- ized immediately as steam is brought in contact with the bellows, and causes the latter to expand and thus close the valve. The temperature of the con- densate from the radiator is slightly below the temperature of the steam but is not sufficiently high to vaporize the liquid. The valve therefore remains open and will pass the water of condensation and air until the steam fetarts to flow, when it immediately closes. These valves are very sensitive, and when prop- erly adjusted and in order will not blow steam. One type of thermostatic VALVE is shown in Fig. 26. It is cus- tomary practice to connect a K-in cold- water line to the main return at the pump, which serves to condense any steam that may leak by the vacuum- Connected to Return-Pipo Fig. 26. Thermostatic Valve or Vacuum- trap Fig. 27. Detail Showing Method of Draining Bottom of Steam-riser in an Overhead System valves due to dirt getting under the seat and preventing the valve from closing tight. Figs. 27, 28 and 29 show clearly the application of vacuum- traps to the two-pipe system. It will be observed by inspection of Table XXVII that the return-connections for a vacuum system are much smaller than ar^ used in the ordinary two-pipe system, Table XXVI. The vacuum Direct Steam -Heating 1289 Punham Air-Tra system is largely employed In connection with exhaust steam-heating, where it is important to keep down the back-pressure on the steam-engines or tur- bines to approximately 5 lb per sq in. A by-pass with reducing-valve is used to cross-connect the live-steam main with the heating system. This valve automatically opens and allows Hve steam at a reduced pressure (usually from 2 to 5 lb) to flow into the heating Discharge to Open Drain Ail-Trap not ^ necessary |if BoilerTEeed oPump ia usedl Fig. 28. Detail Showing Method of Drip- ping Rise in Steam-main Fig. 29. Detail Showing Method of Con- necting Rotary Vacuum-pump when Return-line is Below Vacuum-pump system whenever the demand is greater than the supply from the engines, or when the engines are not in operation. (See Fig. 30.) Exhaust from Engine Fig. 30. Exhaust Steam-heating Vacuum System The vacuum maintained by the pump on the main-return line is ordinarily about 10 in of mercury. This pump is placed under automatic control. The controller being operated by the pressure in the return-line. 1290 Heating and Ventilation of Buildings Table XX. Capacities of Dunham Vacuum-Traps Part 3 Capacity, Pipe- Diameter Number Size. direct radiation, connec- tion, Weight, of port. Lift, in sq ft m lb in m I Vi 100 Vi i>^ 2 H 350 Vi 2 3-2 % H 3 4S0 H B.T. % I 500 % 13 % 3/16 B.T. I 3 000 I 21 I These traps are designed for steam-pressures not in excess of lo-lb gauge. For main and riser-drips, use no smaller trap than the No. 3, and install trap as per details. Care must be exercised in selecting a trap or traps of the proper size for hot-blast heating-coils. The capacity-ratings for all traps are in terms of direct cast-iron radia- tion, on a condensation-basis of approximately 0.25 lb per sq ft per hr. Every unit of blast-coil must be reduced to that basis before trap-sizes are chosen and specified. (See Hot-Blast Heating for further details in reference to rating of vacuum-traps for hot- blast coils.) Size of Vacuum-Pump Required. The following table by the Warren Webster Co. may be used in determining the size of steam-driven vacuum-pump necessary. To determine the size of pump required the following empirical formula is used: Square feet of direct radiation + (number of units X 100) = F. Choose the nearest size corresponding to the value of F given in the table. The steam- cylinders are proportioned on a basis of 80-lb pressure and for lower pressures the steam-cylinder must be proportioned accordingly. Example. Required the size of pump for 5 000 sq ft of direct radiation in 150 radiators. 5 000 + (150 X 100) = 20 000. Use a 5 X 6 X lo-in pump. Table XXI. Sizes and Capacities of Vacuum-Pumps Size Steam, in Exhaust, in Suction, in Dis- charge, in F Floor- space 4 XS 4 X4 X 6. 4 X4 X 8. 5 XS 4 XS X 6. 4 XS X 8. 4MXSMX 8. 6 XS 6 X7 4MX6 X 8. 5 X6 Xio. 7 X7HX10. 6 X7MX12. 7 X8 Xi6. 6 X8 X12. % Vs H I H I '"y I iM I I 2H 2M 3 3 3 3 4 S s s s 2 2 ' 2 K * 2Vi 2H 3 S 4 4 4 6 830 7 270 8 000 10 680 11 3S3 12 500 IS 125 IS 990 17 215 18 000 19 390 28 256 30 60s 34 470 36 620 11X34 II X34 13X36 13X38 13X38 13X38 18X50 18X52 19X54 18X52 19X54 This table may also be employed in determining the size of motor-driven reciprocating vacuum-pumps, the last two figures under Size being the diameter Design of Low-Pressure Steam-Heating 1291 and stroke, respectively, of the pump. A vacuum-pump should be specified to have a displacement of at least from lo to 15 times the volume of the con- densate when operating at its normal rated speed. Table XXII. Capacity and Size of Steam-Driven Vacuum-Pumps Drain- Drain- Steam- cylinder diam- eter. Water- cylinder diam- eter. Stroke, Steam- pipe, Ex- haust- pipe, Suc- tion- pipe, Dis- charge- pipe, ing ing capacity capacity direct con- radia- densed Floor- space, in in in in in in in sq ft lb in 3 2^ 4 H H !}-€ iM 2 700 810 30 X 6 4 4 6 Vi M 2 iH 7 000 2 \QQ 4 8d^ 40 Xio 6 6 10 I iM 4 3 16 000 59X14 10 ID 12 iM 2 6 5 40 800 12 240 72X20 10 12 12 iJ4 2 8 7 62 000 18 600 72X20 10 14 12 iM 2 10 8 85 000 25 500 10 16 18 iH 2 12 10 92 000 27 600 10 18 18 i^ 2 12 10 128 000 38 400 * Condensation figured at 0.3 lb per sq ft radiating-surface per hour. Vacuum-pumps with belted electric motors are made by the Bjshop-Babcock- Becker Co., with capacities of 2000, 5000, 10 000, 17000 and 25000 sq ft of direct radiation. This pump should be under the control of a reliable vacuum-pump governor so that when the requured vacuum has been produced the pump will stop. Design of Low-Pressure Steam-Heating Systems Amount of Radiation Required. The heat-loss, //, of the various rooms is calculated as previously indicated, and // is divided by 250. The result is the amount of direct radiation in square feet required. The heat-emission of cast- iron radiation for pressures up to 5 lb per sq in may be assumed as 250 Btu for all practical purposes of calculation. Rating of Boiler Required. If anthracite coal is to be used for fuel add not less than 50% to the total amount of direct radiation to be installed and 65% if bituminous coal is to be used, to allow for radiation-loss of boiler, mains, returns, etc. The steam-mains and risers should always be covered. Size of Mains, Branches and Return-Pipes. Steam-mains in low-pressure gravity systems should be so proportioned that the loss in pressure, due to pipe- friction, does not exceed approximately i oz or 0.062 lb per sq in, per 100 ft of run. The reason for thus limiting the pressure-loss is apparent from an inspec- tion of Fig. 31. Owing to the fact that the steahi is losing pressure as it flows through the main, it follows that 1 he pressure at the last riser will be lower than in the boiler. The difference in pressure, or pressure-loss, P, causes the water in the return-main to stand higher than the water-line of the boiler. The added height Z is equal to the height of a column of water which pressure P will support. Thus, if the boiler-pressure is 2 lb per sq in and the pressure at the far end of the main is, say i>^ lb, with water weighing 61 lb per cu ft, or 0.035 lb per cu in, the water in the return will stand (2 —1.50) -h 0.035, or -^ =14 in above the water-line of the boiler for a >^-lb loss in pressure between the boiler and the end of main. It is apparent in this instance that unless the water-line 1292 Heating and Ventilation of Buildings Parts of the boiler is about 1 8 in or more below the last riser, or radiatoi*-connectioa, water is quite likely to flood the steam-main and to be accompanied by a ham- mering and a poor circulation in the radiators located at or near the end of the run. Steam-mains are graded in the direction of flow approximately i in in lo ft. Fig. 31. Location of Boiler and Arrangement of Pipes for Low-pressure Steam-heating Systems Referring to Fig. 31, and assuming a 7 ft-6 in, or 90 in, clear height of base- ment, and a boiler having a 7 2-in water-line and a length of steam-main of icx) ft, it is evident that the boiler must be located in a pit, the depth, A', of which is 6 4- 10 -f 18 -1- 72 .90 16 in in order to maintain t8 in between the water-line in the boiler and the end of steam-main. The distance in practice should not be made less than from 18 to 24 in. The extreme pressure-load stated, ^ lb, in this illustration, is never approached in normal operation, when the mains are designed for i-oz drop per 100 ft, but may approach the value stated when the system is being started up with cold radiators, when the rate of condensation is very much higher. The pressure-loss in a pipe flowing full of steam may be approximated by Babcock's formula IF =87.5 i, ypd^ h'i) in which W is the weight of steam flowing per minute in pounds, L the length of pipe in feet, d the diameter of pipe in inches, y the density of the steam and p the loss in pressure in pounds per square inch. One square foot of direct radiation will condense, under nonnal conditions of operation, 0.25 lb per hr, and the density of steam, y, is 0.043 lb for a 2.3-lb pressure. The sizes of steam-mains given in the tables were calculated by the above formula, the pressure-loss, p, being limited to i oz, or 0.062 lb per sq in per 100 ft of straight pipe. To allow for the fittings approximately twice this, or }4 lb per sq in per 100 ft of pii^e may be assumed. The pipe-sizes for the one- pipe system are given in Table XX III, corresponding to the amounts of direct radiation stated in the last column. Branches and risers may l)e taken from Table XXIV, and reliefs for risers from Table XXV. For the two-pipe and also the one-pipe relief system the steam-main may be reduced in size as rapidly as the radiation carried will permit. The steam-main should not, however, be of any smaller size than risers called for in Table XXIV. For one-pipe circuit systems, unless the steam-main is frequently dripped, p' Design of Low-Pressure Steam -Heating 1093 THE MAIN MUST BE RUN FULL SIZE to the end, at which point an automatic air- yalve should be installed and the main dripped into the return. This system is generally used for the heating of residences not exceeding two stories in height. For buildings two stories or more in height the one-pipe relief system <^ 2nd SECOND AND T^|llRD FLOOR RADIATORS 1)^' riir Main-J^l>^^ '{^^ I'Relief or Drip Branch ^^t^^ j^^^^^^ ^^^^^ j,j^^^) ^ 1st Y I ,i&«lH FIRST-FLOOR RADIATOR Fig. 32. One-pipe Relief System X •>[crGT Cable XXm. Pipe-Sizes for One-Pipe Low-Pressure Gravity Heating Systems. Main-Table Steam-main, Dry return,* Radiation, m m sq ft I I 40 iH I 75 I }4 iH 126 2 iH 286 2y2 2 535 3 2M 890 3H 2^4 I 360 4 3 I 950 5 3 3 600 6 4 5 900 8 4 12 700 10 s 22 900 12 6 37 000 * For wet returns reduce one size, with iK in as a minimum size 1294 Heating and Ventilation of Buildings Parts may be employed, in which case the risers supplying the radiation for the second floor and above are dripped into the return as shown in Fig. 32. The minimum size for a wet return should not be less than i J< in, as a smaller pipe is Hkely to become plugged with an accumulation of dirt and scale. Table XXIV. Pipe-Sizes for One-Pipe Low-Pressure Gravity Heating Systems, Branch and Riser-Table Radiation, sq ft Radiator- tapping, in Branch- riser, radiator- arm, in to 20 I I 21 to 24 I i>i 25 to 40 41 to 6o 6i to 8o 8i to 100 lOI to 200 201 to 300 2 2 3 For risers carrying more radiation than given by the table, use the table fo Steam-mains and increase one size. Table XXV. Pipe-Sizes for One-Pipe Low-Pressure Gravity Heating Systems Reliefs for Risers (One-Pipe Relief System) Riser, in i Relief, in H I I 2 2H i?/2 3 3^ 2 2 4 2H 4^ 3 5 3 Table XXVI. Pipe-Sizes for Two-Pipe Gravity Systems msH'tr^. '^ni Direct Diameter Diameter of radiation- of supply. dry return,* surface -Ul-OitiM supplied. m m sq ft H H 20 I % 36 i}4 I 72 iK iH 120 2 I'A 280 2V2 2 530 3 2^ 900 3M 2K I 320 4 3 I 920 4M 3 2 760 S 3H 3 720 6 33^ 6 000 8 4 12 800 9 4K 17 800 10 5 23 200 12 6 31 000 * For wet returns, reduce one pipe-size, with 1)^ in as a nunimtUti. Design of Low-Pressure Steam-Heating 1295 Pipe-Sizes for Two-Pipe Low-Pressure Gravity Heating Systems. Table XXVI may be used in determining the sizes of mains, branches and risers for a two-pipe gravity system. i^'" Fig. 33. Riser-diagram for Down-feed Mechanical Vacuum System 1296 Heating and Ventilation of Buildings Part 3 Pipe-Sizes for Two-Pipe Mechanical Vacuum Systems. The sizes of branch-supplies to radiators, risers, steam-mains, radiator-returns with ther- mostatic valves and main-returns may be taken from Table XXVII. (See Example, Fig. 33.) Table XXVII. Two-Pipe Mechanical Vacuum Systems Size of pipe. in Rating direct radiation Radiator-connections Steam- mains and risers, sq ft Return- mains and return-risers, sq ft Size of radiator, sqft Size of steam- connection, in Size of return- connection and valve, in I iK 2 2H 3 3H 4 4H S 6 8 9 10 12 14 5 20 40 75 150 300 500 900 1 500 2 000 2 800 3 600 6 000 13 000 18 Qbo 23 obo 37 000 40 160 320 600 1 200 2 400 4000 7 200 12 000 16 000 22 400 28 800 48 000 i 72 000 1 30 50 .75 100 125 150 200 300 I iH 2 2 H K K 'A A ' 55 000 Table XXVIII. Direct Radiation Required for the Factory OflBce-Building Shown in Figs. 9 and 34. Room-designation Btu- loss per hr Direct rad'n required, column 2-7-250 Ra diation to be installed No. radiators No. cols. and height No. sect's each radiator •'Total, sq ft I 2 3 4 " S \ 6 7 Sample rm Hall 54 900 19 123 27 358 19 482 7 380 31 306 19 224 70 247 31 306 219 77 95 77 29 125 78 281 125 4 I 2 I I 2 I 4 2 Z-Z2" 3-38" 3-32" 3-32" 3-32" 3-32" 3-38'' 3-32" 3-32" 12 15 II 17 7 14 16 16 14 216 75 99 76K 31M 126 80 288 r26 Laboratory Storage Toilet Mgr's office Hall Gen'l office Sup*t's office . .-. . Totals I 108 Design of Low-Pressure Steam-Heating 1297 Pipe-Sizes for Indirect Gravity Radiation. Multiply square feet of indirect radiation by 2 and use Table XXVI. Design of One-Pipe Low-Pressure Gravity Heating System. Direct Radiation. Let it be required to design a heating system of this type Flanges NOTE:- All Radiators 2-Col. 32" high unless otherwise noted. Fig. 34. Single-pipe Low-pressure Steam-heating System for Factory Office-building. (See, also, Fig. 9.) for the factory office-building shown in Figs. 9 and 34, the heat-losses being as previously calculated and given by Table VII. The location of the radiators are as indicated on the floor-plans, Fig. 9. 1298 Heating and Ventilation of Buildings Part 3 Direct Radiation Required. The total Btu-loss for each room is repeated in column 2 of Taljle XXVI IT. The amounts of radiation required for these losses is given in column 3 and were obtained l^y dividing the Btu-loss in each case by 250, the average heat-emission of direct radialion (Btu) per square foot per hour for a room- temperature of 70° and 2 lb steam-pressure. Boiler-Capacity Required. The boiler-capacity must be such that it will carry the radiation installed plus the extra heat-loss from the steam-mains return-mains and boiler. The steam-mains are to be covered and anthracite fuel is to be used. The fuel-capacity of the fire-pot is to be sufficient for an 8- hi firing-period. Adding 50% to the sq ft of radiation installed, 1.5 X 1.108 = I 662 sq ft, the boiler-rating required. The fuel-holding capacity of the fire-pot should be checked for the boiler proposed as previously stated under Boilers. Chimney-Size. The size of chimney may be taken from Table XVn, and, in this case, is 12 X 12-in inside dimensions, by a 40-ft height. The nearest size, for Hue-lining, Table XVI, is 13 X 18 in. Design of Piping System. The layout of the basement-mains and risers for a ONE -PIPE CIRCUIT SYSTEM is given in Fig. 34. The risers are not dripped in this case. Steam-main A supplies 623 sq ft of radiation, and, according to Table XXIII must be 3 in in diameter. The diameter must be carried to the end where it is dipped into the return-main by a i ^-m relief, as indicated in Table XXIII, for a dry return-pipe. In order to keep the steam-main as close to basement-ceiling as possible, where it passes beneath the floor-girder, a rise is made, and consequently a i M-in drip must be provided to take care of 234 sq ft of radiation. The main wet return takes care of 1108 sq ft of radiation and is therefore made 2-in diameter. The risers and branches are proportioned by Table XXIV, Gravity Indirect Heating General Description. A satisfactory means of providing for the heat-loss in a room, and, at the same time, supplying air-ventilation, is accomplished by this system. The radiators properly encased with a sheet-metal casing, cov- Table XXIX. Final Temperature of Air Passing Over Indirect Radiation. Ex- tended-Surface Type. Initial Temperature of Air, 0° F. Heater, One Stack in Depth. Four-Inch Spacing of Sections Velocity of air through free area of heater, in ft per min, v* Final temperature, /2, in degrees Fahrenheit Steam at 2-lb pressure Hot water, 180° F. SO 100 125 150 175 200 122 100 95 90 86 82 147 127 120 113 106 102 ♦Measured At 70" F. For first-floor registers a velocity of 150 ft per min through ree area and 150 ft per min for second-floor registers is the usual assumption. Gravity Indirect Heating 1299 ered with insulation, are ordinarily hung from the basement ceiling by means of light angle-iron or strap-iron, as shown in Fig. 35. Each radiator is ordinarily 1 Clean-Out> or T Iron belaw^ Casing -^ Fig. 35. Indirect Radiators, Casings, Connections, etc. ibove W.L. for V.Clean--Out I Clean-Ontl aravitj-Steain Systems Ciean-UUt „ , i ^ ELEVATION. INDIRECT RADIATOR WITH ^Tlfon bSS G.I. CASING AND DUCTS provided with a fresh-air inlet and hot-air duct connecting the radiator with the room-register. A recirculating duct may be provided, as indicated, in order to economize on the heating in ex- tremely cold weather if desired. There should be a separate ver- tical hot-air duct for each register to be supplied, connected with its own indirect radiator. At- tempting to supply more than one register from an indirect radiator is not usually success- ful, or recommended, unless a fan system is employed to give a positive air-flow as with the hot-blast system, described later. The hot-air ducts for the upper floors, for best results, should be double pipe as later shown under furnace-heating. The indirect radiator is designed to present a maximum of heating-surface to the air passing over same. Among the various standard types for gravity indirect heating rriay be men- tioned the Indirect Pin Radiator (Fig. 36), Excelsior, Sterling and Vento. Indirect radiators are now rated according to the temperature-increment, or Fig. 36. School Pin Indirect Radiator for Steam or Water 1300 Heating and Ventilation of Buildings Parts rise, which they are capable of giving to the air passing between and over the sections of the heater for various velocities of air, initial temperature, and tem- perature or pressure of the steam, or temperature of the hot water. The veloc- ities stated are, for convenience in rating, based on air at 70°. The free or unob- structed area means the net area between heater-sections after deducting the area of the projecting surfaces from the gross area. Limitations of space pre- vent giving more than these data for one type of indirect radiator. rjyjr\ -+t4 HI 7M an xjmj- ipct 1+ + + 2 Pipe Tap, Fig. 37. Vento Thirty-inch Indirect Heater-section Tables XXIX and XXX give the results of tests made on Vento, indirect radiation, American Radiator Company. (See Fig. 37.) Table XXX. Dimensions, etc., Vento Indirect Radiation Size Heating- surface, 5, sqft Height, in Width, in Free area between sections, (a), sqft 30-in section 40-in section 50-in section 60-in section 8.00 10.75 13.50 16.00 29 J'S SO 2042 601H6 9H 9M 9K 9K 0.256 0.3S 0.428 0.511 Spacing of sections, 4 in on centers for gravity air-circulation. Weight of Air to be Circulated per Minute, W. U = temperature of air leaving register. / = temperature of room. 0.24 = sp heat of air. H — heat- loss of room to be warmed in Btu i^er hour. V = volume of air in cubic feet per minute measured at 70°. Then W = ///[60 X o.24(/i — /)], lb of air per min Y = IF/ (0.075 = the density of the air at 70**) Gravity Indirect Heating 1301 Area of Indirect Heating-Surface Required, S. k = initial temperature of air entering indirect heater, ti = final temperature air leaving heater = ti +5° (assumed temperature-loss in hot-air duct). V = velocity through free area of heater in feet per minute, measured at a temperature of 70°. F = total fire- area required in heater, in square feet, a = free area for one section of heater in square feet, n = number of sections required. Then F = V/v = W /0.75V, n = F/a and 5 = n X 5 Example. Required the amount of indirect low-pressure steam-surface of the extended-surface type, the number and size of sections, and the over-all dimensions of an indirect radiator to supply the necessary heat to warm a first-floor room, the heat-loss of which is ^ =20 000 Btu per hour. All the air is to be taken from the outside, the temperature of which is / = 0° F. The inside temperature to be maintained is / = 70° F. Solution. It is first necessary to assume a temperature, h, for the air entering the room, in order to calculate the amount or weight, W, of air required to be circulated to convey the heat required to make up the heat-loss //. Assume h =95° and ^2 = /i + 5 (loss) = 100°; and v = 100 ft per min, from Table XXIX. Then W = 20 oco/[6o X 0.24(100 — 70)] = 46.3 lb per min and V = 46.3/0.75 = 617 cu ft per min, measured at 70° F. Assume 40 in as the length of section desired in this installation, a =0.35 (Table XXX); F = 617/100 = 6.17, the total square feet of free area required; n = 617/0.35 = i3, the number of sections of 40 in. Vento is, therefore, required, giving a total heating-surface of S = 10.75 X 18 = 193.5 sq ft Dividing this equally between two indirect radiators the width of each heater is equal to nine (sections) X 4 (spacing-sections) = 36 in. Low-Pressure Boiler-Rating Required for Gravity Indirect Radiation. The amount of heat given up to the radiator is h = o.24W{l2 - to) X 60 Btu per hr The equivalent rating in square feet of direct radiation is therefore R = h/250, plus 25% for radiation of mains, returns, etc. Example. Required the equivalent low-pressure boiler-rating to supply the indirect radiation in preceding example. Solution. h = 0.24 X 46.3 (100 — o) X 60 =66 672 Btu per hr R = (66 672/250) X 1.5 = 399 sq ft In other words, i sq ft of low-pressure steam indirect radiator with gravity- circulation is practically equivalent to 2 sq ft of direct radiation; or the amount of indirect surface is approximately 0.4 of the amount of direct radiation required. Area of Hot-Air Ducts for Gravity-Circulation. A velocity of approxi- mately one third of the theoretical velocity attainable by natural draft, due to 1302 Heating and Ventilation of Buildings Part 3 the smaller density of the heated air, is assumed in practice in proportioning the area of the hot-air ducts. Table XXXI. Theoretical Velocity (V) of Air, in Feet per Second, Due to Natural Draft Height of flue Excess of temperature in flue above external air in feet. E 1 10" 15° 20" 25° 30° 50° 100° 150" I I . I 1.4 1.6 1.8 2.0 2.5 3.6 4.4 5 2.5 3-1 3.6 4.0 4-5 5.6 8.1 9.^^; ID 3.6 4-4 5.1 5.7 6.6 8.1 II. 4 14.0 ? IS 4-4 5.4 6.3 7.0 7.7 9-9 14.0 17.1 20 5.1 6.3 7.2 8.1 8.8 11.4 16. 1 19.8 25 5.7 7.1 8.1 9 9-9 12.8 18.0 22.1 30 6.3 7.8 8.8 9-9 I0.8 14.0 19.8 24.2r;.t 35 6.8 8.4 9-5 10.7 IT. 7 15. 1 22.3 26.1.1 40 7.3 8.9 10.2 II.4 12.5 16. 1 22.8 27.9 Example. Required the size of hot-air duct for each of the indirect radiators in the preceding examples for a first-floor installation, the effective height E being 5 ft. Solution. The excess of temperature in the flue above the external air is 100 — o = 100°. The theoretical velocity in the duct, from Table XXXI, is 8.1 X 60 = 486 ft per min. The actual velocity is approximately one third of this, or 162 ft per min. The weight of air per minute passing through the flue is 23 lb, or 23/(0.07 1 (density at ioo°)] = 324 cu ft The required area of the flue is therefore 324/162 = 2 sq f t = 288 sq in The gross area of the register-face must be approximately 1.8 this amount or 518 sq in, to obtain the same free area through the register-grill as exists in the flue or duct. Sizes of standard registers are given in the section on Fur- nace-Heating. Direct Hot- Water Heating Systems in Use. Systems for heating with direct hot-water radiators, like the direct steam heating systems, may be divided into two general classes, the first of which includes all those systems operating by gravity only, depending on the difference in density of the water-columns in the flow and return-lines to cause circulation. The second class includes those systems in which a forced circulation is maintained by means of a pump placed on the return-line just before it enters the boiler or heater. These latter systems are employed usually only in large installations or in district-heating service. Gravity Hot-Water Heating Systems. The gravity systems are divided into the upfeed systems^ using basement-mains, and the downfeed systems, using overhead or attic-mains. The upfeed systems may have either a one-pipe basement-main or two-pip>e basement-mains, and the latter type may have either a direct or a reversed retuni-mahi. (See Figs 38 and 39 for reversed Direct Hot- Water Heating 1303 return.) The downfeed systems may have either SINGLE OR double risers; Either system may be operated with an open or closed expansion-tank, as shown in Figs. 42 to 46. In general, the downfeed or overhead systems are more positive, permit the use of smaller mains and risers, and provide for the automatic removal of air from the radiators and piping. It is necessary, how- ever, that the headroom or clear space in the attic should be at least 4 or s ft if the overhead mains and branches are to be properly installed. It is sometimes possible to run the overhead mains at the ceiling of the top floor, and in such cases the above restriction does not apply. Mains run in attics must be well insulated to prevent freezing. The underfeed systems are used where fote:- First-floor-supply riser-connections ;o be taken from top of main, and risers ibovo first at 45. All z-eturns into side »f main, (or bottom). 3ee below. Fig. 38 BASEMENT HEATING PLAN Figs. 38, 39, 40 and 41. Hot-water Heating. Two-pipe Up-feed System basement-space is available, and of little or no value, and the radiation is located on two or more floors; or where attic-space is so limited that it would not be possible to install overhead mains and branches. Underfeed systems are liable to prove unsatisfactory in buildings less than two stories in height, as the motive head with radiators on the first floor only is so slight that faulty or deficient circulation is quite likely to result. The Upfeed One-Pipe System. The upfeed one-pipe system is in very general use today, and is employed almost exclusively by the United States Treasury and War Departments whenever upfeed hot-water systems are to be installed. In this system, as shown in Figs. 43 and 45, the supply-main rises close to the basement-ceiling just above the boiler and grades down in the direc- tion of flow, with a uniform grade of % in in lo ft. Branches are taken from the top of this main for supplying flow-risers and the return-branches are made into 1304 Heating and Ventilation of Buildings Parts the side or bottom. (Fig. 40.) Flow-connections should always be made from the top, or at an angle of 45** in the case of branches near the boiler, or for branches HOT-WATER HEATING - EXPANSION TANKS (OPEN AND CLOSED SYSTEMS) _ S.A.O. Connection f for Cold Climateff ^'■^ CJbeck-Valvo TableV.,. Expansion-Tanlcs Size in Inches 10x20 22 X CO Capa- citjr Gal. 100 Sq. ft of Rad- iation 250 6000 l^ote.- Galvanized Steel, Tested at 100 lb. Tapped lX"Top and Bottom, and for Gauge- Glass Runs full Size, drop after Serving last Radiator ^ ^ Grade ^Si^in lo'-O" jij^l' Fig. 43 ONE-PIPE UNDERFEED SYSTEM, OPEN TANK For-Piping-Si^es See Tables 3cXXIl-and XXXIII n H K— 2^0* -H Grade Dowa ^ at least 5 Figr. 45 1 PLAN ^ Fig. 46 :^~f USUAL METHOD 2 3* FOR SMALL SYSTEMS From system^ Fig. 4r, HONEYWELL GENERAT6R, FOR USE WITH A CLOSED- TANK SYSTEM Figs. 42, 43, 44, 45 and 46. Hot-water Heating. Expansion-tanks. One-pipe Underfeed System suppl5ang only upper-floor radiators. It will be seen that in the case of branches supplying radiators on all floors the upper-floor radiators may be made to pull Direct Hot-Water Heating 1305 or augment the circulation of the first-floor radiators by taking the basement- branch for the former from the side of the branch running to the latter radiator. The first-floor branch is usually run full size all the way to favor the lowest radiator, as shown in Fig. 45. After having served all the radiator-branches the main drops and returns to the boiler, continuing the same size for the entire circuit. Connections (Fig. 43) to radiators should be made at the top on the supply-end, using a union elbow, and at the bottom on the return-end, using a quick-opening hot-water radiator-valve with union connection. By this arrangement only one valve is required to control the radiator. Since the temperature of the water in the one-pipe main gradually drops, due to the return of water at a lower temperature from the radiators served in the course of the main around the building, it is advisable to increase the last radiators on the main from 5 to 10% in area and to increase the size of branch and riser-connec- tions at the end of the main by a one-pipe size. Pipe-sizes may be taken from Tables XXXH and XXXIII. In using the tables all mains must be measured back to the boiler, and risers to any floor are proportioned to supply all the radiation above that floor as well as the radiator actually installed on that floor, as shown in Figs. 43 and 45. Table XXXII. Hot-Water Heating. Piping-Sizes. Basement-Mains Mains up to 100 ft Open-Tank (Upfeed with Pipe-size in inches Direct radiation Indirect radiation in square feet in square feet iK 135 100 iH 220 135 2 350 225 2H 460 320 3 67s 500 3V2 850 650 4 I 100 850 4H I 350 I 050 S I 700 I 3SO 6 3 600 2 900 7 4 800 3 900 8 6 200 5 000 9 7 700 6 300 10 9 800 7 900 12 14000 II 400 Table XXXII was compiled by J. J. Hogan, and is to be used for either one or two- pipe work. Length of main must be measured back to boiler. For mains over 100 ft, reduce capacity in the ratio The Upfeed Two-Pipe System. The upfeed two-pipe system is also in very general use, and if installed with a reversed return, as shown in Figs. 38 and 39, will give good results. It a direct return is used so that the water circulates first through the radiators nearest the boiler, and then through each succeeding group in turn, the ends of mains will be slow in warming up, the last radiators may be cold, and the system prove unsatisfactory. With the re- 1306 Heating and Ventilation of Buildings Parts Table XXXIII. Hot-Water Heating. Piping-Sizes. Open-Tank (Upfeed with Basement-Mains) Branches and Risers Pipe-size Floor First Second Third Fourth in inches Direct radiation in square feet % 30 45 55 70 I 6o 75 85 95 iM no 120 135 150 i3^ i8o 195 210 230 2 290 320 350 370 23^ 400 490 52s 550 3 620 650 690 730 2>y^ 820 870 920 970 4 I 050 I 120 I 185 I 250 4^ .1 32s I 400 1485 I 560 Table XXXIII was compiled by J. J. Hogan, and is to be used for either one or two- pipe work. VERSED-RETURN SYSTEM cach group of radiators has exactly the same length of water-travel, and hence the resistance to be overcome is practically the same, irrespective of the distance of the radiator-group from the boiler. It will be noted that the return begins at the first radiator served and flows in the same DIRECTION as the flow-main, increasing in size while the latter decreases. The flow-main grades up uniformly ^ in in 10 ft, and the return grades down toward the boiler^with the same pitch. Pipe-sizes may be taken from Tables XXXII and XXXIII as in one-pipe work, and the main-size reduced or increased as rapidly as the change in radiation supplied will permit. It is also customary in government work to install a starting-pipe (Fig. 38), between the main flow anci return at the boiler, in underfeed systems. This pipe ranges from i M to 2K in in size, depending upon the capacity of the boiler, and is intended to assist in the estabhshment of an initial circulation between flow and return-headers, even before the water in the mains is moving. Equalization-Table. In Federal-building work N. S. Thompson makes use of the following Equalization-Table in proportioning mains and risers serving more than one radiator in both upfeed and downfeed systems. The equal- izing-numbers represent the relative capacities of the different sizes of pipes for Table XXXIV. Equalization-Table for Mains and Risers = 2 = 60 = 650 in y^ = 5 2^2 = no 6 = I 050 m I = 10 3 = 175 7=1 600 m i\i =■ 20 3 M = 260 8 =2 250 iH = 30 4 = 380 Example. A iM-in, iH-in and 2-in pipe have a total value of no units, and hence are equivalent in carrying capacity to a 2 yi-\xi main. Direct Hot- Water Heating 1307 the same friction-pressure loss per loo ft of run, and are proportional to the 5/2 powers of the diameters. Thus the weight of water flowing varies as shown by the relation, W = Kdy^^, in which W = weight, / = a constant, and d = pipe- diameter. Details of Piping Systems and • Connections for Direct Hot-Water Heating. The distinctive piping-details of each system of hot-water heating have been discussed under that system, as described in the preceding para- graphs. In general all main piping and branches must be uniformly graded, as already indicated, and ample provision made for expansion and contraction, and the ready removal of air from all parts of the system. Air-traps or pockets in a hot-water system are fully as serious as water-pockets in a steam system. Hence a hot-water main grading down in the direction of flow cannot be relayed unless an air-outlet is provided at the top of the relay. If the main is reduced in size at any point an eccentric fitting must be used to keep the top of the large and small main in the same plane and avoid an air-pocket. Not only must all the piping be designed to permit the removal of air, but free and com- plete drainage of water must be provided for as well, so that when the drain or blow-off cock is opened at the boiler the entire system can be emptied of water. If branch-mains are taken from a header at the boiler they must all rise to the same elevation so that the tops of all the branches will lie in the same plane as they start away from the boiler. The fittings on all main piping and branches must be of the long-sweep pattern, and all pipe should be carefully reamed to remove burrs and sharp edges. Where the same riser supplies radiators on two or more floors the branches to the radiators on the intermediate floors may be connected with special tees (Fig. 41) known as O. S. fittings, with a deflector arranged to divert the current of flow into the outlet of the tee, and thus favor the radiators on the intermediate or lower floors. By using top-flow and bottom-return connections at each radiator it is possible to positively control each unit by a single valve, except for the slight circulation intended to prevent freezing, which takes place through the I'ie-in-diameter hole drilled in the valve- disc or sleeve, when the valve is closed. If both connections are made at the bottom tappings, and only one valve is used, it is entirely possible that the radiator may still be supplied with hot water through the unvalved connection even when the valve is closed. Air-Removal in Hot- Water Systems. Suitable provision must be made for the removal of air from all hot-water radiators, wherever an upfeed system is installed. Usually small air-cocks are attached to the highest point of each radiator and are periodically opened to relieve any accumulation of air. If these cocks are forgotten a radiator may become air-bound and fail to heat because of faulty circulation; hence automatic air- valves are sometimes installed for this purpose. The automatic air-valve for hot-water radiators is not very generally used, due to its HabiUty to pass water as weU as air; but a standard type, made by the Monash-Younker Company, may be mentioned. Expansion-Tanks for Hot- Water Heating. Open-Tank Systems. The low-pressure system of hot-water heating is not a closed system, as provision must be made for expansion and contraction of the water within the system. An open tank is provided at a suitable elevation, not less than 3 ft above the highest radiator, and connection made to the nearest return-riser; or preferably a separate expansion-Hne is run to the flow or return-main in the basement. The size of the expansion-tank varies with the amount of water in the system, and also with the range in temperature of same, and its capacity is determined as follows: The increase in volume of a given weight of water heated from 32° to 212° ig 1308 Heating and Ventilation of Buildings Part 3 about Hs, or approximately 4.33%; so that for every 23 gal in the system at 32°, an allowance of i gal must be made in the expansion-tank when the water in the system is raised to 212°. Cast-iron radiators have an internal volume of ij^ pints per sq ft, while steel radiators and i-in pipe hold about i pint per sq ft. Assuming the internal volume of the radiators to be about 50% of the entire system, we have for 3 000 sq ft of actual radiation, 3000 X 2 X H gal = 750 gal of water. This water will increase Hs X 7So = 33 gal on being heated from 32° to 212°. Hence an expansion-tank of 2 X 33 = 66-gal capacity is necessary, the tank being made double the theoretical volume for practical considerations. A list of expansion-tank capacities and dimensions is given in a table (included with Figs. 42 to 46), from which a commercial tank may be readily selected for systems under 6 000 sq ft. For larger systems the size of tank should be separately determined and the nearest commercial tank-size, as taken from the manufacturer's list, should be specified. These tanks should have i or i34-in top and bottom tappings with J^-in water-gauge tappings, for con- necting a gauge-glass, at least 12 -in long, on the side of the tank as shown in Fig. 43. The tank must be securely supported well above the highest radiator in the system, and in the larger installations special framing must often be designed to carry the weight of tank and water. Automatic expansion-tanks equipped with a ball-cock and overflow are sometimes installed, and the altitude- gauge on boiler, and the gauge-glass and fittings on tank omitted. These tanks may be covered with hardwood and varnished if it is necessary to place them in a finished room or apartment. Expansion-Tank Connections. The most approved method of connecting an expansion-tank to a low-pressure one-pipe system is shown in Fig. 43, where an expansion-and-vent line is run from the top of the main, at the high point just above the boiler, and connected to a return-bend just beneath the tank. A return circulating-line is taken from the other side of this bend and connected with the return-main at the boiler. The circulation of water in this loop will prevent freezing at the tank. From the top of the tank a iJi-in vent-line is taken through the roof, and a iM-in overflow is taken out of this vent-line at a tee just above the tank. This overflow should discharge into an open sink or drain near the boiler so that it will be immediately evident to a person in the boiler-room, filling the system, just when the water has risen to the overflow above the tank. The movable hand on the boiler altitude-gauge can then be set to correspond with the middle of the gauge-glass, and the water-level brought to this point with the system cold. No valves should ever be installed on either the expansion or the overflow-lines, and in case the system is valved at the boiler the expansion-line must be connected on the boiler-side of this valve; and where two boilers are installed this line must be carried to a point above the water- line in the expansion-tank to prevent siphoning the water out of the entire system in case it is necessary to drain OHly one boiler. Expansion or vent-pipe connections must always be so made to main-piping in basement so that all air will be automatically removed from high points. Wherever possible risers or branches to risers may be used for reUeving any accumulation of air in the main- piping. In SMALL INSTALLATIONS the expansion-Une may be connected to the return-riser of one of the highest radiators, and no overflow other than the vent need be provided for, as shown in Fig. 46. This is a cheap method, and should not be resorted to unless extreme economy must be practised. The tank must be in the same room with the radiator to prevent freezing, as no circulation is provided for, and the overflow is simply discharged out of doors and usually upon the roof. The usual result is that an unsightly appearance is soon created. The United States Treasury Department employs a special vent and overflow- Direct Hot-Water Heating 1300 connection (Fig. 42) in cold climates, where there is liability of the vent-line freez- ing up if run out through the roof, due to the condensation and freezing of vapor passing out through this line. The vent-line is made only 2 ft high above the tank so that it is kept within the building, and it is equipped with a check-valve to prevent the escape of water through the same in case the tank should sud- denly overflow. The closing of the check-valve will compel the excess water to pass down the overflow, and prevent the flooding of the building. Closed-Tank Systems. The permissible temperatures in any hot-water system are limited by the pressure on the system, which latter factor determines the point at which boiling will take place. The pressure at any elevation in an open-tank hot-water system will vary directly with the distance below the level of the water in the expansion-tank, and hence it will be possible theoretically to carry the water in the boiler at a temperature corresponding to the hydrostatic pressure at the boiler before boiling would occur. The relation between hydro- static head, pressure and boiling-point are given in the following table: Table XXXV. Relation between Hydrostatic Head, Pressure and Boiling-Point Hydrostatic head in feet Pressure in pounds per square in Boiling-point 12 24 37 49 61 74 87 100 113 125 5 ID 15 20 25 30 35 40 45 SO 212 227 239 250 259 268 274 281 287 292 298 Practically it would be quite impossible to carry temperatures in excess of 2 1 2 ° in any part of an open-tank system, as the high-temperature water would imme- diately rise into the open tank and boil. In order to overcome the hmitations of the open-tank system, in which water will always boil as soon as a tempera- ture of 212° F. is reached, various means of increasing the pressure in these systems have been resorted to in the attempt to carry a higher water-tempera- ture in the radiators in very cold weather than would be possible with an open- tank system. These devices have usually been installed on the expansion-line, either at the boiler or else just below the expansion-tank and the static head increased by interposing a column of mercury in the path of the expanding water as it flows into the expansion-tank. A common form of the apparatus, known as the Honeywell Heat-Genera- tor, is shown in Fig. 44, in which it is seen that water entering the generator from the system wiU force the mercury up the inner tube A until a head of 20 in or 10 lb is established, at which time the entrance to this tube will be uncovered by the mercury and water or air may enter it and pass to the expansion-tank. Any excess of mercury above that required to just fill tube A is returned by tube B to the reservoir in the base. When the system cools off water can flow back down tube A as soon as the mercury-column drops in it, and the slight head of mercury then existing at the outlet of this tube is easily overcome by the head of water in the expansion-tank above this point. This increase of 10 lb in static pressure makes it possible to carry a maximum water-temperature of 240**, nearly 30° higher than would be possible in an open-tank system. While a temperature as high as this could theoretically be carried at the boiler in an open-tank system with a static head of 24 ft, just as soon as this water rose in the system it would boil, and escape from the expansion-tank, at the same time emptying the system of water. In fact with the open-tank system the water is liable to be driven out at a temperature of 212° F. The use of pressure-gene- rators similar to the above makes it possible to use smaller radiators in the 1310r Heating and Ventilation of Buildings Part 3 heated rooms, as it is entirely possible to maintain steam-temperatures in the radiators whenever desired. Since higher temperatures are used, the difference between flow and return-riser temperatures becomes greater than in the open- tank system, and hence a greater motive head exists and smaller mains and risers may be used with this system. The Honeywell Company recommends the following schedule of radiator-tappings: Table XXXVI. Riser- Sizes for Honeywell System Pipe-size in inches Capacity in square feet of hot- water radiation 1st floor* 2nd floor 3rd floor I 30 75 75 up 40 100 100 up 50 125 125 up It should be remembered that since radiators and pipes are smaller in this system there is much less water than in the open-tank system, making it more sensitive in warming up and also in cooling off. The generator should not be placed close under the expansion-tank. Otherwise than this its location may be anywhere in the expansion-line, as the same hydrostatic head is always acting in addition to the head of mercury-column. Furnace-Heating The Furnace and Its Location. The method of warming or heating a building by what is generally known as a warm-air furnace is termed furnace - HEATING. The furnace consists briefly of a cast-iron or steel heater, containing a combustion-chamber, fire-pot and grate. The heater is usually set in or encased by a double-wall galvanized sheet steel jacket (Fig. 47), although brick is sometimes used instead of the steel jacket for this purpose. Furnaces for soft coal are usually designed with a secondary air-supply or overdraft for admitting heated air just at the surface of the fire in order to produce a more perfect combustion of the volatile combustible gases which are liberated from this fuel immediately after firing. This overdraft should be under positive con- trol so that it may be checked or closed after the fuel has been coked. Soft coal may also be burned efficiently in the underf eed-type of furnace in which coal is fed from below by means of a plunger operating in a feed-chute discharging through the center of the grate. The furnace should be located in the basement in an approximately central position with reference to the rooms to be heated, and preferably toward the side or sides from which the prevailing winds blow in the winter-time. This arrangement not only favors the more exposed rooms on the floors above by shortening the leaders to these rooms, but also makes it possible to reduce the length of the cold-air duct, which should always be run from the exposed side of the building to the cold-air pit below the furnace. (Figs. 53 and 54.) In operation cold air is drawn from the outside through the cold-air DUCT, passed through the space between the heater and its jacket, and warmed by coming in contact with the outside heated surface of the combustion-chamber and the radiator, which is usualUy just above the combustion-chamber. It is Furnace-Heating 1311 then discharged through flues connected at the top of the jacket, Ftfki^AGE-GAi, or BONNET to the rooms to be warmed. Collar' Fig. 47. Warm-air Furnace with Galvanized Sheet Steel Jacket Leaders and Stacks. These connecting flues are made up of two sections, (i) the nearly horizontal round pipes in the basement, known as leaders (Figs. 48 and 49), which connect to the collars on the top or conical sides of the r Piping-Plan. AH Collars lined from Center of Furnace Same Piping-PIan. As for Fig.48. All Collarfl lined from Regl8t«r-0utleta Tig. 48. Warm-air Furnace-leaders with Fig. 49. Elbows Warm-air Furnace-leaders with- out Elbows bonnet, and (2) the vertical rectangular pipes called stacks (Fig. 50), which connect the boot at the outer end of the leader, with the double- walled register- box (Fig. 51) into which the register-grille covering the opening into the room, is fitted. The leaders should have an upward pitch toward the base of the 1312 Heating and Ventilation of Buildings Parts stack of at least i in per foot, and for the best results they should not be more than from 1 2 to 15 ft in length. The boots are made in a great variety of shapes to suit actual conditions, and are simply adapters for the purpose of changing from round leaders to rect- angular stacks. The stacks are usually run between the studding of interior walls or partitions (Figs. 50 and 51), since if they are placed in outside walls the cooling effect reduces their efficiency not only in temperature of air, but also in velocity of flow. The METAI, used for leaders and stacks is usually bright Ai^ wm m r ' p7tr:''y/r)iMm ■^tr2iz:j^^_'rT'";'Wt±iq IX tin, although for leaders 1 Iflll " llll I P | ||== larger than 12 in, galvanized \ P -^ II I I j f li — st^^^ o^ N^- 26 United States llinilil Standard gauge is usually employed. The covering of all leaders, boots and stacks, as well as the furnace itself, is mast important, and either a heavy grade of asbestos paper is pasted on the outside, or, as in the case of leaders .and the furnace itself, asbestos air-cell covering, about %'in thick may be used and secured with brass bands or wire. Since the stacks must run, generally, in a 4-in studding- space, with a net depth of about z% in, every effort must be made to keep them as deep as possible; and steel lathing or expanded metal should be used in front of all such stacks, which ordinarily have only a single layer of asbestos-paper covering. A more effective insulation may be provided by using a double-wall stack, in which there is an air-space between the inside and outside pipes, and no asbestos covering is used. See Table XLII for this equipment, as made by the Excelsior Steel Furnace Company. Attention of the architect is here called to the fact that in the case of large second-floor rooms to be warmed by one register, 6-in stud partitions are generally required for the first floor. Fig. 50. Vertical Stack with Side-wall Register The Design of a Burnace Heating System. Heat-Loss and Air Required. Tlie determination of the size of the furnace, and the connecting leaders, stacks, registers, ducts, etc., is based on: (i) The actual heat-loss from each room in the biiilding, including wall and glass-trans- mission losses, as wefl as loss due to infiltration; and (2) the amount of air to be circulated per hour, wliich in turn is based on this heat-loss, A building is The Design of a Furnace-Heating System 1313 warmed or heated by hot air by introducing the air into the rooms at a higher temperature than that required to be maintained in the rooms at the breathing- line (approximately 70° F.) The air in cooling gives up per pound, 0.24 Btii (specific heat of air at con- stant pressure) for each degree drop in tempera- ture, and in this way sup- plies the iveat necessary to offset the heat-transmis- sion of the walls, etc., and at the same time provides a supply of fresh air for ventilation. The maxi- mum temperature of the air leaving the heater-cap is approximately 190° F., and it leaves the registers at 175° F., allowing a drop in temperature of 15° be- tween the furnace-bonnet and the registers. These figures are maximum values not to be exceeded, outside temperature is 1 Fig. 51, Vertical Stack and Register-box If the air is all drawn from the outside, and the °, then the air is heated from 0° to 190°, and cooled, in entering the room, from 175° to 70°, or 105°. In other words, 0.24 Xios or 25 Btu is apparently thrown away, for every pound of air circulated. If all the air must be brought in from the outside in order to supply a sufficient amount for ventilation, then this is the price which must be paid for ventilation, and it would be the same, no matter what system of heating is employed, for equally good ventilation. It is almost invariably the case, however, that a con- siderable portion of the air may, if desired, be recirculated, in which event, for equal ventilation effect, the furnace system of heating requires no more expendi- ture of heat in the form of fuel burned than a direct steam or hot- water system, and is therefore just as economical to operate when correctly designed, installed and operated. The head producing the flow or circulation is due to the differ- ence in weight between the ascending column of heated air and the weight of an imaginary column of the colder intake air. The system may be proportioned for recirculating all of the air during the extreme cold weather. Weight of Air to be Circulated per Hour. It is first necessary to deter- mine the weight of air required per hour which must be suppUed to each room. Let W = pounds of air to be circulated per hour; / = inside temperature to be maintained; td = temperature of air leaving the registers (assumed 15" lower than the temperature leaving the furnace-cap or bonnet); H = Btu to be supplied to room per hour as determined by heat-loss calculations; 0.24 (Jd — "= Btu given up per pound of air circulated. Then W = U/[o.2^{td - t)]. The maximum value for td is 175° F., and t = 70° F. Then W =H/2S', d = density of air, entering at temperature 175° =.063; Q = cubic feet of warm air entering room per hour = PF/.063 = H/1.5S, 1314 Heating and Ventilation of Buildings Parts Heat Required from Heater per Hour, Based on Recirculation. The heat required per hour from the heater will depend on the temperature of the entering air and will be a maximum when all the air circulated is taken from the outside and a minimum when all of the air is recirculated. Let h =Btu required from heater per hour; te = temperature of dr entering heater = 65°; tji te temperature of air leaving heater = 190°. Then h = 0.24 W{ih - h)^ Substituting the values given above for W, tn, and te, h = 1.2 //. Size of Furnace. The capacity of a furnace for heating air depends primarily upon the amount of coal that may be burned per hour, which is the product of the RATE OF COMBUSTION by the grate-area. With an assumed or fixed rate of combustion, the capacity of the furnace is dependent upon the grate-area. The grate-area is therefore used as a basis for the rating and comparison of warm-air furnaces. The average rate of combustion usual in furnace-heating ranges from 3 to 4 lb per sq ft of grate-surface per hour, but in zero weather this rate may run as high as 6 lb, and is readily obtainable with the ordinary height of residence-chimney; that is, at least 35 ft. A properly designed furnace will have a combined furnace and grate-efficiency of from 55 to 60%. Higher effi- ciencies have been obtained in tests. Commercial Ratings of Furnaces. Manufacturers rate their furnaces according to the amount of space, cubical contents, in the ordinary residence- construction they will heat to 70° F. in zero weather. Maximum temperature of air leaving registers = 175° F. The detailed dimension and capacity-data, other than grate-area and space heated, of most furnaces are seldom published by the manufacturer, although there are a few notable exceptions. The actual size of the furnace naturally depends upon the heat-transmission of the walls, floors and roofs, plus the infiltration-losses, as already explained. The claim, however, is made that these "in turn bear a reasonably uniform relation to the cubical contents of the ordinary house," with the usual proportions and ratios of wall to glass-surface, and that therefore the rating, as given, is justifiable. Tables XXXVH and XXXVHI were taken from the Warm Air Furnace Hand- Table XXXVII. Capacity of Warm-Air Furnaces of Ordinary Construction in Cubic Feet of Space Heated Divided space in cubic feet Fire-pot Undivided space in cubic feet -f 10° 0° — 10° Diam- eter, in Area, sq ft H-io'' 0° —10° 12 000 10 000 8 000 18 1.8 17 000 14 000 12 000 14000 12 000 10 OOQ 20 2.2 22 000 17 000 14 000 17 000 14000 12 000 22 2.6 26000 22 000 17 000 22 000 18 000 14 000 24 3.1 30 000 26 000 22 000 26 000 30 000 22 000 26 000 18 000 22 000 26 28 3.7 4.3 35 000 40 000 30 000 35 000 26 000 30 000 35 000 30 000 26 000 30 4-9 SO 000 40 000 35 000 The Design of a Furnace-Heating System Table XXXVIII. Air-Heating Capacity of Warm-Air Furnaces 1315 Fire-pot Casing * Total cross- sectional area of heat- pipes, a, sq in Number and size of heat- pipes that may be supplied Diameter, in Area, sq ft Diameter, in i8 20 22 24 26 28 30 1.8 2.2 2.6 3.1 3-7 4-3 30-32 34-36 36-40 40-44 44-50 48-56 180 280 360 470 565 650 730 3-9" or 4-8" f 2-10 and 2-9" \ 2-9" and 2-8" 1 3- 10" and 2-9" I 4-9" and 2-8" r3-io" and 1-9" I 2-10" and 5-8" f 5-10", 3-9" 1 3-10", 4-9" and 2-8" f 2-1 2", 3-10" and 3-9" I 5-10", 3-9" and 2-8" f 3- 1 2", 3-10" and 3-8" \ 5-10", 5-9" and 1-8" 4.9 52-60 * The casing-diameter should be such that the minimum cross-sectional area M, between casing and radiator, will be at least 20% greater than the total cross-sectional ^rea of all the heat-pipes, a,ox M = 1.2 X a sq in. book, published by the Federal Furnace League, an association of United States furntace-manufacturers. This association is no longer in existence. If the majority of the basement or leader-pipes exceed 12 ft in length or have less than 1 in rise to the foot, or if more than one sixth of the outside surface of the building is glass, then the furnace should be increased one or more sizes. The size of the furnace required can also be determined by the combined area of the cross- sections of the warm-air pipes. Furnace-Rating Based on Efficiency and Rate of Combustion. The Btu per hour that a furnace is capable of imparting to the air (not the room) may also be estimated from the grate-area by assuming that the average coal used will contain approximately 12 000 Btu per lb. A combined furnace-and- grate efl&ciency of 55%, and a maximum c©mbustion-rate of 6 lb per sq ft of grate per hour for maximum conditions (coldest weather) are also usually assumed. Grate-Surface Required, Based on Recirculation. The area of the grate is readily calculated as soon as the heat to be supplied to the building per hour has been determined. H = Btu to be supplied building per hour; h = Btu required from furnace per hour for heating the air = .12 H; C = heating value Btu of coal per lb; E = combined furnace-and-grate efficiency; R = rate of combustion, pounds of coal per square foot of grate-surf^-ce per hr; G = grate-area in square feet; h =G XC XE XR =i.2n. Then h = area of grate in square feet X 12 000 X 0.5 5 X 5-5 = 36 300 X G, which is Btu transmitted to the air passing the fur- nace; G = (1.2 X^)/36 300. J 316 Heating and Ventilation of Buildings Parts Measurements of galv. casings and tops, series A. B. C. .5 ::^ :^ :^ m O fO O O CN IT) M O BSSBSSS OOO lotoo >r> 00 lo to r- t^ ti:i t^ « ro '^ iOvD 00 a^ 1 u 3 0) rt ^ c^ c rno cr> N cs«n cnoo m c«« w lA M M M rc -^ c Tro wo o be »-< l|R P. TfvD 00 ►-• fO «n O^ O O O O O O O +J 4J +J +J 4J 4J -U CO -"tvO C7>0 M T^ H M M ?i o SI •-5 0.52 c fO CO -^-^tO lO VD Is ■i'S 02 •^'noo M "d-r- O M M M (N M M fO ^ 0) Oj M M M N <>» N ro The Design of a Furnace-Heating System 1317 The usual assumptions, with anthracite fuel are: j C = 12 ooo Btu per lb; ^ 2? = 4 lb ordinary rate and 5.5 lb for maximum conditions in coldest weather; £=0.55; Then G = h/{i2 000 X 5-5 X 0.55) = h/s6 300 = i. 2/7/36 300. Size of Leaders and Stacks. The area of the air-pipes (leaders and stacks) required for a room depends upon the quantity of air to be indroduced per min- ute and the velocity with which the air will flow with natural circulation. Q/60 = cubic feet of warm air to be introduced into the room per minute; V = velocity of air in feet per minute attainable; H = heat-loss of room; A = area of pipe in square feet; Q/60 == AV, and substituting value of ^ = H/1.5S; A =H/(95XV). The following velocities are approximately obtained in the leaders and stacks for the floors as stated: First floor, 175 ft per min; Second floor, 240 ft per min; Third floor, 310 ft per min. The above velocities have been observed in practice in well-designed systems. Then for various floors, substituting in the above equation, in square inches: Ai = ///115 for first-floor pipes, leaders and stacks; A2 = H/160 for second-floor pipes, leaders and stacks; An = H/206 for third-floor pipes, leaders and stacks. See Bulletin No. 112, Engineering Experiment Station, University of Illinois, 1919- Actual leader and stack-sizes are based on the above areas, using the nearest half-inch for leader the diameter (Table XL), and keeping the stacks of such proportions that the cross-sectional dimensions are never in a greater ratio than 3 to I . For example, a stack 4 by 20 in is seldom effective over its full area, as it is too narrow, and as its large rubbing-surface causes excessive friction. The actual velocities obtained, however, will depend upon the head or pressure causing the flow and the friction-head, and will seldom exceed 50% of the theoret- ical velocities. Table XL has been recommended by the Federal Furnace League and gives the sizes of round pipe for leaders, the size of wall-pipe for stacks, and free areas of registers to connect with same. Leaders over 12 ft in length should be increased i in in diameter for each 5 ft beyond 12 ft. Registers. The free area through the ordinary register-grille is only ap- proximately 55% of the gross area, and consequently a register must be selected that has a gross area of double the area of the pipe with which it connects, in order that the air-passage may not be contracted and the capacity reduced. Commercial register-sizes are based on the actual inside dimensions of the grilled opening and are made either of pressed steel or cast iron, with a variety of fancy or plain grilles. The plain rectangular grille is to be preferred, finished to suit the decorative scheme, in black japan or electro-plated in brass, bronze or copper finish. Warm-air registers may be placed in the floor, but preferably in inside partitions, for first-floor rooms. By using the modern base-board REGISTER, Fig. 52, it is usually possible to secure the required capacity without 1318 Heating and Ventilation of Buildings Part 3 Table XL. Capacities and Dimensions of Warm-Air Piping and Registers Diameter of round cellar Proper size of rectangular Area of riser-pipe. Required area of register-face, or riser-pipe, riser-pipe, in* in* sq in sq in * 6 3 X 9H 28 52 6M 3H X 9H 33 62 7 3M X II 38 72 iVi ZVl X I2M 44 84 8 3H X 14 50 96 8M 4 Xi4 57 108 9 4 X i6 64 120 9H 4 X i8 71 134 10 4 X 20 78 142 10 H 6 X iaYi 86 158 II 6 X i6 95 176 11^ 6 XI7H 104 194 12 6 X 19 113 204 12^ 6 X 2oH 122 222 13 6 X 22 132 242 13 H 8 Xi8 143 254 14 8 X 19 154 276 14 H 8 X20^ i6s 298 15 8 X 22 176 320 i6 8 X 25 201 358 17 10 X22H 227 410 i8 10 X25 3^ 254 450 19 12 X233^ 283 508 20 12 X 26 314 554 21 12 y.2^yi 346 618 22 14 X 27 380 686 23 14 X29M 415 707 24 14 X 32 452 770 * When the required size of pipe falls on the odd half -inch (as 7H, 8H, 9H, etc.), the size may be increased to the even inch (as 8 instead of 7H, 9 instead of 8.1^, etc.), for the first-floor rooms and bath-rooms; provided that the pipes for upper-floor rooms, other than bath-rooms, be decreased by Vi in when the required sizes fall on the odd half-inch. It is better, however, to use pipes of the sizes given in the above table, with proper allowances for length of pipe, extra bends, etc., beyond straight runs 12 ft long. resorting to floor-registers. These base-board registers can be connected to a flue from 3 to 4 H in deeper than the studding. This has been accomplished by making the special base-board register so that it projects 2 in into the room at the floor-line, necessitating the cutting out of the floor, and also utilizing the space of about i in occupied by the lath and plaster, or a total increase in depth of flue of about 3 in. For upper-floor rooms registers should be placed in inside partition walls, using convex registers for shallow stacks. As a general rule warm-air registers should be so placed as to shorten leader and stack-connections as much as possible. The use of a floor-register may be permitted in an entrance- hall for drying shoes and garments, but it is unsanitary and cannot fail to collect dirt and filth of all kinds. In case such registers are used, however, suitable REGISTER-BOXES must be provided, and they are preferably constructed with double walls. Example in Furnace- Heating. A gravity furnace-heating system is to be designed for the two-story frame building shown in Fig. 55, with inside and out- The Design of a Furnace-Heating System 1319 Base-board Register used on First Floor takes the supply from a Flue? in. Deep or 3 in. Deeper than Studding COLD-AIR DUCTS Fig. 53. Cold-aid Ducts for Warm-air Furnaces FRESH - AIR ROOM WITH DUST-COLLECTOR 1320 Heating and Ventilation of Buildings Parts Table XLI. Table of Sizes of Floor-Registers, Base-Board Registers and Register-Boxes Size of Size of register-box Size of Size of Size of Size of register- box to Size of base-board to base- board base-board register round cellar- round floor- rectangular floor- base-board where studs register where studs register where there is no limit to depth of where there is no limit pipe, register. register. are not more than are not more than to depth of register- 4 in deep, 4 in deep, register- box, box. in in in in in in in 6 9 8X8 2% Xio 7 X 10 2H X 10 7 X 10 6H 9 8X8 3M X 10 7 X 10 SH Xio 7 X 10 7 10 8 X 10 ZH X 10 7 X 10 3M X 10 7 X 10 7^ 12 8 X 12 4H X 10 7 X 10 4H X 10 7 X 10 8 12 8 X 12 4H X 12 7 X 12 4H X 12 7 X 12 8H 12 9 X 12 4H X 12 7 X 12 4H X 12 7 X 12 9 14 10 X 12 S X 13 8 X 13 5 X 13 8 X 13 9H 10 14 14 10 X 14 10 X i6 6 X 12 6^^ X 12 10 X 12 6 X 12 10 X 12 10 X 12 10 X 12 6H X 12 loH i6 10 X i6 ey2 X 13 ^0 X 13 ey2 X 13 10 X 13 II i6 12 X IS 6M Xi4 12 X 14 en X 14 12 X 14 iiM i6 12 X i8 7 X IS 12 X IS 7M X 14 12 X 14 12 i8 12 X 20 6H X i8 12 X i8 7H X IS 12 X IS I2H i8 14 X i6 6^ X i8 12 X i8 eu X i8 12 X i8 13 i8 14 X i8 7H X i8 12 X i8 13 J^ i8 14 X 20 8 X i8 12 X i8 Table XLII. Dimensions of Excelsior Double Wall-Pipe Excelsior Steel Furnace Company Number Measurements Area of stack, sqMn Nominal, in Inside, in Outside, in 4 6 7 8 9 12 . 14 3 Xio 3 Xi2 4 Xii 2HXI0 lHXl2 i Xio 5 X12 X13 X12 HX13 3 XioH 3 Xi2ys 3^X10^ 3^Xi2H 3^Xi3H S^^Xi2H 6KX13H 24 28H 30 36 39 60 72 4 Xi3 4 Xi4 6 Xi3 6HXI4 5 Number Collar-diameter, in Area of collar, sq in Register-size, convex or wafer, sq in 4 6 7 8 9 12 14 7 8 and 9 8 and 9 8, 9 and 10 9 and 10 9 and 10 10 and 12 39 SI and 63 61 and 53 SI and 78H 63 and 78 H 63 and 78 M 78H 6X8— SXio 8X10— 0X12 8X10— 9X12 8 Xio— 10X14 10X12— 10X14 10 X12 — 10X14 10X14 — 12X14 The Design of a Furnace-Heating System 1321 side temperatures of 70° and 0° F. respectively, and the air all recirculated in zero weather. Transmission and infiltration-losses are as computed in Table Fig. 55. Furnace-heating Layout. (See data in Table XL VI) XL VI, which 'also gives the size of heat-pipes, leaders and stacks, and register- sizes. Size of Furnace and Grate. The size of the furnace is calculated on the assumption that all the air is taken from the outside. The total calculated heat- loss from building per hour is 124 558 Btu. which, multiplied bj^ 1.2, and divided 1322 Heating and Ventilation of Buildings Table XLIII. Dimensions of Excelsior Single Furaace-Pipe Excelsior Steel Furnace Company Parts Measurement Size of boot- Capacity of Capacity of in inches collars, diameter, collars, pipe, in sq m sq m 3 Xio 8 51 30 3HX10 8 SI 35 3 X12 8 and 9 51 and 63 36 3HX12 9 63 42 3MX13 9 and 10 63 and 78 45 SMX12 10 78 66 SHX14 12 114 77 sJ^xie 12 and 14 114 and 154 88 7HX16 14 154 112 Note. Stacks sH in deep, made to order only. With frictionless boots, collars in same can be made with a diameter equal to width of stack. Collars 11 in in diameter furnished when so ordered. -> Table XLIV. Capacities and Dimensions of Fresh-Air Ducts, Rooms, Etc. Size of hori- Size of hori- Cross-section area of hori- zontal portion of fresh-air duct. Size of fresh- air-room ; Size of fresh- air intake zontal portion zontal portion •length and (area of of rectangular fresh-air duct. of round fresh- air duct. width (height same as depth of cellar). woven-wire netting, not including frame) , in in in in in 8X18 1-14 144 18 X48 12X16 8X21 1-15 168 21X48 14X16 8X24 1-16 192 24X48 16X16 10X21 1-16 210 21 X60 14X20 10X24 1-18 240 24X60 16X20 10X27 2-13 270 27X60 18X20 10X30 2-14 300 30X60 20X20 12X27 2-14 324 27X72 18X24 12X30 2-15 360 30X72 20X24 12X33 2-16 396 33X72 22X24 12X36 2-17 432 36X72 24X24 12X39 2-17 468 39X72 24X26 14X36 2-18 504 36X84 24X28 14X39 2-19 546 39X84 26X28 14X42 2-19 588 42X84 28X28 14X45 2-20 630 45X84 28X30 14X48 2-21 672 48X84 28X32 14X51 2-21 714 51X84 28X34 16X48 2-22 768 48X96 32X32 16X51 2-23 816 51X96 32X34'' 16X54 2-24 864 54X96 32X36 16X57 2-24 912 57X96 32X38 16X60 2-25 960 60X96 32X40 The Design of a Furnace-Heating Surface 1323 Table XLV. Sizes and Capacities of Wooden Register-Faces for Cold-Air Ducts Nearest size Nearest size Size Net area of air-space, of round pipe of equivalent area, Size, Net area of air-space. of round pipe of equivalent area. sq m m in sq in in 12X20 135 12 24X24 323 20 12X24 161 14 24X26 349 20 12 X30 202 16 24X30 403 ■ 22 , 14X20 157 14 28X28 439 22 14X26 203 16 30X30 504 26 16X20 179 14 36X20 403 22 16X24 215 16 36X24 484 24 16X30 269 18 36X30 60s 28 18X24 242 18 36X36 72s 30 18X30 303 20 72X18 726 ■ 20X20 20 X24 224 269 16 18 72X20 72 X24 806 968 20X26 291 18 72X30 I 210 20 X30 336 20 72 X36 I 450 Table XL VI. Furnace-Heating Example (See Fig. 65) First floor Parlor Hall Dining- room Library Kitchen Cubic feet Heat-loss, H, in Btu per hour. . . . Area of heat-pipe, H ■ sq in 115 Diameter of leader in inches Size of register in inches 2 280 14855 127 13 12X18 2 170 13 400 116 12 12X18 2 400 II 655 lOI II 12X15 2 280 II S15 100 11 12X1S 3 600 II 127 96 II 12X1S Heat-loss of kitchen is based on kitchen- . range ' supplying one^half the required amount. Second floor Chamber No. I Chamber No. 2 Chamber No. 3 Chamber No. 4 Chamber No. 5 Bath- room Contents in cubic feet 2 052 14 370 89 loH 5^X16 12 X14 I 458 12 000 75 10 SHX14 10X13 I 746 10 413 65 9 53^X12 10X12 I 206 9 070 56 9 5HX12 9X12 I 242 10 883 68 9 5HX12 10X12 5,6 5 400 34 8 5 H X.IO 10X12 Heat-loss in Btu per hour. . Area of heat-pipe, // 160 Diameter of leader in inches Stack, in inches . . . Size of register in inches *. . . . The net area of register-faces is assumed to be 55% of the gross area. The gross area equals 1.8 times the area of the leader-pipe. 1324 Heating and Ventilation of Buildings Part ^ by 36 300, the heat available from 1 sq ft of grate when burning 5.5 lb of coal, of 12 000 Btu heat-value per pound, at 55% efficiency, gives 4.1 sq ft as the grate-area. This will require a grate of 28-in diameter. This building has a net volume of 26 000 cu ft, and by reference to Table XXXVII it is seen that a 28-in grate is recommended for this amount of divided space. The furnace, in this problem, has been located practically in the center of the house, but on the north side of its east and west axis, giving a direct cold-air connection from the north wall and short direct runs for most of the leaders. Leader-Layout. The leaders may be laid off. as shown in Fig. 55 and in Fig. 48, by dividing up the circumference of the bonnet into areas proportional to the amount of air to be distributed by each leader, and then connecting collar and leader radially to furnace-cap, making one or more elbows in the leader, if necessary to connect with stack. Another method is to run practically all leaders direct from furnace to foot of stack (Fig. 49) and cut the collars in on the angles at which they intersect the casing. The former method is recommended, and requires less skill in installation. The basement heating-plan is shown on the first-floor plan, which also shows all stack-sizes to both floors. Floor- registers have been shown on the first-floor plan in order to simplify the layout and make the plan clearer. In general, base-board registers are to be preferred. The sum of the areas of leader-pipes is 927 sq in. Hot-Blast Heating General Features. The mechanical indirect method of heating, commonly known as the blower system or hot-blast system, particularly adapted to the warming and ventilating of large structures, is made up of three units: (i) A heater constructed of pipes, tubes, or cast-iron sections, through which steam, hot water or hot gas may be passed. (2) A fan or blower to circulate air over the heater-surfaces, the air acting as a heat-carrier or medium of heat- transfer. (3) A system of ducts or pipes to convey the heated air from the heater to points where heat may be required. When the heater is located between the fan and main duct, the combination is termed blow-through, and when the fan is installed between the heater and the duct, the arrangement is known as draw-through. These two arrangements are shown in Fig. 57. The draw- through combination is more often used for shop and factory-installations where compactness is desirable, the blow-through combination being used principally for hot-and-cold systems as installed in schools and public buildings. ^" Advantages of the Blower or Hot-Blast System. The advantages of the blower or hot-blast system over those of direct radiation, briefly summarized, are: • (i) When ventilation is a requirement in order to maintain a healthful atmos- phere, this method affords a positive means of accomplishing this particularly desirable result, which is entirely independent of the changing climatic con- ditions. (2) When a standard humidity of the air is to be maintained, a feature which is becoming to be more generally recognized as desirable in any heating-and- ventilating installation, and quite essential to the successful manufacture of some materials, the humidifying-apparatus may readily be made an integral part of the system. (3) A much smaller amount of radiating-surface is required to perform an equal heating-duty, with a consequent reduction in the number of steam-tight joints, unions and valves to keep in repair. (4) The air-leakage being mostly outward, the building will in general be freer Hot-Blast Heating 1325 from drafts and more uniformly heated. If the air is simply recirculated, no fresh air being taken into the heating system from the outside, the above state- ment does not apply. The pressure of the air in the building, even when all of the air is taken into the heating system from the outside, is comparatively feeble, and some air will enter by infiltration through the window and door-cracks on the windward side of the building, although the statement is often made that the leakage being all outward, prevents the infiltration of cold air from the outside. (5) This system is more easily regulated, and readily responds to changing outside temperatures. (6) The air entering for ventilation may be conveniently cooled in summer, either by the circulation through the heater of cold water or of brine previously cooled by mechanical refrigeration, (7) Simply running the fan will in itself greatly relieve the oppressiveness in hot sultry weather, and when cold water is circulated through the coils the difference is very noticeable. Typical Arrangements. When ventilation is not a requirement, or when it is relatively unimportant, as is frequently the case in shop or factory-heating where the number of persons vitiating the air is small compared with the cubical con- tents of the building, the air may be simply recirculated, sufficient fresh air for ventilation being supplied l:)y infiltration. The amount of heat to be sup- pUed the heater in this case is the same as would be required for a direct-radiation installation. When ventilation is a requirement to be met a cold-air intake is provided. Since the amount of air necessar}'' for heating is generally in excess of the amount required for ventilation considerable economy may be effected by recirculating a portion of the air. In this case only sufficient fresh air is drawn into the system from the outside to meet the ventilation requirement and the remainder of the air necessary for heating, is recirculated. This may be readily effected by an arrangement of ducts and dampers on the suction-side of the fan. If the fresh air introduced is to be washed or conditioned the washer or humid- ifier and tempering-coil may be added between the inlet for the recirculated air and the fresh-air intake. Amount of Air to be Circulated for Heating. The weight of air to be cir- culated per hour for heating a room or building is found by dividing the heat- loss (//) by the amounts of heat given up by i lb of air in cooling from the tem- perature at the duct-outlets to the mean room-temperature. Let // = heat-loss of room, Btu per hr; M = weight of air to be introduced in room per hour; / = mean inside temperature; td = temperature of air leaving duct-outlets. • Then M = II/[o.24(ta - t)] The temperature fd depends upon the temperature of the air entering the heater, the velocity through the clear area, the amount of heating-surface and the temperature of the steam. This temperature in practice ordinarily ranges from 125° to 150° F. and may be readily determined for any specified condition by the data given later under Hot-Blast Heaters. The temperature of the air leaving the duct-outlets for ordinary installations, when the ducts are not run underground or in outside walls, may be assumed to be the same as the tempera- ture (h) of the air leaving the heater. Any loss in temperature in this case goes toward heating the building and is therefore not a direct loss. If, how- ever, the ducts are run underground or in outside walls, a considerable loss in 1326 Heating and Ventilation of Buildings Part 3 temperature may occur, which is a direct loss, and must be provided for by INCREASING THE TEMPERATURE OF THE AIR LEAVING THE HEATER by an amount equal to the estimated temperature-drop in the ducts. Temperature of Air Entering Heater. Let h = temperature of air entering heater; /2 = outside temperature; t = mean inside temperature; tz — temperature of air leaving heater; («) When the air is all recirculated, k = t; ' {h) When fresh air only is circulated, h = to] (c) W^hen a ix)rtion of the air is recirculated the resulting temperature of the mixture of fresh and recirculated air may be found by the method of mixtures. Let Mv = weight of fresh air, pounds required per hour for ventilation (30 cu ft per min per person) ; = 0.075 X I 800 X number of persons (usual requirements); Mr = weight of air that may be recirculated; M =Mv -{-Mt H = 0.24 {Mt + Mr) {td - /). Having assumed or fixed the value of tdt the only unknown quantity is Mr. Jl/r-///[o.24(/rf -0] -Mv The temperature h may then be found as follows: Mv X {to + 460) = A Mr X{t -\- 460) = B {Mv + Mr) {h + 460) = A i-B or ^ r\ V ^5^ A \ \ \ \\ \\ \ \5 s^ ^\ ^ ^ \\ V^ J\ ^\ \ % \ ^\ ^ A^ ^ ^ V ^ \ \ K^ "0 SrV ^ ^ ^ ^ vV ^ ^ \ \ ^ \x A — ^ K % W ^ V -^^ ^*^ '\^\ ^ -^^^^^ s^. ^^v ^ - '^ ^^^ Vo: \ v^ '^&. .Al ^ \^ S^"^^ V'Ss'* Vv ^ v^ K^VN "•^ ^ 5^ ^^^^ vV^ ^ V ^ ^ ^ \ , %r^ ^Yv^ VV ^' \ \^ C^' ^ rv \ ^ 1^^ w ;/ \ a ^ z^\^^ ^ C^ ^ ^ \ ^ \'^ ^ ^ A^ K \- v; V r^ w\ x^ :^ ^ ^ X '"'j^ ^ V^ << \ ^ ^ w - ^^ ^ X' ■^ \ ^-\ Y.,^ v^ Ve ^"^ V v-V^ ^^ ^ \ Jl'^ \ \.^'^\ t^s^^ \ r V'N \ rV^ y^ ^ 3c^ \ vr* v^'^^ > \ V \r^^ y^ ^ V UV^i^ c \ ^ \ ^ .^' ^ ^ ^ ^ v^ V \ \ vA' n " ^ ^ \\ \ \ c\ \^ %<^ \ ^ \ r. ^ ^ V \\^ V ^ \ 3^ V^ n^ :^ ^ ^ ^ > \\l \ ^ \ \ V ■.^ L/ , ^ ^ ^ '\^ \ V X ^ ^V ^ ^ ^ ■^ -^ ^ ^ w\ ^ ^ A * 'A Diameter of Tipe Fig. 63. Diagram of Friction-pressure Loss Design of Air-Ducts 1335 DIAMETER OF A ROUND DUCT for various velocitics, and the pressure-loss or RESISTANCE foF various quantities of air flowing, may be found without solving the above equation. Cubic Feet of Air per Minute, Q ||.§8§§ i§ §§8S8g go 2 Diameter of Pipe Fig. 64. Diagram of Friction-pressure Loss Example. What should be the size of a round duct required to convey i 500 cu ft of air per minute with a velocity of i 800 ft per min; and what is the pres- sure-Joss per 100 ft of duct. 1336 Heating and Ventilation of Buildings Parts Solution. Locate i 500 on the upper side of the pipe-diagram in Fig. 64, and pass horizontally downward until the i 800-ft-velocity diagonal line is inter- sected. The duct which comes nearest to the required size has a diameter of 12 in. At this intersection pass to the right side to the base-hne and read 0.48- in water-pressure loss. Allowable Velocity of Air in Ducts and Flues. In order to limit the resist- ance or pressure-loss in the duct system the designer should, in general, keep the velocities within the Umits stated in Table LII. In pubHc-building work the air should be delivered to a room at a velocity that will insure its movement to the desired points in the room without objectionable draft or noise in passing through the register-grills. Table LIT. Allowable Velocities in Hot-Blast Systems 4 Types of buildings Allowable velocity in feet per minute Public buildings Throuffh free area of wall-registers . . 400- 500 200- 300 600- 750 800-1 000 I 500-2 500 I 200-1 500 600- 900 I 500-2 400 900-1 500 Through free area of floor-registers Vertical flues to registers Connections to base of flues. . . . Main horizontal distributing ducts Manufacturing plants In plants where the occupation is more or less sedentary and the employe sits -ell day feeding automatic machinery: Main ducts '. Branches In plants where the employe stands all day, as in machine- shops, foundries, etc.: Branches The velocity through the fan-outlet, under the ordinary conditions that obtain in heating work, varies from i 500 to 2 500 ft per min. Table LIU. Metal Gauges for Ducts American Blower Company Heating and ventilating Thickness and weight Blowpiping and exhaust work « Diameter in inches United States standard gauge- number Thickness in inches and weight in pounds per square foot Diameter in inches United States stanaard gauge- number 6-18 19-36 38-48 SO-60 63-72 26 24 22 20 18 in lb per sq ft 0.1087 0.91 0.025 i.i6 0.0312 I. 41 0.0375 1-66 0.05 2.16 3- 5 6- 8 y-15 16-24 26-30 26 24 22 20 18 Design of Air-Ducts 1337 Sheet-Metal Pipes and Ducts. The recommended gauge (United States sheet-metal gauge) for various sizes of galvanized sheet-steel pipes for heating and ventilating work, blowpiping and exhaust work, is given in Table LIII. Pressure-Loss of Rectangular Ducts. The simplest method of determining this is to. proportion the system for round ducts throughout, and then transfer to RECTANGULAR SIZES giving equal pressure-losses (not equal areas) by means of Table LIV. Table LIV. Round and Rectangular Ducts of Equal Pressure-Losses Side of rectangular duct in inches 4 6 8 10 12 14 15 16 18 20 22 24 Equivalent diameters in inches 4 5 6 7 8 9 10 II 12 13 14 15 i6 17 I8 19 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 6o 62 64 66 68 4-4 4-9 5-4 5.8 6.1 6.5 6.8 7.1 7.4 7.6 7.6 8.2 8.4 8.6 8.9 9-1 9-3 9.7 10. 10.4 10.8 II .0 II. 3 II. 6 II. 9 12.2 12.5 12.7 13.0 13. 3 13.5 13.7 13-9 14. 1 14-3 14.6 14-7 15.0 15. 1 15-3 IS. 5 6.6 7.0 7.6 8.0 8.4 8.8 9-2 9.6 9.9 10. 2 10. 5 10.8 11. I II. 4 11. 6 12. 1 12.6 13-1 13.5 13.9 14.3 147 15. 1 15.4 15.7 16. 1 16.4 16.7 17.0 17.3 17.6 17.9 18.2 18.4 18.7 19-0 19.2 19.5 19.7 8.8 9.3 9.8 10.2 10.7 II. I II. 5 II. 9 12.3 12.6 13.0 13.3 13.6 14.2 14.8 15.4 15.9 16.4 16.9 17.3 17.7 18.2 18.6 19.0 19.4 19.8 20.1 20.4 20.8 21. 1 21.5 21.8 22.1 22.4 22.7 23.0 23-3 II. II. 5 12.0 12.5 12.9 13.4 T^ 8 13.2 13.7 14-3 14.7 15.2 15.4 16.0 16.5 17.0 17.4 17.9 18.4 19.2 20.0 20.8 21.5 22.2 22.9 23.5 24.2 24.8 25.4 25.9 26.5 27.0 27.5 28.0 28.5 29.0 29-5 30.0 30.5 30.9 ^1.3 le^s 17. 1 17.6 18. 1 18.6 19.0 19-9 20.8 21.6 22.4 23.1 23.8 24.4 25.1 25.8 26.4 26.9 27.5 28.1 28.6 29.2 29.6 30.1 30.6 31. 1 31.6 32.1 32.6 33.0 33.4 17*6 18.2 18.7 19.2 19-7 20.6 21.5 22.3 23.1 23.9 24.6 26.3 26.0 26.7 27.3 27.9 28.5 29.1 29.6 30.3 30.7 31.2 31.7 32.2 32.7 33.2 33.7 34-2 34.7 19^8 20.4 20.9 21.9 22.8 23.8 24.6 25.4 26.2 26.9 27.7 28.4 29. 1 29.8 30.3 31.0 31.6 32.2 32.9 33.4 33.9 34-4 34-9 35.4 35.9 36.4 36.9 22.0 23.1 24.0 25.1 26.0 26.8 27.7 28. s 29-3 30.0 24.2 25.2 26.3 27.3 28.2 29.1 30.0 30.8 31.5 26.4 27.5 28.5 29.5 30.5 31.3 32.2 33.1 33.9 34.5 35.3 36.2 37.0 37.6 38.3 38.9 39-6 40.3 40.9 41.6 42.2 42.8 43.4 14.2 14.6 15.0 15.4 16. 1 16.8 17.3 18.0 18. 5 19. 1 19.6 20.1 20. 6 21. 1 21.6 22.0 22.4 22.8 23.2 23.6 24.0 24.4 24.7 25.1 25.5 25.9 26. 2 26. 5 15.7 16. 1 16. S 17.0 17.8 18.5 19.2 19.8 20.5 21. 1 21.6 22.2 22.8 2-3.3 23.8 24.3 24.8 25.2 25.7 26.2 26.6 27.0 27.4 27.8 28.2 23.6 31-4 31.2 32.8 33.4 34-1 34.7 35.3 35.9 36.4 37.1 37.7 38.2 38.7 39-2 32.4 33 33-7 34.6 35.2 35.9 36.5 37.2 37.8 38.4 39.1 39.6 40.2 40.8 41.4 29.0 29-4 31.7 33.1 1338 Heating and Ventilation of Buildings Parts Example. What is the width of a rectangular duct 6 in high equivalent to the pressure-loss for a duct 12-in in diameter? Solution. 22 in. Table LV. Friction Pressure-Loss of 90° Elbows Radius of throat in diam- eters of pipe M H % I iM 13-^ 2 3 4 5 Number of diameters of straight pipe of equiva- lent pressure-loss 67 30 16 10 7-5 6 4-3 4.8 5-2 5.8 Example. A duct 12 in in diameter and 120 ft long contains two 90° elbows. The ratio of the radius of throat to pipe-diameter is 3. The amount of air flow- ing is I 500 cu ft per min and the velocity i 800 ft per min. Solution. The total equivalent length of duct is 120 H- (2X4.8)= 129.6 ft The pressure-loss, from the diagram of Fig. 64 is 0.48 in per 100 ft. The loss is therefore 0.43 X (i 29.6/100) = 0.62 in of water The pressure-loss for square elbows is o.85z>2/2^ in of water for round pipes and i.2sv'^/2g for square pipes, v is the velocity in feet per second. The pressure- loss through register-grills may be taken at 0.023 in for a velocity of 400 ft per min through free area. The gross area of registers is twice the free area. The pressure-loss in air-washers and humidifiers for a velocity of 400 ft per min through free area is 0.15 in of water. The pressure-loss through hot-blast heaters may be taken from Table LVI. Table LVI. Friction of Air through Vento Heaters Friction-loss, in inches of water, due to air passing through Vento stacks. Regular sec- tion. Standard 5-in spacing of loops. Air-temperature 70° F. Velocity in feet per minute One Two Three Four Five Six Seven stack stacks stacks stacks stacks stacks stacks 800 0.037 0.070 0.103 0.135 0.167 0.200 0. 232 900 0.047 0.088 0.129 0.170 0.211 0.252 0.293 I 000 0.059 0, 109 0.160 0.211 0.262 0.313 0.364 I 100 0.071 0.132 0.193 0.255 0.316 0.377 0.438 I 200 0.084 0.IS7 0.230 0.303 0.376 0.449 0.522 I 300 0.099 0.18s 0.271 0.356 0.442 0.528 0.614 I 400 0.115 0.214 0.314 0.414 0.513 0.612 0.712 I 500 0. 132 0.246 0.360 0.474 0.588 0.702 0.816 I 600 0.150 0.280 0.410 0.540 0.670 0.800 0.930 I 700 0. 169 0.316 0.463 0.609 0.756 0.903 1.049 I 800 0.190 0.354 0.518 0.683 0.848 1. 012 1. 177 Effect of Temperature on Pressure-Losses. The preceding data on pres- sure-losses in ducts, registers and heaters are based on an air-temperature of 70°. Design of Air-Ducts 1339 For other temperatures, the pressure-losses are to be multiplied by the ratio, density of- air at actual temperature to density at 70**. These ratios are given in Table LVII. For heaters use the average temperature of the air passing through the heater. Table LVII. Ratios of Density of Air at Actual Temperature to Density at 70° F. Temperature Factor Temperature Factor 100 120 130 0.945 0*. 910 0.890 140 ISO 160 0.880 0.865 0.850 Design of Duct Systems. There are two schemes used in proportioning air-ducts: (i) the velocity method, and (2) the method of equal friction pres- sure-loss per foot of length. The first method involves the fixing of the veloci- ties (see Table LII) in the various sections, and the gradual reduction of the velocity from the beginning of duct to the point of discharge. In this case the pressure-loss is computed separately for each section having a different velocity and the various pressure-losses added together to obtain the total loss in pres- sure. The second method is used principally in the design of duct systems for factory- heating. The velocity in the outlet farthest from the fan is fixed and the area and diameter of this branch are determined by the volume of air to be delivered. The friction pressure-loss per 100 ft of a duct of this size is deter- mined by the diagrams in Figs. 63 and 64. The remainder of the main duct is then proportioned for this same pressure-loss per 100 ft. Example. The first method is illustrated in Fig. 65, showing a single-duct system. The risers are figured for a velocity of 600 ft per min, or 10 ft per sec; -16* < 13* i^'L^-^^ _ 39'. !''_]_ J I <— 20 - 5H- PLAN ' Fie. 69. Hot-blast HeatiriK for a Factory-buildinc. (See Example for Computations) 1344 * Heating and Ventilation of Buildings 1 ■ Parts c 000 0% 00 in . 00 "^ O MOO 00 lO • o ^ H M oo ^n VD r0»O t^ O M . M "^ O ^PO o r- t^ lO M . M ^ OVD M lO M ■ N i^ o oo 00 M M MOOO rt(NOO ID POM O 00 M • O POi- 1^00 lO l£> M • o - M O o »o cnM o PO w lo r^oo VO M • OOO t^ VO P^ M t- M • M '^ N :^ t^ o o O N ro O O M loa^M N (N ro O O Application of Hot-Blast Heating-Data O fOiO -^N i>»/^ fon W Tf M »o N 10 -^00 000 00 «0 ro -^ M . • 000 • t- • 0»£> • 10 • Tf • ro • (N • lO 10 M M « C^MM ^""s lO "^ KD t^ 00 o% N ^ u-> ^ ^ *^ M M O M lo ir> »o M^D 000 OOVO cr> OOO. rovO t^»o M fO Ooo r'-joc 10 I- • 10 • ^ • ro • ro • <^ ■ M . M • tT) Oi ■ lO M t- l^ M (N l> M^D 10 M M M<£) M N M 00 00 M 10 ^ M T- CO ^ ro ^ t ^ ^ -^ a. -^ r. "^ to >^ ^ •* •X> 00 a ro 10 ^ M O Tfio 000 10 M -^10 ino OVDOO a^ 00 - M M ro O 'OO W M 000 00^ w ro « i'^ OVO^O »o ioa> M Tt O'^ -t »0 00 r^ • ro • fO M C» 10 MVO • o • M M . t> M • M to a»M . M 10 ^"2 "+ M (N ^ *" o. 2* 00 ^ a. ^ 0. ^ M '^ ro ^ fO "^ 10 «X) 00 CT> ^^ H N 'O 10 00 - 000 ■ 000 • t^ • W w • 00 M • M 0% CT>M fO M Tt ■ " 00 ^ r- f, vo "^ VO "^ ^ ^ ro fO '^ .0 »o "^ 00 a. t^ n t~- "^ cr>M c^ 10 OOvD 000 i/»ro M 10 t>-PO -rt-u^ 10 M 00 100 10 cnro 10 cr.M 000 000 • t^ 10 t>. M invo . OVO • ro M ■ fO t-i • 00 ^o a% 00 t^ t^ M ro N KO ^ M ^ ^ ^ M "^ cr> ^ 10 ro ^ 2 CO ^ t^ "^ M m fO ^ ^ 10 VO i> *^ t>. 00 M QC l/l M OMT) rt-t- t- 00 fO COM N t^»o u-i N «/^00 t^ r- M crxXJ 10 to 00 00 o« >r) r- »0 (N »ot^ lOTfN rt-00 fO 00 -+ ^o 00 00 cs t- vo 00 " M '^ ^ ^ C7^ ^ ^ ^ 00 ^ ro -^^ a. ^ ^ "^ '^ M (N (S fO ro ''t 't »o lO ^'^■f^' ^■^'f^' 'i^p^ ^^^ ^■^*fi: ^'s'fi: ^^^ ^^^ ^'icu ^'^'(^* feo^m feCLn'K feC^ffi f^M fe'flH'a fecCw ^M f^^tJ^ feoia feP^ffi dp:ipq O'p^'pq op^im dp^"pq dp^ffl dp^'w dp:; pq dp^'m dp:ipq ddpq 10 n 00 Tf - 00 •o% a> M M H fO -+ JO 00 CT> M 1346 Heat'mg and Ventilation of Buildings Part 3 The total heating-surface is 8s X i6 = I 360 sq ft Weight of Steam or Condensation per Hour. This is I 360 X 1.09 (Table LI) = i 482 lb The equivalent amount of direct radiation is I 482/0.25 = 5 929 sq ft Design of Duct System. The round ducts will be designed for equal-friction pressure-loss per foot of length. The final velocity at the last or most remote outlet from fan will be taken at 1275 ft per min. The friction pressure-loss for this velocity, as read from the diagram in Fig. 64, is 0.25 in of water per 100 ft of length. There are to be eighteen outlets. The total volum'^ of air to be dis- charged, measured at 145° F., is I 163/0.065 =18 000 cu ft per min or 18 000/18 = I 000 cu ft per min per outlet The cross-sectional area of the outlet or last section is i 000/ 1 275 sq ft, cor- responding to a circular section with a diameter of 12 in. The branch-outlets may all be made the same size and provided with dampers to adjust or equalize the flow. The friction pressure-loss in the duct system is therefore (212/100) X 0.25 = 0.53 in of water The siT^e of each section of duct is determined by locating the quantity of air at the right of the diagram and passing horizontally to the intersection with the o.2S-in pressure-loss Hue. Table LX. Data for Design of Ducts in Fig. 69 Section Quantity of air in cubic feet Duct- diameter in Velocity in feet per Measured length plus allowance for per minute 145° F. inches minute ells, in feet A B C D E F G H I J 1 000 2 000 3 000 4 000 5 000 6 000 7 000 8 000 9 000 18 000 12 16 i8J4 21 23 25 26 28 29 38 I 275 25+[iX(6+3)]-34 15 IS 15 15 IS IS IS 3S+[2.4(6-fio)l-73 2 285 Total length =212 Selection of Fan for Draw-Through Arrangement. The statir pressure rating required, referred to a temperature of 70°, is: Pressure-loss in heater (data from Table I.VT) — 0.26 in Pressure-loss in duct (data from chart, Fig. 04) = 0.53 in Total = 0.79 in Application of Hot-Blast Heating-Data 1347 The actual pressure-loss wHI be somewhat less, owing to the fact that the air- temperature is higher (145° F.) and the density less than for air at 70° F. The actual estimated pressure-loss is therefore assumed to be % in. The volume of air the fan must handle in this example is 18 000 cu ft per min, measured at 145° F. As stated under Rating of Fans, to maintain a constant pressure the tabulated speed, volume and horse-power must be multiplied by the square root of the ratio of densities, or Vo.075/0.066 = 1.07 (nearly) (Table IT) We therefore select from Table LIX a fan having a capacity, measured at 70° F., equal to 18 000/1.07 = 16 822 cu ft per min (approximately 17 000) when operating with a static pressure of % in. A No. 8 Sirocco fan fulfills this requirement. The tabulated speed and horse-power when multiplied by the factor 1.07 gives 196 X 1.07 =210 R.P.M. and 3.76 X 1.07 = 4.02 brake horse-powei: Selection of Fan for Blow-Through Arrangement. In this case fhe fan may be called upon to handle air at a temperature of 0° F., or lower. Assum- ing the same weight of air, or 70 000 lb per hr, to be handled by the fan at a static- pressure of % in, the volume at 0° is 70 000/(0.086 X 60) = 13 566 cu ft per min Referring to Table LVIII, the ratio between the speed, volume and power neces- sary to produce the same pressure for air at 0° and air at 70°, is found to be 0.932. We therefore choose a fan with a capacity of 13 566/0.932 = 14 557 cu ft of air at 70° and with a static pressure of % in. Fan-Engine. When high-pressure steam is available an automatic high- speed engine is frequently employed for fan-driving, and the exhaust from the engine is used in the first section of the heater. Selection of Motor for Fan-Driving. It is considered good practice to add from 10 to 15% to the brake horse-power, as determined from the fan -tables, for the rating of the motor, to allow for a possible overload due to the fact that the fan may not be operated under exactly the same conditions as to pressure and speed as those under which it was originally rated. For the preceding exam- ple (D raw-Thro ugli Arrangement) a 5 -horse-power motor would be selected. Additional Heating Requirement. It is frequently desirable to proportion the heating- apparatus large enough so that the fan may be shut down at night and started up about two hours before the shop or factory is opened in the morning. In this event it may be safely assumed that the temperature of the air in the building will not be below 30° F. when the fan is started, and that the air is all recirculated. The fan and heater must be of sufficient capacity to take care of the heat-loss from the building, including the infiltration, and in addition to warm up the contained air f^om 30° to 60° in two hours. Assum- ing the same data as given in the preceding example, the additional heat re- quired will be, if the cubic contents of the building are 328 000 cu ft, (328 000 X 0.08 X 0.24 X Zo)/2 = 94 464 Btu per hr 1348 Heating and Ventilation of Buildings Parts This amounts to an increase of approximately 7% in the heating requirements as previously calculated and is readily provided for by increashig ?he steam pressure carried m the heater to approximately lo-lb gauge. Catalogue, bul- letins etc on the subject of hot-blast heating, air-washing and humfd fiction may be obtamec^ from the American Blower Company, the B F. SturtTvant Com pany, the Buttalo Forge Company, and the Carrier Air Conditioning Company. Ventilation Natural and Mechanical Ventilation. Ventilation, whether naturai. or MECHANiGA., consists m the displacement of vitiated air from an apartm^and S^JmCl Ventilation 13^ its replacement by fresh aif. To state that the air in an apartment is renewed any given number of times per hour is not strictly accurate, as a positive change does not actually occur; the incoming air mixes with and dilutes the foul air to a point suitable for healthful respiration. In natural-ventilation systems the movement of the air in flues, ducts, etc., is induced solely by the thermal head produced by the difference between the density of the column of air in the ducts and that of the outside atmosphere; the higher the temperature in the ducts the more powerful the draft. The direction and velocity of the wind materially affect the natural ventilation, retarding or accelerating the move- ment of the air through ducts and flues, according to the exposure of the building and the position of inlets and outlets. In mechanical ventilation the move- ment of air is maintained by means of various types of fans, driven by a steam- engine, electric motor, or other prime mover. With fans of known efficiencies ' the results can be accurately estimated. The principal advantages of the use of mechanical systems of heating and ventilation have already been stated under Hot-Blast Heating. Systems of Ventilation. Ventilation systems are also broadly divided into two general classes known as the upward system and the downward system."" The UPWARD system (Fig. 70) is generally used for audience-rooms where there is strong natural tendency for the heat given off by the large number of occupants to rise and take with it the vitiation-products due to respiration. The air is sup- plied NEAR THE FLOOR-LINE through mushroom ventilators in the floor, or through the hollow pedestals of the chairs themselves, or through low registers. The viTiATED-AiR OUTLETS ARE IN OR NEAR THE CEILING. This systcm makes it rather difficult to heat the room in advance of the arrival of the audience as the outlets allow the warmed air to escape almost as rapidly as it can be. introduced. The DOWNWARD SYSTEM is Very generally used in school-rooms, hospitals, institutions, etc. The occupants are not as closely placed as in the former case, and a more even distri- bution of air and more uniform heating can be secured when the air is supplied eight FEET OR more ABOVE THE FLOOR, and the vitiated air REMOVED AT OR NEAR THE FLOOR-LINE. On account of the elevation of the inlets abovethe headsof the occupants there is little liability of drafts, and if the outlets are on the same side wall as the in- lets there is very little opportunity for short-circuiting between inlet and outlet, since the incoming air must flow out across the room to the cold outside wall before it can cool and drop to the floor-level. It is, however, necessary in the downward system, to overcome the natural tendency of the heated air from the bodies of the occupants to rise and oppose the uniform downward tendency of the incoming fresh air. The selection of either system must depend entirely on the conditions to be met. These have been outhned in the above paragraphs. Distribution of the Air. In general, it should be observed that whether upward or downward ventilation is employed there should always be a definite system of vitiated-air removal, designed to provide for uniform distribution and SIZES OP "ABC" MUSHROOM VENTILATOR. Size. Approximate Inside Diameter. Approximate Weight . 4 6 6 0% 61b. 10 lb. 15 1b. Fig. 71. Section through ABC Mushroom Ventilator 1350 Heating and Ventilation of Buildings Parts prevent short-circuiting between inlets and outlets. A practically complete diffusion can only be attained when inlet and outlet are placed in the same inside wall, with the former at least from 7 to 8 ft above the latter. Multiple Flanges (Bolted) Return-Main, Steam and Water f Union (Screwed) Hot-Water Main, (Flow) J-^ . 1 . 1 Tee and Ell, Long Sweep ( Same Plane) Tee and Ell, Close (Same Plane) Drop ■+0- Plan Oast -Iron Boiler and Conuoctious Deflecting and Mixing Damper* Heat and Vent-Flues with Regifcters ^ \ Two-Piw - 5 AQ Elbows in Rounds Duct i Fig, 72. Heating and Ventilating Symbols INLETS and MUSHROOM VENTILATORS, in Order to secure a better mechanical distribution of the air, are being made useof in many systems of upward ventila- tion for audience-rooms with fixed seats. In this case a false flojr or plenum CHAMBER must be constructed iiist bc'Iow the mnin flexor throiifirh wbuh the Mir Ventilation 1351 is to be supplied. Mushroom ventilator-heads (Fig. 71) are then located under every second or third seat and adjusted to give a uniform discharge of tempered air over the entire seating-area. These heads are either mounted on an ad- I k $1 — K) Boiler r i t ii( '2^ Blow-off or Drain H> Boiler t-i I (Alternate) coner ^Expansion-arm Typical Elow-Connections. Plan Header JRelurn -/ r- 1, \^ Boiler C» — F" ii I 4 leometric-Perspective Sectional C. I. Type. Steam.or FloW ' Blow- , l0j ri: n Boiler — O \i u Header^ Twin-Boiler Connections. Plan Hound d. I. Type Elevation. Fig. 73. Heating-boiler Connections . instable spindle (Fig. 70), which is supported centrally in the cast-iron floor- sleeve (^r flange, or else they have a non-adjustable spindle similarly supported, and are cauipped with a control-damper. In either case the adjustable h«a4 or 1352 Heating and Ventilation of Buildings Part 3 damper must be locked positively in the finally adjusted position. In the case of concrete floors it is very desirable to use a cast-iron sleeve and flange (Fig. 70) rather than a galvanized sleeve and cast-iron flange. The Effect of Vitiated Air. The amount of carbon dioxide present in vitiated air has been, until recently, quite generally understood to be the element of danger that should be kept within safe Umits. Dr. Ira Remsen has pointed out that the presence of carbon dioxide in itself is not dangerous to health except that it reduces the supply of oxygen by displacing it. Carbon dioxide is not poisonous, but the organic impurities that are exhaled at the same time with other gases that are given off may prove a menace to health. The ill effects of breathing air in a poorly ventilated room are due to the small quantities of decomposing organic matter and unhealthful gases. The carbon dioxide gen- erated by the lungs and given off at the same time as the other impurities serves more or less as an indicator of the presence of the real danger. Any lowering of the oxygen-supply that is actually required for the proper and necessary transformation of the potential heat-value of the food into the physical and nervous energy required to keep the human machine running, and to readily supply the additional demand made upon that machine to perform external work, means that industrial workers who perform their duties in a vitiated atmosphere do so at the expense of a lowered vitahty, and are naturally less productive. Satisfactory ventilation consists not only in constantly supplying, in a pure condition, fresh air free from dust and other impurities, at the proper temperature and with the proper amount of moisture present, but also in efficiently removing the vitiated air. This cannot be positively accom- pHshed during the heating-season by simply opening the doors and windows. Some mechanical means must be employed. Many physicians, however, do not believe in mechanical ventilation for hospitals, and advocate ventilation by the open- window method; and many hospitals are now constructed without any provision for mechanical ventilation except for the toilets and operating- rooms for which exhaust-fans are provided. Relation between Humidity and Temperature. The proper and healthful RELATIVE HUMIDITY OF THE AIR in buildings has only in recent years been given the thought and attention it rightfully deserves. Heated or warmed air, whether purposely introduced into a building for warming, or naturally entering by infiltration, on being expanded by heat, has its percentage of moisture or rela- tive humidity lowered, and consequently its capacity for absorbing moisture greatly increased. There is, therefore, experienced the sensation due to so-called DRY HEAT. This causes an excessive and unnatural evaporation of moisture from the skin and from the membranes of the respiratory organs. Evaporation takes place by the direct application of heat and is essentially a refrigerating or cooling process. The abstraction of heat from the body for this purpose, nat- urally tends to lower the surface-temperature, and one feels several degrees cooler than the temperature recorded by the thermometer in the room. Dr. H. M. Smith's many observations and experiments upon the sensations produced by different percentages of satltiation, led him to make the following state- ment: "It may be accepted as a cardinal rule that if a room is at 68° and is not warm enough for any healthy person, it is because the relative humidity is too low." A standard relative humidity may be obtained when mechanical ventilation is used by the addition of a humidifier to the system. The subject of air-conditioning is fully treated in Heating and Ventilating, Vol. I, by Harding and Willard. Requirements for Good Ventilation. There is quite a diversity of opinion among various authorities as to what constitutes good ventilation in many Ventilation 1353 instances. The following data by G. D. Small represent good practice in this respect: Types of Buildings. Air-Changes to be Allowed f Portions above grade One change per hour. Office -Buildings j Basement, general Four changes per hour. [ Mechanical plant Ten changes per hour. Factory-Buildings which have no mechanical or natural ventilation, one change per hour. For factories in which large doors from the outside are frequently opened, about four air-changes per hour. Residences which have loose windows, two changes per hour. Churches. Four changes per hour, except small rooms, which should have five or six changes per hour. These data for churches contemplate mechanical ventilation. The majority of public buildings and many of the factories require ventilation or the fan system of heating. . The Usual Requirements for Air Supplied per Person are as Follows Hospitals (O'"'^^''^ from 35 to 40 cu ft per min I Epidemic 80 cu ft per mm Air-change Detention-rooms 6 min Toilet-rooms 6 min Bath-rooms and duty-rooms 8 min Kitchens 3 min Serving-rooms 10 min Fumigating-rooms 10 min Workshops 25 cu ft per min Prisons 30 cu ft per min Theaters from 20 to 30 cu ft per min Meeting-Halls 20 cu ft per min Schools 30 cu ft per min per child and 40 cu ft per min per adult The Usual Time-Intervals for One Air-Change are as Follows Hotels Room Air-change Room Air-change Engine-room 6 min Cafe 8 min Kitchen 1^-5 min Lobby under balcony. . 8 min Restaurant 6 min Main lobby 20 min Base-toilet 5 min Banquet-hall 15 min Billiard 10 min Retiring-room 10 min Barber-shop 8 min Kitchens 8 min Dining-room 15 min All others 15 min Palm-room 12 min Toilets 6 min Buffet 8 min Libraries Corridors 15 min Inside rooms 8 min Basement-rooms 15 min Corner rooms * . . . 7 min Reading-rooms 12 min Toilet-rooms 5 min Laundries should have an air-change every 4 to 6 min. Note. Radiation on sides of buildings subjected to prevailing and cold winds should be increased 10% up to the loth floor and 15% above that floor. 1354 Heating and Ventilation of Buildings Part 3 Ventilation-Laws. The number of ventilation-laws has increased very rapidly in the last few years, not only as regards the number of states which nave added such laws to their codes, but also as to the scope and effectiveness of these statutes. In many cases a special ventilation-officer or commission has been appointed to see to the enforcement and extension of the requirements for compulsory ventilation, so that it behooves the architect or engineer to become thoroughly famiHar with the law of the state or states wherein he practices. A summary of the law recently enacted by the legislature of the state of Ohio is given in the following paragraphs as an example of the regulations with which architects and engineers must conform in preparing plans and specifica- tions. This law as well as the law of Massachusetts, attempts to provide very definite regulations for heating and ventilating all classes of buildings. Future legislation in other states will undoubtedly take a more specific form, establishing complete and definite codes for the heating and ventilation not only of public buildings but of workshops, factories and mercantile establishments as well. Requirements of the Department of Inspection of the Industrial Commission of Ohio for the Heating and Ventilation of Public Buildings, Hospitals, Asylums and Homes Temperature A heating system shall be installed which will uniformly heat the various parts of the building to the following temperatures in zero weather. Theaters and Assembly-Halls. All parts of the buildings, except storage- rooms, 65° F. Churches. Auditorium, social and assembly-rooms, 65° F. All other parts of the building, except storage-rooms, 70° F. School-Buildings. Corridors, hallways, play-rooms, toilets, assembly- rooms, gymnasiums and manual-training rooms, 65° F. All other parts of the buildings, 70° F. Hospitals, Asylums and Homes. Operating-rooms, 85° F. All other parts of the buildings, except storage-rooms, 70° F. Change of Air The heating system shall be coml)ined with a system of ventilation which at normal temperature will change the air the following number of times, or supply to each person the following number of cubic feet of air per hour. Theaters. Parlors, retiring, toilet and check-rooms, six changes per hour. Auditoriums, i 200 cu ft of air per person per hour. Assembly-Halls. When used in connection with a school-building, lodge- building, club-house, hospital or hotel, six changes per hour; and in all other assembly-halls, i 200 cu ft of air per hour per person. Churches. Auditoriums, assembly-rooms and social rooms, six changes per hour. School-Buildings. All parts of the buildings, except corridors, halls and storage-rooms, six changes per hour. Requirements for Heating and Ventilation of Buildings 1355 Asylums, Hospitals and Homes, (i) Rooms with fixed capacity: Adults Children Babies Hospitals, contagious and epidemic 6 ooo 4 000 3 000 Hospitals, surgical and medical 3 000 2 400 i 500 Penal institutions i 800 i 800 All other buildings i 800 i 500 (2) Rooms with variable capacities: Hospitals, contagious and epidemic 12 times per hour Hospitals, surgical and medical 12 times per hour All other buildings 6 times per hour Rooms accommodating four or less persons need not be provided with a system of ventilation. Radiators No radiator shall be placed m any aisle, foyer or passageway of a new theater, assembly-hall or church, but such radiators may be placed in recesses in the walls. Registers No floor-registers shall be used in theaters, assembly-halls, or hospitals. No floor-registers, except foot-warmers, shall be used in a school-building. Floor-registers may be used in churches. Otherwise all vent-registers shall be placed not more than 2 in above the floor^ line, and warm-air registers not less than 8 ft above the floor-line (except when such registers are used when a change of air is not prescribed). Systems to be Installed Where a Change of Air is Required The system to be installed when a change of air is required shall be either a gravity or mechanical furnace system, gravity indirect steam system, or hot- water system; mechanical indirect steam or hot-water system, or split steam or hot- water system; except in hospitals, where a direct-indirect system may be used in connection with an exhaust-fan. The fresh-air supply shall be taken from outside the building and no vitiated air shall be reheated. All vitiated air shall be conducted through flues or ducts and be discharged above the roof of the building. Exceptions. Standard ventilating stoves may be used in the following buildings: Assembly -halls seating less than 100 persons. Churches seating less than 100 persons. All school-buildings, hospitals, asylums and homes. Furnaces Furnaces may be used in all classes of buildings. Gravity Indirect Hot-Water or Steam-Radiator Systems Indirect hot-water or steam-radiators shall be located in basement fresh-air rooms ■ directly at the base of masonry hot-air flues, and shall be properly con- nected to same with galvanized-iron housing. 1356 Heating and Ventilation of Buildings Part 3 Indirect Radiating-Surface for Heating and Ventilating Purposes One square foot of radiating-surface shall be provided to heat not more than the following number of cubic feet of air per hour: Hot Height Steam water First story 200 125 Second story 250 160 Third story 300 200 Fourth story 250 235 For Heating Wall- Surfaces and Glass-Surfaces. The amount of radiating-surface for the heating of the glass-surface and wall-surface shall not be less than that obtained by adding together the glass-surface and one fourth the exposed wall-surface, both in square feet, and multiplying by the following factors: Hot Height Steam water First story 0.7 i . 05 Second story 0.6 0.9 Third story 0.5 0.75 Fourth story 0.4 0.5 Accelerating or Aspirating Coils for Vent-Flues. Vent-flues used in connection with a gravity indirect steam or hot-water system shall be provided with accelerating coils placed i ft above the vent-openings. Mechanical Fan Plenum System This system shall be designed with furnaces, tempering coils or blast-coils so as to furnish heated air, and is to have cleaning-screens, fan plenum chamber, galvanized-iron or masonry horizontal ducts, masonry hot-air flues, electric motor, gas or gasoline engine, or a low-pressure steam-engine operating on a steam-pressure not to exceed 35-lb gauge to operate fan and such other device as is necessary to make this a complete working system. All parts and apparatus in connection with the installation are to be of ample size to make a perfectly free and easily working system, which must thoroughly heat all portions of the building without forcing. Velocity of Air The velocity of the air traveling through ducts, flues, etc., shall never exceed the following number of feet per minute: Feet per Ducts, Flues, etc. minute Fresh-air screens, small mesh 600 Fresh-air ducts, gravity system 300 Fresh-air ducts, mechanical system 850 Tempering coils, gravity system 300 Tempjering coils, mechanical system i 000 Furnaces, gravity system 400 Furnaces, mechanical system 900 Trunk-ducts, mechanical system i 000 Laterals, branches and single ducts, mechanical system • 75° Vertical flues, mechanical system 500 Specifications for Furnace-Work 1357 Vertical warm-air flues, gravity system, first story 300 Vertical warm-air flues, gravity system, second story 350 Vertical warm-air flues, gravity system, third story 390 Vertical vent-flues less than 20 ft high 300 Vertical vent-flues from 20 to ss ft high 350 Vertical vent-flues from 33 to 46 ft high 390 Vertical vent-flues from 46 to 60 feet high 440 Warm-air registers 300 Vent-registers 300 Maximum Speed of Fans The maximum speed of fans used in connection with either an exhaust or plenum system of heating or ventilating, under normal conditions, shall never exceed the following: Diameter of fan in inches. .. . 18 24 36 48 60 72 96 120 180 Revolutions per minute 700 550 400 300 225 175 150 125 75 Location of Heater-Room No heater-room shall be located under the auditorium, stage, lobby, passage- way, stairway or exit of a theater; noF, under any exit, passageway, public halJ or lobby of an assembly-hall, church, school-building, asylum, hospital or home. This applies to new buildings, and a changed location of a heater-room in an existing building. No cast-iron boiler carrying more than lo-lb pressure or steel boiler carrying more than 30-lb pressure shaU be located within the main walls of any school-building. Standard Fire-Proof Heater-Room for New Buildings All furnaces and boilers, including the breeching, fuel-rooms and firing-spaces shall be enclosed by brick walls not less than 1 2 in thick, or by monolithic con- crete walls not less than 8 in thick. The ceiUng over the same shall not be less than the following: reinforced-concrete slab, 4 in thick; brick arches, 4 in thick, covered with i in of cement mortar and supported by fire-proof steel with the necessary tie-rods; or hollow-tile arches, 6 in thick, covered with 2 in of concrete, plastered on the under side and supported by fire-proof steel with the necessary tie-rods. Specifications for Furnace-Work The following form is given as a guide to architects in preparing the specifi- cations for furnace-work : Specifications for Furnace -Work in Residence for Mr to bb BUILT AT Architect Furnace. Furnish and set up complete, where shown on basement-plan, one (. . . name . . .) furnace, or approved equal, portable-pattern, with double casings. Connect the furnace with the chimney with a No. 22 galvanized-iron smoke-pipe of the same size as the collar on the furnace; all bends. or turns to be made with three-piece elbows; the pipe to be strongly supported by wire, and to be kept 12 in below the ceiling. Air-Pit. Excavate for and build a cold-air chamber under the furnace not less than 18 in deep, with 8-in brick walls, laid and plastered with cement; also 1358 Heating and Ventilation of Buildings Parts cement the bottom of the chamber. Build the cold-air duct under cellar-floor, where shown on plan, — ft long, 14 in deep in the clear, and — in wide, with sides of hard brick in cement, and with the sides and bottom smoothly plastered with cement. Cover the duct with 3-in flagstones with tight joints, leaving opening of proper side for the wooden box to be built by the carpenter (wooden box should be included in carpenter's specifications). Hot-Air Pipes. Furnish and properly connect with furnace and register-boxes, leaders and stacks of the following sizes, all to be made of bright IX tin, and the stacks are to be double with an air-space. All turns in leaders to be made by three-piece or four-piece elbows, and the stacks to have boots or starters of approved pattern. Sizes of Pipes and Registers Hall 11" leader, no stack Parlor 11 y^" leader, Dining-room 12" leader. Library loV^" leader, Chamber No. i 10" leader, Chamber No. 2 9" leader, Chamber No. 3 8H" leader: 12" X 14" register. no stack 12" X 15" register no stack 12" X 15" register no stack 12" X 14" register 4" X 15" stack, 10" X 14" register 4" X 13" stack, 10" X 12" register 4" X 13" stack, 10" X 12" register Registers. All registers are to be of sizes given in the foregoing list, of the (. . .name. . .) or approved equal, manufacture; japanned, except those in the first story, which are to be electro-bronze-plated. All floor-registers are to be set in iron borders corresponding with the registers. Register-Boxes. All register-boxes to be made double; for first-story boxes the JOISTS ARE TO BE LINED WITH TIN and provided with ceiling-plates the full size of the registers, with plaster-collars attached, so that pipes and boxes can be removed without disturbing the plastering or defacing the ceiHng. Miscellaneous. All horizontal pipes in the basement are to be round, and where they pass through partitions they are to be provided with collars, so that the pipes can be removed without disturbing the plastering. All leaders are to be provided with dampers and tin tags designating the different rooms they supply; and whenever pipes run near woodwork the same is to be properly covered with tin and protected from any danger from fire. The contractor is to remove afl rubbish made by him, clean up all ironwork, leave the whole apparatus in complete working order, and furnish a poker of proper size. Guarantee. The contractor is to guarantee, if he furnishes the heating- drawings, that the furnace shall, under proper management, heat all rooms with registers connected with the furnace, to 70° F., when the temperature outside indicates 0°. In the event of the failure of the furnace to do this, the contractor, at his own expense and without unnecessary delay, is either to make the furnace heat said rooms or substitute another furnace that will heat them. Hot-Air-and- Water Combination-Furnaces Combination-Furnaces. It is quite difficult, if not impossible, to heat dwellings covering throughout, more than i 400 sq ft with warm air alone. On account of the much larger exposure and the increased length of leaders, it becomes necessary to supplement the warm air with an auxiliary heat which Specifications for Furnace-Work 135W can be carried to remote and exposed parts of the house, and which will not be affected by pressure of wind or long and crooked pipes. For supplying this auxiliary heat, hot water has been found best adapted as a rule, and a variety of COMBINATION-FURNACES are now made which contain provisions for heating water which may be carried by pipes to radiators located in those parts of the house most difficult to heat by warm air. Such combination-systems have been used with success. The construction of the parts for heating the water varies with different makes of furnaces. Some furnaces have a portion of the fire-pot hollow, and the water is heated there; others have a separate heater suspended over the fire-pot. As a rule, the parts of the house which should be heated by the hot water afe the halls, bath-rooms, and pferhaps the rooms on the north or west sides of the 'house. The same rules govern the size of the radiators and piping and the manner of installing as in an entire hot-water plant. Specification for Hot- Water Heating-Apparatus in a Residence This specification contemplates a complete upfeed two-pipe gravity hot-water heating system, to be installed in accordance with the drawings covering the same. Heater. Furnish and set up in cellar, where shown on plan, one ( . . . name . . . ) water-boiler, or approved equal, guaranteed free from all flaws and defects. The heater to be set on a substantial foundation of hard brick laid in cement mortar and put in by the heating-contractor. Furnish and deliver one set of fire-tools, consisting of one poker, one sUce-bar and one fine brush and handle. Smoke-Pipe. Connect the boiler to the chimney by means of smoke-pipe made of No. 22 galvanized iron, the diameter of the pipe to be equal to the outlet on the heater. Trimmings. The boiler is to be provided with one thermometer registering from 80° F. to 250° F., and one Standard altitude gauge.* Water-Connections and Blow-off. Feed-water with its supply-pipe will be brought within 6 ft of the boiler by the plumber and left with one 54-in cast-iron fitting for boiler-connection, which is to be made by this contractor, with suit- able cock. Draw-off cock to be placed on lowest point of system and to be fitted for hose-attachment. Pipes. Furnish and run all necessary flow and return-mains of ample size, connecting them to radiators with risers of ample size to insure the free flow of hot water to and from the radiators. All connections from risers to radiators to be made below floors. Quality of Materials. All materials used in the construction of this apparatus are to be the best of their respective kinds, all fittings to be heavily beaded and made of the best gray iron with clean-cut threads, and, when practicable, Y's and 45° L's are to be used. Reaming. The ends of all pipes used in the construction of this apparatus are to be reamed and all obstructions removed before pipes are placed in position. All flow and return-mains in the basement are to be supported by neat, strong, adjustable hangers, arranged to suit expansion and contraction, and properly secured to timbers overhead. * At all points where pipes pass through ceilings, * An altitude-gauge indicates the amount of water in the system and is a convenient attachment which avoids the necessity of consulting the gauge-glass in the tank. It can be dispensed with if desired. 1360 Heating and Ventilation of Buildings Parts floors, or partitions, tin thimbles are to be provided and the holes protected with floor or ceiling-plates. Expansion-Tank. The expansion-tank is to be constructed of galvanized iron, and is to be furnished with a proper gauge-glass with brass mountings complete. It is to be placed at least 3 ft above the highest radiator in a suitable place and supported on a proper shelf. From this tank an overflow-pipe will be run to the basement or other suitable place with a vent-pipe through the roof, properly flashed. Radiators. Furnish, set up, and pipe the following radiators: Rooms Number of radiators Radiating- surface. sq ft I indirect radiator 108 I indirect radiator 120 I direct radiator 40 I direct radiator 60 I direct radiator 40 I direct radiator 44 I direct radiator 36 I direct radiator 32 I direct radiator 32 Main hall Sitting-roon Library Dining-room Sitting-room chamber. Library chamber Dining-room chamber, Kitchen chamber Bath-room 9 radiators In all there are to be 284 sq ft of direct surface and 228 sq ft of indirect; total surface, 512 sq ft. The direct radiators to be (. . .name. . .) hot-water pattern, or approved equal, 38 in high. Air-Valves. Each radiator is to be provided with a nickel-plated key-type air-valve. Radiator-Valves. Each direct radiator is to be promptly connected to the system of piping with a quick-opening nickel-plated radiator-valve and union elbow. Indirect Radiation. The indirect radiators are to consist of two stacks of ( . . . name . . . ) hot- water radiation, or approved equal, connected together with tight joints and firmly suspended from the basement-ceiling by suitable wrought-iron hangers. The stacks are to be so piped and hung as to permit a noiseless and constant flow throughout of the heated water. Each stack is to be enclosed in a galvanized-iron chamber with proper fresh-air inlet-duct and a corresponding outlet-duct for warm air, connected to the register in the room which the stack is intended to heat. The registers are to be of the (. . .name. . .) pattern, electro-bronze-plated, and of the following sizes: hall, 12 by 19; sitting-room, 14 by 22 in. Registers are to have floor-borders and to be set in register-boxes. The duct connecting the stack and register is to be so arranged that all fresh air coming in wiU be properly heated and con- veyed, with least loss, to its destination. In arranging indirect boxes, care is to be exercised in getting ample space for cold air under the stack, and a corresponding space for warm air over the stack. Covering of Pipe. All flow and return-pipes and fittings in cellar above the floor are to be properly covered with i-in hair-felt neatly sewed up in canvas specifications for Furnace-Work 1361 and painted one coat of good white lead, or covered with asbestos or magnesia sectional covering, with canvas cover, and secured by lacquered-brass bands. Boiler-Covering. All exposed parts of the boiler, except the front, are to be covered with plastic asbestos, i ^ in thick, neatly applied and troweled, smooth. Workmanship. All work is to be done in a neat, substantial and workman- like manner, and the apparatus, when completed, is to be thoroughly tested and left in good working order. Guarantee. The contractor is to guarantee, if he is to furnish the heating- drawings, that the apparatus he installs will be of ample capacity to evenly maintain a temperature of 70° F. in the rooms in which radiators are located, when the outside temperature is at zero, and that the apparatus throughout will have a free circulation when in operation. Steam-Heating for Residences General Requirements. For very large residences, the author would recommend steam-heat, all of the principal rooms to be heated by indirect radiation, and only the bath-room, halls, and perhaps the attic and one or two rooms on the north side, which generally includes the dining-room, by direct radiation. For dining-rooms a special direct radiator, containing a warming- closet, is made. The air-supply to the indirect stacks should be very large and provided with a damper, so that the supply may be regulated according to the weather. The boilers used in residence-heating are generally of the cast- iron sectional type described on page 1278. The single-pipe system is com- monly used in dwellings, all indirect radiators, however, being two-pipe. Specification for a Low-Pressure Steam-Heating Apparatus for Heating by Direct Radiation Intention. This specification is intended to cover everything necessary to fully finish and install in the above-mentioned building a complete steam-heat- ing system in strict accordance with the plans and this specification, as prepared by , architect. Plans. The drawings herewith are intended to show only the location of the boiler, piping and radiators; the arrangement of the piping will be left largely to the contractor, subject to the approval of the architect. General Requirements. This contractor is to provide all necessary tools and appliances for the erection and completion of the work, and when completed, is to remove all apparatus, refuse and debris from the building and grounds, leaving the work in a clean, uninjured and perfect condition. No cutting of any description tending to weaken the building structurally is to be undertaken" without consulting the architect. This contractor is to be fully responsible for the safety and good condition of the work and material embraced in this contract until the completion and acceptance of the same. All work is to be of the best quality, and should at any time improper, imperfect, or unsound material or faulty workmanship be observed, whether before or after same has been built into the structure, this contractor, upon notice from the architect, is to remove same and substitute good and proper material and workmanship without delay in place thereof, in default of which the architect is to effect same by other means as may be deemed best, and is to deduct the cost of such alterations from the sura due the contractor under this contract. 13G2 Heating and Ventilation of Buildings Part 3 System. The heating is to be effected by direct radiation distributed through- out as shown on the drawings, and the circulation of the steam is to be by the one-pipe circuit system. Boiler. This contractor is to build the foundation for the boiler, where shown, 12 in deep, of common hard brick laid in cement mortar. He is to leave an ash-pit for the boiler of proper size, 12 in deep, cemented, and made water-tight. He is to furnish and set up one (. . .name. . .) cast-iron sectional, or approved equal, boiler, provided with 6-in low-pressure brass-cased steam- gauge, water-gauge, and glass, gauge-cocks, combination-column, safety-valves and blow-off valves, and all other usual and necessary trimmings to complete the boiler,* and a full set of fire-tools, consisting of one slicing-bar, one hoe, one poker, and a cleaning-brush. He is to cover the boiler with i M-in of asbestos cement, neatly troweled to a smooth finish. Water-Supply. The plumber is to bring the water-supply to within 6 ft of boiler, but this contractor is to make connection with boiler with ^-in iron pipe, stop-cock and check- valve. Smoke-Pipe. Contractor is to connect the boiler with the chimney with a round smoke-pipe made of No. 22 galvanized iron with suitable balance-damper. This connection to be of same size as left for this purpose by maker of boiler. Main Pipes and Risers. The steam-main is to be run full size for the entire length and provided with an automatic air-vent at the end of the run. It is to be of ample size to carry all the risers and radiators attached to the system, and is to be graded i in in 10 ft in the direction of the flow. From the top of this main the various branches are to be taken to radiators and risers, the connections for which are to be so made that no traps are formed. If a trap cannot be avoided, a drip connected with the return-main is to be installed. Radiators on first story are to be connected direct to steam-main. Radiators for the second and third floors may be taken off the same riser. The main, after serving the last radiator, is to drop below the water-line of the boiler, and its size reduced, and it is to run back to the boiler as a wet-return-main. The steam-main at the end of the run is to be 24 in or more above the water-line of the boiler. The boiler is to be installed in a pit if necessary to accomplish this. Pipes and Fittings. All pipe used throughout is to be of the best quality wrought-iron or steel pipe of standard weight and thickness, with the ends reamed, free from imperfections, and true to shape. All threads are to be clean-cut, straight and true. All fittings are to be of the best heavy gray iron, with taper-threads, and are to be heavily beaded. No inferior pipe or fittings will be allowed. Supports. AH piping is to be supported by approved expansion-hangers or rollers, not to exceed 10 ft apart. Neat cast-iron floor and ceiling-plates are to be used where pipes pass through floors, ceilings and partitions. Radiators. Direct radiation is to be furnished to the amount enumerated on the drawings of the ( . . . name . . . ) rnake, or approved equal. Radiator-Valves. The radiators are to be furnished with removable disk- type union valves, rough nickel-plated, and are to have hard-wood hand-wheels. Air-Valves. Radiators throughout the entire building are to be furnished with ( . . . name . . . ) automatic air- valves, or approved equal. * For house-heating plants it is well to specify also "one automatic damper-regulator of approved pattern, with connection for operating draft-door and cold-air check." Specifications for Furnace- Work 1363 Pipe-Covering. All pipes in the cellar above the floor are to be covered with I -in asbestos (or magnesia) sectional covering with canvas cover and secured by lacquered-brass bands. Painting and Bronzing. AH radiators and exposed pipes in rooms or halls are to be neatly painted two coats of best radiator-enamel, or bronzed in desired colors. Finally. When completed, the apparatus is to be tested to lo-lb steam- pressure and made tight at that pressure, said test to be conducted under the supervision of the architect. Fuel for the test is to be furnished by the owner, and when accepted, the apparatus is to be turned over to the owner in com- plete working order. All valves and stuffing-boxes are to be properly packed and the plant completed in all its parts, it being understood that this contractor ' is to furnish all miscellaneous material, tools, labor, etc., necessary to complete the work in a first-class and workmanlike manner. Guarantee. This contractor is to guarantee that when the apparatus is completed it will be free from all mechanical defects and, if he is to furnish the design and layout, that the installation shall be of ample capacity to heat all rooms where radiation is placed to a temperature of 70° F. when the outside temperature is 0° Fo 1364 Chimneys Part 3 CHIMNEYS* By L. A. HARDING FORMERLY PROFESSOR OF MECHANICAL ENGTNEERING, PENNSYLVANIA STATE COLLEGE Draft. To burn a fuel at a given rate (pounds per square foot of grate-surface per hour) requires a definite weight of air to be supplied for combustion. The air passes under the grate and through the fuel-bed and meets with considerable resistance in its flow, not only through the fuel-bed, but through or around the boiler-tubes and smoke-flue or breeching. The motive force causing the air-flow in a natural-draft plant is suppHed by the chimney. The difference between the atmospheric pressure and the pressure existing at any point in the furnace or in the flue is termed the draft at that particular point. This pressure is ordinarily measured by means of a U tube filled with water, the draft being recorded in inches of water, and is the difference in the heights of the water- columns in the two legs of the U tube. Height. The intensity of draft that a chimney is capable of producing at the base is a fimction of its height, the temperature of the flue-gases, and the temperature of the outside air, which is generally assumed to be 60°. The tem- perature of the flue-gas is ordinarily assumed to be 550°. The intensity of draft produced, per foot height, measured in inches of water is H = 0.0071 L L = height of chimney above grate, in feet. The flue-gas temperature is taken at 550° and the outside temperature at 60°. Ordinarily 0.8// is taken as rep- resenting the available draft, in order to allow for the cooling of the chimney- gases. Then o.&H must be equal to or greater than the sum of the expected draft-losses as given in the following paragraphs. Draft-Losses. The draft-losses through the fuel-bed depends upon the rate of combustion required and the kind of fuel. This loss may be approxi- mated by using the data in Table I. The loss of draft between the grate or furnace and a point just beyond the damper-box of a boiler is about as shown in Table II when the boilers are oper- ated at normal rating; bituminous coal burned at the rate of from 25 to 30 lb per sq ft of grate-surface per hour. The loss of draft through the boiler will depend largely upon the method of baffling employed, and increases with the per-cent rating at which the bpiler is operated. The precipitating-figures should be increased by approximately 55% when the boiler is operated at 150% of its rated capacity, and by 75% when it is run at 200% rating. Velocity of Gases through Flue and Chimney. In preliminary estimates 5 lb coal per boiler horse-power developed, and 24 lb air per lb of coal is usually * See, also, Chimneys for Heating Boilers, page 1281; Flues for Kitchen Ranges an4 F'replace§, page 1282, and Selection of Chimney Flues, page 1282. Velocity of Gases through Flue and Chimney 1365 Table I. Loss of Draft between Furnace and Ash-Pit to Burn Coal Kind of coal 111., Ind., Kan., bituminous. . . Ala., Ky., Pa., Tenn.. bituminous Md., Pa., Va., W. Va., semibitu minous Anthracite pea Anthracite buckwheat No. i . . . Combustion-rate, R, in pounds of dry coal per square foot of grate per hour 15 20 25 30 35 40 45 Force of draft in inches of water 14 .20 .26 .33 .40 .48 16 .23 .31 .40 .49 .60 18 .26 .35 .45 .57 .71 30 .45 .64 .88 1.23 43 .68 1. 00 I. SO .57 .72 .87 Table II. Loss of Draft between Grate •r Furnace and a Point Just beyond Damper-Box Horizontal return tubular Babcock & Wilcox Stirling Vertical tubular . 25 to .30 in of water . 20 to .35 in of water .51 in of water .43 in of water assumed. The customary allowable velocities of gases in chimneys, when the design is based on 1 20 lb of the flue-gas per hour per rated boiler horse-power, varies from 17 ft per sec for a diameter of stack equal to 24 in, to 31 ft per sec for a 72-in or larger diameter. These figures correspond to a weight of 0.68 and 1. 10 lb per sq ft of area. The formula that is supposed to give the most economical diameter for an unlined steel chimney or stack, and used by many engineers in this country isd = 4 .68/(h.p.) ; in which d is the diameter in inches and h.p. is the rated capacity of the boilers served. The following figures are frequently used by engineers for approximating the loss of draft in flues or breechings: (i) Horizontal flues, square or rectangular, from 0.13 to 0.15 in of water per 100 ft. Increase these values 50% for brick-lined flues. Loss of draft for easy right-angle bends, 0.05 in of water. (2) When economizers are to be installed the temperature of the flue-gas is reduced to from 250° to 325°, and the total head, //, should be calculated on a basis of these temperatures. (3) The loss of draft through the economizers should not be figured less than 0.3 in of water. (4) The turns which the flue makes in leaving the damper-box of the boiler, where it enters the main flue and at the stack, should be considered and allowed for. (5) It is customary to make the flue or breeching approximately from 10 to 15% greater in area than the stack to which it connects. The cross-section is re- duced in proportion to the volume of gas to be handled as the flue passes the boilers in succession. The width of the flue or breeching, where it enters the 1366 Chimneys t'art 3 chimney, should never exceed one third the outside diameter of the chimney at its base. Example. The method of procedure in determining the dimensions of a chimney and breeching is explained in the following example. Three 150-1 h.p. return tubular boilers with a total of i 500 sq ft of heating-' surface are to be served. The total area of the grate-surface is 90 sq ft. The measured length of the breeching is 40 ft. The gas makes two right-angle turns, one at the entrance to the breeching, and one on entering the chimney. The . fuel assumed is Pennsylvania bituminous coal. If 5 lb of coal per boiler horse- power per hour is assumed as the fuel-consUmption, the rate of combustion is (3 X 150 X 5)/9o = 25 lb per sq ft of grate-surface per hour. The weight of flue-gas per second is (3 X 120 X i5o)/(6o X 60) = IS lb Assuming a temperature of 550°, the volume of the flue-gas per second is iS/0.0393 = 382 cu ft. Assuming an allowable velocity through the chimney- area of 25 ft per sec, the required area is, 382/25 = 15.3 sq ft corresponding to S4-in diam, approximately The area of the flue is to be 15% greater, or 15.3 X 1.15 = 17-6 sqft at the last boiler next to the chimney. The chimney must produce sufficient * draft to overcome the following resistance. The loss of draft through fuel-btd based on a rate of combustion of 25 lb per sq ft per hr (Table I) is 0.31 in. The loss of draft through return tubular boilers (Table II) is 0.27 in. The loss of draft through the breeching is 0.15 X 40/100 = 0.06 in The loss of draft occasioned by two turns is 2 X 0.05 = 0.10 in The total loss is . 0.31 4-0.27 +0.06 +0.10 = 0.74 in Then // = 0.74/0.8 = 0.92 in or approximately i in. Substituting this value of // in the equation // = 0.007 iL the height, L, of the stack is 1/.0071 = 140 ft -measured above the grate. Kent's Chimney-Formulas. The following chimney-formulas by William Kent are largely used by engineers in this country: The formula is based on the assumption that the friction-head in the chimney is considered equivalent to a diminution of the area by an amount equal to a lining of inert gas, 2 in in thickness. ^ Size of Chimneys for Steam-Boilers 1367 •r; <-- MrtlO . O rovD o fO t- « M M • N C4 rj ro ro fO Tt lovD . irj fo^o fO O 00 VO u^«0 00 . VD O M ir> M . i/^OO ro O 0% O rOOO »/5 ic fO • MMOt^POr^-OMHOooovD . 00 00 o fO a^'£:> >o t- o "^ O (^ - M tJ-VD QOMTj-t^MTi-NO . looo ooir>OMOt^ONOv;cT»M .O^-i-MOMrOt^NOCiONNO '^NMMrot^ro a«0 00 ro lo . ro -^ »OVC 00 O vD fO . o ^00 00 o ror»^oa»Mrt-cy> . <£) M (7. M lo C^ rOOOvDoO rt . lO cr» O^ N i^ ro M M M «>< fO -"t lO t^OO O N ■ • M '1-0O M ic Tj- TtvD j ro TJ- lovo 00 • <0 00 ro M rooo lO o r^«o • cooow rM^C ^rON ro MMMNC^rOrfl/) CT» rf ro t^ ro rovD m m t '^'ii 00 O rovD C3% ro M M M M M ci ro 6^- 1368 Chimneys Part 3 If A = the actual area in square feet; E = the effective area in square feet; D = the diameter in feet; Then E = A -o.6oV^. The draft-power of a chimney varies directly as the effective area, E, and as the square root of the height, L. The formula for the horse-power of a chimney will take the form, h.p. = CE^ L, in which C is a constant. The value of C as obtained by Kent from an examination of a large number of chimneys is 2,.:s:s when 5 lb of coal is burned per boiler horse-power per hour. The formula for the horse-power rating of a chimney is, therefore, h.p. = 2>.2>2>^^1^ = 2>-2>Z {A - o.WJWT or E = 0.3 h.p./VL The Babcock & Wilcox Company recommend that when the fuel used is low- grade bituminous coal of the Middle or Western States, the sizes given in Table III be increased from 25 to 60%, depending upon the nature of the coal and the capacity desired. If the gas makes more than two turns it is advisable to increase the diameter given in the table by one size. The height must be increased at least 30% if economizers are used. Table III may be applied to heating-boilers, the equivalent rating in square feet of direct radiation being approximately equal to the horse-power rating X 100. Chimneys for Tall Office and Loft-Buildings. The chimney or stack for a tall building is a special case in which the height is frequently fixed by the height of the structure itself or the height of the adjoining buildings. In this case a diameter is assumed and the method outlined in the preceding example apphed. General Formulas for the Design of Brick Chimneys. See Fig. 1. Let P = horizontal wind-pressure in pounds per square foot, ordinarily assumed as 25 lb per sq ft for round chimneys : any section distant z from top of chimney (d -f dA ■■ projected area above xx ■■ horizontal wind-load in pounds Pz m y = distance from xx to center of gravity of portion above xx M = wind-moment in foot-poimds = Pzy m Properties of Section di = outside diameter di = inside diameter c = di/2 I = moment of inertia of section A = area of section in square feet = 0.7854 {di^ - d2^) — = section-modulus General Formulas for the Design of Brick Chimneys 1369 / 0.0982 {di^ - ^2") c di W = weight of chimney above xx, in tons Si = compressive stress at edge on leeward side due to W, in tons per square foot 52 = compressive stress at edge on leeward side due to M, in tons per square foot W Mc W Windward side, Sw = ~ — A W Leeward side, 5/ =~ + A Mc ^ . X — - (tension) -— — (compression) ] ] / Sw and Si should not exceed tlie following values, in tons per square foot, for Radial Brick Chimneys: Maximum tension Maximum compression Below 150 ft 2 to 2 H 200 ft and below 19 From 150 to 200 ft. . . i to i J/2 Above 200 ft 21 Above 200 ft o Foundations. Calculate wind-moment, M\ for chimney above groun*d-line. Ml = Phyi (--:-•) / = length of side of square base in feet Ai = P = area of base in square feet / P — = — = section-modulus of base c 6 Wi = combined weight of chimney and foundation Example. It is required to determine the maximum compression, in tons per sq ft at the base of the column, for the chimney shown in Fig. 2, and also the maximum soil-pressure in tons per sq ft. The assumed wind-pressure is 25 lb per sq ft. (See General Formulas for the Design of Brick Chimneys, and Fig. 1.) The area of section at base, A = 0.7854 (162 — 12.32) = 80.9 sq ft. The section-modulus at base, I/c = [0.0982 (16* — i2.30]/i6 = 257. The total weight of brick column (Table Y) isW = 495 tons (interp olated). The projected area of column is H X (8.75 -f 16) X 180 = 2 228 sqft. The horizontal wind-load, i^ = 2 228 X 25 = 55 700 lb = 27.8 tons. The moment-arm of i^ is y = 1^ X i8o[(2 X 8.75) + i6]/(8.75 + 16) = 81 ft. The wind-moment, M = 81 X 27.8 = 2 252 ft tons. •S*! = 495/80.9 = 6.2 tons per sq ft. 52 = ± 2 252/257 = 8.7 tons per sq ft. The maximum compression on the leeward side, 5i -1-52 =6.2 -[-8.7 = 14.9 tons per sq ft. The maximum tension on the windward side, 5i — 52 = — 2.2 tons per sq ft. The following computations are for a square base: Foundation. The length of base, I =25.5 ft, Ai = /2 = 650 sq ft, I/c = 255^/6 = 814. The weight of foundation, based on 1.9 tons per cu yd, is 266 tons. The weight of the 4,V^-in lining is 36 X n X 0.063 = 25 tons. The total weight of column, lining and foundation, is Wi = 495 -|- 25 -f- 266 = 786 tons. The moment-arm for R may be assumed the same as before, or 81 ft. . Then M = 2 252 ft-tons. The section-modulus of the base, I/c = l^/& = 814. Si = 786/650 =1.2 tons per sq ft. 52 = 2 252/814 = 2.8 tons per sq ft, The maximum soil-pressure,' 5i -j- 52 = 1.2 4-2.8 =4 tons per sq ft. 1370 Chimneys Resultant Soil-pressure ia Tons per square foot Si = — - = compression per sq ft due to Wi S2 = —r- = compression por sq ft due to Mi Fig. 1. Details of Construction of Tall Bnck Chimney General Formulas for the Design of Brick Chimneys 1371 ^Cement Cap, 1-3 mix. 7M-?- 11^^:^*- i3K-»"^*- 16^H Is 18)<->>N: i p 2034'-> 5^ X 3 W.I. Retaining- ring set ih Cull Bed of Cement Mortar yEAD OF CHIMNEY (ENLARGED) Outsiilo Filler-wall to prot«'C't Bti.iras from Atmosphere l''Ri8e to Arch for^T eaoli 2 ft. of Fiue- U opening Width Solid Concrete 1-3 mix. <. 4)^" Lining " Five 6 I Beams over Fluo-opening * •with Ji,"Bearipg-plat€ VERTICAL SECTION THROUGH FLUE-OPENING (ENLARGED) ,22K-^ Minimum Air-space of ii between Lining and Main Wall I Beams over Flue- opening sufficient to carry Weight Add 2" to thickness^ of Pilaster for each Foot of Flue-opening Width, starting with 12^1 !*— ^'^^ Pilaster to 3-ft. Opening^ CROSS-SECTION A'A (ENLARGED) Fig. 2. Details of Tall Radial-brick Chimney 1372 Chimneys Parts 3 I "b a> 00 o u H 00 t^ 1-4 a y3 "io ^ V V vb >3 *"rO ■) UO »0 IO VO kO to »£> I^ t^ t^ I>00 00 00 o% o^ • rt--t'+»'3U0'^«O»O'X><£lVOVOo iT) in irjto to ^O «3 r^ r^ t^ r-oo oo oo Oi • r^r<)-rt-'ri-ri--r)-in\nin xr^KC to ^o vD t-- r I e>) c^ fOf*>fO'+'^'1">A>>/^io tmo to 'X) vo r^ i> I fOrocO'Tj-'tTj-rtioiA u^tO «0 to to t^ 4 M M o> cs n n rororO'^-^rf-'Tt-ioifl u^tO tO tO t^ IDCOOOO t^ O fO»0 00 M '^00 M W M P< «0 C3%rO00 rOoO M rtoO M »O00 rooo cj m O M M M M M MM !!!!!!!!!! a^OOOOOOOt-"MM(>,M(v,f/5rortrtTt-ii 0%0^0% O". o%o o o ►■ I N fT) tf) r*^ Tt ^ \n ^J 00 a>a»a>cj»a^o o o *-* ► » 05 cq rorOfO't'+'^io 000000CT«O*a>OOOMMMWNror0r0'^Tj-'- o »o o ^g lii »i^ ir> lo lo looo N ir> cTi N cT>cy»o o o M M M M M ro ro CO -^ MM Tt-00 - : oi -^oo ro t^ N 00 fo to O fOt-O Tft-M t— 000000 a>o%o^o o o ^ t^ r^oO 0000OM3^OOO"- bc o C toOiOO»00>00»'50»'50>/50»00>00>00>00»00»0 0"^0»00>>^ t-0000 a%a^o o m m p< 'H'5toA. BASE Fig. 3. Details of Tall Reinforced-concrete Chimney The Weber Chimney Company, Chicago, 111., designed and constructed, among other tall chimneys, the great reinforced-concrete chimney at Saganoseki, Japan, for the Oriental Compressol Company, for the copper smelter. It was completed in January, 19 17, and ranks with the highest in the world, being 570 ft above the foundations and 261^ ft in internal diameter at the top. 1376 Chimneys Part 3 Self-Sustaining Steel Chimneys* are largely used, especially for tall chimneys of iron-works and power-houses from 150 to 300 ft in height. "The advantages claimed are: Greater strength and safety; smaller space required; smaller cost by 30 to 50% as compared with brick chimneys; avoid- ance of infiltration of air and consequent checking of the draught, common in brick chimneys. They are usually made cylindrical in shape, with a wide curved flare for 10 to 25 ft at the bottom. A heavy cast-iron base-plate is provided, to which the chimney is riveted, and the plate is secured to a massive foundation by holding-down bolts. No guys are used.".t The largest self-sustaining steel chimney in the world (19 19) is that built by the Chicago Bridge and Iron Works at the plant of the United Verde Copper Company, Clarkdale, Arizona. It is 30 ft 93/2 in in diameter and 400 ft in height. The thickness of plates varies from % in at the top to Hie in for the bell-shaped portion at the bottom. The weight of steel is 800 cxx) lb. The stack is anchored to the foundation by thirty-six bolts, each 4 in in diameter, upset, and spaced equidistant in a bolt-circle of 25 ft 4H in radius. Table VHI. Sizes of Foundations for Self-Sustaining Steel Chimneys, Half- Lined t Diameter, clear, in feet. . . 3 4 S 6 7 9 II Height ft in ft in ft in ft in ft in ft in ft in 100 IS 9 6 6 100 IS 3 7 125 17 6 7 6 150 20 4 9 200 23 8 10 ISO 21 10 8 200 25 10 150 22 7 9 250 29 8 12 175 25 9 10 27s 33 6 12 225 29 II 13 300 36 14 Least diam. of foundation Least depth of foundation Height Least diam. of foundation Least depth of foundation The governing feature in the design of a self-sustaining steel chimney or STACK is the force of the wind. The cylinder above any horizontal plane section may be assumed to act as a cantilever beam in which the bending moment, in foot-pounds, is M =HD XP Xy2H = ViHWP in which H is the height in feet above the section considered, D the diameter in feet and P the assumed pressure of the wind in pounds per square foot on a ver- tical cross-section. The fiber-stress S, in pounds per square inch, according to the formula for flexure, is 5 = Mc/I. For hollow cyHnders of large diameter and small thickness, the moment of inertia I = irR'^t, in which R = mean radius in feet (equivalent to c in the flexure formula) and / = thickness of shell in inches. Hence S = MR/httRH = o.ioUI/DH, and / = o.io6M/SD'^. The stress S is tensile on the windward side and compressive on the leeward side. * Compiled from data furnished by Robins Fleming, t Mechanical Engineers' Pocket Book. Kent. X These dimensions were taken from a pamphlet published by the Philadelphia Engineer- IDK Works. Radial Brick Chimney 1377 There is also a small compressive stress due to the weight of the stack. The value of P may be taken at 25 lb per sq ft and of 5 at 16 000 lb per sq in, as given in the Specifications for the Structural Steel Work for Buildings, Chapter XXX. As stacks are built for durability as well as strength it is often advisable to increase the theoretical thickness of the shell. No plate should be used with a thickness less than ]i in. It is important that the stack be securely anchored to the foundation. Many methods have been proposed for determining stresses in anchor-bolts. As the problem depends for its solution on the physical con- ditions of stack, base and bolts, no exact analysis is possible. (See editorial dis- cussion after article, Anchor-Bolt Tension, in Engineering News, April 30, 19 14.) The most severe assumption is that the bolts are screwed up with a high initial tension. The anchor-bolt ring can then be considered in the same way as a ring of the cylinder. The maximum stress at any point of the bolt-circle is devel- oped when the wind is blowing parallel to the radius through that point. The stress for each circumferential inch is 0.106M / {iRi)'^, 2R1 being the diameter of the bolt-circle. Let b be the circumferential distance in inches between adjacent anchor-bolts, N the number of bolts equidistant on the bolt-circle and W the weight of the stack. For the anchor-bolt on the windward side there is a tensile stress, Sw, due to the wind, Sw =0.I06Wf/(2i?l)2] Since b = (2R1 X 12 X 7r)/iV Sw = 2M/R1N Deducting the weight of the portion of the stack between adjacent bolts, the maximum tensile stress in any anchor-bolt may be expressed by the equation Sw = {2M/RyN) -W/N Radial-Brick Chimneys. These chimneys are built with special blocks formed to suit the circular and radial lines of each section of the chimney so that the finished brickwork has joints of an even thickness throughout and a perfectly smooth surface. The blocks being much larger than common bricks, there are only from one third to one half as many joints. Radial-brick chim- neys are always circular in plan above the base. The best form of base is octag- onal in cross-section so as to permit the breeching to enter the chimney at a flat surface and at the same time comply best with the rules of stability. Except for chemical-works, refineries, furnaces, etc., radial-brick chimneys are built with a single shell, a lining only being provided in the immediate vicinity of the flue-entrance. All radial bricks are perforated vertically and this insures thorough burning and allows the mortar to enter the perforations, thus forming a vertical anchorage. Radial blocks for chimney-construction have been used extensively in England, Germany, France and Russia since 1870. They were not introduced into this country, however, until 1898. About forty-five years ago (1869 or 1870) Alphons Custodis, of Diisseldorf, Germany, originated a method of building tall chimneys of perforated radial blocks, made from selected clays and burned at a very high temperature, and in 1898 an American company * was formed for the purpose of erecting chimneys by this method of construction. Since * Alnhons Custodis Chimnev Construction Comnanv. New York Citv. 1378 Chimneys Part 3 that time the company through various agencies has built more than six thousand chimneys in all parts of the world. The tallest chimney in the world (1919), 585 feet high and 60 ft in internal diameter at the top, was built by this company in 19 18 for the Anaconda Copper Company, at Ana- conda, Mont. Mr. H. R. Heinicke,* of Chemnitz, Germany, builder of the 460-ft stack at Halsbriicke, Germany, has employed radial bricks made especially for each chimney. This firm through long and costly research has done much to make chimney-building a science. The chimney at Halsbriicke is a very remarkable one on account of its proportions. In a height of 460 ft, the diameter at the top is only 8 ft, whereas the 585-ft stack at Anaconda, Mont., has a diameter of 60 ft at the top. The Heine Chimney Company f has erected many important high chimneys. The essential difference in the methods of construction used by this company from those of the other chimney-constructors is that the Heine Chimney Com- pany uses perforated, interlocking, radial bricks. It is claimed that this interlocking-fcature has an advantage over the straight-sided bricks in acting as a preventive of deep weathering of the joints and of air-leaks. In addition to this it is claimed that the circumferential strength of the walls when built of this type of brick is considerably greater than when built with plain-sided or corrugated bricks. The perforations in these bricks arc fewer but larger than those of some of the other constructors. The brickwork is laid on full-mortar beds with shoved joints. These large perforations allow the mortar to rise in them, thus forming pins which give the walls great strength and enable them to withstand the stresses due to expansion caused by the high temperature of the flue-gases. In walls more than one brick thick, the bricks are laid up in English bond, that is, with alternate header and stretcher-courses. This com- pany advocates this method of construction even in chimneys built with the ordinary straight-sided common building-bricks. Among the many important chimneys constructed by the Heine Chimney Company is the one erected at the St. Joseph Lead Company's plant, at Herculaneum, Mo. The height of this chimney is 350 ft and the inside diameter at the top 20 ft. (Seepage 1706.) The W. M. Kellogg Company J has designed and built many radial-brick chimneys for power-plants, chemical-works and other purposes. Several of the iniportant chimneys put up by them are mentioned in the hst of tall chimneys (page 1379). Some of the details of construction differ from those of the other companies mentioned. One of the points of difference is the detail relating to the corrugations on their bricks. These corrugations are 3i in wide and }4 in deep and are placed along the vertical sides of the bricks as they lie in the wall. The adhesion between the bricks and mortar is increased by this increased area, It is claimed that tests made show that this is the case. On account of these corrugations it is not considered necessary to embed any ironwork in these chimneys to prevent the development of cracks due to heat-expansion. Iron- work has sometimes been inserted when plain-sided bricks have been used. It is claimed that this design is somewhat heavier than that employed by some other constructors, this company holding that it is not safe to figure on wind- pressure of less than 25 lb per sq ft of projected area. Among the many tall chimneys erected by this company may be mentioned especiall}' the * H. R. Heinicke, Incorporated, New York City, t The Heine Chimney Company, Chicago, 111. Partial List of Tall Chimneys 1379 chimney at Douglas, Ariz., erected for the Copper Queea Consolidated Mining Company, There are other reliable companies which design anfl construct tall chimneys. Those mentioned here were the pioneers in this work. Partial List of Tall Chimneys Over 300 Feet in Height It is to be noted that this list is constantly added to from year to year. ' Diam. Height, inside ft at top, ft *Anaconda, Mont., Anaconda Copper Co. (19 18) 585 60 *Tacoma, Wash., American Smelting & Refining Co. (1917) . . . 573 25 t Saganoseki, Japan, Oriental Compressol Co. (1917) 570 263^ *Great Falls, Mont., Boston & Montana Consolidated Copper and Silver Mining Co. (1907) 506 50 X Freiberg, Saxony, Germany, Halsbriicke Foundry 460 8 Glasgow, Port Dundas, Scotland, F. Townsend 454 Glasgow, St. Rollox, Scotland, Tenant & Co 436 3^ *Jerome, Ariz., United Verde Extension Mining Co. (191 8) 425 30 Creusot, France, Messrs. Musprath Chemical Works 406 §Clarkdale, Ariz., United Verde Copper Co 400 ^0% *E1 Paso, Tex., Consolidated Kansas City Smelting & Refining Co. (1916) 400 30 *Hayden, Ariz., American Smelting & Refining Co. (191 1) 400 25 *East Helena, Mont., American Smelting & Refining Co. (1917). 400 16 Hahfax, Dean Clough Mill, Scotland, Messrs. Crossley's 381 *Easton, Pa., C. K. Williams & Co. (191 1) 375 7 Lancashire, Bolton, England, DolDson & Barlow 367 ♦Rochester, N. Y., Eastman Kodak Co. (two) (1906, 191 1) 366, 9 and 13 ♦Constable Ilook, N. J., Orford Copper Co. (two) (1900, 1910). . 365 10 ♦Garfield, Utah, Garfield Smelting Co. (1913) 350 22 iJHerculaneum, Mo., St. Joseph, Lead Co 350 20 Boston, Mass., Fall River Iron Co 350 n *Newark, N. J., Heller Merz Co (1904) 350 8 East Newark, N. J., Clark Thread Co 335 Barmen, Prussia, Germany, Wessenfield & Co 331 Edinburgh, Scotland, Gas-Works 329 JCopper Hill, Tenn., Tennessee Copper Co 325 20 JIndianapohs, Ind., Indianapolis Traction Co 320 13 Huddersfield, England, Brook & Son, Fire-clay Works 315 Smethwick, England, Adams Soap- Works 312 ♦Providence, R. I., Rhode Island Suburban Railway Co 308 16 ♦New York City, N. Y., New York Steam Co. (1904) 308 15 Carhsle, England, P. Dickon & Son 300 Bradford, England, Mitchell Brothers 300 * Constructed by the Alphons Custodis Chimney Construction Company, New York City. t Reinforced concrete, The Weber Chimney Company, Chicago, 111. i Constructed by H. R. Heinicke, Incorporated, New York City. § Self-sustaining steel chimney, the largest (of this type) in the world (1919). II Constructed by The Heine Chimney Company, Chicago, 111. 1380 Chimneys Part 3 Partial List of Tall Chimneys over 300 Feet in Height (Continued) Diam. Height inside ft at top ■ ft ♦Garfield, Utah, American Smelting and Refining Co. (1905) 300 30 *Hayden, Ariz., American Smelting and Refining Co 300 25 t Douglas, Ariz. Copper Queen Consolidated Mining Co 300 22 ITacoma, Wash., Tacoma Smelting Co 300 18 §McGill, Nev., Steptoe Valley Traction Co 300 15 ♦Brooklyn, N. Y., Nichols Chemical Co. (1905) 300 12 *Claymont, Del., General Chemical Co. (1912) 300 8 * Constructed by the Alphons Custodis Chimney Construction Company, New York City. t Constructed by The M. W. Kellogg, Company, New York City. X Reinforced concrete, The Weber Chimney Company, Chicago, III. § Constructed by H. R. Heinicke, Incorporated, New York City. Hydraulics 1381 HYDRAULICS, PLUMBING AND DRAINAGE, ILLUMI- NATING-GAS AND GAS-PIPING By J. J. COSGROVE CONSULTING SANITARY ENGINEER (i) HYDRAULICS Water is practically an incompressible liquid, weighing, at the average temper- ature of 62° F., 62.355 lb to the cu ft and 8.335 lb to the gallon. These figures change slightly with changes in temperature and atmospheric pressure, and a sUght variation for the same temperature will be found in different works. Pressure of Water. The pressure of still water in pounds per square inch against the sides of any pipe or vessel of any shape whatever is due alone to the HEAD, or height of the surface of the water above the point considered pressed upon, and is equal to 0.433 lb per sq in for every foot of head at 62° F. The fluid-pressure per square inch is equal in all directions. To find the total pres- sure of quiet water against and perpendicular to any surface, whether vertical, horizontal, or inclined at any angle, whether it be flat or curved, multiply together the area in square feet of the surface pressed, the vertical depth of its center of gravity below the surface of the water, and the constant 62.4. The product will be the required pressure in pounds. This may be expressed by formula as follows: P = 62.4.AD in which P = the pressure in pounds of quiescent water on the surface considered; A = the area pressed upon in square feet; and D = the vertical depth in feet of center of gravity of surface considered. Table A. Pressure in Pounds per Square Inch for Different Heads of Water in Feet Head, ft I 2 3 4 S 6 7 8 9 0.433 0.866 1.299 1.732 2.165 2.598 3.031 3.464 3.897 10 4 330 4.763 5.196 5.629 6.062 6.495 6.928 7.361 7.794 8.227 20 8.660 9.093 9.526 9.959 10.392 10.825 11.258 II. 691 12.124 12.557 30 12.990 13.423 13.856 14.289 14.722 15.155 15.58S 16.021 16.454 16.887 40 17.320 17.753 18.186 18.619 19.052 19.485 19.918 20.351 20.784 21.217 50 21.650 22.083 22.516 22.949 23.382 23.815 24.248 24.681 25.114 25.547 60 25.980 26.413 26.846 27.279 27.712 28.145 28.578 29.011 29.444 29.877 70 30.310 30.743 31.176 31.609 32.042 32.475 32.908 33.341 33.774 34.207 80 34.640 35.073 35.506 35-939 36.372 36.805 37.238 37.671 38.104 38.537 90 38.970 39.403 39.836 40.269 40.702 41 . 135 41.568 42.001 42.436 42.867 The pressure for greater heads can be readily found by multiplication or addi- tion; thus, the pressure for a head of 1 10 ft is ten times that for- 11 ft. The presc» sure for 118 ft is equal to the pressure for no ft plus that for 8 ft. 1382 Hydraulics, Plumbing and Drainage, and Gas-Piping Part 3 Flow of Water in Pipes. Owing to the- many practical and variable con- ditions which affect the flow of water in pipes, such as the smoothness of the pipe, number and character of the joints, bends and valves in the pipe, to say nothing of the size and length of the pipe, all formulas for the velocity and discharge of water in and through pipes can only be considered as approximate. The following formulas and data are taken largely from the National Tube Company's Book of Standards, 1902 edition. They agree fairly well with similar tables by Kent and Trautwine, both of whom devote much space to this subject. The quantity of water pmssing through a given pipe is governed by the sectional area of the pipe or outlet and the mean velocity. The velocity depends primarily upon the pressure or head, and is greatly affected by FRICTION, which again varies with the smoothness of the bore, the diameter and length of the pipe, and whatever obstructions there may be in the pipe. The head is the vertical distance from the surface of the water in the reservoir to the center of gravity of the lower end of the pipe when the discharge is into the air, or to the level surface of the lower reservoir when the discharge is under water. When the pressure is produced by mechanical means, the head of water in feet may be readily determined by the following table: Table B.* For Converting Pressure in Pounds per Square Inch into Head of Water in Feet Pres- sure I 2 3 4 5 6 7 8 18.476 9 2.309 4.619 6.928 9-238 11.547 13.857 16.166 20.785 10 23.0947 25.404 27.714 30.023 32.. 333 34.642 36 952 39.261 41.570 43.880 20 46.1894 48.499 50.808 53.118 55.427 57. 737 60.046 62.356 64.665 66.975 30 69.2841 71.594 73.903 76.213 78.522 80.831 83.141 85.450 87.760 90.069 40 92.3788 94.688 96.998 99.307 101.62 103.93 106 . 24 108.55 110.85 113 16 50 115.4735 117.78 120.09 122.40 124.71 126.02 129.33 131.64 133.95 136.26 60 138.5682 140.88 143.19 145.50 147.81 150.12 152.42 154.73 157.04 159 35 70 161.6629 163.97 166.28 168.59 170.90 173.21 175.52 177.83 180.14 182.45 80 184.7576 187.07 189.38 191.69 194.00 196.. 31 198.61 200.92 203.23 205.54 90 207.8523 210.16 212.47 214.78 217.09 219.40 221.71 224 . 02 226.33 228.64 * Tables A and B are exact for water at 62° F. ^nd for atmospheric pressure at 14.7 lb per sq in. To find the velocity of water discharged from a pipe-line longer than four times its diameter, knowing the head, length and inside diameter, use the following formula: J hd V z -I- 54 £ in which V = approximate mean velocity in feet per second; m = coefficient from the table below; d = diameter of pipe in feet; h = total head in feet; L = total length of hne in feet. The following coefficients are averages deduced from a large number of experi- ments. In most-cases of pipes carefully laid and in fair condition, tbey should give results varying not more than from 5 to xo%, Hydraulics Values of Coefficient m 1383 Diameter of pipe in feet J hd ▼ L + 54 ^/ 0.05 O.IO 0.50 I 1.5 2 3 4 m m m m m m m m 0.005 29 31 33 35 37 40 44 47 O.OI 34 35 37 39 42 45 49 S3 0.02 39 40 42 45 49 52 56 59 0.03 41 43 47 50 54 57 60 63 0.05 44 47 52 54 56 60 64 67 O.IO 47 50 54 56 58 62 66 70 0.20 48 51 55 58 60 64 67 70 Example. Given the head, h= 50 ft; the length, L= s 280 ft and the diam- eter, d= 2 it; to find the velocity and quantity of discharge. Substituting these values in the foregoing formula, we get A/dxh _ 4 / 2 X 50 _ 4 / 100 _ V LTs4~d ~ V 5280+108 " V ^388 ~ °"'^ In column headed find O.IO, which is the value nearest to 0.136, and look along this line until column headed 2 is reached; then read 62 as the value of coefficient m. Then z) = 62 x 0.136 = 8.432 ft per sec, the velocity required. To find the discharge in cubic feet per second, multiply this velocity by area of cross-section of pipe in square feet. Thus, 3.1416 X (i)^ X 8.432 =- 26.49 cu ft per sec. Since there are 7.48 gal in a cubic foot, the discharge in gallons per second == 26.49 X 748= 198.2. The above formula is only an approximation, since the flow is modified by bends, joints, incrustations, etc. To find the head in feet necessary to give a stated discharge in cubic feet, use the formula 0.000704 Q2 (L -^ 54 d) h- d^ in which h = total head in feet; L = total length of line in feet; d = diameter of pipe in feet; Q = quantity of water in cu ft per second. Example. Given the diameter of pipe, d= 0.5 ft; the length of pipe, L =» 20 ft; and the quantity of water to be discharged, q= 3.07 cu ft per sec; to find the necessary head. Substituting these values in the above formula, we get 0.000704 X 9.4 X (20+ 27) (0.5)^ 0.000704 X 9.4 X 47 0.03125 = 9-95 ft, the required head. 1384 Hydraulics, Plumbing and Drainage, and Gas-Piping Part 3 The following fonnula is simpler and can be used when 54 d in relation to L is so small as to be negligible: 0.000704 Q^x L * d^ — If the pipe instead of being straight has easy curves (say with radius not less than five diameters of the pipe) either horizontal or vertical, the discharge will not be materially diminished so long as the total heads and total actual lengths of pipe remain the same, but it is advisable to make the radius as much more than five diameters as can conveniently be done. To find the diameter of a pipe of given length to deliver a given quantity of water under a given head use the following, d = 0.234 ' fQ^L in which d = diameter of pipe in feet; Q = cubic feet per second delivered; L = length of line in feet; h = head in feet. Example. Given the head, h= 700 ft; the length of pipe, L= 3000 ft; the quantity to be delivered, Q = 4 cu ft per sec; required the diameter of pipe necessary. Substituting these values in the foregoing formula, we get : \A 6 X 3 000 5 /— — = 0.234 V 68.57 = 0.545 ft = 6.54 m 700 To find the diameter of pipe required to deliver a given quantity of water with a given head. Rule, (i) Reduce the head to feet per 100 ft; (2) from Table C, page 1385, find the discharge for the head thus obtained through a pipe i ft in diameter; (3) divide the required discharge by that obtained from Table C; look for the quotient in the column of Table D, page 1386, headed Ratio of Discharge, etc., and opposite it, in the adjoining columns of the table, will be found the re- quired diameter. Note. The use of Tables C and D gives results sufficiently correct for pipes less than 700 diameters in length. Example. If the head of water from a reservoir to the point of delivery is 20 ft in a distance of i 860 ft, what is the diameter of a pipe required to deliver 6 cu ft of water per second? 20 ft head in i 860 ft = 20/18.60 ft in 100 ft, or 1.075 ft in 100 From Table C we find that the discharge per second with a head of 1.136 is 3.989 cu ft; for a head of 1.075 it would be about 3.8 cu ft. Dividing the re- quired discharge 6, by 3.8 cu ft per sec, we have 1.58. From Table D the diameter of pipe having a ratio of discharge equal to 1.58 is found to be about 14H in; therefore we must use a 15-in pipe to obtain the required discharge. If the required discharge is in gallons, divide by 7.5 to reduce to cubic feet. If in cubic feet per minute, divide by 60 to reduce to feet per second, Hydraulics 1385 Table C. Velocities and Discharges Through a Straight, Smooth Pipe One Foot in Diameter and One Mile, or s 280 Diameters, in Length Head in feet per 100 ft Head in feet per mile Velocity in feet per sec Discharge in cubic feet per sec Discharge in cubic feet per 24 hours 0.0568 3 1. 13 0.8914 76982 O.Q758 4 1.31 1.028 88 862 0.0947 5 I 47 1. 150 99403 0.1136 6 1. 61 1.264 109209 0.1325 7 1.74 1.366 118 022 0.1514 8 1.86 1-455 125 740 0.1703 9 1.96 1-539 132 969 0. 1894 10 2.08 1-633 141 145 0.2273 12 2.27 1.782 153 964 0.2652 14 2.45 1.924 166 233 0.3030 16 2.62 2.057 177 724 0.3409 18 2.78 2.183 188 611 0.3788 20 . 2.93 2.301 198806 0.4735 25 3.28 2.572 222 156 0.5682 30 3 59 2.819 243 604 0.6629 35 3.88 3.047 263260 0.7576 40 415 3.267 282 288 0.8523 45 4.40 3 451 298 209 0.9470 50 4.64 3.638 314 352 1. 136 60 5. 08 3-989 344 649 1.326 70 5.49 4 311 372 470 1. 515 80 5.85 4.602 397 613 1.704 90 6.23 4.900 423 435 1.894 100 6.56 5.144 444 312 2.083 no 6.87 5.395 466 128 2.272 120 7.18 5 639 487 209 2.462 130 7.47 5866 506822 2.652 140 7.76 6.094 526 521 2.841 150 8.05 6.322 546 048 3.030 ■ 160 8.30 6.534 564 576 3.219 170 8.55 6.715 580 176 3408 180 8.80 6.903 596 418 3.596 190 9.04 7.100 613 440 3.788 200 9.28 7.276 628 704 4.261 225 9-84 7.696 664848 4.735 250 10.4 8.168 705 728 5.208 275 10.8 8.482 732 844 5. 682 300 II. 3 8.914 769 824 6.629 350 12.3 9.621 831 168 7.576 400 13 I 10.28 888 624 8.532 450 13.9 10.91 943 056 9-47 500 14.7 11.50 994 032 10.41 550 15.4 12.09 I 044 576 11.36 600 16. 1 12.64 I 092 096 12.30 650 16.7 13. II I 132 704 13-25 700 17-4 13.66 I 180 224 14.20 750 18.0 14.13 I 220 832 15.15 800 18.6 14.55 I 257 408 16.09 850 19. 1 15 00 I 296 000 17.04 9CO 19.6 15 39 I 329 696 17-99 950 20.3 15 94 I 377 216 18.94 I 000 20.8 16.33 I 411 456 22.73 I 200 22.7 17.82 I 539 648 26.52 I 400 24.5 19.24 I 662 336 30.30 I 600 26.2 20.57 I 777 248 34 08 I 800 27.8 21.83 I 886 112 37.87 2 000 29-3 23.01 I 988 064 47.35 2 500 32.8 25.72 2 221 560 56.81 3000 35.9 28.19 2 436 040 1386 Hydraulics, Plumbing and Drainage, and Gas-Piping Part 3 Table D. Diameters of Pipes and Ratio of Discharge Ratio of dis- Ratio of dis- Diameter of pipe, in Diameter of pipe, ft charge to that through a i-ft pipe with the same head per mile Diameter of pipe, in Diameter of pipe, ft charge to that through a i-ft pipe with the same head per mile I 0.0833 0.0020 12H 1.042 1. 106 i\^ 0.1250 0.005s 13 1.083 1. 221 2 0.1667 0.0113 14 1. 167 I 470 2H 0.2083 0.0198 15 1.250 1.746 3 0.2500 0.0310 16 1.333 2.053 3H 0.2917 0.0458 17 1. 417 2.388 4 0.3333 0.0643 18 1.5 2.754 4^2 0.3750 0.0857 .19 1.583 3 153 S 0.4167 0.1119 20 1.667 3.585 sVi 0.4583 0.1422 21 1.75 4.051 6 0.5 0.1767 22 1.833 4.551 6\i 0.5417 0.2159 23 1.917 5.084 7 0.5833 0.2600 24 2 5. 649 7H 0.6250 0.3090 24H 2.052 6.000 8 0.6667 0.3631 26 2.167 6.912 m 0.7083 0.4220 28 2.333 8.319 9 0.75 0.4871 30 2.5 9.822 9M 0.7917 0.5575 30j<4 2.521 10. 10 0.8333 0.6337 32 2.667 II. 6 10K2 0.8750 0.7157 34 2.833 13.5 II 0.9167 . 8044 36 3 15. 5 11'/^ 0.9583 0.8987 38 3.167 17.8 12 I I 40 3.333 20.2 This table shows, also, the relative discharging capacities of long pipes. Thus, one i2-in pipe is equal to two 9-in pipes, to nearly six 6-in pipes, or to thirty- three 3-iii pipes. Hydraulics Table E. Flow of Water in House Service-Pipes Thomson Meter Company To find the discharge in gallons, multiply by 7.47 1387 Condition of discharge Pres- sure in main, lb per sq in Discha rge in cubic feet per minute from the pipe Nominal diameters of iron or lead service-pipe in inches Yz % ¥i I iVi 2 3 4 6 Through 35 ft of service- 30 1. 10 1.92 3.01 6.13 16.58 33.34 88.16 173.85 444.63 40 1.27 2.22 3.48 7.08 19.14 38.50 101.80 200.75 513.42 50 1.42 2.48 3.89 7.92 21.40 43.04 113.82 224.44 574.02 pipe; no 60 1.56 2.7.1 4.26 8.67 23.44 47.15 124.68 245.87 628.81 back- 75 1.74 3.03 4.77 9.70 26.21 52.71 139.39 274.89 703.03 pressure 100 2.01 3 50 5.50 11. 20 30.27 60.87 160.96 317.41 811.79 130 2.29 3.99 6.28 12.77 34.51 69.40 183.52 361.91 925.58 Through 100 ft of 30 0.66 1. 16 1.84 3.78 10.40 21.30 58.19 118. 13 317.23 40 0.77 1.34 2.12 4.36 12.01 24.59 67.19 136.41 366.30 service- pipe; no back- 50 0.86 I. SO 2.37 4.88 13.43 27.50 75.13 152.51 409.54 60 0.94 1.65 2.60 5. 34 14.71 30.12 82.30 167.06 448.63 75 1.05 1.84 2.91 5.97 16.45 33.68 92.01 186.78 501.58 pressure 100 1.22 2.13 3.36 6.90 18.99 38.89 106.24 215.68 579-18 130 1.39 2.42 3.83 7.86 21.66 44.34 121. 14 245.91 660. 3<> Through 100 ft of service- pipe and IS-ft ver- tical rise 30 0.55 0.96 1.52 3.11 8.57 17.55 47.90 97.17 260.56 40 0.66 1.15 1. 81 3.72 10.24 20.95 57.20 I 16. 01 311.09 50 0.75 I-3I 2.06 4.24 11.67 23.87 65.18 132.20 354.49 60 0.83 1-45 2.29 4.70 12.94 26.48 72.28 146.61 393 13 75 0.94 1.64 2.59 5.32 14.64 29.96 81.79 165.90 444.85 100 1. 10 1.92 3 02 6.21 17.10 35.00 95.55 193.82 519-72 130 1.26 2.20 3.48 7.14 19.66 40.23 109.82 222.75 597-31 Through 100 ft of 30 0.44 0.77 1.22 2.50 6.80 14. II 38.63 78.54 211 54 40 0.55 0.97 1-53 3.15 8.68 17.79 48.68 98.98 266.59 50 0.65 1. 14 1.79 3.69 10.16 20.82 56.98 115.87 312.08 service- pipe and 30-ft ver- tical rise 60 0.73 1.28 2.02 4.15 11.45 23.47 64.22 130.59 351-73 75 0.84 1.47 2.32 4.77 13.15 26.95 73.76 149.99 403.98 100 1.00 1.74 2. 75 5.65 15.58 31.93 87.38 177.67 478.55 130 1. 15 2.02 3.19 6.55 18.07 37.02 101.33206.04 554.96 Table E may also be used when the pressure is In feet-head of water by reducing the head in feet to pounds per square inch by Table A. Thus, if we wish the discharge per minute through a %-in pipe 100 ft long with a head of 70 ft, we find from Table A that a head of 70 ft corresponds to a pressure of 30 lb per sq in, and from Table E we find the discharge through a %-in pipe 100 ft long with a pressure of 30 lb to be 1.84 cu ft per minute. 1388 Hydraulics, Plumbing and Drainage, and Gas-Piping Part 3 Table F. Friction of Water in Pipes Based on Ellis and Rowland's Experiments The following table gives the friction-loss in pounds-pressure per square inch for EACH loo ft of length in clean iron pipes of different sizes, discharging given quantities of water per minute. This friction-loss is greatly increased by bends or irregularities in the pipe. To find the friction-head in feet, multiply by 2.3 Gallons per minute Sizes of pipes, inside diameter % in I in i'/4 in ij'i in 2 in 2y2 in 3 in 4 in IS 20 25 30 35 40 45 50 75 IOC 125 150 175 200 250 300 350 400 450 500 600 700 3.3 13.0 28.7 50.4 78.8 0.84 3.16 6.98 12.3 19.0 27.5 37.0 48.0 0.31 1.05 2.38 4.07 6.40 915 12.4 16. 1 24.9 56.1 0.12 0.47 0.97 1.66 2.62 3.75 5. 05 6.52 8.15 10. o 22.4 390 0.12 0.26 0.42 0.64 0.91 1.22 1.60 2.02 2.44 5.32 946 14.9 21.2 28.1 37.5 21 I 3 4 7 9 12 19 28 81 80 20 89 00 46 47 66 06 0.20 0.35 0.74 1. 31 1-99 2.85 3.85 5.02 7.76 II. 2 15.2 19 5 25.0 30.8 0.09 0.23 0.33 0.49 0.69 0.94 1.22 1.89 2.66 •^.65 4.73 6.01 7.43 9-54 14.32 Water-Pipe is usually tested to 300 lb pressure per square inch before delivery, and a hammer-test should be made while the pipe is under pressure. The usual length for each section of cast-iron water-pipe is from 12 ft 4 in to 12 ft 6 in, de- pending upon the depth of the socket, each length making approximately 12 ft of pipe when laid. Pipes from 2 to 4 in diameter are sometimes made in 8 or 9-ft lengths. Hydraulics 1389 Safe Pressures and Equivalent Heads of Water for Cast-Iron Pipes of Different Sizes and Thicknesses Calculated by F. H. Lewis from Fanning's Formula Thick- Size of pipe, in 4 6 3 10 12 14 ness, in 2? 1- ia ia 1 1"^ ta Mr. 112 258 49 112 18 42 Vi 224 516 124 280 74 171 44 lOI 24 55 9/i6 336 774 199 458 130 300 89 205 62 143 42 97 % 274 631 186 429 132 304 99 228 74 170 iHe 177 . 408 137 316 106 244 % 224 S16 174 401 138 316 ^U 212 488 170 392 H 249 574 202 465 1^6 234 538 I 266 612 i6 18 20 24 30 36 - H 56 129 41 95 ^VlQ 84 194 66 152 SI 118 30 69 3/4 112 258 91 210 74 170 49 113 24 55 13/16 140 323 116 267 96 221 68 157 39 90 % 168 387 141 325 119 274 86 198 54 124 32 74 1^6 196 452 ibb 382 141 32s 105 242 69 159 44 lOI I 224 516 191 440 164 378 124 286 84 194 57 131 iH 216 497 209 481 161 371 114 263 82 189 iH 256 589 199 458 144 332 107 247 iH 237 546 174 401 132 304 i^A 204 470 157 362 iH 234 538 182 419 iH 207 477 Weights of Lead and Gaskets for Pipe- Joints Dennis Long & Company Diameter Lead, Gasket, Diameter Lead, Gasket, of pipe. lb lb of pipe. lb lb in m 2 2.5 0.I2S 12 15 0.250 3 3 5 0.170 14 18 0.375 4 4-5 0.170 16 22 0.500 6 6.5 0.200 18 26 0.500 8 90 0.200 20 33 0.62s 10 130 0.250 1390 Hydraulics, Plumbing and Drainage, and Gas-Piping . Part 3 Weights, per Foot, of Cast-iron Pipes in General Use, Including Socket-Ends and Spigot-ends Dennis Long & Company, Inc., Louisville, Ky. Diam- Thick- Weight Diam- Thick- Weight Diam- Thick- Weight eter, ness, per ft, eter, ness, per ft. eter, ness, per ft, in in lb in 16 in lb in in lb 3 H 12'/^ % 129 2 66e 30 Vu 15 U 152 36 % 334 H i8 I 175 I 382 Ha 2oyi. 18 H 120 1% 432' H 23 H 146 iH 482 4 H 17 % 171 iH 532 Vie 20 I 197 iH 587 H 2ZVl iKs 223 iH 632 «/|6 26^4 iK 249 iH 683 H 30 20 iHe 148 1% 734 6 M6 + 30 M 161 2 786 H 34 % 190 42 I 445 »/l6 38H I 216 iH 471 H 42?.^ iH 247 iH 560 H 52 iK 276 iH 629 8 Vie 40 iH 305 iH 675 Vi 43K2 i].i 334 iH 734 Vie 49% 24 H 191 iH 794 H 56 li 225 1% 853 H 68 I 258 2 912 10 lU 50 1% 293 48 iH 572 \h 54 iH 327 iH 637 «/i6 60 iH 361 r)i 701 % 68 iH 395 iH 768 % 82 1% 430 1% 835 12 H 70 1% 465 iH 901 Me 76 30 1^6 258 1% 967 H 82 % 278 2 1034 Vi. 99 I 319 60 iH 797 % 117 1% 360 iH 880 14 9l6 85 m 405 iH 964 H 94 1% 448 iH 1049 % 113 m 489 iH I 133 i6 9l6 137 100 1% 532 575 2 I 216 1300 1% ^^ 108 1% 619 2H 1470 There is no standard weight of pipe for any given pressure. Private Water-Supply. Pumps Private Water-Supplies. The architect is frequently required to furnish a water-supply for isolated buildings, and even in cities it is becoming quite common for manufacturing establishments and large buildings to have their " own water-supply; so that some knowledge of the various methods of sup- plying water is requisite. Power-pumps are of so many kinds and so intri- cate in construction that no attempt will be made to describe them. The Hydraulic Ram. Where a small stream of water having a fall of 2 ft or more flows near the premises, an hydraulic ram may be used to great advan^ Private Water-Supply. Pumps 1391 tage to furnish water for domestic purposes, or even for irrigation. The ram is operated by the momentum of the water flowing through the drive-pipe and dehvers water into an open tank. Wate^; can be conveyed by a ram 13 000 ft when elevated 500 ft, provided there is sufficient fall. The drive-pipe supplying the ram should be 30 or 40 ft long to give the necessary momentum. The use of the ram is the most economical method of pumping water, as there is no expense for maintenance except for repairs, and the cost of installation, also, is small. The Capacities of the Rife Rams are given in the following table. The capacities are determined from the table by multiplying the available supply of water per minute, or the rated amount of water a Rife ram will use, by the factor found in the table at the intersection of the line giving the fall available, for the drive-pipe, and the column showing the height the water is to be elevated. The factor for a lo-ft fall and 50-ft discharge is 192, and this multiplied by the supply of water per minute will give- the delivery per day. This is shown by the example worked out in the corner of the table. These capacities are based on efficiencies dependent on the ratio of fall to lift. A fall of 10 ft and a lift of 50 ft give a ratio of i to 5, and an efficiency of 66%%. The efficiencies of Rife rams based on various ratios, are also given in the table. Deep "Wells and Plunger-Pumps. The common method of obtaining a private water-supply is to drive a deep well until a sufficient supply of water is obtained. The depth to which a well must be driven will, of course, depend upon the locahty, and can only be determined by drillings. As the well is driven, a large wrought-iron pipe is sunk to form the casing. Casings are seldom less than 6 or more than 10 in inside diameter, 8 in being the common size. When the water-pocket has been reached, the water will usually rise and stand in the pipe several hundred feet above its bottom, and the amount of water that can usually be pumped from such wells, with- out lowering the water, is prac- tically unHmited. The cost of drilling deep wells, per foot of depth, INCLUDING THE CASING, differs, of course, with the strata, location and other local conditions. As a rule, however, it will average about $5 per foot for a well driven through rock and $6 per foot for a well through sand. For raising the water into an open tank a single-acting pump consisting of a working- head, (Fig. 1), which operates a cylinder placed in a smaller pipe lowered into the well through which the water is raised, is commonly employed. The cylinder should preferably be placed below the water-line in the well, and is usually connected with the working-head by wooden sucker-rods. The working- Fig. 1. Working- head for Deep- well Pump Fig. 2. Deep-well Working- head for Belt-attachment 1392 Hydraulics, Plumbing and Drainage, and Gas-Piping Part 3 Table of Water Required for Rife Rams Dimensions Size of Size of Gallons per minute Least no. of feet of Num- drive- deliv- required fall Weight, ber Height, ft in Length, ft in Width, ft in pipe, in ery- pipe, in to operate engine, gal recom- mended, ft lb 10 2 I 3 2 I 8 iM % 3 to 6 3 150 IS 2 I 3 4 I 8 i\^ % 5 to 12 3 175 *20 2 3 3 8 I 9 2 I 10 to 18 2 225 25 2 3 3 9 I 9 2I/2 I II to 24 2 250 30 2 7 3 10 I 10 3 iM IS to 3S 2 275 40 3 3 4 4 2 O 4 2 30 to 7S 2 600 8o 7 4 8 4 2 8 8 4 ISO to 3SO 2 2500 *I20 12 5 6 375 to 750 750 to I 500 2 3 000 tl20 8 9 9 6 3 8 12 (two) 2 5500 • Singl« '• t Dupl ex. Table of Capacities of Rife Rams Power- head or fall in ft Height or head in feet the water is to be delivered 4 10 15 20 30 40 *So 60 70 80 90 100 120 140 160 180 200 2 3 4 S 6 7 8 9 *I0 12 14 16 18 20 22 24 26 28 30 540 J 02 301 432 540 128 192 256 345 432 505 96 144 192 240 302 378 432 485 540 64 96 128 160 192 235 270 300 360 430 505 43 72 96 120 144 168 192 216 252 301 353 432 486 540 29 58 77 96 115 134 154 173 *I92 230 270 323 390 430 475 520 24 43 64 80 96 112 128 144 160 192 224 257 303 336 370 405 470 505 540 37 55 69 82 96 no 124 137 165 192 220 247 288 303 346 375 430 465 27 43 60 72 84 96 108 120 144 168 192 2:6 24c 264 288 328 354 405 24 38 53 64 75 86 96 107 128 150 171 192 214 235 256 278 300 336 29 43 57 67 77 86 96 115 135 154 173 192 2X2 230 250 269 288 24 30 43 50 64 72 So 96 112 128 144 160 176 192 208 224 24c 26 31 36 55 62 68 82 96 no 124 137 151 164 178 192 206 27 31 43 54 60 72 84 96 108 120 132 144 156 168 180 24 28 38 64 75 85 96 IC7 118 128 139 149 160 25 29 39 43 57 67 77 86 96 IC5 lis 125 134 144 Example With a supply of I 400 gal per min, lo-ft fall, 50-ft ele- vation. No. 120 en- gine will deliver 268 800 gal per day . 140 0X1 92 = 268 800 * Multiply factor opposite power-head and under pumping-head by the number of gallons per minute used by the engine; the result will be the number of gallons deliV' ERED per day. The efficiency developed is governed by the ratio of fall to pumping-head. 75% for a ratio of i to 2 3'4 The efficiency of rife rams is based on. . . . 70% for a ratio of i to 3 66?^% for a ratio up to i to 18 60% for a ratio up to i to 23 . gal per hour and will deliver water from 50 to 350 ft above the surface of water in the well, although the higher the water is raised the less will be the quantity delivered. The cost of these engines, with pump at- tached, varies from $110 for the smallest size, having a capacity of 150 gal per hour raised 50 ft, to $540 for the largest size, having a capacity of 3 500 gal per hour raised 50 ft. The smaller size requires about i quart of kerosene or 3 lb of anthracite coal per hour. Hot-air engines should be placed close to the source of supply, and when the latter is a deep well the engine must be placed so that the pump-rod will, be in a vertical line above the cylinder in the well, the operation of pumping being the same as that of the ordinary single-acting deep-well pump. It is not practicable to draw water more than from 20 to 25 ft, in height, with any form of suction-pump, because of the difficulty of keeping the pipe, valve and fittings absolutely air-tight. For further information, see the catalogue of the Rider-Ericsson Engine Company. Action of Wind and Capacities of Pumping Windmills Velocity per hour in miles 25 30 40 50 60 80 100 Pressure * per square foot in pounds 0.045 0.125 0.33 0.5 1 . 125 2 3.125 45 8 12.5 18 32 50 Description of wind Just perceptible. . . . Pleasant wind Fresh breeze Average wind Good working wind Strong wind Very strong wind. . . Gale Storm Severe storm Violent storm ...... Hurricane Tornado Action of wind and windmills Windmills will not run Might start if lightly loaded Will start pumping Pumps nicely if properly loaded Does excellent work • Gives best service Maximum results secured Should be furled out of wind I Well-constructed mills and I towers safe if properly erected i Buildings, trees, etc., might be [ injured [ Buildings, trees, etc., would ' be injured Ruin Froi 1 the above table it will be seen that the only available winds are those blowing with a velocity of from 8 to 25 miles per hour, and that a 15-milc wind can be utilized to the best advantage. It is therefore advisable to load a windmill for a 15-mile wind. It then starts pumping in an 8-mile wind, does excsllent work in a is-mile wind and reaches the maximum results in a 25-mile wind. * The pressures per square foot in pounds will vary slightly from the values given according to the formula which is used to obtain such pressures. See, also, Chapter XXVII, pages 1052-3, Chapter XXX, page 1199, and page 1717. Windmills. In the country and on large suburban estates, windmills are extensively used for pumping water. Aside from the noise of operation, the only objection to the windmill, where it can be used, is the irregularity of its supply, but with a large storage-tank this is not a serious objection when used for domestic purposes only. Professor Thurston says, regarding windmills: *'In estimating the capacity, a working-day of eight hours is assumed, but the Private Water-Supply. Windmills 1395 machine, when used for pumping, may actually do its work twenty-four hours a day for days, weeks, and even months together, whenever the wind is stiff enough to turn it. It costs for work done only one-half or one-third as much as steam, hot-air, or gas-engines of similar power." The action of wind of different, velocities, the pressure per square foot of sail-s*irfacc and its relation to the pumping capacity of pumps can be found in the following table, compiled by Fairbanks, Morse & Company. The windmill operates the plunger in the well, the process of pumping being the same as that of the single-acting pumps described above. The following table of capacity was prepared by Alfred R. Wolff, and is sufficiently accurate for all practical purposes: Capacity of the Windmill Desig- Veloc- Gallons of water raised per minute Equiva- nation ity of Revolu- to an elevation of lent • of mill wheel, ft wind in miles per hour tions of actual wheel per minute 25 ft 50 ft 75 ft 100 ft 150 ft 200 ft useful h.p. developed SH i6 40 to 50 6.192 3.016 0.04 10 i6 .35 to 40 19.179 9.563 6^638 4.750 0.12 12 i6 30 to 35 33.941 17.952 II. 851 8.435 5.680 0.21 14 i6 28 to 35 45.139 22.569 15.304 11.246 7.807 4.998 0.28 "^ i6 i6 25 to 30 64.600 31.654 19.542 16.150 9 771 8.075 0.41 i8 i6 22 to 25 97.682 52.165 32.513 24.421 17.485 12. 211 0.61 20 i6 20 to 22 124.950 63.750 40.800 31 248 19.284 15.938 0.78 25 i6 16 to 18 212.381 106.964 71.604 49.725 37.349 26.741 1.34 The horse-power of windmills of the best construction is proportional to the squares of their diameters and inversely as their velocities; for example, a 10-ft mill in a 16-mile breeze will develop 0.15 horse-power at 65 revolutions per min- ute; and with the same breeze: a 20-ft mill, at 40 revolutions per minute, i horse-power; a 25-ft mill, at 35 revolutions per minute, 1% horse-power; a 30-ft mill, at 28 revolutions per minute, 3H horse-power". The wheels of very few windmills are larger than 25 ft in diameter. There are no pumps which will enable the user of a wihdmill to utilize the increased power obtained from winds of high velocity, so that in practice the amount of water pumped by windmills in high winds is but little more than is pumped by the same mills in winds having velocities of from 12 to 18 miles per hour. For this reason it is customary to regulate windmills to govern at about 25 miles an hour. Theoretically the increase in power from increased velocity of wind is equal to the square of its proportional velocity; as, for example, the 25-ft mill rated above for a 16-mile wind will, with a 32-mile wind, have its horse-power increased to 4 X 1% = 7 horse-power. A windmill "will run and produce work in an 8- mile breeze." Windmills have also been used for the generating and storage of electricity for small lighting-plants.* Air-Lift Process. Compressed air is now being used to an increasing extent for raising water from artesian wells. The process in general consists of sub- merging a discharge-pipe in a closed well, with a smaller pipe inside delivering * See Kent's Mechanical Engineers' Pocket-Book. 1396 Hydraulics, Plumbing and Drainage, and Gas-Piping Part 3 compressed air into it at the bottom. The compressed air by its inherent ex~ pansive force lifts a column of mingled air and water which is conveyed to an open tank, to permit of the escape of the air. If desired the water may then be conveyed by gravity into a series of closed tanks, and forced by air-pressure to different parts of a building, ^the only machinery required being an air-com- pressor and power for driving it The slip of the bubl)le constitutes the chief loss of energy in the air-lift. The method of piping a well differs according to its general conditions and the quantity of water to be pumped. "No two wells are alike, and consequently the method of piping which might be applied to one would be unsuited to another." Information as to the best method of piping any particular well may be obtained from the Ingersoll-Sergeant Drill Company. Advantages of the Air-Lift Process. From two to six times as much water may be obtained from a given diameter of well as with any other known system, because there are no valves, cylinders, or rods to hinder the rapid discharge of water. One air-compressor operates any number of wells, which may be any distance apart so as not to affect one another. There is nothing outside the engine-room to look after or wear out. Nothing but common pipe in the wells. Sand or gravel does no harm. The cost of raising i ooo gal of water by this method, including fuel, labor, oil, interest on cost of well, boiler, compressor, foundations, pipes, real estate, erection and taxes, including 15% for depre- ciation, runs from 2H cts down to H ct, according to the size of the plant, height of lift, and other local conditions. With the average outfit of medium or small size, it is usually under lYi cts.* The air-lift process is now exten- sively used in ice-works, breweries, cold-storage houses, textile mills, dye-works, . etc., and a great variety of industrial plants, and for the water-supply of' quite a number of the smaller cities. In Newark, N. J., pumps of this type are at work having a total capacity of i 000 ocx> gal daily, lifting water from three 8-in artesian wells. f Pneumatic Water-Supply Systems. The pneumatic system of supplying water to buildings is used extensively in buildings and institutions remote from public water-supplies. With the pneumatic system, instead of an open ele- vated tank, a closed water-tight tank of iron or steel is used, and this tank may be located at any level, for the water is forced from it by means of compressed air confined in the top of the tank. This fact makes it possible to bury the tank in the ground below the frost-line, away from the heat of the sun, and where the water will have an almost uniform temperature the year round. The water is protected from possible contamination from insects, rats, birds, dust, or other agencies, while the tank takes up no valuable space above ground, imposes no weight upon the attic-floor of a building, and does not disfigure the landscape. The principle of operation is this: Air is compressible, while water is not. If then, water is pumped into a closed tank at the bottom, it will trap the air within, and the more water pumped in, the greater the compression, of the air. The elasticity of the air, then, will force the water out again, whenever a faucet is opened, and the water will continue to flow as long as the air is under sufficient pres- sure in the tank. In practice the air would become absorbed by the water in the tank, and in a short time become exhausted, if it were not supplied as fast as used. This is accomplished by injecting a proportionate amount of air with each stroke of the pump, by means of a snifter-valve air-compressor, or other device. All connections to the tank are taken from the bottom, to prevent the escape of air which would occur if the connections were taken from the top of the tank. * InKersoll-Sergeant Drill Company. t Kent. Fire-Streams 1397 Horse-Power Required to Raise Water to Different Heights General Principles. The power required to raise a certain quantity of water to a certain height varies directly with the quantity to be raised, and also with the height. For instance, it requires twice as much power to raise 200 gal per minute 10 ft high as it does to raise 100 gal to the same height and in the same time; and to raise 100 gal 20 ft high requires twice as much power as it does to raise 100 gal 10 ft high. To find the theoretical horse-power necessary to elevate water to a given height, multiply the number of gallons per minute by 8.335, the weight of i gal, and this result by the total number of feet the water is raised, that is, from the surface of the water to the highest point to which the water is raised, and the result gives the power in foot-pounds; divide by 33 000, and the quotient is the horse-power. To the theoretical power a liberal allowance must be made for the inefficiency of the pump. For a cylinder-pump add from 75 to 100%. To the actual height to which the water is to be raised add the friction-loss in feet, given in Table F, page 1388, when the discharge is to be piped any distance. Example. Find the theoretical horse-power required to raise 100 gal per minute 120 ft high, through a 3-in pipe, 200 ft leng. Solution. From Table F, the friction-head for 100 gal per min in a 3-in pipe, 100 ft long, is 1.3 1 X 2.3 or 3 ft. For 200 ft it will be 6 ft, which, added to 120, gives 126 ft for the height. Then theoretical horse-power = 100 x 8.35 x 126/ 33000= 3.2 h.p. The actual horse-power required will probably vary from 5 to 6, according to the efficiency of the pump. The mistake of using too small a discharge-pipe can easily be seen from Table F. For instance, if one attempted to force 100 gal per minute through 100 ft of 2-in pip'ep- the back-pressure would be equivalent to raising the water 22 ft high. The fuel used would be correspondingly increased. Right-angle turns are to be avoided, as the friction is verj^ materially increased, being practically equal to the friction of 25 ft of straight pipe. Table of Effective Fire-Streams Using 100 ft of 2y2-\n ordinary best-quality rubber-lined hose between nozzle and hydrant or pump Smooth nozzle %\n , ^^in 32 54 65 75 86 34 57 69 80 30 50 60 70 80 30 50 60 70 48 67 72 76 79 49 71 77 81 37 50 54 68 62 42 55 61 (i^ 90 116 127 137 147 123 159 174. 188 Pressure at hydrant, lb . . Pressure at nozzle, lb Vertical height, ft Horizontal distance, ft. . Gal discharged per min. . Smooth nozzle Pressure at hydrant, lb. . Pressure at nozzle, lb. . . . Vertical height, ft Horizontal distance, ft. . Gal discharged per min. . I in ij'^in 37 62 75 87 100 42 70 84 98 30 50 60 70 80 30 SO 60 70 51 73 79 85 89 52 75 83 88 47 61 67 72 76 50 66 72 77 161 208 228 246 263 206 266 291 314 Fire-Streams. The following is an extract from a paper read by John R. Freeman at a meeting of the New England Waterworks Association, entitled Some Experiments and Practical Tables Relating to Fire-Streams, 1 loUS Hydraulics, Plumbing and Drainage, and Gas-Piping Part 3 *'When unlined liiieii hose is used the friction or pressure-loss is from 8 to 60%, increasing with the pressure. This kind of hose is best for inside use in short lengths. Mill-hose is better than unlined Hnen hose for long lengths, but ordinarily the best quality of smooth rubber-lined hose is superior to the mill-hose, having less frictional resistance. The ring-nozzle is inferior to the smooth nozzle and actually delivers less water than the smooth nozzle. For instance, the J6-in ring-nozzle discharges the same quantity of water as a 94-in smooth nozzle, and a i-in ring-nozzle the same as a ^^-in smooth nozzle. Two hundred and fifty gallons per minute is a good standard fire-stream at 80-lb pressure at the hydrant; loo-lb pressure should not be exceeded except for very high buildings or lengths of hose exceeding 300 ft." Notes on the Construction of Cylindrical Wooden Tanks* Material should be either cedar, cypress, juniper, fir, yellow pine, or white pine, free from imperfections and thoroughly air-dry. Clear Louisiana red, Gulf cypress makes the most durable tanks. Staves and Bottom of tanks of greater capacities than 15 000 gal should be made of 2y>-'m, dressed to about 2^ in, stock for tanks 12 ft and not exceeding 16 ft diameter or 16 ft deep. For larger tanks 3-iR, dressed to about 2% in, stock should be used. For smaller tanks 2-in stock may be used. Staves should be connected about one-third the distance from the top by a %-m dowel to hold them in position during erection. The bottom yjlanks should be dressed on four sides, and the edges of each plank should be bored with holes not over 3 ft apart for ^i-in dowels. • Taper. The batter to each side should not be less than H in nor more than ^ in per ft. Hoops should be of round wrought iron or mild steel of good quality. Wrought iron is preferable because it does not rust as easily as steel. There should be no welds in any of the hoops. Where more than one length of iron is necessary, lugs should be used to make the joints; and when more than one piece is necessary the several pieces constituting one hoop should be tied together in preparing for shipment. Hoops for fire-tanks should be of such size and spacing that the stress in no hoop will exceed 1 2 500 lb per sq in when computed from the area at root of thread. For general purposes, a stress of 15 000 lb per sq in is permissible. On acccount of the swelling of the bottom planks, the hoops near the bottom may be subjected to a stress greater than that due to the water-pressure alone; additional hoops, therefore, should be provided. For tanks up to 20 ft in diam.- eter, one hoop of the size used next above it should be placed around the bottom opposite the croze and not counted upon as withstanding any water-pressure. For tanks 20 ft or more in diameter, two hoops, as above, should be used. Hoops with UPSET ends must not be used. The top hoop should be placed within 2 in of the top of staves, so that the overflow-pipe may be inserted as high as possible. Hoops should be so placed that the lugs will not be in a vertical line. No hoop should be less than % in in diameter. All should be cleaned of mill-scale and rust and painted one coat of red lead, lampblack and boiled oil before erecting. Note. The strength of a tank depends chiefly on its hoops. Round hoops are specified because they do not rust rapidly; a slight amount of rust does * These notes have been condensed from specifications published by the Inspection Department of the Factory Mutual Fire Insurance Company, 31 Milk Street, Boston; ft most excellent pamphlet. ' J Wooden Tanks 1399 not have the same weakening effect as on a flat hoop, and round hoops are not likely to burst when the tank swells, as they will sink into the wood. Spacing of Hoops. The hoops should be spaced so that each one will have the same stress per square inch, and no space should be greater than 21 in. To meet this requirement the hoops must be spaced quite close together at the bottom, the space between them gradually increasing towards the top. ^^1 Tt- ^^ Fig. 5. Support for Bottom of Tank - — Fig. 3 shows the proper spacing of hoops for a tank 18 ft in diameter, with 18-ft staves. The spacing for seven other sizes of tanks is given in the pamphlet referred to. It may be computed by the following formula: Spacing of hoops in inches = 2.6 X diameter in feet x // For strength of a H-in rod use 3 750; of a %-in rod, 5 250; of a i-in rod, 6 875; and of a ij^i-in rod, 8 625. H is the distance from surface of the water to center of hoop in feet. Example. How far apart should i-in hoops be placed, at 15 ft 2 in from top of tank, on a tank 20 ft diameter? 6875 Fig. T 3. Diagram of Hoop-spacing for Tanks Solution. Spacing = - = 8% in 2.6 X 20 X 15 Lugs should be as strong as the hoops. A lug similar to Fig. 4 is simple and fulfils the requirement for strength. Malleable lugs are required. Support. The weight of the tank should be supported entirely from its bottom; and in no event should any weight come on the bottom of the staves. The planks upon which the tank-bottom rests should cover at least one-fifth the area of the bottom, should be not over 18 in apart, and of such thickness that the bottom of the staves will be at least i in from the floor (see Fig. 5). The Discharge-Pipe should preferably leave the bottom of the tank at its center and extend up inside of the tank 4 in, to allow the sediment to collect in the bottom of the tank. 1400 Hydraulics, Plumbing and Drainage, and Gas-Piping Part 3 The Overflow-Pipe should be placed as near the top of the tank as possible, discharging either through side or bottom, as may be desired. An overflow is much to be preferred to a telltale, as the latter is liable to get out of order. Heating. Tanks of moderate size need to be provided with some means to prevent freezmg. When a tank is in an enclosed room, as in a mill-tower, the best method is to keep the room warm by a coil of steam-pipe with a return to the boiler-room. A covered tank out of doors may often be similarly heated by placing the steam-pipe in the bottom of the tank. With a tank located on a high trestle, or at a distance from the steam-supply, it is often impracti- cable to arrange a return-pipe. In this case steam may be blown directly into the water in the tank. A i-in pipe is generally sufficient for this purpose. It should be carried to the top of the tank and there bend over and dip down- wards, so that its outlet is about i ft below the high-water line. A check- valve should be placed in this 2 in. horizontal nailing strips spaced about 3 ft. apart.;. :i in. ail '^p.lce 2 in . ait ^])! ^ g Num- ber of Size, in A, in B, in c, in 10 coo 13 4 12 2H 2\i 3K2 % 2H II H 15 000 14 6 14 2% 2M 3'/2 H 2% 14 H 20 000 IS 6 16 2M 2H 3V2 % 2H h? H % 25000 17 6 16 2% 2% 3H H 2% ! 4 12 30000 18 18 2% 23/4 3K2 % 2') 8 4 16 SO 000 22 20 2% 2X1 3H H 2-)8 4 75 000 24 6 24 2% 2% 3H H 2% ( 21 I 100 000 28 6 24 2?.i 2Y^ 3K2 H 2% 5 29 I Pumps for Fire taction in buildings, the following table. •Streams. The dimensions of steam-pumps for fire-pro- approved by the Board of Underwriters, can be found in Underwriter Steam Fire-Pumps Size in inches 1^ Size in inche? Over-all dimen- .ti CI sions of largest pump of given .§1 •*- c U-, ^ 0) la SB If Q g ■ft ,0 bO Q m ft ft n > 1 c2 1 1 > 1 capacity ft M 1 in in in h.p. in in in in in in in ft in ft in ft in gal (14 7 12 1 12^ Soo 14 7H 80 8 6 3 4 3 2 I 9 ^^ 5 2 7 5 250 (16 8 10) 750 ji6 1 16 9 12 j 12 \ "5 10 7 3K2 4 33'^2 2M ii/i 9 5 5 2 8 375 1000 (18 1 18H 10 101/2 12 10 150 12 8 4 5 4 2-)^ iV^ 10 8 5 7^2 8 10 500 1500 20 12 16 200 14 10 5 6 5 2I/2 iH 12 5 5 7 . 8 11 750 The capacities given in last column are desirable; but in case the suction-pipe is short and the lift low, a tank of not less than one-half the capacity stated may sometimes bo used. 1402 Hydraulics, Plumbing and Drainage, and Gas-Piping Part 3 Notes on Steel Tanks* Steel Tanks of sizes commonly used for fire-protection cost from 40 to 100% more than wooden tanks. The additional cost for large tanks is relatively less than for small tanks. A steel tank of about 40 000-gal capacity or over can be erected on a steel trestle at about the same cost as a wooden tank, since a saving can be made in the cost of supports by making a hemispherical or conical bottom to the steel tank and supporting the tank directly on the legs of the trestle, thus saving the expense of horizontal supporting beams. A steel tank is superior to a wooden tank for the following reasons: (i) It will last for an indefinite time if kept thoroughly painted inside and out, whereas a wooden tank will have to be replaced in from twelve to thirty years, usually in about fifteen years; (2) it will be absolutely tight when once well erected and properly cared for, whereas a wooden tank will shrink and leak if the water gets low; (3) it will not be at all Hkely to burst suddenly, if originally correctly designed, even if painting is neglected, for experience shows that a few spots will first rust through and thus show the weak condition by small leaks, whereas a wooden tank, if neglected, may burst its hoops suddenly and cause serious damage. The objections to steel tanks are that: (i) They require skilled boiler- makers to erect them, thus adding considerable to the cost when erected at a distance from a boiler-shop; (2) they are more difficult to protect against freez- ing; (3) they give more trouble by sweating when placed in a mill-tower; (4) they deteriorate rapidly if painting is neglected. Stresses in Cylindrical Tanks. f The intensities of stresses in lb per sq in found in cylindrical tanks are as follows: A tensile stress due to hj'dro- static pressure at any vertical joint or section of the shell of a tank filled with water, S = 62.5 IJD/{2 X 12 /) = 2.6 HD/t A compressive stress at any horizontal joint or section, due to the weight of the stack, S = IV/iwD X 12 = 0.026 W/Dt A stress at any horizontal joint rr section, tensile on the windward side and compressive on the leeward side, due to the wind, ^'2 = 0.106 M/DH. (See Self-Sustaining Steel Chimneys, page 1376.) In the above equation, // = height of tank in ft above section considered, D = diameter in ft, t = thickness of shell in in, W = weight of tank in lb, and M = bending moment in ft-lb. The conditions for overturning from wind are most severe when the tank is empty. Stand-Pipes wore much used for storage-reservoirs at one time. They usually varied from 12 to 30 ft in diameter and from 35 to 120 ft in height. A tank built in 1889 at Greenwich, Conn., was 80 ft in diameter and 30 ft in height. Its capacity was i 300 000 gal. A stand-pipe built in 1876 at Winona, Minn, was 4 ft in diameter by 210 ft in height. The steel cylinder was sur- rounded by a masonry tower. A long list of failures, mostly due to faulty design, are recorded against the stand-pipe. Because of this and the superior advantage of the elevated water-tower, few are now built. General Specifica- tions for Elevated Steel Tanks on Towers, and for Stand-pipes (Trans. Am. Soc. C. E., Vol. 64, 1909, pages 548 to 566), and General Specifications for Steel, Water, and Oil-Tanks (Proc. Am. Ry. Eng. Asso., vol. 13, 191 2), are both reprinted in Ketchum's Structural Engineers' Handbook. * Inspection Department of the Factory Mutual Insurance Company, Boston. t From Notes by Robins Fleming. Capacities of Pipes and Cylinders 1403 Contents in Cubic Feet and U. S. Gallons of Pipes and Cylinders of Various Diameters and One Foot in Length I gallon = 231 cu in. i cu ft = 7.4805 gal For [ft in Fori ft in Fori ft in Diam- length Diam- length length Diam- eter in Cuft, U.S. eter in Cuft, U.S. eter in Cu ft, U. S. inches * also gal inches also gal. inches also gal. area in 231 area in 231 area in 231 sq ft cu in sqft cu in sqft cu in H . 0003 0.0025 6H 0.248s 1.859 19 1.969 14-73 Ma . 000s . 0040 7 0.2673 1.999 19K2 2.074 IS. SI H 0.0008 0.0057 7H 0.2867 2.145 20 2.182 16.32 Via O.OOIO 0.0078 7H 0.3068 2.295 20l/^ 2.292 17 15 Vz 0.0014 0.0102 7-Xi 0.3276 2.450 21 2.40s 17.99 He 0.0017 0.0129 8 0.3491 2. 611 21 1/^ 2.521 18.86 % 0.0021 0.0159 8K 0.3712 2.777 22 2.640 19-75 iMe . 0026 . 0193 m 0.3941 2.948 22H 2.761 20.66 % 0.0031 . 0230 m 0.4176 3.125 23 2.885 21.58 i-Mo 0.0036 . 0269 9 0.4418 3.30s 23K2 3 012 22.53. y^ 0.0042 0.0312 9H 0.4667 3.491 24 3.142 23.50 ^•}U 0.0048 0.0359 9K2 0.4022 3-682 25 3.409 25 50 1 0.005s 0.0408 9% 0.S185 3.879 26 3.687 27.58 iH 0.0085 0.0638 10 0.54S4 4.080 27 3.976 29.74^ ~ lYi 0.0123 0.0918 ioi/4 O.S730 4.286 28 4.276 31-99 m 0.0167 0.1249 10 '/i 0.6013 4.498 29 4.587 34-31 : 2 0.0218 0.1632 loYi 0.6303 4.71s 30 4.909 36.72 2H 0.0276 0.2066 II 0.6600 4.937 31 5. 241 39-21 2K2 0.0341 0.25.50 iiKi 0.6903 5.164 32 5.585 41.78 2H 0.0412 0.3085 II 1/2 0.7213 5.396 33 5-940 44-43 3 0.0491 0.3672 ii-M 0.7530 5.633 34 6.305 47-16 3H 0.0576 0.4309 12 0.78.54 5.875 35 6.681 49 98 3'/2 0.0668 0.4998 12K2 0.8522 6.375 36 7.069 52.88 M 0.0767 0.5738 13 0.9218 6.895 37 7.467 55.86 4 0.0873 0.6528 13K2 0.9940 7.436 38 7.876 58.92 4H 0.0985 0.7369 14 1.0690 7.997 39 8.296 62.06 4H 0.1134 0.8263 14K' I . 1470 8.578 40 8.727 65.28 4% 0.1 231 . 9206 IS 1.2270 9.180 41 9 168 68.58 S 0.1364 1.0200 15K2 I. 3100 9.801 42 9.621 71.97 SH 0.1503 I. 1250 16 1.3960 10.440 43 10.085 75.44 S'/2 0.1650' I . 2340 i6J^^ 1.4850 II. no 44 10. 559 78.99 sH 0.1803 1.3490 17 1.5760 11.790 45 11.045 82.62 6 0.1963 I . 4690 I7'/2 I . 6700 12.490 46 II. 541 86.33 6H 0.2131 I . S940 18 1.7680 13.220 47 12.048 90.13 GVz 0.2304 1.7240 iSVz 1.8670 13.960 48 12.566 94.00 * Actual. To find the capacity of pipes greater than those given, look In the table for a pipe of one-half the given size and multiply its capacity by 4, or one of one- third its size and multiply its capacity by 9, etc. To find the weight of water in any of the given sizes, multiply the capacity in cubic feet by the weight of a cubic foot of water at the temperature of the water in the pipe. To find the capacity of a cylinder in U. S. gallons, multiply the length by the square of the diameter and by 0.0034, 1404 Hydraulics, Plumbing and Drainage, and Gas-Piping Part 3 Cylindrical Vessels, Tanks, Cisterns, Etc. Diameter in feet and inches, area in square feet, and U. S. gallons capacity for i ft in dep:h I gallon = 231 cu in = 0.1337 cu ft Diam, Area, Gal, i-ft depth Diam Area, Gal, i-ft depth Diam, Area, Gal. I-ft depth ft in sqft* ft in sqft* ft in sqft* 0.785 5.87 5 8 25.22 188.66 19 283.53 2120.9 I I 0.922 6. 8 J 5 9 ^^5. 97 194.25 19 3 291.04 2177. I I 2 1.069 8.00 5 10 26.73 199.92 19 6 298.65 2234.0 I 3 1.227 9.18 5 II 27 49 205 . 67 19 9 306.35 2291.7 I 4 1.396 10.44 6 28.27 211. 51 20 314 16 2350.1 I 5 1.576 11.79 6 3 30.68 229.50 20 3 322.06 2409.2 I 6 1.767 13.22 6 6 33.18 24S.23 20 6 330.06 2469.1 I 7 1.969 14.73 6 9 35.78 267.69 20 9 3.38.16 2529.6 I 8 2.182 16.32 7 3S.43 287.83 21 346.36 2591 I 9 2.405 17-99 7 3 41.28 308.81 21 3 354 66 2653.0 I 10 2.640 19-75 7 6 44-18 330.48 21 6 363.05 2715.8 I II 2.88s 21.58 7 9 47.17 352.88 21 9 371.54 2779 3 2 3 142 23.50 8 50.27 376.01 22 380.13 2843.6 2 I 3.409 25.50 8 3 53.46 399.88 22 3 388.82 2908.6 2 2 3.687 27.58 8 6 56.75 424.48 22 6 397.61 2974.3 2 3 3.976 29.74 8 9 60.13 449.82 22 9 406.49 3040 . 8 2 4 4.276 31.99 9 63-62 475.89 23 415-48 3108.0 2 5 4.587 34 31 9 3 67.20 502.70 23 3 424-56 3175.9 2 6 4-909 36.72 9 6 70.88 530.24 23 6 433.74 3244.6 2 7 5 241 39 21 9 9 74 66 558.51 23 9 443.01 3314.0 2 8 5.585 41.78 10 78.54 587.52 24 452.39 3384.1 2 9 5 940 44.43 10 3 82.52 617.26 24 3 461.86 3455.0 2 10 6.305 47.16 10 6 86.59 647.74 24 6 471.44 3526.6 2 II 6.681 49.98 10 9 90.76 678.95 24 9 481. II 3598.9 3 7.069 52.88 II 9.5.03 710.90 25 490.87 3672.0 3 I 7.467 55.86 II 3 99-40 743.58 25 3 500.74 3745.8 3 2 7.876 58.92 II 6 103.87 776.99 25 6 510.71 38203 3 3 8.296 62.06 II 9 108.43 811 14 25 9 520.77 3895.6 3 4 8.727 65.28 12 113.10 846.03 26 530.93 3971 6 3 5 9.168 .68.58 12 3 117.86 881.65 26 3 541.19 4048.4 3 6 9 621 71.97 12 6 122.72 918.00 26 6 551.55 4125.9 3 7 10.085 75.44 12 9 127.68 955.09 26 9 562.00 4204.1 3 8 10.5.59 78.99 13 132.73 992.01 27 572.56 4283 3 9 11.045 82.62 13 3 137.89 1031.5 27 3 588.21 4362.7 3 TO II. 541 86.33 13 6 143.14 1070.8 27 6 593.96 4443.1 3 II 12.048 90.13 13 9 148.49 mo. 8 27 9 604.81 4.S24.3 12.566 94.00 14 153.94 1151.5 28 615.75 4606.2 4 I 13.095 97.96 14 3 159.48 "93 28 3 626.80 4688.8 4 2 13.635 102.00 14 6 165.13 1235.3 28 6 637.94 4772.1 4 3 14.186 106.12 14 9 170.87 1278.2 28 9 649.18 4856.2 4 4 14.748 110.32 15 176.71 132 I. 9 29 660.52 4941.0 4 5 15.321 114 61 15 3 182.65 1366.4 29 3 671.96 5026 . 6 4 6 15.90 118.97 15 6 1S8.69 1411.5 29 6 683.49 5112.9 4 7 16.50 123.42 15 9 194.83 1457.4 29 9 695.13 5199.9 4 8 17.10 127.95 16 201.06 1504. I 30 706.86 5287.7 4 9 17.72 132.56 16 3 207.39 155 I. 4 30 3 718.69 5376.2 4 10 18.35 137-25 16 6 213 82 1599.5 30 6 730.62 5465.4 4 II 18.99 142.02 16 9 220.35 1648.4 30 9 742.64 5555.4 19 63 146.88 17 226.98 1697.9 31 754.77 5646.1 5 I 20 29 151.82 17 3 233.71 1748.2 31 3 766.99 5737.5 5 2 20.97 156.83 17 6 240.53 1799.3 31 6 779 31 5829.7 5 3 21.65 161.93 17 9 247.45 1851.1 31 9 791-73 5922.6 S 4 22.34 167.12 18 254.47 1903.6 32 804 . 25 6016.2 5 S 23.04 172.38 18 3 261.59 19.56.8 32 3 816.86 6110.6 5 6 23.76 177.72 18 6 268.80 2010.8 32 6 829.58 6205.7 5 7 24.48 183.15 18 9 276 . 12 2065.5 842.39 6301.5 * AI30 cubic feet for i ft in depth. Capacities of Cisterns and Tanks 1405 Capacity of Cisterns and Tanks Number of barrels ^iH gal) in cisterns and tanks Diameter, ft Depth, ft 5 6 7 8 9 10 II 12 13 5 23. 3 33.6 45.7 59-7 75.5 93.2 112. 8 134.3 157.6 6 28.0 40.3 54.8 71.7 90.6 111.9 135.4 161. 1 189. 1 7 32.7 47-0 64.0 83.6 105.7 130.6 158.0 188.0 220.6 8 37. 3 53.7 73.1 95.5 120.9 149.2 180.5 214.8 252.1 9 42. o 60.4 82.2 107.4 136.0 167.9 203 . 1 241.7 283.7 10 46.7 67.1 91.4 119-4 151.1 186.5 225.7 268.6 315.2 II 51.3 73.9 100.5 131-3 166.2 205 . 1 248.2 295.4 346.7 12 56.0 80.6 109.7 143-2 181.3 223.8 270.8 322.3 378.2 13 60.7 87.3 118. 8 155.2 196.4 242.4 293 -4 349.1 409.7 14 65.3 94.0 127.9 167. 1 211. 5 261. 1 315.9 376.0 441.3 15 70.0 100.7 137. 1 1790 226.6 289.8 338.5 402.8 472.8 i6 74-7 107.4 146.2 191-0 241.7 298.4 361 . 1 429.7 504.3 17 79.3 114. 1 155.4 202.9 256.8 317.0 383.6 456.6 535.8 i8 84.0 120.9 164.5 214.8 272.0 335.7 406.2 483.4 567.3 19 88.7 127.6 173.6 226.8 287.0 354.3 428.8 510.3 598.0 20 93.3 134.3 182.8 238.7 302.1 373.0 451.3 537.1 630.4 Diameter, ft Depth, • 14 15 16 17 18 19 20 21 22 5 182.8 209.8 238.7 269.5 302.1 336.6 373.0 411. 2 451.3 6 219.3 251.8 286.5 323-4 362.6 404.0 447.6 493.5 541.6 7 255.9 293.7 334.2 377.3 423.0 471.3 522.2 575.7 631.9 8 292.4 335.7 382.0 431.2 483.4 538.6 596.8 658.0 722.1 9 329.0 377.7 429.7 485.1 543.8 605.9 671.4 740.2 812.4 10 365 5 419.6 477-4 539.0 604.3 673.3 746.0 822.5 902.7 II 402.1 461.6 525.2 592.9 667.7 740.6 820.6 904.7 992.9 12 438.6 503.5 572.9 646.8 725.1 807.9 895.2 987.0 1083.2 13 475.2 545.5 620.7 700.7 785.5 875.2 969.8 IC69.2 1173.5 14 511. 8 587.5 668.2 754.6 846.0 942.6 1044.4 II51.5 1263.7 15 548.3 629.4 716.2 808.5 906.4 1009.9 IIIQ.O 1233.7 1354.0 i6 584.9 671.4 773.9 862.4/ 966.8 1077.2 1193.6 1315.9 1444.3 17 621.4 713.4 811. 6 916.3 1027.2 1044 . 6 1268.2 1398.2 1534.5 i8 658.0 755.3 859.4 970.2 1087.7 1211.9 1342.8 1480.4 1624.8 19 694 -5 797.3 907.1 1024. I 1148.1 1279.2 1417.4 1562.7 1715.1 20 731. 1 839.3 954.9 1078.0 1208.5 1346.5 1492.0 1644.9 1805.3 Diameter, ft Depth, 23 24 25 26 27 28 29 30 5 493.3 537.1 582 8 630.4 679.8 731.1 784.2 839.3 6 592.0 644. 5 699 4 756.5 815.8 877.3 941. 1 1007. I 7 690.6 752.0 815 9 882.5 951.7 1023.5 1097.9 1175.0 8 789 -3 859.4 932 5 1008.6 1087.7 1169.7 1254.8 1342.8 9 887.9 966.8 1049 I 1134.7 1223.6 1316.0 I4II.6 1510.7 10 986.6 1074.2 1165 6 1260.8 1359.6 1462.2 1568.2 1678.5 II 1085.2 1181.7 1282 2 1386.8 1495.6 1608.7 1723.0 1846.4 12 1183.9 1289. I 1398 7 1512.9 1631.5 1754.6 1882.2 2014.2 13 1282.6 1396.5 151S 3 1639.0 1767.5 1900.8 2039.0 2182.0 14 1381.2 1503.9 1 63 1 9 1765.1 1903.4 2047.1 2195.9 2343.9 IS 1479-9 1611.4 1748 4 1891 . I 2039.4 2193 3 2352.7 2517.8 i6 1578. 5 1718.8 1865 2017.2 2175.4 2339.5 2509.6 2685.6 17 1677.2 1826.2 1981 6 2143.3 2311.3 2485.7 2666.4 2853.5 i8 1775-9 1933.6 2098 I 2269.4 2447.3 2631.9 2823.3 3021.3 19 1874-5 2041 . I 2214 7 2395.4 2583.2 2778.1 2980.1 3189.2 20 1973.2 2148.5 2321 2 2521.5 2719.2 2924.4 3137.0 3357.0 For tanks that are tapering, measure the diameter four-tenths from large end. 1406 Hydraulics, Plumbing and Drainage, and Gas-Piping Part 3 Number of U. S. Gallons in Rectangular Tanks For One Foot in Depth I cu ft = 7-4805 gal Width, ft 2.5 3 35 4 4.5 S 55 6 6.5 7 Length of tank, ft 29.92 37-40 46.75 44-88 56.10 67.32 52.36 65.45 78.54 91.64 67.32 84.16 100.99 117.82 134-65 151.48 74.81 93-51 112.21 130.91 149.61 168.31 187.01 82.29 102 . 80 123-43 144.00 164-57 185 . 14 205.71 226.28 89.77 112. 21 134.65 157.09 179-53 201 . 97 224.41 246.86 269.30 6.5 97-25 121.56 145-87 170.18 194-49 218.80 243 II 267.43 291-74 316.05 104-73 130.91 157 09 183-27 209.45 235-63 261.82 288.00 314.18 340.36 366.54 Width, ft 2.5 3 3 5 4 4-5 5 5^5 6 6.5 7 7.5 8 8.5 9 9-5 10 10.5 II II. 5 Length of tank, ft 112. 21 140.26 168.31 196.36 224.41 252.47 280.52 308.57 336.62 364.67 392.72 420.78 134-65 168.31 202 . 97 235-63 269.30 302.96 336.62 370.28 403-94 437-60 471.27 504-93 538.59 572.25 605.92 142.13 177.66 213.19 248.73 284.26 319-79 355-32 390.85 426.39 461 . 92 497-45 532.98 568.51 604 . 05 639.58 675 149.61 187.01 224.41 261.82 299 . 22 336.62 374-03 411 43 448.83 486.23 523 64 561.04 598.44 635.84 673 .25 710.65 748.05 157.09 196.36 235 63 274.90 314 18 353 45 392.72 432.00 471 • 27 510.54 549-81 589-08 628.36 667.63 706 . 90 746.17 785-45 824.73 164-57 205 . 71 246.86 288.00 329- 14 370.28 41143 452.57 493-71 534-85 575-00 617.14 658.28 690.42 740.56 781.71 822.86 864.00 905.14 172.05 215.06 258 . 07 301 . 09 344 10 387.11 430.13 473.14 516.15 5.50.16 602.18 645 . 19 688.20 731.21 774-23 817.24 860.26 903.26 946.27 989.29 179 53 224.41 269.30 314- 18 359 06 403-94 448.83 493-71 538.59 583.47 628.36 673.24 718.12 703.00 807.89 852.77 897-66 942.56 987 .43 1032 3 1077 . 2 To find weight of water in pounds at 62° F., multiply the number of gallons by 8H. Example. To find number of gallons in a rectangular tank that is 7.5 ft by 10 ft., the water being 4 ft deep. Look in the extreme left-hand column for 7.5 and opposite to this in the column headed 10 read 561.04, which being multiplied by 4, the depth of water in the tank, gives 2244.2, the number of gallons required. Plumbing and Drainage 1407 (2) PLUMBING AND DRAINAGE Reliable Rules for Plumbing and Drainage. The water-supply of buildings, including the apparatus for heating water, the system of drainage and sewage, and the various fixtures connected therewith, are installed by the plumber, usually in accordance with specifications prepared by the architect and subject to municipal regulations. An efficient and safe system of plumbing is a matter of vital importance. The following may be used as a rehable guide in any locality. Extracts * from the Rules and Regulations of the Department of Buildings of the City of New York, Adopted April 23, 19 12 Definitions of Terms (i2)t The term private sewer is applied to main sewers that are not con- structed by and under the supervision of the Department of Sewers. (13) The term house-sewer is applied to that part of the main drain or sewer extending from a jxiint 2 ft outside of the outer wall of building-vault or area to its connection with public sewer, private sewer or cesspool. (14) The term house-drain is applied to that part of the main horizontal drain and its branches inside the walls of the building-vault or area and extend- ing to and connecting with the house-sewer. (15) The term soil-pipe is applied to any vertical line of pipe extending through roof, receiving the discharge of one or more water-closets with or with- out other fixtures. (16) The term waste-pipe is applied to any pipe, extending through roof, receiving the discharge from any fixtures except water-closets, (17) The term vent-pipe is applied to any special pipe provided to ventilate the system of piping and to prevent trap-siphonage and back-pressure. Materials and Workmanship Soil-Pipe and Vent-Pipe. (19) All cast-iron pipes and fittings must be uncoated, sound, cylindrical, and smooth, free from cracks, sand-holes and other defects, and of uniform thickness and of the grade known in commerce as EXTRA heavy. (20) Pipe, including the hub, shall weigh not less than the following average weights per linear foot: » Diameters Weights per linear foot, lb 2 in 13 17 20 27 33H 45 54 3 in , . 5 in . . 7 in . 8 in 12 in * These numbered paragraphs, from (12) to (174). extracts from Building Regulations, are unedited, except in those details which affect typographical uniformity throughout the book. Editor-in-chief. t Paragraph-numbers are the same as those in the Official Regulations. Missing num- bers indicate Daraeraohs Durooselv omitt«d. 1408 Hydraulics, Plumbing and Drainage, and Gas-Piping Part 3 (22) All joints must be made with picked oakum and molten lead and be made gas-tight. Twelve (12) oz of line, soft pig lead must be used at each joint for each inch in the diameter of the pipe. (24) Wrought-iron and steel water-pipes, vent-pipes, waste-pipes and soil- pipes must be galvanized. (29) All brass pipe for soil-pipes, waste-pipes, and vent-pipes and solder-nip- ples must be thoroughly annealed, seamless-drawn, brass tubing of standard iron-pipe gauge. Lead Waste-Pipes. (37) The use of lead pipes is restricted to the short branches of the soil-pipes and waste-pipes, iiends, traps, and roof-connections of inside leaders. Short branches of lead pipe shall be construed to mean not more than 8 ft of 1 3. 2 -in pipe 5 ft of 2-in pipe 2 ft of 3 -in pipe 2 ft of 4-in pipe (sS) All connections between lead pipes and between lead and brass or copper pipes must be made by means of wiped solder joints. (39) All lead waste, soil, vent, and flush-pipes must be of the best quality, known in commerce as D, and of not less than.the following weights per linear foot: Diameters Weights per linear foot, lb iH in (for flush-pipes only) . i^^ in 2 in 3 in 4 and 4^ in 2H 3 4 6 (40) All lead traps and bends must be of the same weights and thicknesses as their corresponding pipe-branches. Sheet lead for roof-flashings mu.st be 6-lb lead and must extend not less than 6 in from the pipe, and the joint made water-tight. (41) Copper tubing when used for inside leader roof-connections must be' seamless-drawn tubing not less than 22 gauge, and when used for roof -flashings must be not less than 18 gauge. Yard, Area and Other Drains (54) All yards, areas, and courts exceeding 15 sq ft in area must be drained into the sewer. A shaft open at the top and not exceeding 25 sq ft in area, and which cannot be connected in back of a leader, yard, court, or area drain-trap, may be drained into a publicly placed, water-supplied, properly tapped and vented slop-sink. (59) These drains, when sewer-connected, must have connections not less than 3 in in diameter. They should be controlled by one trap, the leader-trap if possible. Leaders (60) Every building shall be kept provided with proper metallic gutters and rain-leaders for conducting water from all roofs in such manner as shall protect the walls and foundations of said buildings from injury. In no case shall the water from any rain-leader be allowed to flow upon the sidewalk or adjoining property, but the same shall be conducted by proper pipes to the sewer. If there be no sewer in the street upon which the buildings front, then the water House-Sewer and Fresh-Air Inlet 1409 from said leaders shall be conducted by proper pipes below the surface of the sidewalk to the street-gutter, or may be conducted by extra-heavy cast-iron pipe to a leeching cesspool located at least 20 ft from any building. No plumb- ing fixtures shall discharge into a leeching cesspool. (61) Inside leaders must be made of cast iron, wrought iron, or steel, with roof-connections made gas-tight and water-tight by means of a heavy lead or copper-drawn tubing wiped to a brass ferrule or nipple calked or screwed into the pipe. (62) Outside leaders may be of sheet metal, but they must connect with the house-drain by means of a cast-iron pipe extending vertically 5 ft above the grade-level. (63) Leaders must be trapped with cast-iron running traps so placed as to prevent freezing. (64) Rain-water leaders must not be used as soil-pipes, waste-pipes or vent- pipes, nor shall any such pipe be used as a leader. The House-Sewer, House-Drain, House-Trap and Fresh-Air Inlet (70) The house-drain must properly connect with the house-sewer at a point 2 ft outside of the outer front vault or area-wall of the building. An arched or other proper opening in the wall must be provided for the drain to prevent damage by settlement. (71) The house-drain if above the cellar-floor, must be supported at inter- vals of 10 ft by 8-in brick piers or suspended from the floor-beams, or be other- wise properly supported by heavy iron-pipe hangers at intervals of not more than 10 ft. (72) No steam-exhaust, boiler blow-ofT, or drip-pipe shall be connected with the house-drain. Such pipes must first discharge into a proper condensing tank, and from this a proper outlet to the house-sewer outside of the building must be provided. In low-pressure steam-systems the condensing tank may be omitted, but the waste-connection must be otherwise as above required. (73) The house-drain and house-sewer must be run as direct as possible, with a fall of at least H in per ft, all changes in direction made with proper fittings, and all connections made with Y branches and one-eighth and one-six- teenth bends. Size of House-Sewer. (74) The house-sewer and house-drain must be at least 4 in in diameter where water-closets discharge into them.. Where rain- water discharges into them, the house-sewer and house-drain up to the leader- connections must be in accordance with the following table: Diameter of For a fall of For a fall of Yi in per foot. \i in per foot. pipe, sq ft of drainage- sq ft of drainage- area area 3 I 200 I 500 4 2 500 3 200 5 4500 6000 6 8000 10 000 7 12 400 15 600 8 18 000 22 500 9 25 000 31 500 10 41 000 59000 12 69000 98 000 1410 Hydraulics, Plumbing and Drainage, and Gas-Piping Part 3 (75) Full-size Y and T-branch fittings for hand-hole clean-outs must be pro- vided where required on house-drain and its branches. No clean-out need be larger than 6 in in diameter. (76) An iron running-trap must be placed on the house-drain near the wall of the house, and oji the sewer-side of all connections, except a Y fitting used to receive the discharge from an automatic sewage-lift, oil-separator or a drip- pipe where one is used. If placed outside the house or below the cellar-floor it must be made accessible in a brick manhole, the walls of which must be S in thick, with an iron or flagstone cover. When outside the house it must never be less than 3 ft below the surface of the ground. (79) A FRESH-AIR INLET must be Connected with the house-drain just inside of the house-trap and extended to the outer air, terminating with a return-bend, with open end i ft above the grade at most available point, to be determined by the superintendent of buildings and shown on plans. The fresh-air inlet-pipe must be of the same diameter as the house-drain. An automatic device approved by the superintendent of buildings may be used when set in a manner satis- factory to him. Note. The fresh-air inlet and running trap prescribed by Sections 76 and 79 are not required in many cities, and it is better to omit them where not re- quired. Soil-Pipes, Waste-Pipes and Vent-Pipes (8t) All main, soil, waste or vent-pipes must be of iron, steel, or brass. (90) The diameters of soil-pipes and waste-pipes must not be less than those given in the following table: Main soil-pipes 4 in Main soil-pipes for water-closets on five or more floors 5 in Branch soil-pipes 4 in Main waste-pipes 2 in Main waste-pipes for kitchen-sinks on five or more floors 3 in Branch waste-pipes for laundry-tubs iH in When set in ranges of three or more 2 in Branch waste for kitchen-sinks 2 in Branch waste for urinals 2 in Branch waste for other fixtures 1 1 2 in (97) The SIZES OF VENT-PIPES throughout must not be less than the follow- ing: For main vents, 2 in in diameter; for water-closets on three or more floors, 3 in in diameter; for other fixtures on less than seven floors, 2 in in diameter; 3-in vent-pipe will be permitted for less than nine stories; for more than eight and less than sixteen stories, 4 in in diameter; for more than fifteen and less than twenty-two stories, 5 in in diameter; for more than twenty-one stories the size of vent-pipe shall be determined by the superintendent of buildings. For fixtures other than water-closets and slop-sinks and for more than eight stories, vent-pipes may be i in smaller than above stated. Traps (loi) Every fixture must be separately trapped by a water-sealing trap placed as close to the fixture-outlet as possible and no trap shall be placed more than 2 ft from any fixture. Water-closets 1411 (102) A set of not more than three wash-trays may connect with a single trap, or into the trap of an adjoining sink, provided both sink and tub waste-outlets are on the same side of the waste-line and the sink is nearest the line. When so connected the waste-pipe from tlie wash-trays must be branched in below the water-seal. (103) The discharge from any fixture must not pass through more than one trap before reaching the house-drain. (109) All earthenware traps must have approved heavy brass floor-plates properly secured to the branch soil-pipe and bolted to the trap-flange and the joint made gas-tight. The use of rubber washers -for floor-connections is pro- hibited. All floor-flanges must be set in place and inspected before any water- closet is set thereon. (no) No trap shall be placed at the foot of main soil- and waste-pipe lines. (112) The sizes for traps must not be less than those given in the following table: Traps for water-closets 4 in in diam. Traps for slop-sinks 2 in in diam. Traps for kitchen-sinks 2 in in diam. Traps for wash-trays 2 in in diam. Traps for urinals 2 in in diam. Traps for shower-baths 2 in in diam. Traps for other fixtures i V^ in in diam. Traps for leaders, areas, floor and other drains must be at least 3 in in diam- eter. Water-Closets (124) In tenement-houses, lodging-houses, factories, workshops, and all public buildings the entire water-closet apartment and side walls to a height of 6 in from the floor, except at the door, must be made water-proof with asphalt, cement, tile, metal, or other water-proof material as approved by the superin- tendent of buildings. (127) The general water-closet accommodation of any building cannot be placed in the cellar nor can any water-closet be placed outside of a building, except to replace an existing water-closet. (130) In all sewer-connected occupied buildings there must be at least one water-closet, and there must be additional closets so that there wiU never be more than fifteen persons per closet. (123) In lodging-houses there must be one water-closet on each floor, and when there are more than fifteen persons on a floor, there must be one additional water-closet for every fifteen additional persons or fraction thereof. (135) Water-closets and urinals must never be connected directly with or flushed from the water-supply pipes, except when flushometer-valves are used, (139) Iron water-closet and urinal-cisterns and automatic water-closets and urinal-cisterns are prohibited unless approved by the superintendent of buildings. (140) The copper lining of water-closets and urinal-cisterns must not be lighter than To-oz copper. (141) Water-closet flush-pipes must not be less than iH in and urinal flush- pipes I in in diameter, and if of lead must not weigh less than 2H lb and 2 lb per lin ft. Flush-couplings must be of full size of the pipe. 1112 Hydraulics, Plumbing and Drainage, and Gas-Piping Part 3 Sinks and Wash-Tubs (147) In all houses sinks must be entirely open, on iron legs or brackets, without any enclosing woodwork. (148) Wooden wash-tubs are prohibited, except when used in hotels, restau- rants or bottling establishments for washing dishes or bottles. Cement or artificial stone tubs will not be permitted unless approved by the superintendent of buildings. Testing the Plumbing-System (171) The entire plumbing and draining-system within the building must be tested by the plumber, in the presence of a plumbing inspector, under a water- test. All pipes must remain uncovered in every part until they have success- fully passed the test. The plumber must securely close all openings as directed by the inspector of plumbing. The use of wooden plugs for this purpose la prohibited. (172) The water- test will be applied by closing the lower end of the main house-drain and filling the pipes to the highest opening above the roof with water. The water-test shall include at one time the house-drain and branches, all vertical and horizontal soil, waste and vent and leader-lines and all branches therefrom to point above the surface of the finished floor and beyond the fin- ished face of walls and partitions. If the drain or any part of the system is to be tested separately, there must be a head of water at least 6 ft above all parts of the work so tested, and special provision must be made for including all joints and connections in at least one test. (17,3) After the completion of the plumbing-work, in any new or altered building and before the building is occupied, a final smoke-test must be applied in the presence of the plumbing-inspector. Except that for a building not over six stories in height, a peppermint-test may be apphed. (174) The material and labor for the tests must be furnished by the plumber. Where the peppermint-test is used, 2 oz of oil of peppermint must be provided for each line up to five stories and cellar in height, and an additional ounce of oil of peppermint must be provided for each line when lines are more than five stories in height. Traps A trap is a device which permits the free passage of liquids through it, and also of any solid matters that may be carried by the liquid, while at the same time preventing the passage of air or gas in either direction. Traps used for plumbing purposes are shaped so that an amount of water sufficient to close the passage and prevent the passage of air will stand in them at all times. The principle of the common trap is shown in Fig. 7. The pipe T receives the waste from a sink or wash-basin, while the lower end B connects with the sewer. Sewer-gas rises in pipe B, but is prevented from passing to the fixture by the water which stands in the trap. The depth of water through which gas must pass to efi'ect a passage is termed the watek-seal. The water-seal in the trap, Fig. 7, is the distance S. All plumbing-pipes which connect with a sewerage- system require to be trapped to prevent sewer-gas from passing through them to the fixture and into the room in which the fixture is located. Ventilation of Traps. When a considerable body of water rushes down through a pipe it forms a suction, and if the pipe is made air-tight, this suction is often sufficient to prevent enough water remaining in the trap to form a seal, thus leaving an opening for the passage f 1 sewer-gas, as in Fig. 8. By connecting the upper bend of a trap with the outs' de air by means of a pipe, as at F, Fig. 8^ ,| Traps 1413 the suction will be stopped, and the water in the pipe T will not fall below the level of the outlet at h. Several non-siphoning traps have been patented for the purpose of obviating the necessity of back-venting, but they are used to a comparatively limited extent. There are also several varieties of back-pressure Fig. 7. Water-seal of Trap Fig. 8. Water-trap Unsealed traps, designed to prevent the sewage from flowing back into the house-drain. These are in the nature of check-valves, and are used principally in seaport- towns where tide- water might possibl}' force the sewage back. The more com- mon shapes of lead traps used in plumbing, with their trade names, are showii Half S y or P /A V ^ Fig. 9. Types of Traps in Fig. 9. The same shapes are also made of cast iron. The pipes marked V are the vent-connections. The drum-trap shown in Fig. 10 has a deeper seal than those shown in Fig. 9, and is commonly used under kitchen-sinks, bath-tubs and wash-trays. Drum-traps are not easily siphoned, even when not vented. The traps for water-closets are commonly formed in the fixture. 1414 Hydraulics, Plumbing and Drainage, and Gas-Piping Part 3 Grease-Traps. The waste-water from kitchen-sinks always contains con- siderable grease, which if permitted to enter the soil-pipe system is liable to clog the pipes by adhering to the walls. In certain localities grease gives much more trouble than in others, due to the chemical composition of the water. In Col- orado and many other places it is necessary to connect the waste from kitchen- ^Top of Ground Fig. 10. Drum-trap Fig. 11. Outdoor Grease-trap sinks with a large grease-trap, which collects and holds the grease, but permits the water to pass into the sewer system. After a time the accumulated grease fills the trap and must be removed. On account of this it is desirable to use a large trap, and whenever possible it should be placed underground, just outside the house, and as near to the sink as practicable. Grease-traps to be placed underground are commonly made of 24-in vitrified drain-tile or cement pipe, and should be about 4 ft deep. They may also be built of brick in cement mortar. Fig. 11 shows a section ■J TT — ^^ Q < I / through such a grease-trap and the ^ J ^ [j--- "^^y'---*-T4-'-'-ir-- "^^^^ ^"^ outlet-pipes. When the sink <'.^ Or ^ v.^zc^^-.r-r- <^, <: is in a basement or an upper story, or when the building occupies the entire lot, the grease-trap must be placed under the sink. When so placed, a round lead trap 12 or 14 in in diameter may be used, with a large trap-screw in the top for removing the grease. Fig. 12 shows a section through such a trap and the way in which the connec- tions should be made. A better form Some city ordinances require that inside Fig. 12. Lead Grease-trap of grease-trap is made of ca.st iron. grease-traps shall have a chiUing-jacket for the purpose of more perfectly separating the grease and thus preventing any of it from entering the waste- pipes. To be effective, a grease-trap must have a capacity of at least twice the amount of greasy water that will be discharged into it at any one time. Supply-Pipes and House-Tanks 1415 Supply-Pipes. These may be of lead, brass, galvanized iron, tin-lined lead, or block tin. Lead pipe offers the least resistance to the flow of water, is easily bent to suit any situation, and easy curves are readily made. It is generally considered more durable underground than galvanized-iron pipe. The grade known a.s A, or strong, is the lightest that should ever be used, and when the supply is taken from city mains, in which there is a considerable pressure, A A, or extra-strong pipe, should be used. Galvanized-iron pipe is probably more extensively used than any other material for water-supply pipes in buildings, except where nickel-plated pipe is required, in which case brass piping is com- monly used. Brass pipe used for water-supply should be what is known as iron- pipe SIZE. Brass piping is preferable to galvanized iron or lead for conveying hot water, and is largely used in the better class of buildings. Tin-hned iron and lead pipes and pipes of block tin are usually considered as offering the greatest resistance to corrosion or chemical action, and should always be used for conveying ale, beer and other liquors. Tin-lined iron pipe is made by pouring melted tin into a wrought-iron pipe. While in a fluid state the tin is inseparably united to the iron, and the result is one solid pipe composed of two metals which CANNOT BE TORN APART. It IS essentially different from iron pipe merely dipped in tin, and immeasurably superior to iron pipe lined with a separate tin pipe that will become detached. Its fittings are lined with tin to match. Hot water will not injure it, rats will not gnaw it, and thieves will not cut it out. Either hot or cold water may stand in block-tin pipes and yet be drawn from them pure and free from poison or rust. Lead-lined pipe is made in the same way and insures delivering the water to the house just as it comes from the mains unchanged by the chemical action which often results from contact with' wrought-iron pipe. Seamless-Drawn Benedict Nickel Tubing is used to some extent for the exposed plumbing-pipes in high-class residences, ofTice and public buildings. Being pure white metal throughout it cannot rub or wear brassy or become discolored. It is made in all the regular iron-pipe sizes, and necessary fittings are supplied of the same metal.* House-Tanks. Where the pressure in the street-mains is not great enough to furnish a sufficient volume of water for supplying the fixtures at all times, or in cases of a private water-supply, a tank should be placed in the attic, or ele- vated at least 6 ft above the highest fixture to be supplied. In some cases the fixtures in the lower story are supplied direct from the street mains, while those in the upper story are supplied from a tank. The advantage of a tank is that it will fill gradually from a very small stream, and thus form a reservoir from which a larger volume can be drawn in a shorter space of time than could be obtained direct from the service-pipes. Storage-tanks should always be pro- vided with an overflow-pipe of ample size and when supplied from the street- mains the supply should be controlled by a ball-cock and float. Storage-tanks of moderate size are preferably made of wood lined with planished or tinned copper. Sheet lead, zinc or galvanized iron should not be used for lining tankij containing water for drinking or cooking purposes, and are not as durable as copper, even when the effect on the water need not be considered. The Size of Tank Required will depend largely upon the character of the supply. Tanks supplied from the street-main in which the pressure is fairly constant need not have a capacity exceeding i6o gal. W^here the water is pumped into the tank by a windmill or hot-air engine, the tank should have a capacity sufiicient for a three or four days' supply at least. * For further information consult the Benedict & Burnham Manufacturing Company, .Waterbury, Conn. 1416 Hydraulics, Plumbing and Drainage, and Gas-Piping Part 3 Amount of Water Required for Various Purposes. The amount of water required for household purposes has been found to be about 25 gal for each person, large or small, but waste will triple that amount sometimes. A horse will drink about 7 gal per day and a cow from 5 to 6 gal per day. A carriage re- quires from 9 to 16 gal for washing. Size of Supply-Pipes. The proper diameter of supply-pipes depends upon several considerations, such as the number and size of faucets that are hkely to be discharging water at the same time, the urgency of the demand, the length of the pipes and number of angles, and upon the pressure. There is no objection to having a pipe larger than is really necessary, except from the standpoint of cost. Service-pipes should always be one size larger than the tap in the street- main. The following table affords a fair guide for proportioning the supply- branches to plumbing-fixtures. If the pressure is less than 20 lb per sq in the system may be rated as low pressure, and if above 20 lb as high pressure. Supply-branches Low pressure. High pressure, To Bath-cocks Basin-cocks Water-closet flush-tank . Water-closet flush-valve Sitz or foot-bath Kitchen sinks Pantry sinks Slop-sinks Urinals H to I iH to iH \*i to Yk H to y^ % to ^4 H to y^ Hto H iH to \\h 1/^tO % Hto H With high-pressure systems, dwellings of five or six rooms are sometimes, for economy, supplied entirely through H-'m pipe. Minimum Diameter of Waste-Pipes. The following are considered as the smallest diameters allowable for waste-pipes. The diameters required in New York City are given on page 1410. Bath and sink-wastes, iM in. Basin and urinal-wastes, iH in. Wash-trays, i^ in from each compartment, entered into 4-in drum-trap and 3-in outlet from trap. Water-closet trap, 2}^^ in. Approximate Spacing for Tacks on Lead Pipes Size of pipe, Vertical pipe Horizontal pipe Distance apart Distance apart Hot, Cold. Hot. Cold. m m in in H 19 25 14 17 H 20 26 IS 18 % 21 27 16 19 I 22 28 17 20 iH 23 29 18 21 iH 24 30 18 22 Lead Pipe 1417 Designation of Lead Pipe. The different thicknesses of lead pipe were formerly designated by letters as in Table H, page 1418, but are now more commonly designated as in Table G, following, which may be considered as generally accepted by dealers. Table G. Weights and Sizes of Lead Pipe Caliber H-in Tubing Fish seine ^i-in Aqueduct Extra light Light Medium Strong Extra strong H-in Aqueduct Extra light Light Medium Strong AA Extra strong Extra extra strong. . ^^-in Aqueduct Extra hght Light Medium Strong Extra strong Extra extra strong.. ^4-in Aqueduct Extra light Light Medium Strong Extra strong Extra extra strong, ^^-in Aqueduct Extra light Light i-in Aqueduct Extra light Light Medium Strong Extra strong Extra extra strong. iH-in Aqueduct Extra light Light Medium Strong Extra strong Extra extra strong. Weight per foot lb Caliber i3'^-in Aqueduct Extra light Light Medium Strong Extra strong Extra extra strong. . iJ4-in Extra light Light Medium Strong Extra strong 2-in Waste Extra light Light Medium Strong Extra strong Extra extra strong . . 2j'^-in Waste Light Medium, Me thick. Strong, V4 thick... . Extra strong, YiQ thick Extra extra strong, ^^ thick 3-in Waste Light Medium, Me thick. Strong, H thick Extra strong, Me thick Extra extra strong, ^i thick 3^i-in Waste Strong, Vi thick — Extra strong, Me thick 4-in Waste Medium Strong, H thick Extra strong, Me thick Extra extra strong, ^i thick S-in Waste Weight per foot 1418 Hydraulics, Plumbing and Drainage, and Gas-Piping Part i Coils of supply-pipe weigh about 200 lb; aqueduct about 90 lb; suction- pipe, loo to 180 lb each. Block-tin pipe is stronger for a given weight per foot than lead pipe or tin \ined lead pipe. As compared with lead pipe its strength is as shz to i. Tin-lined and lead-lined iron pipe is made with inside diameters of H, H, ij iH, iy-2 and 2 in, and in lo-ft lengths, threaded without couphngs. Tin-lined and lead-lined fittings are also made (see page 1415). Weights and Sizes of Sheet Lead 1 ^ Thickness, in, . . K21 Ho He He full H4 %2 H M H full % H % Lb per sq ft 2H 3 3H 4 5 6 8 10 12 14 16 20 24 Table H. Thickness and Strength of Lead Pipes Mean Safe Mean Safe Cali- Weight Thick- burst- work- Cali- Weight Thick- burst- work- ber. Mark per foot, lb oz ness, ing- ing ber- Mark per foot, lb oz ness, ing- ing in in pres- sure, pres- sure, in in pres- sure, pres- sure, lb lb lb lb H AAA I 12 0.18 1968 492 I A 4 0.21 857 214 H AA I S o.is I 627 406 I B 3 4 0.17 745 186 H A I 2 0.13 I 381 347 I C 2 8 0.14 562 140 H B I 0.125 1342 335 I D 2 4 0.125 518 129 C 14 10 O.II I 187 296 271 I I E 2 I 8 O.IO 0.09 475 325 118 81 0.087 1085 Vie gYz 0.08 775 193 iH AAA 6 12 0.275 962 240 H AAA 3 0.25 1787 446 iH AA 5 12 0.25 823 205 H 2 8 0.225 1655 413 iH A 4 II 0.21 685 171 H AA 2 0.18 1393 343 iH B 3 II 0.17 546 136 H A I 10 0.16 1285 321 iH C 3 0.135 420 105 H B I 3 0.125 980 245 iH D 2 8 0.125 350 87 H C I O.IO 782 195 iH 2 0.095 322 80 H D 9 0.065 468 117 iH AAA 8 0.29 742 185 V2 10 0.07 556 139 iH AA 7 0.25 700 175 H 12 0.09 625 156 iH A 6 4 0.22 628 157 H AAA 3 8 0.23 1548 387 iH B 5 0.18 S06 126 % AA 2 12 0.21 1380 345 H C 4 4 0.15 430 107 5/i A 2 8 0.18 I 152 288 H D 3 8 0.14 31S 78 % B 2 0.16 987 246 m 3 0.12 245 61 H C I 7 O.II7 795 198 iM B 5 116 H D I 4 O.IO 708 177 iK C 4 93 H AAA 4 14 0.29 1462 365 1% D 3 10 0.125 318 79 H AA 3 8 0.225 I 225 306 2 AAA 10 II 0.30 611. 152 H A 3 0.19 I 072 268 2 AA 8 14 0.25 5" 127 H B 2 3 O.IS 865 216 2 A 7 0.21 40s lOI H I 12 0.125 782 19s 2 B 6 0.19 360 90 H D I 3 0.09 S05 126 2 C 5 0.16 260 65 I AAA 6 0.30 I 230 307 2 D 4 0.09 200 50 I AA 4 8 0.23 910 227 Sewer-Pipe Weight and Sizes of Pure Block-Tin Pipe 1419 Size inside diameter Weight per foot, 4 4.5,6 4. S.*6. 8 4. 5. 6, 8 5,6,8, lo 9, 12, i6 Size inside diameter Weight per foot, lb 9, 12, i6 12, i6 20, 28 24 and upwards 32 and upwards Sewer-Pipe There are three kinds of sewer-pipe or drain-pipe offered in the market, (i) SALT-GLAZED VITRIFIED CLAY PIPE, (2) SLIP-GLAZED CLAY PIPE and (3) CEMENT PIPE. The name of the latter sufficiently indicates what it is without any de- scription. The SLIP-GLAZED CLAY PIPE is made of what is known as fire-clay, such as fire-brick clay, which retains its porosity when subjected to the most intense heat. It is glazed with another kind of clay, known as slip, which, when subjected to heat, melts, creating a very thin glazing, and which, being a foreign SUBSTANCE TO THE BODY OF THE PIPE, is liable to wear or scale off . Salt-glazed CLAY PIPE is made of a clay, which, when subjected to an intense heat, becomes vitreous or glass-like. It is glazed by the vapors of salt, the salt being thrown in the fire, thereby creating a vapor which unites chemically with the clay, and forms a glazing, which will not scale or wear off, and is impervious to the action of acids, gases, steam, or any other known substance. It unites with the clay in such a manner as to form part of the body of the pipe, and is therefore indestructible. Salt-glazed pipe can only be made from clay that will vitrify, that is, when subjected to an intense heat will become a hard, compact, non- porous body. It should be borne in mind that slip-glazing is only resorted to when the clays are of such a nature that they will not vitrify. The Material of Drain-Pipes should be a hard, vitreous substance; not porous, since this would lead to the absorption of the impure contents of the drain, would have less actual strength to resist pressure, would be more affected by the frost or by the formation of crystals in connection with certain chemical combinations, or would be more susceptible to the chemical action of the con- stituents of the sewerage. Sewer-Pipes Should be Salt-Glazed, as this requires them to be subjected to a much more intense heat than is needed for slip-glazing, and thus secures a harder material. Cement pipes made without metal reinforcement have not proved sufficiently strong and durable to be used with confidence in any im- portant work. When reinforced with metal, however, they have ample strength, and reinforced-cement sewer-pipes of large diameter are used to a considerable extent in Europe. For determining the diameter of house-sewers, the table on page 1409 will serve as a good guide. Storm-sewers should be proportioned to the area drained. The maximum rainfall, as shown by statistics, is about i in per hour, except during very heavy storms, equal to 27 225 gal per hour for each acre, or 453 gal per minute per acre. Owing to various obstructions, not more than from 50 to 75% of the rainfall will reach the drain within the same hour, and allowance should be made for this fact in determining size of storm-sewer required. 1120 Hydraulics, riumbing and Drainage, and Gas-l^iping Part 3 Carrying Capacity of Sewer-Pipfe Gallons per minute Size of pipe. Fall per loo ft in I in 2 in 3 in 6 in 9 in I ft 2 ft 3 ft 3 4 6 13 27 75 19 38 105 23 47 129 32 66 183 40 8i 224 46 93 258 64 131 364 79 163 450 8 9 10 153 205 267 216 290 378 265 355 463 375 503 755 460 617 803 527 712 926 750 I 006 I 310 923 I 240 I 613 12 15 i8 422 740 I 168 596 I 021 I 651 730 . 1 282 2 022 I 033 I 818 2860 I 273 2224 3508 I 468 2464 4045 2 076 3617 5 704 2554 4467 7047 24 .27 30 36 2396 4407 5906 9707 3 387 6 211 8352 13769 4 155 7674 10223 16 816 5874 10883 14298 23763 7202 13257 17 714 29 284 8303 15344 20 204 33722 II 744 21 771 28 129 47523 14466 26 622 35513 58406 Quantities of Cement, Sand and of Cement Mortar for Sewer-Pipe Joints Prepared by J. N. Hazlehurst For each 100 ft of sewer (with Portland cement, 375 lb net per bbl) Size of Proportions: I Cement to I Sand 2 Sand pipe, in Length, • ft Mortar, cu yd Pipe per Pipe per Cement, Sand, bbl Cement, Sand, bbl bbl cu yd cement, linft bbl cu yd cement, linft .6 2V2 0.003 0.01248 0.00201 803 0.00855 0.00252 1168 8 2l/i 0.038 0.15808 . 02546 633 0.10830 0.03192 923 10 2\^ 0.058 0.24128 0.03886 410 0.16530 0.04872 605 12 ^Vi 0.089 0.37024 0.05963 270 0.25365 0.07476 394 15 2\i 0.123 0.51268 0.08241 195 0.35055 0.10332 285 18 2\i 0.167 0.69472 0.11189 144 0.47595 0.14018 210 20 2\^ 0.237 0.98592 0.15879 lOI 0.67545 0.19908 148 24 2\<, 0.299 1.24384 0.20033 80 0.85215 0.25116 117 27 3 0.492 2.04672 0.32964 49 I . 40220 0.41328 71 30 3 0.548 2.27968 0.36716 44 I. 56180 0.46032 64 36 3 0.849 3.53184 0.56883 29 2.41965 0.71316 41 Plumbing Specialties The Kenney Flushometer. This is a gravity valve designed for flushing all water-closets, urinals and slop-sinks in a building direct from one tank situated in the attic or where most desirable, thus dispensing with the individual overhead tank. The pipe from the main tank is run down to the different floors either exposed or concealed and branches taken off from there to the flushom- Plumbing Specialties 1421 eter. The operation of the flushomcter is to pull the handle forward, which raises the main valve off its seat, making a direct connection from the flushom- cter to the tank. After the handle is released the valve closes slowly of its own accord against a high or low pressure. It is constructed without springs or cup-leathers and closes by gravity, is built to stand the hardest service, and yet is so simple in construction and operation that the same valve is used for all requirements, the only differences in adjustment being those necessary for work on high or low pressure. The flushometer is extensively used for flushing closets in buildings in the Eastern States, including many large office- buildings, factories, schools, hospitals, and the better class of residences; also on steamships and yachts. Filters. There are few cities in which the public water-supply is not greatly improved in wholesomeness by being filtered, and in many places filtering is absolutely necessary. The filter should be large enough so that the velocity of the water passing through it will be low and it should be so arranged that the flow of water can be reversed and the accumulated impurities washed into a waste-pipe. In the country a filter suitable for rain-water may be built un- derground, the filtering process being accomplished by beds of sand and gravel. For city buildings, however, a portable filter located in the basement should be used. An ordinary sand filter, either pressure or gravity, will clarify water of all mechanical impurities, suitable for plunge-baths, and other general uses in a building. To provide a perfectly sterile water, however, the filter must be fitted with a coagulating apparatus to automatically feed a proportionate dose of coagulant to the raw water. Those so-called filters which are made to screw onto the nozzle of an ordinary faucet should be considered merely as strainers, and even for that purpose they soon become foul. Instantaneous Water-Heaters are a great convenience for heating water for baths and wash-basins in buildings in which a constant supply of hot water is not provided, and especially in residences where the cooking is done by gas. They are cylindrical in shape, made of nickel-plated copper, and are usually set on a nickel-plated shelf attached to the wall close to the fixture to be supplied. A heater io|.^ in in diameter and 30 in high will heat 20 gal of water in eight minutes at a cost of i^ to 2 cts with gas at $1 per i 000 cu ft. A large line of these heaters is made by the Humphry Manufacturing and Plating Company, Kalamazoo, Mich., for both gas and gasolene, although gas is preferable when it can be had. The cost of heaters varies from $15 to $45, according to size. An Automatic Water-Heater which maintains water at any desired tem- perature without attention, provided the building has a supply of live steam, is made by James B. Clow & Sons, the supply of steam being automatically regu- lated by a thermostat. It will be found especially desirable in hospitals, hotels, apartment-houses and public institutions. The heater is made in four sizes, with capacities of i 500, 2 500, 4 000 and 6 500 gal per hour. The Climax Cellar-Drainer * is a simple device for raising water from 6 to 10 ft without attention or power, except a supply of steam or water. It is used principally for draining cellars, wheel-pits, furnace-pits, etc., when they are too low to drain into the sewer. For such places a box or barrel is sunk so that all of the water will run into it, and the drainer is set in this receiver and the dis- charge-pipe run to a sink or open drain. The drainer performs its functions by passing water or steam under pressure through the drainer-point or jet, thus creating a suction which draws the water from the receiver in which it is placed into the discharge-pipe, and both the jet-water and cellar-water are discharged • Manufactured by Jas. B, Clow & Sons. 1422 Hydraulics, Plumbing and Drainage, and Gas-Piping Part 3 together. As long as the city water or steam passes through the drainer-pipe, this suction and discharge continues. The supply of water or steam is turned on or off automatically, so that there is no consumption of city water or steam except when the drainer is removing water. This drainer will operate with a pressure of 15 lb or more, the heavier the pressure the greater the amount of dead water discharged. When the drainage- water does not have to be raised more than 10 ft, this is the most economical apparatus that can be used, as the amount of city water consumed is very small. The Climax Drainer is made in six sizes, costing from $25 to $160. Sewage-Ejectment. Mechanical ejectment of sewage is resorted to in cases where the street-sewer is abov^e the level of the area to be drained. This con- dition is found principally in the subbasement-lloors of tall buildings, under- ground public-comfort stations and underground passenger-stations. A system of mechanical ejectment consists of a gravity drainage-system to a receiving tank or sump located in a water-tight pit at the lowest part of the drainage- system, and a pump or conpressed-air ejector to raise the sewage and discharge it into the street-sewer. There are three types of apparatus used to raise sew- age to the street sewers, centrifugal pumps, piston-pumps, and compressed-air ejectors. The compressed-air ejectors, however, are commonly used owing to their numerous advantages. They are automatic and almost noiseless in opera- tion, are perfectly odorless, and have but few working parts that can get out of order. Sewage-ejectment apparatus is generally installed in duplicate so that one set may be cut out of service for cleaning or repairs, without inter- rupting the drainage-service. Plunge-Baths An Example of the Construction and Details of a Small Plt^nge- Bath or Swimming-Bath. The following is a description, with illustrations, of the bath in the house of the Racquet and Tennis Club on Forty-third Street, New York City.* "The swimming-bath has inside dimensions of 15 by 22 ft and is about 9 ft in total depth. It was built in a pit about 19 by 26 ft and about 8 ft deep below the main excavation, which was blasted out of solid rock. A concrete invert I ft or more in thickness was laid over the bottom, serving as a footing on which the 12-in walls of common red brick were laid in cement. They were built close to the rough vertical faces of the excavation, and the spaces behind them were filled with concrete or cement mortar or were flushed with grout. Then on the inner surface of the walls and on top of the concrete Iwttom lining a waterproofing of six layers of felt with lapped joints was mopped on with hot tar and flashed around the iron outlet-pipe, which also had a wide calked lead flange extending between the layers of felt. On the bottom of this water-proof coat an 8-in inverted segmental flat floor-arch of common brick was laid, and on its skewbacks 4-in vertical brick walls were built against the water-proofed sides. The bottom was then lined with vitrified white tile and the sides were faced with English white enameled brick. The tops of the walls were coped with beveled and molded white-marble slabs which are about 2 ft above the floor-level and are surmounted at one side and one end by a low heavy rail with twisted orna- mental posts, all of brass. A similar horizontal hand-rail is carried along the inside wall of the bath just above water-level and a curved brass hand-rail is fastened to the wall above the narrow brick-and-marble stairs at one end. The * The illustrations and accompanying descriptions are taken by permission from the Engineering Record of Nov. 3, 1900. Plunge-Baths 1423 swimming-bath occupies one corner of the room and its elevated marble plat- form extends entirely across it, forming a diving-platform which is reached by two marble steps. All the water-supply is filtered and it can be warmed by in- jecting steam into the delivery-pipe at the filter. The water enters through the open upturned end of a 2-in brass pipe projecting a foot or more through the wall above the top of the bath and delivering a solid jet unless it is reduced by the regulating valve or is formed into a fan-shaped cascade by means of a I Brass _ Railing Floor Strainer Inlet ^ WA .=2=t CROSS-SECTION Brass- Railing i I id I ELEVATION Fig. 13. Plunge-bath special nozzle which can be screwed in the open end of the pipe. When the bath is much used a small stream of water is constantly admitted and causes a continual gentle circulation and corresponding overflow, and the entire con- tents are pumped out and the bath cleaned every two or three days. There are two overflows, an open one about 8 ft above the bottom and a valved one a foot lower. C. L. W. Eidlitz was the architect of the house and the water- proofing was done by the T. New Construction Company." Symbols for Plumbing. Figs. 14, 15 and 16 show the symbols suggested in " Plumbing-Plans and Specifications " for designating plumbing-work on plans 1424 Hydraulics, Plumbing and Drainage, and Gas-Piping Part 3 and details, and generally accepted for the purpose. It is just as necessary to have conventional symbols to indicate plumbing-work and fixtures, as it is to have symbols to show-windows, doors, steps, partitions and other struc- ^ Ferrule Ct^ Symbol for lead pipe . Cold water ) • Hot -water > Fresh- water pipes • Circulation ) - Cold water ) - Hot-water V Salt-water pipes Circulation} Symbols for water-pipes Symbol for cast-iron pipe Symbol for wrought pipe Globe valve Gate-valve Plain view of valve Angle- valve One-line symbols for valycs T Check- valve Plan of T-handlo stop-cock Fig. 14. Symbols for Plumbing-pipes and Valves tural details on architectural drawings. Before these symbols became generally used there was no unifonnity in the drawing of plumbing-plans, and this lack of standards often led to serious confusion. For instance, if plans from teo Symbols for Plumbing- Work 1425 different offices were examined, the chances were that on no two of them would the symbols have been alike. Further, plans prepared in the same office at Side view T-handle Plan-view of Side view of Btop-cocic .lever-handle stoi)-cock lever-handle * stop- cock. Symbol for faucet Top view' of faucet • # • 1' vx" %" hot cold circulation. Plan-symbols for water-supply risers Inlet ^"%^ I Beams f 1 [I % 4x6x3 deep Symbol for a suction-tank 3" soil 2 Vent? Symbols for soil and Vent-stacks Qnj)lans Symbol foi non-6iphon.trap I BeamN Symbdljor house -tank Sy^mbol for meter Plan-symbol for a water-heater X {™} 4^fTTTTTn^ Elevation-symbol for a water-heater Fig. 15. Miscellaneous Plumbing-symbols Symbol for hot- water tank different times, or one set of plans on which several different draughtsmen had worked, would often show as many different symbols for a water-closet or lava- tory as there were workmen engaged on the drawings. That was rather con- 1426 Hydraulics, Plumbing and Drainage, and Gas-Piping Part 3 fusing to plumbers who had to take off quantities from the plans; for, often the symbols were so strange and bore so little resemblance to the fixtures or apparatus that some of them were liable to be overlooked. It is owing to this Symbol for plan of pump Symbol for elevation of pump ' Plan-symbol for bath-tub /Si mz ^ "tf- o. Elevation-symbol for bath-tub plan-symbol for £levatioii-symbol Plan-sym"bol for lavatory for lavatory water-closet Ort^ End-symbol for Side-symbol for water-closet water-closet Plan symbol for sink _il_ V 1 k 9 Elevation-symbol for sinTc Fig. 16. Symbols for Plumbing-fixtures Elevation-symbol for ■ ^eedle, shower and spray -bath Plan-symbol for needle, shower and^spray-bath uncertainty wherever it exists from this cause, that there is a wide range of prices in the bids submitted, and all of them are unreasonably high for the amount of work to be done. To avoid confusion and secure good piices, these standard symbol shoul'^ he used. Expansion of Plumbing-Pipes 1427 Expansion of Soil and Waste-Stacks. In tall buildings, provision should be made in the soil-stacks and connections to take care of the expansion, con- traction, settlements, swaying and other movements of the building. This movement is no inconsideral)le amount, in some localities the settlement alone amounting to as much as 5 in when the foundations are not carried to l)ed-rock. In Chicago, for instance, most of the sky-scrapers which were built on com- pressible foundation-beds are out of plumb and lean far out over the plumb- line. One building in particular leaned so that the top was 30 in outside of the line of the foundation. Most of the earlier heavy buildings there erected on " floating foundations " are carried on jacks, and periodically jacked up as settlement occurs. When the building finally comes to rest, the jacks are removed and the walls filled in with masonry. The settlement which takes place will range in such buildings from 3 to 5 in. These various move- ments, expansion, contraction, settlement, racking out of plumb, also sway- ing of high buildings as they follow the sun in its course from East to West, will prove destructive to steam-pipes and plumbing-pipes if provision is not made to take care of them. Steam-pipes always have expansion-loops, but it is only recently that the proper attention has been given to soil and vent-stacks and pipes; and then only after as many as 150 water-closets in one build- ing were broken through faulty installation, or rigid connec- tions. The remedy is to put expansion- joints (Fig. 17) in the soil and vent-stacks of Normal Collapsed Expansion- joints Stretched, Bent Fig. 17. tall buildings, and to connect all water-closets to the soil-pipes by means of flexible or collapsible connections which will stretch, collapse, or stretch on one side, and collapse on the other, according to the stress to which they arft subjected. These flexible fittings should be placed as close to the closets as possible, and should be used also in connection with slop-sinks and inside rain- leaders. For inside rain-leaders the number of corrugations can be increased in proportion to the height of the building. Ordinary stock fittings have a range of about 2 in. That is, they will stretch about i in and collapse i in. For rain-leaders in tall buildings, however, greater range than that is desirable. Two corrugations would be sufficient for a rain-leader in an ordinary building not over 100 ft in height; then, for taller buildings, it is well to allow an extra corrugation for each additional 100 ft or fraction thereof. The flexibility of these fittings can be seen in the accompanying illustrations of Fig. 17. Shrinkage in Buildings. Ninety-seven per cent of buildings erected have wooden floor-construction, and the floor-joists, when they dry out, shrink. This is the cause of many thousands of closets being broken annually, and the destroying of the seal at the closet-connection of those which are not broken, unless they are provided with a flexible floor-flange or fitting. The amount of shrinkage of floor-beams of difl'erent depths, can be found in the following table, compiled from information furnished by the United States Government, Department of Agriculture, Division of Forestry, in Bulletin No. 10. Besides the shrinkage of the individual tiers of joists, there is the multiple shrink- age of all the tiers when bearing-partitions, supporting the joists at the middle in a building, rest on sills at each floor which are laid on top of the joists, instead of extending down through to the plate which supports the tier of joists. When the framing is properly done, there is only the shrinkage of the one tier of beams to take into consideration. When improperly framed. 1428 Hydraulics, Plumbing and Drainage, and Gas-Piping Part 3 there might be three or four shrinkages affecting the top floor of the building. Even though the timbers are dry and seasoned when put in, by the time the plasterers are through the joists are wet and swollen from the moisture in the plaster and from the rain which saturates the timbers before the building is en- closed. It is safe to assume, therefore, that a 12-in joist will shrink almost H \n, and an i8-in joist about % in. Table of Shrinkage of Timbers Depth of green or wet timber, in Amount lost by shrinkage, 4%, in Depth of timber when dry, in 6 0.24 5.76 • 8 0.32 7.68 10 0.40 9.60 12 0.48 11.52 14 0.56 13-44 16 0.64 15.36 18 0.72 17.28 20 0.80 19.20 Floor-Connections for Water-Closets. No water-closet can be considered sanitary which depends upon a putty-joint, slip-joint, rigid-gasket joint or rigid connection of any kind for a seal. Improved metal-to-metal floor-flanges now cost no more than rigid-gasket joints formerly did, and they are flexible, water-tight, will remain permanently tight, and protect the closets from being broken by shrinkage or other movement of the building or piping. The only way to get a perfectly sanitary water-closet is to specify a flexible, metal-to- metal, closet floor-flange with it. Expansion of Hot-Water Pipes. In all tall buildings expansion-loops ought to be placed in both the hot-water and the circulation-pipes, to permit the expansion and contraction of the lines without injury to the system. These loops are usually from 6 to 8 ft long, made up with elbows, and extend into the floor of the building. Generally the hot-water and circulation-pipes are sup- ported midway between loops so that they can expand both up and down. The length that water-pipes will expand depends upon the degree to which they are heated, and the materials of which the pipes are made. The first of the follow- ing three tables gives the expansion of cast-iron pipes, the second the expansion of wrought-iron pipes, and the third the expansion of brass pipes. Expansion of Cast-iron Pipes Temper- ature of air when pipe is fitted, degrees F. Length of pipe when fitted, ft Length of pipe when heated to 215° F. ft in 265° F. ft in ■ 297° F. ft in 338° F. ft in 32 64 100 100 100 100 1.59 100 I . 36 100 I. 12 100 1.96 100 1.6s 100 1.43 100 2.20 100 1.96 100 1.73 100 2 . 50 100 2 . 27 100 2.00 Softening Hard Water Expansion of Wrought-Iron Pipe 1429 Temper- ature of air when pipe is fitted, degrees F. Length of pipe when fitted, ft Length of pipe when heated to 215° F. ft in 265° F. ft in 297° F. ft in 338° F. ft in 32 64 100 100 100 100 1.72 100 1.47 100 I. 21 100 2.21 100 1.78 100 I. 61 100 2.31 100 2.12 100 1.87 100 2.70 100 2.45 100 2.iy Expansion of Brass Pipe Temper- ature of air when pipe is fitted, degrees F. Length of pipe when fitted, ft Length of pipe when heated to 215 ft ^F. in 265° F. ft in 297° F. ft in 338° F. ft in 32 64 100 100 100 100 100 100 2 58 2 19 I 81 100 3 18 100 2.79 100 2 . 41 100 3.56 100 3.18 100 2.79 100 4.05 100 3 67 100 3 28 Softening Hard Water for Domestic Use. In many parts of the country the water is temporarily hard, permanently hard or both temporarily AND PERMANENTLY HARD. This is due to the fact that in those regions the underlying rock is limestone, and in percolating through the limestone the water, which originally was soft, dissolves carbonates and sulphates of lime or magnesia from the rock. The solvent capacity of water for lime and magnesia is greater when the water is cold than when it is hot. Therefore, deep- well water in limestone-regions is usually saturated with lime or magnesia, and when heated in water-tanks or boilers the point of saturation is lowered and lime 13 precipitated or liberated in the form of hard scale or incrustation. The effect of boiler-incrustation is to shorten the life of the boiler and decrease the efificiency of the boiler while in use. It is estimated that: He-in lime-scale means a loss of 13% of fuel. H-in lime-scale means a loss of 22% of fuel. H-in lime-scale means a loss of 38% of fuel. %-in lime-scale means a loss of 50% of fuel. y2-'m lime-scale means a loss of 60% of fuel. %-in lime-scale means a loss of 91% of fuel. These values are probably a little high, but making due allowance, the table will serve to show the loss due to the use of hard water. In the laundry the increased consumption of soap to soften hard water is a further item of expense. It requires about i lb of soap to soften 100 gal of moderately-hard water, besides the soap required for washing after the water has been softened. Besides the expense, hard water forms an insoluble curd when washing which makes it particularly annoying to hotel-guests; therefore, it is advisable to treat all hard water for large hotel-buildings, laundries and for many indus- trial purposes. Permanently hard waters contain sulphates of lime or mag- nesia. Temporarily hard waters contain carbonates of lime or magnesia. 1430 Hydraulics, Plumbing and Drainage, and Gas-Piping Part 3 Temporaiily and permanently hard waters contain both carbonates and sulphates of hme or magnesia. Temporarily hard waters are softened by adding lime-water to the raw water to remove the carbonates of lime. This is known as the Clark Process. Permanently hard waters are softened by the Porter Process, which consists of adding soda-ash to the raw water. Stock types of apparatus are manufactured for this purpose, and may be hud with capacities of any required amount. Heating Water with Steam-Coils. The following constants will be found convenient for proportioning steam-coils for heating water: W = gallons of water to be heated. W -r- lo = sq ft of iron pipe-coil required for exhaust-steam. W -r- 15= sq ft of copper pipe-coil required for exhaust-steam. W X 0.07 = sq ft of iron pipe-coil for 5 lb pressure-steam. W X 0.045 = sq ft of copper pipe-coil for 5 lb pressure-steam. W X 0.05 = sq.ft of iron pipe-coil for 25 lb steam-pressure. W X 0.035 = sq ft of copper pipe-coil for 25 lb steam-pressure. W X 0.04 = sq ft of iron pipe-coil for 50 lb steam-pressure. W X 0.25 = sq ft of copper pipe-coil required for 50 lb steam-pressure. W X 0.03 = sq ft of iron pipe-coil required for 75 lb steam-pressure. W X 0.02 = sq ft of copper pipe-coil required for 75 lb steam-pressure. Capacity of Water-Backs. The average size of water-back having about 110 sq in, or about ^i sq ft of exposed surface, will heat to the ordinary temper- ature of domestic hot water, 180° F., about 21 gal of water an hour. It will heat about 17 gal of water to the boiling-point with an ordinary fire. With a fire such as is used for roasting, washing, or baking, a water-back of this same size will heat about 23 gal of water to the boiling-point, or 27 gal to a temperature of 180° F. Wrought-iron pipe heating-coils will heat from 30 to 40 gal of water under the same conditions, and copper pipes will heat from 45 to 60 gal per hour for each square foot of surface exposed to the fire. In calculating the heating capacity of water-backs or coils, the average temperature of the water is taken. Thus, if water at 60° is heated to 200° F., the average temperature of the water would be (60 -|- 200) -^ 2 = 130° F., and the range of temperature through which it is heated would be 200 — 60 = 140° F. Value of Pipe-Covering. Hot-water pipes and hot-water tanks when uncovered lose by radiation from their surface about 13 heat-units per minute per square foot of surface. To prevent this loss of heat and consequent extra consumption of coal, hot-water pipes, circulation-pipes and hot-water tanks in large institutions are generally covered with some non-heat-conducting material. The value of pipe-covering is not proportional to its thickness. Sectional pipe- coverings average about 1% in in thickness and reduce the loss by radiation about 90%. Doubling the thickness of pipe-covering saves only about another 5% of heat-loss. In specifying covering for pipes and boilers, therefore, a thick- ness of I H in will be sufTicient. Carbonate of magnesia is a very poor conductor of heat. Therefore, it is a good material for covering hot-water pipes. Carbon- ate of lime, on the other hand, is not a good covering material, although it often masquerades as carbonate of magnesia. When magnesia pipe-covering is specified, therefore, it is well to require a composition containing from 80 to 90% of magnesia, and require a test to be made at the expense of the contractor, but by a chemist named by the architect. The following coverings are the best materials for hot-water pipes, in the order in which they are named. Nonpareil Cork, Magnesia, Asbestos Air-Cell and Imperial Asbestos. Illuminating-Gas 1431 (3) ILLUMINATING-GAS AND GAS-PlPlNG* Varieties of Gas. Five varieties of gas are now commonly used for light- ing and cooking, namely: (i) Coal-Gas, which is made by heating bituminous coal in air-tight retorts. This is the most common variety of gas furnished for the lighting of cities and towns. (2) Water-Gas, which is made usually from anthracite coal and steam, and is quite extensively used in Eastern cities. Gas made by this process contains less carbon than good coal-gas, and conseciuently does not give as bright a light, although it burns perfectly in heating-burners. When used for lighting purposes it is enriched in carbon by vaporizing a quantity of petroleum by heat and in- jecting it into the hot gas before it leaves the generator. Pure water-gas is lighter and has less odor than coal-gas. (3) Natural Gas is obtained from holes or wells which are drilled in the ground. In localities where it can be obtained it furnishes cheap light and fuel. The natural gas obtained in the hard-coal regions develops more heat per cubic foot in burning than any other kind of gas except acetylene. Natural gas is usually under greater pressure in the street-mains and house-pipes than manufactured gas. (4) Acetylene-Gas. Used almost exclusively for the lighting of isolated buildings, or for public buildings in towns or cities where there is no public gas- supply, and commonly generated on the premises. It is formed by bringing water and calcium carbide in contact. Calcium carbide is produced by the electrical fusion of coke and lime. It is now a commercial article produced in large quantities and sold at a moderate price. It is a very hard substance like dark granite, has a very slight odor, will not burn or explode, and can be handled in any quantity with perfect safety. The fact that carbide begins to disintegrate and give off acetylene at the slightest touch of moisture makes it practicable to generate the gas in small quantities for single buildings. Process of Generating Acetylene-Gas. The satisfactory production of acety- lene-gas requires a generator which shall feed carbide of sufficient size and weight to be plunged a sufficient depth under the water in the generator-chamber to insure coolness and proper washing. The carbide-chamber must be so arranged and protected that no gas can return to it to be wasted when the chamber is refilled and permeate the house with its smell. It must feed carbide loosely and in very small quantities, in order to provide for perfect coolness by free access of water to all of the carbide. It must work automatically and with absolute certainty. Acetylene-gas to be pure must be thoroughly washed. Impure acetylene, as with any other illuminating-gas, means a discoloration of the flame, diminished illuminating power, clogging of pipes and burners with carbon and other foreign matter, and smoky burners, causing blackening of ceilings and tarnished and soiled woodwork and upholstery. It is now gener- ally agreed that the requirements above outlined can be attained only by a generator of the plunger-type. Portable generators which may be set in the cellar or basement of any building are manufactured in great variety; it is esti- mated that 100 000 acetylene-gas generators are now in use in the United States. They are made in sizes of 5, 10, 15, 20 and up to 500-Hghts capacity. In all machines dropping carbide into water there should be a connection open from the carbide-holding receptacle to the safety-vent run out of doors from the gasometer. It is claimed that for a given degree of illumination, acetylene is cheaper than dollar gas. A large residence may be lighted for about $2.50 a • See, also, Lighting and Illumination of Buildings, page i437- 1432 Hydraulics, Plumbing and Drainage, and Gas-Piping Part 3 month. To develop the full illuminating power of the gas it is necessary to use a burner-tip having the thinnest slit obtainable, the illuminating power of the gas being about fifteen times that of coal-gas, for the same consumption. The light is a clear white, very nearly resembling sunlight in color and dif- fusiveness, with none of the red of the incandescent lamp, the orange of the ordinary gas-flame, or the green tone of the incandescent mantle; and it possesses the quaHty, unique among artificial ilUiminants, of reproducing even the most delicate shades of color as faithfully as sunlight. Even when used with mantle- burners, as it may be with great economy, acetylene-light presents a strong dis- similarity from ordinary gas under the same conditions. Acetylene corrodes silver and copper, but does not affect brass, iron, lead, tin, or zinc. A govern- ment specification for a complete apparatus for acetylene-gas was published in Engineering News of Feb. 4, 1904. (5) Gasoline-Gas is a mixture of gasoline vapor with air. It is never piped but is generated close to the burner, and is seldom used for lighting except for street stands, and the like. It is much used for fuel, however. Gasoline changes from the liquid to the gaseous form under ordinary atmos- pheric pressure, at temperatures above 40° ¥., the evaporation being - cry slow at 40°, quite rapid at 70°, and furious at 212°. If a tank containing liquid gaso- line is left open to the air, the liquid will all pass away in the form of gas. Although generally considered dangerous, it is only so when carelessly or ignorantly handled. To produce i 000 cu ft of gas of good quaHty requires about 4^^ gal of the best grade of gasoHne. An ordinary burner consumes about 5 cu ft per hour. Piping a House for Gas*t General Principles and Requirements. Ordinary wrought-iron pipe, such as is used for steam or water, is suitable and proper for all kinds of gas. Galvanized malleable-iron fittings, in distinction from plain iron, are very superior. The coating of zinc inside and out effectually and permanently covers all blow-hofes, makes the work solid and durable, and avoids the use of perishable cement. Before the pipe is placed in position it should be looked and blown through. It is not infrequently obstructed, and this pre- caution will save much damage and annoyance. What is known as gas-fitters' cement never should be used. It cracks off easily, in warm places it will melt, and it can be dissolved by several different kinds of gas. Nothing but solid metals is admissible for confming gas of any kind. When pipes under floors run across floor-timbers, the latter should be cut into near their ends, or where supported on partitions, and not near the middle of spans. It is evident that a lo-in timber notched 2 in in the middle is no stronger than an 8-in timber. All branch outlet-pipes should be taken from the sides or tops of running lines. Bracket-pipes should run up from below, and not drop from above. Never drop a center pipe from the bottom of a running line. Always take such outlet from the side of the pipe. The whole system of piping must be free from low places or traps, and decline toward the main rising pipe, which should run up in a partition as near the center of the building as is practicable. It is obvious that where gas is distributed from the center of a building, smaller running lines of pipe will be needed than when the main pipe runs up on one end. Hence, timbers will not • Circular issued by tlie Gilbert & Barker Manufacturing Company, t See, also, Lighting and Illumination of Buildings, pages 1437 to 1456. Gas-Piping 1433 require as deep cutting, and the flow of gas will be more regular and even. For the same reason in large buildings, more than one riser may be advisable. When a building has different heights of post, it is always better to have an in- dependent rising pipe for each height of post, than to drop a system of piping from a higher to a lower post, or to grade to a low point and establish drip-pipes. Drip-pipes in a building should always be avoided. The whole system of piping should be so arranged tliat any condensed gas will flow back through the system and into the service-pipe in the ground. All outlet-pipes should be so securely and rigidly fastened in position that there will be no possi- bility of their moving when the gas-fixtures are attached. Center pipes should rest on a solid support fastened to the floor-timbers near their tops. The pipe should be securely fastened to the support to prevent lateral movement. The drop-pipe must be perfectly plumb, and imss through a guide fastened near the bottom of the timbers, which will keep them in position despite the assault of lathers, masons and others. In the absence of express directions to the contrary, outlets for brackets should generally be 5 ft 6 in high from the floor* except that it is usual to put them 6 ft high in halls and bath-rooms. The upright pipes should be plumb, so that the nipples that project through the walls will be level. The nipples should project noj: more than % in from the face of the plastering. Laths and plaster together are usually % in thick; hence the nipples should project 1I/2 in from the face of the studding. Drop center pipes should project iVz in below the furring, or timbers if there is no furring, where it is known that there will be no stucco or centerpieces used. Where center- pieces are to be used, or where there is a doubt whether they will be or not, then the drop-pipes should be left about a foot below the furring. All pipes being properly fastened, the drop-pipe can be safely taken out and cut to the right length when gas-fixtures are put on. Gas-pipes should never be placed on the bottoms of floor-timbers that are to be lathed and plastered, because they are inaccessible in the contingency of leakage, or when alterations are desired, and gas-fixtures are insecure. The whole S3'stem of piping should be proved to be air and gas-tight under a pressure of air that will raise a column of mercury 6 in high in a glass tube. The pipes are either tight or they leak. There is no middle ground. If they are tight the mercury will not fall a particle. A piece of paper should be pasted on the glass tube, even with the mercury, to mark its height while the pressure is on. The system of piping should remain under test for at least a half-hour. It should be the duty of the person in charge of the construction of the building to thoroughly inspect the system of gas-fitting; surely as much so as to inspect any other part of the building. He should know from personal observation that the specifications are complied with. After being satisfied that the mercury does not fall he should cause caps on the out- lets to be loosened in different parts of the building, first loosening one to let some air escape, at th,e same time observing if the mercury falls, then tightening it and repeating the operation at other points. This plan will prove whether the pipes are free from obstruction or not. When he is satisfied that the whole work is properly and perfectly executed, he should give the gas-fitter a certificate to that effect. The following requirements from specifications published by the Denver Gas and Electric Company are worthy of attention. Always use fittings in making turns; do not bend pipe. Do not use unions in concealed work; use long screws or right-and-left couplings. Long runs of approximately horizontal pipe must be firmly supported at short intervals to prevent sagging. 1434 Hydraulics, Plumbing and Drainage, and Gas-Piping Part 3 Rules and Table for Proportioning Sizes of House-Pipes for Gas*t Rules Governing Sizes of Gas-Pipes. The table on page 143S is based on the well-known formula for the flow of gas through pipes. The friction, and therefore the pressure necessary to overcome the friction, increases with the quantity of gas that goes through, and as the aim of the table is to have the loss in pressure not exceed Ho in water-pressure in 30 ft, the size of the pipe increases in going from an extremity toward the meter, as each section has an increasing number of outlets to supply. The quantity of gas the piping may be called on to pass through is stated in terms of f^-in outlets, instead of cubic feet, outlets being used as a unit instead of burners, because at the time of first inspection the number of burners may not be definitely determined. In making the table, each H-in outlet was assumed to require a supply of 10 cu ft per hour. In using the table observe the following rules: J (i] No house-riser shall be less than % in. The house-riser is considered to extend from the cellar to the ceiling of the first story. Above the ceiling the pipe must be extended of the same size as the riser, until the first branch line is taken off. (2) No house-pipe shall be less than % in. An extension to existing piping may be made of H-in pipe to supply not more than one outlet, provided said pipe is not over 6 ft long. (3) No gas-range shall be connected with a smaller pipe than % in. (4) In figuring out the size of pipe, always start at the extremities of the system, and work toward the meter. (5) In using the table, the lengths of pipe to be used in each case are the lengths measured from one branch or point of juncture to another, disregarding elbows or turns. Such lengths will be hereafter spoken of as sections. No change in size of pipe may be made except at branches or outlets, each section therefore being made of but one size of pipe. (6) If any outlet is larger tlian % in it must be counted as more than one, in accordance with the schedule below: Size of outlet, inches H % i iH iH 2 2H 3 4 Value in table .... 2 4 7 11 16 28 44 64 112 (7) If the exact number of outlets given cannot be found in the table, take the next larger number. (8) If, for the number of outlets given, the exact length of the section which feeds these outlets cannot be found in the table, the next larger length, corre- sponding to the outlets given, must be taken to determine the size of pipe re- quired. Thus, if there are eight outlets to be fed through 55 ft of pipe, the length next larger than 55 in the eight-outlet line in the table is 100, and as this is in the i34-in column, that size pipe would be required. (9) For any given number of outlets, do not use a smaller size pipe than the smallest size that contains a figure in the table for that number of outlets. Thus, to feed 15 outlets, no smaller size pipe than i in may be used, no matter how short the .section may be. (10) In any piping- plan, in any continuous run from an extremity to the meter, there may not be used a longer length of any size pipe than found in the table for that size, as 50 ft for % in, 70 ft for i in, etc. If any one section would exceed the limit length, it must be made of larger pipe. Thus, 6 outlets could * The Denver Gas and Electric Company. i t Sec, also, Lighting and Illumination of Buildings, pages 1437 to 1456. t With the exception of tyix)graphical changes made to conform to the rest of the base, these rules are quoted literally. Editor-in-chief. Gas-Piping 1435 Table Showing the Correct Sizes of House-Pipes for Different Lengths of Pipes and Number of Outlets Number of %-m Lengths of pipes in feet outlets ^i-in i/^i-in %-in I -in iH-in iH-in 2-in 2yz-m 3-in 4-in pipe pipe pipe J ipe pipe pipe ' pipe pipe pipe pipe I 20 30 50 70 100 150 200 300 400 600 2 27 50 70 100 150 200 300 400 600 3 12 50 70 100 150 200 300 400 600 4 50 70 100 150 200 300 400 600 5 33 70 100 150 200 300 400 600 6 24 70 100 ISO 200 300 400 600 7 18 70 100 150 200 300 400 600 8 13 50 100 150 200 300 400 eoo 9 44 100 150 200 300 400 600 10 35 100 ISO 200 300 400 600 II 30 50 150 200 300 400 600 12 25 . 75 ISO 200 300 400 600 13 21 60 ISO 200 300 400 600 14 18 53 130 200 300 400 600 15 16 45 IIS 200 300 400 600 i6 14 41 100 200 300 400 600 17 12 36 90 200 300 400 600 i8 32 80 200 300 400 60Q^^ 19 29 73 200 300 400 600 20 27 65 200 300 400 600 21 24 58 200 300 400 600 22 22 53 200 300 400 600 23 20 49 200 300 400 600 24 18 45 196 300 400 600 25 17 42 175 300 400 600 30 12 30 120 300 400 600 35 22 90 270 400 600 40 17 70 210 400 600 45 13 55 165 400 600 50 45 135 330 600 65 27 80 2CO 600 75 20 60 ISO 600 TOO 33 80 360 125 22 so 230 150 15 35 160 175 28 120 200 ' 21 90 250 ' 14 59 not be fed through 75 ft of i-in pipe, but i\i in would have to be used. When two or more successive sections work out to the same size of pipe and their total leagth or sum exceeds the longest length in the table for that size pipe, make the section nearest the meter of the next larger size. For example, if we have 5 out- lets to be supplied through 45 ft of pipe, and these 5 and 5 more, making 10 in all, through 30 ft of pipe, we should find by the table that 10 outlets through 30 ft would require i-in pipe, and that 5 outlets through 45 ft would also require I -in pipe, but as the sum of the two sections, 30 plus 45 equals 75 ft, is longer than the amount of i in that may be used in any continuous run, the 30-ft sec- tion, being the one nearer the nieter, m"'=it be made of iH-in pipe. The applica* 1436 Hydraulics, Plumbing and Drainage, and Gas-Piping Part 3 tion of the limit in length of any one size in a continuous run may also be shown as follows: Eight outlets will allow of 13 ft of %An pipe in the section between the eighth and ninth outlet (counting from the extremity of the system toward the meter), provided that this 13 ft added to the total length of %-in pipe that may have been used between the extremity of the run and the eighth outlet does not exceed 50 ft, which, according to the table, is the greatest length of % in allowable in any one branch of the system. Therefore, up to the eighth outlet, 37 ft of H-in pipe could have been used, and yet allow 13 ft of % in to be used in the section between the eighth and ninth outlet. If more than 37 ft had been used, then the entire 13 ft between the eighth and ninth outlets would have to be of i-in pipe. Fig. 18. Diagram of Gas-piping (11) Never supply gas from a smaller size of pipe to a larger one. If we have 25 outlets to be supplied through 200 ft of pipe, and these 25 and 5 more, making 30 in all, through 100 ft of pipe we should find by the table that 25 outlets through 200 ft would require 2j^-in pipe, and 30 outlets through 100 ft would require 2-in piping, but as under this condition a 2-in pipe would be supplying a 2j'^-in pipe, the loo-ft section must be made 2\i in. The sizes of pipes In Fig. 18 are in accordance with the foregoing rules and the table. Lighting and Illumination of Buildings 1437 LIGHTING AND ILLUMINATION OF BUILDINGS* By W. H. TIMBIE ASSOCIATE PROFESSOR OF ELECTRICAL ENGINEERING, MASSACSUSETtS INSfiTUTE OF TECHNOLOGY General Principles. Objects are illuminated for the sole purpose of making them visible to the eye. The eye, then, is the natural starting-point. When passing upon the merits of any scheme of ordinary illumination, that which should mark it as a success or failure should be the general effect of the scheme upon the eye. Success should be measured largely by the degree of clearness with which the objects are perceived by the eye, as to shape and color. If cer- tain parts of a room or street are too brilUantly lighted, objects in the dimmer portions are not perceived by the eye. If a certain side of one object is too highly illuminated, the general shape of the object is lost, as the eye does not readily perceive its more dimly lighted parts. This is because the eye auto- matically adjusts itself to the most brilliantly lighted area within its view, and, accordingly, is out of adjustment for perceiving the rest. We should get rid of the idea, therefore, that a light of intense brilliancy is the thing to be sought. It is, in general, highly undesirable. A room may appear brilliantly lighted and yet objects looked at may not be sufficiently well illuminated for reading or for working purposes. The lights appear brilliant to the eye, but because they throw their strongest rays in other directions than those in which they are needed for use, they do not give efficient illumination. Distinction between Light and Illumination. There is not only a great difference between light and illumination, but there is a great difference be- tween a brilliantly lighted room and a well-illuminated one. When anybody is asked whether a room is well illuminated or not, the chances are ten to one that he at once looks at the light itself. If the fight appears to him to be brilliant and dazzling, he will invariably say, "Why, of course, the room is well lighted." He should first look away from the light at the objects around the room or under- neath the light. If these can be seen clearly and easily, then the room is well ILLUMINATED. Afterwards he should look at the lights themselves, and if they ap- pear soft and pleasing to his eyesight the room is well lighted. A room in which the lights appear soft to the eye and yet in which the eye can distinguish objects clearly is both well Hghted and well illuminated. A room in which the objects appear clear to the eye while the lights remain dazzling is well illuminated but badly lighted. A room in which the fights appear soft to the eye and the objects not clearly iUuminated, is well lighted, but badly illuminated. A room in which the lights appear dazzling to the eye and the surrounding objects or those under- neath appear not clear to the eyesight is both badly lighted and badly illuminated. An axiom in good artificial illumination is to keep the illumination of objects as strong as is necessary, but the intensity or brilliancy of the lights as low as pos- sible. By doing the first we enable the eye to see better; by doing the second we enable the eye to feel better and suffer less from temporary discomfort or per- manent' injury. It is not generally understood that a light which is dazzling and brilliant to the eyesight may not be giving as much illumination as another source of light which appears soft, or even dim, by comparison. Thus an open gas-fight is more dazzling than an enclosed fight, but is less efficient in illumi- • See. also. Illuminatine-Gas and Gas-Piping, pages 1431 to 1436. 1438 Lighting and Illuminaition of Buildings Part 3 nating a room. The problem, then, resolves itself into two parts. The first step should be to secure a kind of lamp which will cause objects to appear in their accustomed colors; that is, the colors in which they appear by sunlight. The second is to so distribute the lamps that the several illuminated surfaces receive their share of the light, and yet no bright light is thrown directly into the eyes. Nature of Light. All space is supposed to be filled with a medium infinitely lighter than air, called ether. The sensation of light is experienced when certain wave-motions in this ether are transmitted to the eye. These wave-motions are called LIGHT- WAVES. Light-waves differ from one another in length and violence. The DIFFERENCE IN LENGTH causes a difference in color. Thus short waves may be blue or violet, while longer waves may be red or orange. If we have a source of light which sends out long ether-waves, we may expect a predominance of red and orange light in it. The sunlight contains waves of practically all lengths and thus is composed of all colors. The difference in violence of the waves gives rise to a difference in intensity of the light. When these light-waves strike any object, they are partly reflected and partly absorbed. Substances differ widely as to the percentage of light they absorb and the percentage they reflect. If two objects are illuminated by the same amount of light, the one which absorbs the less light and reflects the more will appear the brighter. Some objects reflect light-waves of a certain length only, and absorb all the rest. It is this prop- erty that gives color to objects. Suppose, for instance, that a piece of cloth were receiving light from the sun, all of which it absorbed except the waves of proper length to cause a sensation of green to the eye. The green waves only would then come from the cloth to the eye, all the rest being absorbed, and the cloth would appear green. If it absorbed waves of all lengths, it would appear black, because no light would be reflected from it to the eye. If now the piece of cloth, which absorbs all wave-lengths except that of green, were exposed to a source of light which was emitting all colors except green, there being no green waves to be reflected from it, the cloth in this light would appear black. Sup- pose a piece of cloth absorbed all colors but two, say violet and red. When light having all wave-lengths fell upon it, it would absorb all the waves except violet and red. These two, the cloth would reflect as a mixture and would appear purple. If, however, the source of light contained no violet waves, it could only reflect the red waves and appear red. This light, then, would not cause the cloth to show its normal color. So in choosing an artificial source of light, it is necessary to select one which will send out all wave-lengths, if we wish to have the different objects appear in their normal colors. Table I. Colors of Light-Sources* Sun (at zenith) White (all colors) Electric arc Violet-white Candle Orange-yellow Kerosene Pale orange-yellow Gas-flame Pale orange-yellow Wekbich r^aO S Nearly white to amber, depending upon WelsDacn ^gas) j romposition of mantle Acetylene-flame Almost white Carbon, incandescent Reddish white Tungsten or Mazda Yellowish white Mercury-arc. Blue-green Moore tube (carbon dioxide) White • Compiled by R. F. Pierce, Welsbach Company. Intensity of Illumination 14S9 Experiment has shown that no artificial Hght except the CO2 Moore tube is even a remote approximation to dayhght. The Welsbach white mantle gives a much whiter light than the tungsten-lamp, although neither can be said to approximate daylight. Light-Intensity or Brilliancy. Candle-Power. The brilliancy of a source of Hght is stated as its candle-power; that is, the number of standard candles to which it is equivalent. Thus an ordinary open gas-flame, consuming 5 cu ft of gas per hour, is equivalent in brilliancy to about 18 candles, and is said to have an intensity of 18 candle-power. Welsbach lamps, consuming 3 cu ft per hour, average about 75 candle-power; that is, they are equivalent to 75 candles. Since no two sources of light have the same amount of luminous surface, it is customary to rate a lamp by the number of candle-power per square inch of its apparent (or projected) surface. Thus an ordinary candle-flame has about H sq in of area, and its intensity would be rated as 3 candle-power per square inch; that is, the candle-power it would have if its area consisted of exactly i sq in. This is often called the intrinsic brilliancy of a light-source.* Table II. Accepted Values of Intrinsic Brilliancy for Various Light- Sovirces now in Use * Light-Source Candle-power per sq in Moore tube Frosted electric incandescent-lamp Candle Gas-flame Oil-lamp Cooper-Hewitt lamp Welsbach gas-mantle Acetylene-burner Enclosed alternating-current arc-lamp .... Enclosed direct-current arc-lamp Incandescent lamps: Carbon, 3.5 watts per candle Carbon, 3.1 watts per candle Gem, 2.5 watts per candle Tantalum, 2.0 watts per candle Mazda or tungsten 1.25 watts per candle Mazda or tungsten, i.o watt per candle . Nernst, 1.5 watts per candle Sun, on horizon Flaming arc-lamp Mazda, nitrogen-filled Open arc-lamp Open arc-crater Sun, 30° above horizon Sun, at zenith 0.3-1. 75 ^5 3-4 3-8 3-8 17 20-50 75-100 75-200 ioa-500 375 480 625 750 875 1 000 2 200 2 000 5000 7 700 3 OOa-50 000 200 000 500 000 600 000 * E. B. Rowe, Holophane Works. Intensity of Illumination. Foot-Candle. The extent to which a surface is illuminated is measured in foot-candles. A surface has i foot-candle illumi- * The total amount of light given out by a light-source is measured in lumens. the definition and use of this term see any standard book on illumination. For 1440 Lighting and Illumination of Buildings Part 3 nation when it is placed, at right-angles to the light-rays, i ft away from a light of I candle-power intensity. Thus a paper placed i ft away from a i6-candle- power incandescent lamp would be illuminated to 16 foot-candles. Law of Inverse Squares. The farther away from the light the above paper is held the less the illumination. But if it were held 2 ft away, that is, twice as far as stated above, it would not have one-half the illumination. The illumi- nation which an object receives varies inversely as the square of the distance from the source. Thus, in this example the paper would receive one-fourth as much illumination, or 4 foot-candles. If it were held 3 ft away, it would be il- luminated by one-ninth of 16, or 1.6 foot-candles. Rule. To find the intensity of illumination on any surface, at right-angles to light-rays, divide the candle-power of the lamp by the square of the distance in FEET. The result will be foot-candle illumination. This is called the law OF INVERSE squares. Accordingly, an unshaded 32-candle-power lamp will illuminate a surface facing it squarely and i ft away from it with an intensity of 32 foot-candles, but a surface 4 ft away, with only 32/4^, or 2 foot-candles. Candle-Power and Foot-Candle. Careful distinction should be made between candle-power and foot-candle. Candle-power is the measure of the intensity of a source of light. The foot-candle is the measure of the intensity of illumination of some surface upon which the light falls. Example i. What is the illumination on a surface 5 ft from a 32-candle- power lamp? 32 Solution. = 1.28 ft-candles. 5x5 Example 2. The illumination required on a printed page for easy reading is about 2 foot-candles, (i) How high above a reading-table should a i6-candlc- power lamp be hung? (2) A 32-candle-power lamp? Solution. — = 2 x^=S x=Vs= 2.83(1 (i) —„ = 2x^=i6x = 4h (2) x^ The Primary Function of a Lighting-Installation is to supply sufficient illumination as required by the character of the work to which the lighted space is devoted. The following table can be used in computing the amount of elec- tric power or of gas necessary to satisfactorily illuminate the various rooms in- cluded. Since the lower efficiencies of the indirect and semiindirect systems are largely compensated by the lower intensities required as compared to direct lighting, the same watts per square foot may be allowed in either case, provided the con- ditions are fairly favorable to the use of the indirect and semiindirect systems, namely, light-cream or yellow ceilings. The following table is based upon rooms of average proportions with light-cream, or yellow ceilings and medium walls. High, narrow rooms may require about 10% more, and low, wide rooms about 10% less, energy. Similar allowances may be made for dark or light walls, respectively. Three Systems of General Illumination. To secure the proper illumina- tion, as indicated in Table III, there are three general systems. Power Required for Illumination Table III. Amount of Gas or of Electric Power Required to Illumi- nate Rooms Used for Various Purposes Class of service Armory or drill-hall Auditorium Barber-shop Church (see Auditorium) Draft in g-rooin Factory (general illumination) Hospital (corridor) Hospital (operating-room) Hotel (lobby) Hotel (ball-room) Hotel (dining-room) Hotel (restaurant) Hotel (kitchen) Hotel (writing-room, general illumination only) Hotel (billiard-room, general illumination only) Hotel (buffet) Library (reading-room) Library (stacks) Oflfice (banking and accounting) Office (general) Oflfice (private) Ofifice (stenographic) Residence (bedroom) Residence (dining-room) Residence (hall) Residence (living-room) Residence (music-room) Residence (kitchen) School (assembly or class-room) School (class-room, business colleges) Stores (piano, furniture, haberdashery, dry-goods, automobile, clothing, cigar) Stores (book, shoe, hardware) Warehouses * Cu ft of gas per sq ft per hour 0.02 -0.02S 0.04 -o.os 0.06 -0.07 O.IO -0.II2 O.OI -0.02 0.016-0.02 0.14 -0.15 0.06 -0.065 0.05 -0.052 0.04 -0.045 0.06 -0.07 o.os -0.052 0.052-0.06 0.06 -0.065 0.065-0.072 0.055-0.06 0.012-0.024 o 06 -0.065 o . 052-0 . 06 0.05 -0.52 0.06 -0.07 0.012 0.036-0.04 0.008 0.036-0.04 0.02 -0.025 0.05 -0.052 0.04 -0.045 o . 055-0 . 06 0.06 -0.07 0.055-0.06 0.012-0.036 *Watrts per sq ft 0.5-0.6 10-1.3 I -5-1 7 2.5-2.8 2.5-0.5 0.4-0.5 3.5-3.9 1. 5-1-6 I 2-1.3 l.O-I.I I. 5-1. 7 I. 2-1. 3 I 3-1. 5 I. 5-1. 6 I. 6-1. 8 1.4-1.5 0.3-0.6 1. 5-1. 6 I 3-1 5^ I 2-1.3 I-S-I.7 0.3 0.9-1.0 0.2 0.9-1.0 0.5-0.6 I. 2-1. 3 I.O-I.I 1-4-1.5 I 5-1-7 I 4-1 - 5 0.3-0.9 * These figures are based upon the use of Welsbach reflex lamps and Mazda electric lamps. For Welsbach klmrtic lamps and nitrogen-filled tungsten-lamps (type C Mazda) use about 0.6 the values in the first and second columns, respectively. Data on gas supplied by R. F. Pierce, Welsbach Company. (i) Direct Lighting. A system is designated as dirfxt when more than one- half the light reaches the area to be illuminated by coming directly from the light-source, without being reflected from the ceiling or walls. This includes all systems using lamps with clear, frosted, translucent, or opalescent globes, or reflectors, in which the light is reflected downward. It is the most efficient sys- tem, was the first to be used, and is still the most common. The color of the walls or ceiling has less efl"ect in this system than in the others. (2) Indirect Lighting. A system is designated indirect when all the light is thrown first on the ceiling and walls, and reflected from these to the surface to be illuminated. Any system which conceals the source of light by opaque reflec- tors is thus INDIRECT. Light finish must always be used on the walls and ceiling 1442 Lighting and Illumination of Buildings Part 3 with this system. Even then, the efficiency is usually lower than that of a direct system, but the total absence of glare and shadows and the even distribution of light make this a popular scheme in restaurants, show-rooms, etc., where deco- rative lighting is desired. (3) Semiindirect Lighting. This system throws most of the light to the walls and ceiling, but allows a small percentage to be diffused through the reflector straight to the area to be illuminated.' This system is rapidly coming into favor because apparently we have become accustomed to looking for the source of light and miss it when it is concealed as in the indirect system. The totally indirect fixtures often show up rather unpleasantly as a dark spot against a light background.* This is avoided in the semiindirect system. The slightly higher efficiency of this system is another advantage over the indirect. Any given room may usually be lighted by any one of the three systems al- though it is generally true that conditions are such as to make one of the three more desirable than either of the other two. The following paragraphs show in detail how each system may be worked out for a given room. General Considerations f in Direct Lighting Outlets and Lamps. Outlets should hd located in the centers of as nearly as possible square and equal areas into which the ceiling, for the purpose of calcu- lation, may be subdivided. The greater the number of outlets the more uniform the illumination and the greater the freedom from annoying shadows. Unless great care is used in planning the directions in which the light is received by illu- minated surfaces, a disagreeable glare from glazed paper is likely to be present. The greater the height of lamps above the illuminated area, the more uniform the illumination. Figures suggestive of good practice in selection of mount- ing-heights are given in Table IV, page i444- General Considerations in Indirect and Semiindirect Lighting Outlets and Lamps. The location of outlets should in general conform to the requirements for direct lighting, that is, at the centers of approximately square and equal areas. Since glare from glazed papers is minimized when most of the light is received from ceiling-reflection, larger and fewer units are permis- sible than in the case of direct lighting. The nearer to the ceiling the lamps are placed, the less uniform the illumination and, within reasonable limits, the higher the illuminating efficiency of the installation. Generally speaking, lamps should not be placed less than 2 ft from the ceiling. Aside from this, the position of a fixture should be determined by artistic considerations and reflectors selected which will direct most of the light upon the ceiling without concentrating it enough to illuminate the ceiling unevenly. A. The Interior Colorings and Finishes. t (i) Ceilings especially should be of nearly white, cream, or light-buff colors to efficiently diffuse the light down- ward. Dark greens, reds, or blues are not advisable since the reduction in illumi- nation caused by a green color, over a cream tint, may easily be from 30% to 60%. On the other hand, this system shows very plainly all dirt and discolor- ations on the ceiling, and no colors should be used that are so light as to easily show dirt, where there may not be careful cleaning. * This unpleasant effect can sometimes be avoided by illuminating the underside of the fixture. t By R. F. Pierce, Welsbach Company and G. S. Fobes, Macbeth-Evans Compaoy. i By G. S. Fobes, Macbeth-Evans Company. General Considerations in Indirect and Semiindireet Lighting 1443 (2) Finishes preferably should be matt, or satin, rather than glazed or var- nished. From the matt ceiling-surface the maximum light will always be down- ward, but the varnished ceiling will reflect specularly, directing light sidewise or showing lamp-images and glare. (3) Tints and details of decoration should be considered together with the lighting-system, so that daylight-colors and reliefs will not be reversed or dis- torted by colored light from artificial illuminants and shadows. B. The Positions of Outlets and of Fixtures, (i) Semiindireet units should, if possible, be placed above the places where maximum light is wanted. (2) Fixtures should not be so close to side walls as to cause light-spots running down across picture-moldings, etc. (3) Outlets should be placed logically with reference to the ceiling-panels, so that the more brightly illuminated ceiling-areas will be the ones that on account of their tints, shapes, or decorations, will naturally bear emphasis. If the panels are deep (deep beams), and one outlet is in each panel, it will ordinarily be located at the center. If several panels intervene between units, the fixtures should be on the beams rather than in the panels, to prevent dark ceiling-areas in the shadows of the beams. (4) Spacing should be such as to have the illuminated ceiling-areas overlap if tiie ceiling-surfape is uniform. C. The Proper Lamp and Bowl-Sizes, (i) Ordinarily the symmetrical appearance of fixtures with respect to the other interior furnishings will largely determine their sizes, although the bowls should never be so small as not to com- pletely conceal and nearly surround the lamp-bulb. (2) The smaller the bowl and the brighter the lamp, the less effective the semi- indirect system becomes, and the more the effect approaches direct lighting. D. Shapes and Styles of Bowls, (i) Bowls used close together or hung far from the ceiling should be of the focusing (upward) distribution, while broadly distributing bowls are better when used singly, or when fairly wide apart and close to the ceiling. (2) Bowls too flat in shape may waste considerable light sidewise to the upper walls and therefore be inefficient. (3) Wide open-top bowls should not be used in halls, etc., where the bare lamps are visible to the observer from above, nor on or below the level of a bal- cony or mezzanine. E. Care of Fixtures, (i) The average saving in light (expressed in terms of cost of current) that results from washing once and dusting once monthly, will be from four to ten times the cost of such cleaning. Bowls often collect films of dust which are not visible and which materially reduce the efficiency both of reflection and transmission. (2) A bowl with a dust-cap, button-ornament, or small area of thick glass at the bottom, will allow dead insects or dirt to collect at that point without marring the appearance of the unit. (3) Dilute ammonia is an excellent glass-cleanser. • (4) Fixtures should be arranged to be lowered, for cleaning, from above if on a very high ceiling in a church or similar structure. (5) It should be possible to easily raise the lamp or lamps from within the bowl, to allow of dusting or wiping out. Figures suggestive of good practice in the selection of mounting-heights and types of light-distribution are given in Table VI. 1444 Lighting and Illumination of Buildings Table IV. Direct System LAMP-SIZE, MOUNTING-HEIGHT AND SPACING* I>art 3 Commercial Watts per square foot = IV Ideal spacing Mount- size of lamps = di stance Minimum Maximum ing- in watts = W and cubic /i spacing- spacing- height and cubic feet feet per V distance distance per hour square foot V w ft Watts cu ft Watts cu ft ft in ft in ft in 7 to 10 40 1.6 0.5 0.02 9 8 10 1.5 0.06 5 2 4 6 6 2.5 "o.io 4 3 9 4 3 8 to 13 6o 3.0 0.5 0.02 II 9 6 12 9 1.5 0.06 6 4 5 6 7 3 2.5 o.io 4 II 4 6 5 6 12 to l6 loo 4.0 0.5 0.02 14 5 12 6 16 1.5 0.06 8 2 7 9 6 2.5 O.IO 6 4 5 8 7 14 to 20 150 6.0 0.5 0.02 17 4 15 20 1.5 0.06 10 9 II 2.5 O.IO 7 9 7 8 6 17 to 27 250 10. 0.5 0.02 22 5 20 25 1.5 0.06 12 II II 9 14 3 2.5 O.IO 10 9 II 25 to 35 400 16 . 0.5 0.02 28 2 25 31 6 I. 5 0.06 16 4 15 17 9 2.5 O.IO 12 7 II 6 13 6 30 to 40 500 20.0 0.5 0.02 31 7 28 35 6 1.5 0.06 18 6 16 6 20 9 2.5 O.IO 14 2 12 6 15 * To determine the size of equivalent Welsbach lamps allow i cu ft per hour for each 25 watts. Adapted from the Electric Journal, by A. J. Airston. The Designing of General Illumination by Each System Using Tungsten or Welsbach Lamps (i) From Table III should be determined the watts per square foot desirable for the given class of work, and the total number of watts necessary should then be computed. (2) From Table IV should be obtained the size of unit desirable for a given height of room and the number and spacing of fixtures then computed. (3) The ceiling should be laid off in squares the sides of which are as nearly as possible equal to the value of the ideal spacing. One fixture should be located at the center of each square. (4) Each lamp should be checked up on the plan to see that it is useful and clear of obstacles, and the layout incorporated into the building plans using the standard methods and symbols for electricity or gas as the case may be. Standard Symbols for Gas-Piping Plans 1445 Table V. Standard Symbols for Gas-Piping Plans* W 4 Ceiling-outlet; gas only. Numeral indicates the number of single-mantle gas-lamps. ® Single-lamp outlet (ceiling-units, pendants, etc.); gas only. Ceiling-outlet; combination. f indicates 4 electric lamps and 2 single-mantle gas-lamps. Bracket-outlet; gas only. Numeral indicates the number of gas-lamps. |DJ< J_ Bracket-outlet; combination. f indicates 4 electric lamps ^ and 2 gas-lamps. m^ 2 Baseboard-outlet; gas only. Numeral indicates number of gas-lamps. )il( Floor-outlet; gas only. Q Special outlet (for portable lamp, heater, etc.) ; gas only. 2 Outlet for outdoor-standard or pedestal; gas only. | indi- jSS "s" cates 2 gas-lamps, with 5 mantles per lamp. Outlet for outdoor standard or pedestal; combination. Ys ^ ^ indicates 6 electric lamps, and 2 gas-lamps, with 5 mantles ^ per lamp. Arc-lamp outlet; gas only. Numeral indicates the number W ^ of mantles. p-j-. 2 Pump or pneumatic lighting-system. Numeral indicates the number of lamps to be operated from one pump. Push-button for magnet-valve. The numeral indicates the number of lamps to be operated from one push-button switch. Meter-outlet. Main or supply-pipe concealed under floor. Main or supply-pipe concealed under floor above. Main or supply-pipe exposed. Branch pipe concealed under floor. Branch pipe concealed under floor above. Branch pipe exposed. —0^-0 ' Street gas-main. l|l|l| Battery-outlet. Riser. ' Illuminating Engineering Laboratories, Welsbach Company. 1446 Lighting and Illumination of Buildings Part 3 Distance from Floor to Center of Wall-Outlets * Living-room . Chambers Offices Corridors . . . . Push-button switches or pneumatic pumps • Illuminating Engineering Laboratories, Welsbach Company. Examples of Design of Lighting-System for accounting-office, 63 by 25 ft with 13-ft ceiling (Fig. 1). Walls and ceiling-light in color. ^ ^ <>■ A A A <^ A A A _ J ~ -<>- A A A A A A A A A { <>• ^ ^>- A A •<;^ <;^ A A A i ^ ^ A A A A A A A A ^ Watts per sq ft Total watts Unit, size of Number of .units Spacing (average) desired = 6 ft 4 in (Table IV) Number of rows = 25/6H = four Number of outlets per row == 40/4 = ten Spacing between rows = 25/4 = 6H ft Spacing in rows = 63/10 = 6H ft Spacing-average = 6 ft 4 in. . Fig. 1. Plan of Ceiling-lights Direct System = 1. 5 (Table III) 1^ = 1.5 X 63 X 25 = 2 400 (nearly) = 60 watt electric (Table IV) = 3 cu ft per hour, ordinary inclosed gas, or ) u^ 1.1 = 2 cu ft per hour, Welsbach kinetic ) ^ ^ 2 400/60 == forty -63 ft— K Fig. lA. Modification of Plan Shown in Fig. 1 Fig. 1a is a modification of the plan shown in Fig. 1, and is a great improve nent. It will not produce such even illumination but will result in a much more Distrioution of Light by Reflectors 1447 artistic effect, especially if fixtures are chosen which harmonize with the fur- nishings of the room. The lamps are placed in groups of four on ten fixtures and these are equally spaced throughout the room. Here again it is always possible to use lamps of higher wattage at any point where the illu- mination is not sufficient. The importance of a proper choice of reflector is shown from a study of Figs. 2 to 5.* It will be noted in Fig. 2 how a bare tungsten-lamp throws the greater part of its light to the walls. The distribution of any light can be controlled to a remarkable extent by the use Distribution of Candle-power about a Bare Tungsten Lamp Fig. 3. Holophane Reflector. Extensive Fig. 4. Holophane Reflector. Intensive Distribution of Light Distribution of Light of the proper reflector. Figs. 3 to 5 shdw hoW the' several types 61 Hoiophand teflectors distribute the light. * Furnished by E. B. Rdwe', df t^e Hotophairie Works; 1448 Lighting and Illumination of Buildings Parts Fig. 5. Holophane Reflector. Focusing Effect on Light Fig. 6. Example of Type of Fixtui Used in Semiindirect System. Mac beth-Evans Company Indirect or Semiindirect Systems, for Electricity Watts per sq ft Total watts Average spacing Select 25/2 Number of units in row Spacing in row Type of reflector Distance from reflector to ceiling Number of units Watts per unit Lamps per unit = i.S (Table III) = 2 400, nearly - 14 to 24 ft (Table VI)* = 14 ft for lamps in two rows = 63/12.5 = five == 63/5 = 12 ft 7 in, about = Concentrating (Table VI) = 30 in (Table VI) = two rows of five each = ten = 2 400/10 =« 240 = one, 250 watts four, 60 watts six, 40 watts Calculations for this Example for Gas-Lighting Welsbach kinetic burner used. Cu ft per hour per sq ft = 0.06 X 0.6 = 0.036 (Table III) Total hourly consumption = 63 X 25 X 0.036 = 57 cu ft per hour. Average spacing (see above) = 12^6 ft Number of units = ten Consumption per unit = 57/10 = 6 Reflector and mounting-height as in preceding problem Lamps per unit = one, 6 cu ft Lamps per unit = two, 3 cu ft, etc. * See How to Use Table VI, immediately following the Table. Ceiling-Outlets and Reflectors 1449 Table VI. For Determining Number of Ceiling-Outlets, Type of Reflector and the Distance from Top of Reflector to Ceiling for Indirect and Semiindirect Lighting * a 1 1 20 19 i8 17 i6 15 14 13 12 II 10 9'/2 9 SH 8 Distributing 48 48 48 5'-o 6'-6 u ^O K Concentrating Distributing Concentrating Distributing Concentrating Distributing Concentrating 48 5'-o 6'-6 f-o 48 48 5'-o 6'-o 48 6'-o 6'-6 6'-6 42 48 48 6'-o 42 5'-o 6'-o 6'-o 42 4'-6 C'-o 36 4'-6 6'-o 6'-o 42 42 4'-6 5'-6 Distributing Concentrating Distributing Concentrating Distributing Concentrating Distributing Concentrating Distributing Concentrating Distributing Concentrating Distributing Concentrating Distributing Concentrating Distributing Concentrating Distributing Concentrating Distributing Concentrating Distributing Concentrating Distributing Concentrating 36 42 5'-6 5'-^ '30 4'-6 30 36 4'-6 S'-o 30 5'-o 30 48 5'-o 30 30 30 36 48 24 30 42 30 48 24 24 36 48 24 36 24 30 42 48 24 42 24 36 42 i8 i8 30 30 18 42 18 24 36 18 30 36 18 24 30 18 24 12 18 1 ••■]■■■ ••"T"" 1 lO 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 One side of the limiting square in feet that can be uniformly illumi- nated from one center outlet Table VI gives the distance in inches (except as noted) from the top of the rellector to the ceiling to obtain the desired distribution of light from one ceiling-outlet. Where values are not given to the left, it is advisable to submit data to illuminating engineers and for greater ceiling-heights than 20 ft. * H. B. Wheeler, X-Ray Eye-Comfort Company. 1450 Lighting and Illumination of Buildings Part 3 An idea of the appearance of some of the typical modern fixtures using gas or electricity in these systems of lighting may be obtained from Figs. 6, 7 and 8. m Fig. 7. Type of Fixture in Indirect Illumination. National X-Ray Reflector Company Fig. 8. Fixture Used for Gas by Either Indirect or Semiindirect System How to Use Table VI. In the first column of Table VI is located the height of ceiling, in this case, 13 ft. The last square to the right of this figure, which has a number in it, is noted. In this case the last square to the right of 13 ft^ which has a number in it, contains the number 48. By following this column containing the number 48 down to the figures printed in heavy type at the bottom of the table, the heavy-faced number in this case is found to be 24. This 24 is the length of the side of the largest square which a single fixture can properly illu- minate when the ceiling is 13 ft high. The 48 which is opposite the 13 is merely the number of inches the fixture must be hung from the ceiling. Thus the largest squares into which we can possibly divide the ceiling have 24-ft sides. But a room 25 ft wide cannot be divided into 24-ft squares. We are compelled, therefore, to divide it into squares of a smaller size, since the fixtures will not illuminate any larger square. The greatest length into which we can divide 25 ft is 121.^ ft. We may, then, decide to use fixtures which will illuminate 14-ft squares. Locate the number 14 in heavy type at bottom of table, and trace up the column in which it is found until the square is reached which is opposite the ceiling-height of 13 ft. Plere the number 30 is found. This means we must hang the fixture so that the top of it is 30 in from the ceiling in order to get the desired results. Looking along the squares to the right of the one in which we find the 30, we find the word concentrating, which signifies the. tvne of reflector advised for this installation. Illumination by Gas 14Si School-Room Lighting.* The following illumination-constants have been worked out by experiments and experience covering a wide range of conditions. In each of the following cases light tinted walls and ceilings are taken as a standard. Auditoriums and Lecture-Halls. Since no continuous reading is required here, 0.75 watt per sq ft, direct system, is all that is needed, if it is properly diffused to a pleasant softness. Class-Rooms and Laboratories. These must be lighted for the purpose of writ- ing notes and taking accurate readings of instruments. Thus iH watts per sq ft,, direct system, are required. Wood- Working Shops. The surfaces here are generally high and offer good reflecting properties, so that iH watts per sq ft, direct system, are sufficient. Machine-Shops. Because the belts, machines and dingy floors offer great absorbing surfaces at least 2 watts per sq ft, direct system, are necessary. Foundries. The dark molding-sand and the dust and smoke in the air make 3 watts per sq ft, direct system, necessary. Drafting-Rooms. The semiindirect system with 2H watts per sq ft (about the equivalent of 1^4 watts per sq ft, direct system) has proved highly satis- factory. Illumination by Gas.f Recent progress in incandescent gas-lighting has resulted in the development of appliances in which practically all of the short- comings of previous types are overcome, and except for inaccessible locations, or where lamps are very infrequently lighted, there is little to choose between the- two illuminants, gas and electricity, upon the score of convenience or of artistic possibiHties, while the greater economy of gas-lighting (often in the ratio of about 2y2 to i) coupled with the freedom from interruption which characterizes gas- service makes it desirable to pipe all buildings, particularly residences, for gas throughout, preferably installing combination-fixtures and providing wall-out- lets and baseboard-outlets for the connection of the various gas-operated con- veniences which are being developed in rapidly increasing numbers. Welsbach Kinetic-Burner Lamps With Nearest Equivalent Sizes in Electric Incandescent Lamps Lamps Mazda watts Nitrogen-filled Mazda (Type C> watts T mantle 2 mantles 3 mantles 4 mantles 5 mantles 6 mantles 8 mantles 10 mantles 2.5 cu ft per hour. 5.0 cu ft per hour. 7.5 cu ft per hour, lo.o cu ft per hour. , 12.5 cu ft per hour., 15.0 cu ft per hour.. 20.0 cu ft per hour. , 25,0 cu ft per hour. , two, 40 ISO •250 six, 40 400 Soo Soo 750 Gas-Lamps are available in a variety of types and sizes. The most recent development is the kinetic burner of the Welsbach Company in which the efficiency is increased by from 50% to 100% over the previous types. With this burner no enclosing glassware or housings are required, and the lamp is said A. L. Williston. f R. F. Pierce, Welsbach Company. 1452 Lighting and Illumination of Buildings Part 3 to require no attention beyond the renewal of mantles every 2 cxx5 burnirtg- hours. There is practically no depreciation in candle-power during this interval. Ignition is accomplished either by a pilot-flame burning about Ho cu ft per hour, or by electrical means, and several types of distant control are available. The following table gives the sizes in which these lamps may be obtained and the nearest equivalent sizes in electric incandescent lamps. Selection of Illuminants (i) Factors favorable to the use of electricity: Units less than 60 candle-power required. Lamps in inaccessible positions. Lamps lighted at infrequent intervals. Lamps placed very close to ceiling (12 in or less). Poor gas service as regards: Pressure-regulation (more than 50% variation from minimum). Non-uniformity of gas-quality. Imperfect purification. Good electric service as regards: Voltage-regulation. Freedom from liability to derangement by accident. Non-rigid fixtures. (2) Factors favorable to the use of gas: Units of 60 candle-power or more. Accessible locations. Frequent use of lamps. Lamps placed 15 in or more from ceiling. Good gas service as regards: Pressure-regulation (not more than 50% variation from minimum). Uniformity of gas-quality (chemical composition). Proper purification. Poor electric service as regards: Voltage-regulation (more than 5% variation from maximum) most likely on alternating-current circuits. Liability to derangement by accident (overhead circuits). Rigid fixtures. Hygiene.* From the hygienic point of view there is little to choose between the two illuminants. The investigations of Dr. Rideal have shown that: (i) Gas- light positively improves the air for breathing purposes under the actual condi- tions of use. The causes of this improvement are the acceleration of ventila- tion, the destruction of disease-germs and the addition of necessary' moisture. Gas-burners give rise to stronger air-currents and invariably produce a more active ventilation and diffusion of air than electric lights; hence, along with the products of the gas-burner, the exhalations of persons present are more rapidly removed; (2) The ascending currents of air from the gas-lights on reaching the ceilings rapidly part with their heat, which is conducted away by the rafters and joists; (3) The electric lamps produce more heat than is com- monly accredited to them, and this is the explanation of the unexpected result that the average temperature of the room is practically the same under either il- luminant, and that the electric light does not show the superiority in coolness usually claimed. When excessive temperatures are encountered in gas-lighted * See Relative Hygienic Values of Gas and Electric Lighting, by Samuel Rideal, Trans- actions Royal Sanitary Institute, March, 1908. Diffusion of Light through Windows 14^ rooms, it will be found due to the radiant heat from low-hung lamps of ex- cessive size. On "account of the economy of gas-lighting, it is a common prac" tice to provide from four to six times as much illumination as is required- Dr. Rideal's tests also emphasized, what is a matter of common experience, that under direct lighting, the lower brilliancy of the gas-mantle reduced the glare from glazed papers to such an extent as to be noticeable in the results: "The sensitiveness of the eye to light as measured in the perception-test dimin- ished very markedly after exposure to the electric light, while no corresponding effect is noticeable after the eye has been subjected to gaslight. All the results point strongly in the same direction, namely, that gaslight, as used in these experiments, is less fatiguing to the eye than electric light." Under senii- indirect or indirect lighting, of coursej no such disparity in effect is found. The Foregoing Rules Indicate the General Practice in planning the illu- mination of a room. It must be said, however, that this set of rules must not be followed too slavishly. In illumination no rules can take the place of judgment and intelligence. Each project must be considered more or less as a problem by . itself, for which previous experience and former installations should be made to furnish data and to suggest methods. It is well, therefore, when planning the illumination of a room, to visit as many similar rooms as possible, note the effect of the systems in use and obtain data as to their efficiency, cost, etc. The most successful scheme may then be used as the basis for planning the desired instal- lation. The Diffusion of Light through Windows * Tests on the Diffusion of Light by Glass. Abstracts from report of Charles L. Norton, on an elaborate series of tests made at the Massachusetts In- stitute of Technology :t The results of the tests on a score or more of different glasses may be stated briefly. We may increase the light in a room 30 ft or more deep to from three to fifteen times its present effect by using factory- ribbed GLASS instead of plane glass in the upper sashes. By using prisms we may, under certain conditions, increase the effective light to fifty times its present strength. The gain in effective light on substituting ribbed glass or prisms for plane glass is much greater when the sky-angle is small, as in the case of windows opening upon light-shafts or narrow alleys. The increase in the strength of the light directly opposite a window in which ribbed glass or prisms have been substituted for plane glass is at times such as to light a desk or table 50 ft from the window better than one 20 ft from the window had pre- viously been lighted. The Kinds of Glass Tested were as follows: (i) Ground glass of different degrees of fineness. (2) Rough plate or hammered glass. (3) Ribbed or corrugated glass, with five, and eleven and twenty-one ribs to the inch, the corrugations being sinusoidal in outline, as in A, Fig. 9, and the back of the plate smooth. (4) Glass known as maze, Florentine or figured, in which a raised pattern is worked upon one side, practically roughening the whole surface. (5) Wash-board glass, corrugated, with twenty-one ribs to the inch on one side and five ribs to the inch on the other side, the ribs being parallel. (6) Skylight-glass, which has five ribs to the inch on each side, the groove on one side being opposite the rib on the other, giving a sinuous section B, Fig. 9. ♦ See, also, the subjects Pressed Prism-Plate Glass and Prism Glass, Part III, pages IS77 to 1579. t From Report No. Ill, Insurance Engineering Experiment Station, September, 1903, 1454 Lighting and Illumination of Buildings Part 3 Fig. 9. Types of Ribbed or Prism-glass (7) Ripple-glass, with rippled surfaces on both sides; of very beautiful appear- ance and a clear white color. (8) Glass ribbed on one side and figured on the other. (9) Ribl)ed glass with a wire net pressed into it, to increase its resistance to fire. Of these several specimens, one or two may be dismissed with brief mention. Groiuid glass is of little value, except as a softening medium for bright sunlight. Its rapidly increasing opaqueness with moisture and dust makes it undesirable as a window-glass. The common rough plate has very little action as a difl^using-medium, giving no perceptible change in the effective light. Ripple-glass has great value as a diffusing- medium in small rooms with nearly open horizon. Of the ribbed glasses, the fine Factory-Ribbed, with twenty-one ribs to the inch, is distinctly the best, not in all probability because of the fine- ness, but because of the greater sharpness of the corrugations. The Ribbed wire-glass is about 20% less effective than the ordinary Factory- Ribbed glass. The addition of a second corrugation upon the back of the plate giving the Skylight and Wash-Board glass is of no apparent value. The raised pattern imprinted upon one surface of the glass, as in the case of the Maze glass, gives the widest diffusion, especially in bright sunlight. A raised figure, when worked upon the back of the Ribbed glass, renders it less offensive to the eye in bright sunlight, but less effective in deep rooms. The only glasses of this group which it is worth while, then, to discuss further are the F'actory- Ribbed and the Maze glass. The second group comprises the following glasses: (i) The Luxfer prisms. (2) The Solar prisms. (3) The Daylight-prisms. (4) The glass of prismatic section made by the Mississippi Glass Company. (5) Three-way prisms. (6) Maltby prisms. The Luxfer prism consists of a plate smooth on one side and deeply notched on the other as in C, Fig. 9, the teeth or prisms being of very flat, smooth faces of brilliant appearance. The glass is clear white, and the prisms used in canopies and in the major part of the vertical glazing are made in tiles or plates about 4 in square. Tiles are built up in large sheets in frames of copper or brass, so made as to give to the sheets of tiles a strength and durability far in excess of a single sheet of the same size. The Luxfer prisms are made for factory- use in large sheets, as well as in the small tiles. The Solar prisms are made in small tiles, which are held together in a metal frame to make large sheets. The main difference between the Solar and Luxfer prisms is that the under face of the former prism is curved instead of plane, as in D, Fig. 9. The Daylight-prisms tested were made in large sheets and of approximately the same cross-section and general app>earance as the Luxfer prisms for factory-use. No tiles of Daylight- prisms were tested, as none came to hand in time for the test. The Mississippi prism glass is much like the other prisms is cross-section, but the ridges or Diffusion of Light through Windows 1455 Refraction of Light in Prism-glass Ribbed and prisms do not run across the plate in a straight line, but in a wavy or sinuous line. No advantage arising from this over the straight-edge prism was detected. Conclusions, (i) The conditions in a room less than 15 ft deep are such that, except with a skyhght of less than 45°, it is not advisable to alter the general course of the light by using a prismatic or ribbed glass. A nearly hemispherical diffusion, such as is given by the Maze or Ripple-glass, is ordi- narily preferable. (2) When a room is from 20 to 60 ft deep, or even more, and has a skylight of 60° or less, the ribbed and prismatic glass results in a very great gain in effective light. The gain in brilHancy is such as to make a basement with prism-canopies as light as a second story with plane glass. Rooms with windows opening upon light-shafts and narrow alleys with very limited openings to the sky, where the available hght is now small, may have the light 20 ft back from the window increased ten or twenty times by using prisms; and, by using canopies of prisms, it is some- times possible to strengthen the light fifty to one hundred times. With sky- angles of 30°, or less, and in deep rooms, the relative efficiency of the prism tile increases greatly. The refraction of the incident ray in a case of the ribbed glass and prism is shown in Fig. 10. Ribbed and maze glass are of very great value in softening the light, especially in the case of such windows as are exposed to the direct sun, aside from their effectiveness in strength- ening the light at distant points. With the Maze glass, the artist may have, in all weather and in all directions, what is in effect a much-desired north light. The photog- rapher may have in this way as well diffused a light as he now has with cloth screens or shades, and with a much greater intensity. To be efficient in rooms 20 ft deep or more, ribbed glass should be set with its ribs hori- zontal, and where the sunlight falls upon it, it should be provided with thin white shades. All inferences drawn from the test are made upon the assumption that the windows are to be glazed with diffusing glass only in the upper half, which is the common practice. If the lower sash is to be glazed a further increase of about 25% may be Fig. 11. Basement and First Story Lighted from Court with diffusing glass as well, expected. Considering both expense and efficiency, the following general suggestions are given: Use Maze or Ripple-glass in small rooms or offices not more than 15 or 20 ft deep; use Factory-Ribbed glass in rooms from 30 to 50 ft deep, with sky-angles of 60° or more; use prisms or Factory-Ribbed glass, in sheets, in all vertical win- 1456 Lighting and Illumination of Buildings Part c dows in rooms more than from 50 to 60 ft deep, with sky-angle of less than 45** With a sky-angle of less than 30° use prisms in canopies. Fig. 11 shows ar effective method of lighting the basement and first story where the light mus1 come from a court. Reference Books on Illumination Practical Illumination, 1907. Cravath and Lansingh. Art of Illumination, 1902. Louis Bell. Electrical Illuminating Engineering, 1908. Barrows. Light, Visible and Invisible. Sylvanus Thompson. American Practice of Gas-Lighting. \V. P. Gerhard. Color Values. C. R. Clifford. Radiation, Light and Illumination, 1909. C. P. Steinmetz. Illumination and Photometry, 19 10. Wickenden. Electric-Lamps, 1908. Maurice Solomon. Illumination, its Distribution and Measurement, 19 10. Alex. Pelhan Trotter Photometric Measurements, 1904. W. M. Stine. Proceedings and Transactions of Illuminating Engineering Society. Proceedings and Transactions of American Institute of Electrical Engineers. Proceedings and Transactions of National Electric Light Association. Proceedings and Transactions of American Gas Institute. The Illuminating Engineer (New York). The Illuminating Engineer (London) with which is combined the Transactioni of the London Illuminating Engineering Society. Foster's Engineers' Pocket-Book, 1908. Standard Handbook for Electrical Engineers, 1908. .Engineering Section, Holophane No. 2 Data Book. Bulletins of the Engineering Department, National Electric Lamp Association Bulletins of the General Electric Company. Tungsten Illumination, 19 10. Westinghouse Company. The Electrical SoHcitor's Handbook, 19 10. National Electric Light Associa tion. Gas Solicitor's Handbook, 1910. Welsbach Company, Factory Lighting, C. E. Clewell. American Electricians' Handbook, Terrell Crofto Electric Work for Buildings 1457 ELECTRIC WORK FOR BUILDINGS By W. H. TIMBIE Associate professor of electrical engineering, Massachusetts institute of technology General Considerations and Definitions. Electrical energy is now in com- mon use, furnishing power, heat and light, operating bells and buzzers, and transmitting messages by telephone and telegraph. In order to accomplish these results, a current of electricity must flow around an electric circuit. The nature of electricity is not known, but the flow of it through an electric circuit is analogous to the flow of water through a system of pipes. Current. Amperes. The flow of water is measured in gallons per second. The flow of electricity is measured in amperes. An ampere-flow of electricity is analogous to a gallon-per-second flow of water.. The amperes thus indicate the quantity of electricity flowing through an electrical appliance in one second. About y2 ampere is flowing through an ordinary carbon-filament incandescent lamp when it is glowing at 1 6 candle-power. The same -I current of y2 ampere causes a ^ modern tungsten lamp to pro- duce over 40 candle-power. An arc-lamp usually requires a flow of from 5 to 10 amperes. Pressure. Volts. When a current of water flows from one point to another in a pipe- system, it is always because there is a hydraulic pressure present causing it to flow. This pressure is usually meas- ured in pounds per square inch. Similarly, when a cur- rent of electricity flows from one point to another in -an electric circuit, it is because there is an electric pressure present which causes it to flow. This electric pressure is measured in volts. An electric pressure of i volt is analogous to a hydraulic pressure of i lb per sq in. The pressure which causes the J^i-ampere current to flow through an incandescent lamp is usually no volts. The electric company instals at least two wires in a residence and then maintains an electric pressure of no volts between them just as the water company maintains a pressure in the water-pipes. This electric pressure is at all times tending to force electricity from one wire to the other wire across the space between the two wires, just as the water-pressure tends to force the water out from the pipe. The rubber insulation is put on to prevent this flow, very much as the strength and compactness of the iron pre- vents the flow of water through the walls of the pipe. But when one terminal of a lamp is connected to one wire and the other terminal to the other wire, the electric pressure tending to send a current from one wire to the other, sends a current through the lamp and causes it to glow. We mark the wire bringing the ^110^ volts + X • s y J -A . J ■3 + ^ . + ^ - Fig. 1. Current Always Flows from (+) to (— ) 1458 Electric Work for Buildings Part 3 current to the lamp (+). The wire taking the current away, we mark (— ). Thus in Fig. 1, if the current comes in on the wire marked (.r), this wire is (+) and the wire {y) is ( — ). A pressure of no volts is maintained which tends to cause a current to flow across from the wire (x) to the wire {y). No current can flow, however, unless some path is afforded between the two wires. For in- stance, no current is flowing through lamp Li, because the open switch A makes a gap across which the current cannot pass. Switch B, however, is closed, thus allowing the pressure to force a current from the wire (x) through the lamp Li to the wire (y) and back into the street-mains. Of course the electric com- pany maintains the no-volt pressure between the wires (x) and (y) whether any current is drawn from the wires or not, just as a water company maintains the pressure in the water-mains whether any water is drawn from the pipes or not. Resistance. Ohms. The fact that a current of only ^ ampere flows through an incandescent lamp when a pressure of no volts is applied to it, is due to the RESISTANCE of the fine filament. This resistance of the filament is analogous to the resistance which a pipe of small bore ofl"ers to the flow .of water. The resistance of an electrical appliance is merely the ratio of the pressure to the current which that pressure can force through it. As an equation, it is expressed , pressure Resistance = current When the pressure is measured in volts and the current in amperes, the re- sistance is then in ohms. Thus Ohms = ■ amperes Thus, since a pressure of no volts forces H ampere through an ordinary in- candescent lamp, the resistance of the lamp is wojy^ = 220 ohms. Ohm*s Law. This relation between pressure, current and resistance is called Ohm's law. It is written in symbols in the three forms R = E/I E = IR I = E/R where * R = resistance in ohms; E = pressure in volts; I =» current in amperes. Example. An electric flat-iron has a resistance of 35 ohms. What current will flow through it when it is put across a no- volt circuit? / = E/R = 110/35 = 3.14 amperes Example. An electric toaster takes il^ amperes when on a 115-volt circuit. What resistance does it have? R = E/I = 115/1.5 = 76.6 ohms Insulators and Conductors. In order that practically no current may leak from one wire to the other, the wires are covered with rubber. This rubber covering offers such high resistance to the flow of an electric current that, al- though two wires may lie very close to one another with only this rubber be- tween them, practically no current leaks through the rubber from one wire to the other. Materials such as rubber, glas^, porcelain, dry wood, etc., have this resisting property and are said to be insulators. Metals, on the other hand, offer very little resistance to the flow of an electric current and are called con- Power in Electric Work 14^ DUCTORS. A copper wire Ho in in diameter has a resistance of only Hooo of an ohm per foot. Accordingly, because of their low resistance, copper wires are generally used to carry electric currents, and because of its high resistance, rubber is generally used as a covering of the copper wires to prevent leakage from one wire to another. Wire, approved by the National Board of Fire Under- writers and installed according to their rules, will have the proper insulating covering for each installation. ^ Power. Watts. The flow of an electric current has been likened to the flow of water through a pipe. A current of water is measured by the number of gallons, or pounds, flowing per minute; a current of electricity is measured by the number of amperes. The power required to keep a current of water flowing is the product of the current in pounds per minute by the head, or pressure, in FEET. This gives the power in foot-pounds per minute. To reduce to horse-power, it is necessary merely to divide by s^ coo. Thus (pounds per minute) x (feet) ■ • = horse-power 33 ooo In exactly the same way, the power required to keep a current of electricity flowing is the product of the current in amperes by the pressure in volts. This gives the power in watts. Watts = amperes x volts The term watt is merely a unit of power, and denotes the power used when one volt causes one ampere of current to flow. The watts consumed when any given current flows under any pressure can always be found by multiplying the- current in amperes by the pressure in volts. Thus, if an incandescent lamp takes 0.5 iampere when burning on a iio-volt line, the power consumed equals . 0.5 X 110=^ 55 watts That is, Power = current x pressure or Watts = amperes x volts Example. What power is consumed by a motor which runs on a 2 20- volt circuit, if it takes 4 amperes? Watts = amperes x volts = 4 X 220 Power = 880 watts Incandescent lamps are rated as to the voltage of the line on which they can run, and also as to the amount of electric power it takes to keep them glowing. Thus, a carbon-filament lamp may be rated as a no-volt, 50- watt lamp. A tungsten-lamp may be rated as a no-volt, 25-watt lamp. This means that both lamps are intended to run on a no- volt circuit, but that it takes twice as much power to keep the carbon-filament lamp glowing as it does to keep the tungsten- lamp glowing. H The Power-Equation. The above relation between volts, amperes and watts is usually expressed in the form of an equation: P = 7E I = P/E E = P/I where p = power in .watts; I = current in amperes; E = pressure in volts. 1460 Electric Work for Buildings Part 3 Example. What current does a 40-watt tungsten-lamp take when running on a 1 1 5- volt circuit? I «= P/E = 40/115 = 0.348 arripere Power. Kilowatt and Horse-Power. Because the watt is so small a unit of power, being only 0.74 ft-lb per second, a larger unit, the kilowatt, is gener- ally used in connection with machines, etc. I kilowatt = I 000 watts = i H horse-power Thus a motor drawing 10 amperes from a 220-volt line would take 10 X 220 = 2 200 watts = 2 200/1 000 =2.2 kilowatts. At 80% efficiency this motor would give out 80% of 2.2 = 1.76 kilowatts = 1.76 X i]'i= 2yi horse-power. Horse-Power-Hour. Kilowatt-Hour. When a -man buys mechanical power to run machinery, he has to pay not only according to the horse-power he uses but also according to the number of hours he uses the power. For in- stance, he may use 40 horse-power for i hour and pay $1.20 for it, that is, at the rate of 3 cts for each horse-power-hour. If he uses 40 horse-power for 2 hours he would have to pay twice as much, because he has used the same power twice as long. Another way of stating the same fact is to say that he used twice as many horse-power-hours. For in the first instance he used 40 X I, or 40 horse-power-hours, and in the second 40 X 2, or 80 horse-power- hours. In other words, he did twice as much work in the second case as he did in the first, or received twice as much energy. The unit of work or energy, then, is the horse-power-hour, and is the work done in i hour by a i -horse- power machine. Example. How much work is done by a machine dehvering 15 h.p. when it is run for 8 hours? I h.p. in I hr does i h,p.-hr 15 h.p. in I hr does 15 h.p.-hr 15 h.p. in 8 hr does 8 x 15, or 120 h.p.-hr That is Work = horse-power x hours or 15 X 8= 120 h.p.-hr Similarly, electric power is sold by the kilowatt-hour. This unit is the work or energy delivered in one hour by a i -kilowatt machine. For lighting purposes electrical energy is usually sold for from 10 to 15 cts per kilo watt- hour. Thus at 1 2 cts per kw-hr the monthly bill for burning a 40-watt lamp on an average of 5 hours per day would be computed as follows: For I month of 30 days the lamp is burning 30 X 5 = 150 hours To use a 40-watt lamp 150 hours consumes 40 X 150 = 6 000 watt-hours = 6 000/ 1 000 = 6 kilowatt-hours At 12 cts per kw-hr, 6 kw-hr cost 6 X 12 = $0.72 An instrument called a kilowatt-hour meter is placed in each house to meas- ure the number of kilowatt-hours which each customer consumes. See M in Fig. 13 for location of Kilowatt-hour meter, and Fig. 18 for method of con- nection in typical installation. Heating-Effect of Current. An electric current always heats the material Fuses and Circuit-Breakers 1461 the current heats the fine tungsten wire until it glows; the electric heaters for chafing-dishes, toasters, etc. Even the wires carrying the current to and from the lamps are heated by the passage of the current through them. But since the heating elTect for a given current is directly proportional to the resistance of the conductor, and the conductors always have very little resistance, the heat- ing here is very slight indeed. If conductors of smaller size, and therefore of a higher resistance, were used, the heating would be very pronoimced; in fact, it would soften the rubber insulation and might even produce a temperature high enough to set fire to the building. For this reason The National Board of Fire Underwriters issues a table specifying the size of wire which must be used f jr each amount of current. If smaller wire is used, the resistance of it might be great enough to raise the temperature to a dangerous degree. On the other hand, if a greater current than allowed by this table is sent over the wire, the temperature will also rise, because the heating of a current is also directly pro- portional to the SQUARE OF THE CURRENT. Thus, doubling the current which a certain wire is carrying will quadruple the amount of heat which the wire must radiate. For this Tables III and IV, see pages 1473 and 1474. Fuses and Circuit-Breakers. Use is made of the heating effect of a current to protect a circuit against too much current, very much as a boiler is pro- tected by a safety-valve against too much pressure. A small piece of fusible metal, generally a mixture of lead and bismuth, is inserted in the circuit in such a way that all the current which passes through the circuit must also pass through Fig. 2. Enclosed Fuse this piece of metal. This device is called a fuse: Any current which would be dangerous to the circuit melts this fuse, opens the circuit at this point, and thus protects the rest of the circuit from the effects of the current. The cause of the large current may be then removed and a new fuse inserted in place of the old one. Circuit-breakers are also used to protect a circuit against too much current. They are automatic switches controlled by an electro-magnet and are made in a variety of styles. They operate upon the principle that when an electric current passes through a coil of wire it makes a magnet of the coil. The coil is so adjusted that when a current of a certain number of amperes passes through it, it attracts to itself a small piece of iron. The motion of this piece of iron opens the circuit. Fuses and circuit-breakers are thus automatic safety-devices required for the protection of all constant-potential systems whatever the voltage. Both are for the purpose of protecting the wires from damage due to the presence of too much current from any cause whatever. The ordinary fuse consists of a porcelain base that has suitable terminals for inserting a fuse between the ends of a wire. It must be constructed so that the blowing out of a fuse can do no damage, that is, set anything on fire, and placed where it can easily be reached to replace the fuse. Formerly a piece of fuse-wire, called a link-fuse, was used in cut-outs, but the underwriters now require en- closed fuses (Fig. 2) or fusible plugs which screw into a receptacle. Fuse- 1462 Electric Work for Buildings Part 3 plugs may be used for currents up to 30 amperes; above that enclosed fuses must be used. Fuse-plugs and enclosed fuses are somewhat more expensive than the link-fuse, but are considered safer. A fuse cut-out or circuit- Breaker is required at or near the place where the wires enter a building, and every circuit of twelve i6-c.p. carbon-lights or of sixteen 40-watt tungsten-lights must be protected by a cut-out. Circuit-breakers are more expensive than fusible cut-outs, and are generally used only on switchboards for large in- stallations and where it is desirable to open the circuit instantly on certain loads, which a fuse cannot be depended on to do with any degree of accuracy, owing to both time and surrounding temperature-factors. Circuit-breakers are also used largely on installations where the variation in load is large and fre- quent and the repeated burning out of fuse would become expensive not only for renewals but also on account of the time required to replace them. Lamps. Two kinds of lamps are used for electric lighting, incandescent LAMPS and ARC-LAMPS. The former are used principally for interior illumination, although sometimes used for street-lighting, especially where the streets are thickly shaded by trees. Arc-lamps are especially adapted for street-lighting and for large interiors where they can be kept concealed or above the range of the eye, as in railway-stations, stores, etc. An incandescent lamp as com- monly made consists of a glass bulb containing a simple carbon or a tungsten conductor the ends of which are connected to the source of the electric current. When the current flows through the filament it heats it to such a degree that it becomes incandescent; hence the name of the lamp. The lamps with the fila- ment of finely-drawn tungsten represent the latest type and are superior in every way to those having a carbon filament. Tungsten-lamps require about one-third as much power to produce the same candle-power as carbon-lamps, and have a much longer life. Voltages. In order that the current shall cause the lamp to give its rated CANDLE-POWER, it must be designed for the voltage at which the system is run. If the voltage of the current is much greater than that for which the lamp is designed it will quickly burn out the filament, while if the voltage of the current is below that of the lamp, it will not give its rated candle-power, a voltage 10% lower reducing the candle-power about one-half. The voltage commonly used for tungsten-lamps is from 100 to 130. Tungsten-lamps are also made for volt- ages of from 20 to 260. Two to four candle-power lamps, for illuminating signs or decorative purposes, are made for from 10 to 13 volts by 3.^-volt steps, these lamps being commonly used in series, ten lamps on a 100 to 130- volt circuit. Two 5-watt lamps, 50 volts, are also often used in series on a loo-volt circuit. Candle-Power. Incandescent lamps of from 100 to 130 volts are commonly made 15, 20, 25, 40, 60, 100, 150, 250, 400 and 500 watts. These lamps average I candle-power for every i.i watts. For the method of computing the number, size and distribution of tungsten-lamps for illuminating a given room see pages 1476 to 1478. Arc-Lamps. These are of two kinds, open arc-lamps and enclosed arc- lamps, the latter being generally used for interior illumination. The light from the enclosed arc is much softer and steadier than that from the old-style open arc; there are no sparks, and the life of the carbon is from twelve to fifteen times as great as in the open arc. " Direct-Current Open Arcs usually require about 10 amperes at 45 volts, or 450 watts. The range of voltage is from 42 to 52 for ordinary con- stant-current arcs. The most satisfactory light is given by from 45 to 47 volts. Electric Machines and Currents 1403 Arc-lights used for stereopticon-lan terns may use as high as 25 amperes and provision should always be made in the wiring-plans for such a light for suffi- ciently large wires to be installed to carry one and one-half times this current. ** Direct-Current Enclosed Arcs consume about 5 amperes at 80 volts, or 400 watts." Arc-lamps generally require a resistance in series with the arc in order to regulate properly. This resistance is usually placed within the struc- ture of the lamp, and may be so adjusted that a single lamp can be made to burn well on any circuit from 100 to 130 volts. Dynamo-Electric Machines. There are three classes of dynamo-electric machines: (i) Generators for generating an electric current. (2) Motors for converting electrical into mechanical energy. (3) Transformers and rotary converters. (a) Transformers for converting one voltage into a higher or lower voltage. Converters and transformers belong to the same class. (b) Rotary converters for changing alternating currents to direct currents or vice versa. A dynamo is either a motor or a generator. A motor is the same machine as a generator, but with the nature of its operation reversed. Generators are of two general classes, namely, continuous-current and alternating-current machines; the latter are commonly called alternators. Generators and motors of all kinds vary in voltage, current and speed, according to the pur- pose for which they are designed. A transformer consists essentially of tw6~ coils of wire, one coarse and one fine, wound upon an iron core. Its function is to convert electrical energy from one voltage to another. If it reduces the voltage it is known as a step-down transformer, and if it raises it, it is known as a step-up transformer. A transformer has no moving parts and requires no attendant. Kinds of Currents Produced. There are two kinds of electrical currents commonly used for light and power in buildings, (i) direct currents, and (2) alternating currents. "A direct current is uniform in strength and direction, while an alternating current rapidly rises from zero to a maximum, falls to zero, reverses its direction, attains a maximum in the new direction and again returns to zero. A complete set of these changes is called a cycle. The number of times the current goes through these changes during each second is called the frequency of the current. The frequency commonly used for incandescent lighting is 60 cycles per second; that is, the current goes through the above changes in value 60 times per second. A frequency of 25 cycles is also in common use, especially for run- ning motors, although it is not so satisfactory for use with incandescent lights. If a direct current is likened to the steady flow of water through a pipe-system, an alternating current may be likened to the rapid surging back and forth of water in a pii)e-system. More difficulty was experienced in utilizing these rapid surges of electricity than in developing direct-current apparatus. Consequently the use of the alternating current was retarded but is now becoming general. The advantages of alternating over direct currents are: (i) Greater simplicity of dynamos and motors, no commutators being required in some types; (2) the feasibility of obtaining high voltages by means of transformers for cheapening the cost of transmission; (3) the facility of transforming from one voltage to another, either higher or lower, for different purposes. " * • Adapted from Kent's Pocket Book. 1464 Electric Work for Buildings Part 3 Table I. Average Current Taken by Direct-Current Motors Horse- power Amperes on I ID- volt line Amperes on 220-volt line Horse- power Amperes on 1 10- volt line Amperes on 220-volt line % I 2 3 5 lO 15 20 3 5-4 9 17 25 40 58 76 114 150 1.5 2.7 4.5 8.5 12.5 20 29 38 57 75 25 30 35 40 50 60 75 85 100 186 222 - 260 296 93 III 130 148 18S 220 275 312 366 The current taken by single-phase alternating-current motors can be found by noting the current taken by a direct-current motor of the same size and volt- age, and dividing this current by the power-factor of the alternating-current motor. To find the current taken by each terminal of a three-wire, three-phase alternating-current motor, divide the current taken by a single-phase alternat- ing-current motor of the same size and voltage by 1.73. Example. What current is taken by a 5 -horse-power, alternating-current, 220-volt, induction-motor of 80% power-factor? Soiution. A 5 -horse-power, direct-current, 220-volt motor takes 20 amperes. A single-phase, 5-horse-power, 220-volt motor of ^0% power-factor takes 20/. 80 = 25 amperes. Electric-Lighting Systems Commonly Used for Supplying the Electrical Energy to Lamps Direct-Current, Constant-Potential Systems. The systems most used in America are: (i) Two-wire system largely used for incandescent lighting from small plants, as for a large office-building or factory. It is usually operated at no volts. (2) Three- WIRE system used in small towns for the lighting of buildings from the public mains, usually operated at 220 voltsr Also in large cities with under- ground conduit-system. See pages 1466 to 1468. Five-wire and seven-wire systems with high voltage have been used in Europe, but very little in America. Alternating-Current, Constant-Potential Systems. There are two sys- tems: (i) Single -PHASE system. Current transmitted to building at from i 000 to 2 000 volts and reduced to from 50 to no volts by a transformer. The term phase is used in connection with alternatiiig-current systems only in the sense of circuit. Thus a single-phase system means an alternating-current system sending out power from one circuit only of the generator. A three-phase system has three circuits. (2) Three-phase system. Three or four wires are used. This system is most used for lighting from public plants, principally because it enables both lights and motors to be operated from the public dynamo and is the most econom- ical in wire. (See Table II.) Both of these systems are used for incandescent lighting and for power from central stations. For a comparison of a three- wire direct current with a three-phase, three-wire alternating current, see pages no no f«volt,s|«volts>- — Lfm ■ ' ■ ■nr — i no T no 1 no ^volts^ <— 550-v volts Tl 1 Fig. 3. Five Lamps in Series on a 5 50- Volt Line. Each Lamp has a Voltage of no Volts Across It Electric-Lighting Systems 1465 1468-9. An alternating current may be changed to a direct current at a sub- station by a rotary converter or by a mercury-arc rectifier. The latter is very generally used in garages in order to convert an alternating current into a direct current for charging storage- batteries. Methods of Connecting Lamps. There are three ways of connecting lamps to the dis- tribution-wires: (i) in series; (2) in parallel; and (3) in parallel series. (i) Lamps in Series. Lamps are said to be connected in series when they are arranged one after the other, so that the same current flows through all the lamps. The most com- mon example of this system is the lighting of electric cars and the stations on an electric-railway line. The voltage of such lines is usually 550 volts. Since the ordinary incandescent lamp requires but no volts, five .of these are placed in series as in Fig. 3. Each lamp now has a pressure of no volts across it, and the set of five lamps requires 550 volts across it, and so can be placed across the railway supply-wires. When lamps are arranged in series the total resistance of the circuit is the sum of the resistances of the several parts, and the voltage required to force the current through a number of lamps in series is the sum of the voltages required for the separate lamps. Thus the voltage required to supply the proper current for four 52-volt lamps is 4 X 52 = 208 volts. Arc-lamps for street-lighting are often connected in series, but incandescent lamps are very seldom connected in series except as described above or for decorative purposes or electric signs. Where lamps of low voltage, as in signs, etc., are used on no-volt systems it is necessary to connect them in series. The underwriters, do not approve connecting incandescent lamps in series. The series system requires that the same current flow through each lamp, and if one lamp burns out the circuit is broken and all of the lamps will go out, unless some provision is made for maintaining the circuit around the dead lamps. (2) Lamps in Parallel. This is the common method of connecting incandescent lamps. It is illustrated in Fig. 4. With this system the pressure in each lamp is the same as in the distributing fines, and any lamp may be turned on or off without affecting the other lamps. For this system the pressure or voltage must be kept con- stant, while the current or quan^ty of electricity flow- ing in the lines will depend upon the number of lamps that are burning. Thus with twelve i6-candle-power lamps of no voltage on a parallel circuit, each lamp requiring 0.51 ampere when all the lamps are burning, a current of 6.12 amperes, or 673.2* watts, will be required. With but one lamp burning, • Watts being equal to amperes times voltage. 4. Four Lamps in Parallel. Each Lamp Has the Full- line Pressure of no Volts Across It 1466 Electric Work for Buildings Part 3 a current of only 0.51 ampere will flow. The voltage, however, must be the same for one lamp as for the twelve. For lamps in parallel, therefore, a con- stant-potential system is required. The current for lamps m parallel may be turned on or off at the lamp, or a switch-loop may be run any distance and the contact made by a switch (5) as for the lower lamp (Fig. 4). (3) Lamps in Parallel Series. This method is a xrombination of the other two. Parallel lines are run as in the parallel system, but two or more lamps ^IIO-Vt^ Fig. 5. Lamps in Parallel Series Fig. 6. Lamps in Parallel Series are connected in series between them as in Figs. 5 and 6. This method of con- necting lamps is used principally in places where it is desired to operate lamps on a power system. Fig. 5 shows a series of five lamps operated on a 500-volt system and Fig. 6 a series of two lamps on a 220-volt system using no-volt lamps. Any number of series may be connected across the mains, each series __ being independent of the Fig. 7. The Three-wire Edison System. 220 Volts Between Outside Wires; Only no Volts Between Either Outside Wire and Neutral Wire others. But in each series if one light burns out, the others in the same series will be use- less, and one lamp alone cannot be used. The sum of the voltages of the lamps in series must be approximately equal to the voltage between the mains. There are a number of special cases in which this method of connection may be used. The Edison Three-Wire System. Figs. 4, 5 and 6 are examples of the two-wire system of distribution, which is the system recommended for average- sized office-buildings, apartment-houses, theaters and stores. Where power for motors is to be taken from the same plant as the lighting current, and where the power is not too great a portion of the capacity of the installation, this two- wire system may also be used. Separate mains, however, should under all cir- cumstances be run for the motors, as the variation in load and, consequently, the current-demand on the mains would cause a very appreciivble fluctuation in Electric-Lighting Systems 1407 candle-power of the lamps, if on the same mains with the motors. Where com- paratively long Unes are required and the amount of current to be supplied is D. denotes Dynamo CO. L. M. Cut-out Lamp Motor JioV, 220 V. ic.ol Fig. 8. Example of Three-wire System of Wiring large the titree-wire system is ur>cd. By this system two voltages or pressures can he supplied, no and 220 volts being those generally adopted, the no-volt circuit supplying the arc and To Cut-out Cabinet Second Story incandescent lights and the 220-volt circuit the motors. Fig. 7 shows how the wires are run and connections made. The pressure between the two outside wires is the full voltage transmitted from the generator, usually 220 volts for interior wiring. The current in these two wires flows in opposite direc- tions. The middle wire, called the neutral wire, forms one side of two cir- cuits, the current from one circuit tending to flow in one direction and that from the other circuit in the oppo- site direction; consequently when currents of the same strength, in amperes, are flowing in both circuits they neutralize each other in the middle wire and there will be no current flowing in this wire. With a current of 10 amperes flowing in one circuit and one of 6 amperes in the other circuit, the current flowing in the neutral wire will be 4 Fig. 9. The Wiring of a Cabinet. Showing How to Divide a Three- wire System into Six Two-wire Cir- cuits, Three Circuits to Each Leg 1468 Electric Work for Buildings Part 3 Phase ^110-> volts Phase ~No.3 Phase No.2 amperes. To obtain the greatest benefit from this system, it should always be installed so that there will be nearly the same load or number of lamps on each side of the neutral wire. Even then there will be times when more lamps will be burning on one side than on the other, so that it is necessary to give some size to the neutral wire. The neutral wire is seldom made less than one-half the cross-section of the outer wires. For distributing mains in buildings carrying lamps only, the neutral wire should be of the SAME SIZE as the outer wires. From Table II it will be seen that the three-wire system effects a considerable saving in copper, amounting to fully 60% of the ordinary two-wire no- volt system. As a rule, in supplying current for light and power from one plant, the main^wires only are arranged on the three-wire system and the distributing wires are run Fig. 10 Alternating Current. To Street Mains Three-phase, Three-wire System, Compare with Fig. 11 on the two-wire system as in Fig. 8. When using the three-wire system for lighting only, the three wires are usually run no farther within the building than to the centers of disfribu- tion, and from these centers two wires are run for each cir- cuit, the circuits being divided as equally as possible on the two sides of the three-wire system as shown by Fig. 9. Three-wire mains are now very commonly used where the cur- rent exceeds 100 amperes. When motors are operated from the three- wire system they are usually connected only to the outside wires. Motors used on three-wire incandes- cent-lighting systems should be wound for 220 volts. Comparison of the Three- Phase and Three-Wire Edi- son Systems. The wiring for the Edison three-wire direct- current system is the same as that for the three- wire, three- phase alternating-current sys- Leg N0.1 -220^ volts Leg N0.2 To Street Mains Fig. 11. Three-wire System, Direct Current. Compare with Fig. 10 tem, the only difference being that the voltage between any two wires of a three-phase system is the same. Thus in Fig. 10 which represents a three- wire, tbree-ph^sc system the voltage between the wires A and B (phase No. i) Wire-Calculations 1469 IS no volts; between B and C (phase No. 2) is no volts; and between A and C (phase No. 3) is no volts. But in Fig. 11, which represents a three- wire direct-current system, in which the voltage across A and B, and B and C, is no volts, the voltage across A and C is 220 volts or twice that across either leg. Table II. Relative Weight of Copper Required in Different Systems for Equal Effective Voltage Direct-current, ordinary two- wire system Direct-current, three-wire system, all wires of same size . Direct-current, three-wire system, neutral, one-half size.. Alternating-current, single-phase two-wire system Three-phase three-wire Three-phase four-wire i .000 0.375 0.313 1 .000 0.750 0.333 Wire-Calculations Wire-Gauges.* As the diameter of wires is ordinarily designated by the number of a wire-gauge, and as there are a number of wire-gauges in common use, some knowledge of those used for copper wire is necessary. The Brown & Sharpe, or B. & S., gauge (see page 1474) is almost exclusively used in America in connec- tion with electrical work, except where the size of the wire is designated in cir- cular mils. The sizes of wire given by this gauge range from No. 0000 (0,46 in) to No. 40 (0.0031 in), but No. 14 is the smallest size permitted for interior wiring. The No. 10 wire has a diameter of about Ho in and its resistance per i 000 ft is very nearly i ohm. For any given number of this gauge a wire three numbers higher has verj'- nearly half the cross-section, and one three numbers lower has twice the cross-section; thus a No. 13 wire has very nearly one-half the cross- section of a No. 10 wire, and a No. 7 has twice the cross-section of a No. 10, or four times that of a No. 13. The Circular-Mil Wire-Gauge. This gauge was designed by the engineer- ing department of the Edison Company especially for the designation of copper wire for electrical work, and is now in general use in this country. In practice the B. & S. gauge is commonly used for designating wires up to No. o or No. 00, and all wires above that size are designated by circular mils (cm.). The size of wire required is often determined in circular mils and designated by the corre- sponding B. & S. gauge-number, which is readily done by means of Table III, page 1473. Copper wire is sold by the pound if bare or of the numerous weather-proof varieties, but rubber-covered wire is sold by the i 000 ft. The basis of the circular-mil gauge is the area of a wire Mooo in in diameter (i mil = o.ooi in); consequently, i cm. = 0.0000007854 sq in. As the areas of circles vary as the squares of their diameters, it follows that the sectional area of a wire 2 mils in diameter = 4 cm., of a wire 10 mils in diameter 100 cm., and so on. When wires are designated by circular mils, the sectional area and not the diameter is generally given, cm. always referring to sectional area. The diam- eter of a wire in mils or in thousandths of an inch = square root of its area in circular mils. Thus the diameter of a wire of 3 600 cm. = 60 mils, or 0.060 in. The diameter of a wire 14 400 cm. = 120 mils =0.12 in. The area of a wire 0.162 in in diameter, or 162 mils, = 1622= 26244 cm. * For other causes, see pages 401, 402, 403, i473, 1509, 1510. IS12 and 1600. 1470 Electric Work for Buildings Part 3 To reduce circular mils to square inches. Multiply by 7 854 and point off ten places of decimals. Thus, 5 000 cm. = 7 854 x 5 000 = o.oo39270cxx3 sq in. To obtain the sectional area of a square or rectangular bar in circular mils. Multiply together its dimensions in mils and the product by 1.273. Example. What is the sectional area in circular mils of a bar H in X H in? Solution. H in =0.125 in = 125 mils, H in = 0.250 in = 250 mils; 125 x 250 X 1.273 = 39781.25 cm. The weight of bare copper wire per i 000 ft = cm. x 0.003027 lb. Thus the weight of I 000 ft of copper wire having a sectional area of 2 000 cm. = 0.003027 x 2 000 = 6.054 lb. Table IV, page i474» gives the dimensions and weights of bare copper wire from No. 18 to No. 0000 B. & S. Carrying Capacity of Copper Wire. The safe carrying capacity of copper wire for interior wiring is practically fixed by the underwriters, and if the ca- pacity-limits given in the table published by them are exceeded it would tend to destroy the right to recover insurance in case of fire. The safe carrying capacity of rubber-covered and weather-proof wires given by the National Board of Fire Underwriters is shown by Table III, page 1473.', The lower am- pere-capacity assigned to rubber-covered wires is due to the fact that the rubber insulation would deteriorate in quality under a temperature as high as that allowed for weather-proof wire; that is, the rubber covering makes necessary a lower rate ot heat-development than is required for safety from fire. No wire smaller than No. 14 may be used under insurance-rules, except that No. 16 may be used for flexible cord and No. 18 for fixture-wiring. Nos. 13, II, 9 and 7 are not usually carried in stock and can only be purchased on special order. Rubber-covered wire must be used for service-wires, for mold- ing-work and in damp places; it is more expensive than weather-proof wire. The latter wire may be used in open or exposed places and for outside line-wires. Drop of Potential. When an electric current flows through a wire of any appreciable length the pressure becomes reduced by the resistance of the wire, so that if the current enters the wire at, say, no volts, at the extreme end of the circuit it will be somewhat less, depending upon the length and sectional area of the wire. This loss in voltage is called drop of potential. Drop of potential corresponds to loss of head in hydraulics. As a drop of voltage materially below that for which the lamps are designed means diminished candle-power, it is very important that the wires be proportioned so that the drop shall not be sufficient to affect the illumination. The table for safe carrying capacity for wires has nothing to do with the drop of potential which these currents will cause in the wires. Accordingly, mains and distributing wires may be capable of carrying the number of amperes in accordance with Table III, page 1473, and yet cause a drop of potential of such magnitude that the most distant lamps will burn only at a dull red. It is therefore necessary, in computing the size of these mains and distributing wires, to consider two things: (i) That the wire is large enough, according to the underwriters' table, to carry the current safely. (2) That the potential drop from the generator to the farthest lainp shall not be excessive. An excessive drop in voltage also means increased cost for light and not enough copper in the wires. Where the current is supplied from the public mains it is usual to specify a 2% drop, but where the current is produced cheaply, as by a dynamo on the premises, a 3% or 5% drop may be allowed. Not more than a 5% drop on short r!i , . Resistance = — -. (2) N Xc X2d In both these form.ulas d = distance in feet, one way, from cut-out to load- center (see page 1471) for distributing wires, or from entrance cut-out or source of current to distributing center for main lines or feeders, c = current in am- peres PER LAMP. N = number of lamps supplied, v = drop in volts. Both formulas apply to any voltage and to any two-wire system. To use these formulas for the ordinary three-wire system, let N = maximum number cf lamps on one side of the neutral wire and double the drop in volts. The neutral or middle wire should be of the same size as the outside wires. Example. The distance from the cut-out to load-center of a circuit carrying sixteen 40-watt, iio-volt lamps is 50 ft. What size of wire should be used for a drop of 2 volts? Solution. d= 50; N = 16; c= 40/110= 0.364; and v= 2. By Formula (i), „. , ., 10.4 X 100 X 16 X 0.364 Circular mils = = 3 030 2 Table III, page 1473, shows that the next larger size of wire is 4 107 cm., equivalent to a No. 14 wire. By Formula (2), I 000 X 2 Resistance per i 000 ft = = 4.59 12 X 0.364 X 100 which we see from Table IV, page 1474, is about the resistance of a No. 16 wire; but as No. 14 is the smallest wire permitted that size must be used. Example. The distance from the entrance cut-out, where the wires enter the building, to the main distributing center of a building is 100 ft. The total num- ber of i6-candle-power, iio-volt carbon-lamps supplied is ninety. What is the size of the mains that should be used on the two-wire system with a drop of 2 volts? (A i6-candle-power no- volt carbon lamp takes approximately 0.51 ampere.) Solution. d= 100; A^ = 90-; c= 0.51; v= 2 By Formula (i), . 10.4 X 200 X 90x0.51 Circular mils = = 47 800 2 In Table III it is seen that No. 3 wire must be used. If a drop of 3 volts is allowed the sectional area required will be 33 048 cm., which requires a No. 5 wire. The weight per i 000 ft of No. 3 weather-proof wire (Table IV) is 200 lb and of No. 5 wire 125 lb; consequently, the saving in weight of wire by using a drop of 3 volts instead of 2 is 75 lb, or 37^% of 200, and as wire is sold by the pound, the saving in cost with a 3% drop ranges from 30 to 40% of a 2% drop. Example. With the same conditions as given in the preceding example what is the size of the wire that will be required for the ordinary three-wire Wire- Calculations Table IH. Carrying Capacity of Wires and Cables FOR INTERIOR CONDUCTORS, ALL VOLTAGES From the National Electrical Code No. of Capacity in amperes wire, Circular B.&S. mils Rubber- Weather- gauge * covered proof i8 I 624 3 5 i6 2583 6 10 14 4 107 15 .20 12 6530 20 25 10 10380 25 30 8 16 510 35 50 50 70 6 26 250 5 33100 55 80 4 41 740 70 90 3 52630 80 100 2 66 370 90 125 I 83690 100 150 105500 125 200 00 133 100 150 225 000 167 800 175 275 0000 211 600 225 325 Cables 200 000 200 300 300 000 275 400 400 000 32s Soo 500 000 400 600 600000 4SO 680 700 000 500 760 800 000 550 840 900 000 600 920 I 000 000 650 I 000 I 100 000 690 1080 I 200 000 730 I 150 I 300 000 770 I 220 I 400 000 810 I 290 I 500000 850 1360 I 600 000 890 I 430 I 700 000 930 I 490 I 800 000 970 1550 I 900 000 I 010 I 610 2 000 000 I 050 1670 A current of one ampere will supply two i6-candle-power carbon lamps. Solution. In this case we use one-half of iV", or 45, and 2 v instead of v; then Circular mils = 10.4 X 200 X 45 X o.5i ■■ II 920 or just ONE-FOURTH the section required for the two-wire system. The size of wire required is No. 8; a No. 9 would answer if it could be had. Comparing the weight of wire required with the two-wire system gives two No. 3 wires weighing 400 lb per i 000 ft, and with the three-wire system three No. 8 wires weighing 207 lb; hence, the saving in cost is nearly 50% and if No. 9 wire were obtainable the saving would be 55%. With a drop of 3% (s-S volts) the cir- 1 -1 ' A e ^u 4.1. ' ' 4. ^°-4 X 200 X 4 5 X 0.51 Cular mils required for the three-wire system = ■ — = 7 230, 6.6 im Electric Work for Buildings Part 3 requiring No. lo \^ires. The current in amperes in the two-wire system = N x c = 45.9, and in the three-wire system Yi N x c= 22.95. Referring to Table III it is seen that the smallest size of weather-proof wire permitted for 45.9 amperes is No. 8; consequently, No. 8 wire could be used with the two-wire system and comply with the underwriters' rules, but the drop in potential would be 45.9 X 0.2 X 0.6285 (amperes x resistance of line) = 5.77 volts; or over 5%. For the three-wire system, the current being 23 amperes, the smallest weather- proof wire permitted by Table III is No. 12, which would give a drop of 7.4 volts, or 3.8 volts on each side, or about 3^% of the lamp-voltage. Except on very short lines a 2% drop will always demand larger wires than required by the underwriters, and this is also usually true of a 3% drop. Tab^e IV. Dimensions, Weights and Resistances of Copper Wire Weight in lb per Gauge- number, B.&S. Diameter in mils Area in cir. mils Area in sq in I 000 ft Bare Weather- proof* wire Ohms per I 000 ft wire at 20° C. or 68° F. OCXXJ 460 211 600 0.166190 640.73 800 0.04893 000 410 167800 0.131790 508. 12 666 0.06170 00 36s 133 100 0.104520 402.97 500 0.07780 325 105 500 0.082887 319-74 363 0.09811 I 289 83690 0.065732 253 43 313 0.1237 2 258 66370 0.052128 200.98 250 0.1560 3 229 52630 0.041339 159.38 200 0.1967 4 204 41 740 0.032784 126.40 144 0.2480 5 182 33 100 0.02S999 100.23 125 0.3128 6 162 26250 0.020618 79-49 105 0.3944 7 144 20 820 0.016351 63 -03 87 0.4973 8 128 16.510 012967 49-99 69 0.6271 9 10 114 102 13090 10380 0.010283 0.008155 39-65 31-44 0.7908 0.9972 50 II 91 81 8234 6 530 0.006466 0.005129 24-93 19.77 1-257 1.586 12 31 13 14 72 64 5 178 4 107 0.004067 0.003225 15.68 1-999 2.527 12.44 22 15 16 57 51 3 257 2 583 . 002558 9.86 3 179 4.009* 0.002'528 7.82 14 17 18 45 40 204S 1 624 00160" 6.20 5.055 0.001275 4.92 " 6 374 * Approximate weigRt oi w«atlref-proof line-wire for outdoor work is 10% Ife^ than here given. To find the smallest size of wire that will comply with the underwriters' rules it is only nfeccssary to compute the total current in amperes, and from Table III select the wire having a capacity equal to or next above the required number of amperes. Table VI shows at a glance the maximum number of i6-candle-powci.' iid-volt carbon lamps permitted by the National Code. Formulas (i) and (2), page 1472, may also be used for motor- wiring, if the required current in amperes is known, by substituting the given rmmber of am- peres for N X c. Wire-Calculations 1475 Table V. Maximum Length of Line for Given Number of Lamps tiiat can be Used with a Two-Per-Cent Drop. Two-Wire System Based on Vz ampere per carbon-lamp. One 3 2 -candle-power carbon-lamp = two i6-candle-power carbon-lamps. Four 40-watt tungsten- lamps = three i6-candle-Rower carbon-lamps No. of wire, B.&S. gauge Number of i6-candle-power, no- volt carbon-lamps Maximum length of line, one side, in feet 139 104 83 76 70 52 42 221 166 133 120 no 83 66 264 211 192 176 132 105 326 297 272 440 204 334 163 267 Number of i6-candle- power, no- volt lamps 36 60 70 Maximum length of line, one side, in feet 35 55 88 136 220 44 70 109 178 225 37 58 91 148 187 236 52 81 133 168 212 268 42 65 107 135 170 214 270 54 89 112 141 180 225 285 37 76 96 121 153 193 243 40 66 84 106 134 169 213 59 75 94 119 150 190 53 67 85 107 135 170 For three-wire mains with 220 volts between outer wires and same number of lamps on each side, length of wire may be increased four times. Table VI. Maximum Carrying Capacity of Wires in Terms of i6-CandIe- Power iio-Volt Lamps, However Short the Wires May Be Based on H ampere per lamp Four 40-watt tungsten-lamps = three i6-candle-power carbon-lamps No. of Number of lamps No. of Numbpr of lamps wire. B.&S. Rubber- Weather- B.&S. Rubber- Weather- gauge covered , proof gauge covered proof 14 24 32 4 130 184 12 34 46 3 152 220 10 48 64 2 180 262 8 66 92 I 214 312 6 92 130 254 370 5 108 154 00 300 440 1476 Electric Work for Buildings Part 3 Example. What should be the size of the wires to be run to a motor that i-equires 30 amperes at 220 volts and is situated 200 ft from the distributing pole, the drop in volts not to exceed 2%? Solution. Using Formula (i), and substituting 30 ior N X c, we have Circular mils ■■ 10.4 X 400 X 30 4.4 = 26400 which requires a No. 5 wire. Either the watts or the current in amperes is stamped on every motor. If watts are given, the current in amperes may be found by dividing the watts by the voltage. If kilowatts are given, multi- ply by I 000 and then divide by the voltage. Wiring-Tables. Sev- eral forms of wiring-tables which are very useful to electricians are published in various books on electric- ity. For ordinary interior wiring for iio-volt, 16- candle-power carbon- lamps, Table V, computed by Mr. Kidder, will show at a glance the number of wire, B. & S. gauge, required to supply the given number of lamps by first ascertaining the length of line (one way) through which the average current flows, as explained under Load-Center. (See page 1471 and Fig. 12.) Simple Example of Wiring. To show the method of wiring an or- dinary building for incan- descent lighting we will take a two-story building having a floor-plan as shown in Fig. 13. Most of the light-outlets are on . the ceiling and are indi- cated by a small circle. The outlet marked £ is a special outlet for heating, etc., and must be described in the specifications. Let us assume it is to take 320 watts. This is equiva- lent to adding eight 40-watt lamps to this circuit. F and G are wall-outlets. The meanings of the symbols used are explained on pages 1484-5- The numbers Fig. 13. Wiring-diagram for Second Story. For Mean- ing of Symbols, see pages 1484-5- Wire-Calculations 1477 I and 2 inside the circles denote the number of i6-candle-power carbon-lamps to the outlet. The same number of 25-watt or 40- watt tungsten-lamps may always be used without overloading the circuits. See pages 1398 and 1399 for Standard- Wiring Symbols. The current to be obtained from the wires of the public lighting company, which carry a current at 220 volts between the outside wires, and at no volts between either outside wire and the neutral wire. The feed-wires for the building should enter through the alley-wall at about the level of the second floor and should drop in the partition just inside the wall for the main fuse-block and switch, which should be in a small cabinet and the meter (M). The distribu- tion-cabinet should be lo- cated near the center of the building, say at DC, and there should be a cabinet in each story. From this cabinet we will run four cir- cuits for each story, which are indicated by the letters A, B, C and D. Circuit A shows the wires run for a switch on the wall near the door of each of four rooms to control the lights in those rooms. All of the lights on circuit C should be controlled by keys in the lamp-sockets. F.F, FUSE-PLUGS S.8, KNIFE-SWITCHES Fig. 14. Cabinet-wiring for Knife-switch Control The lights on circuits B and D are not switched, except the outlet at head of stairs, which is controlled by a snap or push-button switch at S. For a first-class job all of the four circuits would be controlled by knife-switches in the cabinet, as shown in Fig. 14; but this is not absolutely necessary. Size of Wires. The load-center of circuits A, C, and D would be at about the points marked X (Fig. 13). For circuit B take one-half the distance ab and add to it the distance from c to the cabinet. In figuring the length of line, 6 ft should be added for the drop from ceiling to the cabinet. Let us as- sume that tungsten-lamps are to be used. In computing the current taken by each lamp it is always assumed that no smaller than a 40-watt tungsten is used. The drop-lights, marked -Q- would probably be 25-watt lamps, but must be counted as 40-watt, according to the underwriters* rules. The number of 40- watt lamps and length of wire for each circuit are as follows: Circuit A, 8 lights, 41 ft one way to load-center. Circuit B, II lights, 52 ft one way to load-center. Circuit C, 16 lights, 37 ft one way to load-center. Circuit D, 12 lights, 59 ft one way to load-center. Total number of lamps, 47. From Table V we see that the maximum length of line one way for No. 14 wire carrying twelve carbon or sixteen 40-watt lamps is 70 ft. Consequently, all of the lamp-circuits can be No. 14 wire, which is the smallest size permittM. 147S Electric Work for Buildings Part 3 Feed-Wires. These should be run on the three-wire system. Allowing for ? X 47 or 94 lamps in first and second stories and eight in basement, the feed- wires must be capable of supplying 102 lamps. Each 40-watt lamp would take 40/110 = 0.364 ampere. The distance from outside the building to distribution- cabinet is about 72 ft, allowing for three drops. Using Formula (1), and assuming that there will be fifty-one lamps on each side of the three-wire system, and doubling the drop in volts, gives ^. , ., 10.4 X 1 44 X 0.364 X 51 r, . Circular mils = = 6 960 cm. which calls for No. 11 wire; but as this size is not carried in stock we must use No. 10. From the second story to the third No. 12 wires could be used. For almost all buildings lighted from a central station the lamp-circuits will not usually require a wire larger than No. 14, so that about the only wires which the architect needs to look after are the wires which run to the distribution- cabinets. Switches. A switch is a device for opening or closing a circuit at will either at the fixture or at any other point. In the better class of buildings the majority, if not all, of the ceiling-lights are controlled by switches placed at a convenient place on a side wall. Lights may be controlled at any distance from the fixture by running a switch-loop. For controlling either a single lamp or fixture, or any number of lamps, a switch-loop is run as shown on circuits A and C, as in Fig. 13. As shown also in Fig. 4, one side of the loop must be connected with one of the distributing X <^Lamp InBulating Material A B Cy D E ^~a z ^r^ Fig. 15. The Lamp May Be Turned Ofif or On From Any of the Five Points, A, B, C, Z>, or£ Fig. 16. The Lamps May Be Turned Off or On From Either the First or Second Story wires and the other side to the lamp. When a number of lamps are to be controlled by one switch, as in the case of hall-lights, and the lamps in large rooms, such as churches, theaters, concert-halls, etc., a separate circuit is usually run for those lamps, and a switch anywhere in one of the distributing lines will turn on or ofif all of the lights on that line. As the underwriters do not permit more than twelve i6-candle-power carbon or sixteen 40-watt tungsten-lamps on one circuit, not more than these numbers of lamps can be controlled by one switch, except where the switch is placed on the mains. It is also practicable to control one lamp from two or three places. Thus by a duplex or three-point switch and proper wiring, a lamp may be lighted or turned ofif from either the first or second story at will. By means of two three-point switches and one four-point switch a first-story hall-lamp may be Conduit-Systems 1479 controlled at will from either the first, second or third stories. Fig. 15 shows the method of control from any number of points, since any number of 4-point snap-switches, such as B, C and D, can be inserted between the 3-point switches A and E if more points of control are needed. Fig. 16 shows one method of wiring for controlling a hall-light from first and second stories by means of two 3-point switches. With the switches in the position shown the circuit is broketi, as there is no connection between the lamps and line B. By turning either switch a connection is made with line B and the current will flow. Kinds of Switches. For controlling lamps from one point three kinds of switches are used, namely, snap-switches, flush or push-button switches and knife-switches. When less than eight lamps are controlled by the switch, a flush or push-button switch is commonly used where a neat appearance is desir- able, and in places where this is of no importance, a snap-switch is used, as it is the cheaper. Where a circuit of twelve or more lamps is controlled by a switch, a double-pole (d.p.) knife-switch (Fig. 17) is commonly used, being generally placed in a cabinet. Knife-switches should always be used on main wires. Snap and push- button switches are made both single and double pole. A single-pole switch opens only one side of the circuit and a double- pole switch both sides. A double-pole knife-switch necessarily opens both sides. Fig. 17. Common Knife-switch A switch used on a three-wire system must have three poles. Double-pole snap and push-button switches are seldom used for less than twelve lamps. Duplex switches, sometimes called three- point switches, are usually of the snap or of the push-button type. Conduit-Systems. As weather-proof or rubber-covered wire cannot be run in brick walls or floors of brick, terra-cotta, or concrete without some protection other than the covering of the wires, it is necessary in such places to run the wires in tubes or conduits, and in fire-proof buildings all of the lighting-wires are generally run in a system of conduits. Kinds of Conduits. There are two kinds of interior conduits now in com- mon use: (i) Lined Mild-Steel Pipe. The lining consists of a thin coat of enamel which must be impervious to water, sulphuric acid, acetic acid, hydrochloric acid and carbonate-of-soda solutions. For regular conduit systems only mild- steel piping of the same thickness as ordinary gas-piping is approved by the underwriters. The conduit must be continuous from outlet to outlet or junction- boxes or cabinets and must properly enter and be secured to all fittings, and the entire system must be mechanically secured in position. Mild-steel pipe may be galvanized, coated, or enameled on the outside, but it must be enameled on the inside as stated above. Rigid conduit, whether lined or unlined, are installed in the same manner as a good job of gas-fitting, except that for conduits the pipe may be bent to a curve and no elbow can be used having less than sM-\n radius for the inner edge. Wherever branches are taken off, junction- boxes must be provided and every outlet must have an approved outlet-box or plate. The wire drawn into conduits must be of at least No. 14 size, rubber- covered and with double braid. All conduit-systems must be grounded by connecting the steel pipe by a conductor to the gas or water system. 1480 Electric Work for Buildings Part 3 (2) Flexible Armored Conduit. This is made of metal ribbon wound spirally, is generally used in wiring old houses because it is easier to install. Circular LOOM is flexible woven tubing treated with insulating material that makes it hold its shape. This may be used in dry places and for outlets through plastering if it extends back to the nearest porcelain knob holding the wire which the conduit covers. National Electrical Code. The National Board of Fire Underwriters, in conjunction with committees from the American Institute of Architects, and from the national associations of electrical, mechanical and railway engineers, have prepared a code of rules and requirements for the installation of electrical lighting which is the generally recognized standard and with which all interior wiring must comply if it is desired to obtain insurance on the building. This code has also been made a part of the ordinances of most of the larger cities. It is revised every two years, in the odd-numbered years. The National Board of Underwriters also publishes, semi-annually, a supplement to the National Electrical Code which contains a list of all articles that have been examined and approved for use in connection with the code, together with the names of the manufacturers. Articles not included in this list will not be passed by the inspectors. Copies of the code and supplement can be obtained from the nearest Underwriters' Inspection Bureau, or by writing to the Underwriters' Labora- tories, 382 Ohio Street, Chicago, 111. The following requirements apply to almost every installation, and every architect should be conversant with them. Extracts from the National Electrical Code* (i) All wire for concealed work must be of the best approved rubber-covered brands, as shown in List of Fittings. No wire smaller than No. 14 B. & S. gauge to be used. All wire run in conduits must have double-braid covering. (2) Where wires are concealed and run parallel to joists they must be sup- ported on porceMn knobs which hold the wires at least i in from woodwork or surface wired over. Knobs must be securely fastened and must be placed EVERY 4H FT. Where wires are run through joists they must be bushed with porcelain tubes the entire width of joists. All wires must be drawn tight, so as to have all slack removed. (3) In concealed work all wires must be separated from each other by AT least 5 IN. Where wires run down partitions, especially partitions formed by 2 by 4-in studs, the wires must be so supported as to run in the middle of partition. If more than two wires are run down partition between studs, they must be separated by at least 5 in. (4) Where wires pass through floors they must be protected from the floor up to a point 5 ft above the floor with conduit or with boxing. There must always be a space of i in between the wires and the boxing. (5) All joints must be securely soldered and taped. A splice to be approved must be both mechanically and electrically secure without solder, but must be soldered unless made with some form of approved splicing-device. Joints to be properly taped require, where rubber-covered wire is used, first to be taped with rubber tape and then with friction-tape. The insulation of a joint must equal that on the conductors. (6) Where wires enter the building they must be provided with drip-loops. (7) There must be a main cut-out and switch installed in an easily acces- sible place, as near as possible to the point where the wires enter the building. * The numbers here given do not correspond with those in the code, and several of the rules are much abridged. They are intended to give the substance, rather than the exact language. General Suggestions for Electric Work 1481 This will require that cut-out and switch be placed where there is no need of a 1 2 -ft ladder to reach them. (8) Every lighting-circuit of 66o watts must be protected by a cut-out. This will limit the number to twelve i6-candle-power or sixteen 40-watt lights on a two-wire, iio-volt circuit, and to thirty-two 40-watt or twenty i6-candle- power lights on a three- wire, 2 20- volt circuit. By special permission, where No. 14 wire is carried directly to keyless sockets, and where the location of the sockets is such as to render unlikely the attachment of flexible cords thereto, the circuits may be so arranged that not more than i 320 watts (or 32 sockets) may be de- pendent upon the final cut-out. Sockets are to be considered as requiring not less than 40 watts each. (9) All cut-outs must be placed in an asbestos-lined cabinet. The as- bestos must be at least H in in thickness and securely held in place by shellac and tacks. Lumber of which cabinet is made must be at least % in in thickness. Cabinet must be furnished with snug-fitting door; door to be hung by strong hinges and to be furnished with a suitable catch. (10) Cut-outs to be approved must be of the plug or of the cartridge-type. (11) Enclosed arc-lamps and incandescent lamps must not be placed on same circuit. Arcs must be on separate circuits by themselves. Each arc-light must be protected by an approved cut-out. The cut-outs are to be placed in an as- bestos-lined cabinet. (12) The practice of using fused rosettes will not be approved, except in mills. (13) Where wires run down the side wall they must be protected from me- chanical injury. (14) All outlets must be made to conform to Rule 24, National Electrical Code. (15) Fans in series will not be approved. (16) Runs of lamp-cord will not be approved. Lamp-cord is designed to be used for drops only. Ordinary insulated wire must be run to place desired. (17) Electric heaters must be installed in accordance with Rule 25 a-f, National Electrical Code. General Suggestions for Electric Work* General Principles and Recommendations. In all electric-work con- ductors, however well insulated, should always be treated as bare, to the end that under no conditions, existing or likely to exist, can a grounding or short circuit occur, and so that all leakage from con- ductor to conductor, or between conductor and ground, may be reduced to the minimum. In all wiring special atten- tion must be paid to the mechanical execution of the work. Careful and neat running, connecting, soldering, taping of conductors, and securing and attaching of fittings, are specially conducive to security and efficiency, and will be strongly insisted on. In laying out an installation, except for constant-cur- rent systems, the work should, if possible, be started frora a center of distri- bution, and the switches and cut-outs, controlling and connected with the several branches, be grouped together in a safe and easily accessible place, where they can be readily got at for attention or repairs. The load should be divided as * Preface to the National Electrical Code Fig. 18. Potential Wire Main Fuse Block Outside Wall Main Switch, Fuse-block and Meter Located Near the Point of Entrance of the Service-wires 1482 Electric Work for Buildings Part 3 erenly as possible among the branches, and all complicated and unnecessary wiring avoided. The use of wireways for rendering concealed wiring per- manently accessible is most heartily indorsed and recommended; and this method of accessible concealed construction is advised for general use. Arch- itects are urged, when drawing plans and specifications, to make provision for the channeling and pocketing of buildings for electric-light or power-wires, and in specifications for electric gas-lighting to require a two-wire circuit, whether the building is to be wired for electric lighting or not, so that no part of the gas-fixtures or gas-piping be allowed to be used for the gas-lighting circuit. Fig. 18 shows a common arrangement of main cut-out, switch and meter, to comply with Rule 7, page 1480. The main cut-out and switch should be as near as possible to the outside wall, but the meter may be at some distance from the switch if desirable for any reason. Specifications for Interior Wiring* Specifications for Interior Wiring should provide: (i) That the wiring shall be installed in accordance with the latest rules and requirements of the National Board of Fire Underwriters, the local ordinances, and the rules of the local electric light company, where current is to be taken from the public mains. (2) No electrical device or material of any kind to be used that is not approved by the Underwriters' National Electric Association, and all articles must have the name or trade-mark of the manufacturer and the rating in volts and amperes or other proper units marked where they may readily be observed after the device is installed. Requirements (i) and (2) are sufficient to insure a safe installation. (3) Contractor must obtain a satisfactory certificate of inspection from the city inspector or from the inspector of the local board of fire-underwriters. (4) If the wires are to run in a conduit system it should be so specified. When a conduit system is used, the wires should not be drawn in until all mechan- ical work as far as possible is completed. It is best to wait until after the plastering is dry. All conduit systems must be grounded, (5) Size of Wires. The best method is to specify the size of all wires, no wire to be less than No. 14 B. & S. gauge; but if the architect does not care to do this, the following clause is sufficient, provided he can have confidence that the contractor will comply with it: "All wires must be of such size that the drop in potential at farthest light-outlet shall not exceed 2% under maximum load." (6) Cut-out cabinets and where they are to be placed; also location of main- line cut-out and fuse. For buildings containing not more than forty lights, one distributing point is generally sufficient, although in large houses it is often convenient to have a cut-out cabinet in each story. (7) Number and kind of switches. All outlets should be marked on the plans, and the number of lights indicated by figures 1, 2, 3, 4, etc., as in Fig. 13. See pages 1484 and 1485 for standard symbols. The location of all switches for controlling lights should also be indicated on the plans. Approximate Cost of Wiring for Incandescent Lighting. Approximate estimates of the cost of wiring buildings for electric lighting are usually based on the number of outlets (not lamps). The actual cost will depend upon the num- ber of pounds of wire required, the kind and number of switches, character of cut-oiit cabinets, etc., and the time required to do the work, so that a close * Wiring specifications for buildings having their own generating plant shoxild be pre- pared by an expert. Specifications for Interior Wiring 1483 estimate cannot be made without plans and specifications. Again, wages and prices of material vary to a considerable extent in different parts of the country, so that an estimate that would be about right for one locality would not sufl5ce for another. The following figures,* however, will enable anyone to form an approximate idea of what any proposed wiring-job will cost. Count cost of labor as not more than one-third the cost of the installation. For knob-and-tube work in new houses of less than • seventeen outlets or twenty-five lamps, with no switches except main switch and a rough cut-out box lined with asbestos, allow $1.50 per outlet. For same class of work, from 25 to 100 lamps, allow $1.75 to $2.00 per outlet. The extra labor involved in wiring old buildings will add from 30 to 50% to the above figures. For each switch-loop with a single-pole snap-switch, add from $1.50 to $1.75. For each switch-loop with single-pole push-button switch, add from ^2.25 to $2.50. For each lamp controlled by duplex or three-point switches, add from $5 to $6. For each hardwood cut-out cabinet with door and lock, add from $7 up ac- cording to number of circuits and finish. Iron cut-out cabinets cost from $8.50 up. Ordinary exposed wiring, as in factories, can usually be run for from $1.00 to $1.75 per drop, including rosettes, cord and sockets, the cost depending very largely upon how closely the drops are spaced. Small installations with iron-armored conduit will probably cost from $5 to $6 per outlet. Large installations will cost somewhat less. A private lighting-plant of 200 lamps, wired on the concealed knob-and-tube system, will cost from $1 250 to $1 500, and a similar plant with 600 lamps will cost from $2 500 to $3 000. These prices include engine, dynamo-switchboard, etc., complete, and wiring, but no switches for controlling lamps. The iron-armored conduit-system will add about $2.75 per outlet. None of the above estimates include the cost of fixtures except in the case of exposed wiring. Drop-cord and sockets cost about 90 cts per lamp. Single-lamp fixtures may be purchased from $1.25 upwards; double-lamp fixtures from $2 upwards. Combination-fixtures cost about 25% more than straight electric fixtures. The price of rubber-covered wire varies from $8 to $60 per i 000 ft according to size, and of weather-proof wire from 16 cts to 25 cts per pound. * These are pre-war prices and the data are retained for purposes of comparison of relative values. 1484 Electric Work for Buildings Part 3 I* .21 . Standard Wiring-Symbols Adopted by the National Contractors' Association and the American Institute of Architects Copyrighted VtV Ceiling-outlet; electric only. Numeral in center indicates number of y~^ standard i6-c.p. incandescent lamps.* y%(.\_ Ceiling-outlet; combination. % indicates 4-i6c.p. standard ^^ \m\% incandescent lamps and 2 gas-burners. If gas only. 59^ ^ Yl^ Bracket-outlet; electric only. Numeral in center indicates W)^^^ number of standard i6-c.p. incandescent lamps. ^)^^4. Bracket-outlet; combination. \ indicates 4-16 c.p. stand- ^T/ms^ ard incandescent lamps and 2 gas burners. If gas only. Wall or baseboard receptacle-outlet. Numeral in center indi- cates number of standard i6-c.p. incandescent lamps. Floor-outlet. Numeral in center indicates number of Standard i6-c.p. incandescent lamps. Outlet for outdoor standard or pedestal, electric only. Numeral indicates number of standard i6-c.p. incandescent lamps. Outlet for outdoor standard or pedestal; combination. % indicates 6-16 c.p. standard incandescent lamps; 6 gas-burners. Drop-cord outlet. One-lamp outlet, for lamp- receptacle. Arc -lamp outlet. Special outlet for lighting, heating specifications. Ceiling-fan outlet. S. P. switch-outlet. D.P. switch-outlets. 3-way switch-outlet. 4-way switch-outlet. Automatic door switch -outlet. Electrolier switch-outlet. Meter-outlet. and power-current, as described in Show as many symbols as there are switches. Or in case of a very large group of switches, indicate number of switches by a Roman numeral, thus; S'XII, meaning 12 single-pole switches. Describe type of switch in speci- fications, that is, Hush or sur- face, push-button or snap. ^^^^H Distribution-panel. ^^^^P Junction or pull-boK. J(^h)/ Motor-outlet. Numeral in center indicates horse-power. L^>-- 3? -- ~__ — ■ -~ .i~' --?; --": ---^ -w- ^2. se= r^-£- ^^ i^ Wi m :m &^ 10 20 30 40 50 CO 70 80 90 100 110 120 130 110150 120 180 240 300 360 420 640 720 900 1080 1200 Total absorbing material Fig. 3. Curves Entered as Parts of their Corresponding Rectangular Hyperbolas. Three Scales are Employed for the Volumes, by Groups, 1-7, 8-1 1, and 12 Architectural Acoustics 1491 12 150 450 300 '11 / i^ / 9000 10800 12C00 aflOO r/ ^ X 1 / » ~~ ^60 / 1200 1800 2400 3000 3000 4200 ^ n^/1 : /J '3 600 800 1000 Volumes of rooms C 74096, but included only the C notes, seven notes in all. Moreover, bearing in mind the experiences of the previous summer, it was recognized that even seven notes would come dangerously near overtaxing the patience of the audience. Inasmuch as the COEFFICIENT OF AB- SORPTION for C4512 hac^ already been determined six years before, in the in- vestigations mentioned, the coefficient for this note was not redetermined. The experiment was therefore carried out for the lower three and the upper three notes of the seven. The audience, on the night of this experiment, was much larger than that which came the previous summer, the pj^ 4 The Parameters ;&, Plotted Against the Volumes night was a more com- ^^f the Rooms, Showing the Two Proportional fortable one, and it was possible to close the windows during the experiment. The conditions were thus fairly satisfactory. In order to get as much data as possible, and in as short a time, there were nine observers stationed at different points in the room. These observers, whose kindness and skill it is a pleasure to acknowledge, had pre pared themselves, by previous practice, for this one experiment. The results of the experiment are shown on the lower curve in Fig. 5. This curve gives the coefficient OF ABSORPTION PER PERSON. It is tO be observed that one of the points falls clearly ofif the smooth curve drawn through the other points. The observations on which this point is based were, however, much disturbed by a street-car passing not far from the building, and the departure of this observation from the curve does not indi- cate a real departure in the coefficient, nor should it cast much doubt on the rest of the work, in view of the circumstances under which it was secured. Counteracting the, perhaps, bad impression which this point may give, it is considerable satisfaction to note how accurately the point for C4512, determined six years before by a different set of observers, falls on the smooth curve Fig. 5. Absorbing Power of an Audi- through the remaining points. The upper ence for Different Notes curve represents the absorbing power of an audience per square meter, as ordinarily seated. The vertical ordinates are expressed in terms of total absorption by a square meter of surface. For the upper curve the ordinates are thus the ordinary coefficients of absorption. The several notes are at octave-intervals 9 -^ ,8 -/ V bp 3 —^ 2 J- 1 C« 1492 Architectural Acoustics Part 3 as follows: C164, C2128, C3 (middle C) 256, C4512, €51024, C6^04$, C74096. In the audience on which these observations were taken there were 77 women and 105 men. The courtesy of the audience in remaining for the experiment and the really remarkable silence which they maintained are gratefully acknowledged. Absorption of Sound by Wooden Sheathing. • The next experiment waS on the determination of the absorption of sound by wooden sheathing. It is not an easy matter to find conditions suitable for this experiment. The room in which the absorption by wooden sheathing was determined in the earlier exper- iments was not available for these. It was available then only because the building was new and empty. When these more elaborate experiments were under way the room became occupied, and in a manner that did not admit of its being cleared. Quite a little searching In the neighborhood of Boston failed to dis- cover an entirely suitable room. The best one available adjoined a night-lunch room. The night-lunch was bought out for a couple of nights, and the experiment was tried. The work of both nights was much disturbed. The trafBc past the building did not stop until nearly two o'clock, and began again at four. The interest of those passing on foot through- out the night, and the necessity of repeated explanations to the police, greatly inter- fered with the work. This detailed state- ment of the conditions under which the experiment was tried is made by way of explanation of the irregularity of the observations recorded on the curve, and of the failure to carry this particular line of work further. On the first night seven points were obtained for the seven notes C164 to C74096. The reduction of these results on the following day showed variations indicative of maxima and minima, which, to be accurately located, would require the determination of inter- mediate points. In the experiment on the following ni:;ht, points were deter- mined for the E and G notes in each Other points would have been determitied, .12 .11 •^ "^, J / •\ V / .10 .09 .08 .07 .06 ,05 .04 .03 .02 .01 / \ / / \ I J / / v.^ / -2 C3 C, C," c, c, Absorbing Power of Wooden Sheathing octave between C212S and CC2048. but time did not permit. It is obvious that the intermediate points in the loWer and in the higher octave were desirable, but no pipes were to be had on such short notice for this part of the range, and in their absence the data could ftot be obtained. In the diagram, Fig. ^6, the points lying on the vertical lines were determined the first night. The pv)ints lying between the vertical lines were determined the second night. The shea thin-? of the room is of North Carolina pine, 2 centimeters thick. The absorption is here due almost wholly to yielding of the sheathing as a whole. It is not possible now to learn as much in regard to the framing and arrangement of the studding in the particular room tested as is desirable. The accuracy with which these points fall on a smooth curve Is, perhaps, all that could be expected in view of the difficulty under which the ob- Architectural Acoustics 1493 servations were conducted and the limited time available. One point in par- ticular falls far off from this curve, the point for C3256, by an amount which is, to say the least, serious, and which can be justified only by the conditions under which the work was done. The general trend of the curve seems, how- ever, established beyond reasonable doubt. It is interesting to note that there is one point of maximum absorption, which is due to resonance between the walls and the sound, and that this point of maximum absorption lies in the lower part, though not in the lowest part, of the range of pitch tested. It would have been interesting to determine, had the time and facilities permitted, the shape of the curve beyond C74096, and to see if it rises indefinitely, or shows, as is far more likely, a succession of maxima. Absorption of Sound by Cushions. The experiment was then directed to the determination of the absorption of sound by cushions, and for this purpose return was made to the constant-temper- ature room. Working in the manner indicated in the earlier papers for sub- stances which could be carried in and out of a room, the curves represented in Fig. 7 were obtained. Curve i shows the ABSORPTION-COEFFICIENT for the Sanders Theater cushions, with which the whole investigation was begun ten years ago (1904). These cushions were of a partic- ularly open grade of packing, a sort of wiry grass or vegetable fiber. They were covered with canvas ticking, and that, in turn, with a very thin, cloth covering. Curve 2 is for cushions borrowed from the Phillips Brooks House. They were of a high grade, filled with long, curly hair, and covered with canvas ticking, which was, in turn, covered by a long-nap plush. Curve 3 is for the cushion of Appleton Chapel, hair-covered with a leatherette, and showing a sharper maximum and a more rapid diminution in absorption for the higher frequencies, as would be ex- pected under such conditions. Curve 4 is probably the most interesting, because for more standard commercial con- ditions ordinarily used in churches. This curve is for the elastic-felt cushions of commerce, of elastic cotton covered with ticking and short-nap plush. The absorbing power is per square meter of surface. It is to be observed that all four curves fall off for the higher frequencies, all show a maximum located within an octave, and three of the curves show a curious hump -in the second octave. This break in the curve is a genuine phenomenon, as it was tested time after time. It is perhaps due to a secondary resonance, and it is to be observed that it is the more pronounced in those curves that have the sharper resonance in their principal maxima. Effects of Interference of Sound- Waves. In both articulate speech and in music the source of sound is rapidly and, in general, abruptly changing in pitch, quality and loudness. In music one pitch is held during the length of a note. In articulate speech the unit or element of constancy is the syllable. Indeed, in speech it is even less than the length of a syllable, for the open- vowel. .9 / \ .8 I \ ^ V \ .6 T / 7 \ N ^\ .5 .4 .3 / '1/ ^ \ \ V 7 \ \ /^ r >, \ \ ^6 Fig. 7. Absorbing Power of Cushions 1494 Architectural Acoustics Part 3 sound which forms the body of a syllable usually has a consonantal opening and closing. During the constancy of an element, either of music or of speech, a train of sound-waves spreads spherically from the source, just as a train of cir- cular waves spreads outward from a rocking boat on the surface of still water Different portions of this train of spherical waves strike different surfaces of the auditorium and are reflected. After such reflection they begin to cross each other's paths. If their paths are so different in length that one train of waves has entirely passed before the other arrives at a particular point, the only phenomenon at that point is prolongation of the sound. If the space between the two trains of waves is sufficiently great, the efifect will be that of an echo. If there are a number of such trains of waves thus widely spaced, the effect will be that of multiple echoes. On the other hand, if two trains of waves have traveled so nearly equal paths that they overlap, they will, dependent on the difference in length of the paths which they have traveled, either reinforce or mutually destroy each other. Just as two equal trains of water-waves crossing each other may entirely neutralize each other if the crest of one and the trough of the other arrive together, so two sounds, coming from the same source, in crossing each other may produce silence. This phenomenon is called interfer- ence, and is a common phenomenon in all types of wave-motion. Of course, this phenomenon has its complement. If the two trains of water-waves so cross that the crest of one coincides with the crest of the other and trough with trough, the effects will be added together. If the two sound-waves are similarly retarded, the one on the other, their effects will also be added. If the two trains of waves are equal in intensity, the combined intensity will be quadruple that of either of the trains separately, as above explained, or zero, depending on their relative retardation. The effect of this phenomenon is to produce regions in an audito- rium of LOUDNESS and regions of comparative or even complete silence. It is a partial explanation of the so-called deaf regions in an auditorium. Distribution of Intensity of Sound. It is not difficult to observe this phenomenon directly. It is difficult, however, to measure and record the phe- nomenon in such a manner as to permit of an accurate chart of the result. With- out going into the details of the method employed, the result of these measure- ments for a room very similar to the Congregational Church in Naugatuck, Conn., is shown in the accompanying chart. The room experimented in was a simple, rectangular room with plain side walls and ends and with a barrel or cylindrical ceiling with the center of curvature at the floor-level. The result is clearly represented in Fig. 8, in which. the intensity of the sound has been indicated by contour-lines in the manner employed in the drawing of the geo- detic survey-maps. The phenomenon indicated in these diagrams was not ephemeral, but was constant so long as the source of sound continued, and re- peated itself with almost perfect accuracy day after day. Nor was the phenom- enon one which could be observed merely instrumentally. To an observer moving about in the room it was quite as striking a phenomenon as the dia- gram suggests. At the points in the room indicated as high maxima of inten- sity in the diagram the sound was so loud as to be disagreeable, at other points so low as to be scarcely audible. It should be added that this distribution of intensity is with the source of sound at the center of the room at tha head-level. Had the source of sound been at one end and on the axis of the cylindrical ceiling, the distribution of intensity would still have been bilaterally symmetrical, but not symmetrical about the transverse axis. Interference-Systems and Reverberation. When a source of sound is main- tained constant for a sufficiently long time, a few seconds will ordinarily sufficej the sound becomes steady at every point in the room. The distribution of the- Architectural Acoustics 1495 intensity of sound under these conditions is called the interference-system, for that particular note, of the room or space in question. If the source of sound is suddenly stopped, it requires some time for the sound in the room to be ab- sorbed. This prolongation of sound after the source has ceased is called rever- beration. If the source of sound, instead of being maintained, is short and sharp, it travels as a discrete wave or group of waves about the room, reflected Distribution of Intensity of Sound from wall to wall, producing echoes. In the Greek theater there was ordinarily but one echo, "doubling the case-ending, " while in the modern auditorium there are many, generally arriving at a less interval of time after the direct sound, and therefore less distinguishable, but stronger and therefore more disturbing. Photographing Air-Disturbances. The formation and the propagation of ECHOES may be admirably stuiiied by an ailaptation of the so-called schlieren- 1493 Architectural Acoustics Part 3 Fig. 9. Photograph of Sound-wave. Vertical Section Fig. 10. Photograph of Sound-wave, Vertical Section Architectural Acoustics 1497 Fig. 11. Photograph of Sound-wave and Echoes. Vertical Section Fig. 12. Photograph of Sound-wave and Echoes. Vertical Section 1498 Architectural Acoustics Part 3 METHODE device for photographing air-disturbances. It is suflScient here to say that the adaptation of this method to the problem in hand consists in the con- struction of a MODEL in proper scale, of the auditorium to be studied and an inves- Fig. 13. Photograph of Sound-wave and Echoes. Horizontal Section 'ligation of the propagation through it of a proportionally scaled sound-wave. To examine the formation of echoes in a vertical section, the sides of a model are taken oflf and, as the sound is passing through it, it is illuminated instantaneously Fig. 14. Photograph of Sound-wave and Echoes. Horizontal Section by the light from a very fine and somewhat distant electric spark. In the accom- panying illustrations, reduced from the photographs, the silhouettes show parts of the shadows cast by the model, and all within are direct nhotographs of the actual Architectural Acoustics , 1499 sound-wave and its echoes. Figs. 9 to 12 show the sound and its echoes at different stages in their propagation through the room, the particular part of the auditorium under investigation being the New Theater in New York City. It Fig. 15. Photograph of Sound-wave and Echoes. Horizontal Section is not difificult to identify the master-wave and the various echoes which it generates, nor, knowing the velocity of sound, to compute the interval at which the echo is heard. To show the generation of echoes and their propagation in Fig. 18. Photograph of Sound-wave and Echoes. Horizontal Section a horizontal plane, the ceiling and floor of the model are removed and the photo- graph taken in a vertical direction. The photographs shown in Figs. 13 to 16 show the echoes produced in the horizontal plane passing through the marble parapet in front of the box. 1500 Specific Gravity Part 3 Solution of Problems Possible in Advance of Construction. While these several factors, reverberation, interference and echo, in an audi- torium at all comphcated are themselves complicated, nevertheless they are capable of an exact solution, or, at least, of a solution as accurate as are the architect's plans in actual construction; and it is entirely possible to calculate in advance of construction whether or not an auditorium will be good, and, if not, to determine the factors contributing to its poor acoustics and a method for its correction. SPECIFIC GRAVITY The Specific Gravity of a substance is the number which expresses the ratio that the weight of a given volume of the substance bears to the weight of the same volume of distilled water at a temperature of 62° F.; or, the specific gravity of a body is equal to its weight divided by the weight of an equal volume of water. The specific gravity of a substance, multiplied by the weight of a cubic foot of water, will give the weight of a cubic foot of the given substance. The weight of a cubic foot of water, at 62° F. and at the sea-level, is about 62.355 lb.* The specific gravity of a solid substance may be determined by first weighing a por- tion of it in air and then in water and dividing the weight in air by the loss of the weight in water; the quotient is the specific gravity required. Example. A piece of granite weighs 5.32 lb in air; when immersed in water it weighs 3.32 lb. Solution. Weight in air (5.32 lb) divided by loss of weight in water (2 lb) =* 2.66, the specific gravity. 2.66 X 62.355 lb = 165.84 lb = weight per cubic foot Note, i cu ft = 7.48 gal. * The textbooks differ slightly in regard to this value. Specific Gravity 1501 Specific Gravities and Weights per Cubic Foot of Various Substances* The basis for specific gravities is pure water at 62° F., barometer 30 in. Weight of i cu ft of water, 62.355 lb Agate, 2. 5 to 2 . 8 Air, atmospheric at 60° F., under pressure of one atmos- phere, or 14.7 lb per sq in, weight His the weight of water Alabaster, carbonate 2 .61 to 2 . 76 Alcohol, absolute, at 32° F Alcohol, 50 per cent Alcohol, 95 per cent Alcohol, commercial Alder, dry j 0.42 to i.oi Alum Aluminum, hammered Aluminum, drawn Aluminum, sheet Aluminum, pure Aluminum, cast Amalgam 13.7 to 14. i Amber Ambergris Ammonia, 60° F Antimony, cast Antimony, native Apple-wood, dry f 0.66 to i . 25 Arsenic 5-7 to 5 • 8 Asbestos 2.1 to 3 • o Asbestos sheathing-paper Ash, American white, dry t Ashes of soft coal, solidly packed Asphalt, for street-paving Asphaltum i.ii to 1.23 Ballast, brick, gravel Bamboo, dry f Barium Bary tes Basalt or trap-rock, average Jersey City, N. J Duluth, Minn Staten Island, N. Y Beech, dryf 06. 5 to 1. 12 Beeswax Benzine Beer. Birch, dry t 0-52 to 1.08 Bismuth, cast 9-76 to 9.90 Blood, at 32° F Bone 1.8 to 2 . o Borax 17 to 1.8 Boxwood, French, dry t Average specific gravity. Water = i 2.6 0.794 0-934 0.815 0.833 0.55 1.72 2.75 2.68 2.67 2.67 2.56 13.92 1.08 0.87 0.894 6.70 6.67 0.75 5.73 2.81 1.20 0.61 0.70 1.60 1.15 1.79 0.36 3.88 4.45 2.96 3-00 2.9s 2.86 0.74 0.95 0.69 1.04 0.65 9.82 1.06 1.90 1.75 1-33 * The values given in this table for specific gravities and for weights per cubic foot are AVERAGE values. In the computations and compilations of these tables the Editor is greatly indebted to Mr. T, Z. Talley for valuable assistance. t The word "dry" in this connection indicates that the wood contains not more tkan 15% of moisture, Green timbers usually weigh from one-fifth to nearly one-half more than dry; ordinary building-timbers, tolerably seasoned, one-sixth more. 1502 Specific Gravity Part Specific Gravities and Weights per Cubic Foot of Various Substance^ * (Continued) The basis for specific gravities is pure ift^ater at 62° F., barometer 30 in. Weight of i cu ft of water, 62.355 ib Boxwood, Dutch, dry f Boxwood, Brazilian, dry f Brass (copper and zinc), cast 7.8 to 9. Brass, rolled Brass, sheet Brass, wire Bricks, building Bricks, common . Bricks, light, inferior . Bricks, lime-sand Bricks, Magnesia • Bricks, pressed Bricks, pressed, hard Bricks, soft Bricks, fire Bricks, paving * Brickwork, pressed brick, fine joints Brickwork, medium quality Brickwork, coarse, inferior, soft Brickwork, at 125 lb per cu ft, i cu yd equals 1.507 tons and 17.92 cu ft equal i ton Bromine Bronze, coin Bronze, gun-metal Bronze, ordinary , Bronze, aluminum Butter Butternut-tree, dry t Cadmium 8 . 6 to 8 . 7 Calcite 2 . 6 to 2 . 8 Calcium Camphor, dry Caoutchouc (India Rubber) Carbon disulphide Castor-oil Cedar, red and white, dry t Cement, Natural (Rosendale) , loose Cement, Portland , loose Cement, Natural, solid Cement, Portland, solid Chalk Champagne Charcoal of pines and oaks , Cherry, dry t Chestnut, dry f Chromium Cider Average specific gravity. Water = i I 035 8.45 8.56 8.24 8.69 1.922 1.442 2.163 2.643 2.163 2.403 1.602 2.403 2.24 2.00 1.60 319 8.66 8.60 8.40 7.70 0.86 0.38 8.65 2.70 1.58 0.99 0.93 1.29 0.96 0.45 1.04 1-35 2.9s 315 2.35 0.99 0.66 0.63 500 1.02 * The values given in this table for specific gravities and for weights per cubic foot are AVERAGE values. t The word " dry " in this connection indicates that the wood contains not more than 15% of moisture. Green timbers usually weigh from one-fifth to nearly one-half more than dry; ordinary building-timbers, tolerably seasoned, one-sbcth more. Specific Gravity 1503 Specific Gravities and Weights per Cubic Foot of Various Substances ♦ (Continued) The basis for specific gravities is pure water at 62° P., barometer 30 in. Weight of i cu ft of water, 62.355 lb Cinnabar Clay, potters', dry 1.8 to 2.1 Clay, dry, in lump, loose Coal, anthracite, 1.3 to 1.84; of Penn., 1.3 to 1.7 Coal, anthracite, broken, of any size, loose, average Coal, anthracite, broken, moderately shaken Coal, anthracite, broken, heaped bushel, loose, 77 to 83 lb Coal, anthracite, broken, a ton loose occupies 40 to 43 cu ft Average specific gravity. Water = i Coal, bituminous, solid, i . 2 to i . 5 Coal, bituminous, solid, Cambria Co., Pa., 1.27 to 1.34. Coal, bituminous, broken, of any size, loose Coal, bituminous, moderately shaken Coal, bitumirious, a heaped bushel, loose, 70 to 78 Coal, bituminous, i ton occupies 43 to 48 cu ft Coke, loose, good quality Coke, loose, a heaped bushel, 35 to 42 lb Coke, loose, i ton occupies 80 to 97 cu ft Concrete, stone 130 to 150 Concrete, cinder 100 to no Copper, hammered 8.8 to 9.0 Copper, rolled 8 . 9 to 9 . o Copper, drawn wire 8.8 to 9.0 Copper, sheet Copper, cast , 8. 6 to 8.9 Copper, melted Cork, dry Corundum, pure 3.92 to 4.01 Creosote oil i . 04 to i . 10 Cypress, American, dry f Dogwood, dry f Douglas fir, dry f Earth, common loam, perfectly dry, loose Earth, common loam, perfectly dry, shaken Earth, common loam, perfectly dry, rammed Earth, common loam, slightly moist, loose Earth, common loam, more moist, loose Earth, common loam, more moist, shaken Earth, common loam, more moist, packed Earth, common loam, as soft, flowing mud Earth, common loam, as soft, flowing mud, well-pressed Ebony Elder-pith . . Elm, dryf. Elm, rock. . Emerald . . . 8.12 1.90 1. 01 I. SO 2.33 1.68 8.9s 8.9s 8.89 8.72 8.82 8.23 0.24 3.96 1.07 0.55 -0.7s o.Si 1.22 1.09 0.076 0.56 0.80 2.70 * The values given in this table for specific gravities and for weights per cubic foot are AVERAGE values. t The word "dry" in this connection indicates that the wood contains not more than 15% of moisture. Green timbers usually weigh from one-fifth to nearly one-half more than dry; ordinary building-timbers, tolerably seasoned, one-sixth more. 1504 Specific Gravity Specific Gravities and Weights per Cubic Foot of Various Substances *1 (Continued) The basis for specific gravities is pure water at 62° F., barometer 30 in. Weight of i cu ft of water, 62.355 lb Emery Fats Feldspar Filbert-tree, dry f Fir, Douglas (see Douglas Fir) . Flint... Gamboge Garnet 3-4 to 4-3 Glass, optical Glass, flint Glass, white '. '. Glass, plate Glass, green Glass, floor, heavy Glass, window Gneiss (see Granites). Gold, pure Gold, hammered, nati>:e Gold, cast Granites and gneiss, Connecticut, Greenwich California, Penryn (hornblende) Nev/ York Maryland, Port Deposit Massachusetts, Quincy (hornblende) Wisconsin, Athelstane Georgia, Lithornia and Stone Mountain Minnesota California, Rocklin (muscovite) Rhode Island, Westerley Connecticut, New London New Hampshire, Keene Maine, Hallowell New Hampshire, Concord Vermont, Barre Wisconsin, Montello Colorado, Georgetown (biotite) Maine, Fox Island Massachusetts, Rockport Graphite Gravel, dry -. Gravel, wet Greenstone, trap 2.8 to 3.2 Grindstone Gum arabic Gun-metal (see Bronze). Gunpowder (granular) , Gutta-percha Average Average specific weight of gravity. icuft Water = i lb 4.00 249. 5 0.93 58.0 2.57 160.2 0.60 37-5 2.63 164.0 1.20 74.8 3.85 240.1 3.45 215.0 3.00 187.0 2.89 180.2 2.80 174-6 2.67 166.5 2.53 158.0 2.50 156.0 19.50 I 215.9 19.40 I 209.7 19.258 I 200.8 2.84 177.3 2.77 172.9 2.74 171. 2.72 169.6 2.70 168.5 2.70 168.5^ 2.69 167. 9fl 2.68 167.3'" 2.68 167.3 2.67 166.7 2.66 166.0 2.66 166.0 2.6s 165.2,^ 2.65 165.^ 2.65 165. 2:S 2.64 164.6 2.63 164.0 2.63 164.0 2.61 162.7 2.26 140.0 1.79 112. 2.00 125.0 3.00 187.0 2.14 133. s 1.32 82.5 I. GO 62.4 0.98 61.0 * The values given in this table for specific gravities and for weights per cubic foot are AVERAGE values. t The word " dry " in this connection indicates that the wood contains not more than 15% of moisture. Green timbers usually weigh from one-fifth to nearly one-half morf , than 4ry; ordinary building-timbers, tolerably seasoned, one-sixth more, jfll specific Gravity 1505 Specific Gravities and Weights per Cubic Foot of Various Substances * (Continued) The basis for specific gravities is pure water at 62° F., barometer 30 in. Weight of i cu ft of water 62.355 lb Average specific gravity. Water = i Average weight of I cu ft lb Gypsum, natural rock, free from surface-water Gypsum, crushed rock, not calcined, all passing i-in ring Gypsum, ground rock, 90% passing 100 mesh, dried, not calcined Gypsum, Plaster-of-Paris, stucco, stiff mortar, set and dried out Gypsum, Plaster-of -Paris, stucco, ground rock, 90% passing 100 mesh, calcined, loose well shaken down or in bins ♦. . . . Hackmatack (see Larch). Hay, loose, in stacks, about 512 cu ft per ton Hemlock, dry t Hickory, pignut, dry f . . . . '. Hickory, mocker-nut, dry f • • •• Hickory, shagbark, dry t Hickory, nutmeg, dry f Hickory, pecan, dry f Hickory, bitternut, dry f Hickory water, dry f Holly Honey Horn Hornblende 3.0 to 3.5 Ice 88 to .914- Iodine Iridium, pure Iron, cast 6.9 to 74 Iron, gray, foundry, cold Iron, gray, foundry, molten Iron, wrought Ivory Juniper-wood Kaolin Lava ■ Larch, or hackmatack, dry + • Lard Lead, commercial, cast Lead, commercial, sheet Lead, pure Lead, molten Lignum-vitjr, dry f . . . o. 65 to i . 33 Limestone, Illinois Indiana Kentucky Michigan Minnesota Missouri New York Average of limestones Linseed-oil 2.30 1-52 1-25 1.22 0.96 1 .11 0.42 0.89 0.85 0.81 0.78 0.78 0.77 0.73 0.76 1 •45 1.69 3-25 0.89 4-94 22 . 12 7.2 7. 21 6.94 7.70 1.88 0.57 2. 20 2 .65 0.5s o . 9 1 II .36 II .40 II .42 10.40 0.99 2.57 2.50 2.68s 2.44 2.655 2.32 2.71 2.60 0.935 143 -o 950 78.0 77.0* 60.0 70.0 26.2 SS.6 53.1 50.6 45 -o 47-4 90.5 105.5 202.7 56.0 308.0 I 3790 448.9 450.0 433 -o 480.0 117. 35.6 137-2 165.2 34-3 58.7 708.0 710.8 713.0 648.8 41 to 84 160.4 155-8 167.4 152 .1 165-6 144-8 169.0 162 . 1 58.3 * The values given in this table for specific gravities and for weights per cubic foot are VERAGE values. fThe word "dry" in this connection indicates that the wood contains not more than .5% of moisture. Green timbers usually weigh from one-fifth to nearly one-half mo'"' han dry; ordinary builditig-timbers, tolerably seasoned, one-sixth more. 1506 Specific Gravity Specific Gravities and Weights per Cubic Foot o| Various Substances * (Continued) The basis for specific gravities is pure water at 62° F., barometer 30 in. Weight of i cu ft of water, 62.355 lb Locust, dry f . • , Magnesite , Magnesium, pure Mahogany 0.56 to 1.06 Manganese, pure Manganese, ore, red Manganese, ore, black Marble, average 2.6 to 164.4 domestic. New York California Georgia Vermont, Dorset foreign, Parian African Carrara Biscayan British French Marl Masonry, brickwork (see Brickwork) Masonry, concrete, stone Masonry, concrete, cinder Masonry, granite, dressed Masonry, granite, rubble in cement Masonry, Hmestone, dressed Masonry, marble, dressed for buildings. Masonry, sandstone Mastic, gum resin Mercury, at 32° F Mica , Milk, at 32° F Molybdenum, pure Mortar, lime Mortar, cement Mud, dry, close Mud, wet, moderately pressed Mud, wet, fluid Mulberry-tree, dry f Naptha-oil, wood, at 32° F Nickel .2.75 to 3.1 Oak, live, dry f 0.88 to 1.02 Oak, white, dryf 0.66 to 0.88 Oak, red and black, dry f Ochre Olive-oil, 32° F Average specific gravity. Water = i 0.71 3.0 1.72 o.8i 8.00 4.01 3.45 2.6 2.83 2.75 2.73 2.66 2.84 2.80 2.72 2.71 2.71 2.6s 2.10 2.33 1.68 2.64 2.48 2.60 2.72" 2.41 0.8s 13.62 2.93 1.032 8.63 1.65 1.68 0.75 0.85 8.56 0.95 0.77 350 0.916 * The values given in this table for specific gravities and for weights per cubic foot are AVERAGE values. t The word " dry " in this connection indicates that the wood contains not more than 15% of moisture. Green timbers usually weigh from one-fifth to nearly one-half more than dry; ordinary building-timbers, tolerably seasoned, one-sixth more. Specific Gravity 1507 Specific Gravities and Weights per Cubic Foot of Various Substances "*= (Continued) The basis for specific gravities is pure water at 62° F., barometer 30 in. Weight of i cu ft of water, 62.355 lb Oolitic stofies . , Opal. Opium Orange-tree . Palladium . . . Paper . ParafHn Pear-tree wood, dry f Peat, pressed Petroleum, oil Pine, Cuban, dry t Pine, yellow, long-leaf, dry. . . Pine, loblolly, dry Pine, yellow, short-leaf, dry. Pine, red, Norway, dry Pine, spruce, dry Pine, white, dry Pitch Plaster of Paris (see Gypsum) . Platinum Plumbago Poplar, dry f Porcelain, china Porphyry Potash Potassium Pumice-stone Quartz Quince-tree wood, dry f Red lead Resin Rock-crystal . Rosewood Rosin Rubber, India , Ruby Salt, coarse, per struck bushel, Syracuse, N. Y., 56 lb. . Saltpetre Sand, of pure quartz, perfectly dry and loose Sand, of pure quartz, voids full of water Sand, of pure quartz, very large and small grains, dry. . , Sandstone, average Massachusetts, Longmeadow Connecticut, Portland New York 2.40 to 2.70 New Jersey, Belleville Pennsylvania Virginia, BrivStow Average specific gravity. Water = i a. 25 2. IS 1-34 0.71 11,80 0.9s 0.88 0.67 0.72 0.878 0.63 0.61 0.53 o.Sl 0.50 0.44 0.38 1.08 2.25 21.50 2.10 0.47 2.30 2.76 2.26 0.86s 0.92 2.65 0.71 8.94 1.09 2.60 0.73 1. 10 0.93 390 2.02 2.44 2.49 2.50 2.60 2.40 2.63 2.60 ' The values given in this table for specific gravities and for weights per cubic foot are AVERAGE values. t The word " dry " in this connection indicates that the wood contains not more than 15% of moisture. Green timbers usually weigh from one-fifth to nearly one-half more than dry; ordinary building-timbers, tolerably seasoned, one-sixth more. 1508 Specific Gravity Part Specific Gravities and Weights per Cubic Foot of Various Substances* (Continued) The basis for specific gravities is pure water at 62" F., barometer 30 in. Weight of i cu ft of water, 62.355 lb Sandstone, (continued) Ohio Michigan Wisconsin Minnesota .Colorado California, Angel Island. Shales, red or black Silica Silver Slate Snow, freshly fallen Snow, moistened, compacted by rain. Soapstone Sodium Spelter Spirit, rectified • Spruce Steel, cast Steel, wrought Sugar. Sycamore, dry. Talc Tallow Tamarack Tar Teak Tellurium Tiles, solid Tin, rolled Tin, cast Tin, molten Trap (see Basalt). Tungsten Turpentine Type-metal, cast. . Uranium Urine Vinegar Walnut, black, dry Water, pure rain, distilled, at 32° F., barometer 30 in Water, pure rain, distilled, at 62° F., barometer 30 in Water, pure rain, distilled, at 212° F., barometer 30 in Water, sea. .• i .026 to i .030 Wax (see Beeswax). Willow Wine Zinc or spelter 6.8 to 7.2 Average specific gravity. Water = i 2.22 2.35 2.22 2.25 2.33 2.73 2.60 2.66 10.50 2.81 2.73 0.978 7.10 0.824 0.40 7.9 7.85 1.60 0.58 2.81 0.94 0.38 1. 00 0.70 6.27 2.20 7.40 7.30 7.02 19.129 0.87 10.45 18.49 1.02 1.08 0.60 1. 00 1.028 0.49 1. 01 7.00 * The values given in this table for specific gravities and for weights per. cubic foot are AVERAGE values. t The word " dry '* in this connection indicates that the wood contains not more than 15% ^f moisture. Green timbers usually weigh from one-fifth to nearly one-half more than dry; ordinary building-timbers, tolerably seasoned, one-sixth more. Wire-Gauges and Metal-Data 1509 WIRE-GAUGES* AND METAL-DATA A Wire-Gauge is a method^of designating the diameter of wires or the thick- ness of sheets of metal by the numbers of a table arranged on a certain fixed basis. There are at the present time several gauges, resulting in great confusion, Table XIII, page 402, gives the diameters of the gauges in common use. The only legal gauge in this country is the United States standard gauge, described on page 1600. It is used by most of the manufacturers of sheet iron and steel and tin plate. The Brown & Sharpe gauge is commonly used for designating size of copper wires (see page 15 10); also for sheet copper and brass. Nearly all copper wire, bare and insulated, is ordered, manufactured, and carried in stock in accordance with this gauge. This might be called the Copper Wire Gauge. The American Steel & Wire Company uses the old Washburn & Moen and Roebhng gauges for ail their steel and iron wire and also for wire nails. The sectional areas for these gauges are given on pages 403 and 15 12, taken from the Roebhng and American Steel & Wire Company's lists. When placing orders for sheets and wire, it is always best to specify the weight per square or linear foot or the thickness or diameter in thousandths of an inch or in circular mils. The gauge for steel wire, used by the J. A. Roebhng's Sons Company, is given on page 403, and the circular-m.il gauge on page i473- The gauge used bj^ this company is the same as the Washburn & Moen gauge, or the American Steel & Wire gauge, except that the diameters in. most cases are given to the nearest mil. This gauge is so generally used for steel wire that it is sometimes called the Steel Wire Gauge or the Market Wire Gauge. The Birmingham Wire gauge is the same as Stubs' Iron-Wire gauge, but entirely different from Stubs' Steel- Wire gauge. Galvanized telegraph and telephone-v/ire, both bare and insu- lated, and galvanized armor-wire are usually designated by this gauge. Its use is not very extensive and is becoming less. The new British Standard gauge is the legal standard for Great Britain and is used there for all kinds of wire. Its use in this country is very limited. It is known, also, as the English Legal standard gauge and the Imperial Wire gauge. * See, also, pages 401, 402, 403, 1469, 1473, 1510, 1512, and i6o«. 1510 Wire-Gauges and Metal-Data Weights in Pounds per Square Foot of Sheets of Wrought Iron, Steel, Copper, * and Brass Thickness by American (Brown & Sharpe) gai^ge • No. of gauge Thickness in inches Iron Steel Copper Brass oooo 0.46 18.40 18.77 20.84 19.69 ooo 0.4096 16.39 16.71 18.56 17-53 oo 0.3648 14-59 14.88 16.53 15.61 o 0.3249 12.99 13.25 14.72 13.90 I 0.2893 11.57 11.80 13 II 12.38 2 0.2576 10.31 10.51 11.67 11.03 3 0.2294 918 9.36 10.39 9.82 4 0.2043 8.17 8.34 9.26 8.74 5 0.1819 7.28 7.42 8.24 7.79 6 0,1620 6.48 6.61 7.34 6.93 7 0.1443 5. 77 5. 89 6.54 6.18 8 0.128S 5. 14 5.24 5.82 5.50 9 0.1144 4.58 4.67 5.18 4.90 10 0.1019 4.08 4.16 4.62 4.36 II 0.0907 . 3.63 3.70 4 II 3.88 12 0.0808 3-23 3-30 3.66 3.46 13 0.0720 2.88 2.94 3.26 3-08 14 0.0641 2.56 2.61 2.90 2.74 15 0.0571 2.28 2.33 2.59 2.44 i6 0.0508 2.03 2.07 2.30 2.18 17 0.0453 1. 81 1. 85 2.05 1-94 18 0.0403 1. 61 1.64 1.83 1.73 19 0.03S9 1.44 1.46 1.63 1.54 20 0.0320 1.28 1.30 1. 45 1.37 21 0.0285 1. 14 1.16 1.29 1.22 22 0.0253 1. 01 1.03 I. IS 1.08 23 0.0226 0.903 0.921 1.02 0.966 24 0.0201 0.804 0.820 0.911 0.860 25 0.0179 0.716 0.730 0.811 0.766 26 0.0159 0.638 0.650 0.722 0.682 27 0.0142 0.568 0.579 0.643 0.608 28 0.0126 0.506 0.516 0.573 0.541 29 0.0113 0.450 0.450 0.510 0.482 30 O.OIOO 0.401 0.403 0.454 0.429 31 0.0089 0.3S7 0.364 0.404 0.382 32 0.0080 0.318 0.324 0.360 0.340 33 0.0071 0.283 0.289 0.321 0.303 34 0.0063 0.252 0.257 0.286 0.270 35 0.0056 0.224 0.229 0.254 0.240 Specific gravity 7.704 480.00 7.85 489.60 8.72 543.6 8.24 513.6 Weight per cubic foot Weight per cubic inch 0.2778 0.2833 0.3146 0.2972 ♦ For other gauges see pages 401, 402, 403, 1469, 1473, 1509, 1512, and 1600, Weights of Metal Sheets and Bars 1511 n xr-i sfO NfO sfO Nr-i ^ V*" N!-< ^90 SfH sf eS^.spO io~s NpO v-* nJO \f 1 N?0 v* Np6 rOMiOTra»QrOQvQOOQOOOOOOOQOOC>v? OOOOOMMMC^roiOt^OiM rovO 00 m -rj-oo '£> ^r ro fO -^VO ro 0000000000000^ I M fO "* 10<0 t^CSO Oi iH ■rt Tf rvj (o CO t-> fOvO ro« O M fO 1000 N t— M 10 C OOOOOMMNroii )OQOOOOOOOOOOC < -^ r^ o ro t^ M ■ ro >0 t^ cy> 00 O ► ioCT>'+oo M Ttr^o looo o o o ooop '" ■ ■ ~~ Sr ri rr J!!? ii** "-^ — " -^ -* ^ .^ O O O M M N CO 'to a>N locTifOt^csoO rooifs r-rocN m ci looo ooooooooooo> H N M fo 00 ^ 'to t^ a. M ro lo I- a» M ro lo r» a> I- ^ 8- 1512 Wire-Gauges and Metal-Data Sizes and Weights of Smooth Steel Wire* As made by the Amefican Steel & Wire Company No. of gauge oooooo ooooo coco ooo CO 5 l6 13 14 IS i6 17 i8 19 23 24 Diameters Fractions of inch ^%2 %2 "h" %2 Me 1/^2 Decimals of inch 0.461S 0. 4375 0-4305 0.40625 03938 0.3750 0.3625 0.34375 0.3310 0.3125 0.306s 0.2830 0.2812s 0.. 2625 0.2500 0.2437 0.2253 0.21875 . 2070 0.1920 0.1875 0.1770 0.1620 0.15625 0.1483 0.1350 0.125 0.1205 0.1055 0.09375 0.0915 0.0800 . 0720 0.0625 0.0540 0.0475 0.0410 0.0348 0.0317 0.03125 0.0286 0.0258 0.0230 Milli- meters 11.72 II. II 10.93 10.32 10.00 9.525 9 2075 8.731 8.407 7.938 7.785 7.188 7.144 6.668 6.350 6.190 5.723 5. 556 5.258 4.877 4.763 4.496 4. 115 3.969 3.767 3.429 3.17s 3061 2.680 2.381 2.324 2.032 1.829 1.58S 1-372 1.207 1. 041 0.8839 0.8052 0.7938 0.7264 0.6553 0.5842 Sectional area, sq in 0.16728 0.15033 0.14556 0.12962 0.12180 0.11045 0.10321 0.092806 0.086049 0.076699 0.073782 0.062902 0.062126 0.0541 19 o . 049087 0.046645 0.039867 0.037583 0.033654 0.028953 0.027612 0.024606 0.020612 0.019175 0.017273 O.OI4ST4 0.012272 o. 01 I 404 0.0087417 0.0069029 0.0065755 0.0050266 0.004071S 0.0030680 0.0022902 0.0017721 0.0013203 0.00095115 o . 00078924 0.00076699 0.00064242 0.00052279 0.00041548 Weight t Pounds per 100 feet 56.81 51.05 49-43 44.02 41.36 37.51 35.05 31-52 29.22 26.05 25.06 21.36 21.10 18.38 16.67 15-84 13-54 12.76 11-43 9-832 9 -.377 8.356 7.000 6.512 5.866 4.861 4.168 3.873 2.969 2.344 2.233 1.707 1.383 1.042 0.7778 0.6018 0.4484 0.3230 0.2680 0.2605 0.2182 0.1775 0.1411 Pounds per mile 2999-0 2696.0 2610.0 2324 -0 2184.0 1980.0 1851 -o 1664.0 1543 o 1375-0 1323 -0 1128.0 1114.0 970.4 880.2 836.4 714-8 673-9 603.4 519-2 495.1 441 -2 369.6 343.8 309.7 256.7 220.0 204.5 156.7 123.8 117.9 90.13 73.01 55-01 41.07 31-77 23.67 17 05 14 15 13 75 11-52 9-37 7-45 * For other gauges, see pages 401, 402, 403, 1469, 1473, 1509, 1510 and 1600. t For iron wire, the values in columns 6 and 7 should be multiplied by 0.98 and for copper wire, by 1.12. Kinds of Wire 1513 Kinds of Wire Manufactured by the American Steel and Wire Company Market-wire, Nos. oooo to i8. Annealed stone-wire or weaving-wire, Nos. i6 to 47. Tinned market- wire, Nos. o to 18. Tinned stone-wire, Nos. 16 to 40. Gun-screw wire, finished with great care as regards roundness and exactness to gauge, Nos. 18 to 50. Machinery-wire, Nos. 00000 to 18. Cast-steel wire, y2-m diameter, down to No. 26. Drill and needle-steel wire, Nos. 12 to 25. The term market-wire applies to the ordinary and most used forms of Bes- semer ANNEALED, BRIGHT, GALVANIZED, TINNED and COPPERED wireS. Galvanizied-Iron-Wire Strand. The diameter, list-price per 100 ft, weight per 100 feet and approximate breaking-load in poimds for this wire is given in Tabic XVI, Chapter XI. 1514 Metal-Data Part Weights and Areas of Square and Round Bars and Circumferences of Round Steel Bars* Weights are for steel, at 489.6 lb per cu ft Thickness or diameter. Weight of D bar I ft long. Weight of bar I ft long, Area of n bar, Area of bar. Circumfer- ence oi bar, in lb lb sq in sq in in M« 0.013 O.OIO . 0039 . 0031 0.1963 5/64 0.021 0.016 0.0061 0.0048 0.2454 H2 0.030 0.023 0.0088 0.0069 0.2945 lU. 0.041 0.032 0.0120 0.0094 0.3436 H 0.053 0.042 0.0156 0.0123 ■ 0.3927 9/64 0.067 0.053 0.0198 0.0155 0.4418 ^A2 0.083 0.065 0.0244 0.0192 0.4909 lj'64 O.IOO 0.079 0.0295 0.0232 0.5400 3/6 0.120 0.094 0.0352 0.0276 0.5890 1^4 0.140 O.IIO 0.0413 0.0324 0.6381 ^^2 0.163 0.128 0.0479 0.0376 0.6872 1%4 0.187 0.147 0.0549 0.0431 0.7363 h' 0.213 0.167 0.0625 0.0491 0.7854 1%4 0.240 0.188 0.0706 0.0554 0.834s %2 0.269 0.2II 0.0791 0.0621 0.8836 1^4 0.300 0.235 0.0881 0.0692 0.9327 Me 0.332 0.261 0.0977 0.0767 0.9817 IH2 0.402 0.316 0.1182 0.0928 1.0799 H 0.478 0.376 0.1406 0.1104 1.1781 1^2 0.561 0.441 0.1650 0.1296 1.2763 TU 0.651 O.5II 0.1914 O.I5C3 1.3744 1^2 0.747 0.587 0.2197 0.1726 1.4726 1/^ 0.850 0.668 0.2500 0.1963 1.5708 15:^2 0.960 0.754 0.2822 0.2217 1.6690 He 1.076 0.845 0.3164 0.2485 I. 7671 1%2 II99 0.941 0.3525 0.2769 1.8653 ^4 1.328 1.043 0.3906 0.3068 1.9635 ii/a 1.607 1.262 0.4727 0.3712 2.1598 M 1-913 1.502 0.5625 0.4418 2.3562 13/6 2.245 1.763 . 6602 0.5185 2.5525 Ti 2.603 2.044 0.7656 0.6013 2.7489 15/6 2.989 2.347 0.8789 0.6903 2.9452 • Adapted from the 191 2 Edition of the Handbook of the Cambria Steel Company, Johnstown, Pa. Weights and Areas of Steel Bars 1515 Weights and Areas of Square and Round Steel Bars * Weights are for steel, at 489.6 lb per cu ft Thick- D Thick- D ness, Weight Weight ness, Weight • \ Vcight in Area, per Area, per in Area, per Area, per sq in foot, lb sq in foot, lb sq in foot, lb sq in foot, lb I 1. 000 3.400 0.785 2.670 3 9.000 30.60 7.069 24.03 Me 1. 129 3.838 0.887 3.014 He 9.379 31-89 7.366 25.04 ' H 1.266 4-303 0.994 3-379 H 9.766 33.20 7.670 26.08 3/i6 1. 410 4.795 1. 108 3-766 Vie 10.16 34.55 7.980 27.13 H 1.563 5.312 1.227 4-173 H 10.56 35.92 8.296 28.20 Vl6 1-723 5 857 l.35i 4.600 Mo 10.97 37.31 8.618 29 30 % 1.891 6.428 1.485 5- 049 H 11.39 38.73 8.946 30.42 Mo 2.066 7.026 1.623 5.518 Mo 11. 82 40.18 9.281 31.56 H 2. 250 7.650 1.767. 6.008 H 12.25 41.65 9.621 32.71 »/l6 2.441 8.301 1. 918 6.520 He. 12.69 43 14 9.968 33 90 H 2.641 8.978 2.074 7.051. H 13.14 44.68 10.32 35.09 1H6 2.848 9.682 2.237 7.604 Hie 13-60 46.24 10.68 36.31 H 3 063 10.41 2.405 8.178 H 14.06 47.82 11.05 37.56 1^6 3.285 II. 17 2.580 8.773 '3/i6 14.54 49.42 11.42 38.81 ^i 3 -516 11.95 2.761 9 388 li 15.02 51. OS 11.79 40.10 1^6 3-754 12.76 2.948 10.02 15/16 15.50 52.71 12.18 41.40 2 4.000 13.60 3.142 10.68 4 16.00 54.40 12.57 42.73 Mo 4-254 14.46 3 341 11.36 i/ie 16.50 56.11 12.96 44.07 }4 4 516 15.35 3.547 12.06 H 17.02 57.85 13.36 45.44 3/16 4.785 16.27 3.758 12.78 •Me 17.54 59.62 13 77 46.83 H 5.063 17.22 3.976 13.52 H 18.06 61.41 14.19 48.24 Me 5.348 18.19 4.200 14.28 Me 18.60 63.23 14.61 49.66 % 5.641 19.18 4.430 15.07 H 19.14 65. oS 15.03 51. II Me 5.941 20.20 4.666 15.86 Mo 19.69 66.95 15-47 52.58 U 6.250 21.25 4.909 16.69 H 20.25 68.85 15.90 54.07 »/l8 6.566 22.33 5.157 17.53 Me 20.82 70.78 16.35 55.59 H 6.891 23.43 5.412 18 40 H 21.39 72.73 16.80 57.12 iHe 7.223 24.56 5.673 19.29 iHe 21.97 74.70 17.26 58.67 3/4 7.563 25 71 5.940 20.20 H 22.56 76.71 17.72 60.25 1^6 7.910 26.90 6.213 21.12 me 23.16 78.74 18.19 61.84 'A 8.266 28.10 6.492 22.07 % • 23.77 80.81 18.67 63.46 15/16 8.629 29.34 6.777 23.04 iMe 24.38 82.89 19 15 65.10 * Adapted from the 19 12 Editioa of the Handbook of the Cambria. Steel Comoany, Johnstown, P^v 1516 Metal-Data Part 3 Weights and Areas of Square and Round Steel Bars ' Weights are for steel, at 489.6 lb per cu ft (Continued) Thick- a Thick- D ness, • Weight Weight ness, Weight \ Veight in Area, per Area, per m Area, per Area, per sq in foot, lb sq in foot, lb sq in foot, lb sq m foot, lb 5 25.00 85.00 19-64 66.76 7 49.00 166.6 38.49 130.9 Me 25.63 87.14 20.13 68.44 M 52.. S6 178.7 41.28 140.4 H 26.27 89.30 20.63 70.14 \'i 56.25 191 3 44.18 150.2 Me 26.91 91.49 21.14 71.86 % 60.06 204.2 47.17 160.3 M 27.56 93.72 21.65 73.60 8 64.00 217.6 50.27 171. Me 28.22 95.96 22.17 75.37 \i 6^.06 231.4 53.46 181. 8 % 28.89 98.23 22.69 77.15 'A 72.25 245.6 56.75 193.0 Me 29.57 100.5 23.22 78.95 M 76.56 260.3 60.13 204.4 \^ 30.25 102.8 23.76 80.77 9 81.00 275.4 63.62 216.3 Me 30.94 105.2 24.30 82.62 M 85.56 290.9 67.20 228. 5 % 31.64 107.6 24.85 84.49 \h. 90.25 306.8 70.88 241.0 iHe 32.35 IIO.O 25.41 86.38 Ml 95.06 323.2 74.66 253.9 'M 3306 112. 4 25.97 88.29 10 100. 340.0 78.54 267.0 iMe 33 79 114. 9 26.54 90.22 H 105. 1 357-2 82.52 280.6 % 34.52 117. 4 27.11 92.17 Vi no. 3 374.9 86.59 294.4 iMe 35.25 "99 27.69 94.14 M 115. 6 392.9 90.76 308.6 6 36.00 122.4 28.27 96.14 II 121. 411. 4 95.03 323.1 % 37.52 127.6 20.47 100.2 \\ 126.6 430.3 99.40 337-9 M 39 06 132.8 30.68 104.3 ¥2 132.3 449-6 103.9 353-1 34 40.64 138.2 31.92 108.5 M* 138. 1 469.4 108.4 368.6 ^^ 42.25 143.6 33.18 112. 8 12 144.0 489.6 113. 1 384.5. H 43.89 149.2 34-47 117. 2 M 45.56 154.9 35.79 121. 7 ^4 47.27 160.8 37.12 126.2 * Adapted from the 19 12 Edition of the Handbook of the Cambria Steel Company, Johnstown, Pa. Weights of Flat Steel Bars Weights in Pounds of Flat Rolled Steel Bars PER LINEAR FOOT One cubic foot of steel weighs 489.6 lb For thicknesses from He in to %& in and widths from H in to % in Width of bar. inches Thickness, inches \i Me % Me \2 Yi^ Y^ iHe 3/4 M6 0.053 0.066 0.080 0.093 0.106 0.120 0.133 0.146 O.IS9 %4 0.066 0.083 O.IOO 0.116 0.133 0.149 0.166 0.183 0.199 %2 0.080 O.IOO 0.120 0.139 O.IS9 0.179 0.199 0.219 0.239 yU 0.093 0.II6 0.139 0.163 0.186 0.209 0.232 0.256 0.279' H 0.106 0.133 0.159 0.186 0.212 0.239 0.266 0.292 0.319 %4. 0.120 0.149 0.179 0.209 0.239 0.269 0.299 0.329 0.3.59 ^M 0.133 0.166 0.199 0.232 0.266 0.299 0.332 0.365 0.398 1Kg4 0.146 0.183 0.219 0.256 0.292 0.329 0.365 0.402 0.438 M6 0.159 0.199 0.239 0.279 0.319 0.359 0.398 0.438 0.478 1%4 0.173 0.216 0.259 0.302 0.345 0.388 0.432 0.475 0.518 7/32 0.186 . 232 0.279 0.325 0.372 0.418 0.465 0.511 0.558 1%4 0.199 0.249 0.299 0.349 0.398 0.448 0.498 0.548 0.598 M 0.213 0.266 0.319 0.372 0.425 0.478 0.531 0.584 0.638 1%4 0.226 0.282 0.339 0.395 0.452 0.508 0.564 0.621 0.677 %2 0.239 0.299 0.359 0.418 0.478 0.538 0.598 0.657 0.717 1%4 0.252 0.31S 0.379 0.442 0.505 0.568 0.631 0.694 0.757 Mfl 0.266 0.332 0.398 0.465 0.531 0.598 0.664 0.730 0.797 2144 0.279 0.349 0.418 0.488 0.558 0.628 0.697 0.767 0.827 11/^-2 0.292 0.365 0.438 0.511 0.584 0.657 0.730 0.804 0.877 2)64 0.305' 0.382 0.458 0-535 0.611 0.687 0.764 0.840 0.916 3/^ 0.319 0.398 0.478 0.5.58 0.638 0.717 0.797 0.877 0.956 2 5/64 0.332 0.41S 0.498 0.581 0.664 0.747 0.830 0.913 0.996 l-%2 0.34s 0.432 0.518 0.604 0.691 0.777 0.863 0.950 1.04 2/64 0.359 0.448 0.538 0.628 0.717 0.807 0.896 0.986 1.08 lu 0.372 0.465 0.558 0.651 0.744 0.837 0.930 1.02 1. 12 2%4 0.38s 0.481 0.578 0.674 0.770 0.867 0.963 1.06 1. 16 1-/32 0.398 0.498 0.598 0.697 0.797 0.896 0.996 1. 10 1.20 3^.4 0.412 0.515 0.618 0.721 0.823 0.926 1.03 1.13 1.24 /2 0.42s 0.531 0.638 0.744 0.850 0.956 1.06 1. 17 1.28 3%4 0.438 0.548 0.657 0.767 0.877 0.986 1. 10 1. 21 1. 31 17/^2 0.452 0.564 0.677 0.790 0.903 1.02 1.13 1.24 1.35 35/^4 0.465 0.581 0.697 0.813 0.930 1.05 1. 16 1.28 1.39 9-16 0.478 0.598 0.717 0.837 0.956 1.08 1.20 1.31 1.43 1518 Metal-Data Weights in Pounds of Flat Rolled Steel Bars (Continued) PER LINEAR FOOT For thicknesses from Me to 2 in and widths from i to 3 in Width of bar. inches Thickness, inches I \\k 1M2 iM 2 2M 2M 2-3-1 3 Ms 0.21 0.26 0.32 0.37 0.43 0.48 0.53 0..58 0.63 H o.*42 0.53 0.64 0.7s 0.85 0.96 1.06 1.17 1.28 3/16 0.63 0.79 96 I. II 1.28 1.44 1.59 1-75 1.91 M 0.85 1.06 1.28 • 1.49 1.70 I-9I 2.12 2.34 2.55 •Me I 06 1.33 1.59 1.86 2.12 2.39 2.65 2.92 3.19 % 1.28 I 59 1.92 2.23 2..SS 2.87 3-19 3 51 3 83 lU 1.49 1.86 2.23 2.60 2.98 3 35 3.72 4.09 4.46 Vi 1.70 2.12' 2.55 2.98 3.40 3.83 4-25 4.67 5.10 Mo 1.92 2.39 2.87 3.35 3.83 4 30 4.78 5.26 5.74 % 2.12 2.65 3.19 3 72 4.2s 4.78 5 31 5.84 6.38 iMo 2.34 2.92 3.51 4.09 4.67 5.26 5.84 6.43 7.02 M 2.55 3- 19 3.83 4-47 5.10 5.7s 6.38 7.02 7.65 i-Me 2.76 3.45 4.14 4.84 5.53 6.21 6.90 7.60 8.29 Ms 2.98 3.72 4-47 5.20 5.95 6.69 7-44 8.18 8.93 iMe 3 19 3-99 4.78 5.58 6.38 7.18 7-97 8.77 9-57 I 3-40 4-25 510 5.95 6.80 7.65 8.50 9.35 10.20 iMe 3.61 4.52 5. 42 6.32 7.22 8.13 9 03 9 93 10.84 1 1/8 3.83 4.78 5-74 6.70 7. 65 8.61 9 57 10.52 11.48 iMe 4.04 5.05 6.06 7.07 8.08 909 10.10 11. II 12.12 i'/4 4-25 5. 31 6.38 7-44 8.50 9-57 10.63 11.69 12.75 iMe 4.46 5.58 6.69 7.81 8.93 10.04 II. 16 12.27 13.39 i5i 4.67 5.84 7.02 8.18 9 35 10.52 11.69 12.85 14.03 iMo 4.89 6. II 7-34 8.56 978 11.00 12.22 13.44 14.66 1M2 S-io 6.38 7.*65 8.93 10.20 11.48 12.75 14.03 15.30 iMe 5-32 6.64 7 97 9 30 10.63 11.95 13 28 14.61 15 94 154 5.52 6.90 8.29 9 67 II. OS 12.43 13.81 15-19 16.58 i^Me 5-74 7.17 8.61 10.04 11.47 12.91 14 34 15.78 17-22 iM 5. 95 7-44 8.93 10.42 11.90 13.40 14.88 16.37 17.85 iiMe 6.16 7.70 9.24 10.79 12.33 13-86 15.40 16.95 18.49 1^4 6.38 7.97 957 II. 15 12.75 14 34 15.94 17.53 19.13 i^Me 6.59 8.24 9.88 11.53 13 18 1483 16.47 18.12 19 77 2 1 6.80 8.50 10.20 11.90 13.60 15.30 17.00 18.70 20.40 Weights of Fiat Steel Bars Weights in Pounds of Flat Rolled Steel Bars (Continued) PER LINEAR FOOT For thicknesses from He to 2 in and widths from 33^ to 7 H in Width of bar, nches Thickness, inches 3H 4 4V2 5 5H 6 6H 7 lYi M6 0.75 0.85 0.96 1.06 1. 17 1.28 1-39 1-49 1.60 'A 1-49 1.70 1.92 2.13 2.34 2.55 2.77 2.98 3-19 3/l6 2.23 2.55 2.87 3-19 3 51 3-83 4.14 4.46 4-78 H 2.98 3.40 3.83 4-25 4-67 S-io 5 53 5-95 6.36 Me 3-72 4-25 4.78 5 31 5.84 6.38 6.90 7-44 7-97 % 4-47 5-10 5.74 6.38 7.02 7.65 8.29 8.93 9-57 Vi6 5. 20 5.95 6.70 7-44 8.18 8.93 9.67 10.41. 11.16 V2 5.95 6.80 7-65 8.50 9-35 10.20 11.05 11.90 12.75 9/16 6.70 7.65 8.61 9-57 10.52 11.48 12.43 13.39 14-34 % 7-44 8.50 9-57 10.63 11.69 12.75 13 81 14.87 15.94 me 8.18 9-35 10.52 11.69 12.85 14.03 15-20 16.36 17-53 % 8.93 10.20 11.48 12.75 14.03 15.30 16.58 17.85 19-13 13/16 967 11.05 12.43 13-81 15.19 16.58 17-95 19-34 20.72 Ti 10.41 11.90 13.39 14.87 16.36 17-85 19-34 20.83 22.32 15/16 II. 16 12.75 14 34 15.94 17.53 19.13 20.72 22.32 23.91 I 11.90 1360 15-30 17.00 18.70 20.40 22.10 23.80 25-50 iMs 12.65 14-45 16.26 18.06 19-87 21.68 23.48 25 -29 27.10 iH 13.39 15.30 17.22 19.13 21.04 22.95 24 87 26.78 28.68 iMe • 14 13 16.15 18.17 20.19 22.21 24.23 26.24 28.26 30.28 iH 14.87 17.00 1913 21.25 23-38 25.50 27.62 29.75 31.88 I Ms 15.62 17.85 20.08 22.32 24-54 26.78 29.01 31.23 3348 m 16.36 18.70 21.04 23.38 25-71 28.05 30.39 32.72 35 06 iV\& 17.10 19 -85 21.99 24.44 26.88 29-33 31.77 34-21 36.66 l\i 17.85 20.40 22.95 25 50 28.05 30.60 33-15 35-70 38-26 i^ie 18.60 21.25 23.91 26.57 2^.22 31.88 34-53 37-19 39-84 iH 19 -34 22.10 24.87 27.63 30.39 33.15 35-91 38.67 41.44 ii/ie 20.08 22.95 25.82 28.69 31-55 34.43 37-30 40.16 43-03 1% 20.83 23.80 26.78 29.75 32.73 35.70 38.68 41.65 44-63 i^Me 21.57 24.65 27.73 30.81 33-89 36.98 40.05 43-14 46.22 l7/i 22.31 25 50 28.69 31.87 35-06 38.25 41.44 44-63 47-82 115/6 23.06 26.35 29.64 32.94 36.23 39 53 42.82 46.12 49.41 2 23.80 27.20 30.60 34.00 37.40 40.80 44.20 47.60 51.00 1520 Metal-Data Weights in Pounds of Flat Rolled Steel Bars (Continued) PER LINEAR FOOT For thicknesses from He to 2 in and widths from 8 to 12 in Width of bar. inches Thickness, inches 8 SH 9 9M2 10 io3^ 11 iiH 12 Me 1.70 i.8i 1. 91 2.02 2.13 2.23 2.34 2.45 2-55 % 340 3.61 3.82 4.04 4.25 4.46 4.68 4-89 5-10 3/lG 5 10 5.42 5.74 6.06 6.38 6.70 7.02 7.32 7.6s H 6.80 7.22 7.65 8.03 8.50 8.92 9.34 9-78 10.20 Mo 8.50 903 9.56 10.10 10.62 11.16 11.68 12.22 12.75 % 10.20 10.84 11.48 12.12 12.75 T3.39 14.03 14.68 15.30 I'ia 11.90 12.64 13.40 14.14 14-88 15.62 16.36 17.12 17.85 u ■ 13.60 14.44 15.30 16.16 17.00 17.85 18.70 19.55 20.40 Vie 15.30 16.26 17.22 .18.18 19.14 20.08 21.02 22.00 22.95 % 17.00 18.06 19-13 20.19 21.25 22.32 23.38 24.44 25 -50 iHe 18.70 19.86 21.04 22.21 23.38 24-54 25.70 26.88 28.05 % 20.40 21.68 22.96 24.23 25.50 26.78 28.05 29 .33 30.60 i-Me 22.10 23.48 24.86 26.24 27.62 29.00 30.40 31.76 33.15 % 23.80 25.30 26.78 28.26 29.75 31.24 32.72 34.21 35.70 15/16 25.50 27.10 28.69 30.28 31.88 33.48 35.06 36.66 38.25 I 27.20 28.90 30.60 32.30 34.00 35.70 37.40 39.10 40.80 iMe 28.90 30.70 32.52 34.32 36.12 37.92 39.74 41.54 43.3s iH 30.60 32.52 34-43 36.34 38.25 40.17 42.08 44-00 45.90 I-/16 32.30 34.32 36.34 38.36 40.38 42.40 44.42 46:44 48.4s I'/i 3400 36.12 38.26 40.37 42.50 44.63 46.76 48.88 51.00 iMe 35.70 37.93 40.16 42.40 44.64 46.86 49.08 51-32 53-55 l3.^ 37.40 39-74 42.08 44-41 46.75 49.08 51.42 53-76 56.10 iMe 39.10 41.54 44 00 46.44 48.88 51.32 53 76 56.21 58.6s 1V2 40.80 43.35 45.90 48.45 51.00 53.55 56.10 58.65 61.20 iy\& 42.50 45.16 47-82 50.48 53.14 55.78 58.42 61.10 63 75 iH 44.20 46.96 49-73 52.49 55.25 58.02 60.78 63.54 66.30 iiMe 45.90 48.76 51-64 54.51 57-38 60.24 63 10 65.98 68.85 1% 47.60 50.58 53-56 56.53 59.50 62.48 65.45 68.43 71-40 ii^e 49.30 52.38 55.46 58.54 61.62 64.70 67.80 70.86 73-95 iVs 51.00 54.20 57.38 60.56 63.7s 66.94 70.12 73.31 76.50 i»Mfl 52.70 56.00 59.29 62.58 65.88 69.18 72.46 75-76 79-05 2 54.40 57.80 61,20 64.60 68.00 71.40 74.80 78.20 81.60 Estimating Weights of Metals 1521 Rtiles for Estimating the Weight of any Piece of Wrought Iron, Steel or Cast Iron Wrought Iron. One cubic foot of wrought iron weighs 480 lb One square foot, one inch thick, weighs 40 lb One square inch, one foot long, weighs 3^^ lb To find the weight per square foot of sheet iron, multiply the thickness in inches by 40. To find the weight per linear foot of bars of any section, multiply the cross- sectional area in square inches by 3H. Steel. One cubic foot of steel weighs 489.6 lb (Or just 2% more than wrought iron.) One square foot, one inch thick, weighs 40.8 lb One square inch, one foot long, weighs 3.4 lb To find the weight per linear foot, of bars of any section, multiply the cross- sectional area in square inches by 3.4; or, if the weight is known, the exact sec- tional area may be obtained by dividing by 3.4. Cast Iron. One cubic foot of cast iron weighs 450 lb One square foot, one inch thick, weighs sjHlh One square inch, one foot long, weighs . , 3H lb One cubic inch weighs 0.26 lb The weight of irregular castings must be estimated by the cubic inch. Rules for Weights of Castings Multiply the weight of the pattern by 18 for cast iron, 13 for brass, 19 for lead, 12.2 for tin, 1 1.4 for zinc; the product is the weight of the casting. Reduction for Round Cores and Core-Prints Rule. Multiply the square of the diameter by the length of the core in inches, and the product multiplied by 0.017 is the weight of the pine core to be deducted from the weight of the pattern. Shrinkage in Castings Pattern-makers' Rule Cast iron . . H Brass He Lead % Tin M2 Zinc Mq of an inch longer per linear foot 1522 Metal-Data Part 3 Weights of Square Ca&t-Iron Columns in Pounds per Linear Foot* an b 20 + 2b t Thicknes s of metal, inches •H in, Vi in, % in. I in, iH in. iH in, iy2 in. 1% in. 2 in, lb lb lb lb lb lb lb It) lb If -Ml. .<>!!;; 18.6 21. 1 23.3 25.0 26.4 27-3 28.1 ..... Mt vi.. 22.5 25.8 • 28.7 3^3 33.4 35.1 37.5 i6 26.4 30.5 34.2 37.5 40.4 45- 46.9 49.2 50.0 i8 30.3 35.2 39.7 43.8 47.4 50.8 56.3 60.2 62.5 20 34 2 39-8 45.1 50.0 54-5 58.6 65.6 71.1 75.0 22 38.1 44.5 50.6 56.3 61.5 66.4 75.0 82.0 87.5 24 42.0 49.2 56.1 62.5 68.5 74.2 84.4 ! 930 100.0 26 45.9 53.9 61.5 68.8 75.6 82.0 93.8 103-9 112.5 28 49-8 58.6 67.0 75.0 82 6 89.8 103.1 114.8 125.0 ■',^1 ,k :,53.7 63.3 72.5- 81.3 89.6 97.7 112.5 125.8 137.5 ^ ^ 57.6 68.0 77.9 87.5 96.7 105. 5 121. 9 136.7 150.0 34 61.5 72.7 83.4 93.8 103.7 113.3 131. 3 147-7 162.5 36 65.4 77.3 88.9 100. 110.7 121. 1 140.6 158.6 175.0 38 693 82.0 94.3 106.3 117. 8 128.9 150.0 169.5 187.5 40 73.2 86.7 99-8 112.5 124.8 . 136.7 159.4 •180.5 200.0 42 771 91-4 105. 3 118. 8 131. 8 144.5 168.8 191.4 212.5 44 81.0 . 96.1 no. 8 125.0 138.8 152.3 178.1 202.3 225.0 46 849 100 8 116. 2 131. 3 145 9 160.2 187.5 213-3 237.5 48 88.8 105. S 121. 7 137.5 152 9 168.0 196.9 224.2 250.0 50 92.8 no. 2 127.2 143.8 159.9 175-8 206.3 235.2 262.5 52 96.7 114.^ 13I2.6 iSO.o 167.0 183.6 215.6 246.1 275.0 54 100.6 119-5 138.1 156.3 174.0 191.4 225.0 257.0 , 287.5 56 104.5 124.2 143-6 162,5 181. 199-2 234.4 268.0 300.0 58 108.4 128.9 149.0 168.8 188.1 207.0 243.8 278.9 312.5 60 112. 3 133.6 154.5 175.0 195.1 214.9 253.2 289.8 325.0 62 116. 2 1383 160.0 181.3 202.1 222.7 262.5 300.8 337.5 64 120 I 1-43-0 16S.4 187.5 205.2 230.5 271.9 311. 7 350.0 66 124.0 147.7 170.9 193-8 216.2 238.3 281.3 322.7 362.5 68 127.9 152.3 176.4 200.0 223.2 246.1 290.6 333.6 375-0 70 131. 8 157.0 181. 8 206.3 230.3 253-9 300.0 344. 5 387.5 72 135.7 161. 7 187-3 212.^ 237.3 261.7 309.4 355.5 400.0 74 139.6 166.4 192.8 218.8 244 -3 269.5 318.8 366.4 412.5 76 143 5 171. 1 198.3 225.0 251-3 277.3 328.1 377.3 425-0 78 1-47.4 175.8 203.7 231.3 2.58.4 285.2 337.5 388.3 437-5 fea 151. 3 180.5 207.2 237-5 265.4 293.0 346.9 399.2 450.0 * Birkmire. t a and b = either side, outside measurement, been made in this table for corners counted twice. 2 a -\- 2 b = number. Allowance has Example. What is the weight per linear foot of a 12 by 16 by i in thick column? Solution. 2 a-\- 2b= 24+ 32 = 56. Opposite this number, under i-in-thick metal, we find 162,5, or weight per linear foot of a column 12 by 16 by i-in-thick. Note. For flanges, brackets, etc., calculate the cubical contents of same and multiply by 0.26; cast iron averages 450 lb per cu ft. Weights of Cast-iron Columns 1523 Weights per Linear Foot of Circular Cast-iron Columns * f Outside Thickness of metal, inches diameter, /z in. H'm, Hin, >Hn, I in, iH in. iH in. 1% in. lb lb lb lb lb lb lb lb 3 12.3 14.6 16.60 18.30 19.6 4 17.2 21.0 24.00 27.00 29-S 32.1 33*8 35. 4 5 22.1 27.0 31.30 35.50 39.3 43.0 46.0 49.0 6 27.0 33.0 39.00 44.00 49-1 54.1 58.3 62.4 7 32.0 39-1 46.00 53.00 59-0 65-1 70.6 76.1 8 36.8 45.3 53.40 61.20 69.1 76.1 83.1 89.5 9 41.7 51.4 61.10 70.00 78.6 87.1 95-1 103.1 10 46.6 57-5 68.13 78.41 88.4 98.0 107.4 116. 4 II 51.6 64.0 75.50 87.10 98.2 109.1 120.1 130.1 12 56.5 70.0 82.87 96.10 108.0 120.0 132.1 143.5 13 61.4 76.0 90.23 104.20 118. 1 131 -2 144-2 157. 1 14 66.3 82.1 97-60 113.20 128.1 142.0 156.5 170.4 15 71.2 88.2 104.96 121.40 137 -5 153-3 169.4 184. 1 i6 76.1 94.4 112.33 130.10 147-3 164-3 181. 197.4 17 81.0 100.5 120.10 139 -10 157 -I 175-4 193.3 211.0 i8 86.0 107.0 127.00 147 00 167.0 186.4 206.0 224.4 19 gi.o 1130 134-40 156.00 177. 1 197 -5 218. 1 238.0 20 96.0 119. 142.10 164.30 186.6 208.8 230.1 i 251.5 21 I 00.6 125.0 149- 10 173.10 196.6 219.6 242.4 1 265 . 22 I 05.6 131.2 156.50 181. so 206.2 230.6 255.0 278.0 23 I 10.5 137-3 -164.10 190.10 216. 1 242.0 267.0 292.0 24 I 15.4 143.5 171.20 199.00 ^26.6 253-0 279-2 30s. 4 Thick] less of m etal, ind les Outside _ diameter, ^ inches K2 in, IH in, 2 in. 2\i in. 2K in, 2% in. 1^4 in, 1% in. -lb lb lb lb lb lb lb lb 3 4 5 51.54 54.1 55.84 57.5 6 66.30 69.9 73.02 76.0 "78'6 80.84 82.83 7 81.00 85.6 90.20 94.3 98.2 ioi.70 105.00 107.84 8 95.80 101.8 107.40 ■ 112. 8 117. 8 122.60 127.00 131.20 9 I 10.50 117.7 124.60 131 -2 137 5 143-40 149 10 154.50 10 I 25.20 133.7 142. CO 149-6 157.1 164.30 171.20 177.80 II I 40.00 149.6 159.00 168.0 176.8 185.20 193-30 201 . 10 12 I 54.70 165.6 176.00 186.4 196.4 206.00 215.40 224.40 13 I 69.40 181. 5 193.30 204.8 216.0 226.90 237.50 247.70 14 I 84.10 197.4 210.50 223.2 235.7 247.70 259 60 271.10 15 I 98.90 213.4 527-70 241.6 255.3 268.20 281 . 70 294.40 l6 2 13.50 229.4 244 -90 260:0 274.9 '289.50 303 -70 317.70 17 2 28.30 245.3 262.00 278.4 294. 5 310.30 325.80 341 00 I8 2 43.00 261.3 279-20 296.8 314.2 331.20 348.00 364-30 19 2 57.70 277.2 296.40 315.2 338.8 352.10 370.00 387-70 20 2 72.50 293.2 313.60 333-6 353.4 372.90 392 . 10 411.00 21 2 87.20 309.0 330.80 352. 1 373.1 393.80 414.20 434.30 22 3 02.00 325 I 348.00 370.5 393.0 414.60 436.30 457.60 23 3 16.70 341 365.10 388.9 412.3 435.50 458.40 481.00 24 3 31.40 357.0 382.30 407.3 432.0 456.40 480.50 504.20 * Birkmii'^. t The table is arranged for the weight of plain shaft. For brackets, flanges, etc., cal- culate the cubical contents and multiply by 0.26, 1524 Metal-Data Part 3 Weight of Cast-iron Plates Weights, in Pounds, of Cast-iron Plates One Inch Thick Calculated at 450 lb per cu ft Width, inches Length, inches 6 in. 8 in. 10 in, 12 m, 14 m. 16 in, 18 in, 20 m, 24 m, 30 m, lb lb lb lb lb lb lb lb lb lb 4 6.25 8.3 10.4 12.5 14.6 16.6 18.7 20.8 25 31 6 9.37 12. 5 15.6 18.7 21.8 25.0 28.1 31.2 38 47 8 12.50 16.6 20.8 25.0 29.1 33.3 37.4 41.6 50 62 10 15.60 20.8 26.0 31.2 36.4 41.6 46.8 52.0 63 78 12 18.70 25.0 31.2 37.5 43.7 49-9 56.2 62.4 75 94 14 21.80 29.2 36.4 43.7 51.0 58.2 65.5 72.8 88 109 16 24.90 33.3 41.6 50.0 58.2 66.6 74.9 83.2 100 125 18 28.10 37.5 46.8 56.2 65. 5 74.9 84.2 93.6 113 140 20 31.20 41.6 52.0 62.3 72.8 83.2 93.6 104.0 125 156 22 34.30 45.8 57.2 68.6 80.1 91-5 103.0 114. 4 138 172 24 37.50 50.0 62.4 75.0 87.4 99.8 112. 3 124.8 150 187 26 40.60 54.0 67.6 81.2 94.6 108.2 121. 7 135.2 163 203 28 43.60 58.2 72.8 87. S 101.9 116. 5 131. 145.6 175 218 30 46.80 62.4 78.0 93.7 109.2 124.8 140.4 156.0 188 234 32 49.80 66.6 83.2 100. 116. 5 133. 1 150.3 166.4 200 250 36 56.10 75.0 93.6 112. 5 131 150.0 168.4 187.2 225 281 For larger plates take size of plate one-half smaller and multiply by 2. Thus a plate 28 by 32 in will weigh twice as much as one 14 by 32 in. For plates more or less than one inch in thickness multiply weight of plate by thickness in inches. Approximate Weights of Square-Ribbed Cast-Iron Column-Bases The following table, giving the weight of cast-iron column-bases, will be useful when estimating the steel and iron in tall buildings.* Size of Size of square Weight, square Weight, base. lb base, lb in . in 22X22 600 32X32 1340 24X24 750 34X34 1450 26X26 880 36X36 I 600 28X28 I 020 38X38 I 720 30X30 I 180 40X40 I 850 ' H. G. Tyrrell, in Architects and Builders Magazine, January, 1903, Screw-Threads, Nuts and Bolt-Heads 1525 Screw-Threads, Nuts, and Bolt-Heads Standard Screw-Threads Recommended by Franklin Institute, December 15, 1864, and adopted by Navy De- partment of the United States; by the R. R. Master Mechanics' and Master Car-Builders* Associations; by Jones & Laughlin Steel Company; and by many other of the promi- nent engineering and mechanical establishments of the country. Angle of thread 60**. Flat at top and bottom H of pitch. Diam Diam at Area at Diam Threads Diam at Area at of Threads root of root of of root of root of screw, per inch thread, thread. screw, per inch thread, thread, in in sq in in in sq in M 20 0.185 - 0.027 2 4H 1. 712 2.302 Vxi, 18 0.240 0.045 2\i 4H 1.962 3.023 v% 16 0.294 0.068 2I/2 4 2.176 3.719 Me 14 0.344 0.093 2Y^ 4 2.426 4.620 V2 13 0.400 0.126 3 3V2 2.629 5.428 %6 12 0.454 0.162 3H 3H 2.879 6.510 % II 0.507 0.202 Z\'i 3H 3 100 7 548 % 10 0.620 0.302 3% 3 3.317 8.641 % 9 0.731 0.420 4 3 3 567 9 963 I 8 0.837 0.550 aH 2li 3 798 11.329 \M 7 0.940 0.694 aYi 23/4 4.028 12.753 iH 7 1.065 0.893 4^4 2% 4.256 14.226 ^% 6 1. 160 1.057 5 2H 4.480 15.763 iH 6 1.284 1.295 sH 2H 4 730 17.572 iH 5K2 1.389 1.51S 5^2 2% 4.953 19.267 1% 5 1. 491 1.746 5H 2% 5.203 21 . 262 l7/i 5 1. 616 2.051 6 2U 5. 423 23.098 Nuts and Bolt-Heads are determined by the following rules, which apply to both square and hexagon nuts: Short diameter of rough nut = iVz X diam of bolt + \^ int. Short diameter of finished nut = i^^i X diam of bolt + He in. Thickness of rough nut = diam of bolt. Thickness of finished nut = diam of bolt — Me in. Short diameter of rough head = iVz X diam of bolt -{- H in. Short diameter of finished head = iVz X diam of bolt + Me in. Thickness of rough head = Vz short diam of head. Thickness of finished head = diam of bolt — Me in. The long diameter of a hexagon nut may be determined by multiplying the short di- ameter by 1.15 s, and the long diameter of a square nut by multiplying the short diameter by 1. 414. 1526 Metal-Data Standard Dimensions of Nuts and Bolt-Heads Thick- Thick- Thick- Short Short Long Long ness, ness, ness, Diam of bolt diam, rough f diam, inished diam, rough diam, rough rough. Nut finished. Both r, 11,1 rough. Head ^ ri!!^' u H H 7/16 3^64 Mo H Me H Me 1?§2 m2 iHe 1M2 Me H 1%4 H ^He H S^4 6%4 H Me 11/^2 Me 2%2 2 3/^2 9/10 IM64 Me 3/^ 25/^4 H ^^ 1^6 I 1I564 H Me Me 916 31/^2 2^k 1% 12 3/64 M6 H 31/^4 H iHe I I>^2 iMe 1I/2 l4%4 5i M Me iMe 1M32 H iH 1^6 H 1^6 l3/i 12H2 2H2 H iMe 2^2 I IH iMe iH 2l%4 I iMe IMe iH iiM« l3/4 2H2 2M6 iJ^ iMc 2%2 iH 2 11^6 25/6 25 36.1 iKi iMe . I i3/i 2-M6 2H 2l%2 33/^2 I3/^ iMe l3/2 iH 23/^ 2^6 234 32M64 m iMe iMe iH 2M6 21/^ 231/^2 3% iH iMe l%2 1% 23/4 211/6 3'M6 3"/64 iM iiHo iH l74 2IM6 2j-i 3»H2 4^32 i>i iiMe llMl2 2 3^ 3M6 3H 42}^64 2 iiMe iMe 2M 3H 3M6 4M6 4«>'64 21/ 2M6 iM 2H 3T^ 3IM6 4H 531/64 2H 2M6 iiMe 23/1 4H 4M6 42^62 6 23/4 21 1/6 2H 3 4H 4^6 53/^ 6i7;i2 3 2iMe 2M6 3'/4 5 A'YlB 51 Me 7M6 3V4 3Me 21/2 3V2 5H SMe 6%4 73 9/64 3H 3Me 21H6 3% 5% 51 He 621,^2 8ii 3M 31 He 2li 4 6\i 61/6 7H2 841/64 4 3iMe 3H6 4M m 7^6 7M6 9M6 4}4 4M6 3H 4V^ m 613/6 731,^2 9M 4I/2 4M6 3M6 4% 7H 7Me 81^2 loH 4M 4HI6 3-H 5 7H 7«/l6 82 ^^2 I049/^4 5 4IM6 3»Me 5H 8 7iMe 9?'32 Il2%4 5^/4 She 4 5H mi 85/ e 92 3/^2 1174 5H 5146 4M6 5M SH 811/6 I0-)^2 1234 SKi 5^ Me 4% 6 9H 9M6 1019^2 i2iMe 6 5»M6 4M6 Weights of Bolts and Nuts Weights of One Hundred Bolts With Square Heads and Nuts INCLUDES WEIGHT OF NUT Hoopes & Townsend's List 1527 Length under head to point in r>4 2 2H 2H 2'H 3 4 5 6 7 iM 8 9 13 14 15 i6 17 i8 19 Diameter of bolts lb 7.00 7. SO 8. CO 8.50 9.00 9 50 10.00 11.00 12.00 13 00 14.00 15.00 16.00 lb 10.50 11.25 12.00 12.75 13.50 14.25 15.00 16.50 18.00 19.50 21.00 22.50 24.00 25.50 27.00 28.50 30.00 lb 15 . 20 16.30 17.40 18.50 19.60 20.70 21.80 24.00 26.20 28.40 30.60 32.80 35.00 37.20 39.40 41.60 43.80 46.00 48:20 50.40 52.60 Y'z in, lb 4.18 22.50 23.82 25.15 25.47 27.80 29.12 30.45 33.10 35.75 33. 40 41.05 43.70 46.35 49.00 51.65 54 30 59 -60 64.90 70.20 75.50 80.80 86.10 91.40 96.70 102.00 107.30 112.60 117.90 123.20 5.45 39.50 41.62 43-75 45.88 48.00 50.12 52.25 56.50 60.75 65.00 69.25 73.50 77.75 82.00 86.25 90.50 94.75 103.25 III. 75 120.25 128.75 137.25 145.75 154.25 162.75 171.00 179.50 188.00 206.50 8.52 Vi m, lb 63.00 66.00 6^.00 72.00 75.00 78.00 81.00 87.00 93.10 99 05 IQS.20 III. 25 17.30 123-35 29.40 135.00 141.50 153.60 165.70 177.80 189.90 202.00 214.10 226.20 238.30 250.40 262 . 60 274 70 286.80 /'S in, lb 109.00 113 25 117.50 121.75 126.00 134.2s 142.50 151.00 159. 55 168.00 176.60 185.00 193.65 202.00 210.70 227.7s 224.80 261.85 278 . 9c 295.9s 313.00 330.05 347.10 364 IS 381.20 398.25 415.30 16.70 Weights of Nuts and Bolt-Heads, in Pounds For calculating the weight of longer bolts Diameter of bolt, in inches M % Yz 5^ H % Weight of hexagon nut and head. . . Weight of square nut and head 0.017 0.021 0.057 0.069 0.128 0.164 0.267 0.320 0.43 0.55 0.73 0.88 Diameter of bolt, in inches . I m 1K2 1% 2 2\i 3 Weight of hexagon nut and head . . . Weight of square nut and head 1. 10 1. 31 2.14 2.56 3.78 4.42 5.6 7.0 8.75 10.50 17 21 28.8 36.4 1528 Metal-Data Part 3 Weights of Rivets and Round-Headed Bolts Without Nuts. Steel POUNDS PER HUNDRED Length, H in ■}4 in ^6 in I in 1% in iH in I'^iin H'm in diam diam diam diam diam diam diam diam iH 5.5 12.8 22.0 293 43.9 66.6 93-3 127 iVz 6.3 14.2 24.1 32.4 48.2 72.1 100 136 iH 7.0 15.5 26.3 35. 5 52.5 77-7 107 145 2 7.9 16.9 28.5 38.7 56.7 83.3 114 153 2H 8.7 18.3 30.7 41.8 61.0 88.8 121 162 2yz 9-4 19.7 32.8 44.9 65.2 94-4 128 171 2->4 10.2 21. 1 3S.0 48.0 69. 5 100. 136 179 3 II. 22.5 37.2 51. 1 73.7 105. 143 188 3H II. 7 23.9 39-3 54.3 78.0 Ill 150 197 s'A 12.6 25.3 41.5 57.4 82.3 116 157 205 3% 13.4 26.7 43.7 60.5 86.5 122 164 214 4 14. 1 28.1 45.9 G3.6 90.8 128 170 223 4U 14-9 29.4 48.0 66.7 95.0 134 177 231 4H 15.7 30.8 50.2 69.9 99-3 139 185 240 4% 16.5 32.2 52.4 730 104 145 192 349 5 17.2 33.6 54. 5 76.1 108 150 199 258 SH 18. 1 35.0 56.7 79-2 112 156 206 266 sVz 18.8 36.4 58.9 82.3 116 161 213 275 sH 19.6 37.8 61. 1 •85.5 120 166 220 284 6 20.4 39.2 63.2 88.6 124 172 227 292 6H 21.9 42.0 67.6 95.1 133 184 241 310 7 235 44.7 71.9 lOI 142 195 255 327 7K2 25.1 47.5 76.1 108 150 206 269 345 8 26.6 SO. 3 80.6 114 159 217 284 362 8H 28.2 53.1 85.0 120 167 227 •298 379 9 29.8 55.9 89.3 126 176 239 312 397 9H 31-3 58.7 93-7 133 18S 250 325 414 10 32.8 61.4 98.0 139 193 261 340 431 loV^ 34-5 64.2 103 145 202 272 354 449 II 36.0 67.0 107 151 210 284 368 466 iii/i 37.6 69.8 III 158 218 295 382 484 12 39-2 72. 5 115 164 227 306 396 501 Heads 1.8 5.8 II. I 13.6 22.6 39- 58.0 83.5 For length of shaft re quired to form riv€ t-head, s i^ Table IV, page 420. Nails 1529 NAn.S AND SCREWS* Nails. Based upon the process of manufacture there are three kinds of nails in common use, namely, plate or cut nails, wire nails, and clinch-nails. These are briefly described in the following subdivisions of this article and other data bearing on the subject is included. (i) Cut Nails. Cut nails are made from a strip of rolled iron or steel of the same thickness as the finished nail and a little wider than its length, the fiber of the iron being parallel with the length of the nail. Special machinery cuts the nails out in alternate wedge-shaped slices, the heads are then stamped on them and the finished n'ails droj^ped into the casks. Cut nails made from iron are generally preferred for use in exposed positions. Cut nails are made in a variety of shapes to suit special uses. For ordinary use in building, nails of three different shapes are made, and the nails are called common nails, finish-nails and CASING-NAILS. The common nails are used for rough work, finish-nails for finished work, and casing-nails for flooring, matched ceiling and sometimes for pine casings, although the heads are rather too large for finish-work. Cut nails are beginning to return to favor as they have holding power and lasting qualities superior to wire nails. (2) Brads. Brads are thin nails with a small head, used for smaU finish, panel- moldings, etc. They vary from H to 2 in in length. (3) Clout-Nails. Clout-nails are made with broad, flat heads, and are sold in sizes varying from % to 2y> in in length. They are used chiefly for fastening gutters and metal- work. Special nails are also made for lathing, slating, shing- ling, etc. (4) Wire Nails. These have of late years become as common as the cut nails, and are sold at about the same price. They are said to be stronger for driving than the cut nails, not so liable to bend or break, especially when driven into hard woods, and less liable to split the wood; for these reasons they are generally preferred by carpenters. Wire nails are made from wire, of the same section- diameter as the shank of the nail, by a machine which cuts the wire in even lengths, heads and points them, and; when desired, also barbs them. In general the same classification is used for cut nails. It should be noticed that the gauge of the wire and the shape of the head vary in the different kinds, and that some are barbed, others plain. The various types of wire nails are drawn round, SMOOTH or BARBED, for the domestic trade; for export they are drawn oval, SQUARE, or DIAMOND-SHAPED, according to the country to which they are to be shipped and its requirements. It is customary to charge 15 cents more per 100 lb for standard nails, barbed, than for the same nails, smooth. (5) Clinch-Nails. These are made from open-hearth or Bessemer-steel wire. Any ordinary wire nail will chnch, especially when made with duck-bill or flattened points for clinching purposes, or even otherwise, if annealed. These nails are used only in places where it is desired to turn over the ends of the nails to form a clinch, as in the case of battens or cleats. (6) Length and Weight of Nails. The length of nails is designated by pen- nies id's). This classification originally represented the price in English pence per 100 nails, as 2d per 100, etc. In that sense it is of course now obsolete, but it is stiU retained and is practically uniform with the various manufacturers, both for cut and wire nails. The weights expressed in pennies run from two pennies to sixty pennies, the larger sizes being designated by fractions of an inch. * Condensed from article by Thomas Nolan in chapter on Builders' Hardware in re- vised edition of Building Construction and Superintendence, Part II, Carpenters' Work' by F. E. Kidder, 1530 Nails and Screws Part 3 The sizes and lengths of various kinds of nails and tacks are given in tables on pages 153 1 to 1534. (7) Sizes of Nails for Different Classes of Work. It is imperative for first- class work that nails of proper size should be used and to insure the best results it is well in certain classes of work to specify the sizes which are to be used. For framing, twentypenny, fortypenny and sixtypenny nails, or spikes, are used, according to the size of the timber. For sheathing and roof-boarding, under- floors and cross-bridging, tenpenny common nails should be used. For over- floors tenpenny floor-nails or casing-nails should be used for jointed boards, and ninepenny or tenpenny for matched flooring, although eightpenny nails are sometimes used. Ceiling when H in thick is generally put up with eightpenny casing-nails, and when thinner stuff is used, with sixpenny nails. For inside finish any size of finish-nails or brads from eightpenny down to twopenny is used, according to the thickness and size of the moldings. For pieces exceeding i in in thickness, tenpenny nails should be used. Clapboarding is generally put on with sixpenny finish-nails or casing-nails. Fourpenny nails should be used for shingling and slating, and threepenny for lathing. For slating, galvanized nails should be used, and they are also better for shingling. Whether wire or cut nails should be used may generally be left to the builder; but in places where there is any danger of the nails being drawn out either by the warping of the boards or from the pull of the nail, cut nails should be used, as they have greater holding power than the wire nails under certain conditions. It is generally understood that a wire nail will hold more firmly when barbed than when smooth. (See page 1 531 for tests.) (8) Copper and Brass Nails. Nails are also made of copper and cast brass, and these are sometimes used in connection with boat-building, refrigerator- work, etc. One wing of the Physical Laboratory Building of Harvard College is put together entirely with brass and copper. As the rooms were intended for use in delicate electrical work, no iron was used in their construction. (9) Cement-coated Wire Nails. The coating consists of various resinous gums mixed by a secret formula, and put on the nails by a baking-process which involves the use of quite complicated machinery. Although the chief market for coated nails is among the users of packages to be shipped, there is a limited market for them among builders, for construction-purposes. The chief merit of the coating is that it gives the nail an adhesive resistance approximately twice that of ordinary wire nails. This quality appeals especially to the manufacturers and users of packages to be shipped, for which strength is particularly wanted. It is desirable for construction-purposes also, but the lack of holding power in plain wire nails is not so apparent in building. About 90% of the output goes to box- factories and large shippers.* Cement-coated nails are quite widely used, also, in laying both ordinary and parquetry-flooring. The use of these nails, with a special head which leaves a small hole, gives a firm floor and prevents springing. Though the makers do not claim that the nails are absolutely rust-proof, they do claim that nails thus treated will resist the effects of moisture from 20 to 50% better than the uncoated wire nails. But it is when in use that the non-rusting quality is most evident. There is more coating on the nails than is actually necessary for holding power. The heat caused by the friction of driving the nail softens the coating and the surplus is forced toward the head, completely closing the opening; this prevents the admission of moisture between the wood and the nail. Under similar conditions, the life of a cement-coated nail will be about twice as long as that of an uncoated one. Less force is needed to drive a coated nail as the softened coating forms a lubricant. These nails are made in * Of this amount about 60% is made by the J. C. Pearson Company. Holding Power of Nails 1531 two types, differing only in the heads, and are either coolers or sinkers. The former have large flat heads; the latter, heads slightly reinforced by counter- sinking. They are made to replace common nails, in sizes from H in to i in, and are used for framing, boarding, shingling and staging, and for boxes and crates. Results of tests made with cement-coated nails to determine their adhesive resistance in comparison with the common smooth-wire nails are given below. The following table shows the result of tests made at the United States Arsenal, Watertown, Mass., in 1902, the wood being pine: Comparative Adhesive Resistance of Common Smooth- Wire Nails and Cement-Coated Nails All nails were driven into the same piece and were perpendicular to the grain Size and name Tenpenny, common, smooth. . , Tenpenny, coated Ninepenny, common, smooth. . Ninepenny, coated • Eightpenny, common, smooth. Eightpenny, coated Sixpenny, common, smooth. . . , Sixpenny, coated Diameter, 0.145 0.117 0.132 0.114 0.132 0.112 0.097 0.092 Length driven,* 2; 2 2H iH Adhesive resistance, t lb 167 418 182 327 189 316 106 226 * All of the nails were left with their heads projecting from ] t Average of three trials. : to H Holding Power of Nails. A committee appointed by the Wheeling nail- manufacturers, a number of years ago, to test the comparative holding power of cut and wire nails, published the following data, although the kind of wood is not named. Pounds Required to Pull Nails Out Cut Wire Cut Wire Twentypenny Tenpenny Eightpenny I 593 908 597 703 31S 227 Sixpenny 383 286 200 123 Fourpenny . The holding power of nails varies with the kind of wood into which they are driven. Austin T. Byrne gives the relative holding power of woods as about ad follows: White pine, i; yellow pine, 1.5; white oak, 3; chestnut, 1.6; beech, 3.2; [feycamore, 2; elm, 2; basswood, 1.2. Comparative Holding Power of Cut and Wire Nails Very thorough tests of the comparative holding power of wire nails and cut tiails of equal lengths and weights were made at the U. S, Arsenal in 1892 and 1893. From forty series, comprising forty sizes of nails driven in spruce wood, it was found that the cut nails showed an average superiority of 60.50%, the com- mon nails showing an average superiority of 47 -51% and the finishing-nalls an iivera^e of 72.22%. In eighteen series, comprising six sizes of box-nails driverb into pine, wood, in three ways the cut nails showed an average superiority o^ 99-93%' I" "<^ series of tests did the wire nails hold as much as the cut nails* 1532 Nails and Screws Quantity of Nails Required for Different Kinds of Work For I coo shingles allow 5 lb fourpenny nails or 3\i lb threepenny I 000 laths, 7 lb threepenny fine, or for 100 sq yd of lathing, 10 lb threepenny fine I 000 sq ft of beveled siding, 18 lb sixpenny I 000 sq ft of sheathing, 20 lb eightpenny or 25 lb tenpenny I 000 sq ft of flooring, 30 lb eightpenny or 4O lb tenpenny I 000 sq ft of studding, 15 lb tenpenny and s lb twentypenny I 000 sq ft of I by 2H-in furring, 12-in centers, 9 lb eightpenny or 14 lb tenpenny I 000 sq ft of I by 2^^-in furring, i6-in centers, 7 lb eightpenny or 10 lb tenpenny Cut Steel Nails and Spikes Sizes, lengths, and approximate number per pound Taken from the Handbook of the Cambria Steel Company Sizes Ivength, inches Common Clinch Finishing Casing and box Fencing Spikes 2d 3d Ad Sd 6d Id 8d gd lOd I2d i6d 20d 25d 30d 40d sod 6od I iy2 2 2% 2\^. 2% 3 3K2 4 A\i A\i 5 5K2 6 7 740 460 280 210 160 120 88 73 60 46 33 23 20 12 10 8 4CO 260 180 I 100 880 530 17 14 II 9 6 sVi 5 420 300 210 180 130 107 88 70 52 38 125 100 80 68 52 48 40 34 24 350 300 210 168 130 104 96 86 76 100 80 60 52 38 26 20 18 16 30 26 20 16 Sizes Length, inches Barrel Light barrel Slating Sizes Lent incl Jth, les Flat grip, fine I 462 I 300 I 100 800 650 Edge- grip, fine "96o' 750 600 '"2d" ""3d" ""^d" 5d M Id M 9d lod I2d i6d % I iH i|4 iVs iH i?4 2 2H 2H 2% 3 3H 3H 750 600 Soo 450 310 280 210 190 400 304 224 I 2d 3d Ad 340 280 Tobacco Brads Shingle 220 180 130 97 85 68 58 48 120 94 74 62 50 40 27 90 72 60 Nails, Spikes and Tacks 1533 Steel-Wire Nails, Spikes, and Tacks SIZE, LENGTH, GAUGE AND APPROXIMATE NUMBER TO THE POUND Compiled from Catalogue of American Steel and Wire Company, 1910 American Steel and Wire Company's gauge. (See page 151 2.) Common nails and brads * Casing-nails \ Finishing-nailst Number Number Number Size Length, Gauge to Gauge to Gauge to in pound pound pound 2d I 15 876 15I/2 . I 010 16I/2 I3SI 3d iM 14 568 I4V^ 63s 15K2 807 4 4 23 30d 3 17 Fine nails 4od sod 5 5H 2 I 13 10 2d I 16K2 I3SI God 6 I 5/ tt 9 3d 1% IS 778 1" 8" 9" 7 8 9 716 7 4 3H 4d 2d extra fine 1I/2 } ^ 14 17 473 iS6o 10" 10 w 3 3d extra fine 1 iH 12" 12 w 2\^ 16 I CIS * Common brads differ from common nails only in the head and point, t Lengths are the same as common nails for corresponding size. X Spikes are made with chisel-points and diamond points; also with convex heads and fiat heads. 1534 Nails and Screws Part 3 Steel-Wire Nails (Continued) Clinch-nails Fence-nails * Slating-nails * Number Number Number Size Length, Gauge to Gauge to Gauge to in pound pound pound 2d I 14 710 12 411 3d iH 13 429 No 5 smallest 10K2 225 4d 5d i\^ 274 235 I0l/'2 187 1)4 12 10 142 10 142 6d Id U 2 2H 2H II II 10 157 139 99 10 9 9 124 92 82 9 103 Barbed roofing-nails t 9d 2-Xl 10 90 8 62 ^4"XNo 13 714. lOd 3 9 69 7 50 ^8"XNoi2 469 12d 3H 9 62 6 40 i"XNo 12 411 i6d 3li 8 49 5 30 iH"XNoi2 365 20i 4 7 37 4 23 iH"XNoii 251 * Length same as clinch-nails of corresponding size. t Roofing-nails are designated by the length, not by penny. These nails are made in lengths up to 2 in. Wire Tacks Title, ounce Number Title, ounce Length, in Number per pound Title, ounce Length, in Number per pound in per pound I 2 2H 3 H Me 16 000 10666 8000 6 400 5 333 4 6 8 10 12 Me •Me iHe % 4 000 2666 2 000 I 600 1333 14 16 18 20 22 24 i-Me iMe I iHe iH I 143 I 000 888 800 727 666 Wire carpet -tacks are made polished, blued, tinned, or coppered; there are also uphol- sterers' and bill-posters' or railroad tacks. Expansion-Bolts. These are commonly used for bolting wood or iron to masonry that is already built. A hole is drilled in the masonry of such size that the expansion-nut will fit closely, and when the bolt is screwed up the nut expands and binds firmly in the masonry. The illustration shows the Evans expansion-bolt, which is also furnished with screw-head bolts. There are other forms of expansion-bolts on the market. From experiments on expansion-bolts it was found that the holding capacity was 264 lb per sq in when embedded in i : 2 Portland cement mortar, 843 per sq in when embedded in sulphur and 485 lb per sq in when embedded in lead. For average working unit-stresses it is safe to use about one-fifth of . When the work is exposed to rain or moisture sulphur should Expansion-bolt the values given Screws 1535 not be used as the acid which results will rust the metal and will also tend to disintegrate the masonwork at the point of entrance of the bolt. Screws. The substitution of screws for nails in building operations is a marked feature of modern work. Trimming hardware of all descriptions is put on with screws, and a great deal of panel-work, inside finish, etc., is put together with them. Stop-beads, the casings of plumbing-fixtures, etc., should be fas- tened with screws, as well as all kinds of store and office-fixtures, and cabinet- work in general, except where the joints are glued. Screws are also largely used in making furniture. They present a neater appearance than nails, have greater holding power and are less apt to injure the material if it should be removed and replaced. By making holes for the screws with a bit, all danger of splitting the finish is averted. The ordinary type of screw has a gimlet-point by which it can be turned into the wood without the aid of a bit. The heads are made in various forms to suit different uses. Screws are made ordinarily of steel, but sometimes; of brass and bronze. The latter sort are used for screwing in place finished hard- ware of the same material, and have heads finished to correspond with the trim- mings. Steel screws, also, are finished with blue, bronze, lacquered, galvailized, or tinned surface, to match the cheaper class of trimmings. The galvanized finish is used in building operations at the seasliore. Screws with blue surface, called RLUED screws, are generally used with japanned hardware and for stop- beads, and wherever a cheap round-headed screw is desired. Silver, nickel, and gold-plated screws are also manufactured for use in connection with similar hardware. Steel screws for wood are made in twenty different lengths, varying from li to 6 in, and each length of screw has from six to eighteen varieties in thickness, there being in all thirty-one dif- ferent gauges; so that altogether there are in the market about two hundred and fifty different sizes of ordinary screws used for woodwork. The most common shapes are the ordinary flat head, round head and oval head. The oval-head screw is tapered for countersinking but is slightly rounded on top. Lag and Coach-screws Patent diamond-point steel screws are made especially for driving with a hammer. These can be driven with a hammer their entire length into any hard wood, and then held by one or two turns as securely as the ordinary screw. In ordering screws both the length and number of the gauge or diameter of the shank, the material and finish, and the use to which they are to be put, should be given. Screws for Metal have the same diameter throughout and the threads are V- shaped. Sizes of Screws. The sizes of screws are given in length in inches and the number of the gauge, the gauge denoting the diameter. Thus, a i-in No. 12 screw is I in long and 0.2158 in in diameter. The gauge-numbers range from o to 30 and the lengths from H to 6 in. The lengths vary by eighths of an inch up to I in, by quarters of an inch up to 3 in and by halves of an inch up to 5 in. Screws from % to 4\-2 in long are made in about sixteen different gauge-numbers. Table XIII, page 402, gives the diameter to four places in decimals of an inch of the American screw-gauge. It should be noticed that, unlike the ordinary wire- gauges, the o of the screw-gauge indicates the diameter of the smallest screw while the diameter of the screw increases with the number of the gauge. Lag-Screws and Coach-Screws are large, heavy screws used where great strength is required, as in heavy framing, and for fixing ironwork to timber. D 1536 Data on Excavating Part 3 Lag-screws with conical point are made with diameters of Me, H, Me, Vz, ^le, H, %, and I in, and in lengths from 1^2 to 12 in; coach-screws in diameters from Me to % in and in lengths from 1^2 to 12 in. For putting in lag-screws a hole should be bored which has a diameter a little greater than the unthreaded shank of the screw and it should be bored to a depth corresponding to the length of the unthreaded shank. A second hole should then be bored at the bottom of the first hole of a diameter somewhat less than that of the threaded shank and to a depth of about half its length. Holdmg Power of Lag-Screws Tests made by A. J. Cox, University of Iowa, 1891, quoted by Kent, page 324 Kind of wood Size of screw, in Size of hole bored, in Length in wood, in Maximum resist- ance, lb Number of tests Seasoned white oak 'A 9/16 I2 4H 3 4K2 4 4 8037 6480 8780 3800 3 40.'5 3 I 2 2 2 Seasoned white oak Seasoned white oak Yellow-pine st'ck .... White cedar, unseasoned Hoopes & Townsend give the force required to draw screws out of yellow pine as follows: Screw Wood, depth Force, pounds \^ in 3M in 4960 'H in 4 m 6 000 4 m 7 685 T^in 5 in II 500 6 in 12620 Wooden-screws are sold by the gross, lag-screws and coach-screws by the pound. DATA ON EXCAVATING * Excavating is almost invariably measured by the cubic yard of 27 cu ft. For measuring excavations of irregular depth see page 65. For computing the con- tents of wells and cesspools, the circular area in square feet may be obtained from the table on page 51, and this circular area multiplied by the depth in feet will give the contents in cubic feet. The cost of excavating and removing earth is ordinarily made up of the following items: (i) Loosening the earth for the shovelers; (2) Loading by shovels into carts or barrows; I3) Hauling or wheeling it away, including emptying and returning; (4) Spreading it out on the dump; For every large job, such as railroad-work, it is also necessary to make an al- lowance for keeping the hauling-road in repair, for sharpening and repair of tools, and for carts, harness, superintendence and water-carriers. Where the dirt excavated can be spread over the ground immediately surrounding the excava- tion the loosened dirt may be removed by scrapers without shoveling. Data for Estimating Cost of Loosening Earth. Two men with a plough and team of horses will loosen from 20 to 30 cu yd of strong, heavy soil per hour or * All prices given are pre-war prices and are retained for purposes of comparison of Data on Excavating 1537 from 40 to 60 cu yd of ordinary loam. One man with a pick will loosen iH yd per hour of stifiE clay or cemented gravel, 4 yd of common loam, or 6 yd of light sand. The average quantity of loosened earth that a man can shovel into a cart per hour is: Loam or sand .• 2 .0 cu yd Clay and heavy soils i . 7 cu yd Rock ' 1.0 cu yd Average earth when loosened swells to from iH to iH times its original bulk in place. The capacity of vehicles used for moving excavated materials is about as follows: Wheelbarrows " 3 to 4 cu f t One-horse dump-carts 18 to 22 cu ft Two-horse dump-wagons 27 to 45 cu ft * Drag-scrapers 3 to 7 cu ft Wheel-scrapers 10 to 17 cu ft Dump-cars on rails 27 to 80 cu ft The Economical Length of Haul with drag-scrapers is about 150 f t ; with wheeled scrapers, 500 ft; with wheelbarrows, 250 ft; with one-horse dump-carts, 600 ft.f The average speed of horses is given as about 200 ft per minute. Much valuable data for estimating % the cost of excavating may be found in the Civil Engineer's Handbooks. Weight of Earth, Sand and Gravel. For general calculations the following average values may be taken: 14 cu ft of chalk weigh i ton 18 cu ft of clay weigh i ton 21 cu ft of earth weigh i ton 19 cu ft of gravel weigh i ton 22 cu ft of sand weigh i ton Rock-Excavation. A cubic yard of rock, in place, when broken up by blasting for removal by wheelbarrows or carts, will occupy a space of about iH cu yd; consequently the cost of hauling or removal is abo«ut 50% more than for dirt. *' With labor at $1 per day, the actual cost for loosening haid rock, including tools, drilHng, powder, etc., will average about 45 cents per cubic yard, in place, under all ordinary circumstances. In practice it will generally range between 30 and 60 cents, depending on the position of the strata, hardness, toughness, water and other considerations. Soft shales and other allied rocks may frequently be loosened by pick and plough as low as 15 to 20 cents, while on the other hand shal- low cuttings of very tough rock with an unfavorable position of strata, especially in the bottoms of excavations, may cost $1 per cu yd, or even considerably more. The quarrying of average hard rock requires about H to H lb of powder per cu yd, in place, but the nature of the rock, the position of the strata, etc., may increase it to 1^2 lb or more. Soft rock frequently requires more powder than hard. A good churn-driller will drill 8 to 10 ft in depth of holes about 2^/^ ft deep and 2 in diameter per day in average hard rock, at from 12 to 18 cents per ft." § * The ordinary load for two-horse wagons such as are commonly used for hauling dirt, sand and gravel is from i M to i y2 cu yd. t Inspectors' Pocket-Book, by A. T. Byrne, i See, also, Handbook of Cost Data, by H. P. Gillette. I The Civil Engineer's Pocket-Book, J. C. Trautwine. 1538 Data on Stonework Part 3 DATA ON STONEWORK* Kinds of Stonework. The commonest kind of stonework, that is, for walls, is called rubblework. No work whatever is done on the stones except to break them up with a hammer. If the wall is built in courses it is designated COURSED RUBBLE. When the stones showing on the outside face of the wall are squared, the work is designated ashlar. Ashlar is of two kinds: coursed ASHLAR, in which the stones are laid to form courses around the building, all of the stones in any course being of the same height, and broken ashlar, in which stones of different heights are used. Hammer-dressed ashlar designates work where the stones are roughly squared with a hammer. This is a very cheap class of work. Good ashlar work should be squared on the bench with chisels, and with beds and end-joints cut sc^uare to the face. Stonework which requires a chisel or any other tool except a hammer for dressing is called cut work. Cut work costs considerably more than hammer-dressed work. Measurement of Stonework. Rough stone from the quarry is usually sold under two classifications: rubble-stone and dimension-stone. Rubble includes the pieces of irregular size most easily obtained from the quarry, and suitable for cutting into ashlar 12 in or less in height and about 2 ft long. Stone ordered to be of a certain size, to square over 24 in each way and to be of a particular thick- ness, is called dlmension-stone. The price of the latter varies from two to four times the price of rubble. Rubble is generally sold by the ton or car- load. Footings and flagging are usually sold by the square foot; dimension- stone by the cubic foot. In Boston, granite blocks for foundations are usually sold by the ton. In Estimating on the Cost of Stonework put into a building, the custom varies with different localities, and even among contractors in the same city. Dimen- sion-stone footings, that is, squared stones 2 ft or more in width, are usually measured by the square foot. If built of large rubble or irregular stones the footings are measured in with the wall, allowance being made for the projections of the footings. Rubblework is almost universally measured by the perch of i6)>^ cu ft. The author has been unable to find any locality where the legal perch of 24% cu ft is used by stone-masons. In Philadelphia, St. Louis and some sections of Illinois, 22 cu ft are called a perch. Railroad- work is usually meas- ured by the cubic yard. When stonework is let by the perch, the number of cubic feet to the perch should be stated in the contract, and it should be stated, also, whether or not openings are to be deducted. As a rule no deductions are made for openings of less than 70 superficial feet. Data for Estimating Cost.f The price of common rubble as it comes from the quarry will vary from 55 cts to $1.65 per ton, free on board cars at point of delivery, according to the cost of quarrying, transportation, etc. $1.35 a perch is probably a fair average. A ton of most of the different kinds of stones will make from i perch to iH perches. The cost of laying one perch of stone may be estimated by the following items: Labor: mason 2% hrs, helper 1% hrr>, based on two helpers to three masons; sand Vs load; lime M bu, or if laid in all-cement mortar, one perch will require from H to Yi bbl of cement. At average wages, rubble cellar- walls, from 18 in to 2 ft thick, laid in lime mor- * The prices given are pre-war prices. t For wages dififerent from those named, the average costs may be calculated by pro- portion. Flagstones and Curbing 15S9 tar, vary in cost from $2.75 to $4.50 per perch, $3.50 a perch being a fair a\^ragei in all-cement mortar, from $3.50 to $4.50 per perch. The cost of ashlar depends very largely upon the kind of stone used and the distance it has to be brought. The price of the rough stock on the cars at the point of deUvery may vary from 75 cts to $1.35 per cu ft for granite and from 60 cts to $1.10 for sandstones and limestones, depending largely upon cost of transportation, i cu ft of stone should make 2 sq ft of ashlar, at least. Some quarries get out stone especially suitable for ashlar and sell it at about 30 cts per lin ft for courses 12 in high. The cost of cutting ashlar, with stone-cutters' wages at $4 per day, will average about 15 cts per sq ft for soft stones, from 15 to 20 cts per sq ft for hard sand- stones and limestones, and from 25 to 30 cts for granite. The cost of setting ash- lar will vary from 10 cts per sq ft to 25 cts for soft stones or 30 cts for granite, 15 cts being an average price for sandstones and limestones. The cost of cut-stone trimmings depends so largely upon the kind of stone that it is quite impossil^le to give prices that would be of very much service. The following figures, however, may serve as a general guide in forming a rough estimate, the prices if anything being probably a little above the cost of th^ local stone in most localities. Flagstones for Sidewalks, ordinary stock, natural surface, 3 in thick, with joints pitched to Hue, m lengths, along walk, from 3 to 5 ft, will cost, for a 3-ft walk, about 10 cts per sq ft, or if 2 in thick, 7 cts; for a 4-ft walk, 10 cts; and for a s-ft walk, 12 cts per sq ft. The cost of laying all sizes will average about 4 cts per sq ft. The above figures do not include the cost of hauUng. Curbing. 4 by 24-in granite will cost at the quarry from 3oto 35 cts per lin ft; digging and setting will cost from 12 to 14 cts additional; and the cost of freight and hauling must also be added. -. Cut Bluestone. The following figures show the approximate cost of cut bluestone for various uses: Flagstone, 5 in, size 8 by 10 ft, edges and top bush-hammered, per square foot face-measure Flagstone, 4 in, size 5 by 5 ft, select stock, edges clean-cut, natural top, per square foot Door-sills, 8 by 12 in, clean-cut, per Hnear foot Window-sills, 5 by 12 in, clean-cut, per linear foot Window-sills, 4 by 8 in, clean-cut, per linear foot W^indow-sills, 5 by 8 in, clean-cut, per linear foot Lintels, 4 by 10 in, clean-cut, per linear foot Lintels, 8 by 12 in, clean-cut, per linear foot Water-table, 8 by 12 in, clean-cut, per linear foot Coping, 4 by 21 in, clean-cut, fier linear foot Coping, 4 by 21 in, rock-face edges and top, per linear foot Coping, 3 by 15 in, rock-face edges and top, per linear foot Coping, 3 by 18 in, rock-face edges and top, per linear foot Steps, sawed stock, 7 by 14 in, per linear foot Platform, 6 in thick, per square foot To the prices of cut stone above given must be added the cost of setting, which, for water-tables, steps, etc., will be about 10 cts per linear foot, and for window- sills, etc., about 5 cts per Hnear foot. For fitting, about 10 cts per cu ft, and for trimming the joints after the pieces are set in place, about 5 cts per cu ft should also be added. 1540 Data on Bricks and Brickwork Part 3 DATA ON BRICKS AND BRICKWORK * Clay Bricks. The word brick as commonly used refers to a block made from clay, molded into the required shape and burned in a kiln; and, until quite re- cently, practically all bricks were made from clay. At the present time, how- ever, bricks are also made from sand and lime. Clay bricks may be broadly classified as common bricks, face-bricks, fire-bricks and paving-bricks. As to the process of manufacture, bricks are classified as soft-mud bricks, stiff-mud bricks, dry-pressed bricks and repressed bricks. Soft-Mud Bricks are made by tempering clay with water until it becomes soft and plastic and then pressing it into molds either by hand or by a machine. Practically all handmade bricks are soft-mud bricks. Soft-mud bricks are often REPRESSED to make face-bricks. Stifif-Mud Bricks are machine-made. The clay is first ground, and only enough water is added to make a stiff mud. The stiff clay is forced through a die or dies in the machine in a continuous stream, which is cut up automatically into pieces the size either of the end or side of the brick. If the opening is the size of the end of the brick, the bricks are end-cut bricks; if of the size of the side of the brick, they are side-cut bricks. Stiff-mud bricks can readily be distinguished from soft-mud bricks by their appearance. As good if not better bricks can be made by the soft-mud process as by the stiff-mud process, and in the Eastern States the soft-mud bricks are probably the stronger. As far as the author's observation has extended in the Western States, the stiff-mud bricks are as a rule preferable to those made by the soft-mud process. Stiff-mud bricks are usually heavier than soft-mud bricks or hand-made bricks. Dry-pressed Bricks are made almost entirely for face-work, although in some localities dry-pressed bricks are also used as common bricks. Hydraulic-pressed bricks are dry-pressed. Molded Bricks are always dry-pressed. Very fine bricks are made by this process. Burning of Bricks. Bricks made by any of the above processes require to be burned in a kiln. According to their position in the kiln, common bricks are designated arch-bricks or hard-burned bricks, red bricks or well-burned bricks, and salmon bricks or soft bricks. As a rule, salmon bricks are not fit to use in an exterior or bearing- wall. Color of Bricks. The color of bricks depends principally upon the presence of iron, lime, or magnesia in the clay. A large proportion of oxide of iron gives a clear bright red. Magnesia produces a brown color, and when in the presence of iron, a light-drab color. Dry-pressed bricks are often colored artificially either by mixing clays of different composition, or by mixing mineral colors with the finely ground clay. Fire-Bricks are ordinarily made from a mixture of flint clay and plastic clay. They are usually white, or white mixed with brown, in color and are used for the lining of furnaces, fireplaces and tall chimneys. Paving-Bricks are very hard bricks, usually vitrified or annealed. They are much more expensive than common bricks and are seldom used in buildings. Size and Weight of Clay Bricks. In this country there is no legal standard for the size of bricks, and the dimensions vary with the maker and also with the * For a complete description of clay bricks, their process of manufacture, etc., and also of all kinds of brickwork, see Chapter VII, Part I, of Building Construction and Super- intendence, by F. E. Kidder. Sand-Lime Bricks 1541 locality. Common standard sizes are 8 by 3,'^Ahy 2)4 in. and 8 by 3J^ by 2}i in. In the New England States the common brick averages about 7^4 by 3% by 2V4 in. In most of the Western States common bricks measure about 8K' by /^% by iVz in, and the thicknesses of the walls measure about 9, 13, 18 and 22 in for thicknesses of I, i\-2, 2 and 2M> bricks. The sizes of all common bricks vary considerably in each lot, according to the degree to which they are burned; the hard bricks being from H to -Me in smaller than the salmon bricks. In England the common standard is 8-)4 by 4}^ by 2>.i in. Pressed bricks or face-bricks are more uniform in size, as most of the manufacturers use the same size of mold. The prevailing sizes for pressed bricks are 8^8 l)y ^M by 2% and 8^i by 4 by 2>4 in. Pressed bricks are also made iK> in thick and 12 by 4 by iK" in, those of the latter size be- ing generally termed^ roman bricks or tiles. The WEIGHT OF I5RICKS varies considerably with the quality of the clay from which they are made, and also, of course, with their size. Common bricks average about ^Yi lb each, and pressed bricks vary from 5 to 5^/2 lb each. For the STRENGTH OF BRICKS and brickwork, see Chapter V. The fire-bricks are made in various forms to suit the required work. A straight brick measures 9 by /[Yi by 2K' in and weighs about 7 lb. To secure the best results fire-bricks should be laid in the same clay from which they are manufactured, this being mixed with water into a thin paste. The thinner the joint, the better the wall will stand heat. For paving-bricks the size and weight vary according to the locality and to the requirements of the specifications. Former standards were, 2y2 by 4 by 8 in, required 61 bricks to the square yard, on edge, and weighed 7 lb each. Repressed bricks, 21^2 by 4 by 8^^ in, require 58 to the square yard and weigh 6^^ lb each. Metropolitan bricks were 3 by 4 by 9 in, required 45 to the square yard, and weighed <^\i lb each.* Lime-Mortar Bricks. f General Description. The so-called sand-lime bricks were originally made of lime mortar, molded in brick form and hardened by exposure to the air. Such bricks are said to have been largely used in ancient times, and it is claimed that remains of such materials are now in evidence and in a good state of preservation. It is known that they were formerly used in Europe in localities where other materials were not readily available, and that they have been used in some localities in this country during the past thirty-five years. The writer knows of several houses in Haddonficld, N. J., built of such bricks, generally with the exterior surfaces plastered. One of them, however, said to be about twenty-five years old, has not been plastered, and an inspection (19 15) shows the bricks to be in an excellent state of preservation. Lime-mortar bricks harden by the absorption of carbonic-acid gas from the air. This gas enters into combination with the lime, forming carbonate of lime. I he hardening proc- ess requires several weeks' exposure under cover and the product has not virtues sufTicient to commend it where other materials are available. Sand-Lime Bricks. It was discovered in Germany about 1875 that lime- mortar bricks could be hardened in a few hours under heat and pressure, and it was found later that the chemical reaction under the new process differs essen- tially from that just described, and that the percentage of lime can be greatly reduced. The fundamental principles of sand-lime-brick n;i^nufacture are now common property and only the details of the manufacture are patentable. Sand-hme bricks were first made in Germany about 1880, and the more extended commercial development of the industry dates back in Europe to about 1888, * Building Inspectors' Pocket-book, A. T. Byrne. t Condensed from article on Sand-Lime Bricks by Professor Thomas Nolan in the re- vised edition of Building Construction and Superintendence, Part I, Masons' Work, by F. E. Kidder. 1542 Data on Bricks and Brickwork Part 3 and in this country, to about 1900. There are now (1915) several factories in operation in this country. Manufacture of Sand-Lime Bricks. Pure sih'ca sand, mixed with from 5 to 10% of high-calcium Hme and a certain proportion of water, is molded under very high pressure into the form of bricks. These are piled loosely on cars hold- ing about 1000 bricks each and placed in a steel cylinder large enough to hold from TO to 20 cars. The cylinder is then closed and steam is turned in and main- tained at a pressure of from 1 20 to 135 lb to the square inch for from 8 to 10 hours, when the cylinder is opened and the bricks removed, ready for use. The tre- mendous pressure, which is said to be 100 tons on each brick, under which the bricks are formed, causes great density and a bringing of the component elements into close contact. The heat in the cylinder dries the bricks and causes a chemi- cal reaction between the lime and a portion of the silica, forming a hydrosilicate of lime, an insoluble and durable element, which bonds the remaining particles of the sand together and forms a comparatively strong cementing material. The small residue of uncombined lime combines, in the course of time, either with silica or with carbonic-acid gas from the air, until no free lime remains. The bricks thus become harder and stronger with age. In regard to the constitution of sand-lime bricks, Edwin C. Eckel says:* "It may be safely assumed that a sand-lime brick as marketed consists of (i) sand-grains held together by a net- work of (2) hydrous lime silicate, with probably (if a magnesian lime is used) some allied magnesium silicate, and (3) Hme hydrate or a mixture of lime and magnesia hydrates. These three elements will always be present, and the struc- tural value of the l)rick will deixind in large part on the relative percentage in which the sand and the hydrates occur." Quality of Sand-Lime Bricks. The quality of the product depends mainly upon the selection and treatment of the sand and the lime. Pure silica sands, containing a large percentage of fme grains passing through screens of from 80 to 150 mesh, are preferal)le. Clay or kaolin are dangerous elements and should not be present in quantities of more than 5%. The lime should be, preferably, high- calcium lime, the magnesium silicates formed by impure limes not being as strong as calcium silicates. Some manufacturers use ready-hydrated lime, others hydrate the lime themselves, before mixing it with the sand, and others grind the quicklime, mix it with the sand and slake it in the sand. The other most im- portant element affecting quality is the press. After pressing and before steam- ing, the bricks are very fragile and the press should be such that they are subjected to no shaking or friction after the pressure is removed from the mold. Vertical clay-brick presses have been commonly used, but do not appear to be well adapted to the purpose. The rotary table-presses seem to be most successful. Tests of Sand-Lime Bricks. If the sand is reasonably clean and pure, and the lime finely divided, and if the bricks are sound and have a good metallic ring, they will stand weather-exposure well. If a brick stands in still water for an hour and the moisture rises more than Vi in, it is not a first-class brick; if the moisture rises 2 in, its use for facings is questionable; and if the moisture rises 3 in, it should not be used on outside work of any importance. Authentic tests f have been made forrrushing, fire-resistance, frost-resistance, acid-resistance and absorption, from which it may be concluded that under proper conditions of * " The Production of Lime and Sand-lime Brick in 1906," in the Government Report, dated 1907 and published in 1908, on The Mineral Resources of the United States for the Calendar Year, 1906. t See, also, Tests Upon Sand-Lime Bricks, made by Ira H. Woolson, November, 1905, at the Testing Laboratory, Columbia University, New York, for The National Association of Manufacturers of Sand-Lime Products. Glazed and Enameled Bricks 1543 manufacture sand-Hmc l)ricks arc produced having the following physical char- acteristics: Crushing strength, average, between 2 500 and 3 000 lb per sq in, al- tliough some specimens have shown over 5 000 lb per sq in; modulus of rupture, average, about 450 lb per sq in; fire-resistance, but little inferior to that of fire- brick; frost-resistance, generally good; acid-resistance, superior; absorption, from 7 to 10% in 48 hours; rate of absorption, slower than for clay bricks; average absorption for complete saturation, 14%; reduction of compressive strength by saturation for absorption-test, average 33%. Special Properties of Sand-Lime Bricks. The bricks are square, straight, uniform in size and homogeneous in composition and density. They cleave accurately under the stroke of the trowel and present a weather-surface with the good qualities of stone. They can be cut, carved or sand-blasted, are easily washed clean and show no efflorescence. These claims are well established for properly manufactured sand-hmc bricks. It should be further stated that com- mon bricks and facings are made in the same press, the only aifference being in the selection of the materials and in the handUng of the raw bricks. It is there- fore claimed that a rational and homogeneous exterior wall-structure is possible, since backings and facings may be built and bonded in even courses, with Flemish or other ornamental bonds. Some factories, however, manufactured, at first, inferior bricks and care should still be taken in selections from their out- puts. Freciuently the ordinary runs of sand-lime bricks are not as strong as the average clay building bricks and some of them are too low in their resistance to frost. Colors of Sand-Lime Bricks. The natural color is pearl-gray, varying in warmth with the composition of the sand. Permanent colors are produced by introducing mineral oxides with the raw materials in quantities varying accord- ing to the intensity of color desired; but as the oxides are foreign materials in the bricks, they affect the ciuality of the latter in proportion to the quantity used. Glazed and Enameled Bricks. The terms glazed brick and enam- eled BRICK, as commonly used, refer practically to the same product, and neither includes what is known as salt-glazed brick. The enameled or glazed bricks are generally dipped or sprayed and then burned, whereas the . salt-glaze is obtained by the Introduction of salt into the fire-boxes of kilns while the bricks are being burned. Glazed or enameled bricks are generally divided into two classes: (1) true enameled bricks, which have a glaze contain- ing the coloring matter applied to it without any intermediate slip; (2) bricks which have a transparent glaze placed over a white or colored slip, the slip coming between the glaze and the material to be glazed. The latter is the process most used in this country. Manufacturers differ as to which process produces the best bricks although it would seem as though the true enamel would not chip or peel as readily. These bricks can be made in a variety of colors, from white to dark green or chocolate, and either in a highly glazed FINISH or in a dull, satin-finish, the latter finish being quite desirable in many instances on account of its doing away with the glare of the more highly glazed bricks or tiles. An enameled surface may be distinguished from a glazed surface by chipping off a piece of the brick. The glazed brick will show the layer of slip between the glaze and the body of the brick; while the enam- eled brick will show no line of demarcation between the body of the brick and the enamel. American enameled and glazed bricks are now extens'vely used for the exterior surfaces of buildings, particulariy for street-fronts and light- courts, and for interior side walls and partitions of rooms or buildings used for a great variety of purposes. 1544 Data on Bricks and Brickwork Part 3 Sizes of Enameled Bricks. Enameled bricks are made in two regular sizes: (i) English oize, 9 by 3-in enameled surface, 41'j-in bed, and (2) American size, 8^8 by 2K-in enameled surface, 4H-in bed. The English-size bricks cost about $10 per I 000 more than the American, but on account of the saving in the number of bricks, labor of laying and mortar in joints, the former really effect a saving of about 7 cts per sq ft. Enameled bricks are made, also, with a 12 by 4H-in enameled surface, 2H-in bed. Cost of Enameled Bricks.* The selling price of enameled bricks varies from $75 per I 000 for the American size to $85 for the English size and Gioo for the 12 by 4\i by 2i/4-in size; and at these prices the cost of the bricks per square foot is: cts American size, 7 bricks to the foot ." . . . .' 52H EngHsh size, 5 H bricks to the foot 4SH English flat, 3% bricks to the foot 36 12 by 4H by 2H-)n, 3 bricks to the foot 30 Colors of Enameled Bricks. The standard colors carried in stock are white, cream and buff; other colors are made to order. Estimating Quantities and Cost of Brickwork * Methods of Calculation. The almost universal method of calculating the cost of brickwork is by estimating the number of thousands of bricks, wall- measure, and then multiplying by a certain price per thousand, which is usually determined by experience and which is intended to include every item affecting the cost, and very often the profit. All of the common brickwork in any given building is usually figured at the same price per thousand bricks, the adjustment for the more expensive portions of the work being made in the manner of measur- ing. The principle underlying this system is explained as follows: " The plain dead wall of brickwork is taken as the standard, and the more difficult, complicated, ornamental, or hazardous kinds of work are measured up to it so as to make the compensation eciual. To illustrate, if, in one day, a man can lay 2 000 bricks in a plain dead wall, and can lay only 500 in a pier, arch, or chimney-top in the same time, the cost of labor per thousand in such work is four times as much as in the dead wall, and he is entitled to extra compensation; but instead of varying the price, the custom is to vary the measurement to com- pensate for the difference in the time, and thus endeavor to secure a uniform price per thousand for all descriptions of ordinary brickwork, instead of a differ- ent price for the execution of the various kinds of work."t Measurements of Brick- Quantities. Plain walls are quite universally figured at IS bricks to the square foot of an 8 or 9-in wall, 22V2 bricks per square foot of a 12 or 13-in wall, 30 bricks per square foot of a 16 or 17-in wall, and 7H bricks for each additional 4 or 4} 2 in in the thickness of the wall. These figures are used without regard to the size of the bricks, the effect of the latter being taken into account in fixing the price per thousand. No deduction is made for OPENINGS of less than 80 sup ft, and when deductions are made for larger openings the width is measured 2 ft less than the actual width. Hollow walls are also measured as if solid. To the number of bricks thus obtained is added the * The prices given are pre-war prices. t From Rules of Measurement adopted by the Brick Contractors' Exchange of Denver, Col. Measurements of Brick-Quantities 154?5 measurement for piers, chimneys, arches, etc. Footings are generally measured in with the wall by adding the width of the projection to the height of the wall. Thus if the footings project 6 in on each side of the wall, i ft is added to the actual height of the wall. Chimney-breasts and pilasters are measured by multi- plying the girth of each breast or pilaster from the intersections with the wall by the height, and then by the number of bricks corresponding with the thickness of the projection. Flues in chimneys are always measured solid. Detached chimneys and chimney-tops are measured as a wall having a length equal to the sum of the side and two ends of the chimney, and a thickness equal to the width of the chimney. Thus a chimney measuring 3 ft by i ft 4 in would be measured as a 16 or 17-in wall, 5 ft 8 in long. The rule for independent piers is to multiply the height of each pier by the distance around it in feet, and consider the product as the superficial area of a wall whose thickness is equal to the width of the pier. In practice, many masons measure only one side and one end of a pier or chimney. Arches of common bricks over openings of less than 80 sup ft are usually disregarded in estimating. If the arch is over an opening larger than 80 sq ft, the height of the wall is measured from the springing-line of the arch. No deduction is made in the wall-measurement for stone sills, caps, or belt- courses, nor for stone ashlar, if the same is set by the brick-mason. If the ashlar is set by the stone-mason, the thickness of the ashlar is deducted from the thick- ness of the wall. The sum of all of these measurements represents a certain number of thousands of bricks, and the whole is then multiplied by a common price per thousand, as $6, $8, $12, or $16, according to whatever the cost of plain brickwork may be. If the building is to be faced with pressed bricks, the actual cost cf the pressed bricks, as nearly as it can be computed, is added to the esti- mated price of the common brickwork, nothing being added for laying the pressed bricks, nor anything deducted from the common-brick measurement, the meas- urement of the common work displaced by the pressed bricks being assumed to offset the difference in the cost of laying the pressed and common brickwork. In arriving at the cost of the pressed bricks, the external superficial area of the walls faced with such bricks is computed, and all openings, belt-courses, stone caps, etc., are deducted. Five-in stone sills are not usually deducted. If a por- tion of the wall is covered by a porch, so that common bricks may be used back of it, this space, also, is deducted. The net pressed-brick surface is then multi- plied by 6, 6K', or 7 to obtain the number of bricks required, 6y2 giving about the number of pressed bricks of the standard size required to the square foot. The topping out of chimneys, if of face-brick, is measured by girting the chim- neys, multiplying by the heights, and adding the sums to the wall-area. Example. As a simple example of this system of estimating consider a small brick house, 28 by 32 ft in plan, without cross- walls, the basement-walls being 13 in thick, with footings 2 ft 6 in wide; the first-story walls, 13 in thick; the second-story walls, 9 in thick; the height of the basement- walls from the trench to the top of the first-story joists, 8 ft 6 in; the height of the walls from the first- story joists to the top of the second-story joists, 10 ft 6 in; and from the second- story joists to the plate, 9 ft. Wall-Measurements. Basement- walls: 120 ft (girth of building) by 9 ft 10 in (height and projection of footing) by 2 2j'i bricks per square foot; equal to 26 550 bricks. First-story walls: 120 ft by 10 ft 6 in by 22 J.^ bricks per square foot; equal to 28 360 bricks. Second-story walls: 120 ft by 9 ft by 15 bricks per square loot; equal to 16 200 bricks. Topping out two chimneys, each i ft 9 in by i ft 5 in by 14 ft high above roof; 1546 Data on Bricks and Brickwork Part 3 2 by 14 ft by (1 ft 5 in plus 1 ft 9 in plus i ft 5 in) by 30 bricks per square foot; equal to 3 850 bricks. Total brickwork: 74 960 bricks. At $9 per i 000, the cost is $674.64. Pressed Bricks. From the grade to the under side of the plates, the wall measures 22 ft 6 in and it is to be faced with pressed bricks of the standard size, costing $15 per i 000. The door-openings and window-openings measure 384 sup ft. The surface of pressed bricks equals 120 by 2 2 3' 2 ft, equal to 2 700 sq ft The deduction for openings is 384 sq ft Area, after deduction 2 316 sq ft Addition for two chimneys, 2 by 14 by 6 ft 4 in, equal to 177 sq ft Total 2 493 sq ft 2 493 by 6y2 equals 16 204 pressed bricks, which, at $15 per i 000 cost, equals $243. The total amount of the bid is $674.64 plus $243, or $917.64. The above figures are supposed to include the necessary lime, sand, water, scaffolding, etc., required to make the mortar and put up the walls, and also a, profit for the contractor; but anything in the way o£ ironwork, such as ties, thimbles, ash-doors, etc., are figured as additions to this amount. Detailed Estimates of Brickwork. In estimating by the above method, the price per thousand is to some extent a matter of guesswork, and while an expe- rienced contractor may perhaps make as accurate an estimate by this method as is possible by any, yet it is often necessary to estimate the work in detail; and even when the work has been estimated as above, it is necessary for the con- tractor to know how many bricks and how much sand and lime will be required to do the work. The following data will assist in making such detailed estimates. With the size of bricks used in the Western States, from 16^2 to 17^^ common bricks are required to the cubic foot after deducting openings, and figuring the thickness of walls at 8, 12, 16, 20 in, etc., the actual number of bricks required will run about two-thirds of the wall-measure when the openings are of about the average number and size. The number of pressed bricks will be about 6 or Syi bricks to the foot, after deducting openings. To lay I 000 common bricks, kiln-count, requires 2V2 bushels or 200 lb of white lime and H cu yd of sand. For a good lime-and-cement mortar, allow 2 bushels of lime, I bbl of cement and H cu yd of sand. For i : 3 cement-and-sand mortar, allow iVi bbl of cement and % cu yd of sand, or one-half a load. To lay I 000 pressed bricks with buttered joints will require 2 bushels of lime (160 lb) and H cu yd of sand; with spread joints, from 2 to 2^2 bushels of lime and from % to yz cu yd of sand. If colored mortar is used, about $1 per i 000 bricks should be added for the mortar-color. A brick-mason, working on a city job under a good foreman, will lay, on an average, 60 pressed (face) bricks per hour, and from 150 to 175 common bricks per hour, 160 being a fair average. In country towns the average is nearer 120 per hour. With wages at 62 ^/^ cts per hour for masons, 31 M cts for hod-carriers, and 34% cts for mortar-mixers and carriers, sand at 60 cts per cu yd, and lime at 40 cts per bushel of 80 lb, brick-masons in Denver state that the average cost of laying common bricks in 12-in walls is about $6 per i 000, kiln-count, and of laying pressed bricks about $10 per i 000. Mortar-Colors. Efflorescence 154"/ For common brickwork, one helper will be required for every mason, and on 9-in walls, faced with pressed bricks, one helper to every two masons. In build- ing common-brick fireplaces and chimneys one mason and heli)er will lay about 600 bricks in a day of nine hours. As a rule, chimneys built of common bricks and with 4-in walls cost about 50 cts per running foot, in height, for single flues, and 90 cts for double flues. Space Required for Piling Bricks. One thousand bricks closely stacked occupy about 56 cu ft of space. One thousand old bricks, cleaned and loosely stacked, occupy about 72 cu ft. A brick-layer's hod measures 21 by 7 by 7 in, and will hold 18 bricks. A mortar-hod measures 24 by 12 by 12, and 12 in across the top. Mortar-Colors are usually in the form of dry powders, or of pulp or paste. The powders are put up in barrels, the number of pounds to the barrel and price per pound being about as follows: Red, in 500-lb barrels, dry from 1^4 to 2 cts per lb Brown, in 450-lb barrels, dry from iH to 2^ cts per lb Buff, in 400-lb barrels, dry from 1% to lYz cts per lb Black, in i 000-lb barrels, dry from 3 to 3)2 cts per lb For lots of less than full barrels an extra charge is sometimes made for packing and drayage. In pulp or paste-form: Red, brown and buff 1^4 cts per lb Black 3 cts per lb All other colors 2 cts per lb Colors in paste-form can be obtained in casks, barrels, half-barrels and kegs, all (except black and buff) weighing, in casks, 900 lb; in barrels, 550 lb; and in half-barrels, 375 lb. The buff weighs, in casks, 700 lb; in barrels, 450 lb; and in half-barrels, 300 lb. Black weighs, in barrels, 450 lb; and in half-barrels, 275 lb. To color the mortar for laying i 000 bricks with H-'m joints requires about 50 lb of red, terra-cotta color, amber, fern-green and salmon; 40 lb for buff, brown, colonial drab or French gray; and 25 lb for black. For wider joints, a larger quantity of stain must be used. For paste-colors an average mixture is, i bucket of paste-color to 7 buckets of mortar for brickwork with 14-in joints. When the colors are in the form of dry powder they are first mixed with dry sand, the cold slaked lime is then added and again mixed thoroughly. It is very important that the color be uniformly mixed. If it is not added at first, but left until the mortar is made, the labor of mixing is doubled. The more thorough the mixing the less color is required. Mortar colors should never be mixed with hot lime. When the color is in the form of a pulp or paste, it should be thor- oughly hoed in, in order to secure a uniform and smooth shade. For very fine pressed bricks, the stained mortar should be strained through a coarse sieve. Efflorescence on Brickwork. A white efflorescence often appears on brickwork, especially in moist climates and damp places. It may spread over large areas of the wall-surface although originating in the mortar joints. Solu- ble salts, principally of soda, potash and magnesia, in the cement or lime mortar, are dissolved by the water absorbed by the mortar and later precipitated on the surface of the brickwork as a white deposit, when the water evaporates. This deposit seems to be greater with the natural than with the Portland-cement mor- tars and still heavier with lime mortar. The origin of the eflioresence may be m the bricks themselves as well as in the mortar used. This is the case when the bricks are made from clays containing iron pyrites or burned with sulphurous 1548 Lime Part 3 coal. Moisture in such bricks tends to dissolve the sulphate of magnesia arid sulphate of lime, which, in the evaporation of the water, are deposited on the surface as crystals of these salts. Efflorescence may result, also, from water impregnated from the mortar, absorbed by the bricks and then evaporated, leaving the whitish deposits; and it is sometimes caused by adulterations in certain mortar-colors. As a preventive. General Gilmore recommended the addition to every 300 lb of the cement powder, 100 lb of quicklime, and from 8 to 12 lb of any cheap animal fat, whix^h is to be thoroughly incorporated with the quicklime before the latter is slaked, preparatory to adding it to the cement. The alkaline salts tend to be saponieied by the fat. This is not an entirely satisfactory treatment, and as a rule it only partly prevents or removes the objectionable deposits; and this addition to the cement retards its setting and somewhat diminishes its strength. It is claimed by some that boiled linseed- oil, applied to brickwork in two coats, will lessen the absorption of moisture for from one to three years and thus lessen the tendency to efflorescence. It is usually mixed in the proportion of 2 gal of oil to 300 lb of dry cement, either with- er without lime; but it is injured by the mortar and, like the fat, retards the setting of the cement mortar and weakens it. In order to diminish the chances of efflorescence on brickwork, the walls should be made as impervious as possible by laying the bricks in a rich well-mixed Portland-cement mortar and filling all joints full and solid. If the building is on damp ground, carefully constructed DAMP-PROOF courses of the proper materials should be built into the walls or a course of horizontal joints near the bottom of the walls should be waterproofed. Reasonably hard bricks should be used for facing, projections and exposed top surfaces waterproofed and provided with drips, and the roof, cornice and gutters made water-tight. When efflorescence is due to the penetration of rain-water or moisture into the brickwork and it is required to preserve the texture and color of the work, the surface may be coated with preparations of paraffine or with various patented waterproofing mixtures. The preparations containing paraffine are usually applied hot, and the walls, also, are heated by portable heaters previous to the application. They give fairly good results, but are quite expensive, owing to the time and labor required for their application. Brick walls may be rendered impervious to moisture by washes applied by the Sylvester process. These washes consist of an alum-solution made by dis- solving I lb of alum per gallon of water, and a soap-solution made by dissolving 2H lb of pure hard soap per gallon of water. The brick walls should be dry and clean and it is recommended that they should not be colder than 50° F. The soap- wash is made boiling hot and then applied to the brickwork. The tem- perature of the alum-solution is usually from 60° to 70° F. when put on. One wash is applied and allowed to dry for about 24 hours, after which the other wash is put over it. When aluminium sulphate, improperly called alum, is substi- tuted for the alum, the cost of the wash is less, only two-thirds as much sulphate as alum is required and the results are better. LIME* Nature and Properties of Lime. Chemically, lime is calcium oxide. Used in a broader sense, it is the class-name of a great variety of products manu- factured by the calcination of limestone. Limestone consists of the carbonates of calcium and magnesium which vary widely in their ratio to each other. The limestones used in the manufacture of lime products may be divided into two • Valuable practical data relating to lime and plaster has been furnished by the Charles Warner Company, of Wilmington, Del. Specifications for Quicklime 1549 classes, calcium limestones and dolomitic limestones. High-calcium lime- stones contain only a relatively low percentage of magnesium carbonate, while dolomitic limestones contain a considerable amount of it. Dolomitic hmestone usually corresponds roughly to the theoretical formula of dolomite (CaCOa) (MgCOs). The CALCINATION of limestone consists of heating to expel the carbon dioxide. The product resulting from calcination of limestone is known as quicklime and possesses great affinity for water. Slaking is the process of adding water to quicklime. During the process of slaking, heat is energetically evolved and much of the water driven off in the form of steam. During this slaking process, also, high-calcium quicklimes must be agitated and stirred con- tinually or a portion will fail to receive the proper quantity of water and will contain unslaked particles which are likely to slake after being used in the work, causing popping, pitting and disintegration. Dolomitic hmes do not slake so energetically, and while they should be stirred while slaking, this is not so neces- sary as with high-calcium lii.ies. Either class of quicklime, through faulty manu- facture, is likely to contain over-burned portions which slake with difficulty and may cause popping, etc., if the lime-paste is not carefully screened before use. The setting and hardening of common lime mortar is due, first, to the drying out and, secondly, to the absorption of carbon dioxide from the atmosphere and the formation of crystals of calcium carbonate to which the strength of the mor- tar is ascribed. In the manufacture and use of common lime mortar, therefore, the raw material, limestone, is first calcined, and the carbon dioxide expelled; it is then slaked with water and forms calcium hj^droxide, in which the water is gradually replaced by carbon dioxide. The lime thus eventually returns to its original carbonate form. As far as the ultimate result is concerned, there is generally little ditference between high-calcium and dolomitic quicklimes. Owing to greater familiarity with one or the other of the classes of lime, archi- tects and builders in certain sections of the country prefer one to the other. Specifications for Quicklime. The lime industry has in recent years been made the subject of careful study and the following clauses give the various requirements of Standard Specifications for QuickUme adopted by the American Society for Testing Materials in 1915. 1. Definition. Quicklime is a material the major part of which is calcium oxide or calcium and magnesium oxides, which will slake on the addition of water. 2. Grades. Quicklime is divided into two grades: (a) Selected. Shall be well -byrned, picked free from ashes, Core, clinker or other foreign material. (b) Run-of-Kiln. Shall be well-liurned, without selection. 3. Forms. Quicklime is shipped in two forms: (a) Lump. Shall be kiln-size. {b) Pulverized Lime. Lump lime reduced in size to pa«s a K-in screen. 4. Classes. Quicklime is divided into four classes: (a) High-Calcium; (b) Calcium; (<:).Magnesian; (d) High-Magnesian. 5. Basis of Purchase. The particular grade, form and class of quicklime desired shall be specified in advance by the purchaser. I. Chemical Properties and Tests (A) Sampling 6. Lime in Bulk. When quicklime is shipped in bulk, the sample shall be so taken that it will represent an average of all parts of the shipment from top to bottom, and shall not contain a disproportionate share of the top and bottom layers, which are most subject to changes. The samples shall comprise at least 10 shovelfuls taken from different parts of the shipment. The total sample 1550 Lime Parts taken sh;ill weigh at least loo lb and shall he crushed to pass a i-in ring and quartered to provide a 15-lb sample for the laboratory. 7. Lime in Barrels. When quicklime is shipped in barrels, at least 3% of the number of barrels shall be sampled. They shall be taken from various parts of the shipment, dumped, mixed and sampled as specified in Section 6. 8. Laboratory Samples. All samples to be sent to the laboratory shall be immediately transferred to an air-tight container in which the unused portion shall be stored till the quicklime is finally accepted or rejected by purchaser. (B) Chemical Tests 9. Chemical Properties, (a) The classes and chemical properties of quick- lime shall be determined by standard methods of chemical analysis, (b) Samples shall be taken as specified in Sections 6, 7 and 8. (c) Quicklime shall conform to the following requirements as to chemical composition: Chemical Composition Properties considered High-Calcium Calcium Magnesian High- Magnesian Select- ed Run of kiln Select- ed Run of kiln Select- ed Run of kiln Select- ed Run of kiln Calcium oxide, per cent. . Magnesium oxide, per ct . Calcium oxide plus mag- nesium oxide, min, per cent . 90 (min) 90 3 5 90 (min) 5 7- =) 85-90 90 3 85-90 85 5 7 • "5 10-25 90 3 5 10-25 85 5 7.5 25 (min) 90 3 5 25 (min) 5 7.5 Carbon dioxide, max, per cent Silica plus alumina plus oxide of iron, max, per n. Physical Properties and Tests 10. Percentage of Waste. An average 5-lb sample shall be put into a box and slaked by, an experienced operator with suflicient water to produce the maximum quantity of lime putty, care being taken to avoid burning or drown- ing the lime. It shall be allowed to stand for 24 hours and then washed through a 20-mesh sieve by a stream of water having a moderate pressure. No material shall be rubbed through the screens. Not over 3% of the weight of the selected quickhme nor over 5% of the weight of the run-of-kiln quicklime shall be retained on the sieve. The sample of lump lime taken for this test shall be broken so that all of it will pass a i-in screen and be retained on a }4-m screen. Pulverized lime shall be tested as received. III. Inspection and Rejection 11. Inspection, (a) All quicklime shall be subject to inspection. (b) The quicklime may be inspected either at the place of manufacture or the point of delivery, as arranged at time of purchase. (c) The inspector representing the purchaser shall have free entry, at all times while work on the contract of the purchaser is being performed, to all parts of the manufacturer's works which concern the manufacture of the quicklime ordered. The manufacturer shall afford the inspector all reasonable facilities for inspection and sampling, which shall be so conducted as not to interfere un- necessarilv with the operation of the works. Specifications for Hydrated Lime 1551 (d) The purchaser may make the tests to govern the acceptance or rejection of the ciuicklime in his own laboratory or elsewhere. Such tests, however, shall be made at the expense of the purchaser, 12. Rejection. Unless otherwise specified, any rejection based on failure to pass tests prescribed in accordance with these specifications shall be reported within five days from the taking of samples. 13. Rehearing. Samples which represent rejected quicklime, shall be pre- served in air-tight containers for live days from the date of the test-report. In case of dissatisfaction with the results of the tests, the manufacturer may make claim for a rehearing within that time. Hydrated Lime. The slaking of quicklime is an operation which is almoslj invarial:)ly carried on by laborers who have little or no conception of the impor-' tance of their task. As a result, many failures have been charged to lime in the past which actually w-ere due to improper preparation during the slaking opera- tion. The new product knov/n as hydrated lime has been offered widely to the trade in recent years and has met with much success. Hydrated lime is a dry flocculent powder resulting from the slaking of quicklime by mechanical means,, with an amount of water which is sufBcient to satisfy the calcium oxide, but insufRcient to make a paste or putty. Hydrated lime is manufactured in me- chanical hydrators in which the batches of .quicklime and water used are carefully proportioned by weight. After passing from the hydrator, hydrated Hme is subjected to a mechanical system of separation which eliminates the coarse or impure particles which may cause popping, etc. Hydrated lime is sold in bags of definite weight and requires only to be mixed with sand and water to make the mortar. The bags have usually been made of heavy burlap or duck cloth, con- taining 100 lb, or of paper, containing 40 lb. Several of the more prominent manufacturers of hydrated lime in the United States employ chemists who regularly superintend the manufacture of hydrated lime, just as the chemists in Portland-cement factories superintend the proportioning of the raw mix going to the kilns to be burned for Portland cement. The hydrated lime manufac- tured under such chemical supervision is a reliable product free from tendencies which might give rise to popping, pitting or disintegration. Hydrated lime of good quality may l)e used for almost any purpose for which lime mortar is used, and is by some considered a more reliable product than quicklime. Among the newer uses for hydrated lime may be mentioned its employment in cement mor- tars and concrete. An addition of about 15% of hydrated lime to cement mortar or concrete decreases its permeability to water, reduces the cracking due to shrinkage, etc., and increases the plasticity of the mortar or concrete, thus preventing separation of the sand, stone and cement and causing the mix- ture to flow and fill the forms more readily. (See Macgregor tests, page 276.) Specifications for Hydrated Lime. The following clauses give the various requirements of Standard Specifications for Hydrated Lime adopted by the American Society for Testing Materials in 1915. 1. Definition. Hydrated lime is a dry flocculent powder resulting from the hydration of quicklime. 2. Classes. Hydrated Hme is commercially divided into four classes: (a) High-Calcium; (b) Calcium; (c) Magnesian; (d) High-Magnesian. 3. Basis of Purchase. The particular type of hydrated lime desired shall be specified in advance of purchase, I. Chemical Properties and Tests 4. Sampling. The sample shall be a fair average of the shipment. Three j)er cent of the packages shall be sampled. The sample shall be taken from the surface to the center of the package. A 2-lb sample to be sent to the laboratory 1552 Lime Pari 3 shall immediately be transferred to an air-tight container, in which the unused portion shall be stored until the hydrated lime has been finally accepted or re- jected by the purchaser. 5. Chemical Properties, (a) The classes and chemical properties of hy- drated Ume shall be determined by standard methods of chemical analysis, (b) The non-volatile portion of hydrated Hme shall conform to the following require- ments as to chemical composition: Chemical Composition Properties considered High- Calcium Calcium Magnesian High- Magnesian Calcium oxide, per cent Magnesium oxide, per cent. . Silica plus alumina plus oxide of iron, max, per cent Carbon dioxide, max, percent Water £9o(min) 5 Sufficient to hydrate the calcium-ox- ide content 85-90 5 Sufficient to hydrate the calcium-ox- ide content 10-25 5 Sufficient to hydrate the calcium-ox- ide content 25 (min) 5 Sufficient to hydrate the calcium-ox- ide content II. Physical Properties and Tests 6. Fineness. A loo-g. sample shall leave by weight a residue of not over 5% on a standard loo-mesh sieve and not over 0.5% on a standard 30-mesh sieve. 7. Constancy of Volume. Hydrated lime shall be tested to determine its constancy of volume in the following manner: Equal parts of hydrated lime under test and volume-constant Portland cement shall be thoroughly mixed together and gauged with water to a paste. Only sufficient water shall be used to make the mixture workable. From this paste a pat about 3 in in diam- eter and 1 2 in thick at the center, tapering to a thin edge, shall be made on a dean glass plate about 4 in square. This pat shall be allowed to harden 24 hours in moist air and shall be without popping, checking, cracking, warping or disintegration after 5 hours' exposure to steam above boihng water in a loosely closed vessel. in. Packing and Marking 8. Packing. Hydrated lime shall be packed either in cloth or paper bags and the weight shall be plainly marked on each package. 9. Marking. The name of the manufacturer shall be legibly marked or tagged on each package. IV. Inspection and Rejection 10. Inspection, (a) All hydrated lime shall be subject to inspection. (b) The hydrated Hme may be inspected either at the place of manufacture or the point of delivery, as arranged at the time of purchase. (c) The inspector representing the purchaser shall have free entry, at all times while work on the contract of the purchaser is being performed, to all parts of the manufacturer's works which concern the manufacture of the hydrated Hme ordered. The manufacturer shall all'ord the inspector all reasonable facilities for inspection and sampling, which shall })e so conducted as not to interfere un- necessarily with the operation of the works. (d) The purchaser may make the tests to govern the acceptance or rejection of the hydrated lime in his own laboratory or elsewhere. Such tests, however, shall be made at the expense of the purchaser. Sand and Gravel 1553 11. Rejection. Unless otherwise specified, any rejection based on failure to pass tests prescribed in these specifications shall be reported within five working days from the taking of samples. 12. Rehearing. Samples which represent rejected hydrated lime shall be preserved in air-tight containers for five days from the date of the test-report. In case of dissatisfaction with the results of the tests, the manufacturer may make claim for a rehearing within that time. Alca Lime. A recent development in the lime industry is Alca Lime.* This is a matendl said to combine the plasticity and sand-carrying qualities of lime mortar with the strength, hardness and quicker set of the gypsum plasters. It is composed of approximately 85% of hydrated lime and 15% of a specially prepared material containing alumina and silica in such proportions as to com- bine, forming bodies which greatly contribute to the strength, hardness and plasticity of the product. It is sold in loo-lb packages and requires only to be mixed with sand and water before use. When used for plastering, it has the characteristics of lime mortar, and while it becomes hard and strong, it is claimed that it is free from the so-called sounding-board effects noticed in some hard-wall plasters. It is not injured by water and is often used for outside stucco-work and also as a brick-laying mortar in place of lime mortar gauged with Portland cement. The manufacturers' directions for the use of Alca Lime should be care- fully observed, and this may be said of all prepared plastering or cementing materials. Useful Data on Quicklime. Quicklime is shipped either in barrels or in bulk. In dry climates it will keep for a long time in bulk, but in damp climates and along the coast it soon slakes unless enclosed in barrels. By Act of Congress, August 23, 19 1 6, it is required that Hme in barrels shall be packed only in barrels containing 280 lb or iSo lb, net weight. When shipped in bulk it is generally sold by the bushel of 80 lb, 3H bushels or 280 lb, net, of Hme being considered as equivalent to a large barrel. Other weights are 180 lb, net, per small barrel, and 64 lb per cu ft. The average yield of lime-paste from the best Easfern limes has been found to be 2.62 times the bulk of unslaked lime. A barrel of good quality well-burned lime should make 8 cu ft, or 20 pails, of lime-paste or putty. Careful experiments conducted by United States engineers have demonstrated that the best mortar is obtained by mixing one part of lime paste to two parts of sand. Cements. For data on cements, see Chapter III. SAND AND GRAVEL Sand is obtained from banks or pits, from river-beds and from the seashore. Pit-sand or bank-sand, free from clay or earthy materials, is generally considered the best for mortar, although excellent sand is often obtained from river-beds. Sea-sand contains alkaline salts which attract and retain moisture and which, unless thoroughly washed, cause efiiorescence when used in brickwork. Both sea-sand and river-sand have more or less rounded grains, to which lime or cement will not adhere as well as to sharp, angular grains. Both are extensively used, however, for lack of better materials. The use of sand in mortar is to prevent excessive shrinkage and to save the cost of lime or cement. Sand, when used in the proportion of i : 2, strengthens lime mortar, but any addition of sand to cement weakens it. Screening Sand. Sand for mortar must ordinarily be screened. Sand for brown mortar for plastering or common brickwork is ordinarily run through a * This is a patented article and is offered for sale by many licenses in the United States under the Spackraan patents. 1554 Lathing and Plastering Part 3 No. 4 screen having 4 by 4 meshes to the inch. For sand finish and mortar for pressed brickwork, either a No. 10 or a No. 12 screen with 10 by 10 or 12 by 12 meshes to the inch is commonly used. For rubble stonework the sand is not ordinarily screened, unless it contains much gravx'l, in which case it should be screened through a ^-in mesh. . Weight of Sand. Dry sand weighs from 80 to 115 lb per cu ft. The aver- age weight of damp (not wet) sand is about 96 lb per cu ft, or about 2 600 lb per cu yd. The voids for ordinary sand range from 0.3 to 0.5 of the volume, the average for screened sand suitable for mortar being 0.35 of the volume. ' The more uneven the grains in size the smaller the percentage of the voids. A one-horse load of sand contains about 22 cu ft. Two-horse loads vary from iM to 2 yd. The amount hauled per load in the larger cities is generally fixed by the Team Owners' Association. i}4 yd is a fair load, i>^ yd a good load and 2 yd a large load. LATHING AND PLASTERING Wooden Laths should be well seasoned, free from sap, bark and dead knots. Bark on laths is quite sure to stain the plaster. White pine is generally con- sidered the best wood for laths, although spruce and hemlock laths are much used. Hard pine is not a good material, as it contains too much pitch. The regular size of laths is K in by i y-z in by 4 ft. The width and thickness vary some- what in different rpills. There is a new lath on the market, which is only 32 in long and which costs from $1.75 to $2 less than the 48-in lengths. Laths are sold by the thousand, in bunches containing 100 laths, from $4.50 to $5.50 be- ing about the average prices. (Pre-war prices.) Metal Lathing. (See Chapter XXIII, pages 883 to 887.) Plastering on laths is generally done in three coats.* The first coat is called the scratch-coat; the second, the brown coat, and the third, the white coat, SKiM-co.\T, or FINISH. On brickwork or stonework the scratch-coat is generally omitted. For first-class work each coat should be permitted to dry thoroughly before the next coat is appHed, and under no circumstances should the finish- coat be applied before the brown coat is thoroughly drJ^ Drawn Workjs a brown coat appUed to a scratch-coat from the same staging, immediately after the scratch-coat is applied. It is a little cheaper than dry SCRATCH, and much of it is done in the Western States. The Scratch-Coat should always be made rich iii lime, and should contain 1 H bu of hair, or an equivalent quantity of fiber to each cask of lime, or i bu of hair to 2 of lime. A proportion of one part hme-paste to two parts of sand will re- 'quire I cask (23.^ bu) of Hme to 5H bbl of screened sand. ,; The Brown Coat should contain i cask (2^2 bu) of lime to 7 bbl of screened sand, and i bu of hair to 5 of lime. Very Httle plaster is mixed by measure, how- ever, the usual custom being to mix as much sand with the slaked hme as the mortar-mixer thinks it will stand and give satisfaction, the tendency being always to make the lime go as far as possible. The Third or Finishing Coat is designated by various terms, such as skim- coat, WHITE COAT, putty-coat, sand-finish, ctc. The skim-coat as used in the ♦ In the Eastern States, dwellings of moderate cost are generally plastered with two- coat work, the first or scratch-coat being brought nearly to the grounds, and carefully straightened to receive the skim-coat. Plastering 1555 Eastern States is generally composed of lime-putty and washed beach-sand in equal proportions. Sand Finish, which has a rough surface resembling coarse sandpaper, is mixed in the same way, only that coarser sand and more of it is used, and it is finished with a wooden or cork-faced float. White Coating or Hard Finish generally means a composition of lime-putty and plaster of Paris, to which marble-dust is sometimes added. Plaster of Paris and marble-dust when used should not be mixed with the lime-putty until a few moments before using, and no more should be prepared at one time than can be used up at once, as it soon SETS, after which it should not be used. The skim- coat or hard finish should be finished with a steel trowel and wet brush. The more the work is troweled the harder it becomes. A superior hard finish is ob- tained by mixing 4 parts of Best's Kecne's cement to i part hme-putty. Mortar for Plastering. . To make sure that the lime is well slaked, it Is cus- tomary to require that the mortar for plastering shall be mixed at least seven days before it is used. Hair such as is used by plasterers is obtained from the hides of cattle, and after being washed and dried is put up in paper bags, each bag being supposed to con- tain I bushel of hair when beaten up. Each package is supposed to weigh from 7 to 8 lb but the weight often falls short. Asbestos and Manilla fiber are both used in place of hair; they are cleaner than hair and are said to be less injured by the lime. It is much better to add the hair to the lime-paste after it is cold and before mixing in the sand, as hot lime, and the steam caused by the slaking, burn or rot the hair so as to greatly weaken it. The common practice is to put the hair in the mortar-box, run off the hot lime as soon as it is slaked, throw in the sand and mix the whole together. It is then thrown out of the box into a pile and a new batch mixed up. Machine-Made Mortar. In several of the larger cities plants have been equipped for the mixing of mortar by machinery. Machine-mixed mortar should be much better than the ordinary hand-mixed mortar, for the reason that time can be given for the lime to slake, the lime and sand can be accurately measured, and the hair and lime are not mixed with the lime until just before delivery. The mixing may also be more thoroughly and evenly done by machinery than is possible by hand. Improved Wall-Plasters. Owing to the difficulty of obtaining sufficient space in building operations in central sections of large cities to properly slake sufficient lime mortar to carry on the plastering with the necessary speed, other kinds of plastering materials have come into existence in recent years. These are known as gypsum plasters or hard-wall plasters. The base of these products is calcium sulphate or gypsum which has been calcined to partially expel the water. The setting and hardening of these products is dependent upon their combining chemically with the gauging water and crystallizing in the same chemical form as the material possessed before calcination. All hard-wall plasters contain material added for the purpose of controlling the set. The straight calcined gypsum sets in a very few minutes, which time would be en- tirely too short to permit the workmen to apply the plaster to the wall and straighten it up before it had set. These plasters are characterized, also, by their inability to carry as much sand as lime mortar. Many of them contain other substances, such as clay or hydrated lime, added to improve their plastic- ity. Hard-wall plasters manufactured in the eastern part of the United States from rock-gypsum invariably contain 15%, more or less, of clay or hydrate, '^,dHed for this purpose. Plasters made in Kansas, Oklahoma, Texas and other 1556 Lathing and Plastering Part 3 Western and Southwestern States are made from earth-gypsum. In the case of these materials, clay and hydrated lime are not added, for the reason that the earth-gypsum contains considerable clay matter, which renders further additions unnecessary. Use of Hard-Wall Plasters. Hard-wall plasters are found to be very con- venient in cases where space and time are the most important elements in the building operation. They set more rapidly than lime plasters, thus permitting the white coating and finishing of the job to be completed earlier. While hard- wall plasters become extremely hard, this property is sometimes considered objectionable, as it may give rise to what is called the sounding-board effect. Keene's Cement Plasters. Asdistinguished from theordinary hard-wall plasters, there exists another class of gypsum-products which, however, are somewhat different in the method of preparation and behavior. In the manufacture of these materials, the gypsum is calcined, immersed in a bath of alum or similar chemical and recalcined. The name Keene's cement is usually applied to these materials, which are made by several manufacturers in this country. These are slow-setting and ultimately attain great strength and hardness. Keene's cement is generally used with considerable Hme-putty or hydrated lime. The use of equal parts of hydrated lime and Keene's cement in making a plastering material is often recommended and found in specifications. (For Alca lime used as a wall-plaster, see page 1553.) Advantages of Improved Wall-Plasters. Among the advantages gained by the use of these plasters are uniformity in strength and quality, extra hardness and toughness, freedom from pitting, saving in time required in making and dry- ing, minimum danger from frost while being applied and before set, less weight and moisture in the building, and, in some cases, greater resistance to the action of fire. Measuring Plasterers' Work. Lathing is always figured by the square yard and is generally included with the plastering, although in small country towns the carpenter often puts on the laths. Plastering on plane surfaces, such as walls and ceilings, is always measured by the square yard, whether it is one-coat, two- coat, or three-coat work, or lime or hard plaster. In regard to deductions for openings, custom varies somewhat in different parts of the country and also with different contractors. Some plasterers allow one-half the area of openings for ordinary doors and windows, while others make no allowance for openings of less than 7 sq yd. Miscellaneous Details. Returns of chimney-breasts, pilasters and all strips less than 12 in in width should be measured as 12 in wide. Closets, soffits of stairs, etc., are generally figured at a higher rate than plain walls or ceilings, as it is not as easy to get at them. For circular or elliptical work, domes or groined ceilings, an additional price is made. If the plastering cannot be done from trestles an additional charge must be made for staging. Whenever plastering is done by measurement the contract should definitely state whether or not open- ings are to be deducted, and a special price should be made for the stucco-work, based on the full-size details. Cornices and Moldings. Stucco cornices and molded work are generally measured by the superficial foot, measuring on the profile of the molding. When less than 1 2 in in girth they are usually rated as i ft. For each internal angle i lin ft should be added, and for external angles, 2 lin ft. For cornices on circular or elliptical work an additional price should be charged. Enriched moldings are generally figured by the linear foot, the price depending upon the design and size of the mold. Cost of Lathing and Plastering 1557 Quantities of Materials for Lathing and Plastering Miscellaneous Data. To cover loo sq yd requires from i 400 to 1 soolaihs, or say i 450 for an average jol), and 10 lb of threepenny fine nails. Three-coat plastering on wooden laths, plaster-of-Paris finish, will require from 10 to 12 bu of lime, 13^2 cu yd of sand, 2 bu of hair and 100 lb of plaster of Paris per 100 sq yd. If the finish-coat is omitted, deduct 2 bu of hme and all of the plaster of Paris. If sand-finished, omit the plaster of Paris and add J-^ cu yd of sand. To cover 100 sci yd with two coats on brick or stone walls, tlie brown coat and finishing coats, will require from 8 to 10 bu of lime, i^{! cu yd of sand, and 100 lb of plaster of Paris, to 100 sq yd. Using Best's Keenc's cement for brown mortar and Keene's finish on expanded- metal lath will require, for brown mortar, 550 lb of cement, 5V2 bu of lime, 2 cu yd of sand and 2 bu of hair; for the finish, joo lb of cement and i bu of lime per 100 yd. Hard plasters on expanded-mctal lath, plaster-of-Paris finish, require, for brown mortar, 2 000 lb of plaster and 2 cu yd of sand; for the finish, i bu of lime and 100 lb of plaster of Paris per 100 yd. Cost of Lathing and Plastering. The average price for putting on wooden laths, labor only, is 4^4 cts per yard. For expanded or sheet-metal laths on wooden studding, s^i cts; on steel studding, wired, from 10 to 12 cts. The cost of putting three coats on laths, plaster-of-Paris finish, labor only, runs about 22 cts per yard. With sand finish the cost is about 23 cts. These figures are based on plasterers' wages at 75 cts per hoiir, and 50 cts- per hour for hod-carriers and mortar mixers. The following schedule * gives the average cost of different kinds of plastering, based on lime at 40 cts per bushel, sand at 75 cts per load of lU' cu yd, hair at 40 cts per bushel, plaster of Paris at 50 cts per 100 lb. Scratch and brown coat (lime) on wooden laths 25 cts per sq yd. Three coats (lime) on wooden laths, plaster-of-Paris finish . . 30 cts per sq yd. Three coats (lime) on wooden laths, sand finish 30 cts per sq yd. Brown coat and finish on brick walls 23 cts per sq yd. For hard-wall plaster instead of Hme, add 3 cts per sq yd. Three coats (lime), plaster-of-Paris finish, metal lath on wooden studding 65 cts per sq yd. Three coats (lime) plaster-of-Paris finish, metal lath on steel studding 68 cts per sq yd. For Keene's cement finish, add 10 cts per sq yd. For blocking in imitation of tile, add 50 cts per sq yd. Two coats hard-wall plaster, pLister-of-Paris finish, metal lath, wooden studding '. 70 cts per sq yd. Two coats hard-wall plaster, plaster-of-Paris finish, metal lath on steel studs 73 cts per sq yd. For Keene's cement finish, add 10 cts per sq yd. Portland cement, brown coat, finished with Keene's cement blocked in imitation of tile, 3 by 6 in $2.80 per sq yd. For running base," 9 in high, in Best's Keene's cement 10 cts per ft. For running plain moldings in plaster of Paris, from 3 to 5 cts per inch of girth. For finishing shafts of columns, from 16 to 24 in in diam., from 12 to 14 ft high, $3 per column (labor only). * These are pre-war prices and the unit values per sq yd must be largely increased on account of the increase in wacres and materials. 155S Lumber and Carpenters' Work Parts These prices, of course, vary somewhat in different sections of the country. In some locaHties prices for materials or labor are less, in others higher. Staff is a composition of plaster of Paris and hemp-fiber, cast in molds, and nailed or wired in place. All of the buildings of the Columbian Exix>sition at Chicago (1893) were covered with this material and all of the temporary build- ings of the St. Louis Exposition (1904). It is not sufficiently durable for per- manent work unless it is frequently painted. The cost of staff, as used on the buildings at Chicago in 1893, varied from $2 to $2.25 per sq yd. DATA ON LUMBER AND CARPENTERS' WORK* Relative Hardness of Woods. Taking shell-bark hickory as the highest standard of our forest-trees, and calling that 100, other trees will compare with it for hardness as follows: Shell-bark hickory 100 Pignut hickory 96 White oak 84 White ash 77 Dogwood 75 Scrub-oak 73 White hazel 72 Apple-tree 70 Red oak 69 White beech 65 Black walnut 65 Black birch 62 Yellow oak 60 Hard maple 56 White elm 58 Red cedar 56 Wild cherry 55 Yellow pine 54 Chestnut 52 Yellow poplar 51 Butternut 43 White birch 43 White pine 30 Weight of Rough Lumber per i 000 Feet BOARD-MEASURE, APPROXIMATE For weight of various woods see tables on pages 1501 to 1508 Kind of wood Ash Chestnut Hemlock Maple, hard. . . Maple, soft . . . . Oak, red Oak, white Pine, long-leaf Pine, white Poplar Spruce Sycamore W^alnut, black. Green from saw, lb 4 600 4 200 5400 5 000 5 500 5 700" 4500 3500 4 000 3 ISO 4 750 4900 Shipping- dry, lb 3000 4150 3650 4250 4500 3500 2 500 3000 2 700 3 200 4 000 Well- seasoned, lb 3 500 3900 3300 4 000 4 100 2 400 2 900 2300 3000 3800 Kiln-dried, lb 3 200 3400 3000 3400 3600 2 200 2400 2 200 * A comprehensive booklet giving the rules for the grading and classification of yellow- pine lumber and dressed stock may be obtained from The Southern Pine Association, New Orleans, La. Measurement of Rough Lumber 1559 Framing-Lumber may commonly be purchased in any of the following nomi- nal sizes, except that common pine, spruce, and hemlock cannot usually be ob- tained in larger sizes than 12 by 12 in. Nominal Sizes of Framing-Lumber ill in in in 2X4 3X 6 4X12 8X12 2 X 6 3X 8 4X14 8X14 2X8 3X10 6X 6 ^ 10X10 2 Xio 3X12 6X 8 10X12 2 X12 3X14 6X10 10X14 2 X14 3X16 6X12 10X16 2 X16 4X 4 6X14 12X12 2I/2X12 4X 6 6X16 12X14 2V2X14 4X 8 8X 8 12X16 2HX16 4X10 8X10 14X14 14X16 In some of the New England mills, the following sizes, also, are sawed: 2 by 3, 2 by 5, 2 by 7, 2 by 9, 3 by 4 and 3 by 5 in. These sizes are not commonly carried in stock, and in .most localities would have to be obtained by ripping larger gizes. Most of the long-leaf yellow pine and Douglas fir is shipped surfaced ONE SIDE AND EDGE, the actual dimensions being from Yi in to % in, and some- times y2 in, scant of the nominal dimensions. When framing-lumber is required^ to be full to dimensions it should be ordered in the rough, and a Special contract made on that understanding. Lengths oi Framing-Timbers. All timber is cut and sold in even lengths, as 10, 12, 14 and 16 ft. Odd and fractional lengths are counted as the next higher even length; consequently it is, in certain cases, possible and economical to plan buildings so that timbers of even lengths may be used without waste. Measurement of Rough Lumber. All rough lumber is sold by the foot, board-measure, one foot being the equivalent of a board i ft wide, i ft long, and I in thick. To compute the board-measure in any board, plank, or timber, di- vide the nominal sectional area, in inches, by 12, and multiply by the length in feet. Thus the number of feet in a 2 by 4-in scantling, 8 ft long = (2 x 4/12) X 8= 51,^ ft, board-measure. A lo-in board, 12 ft long, contains (i X 10/12) x 12 = 10 ft, board-measure. Extensive tables are published showing the feet, in board measure, for almost any commercial size of timber. The following table, however, although compact, will enable one to readily estimate the number of FEET in any of the standard sizes of boards, planks, or timbers. To use the table, find the product of the lateral dimensions of the cross-section; then in the column having a heading equal to this product, and in the horizontal line oppo- site the given length will be found the number of feet in board-measure. Thus, for a 3 by 4, 2 by 6, or i by 12-in timber look in the column headed 12; for a 2 by 12, 4 by 6, or 3 by 8-in piece, look in the column headed 24. For lengths not given in the table, take either twice the length and divide by 2, or one-half the length and multiply by 2. Where timbers of the same size abut end to end, it economizes labor in reducing to board-measure to take the full length; for this reason the lengths in the table are carried beyond those for single sticks. Lumber and Carpenters' Work Part 3 Table of Board-Measure For explanation, see page 1559 Sectional area in square inches Length 1- in feet 4 6 8 IC 12 14 16 18 20 ft in ft* ft in ft in ft* ft in ft in ft* ft in 6 2 3 3 4 5 6 7 8 9 10 8 2 8 4 5 4 6 8 •8 9 4 10 8 12 13 4 10 3 4 5 6 8 8 4 10 II 8 13 4 15 16 8 12 4 6 8 10 12 14 16 18 20 14 4 8 7 9 4 11 8 14 16 4 18 8 21 23 4 i6 5 4 8 10 8 13 4 16 18 8 21 4 24 26 8 18 6 • 9 12 15 18 21 24 27 30 20 G 8 10 1^ 4 16 8 20 23 4 26 8 30 33 4 22 7 4 II 14 8 18 4 22 25 8 29 4 33 36 8 24 8 12 16 20 24 28 32 36 40 26 8 8 13 17 4 21 8 26 30 4 34 8 39 43 4 28 9 4 14 18 8 23 4 28 32 8 37 4 42 46 8 30 10 15 20 25 30 35 40 45 50 32 ID 8 16 21 4 26 8 32 37 4 42 8 48 53 4 34 II 4 17 22 8 28 4 34 39 8 45 4 51 56 8 36 12 18 24 30 36 42 48 54 60 38 12 8 19 25 4 31 8 38 44 4 50 8 57 63 4 40 13 4 20 26 8 33 4 40 46 8 53 4 60 66 8 42 14 21 28 35 42 49 56 63 70 Sectional ar ea in sc luare inc hes 24 28 30 32 35 36 40 42 48 6 ft* ft in ft* ft in ft in ft* ft in It * ft* 12 14 15 16 17 6 18 20 21 24 8 16 18 8 20 21 4 23 4 24 26 8 28 32 10 20 23 4 25 26 8 29 2 30 33 4 35 40 12 24 28 30 32 35 36 40 42 48 14 28 32 8 35 37 4 40 16 42 46 8 49 56 i6 32 37 4 40 42 8 46 8 48 53 4 56 64 18 36 42 45 48 52 6 54 60 63 72 20 40 46 8 50 53 4 58 4 60 66 8 70 80 22 44 51 4 55 58 8 64 2 66 73 4 77 88 24 48 56 60 64 70 72 80 84 96 26 52 60 8 65 69 4. 75 ro 78 86 8 91 104 28 56 6S 4 70 74 8 81 8 84 93 4 98 112 30 60 70 75 80 87 6 90 100 105 120 32 r>4 74 8 80 85 4 93 4 96 106 8 112 128 34 68 79 4 85 90 8 99 2 102 113 4 119 136 36 72 84 90 96 105 108 120 126 144 38 76 88 8 95 lOI 4 no 114 126 8 133 152 40 80 93 4 100 106 8 116 8 120 133 4 140 160 42 84 98 105 112 122 6 126 140 147 168 * The mca»ur<;ments in these columns come out in even feet. Board-Measure 1561 Table of Board-Measure (Continued) For explanation, see page 1559 Length Sectional area in square inches • _ in feet 56 60 64 72 8a 84 96 100 112 1 ft in ft* ft in ft* ft in ft* ft* ft in ft in 4 18 8 20 21 4 24 26 8 28 32 33 4 37 4 6 28 30 32 36 40 42 48 50 56 . 8 37 4 40 42 8 48 53 4 56 64 66 8 74 8 10 46 8 50 53 4 60 66 8 70 80 83 4 93 4 12 56 60 64 72 80 84 96 100 112 14 65 4 70 74 8 84 93 4- 98 112 116 8 130 8 16 74 8 80 85 4 96 106 8 112 128 133 4 149 4 18 84 90 96 108 120 126 144 150 168 20 93 4 100 106 8 120 133 4 140 160 166 8 186 8 22 102 8 110 117 4 132 146 8 154 176 183 4 205 4 24 112 120 128 144 160 168 192 200 224 26 • 121 4 130 138 8 156 173 4 182 208 216 8 242 8 28 130 8 140 149 4 168 186 8 196 224 233 4 261 4 30 140 150 160 180 200 210 240 250 280 32 149 4 160 170 8 192 213 4 224 256 266 8 298 8 34 158 8 170 181 4 204 226 8 238 272 283 4 317 4 36 168 180 192 216 240 252 288 300 336 38 177 4 190 202 8 228 253 4 266 304 316 8 354 8 40 186 8 200 213 4 240 266 8 280 320 333 4 373 4 42 196 210 224 252 280 294 336 350 392 44 205 4 220 234 8 264 293 4 308 352 366 8 410 8 46 214 8 230 245 4 276 306 8 322 36S 383 4 429 4 48 224 240 256 288 320 336 384 400 448 50 233 4 250 266 8 300 333 4 350 400 416 8 466 8 52 242 8 260 277 4 312 346 8 364 416 433 4 485 4 54 252 270 288 324 360 378 432 450 S04 56 261 4 280 298 8 336 373 4 392 448 466 8 522 8 58 270 8 290 309 4 348 386 8 406 464 483 4 541 4 60 280 300 320 360 400 420 480 500 560 62 289 4 310 330 8 372 413 4 434 496 516 8 578 8 64 298 8 320 341 4 384 426 8 448 512 533 4 597 4 66 308 330 352 396 440 462 528 550 616 68 317 4 340 362 8 408 453 4 476 544 566 8 634 8 70 326 8 350 373 4 420 466 8 490 560 583 4 653 4 72 336 360 384 432 480 504 576 600 672 74 345 4 370 394 8 444 493 4 518 592 616 8 690 8 76 354 8 380 405 4 456 506 8 532 608 633 4 709 4 78 364 390 416 468 520 546 624 650 c 728 80 373 4 400 426 8 480 533 4 S6o 640 666 8 746 8 82 382 8 410 437 4 492 546 8 574 656 683 4 765 4 84 392 420 448 504 560 588 672 700 784 — , — if * The measurements in these columns come out in even feet. 1562 Lumber and Carpenters' Work Table of Board-Measure (Continued) For explanation, see page 1559 Length Size and sectional area in inches in feet 120 140 144 160 168 192 196 224 10X12 loX 14 12X12 10X16 12X14 12X16 14X14 14X16 ft* ft in ft* ft in ft* ft* ft in ft ■ in 4 40 46 8 48 53 4 56 64 65 4 74 8 6 60 70 72 80 84 96 98 112 8 80 93 4 96 106 8 112 128 130 8 149 4 10 100 116 8 120 133 4 140 160 163 4 186 8 12 120 140 144 160 168 192 196 224 14 140 163 4 168 186 8 196 224 228 8 261 4 16 160 186 8 192 213 4 224 256 261 4 298 8 18 180 210 216 240 252 288 294 336 20 200 233 4 240 266 8 280 320 326 8 373 4 22 220 256 8 264 293 4 308 352 359 4 410 8 24 240 280 288 320 3.36 384 392 448 26 260 303 4 312 346 8 364 416 424 s 485 4 28 280 326 8 336 373 4 392 448 457 4 522 8 30 300 350 360 400 420 480 490 560 32 320 373 4 384 426 8 448 512 522 8 597 4 34 340 396 8 408 453 4 476 544 555 4 634 8 36 360 420 432 480 504 576 588 672 38 380 443 4 456 5o5 8 532 60S 620 8 709 4 40 400 466 8 480 533 4 560 640 653 4 746 8 42 420 490 504 560 588 672 686 784 44 440 513 4 528 586 8 616 704 718 8 821 4 46 460 536 8 552 613 4 644 736 ■751 4 858 8 48 480 560 576 640 672 768 784 896 SO 500 583 4 600 666 8 700 800 816 8 933 4 52 520 606 8 624 693 4 728^ 832 849 4 970 8 54 540 630 648 720 756 864 882 I oc8 56 560 653 4 672 746 8 784 896 914 8 1045 4 58 580 676 8 696 773 4 812 928 947 4 I 082 8 60 600 700 720 800 840 960 980 I 120 62 620 723 4 744 826 8 868 992 I 012 8 r 157 4 64 640 746 8 768 853 4 896 1024 I 045 4 I 194 8 66 660 770 792 880 924 I 056 I 078 I 232 68 680 793 4 816 906 8 952 1088 I no 8 I 269 4 70 700 816 8 840 933 4 980 I 120 I 143 4 I 306 8 72 720 840 864 960 I 008 I 152 I 176 1344 74 740 863 4 888 986 8 I 036 I 184 I 208 8 I 381 4 76 760 886 8 912 I 013 4 I 064 I 216 I 241 4 I 418 8 78 780 910 yi6 I 040 I 092 I 248 I 274 I 456 80 800 933 4 960 T 066 8 I 120 I 280 L306 8 I 493 4 82 820 956 8 984 I 093 4 I 148 I 312 1339 4 I S30 8 84 840 980 I 008 I 120 I 176 I 344 I 372 I 568 ' The measurements in these columns conxe out in even feet. Measurement ot Lumber 1563 Measurement of Finishing-Lumber, Flooring, Ceiling, Etc. Most, if not all, lumber for finishing is sawed for use in thicknesses of i in, iH in, lYz in, and 2 in, and some woods, such as white pine and poplar, are sawed into thicknesses of 2y2 in and 3 in. When surfaced both sides, the thickness is reduced to ^He, iHe, iMe, iH, 2H, and 2^yi6 in. All dressed stock is measured and sold strip-count, that is, full size of rough material necessarily used in its manufacture. Thus iHe-in boards are measured as though iH in thick. The number of feet, board-measure, for i^-in stock (iHe finished) is iH times that in a i-in board, and in the same way for iH-in and 2y2-'m stock. 1^4 -in planks are always measured 2 in thick, and 2H-in stock, 2H in thick. Boards less than i in thick are measured the same as i-in boards, but for ^^-in and %-m stock a reduced price is generally made. Matched Ordinary Flooring.* The standard sizes for flooring (other than hardwood, parqueting or parquet-flooring) are i by 3, i by 4 and i by 6; or iH by 3, 1 1/4 by 4 and iH by 6. The thickness of i-in flooring should be ^Vie in, and of iH-in flooring, i%2 in. 3-in flooring should show 21/4 in on the face, after it is laid; 4-in, 33.4 in; and 6-in, 5H in. Matched Maple Flooring is usually made in 2-in, 2 1 4-in and 3i/4-in face, and in thicknesses of i^le, iMe and i^g in. Ceiling, matched and beaded boards, is regularly stuck in the same widths as flooring. The standard (nominal) thicknesses of yellow-pine ceiling are H, \i, % and H in, the actual thickness of each being Me in less. The %-'m ceihng is dressed one side only, the other thicknesses both sides. Yellow Pine Drop-Siding. Dressed and matched yellow pine drop-siding H Vi by 3!/^ and % by 53'^ in, showing 3I/4 and sH-in face; and worked shiplap H % by 3>^ and % by 5 J- 2 in, showing 3 and 5-in face. Beveled Siding is resawed on a bevel from stock i^ie by 3H and i^e by 5H in^ after surfacing. New England Clapboards are 4 ft long, 6 in wide, y2 in*thick at the butt, and about % in thick at the other edge. They are put up in bunches and sold by the thousand. Rules for Estimating Quantities of Sheathing, Flooring, Etc. For com- mon sheathing laid horizontally on a wall or roof without openings, add one- tenth to the actual superficial area to allow for waste. On the walls of dwellings, figure the walls as though without openings and allow nothing for waste. If sheathing is laid diagonally, add one-sixth to the actual superficial area. For tight sheathing laid horizontally, add one-fifth for 6-in boards, one-seventh for 8-in boards, and one-ninth for lo-in boards. If laid diagonally add one- fourth for 6-in boards, one-sixth for 8-in boards, and one-eighth for lo-in boards. Bor 3-in matched flooring add one-half to the actual superficial area to be covered. For 4-in flooring add one-third and for 6-in flooring add one-fifth. Ceiling is measured the same as flooring. For drop-siding, add one-fifth to the superficial area. For lap-siding, laid 4 in to the weather, add one-half to the actual superficial area; if 4y2 in to the weather, add one-third. * Everywhere except in New England flooring is always understood to be tongued and grooved. 1564 Building Papers, Felts and Quilts Parts Cost of Labor for Carpenters' Work. There are so many items and con- ditions which enter into the cost of carpenters' work, and the cost varies so widely with the locality, that it is quite impossible to give figures which are of general practical value, although several books * have been published on esti- mating labor and materials for buildings. The following figures of the cost,t for labor and nails, of framing and putting on sheathing and siding and laying flooring were computed on the basis of car- penters' wages at $3 a day of eight hours (37^2 cts per hour). The cost. of framing is almost always figured at a certain price per thousand feet of lumber, board-measure. The cost of laying flooring, sheathing, etc., is almost always figured by the square of 100 sq ft (10 by 10 ft). Character of work Cost For setting up studding and framing walls of wooden $10.00 per 1000 $9.00 to $10.00 per 1000 $ 8.50 per 1000 10.00 per 1000 $1 1 . 00 to $12 . 00 per 1000 $1.25 60 cts per square 75 cts per square $2 . 00 per square 2.25 per square 2 . so per square 3 75 per square 6.00 per square 8.00 per square $10.00 to ?i2.oo per sq For framing and setting floor- joists, 2 by 8 to 2 by 12. . . Framing and setting heavy joists and girders, 6 by 12 to Framincf crable roofs and settincf in olace Framing hip-roofs and setting in place For ptrtting in bridging, after it is cut, per 100 lin ft in the row For covering the sides or roofs of wooden buildings with dressed sheathing, laid horizontally The same, if lairl^ diagonally The cost of labor and nails for laying 6-in flooring, blind- nailed to every joist, without dressing after laying, is about For 4-in flooring not dressed allow ... For 3-in hard-pine flooring, hand-smoothed or traversed. For 3-in red-oak flooring, hand-smoothed or traversed. . For 3-in white-oak flooring, hand-smoothed or traversed For 3-in maple flooring, hand-smoothed or traversed BUILDING PAPERS, BUILDING FELTS AND QUILTS Sheathing-Papers,t Felts, Quilts, Etc. It is well known that frarne build- ings when merely sheathed and clapboarded or shingled on the outside and simply lathed and plastered on the inside, are almost sure to be hot in summer and cold in winter; and as the wood almost always shrinks, cracks result through which the wind finds its way. For these reasons some extra provision should be made for keeping out the wind and the heat and cold; and it is generally admitted that * Readers are referred to The Building Estimator's Reference Book, by F. R. Wa|ker, The New Building Estimator, by William Arthur, Handbook of Cost Data, by H. P. Gillette and the Estimators' Price Book, by I. P. Hicks. To all of these, architects and builders are referred for detailed information and valuable data on costs of laboi and material. t The wages of carpenters varied (1916) in the United States from 35 to 70 cts per hour, or from $2.80 to $5.60 per day of 8 hours. For rates per day higher than those given the figures showing the cost's in the schedule must be raised proportionately. t The terms building paper and sheathing-paper are by the public indiscriminately applied to all kinds of paper used in connection with building-construction. In the trade, however, the term building paper is confined to the rosin-sized and cheaper grades of paper, while the he? "«'"'■ and better grades are classed as sheathing-papers. Building Papers, Building Felts and Quills 1565 there is no material that will do this so well and at so small an expense as good sheathing-papers or sheathing-felts. The papers made for this purpose are com- monly known as sheathing-papers or building papers. There -is a great variety of sheathing-papers manufactured, many of them of great excellence, and even the best are comparatively inexpensive, costing only about $i.oo per IOC sq ft; so that only the better qualities of any kind of felt or paper should be specified. Where the cost of the sheathing-paper on an ordinary house is only a few dollars, it is poor economy to use a cheap paper, as the labor of applying it is an important item and the poorer the paper the more difficult the work of put- ting it on. The qualities which good sheathing-paper should possess are per- manence, impenetrability to air and water and sufficient strength to permit of applying without tearing. Protection or proof against vermin and insects i$ another important requirement. It should not be brittle nor have a lasting strong odor and, for the convenience of the builder, should be clean for handling. There are so many papers possessing all or most of these qualities that it is deemed inexpedient to mention particular brands. The architect should decide for him- self, from the samples with which he has probably been furnished, what papers are best adapted to the particular conditions; and he should then specify those brands, giving, also, the manufacturers' names, instead of leaving the choice to the builder, who will be quite sure to be guided by price rather than by quality. Many object to tarred or saturated sheathing-papers and felts because of their tendency to become brittle and because they emit a strong odor and are some- what disagreeable to handle. On the other hand, the advocates of tarred felts emphasize their cheapness, warmth and even their odor, which makes them vermin-proof. The odor gradually disappears after the clapboards, siding or shingles are put on and the inside walls finished. Sheathing-paper is usually applied just previous to putting on the clapboards, siding, or shingles. It is generally placed horizontally and should lap about 2 in over each sheet and over the paper previously placed around the window and door-frames. If sheathing- quilt or similar material is to be placed under the clapboards or siding, laths should be nailed vertically over it, opposite each stud, and the siding or clap- boards nailed to the laths; otherwise it will be difficult to put them on evenly, owing to the thickness and elastic quality of the quilt. Shingles, however, may be applied directly over it. Sheathing-quilt possesses marked fire-resisting properties. The sheathing-paper and the labor of putting it on should be in- cluded in the carpenter's specifications. Rosin-Sized Building-Papers. These are the common grades of building paper; they are not water- proof, and should not be used on roofs or on walls in damp climates. In dry places they protect from dust, draughts, and to some extent from heat and cold. They are generally either a dull red or gray in color, have a hard, smooth surface, and are clean to handle. They are always put up in rolls 36 in wide and usually contain 500 sq ft. The weight varies from 18 to 40 lb to the roll of 500 sq ft. Insulating and Deadening- Quilts. Among the insulating and dcadening- quilts much in use are those mentioned below. There are also other good ma- terials in this line which are manufactured and used for insulating and deadening purposes. Sheathing- Quilt.* This consists of a felted matting of eel-grass held in place between two layers of strong Manila paper by quilting. "The long, flat fibers of eel-grass cross each other at every angle and form within each layer of quilt innumerable minute dead-air spaces, that make a soft, elastic cushion. This * Made by Samuel Cabot (Inc.), Boston, Maae. 1566 Building Papers, Felts and Quilts Part 3 gives the most perfect conditions for non-conduction." Eel-grass is chosen for the filling because of its long, Hat fibers, which especially adapt it for felting; because of its great durability,* and its resistance to fire; and because, owing to the large percentage of iodine which it contains, it is repellent to rats and vermin. This. quilt is made in single and double-ply thickness, and is put up in bales of 500 sq ft. It is also now made with a covering of asbestos, which tend.rs it thoroughly fire-proof. The material is also very efficient for heat- in sulatio . When used for this purpose there is no objection to nails passing through it. Keystone Hair Insulator. Another material used for similar purposes is the Keystone Hair Insulator.f This consists of thoroughly cleansed catties' hair, between two layers of strong, non-porous building paper, securely stitched to- gether. The hair is chemically treated, so that it is coated with lime, which makes the finished material vermin-proof and odorless. Mineral -Wool Deadeners, which are fire-proof sound-deadening quilts of rock-fiber wool stitched between two sheets of building paper or of asbestos paper according to the grade desired, are made by the Union Fibre Company oT Winona, Minn., and other firms. This company makes, also, what is called Lith and Feltlino, which are sound-deadening materials in board form. They manufacture, also, Linofelt, a building-quilt of flax-fibers (unbleached linen threads), stitched between water-proof paper or asbestos paper according to need. It is H in thick. Linofelt for sheathing in place of ordinary building paper adds from I to i\^2% to the cost of a house. Felt-Papers. There are a great many felt-papers for lining floors and a few are made fire-proof by means of chemicals. As a rule these felts are cheaper than Cabot's QUILT, although the saving in an ordinary residence would be but little, and even among the felts themselves there is quite a difference in cost. In choosing a felt-paper for lining, the architect should select one that is soft and elastic enough to form a cushion, and the thicker the felt, provided it has the above qualities, the greater will be its non-conduction. Some felts are made water-proof by an asphalt center, which is an advantage in case of fire or leaks, but some authorities think that it is doubtful if such felts obstruct the passage of sound as well as felts without the asphalt center. The experience of some acoustical experts seems to show that one of the best methods of deadening is by a combination of he'avy hair-felt or felt-paper with sheets of galvanized iron. Two layers of felt, each from ^2 to i in thick, are placed on either side of a single layer of galvanized iron, the latter resting freely between the felt layers. This form of construction is to be preferred where the deadening-material is not at- tached to the enclosing woodwork. An additional layer of iron and of felt increases the effectiveness of the combination. Saturated Felts.J Common roofing-felts are made by saturating common dry felt with coal-tar pitch. Roofing-felts are commonly made in weights of 12, 15, and 20 lb to the 100 sq ft. Nothing lighter than 12 lb should be used for roofing. They are usually sold by weight. Asphalt-felts are commonly made in the same weights. Dry Saturated Tarred Felts are specially run through a tier of calenders to give a hard, uniform surface and contain a minimum amount of coal-tar. • A sample of eel-grass 250 years old and in a perfect state of preservation, may be seen at Mr. Cabot's office. t Made by H. W. Johns-Manville Company, New York. X The Barrett Manufacturing Company and others make numerous brands of these eiicathing and roofing-papers. Building Papers, Building Felts and Quilts 1567 They are especially adapted for slaters' use, as they will carry a chalk line and are easy to handle. The rolls are 36 in wide, contain 500 sq ft and weigh about 30 lb. Asbestos Building Felts are usually made about 6, 10, 14 and 16 lb to the 100 sq ft, although different manufacturers make different weights. They come in rolls 36 in wide and are sold by weight. Sound-Deadening Felts. These deadening- felts are made by various manu- facturers. In one of these felts * the material itself is rather hard and thin, but it is pressed in such a way as to form small indentations or air-cells. This makes it elastic and breaks up the sound-waves. Asbestos Sheathing. Sheathing-papers or building felts, made of asbestos, are used to a considerable extent for floor-linings and for covering the outside walls of wooden buildings, principally on account of their fire-proof and vermin- proof qualities. These papers are well known in the trade and can be procured without difficulty. They are supplied by the manufacturers in 50 or loo-lb mUs, 36 in wide, on a basis of the following scale of weights: 4 lb to the 100 sq ft 18 lb to the 100 sq ft 6 lb to the 100 sq ft 20 lb to the 100 sq ft 8 lb to the 100 sq ft 24 lb to the 100 sq ft 10 lb to the 100 sq ft 32 lb to the 100 sq ft 12 lb to the 100 sq ft Me in thick 14 lb to the 100 sq ft %2 in thick 16 lb to the 100 sq ft H in thick The sheathing in the Me, ^2 and H-'m thicknesses is used only for special pur- poses where an unusually thick lining is desired for possible fire-protection around exposed flues, for chimney-breasts, etc. When the weight of paper ex- ceeds 32 lb to the square foot it is known as roll-board and is no longer classed by weight per 100 sq ft, but by thickness. For floor-linings, i6-lb paper is gen- erally employed, this weight being sufficiently thick and strong to resist ordi- nary damage in application and in handling. Asbestos felts and building papers appear to have approximately the same effect in retarding the passage of sound- waves as other felt-papers of a relatively similar thickness and quality, while their fire-proof and vermin-proof qualities are a distinct advantage. The cost of asbestos paper and building-felt, while somewhat greater than that of the ordi- nary papers used for similar purposes, is not excessive. The market price varies and depends upon the fluctuations of the market. For example, the cost of 100 sq ft of i6-lb asbestos paper varied from 32 to 40 cts, according to the market, before the war.f Water-Proof Papers. Neponset Black Sheathing is water-proof and air-proof, odorless and clean to handle, and is an excellent paper under siding, shingles, slate, or tin. The rolls are 36 in wide, containing 250 and 500 sq ft. Neponset Red Rope Sheathing and Roofing. This is made of rope- stock, has great strength and flexibility, and is absolutely water-proof and air- tight. It is one of the best sheathing-papers and makes a good cheap roofing for sheds, poultry-houses, etc. The rolls are 36 in wide, containing 100, 250 and 500 sq ft. * Neponset Florian Sound-Deadening Felt, made by F. W. Bird & Son, East Walpole, Mass. t These prices are now much higher. 1568 Paint and Varnish Part 3 Parchment Water-Proof Sheathing. There are various parchment-sheath- ings on the market which are semitransparent, have smooth surfaces, and are odorless, water-proof, air-proof and vermin-proof. They are adapted for general sheathing purposes. In general i-ply weighs 25 lb to 900 sq ft; 2-ply, 25 lb to 500 sq ft; 3-ply, 25 lb to 275 sq ft. They are 36 in wide. Cost of Building and Sheathing-Papers in Place.* The following, al- though necessarily restricted to a few lines, will give a general idea of the cost of different kinds and grades of sheathing-papers, the prices given being fair aver- ages for the materials applied to an outside wall or roof: Price per 100 .square feet Common tarred felts (15 lb per square) 30 cts Red rosin-sized sheathing, best grades 25 cts Monahan's parchment sheathing, single-ply 26 cts Monahan's parchment-sheathing, double-ply • 40 cts Monahan's ship-rigging tar-sheathing, 2-ply 75 cts "Neponset" black (water-proof) paper 45 cts "Neponset" red-rope roofmg $1.20 Sheathing-papers with asphalt center 40 to 50 cts Asbestos building or sheathing-felt, 10 lb per square 22^^ cts Asbestos building or sheathing-felt, 14 lb per square : 31]^^ cts Cabot's sheathing-quilt, single-ply $1.05 Cabot's sheathing-quilt, double-ply $1.25 Barrett's specification-felt 35 cts Barrett's defender, felt -sheathing 80 cts Sackett's water-proof sheathing 30 cts Empire parchment-sheathing, i-ply 25 cts Empire parchment-sheathing, 2-ply 36 cts Empire parchment-sheathing, 3-ply 50 cts Barrett's red rope $1.00 Barrett's black, water-proof sheathing 40 cts PAINT AND VARNISH f Pigments and Vehicles. The solid ingredient of a paint is called the pigment, and is a line powder, nearly all of which will pass through a brass-wire sieve of 100 meshes to the linear inch; in fact, most pigments are much finer than that, and those formed as precipitates by chemical processes are so fine that there is no way to measure them. The liquid part is called the vehicle. This is usu- ally linseed-oil, sometimes with the addition of a little turpentine or other volatile solvent. In the enamel paints it is varnish and in kalsomine and other cold- water paints it is a solution of glue, casein, albumen, or some similar cementing material. The cementing material is sometimes called the binder. Ingredients of Oil-Paint. White lead and white zinc are the common white pigments. There are white pigments of variable composition called leaded zinc and zinc lead, furnace-products, composed of zinc oxide and lead sulphate. There is also a basic lead sulphate, commercially called sublimed white lead, which is a similar furnace-product consisting chiefly of sulphate of lead. These composite white pigments are largely used in mixed paints, lithopone is a mixture of sulphide of zinc and sulphate of barium. It is very white, fine * All prices quoted are pre-war prices and the data are retained for purposes of com- parison and relative values. t The editor is indebted to Professor Alvah H. Sahin for valuable assistance in the Outside Painting 1569 and opaque and largely used as the basis of flat wall-finishes for interior work, but is not durable for exterior work. It is discolored (grey) by strong light, but this is not a very serious practical objection. White lead is used everywhere, but tends to yellow somewhat in the dark. White zinc is chiefly used on interior work, being the whitest paint known. Both are often mixed and both are used in mixed paints. Yellow paint is commonly chromate of lead, or chrome yellow; green is chrome green, which is a mixture of chrome yellow and Prussian blue; blue is ultramarine, or sometimes Prussian blue. The brilliant reds are coal-tar colors as a rule; the dull reds and browns are oxides of iron. Ochres are dull yellow. Carbon forms the base of all black paints, either as lampblack, drop- black (boneblack), or graphite. Linsecd-oil is either raw or boiled. Raw oil is the oil in its natural state as it is extracted from the seed; it should be settled and filtered perfectly clear; it is yellow or greenish yellow in color. Boiled oil is raw oil which has been heated to 400° or 500° F. with compounds (usually oxides) of lead and manganese; it is darker in color than raw oil, and dries quicker. Raw oil exposed in a thin film to the air is converted in about five days into a tough leathery substance; boiled oil undergoes this change in from 10 to 24 hours. Driers. These are compounds of lead and manganese, dissolved in oil, and this solution thinned with turpentine or benzine. They act as carriers of oxygen between the air and the oil, and their addition to a paint makes it dry more rapidly. Some driers are also called japans. Not more than 10% by volume of any of these liquid driers should be added to oil. Excess of drier causes the paint to lack durability. Cheap driers often contain rosin. It iS well to specify that driers and japans should be free from rosin (not resin, as varnish-resins are present in some of the best driers). ''^ Priming Coat. This is the first coat applied to the clean surface. A priming coat for wood is chiefly oil, and is usually equivalent to a gallon of ordinary paint thinned with a gallon of raw linseed-oil. Paint, however, is not thinned to make a priming coat for structural metal. In all wood-work, nail-holes and other de- fects are filled with putty after the priming coat has been applied; but if the wood is resinous, knots and resinous places must be covered with shellac varnish before the priming coat is put on. Pitchy woods, such as southern yellow pine and cypress, do not readily absorb oil, and turpentine should be substituted for part of the oil. Red lead is successfully used as a primer (2 parts to i of white lead) on such woods; this is the standard practice in England, and is better than the use of all white lead. Outside Painting. The priming coat having largely been absorbed by the wood, a second and third coat of paint are to be applied. The most common paint used on houses is white lead. This is commonly sold as paste white lead, containing 8% of oil; 100 lb of this is equal to 2.8 gal in volume, and is commonly mixed with sVi gal of raw Hnseed-oil, i qt of turpentine and i pt of drier to make 6ys gal of paint for the second coat; or with 4 gal of oil, i pt of turpentine and i pt of drier for the finishing coat. If white zinc is used, gV^ lb of dry zinc oxide and 5.7 lb of oil make i gal of paint; to this, turpentine and drier should also be added. White lead, after about a year, begins to chalk, that is, its surface becomes dry and chalky; this does not indicate failure, however, and it makes a good surface for repainting. Finely reticulated checking, not extending through the film, occurs later, and when sufficiently marked indicates need of repainting. In any paint, when cracks begin to extend through to the wood, repainting is called for; these cracks occur sooner on pitchy woods. White zinc, if used alone on outside (not inside) work, is very hard and tends to peel off. Mixed paints (prepared proprietary paints) generally contain zinc mixed with either white lead or some of the pigments based on basic lead sulphate, and some auxiliary 1570 Paint and Varnish Part 3 pigments, such as barytes, China clay, etc., ground in oil and turi)entine and containing the necessary drier. The best of these are excellent, but some are very poor; the safest way to use th^m is to specify them bj' name, and use them according to the maker's directions. Colored paints are commonly made by adding colored pigments to lead or zinc; but some dark paints contain only iron oxides, ochers, etc., as pigments; these weigh from 12 to 14 lb per gal. Painting should always be done in dry weather and no painting should be done until the inside plastering is dry. Paint should not be applied to lumber that is not dry. A week or more should be allowed between successive couts. In painting the out- side of a house, the trim should be painted first; then the body-color can be laid neatly against it. The final brushing should be in the direction of the grain of the wood. It is good practice to have the successive coats (except for white paint) vary a little in color, to facilitate inspection. White, light blue and light green are less durable colors than yellow, gray, or dark colors in general, owing to the fact that the chemical rays of light penetrate the former more easily. A gallon of paint will cover from 400 to 600 sq ft of surface, dcpendihg upon the character of the surface. Roof-paints should contain a larger proportion of oil, and a smaller amount of drier or none at all. Three coats are desirable. Tin roofs and galvanized-iron work should be thoroughly scrubbed and then dried before painting. The shingles on the walls and roofs of a house are sometimes stained with creosote stain, which consists of a pigment suspended in creosote or some similar liquid. The creosote has some preservative effect. Inside Painting. Door-frames and window-frames should receive a priming coat of paint in the shop; if they are to be finished in varnish this paint will be applied to the back only. As has already been said, before any painting is done any resinous knots should be varnished with shellac. All interior surfaces which are to be painted should be puttied after the priming coat and the putty should be applied with a wooden spatula, not a steel one, to avoid marring the surface. The paint for the second coat should contain as much turpentine as oil, that is, its vehicle should be half oil and half turpentine. The effect of this is to make the paint dry with a dull instead of a glossy surface, flat surface being the painter's term. To this the next coat will adhere well. If the next is the final coat, it may be an ordinary oil-paint. When thoroughly dry the gloss may be removed bj'^ lightly rubbing it with pumice and water. Enamel paint consists of pigment with varnish as a vehicle. It is harder and makes a finer finish than oil-paint. It is also more expensive. It is usual to apply it over oil-paint, in which case the last coat of oil-paint should be lightly sandpapered when quite hard and dry. A coat of enamel paint is then put on, and when it is dry it should be sandpapered or rubbed with curled hair. The final coat of enamel is then laid on and it may be rubbed in a Uke manner if a flat surface is desired, or it may be left with the gloss. It is also common practice for painters to make a final enamel finish by adding varnish to white lead or white zinc, very little oil being used in this case. The best varnish for this purpose is a spar-varnish from a thoroughly reliable maker. The quicker-drying varnishes will crack and ALLIGATOR. Varnish. There are two principal kinds of varnish, (i) spirit varnishes, of which shellac varnish is the most important, and which consists essentially of a resin dissolved in a volatile solvent, and (2) oleoresinous varnishes, in which the resinous ingredient is combined with linseed-oil, and this compound is dissolved in turpentine or benzine. The oleoresinous varnishes are commercially the more important, and are largely used in interior finishing. A gallon of varnish covers 500 sq ft, one coat. Surfaces to be varnished are treated in the following manner. If the wood is open-grained, as oak, chestnut, or ash, it first receives a Repainting 1571 coat of paste-filler. Liquid fillers are not desirable, as they form a poor base for subsequent work. A paste- tiller is really a sort of paint, the pigment being silex, or ground quartz, and the vehicle is a quick-drying varnish made thin with tur- pentine or benzine. This is rubbed strongly in on the grain of the wood with a short stiff brush, and as soon as it has set, usually within half an hour, it is rubbed off with a harsh cloth or a handful of excelsior, the rubbing being hard across the grain of the wood. If it is desired to stain the wood, the oil-stain may be mixed with the filler; but if a close-grained wood is used, which needs no filler, the oil- stain may be thinned to the desired color with turpentine or benzine and applied as a wash. In cleaning the filler out of moldings, corners, etc., a suitably shaped stick, but not a steel implement, may be used. If any puttying is necessary it is done next. After two days the first coat of varnish is appHed; after five days it should be rubbed with curled hair or fine sandpaper to remove the gloss, so that the next coat will adhere well; then one, two or three more coats of varnish are added, five days or more apart, each coat being rubbed. The last coat may be rubbed or left with the natural gloss. Outside doors, window-sills, jambs, inside blinds, and all surfaces exposed to the direct rays of the sun, should be varnished with spar-varnish and left glossy. If shellac varnish is used as the in- terior finish it is applied in the same way, but at least six coats should be applied. Floors which are to be varnished should be treated as has been described; but if they are to be waxed they should receive one or two coats of shellac varnish, then five or six coats of wax, at intervals of a week, each coat beii>g well polishec? with a weighted tloor-brush made for the purpose. Floor-wax is not beeswax, but is a compound wax made for the purfx)se. Shellac is a good floor-varnish; it discolors the wood less than any other varnish, and dries rapidly. Painting Plastered Walls. Plastered walls which must be painted are usu- ally washed with a solution of soap and then with a solution of alum. When this is dry it is sponged off, then allowed to dry, then oiled, then painted. If the paint is apphed to the fresh piaster the lime in the plaster will attack the paint. Repainting. The exterior woodwork of a house needs repainting once in five to ten years, according to climate and other conditions, although if not done with proper material or sufficient care it will not last as long as this; the interior should, with good care, stand from fifteen to twenty years, and then may not require complete renewal. Exterior paint sometimes loses its luster, while the body of the paint is still good, and in cases of this kind it is sufficient to wash the surface and then give it a coat of oil. This replaces the oil which has superficially perished, imparts a gloss and brings out the color. If the paint is worn off so as to show the wood in places, or is peeling, it must be very carefully examined. In extreme cases it is necessary to burn off the old paint; this is done with a painter's torch, a lamp which burns alcohol, naphtha, or kerosene, and which furnishes a flaring blast of flame, which is directed against the painted surface just long enough to soften the paint which is at once removed with a scraper while still hot. The paint is not actually burned, but only softened by the flame; it may, however, be removed as well as softened by this method. Houses cov- ered with pitchy wood, like southern pine, sometimes require this treatment, and the next painting is found to be more lasting. In many cases it is sufficient to thoroughly scrub the surface with a stiff steel- wire brush. Interior surfaces may be cleaned (if the removal of the old paint and varnish is necessary) with varnish-remover; this is a mixture of solvent liquids, which penetrate the old paint or varnish and soften it, when it may be removed with scrapers or brushes. There is less danger of fire with this method than with the burning-off method, but it is slower and costs more. It must not be forgotten that varnish-remover is volatile and highly inflammable and must not be used in a room where there is 1572 Paint and Varnish Part 3 a fire. It is especially suitable for cleaning out moldings and all irregular sur- faces from which the varnish may then be removed with stiff brushes, if it is not convenient to use scrapers. It is especially desirable to have floors occasionally cleaned in this way; but if a house has been varnished originally with a first- class varnish it may be necessary only to wash it thoroughly and then apply an- other coat of varnish. Smoke and dirt may often be thoroughly removed from ceilings with the crumbs of fresh bread, where washing would not be desirable. A io% solution of carbonate of soda (sal soda) in hot water may be used to remove old floor-wax. The Painting of Structural Steel. Steel being usually more perishable than wood, as well as more expensive, and used for service where its strength is essential to the stability of the structure, its protection from corrosion by paint- ing is of much importance. It must first of all be recognized that the precaution always taken in painting wood, to secure a clean surface for the paint, must not be omitted with steel. Mud and dirt must first be removed from the steel; then It must be examined for rust, and any rust-spots must be thoroughly cleaned. Loose scale may be removed with wire brushes, but thick and closely adherent rust must be removed with steel scrapers, or with hammer and chisel if necessary. No doubt the best way to clean steel is to use the sand-blast, but it is not available for much architectural work. In an^^ case much care must be taken to obtain a clean surface. On wood the priming coat sinks into the wood and forms a perfect bond between it and the succeeding coats; but on metal no such thing is pos- sible and it is a case of simple adhesion, which demands a clean surface for effi- cient results. The paint for structural metal should be tough and elastic, and to as great a degree as possible it should be water-proof. Less than two coats should never be applied, and three are better. Paint is always thin on edges and angles, and also on bolt and rivet-heads; it is therefore good practice, after the first full coat, to apply a partial or striping coat, covering the angles and edges and the surface for at least i in JDack from the edges, and covering all bolt- heads and rivet-heads. After this striping coat has become dry, the second full coat is applied, and it may then be assumed that the whole surface has received two full coats. At least a week should elapse between coats. In designing the steelwork, all cavities which may be filled with rain during erection should be properly drained; and during erection all small cavities should be filled with cement, and all contact-surfaces thickly painted. Kinds of Paint for Structural Steel. Red lead is more generally used than anything else as a paint for structural steel. It is a " true red lead " (Pb304), usu- ally made from litharge (PbO), and frequently containing from lo to 20% of the latter. If it contains much litharge, it rapidly thickens when mixed with oil and finally hardens; this makes it a paint difficult to apply. If, however, the material from which it is made is reduced to a sufficiently fine powder before it is oxidized, an almost completely oxidized red lead is produced, which is as easily worked as white lead, and better in every respect. The requirements of the govern- ment of the United States have for years called for red lead of not less than 94% of " true red lead " (Pb304), and the Navy Department, as well as several large railway companies, is now using large amounts of red lead which has not less than 98% of " true red lead." It may now be obtained in paste-form, similar to white lead and containing about 6)2% of raw linseed-oil. 32, lb of red lead (dry pig- ment) to I gal of oil is the maximum and this is especially suitable for hydraulic work; 28 lb to i gal of oil (containing 20 lb of pigment in a gallon of paint) is more common; while 25 lb to a gallon of oil is a common requirement for rail- road-specifications. Finely ground graphite in linseed-oil is a favorite paint for metal; it flows well, is easily applied, less expensive than red lead, and if well Window-Glass and Glazing 1573 made gives excellent results: Graphite is sometimes mixed with lampblack, prob- ably with advantage. Boneblack is also an important ingredient of carbon PAINTS. Formerly oxide of iron in Unseed-oil was used more than all other paints for this purpose; but while many engineers still like it, its use has very greatly di- minished. AsPHALTUM has been used and is still used,, as a varnish either alone or in combination, and some of these asphaltic preparations are fairly satis- factory. The fact is, that a really competent paint-manufacturer can make a reasonably good paint out of any of these, and if the paint is carefully apphed the results will be satisfactory. There are great differences in painters. In re- gard to the surface of structural steel covered by a gallon of paint, there is a great difference of opinion among experts. Some say from 300 to 400 sq ft, others 1000 or 120Q sq ft. The truth is that any paint may be brushed out into an exceedingly thin film by a skilled workman, while ordinary usage results in a film at least twice as thick. The general opinion is that it is not wise to esti- mate more than 400 sq ft to the gallon for one coat. Varnish-paints cover less than oil-paints, but if well made they are very durable. Painting on Cement and Concrete. Cement and concrete-work are diffi- cult to paint, because they are strongly alkaline and even caustic when new. Work in these materials should be allowed to stand a year or two if possible be- fore it is painted; then it may be painted with any ordinary paint. A practice which has been highly recommended is to wash the surface, repeatedly if possible, with a strong solution of zinc sulphate, the sulphuric acid uniting with the free lime and the zinc being left in the pores as an oxide or hydrate. Some prepara- tions for this purpose are on the market; and while some are probably good, others are to be distrusted. The best way is to allow the surface to age, if this is at all possible. WINDOW-GLASS AND GLAZING* Glazing. The glazing of windows originally belonged to the painter's trade» and when glass is broken, it is still customary to go to a painter to have it re- placed; but custom has so changed in some parts of the country, that when new windows are to be glazed, the work is sometimes done at the mill or factory where the sashes are made, sometimes by the local glass-jobber in the town where the building is being erected, and again, in other localities, the glazing of new buildings is still done by the painter. Common window-glass is usually set with putty and secured with triangular pieces of zinc called glaziers' points, driven into the wood over the glass and covered with putty. In the best work, a thin layer of putty is first put in the rebate of the sash and the glass is then placed on it and pushed down to a solid bearing. This is called back-puttying. The points are then driven about 8 or 10 in apart and the putty applied over the glass and points so as to fill the rebate. Outside windows should always be glazed on the outside of the sash. Common window-glass has a slight bend in it, the re- sult of its original cylindrical shape; it should be glazed, therefore, with the convex side out, as this reduces to a minimum the effects of the waviness when looking through it either from the outside or inside. Plate glass, in window- sashes and door-lights, should be back-puttied and secured by wooden beads. Leaded Glass. It was formerly a common practice for architects to name in the specifications a certain sum of money to be allowed by the carpenter tor the leaded glass and to be expended under the direction of the architect. Where * Condensed from article on Window-Glass and Glazing by Professor Thomas Nolan in Building Construction and Superintendence, Part II, Carpenters' Work, by F. E. Kidder. 1574 Window-Glass and Glazing Part 3 clear glass was used, the pattern was sometimes shown on the drawings and the glass was specified in the same manner as any other work. When colored glass was to be used, it was customary to make a definite allowance and then to en- trust the work to a good art-glass manufacturer. But leaded glass should be designed, furnished and put in place by those who are entirely familiar with its manufacture and its limitations; the purchase of the same should be left entirely in the hands of the owner; ajid no specification as to its price or make should be used by the architect. The colored-glass windows should show as much indi- vidual artistic taste as any other picture or decoration used in the Ijuilding. The' cheap and inartistic leaded glass is fast becoming a thing of the past and owners are confining themselves to purely works of art placed in some appropriate location in the building. Sheet Glass. General Description. Common window-glass is technically known as sheet glass or cylinder glass. "It is made by the workmen dip- ping a tube with an enlarged end in the molten glass or metal until from 7 to 10 lb are gathered up. Then it is blown out sli^^htly by the workman, taken on a blowing-tube and still further blown and manipulated, until a cylinder about 15 in in diameter and 60 in long is formed. This cylinder has the two ends trimmed off and is then cut longitudinally and gradually warmed. It is then placed on a large flat stone supported by a carriage, where it is heated until it softens sufficiently to open out flat; the carriage is then pushed into the anneal- ing-chamber and the sheet taken off." About the year 19 10, sheet glass blown by machinery, utilizing compressed air, was perfected, and the result has been a gradual decrease in its cost. The cylinder blown by compressed air is split open and flattened out in just the same manner and by the same process as in the mouth-blown cylinder. Grades and Qualities of Sheet Glass. Sheet glass is graded as double-thick, or single-thick, and each thickness is further divided into three qualities, first, second, or THIRD, according to its relative freedom from defects. The price varies according to the strength and quality. It should be remembered that sheet glass is always wavy, the result of the flattening of the cylinder. Many suppose that by designating sheet glass, crystal-sheet glass, selected-sheet glass, or SHEET glass FREE FROM WAVES AND IMPERFECTIONS, a sheet glass free from waves and blemishes can be obtained. The terms and names do not change the nature of this glass, which still remains sheet glass, characterized by the defects inherent in the method by which it is manufactured. To obtain a thin glass, free from waviness, plate glass, H in thick, sometimes known as crystal plate, or plate glass Me in thick, must be specified. Since the improvement in the manufac- ture of window-glass in this country, scarcely any sheet glass is now imported for glazing purposes. A small amount of Belgian sheet glass is brought to this country and used along the Atlantic seaboard for picture-framing. The low prices of the American sheet glass, and its excellent quality, have practically forced imported sheet glass out of the market. All common sheet glass, without regard to quality, is graded according to thickness, as single-thick or double- thick. The thickness of the double-thick glass is a scant H in while that of the single-thick averages about VI2 in. It is customary to use the double thickness for sheet glass over 24 in in width. The best quality of sheet glass is specified as A A, the second as A and the third as B. Sizes of Sheet Glass. The regular stock -sizes vary by inches from 6 to 16 in in width. Above that they vary by even inches up to 60 in in width and 70 in in length for double thickness, and up to 30 by 50 in for single thickness. Cost of Sheet Glass. The prices for sheet glass, as for all other clear glass, vary with the size, strength and quality. Prices are determined by a schedule Sheet Glass 1575 or price-list,* giving the price for each size, in both thicknesses, and all qualities; and from these prices a very large discount is allowed. Fluctuations in prices are regulated by the discount, the list usually remaining unchanged for a number of years. The price-list prevailing in 19 13 was in use from October i, 1903. The only way to ascertain the price of a light of glass of a given size is to find it from the price-list, from which the discount, quoted by the glass-dealer, must be deducted. For the benefit of the Pacific Coast trade there is a Western Glass List t which differs somewhat from the Eastern list. The list is for sheet glass, the plate glass lists being the same in the East and West. The price per square foot increases rapidly as the size of the pane increases, so that it is much cheaper to divide a large window into eight or twelve lights than into two lights. Com- pared with the cost of the building, however, the glass is a small item and in the better classes of buildings each sash is usually glazed with a single Hght of glass. In factories, workshops, etc., where there is usually a large amount of glass- surface, the size of the lights is not of so much importance, while the saving by using small lights is quite an item; hence twelve-light and even sixteen-light windows are generally used in such buildings. The following table shows quite clearly the relative cost (19 13) per square foot of different-sized panes of Ameri- can glass, the prices given being an average at that time for the whole country. Comparative Cost (1913) of American Sheet Glass per Square Foot, Based Upon a Discount of 90 and 20 Per Cent on the List of October 1, 1903 t • Grades Sizes of lights in inches 10X12 15X20 24X34 30X36 36X40 40X60 60X70 1 Prices hi cents per square foot Double strength: First quality Second quality Single strength: First quality Second quality — 7.0 6.0 5.0 4.3 8.3 7-3 4.8 4.5 9-4 8.3 6.4 5.6 10. 9.0 6.8 6.0 10.8 10.0 14.0 14.4 29.2 27.0 1 Crystal-Sheet Glass, 26-Ounce. This glass is made by the cylinder-process, but is a little thicker than the ordinary double-strength glass. It is probably the best glass made, next to plate glass, but owing to the method of its manu- facture is necessarily characterized by a wavy appearance. If good glass is required for first-class residences, hotels, office-buildings, etc., polished plate glass should be used. The latter invariably gives satisfaction, while sheet glass, no matter of what thickness, is usually disappointing in its appearance. Defects of Sheet Glass. All sheet glass, when looked upon from the outside, has a wavy, watery appearance, like the surface of a lake slightly agitated by * The price-lists of glass have been omitted as they can readily be obtained from the glass-dealers in any city. Such lists are not of much service unless they are complete; and the full lists are too long to be inserted in a condensed handbook. t This list, with discounts from the prices given, may be obtained from the W. P. Fuller Company, San Francisco, Cal. t Much valuable information in regard to Window-Glass and Glazing was furnished by Mr. S. C. Gihnore of the Hires-Turner Glass Company, Philadelphia, Pa. 1576 Window-Glass and Glazing Part 3 the wind; and when the sunshine falls upon it the irregularity of the surface is greatly emphasized. This characteristic of sheet glass is due to its being made in the shape of a cylinder and then stretched or flattened out into a sheet, and it cannot be wholly avoided. Besides this universal defect, the cheaper grades are often STRINGY, BLiSTERY, SULPHURED, SMOKED, or STAINED; SO that, in looking through the glass, objects seen at a distance are deformed and distorted. Plate Glass. General Description. Plate glass is commonly known as POLISHED PLATE GLASS because its surface is finely polished and thus made clear and transparent. It is more largely used every year for windows of fine resi- dences, hotels and office-buildings, where transparency is desired from the inside and an elegant appearance required on the outside. The process of manufacture of plate glass is entirely different from that of sheet glass. In making plate glass the metal, which is prepared with great care, is melted in large pots and then cast on a perfectly flat cast-iron table. "The width and thickness of the plate is determined by means of metal strips called guns, which are fastened on, and on which a heavy, metal roller travels. The ends of the guns are tapered so that when the roller is at one extremity, it and the guns form three sides of a shallow, rectangular dish. The molten metal is poured on and the roller passed along slowly, forcing the metal in front of it and rolling out the sheet." The sheet is then annealed and forrris what is known as rough plate, which is used for vault- lights, skylights, floor-lights and the like. "For polished plate the rough plate is carefully examined for flaws, which are cut out, leaving the largest-sized sheet practicable. The plate is then fastened to a revolving table by means of plaster of Paris, and two heavy shoes, shod with cast iron, are mounted over it. The table is then revolved and sand and water fed onto the surface; the shoes revolve also, going over all parts of the plate and grinding it down to a true j^lane. Emery-powder is then fed on, in successive degrees of fineness until the plate is made absolutely smooth and all grit removed. After this, new rubbers, shod with very fine felt, are put on and liquid rouge is added for the polishing. When one side is completed the other side is similarly treated, the plate losing about 40% in weight by the operation." Qualities of Polished Plate Glass. For glazing purposes there is but one quality of plate glass on the market. The best of this is selected for manufactur- ing mirrors. At one time, plate glass was extensively imported, but the gradu- ally improving methods of the American manufacturers, as well as the great cheapening of the process, have practically eliminated imported plate glass from the market. The American plate glass is equal in every respect to that which was imported. The usual thickness of polished plate glass is from yi to Mo in, but it can be made thinner than this; and when required for residence- windows or car-windows, may be obtained in ^le or H-in thicknesses. It is manufactured from the same thickness of rough plate used for the ordinary thicknesses, but is ground down thinner and, owing to the additional cost of grinding, as well as to the risk, is more expensive than glass of the ordinary thickness. Cost* of Polished Plate Glass. The cost of plate glass of ordinary thickness varies with the size of the lights. The net price of polished plate glass (1913) glazing quality, was about 45 cts ($0.45) per sq ft, for sizes of not more than 10 sq ft per plate, 50 cts ($0.50) per sq ft for sizes containing from 10 to 50 sq ft per plate, and 65 cts ($0.65) per sq ft for sizes containing not more than 120 sq ft per plate. For larger sizes the price increased rapidly up to $2.00 per sq ft. The price, however, can be accurately determined only by means of a price-list and discount. The price-list in use (19 13) was introduced in March, 19 10, and the * These are pre-war prices and the data are retained for purposes of comparison, Window- Glass 1577 discount was about 90%. Plate glass -yieln thick costs 15% more than glass of the regular thickness on account of the extra expense of grinding it down. Plate glass H in thick costs from 25 to 40% more than glass of the regular thickness. Sizes of Polished Plate Glass. Plate glass is cut into stock sizes, varying by even numbers from 6 by 6 in up to 144 by 240 in, or 138 by 260 in. Comparative Cost of Different Kinds of Window-Glass. The following table gives an idea of the comparative cost of the different kinds and qualities of glass used in this country for g'azing. The prices for the sizes are the 19 14, net, average prices. The first column of the table gives the kinds of glass, and includes both the American plate and the American sheet glass. The other columns of the table give the sizes of the different lights in inches. Comparative Cost of DiflFereat Kinds of Window Glass • Kinds of glass American Plate Glass Glazing-quality Crystal-sheet glass, 26-oz American Sheet Glass Double-strength, first quality Double-strength, second quality. . Single-strength, first quality , Single-strength, second quality Sizes of lights in inches 24X32 30X36 36X40 48X60 $2.35 1. 00 0.54 0.47 0.37 0.32 $3.38 1. 54 0.83 0.73 0.56 0.50 $4.60 2.34 .25 • 13 $9.80 6.66 3-55 330 It will be seen from this table that the relative difference in the cost of plate and sheet glass decreases rapidly as the sizes of the lights increase. The prices in this table are based on the list of October i, 1903, on a discount of 90% for plate glass, 90 and 20% for American sheet glass and 85% on A A double- thick for 26-OZ crystal-sheet glass. Wire-Glass. This is described in Chapter XXIII, page 821. Figured Rolled Glass. This is a translucent or obscured glass with a pat- tern stamped on one surface. As the molten metal is rolled out on the table, the design, cut into the table, imprints itself into the soft glass. This kind of glass has almost entirely supplanted the ordinary ground glass because of its greater cleanhness. There are several popular designs on the market, made by various manufacturers. Some of the designs in common use are known as moss, maze, COLONIAL, FLORENTINE, COBWEB, etc. This glass is usually made H in thick and in large sheets from 24 to 42 in wide and from 8 to 10 ft long. Maze, Floren- tine and COBWEB designs can be had either with or without the wire mesh in them. One important property of figured rolled glass is that of diffusing the light which passes through it. (See, also, pages 1453 and i554-) . Pressed Prism-Plate Glass, f This is manufactured in different patterns and for different purposes and includes (i) Imperial Prism-Plate Ornamental Glass in five different patterns, (2) Imperial Prism-Plate Glass and (3) Imperial Sky- light Prism Glass. The general description is as follows: * These are pre-war prices and the data are retained for purposes of comparison. t Manufactured by the Pressed Prism Plate Glass Company, Chicago, 111. See, also, pages 1453 to 1456. 1578 Window-Glass and Glazing Part 3 (i) Imperial Prism-Plate Ornamental Glass is plate glass ground and polished on one side. It is manufactured in plates, 54 by 72 or 72 by 54 in, can be cut into smaller sizes, and is made in five different stock patterns. It is used in modern mercantile, office and public buildings for partitions, transoms, door- lights, vestibule doors, ornamental ceiling-lights, bank-windows and other street- windows, and in all places where semiobscurity and ornamental effect are desired. On account of its prismatic qualities it gives a strong diffusion of light for office- use where privacy is desired. (2) Imperial Prism-Plate Glass. This is manufactured in large sheets, 54 by; 72 or 72 by 54 in, and can be cut into smaller sizes. It is made in several different angles in order to obtain the proper diffusion of Ught for varying conditions. It is a plate glass, ground and polished on one side. There are no wires or bars to collect dirt and retard the light and it is very easily cleaned. It is used in the upper sashes of windows and in transoms, store-fronts, etc. (3) Imperial Skylight Prism Glass. This is made in unit plates, 18 by 60 in, with a H-in back, and conforms to the requirements of the Board of Fire Insur- ance Underwriters. It is used for skylights, roofs over areaways and in light- Wells, etc. The possibility of leakage is lessened on account of the large-sized plates in which it may be obtained. These plates, however, can be cut into smaller sizes if required. It is particularly adapted for lighting the rear parts of stores and for railway-stations, sheds, etc. Prism Glass, for glazing windows, skylights and sidewalk-lights, is now manu- factured in a large number of forms in both prisms and sheets, and by several companies. The diffusing properties of several types are described on pages 1453 to 1456 under the subject of Illumination. This glass is made with sharp prisms which are glazed horizontally in the windows and by refracting the light throw it back horizontally into the rooms, adding very materially to the in- terior lighting. It is manufactured by several companies and can be procured from glass-jobbers in practically all the cities of the .Umted States. (See, also, page 821.) Glass prisms for lighting are made of pieces of glass of standard dir mensions, about 4 in square, with a smooth outer surface and an inner surface di- vided into a series of prisms. They are, in many cases, formed into plates by the process of electroglazing, the edges of the prism-lenses being welded together, so to speak, by a narrow line of copper which gives the desired stiffness and strength for use in large frames, and also an attractive appearance considered by some to be superior to ordinary leaded work. These prism-plates can be made in any desired size, but for very large surfaces two or more plates, divided by means of metal sash-bars, are generally used. (See, also, page 821.) The commercial value of these prisms depends on that property of glass which causes what is known as retraction. Prism-plates recei\ c the light from the sky, not necessarily from the sun, and refract or turn it back into the room which is to be lighted. With an ordinary window the light from the sky, passing through the glass, strikes the floor at a point not very far distant from the window. As the color of the floor is usually dark, reflecting perhaps only one-tenth part of the light falling on it, the rear parts of the room receive only a small portion of the light which enters the window. For this reason it has been necessary to make very high stories for deep rooms, in order to light, even moderately, those parts which are at a distance from the window. When prisms are substituted for the common window-glass or plate glass, the rays of light as they enter the glass are refracted, and by employing prisms of the proper angle, the rays may be given almost any direction. Moreover, by utilizing different prisms in the same plate, some of the rays may be directed to the rear of the room while others are thrown so as to strike near the front. The prism-plates do not increase the Prism Glass 1579 quantity of light entering the window, but simply redistribute it, directing it into those portions of the room in which it is most needed. By thus changing the direction of Hght-rays a room with a low ceiling can be better lighted than when sheet or plate glass is used. To insure success in the lighting of interiors by means of prisms requires, however, a superior quality of glass, and careful scientific calculations and experiments, besides practical and attractive means of glazing and methods of installation. These requirements have been met by the several companies making these prisms and their products may be con- sidered among the relatively new building materials. They have been very successfully applied to the lighting of dark rooms by daylight. The application of prisms to any particular building depends upon the surrounding conditions and requirements, each case requiring some special treatment; but in a general way the various appliances used in the installations may be divided into four classes as follows: (i) Vertical Plates, which are set directly in the sashes in place of the ordinary window-glass. They are commonly used for the transom-lights of store-windows and the upper sashes of double-hung windows. They may also fill the entire window. (2) Foriluxes, which are vertical prism-plates set in independent frames and placed in window-openings substantially flush with the face of the wall. (3) Canopies, which are external prism-plates in independent frames, placed over window-openings and set at an angle with the vertical, a position similar to that of an ordinary awning. (4) Pavement-Prisms, which are set in iron frames in the pavements or side- walks, in place of the ordinary bull's-eye lights. In connection with the pave- ment-prisms, when a well-lighted basement is desired, vertical plates of prisms, hung below and opposite the pavement- lights, are often used. These hanging, vertical plates receive the light from the pavement- prisms, and again chang- ing its direction, project it horizontally into the basement. This feature is illustrated in the figure here given, reproduced through the courtesy of the Luxfer Prism Company. The canopies may be made either stationary or adjustable and may be em- ployed in a variety of ways, combining the useful with the ornamental. The hanging, vertical plates lend themselves to a highly decorative treatment. In both the fixed and hanging vertical plates the prisms may be arranged to pro- duce ornamental effects, and designs may be inwrought on the face of the prism- plates to correspond with the designs worked into the surfaces of the building and with the style of the entire facade. The prism-plates weigh no more, and often less, than plate glass of the same size, while they are much stronger in resisting wind-pressure, the action of hail and the impact of flying fragments. Although transmitting a very large amount of light, these prism-plates are not transparent in the ordinary sense, and may thus be used as screens to hide un- attractive views or to prevent persons looking either in or out of a window. At Refraction and Transmission of Light by Prisms 1580 Window-Glass and Glazing I'art 3 t;he same time a maximum quantity of light is admitted. Tiie prism-plates, owing to the still, durable manner in which they are united by the electro- glazing process, serve, also, as a fire-retardant or as a partial substitute for the ordinary iron tire-shutters. The copper glazing forms, as it were, a continuous rivet, which holds the individual prism-lights together, even after they have become badly cracked by the action of fire and water. The details of the vari- ous makes of piisms are too complicated to be set forth in a few pages, but they are well described in the various handbooks and catalogues published by the different manufacturers. From a commercial point of view the special ad- vantages of these systems of interior lighting are manifold. They transform rooms, particularly basements, otherwise too dark for occupancy, into income- producing spaces; in many buildings they do away with the use of light-shafts, thus saving a large amount of valuable floor-space; and in all large or deep rooms they effect a great saving in artificial lighting. Once installed, there is no cost for maintenance. The extent to which these prisms have been used by architects, in both new and old buildings, shows that they have had. a decided influence upon commercial architecture. Glass for Skylights. General Description. The glass ordinarily used now for skylights is either rough or ribbed skylight-glass, and since the great cheapen- ing in the process of manufacturing glass with wire mesh in it, wire-glass, also, is being largely used for this purpose. The sizes used depend largely upon the pitch of the skylight, small sizes being more desirable when the pitch is slight. The weight of rough or ribbed glass, with or without wire mesh, is approximately as follows: Weight of Rough 01 Ribbed Glass ' Thickness in inches. Weight in pounds . . . 1/8 2 Me 2 1/2 H 3I/2 5 7 81.4 10 I I2K2 Cost of Skylight-Glass.* The different kinds of skylight-glass in small quan- tities were quoted (1914) about as follows: Cost of Skylight-Glass Kinds of glass Cost Rough or ribbed skylight-glass, ^'^-in 6 cts per sq ft 8 cts per sq ft 12 cts per sq ft 16 cts per sq ft 20 cts per sq ft 20 cts per sq ft Roueh or ribbed skvlicht-class M-in Rough or ribbed wire-glass, /i-in . Maze Cobweb, or Florentine wire-glass Sheet prism glass Glass for Mirrors. Mirrors are made by silvering one side of a sheet of pohshed plate glass. This is the only kind of glass suitable for making mirrors, because, unless the surface of glass is polished, the reflection is distorted. A generation ago, mirrors were made by the old-style process of pressing the glass by means of heavy weights onto mercury, backed by tinfoil, the affinity of mer- cury for tin forming an amalgam which protected the back of the mirrors and gave the reflection. This was a very slow and expensive process. During the twenty-five years prior to 1913, practically all of the mirrors made were manufactured by what is known as the patent-back process, in which nitrate * The prices have materially advanced and as they change from year to year, the man- ufacturers' lists must be consulted. Memoranda on Roofing 1581 of silver is precipitated in a film over the surface of the glass, thus giving it the property of reflecting. This film is afterward covered and protected by shellac, varnish and paint. This modern method of manufacture has made it possible to supply mirrors in considerably less time, and at a very much lower cost, than when manufactured by the old-fashioned mercury-back process. There are many who claim that in spite of modern processes of manufacture, the old method produced the best results as far as durability is concerned. This is evidenced by the following statement inserted by Mr. Kidder in the preceding editions of the Pocket-Book: "There are two kinds of mirrors on the market, one the old time reliable mercury-back mirror, the other the nitrate of silver, or what is better known to the trade as the patent-back mirror. The latter is now and has, in recent years, been most extensively sold as a substitute for the former. In the manufacture of mercury-back mirrors no chemicals are used, only two metals, mercury and tin-foil. The aflinity of mercury for tin forms an amalgam impervious to and not affected by the atmosphere. A mercury-back mirror is universally considered to be the only durable and permanent mirror. A nitrate- of-silver 6r patent-back mirror is produced by the precipitation of a chemical solution of nitrate of silver and other media on the surface of the glass, to which is added one coat of shellac varnish overlaid with one or more coats of paint. This mirror, irrespective of the quality of the glass from which it is made, will steadily deteriorate from the date of its manufacture to that of its final collapse, which may occur at any time from a few months, but certainly within a few years." MEMORANDA ON ROOFING Shingles.* The best shingles are those made from cypress, cedar, redwood, white and yellow pine and spruce, in the order mentioned. Redwood, while perhaps not quite as durable as cypress, is less inflammable; sawed pine shingles are inferior to cedar, and spruce shingles are not suitable for good work. Number and Weight of Cedar and Pine Shingles Per Square of One Hundred Square Feet Number Weight per square Number Weight Length, Assumed Weather of of of nails width, ,or gauge. shingles nails per m m per Cedar. Pine, per square, square f lb lb square lb 14 4 4 900 210 233 I 800 4.50 15 4 A'A 800 200 222 1600 4.00 16 4 5 720 192 213 I 440 3.60 18 4 SV2 r)=;5 197 218 I 310 3.28 20 4 6 600 200 222 I 200 3 00 22 4 6j/2 554 203 226 I 108 2.77 24 4 7 S.3 20(3 229 I 030 2.58 Sizes of Shingles. Cedar and redwood shingles as commonly sawed are 20 in in length, and cypress shingles usually from 20 to 24 in long, the longer ones allow- * For more complete information see Kidder's Building Construction and Superinten- dence, Part II, Carpenters' Work, pages 321 to 325. t To allow for waste, add from 6 to 10%. the greater allowance being for the sbortei shingles. 1582 Memoranda on Roofing Part 3 ing a greater exposure to the weather. Redwood shingles and the cedar shingles from the States of Washington and Oregon, which States furnish most of the shingles used west of the Mississippi, are He and ^le in thick at the butt; cypress shingles are usually sawed thicker. Those used in Boston are %& in thick. Ordinary roofing-shingles are of random widths, varying from 2y2 to 14 and sometimes 16 in. They are put up in bundles, usually four bundles to the thousand. A thousand common shingles means the equivalent of i 000 shingles 4 in wide. Dimension-Shingles are sawed to uniform width, either 4, 5, or 6 in. Dimen- sion-shingles with the butt sawed to various patterns are also carried in" stock. On hip-roofs, or for four valleys, add 5% for cutting. On irregular roofs with dormer-windows, add 10%. It is claimed that redwood shingles will go farther than cedar shingles. With a rise to the roof of from 8 to 10 in to the foot, cedar shingles, or any shingles 16 or 18 in in length, should be laid from 4 to 4H in to the weather; with a rise from 10 to 12 in, from 4H to 4% in to the weather; and on steeper roofs they may be laid from 4y2 to 5 in. Redwood shingles may be laid H in more to the weather. Some authorities allow slightly greater ex- posures for these lengths. Where the longer shingles are used the exposure to the weather may be increased up to 7 in for the 24-in lengths. On walls cedar shingles are commonly laid 5 in to the weather, and redwood shingles 6 in. Labor. An average shingler should lay i 500 shingles in 9 hours on plain work; on irregular roofs with dormers, i 000 per 9 hours. Nails. It requires about 5 lb of threepenny or 7>i lb of fourpenny nails to I 000 shingles. Slate Roofs Characteristics of Good Slate. A good slate should be both hard and tough. If the slate is too soft, however, the nail-holes will become enlarged and the slate will become loose. If it is too brittle the slate will fly to pieces in the process of squaring and holing and will be easily broken on the roof. "A good slate should give out a sharp metallic ring when struck with the knuckles; should not splinter mder the slater's axe; should be easily holed without danger of fracture, and should not be tender or friable at the edges." The surface when freshly split should have a bright metallic luster and be free from all loose flakes or dull sur- faces. Very few of the Vermont slates, however, have the metallic luster or ribbons. Most slates contain ribbons or seams which traverse the slate in approximately parallel directions. Slates containing soft ribbons are inferior and should not be used in good work. Color. The color of slates varies from dark blue, bluish black, and purple to gray and green. There are also a few quarries of red slate. The color of the slate does not appear to indicate the quality. All slate quarried in Maine is black as is also that quarried in Virginia, while that quarried in Pennsylvania and Maryland is also black but borders on dark blue and is advertised by some firms as dark blue. Slate quarried i-n New York State is red, of various tints, while that quarried in Vermont is of various colors, such as green, purple, varie- gated, etc. The red and dark colors were formerly considered the most effec- tive but at the present time the greens are going on some of the largest and finest of the new residences. Some slates are marked with bands or patches of a different color, and the dark-purple slates often have large spots of light green on them. These sp^ots do not as a rule affect the durability of the slate, but they greatly detract from its appearance. Grading and Laying Slates 1583 Grading of Slates. The Monson, Me., slates and Brownville, Me., slates are graded as follows: No. i. Every sheet to be full Mo in thick, both sides smooth and all corners full and square. No pieces to be winding or warped. No. 2. Thickness may vary from M to H in, all corners square, one side gener- ally smooth, one side generally rough, no badly warped slates. The Bangor, Pa., slates are graded: No. I Clear. A pure slate without any faults or blemishes. No. I Ribbon. As well made as No. i Clear, except that it contains one or more ribbons (a black band or streak across the slate), which, however, are high enough on the slate to be covered when laid, thus presenting a No. i roof. No. 2 Ribbon. This contains several ribbons, some of which cannot be covered when laid. No. 2 Clear. A slate without ribbons, made from rough beds. Hard Beds. A clear Bangor slate, not quite as smooth as No. i Clear, but much better than No. 2 Clear. Ordinary Bent Slate. A smooth slate similar to No. i Clear, but bent at a radius of about 1 2 f t. Punching. Formerly nail-holes in slates were punched on the Job; now, how- ever, slates are bored and countersunk at the quarry, when so ordered. Archi- tects should always specify that the slates are to be bored and countersunk, as punching badly damages the slates. Sizes. The sizes of slates range from 9 by 7 in to 24 by 14 in, there being some thirty-seven different sizes; the more common sizes, however, are the following: The sizes of slates best adapted for plain roofs are the large wide slates, such as 12 by 16 in, 18 by 12 in, 20 by 12 in, or 24 by 14 in. Slates from 8 by 16 to 10 by 20 in are popular sizes, 9 by i8-in slates being pr«bably used oftener than those of any other size. The 11 by 22 and 12 by 24-in slates are used principally on very large high buildings. The lower grades of slate are used largely on ware- houses and barns. The larger sizes make fewer joints in the roof, require fewer nails, and diminish the number of small pieces at hips and valleys. For roofs cut up into small sections the smaller sizes, such as 14 by 7 in or 16 by 8 in, look the best. Thickness. Slates vary in thickness from H to % in; Yie in is the usual thick- ness for ordinary sizes (see Grading of Slates in the preceding paragraphs). It is of utmost importance for architects to specify the thickness of slates, either fully Me in thick, or fully H in thick, to secure u strong and durable roof. Laying. Slates are laid either on a board sheathing (rough, or tongued and grooved) covered with tarred or water-proof paper or felt, or on roofing-laths from 2 to 3 in wide and from i to i H in thick, nailed to the rafters at distances apart to suit the gauge of the slates. Each slate should lap the slate in the second course below, 3 in. The slates are fastened with two threepenny or four- penny nails, one near each upper corner. For slates 20 by 10 in or larger, four- penny nails should be used. Copper, composition, tinned, or galvanized nails should be used. Plain-iron nails are speedily weakened by rust, and they break and allow the slates to be blown off. On iron roofs slates are often placed directly on small iron purlins spaced at suitable distances apart to receive them, and fastened with wire or special forms of fasteners. The gauge of a slate is the portion exposed to the weather, which should be one-half the re- mainder obtained by subtracting 3 in from the length of the slate. Roofs to be covered with slate should have a rise of not less than 6 in to the foot for 20-in or 24-in slates, or 8 in for smaller sizes. 1584 Memoranda on Roofing Part 3 Elastic Cemfent. In first-class work, the top course of slate on the ridge, and slate for from 2 to 4 ft from all gutters and i ft each way from all valleys and hips, should be bedded in elastic cement. Flashings. By flashings are meant pieces of tin, zinc, or copper laid over slate and up against walls, chimneys, copings, etc. Coimterflashings are of lead or zinc, and are laid between the courses in brick, and turned down over the flashings. In flashing against stonework, grooves or reglets often have to be cut to receive the counterflashings. Close and Open Valleys. A close valley is one in which the slates are mitered and flashed in each course and laid in cement. In such valleys no metal can be seen. Close valleys should only be used for pitches above 45°. An open valley is one formed of sheets of copper or zinc 15 or 16 in wide, over which the slates are laid* Old English Method of Laying Slates.* This method of laying slate in- volves the use of different shades of colored slates in graduated courses and in random widths beginning at the eaves, for example, with slates 28 in long and iH in thick, and using the different thicknesses from i H to % in, in shorter lengths, in working upward on the roof. The use of this kind of work for roofs has in- creased in recent years and the method possesses vast possibilities for carry- ing out architects' ideas for varied artistic effects. The slates are made with ' rough-cut edges in all thicknesses from Me to lYz in, in a combination of various shades carefully selected in such prop>ortion as to produce the best possible har- mony, when laid. As all of these colors and shades are unfading, the weathered effect is obtained at once and is permanent. These slates are made not only in usual sizes, but in the old English style, to be laid in graduated courses of dif- ferent lengths and in random widths. The Old English color-combination roof- ing-slates should be specified^to secure the light -and-shadow effect, and it is of the utmost importance to specify the thickness desired, as the price is the same for all sizes, while the cost varies according to thickness. When graduated courses are desired, specifications should call for the number of courses to be laid in each length and thickness beginning at the eaves courses, where the thickest slates are used in the largest sizes, sometimes 30 or even 36 in in length, and working upward on the roof with the shorter lengths and thinner slates to the ridges where the smallest sizes and thinnest slates are used. To secure a rough effect at mini- mum cost, specifications should call for Old English color-combination, all slates to be fully Vi in thick with rough cut edges and graduated courses in sizes rang- ing from 24 by 16 to 12 by 6 in, with nail-holes drilled and countersunk. To secure the best rough effect, specifications should call for eaves-courses not less than % in thick, stating the thickness desired for the eaves, and the number of courses desired in each length and thickness. Among the good specimens of tho Old English style of roofing may be mentioned the buildings of Princeton Uni- versity for the Graduate College, where different shades of unfading-green slates are used in thicknesses running from 1 34 in at the eaves to ^i in at the ridge. Measurement. Slates are sold by the square, by which is meant a sufficient number of slates of any size to cover 100 sq ft of surface on a roof, with 3 in of lap, over the head of those in the second course below. The square is also the basis on which the cost of laying is measured. "Eaves, hips, valleys, and cut- tings against walls or dormers are measured extra; i ft wide by their whole * Full information in regard to the details of the slates for this purpose and the methods employed in laying them can be obtained from the various companies. Cost of Slates 1585 lengtji, the extra charge being made for waste material and the increased labor reouired in cutting and fitting. Openings less than 3 sq ft are not deducted, and all cuttings around them are measured extra. Extra charges are also made for borders, figures, and any change of color of the work and for steeples, towers, and perpendicular surfaces."* Cost.f The cost of slates varies with the size, color and quality. The prices given in the following table were about the average in 19 15 for blue-black slate, of No. I grade, loaded on the cars at the Pennsylvania quarry. The freight in car-load lots of 60 scjuares or over to Philadelphia from Bethlehem, Pa., was 60 cts per square, from Pennsylvania to Omaha, Neb., $2.60 and from Vermont, about the same. It will be seen that slates of the medium sizes cost the most, and those of the larger and smaller sizes the least. Special prices' are quoted for special sizes. The larger sizes make the cheapest roofs. Red slates cost from 60 to 150% more than black slates. The green slates are more expensive than the black with the exception of the Maine and Peach Bottom varieties. Number and Cost t of Slates, and Pounds of Nails to 100 Square Feet of Roof 3-inch Lap Sizes of Exposed Number to Weights of galvanized Cost per slates, when laid, a square nails, square at in in lb oz quarry 14X24 loV^ 98 I 6 $4-50 12X24 io!-2 115 I 10 4.50 12X22 9'/^ 126 Ad- I 12 4-75 11X22 9K2 138 I 15 4-75 11X20 8K> 155 2 5.2s 10X20 SVi 170 2 6 5.2s i2Xi8 10X18 7M2 160 1 13 2 3 192 5.25 9X18 iVi 214 2 7 5.25 12X16 10X16 9X16 6V2 61/2 61/2 18S 222 2 2 2 8* 247 3 5.25 8X16 61/2 277 3d- 3 2 5.2s 10X14 sYi 262 3 8X14 5!/2 328 3 12 4.75 7X14 5/2 375 4 4 4-75 8X12 A\i 400 4 9 7X12 . aVi 457 5 3 4.25 6X12 4/2 534 6 I 4 25 The cost' of blue-black-slate roofs, complete, varies from $9 to $16 per square, depending on the class of work and remoteness from the quarries. The addi- tional cost of laying slate in elastic cement varies from $1.75 to $2.50 per square. An experienced roofer will lay, on an average, 2I/2 squares of slate in 8 hours. Weight. Slate roofing Vie in thick will weigh on the roof about 6K2 lb per sq ft, and if i/4 in thick, 8% lb, the smaller sizes weighing the most on account of the lap. The actual weight of a square foot of slate H in thick is 3.63 lb. A cubic • The Building Trades Pocket-book. t These prices have advanced and the manufacturers' lists must be consulted. 1586 Memoranda on Roofing Part 3 foot of Vermont slate weighs approximately 175 lb. The average shipping weight for No. i, ^le-in slates, is approximately 725 lb; for H-in slates, i 000 lb; for H-in slates, 2 000 lb, etc. Roofing-Tiles General Notes on Roofing-Tiles. The term roofing-tile is commonly understood to refer to exterior roof-covering made from clay in units of various shapes and laid with overlapping edges. Clay or terra-cotta roof-tiles have long been very largely used in Europe, where their cost is much less than in America. Since the year 1893 the advance here in the character and extent of ■ roofing-tile has been marked and rapid. This material can now be had at much lower prices than formerly prevailed, and the result has been that thousands of squares of terra-cotta tiles have been placed on shops and factories which would under former conditions have been covered with slate or metal. Whether or not a tile roof is as durable and satisfactory as one of No. i slate is a much-dis- puted question. Mr. Kidder was of the opinion that, considering the quantities used, slates have given better satisfaction than tiles. A tile roof, however, is certainly more attractive than a slate roof, and it is generally held that there are many roofing-tiles on the market which if properly laid prove as tight and durable as slates. There are so many patterns of roofing-tiles that it is impos- sible here to enter into a description of them. Of the various patterns, those which interlock are considered from a practical standpoint, to make the most satisfactory roof. Laying Roofing-Tiles. Roofing-tiles have been laid directly on a porous book tile or concrete base or on a sheathed surface over such base, or they have been fastened to stripping over the sheathing or wooden or steel purlins by means of copper wires. When thus fastened by wires, the joints were usually pointed on the under side after they were laid, to prevent the entrance of dust or dry snow. Tiles of the older patterns were nailed to the sheathing, but later on this iuethod was superseded by the practice of fastening with copper wires from pierced lugs near the lower ends of the tiles. The best modern method, however, seems to be the one involving a solid continuous base for the roofing-tiles, whether or not purlins are used. "Such purlins should be filled in between either with book tiles or a concrete base and felt should be laid thereon. The book tiles, if used, should be of a porous quaUty. Instead of regarding the nailing of tiles as a defective method, we have returned to it as the only proper method of fasten- ing tiles and have eliminated tlie stripping of sheathed roofs and the use of copper wires. Such methods Would do in some portions of central Europe where the winds and other climatic conditions are not severe, but through a twenty-five- years' experience in the varied climatic conditions of the United States, we have found that the nailing of tiles with copper nails is the only satisfactory method of application. We have also found that a roof should be sheathed and covered with a good asphaltum-felt to prevent wind-suction." * Roofing-tiles weigh from 750 to I 200 lb per square of 100 sq ft. •Specifications for Tile Roofing The following specification t contains valuable suggestions for the proper lay- ing of tile roofs: All pitched roofs shall be covered with ( ) tiles with fittings suitable for * Quoted by permission from data on roof-tiling, by the Ludowici-Celadon Company, Chicago, III. t Prepared from data furnished by the Ludowici-Celedon Companyj Chicago, 111. Roofing-Tiles 1587 each pattern unless otherwise selected by the architect. The tiles as specified above are to be hard-burned, of red color, and in accordance with samples de- posited in the office of the architect. (i) Preparation of Roof. Before the roofer is sent for, the owner or general contractor is to construct the roofs in strict accordance with the plans, sheath the roofs TIGHT, have all chimneys and walls above the roof-line completed, have all vent-pipes put through the roofs, furnish all strips of required width used under hip-rolls, furnish all i by }i-'m cant-strips used under the tiles at the eaves and have all the scaffolding ready for the roofers' use. The metal-contractor is to have all gutters in place on the roof (gutters, whether box, hanging or secret' gutters, are to extend over the roof -sheathing and cant-strips, and run under the felt and tiles at least 8 in) and is to have in place, also, all valley-metal, the width of which is to be not less than 24 in, with both edges turned up H in through the entire length of the valley. The valley-metal is to be fastened with clips and never nailed or punctured in any manner. The valley-metal is to be laid over one layer of felt running lengthwise the entire distance of the valley. The metal-contractor is to have in readiness all flaghing-metal used alongside and in front of dormers, gables, skylights, towers and perpendicular walls, and around vent-pipes and chimneys, and is to place the same after the arrival of the tile-roofer and under his direction. (2) Laying the Felt. After the roofs have thus been prepared to receive the felt and tiles, the tile-roofer is to cover the sheathing of the roofs with one thick- ness of asphalt roofing-felt weighing not less than 30 lb to the square, laying the same with a 2H-in lap and securing it in place by capped nails. The felt is to be laid parallel with the eaves, lapped over all valley-metal about 4 in and laid imder all flashing-metal about 6 in. (3) Laying the Tiles. The roof having thus been prepared, the tile-layer is to fasten the tiles with copper nails. The roofer is to see that the tiles are well locked together and that they lie smoothly, and no attempt is to be made to stretch the courses. The tiles are to be laid so that the vertical lines are parallel with each other and at right-angles to the eaves. The tiles that verge along the hips are to be cut close against the hip-boards, and a water-tight joint made by cementing cut hip-tiles to the hip-boards with elastic cement. Each piece of hip-roll is then to be nailed to the hip-board, and the hip-rolls are to be cemented where they lap each other. The interior spaces of hip-rolls and ridge-rolls are not to be filled with the pointing-material. Cost of Roofing-Tiles.* The prices of tiles vary from $7 to $30 per square, according to the character of the surface-finish and to the pattern. The cost of laying, including asphalt-felt, varies from $5 to $10 per square, according to the pattern of tiles used, the number of layers of felt and the character and extent of the roof. If roofing-tiles are laid on book tiles or on cement, 20% must be added to the cost for laying on wooden sheathing. Fluctuating values of copper make the item of copper nails, when these are used, one of im- portance. Sheet-Metal Tiles. Roofing-tiles stamped from sheet steel, plain or galvan- ized, and also from sheet copper, in imitation of clay tiles, are made by several manufacturers and have been extensively used for factories and buildings of secondary importance. The first cost of these tiles, except those made of copper, is much less than that of clay tiles and they do riot require as heavy roof-framing. Tin or galvanized-iron tiles, however, niust be painted every few years, so that for a long period of years they probably cost as niuch as clay tiles and more than slate. • These tirices have erdvailced sad the ni&nxUUiiiievs' lists riiuit bd coiisuUed. 158& Memoranda on Roofing Part 3 Tin Roofs The Sheets. Roofing-plates are made of soft steel of various special analyses, or wrought iron (more commonly of the former), covered with a mixture of lead and tin, and are designated terne-plates, in distinction from plates coated only with tin and therefore called bright tin. Roofing-plates are coated by two methods, (i) The original method of coating the plates consisted in dip- ping the black plates by hand Into the mixture of tin and lead, and allowing the sheets to absorb all the coating that was possible; and at least one brand of .roofing-tin is still made by this process. (2) The other process, by which the ma- jority of roofing-plates are now made, is known as the patent-roller-process, by which the plates are put into a bath of tin and lead, and are passed through rolls. The pressure of these rolls leaves on the iron or steel a thickness of coating which, to a great extent, determines the value of the plates. These rolls can be adjusted to leave a relatively large amount of coating on the plate, an ordinary coating, or a very scant coating. The heavier the coating the more valuable the plate. Some makers employ a variation of this patent process, by which the plates are given an extra dip, by hand, in an open pot, to give a hand-dipped FINISH. It is claimed that hand-dipped plates will last much longer than those made by the new process, although the latter process is much more extensively used and many good roofing-sheets are made by it. Brands. The best roofing-plates always have the brand stamped on them, and as the manufacturers have a pecuniary interest in keeping up the reputation of these brands, the only way of being sure of a good tin roof is to specify a brand of tin that has a reputation for quality and durability. Some of the best-known brands are Taylor's Target-and-Arrow (formerly Old Style); Merchant's Old Method, MF; Follansbee's Banfield Process; and Margaret. Machine-made plates are usually stamped with the weight of coating per box of 112 sheets, 28 by 20-in size. Sizes of Sheets. The common sizes of tin plates are 10 by 14 in and multiples of that measure. The sizes generally used are 14 by 20 in and 28 by 20 in. The larger size is the more economical to lay, and hence roofers prefer to use it; but for flat roofs the 14 by 20-in size makes the better roof. Thicknesses of Sheets. Terne-plates are made in two thicknesses, IC, in which the iron body weighs about 50 lb per 100 sq ft, and IX, in which it weighs 62^^ lb per 100 sq ft. For roofing, the IC, or lighter weight, is to be preferred, because the seams do not contract and expand as much as they do when the thicker plates are used. For spouts, valleys and gutters, however, IX plates should always be specified, and should preferably be used for flashings, as they are stiffer and less liable to be dented or punched. The thickness of the iron does not add to the durability of the plates, as this depends entirely upon the tin coating. Weights of Sheets. The standard weight of 14 by 20-in IC terne-plates is 107 lb for 112 sheets, the number usually packed in one box, and of 14 by 20-in IX sheets, 135 lb. The 28 by 20-in sheets should weigh just twice as much. The black sheets, before coating, should weigh, per 112 sheets, from 95 to 100 lb for IC, 14 by 20-in sheets, and from 125 to 130 lb for IX, 14 by 20-in sheets. The difference between the weights of the black sheets and finished sheets is the weight of the tin. A heavily coated tin should weigh from 115 to 120 lb per 112 sheets for IC, 14 by 20-in sheets, and from 145 to 150 lb for IX, 14 by 20-in sheets. The 28 by 20-in sheets should, of course, weigh twice as much. The Roof. Roofs of less than one-third pitch are made with flat seams and should preferably be covered with 14 by 20-in sheets rather than with 28 by 20-in Tin Roofs 1589 sheets, because the larger number of seams stiffens the surface and helps to pre- vent buckles and rattling in stormy weather. For a flat-scam roof, the edges of the sheets are turned y2 in, locked together and well soaked with solder. The sheets are fastened to the sheathing-boards by cleats spaced 8 in apart and locked in]the seams. Two i-in barbed and tinned-wire nails are used in each cleat. No nails should be driven through the sheets. The seams must be made with great care and sufficient time taken to properly sweat the solder into the seams. Steep tin roofs should be made with standing seams and with 28 by 20-in sheets. The sheets are first single-seamed or double-seamed and usually soldered to- gether, preferably end to end, into long strips that reach from eaves to ridge. The sloping seams are composed of two upstands, interlocked at the upper edge, and held to the sheathing-boards by cleats. The standing seams are usually not soldered but simply locked together with the cleats folded in about i ft apart. Nails should be driven into the cleats only. The use of acid in soldering the seams of a tin roof should be carefully avoided as acid coming in contact with the bare iron on the cut edges and corners, where the sheets are folded and seamed together, causes rusting. No other soldering-flux but good rosin should ever be used. Durability of Tin Roofs. A tin roof of good material, properly put on, and kept properly painted, will last from forty to fifty years, or longer. All traces of rosin left on the roof should be removed as soon as the tin is laid and soldered, and one coat of paint should be applied promptly; a second coat should follow two weeks after the first. One or more layers of felt or water-proof paper should be placed under the tin, to serve as a cushion, and also to deaden the noise pro- duced by rain striking the tin. The durability of tin roofing, and especially of tin gutters, valleys and flashings, is generally increased by painting the tin on the back before laying. An excellent paint for tin roofs is composed of 10 lb of Venetian red, i lb of red lead and i gal of pure Unseed-oil. Maintenance of Tin Roofs. The tin roof should be given one coat of paint after it is laid and an additional coat of paint at four-year or five-year intervals should be amply sufficient to keep its upper surface in first-class condition as long as the building stands. With each painting the roof is fully restored to its original condition. Graphite and tar paints should be avoided on tin roofs. Metallic brown, Venetian red, red oxide or red lead, only, should be used as pigments, with pure linseed-oil. Tinned gutters should be swept clear of accu- mulations of leaves, dirt, etc., and if water has a tendency to lie in the gutters they should be painted yearly. Number of Sheets Required to a Square. For flat-seam roofing a sheet of tin 14 by 20 in, with H-in edges, measures, when edged or folded, 13 by 19 in, or 247 sq in; but its covering capacity when joined to other sheets on the roof is only 12H by i8J^ in, or 231.25 sq in. The number of sheets to a square, there- fore, equals 14 400 divided by 231.25 or 63, and an area of i 000 sq ft requires 625 sheets. A box of 112 14 by 2c5-in sheets will cover, approximately, 180 sq ft. Sheets 28 by 20 in, when edged or folded, have a covering capacity of 490.25 sq in, each. To cover i 000 sq ft (10 squares) requires 294 sheets. For standing- seam roofing the locks require 2^4 in off the width and ij^ in off the length of the sheet. A 28 by 20-in sheet, with the seams on the long edges, will cover 463 sq in. To cover i 000 sq ft requires 312 sheets. The Cost* of Tin Roofing varies from $8 to $12 per square, according to the grade of the tin, the locality and nature of the work and the scale of wages. Standing-seam roofs cost about 50 cts a square less than flat-seam roofs. The cost, when 14 by 20-in sheets are used, is about 25% more than for 28 by 20-in * Variations in cost must be ascertained from manufacturers' lists. 1590 Memoranda on Roofing Part 3 sheets, owing to the greater number of seams; hence, more tin, solder, cleats and work are required. How a Tin Roof Should he Laid* The Slope of the Roof. If the tin is laid with a flat seam or flat lock, the roof should have an incline of ^ in or more to i ft. If laid with a standing seam, there should be an incline of not less than 2 in to i ft. Although tin is used on roofs of less pitch than this and on some which are almost flat, a good pitch is desirable to prevent the accumulation of water and dirt in shallow puddles. Gutters, • valleys, etc., should have sufficient incline to prevent water from standing in them or backing up far enough to reach standing seams. Tongued and grooved sheathing-boards of well-seasoned dry lumber are recommended. Narrow widths are preferable, and the boards should be free from holes, and of even thick- ness. A new tin roof should never be laid over old tin, rotten shingles, or tar roofs. Sheathing-paper is not necessary where the boards are laid as specified above. If steam, fumes, or gases are likely to reach the under side of the tin, some good water-proof sheathing-paper, such as black Neponset paper, should be used. Tarred paper should never be used. No nails should be driven through the sheets. Flat-Seam Tin Roofing. When the sheets are laid singly, they should be fastened to the sheathing-boards by cleats, using three to each sheet, two on the long side and one on the short side. Two i-in barbed-wire nails should be used to each cleat. If the tin is put on in rolls the sheets should be made up into long lengths in the shop, and the cross-seams locked together and well soaked with solder. They should be edged yi in, and fastened to the roof with cleats spaced 8 in apart, and the cleats locked into the seam and fastened to the roof with two I -in barbed-wire nails to each cleat. Standing-Seam Tin Roofing. The sheets should be put together in long lengths in the shop, and the cross-seams locked together and well soaked with solder. They should be applied to the roof the narrow way, and fastened with cleats spaced i ft apart. One edge of the course is turned up i H in at a right angle, and the cleats are installed. The adjoining edge of the next course is turned up i Vi in, and these edges are locked, turned over and the scam flattened to a rounded edge. Valleys and Gutters. These should be lined with IX tin, and formed with flat seams, the sheets being applied the narrow way. It is important to see that good solder, bearing the manufacturer's name, is used, that it is guaranteed one- half tin and one-half lead, new metals, and that nothing but rosin is used as a flux. The solder should be well sweated into all seams and joints. Painting. All painting should be done by the roofer. The tin should be painted one coat on the under side before it is applied to the roof. The upper surface of the tin roof should be carefully cleanecf of all rosin-spots, dirt, etc., and immediately painted. The approved paints are metallic brown, Venetian red, red oxide, arid red lead, mixed with pure linseed-oil. No patent drier or tur- pentine should be used. All coats of paint should be applied with a hand-brush, and well rubbed on. A second coat should be applied two weeks after the first and a third coat one year later. Caution. No unnecessary walking over the tin roof, or use of it for storage of materials, should be allowed at any time. Workmen should wear rubber-soled * These suggestions are in accordance with the standard working specifications adopted by the National Association of Sheet Metal Contractors. Covering Capacity of Roofing-Tin 1501 shoes or overshoes when on the roof. Wherever the slope is steep enough the tin should be laid with standing seams, which allow for expansion and contraction. Sizes, Weights, Etc., of Roofing-Tin * Roofing-tin is usually furnished in two sizes, sheets 14 by 20 in and 28 by 20 in, packed 112 sheets to the box. Target-and- Arrow tia is furnished in three thick- nesses: IC thickness, approximately No. 30 gauge, U. S. Standard; IX thickness, approximately No. 28 gauge, U. S. Standard; 2X thickness, approximately No. 27 gauge, U. S. Standard, etc. Weight per 100 sq ft laid on the roof, about 65 lb for IC thickness. Covering Capacity of Roofing-Tin Flat-Seam Tin Roofing. The following table shows the quantity of 14 by 20-in tin required to cover a given number of square feet with flat-seam tin roofing. A sheet 14 by 20 in with y2 in edges measures, when edged or folded, 13 by 19, or 247 sq in, but its covering capacity when joined to other sheets on the roof is only i2i/i by 18H in, or 231.25 sq in. In the following table each fractional part of a sheet is counted a full sheet'. No. of square feet . Sheets required . . . 100 63 no 69 120 75 130 140 150 160 170 106 180 112 190 119 200 125 81 88 94 100 No. of square feet. Sheets required . . . 210 131 220 137 230 144 240 150 250 156 260 162 270 169 280 175 290 i8i 300 187 310 193 No. of square feet. Sheets required . . . 320 200 330 206 340 212 350 218 360 224 370 231 380 237 390 243 400 249 410 256 420 262 No. of square feet . Sheets required . . . 430 268 440 274 4SO 281 460 287 470 293 480 299 490 305 500 312 510 318 520 324 630 393 530 330 640 399 No. of square feet . Sheets required . . . 540 337 550 343 560 349 570 355 580 362 590 368 600 610 380 620 386 No. of square feet . Sheets required . . . 650 405 660 411 670 418 680 424 690 430 700 436 710 442 720 448 730 455 740 461 750 467 No. of square feet . Sheets retiuired . . . 760 474 770 480 780 486 790 492 800 499 810 50s 820 511 830 517 840 523 850 530 860 536 No. of square feet . Sheets required . . . 870 542 880 548 890 554 900 561 910 567 920 573 930 579 940 586 950 592 960 598 970 604 No. of square feet . Sheets required . . . 980 610 990 617 1000 625 A box of 112 sheets 14 by 20 in laid in this way will cover 180 sq ft. Flat-Seam Tin Roofing. The following table shows the number of 28 by 20-in sheets required to cover a given number of square feet with flat-seam tin roofing. The flat seams edged V' in take iH in off the length and width of the sheet. The covering capacity of each sheet is, therefore, 26y2 by 18^2 in, or 490.25 sq in. In the following table each fractional part of a sheet is counted a full sheet. ■ • The following tables of sizes, weights, covering capacities and costs are adapted from useful data compiled for the use of sheet-metal workers by th« N. & G. Taylor Company, Philadelphia, Pa. 1592 Memoranda on Roofing Part 3 No. of square feet . Sheets required . . . lOO 30 110 33 120 36 130 39 140 42 150 45 160 47 170 50 180 53 190 56 200 59 No. of square feet. Sheets required . . . 210 62 220 65 230 68 240 71 250 74. 260 77 270 80 280 83 290 86 300 89 310 92 No. of square feet . Sheets required . . . 320 94 330 97 340 100 350 103 360 106 370 109 380 112 390 115 400 118 410 121 420 124 No. of square feet. Sheets required . . . 430. 127 440 130 133 460 136 470 139 480 141 490 144 500. 147 510 ISO 520 153 530 156 No. of square feet. Sheets required . . . 540 159 550 162 560 165 570 168 580 171 590 174 600 177 610 180 620 183 630 186 640 188 No. of square feet . Sheets required . . . 650 191 660 194 670 197 680 200 690 203 700 206 7T0 209 720 212 730 215 740 218 750 221 No. of square feet . Sheets required . . . 760 224 770 227 780 230 790 233 800 235 8to 238 820 241 830 244 840 247 850 250 86c 253 No. of square feet. Sheets required . . . 870 256 880 259 890 262 qoo 265 910 268 920 271 930 274 940 277 950 280 960 282 970 285 No. of square feet . Sheets required . . . 980 288 990 291 1000 294 A box of 112 sheets 28 by 20 in laid in this way will cover 381 sq ft. Standing-Seam Tin Roofing. The following table shows the number of 14 by 20-in sheets required to cover a given number of square feet with standing-seam roofing. The standing seams, edged iH and i^/i in, take 2% in off the width; and the flat cross-seams, edged % in, take i \i in off the length of the sheet. The covering capacity of each sheet is, therefore, iiH by 18^6 in, or 212.34 sq in. In the following table each fractional part of a sheet is counted a full sheet. No. of square feet. Sheets required . . . 100 68 no 75 120 82 130 89 140 95 150 102 160 109 170 116 180 123 190 129 200 136 No. of square feet. Sheets required . . . 210 143 220 150 230 156 240 163 250 170 260 177 270 184 280 190 290 197 300 204 310 211 No. of square feet . Sheets required . . . 320 218 330 224 340 231 350 238 360 245 370 251 380 258 390 265 400 271 410 •279 420 285 No. of square feet . Sheets required . . , 430 292 440 299 450 306 460 312 470 319 480 326» 490 333 Soo 340 510 346 520 353 530 360 No. of square feet. Sheets required . . . 540 367 550 374 560 379 570 387 580 393 590 401 600 407 610 414 620 421 630 428 640 435 No. of square feet. Sheets required . . . 650 441 660 447 670 455 680 462 600 468 700 475 710 482 720 489 730 495 740 501 750 509 No. of square feet. Sheets required . . . 760 515 770 523 780 529 790 536 800 543 810 550 820 557 830 563 840 570 850 577 860 584 No. of square feet. Sheets required . . , 870 590 880 597 890 604 QOO 611 910 618 920 623 930 630 940 637 950 644 960 651 970 658 No. of square feet. Sheets required . . . 980 66s 990 672 1000 679 ... ... ... A box of 112 sheets 14 by 20 in laid in this way will cover 165 sq ft. Covering Capacity of Roofing-Tin 1593 Standing-Seam Tin Roofing. The following table shows the number of 28 by 20-in sheets required to cover a given number of square feet with standing-seam roofing. The standing seams take 2% in off the width, and the flat cross-seams, edged Vs in, take iH in off the length of the sheet. The covering capacity of each sheet is, therefore, 26% by 17 H in, or 463.59 sq in. In the following table each fractional part of a sheet is counted a full sheet. No. of square feet . Sheets required . . . 100 32 lie 35 120 38 130 41 140 44 ISO 47 160 50 170 53 180 56 190 59 200 62 No. of square feet. Sheets required . . . 210 65 220 68 230 71 240 74 250 77 260 80 270 84 280 87 290 90 300 94 310 97 No. of square feet . Sheets required . . . 320 100 330 103 340 106 350 109 360 112 370 115 380 118 390 121 400 125 410 128 420 131 No. of square feet. Sheets required . . . 430 134 440 137 450 141 460 144 470 147 480 150 490 153 500 156 510 159 520 162 530 165 No. of square feet. Sheets required . . . 540 168 550 171 S6o 174 570 177 580 180 590 184 600 187 610 190 620 193 630 196 640 199 No. of square feet. Sheets required . . . 650 202 660 205 670 208 680 211 690 214 700 218 710 221 720 224 730 227 740 230 750 233 No. of square feet. Sheets required . . . 760 236 770 239 780 242 790 245 800 249 810 252 820 255 830 258 840 261 85c 265 860 268 No. of square feet. Sheets required . . . 870 271 880 274 890 277 900 280 910 283 920 286 930 289 940 292 950 296 960 299 970 302 No. of square feet. Sheets required . . . 980 305 990 308 ... A box of 112 sheets 28 by 20 in laid in this way will cover 360 sq ft. Laying 'the Long or Short Way. Sheets 14 by 20 in can be laid either the long or short way. The best roof is made by laying the sheets the 14-in way; similarly, in using the 28 by 20-in sheets, they should always be laid the 20-in way, that is, with the short dimension crosswise. Cost of Roofing-Tin Cost of Tin for* Standing-Seam Roofing Sheets 28 by 20 in. Price per box and per square foot When tin costs ■- per box $11.00 $11.50 $12.00 $12.50 $13.00 $13.50 $14.00 $14-50 $15.00 $15.50 Standing-seam roofing costs per sq ft 0.0297 0.0310 0.0324 0.0337 0.0351 0.0364 0.0378 0.0391 0.0404 0.0418 When tin costs per box.... .. 16.00 16.50 17.00 17.50 18.00 18.50 19.00 19.50 20.00 20 . 50 Standing-seam roofing costs per sq f t 0.0432 0.0446 0.0459 0.0473 0.0486 0.0500 0.0513 0.0526 0.0540 0.0553 When tin costs per box 21.00 21.50 22.00 22.50 23.00 23.50 24.00 24 -50 25.00 Standing-seam roofing costs per sq ft 0.0567 0.0580 0.0594 0.0607 0.0621 0.0634 0.0648 0.0661 0.0675 The above estimates do not include cost of laying. The cost, using 14 by 20-in sheets, will amount to about 25% more than the cost, using 28 by 20-in sheets, owing to the greater number of seams. More tin, solder, cleats and work are therefore necessary. 1594 Memoranda on Roofing Tin in Rolls, or Gutter-Strips Number of sheets required per linear foot for 20 and 28-in widths Widths Widths Widths Hun- Widths Feet Feet Feet dred 20 28 20 28 20 28 feet 20 28 I I I 3S If) 23 69 31 44 2 89 128 2 I 2 36 16 23 70 32 45 3 134 192 3 2 2 37 17 24 71 32 45 4 178 256 4 2 3 38 17 24 72 32 46 5 223 320 5 3 4 39 18 25 73 33 47 6 267 384 6 3 4 40 18 26 74 33 47 7 3T2 444 7 4 5 41 19 27 75 34 48 8 356 512 8 4 s 42 19 27 76 34 48 9 401 576 9 4 6 43 20 28 77 35 49 10 445 64c 10 5 7 4; 20 28 78 35 50 II 495 704 II 5 7 4S 20 29 79 36 SO 12 540 768 12 6 8 46 21 2J 80 36 SI 13 585 832 13 6 9 47 21 30 81 36 52 14 630 896 14 7 9 48 22 31 82 37 52 15 675 060 IS 7 10 49 22 31 83 37 53 16 720 I 024 16 8 II SO 23 32 84 38 54 17 765 I 088 17 8 n SI 23 33 85 38 54 18 810 I 152 18 8 12 S2 24 33 86 39 55 19 855 I 216 19 9 12 S3 24 34 87 39 55 20 900 I 280 20 9 13 S4 24 34 83 40 56 21 945 1344 21 22 10 10 14 14 ss 25 35 36 89 90 40 40 57 57 22 23 990 1035 1408 I 472 S6 25 23 II IS S7 25 36 91 41 58 24 I oSo 1536 24 II 16 S8 26 37 92 41 59 25 1^35 I Geo 25 12 16 S9 27 33 93 42 59 26 I 170 1664 26 12 17 60 27 38 94 42 60 27 I 215 1738 27 12 18 61 28 39 95 43 (n 28 1 2G0 I 792 2i 13 18 62 28 40 96 43 62 29 I 305 1856 29 13 19 63 28 40 97 44 62 30 I 350 I 920 30 14 19 64 29 41 98 44 63 31 I 395 1984 31 14 20 65 29 41 99 44 64 32 I 440 2048 32 IS 21 66 30 42 100 45 64 33 T 485 2 112 33 IS 21 67 30 43 34 I 530 2176 34 16 22 68 31 43 35 I 575 2 240 Cost of Tin in Rolls or Gutter-Strips Labor, solder, paint, rosin and other materials not included A box of 112 sheets in 28-in roll will cover 175 lin ft A box of 112 sheets in 20-in roll will cover 248 lin ft A box of 112 sheets in 14-in roll will over 350 lin ft A box of 112 sheets in lo-in roll will cover 496 Hn ft Cost per box (28 by 20 in) Cost per linear foot, 28 in wide. Cost per linear foot, 20 in wide. $10 00 0.05714 o . 04032 $II.Od| $12.00 0.052^5,0. o53-;6 0.0443510.04838 $13 00 0.07426 0.05241 $14.00 o . 07998 0.05644 Cost per box (28 by 20 in) Cost per linear foot, 28 in wide, . ; . Cost per linear foot, 20 in wide. , , . $16 00 0.09149 d. 06450 $17.00 O.C17II Si8,oo 0.10282 d.^7256 $19.00 0.10853 0.07659 $20.00 0.11424 ,©.68062 Slag and Gravel Roofing 1595 Tin in Rolls. For the convenience of roofers and for rush-orders, Target-and- Arrow tin is put up in rolls 14, 20 and 28 in wide. Each roll contains 108 sq ft; (al^out 63 lin ft, 28 by 20-in sheets laid 20 in wide). The tin is painted on one or both sides, as wanted, with an approved metallic brown paint. The seams arc carefully soldered by hand, good 100 to 100 solder and rosin being used as a tlux. ^9|HH| '■^if^sm^ Slag or Gravel Roofing The Ordinary Gravel Roofing over boards is formed by first covering the surface of the roof with dry felt (paper) and over this laying three, four, or five Jayers of tarred or asphaltic felt lapping each other like shingles, so that only from 6 to 10 in of each layer are exposed. In laying roofs over concrete the dry felt is omitted, a mopping of pitch is placed directly on the concrete and the first layer of the felt embedded in it. Flashing against walls, chimneys, curbs of skylights, etc., is done by turning the felt up 6 in against the walls. Over this is laid an 8-in strip with half its width on the roof. The upper edge of the strip and of the several layers of felt is then fastened to the walls by nailing wooden strips or laths over the felt and into the walls. Metal flashings to protect the felt are better than the wooden stiipg and should be used when possible. At the eaves and on all exposed edges, metal gravel-stops should be used. A Better Method of Slag or Gravel Roofing is to lay two plies of tarred felt, lapping each other 17 in, and then spreading a coat of pitch over the entire roof 4 On this again three more layers of felt are laid and then coated with pitch, into which the crushed slag or screened gravel is embedded. Specifications for Pitch-Slag or Gravel Roofing. The following specific cation-notes * describe the latter method more in detail and also the material^ that should be used to secure a first-class job. These roofs are most efficient and durable on comparatively flat inclines. The usual built-up roof consists of suc- cessive layers of saturated felt cemented together and surfaced with coal-tar pitch or asphalt, into which is embedded the gravel or slag. Tile is also used as a surfacing material. The saturants used in the felt are generally coal-tar or asphalt-compounds. (i) Specification for Pitch-Slag or Pitch-Gravel Roofing Over Wooden Sheathing This specification should not be used when the roof-incline exceeds 3 in to i ft. Lay one thickness of sheathing-paper or unsaturated felt weighing not less than 5 lb per 100 sq ft, lapping the sheets at least i in. Over the entire surface lay two plies t of tarred felt, lapping each sheet 17 in over the preceding one, and nail as often as is necessary to hold them in place until the remaining felt is laid. Coat the entire surface uniformly with pitch. * Condensed and adapted from specifications published by the Barrett Manufacturing Company and known, in their full form, as "The Barrett Specifications," They can be obtained from the manufacturers. t In the Western States the number of "plies" is construed to mean the total num- ber of layers, including dry as well as saturated felt, and the terms 3-ply, S-ply, etc., are hereinafter used on that basis. In the Eastern States, 3-ply, 5-ply, etc., usually refers to the number of layers of saturated left; The total number of layers should always be specified if there ia any doubt as .to the exact meaning of the term as used, in the speci- ficatigns, '"' ^^^'^ tiOJuj iu iitnit^uj mioiiau >■ ] 13V0 bfiSiq : * 1596 Memoranda on Roofing Part 3 Over the entire surface lay three plies of tarred felt, lapping each sheet 22 in over the preceding one and mopping with pitch the full 22 in on each sheet, so that in no place felt touches felt. Do such nailing as is necessary so that all nails are covered by not less than two plies of felt. Diagram of Gravel or Slag Roofing on Wooden Sheathing Diagram of Gravel or Slag Roofing on Concrete Base Spread over the entire surface a uniform coating of pitch, into which, while hot, embed not less than 400 lb of gravel or 300 lb of slag to each 100 sq ft. The grains of the gravel or slag are to be from H to H in in size, and dry and free from dirt. The roof may be inspected before the gravel or slag is applied, by cutting a slit not less than 3 ft long at right-angles to the direction in which the felt is laid. All felt and pitch is to bear the manufacturer's label. (2) Specification for Pitch-Slag or Pitch-Gravel for Roofing over Concrete This specification should not be used when the roof-incline exceeds 3 in to the foot. When the incline exceeds i in to i ft the concrete must permit of nailing or nailing-strips must be provided. Coat the concrete uniformly with hot pitch. Over the entire surface lay two plies of tarred felt, lapping each sheet 17 in over the preceding one, mopping with pitch the full 17 in on each sheet, so that in no place felt touches felt. Coat the entire surface uniformly with pitch. Over the entire surface lay three plies of tarred felt, lapping each sheet 22 in over the preceding one and mopping with pitch the full 22 in on each sheet, so that in no place felt touches felt. Spread over the entire surface a uniform coating of pitch, into which, while Slag and Gravel Roofing 1597 hot, embed not less than 400 lb of gravel or 300 lb of slag to each 100 sq ft. The grains of the gravel or slag are to be from \i to H in in size, and dry and free from dirt. The roof may be inspected before the gravel or slag is applied, by cutting a slit not less than 3 ft long at right-angles to the direction in which the felt is laid. All felt and pitch is to bear the manufacturer's label. Notes on Slag and Gravel Roofing. The difference between slag and gravel roofing is that for the former crushed slag is used instead of gravel. The greater the number of plies of tarred felt, the greater the amount of pitch that it is prac- tical to use, and it is the pitch that gives life to the roof. As there are several different weights and qualities of tarred felt, a specification should state either the minimum weight per 100 sq ft, single thickness (the most practical weight is from 14 to 16 lb), or some known quality, such as Barrett's " Specification Tarred Felt." Felt weighing less than 12 lb per 100 sq ft is not economical even on the cheaper work. To comply with the Barrett specification the materials neces- sary for each 100 sq ft of completed roof are approximately as follows: Over boards Material Over concrete 108 sq ft 80 to 8s lb 120 to i6o lb 400 lb 300 lb Sheathing-paper Specification tarred felt Specification-pitch Gravel Slag None 80 to 8s lb 180 to 225 lb 400 lb 300 lb In estimating felt, the average weight is practically 15 lb per 100 sq ft, single thickness, and about 10% additional is required for laps. In estimating pitch the weather-conditions and expertness of the workmen will affect the amount necessary for the moppings and for a proper embedding of the gravel or slag. As there are several qualities of pitch, a specification should either specify it by name, such as "Specification-Pitch" or "Straight-Run Coal-Tar Pitch," or in specifying asphalt-pitch, the brand or origin should be plainly defined. The use of an under-layer of sheathing-paper next to board-sheathing is mainly for the purpose of preventing any pitch which might penetrate the felt from cement- ing the roofing to the sheathing. It is also of value in preventing the drying out of the roof from belovv^ through open joints. Where a less expensive roof is de- sired, four plies or three plies of saturated felt may be used. With the four plies there should be used from 90 to 100 lb of pitch per 100 sq ft of completed roof; and with the three plies from 70 to 80 lb of pitch. Durability of Slag or Gravel Roofs. These roofs, mentioned in the pre- ceding paragraph, will last from five to ten years, or even longer, depending upon the quaHty of the materials used and the care with which they have been applied. Roofing put on strictly as provided for in the standard specifications will last twenty years or more, and if a tile surface is used, instead of gravel or slag, the roofing will last as long as the structure itself. Resistance to Fire, Acid-Fumes, Etc. The fire-resisting properties of the slag or gravel roof are due principally to the incombustible material on the sur- face. It is claimed that the gravel or slag tends to prevent the successive layers of felt and pitch from burning and the whole mass has a blanketing influence on fires originating within the building. Some carefully conducted tests seem to indicate that gravel roofing protects a wooden roof better than tin. The general effect of a fire upon gravel roofing is to soften the pitch or asphalt in the roofing, 1598 Memoranda on Roofing Part 3 to burn out the inflammable oil in them and to cause the residue to swell and form a porous, incombustible coke. This type of roofing is not attacked by corrosive gases or acid-fumes, and is used extensively on railroad-roundhouses and other structures where the conditions are particularly severe. Coal-tar or tar-oil should not be added to the pitch to soften it. Guarantee. Roofers generally give a five-year guarantee with gravel roofs. Cost * of Pitch-Slag or Gravel Roofing'. The cost of this type of roofing varies greatly, depending on the location, size and quality of the work, the ex- tremes being approximately $2.50 and $3.50 per square for three-ply, $3.50 and $4.50 per square for four-ply, and $4.50 and $7.00 per square for five-ply roofing-. Asphalt-Gravel Roofing Asphalt-Gravel or Asphalt-Slag Roofing differs from coal-tar roofing princi- pally in the substitution of asphalt or asphaltic cement for the coal-tar pitch, for saturating the felt as well as for mopping and surface-coating. It is claimed that the oils of asphalt do not evaporate as quickly as do those of coal-tar pitch under ordinary temperatures and that therefore the flexibility and life of asphaltic felts and coatings are not as quickly destroyed. As. a matter of fact, asphalt roofs do not always last longer than some coal-tar roofs, but the chances are that they will last fully as long and possibly longer, depending upon the quality of the materials and the workmanship. The asphalt used for roofing is obtained prin- cipally from the island of Trinidad. Specifications for Asphalt Roofing, f The following specifications were prepared by the above-named company and are for Warren's heavy standard Anchor-brand roofing. The manner of laying the felting differs from that ordi- narily employed for coal-tar roofing. (i) Specification for Asphalt-Gravel Roofing Over Wooden Sheathing Cover the roof with two thicknesses of Warren's Composite roofing-felt, manila-paper side down, lapping each sheet 17 in over the preceding one, and securing with nails through tin discs about 2y2 ft apart. Over the entire surface of the Composite felt thus laid, mop an even coating of Warren's Anchor Brand roofing-cement, into which, while hot, lay two thicknesses of Anchor Brand felt, lapping each sheet 17 in over the sheet preceding, sticking these laps the full width with hot Anchor cement and securing with nails through tin discs not more than 20 in apart. Over the entire surface of the felt thus prepared, spread an even coating of the cement, covering it immediately with a sufficient body of well-screened, dry gravel or crushed slag. If the roofing is applied in cold weather the gravel or slag must be heated. Slag only should be used if the incline of the roof exceeds 3 in to the foot. All layers of felt must be turned up at least 4 in over battlement-v/alls, sky- light-curbs, or any projections raised above the roof. (2) Specification for Asphalt-Gravel Roofing Over Concrete The concrete foundation is to be smooth and perfectly graded to carry the water to the outlets or gutters. Over the entire surface of the concrete first mop a smooth, even coating;: of Eclipse Asphalt cement, into which, while hot, lay two thicknesses of Warren's Anchor Brand roofing-felt, lappmg each sheet 17 in over the sheet preceding. * These rvrices have advanced and the manufacturers' lists must be consulted. tThe asphalt -roofing materials manufactured by the Warren Chemical tk Manufac- turing Company of New York have been used for many years and have given good Corrugated Iron and Steel Sheets 1599 Mop back for the full width between the laps of the felt thus laid, with War- ren's Anchor Brand roofing-cement. Ovci the entii-e exposed surface of the felt mop an even coating of said Anchor cement, into which, while hot, lay two thicknesses of Anchor Brand felt, lapping each sheet 17 in over the sheet preceding, and sticking these laps thoroughly the full width with hot cement. Over the entire surface of the felt thus prepared, spread an e.ven coating of the cement, covering it immediately with a sufficient body of well-screened, dry gravel or crushed slag. If the roofing is applied in cold weather, the gravel or slag must be heated. Slag only should be used if incline of roof exceeds 3 in to the foot. On steep surfaces naihng-strips should be provided in the concrete, unless the latter is sufficiently soft to admit of naiUng. All layers of felt must be turned up at least 4 in over battlement-walls and skylight-curbs, or any projections raised above the roof. Cost of Asphalt-Gravel or Slag Roofing. Asphalt-gravel roofing costs a little more than pitch-gravel roofing of the same grade. (See Cor^t of Pitch- Slag or Gravel Roofing, page 1598.) Roof-Incline.* Asphalt-gravel or asphalt-slag roofing should not be applied to roofs which are steep enough to make the material run in hot weather. The manufacturers of various roofings will guarantee the permanency of their roofings for certain maximum slopes. Prepared Roofing. There is a large number of so-called prepared roofings or READY ROOFINGS, which are made by cementing together two, three, or more layers of saturated felt or felt and burlap and then coating the combination either with a hard solution of the same cementing material, or with hot pitch or asphalt into which is embedded sand or fine gravel. These roofings are commonly put up in rolls 36 in wide and are applied by lapping the strips 2 in with a coat of cementing material between, and naiUng every 2 or 3 in with tin-capped roofing- nails. A sufficient quantity of cement, nails and tin caps is packed in the middle of the rolls. The particular advantage of these roofings is that no previous expe- rience is required for laying them and no kettles are required; for this reason they are extensively used in the country, and on railroad-shops, factories, and mill- buildings. In cities there is no particular advantage in using them except for roofs that are too steep for coal-tar pitch, as they cost on the roof about the same as good gravel roofing. Many of these prepared roofings are as durable under or- dinary conditions as the light-weight gravel roofs. In Colorado, however, it has been found that they are badly damaged by severe hail-storms, probably owing to the lack of the protecting gravel. For roofs having a rise of i in or more to the foot, these roofings make economical and durable roofs, and for some build- ings are to be preferred to other materials. Corrugated Iron and Steel Sheets Corrugated Sheets of iron and steel are very extensively used for the roofing and siding of mills, sheds, grain-elevators and warehouses. The best grades of corrugated sheets are now made of double-refined box-annealed iron or steel.f * The Editor has been notified by the Warren Chemical & Manufacturing Company, New York, that when put on according to their directions, their Anchor Brand roofing has been successfully used on relatively steep surfaces v/here the slope was as high as 9 in to the foot. t It is claimed that "the life of a genuine puddled-iron sheet when exposed only to the pure air and natural elc.nents is froiT> five to eight times longer, and when exposed to 1600 Memoranda on Roofing Part 3 The corrugations are usually made lengthwise of the sheet, either by passing them through rolls or by pressing the plain sheets in a press made to give the desired corrugations. It is claimed that the latter method gives the more per- fect and uniform corrugations. The weight and thickness of the metal is rep- resented by the gauge-number of the black sheets from which the corrugated sheets are made. The standard gauge* for sheet iron and steel in this country is that established by act of Congress, March 3, 1893. (See page 402.) Gauges. The following table gives the weights and thicknesses of the differ- ent gauges, from No. 7 to No. 30, for flat black sheets. The gauge extends from No. 7-0, H in thick, up to No. 40, 0.005469 in thick, but sheet steel is not commonly made thinner than No. 30, and above Ms in, the thickness is gener- ally designated by fractions of an inch. Section 3 of the act of Congress pro- vides that in the practical use and application of this gauge, a variation of 2H% either way may be allowed. United States Standard Gauge for Sheet Iron and Steel * Num- Thicknesses Weights ber of Approximate Approximate Weight per Weight per gauge thickness in thickness in square foot square foot fractions of decimal parts ^n ounces, in pounds an inch of an inch avoirdupois avoirdupois 7 3/i« 0.1875 120 7.5 8 H64 0.171875 no 6.875 9 H2 0.15625 100 6.25 10 %4. 0.140625 90 5-625 II H 0.125 80 5.0 12 7/64 0.109375 70 4. 375 13 ^A2 0.0937s 60 3.75 14 %4 0.078125 50 3.125 IS %2% 0.0703125 45 2.8125 16 Ma 0.0625 40 2.5 17 Meo 0.05625 36 2.25 18 \^o 0.05 32 2.0 19 lUo 0.04375 28 1-75 20 Ho 0.0375 24 1.50 21 l»'^20 0.034375 22 1.375 22 \i2 0.0312s 20 1.25 23 ^20 0.028125 18 1. 125 24 Ho 0.025 16 1.0 25 J^20 0.021875 14 0.875 26 Meo 0.01875 12 0.75 27 ^Voio 0.0171875 II 0.6875 28 \U 0.015625 10 0.625 29 9^40 0.014062s 9 0.5625 30 ^60 0.0125 8 0.5 Galvanizing the Sheets adds approximately 2H oz per sq ft to the above weights. The regular sizes of the corrugations are 2\h, iH, % and M« in, measured from center to center. Besides these sizes, 5-in, 3-in and 2-in corru- sulphurous and other gases from ten to twenty times longer, than a sheet of steel or semi- steel of the same gauge, or a light-gauge sheet made from pure puddled pig-iron; and that it will wear longer than steel sheets of the heaviest gauges, or galvanized sheets of the same gauge. " * For other gauges, see pa^es ^01, 402, 403, 1469, 1473, 1509, isioan^ 1513. Corrugated-Steel Roofing 1601 gations are made by one or two corrugating companies. Corrugated sheets are carried in stock in 4-ft, 5-ft, 6-ft, 7-ft, 8-ft, 9-ft and lo-ft lengths. Sheets can be obtained as long as 12 ft at a cost of 5% extra. The 8-ft length, however, is most commonly used. The width of the sheets, as a rule, is 24 in between cen- ters of the outer corrugations, so that the covering width is 24 in when one corrugation is used for the side lap. This appHes to all sizes of corrugations, all though one or two mills make wider sheets. The 2-in, 2H-in and 3 -in corrugated sheets are made in all gauges from No. 16 to No. 28, the ij^i-in corrugated sheets from No. 22 to No. 28, the ^i-in corrugated sheets from No. 24 to No. 28 and the yiQ-'m corrugated sheets in Nos. 26, 27 and 28 only. No. 28 gauge is the one com- monly used for all purposes. The sheets are generally painted with a red mineral paint before shipping and galvanized sheets, also, can be obtained if desired. All corrugated sheets are sold by the square (100 sq ft), measuring the actual widths and lengths of the corrugated sheets. Corrugated-Steel Roofing * Useful Data. For covering roofs, either 3-in, 23'i-in, or 2-in corrugations should be used, the 2H-in being the most common size. The thickness or gauge • depends upon the distance between the supports on which the sheets are laid. Nos. 26 to 28 gauges should be laid on close sheathing, or strips not more than from i to 2 ft on centers. The maximum distances between supports for other gauges should be as follows: t For No. 24 gauge, from 2 to 2H ft, center to center. For Nos. 22 and 20 gauge, from 2 to 3 ft, center to center. For No. 18 gauge, from 4 to s ft, center to center. For No. 16 gauge, s to 6 ft, center to center. The least pitch which should be given to roofs that are to be covered with corrugated sheets is 3 in to the foot, and for trussed roofs it is not desirable to Fig. 1. Approved Method of Laying for Side Lap have less than a one-fourth pitch (6 in to the foot). When laid on a roof, corru- gated sheets should have a lap at the lower end of from 3 to 6 in, according to the pitch of the roof. For a H pitch, a 3-in lap is used; for a H pitch, a 4-in lap; and for a ^ pitch, a 5-in lap. For the side lap it is recommended that each alternate sheet be laid upside down and lapped as shown in Fig. 1. By this method, when water is blown through the first lap, it will stop and not pass the half lap, but run down and out at the end of the sheet. A great deal of roofing, however, is laid as in Fig. 2. In applying to sheathing or wooden strips, the sheets are secured by nailing through the tops of the corrugations, the nails being driven through every alternate corrugation at the ends, and about 8 in * Much practical information regarding the use of corrugated sheets on mill-build- ings, with many details, is contained in Steel Mill Buildings and in the Structural En- gineers' Handbook, by Milo S. Ketchum. t For the strength of corrugated sheets, see the books above mentioned. 1602 Memoranda on Roofing Part 3 apart at the sides. When applied to iron or steel purlins, the side laps should extend over at least i^ corrugations, and the sheets should be riveted together every 8 in on the sides and at every alternate corrugation at the ends. The Cincinnati Corrugating Company makes a patent edge-corrugation which makes a tight joint with a lap of only one corrugation. To fasten the sheets to Common Method of Laying for Side Lap the purlins, which are usually steel angles, cleats of band-iron, % or li in wide, may be passed around or under the purlins and riveted at both ends to .the sheets, as shown in Fig 3. By contracting or pressing these cleats toward the web, a tight, secure fastening results, which allows for contraction and expansion of the sheets. Cleats, however, are generally used only with channel or Z-bar V\g. 3. Sheets Fastened to Angle- purlin by Band-iron Cleats / Sheets Fastened to Angle-purlin by Clinch-nails jDurlins. For angle-iron purlins, clinch-nails, made of soft-iron wire, are com- monly used, as shown in Fig. 4; they make very satisfactory fastenings. The following table shows the sizes of clinch-nails to be used with different sizes of angle-purlins and also the number of nails to the pound in each instance: Purlin-angle^ , ^^^^.^ .^^j,.„ ...... 2X^ in Lengths of nails. ».•*..,. 41 Number of nails peVy-^'^^ '*' ' HXsin 3HX3H in 4X4H in 5 m 6 in 7 m 38 33 27 . ^ . ^^^ , . , The nails should be placed through the top of every second or third corruga- tion. At the eaves of the building and along the edges of the ventilators special pains should be taken in fastening the roofmg, as these are the places where the force of the wind is the greatest and where it tends to strip the roofing from the purlins. For these parts of the roof the best method of fastening is that shown in Fig. 5. These fastenings consist of strips of sheet iron about 2 in wider than the purlins, made of No. 12 iron and riveted to the purlins with ^4-in rivets spaced 10 in apart. To these strips the corrugated sheets are riveted, every 5 in or every two corrugates, with 6-lb rivets. The method of fastening shown in Fig. 6, also, answers very wdil and is less expensive. Corrugated Siding 1603 In ordering corrugated sheets an allowance must be made for the laps. The following table gives the number of square feet necessary to cover one square of Fig. 5. Approved Fastening for Sheets at Eaves Fig. 6. Alternate Method of Fastening at Eaves actual surface, using sheets 8 ft long. If shorter sheets are used, the allowance must be slightly increased. Number of Square Feet of Corrugated Sheets to Cover loo Square Feet of Roof End-laps I in 2 in 3 in 4 in 5 in 6 in Side lap, i corrugation Side lap, ly^ corrugations Side lap, 2 corrugations sqft no 116 123 sqft III 117 124 sqft 112 118 125 sqft 113 119 126 sqft 114 120 127 sqft 115 121 128 Approximate Weights in Pounds of 100 Square Feet of 2}i-ia. Corrugated Sheets Gauge No. 28 No. 27 No. 26 No. 24 No. 22 No. 20 No. 18 No. 16 Painted.... Galvanized. 69 86 77 93 84 99 III 127 138 154 165 182 220 236 275 ^91 Anti-Condensation Lining. Wherever corrugated steel is laid on puriins with no sheathing or paper underneath, if the building is heated, moisture will invariably collect on the under side, and if the air in the building is warm and humid, considerable dripping will result. To prevent this dripping, it is neces- sary to protect the under side of the corrugated steel with paper or felt. This may be done by first stretching poultry-netting over the purlins, from eaves to ridge, and wiring the strips together at the edges. Over this should be laid one thickness of asbestos paper and one or two layers of saturated felt. The cor- rugated steel may then be fastened to the purlins in the usual way. The side laps may be secured by stove-bolts, with i by H by 4-in plate washers on the under side, to support the lining. Corrugated Siding For Siding, either the 2y2, 2, or iH-in corrugations are used. The iH-in size, however, makes the best appearance. For the laps, i in at the bottom and one corrugation at the sides are sufficient. For Sheds, etc., the sheets may be nailed to cross-pieces cut in between the studs horizontally and spaced from 2 to 3 ft apart, the studs being from 3 to 4 ft 1604 Memoranda on Tiling Part 3 on centers. For elevators, either cross-corrugated sheets or sheets not more than 32 in long should be used. The nails should be driven in the trough of each alternate corrugation, 2 in above the lower end of the sheet, which will be I in ABOVE the top end of the under sheet. This allows the sheet to slide i in in 32 in as the building settles, before the nail will strike the upper end of the lower sheet. The side lap should not be nailed. Ceilings. For 'the ceilings of stores, stables, etc., fie or ^^-in corrugated sheets are much used; and the construction is an excellent one for this purpose. Galvanized Iron. This term is commonly applied to all galvanized sheet metal. Formerly most of the galvanized sheets had a steel base, but since about 1906 a nearly pure iron, called Toncan Metal, has been largely used for sheets of very fine quality. Galvanized sheets come in lengths of 6, 7 and 8 ft in United States Gauge-Nos. 14, 16, 18, 20, 22, 24, 26, 27, 28 and 30, and in widths of 24, 26, 28, 30 and 36 in for all gauges except No. 30, which is made only in widths of 24, 26 and 28 in. Sheets of No. 28 gauge are also made in widths of 32 and 34 in. The widths commonly carried in stock are 24, 28 and 30 in. Most of the galvanized iron used for cornices and ornamental work is No. 27 gauge. No. 28 is sometimes used for gutters and conductors. Copper for Roofs Method of Applying. This is usually in 2\i by 5-ft sheets, making iiVi sq ft and weighing from 10 to 14 lb per sheet. It is laid on boards to which it is fastened by copper cleats. No solder is employed, as it is in tin roofs, in the horizontal joints, and the horizontal and sloping joints are made by simply over- lapping and bending the sheets. The horizontal joints are locked together and then tightly flattened down. MEMORANDA ON TttlNG Floor-Tiling and Wall-Tiling Tile Floors are extensively used in the better class of buildings, and par- ticularly in those portions which are used by the pubhc, on account of their great durability, sanitary qualities and decorative effects. As a matter of fact, a good tile floor is also cheaper in the long run than a wooden floor if it is subject to much wear. The materials used for tiling floors are tiles made from diff'erent grades of clay, marble, slate, glass and rubber. Of these probably the most durable and sanitary are the vitreous clay tiles. For walls and wainscotings, glazed tiles, marbles and glass are extensively used. Floor-Tiles. The following include some of the principle kinds of clay tiles: (1) Common Encaustic Tiles. These belong to the cheapest grades, and are made of naturally colored clays, red, buff, gray, chocolate and black. These tiles are of a porous, absorbent nature and are used for common floors where sanitary requirements are not exacting. (2) Semivitreous Tiles. These belong to a somewhat better grade than the first mentioned and are less porous and absorbent. (3) Vitreous Tiles. These are the hardest tiles known, cannot be scratched by steel or sand, and are non-absorbent and thoroughly aseptic. They are used principally for floors requiring a perfect sanitary condition and are manufactured in white, blue, gray, green and pink colors of great delicacy. Classification of Tiles 1605 (4) Ceramic Tiles or Ceramic Roman Mosaic. This material is made of VITREOUS clay in tesseral pieces representing the tesserae of the Roman mosaics. It is made into regular tiles ranging from yz to %-in squares and also in hexagonal shapes from % in to i in in size. A rounded lozenge tile is also manu- factured to be laid in tesseral paving. (See, also, Flooring of Mosaic, Terrazzo, etc., page 1607.) The material itself is of great hardness and well suited for work of a monu- mental or public character. The even and regular texture of the tesserae admits the adoption of damask designs which have become identified and associated with this material. The minuteness of the tesserae admits of a great range in designing and the following of the architectural lines. The ceramic Roman mosaic is much preferred to mosaic consisting of natural marbles, because of the great variety in colors and its greater durability. The vitreous-clay tiles are impervious to attacks of any acids contained in the atmosphere, while marbles, especially, are subject to rapid disintegration caused by the sulphuric acid con- tained in the smoke-laden atmosphere of our cities. (5) Florentine Mosaics and Flint Tiles. These are the largest and heaviest tiles manufactured in this country. They are either plain or inlaid and are in use especially in ecclesiastic work on account of their relation to mediaeval application. The material is vitreous, annealed and tougher than it is brittle. It is also in use for exterior polychrome work. (6) Aseptic Tiles. These are large, heavy and thoroughly vitreous tiles used for institute work. They are the only vitreous tiles of large size made in this country. As the tiles are large and generally of hexagonal shape, the joint- spaces are reduced to a minimum, and they are, therefore, especially adapted ' for hospitals, operating-rooms and wards for contagious diseases. Enameled Tiles, Wall-Tiles and Mantel-Tiles. The following include some of the enameled tiles: (1) White, Wall-Tiles. These are glazed tiles for wainscots. They have a white, soft body and a surface covered with a clear glaze. The brilliancy of this glaze and its reflecting properties make the white wall-tiles especially de- sirable for dark passages. (2) Colored, Glazed or* Enameled Tiles. These tiles are about the same as the former In quality; the glaze or enamel, however, is stained with metallic oxides, which produces a brilliant decorative effect. (3) Dull-Satin, etc., Finished, Enameled Tiles. These are glazed tiles with a DULL or BLIND enamel-finish. The dull finish is produced either by sand- blasting or by devitrifying enamels. It is principally used for quaint decorative effects in mantel-work. (4) Glazed Roman Mosaics. This is a type of enameled tiling which has great decorative possibilities. It has the same tesseral texture as the ceramic floor-tiles and is readily applied to wainscots and mantel-work. Setting of Tiles. Clay tiles are set in Portland-cement mortar as a rule, and flooring of this character should always be provided with a substantial concrete base. Ceramic mosaics are sometimes laid on a flexible base. With this construction wooden floors can be provided with tile covering, and owing to the elasticity and lightness of the material, floors in elevators, boats and other ambulant structures can be safely tiled. Marble Tiles, from 9 to 12 in square, have been extensively used for flooring, principally on account of their decorative effect. None of the marbles, however, jg as hard and. consequently as durable as the vitreous and ceramic tiles, and 160« Memoranda on Tiling Part 3 from all practical standpoints the marbles do not make as good floor-coverings. When used, they should be iH in thick and not over 12 in square, and should be bedded in cement on a concrete base. Marbles should not be used for flooring in hospitals, as they yield rapidly to the usual antiseptic floor- washes. Slate, although non-absorbent and not affected even by dilute mineral acids, is too cold and dingy to commend itself for floor-tiles, but because it is conven- iently handled in large slabs it is valuable as a cheap base and as a cover for wiring and pipe- trenches in the floors. As these often follow a wall, it may serve in the capacity of a border and as such be extended around the floor-space. Slate slabs for floors should be about iK in thick. Marbleithic Tiles or Slabs are made of small pieces or chips of marbles of irregular shapes, set in a backing of sand and Portland cement. After the ce- ment has set, the top surface is rubbed until it becomes flat and smooth. Mar- bleithic resembles mosaic or Terrazzo, except that it is laid in the form of tiles instead of being put down on the floor in a plastic condition. Much objection has been made to Terrazzo because of the cracks which commonly occur in it, due to the sBght settlements which are unavoidable in a new building. (See, also, Flooring of Mosaic, Terrazzo, etc., page 1607.) With tile floors of any material the joints allow for any slight movement of the floor-construction, without causing visible cracks. By the process of manufacture, marbleithic is made much harder than it is possible to make mosaic floors that are laid in a plastic condition, so that they have a much better wearing surface. Floors of this material have been in use since 1895 and show little if any wear. Marbleithic tiles are made of various colored marbles and in different sizes, shapes and patterns, so that a great variety of effects may be produced. Sanitary coved bases, stair-treads, and wainscotings, also, are made of this material. Cast-Glass Tiles, while quite resistant to a blow when the polish is un- broken, will break very easily when the surface is scratched. All glass tiles should, therefore, be very thick and small or protected by metal framing. Novus Sanitary Glass * is a sanitary structural glass manufactured in all thicknesses from H in up to 2 in and in slabs of all widths and lengths up to 100 in in width and 180 in in length. It is made in various colors and designs and in the following finishes: natural-fire finish, hone, semipolished and polishe^. It can be worked and handled the same as marble, it is readily drilled and shaped to accommodate fixtures, etc., and is very handsome in appearance. It is im- pervious to discoloration and is non-crazing. These qualities make it especially desirable for floors, wainscoting, tables, shelves, etc., in all places where an abso- lutely sanitary condition combined with a handsome appearance is required. Interlocking Rubber Tiling General Description. There is an interlocking rubber tiling, f which, be- cause of its being noiseless, non-slippery, and more comfortable to the feet than inelastic substances, has met with great favor for floors in banking-rooms, counting-rooms, vestibules, elevators, stairs, cafes, libraries, churches, etc. For elevators it is one of the most durable and practical floors that can be laid;' it is also especially and peculiarly adapted for floors of yachts and steamships. The interlocking feature unites the tiles into a smooth, unbroken sheet of rubber, unlimited in area. The tiles do not pull apart or come up, and each being distinct, almost any color-scheme can be employed, the tiles bei»ng made in a carefully selected variety of colors. The tiles are laid directly over the • Made by the Penn-American Plate Glass Company, Pittsburgh, Pa. I M2^n\ifactured by the I c tc £-? (U O fl O X5 J3 ja >. .^ 'Cl ^ '^ '^ O ,„ J2 &jJ,y ,5:i ti -^ o o o o o o o Ti o a> ■=!■ »^ 6 W.S =< H M m -s^ -^^ ii' illllli -:! i2 J: vn li, :;» ^i: J^3 •^ =:: P^ w o Fi *j 4> id ^ H fci. < XI i? (U n H -n o is rtK K ^^ C/5 J3 „ o "^-a if fe- ll 'T3 ffi 0) ^ "r< a ^ .. o '^ t« C3 C.S2 Sc.:^ T^B Ic! I'S 5*, JS Is » -♦— H S 1618 Estimating the Cost of Buildings Part 3 The Grand Central Station, as a complete terminal, is a very complex struc- ture, but there is a distinct part which contains the passenger-concourse and the waiting-rooms, restaurant and other parts that are considered necessary to care for the traflBc. The cubic contents of this part total about 14 000 000 cu ft. Other ])art5 of the building are not considered in the present reference. Some interesting facts as to the main station, only, are: Cost, * about. . . i $8 000 000 Ground-area above street-level, square feet 266 000 Additional station-facilities under street, square feet 80 000 Floor-area devoted to station-purposes, square feet i 188 000 Cubic contents, about, cubic feet 32 857 800 Steel used in construction, tons 35 767 Weight of largest girder used, tons 30 Costs* of Pre-war Reinforced-Concrete Buildings. fi In judging the cost of a building by cubical content or by areas of floors the shape of the build- ing in plan should be taken into consideration. A long, narrow building will cost more per cubic or sqliare foot than one more nearly square in plan; and in computing costs by the cubic-foot or square-foot unit prices these conditions as well as the judgment and experience of the architect or engineer who makes the estimates affect the accuracy of the results. The following notes quoted from data furnished by the architects and engineers of the buildings mentioned include useful information relating to costs of some reinforced-concrete buildings of different types, erfccted in Philadelphia and vicinity (1906-19 15). (1) * A reinforced-concrete building of the factory-type, erected (i 914-15) in the City of Philadelphia. It is a concrete cage, with no brick veneer, four st )ries in height, no basement, size, 60 by 159 ft, stair-shafts and elevator- shafts projecting beyond the building; cubical contents, 603 000 cu ft. The cost, without equipment, was 7K cts per cu ft. Drainage is included in this price, but no plumbing, heating^ lighting or elevators. The total floor-area of the building is 40 140 sq ft and the cost per square foot is $1.1414. This is built according to the building laws of Philadelphia. (2) "A mill-con.structed building, about the same size as building (i), recently erected in a manufacturing town forty miles from Philadelphia. It is four stories in height and has a part-basement, a wing 30 by 40 ft, and a one- story boiler-room and engine-room. The total cubical contents are 524 160 cu ft, and the cost, 6H cts per cu ft. The total floor-area is 37 gco sq ft, and the cost, $0.85 H per sq ft. This is without power^ heat, or light. There are a few plumbing-fixtures in this building. "In comparing the costs of the two buildings, it must be borne in mind that one is located forty miles from Philadelphia, and was not erected under the rigid building laws that are in force there. It is usually possible to erect a building of any type at less expense outside of Philadelphia than in that city and this can probably be said of any city where there are no state building codes. (3) "A mill-constructed building, three stories in height, erected in 1906 in Camden, N. J., and having 575 044 cu ft. It cost 7 cents per cu ft. It has 38 912 sq ft of floor-area, at a cost of $1.04 per sq ft. This price is without power, heat, Hght, of elevators, but includes some plumbing. (4) "The new municipal repair-shop of the City of Philadelphia. This is a reinforced-concrete building with brick veneer of an ornamental type, and cost 9}^ cts per cu ft for i 080 591 cu ft or $1.74 per sq ft for 57 323 sq ft of total * See notes on costs on pa^ 1614. Prices given must be at least doubled (1920). t Valuable data on ibis subject have been furnished the Editor by Ballinger & Perrot, the architects and engineers of the five reinforced-cohcrete buildings described. 1 See, also, page 1613. Division of Cost of Fire-Proof Buildings 1619 lloor-area. This is without plumbing, power, heat, light, or elevators. The relatively high cost per square foot for this building is due to the fact that the crane run-way takes up a considerable portion of the building, so that a floor is omitted where the crane is placed, and the floor-area accordingly reduced. (5) "The new building for the Automobile Club of Philadelphia. This is a three-story building, of reinforccd-concrete cage-construction, and contains I 341 966 cu ft, at a cost of 10% cts per cu ft. The total floor-area is 90 602 sq ft, costing $1.54 per sq ft. This is without power, heat, light, or any equip- ment, but includes plumbing. The shape of this building favors economy o( construction, as it is nearly square in plan." In summing up the conclusions arrived at in regard to the average costs of reinforced buildings, E. G. Perrot states * that the cost can best be considered by classifying them under three general heads: (i) Warehouses and manufactories. Cost, from 8 to 11 cts per cu ft. (2) Stores and loft-buildings. Cost, frorh 11 to 17 cts per cu ft. (3) Miscellaneous buildings, such as school-houses, hospitals, etc. Cost from 15 to 20 cts per cu ft. Cost of Mills and Factories Built on the Slow-Burning Principle. For data relating to total and unit costs of buildings of this type, see Chapter XXII, pages 802 to 810., Percentages of Cost of Items of Construction in Fire-Proof Buildings The tables t on the following six pages show, on pages 1620 to 1625, the DIVISION OF THE COSTS of fire-proof buildings among the different materials and parts of the construction, the data having been furnished the compiler hy architects and builders in the cities mentioned in the tables. Each column of values in the tables gives the data for an individual building, except the values for New York City, in the second, third and fifth columns, which show the averages for a large numl^cr of buildings. The tables on the first four pages include only buildings approximating closely the standard specifications of the National Board of Fire Underwriters. The tables show that the foundations and steel frames, the Only parts little damaged in conflagrations, represent, approximately, only 25% of the entire sound value of a building. For examplci in the tables on the first four pages, the average cost of all the foundations is 8%, while the average cost of the steel frames is 17.88%. The tables show, also, on pages 1624 and 1625 the percentages of cost of the classified items of construction of eight buildings damaged by the Baltimore conflagration (1904)} the averages of these eight buildings being given in the last column. * See "Comparative Costs of Reinforced Concrete Buildings," by E. G. Perrot, in Proceedings of the National Association of Cement Users, Vol. V, 1909. See, also, notes on costs on page 1614. t The tables on the first four pages were compiled by F. J. T. Stewart, Continental Insurance Company, and those on the last two pages by the Baltimore Committee of the National Board of Fire Underwriters. All are reproduced, by permission, from J. K. Freitag's Fire Prevention and Fire Protection. Those parts of the Baltimore tables which gave the proportion of fire-damage to sound value of the various items have been omitted as this article of the Pocket-Book deals more especially with original costs. 1620 Estimating the Cost of Buildings Part 3 • rj t^ o M id • ro O ro • • tOOO '<»-Mi-iOOO oqvOh • 4 cs c « .^^ a=^ 2S a O o ^ •cd : rt'S : ro r^ c>j Tf r O O cvj ro ^ vcJNioddvooM o%oo o lo f^ 6 ^ ^ 6>6 6 MO • ro O M-od ooo vo lO (U s T ^ w 03 r? „; r-; ^ ^ a O . - u. ^ .v "^^ >. >i d oT s» -»-J -tJ TO en o C C ^ ^^ o ■G T; "5 w .';3 « (720 1622 Estimating the Cost of Buildings Part .S2 c O ^ OT eg o o o» tx • 2J^ N 00 • MO •00 lO • MOO SK • W Vh J? I'd ^•^'§3 •J:S -^ bO c3 flj'-l ca ra {-< _-i Jii ca a rt vh c^ 3^ o ^^ o ^.-2 : a : : • S o g-^ :> : • -^ S 8 § rti ^|.S ifj^ i§ :£ o w G : ^^ ^ • u O.b 03 ^.S^.H.2.2 e o ^'-;l o C3 t- ^'Si w > w Division of Cost of Fire-Proof Buildings lessl 1 W S H . ; ; 1 i ! I i I ! ! I i ^ : : : i : : s , H 1 1 ; ' ;:^ : : : : : : ' 1 g^^iofo . c^ . ^ vr> -00 • . • . • : : : : ^ : : ? : • • '. i Cvj .' * M • N •^ lO lOVO t^ a .M . . . . . . fO .00 • • t^ • ^ ■]Q • ' • • • • tT ■ C>< . . N . K, ^ '^ t^ rf Ol fn ^ •> • • • • in • • r- -vo • • o • t3 N 13 t^ ■'^ ro (v^ . lO . • . . . . O • (N • .VO • vo .J. . . . . . . c>« • rc . . fo • ^ N ?; .^SmYi % fn • 00 • • • • . .vo • -^ • ■ in • VO .^ . . . . - • MMO%0 O Oo • Tt . • • • . . . . M • • 0< . «*-. ? Oo to M lO o,vo lo ; ; : : ^ : : : : : : ^ .c . . . . ;^ -^i • • • • ::g:5::^: O '^ rt o C .'::? ^ E:^ '^ ^ ^ 12 .<^ S VO .00 . • • • . .CO .^, . .J . ^, I lo t^ rn !;■ & S ro O.'^ . i^ ^ .VO • • • • > J H .CO . . . . • • « • CO • • M . ^ r? "* 00 ?" ^'g^lSoop; -^ j:^ .^ . . . . j^ .j^ . . . . 00 D- ii I F ^ (N 0000 CN lO "s . s . . . . CO ro O M |,. "" c. 7^ oJo ?^ 8 ... =? :^ : : : : O, i ro I • • • >-H Hi • 8 u :::::, :::::::::: : : : :^ : : : : : : : i^ itJ : : : : :.s : : ^ ^ i ; :.s ;| M ; i ill M • • • : :.t! :i : : : : :i'S : : : : : • -^ -i : : :-g :^-S ; ; • : :a :S :-H : : -1 i-^g : : • c : ^ : +^ . ^ . . : bo . cd trt . . ■a'H,bi>?g^ :„' :i^a-43 : fe g oJ o ? iL r 1 i3 f-'n • o • t, cJ cj • X 3) v;-- ::::::: : : : :| : : : ;!:!:!!!;;! I'm ' '. '. ::::::::::: i'o :-h' : ; i ; ; ; ; ; I ; : ; ;| ;l ; ;;;;:;;;;: ;*-| ;i ; .pp;::;:-:|i.e^ ; |S>c_e« : : : : : : gj- g • Hint illl ill III l" 1624 Estimating the Cost of Buildings Part fe'sis J M d d d ■I o o -=i-avO K o.*d ^7 ■* pq ^ 5 ^^ ^Division of Cost of Fire-Proof Buildings 1625 <^1 t cs cs o o 6 o w N o d i/) o ^^1 00 '^ Ova> o \0 M IT) bO Co a» t^ IN IT) d Jean's \0 lo O 't l> tv,00 d lo d CO a> d ID 4 ^ • to d (v^VO 00 ■^ d H 1c2 moo O M H d d d d d d M H (N vd d 2.S 4 lO H M H >'0 O^ r^ ■^ d d d >o cy>Hi a>oo M >0 »0 fO (N 00 M K. csi >* d d t^ tie PQ ^ONIJ^OOVOOH O>00 < o< d cs N ov d d lis I sill iii ct3 rt _ o C d te; > a; o ^ .. rt £^ 1^ f^ o^ cg^ vi"3^ 1:: 5 & C/20 S w c 1626 Estimating the Cost of Buildings Part 3 Costs * of Different Kinds of Work per Cubic Foot of Building Some estimates f have been made by F. W. Fitzpatrick showing the propor- tionate COST OF THE DIFFERENT BRANCHES OF WORK which gO tO make Up 3 completed building. Believing that these data will be found useful in making up approximate estimates, Mr. Kidder obtained permission to use them in the Pocket-Book. The following figures represent the actual cost of a ten-stor^ OFFICE-BUILDING, 6o by 130 ft in plan, built in the Middle West, a first-class fire-proof structure, with two street-fronts faced with granite and resting on a pile foundation. Kind of work Per cubic foot of entire building, cents Kind of work Per cubic foot of entire building, cents Foundations 1% 2 Ms Heating ; iH Steel framing Plumbing . . Vi Granite and all masoni-y . . Cornice, roofs and sky- lights Elevators I Stairs, scenic structural framing, "making ends meet," lamp-fixtures, etc. What might be called a fair amount for " contingencies " in such a building, includ- ing lesser items net men- tioned here but grouped together Fire-proof floors Partitions, tile All plastering and stucco. . Elevator-fronts and all oir- namental metal work Marble work Hardware Joiners' work 42^20 Glass Architect's fee !•% Painting and varnishing. . . Electric wiring Total 34M2 The Chicago post-office building, containing 12 000000 cu ft and of monu- mental character and finish, cost, * in some of its items, as follows: Kind of work Foundations Steel framing Granite and masonry Fire-proof floors Plaster, plain and orna- mental Per cubic foot of entire building, cents i94 2\^ 13H m Kind of work Ornamental metalwork Marble Plumbing Heating Per cubic foot of entire building, cents 2H 1% It will be noticed that the relative cost of several .of these items is the same •^.s in the office-building. The total cost * of this building was 42^ cts per cu ft. * These pre-war figures must be increased from 50% to 100%. t Published in " Fireproof^'^Mfrchj 1903, Cost of Buildings per Square Foot iSSt Cost * of Buildings per Square Foot One-Story Buildings of Large Area, such as exposition-buildings, etc., may be estimated almost as accurately by the square foot of ground covered as by the cubic foot of building, as there are few or no interior partitions, and usu- ally no plastering or interior finish. Iron and Steel Buildings. "Roughly speaking, the cost of one-story iron and steel buildings, complete, is, for sheds and storage-houses, from 40 to 60 cts per sq ft of ground, and for such buildings as machine-shops, foundries, and electric-light plants, that are provided with traveling cranes, the cost is from 60 to 90 cts per sq ft of ground covered." f Structural Steel. For estimates of cost of structural steel for buildings, see pages 1204 to 1207. Wooden and Brick Mills and Warehouses. See Chapter XXII, pages 802 to 810. Exposition-Buildings. The cost t of the World's Fair buildings (Chicago, 1893) per square foot of ground covered, including sculpture and decoration, was as follows: Manufactures and Liberal Arts Building $1 .39 Transportation Building i . 08 Electricity Building i . 69 Machinery Hall 2.12 Agricultural Building i . 44 Administration Building 9.18 Horticultural Building i . 41 Mines and Mining Building i .04 Fisheries Building 2.35 Forestry Building 0.75 Cost* of Structures for the St. Louis Exposition (1904). The following figures were issued by Isaac S. Taylor, at that time Director of Works, of the Building Art Two Art Pavilions, each Art Building Annex Government Building Government Fisheries Mines and Metallurgy Liberal Arts Education and Social Economy . . Manufactures Electricity Varied Industries Machinery Steam, Gas and Fuel Transportation • . Horticulture Agriculture Forestry, Fish and Game Festival Hall Dimensions, Area, Total cost Cost. ft acres sq ft 161X346 144X423 1.42 1 3.i4i S967 833.90 $5.45 106X150 0.41 39388.99 2.48 200X736 3.86 328980.00 2.23 136X136 0.42 45 000.00 2.43 525X750 9.08 488848.50 1.24 525X750 8.80 471 820.95 1.20 525X758 7.70 323950.75 0.81 525X1 200 13.47 711 510.00 1. 13 525X758 6.67 408531.57 1.03 525X1 200 10.28 704067.96 1.12 525X1 000 51.48 509 110.50 0.97 301X326^^ 2.25 135 480.00 1.38 525X1 300 15.70 674853.42 0.99 374X782 5.42 225342.27 0.77 500X1 600 18.62 520491.07 0.58 300X600 4.07 168883.38 0.94 195 in diam- 1 eter, exclusive ? 109 215899.00 of annex ) eased from 50^ I to 100%. fH. G .Tyrell.^ 1628 Estimating the Cost of Buildings Part 3 World's Fair, showing the area and cost of the principal exhibition-buildings. The total area of twenty-two buildings was 123.51 acres, and the total cost $6 939 992.26. The cost was for the bare buildings, and did not include sculp- tural or other decorations, or the architects' compensation. Recent Exposition Buildings. The cost of buildings of this character, erected since 1904, shows a pretty general increase up to 19 14, with occasional variations in the rate of change, of from i to 2% per year. Increase since 1914 would be from 50 to 100%. Cost * of United States Government Buildings. There was published in 1900, by the United States Treasury Department, a history of the public buildings of the United States, giving their cost, and in 1902, there was pub- lished t a list of 287 buildings, giving the cost per cubic foot, the material used for the walls and the date of erection. There was also published, in 1910, by the Committee on Public Buildings and Grounds of the United States Senate, a list of sites and plans for pul^lic buildings, giving data of much value in regard to the cost of public buildings, their cubical contents and their cost per cubic foot, including buildings erected from 1816 to 1910. "As a rule, these buildings have cost more per cubic foot than private buildings, so that their cost cannot always be used as a guide, except for government buildings." | Unit Prices * per Cubic Foot for Recent Government Buildings of the Same Type.§ The data included in the following paragraphs relate to federal buildings erected before or in process of construction in 19 14. They are of certain fixed types and in different parts of the United States. The buildings are post-office buildings and the location, brief description of the general con- struction, ground-area covered, cubical contents and comparative rates per cubic foot are given. The buildings are grouped under five different types, and the VARIATIONS IN COSTS PER CUBIC fOot of similar or identical buildings in each type, located in different sections of the country, are shown. Following these five types is a list of buildings of various .sizes and descriptions showing the variations in the cubic-foot rates. The conclusions arrived at and summarized at the end of the lists, include a table which shows what was considered by the office of the Supervising Architect to be a fair difference in cost of buildings OF THE SAME TYPE in different sections of the United States. It wns con.sidered, also, by that office, that the method of estimating the cost of buildings by a CUBIC-FOOT unit PRICE is productive of very uncertain results, inasmuch as there are many variable conditions entering into the construction of buildings located in different localities. The principal items affecting the cost of similar types of buildings are: (i) Labor; rates and efficiency. (2) Materials; quality and freight-rates. (3) Season; time of year when building is constructed. (4) Contractors; finances, abihty, equipment, overhead expenses and margin of profit desired. * Pre-war figures must be increased from 50% to 100%. t Published in the Architects' and Builders' Magazine, Aug., 1902, and in the Inland Architect, April, 1902, t F. E. Kidder, in previous editions of the Pocket-Book. § The information relating to the cost of recent government buildings of certain types was furnished by J. W. Ginder, Superintendent of the Computing Division, Office of the Supervising Architect, by permission of Mr, O. Wenderoth, the Supervising Archi- tect, throui^h whose courtesy and valuable assistance the editor is able to present the data referred to. The editor regrets that limited space prevents the reproduction of a carefully prepared and most interesting series of photographs of the plans, elevations and sections of the government buildings, the costs of which per cubic foot are here discussed. Cost of Government Buildings 1629 (c) Location; as to supply-centers, distance from railroads, and facilities for handling mtaerials. Variations in Unit Costs * of Identical Buildings in Different Localities In order to compare the costs of identical buildings, with slight modification only, the following are given as examples, to show the variance in different localities. Type I. Post-office buildings at Grenada, Miss., Bennettsville, S. C., Cov- ington, Tenn., and Burhngton, N. J. Description. Main building, two stories and basement; rear projection, one story and basement; non-fire-proof construction throughout; brick facing; stone trim; wooden cornice; slate-covered gable roof, with dormers over two-story portion, and flat, composition roof over one-story portion. Area and contents Ground-area Cubical contents . 3 825 sq ft 138 210 cu ft Rate per cubic foot * Location Grenada, Miss Covington, Tenn. . Bennettsville, S. C, Burlington, N. J... Non-fire-proof $0,322 0.31S 0.304 0.293 First floor, fire-proof $0,327 o 324 0.309 0.298 , and Type 2. Post-office buildings at Winchester, Tenn., McPherson, Kan., Longview, Tex. . . , Description. Main building, two stories; rear projection, one story; partly excavated basement; non-fire-proof construction throughout; brick facing; stone trim; wooden cornice and pilasters at front entrance; slate-covered gable roof with dormers over two-story portion, and flat, composition roof over one- story portion. Area and contents 3 825 sq ft 138 210 cu ft Cubical contents Rate per cubic foot * , Location Non-fire-proof First floor, fire-proof $0,344 0.346 0.332 $0,350 0.351 0.337 .♦ These pre-war figures must be increased from 50 to 100%. 1630 Estimating the Cost of Buildings Part 3 Type 3. Post-office buildings at Cookeville, Teiin., and Jackson, Ky. Description. Three-story-and-basement building; stone-faced to top of course over water-table; selected, common-brick facing and ornamental terra- cotta trim; composition and slate roof and non-fire-proof construction, except the first floor. Area and contents Ground-area 4 942 sq ft 290 300 cu ft Cubical contents Rate per cubic foot * Cookeville, Tenn So. 275 0.269 Jackson, Ky Type 4. Post-ofTice buildings at Garden City, Kan., and Lake City, Minn, (identical buildings). Description. One-story-and-basement, brick-faced building, with stone water- table course and trimmings and ornamental terra-cotta cornice, architrave and parapet-coping; non-fire-proof construction, except the first floor; composition roof. Area and contents Ground-area 3 888 sq ft 141 456 cu ft Cubical contents Rate per cubic foot * Garden City, Kan $0,405 0.341 Lake City, Minn Type 5. Post-office buildings at Abilene, Kan., and Bellefontaine, Ohio. Description. One story and basement; stone facing; granite steps, etc.; tin roof; fire-proof construction, except roof. Area and contents Ground-area 5 000 sq ft 183 000 cu ft Cubical contents Rate per cubic foot * Abilene Kan $0,359 0.367 Bellefontaine, Ohio Buildings of Various Sizes and Descriptions. The following li.st is for buildings of various sizes and descriptions throughout the country and shows the variance in the cubic- foot rate. * These pre-war figures must be increased from 50 to 100%. Cost of Government Buildings 1631 Post-office building at New Rochelle, N. Y. , , * Description. This building is of an irregular plan; two-story and basement; •enter pavilion; sides and rear one-story and basement; clearstory over work- •oom; stone facing to first-floor level; brick facing above this point, with terra- :otta'trim and cornice; composition roof; fire-proof construction. _ Ground-area Cubical contents Rate per cubic foot * . 7 512 sq ft 258 900 cu ft $0,259 Post-office building at Mobile, Ala. Description. Front portion, two stories, and rear portion, one story over workroom Only a small portion of basement excavated for heating-plant. Main building faced with limestone and rear second story portion with orna- mental terra-cotta. Fire-proof construction; long and short spans and con- crete joists with terra-cotta fillers; copper deck and Spamsh-tile roofs. Ground-area Cubical contents Rate per cubic foot * . 18 054 sq ft 670 476 cu ft $0,341 Post-ofhce building at Muskogee, Okla. Description. A four-story-and-basement building, floor line, stone-faced above (except in interior court, which is brick) cotta cresting at roof; copper roofing and fire-proof construction throughout. Both standard types of concrete and terra-cotta floor-co^nstruction, M.n,. mental in design. Corinthian colonnade at entrance, lamp-standards. Six flights of marble stairs, very ornamental plaster-work in lobby and court-room. Granite to the first- terra- jhout. Monu- Eight heavy bronze Entire lobby of marble, and Ground-area Cubical contents Rate per cubic foot *. 20 400 sq ft I 326 612 cu ft $0.43 Post-office building at New Bedford, Mass. Description. One story, basement and mezzanine ce^t^d portion; granite facing, except ^l-story w^^^^^^^^^^ cotta; main roof of composition; clearstory roof of copper, struction. vith clearstory over fire-proof con- Ground-area Cubical contents Rate per cubic foot * . 27 750 sq ft I 080 690 cu ft $0,323 Pnqt office building at Newark, Ohio. Dccript on Two-story, basement and unfinished attic The workroom ex- tendtthrough two stories. Offices in second story over ba ance of bu.ldmg. Firrnroof construction throughout. Terra-cotta floors, ce.lmgs roo s, parti- fion?furri.g etc Exterior faced with pink granite to the first-floor level and rhwhte marble above, including cornice, parapet etc Flat t." roof; bron.^ Grille, at first and second-story windows on front of bu.ldmg Cast-iron grilles ! first story and basement-windows on sides and rear; bron.e-faced post- offict iree7 desks, revolving doors, vestibules, etc., and drawn-bronze covered f hes wTnd^w-fra^es, doors, etc., in lobby. Caen-^stone cormce and coSered ceiling in lobby. Bronze and marble stairs to second story. ♦ These nre-war figures must be increased rrom so to 100%. 1632 Estimating the Cost of Buildings Part c Ground-area ..... 6 912 sq ft 369 640 cu ft $0,487 Cubical contents Rate per cubic foot * Post-office building at Mi not, N. D. Description. Three-story-and-basement building; fire-proof, except roof which is plank on steel beams; stone facing to second-story window-sills; bricl lacing above, with stone cornice, parapet-coping, etc. Oround-area . . 6 700 sq ft 427 300 cu ft $0,328 Cubical contents Rate per cubic foot * Post-office building at McAlester, Okla. Description. Three stories and basement; fire-proof, except roof; terra cotta floors, etc.; suspended ceilings; stone facing to second-floor level; bricl facing above, with stone trim; cornice and balustrade; tin roof. Ground-area 7 482 sq ft 394 765 cu ft $0.38 Cubical contents Rate per cubic foot * Post-ofiice building at North Tonawanda, N. Y. Description. The building has two stories and basement; granite to th( first-floor line; brick-faced above with stone trimming and slate roof; fire-proo construction to and including the second floor. Ground-area 5 475 sq ft 276 320 cu ft $0,289 Cubical contents Rate per cubic foot * . Conclusions Regarding Variations in Unit Costs. In the foregoing unit costs, the approach-work, such as walks, platforms, terraces, etc., is in eluded. This, in some cases, is quite expensive, and is generally from 5 to lO/^ of the entire cost of the building. In federal buildings, there are many require ments not met with in the ordinary mercantile buildings, and the permanent character of the building necessitates all materials, workmanship and construe tion to be of the very best in each case. This is guaranteed by iron-clad speci- fications, long-time guarantees for several items of the work, and persona government inspection. The office of the supervising architect has deter- mined that the rel.ative increase in cost of buildings throughout the country over the cost in the Mississippi Valley district was about as follows, taking the Mississippi Valley district, as a base, at 100%, and the labor and market-con- ditions which prevailed in October, 19 14. ! Per cent Mississippi Valley district . ... 100 no H5 100 130 120 125 New England (except Maine) Maine . . . . Southern States Northwest Mountain district Southwest Mountain district Pacific Coast '. * These pre-war figures must be increased from 50 to 100%. Cost of Government Buildings 1633 In the grouping of districts, the Mississippi Valley district is intended to cover the Middle States as far east as Ohio and Pennsylvania, and the states, generally, bordering on the western bank of the Mississippi River. This is found to be a part of the country in which the lowest prices have been ob- tained. The other districts represent the approximate greater cost for buildings over that in the Mississippi Valley or Middle States, and is intended to repre- sent the DIFFERENCE IN COST AT ANY TIME; but is not intended to represent the diiTerence in cost at different periods. Illustration of Variation in Cost * of Buildings of Identical Area and Contents. The following notes are taken from photographs of drawings, and from data accompanying them.f The drawings were for a Post-Office build- ing at Menomonie, Wis. This building contains 4 770 sq ft of ground-area, and the cubical contents are 147 570 cu ft. The contract was awarded (19 13) for $45 380, or at the rate of $0,308 per cu ft. It is a one-story-and-basement building, faced with brick, with stone water-table, brick parapet and tin and composition roof. The first floor, only, is fire-proof. Proposals were opened (19 14) for a Post-Office building at Uvalde, Tex. This building, except for some slight modifications, is as nearly like the Menomonie building as it is possible to make it without using the same drawings. The ground-area of the Uvalde building is 4 672 sq ft and the cubical contents, 151 875 cu ft. The work in connection with the approaches is practically the same as that at Menomonie. If these buildings had been erected in the same town, it does not appear that there would have been any difference in the costs, but the lowest proposal received for the Uvalde building was $56 400, or at the rate of $0,371 per cu ft. A comparison of the amounts for these two buildings further illustrates the unreliability of any universal appHcation of the cubic-foot rate in determining the costs of buildings, and also shows that the difference in cost of construction of buildings in different sections of the country varies considerably. Cost per Cubic Foot of Some Important Federal Buildings. The follow- ing tabulations contain additional unit costs and other data for public buildings. Cost * per Cubic Foot of Some Important Federal Buildings. Location and building New York, N. Y., Custom-House (completed 1908) Cleveland, Ohio, Post-Office, Custom-House and Court-House. ..... San Francioco, Cal., New Post-Office and Court-House (completed 1906) Denver, Col., new Mint (completed 1905) San Francisco, Cal., Subtreasury Building (estimated) Baltimore, Md., new Custom-House (completed 1908) Washington, D. C, Senate Office-Building Salt Lake City, Utah, Post-Office (completed 1905) : Indianapolis, Ind., new Post-Office (completed 1906) Philadelphia, Pa., new Mint (completed 1901) Washington, D. C, National Museum Building Washington, D. C, Agricultural Buildings (portions completed) Washington, D. C, House Office-Building Cost per cubic foot, cents • 74 68 66 65 60 55 50 47 46 45 43 40 36 * These pre-war figures must be increased from 50 to 100%. t These photographs of plans, elevations and sections, together with many others, and accompanying explanations and data, were furnished the editor by J. W. Cinder, Super- intendent of the Computing Division, Office of the Supervising Architect, by permission of Mr. O. Wenderoth, the Supervising Architect (1914), and have been of great assistance in the nresentation of notes on the costs of buildings. 1634 Estimating the Cost of Buildings Part 3 Cost * per Cubic Foot and per Square Foot of Some New Public Buildings t Location Facing Cost Contents, cuft Area, sqft Cost ] Cuft Sqft Bangor, Me Granite Marble Stone Limestone Brick Limestone Granite $271 297 288800 132 702 95200 81532 116 689 295051 793 720 576000 377668 256 210 256 210 448300 I 080 000 15600 II 000 II 000 6470 6470 9984 21 732 $0,342 0.500 0.350 0.373 0.318 0.360 0.300 $17-40 26.20 12.00 14.80 12.60 11.70 13.50 Augusta, Ga South Chicago, 111 Long Branch, N. J Plymouth, Mass Piqua, Ohio New Bedford, Mass. . . Depreciation of Buildings | Discounts from Values of New Buildings. The figures given on the pre- ceding pages are for new buildings. To ascertain their value at any time sub- sequent to their erection, a discount from the value when new should be made as follows: Per cent per year Brick, occupied by owner i to 1 ^ Brick, occupied by tenant iH to ij^^ Frame, occupied by owner 2 to 2}-^ Frame, occupied by tenant 2»'i to 3 If built of long-leaf yellow pine, or of spruce from the New England States, add from 20 to 30%, or if of short-leaf yellow pine, add from 40 to 50% to these values. If of redwood or cedar from the Pacific Coast, use about one-half these estimates, which are for white pine or white pine with oak framing-timbers. These figures for depreciation are to include buildings in which ordinary repairs have been made. If extraordinary repairs have been made, the discount should not be so heavy. Good judgment must be used in estimating the amount of depreciation in buildings. The Depreciation of Mill-Buildings. The annual depreciation of a mill- building of slow-burning construction varies from i to iyi%, while the de- preciation of a reinforced-concrete factory-building is relatively much less, since it is confined entirely to such details as windows, doors, roofing, etc. The Wear and Tear of Building Materials. At the tenth annual meeting of the Fire Underwriters' Association of the Northwest, held at Chicago in September, 1879, Mr. A. W. Spalding read a paper on the wear and tear of building materials and tabulated the results of his investigations in the follow- ing form: * These pre-war figures must be increased from 50 to 100%. t Reproduced, by permission, from the Journal of the Society of Constructors of Federal Buildings, September, 1914, through the courtesy of C. R. Marsh, Editor of Publications of the Society of Constructors of Federal Buildings. This Journal, published monthly, contains data of much interest to architects and builders. X From Tiffany's Estimate of Depreciation, used by the United States Government. Quantity System of Estimating 1635 Material in building Brick Plastering Painting, outside... Painting, inside Shingles Cornices Weather-boarding. . Sheathing Flooring Doors, complete. . . . Windows, complete. Stairs and newels. . . Bases Inside blinds Building hardware. Piazzas and porches Outside blinds. . Sills and first-floor joists Dimension-lumber These figures represent the averages deduced from the replies made by eighty- three competent builders unconnected with fire-insurance compames m twenty- seven cities and towns of the eleven Western States. THE QUANTITY SYSTEM * Explanation of the System. The quantity system is not, as some persons have supposed, merely the taking off of a list of items by one person probably with uncertain accuracy, for some other person's use. It means the careful measurement by a disinterested expert specially trained in this kmd of work, that is a quantity surveyor. This specialist proceeds in a manner quite different from that of the average contractor. He follows a certain recognized order and system in taking off quantities, abstracting and billing, with a view to eliminating errors. He uses certain uniform standards of measurements and expressions well understood by bidders. His checking and rechecking methods to ensure accuracy must be studied to be appreciated by those to whom the quantity system is unknown. A record is kept of every item, however small, having a money-value. These items are classified and arranged, each under its proper trade or department, in methodical order. Guess-work methods * The quantity "system" which is not merely a survey of items, has been systematically advocated since 1891 by G. Alexander Wright, A.I.A., 354 Pine Street, San Francisco who is the founder of the movement to adapt the Quantity System to American building nractice It has attracted much attention among contractors, architects, and engineers. In course of time this system of estimating must be adopted, as it stands for a square deal between owner and contractor. The movement in aid of this work is purely a voluntary one, an honest effort to bring about better methods. 1636 Quantity System of Estimating Part 3 are unknown to the quantity surveyor, while his accuracy and attention to even small details is worthy of comment. Every l^idder figures from a copy of the surveyor's quantities furnished to each one, with (if desired) the plans and specifications. The surveyor who does this work is a professional man similar to the engineer or the architect. He should, in fact, have, and he usually has had, experience in these professions, and in addition, a practical experience acquired in the field in actual contact with and superintendence of construction- work. Method of Procedure. Such a surveyor, in taking off quantities from an architect's or engineer's drawings, readily detects any discrepancies due to hasty preparation or other cause. The attention of the architect or engineer is called to such matters by the quantity surveyor, as he goes on with his work. De- tected in this way, all uncertainties are at once corrected and adjusted, so that by the time the drawings and specifications reach contractors, everything has been made plain and accurate and the possibility of error in quantities can therefore be disregarded. The resulting document, the bill of quantities, is then either printed or otherwise reproduced, and a facsimile copy supplied free of cost to each bidder who inserts his unit price opposite each item and in an hour or two foots up the money-cost in dollars and cents. This is really all that a contractor should be expected to do (for nothing). The bill of QUANTITIES contains everything the contractor is called upon to perform or furnish, in order to complete his contract. In short, the bid becomes a pro- posal to do a certain fixed quantity of work, no more and no less. This then, briefly, is the main underlying principle of the quantity system: a definite quantity of work for a definite price, and the elimination of every condition which now compels bidders to take chances. The Present Unsatisfactory Conditions. Most architects are familiar with the wasteful, unsatisfactory methods followed to-day. They injure both parties to a contract because of bidders' mistakes in figuring, accuracy being so often sacrificed for speed. While wonderful strides in methods of construc- tion have been made, no attention has been given to standardizing methods of measuring builders' work, and so both owner and contractor suffer. As a result of the movement in aid of better methods (initiated in San Francisco in 1 891) more conservatism, and a closer adherence to business principles are being preferred in place of gambling methods of estimating. Architects or engineers who now permit an unduly low bidder to take a contract are courting trouble every time. Use of the Quantity System in Other Countries. The principle of pay- ment by measurement is based upon equity and square dealing. On large work it is used in England, Ireland, Scotland, France, Germany, Austraha, and South Africa, and to some extent in the United States and Canada. It is a significant fact, that in no instance in which this measurement system has been once established, has it ever been abandoned for the former haphazard methods. Advantages Claimed for the Quantity System. The following are the advantages claimed for the system: (i) An immense saving of time and money now wasted by bidders; all doing the same thing, going over the same ground, and each arriving at a different result. (2) Safer bids, as the work to be performed is clearly written out in the ^ill of quantities, which can be the essence of the contract. • Quantity System of Estimating 1637 (3) No expense to the bidder; the owner pays for the quantities knowingly, The owners pay now, but this fact is not brought to their attention, and it (lots not occur to them. The percentage added to a bidder's net cost is not all profit, a certain portion being absorbed in overhead charges, inchiding cost of estimating, which, of course, is ultimately borne by owners. (4) Saving of disputes arising from ambiguities, oversights, and even errors, .ill ( ausing extra claims more or less just, but usually vexatious, and sometimes embarrassing. (5) Better opportunities for the competent bidder, as the bidders all work up and price from the same basis. (6) Better work and greater harmony. If no part of the work is omitted there is less reason to skin the work, a proceeding which produces friction, or worse. (7) Misunderstandings are reduced. The bill of quantities states clearly what is intended, and is a sort of clearing-house for the drawings and specifica- tions. (8) Neither party can obtain an advantage over the other on quantity or description of work. (9) No disputes with subbidders, it being clearly stated what each trade is to furnish. (10) Contractors have no figuring of quantities to do and can therefore devote more time to buildings in hand and save profits now lost for want of their personal supervision. (11) Fewer inferior contractors as lowest bidders. (12) Fewer extras, which are usually a trouble to all concerned. (13) The architect or engineer has the assistance by collaboration of the professional quantity surveyor, who is available, also, for preliminary figures. This advance-information, now so often furnished by a prospective bidder, creates undesirable obligations. (14) No change or reorganizing of architects' offices is entailed. Much detail-work now involved in receiving bids could be taken care of in the quantity surveyor's office. (15) The drawings and specifications having been previously made as com- plete as possible, subsequent inconvenience to contractors and foremen on the job, and inquiries at the architects' offices for explanations become unneces- sary. The BILL OF QUANTITIES gives detailed information which cannot be well given by drawings. Adaptation to American Practice. In the United States any such uni- versal system must conform to American needs and sentiment, and be a prac- tical system. For many reasons it would be unpractical to follow the English practice. The principles it stands for can, however, be accepted and applied anywhere with great advantage. DIMENSIONS AND DATA USEFUL IN THE PREPARA- TION OF ARCHITECTS' DRAWINGS AND SPECIFICATIONS* Dimensions for Furniture. For the convenience of draughtsmen when designing furniture or providing space for a special article the following dimen- sions are given: f * See, also, the additional tables with more detailed and classified lists, t Many of these dimensions were first contributed to the American Architect of NQ' Vf^ber IP, 1894, by Alvin C. Nye. 1638 Dimensions and Data Parfl a-L IS, t size^ '1 ingB Chuirs ai4d Seats. The average figures taken from a variety of good < are: Height of the seat above the floor, i8 in; depth of the seat, 19 in; the tof*' of the back above the floor, sS in.. Usually the seat increases in depth as it decreases in height, while the back is higher and slopes more. Twenty inches inside is a comfortable depth for a seat of moderate size. Chair-arms are about 9 in above the seat. The slope of the back should not be more than one-fifth the depth of the seat. A lounge is 6 ft long and about 30 in wide. Tables vary in shape and size almost as much as chairs. Writing-tables and dining-tables are made 2 ft 5 in high, and the type of sideboard called a carving- table is made 3 ft high to the principal shelf; but tables for general use are '2 ft 6 in high. Dining-tables are made from 3 ft 6 in to 4 ft wide and to extend from 12 ft to 16 ft by means of slides within the frame. This frame should not be so deep as to interfere with the knees of any one sitting at the table; that is, there must be about 2 ft clear space between it and the floor. The smallest siz^ practicable for the knee-holes of desks and library-tables is 2 ft high by i ft 2 wide, the width to be increased as much as possible. Bedsteads are classed as single, three-quarters, and double. A singli bed is from 3 to 4 ft wide inside; a three-quarter bed, from 4 ft to 4 ft 6 in; a double bed, 5 ft. Bedsteads are from 6 ft 6 in to 6 ft 8 in long inside. Foot- boards are from 2 ft 6 in to 3 ft 6 in and headboards from 5 ft to 6 ft 6 in high. Single beds for dormitories are often made only 2 ft 8 in wide. Bureaus vary in shape and size to such an extent that it is almost impossible to say that any dimension is fixed. Convenient sizes are: body, 3 ft 5 in wid T ft 6 in deep and 2 ft 6 in high; or 4 ft wide, i ft 8 in deep and 3 ft high. Commodes are i ft 6 in square on the top atid 2 ft 6 in high. Chiffoniers ace about 3 ft wide, i ft 8 in deep and 4 ft 4 in high. Cheval-Glasses are made, if large, 6 ft 4 in high and 3 ft 2 in wide. If small, 5 ft high and i ft 8 in wide. If medium, 5 ft 6 in high and 2 ft wide. Wash-Stands of large sizes are 3 ft long, i ft 6 in wide and 2 ft 7 in high. Small sizes are from 2 ft 4 in to 2 ft 8 in long. Wardrobes may be 8 ft high, 2 ft deep and 4 ft 6 in wide; or 6 ft 9 in I ft 5 in deep and 3 ft wide. Sideboards may be from 4 to 6 ft long and from 20 in to 2 ft 2 in deep. Upright Pianos vary from 4 ft 10 in to 5 ft 6 in in length, from 4 to 4 ft ^| in height and are about 2 ft 4 in deep over all. Miniature and Baby-Grand Pianos vary from 5 ft 10 in to 6 ft in length, an3 are about 4 ft 10 in in width. Parlor-Grand Pianos vary from 5H ft to 6 ft 10 in in length, and are about 4 ft 10 in in width. Concert-Grand Pianos are about 8 ft 10 in in length and 5 ft in width. Billiard-Tables (Collender), 4 by 8 ft, 4 ft 2 in by 9 ft and 5 by 10 ft. of room required 13 by 17 ft, 14 by 18 ft and 15 by 20 ft, respectively. Classified Tables * of Furniture-Dimensions. The following more tailed and classified tables of average dimensions of furniture are added to those already given and are taken from recent data furnished by manufacturers of * These additional tables were compiled by E. S. Hand, and much of this data in the several editions of the Pocket-Book has been taken, by permission, from the valuable treatise on Furniture Designing and Draughting, by A. C. Nye, ^^1 i Dimensions of Tables and Chairs 1639 furniture. While some of these measurements vary sHghtly from the dimen- sions given in the preceding paragraphs they represent average dimensions of furniture as made at the present time. Dimensions of Tables Kind of table Bedroom-table . Bedi-oom-table . Bijou-table Carving-table . . Dressing-table . Extension table Extension table Library-table... Library-table . . . Library-table . . . Library-table . . . Tea-table Length Width Height Remarks 30 42 36 66 54 51 42 54 60 13 18 23 30 66 54 41 27 34 36 13 18 17 23 29 30 30 36 30 30 30 30 29 29 29 20 24 29 18 Commode Round Square Oval Round Square Upper shelf Lower shelf All dimensions are in inches. Heights are from the floor. Dimensions of Chairs Kind of chair Bedroom-chair Baby's high chair *.. Check-chair f Chip-chair Chip-chair Dining-chair Dining-chair Dining-chair Dining-chair Easy chair , Easy chair f Hepplewhite chair. . . Parlor-chair I Parlor-chair f Parlor-chair f Parlor-chair § Piano-bench. Reception-chair li . . . Rocking-chair Roundabout chair. . Rubens chair Slipper-chair Height 17 17 18 19 18 17 17 18 16K2 14 18 18 20 17 16 18 Seat-width, Front Back 16 14 29 24 19 19 20 33 27 26K2 23y. 18 18 25 17V2 17 22 17 17 15 28 25 17 193-^ 21 22 H 13 19 20 H 18 17^2 15 Depth, outside 17 13K2 2^y2 17 17% 22 19 18 IS 241 27 K2 17 mi 18 u 26 1/2 19 15 21 18 IS 17 Back Height Slope 34 37 44 39 38 45 43 38'/^ 36 43 41 34^/^ 36 29 37 30 41 29l/i2 40 28 2K2 2 1K2 5 6K2 Arms, height from floor 26K2 21 26 27 25H 25 23 24 2SH * Foot rest 12 in above floor, t Overstuffed. t French cane seat and back. § Wooden arm and back. II Upholstered seat. H Depth mside. All dimensions are in inches. Heights are from the floor. The slope of the back is meas- ured at the seat-lavel to a pe-oendicular through the highest pomt of the back. 1640 Dimensions and Data Part 3 Dimensions of Sofas Kind of sofa Small Extra large . . . Ordinary sofa Lounge Lounge. Height i8 16. IS 17 17 Seat-width Front Back 43 78 54 68 57 40 76 51 Depth, outside Back 36 24 28 29 Height Slope 32 H 29 34 35 23 5^^ 2 1/2 Arms, height from floor 24 25 24 29 34 All dimensions are in inches. Heights are from the floor. The slope of the back is measured at the seat-level to a perpendicular through the highest point of the back. Dimensions of Case-Work Kind of case-work Body Remarks Width Depth Height Bureau 45 51 48 54 60 60 39 36 25 16 84 36 54 20'/^ 23 22 20 33 32 20 20 "16' 32 19 24 37 > 2 36K2 42 42 44 48 51 65 31 30 69 96 Bureau Bureau Bookkeeper's desk Bookkeeper's desk Chiffonier Deck, II in; slope, 22 in Chiffonier Cheval-glass Commode Sideboard Wardrobe Wardrobe All dimensions are in inches. Heights are from the floor. The slope of the back is meas- ured at the seat-level to a perpendicular through the highest point of the back. Dimensions of Bedsteads Kind of bed Inside Heights Height, Width, bottom side rail of side rail Length Width Foot Head Single bed Single bed Double bed Double bed 78 78 78 78 42 42 56 40 41 42 36 62 60 63 67 gy> 9K2 10 10 11 10V2 13 9V2 All dimensions are in inches. Heights are from the floor. Dimensions of Plumbing-Fixtures. Enameled-Iron Bath-Tubs. Standard sizes for roll-rim baths with sloping ends are: nominal lengths, 4 ft, 4V2 ft, 5 ft, SH ft and 6 ft; width over all, from 30 to 34 in. Specially narrow tubs are made from 25 to 29 in wide. The actual length over rim is usually i or 2 in more than the nominal length, and 2 in will include an ordinary overflow-pipe. Dimensions of Plumbing-Fixtures 1641 Wash-Basins. Crockery basins, to go with marble slabs, are made round and oval. Round bowls are made lo, 12, 13, 14 and 16 in in diam, measured from the outside of the rim. Oval bowls, 14 by 17 in, 15 by 19 in and 16 by 21 in. The 12 and 14-in rounds and 15 by 19-in oval, are commonly used. Marble Basin-Slabs may be 20 by 24 in, 20 by 30 in, 22 by 28 in, or 24 by 30 in, the last being a very common size. They can be made any size, to order. They should be iV4 in thick, countersunk on top, and should have molded edges where exposed. Corner-Slabs are commonly made 21 by 21 in and 24 by 24 in. Marble backs are usually 8 or 10 in high, and sometimes 12 in. Enameled-Iron Wash-Basins or Lavatories made in one piece: common sizes are 16 by 20 in, 11 by 14-in basin; 18 by 21-in, 11 by 15 in basin; 18 by 24 in, 12 by 15-in basin; back, 10}'^ in high. The smallest-sized wash-basin is 13 in wide at the back. Corner-Basins, i2y2 by 12I/2 in, 12-in round basin; 15 by 15 in, 11 by 14-in basin; 16 by 16 in, 11 by 14-iiTbasin; 19 by 19 in, 11 by 15-in basin. The stand- ard height of wash-basins is 2 ft 6 in from the floor. Foot-Baths, enameled iron, roll-rim, are 22yz by 19 in; width, including fittings, I ft II in; height 17 in; depth inside, 11 in. Seat-Baths, enameled iron, average about 32 in long over fittings, and 27 in wide. Water-Closets. The dimensions of water-closet bowls vary considerably, the following being about an average: width of bowl over all, 13 in; depth from wah to front of seat, 23 in; height from floor to seat, 17 in; width of seat, from 15 to 16 in. Closets with low-down tanks measure about 28 in from front of seat to wall. The distance from center of outlet-opening to the walls, or the ROi'GHiNG-iN dimensions, are given in manufacturers' catalogues, as they vary with difierent closets. The smaflest space permissible for water-closet compart- ments, where doors open out, is 2 ft 4 in by 4 ft. If the doors open in, the com- partment should be 3 by 5 ft. Closet-Ranges, used in schools and factories, are made 24, 27 and 30 in, center to center of partitions. For graded schools, 24 in is ample, and for factories, 27 in. The range usually occupies a space 28 in in depth, if set against a wall. Urinal-Stalls should be from 24 to 27 in, center to center of partitions; depth of partitions, 20 or 22 in; of ends, 2 ft; of bottom slab, 2 ft; height of partitions, from 4 ft 6 in to 5 ft 6 in. Kitchen-Sinks of cast iron are made in a great variety of sizes, those most commonly used being 16 by 24 in, 18 by 30 in, 18 by 36 in, 20 by 30 in and 20 by 36; 24 by 50 in is the largest size for enameled sinks. Th^ depth inside, for the sizes given, is 6 in. Plain cast-iron sinks are made as large as 32 by 56 in, or 28 by 78 in. Steel sinks are made in all of the above sizes up to 20 by 40 in. Porcelain Sinks. Common sizes of porcelain sinks are 20 by 30 in, 23 by 36 in and 24 by 42 in. Cast-iron Slop-Sinks, common sizes, are 16 by 16 in, 16 by 20 in, 18 by 22 in and 20 by 24 in; 12 in deep. Copper Pantry-Sinks. Common sizes are 12 by 18 in, 14 by 20 in and 16 by 24 in. Laundry-Tubs of slate or soapstone are commonly made 2 ft wide over all, and 16 in deep. Lengths over all, two-part tubs, 4 ft and 4 ft 6 in; three- 1642 Dimensions and Data Part 3 part tubs, 6 ft, 6 ft 6 in and 7 ft. Earthen and porcelain tubs come separately, and are connected as required. The dimensions of each tub are 2 ft or 2 ft 'jy2 in in length, 2 ft iVz in in width and 15 in in depth, inside. The length required for two 2-ft tubs is 4 ft i in; for three tubs, 6 ft 2 in; and for four tubs, 8 ft 3 in. WoltT's roll-rim enameled-iron wash-tubs are 55 in. over all, for two tubs, and 82 in for three tubs. Range-Boilers are 12 in diameter for 30-gal, 14 in for 40-gal, 16 in for 52- gal and 63-gal, 22 in for loo-gal and 120-gal boilers. Dimensions of Carriages. Covered Buggy (Goddard). Length over all, 14 ft; width, 5 ft; height, 7 ft 4 in. Will turn in space from 14 to 20 ft square, according to skill. Coupe. Length over all, 18 ft; width, 6 ft; height, 6 ft 6 in. Buggy (Piano-Box). Length over all, 14 ft; width, 4 ft 10 in. Landau. Length over all, 19 ft 6 in; width, 6 ft 3 in; height, 6 ft 3 in; length of pole, 8 ft o in. Stanhope Gig, Two Wheels. Length over all, 10 ft 6 in; width, 5 ft 8 in; height, 7 ft 6 in. Victoria. Length, without pole, 9 ft 6 in; length of pole, 8 ft; width over all, 5 ft 4 in. Light Brougham. Length, without pole or shaft, 9 to 11 ft; width over all, 5 ft 4 in; height, 6 ft 4 in. Automobiles. Length, from m to 19 (average 16) ft; width, 6 ft; height, 7 ft. Dimensions and Weight of Fire-Engines. From measurements of differ- ent fire-engines belonging to the city .of Boston, it was found that the greatest length, including pole, was 22 ft 6 in. The widths varied from 5 ft to 5 ft 11 in, the average height being 8 ft 8 in. The average weight (computed from 29 engines), 8 000 lb; the greatest weight, 9 420 lb and the least, 4 780 lb. Dimensions and Weight of Hose-Carriages. Extreme length with horse, 19 ft 6 in, without horse, 17 ft 6 in; width, from 5 ft 9 in to 7 ft; height, from 6 ft 8 in to 7 ft; average weight (computed from 11 carriages), 2 943 lb; greatest weight, 3 500; least weighs 2 120. Dimensions and Weight of Ladder- Wagons. Length of truck, 33 ft; total length, with ladders on, 45 ft; width, 6 ft 2 irt; average weight (com- puted from 12 wagons), 6 660 lb; greatest weight, 8 800; least, 4 350. Dimensions of Locomotives and Cars. The dimensions of locomotives and freight-cars vary considerably, but the following will cover those in com- mon use: Locomotives. From 15 ft 4 in to 15 ft 10 in to top of stack from top of rail; extreme width o^ cab, 10 ft 2 in. Doors to admit locomotives should be from 12 to 13 ft wide and 18 ft high. Furniture-Cars are 14 ft i in, from top of track to top of brake-staff; floor, 3 ft 8 in from track; extreme width, 9 ft 10 in. Stock-Cars, 13 ft 5 in, from top of track to top of brake-staff; floor, 4 ft from track; extreme width, 9 ft 8 in. Refrigerator-Cars, 14 ft 6 in, from top of track to top of brake-staff; floor, 4 ft from track; extreme width, 9 ft 7 in. Ordinary Freight-Cars are about 13 ft high to top of brake-staff and 9 ft 4 in in extreme width. The height of floor of freight-cars varies from 3 ft 8 in to 4 ft above top of track for standard-gauge, and from 3 ft to 3 ft 6 in for nar- row-gauge cars. Standard-gauge, 5 ft S^ in. Dimensions of Bowling-Alleys 1643 Passenger-Coaches vary from 14 to 16 ft in height and from 10 to 11 ft in width. Doors to admit cars should give at least 12 in clearance on each side, and 2 ft overhead. Street Trolley-Cars are about 8 ft 6 in wide for the car proper, and the steps project about 8 in. Height from track to top of coach, 11 ft 6 in; the trolley- stand is 18 in higlier. The length varies, up to 42 ft. Trucks for a 41 ft 6 in car are about 24 ft apart. Wheel-bases, 4 ft center to center. Radius of short- est curve in Denver, Colo., 35 ft to midway between rails. The gauge of a rail- road track is the distance between the inner sides of the heads of tine two rails. The standard or broau gauge is 4 ft 8^2 in; standard narrow gauge, 3 it 3]^^ in. Capacity of Freight-Cars. Car-Loads. The capacity of freight-cars, and the minimum car-loads, vary so greatly that no accurate general information can be given. For heavy freight, 25 tons is an average load; for light freight, from 12 to 15 tons; for household goods, 10 tons is about the minimum; for lime, 15 tons is about a minimum load; for cement, 20 tons. The minimum car-load, to obtain car-load rates, varies with different roads, and also with the rate made; a low rate is usually made on the basis of a big load. Thirty tons is a good load for heavy freight, and 40 tons is about the maximum,* except for special cars. Miscellaneous Dimensions. Horse-Stalls. Width, from 3 ft 10 in to 4 ft or else 5 ft or over; length, 9 ft. The width should never be between 4 ft and 5 ft. as a horse is liable to cast himself. Dimensions of Standard Bowling-Alleys.* For one pair of alleys: Room necessary, 83 ft over all; li ft 6 in wide, 60 ft from foul-line to head pin, 3 ft for pins to back of alley, 4 ft for pin-pit,. 8 in deep in front, 6 in in back; alleys^ of maple flooring, should extend on and beyond the foul-line 12 ft, and then 4 ft more, making a i6-ft approach to the foul-line for the player to run to deliver the ball. For one alley: Same length, 8s ft; width, 6 ft 3H in; closer dimen- sions; beds 42 in, gutters 9 in, division-pieces 2% in, ball-return 9% in. In In One alley: Ball-return 9% One pair of alleys: Ball-return 9% First-division piece 2% First-division piece 2% Gutter . ." 9 Gutter 9 Bed 42 Bed 42 Gutter 9 Gutter 9 Second-division piece 2% Second-division piece 2% 6 ft sVi in *= 7SH 6 ft 3H in = 7SH To the 75 H in of the pair of alleys, should be added Gutter 9 Bed 42 Gutter 9 Third-division piece 2% 138 Additional room should be provided for the bowlers and spectators as these dimensions are for the alleys only. Dimensions of Drawings for Patents (United States). 10 by 15 in, with border-line i in inside all around. * Dimensions furnished by The Brunswick-Balke-Collender Company, New York City. 1644 Dimensions and Data Part 3 Dimensions of a Barrel. Diameter of head, 17 in; diameter at bung, 19 in; length, 28 in; volume, 7 680 cu in. Miscellaneous Memoranda. Weight of Men and Women. The average weight per person of twenty thousand men and women weighed at Boston, Mass., in 1864, was, men, 141^^2 lb; women, 1 24)^2 lb. Wooden Flagpoles. For a flagpole, extending from 30 to 60 ft above the roof, the following proportions give satisfactory results: The diameter at the roof should be lio .the height above the roof, and the top diameter one-half the lower. To profile the pole, divide the height into quarters; make the diameter at the first quarter above the roof, fifteen-sixteenths of the lower diameter; at the second quarter, seven-eighths, and at the third quarter, three-quarters the lower diameter.* Steel Flagpoles, t The Department of Education, City of New York, has abandoned the use of wooden flagpoles and is using steel flagpoles. For an ordinary building, 60 ft in height above the curb, a pole 4SV2 ft in height is used, which is sufficient for the tackle of a large or post-flag, for the reason that roof- parapets are very low. Each pole is required to be fitted complete with a cast- iron, galvanized, revolving truck, mounted on crucible-steel pins, the cap be- neath it, also, being of galvanized iron. The truck is fitted with two 4^4-in bronze sheaves on Tobin-bronze pins, surmounted with an 8-in 20-oz copper ball, acid-cleaned and painted with four coats of the best English weather-proof sizing, and covered with XXXX leaf-gold. One or more field-joints are per- mitted in the length of the pole, which are determined according to standard details, the bands being secured to the male tube, and both edges of the inner band and the shoe being machine-beveled to insure a perfect fit. The female tube is drilled and secured to the male shoe with tap-screws of sufl5cient strength to carry the upper section of the pole, and the ends of the screws are upset. The exposed ends of the female tube are chamfered and caulked tight. A steel collar or band, to receive the copper flashing, is secured to the pole and braced just above the roof-lines. Dimensions of Schoolrooms, Boston Schools. t The sizes of the rooms in the Boston school-houses, as adopted by the school board, are, for grammar- schools, 28 by 32 ft in plan by 13 ft 6 in in height; for primary schools, 24 by 32 by 12 ft. This accommodates 56 scholars per room, in each grade, allowing 216 cu ft per scholar in the grammar schools, and 165 cu ft in the primary grade. A width of 27 ft is very satisfactory for schoolrooms, and is commonly adopted because it permits of the use of 28-ft joists, without waste. Heights of Blackboards in Schoolrooms. | The heights from floor to top of chalk-rail should be about as follows: For third and fourth grades, chalk-rail 2 ft i in from floor For fifth grade, chalk-rail 2 ft 2H in from floor For sixth grade, chalk-rail 2 ft 4 in from floor For seventh and eighth grades, chalk-rail 2 ft 6 in from floor Slate blackboards are made 3 ft 6 in, 4 ft and 4 ft 6 in high, 4 ft being a very common and satisfactory height. * The Building Trades Pocketbook. t From data compiled by E. S. Hand from notes furnished by C. B. J. Snyder, Super- intendent of School Buildings, New York City. X F. E. Kidder, in previous editions. Dimensions of School-Furniture 1645 Sizes of Seats and Desks for Schools and Academies * Space occupied Nuniber of Age of scholar Height of seat Height of desk by desk and desk or chair (next scholar) seat (back to back) years in in ft in i6 to i8 i6% 29^/i 2 9 I 14 to i6 I5H 28 2 9 2 12 to 14 15 K2 27K2 2 8 3 10 to 12 i4'/i 26V^2 2 7 4 8 to 10 iM 25H 2 5 5 7 to 8 121/4 24 2 4 6 6 to 7 ii'/i 22V2 2 3 7 5 to 6 101/2 21 2 2 4 to 5 ■ 9K2 19 2 Desks for two scholars are 3 ft 10 in long, and for a single scholar, 2 ft long. Aisles are from 2 ft to 2 ft 4 in wide, according to age of scholars and size of room. Additional Dataj on School-Houses Sizes of Rooms. The Department of Education, New York City, has adopted, for the dimensions of the schoolrooms, the German standard of 22 by 30 ft in plan by 14 ft in height, with unilateral lighting. These dimensions are used for all grades of elementary schools, the sittings being on the basis of 15 sq ft of floor-space per pupil. Good light cannot be had on desks which are placed at a greater distance from the windows than one and one-half times the height of the top of the upper sash from the floor. Sizes of Seats and Desks for Elementary and High Schools Space § occupied Nunil^er of desk Age of scholar Height X of seat or chair Height X of desk by desk and seat (back to back) years in in in f 16 to 18 17 31 32 I 14 to 16 16 30 32 2 12 to 14 IS 28 31 3 ID to 12 14 26 30 4 8 to ID 13 24 29}-^ 5 7 to 8 12 23 27 6 6 to 7 II 22 27 7 5 to 6 10 20 H 26 Blackboards. For first and second-year scholars the chalk-rail is placed 2 ft from the floor, and the boards are 4 ft high. This allows the smaller children * F. E. Kidder, in previous editions. t From cLata compiled by E. S. Hand from notes furnished by C. B. J. Snyder, Super- intendent of School Buildings, New York City. X Heights are measured as follows: From the floor to the top of ink-well strips of desks, and from floor to top of front edge of seats, and should not vary more than H »n from the heights given in this table. Aisles have a minimum width of 18 in for the lower grades and 22 in for the upper grades. § If chairs are used, this distance must be increased from lYz to 2 in. Dimensions and Data Part 3 a nP* v!M VTf mm V* v^ v^N NJ14 s0t-<:?iOO(N'*I^Mo>o>a>a>o i X"*" vP> x* spO X"*" ^ ^P» NpO x* spO X* ^f ^P» Nf^ ,-x ^x ccN loN ^x i~x ,-iX r-x eox pjv r-Js r-fv —n ^x ^OOiOfOt^oOOMMPO-tOOOMNOirOO-^M .r*t>»t^r-t^oooooooooooo 0\ o o i M N Nf^ v^ xc^ MN o fOo o i S» x* NpO sfl vpO NTf spO I0l/^10<0'O^OVOVOVO»0 -l^t^t^OOOO O^CJiO ocvjiot^OMOi-irO'*iovooooMvoM'cs io»oioioioioo v-f ^fl -— C s!« x-t nQO vfi^ sJO x* ~^90 V7^ vf^l Nf^ spi ^X ^X roX ^X rtX C^ rJS inN PJN hX _X ^\ _X r-X oio>oio»/^"00 nP» Vpl ,JS r-.X CON «0X —X t-N i-X r-iX CON COX ,-N ,-*k ^X ^X vor^oooiMHOOMfsNfO^io'OO^MC^Ttt^i/^o (N o«oo t^-i^oo a>o o (N 'i-.000>0>0^0 O O M M O O M r0rfo' N^ vpo X* NPO v*« N^ s^ NpO X"* ^f« ^P* ^P» ^ — ix c«?x .-ix .-hX co\ •- .S VO t- W ro ** ^ ic 0^0 cor^o M 1000 o0 M CN rooo O ^ „ ^ „„„„„„„„ ^^ ^^ ^^ ^^ ^^ ^_,| VO '0 VO "S (N ro ro ^ ^ N-M sfO s^ \0O N-r NPO ^ ^ nM v^ t^ "o Th '^ T-^ "o" Ih '^ 00 "w 00 a» oi '0 M M M ..MMM^^^^„^„„„„„„„. _,..., .., OMrt-t^OMTl-a>rOrOMH M, 1000 M i>.«o tO"<*ro(N 000 M rOfOroroPO-rf'^t'sJ-intoto r^oo ct>0 roi/- NPO X1< VS» sri N30 N"«< vW v^. .?^ SPJ vTl lON >-lN KS rJN r-iN CON fJN >-(V r-iN ^N .-K rOiOOO M -^vo 0^0 too a>t-vO ■^POCJivO ->!tiOiO o^ n90 \-f NDO nTI n?0 \f v(0 -,-t VTI s-N x!N CON CON rJN ,-K lOv —N ox coN -.N -JN ^N MfOiOooOOroioooOiOfOOOt^«Ol^ a> tOoo'o'oro'io'r^'aio'^CkO fOO 0>t0'0 O0OMMMMMPI«NN c^x ^N LON CON t-N ,-JV t-JN tJx rJx MHcoioi>a>MMTfoooa>»o '^OOO 0%0 00 MM (N (NfO-^rtt^OO srf Np» yjjl t^ f- 00 00 NPO v-* N» ^■?l N» Nf xpO "^"^ ^ ^ "^ ooooa^o%o»o»o^c^oooMMdPO po*o t>. J .-is, ^N CON ^O VO vo « t^i>i>r-t^«>«>t^ooooooa>cr.o m ro-^ 1648 Dimensions and Data Part 3 to use the lower portion. The upper part of the surface is at a height convenient for the use of the teacher, there being much display-work employed in the lower grades. For scholars in grades from the third to the eighth year, inclusive, and for high schools the chalk-rail is placed 2y2 ft from the floor and the boards are 3 ft 6 in in height. Doors and Stairways. Wardrobes should be entered from the classrooms only. Classroom-doors should open into the rooms, so as to afford the teacher control in case of panic. All exit-doors should open out. All stairways should be shut off from corridors by means of self-closing doors, which, together with the stairways and the enclosures, should be of lire-proof materials. Stairways should be of sufficient number to permit of the building being vacated within three minutes from the time a signal is given. This can be effected by allowing a lineir width of 4 ft for the first 50 persons and 12 in additional for each 100 persons in excess thereof. No stairway is to be less than 4 ft nor more than 5 ft in width. Exits should be planned so as to provide 15 lin ft for the first 500 persons and 6 in additional for each 100 persons in excess thereof. No stairway should have more than 15 steps in any one flight, changes in direction being effected by a square platform and no winders being used. No stair-door or exit-door should open out over a step. Platforms are to be provided for such doors and are to extend at least i ft beyond the edge of the door when standing ©pen. Stairs,* The rise of a stair is the height from the top of one step to the top of the next. The total rise is the height from floor to floor. The run is the horizontal distance from the face of one riser to the face of the next. Risers are the upright boards or other materials forming the faces of the steps, and the treads are the horizontal pieces or surfaces on which the feet tread. Treads are usually from \M to 1^4 in wider than the run, on account of the NOSING. The height of an individual riser or the rise of any stairs is found by dividing the total rise by the number of risers. The run of the stairs may be flxed at will unless the space is cramped, but to secure a comfortable stair the run must bear a certain relation to the rise. Rules for Dimensions of Treads and Risers. For ordinary use a rise of from 7 to 7'/2 in makes a very comfortable flight of stairs. For schools and for stairs used by children the rise should not exceed 6 in. Stairs having a rise greater than 7^/4 in are steep. The width of the run should be determined by the height of the rise; the less the rise the greater should be the run, and vice- versa. Several rules have been given for proportioning the run to the rise: (i) The sum of the rise and run should be equal to from 17 to \^y1 in. (2) The sum of two risers and a tread should not be less than 24 nor more than 25 in. (3) The product of the rise and run should not be less than 70 nor more than 75. These rules apply only to stairs with nosings. Stone stairs without nosings should have at least 12-in treads for adults. (See Tables, pages 1646-7.) Height of Hand-Rail. In dwellings, hotels, apartments, etc., the height of the rail should be about 2 ft 6 in above the tread, on a line with the face of the riser. For grand staircases the height may be reduced to 2 ft 4 in. On steep stairs the height should be from 2 ft 7 in to 2 ft 9 in. The rail should also be raised over winders. On landings, the height of the rail should be equal to the height of the stair-rail, measured at the center of the tread, the usual height in residences being from 2 ft 8 in to 2 ft 10 in. * This subject is quite fully treated in Building Construction and Superintendence, Part II, Carpenters' Work, by F. E. Kidder. Sash- Cords 1649 Sash-Cords.* Until a few years ago, linen or cotton cord only was used for connecting weights with the sashes of double-hung windows, and cord is still more extensively used than either riblx)ns or chains. For windows of ordinary size a good brand of cord will wear for a long time, and this material will prob- ably never be entirely displaced by metal. "Tests made at the Massachusetts Institute of Technology show that cords wear much longer than chains, though they have less tensile strength. Cords should be smooth and round, so that each strand bears its part of the stress, and well glazed, so that they have a smooth surface aiid consequently less wear from friction with the wheel of the pulley." It has been found that cord can be braided too hard for durability, yet if it is braided so as to be very flexible it may be so soft that it will stretch and cause great annoyance by permitting the weight to hit the bottom of the weight-box. The architect, however, shjuld always specify the particular brand and size of cord to be used, and also the diameter of the pulley. Among the leading brands of sash-cord at present are the Samson Spot,! and the Silver Lake A. J These brands are superior to the ordinary braided cords, which are made from inferior yarns to meet the jobbers' requirements for price. In addition to other most excellent qualities, the Samson cord offers an additional advantage that architects will appreciate; it has a colored strand woven through it, which shows in spots on the surface and thus enables one to tell at a glance that no other cord has been substituted. The Silver Lake A sash-cord has the name Silver Lake A branded on every foot of cord; but unless the letter A accompanies the name a second grade of cord is denoted. The marking of the cord by color, or any other device, does not alter the quality of the cord. Special marks may be applied to inferior cords as well as to the best. The following numbers should be specihed for the different weights of sash- weights: Relative Sizes of Sash-Cords, Weights and Piilleys Size-number Diameter in inches. . . . Feet per pound Suitable for weights in pounds up to Minimum diameter in inches of pulley allowable . . 6 7 8 9 10 12 3/i6 li2 H %2 Me H 66 55 44 36 27 20 5 12 20 30 40 50 iH 1% 2 2H 2^/^ 3 For hanging* sashes weighing over 40 lb, only the largest size of Samson c Silver Lake A cord, or some form of sash-chain or sash-ribbon, should be used, and the pulleys should be selected to fit the cord or chain. A guarantee that the cord will last at least twenty years may be had from either of the manufacturers mentioned above. The Samson wire-center sash-cord has recently been put on the market. This is really a metal sash-cord protected by a braided-cotton sur- face which acts as a noiseless cushion. It is claimed that it harmonizes with the window-finish and that it has greater durability than other sash-cords or metal devices. (See record of tests made at Massachusetts Institute of Technology, page 165 1.) The standard color is that of dark mahogany, but this cord is made to order for large buildings in other colors to match the finish. * The following notes, relating to Sash-Cords, Sash-Chains, Sash-Ribbons, Sash- Weights and Sash-Balances, are condensed and revised from articles by Professor Thomas Nolan, in Kidder's Building Construction and Superintendence, Part II, Carpenters' Work. t Manufactured by the Samson Cordage Works, Boston, Mass. I Manufactured by the Silver Lake Company, Boston, Mass. 1650 Dimensions and Data Part 3 Sash- Chains. Of several styles of sash-chains on the market, the style most largely used is the flat-link chain.* This chain is made either of steel, or of bronze composed of 95% copper and 5% of tin. For suspending very heavy sashes, doors and gates, a cable-chain has been extensively used. Star f sash-chain is made of bronze-metal. The manufacturers of the Norris sash-pulley claim that a riveted chain that has joints only one way is almost sure to break when even slightly twisted, and that it is better to use two chains of the link-pattern run- ning side by side over the same pulley. The strongest sash-chains are of steel, made rust-proof by the hot-galvanizing process, and electro-copperplated to give a bronze finish; and of a bronze-mixture which looks like copper, but is tougher and harder. One firm J claims that its galvanized-steel sash-chain is from II to 45% stronger than any bronze or copper sash-chain and that it will resist fire for a much longer period. The tensile strength of their chain varies from 475 to 850 lb, according to the weight used. Sash-Ribbons. These are now also extensively used in hanging the sashes of the better class of buildings. The ribbons are made of steel and aluminum- bronze or of some mixture of aluminum, and in %, Yz, ^^, ^4 and %-m. widths. They are claimed to be practically indestructible, but according to one series of tests it would appear that in some cases they do not wear as long as sash-cords or sash-chains. Some people object that the ribbons snap against the pulley- stiles, when the sash is raised or lowered, and thus make considerable noise. The %-m ribbon may be used for a sash weighing up to 100 lb and requiring 50-lb weights. For a window 6 ft 10 in high and 3 ft wide, glazed with plate glass, the ribbons with attachments cost about 75 cts. Sash-ribbons are now manu- factured by a number of firms who also make the necessary attachments for weight and sash. For the best working of windows hung with ribbons, pulleys «f the following sizes should be used: For sashes weighing not over 40 lb, 2 in For sashes weighing not over 60 lb, 2]i in For sashes weighing not over 100 lb, 2y> in For sashes weighing not over 150 lb, 3 in For sashes weighing not over 250 lb, zVi in For sashes weighing not over 300 lb, 4 in For sashes weighing not over 350 lb, ^Yi in Comparative Strength of Sash-Cords and Chains. The comparative strength and durability of sash-cords and chains have been determined by careful tests, but there is a great variation in both cases, due partly to variation in mate- rial, but principally to the relative sizes of the chain and pulley or cord and pulley. The cords or chains may be too light for the weights used, or the pulleys too small in diameter to carry the cord without undue bending. The pulleys may also have too narrow a groove or an uneven groove with sharp edges which cut the cords. The larger the diameter of the pulley, the longer the wear. Tests § on Wire-Center Sash-Cord and Bronze Sash-Chains. The cord tested was size No. 8, Y\-m diam, Samson solid braided cotton cord with steel- * One type of this kind of sash-chain is manufactured by the Bridgeport Chain Com- pany, Bridgeport, Conn. , t Manufactured by the U. T. Hungerford Brass & Copper Company, New York City. X The Oneida Community, Ltd., Oneida, N. Y. § Made at the Massachusetts Institute of Technology, May, 1914, by Professor E. F. Miller. Sash-Cords, Chains and Weights 1651 wire cable center, He in in diam. The chains tested were of two different makes of bronze, size No. 2, purchased in the open market as typical bronze sash-chains, each recommended by a reputable dealer as the proper chain, for use with a 25-lb window-weight. The tests for the better of the two chains are those given. Durability-tests were made by raising and lowering a 25-lb weight over a 2-in pulley, each movement corresponding to once opening and shutting a window. The cord was tested over the regular round grooved pulley ordinarily used for cords, and the chains were tested over the combina- tion grooved pulley usually furnished for sash-chains. For the fire-tests the cords or chains were hung through an asbestos box in which a Buflsen flame under pressure was applied to all alike, the temperature being about 2 200° F. A 25-lb weight was attached in each case to keep the cord or chain under the same tension. The wire-center cord took about twice as long to burn through and wore about seventeen times as long as the bronze chain. Tests on Wire-Center Sash-Cord and Bronze Sash-Chain Durability-tests Fire-tests Number of lifts before breaking Length of time before parting Bronze chain Samson wire- center cord Bronze chain, sec Samson wire- center cord, sec 34 944 37486 37381 32948 40 356 31 234 40 790 27874 Average 35 377 6S9 892 592 559 632 230 594 114 631 286 577 154 504 032 637 796 Average 603 633 42.5 40 39 32 78.S 75.5 77 75 Average 38.4 Average 76.5 Weights of Sashes and Glass. In figuring the weights of windows, the weight of the glass may be taken at 3V2 lb per sq ft for plate glass, iH lb for double-strength glass and i lb for single-strength glass. For the weight of the wooden sash, add together the height and width, in feet, of each sash, and mul- tiply by 2.1 for 2H-in sash, by 1% for iM-in sash and by i}i for i^6-in sash. These values are sufficiently accurate for determining the size of sash-cords and pulleys, but the weights should be determined by weighing each sash after it is glazed, as the weight of the glass varies considerably. Iron Sash-Weights. The weights ordinarily used for balancing windows are made of cast iron, in the form of solid cylinders from 1% to 2% in in diameter, and from 7 1'^ to 31 in long, with an eye cast in the upper end of each. The lengths vary with the weights, which are from 2 to 25 lb. Flat weights, which usually are calbd for in the Philadelphia and some other markets, are from 6 to 34^/^ in long, from 2 to 30 lb in weight, and from iH by 1% to iH by 2% in in cross- section. In ordering sash-weights the number of pounds of each weight, and the sections and lengths of the boxes in which the weights will work, should be given. Ordinary weights have very rough eyes for the sash-cords. There are a few manufacturers in the East who make weights with a patent eye that will 1652 Dimensions and Data Part 3 not cut the cord. A sectional sash-weight* made with a well-designed hooking- device which has given satisfaction, is said to be one of the best on the market. Usually from three to six sections are required on each side to balance a sash properly. If the hooking-device fails near the top the upper sash cannot be closed and if at the bottom the window cannot be opened. It is then necessary to open the weight-box and rehang the sections before the window can be oper- ated. In theory, sectional weights are ideal; in practice, however, they are not considered as satisfactory as solid weights. The Brown f sectional weights are made 2^ by 2>H in and in weights of 6, 7, 8, 9 and 10 lb. They are made of both cast-iron and lead. It frequently occurs after a contract is let, that the glass is changed from double-thick to plate or prism glass. This means increased weight; but the length of the sash-weight cannot be increased and it, therefore, becomes necessary to increase the area of its cross-section. If the weight-box is detailed to take the regular round sash-weight, its general construction will be such that it will take a 2-in round sash-weight, but not a 2-in square sash- weight. This difficulty can be avoided by a little thought at the start. An added depth of K in in the weight-box permits the use of a rqptangular cast-iron sash- weight. The Sanborn sectional sash- weight i is intended for use in large buildings of heavy construction. Because of the lack of uniformity in the weight of plate glass the required weights of sash-weights cannot be accurately determined previous to the hanging of the sashes. By the use of a sectional sash-weight, combinations of units can be made up to suit the requirements. The units are made square or rectangular in section in order to secure a max- imum weight with a minimum length. An opening of 12 in in the side of the pocket is sufficient for hanging the largest unit. These units are manufactured in standard sizes to meet the general conditions found in the building trades. Lead Sash-Weights. It often happens that for wide and low windows the weights if of iron would be so long that they would touch the bottom of the pocket before the bottom sash was fully raised. Iri such cases lead weights are usually resorted to, lead being 80% heavier than cast iron. By casting the weights square in section, whether of iron or lead, a considerable saving can be made in the lengths. One sash-weight manufacturer! makes a specialty of compressed-lead sash-weights, with wrought and malleable-iron fastenings, centered so that the weights hang perfectly plumb; and when lead weights are necessary the architect will do well to specify the weights made by this com- pany. These weights are made under hydrauHc pressure, by which greater smoothness, solidity and density of metal is secured than is possible by the casting-process. A wrought-iron rod is run through the center, to which are securely attached the malleable-iron fittings. In hanging the sashes the weights for the upper sash should be about y2 lb heavier than the sash, and for the lower sash, y2 lb lighter. Sash-Balances. Within a comparatively few years several devices have been patented for balancing sashes by means of springs instead of weights, but the author believes that only one type, known as the sash-balance, has proved a practical success. The sash-balance consists of a drum on which the ribbon is wound, and which contains a coiled-steel clock-spring, immersed in oil; the spring sustains the weight of the sash. The common type very much resembles in outward appearance the ordinary sash-pulley, and is applied in practically the same way; the ribbons, which are made usually of aluminum-bronze, are * Manufactured by E. E. Brown & Company, Philadelphia, Pa. t Manufactured by E. E. Brown & Company, Philadelphia, Pa. t Manufactured by the Lidgerwood Manufacturing Company, New York City. § Raymond Lead Company, Chicago, III. Seating-Space in Churches and Theaters" 1653 attached to the sashes in the same manner as cords when weights are used. While the sash-balance in its best form works very satisfactorily, it will probably never entirely supplant the weight and axle-pulley for ordinary windows. There are many windows, however, for which sufficient pocket-room for weights cannot be obtained without spoiling the effect desired or narrowing the glass, as in some bay windows, or where it is undesirable to break the frame into the brick jamb. In such cases the sash-balance is almost invaluable. For hanging the glass doors of show-cases, sash-balances are usually preferable to weights. Sash- balances are made in both side and top-patterns, but the former are recommended wherever there is room at the side of the frame for the depth of mortise required. For windows of the sizes usually found in residences, the depth of the sash- balance measured from the face of the pulley-stile will vary from 3 to 4 in; this can be provided for usually by cutting a hole, if necessary, in the masonry or studding back of the frame. As sash-balances require only a plank frame, the consequent reduction in the cost of the frame offsets the extra cost of the balance. In remodeling old buildings which have plank frames without weights, sash- balances are found to be a great convenience, since they can easily be in- serted in the old frames. An advantage which all spring-balances possess is that they act most strongly when the sash is down, and so enable one to raise a binding window more readily than if it were hung with weights; while when the sash is up the springs barely suffice to hold it in position, and do not offer resistance to drawing it down. Of the various sash-balances on the market, the Pullman* and the Caldwell f are the most extensively used, and are undoubtedly reliable. The Pullman Unit sash-balance has been on the market many years and has proved satisfactory. These balances are now made with uniform-size face-plates for the various weights of sash with which they are to be used, -and thus make it possible to have all mortises for the balances cut at the mill, as is now done for the regular cord-pulleys. The Caldwell sash-balance, both top and side-types, is much used by the United States Post Office and Navy Depart- ments. It is used also by the leading car-builders. The springs are made of high-grade cold-rolled tempered-steel wire, a material similar to that used for clock-springs. The manufacturers guarantee these sash-balances for from ten to fifteen years. Seating-Space in Churches and Theaters. The minimum spacing for pews, back to back, is 30 in. This spacing is fairly comfortable for occupants, but is a little cramped for persons passing by others into or out of the pews. A spacing of 32 in is to be preferred, and if there is abundance of room, the spac- ing may be made ss ii^- Anything over 33 in is a waste of room. A space of 18 in in the length of the pew is considered a sitting. t Opera or Theater-Chairs are made 19, 20, 21 and 22 in wide, center to center of arms, and in arranging them in rows where the aisles converge, the ends are brought to a line on the aisles by using a few chairs that are either narrower or wider than the standard width. For churches, a standard width of 20 in is the least that is desirable. For theaters, 21 or 22-in chairs are commonly used in the parquet, 20 or 21-in in the dress-circle, and 20 and 19-in in balcony and gallery, although there is no accepted rule in this respect. On account of the seat-lifting, opera or theater-chairs may be comfortably spaced 31 in, back to back, and this is the usual spacing in halls and churches. In theaters the chairs are usually set on steps. In the upper gallery these steps should not be more than 30 in wide; in the balcony they are usually made either 30 or 31 in * Manufactured by the Pullman Manufacturing Company, Rochester, N. Y. t Manufactured by the Caldwell Manufacturing Company, Rochester, N. Y. X For dimensions of pew-bodies see page 48 of Churches and Chapels, by F, E. Kidder, 1654 Dimensions and Data Part 3 wide, and in the parquet, 31 or 32 in wide. As a rule the higher- priced scats arc more commodious than the lower-priced. Estimating Sealing Capacity. The actual seating capacity of theaters and audience-rooms can be determined only by drawing the seats to an accurate scale, on the floor-plan, and then counting the number of chairs, or measuring the linear feet of pews. Approximate Seating Capacity. For approximate purposes the seating capac- ity or required size of room may be determined by allowing from 7 to 8 sq ft to each seat, or sitting, when on a curve, and from 6 to 7 sq ft to each sitting when in straight rows, the smaller number being used only for large rooms. This allows for aisles and pulpit-platform. For small concert-halls and narrow rectangular rooms, 6 sq ft per sitting will usually be sufficient allowance, pro- vided only that the actual floor-space utilized for seats and aisles is considered. Seating Capacity of Several of the Older Cathedrals, Churches, Theaters and Opera-Houses * European Cathedrals and Churches Estimating that one person occupies an area of 19.7 inches square f St. Peter's, Rome Milan Cathedral St. Paul's, Rome St. Paul's, London St. Petronio's, Bologna Florence Cathedral Antwerp Cathedral St. Sophia's, Constantinople, St. John Lateran, Rome. . . . 54 000 37 000 32 000 25 600 24 400 24300 24 000 23 000 22 900 Notre Dame, Paris Pisa Cathedral St. Stephen's, Vienna St. Dominic's, Bologna St. Peter's, Bologna Cathedral of Sienna St. Mark's, Venice Spurgeon's Tabernacle, London 21 000 13 000 12 400 12 000 II 400 II 000 7 000 7 000 European Theaters and Opera-Houses Carlo Felice, Genoa Opera-House, Munich Alexander, St. Petersburg. . San Carlo, Naples Imperial, St. Petersburg — La Scala, Milan Academy of Paris 2560 2370 2332 2240 2 160 2 113 2092 Drury Lane, London Covent Garden, London. Opera House, Berlin Adelphi, London Lancaster, London Globe, London 1948 3000 1636 2300 I 850 I 100 Some Early American Theaters and Opera-Houses, outside of New York The Auditorium, Chicago. .^ Academy of Music, Phila- delphia Boston Theater, Boston 3124 3000 Castle Square Theater, Boston Gaiety Theater, Boston. . . j Grand Opera-House, Cin- I 600 to I 800 nearly 3000 I 736 * The table following this one gives the seating capacities of theaters in use in 1914 in some of the boroughs of New York City. The above table of seating capacities of some of the earlier churches and theaters is retained for purposes of comparison. So many important structures of these types have been erected in. recent years in the larger cities of the world, or are now in process of erection, that it has been found impossible to make any list that would be and would remain, for any length of time, complete. t See note on page 1655. Seating Capacity of New York Theaters Seating Capacity of New York Theaters (1914) 1655 Boroughs of Manhattan and the Bronx Name Academy of Music Alhambra American American, Roof Astor Belasco Berkley Lyceum Bijou Broadway Bronx Carnegie Hall Carnegie Lyceum Casino Century Century, Roof Circle City Clinton Street (Odeon) . . . George M. Cohan Colonial Columbia Comedy • Criterion '. . Daly's Delancy Street Foxes (Dewey) 86th Street Eltinge Empire Family Fifth Avenue (Proctor's) . 14th Street 48th Street (Brady's) Fulton Seating capacity 2653 1389 1683 I 134 I 137 984 416 814 1 776 1764 2 632 640 1465 2 078 I 150 1 684 2 289 904 I 072 I 541 131S 696 916 1074 I 242 I 310 1436 89s I 099 687 I 204 I 255 969 662 Name Gaiety Garden Garrick Globe Gotham Grand Grand Opera-HoUse Greeley Square (Loew's) Harlem Casino Harlem Opera-House Harris Herald Square Hippodrome Hudson Hurtigand Seamon's (Music- Hall) Illington Irving Place Keith's Union Square Kessler's 2nd Avenue Kessler's 2nd Avenue, Roof. Knickerbocker Lafayette Liberty Lincoln Square Lipzin Little Longacre Loew's Fifth Avenue Loew's 7th Avenue Loew's National Lyceum Lyric* Madi son Square Garden . . . . Seating capacity I 090 844 I 194 I 626 1888 2093 1393 847 I 160 4588 1077 1093 * 1079 I 080 1803 734 I 351 I 042 I 2H 1547 I 030 299 « 964 I 626 2333 957 I 452 3366 * Data not furnished. Note Regarding Unit Area for Seating Capacity. The unit area given in the table on page 1654 appears in the former editions of this book and seems to be too small. The original authority for the data cannot be determmed. A more reasonable minimum area would be about 23^2 inches square, or about 18 by 30 iji, or 540 sq in, or about 3.8 sq ft. Editor. 1656 Dimensions and Data Seating Capacity of New York Theaters (1914) (Continued) Boroughs of Manhattan and the Bronx Name Madison Sq Garden, Roof.. Manhattan Opera-House Maxine Elliott Metropolis Metropolitan Opera-House. . McKinley Square Miner's Bowery , Miner's Bronx (Acme) Miner's 8th Avenue Minsky Moulin Rouge Murray Hill Mount Morris Nemo New Amsterdam New Amsterdam, Roof. . . . New York Theater, Roof. . Olympic ii6th Street Odeon 145th Street Park People's Philipps Plaza Playhouse Seating capacity 700 3200 904 I ISO 330s I 500 I 168 1798 I 178 1866 I 61S I 224 * 941 I 618 610 1337 745 I 743 904 I 513 1693 * 1544 879 Name Proctor's 23rd Street Proctor's 58th Street Proctor's 125th Street Prospect Republic Richmond Riverside Savoy Star St. Nicholas Thalia Third Avenue (Keeney's) . . . 39th Street Tremont Victoria. Victoria, Roof Wadsworth Wallack's Washington Weber's West End Weber and Field Music-Hall Winter Garden Yorkville Seating capacity ■ Data not furnished. Borough of Brooklyn Academy of Music . . . Amphion Bijou Broadway Bushwick Casino Columbia Comedy Crescent DeKalb Empire Fifth Avenue Folly Fulton Gayety Gotham Grand Opera-House. Greenpoint 2 200 I 589 I 562 I 969 •2228 ISO3 1673 I 123 I 610 2232 I 740 I 063 I 840 1492 1455 958 I 515 I 776 Jones Liberty Linden Lyceum Lyric Majestic Myrtle New Montauk. Novelty Olympic Orpheum Oxford Payton's Prospect Hall . . Royal Shubert's Star Dimensions of Theaters and Opera-Houses 1657 Dimensions of Some Theaters and Opera-Houses ** The following are the dimensions, in feet, of some of the earlier theaters in this country and in Europe. Name and location Auditorium Proscenium- opening Stage Alexander, St. Petersburg. . , Berlin La Scala, Milan San Carlo, Naples Grand, Bordeaux Salle Lepeletier, Paris Covent Garden, London. . . Drury Lane, London Boston, Boston Academy of Music, New York Academy of Music, Phila- delphia Globe, Boston Museum, Boston Metropolitan Opera-House, New York § The Auditorium, Chicago. . Empire, New York Knickerbocker, New York. Garrick, New York Fifth Avenue, New York.. American, New York Proctor's Pleasure Palace, New York Hudson, New York Grand Opera-House, Cin- cinnati Castle Square, Bostonll Gaiety, Boston 69 70% '74K2 67I4 67 79K2 77 66 79 52 74K2 67 69 85!/^ 80% 58 47?^3t 7ot 34 II 30 75 92 86 66 80 78 86 48 87 83 90 62 68 100 no 67 40 71 K2 80 77-K 70 67 H 67 68 60 72 38 46 73 70 30 65'/2 28'/^ 35 43H 40 302^i 41 45^/2 42 73H Notes on Theater-Dimensions.ft "The utmost distance from the front of the stage to the rear ought not to exceed 75 ft, or the limit the voice is capable of expanding in a lateral direction." "Measured from the curtain-line, the San Carlo Theater in Naples is 73 ft; the * From the curtain or back line of proscenium opening, t Measured from stage to center of ceiling. j To the "gridiron" or rigging-loft. § As remodeled in 1893. II Can be enlarged to 40 by 40 ft. II The plan of this theater is in the shape of a horseshoe. ** See footnote with table of Seating Capacities of Churches, Theaters, etc., page 1654, in regard to data relating to recently constructed buildings of these types. . tt From The Planning and Construction of American Theaters, by Wm. H. Birkmir*. 1658 Dimensions and Data Part 3 theater at Bologna, 74 ft. Of the London theaters, the Adelphi is 74 ft, Covent Garden 80 ft, the Gaiety 53 ft 6 in, Lancaster 58 ft 4 in, Marylebone 74 ft and the Globe 47 ft 6 in." 1 The width of the ideal theater, between inside walls, should be from 70 to 75 ft, and "the ceiling should be from 55 to 65, or even 70 ft above the stage- level." "The^depth of the parquet-floor at the orchestra-rail is governed by the stage-level, and is generally from 3 ft 6 in to 4 ft 3 in below the stage. A depth of 3 ft 9 in is a good height, as it fixes the eye of the spectator 5 in above the stage-level." "The height of the stage, that is, from the floor to the bottom of the 'gridiron' or rigging-loft, should be 2 or 3 ft over twice the height of proscenium-opening, in order that the fire-curtain may be raised the full height of the opening." There should be a height of 7 ft above the gridiron to enable the fly-men to adjust their ropes with facility. Proportioning Gutters and Conductors to the Roof-Surface. The size of gutters and down-spouts and their distance apart for roofs of mill-buildings with a H pitch and of different spans are shown in the following table: * One-half roof-span, in feet Size of gutter', in inches Size of down-spouts, in inches. . Spacing of down-spouts, in feet. 10 20 30 40 50 60. 70 80 5 5 6 6 7 7 8 8 3 3 4 4 5 5 6 6 50 SO 50 50 40 40 40 40 The specifications of the American Bridge Company provide as follows foi the size of gutters and conductors: f Span of roof Gutters Conductors Up to so ft From so to 70 ft From 70 to 100 ft 6 in 7 in Sin 4 in every 40 ft 5 in every 40 ft 5 in every 40 ft Hanging gutters should ha^ e a slope of about i in in every 16 ft. "The Produce Exchange Building in New York City, with a roof-area of three-fourths of an acre, roughly speaking, has twelve leaders, each about 5 in in diameter. The roof, which is paved with fire-brick, is graded with slopes of perhaps one in fifty toward the points at which the leader-openings are placed, most of these draining-surfaces being about 40 by 70 ft each. The provision here made is equivalent to about i sq in of leader-opening to 140 sq ft of roof- surface. On the Sioane Building, at 19th Street and Broadway, New York City; with a roof-area of 18 000 or 20 000 sq ft, sloping one in twenty-five, there are two leaders, each about 6 in in diameter, and a third rectangular leader, 4 by 6 in in cross-section. This gives an allowance of 240 sq ft of surface to the square inch of leader-opening, while on the Massachusetts Hospital Life Insur- ance Company's Building and the Hemenway Building, in Boston, the proportion is only from 60 to 70 sq ft to the square inch of opening. " J * H. G. Tyrrell. t M. S. Ketchum. i Dwight Potter in The Technology Quarterly, Elevator-Service in Buildings 1659 ELEVATOR-SERVICE IN BUILDINGS* General Considerations. An efBcient elevator-service may be obtained by machines of any one of several types, the choice of the one decided upon for any building depending upon varying conditions. The following is a general classi- fication of elevators (see, also, page 1668): 1. Hydraulic elevators: (i) Vertical, geared hydraulic type. (2) Horizontal, geared hydraulic type. (3) Direct-lift plunger-type. (4) Inverted (high pressure) plunger-type. 2. Electric elevators: (i) Drum-type. (2) Worm-gear traction-type. (3) Helical-gear type. (4) Gearless, traction-type. (a) Direct-drive (one-to-one) type. (b) Two-to-one type. In addition to these, there are also the belt-driven type of elevators, and the HAND-POWER elevators. The belt-driven type may be either single-belt or DOUBLE-BELT driven, the former being used with a reversible motor and the latter where driving-power is taken from a line-shaft. In view of varying and sometimes conflicting claims of competing manufacturers, the architect's de- cision must be governed by impartial engineering judgment rendered after a careful study of the problem in each case. Geared Versus Gearless Types of Elevators. (See, also, page 1669.) There has been much discussion regarding the merits and demerits of geared and gearless machines for elevators and the efficiency and future of each. Manufacturers of gearless traction-machines have claimed that the use of the heHcal gear, for example, for elevator-machines, being a relatively recent devel- opment, has not extended over a sufficient length of time to permit of extensive or definite data; that they are used for different and less severe service than that for which the gearless traction-machines are employed; and that they can- not rival the gearless traction-machines from the standpoint of efficiency. On the other hand, the manufacturers of helical-gear elevator-machines claim that gears have been in successful use for many years, the substitution of helical gears for worm-gears being the only difference made in the application to their type of elevators; that the helical-gear elevators installed in some of the highest office-buildings are doing as much work as any gearless traction-machines; and that the mechanical efficiency of the helical-gear machines is only a little below that of the gearless traction the electrical efficiency under local or ordinary running conditions, greater, and the car-mile consumption in kilowatt-hours, less. Questions of Cost and Efficiency of Elevators. The principal demerit of elevator-machines of the gearless type is their relatively high first cost, al- though even that is much lower than the initial cost of elevators of the plunger- type. The use of any gear, whether of the helical, worm or spur-type, is, in the opinion of many engineers, to be recommended only for the purpose of obtaining * The matter relating to elevators and elevator-service is condensed and adapted by permission, from data furnished by various engineers and manufacturers, and papers by the Otis Elevator Company, New York City; The H. J. Reedy Company, Cincinnati, Ohio; R. P. Bolton of The R. P. Bolton Company, Consulting Engineers, New York, and author of " Elevator Service"; C E. Knox, Consulting Engineer, New York; M. W. Ehrlich, Consulting Engineer, New York; and others, 1660 Elevator-Service in Buildings Part 3 a higher-speed motor, because a higher-speed motor costs less than a low-speed motor. The heHcal gear is generally considered a more efficient type of gear than the worm-gear and has a deserved place in the development of the eleva- tor-industry. The helical-geared traction-elevators will undoubtedly be ex- tensively used, for the reason that, even if they are not considered b> some engineers to be as good in some details as machines of the gearless, traction- type, they are less expensive. It is undoubtedly true, however, that the intro- duction of any gear means some los5 in power, and it is claimed that tests show that low-speed motors can be designed which arc in every way as efficient as high-speed motors. The data and statements in the following paragraphs relat- ing to elevator-service in buildings are presented as useful aids to architects, and include some opinions and conclusions which are to be accepted or modified in the light of constant additions to engineering knowledge. A. General Conditions Affecting the Requirements of Specifications for Elevator-Service * Electric Versus Hydraulic Elevators. The question of the type of eleva- tors, whether electric or hydraulic, is best determined by the local conditions, or the special conditions which exist in every plant. The relation of the elevator- equipment to the entire mechanical equipment should be carefully considered, and should be decided only after mature deliberation and consultation with unprejudiced engineers and elevator-manufacturers. At the present time (19 14) about 90% of the elevators being installed are electric, and this includes all types of buildings from the small one with but one elevator to the tall sky- scrapers of the big cities. The electric equipment recommends itself, for while it has all of the safety-features of the hydraulic equipment, it is a more flexible system, is more adaptable to all kinds of conditions, and requires much less space. The question of space is a particularly important consideration in office-buildings. Furthermore, the control-system is more automatic, the acceleration and retarda- tion of the car can be made more rapid, and the stops more accurate; the effi- ciency, also, is higher and in most cases the cost of operation lower. (See, also, paragraph on Comparison of Merits of Electric, Traction and Hydraulic, Plunger- Elevators, page 1670.) Location of Hoistways and Machinery-Room. The location of the hoist- ways is rather a matter for the good judgment of the architect. In the larger equipment all elevators serving one portion of the building and for the same character of service, should be placed in one bank and not distributed or sepa- rate 1. Thus, all express-elevators should be together and in one bank, as should, also, the locals. The hoistways should be so placed that the entrances, in all stories, are on the same side of the car. In some of the larger cities, two en- trances for a passenger-car are not permitted, unless the doors ca 1 be controlled by the attendant without leaving the operating-device. The machinery-room should be well ventilated, light and clean as possible, in order that the machinery may be given proper attention. This room should also be largo enough to make iihe machines readily accessible for repairs and inspection. Where the machines have heavy parts, which it may be necessary to remove from time to time for repairs, it is advisable to locate a trolley-beam with hand-hoist above them to facilitate the handling of these parts. * The Otis Elevator Company, New York, has been of assistance in furnishing much of the engineering data of Section A, of this article on elevators. Among other details it considers especially those conditions which should be considered and made definite by the architect preliminary to the preparation of the elevator-specifications. The paragraphs of Section A sliould be read in connection with those of Section B, page 1667, and the data compared. Number and Size of Elevators 1661 Number and Sizes of Elevators. (See, also, pages 1673 and 1675.) The number and sizes of elevators are governed by the following considerations: (i) the character of the building, (2) the height of the building, (3) the rentable area, (4) the time-intervals between the departures of cars, (5) the number of stories to be served, (6) the average number and length of stops per trip, (7) the speed of the elevators and (8) the type of elevators used. No iron-clad rules can be given for all types of buildings, but the larger office- buildings, loft-buildings or light-manufacturing buildings have been sufficiently regular in design to warrant same general rules, based upon experience; even in these cases, however, the governing conditions vary with the size of the building. One of the most essential requirements for a satisfactory plant is quick ser- vice and in first-class office-buildings the intervals between cars should not exceed 30 seconds. The number of stories to be served by a car should be a consideration. For example, in a fifteen-story building, assuming that stops are made at 80% of the stories for one passenger each, and allowing 2 sq ft for each passenger, and 4 sq ft for the operator, the car should have an inside area of about 28 sq ft. In order to facilitate unloading and thus increase the efficiency of the system, it is desirable to have the width of the car greater than the depth. In the above case, a car with outside dimensions of about 6 ft wide by 5 ft deep would give the best results, showing a difference of from 15 to 20% between tho depth and width. In specifying the equipment, it is better to call for several moderate-sized cars and a high speed, than for a few large cars of slower spee({ and larger capacities. Thus, three cars, each carrying one-third of all the passen- gers, are better than two cars, each carrying one-half, as the service is increased by making the period between cars less. As the elevator-service largely deter- mines the success of a building, it is of vital importance that a sufficient number of elevators be installed to handle the regular traffic, as well as emergency-con- ditions in case of a shut-down. To illustrate what is considered the proper proportion of passenger-elevators for buildings of various heights, the following table is given, based upon a rentable area of 8 000 sq ft per story and 125 sq ft per person. This table shows the various combinations for elevators with a speed of from 400 to 500 ft and of 600 ft per min for buildings of from 10 to 30 stories above the ground. Table Showing Number of Elevators Required Number of stories Express 600 ft per min Local 600 ft per min Express 600 ft per min Local 500 ft per min Express 500 ft per min Local 400 ft per min 10 12 15 18 18 20 20 25 30 4 5 6 7 I to II 5 All locals 8 I to 12 5 I to IS 6 I to 18 7 S 5 7 8 I to ID 5 5 6 7 8 (- 500 ft ^ per min |i ton Express to 11 5 j Express to 10 5 ! Express to 11 s f Express to 12 5 Express to 15 6 Express to 18 7 i Express to 11 5 Express to 14 6 Express to 17 7 I to 11 5 I to 14 6 I to 17 7 Express to 12 6 Express to 15 7 Express to 18 8 I to 12 6 I to 15 7 I to 18 8 1662 Elevator- Service in Buildings Part 3 Buildings equipped with both local and express-service should have the same number of elevators for each class of service. In the case of the twenty-five story building for 600 ft-per-min speed, it is to be noted that the local elevators are shown serving from the first to fifteenth story, whereas the express-elevators serve from the fifteenth to the twenty-fifth story. The express-elevators can- not serve as many stories as the locals on account of the extra time consumed in the run to the first express-landing. With the distribution as shown, the service for all stories is about equal, and both express-elevators and local elevators operate on about the same schedule. In the fourth and fifth columns are shown what is considered the best arrangement with the express-elevators operating at a 6cx3 and the locals at a 500 ft-per-min speed. Upon comparison with the second and third columns, it will be noted that the express-elevators are to serve one additional story. This is due to the difference in si3eed between the express-elevators and local elevators and is. done so that the schedule may still remain the same for both. (See, also, paragraph on the Local and Express Round-Trip Time, page 1675.) Loads and Speeds. The sizes of the machines or hoisting-apparatus are determined by the loads and speeds. The loads for passenger-cars should be figured on a basis of 75 lb per sq ft of inside area of platform. The speed is a very important factor, as the foregoing indicates. This is usually limited by local ordinances, and in New York City, cars stopping at all stories are not per- mitted to exceed a speed of 500 ft per min. For express-service, in that portion of the shaft where no stop is made, a speed of 700 ft per min is allowed. This NO-STOP DISTANCE must be at least 80 ft or. more. The best companies for ele- vator-insurance will not permit electric-drum elevators for a speed much over 400 ft per min, whereas the gearless, traction-drive type and the hydraulic types are approved up to the limits, as noted above. In hydraulic plants it is necessary to specify the number of round trips per hour for the entire elevator-equipment. This is required in order to determine an adequate pumpin^-plant. Hoistways. The hoistways should be finished to plumb-line dimensions, so that the car running on guide-rails set to plumb-line will at all points have the same clearance. Supports should be provided adjacent to the hoistway for the overhead beams at a distance, if possible, of at least 4 ft from the top of car- frame when the platform is flush with the top landing. This distance should be increased where possible so that the car will have ample clearance, thus preventing accidents due to striking the overhead work, in case it should run past the top landing. The minimum clearances between the top of the car- frame and the overhead apparatus are usually limited by the local building regu- lations, and these should be consulted. In the case of the elevators operating at a speed greater than 350 ft per min, the distance given above would probably have to be increased in order to comply with these regulations. A pit should be provided at the bottom of the shaft. This should be at least 3 ft deep, and as is the case with the overhead clearances, the depth is usually regulated by the building regulations, in accordance with the speed of the elevator. Wherever possible, the hoistways should be so planned that the main guide-rails may be placed at the sides of the car. Supports should be provided at all the floors for these rails, and where the distance between floors is greater, than 12 ft, inter- mediate supports should be provided. The distance from the supports for the overhead beams, to the penthouse or skylight-roof, varies with the type of in- stallation, but can be accurately obtained from the elevator-manufacturer. Protection of Counterweights. In New York City the Bureau of Buildings requires that where the counterweights run in the same shaft as the car, they must be protected with a substantial screen of iron from the top of the rail to a Specifications for Elevator-Installation 1GG3 point 15 ft below, except where the plunger-type or traction-type elevator is used. Building Laws Governing Elevator-Installation. The Bureau of Build- ings, Borough of Manhattan, New York City, issued regulations * governing the construction, inspection and operation of all types of elevators, and the special attention of all architects is called to them, as they are not only obligatory there, but are excellent guides to practice at all times. The foregoing paragraphs are intended to give an idea of what the architect must consider and provide in a building for the reception of the elevator-apparatus, and what he must determine in order to enable the manufacturer to intelligently design and lay out his machinery. Standard Designs and Special Apparatus. The specifying of apparatus of special construction is, as a rule, not to be recommended. Standard designs should be used as much as possible, as (i) they are more apt to be well designed, tested and built, (2) they are undoubtedly less expensive, both in initial cost and maintenance and (3) repair-parts may be more easily and quickly obtained and at less cost. Specifications for Elevator-Installation. The specifications should include data included in the following classification. (i) Kinds of service and number of elevators of each service. (2) Maximum load wanted. (3) Maximum speed. (4) Load with maximum speed. (5) Maximum number of round trips per hour for each elevator. (6) Method of control. For electric elevators, car-switch control should be used for passenger-service and for all elevators for a speed over 150 ft per min. (7) Size of hoistways and area of car-platforms. (8) Travel of car-pkitform in feet, number of car-landings, and number of openings at each landing. (9) System used. If electric, direct or alternating current, the voltage and, also, the phase of cycles for alternating current should be given. If hydraulic, the steam-pressure or electric current characteristics for the pump-motors or the water-pressure, if the purchaser provides the pumps, tanks or other source of water-pressure supply. (10) A sketch-elevation showing landings, supports for overhead beams, space for the overhead sheaves, and runbys at top and bottom; a sketch-plan showing size and shape of hoistways, entrances, position of car and counterweight, guide-rails, and location of space available for machines, pumps, tanks, etc., with reference to hoistways. (11) Car and counterweight guide-rails, whether of wood or steel. (12) Supports for fastening the rails, character of these supports, and where and how located. (13) Value of finished car or cage, that is, the specified amount to be allowed for each, the design being subject to the approval of the architect. (14) Number and size of ropes, if not left to the judgment of the elevator- contractor. The largest sheaves possible should always be required, as this factor determines largely the life of the ropes. (15) System of signals, that is, (a) annunciators in the cars with push-buttons at the landings, {b) up and down signals in the cars, with up and-DOWN buttons at the landings, so arranged that a car going up receives only * Published in the Record and Guide, July 29th, 191 1. 1664 ^ Elevator-Service in Buildings Part 3 UP signals, and a car going down receives only down signals, each signal being automatically reset b}'^ the first car stopping at the story from which the signal is given. This system adds greatly to the efficiency of a battery of elevators, as it avoids the confusion of more than one car answering a signal, or a car going in one direction stopping for a passenger going in the opposite direction. The number of stories at which each car is to land should always be specified. (i6) Indicators. Whether at the ground-fioor only, for the information of the starter regarding the position of the cars, or at all floors. Indi- cators are unnecessary with the automatic signals last described, except at the ground-floor, as there is at each floor an up and down signal to show the first available car in either direction. (17) Source of power. It should be specified whether the connections will be brought to the elevator-apparatus by the purchaser or by the ele- vator-contractor. If by the latter, a sketch should be made showing the distance, and for the electric system the specifications should state whether the wiring is to be open, that is, on cleats, in moldings, or in conduits; the sizes of wire, and the switches, cut-outs, etc. For an hydraulic system, the size of pipe for steam-supply should be given. The sizes of water-piping should be left to the elevator-contractor and he should be held responsible for them. Also, in the case of an hy- draulic system operating from street-mains, the specifications should state by whom the piping is to be done and who is to furnish the water- meter. (18) Pumps and tanks in hydraulic plants. These should be furnished by the contractor. The specifications should state whether the capacity is to be just ample J;o do the work, or whether there is to be a reserve- capacity, with reserve-units, to provide against interference with the service in case of accident to a pump or tank, or for future elevators; but the sizes and design should be left to the judgment of a responsible elevator-contractor, (19) Foundations for the machine, whether they are to be provided by the purchaser or by the contractor. (20) Miscellaneous. Gratings underneath the overhead work, pitpans, paint- ing in addition to the standard factory-finish and all items not men- tioned above are generally furnished by tlie purchaser under separate contracts, but this should be clearly set forth in the elevator-specifi- cations. Safety-Devices for Elevators. (See, also, page 1672.) The question of safety-devices cannot be too carefully considered for all elevators, and for passenger-elevators in particular only the best and most thoroughly tested apparatus should be installed. Each car should be equipped with the me- chanical device designed to grip the rails and stop the car in case it exceeds a predetermined maximum descending-speed, either from breaking of the cables or from any other causes. This safety-device should be mounted upon the car-frame beneath the platform, and should be operated by means of a speed- governor located overhead. For speeds above 150 ft per min, this gripping of the rails should be done gradually. In New York City the instantaneous stop- ping is not allowed above a speed of 100 ft per min. A switch for emergency- use should be placed in the car of electric elevators. The opening of this switch should stop the car immediately and independently of the regular oper- ating-device. All electric^ elevator-machines should be equipped with an electric brake. This brake should be automatically applied when the car stops or when Geatless Traction-Elevators 1665 the current-supply is interrupted. The brake should be released electrically and applied by means of spring-pressure. Automatic limits should be placed at the top and bottom of the hoistway, to automatically slow down and stop tha car at the limits of travel, independently of the operator. Gearless Traction-Elevators.* Among the more recent developments of the elevator industry is the electric, gearless, traction-elevator (Figs. 1 and 2). (See, also, Fig. 5.) The designing of an efficient slow- speed motor made it practical to build a traction-machine with the driving-sheave mounted directly upon the arma- ture-shaft, thus eliminating the use of gears to reduce to the desired car- speed. This gearless machine is used for speeds from 250 ft per min and above. The manufacturers of this type of machine claim that it is the outcome of a general tendency toward simplicity in design with efficiency in operation. The machines are gener- ally located over the hatchway. The car is supported by cables which lead from the car directly over the driving- sheave, with overhead installation, then partially around the auxiliary idler or leading-sheave and again over the driving-sheave to the counter- weight. With this arrangement a complete turn around the driving- sheave and the idler-sheave is ob- tained, giving sufficient tractive effort to drive the car. The machine being placed overhead, the cables can lead directly to the car and counter- weights; and as this allows the cables to bend in the same direction, it is claimed by the manufacturers that it is an advantage and that the life of the cables is appreciably lengthened. Special hitches are used for connections to the car and counterweight to counteract the twisting effort due to the reaving of the cables. As soon as cither the car or counterweight is obstructed, the tension in the cables is decreased and consequently the tractive effort reduced. This arrangement, it is claimed, brings either the car or counterweight to rest and prevents running by the limits of travel, and into the overhead beams, should either member land on the buffers at the bottom of the shaft. Underneath both car and counterweight are placed oil-buffers designed to bring the car or counter- weight to rest at the limits of travel, from full speed. At the top and bottom of the hatchway the car is stopped automatically by a scries of electric switches. The operation of these switches is so timed that the car is brought to a smooth and gradual stop. The slow-speed shunt-motor, with its control, makes a flex- ible system. The acceleration and retardation may be arranged to suit the particular service-requirements. For speeds below 450 ft per min, it is the prac- tice to obtain the slow speed by passing the cables around sheaves mounted in * For full and valuable data relating to the relative advantages of the helical-gear elevators as compared with those of the traction-type, see papers published by the H. J. Reedy Company, Cincinnati, Ohio, and others advocating the geared machines. Editor. / Fig. Compensating Cables 1. Roping for to I Traction- machine Cojxnterweight L Compensating Cables Fig. 2. Roping for 2 to I Traction- machine 1666 Elevator-Service in Buildings Part 3 the cross-head of the car and of the counterweight, and anchoring the ends of the cables at the top of the hoistway. These sheaves, with their ball bearings, are specially made to withstand the heavy service to which they are subjected. In addition to the above details, elevators of this type should be provided with all of the regular safety-devices used with passenger-elevators. Electric Elevators with Push-Button Control. One of the most ingenious and serviceable developments in the elevator-industry is that of the automatic electric elevator with push-button control. In New York City this type of elevator is permitted only in residences, but in other cities it is used in apart- ments/hospitals, and other places where the service is very light and intermittent, and it is desired to dispense with an attendant. In the design of these elevators it has been the aim to provide all safety-devices and appliances to make the in- stallation absolutely safe, so that the elevators may be operated even by a child alone, without danger. In each story is located a button, similar in appearance to the ordinary signal-button, and the passenger, by pressing this, may call the car, if it is unoccupied or not in use, to any story. The car comes to the story at which it is required, and stops automatically. When it comes to rest in this story, the entrance-door to the hoistway is automatically unlocked, and it is then possible for the passenger to open the door and the car-gate, and enter the Fi?. 3. Standard Hatchway and Car- Fig. 4. Standard Hatchway and Car- platiorm. Side-guides platform. Corner-guides car. The hoistway-gates and the car-gate are so arranged that the machine is inoperative until both are tightly closed. The hoistway-doors can be opened from a hall, only when the car is at the landing of that particular hall. In the car is a bank of buttons corresponding to the various stories served, and also a stop-button or emergency-button. After entering the car, and closing the hatchway-door and the car-gate, the passenger can push the button in the car corresponding to the story to which he desires to go. The car will proceed to the designated story and stop automatically. Should the passenger desire, for any reason, to stop the car at any point of its travel, he can do so by pushing the stop or pmergency-button. The car is in the complete control of the pas- senger, as, after the initial operation of calling or sending it to a landing, its further operation cannot be interfered with until after both the hatchway-door and the car-gate are opened and closed. This means that no other person can call the car until after the passenger has reached the desired landing, left the car, and closed the gate and door. In some equipments for elevators of this type, the device for releasing the door-lock is prevented from operating while the car is in motion. This is a very desirable safety-feature, as otherwise each lock Electric-Elevator Service 1667 is temporarily released as the car passes up or down the hoistway, and a person on a landing can open the door during the momentary period that it is unlocked. In some cases the gate on the car is omitted; but this is a very dangerous prac- tice and should not be permitted. Elevators of this type are designed for oper- ation with direct current or alternating current, and single or multiphase circuits. Single phase should be avoided, if possible, and before deciding upon this type of current, the consent of the electric power company should be ob- tained for placing upon their lines a motor with the heavy inrush of current required at starting. Standard Relations of Hatchway, Platform and Car-Sizes. (See, also, page 1675.) In Figs. 3 and 4 are shown some typical elevator layouts for electric installations, with side and corner-posts and steel construction. (See, also. Fig. 7.) The clearances shown are for elevators traveling at a speed of 450 ft per min or more, and may be reduced about i Vz in for elevators of slower speed. Some of the minimum dimensions given, with Figs. 3 and 4 vary slightly from those given with Fig. 7 and in Table D, page 1676, but agree in the essen- tial requirements. B. Electric, Passenger-Elevator Systems * Elevator-Development. The object in view in presenting this material is not to discuss all the details of elevator-construction or the mechanical features, but to outline the results of a study in connection with the economic division of passenger-elevators and an efficient elevator-service for the traffic of the modera commercial or distinct type of office-building. The requirement of such build- ings is a very ample and adequate elevator-service, not only because the mon- etary value of the building may otherwise be affected, but in time of necessity, as during a fire or other panic, the occupants must be readily brought to safety. During the early development of the sky-scraper the necessity for a proper elevator-service was partly overlooked, and perhaps not altogether realized, for some of the older buildings suffer from a lack of traveling-facilities, resulting in an inconvenience to the many occupants. The tenants of the upper stories are therefore obliged to wait on the up trip of the elevator, and the people occu- pying the lower portion of the building are left behind on the down trip. The Extensive Use of Elevators. To fully indicate the extensive use to which the elevator has been adopted for passenger traffic in large cities, the in- stance of the Borough of Manhattan of New York City is given. There were in 19 14 about 10 000 machines in service, twice the number that were in oper- ation in 1904, and these were divided among the different classes of buildings approximately as follows: 5 000 elevators in office-buildings over 10 stories high. I 500 elevators in office-buildings under 10 stories high. 500 elevators In loft-buildings. 700 elevators in residences. 800 elevators in apartment-houses. 500 elevators in department and other stores. I 000 elevators in hotels, clubs, institutions, etc. * The matter in Section B of this article on Elevators is, by permission, condensed and adapted from data contained in papers by M. W. Ehrlich, consulting engineer. The papers first appeared in the Aprii, May and June, 1914, issues of Electrical Engineering, and afterwards were published in condensed form in Lefax, by the Standard Corpora- tion of Philadelphia. Section B includes a brief outline of elevator-development, some economic considerations and some installation-data, and the paragraphs of this Section should be read in connection with those of Section A, page 1580, and the data compared. 1668 Elevator- Service in Buildings Part 3 Besides these passenger-cars, the buildings requiring freight-service involved an additional lo ooo machines. Two Common Types of Elevators. In modern elevator-practice there are but two comm3n types of successful machines in use, the hydraulic and elec- tric elevators. These may both be subdivided in the classification according ^^/'TcL Motor and '^^~^. Driving Sheave Idler Sheave U' Counter weight Elevator- car GEARLESS.TRACTION, ELECTRIC OVERHEAD-DRIVE Counter weight Idler Sheave 1 Motor and \V^ Driving Sheavo WORM-GEAR, ELECTRIC BASEMENT- DRIVE ^^ CyKnder ^Pressure Tank Casing Pump — I ] Discharge -Tank VERTICAL CYLINDER.HYDRAULIC DIRECT-ACTING.PLUNGER Fig. 5. Some Types and Varieties of Elevators to the mode of drive or operation and the transmission of ix)wer, thereby showing an apparent variety of elevators. The machine of the hydraulic type may be of the vertical-cylinder pattern or of the plunger-type, while the electrical appa- ratus may be of the drum, worm-gear or gearless traction-type. Some of the types and varieties are illustrated in Fig. 5. (See, also, Figs. 1 and 2, page 1665, and general classification on page 1659.) A Short Historical Account of the Development of the Commercial Passenger-Elevator brings one back a little more than half a century to the Traction and Geared Elevators 1669 introduction of the first steam-elevator. This fjorm of drive was soon replaced by the water-balance type of hydraulic elevator, which, even though a faster machine, proved to be, in operation, quite dangerous. P'or a number of years this type enjoyed the distinction of being the only high-speed apparatus until the advent of the vertical-cylinder hydraulic elevator, about twenty years later. Running-speeds as high as 400 ft per min were readily attained, and on account of the ease in handling and the safety in operation, these ele- vators soon gained favor and were the only types of machines installed in the then tall buildings. The electric drum-machine made its first appearance in New York during the year 1889, and owing to the merits of this new system, the electric machine soon established itself as a successful competitor with the hydraulic type. The only obstacle remaining was to overcome the slower speed, and this brought out the Sprague long-screw electric elevator. Elevators of this type proved quite costly to maintain and operate, but on account of their possibilities of speed and high rise, were installed in several tall structures. These different types of elevators helped considerably in the development of the sky-scraper buildings, and as further building projects brought on an extension in height, a hitherto unknown condition of passenger- elevator service had to be met. About the year 1900 the direct- acting PLUNGER hydraulic ELEVATOR was introduced to fulfil this increasing demand of continued high rise with high, speed. The inherent safety in operation and the relatively high economy allowed for no doubt as to the possibilities of the PLUNGER, but after several years, experience painted out that the advantages of the hydraulic plunger-elevator were somewhat limited in certain directions, and only under conditions of a rise not exceeding 150 ft could the character- istics of the safe and economical plunger-elevator be maintained. Traction and Geared Elevators. (See, also, page 1659.) Recent experi- ments conducted to perfect an electric elevator that would meet the growing requirements of heavy passenger traffic in the newest form of tall office-build- ings have resulted in the production of what is now commercially known as the ONE-TO-ONE, or GEARLESS TRACTION-ELEVATOR. Among the earliest New York installations of this type of electric elevator may be named those in the Singer Building and Tower, and later those in the Metropolitan Building and Tower, while the latest developments include the Woolworth and the Equitable Build- ings. The apparatus used in the Municipal Building is one in which the machines are an adaptation of the usual double-worm-and-gear drive between a relatively high-speed motor and a cable-drum, a double set of intermeshing spur-gears being employed between the two gear-shafts. In summarizing, it might be well to mention that the commercial or useful life of an elevator and its combined mechanisms seldom exceeds fifteen years, and that where remod- eling has been resorted to, the electric drum and worm-gear traction have usually been substituted for the hydraulic type in buildings not exceeding from twelve to sixteen stories in height; and that in higher structures the gearless traction-elevator or its modification in the form of an electric two- to-one traction-elevator has been resorted to. Safety of Electric and Hydraulic Elevators. (See page 1664.) It is true, however, that both the electric and hydraulic types of elevators have been perfected to a state of high efficiency, and they may, therefore, be used with entire safety. Of the hydrauHc types it may be said that the plunger- elevators are inherently safer than those which are suspended, or than even the more modern electric traction-elevators; but it cannot be denied that the many refinements and improved appliances attached to elevators of the various electric types have made the latter as reliable as hydraulic machines designed according 1670 Elevator- Service in Buildings Part 3 to best practice. It is claimed that the electric traction-elevator is relatively free from the element of danger because of the improved methods of power- transmission and the peculiar form of windings used for the drive. Comparison of Merits of Electric, Traction, and Hydraulic Plunger- Elevators. In narrowing down the question as to the merits of the electric TRACTION-ELEVATOR and of the HYDRAULIC PLUNGER-ELEVATOR for passeugcr- service in tall office-buildings of to-day, it might be well to note that the new elevator-installations, almost without exception, have favored the electric. Not only is the cost of installing the traction-machine from 25 to 35% less than that of the plunger-type, but the room occupied by the driving-machinery is reduced to a minimum, and, as a matter of fact, may be placed at the head and directly over the elevator-shaft. If no local supply of electricity is available on the premises, the public source may be resorted to. The difficulty with the plunger-elevator for high-rise, high-speed work lies in the requirement for mov- ing the mass of water and the massive plunger proper, and as this immense weight cannot be readily and smoothly stopped, the result is a sluggishness in starting and stopping. At any rate, it remains an open question as to whether the economic values attached to modern buildings would favor the installation of the plunger-elevator, with its accompanying pumping-plant, which neces- sarily occupies considerable floor-space. The choice, therefore, would tend to favor the high-rise, high-speed electric traction-elevator for passenger- service. (See, also, paragraph on Electric Versus Hydraulic Elevators, page 1660.) Table A. Relative Operating-Costs of Elevators Costs Per cent of rentals Cents per car-mile . Dollars per car per annum Per cent of all oper- ating-costs Office-building 25 7.2 22 1850 6.8 I 680 II. 3 6.5 19 I 600 Loft-building Apartment-house 23.8 II. o 18.015.4 6.5 19 14.8 6.2 18 14.0 560 13-6 6.0 18 5-5 17 480 53 16 10.6 Relative Operating-Costs of Elevators. The figures given in Table A may prove of interest in pointing out the relatively higher operating-costs of the different electric types over the vertical-cylinder hydraulic and plunger- elevators. The values given represent only the cost of labor, power, repairs and supplies. By a close perusal of the amounts listed, it will be confirmed that the economies of the plunger cannot be utilized beneficially in tall office- buildings, on account of the mechanical difficulties, and in other types of smaller buildings, allowing for a low rise, the installation cost becomes exorbitant. If the relatively high first cost of this type of machine were taken into considera- tion, with an addition for the extra cost in building-construction necessary for the space occupied by the pump and tank-equipment, the total expenditure on the whole would show no great favor either way. In explaining the values given in Table A, it should be understood that the figures are computed on a basis of actual records of several buildings that have been brought to the writer's Power-Diagrams 1671 notice. The general method of comparing records in business buildings is to compare the costs with the total annual income or rental. The total oper- ating-costs include the expense in the mechanical, electrical and building departments, covering all costs of labor and material for the maintenance of the different divisions of service. Therefore the annual cost of operating an ele- vator-system is given as a percentage of the gross rentals received, and is further stated as a percentage of the total operating-expenditure of the build- ings under consideration. The average cost in cents per car-mile traversed is also given, together with the average annual cost in dollars to pay for the labor of operating and repairing, the necessary power, and the material and supplies required per single elevator. Economic Considerations. The efficient operation of an elevator-system does not rest altogether on the economic division and disposition of the cars, as the human element becomes one of the main factors. It is self-evident, there- fore, that the service of an elevator is limited not only by the different classes of passengers entering, riding and leaving the conveyance, but by the experience of the hallman or starter and his ability to understand the demands of the traffic and the personal peculiarities of the elevator-operators. Time-Schedules. It is now common practice to dispatch the various ma- chines of an elevator-system on a predetermined time-schedule, thus avoiding to a great extent any confusion or overcrowding that would otherwise arise. It has been well established that the travel of elevators under consecutive-trip schedule-operation allows for a hi::;hly efficient service, not only in the handling of the traffic, but in the demand for power, which is thereby reduced to a min- Tiuie in SeconUs. Up-Trip Time in Seconds. Down- Xrip Ca) Operation of one car " 1^ ^ > / l\ B / 7 V. r y'^ ,"(1 1 , r \.y .sr i ^ -:^;#%";4^7--^c^ f-WS..;-;,:, -/^N ^•^I^KJ '[ -^^^^M 1 ■' * r±:"':: "■■::: 1" ± - Scale of Time in Seconds per Round Trip (b) Operation of a bank of elevators Fig. 6. Recorded Current-consumption of Gearless Traction-elevators Power-Diagrams. The Power-diagrams (Fig. 6) point to the effect of a poor and a proper service under different conditions. The upper curve (a) was taken under test-conditions and represents the operation of one elevator. The load in the single car is approximately eciual to the designed machine-balance, both on the up and down trips, and the number of stops corresponds to the average per car per mile under actual service in office-buildings. This diagram is given mainly to allow for a proper understanding of the combined curve (b), showing the actual round-trip operation of a bank of elevators in one of the New York sky-scraper buildings at an early-morning hour. The full or solid-line curve shows an excessive power-demand due to an inconsistent schedule, the 1672 Elevator-Service in Buildings Part 3 cars having been dispatched by a starter who may be identified as A", while the dotted or broken-line curve shows the more expert handling under the consecutive trips by starter Y, the same operators running the cars in each case. Safety-Appliances. (See, also, page 1664.) To minimize the many acci- dents in elevator-practice, a safety-lock is recommended, so attached that it will not permit the elevator to leave a landing until the gate has been locked. ; Accidents are seldom, if ever, due to the faulty behavior of the elevator proper, but sometimes the breaking of suspension-ropes, as recorded by a relatively few cases, will result in a serious accident. The most frequent cause of accidents connected with the operation of elevators, is that due directly to the negli- gence of the operator in handling the doors or elevator-gates, and this may be avoided by the installation of the safety-locks above recommended. So far as has been practically demonstrated, many of the safety-appHances on the older installations designed to stop a falling elevator have usually failed to act; but the improved wedge-type of jaw-safety, actuated bj^ a speed-governor and attached to the more recent installations, usually acts when the elevator exceeds its normal running-speed. This generally occurs when the designed or safe-distance limit has been passed, and the jar occasioned by the final stopping of the car is not altogether a pleasant experience. The serious injuries and fatalities due to the falling of an elevator are proportionately small when com- pared with the entire list, and amount to about 20% of the total, whereas the loss of life caused by open and unlocked gates in elevator-practice today accounts for the remaining 80%, The only safety-device, therefore, that may be called useful, as it eliminates the personal element, is a safety-lock. Of the several automatic devices now available for this provision of safety, all de- serve merit; and while some are purely mechanical, others are actuated elec- trically, and only by the installation of such automatic locks will unnecessary elevator-accidents be avoided. Signal-Systems. A signal-system is essential to an efficient service. Auto- matic electric-light indicators at the different landings, with a mechanical indicator on the ground-floor or street-landing, will be found highly efficient even though not the simplest. Briefly described, the system is composed of a dynamotor supplying current for the magnets, push-buttons and lamps. At each landing one or more sets of push-buttons are arranged for both the up and DOWN signal, and over each elevator-gate two lamps of different color, one over another, to indicate the direction of car-travel; and each elevator-car is also provided with a signal-lamp and a transfer-switch or push-button. A mechan- ical indicator on the main landing informs the starter as to the location of the different elevators, and thereby aids him in exercising full discretion as to when to dispatch the next car. The general system operates in a manner approxi- mately as follows: When a push-button is pressed for either direction in any story, it actuates a magnet corresponding to that story, which iji turn signals to the operator in any approaching car, thereby indicating a waiting passenger; and, according to the movement of the elevator, further contact is made with the outside signal-lamps at that story showing to the waiting person the car approaching that floor. In a properly proportioned elevator-system the trans- fer-switch is seldom used, but in buildings in which the travel becomes overtaxed during the rush-hours, and when an approaching car is filled to its capacity, the operator may press the transfer-button and thereby signal the car following. Traffic-Capacity of Elevators. The traffic-capacity of an elevator, or its passenger accommodations must necessarily be of such proportions as to handle the travel of the tenants of the building and also of their visitors and in- sure a proper working schedule. From a study of existing systems in which the Formulas for Elevator- Service 1673 elevator-service is considered adequate, it is found that the questions of build- ing-occupancy as related to building-area and elevator traffic-capacity may be combined into a consideration of a proper unit area for the elevator. In regard to the determination of the maximum traffic-capacity of a passenger- elevator, experience shows that an average weight of 140 lb may be allowed for each passenger, and as each size of car has its corresponding load at the rated speed, the total load divided by 140 gives the maximum number of passengers an elevator can accommodate at its designed speed. In another simple computa- tion for this result, an allowance of 2 sq ft of car is made for each passenger. The maximum capacity of an elevator may be of interest in computing the time re- quired to empty a building in case of emergency; but when a car of proper unit area is installed, this condition is taken care of. Tests have shown that the average passenger traffic of an elevator-system bears a definite relation to the tenancy of the building, and to the maximum travel, the result being that expressed in Formula (6). Number of Elevators. (See, also, page 1661.) Modern practice tends to show that the number of elevators required for any office-building is really governed by the physical aspects and conditions of that building. Wherever it is not practicable to use a car of large area, the number required will certainly be in excess of that necessary when large cars are used. It is not advisable, therefore, to base any conclusions on the number of cars to adequately satisfy a certain condition, unless the unit area of the car is considered. Local and Express-Elevators. Another important consideration is the division so common in high-class office-buildings, namely, the proper service of LOCAL and EXPRESS-elevators. Formulas for Elevator-Service. The formulas given below are well sub- stantiated, and give economical service-conditions based on existing systems in the larger cities of the United States. By these formulas the number of eleva- tors required, the division of service, and their operation may be determined. E = 74/24000 (i) f=n/2-{-2 (2) Te = (25/5 4- 5/100) n and Tl = (25/5 -h //lo) n (3) Me = 2 w/7 Te and Ml = 2 n/l Tl (4) Ce= 115 n/100 Te and Cl= 115 n/ioo Tl (5) pe = $00/ Te and pi = 300/ Tl (6) The notations in the formulas are: E = number of elevators required A = square feet of gross building-area served / = story at which express-run terminates n = total number of stories served s = speed of elevator, in feet per minute Tl = local round-trip time, in minutes Te = express round-trip time, in minutes Ml = miles traveled per hour by local Me = miles traveled per hour by express CI = current consumed per hour by local, in kilowatt-hours Ce = current consumed per hour by express, in kilowatt-hours pi = passengers carried per hour by local, one way, up or down pe = passengers carried per hour by express, one way, up or down The figures in Table B represent the average load and speed-combinations for various heights of buildings, together with the usual area of the elevator- 1074 Elevator-Service in Buildings Part 3 CAR consistent with the standard sizes manufactured, and should be used as a basis for selecting the proper unit areas in connection with l^onnula (i). Tho many factors entering into the operation of an elevator would affect tho current- consumption to a considerable extent, as may be seen in Fig. 0, previously ex- plained. But Formula (5) agrees with modern service under average operating- conditions. Table B. Unit Area, Load and Speed-Combinations Number of stories Car-area, sqft Load, lb Speed, ft per min 8 to 13 14 to 22 23 to 30 25 30 40 I 700 2000 3000 250 to 350 350 to 600 400 to 600 Table C. Elevator-Installation Data I 2 3 4 1 5 6 1 . 7 Building Number of elevator? required Number of stories Gross area, sqft Total car-area, sqft Cars at 25 sqft Cars at 30 sqft* Cars at 40 sqft By Formula (i) 8 10 12 14 16 18 20 25 30 80 000 100 000 120 000 210 000 240 000 270000 300000 375000 800 000 89 III 133 262 300 337 375 577 I 221 4 4 5 II 12 14 4 4 5 9 10 II 13 16 33 9 10 II 13 19 40 15 10 15 30 Number of stories 8 9 10 1 II 12 Round trip time in minutes /.or express-run, in stories Tl at 350 ft per min Tl at 500 ft per min Teat 500 ft . per min Te at 600 ft per min 8 10 12 14 16 18 20 25 30 1.3 1-7 2.0 2.4 2.7 2.1 2.4 2.7 3 1.6 1.8 2.0 2.5 3 10 II 12 15 TT 1.8 2.3 2 T Hatchways and Car-Platforms X675 Installation-Data. In order to facilitate the ready understanding of the various formulas given, Table C, embodying the computations, is presented. The various headings included are numbered in respective order from i to i2,l so that an explanation of the items considered will not be confusing. Under' column I is listed the heights of buildings, with the assumed floor-areas, extend-! ing the full height of the structure, given in column 2. In column 3 are listed the actual square feet of car-area now provided in many buildings of similar floor-space and with an adequate service. This is intended as a guide where the considerations in planning the building have included a means of accom- modating the standard-sized elevators most suitable for that building and where serious attention has been given to the disposition of the cars. But, on the other hand, the values listed may also be used to advantage in proportioning the number of elevators required under any conditions, and where the physi- cal aspect of the building does not allow for an economic disposition of the} elevators. Any conservative unit area best suited to the conditions may then be allotted for each car, and the numl^er of elevators then determined. Col- umns 4, 5 and 6 give the numbers of cars for various standard unit areas, while the values in column 7 are computed by Formula (i). The Local and Express Round-Trip Time for different running-speeds is given in columns 8, 9, 10 and 11 of Table C, and the value for / as given in Formula (2) is given in column 12. It will be noticed that in columns 8 and 9 the time occupied in traversing the heights of buildings exceeding eighteen stories is slightly more than would actually prove economical. It might be well, therefore, to point out that the speeds of local elevators for high buildings might be increased to advantage; but whether the service is local or express, it is not advisable to exceed a speed-rate of 600 ft per min. In order to rectify this con- dition, under the speeds considered, the numl:)er of express-elevators must then be more than half the total number in the system, and a subdivision of express- service proper is also necessary. (See, also, Table Showing Number of Eleva- tors Required and notes following, page 166 1.) Sizes of Hatchways and Car-Platforms. (See, also, page 166 1.) The sizes of elevator-car p'atforms and hatchways of unit areas heretofore con- HW- ////////////////////////^^///// , /2;^^^^^^^ ^.^ ^5^^^^^^^^^^^^^ ^ >HD B Fig. 7. Typical Layouts for Elevator-hatchways and Car-platforms sidered are shown in the following diagrams (Fig. 7) illustrating three typical forms of modern installations with steel guide-rails. (See, also, Figs. 3 and 4.) The gate or door-opening may be either right-hand or left-hand, as best suited to planning, structural, or other conditions. The clear inside dimensions of the necessary hatchway are given, and also the clearances required between this and the car. Some of the minimum dimensions given with Fig. 7 and in Table D vairy slightly from those given with Figs. 3 and 4, page 1666, but agree in the 1676 Elevator-Service in Buildings Part 3 Table D. Sizes of Elevator-Car Platforms and Hatchways Dimensions Area of car-platform 25 sq ft ft in 30 sq ft ft in 40 sq ft ft in PF= inside width of car 6 p 4 3 2 3 3 9 7 7 4 7 3 5 I 4 9 5 2 6 3 4 9 2 3 4 7 3 7 7 7 6 5 7 5 3 5 8 7 o 5 9 2 3 4 9 8 8 4 8 3 6 7 6 3 6 8 D = inside depth of car 0= space for operator G = gate-opening // W= hatch-width, car A car B car C II D = hatch-depth, car A car B car C. . . 90 / 1 / 1 /^ / / 7 i^^5 it vV / / / / 80 / Vl 1 fl V /•«; / / / / 1 7 h rj f / / 70 / 1 1 '/ // / ^% ¥ / / // / / ' /I / / ^. / u % o60 1 / 'h 1/ / / / 7 / t- 50 1 1 // m A / / / c f >/" / / / / / i i O o 40 1 I V, // / / / / 4> } 1 , // // / / / /^ m / 1 m / // / /' \ / ^ 20 15 § k // / / y' y^ y^ '//. /. y / X ^ -^ j^ ^j^ y. -"/ ^ ^ ^^ ^ 100 150 200 :300 400 500 Speed of Machine. Feet per Miixute Fig. 8. Motor-sizes for Electric Elevators 600 Mail-Chutes 1677 Size of Motor. It is often helpful to be informed as to the size of motor re- quired for an installation, and the diagram (Fig. 8) may be used for this purpose. For .sake of illustration in the use of the diagram, a speed of 400 ft per min is assumed, with a combined load of 2 500 lb. Following the line marked with an arrow from the speed of 400 ft, the point of intersection is then at 2 500 lb. From this point follow the line as indicated to the scale of motor-sizes, and the result is about 40 horse-power. Table E. Current-Consumption Motor-size Starting- current Running- current 20 horse-power 40 horse-power 60 horse-power 102 amperes 202 amperes 292 amperes 74 amperes 147 amperes 213 amperes Current-Consumption. Table E gives the current-consumption of motor- sizes common in elevator-practice. The figures are for direct-current motors operating at 230 volts and are based on the results of tests. Electric Feeders. To aid in the selection of well-proportioned electric FEEDERS for clcvator-motors, Table F is given. The figures are for 230-volt, direct-current machines. Table F. Wire and Conduit-Sizes for Electric Elevators, 2-Wire, 230-Volt, Direct-Current Systems Wire Max- Conduit Motor- imum run or distance Under- Trade Inside Outside h.p. Size of each wire carrying capacity, for 2% drop, ft size for 2 wires diam- eter, in diam- eter, in amperes 15 No. 3 80 154 iKi 1.38 1.66 20 No. I 100 174 1^/2 1. 61 1.90 25 No. 125 186 iVz 1. 61 1.90 30 No. 00 150 198 2 2.06 2.37 35 No. ODD 175 212 2 2.06 2.37 40 No. 0000 225 226 2 2.06 2.37 45 No. 0000 225 226 2 2.06 2.37 50 300000 cm.* 275 248 2\^ 2.46 2.87 55 300 000 cm.* 275 248 2H 2.46 2.87 60 400 000 cm.* 325 272 3 3.06 3.50 • Circular mils. MAIL-CHUTES General Description. This system of mailing letters by means of a specially constructed chute connected with the receiving-box at the bottom, has come into such general use in public buildings, office-buildings, apartment-houses ^nd hotels, that the restrictions affecting the same and what is required in the way of preparaLion should be known to architects. The system is installed by the patentees, under regulations of the Post-Office Department governing itg 1078 Mail-Chutes Part 3 coMstruction and location, and for this reason it is well to consult the makers* before permanently locating the apparatus on the plans. It may be placed in any building of more than one story, used by the public, where there is a free delivery and collection-service, in the discretion of the local postmaster, subject to whose approval the contracts are made. The Chute and Receiving-Box. The chute is required to be made with a removable front and a continuous, rigid, vertical support is absolutely necessary. It must be of metal, its front must be of plate glass, and it mu; t bear the insignia prescribed by the department; and the whole apparatus, when erected and the Government lock put on the box, passes under the exclusive care and control of the Post-Office Department, and the chutes become a part of the receiving- boxes. These boxes may be of various patterns and highly ornamented and are furnished by the makers in connection with the chutes. The work of preparing a rigid support for the chute and cutting and finishing the openings in the floors is of the utmost importance, and details showing the usual arrangements are always given. Preparatory Work. The requirements for what the manufacturers call PREPARATORY WORK include a flat, vertical, continuous surface not less than W//////////^///////yM LineTof Fig. 1. Wooden Support for Mail-chute 'Elevator-Screen'-Nv. Fig. 2. Steel Support for Mail-chute Elevator-Screen-^ ' S>%'- I2V2XX' n .Angles ... Floor- Thimble Fig. 3. Alternate Steel Support for Mail- chute Fig. 4. Preparatory Work Complete for Mail-chute io>^ in wide, extending from the floor of the ground-story to a point 4 ft 6 in above the finished floor in the top story, and an opening in each floor directly in front of and centered upon this surface. These openings are neatly finished, and their size and shape determined by setting in them thimbles of iron which ♦ The Cutler Mail Chute Company, Rochester, N. Y. Refrigerators 1679 are furnished and delivered by the patentees, as part of their contract. In ordinary installations a casing of wood, suitably molded and finished to match the trim of the building, answers every purpose. Such a casing is shown in plan. Fig. 1, with the opening finished by the iron thimble. In buildings, or some- times in a few stories, where a more elaborate finish is desired, marble is sub- stituted for wood, the form and construction of the casing being adapted to the material, but of course without disturbing the size and form of the front surface. Steel angles are used where the use of wood is objected to, or where it is necessary to run the chute in front of an elevator-screen, or in other locations where a solid wall is not available to support the casing. Steel square-root angles, 2 by 2 by H in in section, are generally used, and set as in Fig. 2, but sometimes, where it is desirable to fill up the space between them and the elevator-screen, they are reversed, as in Fig. 3. The angles are usually bolted to the beams, and in any case must be straightened so that they are without twists or kinks, and the sur- face which receives the mail-chute plumb and flush in all stories. Fig. 4 gives a general view of the mail-chute casings and floor-openings ready to receive the chutes themselves. This work of preparing the building, except the cutting or leaving ready the necessary openings in the floors, is now usually included in the mail-chute contract, as it has been found for many reasons undesirable to sepa- rate it. The necessary openings in floors, and all patching around such open- ings, should be included in the mason's or other proper specifications. Essential Points to be remembered are (i) that no bends or offsets can be made, a vertical fall being absolutely essential, and (2) that the entire apparatus must be exposed to view and must be accessible, that is, it is not permitted to extend the work behind an elevator-screen or partition or through any part of the building except a public corridor. REFRIGERATORS * General Requirements. The following information is given as a guide to architects in providing for refrigerators in large residences, hotels, clubs, hospitals and other institutions. Consultation with a reliable refrigerator-builder, how- ever, is always desirable before deciding upon spaces to be occupied by refriger- ators, refrigerating-rooms, etc., as a satisfactory refrigerator cannot be adapted to a badly proportioned space. (See, also, Design of Refrigerators, under Mechanical Refrigeration, page 1691.) Residence-Refrigerators. Care should be taken to select a refrigerator which is simple in operation and easily cleansed, as modern sanitary science has traced much illness to faulty refrigeration. Thorough insulation is an important feature in a refrigerator, as upon this depends economy in the use of ice and the securing and maintaining of the low temperature necessary to the proper preser- vation of food. Fig. 1 shows a kitchen-refrigerator for use of families of ordi- nary size. The ice-compartment is located in the middle division. The depth should not be more than 3 ft nor less than 2 ft, and the height may vary from 4 ft 6 in to 7 ft. The length of the front largely determines the capacity and should range from about 4 to 7 ft. Fig. 1 shows, also, a most satisfactory method of accomplishing the outside-icing feature which consists of a double outside icing-door complete, with frame and jamb. This is provided by the refrigerator- builder to fit the rough opening furnished by the owner in the outside wall of * Valuable data and the drawings relating to this subject were furnished the author and editor by The Jewett Refrigerator 'Company, Buflfalo, N. Y. Practical data were furnished, also, by The Brunswick-Balke-Collender Company, New York City. There are numer- ous other reliable firms whose refrigerator-work has the highest reputation. 1680 Refngerators Part 3 the building. With this method a minimum outside opening is required to furnish a maximum inside opening for ice. The drain-pipes should be as short and straight as possible and should be readily detachable for cleansing pur- poses. The drain should be properly trapped in the floor of the refrigerator and carried through the floor of the building, discharging over the plumber's open connection as shown in the elevation of Fig. 1. Fig. 2 shows a refrigerator for use in a butler's pantry where economy of space is important. The ice-compartment is of galvanized steel throughout and is removable for con- venience in filling as it slides on roller-bearing runways. When the ice-compartment is replaced in position the out- side door closes over it. The adjoining storage-compart- ment is generally fitted with one removable shelf, below which is a bottle-rack for horizontally placed bottles and a space for standing bottles. The depth should be about 2 ft and the height 2 ft 8 in, under counter-top. The length of the front determines the capacity, but it should never be less than 3 ft. For a double refrigerator with a central ice- compartment and storage-com- partments at either side, 5 ft is a convenient length. The ex- terior finish and hardware should correspond with the adjacent trim. The most sanitary and attractive interior finishfor storage-compart- ments consists of white plate glass for the walls and ceilings and tile for the flooring. The usual complement of refrigerators for use in ordinary families ronsist«i of one adjacent to the kitchen and one in the butler's pantry. For large families the number could be the same with the capacity greater. Refrigerators for Hotels, Clubs, Etc. Mechanical refrigeration has largely superseded ice as a cooling-agent where the refrigerator-equipment con- sists of several units, as in hotels, clubs and institutions. (See, also. Mechan- ical Refrigeration, page 169 1.) The arrangement of refrigerators is similar to that employed where ice is used, as the refrigerating-coils are often contained in compartments corresponding to ice-compartments; the alternative method is to .place the coils against walls of storage-compartments. Refrigerating-coils are generally of i}4-in pipe, the length of coil depending upon the temperature required. Fig. 3 shows a practical layout for- the working-department of a * The Jewett Refrigerator Company. KITCHEN PANTRY PLAN Fig. 1.* Kitchen-refrigerator for Small Family Refrigerators for Hotels, Clubs and Hospitals 1681 ELEVATION Removable Ice-compartment on Roller-bearing Runways-^ good-sized club, and illustrates the proper complement of mechanically cooled refrigerators, together with adjacent operating-equipment. No. i, a store-room refrigerator, has the front arranged in one full-height door and is fitted with three tiers of shelves throughout. No. 2, a meat-refrigerator, is also accessible through a full-height door and is fitted with shelves and meat-racks. No. 3, a broiler and fish-refrigerator, has the front arranged in two doors, each door opening onto a series of six galvanized sheet-steel pans sliding on self-sus- taining roller-bearing runways. No. 4, a serving-pantry refrigerator, is subdivided by an insulated partition into three separate and distinct com- partments, those at the left and right being each accessible through two doors, while the middle compartment is accessible through one door, below which is a series of four drawers sliding on self-sustaining roller-bearing runways. The doors open onto re- movable shelves throughout. No. 5, an ice-cream refrigerator, occupies a position in the serving-pantry counter and has the top arranged in one lift- off cover. Its interior fittings consist of three 20-quart porcelain-lined ice- cream jars and one glace-frame for fancy forms of ice-cream. No. 6, a pastry-refrigerator, has the front ar- ranged in four doors, two upper doors opening onto removable shelving, and two lower doors onto pastry-pans sliding on angle-iron runways. No. 7, a bar-refrigerator, is subdivided by an insulated partition into two sepa- rate and distinct compartments, each accessible through four doors. The upper doors open onto three tiers removable shelves for standing bottles, while the lower doors open onto five tiers of racks arranged specially for horizontal bottles. The equipment described above will also satisfactorily cover the requirements of a moderate-sized hotel. Refrigerators for Hospitals. The usual complement of refrigerators for small hospitals consists of one large storage-refrigerator, one refrigerator for the chef's use in or neat the kitchen, one for milk and butter and one iron-lmed chest for broken ice. For large hospitals the same number with increased ca- pacity and with the addition of small diet-kitchen refrigerators, and possibly a mortuary-refrigerator for two or three bodies, will meet the requirements. The Height of Large Refrigerators for hotels, clubs and institutions, to be entered through full-height doors, should be from 10 to 12 ft, if equipped with overhead ice or coil-compartments; with side ice-compartments or coils placed against walls, the height should be 7 ft 6 in or 8 ft. The smaller refrigerators, * Tht Jewett Refrigerator Company Cupboards Cupboards BUTLER'S PANTRY PLAN Fig. 2.* Refrigerator for Butler's Pantry of 1682 Refrigerators Private Dining-Room Enclosed Porch Main .Dinlng-Koom Fig. 3.* Plan of Refrigerators for Large Club-house * The Jewett Refrigerator Company. Mortuary- Refrigerators 1683 I /^SyCement TT^f Platform ELEVATION accessible through half-height doors, hinged covers, drawers, etc., should be placed on a 3-in sanitary cement platform finished with cove to floor of building. These refrigerators should not be higher than 6 ft 6 in unless provided with over- head ice or coil-compartments, in which case the height should be from 8 to 9 ft. Insulation. (See, also. The Value of Good Insulation, page i6qo.) Refrigerators in modern hotels, clubs, institutions, etc., are insulated with Government-standard corkboard, the large refrigerators being constructed of 4-in cork throughout, in two courses of 2 in thickness, and with all joints broken. Cork is applied to adjacent walls of a building with Portland cement, H in thick, and this cement is used, also, in applying the inner course of cork to the outer course in walls, partitions and ceilings. All cork in the flooring is asphalted water-tight. Interior finish may be of Portland cement throughout or of galvanized sheets on walls and ceil- ings and of Portland cement on floors. Or the walls and ceilings may be of f used-on porcelain or white plate glass, and the floors of tile, all depending upon the grade and character of the building to be equipped. The in- sulation of smaller refrigerators con- sists of (1) an exterior course of ^^-in tongued and grooved lumber, (2) twa courses of water-proof insulating- paper and (3) a 3-in thickness of sheet cork in two ij^^-in courses, all joints being broken. To this insula- tion is applied the interior lining. Mortuary-Refrigerators. Mor- tuary-refrigerators should be cooled by mechanical refrigeration, the coils being placed longitudinally on both sides of the mortuary-trays. Fig. 4 illustrates a mortuary-refrigerator for three bodies. This may be used as a unit in designing mortuary-refrigera- tors of larger capacity, or the height may be reduced to 5 ft and the bodies placed in two instead of three PLAN Fig. 4.* Mortuary-rctrigerator horizontal tiers. Mortuary-refrigerators sometimes have both fronts finished and equipped with doors so that bodies are accessible for identification or examination from both fronts. * The Jcwett Refrigerator Company. 16S4 Mechanical Refrigeration Part 3 MECHANICAL REFRIGERATION* A Brief Description of Methods in Common Use for Producing and Applying Refrigeration, with Special Reference to Small Plants A British Thermal Unit, (Btu), is the quantity of heat required to raise the temperature of i lb of water i° F. Heat used in this way, that is, to raise the temperature of water or other substance, is said to be present in that sub- stance as SENSIBLE HEAT, or, in other words, beat, the presence of which we can feel, or sense. The Heat of Liquefaction, or so-called latent heat of liquefaction of a mass of ice, is the amount of heat it will absorb in melting. One pound of ice at 32° F. will absorb 144 Btu in melting to water at 32° F. Heat coming into a cake of ice is thus absorbed in melting the ice and becomes what is known as latent heat, or heat absorbed without any rise in temperature. If the ice is at a lower temperature than 32° F., or if the water resulting from the melting rises above 32° F., additional heat will be absorbed as sensible heat. The Specific Heat of a substance is the ratio of the quantity of heat required to raise the temperature of a certain weight of the substance one degree to that required to raise the same weight of water from 62° to 63° F. The Heat of Vaporization of water or of any other liquid is the amount of heat it will absorb in vaporizing, in evaporating from a liquid to a gas, or will give out in returning from the gaseous to the liquid state. Transfer of Heat occurs in three ways: (i) by convection, (2) by radiation , and (3) by conduction. For instance, if particles of air in a refrigerator ad- jacent to a source of heat become warmed they circulate and distribute the heat by convection through the refrigerator-box. Heat will pass from a warm sub- stance, as from the filament of an incandescent lamp, out into the box by RADIATION. Heat will enter the box through the walls by conduction. Heat-Transmission. When the temperatures on opposite sides of any sur- face, as for instance, a wall, are unequal, heat will pass by conduction through the material from the warmer to the cooler side. The rate of this movement is the RATE OF heat-transmission and is stated in terms of the quantity of heat called (Btu) which will pass through i sq ft of surface in 24 hours, per degree temperature-difference between the two sides of the wall. Some Advantages Claimed for Mechanical Refrigeration. (i) Lower temperatures can be obtained with refrigcrating-machines than with ice. (2) The inconvenience of handling ice is avoided. (3) There is no accumulation of slime in the refrigerators as from the melting of even the best, ice. (4) Refrigerators cooled mechanically are dryer than ice-cooled boxes because the moisture is frozen out of the air and deposited on the cooling surfaces. (5) There is generally a better air-circulation, resulting in a more uniform temperature and dryer atmosphere throughout the compartment. (6) With proper design of refrigerator and refrigeratirig-machine any de- sired temperature can be obtained. (7) Refrigeration produced mechanically is oftei^ p^eaper than refrigeration produced by melting ice. (See page 1695.) * CompUed and adapted, by permission, frqm data included in a paper by R. F. Massa, See, also, Refrigerators, pages 1679 to 1683, Types of Refrigerating-Ma chines 1685 Operation of Refrigerating-Machines. In almost all methods of producing cold, advantage is taken of the fact that when a liquid evaporates it usually cools both itself and its surroundings, and changes into a gas or vapor. There are several liquids which are easily made to evaporate and produce this cooling effect, and were it not for their cost, refrigeration could be very simply produced by supplying a steady stream of the hquid and allowing the vapor or gas evapo- rated to escape into the atmosphere. A refrigerating-machine is practically an apparatus for saving this gas which has evaporated and returning it to its liquid form to be used over again. In this process of recovery and condensation the gas gives out the heat which it has previously absorbed in evaporating. This heat is carried away by flowing water, which, in absorbing the heat, rises in -temperature. Types of Refrigerating-Machines. In the (i) compression-type of re- frigel-ating-machines the recovery of the gas is elTected by drawing it away from the point where it has been evaporated and pumping it under increased pressure into a chamber where it gives out its heat to the water-cooled walls of the chamber and returns to the liquid state ready to be used over again. In the (2) ABSORPTION-TYPE of refrigerating-machines ammonia is generally used and the recovery of the gas is elTected by bringing it into contact with water with which it unites chemically. The solution thus formed is pumped into another chamber, and heat is applied to drive off the ammonia-gas which is then condensed under high pressure. It is now ready to be reevaporated and reproduce its cool- ing effect. In all cases of large units, and in all cases of either large or small units where exhaust-steam is available in sufficient quantities, absorption re- frigerating-machines are very economical. Liquids Used in Refrigerating-Machines. A number of liquids have been used in refrigerating-machines, the ones commonly employed being (i) am- monia, (2) carbon dioxide and (3) sulphur dioxide. Various practical considerations determine which is to be used in any particular design of machine. With (i) ammonia the advantage is the lower working pressures, from 15 to 300 lb per sq in, which are easy to deal with. An advantage over carbon dioxide is that leaks are very easily located. Ammonia-fumes, however, are offensive and sometimes dangerous in case of a break. With (2) carbon dioxide the advantage is in its inoffensive odor. Its disadvantages are the high pressure at which it works, from 300 to i 200 lb per sq in, the relative difficulty of holding these pressures and of finding small leaks, owing to its slight odor and chemical inactivity. With (3) sulphur dioxide the advantage is its comparatively low working pressure, which is not above 75 lb per sq in. Its great disadvantage is that with moisture it forms an acid which rapidly corrodes the apparatus. At one time this disadvantage was fatal, since with the old-type machines, air and moisture were constantly being drawn into the system more or less rapidly and mixed with the sulphur dioxide. This difficulty has recently been overcome in some modern types of machines * in which the refrigerant is hermetically sealed in the machine and chemical action, therefore, prevented. Rating of Refrigerating-Machines. A i-TON refrigerating-machine is a machine which, if operated for 24 hours, -will absorb the amount of heat which I ton of ice would absorb in melting. If the machine is operated a shorter time per day, a less amount of heat will of course be absorbed, and in order to main- tain the temxperature during the period when the machine is not running, some * The Audiffren Refrigerating-Machine, a small machine intended for domestic uses and sold by the H. W. Johns-Manville Company, New York. There are many other reliable firms making refrigerating-machines of other distinct types, and the architect should look carefully into the merits and claims of each when called upon to specify them. 1G86 Mechanical Refrigeration t*art 3 means must be adopted for storing cold. (See paragraph below.) Ref rigerating- machines are sometimes rated in terms of ice-making capacity, that is, in terms of the amount of ice the machine will make in 24 hours. This is always less than the refrigerating capacity because some refrigerating effect is required to cool the water down to 32° F. before the freezing can begin, and the ice is usually cooled several degrees below*32° F., which requires a still greater capacity. There is also some flow of heat into the apparatus. These elements vary considerably so that from some points of view ice-making capacity might be considered an unsatisfactory method of rating some refrigerating-machines. Applying the Cold. According to one classification there are three common systems of applying the cold. These are, (i) the direct-expansion system, (2) the brine-system and (3) the cold-air system. (i) In the direct-expansion system the refrigerant is evaporated in coils of pipe placed directly in the room to be cooled. (2) In the brine-system the refrigerant is used to cool brine, which is then circulated through coils of pipe in the room to be cooled. (3) In the COLD-AIR system a current of air is chilled by passing it over coils of pipe cooled directly by the evaporating refrigerant, or by brine, or by passing it through a spray of cold brine; and this chilled air is then passed into the room and circulated back to the cooling-coils, the whole operation being repeated indefinitely. All of these systems have their advantages and disadvantages. While the brine-system is a little more expensive to operate in large plants, the temper- ature is more easily controlled than with the direct-expansion system, and in practice in small plants it is found as economical in operation in spite of its theoretical disadvantage. Furthermore, in case of any breakdown in the ma- chine, the temperature can be held for a time by circulating the brine until it becomes too warm to be of use, whereas with direct expansion the temperature will begin to rise immediately upon the stopping of the machine. The cold-air system is not as applicable where any drying of the goods stored would be harm- ful and there is some risk of carrying fire in the air-passages. It is much used, nevertheless, for such service as chocolate-dipping rooms, ice-cream hardening, fur-storages, etc. Storage of Cold. When temperatures are to be maintained while the refrig- erating-machine is shut down, cold must be stored. In the brine-system this is effected by cooling a comparatively large body of brine which warms slowly as it is circulated. Where the brine-circulating pump as well as the machine must be stopped, so-called pressure-tanks may be placed in the piping- system in the room being cooled; the mass of brine in these tanks absorbs the heat and helps to maintain an approximately even temperature. Where the direct-expansion system is used, a part of the cooling-coils may be immersed in a tank of brine placed in the room and the remainder of the coils arranged for the direct cooling of the room. In some places the spaces avfiilable will not permit the use of brine-storage tanks. In cases of this kind smaller tanks may be used and filled with water, or a weak brine which will freeze at a tempera- ture a little below 32° F. Since i lb 'of ice in melting will absorb 144 Btu and 1 lb of brine rising in temperature, say 26^, will absorb only from 14 to 16 Btu, the saving of space is apparent. It must be absolutely certain that the refrig- erant reaches the tank first at the bottom and that the air to be cooled reaches it first at the top so that the ice in forming shall not bulge or burst the tank. If the congealing mass were to freeze from the top down the tank would be strained and finally leak, because of the expansion of the ice in freezing. An- other fact to be considered is that where water, only, is frozen, a resulting high Description of Refrigerating-Machines 1687 temperature may be olitaincd in the refrigerator, since the brine must be warmer than the ice in order to melt it, and the refrigerator just that much warmer, or warmer than an ice-cooled box. In calculating the proper sizes of tanks for storing brine, it should be remembered that, usually, the period during which the machine is shut down coincides with the period during which the demand for refrigeration in the box is the least. The amount of heat to be absorbed is usually only that entering through the insulation, as the doors are shut and no food is put in or removed. Description of Refrigerating-Machines. As explained in the preceding paragraphs refrigerating-machincs may be divided generally into two classes, (i) the COMPRESSION-TYPE and (2) the absorption-type. (i) The Compression-Type of Refrigerating-Machines may be subdivided as follows: (a) The open type of machine, which is made both vertical and horizontal, and both single and double-acting, that is, compressing the gas at one end or at both ends of the cylinder, {b) The partially enclosed type of machine, in which all the moving parts of the compressor proper are enclosed within the frame of the compressor, except the fly-wheel and the main shaft which enters the frame of the machine through a stuffing-box. Such valves, also, as are required in the system are exposed, (c) The wholly enclosed type of machine,* in which all of the working parts are enclosed in a hermetically sealed container. (a) One advantage of the open type of machine is that any lack of adjustment due to wear can be readily corrected; so that, with proper attention, it gives excellent results. For large installations this is considered by many to be a most efficient type of machine. (b) The enclosed type of machine resulted from the effort to reduce the amount of attention required by the open machine, to cheapen its construction and to reduce the possibility of trouble from inexpert tampering. An objection to machines of this type is that when adjustments have to be made the working parts are relatively inaccessible. (c) With the wholly enclosed type of machine it is claimed that the loss of the refrigerant is prevented by the hermetical sealing of the apparatus, and that the working parts, being completely enclosed, are protected from deterioration due to outside causes or tampering. (2) The Absorption-Type of Refrigerating-Machines are of two kinds, differ- ing principally in the .proportioning of the parts. In the one machine high-pres- sure steam is used; in the other the proportions are such that low-pressure or exhaust-steam may be used. Where exhaust-steam is available machines of this type are found to be very economical, and this is true, also, for all large units whether or not exhaust-steam is used. Full descriptions of these machines with detailed plans and layouts may be obtained from the various manufacturers. Calculations for the Capacity of a Refrigerating-Machine. Heat enters the refrigerated compartments, (i) through the walls, (2) with warm goods, (3) by the interchange of the outside air when doors are opened and by air-leaks, since the cooled air is the heavier and immediately flows out when a door is opened, (4) from lights or from the heat of the bodies of workers, and (5) from any change of state occurring in the goods, such as freezing, fermenting, etc. In large rooms these various sources of heat should be analyzed sepa- rately. In small refrigerators, as in hotels, kitchens, dwellings, etc., a rough rule, quite as accurate as a more elaborate analysis, allows a certain number of Btu per cubic foot of refrigerated space per 24 hours. This amount varies ? Referred to on page 1685. 1688 Mechanical Refrigeration Part 3 with the character and location of the box, the nature of its insulation, the tem- peratures desired and so on. It will be seen that the insulation, while of great importance, is not by any means the only important factor in this class of boxes. For domestic refrigerators in which a temperature of from 35 to 50° F. is maintained, soo Btu per cu ft of refrigerator per 24 hours should be allowed. For boxes in hotel or restaurant-kitchens, 600 Btu, or even 900 Btu in ex- treme cases and where low temperatures are required, should be allowed. For butchers' coolers or large storage-boxes in hotels, etc., from 2cx> to 250 Btu per cu ft per 24 hours should be allowed. A check on the above figures for the large type of box is the following: * "When the exact conditions under which cold-storage rooms are to be operated are known, namely, the size and shape of the rooms, the quality of the insulation, the kind and quantity of goods to be handled per day and the temperatures at which they are received and at which they are to be held, the amount of refrigeration required can be estimated very closely by the following rule: (i) Calculate the exact area of exposed surface in the walls, floor and ceiling of the room in square feet, multiply the total num- ber of square feet by the number given in the table for the required tempera- ture and divide the product by 288 000. (2) Multiply the amount of goods, in pounds, to be stored per day by the number of degrees of heat to be extracted by the specific heat of the goods, and divide by 288 000. This will give the amount of refrigeration, in tons per day, necessary to maintain the tempera- ture required for the goods. (3) Add these two amounts together. The total will be the amount of refrigeration, in tons per day, required to maintain the temperature required for the goods and for the room. (4) If the goods are to be frozen, the latent heat of freezing should be added to the number of Btu to be extracted." For rooms containing less than i 000 cu ft If maintained at 0° F. multiply the exposed surface by t 775 If maintained at 5° F. multiply the exposed surface by 710 If maintained at 10° F. multiply the exposed surface by 535 If maintained at 20° F. multiply the exposed surface by 3^5 If maintained at 32° F. multiply the exposed surface by 265 If maintained at 36° F. multiply the exposed surface by 180 For rooms containing from i 000 to 10 000 cu ft If maintained at 0° F. multiply the exposed surface by ] 250 If maintained at 5° F. multiply the exposed surface by 600 If maintained at 10° F. multiply the exposed surface by 300 If maintained at 20° F. multiply the exposed surface by.. 190 If maintained at 32° F. multiply the exposed surface by 160 If maintained at 36° F. multiply the exposed surface by 125 For rooms containing more than 10 cxx) cu ft If maintained at 0° F. multiply the exposed surface by ] 100 If maintained at 5° F. multiply the exposed surface by 550 If maintained at 10° F. multiply the exposed surface by 275 If maintained at 20° F. multiply the exposed surface by 180 If maintained at 32° F. multiply the exposed surface by 140 If maintained at 36° F. multiply the exposed surface by no * Taken from Levey's Refrigeration Memoranda, page 41. Capacities of Refrigerating-Machines 1689 With small machines it is necessary to allow a greater capacity of machine for a given size of box than with large machines, since, with the latter, one can always throw a large part of the machine-capacity to any given box where special need may exist; whereas to do this with the small machine would almost certainly rob some other box, if indeed there happened to be another box. It is never possible to determine with mathematical certainty exactly how much refrigeration is required for a given case. It is best to allow for this fact and to be sure the machine is amply large. Where an existing ice-cooled box is to be cooled mechanically one check upon the size of the machine required is the amount of ice used. This check is more apt than any other, however, to lead to erroneous conclusions unless the figures are properly analyzed. Another Method of Determining the Capacity of a Refrigerating-Machine. The following is a method that gives good results, except that allowance may be made in the larger boxes and where brine-storage tanks are provided in the box for the steadying effect of the mass of cold brine: (i) The ice-consumption for the hottest month of the year should be deter- mined. This will give the average ice-consumption for that month. (2) The average temperature that is maintained in the box with ice should then be accurately determined. This will usually be from 55 to 65° F. It will commonly be stated to be anywhere from 40 to 45° F., but these temperatures are seldom obtained. Even if they are, with a full ice-chamber and the box closed for long periods the average will be above these figures. Unless, there- fore, there is positive assurance to the contrary, from 55 to 60° F. should be considered the average temperatures. (3) A calculation should then be made of the heat-inflow through the insula- tion, with a temperature of 55° F. in the box and with the average summer temperature outside. The difference between the heat-inflow through the insulation and the total heat actually absorbed by the melting of the ice is the amount entering the box from other sources than through the insulation. This access of heat ordinarily occurs during the hours of daytime only, that is, when the box is being opened, since at night the box will remain closed. A machine of sufficient capacity to produce the temperature actually obtained with ice must, therefore, be of larger rated capacity than that indicated by the actual ice-consumption; and how much larger it should be can be determined by this method. (4) A further fact which it is claimed should be taken into account m deter- mining the proper size of a machine is that temperatures obtainable with ice are often unsatisfactory. If they were always satisfactory one reason for put- ting in cooling-machinery would be done away with. Where 55° F. is obtained with ice, from 35 to 45° F. will be required with mechanical cooling and the machine-size must be further increased in the ratio of the temperature-differ- ences between average summer temperatures and 35° F., and average summer temperatures and 55° F. . , , /- 1 j (5) The cooling-machine if installed in accordance with these figures would handle average-weather conditions but would not be adequate for extreme hot-weather conditions, the most important conditions to be met by cooling- machinery. It is necessary, therefore, to further increase the size of the machine in the ratio of the difference in temperature between maximum summer tem- perature and 35° F., and average summer temperature and 35° F. (6) A further allowance should be considered, namely, the fact that in many cases for one reason or another, it is not possible, or else not desirable, to oper- ate the machine except during certain periods of the day, and the machine-size must be increased as much as may be required to take care of these conditions. 1690 Mechanical Refrigeration Part 3 f ^ (7) If the machine is not placed directly at the box to be cooled, allowance must be made for the heat-inflow into the insulated brine-mains. The amount of heat entering from this source is often of considerable importance, particu- larly with small machines. The table below gives heat transmissions for cork pipe-covering and some other materials. Water and Milk-Cooling. Mechanical refrigeration as apphed to cooling Water and milk differs in one respect from other classes of refrigerating-work. A relatively intense quantity of cooling effect is called for in a brief interval of time. For instance, in a drinking-water system the heaviest requirements may come at the noon-hour. In a bakery, also, the demand for chilled water will be intermittent, a large quantity of water being required for the dough- mixing. In dairy- work the milk must be cooled very rapidly to check the development of bacteria which grow with incredible rapidity within the tem- perature-rangc of from no to 50° F. To install a large enough refrigerating- machine to produce the required cooHng effect as it is needed would in most cases call for a very large machine. This is overcome by using a smaller machine and allowing it to operate for a longer time, say throughout the day, storing the refrigerating effect produced by cooling a large body of brine, or melting the ice as rapidly as may be required. For instance, if 50 cans of milk, of 40 qts each, are to be cooled from a temperature of from, say, 75 to 35° F., in I hour, the refrigcjation required will be 50 cans times 40 qts times 2 lb per qt times (75° F. — 35° F.), which eciuals 320000 Btu. Milk is treated in the calculation as having the same specific heat as water, since water forms so large a percentage of its total weight. This amount of refrigeration pro- duced by a machine running 12 hours per day would require the machine to absorb 320000 Btu divided by 12, or 26 000 Btu per hour. The quantity of brine necessary to store the cooling effect may be calculated closely enough for practical purposes by using the following approximate figures. The specific heat of brine is 0.75. The weight of the brine is 9 lb per gallon. The permis- sible temperature-range of the brine dei^cnds upon the conditions and may be from, say, 30 to 15° F., or lower. In other words, the temperature to which the brine can be permitted to rise is limited to the temperature it must produce in the room or in the substance being cooled, and the temperature to which the brine can be cooled in storing cold is limited by the decrease in economy of the rcf rigerating-machine at the low, temperatures. The Value of Good Insulation. (See, also, Insulation, page 1683 ) The importance of good insulation cannot be too strongly emphasized. A cold- storage room or refrigerator and its contents may be cooled by ice or mechani- cal means, but unless the walls are adequately insulated, the demand caused by the inflow of heat through the poor insulation may be more than the ice- supply or refrigerating-machine can meet to maintain the required tempera- ture. The almost universal standard of insulation for cold-storage rooms is a 4-in thickness of pure-cork sheet. The following table shows the heat trans- mitted through I in in thickness of each of the substances, per square foot of exposed surface per degree difference in temperature j>er 24 hours. Pure-cork sheets 6.4 Btu Hair-felt 7-3 Btu Impregnated cork boards 8.5 Btu Rock-wool blocks 8 . o Btu Waterproofing lith-blocks ' 8.5 Btu SprUce, clear and dry 16 . o Btu White oak 26.0 Btu \ Design of Refrigerator 1691 Design of Refrigerators. Disposition of Cooling-Surfaces. (See, also, subject of Refrigerators, page 1679.) No attempt need be made to describe all of the many arrangements of refrigerated compartments that are to be found in service. The intention is to point out some of the more important things to be considered in determining upon the design of a box. It is desirable in a refrigerator to produce not only a low temperature, but a relatively dry atmos- phere. Cooling-Surface and Temperature. Securing the low temperature is merely a question of supplying sufficient cooling-surface to produce the desired results with the temperature available in the refrigerant. The amount of surface required is influenced by the arrangement of the box, that is, whether or not the air passes freely or sluggishly over the surface, whether the cooling-surface is placed on the ceiling or walls of the compartment or in a loft and, if the latter arrangement is used, whether or not the air-passages are of proper size and the circulation between the loft and the compartment sufficient. Dryness of Atmosphere and Temperature. To secure a box of satisfactory dryness it is necessary to have a relatively low temperature in the refrigerant. The air which passes over the cooling-surfaces is practically in a saturated con- dition when it leaves them. If it is to be dry at the temperature required in the box, it must have been, necessarily, cooled well below the box-temperature. For instance, in a box, the temperature of which is maintained at 35° F., the brine should be run at a temperature of from about 20° to 25° F. It is further desirable to so locate the cooHng-surface that frost in melting will pass out of the box quickly and not remain to be reabsorbed by the air in the box. Arrangements of Cooling~Surface&. There are several common arrangements of cooling-surfaces in refrigerators. Sometimes the coils are arranged overhead, but directly in the compartment to be cooled. This is one of the efficient ways in which a cooling-surface can be arranged, so far as the cooling effect alone is concerned. It is not, in general, a good arrangement, however, since frost melting from the coils drips on the goods. In another arrangement the cooling- surfaces are on the wall. This is preferable to the ceiling-arrangement, as far as the dripping is concerned. The objection to it is that goods placed close to the walls are apt to be overchilled, while goods nearer the center of the com- partment are not cooled quickly enough. It also wastes floor-space, because packing goods close to the coils is not practicable on account of possible over- chilling and also on account of the liability of retarding the air-circulation. The wall-arrangement for cooling-surfaces is, nevertheless, often the most practica- ble method. Another method involves a modified form of wall-coil arrangement in which a brine-storage tank is used to assist in maintaining the temperature when the machine is shut down. A further modification is often introduced, in which a partition or baffle-plate is used in front of the coils. The best types of box-arrangement are those in which the cooling-surface is separated from the storage-space and is so arranged as to secure an active circulation of the air over the coils and through the compartments. In all of these plans the one requirement calling for the .greatest care is that the air-passages shall be as direct as possible and of ample size. The force causing the air to circulate, namely, the difference in weight due to differences in temperature and density between the column of air in the coil-compartment and that in the storage- compartment, is so extremely small that any slight interference is a serious matter. An extra turn in the passage or a slight reduction in the size of the passage will produce a marked effect. A good rule to follow is to make the passage as large as it can be made without allowing any drip to reach the storage-compartment. This will work out in many cases to show a ratio of 1692 Mechanical Refrigeration Part 3 I to 8 or 9 between the area of the passage and the floor-area of the compart- ment; but even i to 6 is just that much better if it can be secured. The matter of proportioning the size of the air-passages is of much less importance where the air is circulated by fans. Forced circulation is not usual, however, except in large storage-refrigerators, and no attempt will be made here to consider it. One precaution that must be taken in arranging the cooUng-surface, especially in small and frequently opened boxes, is the avoidance of any undue cooling of walls or ceilings that are exposed to currents of warm air when the door is opened. Moisture from the incoming air deposits on these surfaces and causes the offensive so-called sweating of the box. This is most often seen on the storage-compartment side of uninsulated coil-compartment floors or partitions, and also occurs on walls or ceihngs where the cooling-pipes are set very close to these surfaces. The obvious and effective cure is to insulate the partitions between coil-compartments and storage-compartments and keep cooling-sur- faces well away from walls or ceilings, from 3 to 8 in, depending upon the tem- perature of the brine. Incidental Notes on Refrigerators. Drawers. In restaurant-kitchens and elsewhere it is sometimes convenient to have a box fitted with a number of refrigerated drawers. The heat-leakage through the many joints, through shdes which are invariably only partially closed, and through the poor insula- tion of the drawers, is very great. Where it is at all possible to do so, it is best to arrange an insulated door covering the entire drawer-space. Anterooms. In storage-rooms of medium to large size the air-interchange due to opening doors is reduced to a minimum by arranging an anteroom or entry which, after it is entered, has its outer door closed before the door to the storage-room proper is opened. Where two rooms are side by side, it is often possible to reduce the interchange of air by treating the one room as an ante- room of the other, having but one door to the outside air. Doors.' Special note should be made as to the design of doors for refrigerated rooms or boxes. There is a common idea that a refrigerator-door should be beveled. As a matter of fact no more certain means of ensuring air-leakage could be devised. A perfectly fitted beveled door, hung accurately in place, could perhaps be made tight in the beginning. This door in service at once begins to sag, since a refrigerator-door is always heavy. It immediately be- comes impossible to force it to a tight seat and continuous leakage of air begins. A refrigerator-compartment door is most readily made tight by having a flat surface on the door come up against a corresponding surface on the frame, with a soft gasket of some kind between them. There are several well made re- frigerator-doors on the market at prices low enough to make it doubtful economy to attempt the home-made article. Arrangement of Brine-Mains. In laying out mains to carry brine from the refrigerating-machine to the refrigerator, there are a few simple points to be cared for. For the convenience of the pipe-covering man, the flow and return lines should be placed far enough apart so that he can get his covering onto each pipe without cutting it to pieces, or else they should come close together so as to be covered together. A common difficulty experienced in brine-sys- tems of refrigeration, where the cooling-coils in several compartments are fed from the same main, is that when the adjustment of the valve controlling the flow of brine through one coil is changed, it upsets the adjustment of the whole system. This is due to too small mains or too small a pump, or both. A similar action is observed when the opening of a faucet on a water-pipe checks the flow from other open faucets on the line. The ideal cross-section area of Calculations for Cooling- Surfaces 1693 the brine-mains is as nearly as possible equal to the combined cross-section area of the coils which they serve at any one time. Even with this proportion, however, it is not possible to absolutely ensure that the lower coils will not rob the upper ones, or even drain them completely in some systems of piping. A most effective, even if somewhat expensive method of overcoming this diffi- culty, is by the addition of a third main. In this arrangement it is not possible for one coil to rob another to the point of draining it. Calculations for the Necessary Amount of Cooling-Surfaces. No hard and fast rule can be given regarding the proper amount of coohng-surface for compartments of various sizes, since the design and arrangement of the cooling-surface and the freedom with which the air circulates over it greatly affect the amount required. As a general guide, however, and where the con- ditions are such as to permit a good circulation of the air, the following formula will give good results. It will be understood, of course, that the refrigeration required in the given room has been determined as previously indicated. The cooling-surface required, in square feet, per ton of refrigeration equals 4 7oo/(r— t) in which T is the temperature desired in the compartment, and i the average temperature of the brine. Approved Cold-Storage Temperatures Articles stored Degrees Fahrenheit Beef Lamb and mutton • • Hogs Veal M'eats, in pickle or brine Butter, must be kept separate from other goods Eggs Cheese Lard Poultry, to freeze Poultry, when frozen Game, to freeze Game, when frozen Fish, retail fish-counters should be cooled with ice rather than mechanically Oysters Beer Wines Cider Fruits Vegetables • Canned goods Flour and meal Furs Brine for ice-cream freezing Ice-cream, air-hardening Ice-cream, serving-temperature 36 to 40 32 to 36 29 to 32 34 to 36 35 to 40 oto38 29 to 32 32 to 34 38 to 40 5 to 10 25 to 28 5 to 10 25 to 28 25 to 28 33 to 45 33 to 42 40 to 45 30 to 40 33 to 36 34 to 40 38 to 40 40 25 to 32 5 to 10 S 14 to 16 Ice-Making. If the following facts of physics are kept in mind in consider- ing methods of making ice the results obtainable may be understood or pre- 1694 Mechanical Refrigeration Part 3 (i) Chemically pure water will freeze solid and clear. (2) Water containing impurities in solution tends in freezing to force these impurities out of solution. The slower the process of freezing the more completely is the purification effected. (3) Ice forming in still water sends out long slender crystals which increase in number and size, forming a meshwork that gradually becomes a solid mass. (4) Agitation of water during freezing aids in the separation of impurities and therefore in forming solid, clear ice. (5) Practically all natural waters contain more or less organic or inorganic material in solution and invariably contain air in solution. These substances are, therefore, frozen out of solution and tend to cause the ice formed to be opaque, the lighter substances tending to rise and collect near the surfaice, and the heavier ones tending to sink. (6) The rate of freezing of ice decreases as the thickness already formed increases, so that the time required to freeze increases as the square of the thickness to be frozen. In the formation of natural ice the freezing is from the top down and impurities frozen out of solution fall. This and the motion of the water, especially in quiet running streams, tends to make naturally frozen ice transparent. American manufac- turers of ice have always tried to duplicate this clearness- Methods of Ice-Making. The method first adopted in this country was the one in which distilled water was used. From a sanitary point of view such ice would be theoretically ideal. Practical difiicultics make it almost impos- sible to secure pure ice in this way. Some of these difl5culties are: (i) Removal of oil from the distilled water, this oil being picked up as the steam passes through the cylinder of the engine. It is difficult to remove organic oil which is present in the lubricant. (2) Assurance that the filters are in proper shape, an assurance often impos- sible to obtain since this apparatus is ordinarily used the season through without overhauling. (3) Possibility of contamination in the storage-tank where the distilled water is held and usually precooled to as near 32° F. as possible, before passing to the freezing-cans, thus saving time in the freezing process in the tank. (4) Possible contamination from handling the cans and the wooden covers over them. These covers form the top of the freezing-tank in which the cans of water are immersed in cold brine for freezing and are tramped over by the ice-harvester with the consequent possibility of dirt getting into the cans. A second system of ice-making in common use in this country is the plate system. In this process the ice is formed on vertical steel plates. Natural or raw water is used and the bath is agitated by various methods. The re- sulting ice is very clear and dense. In this system when the ice is formed to the desired thickness, usually about 12- in, it is loosened from the freezing- plate by various thawing-arrangements in different forms of the apparatus. The ice-plates, often 9 by 16 ft by 12 in in thickness, are lifted from the tanks by overhead cranes and carried to a table where they are cut to commercial sizes. While the plate process is usually very slow on account of the fact that the freezing is from one side only, it is largely used and lends itself to great economy in steam-consumption, whereas in the old-style distilled-water ice- • making plant the amount of steam required to make the ice was more than an Tower-Clocks 1695 economical engine would use and it was not possible to obtain fuel-economy. One modified form of this system, now coming into considerable favor, is aiiaiiged so that stationary CANS are filled with raw water and kept agitated l)y compressed air bubbling up through it. When the freezing has progressed somewhat the remaining water is drawn off and replaced by fresh water, thus removing the greater part of the impurities that have been frozen out of solu- l ion. Various other modifications of these two systems of ice-making have been and are being developed. All of them depend, however, upon the series of pli\sical facts stated in the preceding paragraphs, and the results may be analyzed by reference to them. Relative Economy of Producing Refrigeration Mechanically and by Ice. (i) In determining the cost of refrigeration by ice, account must 1)1' taken not only of the cost of the ice but of melting, of the uncertain ice- harvest, of the amount of ice left over at the end of the season and of that ffo/cn together in the storage and, therefore, practically useless. Regarding the melting, it may run anywhere up to 50% of the total ice-harvest. The c, which it resembles when on the base of a column; scotia^ from SKOTiA, darkness, because of the strong shadow cast in its hollow, and which is increased by the projection of the torus above it; ovolo, from ovum, an egg, which this member resembles when carved, as in the Ionic capital; cavetto, from CAVus, hollow; cymatium, from Annulet, iand, ciucturl. fillet. Aat L«. or bei KUMATON, a WaVC. 3 [^ ""^^''"^^^ "^^^ Characteristics of Moldings. None of these moldings is pecuHar to any one of the orders of architecture; and although each has its appropriate use, it is by no means confined to any certain position in an assemljlage of OtoIo, quarter-round, or echinus. Cavetto, cove, or hollow. moldiugS. The USC of tllC fillet and also of the astragal and torus, which resemble ropes, is to bind the parts. The ovolo and cyma-reversa are strong C7 XT Cjmatium,orcyma-re.ta. i-^verte^cymatium, or ^t their uppcr extremities, and are therefore used to support projecting parts above them. The cy ma-recta and cavetto, being weak at their upper extremities, are not used as supporters, but are placed uppermost to cover and shelter the upper parts. The scotia is introduced in the base of a column to separate the upper and lower torus, and to produce a pleasing variety and relief. The form of the bead and that of the torus are the same; the reason for giving distinct names to them is that the torus, in every order, is always considerably larger than the bead and is placed among the base-moldings, whereas the bead is never placed there, but on the capital or entablature. •The torus, also, is seldom carved, whereas the bead is; and while the torus, among the Greeks, was frequently elliptical in its form, the bead retains its circular shape. While the scotia is the reverse of the torus, the cavetto is the reverse of the ovolo, and the cyma-recta and cyma-reversa are combinations of the ovolo and cavetto. THE CLASSICAL ORDERS* Origin of the Orders. "In the classical styles several varieties of column and entablature are in use. These are called the orders. Each order comprises a COLUMN with a base, shaft and capital, with or without a pedestal, with its BASE, DIE and CAP, and is crowned by an entablature, consisting of architrave, FRIEZE and CORNICE. The entablature is generally about one-fourth as high as the column, and the pedestal one-third, more or less. Among the Greeks the forms used by the Doric race, which inhabited Greece itself and had colonies in Sicily and Italy, were much unlike those of the Ionic race, which inhabited the western coast of Asia Minor, and whose art was greatly influenced by that of Assyria and Persia. Besides the Ionic and Doric styles, the Romans devised a third, which employed brackets, called modillions, in the cornice, and was much more elaborate than either of them; this they called the Corinthian. They used also a simple Doric called the Tuscan, and a cross between the Corinthian and Ionic called the composite. These are the five orders. The * The paragraphs in quotation-marks are taken from The American Vignola by Pro- fessor W. R. Ware, by permission of the owners of the copyright, the International Text- book Company, Scranton, Pa., proprietors of the International Correspondence Schools. The engravings were made especially for this book, and correspond with the original drawings prepared by Giacorao Barozzi da Vignola. Tuscan, Doric and Tonic Orders 1699 ancient examples vary much among themselves and diftcr in different places, and in modern times still further varieties are found in Italy, Spain, France, Germany and England. The best known and most admired forms for the orders are those worked out by Giacomo Barozzi da Vignola in the sixteenth century from the study of ancient examples." The Tuscan Order. "The distinguishing characteristic of the Tus- can ORDER (Fig. 1) is simplicity. Any forms of pedestal, column and entablature that show but few moldings, and those plain, are con- sidered to be Tuscan." The Doric Order. "The distinguishing characteristics of the Doric order are fea- tures in the frieze and in the bed-mold above it called triglyphs and MUTULES, which are sup- posed to be derived from the ends of beams and rafters in a primitive wooden construction with large beams. Un- der each triglyph, and beneath the taenia which crowns the architrave, is a little fillet called the REGULA. Under the regula are six long drops, called GUTT^, which are sometimes conical, some- times pyramidal. There are also either eighteen or thirty-six short cylin- drical guttai under the soffit of each mutule. The guttai are supposed to represent the heads of wooden pins, or treenails. Two different Doric cor- Dices are in use, the mutulary with bracket and the denticulated with dentils, the principal difference being in the bed-mold." The order shown in Fig. 2 has the denticulated cornice. The Ionic Order. "The prototypes of the Ionic order (Fig. 3) are to be found in Persia, Assyria, and Asia Minor. It is characterized by bands in the architrave and dentils in the bed-mold, both of which are held to represent small sticks laid together to form a beam or a roof. But the most conspicuous Dimensions are in 24thK of Diameter, Fig. 1. The Tuscan Order 1700 Classical Orders Part 3 and distinctive feature is the scrolls which decorate the capital of the column. These have no structural significance, and are purely decorative forms derived from Assyria and Egypt. Originally the Ionic order had no frieze and no ECHINUS in the capital. These were borrowed from the Doric order, and, in X T II U-iuuuaiuuuTxi r— t^ T . I I > ,k- :lrD^2i Dimensions are in 2iths of Diameter Fig. 2. The Doric Order like manner, the dentils and bands in the Doric were borrowed from the Ionic. The Ionic frieze was introduced in order to afford a place for sculpture, and was called by the Greeks the zoophorous, or figure-bearer. The typical Ionic base is considered to consist mainly of a scotia, as in some Greek examples. It is common, however, to use instead what is called the Attic base, consisting of a Ionic Order 1701 ^ ^i^p jz;j Plmeusions are ia 24ths of Diameter. Fig. 3. The Ionic Order 1702 Classical Orders Part 3 SCOTIA and two fillets between two large toruses, mounted on a plinth, the whole half a diameter high. The plinth occupies the lower third, or one-sixth of a diameter. Vignola adopted for his Ionic order a modification of the Attic base, substituting for the single large scotia two small ones, separated by one or two beads and fillets, and omitting the lower torus. " This is the base shown in Fig. 3. "The Ionic frieze is plain, except for the sculpture upon it. It sometimes has a curved outline, as if ready to be carved, and is then said to be PULViNATED, from pulvinar, a bolster, which it much resembles. The shaft of the column is ornamented with twenty-four FLUTmos, semicircular in section, which are separated not by an arris, but by a fillet of about one-fourth their width. This makes the llutings only about two-thirds as wide as the Doric channels, or about one-ninth of a \ ! ', diameter, instead of one-sixth." \ l\ ; To Describe the Ionic Volute. \ I \ I There are several methods of doing ^^_Juj>l this, the simplest being by means of /^ /'''^ ^v |\ centers found as shown by the diagram /__h^_l_\_xA^ \ i" Fig. 4. First locate the center of ---/■-/^p^^4A--^^5\^\ the EYE M D vertically below the ""//^^■"^"t^vj^ \J point A, Fig. 3. Then describe a f\ 1 1^3^^^^^-'----/ circle with a diameter equal to Ms D, \^\'/rT~''" 8^7,7^7 ^^ ^^''"^ ^^^ ^y^- Inside of this circle \ ^\ f'^~~~/* / inscribe a square at 45 degrees to a \s! \^ I / 'y horizontal ; then draw the axes 1-3 _i^^jr-N/l-'^■"'^ and 2-4, and divide each of these into ' J I six equal parts. Then with the point I ! ! I as a center, and a radius extending ' ' to /!, Fig. 3, draw a quarter-circle to Fig. 4. The Ionic Volute line 1-2 produced, with 2 as a center, continue the curve until it intersects 2-3 produced, and so on. The centers for the outer curve of the volute are at the points i, 2, 3, 4, 5, 6, etc. For the centers for the inner curve, start with a point one-third the way from i to 5, then a point one-third the way from 2 to 6, and so on. The Corinthian Order. "The three distinguishing characteristics of the Corinthian order (Fig. 5) are a tall, bell-shaped capital, a series of small brackets called modillions, which support the .cornice instead of mutules, in addition to the dentils, and a general richness of detail which is enhanced bv the use of the acanthus leaf in both capitals and modillions. Here, again, the Attic base is commonly used, but sometimes, especially in large columns, a base is used which resembles Vignola's Ionic base, except that it has two beads between the scotias instead of one, and also a lower torus. The shaft i^ fluted like the Ionic shaft, with twenty-four semicircular flutings, but the^ are sometimes filled with a convex molding or carle to a third of their height. Almost all the buildings erected by the Romans employ the Corinthian order." The Composite Order. "The composite order is a heavier Corinthian, just as the Tuscan is a simplified Doric. The chief proportions are the same as in the Corinthian order, but the details are fewer and larger. It owes its name to the CAPITAL, in which the two lower rows of leaves and the caulicoli are the same as in the Corinthian. But the caulicoli carry only a stunted leaf-bud, and the upper row of leaves and the sixteen volutins are replaced by the large echinus, scrolls and astragal of a complete Ionic capital. Vignola's com- posite entablature differs from his Ionic chiefly in the shape and size of the Corinthian Order 1703 (H%- r~\ %' dL- -■ 7- " J --- - D = 21 v^ - - I I k I 1- t_.J J Dimensions are in 24ths of Diameter THE CORINTHIAN ORDER E«. 5. The Corinthian Order 1704 Lightning-Conductors Part 3 DENTILS. They are larger, and are more nearly square in elevation, being one- fifth of a diameter high and one-sixth wide, the interdentil being one-twelfth, and they are set one-fourth of a diameter apart, on centers. The composite capital is em- ployed in the Arch of Titus in Rome, and elsewhere, with a Corinthian entablature, and the BLOCK CORNICE occurs in the so- called FRONTISPIECE of Nero, as well as in the temple at Athens, in connection with a Corinthian capital." Egyptian Style.* The archi- tecture of the ancient Egj^'ptians is characterized by boldness of outline, solidity, and grandeur. The principal features of the Egyptian style of architecture are: uniformity of plan, never deviating from right lines and angles; thick walls, having the outer surface slightly deviating inwardly from the perpendicular; the whole building low; roof flat, composed of stones reaching in one piece from pier to pier, these being supported by enor- mous columns, very stout in proportion to their height; the shaft sometimes polygonal, hav- ing no base, but with a great variety of handsome capitals, the foliage of these being of the palm, lotus and other leaves; entablatures having simply an ARCHITRAVE, crowned with a huge CAVETTO ornamented with sculpture; and the intercolum- NiATiON, very narrow, usually 1 1/2 diameters and seldom ex- ceeding 2 3^2. A great dissimi- larity exists in the proportions, forms and general features of Egyptian columns. For practical use the column shown in Fig. 6 may be taken as a standard of the Egyptian style. Fig. 6. An Egyptian Order. Diameter Divided into Sixty Parts LIGHTNING-CONDUCTORS Rules for the Erection of Lightning-Conductors. The following rules for the erection of lightning-conductors were issued in 1882 by the Department of Explosives of the English Home Office to the occupiers of all factories and maga-: ' From The American House Carpenter, by R. G. Hatfield. Lightning-Conductors 1705 zines for explosives, and to those local and police authorities upon whom de- volves the inspection of stores of explosives: (i) Material of Rod. Copper, weighing not less than 6 oz per ft run, the {electrical conductivity of which is not less than 90% of that of pure copper, [either in the form of rod, tape, or rope of stout wires, no individual wire being less than No. 12, Birmingham Wire-Gauge (0.109 in) the English standard wire-gauge. Iron may be used, but should not weigh less than 2H lb per foot of run. (2) Joints. Every joint, besides being well cleaned and screwed, scarfed, or riveted, should be thoroughly soldered. (3) Form of Points. The point of the upper terminal * of the conductor should not have an angle sharper than 90°. A foot below the extreme point a coi)[)cr ring should be screwed and soldered on to the upper terminal, in which ring should be fixed three or four sharp copper points, each about 6 in long, it is desirable that these points should be so platinized, gilded, or nickel-plated as to resist oxidation. (4) Number and Height of Upper Terminals. The number of conductors or upper terminals required will depend upon the size of the building, the material of which it is constructed, and the comparative height above ground of the several parts. No general rule can be given for this, except that it may be as>umed that the space protected by the conductor is, as a rule, a cone, the radius of whose base is equal to the height of the conductor from the ground. (5) Curvature. The rod should not be bent abruptly around sharp corners. In no case should the length of a curve be more than half as long again as its chord. A hole should be drilled in string-courses or other projecting masonry, when possible, to allow the rod to pass freely through it. (6) Insulators. The conductor should not be kept from the building by glass or other insulators, but attached to it by fastenings of the same metal as that of the conductor itself. (7) Fixing. Conductors should preferentially be taken down the side of the building which is most exposed to rain. They should be* held firmly, but the holdfasts should not be driven in so tightly as to pinch the conductor or prevent contraction and expansion due to change of temperature. . (8) Other Metalwork. All metallic spouts, gutters, iron doors, and other masses of metal about the building should be electrically connected with the- conductor. (9) Earth-Connection. It is most desirable that, whenever possible, the lower extremity of the conductor should be buried in permanently damp soil. Hence, proximity to rain-water pipes and to drains or other water is desirable. It is a very good plan to bifurcate the conductor close below the surface of the ground, and to adopt two of the following methods for securing the escape oi the lightning into the earth: (a) A strip of copper tape may be led from the bottom of the rod to a gas or water-main (not merely to a leaden p'pe), if such exist near enough, and be soldered to it; (6) a tape .may be solderea to a sheet of copper, 3 by 3 ft by Me in thick, buried in permanently wet earth and sur- rounded by cinders or coke; (c) many yards of copper tape may be laid in a trench filled with coke, having not less than 18 sq ft of copper exposed. (10) Protection from Theft, etc. In places where there is any likelihood of the copper being stolen or injured, it should be protected by being enclosed * The upper terminal is that portion of the conductor which is between the top of the edifice and the point of the conductor. 1706 Lightning-Conductors Part 3 in an iron gas-pipe, reaching lo ft (if there is room) above ground and some distance into the ground. (ii) Painting. Iron conductors, galvanized or not, should be painted. It is optional with copper ones. (12) Inspection. When the conductor is finally fixed it should in all cases be examined and tested by a qualified person, and this should be done in the case of new buildings after all work on them is finished. Periodical examina- tion and testing, should opportunities offer, are also very desirable, especially when iron earth-connections are employed. Lightning-Protection for High Chimneys. The following is a descrip- tion of the system of lightning-protection * for the radial-brick chimney-stack, 350 ft in height, for the plant of the St. Joseph Lead Company, Herculaneum, Mo. Conductor. The conductor used is of commercially pure copper. No. 1 1, Brown & Sharpe gauge, in the form of a cable, consisting of twenty-eight wires, seven strands, four wires to the strand, and % in in diameter, 230 552 circular mils. The vertical conductors are of continuous lengths from the top of the chimney to and into the ground. A circuit-conductor is placed 5 ft below the top of the chimney and connected to each down-conductor by a 12-in two-way splice. Points. The air-terminals are eight in number equally spaced around the top of the chimney, and consist of solid, copper bars i in in diam and 10 ft in length, the upper 12 in tapering to a point and covered with a 12-in thimble of genuine platinum. Air-terminals extend 5 ft above the top of the stack and the lower end of each copper bar is set in a heavy copper T coupler, which con- nects the same into the circuit-conductor. Each rod is held in place by heavy anchor-fasteners, bolted from the inside of the stack. These anchors are en- cased in copper tubes set in the solid masonry. Grounding. At a point below the ground-level and at the chimney-line, the conductor is carried in a downward course from the chimney, in a trench bedded in charcoal, to a point 5 ft outside the foundation-line. An additional conductor is spliced into the main cable at this point, forming a Y with branches terminating 15 ft apart. Two well-holes are bored to a depth of ap- proximately 20 ft into permanent moisture. The end of each Y conductor is electrically soldered into perforated, copper reservoirs 4^/2 in in diam and 28 in in length, and filled with pea-size charcoal. The effect of the reservoir is to give the required amount of surface-contact with the earth and to insure per- manent moisture through the charcoal by capillary attraction. Each main conductor is thus grounded in two places instead of in one place. Lead Covering. To preserve the conductor system against decomposition in ozone, in which sulphuric or other acid gases may exist, all of the conductor system at the top, and to a point 75 ft below the top of the chimney is covered with lead H in in thickness. Exception is made to the platinum-covered 12-in top of each rod, which requires no lead covering. Where splices are made and anchor-fasteners set, the whole is covered with lead sleeves or hoods thoroughly wiped and hermetically sealed. Connections of point-bar T's etc., are all soldered, lead-covered and sealed. Practical experience seems to show that all lightning-conductor systems on chimneys should be lead-covered and hermetically sealed to a point, approximately 25 ft downward from the top, to protect the copper against decomposition, not necessarily as thick as on this chimney, but, say, He in, the thickness being determined by the size and usage • Installed by the Ajax Conductor and Manufacturing Compauy, Chicago, IlL Automatic Telephones for Intercommunicating Service 1707 of the stack. It has been found that in from three to five years there is a de- cided honeycombing of the copper, through the action of the sulphuric and other acid gases. It has often been necessary to replace points, sections of cable, etc., entirely eaten away from this cause. INTERPHONES. AUTOMATIC TELEPHONES FOE INTERCOMMUNICATING SERVICE Description. The interphone system is an application of the telephone for interior use. It is an automatic, intercommunicating system, requiring neither switchboard nor operator, and being self-contained within the walls of the estab- lishment for whose benefit it has been installed. Advantages. In brief, the advantages of such a system are these: (i) the mere pressing of a button gives a person telephone-connection with any desired party, without the loss of time involved in first calling up a third party; (2) re- course to directory or information bureau is made unnecessary through the use of labels, properly inscribed, on the face of the instrument; (3) no maintenance- expense is involved, and the system, consequently, is as inexpensive to operate as an electric door-bell; (4) the wiring-arrangement is such that the system ma^ be provided for when the original plans for a new building are being drawn up, and in this respect it does not differ much from a system of electric lights or plumbing. The Use of Interphones in residences, schools, hospitals, factories, mills, offices, stores and clubs is constantly increasing. The same general features apply to all of these types of installations, and in practically every case it is the simplicity of the system that especially recommends it for service. The interphone usually fits in where formerly call-bells, speaking-tubes, messenger service and other inadequate methods were the rule. The interphone field of service is in the estabhshmcnt whose needs call for from four to thirty-two telephone-stations. When there are more than thirty-two the installation of a private telephone-exchange, with a switchboard, is better practice. Types of Interphones. There are several types of interphones for varying degrees of service. (i) The most familiar instrument is a wall-interphone, of the non-flush TYPE. The telephone is of metal, with connecting buttons, labels, bells, mouth- piece, hook and receiver, all mounted on its face. This instrument is to be at- tached directly to the wall. (2) The FLUSH TYPE resembles the first-mentioned type in every particular but the one implied in its title. The instrument is mounted into the wall, with its face flush with the rest of the wall-surface. These two instruments are most popular for installation in club-halhvays, in stores and factories, in residences, and in all places where wall-telephones would ordinarily be used. Busy offices and stores often employ variations of types (i) and (2) and use a desk-set, a separate instrument taking care of the connecting buttons and labels, or a hand- set. (3) The DESK-STAND telephone is of the type often used for local and long- distance service. Connected with it is a metal box containing the rows of buttons and labels, each label being opposite the button through which is se- cured connection with the corresponding station. The telephone in this case stands on the desk, and the key-box is conveniently close at hand, either on the desk or on the wall. 1708 Vacuum-Cleaning Part 3 (4) Some prefer for this service the hand-set, with the receiver and trans- mitter in one piece. This is a convenient, compact instrument, well fitted for use in an office. (5) From two to six instruments of still another type make up a party-line INTERPHONE SYSTEM. Here there are no connecting buttons, the principle in- volved being the same as that of the elementary, farmers' Hne. This makes a convenient private-line system for a small residence, and is appropriate for a house-to-garage circuit. Variations from Standard Types. There are systems with variations from the standard types. Many schools are using a combination of interphones of type (i) or (2) with (5). In the principal's office is an instrument of type (i) or (2) with a connecting button for each outside station, while the class- room-telephones are all of type (5). With this system the principal can at any time call up any teacher; but a teacher can call up another classroom only through the medium of this master-station, which acts as a sort of ex- change. The advantages of this arrangement for a school are obvious. In a hospital the instruments are usually placed outside of the more important operating-rooms and wards and in the offices and reception-rooms. Wiring and Batteries. All wiring is enclosed in cables. Energy is obtained from dry cells. The only maintenance-expense connected with an interphone system is the occasional renewal of these batteries^. VACUUM-CLEANING General Description. Vacuum-cleaners are appliances which have come into use during recent years and which are for the purpose of removing dirt and dust from rooms of buildings, cars, steamships, etc., or from furniture, carpets, curtains, or other interior fittings. The dust and dirt are removed by suction and the apparatus consists of an air-pump which is arranged to draw the air and the dirt or dust contained in it through pipe and nozzle. This nozzle is drawn or passed over the surfaces which are to be cleaned. Screens of musUn or other appropriate cloth are used to separate by filtration the dust and dirt which are borne along with the stream of air; and in some types of apparatus this process is assisted by what are called baffle-plates which are added to make the heavier particles of dust drop by their own weight to the lower part of the receptacle placed to receive them. About the year 1890 compressed air was used for the first time in railroad-cars for purposes of cleaning and dust- removal. There were serious objections to this method of cleaning, however, as it was found that the jets of compressed air blew out the dust and dirt in such a way that it was difficult to arrange for their collection and retention; the principle of suction was consequently introduced to overcome these difiiculties. Types of Vacuum-Cleaners. The machines belonging to the earliest types usually consist of a pump, the motor-power of which is cither a gas-engine or an electric motor, the machines being portable. They can be moved about from one building to another as occasion demands. Cleaners of the next type intro- duced involve an installation in the basement or lower part of a building and a fixed and permanent position. From the central plant pipes art* run to various rooms and apartments and are fitted in such rooms or apartments or in adjacent halls or corridors, with valves to which are attached the hose with the cleaning- appliances at the end. In some cases this vacuum-arrangement is combined with another for washing floors, the secondary system including a second set of pipes from a tank filled with soap and water. Compressed air is employed to spray the latter over the floor, and both dirt and water are finally removed Waterproofing for Foundations 1709 'Ugh pipes to the street-sewers. A portable tank is used for the soap and rv. Vacuum-cleaners of a third type consist of small machines which take place of the brooms and dusters or are used in connection with them. They now very generally used and may be driven by an electric motor, by foot, or ■ and. These last-mentioned, smaller, portable cleaners are used for many r purposes than the ordinary cleaning of rooms and furniture. etails and Specifications for Vacuum-Cleaning Installations. Com- ' plans and specifications for the installation of a vacuum-cleaning plant for ilding may be obtained from any of the numerous manufacturers making I apparatus and taking contracts to put it in place. There are several types uichines and systems of installation and detailed descriptions would exceed limits of space in this handbook. WATERPROOFING FOR FOUNDATIONS* The Waterproofing of Substructure Work is, comparatively speaking, a ]iiv)dcrn branch of engineering. It is only within recimt years that it has become accessary to construct deep basements for buildings. In the past, the more imoortant structures, such as cathedrals, capitols, state-buildings and the like, were usually built upon high ground, and water was prevented from entering ih-- basements of such buildings by means of drainage. Waterproofing, as we know it, was generally unnecessary. With the advent of the so-called sky- I ! )ers, however, requiring large mechanical plants, deep basements became an actual necessity, and as these basements are usually carried below ground- water level, and in many instances below tide-level, the question became one of utmost importance. Like almost every detail of a modern building, water- proofing is a specialty. Each building presents its own problems, and the safest plan is to leave the solution of these problems to some one expert in the knowledge of waterproofing who has made it a special study and knows how best to over- come the existing difficulties. It may be laid down as an invariable rule that, where conditions are at all serious, the owner or the general contractor will save money in the long run if he employs the services of an expert waterproofer to place his waterproofiug-seal, regardless of the method he wishes to use. Pressure-Resistance Versus Waterproofing. In waterproofing large base- ments where actual pressure exists, it is a question for the engineer to decide whether it is more economical to attempt to secure an absolute pressure-job or a WATER-PROOF JOB in connection with a drainage system. As a general rule, it may be stated that where a building is generating its own power, it is more economical to use a drainage system with an open sump than to construct a pressure-cellar, the cost of pumping being much less than the interest charges on the cost of a floor-slab sufficiently strong to withstand the pressure. Waterproofing Concrete Foundations. The three following subdivisions of this subject, discussing the causes of permeability of concrete, the addition of substances to render it more water-proof, and the treatment of its surfaces to make it less permeable, embody the conclusions of Committee D-8 of the Amer- ican Society for Testing Materials, f This committee, since its organization in 1 90s has, through laboratory-tests and experiments, together with examinations of work during construction and after completion, 4s well as the study of liter^ ature on the subject, sought to secure sufficient information to enable it to for- * For foundations in general, see Chapter II. tThis article, to the middle of page 1713, is the substance of a Report submitted to the American Society for Testmg Materials at its meeting, June 24-28, 19 13. This society has (1920) no Standard Specifications for Waterproofing, but published in 1918 ftmr Tentative Soecificatioris on this subject. 1710 Waterproofing for Foundations Part 3 miilate definite methods for securing water-proof concrete structures. The work of the committee was compHcated by reason of the facts that there seemed to be so httle concordance between results of tests obtained under laboratory-condi- tions and in the field and that it was necessary to extend its investigations over a period of years in order to determine the permanency of the action noted. The committee reported that while it had not been able to arrive at sufficiently definite conclusions to enable it to formulate specifications for the making of concrete structures water-proof or for materials to be used in such work, it had reached certain general conclusions which might be of assistance to the constructor in securing the desired result of impermeable concrete. Early in the investigation, the work was found to subdivide naturally into three branches, and the con^ elusions reached will be grouped in order under these subdivisions, which are: (i) The determination of causes of the permeability of concrete as usually made from mixtures of Portland cement, sand and stone, or other coarse aggre- gate, in proportions of from i of cement, 2 of sand and 4 of stone, to i of cement, 3 of sand and 6 of stone, and the best methods of avoiding these causes. V (2) The rendering of concrete more water-proof by adding to ordinary mix- tures of cement, sand and stone, other substances which, either by their void- filling or repellent action, would tend to make the concrete less permeable. (3) The treatment of exposed surfaces after the concrete or mortar has been put in place and hardened more or less, either by penetrative, void-filling or repellent liquids, making the concrete itself less permeable; or by extraneous protective coatings, preventing water from having access to the concrete. Considering these several subdivisions separately and in the order named, the committee arrives at the following conclusions: (i) Causes of Permeability of Concrete. In the laboratory and under test- conditions where properly graded and sized coarse and fine aggregates are used, in mixtures ranging from i of cement, 2 of sand and 4 of stone, to i of ce- ment, 3 of sand and 6 of stone, impermeable concrete can invariably be pro- duced. Even with sand of poor granulometric composition, with mixtures as rich as i of cement, 2 of sand and 4 of stone, permeable concrete is seldom, if ever, found and is a rare occurrence with mixtures of i of cement, 3 of sand and 6 of stone. But the fact remains, nevertheless, that the reverse often ob- tains in actual construction, permeable concretes being encountered even with mixtures of i of cement, 2 of sand and 4 of stone and are of frequent occurrence where the quantity of the aggregate is increased. This the committee attributes to: (a) Defective workmanship, resulting from improper proportioning, lack of thorough mixing, separation of the coarse aggregate from the fine aggregate and cement in transporting and placing the mixed concrete, lack of density through insuflicient tamping or spading, improper bonding of work-joints, etc. (b) The use of imperfectly sized and graded aggregates. (c) The use of excessive water, causing shrinkage-cracks and formation of laitance-seams. (d) The lack of proper provision to take care of expansion and contraction, causing subsequent cracking. Theoretically, none of these conditions should prevail in properly designed and supervised work, and they are avoided in the laboratory and in the field, under test-conditions, where speed of construction and cost are negligible items, instead of being governing features as they must be in actual construction. Properly graded sands and coarse aggregates are rarely, if ever, found in nature in sufficient quantities to be available for large construction, and the effect of poorly graded Waterproofing for Foundations 1711 aggregates in producing permeable concrete is aggravated by poor and inefficient field-work. Even if the added expense of screening and remixing tlie aggre- gates could be afforded, so as to secure proper granulometric composition to give the density required to make untreated concretes impermeable, it is seem- ingly often a commercial impossibility on large construction to obtain work- manship, even approximating that found in laboratory- work. (2) Addition of Foreign Substances to Cement Before or During Mixture. The committee finds that in consequence of the conditions outlined above, sub- stances calculated to make the concrete more impermeable, either incorporated in the cement or added to the concrete during mixing, are often used. This has resulted in the development and placing on the market of numerous patented or proprietary waterproofing-compounds, the composition of which is more or less of a trade-secret. While it has been impossible for the committee to test all of the special waterproofing-compounds being placed on the market, it has investigated a sufficient number of these, as well as the use of certain very finely divided, naturally occurring or readily obtainable commercial mineral products, such as finely ground sand, colloidal clays, hydrated lime, etc., to form a general idea of the value of the different types. The committee finds: (k) That the majority of patented and proprietary integral compounds tested have little or no immediate or permanent effect on the permeability of concrete and that some of these even have an injurious effect on the strength of mortar and concrete in which they are incorporated. (b) That the permanent effect of such integral waterproofing-additions, if dependent on the action of organic compounds, is very doubtful. (c) That in view of their possible effect, not only upon the early strength, but also upon the durability of concrete after considerable periods, no integral waterproofing-material should be used unless it has been subjected to long-time practical tests under proper observation to demonstrate its value, and unless its ingredients and the proportion in which they are present are known. (d)°That in general, more desirable results are obtainable from inert com- pounds acting mechanically, than from active chemical compounds whose efficiency depends on change of form through chemical action after addition to the concrete. , u i (e) That void-filling substances are more to be relied upon than those wliose value depends on repellent action. (f) That, assuming average quality in sizing of the aggregates and reasonably good workmanship in the mixing and placing of the concretes, the addition ot from 10 to 20% of very finely divided void-filling mineral substances may be expected to result in the production of concrete which, under ordinary conditions of exposure will be found impermeable, provided the work-joints are properly bonded, and cracks do not develop on drying, or through change m volume dus to atmospheric changes, or by settlement. (3) External Treatment. While external treatment of concrete would not be necessary if the concrete itself, either naturally or by the addition of wat^er- prfing-material, was impermeable to water, it has ^een ^ound m pra^^^^^^^^ in large construction, no matter how carefully the concrete itself has been made^ cracks are apt to develop, due to shrinkage in drying out, ^^^^^^'^^^^^^^^^^ tion under change of temperature and moisture-content and t« se^^^^^^^ ment It is therefore, often advisable in important construction to anticipate Xrovide'for the possible occurrence of such cracks by external^t^^^^^^^^ with a protective coating. Such coating must be sufficiently ^i^f ^ ^^^^^^^^^ to Drevent the cracks extending through the coating itself. The application ot merel7 penetrative void-filling liquid washes will not prevent the passage of 1712 Waterproofing for Foundations Part 3 water due to cracking of the concrete. The committee has, therefore, consid- ered surface-treatment under two heads: (a) Penetrative void-iiiHng Hquid washes. (b) Protective coatings, including all surface-applications intended to prevent water coming in contact with the concrete. Penetrative Washes. While some penetrative washes may be efficient in rendering concrete water-proof for limited periods, their efficienci^ may decrease with time and it may be necessary to repeat such treatment. Some of these washes may be objectionable, due to discoloring the surface to which they are applied. The committee, therefore, believes that the first effort should be made to secure a concrete that is impermeable in itself and that penetrative void- filling washes should only be resorted to as a corrective measure. Protective Coatings. While protective extraneous bituminous or asphaltic coatings are unnecessary, so far as the major portion of the surface of the con- crete is concerned, provided the concrete, either in itself or through the addition of integral compounds, is made impermeable, they are valuable as a protection where cracks develop in a structure. It is therefore recommended that a com- bination of inert void-filling substances and extraneous waterproofing be adopted in especially difficult or important work. Bituminous or Asphaltic Coatings. Considering the use of bitum.inous or asphaltic coatings, the committee finds: (a) That such protective coatings are often subject to more or les.^ deteriora- tion with time, and may be attacked by injurious vapors or deleterious substances in solution in the water coming in contact with them. (b) That the most effective method for applying such protection is either the ■ Z2tting of a. course of impervious brick dipped in bituminous material into a solid ^ed of bituminous material, or the application of a sufficient number of layers of satisfactory membranous material cemented together with hot bitumen. (c) That their durability and efficiency are very largely dependent on the care with which they are applied. Such care refers particularly to proper cleanhig and preparation of the concrete to insure as dry a surface as possible before appli- cation of the protective covering, the lapping of all joints of the meinbranous * layers, and their thorough coating with the protective material. The use of this method of protection is further desirable because proper bituminous cover- ings offer resistance to stray electrical currents, the possible attack from which is referred to in succeeding paragraphs. Rich Mixtures. So far, the committee has considered only concretes of the usual proportions, namely, those ranging from i of cement, 2 of sand and 4 of stone, to I of cement, 3 of sand and 6 of stone. It has been suggested that im- permeable concretes could be assured by using mixtures considerably richer in cement. While such practice would probably result in an immediate imperme- able concrete, it is believed by many that the advantage is only temporary, as richer concretes are more subject to check-cracking and are less constant in volume under changes of conditions of temperature, moisture, etc. Therefci . the use of more cement in mass-concrete would cause increased cracking, unk some means of controlling the expansion and contraction is discovered. Wi: reinforced concretes the objection is not so great, as the tendency to crackii is more or less counteracted by the reinforcement. Fine Flour Mixtures. It has also been suggested that the presence in the : cement of a larger percentage of very fine flour might result in the production of u denser and more impermeable concrete, through the formation of a larger timount of colloidal gels. Neither of these suggestions has been especially in- vestigated by the committee. Both appeal to the committee, however, for the Waterproofing for Foundations 1713 reason that they substitute active cementitious substances for the largely 'in- active void-filUiig materials previously recommended, thus increeteing the strength of the concrete. Character of Workmanship. In conclusion, the committee would point out that no addition of waterproofing-compounds or substances can be relied upon to completely counteract the effect o/ bad workmanship, and that the produc- tion of impermeable concrete can only be hoped for where there is determined insistence on good workmanship. Saline Waters. Electrical Action. The production of impermeable concrete has assumed greater importance since the appointment of this committee, owing to the well-known injurious action of saline or alkaline waters and to the suggested possible effect of the moisture in concrete occasioning or aggravating electrical action from stray currents. Originally, the question of waterproofing involved mainly the physical troubles resulting from water passing through concrete without any special consideration of its effect on its durabiUty, other than a gradual leacliing out of the cement. Recent developments suggest the possibility that, owing to the increased conductivity of damp concrete to elec- trical currents, such currents, if present, may so affect damp concrete as to seri- ously lessen its integrity; and this possibility further emphasizes the importance of the recommendation that no waterproofing-compound of unknown chemical composition be added to concrete, as recent tests seem to show that the action of electrical currents is aggravated by the presence of certain solutions. Waterproofing by External Linings of Brick, Tar, or Asphalt, and Felt, The oldest method of waterproofing is the one involving the use of a tar-and-felt or asphalt-and-felt seal (Fig. 1). This consists of building first a supporting wall arid a supporting concrete slab to hold the seal. On the floors, this slab is usually composed of concrete, 4 in thick. The walls are generally of brick from 4 to 8 in thick, but occasionally 4-in terra-cotta tiles are used. Upon this base a swabbing of tar or asphalt is placed and before this has become cold or set, one thickness of paper, saturated with coal-tar, is laid. This paper receives a swabbing of coal-tar and asphalt and another layer of paper is placed, the operation being continued until there are three or more layers of paper with four or more swabbings of tli^ tar or asphalt. For damp-proof work, three layers of paper with four swabbings of tar are usually sufficient. For waterproofing- work not less than five and usually six layers of paper with from six to seven swabbings of tar are used. The main walls of the structure are then built against the wall-waterproofing, and after these are in place, the main concrete basement- floor is laid immediately on top of the floor-seal, the idea being to form a con- tinuous water-proof seal enveloping the entire basement below grade.^ The difficulties of this system consist chiefly in securing perfect laps at all points in the work, and unless extreme care is used and unless there is perfect cooperation between the waterproofer and the mason-contractor, there is apt to be a break somewhere in the seal, usually where the wall-waterprooflng is supposed to be joined to the floor-work. The disadvantages of this system are due to the fact that the seal is not permanent in all soils as the subsurface water frequently contains acids which destroy the seal. Then again, the seal may be easily punctured by the mas6n-contractor in building his wall against it or in laying the concrete floor upon the flat work. The chief disadvantage, however, is that the waterproofing- seal is invariably buried behind a mass of masonry, either brick or concrete, which means that should there be a leak, due to either care- lessness or accident, through the waterproofing-seal, it is frequently impossible to stop it. It not infrequently happens that when a leak has developed in tar- and-felt work, the actual presence of the water does not show opposite the leak, 1714 Waterproofing for Foundations Part 3 but following some line of least resistance, appears from 50 to 100 ft, or more, away from where the actual damage causing the leak occurs. In actual water- proofing work it is seldom attempted to secure a bottle-tight job with tar and felt. Instead, some system of drainage is installed beneath the water-proof seal which is on the floors of the building, and the water is conducted through tile Brick wall 4 in. Tile blocks A in. Waterproofing JS^in. Bricks lin. Concrete 30 in. Furring and plaster Total thickness of wall 4 in. 465^ in. Total thickness of floor 16 In. Fig. 1.* Felt-Waterproofing for Foundations or other pipes to some central sump from which it is mechanically pumped to a sewer. The purpose of the waterproofing in this case, therefore, is to con- centrate or drive the water to this sump. For shallow cellars and especially dampproofing-work, this tar-and-felt method is the most economical and most frequently employed. Waterproofing by Coating with Water-Proof Cement. For deep and difficult work a comparatively new method of waterproofing is often used (Fig. 2). This consists of placing a coating of water-proof cement upon the interior surface of the exterior walls of the building and over the upper surface of the concrete floor-slab in the basement or subbasement. Fig. 3 shows a foundation for an engine, the concrete being waterproofed as shown. The pit is made somewhat larger than the foundation, the extra space being filled in with cinders, dry bricks or terra-cotta blocks, which may be readily removed to allow access to the bed-plate bolts for which hand-holes have been cast in the concrete, thus permitting the complete removal of the engine. The figure * Reproduced, by permission, from a pamphlet published by The Waterproofing Com- pany. New York, and showing the greater thickness of walls and floor required for the outside-surface brick -and-felt method of waterproofing as compared with the inside- surface waterproof -cement coating. Taken from design for waterproofing in a prominent New York building. See, also, Fig. 2. Waterproofing for Foundations 1715 shows a 2-in sand cushion and a 2-in layer of planks under the engine-foundation. This is not a part of the waterproofing but is put in to prevent the communica- tion of^ vibration. Fig 4 shows rcinforced-concrete floors for an engine-room and boiler-room, the concrete slab being 12 in thick under the former and 24 in Concrete wall 30 in. Waterproofing ^irx. Total thickness of wall 30X in. Total thickness of floor 11 in. Fig. 2.* Cement Waterproofing for Foundations thick under the latter. Both floors are covered with a i-in course of water-proof cement. The reinforcement is put in as shown and in sizes and spacing as follows: i2-in slab 24-in slab Rods in two courses Rods in three courses Lower rods, 4 in on centers, 6 in from Lowest rods, 3 in on centers, 12 in from surface surface Upper rods, 6 in on centers, 2 in from Intermediate rods, 3 in on centers, 7 in surface from surface For five rods, total area of cross-section Upper rods, 6 in on centers, 2 in from is 0.703 sq in; per square foot of sur- surface - face, 2.39 lb For ten rods, total area of cross-section. 1.4 sq in; per square foot of surface. 4.78 lb * From a pamphlet published by The Waterproofing Company, New York, and show- ing reduced total thickness of walls and floor required for the inside-surface water-proof cement method of waterproofing. Taken from design for waterproofing of the same building shown in Fig. 1. The walls and floors were put in place in the monolithic form. 1716 Waterproofing for Foundations Part 3 There are many compounds.advertised to make cement or concrete water-proof. Besides these, there are water-proof cements manufactured by secret processes and applied by companies that make a specialty of waterproofing. Some of the many waterproofing-compounds have merit; but the main factors of a Fig. 3.* Engine-foundation with Water-proof Cement successful job of waterproofing are the skill and experience of the waterproofers who do the work. It is claimed that to apply cement waterproofing so as to obtain efficient results requires more skill than to apply a tar-and-felt seal; but a cement waterproofing, once properly applied, seems to possess some advantages Fig. 4.* Reinforced-concrete Floor with Water-proof Cement over the older method of tar and felt. One advantage is that the waterproofing is accessible, and that if any leaks develop, they are apparent and can be readily and economically repaired by cutting out the old waterproofing and placing a new coating where the damage exists. Another advantage claimed is that cement waterproofing is generally permanent and not damaged by the ordinary * Reproduced by permission of The Waterproofing Company, New York. Force of the Wind 1717 acids found in solution with water in soil. By the cement method the cost of the brick supporting walls and the concrete supporting slab is eliminated as is also the corresponding cost of the necessary excavation for them; and finally, the waterproofing on the floor serves the double purpose of waterproofing and wearing-surface, thus saving the cost of the cement finish usually found in basements and subbasements. One of the disadvantages of cement water- proofing is that the material is rigid and is fractured by any settlement of the building or contraction in the concrete upon which it is placed. Experience has shown, however, that settlement-cracks usually take place before the water- proofing contractor has left the building and that there is little or no trouble from these causes after his work is completed. Contraction-cracks in concrete, however, seem to develop at any time within twenty-four months after concrete has been placed. In order to prevent these cracks, users of the cement water- proofing have adopted a system of reinforcement in the concrete, and it is claimed that this reinforcement is, in the long run, an economy, as it permits of less con- crete and gives a better and stronger floor or wall. On brick and stone walls no trouble is experienced from contraction and expansion. . It should be re- membered that this work is all below grade where contraction and expansion are reduced to a minimum, regardless of the materials used. Waterproofing by Adding Substances to Cement. This is another method of waterproofing now being advocated by some. If this method could always be made efficient, it would be highly advantageous. It is claimed by the manufacturers of these compounds that in order to secure a water-proof basement, for example, a certain percentage of the compound is to be mixed with the cement before it is incorporated in the concrete. The opponents of this method claim, however, that it is impossible to construct a basement in this way without incurring the danger of serious leaks at the joinings of one day's work with that of another; that leakage at these points of cleavage may be increased by the use of waterproofing-compounds; and that their principal merit is that they produce a very dense mass of concrete. It is always difficult to bond old concrete to new, and if concrete is made water-proof, or, in other words, nonabsorbent, the difficulty of joining new concrete to a nonabsorbent mass of old concrete is increased. This method is effective, however, and is to be recommended in work which can be carried on without interruption, such, for instance, as small elevator-pits or small swimming-pools, where the concrete can be started in the morning and completed by night or before any part of the work has had time to attain its initial set. FORCE OF THE WIND Relation Between the Pressure and Velocity of Wind. According to experiments made in 1890 or thereabouts, by C. F. Marvin, United States Signal Service, the relation between wind-pressure and velocity is given very accurately by the formula p = 0.004 V'-, where p is the pressure in pounds per square foot on a flat surface normal to the direction of the wind, and V the velocity of the wind in miles per hour. Smeaton considered the pressure as equal to 0.005 F^. The following table, based on Marvin's formula,* is quoted by Turneaure and Ketchum.f * If Marvin's formula is written p = 0.0032 V^ the values in this table will be slightly changed. See Chapter XXVII, pages 1052 and 1053; Chapter XXX, page 1199; and also page 1394. The formula used by the United States Signal Service is /> = 0.004 V^- The true pressure is probably somewhere between 0.005 V'^ and 0.004 V-, near the former for very low velocities and near the latter for high velocities. t See, also. Trautwine's Pocket-Book, page 321. 1718 Copies of Tracings PaiiH Table Showing the Force of the Wind H Miles per hour Feet per minute Feet per second Force, in pounds, per square foot Description I 2 , 3 4 5 10 IS 20 25 30 . 35 40 45 SO 60 70 80 100 88 176 264 352 440 880 1 320 1 760 2 200 2 640 3080 3520 3960 4400 5280 6160 7040 8800 1.47 2.93 4.40 5.87 7.33 14.67 22.0 29-3 26.6 44.0 51.3 58.6 66.0 73.3 88.0 102.7 117. 3 146.6 0.004 0.014 / 0.036 j 0.064 ( 0.1 i 0.4 ( 0.9 j 1.6 / 2.5 ( 3.6 j 4.9 j 6.4 I 8.1 ( 10. 14.4 j 19.6 ( 25.6 40.0 ( Hardly perceptible Just perceptible Gentle breeze Pleasant breeze Brisk gale High wind Very high wind Storm Great storm Ilurricane COPIES OF TRACINGS Blue-Prints from Tracings. The following directions * cover the whole ground. The sensitized paper can be procured, all prepared, at stores where artists' materials are sold, so that the process of preparing the paper by means of chemicals can then be omitted. The materials required are as follows: (i) A board a Httle larger than the tracing to be copied. The drawing- board on which the drawing and tracing are made can always be used. (2) Two or three thicknesses of flannel or other soft white cloth, which is to be smoothly tacked to the board to form a smooth surface, on which to lay the sensitized paper and tracing while printing. (3) A plate of common double-thick window-glass, of good quality, slightly larger than the tracing to be copied. The function of the glass is to keep the tracing and sensitized paper closely and smoothly pressed together while printing. (4) The chemicals for sensitizing the paper. These consist simply of equal parts, by weight, of citrate of iron and ammonia, and red prussiate of- potash and can be obtained at any drug-store. The price should not be over 8 or 10 cts per ounce for each. (5) A stone or yellow-glass bottle to keep the solution of the above chemicals in. If there is but little copying to do, an ordinary glass bottle will do, and the solution can be freshly made whenever it is wanted for immediate use. (6) A shallow earthen dish in which to place the solution when using it. A * common dinner-plate is as good as anything for this purpose. (7) A soft paste-brush, about 4 in wide. (8) Plenty of cold water in which to wash the copies after they have been exposed to the sunlight. The outlet of an ordinary sink may be closed by placing a piece of paper over it with a weight on top to keep the paper down, and the sink filled with water, if the sink is large enough to lay the copy in. * Taken from The Locomotive. Blue-Prints and Black-Line Prints 1719 If it is not, it is better to make a water-tight box 5 or 6 in deep, and 6 in wider and longer than the drawing to be copied. (9) A good quality of white book-paper. The following directions are to be followed: Dissolve the chemicals in cold water in these proportions: i oz of citrate of iron and ammonia; i oz of red prussiate of potash; and 8 oz of water. They may all be put into a bottle together and shaken up. Ten minutes will suffice to dissolve them. Lay a sheet qf the paper to be sensitized on a smooth table or board, pour a little of the solution into the earthen dish or plate, and apply a good even coat- ling of it to the paper with the brush. Then tack the paper to a board by two adjacent corners, and set it in a dark place to dry. One hour is sufficient for 'the drying. Place the paper, with its sensitized side up, on the board on which ycu have smoothly tacked the white flannel cloth; lay the tracing to be copied on top of it; on top of all lay the glass plate, being careful that paper and tracing arc Ijoth smooth and in perfect contact with each other, and lay the whole thing out in the sunlight. Between eleven and two o'clock in the summer-time, on a clear day, from 6 to 10 minutes will be sufficiently long to expose it; at otficr seasons a longer time will be required. If the location does not admit of direct sunlight, the printing may be done in the shade, or even on a cloudy day; but from 1 to 2y2 hours will be required for exposure. A httle experience will soon enable any one to judge of the proper time for exposure on different cia\s. After exposure, place the print in the sink or trough of water before nuMitioned, and wash thoroughly, letting it soak from 3 to 5 minutes. Upon ininicrsion in the water, the drawing, hardly visible before, will appear in clear wltite lines on a dark-blue ground. After washing, tack up against the wall, jr other convenient place, by the corners, to dry. This finishes the operation, which is very simple and thorough. After the copy is dry, it can be written on witli a common pen and a solution of common soda, which makes a white line. Alternate Recipe for Making Blue-Prints. The following is an alternative recipe to the one given above. The paper should be prepared by floating it lor one minute in a solution of ferricyanide of potassium (red prussiate of potash), I <»z, and water, 5 oz. It should then be dried in a dark room, afterwards ex- )o-td beneath the negative until the dark shades have assumed a deep blue oK-r, and immersed in a solution of water, 2 oz, and bichloride of mercury, i gr. Ilu; print should be washed, immersed in a hot solution of oxalic acid, 4 drm, md water, 4 oz, washed again and dried. Where a copy of a drawing is to be iuide the prepared paper is placed, sensitive side uppermost, on a flat board a)\ cred with two or three thicknesses of blanket or its equivalent. A tracing )f the drawing is made, laid on the sensitized paper and held in place by a sheet 'f ^Mass clamped to the board. The sensitized paper is exposed to the sunlight roni 4 to 10 minutes or to a clear sky from 20 to 30 minutes and then removed, vashed and dried. The only requisite as to paper is that it must stand wash- ng. Prepared paper may be purchased. Black-Line Copies from Tracings.* The directions for making the sensitiz- ng solution used in this process are as follows: Dissolve separately, gum arabic, 3 4 For bells above i 800 lb ^i to i The Largest Bells in the World * Actual Diam- Sound-bow Names and locations Date vibra- Key- eter, Weight. of bells cast note lb tion in Inches Stroke Moscow, T7.ar Kolokol f- 1733 74 D 272 23 0.84 443 772 Burmah, Mingoon 94 Ft 203? 16? 0.80 201 600 Moscow, St. Ivan's 1819 105 Gi 185 14.75 0.80 127 350 Pekin, Great Bell 156 120 000 Burmah, Maha Ganda. . 125 B 155 12. 5 0.80 95000 Nishni Novgorod. ...:.. 125 B 151 12 0.80 69664 Moscow, Church of Re- deemer 1879 141 ct 136.3? 10.6 0.80 60 736 Nankin, China 112 45000 London, St. Paul's 1881 157 Ej 114.25 8.75 0.76 42000 Olmutz, Bohemia 157 E(7 121 9.125 0.75 40320 Vienna, Austria 1711 157 Eb 118 9.5 0.80 40 200 Westminster, London — 1856 166 E 113. 5 9-375 0.83 35620 Erfurt, Saxony 1487 176 F 103.6 g.75 75 30 800 Notre Dame, Paris 1680 166 E 103 7.5 0.73 28670 Montreal, Canada 1847 176 P 103 7.8 0.76 28560 York, England 1845 187 n 100 8 0.80 24 080 St. Peter's, Rome 1786 187 Fit 97.25 7-5 0.77 18 000 Great Tom, Oxford 1680 210 Git 84. 6.125 0.73 17 024 Cologne, Germany 1477 . 198 G 95 7.2 0.75 16 016 Brussels, Belgium 210 Git 95.81 7.75 0.71 15848 State-house, Philadelphia i87S 198 G 88 6.375 0.73 13 000 Lincoln, England 1834 210 Git 82.85 6 0.73 12096 St. Paul's, London 1716 222 A 81 6.08 0.75 II 500 Exeter England 1675 210 Git 76 5 66 10 080 Old Lincoln, England. . . 1610 249 B 75. 5 5.94 0.78 9 856 Westminster^ London.... i8S7 249 B 72 5.75 0.79 8960 ^ * John W. Nystrom, in the Journal of the Franklin Institute, Philadelphia. t This bell is fractured and has not been rung for many years. Circular of Advice on Professional Practice 1727 SYMBOLS FOR THE APOSTLES AND SAINTS From the constant occurrence of symbols in the edifices of the Middle Ages and many of the cathedrals of the present day, the following list of symbols, as commonly attached to the apostles and saints, may be found useful: Holy Apostles St. Peter. Bears a key, or two keys with different wards. St. Andrew. Leans on a cross so called from him; called by heralds the saltire. St. John the Evangelist. With a chalice, in which is a winged serpent. When this symbol is used, the eagle, another symbol of him, is never given. St. Bartholomew. With a flaying-knife. St. James the Less. A fuller's staff bearing a small square banner. ■ St. James the Greater. A pilgrim's staff, hat and escalop-shell. St. Thomas. An arrow, or with a long staff. St. Simon. A long saw. St. Jude. A club. St. Matthias. A hatchet. St. Philip. Leans on a spear or has a long cross in the shape of a T. St. Matthew. A knife or dagger. St. Mark. A winged lion. St. Luke. A bull. St. John. An eagle. St. Paul. An elevated sword, or two swords in saltire. St. John the Baptist. An Agnus Dei. St. Stephen. With stones in his lap. Saints St. Agnes. A lamb at her feet. St. Cecilia. With an organ. St. Clement. With an anchor. St. David. Preaching on a hill. St. Denis. With his head in his hands. St. George. With the dragon. St. Nicholas. With three naked children in a tub, in the end whereof rests his pastoral staff. St. Vincent. On the rack. CIRCULAR OF ADVICE RELATIVE TO PRINCIPLES OF PROFESSIONAL PRACTICE AND THE CANONS OF ETHICS, BY THE AMERI- CAN INSTITUTE OF ARCHITECTS * ■ A Circular of Advice Introductory. The American Institute of Architects, seeking to maintain a high standard of practice and conduct on the part of its members as a safeguard of the important financial, technical and esthetic interests entrusted to them, offers the following advice relative to professional practice: The profession of architecture calls for men of the highest integrity, business capacity and artistic *The American Institute of Architects, Document No. 141, Washington, D. C, April 29, 1919. Reprinted by permission. This circular relates to the principles of professional practice and the canons of ethics. 1728 Circular of Advice on Professional Practice Part 3 ability. The architect is entrusted with financial undertakings in which his honesty of purpose must be above suspicion; he acts as professional adviser to his client and his advice must be absolutely disinterested; he is charged with the exerdse of judicial functions as between client and contractors and must act with entire impartiahty; he has moral responsibilities to his professionil associates and sabordinates; finally, he is .engaged in a profession which carries with it grave responsibility to the public. These duties and responsibilities cannot be properly discharged unless his motives, conduct and ability are sujh as to command respect and confidence. No set of rules can be framed which will particularize all the duties of th2 architect in his various relations to his clients, to contractors, to his professional brethren, and to the public. The following principles should, however, govern the conduct of members of the pro- fession and should serve as a guide in circumstances other than those enumer- ated: (i) On the Architect's Status. The architect's relation to his client is primarily that of professional adviser; this relation continues throughout the entire course of his service. When, however, a contract has been executed between his client and a contractor by the terms of which the architect becomes the official Interpreter of its conditions and the judge of its performance, an additional relation is created under which it is incumbent upon the arcliitect to side neither with client nor contractor, but to use his powers under the con- tract to enforce its faithful performance by both parties. The fact that the architect's payment com^s from tha client does not invalidate his obligation to act with impartiahty to both parties. (2) On Preliminary Drawings and Estimates. The architect at the out- set should impress upon the client the importance of su'iicient time for the preparation of drawings and sp3cifications. It is the duty of the architect to make or secure preliminary estimates when requested, but he should acquaint the client with their conditional character and inform him. that complete and final figures can be had only from complete and final drawings and specifications. If an unconditional limit of cost be imposed before such drawings arc m;ide and estimated, the architect must be free to make such adjustments as seem to him necessary. Since the architect should assume no responsibility that may pre- vent him from giving his client disinterested advice, he should not, by bond or otherwise, guarantee any estimate or contract. (3) On Superintendence and Expert Services. On all work except the simplest, It is to the interest of the owner to employ a superintendent or clerk OF THE WORKS. In many engkieering problems and in certain specialized esthetic problems, it is to his interest to have the services of special experts and the architect should so inform him. The experience and special knowledge of the architect make it to the advantage of the owner that these persons, although paid by the owner, should be selected by the architect under whose direction they are to work. . (4) On the Architect's Charges. The Schedule of Charges of the American Institute of Architects is recognized as a proper minimum of payment. The locality or the nature of the work, the quality of services to be rendered, the skill of the practitioner or other circumstances frequently justify a higher charge than that indicated by the schedule. (5) On Payment for Expert Service. The architect when retained as an EXPERT, whether in connection with competitions or otherwise, should receive a compensation proportionate to the responsibUity and difficulty of the service. Nq duty of the arcliitect is more exacting than such service, and the honor of Circular of Advice on Professional Practice 1729 the profession is involved in it., Under no circumstances should experts know- ingly name prices in competition with each other. (6) On Selection of Bidders or Contractors. The architect should advise the client in the selection of bidders and in the award of the contract. In advising that none but trustworthy bidders be invited and that the award be made only to contractors who are rehable and competent, the architect protects the interests of his client. . (7) On Duties to the Contractor. As the architect decides whether or not the intent of his plans and specifications is properly carried out, he should take special care to see that these drawings and specifications are complete and accurate, and he should never call upon the contractor to make good oversights or errors in them nor attempt to shirk responsibility by indefinite clauses in the contract or specifications. (8) On Engaging in the Building Trades. The architect should not directly or indirectly engage in any of the building trades. If he has any financial interest in an}^ building material or device, he should not specify or use it without the knowledge and approval of his chent. (9) On Accepting Commissions or Favors. The architect should not receive any commission or any su])stantial service from a contractor or from any interested person other than his client. (10) On Encouraging Good Workmanship. The large powers with which the architect is invested should be used with judgment. While he must con- demn bad work, he should commend good work. Intelligent initiative on the part of craftsnen and workmen should be recognized and encouraged and the architect should make evident his appreciation of the dignity of the artisan's fltnction. (11) On Offering Services Gratuitously. The seeking out of a possible client and the offering to him of professional services on approval and without compensation, unless warranted by personal or previous business relations, t-cnds to lower the dignity and standing of the profession and is to be condemned. (i?) On Advertising. PubUcity of the standards, aims and progress of the profession, both in general and as exemphfied by individual achievement, is ei^sential. Advertising of the individual, meaning self-laudatory publicity procured by the person advertised or with his consent, tends to defeat its own ends as to the individual as well as to lower the dignity of the profession, and is to be deplored. (13) On Signing Buildings and Use of Titles. The unobtrusive signature OF BUILDINGS after completion is desirable. The placing of the architect's NA\rE ON A building DURING CONSTRUCTION serves a legitimate purpose for public information, but it is to be deplored if done obtrusively for individual publicity. The use of initials designating membership in the Institute is desirable in all professional relationships, in order to promote a general under- standing of the Institute and its standards through a knowledge of its members and their professional activities. Upon the members devolves the responsibility to associate the symbols of the Institute with acts representative of the highest standards of professional practice. fi4^ On Competitions. An architect should not take part in a competition as a compf.titor or juror unless the competition is to be conducted according to the !)est practice and usage of the profession, as evidenced by its havmg received the approval of the Institute, nor should he continue to act as pro- fession \l a-dviser after it has been determined that the program cannot be so X730 The Canons of Ethics Part 3 drawn as to receive such approval. When an architect has been authorized to submit sketches for a given project, no other architect should submit sketches for it until the owner has taken definite action on the first sketches, since, as far as the second architect is concerned, a competition is thus established. Except as an authorized competitor, an architect may not attempt to secure work for which a competition has been instituted. He may not attempt to influence the award in a competition in which he has submitted drawings. He may not accept the commission to do the work for which a comf>etition has been instituted if he has acted in an advisory capacity either in drawing the program or in making the award. (15) On Injuring Others. An architect should not falsely or maliciously injure, directly or indirectly, the professional reputation, prospects or business of a fellow architect. (16) On Undertaking the Work of Others. An architect should not under- take a commission while the claim for compensation or damages or both, of an architect previously employed and whose employment has been terminated remains unsatisfied, unless such claim has been referred to arbitration or issue has been joined at law; or unless the architect previously employed neglects to press his claim legally; nor should he attempt to supplant a fellow architect after definite steps have been taken toward his employment. (17) On Duties to Students and Draughtsmen. The architect should advise and assist those who intend making architecture their career. If the beginner must get his training solely in the office of an architect, the latter should assist him to the best of his ability by instruction and advice. An architect should urge his draughtsmen to avail themselves of educational opportunities. He should, as far as practicable, give encouragement to all worthy agencies and institutions for architectural education. While a thorough technical prepar- ation is essential for the practice of architecture, architects cannot too strongly insist that it should rest upon a broad foundation of general culture. (18) On Duties to the Public and to Building Authorities. An archi- tect should be mindful of the pubHc welfare and should participate in those movements for public betterment in which his special training and experience quality him to act. He should not, even under his client's instructions, engage in or encourage any practices contrary to law or hostile to the pubUc interest; fo*- as he is not obliged to accept a given piece of work, he cannot, by urging that he has but followed his client's instructions, escape the condemnation attaching to his acts. An architect should support all public officials who have charge of building in the rightful performance of their legal duties. He should care- fully comply with all l^uilding laws and regulations, and if any such appear to him unwise or unfair, he should endeavor to have them altered. (19) On Professional Qualifications. The public has the right to expect that he who bears the title of architect has the knowledge and abiUty needed for the proper invention, illustration and supervision of all building operations which he may undertake. Such quaUfications alone justify the assumption of the title of architect. The Canons of Ethics * The following Canons are Adopted by The American Institute of Architects as a general guide, yet the enumeration of particular duties should * Adopted, December 14-16, 1909. Revised, December 10-12, 191 2. Revised, April 2«, 1918. Circular of Advice on Professional Practice 1731 not be construed as a denial of the existence of others equally important although not specially mentioned. It should also be noted that the several sections indicate offenses of greatly varying degrees of gravity. It is unprofessional for an architect (i) To engage directly or indirectly in any of the building or decorative trades. (2) To guarantee an estimate or contract by bond or otherwise. (3) To accept any commission or substantial service from a contractor or from any interested party other than the owner. (4) To take part in any competition which has not received the approval of the Institute or to continue to act as professional adviser after it has been de- termined that the program cannot be so drawn as to receive such approval. (s) To attempt in any way, except as a duly authorized competitor, to secure work for which a competition is in progress. (6) To attempt to influence, either directly or indirectly, the award of a com- petition in which he is a competitor. (7) To accept the commission to do the work for which a competition has been instituted if he has acted in an advisory capacity, either in drawing the pro- gram or in making the award. (8) To injure falsely or maliciously, directly or indirectly, the professional reputation, prospects, or business of a fellow architect. (9) To undertake a commission while the claim for compensation, or damages, or both, of an arcliitect previously employed and whose employment has been terminated remains unsatisfied, until such claim has been referred to arbitration or issue has been joined at law, or unless the architect previously employed neglects to press his claim legally. (10) To attempt to supplant a fellow architect after definite steps have been taken toward his employment, that is, by submitting sketches for a project for which another architect has been authorized to submit sketches. (ii) To compete knowingly with a fellow architect for employment on the basis of professional charges. Professional Practice of Architects. Details of Service to be Rendered and Schedule of Proper Minimum Charges * (i) The architect's professional services consist of the necessary conferences, the preparation of preliminary studies, working drawings, specifications, large- scale and full-size detail drawings; the drafting of forms of proposals and contracts; the issuance of certificates of payment; the keeping of accounts, the general administration of the business and supervision of the work, for which, except as hereinafter mentioned, the minimum charge, based upon the total cost of the work t complete, is 6 per cent. (2) On residential work, alterations to existing buildings, monuments, furni- ture, decorative and cabinetwork and landscape-architecture, it is proper to make a higher charge than above indicated. *As adopted at the Washington, D. C, Convention, December 15-17, 1908, and as revised in form at the Minneapolis convention, December 6-8, 1916. t The words "the cost of the work," as used in Articles (i) and (9) hereof, are ordinarily to be interpreted as meaning the total of the contract-sums incurred for the execution of the work, not including architect's and engineer's fees or the salary of the clerk of the works, but in certain rare cases, that is, when labor or material is furnished by the owner below' its market cost or when old materials are reused, the cost of the work is to be interpreted as the cost of all materials and labor necessary to complete the work, as such cost would have been if all materials had been new and if all labor had been fully paid at market prices current when the work was ordered, plus contractor's profits and exuensps 1732 Schedule of Charges Part 3 (3) The architect is entitled to compensation for articles purchased under his direction, even though not designed by him. (4) Where the architect is not otherwise retained, consultation-fees for pro- fessional advice are to be paid in proportion to the importance of the question involved and services rendered. (5) The architect is to be reimbursed for the costs of transportation and living incurred by him and his assistants while traveling in discharge of duties connected with the work, and the costs of the services of heating, ventilating, mechanical, and electrical engineers. (6) The rate of percentage arising from Articles (i) and (2) hereof, that is, the basic rate, applies when all of the work is let under one contract. Should the owner determine to have certain portions of the work executed under separate contracts, as the architect's burden of service, expense, and responsi- bility is thereby increased, the rate in connection with such portions of the work is greater (usually by 4 per cent) than the basic rate. Should the owner deter- mine to have substantially the entire work executed under separate contracts, then such higher rate applies to the entire work. In any event, however, the basic rate, without increase, applies to contracts for any portions of the work on which the owner reimburses the engineer's fees to the architect. (7) If, after a definite scheme has been approved, the owner makes a decision which, for its proper execution, involves extra services and expense for changes in or additions to the drawings, specifications, or other documents; or if a con- tract be let by cost of labor and materials plus a percentage or fixed sum; or if the architect be put to labor or expense b\' delays caused by the owner or a con- tractor, or Ijy the delinquency or insolvency of either, or as a result of damage by fire, he is to be equitably paid for such extra service and expense. (8) Should the execution of any work designed or specified by the architect or any part of such work be abandoned or suspended, the architect is to be paid in accordance with or in proportion to the terms of Article (9) of this Schedule for the service rendered on account of it, up to the time of such abandonment or suspension. (9) Whether the work be executed or whether its execution be suspended or abandoned in part or whole, payments to the architect on his fee are subject to the provisions of Articles (7) and (8), made as follows: Upon completion of the preliminary studies, a sum equal to 20 per cent of the basic rate computed upon a reasonable estimated cost. Upon completion of specifications and gen- eral working drawings (exclusive of details) a sum sufiicient to increase pay- ments on the fee to sixty per cent of the rate or rates of commission agreed upon, as influenced by Article (6), computed upon a reasonable cost estimated on such completed specifications and drawings, or if bids have been received, then computed upon the lowest bona-fide bid or bids. From time to time during the execution of work and in proportion to the amount of service ren- dered by the architect, payments are made until the aggregate of all payments made on account of the fee under this Article reaches a sum equal to the rate or rates of commission agreed upon as influenced by Article (6), computed upon the final cost of the work. Payments to the architect, other than those on his fee, fall due from time to time as his work is done or as costs are incurred. No deduction is made from the architect s fee on account of penalty, liquidated damages or other sums withheld from payments to contractors. (10) The owner is to furnish the architect with a, complete and accurate survey of the building-site, giving the grades and Hnes of streets, pavements and adjoining properties; the rights, restrictions, easements, boundaries and contours of the building-site, and full information as to sewer, water, gas and Architectural Competitions 1733 electrical service. The owner is to pay for borings or test-pits and for chemical mechanical or other tests, when required. (ii) The architect endeavors to guard the owner against defects and de- ficiencies in the work of contractors, but he does not guarantee the performance of their contracts. The supervision of an architect is to be distinguished from the continuous personal superintendence to ]je obtained by the employment of a clerk of the works. When authorized by the owner, a clerk of the works, acceptable to both owner and architect, is to be engaged by the architect at a salary satisfactory to the owner and paid by the owner, upon presentation of the architect's monthly certificates. (12) When requested to do so, the architect, makes or procures preUminary estimates on the cost of the work and he endeavors to keep the actual cost of the work as low as may be consistent with the purpose of the building and with proper workmanship and material, but no such estimate can be regarded as other than an approximation. (13) Drawings and specifications, as instruments of service, are the property of the architect, whether the work for which they are made be executed or not. ARCHITECTURAL COMPETITIONS * This Circular of Advice furnishes information as to the best methods of conducting architectural competitions and states the conditions which are pre- requisite to participation in them by members of The American Institute of Architects. It does not apply to competitions for work to he erected elsewhere than in the United States, its territories and possessions. The Attitude of The American Institute of Architects to Competitions. Since its foundation, more than sixty years ago (1857), The American Institute of Architects has given much attention to the conduct of architectural cx)M- PETiTiONS. These contests, instituted when the direct selection of an architect could not be made, were for many years conducted without proper regulation and often in disregard of the interests both of the owner aiad of the competitors. The owner, totally unfamiliar with the intricacies of the subject, assumed, with- out skilled assistance, to prepare the programme, laying down, or more frequently ignoring, rules to govern procedure. With the growth of the countr\', the in- crease in expenditures for pubHc and private buildings, and the increase in the number of architects, all the evils of ill-regulated competitions became more marked. Programmes varied from loose and careless forms, difficult to under- stand and often open to the suspicion that only the initiated knew what they meant, to over-elaborate ones necessitating useless study of details and needless drawings. Those instituting the competition often had no legal authority to pay any competitors, still less to employ the winner. There was great economic waste, the total cost of participation exceeding the total net profit accruing to the profession from work secured through competitions. Architects have learned that the outcome of a competition, unless governed by well-defined agreements, is largely a matter of chance. The owner has, to be sure, a choice of designs, but *The American Institute of Architects, Document 114. Reprinted by permission. Authorized by the 43d annual convention at Washington, D. C, December 14-16, 1909; issued March 30, 1910, amended June 10, 1910; and January 3, 1911; ratified by the 44th annual convention at San Francisco, January 16-21, 1911; reaffirmed by the 45th annual convention at Washington, D. C; amended January 3, 1912, as authorized by the convention; amended December 9, 191 2, and ratified hy the 46th annual convention at Washington, D. C, December 10-12, 191 2; amended December 2, 1913, and ratified by the 47th annual convention at New Orleans, La., December 3-5, 1913; amended and ratified by the 48th annual convention at Washington, D. C, December 2-4, 1914. 1734 Architectural Competitions Pa^^ he is no more likely to make the wisest selection or to obtain the best building than if he selects his architect directly, guided by the results previously achieved by the men he is considering. When a competition is necessary or desirabb it should be of such form as to establish equitable relations between the owner and the competitors. To insure this: (i) The REQUIREMENTS should be clear and definite, and the statement of them, since it must be in technical terms, should be drawn by one familiar mih such terms. (2) The COMPETENCY of all competing should be assured. The drawings sub- mitted in a competition are evidence, only in part, of the ability of the architect to execute the building. The owner, for his own protection, should admit to the competition only those to whom he would be willing to entrust the work; that is, to men of know^n honesty and competence. (3) The AGREEMENT between the owner and the competitors should be definite, as becomes a plain statement of business relations. (4) The JUDGMENT should be based on knowledge, and since ideas presented in the form of drawings are intelligible only to a trained mind, judgment should not be rendered until the owner has received competent technical advice as to the merits of those ideas. To sum up: To insure the best results, a competition should have (i) a clear programme, (2) competent competitors, (3) a business agreement, (4) a fair judgment. Fifteen years ago many competitions had none of these provisions and few had all of them. The commonest form of competition was one that was open to all, had a programme prepared by a layman, was judged by the owner without professional assistance, contained no agreement, and made no provision to eliminate the incompetent. All this demanded correction. The Institute, seeking a means of reform, perceived at once that its relation to the owner could be only an advisory one. It might advise him how to hold a competition, but it could go no further. To architects in general the Institute could scarcely presume to offer even its advice, but being a professional body charged with maintaining ethical standards among its own members, its duty was to see that they did not take part in competitions that fell below a reason- able standard. It was, therefore, voted in convention of the Institute that members should be free to take part in competitions only when their terms had received the APPROVAL OF THE INSTITUTE. Thereupon the Institute fully stated the prin- ciples which should govern competitions and defined the conditions prerequisite to the giving of its approval. These are contained in the Circular of Advice here following, which is intended as a guide to all who are interested in com- petitions. Committees of the Institute throughout the country are authorized to give its approval to competitions when properly conducted, but unless a programme has received such approval members of the Institute do not accept a position as competitor or juror, nor does a member continue to act as profes- sional adviser after it becomes evident that the owner will not permit his programme to be brought into harmony with the principles approved by the Institute. The position thus taken by the Institute is by no means an arbitrary one, since it governs the action of none but its own members. To the owner its service has been of great value in giving him information and useful advice and in saving him from the delays, cost and disappointment incident to the amateur conduct of a competition. The owner who disregards the standard set by the Institute finds it increasingly difficult to get men of standing in the profession to enter. He who raises his programme to that standard has no difficulty in securing the Architectural Competitions 1735 services of architects of the greatest ability. Even in the few years since the Institute first made its firm stand against the abuses of competitions, the effect of that action has been far greater than could have been foreseen. It has not altogether eliminated ill-regulated competitions, but it has greatly reduced their number, and it is safe to say that no competition of prime importance is now conducted except in accordance with the principles stated in the following Cir- cular OF Advice: A Circular of Advice and Information Relative to the Conduct of Architectural Competitions Competitions are instituted to enable the owner * to choose an architect through comparison of the designs submitted. The American Institute of Archi- tects, believing that the interests of both owner and competitors are best served by fair and equitable agreements between them, issues this circular as a state- ment OF the principles which should underlie such agreements. The Institute does not assume to dictate the owner's course in conducting competitions, but aims to assist him by advising the adoption of such methods as experience has proved to be just and wise. So important, however, does the adoption of such methods appear to architects that members of the Institute do not take part in competitions except under conditions based on this circular and specifically set forth in Articles (i6) and (i8). (i) On Competitions in General. A competition exists when two or more architects prepare sketches at the same time for the same project, but no archi- tect who prepares drawings for comparison in problems of an altruistic or edu- cational nature, where the problem does not involve a definite proposed building operation, shall be held as having taken part in a competition, within the mean- ing of this circular of advice. (2) On the Employment of a Professional Adviser. No competition shall be instituted without the aid of a competent adviser. He should be an architect of the highest standing and his selection should be the owner's first step. He must be chosen with the greatest care, as the success of the competition will depend largely upon his experience and abiUty. The expert's advice is of great value to the owner, for example, in so drawing the programme as to safeguard him against the employment of an architect who submits a design largely exceeding in cost of execution the sum at his disposal, and in helping him to avoid the disappointment, embarrassment and litigation which so often result from competitions conducted without expert technical advice. The duties OF the expert are to advise those who hold the competition as to its form and terms, to draw up the programme, to advise in choosing the competitors, to answer their questions, and to conduct the competition. (3) On the Forms of Competition. The following forms of competition are recognized: . u c w Limited. In this form, participation is limited to a certam number of archi- tects whose names should be stated in the programme and to any one of whom the owner is wiUing to entrust the work. In a limited competition the com- petitors may be chosen (a) from among architects whose ability is so evident that no formal inquiry into their qualifications is needed, or (b) from among architects who make application accompanied by evidence of their education and experience. The Hmited form has the advantage that the owner and the professional adviser may meet competitors and discuss the terms of the com- * The person, corporation or other entity instituting? a competition, whether acting directly or through representatives, is heroin called the owner. 1736 Architectural Competitions Part 3 petition with them before the issuance of the programme Form (a) is the simplest and most direct form of competition. Open. The Institute believes that a competition open to all who wish to participate without regard to their qualifications is detrimental to the interests alike of owner and of architects. It will, therefore, give its approval to that form only when conducted in two stages, since by that means alone it is possible to insure anonymity of submission while safeguarding the owner's interests against the selection as winner of a person lacking the qualifications set forth in Article (4) hereof. In this form there is a first stage open to all, in which the com- petitive drawings are of the slightest nature, involving only the fundamental ideas of the solution. These drawings are accompanied by evidence of the com- petitor's education and experience. From the first stage a small number who have thus demonstrated their competence to design the work and to carry it successfully into execution are chosen to take part in a final and strictly anony- mous stage involving competitive drawings of the type indicated in Article (8) hereof. (4) On the Qualification of Competitors. The interests of the owner may be seriously prejudiced by admitting to a limited competition or to the second stage of an open competition any architect who has not established to the satisfaction of the owner his. competence to design and execute the work. It is sometimes urged that by admitting all who wish to take part some unknown but brilliant designer may be found. If the object of a competition were a set of sketches, such reasoning might be valid. But sketches give no evidence that their author has the matured artistic ability to fulfil their promise, or that he has the technical knowledge necessary to control the design of the highly com- plex structure and equipment of a modern building, or that he has executive ability for large afifairs, or the force to compel the proper execution of contracts. Attempts have often been made to defend the owner's interests by associating an architect of ability with one lacking in experience. These have generally resulted in failure. As the owner should feel bound, not only legally, but in point of honor, to retain as his architect the competitor to whom the award is made, it is essential that the competitors in a limited competition, or in the second stage of an open competition, should be selected with the greatest care in consultation with the professional adviser, and that there should be included among them only architects in whose ability and integrity the ov/ner has abso- lute confidence, and to any one of whom he is willing to entrust the work. (5) On the Number of Competitors. Experience has demonstrated that the admission of many competitors is detrimental to the success of a competi- tion. When there are many, each knows that he has but a slight chance of success, and he is therefore less aroused to his best effort than when there are but a few. As the owner is interested only in the best result, he is ill-advised to sacrifice quality for quantity. (6) On Anonymity of Competitors. Absolute and efifective anonymity is a necessary condition of a fair and unbiased competition. The signing of DRAWINGS should not be permitted nor should they bear any motto, device or distinguishing mark. Drawings and the accompanying sealed envelopes con- taining their authors' names should be numbered upon receipt, the envelopes remaining unopened until after the award. (7) On the Cost of the Proposed Work. No statement of the intended cost of the work should be made unless it has been ascertained that the work as described in the programme can be properly executed within the sum named. Jn general it is wiser to limit the cubic contents of the building than to state a Architectural Competitions 1737 limit of cost. The programme slioiild neither require nor permit competitors to furnish their own or builders' estimates of the cost of executing the work in accordance with their designs. Such estimates are singularly unreliable. If the cubage be properly limited they are unnecessary. (8) On the Jury of Award. To insure a wise and just award and to pro- tect the interests of both the owner and the competitors, the competitive draw- ings should be submitted to a jury sj chosen as to secure expert knowledge and freedom from personal bias. Such a jury thoroughly understands and can explain the intent of the drawings. It discovers from them their authors' skill in design, arrangement and construction. Because of its trained judgment its advice as to the merits of the designs submitted is of the highest value to the owner. The jury must consist of at least three members, one of whom must, and a majority of whom should, be PRACTicmo architects. One or more members of the jury may be chosen by the competitors. It is the duty of the JURY to study carefully the programme and all conditions relating to the problem and the competition before examining the designs submitted; to refuse to make or recommend an award in favor of the author of any design that does not fulfil the conditions distinctly stated as mandatory in the programme; to give ample time to the careful study of the designs; and to render a decision only after mature consideration. The jury should see to it that a copy of its report reaches every competitor. The professional adviser should not be a member of the jury, as his judgment is apt to be influenced by his previous study of the problem. (9) On the Competitive Drawings. The purpose of an architectural com- petition is not to secure fully developed plans, but such evidence of skill in treat- ing the essential elements of the problem as will assist in the selection of an ARCHITECT. The drawings should, therefore, be as few in number and as simple in character as will express the general design of the building. A jury of experts does not need elaborate drawings. (10) On the Programme. The programme should contain rules for the conduct of the competition, instructions for competitors and the jury, and t;he agreement between the owner and the competitors. Uniform conditions for all competitors are fundamental to the proper conduct of competitions. Lengthy programmes and detailed instructions as to the desired accommodations should be avoided as they confuse the problem and hamper the competitors. The problem should be stated broadly. Its solutions should be left to the competi- tors. A distinction should be clearly drawn between the mandatory and the ADVISORY provisions of the programme, that is, between those which, if not met, preclude an award in favor of the author of a design so failing, and those which are merely optional or of a suggestive character. The mandatory requirements should be set forth in such a way that they cannot fail to be recognized as such. They should be as few as possible, and should relate only to matters which cannot be left to the discretion of the competitors. It is difficult to summarize briefly the progranime, but it should at least: (a) Name the ov/ner of the structure forming the subject of the competition, and state whether the owner institutes the competition personally or through representatives; if the latter, name the representatives, state how their author- ity is derived, and define its scope. (b) State the kind of competition to be instituted, and in limited conipetitions name the competitors; or in open competitions, if the competition is limited geographically or otherwise, state the limits. (c) Fix a time and place for the receipt of the designs. The time should not be altered except with the unanimous consent of the competitors. (d) Furnish exact information as to the site. 1738 Architectural Competitions Part (e) State the desired accommodation, avoicling detail. (f) State the cost if it be fixed or, better, Hmit the cubic co-ntents. (g) Fix uniform requirements for the drawings, giving the number, the sc; or scales, and the method of rendering. (h) Forbid the submission of more than one design by any one competitor. (i) Provide a method for insuring anonymity of submission. (j) Name the members of the jury or provide for their selection. Define their powers and duties. If for legal reasons the jury may not make the final award, state such reasons and in whom such power is vested. (k) Provide that no award shall be made in favor of any design until the jury shall have certified that it does not violate any mandatory requirement of the programme. (1) Provide that during the, competition there shall be no communication relative to it between any competitor and the owner, his representatives, or any member of the jury, and that any communication with the professional adviser shall be in writing. Provide also that any information, whether in answer to such communications or not, shall be given in writing simultaneously to all competitors. Set a date after which no questions will be answered. (m) State the number and amount of payments to competitors. (n) Provide that the professional adviser shall send a report of the competi- tion to each competitor, including therein the report of the jury. (o) Provide that no drawing shall be exhibited or made public until after the award of the jury. (p) Provide for the return of unsuccessful drawings to their respective authors within a reasonable time. (q) Provide that nothing original in any of the unsuccessful designs shall be used without consent of, and compensation to, the author of the design in which it appears. (r) Include the contract between the owner and the competitors. (s) Include the contract between the owner and the architect receiving the award. (ii) On the Agreement. An owner who institutes a competition assumes a moral obligation to retain one of the competitors as his architect. In order that architects invited to compete may determine whether they will take part it is essential that they should know the terms upon which the winner will be employed; and it is of the utmost importance to the owner that those terms should be so clearly defined that no disagreement as to their meaning can arise after the award is made. Unless they be so defined, delay is likely to occur and disagreements to arise at a time when a complete understanding between owner and architect is most important for the welfare of the work. Therefore, there must be included in the programme a form which guarantees the appointment of one of the competitors as architect and provides an agreement operative up^n that appointment, defining his employment m terms consonant with the best practice. This must conform in all fundamental respects to the typical form of agreement appended to this circular. (12) On Payments to Unsuccessful Competitors. In a limited com- petition and in the second stage of an open competition each competitor, except the winner, should be paid for his services. (13) On Legality of Procedure. It is highly important tliat each step taken in coiiaecLijii with a co.npelition and every provision of the jorogramrae should be in consonance with law. Those charged with holding the competition should know and state their authjrity. If they are not empowered to Ijind their principal by contracts with the competitors, they should seek and receive such Architectural Competitions 1739 authority before issuing an invitation. If authority cannot legally be granted to the jury to make the award, that fact should be stated, and the body named in which such authority is vested. (14) On the Conduct of the Owner. In order to maintain absolute impartiahty toward all competitors, the owner, his representatives and all con- nected with the enterprise should, as soon as a professional adviser has been appointed, refrain from holding any communication in regard to the matter with any architect except the adviser or the jurors. The meeting with com- petitors described in Article (3) is of course an exception. (15) On the Conduct of Architects. An architect should not attempt in any way, except as a duly authorized competitor, to secure work for which a competition is in progress, nor should he attempt to influence, either directly or indirectly, the award in a competition in which he is a competitor. An archi- tect should not accept the commission to do the work for which a competition has been instituted if he has acted in an advisory capacity, either in drawing the programme or making the award. An architect should not submit in competi- tion a design which has not been produced in his own office or under his own direction. No competitor should enter into association with another architect, except with the consent of the owner. If such associates should win the com- petition, their association should continue until the completion of the work thus won. During the competition, no competitor should hold any communi- cation relative to it with the owner, his representatives or any member of the jury, nor should he hold any communication with the professional adviser, except it be in writing. When an architect has been authorized to submit sketches for a given project, no other architect should submit sketches for it until thf? owner has taken definite action on the first sketches, since, as far as the second architect is concerned, a competition is thus established. (16) On the Participation of Members of the Institute. Members of The American Institute of Architects do not take part as competitors or jurors in any competition the programme of which has not received the formal approval of the Institute, nor does a member continue to act as professional adviser after it has been determined that the programme cannot be so drawn as to receive such approval. (17) Committees. In order that the advice of the Institute may be given to those who seek it and that its approval may be given to programmes in con- sonance with its principles, the Institute maintains the following committees: (a) The Standing Committee on Competitions, representing the Institute in its relation to competitions generally. This committee advises the subcom- mittees and directs their work and they report to it. . (b) A subcommittee for the territory of each chapter, representmg the Institute in its relation to competitions for work to be erected within such The president of the chapter is ex-officio chairman of the subcommittee, the other members of which he appoints. The subcommittees derive their authority from the Institute and not from the chapters. An appeal from the decision of a subcommittee may be made to the standing committee The standing committee may approve, modify or annul the decision of a subcom- mittee. (iS) The Institute's Approval of the Programme. The approval of the Institute is not given to a programme unless it meets the following essential conditions: (a) That there be a professional adviser. .,. j . a .- 1 / ^ (b) That the competition be of one of the forms described m Article (3). 1740 Arcjiitectural Competitions Part 3 (c) That the programme contain an Agreemknt and Conditions of Con- tract between architect and owner in conformity with those printed in the Appendix of this circular, that it include no provision at variance therewith, that it ontain terms of payments in accord with good practice, and that it spe- cifically set forth the nature of expert engineering services for which the architect will be reimbursed. (d) That the programme make provision for a jury of at least three persons. (e) That the programme conform in all particulars to the spirit of this cir- cular. When the programme meets the above essential conditions, the approval of the Institute may be given to it by the subcommittee for the territory in which the work is to be erected, or if there be no subcommittee for that territory, then by the standing committee on competitions. If, for legal or other reasons, the standing committee deem that deviations from the essential conditions are justified, it may give the approval of the Institute to a programme containing such deviations. Power to give approval in such cases is, however, vested only in the standing committee. The professional adviser, when duly authorized in writing by the proper committee, may print the Institute's approval as a part of the programme or otherwise communicate it to those invited to compete. ^ Typical Form of Agreement between Owner and Competitors In consideration of the submission of drawings in this competition (here insert the name of the owner or of the body duly authorized to enter into contracts on behalf of the owner), hereinafter called the owner, agrees with the competi- tors jointly and severally that the owner will, within days of the date set for the submission of drawings, make an award of the commission to design and supervise the work forming the subject of this competition to one of those competitors who submit drawings in consonance with the mandatory require- ments of this programme, and will thereupon pay him, on account of his services as architect, one-tenth of his total estimated fee as stated below. And further, in consideration of the submission of drawings as aforesaid and the mutual promis3s enumerated in the subjoined Conditions of Contract between Architect and Owner, the owner agrees and each competitor agrees, if the award be made in his favor, immediately to enter into a contract containing all the Conditions here following, and until such contract is executed to be bound by the said Conditions. Conditions of Contract between Architect and Owner Article I. Duties of the Architect (x) Design. The architect is to design the entire building and its immediate surroundings and is to design or direct the design of its constructive, engineering and decorative work and its fixed equipment and, if further retained, its movable furniture and the treatment of the remainder of its grounds. (2) Drawings and Specifications. The architect is to make such revision of his competitive scheme as may be necessary to complete the preliminary studies; and he is to provide drawings and specifications necessary for the con- duct of the work. All such instruments of service are and remain the property of the architect. (3) Administration. The architect is to prepare or advise as to all forms connected with the making of proposals and contracts, to issue all certificates Architectural Competitions 1741 •f payment, to keep proper accounts and generally to discharge the necessary administrative duties connected with the work. (4) Supervision. The architect is to supervise the execution of all the work committed to his control. Article II. Duties of the Owner (i) Payments. The owner is to pay the architect for his services a sum e<^l^a^ to per cent * upon the cost of the work. (The times and amounts of payments should be here stated.) f (2) Reimbursements. The owner is to reimburse the architect, from time to time, the amount of expenses necessarily incurred by him or his deputies while traveling in the discharge of duties connected with the work. (3) Service of Engineers. The owner is to reimburse the architect the cost of the services of such engineers for heating, mechanical and electrical work as are specifically provided for in each programme. The selection of such engineers and their compensation shall be subject to the approval of the owner. (4) Information, Clerk of the Works, etc. The owner is to give all in- formation as to his requirements; to pay for all necessary surveys, borings and tests, and for the continuous services of a clerk of the works, whose competence is approved by the architect. Standard Form of Competition- Programme J The following standard form of Competition-programme, prepared by The American Institute of Architects, contains those provisions which the Institute considers essential to the fair and equitable conduct of a competition. The Institute in no way assumes or attempts to dictate an Owner's course in con- ducting a competition; it claims only the right to control its own members, and having found by experience the danger to the interests of both Owner and Competitor from a competition in which such provisions are lacking, it per- mits no member to take part in any competition which does not meet those essential conditions, and the programme of which has not been specifically approved. A competition should be of such form as to establish equitable rela- tions betv/een the Owner and the Competitor. To insure this, the require- ments should be clear and definite; the competency of the Competitors should be assured; the agreement between the Owner and Competitors should be definite, as becomes a plain statement of business relations; and the judgment should be based on expert knowledge. The following programme will, if adhered to, be duly approved by the Institute Subcommittees on Competitions for the various chapters of the Institute, and by the Standing Committee on Competitions of the Institute. * The percentage inserted should be in accord with good practice. t Good practice has established the payments on account as follows: Upon completion of the preliminary studies one-fifth of the total estimated fee less the previous payment; upon completion of contract-drawings and specifications two-fifths additional of such fee; for other drawings, for supervision and for administration, the remainder of the fee, from time to time, in proportion to the progress of the work. JAs authorized by the 48th annual convention, 1914. The American Institute of Architects, Document, Series A, No. 115, Washington, D, C., January, 1918. Reprinted by permission. 1742 . Architectural Compotitivons Part 3 Programme of Competition for (Insert name of proposed building) NOTE. Throughout this programme the word Owner is used to indicate either the owner in person, or those to whom he has delegated his powers. PART I (i) Proposed Building. The (Insert name of owner) proposes to erect a new (Insert name of building) on the site at (Insert location) (2) Authority. The (Insert name of owner) has (delegated to > (Insert name or names of individuals) authority to select an architect to prepare the plans for, and supervise thfe erection of the building. NOTE. If authority for the erection of the proposed building is granted by act of legislature, ordinance, etc., it is desirable to make clear the source of such authority. (3) Architectural Adviser. The Owner has appointed as his expert Pro- fessional Adviser (Insert name and address of adviser) to prepare this programme and to act as his Adviser in the conduct of this competition. NOTE. No competition shall be instituted without the aid of a competent adviser. He should be an architect of the highest standing and his selection should be the Owner's first step. He should be chosen with the greatest care, as the success of the competition will depend largely upon his experience and ability. The duties of the expert are to advise those who hold the competition in regard to its form and terms, to draw up the programme, to advise in choosing the Competitors, to answer inquiries from Competitors and in general to direct the competition. (4) Competitors. Participation in this competition is limited (A), to the following architects: (Insert names of invited competitors) and ^^^ ^^ ^^^^ architects as shall have made application on or before (Insert date) accompanied by evidence of their education and experience, satisfactory to the Owner and the Professional Adviser. It is agreed that the names of all those admitted to the competition shall be made public on or before (Insert date) The Owner agrees that he will admit no one as a Competitor to whom he k not willing to award the commission to erect the building, in case of his success in the competition. Architectural Competitions 1743 (5) Tury of Award. The Owner agrees that there will be a Jtjry of Award {A) which will consist of the following members: (Insert names of jury) Or (B) which will consist of members. Of these, the Owner (Insert number) has appointed the following: and (Insert names of those so selected) the Competitors will select the remaining members of the Jury. NOTE. To insure a just and wise award and to protect the interests of both the Owner and the Competitors, the drawings should be submitted to a Jury chosen to secure expert knowledge and freedom from personal* bias. The Jury shall consist of at least three members, one of whom must, and the majority of whom should, be practicing architects, for example, a layman and an architect selected by the Owner or the Building Committee, and an architect selected by the Competitors. For work of great impor- tance it is desirable to increase the size of the Jury, adding to it architects and specially qualified laymen. Some of the advantages of a Jury so constituted are that it thoroughly understands and can explain the intent of the drawings, and discovers from them their author's skill in design, arrangement and construction. Because of its expert knowledge, its judgment on the merits of the designs submitted is of the highest value to the Owner. The adaption of the recommendation that the architectural members of the Jury be in the majority, is not necessarily a cause of expense, for the reason that in order to insure the proper conduct of competitions, many architects of standing are willing, if the occasion warrants, to serve as Jurors without payment, other than actual expenses. It is cus- tomary and desirable that the Competitors should elect one or more of the architectural members of the Jury. It is not advisable that the Professional Adviser, who has drawn up the programme, be permitted to vote as a member of the Jury, although he may with advantage take part in the deUberations of the Jury. (6) Authority of Jury. The Owner agrees that the Jury above named, or selected as above provided, will have authority to make the award and that its decision in the matter shall be final. Moreover, this Jury will make an award to one of those taking part in this competition, unless no design is submitted which fulfils the mandatory requirements of this programme. The Owner further agrees to employ as architect for the work as more fully set forth herein- after, the author of the design selected by the Jury as its first choice. NOTE. If, under the law, authority to make the award cannot be delegated to the Jury, the following form should be substituted for Section (6): The Owner agrees that the Jury above named or selected as above provided, will select the design which appears to it to be the most meritorious and make a written report to the Owner, designating it by number. The Owner will then consider this design and the report of the Jury and will thereupon, without learning the identity of the Com- petitors, select as the winner of the competition the author of the design selected by the Jury, unless in his judgment there be cause to depart from such selection, in which case he will, still without learning the identity of the Competitors, select one of the other designs submitted in competition. The Owner further agrees that he will pay to the author of the design designated as most meritorious by the Jury, in case he should not be appointed Architect of the building, a prize of $ (State amount of prize) The opening of the envelope containing the name of the author of the design selected by the Owner will automatically close the contract between him and the Owner, printed as Part III hereof. (7) Examination of Designs and Award. The Professional Adviser will examine the designs to ascertain whether they comply with the mandatory re-. quirements of the programme, and will report to the Jury any instance of failure to comply with these mandatory requirements. The Owner further agrees that the Jury will satisfy itself of the accuracy of the report of the Professional Adviser, and will place out of competition and make no award to any design which does not comply with these mandatory requirements. The Jury will carefully study the programme and any modifications thereof, which may have been made through communications (see Section (12)), and will then consider the remaining designs, holding at least two sessions on separate days, and consider- ing at each session all the drawings in competition, and will make the award, and the classification of prize-winners, if prizes are given, by secret ballot, and by majority vote, before opening the envelopes which contain the names of the Competitors. In making the award the Jury will thereby affirm that it has made no effort to learn the identity of the various Competitors, and that it has remained in ignorance of such identity until after the award was made. The opening of the envelope containing the name of the author of the selected design, will automatically close the contract between him and the Owner, printed as Part III hereof. (8) Report of the Jury. The Jury will make a full report which will state its reasons for the selection of the winning design and its reason for the classifica- tion of the designs placed next in order of merit, and a copy of this report, accom- panied by the names of prize-winners, if prizes are given, will be sent by the Professional Adviser to each Competitor. Immediately upon the opening of the envelopes, the Professional Adviser will notify all Competitors, by wire, of the result of the competition. (9) Compensation to Competitors. The Owner agrees to pay to the suc- cessful competitor within ten days of the judgment, on account of his fee for services as architect, one-tenth of his total estimated fee. In full discharge of his obligation to them (in case prizes or fees are ofifered), the Owner agrees: (A) To pay the following prizes to those ranked by the Jury next to the suc- cessful design: To the design placed second $ , to the design placed third $ , to the design placed fourth $ , to the design placed fifth $ , etc., within ten days of the judgment, or (B) To pay to each of the Competitors invited to take part in this competi- tion, other than the successful Competitor, a fee of $ within ten days of the judgment. (10) Exhibition of Drawings. It is agreed that no drawings shall be ex- hibited or made public until after the award of the Jury. There will be a public exhibition of all drawings after the judgment, and all drawings, except those of the successful competitor, will be returned to their authors at the close thereof. (11) Use of Features of Unsuccessful Designs. Nothing original in the unsuccessful designs shall be used without consent of, or compensation to, the author of the design in which it appears. In case the Owner de ires to make use of any individual feature of an unsuccessful design, the same may be obtained by adequate compensation to the designer, the amount of such compensation to be determined in consultation with the author and the Pro- fessional Adviser. (12) Communications. (Mandatory.) If any Competitor desires infor- mation of any kind whatever in regard to the competitition, or the programme, he shall ask for this information by anonymous letter addressed to the Pro- fessional Adviser, and in no other way, and a copy of this letter and the -^ Architectural Competitions 1745 answer thereto will be sent simultaneously to each Competitor, but no re- quest received after (Insert date) will be answered. (13) Anonymity of Drawings. (Mandatory.) The drawings to be sub- mitted shall bear no name or mark which could serve as a means of identification, nor shall any such name or mark appear upon the wrapper of the drawings, nor shall any Competitor directly or indirectly reveal the identity of his designs, or hold communication regarding the competition with the Owner or with any member of the Building Committee or of the Jury, or with the Professional Adviser, except as provided for under Communications. It is understood that in submitting a design, each Competitor thereby affirms thart he has complied with the foregoing provisions in regard to anonymity and agrees that any vio- lation of them renders null and void this agreement and any agreement arising from it. With each set of drawings must be enclosed a plain, opaque, sealed envelope without any superscription or mark of any kind, same containing the name and address of the Competitor. These envelopes shall be opened by the Professional Adviser after the final selection has been made, and preferably in the presence of the Jury. (14) Delivery of Drawings. (Mandatory.) The drawings submitted in this competition shall be securely wrapped, addressed to the Professional Ad- viser at . in plain lettering and (Insert address for delivery of drawings) with no other lettering thereon, and delivered at this address not later than (Insert date and hour) In case drawings are sent by express, they may be delivered to an express com- pany at the above date and hour, in which case the express company's receipt, bearing date and hour, shall be mailed immediately to the Professional Ad- viser as evidence of delivery. PART II (15) Site. The site of the building is as follows (Insert description of site, and provide topographical map giving dimensions, grades, etc.) NOTE. The site should be carefully described and a survey of the property should be attached and included as part of the programme. Conditions pertaining to the site and to neighboring buildings frequently become determining factors in a design. Photo- graphs showing surrounding buildings and landscape-conditions may with advantage be included. (16) Cost. (Mandatory.) For the purpose of this competition the cost of the building shall be figured at cts per cu ft, and the total thereof (Insert number) figured on this basis shall not exceed (Insert limit of cost) (17) Cubage. (Mandatory.) Cubage shall be so computed as to show as exactly as possible the actual volume of the building, calculated from the finished level or levels of the lowest floor to the highest points of tlTe roofs, and contamed within the outside surfaces of the walls. Pilasters, cornices, balconies and other similar projections shall not be included. Porticos with engaged columns and similar projections shall be taken as solids and figured to the outer face of the columns. When columns are free-standing, one-half of the volume of the Dorti- 1746 Architectural Competitions Partfl cos shall be taken. There shall also be included in the cubage the actual volume of all parapets, towers, lanterns, dormers, vaults, and other features adding to the bulk of the building, also the actual volume of exterior steps above grade. Light-wells of an area of loss than 400 sq ft shall not be deducted. In calculat- ing cubage, account shall be taken of variations in the exterior wall-surface, as for example, the projection of a basement-story beyond the general line of the building. A figured diagram showing method adopted in cubing shall accom- pany each set of drawings. (18) Drawings. (Mandatory.) The drawings submitted shall be made according to the following hst, at the scale given, and rendered as noted; and no other drawings than these shall be submitted: (Insert list, scale and method of rendering) NOTE. The drawings submitted should be the least number necessary to set forth clearly the solution of the problem, and the scale of these drawings the smallest com- patible with the requirement that the intention of each Competitor be made clear to an expert Jury. Where the number and scale of drawings is reduced to the minimum, and simple methods of rendering imposed, the Competitors are enabled to devote their time and energy to the study of the problem, which is the serious business of a competition, instead of upon draughtsmanship and rendering, which when carried beyond a certain point, are of no value whatever in determining the fitness of the Competitors to handle the work of erecting the building, for which the competition is being held. PART III Agreement between Owner and Competitors In consideration of the submission of drawings in this competition, and the mutual promises enumerated in the subjoined Conditions of Contract be- tween Architect and Owner the Owner agrees, and each Competitor agrees if the aw.ird be made in his favor, immediately to enter into a contract contain- ing all the Conditions here following, and until such contract is executed, to be bound by the said Conditions. Conditions of Contract between Architect and Owner Duties of the Architect (i) Design. The architect is to design the entire building and its imme- diate surroundings and is to design or direct the design of its constructive, engineering and decorative work and its fixed equipment and, if further re- tained, its movable furniture and the treatment of the remainder of its grounds.' (2) Drawings and Specifications. The architect is to make such revision of his competitive scheme as may be necessary to complete the preliminary studies; and he is to provide drawings and specifications necessary for the con- duct of the work. All such instruments of service are and remain the prop- erty, of the architect. (3) Administration. The architect is to prepare or advise as to all forms connected with the making of proposals aud contracts, to issue all certificates of payment, to keep proper accounts and generally to discharge the necessary aiiministrative duties connected with the work. (4) Supervision. The architect is to supervise the execution of all the work committed to his control. Architect uru.1 Competitions 1747 Duties of the Owner (5) Payments. The Owner is to pay the architect for his services a sum equal to per cent upon the cost of the work. NOTE. The percentage inserted should be in accord with good practice. The times and amounts of payments should be here stated. Good practice has established the payments on account as follows: Upon completion of the ,preliminary studies one-fifth of Hie total estimated fee less the previous payment; upon completion of contract-drawings ar.d specifications two-fifths additional of sucK fee; for other drawings, for supervision and for administration, the remainder of the fee, from time to time, as the work progresses. (6) Reimbursements. The Owner is to reimburse the architect from time to lime, the amount of expenses necessarily incurred by him or his deputies while traveling in the discharge of duties connected with the work. (7) Service of Engineers. The Owner is to reimburse the architect, the cost of the services of engineers for (Insert nature of \v6rk for which the Owner agrees that engineers shall be employed at his expense) The selection of such engineers and their compensation shall be subject to the approval of the Owner. (8) Information, Clerk of the Works, Etc. The Owner is to give all in- formation as to his requirements; to pay for all necessary'' surveys, borings and tests, and for the continuous services of a clerk of the works whose competence is approved by the architect. PART IV Requirements of the Building NOTE. For the same reason that elaborate drawings are undesirable, it is advisable to avoid hngthy and detailed instructions as to the desired accomniodations, as they confuse the problem and hamper the Competitors; and the Owner loses thereby the benefit he might gain in allowing the Competitors freedom to develop solutions which they would not otherwise be at liberty to suggest. It should be borne in mind that either the cost of the building, as determined by its cubical contents, should be fixed, or the requirements of the Owner in regard to the design, materials of construction, dimensions of rooms, etc., should be fixed, but not both. If, on the one hand, the cubical contents and cost is fixed, it should be stated that the requirements of the Owner must be adhered to as closely as possible by Competitors; if, on the other hand, the requirements of the Owner are definitely fixed, it may be stated that the cubical contents of each design, while not limited, will be taken into consideration in making the award. In case the sizes of certain rooms, etc., are definitely fixed, the word Mandatory should be placed at the head of the paragraph referring to these rooms. Here should follow a list of rooms required, together with sizes and other data which apply to the building under consideration. 1748 Standard Documents Part C THE STANDARD DOCUMENTS OF THE AMERICAN INSTITUTE OF ARCHITECTS* Introductory Notes. This introductory paragraph is from an article t by R. Clipston Sturgis, President of The American Institute of Architects. " For many years builders' and owners have commonly used an agreement recognized as in- adequate and imperfect, and one apt to lead to serious misunderstandings, if not to legal diflGiculties. Architects entrusted with important work and its accom- panying responsibilities have endeavored to have agreements drawn which would adequately safeguard the interests involved. When, some nine years ago (1907), the Institute attempted to prepare a new standard agreement, it found already in use a considerable number of forms prepared by architects, differing in detail but agreeing in one main point. This one point was that the contract and the conditions of the contract should be treated as two branches of the same agree- ment, not as one document, nor yet as two. The contract was to be as brief as possible, stating simply what the obligation was. The conditions of the contract, complicated and involved, yet essential to the contract, were of necessity com- paratively lengthy. The most difficult part of the work, surveying the field and breaking out the way, was done by the Committees on Contracts and Specifica- tions during the years 1906 to 191 1, and resulted in the first edition of the STANDARD DOCUMENTS, pubHshed in 1911. At that time some thought the prob- lem solved; others thought it but an important step forward; which latter proved to be the fact. These first documents, excellent as they were as text-books, were not suitable for everyday use. The Institute again took up the problem, this time with the definite aim to produce a document which should entirely replace the uniform agreement when the contract for its publication expired in May, 19 1 5. This has been done and the carefully studied agreement and condi- tions OF THE contract presented to the convention in December, 19 14, have been further studied and improved and are now (19 15) on the market for general use. In the final study between January and May, 1915, the Institute had the advantages of cooperation with representatives of many of the building trades and the advice of counsel representing the Institute and counsel representing the building trades. The document, like its predecessor, will now come to the test of actual use. It will prove to be imperfect and revised sections will be necessary, but it is believed to be in the main a fair and comprehensive agree- ment and one that is practical and fit for general use. Architects everywhere are urged to use and test this form, and criticism from owners and builders will be gladly received and considered. In addition to this most important docu- ment the committee has prepared and the Institute has published a form of BOND, a LETTER OF ACCEPTANCE by a Contractor of a sub-contractor's bid, and an agreement between a contractor and sub-contractor. Many architects who have done work on which a bond has been required have been surprised at the ease with which the obligations of the bond could be evaded. In most cases, because someone, architect, contractor, or owner, had invalidated the bond. The new form of bond is prepared for insuring, as far as possible, that the bonding com- pany shall discharge its obligations and protect the owner who pays for this protection. The letter from contractor to sub-contractor is intended to provide a simple form whereby the mutual obhgations of the two shall be clearly defined. The agreement between contractor and sub-gontractor accom- plishes the same purpose in a somewhat more formal way." * Third Edition, copyrighted by The American Institute of Architects, 1915-1918, and inserted here by permission. t Published in the Journal of The American Institute of Architects, June, 1915. Standard Documents 1749 The Development of the Standard Documents. In the year 1887 The American Institute of Architects, the Western Association of Architects and the National Association of Builders, thinking it desirable to estabhsh better practice in the matter of building contracts, undertook the preparation of a form of con- tract satisfactory to all. Under the name of the uniform contract this form attained wide acceptance and has been long in use. About the year 1907, feeling that practice had advanced to a point no longer fully reflected by the uniform CONTRACT, the Institute undertook a general study of the subject with a view to developing a form of contract clear in thought, equitable, applicable to work of almost all classes, binding in law and a standard of good practice. The work was entrusted to the Standing Committee on Contracts and Specifications, who spent four years on it, studying the uniform contract and forms in use by some thirty well-known architects, and submitted various drafts for criticism to the chapters of the Institute and to engineers, contractors and architects throughout the country. The documents were prepared under the advice of Francis Fisher Kane, counsel for the Institute, and Ernest Eidlitz, and with the able and careful criticism of Professor Samuel Williston of the Harvard Law School, and with the assistance of James W. Pryor, in their editing. The Institute gave its approval to the work in 191 1. The Standing Committee on Contracts and Specifications, during the preparation of the first edition of the standard forms, consisted of Grosvenor Atterbury, Chairman; Allen B. Pond, Secretary; Frank Miles Day» William A. Boring, Frank C. Baldwin, Frank W. Ferguson, Alfred Stone and G. L. Heins. Criticisms of the first edition of the documents were invited by the Institute and during the year 19 13 a group of architects and builders in Bos- ton, known as the Joint Committee of the Boston Society of Architects, and of the Master Builders' Association, gaVe much sincere study to the subject. At the same time the National Association of Builders' Exchange offered a detailed criticism of the documents. In 19 1 4 the Institute instructed its Standing Committee on Contracts and Specifications to undertake a general revision with a view to making the con- ditions simpler in wording and more equitable. The committee was empowered to hold conferences with organizations so desiring. Subcommittees for the terri- tory of the several chapters of the Institute were appointed and collaborated with the standing committee. The Boston group presented its ideas in the form of an entirely new draft which proved of high value and its Chairman, W. Stanley Parker, was present with the Standing Committee at nearly all its meetings. The Committee had a joint meeting with representatives of the National Asso- ciation of Builders' Exchanges and thereafter the counsel of the Association, W. B. King, and the counsel of the Institute, Louis Barcroft Runk, collabo- rated most effectively with the committee. The general conditions were entirely rewritten and in response to the strong desire of contractors and subcon- tractors, the principle of general arbitration, subject to limitations in the documents, was adopted, and provisions relative to the relations of the con- tractor and his subcontractors were included in the documents. After much study, conference and criticism, a draft of the second edition was issued by authority of the Institute, April i, 19 15. During the revision of the documents, the Standing Committee on Contracts and Specifications consisted of Frank Miles Day, Chairman; Allen B. Pond, Sullivan W. Jones, Clarence A. Martin, Norman M. Isham, Octavius Morgan, Thomas Nolan, A. O. Elzner, M. B. Medary, Jr., Jos.' Evans Sperry, Frank W. Ferguson and Samuel Stone. The Construction of the Standard Documents. An agreement, and drawings and specifications are the necessary parts of a building contract. Many conditions of a general character may be placed at will in the agreement 1750 Standard Documents Part 3 or in the specifications. It is, however, wise to assemble them in a single document and, since they have as much bearing on the drawings as on the SPKCiFicATiONS, and even more on the business relations of the contracting parties, they are properly called the general conditions of the contract. As the AGREEMENT, GENERAL CONDITIONS, DRAWINGS and SPECIFICATIONS are the constituent elements of the contract and are acknov/ledged as such in the Agreement, they are correctly termed the contract documents. Statements made in any one of them are just as binding as if made in the agreement. The Institute's forms, although intended for use in actual practice, should also be regarded as a code of reference representing the judgment of the Institute as to ' what constitutes good practice and as such they may be drawn upon by archi- tects in improving their own forms. Although the forms are suited for use in connection with a single or general contract, they are equally applicable to an operation conducted under separate contracts. Titles of the Standard Contract Documents.* The new standard con- tract DOCUiffiNTS of The American Institute of Architects are now on salef by dealers in office and drafting-supphes in all the large cities of the country, and replace the old uniform contract. The following are the titles of the standard documents: a. i. form of agreement and a. 2. general Conditions of the Contract. B. Bond of suretyship. C. Form of Subcontract. D. Letter of Acceptance of Subcontractor's Proposal. A cover in heavy paper with valuable explanatory notes is sent without charge with each complete set of the documents. These documents have received the full approval of the Institute, through its conventions, board of directors and officers. They are the outcome of nine years of continuous work, by a Standing Committee on Contracts and Specifications. This committee, com- prising some of the ablest American architects, was assisted by the Institute's thirty-nine chapters; advised by eminent legal specialists in contract law and aided by representatives of the Building and Trade Associations of the United States. The Standard Documents have received the formal approval of the * Third Edition, copyrighted by the American Institute of Architects. t Notice to Architects, Builders and Contractors. The contract forms may be obtained singly or in lots from the local dealers. If your dealer cannot supply you send your order and his name to The Executive Secretary, A. I. A., The Octagon, Washington, D. C. All orders must include the necessary remittance irrespective of A. I. A. member- ship and irrespective of commercial standing of purchaser. The Institute has adopted these CASH terms, from which no exception will be made to anybody, in order to reduce cost of accountancy and thereby reduce expense to the user. Remittances may be by check, money-order, cash, or stamps. Prices for Single Copies: Agreement and General Conditions in cover, $0.14; General Conditions without Agreement, $0.10; Agreement without General Conditions, $0.03; Bond of Suretyship, $0.02; Form of Subcontract, $0.03; Letter of Acce{)tance of Sub- contractor's Proposal, $0.02; Cover (heavy paper, with valuable notes), $0.01; Com- plete set in cover, $0.20. A Trial set will be delivered upon receipt of ten 2-ceut stamps. Prices for Quantities and Discounts to Architects, Builders and Contractors. Orders for quantities are subject to the following discounts (which are also given by all dealers) : Five per cent on lots of 100 (one kind or assorted); 10% on lots of 500 (one kind or assorted); 15% on lots of i 000 (one kind or assorted). As these documents are printed on sheets, 8 H by 11 ins, and in large quantities, they cannot be supplied with any indi- vidual names or printing different from the standard forms. The Institute does not wish to encourage the use of the agreement with general conditions other than those endorsed by it, but on request will sell the agreements separate from tlic standard GENERAL CONDITIONS at 3 cts each. Standard Documents 1751 National Association of Builders' Exchanges, the National Association of Master Plumbers, the National Association of Sheet Metal Contractors of the United States, the National lilectrical Contractors' Association of the United States, the National Association of Marble Dealers, the Building Granite Quarries Association, the Building Trades Employers' Association of the City of New York, and the Heating and Piping Contractors' National Association. A. I. THE STANDARD FORM OF AGREEMENT BETWEEN CONTRACTOR AND OWNER* ISSUED BY THE AMERICAN INSTITUTE OF ARCtllTECTS t This form has been approved by the National Association of Builders' Exchanges, The National Association of Master Plumbers, the National Association of Sheet Metal Contractors of the Utiited States, the National Electrical Contractors' Association of the United States, the National Association of Marble Dealers, the Building Granite Quarries Association, the Building Trades Employers' Association of the City of New York, and the Heating and Piping Contractors' National Association. THIRD EDITION, COPYRIGHT 1915-1918, BY THE AMERICAN INSTITUTE OF ARCHI- TECTS, THE OCTAGON, WASHINGTON, D. C. THIS FORM IS TO BE USED ONLY WITH THE STANDARD GENERAL CONDITIONS OF THE CONTRACT THIS AGREEMENT, made the day of in the year Nineteen Hundred and by and between (Two blank lines) t hereinafter called the Contractor, and (Two blank lines) hereinafter called the Owner WITNESSETH, that the Contractor and the Owner for the considerations hereinafter named agree as follows: Article i . The Contractor agrees to provide all the materials and to perform all the work shown on the Drawings and described in the Specifications entitled (Here insert the caption descriptive of the work as used in the Proposal, General Con- ditions, Specifications, and upon the Drawings.) (Five blank lines) prepared by (Two blank lines) acting as, and in these Contract Documents entitled the Architect, and to do everything required by the General Conditions of the Contract, the Specifica- tions and the Drawings. Article 2. The Contractor agrees that the work under this Contract shall be substantially completed. (Here insert the date or dates of completion, and stipulations as to liquidated damages if any.) (Eight blank lines) Article 3. The Owner agrees to pay the Contractor in current funds for the performance of the Contract. ($ ) subject to additions and deductions as provided in the General Conditions of the Con- * Published by permission of The American Institute of Architects, t For use when a stipulated sum forms the basis of payment. t Dotted lines, as indicated, are in the standard documents and are omitted here to save space. 1752 Standard Documents Part S tract and to make payments on account thereof as provided therein, as follows On or about the day of each month per cent of the value, proportionate to the amount of the Contract, of laboi and materials incorporated in the work up to the first day of that month as estimated by the Architect, less the aggregate of previous payments. On substantia' completion of the entice work, a sum sufficient to increase the total payment; to per cent of the contract price, and days thereafter, provided the work be fully completed and th( Contract fully performed, the balance due under the Contract. (Five blank lines) Article 4. The Contractor and the Owner agree that the General Condition; of the Contract, the Specifications and the Drawings, together with this Agree ment, form the Contract, and that they are as fully a part of the Contract as ij hereto attached or herein repeated; and that the following is an exact enumera- tion of the Specifications and Drawings: (Thirty-five blank lines) The Contractor and the Owner for themselves, their successors, executors administrators and assigns, hereby agree to the full performance of the covenant; herein contained. IN WITNESS WHEREOF they have executed this agreement, the day anc year first above written. A. 2. THE GENERAL CONDITIONS OF THE CONTRACT * STANDARD FORM OF THE AMERICAN INSTITUTE OF ARCHITECTS This form has been approved by the National Association of Builders' Exchanges, The National Association of Master Plumbers, the National Association of Sheet Metal Contractors of the United States, the National Electrical Contractors' Association of the United States, the National Association of Marble Dealers, the Building Granite Quarries Association, the Building Trades Employers' Association of the City of New York, and the Heating and Piping Contractors' National Association. THIRD EDITION, COPYRIGHT 1915-1918, BY THK AMERICAN INSTITUTE OF ARCHITECTS, THE OCTAGON, WASHINGTON, D. C. Index to the Articles of t!ie General Conditions I. Definitions. 8. Samples. 2. Documents. 9- The Architect's Status. 3>. Details and Instructions. 10. The Architect's Decisions. 4- Copies Furnished. II. Foreman, Supervision. %. Shop Drawings. 12. Materials. Appliances, Employees. 6. Drawings on the Work. 13- Inspection of Work. 7- Ownership of Drawings. 14. Correction Befoxe Final Payment. •Published by permission of The American Institute of Architects. Standard Documents 1753 32. Use of Premises. 33. Cleaning Up. 34. Cutting, Patching and Digging. 35. Delays. 36. Owner's Right to Do Work. 37. Owner's Right to Terminate Contract. 38. Contractor's Right to Stop Work or Terminate Contract. 39. Damages. 40. Mutual Responsibility of Contractors. 41. Separate Contracts. Assignment. Subcontracts. Relations of Contractor and Subcon- tractor. Arbitration. 42. 43- 44. 45- 5. Deductions for Uncorrected Work. 6. Correction After Final Payment. 7. Protection of Work and Property. :8. Emergencies. :9. Contractor's LiabilHty Insurance. >o. Owner's Liability Insurance. Fire Insurance. !2. Guaranty Bonds. >3. Cash Allowances. !4. Changes in the Work. !5. Claims for Extras. >6. Applications for Payments. 17. Certificates and Payments. >8. Payments Withheld. >9. Liens. JO. Permits and Regulations. . Royalties and Patents. Art. I. Principles and Definitions. (a) The Contract Documents consist of the Agreement, the General Con- iitions of the Contract, the Drawings and Specifications, including all modi- ications thereof incorporated in the documents before their execution. These iorm the Contract. (b) The Owner, the Contractor and the Architect are those named as such in the Agreement. They are treated throughout the Contract Documents as if each were of the singular number and masculine gender. (c) The term Subcontractor, as employed herein, includes only those having a direct contract with the Contractor and it includes one who furnishes material worked to a special design according to the plans or specifications of this work, but does not include one who merely furnishes material not so worked. (d) Written notice shall be deemed to have been duly served if delivered in person to the individual or to er cent of the insurable value thereof. The loss, if any, is to be made adjustable with and payable to the Owner as Trustee for whom it may concern. All policies shall be open to inspection by the Contractor. If the Owner fails to show them on request or if he fails to effect or maintain insurance as above, the Contractor may insure his own interest and charge the cost thereof to the Owner. If the Contractor is damaged by failure of the Standard Documents 1757 Owner to maintain such insurance, he may recover under Art. 39. If required in writing by any party in interest, the Owner as Trustee shall, upon the occun:ence of loss, give bond for the proper performance of his duties. He shall deposit any money received from insurance in an account separate from all his other funds and he shall distribute it in accordance with such agreement as the parties in interest may reach, or under an award of arbitrators appointed, one by the Owner, another by joint action of the other parties in interest, all other procedure being in accordance with Art. 45. If after loss no special agreement is made, replacement of injured work shall be ordered under Art. 24. The Trustee shall have power to adjust and settle any loss with the insurers unless one of the contractors interested shall object in writing within three working days of the occurrence of loss and thereupon arbitrators shall be chosen as above. The Trustee shall in that case make settlement with the insurers in accordance with the directions.of such arbitrators, who shall also, if distribution by arbitra- tion is required, direct such distribution. Art. 22. Guaranty Bonds. The Owner shall have the right to require the Contractor to give bond covering the faithful performance of the contract and the payment of all obligations arising thereunder, in such form as the Owner may prescribe and with such sureties as he may approve. If. such bond is required by instructions given previous to the receipt of bids, the premium shall be paid by the Contractor; if subsequent thereto, it shall be paid by the Owner. Art. 23. Cash Allowances. The Contractor shall include in the contract sum all allowances named in the Contract Documents and shall cause the work so covered to be done by such contractors and for such sums as the Architect may direct, the contract sum being adjusted in conformity therewith. The Contractor declares that the contract sum includes such sums for expenses and profit on account of cash allowances, as he deems proper. No demand for expenses or profit other than those included in the contract sum shall be allowed. The Contractor shall not be required to employ for any such work persons against whom he has a reasonable objection. Art. 24. Changes in the Work. The Owner, without invalidating the contract, may make changes by altering, adding to or deducting from the work, the contract sum being adjusted accordingly. All such work shall be executed under the conditions of the original contract except that any claim for extension of time caused thereby shall be adjusted at the time of ordering such change. Except as provided in Articles 3, 9 and 18, no change shall be made unless m pursuance of a written order from the Owner signed or countersigned by the Architect, or a written order from the Architect stating that the Owner has authorized the change, and no claim for an addition to the contract sum shall be valid unless so ordered. The value of any such change shall be determined in one or more of the following ways: (a) By estimate and acceptance in a lump sum. (b) By unit prices named in the contract or subsequently agreed upon. (c) By cost and percentage or by cost and a fixed fee. (d) If none of the above methods is agreed upon, the Contractor, provided he receive an order as above, shall proceed with the work, no appeal to arbitra- tion being allowed from such order to proceed. In cases (c) and (d), the Contractor shall keep and present in such form a? the Architect may direct, a correct account of the net cost of labor and mate- rials together with vouchers. In any case, the Architect shall certify to the 1758 Standard Documents Part 3 amount, including a reasonable profit, due to the Contractor. Pending final determination of value, payments on account of changes shall be made on the Architect's certificate. Art. 25. Claims for Extras. If the Contractor claims that any instruc- tions, by drawings or otherwise, involve extra cost under this contract, he shall give the Architect written notice thereof before proceeding to execute the work and, in any event, within tw^o weeks of receiving such instructions, and the procedure shall then be as provided in Art. 24. No such claim shall be valid unless so made. Art. 26. Applications for Payments. The Contractor shall submit to the Architect an application for each payment and, if required, receipts or other vouchers showing his payments for materials and labor as required by Article 44. If payments are made on valuation of work done, such application shall be submitted at least ten days before each payment falls due, and, if required, the Contractor shall before the first application, submit to the Architect a schedule of values of the various parts of the work, including quantities, aggre- gating the total sum of the contract, divided so as to facilitate payments to subcontractors in accordance with Article 44 (e), made out in such form, and, if reciuired, supported by evidence as to its correctness, as the Architect may direct. This schedule when approved by the Architect j shall be used as a basis for certificates of payment, unless it be found to be in error. In applying for payments, the Contractor shall submit a statement based upon this schedule and, if required, itemized in such form, and supported by such evidence, as the Architect may direct, showing his right to the payment claimed. Art. 27. Certificates and Payments. If the Contractor has made applica- tion as above, the Architect shall, not later than the date when each payment falls due, issue to the Contractor a certificate for such amount as he decides to be properly due. No certificate issued nor payment made to the Contractor, nor partial or entire use or occupancj^ of the work by the Owner shall be an acceptance of any work or materials not in accordance with this contract. The making and acceptance of the final payment shall constitute a waiver of all claims ])y the Owner, otherwise than under Articles 16 and 29 of these con- ditions or under requirement of the specifications, ai^d of all claims by the Contractor, except those previously made and still unsettled. Should the Owner fail to pay the sum named in any certificate of the Architect or in any award by arbitration, upon demand when due, the Contractor shall receive, in addition to the sum named in the certificate, interest thereon at the legal rate in force at the place of building. Art. 28. Payments Withheld. The Architect may withhold or, on account of sulisequently discovered evidence, nullify the whole or a part of any certificate for payment to such extent as may be necessary to protect the Owner from loss on account of: (a) Defective work not remedied. (b) Claims filed or reasonable evidence indicating probable fifing of claims. (c) Failure of the Contractor to make payments properly to subcontractors or for material or labor. (d) A reasonable doubt that the contract can be completed for the balance then unpaid. (e) Damage to another contractor under Article 40. • When all the alcove grcimds are removed certificates shall at once be issued for amounts withheld because of them. Art. 29. Liens. Neither the final payment nor any part of the retained Standard Documents 1759 percentage shall become due until the Contractor, if required, shall deliver to the Owner a complete release of all liens arising out of this contract, or receipts in full in lieu thereof and, if required in either case, dn affidavit that so far as he has knowledge or information the releases and receipts include all the labor and material for which a lien could be filed; but the Contractor may, if any subcontractor refuses to furnish a release or receipt in full, furnish a bond satisfactory to the Owner, to indemnify him against any claim by lien or otherwise. If any lien or claim remain unsatisfied after all payments are made, the Contractor shall refund to the Owner all moneys that the latter may be compelled to pay in discharging such lien or claim, including all costs and a reasonable attorney's fee. Art. 30. Permits and^Regulations. The Contractor shall obtain and pay for all permits and Hcenses, but not permanent easements, and shall give all notices, pay all fees, and comply with all laws, ordinances, rules and regulations bearing on the work, as drawn and specified. If the Contractor observes that drawings and specifications are at variance therewith, he shall promptly notify the Architect in writing, and any necessary changes shall be adjusted under Art. 24. If the contractor performs any work knowing it to be con- trary to such laws, ordinances, rules and regulations, and without such notice to the Architect, he shall bear all costs arising thereform. Art. 31. Royalties and Patents. The Contractor shall pay all royalties and Hcense fees. He shall defend all suits or claims for infringement of any patent rights and shall save the Owner harmless from loss on account thereof, except that the Owner shall be responsible for all such loss when the product of a particular manufacturer or manufacturers is specified; but if the Contractor has information that the article specified is an infringe- ment of a patent he shall be responsible for such loss unless he promptly gives such information to the Architect or Owner. Art. 32. Use of Premises. The Contractor shall confine his apparatus, the storage of materials and the operations of his workmen to Hmits indicated by law, ordinances, permits, or directions of the Architect and shall not unreason- ably encumber the premises with his materials. The Contractor shall not load or permit any part of the structure to be loaded with a weight that will endanger its safety. The Contractor shall enforce the Architect's instructions regarding signs, advertisements, fires and smoking. Art. 33. Cleaning l^. The Contractor shall at all times keep the premises free from accumulations of waste material or rubbish caused by his employees or work and at the completion of the work he shall remove all his rubbish from and about the building and all his tools, scaffolding and surplus materials, and shall leave his work "broom clean" or its equivalent, unless more exactly specified. In case of dispute the Owner may remove the rubbish and charge the cost to the several contractors as the Architect shall determine to be just. Art 34 Cutting, Patching and Digging. The Contractor shall. do all cuttin- fitting, or patching of his work that may be required to make its several parts come together properly and fit it to receive or be received by work of other contractors shown upon, or reasonably implied by, the Drawings and Specifica- tions for the completed structure, and he shall make good after them, as the Architect may direct. Any cost caused by defective or ill-timed work shall be borne by the party responsible therefor. The Contractor shall not endanger any work by cutting, digging, or otherwiseand shall not cut or alter the work of any other contractor, save with the consent of the Architect-. Art. 35. Delays. If the Contractor is delayed in the completion of the work 1760 Standard Documents Part 3 by any act or neglect of the Owner or the Architect, or of any employee of either, or by any other contractor employed by the Owner, or by changes ordered in the work, or by strikes, lockouts, fire, vmusual delay by common carriers, unavoid- able casualties, Or any causes beyond the Contractor's control, or by delay authorized by the Architect pending arbitration, or by any cause which the Architect shall decide to justify the delay, then the time of completion shall be extended for such reasonable time as the Architect may decide. No such extension shall be made for delay occurring more than seven days before claim therefor is made in writing to the Architect. In the case of a continuing cause of delay, only one claim is necessary. If no schedule is made under Art. 3, no claim for delay shall be allowed on account of failure to furnish drawings until two weeks after demand for such drawings and not then unless such claim be reasonable. This article does not exclude" the recovery of damages for delay by either party under Article 39 or other provisions in the Contract Documents. Art. 36. Owner's Right to Do Work. If the Contractor should neglect to prosecute the work properly or fail to perform any provision of this contract, the Owner, after three-days' written notice to the Contractor, may, without prejudice to any other remedy he may have, make good such deficiencies and may deduct the cost thereof from the payment then or thereafter due the Contractor; provided, however, that the Architect shall approve both such action and the amount charged to the Contractor. Art. 37. Owner's Right to Terminate Contract. If the Contractor should be adjudged a bankrupt, or if he should make a general assignment for the benefit of his creditors, or if a receiver should be appointed on account of his insolvency, or if he should, except in cases recited in Article 35, persistently or repeatedly refuse or fail to supply enough properly skilled workmen or proper materials, or if he should fail to make prompt payment to subcontractors or for material or labor, or persistently disregard laws, ordinances or the instructions of the Archi- tect, or otherwise be guilty of a substantial violation of any provision of the con- tract, then the Owner, upon the certificate of the Architect that sufficient cause exists to justify such action, may, without prejudice to any other right or remedy and after giving the Contractor seven-days' written notice, terminate the employment of the Contractor and take possession of the premises and of all materials, tools and apphances thereon and fmish the work by whatever method he may deem expedi.^nt. In such case the Contractor shall not be entitled to receive any further payment until the work is finished. If the unpaid balance of the contract price shall exceed the expense of finishing the work, including compensation to the Architect for his additional services, such excess shall be paid to the Contractor. If such expense shall exceed such unpaid balance, the Contractor shall pay the difference to tiie Owner. The expense incurred by the Owner as herein provided, and the damage incurred through the Con- tractor's default, shall be certified by the Architect. Art. 38. Contractor's Right to Stop Work or Terminate Contract. If the work should be stopped under an order of any court, or other public authority, for a period of three months, through no act or fault of the Con- tractor or of any one employed by him, or if the Owner should fail to pay to the Contractor, within seven days of its maturity and presentation, any sum certified by the Architect or awarded by arbitrators, then the Contractor may, upon three-days' written notice to the Owner and the Architect, stop work or terminate this contract ^and recover from the Owner payment for all work exe- cuted and any loss sustained upon any plant or material and reasonable profit &nd damages, Standard Documents I76l Art. 39. Damages. If either party to this contract should suffer damage in any manner because of any wrongful act or neglect of the other party or of any one employed by him, then he shall -be reimbursed by the other party for such damage. Claims under this clause shall be made in writing to the party liable within a reasonable time of the first observance of such damage and not later than the time of final payment, except in case of claims under Article 16, and shall be adjusted by agreement or arbitration. Art. 40. Mutual Responsibility of Contractors. Should the Contractor cause damage to any other contractor on the work, the Contractor agrees, upon due notice, to settle with such person by agreement or arbitration, if he will so settle. If such other contractor sues the Owner on account of any damage alleged to have been so sustained, the Owner shall notify the Contractor, who shall defend such proceedings at the Owner's expense and, if any judgment against the Owner arise therefrom, the Contractor shall pay or satisfy it and pay all costs incurred by the Owner. Art. 41. Separate Contracts. The Owner reserves the right to let other contracts in connection with this work. The Contractor shall afford other con- tractors reasonable opportunity for the introduction and storage of their mate- rials and the execution of their work and shall properly connect and coordinate his work with theirs. If any part of the Contractor's work depends for proper execution or results upon the work of any other contractor, the Contractor shall ins})ect and promptly report to the Architect any defects in such work that render it unsuitable for such proper execution and results. His failure so to inspect and report shall constitute an acceptance of the other contractor's work as iU and proper for the reception of his work, except as to defects which may d('\ clop in the other contractor's work after the execution of his work. To insure the proper execution of his subsequent work the Contractor shall measure work already in place and shall at once report to the Architect any discrepancy between the executed work and the drawings. Art. 42. Assignment. Neither party to the Contract shall assign the con- trai t without the written consent of the other, nor shall the Contractor assign an>- moneys due or to become due to him hereunder, without the previous written consent of the Owner. Art. 43. Subcontracts. The Contractor shall, as soon as practicable after thi; signing of the contract, notify the Architect in writing of the names of sill) contractors proposed for the principal parts of the work and for such others as the Architect may direct and shall not employ any that the Architect may within a reasonable time object to as incompetent or unfit. If the Contractor has submitted, before signing the contract, a list of subcontractors and the. change of any name on such list is required or permitted after signature of agreement, the contract price shall be increased or diminished by the difference between the two bids. The Architect shall, on request, furnish to any subcon- tractor, wherever practicable, evidence of the amounts certified to on his account. The Contractor agrees that he is as fully responsible to the Owner for the acts or omissions of his subcontractors and of persons either directly or indirectly employed by them, as he is for the acts and omissions of persons di- rectly employed by him. Nothing contained in the Contract Documents shall create any contractual relation between any subcontractor and the Owner. Art. 44. Relations of Contractor and Subcontractor. The Contractor, agrees to bind every subcontractor and every subcontractor agrees to be bound, by the terms of the General Conditions, Drawings and Specifications, as far as applicable to his work, including the following provisions of this Article, unless 1762 Standard Documents Part 3 specifically noted to the contrary in a subcontract approved in writing as adequate by the Owner or Architect. This does not apply to minor sub- contracts. The Subcontractor agrees: (a) To be bound to the Contractor by the terms of the General Conditions, Drawings and Specifications and to assume toward him all the obligations and responsibihties that he, by those documents, assumes toward the Owner. (b) To submit to the Contractor applications for payment in such reasonable time as to enable the Contractor to apply for payment under Article 26 of the General Conditions. (c) To make all claims for extras, for extensions of time and for damages for delays or otherwise, to the Contractor in the manner provided in the General Conditions for like claims by the Contractor upon the Owner, except that the . time for making claims for extra cost as under Article 25 of the General Condi- tions is one week. The Contractor agrees: (d) To be bound to the Subcontractor by all the obligations that the Owner assumes to the Contractor under the General Conditions, Drawings and Specifi- cations and by all the provisions thereof affording remedies and redress to the Contractor from the Owner. (e) To pay the Subcontractor, upon the issuance of certificates, if issued under the schedule of values described in Article 26 of the General Conditions, the amount allowed to the Contractor on account of the Subcontractor's work to the extent of the Subcontractor's interest therein. (f ) To pay the Subcontractor, upon the issuance of certificates, if issued other- wise than as in (e), so that at all times his total payments shall be as large in proportion to the value of the work done by him as the total amount certified ta the Contractor is to the value of the work done by him. (g) To pay the Subcontractor to such extent as may be provided by the Contract Documents or the subcontract, if either of these provides for earlier or brger payments than the above. (h) To pay the Subcontractor on demand for his work or materials as far as executed and fixed in place, less the retained percentage, at the time the certifi- cate should issue, even though the Architect fails to issue it for any cause not the fault of the Subcontractor. (j) To pay the Subcontractor a just share of any fire-insurance money received by him, the Contractor, under Article 21 of the General Conditions. (k) To make no demand for liquidated damages or penalty for delay in any sum in excess of such amount as may ))e specifically named in the subcontract. (1) That no claim for services rendered or materials furnished by the Con- tractor to the Subcontractor shall be valid unless written notice thereof is given by the Contractor to the Subcontractor during the first ten days of the calendar month following that in which the claim originated. (m) To give the Subcontractor an opportunity to be present and to submit evidence in any arbitration involving his rights. (n) To name as arbitrator under Article 45 of the General Conditions the person nominated by the Subcontractor, if the sole cause of dispute is the work, materials, rights, or responsibilities of the Subcontractor; or, if of the Sub- contractor and an}- other subcontractor jointly, to name as such arbitrator the person upon whom they agree. The Contractor and the Subcontractor agree that: (o) .In the matter of arlntration, their rights and obligations and all procedure shall be analogous to those set forth in Article 45 of the General Conditions. Standard Documents 17G3 Nothing in this Article shall create any obligation on the part of the Owner to pay to or to see to the payment of any sums to any Subcontractor. Art. 45. Arbitration. Subject to the provisions of Article 10, all questions in dispute under this contract shall be submitted to arbitration at the choice of cither party to the dispute. The Contractor agrees to push the work vigor- ously during arbitration proceedings. The demand for arbitration shall be filed in writing with the Architect, in the case of an appead from his decision, within ten days of its receipt and in any other case within a reasonable time after cause thereof and in no case later than the time of final payment, except as to questions arising under Article t6. If the Architect fails to make a decision within a reasonable time, an appeal to arbitration may be taken as if his decision had been rendered against the party appealing. No one shall be nominated or act as an arbitrator who is any way financially interested in this contract or in the business affairs of either the Owner, Contractor or Architect. The general procedure shall conform to the laws of the State in which the work is to be erected. Unless otherwise pfovided by such laws, the parties may agree upon one arbitrator; otherwise there shall be three, one named, in writing, by each party to this contract, to the other party and to the Architect, and the third chosen by these two arbitrators, or if they fail to select a third within ten days, then he shall he chosen by the presiding officer if the Bar Association nearest to the location of the work. Should the party demanding arbitration fail to name an arbitrator within ten days of his demand his right to arl)itration shall lapse. Should the other party fail to choose an arbitrator within said ten days, then such presiding officer shall appoint such arbitrator. Should either party refuse or neglect to supply the arbitrators with any papers or information demanded in writing, the arbitrators are empowered by both parties to proceed ex parte. The arbitrators shall act with promptness. If there be one arbitrator his decision shall be binding; if three the decision of any two shall be binding. Such decision shall be a condition precedent to any right" of legal action, and wherever permitted Ijy law it may be filed in Court to carry it into effect. The arbitrators, if they deem that the case demands it, are authorized to award to the party whose contention is sustained such sums as they shall deem proper for the time, expense and trouble incident to the appeal and, if the appeal was taken without reasonable cause, damages for delay. The arbitrators shall fix their own compensation, unless otherwise provided by agreement, and shall assess the costs and charges of the arbitration upon either or both parties. The award of the arbitrators must be in writmg and, if in writing, it shall not be open to objection on account of the form of the proceedings or the award, unless otherwise provided by the laws of the State in which the work is to be erected. In the event of such laws providmg on any matter covered by this article otherwise than as hereinbefore specified, the method of procedure throughout and the legal effect of the award shaU be wholly in accordance with the said State laws it being intended hc^reby to lay down a principle of action to be followed, leaving its bcal apphcation to be adapted to the legal requirements of the place in which the work is to be erected. B THE STANDARD FORM OF BOND * •" "■ " =sr r-r.: »= » - == "" °' * Published by permission of The American Institute of Architects. 1764 Standard Documents Part 3 Contractors of the United States, the National Electrical Contractors' Association of the United States, the National Association of Marble Dealers, the Building Granite Quarries Association, the Building Trades Employers' Association of the City of New York, and the Heating and Piping Contractors' National Association. COPYRIGHT 19 1 5 BY THE AMERICAN JNSTITUTE OF ARCHITECTS, THE OCTAGON, WASHINGTON, D. C. KNOW ALL MEN: That we (Here insert the name and address or legal title of the Contractor.) (Two blank lines)* hereinafter called the Principal, and [l^Here insert the name and address or legal title of one or more sureties.) (Two blank lines) and (Two blank lines) and hereinafter called the Surety or Sureties, are held and firmly bound unto (Here insert the name and address or legal title of the Owner.) "; (Two blank lines) hereinafter called the Owner, in the sum of (Two blank lines) ($ ) for the payment whereof of the Principal and the Surety or Sureties bind them- selves, their heirs, executors, admini.strators, succes.sors and assigns jointly and severally, firmly, by these presents. Whereas, the Principal has, by means of a written Agreement, dated entered into a contract with the Owner for (Two blank lines) a copy of which Agreement is by reference made a part hereof: Now, Therefore, the Condition of this Obligation "is such that if the Principal shall faithfully perform the Contract on his part, and satisfy all claims and demands, incurred for the same, and shall fully indemnify and save harmless the Owner from all cost and damage which he may suffer by reason of failure so to do, and shall fully reimburse and repay the Owner all outlay and expense which the Owner may incur in making good any such default, and shall pay all per- sons who have contracts directly with the Principal for labor or materials, then this obligation shall be null and void; otherwise it shall remain in full force and effect. Provided, however, that no suit, action or proceeding by reason of any default whatever shall be brought on this bond after months from the day oh which the final jpayment under the Contract falls due. And Provided, that any alterations which may be made in the terms of the Contract, or in the work to be done under it, or the giving by the Owner of any extension of time for the performance of the Contract, or any other forbearance on the part of either the Owner or the Principal to the other shall not in any way release the Principal and the Surety or Sureties, or either or any of them, their heirs, executors, administrators, successors, or assigns from their liability here- under, notice to the Surety or Sureties of any such alteration, extension, or for-r bearance being hereby waived. Signed and Sealed this day of In Presence of (Repeated three times) } as to (Repeated three times) " Dotted lines, as indicated, are in the standard documents and are omitted here to I Standard Documents 1765 C. THE STANDARD FORM OP AGREEMENT BETWEEN CON- TRACTOR AND SUBCONTRACTOR * OK I'SE IN CONNECTION WITH THE THIRD EDITION OF THE STANDARD FORM OF AGREEMENT AND GENERAL CONDITIONS OF THE CONTRACT This form has been approved by the National Association of Builders' Exchanges, The iNjational. Association of Master Plumbers, the National Association of Sheet Metal ;"ontractors of the United States, the National Electrical Contractors' Association of he United States, the National Association of Marble Dealers, the Building Granite Quarries Association, the Building Trades Employers' Association of the City of New ii^ork, and the Heating and Piping Contractors' National Association. COPYRIGHT 19 1 5 BY THE AMERICAN INSTITUTE OF ARCHITECTS, THE OCTAGON, WASHINGTON, D. C THIS AGREEMENT, made this. day of 19. . )y and between . . . ., heroinafter called he Subcontractor and lereinafter called the Contractor. WITNESSETH, That the Subcontractor and Contractor for the considera- ions hereinafter named agree as follows: Section i. The Subcontractor agrees to furnish all material and perform all rork as described in Section 2 hereof for (Here name the kind of building). . . . (Blank lines) '■ or ... .^ (Here insert the name of the Owner) • _\ (Blank lines) lereinafter called the Owner, at (Here insert the location of the work.). . . . (Blank lines) accordance with the General Conditions of the Contract between the Owner tnd the Contractor, and in accordance with the Drawings and the Specifications )repared by hereinafter called the Architect, all of vhich General Conditions, Drawings and Specifications signed by the parties hereto or identified by the Architect, form a part of a Contract between the :ontractor and the Owner dated i9- • and hereby become a )art of this Contract. Section 2. The Subcontractor and the Contractor agr:e that the materials :o be furnished and work to be done by the Subcontractor are (Here )nsert a )recise description of the work, preferably by reference to the numbers of the Drawmgs md the pages of the Specifications.) (Blank lines) * Section 3. The Subcontractor agrees to complete the several portions and Lhe whole of the work herein sublet by the time or times following: . ......... (Here insert the dates or date and if there be liquidated damages state them.). . . . . (Blank lines) Section 4. The Contractor agrees to pay the Subcontractor for the perform- ance of his work the sum of (Blank line). . ... ■ • • ••($ ■-> in current funds, subject to additions and deductions for changes as may be agreed upon, and to make payments on account thereof in accordance with Section 5 hereof. Section 5. The Contractor and Subcontractor agree to be bound by the terms of the General Conditions, Drawings and Specifications as far as apphcable to this subcontract, and also by the foUowing provisions:! ; isi ^rrsissitfo^src:^^^ ^n ... ... ... exception of references to other articles, See page 1761, _ 1766 Standard Documents Part 3 Section 6 . (One page of blank lines) . Finally. The Subcontractor and Contractor, for themselves, their heir., successors, executors, administrators and assigns, do hereby agree to the full performance of the covenants herein contained. IN WITNESS WHEREOF tliey have hereunto set their hands the day and date first above written. In Presence of Suhcontr actor. Contractor. D. STANDARD FORM OF ACCEPTANCE OF SUBCONTRACTOR'S PROPOSAL * FOR USE IN CONNECTION WITH THE THIRD EDITION OF THE STANDARD FORM OF AGREEMENT AND GENERAL CONDITIONS OF THE CONTRACT This form has been approved by the National Association of Builders' Exchanges, The National Association of Master Plumbers, the National Association of Sheet Metal Contractors of the United States, the National Electrical Contractors' Association of the United States, the National Association of Marble Dealers, the Building Granite Quarries Association, the Building Trades Employers' Association of the City of New York, and the Heating and Piping Contractors' National Association. COPYRIGHT 19 1 5 BY THE AMERICAN INSTITUTE OF ARCHITECTS, THE OCTAGON, WASHINGTON, D. C. Dear Sir: Having entered into a contract with (Here insert the name and ad- dress or corporate title of the Owner. ) (Blank line) for the erection of (Here insert the kind of work and the place at which it is to be erected. ) (Blank line) in accordance with plans and specifications prepared by (Here insert the name and address of the Architect.) ." . . (Blank line) and in accordance Vi ith the General Conditions of the Contract prefixed to the specifications, the undersigned hereby accepts your proposal of (Here insert date.) to provide all the materials and do all the work of (Here insert the kind of work to be done, as plumbing, roofing, etc., accurately describing by number, page, etc., the drawings and specifications governing such work.) (Blank lines) The Undersigned agrees to pay you in current funds for the faithful perform- ance of the subcontract established by this acceptance of your proposal the sura of .^ ($ Our relations in respect of this subcontract are to be governed by the plans and specifications named above, by the General Conditions of the Contract as far as applicable to the work thus sublet and especially by Article 44 of those conditions printed on the; reverse hereof, t Very truly yours, •Published by permission of The American Institute of Architects, t Article 44 of the Cieneral Conditions of the Contract is printcfl in full on the reverse side of the Institute's standard form. See page 1761. Official Institute Documents of a Permanent Nature 17G7 The Subcontractor entering into this agreement should be sure that not merely the above Article 44, but the full text of the General Conditions of the Contract as signed by the Owner and Contractor is known to him, since such full text, though not herein repeated, is binding on him. OFFICIAL INSTITUTE DOCUMENTS OF A PERMA- NENT NATURE PUBLISHED (1921) BY THE AMERICAN INSTITUTE OF ARCHITECTS. TITLES AND PRICES The Journal of the American Institute of Architects, monthly, 50 cts; yearly, to A. I. A. members $3 . 50 Yearly, to non-Institute members 5 .00 The Monograph on the Octagon (Thirty Drawings, 12 X 18, Photographs and Text) 12 . 50 The Standard Contract Documents: Agreement and General Conditions in Cover 14 General Conditions without Agreement 10 Agreement without General Conditions 03 Bond of Suretyship .02 Form of Subcontract 03 Letter of Acceptance of Subcontractor's Proposal 02 Cover (heavy paper, with valuable notes) 01 Complete set in Cover 20 The Standard Form of Agreement between Owner and Architect (Per- centage Basis) 03 A Circular of Information on the Fee-Plus-Cost System of Charges Free (Explanatory of Owner-Architect Agreement on Fee-Plus-Cost Basis) A Form of Agreement between Owner and Architect (Fee-Plus-Cost System) $0.03 A Form of Agreement between Owner and Contractor (Cost-Plus-Fee Basis) 05 Circular of Information Relative to Cost-Plus-Fee System of Contracting Free (Explanatory of Contractor-Owner Agreement) A Circular of Advice and Information Relative to the Conduct of Archi- tectural Competitions Free Standard Form of Competition-Programme $0.08 Proceedings of the Convention ^J^^ Annuary to Institute Members J*^^ To Commercial Firms $5.00 Circular of Information Concerning Requirements for Institute Member- ship Free Circular of Information Concerning Requirements for Chapter Associate- , . Free ship Pj.ee Constitution and By-laws „ Standard Form of Chapter Constitution and By-laws. . . . .^. . • .. •.•.•• ^ree A Circular of Advice Relative to Principles of Professional Practice, The ^^^^ Canon of Ethics $0 02 Schedule of Proper Minimum Charges V : " ^V \ir' ^4^ \. Fr*.#» Circular Relative to the Size and Character of Advertising Matter Free 176S Regulation of Practice of Architecture by State Legislation Part 3 Model Registratwn Law Free List of Institute Documents Free For the convenience of the members of the Institute, and the profession generally, who use in .their practice, by reference or otherwise, the various official documents of the American Institute of Architects, the above schedule of Titles and Prices is issued. On single copies of pamphlet-documents postage will be prepaid, otherwise not. The prices quoted in practically every case are to cover the actual cost of printing and handling. The Institute has no desire to make a profit on documents issued primarily for the benefit of the profession. For distinctly educational work, and for Chapter-work, no charge will be made for small quantities of documents, except for postage. Requests of this kind should come through the Chapter-Secretary or a Committee- Chairman. Communications and remittances should be sent to the Executive Secretary, The Octagon House, Washington, D. C. All orders are filled on the day received. REGULATION OF THE PRACTICE OF ARCHITEC- TURE BY STATE LEGISLATION* States Having Registration Laws (1920). Sixteen States have registra- tion or license laws (1920) affecting the practice of architecture, as follows: California, Colorado, Florida, Georgia, Idaho, IlUnois, Louisiana, Michigan, Montana, New Jersey, New York, North Carolina, North Dakota, Oregon, Pennsylvania, South Carolina, Utah, Virginia, Washington, and Wisconsin. Laws are pending (1921) in Indiana, Iowa, and Minnesota!. Theory of Registration Laws. The reason for the regulation of archi- tectural PRACTICE BY LAW is the fact that men improperly qualified to practice can otherwise, at will, assume the title of architect and impose upon the public, thereby discrediting the profession. In some States and in Canada it seems evident that legislation was enacted for protection of local architects against encroachment on the part of non-resident architects. Such a motive is unworthy of the profession, whose efforts through legislation should be to encourage design of higher artistic quahty and to insure safe construction. Some laws, like the first one formulated (Illinois 1897), are license laws in that they tax every architect. Other laws, that in New York, for example, called registration laws, undertake to issue certificates only to those qualified to practice. Registration laws should not in a retroactive way attempt to deprive those of their right who, by virtue of having been in bona-fide practice when the law was enacted, have the legal right to continue in such practice, S'ubject to the effect of pubHc sentiment which may be created against non-registered architects, and subject also to responsibihties imposed by building ordinances requiring safe construction. The theory of the registration law is that an architect should attain to a certain minimum general education, a certain minimum technical education, plus a certain minimum of practical experience, before beginning practice on his own account. That theory is carried into effect by requiring under penalty that no person may assume the title architect whether he is a new practitioner, or an experienced practitioner from without the State, without first estabhshing his qualifications and receiving a certificate authorizing him to use that title. The new york state law, printed here- * This matter was prepared by D. Everett Waid, President of the New York State Board of Examiners and Registration of Architects (term expires, 1922). Registration of Architects. New York State 17G9 with, is typical of recent laws which attempt to embody this theory. References here are made to this law and the notation also that the American Institute of Architects is prepared to cooperate with any persons interested who desire to improve upon the laws already passed when trying to secure in other States such legislation as will tend to raise the standard of quaUfications of architects. Such legislation will certainly achieve its highest end if looked upon as educa- tional in purpose. Incidentally it may be remarked that the best interests of all will be conserved if earnest efforts are made toward a common standard which will encourage reciprocal relations among the States. An architect who has demonstrated his quahfications by passing a proper examination in one State should not be harassed by repetitions of the test in other States in which he may choose to practice. Standards of Education.. The general education required under the New York law is the completion of a high-school course, or equivalent thereof; also the satisfactory completion of such courses in mathematics, history, and one modern language, as are included in two years of an approved institution granting the degree of A.B. Five years' practical experi];:nce in the office of a reputable architect, beginning after the high-school course, is required before a candidate can take the technical examination conducted by the Board of Examiners. This technical examination is not required of graduates of recognized schools of architecture who shall have had, also, three years' prac- tical experience. Administration of Registration Laws. In New York State, architects are admitted to practice by the Regents of the University of the State, who administer the law through a Board of Examiners and Registration of Architects. In other States, the Boards of Examiners are appointed by the Governors. Application for Certificates. AppUcation-blanks and information regard- ing admittance to practice, dates of examinations, etc., can be obtained by addressing the Board of Examiners and Registration of Architects, Education Building, Albany, N. Y. In other States, such inquiries may be addressed to the Secretary of State. Model Registration Law. Those interested in state legislation regu- lating THE practice OF ARCHITECTURE AND THE EDUCATION OF ARCHITECTS may secure copies of a bill issued to serve as a basic model which, with suitable modifications, may be enacted in any State. Address the Secretary, American Institute of Architects, The Octagon House, Washington, D. C. REGISTRATION OF ARCHITECTS IN THE STATE OF NEW YORK* The law in relation to the practice of architecture and the rules of the State Board of Examiners and Registration of Architects approved by the Regents of The University of the State of New York The Assistant Commissioner and Director of Professional Education is in charge of universities, colleges, professional and technical schools, the execution of the laws concerning the professions, and the relations and chartering of institutions. All correspondence relating to the issuance of certificates, the details of licensing examinations, and admissions to the practice of architecture * The form of the law itself and of the State official documents, with the exception of the type, are inserted as enacted and printed, without further editing. 1770 Registration of i\rcliitccts. New York State Part 3 should be addressed to the Director of the Examinations and Inspections Division, Albany, N. Y. REGISTERED ARCHITECTS General business law (L. 1909, Ch. 25) Chapter 20 of the consolidated laws, became a law February 17, 1909 Article 7-A, Registered Architects Became a law April 28, 19 15 (Laws of 1915, Chapter 454). As amended by Laws of 1918, Chapter 77. Section 77. Registered Architects. Section 78. Board of Examiners. Section 79. Qualifications. Examinations. Fees. Section 79a. Certificates. Section 79b. Violation of Article. 77. Registered Architects. Any person residing in or having a place of business in the State, who, before this article takes effect, shall not have been engaged in the practice of architecture in New York State, under the title of architect, shall, before being styled or known as an architect, secure a cer- tificate of his qualification to practice under the title of architect, as provided by this article. Any person who shall have been engaged in the practice of architecture under the title of architect, before this article takes effect, may ■ secure such certificate, in the manner provided by this article. Any person having a certificate pursuant to this article may be styled or known as a regis- tered architect. No other person shall assume such title or use the abbreviation R. A., or any other words, letters or figures to indicate that the person using the same is a registered architect; but this article shall not be construed to prevent persons other than architects frorn filing applications for building permits or obtaining such permits. 78. Board of Examiners and Registration. There shall be a State Board of Examiners and Registration of. Architects, who, and their successors, shall be appointed by and hold during the pleasure of the Board of Regents of The University of the State, and who, subject to the approval and to the rules of the Regents, may make rules for the examination and registration of candidates for the certificates provided for by this article. Such board of examiners shall be composed of five architects, who have been in active practice in the State of New York for not less than ten years, previous to their appointment, selected by the Regents. Such examiners shall be entitled to such compensation for their services under this article as the Board of Regents shall determine, not exceeding in the aggregate the amount of fees collected from applicants for certificates. 79. XJualification. Examination. Fees. Any citizen of the United States, or any person who has duly declared his intention of becoming such citizen, being at least twenty-one years of age and of good moral characteri may apply for examination or certificate of registration under this article, but before securing such certificate shall submit satisfactory evidence of having satisfactorily completed the course in high school approved by the Regenti of the University or the equivalent thereof and subsequent thereto of havini satisfactorily completed such courses in mathematics, history and one moderi language, as are included in the first two years in an institution approved b] the Regents, conferring the degree of bachelor of arts. Such candidate shall h Registration of Architects. New York State 1771 addition submit satisfactory evidence of at least five years' practical experience in the office or offices of a reputable architect or architects, commencing after the completion of the high school course. The board of examiners may accept satisfactory diplomas or certificates from approved institutions covering the course required for examination. Upon complying with the above require- ments, the applicant shall satisfactorily pass an examination in such technical and professional courses as are established by the board of examiners. The board of examiners in lieu of examinations may accept satisfactory evidence of any one of the quahfications set forth under subdivisions i and 2 of this section. 1. A diploma of graduation or satisfactory certificate from an architectural college or school approved by the Regents, together with at least three years' practical experience in the office or offices of a reputal^le architect or architects; but the three years' experience shall be counted only as beginning at the com- pletion of the course leading to the diploma or certificate; the State Board of Examiners and Registration of Architects may require applicants under this subdivision to furnish satisfactory evidence of knowledge of professional prac- tice; 2. Registration or certification as an architect in another state or country, where the qualifications required for the same are equal to those required in this State; 3. The board of examiners in lieu of all examinations shall accept satisfactory evidence as to the applicant's character, competency and qualifications, and that he has been continuously engaged in the practice of architecture for more than two years next prior to the date when this article shall take effect, or that he has been actually engaged in the practice of architecture on his own account or as a member of a reputable firm or association for more than one year prior to the date when this article shall take effect; providing the apphcation for such certification shall be made on or before January i, 19 18. Any architect who has lawfully practiced architecture for a period of more than ten years without the State shall be required to take only a practical examination, which shall be of the nature to be determined by the State Board of Examiners and Registration of Architects. Every person applying for examination or certifi- cate of registration under this article shall pay a fee of twenty-five dollars to the Board of Regents. 79a. Certificates, i. The result of every examination, or other evidence of quahfication, as provided by this article, shall be reported to the Board of Regents by the board of examiners, and a record of the same shall be kept by the Board of Regents, and such board shall, unless deemed otherwise advis- able, issue a certificate of registration to every person certified by the board of examiners as having passed such examination or as being otherwise qualified to be entitled to receive the same. 2. Every person securing such certificates shall register in the office of the county clerk of the county in which he maintains a place of business, in a book kept by the clerk for such purpose, his name, residence, place and date of birth and post office address, source, number and date of his certificate of registration to practice architecture and the date of such registration, which registration he shall be entitled to make only upon showing to the county clerk his certificate of registration and making an affidavit of the above facts, and that he is the identical person named in the certificate; that before receiving the same he complied with all of the preliminary requirements of this article and the rules of the Regents and the board of examiners as to the terms and the amount of c^tudy and examination; that no money other than the fees prescribed by 1772 Registration of Architects. New York State Part 3 this article and such rules was paid directly or indirectly for such registration, and that no fraud, misrepresentation or mistake in material regard was em- Jjloyed or occurred in order that such certificate should be made, which affidavit shall be preserved in a bound volume by the county clerk. The county clerk shall indorse or stamp on the back of the certificate the date and his name preceded by the words '* registered as authority to practice as a registered architect, in the clerk's office of county"; and shall issue to each person duly registering and making such affidavit a certificate of registration in his county which shall include a transcript of the registration. Such transcript and the certificate of registration may be offered as presump- tive evidence in all courts of the facts stated therein. The county clerk's fee for taking such registration and affidavit and issuing such certificate shall be one dollar. Any person who, having lawfully registered as aforesaid, shall thereafter change his name in any lawful manner, shall register the new name with a marginal note of the former name, and shall note upon the margin of the former registration the fact of such change and a cross-reference to the new registration. A county clerk who knowingly shall make or suffer to be made upon the book of registry of architects kept in his office any other entry than is provided for in this article shall be guilty of a misdemeanor. 3. An architect having duly registered to practice as a registered architect in one county and removing his practice or a part thereof to another county or regularly engaging in practice or opening an office in another county, shall show or send, by registered mail, to the clerk of such other county, his certificate of registration. If such certificate clearly shows that the original registration was duly issued Under seal l:)y the Board of Regents, the clerk shall thereupon register the applicant in the latter county on receipt of a fee of 25 cents and shall stamp or indorse on such certificate the date and his name, preceded by the words "Registered also in county," and return the certificate to the applicant. 4. The Board of Regents may revoke any certificate, if such action be recom- mended by the board of examiners, after thirty days' written notice to the holder thereof and after a hearing before the board of examiners, upon proof that such certificate has been obtained by fraud or misrepresentation, or upon proof that the holder of such certificate has been guilty of felony in connection with the practice of architecture. 79b. Violation of Article. Any violation of this article shall be a mis- demeanor, punishable for the first offense by a fine of not less than fifty and not more than one hundred dollars, and for a subsequent offense by a fine of not less than two hundred nor more than five hundred dollars, or imprison- ment for not more than one year, or both. SYNOPSIS OF SUBJECTS ON WHICH EXAMINATIONS ARE BASED • The examinations of applicants for certificates shall be based on the four following subjects or groups: a. History of Architecture. The candidate shall give evidence in the examination that he understands the essentials that give character to the various historic styles of architecture by clear descriptive analyses of plan, construction, general expression and ornament. Questions will be asked relating to: (i) Architecture in various countries. * Taken from the Rules of the New York State Board of Examiners and Registration of Architects. Registration of Architects. New York State J773 (2) Styles and orders. Sketches and names of examples. (3) Sculpture and painting and color as applied to architecture. (4) Furniture and decoration. b. Architectural Composition. The candidate shall give evidence that he understands the broad principles underlying the subject of architectural plannmg by the application of the same to specific problems stated in the examination. The social, economic and physical requirements of several architectural problems will be outlined and the candidate will be asked to state the principal considerations that would guide him in the choice of an arrangement of plan that would most adequately express and fulfill the con- ditions suggested. Small sketches will be required to illustrate the application of the principles involved. Questions will refer to: (i) Principles of Planning: Problems in planning individual buildings, groups and towns; illustrations may "be asked to show how plans may be influenced by considerations, esthetic, structural, and as to kinds of materials, and modifications of plan due to considerations of occupancy and of fire pre- vention both for fireproof and non-fireproof buildings. (2) Esthetic Design: Original examples will be required illustrating prin- ciples involved in the solution of practical problems and the relation of plan to elevation. c. Architectural Engineering. In this examination the candidate shall give evidence that he has a thorough understanding of the appropriate use of the various materials used in buildings. He will be required also to solve certain technical problems siich as the calculation of the proper economic dimensions of various structural members common to buildings, in the several materials noted. Candidates will not be required to make complicated calcu- lations, and the use of handbooks will be permitted. Questions will be asked as to the knowledge of these subjects that an architect should possess in order properly to advise his clients and to design or to direct the designing of suitable mechanical equipment for buildings of different classes. Questions will be asked relating to: (i) Structural Design: Column, girder, joist and truss designs. Wind bracing for buildings of different classes. Various types of foundations and conditions under which their use is advisable. Various kinds of bottom met with in ordinary practice and unit loads allowable under foundations in each case. Different types of concrete floor slab construction in common use. Structural design as affected by fire and resistive quaUties of different build- ing materials. (2) Use of Materials: Strength of materials, durability and considerations of wear and repair. Esthetic reasons for use of different materials. (3) Heating and Ventilating: Various systems and reasons for and against use under specific conditions. Important features of design that should be specified. (4) Electric Equipment: General questions rather than technical. Various kinds of current and considerations involved. Kinds of wiring and insulation; methods and materials. Light distribution. . u • 1 Lighting fixtures; esthetic and practical design; important mechanical details. 1774 Registration of Architects. New York State Part 3 Generators, motors, storage batteries, and advice to clients regarding the same. Independent power plant considerations. (5) Plumbing and Fire Protection Equipment: Supply and waste systems. Kinds of material for piping and reasons for use. Kinds of materials for fixtures. Sewage disposal plants and considerations involved. Water supply, different systems and considerations of supply and filtration. Sprinklers and other fire protection equipment. (6) Elevators: Types of elevators. Arrangement and location of elevators. d. Architectural Practice. In this examination the candidate shall give evidence that he understands the moral and the legal responsibilities of the architect in the proper performance of his duties as such. He will be required to outline or draft clauses of contracts between owner and architect and to state specifically the content of the clauses included in the contract between owner and contractor which are incorporated for the purpose of defining the architect's authority and responsibility to both parties of the contract. Each candidate will be required to show that he understands the major provisions of state, county and municipal building laws and ordinances and how the same affect the different classes of buildings. He shall be able also to cite the com- petent authority under whose jurisdiction permits for the erection and occupancy of various types of buildings must be obtained. Questions will be asked relat- ing to: (i) Business and Professional Functions of Architects: Professional relation of clients and contractors. Essential provisions in contract between architect and his client. When the architect is disinterested arbitrator, and when he properly may act as an agent. Relation of architects to each other in ordinary practice, in association, and in consultation, and when one architect displaces another on a given piece of work. Sources and kinds of compensation for architect's services. Responsibilities of architects and methods of conducting their business. Scope of architect's work, esthetic and structural. When expert's services should be advised. Scope of architect's work, administrative business, and legal contracts, arbitrations, court evidence, contractors in default, when counsel of client's lawyer should be advised. (2) Building Laws: State, county and municipal laws, ordinances and regulations, and how they affect different classes of buildings. Filing drawings and specifications and obtaining permits. (3) Contracts: Drawings, specifications and agreement as essential parts of the customary contract between owner and builder. Variations in kinds and forms of agreements and contracts. Definition of architect's authority. Provisions as to bids, letting contracts, unit prices, requisitions, certificatl and payments. Insurance: fire, liability, compensation. 1 Registration of Schools of Architecture 1775 Bonding contractors. (4) Specifications: General conditions, purp -ises and scope. Scope and purposes and limitations of general clauses. Principles which should he observed in writing specifications. Right and wrong methods of specifying qualities of materials and workman- ship. (5) Drawings: Purposes, use and limitations of preliminary drawings. Essentials which should be embodied in contract drawings. Purposes and limitations of detail and other working drawings which are not contract drawings. REGISTRATION OF SCHOOLS OF ARCHITECTURE • A school of architecture may be registered as maintaining a satisfactory standard and may be legally incorporated. Incorporation by the Regents will be made on formal appHcation and inspection by the Department which show that the school possesses the minimum requirements. Application. An educational institution desiring admission to or incor- poration or registration by the University must file a written application giving the information requested in the form prescribed by the Commissioner of Education. A form will be mailed on application to the Assistant Commissioner for Higher Education. Such application must be on file in the Education Department at least 10 days before the meeting of the Regents at which action thereon is to be taken. Accrediting. Institutions unable to meet the standards required by the Regents for registration in fall shall be accredited by the Department for one or more years of professional training as they meet the requirements for admission and for professional training set by the Regents standards. Recognition Accorded Accredited Professional Schools. Professional schools registered by the Regents shall give the work of accredited institutions no higher recognition than that accorded such institutions in the Department's accredited Ust, viz.: (1) The successful completion of a four-year course in a professional school accredited by the Department for three years shall be accorded three years' recognition only; (2) the successful completion of a three- year course in a professional school accredited by the Department for two years shall be accorded two years' recognition only; (3) the successful completion of a two-year course in a professional school accredited by the Department for one year shall be accorded one year's recognition only. A registered school may refuse to accord an accredited institution the recognition given it by the Department but it may not give it any higher recogmtion. Comity of Action in the Transfer of Students from One Professional School to Another. The Department does not consider a course in a school of architecture satisfactory if more than two conditions, one major of 100 hours and one minor of 50 hours, are allowed students for promotion from one year s class to the next. * T^oton from thp Rulcs of thc Ncw Yofk State Board of Examiners and Registration of ATctTectrls — U be added to the accredited lists, these Usts must be revised from time to time. 1776 Regents' Rules. Schools of Architecture Part 3 REGENTS' RULES Schools of Architecture * 440. Definitions. School of Architecture means any college or school of architecture, or school, department or course of architecture in a college or university, whatever the corporate title. 441. Requirements. A School of Architecture, legally incorporated, may be registered as maintaining proper standards. It must afford satis- factory instruction in such technical and professional courses as are established by the board of examiners, for admission to the examinations in the history of architecture, architectural composition, architectural engineering and archi- tectural practice. 442. General Education. A. Preliminary. For admission to a school of architecture, evidence shall be required showing the satisfactory completion of a four-year course in a secondary school approved by the Board of Regents, or the equivalent, 72 counts in the academic examinations. B. Higher. For admission to the examinations for the certificate of R. A. evidence shall be required of such courses in mathematics, history and modern languages as ?ire included in the first two years of the curriculum leading to the degree of bachelor in arts, or the equivalent, graduation from a junior college approved by the Board of Regents. SCHOOLS OF THE UNITED STATES AND CANADA REGISTERED OR ACCREDITED.! JUNE, (1918) Alphabetically Arranged by States United States California. Registered: School of Architecture, University of California, Berkeley. (Graduate course, one or two years.) District of Columbia. Registered: Department of Architecture, George Washington University, Washington. (Course, four years.) Georgia. Registered: Department of Architecture, Georgia School of Technology, Atlanta. (Course, four years.) Illinois. Registered: Chicago School of Architecture, Armour Institute of Technology, Chicago. (Course, four years.) Department of Architecture, University of Ilhonis, Urbana. (Course, four years.) Indiana. Registered: College of Architecture, University of Notre Dame, Notre Dame. (Course, four years.) Department of Architectural Engineering, Rose Polytechnic Institute, Terre Haute. (Course, four years.) Kansas. Department of Architecture, Kansas State Agricultural College, Manhattan. (Course, four years.) Department of Architectural Engineering, University of Kansas, Lawrence. (Course, four years.) • Taken from the Rules of the New York State Board of Examiners and Registration of Architects. As schools may be added to the accredited lists, these lists must be revised from time to time. t This is the list of Schools or Departments of Architecture in the United States and Canada, registered or accredited by the New York State Board of Examiners and Regis- tration of Architects, and must be added to from time to time. Schools Registered or Accredited 1777 Louisiana. Registered: School of Architecture and Architectural Engi- neering, Tulane University, New Orleans. (Courses, four years.) Massachusetts. Registered: Departments of Architecture and Archi- tectural Engineering, Massachusetts Institute of Technology, Cambridge. (Courses, four years.) School of Architecture, Harvard University, Cambridge. (Graduate Course, three years.) Michigan. Registered: College of Architecture, University of Michigan, Ann Arbor. (Course, four years.) Minnesota. Registered: Department of Architecture, University of Minnesota, MinneapoHs. (Course, four years.) Missouri. Registered: School of Architecture, Washington University, St. Louis. (Course, four years.) Nebraska. Registered: Department of Architectural Engineering, Uni- versity of Nebraska', Lincoln. (Course, four years.) New York. Registered: College of Architecture, Cornell University, Ithaca. (Course, four or five years.) Department of Architecture, Syracuse University, Syracuse. (Course, four years.) School of Architecture, Columbia University, New York. (Course, four years.) Ohio. Registered: Department of Architecture, Ohio State University, Columbus. (Course, four years.) Oklahoma. Registered: Department of Architecture, Oklahoma Agri- cultural and Mechanical College, Stillwater. (Courses, four years.) Pennsylvania. Registered: Department of Architectural Engineering, Pennsylvania State College, State College. (Course, four years.) Department of Architecture, University of Pennsylvania, Philadelphia. (Courses, four years.) Department of Architecture, Carnegie Institute of Technology, Pittsburgh. (Course, four years.) Texas. Registered: Departments of Architecture and Architectural Engineering, Agricultural and Mechanical College of Texas, College Station. (Courses, four years.) School of Architecture, University of Texas, Austin. (Course, four years.) Canada Ontario. Registered: Department of Architecture, University of Toronto, Toronto. (Course, four years.) Quebec. Department of Architecture, McGill University, Montreal (Course, five years.) SYNOPSIS OF REGISTRATION LAWS* • This study t is made for those who would see at a glance the statutory requirements for the practice of architecture throughout the Umted States. *As States are added to the list of those which have laws f«^the Registration of Architects these lists must be revised from time to time. Georgia, Michigan, Penn- syTvant Vi gS^ Washington have been added to the list up to January x92x^ t Taken from Handbook No. 35, published annually by The University of the State of New Yortand containing information relating to the Registration of Architects, 1778 Synopsis of Registration Laws Part 3 There are four distinct lines of statutory requirements: (i) Preliminary educa- tion; (2) professional training; (3) licensing test; (4) registry. These four items with (5) the title of the executive officer and the administrative board are given uniformly in this synopsis.* If there are no statutory requirements the word "none" covers the item. California, (i) None; (2) none; (3) examination; (4) with the recorder of the county of residence annually; (5) secretary, State Board Architecture, San Francisco. Colorado, (i) None; (2) none; (3) examination or certificate from a similarly constituted board of another state; (4) with the secretary of state and annually with the board; (5) Secretary, State Board of Examiners of Archi- tects, Denver. Idaho, (i) Approved high school course or its equivalent and in addition a two-year course in English and mathematics such as is required in an approved B. A. course; (2) three years' practical experience in the office of a reputable architect; (3) examination or in lieu of all examinations, graduation from an approved architectural school or registartion as an architect in another state whose standard equals that of this board; (4) with the secretary of state; (5) Secretary, State Board of Examiners of Architects. Illinois, (i) None; (2) none; (3) examination; (4) with the clerk of the county of practice, annually; (5) Secretary, Department of Registration and Examination, Springfield. Louisiana, (i) Good primary education; (2) none; (3) examination or diploma from an approved school of architecture; (4) with the district court clerk of the parish of residence and annually with the board; (5) Secretary Board of Architectural Examiners, New Orleans. Montana, (i) None; (2) none; (3) examination or a license from another state l)oard; (4) with the clerk and recorder of the county of residence and annually with the state treasurer; (5) Secretary, Board of Architectural Exami- ners. New Jersey, (i) None; (2) none; (3) examination or a license from a similarly constituted board of another state or membership in the American Institute of Architects; (4) with the board, annually and with the secretary of state; (5) Secreta'-y, State Board of Architects, Trenton. New York, (i) Approved high school course or the equivalent and in addition such course in mathematics, liistory and one modern language as are included in an approved two-year B. A. course; (2) at least five years' practical experience in the office of a reputable architect; (3) examination or graduation from an approved architectural school with three years' experience or regis- tration in another state or country having standards equal to that of this board; (4) with the Board of Regents; (5) Secretary, State Board of Examiners and Registration of Architects, New York. North Carolina, (i) Prescribed bj'- the board; (2) prescribed by the board; (3) examination or a certificate from a similarly constituted board in another state or membership in the American Institute of Architects; (4) with the clerk of the superior court of the county of residence; (5) Secretary of the Board of Architectural Examination and Registration. North Dakota, (i) Approved high school course or its equivalent; (2) three years' practical experience in the office of a reputable architect; (3) * The names of the executive officers, Secretaries of the Boards, etc., are omittec} here, as the personnel is constantly changing. Institutions Teaching Architecture 1779 examination or a license from another state board whose standard equals that of this board or membership in the American Institute of Architects; (4) with the secretary of state and annually with the board; Secretary, State Board of Architecture, Bismarck- South Carolina, (i) None; (2) at least two years' experience in archi- tectural work; (3) examination or graduation from an approved school of architecture; (4) with the board, annually; (5) Secretary, State Board of Architectural Examiners, Columbia. Utah, (i) None; (2) none; (3) examination; (4) with the board, annually; (5) Secretary, State Board of Architecture. Wisconsin. (0 None; (2) at least five years' practical experience in the ofhce of a reputable architect; (3) examination or a satisfactory certificate from a recognized architectural school with three years' experience or registra- tion with the 1)oard of another state or country whose standards are not lowe. than those of this board; (4) with the Industrial Commission; (5) Secretary of the Board of Examiners of Architects, Madison. FmiCATIONAL INSTITUTIONS IN THE UNITED ??ATES AND CANADA OFFERING COURSES IN ARCHITECTURE. TRAVELLING FELLOW- SHIPS AND SCHOLARSHIPS 1. Association of Collegiate Schools of Architecture A • ♦•«« nf rnlleeiate Schools of Architecture. Organized in 1912 and ftl^Sme ieT.^ M^^^^^^^^ "^ Technology. (Office-9- pl^trEmilLorch; Vice-Presid»t.^V^Ham Emerson^ broadly sun^marized as follows: ( ^^^^^^^^^^^^ „f both general and Foundation; (2) A course of at least "° ^f;"^ anoroved method of presen- professional studies of cenamm^^^^^^^^^^^^ tat on, leading to a degree not le.s cna adequacy of equipment of staff and administration, ^andrngj^co^^^^^^^ as will reasonably assure quahty .«' /^f "™^^^'f 'f^;; years. The Association of all American schools are welcomed. 2. Educational Institutions. Fellowships, and Scholarships Academy of Architecture and Indusu; IS ie„ce.^ ^^^ is a private school ^""ded by Mr^ Maj^A^n 5. .^^ ^^^^ ^^^^ .„ ^^^ 1780 Institutions Teaching Architecture Part 3 understanding of the plans and details of complicated buildings. There is also a special course for those desiring to fit themselves for positions as draughts- men in architects' offices. Tuition for the regular course is $50 for a three- months' term, or $300 for the full course of eight terms, or $100 for the year. Several special courses with varying tuition. Alabama Polytechnic Institute, Auburn, Ala. Department of Architecture, (i) Full four-year course leading to the degree of Bachelor of Science in Architecture. (2) Full four-year course leading to the degree of Bachelor of Science in Architectural Engineering. (3) Two-year special course for draftsmen and college graduates. Tuition free to residents of Alabama; $20 per year for others. About two dozen loan-scholarships of $100 or more per annum. Limited number of fellowships of $250 for post- graduates. Illustrated Announcement giving details, sent on request. American Academy in Rome, Fellowship in Architecture. Roman Prize. The fellowship is awarded annually and is of the value of $1 000 a year for three years. The award is made on competitions which are open only to unmarried male citizens of the United States, who comply with the regulations of the Academy. Candidates are required to be (i) graduates of one of the architectural schools included in the accepted list of the Academy; or (2) grad- uates of a college or university of high standing who hold certificates of at least two years* study in one of such architectural schools; or (3) Americans who are pupils of the first class of the School of Fine Arts at Paris, and who have obtained at least three values in that class. There is no age-limit. Information as to the terms and conditions of the competitions may be obtained from the Secretary of the Academy, 10 1 Park Avenue, New York City. American School of Correspondence, Chicago, 111. Correspondence- courses in Architecture, Architectural Engineering, Contracting and Building, Reinforced Concrete, Architectural Design, and Structural Draughting. Bulle- tin sent on application. Armour Institute of Technology, Chicago, III. Full four-year course leading to the degree of Bachelor of Science in Architecture. Applicants for admission must have completed the regular four-year high-school course. A Home Traveling- Scholarship, four prizes, and a medal are awarded annu- ally. Tuition, $180 per year. Beaux ATts Institute of Design, 126 East 75th Street, New York, N. Y. Department of Architecture. (Address all communications to this depart- ment.) The course, established in 1893, consists (1920) of a seriesof thirty-five competitions, issued annually, for the study of architectural design and the styles of architecture, open to the draughtsmen and students in architectural schools in the United States and Canada, and modeled on the system of instruction adopted by the Ecole des Beaux Arts in Paris. The course is free, except for the annual fee of $2 for registration of each student. There are no restrictions as to the age, nationality, or sex of the students. No preliminary examinations are given, but new students are expected to have a knowledge of the five orders of architecture. Bronze and silver medals are awarded for excellence in design and money-prizes are offered in special prizes for decoration, group- planning of buildings, etc. Certificates are presented to all students of Class A completing the course as defined in the circular of information, which is furnished on request. During the season 1917-1918 the work was carried on by one hundred and eleven correspondents of the Institute in eighty-eight different cities, with a total of seven hundred and seventy- four students. Department of Interior Decoration (Address all communications to this \ Institutions Teaching Agriculture 1781 department). The course consists of programmes for competitions issued every sLx weeks to those who apply for them. These may be executed by students situated in any locaUty and sent in to the Institute where they will ' be criticized and judged on fixed dates by a jury of experts. Bkonze and SILVER MEDALS are awarded for excellence. An atelier for male students under the instruction of several decorators exists in the building of the Institute. There are no fees of any kind. No formalities or examinations are necessary for admission to the atelier. A circular is furnished on request. Department of Sculpture. (Address all communications to this depart- ment). Ateliers for male students for each one of the three courses (Archi- tectural Ornament, Life Drawing, and Modeling and Composition) exist in the building of the Institute. No examinations, formalities, or fees of any kind. Open all day all the year round. Instructors visit their classes twice a week. Judgments by expert juries every four weeks on the work of the preceding month. Bronze and silver medals awarded. A circular is fur- nished on request. Department of Mural Painting (Address all communications to this department). The course consists of pioblems, programmes of which are issued every month to those who apply for them. Judgments by a jury of artists every month on the designs handed in. Bronze and silver medals awarded. No examinations, formalities, or fees of any kind. There is no atelier for this department at the Institute and students work up their problems under their own instructors wherever they may be situated. A circular is furnished on request. Beaux Arts Archhects, Society of. 126 East 75th Street, New York, N. Y. The course in Architectural Design estabUshed in 1893 and formerly conducted by the Committee on Education of this Society, is now carried on by the Beaux Arts Institute of Design. (See Beaux Arts Institute of Design.) Paris Prize. This scholarship-prize is usually conducted annually by the Society of Beaux Arts Architects. Under its conditions the winner re- ceives $1 200 per annum for two years and a half, to study architecture in Paris at the Ecole des Beaux Arts, into the upper class of which he is received without further examinations. The competition beginning January loth, 1920, for this scholarship consisted of two preliminaries and one final com- petition and was open to all male citizens of the United States under thirty.-two years of age on July ist, 1920. A circular is furnished on request. Carnegie Institute of Technology, Pittsburgh, Pa. Division of the Arts; School of Architecture, (i) A complete course in architecture for day- students for which the degree of Bachelor of Architecture in Design is awarded to those speciaHzing in design and allied subjects (Option i). and the degree ot Bachelor of Architecture in Construction to those in construction and allied subjects (Option 2). From four to five years are required for the ^omPleUon of prescribed work. (2) For graduate day-students a course of ^d^^ced studies in design and allied subjects, scheduled to cover one y^l^^"}^.^'^^^^^^ degree of Master of Arts. (3) A partial day-course schedukd ^ cov^^^^^^^ years, for experienced draughtsmen and designers. f^^^^^^^Vh a Scate proficiency is awarded. (4) A course for night -students for which a Certificate Tpr'toy is awarded'^ This course includes the same w-k as is requned of day-students in design, freehand drawing and modehng. Tuition. For day school, $7s: for night-school, $20 per year. Columbia University. New York. N. Y. f^'Twof ^4?™' (i). FuU four-year course leading to the degree of Baciielor of Architecture. 1782 Institutions Teaching Architecture Part 3 Receives only students with at least two years of college training. In con- nection with Columbia College, there is a six-year course giving the degree of A.B., at the end of four years and B.Arch. at the end of six years. (2) Advanced courses leading to the degree of Master of Science in Architecture. Tuition $6 per "tuition-point," totahng about $250 per year. There are three Traveling-Fellowships, awarded as follows: One is available each year, with a stipend of about $1 500; the McKim Fellowship every third year, beginning 19 16-17; the Schermerhorn Fellowship, every third year, begin- ning 19 18-19; and the Perkins Fellowship, every third year, beginning 1920-21. Each of these requires the winner to devote one year to foreign travel and study. Extension-Teaching, evening and afternoon courses. A course leading to a Certificate of Proficiency in Architecture is offered. This covers roughly six years, depending on how much is taken each year. Equivalent of day-course in instruction. Tuition, $6 per "tuition-point," each course having a stated point-value. Graduation accepted in lieu of examinations for state Hcense. There are Special Students, also, under Extension-Teaching who select their own course of study in subjects for which they are quahfied. All information may be obtained from the Curator, Cornell University, Ithaca, N. Y., College of Architecture, (i) A four-year general course in architecture, leading to the [degree of Bachelor of Architecture, and a similar course with engineering elcctives, leading to the degree of Bachelor of Science in Architecture. (2) Five-year courses in archi- tecture, the same as the above, but with additional work in the arts and sciences, leading to the same degrees. (3) Six-year courses in arts and sciences and architecture, or in engineering and architecture, leading to the degrees of A.B. and B.Arch., or C.E. and B.S.Arch. (4) A two-year special course in archi- tecture, leading to a certificate. (5) Graduate courses in architecture, leading to the degree of Master of Architecture. Tuition, $200 a year. Georgia School of Technology, Atlanta, Ga. Department of Archi- tecture, (i) Full four-year course leading to the degree of Bachelor of Science in Architecture. (2) Two-year special course leading to a certificate of proficiency. Tuition, $25 per year for residents of Georgia; $100 for non-residents. The Georgia Chapter of the American Institute of Architects has provided a loan-fund in this department for one or two students needing pecuniary assist- ance. George Washington University, Washington, D. C. Department OF Arts and Sciences. Course in Architecture. Four-year course in archi- tecture, leading to the degree of Bachelor of Science in Architecture. Courses of instruction open to qualified special students, without reference to any degree. Full tuition $180; part-time students pay $6 for each semester-hour credit. Harvard University, Faculty of Architecture, Cambridge, Mass. School of Architecture. Professional training in architecture, (i) Open to graduates of colleges, scientific schools and professional schools of good stand- ing, leading to the degree of Master in Architecture, or Master in Architecture in Architectural Engineering. Length of period of study for men with no professional preparation, commonly three years, depending on ability and pre- vious training. (2) Open to competent special students, who must be over twenty-one years of age, and must hare had at bast three years of oflFice- experience; admitted to special course leading to certificate. Tuition $200 per year. Institutions Teaching Architecture 1783 School of Landscape- Architecture, (i) Professional training in landscape- architecture, open to graduates of colleges and technical schools of good standing, leading to the degree of Master in Landscape-Architecture. (2) Competent special students admitted to any courses for which their previous training fits them. Tuition, $200 per year. Two Traveling-Fellowships, the Julia Amory Appleton and the Robin- son, are offered for competition in alternate years, each having an annual value of $1 100, tenable for two years, for travel and study in Europe under the direction of the School of Architecture. The Charles Eliot Fellow- ship IN Lansdcape-Architecture (stipend $1 100) is offered for travel and study in landscape-architecture, under the direction of the School of Landscape- Architecture. These fellowships are open for competition to graduates in architecture and in landscape-architecture, respectively. Resident Scholarships. Two Austin Scholarships in Architecture and one in Landscape-Architecture, annual value, $350. The Cummings Scholarship in Landscape-Architecture, annual value, $350. One Eveleth Scholarship in Architecture, annual value, I250. Three Scholarships FOR Special Students in Architecture, open to competition to properly quahfied draughtsmen, annual value, $200. Six University Scholarships open to regular students in Architecture or Landscape-Architecture, annual value, $200. Other scholarships available to candidates of special claims as to residence, college, or descent. International Correspondence Schools, Scranton, Pa. A corporation formed to furnish instruction by correspondence and to hold examinations to establish proficiency. The architectural course is designed particularly to meet the wants of those already engaged in the building trades or drafting-room. It includes sixty-one subjects covering the elements of building-construction, masonry, carpentry, plumbing, etc., and the principles of design, drawing, rendering, and specification-writing. The tuition includes text-books and instruction, that is, criticisms on written lessons, sent to the schools, and also answers to questions on subjects connected with the course, that may be asked by the students. Information regarding fees can be obtained on inquiry. Shorter courses are available for building-contractors, building-foremen, and also special courses in structural engineering. Kansas State Agricultural College, Manhattan, Kan. Department of Architecture. Full four-year course in architecture, leading to a degree in Bachelor of Science. Tuition free to residents of the state. Incidental fees amount to about $12 a semester. Massachusetts Institute of Technology, Boston, Mass. Two four-year courses are offered in architecture, leading to the degree of Bachelor of Science: (i) Course in general architecture; (2) Course in architectural engineering. Opportunities are offered in each course for. advanced professional work leading to the degree in (i) of Master in Architecture and in (2) of Master of Science. Special students must be college-graduates, or twenty-one years of age, with not less than two years of office-experience. In all cases they must demonstrate their fitness for the work of the department by personal conference with the head of the department, or his representative, and by the presentation of letters from former employers, together with drawings covenng their experience as fully as possible. All special students must take in their first year of residence at the Institute courses in descriptive geometry and mechanical drawing, unless these subjects have been passed at the September examinations for advanced standing, or excuse from one or both has been obtained on the basis of equivalent 1784 Institutions Teaching Architecture Part 3 work accomplished elsewhere. Tuition, $250 per year. An Annual Traveling- Fellowship amounting to $1 000 is given solely on the basis of distinguished merit, candidates being received from both regular and special students. Eight prizes, varying from $10 to $200 each, are equally divided between the regular and the special students. Certain funds are available for the assistance of well- quahfied regular students for undergraduate and for post-graduate work. McGill University, Montreal, Canada. Department of Architecture. (i) Full five-year course leading to the degree of Bachelor of Architecture. (2) Competent special students are admitted to take a partial course, but no university certificate is granted for this work. Tuition, $150 per year. North Dakota Agricultural College, Fargo, N. D. Department of Engineering. Draughtsmen's and builders' course of three years (six months each). Full four-year course in architecture, leading to Bachelor of Science in Architecture. Full four-year course in Architectural Engineering, leading to Bachelor of Science in Architectural Engineering. Tuition free. Fees amounting to $35 per year. Ohio Mechanics- Institute, Cincinnati, Ohio. Department of Archi- tecture. Technical high- school course preparatory to architecture, cover- ing four years. Two-year intensive course in architecture. Evening classes in architectural drawing and alUed building-trade subjects. Graduates of grammar-schools are trained in draughting and elementary architectural subjects simultaneously with their high-school subjects. Graduates of high- schools are trained intensively in technical architectural work, including colle- giate mathematics and sciences, and receive a Certificate of Proficiency in Architecture. Tuition, $75 per year. Ohio State University, Columbus, Ohio. Course in Architecture. Two four-year courses, leading to the degrees of Bachelor of Architecture and Bachelor of Architectural Engineering. Tuition free. Oklahoma Agricultural and Mechanical College, Stillwater, Okla. Departments of Architecture and Architectural Engineering. Four- year course in Architecture and Architectural Engineering, leading to a degree of Bachelor of Science. Two-year special course for draftsmen, leading to a certificate of completion in this work. Tuition free. The registration-fee is $2 a semester. Pennsylvania State College, State College, Pa. Course in Architec- tural Engineering. Full four-year course, leading to the degree of Bachelor of Science in Architectural Engineering. Tuition is free. Incidental fees amount to about $30 per semester, these fees including the college fees. No course in architectural design. Pratt .Institute, Brooklyn, N. Y. Course in Architecture. School of Fine and Applied Arts, (i) Two-year course in architectural design. (2) Two-year course in architectural construction. (3) Full three-year course in architectural design and architectural construction. The course in archi- tectural design aims to give students a general training thaj: will prepare them to pursue the profession of architecture as competent assistants in architects' offices, and leads to positions of responsibility and independence. The course in architectural construction aims to fit the student for general draughting in builders' offices, or for general detailing and construction-work in an architects' ofiice, and leads to the position of superintendent of construction- work. Tuition, $80 per year. Princeton University, Princeton, N. J. School of Architecture. Institutions Teaching Architecture 17,S5 Three courses in Architecture: (i) For students enrolled as candidates for the degree of Bachelor of Arts on graduation and for the degree of Master of Fine Arts in Architecture after two years of graduate work. (2) For students who have not begun the study of architecture in the sophomore year, but who wish to receive the degree of Bachelor of Arts on graduation and the degree of Master of Fine Arts in Architecture after two years of graduate work. (3) For students entering the School as candidates for the degree of Master of Fine Arts in Architecture without previous study in architecture. For the average student, three years and a half are required for this course. Tuition, $100 a year for students on full time, and $40 for those on part time. Annual fees, $15. The graduate fellowship and scholarships of the University are open to members of the School. They are over fifty in number, and range in stipend from $150 to $1 000 per annum. Rice Institute, Houston, Tex. Architectural Department. Full four-year course leading to the degree of Bachelor of Science in Architecture. Tuition free. Rochester Athenaeum and Mechanics Institute, Rochester, N. Y. Department of Applied Arts. Three-year courses in Architectural Drawing and Design, and Architectural Construction, leading to Diplomas. There are also courses for properly prepared students who do not wish to take the diploma-courses. Tuition for full courses, $90 per year; for part-time students, $4 per term of twelve weeks for one session per week. Rose Polytechnic Institute, Terre Haute, Ind. Department of Archi- tectural Engineering. P'ull four-year course, designed to give a thorough training in architectural engineering, together with systematic instruction irv architectural design. Tuition and incidental fees, $110. Rotch Traveling-Scholarship, Inc. (For particulars address the Secretary, 20 Beacon Street, Boston, Mass.) Candidates must be under thirty years of age at the date of the beginning of the preliminary examinations. At that date they must have been engaged in professional work during two years in Massachusetts in the employ of a practicing architect resident in Massa- chusetts, and will be required to pass preliminary examinations upon the follow- ing subjects: (i) History of architecture; (2) Freehand drawing from the cast; (3) Construction, theory and practice; (4) An elementary knowledge of the French language. Holders of a degree in Architecture from the Massa- chusetts Institute of Technology, Columbia University, University of Penn- sylvania, Cornell University, Harvard University, or University of Illinois will be allowed to present such diploma which will be accepted in lieu of the examinations in the preliminaries. Candidates who pass in these preliminary examinations' are admitted to a competition in design, the successful can- didate in which is awarded the scholarship and receives annually, for two years, $1 400, to be expended in foreign travel and study. The Boston Society of Architects, through a committee, has complete charge of the examinations, and supervises the. work of the scholar. The Society of Architects awards the sum of $75 as a second prize. Syracuse University, Syracause, N. Y., College of Fine Arts. Depart- ment OF Architecture. This school offers: Four-year courses in (i) Ardu- tecture, (2) Architectural Design, (3) Architectural Engineering, all leading to the degree of Bachelor of Architecture (BAr.); (4) Special two-year course for architectural draughtsmen of two or more years' experience; (5) Graduate course in architecture; (G) Interior architectural design and decoraUon.. 1786 Institutions Teaching Architecture Part 3 Tuition, $150 per year. Bulletins and full information available from the Registrar. Texas. Agricultural and Mechanical College of Texas, College Station, Tex. Department of Architecture. Four-year course in architecture, offering an option through the junior and senior years in architectural eng'ineer- ing. Qualified special students admitted. Tuition free. Tulane University of Louisiana, New Orleans, La. Department of Architecture in the College of Technology, (i) Full four-year course leading to a degree in architecture. (2) Special courses for students not can- didates for a degree. Tuition, $100 per year. Special attention given to subtropical conditions. University of California, Berkeley, Cal. School of Architecture. (i) Full four-year course leading to the degree of Bachelor of Arts. (2) One- year-graduate course leading to the degree of Master of Arts. (3) Two-year graduate course leading to the degree of Graduate in Architecture. (4) Special or elective courses for students not candidates for a degree. Tuition free to residents of the state of California. University of Illinois, Urbana, 111. Courses in Architecture and Architectural Engineering, (i) Full four-year course leading to tlie degree of Bachelor of Science in Architecture. (2) Full four-year course, leading to the degree of Bachelor of Science in Architectural Engineering. Tuition is free. Incidental fee, $30 per year. Plym Traveling-Fellowship, $1 coo for one year of travel abroad; awarded by comi:)etition to graduates of the Departmtrnt of Architecture of the University of Illinois. University of Kansas, Lawrence, Kan. Department of Architecture AND Architectural Encinekring. Full four-year course in Architecture, leading to the degree of Bachelor of Science in Architecture. Full four-year course in Architectural Engineering, leading to the degree of Bachelor of Science in Architectural Engineering. Four-year courses in each, based on one year in the College of Liberal Arts, leading to the degree of Bachelor of Science. Tuition free. Fees amounting to $15 per year for residents of the state, and $25 per year for non-residents. University of Michigan, Ann Arbor, Mich. College of Architecture (i) A general four-year course leading to the degree of Bachelor of Science in i.\rchitecture. (2) A four-year course in which architectural design is em- phasized, leading to the same degree. (3) A four-year course in which there is a large proportion of engineering subjects, leading to the degree of Bachelor of Science in Architectural Engineering. (4) Five-year courses leading to the degrees of Master of Science in Architecture and Master of Science in Archi- tectural Engineering. (5) A two-year course, leading to a Certificate, for special students (experienced draughtsmen or college-graduates). (6) Students may earn the degree of Bachelor of Arts and the degree in Architecture in from five to six years. There are two scholarships. Annual fees, $57 for students from Michigan and $87 for others. University of Minnesota, Minneapolis, Minn. Department of Archi- tecture. Full four-year course, leading to the degree of Bachelor of Science in Architecture. Fifth year, leading to the degree of Master of Science in Architecture. Special students of maturity and practical experience are admitted. Instruction is provided in Architectural Engineering. Tuition ii^-r.. Incidental fee, $60 per year. University of Nebraska, Lincoln, Neb. College of Engineer: Institutions Teaching Architecture 1787 Full four-year course in architectural engineering, leading to Bachelor of Science in Architectural Engineering. Tuition free. Total fees for four years, $iio. University of Notre Dame, Notre Dame, Ind. Department of Archi- tecture, (i) Full four-year course in design leading to the degree of Bachelor of Science in Architecture. (2) Full four-year course in architectural engi- neering leading to the degree of Bachelor of Science in Architectural Engineering. (3) Two-year special course leading to a Certificate of Proficiency. Tuition, $120 per year; room $60 and upwards; board, $180 and upwards. University of Oregon, Eugene, Ore. School of Architecture and Allied Arts. Two architectural options in design and structural work, (i) Four-year course leading to the degree of Bachelor in Architecture. (2) Five-year course leading to the degree of Master in Architecture. (3) Ex- tension-courses in Portland, Ore., in design, etc. (4) Special courses for ex- perienced draughtsmen. Tuition free for university-courses; $5 a term for extension-courses. University of Pennsylvania, Philadelphia, Pa. School of Fine Arts, Department of Architecture, (i) Four-year course leading to the degree of Bachelor of Architecture. (2) Graduate course of one year, with choice between major subjects, leading to the degree of Master of Architecture. (3) Two-year special course leading to a professional certificate. (4) Six-year arrangement of courses in liberal arts and architecture leading to the degrees of A. B. and also B. Arch. (5) Option in Architectural Engineering leading to the degree of Bachelor of Architecture. Summer school providing instruction in many architectural subjects of the regular session. The degree and certificate are accepted by the American Institute of Architects in satisfaction of its educational requirements for membership and are credited by State Boards for licensing of architects. Tuition $300 per year. Descriptive circular, includ- ing information concerning all courses in the School of Fine Arts, on applica- tion to the Dean of the School of Fine Arts, University of Pennsylvania, Phila- delphia, Pa. The Woodman Scholarship in Architecture of the University of Penn- sylvania, for one year of foreign travel and study, is open to graduates of this school, they being also eligible to the general competition for the Fellowship OF THE American Academy in Rome. The Paris Prize of the Beaux-Arts Institute of Design is open to seniors and graduates and the Stewardson Traveling-Schot.arship is available to students who are residents of Penn- sylvania. The medals of the American Institute of Architects and the SociETE DES Architectes Diplomhs are conferred in this school as well as other medals and prizes open to its students alone. University of Southern California, Los Angeles, Cal. Four-year general course in architecture, leading to the degree of B.S. in Architecture. University of Texas, Austin, Tex. School of Architectitre. (i) Four-year and five-year courses leading, respectively, to the degrees of Bachelor of Science in Architecture, and Master of Science in Architecture. (2) Four- year course leading to the degree of Bachelor of Science in Architectural Engineering. Tuition free. University of Toronto, Toronto, Canada. Department of Archi- tecture Full four-year course leading to the degree of Bachelor of Applied Science (B A Sc ) with an option of architectural engineering, replacing archi- tectural design in the fourth year. The fees are, first year, $100; second year, $110; third and fourth years, $120. The university is supported by the Province of Ontario. 1788 Architectural Societies and Organizations of the World Part 3 University of Virginia. McIntire School of Fine Arts. Four-year course in architecture, leading to the degree of Bachelor of Science in Archi- tecture. Annual average of tuition and laboratory fees: For non- Virginians, $i8o; for Virginians, $75. University of Washington, Seattle, Wash. Course in Architecture. Four-year course, leading to the degree of Bachelor of Architecture. There is a fourth-year option in architectural engineering. Tuition, $20 per year., Entrance fee, $10; graduation fee, $5. Washington, The State College of, Pullman, Wash. Department op Architecture, (i) Full four-year course leading to the degree of Bachelor of Science in Architecture. (2) Two-year special course leading to a Certificate of Proficiency. (3) Special students, adequately prepared, are admitted to all classes. Tuition free. Washington University, St. Louis, Mo. School of Architecture (i) Four-year courses in architecture and in architectural engineering leading to the degrees of Bachelor of Architecture, and Bachelor of Science in Archi- tectural Engineering, respectively. (2) One-year course leading to the degree of Master of Architecture. (3) Special two-year course with Certificate. Tuition, $150 per year. Wentworth Institute, Boston, Mass. Courses in architectural con- struction, carpentry and building, and twelve other technical trades or indus- tries, (i) Two-year course in architectural construction trains for positions of foremen, superintendents, detail-designers, etc. Tuition, $54 per year and $15 laboratory fee. (2) One-year course in carpentry and building planned for those wishing to enter the wood-working-trades and industries as advanced apprentices or high-grade artisans. Tuition $30 per year and $15 laboratory fee. Yale University, New Haven, Conn. Department of Architecture. Regular course covers four years. Special degree. Bachelor of Fine Arts, to be competed for at end of course. Portions of the first-year's work, including lectures on history of chief styles of architecture and principles of composition and practice in elementary design, may be taken as electives by juniors and seniors in the academic course. Alice Kimball English Scholarship, sup- ported from fund of $11 000, for a year's travel abroad. William Wirt Win- chester Scholarship, supported from fund of $20000, for a year's travel abroad. Tuition, $180 per year. ARCHITECTURAL SOCIETIES AND ORGANIZA- TIONS OF THE WORLD I. United States (i) THE AMERICAN INSTITUTE OF ARCHITECTS •The Octagon, Washington. D. C. List of Chapters (192 i) of the The American Institute of Architects The year indicates the date of the chapter's organization Alabama Chapter. 19 16 Central New York Chapter. 1887 Baltimore Chapter. 1870 Cincinnati Chapter. 1870 Boston Chapter. 1870 Cleveland Chapter. 1890 Brooklyn Chapter. 1894 Colorado Chapter. 1892. Buffalo Chapter. 1890 Columbus (Ohio) Chapter. 19 13 Architectural Societies and Organizations of the World 1789 Connecticut Chapter. 1902 Dayton Chapter. 1899 Georgia Chapter. 1906 Illinois 'Chapter. 1869 Iowa Chapter. 1903 Kansas City Chapter. 1890 Kentucky Chapter. 1908 Louisiana Chapter. Michigan Chapter. Minnesota Chapter Nebraska Chapter. New Jersey Chapter. New York Chapter North Carolina Chapter. 1913 Oregon Chapter. 191 1 1910 1919 1900 1S67 Philadelphia Chapter. 1869 Pittsburgh Chapter. 1891 Rhode Island Chapter. 1875 St. Louis Chapter. 1890 San Francisco Chr.pter. 1881 South Carolina Chapter. 19 13 Southern California Chapter. 1894 Southern Pennsylvania Chapter. 1909 Tennessee Chapter. 19 19 Texas Chapter. 1913 Toledo Chapter. 1914 Virginia Chapter. 1914 Washington (D. C.) Chapter. 1887 Washington State Chapter, 1894 Wisconsin Chapter. 191 1 [921: Arkansas, Florida, Indiana, Note. — ^These new chapters were organized in Kansas State, Montana, and Utah. List of State Associations of The American Institute of Architects New York State Society of Architects. 1919 Ohio State Association. 19 15 Pennsylvania State Association. 1909 (2) MISCELLANEOUS SOCIETIES * \merican Society of Landscape Architects \rchitects' Association of Indianapolis Architectural Club of Minneapohs Architectural League of Pacific Coast Architectural League of New York Architectural Society of the University of California . Architectural Society of the University of Pennsylvania Association of Collegiate Schools of Architecture Baltimore Architectural Club Birmingham Society of Architects Boston Architectural Club Boston Society of Architects Brooklyn Institute of Arts and Sciences Chicago Architects' Business Association Chicago Architectural Club Chicago Association of Architects Cincinnati Architectural Club Cleveland Architectural Club Columbus Society of Architects Detroit Architectural Club Duluth Architectural Club . .„ x- Engineers' and Architects' Club of Louisville, Ky. Florida Association of Architects Gargoyle Club of St. Paul Georgia Architectural Association Indianapolis Architectural Club Kansas State Architects' Association 1790 Architectural Societies and Organizations of the World Part 3 Los Angeles Architectural Club I^.Iassachusetts Institute of Technology Architectural Association IMinneapolis Architectural Club Minneapolis Society of Architects New Orleans Architectural Club New York Society of Architects Norfolk Society of Architects North Carolina Architectural Association Oakland Architects' Association Oakland Architectural Club Oklahoma State Association of Architects Pittsburgh Architectural Club Portland, Oregon, Architectural Club Portland, Oregon, Association of Architects St. Joseph, Missouri, Society of Architects St. Louis Architectural Club St. Paul Architectural Club San Antonio Society of Architects San Diego Architectural Association San Francisco Architectural Club Society of Architects of Akron, Ohio Society of Architects of Columbia University Society of Beaux-Arts Architects Society of Naval Architects and Marine Engineers South Bend Architectural Club South Carolina Association of Architects Southern States Engineering Society Spokane Architectural Club T Square Club of Philadelphia Tacoma Society of Architects Texas State Association of Architects Utah Association of Architects Washington, D. C, Architectural Club 2. Argentine Republic Sociedad Central de Arquitectos. Buenos Aires 3. Austria Austrian Society of Civil Engineers and Architects. Vienna Architekten-Kiub der Weiner Kunstlergenossenschaft. Vienna Gesellschaft Osterreichischer Architekten. Vienna Weiner Bauhiitte. Vienna Towarzystwo Politechniczne we Lwowie. Leopoi Towarzystwo Technisczne we Krakowie. Cracow 4. Belgium Association des Architectes, de Liege. Liege i Societe Centrale D Architecture de Belgique. Brussels Societe Roy ale des Architectes D'Anvers. Antwerp Kring Voor Bouwhunde D'Anvers. Antwerp Chambre Syndicate des Architectes de Bruxelles. Brussels Foreign Architectural Societies 1791 Association des Architectcs de Bruxelles. Brussels Societe des Architectes de la Flandre Orientale. Ghent Societe des Architectes de la Flandre Orientale. Bruges 5. Bulgaria Societe des Ingenieurs et des Architectes Bulgares. Sofia 6. Canada Architectural Association of Canada Royal Architectural Institute of Canada. Montreal Alberta Association of Architects. Calgary and Ed^nonton, Alta. Architects' Association of Victoria. Victoria, B. C. British Columbia Association of Architects. Calgary Architectural Club Manitoba Association of Architects. Winnipeg, Man. Ontario Association of Architects. Toronto Province of Quebec Association of Architects. Montreal Regina Architectural Association. Regina, Sask. Saskatchewan Association of Architects. Regina, Sask. 7. Cuba Society of Engineers and Architects of Havana. Havana 8. France Permanent Committee of International Congresses of Architects. Paris Societe des Architectes Diplomes par le Gouvernement. Paris. Societe Nationale des Architectes de France. Paris. Societe Centrale des Architectes Frangais. Paris Union Syndicale des Architectes Frangais. Paris Societe des Diplomes de I'Ecole Speciale d'Architecture. Paris Association Provenciale des Architectes Frangais. Versailles Societe. Regionale des Architectes du Centre de la France. Bourges Societe Regionale des Architectes de Dauphine et de la Savoie. Grenoble Societe des Architectes de I'Est de la France. Nancy Societe Regionale des Architectes du Limousin, de TAngoulerae et du Perigord. Gueret (Creuse) Societe Regionale des Architectes du Midi. Toulouse Societe Regionale des Architectes du Nord. Lille Societe Regionale des Architectes du Poitou et de la Saintonge. Parthenay Societe Regionale des Architectes du Puy-de-D6me, du Cantal, de la Haute- Loire et de I'Allier. Clermont-Ferrand Societe Regionale des Architectes de Saone-et-Loire, de I'Ain et du Jura. Cha- lons-sur-Sa6ne Association Regionale des Architectes du Sud-Est Nice Societe des Architectes de I'Aisne. St. Quentin Societe des Architectes de I'Allier. Moulins Societe des Architectes de I'Anjou. Angers Societe des Architectes de I'Aube. Troyes Societe des Architectes de Blois. Blois Societe des Architectes de Bordeaux et du Sud-Ouest. Bordeaux ^ Societe des Architectes des Bouches-du-Rhone. Marseilles 1792 Architectural Societies and Organizations of the World Part 3 Socicti des Architectes du Doubs; Besangon Societe des Architectes de la Drome et de I'Ardeche. Valence Societe des Architectes d'Eure-et-Loir. Chartres Societe Amicale et Syndicat des Architectes du Gard. Nlmes Societe des Architectes de la Haute-Marne. Chalons-sur-Mame Societe Academique d'Architecture de Lyon. Lyon Societe des Architectes de la Marne. Paul-Chandon Societe des Architectes de Nantes. Nantes Societe des Architectes de I'Oise. Compiegne Societe des Architectes d'Orleans. Orleans Societe des Architectes de Rennes. Rennes Societe des Architectes de la Seine Inferieure et de I'Eure. Rouen Societe des Architectes de Seine-et-Marne. Melun Societe des Architectes de Seine-et-Oise. Versailles Societe des Architectes de la Touraine. Tours Societe des Architectes de I'Yonne. Joigny Association Amicale des Architectes. Paris Reunion Amicale des Anciens Eleves de I'Atelier Quest el- Pascal. Paris Union Mutuelle des Architectes. Paris Association Provinciale des Architectes Frangais. Bordeaux Societe des Architectes de la Cote-d'Or. Dijon Societe dss Architectes du Nord-Ouest. Guingamp (C6tes-du-Nord) Societe des Architectes de la Loire. Saint-Etienne Societe des Architectes du Loiret. Orleans Societe des Architectes, Geometres et Experts de la Lozcre. Mende Syndicat des Architectes du Rhone. Villeurbanne Societe des Architectes du Havre. Le Havre (Seine-Inferieure) Union Architecturale de Lyon. Lyon Association des Architectes Fran^ais. Marseilles Syndicat des Architectes de Basse-Normandie. Caen Societe Historique de Campiege. Campiege Societe d'Assistance Confraternelle des Architectes Frangais. Versailles 9. Germany Architekten-Verein zu Berlin. Berlin. W. Verbund. Deutscher Architekten-und-Ingenieur-Vereine. Berlin. S.W. Wiirttembergerischer Verein fur Baukunde. Stuttart Sachsischer Ingenieur-und-Architekten-Verein. Dresden Vereinigung Berliner Architekten. Berlin. W. Architekten-und-Ingenieur-Verein zu Hannover. Hannover Architekten-und-Ingenieur-Verein zu Osnabriick. Osnabriick Architekten-und-Ingenieur- Verein zu Hamburg. Hamburg Architekten-und-Ingenieur-Verein zu Cassel. Cassel Architekten-und-Ingenieur-Verein zu Liibeck. Lubeck Schleswig-Holsteinischer, Architekten-und-Ingenieur-Verein. Keil Baierischer Architekten-und-Ingenieur- Verein. Munich Architekten-und-Ingenieur-Verein zu Breslau. Breslau Badischer Architekten-und-Ingenieur-Verein. Karlsruhe Architektenrund-Ingenieur- Verein zu Oldenburg. Oldenburg Ostpreussischer Architekten-und-Ingenieur-Verein. Konigsberg Frankfurter Architekten-und-Ingenieur- Verein. Frankfort-on-Main Westpreussicher Architekten-und-Ingenieur- Verein zu Danzig. Danzig Architekten-und-Ingenieur- Verein fiir Elsass-Lothringen. Strassburg Foreign Architectural Societies l'J^93 Mittelrheinischer Architekten- und Ingenieur-Verein. Darmstadt Dresdener Architekten-Verein. Dresden Architekten-und-Ingenieur-Verein fur Niederrhein und Westfalen. Cologne Verein Leipziger Architekten. Leipzig Architekten-und-Ingenieur-Verein fiir das Herzogtum Braunschweig. Bruna" wick Architekten-und-Ingenieur- Verein zu Madgeburg. Magdeburg Architekten-und-Ingenieur-Verein zu Bremen. Bremen Architekten-und-Ingenieur- Verein zu Aachen. Aix-la-Chapelle Architekten-und-Ingenieur- Verein zu Metz. Metz Mecklenbiirgischer Architekten - und - Ingenieur - Verein zu Schwerin, i.M. Schwerin Vereinigung Berliner Architekten. Berhn. W. Architekten-und-Ingenieur- Verein zu Diisseldorf. Diisseldorf Bromberger Architekten-und-Ingenieur-Verein. Bromberg Architekten-und-Ingenieur-Verein zu Munster, i.W. Miinster Architekten-und-Ingenieur-Verein zu Potsdam. Potsdam Architekten-und-Ingenieur-Verein zu Stettin. Stettin Architekten-und-Ingenieur-Verein zu Posen. Posen Architekten-und-Ingenieur- Verein zu Erfurt. Erfurt Verein der Architekten und Bauing-Enieure zu Dortnaund. Dortmund Vereiningung Schlesischer Architekten. Breslau Towarzystwo Przyjaciol Nauk. Posen 10. Great Britain Royal Institute of British Architects. London, W. Northern Architectural Association. Newcastle-upon-Tyne Leeds and Yorkshire Architectural Society. Leeds Sheffield Society of Architects and Surveyors. Sheffield Manchester Society of Architects. Manchester Liverpool Architectural Society (Inc.). Liverpool Nottingham Architectural Association. Nottingham Birmingham Architectural Association. Birmingham Leicester and Leistershire Society of Architects. Leicester Bristol Society of Architects. Bristol Cardiff, South Wales and Monmouth Architects' Society. Cardiff Devon and Exeter Architectural Society. Exeter Glasgow Institute of Architects. Dundee Dundee Institute of Architects. Dundee Aberdeen Society of Architects. Aberdeen Edinburgh Architectural Association. Edinburgh York and Yorkshire Architectural Society. York Royal Institute of Architects of Ireland (Inc.). Dublin Architectural Association of Ireland. Dublin Institute of Architects of New South Wales (Inc.). Sydney Royal Victorian Institute of Architects (Inc.). Melbourne West Australian Institute of Architects (Inc.). Perth Cape Institute of Architects. Cape Town, South Africa Transvaal Institute of Architects. Johannesburg. Transvaal, South Afnca Natal Institute of Architects. Durban. Natal, South Afnca The Architectural Association. London, E.C. 1794 Architectural Suciviub and Organizations of the World Part 3 11. Greece Melienic Polytechiiical Society. Athens n, Holland Society for the Propagation of Architecture. Amsterdam Genootschap Architectura et Amicitia. Amsterdam Bouwhunst en Vriendschap. Rotterdam 13. Hungary Society of Engineers and of Architects. Budapest Magyar IVIernok-es Epitesz-Egylet. Budapest Society of Private Architects. Budapest 11. Italy Societa degli Ingegnerie e degli Architetti. Rome Associazione Artistica fra i Cultori di Architettura. Rome College dcs Ingenieurs et des Architectes de Gjncs. Genes Collegio degli Ingegneri ed Architetti in Palermo. Palermo Collegio Toscano degli Ingegneri ed Architetti in Firenze. Florence Societa degU Ingegneri di Bologna. Bologna Collegio degli Ingegneri ed Architetti di Milano. Milan Collegio degli Ingegneri ed Architetti di Torino. Turin Collegio degli Ingegneri ed Arciiitetti di Messina Collegio degli Ingegneri ed Architetti PugUe. Bari Collegio Veneto degh Ingegneri Venezia. Venise 15. Japan Society of Architects. Tokyo 16. Norway Societe des Architectes et des Ingenieurs. Christiania 17. Portugal Real Associo dos Architectos Civis e Archeologos Portuguezes. Lisbon Sociedad dos Architectos Portuguezes. Lisbon 18. Russia Societe Imperiale des Architectes Russes. Petrograd Societe des Architectes de Moscow. Moscow Stowarzyszenie Technikow Kolo Architektow. Varsovie 19. Spain Sociedad Centrale de Arquitectos de Madrid. Madrid Associacion des Architectes de Cataluna. Bajos Associacion des Architectes de Vizcaya. Bilboa Associacion des Architectes de Navarra. Pamplona Associacion de Arquitectos de Valencia. Valencia Associacion de Arquitectos de Galicia. Santiago (Coruna) Associacion de Arquitectos de Guipuzcoa. San Sebastian Agrupacion Regional Central dc Arquitectos de Castilla la Nueva. Madrid Foreign. Architectural Societies 1795 Acrupacion Regional de Arquitcctos do Castilla la Vieja. Zamora Agrupacion Regional de Arquitcctos de Norte. Bilboa Agrupacion Regional de Arquitcctos de Catalana-Balear. Bajos Agrupacion Regional de Arquitcctos de Andalucia. Cadiz Agrupacion Regional de Arquitcctos de Galicia. Santiago (Coruna) Agrupacion Regional de Arquitcctos de Cantabrico-Lconcsa. Santander Agrupacion Regional de Arquitcctos de Aragon. Teruel Agrupacion Regional de Arquitcctos de Levante. Valencia Agrupacion Regional de Arquitcctos de Canarias. Canaries Agrupacion Regional de Arquitcctos de Occidente. Caceres 30. Sweden . Societe des Architectes et Ingenieurs. Stockholm Svepska Teknologforenique. Stockholm 31. Switzerland Scheizerischer Ingenieur und Architekten Verein. Bale 33. Venezuela Sociedad de Arquitectura y Construccion du Venezuela. Caracas 1796 Glossary Parts CORINTHIAN ABACUS GLOSSARY * Technical Terms, Ancient and Modern, Used by Architects, Builders, and Draughtsmen Aaron*s-Rod. An ornamental figure representing a rod with a serpent twined about it. It is sometimes confounded witli the caduceus of Mercury. The distinction between tiie caduceus and the Aaron's-rod is that the former has two serpents twined in opposite directions, while the latter has but one. Abacus. The upper member of the capital of a column. It is sometimes square and sometimes curved, forming on the plan segments of a circle called the arch of the abacus, and is commonly decorated with a rose or other ornament in the center, having the angles, called horns of the abacus, cut. off in the direction of the radius or curve. In the Tuscan or Doric, it is a square tablet; in the Ionic, the edges are molded; in the Corinthian, its sides are concave and frequently enriched with carving. In Gothic pillars it has a great variety of forms. Abbey. A term for the church and other build- ings used by conventual bodies presided over by an abbot or abbess, in contradistinction to cathedral, which is presided over by a bishop; and priory, the head of which was a prior or prioress. Abutment. That part of a pier from which the arch springs. Abuttals. The boundings of a piece of land on other land, street, river, etc. Acanthus. A plant found in the south of Europe, representations of whose leaves are employed for decorating the Corinthian and Composite capitals. The leaves of the acanthus are used on the bell of the capital, and distinguish the two rich orders from the three others. Acroteria. The small pedestals placed on the extremities and apex of a pediment. They are usu- ally without bases or plinths, and were originally intended to receive statues. Aile, Aisle. The wings; inward side porticos of a church; the inward lateral corridors which enclose the choir, the presbytery, and the body of the church along its sides. Any one of the passages in a church or hall into which the pews or seats open. Alcove. The original and strict meaning of this word, which is derived from the Spanish alcoba, is confined to that part of a bed-chamber in which the bed stands, separated from the other parts of the room by columns or pilasters. It is now commonly used to express any large recess in a room, generally separated by an arch. Alipterion. In ancient Roman architecture, a room used by bathers for anointing themselves. * This Glossary was compiled by Mr. Kidder from various sources, and with the exception of some changes in typographical details to make it conform generally to the matter in the rest of the book, it is left as published in the preceding editions. ACANTHUS Glossary 1797 Almonry. The place or chamber where alms were distributed to the poor in churches, or other ecclesiastical buildings. At Bishopstone Church, Wiltshire, England, it is a sort of covered porch attached to the south transept, but not communicating with the interior of the church. At Worcester Cathedral, Eng- land, the alms are said to have been di':tributed on stone tables, on each side, within the great porch. In large monastic establishments, as at Westminster', it seems to have been a separate building of some importance, either joining the gate-house or near it, that the establishment might be disturbed as little as possible. Altar. In ancient Rom.an arc hitecture, a place on which offerings or sacri- fices were made to the gcds. In Protestant churches, t!ie communion table is often designated as the Altar, and in Roman Catholic churches it is a square table placed at the east end of the church for the celebration of mass. Altar of Incense. A small table covered with plates of gold on which was placed the smoking censer in the temple at Jerusalem. Altar-piece. The entire decorations of an altar; a painting placed behind an altar. Altar-screen. The back of the altar from which the canopy was suspended, and separating the choir from the lady chapel and presbytery. The Altar-screen was generally of stone, and composed of the richest tabernacle work of niches, finials, and pedestals, supporting statues of the tutelary saints. Alto-rilievo. High relief. A sculpture, the figures of which project from the surface on which they are carved. Ambo. A raised platform, a pulpit, a reading desk, a marble. -pulpit — an oblong enclosure in ancient churches, resembling in its uses and positions the modern choir. Ambry. A cupboard or closet, frequently found near the altar in ancient churches to hold sacred utensils. Ambulatory. An alley — a gallery — a cloister. * Amphiprostylos. A Grecian temple which has a columned portico on both ends. Amphitheater. A double theater, of an elliptical form on the plan, for the exhibition of the ancient gladiatorial fights and other shows. Its arena or pit, in which those exhibitions took place, was encompassed with seats rising above each other, and the exterior had the accommodation of porticos or arcades for the pubHc. Amphora. A Grecian vase with two handles, often seen on medals. Ancones. The consoles or ornaments cut on the key-stones of arches or on the sides of door-cases. They are sometimes made use of to support busts or other figures. Angle-bar. In joinery, an upright bar at the angles of polygonal windows; a mullion. Angle-capital. In Greek architecture, those Ionic capitals placed on the flank columns of a portico, which have one of their volutes placed horizontally at an angle of a hundred and thirty-five degrees with the plane of the frieze. Annulated Columns. Columns clustered together by rings or bands; much used in English architecture. Annular Vault. A vault rising from two parallel walls— the vault of a corridor. Ssune as Barrel Vault. 1798 Glossary Part 3 Annulet. A small square molding used to separate others. The fillet which separates the flutings of columns is sometimes known by this term. Anta, Antae. A name given to a pilaster when attached to a wall. Vitruvius calls pilasters par- asiatcB when insulated. They are not usually di- minished, and in all Greek examples their capitals are ANNULET different from those of the columns they accompany. Antechamber. An apartment preceded by a vestibule and from which is approached another room. Antechapel. A small chapel forming the entrance to another. There are examples at Merton College, Oxford, and at King's College, Cambridge, England, besides several others. The antechapel to the lady-chapel in cathedrals is generally called the Presbytery. Antechoir. The part under the rood loft, between the doors of the choir and the outer entrance of the screen, forming a sort of lobby. It is also called the Fore-choir. Antefixa. In classical architecture (gargoyles, in Gothic architecture), the ornaments of hons' and other heads below the eaves of a temple, through channels in which, usually by the mouth, the water is carried from the eaves. By some this term is ap- plied to the upright ornaments above the eaves in ancient architecture, which hid the ends of the Harmi or joint tiles. Apophyge. The lowest part of the shaft of an Ionic or Corinthian cplumn, or the highest member of its base if the column be considered as a whole The Apophyge is the inverted cavetto or concave sweep, on the upper edge of which the diminishing shaft rests. Apron. A plain or molded piece of finish below the stool of a window, put on to cover the rough edge of the plastering. Apse. The semicircular or polygonal termination to the chancel of a church. Apteral. A temple without columns on the flanks or sides. Aqueduct. An artificial canal for the conveyance of water, either above or under ground. The Roman aqueducts are mostly of the former construction. Arabesque. A building after the manner of the Arabs. Ornaments used by the same people, in which no human or animal figures appear. Arabesque is sometimes improperly used to denote a species of or- naments composed of capricious fantastics and imaginary repre- sentations of animals and foliage so much employed by the Romans in the decorations of walls and ceiHngs. Arabian Architecture. A style of architecture the rudiments ^ of which appear to have been taken from surrounding nations, the Egyptians, Syrians, Chaldeans, and Persians. The best preserved specimens partake chiefly of the Gra^co-Roman, Byzantine, and Egyptian. It is supposed that they constructed many of their finest buildings from the ruins of ancient cities. Araeostyle. That style of building in which the columns are distant from one another from four to five diameters. Strictly speaking, the term should be limited to intercolumniation of four diameters, which is only suited to the Tuscan order. Ar»osystylos. That style of building in which four columns arabesqte are used in the space of eight diameters and a half; the central Glossary I799 intercolumniation being three diameters and a half, and the others on each side being only half a diameter, by which arrangement coupled columns are mtroduced. Arbores. Large bronze candelabra, in the shape of a tree, placed on the floor of ancient churches, so as to appear growing out of it. Arcade. A range of arches, supported cither on columns or on piers, and detached or attached to the wall. Arch. In building, a mechanical arrange- ment of building materials arranged in the form of a curve, which preserves a given form when resisting pressure, and enables them, supported by piers or abutments, to carry weights and resist pressure. Arch-buttress. Sometimes called a flying arcade buttress; an arch springing from a buttress or pier. Architrave. That part of an entablature which rests upon the capital of a column, and is beneath the frieze. Architrave Cornice. An entablature consisting of an architrave and cor- nice, without the intervention of the frieze, sometimes introduced when incon- venient to give the entablature the usual height. Architrave of a Door. The finished work surrounding the aperture; the upper part of the lintel is called the traverse; and the sides, the jambs. Archives. A repository or closet for the preservation of writings or records. Archivolt. A collection of members forming the inner contour of an arch, or a band or frame adorned with moldings running over the faces or the arch- stones, and bearing upon the imposts. Area. The superficial contents of any figure; an open space or court within a building; also, an uncovered space surrounding the foundation walls to give light to the basement. Arena. The plain space in the middle of the amphitheater or other place of public resort. Arris. The meeting of two surfaces producing an angle. Arsenal. A public storehouse for arms and ammunition. Artificer, or Artisan. A person who works with his hands, and manufac- tures any commodity in iron, brass, wood, etc. Ashlar, or Ashler. A facing made of squared stones, or a facing made of thin slabs, used to cover walls of brick or rubble. Coursed ashlar is where the stones run in level courses all around the building; random ashlar, where the stones are of different heights, but level beds. Common freestones of small size, as they come from the quarry, are also called ashlar. Asphaltum. A kind of bituminous stone, principally found in the province of Neufchatel. Mixed with stone, it forms an excellent cement, incorruptible by air and impenetrable by water. Astragal. A small semicircular molding, sometimes plain and sometimes ornamented. Asymptote. A straight line which continually approaches to a curve with- out touching it. 1800 Glossary Part 3 Atlases, or Atlantes. Figures or half-figures of men, used instead of col- umns or pilasters to support an entablature; • called also Telamoncs. ^ Atrium. A court in the interior division of Roman houses. Attached Columns. Those which project three-fourths of their diameter from the wall. Attic. A low story above an entablature, or above a cornice which limits the height of the main part of an elevation. Although the term is evidently derived from the (ireek, we find noth- ing exactly answering to it in Greek architec- ture; but it is very common in both Roman and Italian practice. What are otherwise called tholobates in St. Peter's and St. Paul's Cathe- atlantes drals are frequently termed attics. Attic Order. A term used to denote the low pilasters employed in the decoration of an attic story. Attributes. In painting and sculpture, symbols given to figures and statues la indicate their office and character. Auditory. In ancient churches, that part of the church where the people usually stood to be instructed in the Gospel, now called the nave. Aula. A court or hall in ancient Roman houses. Aviary. A large apartment for breeding birds. Axis. The spindle or center of any rotative motion. In a sphere, an imag- inary line through the center. Back-choir. A place behind the altar in the principal choir, in which there is, or was, a small altar standing back to back with the former. Backing of a Rafter or Rib. The forming of an upper or outer surface, that it may range with the edges of the ribs or rafters on either side. Backing of a Wall. The rough inner face of a wall; earth deposited behind a retaining wall, etc. Back of a Window. That piece of wainscoting which is between the bottom of the sash frame and the floor. Balcony. A projection from the face of a wall, supported by columns or con- soles, and usually surrounded by a balustrade. Baldachin. A building in the form of a canopy, supported with columns, and serving as a crown or covering to an altar. Baluster. A small pillar or column, supporting a rail, of various forms, used in balustrades. Baluster Shaft. The shaft dividing a window in Saxon architecture. At St. Albans are some of these shafts, evi- dently out of the old Saxon church, which have been fixed up with Norman capitals. Balustrade. A series of balusters connected by a rail. Band. A sort of flat frieze or fascia running horizon- tally round a tower or other parts of a building, particu- larly the base tables in perpendicular work, commonly used with the long shafts characteristic of the thirteenth cen- tury. It generally has a bold, projecting molding above PAI^ACHIN Glossaiy jgQ^ and below, and is carved sometimes with foliages, but in general with cusped circles, or quatrefoils, in which frequently are shields of arms. of fh?.t ?L^ fo^^^^- A series of annulets and hollows going round the middle of the shafts of columns, and sometimes of the entire pier. They are often beau- tif ully carved with foliages, etc., as at Amiens. In several cathedrals there are rings ot bronze apparently covering the junction of the frusta of the columns At Worcester and Westminster they appear to have been gilt; they are there more properly called Shaft-rings. Baptistery. A separate building to contain the font, for the rite of baptism Ihey are frequent on the Continent; that at Rome, near St. John Lateran and those at Horeace, Pisa, Pavia, etc., are all well-known examples. The only ex- amples in England are at Cranbrook and Canterbury; the latter, however is supposed to have been originally part of the treasury. Barbican. An outwork for the defence of a gate or drawbridge; also, a sort of pent-house or construction of timber to shelter warders or sentries from arrows or other missiles. Barge Board. See Verge Board. Bartizan. A small turret, corbeled out at the angle of a wall or tower, to pro- tect a warder and enable him to see around him. They generally are furnished with oylcts or arrow- slits. Basement. The lower part of a building, usu- ally in part below the grade of the lot or street. Base Moldings. The moldings immediately above thf^. plinth of a wall, pillar, or pedestal. Base of a Column. That part which is between bartizan the shaft and the pedestal, or, if there be no pedes- tal, between the shaft and the plinth. The Grecian Doric had no base, and the Tuscan has only a single torus, or a plinth. Basilica. A term given by the Greeks and Romans to the public buildings devoted to judicial purposes. Bas-relief. See Basso-rilievo. Basse-cour. A court separated from the principal one, and destined for stables, etc. Basso-rilievo, or Bas-relief. The representations of figures projected from a background without being detached from it. It is divided into three parts: Alto-rilievo, when the figure projects more than one-half; Mezzo-rilievo, that in which the figure projects one-half; and Basso-rilievo, when the projection of the figure is less than one-half, as in coins. Bat. A part of a brick. Batten. Small scantlings, or small strips of boards, used for various purposes. Small strips put over the joints of sheathing to keep out the weather. Batten-door. A door made of sheathing, secured by strips of board, put crossways, and nailed with cHnched nails. Batter. A term used by bricklayers, carpenters, etc., to signify a wall, piece of timber, or other material, which does not stand upright, but inclines from you when you stand before it; but when, on the contrary, it leans toward you, it is said to overhang. 1802 Glossary Part 3 Battlement. A parapet with a series of notches in it, from which arrows may be shot, or other instruments of defence hurled on besiegers. The raised portions are called merlons; and the notches, em- brasures or crenelles. The former were intended to cover the soldier while dis- charging his weapon through the latter. Their use is of great antiquity; they are found in the sculptures of Nineveh, in the tombs of Egypt, and on the famous Fran- battlement gois vase, where there is a delineation of the siege of Troy. In ecclesiastical architecture the early battlements have small shallow embrasures at some distance apart. In the Decorated period they are closer together, and deeper, and the moldings on the top of the merlon and bot- tom of the embrasure are richer. During this period, and the early part of the Perpendicular, the sides or cheeks of the embrasures are perfectly square and plain. In later times the moldings were continued round the sides, as well as at top and bottom, mitring at the angles, as over the doorway of Magdalen Col- lege, Oxford, England. The battlements of the Decorated and later periods are often richly ornamented by paneling, as in the last example. In castellated work the merlons are often pierced by narrow arrow-shts, (See Oylel.) In South Ital}^ some battlements are found strongly resembling those of old Rome and Pompeii; in the Continental ecclesiastical architecture, the parapets are very rarely embattled. • Bay. Any division or compartment of an arcade, roof, etc. Thus each space, from pillar to pillar, in a cathedral, is called a bay, or severy. Bay Window. Any window projecting outward from the wall of a building, either square or polygonal on plan, and commencing from the ground. If they are carried on projecting corbels, they are called Oriel windows. Their use seems to have been confined to the later periods. In the Tudor and Elizabethan styles they are often semicircular in plan, in which case some think it more correct to call them Bow Windows. Bazaar. A kind of Eastern mart, of Arabic origin. Bead. A circular molding. When several are joined, it is called Reeding; when flush with the surface, it is Called Quirk-bead; and when raised. Cock-bead. Beam. A piece of timber, iron, stone, or other material, placed horizontally^ or nearly so, to support a load over an opening, or from post to post. Bearing. The portion of a beam, truss, etc., that rests on the supports. Bearing Wall, or Partition. A wall which supports the floors and roofs in a building. Beauf et, or Buffet. A small cupboard, or cabinet, to contain china. It may either be built into a wall, or be a separate piece of furniture. Bed. In bricklaying and masonry, the horizontal surfaces on which the stones or bricks of walls lie in courses. Bed of a Slate. The lower side. Bed Moldings. Those moldings in all the orders between the corona and frieze. Belfry. Properly speaking, a detached tower or campanile containing bells, as at Evesham, England, but more generally applied to the ringing- room or loft of the tower of a church. See Tower. Glossary 1803 Bell-cot, Bell-gable, or Bell-turret. The place where one or more bells are hung in chapels, or small churches which have no towers. Bell-cots are some- times double, as at Northborough and Coxwell, England; a very common form in France and Switzerland admits of three bells. In these countries, also, they are frequently of wood, and attached to the ridge. Those which stand on the gable, dividing the nave from the chancel, are generally called Sanctus Bells. A ^ery curious and, it is beheved, unique example at Cleves Abbey, England, juts out from the wall. In later times bell-turrets were much ornamented; these are often called Fleches. Bell of a Capital. In Gothic work, immediately above the necking is a deep, hollow curve; this is called the bell of a capital. It is often enriched with foli- ages. It is also applied to the body of the Corinthian and Composite capitals. Belt. A course of stones or brick projecting from a brick or stone wall, gen- erally placed in a line with the sills of the windows; it is either molded, fluted, plane, or enriched with patras at regular intervals. Sometimes called Stone String. Belvedere, or Look-out. A turret or lantern raised above the roof of an observatory for the purpose of enjoying a fine prospect. Bema. The semicircular recess, or hexedra, in the basiUca, where the judges sat, and where in after-times the altar was placed. It generally is roofed with a half-dome or concha. The seats of the priests were against the wall, looking into the body of the church, that of the bishop being in the center. The bema is generally ascended by steps, and railed off by cancelli. Bench Table. The stoiie seat which runs round the walls of large churches, and sometimes round the piers; it very generally is placed in the porches. Bevel. An instrument for taking angles. One side of a soHd body is said to be beveled with respect to another, when the angle contained between those two sides is greater or less than a right angle. Bezantee. A name given to an ornamental molding much used in the Nor- man period, resembling bezants, coins struck in Byzantium. Billet. A species of ornamented molding much used in Norman, and some- times in Early English work, like short pieces of stick cut off and arranged alter- nately. Blocking, or Blocking-course. In masonry, a course of stones placed on the top of a cornice crowning the walls. Bond. In bricklaying and masonry, that connection between bricks or stones formed by lapping them upon one another in carrying up the work, so as to form an inseparable mass of building, by preventing the vertical jomts falhng oyer each other. In brickwork there are several kinds of bond. In common bnck walls in every sixth or seventh course the bricks are laid crossways of the wall called Headers. In face work, the back of the face brick is clipped so as to get in a diagonal course of headers behind. In Old Enghsh bond, every a erna e course is a header course. In Flemish bond, a header and stretcher alternate in each course. Bond-stones. Stones running through the thickness of the wall at nght ani,^les to its face, in order to bind it together. Bond-timbers. Timbers placed in a horizontal direction in the walls o a I. i 1 buildL in tiers, and to which the battens, laths, etc., are secured. In rub- l,U work walls are better plugged for this purpose. Border. Useful ornamental pieces around the edge of anythmg. 1804 Glossary Parts Boss. An ornament, generally carved, forming the key-stone at the intersec- tion of the ribs of a groined vault. Early Norman vaults have no bosses. The carving is generally foliage, and resembles that of the period in capitals, etc. ■ Sometimes they have human heads, as at Notre Dame at Paris, and sometimes grotesque figures. In Later Gothic vaulting there are bosses at every intersection. Boutell. The mediaeval term for a round molding, or torus. When it follows a curve, as round a bench end, it is called a Roving Boutell. Bow. Any projecting part of a building in the form of an arc of a circle. A bow, however, is sometimes polygonal. Bow Window. A window placed in the bow of a building. Brace. In carpentry, an inclined piece of tim]3cr, used in trussed partitions, or in framed roofs, in order to form a triangle, and thereby stiffen the framing. When a brace is used by way of support to a rafter, it is called a strut. Braces in partitions and span-roofs are, or always should be, disposed in pairs, and introduced in opposite directions. Brace Mold. [ \ J Two rcssaunts or ogees united together like a brace in printing, sometimes with a small bead between them. Bracket. A projecting ornament carrying a cornice. Those which support vaulting shafts or cross springers of a roof are more generally called Corbels. Break. Any projection from the general surface of a building. Breaking Joint. The arrangement of stones or bricks so as not to allow two joints to come immediately over each other. See Bond. Breast of a Window. The masonry forming the back of the recess and the parapet under the window-sill. Bressummer. A hntcl, beam, or iron tie, intended to carry an external wall and itself supported by piers or posts; used principally over shop windows. This term is now seldom used, the word beam, or girder, taking its place. Bridging. A method of stiffening floor joist and parti- tion studs, by cutting pieces in between. Cross bridging of floor joist is illustrated in cut. Bulwark. In ancient fortification, nearly the same as Bastion in modern. Burse, or Bourse. A public edifice for the assembly of merchant traders' an exchange. Bust. In sculpture, that portion of the human figure which comprises the head, neck, and shoulders. Buttery. A store-room for provisions. Butt-joint. Where the ends of iwo pieces of timber or molding butt together. Buttress. Masonry projecting from a wall, and intended to strengthen the same against the thrust of a roof or vault. Buttresses are no doubt derived from the classic pilasters wliich serve to strengthen walls where there is a pressure of a girder or roof-timber. In very early work they have little projection, and, in fact, are "strippilasters." In Norman work they are wider, with very Httle projection, and generally stop under a cornice or corbel table. Early English buttresses project con- siderably, sometimes with deep sloping weatherings in several CROSS-BRIDGING FLYING BUTTRESS Glossary 1.S05 stages, and sometimes with gabled heads. Sometimes they are chamfered, and sometimes the angles have jamb shafts. At Wells and Salisbury, England, they are richly ornamented with canopies and statues. In the Decorated period they became richly paneled in stages, and often finish with niches and statues and elegantly carved and crocketcd gablets, as at York, England. In the Perpendicular period the weatherings became waved, and they frequently terminate with niches and pinnacles. Buttress, Flying. A detached jjuttress or pier of masonry at some distance from a wall, and connected therewith by an arch or por- tion of an arch, so as to discharge the thrust of a roof or vault on some strong point. Buttress Shafts. Slender columns at the angle of buttresses, chiefly used in the Early English period. Byzantine Architecture. A style developed in the Byzantine Empire. The capitals of the pillars are of endless variety and full of invention; some are founded on the Greek Corinthian, some resemble the Norman and the Lombard style, and arc so varied that no two sides of the same capital are alike. They are comprised under the style Romanesque, which comprehends the round- arch style. Byzantine architecture reached its height in the Church of St. Sophia at Constantinople. Cabinet. A highly ornamented kind of buffet or chest of drawers set apart for the preservation of things of value. Cabling. The flutes of columns are said to be cabled when they are partly occupied by solid convex masses, or appear to be refilled with cylinders after they had been formed. Caduceus. Mercury's rod, a wand entwined by two serpents and surmounted by two wings. The rod represents power; the serpents, wisdom; and the wings, diligence and activity. Caisson. A panel sunk below the surface in flat or vaulted ceil- ings. See Cassoon Caisson. In bridge building, a chest or vessel in which the piers of a bridge are built, gradually sinking as the work advances till its bottom comes in contact with the bed of the river, and then the sides are disengaged, being so constructed as to allow of their being thus detached without injury to its floor or bottom. Caliber, or Caliper. The diameter of any round body; the width of the mouth of a piece of ordnance. Camber. In carpentry, the convexity of a beam upon the surface, in order to prevent its becoming concaVfe by its own weight, or by the burden it may have to sustain. Campanile. A name given in Italy to the bell-tower of a town-hall or church. In that country this is almost always detached from the latter. Candelabrum. Stand or support on which the ancients placed their lamps. Candelabra were made in a variety of shapes and with much taste and elegance. The term is also used to denote a tall ornamental candlestick with several arms, or a bracket with arms for candles. Canopy. The upper part or cover of a niche, or the,projection or ornament over an altar, seat, or tomb. The word is supposed to be derived from cone- 1806 Glossary Part 3 paeum, the gauze covering over a bed to keep off the gnats; a mosquito curtain. Early English canopies are generally simple, with trefoilcd or cinque-foiled heads; but in the later styles they are very rich, and divided into compartments with pendants, knots, pinnacles, etc. The triangular arrangement over an Early Eng- lish and Decorated doorway is often called a canopy. The triangular canopies in the North of Italy are peculiar. Those in England are generally part of the arrangement of the arch moldings of the door, and form, as it were, the hood- molds to them, as at York. The former are above and independent of the door moldings, and frequently support an arch with a tympanum, above which is a triangular canopy, as in the Duomo at Plorence. Sometimes the canopy and arch project from the wall, and are carried on small jamb shafts, as at San Pietro Martiro at Verona. Canopies are often used over windows, as at York Minster over the great west window, and lower ties in the towers. These are triangular, while the upper windows in the towers have ogee canopies. Ca'pital. The upper part of a column, pilaster, pier, etc. Capitals have been used in every style down to the present time. That mostly used by the Egyp- tians was bell-shaped, with or without ornaments. The Persians used the double- headed bell, forming a kind of bracket capital. The Assyrians apparently made use of the Ionic and Corinthian, which were developed by the Greeks, Romans, and Italians into their present well-known forms. The Doric was apparently an invention or adaptation by the Greeks, and was altered by the Romans and Italians. But in all these examples, both ancient and modern, the capitals of an order are all of the same form throughout the same building, so that if one be seen the form of all the others is known. The Romanesque architects altered aU this, and in the carving of their capitals often introduced such figures and emblems as helped to tell the story of their building. Another form was intro- duced by them in the curtain capital, rude at first, but afterward highly deco- rated. It evidently took its origin from the cutting off of the lower angles of a square block, and then rounding them off. The process may be distinctly seen, in its several stages, in Mayence Cathedral. But this form of capital was more fully developed by the Normans, with whom it became a marked feature. In the early English capitals a peculiar flower of three or more lobes was used spreading from the necking upward in most graceful forms. In Decorated and Perpendicular styles this was abandoned in favor of more realistic forms of crumpled leaves, enclosing the bell like a Wreath. In each style bold abacus moldings were always used, whether with or without foliage. Caravansary. A huge, square building, or inn, in the East, for the reception of travelers and lodging of caravans. Carriage. The timber or iron joist which supports the steps of a wooden stair- Carton, or Cartoon. A design made on strong paper, to be transferred on the fresh plaster wall to be afterward painted in fresco; also, a colored design for working in mosaic tapestry. Cartouche. An ornament which like an escutcheon, a shield or an oval or oblong panel has the central part plain, and usually slightly convex, to receive an inscription, armorial bearings, or an ornamental or significant piece of painting or sculpture. Frequently used in French Renaissance and Modern Architecture. Caryatides. Human female figures used as piers, columns, or supports. Caryatic is applied to the human figure generally, when used in the manner of caryatides. Cased. Covered with other materia^ generally of a better quality. Glossary 1807 Casement. A glass frame which is made to open by turning on hinges affixed to its vertical edges. Casspon, or Caisson. A deep panel or coffer in a soffit or ceiling. This term is sometimes written in the French form, caisson; sometimes derived directly from the Italian cassone, the augmentative of cassa, a chest or coffer. Cast. A term used in sculpture for the impression of any figure taken in plaster of Paris, wax, or other substances. Catacombs. Subterranean places for burying the dead. Those of Egypt, and near Rome, are believed to be the most important. Catafalco. An ornamental scaffold used in funeral solemnities. Cathedral. The principal church, where the bishop has his seat as diocesan. Cauliculus. The inner scroll of the Corinthian capital. It is not uncommon, however, to apply this term to the larger scrolls or volutes also. Causeway. A raised or paved way. Cavetto. A concave ornamental molding, opposed in effect to the ovolo — the quadrant of a circle. Ceiling. That covering of a room which hides the joists of the floor above, or the rafters of the roof Most European churches either have open roofs, or arc groined in stone. At Peterborough and St. Albans, England, there are very old flat ceilings of boards curiously painted. In later times the boarded ceilings, and, in fact, some of those of plaster, have molded ribs, locked with bosses at the intersection, and are sometimes elaborately carved. In many English churches there are ceilings formed of oak ribs, filled in at the spandrels with narrow, thin pieces of board, in exact imitation of stone groining. In the Elizabethan and subsequent periods the ceilings are enriched with most elaborate ornaments in stucco. Matched and beaded boards, planed and smoothed, used for wainscoting. In the New England States it is called sheathing. Cenotaph. An honorary tomb or monument, distinguished from monuments in being empty, the individual it is to memorialize having received interment elsewhere. Centaur. A poetical imaginary being of heathen mythology, half-man and half-horse. Centring. In building, the frames on which an arch is turned. Chamfer, Champf er, or Chaumf er. When the edge or arris of any work is cut off at an angle of 45° in a small degree, it is said to be chamfered; if to a large scale, it is said to be a canted corner. The chamfer is much used in mediaeval work, and is sometimes plain, sometimes hollowed out, and sometimes jmolded. Chamfer Stop. Chamfers sometimes simply run into the arris by a plane face; more commonly they are first stopped by some ornament, as by a bead; they are sometimes terminated by trefoils, or cinque-foils, double or single, and- in general form very pleasing features in mediaeval architecture. Chancel. A place separated from the rest of a church by a screen The word is now generally used to signify the portion of an Episcopal or Catholic church containing the altar and communion table. Chantry. A small chapel, generally built out from a church. They generally contain a founder's tomb, and are often endowed places where masses might 1808 Glossary Parts CHAPTREL be said for his soul. The officiator, or mass priest, being often unconnected with the parochial clergy. The chantry has generally an entrance from the outside. Chapel. A small, detached building used as a substitute for a church in a large parish; an ai:)artment in any large building, a palace, a nobleman's house, a hospital or prison, used for pubhc worship; or an attached building running out of and forming part of a large church, generally dedicated to different saints, each having its own altar, piscina, etc., and screened off from the body of the building. Chapter House. The chamber in which the chapter or heads of the monastic bodies assembled to transact business. They are of various forms; some are oblong apartments, some octagonal, and some circular. Chaptrel. In Gothic architecture, the capital of a pier or column which receives an arch. Charnel House. A place for depositing the bones which might be thrown up in digging graves. Sometimes it was a portion of lli. crypt; sometimes it was a separate building in the church-yan sometimes chantry chapels were attached to these buildings. . Al. Viollet-le-Duc has given two very curious examples of ossuaires — one from Fleurance, the other from Faouet. Cherub — Gothic. A representation of an infant's head joined to two wings, used in the churches on key-stones of arches and corbels. Chevron — Gothic. An ornament turning this and that way, like a zigzag, or letter Z. Chiaro-oscuro. The effects of light and shade in a picture. Choir. That part of a church or monastery where the breviary service, or "hora;," is chanted. Church. A building for the performance of public worship. The first churches were built on CHE\':ron the plan of the ancient basilicas, and afterward on the plan of a cross: a church is said to be in Greek cross when the length of the transverse is equal to that of the nave; in Latin cross, when the nave is longer than the transverse part; in rotundo, when it is a perfect circle; simple, when it has only a nave and choir; with aisles, when it has a row of porticos in form of vaulted galleries, with chapels in its circumference. Ciborium. A tabernacle or vaulted canopy supported on shafts standing over the high altar. Cincture. A ring, list, or fillet at the fop and bottom ot a column, serving to divide the shaft of the column from its capital and base. Cinque-foil. A sinking or perforation, like %. flower, of five points or leaves, as a quatre-foil is of four. The points are sometimes in a circle, and sometimes form the cusping of a head. Civic Crown. A garland of oak-leaves and acorns, given as honorary distinction among the Romans to such as had preserved the life of a fellow-citizen. CINQUE-FOIL Glossary 1809 Clere-story Clear-story. When the middle of the nave of a church rises above the aisles and is pierced with windows, the upper story is thus called. Sometimes these windows are very small, being mere quatre- foils, or spherical triangles. In large buildings, however, they are impor- tant objects both for beauty and utility. The window of the clere- stories of Norman work, even in large churches, are of less importance than in the later styles. In Early English they became larger j and in the Deco- rated they are more important still, being lengthened as the triforium diminishes. In Perpendicular work the latter often disappears altogether, and in many later churches the clere- stories are close ranges of windows. The word clere-story is also used to denote a similar method of lighting other buildings besides churches, es- pecially factories, depots, sheds, etc. Cloister. An enclosed square, like the atrium of a Roman house, with a walk or ambulatory around, sheltered by a roof, generally groined, and by tracery windows, which were more or less glazed. Close. The precinct of a cathedral Sometimes the walls • are but now generally the is only known by tradi- or abbey, traceable, boundary tion. Close String, or Box String. Bath Abbey FLYING BUTTRESS AND CLERE-STORY A, buttress with pinnacle; B, flying method of r,„ishin« the outer edge of Ij^XTroo^rj^T D t'fel^dTiding nave from aisle; E, vaulted roof of nave. tairs, by bull-ding up a sort of curb string on which the balusters set, and the treads and risers stop against it. Clustered. In architecture, the coalition of several members which penetrate each other. Clustered Column. Several slender pillars attached to each other SD as to form one. The term is used in Roman architecture to denote two or four columns which appear to intersect each other at the angle of a building to answer at each return. Coat. A thickness or coveiang of paint, plaster, or other work, done at one rime. The first coat of plastering is called the scratch coat, the second coat (when there are three coats) is called the brown coat, and the last coat is variously known as the slipped coat, skimcoat, or white coat. It varies in composition in different iocaiities. Coffer, A deep panel in a ceiling. 1810 Glossary Parlfl ? watl^B piked !^1: LFTJ cyma-recta .fillet:zz cornice-^ corona_ OVCLO ' fillet; lcavetto FRIEZE-^ FRIEZE TENiAr; ARCHI- J UPPER FASCI RAVE LOWER FASCI I Coffer Dam. A frame used in the building of a bridge in deep watsj similar to a caisson. Collar Beam. A beam above the lower ends of the rafters, and spiked!^ them. Colonnade. A row of columns. The colonnade is termed, according to the number of columns which support the entablature: Tetrastyle, when there are four; hexastyle, when six; octostyle, when eight, etc. When in front of a building they are termed porticos; when surrounding a building, peristyle; and when double or more, polystyle. Colosseum, or Coliseum. The immense amphitheater built at Rome by Flavins Vespasian, A d. 72, after his return from his victories over the Jews. It would contain ninety thousand persons sitting, and twenty thousand more standing. The name is now employed to denote an unusually large audience building, generally of a temporary nature. Colossus. The name of a brazen statue which was erected at the entrance of the harbor at Rhodes, one hundred and five feet in height. Vessels could sail between its legs. Column. A round pillar. The parts are the base, on which it rests; its body, calbd the shaft; and the head, called the capital. The capital finishes with a horizontal table, called the abacus, and the base commonly stands on another, called the plinth. Columns may be either insulated or attached. They are said to be at- tached or engaged when they form part of a wall, projecting one-half or more, but not the whole, of their substance. Common. A line, angle, surface, etc., which belongs equally to several objects. Common centring is a cen- tring without trusses, having a tie beam at bottom. Common joists are the beams in naked flooring to which the joists are fixed. Common rafters in a roof are those to which the laths are attached. Composite Arch. Is the pointed or lancet arch. ^ Composite Order. The most elaborate of the orders of classical arch- itecture. Compound Arch. A usual form of medieval arch, which may be resolved into a number of concentric archways, successively placed within and behind each other. Conduit. A long narrow passage between two walls or underground for secret communication between different apartments; also, a canal or pipe for the conveyance of water. jM APOPHYCES FILLET-~-r-: TORUS r SECTION OF COLUMN AND ENTABLATURE (Divided according to the Tuscan Order.) Glossary 1811 Confessional. The seat where a priest or confessor sits to hear confessions Conge. Another name for tho ecliinus or quarter round. Conservatory. A building for the protection and rearing of tender phmts often attached to a house as an apartment. Also, a public place of instruction,' designed to preserve and perfect the knowledge of som3 branch of learning or the fine arts; as, a conservatory of music. Consistory. The judicial hall of the College of Cardinals at Rome. Consol, or Console. A bracket or truss, generally with scrolls or volutes at the two ends, of unequal size and contrasted, but connected by a flowing line from the back of the upper one to the inner convolving face of the lower. Coping. The capping or covering of a wall. This is of stone, weathered to throw off the wet. In Nor- man times, as far as can be judged from the little there is left, it was generally plain and flat, and projected over the wall with a floating to form a d.ip. After- ward it assumed a torus or bowtell at the top, and be- came deeper, and in the Decorated period there were generally several sets-off. The copings in the Perpendicular period assumed something of the wavy section of the buttress caps, and mitred round the sides of the embrasure, as well as the top and bottom. Corbel. The name, in mediaeval architecture, for a piece of stone jutting out of a wall to carry any superincumbent weight. A piece of timber projecting in the same way was called a tassel or a bragger. Thus, the carved ornaments from which the vaulting shafts spring at Lincoln are corbels. Norman corbels are generally plain. In the Early English period they are sometimes elaborately carved. They sometimes end with a point, apparently growing into the wall, or forming a knot, and often are supported by angles and other figures. In the later periods the foliage or ornaments resemble tho33 in the capitals. In modern architecture, a short piece of stone or wood projecting from a wall to form a support, generally ornamented. Corbel Out. To build out one or more courses of brick or stone from the face of a wall, to form a support for timbers. Corbel Table. A projecting cornice or parapet, supported by a range of corbels a short distance apart, which carry a molding, above which is a plain piece of projecting wall forming a parapet, and covered by a coping. Sometimes small arches are thrown across from corbel to corbel, to carry the projection. Cornice. The projection at the t>p of a wall finished by a blocking-course, common in classic architecture. In Norman times, the wall finished with a cor- bel table, which carried a portion of plain projecting work, which was finished by a coping, and the whole formed a parapet. In- Early English times the para- pet was much the same, but the work was executed in a much better way, espe- cially the small arches connecting the corbels. In the Decorated ixir:od the corbel table was nearly abandoned, and a large hollow, with one or two subordinate moldings, substituted; this is sometimes filled with the ball-flowers, and some- times with running foliages. In the Perpendicular style the parapet frequently did not project beyond the .waH-line below; the molding then became a stnng (thou-h often improperly calleda cornice), and was ornamented by a quatre-foil, or small rosettes, set at equal intervals immediately under the battlements. In many French examples the molded string is very bold, and ennched with fohage ornaments 1812 Glossary Part 3 Corona. The brow of the cornice which projects over the bed moldings to throw off the water. Corridor. A long gallery or passage in a mansion connecting various apart- ments and running round a quadrangle. Any long passage-way in a building. Countersink. To make a cavity for the reception of a plate of iron, or the head of a screw or bolt, so that it shall not project beyond the face of the work. Coupled Columns. Columns arranged in pairs. Course. A continued layer of bricks or stones in buildings; the term is also applicable to slates, shingles, etc. Court. An open area behind a house, or in the center of a building and the wings. Courts admit of the most elegant ornamentations, such as arcades, etc. Cove — Coving. The molding called the cavetto, or the scotia inverted, on a large scale, and not as a mere molding in the composition o^ a cornice, is called a cove or a coving. Cove-bracketing. The wooden skeleton mold or framing of a cove, applied chielly to the bracketing of a cove ceihng. Cove Ceiling. A ceiling springing from the walls with a curve. Coved and Flat Ceiling. A ceiling in which the section is the quadrant of a circle, rising from the walls and intersecting in a flat surface. Cradling. Timber work for sustaining the lath and plaster of vaulted ceilings. Cresting. An ornamental finish in the wall or ridge of a building, which is common on the Continent of Europe. An example occurs at Exeter Cathedral, the ridge of which is ornamented with a range of small fleurs-de-lis in lead. Crocket. An ornament running up the sides of gablets, hood-molds, pinna- cles, spires; generally, a winding stem like a creeping plant, with flowers or leaves projecting at intervals, and terminat- ing in a fiftial. Cross. This religious symbol is almost always placed on the ends of gables, the summit of spires, and other conspicu- ous places of old churches. In early times it was generally very plain, often a simple cross in a circle. Sometimes they take the form of a light cross, crosslet, or a cross in a square. In the Decorated and later styles they became richly floriated, and assumed an endless variety of forms. Of memorial crosses the finest examples are the Eleanor crosses, erected crocket by Edward I. Of these a few yet remain, one of which has recently been reerected at Charing Cross. Preaching crosses were often set up by the wayside as stations for preaching; the most noted is that in front of St. Paul's, England. The finest remaining sepulchral crosses are the old elaborately carved examples found in Ireland. Cross-aisle. An old name for a transept. Cross-springer. The transverse ribs of a vault. Cross-vaulting. A common name given to groins and cylindrical vaults. Crown. In architecture the uppermost member of the cornice; called also Corona and Larmier. Crypt, A vaulted apartment of greater or less size, usually under the choir. Cupola. A small room, either circular or polygonal, standing on the top of a dome. By some it is callec] a Lantern, r H \ i 1 1 CYMA RECTA 1 b "^ • wmA CYMA REVERSA Glossary 1813 Curb Roof, or Mansard Roof. A roof formed of four contiguous planes, each two having an external inclination. ^ Curtail Step. The hrst step in a stair, which is generally finished in the form of a scroll. Cusp. The point where the foliations of tracery intersect. The earliest examplj in England of a plain cusp is probaljly that at Pythagoras School, at Cambridge, of an ornamental cusp, at Ely Cathedral, where a small roll, with a rosette at the end, is formed at the termination of a cusp. In the later styles the terminations of the cusps were more richly decorated; they also sometimes terminate not only in leaves or foHages, but in rosettes, heads, and other fanciful ornaments. Cyclostyle. A structure composed of a circular range of columns without a core is cyclostylar; with a core, the range would be a peristyle. This is the spe- cies of edifice called by Vitruvius monopteral. Cyma. The narhe of a molding of very frequent use. It is a simple, waved line, concave at one end and convex at the other, Hke an Italic /. When the concave part is uppermost it is called a cyma recta, but if the convexity appear above, and the concavity below, it is then a cyma reversa. Cymatium. When the crowning molding of an en- ] tablature is of the cyma form, it is termed the Cyma- tium. Cyrtostyle. A circular projecting portico. Such are those of the transept entrances to St. Paul's Cathedral, London. Dado, or Die. The vertical face of an insulated pedestal between the base and cornice, or surbase. It is extended also to the similar part of all stereobates which are arranged Hke pedestals in Roman and Italian architecture. Dais. A part of the floor at the end of a mediaeval hall, raised a step above the rest of the floor. On this the lord of the mansion dined with his friends at the great table, apart from the retainers and servants. In mediaeval halls there was generally a denp recessed bay window at one or at each end of the dais, supposed to be for retirement, or greater privacy than the open hall could afford. In France the word is understood as a canopy or hanging over a seat; probably the name was given from the fact that the seats of great men were then sur- mounted by such an ornament. Darby. A flat tool used by plasterers in working, especially on ceilings. It is generally about seven inches wide and forty-two inches long, with two handles on the back. Decastyle. A portico of ten columns in front. Decorated Style. The second stage of the Pointed or Gothic style of archi- tecture considered the most complete and perfect development of Gothic archi- tecture the best examples of which are found in England. Demi-metope. The half of a metope, which is found at the retiring or pro- jecting angles of a Doric frieze. . , u , i ^ r r^„-„ Dentil. The cogged or toothed member, common m the hjd-mo^^^ a Conn thian entablature, is said to be dentiled, and each cog or tooth is called a denti . Depressed Arches, or Drop Arches. Those of less pitch than the eqmlateral. application to a technical portion of the design. 1814 Glossary Part 3 Detail. As used by architects, detail means the smaller parts into which a composition may be divided. It is applied generally to moldings and other enrichments, and again to their minutiae. Diameter. The line in a circle passing through its center, or tliickest part, which gives the measure proportioning the intercolumniation in some of the otders. Diameters. The diameters of the lower and upper ends of the shaft of a column are called its inferior and superior diameters, respectively; the former is the greatest, the latter the least diameter of the shaft. Diaper. A method of decorating a wall, panel, stained glass, or any plain sur- face, by covering it with a continuous design of flowers, rosettes, etc., either in squares or lozenges, or some geometrical form resembHng the pattern of a dia- pered table-cloth, from which, in fact, the name is supposed by some to have been derived. Diastyle. A spacious intercolumniation, to which three diameters are assigned. Dipteros. A double- winged temple. The Greeks are said to have constructed temples with two ranges of columns all around, which were called dipteroi. A portico projecting two columns and their interspaces is of dipteral or pseudo- dipteral arrangement. Discharging Arch. An arch over the opening of a door or window, to dis- charge or relieve the superincumbent weight from pressing on the lintel. Distemper. Term applied to painting with colors mixed with size or .. ther glutinous substance. All the cartoons of the ancients, previous to the year 1410, are said to be done in distemper. Distyle. A portico of two columns. This is not generally applied to the mere porch with two columns, but to describe a portico with two columns in anti$. Ditriglyph. An intercolumniation in the Doric order, of two triglyphs. Dodecastyle. A portico of twelve columns in front. The lower one of the west front of St. Paul's Cathedral, London, is of twelve columns, but they are coupled, making the arrangement pseudo-dodecastyle. The Chamber of Depu- ties in Paris has a true dodecastyle. Dog-tooth. A favorite enrichment used from the latter part of the Normaa period to the early part of the Decorated. It is in the form of a four-leaved flower, the center of which projects, and probably was named from its resem- bLnce to the dog-toothed violet. Dome. A cupola or inverted cup on a building. The application of this term to its generally* received purpose is irom the Italian custom of calling an archi- cpiscopal church, by way of eminence, II Duomo, the temple; for to one of that rank, the Cathedral of Florence, the cupola was first applied in modern practice. The Italians themselves never call a cupola a dome; it is on this side of the Alps the application has arisen, from the circumstance, it would appear, that the Ital- ians use the term with reference to those structures whose most distinguishing feature is the cupola, tholus, or (as we now call it) dome. Domestic Architecture. That branch which relates to private buildings. Donjon. The principal tower of a castle, generally containing the prison. Door Frame. The surrounding case into and out of which the door shuts and opens. It consists of two upright pieces, called jambs, and a head, generally fixed together by mortices and tenons, and wrought, rebated, and beaded. Doric Order. The oldest of the three orders of Grecian architecture. Glossary 1815 Dormer Window, ri window belonging to a room in a roof, which conse- quently projects from it with a valley gutter on each side. They are said not to be earlier than the fourteenth century. In Germany there are often several rows of dormers, one above the other. In Italian Gothic they are very rare: in fact, the former have an unusually steep roof, while in the latter country, where the Italian tile is used, the roofs are rather flat. Dormitory. A room, suite of rooms, or building used to sleep in. The name was first applied to the place where the monks slept at night. It was sometimes one long room like a barrack, and sometimes divided into a succession of small chambers or cells. The dormitory was generally on the first floor, and connected with the church, so that it was not necessary to go out-of-doors to attend the nocturnal services. In the large houses of the Perpendicular period, and also in some of the Elizabethan, the entire upper story in the roof formed one large apartment, said to have been a place for exercise in wet weather, and also for a dormitory for the retainers of the household, or those of visitors. Double Vault. Formed by a dupHcate wall; wine cellars are sometimes so formed. Dovetailing. In carpentry and joinery, the method of fastening boards or other timbers together, by letting one piece into another in the form of the expanded tail of a dove. Dowel. A pin let into two pieces of wood or stone, where they are joined together. A piece of wocd driven into a wall so that other pieces may be nailed to it. This is also called plugging. Draw-bridge. A bridge made to draw up or let down, much used in fortified places. In navigable rivers, the arch over the deepest channel is made to draw or revolve, in order to let the masts of ships pass through. Drawing-room. A room appropriated for the reception of company; a room to which company withdraws from the dining-room. Dresser. A cupboard or set of shelves to receive dishes and cooking utensils. Dressing. Is the operation of squaring and smoothing stones for building; also applied to smoothing lumber. Dressing-room. An apartment appropriated for dressing the person. Drip. A name given to the member of a cornice which has a projection beyond the other parts for throwing off water by small portions, drop by drop. It is also called Larmier. Drip-stone. The label molding which serves on a canopy lor an opening, and to throw off the rain. It is also called Weather Molding. - Drop-scene. A curtain suspended by pulleys, which descends or drops m front of the stage in a theater. Drum. The upright part of a cupola over a dome; also, the solid part or vase of the Corinthian and Composite capitals. ^ Drv-rot. A rapid decay of timber, by which its substance is converted mto a dry powderV which issues from minute cavities resembhng the bonngs of "" Dungeon. The prison in a castle keep, so called because the Norman name for thelatter is donfon, and the dungeons, or prisons, are generally m its lowest 'Twarf Wall. The walls enclosing courts above which are raihngs of iron; low walls, in general, receive this name. 1816 Glossary Part 3 Eaves. In slating and shingling, the margin or lower part of the slating hanging over the wall, to throw the water ofif from the masonry or brickwork. Echinus. A molding of eccentric curve, gener- ally cut (when it is carved) into the forms of eggs and anchors alternating, whence the molding is called by the name of the more conspicuous. It is the same as Ovolo. Edifice. Is synonymous with the terms building, fabric, erection, but is more strictly apphcable to arcliitecture distinguished for size, dignity, and grandeur. Efflorescence. In architecture, the formation of a whitish loose powder, or crust, on the surface of stone or brick walls. Egyptian Architecture. The earliest civilization and cultivation of the arts was in Upper Egypt. The most remarkable and most ancient monuments of the Eg3'ptians, with the exception of the pyramids, are nearly all included in Upper Egypt. The buildings of Egypt are characterized' by solidity and massiveness of construction, originality of conception, and boldness of form. The walls, the pillars, and the most sacred places of their religious buildings were ornamented with hieroglyphics and symbolical figures, while the ceilings of the porticos exhibited zodiacs and celestial planispheres. The temples of Egypt were gener- ally without roofs, and, consequently, the interior colonnades had no pediments, supporting merely an entablature, composed of only architrave, frieze, and cornice, formed of immense blocks united without cement and ornamented with hieroglyphics. Element. The outline of the design of a Decorated window, on which the centers for the tracery are formed. These centers will all be found to fall on points which, in some way or other, will be equimultiples of parts of the openings. To draw tracery well, or understand even the principles of its composition, much attention should be given to the study of the element. Elevation. The front facade, as the French term it, of a structure; a geo- metrical drawing of the external upright parts of a building. Embattlement. An indented parapet; battlement. Emblazon. To adorn with figures of heraldry, or ensigns armorial. Embossing. Sculpture in rilievo, the figures standing partly out from the plane. Embrasure. The opening in a battlement between the two raised solid por- tions or merlons, sometimes called a crenelle. Encaustic. Pertaining to the art of burning in colors, apphed to painting on glass, porcelain, or tiles, where colors are fixed by heat; hence, encaustic tiles, bricks, etc. Engaged Columns. Are those attached to, or built into walls or piers, a portion being concealed. Enrichment. The addition of ornament, carving, etc., to plain work; decora- tion; embellishment. Ensemble. Means the whole work or composition considered together, and not in parts. Entablature. The assemblage of parts supported by the column. It coi>^ sists of three parts: the architrave, frieze, and cornice. Entail. In Gothic architecture, dehcate carving. Glossary 1817 Entasis. The swelling of a column, etc. In medic-eval architecture, some spires, particularly those called "broach spires," have a slight swelhng in the sides, but no more than to make them look straight; for, from a particular "deceptio visus," that which is quite straight, when viewed at a height, looks hollow. Entry. A hall without stairs or vestibule. Epistyle- This term may with propriety be applied to the whole entablature, with which it is synonymous; but it is restricted in use to the architrave, or lowest member of the entablature. Escutcheon. (Her.) The field or ground on which a coat-of-arms is repre- sented. (Arch.) The shields used on tombs, in the spandrels of doors, or in tring-courses; also, the ornamented plates from the centre of which door rings, inockers, etc., are suspended, or which protect the wood of the key-hole from :he wear of the key. In mediaeval times these were often worked in a very Deautiful manner. Etching. A mode of engraving on glass or metal (generally copper) by means Df lines, eaten in or corroded by means of some strong acid. Eustyle. A species of intercolumniation to which a proportion of two diam- :ters and a quarter is assigned. This term, together with the others of similar mport — pycnostyle, systyle, diastyle, and araeostyle — referring to the distance 3f columns from one another in composition, is from Vitruvius, who assigns to 2ach the space it is to express. It will be seen, however, by reference to them ndividually, that the words themselves, though perhaps sufficiently applic- ble convey no idea of an exactly defined space, and, by reference to the :olumnar structures of the ancients, that no attention was paid by them to uch limitations. It follows, then, that the proportions assigned to each are >urely conventional, and may or may not be attended to without vitiating the )ower of applying the terms. Eustyle means the best or most beautiful ar- angement; but, as the effect of a columnar composition depends on many hings besides the diameter of the columns, the same proportioned inter- :olumniation would look well or ill according to those other circumstances, o that the limitation of Eustyle to two diameters and a quarter is absurd. Extrados. The exterior or convex curve forming the upper line of the arch tones; the term is opposed to the intrados, or concave side. Eye of a Dome. The aperture at its summit. Eye of a Volute. The circle in its center. Facade, or Face. The whole exterior side of a building that can be seen at ne view; strictly speaking, the principal front. Face Mold. The pattern for marking the plank or board out of which irnamental hand-railings for stairs and other works are cut. Fan Tracery. The very complicated m_ode of roofing used in the Perpen- lieular style, in which the vault is covered by ribs and veins of tracery. Fascia. A flat, broad member in the entablature of columns or other parts of puildings, but of small projection. The architraves in some of the orders are omposed of three bands, or fascia; the Tuscan and the Doric ought to have only ne. Ornamental projections from the walls of brick buildings over any of the /indows, except the uppermost, are called Fasciae. Fenestral. A frame, or "chassis," on which oiled paper or thin cloth was trained to keep out wind and rain when the windows were not glazed. 1818 Glossary Parts fmTmmMMMmm^ immm^ l^&^^^w^^ g^^as^ Im^P (m;^ FESTOON FINIALS Festoon. An ornament of carved work, representing a wreath or garland of flowers or leaves, or both, interwoven with each other. It is thickest in the middle, and small at each extremity, where it is tied, a part often hanging down below the knot. Fillet. A narrow vertical band or listel of frequent use in congeries of moldings, to sepa- rate and combine them, and also to give breadth and firmness to the upper edge of a crowning cyma or cavetto, as in an external cornice. The narrow slips or breadth between the flutes of Corinthian and Ionic columns are also called fillets. In mediaeval work the fiUet is a small, flat, projecting square, chiefly used to separate hollows and rounds, and often found in the outer parts of shafts and boutels. In this situation the center fillet has been termed a keel, and the two side ones, wmgs; but, apparently, this is not an ancient usage. Finial. The flower, or bunch of flowers, with which a spire, pinnacle, gablet, canopy, etc., generally terminates. Where there are crockets, the finial generally bears as close a resem- blance as possible to them in point of design. They are found in early work where there are no crockets. The simplest form more resembles a bud about to burst than an open flower. They soon became more elaborate, as at Lincoln, and still more, as at West- minster and the Hotel Cluny at Paris. Many per- pendicular finials are like, four crockets bound to- gether. Almost every known example of a finial has a sort of necking separating it from the parts below Fish-joint. A splice where the pieces are joined butt end to end, and are con- nected by pieces of wood or iron placed on each side and firmly bolted to the timbers, or pieces joined. Flags. Flat stones, from i to 3 inches thick, for floors. Flamboyant. A name applied to the Third Pointed style in France, which seems to have been developed from the Second, as the English Perpendicular was from the Decorated. The great characteristic is, that the element of the tracery flows upward in long wavy divisions like flames of fire. In most cases, also, every division has only one cusp on each side, however long the division may be. 1 he moldings seem to be as much inferior to those of the preceding period as the Perpendicular moldings were to the Early English, a fact which seems to show that the decadence of Gothic architecture was not confined to one country. Flange. A projecting edge, rib, or rim. Flanges are often cast on the top o! bottom of iron columns, to fasten them to those above or below; the top and bottom of I-beams and channels are called the flange. Flashings. Pieces of lead, tin, or copper, let into the joints of a wall so as to lap over gutters or other pieces; also, pieces worked in the slates or shingles around dormers, chimneys, and any rising part, to prevent leaking. Flatting. Painting finished without leaving a gloss on the surface. Fleche. A general term in French architecture for a spire, but more par- ticularly usad for the small, slender erection rising from the intersection oi the nave and transepts in cathedrals and large churches, and carrying the sanctus bell. Fleur-de-lis. The royal insignia of France, much used in decoration. Glossary 1819 Flight. A run of steps or stairs from one landing to c^notiier. Floating. The equal spreading of plaster or stucco on the surface of walls, by means of a board called a float; as a rule, only rough plastering is floated. ' Floriated. Having florid ornaments, as in Gothic pillars. Flue. The space or passage in a chimney through which the smoke ascends. Each passage is called a flue, while aU together make the chimney. Flush. The continued surface, in the same plane, of two contiguous masses. Flute. A concave channel. Columns whose shafts are channeled are said to be fluted, and the flutes are collectively called Flutings. Flying Buttress. An arched buttress used when extra strength was required for the upper part of the wall of the nave, etc., to resist the outward thrust of a vaulted ceiling. The flying buttress generally rests on the wall and buttress of the aisle. Foils. The small arcs in the tracery of Gothic windows, panels, etc. Foliage. An ornamental distribution of leaves on various parts of buildings. Foliation. The use of small arcs or foils in forming tracery. Font. The vessel used in the rite of baptism. The earliest extant is supposed to be that in which Constantine is said to have been baptized; this is a porphyry labrum from a Roman bath. Those in the baptisteries in Italy are all large, and were intended for immersion; as time went on, they seem to have become smaller. Fonts are sometimes mere plain hollow cylinders, generally a little smaller below than above; others are massive squares, supported on a thick stem, round which sometimes there are smaller shafts. In the Early English this form is still pursued, and the shafts are detached; sometimes, however, they are hex- agonal and octagonal, and in this and the later styles assume the form of a vessel on a stem. Norman fonts frequently have curious carvings on them, approach- ing the grotesque; in later times the foliages, etc., partook absolutely of the character of those used in other architectural details of their respective periods. The font in European churches is usually placed close to a pillar near the en- trance, generally that nearest but one to the tower in the south arcade; or, in large buildings, in the middle of the nave, opposite the entrance porch, and sometimes in a separate building. In Protestant churches in this country, the font is generaUy placed inside the communion rail, or on the steps of the chancel. Footings. The spreading courses at the base or foundation of a wall. ^ When a layer of different material from that of the wall (as a bed of concrete) is used, it is called the Footing. Foundation. That part of a building or wall which is below the surface of the ground. Foxtail Wedging. Is a peculiar mode of mortising, in which the end of the tenon is notched beyond the mortise, and is split and a wedge inserted, which, being forcibly driven in, enlarges the tenon and renders the jomt firm and mi- ■ movable. Frame. The name given to the wood-work of windows, doors, etc.; and m carpentry, to the timber works supporting floors, roofs, etc. Framing. The rough timber work of a house, including the flooring, roofing, partitioning, ceiling, and beams thereof. Freestone. Stone which can be used for moldings, tracery and other work required to be executed with the chisel. The ooht.c and sandstones are those /■er-^rally included by this term. 1820 Glossary Part 3 Fresco. The method of painting on a wall while the plastering is wet. The color penetrates through the material, which, therefore, will bear rubbing or clean-» ing to almost any extent. The transparency, the chiaro-oscuro, and lucidity, as well as force, which can be obtained by this method, cannot be conceived unless the frescos of Fra Angelico or Raphael are studied. The word, however, is often applied improperly to painting on the surface in distemper or body color, mixed with size or white of egg, which gives an opaque effect. Fret. An ornament consisting of small fillets inter- secting each other at right angles. Frieze. That portion of an entablature between-the cornice above and architrave below. It derives its name from being the recipient of the sculptured en- fret richments either of foliage or figures which may be relevant to the object of the sculpture. The frieze is also called the Zoophorus. I Frigidarium. An apartment in the Roman bath, supplied with cold water. Furniture. A name given to the metal trimmings of doors, windows, and other similar parts of a house. In this country the word ''hardware" is more generally used to denote the same thing. Furrings. Flat pieces of timber used to bring an irregular framing to an even surface. Gable. When a roof is not hipped or returned on itself at the ends, its ends are stopped by carrying up the walls under them in the triangular form of the roof itself. This is called the gable, or, in the case of the ornamental and orna- mented gable, the pediment. Of necessity, gables follow the angles of the slope of the roof, and differ in the various styles. In Norman work they are generally about half-pitch; in Early English, seldom less than equilateral, and often more. In Decorated work they become lower, and still more so in the Perpendicular style. In all important buildings they are finished with copings or parapets. In the Later Gothic styles gables are often surmounted with battlements, or enriched with crockets; they are also often paneled or perforated, sometimes very richly. The gables in ecclesiastical buildings are mostly terminated with a cross; in others, by a finial or pinnacle. In later times the parapets or copings were broken into a sort of steps, called corbie steps. In buildings of less pretension the tiles or other roof covering passed over the front of the wall, which then, of course, had no coping. In this case, the outer pair of rafters were concealed by molded or carved verge boards. Gable Window. A term sometimes applied to the large window under a gable, but more properly to the windows in the gable itself. Gabled Towers. Those which are finished with gables instead of parapets. Many of the German Romanesque towers are gabled. Gablets. Triangular terminations to buttresses, much in use in the Early English and Decorated periods, after which the buttresses generally terminate in pinnacles. The Early English gablets are generally plain, and very sharp in pitch. In the Decorated period they are often enriched with paneling and crockets. They are sometimes finished with small crosses, but oftener with finials. Gain. A beveled shoulder on the end of a mortised brace, for the purpose of giving additional resistance to the shoulder. Gallery. Any long passage looking down into another part of a building, or into the court outside. In like manner, any stage erected to carry a rood or an organ, or to receive spectators, was latterly called a gallery, though originally a Glossary 1821 loft. Ill later times the name was given to any very long rooms, particularly those intended for purposes of state, or for the exhibition of pictures. Gambrel Roof. A roof with two pitches, similar to a mansard or curb roof. Gargoyle, or Gurgoyle. The carved termination to a spout which conveyed away the water from the gutters, supposed to be called so from the gurgling noise made by the water passing through it. Gar- goyles are mostly grotesque figures. Gate-house. A building forming the entrance to a town, the door of an abbey, or the enceinte of a castle or other important edifice. They generally had a large gateway protected by a gate, and also a port- cullis, over which were battlemented parapets with holes (machicolations) for throwing down darts, melted lead, or hot sand on the besiegers. Gate-houses always had a lodge, with apartments for the porter, gargoyle and guard-rooms for the soldiers; and, generally, rooms over for the officers, and often places for prisoners beneath. The name is now commonly applied to the gate-keeper's lodge on large estates. Gauge. To mix plaster of Paris with common plaster to make it set quick, called gauged mortar. A tool used by carpenters, to strike a line parallel to the edge of a board. Girder. A large timber or iron beam, either single or built up, used to sup- port joists or walls over an opening. Glyph. A vertical channel in a frieze. Gothic Style. The name of Gothic was given to the various Mediaeval styles at a period in the sixteenth century when a great classic revival was going on, and everything not classic was considered barbarian, or Gothic. The term was thus originally intended as one of stigma, and, although it conveys a false idea of the character of the Mediaeval styles, it has long been used to distinguish them from the Grecian and Roman. The true principle of Gothic architecture is the vertical division, relation and subordination of the different parts, distinct and yet at unity with each other, and while this principle was adhered to, Gothic architecture may be said to have retained its vitality. Grange. A word derived from the French, signifying a large barn or granary. Granges were usually long buildings with high wooden roofs, sometimes divided by posts or columns into a sort of nave and aisles, with walls strongly buttressed. In England the term was appHed not only to the barns, but to the whole of the buildings which formed the detached farms belonging to the monasteries; m most cases there was a chapel either included among these or standing apart as a separate edifice. GriUage. A framework of beams laid longitudinally and crossed by simUar beams notched upon them, used to sustain walls to prevent irregular setting. GriUe. The iron-work forming the enclosure screen to a chapel, or the pro- tecting railing to a tomb or shrine; more commonly found m France than m England. They are of wrought iron, ornamented by the swage and Punch and put together either by rivets or clips. In modern times grilles are used exten- ^vely for protecring L lower windows in city houses, also the glass openmg m outside doors. . ,, i xu . Groin. By some described as the line of intersection of two vaults where they cross eacL other, which others caU the groin point; by others the curved section 1822 Glos iossiiry Part :i GROINED VAULTING or spandrel of such vaulting is called a groin, and by others the whole system of vaulting is so named. Groin Arch. The cross-rib in the later styles of groining, passing at right angles from wall to wall, and dividing the vault into bays or travees. Groin Ceiling. A ceiling to a building com- posed of oak ribs, the sj)andrcls of wiiicli are filled , in with narrow, thin slips of wood. There arc several in England; one at the Early English church at VVarmington, and one at Winchester Cathedral, exactly resembling those of stone. Groin Centring. In groining without ribs, the whole surface is supported by centring during the erection of the vaulting. In ribbed work the 8tone ribs only are sui)ported by timber ribs during the progress of the work, any light stuff being used while filling in the spandrels. Groin Point. The name given by workmen to the arris or line of intersection of one vault with another where there are no ribs. Groin Rib. The rib which conceals the groin point or joints, where the span- drels intersect. Groined Vaulting. The system of covering a building with stone vaults which cross and intersect each other, as opposed to the barrel vaulting, or series of arches placed side by side. The earliest groins are plain, without any rib , except occasionally a sort of wide band from wall to wall, to strengthen the coi btruction. In later Norman times ribs were added on the line of intersection ol the spandrels, crossing each other, and having a boss as a key common to both; these ribs the French authors call ncr/s en ogive. Their introduction, however, caused an entire change in the system of vaulting; instead of arches of uniform thickness and great weight, these ribs were first put up as the main construction, and spandrels of the lightest and thinnest ix>ssible material placed uixjn them, the haunches only being loaded sufikiently to counterbalance the pressure from the crown. Shortly after, half-ribs against the walls (formercts) were introduced to carry the spandrels without cutting into the walling, and to add to the apjx^'arance. 'J'he work was now not treated as continued vaulting, but as divided into bays, and it was formed by keeping up the ogive, or intersecting ribs and their bosses; a sort of construction having some affinity to the dome was formed, which added much to the strength of the groining. Of course, the top of the soffit or ridge of the vault was not h(jriz(^ntal, but rose from the level of the top of the formeret-rib to the boss and fell again; but tliis could not be perceived from below. As this system of construction got more into use, and as the vaults were required to be of greater span and of higher pitch, the spandrels became larger, and re(|uired more support. To give this, another set of ribs was introduced, passing from the springers of the ogive ribs, and going to about half-way between these and the ogive, and meeting on the ridge of the vault; these intermediate ribs are called by the French tiercerons, and began to come into use in the transition from Early English to Decorated. About the same period a system of vaulting came into use called hcxpartite, from the fact that every bay is divided into six compart- ments instead of four. It was invented to cover the naves of churches of unusual width. The filling of the spandrels in this style is very peculiar, and, where the diflerent compartments meet at the ridge, some pieces of harder stone have been used, which give rather a pleasing effect. The arches against the wall, being of smaller span than the main arches, cause the centre springers to be per- Glossary 1823 peiidicular and parallel for some height, and the spandrels themselves are very hollow. As styles progressed, and the desire for greater richness increased, another s(-Ties of ribs, called Hemes, was introduced; these passt;d crossways from the ogives to tin; liercerons, and thence to tiie doublcaux, dividing the spandrels nearly horizontally. 'J'hese various systems increased in the reri)endicu!ar period, so that the walls were (juite a net-work of ribs, and led at last to the Tudor, or, as it is called by many, fan-tracery vaulting. In this system the ribs are no part of the real construction, but are merely carved upon the voussoirs, which form the actual vaulting. Fan Tracery is so called because the ribs radiate from the springers, and sj^read out like the sticks of a fan. These later methods arc; not strii tly groins, for the ixMuIcntives are not square on plan, but circular, and Ihere is, theref(jre, no arris intersection or groin point. Groins, Welsh, or Underpitch. When the main longitudinal vault of any groining is higher than the cross or transverse vaults which run from the windows, the system of vaulting is called unden)it(:li groining, or, as termed by the work- men, Welsh groining. A very fine example is at St. George's Chapel, Windsor, England. Groove. In joinery, a term used to signify a sunk channel whose section is rectangular. It is usually employed on the edge of a molding, stile, or mil, etc., into which a tongue corresponding to its section, and in the substance of the wood to which it is joined, is inserted. Grotesque. A singular and fantastic style of ornament found in ancient buildings. Grotto. An artificial cavern. Ground Floor. The floor of a building on a level, or nearly so, with the ground. Ground Joist. Joist that is blocked up from the ground. Grounds. IMeces of wood embedded in the plastering of walls to which skirting and other joiner's work is attached. They arc also used to stop the plastering around door and window openings. Grouped Columns. Three, four, or more columns put together on the same pedestal. When two are placed together, they arc said to be coupled. Grout. Mortar made so thin by the addition of water that it will run into all the joints and cavities of the mason-work, and fill it up solid. Guilloche, or Guillochos. An interlaced orna- ment like net-work, used most frequently to enrich ^X:"xx««x. Gutta. The small cylindrical drops used to en- rich the mutulcs and regular of the Doric entabla- ture arc so called. Guttei. The channel for carrying off rain-water The medireval gutters differed little from others, except that they are often hollows sunk in .the top of stone cornices, in which case they are generally called chan- CUTT^. nels in English, and chcncaux \n Lrench. , ^ , .. Gymnasium. A building cj-ed in 0. f^st ^^^^^^^ them they instructed the youth m all the arth of peace ana wa . athletic exercises. 1S24 Glossary Part 3 Hall. The principal apartment in the large dwellings of the Middle Ages, used for the purposes of receptions, feasts, etc. In the Norman castle the hall was generally in the keep above the ground floor, where the retainers lived, the basement being devoted to stores and dungeons for confining prisoners. Later halls — indeed, some Norman halls (not in castles) — are generally on the ground floor, as at Westminster, approached by a porch either at the end, as in this last example, or at the side, as at Guildhall, London, having at one end a raised dais or estrade. The roofs are generally open and more or less ornamented. In the middle of these was an opening to let out the smoke, though in later times the halls have large chimney-places with funnels or chimney-shafts for this purpose. At this period there were usually two deeply recessed bay windows at each end of the dais, and doors leading into the withdrawing-rooms, or the ladies' apart- ments; they are also generally wainscoted with oak, in small panels, to the height of five or six feet, the panels often being enriched. Westminster Hall was originally divided into three parts, like a nave and side aisles, as are some on the Continent of Europe. A room or passage-way at the entrance of a house, or suite of chambers. A place of pubHc assembly, as a town-hall, a music-hall. Halving. The junction of two pieces of timber, by letting one into the other. Hammer Beam. A beam in a Gothic roof, not extending to the opposite side; a beam at the foot of a rafter. Hanging Buttress. A buttress not rising from the ground, but supported on a corbel, applied chiefly as a decoration and used only in the Decorated and Perpendicular style. Hanging Stile. Of a door, is that to which the hinges are fixed. Hangings. Tapestry; originally invented to hide the coarseness of the walls of a chamber. Different materials were employed for this purpose, some of them exceedingly costly and beautifully worked in figures, gold and silk. Hatching. Drawing parallel lines close together for the purpose of indicat- ing a section of anything. The lines are generally drawn at an angle of 45° with a horizontal. Haunches. The sides of an arch, about half-way from the springing to the crown. Headers. In masonry, are stones or bricks extending over the thickness of a wall. In carpentry, the large beam into which the common joists are framed in framing openings for Stairs, chimneys, etc. Heading Courses. Courses of a wall in which the stone or brick are all headers. Head-way. Clear space or height under an arch, or over a stairway, and the like. Heel. Of a rafter, the end or foot that rests upon the wall plate. Height. Of an arch, a line drawn from the middle of the chord to the intrados. Helix. A small volute or twist like a stalk, representing the twisted tops of the acanthus, placecf under the abacus of the Corinthian capital. Hermes. A rough quadrangular stone or pillar, having a head, usually of Hermes or Mercury, sculptured on the top, without arms or body, placed by the Greeks ia front of buildings. HERMES Glossary 1825 . Herring-bone Work. Bricks, tile, or other materials arranged diagonally in building. ^ Hexastyle. A portico of six columns in front is of this description. High Altar. The principal altar in a cathedral or church. Where there is a second, it is generally at the end of the choir or chancel, not in the lady chapel. Hip-knob. The finial on the hip of a roof, or between the barge boards of a gable. Hip-roof. A roof which rises by equally inclined planes from all four sides of the building. Hippodrome. A place appropriated by the ancients for equestrian exercises. Hips. Those pieces of timber placed in an inclined position at the corners or angles of a hip-roof. Hood-mold. A word used to signify the drip-stone for label over a window or door opening, whether inside or out. Hotel de Ville. The town-hall, or guild-hall, in France, Germany, and Northern Italy. The building, in general, serves for the administration of justice, the receipt of town dues, the regulation of markets, the residence of magistrates, barracks for police, prisons, and all other fiscal purposes. As may be imagined, they differ very much in different towns, but they have almost invariably attached to them, or closely adjacent, a large clock-tower containing one or more bells, for caUing the people together on special occasions. Hotel Dieu. The name for a hospital in mediaeval times. In England there are but few remains of these buildings, one of which is at Dover; in France there are many. The most celebrated is the one at Angers, described by Parker. They do not seem to differ much in arrangement of plan from those in modern days, the accommodation for the chaplain, medicine, nurses, stores, etc., being much the same in all ages, except that in some of the earlier, instead of the sick being placed in long wards like galleries, as is now done, they occupied large buildings, with naves and side aisles, like churches. Housing. The space taken out of one solid to admit the insertion of another. The base on a stair is generally housed into the treads and risers; a niche for a statue. Hypaethros. A temple open to the air, or uncovered. The term may be the more easily understood by supposing the roof removed from over the nave of a church in which columns or piers go up from the floor to the ceiling, leaving the aisles still covered. Hypogea. Constructions under the surface of the earth, or in the sides of a hill or mountain. Ichnography. A horizontal section of a building or other object, showing its true dimensions according to a geometric scale, a ground plan. Impluvium. The central part of an ancient Roman court, which was un- covered. Impost. A term in classic architecture for the horizontal moldings of piers or pilasters, from the top of which spring the archivolts or moldings which go round the arch. In Antis. When there are two columns between the antai of the lateral waUs and the cella. Incise. To cut in; to carve; to engrave. Indented. Toothed together. 1826 Glossary Part 3 Inlaying. Inserting pieces of ivory, metal, or choice woods, or the like, into a groundwork of some other material, for ornamentation. Insulated. Detached from another building. A church is insulated, when not contiguous to any other edifice. A column is said to be insulated, when standing free from the wall; thus, the columns of peripteral temples were insulated. Intaglio. A sculpture or carving in which the figures are sunk below the gen- eral surface, such as a seal the impression of which in wax is in bas-relief; op- posed to Cameo. Intercolumniation. The distance from column to column, the clear space between columns. Interlaced Arches. Arches where one passes over two openings, and they consequently cut or intersect each other. Intrados. Of an arch, the inner or concave curve of the arch stones. Inverted Arches. Those whose key-stone or brick is the lowest in the arch. Ionic Order. One of the orders of Classical architecture. Iron Work. In mediaeval architecture, as an ornament, is chiefly confined to the hinges, etc., of doors and of church chests, etc. In some instances not only do the hinges become a mass of scroll work, but the surface of the doors is covered by similar ornaments. In almost all styles the smaller and less important doors had merely plain strap hinges, terminating in a few bent scrolls, and latterly in fleurs-de-lis. Escutcheon and ring handles, and the other furniture, partook more or less of the character of the time. On the Continent of Europe the knockers are very elaborate. At all periods doors have been ornamented with nails having projecting heads, sometimes square, sometimes polygonal, and some- times ornamented with roses, etc. The iron work of windows is generally plain, and the ornament confined to simple fleur-de-lis heads to the stanchions. The iron work of screens enclosing tombs and chapels is noticed under Grille, q.v. Jack. An instrument for raising heavy loads, either by a crank, siren and pinion, or by hydraulic power, and in all cases worked by hand. Jack Rafter. A short rafter, used especially in hip-roofs. Jamb. The side-post or lining of a doorway or other aperture. The jambs of a window outside the frame are called Reveals. Jamb-shafts. Small shafts to doors and windows with caps and bases; when in the inside arris of the jamb of a window they are sometimes called Esconsons. Joggle. A joint between two bodies so constructed by means of jogs or notches as to prevent their sliding past each other. Joinery. That branch in building confined to the nicer and more ornamental parts of carpentry. Joist. A small timber to which the boards of a floor or the laths of ceiling are nailed. It rests on the wall or on girders. Keep. The inmost and strongest part of a mediaeval castle, answering to the citadel of modern times. The arrangement is said to have originated with Gun- dulf, the celebrated Bishop of Rochester. The Norman keep is generally a very massive square tower, the basement or stories partly below ground being used for stores and prisons. The main story is generally a great deal above ground level, with a projecting entrance, approached by a flight of steps and drawbridge. This floor is generally supposed to have been the guard-room or place for the soldiery; above this was the hall, which generally extended over the whole area of the building, and is sometimes separated by columns; above this are other apartments for the residents. There are winding staircases in the angles of the Glossary jg27 buildings, and passages and small chambers in the thickness of tho walls The keep was intended for the last refuge, in case the outworks were scaled and the other buildmgs stormed There is generally a well in a mediaeval keep, ingen lousb^ concealed m the thickness of a wall, or in a pillar. The most celebrated of Norman times are the White Tower in London, the castles at Rochester Arundel, and Newcastle, Castle Hedingham, etc. The keep was often circular! Key-stone. The stone placed in the center of the top of an arch The char acter of the key-stone varies in different orders. In the Tuscan and Doric it is only a srniple stone projecting beyond the rest; in the Ionic it is adorned with nioldings m the manner of a console; in the Corinthian and Composite it is a rich-sculptured console. King-post. The middle post of a trussed piece of framing for supporting the tie-beam at the middle and the lower ends of the struts. Knee. A piece of timber naturally or artificially bent to receive another to Xelieve a weight or strain. Knob, Knot. The bunch of flowers carved on a corbel, or on a Boss. Kremlin. The Russian name for the citadel of a town or city. Label. Gothic: the drip or hood-molding of an arch, when it is returned to the square. Label Terminations. Carvings on which the labels terminate near the springing of the windows. In Norman times those were frequently grotesque heads of fish, birds, etc., and sometimes stiff fohage. In the Early English and Decorated periods they are often elegant knots of flowers, or heads of kings, queens, bishops, and other persons supposed to be the founders of churches. In the Perpendicular period they are often finished with a short square, mitred return or knee, and the foliages are generally leaves of square or octagonal form. Lacunar. A paneled or coffered ceiling or soffit. The panels or cassoons of a ceiling are by Vitruvius called lacunaria. Lady-chapel. A small chapel dedicated to the Virgin Mary, generally found in ancient cathedrals. Lancet. A high and narrow window pointed like a lancet, often called a lancet window. Landing. A platform in a flight of stairs between two stories; the terminating of a stair. Lantern. A turret raised above a roof or tower and very much pierced, the better to transmit light. In modern practice this term is generally applied to lacunars in ceiling any raised part in a roof or ceiling containing vertical windows, but covered in horizontally. The name was also often applied to the louver or femerell on a roof to carry off the smoke; sometimes, too, to the open constructions at the top of towers, as at Ely Cathedral, probably because lights were placed in them at night to serve as beacons. Lanterns of the Dead. Curious smaU slender towers, found chiefly in the centre and west of France, having apertures at the top, where a light was ex- hibited at night to mark the place of a cemetery.^ Some have supposed that the round towers in Ireland may have served for this purpose. Lath. A slip of wood used in slating, tiling, and plastering. Lattice. Any work of wood or metal made by crossing laths, rods, or bars, and forming a net-work. A reticulated window, made of laths or slips of iron, 1828 Glossary Part 3 separated by glass windows, and only used where air rather than light is to be admitted, as in cellars and dairies. Lavabo. The lavatory for washing hands, generally erected in cloisters of monasteries. A very curious one at Fontenay, surrounding a pillar, is given by VioUet-le-Duc. In general, it is a sort of trough, and in some places has an almry for towels, etc. Lavatory. A place for washing the person. Lean-to. A small building whose rafters pitch or lean against another build- ing, or against a wall. Lectern. The reading-desk in the choir of churches. Ledge, or Ledgement. A projection from a plane, as slips on the side of window and door frames to keep them steady in their places. Ledgers. The horizontal pieces fastened to the standard poles or timbers of scafifolding raised around buildings during their erection. Those which rest on the ledgers are called putlogs, and on these the boards are laid. Lewis. An iron clamp dovetailed into a large stone to lift it by. Lich-gate. A covered gate at the entrance of a cemetery, under the shelter of which the mourners rested with the corpse, while the procession of the clergy came to meet them. There are several examples ijTi England. Light. A division or space in a sash for a single pane of glass; also a pane of glass. Linen ScroU. An ornament formerly used for filling panels, and so called from its resemblance to the convolutions of a folded napkin. Lining. Covering for the interior, as casing is covering for the exterior surface of a building; also, such as linings of a door for windows, shutters, and similar work. Lintel. The horizontal piece which covers the opening of a _ door or window. Lip Mold. A molding of the Perpendicular period like a hanging lip. i List, or ListeL A little square molding, to crown a larger; also termed a fillet. Lithograph. A print from a drawing on stone. Lobby. An open space surrounding a range of chambers, or seats in a theater: a small hall or waiting room. Lodge. A small house in a park. Loft. The highest room in a house, particularly if in the roof; also, a gallery raised up in a church to contain the rood, the organ, or singers. Loggia. An outside gallery or portico above the ground, and contained within the building. Loop-hole. An opening in the wall of a building, very narrow on the outside, and splayed within, from which arrows or darts might be discharged on an enemy. They are often in the form of a cross, and generally have round holes at the ends. Lombard Architecture. A name given to the round-arched architecture of Italy, introduced by the conquering Goths and Ostrogoths, and which super- seded the Romanesque. It reigned between the eighth and twelfth centuries, during the time that the Saxon and Norman styles were in vogue in England, and corresponded with them in its development into the Continental Gothic. W^- Glossary 1829 LOZENGE MOLDING LOUVER WINDOW Lotus. A plant of great celebrity amongst the ancients, the leaves and blossoms of which generally form the capitals of Egyptian columns. Louver. A kind of vertical window, frequently in the peaks of gables, and in the top of towers, and provided with horizontal slats which permit ventilation and exclude rain. Lozenge Molding. A kind of molding used in Norman architecture, of many dififcrent forms, all of which are char- acterized by lozenge-shaped ornaments. Lunette. The French term for the circular opening in the groining of the lower stories of towers, through which the bells are drawn up. Machicolation.. A parapet or gallery projecting from the upper part of the wall of a house or fortifica- tion, supported by brackets or corbels, and perforated in the lower part so that the defenders of the building might throw down darts, stones, and sometimes hot sand, molten lead, etc., upon their assailants below. Man-hole. A hole through which a man may creep into a drain, cesspool, steam-boiler, etc. Manor-house. The residence of the suzerain or lord of the manor; in France the central tower or keep of a castle is often called the manoir. Mansard Roof. Curb roof, invented by Francois Mansard, a distinguished French architect, who died in 1666. Mansion. A residence of considerable size and pretension. Mantel. The work over a fireplace in front of a. chimney; especially, a shelf, usually ornamented, above the fireplace. Marquetry. Inlaid work of fine hard pieces of wood of different colors, also of shells, ivory, and the hke. Mausoleum. A magnificent tomb or sumptuous sepul- chral monument. Medallion. Any circular tablet on which are embossed figures or busts. Mediaeval Architecture. The architecture of Eng- land, France, Germany, etc., during the Middle Ages, including the Norman and Early Gothic styles. It comprises also the Romanesque, Byzantme and bara- cenic, Lombard, and other styles. Members. The different parts of a building, the different parts of an entab- lature, the different moldings of a cornice, etc. Merlon. That part of a parapet which lies between two embrasures. Metope. The square recess between the triglypns in a Doric frieze. It is sometimes occupied by sculptures. Mezzanine. A low story between two lofty ones. It is called by the French entresol, or inter-story. Mezzo-riiievo. Or mean relief, in comparison with ^Ito-riUevo, or high relief. MACHICOLATION •^^ METOPE 1830 Glossary Parts MINARET MODILLION Minaret. Turkish: a circular turret rising by different stages or divisions, each of which has a balcony. Minster. Probably a corruption of monasterium — the large church at- tached to any ecclesiastical fraternity. If the latter be presided over by a bishop, it is generally called a Cathedral; if by an abbot, an Abbey; if by 3 prior, a Priory. Minute. The sixtieth part of the lower diameter of a column ; it is the measure used by architects to determine the proportions of an order. Miserere. A seat in a stall of a large church made to turn up and afford support to a person in a position between sitting and standing. The under side is generally carved with some ornament, and very often with grotesque figures and caricatures of diJereut persons. Miter. A molding returned upon itself at right angles is said to miter. In joinery, the ends of any two pieces of wood of correspond- ing form, cut off at 45°, necessarily abut upon one another so as to form a right angle, and are said to miter. Modillion. So called because of its arrangement in regulated distances; the enriched block or horizontal bracket generally found under the cornice of the Corinthian entablature. Less ornamented, it is sometimes used in the Ionic. Module. This is a term which has been generally used by architects in determining the relative propor- tions of the various parts of a columnar ordinance. The semi-diameter of the column at its base is the module, which being divided into thirty parts called minutes, any part of the composition is said to be of so many modules and minutes, or minutes alone, in height, breadth, or projection. The whole diameter is now generally preferred as a module, it being a better rule of proportion than its half. Monastery. A set of buildings adapted for the reception of any of the vari^ ous orders of monks, the different parts of which are described in the separate article. Abbey. Monotriglyph. The intercolumniations of the Doric order are determined by the number of triglyphs which intervene, instead of the number of diameters of the column, as in other cases; and this term designates the ordinary intercolum- niation of one trig ly ph. Monument. A name given to a tomb, particularly to those fine structures recessed in the walls of mediaeval churches. Mosaic. Pictorial representations, or ornaments, formed of small pieces of stone, marble, or enamel of various colors. In Roman houses the floors are often entirely of mosaic, the pieces being cubical. The best examples of mosaic work arc found in St. Mark's, at Venice. Mosque. A Mahometan temple, or place of worship. Molding. When any work is wrought into long regular channels or projec- tions, forming curves or rounds, hollows, etc., it is said to be molded, and each separate member is called a molding. In mediaeval architecture the principal moldings are those of the arches, doors, windows, piers, etc. In the Early English style, the moldings, for some time, formed groups set back in squares, and frequently very deeply undercut. The scroll molding is also common. Glossary IH'Sl Small fillets now become very frequent in the keel molding, from its resemblance in section to the bottom of a ship; sometimes, also, it has a pecuHar hollow on each side, like two wings. Later in the Decorated style the moldings are more varied in design, though hollows and rounds still prevail. The undercutting is not so deep, fillets abound, ogees are more frequent, and the wave mold, double ogee, or double ressaunt, is often seen. In many places the strings and labels are a round, the lower half of which is cut off by a plain chamfer. The moldings in the later styles in some degree resemble those of the Decorated, flattened and extended; they run more into one another, having moldings fewer fillets, and being, as it were, less grouped. ^' astragal; b, ogee; One of the principal features of the change is the ^' cymatium; d, cavet- substitution of one, or perhaps two (seldom more), ^o; e, scotia, or case- very large hollows in the set of moldings. These hoi- ment; /, apophyges; lows are neither circular nor elliptical, but obovate, S, ovolo, or quarter like an egg cut across, so that one half is larger round; h, • torus; i, than the other. The brace mold also has a small reeding; j, band, bead, where the two ogees meet. Another sort of molding, which has been called a lip mold, is common in parapets, bases, and weatherings. Moldings, Ornamented. The Saxon and early Norman moldings do not seem to have been much enriched, but the complete and later styles of Norman are remarkable for a profusion of ornamentation, the most usual of which is what is called the zigzag. This seems to be to Norman architecture what the meander or fret was to the Grecian; but it was probably derived from the Saxons, as it is very frequently found in their pottery. Bezants, quatrefoils, lozenges, crescents, billets, heads of nails, are very common ornaments. Besides these, battlements, cables; large ropes round which smaller ropes are turned, or, as our sailors say, "wormed"; scallops, pellets, chains, a sort of conical barrels, quaint stiff foliages, beaks of birds, heads of fishes, ornaments of almost every con- ceivable kind, are sculptured in Norman moldings; and they are used in such profusion as has been attempted in no other style. The decorations on Early English moldings are chiefly the dog-tooth, which is one of the great charac- teristics of this Style, though it is to be found in the Transition Norman. It is generally placed in a deep hollow between two projecting moldings, the dark shadow in the hollow contrasting in a very beautiful way with the light in these moldings. In this period and in the next the tympanum over doorways, par- ticularly if they are double doors, is highly ornamented. Those of the Decorated period resemble the former, except that the foliage is more natural and the dog- tooth gives way to the ball-flower. Some of the hollows, also, arc ornamented . with rosettes set at intervals, which are sometimes connected by a running tendril, as the ball-flowers are frequently. Some very pleasing leaf -like ornaments in the labels of windows are often found in Continental architecture. In the Perpen- dicular period the moldings are ornamented very frequenUy by square four- leaved flowers set at intervals, but the two characteristic ornaments of the time are running patterns of vine leaves, tendrils, and grapes in the hollows which by old writers are called "vignettes in casements," and upright stitt leaves generally called the Tudor leaf. On the Continent moldings partook much of the same character. Mullion, Munion.. The perpendicular pieces of stone, sometimes like col- umns, sometimes like s.^^nder piers, which divide the bays or lights of windows 1832 Glossary Part 3 or screen-work from each other. In all styles, in less important work, the mul- lions are often simply plain chamfered, and more commonly have a very flat hol- low on each side. In larger buildings there is often a bead or boutell on the edge, and often a single very small column with a capital. As tracery grew richer, the windows were divided by a larger order of mullion, between which came a lesser or subordinate set of mullions, which ran into each other. The term is also applied to a wood or iron division between two windows. Multifoil. A leaf ornament consisting of more than five divisions, applied to foils in windows. Mutule. The rectangular impending block under the corona of the Doric cornice, from which guttle or drops depend. Mutule is equivalent to modillion but the latter terra is applied more particularly to enriched blocks or brackets, such as those of Ionic and Corinthian entablatures. Narthex. The long arcaded porch forming the entrance into the Christian basihca. Sometimes there was an inner narthex, or lobby, before entering the church. When this was the case, the former was called exo-narthex, and the latter eso-narthex. In the Byzantine churches this inner narthex forms part of the solid structure of the church, being marked off by a wall or row of columns, whereas in the Latin churches it was usually formed only by a wooden or other temporary screen. Natural Beds. In stratified rocks, the surface of a stone as it lies in the quarry. If not laid in walls in their natural bed the laminse separate. Nave. The central part between the arches of a church, which formerly wa3 separated from a chancel or choir by a screen. It is so called trom its fancied resemblance to a ship. In the nave were generally placed the pulpit and font. In continental Europe it often also contains a high altar, but this is of rare occurrence in England. Necking. The annulet or round, or series of horizontal moldings, which separate the capital of a column from the plain part or shaft. Newel. In mediaeval architecture, the circular ends of a winding staircase which stand over each other, and form a sort of cylindrical column. Newel Post. The post, plain or ornamented, placed at the first, or lowest step, to receive or start the hand-rail upon. Niche. * A recess sunk in a wall, generally for the reception of a statue. Niches sometimes terminate by a simple label, but more commonly by a canopy, and with a bracket or corbel for the figure, in which case they are often called tabernacles. Norman Style. Was that species of Romanesque which was practised by the Normans, and which was introduced and fully developed in England after they had established themselves in it. The chief features of this style are plainness and massiveness. The arches, windows, and doorways were semicircular, the pillars were very massive, and often built up of small stones laid like brickwork. Nosings. The rounded and projecting edges of the treads of a stair, or the edge of a landing. Obelisk. Lofty pillars of stone, of a rectangular form, diminishing toward the top, and generally, ornamented with iriscriptions and hieroglyphics among the ancient Egyptians. Observatory. A building erected on an elevated spot of ground for making astronomical observations. Octostyle. A portico of eight columns in front. Glossary I833 Offsets. When the face of a wall is not one continued surface but sets in b v honzontal jogs, as the wall grows higher and thinner, the jogs are caMsets": ^f ^•* I ^^^T f PP^^^"^ ^^ ^ "'^^^^^'^^' P^^tly a hollow and partly a round and denved no doubt from its resemblance to an O placed over a G. U is rare y found m Norman work, and is not very common in Early English. It is o^fre^ wa?. J^'r ^^^'°'^ff^/«'-k^, where it becomes sometimes double, and is called a wave moldmg; and later still, two waves are connected with a small bead, which IS then called a brace molding. In ancient MSS. it is called a Ressaunt. Ofchestra. In ancient theaters, where the chorus used to dance; in modern ■ theaters, where the musicians sit. Order. A column with its entablature and stylobate is so called. The term is the result of the dogmatic laws deduced from the writings of Vitruvius and has been exclusively applied to those arrangements which they were thought to warrant. Oriel Window. Gothic: a projecting angular window, commonly of a tri- agonal or pentagonal form, and divided by mullions and transoms into different bays and compartments. Orthography. A geometrical elevation of a building or other object in which it is represented as it actually exists or may exist, and not perspectively, or as it would appear. Orthostyle. A columnar arrangement in which the columns are placed in a straight line. Ovolo. Same as Echinus. Pagoda. A name given to temples in India and China. Palace. The dwelHng of a king, prince, or bishop. Pale. A fence picket, sharpened at the upper end. Pane. Probably a diminutive of panneau, a term applied to the different pieces of glass in a window; same as Light. Panel. Properly a piece of wood framed within four other pieces of wood, as in the styles and rails of a door, filling up the aperture, but often applied both to the whole square frame and the sinking itself; also to the ranges of sunken com- partments in wainscoting, cornices, corbel tables, groined vaults, ceilings, etc. Pantograph, or Pentagraph. An instrument for copying on the same, or an enlarged or reduced scale. Pantry. An apartment or closet in which bread and other provisions are kept. Papier-mache, A hard substance made of a pulp from rags or paper mixed with size or glue, and molded into any desired shape. Much used for architec- tural ornaments. Parapet. A dwarf wall along the edge of a roof, or round a terrace walk, etc., to prevent persons from falling over, and as a protection to the defenders in case of a siege. Parapets are either plain, embattled, perforated, or paneled. ^ The last two are found in all styles except the Norman. Plain parapets are simply portions of the wall generally overhanging a little, with coping at the top and corbel table below. Embattled parapets are sometimes paneled, but oftener pierced for the discharge of arrows, etc. Perforated parapets are pierced in various devices — as circles, trefoils, quatrefoils, and other designs— so that the light is seen through. Paneled parapets are -those ornamented by a series of panels, eitner oblong or square, and more or less enriched, but are not perforated. These are common in the Decorated and Perpendicular periods. 1834 Glossary Part 3 Pargeting. A species of plastering decorated by impressing pattern^, on it when wet. These seem generally to have been made by sticking a number of pins in a board in certain lines or curves, and then pressing on the wet plaster in various directions, so as to form geometrical figure j. Sometimes these devices are in rehef, and in the time of Elizabeth represent figures, birds, foliages, etc. Rough plastering, commonly adopted for the interior surface of chimneys. Parlor. A room in a house which the family usually occupy for society and conversation, and for receiving visitors. The apartment in a monastery or nunnery where the inmates are permitted to meet and converse with each other, or with visitors and friends from without. Parochial. Belonging or relating to a parish. Parquetry, or Marquetry. A kind of inlaid floor composed of small pieces of wood either square or triangular, which are capable of forming, by their dis- position, various combinations of figures; this description of joinery is very suitable for the floors of libraries, halls, and public apartments. Party Walls. Partitions of brick or stone between buildings on two adjoining properties. Patera. A circular ornament resembling a dish, often worked in relief on friezes, etc. Pavement. Tessellated, a pavement of mosaic work, used by the ancients, made of square pieces of stone, etc., called Tessera. Pavilion. A turret or small insulated building, and comprised beneath a single roof; also, the projecting part in front of a building which marks the centre, and which sometimes flanks a corner, when it is termed an angular pavilion. patera Pedestal. The square support of a column, statue, etc.; and the base or lower part of an order of columns: it consists of a plinth for a base, the die, and a talon crowned for a cornice. When the height and width are equal, it is termed a square pedestal; one which supports two columns, a double pedestal; and if it supports a row of columns without any break, it is a continued pedestal. Pediment. A low triangular crowning, ornamented, in front of a building, and over doors and windows. Pediments are sometimes made in the form of a segment; the space enclosed within the triangle is called the tympanum. Also, the gable ends of classic buildings, where the horizontal cornice is carried across the front, forming a triangle with the end of the roof. Pendent. A name given to an elongated boss, either molded or foliated, such as hang down from the intersection of groins, especially in fan tracery, or at the end of hammer beams. Sometimes long corbels, under the wall pieces, have been so called. The name has also been given to the large masses depend- ing from enriched ceihngs, in the later works of the Pointed style. Pendent Posts. A name given to those timbers which hang down the side of a wall from the plate in hammer beam trusses, and which receive the hammer braces. Pendentive. A name given to an arch which cuts off, as it were, the corners of a square building internally, so that the superstructure may become an octagon or a dome. In mediaival architecture these arches, when under a spire in the interior of a tower, are called Squinches. Glossary jg^,^ Pendentive Bracketing, or Cove Bracketing. Springing from the rec- tangular wa is of an apartment upward to the ceiling, and forming the horizon- tal part of the ceihng mto a circle or ellipse. Pentastyle. Having five columns in front. Pent-roof. A roof with a slope on one side only. Perch. A measure used in measuring stone work, being 24% cu ft and 16^^ cu ft, according to locality and custom. Periptery. An ediiice or temple surrounded by a peristyle. Peristyle. A range of columns encircling an edifice, such as that which sur- .•ounds the cylindrical drum under the cupola of St. Paul's. The columns of a Greek peripteral temple form a peristyle also, the former being a circular, and the latter a quadrilateral peristyle. Perpendicular Style. The third and last of the Pointed or Gothic styles; also called the Florid style. Perspective Drawing. The art of making such a representation of an object upon a plane surface as shall present precisely the same appearance that the object itself would to the eye situated at a particular point. Pews. A word of uncertain origin, signifying fixed seats in churches, com- posed of wood framing, mostly with ornamented ends. They seem to have come into general use early in the reign of Henry VI, and to have been rented and "well paid for" before the Reformation. Some bench ends are certainly of a decorated character, and some have been considered to be of the Early English period. They are sometimes of plain oak board, two and a half to three inches thick, chamfered, and with a necking and finial, generally called a poppy head; others are plainly paneled with bold cappings; in others the panels are orna- mented with tracery or with the hnen pattern, and sometimes with running foliages. The divisions are filled in with thin chamfered boarding, sometimes reaching to the floor, and sometimes only from the capping to the seat. Picket. A narrow board, often pointed, used in making fences; a pale or paling. Pier-glass. A mirror hanging between windows. Piers. The solid parts of a wall between windows, and between voids gener- ally. The term is also applied to masses of brick-work or masonry "which are insulated to form supports to gates or to carry arches, posts, girders, etc. Pilasters. Are flat square columns, attached to a wall, behind a column, or along the side of a building, and projecting from the wall about a fourth or a sixth part of their breadth. The Greeks had a slightly different design for the capitals of pilasters, and made them the same width at top as at bottom, but the Romans gave them the same capitals as the columns, and made them of di- minished width at the top, similar to the columns. Pile. A large stake or trunk of a tree, driven into soft ground, as at the bottom of a river, or in made land, for the support of a building. (See p. 188.) Pillar, or Pyller. A word generally used to express the round or polygonal piers, or those surrounded with clustered columns, which carry the main arches of a building. Saxon and Early Norman pillars are generally stout cylindrical shafts built up of small stones. Sometimes, however, they are quite square, sometimes with other squares breaking out of them (this is more common m French and German work), sometimes with angular shafts, and sometimes they are plain octagons. In Romanesque Norman work the pillar is sometimes square with two or more semicircular or half-columns attached. In the Early 183G Glossary Part 3 English period the pillars become loftier and lighter, and in most important buildings are a series of clustered columns, frequentlj'' of marble, placed side by side, soinetimes set at intervals round a circular centre, and sometimes almost touching each other. These shafts are often wholly detached from the central pillar, though grouped round it, in which case they are almost always of Purbeck or Bethersden marbles. In Decorated work the shafts on plan are very often placed round a square set anglewise, or a lozenge, the long way down the nave; the centre or core itself is often worked into hollows or otfier moldings, to show between the shafts, and to form part of the composition. In this and the latter part of the previous style there is generally a fillet on the outer part of the shaft, forming what has been called a keel molding. They are also often, as it were, tied together by bands formed of rings of stone and sometimes of metal. The small pillars at the jambs of doors and windows, and in arcades, and also those slender columns attached to pillars, or standing detached, are- generally called shafts. Pin. A cylindrical piece of wood, iron, or steel, used to hold two or more pieces together, by passing through a hole in each of them, as in a mortise and tenon joint, or a pin joint of a truss. Pinnacle. An ornament originally forming the cap or crown of a buttress or small turret, but afterwards used on parapets at the corners of towers and in many other situations. It was a weight to counter- act the thrust of the groining of roofs, particularly where there were flying buttresses; it stopped the tendency to sHp of the stone copings of the gables, and counterpoised the thrust of spires; it formed the piers to steady the elegant perforated parapets of later periods; and in France, especially, served to counterbalance the weight of overhanging corbel tables, huge gargoyles, etc. In the Early Engish period the smaller buttresses frequently finished with gablets, and the more important with pinnacles supported with clustered shafts. At this period the pinnacles were often supported on these shafts alone, and were open below; and in .larger work in this and the subsequent periods they frequently form niches and contain statues. In France, pinnacles, hke spires, seem to have been in use earlier than in England. There are small pinnacles at the angles of the tower in the Abbey of Saintes. At Roullet there are pinnacles in a similar position, each composed of piajj^^CLE four small shafts, with caps and bases surmounted with small pyramidal spires. In all these examples the towers have semicircular headed windows. Pitch of a Roof. The proportion obtained by dividing the height by the span; thus, we speak of its being one-half, one- third, one-fourth. When the length of the rafters is equal to the breadth of the building it is denominated Gothic. Pitching-piece. A horizontal d^rtber, with one of its ends wedged into the wall at the top of a flight of stairs, to support the upper end of the rough strings. Place. An open piece of ground surrounded by buildings, generally decorated with a statue, column, or other ornament. Plan. A horizontal geometrical section of the walls of a building; or indi- cations, on a horizontal plane, of the relative positions of the walls and partitions, with the various openings, such as windows and doors, recesses and projections, chimneys and chimney-breasts, columns, pilasters, etc. This term is often incorrectly used in the sense of Desiirn. Glossary 1837 Planceer. Is sometimes used in the same sense as soflSt, but is more correctly cipplicd to the soffit of the corona in a cornice. Plastering. A mixture of lime, hair, and sand, to cover lath-work between timbers or rough walling, used from the earliest times, and very common in Roman work. In the Middle Ages, too, it was used not only in private, but in public constructions. On the inside face of old rubble walls it was not only used for purposes of cleanHness, rough work holding dirt and dust, but as a ground for distemper painting (tempera, or, as it is often improperly called, fresco), a species of ornament often used in the Middle Ages. At St. Albans Abbey, Eng- land, the Norman work, is plastered, and covered with lines imitating the joints of stone. The same thing is found in English Perpendicular work. On the out- side of rubble walls, and often of wood framing, it was used as roughcast; when ornamented in patterns outside, it is called pargeting. Plate. The piece of timber in a building which supports the end of the rafters. Plinth. The square block at the base of a column or pedestal. In a wall, the term plinth is applied to the projecting base or water table, generally at the level of the first floor. Plumb. Perpendicular; that is, standing according to a plumb line, as, the post of a house or wall is plumb. Plumbing. ' The lead and iron pipes and other apparatus employed in con- veying water, and for toilet purposes in a building; originally the art of casting and working in lead. Ply. Used to denote the number of thicknesses of roofing paper, as three ply. four ply, etc. Podium. A continued pedestal; a projection from a wall, forming a kind of gallery. Polytriglyph. An intercolumniation in the Doric order of more than two triglyphs. Poppy Heads. Probably from the French poupee: the finials or other orna- ments which terminate the tops of bench ends, either to pews or stalls. They are sometimes small human heads, sometimes richly carved images, knots' of foliage, or finials, and sometimes fleurs- de-lis simply cut out of the thickness of the bench end and cham- fered. Porch. A covered erection forming a shelter to the entrance door of a large building. The earliest known are the long arcaded porches in front of the early Christian basilicas, called Narthex. In later times they assume two forms-one, the projectmg erection covering the entrance at the west front of cathedrals, and divided into three or more doorways, etc.; and the other, a kind of covered chambers open at the ends, and having small windows at the sides as a protection from rain. Portal. A name given to the deeply recessed and richly decorated entrance doors to the cathedrals in Continental Europe. Portcullis. A strong-framed grating of oak, the lower points shod with Kon, i-ortcuiiis. t\ birung 6 J j^^ij ijj grooves and sometimes entirely made of nietal, hung »> ^^ to suae p with counterbalances, and intended to protect the gateways of castles, etc. Portico An open space before the door or other entrance to any building, fronted wiih ^olumL. 'a portico is distinguished as prostyle or .» anHs accord- 1838 Glossary Part 3 ing as it projects from or recedes within the building, and is further designated by the number of columns its front may consist of. Post. Square timbers set on end. The term is especially applied to those which support the corners of a building, and are framed into brcssummers or crossbeams under the walls. Posticum. A portico behind a temple. Presbytery. A word applied to various parts of large churches in a very ambiguous way. Some consider it to be the choir itself; others,' what is now named the sacrarium. Traditionally, however, it seems to be applied to the vacant space between the back of the high altar and the entrance to the lady- chapel, as at Lincoln and Chichester; in other words, the back- or retro-choir. Priming. The laying on of the first shade of color, in oil paint, and generally consisting mostly of oil, to protect and fill the wood. Priory. A monastic establishment, generally in connection with an abbey, and presided over by a prior, who was a subordinate to the abbot, and held much the same relation to that dignitary as a dean does to a bishop. Profile. The outline; the contour of a part, or the parts composing an order, as of a base, cornice, etc.; also, the perpendicular section. It is in the just proportion of their profiles that the chief beauties of the different orders of architecture depend. The ancients were most careful of the profiles of their moldings. Proscenium. The front part of the stage of ancient theaters, on which the actors performed. Prostyle. A portico in which the columns project from the building to which it is attached. Protractor. A mathematical instrument for laying down and measuring angles on paper, used in drawing or plotting. Pseudo-dipteral. False double-winged. When the inner row of columns of a dipteral arrangement is omitted and the space from the wall of the building to the columns is preserved, it is pseudo-dipteral. Puddle. To settle loose dirt by turning on water, so as to render it firm and solid. Pugging. A coarse kind of mortar laid on the boarding, between floor joists, to prevent the passage of sound; also called deafening. Pulpit. A raised platform with enclosed front, whence sermons, homilies, etc., were delivered. Pulpits were probably derived in their modern form from the ambones in the early Christian church. There are many old pulpits of stone, though the majority are of wood. Those in the churches are generally hexagonal or octagonal; and some stand on stone bases, and others on slender wooden stems, like columns. The designs vary according to the periods in which they were erected, having paneling, tracery, cuspings, crockets, and other ornaments then in use. Some are extremely rich, and ornamented with color and gilding. A few also have fine canopies or sounding boards. Their usual place is in the nave, mostly on the north side, against the second pier from the chancel arch. Pulpits for addressing the people in the open air were common in the Mediaeval period, and stood near a road or cross. Thus, there was one at Spitalfields, and one at St. Paul's, London. External pulpits still remain at Magdalen College, Oxford, and at Shrewsbury, England. Purlins. Those pieces of timbers which support the rafters to prevent them from sinking. Glossary 1839 Putlog. Horizontal pieces for supporting the floor of a scaffold, one end being inserted into putlog holes, left for that purpose in the masonry. Putty in Plastering. Lump lime slacked with water to the consistency of cream, and then left to harden by evaporation till it becomes like soft putty. It is then mixed with plaster of Paris, or sand, for the finishing eoat. Puzzolana. A grayish earth used for building under water. Pyramid. A solid, having one of its sides, called a base, a plane figure, and the other sides triangles, these points joining in one point at the top, called the vertex. Pyramids are called triangular, square, etc., according to the form of their bases. Pyx. In Roman Catholic churches, the box in which the host, or consecrated wafer, is kept. Quadrangle. A square or quadrangular court surrounded by buildings, as was often done formerly in monasteries, colleges, etc. Quarry. A pane of glass cut in a diamond or lozenge form. Quarry-face. Ashlar as it comes from the quarry, squared off for the joints only, with split face. In distinction from Rock-face, in that the latter may be weather-worn, while Quarry-face should be fresh split. The terms are often used indiscriminately. Quatref oil. Any small panel or perforation in the form ofa four-leaved flower. Sometimes used alone, sometimes in circles and over the aisle windows, but more frequently in square panels. They are generally cusped, and the cusps are often feathered. Queen Truss. A truss framed with two vertical tie-posts, in distinction from the king-post, which has but one. The upright ties are called Queen-posts. Quirk Moldings. The convex part of Grecian moldings when they recede at the top, forming a reentrant angle, with the surface which covers the moldings. Quoins. Large squared stones at the angles of buildings, buttresses, etc., generally used to stop the rubble or rough stone work, and that the angles may be true and stronger. Saxon quoin stones are said to have been composed of one long and one short stone alternately. Early quoins are generally roughly axed; in later times they had a draught tooled by the chisel round the outside edges, and later still were worked fine from the saw. Rafters. The joist to which the roof boarding is nailed. Principal rafters are the upper timbers in a truss, having the same inclination as the common rafters. Rail. A piece of timber or metal extending from one post to another, as in fences, balustrades, staircases, etc. In framing and paneling, the horizontal pieces are called rails, and the perpendicular, stiles. Raking. Moldings whose arrises are inclined to the horizon. Ramp. \ concavity on the upper side of hand railings formed over risers, made by a sudden rise of the steps above. Any concave bend or slope in the cap or upper member of any piece of ascending or descending workmanship. Rampant. A term applied to an arch whose abutments spring from an incUned plane. Random Work. A term used by stone-masons for stones fitted together at random without any attempt at laying them in courses. Random Coursed Work is a like term applied to work coursed in horizontal beds, but the stones are of any height, and fitted to one another. 1840 Glossary Part 3 Range Work. Ashlar laid in horizontal courses; same as coursed ashlar. Rebate. A groove on the edges of a board. Recess. A depth of some inches in the thickness of a wall, as a niche, etc. Refectory. The hall of a monastery, convent, etc., where the religious took their chief meals together. It much resembled the great halls of mansions, castles, etc., except that there frequently was a sort of ambo, approached by steps, from which to read the Legenda Sanctorum, etc., during meals. Reglet. A flat, narrow molding, used to separate from each other the parts or members of compartments and panels, to form frets, knots, etc. Renaissance (a new birth). A name given to the revival of Roman architec- ture which sprang into existence in Italy as early as the beginning of the fifteenth century, and reached its zenith in that country at the close of the century. There are several divisions of this style as developed in different localities; viz., The Florentine Renaissance, of which the Pitti Palace, by Brunelleschi, is one of the best examples. The Venetian Renaissance, characterized by its elegance and richness. The Roman Renaissance, which originated in Rome, under the architects knov/n as Bronte, Vignola, and Michael Angelo. Of this style the Farnese Palace, St. Peter's, and the modern Capitol at Rome are the best examples. The French Renaissance, introduced into France in the latter part of the fif- teenth century, by Italian architects, where it flourished until the middle of the •seventeenth century. The Renaissance style was introduced into Germany about the middle of the sixteenth century, and into England about the sanie time by John of Padua, architect to Henry VIII. This style in England is gen- erally known mider the name of Elizabethan. Rendering. In drawing, finishing a perspective drawing m ink or color, to bring out the spirit and effect of the design. The first coat of plaster on brick or stone work. Reredos, Dorsal, or Dossel. The screen or other ornamental work at the back of an altar. In some large EngHsh cathedrals, as Winchester, Durham, St. Albans, etc., this is a mass of splendid tabernacle work, reaching nearly to the groining. In smaller churches there are sometimes ranges of arcades or panelings behind the altars; but, in general, the walls at the back and sides of them were of plain masonry, and adorned with hangings or paraments. In the large churches of Continental Europe the high altar usually stands under a sort of canopy or ciborium, and the sacrarium is hung round at the back and sides with curtains on movable rods. Reticulated Work. That in which the courses are arranged in a form like the meshes of a net. The stones or bricks are square and placed lozenge-wise. Return. The continuation of a molding, projection, etc., in an opposite direction. Return Head. One that appears both on the face and edge of a work. Reveal. The two vertical sides of an aperture, between the front of a wall and the window or door frame. Rib. A molding or projecting piece upon the interior of a vault, or used to form tracery and the like. The earliest groining had no ribs. In early Norman times plain flat arches crossed each other, forming ogive ribs. These by degrees became narrower, had greater projection, and were chamfered. In later Nor- man work the ribs were often formed of a large roll placed upon the flat band, and then of two rolls side by side wi£h a smaller roll or a fillet between them. Glossary lg41 much like the lower member. Sometimes they are enriched with zigzags and other Norman decorations, and about this time bosses became of very general use. As styles progressed, the moldings were more undercut, richer, and more elaborate, and had the dog-tooth or ball-flower or other characteristic ornament in the hollows. In all instances the moldings are of similar contours to those of arches, etc., of .the respective periods. Later, wooden roofs are often formed into cants or polygonal barrel vaults, and in these the ribs are generally a cluster of rounds, and form square or stellar panels, with carved bosses or shields at the intersections. Ridge. The top of a roof which rises to an acute angle. Ridge-pole. The highest horizontal timber in a roo^, extending from top to top of the several pairs of rafters of the trusses, for supporting the heads of the jack rafters. Rilievo, or Relief. The projection of an architectural ornament. Rise. The distance through which anything rises, as the rise of a stair, or incHned plane. Riser. The vertical board under the tread in stairs. Rococo Style. A name given to that variety of the Renaissance which was in vogue during the seventeenth and the latter part of the sixteenth century. Romanesque Style. The term Romanesque embraces all those styles of ar- chitecture which prevailed between the destruction of the Roman Empire and the beginning of Gothic architecture. In it are included the Early Roman Christian architecture, Byzantine, Mahometan, and the later Romanesque architecture proper, which was developed in Italy, France, England, and Germany. This later Romanesque, which was quite different from the preceding, came into vogue during the tenth century, and reached its height during the twelfth century, and in the thirteenth century gave way to the Pointed or Gothic style. In England, Romanesque architeqture is known under the name of the Saxon, Norman, and Lombard styles, according to the different political periods. Rood. A name appHed to a crucifix, particularly to those which were placed in the rood-loft or chancel screens. These generally had not only the image of the crucified Saviour, but also those of St. John and the Virgin Mary standing one on each side. Sometimes other scants and angels are by them, and the top of the screen is set with candlesticks or other decoration. Rood-loft, Rood-screen, Rood-beam, Jube Gallery, etc. The arrange- ment to carry the crucifix or rood, and to screen off the chancel from the rest of the church during the breviary services, and as a place whence to read certain parts of those services. Sometimes the crucifix is carried simply on a strong trans- verse beam, with or without a low screen, with folding-doors below but forming no part of such support. In European churches the general construction of wooden screens is close paneling beneath, about 3 feet to 3 feet 6 inches high, on which stands screen work composed of slender turned balusters or regular wooden mullions, supporting tracery more or less rich, with cornices, crestnig, etc., and often painted in brilliant colors and gilded. These not only enclose the chancels, but also chapels, chantries, and sometimes even tombs. In English mansions, and some private houses, the great halls were screened off by a low passage at the end opposite to the dais, over which was a gallery for the use of minstrels or spectators. These screens were sometimes close and sometimes glazed. Rood-tower. ^ A name given by some writers to the central tower, or that over the intersection of the nave and chancel with the transepts. 1842 Glossary Part 3 Roof. The covering or upper part of any building. Roofing. The material put on a roof to make it water-tight. Rose Window. A name given to a circular window with radiating tracery; called also wheel window. Rostrum. An elevated platform from which a speaker addresses an audience. Rotunda. A building which is round both within and without. A circular room under a dome in large buildings is also called the rotunda. Roughcast. A sort of external plastering in which small sharp stones are mixed, and which, when wet, is forcibly thrown or cast from a trowel against the wall, to which it forms a' coating of pleasing appearance. Roughcast work has been used in Europe for several centuries, where it was much used in timber houses, and when well executed the work is sound and durable. The mortar for roughcast work should always have cement mixed with it. Rubble Work. Masonry of rough, undressed stones. When only the rough- est irregularities are knocked off, it is called scabbled rubble, and when the stones in each course are rudely dressed to nearly a uniform height, ranged rubble. Rudenture. The figure of a rope or staff, which is frequently used to fill up the flutings of columns, the convexity of which contrasts with the concavity of the flutings, and serves to strengthen the edges. Sometimes, instead of a convex shape, the flutings are filled with a flat surface; sometimes they are ornamentally carved, and sometimes on pilasters, etc. Rudentures are used in relief without flutings, as their use is to give greater solidity to the lower part of the shaft, and secure the edges. They are generally only used in columns which rise from the ground and are not to reach above one-third of the height of the shaft. Rustic or Rock Work. A mode of building in imitation of nature. This term is applied to those courses of stone work the face of which is jagged or picked so as to present a rough surface. That work is also called rustic in which the horizontal and vertical channels are cut in the joinings of stones, so that when placed together an angular channel is formed at each joint. Frosted rustic work has the margins of the stones reduced to a plane parallel to the plane of the wall, the intermediate parts having an irregular surface. Vermiculated rustic work has these intermediate parts so worked as to have the appearance of having been eaten by worms. Rustic chamfered work, in which the face of the stones is smooth, and parallel to the face of the wall, and the angles beveled to an angle of one hundred and thirty-five degrees with the face so that two stones coming together on the wall, the beveling will form an internal right argle. Sacristy. A small chamber attached to churches, where the chalices, vest- ments, books, etc., were kept by the officer called the sacristan. In the early Christian basilicas there were two semicircular recesses or apsides, one on each side of the altar. One of these served as a sacristy, and the other as the biblio- theca or library. Some have supposed the sacristy to have been the place where the vestments were kept, and the vestry that where the priests put them on; but we find from Durandus that the sacrarium was used for both these purposes. Sometimes the place where the altar stands enclosed by the rails has been called sacrarium. Saddle Bars. Narrow horizontal iron bars passing from mullion to mullion, and often through the whole window, from side to side, to steady the stone work, and to form stays, to which the lead work is secured. When the bays of the . windows are wide, the lead lights are further strengthened by upright bars passing through eyes forged on the saddle bars, and called stanchioni. When Glossary lg43 Scoddle bars pass right through the mullions in one piece, and are secured to the jambs, thfry have sometimes been called stay bars. Sagging. The bending of a body in the middle by its own weight, or the load upon it. Salient. A projection. Salon. A spacious and elegant apartment for the reception of company, or for state purposes, or for the rece|5tion of paintings, and usually extending through two stories of the house. It may be square, oblong, polygonal, or circular. Sanctuary. That part of a church where the altar is placed; also, the most sacred or retired part of a temple. A place for divine worship; a church. Sanctus Bell-cot, or Turret. A turret or enclosure to hold the small bell sounded at various parts of the service, particularly where the words "Sanctus," etc., are read. This differs but little from the common bell-cot, except that it is generally on the top of the arch dividing the nave from the chancel. Sometimes, however, the bell seems to have been placed in a cot outside the wall. In Eng- land sanctus bells have also been placed over the gables of porches. In Conti- nental Europe they run up into a sort of small slender spire, ca-Wed fleche in France, and guglio in Italy. Saracenia Architecture. That Eastern style employed by the Saracens, and which distributed itself over the world with the religion of Mahomet. It is a modification and combination of the various styles of the countries which they conquered. Sarcophagus. A tomb or coffin made of stone, and intended to contain the body. Sash. The framework which holds the glass in a window. * Scabble. To dress off the rougher projections of stones for rubble masonry with a stone axe or scabbling ham.mer. Scagliola. An imitation of colored marbles in pla.s.ter work, made by a com- bination of gypsum, glue, isinglass, and coloring matter, and finished with a high polish, invented between 1600 and 1649. Scantling. The dimensions of a piece of timber in breadth and thickness; also, studding for a partition, when under five inches square. Scarfing. The joining and bolting of two pieces of timber together trans- versely, so that the two appear as one. Sconce. A fixed hanging or projecting candlestick. Scotia. A concave molding, most commonly used in bases, which projects a deep shadow on itself, and is thereby a most effective molding under the eye, as in a base. It is like a reversed ovolo, or, rather, what the mold of an ovolo would present. Scratch Coat. The first coat of plaster, which is scratched to afford a bond for the second coat. Screeds. Long narrow strips of plaster put on horizontally along a wall, and carefully faced out of wind, to serve as guides for plastering the wide mtervals between them. . . Screen. Any construction subdividing one part of a h"Mmgf™m another as a choir, chantry, chapel, etc. The eariiest screens are '^e low ^arbk P^dia shutting off the chorus cantantium in the Rr^K^l' . ,'nd nresbvt«s The cancelli enclosing the bema, altar, and seats of the ^f °P^ f "^ p^'.y^^^^^^^^ chief screens in a church are those which enclose the choir or the place where 1844 Glossary Part 3 the breviary services are recited. In Continenta' Europe this is done not only by doors and screen work, but also, when these are of open work, by cur^ins, the laity having no part in these services. In England screens were of two kinds: one, of open wood-work, generally called rood-screens or jubes, and which the French call grilles, clotures du chceiir; the other, massive enclosures of stone work enriched with niches, tabernacles, canopies, pinnacles, statues, crestings, etc., as at Canterbury, York, Gloucester, and many other places. Scribing. Fitting wood-work to an irregular surface. Section. A drawing showing the internal heights of the various parts of a building. It supposes the building to be cut through entirely, so as to exhibit the walls, the heights of the internal doors and other apertures, the heights of the stories, thicknesses of the floors, etc.. It is one of the species of drawings necessary to the exhibition of a Design. Sedilia. Seats used by the celebrants during the pauses in the mass. They are generally three in number — for the priest, deacon, and sub-deacon — and are in England almost always a species of niches cut into the south walls of churches, separated by shafts or by a species of mullions, and crowned with canopies, pinnacles, and other enrichments more or less elaborate. The piscina and ambry sometimes are attached to them. In Continental Europe the scdiha are often movable seats; a single stone seat has rarely been found. Set-off. The horizontal line shown where a wall is reduced in thickness, and, consequently, the part of the thicker portion appears projecting before the thinner. In plinths this is generally simply chamfered. In other parts of work the set-off is generally concealed by a projecting string. Where, as in parapets, the upper part projects before the lower, the break is generally hid by a corbei table. The portions of buttress caps which recede one behind another are also called set-offs. Shaft. In Classical architecture that part of a column between the necking and the apophyge at the top of the base. In later times the term is applied to slender columns either standing alone or in connection with pillars, buttresses, jambs, vaulting, etc. Shed Roof, or Lean-to. A roof with only one set of rafters, falling from a higher to a lower wall, like an aisle roof. . Shore. A piece of timber placed in an oblique direction to support a building or wall temporarily while it is being repaired or altered. Shrine. A sort of ark or chest to hold relics. It is sometimes merely a small box, generally with a raised top Hke a roof; sometimes an actual model of churches; 'sometimes a large construction, like that of Edward the Confessor at Westminster, of St. Genevieve at Paris, etc. Many are covered with jewels ii the richest way; that of San Carlo Borromeo, at Milan, is of beaten silver. Sills. Are the timbers on the ground which support the posts and superstruc- ture of a timber building. The term is most frequently applied to those pieces of timber or stone at the bottom of doors or windows. Skewback. The inclined stone from which an arch springs. Skirtings. The narrow boards which form a plinth around the margin of a floor, now generally called the base. Sleeper. A piece of timber laid on the ground to receive floor joists. Soffit. The lower horizontal face of anything as, for example, of an entab- lature resting on and lying open between the columns, or the under face of an arch where its thickness is seen. Glossary 1845 Sound Board. The covering of a pulpit to deflect the sound into a church, Spall. Bad or broken brick; stone chips. Span. The distance between the supports of a beam, girder, arch, truss, etc Spandrel, or Spandril. The space between any arch or curved brace and the level label, beams, etc., over the same. The spandrels over doorways in Perpen- dicular works are generally richly decorated. Specification. Architect's. The designation of the kind, quality, and quantity of work and material to go in a building, in conjunction with the working drawings. Spire. A sharply pointed pyramid or large pinnacle, generally octagonal in England, and forming a finish to the tops of towers. Timber spires are very common in England. Some are covered with lead in flat sheets, others with the same metal in narrow strips laid diagonally. Very many are covered with shingles. In Continental Europe there are some elegant examples of spires of open timber work -covered with lead. Splayed. The jamb of a door, or anything else of which one side makes an oljlique angle with the other. Springer. The stone from which an arch springs; in some cases this is a capital, or impost; in other cases the moldings continue down the pier. The lowest stone of the gable is sometimes called a springer. Squinches. Small arches or corbeled set-offs running diagonally and, as it were, cutting off the corners of the interior of towers, to bring them from the square to the octagon, etc., to carry the spire. Squint. An oblique opening in the wall of a church; especially, in mediaeval architecture, an opening so placed as to afford a view of the high altar from the transept or aisles. Staging. A structure of posts and boards for supporting workmen and material in building. Stall. A fixed seat in the choir for the use of the clergy. In early Christian times the thronus cathedra, or seat of the bishop, was in the center of the apsis or bema behind the altar, and against the wall; those of the presbyters also were against the wall, branching off from side to side around the semicircle. In later times the stalls occupied both sides of the choir, return seats being placed at the ends for the prior, dean, precentor, chancellor, or other officers. In general, in cathedrals, each stall is surmounted by tabernacle work, and rich canopies, generally of oak. Stanchion. A word derived from the French etancon, a wooden post, applied to the upright iron bars which pass through the eyes of the saddle bars or hori- zon^tai irons to steady the lead lights. The French call the latter /m..r..., the stanchions montants, and the whole arrangement armature. Stanchions fre- quently finish with ornamental heads forged out of the iron. Steeple. A general name for the whole arrangement of tower, belfry, spire, etc. Stereobate. A basement, distinguished from the nearly equivalent term sty- lobate by the absence of columns. Stile. The upright piece in framing or paneling. Stilted. Anything raised above its usual level An arch is stilted when its centre is raised above theline from which the arch appears to spring. Stoop. A seat before the door; often a porch with a balustrade and seats on the sides. 1846 Glossary Part 3 Stoup. A basin for holy water at the entrance of Roman Catholic churches, into wliich all who enter dip their lingers and cross themselves. Straight Arch. A form of arch in which the intrados is straight, but with its joints radiating as in a common arch. Strap. An iron plate for connecting two or more timbers, to which it is screwed by bolts. It generally passes around one of the timbers. Stretcher. A brick or block of masonry laid lengthwise of a wall. String Board. A board placed next to the well-hole in wooden stairs, termi- nating the ends of the steps. The string piece is the piece of board put under the treads and risers for a support, and forming the support of the stair. String-course. A narrow, vertically faced and slightly projecting course in an elevation. If window-sills are made continuous, they form a string-course; but if this course is made thicker or deeper than ordinary window-sjlls, or covers a set-off in the wall, it becomes a blocking-course. Also, horizontal moldings running under windows, separating the walls from the plain part of the parapets, dividing towers into stories or stages, etc. Their section is much the same as the labels of the respective periods; in fact, these last, after pa::sing round the windows, frequently run on horizontally and form strings. Like labels, they are often decorated with foliages, ball-flowers, etc. Studs, or Studding. The small timbers used in partitions and outside wooden walls, to which the laths and boards are nailed. Style. The term style in architecture has obtained a conventional meaning beyond its simpler one, which applies only to columns and columnar arrange- ments. It is now used to signify the differences in the moldings, general out- lines, ornaments, and other details which exist between the works of various nations, and also those differences which are found to exist between the works of any nation at different times. Stylobate. A basement to columns. Stylobate is synonymous with pedeslul, but is applied to a continued and unbroken substructure or basement to columns, while the latter term is confined to insukited supports. The Greek temples gen- erally had three or more steps all around the temple, the base of the column resting on the top step; this was the stylobate. Subsellium. A name sometimes given to the seat in the stalls of churches; same as miserere. Summer. A girder or main-beam of a floor; if supported on two-story posts and open below, it is called a Brace-summer. Surbase. A cornice or series of moldings on the top of the base of a pedestal, podium, etc.; a molding above the base. Surface. To make plane and smooth. Systyle. An intercolumniation to which two diameters are assigned. Tabernacle. A species of niche or recess in which an image may be placed. They are generally highly ornamented and often surmounted with crocketed gables. The word tabernacle is alsc often used to denote the receptacle for relics, which was often made in the form of a small house or church. Tabernacle Work. The rich ornamental tracery forming the canopy, etc., to a tabernacle, is called tabernacle work; it is common in the stalls and screens •f cathedrals, and in them is generally open or pierced through. Tail Trimmer. A trimmer next to the wall, into which the ends of joists are fastened to avoid flues. Glossary 2^^^ Tamp. To pound the earth down around a wall after it has been thrown in. Tapestry. A kind of woven hangings of wool or silk, ornamented with figures and used formerly to cover and adorn the walls of rooms. They were often of the most costly materials and beautifully embroidered. Temple. An edifice destined, in the earliest times, for the public exercise of religious worship. Templet, or Template. A mold used by masons for cutting or setting work. A short piece of timber sometimes laid under a girder. Terminal. Figures of which the upper parts only, or perhaps the head and shoulders alone, are carved, the rest running into a parallelopiped, and sometimes into a diminishing pedestal, with feet indicated below, or even with- out them, are called terminal figures. Terra-cotta. Baked clay of a fine quahty. Much used for b'as-reliefs for adorning the friezes of temples. In modern times employed for archi- tectural ornaments, statues, vases, etc. Tessellated Pavements. Those formed of *esserae, or, as some write it, tessellae, or small '^ubes from half an inch to an inch square, like *ice, of pottery, stone, marble, enamel, etc. Tetrastyle. A portico of four columns in front. Tholobate. That on which a dome or cupola rests. This is a term not in general use, but it is not the less of useful application. What is generally termed the attic above the peristyle and under the cupola of St. Paul's, London, would be correctly designated the tholobate. A tholobate of a different descrip- tion, and one to which no other name can well be applied, is the circular sub- structm"e to the cupola of the University College, London. Throat. A channel or groove made on the under-side of a string-course, coping, etc., to prevent water from running inward toward the walls. Tie. A timber, rod, chain, etc., binding two bodies together, which have a tendency to separate or diverge from each other. The tie-beam connects the bottom of a pair of principal rafters, and prevents them from bursting out the wall. Tiles. Flat pieces of clay burned in kilns, to cover roofs in place of slates or lead. Also, flat pieces of burned clay, either plain or ornamented, glazed or unglazed, used for floors, wainscoting, and about fireplaces, etc. Small square pieces of marble are also called tile. Tongue. The part of a board left projecting, to be inserted into a groove. Tooth Ornament. One of the peculiar marks of the Early English period of Gothic architecture, generally inserted in the hollow moldings of doorways, windows, etc. Torso. A mutilated statue of which nothing remains but the trunk. Columns with twisted shafts have also this term. Of this kind there are several varieties. Torus. A protuberance or swelling, a molding ^ r-r^ ANCIENT TERMINI ig, a momuig ^ whose form is convex, and generally nearly approaches T a semicircle. It is most frequently used in bases, and i.s generally the lowest molding in a base. -L-4.- i; 1S48 Glossary Part 3 Tower. An elevated building originally designed for purposes of defence. Those buildings are of the remotest antiquity, and are, indeed, mentioned in the earliest Scriptures. In mediaeval times tl\ey were generally attached to churches, to cemeteries, to castles, or used as bell-towers in public places of large cities. In churches, the towers of the Saxon period were generally square. Norman towers were also generally square. Many were entirely without buttresses; others had broad, flat, shallow projections which served for this purpose. The lower windows were very narrow, with extremely wide splays inside, probably in- tended to be defended by archers. The upper windows, like those of the preced- ing style, were generally separated into two lights, but by a shaft or short column, and not by a baluster. Early English towers were generally taller, and of more elegant proportions. They almost always had large projecting buttresses, and frequently stone staircases. The lower windows, as in the former style, were frequently mere arrow-slits; the upper were in couplets or triplets, and sometimes the tower top had an arcade all around. The spires were generally broach spires; but sometimes the tower tops finished with corbel courses and plain parapets, and (rarely) with pinnacles. There are a few Early English towers which break into the octagon from the square toward the top, and still fewer which finish with two gables. Both these methods of termination, however, are common in Continental Europe. At Vendome, Chartres, and Senlis the towers have octagonal upper stages surrounded with pinnacles, from which elegant spires arise. In the North of Italy, and in Rome, they are generally tall square shafts in four to six stages, without buttresses, with couplets or triplets of semicircular windows in each stage, generally crenellated at top, and covered with a low pyramidal roof. The well-known leaning tower at Pisa is cylindrical, in five stories of arcaded colon- nades. In Ireland there are in some of the churchyards very curious round towers. Tracery. The ornamental filling in of the heads of windows, panels, circular windows, etc., which has given such characteristic beauty to the architecture of the fourteenth century. Like almost everything connected with mediaeval archi- tecture, this elegant and sometimes fairy-like decoration seems to have sprung from the smallest beginnings. The circular-headed window of the Norman? gradually gave way to the narrow-pointed lancets of the Early English period, and^ as less light was afforded by the latter system than by the former, it was necessary to have a greater number of windows; and it was found convenient to group them together in couplets, triplets, etc. When these couplets were as- sembled under one label, a sort of vacant space or spandrel was formed over the lancets and under the label. To relieve this, the first attempts were simply to perforate this flat spandrel, first by a simple lozenge-shaped or circular opening, and afterward by a quatrefoil. By piercing the whole of the vacant spaces in the window head, carrying moldings around the tracery, and adding cusps to it, the formation of tracery was complete, and its earliest result was the beautiful _ geometrical work such as is found at Westminster Abbey. Transept. That portion of a church which passes transversely between the nave and choir at right angles, and so forms a cross on the plan. Transom. The horizontal construction which divides a window into heights or stages. Transoms are sometimes simple pieces of mullions placed transversely as cross-bars, and in later times are richly decorated with cuspings, etc. Traverse. To plane in a direction across the grain of the wood, as to traverse a floor by planing across the boards. Tread. The horizontal part of a step of a stair. Glossary 1S49 Trefoil. A cusping the outline of which is derived from a three-leaved flowci or leaf, as the quatrefoil and cinque-foil are from those with four and five. Trellis. Lattice-work of metal or wood for vines to run on. Trestle. A movable frame or support for anything; when made of a cross piece with four legs it is called by carpenters a horse. Triforium. The arcaded story between the lower range of piers and arches and the clere-story. The name has been supposed to be derived from trcs and fores — three doors, or openings — that being a frequent number of arches in each bay. Triglyph. The vertically channeled tablets of the Doric frieze are called triglyphs, because of the three angular channels in them — two perfect and one divided — the two chamfered angles or hemiglyphs being reckoned as one. The square sunk spaces between the triglyphs on a frieze are called metopes. Trim. Of a door, sometimes used to denote the locks, knobs, and hinges. Trimmer. The beam or floor joist into which a header is framed. Trimmer Arch. An arch built in front of a fireplace, in the thickness of the floor, between two trimmers. The bottom of the arch starting from the chimney and tlie top pressing against the header. Tuck-pointing. Marking the joints of brickwork with a narrow parallel ridge of fine putty. • Tudor Style. The architecture which prevailed in England during the reign of the Tudors; its period is generally restricted to the end of the reign of Heniy VIII. Turret. A small tower, especially at the angles of larger buildings, sometimes overhanging and built on corbels, and sometimes rising from the ground. Tuscan Order. The plainest of the five orders of Classic architecture. Tympanum. The triangular recessed space enclosed by the cornice which bounds a pediment. The Greeks often placed sculptures representing subjects connected with the purposes of the edilice in the tympana of temples, as at the Parthenon and ^gina. Under-croft. A vaulted chamber under ground. Upset. To thicken, and shorten as by hammering a heated bar of iron on the end. Vagina. The upper part of the shaft of a terminus, from which the bust or figure seems to rise. Valley. The internal angle formed by two inclined sides of a roof. Valley Rafters. Those which are disposed in the internal angle of a roof to form the valleys. Vane. The weathercock on a steeple. In eariy times it seems to have been of various forms, as dragons, etc.; but in the Tudor period the favonte design was a beast or bird sitting on a slender pedestal, and carrying an upn^ht rod, on which a thin plate of metal is hung Hke a flag, ornamented in various ways. Vault. An arched ceiling or roof. A vault is. indeed, a laterally co^^^^^^^^^^ series of arches. The arch of a bridge is, strictly speaking, a vault. I^™^ vaults are said to be groined. See Gro^n^d VaulHng for fuller description of ""^Verge. The edge of the riling, slate or shingles, projecting over the gable of a roof, that on the horizontal portion being called eaves. 1850 Glossary Pari i VERMICULATED Verge Board. Often corrupted into Barge Board; the board under the verge of gables, sometimes molded, and often very, richly carved, perforated, and cuspcd, and frequently having pendants, and sometimes finials, at the apex. Vermiculated. Stones, etc., worked so as to have the appearance of having been worked by worms. Vestibule. An anti-hall, lobby, or porch. Vestry. A room adjoining a church, where the vest- ments of the minister are kept and parish meetings held. In American Protestant churches, the Sunday-school room is often called the vestry. Viaduct. A structure of considerable magnitude, and usually of masonry, for carrying a railway across a valley. Vignette. A running ornament, representing, as its name imports, a little vine, with branches, leaves, and grapes. It is common in the Tudor period, and runs or roves in a large hollow or casement. It is also called Trayle. Villa. A country house for the retreat of the rich. Volute. .The convolved or spiral ornament which forms the characteristic of the Ionic capital. Volute, scroll, helix, and cauliculus are used indifferently for the angular horns of the Corinthian capital. Voussoir. One of the wedge-Uke stones which form an arch; the middle one is called the key-stone. . ' Wainscot. The wooden lining of walls, generally in panels. Wall Plates. Pieces of timber which are placed on top of brick or stone walls so as to form the support to the roof of a building. Warped. Twisted out of shape by seasoning. Water Table. A slight projection of the lower masonry or brickwork on the outside of a wall a few feet above the ground as a protection against rain. Weather Boarding. Boards lapped over each other to prevent rain, etc., from passing through. Weathering. A slight fall on the top of cornices, window-sills, etc., to throw off the rain. Wicket. A small door opening in a larger. They are common in medixval doors, and were intended to admit single persons, and guard against sudden surprises. Wind. A turn, a bend. A wall is out of wind when it is a perfectly flat surface. Wing. A side building less than the main building. Withes. The partition between two chimney flues in the same stack. A Architectural Terms as Defined in Various Building Laws 1851 ARCHITECTURAL TERMS AS DEFINED IN VARIOUS BUILDING LAWS Compiled by The American Architect and Building News, Page 150, Vol. XXXIII (Republished by permission of Ticknor & Co.) Terms Defined [The following terms chance to be defined in sundry building codes, which are nentioned in each case. The fact that other codes are not mentioned is not neces- arily a proof that the term is not also elsewhere in use as defined.] Adjoining Owner. The owner of the premises adjoining those on which vork is doing or to be done. [District of Columbia.] Alteration. Any change or addition except necessary repairs in, to, or upon ny building affecting an external, party, or partition wall, chimney, floor, or tairway, and "to alter" means to make such change or addition. [Boston and )enver] Appendages. Dormer-windows, cornices, moldings, bay-windows, towers, pires, ventilators, etc. [Chicago and Minneapolis.] Areas. Sub-surface excavations adjacent to the building-line for lighting or entilation of cellars or basements. [District of Columbia.] Attic Story. A story situated either in whole or in part in the roof. [Denver nd District of Columbia-] Base. "The base of a brick wall" means the course immediately above the Dundation wall. [Cincinnati and Cleveland.] Basement Story. One whose floor is 12" or more below the sidewalk, and .'hose height does not exceed 12' in the clear; all such stories that exceed 12' igh shall be considered as first stories. [Chicago and Louisville.] A story whose floor is 12" or more below the grade of sidewalk. [Milwaukee.] A story whose floor is 3' or more below the sidewalk, and whose height does ot exceed 11' in the clear; all such stories that exceed 11' high shall he con-. idered as first stories. [Minneapolis.] A story suitable for habitation, partially below the level of the adjoining street r ground.* [District of Columbia and Denver.] (See Cellar.) Bay-window. A first-floor projection for a window other than a tower-pro- ction or show-window. [District of Columbia.] Any projection for a window other than a show-window. [Denver.] Bearing Walls. Those on which beams, trusses, or girders rest. [New York nd San Francisco.] Brick Building. A building the walls of which are built of brick, stone, iron, other substantial and incombustible materials. [Boston, Denver, and Kansas 'ity.] * And below the first floor of joists. [District of Columbia.] 1852 Architectural Terms in Building Laws Jrad Building. Any construction within the scope and purview of these regula- tions. [District of Columbia.] Building Line. The line of demarcation between public and private space [District of Columbia.] Building Owner. The owner of premises on which work is doing or to be done. [District of Columbia.] Business buildings shall embrace all buildings used principally for business purposes, thus including, among others, hotels, theaters, and office-buildings. [Chicago, Louisville, Milwaukee, and Minneapolis.] Cellar. Basement or lower story of any building, of which one-half or more of the height from the floor to the ceiling is below the level of the street* ad- joining.! [Boston, Denver, and Kansas City.] Portion of building below first floor of joists, if partially or entirely belpw the level of the adjoining parking, street, or ground, and not suitable for habitation. [District of Columbia.] Cement-mortar. A proper proportion of cement and sand without the ad- mixture of lime. [Kansas City.] Division Wall. One that separates part of any building from another part of the same building. [Cincinnati and Cleveland.] Floor-bearing walls extending through buildings from front to rear, and sepa- rating stores and tenements in buildings or blocks owned by the same party. [Minneapolis.] (See Partition-wall.) Dwelling-house Class. All buildings except public buildings and buildings of the warehouse class. [Cincinnati and Cleveland.] Shall not apply to buildings accommodating more than three families. [San Francisco.] External Wall. Every outer wall or vertical enclosure of a building other than a party-wall. [Boston, Cincinnati, Cleveland, Denver, District of Columbia, Kansas City, and Providence.] First Story. The story the floor of which is at or first above the level of th€ sidewalk or adjoining ground, the other stories to be numbered in regular ^M cession, counting upward. [Denver and District of Columbia.] 'IHI Footing Course. A projecting course or courses under base of foundation wall. [Cincinnati and Cleveland.] Foundation. That portion of wall below level of street curb,t and, where the wall is not on a street, that portion of wall below the level of the highest ground next to the wall. [Boston, Kansas City, New York, and Providence.] Portion of exterior wall below surface of adjoining earth or pavement, and portion of partition or party wall below level of basement or cellar floor. [Dis- trict of Columbia and Denver.] Foundation, Basement, or Cellar Walls. That part of walls of building that is below the floor or joists, which are on Or next above the grade line. [Detroit.] Portion of the wall below the level of street curb, in front of the central line of building. [San Francisco.] * Ground. [Providence.] t And not suitable for habitation. [Denver.] X " And serve as supports for piers, columns, girders, beams, or other wi iNew York.] 1 Architectural Terms as Defined in Various Building Laws 1853 Incombustible Scantling Partition. One plastered on both sides upon iron lath or wire cloth, and filled in with brickwork 8" high from floor, provided the building is not over 80' high. [Chicago.] Incombustible Roofing. Covered with not less than three (3) thicknesses roofing-felt, and good coat of tar and gravel, or with tin, corrugated-iron, or other fire-resisting material with standing-seam or lap-joint. [Denver.] Lengths. Walls are deemed to be divided into distinct lengths by return walls, and the length of every wall is measured from the center of one return wall to the center of another, provided that such return walls are external or party cross-walls of the thickness herein required, and bonded into the walls so deemed to |je divided. [Cincinnati and Cleveland.] Inflammable Material. Dry goods, clothing, millinery, and the like in stores, flyings or goods in factories, or other substance readily ignited by drop- pings or flyings from electric lights. [Minneapolis.] Lodging-house. A building in which persons are temporarily accommodated with sleeping* apartments, and includes hotels. [Boston and Kansas City.] Any building or portion thereof in which persons are lodged for hire for less than a week at one time. [District of Columbia and Providence.] Any building or portion thereof in which persons are lodged for hire tempo- rarily, and includes hotels. [Denver.] Mansard Roof. One formed with an upper and under set of rafters, the upper set more inclined to the horizon than the lower set. [Denver and District oj Columbia.] Oriel Window. A projection for a window above the first floor. [Distria of Columbia.] Partition. An interior division constructed of iron, glass, wood, lath and plaster, or other destructible natures. [District of Columbia.] Partition-wall. Any interior wall of masonry in a building. [Boston, Kansas City, and Providence.] An interior wall of non-combustible material. [District of Columbia.] Any interior division constructed of iron, glass, wood, lath and plaster, or any combination of those materials. [Denver.] (See Division Wall.) Party-wall. Every wall used, or built, in order to be used, as a separation of two or more buildings. f [Boston, Cincinnati, Cleveland, Denver, Kansas City, ^^td PTOV'tdEftCE 1 A wall built upon dividing line between adjoining premises for their common use. [District of Columbia.] Parking. The space between the sidewalk and the building line. [District of Columbia.] Parking Line. The line separating parking and sidewalk. [District of Columbia.] PubUc Building. Every building used as church, chapel, or other place of public worship; also every building used as a college school P"bl>chal^ hospital theater, public concert-room, public baU-room, P"bl.c lecture-room or for any public assemblage. [Boston. Chicago, Cincnmh. CMand. Denver Kansas City, and Minneapolis.] na^f 1854 Architectural Terms in Building Laws Pa^ Such buildings as shall be owned and occupied for public purposes for | State, the United States, the corporation of the City of Brooklyn, or other pd schools within said city. [Brooklyn.] Public Hall. Every theater, opera-house, hall, church, school, or other b^ ing intended to be used for public assemblage. [Milwaukee and Louisville.] Return Wall. No wall subdividing any building shall be deemed a return wall, as before mentioned, unless it is two-thirds the height of the externa^ party-walls. [Cincinnati and Cleveland.] Shed. A skeleton structure for storage or shelter. [District of Columbia Open structure, enclosed only on one side and end, and erected on the ground. [San Francisco.] Open or closed board structure. [Denver.] Show-window. A store-window in which goods are displayed for sale or advertisement. [District of Columbia and Denver.] Square thereof. The square or level of the walls before commencing the pitch for roof. [District of Columbia.] Standard Depth for Foundations. For brick and stone buildings, 14' below curb line. [San Francisco.] Standard Depth of Cellars. 16', measured down from sidewalk grade at property line. [Memphis.] Standard Iron Door. Made of No. 12 plate- iron, frame or continuous 2" X 2" X %" angle-iron, firmly riveted. Two panel doors, to have proper cross- bars, one panel on either side, fastened together with hooks or proper bolts top and bottom, and with not less than two lever-bars. All doors hung on iron frames of %" x 4" iron, securely bolted together through wall, swung on three hinges, fitting close to frame all around; sill between doors, iron, brick, or stone, to rise not less than two (2) inches above floor on each side of opening. Lintel over door, brick, iron, or stone. Floors of basement, when doors are to swing, stone or cement, in no case wood. [Denver.] Standard Skylight. Constructed of wrought-iron frames, with hammered or desk-light glass not less than ^-'2" thick; not larger than 10' by 12', except by special permission of the Inspector. [Denver.] Storehouse. (See Warehouse Class.) Street. All streets, avenues, and pubhc alleys. [Minneapolis.] Tenement-house. A building which, or any portion of which, is to be occu- pied, or is occupied, as a dwelling by more than three* families living independ- ently of one another, and doing their cooking upon the premises. [Boston, Denver, and Kansas City.] Or by more than two familiesf above the second floor, so living and cooking. [Bosfon and Kansas City.] Building which shall contain more than two rooms in front on each floor, or which shall be built with a passage or arched way between distinct parts of the same building, or which building shall be intended for the separate accommoda- tion of different families or occupants. [Charleston.] Theater. Public hall containing movable scenery or fixed scenery which is not made of metal, plaster, or other incombustible material. [Chicago, Louis- ville, and Milwaukee.] * Two instead of three. [District of Columbia and Minneapolis.] t Upon one floor, but having a common right in the halls, stairways, yards, etc. [Provi' denc€.] Architectural Terms as Defined in Various Building Laws 1855 Thickness of a Wall. The minimum thickness of such wall.* [Boston, ticinnali, Cleveland, Kansas City, Milwaukee, and Providence.] Tinned Covered Fire-door. Wood doors or shutters, double thickness of jod, cross or diagonal construction, covered on both sides and all edges with eet-tin, joints securely clinched and nailed. [Denver.] Tower Projection. A projection designed for an ornamental door-entrance, r ornamental windows, or for buttresses. [District of Columbia.] Vault. \\\ underground construction beneath parking or sidewalk. [District Colmnbia.] Veneered Building. Frame structure, the walls covered above the sill by a wall of brick, instead of clapboards. [Common understanding in Chicago, ilwaukee, and Minneapolis, but not defined by law.] Warehouse Class. Buildings used for the storage of merchandise, manufac- ries in which machinery is operated, breweries, and distilleries. [Cincinnati id St. Louis.] Width of buildings shall be computed by the way the beams are placed; the igthwise of the beams shall be considered and taken to be the widthwise of the lilding. [New York and San Francisco.] Wholesale store, or storehouse, shall embrace all buildings used (or intended be used) exclusively for purpose of mercantile business or storage of goods. 'hicago, Louisville, and Milwaukee.] Wooden Building. A wooden or framef building. [Boston, Kansas City, id Minneapolis.] Any building of which an external or party wall is constructed in whole or in- irt of wood. [Denver and District of Columbia.] Having more wood on the outside than that required for the door and window ames, doors, shutters, sash porticos, and wooden steps, and all frame buildings : sheds, although the sides and ends are proposed to be covered with corrugated on or other metal, shall be deemed a wooden building under this law. [CharUs- n and Nashville.] * As applied to solid walls. [Minneapolis and Providenci.] t Or veneered. [MinneapoHs.l INDEX By CLINTON L. BOGERT Associate Member of American Society of Civil Engineers Numbers refer to Pages. Consult also the Glossary, pages 1796-1850. Abacus (Glossary), 179& Abbreviations of terms, 122, 123 Abutments, arch, 305 pier, 306 Acetylene gas, 1431 , Acoustics, architectural, 1486-1500 Advertising, ethics, 1729 Aetna radiator, 1266 Agate, 130, 1501 Aggregate, concrete, 241, 287,908,909, 945 Agreement, form, 1765 Agreements, 1751 Air-compressor, water-supply, 1390 Air, condUioning, 1352 density, 1247, i339 flow, resistance, i333 hot-water systems, removal, 130? properties, 12 54-1 2 56 quantity, symbol, 1247 specific heat, 1250, 1255 ventilation, requirements, 1260, 1354. 1356 vitiated, effects, 1352 Air-ducts, 1333-1341 Air-lift, 1396 Air-lock, pneumatic caisson, 211 Air-pressure, pneumatic caisson, 211 Alabaster, 131, 1501 Alca lime, is S3 ■, - vA Alcohol, specific gravity and weigMf, 1501 Almonry (Glossary), i797 Alterations, defined, 1851 . Aluminum, specific gravity and weight, Americir Blower Co., heater, 1329- Americ'an' Institute of Architects^ canons of ethics, 173© chapters, 1788 competitions, 1733 documents, 1767 professional practice, 1727 schedule of charges, 1728. I73i standard documents, I74» American Steel & Wire Go's gauge, 401, 402 Amperes, defined, 1457 Anchor, box, 753, 790, 792, 793 reinforced-concrete, 919 steel beams, 619 trusses, 1150, 11S2, 1168 wooden beams, 616, 762, 783-800 Anchor-bolts, adhesion, 240 placing, 1 194 steel beams, 619 steel stacks, 137 7 Ancient measures and weights, 34 Aneroid, barometer, 1249 Angle in geometry, 36 bisected, 69 critical, domes, 12 13 friction, retaining walls, 2S3 measure, two-foot rules, 68 repose, materials, 253, 2S4, 256 Angle of structural steel, 361-367 beams, safe loads, 566, s86-59o connections, beams, 616 double, properties, 370-372 moment of inertia, 339, 362-367 oblique loading, 593 price, X204, 1211 properties of, steel, 362-367 shelf, 787-790 struts, 488, Soi-503 tension-members, loads, 385, 399 deduction, 399, 400, 702 Angle-anchor, 619 Angle-and-plate columns, 475, 47 o Angle-bar (Glossary), i797 Angle-bracket, 422 Angular measure, 30, 68 Anhydrite, 131 Annealing, rivets, 382, 414 Anthracite coal, combustibles, 1271 for hot-air heating, 131 7 Apartment-houses, floor-joists, 737 live loads, i49, "98 I beams in floor, size, 864 steel, weight, 1207 Apatite, 131 1857 1858 Index Apostles and Saints, symbols, 1727 Apothecaries' weight, 29 Apple-tree, wood, hardness, 1558 Apron, retaining-walls, 263 Aragonite, 131 Arbitration, contract, 1763 Arbitration bar, cast-iron test, 380 Arc, arcs, circular, 38, 69, 70 lengths, 54 Arc-lamps, 1462 Arch, arches, masonry, 305-321 (Glos- sary), 1799 angle of friction, 311 brick, 306 center of pressure, 311, 313 centers, 308 concrete, reinforced, 321 cut-stone, 310 depth of keystone, 308-310 elliptical, 306 failure of, 311-313 floor, 827-844 forms of, 306 groined, 1235-1240 inverted, in footings, 227, 228 keystone, 305, 308-310 line of fracture, 316 line of pressure, 311-321 line of resistance, 311-321 load, actual, masonry, 318 loaded, 317 middle third, principle of, 311-315, 1225, 1227, 1240 New York City requirements, 307 plate-girder arches, 1131 pointed, failure of, 312 rings, 308, 317 rise, 307 segmental, 305, 306, 307, 321 semicircular, 306 semielliptical, 321 solid ribs, 1132 stability, determination, 311-321 strength, 306 surcharged, 317 three-centered, 306 thrust, 305, 307, 311-321 tie-rods, for I beams, 619, 865 roof -trusses, 11 20 segmental arches, 307 trussed, 1121 unloaded, 311 voussoirs, :>o5, 311 Arched trusses, 1035-1043 stresses, 11 18- 11 20 wooden, 1020-1024 Architects, canons of ethics, 1730 certificates, 1771 charges, schedule, 1728, 1731 competitions, 1 733-1747 drawings, 1718, L728, 1731, 1754 Architects, estimates, 1728 examinations, 1772 inspection of work, 1755 organizations, 1788-1795 professional practice, 1727 registration laws, 1768-1779 status and decisions, 1754 superintendence, 1728 Architectural acoustics, 1486-1500 Architectural engineering, terms, 124- 128 Architectural fellowships, 1779-1788 medals, 1779-1788 Architectural societies, 1788-1795 Architectural terms (Glossary), 1796- 1850 building laws, 1851-1855 Architecture, schools of, 1779 Areas, circles, tables, 42-54 elementary, 332 geometrical figures, 38-54, 59-61 334-338, 348-351 net sectional, of tension-members 386 Arithmetic, practical, 3-24 Armories, steel, weight, 1208 Artificial cements, 236-240 Asbestic plaster, 818, 819 *' Asbestos, building-lumber, 819 corrugated sheathing, 819 metal, 819 products, 819 roofing-shingles, 819 sheathing, 1501, 1567 specific gravity and weight, 1501 Ash (wood) deflection in beams, 664 hardness, 1558 specific gravity, 1501 ultimate unit stresses, 651 weight, 651. isoi, 1558 Ashes, angle of repose, 256 specific gravity, 1501 weight, 651, 1501, 1558 Ashlar (Glossary), 1799 masonry, 233, 269, 441, 1538, I5S9 Asphalt, 1608 floors, 1608, 1609 mastic, 1608 pavements, 1608 rock, 1608 roofing, 1608 specific gravity and weight, 1501 Asphalt-gravel roofing, 871, 1598 Asphaltum, 1608, 1799 specific gravity and weight, 1501 Assembly-halls, joists, 739, 744- live-loads, 719, 720, 1198 Asylums, non-fire-proof, height, 813 ventilating and heating, 1355 Asymptote (Glossary), 1799 Index 1859 Atlanta building code, loads on founda- tion-beds, 143 office-building loads, 151 Auditoriums, heating and ventilating requirements, 1354 lighting, 1 45 1 live loads, 719, 720, 1198 Augite, 131 Automobile factory, design and cost, 803 Automobiles, dimensions, 1642 Avoirdupois weight, 28 Axial force, definition, 375 Axis, conjugate, 38 neutral, 295, 332-338, 555, 621 transverse, 38 Back, arch, 305 Baltimore, fire, reinforced concrete in, 957 building code, steel columns, 481 Band of column (Glossary), 1801 Barometer, 1249 pressure, measurement, 1249, 1252 Barns, cost, 16 13 Barrel, dimensions, 1644 Barrel vault, 1231-1235 Barrett specifications, roofing, 1595 Bars (steel), 385-398 • areas, 1514-1521 base price, 1205 circumferences, 1514-1521 lacing, 385 reinforcing, 915-921 safe loads, 388-392 standard, classification and cost, 1211 weights, 1514-1521 Bartizan (Glossary), 1801 Basalt, 131 specific gravity and weight, 1501 Base, columns (Glossary), 1801 cast-iron column, 457, 459 material, 1195 mill-construction, 782-788 pipe columns, 470, 471, 47^ pressures, 265, 441, 1200 steel columns, 473-477 Base-plates, 440-445, 1524 Basement, defined, 1851 walls, 228, 229 Basin-slabs, marble, 1641 Bath, foot, 1 64 1 plunge, 1422 seat, 1641 Bath-tubs, dimensions, 1640 symbols for, 1426 Batter, iSoi cellar walls, 229 retaining-walls, 259 Battlement (Glossary), 1802 Bay window (Glossary), 1802 Beam, beams (see also Girders) Beam, bearing on wall, 634, 687 bearing-plate areas, 440-444 bending moment, 324-331, 555, 939 continuous beams, 673 iniluence-lines, 1134 reinforced-concrete, 935 Bethlehem, 357, 358, 592-602 buckling, 183, 565, 567, 569^ girders, 686, 705 separators, 612 wooden, 627 cantilever (see Cantilever, beams) Carnegie, 352-356, 574-591, 605, 606 cast-iron (see Lintels) channel (see Channels) clamps for connecting, 616 coefficient of strength, 556, 628 compound, 652-654, 763 compression in, 555 concrete fire-protection, 860 concrete, not reinforced, 628, 637 connections, steel beams (see Fram- ing, steel beams) wooden beams, 749-757, 789, 790 continuous, 555, 671-680, 979, 980 cross-section irregular, 557 cylindrical, 667 deck, 565 deflection, 663-670 allowed, 566, 628, 664, 736 continuous girders, 674-676 steel, 566, 612, 668-670, 676 wooden, 636, 653, 654, 664, 667 double, 564, 603, 604, 607-611 elasticity, 555, 663 external forces, 325 factors of safety, 556 fixed, strengths, 331, 634 flexure, 324-331, 332-334, 555 reinforced-concrete beams, 924-941 steel beams, 564-573 wooden beams, 627-637, 652-656 floor, steel, specifications, 1201, 1202 . girder (see I beams; also Girders) grillage, foundations, 165-169, 181- 185, 678-680 H beams, 356, 474, 585, 1204 I beams (see I beams) inclined, 564, 665 influence-lines, 1134 internal forces, 325 keyed, 653-655 lateral deflection, 566, 670 loads, general principles, 555, 565. 593, 629, 665 tables (see Beams, steel, etc.) materials used for, 564 neutral axis, definition, 555 neutral surface, definition, 555 overhanging (see Cantilever, beams) reactions, 322-324 1860 Index Beam, rectangular, relative strength, 633,634 stiffness, 665, 666 reinforced-concrete, 924-941, 971-97S resisting moment, 333, 555. 635, 683, 929 shear, 183, 411, 413, 565, 567-570 simple, 323-330, 555 span, 555 span-limit, 566 steel, anchors for, 619 base price, 1204 bending moments, table of maxi- mum, 574-576 Bethlehem, 357, 358, 592-602 buckling, 183, 565, 567, 569, 612, 627 Carnegie, 352-356, 574, 59i, 605, 606 channels (see Channels) connections (see Framing, steel beams) crippling (same as buckling) deflection, vertical (see above) dimensions, 352, 565 economy and strength, 565 end-reactions, 569, 574-576 fiber-stress, 556, 557, 569 fireproofing,. 780-782, 827-842, 844. 849, 854-860 flange-thickness, 592 forms of, 565 framing and connecting (see Framing) H beams, 474, 585, 1204 H beams, properties, 356 heavy, 565 I beams (see I beams) lateral deflection, 566, 670 light, 565 loads, safe, 565, 577-591, 594-602 separators, 612-614, 1202 shearing-stresses, 181-185, 567, 568, 569^ 574, 575 standard, 352 strength affected by dimensions, 556, 565 strut, 571, 572 T beams, 337, 368, 369, 591, 1211, 1212 tie, 572 tie-rods, 619, 865 unit stresses, 1200 web-buckling, 181-185, $65, 567, 569, 612 web-thickness, 592 stiffness, 565, 635, 663-670 stone, 637 coefficients of strength, 556, 628 stresses, 555-557, 567, 569, 603, 604, 628, 635 Beam, strut, steel 571, 572 wooden, 633 supplementary, 352, 561 T beam, 337, 368, 369, 591, 1211, 1212 tension in, 555 tie-beams, steel, 572 wooden, 430-432, 434, 435, 633 wall-support, 612 wooden, 627-668, 717-757, 780, 789- 795 , anchors, 6x6, 762, 783-800 bolted, 429, 653, 655 buckling, 627 built-up, 652, 656 cantilever, 629 cedar, 628, 640, 664 chestnut, deflection, 664 distributed loads, 641 coefficients, 628 compound, 652-654, 763 connections, 749-757, 789, 792 (see also Framing, floors, wooden) conversion factors, 637, 668 cross-sections, 627, 637 cut from log, strongest, 634 cylindrical, 634, 667 cypress, distributed loads, 641 deflection. 636, 653, 654, 664, 667 Douglas fir, 'distributed loads, 628, 642, 664 dressed, 667 Eastern fir, loads, 639 end-bearing, 634 flitch-plate, 655 framing, 749-757 framing to steel beams, 789, 790 hangers (see Hangers) hemlock, loads, 628, 638, 664 keyed, 653-655 loads, safe, 638-646, 667 mill-construction, 758-769 nominal dimensions, 636, 667, 736, 1559 Norway pine, loads, 641, 664 redwood, loads, 640 shear, horizontal, 412, 635 sizes, nominal and actual, 636, 667, 736, 1559 spans, maximum, 737-746 spruce, loads, 628, 639, 664 stiffness, 664 strongest cut from log, 634 strut, 633 tension, 635 tie, 430-432, 434, 435, 633 trussed, 656-662 unit stresses, 557, 627, 635, 647-651 white oak, loads, 643, 664 white pine, loads, 639, 664 yellow pine, 628 • Index 1861 Beam, wooden, yellow pine, deflection, 664 loads, 642, 643, 666 wrought iron, 628 deflection, 664 Beam-box, 753, 762, 790, 792, 793 Beam girders (see I beams) Beam-hangers (see Hangers) Bearing-brackets, cast-iron columns, 445-447 Bearing-plates, 440-445, 1524 pressures, 441, 1200 Bearing values (see materials in ques- tion) Bed, masonry (Glossary), 1802 , Bedsteads, dimensions, 1638, 1640 Beechwood, hardness, 1558 Bell-cot or gable (Glossary), 1803 Bells, 1725 Belt, for shafting, 1721 mill-construction, 764, 765 Bending moments, beams, 324-331, 555, 939 bolts in wooden construction, 429, 431 channels, table, 576 columns, 485 continuous girders, 673 diagrams for beams and girders, 328, 330, 564, 678, 690, 695, 698 footings, 174, 175, 178 I beams, table of maximum, 574, 575 influence lines, 1134 moving loads, 1134-113S pins, 423-429 reinforced concrete, 934, 935 slabs, concrete, 932, 936, 984-991, 994 T beams, concrete, 992 Berger's studding, 881 metal lumber, 852, 858, 881 Bessemer steel, 380 Bethlehem beams, 357, 358, 592, 594- 604 Bethlehem columns, 475, 479, 482-488, loads, 483, 506-515 Bevels, 90 Billard-tables, dimensions, 1638 Birchwood, hardness, 1558 Bitumen, 1608, 1609 Bituminous coal, combustibles, 1271 Blackboards, dimensions, 1644, 1645 Black-line prints, 1719 Block-tin, pipe, 1419 Blocks, hollow building, filling, 287 concrete (see Concrete, blocks) Blower system, heating, 1324 Blue-prints, 17 18 Bluestone, beams, coefl&cient for, 628 flagging, 282, 1539 Board-measure, table, 1 560-1 562 Boiler, 12 73-1 283 connections, 1279 covering, 1361 horsepower, 1274 incrustation, 1429 location, 1357 in mills, 765 in warehouses, 780 rating, 1301 residence, specification, 1362 shops, steel, weight, 1208 symbols, 1351 water, for ranges, 1642 Boiler-plants, mill-construction, 765 Bolsters, mill-construction, 454, 795 Bolt, bolts, anchoring, 240 bearing strength, 429, 439, 1138 bending, 1138 bending moment, 429, 431 beveled washers, 1202 built-up beams, 652, 654 expansion, 1534 fiber-stress, 1138 foot of rafter, 437 girders, 432, 433 heads, 1525-1528 safe bearing in timber, 430 screw-ends, upset, 387 shearing value, 412, 429-439, 1138 shock loads, 1202 steel, table, 431 stresses, 618, 1138, 1200 strap-joints in trusses, 436 swedge, 619 tension, 431, 1138 truss-joints (see Roof-trusses) weight, 1527 wrought iron, table, 431, 1138 Bolt-heads, 15 25-1 5 28, standard dimensions, 1525-1526 weight, 1526-1528 Bonanza reinforced-cement tiles, 868 Bond, brickwork, 268, 306 masonry (Glossary), 1803 timber (Glossary), 1803 Bond-stones in piers, 269 Bonds, form, 1763 guaranty, 1757 Book-stacks, library, 1696 Book-tile, roofing, 868 Borings, for foundations, 144 Boss (Glossary), 1804 Boston building code, column-formula, 460, 481, 493-496 loads on foundation-beds, 142 loads on masonry, 267 office-buildings, assumed loads, 151 rivets, bearing and shear, 419 steel column formula, 481, 493-49^ thickness of walls, 230, 231, 232 1862 Index * Boston, Chamber of Commerce Build- ing, 192 Bostwick lath, 884 Boulders, 134, 136, 141 safe loads on, foundations, 141 Bowling-alleys, dimensions, 1643 Bowstring truss, 1035 stresses, 1094, 1096 Box anchors, beam-supports, 753, 762, 790, 792, 793 Box columns, 467, 479, 484 moment of inertia, 342 plate-and-angle, 479 Box girders, 681-716 bending moment, 683, 695, 697, 698, 699 buckling, 686, 705 construction, details of, 682 cover-plates, 696 end-reactions, maximum, 703, 706- 716 examples, 694-703 ^ flange-area, 683, 692, 696, 699, * framing and connections, 615 moment of inertia, section, 341, 342 rivet-holes, loss of area, 702 shear, 684-687, 690, 691, 696, 698 specification, 1201, 1202, 1203 steel-beam, 607-611 stififeners, 681, 686, 691, 696, 1201, 1203 web-plate, buckling value, 686, 705 shearing value, 684, 703 weight, 687, 701 Box-hangers (see Beam-boxes) Bracing, steel structures, 1202 wind buildings, 1171-1193 Brackets, cast-iron columns, 445-447 terra-cotta, 278 Brads, 1529 Brass, castings, shrinkage, 1521 specific gravity, 1502, 1510, 1511 weight, 1502, 1510, isn Br east- walls, 262-263 Breeching, dimensions, 1366 Breuchaud method, underpinning, 221 Brick, bricks, angle of friction, 253 arches, laying, 306-307 burning, 1540 clay, 27s, 1540 coefficient of friction, 253 color, 1540, 1543, 1544, 1547 cost, 1544 crushing-height, 269 crushing strength, 270, 271 dry-pressed, 1540 enameled, 1543 fiber-stresses, 557 fire, 1540 fire-resistance, 814 flexure, 17$ Brick, footings, 226, 227 glazed, 1543 lime-mortar, 1541 machine-made, 1540 manufacture, 1542 molded, 1540 paving, 1540 piers, 267-276, 278 piling, space required, 1547 repressed, 1540 retaining-walls, 259, 260 sand-lime, 1541 properties of, 1543 size, 1540, 1543 soft-mud, 1540 specffic gravity, 1502 strength, ultimate, 270 stiff-mud, 1540 tests, 270, 275, 281, 1542 vaults, 1238 weight, 1502, 1541 Brickwork, 1 540-1 548 (see, also, Ma- sonry, Walls, etc.) arches, 306 bond, effect on strength, 268 cement mortar required, 239 compared with concrete, 968 cost, 1544-1547 mill-buildings, 808-810 crushing strength, 270-276 data, 1 540-1548 efflorescence, 1547 estimating quantities and cost, 1544- 1546 fire-resistance, 814 floor-arches, 827-828 footings, 226, 227 lintels supporting, 623 loads, safe, 265-268, 287, 441 moisture, 1547 mortar, 239, 276, 818 mortar-colors for, 1547 piers, 267-276, 278 bond-stones, 269 crushing strength, 271-276 safe loads, 267-268 tests, 272-278 pressures, 265, 441, 1200 quantity estimates, 1 544-1 547 specific gravity, 1502 strength, safe, 265-268, 287, 441 tensional strength, 178 walls, safe loads, 265, 441 warehouse, 778 weight, 1502 Bridging (Glossary, 1804) floor-joists, 748, 749 British thermal unit, 33, 1250, 1251, 1255, 1684 Bronze, door-frames, 895 specific gravity and weight, 1502 Index 1863 Bronze, window-frames, 895 Brown & Sharpe wire-gauge, 401, 402, 1469, 1473, 1509, 1510 Brown-line prints, 1720 Brownstone, crushing strength, 279, 281 Buckling, plate girders, 686, 705 steel beams, 565, 567-569, 612, 627 web, box girders, 705 plate girders, 705 wooden beams, 627 Buffalo building code, loads on founda- tion, 142 masonry loads, 267, 287 office-buildings, assumed loads, 151 Building, alterations, 1851 steel, drafting, 1207 cost, 1611-1634 of slow-burning, 758, 802, 1619 per cubic foot, 1611-1634 per square foot, 1627-1634 reinforced-concrete, 1618 cubage, 1612 depreciation, 1634 drainage, 1407-1414, 1419-1421 factory, 968 fire-proof, cost, 802, 812, 1619-1625 fireproofing, 811-905 government, cost, 1628-1634 heating, 1 247-1363 temperatures, 1256 iron and steel, 1627 legal definition, 1852 loads, 1 196 mill-construction, 1618 non-fire-proof, 812, 813 office, specifications, 1194-1212 papers, 1564 protection from outside hazard, 901- 903 reinforced-concrete, 968-997 shrinkage in, 1427-1428 signing by architects, 1729 steel, cost, 1206 weight, 1207 structural-steel specifications, 1194- 1212 veneered, 269, 1855 ventilating, 1348-1354, i356 wind bracing, 1171-1193. 1202 wooden, defined, 1855 Building laws, bearing on masonry, 441 bearing- walls, 269 brickwork, 267 column-protection, 822-826 concrete columns, length of, 94i concrete fire-protection, 955-960 floor-slabs, 937 electric work, 1480-1481 elevator-installation, 1663 fire-proof construction, 811-905, 1618-1620 Building laws, fire-proof paint, 821 fire-proof wood, 820 floor fire tests, 827 flooring, fire-proof, 892-893 floor-loads, 719, 730, 1198 footings, assumed loads on, 151 formulas, steel columns, 481 foundation-beds, loads on, 142 hooped columns, 942 loads, on brickwork, 269 on floors, 719, 730 on foundation-beds, 142 on masonry, 267, 287 non-fire-proof buildings, areas, 812 heights, 812, 813 reinforced-concrete columns, 940, 941 sand in concrete, 908 terms defined, 1851-1855 unit stresses for woods, 647 walls, thickness, 230, 231, 232 wind-bracing, 1171-1172 Building materials, 1634-163 7 depreciation, 1634 estimating, 1635 quantity systern, 1635-1637 wear and tear, 1634 Building papers, 1564-1568 Bureaus, dimensions, 1638, 1640 Butternut wood, hardness, 1558 unit stresses, 651 Buttresses, 1804 center of gravity, 300, 303 stability, 297-304 Cables, carrying capacity, 1473 measure, 25 Caissons, 210-214 Calcareous minerals, 130, 131 Calcite, 131 specific gravity and weight, 1502 Calendar, old and new, 30 California, registration law, 1778 Cambered truss (see Roof-truss, cambered) Calorimetry, 1250 Candle-power, 1439, i440» 1462 Canopy (Glossary), 1805 Cantilever, beams, 555, io43 moments, 325, 326, 558, 559 wooden, 629 buildings as cantilevers, 11 73 compound footings, 178 flat slabs, concrete, 950 foundations, 165-169, 978 truss, 1043-1045, 1105-1107 Canvas roofs, 801 Cap, cast-iron columns, 459 mill-construction, 762 steel-pipe columns, 470, 471 stone (see Coping) wooden columns, 454 1864 Index Cap-plates, 795 Capital (Glossary), 1806 Car-bams, steel, weight, 1209 Carbon, in steel, 381 Carnegie shapes (see Beams, etc.) Carpenter's rule, heat-loss, 1261 Carpenter's work, data on lumber and work, 1 5 58-1 564 cost of labor, 1564 Carriages, dimensions, 1642 Cars, railroad, capacities, 1643 dimensions, 1642 Case-work, dimensions. 1640 Cast iron, 379 appearance, 379 castings, 379, 380 shrinkage, 1521 columns (see Columns) crushing-loads, 449 defects, 379 fiber-stresses, 557 fire-resistance, 819-820 lintels, 620-628 manufacture, 379 modulus of elasticity, 664 plates, weight, 1524 shearing-stresses, 1505 specific gravity, 1505 specifications, 379 strength, 376, 379, 412 tension, 376 weight, 1505, 1521, 1524 estimating, 1505, 1521 weight of castings, 1521 Castings, shrinkage, 15 21 specifications, for cast iron, 379, 1196 steel, stresses, 1138, 1200 structural, painting, 1203 weights, 1521 Cathedrals, seating capacity, 1654 Cedar, beams, deflection, 664 fiber-stress, flexure, 557 safe loads, 640 columns, safe loads, 450, 452 crushing strength, 449, 454 hardness, 1558 specific gravity, 1502 unit stresses, 557, 647, 650 weight, 650, 1502 Ceiling (Glossary), 1807 corrugated metal, 1604 loads, 1 197 matched, 1563 suspended, 871-872 Ceiling-joists, wooden, framing to roof- trusses, 1004 maximum spans, 736, 737, 742 Cellar, defined, 1852 walls, 129, 228, 229 Cellar-drainer, 142 1 Celsius thermometer, 1250 Cement, 235-240, 907, 908 artificial, 236 chemical composition, 237, 908 constancy of volume, 907 corrosion of steel, 960 cost, 238, 248, 910 fineness, 237, 907 grappier, 236 La Farge, 236, 238 manufacture, 236 mixing, 238 mortars, freezing, 239 proportions, 235, 247 specific gravity and weight, 1506 water required, 238 natural, 235, 284 (see Hydraulic lime) neat, 237, 907 painting of, 1573 Portland (see Portland cement) Puzzolan,»236, 237 quantities in concrete, 247, 248, 249 reinforced-concrete, 907 setting, 237, 907 slag, 236, 237, 238 specific gravity, 237, 907, 1502 specifications, 236, 907 stainless, 238 strength, 235, 237, 240, 283, 284, 907 tests, 237, 240, 907 water required, 238 waterproofing, 1711, 1717 weight, 235, 723, 1502 Cement blocks, 269 Cement-gun, column-protection, 826 Cement-plants, steel, weight, 1209 Center, striking for arch, 308 Center of gravity, 127, 291-296 circle, sector and segment of, 293 compound figures, 294, 295 found by moments, 294 irregular figures, 292, 295 lines, 292 particles, heavy, 293, 294 quadrant of circle, 293 quadrilaterals, 292 regular figures, 292 surface, 292 table of, 293 triangles, 292, 293 voussoir of arch, 313, 318 wall and buttress, 300-301 Center of pressure, arches, 311, 313 pier-joints, 300 Centigrade thermometer, 1250 Ceramic tile, 1605, 1607 Certificates, architects, 1771 Chain, 408-410 Chain-blocks, 1723 Chain-cables, 409 Chain-hoists, 1723 Chain-hooks, 1724 Index 1865 Chairs, dimensions, 1638, 1639, 1653 Chalk, 132 specific gravity and weight, 1502 Chamber of Commerce Building, Bos- ton, piiing-plan, 192 Chamfer (Glossary), 1807 Channel, beams, safe loads, 582-584 bending moments, table, 576 buckling, 576 columns, 467, 476-480, 486-489 safe loads, 499, 500, 533-554 deflection, coefficients, 582-584 depth, 576 dimensions of standard, 353, 360 double sections, 359, 373, 374, 499- 500 end-bearing, 576 moment of inertia, 337, 338 oblique loading, 573 properties of, 359, 360, 373, 499, 500 radius of gyration, 337, 338 sections, 359 set flatwise, 572 shearing, 576 small grooved, 360 steel, prices, 1204, 1212 web-resistance, table, 576 weight, 360, 576 Chapel (Glossary), 1808 Charcoal, combustion, 1272 Charges, schedule, 1728, 1731 Charles' law, gases, 1254 Check-nuts, shock-loads, 1202 Chert, 130 Chestnut, beams, coefficients for, 628 deflection, 664 distributed loads, 641 fiber-stress, safe, flexure, 557 columns, safe loads, 450, 452 crushing strength, across the grain, 454 crushing-loads, with the grain,' 449 hardness, 1558 specific gravity, 1502 tension, 376 unit stresses, 647, 648, 651 weight, 651, 1502, 1558 Cherry, hardness, 1558 weight, 1502 Cheval-glasses, dimensions of, 1638, 1640 Chicago building code, bearing pressure, masonry, 441 column-formula, 450, 460, 481, 482 safe loads, 493-495 steel-pipe column, 469, 474, 497, 498 compression, steel members, 495 concrete flat slabs, 997 masonry-loads, 267, 287,441 method of excavating, 209 Chicago building code, office-buildings assumed loads, 151 piers, strength, 268 skeleton construction, 234 thickness of walls, 230, 231, 232 Chiffoniers, dimensions, 1638, 1640 Chimneys, 1281, 1364-1380 for boilers, 1281, 1282, 1283, 1367 for fire places, 1282 for kitchen ranges, 1282 formula, 1366, 1368 for tall buildings, 1283, 1368 gas-velocity, 1364 height, draft-relation, 1281, 1364 radial-brick, 1368-1373, 1377 reinforced-concrete, 1373-1375 steel, 1376 wind load, 1199, 1368 tall, list of, 1379 Chlorite, 131 Chords, of arcs, 38 of truss, definitions, 998 table, 81-89 Churches (Glossary), 1808 air-changes, 1260, 1353 cost, 1613 floor-loads, 719, 720, 1198 seating-space, 1653, 1654 Cinciimati building code, office-build- ings, assumed loads, 151 loads on foundation-beds, 143 Cinder, cinders, angle of repose, 256 Concrete, 242, 250, 909, 930 corrosive action, 818, 960 reinforced work, 242 weight, 250 weight of loose, 256 Circles and parts, 37,38,41 areas, tables, 42-54 arcs, mensuration, 54-59 chords, tables, 81-89 circumferences, 42-54 geometrical problems, 66-74 moment of inertia, 337 radius of gyration, 337 section-modulus, 337 Circuit-breakers, 1461 Circular measure, 30 Circular mil, 1469, 1473 Circular ring, 61 Circumference, 37 circles, 42-54* Cisterns, capacity of, 1404-1405 Clapboards, 1563 Classical moldings, 1697 Classical orders, 1 698-1 704 Clay, angle of repose, 256 bricks, 275 foundation-beds, 135, 138, 139 moisture in, 138 safe loads, 141, 143 1866 Index Clay, specific gravity, 1503 weight, loose, 256, 1503 Clerestory or Clearstory, ( Glossary ) ,1 809 Clerk of the works, 1728, 1733 Cleveland building code, loads on foundation-beds, 143 office-buildings, assumed loads, 151 Clevises, standard, 387, 398 Climax, cellar-drainer, 142 1 floor system, 855 Clinched lath, 886 Clinton stiffened lath, 887 Clips, for steel beams, 616 Clocks, tower, 1695 Closet, water, 141 1, 1428, 1641 Closet-ranges, dimensions, 1641 Coach-screws, 1535 Coal, calorific value, 1271 classification, 1271 composition, 1271 specific gravity and weight, 1503 Coal-bunkers, steel weight, 1209 loads, 1 198 Coal-fields, 1271 Coal-gas, 1273, 1 43 1 Codes, building terms, 1851-1855 Coefiicient of elasticity (see Modulus) Coefficients, beams, 556, 628 deflection, steel beams, 668 expansion, steel, 382 flow of water, 1383 friction, 253 sound absorption, 1488-1493 Coins, weights, 29 Coke, combustion, 1272 specific gravity and weight, 1503 Cold-air ducts, furnaces, 1319 Cold-bending tests, iron and steel, 378, 384, 385, 914 Cold-storage, temperature, 1693 Collar-beam, 1810 Colleges, architectural, 1779 Color, light-sources, 1438 mortar, 1547 Colorado, registration law, 1778 Column, columns, bases (see Bases, columns) • base-plates, 440-445, 1524 bearing-brackets, 445-447 bearing-plates, 440-445, 1524 bending moments, 485. Bethlehem, 475, 479, 482-488 loads, tables, 483, 506-515 box, 342, 467, 479, 484 caps (see Column-caps) cast-iron, 455, 466 advantages and disadvantages, 455 bearing-brackets, 445-447 breaking-loads, 462 connections, 445, 447, 457, 458, Column, cast-iron, cylindrical, 456, 457, 459, 461, 1523' design, 456-459 failure by fire, 780 fireproofing for, 781, 822-826 H-shape, 456, 458 inspection, 456 reinforced-concrete, connections, 945 safe loads, 461-466 square, hollow, 456, 458, 461, 1522 strength, 459-466, 480-482 weight, 1522, 1523 channel (see Channel, columns) classification, 448 concrete, not reinforced, 284 cross-sections, moments of inertia, 342, 343 radii of gyration, 344, 345 definitions, 448, 467, 477, 1810 eccentric loading, pipe columns, 472 eccentric loading, steel columns, 485- 488 eccentric loading, wooden columns, 453, 454 fireproofing for, 468, 780-782, 822- 826, 959, 960 footings (see Column-footings) general principles, 448 H columns, 456, 458, 459 economy, 458, 474, 483 safe loads, cast-iron, 466 safe loads, steel, 506-515 I-beam columns, 474, 488, 504, 505 Lally, 467^ 474, 477 loads, 488, 516 lattice, 477-479 lengths, schedule for, 492 loads, live, proportion, 148-152, 489, 490, 1196, 1198 tables, 488-490, 493-554 mill-construction, 782-788, 969, 976- 978, 980, 981 cost, 810 pipe, 469-474, 488 loads, 488, 497, 498 plate-and-angle (see Columns, steel) reinforced-concrete, 941-946, 969, 980 calculations for, 976, 977 fire-proofed, 958-959 metal-core, 944-945 safe loads, tables, 482, 490, 493- 554 slenderness-ratio, 448 steel, 467-554 bases for, 473-477 beam columns, safe loads, 504-50S box, 342, 343, 467, 479 channel (see Channel, columns) rhniVp of tvne. a67— a68 Index 1867 Column, steel, connections, 468, 470, 471, 473-478, 945-946 connections in wind-bracing, 11 74, 1175, 1179, 1189, 1190 cost, 467, 468, 1207 design, 482-485 eccentric loading, 485-488 examples, 482-488 failure, 469, 819 fireproofing for, 468, 780, 782, 819, 822-826 formulas, 480-482, 485, 493-496 diagram, 496 Gordon's formula, 481, 484, 485, 486, 487, 493-485, 496 Rankine's formula, 481, 484, 493, 469 straight-line, 481, 482, 493, 496, 1139 H-column, table of loads, 483, 504-515 lattice, 477-479 loads, 1196, 1198, 1201 loads, proportion, 148-152, 489- 490, 1196, 1198 loads, tables, 488-490, 493-554 plate-and-angle, 467,488,517-532 (see Plate-and-angle column) reinforced concrete, 946 section, 467, 468 splices, 1201 strength, general principles, 480- 482 stresses, 618, 1138, 1200 struts, angle, safe loads, 488, 501- 503 types, 467, 477 steel-pipe, 469-474 loads, 488, 497, 498 struts in trusses, 480, 499-503 wind-bracing, 1174, 1183, 1189, 1190 wooden, bases for, 782-788 bolsters, 454, 795 eccentric loading, 453, 454 factor of safety, 448 formulas, 450, 11 39 metal caps, 454, 762, 782-788, 795- 800 mill-construction, 782-788 safe loads, 448, 449, 45© tables, 451, 452 strength, general principles, 448- 450 wrought-iron, fireproofing, 780,819 Column-bases (see Bases) Column-caps, metal for wood, 454, 762, 782-788, 795-800 for steel-pipe columns, 470, 471, 472 Column-footings, bearing-plates for, 440-445 • desiern. 178-188 Column-footings, loads for design, 151, 152, 160 moments, 176-178 plan, 1 195 proportioning, 152-164 reinforced concrete, 186, 974, 978-982 Colunin-sheets, 490 Combined stresses, 128, 480, 572, 11 14 Commercial weights and measures, 28 Commodes, dimensions, 1638, 1640 Competitions, architectural, 1 733-1 747 ethics, 1729 Composite Order, 1702 Composite piles, timber and concrete, 198 Composition, forces, 288 Compound sections, moment of inertia, radius of gyration, 344 Compression, 127 members, steel, specification, 1201- 1203 sig-, 1065, 1068 Concrete (see, also, Reinforced con- crete), 240 adhesion to steel, 912, 919, 920, 938, 940 aggregates, 241, 287, 908, 909, 945 effect of heat, 817 strength, 287 beam-protection, 860 beams, not reinforced, 628, 637 coefficients for, 628 fiber-stresses, 557 bearing surface, 285 blocks, 816, 956 fire test, 956, 957 machinery for, 816 walls, 233 bonding old and new, 965 capping of piles, 191 cinder, 242, 250, 909, 930 corrosion of steel, 818, 960, 961 fire-resistance, 818 weight, 250 column-protection, 780-782, 822- 826 columns, 284 compression-tests, 283 compressive strength, 283, 287, 441 tests, 284-286 working stresses, 265-267, 287, 441, 911 consistency, 243, 286 corrosion of steel, 818, 960, 961 cost, 249-250, 910 dehydration of, 245 design of massive, 246 electrical action, 17 13 finish of surfaces, 246, 965 1S6^ Index Concrete, fireproofing, column-protec- tion, 780, 782, 822-826 concrete blocks, 816, 956 roofs, 866, 871 tests, 245, 955-960 warehouse-construction, 780-782 flour-mixtures, 17 12 forms, 245, 962-965 freezing-temperature, 244 gravel, 241, 286, 908 heat, conductivity, 245 effect of, 245, 817, 957-958 I-beam protection, 780, 847 ceilings, 849 roofs, 871 I beams, 854 laitance, 244 limestone, weight, 250 mass, strength, 267 design, 246 materials, proportions, 243, 247, 907, 909-910,945 mechanical analysis, 910 mixers, 963 mixing, 242, 243, 963 mixtures, 909-910, 945, 963-964, 1712 modulus of elasticity, 934, 935 blocks, heated, 956 design, assumption, 924 ratio to steel, 912 modulus of rupture, 284 molds for, 962-966 natural cement, 235, 267, 284 painting, 1573 partitions, 876, 881 penetrative washes, 171 2 permeability, causes, 1710 pile-capping, 191 piles (see Piles) pipe-column filling, 469 placing, 244 plant-cost, 250 Portland-cement, 240-251 pouring, 964 preparing, 242 properties, 240 proportions, 240, 243, 247-249, 907, 910,945, 1712 protective coatings, 171 2 ramming, 964 reinforced (see Reinforced concrete) retempering, 244 rubble, 244 saline waters, 1713 sand in, 241, 247, 908 grading, 241 shearing strength, 284 shrinkage, 245 slag, fire-resistance, 817 specific gravity, 1503 Concrete, stone (see Concrete, aggre- gate) strength (see Concrete, compression) tensile, 284 surface-finish, 246, 965, 1555 temperature-changes, 245 tensile strength, 284 test for hardening, 245 tests, 283-287, 817 tile, strength of, 817 tiles, 816 tools, 963-964 cost, 250 transporting, 964 trap-rock, 250, 817 tremie, use of, 244 under-water, 244 uses, 240, 906 walls, 228-229, 946-947, 965, 966 cost, 250 water used in, 242, 909 waterproofing, 246, 1 709-1 717 weight, 250, 1503 Conductors, electricity, 1458 lightning, 1704-1707 water, roofs, 1658 Conduits, electric-wiring, 1479 Cone, 38 center of gravity, 295 frustum, 38, 61, 63 surface, 61 volume, 63 Conic sections, 38 Coniferous woods, ultimate unit stresses, 649 Connections (see under Columns, Beams, etc.) Consoles (Glossary), 181 1 terra-cotta, 278 Construction, insurance during, 1756 Continuous beams and girders, 555, 671-680, 979, 980 Contract drawings, 1753 Contracts, arbitration, 1763 architect and ov/ner, 1740, 1746 contractor and owner, 1751 forms, 1750, 1752 owner and competitor, 1740, 1746 subcontractor and contractor, 1765 uniform, 1749 Contractor vs. Architect, relation, 1729 Contractor's insurance, 1756 Conversion tables, metric, 33-35 Coping (Glossary), 181 1 stone, 1539 Copper, roofs, 1604 - sheets, 1049, 1510-1511 specific gravity and weight, 1503, 1510 wire, 401, 1469, 1474, 1513 current capacity, 1470 Index 1869 Corbel (Glossary), iSii Cords, sash i,see Sash-cords) Core-borings, foundation-bed testing, 145 Cores, steel, in concrete columns, 441 reduction for, in castings, 1521 Corinthian Order, 1702, 1703 Comer-basins, dimensions, 1641 Comer-slabs, dimensions, 1641 Cornices (Glossary), 181 1 mills, 764, 769 Corr-bars, 916, 923 Corr-mesh, 853 Corrosion, cinder concrete on sleel, 818, 960, 961 Corrugated bars, 916 Corrugated iron and steel roofing, 1046, 1049, i599-'i6o4 Cormgated sheets, 1599-1604 anti-condens- tion lining, 1603 ceilings, 1604 covering capacity, 1603 floors and roofs, 851 galvanizing, 1600, 1604 gauges, 402, 1 5 10, 1600 laying, 1601 sides, building, 1603 weight, 1600, 1603 Cosecants, tables of natural, 117 Cosines, tables of natural, 95 Cost, costs, brickwork, 1 544-1 547 mill-buildings, 808-810 buildings, cubic foot, 1611-1634 building-papers, 1568 carpenters' work, 1564 cement, 238, 248, 910 columns, mill-construction, 810 concrete, 249-250, 9io. i6i3, 1618 cubic foot, buildings, 1611-1634 cut stonework, 1539 drafting, structural steel, 1206 driving wooden piles, 195 ilvvellings, 161 3 elevators, 1659, 1670 enameled bricks, IS44 erecting structural steel, 1206 estimating, buildings, 1611-1635 excavating, 153^^ exposition-buildings, 1627 Federal buildings, 1613, 1626-1633 felts, 1565, 1568 tire-proof partitions, 889 flagstones, i539 floors in mills, 810 glass, 1574-1577 polished plate, 1576 sheet, 1575 skylight, 1580 window, 1577 incandescent lighting, 1482 labor, 1564 Cost, lathing and plastering, 1557 library-stacks, 1697 mill-construction, reinforccd-concreto, 777, 1613, 1618 slow-burning, 758, 77: mineral wool, i6io office-buildings, 1613 partitions, sound-deadening, 889 piles, driving, 195 pitch-slag, roofs, 1598 plumbing-fixtures, 810 public building, 1613, 1628-1634 refrigeration, 1695 reinforced concrete, 250, 910, 1613, 1618 roofs, mill-buildings, 777, 810 roofing, asphalt-gravel, i599 gravel, 1598 slag, 1598 slate, 1046, 1585 tile, 1046, 1587. 1607 tin, 1046. 1589, 1593, 1594 saw-tooth roofs, 777 school-buildings, 1613, 1614, 1616 slates, 1046, 1585 slow-burning construction, 758, 802- 810, 1619 square foot, buildings, 1627-1634 steel, structural, 1204-1212 stonework, 1538 tiles, 1046, 1587, 1607 tin, gutter-strips, 1594 rolls, 1594 roofing, 1046, 1589, 1593, 1594 trusses, steel, 1206 warehouses, 777, 802-810 Cotangents, tables of natural, 115 Cotton, weight, 72a Cotton-mill, design and cost, 803 Cotton rope, 406 Counterbraces, wooden trusses, 1000- 1006, 1034, 1 104 Counterforts, retaining walls, 263 Counter-ties, 3S6 Counterthrust, 305 Cover-plates, box girders, 696 plate girders, 687 riveting, 421,422 Crane, chain, 410 clearance-diagram, 119S load, 1197, 1201 truss, 1069 Creosote, 1570 oil, 1503 Crockery, weight, 723 Cross (Glossary), 181 a Cross-sections, 332-374 Crown, of arch, 305 Crushing strength (see under each ma- terial) Cubage, 161 2 1870 Index Cube, cubes, 38 Cube root, 4 tables, 8-24 Cubic measure, 27 metric, 31 Cummings system, reinforcing, 923 Cupola process, iron, 1379 Curbing-stones, 1539 Cycloid, definition, 80 problems on, 80 Cylinders, 38, 63 contents of, various diameters .1403 Cypress, beams, distributed loads, 641 deflection, 664 flexure-stress, 557, 650 columns, safe loads, 450, 452 crushing-loads, across the grain, 454 with the grain, 449 specific gravity, 1503 ultirtiate stresses, 650 weight, 650, 1503 working stresses, 647 Dahlstrom metal doors, 896 Dams, concrete, cost of, 250 Dead load, definition, 126 Deadening partitions, 890 Deadening-quilts, 1565 Decagon, 37 Decimals of inch, table, 26 Deck-beams, steel, loads, 565 Deflection, beams, 663-670 allowed, 566, 628, 664, 736 steel, 566, 612, 668-670, 677 wooden, 636, 653, 654-657 continuous girder, 674-676 diagram, 670 Deformation, definition, 125 Degree, degrees, of heat, 1250 Density, 1247 Denver building code, masonry-loads, 267, 287 thickness of walls, 231-232 Department-stores, steel, weight, 1208 Depreciation of buildings, 1634 Derrick, rope for, 408 Desks, sizes, 1640, 1645 Details, structural, specifications, 1202 Diagonals, 37 Diameters, 37, 1814 Diamond bar, reinforcement, 917 Diamond bits, foundation-bed, testing, 145 Diamond-mesh lath, 884 Dimensions, useful, 1637-1658 Dodecagon, 37 Dogwood, hardness, 1558 Dolomite, 131, 132 Domes, 1213-1231 (Glossary), 1814 angle, critical, 1213 reintorced concrete, 121 7, 1225-1231 Domes, ribbed, 1222 secondary stresses, 1220 smooth-shell, 12 13 steel, 1222 weight, 1224 Door, doors, fire-resisting, 801 iron, standard, definition, 1854 metal and metal-covered, 894-897, 901-902 school-buildings, 1648 Door-frames, cement, 898 metal, 897 terra-cotta, 898-899 Door-sills, stone, 1539 Doric Order, 1 699-1 700 Double-plenum-chamber system, heat- ing, 1327 Douglas fir, beams, distributed loads, 642 deflection in, 664 flexure, 557, 628, 647, 650 columns, safe loads, 451 crushing-loads, with the grain, 449 crushing strength, across the grain, 454 specific gravity, 1503 unit stresses, 376, 412, 647, 650 weight, 650, 1503 Dovetailing (Glossary), 181 5 Dowel (Glossary), 1815 Documents, American Institute of Architects, list, 1767 standard, American Institute of Architects, 1748 Draft, definition, 1364 natural, air-velocity, 1302 Drafting, structural, cost, 1206 Drain, drains, 1407-1414 area, 1408 cellar, 142 1 house, 1407-1414, 1419-1421 Drain-pipes (see Pipes) Drainage of buildings, 1407-1414, 1419- 1421 Drainer, cellar, 142 1 Drawings, architect's, 1728, 1754 competitive, 1737, I744. I745> 174^ contract, 1753 property of architect, 1733 shop, 1754 working, steelwork, 1195 Drift-pins, 414, 682 Drill-rooms, floor-loads, 719 Drop-hammer, pile-driving, 190 Drum-trap, 141 3 Dry measure, 27 Dry-rot, 759 Du Long's formula, heat of coal, 1272 Duchemin's formula, wind, 1199 Ducts, air, design, 1333-1341 cold-air, furnaces, 1319 Index IS71 Ducts, fresh-air, sizes, 1322 hot-air, area, 1301 metal gauge, 1336 system, design, 1346 Dwellings (see also Residences) cellar walls, 229 cost of constructing, 1613, 1614 floor-joists, 737, 742 floor-loads, 149, 719, 1198 heating, 1256, 1353, 1361-1363 wall-thickness, 230, 232 Dyestaffs, weight of, 723 Earthy material, 132 weight, 1537 Eastern fir, safe load, 639 safe stress, 647 Ecceitric loads (see Loads, eccentric) EchiDes, acoustics, 1487 Edncitioa, registration laws, 1769 Eljcitioaal institutions, 1779 Ejflaressence, brickwork, 1547 Egyptiii long measures, 34 Egyptian style, architecture, 1704 Elastic limit, definition, 126, 381, 913 Elasticity, coefficient or modulus of, 126, 626, 662 reinforced concrete, 912, 934 steel, 381, 912, 934 timbsr. 647, 731-734 Elbows, heating, pressure-loss, 1338 Electric work for buildings, 1457-1485 cabinet-wiring, i477, 1481 center of distributioA, 1471 circuit-breakers, 1461 cods-requirements, 1480-1482 conductors, 1458 conduit system, 1479 cost, of lighting-equipment, 1482 of wiring, 1482 design of lighting systems, 1446-1448 drop of potential, 1470 feed-wires, 1478 fuse, enclosed, 1461 fuse-block, 1481 insulators, 1458 interior wiring, 1482 knife-switch, i477, 1479 lamp-arrangement, 1465, 1466 lamps, number of, 1446, i449» ^475 national electrical code, 1480 power-computations, I4S9 speciflcations, 1482 switches, 1478, I479 systems of lighting, 1464-1469 wire-calculations, 1469-1472 wire, dimensions, weights, i474, i475, 1477 carrying capacity, 1470, I473, I475 wiring-diagram, 1476 symbols, 1476-1478, 1484 Electricity, 1457-1464 Electrolysis, reinforced-concrete foot- ings, 186 Elevator, 1659-1677 car-platform, 1661, 1666, 1675, 1676 comparison of types, 1660, 1664, 1670 cost, 1659, 1670 counterweights, protection of, 1662 development of systems, 1667-1669 economic considerations, 167 1 efficiency, 1659 electric, 1659, 1666, 1669, 1676, 1677 versus hydraulic, 1660, 1664, 1670 passenger systems, 1667-1670 express, 1661, 1673, 1675 geared, 1659, 1669 gearless, 1659, 1665 hatchway, size, 1660, 1667, 1675, 1676 hoistway, 1660, 1662 hydraulic plunger, 1670 versus electric, 1660, 1664, 1670 installation-data, 1663, 1674, 1675 laws governing, 1663 loads, 1662, 1674 local, 1661, 1673, 1675 machinery-room, 1660 motors, current-consumption, 1677 feeders, 1677 sizes, 1676, 1677 number required, i66i, 1673 operating-costs, 1670 power-diagrams, 167 1 push-button control, 1666 safety-appliance, 1664, 1669, 1672 service, formulas for, 1673 signal-systems, 1672 sizes, 1661, 1667, 1675 specifications, 1663 speeds, 1662, 1674 standard designs, 1663 time-schedule, 167 1 towers for, in mills, 764, 765, 768 traction, 1665, 1669, 1670 traffic-capacity, 1672 types, 1660, 1668 use of, 1667 Elevator-tower, mill-construction, 764, 765 storehouse, 768 Ellipse, 38 center of gravity, 293 problems on, 74, 79 Ellipsoids, 60, 65 Elm, ha dne-.3, 1558 specific gravity, 1503 ultimate unit stresses, 651 weight, 651, 1503 working stress, flexure, 557 Elongation, eye-bars, 386 steel, 38T, 384, 913 1872 Index Enamel, painting, 1570 Enameled tile, 1605-1607 Energy, work, 1248 and power, relation, 1250 Engineering, architectural, terms used, 124, 128 Engineering News formula for pile foundations, 193 Engines, fire, dimensions, 1642 foundations for, 1716 hot-air, 1393 Eimeagon, 37 Entasis (Glossary), 1817 Entropy, of steam, 1254 Equilibrium, 124 of parallel forces, 290 polygon, forces, 289, 299, 313-315, 319 Estimates, architects', 1728 guaranteed, 1731 Estimating (see Costs) quantity system of, 1635-1637 Ethics, professional, 1729, 1731 Eustyle (Glossary), 181 7 Evaporation, 1251-1254 equivalent, boiler, 1274 Evolution, mathematics, 3-5 Examination, architects. New York state, 1.772 Excavation, 200-222 below water, 203 bracing, 201 Chicago method, 209 data on, 1536 dredged wells, 210 earth-pressure, 201, 205 freezing process, 214 needling, 218-222 open-caisson method, 210 pneumatic -caisson method, 21 1-2 14 poling-board method, 209 protecting adjoining structures, 214- 222 quicksand, 137, 211 rock, 1537 sheet piling, 200-209 shoring, 214-222 underpinning, 214, 218-222 volume of, computing, 65 well-curb method, 210 well-digger's method, 211 Expanded metal, 846-847, 883-884, 919 Expansion-bolts, 1534 Expansion- tank, 1360 hot-water heating, 1307, 1308 Exposition-buildings, cost of, 1627 Expenses, architects, 1731 Expert, in competitions, i735 services, payment, 1728 Extrados, arch, 305 Eye-bars, 386, 395 Face, arch, 305 Face-wall, definition, 255 Factor of safety, 126, 375, 556 Factories, air-changes, 1260, 1353 brick, 808-810 heating, direct radiation, 1296 hot-blast, 1324, 1336, 1342-1347 temperature, 1256 non-fireproof, height, 813 reinforced-concrete, 968-997 steel, 1210, 1627 wooden construction, 758-810, 1634 Fahrenheit thermometer, 1250 Fan, maximum speed, 1357 ventilation, 1341-1347, 1357 Fj.n system, heating, 13 24-1341 Fan trusses, 1025-1029,1145 stresses, 1058-1060, 1078, 1145 Federal buildings, cost, 1613, 1626 1633 Feed-wires, electric, 1478 Fees, architects', 1731 Feet converted into meters, 34, 35 Feldspar, 131 specific gravity and weight, 1504 Fellowships, architectural, 177 9- 1788 Felts, asbestos, 1567 building, 1564-1568 cost, 1565, 1568 Ferroinclave, floors, 850-851 roofs, 851 stair-construction, 900-901 Fiber-stresses (see, also, under each material), 126, 556, 557 Field-rivets (see Rivets) Fillers, web-stififeners, 686 Filters, water, 142 1 Finial (Glossary), 181 8 Fink truss, 1025-1030, 1161-1164 cambered, stresses, 1079-1081 stresses, 1058-1061 steel members, 1148, 1 161-1 164 Fir, Douglas (see Douglas fir) Eastern, beams, safe loads, 639 unit stresses, 647 Fire-clay, flue-linings, 1281 Fire-doors, metal-covered, 894-897, 901-902 stairways, 779 tin-covered, 901, 1855 Fire-engines, dimensions, 1642 Fire-escapes, warehouses, 764, 765, 778, 779 Fire-extinguishers, 903-905 Fire-protection, alarm system, electric, 903-905 doors (see Fire-doors) fire-extinguishers, 903-905 fire-retardants, 759 hose, 768 hose-reels, 905 outside hazard, 901-903 Index 1873 Fire-protection, partitions, 8oi pumps for fire-streams, 759, 1401 roof nozzles, 801 scuppers, 767 shutters, 759, 778, 801, 901, 902 signaling systems, 905 sprinklers, 801, 903 90S mill-buildings, 759, 7^8 timber-spacing, 777 tanks, 779 stairways, 764, 765, 778, 779 ' standpipes, 768, 801, 905 steam-pumps, 1401 steelwork, 468, 760, 780-782, 819, 822-826 tanks, 779, 1402 water-supplies, 802 wire-glass, 759, 778, 821 Fire-pumps, steam, 759, 1401 Fire -resistance of materials (see Fire- proofing) Fire-stops, mill-construction, 759 Fire-streams, 1397 pumps for, 1401 Fire-tests (see Tests) * Fire-towers, 764, 765, 778, 779 Fire- walls, storehouses, 765 Fireplaces, flues, 1282 Fireproofing, asbestic plaster, 818 asbestos, 819 beams and girders, 780-782, 827-842, 844, 849, 854-860 brickwork, 814 buildings, 811-905 cost of, 802, 812, 1619-1625 percentages of cost, 1619 ceilings, 871-872 columns, cast-iron, 781, 822-826 steel, 468, 780-782, 822-826 wrought-iron, 780, 819 concrete, column-protection, 824-826 concrete blocks, 816-818, 956 floors, 860-866 roofs, 866 tests, 245, 955-960 warehouse-construction, 780-702 flooring, 892-893 floors, 826-866 interior finish and fittings, 893-901 materials, 811-905 fire-resistance, 245, 814-822, 955 960 mortars, 818 municipal definitions, 811, i»53 paint, 821-822, 894 partitions, 873-892 plaster, 818, 878 882, 889-891 plaster of Paris, 818 prism glass, 821 reinforced-concrete, 781, 811, 955 960 Fireproofing, roofs, 801,866-872, 1597 stairs, 899-900. 947, 983 steel, 468, 760, 780, 822- 826 stone, 814 terra-cotta, 234, 814-815, 828, 874 trusses, 860 wall-coverings, 881-892 wire-glass, 821 wood, fire-proof, 820, 894-895 Fires, cast-iron in, 819 steel and wrought-iron in, 819 concrete affected, 245, 955-96o Fish-plate, roof -trusses, 11 55 Flagpoles, dimensions, 1644 Flagstones, 282, 1539 Flashings (Glossary), 1818 Flats, steel,- safe loads, 389 Flexure, 126, 324-331, 332-334, 555 reinforced-concrete beams, 924-941 steel beams, 564-573 wooden beams, 627-637, 647-656 Flint, 130 specific gravity and weight, 1504 tile, 1605 Flitch-plates, beams and girders, 655. 656 Floor, floors, asphalt, 1608 Akme system, 949 beam-and-slab, 968 Berger's metal lumber and concrete, 852,858 brick arches, 827 cantilever flat slab, 95© Climax system, 85s Corr-plate system, 950 Excelsior, tile, 838 expanded-metal and concrete, 847 Ferroinclave, 850-851 fire-proof, brick and tile, 826-842 concrete, 842-866 fire tests, 827 flat reinforced, 845-846, 949-952 Floredome system, 953 Floretyle system, 952-953 framing, steel (see Frammg) girderless, 968, 993-997 _ girders, steel, specifications, 1201, 1202 Guastavino, 841-842, 843, i243 heat-transmission, 1259 heating pipes through, 1360 Herculean, 838-839 I-beam system, concrete, 854-855 Johnson construction, 837-841 joists (see Floor-joists) keys, tile, 835 loads (see Loads) lock-woven fabric, 849-850 M system, 948-949 metal lumber, 858 1874 index Floor, mill, 730, 760, 766, 769, 782-794 (see Mill-construction) New York, tile. S40 reinforced-concrete, 842-856, 924- 940, 948 955, 968, 971 cost, 250 design, 985-99? four-way reinforcement, 949 girderless, 968, 993-997 mushroom system, 950, 993-997 S. M. I. system, 950 top coat, 239 triangular-mesh fabric, 850 reinforced tile, 838-842 sectional systems, 853-854 segmental, concrete, 844-845 tile, 831, 832 separately-molded, 953 - side-construction, 830-833 Siegwart system, 855 skewbacks, tile, 834, 835 square-panel system, 968 steel framing, computations, 861-866 System M, 948 terra-cotta, 828-840, 1604-1607 tie-rods, 307, 832 tile, 828-840, 953, 1 604- 1 607 tile-and-concrete, 951-952 end-construction, 829, 833, 837 Vaughan system, 856 Waite's concrete I-beam system, 854 warehouses, 764, 777 Watson system, 856 weight (see Loads) of wooden construction, 718 welded-metal fabric, 848 wire fabrics, 848-850 wooden, cost, 810 estimating, 1563 framing, 721-731, 746-757 mill-construction, 730, 760, 766 old, strength, 749 plank, 730-735 strength and stiffness, 717-757 warehouses, 764, 777, 893 workshop, 769 Floor-joists, wooden, assembly-halls, maximum span, 739, 744 bridging, 748, 749, 1804 churches, 738, 743 continuous, 717 corridors, 739, 744 dwellings, span, 737, 742 framing-details, 749-757, 782-795 hangers, 750-757, 782-794 nominal and actual sizes, 637 office-buildings, 738, 743 plans, 717, 727, 747 school-buildings, 717, 737, 742 size, 637 spans, maximum, 736-746 Floor-joists, wooden, stiffness, tablei 635, 638-646 stirrups, 750, 751, 754-757, 787-79 stores, span, 739, 744 strength, tables, 635, 638-646 tenements, 737, 742 theaters, maximum span, 738, 743 weight, wooden, 718 Floor-slabs (see Reinforced concrete slabs) Floor-tiling (see Flooring) Flooring, banks, 893 cem^ent, 831, 893 composition, 893 concrete finish, 965 fire-proof, 893 hotels, 893 matched, 1563 mortar over concrete, 965 Mosaic, 1607 slate, 1606 terrazzo, 1607 tiling, 1604-1607 toilet-rooms, 893 • warehouses, 764, 777, 892, 893 wooden, cost, 810 estimating, 1563 mill-construction, 760, 766 old, strength, 749 plank, 730-735 _ strength and stiffness, 717-757 Floredome, 953 Flore tyle, 952-953 Floriluxe, 1579 Flues, 1281-1283, 1365 gas-velocity, 1364 vent, 1356, 1357 Fluid measure, 28 Flushometer, Kenney, 1420 Font (Glossary), 1819 Foot-baths, dimensions, 1641 Foot-car die, 1439, 1440 Footings, 129, 223 (see also, Founda- tions) areas, minimum, 152 bending-stresses, 172-178 brick, 226, 227 cantilever, 165-169, 978 columns, design, 178-188 loads for design, 151, 152, i6o proportioning, 155-164 moments, 176-178. reinforced-concrete, 974, 978-982 compound, 178 concentric loads, 160 concrete, 225, 226 cost, 250 design, 179 reinforced, 186, 946, 978 conditions affecting, 188 continuous beams, 979 Index 1875 Footings, courses, 129, 169-172, 223 cracks in, 224 crushing, failure by, 171 defined, 1852 depth of, minimum, 188 design of, 178, 978 eccentric loads, 162 factor of safety, 178 failure of, 170-172 flexural strength, 178-179 grillage, steel, 166-169, 181-185 homogeneous slabs, 178 inverted arches, 227-228 light buildings, 223 loads, 148-163, 170, 223, 265-267, 978 offsets, 163-165, 179, 223-227 piers (see Footings, columns, and Piers, footings) projection and depth, ratio, 180-181 reinforced-concrete, 186, 946, 978 electrolysis 186 retainiug-vvalls, 261, 262 settlement, 152-160 shear, failure by, 170-171 size and form, 169 slabs, homogeneous, 178 spreading, failure by, 171 steel beams in, 181-185 stone, 223-224 stresses, 169-178 timber, 186-188 unit and separate-layer compared, i8o Foot-pound, 290 Foot-pound-second system, 1247, 1250 to B.t.u., 1251 Force, forces, 124 axial, 375 center of gravity, 127, 291-296 composition, 288, 1065 compression, 127, 1065, 1068-1072 equilibrium, 124, 289, 299, 313-315, 319 external, 125, 325, 1066 graphic statics, 1065 internal, 125, 325, 1066 lever, principle of, 165, 290-294 line of action, 289 magnitude, 288 moments of, 127, 289, 322 parallel, 290-291 parallelogram of^ 289 point of application, 289 polygon of, 289, 1070 reactions, beams, 322-324 trusses, 1066 resolution, 288, 1065 resultant, 288 sense of, 289 signs for, 1065, 1068, 1072 shear, 128 Force, stress (see Stress) tension, 127, 1065, 1068, 1072 torsion, 128 triangle of, 289 Forge-shop, steel, weight, 1209 Forked loop, tension-member, 387 Forms for concrete, 245, 962-965 Fossiliferous limestones, 132 Foundation ( ee, also. Footings and Foundation-beds), 129-222 adjoining excavations, 130, 147 adjoining structures, protecting, 214 brick, 226-227 caisson, 210-214 cantilevers in, 165-169, 978 Cathedral of St. John the Divine, 251 columns, 161-163, 176-178, 184, 974, 978-982 concrete, 225, 226, 249-251 early examples, 251 pile, 188, 196-200 reinforced, 186, 196, 978 conditions affecting, 188 definition, 129, 1852 depth, 188 engine, water-proof cement, 17 16 excavating for, 200-214 (see, also, Excavation) footings (see Footings) general requirements, 129, 130 girdering-method, 166-169 grillage, steel, 166-169, 181-185, 678 light buildings, 223-229 Manhattan Life Insurance Building, 251 mining districts, 147 needling, 218-222 piers, 129, 188 200 pile, reinforced-concrete, 196-200 sheet, 201-209 wooden, 188-196 reinforced-concrete, 186, 946-947,978 screw-jacks, 215, 216, 221 settlement, equal, 152-160 sewers, 147 shafts, 147 shoring, 214-222 spread, 166-169, 181-188, 978, 980 subways, 148 temporary buildings, 187 timber, spread, 186-188 trenches, 147 tunnels, 148 underuinning, 214, 218-222 walls, 129, 200, 228, 229, 979 Washington Monument, 251 waterproofing, 1709-1717 wedges, 215 wells, 147 , » J Foundation-beds (see, also. Founda- tions), 129 -148, 223, 1876 Index Foundation-beds, boulders, 134, 136, 141 clay, 13s, 138, 139, 141, 143 dirt, 135 drill tests, 145 earthy material, 132-133, 135, 138- 140 filled ground, 140 geological considerations, 130 glacial deposits, 133 hard-pan, 135, 141, 143 gravel, 134, 136, 141. i43 loads on, 140-143, 148-160, 223 tests, 142-146 loam, 13s, 143 materials composing, 130-140 mould, 13s mud, 135, 139 peat, 135, 139 pipe-borings, 144, 145 quicksand, 136, 137, 141, 143 river-deposits, 133 rock, 130-132, 134, 135, 141 sand, 134, 136-138, 141, 143 shale, 13 s silt, 135, 139 soil, 132,. 135, 143 testing, 141-146 topographical conditions, 146 trenches for footings, 226 varying pressure on, 163-164 Foundry-castings, 379 Foundry, heating-temperature, 1256 lighting, 1451 steel, weight, 1209 Frames, door, 898, 899 window (see Window-frames) Framing, floors, wooden, 721-731, 746- 757 mill-construction, 760-764, 766, 769, 782-794 saw-tooth roof, 772-777 steel beams, 612-618 cast-iron columns, 445, 447, 457, 458, 946 fire-proof floors, 861-86G Lally columns, 474, 477 steel columns, 468, 470, 471, 473- 478, 945, 946 wooden floors, 616, 752, 753, 755, 786-792 truss-jomts, 1149-1170 arched, 1024, 1039 heel, 434-439, 1003, 11S0-1170 iron ties, 1019 lattice truss, 1008, 1009 pin-connected, 423-429 wind-bracing, 1174-1176, 1183-1193 Freight rates, structural steel, 1205 Freight-cars, capacity, 1643 French truss, 1026 Friction, theorem, 252-254 water in pipes, 1388 Frostproofing, pipes, 1400 Frustum, of cone, 38, 61, 63-64 of pyramid, 38, 61, 64 Fuels, 1 271-1273 air required, 1272 boiler-rating affected, 1277 calorific value, 1271, 1272, 1273 combustion, 1272, 1273 consumption, heating-boilers, 1278 heating, example, 131 7 Fulcrum, grillage, 166 Furnace, combination, 1358 pipes, 1311, 1318, 1322, 1358-1360 ratings, 1314 registers, 1317-1320, 1355, 1358 1360 air-velocity, 1367 pressure loss, 1338 symbol, 1350 stack, 1312, 1317, 1322, 1358 work, specifications, 1357-1359 Furnace-heating, 1310-1324 fuels, 1317 specifications, 1357-1359 where used, 1355 Furnace-iron, 379 Furnace-leaders, 1311, 1317, 1324, i35{ Furniture, dimensions, 1637-1640 metallic, 898-899 weight, 149 Furring, metal, 881, 892 mill-construction, 759 outside walls, 891 Fuses, electric work, 1461 Fusion, latent heat, 1251 Gable (Glossary), 1820 Gallon, capacity, 1247 Galvanized iron and steel, 1600, 1604 Garage, floor-load, 1198 Gargoyle (Glossary), 182 1 Gas, acetylene, 143 1 coal, 143 1 as fuel, 1273 gasoline, 1432 illuminating, 143 1-1436 illumination by, 1448, 1450, 1451 lamps, 1451 natural, 143 1 perfect, 1256 piping for, 1432-1436, 1445 velocities, flue and chimney, 1364 water, 1431 weight, 1273 Gas-pipe, separators, steel beam, 614 Gas-piping, 1432-1436 symbols, 1445 Gaskets, pipe, 1389 Gasoline, 1432 Index 1877 Gauges, American Steel and Wire, 401, 402, 1512 Brown & Sharpe, 401, 402, 1469, 1473, 1509, 1510 circular-mil, wire, 1469, 1473 corrugated sheets, 15 10, 1600 for air-duct metal, 1336 piano wire, 401 pressure, 1248 railroad-tracks, 1642 Roebling's wire, 403, 1509 sheet-thickness, 1509 standard, compared, 400, 402 U. S. standard, metal sheets, 402, 1600 Washburn & Moen, wire, 402, 1509 jears, size and speed, 1720 jener itor, electric, 1463 heat, 1309, 1316 jealo^lcal data, foundations, 130-140 jeo nstrical problems, 66-90 je 3 me try and Mensuration, 36-65 jirder, girders (see, also, Beams) bearing, 634, 687 Bethlehem girder beams, 358, 594- 597 box (see Box girders) built-up, wooden, 652-656 continuous, 555, 671-680, 979-980 deflection, 663-670 continuous girders, 674-676 double-beam, 564, 603, 604 tables, 607-611 fireproofing for, 780-782, 827-842, 849, 854-860 framing (see under Framing) grillage-foundations, 678 I beam, 603-611 latticed, 1008-1010, 1089-1091, 1181 wind-bracing, 1176, 1181, 1182 loads, tables of safe, S74-S9I, 594, 6o2, 605-611 plate (s33 Plate girders) reinforced-concrete, 972-974 riveted (see Box and Plate girders) steel (s3 3 Beams, steel) wall-support, 612, 792 wind-bracing, iiTi wooden (;c3 Beams, wooden) jirdering, cantilever foundations, 166, 169, 978 jliciil deposits, 133 jUss, cast, 1606 cost, 1574-1577 crystal-sheet, 157S defects, 1575 diffusion of light, I453-I456, i577- 1580 figured rolled, i577 grades, 1574 leaded, 1573 Glass, mills and warehouses, 759, 763 764, 769, 772 saw-tooth roof, 775 mirrors, 1580 Novus sanitary, 1606 plate, 1576 prism, 821, 1454-1456, 1578-1580 prism-plate, 1577 polished-plate, 1576 saw-tooth roof, 775 sheet, 1574 sizes, 1574-1577 skylights, 1580 specific gravity, 1504 tile, 1606 types of, for lighting, 1454 weight, 723, 1504. 165 1 window, 1577 wire, fire-protection, 759, 821 Glossary, 1796-1850 Gneiss, 132, 282 specific gravity and weight, 1504 Gold, specific gravity and weight, 1504 Gordon's formula, cast-iron and steel columns, 460, 461, 481, 484, 485, 487, 493-495, 496 Government buildings, cost, 1628-1634 Grain, weight, 723 Granite, 131 angle of friction, 253 beams, coefficients for, 628 fiber-stress, 557 compressive strength, 266, 280, 281, 282 allowed, 267, 287 curbing for sidewalks, 1539 fire-resistance, 814 modulus, of elasticity, '282 of rupture, 282 shearing strength, 282 specific gravity, 282, 1504 tension, 282 weight. 282, 1504 Graphical analysis, arches, 311-321 bending moments in beams, 328- 336, 564, 678, 690, 695, 698 bending moments, in pins, 426-429 column formulas, 496 deflection of beams, 670 domes, 1224 forces, 252, 288-291 friction, 252 moment of inertia, 345 piers and buttresses, 297-304 retaining-walls, 257-259 roof -trusses, 1065-1137 vaults, 1 234-1243 Graphite, specific gravity and weight, 1504 Grappier cement, 236 1878 Index Grate-area, boilers, 1276, 1283 Grate, furnace, 13 21 surface, heating-furnace, 1315 Gravel, angle of repose, 256 beds of, 133, 134 concrete aggregate, 286, 908 graded, 241 cost, 249, 250 definition of, 134, 136 roofing, 871, 1027, i595-i599 safe loads for foundations, 141, 143 specific gravity, 1504 weight, 256, 1504, 1537 Gravity, center of (see Center of grav- ity) Gravity, specific, substances, 1500-1508 Gray-iron castings, 379 specific gravity and weight, 1505 Grease-traps, 141 4 Grecian long measures, 34 Greek letters, symbols, 123 Grillages, beams, spacing, 182 cantilever foundations, 166 column-footings, 184 foundations, 166-169, 181-185 continuous girders, 678 fulcrum, foundations, 167 Groin (Glossary), 1821 Groined vaults, 1235-1240, 1822 Groins, 1235 Grouting, 269 brick footings, 227 Guastavino tile-arch system, 841, 8.12, 1243 Gum wood, unit stresses, 651 weight, 651 Gunnite, column-protection, 826 Gunter's chain, measure, 25 Gusset-plates, truss-joints, 11 60, ti6i wind-bracing, 1176, 1179-1186,1189, 1190, 1193 Gutters, 1590 mill-building, 769 proportioning, 1658 saw-tooth roof, 775 Gutter-strips, tin, cost, 1594 Guys, wire, 406 Gypsinite, partitions, 877-878 Gypsum, 131 floors, 856 plaster, 818, 1555 slabs, heat-transmission, 1259 specific gravity and weight, 1505 Gypsum-block, partitions, 876 Hjyration, radius of (see Radius of gyra- tion) H beams, base price, 1204 loads, table, 585 properties, 356 struts and columns, 474 H columns, 456, 458, 459 Bethlehem, 475, 479, 482-484, 487 table of loads, 483, 506 515 cast-iron, 456, 458, 459 safe loads, 466 Hair in plaster, 1555 Halls, air-changes, 1260, 1353 Hammer-beam truss, 1013-1018, 1087- 1089 Hammers, pile-drivers, 190, 193, 204 sheeting-plank, 202, 203 Hangers, beam and joist, 750-757, 782- 795 box, 753, 790, 792, 793 Duplex, 752-754, 784, 788-791, 793, 794 Goetz, 752, 792, 793 I-beam, 752, 753, 755, 788-790 Ideal, 754, 786 Lane, 756 mill-construction, 782, 785, 789 National, 755, 756 stirrup, 750, 756-757 strength, 756 Van Dorn, 755, 786, 791, 792 wall, 750-757, 783-788, 792-794 Hard-pan, 135, 141, 143 Hardwoods, unit stresses, 649 Hatchway, elevators, 1660, 1667, 1675, 1676 Haunch, arch, 305, 312 arches, filling of, 832 . Havermeyer bar, 917 Hawser-rope, 404 Hazlewood, hardness, 1558 Headers (Glossary), 1824 _ brick footings, 226 floor-framing, 728, 747, 749 Heat, 1249- 1 25 1 absolute, 1250 British thermal unit, 33, 1250, 1084 concrete fireproofing, effect on, 245, 827, 937. 955-959 furnace-rating, 13 14 horse-power equivalent, 1251 insulation, 1360, 1363, 1430, 1610 intensity, 1249-1251 latent, 1251-1252 loss, 1256-1264 furnace heating, 13 12 walls, 1256 measurement, 1247-1250 mechanical equivalent, 1251 of evaporation, 1251 of liquefaction, 1684 of the liquid, 1251 of vaporization, 1684 sensible, 1251 specific, 1250, 1684 steam, 1 249-1 254 thermometers, 1250 Index 1879 Heat, total, vapor, i2,';4 transfer of, 1256-1264, 1684 transmission by walls, 1 256-1264, 1684 Heater-room, location, 1357 Heaters, hot-blast, 1329 Heating, 1247-1363 air-changes per hour, 1260, 1261, 1353, 1354 blower system, 1324 cold-air supply, 1319, 1333 direct-indirect radiation, 1264 direct radiation, 1264, 1283, 1296 fan system, 1324-1341 furnace heating, 1310-1324, 1355 (see Furnace heating) gravity system.s, 1283, 1298 hot-air, 1310-1324 hot-and-cold system, 1327 hot-blast system, 1324-1341, 1346 example, 1342-1347 hot-water, 1302-1310 radiators, 1264, 1270 specification, 1359 Treasury Department, 1303, 1308 U. S. Gov't Buildings, 1303-1306, 1308 where used, 1355 mains and branches, 1284, 1289, 1291, 1350 radiating-surface, walls and win- dows, 1256, 1258, 1259 radiators (see Radiators) re-^isters (see Registers) residences, air-changes, 1353 hot-air, 1310-1324, 1357 hot-water, 1302-1310, 1359 temperatures, 1256 rules, 1354 steam, 1361-1363 requirements, buildings, 1 256-1 264, 1354 saw-tooth roofs, 776 specifications (see under each system) steam, 1264, 1283-1302 Bishop - Babcock - Becker system, 1287 direct, 12 83-1291 gravity system, 1283, 1298 hot-blast, 1324 low-pressure system, 1 291-1298 one-pipe gravity system, 1283-1285 Paul system, 1286 pipes (see Pipes) special gravity system, 1286 specification, 1361-1363 two-pipe gravity system, 1286 where used. 1355 structures, large, 1324 symbol? used, 1350 tanks, 1400 vacuum system, 1 287-1 291 Heating, water, by steam-coils, 1430 workshops, 769, 776 Hemlock, beams, coefficients for, 628 deflection, 664 ilexural strength, 557, 648 columns, safe loads, 452 compression, 449, 454, 647, 648, 650 crushing strength, across grain, 454, 648 crushing strength, with grain, 449, 648 modulus of elasticity, 647 safe loads, 638 shearing-stresses, 412, 647, 648, 650 specific gravity, 1505 tensile strength, 376, 647, 648, 650 weight, 650, 1505, 1558 Hemp rope, 406-408 Hennebique system, 920, 940 Heptagon, 37 Herculean floor-arch, 838-839 Herringbone metal lath, 884, 885 Hexagon, 37 Hickory, hardness, 1558 specific gravity, 1505 unit stress, 651 weight, 651, 1505 Hides, weight, 723 Hip-rafters, lengths and bevels, 90 Hoists, 1723 rope for, 404, 407 Hollow tile (see Terra-cotta) Homes, heating and ventilating re- quirements, 1354 Honeywell heat-generators, 1309, 1310 Hook-splice, roof -trusses, 1155 Hooks, for chains, 1723-1725 Hoops, water-tanks, 1398 Hornblende, 131 specific gravity and weight, 1505 Horse-power, 1248, 1250, 1460, 1720- 1722 boilers, 1274 chimney, 1368 electrical, 1460 heat-equivalent, 1251 machinery, 1720 pumps, 1397 raising water, 1397 transmitted, by belting, 17 21 by shafting, 1722 windmills, 1394 Horse-stalls, dimensions, 1643 Hose, 768 Hose-carriages, dimensions, 1642 Hose-reels, 905 Hospitals, heating-temperature, 1256 and ventilating requirements, I354-I3S7 non-fire-proof, height, 813 ventilation, 1349, i352, I3S3. I3S4- 1357 1880 Index Hot-air engines, 1393 Hot-air heating, 1310-1324 fuels, 13 1 7 Hot-and-cold system, heating, 1327 Hot-blast heating, 1324-1341 example, 1342-1347 radiation, 1324 Hot-water heating, direct, 1302-1310 radiators, 1264 specification, 1359 U. S. Gov't Buildings, 1303, 1306, 1308 where used, 1355 Hotels, fire-hose in, 905 floor-loads, live, 719, 1198 flooring, fire-proof, 892-893 furniture, weicht of, 149 non-fire-proof, height, 813 steel, weight, 1208 ventilation, 1353 House-tanks, size, 141 5 Howe truss, 999-1 ooS design of, 1142-1143 joint-details, 1151-1156 stresses by computation, 1063, 1065 by graphics, 1075-1077, 1102-1105 types, 1000- 1008 weight, 1057 Humidifying-apparatus, hot-blast heat- ing, 1324 Humidity, temperature-relation, 1352 Hydrants, mills, 759 Hydrated lime, 155 1 Hydraulic jacks, shoring, 215, 216. 221 Hydraulic lime, 235 (see Cements) Hydraulic limestone, 132 Hydraulic ram, 1390 Hydraulics, 1381-1406 Hyperbola, 38 problems on, 79-80 Hyperboloid of revolution, volume, 65 Hy-rib, concrete-reinforcement, • 853, 886 I beams, anchors for, 619 bending moments, maximum, 574- 575 Bethlehem, 592 loads, safe, 592, 593, 598-602 properties, 357 buckling of web, 181-185, 565, 567- 569, 612 table, 574, 575 _ Carnegie, dimensions, 352-353 properties, 354, 355 safe loads, 577-581 concrete, 854 connections, anchors, 619 floor-framing, 612-619 limiting values, 618 separators, 612-614, 1202 I beams, connections, standard, 616, 617 with Bethlehem H columns, 473 with built-up columns, 475, 476 with cast-iron co|lumns, 446, 447, ^457, 458 with plate and box girders, 615 continuous, 677-680 cost, base price, 1204 crippling of web (same as buckling) deflection, lateral, 566, 670 vertical, 566, 577-581, 668, 669 dimensions, 352, 353, 565 double-beam girders, loads, 564^ 603, 604, 607-611 economy, relative, 565 end-bearing, minimum, 574-575 end-reactions, 569, 574, 575 fireproofing ' (see Beams, steel, fire- proofing) framing, between columns, 614 to wooden beams and joists, 616, 752, 753, 755, 786-792 girders, 603-611 double, safe loads, 607-611 single, safe loads, 605-606 grillage foundations, 167-169, 181- 185, 678-680 light versus heavy, 565 loads, Bethlehem, table, 594-602 Carnegie, table, 577-581 examples solved, 570-573 moment of inertia, 336 needling, 218-221 oblique loading, 573 properties, 352-355, 357, 358 radius of gyration, 336 separators for, 612-614, 1202 shearing, 181-185, 567, 568, 569 table, 574-575 single-beam girders, loads, 605, 606 span-lengths, limiting, 618 standard, dimensions, 352-353 properties, Bethlehem, 357-358 properties, Carnegie, 352-355 supplementary, 352 tie-rods for, 619, 865 web-resistance, 181-185, 567-569 table, 574-575 Ice, melting- temperature, 1251 specific gravity and v/eight, 1505 Ice-making, 1693- 169 5 Idaho, registration law, 1778 Igneous rocks, 131 Illinois, registration law, 1778 Illuminants, hygiene of, 1452 selection, 1452 Illuminating gas, lighting, 143 1- 1436, 1451 Illumination (see Lighting and Illumi- nation) Incandescent lamps, 1462, 1471. 1482 Index 1881 Incandescent lighting (see Lighting) Inch, equivalents, 25, 26 Inch- pound, 290 Inclined plane, friction, 252 Incrustation, boilers, 1429 Inertia, moment of (see Moment of inertia) Influence lines, 1134-1137 Institutions, educational, architectural, 1779 Insulating quilts, 1565 Insulation, 1683, 1690 heat, 1430, 1566 mineral wool, 1610 pipe, 1430 Insulators, electric, 1458 Insurance during construction, 1756 Interphones, 1707 Intrados, arch, 305 Inverse squares, law, light, 1440 Involution, arithmetic, 3 Ionic Order, 1 699-1 702 Ionic Volute, 1702 Iron, cast (see Cast iron) galvanized, 1604 properties, 375 wire, 400 Iron, wrought (see Wrought iron) Isosceles triangle, 293 Jack, jacks, hydraulic, 216, 221 Jack-rafters, lengths and bevels, 90 Jack-screws, shoring, 215, 216, 221 Jacket, furnace, 13 10, 13 11 Jewish long measures, 34 Johnson floor-construction, 837-840, S41 Joint, rupture, dome, 12 13 Joints (see under each subject) Joist (Glossary), 1826 Joists, floor (see Floor- joists) ceihng (see Ceiling-joists) Joist-hangers (see Hangers) Joule, 1250 Jury, competitions, i737, i743 . Kahn bar, 921 system, 940 Kalamein iron, 894 89s Keene's cement plasters, 1556 Kelsey warm-air generator, 13 16 Kenney fiushometer, 1420 Kent's chimney-formula, 1366 Key expanded-metal lath, 884 Keyed beams, 653-655 Keys, compound beams, 654 Keystone arches, 305, 3o8, 310 (Glos- sary), 1827 Rankine's formila, 308 Trautwine's formula, 309 Keystone hair insulator, 1566 Kilowatts, defined, 1460 King-post truss (see Roof -truss) King-rod truss (see Roof-truss) Kitchen ranges, flues, 1282 Kitchen-sinks, dimensions, 1641 Knee-braces, trusses, 1025-1027 1116- 1118, 1164, 1168 v/ind-bracing, 1179, 1181, 1185-1190 Knife-switch, 1477, 1479 Kno-bum lath, 884 Kno-fur lath, 885 Labor, cost, 1564 Laboratories, lighting for, 1451 Lacing-bars, 385 Ladder-wagons, dimensions, 1642 La Farge cement, 236, 238 Lag-screws, 1535 roof -trusses, 1157 Laitance, 244 Lally columns, 467, 474, 477 loads, 488, 516 Lamps, arc, 1462, 1463 arrangement, 1465, 1466 bowl-size, 1443 brilliancy, 1439 gas, 1451 height, 1444 incandescent, 1462, 1471, 1482 kinetic burner, 1451 location, 1442, 1443, 1446 number, 1446, T449> I47S sizes, 1443, 1444 tungsten, I444, I447 Welsbach, i444, i45i Land, measure, 27 Lard-oil, weight, 723 Lath, metal (see Metal lath) wire (see Metal lath) wooden, 1554 Lathing, 1554 cost, 1557 Lattice-bars, columns, 477-479 specifications, 1202 Lattice columns, 477-479 Lattice girders, 1008-1010, 1089-1091 wind-bracing, 1176, 1181, 1182 Lattice trusses, 1008-1010, 1089-1091 Laundry-tubs, dimensions, 1641 Lava, 131 crushing strength, 280 Lavatories, dimensions. 1641 Laws, building (see Bmlding laws) registration, architects, 1768-17 79 ventilation, 1354 Lead, anchor-bolts, 240 castings, shrinkage, 1521 pipe. 1408, 1413, 1416-1418 sheet, 1418, 1511 specific gravity, 1505 weight, 1505, 1511 1882 Index Leaders, furnace, 131T, 1317, 1324, 1358 Leather, weight, 723 Length, unit of, 1247 Lever, principle of, 165, 290, 293, 294 Libraries, book-stacks, 1696 ventilation, 1353 License law, architects, 1768-1779 Light, brilliancy, 1439 candle-power, 1439, 1440, 1462 diffusion, 1453-1456, 1577-1580 heat, emission, 1261 versus illumination, 1437 intensity, 1439 nature of, 1438 refraction, 1453 -1456, 1577-1580 sources, 1438 colors, 1438 Lighting and illumination, 143 7-1456 accounti.ig-oilices, 1446 auditoriums, 1451 bibliography, 1456 ceiling-lights, 1446 ceiling-outlets,. 1449 class-rooms, 145 1 coloring of ceilings, 1442 design of system, 1444, 1446 diffusion by glass, 1453-1456, iS77" 1580 direct, 1441, 1442. 1446-1448 drafting-rooms, 145 1 electric-lighting systems, 1464-1469 cost, 1482 design, 1446-1448 electric power required, 1441 factories, 969 feed-wires, 1478 fixtures, care of, 1443 in direct systems, 1446-1448 in semiindirect systems, 1448-1450 foundries, 145 1 gas, 1448, 1450, 1451 amount of gas required, 1441 calculations, 1448 pipe, sizes, 1432-1436 piping, symbols, 1445 general principles, 1437 heights of lamps, 1444 Holophane reflector, 1447 hygiene of, 1452 indirect, 1441, 1442, 1448-1450 intensity, 1439, 1440 laboratories, 1451 law of inverse squares, 1440 lecture-halls, 145 1 machine-shops, 1451 mill-buildings, 969 outlets, 1442, 1443, 1446 piping for gas, 1432-1436, 1445 reflectors, 1447, 1448 roof -lights, 775 Lighting and illumination, saw-tooth roofs, 772, 775 school-rooms, 1451 semiindirect, 1442, 1448-1450 single-phase system, 1464 , switches, 1478, 1479, 1481 systems, 1464-1469 three-phase system, 1464-1469 three-wire system, 1464-1469 two- wire system, 1464 windows, 775, 1453-1456 wiring, cost, 1482 workshops, 769, 145 1 Lightning-conductors, 1704-1707 Lignite, combustible, 1271, 1272 Lignum-vitae, ultimate unit stresses, 651 weight, 651 Lime, 1548-1553 Alca, 1553 chemical properties, 1550 classification, 1549 data, 1553 hydrated, 155 1 hydraulic, 235 inspection, 1550, i5S2 nature, 1548 properties, 1548, 1550, 1552 sampling, 1549 specific gravity, 1506 specifications, 1 549-1 551 tests, 1549 weight, 723, 1506 Limestone, 132 beams, coefhcients for, 628 calcite, 131 calcium, 1549 compressive strength, 266, 280, 281, 282, 287 constituents, 1548 dolomitic, 131, 1549 fiber-stresses, 557 fire-resistance, 814 modulus of elasticity, 282 of rupture, 282 shearing strength, 282 specific gravity and weight, 282, 1505, 1506 tensile strength, 282 Line of fracture, arches, 316 Linear measures, 25 metric, 31 Gunter's chain, 25 ropes and cables, 25 Lines, center of gravity of, 292 geometrical problems, 66 Lines of pressure, arches, 31 1-3 21 buttresses, 297-304 Links, strength of, chains, 410 Linseed-oil, 1568, 1569 jS specific gravity and weight, 1505 l|H Index 1883 Lintels, 305 cast-iron, 620-627 cross-section, ideal, 620 deflection, 628, 664 formulas, 620-621 safe lead, tables, 624-627 reinforced-concrete, 975 stone, 1539 Liquid measure, 27 metric, 32 Liquefaction, heat of, 1684 Live loads (see member loaded) definition, 126, 149 Load, loads (see, also, each member loaded; also Weight) cast-iron columns, 461 footings, 162-1-65 eccentric, columns, 489, 946 footings, 162-165 steel column, 485-489 steel-pipe column, 472 wooden column, 453 oblique, steel beams, 573, 593 on columns, method of computing, 148-152, 489, 490 on floors, fire-proof, 833, 837-844, 850-852,856,863-865 mill-buildings, 802-808 reinforced concrete, 936, 948, 967, 971, 984-987 steel, 1 197 various buildings, 149 wooden, 717-749 on foundation-beds, 141-143, 148-160 on masonry, 265-267, 287, 441, 442, 1200 on roofs, 740-741, 745, 746, 1048- 1057, 1196 on reinforced-concrete slabs, 984- 987 safe-load, definition, 125 snow-loads, 1049, 1052-1057 tests, fire-proof floors, 827, 866, 956- 958, 967 foundation-beds, 141-146 wind-loads, 148-160, 1049, 1052- 1057, 1171-1173, 1198 Lock-woven fabric, 849 Locomotives, dimensions, 1642 Locust, safe fiber-stress, flexure, 557, 648 specific gravity, 1506 unit stresses, 651 weight, 651, 1506 Lodging-ho-ase, defined, 1853 Loit buildings, chimneys, 1368 Lofts, cost, 1 61 3 live loads on floors, 149, "97 Logwood, extract of, 723 Loop-eyes, 386 Loop-rods, 386, 396 Louisiana, registration law, 1778 Louisville code, loads on foundation- beds, 143 masonry loads, 287 Lumber (see, also. Timber and differ- ent woods) asbestos, 819 data, 1558-1564 framing, 1559 hardness, relative, 1558 measurement, 1559-1563 metal, 858 specific gravity, 1501-1508 weight, 1501-1508, 1558 Luten truss, 923 McGill University, tests on brick piers, 275 Machine-shop, design and cost, 802-803 saw-tooth roofs, 774 steel, weight, 1209 Machinery, vibration of, 763 Machines, dynamo-electric, 1463 refrigerating, 1685- 1690 Mackolite, partition-blocks, 877 Mahogany, uiiit stresses, 651 specific gravity, 1506 weight, 651, 1506 Mail-chutes, 167 7- 1679 Mains, steam, 1284, 1289, 1291, 1350 Manhattan Life Insurance Building, foundations, 251 Manila rope, 406-408 Mansard roof, tiles for, 870 Mantle-tile, 1605 Maple, deflection in beams, 664 hardness, 1558 unit' stresses, 651 weight, 651, 1558 Marble, beams, coefficients for, 628 compression, 266, 282 crushing strength, 280, 282 fiber-stresses, flexure, 557 fire-resistance, 814 loads, safe, masonry, 266 shearing strength, 282 specific gravity, 282, 1506 strength, 267 tension, 282 tile, 1605 weight, 282, 1506 Marbleithic tile, 1606, 1607 Masonry, 1538, i539 (see, also, Brick- work, Stonework, Walls, etc ) arches (see Arches) bearing pressure, allowable, 441-444 bed (Glossary), 1802 bond (Glossary), 1803 bond-stones, effect of, 269 building codes, 267, 287 cement mortar required, 239, 247 1884 Index Masonry, classification, 1538 coefficients of friction, 253 compressive strength, 265, 441 cost, 1538, 1539 crushing strength of stone, 279-282 footings, 178, 223-225 tensional strength, 178-179 grouting^ 269 measurement, 1538 mortar for, 229-239, 247 piers, 270 pressures allowed, 265, 267, 287, 441, 1200 safe working loads, 265-267, 287, 441 strength, 265-282, 441, 1200 stresses in, 265 thickness of walls, 229-234 walls, 228-234 weii^ht, 1506 Mass-concrete, strength, 267 Mathematical signs and characters, 3 Mathematics, practical, 3-5 McGill University, tests on brick piers, 275 Measure, measures, 25-35 ancient, 34 circular and angular, 30 conversion tables, 33-35 cubic, 27 metric, 31 dry, 27 metric, 32 Egyptian long, 34 fluid, 28 Grecian long, 34 Jewish long, 34 land, 27 linear, metric, 31 liquid, 27 metric, 32 metric system, 30-33 miscellaneous, 26, 28, 34 nautical, 26 Roman long and weight, 34 Scripture and ancient, 34 surface, 27, 31 time, 30 value, 29 volume, 27, 31 weight, 28-29 metric, 32 Mechanical refrigeration, 1684-1695 Mechanics, applied, definition, 124 Mechanics of materials, terms used, 124 Medals, architectural, 17 79-1 788 Melan arch, 844 Mensuration, 38-65 definition, 38 solids, 61-65 surfaces, 38-61 Merchandise, weights, 721-723 Merchant- bar iron, 377 Metal, asbestos-protected, 819 data, 1509 doors, 894-897, 901, 902 finish, 896 sheet, standard gauges, 402 Metal frames, fire-proof buildings, 89-: Metal furring, 881, 892 Metal lath, 882-892, 919 column-protection, 822 expanded, 884 fireproofing, 781 partitions, 878, 882, 888, 890 sheet, 402, 886, 1510, 1599 woven-wire, 887 Metal lumber, 858 Metal-rib plaster-board, 888 Metal sashes, fire-proof buildings, 89 Metallic furniture and fittings, 898-89 Metamorphic rocks, 131, 132 Metric system, 30-32 conversion tables, 32-35 Mica, 131 specific gravity and weight, 1506 Mica-schist, 132 Middle third, theorem of, 254 arches, 311-315 buttresses, 301, 304 domes, 1225, 1227 footings, 164 retaining- walls, 259 vaults, 1233, 1234, 1240 Mill-buildings (see, also, Mill-con struction), brick, 808-810 cost, 808-810, 1206 depreciation, 1634 reinforced concrete, 968-997 steel, cost, 1206 weight, 1208, 1209, 1210 wooden, 758-810 Mill-construction, reinforced-con Crete, 948, 968-997 columns, 969, 976, 978, 980 loads, distribution, 976 cost, 777. 1613, 1618 floors, 968, 971, 993 beams, secondary, 971 formulas for design, 985-997 girderless, 968, 993-997 footings, 978, 982 girders, 974, 975 lighting, 969 lintels, 975 stairs, 899-901, 982, 983 Mill-construction, slow-burning, 758- 810 belts, shafts, 765 boiler-plant, 765, 780 columns, cost, 810 fireproofing, 780, 781, 822-826 Index 1885 Mill-construction, slow-burning col- umns, framing, 769, 782-800 conductors, 775 cornices, 764, 769 cost, 758, 777, 802-810, 1613, 1618 doors, 801 dry-rot, 759 elevator-towers, 764, 768 fire-protection, 768, 777, 779, 801, 903-905 fire-retardants, 759 fire-shutters, 759, 778, 801, 901, 902 fire-stops, 759 fireproofing metal members, 780-782 floors, 760-764, 766 cost, 810 estimating, 1563 framing (see Framing, floors) old, strength, 749 plank, 730-735 strength and stiffness, 717-757 surfacing, 769 warehouses, 777 frames and shutters, 764 framing, steel, 786, 788 general description, 758-760 girder-supports, 792 glass, 759, 763, 764, 769, 772, 775 gutters, 769, 775 hangers, 782, 785, 789 heating, 769, 776 height, of buildings, 777-778, 813 of stories, 765, 810 joist-supports, 792-794 painting, 759, 763 partitions, 759, 801 plumbing-fixtures, 810 post and girder-connections, 795-800 post-caps and bases, 782-788, 791, 795-800 pumps, 759 roofing-materials, 760, 800-801 roofs, 760 cost, 810 example, 769 materials (see Roofing, materials) timber framing, 765 walls, 768 saw-tooth, 772-777 scuppers, 767 shafting, 765 skylights, 765 sprinklers, 768, 777, 779, 801, 904 stairways, 759, 810 tower, 764, 768, 778, 779 steam-pipes, 764 stirrups, wrought-iron, 750, 754" 757, 787-794 storehouses, 765-788 structural details, 782-792, ii94- Mill-construction, slow-buming tim- bers, 759, 762, 763 towers, 764, 768, 778, 779 trusses, 772 ventilation, 769, 775, 776 of timbers, 763 walls, 760, 765, 768, 778, 809 warehouses, 777-782 weave-shed, 773 windows, 763, 769, 772, 775, 778 fire-guards, 759 frames, 764 Milwaukee building code, formula for steel columns, 481 Mineral wool, 1566, 1609, 16 10 Minneapolis building code, formula for steel columns, 481 loads on foundation-beds, 143 office-buildings, assumed loads, 151 thickness of walls, 231-232 Mineral oil, fuel, 1272 Minerals, forming rock, 130 Mirrors, 1580 Modulus of elasticity, 126. 626, 662 concrete, 912, 924, 934, 935, 956 definition, 126 notation, symbols, 122 steel, 381, 912, 934 stone, 282-283 various materials, 647, 664 Modulus of rupture, 126 concrete, mortar, and stone; 282-283 woods, 650-651 Modulus, section (see Section-modulus) Molding (Glossary), 1830 Moldings, classical, 1697, 1698 plaster, 1556 Molds, concrete, 962-966 Moment of force, definitions, 127, 289, 322 Moments, bending (see Bending mo- ments) of inertia (see Moments of inertia) of resistance, 333, 55^ principle of, 289-291, 294, 301, 322- 324 Moments of inertia, areas, 332-352 compound sections, 339-345 definitions, 33 2-333 determined graphically, 345 notation, 122 rectangles, tables, 346-347 structural shapes, 354-359, 362-369 transferring, 338-345 Moments of resistance, flexure-for- mula, 333, 556 Money, United States, 29 Montana registration law, 1778 Mortar, adhesive strength, 240 aggregates, 241 alca lime, 15 53 1886 Index Mortar, brickwork, 227, 271 cement, 235-240 cement-gun, 826 colors, 1547 durability, 818 fire-resistance, 818 floor-tiles, 829 for plastering, 239, 1554-1558 freezing, effect of, 239 grouting, 227^ 269 hair in, 1555 hot water in, 239 hydrated lime, 1551 lime, compressive strength, 282 mixing, cement, 239 natural-cement, 235 compressive strength, 283 Portland-cement, 238 compressive strength, 283 quantity required, 239, 247 relative compressive and tensile strength, 283 salt in, 239 specific gravity, 1506 stone walls, 229, 230 water required, 238 weight, 1506 Mortar-colors, 1547 Mortuary, refrigerator, 1683 Mosaics (see, also, Tile) Ceramic, 1605, 1607 Florentine, 1605 Roman, 1605, 1607 terrazzo, 1607 Motion, definition, 124 rate, 1247 Motor, 1463 for elevator, 1676, 1677 for fan-drive, 1347 heat-emission, 1261 Mud, 139 Mullion and munion (Glossary), 183 1 Mushroom system, reinforced concrete, 950, 993-997 Nails, 1 5 29-1 534 National Board of Fire Underwriters code, masonry-load, 287 concrete, 958 National Electric code, 1480, 1481 Natural cement, 235 concrete, 235, 267, 284 mortar, 235 compressive strength, 283 production, 235 strength, 235, 284 weight, 235 where used, 235 Natural gas, 1431 Nautical measures, 26 Needling, 218-222 Neutral axis, beam-sections, 332-338 555, 621 New Jersey registration law, 1778 New Orleans building code, load on foundation-bed, 142 thickness of walls, 231 New York City building code, arches, 307 bearing pressure on masonry, 44 1, 444 column-formula, cast-iron, 460 compression, steel members, 495 formula for steel columns, 481, 493, 495 loads on foundation-beds, 143 masonry-loads, 267 office-buildings, assumed loads, 151 pipe-column formula, 469, 474, 497, 498 _ rivets, bearing and shear, 419 skeleton construction, 234, 1171 terra-cotta, 276 thickness of walls, 230, 231-232 wind bracing, 1171 New York State, registration law, 1768- 1776, 1778 Nickel tuijing, 141 5 Nicking test, wrought iron, 378 Nonagon, 37 North Carolina, registration law, 1778 North Dakota, registration law. 1778 Novus sanitary glass, 1606 Norway pine, beams, loads, 641 deflection, 664 fiber-stress, safe, 557 columns, safe loads, 450, 452 crushing-load, 449 crushing strength, across grain, 454 specific gravity, 1507 unit stresses, 376, 647, 650 weight, 650, 1507 Notation mathematical, 122, 123 Nozzles, roof, 801 Nuts, 1525 standard dimensions, 1526 weight, 1527 Oak, beams, coefficients for, 628 deflection, 664 distributed loads, safe, 643 fiber-stresses, 557 columns, safe loads, 450, 451 crushing-load, with the grain, 449 ' crushing strength, across the grain, 454 hardness, 1558 shearing-stresses, 412 specific gravity, 1506 unit stresses, 376, 412, 647, 648, 651 weight, 651, 1506, 1558 Obsidian, 131 Octagon 37 J ndex 1887 OfRce-buildings, chimney, 1368 cost, 1613 fire-hose in, 905 floor-joists, 738, 743 floor-loads, 149, 151, 719, 720, 1198 furniture, weight, 149 I beams, sizes, 864 steel, weight, 1207, 1208 Offices, air-change, 1353 Offsets, footings, 163-165, 179, 223-227 Ohm, defined, 1458 Oil, mineral, as fuel, 1272 Open-hearth, steel, 380 Opera-houses, dimensions, 1657 chairs, 1653 seating capacity, 1654-1656 Orders, classical, 1698-1704 Oregon Pine (see Douglas fir) Organizations, architectural, 1788-1795 Ottawa sand, 235, 241, 908 Overdraft, in furnace, 1310 Owner, competitions, 1739, 1740, 1746 Owner's right, in contract, 1760 Paint, Painting, 1568- 1573 cement and concrete, 1573 driers, 1569 enamel, 1570 fire-proof, 821-822, 894 inside, 1570 mill-construction, 759 old work, 1 571 outside, 1569 paints, 1568-1570 pigments, 1568 plastered walls, 1571 priming, 1569 repainting, 1571 steelwork, 1203, 1206, 1572 timbers, 763 tin roofs, 1570, 1589, 1590 varnish, 1568, 1570, 1573 vehicle, 1568 Pantry-sinks, dimensions, 1641 Paper, building, 1564-1568 weight, 722 Paper-mills, cost, 805 steel, weight, 1210 Parabola, 38 center of gravity, 293 problems, 79 Paraboloid of revolution, volume, 65 Parallelogram, 37, 39 of forces, 289 Parallels, 36 Parapets on mills, 768 architecture, 1833 Parchment, water-proof sheathing, 1568 Parking, defined, 1853 Partitions, brick, 873 concrete, 876, 880 Partitions, defined, 1853 double, 880, 890 fire-proof, 873-892 fire test, 873, 889 gypsum-block, 876 heating pipes through, 1358, 1360 hollow-tile, 873-874, 890 mackolite, 877 metal-lath. 878, 882-888, 890 mill-construction, 759, 801 rib-stud, 881 soundproofing, 889-891 scantling, incombustible, defined, i8S3 solid plaster, 878, 880, 890 terra-cotta, 873, 875, 890 types, 873 wooden, ^25-727, 748 Partition-wall, defined, 1853 Party walls, 873 defined, 1853 floor-loads on, 234 Patent rights, payment, 1759 Patterns, castings, 1521 Paul, air-line system, heating, 1286 Pavement-prisms, 1579 Pavements, asphalt, 1608 Payments, on contract, 1758 Pearl-alum, weight, 723 Peat, 139, 1272 Pedestal-piles, 198 Peerless radiators, 1265, 1266 Pentagon, 37 Perimeter, 37 of triangles, center of gravity, 292 Persons, heat-emission, 1261 Pews (Glossary), 1835 Philadelphia building code, bearing pressure on masonry, 444 formula for steel columns, 481, 493 loads on foundation-beds, 143 masonry-loads, 267 pipe-column formula, 469, 474 Phosphorus in steel, 381, 383 Pianos, dimensions, 1638 Piers, arch, 305 brick, 267-269, 271-276, 278 bond-stones, 269 safe loads, 265, 267, 268 strength, 268, 271-276, 278 tests, 275 caisson, 212, 214 center of gravity, 300. 30i, 302 footings for, 161,. 162, 176-178, 184. 185 foundation, 129, 188, 200 line of pressure, 300 on concrete and wooden piles, i99 grillage, 184, 185 pneumatic-caisson method, 212, 214 reinforced-concrete, 980 1888 Index Piers, stability, 297-304 stone, 270 terra-cotta, 276-278 thrust, 297, 298 Pigments, paints, 1568-1570 Pilasters (Glossary), 1835 Pile-drivers, 190, 194-196, 202-204 Piles, durability, 188, 196 iron-pipe, 199 reinforced concrete, 196-200, 945 versus wooden, strength, 196 wooden, 188-196 capping, 190-192, 198 timber-grillage, 191, 192 cost of driving, 195 crushing strength, 196 driving, 189, 190, 194-196, 202-204 durability, 188, 196 ' Engineering News formula, 193 municipal requirements, 189 plan of, for building, 192 safe loads, 189, 193, 195 specifications, 193 strength versus concrete piles, 196 under piers, 199 woods used, 189 Piling, sheet, 200-209 Pillars (Glossary), 1835 Pin, pins, in trusses, 423-429 steel, stresses, 618, 1138, 1200 Pine, specific gravity and weight, 1507 Norway (see Norway pine) white (see White pme) yellow (see Yellow pine) Pinnacle (Glossary), 1836 Pipe, pipes (see, also, Ducts) . block-tin, 1418, 1419 brass, 1429 capacity, 1383, 1403 cast-iron, 1389, 1407, 1427, 1428 conduits, 1479 coverings, 1360, 1363, 1430, 1610 drain, 1407-1412, 1419, 1420 expansion, 1427-1429 flow of water through, 1382-1400, 1420 friction in, 1388 frostproofing, 1400 furnace, 1311, 1318, 1322, 1358, 1360 gas, 1432-1436 hot-water heating, covering, 1360, 1430 size, 1305, 1306 specifications, 1359 hot-water supply, 1415, 1428, 1429 lead, 1408, 1413, 1415, 1416-1418 location, fireproof, 826 sewer, 1407-1409, 1419, 1420-1422 sheet-metal, 1337 smoke, 1362 Pipe, soil, 1407-1410, 1427 steam-heating, 764, 1362 covering, 1363 pressure-loss, 1292 size, 1294 specifications, 1362 steel, 1408 supply, 1390-1398, 1415 symbols, 1350, 1424-1426 tests, 1388, 1412 tin-lined, 1418 vent, 1407, 1410 warm-air, size, 1318 waste, 1407-1411, 1416, 1417, 1427 wrought-iron, 1408, 1429, 1432-1436 Pipe-columns, 469-474, 488 loads, 488, 497-498 Pipe-coverings, steam-pipes, 1360, 1363, 1430, 1610 Pitch of roofs, 867, 869, 1046, 1053 Pitch, gravel roofs, 1595-1599 slag roofs, 1595-1599 specific gravity and weight, 1507 Plane, 36 inclined, 252 Plaster, alca-lime, 1553 asbestic, 818 fire-resistance, 818 gypsum, 818, 1555 hard- wall, 1556 hydrated-lime, 1551 . Keene's cement, 1556 machine-made, 1555 measuring, 1556 mortar for, 239, 1554-1558 staff, 1558 wall, 1555 weight, 723 Plaster-blocks, 876 Plaster of Paris, column-protection, 822 fire-resistance 818 Plastering, 1554-1558 coats, 1554 cornices and moldings, 1556 cost, 1557 Plate, base, forms of, 441 bearing, 440 . pressures, 441, 1200 cast-iron, weight, 1524 cover, riveted joints, 421 steel, 384, 385 base price. 1204, 1205 punching, effect, 382, 414, 688 wall (see Wall-plates) Plate-and-angle columns, 46^, 479 connections, 477 moment of inertia, 343 radius of gyration, 344 tables, 488, 517-532 Plate girders, 681-716 construction, details, 682-683 Index 1SS9 Plate girders, elements, 706-716 end-reactions, maximum, 70s, 706- 716 examples, 688-694 framing and connections, 614- 616, 682 moment of inertia, section, 340-342 safe loads, 706-716 shear, 684-687, 690, 691, 696, 698, 703 specifications, 1201, 1202, 1203 splice-plates, 693 stifTeners, 681, 686, 691, 696, 1201, 1203 stresses, design, 683, 1201 web, 681, 703- 70s buckling, 686, 705 shearing value, 703-704 stresses, 684, 686, 691 weight, 687 Platforms, stone, 1539 Plenum chamber, 1350 Plenum system, ventilating, 1356 Plumbing, 1407-1430 definition of terms, 1407 fixtures (sec Plumbing-Fixtures) pipes (see Pipes) symbols, 1423-1426 testing, 141 2 Plumbing-fixtures, 1410-1415, 1420- i4-'6 cost, mill-buiMings, 810 dimensions, 1640-1642 Plunge-bath, 1422 Plutonic rocks 131, 132 Pneumatic, caisson, 21 1-2 14 water-supply, 1396 Point, 36 Poling-board method, foundations, 209 Polygons, definition, 36 equilibrium, 289, 299, 313-31S, 3i9 factors for determining elements, 40 force, 289, 1070 Polyhedrons, regular, 63 Poplar (see, also. White wood) columns, safe loads, 450, 452 crushing-loads, with the grain, 449 hardness, 1558 specific gravity, 1507 unit stresses, 651 weight, 651, 1507, 1558 Portal bracing, 117 6, 1182 Portland, Ore., building code, loads on foundation-beds, 143 Portland cement, 236-240 adhesive strength. 240 composition, 236 concrete, reinforced, 907, 908 concrete blocks, 233 cost, 238 defined, 237 fineness, 237, 907 Portland cernent, manufacture, 236 mixing, 238 mortar, 238 compressive strength, 283 proportions, 235, 247 specific gravity and weight, 1506 quantities in concrete, 247, 248, 249 setting-time, 237, 907 specific gravity, 237, 907, 1502 specifications, 236, 907 strength, 237, 240, 283, 284, 907 testing, 237, 240, 907 weight, 235, 723, 1502 Post-caps, 782 788, 791, 795-800 Post-office buildings, cost, 1630 Posts (,ce Columns) Pound-feet, 290 Pound-inches, 290 Power, 1248, 1250 Power-hammer, underpinning, 221 Power-houses, steel, weight, 1210 Pratt truss, 1026, 1029, 1031, 1032 economy, 1055 with inclined ties, 1077 Pressure, barometric, 1249 earth, 201, 205 gauges, 1248 Prism, 38, 62 Prism-glass, 1454-1456, 1578-1580 fire-resistance, 821 Prismoid, quadrangular, 62 Prisons, ventilation, 1353 Prizes, architecture, 17 79 -1788 Professional practice, A. I. A., 1727 Programme, competitions, 1737, 1741 Public building (see, also, Federal build- ings) cost, 1613, 1628-1634 defined, 1853 registers, heating, 135S Pulleys, arrangement, 1722 sash, 1649 size and speed, 1720 Pulpit (Glossary), 1838 Pumice, 131 Pumps, air-lift, 1395 deep- well, 1391 fire, 1401 mills, 759 plunger, 1391 pneumatic system, 1396 private water-supply, 139° single-acting, 1393 slip, 1247 . steam, 1401 vacuum, size, 1290 Punchmg, effect on steel plates, 382, 414, 688 Purlins (Glossary, 1838), 998, 1838 channels, 1169 connections, 1153, "69, 11 70 1X90 Index Pml-ns, design, 1144, 1169, 1170 I-beam, 1169 oblique, stress, 573, 593 spacing, 1003-1004, 1006 steel, specifications, 1201, 1204 supports, 1004, 1046, 1047 weight, 1050, 1055 wooden, 1003, ii44> ii53, 1169 workshops, 771 Z-bar, 1 1 59 Puzzolan cement, 236, 237 Pyramid, 38 center of gravity, 293 frustum, 38 surface-area, 61 volume, 64 surface-area, 61 vertex, 38 • volume, 64 Pyrometer, 1249, 1250 Quadrangular prismoid, 62 Quadrangular truss, 1032, 1033, 1091, 1094 Quadrant of circle, center of gravity, 293 Quadrilaterals, 36 center of gravity, 292-293 Quantity system of estimating, 1635- 1637 Quartz, 130 specific gravity and weight., 1507 Quartzite, 132 Queen truss, 999-1004 example, of analysis, 1055, 1139 graphic analysis, 107 1 wind-stresses, 1112-1116 Quicklime, 1549 Quicksand, 136 excavations in, 137, 211 foundation-beds in, 137, 141 pockets, 137 safe load on, 141 Quilts, building, 1564-1568 Quoins (Glossary), 1839 Radial Brick Chimney, 1369-1373, i377 Radiation, 1264-1271 versus hot-blast heating, 1324 Radiators, 1 264-1 271 air-removal, 1285 cast-iron, 1265-1267 concealed, 1270 connections, 1264, 1283 direct, 1264. 1283 direct-indirect, 1264, 1268 hot-water, 1264, 1270 indirect heating, 1264, 1299, 1300, 1356 location, 1355 specifications, 1360, 1362 Radiators, indirect heating, symbol, 1350 materials, 1264 measurement, 1265 pipe coil, 1267, 1269 pressed-metal, 1264, 1265, 1267, 1268 rating, 1265 types, 1265 1270 wall, 1268 Radius of gyration,. 333 areas, 334-338 (see, also. Moments of inertia) compound sections, 344 definition, 333 hollow-round sections, table, 348-349 hollow-square sections, table, 345, 350-351 notation, 122 steel-pipe columns, 472, 497-498 structural shapes, 354^359, 362-374 double angles, 371, 372, 503 double channels, 373, 374, 499, 500 plates and angles, 344, 517-532 plates and channels, 533-554 Rafters, 1003, 1046, 1836 bevel and length, 90 details, 1150-1154 hammer-beam truss, 1014-1016 on steel purlins, 11 69 span, maximum, 740-, 741, 745, 746 stresses, 1140, 1141 weight, 1050 Rags, weight, 722 Rams, hydraulic, 1390 Random work (Glossary), 1839 Range-boilers, dimensions, 1642 Rankine's formula, cast-iron columns, 460-461 depth of keyst ne, 308-309 steel columns, 481, 484, 493-496 Raymond concrete pile, 197 Reactions, beams, 322, 671 Reaming, steel, 382, 414, 423, 682 Reaumur thermometer, 1250 Reciprocals, 7, 8, 24 Rectangles, 37, 39 axis of moments, 335 moment of inertia, 335, 346 radius of gyration, 335 section-modulus, 335 Redwood, beams, loads, 640 deflection, 664 fiber-stress, safe, 557 columns, safe loads, 450, 452 crushing-loads, with the grain, 449 crushing strength, across the grain, 454 shear, 647 tension, sife stress, 376, 647 unit stresses, 647, 650 weight, 650 Reflection, multiple (acoustics), 1487 Index 1891 Refraction of light, I453-I4S6, 1577- 1580 Refrigeration, mechanical, 1684-1695 Refrigerators, 1679-1683, 1691-1693 Register-boxes, 1358 Registers, air- velocity, 1357 furnace, 1317-1320 pressure-loss, 1338 in public buildings, 1355 size, 1358 specifications, 1360 symbol, 1350 Registration of architects, 1768-17 76 Reinforced concrete (see, also, Concrete and Reinforcement), 906-997 adhesion (see bond, below) aggregate, 241, 287, 908, 909, 945 beams, 924-941 bending moments, 935-936 compression-rods, 921-922, 941 diagonal tension, 921, 938 bond, 940 allowed stresses, 911, 912 tests, 919 use in design, 938 cantilever flat-slab system, 950 cast-iron column-connections,945-946 cement used, 907 chimneys, i373-i375 cinders, 242, 250, 909, 930 corrosion of steel, 818, 960-961 columns, 941-946, 969, 980 calculations, 976 fire-proofed, 958, 959 metal-cored, 944-945 compressive strength, 910-91 1 conductivity, 955 connections, 944-947 construction in general, 906-967 corrosion-protection, 960-962 cost, 250, 910, 1613, 1618 Cummings system, 923, 945 design of, 924-947 diagonal tension, 921, 938 electrolysis, 186 erection, 906, 962-963 factors of safety, 911 factory-construction, 968-997 fire tests, 956, 957, 960 Fire Underwriters' requirements, 958 fireproofing, 781, 811. 955, 957-958 flat-slab construction, 949 floors, 842-856, 924-940, 948-955 (see slabs-, below) load tests, 967 surface-finish, 239, 246, 965 footings, 186, 946-947, 978 forms, 245, 962, 964-965. 966 permanent centering, 852, 853 foundations, 186, 196, 946-947, 978 four-way system, 949, 95o, 993-997 Reinforced concrete, gravel, 908 heat, effect of, 245, 827, 937, 955- 959 Hennebique system, 919-920, 940 historical notes, 906 hollow-tile and concrete, 951-952 I beams, reinforced, 854 inspection, 965-966 joining new work to old, 965 Kahn system, 921, 940 metal-core columns, 944-945 materials used, 907-923 mill-construction, 948, 968-997 mixing, 963, 964 mixtures, 909-910, 945, 963, 964 modulus of elasticity, 912, 924, 934, 935, 956 molds, 962, 963, 964-965, 966 permanent centering, 852, 853 Mushroom system, 950, 993-997 piers, 978 piles, 196-200, 945 pouring and ramming, 964, 966 proportions of materials, 240, 247 - 249, 910, 1712 protected from fire, 958 reinforcements (see Reinforcement) retaining-walls, 261-263 roofs, 866-872, 968, 976 sand, 908 sectional systems, 853-854 separately moulded system, 953-955 shear, 912, 921, 937-940 shrinkage-stresses, 937 skeleton construction, 948 slabs (3ee, also, floors, above) bending moments, 932, 936, 984. 987 cost, 250 design, example, 971 diagrams for strength, 984-987 flat-slab construction, 845, 846, 949-952 girderless floors, 968, 993-997 loads, safe, 984-987 rectangular, formulas, 932 separately molded, 953 strength, 932, 97i, 984-987 in T-beam design, 934, 975 stairs, 900, 947, 982, 983 stirrups, 921-923, 939, 940, 973 stone, 908-909, 935 superintendence, 965-966 System M, 948-949 T beams, 932, 933, 937, 94©, 97i. 975, 988-991 temperature-stresses, 937 tension-members, 913-91S tensional stress, 924 tests, adhesion, 920 corrosion, 961 1892 Index Reinforced concrete, tests, fire-resist- ance, 955-960 hooped columns, 942 loads, 967 thickness of concrete, 958 tile-and-concrete floors, 952 tile-protection, 959 two-way tile system, 949-953 types of construction, 948-955, 968 unit system of reinforcement. 922-923 Yaughan system, 856 Waite's concrete I beam, 854 wall-piers, 978 walls, 946, 948; 968, 975-978 water for, 909 wet-concrete mixtures, 963-964 working stresses, 911-913, 935 wrought iron, 907 Reinforcement, 913-924 (see, also, Reinforced concrete) adhesion (see Reinforced concrete, bond) Akme system, 949-95° bars, 915-921 area, 1514-1521 compression, 921, 922, 941 Corr-mesh, 853 corrosion, 960, 961 corrugated bars, 916 Cummings system, 923, 945 deformed bars, 915, 919 Diamond bar, 917 dovetailed corrugated sheets, 850 expanded metal, 846, 883, 884, 919 Ferrornclave, 850-851 grades used, 913 Havermeyer bar, 917 Hennebique system, 919, 920, 940 hollow -tile and reinforced, 951 yiy-rib, 853 Kahn bar, 921, 940 Kalman bar, 918 lock-woven fabric, 849 loop truss, 923 Luten truss, 923 metal fabric, welded, 848 metal lath, 882-888, 922 Monotype, 918 multiplex, Berger's, 852 Ovcid bar, 918 peicentage, 925, 937 permanent centering, 852, 853 Ransome bar, 915 Rib-bar, 917-918 rib-metal, 847-848 rib-truss, 853 rivet-grip bar, 919 rods, number, 937-938 rust, 186 Self-Centering, Duplex, 853 Self-Sentering, 853, 885-886 Reinforcement, spacing, 922, 938 specifications, 904 System M, 948 triangle niesh, 850 types, 843, 855, 880-890, 913-923 unit system, 922-923 welded-metal fabric, 848 wire-fabric, 850 wire-mesh, 919 working stresses, 912, 913 wrought-iron, 907 Repose, slopes and angles, 253, 254, 256 Residences (see, also, Dwellings) air-change, 1353 heat-temperature, 1256 non-fireproof, height, 813 steam-heating specifications, 1361- 1363 Resisting moment, 333, 556 Resolution, forces, 288, 289, 1065 Rest, definition, 124 Resultant, force, 288, 289 Retaining- walls, 252-264 angles of friction, 253 angles of repose, 256, 259-260 batter, 259-260 breast walls, 262-263 cleavage-plane, 257-258 coeflacients of friction, 253 construction, details, 259 footings, 261-262 friction, theorem of, 252 angles of, 253 grouted, 269 internal stresses, 257 pressures on, 257 principles of, 252-255 proportions, 261 reinforced-concrete, 261-26^ slopes of repose, 256 thickness, 260 theories, 255 vault-walls, 263-264 Reverberation, acoustics, 1487 Rhomboid, 37 Rhombus, 37 Rib-bar, 918 Rib-metal, properties, 847-848 Rib-stud, plaster partitions, 881-882 Rib-truss, 853 Richmond building code, loads on foundation-beds, 143 office-buildings, assumed loads, 151 Risers, stairs, rules, 1648 table, 1646-1647 River-deposits, 133 Rivet, rivets (see, also, Riveting), 413 American Bridge Co., standard, table, 420 annealing, 382, 414 Index 1893 Rivet, arrangement, 414, 415 base-price, 1205 bearing value, 415, 416 area used, 416 Boston law, 418 by proportion, 692 column-connections, 469 Cambria, 418 Carnegie, 418 determination of, 415 field-rivets, 618 formula for, 416 live loads, 415 New York law, 418 riveted girders, table, 418 shop-rivets, 618 steel-beam connections, table, 419 steel trusses, table, 419 tables, 418, 4x9 wrought iron, 415 wrought iron, table, 418 bending-stress, 422, 423 bridge-work, 423 butt-joints, comparative efficiency, 421 chain, definition, 421 clearance, 414 columns, number of rows, diagrams, 467 conventional sign, 417 cost, base-price for rivets, 1205 punching holes, 1204 cover-plates, diagrams, 421, 422 diameters, plate and box girders, 682 standard connections, 617 distance from edge of plate, 682 drift-pins, 414, 682 driving-tools, 1203 failure of joints, 415 field, 423 lengths, table, 420 shearing value, 618 symbols, 617 weight, percentage added, 617 grips, table, 420 heads, 413, 414, 682 , diagram, 416 eccentric, 414 holes, 413 aline ment, 414 allowance for errors, 615 deductions, plate girders, tables, 702, 703, 704 - deductions, plates and .angles, tables, 399, 400, 702 deductions, from various authorities, 60 J, 604 diameter, 414, 415? 682 punching, 382, 414, 4i5» 1203 in flange-angles, 687, 691 spacing, specifications, 1202 Rivet, in plate girders, diagram, 615 in stiffeners, 687 initial slip, 422 inspection, 414 lap-joints, diagram, 421 lengths, 413 field-rivets, table, 420 loose, 414 machine-driven, 414, 683 material of, 413 number of, column-connections, 469 equation for determining, 687 examples, 699, 700, 701 joints, 421, 422 plate girders, 691, 696, 701 for double shear, 416 standard connections, 616, 617 pitch (see spacing) proportions, diagrams, 416 punching, diameter of die, 414, 682 reaming, 382, 414, 423, 682 shanks, diagram, 416 shearing value, 411, 413, 416, 692 area used, 416 by proportion, 692 column-connections, 469 determination of, 415 double shear, 411, 416 field-rivets, 618 live loads, 415 shop-rivets, 618 single shear, 411, 416 steel-beam connections, table, 419 steel trusses, table, 419 tables, 418, 419 wrought iron, 415 shop, 414, 417, 423 bearing value, 618 shearing value, 618 signs, conventional diagram, 417 sizes, determination of, 415, 1201 diagrams, 416 for plate-thicknesses, 41 S shop-practice, 415 table, 420 spacing, 414 cover-plates of plate girders, 683 flange-angle, examples, 696, 697, 699-701 .plate girder, example, 691, 692, 693 specifications, 1202 standard connections, 617 steel columns, 469 staggering, 414 standard connections, 616, 617, 618 symbols, 417 taper-rivets, 423 weights, standard connections, 617 steel rivets, 1528 working stresses, 41S, 4i6, 423, 618, 1138, 1200 1894 Index Rivet, working stresses, column-connec- tions, 469 compared, 692 for bridges, 423 standard connections, table, 618 Riveting (see, also, Rivets), 413-^23 definitions, 413, 421 field, compared with shop, 423 machines, 414 shop, 414, 415, 423 single, definition, 421 Rock, angle of repose, 256 argillaceous, 131, 132 boulders, 134, 136 classification, 131-132, 134 composition, 130 disintegration, 133, 134 excavation, cost, 1537 foundation-bed, 130-132, 134, 135,141 loads, 143 igneous, 131 inclined strata, 146 ledge, 134, 13s loose, 134, 135 metamorphic, 131, 132 plutonic, 131, 132 rotten, 134, 135, 256 safe loads, 141, 143 sedimentary, 131 siliceous, 131 testing, 145 under caisson-piers, 214 weight, loose, 256 Rococo radiator, 1265 wall, 1266 Rods and bars, steel, 385-398 forked-loop, 387 looped, 386, 396 safe loads, 388-392 screw-ends, 387, 393-398 weights, 1 514-152 1 Roebling's Sons, wire-gauge, 400 standard wire lath, 887 Roman long measures, 34 weight, 34 Roof, roofs (see, also, Roofing and Roof- trusses) cost, 777, 810 conductors, 1658 dampness, 800 fire-proof, 866-872 fire-protected, 801, 1597 flooding, 801 gutters, 1658 heat-transmission, 1259 leaks, 800 loads, 740, 741, 745, 746, 104S 1057, 1196 mansard, 870-871 mill-constrdction, 760 (see Mill-con- struction) Roof, mill-construction, cost, 810 example, 769 materials (see Roofing, materials) timbers and framing, 765 walls, 768 nozzles, 801 pitch or slope, 867, 869, 1046, 1053 rafters (see Rafters) reinforced-concrete, 866-872, 968, 976 saw-tooth, 772-777 trusses (see Roof -trusses) Roof-loads (see Loads) Roof-trusses, 998-1170 (see, also, Roof and Roofing) anchoring, 1150-1152, 1168 arched trusses, 1035-1043 stresses in, 1118-1123 wooden, 1020-1024 arches, trussed, 1121-1133 bending moments, moving load, 1134, 1 13s bolt-connections, 429-439, 1138 Bow's notation, 1066 bowstring, 1035, 1094, io9S cambered, 1011-1019, 1026, 1028, 1033-1035 (see, also. Scissors truss) stresses in, 1056, 1060, 1061, 1079- 1086, 1093-1095 cantilever, 1043-1045, 1 105 -i 108 car-barn, 1028, 1056, 1209 cost, 1208 counterbracing, 1000-1006, 1034, 1104 crane, 1069 diagrams, lettering, 1066 fan (see Fan truss) Fink (see Fink truss) fireproofing for, 860, 861 fixed arch, 1043, 1131 fixed and free ends, wind-stresees, 1109, mo flat roofs, example, 1057, 1143 stresses, graphics, 1075, 1077, 1089- 1092, 1102-1104 types, 1030-1034 forces acting, 1066, 1070 French, 1026 hammer-beam (see Hammer-beam truss) hinged, 1038-1043, 1121-1130 hook-splice, 11 55 horizontal chords, 1004 horizontal deflection, 1085- 1088 I119, 1 1 29 horizontal thrust, 1085- 1088, 11 10. 1129-1130 Howe (see Howe truss) influence-lines, 1134--1137 joints, steel, 423-429, 1160-1170 wooden, 412, 413, 429-439, 1149 1160 Index 1895 Roof -trusses, king-post, 998, 1000 king-rod, 998, 1153, 1154 stresses, 1048, 1069, io99 knee-braces, 1025-1027, 1116-1118, 1164, 1168 lateral bracing, 1033 lattice, 1008-1010, 1089-1091 loads (see Loads) members, proportioning, 1139 notation. Bow's, 1066 pin-connections, 423-429 use, 1030, 1032, 1034 Pratt, 1026, 1031, 1032, 1077 purlins (see Purlins) quadrangular, 1032, 1033, 1091-1094 queen, 999-1004, 1139, 1140 load-distribution, 1055 stresses, 1071, H12-1116 reactions, 1066 unsymmetrical loads, 1096, 1098 wind-loads, mo roller-bearing, wind-stresses, iiii, 1118 sag-tie, 1025 saw-tooth roofs, 772-777 scissors (see Scissors trusses) shed, 1025 spacing, 1047, 1048, 1051 splicing in wooden, 11 55 steel, 1025-1045, 1144-1149, ii6o- 1170 cost, 1206 saw-tooth roofs, 772-777 secondary stresses, 1137 shop-drawings, 1162, 1207 specifications, 1201 weight, 1050, 1051, 1209 steel columns in trusses, 1139 stresses, 1046-1137, 1138 influence-lines, 1134-1137 coefficients, 1058-1065 graphics, 1065-1137 unit, timber, 1138 wind-load, 1118, 1123-1128 suspended, 1032, 1089 types, 998-1045 unsymmetrical, 1096-1098, iioo- 1107 loads, 1096, 1098 wall-plates, 1 1 50-1 152, 1156, 1158, 1165, 1168 Warren (see Warren truss) weight, 1050-1051 white-pine, 1138 wooden, 439 bolted connections, 429-439 cantilever, 1044 design, 1138-1144 joints, II 49-1 160 types, 998-1024 unit stresses. 1138 Roof- trusses, wooden, washers, 1157- II 60 weight, 1050-1057 Roofing, 1 581 -1604 (see, also, Roofs and Roof -trusses) asbestos, corrugated sheathing, 819 sKingles, 819 asphalt-gravel, 871, 1598 asphaltic materials, 1608 . Barrett, 1595 Bonanza tile, 868, 869 book-tile, 868 canvas, 801 cement tiles, 868, 869 copper, 1049, 1604 corrugated iron, 1046, 1049, 1599- 1604 dampness, 800 felt, weight, 1049 flat roofs, 866, 1046 galvanized, 1604 gravel, 871, 1027, I59S-IS99 fire-resistance, 1597 incombustible, defined, 1853 leaks, 800 materials, 800, 1046, 1567, 1581-1604, 1608 fire-resistant, 819, 817, 1597 weight, 1049 mill-construction, 760, 800 pitched roofs, 867-869, 1046 prepared, 1599 ready, 1027, 1046, 1049, 1599 reinforced-cement tiles, 867, 868 sheathing, 1049, 1055, 1567 paper, 1567 shingles, 1046, 1581 slag, 801, 1595-1599 slate, 871, 1046, 1049, 1582-1586 steel sheets, 1 599-1604 asbestos-covered, 819 tar-and-gravel, 871, 1027 tile, 866, 867, 871, 1586 tin, 801, 1046, 1049, 1588, 1595 (see also, Tin, roofing) warehouses, 800 Roofs, heat-transmission, 1259 Room, fresh air for furnace, 1322 Rope, for bells, 1726 cotton, hemp and Manila, 406-408 weight, 723 wire, 404-406 Ropes and cables, measures, 25 Rosin, weight, 723 • Rotary converter, 1463 Rotten rock, 134, 135, 256 Royalties, payments, 17 59 Round rods, safe loads, 388 Rubble (Glossary), 1842 Rubblework, 266, 441, 1538, 1842 cement, 235 1896 Index Rupture, Modulus of (see Modulus of rupture) Rust, reinforced concrete footings, i86 Safe load, definition, 125 Safety, factor of, definition, 126, 375, 556 appliances, elevators, 1664, 1669, 1672 St. John the Divine, Cathedral, founda- tions, 251 St. Louis building code, loads on foun- dation-beds, 143 loads on masonry, 267 office-buildings, assumed loads, 151 thickness of walls, 230-232 St. Paul building code, loads on foun- dation-beds, 143 office-buildings, assumed loads, 151 Saints, symbols, 1727 San Francisco building code, loads on foundation-beds, 143 thickness of walls, 231 San Francisco fire, tests of materials, 957 Sand, 134, 1553 angle of repose, 256 beds of, 134 chemical analysis, 138 classification and composition, 136 cost, 249 foundation-beds on, 141 in reinforced concrete, 908 Ottawa, 235, 241, 908 proportions, in concrete, 241-243, 247- 251, 908 in lime mortar, 1553 quicksand, 136, 137, 141, 211 safe loads on, 141, 143 screening, 1553 sieve tests, 138, 241 source of, 130, 1553 specific gravity, 1507 voids, 247-249 weight, 248; 256, 1507, I537> I554 Sand-bars, formation of, 133 Sand finish, plastering, 1555 Sandstone, 131 beams, coefficients for, 628 fiber-stresses, 557 tensional strength, 282 bituminous, paving, 1609 crushing strength, 266, 270, 279-282 fire-resistance, 814 loads, safe, 266, 267, 279, 282 modulus, of elasticity, 282 of rupture, 282 shearing strength, 282 specific gravity, 282, 1507. 1508 weight, 282, 1507, 1508 Sash, hollo \v-metal, 897 Sash, weights for, 1649, 1651 Sash-balances, 1652 Sash-chains, 1650 Sash-cords, 1649 Sash- pulleys, 1649 Sash-ribbons, 1650 Sash-weights, 1649, 1651 Saw-tooth roofs, 772-777 Schedule of charges, architects, 1728, 1731 Schists, 132 Schlierenmethode, photographing air- disturbances, 1495-1499 Scholarships, architectural, 1779-1788 School-buildings, 1644- 1648 cost, 1613, 1614, 1616 doors, 1648 flagpoles, 1644 floor-joists, 717 spans, 737, 742 floor-loads, live, 719 720, 1198 heating-temperature, 1256 hot-blast heating, 1324 non-fire-proof, height, 813 size of rooms, 717 stairs, 1648 ventilation, 1353 wa»ter-closets, 1641 Schoolrooms, blackboards, 1644, 1645 desks, 1645 dimensions of, 717, 1644 floor-loads, 719, 720, 1198 heating, 1256, 1324 lighting, 145 1 seats, 1645 ventilation, 1349, 1353 Schools, architectural, 1769, 1775, 1776, ■ _ 1779-1788 Scissors trusses, 1004, 1010-1013, 1055, 1056 stresses, 1081-1087 wall-joint, 1156 Screen (Glossary), 1843 Screw-ends, 386-398 Screw-jacks, 215, 216, 221 Screws, 1535, 1536 lag, 1157, 1535 threads, standard, 1525 Scripture measures and weights, 34 Scuppers, 767 Seat-baths, dimensions, 1641 Seating capacity, 165 3- 1656 Seating-space, churches, 1653, 1654 schools, 1645 theaters, 1653-1656 Seats, dimensions of, 1638, i6;i5, 1653 Seattle building code, masonry loads 287 Secants, table of natural, ii6 SeQtiQn-f actor (see Section-modulus) Index 1897 Section-modulus, 333 elementary sections, 334-338 structural shapes, 354-359, 362-369 Sectar of circle, 38 ceater of gravity, 293 Sedimentary rocks, 131 Segneat of circle, 38 center of gravity, 293 Segnental arch, 305, 307, 321 Seleriite, 131 Senicircle, center of gravity, 293 Separators for steel beams, 612-614, 1202 Services, architects, 1731 Sevige, ejectment of, 1422 Se,v3r-pipes, 1407-1409, 1419, 1420, 1422 Sewers, as afifecting foundations, 147 house, 1409 Sexigon, 37 Shift, elevator, 1659, 1660, 1666, 1675, 1676 fire-proof, 889, 890 for mills, 764, 768 Shafting, loads, 1197 machinery, 1720-1722 Shale, 132, 143 bricks, 275 specific gravity and weight, 1508 Shear, 128, 411 beams (see Beams) baits (see Bolts) buildings, wind-pressure, 1176-1183 cast iron, 412 double, 411 failures, illustrations, 170, 171, 411, 412 girders (see Beams) horizontal, wooden beams, 412, 635 pins, 423, 424 plate girders, 684-687, 690, 691, 696, 698, 703 reinforced-concrete, 912, 921, 937-940 rivets (see Rivets) single, /,.ii steel, 382, 412, 567, 569, 1132 specifications, 1203 vertical, beams, 411, 565, 567 diagrams, 685, 686, 690, 698 wind-bracing, 11 76-1 183 web-plates, in plate girders, 703 wind-bracing, 1176-1183 woods, 412, 647-651, 1138 Shearing, effect on steel, 382, 414, 688 Sheathing, asbestos corrugated, 819 mill-construction, 759 papers, 1564-1568 roof, weight, 1049 wooden, 1049, 1563 Sheathing- quilt, 1564-1568 Sheet lath, 886 Sheet, metal, 402,886, 1510, 1511, 1599 tile, 1587 Sheet- piling, 200-209 Sheet iron and steel, asbestos-covered, 819 base-price, 1205 ceiling, 1604 corrugated, 1599-1604 galvanized, 1604 gauges, 402, 1 5 10, 1600 roofing, 1599-1604 siding, 1603 Shelf-angle, beam-framing, 787-790 Shelf-hangers, 752, 788, 790 Shingles, 1581 asbestos, 819 dimensions, 1582 nails required, 1581, 1582 sizes, 1 581 staining, 1570 tin, 1046, 1049 weight, 1046, 1049, 1581 wooden, 1046, 1049, 1570, 1581 Shop drawings, 1754 Shops, hot-blast heating, 1324 Shoring, excavations, 214-222 Shot-drills, foundation-bed testing, 145 Shutters, fire, 759, 778, 801, 901-902 Sideboards, dimensions, 1638, 1640 Sidewalks, flagstones, 1539 granite curbing, 1539 vault-walls, 263-264 Siding, beveled and drop, wooden, 1563 corrugated metal, 1603 Silica minerals, 130 Silicates, 130 Sills, stone, 1539 Silt, 139 Silver, specific gravity and weight, 1508 Simplex concrete pile method, 197 Sines, table of natural, 95 Sinks, 141 2, 1641 Sirocco, fans, 1341, 1344 Skeleton construction, 234, 948, 11 71 Skewback, arch, 305,307 floor-arches, 834-835 vaults, 1232 Skylights, glass for, 1580 mills and warehouses, 765 saw-tooth, 769, 772-777 standard, defined, 1854 weight, 1049 Sky-signs, wind load, 1199 Slabs, reinforced-concrete (see Rein- forced concrete) Slag, in cement, 236, 237 roofing, 801, 1595-1599 Slag' cements, characteristics, 236, 237, 238 Slag concrete, fire-resistance, 817 1898 Index Slate, 132, 1582 beams, coefficients for, 628 safe fiber-stress, 557 cost, 1046, 1585 crushing strength, 282 flooring, 1606 grading of, 1583 laying, 1583 Old English method, 1584 measurement, 1584 modulus of elasticity, 282 modulus of rupture, 282 nails required, 1585 punching, 1583 roofs, 871, 1046, 1049, 1582-1586 sizes, 1583 specific gravity, 282, 1508 strength, 282, 557 thickness, 1583 tile, 1606 weight, 282, 1049, 1508, 1585 Sleeve-nuts, 386, 387, 397 Slenderness-ratio, columns, 448 Slip, in pump action, 1247 Slop-sinks, dimensions of, 1641 Slope, of roofs, 867, 869, 1046, 1053 of repose, 256 Slow-burning construction (see Mill- construction, slow-burning) Smoke-pipe, 1362 Snow-loads, 1049, 1052-1057 Soapstone, 131 Societies, architectural, 1 788-1 795 Sofas, dimensions, 1640 Soffit, arch, 305 Softwoods, ultimate unit stresses, 649- 651 Soil, 132 angle of repose, 256 foundation-beds, 135-148, 980 weight of loose, 256 Soil-pipes, 1407, 1410, 1427 Solids, m.ensuration of, 61 Sound (see Acoustics) Soundproofing, partitions, 891 South. Carolina, registration law, 1779 Span, arch, 305 beams, definition, 555 wooden joists, 736-746 Spandrels, arch, 305 Specifications, cast iron, 379 column-connections, cast-iron, 457, 458 electric wiring, 1482 elevator-installation, 1 663-1664 fire-shutters, tinned, 901-902 furnace-heating, 1357-1359 gravel roofing, 1 595-1 599 hot-water heating, 1359 hydrated lime, 1551 lime, 1549 Specifications, paint, fire-proof, 821 plate girders, 682 plumbing-fixtures, 1640 Portland cement, 236, 907 reinforcing-steel, 914 roofing-tiles, 1586 slag roofing, 1 595-1 599 standard, A. I. A., 1752-1764 steam-heating, 1361^ steel, in reinforced concrete, 914 structural, 383, 1194-1204 tile roofing, 15S6 wiring, electric work, 1482 wooden-pile foundations, 193 wrought iron, 377 Specific gravity, 1500-1508 Specific heat, 1250, 1684 Specific volume, gases, 1256 Spheres, 38, 60, 64 Spheroids, 60, 65 Spider, domes, 1222 Spikes, cut steel, 1532 steel-wire, 1533 Spinning-mills, cost, 805 Spring-hne, arch, 305 Spring-needles, 221 Springers, arch, 305 Sprinklers, automatic, 801, 903-905 framing to accommodate, 777 mills, 759, 768 tanks, 779 Spruce, beams, coefficients for, 628 deflection, 664 distributed loads, safe, 639 fiber-stress, 557, 647, 648 columns, safe loads, 451 crushing-loads, with the grain, 449 crushing strength, across the grain, 454 modulus of elasticity, 647, 664 shearing strength, 412, 647, 648 specific gravity, 1508 stiffness, 664 tension, 376, 647, 648 unit stresses, 376, 412, 647, 648, 650 weight, 650, 1508, 1558 Square, squares, 37, 39 hollow, moment of inertia, 335 pleasures, 27 moment of inertia, 334 radius of gyration, 334 section-modulus, 334 tables of, 8-24 Square roots, 3 tables, 8-24 Stability of structures, definition, 125 Stack, looilcr, 1283 furnace, 1312, 1317, 1322, 1358 steel, 1376 anchor-bolts, 1377 tall buildings, 1283, 1368 Index 1.S99 Staff, 1558 Stainless cements, 238 Stairs, dimensions, 1646, 1647, 1648 Ferroinclave foundation, 900 fire-proof, 899-900, 947, 983 hand-rail, 1648 hollow-tile steps, 899, 904 mill-construction, 759, 810 tower, 764, 768, 778, 779 reinforced-concrete, 900, 947, 983 risers, 1648 table, 1646, 1647 school-houses, 1648 towers for, 764, 768, 778, 779 treads, 899, 1648 table, 1646, 1647 Stairways, loads, 1198 protection, fire, 764, 765, 778, 779 Standpipes, 768, 801, 905 States, registration of architects, 1768, 1777 Stitistics, definition, 124 Stitis, architects, 1728, 1754 Sieim, 1251-1254 consumption, engines, 1247 heating, 1264, 1 283-1302 (see Heat- ing, steam) saturated, properties, 1253 Steitn-coils, hcaiing water by, 1344 Steam-heating (see Heating) St3el, adhesion to concrete, 912, 919, 920, 938, 940 bars, 385-398 areas, etc., 1514-1521 safe loads, 388-392 weight, 1514-1521 bas3-price, 1204, 1210-1212 beams (see Beams) Bessemer process, 380 branding, 385 carbon-content, 381 chemical properties, 383 chimneys, 1376 coefficient of expansion 382 cold-bend test, 378, 384, 385,914 columns (see Columns) compressive strength, 449 corrosion in concrete, 960-962 corrugated, base-price, 1205 weight, 1600, T603 cost, 1 204-1212 defined, 380 elastic behjivior, 381 elastic limit, 381, 913 eloi^ation, 381, 384, 9^3 eye-bars, 386, 595 finished material, 384 fire-resistance, 819 form of test-specimen, 384 manufacture, 380, 383 merchant, cost, 12 10 Steel, modulus of elasticity, 381, 912, 934 open-hearth process, 380 plates, 384, 385, 1204 phosphorus-content, 381, 383 properties, chemical and physical,.383 punching, effect on plates, 382, 414, 688 reinforcing (see Reinforcement) roof-trusses (see Roof-trusses) rope, 404-406 rupture-stress, 381 shearing, 382, 412, 567, 569, 1138 sheet, 1 599-1604 asbestos-covered, 819 base-price. 1205 corrugated, 1205, 1599-1604 gauges, 402, 1510 specifications, 383 specimens for tests, 383, 384, 407 strength, 407, 914 carbon and phosphorus, effect, 381 specification, 383 ultimate, 482 wire, 401, 406 working, 376, 412, 557, 1138, 1199 stress-strain diagram, 382 stresses (see strength) structural (see Structural steel) tests, 383-385, 1195 thickness, corrosive agents, 1202 weight, 382, 1510-1521 estimating, rule for, 152 1 sheets, 1510, 1511 variation in, 385 wire, 400-406, 1512 weight, 1512 yield-point, 381, 383, 912, 913 Steel-pipe columns, 469-474, 488 safe loads, 488, 497, 498 Steelwork, 1194-1206 bolted connections, 1204, 1206 buildings, weight, 1 207-1 209 cost-data, 1204- 1 212 cut to length, 1206 design, 1201 drafting, cost, 1206 erection, 1203, 1206 fire-protection, 468, 760, 780, 822- 826 foundations, 1203 freight-rates, 1205 inspection, 1203, 1205 mill-buildings, 786, 788, i2to painting, 1203, 1206, 1572, I573 specifications, 383, 1 194-1204 stresses, 618, 1138, ii99 weight, estimates, 1207-1210 workmanship. 1202 Steps, hollow-tile, 899 stone, 1539 1900 Index Stevedore-rope, 407 Stiffeners, girder-webs, 681, 686, 691, 921-923, 939, 940, 973 Stiffness, definition, 125 Stirrups, reinforced-concrete beams, 921-923, 939, 940, 973 wooden beams, 750, 754-757, 787- 794 Stone (see, also, Stonework and each kind of stone) angle of friction, 253 beams, 628 fiber-stress, 557 building-data, 282 caps, 1539 coefiicient of friction, 253 concrete, 908 coping, 1539 cost, 1538, 1613 crushed, cost, 249 crushing height, 269 crushing strength, 279-282 fire-resistance, 814 footings, 223, 224 lintels, 1539 masonry, 265-270, 1538 modulus of elasticity, 282, 283 piers, 270 quantities in concrete, 247-249 sills, 1539 steps, 1539 strength, 265-770, 279-282 weights, 282 Stonework (see, also, Masonry, Stone, Walls, etc.) ashlar, 441, 1538 bluestone, cut, 1539 coefficients of friction, 253 cost, data for estimating, 1538 crushing strength, 265 cut-work, 1538 data, 1538-1539 hammer-dressed, 1538 loads, safe, 266 measurement, 1538 rubble, 441, 1538 sidewalks, 1539 Storehouse-construction, 765-788 Straight-line formula, cast-iron columns, 460-461 depth of keystone, 308-309 steel columns, 481-482, 493-496 Strain, definition, 125 Strength, beams, law of variation, 565 breaking, 556 coefficient of, 556, 628 compressive, 448 definition, 125 elastic, 126 elongation-relation, steel, 381 flexural, definition, 125, 556, 635 Strength, of materials, definition, 125 shearing, 411, 635, 657, 667 tensile, 375 ultimate, definitions, 125, 375, 381 • 411, 448 working, definition, 125, 375 Strength of materials (see name of ma terial in question) definition, 125 Stress, stresses, 125, 254 (see, also materials in question) bearing, 415 bending, 265, 628, 647 combined, 128, 480, 572, 1114 compressive, 127, 647 constants, wooden beams, 628 diagrams and formulas, 1065-1137 distribution of, 254 elastic limit, 126, 381 fiber, 126. 32s, 555, 556 flexural, 126, 325, 333, 555 intensity, definitions, 125, 254, 375 modulus of rupture, 126 notation, 122 resultant, 254, 1183 reversal of, 1104 rupture, 381 secondary, 1137 shearing, 128, 411, 415, 647 horizontal, 635, 687 shrinkage, in concrete, 937 stress-strain diagram, 382 temperature, in concrete, 937 trusses, 11 28 tensional, 127, 375, 415, 647 torsion, 128 transverse, 265, 480, 555, 628 ultimate, 375 uniform, 254 unit, definitions, 125; 126, 375, 1172 varying, 254 wind, trusses, 1109-1118, 1123-1128 wind-bracing, 1176-1183 working, definitions, 125, 375 yield-point, 381 Stress-strain diagram, 382 String-course (Glossary), 1846 Structural shapes, 332-374 (see Angles, Channels, I beams, etc.) Structural steel (see Steelwork) Structures, definition, 124 domical, 1213-1231 large, heating, 1324 theory of, 124 vaulted, 1231-1243 Struts, angle, tables, 488, 501-503 as beams, 571, 572 bracing, formulas, 495 cast-iron, trussed girders, 661 channel, loads, table, 499-500 compression-formulas, 496 Index 1901 Struts, double-steel-angle, loads, 503 eccentric loads, 453, 489 I-beam, strength of, 489 in trusses, steel, 480 loads, 1 201 tables, 488, 493-495 single-steel-angle, loads, 501 trusses, 998 wood, 633 strength of, 448-452 trussed girders, 661 Subcontractor's agreement, 1765 Subcontracts, 1761 Sugar, specific gravity, 1508 weight of, 723, 1508 Sulphur, anchoring-bolts, 240 Superintendent, architects, 1728 Surcharges, 306 Surface, center of gravity, 292 finish, concrete, 246, 965, 1555 measures, 27 metric, 31 Sway-rods, wind-bracing, 11 76, 1181 Swedge-bolts, steel columns, 619 Switches, electric lighting, 1478, 1479, 1481 Sycamore, specific gravity, 1508 weight, 1508, 1558 Syenite, 131 compression, 282 tension, 282 Symbols, Apostles and Saints, 1727 electric wiring, 1476-1478, 1484 gas-piping, 1445 mathematical 122. 123 pipes and fittings, 1350 plumbing, 1424-1426 System of units, engineers', 1247 T beams, reinforced concrete, diagrams for strength, 988-991 example, 971, 97 5 formulas, 933-934 reinforcement, 937, 94° Tsectioris, steel, base-price, 1212 fire-proof ceilings, 872 girder flange, 682 size and properties, 337, 3^8, 369, 5^5 strength, as beams, 591,682 Tables, furniture, dimensions, 1638. 1639 Tacks, wire, i533, iS34 Tail-beams, floors, 749 Talc, 131 specific gravity and weight, 1508 Tall buildings, stack, 1283, 1368 . Tangents, 38 tables of natural, 104 Tanks, capacity, 1 404-1406 construction, 1398-1402 expansion-tanks, 1307, 1360 Tanks, frost-proofing pipes, 1400 gravity-tanks, water, 779 heating, 1400 house-tanks, 1415 incrustation, 1429 materials, 1398 standard sizes, 1401 steel, 1402 wind-load, 1199 wooden, 1398 Telephones, automatic, 1707 Telltale (Plumbing), 1400 Temperature, absolute, 1250 concrete, 244, 245 humidity-relation, 1352 inside, table, 1256 maintenance, heating buildings, 1256 outside, in U. S. table, 1257 roof -trusses affected by, 11 28 United St'.tes, 1257 Tempering-coil, heating, 1328 Tenement-house, defined, 1854 floor loads, 719, 1198 specifications, 1200 • Tension, 127, 375 building materials, 376 members, steel, 385-387 - safe loads, 388-392, 399 sign, 1065, 1068, 1072 Terms, architectural (Glossary), 1796- 1850 building codes, 1851-1855 building laws, 1851-1855 engineering, 124-129 technical, 1796-1855 Terra-cotta, beam-protection, 782 book-tile, 867, 868 column-protection, 782, 822-826 composition, 276, 814 dense, 814, 816, 875 facing of walls, 269 fire-resistance, 234, 815, 816, 828, 874 floors, 828-840, 1604-1607 heat-transmission, 1258-1259 hollow walls, 233-234 ornamental, fire-resistance, 814 inside finish, 898-899 staircases, 899 partitions, 873-875, 889 piers, 276-278 porous, 815, 875 properties, 276 roof -construction, 866, 867, 871, 1586 semiporous, 815 sound-resistance, 889, 890 strength, 266, 276-278, 287, 815 tests, 276-278, 816, 873 truss-protection, 860 weight, 278 1902 Index Terrazzo flooring, 1607 Tests (see, also, materials in question) brick piers, 272-278 bricks, 270, 281, 1542 cast iron, 380, 446, 819-820 cement, 236-237, 240, 907 chains, 408-410 column-coverings, 822-823 columns, cast-iron, 460, 823 steel, 822 steel-pipe, 472 wooden, 449 concrete, 283-287, 817, 911 eye-bars, 386 fire-proof floors, 827, 841, 844, 866 fire-proof partitions, 828, 873, 889 fire-proof wood, 820 floors, 720-721, 866, 967 foundation-beds, 141 -146 joist-hangers, 756, 794 mortar, 283 nails, holding-power, 1531 pipe, water, 1388 plumbing, 1412 reinforced-concrete, adhesion*, 919-' 920 corrosion, 961 elastic properties, 935 fire-resistance, 955-960 hooped columns, 942 loads on floors, 967 sash-cords and sash-chains, 1650 sound-absorption, 1486-1500 steel, 382-385 stone, 279-281 terra-cotta, 276, 278, 816, 873-874 wooden beams, built-up, 652-654 columns, 449 wrought iron, 377-379 Theater-curtains, asbestos, 819 Theaters, chairs, 1653 defined, 1854 dimensions of, 1657 floor-loads, 719, 720, 1198 heating and ventilating layout, 1348, 1353 seating capacity, 1654-1656 seating-space, 1653 Thermometers, thermometry, 1249 Threads of screws, standard, 1525 Thrusts, 305 Tie-beams, wooden, 430, 432, 434, 43s, 633 built-up, 432 steel, stresses in, 572 Tie-plates, steel, 1202 Tie-rods, for 1 beams, 619, 865 roof -trusses, 11 20 segmental arches, 307, 832 Tile, 1 604-1 607 aseptic, 1605 Tile, cast-glass, 1606 cement, reinforced, 867—869 ceramic, 1605, 1607 concrete, 8i6 copper, 1587 cost, 1046, 1587, 1607 enameled, 1605, 1607 encaustic, 1604, 1607 faience, 1607 fireproofing, 234, 815, 828, 874 flint, 1605 flooring, 892-893, 1604-1607 Florentine mosaic, 1605 glass, 1606 glazed, 1605, 1607 hollow (see Terra-cotta) and concrete, 951-952 interlocking rubber, 1606 lozenge, 1605 Ludowici, 1049 mantel, 1605 marble, 1605 mosaic, 1607 piers, 278 reinforced, 838-842 reinforced-cement, 867-869 Roman, 1049, 1605, 1607 floor-construction, 953 roofing, 866, 1586 cost, 1587 laying, 1586 specifications, 1586 rubber, 1606 semivitreous, 1604 sheet-metal, 1587 slate, 1606 Spanish, 1049 specific gravity, 1508 steel, 1587 terrazzo, 1607 tin, 1587 vaults, 1243 vitreous, 1604, 1605, 1607 wall, 1604, 1606, 1607 weight, 1049, 1508 Tile-arch, Guastavino, 841, 842, 1243 Timber (see, also. Lumber and different woods ) board-measure, 1560-1562 bond (Glossary), 1803 data, 1558-1563 footings, temporary buildings, 186, 187 framing, sizes, 1559 hardness, relative, 1558 measurement, 1559-1563 modulus of elasticity, 647, 731- 734 painting, 763 piles, 188-196, 198 shrinkage, table, 1428 Index 1903 Timber, sizes in slow-burning construc- tion, 759, 762 stresses (see woods in question) ventilation, 763 weight, 1501-1508, 1558 working unit stresses, 647, 648, 650, 1138 Time, measures, 30 unit of, 1247 Tin, block, pipe, 1419 brands, 1588 casting, 1521 fire-doors, 894-897, 901-904, 1853 gutters, 1590 lined pipe, 141 5 roofing, 801, 1588-1595 cost, 1046, 1589, 1593, 1594 covering capacity, 1591-1594 durability, 1589 gutters, 1590 laying, 1 590-1 593 painting, 1570, 1589, i59o rolls, 1594 valley, 1590 sheets, 1588 specific gravity, 1508 terne-plates, 1588 weight, 723, 1049, 1508, 1521, 1588, 1591 Tinned fire-doors, 894-897, 901-904, 1853 Toncan metal, 1604 Torsion, definition, 128 Tower (Glossary, 1848), belt, 764, 765 elevator, 764, 765, 768 fire-escape, 779 stairway, 764, 765 warehouses, 768, 779 water, wind-bracing, 1184 Tower-clocks, 1695 Tracings, 1718-1720 black-line copies, 17 19 blue-prints, 17 18 brown-line copies, 1720 Train-sheds, steel, weight, 12 10 trusses for, 1039 Transferred heat, 1684 Transformers, current, 1463 Transmission of heat, 12 56-1 2 59, 1684 Trapezium, 37 Trapezoid, 37, 4° moment of inertia, 336, 337 radius of gyration, 336 section-modulus, 336 Trap-rock, 131 compressive strength, 282, 287 concrete aggregate, 817 specific gravity and weight, 282, 1508 Traps, plumbing, 1410. 1412-1414 drum, 1413. 1414 grease, 1414 Traps, sewer, 1409 ventilation, 141 2 Trautwine's formula, depth of keystone, 309 Travertine, 131 Treads, marble, 900 rules for, 1648 slate, 900 table, 1646, 1647 Treasury Department, hot-water heat- ing, 1303, 1308 Tremies, 244 Trenches, as afi'ecting foundations, 147 preparing for footings, 226 Triangles, 36, 39, 7i center of gravity, 292 moment of inertia, 336 oblique-angled, 92 of forces, 289 radius of gyration, 336 section-modulus, 336 trigonometrical functions, 91-94 Trigonometry, 90-117 Trim, cement, 898 electroplated, 898 hollow-tile, 898, 899 metal-covered, 894-899 Trimmers, floor, 728, 748 safe loads, 747 Troy weight, 29 Truss-metal lath, 885 Trusses (see Roof-trusses) Tubing, Benedict nickel, 141 5 seamless-drawn, 141 5 Tungsten, specific gravity and weight, 1508 Tungsten-lamps, 1444, i447 Tumbuckles, 386, 387, 397 Tuscan Order, 1699 Underpinning, 214, 218-222 Unit stress, definitions, 125, 126, 332. 375, 1172 Unit system, reinforcement, 922 Units, system of, 1247 electrical and mechanical, equiva- lents, 1248 foot-pound-second system, 1247 University of Illinois, tests on brick piers, 275 tests on terra-cotta piers, 277 Urinal-stalls, dimensions of, 1641 United States Goverment buildings, hot- water heating, 1303, 1306, 1308 United States measure of value, 29 United States Naval Observatory, foundations, 251 Utah, registration law, i779 V cuum-cleaners, types, 1708 ,num-gauges, 1248 1904 Index Vacuum, pumps, size, 1290 systems, steam-heating, 1287-1291 Valleys and gutters, 1590 Valves, equalizing, caissons, 212 heating, symbol, 1350 Vapor, 1249-1254 (see Steam) Vaporization, heat of, 1684 Varnish, 1568, 1570, 1573 Vault, 1 231-1243 barrel, 1231-1235 (Glossary), 1849 framed, 1243 groined, 1235-1240, 1822 legal definition, 1855 ribbed, 1240 tile, 1243 Vault-walls, 263-264 Vaulting (Glossary), 1822 Velocity, unit, 1247 Veneer, buildings, 269 defined, 1855 Vent-flues, air-velocity, 1357 coils, 1356 Vent-pipes, plumbing, 1407, 1410 sizes, 1410 Vent-shafts, fire-proof, 889 Vento heater, 1330-1332, 1338 Ventilating fans, 1341-1347, 1357 Ventilation, 1348-13 54 air required, amounts, 1260, 1354, 1356 buildings, 1348-1354, 1356 capacity of fans, 1341 fans, 1341-1347, 1357 furnace-heating, 1313 gravity indirect heating, 1299 hot-blast system, 1325, 1327 laws, 1354 mill-buildings, 769, 775-776 saw-tooth roofs, 776 systems, 1349 timbers, 763 warehouses, 776 workshops, 769, 1353 Verona radiators, 1266 Vibration of machinery, 763 Volt, defined, 1457 Voltage, candle-power, 1462 Volume, measures, 27, 31, 1247 Volumes, geometrical, 38, 60-65 Voussoirs, arch, 305, 311, 313 center of gravity, 313, 318 Walks, cement, 239 Wall (see, also, Brickwork, Masonry, Stonework, etc.) ashlar, thickness, 233 basement, 228, 229 bearing-plates on, 442 breast, 262-263 brick, 229 backing, 269 Wall, brick, over openings, 318 safe loads, 265, 441 buckling, 229 buildings, mercantile, 230-232 cantilevering, 169 cellar, 129, 228, 229 cement-block-faced, 269 center of gravity, 300, 301 concrete, 229, 946-947, 965, 966 cost, 250 concrete blocks, 233 crushing height, 269, 270 curtain, 234 dwellings, 230, 232 external, thickness, 229, 231 face, 269 faced, with ashlar, 233, 269 with cement blocks, 269 with terra-cotta, 269 fire, 765 fire-resistance, 229, 234 footings (see Footings) foundation, 129, 200,. 228, 229, 979 heat-transmission, 1256 hollow-tile, 233 loads over openings, 318 mills and factories, 760, 765, 768, 778, 809 needling, 218-222 openings in, 318, 778 parapet, 768 party, 234 reinforced-concrete, 946, 948, 968, 975, 978 retaining (see Retaining- wall) roof, 768 safe loads, 265-267 self-sustaining, 234 shoring, 214-222 skeleton construction, 234 stability, 229, 301 stone, 229, 233 safe loads, 266, 267 stone-faced, 233, 269 ashlar, 233, 269 strength, 265-267, 269, 270 superstructure, 229-234 supports, girders, 792 terra-cotta facing, 269 thickness, 229-234, 260-261, 269, 760 tile, hollow, 233 tiling, 1604, 1605, r6o7 underpinning, 214, 218-222 vault, 263-264 warehouses, 230-232, 768, 778 Wall-boards, asbestos, 819 metal-rib, 888 Wall-boxes, 782, 785, 786; 792, 793 Wall-hangers (see Hangers) Index 1905 Wall-openings, 31 8, 778 Wall-pipe (furnaces), dimensions, 1320 Wall-plasters (see Plaster) Wall-plates, beams and girders, 783, 785, 787, 788, 793 roof-trusses, 1150-1152, 1156, 1158 1165, 1168 Walnut, hardness, 1558 specific gravity, 1508 unit stresses, 651 weight, 651, 1508, 1558 War Department, hot-water heating, 1303 Wardrobes, dimensions, 1638, 1640 Warehouses, basement walls, 229 beams, 762, 763, 779, 800 boilers, 780 cast-iron columns, 780, 781 cement floors, 892 construction, general, 758-810 cost, 777, 802-810 defined, 1855 fire-escape, 768, 778 fireproofing, 780-782 fire-protection (see sprinklers, below) floor-areas, 765, 777, 778 floor-loads, 721, 1198 floors, 764, 777, 892, 893 size and weight of I beams, 865" girders, 762, 763, 779-800 gravity-tanks, 779 heating, 776 height, 777 live loads, 721 mill-construction for, 777-782 openings in walls, 778 roofs, 768, 772, 800 roofing-materials, 800, 801 scuppers, 767 sprinklers, 768, 777, 779> 801, 903- 905 stairs, 759, 764, 768, 778, 779, 810 standpipes, 768, 801, 905 steel, weight, 1208 story-heights, 765 structural details, 780, 788, 810 towers, 768, 779 ventilation, 776 walls, 230-232, 768, 778 wooden columns versus iron and steel, 780 water-supplies, 802 Warren truss, types, 1030, 103 1 stresses, 1089-1091 Wash-basins, dimensions, 1641 Washers, 437, 1157-1160 beveled, 437, 1202 Washington building code, steel col- umns, 481 Washington Monument, foundations, 251 Wash-pipes, foundation-bed testing, 144 Wash-stands, dimensions of, 1638 Wash-tubs, 141 2 Waste-pipes, 1407-1411, 1416, 1417, 1427 Waste-stacks, expansion, 1427 Water, density, 1247 evaporation, 1251-1254 filters, 142 1 flow in pipes, 1382-1388 freezing-point, 1250 hard, softening, 1429 head, 1381-1383, 1389 heating, house-supply, 1430 incrustation of tanks, 1429 pressure, 1381, 1382, 1389 properties, 1381 required for mortar, 238 softening, 1429 specific grav ty, 1381, 1500, 1508 supply, 802, 1390-1398, 141S tanks (see Tanks) temperatures, boiling, 1251 weight, 1381, 1500, 1508 Water-backs, capacity, 1430 Water-closets, 141 1, 1428, 1641 Water-curtains, 901, 903 Water-filters, 142 1 Water-gas, 1431 Water-heaters, 1421, 1425 Water-meters, 1425 Water-pipes (see Pipes) Water-seal, 1413 Water-supply, 1390-1398, 1415 fire-protection, 802 Water-tables, stone, 1539 Water-tanks (see Tanks) Water-towers, wind-bracing, 11 84 Waterproofing, 17 09-1717 cement, 1711, 1717 concrete, 246, 1711, 1717 foundations, 1709 external, 17 13 foundations, 1 709-1 71 7 water-proof cement, 1714 paper, 1567 Watt, 33, 1248, 1459 Web (see, also. Box Girders, Plate girders, and Beams, steel) box girders, buckling value, 686, 705 shearing value, 684, 703 stiffeners, 681, 686, 691, 696, 1201, 1203 domes, 1241 plate girders, 681, 703-716 buckling value, 686, 705 shearing value, 703 stresses, 684, 686, 691 steel beams, web-buckling, 181-185, 565, 567-569, 612, 627 w«b-thickness, 592 1906 Index Wedges, shoring, 215 Weight (see each substance, and also Loads) adult persons, 1644 measures of, 28-29 metric system, 32 merchandise, 721-723 sash, 1649-1651 substances, per cubic foot, 1501-1508 unit of, 1247 Weights and measures, 25-35 Weld, iron, 377 steel, 377 Welded-metal fabric, 948-949 Wellington's formula for pile founda- tions, 193 Wells, dredged, foundations, 210 driven, water-supply, 1391 foundations affected, 147 Welsbach lamps, 1444-145 1 Wemlinger sheet-piling, 209 Wheat, weight, 723 White-coating, plastering, 1555 White pine, beams, coefficients for, 62S deflection, 664 fiber-stress, flexure, safe, 557, 647, 648, 1138 safe loads, 639 columns, safe loads, 450, 452 crushing-loads, with the grain, 449, 650 crushing strength, across the grain, 454, 650 hardness, 1558 modulus, of elasticity, 647, 664 of rupture, 650 safe loads on columns, 450, 452 shearing-stresses, 412, 647, 648, 1138 specific gravity, 1507 stiffness, 664 tension, 376, 647, 648, 650, 1138 unit stresses, 376, 412, 647, 650, 1138 weight, 650, 1507, 1558 White wood (poplar), columns, safe loads, 450, 452 crushing-loads, with the grain, 449 hardness, 1558 specific gravity and weight, 651,1507 unit stresses, 651 Wind, force of, 17 17 pressure, 1171-1173 resistance, 1175 stresses, bracing, 11 76-1 183 trusses, 1109-1118, 1123-1128 Wind-bracing, 1171-1193 building law, 1171-1172, 1176, 1202 column-connections, 1174-1175, 1179, IT89, 1190 columns, types, 1183 conditions determining, 1172 details, 1189, 1190 Wind-bracing, examples, 1187-1193 general theory, 1173-1174 gusset-plate type, 1176, 1179, 1189, 1190 knee-brace type, 1176, 1179, 1180 lattice-girder type, 11 76, 1181 moment-increments, 1176, 1178 portal type, 1176, 1182 resistance-factors, indeterminate, 1 178 stresses, computation of, 1176-1183 sway-rods, 11 76, 1181 types, 1174-1176, 1187-1193 water-towers, 1184 Wind-loads, 1053, 1198 Wind-shields, scuppers, 767 Wind-stresses (see Stresses) Windmills, capacity, 1394 Window-frames, bronze, <395 fire-resisting, 902 Kalamein iron, 895 metal, 897 metal-covered, 895 mill-construction, 764 Window-sashes, fire-resisting, 902 metal, 897 metal-covered, 895 weights, 1649- 1651 Window-sills, stone, 1534 Windows, bay (Glossary), 1802 fire-protection, 901 glazing, 1573-1580 heat-transmission, 1258 loads over, 318 metal-frame-and-wire-glass, 901-902 mill-construction, 759, 763, 769 saw-tooth, 772, 775, 778 sheet-metal, 902 water-curtains, 901, 903 wire-glass in warehouses, 778 Winslow formula, wooden columns, 450 Wire, 402, 403 annealed, 1513 aviator, 401 Bessemer, 1513 bright, 1513 copper, 401, 1469, I470» i474, iSi3 electric wiring, 1466-1485 (see, also, Wiring) calculations, 1469-1479 lighting, 1469 resistance, 1474 fabric, reinforcement, 850 feed, 1478 finish, 400 fire-detecting, 903 galvanized, 406, 1513 gauges, 401, 1469, 1509, 1512 gun-screw, 1513 in glass, 759, 821 iron, 401 lath, 887 Index 1907 Wire, length per pound, 403 machinery, 15 13 manufacture, 400, 1513 market, 15 13 nails, 1529 piano, 401 plough, 401 rope, 404-406 _ weight, 403, 1474, 1512 size and weights, 403, 1474, 1475, 1477, 1512 steel, 400, 401, 403, 404, 406, 1 5 13 strength, 400-401, 403, 1512 telegraph, 401 telephone, 401 tinned. 15 13 uses, 401 Wire-glass, 759, 778, 821 Wire-mesh, 919 Wiring, electric-lighting, 1466-1485 cabinet, 1477 conduits, 1479 cost, 1482 national electrical code, 1480 specifications, 1482 symbols, 1476-1478, 1484 tables, 1475 Wisconsin, registration law, 1779 Wood (see, also, Lumber, Timber, and wood in question) beams (see Beams) columns (see Columns, wooden) .compression, across the grain, 454, 647, 650, 651, 1138 with the grain, 449, 647, 650, 651, 1138 fire-proof, 820, 894 flexure, 557, 647, 650, 651, J138 friction-coefficient, 253 fuel, 1272 hardness, relati^^i, 1558 metal-covered, 894-895 modulus of elasticity, 647, 664 painting, 1569-1572 shear, 412, 647-651, 1138 sheathing, 1049, 1563, 1564 specific gravity, 1501-1508 tension, 376, 647, 650, 651, 1138 weight, 650, 651, 1501-1508, 1558 working stresses, 647, 648, 650, 1138 Wool, weight, 721 Work, contractor's changes, 1757 energy, 1248 Working stresses (see Stress and ma- terials in question) Works, Clerk of the, 1728, 1733 Workshops, slow-burning, 769-771 ventilation, 769, 1353 Wrought iron, 377 appearance, 377 beams, coefficients for, 628 Wrought iron, beams, deflection, 664 stiffness, 664 bending moments, 431 bolts, 431, 1138 bearing strength, 1138 chains, 408, 410 compression, bolts, 1138 crushing-loads, 449 elongation, 378, 410 finish, 378 fire-resistance, 819 flexure, 431, 557, 1138 grades, 378 manufacture^of, 378 modulus of elasticity, 664 physical properties, 377, 378 pipe, 1408, 1429, 1432-1436 reinforcement, 907 rivets, 418 rope, 404-406 shearing-stresses, 412, 431, 1138 specific gravity, 1505, 1510 specifications, 377-378 stirrups, 750, 757 tension, 376, 377-378, 410, 431, 1138 tests, 377-379 use, 377 weight, 1505, 1510, 1521 estimating, 1521 sheets, 1510 welding, 377 yield-point, 378 . Yellow pine, beams, coefficients for, 628 deflection, 664 fiber-stress, flexure, 557, 647, 648 safe loads, 642, 643, 666 columns, safe loads, 450, 451, 452 crushing-loads, with the grain, 449, 650 crushing strength, across the grain, 464, 650 hardness, 1558 modulus of elasticity, 647, 664 modulus of rupture, 650 safe loads on columns, 450, 451 shearing-stresses, 412, 647, 648, 650 specific gravity, 1507 stiffness, 664 tension, 376, 647, 648, 650 unit stresses, 376, 412, 647, 648, 650 weight, 650, 1507, 1508 Yield-point, steel, 381, 383, 912, 913 wrought iron, 378 Young's modulus, 126 Z bars, base price, 1204 purlins, 11 69 Zinc, castings, shrinkage, 1521 specific gravity and weight, 1508 Zone of sphere, volume, 64 UNIVERSITY OF CALIFORNIA BRANCH OF THE COLLEGE OF AGRICULTURE THIS BOOK IS DUE ON THE LAST DATE STAMPED BELOW ^^KC-d iBm- * #^16 "^^ 29 '41 JUN 1 1 1942 umzs-m' ,,5,0 l<6Wi*« c^y 1 '®''* JAN 12 SBTB 5/w-8,'26 4CS447 i*4 UNIVERSITY OF CALIFORNIA LIBRARY