GIFT OF 
 J..C. 
 
THE 
 
 ARCHITECT'S AND BUILDER'S 
 POCKET-BOOK 
 
 A HANDBOOK FOR ARCHITECTS, STRUCTURAL 
 
 ENGINEERS, BUILDERS, AND 
 
 DRAUGHTSMEN. 
 
 BY 
 
 FRANK E. BIDDER, C.E., PH.D., 
 
 Consulting Architect and Structural Engineer, Denver, Colo.; 
 
 Fellow of the American Institute of Architects; 
 
 Author of " Building Construction 
 
 and Super i ntendence. ' ' 
 
 ffllustrateD witb 1000 J6n0ratnn06, mostly 
 from riginal 
 
 FOURTEENTH EDITION, REWRITTEN. 
 
 NINTH THOUSAND. 
 TOTAL ISSUE, T\VENliT-IIV THOUSAND. 
 
 NEW YORK : 
 
 JOHN WILEY & SONS. 
 
 LONDON : CHAPMAN & HALL, LIMITED. 
 
 1905. 
 
Copyright, 1884, 1892, 1897, 1904, 
 
 BY 
 
 FRANK E. KIDDER. 
 
 
 PRESS OF 
 
 BRAUNWORTH & CO. 
 
 BOOKBINDERS AND PRINTERS 
 
 BROOKLYN, N. Y. 
 
s Boob 
 
 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.* 
 
 1 Dedication to First Edition. 
 
 288893 
 
 . 
 
THE publishers and the author will be grateful to any of 
 the readers of this volume who will kindly call their attention 
 to errors, typographical or otherwise, discovered therein, in order 
 that these may be corrected before the next edition goes to 
 press, also for suggestions towards making the index more com- 
 plete; 
 
 JOHN WILEY & SONS, 
 
 43 & 45 EAST NINETEENTH STREET, 
 
 NEW YORK. 
 
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 improvements have 
 taken place in the building world, so many articles invented, 
 new methods of construction developed, higher standards estab- 
 lished, 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 and reliable as Trautwine's had been to 
 civil engineers; and with that object constantly 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 
 utilization of those hours which one ordinarily takes for recrea- 
 tion, and at the best more or less interruption to his regular 
 business, and consequent reduction in income, the writer under- 
 
 v 
 
VI PREFACE TO FOURTEENTH EDITION. 
 
 took 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 : 
 
 1st. A reference-book which should contain some informa- 
 tion on every subject (except design) likely to come before an 
 architect, structural engineer, draughtsman, or master-builder, 
 including data for estimating the approximate cost. 
 
 2d. To as thoroughly cover the subject of architectural engi- 
 neering as is practicable in a handbook. 
 
 3d. To present all information in as simple and convenient a 
 form for immediate application 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 "Archi- 
 tectural Engineering" had not been used in its present applica- 
 tion, and the term "Structural Engineering," 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. 
 
 Where it was impossible, for lack of space, to go extensively 
 into any subject, references to other books or sources of infor- 
 mation have been given, so that in this way the book may 
 serve as a general index to the many lines of work, materials, 
 and manufactured products entering into the planning, con- 
 struction, 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 or draught- 
 ing-table, and is seldom carried in the pocket, 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 
 
PREFACE TO FOURTEENTH EDITION. vii 
 
 have been taken to furnish reliable data. A large number of 
 experts in various lines 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. Also 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 stim- 
 ulus 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 sugges- 
 tions looking to the further improvement of the book, will com- 
 municate 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 perfect handbook. 
 
 F. E, KIDDER. 
 DENVER, COLO., July 18th, 1904. 
 
PREFACE TO FIRST EDITION, 1884. 
 
 IN preparing the following pages, it has ever been the aim of 
 the author to give to the architects and builders of this country 
 a reference book which should be for them what Trautwine's 
 "Pocket-Book" is to engineers, a compendium of practical 
 facts, rules, and tables, presented in a form as convenient for 
 application as possible, 1 and as reliable as our present knowledge 
 will permit. Only so much theory has been given as will render 
 the application of the formulas more apparent, and aid the 
 student in understanding, in some measure, the principles upon 
 which the formulas are based. It is believed that nothing has 
 been given in this book but what has been borne out in practice- 
 
 As this book was not written for engineers, the more intricate 
 problems of building construction, which may fairly be said to 
 come within the province of the civil engineer, have been omitted. 
 
 Desiring to give as much information as possible likely to be of 
 service to architects and builders, the author has borrowed and 
 quoted from many sources, in most cases with the permission of 
 the authors. Much practical information has been derived from 
 the various handbooks published by the large manufacturers of 
 rolled-iron beams, bars, etc.; and the author has always found 
 the publishers willing to aid him whenever requested. 
 
 Although but very little has been taken from Trautwine's 
 ''Pocket-Book for Engineers," yet this valuable book has served 
 the author as a model, which he has tried to imitate as well as 
 the difference in the subjects would permit; and if his work 
 shall prove of as much value to architects and builders as Mr. 
 Trautwine's has to engineers, he will feel amply rewarded for 
 his labor. 
 
 As it is impossible for the author to verify all of the dimensions 
 
PREFACE TO FIRST EDITION. 
 
 and miscellaneous information contained in Part III., he cannot 
 speak for their accuracy, except that they were in all cases taken 
 from what were considered reliable sources of information. The 
 tables in Part II. have been carefully computed, and it is believed 
 are free from any large errors. There are so many points of 
 information often required by architects and builders, that it is 
 difficult for one person to compile them all; and although the 
 present volume is by no means a small one, yet the author desires 
 to make his work as useful as possible to those for whom it has 
 been prepared, and he will therefore be pleased to receive any 
 information of a serviceable nature pertaining to architecture or 
 building, that it may be inserted in future editions should such 
 become necessary, and for the correction of any errors that may 
 be found. 
 
 The author, while compiling this volume, has consulted a great 
 number of works relating to architecture and building ; and as he 
 has frequently been asked by students and draughtsmen to refer 
 them to books from which they might acquire a better knowledge 
 of construction and building, the following list of books is given 
 as valuable works on the various subjects indicated by the 
 titles : 
 
 "Notes on Building Construction/' compiled for the use of the 
 students in the science and art schools, South Kensington, Eng- 
 land. 3 vols. Rivingtons, publishers, London. 
 
 "Building Superintendence," by T. M. Clark, architect and 
 professor of architecture, Massachusetts Institute of Technology. 
 J. R. Osgood & Co., publishers, Boston. 
 
 "The American House Carpenter' 7 and "The Theory of 
 Transverse Strains," both by Mr. R. G. Hatfield, architect, 
 formerly of New York. 
 
 "Graphical Analysis of Roof-Trusses," by Professor Charles 
 E. Green of the University of Michigan. 
 
 "The Fire Protection of Mills," by C. J. H. Woodbury, in- 
 spector for the Factory Mutual Fire Insurance Companies. John 
 Wiley & Sons, publishers, New York. 
 
 "House Drainage and Water Service," by James C. Bayles, 
 editor of "The Iron Age" and "The Metal Worker." David 
 Williams, publisher, New York. 
 
 "The Builders' Guide and Estimators' Price-Book," and "Plas- 
 ter and Plastering, Mortars, and Cements," by Fred. T. Hodgson, 
 editor of "The Builder and Wood Worker." Industrial Publi- 
 cation Company, New York. 
 
PREFACE TO FIRST EDITION. xi 
 
 " Foundations and Concrete Works," and "Art of Building/' 
 by E. Dobson. Weale's Series, London. 
 
 It would be well if all of the above books might be found in 
 every architect's office; but if the expense prevents that, the 
 ambitious student and draughtsman should at least make him- 
 self acquainted with their contents. These works will also be 
 found of great value to the enterprising builder. 
 
CONTENTS. 
 
 PART I. 
 
 PAGE 
 
 ARITHMETICAL SIGNS AND CHARACTERS 3 
 
 INVOLUTION 4 
 
 EVOLUTION, SQUARE AND CUBE ROOT, RULES, AND TABLES 4 
 
 WEIGHTS AND MEASURES 25 
 
 THE METRIC SYSTEM 31 
 
 METRIC CONVERSION TABLES 34, 36a 
 
 SCRIPTURE AND ANCIENT MEASURES AND WEIGHTS 36 
 
 MENSURATION 37 
 
 GEOMETRICAL PROBLEMS 70 
 
 TABLE OF CHORDS 88 
 
 HIP AND JACK RAFTERS 97 
 
 TRIGONOMETRY, FORMULAS AND TABLES 98 
 
 PART II. 
 
 STRENGTH OF MATERIALS AND STABILITY OF 
 STRUCTURES. 
 
 INTRODUCTION 127 
 
 EXPLANATION OF SIGNS AND TERMS 128 
 
 CHAPTER I. 
 DEFINITIONS OF TERMS USED IN MECHANICS 130 
 
 CHAPTER II. 
 
 FOUNDATIONS AND SPREAD FOOTINGS , 135 
 
 xiii 
 
xiv CONTENTS. 
 
 CHAPTER III. 
 
 PAGE 
 
 MASONRY WALLS AND FOOTINGS CEMENTS AND CON- 
 CRETES 178 
 
 CHAPTER IV. 
 RETAINING WALLS VAULT WALLS 206 
 
 CHAPTER V. 
 
 STRENGTH OF BRICK AND STONE MASONRY AND CON- 
 CRETE 212 
 
 CHAPTER VI. 
 
 COMPOSITION AND RESOLUTION OF FORCES CENTRE OF 
 
 GRAVITY 231 
 
 CHAPTER VII. 
 STABILITY OF PIERS AND BUTTRESSES 242 
 
 CHAPTER VIII. 
 THE STABILITY OF ARCHES 249 
 
 CHAPTER IX. 
 BENDING MOMENTS AND SUPPORTING FORCES 266 
 
 CHAPTER X. 
 
 MOMENTS OF INERTIA AND RESISTANCE, RADIUS OF 
 GYRATION. DIMENSIONS AND PROPERTIES OF STRUC- 
 TURAL SHAPES 278 
 
 CHAPTER XI. 
 
 RESISTANCE TO TENSION PHYSICAL PROPERTIES OF 
 
 IRON AND STEEL 321 
 
 CHAPTER XII. 
 RESISTANCE TO SHEARING RIVETED JOINTS 360 
 
 CHAPTER XIII. 
 PROPORTIONS OF CAST-IRON AND STEEL BEARING-PLATES 
 
 AND FOR BRACKETS ON CAST-IRON COLUMNS 398 
 
CONTENTS. XV 
 
 CHAPTER XIV. 
 
 PAGE 
 
 STRENGTH OF POSTS, STRUTS, AND COLUMNS. DETAILS 
 
 OF COLUMN CONNECTIONS 407 
 
 CHAPTER XV. 
 
 GENERAL PRINCIPLES OF THE STRENGTH OF BEAMS AND 
 STRENGTH OF STEEL BEAMS. STANDARD CONNEC- 
 TIONS FOR STEEL BEAMS 497 
 
 CHAPTER XVI. - 
 STRENGTH OF CAST-IRON, WOODEN, AND STONE BEAMS . . 554 
 
 CHAPTER XVII. 
 
 STRENGTH OF BUILT-UP WOODEN BEAMS, FLITCH- 
 PLATES, AND TRUSSED GIRDERS 579 
 
 CHAPTER XVIII. 
 STIFFNESS AND DEFLECTION OF BEAMS 595 
 
 CHAPTER XIX. 
 
 STRENGTH AND STIFFNESS OF CONTINUOUS GIRDERS. . . . 608 
 
 CHAPTER XX. 
 RIVETED STEEL-PLATE AND Box GIRDERS 618 
 
 CHAPTER XXI. 
 STRENGTH AND STIFFNESS OF WOODEN FLOORS 651 
 
 CHAPTER XXIL 
 MILL AND WAREHOUSE CONSTRUCTION .- 687 
 
 CHAPTER XXIII. 
 FIRE-PROOFING OF BUILDINGS MATERIALS AND DETAILS 
 
 OF CONSTRUCTION 726 
 
 CHAPTER XXIV. 
 FIRE-PROOF AND INCOMBUSTIBLE FLOORS AND FLAT ROOFS 
 
 FORMULAS FOR REINFORCED CONCRETE 782 
 
 CHAPTER XXV. 
 ROOF-TRUSSES TYPES OF WOODEN AND STEEL TRUSSES. 883 
 
xvi CONTENTS. 
 
 CHAPTER XXVI. 
 
 PAGE 
 
 STRESSES TN ROOF-TRUSSES 941 
 
 CHAPTER XXVII. 
 
 ROOF-TRUSSES; PROPORTIONING MEMBERS OF, AND DE- 
 TAILS OF JOINTS 1037 
 
 CHAPTER XXVIII. 
 WIND STRESSES AND BRACING IN TOWERS AND HIGH 
 
 BUILDINGS 1075 
 
 PART III. 
 
 HEAT, FUEL, WATER, STEAM, AND AIR 1107 
 
 DRYING BY STEAM 1117 
 
 COMPARISON OF THERMOMETERS 1118 
 
 GRAVITY SYSTEMS OF STEAM HEATING 1121 
 
 SYSTEMS OF PIPING FOR STEAM HEATING 1146 
 
 STEAM-PIPE FITTINGS AND VALVES 1153 
 
 RULES FOR PROPORTIONING RADIATING SURFACE 1158 
 
 HOT- WATER HEATING 1168 
 
 FURNACE HEATING 1174 
 
 SPECIFICATIONS FOR HEATING APPARATUS 1188 
 
 TABLES OF HOT-AIR STACKS, REGISTERS, STEAM PIPING, 
 
 ETC 1197 
 
 SMOKE PREVENTION . 1207 
 
 VENTILATION. 1208 
 
 CHIMNEYS 1220 
 
 HYDRAULICS , .^ 1231 
 
 PRIVATE WATER-SUPPLY, PUMPS, WINDMILLS, ETC 1244 
 
 FIRE STREAMS 1251 
 
 CONSTRUCTION OF CYLINDRICAL WOODEN TANKS 1252 
 
 CAPACITY OF TANKS 1258 
 
 PLUMBING DEFINITIONS AND REQUIREMENTS 1262 
 
 PLUMBING MATERIALS AND DETAILS 1269 
 
 PLUMBING SPECIALTIES 1281 
 
 PLUNGE-BATHS 1283 
 
 ILLUMINATING-GAS, VARIETIES OF 1285 
 
 PIPING A HOUSE FOR GAS 1287 
 
 NOTES ON LIGHTING AND ILLUMINATION 1294 
 
 THE DIFFUSION OF LIGHT THROUGH WINDOWS 1300 
 
CONTENTS. xvii 
 
 PAGE 
 
 ELECTRICITY 1305 
 
 ELECTRIC LIGHTING AND WIRING 1311 
 
 SPECIFIC GRAVITIES AND WEIGHTS OF SUBSTANCES 1341 
 
 WIRE AND SHEET-METAL GAUGES 1345 
 
 WEIGHTS OF WROUGHT IRON, STEEL, COPPER, AND BRASS 
 
 SHEETS 1347 
 
 WEIGHT OF LEAD, COPPER, AND BRASS 1348 
 
 SIZE, WEIGHT, AND KINDS OF SMOOTH STEEL WIRE 1349 
 
 WEIGHTS AND AREAS OF ROUND AND SQUARE BARS 1350 
 
 WEIGHTS OF FLAT-ROLLED STEEL BARS 1353 
 
 DATA FOR ESTIMATING WEIGHT OF CAST IRON, WROUGHT 
 
 IRON, AND STEEL 1357 
 
 WEIGHT OF CAST-IRON COLUMNS 1358 
 
 WEIGHT OF CAST-IRON PLATES 1360 
 
 SCREW-THREADS, NUTS AND BOLT-HEADS, DIMENSIONS 
 
 AND WEIGHT. 1361 
 
 WEIGHT OF RIVETS AND ROUND-HEADED BOLTS 1364 
 
 NAILS, KINDS, VARIETIES, SIZES, ETC., HOLDING POWER OF 1365 
 
 SCREWS AND EXPANSION BOLTS 1370 
 
 EXCAVATING 1371 
 
 STONEWORK 1373 
 
 BRICKS AND BRICKWORK. . , 1376 
 
 LIME 1387 
 
 SAND AND GRAVEL , 1388 
 
 LATHING AND PLASTERING 13 r 9 
 
 LUMBER AND CARPENTERS' WORK 1394 
 
 BUILDING PAPERS FELTS AND INSULATING QUILTS 1401 
 
 PAINTS AND PAINTING 1403 
 
 GLASS KINDS AND PRICE LISTS 1415 
 
 TRANSLUCENT FABRIC MIRRORS 1424 
 
 MEMORANDA ON ROOFING SHINGLES, SLATES, TILES, TIN, 
 
 AND GRAVEL 1425 
 
 CORRUGATED IRON AND STEEL SHEETS ROOFING AND 
 
 SIDING . 1437 
 
 GALVANIZED IRON 1443 
 
 FLOOR AND WALL TILING 1443 
 
 ASPHALTUM, ROCK ASPHALT 1448 
 
 MINERAL WOOL 1450 
 
 ESTIMATING THE COST OF STRUCTURAL STEEL 1451 
 
 STANDARD STEEL CLASSIFICATION 1455 
 
 COST OF BUILDINGS PER CUBIC FOOT 1457 
 
xvm CONTENTS. 
 
 PAGE 
 
 COST OF BUILDINGS PER SQUARE FOOT 1467 
 
 DEPRECIATION OF BUILDINGS 1468 
 
 DIMENSIONS OF FURNITURE, PLUMBING FIXTURES, CAR- 
 RIAGES, FIRE-WAGONS, LOCOMOTIVES, AND CARS 1470 
 
 DIMENSIONS FOR HORSE-STALLS, FLAG-POLES, SCHOOL- 
 ROOMS, SCHOOL-SEATS, ETC 1474 
 
 STAIRS 1476 
 
 SASH WEIGHTS 1477 
 
 SEATING SPACE IN CHURCHES AND THEATRES 1478 
 
 CAPACITY OF CHURCHES, THEATRES, AND OPERA-HOUSES. . 1479 
 
 DIMENSIONS OF THEATRES AND OPERA-HOUSES 140 
 
 PROPORTIONING GUTTERS AND CONDUCTORS TO ROOF SUR- 
 FACE 1481 
 
 ELEVATORS 1482 
 
 MAIL CHUTES 1491 
 
 REFRIGERATORS 1492 
 
 TOWER CLOCKS 1494 
 
 LIBRARY STACKS, CAPACITY OF SHELVING 1494 
 
 CLASSICAL MOULDINGS 1496 
 
 THE CLASSICAL ORDERS 1497 
 
 LIGHTNING CONDUCTORS 1505 
 
 ADHESIVE STRENGTH OF SULPHUR, LEAD, AND PORTLAND 
 
 CEMENT FOR ANCHORING BOLTS 1507 
 
 EFFLORESCENCE ON BRICKWORK 1508 
 
 RELATIVE HARDNESS OF WOODS. WEIGHT OF ROUGH 
 
 LUMBER 1509 
 
 FORCE OF THE WIND 1510 
 
 To MAKE BLUE-PRINT COPIES OF TRACINGS 1510 
 
 HORSE-POWER, PULLEYS, GEARS, BELTING, AND SHAFTING 1512 
 
 CHAIN BLOCKS 1516 
 
 PROPORTION OF HOOKS 1518 
 
 THE LONGEST BRIDGES IN THE WORLD. . 1519 
 
 OTHER NOTABLE BRIDGES 1521 
 
 DIMENSIONS* AND WEIGHTS OF CHURCH BELLS 1522 
 
 LARGEST RINGING BELLS IN THE WORLD 1523 
 
 SYMBOLS OF THE APOSTLES AND SAINTS 1524 
 
 HEIGHTS OF COLUMNS, TOWERS, DOMES, SPIRES, ETC 1525 
 
 PRINCIPAL DIMENSIONS OF THE ENGLISH CATHEDRALS. . . 1527 
 
 DIMENSIONS OF THE VARIOUS OBELISKS 1528 
 
 DIMENSIONS OF SOME WELL-KNOWN EUROPEAN BUILDINGS. 1529 
 
CONTENTS. xix 
 
 PAGE 
 
 HEIGHT OF SOME OF THE TALLEST BUILDINGS IN THE 
 
 UNITED STATES 1531 
 
 DESCRIPTION OF NOTABLE AMERICAN BUILDINGS 1533 
 
 ARCHITECTS OF NOTED PUBLIC AND SEMI-PUBLIC BUILD- 
 INGS IN THE UNITED STATES 1537 
 
 LIST OF NOTED ARCHITECTS 1540 
 
 PROFESSIONAL PRACTICE OF ARCHITECTS, A.I.A. SCHED- 
 ULE OF CHARGES 1552 
 
 CONTRACT BETWEEN ARCHITECT AND OWNER 1553 
 
 THE UNIFORM CONTRACT 1555 
 
 ARCHITECTS' LICENSE LAW STATE OF ILLINOIS. 1558 
 
 COLLEGES AND SCHOOLS OF ARCHITECTURE IN THE UNITED 
 
 STATES 1562 
 
 TRAVELLING FELLOWSHIPS AND SCHOLARSHIPS 1565 
 
 LIST OF BOOKS FOR ARCHITECTS, DRAUGHTSMEN, AND 
 
 BUILDERS 1566 
 
 TRADE REFERENCES 1570 
 
 GLOSSARY OF TECHNICAL TERMS, ANCIENT AND MODERN, 
 
 USED BY ARCHITECTS, BUILDERS, AND DRAUGHTSMEN. 1575 
 LEGAL DEFINITION OF ARCHITECTURAL TERMS 1628 
 
PART I. 
 
 PRACTICAL 
 
 ARITHMETIC, GEOMETRY, AND TRIGONOMETRY. 
 
 RULES, TABLES, AND PROBLEMS. 
 
PRACTICAL 
 
 ARITHMETIC AND GEOMETBY. 
 
 SIGNS AND CHARACTERS. 
 
 THE following signs and characters are generally used to denote 
 and abbreviate the several mathematical operations: 
 The sign= means equal to, or equality. 
 
 means minus or less, or subtraction. 
 
 + means plus, or addition. 
 
 X means multiplied by, or multiplication. 
 
 -=-means divided by, or division. 
 
 2 ( Index or power, meaning that the number to 
 
 3 J which they are added is to be squared ( 2 ) or 
 ( cubed ( 3 ). 
 
 : is to } 
 
 : : so is >- Signs of proportion. 
 :to ) 
 \/nieans that the square root of the number before 
 
 which it is placed is required. 
 
 *v/means that the cube root of the number before 
 which it is placed is required. 
 
 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 2 T 5 ir , 0.46 
 
 means T 4 oV 
 
 means degrees, ' minutes, " seconds. 
 .*. means hence. 
 
 3 
 
4 INVOLUTION .EVOLUTION. 
 
 INVOLUTION. 
 
 To square a number, multiply the number by itself, and 
 the product will be the square; thus, the square of 18= 18 X 18= 
 324. 
 
 The cube of a number is the product obtained by multi- 
 plying the number by itself, and that product by the number 
 again; thus, the cube of 14=14X14X14=2744. 
 
 The fourth power of a number is the product obtained 
 by multiplying the number by itself four times; thus, the fourth 
 power of 10=10X10X10X10=10000. 
 
 EVOLUTION. 
 
 Square Root. Rule for determining the square root of a 
 number. 
 
 1st, 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, 1 0236. 8126. 
 
 2d, 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 remainder bring down the next period 
 or a new dividend. 
 
 3d, 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, also, in place of the cipher in the 
 divisor; multiply this final divisor by the number in the quotient 
 just found, and subtract the product from the dividend, and to 
 the remainder 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 down the next period 
 for a new dividend, and annex another cipher to the trial divisor, 
 ? and put a cipher in the quotient, and proceed as before. 
 
 EXAMPLE 10236.8126 ( 101.17 square root. 
 
 1 
 
 201~)0236 
 201 
 
 2021 ) 3581 
 2021 
 
 20227)156026 
 
 141589 
 
 14437 
 
CUBE ROOT. 
 
 Cube Root. To extract the cube root of a number, point 
 off the number 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 to right 
 of 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, and multiply by three, 
 and annex two ciphers for the trial divisor. Find how often 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. 
 
 Desired the ^493039. 
 
 493039 (79 cube root. 
 7X7X7=343 
 
 7X7X3=14700 
 
 7X9X3= 1890 
 
 9X9= 81 
 
 16671 
 
 150039 
 
 150039 
 
 Desired the ^/403583.419. 
 
 403583.419 ( 73.9 cube root. 
 
 7X7X7=343 
 
 7X7X3=14700 
 
 7X3X3= 630 
 
 3X3= 9 
 
 15339 
 
 73X73X3=1598700 
 
 73X 9X3= 19710 
 
 9X9= 81 
 
 1618491 
 
 60583 
 
 46017 
 
 14566419 
 
 14566419 
 
CUBE ROOT, 
 
 Desired the i/1 58252.632929. 
 
 158252.632929 ( 54.09 cube root. 
 5X5x5=125 
 
 
 5X5X3=7500 
 5X4X3= 600 
 4X4= 16 
 
 33252 
 32464 
 
 8116 
 
 540 X 540 X 3 = 87480000 
 540 X 9X3= 145800 
 9X9= 81 
 
 788632929 
 788632929 
 
 
 87625881 
 
TABLE 
 
 SQUARES, CUBES, SQUARE ROOTS, CUBE ROOTS, 
 AND RECIPROCALS, 
 
 -fco 
 
 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 1 to 
 1054. The reciprocal of a number is the quotient obtained by 
 dividing 1 by the number. Thus the reciprocal of 8 is l-j-8= 
 0.125. 
 
 7 
 
SQUARES, CUBES, SQUARE ROOTS, 
 
 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 
 
 . 1*25000000 
 
 9 
 
 81 
 
 729 
 
 3.0000000 
 
 2.0800837 
 
 .111111111 
 
 10 
 
 100 
 
 1000 
 
 3.1622777 
 
 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 
 
 576 
 
 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 
 
 5.3851648 
 
 3.0723168 
 
 .034482759 
 
 30 
 
 900 
 
 27000 
 
 5.4772256 
 
 3.1072325 
 
 .033333333 
 
 31 
 
 961 
 
 29791 
 
 5.5677644 
 
 3.1413806 
 
 .032258065 
 
 32 
 
 1024 
 
 32768 
 
 5.6568542 
 
 3.1748021 
 
 .031250000 
 
 33 
 
 1089 
 
 35937 
 
 5.7445626 
 
 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 
 
 6.0827625 
 
 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 
 
CUBE ROOTS, AND RECIPROCALS. 
 
 No. 
 
 Squares. 
 
 Cubes. 
 
 Square 
 Roots. 
 
 Cube Roots. 
 
 Reciprocals. 
 
 63 
 
 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 
 
 300763 
 
 8.1853528 
 
 4.0615480 
 
 .014925373 
 
 68 
 
 4624 
 
 314432 
 
 8.2462113 
 
 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 
 
 7569 
 
 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 
 
 8464 
 
 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 
 
 10.0498756 
 
 4.6570095 
 
 .009900990 
 
 102 
 
 10404 
 
 1061208 
 
 10.0995049 
 
 4.6723287 
 
 .009803922 
 
 103 
 
 10609 
 
 1092727 
 
 10.1488916 
 
 4.6875482 
 
 .009708738 
 
 104 
 
 10816 
 
 1124864 
 
 10.1980390 
 
 4.7026694 
 
 .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 
 
 .008620690 
 
 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 
 
 34884 - 
 
 1815848 
 
 11.0453610 
 
 4.9596757 
 
 .008196721 
 
 123 
 
 15129 
 
 1860867 
 
 11.0905365 
 
 4.9731898 
 
 .008130081 
 
 124 
 
 15376 
 
 1906624 
 
 11.1355287 
 
 4.9866310 
 
 .008064516 
 
10 
 
 SQUARES, CUBES, SQUARE ROOTS, 
 
 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 
 
 5.02G5257 
 
 .007874016 
 
 128' 
 
 16384 
 
 2097152 
 
 11.3137085 
 
 5.0396842 
 
 .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 
 
 5.0916434 
 
 .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 
 
 2628072 
 
 11.7473401 
 
 5.1676493 
 
 .007246377 
 
 139 
 
 19321 
 
 2685619 
 
 11.7898261 
 
 5.1801015 
 
 .007194245 
 
 140 
 
 19600 
 
 2744000 
 
 11.8321596 
 
 5.1924941 
 
 .007142857 
 
 141 
 
 19881 
 
 2803221 
 
 11.8743421 
 
 5 . 2048279 
 
 .007092199 
 
 142 
 
 20164 
 
 2863288 
 
 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 
 
 12.1243557 
 
 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 
 
 3796416 
 
 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 
 
 12.6491106 
 
 5.4288352 
 
 . 006250000 
 
 161 
 
 25921 
 
 4173281 
 
 12.6885775 
 
 5.4401218 
 
 .006211180 
 
 162 
 
 28244 
 
 4251528 
 
 12.7279221 
 
 5.4513618 
 
 .006172840 
 
 163 
 
 26569 
 
 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 
 
 5268024 
 
 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 
 
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 
 
 7J645373 
 
 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 
 
 206 
 
 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 
 
 10503459 
 
 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 
 
 15.1657509 
 
 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 
 
 SQUARES, CUBES, SQUARE ROOTS, 
 
 No. 
 
 Squares. 
 
 Cubes. 
 
 Square 
 Roots. 
 
 Cube Roots. 
 
 Reciprocals. 
 
 249 
 
 62001 
 
 15438249 
 
 15.7797338 
 
 6.2911946 
 
 .004016064 
 
 250 
 
 62500 
 
 15625000 
 
 15.8113883 
 
 6 . 2996053 
 
 .004000000 
 
 251 
 
 63001 
 
 15813251 
 
 15.8429795 
 
 6.3079935 
 
 .003984064 
 
 252 
 
 63504 
 
 16003008 
 
 15.8745079 
 
 6.3163596 
 
 .003968254 
 
 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 
 
 66049 
 
 16974593 
 
 16.0312195 
 
 6.3578611 
 
 .003891051 
 
 258 
 
 66564 
 
 17173512 
 
 16.0623784 
 
 6.3660968 
 
 .003875969 
 
 259 
 
 67081 
 
 17373979 
 
 16.0934769 
 
 6.3743111 
 
 .003861004 
 
 260 
 
 67600 
 
 17576000 
 
 16.1245155 
 
 6.3825043 
 
 .003846154 
 
 261 
 
 68121 
 
 17779581 
 
 16.1554944 
 
 6.3906765 
 
 .003831418 
 
 262 
 
 68644 
 
 17984728 
 
 16.1864141 
 
 6.3988279 
 
 .003816794 
 
 263 
 
 69169 
 
 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 
 
 71289 
 
 19034163 
 
 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 
 
 16.4924225 
 
 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 
 
 80089 
 
 22665187 
 
 16.8226038 
 
 6.5654144 
 
 .003533569 
 
 284 
 
 80656 
 
 22906304 
 
 16.8522995 
 
 6.573J.385 
 
 .003521127 
 
 285 
 
 81225 
 
 23149125 
 
 16.8819430 
 
 6.5808443 
 
 .003508772 
 
 286 
 
 81796 
 
 23393656 
 
 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 
 
 6.6267054 
 
 .003436426 
 
 292 
 
 85264 
 
 24897088 
 
 17.0880075 
 
 6.6342874 
 
 .003424658 
 
 293 
 
 85849 
 
 25153757 
 
 17.1172428 
 
 6.6418522 
 
 .003412969 
 
 294 
 
 86436 
 
 25412184 
 
 17 . 1464282 
 
 6.6493998 
 
 .003401361 
 
 295 
 
 87025 
 
 25672375 
 
 17.1755640 
 
 6.6569302 
 
 .003389831 
 
 296 
 
 87616 
 
 25934336 
 
 17.2046505 
 
 6.6644437 
 
 .003378378 
 
 297 
 
 88209 
 
 26198073 
 
 17.2336879 
 
 6.6719403 
 
 .003367003 
 
 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 
 
 272709Q1 
 
 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 
 
 .003278689 
 
 306 
 
 93636 
 
 28652616 
 
 17.4928557 
 
 6.7386641 
 
 .003267974 
 
 307 
 
 94249 
 
 28934443 
 
 17.5214155 
 
 6.7459967 
 
 .003257329 
 
 308 
 
 94864 
 
 29218112 
 
 ] 7 . 5499288 
 
 6.7533134 
 
 .003246753 
 
 309 
 
 95481 
 
 29503629 
 
 17.5783958 
 
 6.7606143 
 
 .003236246 
 
 310 
 
 96100 
 
 29791000 
 
 17.6068169 
 
 6.7678995 
 
 .003225806 
 
KUUTS, A1NJJ 
 
 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 
 
 30664297 
 
 17.6918060 
 
 6.7896613 
 
 .003194888 
 
 314 
 
 98596 
 
 30959144 
 
 17.7200451 
 
 6.7968844 
 
 .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 
 
 326 
 
 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 
 
 18.7082869 
 
 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 
 
 .002832861 
 
 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 
 
 128164 
 
 45882712 
 
 18.9208879 
 
 7.1005885 
 
 .002793216 
 
 359 
 
 128881 
 
 46268279 
 
 18.9472953 
 
 7.1071937 
 
 .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 
 
 . 002747253 
 
 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 
 
 50653000 
 
 19.2353841 
 
 7.1790544 
 
 .002702703 
 
 371 
 
 137641 
 
 51064811 
 
 19.2613603 
 
 7.1855162 
 
 .002695418 
 
 372 
 
 138384 
 
 51478848 
 
 19.2873015 
 
 7.1919663 
 
 .002688172 
 
14 
 
 SQUARES, CUBES, SQUARE ROOTS, 
 
 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 
 
 55308341 
 
 19.5192213 
 
 7.2495045 
 
 .002624072 
 
 382 
 
 145924 
 
 55742968 
 
 19.5448203 
 
 7.2558415 
 
 .002617801 
 
 383 
 
 146689 
 
 56181887 
 
 19.5703858 
 
 7.2621675 
 
 .002610966 
 
 384 
 
 147456 
 
 56623 ld4 
 
 19.5959179 
 
 7.2684824 
 
 .002604167 
 
 385 
 
 148225 
 
 57086625 
 
 19.6214169 
 
 7.2747864 
 
 . 002597403 
 
 386 
 
 148998 
 
 57512456 
 
 19.6468827 
 
 7.2810794 
 
 .002590874 
 
 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 
 
 .002531640 
 
 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 
 
 64481201 
 
 20.0249844 
 
 7.3741979 
 
 .002493760 
 
 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 
 
 7.53024.82 
 
 .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 
 
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 
 
 7.5885793 
 
 .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 
 
 .002267574 
 
 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 
 
 2^U87121 
 
 7.6403213 
 
 .002242152 
 
 447 
 
 199809 
 
 89314623 
 
 21.1423745 
 
 7.6460272 
 
 .002237136 
 
 448 
 
 200704 
 
 89915392 
 
 2i.i660105 
 
 7.6517247 
 
 .002232143 
 
 449 
 
 201601 
 
 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 
 
 7.7639361 
 
 .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 
 
 7.7859928 
 
 .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 
 
 7.8890916 
 
 .002036660 
 
 492 
 
 242064 
 
 119095488 
 
 22.1810730 
 
 7.8944468 
 
 .002032520 
 
 493 
 
 243049 
 
 119823157 
 
 22 . 2036033 
 
 7.8937917 
 
 .002028398 
 
 494 
 
 244036 
 
 120553784 
 
 22.2261108 
 
 7.9051294 
 
 .002024291 
 
 495 
 
 245025 
 
 121287375 
 
 22.2485955 
 
 7.9104599 
 
 .002020202 
 
 496 
 
 246016 
 
 122023936 
 
 22.2710575 
 
 7.9157832 
 
 .002016129 
 
16 
 
 SQUARES, CUBES, SQUARE ROOTS, 
 
 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 
 
 263169 
 
 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 
 
 153990656 
 
 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 
 
 159220088 
 
 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 
 
 162771336 
 
 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 
 
 168196603 
 
 23.4946802 
 
 8.2031319 
 
 .001811594 
 
 553 
 
 305809 
 
 169112377 
 
 23.5159520 
 
 8.2080825 
 
 .001808318 
 
 554 
 
 306916 
 
 170031464 
 
 23.5372046 
 
 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 
 
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 
 
 176558481 
 
 23.6854386 
 
 8 . 2474740 
 
 .001782531 
 
 562 
 
 315844 
 
 177504328 
 
 23 . 7065392 
 
 8.2523715 
 
 .001779359 
 
 563 
 
 316969 
 
 178453547 
 
 23.7276210 
 
 8.2572633 
 
 .001776199 
 
 564 
 
 318096 
 
 179406144 
 
 23 . 7486842 
 
 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 
 
 573 
 
 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 
 
 24.1246762 
 
 8.3491256 
 
 .001718213 
 
 583 
 
 339889 
 
 198155287 
 
 24.1453929 
 
 8.3539047 
 
 .001715266 
 
 584 
 
 341056 
 
 199176704 
 
 24.1660919 
 
 8.3586784 
 
 .001712329 
 
 585 
 
 342225 
 
 200201625 
 
 24.1867732 
 
 8.3634466 
 
 .001709402 
 
 586 
 
 343396 
 
 201230056 
 
 24.2074369 
 
 8 . 3682095 
 
 .001706485 
 
 587 
 
 344569 
 
 202262003 
 
 24 . 2280829 
 
 8.3729668 
 
 .001703578 
 
 588 
 
 345744 
 
 203297472 
 
 24.2487113 
 
 8.3777188 
 
 .001700680 
 
 589 
 
 346921 
 
 204336469 
 
 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 
 
 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.^981781 
 
 8.4809261 
 
 .001639344 
 
 611 
 
 373321 
 
 228099131 
 
 24.7184142 
 
 8.4855579 
 
 .001636661 
 
 612 
 
 374544 
 
 229220928 
 
 24.7386338 
 
 8.4901848 
 
 .001633987 
 
 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 
 
 8.5224321 
 
 .001615509 
 
 620 
 
 384400 
 
 238328000 
 
 24.8997992 
 
 8.5270189 
 
 .001612903 
 
18 
 
 SQUARES, CUBES, SQUARE ROOTS, 
 
 No. 
 
 Squares. 
 
 Cubes. 
 
 Square 
 Roots. 
 
 Cube Roots. 
 
 Reciprocals. 
 
 621 
 
 385641 
 
 239483061 
 
 24.9198716 
 
 8.5316009 
 
 .001610300 
 
 622 
 
 386884 
 
 240641848 
 
 24.9399278 
 
 8.5361780 
 
 .001607717 
 
 623 
 
 388129 
 
 241804367 
 
 24 . 9599679 
 
 8.5407501 
 
 .001605136 
 
 624 
 
 389376 
 
 242970624 
 
 24 . 9799920 
 
 8.5453173 
 
 .001602564 
 
 625 
 
 390625 
 
 244140625 
 
 25 . 0000000 
 
 8.5498797 
 
 .001600000 
 
 628 
 
 391876 
 
 245314376 
 
 25.0199920 
 
 8.5544372 
 
 .001597444 
 
 627 
 
 393129 
 
 246491883 
 
 25.0399681 
 
 8.5589S99 
 
 .001594896 
 
 628 
 
 394381 
 
 247673152 
 
 25.0599282 
 
 8.5635377 
 
 .001592357 
 
 629 
 
 395641 
 
 248858189 
 
 25.0798724 
 
 8 . 5680807 
 
 .001589825 
 
 630 
 
 396900 
 
 250047000 
 
 25.0998008 
 
 8.5726189 
 
 .001587302 
 
 631 
 
 398161 
 
 251239591 
 
 25.1197134 
 
 8.5771523 
 
 .001584786 
 
 632 
 
 399424 
 
 252435968 
 
 25.1396102 
 
 8.5816809 
 
 .001582278 
 
 633 
 
 400589 
 
 253836137 
 
 25.1594913 
 
 8 . 5862047 
 
 .001579779 
 
 634 
 
 401956 
 
 254840104 
 
 25.1793566 
 
 8.5907238 
 
 .001577287 
 
 635 
 
 403225 
 
 256047875 
 
 25.1992063 
 
 8.5952380 
 
 .001574803 
 
 636 
 
 404498 
 
 257259456 
 
 25.2190404 
 
 8.5997476 
 
 .001572327 
 
 637 
 
 405769 
 
 258474853 
 
 25 . 2388589 
 
 8.6042525 
 
 .001569859 
 
 638 
 
 407044 
 
 259594072 
 
 25.2586619 
 
 8.6087526 
 
 .001567398 
 
 639 
 
 408321 
 
 260917119 
 
 25.2784493 
 
 8.6132480 
 
 .001564945 
 
 640 
 
 409600 
 
 262144000 
 
 25.2982213 
 
 8.6177388 
 
 .001562500 
 
 641 
 
 410881 
 
 263374721 
 
 25.3179778 
 
 8.6222248 
 
 .001560062 
 
 642 
 
 412164 
 
 264609288 
 
 25,3377189 
 
 8.6267063 
 
 .001557632 
 
 643 
 
 413449 
 
 285847707 
 
 25.3574447 
 
 8.6311830 
 
 .001555210 
 
 644 
 
 414736 
 
 267089984 
 
 25.3771551 
 
 8.6356551 
 
 .001552795 
 
 645 
 
 416025 
 
 268336125 
 
 25.3968502 
 
 8.6401226 
 
 .001550388 
 
 646 
 
 417316 
 
 269585135 
 
 25.4165301 
 
 8 . 6445855 
 
 .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 
 
 274625003 
 
 25.4950976 
 
 8.6623911 
 
 .001538462 
 
 651 
 
 423801 
 
 275894451 
 
 25.5147016 
 
 8.6668310 
 
 .001536098 
 
 652 
 
 425104 
 
 27716780S 
 
 25.5342907 
 
 8.6712665 
 
 .001533742 
 
 653 
 
 426409 
 
 278445077 
 
 25.5538647 
 
 8.6756974 
 
 .001531394 
 
 654 
 
 427716 
 
 279728254 
 
 25.5734237 
 
 8.6801237 
 
 .001529052 
 
 655 
 
 429025 
 
 281011375 
 
 25 . 5929678 
 
 8 . 6845456 
 
 .001526718 
 
 656 
 
 430336 
 
 282300116 
 
 25.6124969 
 
 8 . 6889630 
 
 .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 . 7293607 
 
 8.7153734 
 
 .001510574 
 
 663 
 
 439569 
 
 291434247 
 
 25 . 7487864 
 
 8.7197596 
 
 .001508296 
 
 664 
 
 440896 
 
 292754944 
 
 25.7681975 
 
 8.7241414 
 
 .001506024 
 
 665 
 
 442225 
 
 294079825 
 
 25.7875939 
 
 8.7285187 
 
 .001503759 
 
 666 
 
 443556 
 
 295408298 
 
 25 . 8069758 
 
 8.7328918 
 
 .001501502 
 
 667 
 
 444889 
 
 296740963 
 
 25.8263431 
 
 8.7372604 
 
 .001499250 
 
 668 
 
 446224 
 
 298077632 
 
 25.8456960 
 
 8.7416246 
 
 .001497006 
 
 669 
 
 447561 
 
 299418309 
 
 25.8650343 
 
 8.7459846 
 
 .001494768 
 
 670 
 
 448900 
 
 300763000 
 
 25.8843582 
 
 8.7503401 
 
 .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 
 
 308182024 
 
 25.9615100 
 
 8.7677192 
 
 .001483680 
 
 675 
 
 455625 
 
 307546875 
 
 25.9807621 
 
 8.7720532 
 
 .001481481 
 
 676 
 
 456976 
 
 308915776 
 
 26.0000000 
 
 8.7763830 
 
 .001479290 
 
 677 
 
 458329 
 
 310288733 
 
 26.0192237 
 
 8.7807084 
 
 .001477105 
 
 678 
 
 459684 
 
 311665752 
 
 26.0384331 
 
 8.7850296 
 
 .001474926 
 
 679 
 
 461041 
 
 313046839 
 
 26.0576284 
 
 8.7893466 
 
 .004472754 
 
 680 
 
 462400 
 
 314432000 
 
 26.0768096 
 
 8.7936593 
 
 .001470588 
 
 6S1 
 
 463761 
 
 315821241 
 
 26.0959767 
 
 8 . 7979G79 
 
 .001468429 
 
 632 
 
 465124 
 
 317214568 
 
 26.1151297 
 
 8.8022721 
 
 .001466276 
 
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 
 
 327082769 
 
 26.2488095 
 
 8.8322S50 
 
 .001451379 
 
 690 
 
 476100 
 
 328509000 
 
 26.2678511 
 
 8.8365559 
 
 .001449275 
 
 691 
 
 477481 
 
 329939371 
 
 26.2868789 
 
 8.8408227 
 
 .001447178 
 
 692 
 
 478864 
 
 331373888 
 
 26.3058929 
 
 8.8450854 
 
 .001445087 
 
 693 
 
 480249 
 
 332812557 
 
 26.3248932 
 
 8.8493440 
 
 .001443001 
 
 694 
 
 481636 
 
 33-1255384 
 
 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 
 
 26.4196896 
 
 8.8705757 
 
 .001432665 
 
 699 
 
 488601 
 
 341532099 
 
 26.4386081 
 
 8.8748099 
 
 .001430615 
 
 700 
 
 490000 
 
 343000000 
 
 26.4575131 
 
 8.8790400 
 
 .001428571 
 
 701 
 
 491401 
 
 344472101 
 
 26.4764046 
 
 8.8832661 
 
 .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 
 
 8.9043366 
 
 .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 
 
 .0^1394700 
 
 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 
 
 374805361 
 
 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 
 
 .001379310 
 
 726 
 
 527076 
 
 3*82657176 
 
 26.9443872 
 
 8.9876373 
 
 .001377410 
 
 727 
 
 528529 
 
 384240583 
 
 26.9629375 
 
 8.9917620 
 
 .001375516 
 
 728 
 
 529984 
 
 385828352 
 
 26.9814751 
 
 8.9958829 
 
 .00137,3626 
 
 729 
 
 531441 
 
 387420489 
 
 27.0000000 
 
 9.0000000 
 
 .001371742 
 
 730 
 
 532900 
 
 389017000 
 
 27.0185122 
 
 9.0041134 
 
 .001369863 
 
 731 
 
 534361 
 
 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 
 
 3986S8256 
 
 27.1293199 
 
 9.0287149 
 
 .001358696 
 
 737 
 
 543169 
 
 40031 55;53 
 
 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 
 
20 
 
 SQUARES, CUBES, SQUARE ROOTS, 
 
 No. 
 
 Squares. 
 
 Cubes. 
 
 Square 
 Roots. 
 
 Cube Roots. 
 
 Reciprocals. 
 
 745 
 
 555025 
 
 413493625 
 
 27.2946881 
 
 9.0653677 
 
 .001342282 
 
 746 
 
 556516 
 
 415160936 
 
 27.3130006 
 
 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 
 
 9.1097669 
 
 .001322751 
 
 757 
 
 573049 
 
 433798093 
 
 27.5136330 
 
 9.1137818 
 
 .001321004 
 
 758 
 
 574564 
 
 435519512 
 
 27.5317998 
 
 9.1177931 
 
 .001319261 
 
 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 
 
 .001293061 
 
 774 
 
 599076 
 
 463684824 
 
 27.8208555 
 
 9.1815003 
 
 .001291990 
 
 775 
 
 600625 
 
 465484375 
 
 27.8388218 
 
 9.1854527 
 
 .001290323 
 
 776 
 
 602176 
 
 467288576 
 
 27.8567766 
 
 9.1894018 
 
 .001288660 
 
 777 
 
 603729 
 
 469097433 
 
 27.8747197 
 
 9.1933474 
 
 .001287001 
 
 778 
 
 605284 
 
 470910952 
 
 27.8926514 
 
 9.1972897 
 
 .001285347 
 
 779 
 
 606841 
 
 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 
 
 9.2326189 
 
 .001270648 
 
 788 
 
 620944 
 
 489303872 
 
 28.0713377 
 
 9.23B5277 
 
 .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 
 
 523606616 
 
 28.3901391 
 
 9 . 3063278 
 
 .001240695 
 
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 
 
 28.5482048 
 
 9.3408386 
 
 .001226994 
 
 816 
 
 665856 
 
 543338496 
 
 28.5657137 
 
 9.3446575 
 
 .001225490 
 
 817 
 
 667489 
 
 545338513 
 
 28.5832119 
 
 9.3484731 
 
 .001223990 
 
 818 
 
 669124 
 
 547343432 
 
 28.6006993 
 
 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 
 
 563559976 
 
 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 
 
 9.4166297 
 
 .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 
 
 9.4391307 
 
 .001189061 
 
 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 
 
 9.4652470 
 
 .001179245 
 
 849 
 
 720801 
 
 611960049 
 
 29.1376046 
 
 9.4689661 
 
 .001177856 
 
 850 
 
 722500 
 
 614125000 
 
 29.1547595 
 
 9.4726824 
 
 .001176471 
 
 851 
 
 724201 
 
 616295051 
 
 29.1719043 
 
 9.4763957 
 
 .001175088 
 
 852 
 
 725904 
 
 618470208 
 
 29 . 1890390 
 
 9.4801061 
 
 .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 
 
 9.4986147 
 
 .001166861 
 
 858 
 
 736164 
 
 631628712 
 
 29.2916370 
 
 9.5023078 
 
 .001165501 
 
 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 
 
SQUARES, CUBES, SQUARE ROOTS, 
 
 No. 
 
 Squares. 
 
 Cubes. 
 
 Square 
 Root. 
 
 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 
 
 .001145475 
 
 874 
 
 763876 
 
 667627624 
 
 29.5634910 
 
 9.5610108 
 
 .001144165 
 
 875 
 
 765625 
 
 669921875 
 
 29 . 5803989 
 
 9 . 5646559 
 
 .001142857 
 
 876 
 
 767376 
 
 672221376 
 
 29.5972972 
 
 9.5682982 
 
 .001141553 
 
 877 
 
 769129 
 
 674526133 
 
 29.6141858 
 
 9.5719377 
 
 .001140251 
 
 878 
 
 770884 
 
 676836152 
 
 29.6310648 
 
 9.5755745 
 
 .001138952 
 
 879 
 
 772641 
 
 679151439 
 
 29.6479342 
 
 9.57920&5 
 
 .001137656 
 
 880 
 
 774400 
 
 681472000 
 
 29.6647939 
 
 9.5828397 
 
 .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 
 
 704969000 
 
 29.8328678 
 
 9.6190017 
 
 .001123596 
 
 891 
 
 793881 
 
 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 
 
 719323136 
 
 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 
 
 817216 
 
 738763264 
 
 30.0665928 
 
 9.6691762 
 
 .001106195 
 
 905 
 
 819025 
 
 741217625 
 
 30.0832179 
 
 9.6727403 
 
 .001104972 
 
 908 
 
 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 
 
 .001092896 
 
 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 
 
 920 
 
 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 
 
 9.7504930 
 
 .001078749 
 
 928 
 
 861184 
 
 799178752 
 
 30.4630924 
 
 9.7539979 
 
 .001077586 
 
 929 
 
 863041 
 
 801765089 
 
 30.4795013 
 
 9.7575002 
 
 .001076426 
 
 930 
 
 864900 
 
 804357000 
 
 30.4959014 
 
 9.7610001 
 
 .001075269 
 
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 
 
 .00106C098 
 
 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 
 
 9.8097362 
 
 .001059322 
 
 945 
 
 893025 
 
 843908625 
 
 30.7408523 
 
 9.8131989 
 
 .001058201 
 
 946 
 
 894916 
 
 846590536 
 
 30.7571130 
 
 9.8166591 
 
 .001057082 
 
 947 
 
 896809 
 
 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 
 
 9.8339238 
 
 .001051525 
 
 952 
 
 906304 
 
 862801408 
 
 30.8544972 
 
 9.8373695 
 
 .001050420 
 
 953 
 
 908209 
 
 865523177 
 
 30.8706981 
 
 9.8408127 
 
 .001049318 
 
 954 
 
 910116 
 
 868250664 
 
 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 
 
 31.0000000 
 
 9.8682724 
 
 .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 
 
 31.0966236 
 
 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 
 
 9.9362613 
 
 .001019368 
 
 982 
 
 964324 
 
 946966168 
 
 31 . 3368792 
 
 9.9396363 
 
 .001018330 
 
 983 
 
 966289 
 
 949862087 
 
 31.352830,3 
 
 9.9430092 
 
 .001017294 
 
 984 
 
 968256 
 
 952763904 
 
 31.3687743 
 
 9.9463797 
 
 .001016260 
 
 985 
 
 970225 
 
 955671625 
 
 31.3847097 
 
 9.9497479 
 
 .001C115228 
 
 986 
 
 972196 
 
 958585256 
 
 31.4006369 
 
 9.9531138 
 
 .001014199 
 
 987 
 
 974169 
 
 961504803 
 
 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 
 
 31.4801525 
 
 9.9699095 
 
 .001009082 
 
 992 
 
 984064 
 
 976191488 
 
 31.4960315 
 
 9.9732619 
 
 .001008065 
 
24 SQUARES, CUBES, SQUARE ROOTS, ETC. 
 
 No. 
 
 Squares. 
 
 Cubes. 
 
 Square 
 Roots. 
 
 Cube Roots. 
 
 Reciprocals. 
 
 993 
 
 986049 
 
 979146657 
 
 31.5119025 
 
 9.9766120 
 
 .001007049 
 
 994 
 
 988036 
 
 982107784 
 
 31.5277655 
 
 9.9799599 
 
 .001006036 
 
 995 
 
 990025 
 
 985074875 
 
 31.5436206 
 
 9.9833055 
 
 .001005025 
 
 996 
 
 992016 
 
 988047936 
 
 31.5594677 
 
 9.9866488 
 
 .001004016 
 
 997 
 
 994009 
 
 991026973 
 
 31.5753068 
 
 9.9899900 
 
 .001003009 
 
 998 
 
 996004 
 
 994011992 
 
 31.5911380 
 
 9.9933289 
 
 .001002004 
 
 999 
 
 998001 
 
 997002999 
 
 31.6069613 
 
 9 . 9966656 
 
 .001001001 
 
 1000 
 
 1000000 
 
 1000000000 
 
 31.6227766 
 
 10.0000000 
 
 .001000000 
 
 1001 
 
 1002001 
 
 1003003001 
 
 31.6385840 
 
 10.0033322 
 
 .0009990010 
 
 1002 
 
 1004004 
 
 1006012008 
 
 31.6543836 
 
 10.0066622 
 
 .0009980040 
 
 1003 
 
 1006009 
 
 1009027027 
 
 31.6701752 
 
 10.0099899 
 
 . 0009970090 
 
 1004 
 
 1008016 
 
 1012048064 
 
 31.6859590 
 
 10.0133155 
 
 .0009960159 
 
 1005 
 
 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 
 
 ^2.3728281 
 
 10.1575062 
 
 .0009541985 
 
 1049 
 
 1100401 
 
 1154320649 
 
 32.3882695 
 
 10.1607359 
 
 .0009532888 
 
 1050 
 
 1102500 
 
 1157625000 
 
 32.4037035 
 
 10.1639636 
 
 .0009523810 
 
 1051 
 
 1104601 
 
 1160935651 
 
 32.4191301 
 
 10.1671893 
 
 .0009514748 
 
 10.52 
 
 1106704 
 
 1164252608 
 
 32.4345495 
 
 10.1704129 
 
 .0009505703 
 
 1053 
 
 1108809 
 
 1167575877 
 
 32.4499615 
 
 10.1736344 
 
 . 0009496676 
 
 1054 
 
 1110916 
 
 1170905464 
 
 32.4653662 
 
 10.1768539 
 
 .0009487666 
 
WEIGHTS AND MEASURES. 
 
 25 
 
 WEIGHTS AND MEASURES. 
 Measures of Length. 
 
 12 inches = 1 foot. 
 3 feet = 1 yard = 36 inches. 
 5} yards = 1 rod = 198 inches= 16J ft. 
 40 rods = lfurlong= 7920 inches = 660 ft. = 220 yds. 
 8 furlongs= 1 mile =63360 inches =5280 ft.= 1760 yds.= 
 1 yard =0.0005682 of a mile. [320 rods. 
 
 . GUNTER'S CHAIN. 
 7.92inches=l link. 
 
 100 links = 1 chain =4 rods =66 feet. 
 80 chains =1 mile. 
 
 ROPES AND CABLES. 
 
 6 feet= 1 fathom. 120 fathoms = 1 cable's length. 
 
 TABLE SHOWING 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 
 
 .0104 
 
 .0938 
 
 .1771 
 
 2604 
 
 3438 
 
 .4271 
 
 .5104 
 
 .5938 
 
 .6771 
 
 .7604 
 
 .8438 
 
 .9271 
 
 5-32 
 
 .0130 
 
 .0964 
 
 .1797 
 
 2630 
 
 3464 
 
 .4297 
 
 .5130 
 
 .5964 
 
 .6797 
 
 .7630 
 
 .8464 
 
 .9297 
 
 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 
 
 .7760 
 
 .8594 
 
 .9427 
 
 11-32 
 
 .0286 
 
 .1120 
 
 .1953 
 
 .2786 
 
 3620 
 
 .4453 
 
 .5286 
 
 .6120 
 
 .6953 
 
 .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 
 
 .0365 
 
 .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 
 
 .,6458 
 
 .7292 
 
 .8125 
 
 .8958 
 
 .9792 
 
 25-32 
 
 .0651 
 
 .1484 
 
 .2318 
 
 .3151 
 
 .3984 
 
 .4818 
 
 .5651 
 
 .6484 
 
 .7318 
 
 .8151 
 
 .8984 
 
 .9818 
 
 13-16 
 
 .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 
 
 .9896 
 
 29-32 
 
 .0755 
 
 .1589 
 
 .2422 
 
 .3255 
 
 .4089 
 
 .4922 
 
 .5755 
 
 .6589 
 
 .7422 
 
 .8255 
 
 .9089 
 
 .9922 
 
 15-lfi 
 
 .0781 
 
 .1615 
 
 .2448 
 
 .3281 
 
 .4115 
 
 .4948 
 
 .5781 
 
 .6615 
 
 .7448 
 
 .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 DECIMAL EQUIVALENTS FOR FRACTIONS. 
 DECIMAL EQUIVALENTS FOR FRACTIONS OF AN INCH. 
 
 s-jds. 
 
 &tfa*. 
 
 Decimal. 
 
 Frac- 
 tion. 
 
 B ] 2 ds. 
 
 ^ths. 
 
 Decimal. 
 
 Frac- 
 tion. 
 
 
 1 
 
 .015625 
 
 
 
 33 
 
 .515625 
 
 
 1 
 
 2 
 
 .03125 
 
 
 17 
 
 34 
 
 .53125 
 
 
 
 3 
 
 .046875 
 
 
 
 35 
 
 .546875 
 
 
 2 
 
 4 
 
 .0625 
 
 1/16 
 
 18 
 
 36 
 
 .5625 
 
 9/16 
 
 
 5 
 
 .078125 
 
 
 
 37 
 
 .578125 
 
 
 3 
 
 6 
 
 .09375 
 
 
 19 
 
 38 
 
 .59375 
 
 
 
 7 
 
 . 109375 
 
 
 
 39 
 
 .609375 
 
 
 4 
 
 8 
 
 .125 
 
 1/8 
 
 20 
 
 40 
 
 .625 
 
 5/8 
 
 
 9 
 
 . 140625 
 
 
 
 41 
 
 .640625 
 
 
 5 
 
 10 
 
 .15625 
 
 
 21 
 
 42 
 
 .65625 
 
 
 
 11 
 
 .171875 
 
 
 
 43 
 
 .671875 
 
 
 6 
 
 12 
 
 .1875 
 
 3/16 
 
 22 
 
 44 
 
 .6875 
 
 11/16 
 
 
 13 
 
 .203125 
 
 
 
 45 
 
 .703125 
 
 
 7 
 
 14 
 
 .21875 
 
 
 23 
 
 46 
 
 .71875 
 
 
 
 15 
 
 .234375 
 
 
 
 47 
 
 .734375 
 
 
 8 
 
 16 
 
 .25 
 
 1/4 
 
 24 
 
 48 
 
 .75 
 
 3/4 
 
 
 17 
 
 .265625 
 
 
 
 49 
 
 .765625 
 
 
 9 
 
 18 
 
 .28125 
 
 
 25 
 
 50 
 
 .78125 
 
 
 
 19 
 
 .290875 
 
 
 
 51 
 
 .796875 
 
 
 10 
 
 20 
 
 .3125 
 
 5/16 
 
 26 
 
 52 
 
 .8125 
 
 13/16 
 
 
 21 
 
 .328125 
 
 
 
 53 
 
 .828125 
 
 
 11 
 
 22 
 
 .34375 
 
 
 27 
 
 54 
 
 .84375 
 
 
 
 23 
 
 .359375 
 
 
 
 55 
 
 .859375 
 
 
 12 
 
 24 
 
 .375 
 
 3/8 
 
 28 
 
 56 
 
 .875 
 
 7/8 
 
 
 25 
 
 .390625 
 
 
 
 57 
 
 .890625 
 
 
 13 
 
 26 
 
 .40625 
 
 
 29 
 
 58 
 
 .90625 
 
 
 
 27 
 
 .421875 
 
 
 
 59 
 
 .921875 
 
 
 14 
 
 28 
 
 .4375 
 
 7/16 
 
 30 
 
 60 
 
 .9375 
 
 15/16 
 
 
 29 
 
 .453125 
 
 
 
 61 
 
 .953125 
 
 
 15 
 
 30 
 
 .46875 
 
 
 31 
 
 62 
 
 .96875 
 
 
 
 31 
 
 .484375 
 
 
 
 63 
 
 .984375 
 
 
 16 
 
 32 
 
 .5 
 
 1/2 
 
 32 
 
 64 
 
 1. 
 
 1 
 
MEASURES OF SURFACE AND VOLUME. 27 
 
 NAUTICAL MEASURE. 
 
 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 
 at 6086.07 feet= 1.152664 statute or land miles by the United 
 States Coast Survey. 
 
 3 nautical miles=l league. 
 
 MISCELLANEOUS. 
 
 1 palm = 3 inches. 1 span =9 inches. 
 
 1 hand=4 inches. 1 meter =3.2809 feet. 
 
 Measures of Surface. 
 
 144 square inches = 1 square foot. 
 
 9 square feet = 1 square yard = 1296 square inches. 
 100 square feet = 1 square (architects' measure). 
 
 LAND. 
 
 30 1 square yards = 1 square rod. 
 40 square rods = 1 square rood =1210 square yards. 
 
 4 square roods } = 1 acre = 4840 square yards. 
 10 square chains f = 160 square rods. 
 
 640 acres =1 square mile =3097600 square yards = 
 
 208.71 feet square = 1 acre. [102400 sq. rods= 2560 sq. roods. 
 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 58333 
 grains. 
 
 1 cubic foot contains 7.48 liquid gallons, or 6.428 dry gallons. 
 
 1 gallon dry measure=268.8 cubic inches. 
 
 1 bushel (Winchester) contains 2150.42 cubic inches, or 77.627 
 pounds distilled water at 39.8 F. 
 
 A heaped bushel contains 2747.715 cubic inches. 
 
 DRY. 
 
 2 pints = 1 quart = 67.2 cubic inches. 
 4 quarts = 1 gallon = 8 pints = 268.8 cubic inches. 
 2 gallons = 1 peck = 16 pints= 8 quarts =537.6 cubic inches. 
 4 pecks -1 bushel = 64 pints=32 quarts=8 gals. = 2150.42 
 1 cord of wood= 128 cubic feet. [cu. in. 
 
28 MEASURES OF VOLUME AND WEIGHT. 
 
 LIQUID. 
 
 4 gills = 1 pint =16 fluid ounces. 
 2 pints = 1 quart = 8 gills = 32 fluid ounces. 
 4 quarts = 1 gallon = 32 gills = 8 pints = 128 fluid ounces. 
 In the United States and Great Britain 1 barrel of wine or 
 brandy=31J gallons, and contains 4.211 cubic feet. 
 
 A hogshead is 63 gallons, but this term is often applied to casks 
 of various capacities. 
 
 Cubic Measure. 
 1728 cubic inches = 1 cubic foot. 
 27 cubic feet = 1 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 16 \ feet long, 1 foot high, and 
 1J feet thick, and contains 24f cubic feet. 
 
 A perch of stone is, however, often computed differently in 
 different localities; thus, in most if not all of the States and Ter- 
 ritories west of the Mississippi, stone masons figure rubble by 
 the perch of 16J cu. ft. In Philadelphia, 22 cu. ft. are called a 
 perch. In Chicago, stone is measured by the cord of 100 cu. ft. 
 A ton of shipping is 42 cubic feet in Great Britain and 40 cubic 
 feet in the United States. 
 
 Fluid Measure. 
 60 minims = 1 fluid drachm. 
 
 8 fluid drachms = 1 ounce. 
 16 ounces = 1 pint. 
 
 8 pints = 1 gallon. 
 
 Miscellaneous, 
 
 Butt of Sherry = 108 gals. Puncheon of Brandy, 110 to 120 gals. 
 Pipe of Port =115 gals. Puncheon of Rum, 100 to 110 gals. 
 Butt of Malaga= 105 gals. Hogshead of Brandy, 55 to 60 gals. 
 Puncheon of Scotch Whis- Hogshead of Claret, 46 gals. 
 
 key, 110 to 130 gals. 
 
 Measures of Weight. 
 
 The standard avoirdupois pound is the weight of 27.7015 cubic 
 inches of distilled water weighed in air at 39.83, the barometer 
 at 30 inches; it contains 7000 grains. One pound avoirdupois= 
 1.2153 pounds troy. 
 
MEASURES OF WEIGHT. 29 
 
 Avoirdupois, or Ordinary Commercial Weight. 
 
 1 drachm =27.343 grains. 
 
 16 drachms =1 ounce (oz.). 
 
 16 ounces =1 pound (lb.). 
 
 100 pounds = 1 hundred weight (cwt.). 
 
 20 hundred weight = 1 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 = 1 quarter. 
 
 4 quarters, or 112 lbs.= 1 hundred weight. 
 20 hundred weight = 1 long ton= 2240 pounds. 
 A stone = 14 pounds. 
 
 A quintal =100 pounds. 
 
 The following measures are sanctioned by custom or law: 
 1 bushel = 1.244 cubic feet or 1 J cubic feet nearly. 
 
 32 pounds of oats = 1 bushel. 
 
 45 pounds of Timothy-seed = 1 bushel. 
 48 pounds of barley = 1 bushel. 
 
 56 pounds of rye = 1 bushel. 
 
 56 pounds of Indian corn = 1 bushel. 
 50 pounds of Indian meal = 1 bushel. 
 60 pounds of wheat = 1 bushel. 
 
 60 pounds of clover-seed = 1 bushel. 
 60 pounds of potatoes = 1 bushel. 
 56 pounds of butter = 1 firkin. 
 
 100 pounds of meal or flour = 1 sack. 
 100 pounds of grain or flour = 1 cental. 
 100 pounds of dry fish = 1 quintal. 
 
 100 pounds of nails = 1 cask. 
 
 196 pounds of flour = 1 barrel. 
 
 200 pounds of beef or pork = 1 barrel. 
 80 pounds of lime = 1 bushel. 
 
 Troy Weight. 
 
 USED IN WEIGHING GOLD OR SILVER. 
 
 24 grains = 1 pennyweight (pwt.). 
 
 20 penny weights = 1 ounce (oz.). 
 
 12 ounces =1 pound (lb.). 
 
 A carat of the jewellers, for precious stones, is, in the United 
 States, 3.2 grains: in London, 3.17 grains, in Paris, 3.18 grains 
 
30 MEASURES OF VALUE AND TIME. 
 
 are divided into 4 jewellers' grains. In troy, apothecaries', 
 and avoirdupois weights, the grain is the same, one pound troy 
 being equal to .82286 pound avoirdupois. 
 
 Apothecaries' Weight. 
 
 USED IN COMPOUNDING MEDICINES, AND IN PUTTING UP 
 MEDICAL PRESCRIPTIONS. 
 
 20 grains (gr.) = 1 scruple (3 ). 
 3 scruples = 1 drachm ( 3 ) . 
 
 8 drachms = 1 ounce (oz.). 
 12 ounces = 1 pound (lb.). 
 
 Measures of Value. 
 
 UNITED STATES STANDARD. 
 
 10 mills = 1 cent. 
 10 cents =1 dime. 
 
 10 dimes = 1 dollar. 
 10 dollars = 1 eagle. 
 
 The standard of gold and silver is GOO parts of pure metal and 
 100 of alloy in 1000 parts of coin. 
 
 The fineness expresses the quantity of pure metal in 1000 parts. 
 
 The remedy of the mint is the allowance for deviation from the 
 exact standard fineness and weight of coins. 
 
 Weight of Coin. 
 
 Double eagle =516 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 . 16 troy grains. 
 3-cent piece (nickel) = 30 troy grains. 
 Cent (bronze) = 48 troy grains. 
 
 Measure of Time. 
 
 60 seconds = 1 minute. 
 60 minutes = 1 hour. 
 
 365 days= 1 common year. 
 
 366 days= 1 leap year. 
 
 24 hours = 1 day. 
 
 A solar day is measured by the rotation of the earth upon its 
 axis with respect to the sun. 
 
 In astronomical computation and in nautical time the day com- 
 mences at noon, and in the former it is counted throughout the 24 
 hours. 
 
 In civil computation the day commences at midnight, and is 
 divided into twp portions of 12 hours each. 
 
 A solar year is the time in which the earth makes one revolution 
 around the sun; a^id its average time, called the mean solar year, 
 
THE CALENDER. ANGULAR MEASURE. 31 
 
 is 365 days, 5 hours, 48 minutes, 49.7 seconds, or nearly 365J 
 days. 
 
 A mean lunar month, or lunation of the, moon, is 29 days, 12 
 hours, 44 minutes, 2 seconds, and 5.24 thirds. 
 
 The Calendar, Old aiid New Style. 
 
 The Julian Calendar was established by Julius Caesar, 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, 6 hours, instead of the value given above, thus intro- 
 ducing an accumulative error of 11 minutes, 12 seconds, every 
 year. This calendar was adopted by the church in 325 A.t>., at 
 the Council of Nice. In the year 1582 the anmial error of 11 min- 
 utes, 12 seconds, had amounted to a period of iO days, which, by 
 order of Pope Gregory XIII., was suppressed in the calendar, and 
 the 5th of October reckoned as the 15th. To prevent the repe- 
 tition of this error, it was decided to leave out three of the in- 
 serted 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, 2000, all of which are leap years according to 
 the Julian 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 DETERMIN- 
 ING LATITUDE AND LONGITUDE. 
 
 60 seconds (") = 1 minute ('). 
 
 60 minutes =1 degree (). 
 
 360 degrees = 1 circumference (C.) . 
 
 Seconds are usually subdivided into tenths and hundredths. 
 A minute of the circumference of the earth is a geographical 
 mile. 
 
 Degrees of the earth's circumference on a meridian average 
 69.16 common miles. 
 
 THE METRIC SYSTEM. 
 
 The metric system is a system of weights and measures based 
 upon a unit called a meter. 
 
32 THE METRIC SYSTEM. 
 
 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 names of derived metric denominations are formed by pre- 
 fixing to the name of the primary unit of measure 
 
 Milli (mill'e), a thousandth, 
 Centi (sent'e), a hundredth, 
 Deci (des'e), a tenth, 
 
 Hecto (hek'to), one hundred, 
 Kilo (kiKo), a thousand, 
 Myria (mir'ea), ten thousand. 
 
 Deka (dek'a), 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 1866 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. 
 TABLE. 
 
 10 millimeters (mm.) = 1 centimeter (cm.) = . 3937 in. 
 
 10 centimeters =1 decimeter = 3. 937 in. 
 
 10 decimeters = 1 METER = 39 . 37 in. 
 
 10 meters = 1 dekameter = 393 . 37 in. 
 
 10 dekameters =1 hectometer 328 ft. 1 in. 
 
 10 hectometers =1 KILOMETER (km.) =0.62137 miles. 
 
 10 kilometers =lmyriameter =6.2137 miles. 
 
 The meter is used in ordinary measurements ; the centimeter, or 
 millimeter, in reckoning very small distances; and the kilometer, 
 for roads or great distances. 
 
 A centimeter is about f of an inch; a meter is about 3 feet 3 
 inches and J ; a kilometer is about 200 rods, or f of a mile (see p. 
 35). 
 
 Surface Measures. 
 
 The square meter is the primary unit of ordinary surfaces. 
 
 The are (air), a square, each of whose sides is ten meters, is 
 the unit of land measures. 
 
 TABLE. 
 
 100 square millimeters (sq. mm.) = 1 square ) . , 
 
 v ^ [ =0.155 sq. inch, 
 
 centimeter (sq. cm.) ) 
 
 100 square centimeters= 1 square decimeter = 15.5 sq. inches. 
 
 100 square decimeters = 1 square ) 
 
 N > = 1550 sq. in., or 1.196 sq. yds. 
 
 METER (sq. m.) J 
 
THE METRIC SYSTEM. 33 
 
 ALSO 
 
 100 centiares, or sq. meters, = 1 ARE (ar.) = 119 . 6 sq. yds. 
 
 100 ares = 1 hectare (ha.) =2.471 acres. 
 
 A square meter, or one centiare, is about lOf square feet, or 1J 
 square yards, and a hectare is about 2J acres. 
 
 Cubic Measures. 
 
 The cubic meter, or stere (stair), is the primary unit of a volume. 
 
 TABLE. 
 
 1000 cubic millimeters (cu. mm.) = 1 cubic centimeter (cu. cm.) = 
 
 [0.061 cubic inch. 
 
 1000 cubic centimeters=l cubic decimeter =6 1.022 cubic inches. 
 1000 cubic decimeters =1 cubic METER (cu. m.) = 35.314 cu. ft. 
 
 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 dekastere. 
 
 A cubic meter, or stere, is about 1 J cubic yards, or about 2J cord 
 feet. 
 
 Liquid and Dry Measures. 
 
 The liter (leeter) 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 hectoliter is the unit in measuring large quantities of grain, 
 fruits, roots, and liquids. 
 
 10 milliliters (ml.) = 1 centiliter (cl.) =0.338 fluid ounce. 
 10 centiliters = 1 deciliter = . 845 liquid gill. 
 
 10 deciliters = 1 LITER (1.) = 1 . 0567 liquid quarts. 
 
 10 liters = 1 dekaliter = 2 . 6417 gallons. 
 
 10 dekaliters = 1 HECTOLITER (hi.) = 2 bushels 3 . 35 pecks. 
 
 10 hectoliters = 1 kiloliter = 28 bushels 1J pecks. 
 
 A centiliter is about J of a fluid ounce] a liter is about 1-f^ 
 liquid quarts, or ^ of a dry quart; a hectoliter is about 2f 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 tempera- 
 ture of 39.2 degrees Fahrenheit. 
 
34 THE METRIC SYSTEM. 
 
 TABLE. 
 
 Id milligrams (mg.) =1 centigram = 0.1543 troy grain. 
 
 10 centigrams =1 decigram = 1.543 troy g: 
 
 10 decigrams = lGRAM(g.) = 15.432 troy grains 
 
 10 grams = 1 dekagram = 0.3527 avoir, oz. 
 
 10 dekagrams =1 hectogram = 3,5274 avoir, oz. 
 
 10 hectograms = 1 KILOGRAM (k.) = 2.2046 avoir. Ibs. 
 
 10 kilograms = 1 myriagram = 22.046 avoir. 11 ><. 
 
 10 myriagrams =1 quintal = 220.46 avoir. Ibs. 
 
 10 quintals = 1 TOXXEAU (t.) =2204.6 avoir. Ibs. 
 
 1 kilogram per kilometer = .67195 pounds per 1000 feet. 
 1 pound per thousand feet= 1.4882 kilogrames per kilometer. 
 1 kilogram jter square millimeter = 1423 pounds per square inch. 
 1 pound per square inch = .000743 kilograms 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 (tonno), or metric ton, is used in find- 
 ing the weight of t-ery hedrvy articles. 
 
 A gram is about 15 J grains troy; the kilo about 2J pounds 
 avoirdupois; and the metric ton-, about 2205 pounds. 
 
 A kUo is the weight of a liter of water at its greatest density; 
 and the metric ton, of a cubic meter of water. 
 
 M --trie numbers are written with the decimal-point (.) at the 
 right of the figures denoting the unit; thus, 15 meters, 3 centi- 
 meters, are 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 irieters and 525 millimeters, or 46 and 
 525 thousandths meters. 
 
 In writing and reading metric numbers^ according as the scale 
 is 10, 100, or 1000, each denomination should be allowed one, 
 two, or three orders of figures. 
 
 METRIC CONVERSION TABLE. 
 
 The following metric conversion table has been compiled by 
 Mr. C; W. Hunt, 31. Am. Soe. M r E., President of the C. W. Hunt 
 Company, of New York City, and is most convenient in dealing 
 with metric weights and measures: 
 
METRIC CONVERSION TABLE. 
 
 35 
 
 Millimeters X. 03937 
 
 Millimeters -=-25. 4 
 
 Centimeters X. 3937 
 
 Centimeters -v- 2. 54 
 
 Meters X 39.37 
 
 Meters X 3.281 
 
 Meters X 1.094 
 
 Kilometers X. 621 
 
 Kilometers -=-1.6093 
 
 Kilometers X 3280.7 
 
 Square millimetersX.0155 
 
 Square millimeters -=- 645.1 
 
 Square centimeters X.I 55 
 
 Square centimeters -=-6.451 
 
 Square meters X 10.764 
 
 Square kilometers X 247.1 
 
 Hectares X 2.471 
 
 Cubic centimeters -T- 16.383 
 
 Cubic centimeters-:- 3. 69 
 
 Cubic centimeters -=-29.57 
 
 Cubic meters X 35.315 
 
 Cubic meters X 1 .308 
 
 Cubic meters X 264.2 
 
 Liters X 61. 022 
 
 LitersX33.84 
 
 Liters X. 2642 
 
 Liters -=-3. 78 
 
 Liters -=-28.316 
 
 He'ctolitersX3.531 
 
 HectolitersX2.84 
 
 Hectoliters X. 131 
 
 HectolitersH-26.42 
 
 Grammes X 15. 432 
 
 Grammes X 981 
 
 Grammes (water) -7-29.57 
 
 Grammes -T- 28. 35 
 
 Grammes per cu. cent. -5- 27.7 
 
 Joule X. 7373 
 
 Kilograms X 2.2046 
 
 Kilogrammes X 35,3 
 
 Kilograms -=-1102.3 
 
 Kilograms per sq. cent . X 14.223 
 
 = inches. 
 
 = inches. 
 
 = inches. 
 
 = inches. 
 
 = ins. (Act of Congress.) 
 
 = feet. 
 
 = yards. 
 
 = miles. 
 
 = miles. 
 
 = feet. 
 
 = square inches. 
 
 = square inches. 
 
 = square inches. 
 
 = square inches. 
 
 = square feet. 
 
 = acres. 
 
 = acres. 
 
 = cubic inches. 
 
 = fluid drachms. (U. S. P.) 
 
 = fluid ounce. (U. S. P.) 
 
 = cubic feet. 
 
 = cubic yards. 
 
 = gallons (231 cu. ins.). 
 
 = cu ins. (Act of Congress.) 
 
 = fluid ounces. (U.S. P. 
 
 = gallons (231 cu. ins.). 
 
 = gallons (231 cu. ins.). 
 
 = cubic feet. 
 
 = cubic feet. 
 
 = bushels (2150.42 cu. ins.). 
 
 = cubic yards. 
 
 = gallons (231 cu. ins.). 
 
 = grains. (Act of Congress.) 
 
 = dynes. 
 
 = fluid ounces. 
 
 = ounces avoirdupois. 
 
 = pounds per cubic inch. 
 
 = foot-pounds. 
 
 = pounds. 
 
 = ounces avoirdupois. 
 
 = tons (2000 pounds). 
 
 = pounds per square inch. 
 
36 ANCIENT MEASURES AND WEIGHTS. 
 
 Kilogrammeters X 7.233 = foot-pounds. 
 
 Kilograms per meter X- 672 = pounds per square foot. 
 
 Kilograms per cubic meter X .062 = pounds per cubic foot. 
 
 Kilograms per cheval vapeurX 2. 235= pounds per horse-power. 
 
 Kilo- watts X 1 .34 = horse-power. 
 
 Watts -T- 746 = horse-power. 
 
 Watts -v- .7373 = foot-pounds per second. 
 
 CalorieX3.968 =B. T. U. 
 
 Cheval vapeur X .9863 = horse-power. 
 
 (Centigrade X 1 .8) + 32 = degrees Fahrenheit. 
 
 Francs X . 1 93 = dollars . 
 
 Gravity, Paris =980.94 cent, per second. 
 
 SCRIPTURE AND ANCIENT MEASURES AND 
 
 WEIGHTS. 
 Scripture Long- Measures. 
 
 Feet. Inches. 
 
 Cubit = 1 
 
 Fathom =7 3 . 552 
 
 Inches. 
 
 Digit = 0.912 
 
 Palm = 3.648 
 
 Span =10.944 
 
 Egyptian Long Measures. 
 
 Nahud cubit = 1 foot 5.71 ins. Royal cubit = 1 foot 8.66 ins. 
 
 Grecian Long Measure. 
 
 Feet. Inches. 
 
 Digit = 0.7554 
 
 Pous (foot) = 1 0.0875 
 
 Feet. Inches. 
 
 Stadium =604 4.5 
 
 Mile =4835 
 
 Cubit = 1 1.5984f 
 
 Jewish Long Measures. 
 
 Cubit =1.824 ft. 
 
 Sabbath-day's journey = 3648 ft. 
 
 Mile = 7296 feet. 
 
 Day's journey =33. 164 miles. 
 
 Roman Long Measures. 
 
 Inches. 
 
 Feet. Inches. 
 
 Digit = 0.72575 Cubit = 1 5.406 
 
 Uncia(inch) = 0.967 Passus = 4 10.02 
 
 Pes (foot) = 1 1 . 604 Mile (millarium) = 4842 
 
 Roman Weight. 
 
 Ancient libbra= . 7094 pound. 
 
 Miscellaneous. 
 
 Feet. 
 
 Arabian foot = 1 . 095 
 
 Babylonian foot = 1 . 140 
 Egyptian finger = . 06145 
 
 Feet. 
 
 Hebrew foot =1.212 
 
 Hebrew cubit =1.817 
 
 Hebrew sacred cubit = 2 . 002 
 
FEET INTO METRES. 
 
 36a 
 
 8 
 
 d 
 
 o 
 
 I 
 
 00000 
 rH CM CO rH 
 
 tO CO I>C/J O5 
 
 I 
 
 .S 
 
 Ci 
 
 tO O rH 
 
 rH rH O O Oi 
 
 CO rH Oi t* rH 
 
 rH Oi CO 00 CO 
 1>I> 00 00 Oi 
 
 os oo oo t^ r> 
 
 CM O 00 CO rH 
 00 CO l> CM t^ 
 
 Oi O O rH rH 
 
 Oi 
 
 6 
 
 
 CM to 00 rH rH 
 
 rH rH 
 
 l> rH rH 1> O 
 
 rH CM CM CM CO 
 
 
 s 
 
 00 
 
 CO CO CM C^ rH 
 
 00 CO rH CM O 
 
 CO OO CO 00 CO 
 rH rH to tO CO 
 
 CM tO 00 rH rH 
 
 rH rH 
 
 rH O O Oi O5 
 
 00 CO rH rH O 
 I>CM I>CM CO 
 
 co i> i> oo oo 
 
 I>O CO CO O5 
 rH CM CM CM CM 
 
 00 
 
 11 millimet 
 ished by Sp 
 
 t. 
 
 CO rH IO 
 
 *O tO rH rH CO 
 
 CO rH O5 l> tO 
 
 CO 00 CM l> CM 
 
 rH rH CM CM CO 
 
 CO CM CM rH rH 
 CO rH O5 l> tO 
 
 l> CM CO rH CO 
 
 CO rH rH IO to 
 
 ^ 
 
 11 
 
 
 rH rH 
 
 r^Sc5^S 
 
 
 O o 
 
 CO 
 
 t> rH CO 
 
 OO CO rH CM O 
 00 00 Oi OiO 
 
 tO rH rH CO CO 
 
 O rH rH CM CM 
 
 CO 
 
 | ^ 
 * 
 
 
 rH rH 
 
 r^Sc^SS 
 
 
 rH e3 
 
 ? 
 
 l> CM CO 
 
 Oi Oi 00 00 00 
 
 CO rH Oi I> *O 
 
 CM l>- rH CO rH 
 
 tO tO CO CO l> 
 
 rH rH 
 
 CO rH Oi t^" ^O 
 
 CO rH IO O >O 
 
 1>00 00 Oi Oi 
 CO Oi CM tO 00 
 
 rH rH CM CM CM 
 
 10 
 
 CO 3 
 
 oT 1 
 
 o 3 
 
 tt) "** 
 
 
 
 00 CM l> 
 
 rH rH O O O 
 Oi l> *O CO rH 
 
 rH CO rH CO rH 
 
 CM CM CO CO rH 
 rHrJ< 1>O CO 
 
 Oi 00 001>I> 
 
 to o *o o to 
 
 rf tO tO CO CO 
 CO Oi CM tO 00 
 
 . 
 
 4.11 decim 
 conversion 
 
 CO 
 
 00 CO l> 
 
 CO CO CM CM CM 
 rH CM O 00 CO 
 
 rH CO rH tO O 
 
 Oi Oi O O rH 
 CO I>O CO 
 
 rH rH 
 
 rH O O Oi Oi 
 
 rH CM O I>O 
 
 tOO *O Oi rH 
 rH CM CM CM CO 
 
 CO Oi CM tO 00 
 
 rH rH CM CM CM 
 
 CO 
 
 CO ^ 
 rH O 
 H w 
 
 w 3* 
 
 I a 
 
 li 
 
 CM 
 
 00 CO 00 CM 
 
 !> tO CO rH 
 tO O tO O 
 CO l> l> OO 
 
 COCO CM rH ^H 
 Oi I> IO CO rH 
 
 00 00 Oi OiO 
 
 CM 
 
 rH t W) 
 
 
 CO CO Oi CM 
 
 rH 
 
 tO 00 rH rH 00 
 rH rH CM CM CM 
 
 
 | 1 
 
 rH 
 
 O5 rH 00 CO 
 |> t^ CO CO CO 
 rH CM O 00 CO 
 O tO O rH G5 
 
 to tOrH rH CO 
 rH CM O 00 CO 
 
 rH 
 
 rh T^ 
 
 
 COCO Oi CM 
 
 IO 00 rH rH 1> 
 
 rH rH CM CM CM 
 
 
 3 IK 
 
 O 
 
 rH O5CO 00 
 O5 00 00 l>- 
 t^ tO CO rH 
 
 O O rH rH 
 
 <N l> rH CO O 
 
 r>. co co to to 
 
 Oi l> O CO rH 
 
 CO 00 CO 00 CO 
 CM CM CO CO rH 
 
 
 
 '!; 
 
 
 to ro w -X 
 
 tO 00 rH rH l> 
 rH rH CM CM CM 
 
 
 1" 
 
 CD 
 
 1 
 
 ooooo 
 
 rH CM CO ^ 
 
 tO CO l> 00 Oi 
 
 Q) 
 J 
 
 HH 
 
 c 
 
 c 
 
 r 
 
366 
 
 INCHES INTO MILLIMETRES. 
 
 O5 00 1> CO 
 CO O5 *O rH 
 
 OiO <M rH 
 
 i> oo oo oo 
 
 H CO 
 
 CO 
 
 Oi O 
 
 c^i co *o C 
 
 Oi Oi Oi 
 CM CN (N < 
 
 o 
 t 
 
 Th tOI>. 00 
 iO to to to 
 <N (N <M (N 
 
 IOCO <M rH 
 CO O5 >O rH 
 
 O rH CO 1C 
 
 CD CO CD CO 
 (N (N (M <N 
 
 O 00 
 I>(N 
 
 CO 00 O5 rH 
 CO CO CO 1> 
 <M (N (N CM 
 
 OO O rH CO 
 
 C?iO O O 
 C^l CO CO CO 
 
 tO CO (N rH 
 
 O CD (N 00 
 
 CO <* CO l> 
 l>t^ t^ t^ 
 <M (N (N C^ 
 
 00 1 
 rH t 
 
 o oo t> co 
 
 CO 00 -tf O 
 
 ooo 1-1 e 
 
 <N CO CO C 
 <N (M (N < 
 
 T^ CO 00 O5 
 CO CO CO CO 
 (M (M (M (M 
 
 (N (N < 
 
 f CO 
 
 (N 
 
 l> OiO <N 
 
 HH -HH lO ^O 
 
 (N (N ^A <M 
 
 oooi>c 
 
 <N I>CO 
 
 1C CO <N rH 
 *O rH t> CO 
 
 (N <M (M 
 
 rH <N 
 rH rH 
 
 O 00 !> CO 
 (M (M (M (N 
 
 o oo i> co 
 oo co Oi to 
 
 O CO <N rH 
 rH |> CO O 
 
 i> co 
 
 CO (M 
 
 O <M CO O 
 
 O5 Oi Oi O5 
 
 O CO <N rH 
 
 00^ O CO 
 
 CO 00 
 
 IO CO 
 
 t^ CO 
 
 1C CO C 
 
 O 00 t^CO 
 rH CO (M 00 
 
 >oco oo 
 
 CD CO CO C 
 
 CO O4 rH 
 
 ^ O CO (N 
 
 IO CO <M rH 
 
 O CD CO CO 
 
 Oi t- CO 
 tOrH|> 
 
 1> 00 O rH CO TtH CO 00 _..,,, 
 
 CO CO CO CO CO CO CO CO CO "** ^ ^ T)^ "HH " 
 
 O 
 
 ^O 
 
 I (M rH O Oil> C 
 
 JTHI> cooo Th <: 
 
 >O T^ (N rH 
 
 CD (M 00 ^ 
 
 i-H CO ^ CO 
 
 O O O O 
 
 t^ Oi r 
 
 O (M CO ^ 
 (M (N (N ( 
 
 Oi CD rH rH OiCOCOrH 00 CO CO rH 
 O5'Xt^-CO rtiCOCOrH OiOOt^cD 
 
 rH 1> CO O5 O rH |> CO OO "* O CO 
 
 r^ CO <M rH 
 (N 00 Tjn O 
 
 COI>O5O (NTHOI> 00 O <M CO tocDOOO 
 t-t^l>00 00000000 OOO2OiO5 O5C1O5O 
 
 O5 t^" Ttf rH O5 CO rf rH 
 O5001>CD TFCOCOrH 
 l> CO Oi tO rH I> CO Oi 
 
 5 CD "# rH 
 5 00 1>CO 
 h O CD <N 
 
 O5 CO ^ rH 
 ^ CO (N rH 
 
 oo-^ o CD 
 
 S( 
 1 
 
 t>- 00 O rH CO tO CD 00 Oi rH CO T^ 
 
 tOtOCOCO cOcDCDcO COt^-t^-I^- 
 
 Oi t^-rJH (M 
 
 Tt CO <M rH 
 
 I>CO O5 iO 
 
 rH COrf CO 
 CO CO COCO 
 
 Tt< CD t>- OS 
 
 1C Qi Th 
 
 1^ Tt (M 
 
 00 I>CO 
 
 T^ CO C^ 
 CO Oi ^>rH 
 
 O GO i> CD to CO CO T . 
 I>COOO^ OCDCOGO 
 
MENSURATION. DEFINITIONS. 
 
 37 
 
 MENSURATION. 
 Definitions. 
 
 A point is that which has only position. 
 
 A plane is a surface in which, any two points being taken, tKe 
 straight line joining them will be wholly in the 
 surface. ^ Fig. I 
 
 A curved line is a line of which no portion is A Curved Line 
 straight (Fig. 1). 
 
 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, . Fig. 2 
 
 An angle is the opening between two Parallel Lines, 
 
 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 ob- 
 tuse when it is greater than a right 
 angle. Thus, in Fig. 3, 
 
 A A A A are acute angles, 
 
 oooo are obtuse angles, R R R R ~ L^C 
 are 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 tri- 
 angle has two of its sides equal; an equi- 
 lateral triangle has all three of its sides 
 equal. 
 
 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. 
 
 Fig.3 
 
 Fig. 4. 
 
 Fig. 5. 
 
 Scalene Triangle. 
 
 Fig. 6. Fig. 7. 
 
 Isosceles Triangle. Equilateral Triangle. 
 
38 
 
 GEOMETRICAL TERMS. 
 
 A quadrilateral is a polygon of four sides. 
 
 Quadrilaterals are divided into classes, as follows, the trape- 
 zium (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. 
 
 \ 
 
 \ 
 
 8. 
 
 Fig. 9. Fig. 10. 
 
 A parallelogram whose sides are not equal, and its angles 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 whose sides are all equal is 
 called a square (Fig. 14). Polygons whose sides are all equal are 
 called regular. 
 
 Fig. II. Fig. 12. Fig. 13. Fig, 
 
 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; 
 The octagon (Fig. 18), which has eight sides. 
 
 Fig. 17. 
 
 18. 
 
 Fig. 15. Fig. 16. 
 
 The enneagon has nine sides. 
 
 The decagon has ten sides. 
 
 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. 
 
GEOMETRICAL TERMS. 
 
 39 
 
 A perimeter is the boundary line of a plane figure. 
 
 A circle is a portion of a plane bounded by a curve, all the points 
 of which are equally distant from a point within called the centre 
 (Fig. 19). 
 . The circumference is the curve which bounds the circle. 
 
 A radius is any straight line drawn from the centre to the cir- 
 cumference. 
 
 Any straight line drawn through the centre to the circumfer- 
 ence on each side is 'called a diameter. 
 
 An arc of a circle is any part of its circumference. 
 
 A chord is any straight line joining two points of the circumfer- 
 ence, as bd. 
 
 A segment is a portion of the 
 circle included between the arc and 
 its chord, as A in Fig. 19. 
 
 A sector is the space included be- 
 tween an arc and two radii drawn 
 to its extremities, as B, Fig. 19. 
 In the figure, ab is a radius, cd a 
 diameter, and db is a chord sub- 
 tending the arc bed. 
 
 Fig. 19. 
 
 A tangent is 
 
 a right line which in passing a 
 curve touches without cutting it, as fg, Fig. 19. 
 
 Volumes. 
 
 A prism is a volume whose ends are equal and parallel poly- 
 gons, and whose sides are parallelograms. 
 
 A prism is triangular, rectangular , etc., according as its ends 
 are triangles, 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 parallel circles. 
 
 A pyramid is a volume whose base is a poly- 
 gon, 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 remaining surface tapers uni- 
 formly to a point or vertex (Fig. 20). 
 
 Conic sections are the figures made by a plane cutting a cone. 
 
 Fig. 20. 
 
40 
 
 MENSURATION. 
 
 An ellipse is the section of a cone when 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 at a greater . 
 angle through the base than is 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 through it. The conjugate axis, 
 or short diameter, is a line drawn through 
 the centre, at right angles to the long 
 diameter. 
 
 A frustum of a pyramid or cone is that 
 which remains after cutting off the upper 
 part of it by a plane parallel to the base. 
 
 A sphere is a volume bounded by a 
 curved surface, all points of which are 
 equally distant from a point within, called the centre. 
 
 Mensuration treats of the measurement of lines, surfaces, 
 and volumes. 
 
 RULES. 
 
 To compute the area of a square, a rectangle, a rLombus, or a 
 
 rhomboid. 
 
 RJJLE. Multiply the length by the breadth or height; thus, 
 in either of Figs. 22, 23, 24, tfie area=a6x6c. 
 
 Fig.22 
 b c 
 
 Fig. 20. 
 
 Fig.23 
 
 a 
 Fj 9 .24 
 
 To compute the area of a triangle. 
 
 RULE. Multiply the base by the alti- 
 tude, and divide by 2; thus, in Fig. 25, 
 
 ,, . 7 abXcd 
 
 the area of abc= - . 
 
 To find the length of the hypothcnuse of a 
 right-angled triangle when both sides 
 are known. 
 
 d 
 Fig,25 
 
MENSURATION. POLYGONS. 
 
 41 
 
 RULE. Square the length of each of the sides making the right 
 angle, add their squares together, arid take 
 the square root of their sum. Thus (Fig. 26), F . 2 
 
 the length of ac=3, and of 6c=4; then 
 
 )-9 + 16=25. 
 \/25=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. 
 
 RULE. Multiply the diagonal by 
 the sum of the two perpendiculars fall- 
 ing upon it from the opposite angles, 
 and divide the product by 2. Or, 
 
 To -find the area of a trapezoid (Fig. 28). 
 
 RULE. Multiply the sum of the two par- 
 allel sides by the perpendicular distance be- 
 tween 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 to- 
 gether the areas of all the triangles, as A, B, 
 and C (Fig. 29). 
 
 To find the area of a regular polygon. 
 
 RULE. Multiply the length of a side by 
 the perpendicular distance to the centre (as 
 oo, Fig. 30), and that product by the numbe 
 of sides, and divide the result by 2. 
 
 To compute the area of a reguldr polygon when 
 
 the length of a side only is given. 
 RULE. Multiply the square of the side by 
 the multiplier opposite the name of the poly- 
 gon in column A of the following table : 
 
 Fig.30 
 
42 MENSURATION. POLYGONS AND CIRCLES. 
 
 Name of Polygon. 
 
 isyo. of 
 
 sides. 
 
 A. 
 Area. 
 
 B. 
 
 Radius of 
 circum- 
 scribing 
 circle. 
 
 c. 
 
 Length of 
 the sides. 
 
 D. 
 
 Radius of 
 inscribed 
 circle. 
 
 Triangle 
 
 3 
 
 0.433013 
 
 5773 
 
 1 732 
 
 2887 
 
 Tetragon 
 
 4 
 
 1 
 
 7071 
 
 1 4142 
 
 5 
 
 Pentagon . . . 
 
 5 
 
 1 . 720477 
 
 8506 
 
 1 1756 
 
 6882 
 
 Hexagon 
 
 6 
 
 2 598076 
 
 1 
 
 1 
 
 866 
 
 Heptagon 
 
 7 
 
 3.633912 
 
 1 1524 
 
 8677 
 
 0383 
 
 
 8 
 
 4.828427 
 
 1 3066 
 
 7653 
 
 2071 
 
 Nonagon . 
 
 9 
 
 6 181824 
 
 1 4619 
 
 684 
 
 3737 
 
 Decagon 
 
 10 
 
 7 . 694209 
 
 1.618 
 
 618 
 
 5383 
 
 Undecagon 
 
 11 
 
 9 36564 
 
 1 7747 
 
 5634 
 
 7028 
 
 Dodecagon 
 
 12 
 
 11.196152 
 
 1.9319 
 
 0.5176 
 
 .866 
 
 To compute the radius of a circumscribing circle when the length 
 
 of a side only is given. 
 
 RULE. Multiply the length of a side of the polygon by the 
 number in column B. 
 
 EXAMPLE. What is the radius of a circle that will contain a 
 hexagon, the length of one side being 5 inches? 
 
 Ans. 5X1 = 5 inches. 
 To compute the length of a side of a polygon that is contained in 
 
 a given circle, when the radius of the circle is given. 
 RULE. Multiply the radius of the circle by the number oppo- 
 site the name of the polygon in column C. 
 
 EXAMPLE. What is the length of the side of a pentagon con- 
 tained in a circle 8 feet in diameter? 
 
 Ans. 8 ft. diameters 2= 4 ft. radius, 4X1.1756=4.7024 ft. 
 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 num- 
 ber opposite the name of the polygon in column D. 
 To compute the radius of a circle that can be inscribed in a given 
 
 polygon, when the length of a side is given. 
 RULE. Multiply the length of a side of the polygon by the 
 number opposite the name of the polygon in column Z). 
 
 EXAMPLE. What is the radius of the circle that can be in- 
 scribed in an octagon, the length of one side being 6 inches. 
 
 Ans. 6X1.2071 = 7.2426 inches. 
 
 Circles. 
 
 To compute the circumference of a circle. 
 
 RULE. Multiply the diameter by 3.1416; or, for most pur- 
 poses, by 3^ is sufficiently accurate. 
 
MENSURATION. CIRCLES. 43 
 
 EXAMPLE. What is the circumference of a circle 7 inches in 
 diameter? 
 
 Ans. 7X3.1416=21.9912 inches, or 7X3^=22 inches, the 
 
 error in this last being 0.0088 of an inch. 
 To find the diameter of a circle when the circumference is given. 
 
 RULE. Divide the circumference by 3.1416, 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 one-half the chord, also square the rise; divide 
 their sum by twice the rise; the result will 
 be the radius. 
 
 EXAMPLE. The length of the chord ac, ^~-T 
 
 Fig. 30J, is 48 inches, and the rise, bo, is 6 /^ 
 inches. What is the radius of the arc? / 
 
 OC 2_|_~5 2 24 2 + 6 2 ng.ov* 
 
 Ans. Rad= ^ = =51 ins. 
 
 2bo 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 inches, and a 
 chord of 48 inches. What is the rise? 
 
 Ans. Rise = rad - Vrad 2 -~Jchord 2 = 51 - V2601 - 576 
 
 = 51 45 = 6 inches = rise. 
 To compute the area of a circle. 
 
 RULE. Multiply the square of the diameter by 0.7854, or mul- 
 tiply the square of the radius by 3.1416. 
 
 EXAMPLE. What is the area of a circle 10 inches in diameter? 
 
 Ans. 10X10X0.7854=78.54 square inches, or 5X5X3.1416 
 = 78.54 square inches. 
 
 The following tables will be found very convenient for finding 
 the circumference and area of circles. 
 
44 
 
 MENSURATION. CIRCLES. 
 
 AREAS AND CIRCUMFERENCES OF CIRCLES. 
 
 (For Diameters from fa to 100, advancing by Tenths.) 
 
 Dia. 
 
 Area. 
 
 Circum. 
 
 Dia. 
 
 Area. 
 
 Circum. 
 
 Dia. 
 
 Area. 
 
 Circum. 
 
 0.0 
 
 
 
 5.0 
 
 19.6350 
 
 15.7080 
 
 10.0 
 
 78.5398 
 
 31.4159 
 
 .1 
 
 0.007854 
 
 0.31416 
 
 .1 
 
 20.4282 
 
 16.0221 
 
 .1 
 
 80.1185 
 
 31.7301 
 
 .2 
 
 0.031416 
 
 0.62832 
 
 .2 
 
 21.2372 
 
 16.3363 
 
 .2 
 
 81.7128 
 
 32.0442 
 
 .3 
 
 0.070686 
 
 0.94248 
 
 .3 
 
 22.0618 
 
 16.6504 
 
 .3 
 
 83.3229 
 
 32.3584 
 
 .4 
 
 0.12566 
 
 1.2566 
 
 .4 
 
 22.9022 
 
 16.9646 
 
 .4 
 
 84.9487 
 
 32.6726 
 
 .5 
 
 0.19635 
 
 1.5708 
 
 .5 
 
 23.7583 
 
 17.2788 
 
 .5 
 
 86.5901 
 
 32.9867 
 
 .6 
 
 0.28274 
 
 1.8850 
 
 .6 
 
 24.6301 
 
 17.5929 
 
 .6 
 
 88.2473 
 
 33.3009 
 
 .7 
 
 0.38485 
 
 2.1991 
 
 .7 
 
 25.5176 
 
 17.9071 
 
 .7 
 
 89.9202 
 
 33.6150 
 
 .8 
 
 0.50266 
 
 2.5133 
 
 .8 
 
 26.4208 
 
 18.2212 
 
 .8 
 
 91.6088 
 
 33.9292 
 
 .9 
 
 0.63617 
 
 2.8274 
 
 .9 
 
 27.3397 
 
 18.5354 
 
 .9 
 
 93.3132 
 
 34.2434 
 
 1.0 
 
 0.7854 
 
 3.1416 
 
 6.0 
 
 28.2743 
 
 18.8496 
 
 11.0 
 
 95.0332 
 
 34.5575 
 
 .1 
 
 0.9503 
 
 3.4558 
 
 .1 
 
 29.2247 
 
 19.1637 
 
 .1 
 
 96.7689 
 
 34.8717 
 
 .2 
 
 1.1310 
 
 3.7699 
 
 .2 
 
 30.1907 
 
 19.4779 
 
 .2 
 
 98.5203 
 
 35.1858 
 
 .3 
 
 1.3273 
 
 4.0841 
 
 .3 
 
 31.1725 
 
 19.7920 
 
 .3 
 
 100.2875 
 
 35.5000 
 
 .4 
 
 1.5394 
 
 4.3982 
 
 .4 
 
 32.1699 
 
 20.1062 
 
 .4 
 
 102.0703 
 
 35.8142 
 
 .5 
 
 1.7671 
 
 4.7124 
 
 .5 
 
 33.1831 
 
 20.4204 
 
 .5 
 
 103.8689 
 
 36.1283 
 
 .6 
 
 2.0106 
 
 5.0265 
 
 .6 
 
 34.2119 
 
 20.7345 
 
 .6 
 
 105.6832 
 
 36.4425 
 
 .7 
 
 2.2698 
 
 5.3407 
 
 .7 
 
 35.2565 
 
 21.0487 
 
 .7 
 
 107.5132 
 
 36.7566 
 
 .8 
 
 2.5447 
 
 5.6549 
 
 .8 
 
 36.3168 
 
 21.3628 
 
 .8 
 
 109.3588 
 
 37.0708 
 
 .9 
 
 2.8353 
 
 5.9690 
 
 .9 
 
 37.3928 
 
 21.6770 
 
 .9 
 
 111.2202 
 
 37.3850 
 
 2.0 
 
 3.1416 
 
 6.2832 
 
 7.0 
 
 38.4845 
 
 21.9911 
 
 12.0 
 
 113.0973 
 
 37.6991 
 
 .1 
 
 3.4636 
 
 6.5973 
 
 .1 
 
 39.5919 
 
 22.3053 
 
 .1 
 
 114.9901 
 
 38.0133 
 
 .2 
 
 3.8013 
 
 6.9115 
 
 .2 
 
 40.7150 
 
 22.6195 
 
 .2 
 
 116.8987 
 
 38.3274 
 
 .3 
 
 4.1548 
 
 7.2257 
 
 .3 
 
 41.8539 
 
 22.9336 
 
 .3 
 
 118.8229 
 
 38.6416 
 
 .4 
 
 4.5239 
 
 7.5398 
 
 .4 
 
 43.0084 
 
 23.2478 
 
 .4 
 
 120.7628 
 
 38.9557 
 
 .5 
 
 4.9087 
 
 7.8540 
 
 .5 
 
 44.1786 
 
 23.5619 
 
 .5 
 
 122.7185 
 
 39.2699 
 
 .6 
 
 5.3093 
 
 8.1681 
 
 .6 
 
 45.3646 
 
 23.8761 
 
 .6 
 
 124.6898 
 
 39.5841 
 
 .7 
 
 5.7256 
 
 8.4823 
 
 .7 
 
 46.5663 
 
 24.1903 
 
 .7 
 
 126.6769 
 
 39.8982 
 
 .8 
 
 6.1575 
 
 8.7965 
 
 .8 
 
 47.7836 
 
 24.5044 
 
 .8 
 
 128.6796 
 
 40.2124 
 
 .9 
 
 6.6052 
 
 9.11(56 
 
 .9 
 
 49.0167 
 
 24.8186 
 
 .9 
 
 130.6981 
 
 40.5265 
 
 3.0 
 
 7.0686 
 
 9.4248 
 
 8.0 
 
 50.2655 
 
 25.1327 
 
 13.0 
 
 132.7323 
 
 40.8407 
 
 .1 
 
 7.5477 
 
 9.7389 
 
 .1 
 
 51.5300 
 
 25.4469 
 
 .1 
 
 134.7822 
 
 41.1549 
 
 .2 
 
 8.0425 
 
 10.0531 
 
 .2 
 
 52.8102 
 
 25.7611 
 
 .2 
 
 136.8478 
 
 41.4690 
 
 .3 
 
 8.5530 
 
 10.3673 
 
 .3 
 
 54.1061 
 
 26.0752 
 
 .3 
 
 138.9291 
 
 41.7832 
 
 .4 
 
 9.0792 
 
 10.6814 
 
 .4 
 
 55.4177 
 
 26.3894 
 
 .4 
 
 141.0261 
 
 42.0973 
 
 .5 
 
 9.6211 
 
 10.9956 
 
 .5 
 
 56.7450 
 
 26.7035 
 
 .5 
 
 143.1388 
 
 42.4115 
 
 .6 
 
 10.1788 
 
 11.3097 
 
 .6 
 
 58.0880 
 
 27.0177 
 
 .6 
 
 145.2672 
 
 42.7257 
 
 .7 
 
 10.7521 
 
 11.6239 
 
 .7 
 
 59.4468 
 
 27.3319 
 
 .7 
 
 147.4114 
 
 43.0398 
 
 .8 
 
 11.3411 
 
 11.9381 
 
 .8 
 
 60.8212 
 
 27.6460 
 
 .8 
 
 149.5712 
 
 43.3540 
 
 .9 
 
 11.9459 
 
 12.2522 
 
 .9 
 
 62.2114 
 
 27.9602 
 
 .9 
 
 151.7468 
 
 43.6681 
 
 4.0 
 
 12.5664 
 
 12.5664 
 
 9.0 
 
 63.6173 
 
 28.2743 
 
 14.0 
 
 153.9380 
 
 43.9823 
 
 .1 
 
 13.2025 
 
 12.8805 
 
 .1 
 
 65.0388 
 
 28.5885 
 
 .1 
 
 156.1450 
 
 44.2965 
 
 .2 
 
 13.8544 
 
 13.1947 
 
 .2 
 
 66.4761 
 
 28.9027 
 
 .2 
 
 158.3677 
 
 44.6106 
 
 .3 
 
 14.5220 
 
 13.5088 
 
 .3 
 
 67.9291 
 
 29.2168 
 
 .3 
 
 160.6061 
 
 44.9248 
 
 .4 
 
 15.2053 
 
 13.8230 
 
 .4 
 
 69.3978 
 
 29.5310 
 
 .4 
 
 162.8602 
 
 45.2389 
 
 .5 
 
 15.9043 
 
 14.1372 
 
 .5 
 
 70.8822 
 
 29.8451 
 
 .5 
 
 165.1300 
 
 45.5531 
 
 .6 
 
 16.6190 
 
 14.4513 
 
 .6 
 
 72.3823 
 
 30.1593 
 
 .6 
 
 167.4155 
 
 45.8673 
 
 .7 
 
 17.3494 
 
 14.7655 
 
 .7 
 
 73.8981 
 
 30.4734 
 
 .7 
 
 169.7167 
 
 46.1814 
 
 .8 
 
 18.0956 
 
 15.0796 
 
 .8 
 
 75.4296 
 
 30.7876 
 
 .8 
 
 172.0336 
 
 46.4956 
 
 .9 
 
 18.8574 
 
 15.3938 
 
 .9 
 
 76.9769 
 
 31.1018 
 
 .9 
 
 174.3662 
 
 46.8097 
 
MENSURATION. CIRCLES, 
 
 45 
 
 AREAS AND CIRCUMFERENCES OF CIRCLES. 
 
 (Advancing by Tenths.) 
 
 Dia. 
 
 Area. 
 
 Circum. 
 
 Dia. 
 
 Area. 
 
 Circum. 
 
 Dia. 
 
 Area. 
 
 Circum. 
 
 15.0 
 
 176.7146 
 
 47.1239 
 
 20.0 
 
 314.1593 
 
 62.8319 
 
 25.0 
 
 490.8739 
 
 78.5398 
 
 .1 
 
 179.0786 
 
 47.4380 
 
 .1 
 
 317.3087 
 
 63.1460 
 
 .1 
 
 494.8087 
 
 78.8540 
 
 .2 
 
 181.4584 
 
 47.7522 
 
 .2 
 
 320.4739 
 
 63.4602 
 
 2 
 
 498.7592 
 
 79.1681 
 
 .3 
 
 183.8539 
 
 48.0664 
 
 .3 
 
 323.6547 
 
 63.7743 
 
 '.3 
 
 502.7255 
 
 79.4823 
 
 .4 
 
 186.2650 
 
 48.3805 
 
 .4 
 
 326.8513 
 
 64.0885 
 
 .4 
 
 506.7075 
 
 79.7965 
 
 .5 
 
 188.6919 
 
 48.6947 
 
 .5 
 
 330.0636 
 
 64.4026 
 
 .5 
 
 510.7052 
 
 80.1106 
 
 .6 
 
 191.1345 
 
 49.0088 
 
 .6 
 
 333.2916 
 
 64.7168 
 
 .6 
 
 514.7185 
 
 80.4248 
 
 .7 
 
 193.5928 
 
 49.3230 
 
 .7 
 
 336.5353 
 
 65.0310 
 
 .7 
 
 518.7476 
 
 80.7389 
 
 .8 
 
 196.0668 
 
 49.6372 
 
 .8 
 
 339.7947 
 
 65.3451 
 
 .8 
 
 522.7924 
 
 81.0531 
 
 .9 
 
 198.5565 
 
 49.9513 
 
 .9 
 
 343.0698 
 
 65.6593 
 
 .9 
 
 526.8529 
 
 81.3672 
 
 16.0 
 
 201.0619 
 
 50.2655 
 
 21.0 
 
 340.3606 
 
 65.9734 
 
 26.0 
 
 530.9292 
 
 81.68*4 
 
 .1 
 
 203.5831 
 
 50.5796 
 
 .1 
 
 349.6671 
 
 66.2876 
 
 .1 
 
 535.0211 
 
 81.9956 
 
 .2 
 
 206.1199 
 
 50.8938 
 
 .2 
 
 352.9894 
 
 66.6018 
 
 .2 
 
 539.1287 
 
 82.3097 
 
 .3 
 
 208.6724 
 
 51.2080 
 
 .3 
 
 356.3273 
 
 66.9159 
 
 .3 
 
 543.2521 
 
 82.6239 
 
 .4 
 
 211.2407 
 
 51.5221 
 
 .4 
 
 359.6809 
 
 67.2301 
 
 .4 
 
 547.3911 
 
 82.9380 
 
 .5 
 
 213.8246 
 
 51.8363 
 
 .5 
 
 363.0503 
 
 67.5442 
 
 .5 
 
 551.5459 
 
 83.2522 
 
 .6 
 
 216.4243 
 
 52.1504 
 
 .6 
 
 366.4354 
 
 67.8584 
 
 .6 
 
 555.7163 
 
 83.5664 
 
 .7 
 
 219.0397 
 
 52.4646 
 
 .7 
 
 369.8361 
 
 68.1726 
 
 .7 
 
 559.9025 
 
 83.8805 
 
 .8 
 
 221.6708 
 
 52.7788 
 
 .8 
 
 373.2526 
 
 68.4867 
 
 .8 
 
 564.1044 
 
 84.1947 
 
 .9 
 
 224.3176 
 
 53.0929 
 
 .9 
 
 376.6848 
 
 68.8009 
 
 .9 
 
 568.3220 
 
 84.5088 
 
 17.0 
 
 226.9801 
 
 53.4071 
 
 22.0 
 
 380.1327 
 
 69.1150 
 
 27.0 
 
 572.5553 
 
 84.8230 
 
 .1 
 
 229.6583 
 
 53.7212 
 
 .1 
 
 383.5963 
 
 69.4292 
 
 .1 
 
 576.8043 
 
 85.1372 
 
 .2 
 
 232.3522 
 
 54.0354 
 
 .2 
 
 387.0756 
 
 69.7434 
 
 .2 
 
 581.0690 
 
 85.4513 
 
 .3 
 
 235.0618 
 
 54.3496 
 
 .3 
 
 390.5707 
 
 70.0575 
 
 .3 
 
 585.3494 
 
 85.7655 
 
 .4 
 
 237.7871 
 
 54.6637 
 
 .4 
 
 394.0814 
 
 70.3717 
 
 .4 
 
 589.6455 
 
 86.0796 
 
 .5 
 
 240.5282 
 
 54.9779 
 
 .5 
 
 397.6078 
 
 70.6858 
 
 .5 
 
 593.9574 
 
 86.3938 
 
 .6 
 
 243.2849 
 
 55.2920 
 
 .6 
 
 401.1500 
 
 71.0000 
 
 .6 
 
 598.2849 
 
 86.7080 
 
 .7 
 
 246.0574 
 
 55.6002 
 
 .7 
 
 404.7078 
 
 71.3142 
 
 .7 
 
 602.6282 
 
 87.0221 
 
 .8 
 
 248.8456 
 
 55.9203 
 
 .8 
 
 408.2814 
 
 71.6283 
 
 :8 
 
 606.9871 
 
 87.3363 
 
 .9 
 
 251.6494 
 
 56.2345 
 
 .9 
 
 411.8707 
 
 71.9425 
 
 .9 
 
 611.3618 
 
 87.6594 
 
 18.0 
 
 254.4690 
 
 56.5486 
 
 23.0 
 
 415.4756 
 
 72.2566 
 
 28.0 
 
 615.7522 
 
 87.9646 
 
 .1 
 
 257.3043 
 
 56.8628 
 
 .1 
 
 419.0963 
 
 72.5708 
 
 .1 
 
 620.1582 
 
 88.2788 
 
 .2 
 
 260.1553 
 
 57.1770 
 
 .2 
 
 422.7327 
 
 72.8849 
 
 .2 
 
 624.5800 
 
 88.5929 
 
 .3 
 
 263.0220 
 
 57.4911 
 
 .3 
 
 426.3848 
 
 73.1991 
 
 .3 
 
 629.0175 
 
 88.9071 
 
 .4 
 
 265.9044 
 
 57.8053 
 
 .4 
 
 430.0526 
 
 73.5133 
 
 .4 
 
 633.4707 
 
 89.2212 
 
 .5 
 
 268.8025 
 
 58.1195 
 
 .5 
 
 433.7361 
 
 73.8274 
 
 .5 
 
 637.9397 
 
 89.5354 
 
 .6 
 
 271.7164 
 
 58.4336 
 
 .6 
 
 437.4354 
 
 74.1416 
 
 .6 
 
 642.4243 
 
 89.8495 
 
 .7 
 
 274.6459 
 
 58.7478 
 
 .7 
 
 441.1503 
 
 74.4557 
 
 .7 
 
 646.9246 
 
 90.1637 
 
 .8 
 
 277.5911 
 
 59.0619 
 
 .8 
 
 444.8809 
 
 74.7699 
 
 $ 
 
 651.4407 
 
 90.4779 
 
 .9 
 
 280.5521 
 
 59.3761 
 
 .9 
 
 448.6273 
 
 75.0841 
 
 !9 
 
 655.9724 
 
 90.7920 
 
 19.0 
 
 283.5287 
 
 59.6903 
 
 24.0 
 
 452.3893 
 
 75.3982 
 
 29.0 
 
 660.5199 
 
 91.1062 
 
 .1 
 
 286.5211 
 
 60.0044 
 
 .1 
 
 456.1671 
 
 75.7124 
 
 .1 
 
 665.0830 
 
 91.4203 
 
 .2 
 
 289.5292 
 
 60.3186 
 
 .2 
 
 459.9606 
 
 76.0265 
 
 .2 
 
 669.6619 
 
 91.7345 
 
 .3 
 
 292.5530 
 
 60.6327 
 
 .3 
 
 463.7698 
 
 76.3407 
 
 .3 
 
 674.2565 
 
 92.0487 
 
 .4 
 
 295.5925 
 
 60.9469 
 
 .4 
 
 467.5947 
 
 76.6549 
 
 .4 
 
 678.8668 
 
 92.3628 
 
 .5 
 
 298.6477 
 
 61.2611 
 
 .5 
 
 471.4352 
 
 76.9690 
 
 .5 
 
 683.4928 
 
 92.6770 
 
 .6 
 
 301.7186 
 
 61.5752 
 
 .6 
 
 475.2916 
 
 77.2832 
 
 .6 
 
 688.1345 
 
 92.9911 
 
 .7 
 
 304.8052 
 
 61.8894 
 
 .7 
 
 479.1636 
 
 77.5973 
 
 .7 
 
 692.7919 
 
 93.3053 
 
 .8 
 
 307.9075 
 
 62.2035 
 
 .8 
 
 483.0513 
 
 77.9115 
 
 .8 
 
 697.4650 
 
 93.6195 
 
 .9 
 
 311.0255 
 
 62.5177 
 
 .9 
 
 486.9547 
 
 78.2257 
 
 .9 
 
 702.1538 
 
 93.9336 
 
46 
 
 MENSURATION. CIRCLES. 
 
 AREAS AND CIRCUMFERENCES OF CIRCLES. 
 
 (Advancing by Tenths.) 
 
 Dia. 
 
 Area. 
 
 Circum. 
 
 Dia. 
 
 Area. 
 
 Circum. 
 
 Dia. 
 
 Area. 
 
 Circum. 
 
 30.0 
 
 706.8583 
 
 94.2478 
 
 35.0 
 
 962.1128 
 
 109.9557 
 
 40.0 
 
 1256.6371 
 
 125.6637 
 
 .1 
 
 711.5786 
 
 94.5619 
 
 .1 
 
 967.6184 
 
 110.2699 
 
 .1 
 
 1262.9281 
 
 125.9779 
 
 .2 
 
 716.3145 
 
 94.8761 
 
 .2 
 
 973.1397 
 
 110.5841 
 
 .2 
 
 1269.2348 
 
 128.2920 
 
 .3 
 
 721.0662 
 
 95.1903 
 
 .3 
 
 978.6768 
 
 110.8982 
 
 .3 
 
 1275.5573 
 
 126.6062 
 
 .4 
 
 725.8336 
 
 95.5044 
 
 .4 
 
 984.2296 
 
 111.2124 
 
 .4 
 
 1281.8955 
 
 126.9203 
 
 .5 
 
 730.6167 
 
 95.8186 
 
 .5 
 
 989.7980 
 
 111.5265 
 
 .5 
 
 1288.2493 
 
 127.2345 
 
 .6 
 
 735.4154 
 
 96.1327 
 
 .6 
 
 995.3822 
 
 111.8407 
 
 .61 1294.6189 
 
 127.5487 
 
 .7 
 
 740.2299 
 
 96.4469 
 
 .7 
 
 1000.9821 
 
 112.1549 
 
 .7 
 
 1301.0042 
 
 127.8628 
 
 .8 
 
 745.0601 
 
 96.7611 
 
 .8 
 
 1006.5977 
 
 112.4690 
 
 .8 
 
 1307.4052 
 
 128.1770 
 
 .9 
 
 749.9060 
 
 97.0752 
 
 .9 
 
 1012.2290 
 
 112.7832 
 
 .9 
 
 1313.8219 
 
 128.4911 
 
 ai.o 
 
 754.7676 
 
 97.3894 
 
 36.0 
 
 1017.8760 
 
 113.0973 
 
 41.0 
 
 1320.2543 
 
 128.8053 
 
 .1 
 
 759.6450 
 
 97.7035 
 
 i 
 
 1023.5387 
 
 113.4115 
 
 .1 
 
 1326.7024 
 
 129.1195 
 
 .2 
 
 764.5380 
 
 98.0177 
 
 '.2 
 
 1029.2172 
 
 113.7257 
 
 .2 
 
 1333.1663 
 
 129.4336 
 
 .3 
 
 769.4467 
 
 98.3319 
 
 .3 
 
 1034.9113 
 
 114.0398 
 
 .3 
 
 1339.6458 
 
 129.7478 
 
 .4 
 
 774.3712 
 
 98.6460 
 
 .4 
 
 1040.6212 
 
 114.3540 
 
 .4 
 
 1346.1410 
 
 130.0619 
 
 .5 
 
 779.3113 
 
 98.9602 
 
 .5 
 
 1046.3467 
 
 114.6681 
 
 .5 
 
 1352.6520 
 
 130.3761 
 
 .6 
 
 784.2672 
 
 99.2743 
 
 .6 
 
 1052.0880 
 
 114.9S23 
 
 .6 
 
 1359.1786 
 
 130.6903 
 
 .7 
 
 789.2388 
 
 99.5885 
 
 .7 
 
 1057.8449 
 
 115.2965 
 
 .7 
 
 1365.7210 
 
 131.0044 
 
 .8 
 
 794.2260 
 
 99.9026 
 
 .8 
 
 1063.6176 
 
 115.6106 
 
 .8 
 
 1372.2791 
 
 131.31S6 
 
 .9 
 
 799.2290 
 
 100.2168 
 
 .9 
 
 1069.4060 
 
 115.9248 
 
 .9 
 
 1378.8529 
 
 131.6327 
 
 32.0 
 
 804.2477 
 
 100.5310 
 
 37.0 
 
 1075.2101 
 
 116.2389 
 
 42.0 
 
 1385.4424 
 
 131.9469 
 
 .1 
 
 809.2S21 
 
 100.8451 
 
 .1 
 
 1081.0299 
 
 116.5531 
 
 .1 
 
 1392.0476 
 
 132.2611 
 
 .2 
 
 814.3322 
 
 101.1593 
 
 .2 
 
 1086.8654 
 
 116.8672 
 
 .2 
 
 1398.6685 
 
 132.5752 
 
 .3 
 
 819.3980 
 
 101.4734 
 
 .3 
 
 1092.7166 
 
 117.1814 
 
 .3 
 
 1405.3051 
 
 132.8894 
 
 .4 
 
 824.4796 
 
 101.7876 
 
 .4 
 
 1098.5835 
 
 117.4956 
 
 .4 
 
 1411.9574 
 
 133.2035 
 
 .5 
 
 829.5768 
 
 102.1018 
 
 .5 
 
 1104.4662 
 
 117.8097 
 
 .5 
 
 1418.6254 
 
 133.5177 
 
 .6 
 
 834.6898 
 
 102.4159 
 
 .6 
 
 1110.3645 
 
 118.1239 
 
 .6 
 
 1425.3092 
 
 133.8318 
 
 .7 
 
 839.8185 
 
 102.7301 
 
 .7 
 
 1116.2786 
 
 118.4380 
 
 .7 
 
 1432.0086 
 
 134.1460 
 
 .8 
 
 844.9628 
 
 103.0442 
 
 .8 
 
 1122.2083 
 
 118.7522 
 
 .8 
 
 1438.7238 
 
 134.4602 
 
 .9 
 
 850.1229 
 
 103.3584 
 
 .9 
 
 1128.1538 
 
 119.0664 
 
 .9 
 
 1445.4546 
 
 134.7743 
 
 33.0 
 
 855.2986 
 
 103.6726 
 
 38.0 
 
 1134.1149 
 
 119.3805 
 
 43.0 
 
 1452.2012 
 
 135.0885 
 
 .1 
 
 860.4902 
 
 103.9867 
 
 .1 
 
 1140.0918 
 
 119.6947 
 
 .1 
 
 1458.9635 
 
 135.4026 
 
 .2 
 
 865.6973 
 
 104.3009 
 
 .2 
 
 1146.0844 
 
 120.0088 
 
 .2 
 
 1465.7415 
 
 135.7168 
 
 .3 
 
 370.9202 
 
 104.6150 
 
 .3 
 
 1152.0927 
 
 120.3230 
 
 .3 
 
 1472.5352 
 
 136.0310 
 
 .4 
 
 876.1588 
 
 104.9292 
 
 .4 
 
 1158.1167 
 
 120.6372 
 
 .4 
 
 1479.3446 
 
 136.3451 
 
 .5 
 
 881.4131 
 
 105.2434 
 
 5 
 
 1164.1564 
 
 120.9513 
 
 .5 
 
 1486.1697 
 
 136.6593 
 
 .6 
 
 886.6831 
 
 105.5575 
 
 !e 
 
 1170.2118 
 
 121.2655 
 
 .6 
 
 1493.0105 
 
 136.9734 
 
 .7 
 
 891.9688 
 
 105.8717 
 
 .7 
 
 1176.2830 
 
 121.5796 
 
 .7 
 
 1499.8670 
 
 137.2876 
 
 .8 
 
 897.2703 
 
 106.1858 
 
 .8 
 
 1182.3698 
 
 121.8938 
 
 .8 
 
 1506.7393 
 
 137.0018 
 
 .9 
 
 902.5874 
 
 106.5000 
 
 .9 
 
 1188.4724 
 
 122.2080 
 
 .9 
 
 1513.6272 
 
 137.9159 
 
 34.0 
 
 907.9203 
 
 106.8142 
 
 39.0 
 
 1194.5906 
 
 122.5221 
 
 44.0 
 
 1520.5308 
 
 138.2301 
 
 .1 
 
 913.2688 
 
 107.1283 
 
 .1 
 
 1200.7246 
 
 122.8363 
 
 .1 
 
 1527.4502 
 
 138.5442 
 
 .2 
 
 918.6331 
 
 107.4425 
 
 2 
 
 1206.8742 
 
 123.1504 
 
 .2 
 
 1534.3853 
 
 138.8584 
 
 .3 
 
 924.0131 
 
 107.7566 
 
 is 
 
 1213.0396 
 
 123.4646 
 
 .3 
 
 1541.3360 
 
 139.1726 
 
 .4 
 
 929.4088 
 
 108.0708 
 
 .4 
 
 1219.2207 
 
 123.7788 
 
 .4 
 
 1548.3025 
 
 139.4867 
 
 .5 
 
 934.8202 
 
 108.3849 
 
 .5 
 
 1225.4175 
 
 124.0929 
 
 .5 
 
 1555.247 
 
 139.8009 
 
 .6 
 
 940.2473 
 
 108.6991 
 
 .6 
 
 1231.6300 
 
 124.4071 
 
 .6 
 
 1562.2826 
 
 140.1153 
 
 .7 
 
 945.6901 
 
 109.0133 
 
 .7 
 
 1237.8582 
 
 124.7212 
 
 .7 
 
 1569.2962 
 
 140.4292 
 
 .8 
 
 951.1486 
 
 109.3274 
 
 .8 
 
 1244.1021 
 
 125.0354 
 
 .8 
 
 1576.3255 
 
 140.7434 
 
 .9 
 
 956.6228 
 
 109.641C 
 
 .9 
 
 1250.3617 
 
 125.3495 
 
 .9 
 
 1583.3706 
 
 141.0575 
 
MENSURATION. CIRCLES. 
 
 47 
 
 AREAS AND CIRCUMFERENCES OF CIRCLES. 
 
 (Advancing by Tenths.) 
 
 Dia. 
 
 Area. 
 
 Circum. 
 
 Dia. 
 
 Area. 
 
 Circum. 
 
 Dia. 
 
 Area. 
 
 Circum. 
 
 45.0 
 
 1590.4313 
 
 141.3717 
 
 50.0 
 
 1963.4954 
 
 157.0796 
 
 55.0 
 
 2375.8294 
 
 172.7876 
 
 .1 
 
 1597.5077 
 
 141.6858 
 
 .1 
 
 1971.3572 
 
 157.3938 
 
 .1 
 
 2384.4767 
 
 173.1017 
 
 .2 
 
 1604.5999 
 
 142.0000 
 
 .2 
 
 1979.2348 
 
 157.7080 
 
 .2 
 
 2393.1396 
 
 173.4159 
 
 .3 
 
 1611.7077 
 
 142.3142 
 
 .3 
 
 1987.1280 
 
 158.0221 
 
 .3 
 
 2401.8183 
 
 173.7301 
 
 'A 
 
 1618.8313 
 
 142.6283 
 
 .4 
 
 1995.0370 
 
 158.3363 
 
 .4 
 
 2410.5126 
 
 174.0442 
 
 .5 
 
 1625.9705 
 
 142.9425 
 
 .5 
 
 2002.9617 
 
 158.6504 
 
 .5 
 
 2419.2227 
 
 174.3584 
 
 .6 
 
 1633.1255 
 
 143.2566 
 
 .6 
 
 2010.9020 
 
 158.9646 
 
 .6 
 
 2427.9485 
 
 174.6726 
 
 [7 
 
 1640.2962 
 
 143.5708 
 
 .7 
 
 2018.8581 
 
 159.2787 
 
 .7 
 
 2436.6899 
 
 174.9867 
 
 !s 
 
 1647.4826 
 
 143.8849 
 
 .8 
 
 2026.8299 
 
 159.5929 
 
 .8 
 
 2445.4471 
 
 175.3009 
 
 .9 
 
 1654.6847 
 
 144.1991 
 
 .9 
 
 2034.8174 
 
 159.9071 
 
 .9 
 
 2454.2200 
 
 175.6150 
 
 46.0 
 
 1661.9025 
 
 144.5133 
 
 51.0 
 
 2042.8206 
 
 160.2212 
 
 56.0 
 
 2463.0086 
 
 175.9292 
 
 .1 
 
 1669.1360 
 
 144.8274 
 
 .1 
 
 2050.8395 
 
 160.5354 
 
 .1 
 
 2471.8130 
 
 176.2433 
 
 .2 
 
 1676.3853 
 
 145.1416 
 
 .2 
 
 2058.8742 
 
 160.8495 
 
 .2 
 
 2480.6330 
 
 176.5575 
 
 .3 
 
 1683.6502 
 
 145.4557 
 
 .3 
 
 2066.9245 
 
 161.1637 
 
 .3 
 
 2489,4687 
 
 176.8717 
 
 .4 
 
 1690.9308 
 
 145.7699 
 
 .4 
 
 2074.9905 
 
 161.4779 
 
 .4 
 
 2498.3201 
 
 177.1858 
 
 .5 
 
 1698.2272 
 
 146.0841 
 
 .5 
 
 2083.0723 
 
 161.7920 
 
 .5 
 
 2507.1873 
 
 177.5000 
 
 .6 
 
 1705.5392 
 
 146.3982 
 
 .6 
 
 2091.1697 
 
 162.1062 
 
 .6 
 
 2516.0701 
 
 177.8141 
 
 .7 
 
 1712.8670 
 
 146.7124 
 
 .7 
 
 2099.2829 
 
 162.4203 
 
 .7 
 
 2524.9687 
 
 178.1283 
 
 .8 
 
 1720.2105 
 
 147.0265 
 
 .8 
 
 2107.4118 
 
 162.7345 
 
 .8 
 
 2533.8830 
 
 178.4425 
 
 .9 
 
 1727.5697 
 
 147.3407 
 
 .9 
 
 2115.5563 
 
 163.0487 
 
 .9 
 
 2542.8129 
 
 178.7566 
 
 47.0 
 
 1734.9445 
 
 147.6550 
 
 52.0 
 
 2123.7166 
 
 163.3628 
 
 57.0 
 
 2551.7586 
 
 179.0708 
 
 .1 
 
 1742.3351 
 
 147.9690 
 
 .1 
 
 2131.8926 
 
 163.6770 
 
 .1 
 
 2560.7200 
 
 179.3849 
 
 .2 
 
 1749.7414 
 
 148.2832 
 
 .2 
 
 2140.0843 
 
 163.9911 
 
 .2 
 
 2569.6971 
 
 179.6991 
 
 .3 
 
 1757.1635 
 
 148.5973 
 
 .3 
 
 2148.2917 
 
 164.3053 
 
 .3 
 
 2578.6899 
 
 180.0133 
 
 .4 
 
 1764.6012 
 
 148.9115 
 
 .4 
 
 2156.5149 
 
 164.6195 
 
 .4 
 
 2587.6985 
 
 180.3274 
 
 .5 
 
 1772.0546 
 
 149.2257 
 
 .5 
 
 2164.7537 
 
 164.9336 
 
 .5 
 
 2596.7227 
 
 180.6416 
 
 .6 
 
 1779.5237 
 
 149.5398 
 
 .6 
 
 2173.0082 
 
 165.2479 
 
 .6 
 
 2605.7626 
 
 180.9557 
 
 .7 
 
 1787.0086 
 
 149.8540 
 
 .7 
 
 2181.2785 
 
 165.5619 
 
 .7 
 
 2614.8183 
 
 181.2699 
 
 .8 
 
 1794.5091 
 
 150.1681 
 
 .8 
 
 2189.5644 
 
 165.8761 
 
 .8 
 
 2623.8896 
 
 181.5841 
 
 .9 
 
 1802.0254 
 
 150.4823 
 
 .9 
 
 2197.8661 
 
 166.1903 
 
 .9 
 
 2632.9767 
 
 181.8982 
 
 48.0 
 
 1809.5574 
 
 150.7964 
 
 53.0 
 
 2206.1834 
 
 166.5044 
 
 58.0 
 
 2642.0794 
 
 182.2124 
 
 .1 
 
 1817.1050 
 
 151.1106 
 
 .1 
 
 2214.5165 
 
 166.8186 
 
 .1 
 
 2651.1979 
 
 182.5265 
 
 .2 
 
 1824.6684 
 
 151.4248 
 
 .2 
 
 2222.8653 
 
 167.1327 
 
 .2 
 
 2660.3321 
 
 182.8407 
 
 .3 
 
 1832.2475 
 
 151.7389 
 
 .3 
 
 2231.2298 
 
 167.4469 
 
 .3 
 
 2669.4820 
 
 183.1549 
 
 .4 
 
 1839.8423 
 
 152.0531 
 
 .4 
 
 2239.6100 
 
 167.7610 
 
 .4 
 
 2678.6476 
 
 183.4690 
 
 .5 
 
 1847.4528 
 
 152.3672 
 
 .5 
 
 2248.0059 
 
 168.0752 
 
 .5 
 
 268718289 
 
 183J832 
 
 .6 
 
 1855.0790 
 
 152.6814 
 
 .6 
 
 2256.4175 
 
 168.3894 
 
 .6 
 
 2697.0259 
 
 184.0973 
 
 .7 
 
 1862.7210 
 
 152.9956 
 
 .7 
 
 2264.8448 
 
 168.7035 
 
 .7 
 
 2706.2386 
 
 184.4115 
 
 .8 
 
 1870.3786 
 
 153.3097 
 
 .8 
 
 2273.2879 
 
 169.0177 
 
 .8 
 
 2715.4670 
 
 184.7256 
 
 .9 
 
 1878.0519 
 
 153.6239 
 
 .9 
 
 2281.7466 
 
 169.3318 
 
 .9 
 
 2724.7112 
 
 185.0398 
 
 49.0 
 
 1885.7409 
 
 153.9380 
 
 54.0 
 
 2290.2210 
 
 169.6460 
 
 59.0 
 
 2733.9710 
 
 185.3540 
 
 .1 
 
 1893.4457 
 
 154.2522 
 
 .1 
 
 2298.7112 
 
 169.9602 
 
 .1 
 
 2743.2466 
 
 185.6681 
 
 .2 
 
 1901.1662 
 
 154.5664 
 
 .2 
 
 2307.2171 
 
 170.2743 
 
 2 
 
 2752.5378 
 
 185.9823 
 
 .3 
 
 1908.9024 
 
 154.8805 
 
 .3 
 
 2315.7386 
 
 170.5885 
 
 !3 
 
 2761.8448 
 
 186.2964 
 
 .4 
 
 1916.6543 
 
 155.1947 
 
 .4 
 
 2324.2759 
 
 170.9026 
 
 .4 
 
 2771.1675 
 
 186.6106 
 
 .5 
 
 1924.4218 
 
 155.5088 
 
 .5 
 
 2332.8289 
 
 171.2168 
 
 .5 
 
 2780.5058 
 
 186.9248 
 
 .6 
 
 1932.2051 
 
 155.8230 
 
 .6 
 
 2341.3976 
 
 171.5310 
 
 .6 
 
 2789.8599 
 
 187.2389 
 
 .7 
 
 1940.0042 
 
 156.1372 
 
 .7 
 
 2349.9820 
 
 171.8451 
 
 .7 
 
 2799.2297 
 
 187.5531 
 
 .8 
 
 1947.8189 
 
 156.4513 
 
 .8 
 
 2358.5821 
 
 172.1593 
 
 .8 
 
 2808.6152 
 
 187.8672 
 
 .9 
 
 1955.6493 
 
 156.7655 
 
 .9 
 
 2367.1979 
 
 172.4735 
 
 .9 
 
 2818.0165 
 
 188.1814 
 
48 
 
 MENSURATION. CIRCLES. 
 
 AREAS AND CIRCUMFERENCES OF CIRCLES. 
 
 (Advancing by Tenths.) 
 
 Dia. 
 
 Area. 
 
 Circum. 
 
 Dia. 
 
 Area. 
 
 Circum. 
 
 Dia. 
 
 Area. 
 
 Circum. 
 
 60.0 
 
 2827.4334 
 
 188.4956 
 
 65.0 
 
 3318.3072 
 
 204.2035 
 
 70.0 
 
 3848.4510 
 
 219 9115 
 
 .1 
 
 2836.8660 
 
 188.8097 
 
 .1 
 
 3328.5253 
 
 204.5176 
 
 .1 
 
 3859.4544 
 
 220.2256 
 
 .2 
 
 2846.3144 
 
 189.1239 
 
 .2 
 
 3338.7590 
 
 204.8318 
 
 .2 
 
 3870.4736 
 
 220.5398 
 
 .3 
 
 2855.7784 
 
 189.4380 
 
 .3 
 
 3349.0085 
 
 205.1460 
 
 .3 
 
 3881.5084 
 
 220.8540 
 
 .4 
 
 2865.2582 
 
 189.7522 
 
 .4 
 
 3359.2736 
 
 205.4602 
 
 .4 
 
 3892.5590 
 
 221.1681 
 
 .5 
 
 2874.7536 
 
 190.0664 
 
 .5 
 
 3369.5545 
 
 205.7743 
 
 .5 
 
 3903.6252 
 
 221.4823 
 
 .6 
 
 2884.2648 
 
 190.3805 
 
 .6 
 
 3379.8510 
 
 206.0885 
 
 .6 
 
 3914.7072 
 
 221.7964 
 
 .7 
 
 2893.7917 
 
 190.6947 
 
 .7 
 
 3390.1633 
 
 206.4026 
 
 .7 
 
 3925.8049 
 
 222.1106 
 
 .8 
 
 2903.3343 
 
 191.0088 
 
 .8 
 
 3400.4913 
 
 206.7168 
 
 .8 
 
 3936.9182 
 
 222.4248 
 
 .9 
 
 2912.8926 
 
 191.3230 
 
 .9 
 
 3410.8350 
 
 207.0310 
 
 .9 
 
 3948.0473 
 
 222.7389 
 
 61.0 
 
 2922.4666 
 
 191.6372 
 
 66.0 
 
 3421.1944 
 
 207.3451 
 
 71.0 
 
 3959.1921 
 
 223.0531 
 
 .1 
 
 2932.0563 
 
 191.9513 
 
 .1 
 
 3431.5695 
 
 207.6593 
 
 .1 
 
 3970.3526 
 
 223.3672 
 
 .2 
 
 2941.6617 
 
 192.2655 
 
 .2 
 
 3441.9603 
 
 207.9734 
 
 .2 
 
 3981.5289 
 
 223.6814 
 
 .3 
 
 2951.2828 
 
 192.5796 
 
 .3 
 
 3452.3669 
 
 208.2876 
 
 .3 
 
 3992.7208 
 
 223.9956 
 
 .4 
 
 2960.9197 
 
 192.8938 
 
 .4 
 
 3462.7891 
 
 208.6017 
 
 .4 
 
 4003.9284 
 
 224.3097 
 
 .5 
 
 2970.5722 
 
 193.2079 
 
 .5 
 
 3473.2270 
 
 208.9159 
 
 .5 
 
 4015.1518 
 
 224.6239 
 
 .6 
 
 2980.2405 
 
 193.5221 
 
 .6 
 
 3483.6807 
 
 209.2301 
 
 .6 
 
 4026.3908 
 
 224.9380 
 
 .7 
 
 2989.9244 
 
 193.8363 
 
 .7 
 
 3494.1500 
 
 209.5442 
 
 .7 
 
 4037.6456 
 
 225.2522 
 
 .8 
 
 2999.6241 
 
 194.1504 
 
 .8 
 
 3504.6351 
 
 209.8584 
 
 .8 
 
 4048.9160 
 
 225.5664 
 
 .9 
 
 3009.3395 
 
 194.4646 
 
 .9 
 
 3515.1359 
 
 210.1725 
 
 .9 
 
 4060.2022 
 
 225.3805 
 
 62.0 
 
 3019.0705 
 
 194.7787 
 
 67.0 
 
 3525.6524 
 
 210.4867 
 
 72.0 
 
 4071.5041 
 
 226.1947 
 
 .1 
 
 3028.8173 
 
 195.0929 
 
 .1 
 
 3536.1845 
 
 210.8009 
 
 .1 
 
 4082.8217 
 
 226.5088 
 
 .2 
 
 3038.5798 
 
 195.4071 
 
 .2 
 
 3546.7324 
 
 211.1150 
 
 2 
 
 4094.1550 
 
 226.8230 
 
 .3 
 
 3048.3580 
 
 195.7212 
 
 .3 
 
 3557.2960 
 
 211.4292 
 
 .3 
 
 4105.5040 
 
 227.1371 
 
 .4 
 
 3058.1520 
 
 196.0354 
 
 .4 
 
 3567.8754 
 
 211.7433 
 
 'A 
 
 4116.8687 
 
 227.4513 
 
 .5 
 
 3067.9616 
 
 196.3495 
 
 .5 
 
 3578.4704 
 
 212.0575 
 
 .5 
 
 4128.2491 
 
 227.7655 
 
 .6 
 
 3077.7869 
 
 196.6637 
 
 .6 
 
 3589.0811 
 
 212.3717 
 
 .6 
 
 4139.6452 
 
 228.0796 
 
 .7 
 
 3087.6279 
 
 196.9779 
 
 .7 
 
 3599.7075 
 
 212.6858 
 
 .7 
 
 4151.0571 
 
 228.3938 
 
 .8 
 
 3097 4847 
 
 197.2920 
 
 .8 
 
 3610.3497 
 
 213.0000 
 
 .8 
 
 4162.4846 
 
 228.7079 
 
 
 3107.3571 
 
 197.6062 
 
 .9 
 
 3621.0075 
 
 213.3141 
 
 .9 
 
 4173.9279 
 
 229.0221 
 
 63.0 
 
 3117.2453 
 
 197.9203 
 
 68.0 
 
 3631.6811 
 
 213.6283 
 
 73.0 
 
 4185.3868 
 
 229.3363 
 
 
 3127.1492 
 
 198.2345 
 
 .1 
 
 3642.3704 
 
 213.9425 
 
 .1 
 
 4196.8615 
 
 229.6504 
 
 ' n 
 
 3137.0688 
 
 198.548 7 
 
 .2 
 
 3653.0754 
 
 214.2566 
 
 .2 
 
 4208.3519 
 
 229.9646 
 
 *3 
 
 3147!004C 
 
 198.8628 
 
 .3 
 
 3663.7960 
 
 214.5708 
 
 .3 
 
 4219.8579 
 
 230.2787 
 
 
 3156.9550 
 
 199.1770 
 
 .4 
 
 3674.5324 
 
 214.8849 
 
 .4 
 
 4231.3797 
 
 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 
 
 .6 
 .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 
 235.3053 
 
MENSURATION. CIRCLES. 
 
 49 
 
 AREAS AND CIRCUMFERENCES OF CIRCLES. 
 
 (Advancing by Tenths.) 
 
 Dia. 
 
 Area. 
 
 Circum. 
 
 Dia. 
 
 Area. 
 
 Circum. 
 
 Dia. 
 
 Area. 
 
 Circum. 
 
 75.0 
 
 4417.8647 
 
 235.6194 
 
 80.0 
 
 5026.5482 
 
 251.3274 
 
 85.0 
 
 5674.5017 
 
 267.0354 
 
 .1 
 
 4429.6535 
 
 235.9336 
 
 .1 
 
 5039.1225 
 
 251.6416 
 
 .1 
 
 5687.8614 
 
 267.3495 
 
 .2 
 
 4441.4580 
 
 236.2478 
 
 .2 
 
 5051.7124 
 
 251.9557 
 
 .2 
 
 5701.2367 
 
 267.6637 
 
 .3 
 
 4453.2783 
 
 236.5619 
 
 .3 
 
 5064.3180 
 
 252.2699 
 
 .3 
 
 5714.6277 
 
 267 9779 
 
 .4 
 
 4465.1142 
 
 236.8761 
 
 .4 
 
 5076.9394 
 
 252.5840 
 
 .4 
 
 5728.0345 
 
 268.2920 
 
 .5 
 
 4476.9659 
 
 237.1902 
 
 .5 
 
 5089.5764 
 
 252.8982 
 
 .5 
 
 5741.4569 
 
 268 6062 
 
 .6 
 
 44SS.S332 
 
 237.5044 
 
 .6 
 
 5102.2292 
 
 253.2124 
 
 .6 
 
 5754.8951 
 
 268.9203 
 
 .7 
 
 4500.7163 
 
 237.8186 
 
 .7 
 
 5114.8977 
 
 253.5265 
 
 .7 
 
 5768.3490 
 
 269 2345 
 
 .8 
 
 4512.6151 
 
 238.1327 
 
 .8 
 
 5127.5819 
 
 253.8407 
 
 .8 
 
 5781.8185 
 
 269.54S6 
 
 .0 
 
 4524.5296 
 
 238.4469 
 
 .9 
 
 5140.2818 
 
 254.1548 
 
 .9 
 
 5795.3038 
 
 269.8628 
 
 76.0 
 
 4536.4598 
 
 238.7610 
 
 81".0 
 
 5152.9973 
 
 254.4690 
 
 86.0 
 
 5808.8048 
 
 270.1770 
 
 .1 
 
 4548.4057 
 
 239.0752 
 
 .1 
 
 5165.7287 
 
 254.7832 
 
 .1 
 
 5822.3215 
 
 270.4911 
 
 .2 
 
 4560.3673 
 
 239.3894 
 
 .2 
 
 5178.4757 
 
 255.0973 
 
 .2 
 
 5835.8539 
 
 270.8053 
 
 .3 
 
 4572.3446 
 
 239.7035 
 
 .3 
 
 5191.2384 
 
 255.4115 
 
 .3 
 
 5849.4020 
 
 271.1194 
 
 .4 
 
 4584.3377 
 
 240.0177 
 
 .4 
 
 5204.0168 
 
 255.7256 
 
 .4 
 
 5862.9659 
 
 271.4336 
 
 .5 
 
 4596.3464 
 
 240.3318 
 
 .5 
 
 5216.8110 
 
 256.0398 
 
 .5 
 
 5876.5454 
 
 271.7478 
 
 .6 
 
 4608.3708 
 
 240.6460 
 
 .6 
 
 5229.6208 
 
 256.3540 
 
 .6 
 
 5890.1407 
 
 272.0619 
 
 .7 
 
 4620.4110 
 
 240.9602 
 
 .7 
 
 5242.4463 
 
 256.6681 
 
 .7 
 
 5903.7516 
 
 272.3761 
 
 .8 
 
 4632.4669 
 
 241.2743 
 
 .8 
 
 5255.2876 
 
 256.9823 
 
 .8 
 
 5917.3783 
 
 272.6902 
 
 .9 
 
 4644.5384 
 
 241.5885 
 
 .9 
 
 5268.1446 
 
 257.2966 
 
 .9 
 
 5931.0206 
 
 273.0044 
 
 77.0 
 
 4656.6257 
 
 241.9026 
 
 82.0 
 
 5281.0173 
 
 257.6106 
 
 87.0 
 
 5944.6787 
 
 273.3186 
 
 .1 
 
 4668.7287 
 
 242.2168 
 
 .1 
 
 5293.9056 
 
 257.9247 
 
 .1 
 
 5958.3525 
 
 273.6327 
 
 .2 
 
 4680.8474 
 
 242.5310 
 
 .2 
 
 5306.8097 
 
 258.2389 
 
 .2 
 
 5972.0420 
 
 273.9469 
 
 .3 
 
 4692.9818 
 
 242.8451 
 
 .3 
 
 5319.7295 
 
 258.5531 
 
 .3 
 
 5985.7472 
 
 274.2610 
 
 .4 
 
 4705.1319 
 
 243.1592 
 
 .4 
 
 5332.6650 
 
 258.8672 
 
 .4 
 
 5999.4681 
 
 274.5752 
 
 .5 
 
 4717.2977 
 
 243.4734 
 
 .5 
 
 5345.6162 
 
 259.1814 
 
 .5 
 
 6013.2047 
 
 274.8894 
 
 .6 
 
 4729.4792 
 
 243.7876 
 
 .6 
 
 5358.5832 
 
 259.4956 
 
 .6 
 
 6026.9570 
 
 275.2035 
 
 .7 
 
 4741.6765 
 
 244.1017 
 
 .7 
 
 5371.5658 
 
 259.8097 
 
 .7 
 
 6040.7250 
 
 275.5177 
 
 .8 
 
 4753.8894 
 
 244.4159 
 
 .8 
 
 5384.5641 
 
 260.1239 
 
 .8 
 
 6054. 50S8 
 
 275.8318 
 
 .9 
 
 4766.1181 
 
 244.7301 
 
 .9 
 
 5397.5782 
 
 260.4380 
 
 .9 
 
 6068.3082 
 
 276.1460 
 
 78.0 
 
 4778.3624 
 
 245.0442 
 
 83.0 
 
 5410.6079 
 
 260.7522 
 
 88.0 
 
 6082.1234 
 
 276.4602 
 
 .1 
 
 4790.6225 
 
 245.3584 
 
 .1 
 
 5423.6534 
 
 261.0663 
 
 .1 
 
 6095.9542 
 
 276.7743 
 
 .2 
 
 4802.8983 
 
 245.6725 
 
 .2 
 
 5436.7146 
 
 261.3805 
 
 .2 
 
 6109.8008 
 
 277.0885 
 
 .3 
 
 4815.1897 
 
 245.9867 
 
 .3 
 
 5449.7615 
 
 261.6947 
 
 .3 
 
 6123.6631 
 
 277.4026 
 
 .4 
 
 4827.4969 
 
 246.3009 
 
 .4 
 
 5462.8840 
 
 262.0088 
 
 .4 
 
 6137.5411 
 
 277.7168 
 
 .5 
 
 4839.8198 
 
 246.6150 
 
 .5 
 
 5475.9923 
 
 262.3230 
 
 .5 
 
 6151.4348 
 
 278.0309 
 
 .6 
 
 4852.1584 
 
 246.9292 
 
 .6 
 
 5489.1163 
 
 262.6371 
 
 .6 
 
 6165.3442 
 
 278.3451 
 
 .7 
 
 4864.5128 
 
 247.2433 
 
 .7 
 
 5502.2561 
 
 262.9513 
 
 .7 
 
 6179.2693 
 
 278.6593 
 
 .8 
 
 4876.8828 
 
 247.5575 
 
 .8 
 
 5515.4115 
 
 263.2655 
 
 .8 
 
 6193.2101 
 
 278.9740 
 
 .9 
 
 4889.2685 
 
 247.8717 
 
 .9 
 
 5528.5826 
 
 263.5796 
 
 .9 
 
 6207.1666 
 
 279.2876 
 
 79.0 
 
 4901.6699 
 
 248.1858 
 
 84.0 
 
 5541.7694 
 
 263.8938 
 
 89.0 
 
 6221.1389 
 
 279.6017 
 
 .1 
 
 4914.0871 
 
 248.5000 
 
 .1 
 
 5554.9720 
 
 264.2079 
 
 .1 
 
 6235.1268 
 
 279.9159 
 
 .2 
 
 4926.5199 
 
 248.8141 
 
 .2 
 
 5568.1902 
 
 264.5221 
 
 .2 
 
 6249.1304 
 
 280.2301 
 
 .3 
 
 4938.9685 
 
 249.1283 
 
 .3 
 
 5581.4242 
 
 264.8363 
 
 .3 
 
 6263.1498 
 
 280.5442 
 
 .4 
 
 4951.4328 
 
 249.4425 
 
 .4 
 
 5594.6739 
 
 265.1514 
 
 .4 
 
 6277.1849 
 
 280.8584 
 
 .5 
 
 4963.9127 
 
 249.7566 
 
 .5 
 
 5607.9392 
 
 265.4646 
 
 .5 
 
 6291.2356 
 
 281.1725 
 
 .6 
 
 4976.4084 
 
 250.0708 
 
 .6 
 
 5621.2203 
 
 265.7787 
 
 .6 
 
 6305.3021 
 
 281.4867 
 
 .7 
 
 4988.9198 
 
 250.3850 
 
 .7 
 
 5634.5171 
 
 266.0929 
 
 .7 
 
 6319.3843 
 
 281.8009 
 
 .8 
 
 5001.4469 
 
 250.6991 
 
 .8 
 
 5647.8296 
 
 266.4071 
 
 .8 
 
 6333.4822 
 
 282.1150 
 
 .9 
 
 5013.9897 
 
 251.0133 
 
 .9 
 
 5661.1578 
 
 266.7212 
 
 .9 
 
 6347.5958 
 
 282.4292 
 
50 
 
 MENSURATION. CIRCLES. 
 
 AREAS AND CIRCUMFERENCES OF CIRCLES. 
 
 (Advancing by Tenths.) 
 
 Dia. 
 
 Area. 
 
 Circum. 
 
 Dia. 
 
 Area. 
 
 .Circum. 
 
 Dia. 
 
 Area. 
 
 Circum. 
 
 90.0 
 
 6301.7251 
 
 282.7433 
 
 93.5 
 
 6866.1471 
 
 293.7389 
 
 97.0 
 
 7389.8113 
 
 304.7345 
 
 .1 
 
 6375.8701 
 
 283.0575 
 
 .6 
 
 6880.8419 
 
 294.0531 
 
 .1 
 
 7405.0559 
 
 305.0486 
 
 .2 
 
 6390.0309 
 
 283.?717 
 
 .7 
 
 6895.5524 
 
 294.3372 
 
 .2 
 
 7420.3102 
 
 305.3628 
 
 .3 
 
 6404.2073 
 
 283.6858 
 
 .8 
 
 6910.2786 
 
 294.6814 
 
 Jt 
 
 7435.5922 
 
 305.6770 
 
 .4 
 
 6418.3995 
 
 284.0000 
 
 .9 
 
 6925.0205 
 
 294.9956 
 
 ^ 
 
 7450.8839 
 
 305.9911 
 
 .5 
 
 6432.6073 
 
 284.3141 
 
 94.0 
 
 6939.7782 
 
 295.3097 
 
 .5 
 
 7466.1913 
 
 306.3053 
 
 .6 
 
 6446.8309 
 
 284.6283 
 
 .1 
 
 6954.5515 
 
 295.6239 
 
 .'( 
 
 7481.5144 
 
 306.6194 
 
 .7 
 
 6461.0701 
 
 284.9425 
 
 .2 
 
 6969.3106 
 
 295.9380 
 
 7 
 
 7496.8532 
 
 306.9336 
 
 .8 
 
 0475.3251 
 
 285.2566 
 
 .3 
 
 6984.1453 
 
 296.2522 
 
 JB 
 
 7512.2078 
 
 307.2478 
 
 .9 
 
 6489.5958 
 
 285.5708 
 
 .4 
 
 6998.9658 
 
 296.5663 
 
 .9 
 
 7527.5780 
 
 307.5619 
 
 91.0 
 
 6503.8822 
 
 285.8849 
 
 .5 
 
 7013.8019 
 
 296.8805 
 
 98.0 
 
 7542.9640 
 
 307.8761 
 
 .1 
 
 6518.1843 
 
 286.1991 
 
 .6 
 
 7028.6538 
 
 297.1947 
 
 .1 
 
 7558.3056 
 
 308.1902 
 
 .2 
 
 6532.5021 
 
 286.5133 
 
 .7 
 
 7043.5214 
 
 297.5088 
 
 .1 
 
 7573.7830 
 
 308.5044 
 
 .3 
 
 6546.8356 
 
 286.8274 
 
 .8 
 
 7058.4047 
 
 297.8230 
 
 . 
 
 7589.2161 
 
 308.8186 
 
 .4 
 
 6561.1848 
 
 287.1416 
 
 .9 
 
 7073.3033 
 
 298.1371 
 
 A 
 
 7604. 664b 
 
 309.1327 
 
 .5 
 
 6575.5498 
 
 287.4557 
 
 95.0 
 
 7038.2184 
 
 298.4513 
 
 .5 
 
 7620.1293 
 
 309.4469 
 
 .6 
 
 6589.9304 
 
 287.7699 
 
 .1 
 
 7103.1488 
 
 298.7655 
 
 ."o 
 
 7635.C095 
 
 309.7610 
 
 .7 
 
 6604.3268 
 
 288.0840 
 
 .2 
 
 7118.1950 
 
 299.0796 
 
 .7 
 
 7651.1054 
 
 310.0752 
 
 .8 
 
 6618.7388 
 
 288.3982 
 
 .3 
 
 7133.0568 
 
 299.3938 
 
 
 
 7666.6170 
 
 310.3894 
 
 .9 
 
 6633.1666 
 
 288.7124 
 
 .4 
 
 7148.0343 
 
 299.7079 
 
 !9 
 
 7682.1444 
 
 310.7035 
 
 92.0 
 
 6647.6101 
 
 289.0265 
 
 .5 
 
 7163.0276 
 
 300.0221 
 
 99.0 
 
 7697.6893 
 
 311.0177 
 
 .1 
 
 6662.0692 
 
 289.3407 
 
 .6 
 
 7178.0366 
 
 300.3363 
 
 .1 
 
 7713.2461 
 
 311.3318 
 
 .2 
 
 6676.5441 
 
 289.6548 
 
 .7 
 
 7193.0612 
 
 300.6504 
 
 .2 
 
 77^8.8206 
 
 311.6400 
 
 .3 
 
 6691.0347 
 
 289.9690 
 
 .8 
 
 7208.1016 
 
 300.9646 
 
 .3 
 
 7744.4107 
 
 311.9602 
 
 .4 
 
 6705.5410 
 
 290.2832 
 
 .9 
 
 7223.1577 
 
 301,2787 
 
 .4 
 
 7760.0166 
 
 312.2743 
 
 .5 
 
 6720.0630 
 
 290.5973 
 
 96.0 
 
 7238.2295 
 
 301.5929 
 
 .5 
 
 7775.6382 
 
 312.5885 
 
 .6 
 
 6734.6008 
 
 290.9115 
 
 .1 
 
 7253.3170 
 
 301.9071 
 
 .6 
 
 7791.2754 
 
 312.9020 
 
 .7 
 
 6749.1542 
 
 291.2256 
 
 .2 
 
 726S.4202 
 
 302.2212 
 
 .7 
 
 7806.9284 
 
 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 
 
 303.1637 
 
 100.0 
 
 7853.9816 
 
 314.1593 
 
 .1 
 
 6807.5250 
 
 292.4823 
 
 .6 
 
 7328.9901 
 
 303.4779 
 
 
 
 
 .2 
 
 6822.1569 
 
 292.7964 
 
 .7 
 
 7344.1718 
 
 303.7920 
 
 
 
 
 .3 
 
 68?6.8046 
 
 293.1106 
 
 .8 
 
 7359.3693 
 
 304.1062 
 
 
 
 
 .4 
 
 6851.4680 
 
 293.4248 
 
 .9 
 
 7374.5824 
 
 304.4203 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
MENSURATION. CIRCLES. 
 
 51 
 
 AREAS OF CIRCLES. 
 
 (Advancing by Eighths.) 
 
 AREAS. 
 
 Dia. 
 
 0.0 
 
 w 
 
 o.i 
 
 o.f 
 
 O.J 
 
 o.f 
 
 o.f 
 
 o-l 
 
 
 
 0.0 
 
 0.0122 
 
 ' 0.0490 
 
 0.1104 
 
 0.1963 
 
 0.3068 
 
 0.4417 
 
 6013 
 
 1 
 
 0.7854 
 
 0.9940 
 
 1.227 
 
 1.484 
 
 1.767 
 
 2.073 
 
 2.405 
 
 2.761 
 
 2 
 
 3.1416 
 
 3.546 
 
 3.976 
 
 4.430 
 
 4.908 
 
 5.411 
 
 5.939 
 
 6 491 
 
 3 
 
 7.068 
 
 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 
 
 20.62 
 
 21.64 
 
 22.69 
 
 23.75 
 
 24.85 
 
 25.96 
 
 27.10 
 
 6 
 
 28.27 
 
 29.16 
 
 30.67 
 
 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 
 
 50.26 
 
 51.84 
 
 53.45 
 
 55.08 
 
 56.74 
 
 58.42 
 
 60.13 
 
 61.86 
 
 9 
 
 63.61 
 
 65.39 
 
 07.20 
 
 69.02 
 
 70.88 
 
 72.75 
 
 74.66 
 
 76.58 
 
 10 
 
 78.54 
 
 80.51 
 
 82.51 
 
 84.54 
 
 86.59 
 
 88.66 
 
 90.76 
 
 92.88 
 
 11 
 
 95.03 
 
 97.20 
 
 99.40 
 
 101.6 
 
 103.8 
 
 106.1 
 
 108.4 
 
 110.7 
 
 12 
 
 113.0 
 
 115.4 
 
 117.8 
 
 120.2 
 
 12?. 7 
 
 125.1 
 
 127.6 
 
 130.1 
 
 13 
 
 132.7 
 
 135.2 
 
 137.8 
 
 140.5 
 
 143.1 
 
 145.8 
 
 148.4 
 
 151.2 
 
 14 
 
 153.9 
 
 156.6 
 
 159.4 
 
 162.2 
 
 165.1 
 
 167.9 
 
 170.8 
 
 173.7 
 
 15 
 
 176.7 
 
 179.6 
 
 182.6 
 
 185.6 
 
 188.6 
 
 191.7 
 
 194.8 
 
 197.9 
 
 16 
 
 201.0 
 
 204.2 
 
 207.3 
 
 210.5 
 
 213.8 
 
 217.0 
 
 220.3 
 
 223.6 
 
 17 
 
 226.9 
 
 230.3 
 
 233.7 
 
 237.1 
 
 240.5 
 
 243.9 
 
 247.4 
 
 250.9 
 
 18 
 
 254.4 
 
 258.0 
 
 261.5 
 
 265.1 
 
 268.8 
 
 272.4 
 
 276.1 
 
 279.8 
 
 19 
 
 283.5 
 
 287.2 
 
 291.0 
 
 294.8 
 
 298.6 
 
 302.4 
 
 306.3 
 
 310.2 
 
 20 
 
 314.1 
 
 318.1 
 
 322.0 
 
 326.0 
 
 330.0 
 
 334.1 
 
 338.1 
 
 342.2 
 
 21 
 
 346.3 
 
 350.4 
 
 354.6 
 
 358.8 
 
 363.0 
 
 367.2 
 
 371.5 
 
 375.8 
 
 22 
 
 380.1 
 
 384.4 
 
 388.8 
 
 393.2 
 
 397.6 
 
 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 
 
 461.8 
 
 466.6 
 
 471.4 
 
 476.2 
 
 481.1 
 
 4S5.9 
 
 25 
 
 490.8 
 
 495.7 
 
 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 
 
 562.0 
 
 567.2 
 
 27 
 
 572.5 
 
 577.8 
 
 583.2 
 
 588.5 
 
 593.9 
 
 599.3 
 
 604.8 
 
 610.2 
 
 28 
 
 615.7 
 
 621.2 
 
 626.7 
 
 632.3 
 
 637.9 
 
 643.5 
 
 649.1 
 
 654.8 
 
 29 
 
 660.5 
 
 666.2 
 
 671.9 
 
 677.7 
 
 683.4 
 
 689.2 
 
 695.1 
 
 700.9 
 
 30 
 
 706.S 
 
 712.7 
 
 718.6 
 
 724.6 
 
 730.0 
 
 736.6 
 
 742.6 
 
 748.6 
 
 31 
 
 754.8 
 
 760.9 
 
 767.0 
 
 773.1 
 
 779.3 
 
 785.5 
 
 791.7 
 
 798.0 
 
 32 
 
 804.3 
 
 810.6 
 
 816.9 
 
 823.2 
 
 829.6 
 
 836.0 
 
 842.4 
 
 848.8 
 
 33 
 
 855.3 
 
 861.8 
 
 868.3 
 
 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 
 
 955.3 
 
 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 
 
 1068.0 
 
 37 
 
 1075.2 
 
 1082.5 
 
 1089.8 
 
 1097.1 
 
 1104.5 
 
 1111.8 
 
 1119.2 
 
 1126.7 
 
 38 
 
 1134.1 
 
 1141.6 
 
 1149.1 
 
 1156.0 
 
 1164.2 
 
 1171.7 
 
 1179.3 
 
 1186.9 
 
 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 
 
52 
 
 MENSURATION. CIRCLES. 
 
 CIRCUMFERENCES OF CIRCLES. 
 
 (Advancing by Eighths.) 
 
 CIRCUMFERENCES. 
 
 Dia. 
 
 0.0 
 
 P.* 
 
 o.i 
 
 o,| 
 
 O.J 
 
 o.f 
 
 o.f 
 
 o.| 
 
 
 
 0.0 
 
 0.3927 
 
 0.7854 
 
 1.178 
 
 1.570 
 
 1.963 
 
 2.356 
 
 2.748 
 
 1 
 
 3.141 
 
 3.534 
 
 3.927 
 
 4.319 
 
 4.712 
 
 5.105 
 
 5.497 
 
 5.800 
 
 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 
 
 16.19 
 
 16.88 
 
 17.27 
 
 17.67 
 
 18.06 
 
 18.45 
 
 6 
 
 18.84 
 
 19.24 
 
 19.63 
 
 20.02 
 
 20.42 
 
 20.81 
 
 21.20 
 
 21.59 
 
 7 
 
 21.99 
 
 22.38 
 
 22.77 
 
 23.16 
 
 23.56 
 
 23.95 
 
 24.34 
 
 24.74 
 
 8 
 
 25.13 
 
 25.52 
 
 25.91 
 
 26.31 
 
 26.70 
 
 27.09 
 
 27.48 
 
 27.8S 
 
 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 
 
 31.95 
 
 35.34 
 
 35.73 
 
 36.12 
 
 36.52 
 
 36.91 
 
 37.30 
 
 12 
 
 37.09 
 
 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 
 
 42.80 
 
 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 
 
 54.19 
 
 54.5S 
 
 54.97 
 
 55.37 
 
 55.76 
 
 56.15 
 
 18 
 
 56.54 
 
 56.94 
 
 57.33 
 
 57.72 
 
 58.11 
 
 58.51 
 
 5S.90 
 
 59.29 
 
 19 
 
 59.69 
 
 60.08 
 
 60.47 
 
 60.86 
 
 61.26 
 
 61.65 
 
 62.04 
 
 62.43 
 
 20 
 
 62.83 
 
 63.22 
 
 63.61 
 
 64.01 
 
 64.40 
 
 64.79 
 
 65.18 
 
 65.58 
 
 21 
 
 65.97 
 
 66.36 
 
 66.75 
 
 67.15 
 
 67.54 
 
 67.93 
 
 08.32 
 
 68.72 
 
 22 
 
 69.11 
 
 69.50 
 
 69.90 
 
 70.29 
 
 70.68 
 
 71.07 
 
 71.47 
 
 71.86 
 
 23 
 
 72.25 
 
 72.64 
 
 73.01 
 
 73.43 
 
 73.82 
 
 74.22 
 
 74.01 
 
 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 
 
 82.46 
 
 82.85 
 
 83.25 
 
 83.64 
 
 84.03 
 
 84.43 
 
 27 
 
 84.82 
 
 85.21 
 
 85.60 
 
 86.00 
 
 86.39 
 
 86.78 
 
 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 
 
 93.06 
 
 93.46 
 
 93.85 
 
 30 
 
 94.24 
 
 94.64 
 
 95.03 
 
 95.42 
 
 95.81 
 
 96.21 
 
 96.60 
 
 96.99 
 
 31 
 
 97.39 
 
 97.78 
 
 98.17 
 
 98.57 
 
 98.96 
 
 99.35 
 
 99.75 
 
 100.14 
 
 32 
 
 100.53 
 
 100.92 
 
 101.32 
 
 101.71 
 
 102.10 
 
 102.49 
 
 102.89 
 
 103.29 
 
 33 
 
 103.67 
 
 104.07 
 
 104.46 
 
 104.85 
 
 105.24 
 
 105.64 
 
 106.03 
 
 100.42 
 
 34 
 
 106.81 
 
 107.21 
 
 107.60 
 
 107.99 
 
 103.39 
 
 108.78 
 
 109.17 
 
 109.50 
 
 35 
 
 109.96 
 
 110.35 
 
 110.74 
 
 111.13 
 
 111.53 
 
 111.92 
 
 112.31 
 
 112.71 
 
 36 
 
 113.10 
 
 113.49 
 
 113.88 
 
 114.28 
 
 114.67 
 
 115.06 
 
 115.45 
 
 115.85 
 
 27 
 
 116.24 
 
 116.63 
 
 117.02 
 
 117.42 
 
 117.81 
 
 118.20 
 
 118.60 
 
 118.99 
 
 38 
 
 119.38 
 
 119.77 
 
 120.17 
 
 120.56 
 
 120.95 
 
 121.34 
 
 121.74 
 
 122.13 
 
 39 
 
 122.52 
 
 122.92 
 
 123.31 
 
 123.70 
 
 124.09 
 
 124.49 
 
 124.88 
 
 125.27 
 
 40 
 
 125.66 
 
 126.06 
 
 126.45 
 
 126.84 
 
 127.24 
 
 127.63 
 
 128.02 
 
 128.41 
 
 41 
 
 128.81 
 
 129.20 
 
 127.59 
 
 129.98 
 
 130.38 
 
 130.77 
 
 131.16 
 
 131.55 
 
 42 
 
 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 
 
 138.02 
 
 139.02 
 
 139.41 
 
 139.80 
 
 140.19 
 
 140.59 
 
 140.98 
 
 45 
 
 141.37 
 
 141.76 
 
 142.16 
 
 142.55 
 
 142.94 
 
 143.34 
 
 143.73 
 
 144.12 
 
MENSURATION. CIRCLES. 
 
 53 
 
 AREAS AND CIRCUMFERENCES OF CIRCLES. 
 
 FROM 1 TO 50 FEET. 
 (Advancing by One Inch.) 
 
 Dia. 
 
 Area. 
 
 Circum. 
 
 Dia 
 
 Area. 
 
 Circum 
 
 Dia 
 
 Area. 
 
 Circum. 
 
 Ft. 
 
 Feet. 
 
 Ft. In. 
 
 Feet 
 
 Feet. 
 
 Ft. In 
 
 Ft. 
 
 Feet. 
 
 Ft In 
 
 1 
 
 0.7854 
 
 3 If 
 
 5 
 
 19.635 
 
 15 8i 
 
 9 
 
 63.6174 
 
 28 3} 
 
 1 
 
 0.9217 
 
 3 4f 
 
 1 
 
 20.2947 
 
 15 11| 
 
 1 
 
 64.8006 
 
 28 61 
 
 2 
 
 1.069 
 
 3 8 
 
 2 
 
 20.9656 
 
 16 2f 
 
 2 
 
 65.9951 
 
 28 9*- 
 
 3 
 
 1.2271 
 
 3 11 
 
 3 
 
 21.6475 
 
 16 fit 
 
 J 
 
 67.2007 
 
 29 | 
 
 4 
 
 1.3962 
 
 4 2* 
 
 4 
 
 22.34 
 
 16 9 
 
 4 
 
 68.4166 
 
 29 31 
 
 5 
 
 1.5761 
 
 4 5f 
 
 5 
 
 23.0437 
 
 17 i 
 
 c 
 
 69.644 
 
 29 7 
 
 6 
 
 1.7671 
 
 4 8* 
 
 6 
 
 23.7583 
 
 17 3} 
 
 I 
 
 70.8823 
 
 29. 10i 
 
 7 
 
 1.9689 
 
 4 11| 
 
 7 
 
 24.4835 
 
 17 61 
 
 7 
 
 72.1309 
 
 30 l| 
 
 8 
 
 2.1816 
 
 5 2f 
 
 $ 
 
 25.2199 
 
 17 9S 
 
 8 
 
 73.391 
 
 30 4| 
 
 9 
 
 2.4052 
 
 5 5| 
 
 9 
 
 25.9672 
 
 18 4 
 
 g 
 
 74.662 
 
 30 7} 
 
 10 
 
 2.6398 
 
 5 9 
 
 10 
 
 26.7251 
 
 18 3f 
 
 10 
 
 75.9433 
 
 30 111 
 
 11 
 
 2.8852 
 
 6 * 
 
 11 
 
 27.4943 
 
 18 7i 
 
 11 
 
 77.2362 
 
 31 11 
 
 2 
 
 3.1416 
 
 6 3f 
 
 6 
 
 28.2744 
 
 18 10i 
 
 10 
 
 78.54 
 
 31 5 
 
 1 
 
 3.4087 
 
 6 6* 
 
 1 
 
 29.0649 
 
 19 H 
 
 1 
 
 79.854 
 
 31 8i 
 
 2 
 
 3.6869 
 
 6 9f 
 
 2 
 
 29.8668 
 
 19 41 
 
 2 
 
 81.1795 
 
 31 ll| 
 
 3 
 
 3.976 
 
 7 f 
 
 3 
 
 30.6796 
 
 19 7* 
 
 3 
 
 82.516 
 
 32 21 
 
 4 
 
 4.276 
 
 7 3| 
 
 4 
 
 31.5029 
 
 19 10| 
 
 4 
 
 83.8627 
 
 32 5* 
 
 5 
 
 4.5869 
 
 7 7 
 
 5 
 
 32.3376 
 
 20 11 
 
 5 
 
 85.2211 
 
 32 8| 
 
 6 
 
 4.9087 
 
 7 10i 
 
 6 
 
 33.1831 
 
 20 4| 
 
 6 
 
 86.5903 
 
 32 111 
 
 7 
 
 5.2413 
 
 8 11 
 
 7 
 
 34.0391 
 
 20 8i 
 
 7 
 
 87.9697 
 
 33 2i 
 
 8 
 
 5.585 
 
 8 4* 
 
 8 
 
 34.9065 
 
 20 11* 
 
 8 
 
 89.3608 
 
 33 6i 
 
 9 
 
 5.9295 
 
 8 7 
 
 9 
 
 35.7847 
 
 21 21 
 
 9 
 
 90.7627 
 
 33 9i 
 
 10 
 
 6.3049 
 
 8 101 
 
 10 
 
 36.6735 
 
 21 5* 
 
 10 
 
 92.1749 
 
 34 1 
 
 11 
 
 6.6813 
 
 9 It 
 
 11 
 
 37.5736 
 
 21 81 
 
 11 
 
 93.5986 
 
 34 3* 
 
 3 
 
 7.0686 
 
 9 5 
 
 7 
 
 38.4846 
 
 21 11| 
 
 11 
 
 95.0334 
 
 34 8* 
 
 1 
 
 7.4666 
 
 9 8i 
 
 1 
 
 39.406 
 
 22 3 
 
 1 
 
 96.4783 
 
 34 9f 
 
 2 
 
 7.8757 
 
 9 111 
 
 2 
 
 40.3388 
 
 22 6i 
 
 2 
 
 97.9347 
 
 35 I 
 
 8 
 
 8.2957 
 
 10 2* 
 
 3 
 
 41.2825 
 
 22 9- 
 
 3 
 
 99.4021 
 
 35 4i 
 
 4 
 
 8.7205 
 
 10 54 
 
 4 
 
 42.2367 
 
 23 f 
 
 4 
 
 100.8797 
 
 35 7i 
 
 5 
 
 9.1683 
 
 10 8f 
 
 5 
 
 43.2022 
 
 23 2 r 
 
 5 
 
 102.3689 
 
 35 101 
 
 6 
 
 9.6211 
 
 10 11-i- 
 
 6 
 
 44.1787 
 
 23 61 
 
 6 
 
 103.8691 
 
 36 H 
 
 7 
 
 10.0S46 
 
 11 3 
 
 7 
 
 45.1656 
 
 23 9f- 
 
 7 
 
 105.3794 
 
 36 4* 
 
 8 
 
 10.5591 
 
 11 6i 
 
 8 
 
 46.1638 
 
 24 li 
 
 8 
 
 106.9013 
 
 36 71 
 
 9 
 
 11.0446 
 
 11 91 
 
 9 
 
 47.173 
 
 24 4i 
 
 9 
 
 108.4342 
 
 36 10| 
 
 10 
 
 11.5409 
 
 12 $ 
 
 10 
 
 48.1962 
 
 24 7J 
 
 10 
 
 109.9772 
 
 37 21 
 
 11 
 
 12.0481 
 
 12 31 
 
 11 
 
 49.2236 
 
 24 101 
 
 11 
 
 111.5319 
 
 37 5i 
 
 4 
 
 12.5664 
 
 12 6 
 
 8 
 
 50.2656 
 
 25 1} 
 
 12 
 
 113.0976 
 
 37 8f 
 
 1 
 
 13.0952 
 
 12 9 
 
 1 
 
 51.3178 
 
 25 4f 
 
 1 
 
 114.6732 
 
 37 11* 
 
 2 
 
 13.6353 
 
 13 1 
 
 2 
 
 52.3816 
 
 25 7| 
 
 2 
 
 116.2607 
 
 38 2* 
 
 3 
 
 14.1862 
 
 13 4i 
 
 3 
 
 53.4562 
 
 25 11 
 
 3 
 
 117.859 
 
 38 5f 
 
 4 
 
 14.7479 
 
 13 7i 
 
 4 
 
 54.5412 
 
 26 2i 
 
 4 
 
 119.4674 
 
 38 8 
 
 5 
 
 15.3206 
 
 13 10* 
 
 5 
 
 55.6377 
 
 26 5J- 
 
 5 
 
 121.0876 
 
 39 
 
 6 
 
 7 
 
 15.9043 
 
 16.4986 
 
 14 1| 
 14 41 
 
 6 
 
 7 
 
 56.7451 
 
 57.8628 
 
 26 81 
 26 11* 
 
 6 
 
 7 
 
 122.7187 
 124.3598 
 
 39 3i 
 39 61 
 
 8 
 9 
 
 17.1041 
 17.7205 
 
 14 7* 
 14 11 
 
 8 
 9 
 
 58.992 
 60.1321 
 
 27 21 
 
 27 5f 
 
 8 
 9 
 
 126.0127 
 127.6765 
 
 39 9* 
 40 1 
 
 10 
 
 18.3476 
 
 15 2i 
 
 10 
 
 61.2826 
 
 27 9 
 
 10 
 
 129.3504 
 
 40 3f 
 
 11 
 
 18.9858 
 
 15 5i 
 
 11 
 
 62.4445 
 
 28 | 
 
 11 
 
 131.036 
 
 40 6| 
 
54 MENSURATION. CIRCLES. 
 
 Areas and Circumferences of Circles (Feet and Inches) . 
 
 Dia. 
 
 Area. 
 
 Circum. 
 
 Dia. 
 
 Area. 
 
 Circum. 
 
 Dia. 
 
 Area. 
 
 Circum . 
 
 Ft. 
 
 Feet. 
 
 Ft. In. 
 
 Ft. 
 
 Feet. 
 
 Ft. In. 
 
 Ft. 
 
 Feet. 
 
 Ft. In. 
 
 13 
 
 132.7326 
 
 40 10 
 
 
 IS 
 
 254.4696 
 
 56 GJ 
 
 23 
 
 415.4766 
 
 72 3 
 
 1 
 
 134.4391 
 
 41 li 
 
 
 
 1 
 
 256.8303 
 
 56 9| 
 
 1 
 
 418.4915 
 
 72 6i 
 
 2 
 
 136.1574 
 
 41 4i 
 
 
 2 
 
 259.2033 
 
 57 1 
 
 2 
 
 421.5192 
 
 72 91 
 
 3 
 
 137.8867 
 
 41 7J 
 
 i- 
 
 3 
 
 261.5872 
 
 57 4 
 
 3 
 
 424.5577 
 
 73 A- 
 
 4 
 
 139.626 
 
 41 10t 
 
 
 4 
 
 263.9807 
 
 57 7i 
 
 4 
 
 427.0055 
 
 73 3f 
 
 5 
 
 141.3771 
 
 42 li 
 
 
 5 
 
 266.3864 
 
 57 10i 
 
 5 
 
 430.6658 
 
 73 6| 
 
 6 
 
 143.1391 
 
 42 4^ 
 
 
 6 
 
 268.8031 
 
 58 1-| 
 
 
 
 433.7371 
 
 73 91 
 
 7 
 
 144.9111 
 
 42 8 
 
 
 7 
 
 271.2293 
 
 58 44- 
 
 7 
 
 436.8175 
 
 74 1 
 
 8 
 
 146.6949 
 
 42 Hi 
 
 8 
 
 273.6678 
 
 58 7 
 
 8 
 
 439.9106 
 
 74 4i 
 
 9 
 
 14S.4896 
 
 43 2, 
 
 
 9 
 
 276.1171 
 
 58 10| 
 
 9 
 
 443.0146 
 
 74 7i 
 
 10 
 
 150.2943 
 
 43 5: 
 
 
 10 
 
 278.5761 
 
 58 2 
 
 10 
 
 446.1278 
 
 74 lOf 
 
 11 
 
 152.1109 
 
 43 Si 
 
 
 11 
 
 281.0472 . 
 
 59 5J 
 
 11 
 
 449.2536 
 
 75 If 
 
 14 
 1 
 
 153.9384 
 155.7758 
 
 43 11| 
 
 44 21 
 
 19 
 1 
 
 283.5294 
 286.021 
 
 59 Si 
 59 11* 
 
 24 
 1 
 
 452.3904 
 455.5362 
 
 75 4| 
 
 75 71 
 
 2 
 
 157.625 
 
 44 6 
 
 
 2 
 
 288.5249 
 
 60 2* 
 
 2 
 
 458.6948 
 
 75 11 
 
 3 
 
 159.4852 
 
 44 9i 
 
 
 3 
 
 291.0397 
 
 60 5| 
 
 3 
 
 461.8642 
 
 76 21 
 
 4 
 
 161.3553 
 
 45 -. 
 
 
 4 
 
 293.5641 
 
 60 8| 
 
 4 
 
 465.0428 
 
 76 5i 
 
 5 
 
 163.2373 
 
 45 
 
 
 5 
 
 296.1107 
 
 60 111 
 
 5 
 
 468.2341 
 
 76 8* 
 
 6 
 
 165.1303 
 
 45 6j 
 
 
 6 
 
 298.6483 
 
 60 3i 
 
 6 
 
 471.4363 
 
 76 llf 
 
 7 
 
 167.0331 
 
 45 9^ 
 
 
 7 
 
 301.2054 
 
 61 6i 
 
 7 
 
 474.6476 
 
 77 2f 
 
 8 
 
 168.9479 
 
 46 i 
 
 
 8 
 
 303.7747 
 
 61 9* 
 
 8 
 
 477.8716 
 
 77 51 
 
 9 
 
 170.8735 
 
 46 4 
 
 
 9 
 
 306.355 
 
 61 * 
 
 9 
 
 481.1065 
 
 77 9 
 
 10 
 
 172.8091 
 
 46 7i 
 
 10 
 
 308.9448 
 
 61 3f 
 
 10 
 
 484.3506 
 
 78 i 
 
 11 
 
 174.7565 
 
 46 Hi 
 
 11 
 
 311.5469 
 
 62 6f 
 
 11 
 
 487.6073 
 
 78 3i 
 
 15 
 
 176.715 
 
 47 13 
 
 - 
 
 20 
 
 314.16 
 
 62 91 
 
 25 
 
 490.875 
 
 78 64- 
 
 1 
 
 178.6832 
 
 47 4| 
 
 
 1 
 
 316.7824 
 
 62 li 
 
 1 
 
 494.1516 
 
 78 9* 
 
 2 
 
 180.6634 
 
 47 7^ 
 
 
 9 
 
 319.4173 
 
 63 4i 
 
 2 
 
 497.4411 
 
 79 
 
 3 
 
 182.6545 
 
 47 10i 
 
 
 3 
 
 322.063 
 
 63 7| 
 
 3 
 
 500.7415 
 
 79 31 
 
 4 
 
 184.6555 
 
 48 2J 
 
 
 4 
 
 324.7182 
 
 63 11* 
 
 4 
 
 504.051 
 
 79 71 
 
 5 
 
 180.6684 
 
 4S 5i 
 
 
 5 
 
 327.3858 
 
 63 If 
 
 5 
 
 507.3732 
 
 79 Hi 
 
 6 
 
 188.6923 
 
 43 8- 
 
 
 6 
 
 330.0643 
 
 64 4| 
 
 6 
 
 510.7063 
 
 80 li 
 
 7 
 
 190.726 
 
 48 11 
 
 
 7 
 
 332.7522 
 
 64 71 
 
 7 
 
 514.0484 
 
 80 41 
 
 8 
 
 192.7716 
 
 49 2 
 
 
 8 
 
 335.4525 
 
 64 11 
 
 8 
 
 517.4034 
 
 80 7-| 
 
 9 
 
 194.8282 
 
 49 5: 
 
 
 9 
 
 338.1637 
 
 65 2i 
 
 9 
 
 520.7692 
 
 80 10| 
 
 10 
 
 196.8946 
 
 49 Si 
 
 
 10 
 
 340.8844 
 
 65 51 
 
 10 
 
 524.1441 
 
 81 11 
 
 11 
 
 198.973 
 
 50 
 
 
 11 
 
 343.6174 
 
 65 Si 
 
 11 
 
 527.5318 
 
 81 5 
 
 16 
 
 201.0624 
 
 SO 3i 
 
 21 
 
 346.3614 
 
 65 llf 
 
 26 
 
 530.9304 
 
 81 Si 
 
 1 
 
 203.1615 
 
 50 6i 
 
 1 
 
 349.1147 
 
 66 2| 
 
 1 
 
 534.3379 
 
 81 Hi 
 
 2 
 
 205.2726 
 
 50 9< 
 
 
 2 
 
 351.8804 
 
 66 51 
 
 2 
 
 537.7583 
 
 82 21 
 
 3 
 
 207.3946 
 
 51 3 
 
 
 
 3 
 
 354.6571 
 
 66 9 
 
 3 
 
 541.1896 
 
 82 5i 
 
 4 
 
 209.5264 
 
 51 3j 
 
 
 4 
 
 357.4432 
 
 66 i 
 
 4 
 
 544.6299 
 
 82 8f 
 
 5 
 
 211.6703 
 
 51 6i 
 
 
 5 
 
 360.2417 
 
 67 31 
 
 5 
 
 548.083 
 
 82 m 
 
 6 
 
 213.8251 
 
 51 10 
 
 
 6 
 
 363.0511 
 
 67 6* 
 
 6 
 
 551.5471 
 
 83 3^ 
 
 7 
 
 215.9896 
 
 52 li 
 
 7 
 
 365.8698 
 
 67 9| 
 
 7 
 
 555.0201 
 
 83 61 
 
 8 
 
 218.1662 
 
 52 4: 
 
 - 
 
 8 
 
 3G8.7011 
 
 68 | 
 
 8 
 
 558.5059 
 
 83 9i 
 
 9 
 
 220.3537 
 
 52 7^ 
 
 
 9 
 
 371.5432 
 
 68 31 
 
 9 
 
 562.0027 
 
 84 1 
 
 10 
 
 222.551 
 
 52 10! 
 
 
 
 10 
 
 374.3947 
 
 68 7 
 
 10 
 
 565.5084 
 
 84 3* 
 
 11 
 
 224.7608 
 
 53 li 
 
 
 11 
 
 377.2587 
 
 68 10i 
 
 11 
 
 569.027 
 
 84 6| 
 
 17 
 
 226.9806 
 
 53 41 
 
 22 
 
 380.1336 
 
 69 If 
 
 27 
 
 572.5566 
 
 84 91 
 
 1 
 
 229.2105 
 
 53 8 
 
 
 1 
 
 383.0177 
 
 69 44- 
 
 1 
 
 576.0949 
 
 85 1 
 
 2 
 
 231.4525 
 
 53 Hi 
 
 r 
 
 2 
 
 385.9144 
 
 69 7f 
 
 2 
 
 579.6463 
 
 85 4i 
 
 3 
 
 233.7055 
 
 54 2i 
 
 
 3 
 
 388.822 
 
 69 10| 
 
 3 
 
 583.2085 
 
 85 8i 
 
 4 
 
 235.9682 
 
 54 5i 
 
 
 4 
 
 391.7389 
 
 70 11 
 
 4 
 
 586.7796 
 
 85 111 
 
 5 
 
 238.243 
 
 54 8^ 
 
 
 5 
 
 394.6683 
 
 70 5 
 
 5 
 
 590.3637 
 
 86 1* 
 
 6 
 
 240.5287 
 
 54 11- 
 
 : 
 
 6 
 
 397.6087 
 
 70 Si 
 
 6 
 
 593.9587 
 
 86 4f 
 
 7 
 
 242.8241 
 
 55 2-i 
 
 1 
 
 7 
 
 400.5583 
 
 70 Hi 
 
 7 
 
 597.5625 
 
 86 71 
 
 8 
 
 245.1316 
 
 55 6 
 
 
 8 
 
 403.5204 
 
 71 24- 
 
 8 
 
 601.1793 
 
 86 11 
 
 9 
 
 247.45 
 
 55 9^ 
 
 r 
 
 9 
 
 406.4935 
 
 71 5f 
 
 9 
 
 604.807 
 
 87 2i 
 
 10 
 
 249.7781 
 
 56 - 
 
 
 10 
 
 409.4759 
 
 71 8f 
 
 10 
 
 608.4436 
 
 87 5i 
 
 11 
 
 252.1184 
 
 56 3 
 
 
 11 
 
 412.4707 
 
 71 111 
 
 11 
 
 612.0931 
 
 87 8| 
 
MENSURATION. CIRCLES. 
 
 55 
 
 Areas and Circumferences of Circles (Feet and Inches). 
 
 Dia. 
 
 Area. 
 
 Circum. 
 
 Dia. 
 
 Area. 
 
 Uircum. 
 
 Dia. 
 
 Area. 
 
 Circum. 
 
 Ft. 
 
 Feet. 
 
 Ft. In. 
 
 Ft. 
 
 Feet. 
 
 Ft. In. 
 
 Ft. 
 
 Feet. 
 
 Ft. In. 
 
 28 
 
 615.7530 
 
 87 Hi 
 
 33 
 
 855.301 
 
 103 8 
 
 38 
 
 1134.118 
 
 119 4i 
 
 1 
 
 619.4228 
 
 88 25- 
 
 1 
 
 859.624 
 
 103 Hi 
 
 1 
 
 1139.095 
 
 119 71 
 
 2 
 
 623.105 
 
 88 5f 
 
 2 
 
 863.961 
 
 104 2i 
 
 2 
 
 1144.087 
 
 119 lOf 
 
 2 
 
 626.7982 
 
 88 9 
 
 3 
 
 868.309 
 
 104 5| 
 
 3 
 
 1149.089 
 
 120 2 
 
 4 
 
 630.5002 
 
 89 i 
 
 4 
 
 872.665 
 
 104 8f 
 
 4 
 
 1154.110 
 
 1?0 5i 
 
 5 
 
 634.2152 
 
 89 3i 
 
 5 
 
 877.035 
 
 104 llf 
 
 5 
 
 1159.124 
 
 120 Sfc 
 
 6 
 
 637.9411 
 
 89 6| 
 
 6 
 
 881.415 
 
 105 2 
 
 6 
 
 1164.159 
 
 120 11| 
 
 7 
 
 641.6758 
 
 89 9i 
 
 7 
 
 885.804 
 
 105 6 
 
 7 
 
 1169.202 
 
 121 2i 
 
 8 
 
 645.4235 
 
 90, 
 
 8 
 
 890.206 
 
 105 9i 
 
 8 
 
 1174.259 
 
 121 5f- 
 
 9 
 
 649.1821 
 
 90 3f 
 
 9 
 
 394.619 
 
 106 i 
 
 9 
 
 1179.327 
 
 121 8f 
 
 10 
 
 652.9495 
 
 90 G 
 
 10 
 
 899.041 
 
 106 3| 
 
 10 
 
 1184.403 
 
 121 111 
 
 11 
 
 656.73 
 
 90 Hi 
 
 11 
 
 903.476 
 
 106 61 
 
 11 
 
 1189.493 
 
 122 3i 
 
 29 
 
 660.5214 
 
 91 li 
 
 34 
 
 907.922- 
 
 100 9f 
 
 39 
 
 1194.593 
 
 122 6i 
 
 1 
 
 664.3214 
 
 91 4J 
 
 1 
 
 912.377 
 
 107 i 
 
 1 
 
 1109.719 
 
 122 9i 
 
 2 
 
 668.1346 
 
 91 7i 
 
 2 
 
 916.844 
 
 107 4 
 
 2 
 
 1204.824 
 
 123 i 
 
 3 
 
 671.9587 
 
 91 101 
 
 3 
 
 921.323 
 
 107 7i 
 
 3 
 
 1209.958 
 
 123 3| 
 
 4 
 
 075.7915 
 
 92 If 
 
 4 
 
 925.810 
 
 107 10i 
 
 4 
 
 1215.099 
 
 123 Of 
 
 5 
 
 679.6375 
 
 92 4i 
 
 5 
 
 930.311 
 
 108 11 
 
 5 
 
 1220.254 
 
 123 9i 
 
 6 
 
 633.4943 
 
 92 8i 
 
 6 
 
 934,822 
 
 108 4| 
 
 6 
 
 1225.420 
 
 124 li 
 
 7 
 
 687.3598 
 
 92 Hi 
 
 7 
 
 939.342 
 
 108 7f 
 
 7 
 
 1230.594 
 
 124 41 
 
 8 
 
 691.2385 
 
 93 2f 
 
 8 
 
 943.87.5 
 
 108 10$ 
 
 8 
 
 1235.782 
 
 124 7f 
 
 9 
 
 695 1028 
 
 93 5A- 
 
 9 
 
 948.419 
 
 109 2 
 
 9 
 
 1240.981 
 
 124 10} 
 
 10 
 
 699.0263 
 
 93 8 
 
 10 
 
 952.972 
 
 109 5i 
 
 10 
 
 1240.188 
 
 125 1| 
 
 11 
 
 702.9377 
 
 93 Hi 
 
 11 
 
 957.538 
 
 109 8i 
 
 11 
 
 1251.408 
 
 125 4f 
 
 30 
 
 706.86 
 
 94 2i 
 
 35 
 
 902.115 
 
 109 11| 
 
 40 
 
 1256.64 
 
 125 7| 
 
 1 
 
 710.791 
 
 94 6 
 
 1 
 
 966.770 
 
 110 21 
 
 1 
 
 1261.879 
 
 125 11 
 
 2 
 
 714.735 
 
 94 9i 
 
 2 
 
 971.299 
 
 110 5f 
 
 2 
 
 1267.133 
 
 126 2i 
 
 3 
 
 718.69 
 
 95 f 
 
 3 
 
 975.908 
 
 110 8i 
 
 3 
 
 1272.397 
 
 126 51 
 
 4 
 
 722.654 
 
 95 3i 
 
 4 
 
 980.526 
 
 111 
 
 4 
 
 1277.669 
 
 126 8i 
 
 5 
 
 726.631 
 
 95 C>f 
 
 5 
 
 985.158 
 
 111 3i 
 
 5 
 
 1282.955 
 
 120 111 
 
 6 
 
 730.618 
 
 95 9f 
 
 6 
 
 989.803 
 
 111 ft- 
 
 6 
 
 1288.252 
 
 127 2f 
 
 7 
 
 734.615 
 
 96 I 
 
 7 
 
 994.451 
 
 111 9f 
 
 7 
 
 1293.557 
 
 127 5| 
 
 8 
 
 738.624 
 
 96 4 
 
 8 
 
 999.115 
 
 112 j : 
 
 8 
 
 1298.876 
 
 217 9 
 
 9 
 
 742.645 
 
 96 7i 
 
 9 
 
 1003.79 
 
 112 3: 
 
 9 
 
 1304.206 
 
 128 i 
 
 10 
 
 746.674 
 
 96 101 
 
 10 
 
 1008.473 
 
 112 6| 
 
 10 
 
 1309.543 
 
 128 31 
 
 11 
 
 750.716 
 
 97 li 
 
 11 
 
 1013.170 
 
 112 10 
 
 11 
 
 1314.895 
 
 128 6i 
 
 31 
 
 754.769 
 
 97 41 
 
 36 
 
 1017.878 
 
 113 li 
 
 41 
 
 1320.257 
 
 128 9f 
 
 1 
 
 758.831 
 
 97 7f 
 
 1 
 
 1022.594 
 
 113 4i 
 
 1 
 
 ' 1325.028 
 
 129 f 
 
 2 
 
 762.906 
 
 97 10i 
 
 2 
 
 1027.324 
 
 113 71 
 
 2 
 
 1331.012 
 
 129 3 
 
 3 
 
 766.992 
 
 98 2 
 
 3 
 
 1032.064 
 
 113 101 
 
 3 
 
 1336.407 
 
 129 7 
 
 4 
 
 771.086 
 
 98 5i 
 
 4 
 
 1030.813 
 
 114 If 
 
 4 
 
 1341.810 
 
 129 10i 
 
 5 
 
 775.191 
 
 98 8| 
 
 5 
 
 1041.570 
 
 H4 4} 
 
 5 
 
 1347.227 
 
 130 11 
 
 6 
 
 779.313 
 
 98 Hi 
 
 6 
 
 1040.349 
 
 114 8 
 
 ft 
 
 1352.655 
 
 130 4i 
 
 7 
 
 783.440 
 
 99 2g 
 
 7 
 
 1051.130 
 
 114 Hi 
 
 7 
 
 1358.091 
 
 130 7f 
 
 8 
 
 787.581 
 
 99 5| 
 
 8 
 
 1055.920 
 
 115 2i 
 
 8 
 
 1363.541 
 
 130 lOf 
 
 9 
 
 791.732 
 
 99 8i 
 
 9 
 
 1060.731 
 
 115 51 
 
 9 
 
 1369.001 
 
 131 If 
 
 10 
 
 795.892 
 
 100 
 
 10 
 
 1065.546 
 
 115 9i 
 
 10 
 
 1374.47 
 
 131 5 
 
 11 
 
 800.065 
 
 100 3i 
 
 11 
 
 1070.374 
 
 115 111 
 
 11 
 
 1379.952 
 
 131 8i 
 
 32 
 
 804.25 
 
 100 61 
 
 37 
 
 1075.2126 
 
 116 2f 
 
 42 
 
 1385.446 
 
 131 111 
 
 1 
 
 808.442 
 
 100 9i 
 
 1 
 
 1080.059 
 
 116 6 
 
 1 
 
 1390.247 
 
 132 2i 
 
 2 
 
 812.648 
 
 101 | 
 
 2 
 
 1084.920 
 
 116 9i 
 
 2 
 
 1396.462 
 
 132 5| 
 
 3 
 
 816.865 
 
 101 3| 
 
 3 
 
 1089.791 
 
 117 i 
 
 3 
 
 1401.988 
 
 132 8| 
 
 4 
 
 821.090 
 
 101 6i 
 
 4 
 
 1094.671 
 
 117 34- 
 
 4 
 
 1407.522 
 
 132 Hi 
 
 5 
 
 825.329 
 
 101 10 
 
 5 
 
 1099.564 
 
 117 Gi 
 
 5 
 
 1413.07 
 
 133 3 
 
 6 
 
 829.579 
 
 102 li 
 
 6 
 
 1104.469 
 
 117 91 
 
 6 
 
 1418.629 
 
 133 6i 
 
 7 
 
 833.837 
 
 102 41 
 
 7 
 
 1109.381 
 
 118 f 
 
 7 
 
 1424.195 
 
 133 9i 
 
 8 
 
 838.108 
 
 102 7i 
 
 8 
 
 1114.307 
 
 118 4 
 
 8 
 
 1429.776 
 
 134 * 
 
 9 
 
 842.391 
 
 102 101 
 
 9 
 
 1119.244 
 
 118 7i 
 
 9 
 
 1435.367 
 
 134 31 
 
 10 
 
 846.681 
 
 103 If 
 
 10 
 
 1124.189 
 
 118 10} 
 
 10 
 
 1440.907 
 
 134 Of 
 
 11 
 
 850.985 
 
 103 4i 
 
 11 
 
 1129.118 
 
 119 1| 
 
 11 
 
 1440.580 
 
 134 9i 
 
56 
 
 MENSURATION. CIRCULAR ARCS. 
 
 Areas and Circumferences of Circles (Feet and Inches). 
 
 Dia. 
 
 Area. 
 
 Circum. 
 
 Dia. 
 
 Area. 
 
 Circum. 
 
 Dia. 
 
 Area. 
 
 Circum . 
 
 Ft. 
 
 Feet. 
 
 Ft. In. 
 
 Ft. 
 
 Feet. 
 
 Ft. In. 
 
 Ft. 
 
 Feet. 
 
 Ft. In. 
 
 43 
 
 1452.205 
 
 135 1 
 
 46 
 
 1661.906 
 
 144 64 
 
 49 
 
 1885.745 
 
 153 114 
 
 1 
 
 1457.830 
 
 135 44 
 
 1 
 
 1667.931 
 
 144 91 
 
 1 
 
 1892.172 
 
 154 2f 
 
 2 
 
 1463.483 
 
 135 74 
 
 2 
 
 1673.97 
 
 145 f 
 
 2 
 
 1898.504 
 
 154 54 
 
 3 
 
 1469.14 
 
 125 10* 
 
 3 
 
 1680.02 
 
 145 34 
 
 3 
 
 1905.037 
 
 154 8f 
 
 4 
 
 1474.804 
 
 136 If 
 
 4 
 
 1686.077 
 
 145 6|- 
 
 4 
 
 1911.497 
 
 154 114 
 
 5 
 
 1480.483 
 
 136 4f 
 
 5 
 
 1692.148 
 
 145 94 
 
 6 
 
 1917.961 
 
 155 24 
 
 6 
 
 1486.173 
 
 136 74 
 
 6 
 
 1698.231 
 
 146 14 
 
 6 
 
 1924.426 
 
 155 6 
 
 7 
 
 1491.870 
 
 136 11 
 
 7 
 
 1704.321 
 
 116 4| 
 
 7 
 
 1930.919 
 
 155 94 
 
 8 
 
 1497.582 
 
 137 24 
 
 8 
 
 1710.425 
 
 146 74 
 
 8 
 
 1937.316 
 
 156 4 
 
 9 
 
 1503.305 
 
 137 5} 
 
 9 
 
 1716.541 
 
 146 10f 
 
 9 
 
 1943.914 
 
 156 3* 
 
 10 
 
 1509.035 
 
 137 8-| 
 
 10 
 
 1722.663 
 
 147 n 
 
 10 
 
 1950.439 
 
 156 6 
 
 11 
 
 1514.779 
 
 137 11| 
 
 11 
 
 1728.801 
 
 147 4f 
 
 11 
 
 1956.969 
 
 156 9$ 
 
 44 
 
 1520.534 
 
 138 2$ 
 
 47 
 
 1734.947 
 
 147 7f 
 
 50 
 
 1963.5 
 
 157 4 
 
 1 
 
 1526.297 
 
 138 6| 
 
 1 
 
 1741.104 
 
 147 11 
 
 
 
 
 2 
 
 1532.074 
 
 138 9 
 
 2 
 
 1747.274 
 
 148 24 
 
 
 
 
 3 
 
 1537.862 
 
 139 4 
 
 3 
 
 1753.455 
 
 148 54 
 
 
 
 
 4 
 
 1543.658 
 
 139 34 
 
 4 
 
 1759.643 
 
 148 8| 
 
 
 
 
 5 
 
 1549.478 
 
 139 6t 
 
 5 
 
 1765.845 
 
 148 114 
 
 
 
 
 6 
 
 1555.288 
 
 139 9 
 
 6 
 
 1772.059 
 
 149 2f 
 
 
 
 
 7 
 
 1561.116 
 
 140 f 
 
 7 
 
 1778.28 
 
 149 5| 
 
 
 
 
 8 
 
 1566.959 
 
 140 34 
 
 8 
 
 1784.515 
 
 149 84 
 
 
 
 
 9 
 
 1572.812 
 
 140 74 
 
 9 
 
 1790.761 
 
 150 4 
 
 
 
 
 10 
 
 1578.673 
 
 141 104 
 
 10 
 
 1797.015 
 
 150 34 
 
 
 
 
 11 
 
 1584.549 
 
 141 It 
 
 11 
 
 1803.283 
 
 150 6| 
 
 
 
 
 45 
 
 1590.435 
 
 141 4| 
 
 48 
 
 1809.562 
 
 150 94 
 
 
 
 
 1 
 
 1596.329 
 
 141 74 
 
 1 
 
 1815.848 
 
 151 | 
 
 
 
 
 2 
 
 1602.237 
 
 141 lOf 
 
 2 
 
 1822.149 
 
 151 3f 
 
 
 
 
 3 
 
 1608.155 
 
 142 14 
 
 3 
 
 1828.460 
 
 151 6| 
 
 
 
 
 4 
 
 1614.082 
 
 142 5 
 
 4 
 
 1834.779 
 
 151 104 
 
 
 
 
 5 
 
 1620.023 
 
 142 84 
 
 5 
 
 1841.173 
 
 152 H 
 
 
 
 
 6 
 
 1625.974 
 
 142 iii 
 
 6 
 
 1847.457 
 
 152 4f 
 
 
 
 
 n 
 
 1631.933 
 
 143 2f 
 
 7 
 
 1853.809 
 
 152 74 
 
 
 
 
 8 
 
 1637.907 
 
 143 5J- 
 
 8 
 
 1880.175 
 
 152 lOf 
 
 
 
 
 9 
 
 1643.891 
 
 143 8f 
 
 9 
 
 1866.552 
 
 153 1$ 
 
 
 
 
 10 
 
 1649.883 
 
 143 llf 
 
 10 
 
 1872.937 
 
 153 44 
 
 
 
 
 11 
 
 1555.889 
 
 144 3 
 
 11 
 
 1879.335 
 
 153 84 
 
 
 
 
 Circular Arcs. 
 
 To find the length of a circular arc when its chord and height, or 
 versed sine is given; BY THE FOLLOWING TABLE. 
 
 RULE. Divide the height by the chord; find in the column of 
 heights the number equal to this quotient. Take out the corre- 
 sponding number from the column of lengths. 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? 
 
 Ans. 30^80=0.375. The length of an arc for a height of 
 0.375 we find from table to be 1.34063. 80X 1.34063= 107.2504 
 = length of arc. 
 
MENSURATION. CIRCULAR ARCS. 
 
 57 
 
 TABLE OF CIRCULAR ARCS. 
 
 Hts. 
 
 Lengths 
 
 Hts. 
 
 ,engths 
 
 Hts. 
 
 Lengths 
 
 Hts. 
 
 Lengths 
 
 Hts. 
 
 Lengths 
 
 .001 
 
 1.00001 
 
 .062 
 
 1.01021 
 
 .123 
 
 1.03987 
 
 .184 
 
 1.08797 
 
 .245 
 
 1.15308 
 
 .002 
 
 1.00001 
 
 .063 
 
 1.01054 
 
 .124 
 
 1.04051 
 
 .185 
 
 1.08890 
 
 .246 
 
 1.15428 
 
 .003 
 
 1.00002 
 
 .064 
 
 1T01088 
 
 .125 
 
 1.04116 
 
 .186 
 
 1.08984 
 
 .247 
 
 1.15549 
 
 .004 
 
 1.00004 
 
 .065 
 
 1.01123 
 
 .126 
 
 1.04181 
 
 .187 
 
 1.09079 
 
 .248 
 
 1.15670 
 
 .005 
 
 1.00007 
 
 .066 
 
 1.01158 
 
 .127 
 
 1.04247 
 
 .188 
 
 1.09174 
 
 .249 
 
 1.15791 
 
 .006 
 
 1.00010 
 
 .067 
 
 1.01193 
 
 .128 
 
 1.04313 
 
 .189 
 
 1.09269 
 
 .250 
 
 1.15912 
 
 .007 
 
 1.00013 
 
 .068 
 
 1.01228 
 
 .129 
 
 1.04380 
 
 .190 
 
 1.09365 
 
 .251 
 
 1.16034 
 
 .008 
 
 1.00017 
 
 .069 
 
 1.01264 
 
 .130 
 
 1.04447 
 
 .191 
 
 1.09461 
 
 .252 
 
 1.16156 
 
 .009 
 
 1.00022 
 
 .070 
 
 1.01301 
 
 .131 
 
 1.04515 
 
 .192 
 
 1.09557 
 
 .253 
 
 1.16279 
 
 .010 
 
 1.00027 
 
 .071 
 
 1.01338 
 
 .132 
 
 1.04584 
 
 .193 
 
 1.09654 
 
 .254 
 
 1.16402 
 
 .011 
 
 1.00032 
 
 .072 
 
 1.01376 
 
 .133 
 
 1.04652 
 
 .194 
 
 1.09752 
 
 .255 
 
 1.16526 
 
 .012 
 
 1.00038 
 
 .073 
 
 1.01414 
 
 .134 
 
 1.04722 
 
 .195 
 
 1.09850 
 
 .256 
 
 1.16650 
 
 .013 
 
 1.00045 
 
 .074 
 
 1.01453 
 
 .135 
 
 1.04792 
 
 .196 
 
 1.09949 
 
 .257 
 
 1.16774 
 
 .014 
 
 1.00053 
 
 .075 
 
 1.01493 
 
 .136 
 
 1.04862 
 
 .197 
 
 1.10048 
 
 .258 
 
 1.16899 
 
 .015 
 
 1.00061 
 
 .076 
 
 1.01533 
 
 .137 
 
 1.04932 
 
 .198 
 
 1.10147 
 
 .259 
 
 1.17024 
 
 .016 
 
 1.00069 
 
 .077 
 
 1.01573 
 
 .138 
 
 1.05003 
 
 .199 
 
 1.10247 
 
 .260 
 
 1.17150 
 
 .017 
 
 1.00078 
 
 .078 
 
 1.01614 
 
 .139 
 
 1.05075 
 
 .200 
 
 1.10347 
 
 .261 
 
 1.17276 
 
 .018 
 
 1.00087 
 
 .079 
 
 1.01656 
 
 .140 
 
 1.05147 
 
 .201 
 
 1.10447 
 
 .262 
 
 1.17403 
 
 .019 
 
 1.00097 
 
 .080 
 
 1.0169S 
 
 .141 
 
 1.05220 
 
 .202 
 
 1.10548 
 
 .263 
 
 1.17530 
 
 .020 
 
 1.00107 
 
 .081 
 
 1.01741 
 
 .142 
 
 1.05293 
 
 .203 
 
 1.10650 
 
 .264 
 
 1.17657 
 
 .021 
 
 1.00117 
 
 .082 
 
 1.01784 
 
 .143 
 
 1.05367 
 
 .204 
 
 1.10752 
 
 .205 
 
 1.17784 
 
 .022 
 
 1.00128 
 
 .083 
 
 1.01828 
 
 .144 
 
 1.05441 
 
 .205 
 
 1.10855 
 
 .266 
 
 1.17912 
 
 .023 
 
 1.00140 
 
 .084 
 
 1.01872 
 
 .145 
 
 1.05516 
 
 .206 
 
 1.10958 
 
 .267 
 
 1.18040 
 
 .024 
 
 1.00153 
 
 .085 
 
 1.01916 
 
 .146 
 
 1.05591 
 
 .207 
 
 1.11062 
 
 .268 
 
 1.18169 
 
 .025 
 
 1.00167 
 
 .086 
 
 1.01961 
 
 .147 
 
 1.05667 
 
 .208 
 
 1.11165 
 
 .269 
 
 1.18299 
 
 .026 
 
 1.00182 
 
 .087 
 
 1.02006 
 
 .148 
 
 1.05743 
 
 .209 
 
 1.11269 
 
 .270 
 
 1.18429 
 
 .027 
 
 1.00196 
 
 .088 
 
 1.02052 
 
 .149 
 
 1.05819 
 
 .210 
 
 1.11374 
 
 .271 
 
 1.18559 
 
 .028 
 
 1.00210 
 
 .089 
 
 1.02098 
 
 .150 
 
 1.05896 
 
 .211 
 
 1.11479 
 
 .272 
 
 1.18689 
 
 .029 
 
 1 .00225 
 
 .090 
 
 1.02145 
 
 .151 
 
 1.05973 
 
 .212 
 
 1.11584 
 
 .273 
 
 1.18820 
 
 .030 
 
 1.00240 
 
 .091 
 
 1.02192 
 
 .152 
 
 1.06051 
 
 .213 
 
 1.11690 
 
 .274 
 
 1.18951 
 
 .031 
 
 1.00256 
 
 .092 
 
 1.02240 
 
 .153 
 
 1.06130 
 
 .214 
 
 1.11796 
 
 .275 
 
 1.19082 
 
 .032 
 
 1.00272 
 
 .093 
 
 1.02289 
 
 .154 
 
 1.06209 
 
 .215 
 
 1.11904 
 
 .976 
 
 1.19214 
 
 .033 
 
 1.00289 
 
 .094 
 
 1.02339 
 
 .155 
 
 1.06288 
 
 .216 
 
 1.12011 
 
 .277 
 
 1.19346 
 
 .034 
 
 1.00307 
 
 .095 
 
 1.02389 
 
 .156 
 
 1.06368 
 
 .217 
 
 1.12118 
 
 .278 
 
 1.19479 
 
 .035 
 
 1.00327 
 
 .096 
 
 1.02440 
 
 .157 
 
 1.06449 
 
 .218 
 
 1.12225 
 
 .279 
 
 1.19612 
 
 .036 
 
 1.00345 
 
 .097 
 
 1.02491 
 
 .158 
 
 1.06530 
 
 .219 
 
 1.12334 
 
 .280 
 
 1.19746 
 
 .037 
 
 1.00364 
 
 .098 
 
 1.02542 
 
 .159 
 
 1.06611 
 
 .220 
 
 1.12444 
 
 .281 
 
 1.19880 
 
 .038 
 
 1.00384 
 
 .099 
 
 1.02593 
 
 .160 
 
 1.06693 
 
 .221 
 
 1.12554 
 
 .282 
 
 1.20014 
 
 .039 
 
 1.00405 
 
 .100 
 
 1.02645 
 
 .161 
 
 1.06775 
 
 .222 
 
 1.12664 
 
 .283 
 
 1.20149 
 
 .040 
 
 1.00426 
 
 .101 
 
 1.02698 
 
 .162 
 
 1.06858 
 
 .223 
 
 1.12774 
 
 .284 
 
 1.20284 
 
 .041 
 
 1.00447 
 
 .102 
 
 1.02752 
 
 .163 
 
 1.06941 
 
 .224 
 
 1.12885 
 
 .285 
 
 1.20419 
 
 .042 
 
 1.00469 
 
 .103 
 
 1.02806 
 
 .164 
 
 1.07025 
 
 .225 
 
 1.12997 
 
 .286 
 
 1.20555 
 
 .043 
 
 1.00492 
 
 .104 
 
 1.02860 
 
 .165 
 
 1.07109 
 
 .226 
 
 1.13108 
 
 .287 
 
 1.20691 
 
 .044 
 
 1.00515 
 
 .105 
 
 1.02914 
 
 .166 
 
 1.07194 
 
 .227 
 
 1.13219 
 
 .288 
 
 1.20827 
 
 .045 
 
 1.00539 
 
 .106 
 
 1.02970 
 
 .167 
 
 1.07279 
 
 .228 
 
 1.13331 
 
 .289 
 
 1.20964 
 
 .046 
 
 1.00563 
 
 .107 
 
 1.03026 
 
 .168 
 
 1.07365 
 
 .229 
 
 1.13444 
 
 .290 
 
 1.21102 
 
 .047 
 
 1.00587 
 
 .108 
 
 1.03082 
 
 .169 
 
 1.07451 
 
 .230 
 
 1.13557 
 
 .291 
 
 1.21239 
 
 .048 
 
 1.00612 
 
 .109 
 
 1.03139 
 
 .170 
 
 1.07537 
 
 .231 
 
 1.13671 
 
 .292 
 
 1.21377 
 
 .049 
 
 1.00638 
 
 .110 
 
 1.03196 
 
 .171 
 
 1.07624 
 
 .232 
 
 1.13785 
 
 .293 
 
 1.21515 
 
 .050 
 
 1.00665 
 
 .111 
 
 1.03254 
 
 .172 
 
 1.07711 
 
 .233 
 
 1.13900 
 
 .294 
 
 1.21654 
 
 .051 
 
 1.00692 
 
 .112 
 
 1.03312 
 
 .173 
 
 1.07799 
 
 .234 
 
 1.14015 
 
 .295 
 
 1.21794 
 
 .052 
 
 1.00720 
 
 .113 
 
 1.03371 
 
 .174 
 
 1.07888 
 
 .235 
 
 1.14131 
 
 .296 
 
 1.21933 
 
 .053 
 
 1.00748 
 
 .114 
 
 1.03430 
 
 .175 
 
 1.07977 
 
 .236 
 
 1.14247 
 
 .297 
 
 1.22073 
 
 .054 
 
 1.00776 
 
 .115 
 
 1.03490 
 
 .176 
 
 1.08066 
 
 .237 
 
 1.14363 
 
 .298 
 
 1.22213 
 
 .055 
 
 1.00805 
 
 .116 
 
 1.03551 
 
 .177 
 
 1.08156 
 
 .238 
 
 1.14480 
 
 .299 
 
 1.22354 
 
 .056 
 
 1.00834 
 
 .117 
 
 1.03611 
 
 .178 
 
 1.08246 
 
 .239 
 
 1.14597 
 
 .300 
 
 1.22495 
 
 .057 
 
 1.00864 
 
 .118 
 
 1.03672 
 
 .179 
 
 1.08337 
 
 .240 
 
 1.14714 
 
 .301 
 
 1.22636 
 
 .058 
 
 1.00895 
 
 .119 
 
 1.03734 
 
 .180 
 
 1.08428 
 
 .241 
 
 1.14832 
 
 .302 
 
 1.22778 
 
 .059 
 
 1.00926 
 
 .120 
 
 1.03797 
 
 .181 
 
 1.08519 
 
 .242 
 
 1.14951 
 
 .303 
 
 1.22920 
 
 .000 
 
 1.00957 
 
 .121 
 
 1.03860 
 
 .182 
 
 1.08611 
 
 .243 
 
 1.15070 
 
 .304 
 
 1.23063 
 
 .061 
 
 1.00989 
 
 .122 
 
 1.03923 
 
 .183 
 
 1.08704 
 
 .244 
 
 1.15189 
 
 .305 
 
 1.23206 
 
58 MENSURATION.CIRCULAR ARCS. 
 
 Table of Circular Arcs (concluded). 
 
 Hts. 
 
 Lengths 
 
 Hts. 
 
 Lengths 
 
 Hts. 
 
 Lengths 
 
 Hts. 
 
 Lengths 
 
 Hts. 
 
 Lengths 
 
 .30R 
 
 1.23349 
 
 .345 
 
 1.29209 
 
 .384 
 
 1.35575 
 
 .423 
 
 1.42402 
 
 .462 
 
 1.49651 
 
 .307 
 
 1.23492 
 
 .346 
 
 1.29366 
 
 .385 
 
 1.35744 
 
 .424 
 
 1.42583 
 
 .463 
 
 1.49842 
 
 .308 
 
 1.23636 
 
 .347 
 
 1.29523 
 
 .386 
 
 1.35914 
 
 .425 
 
 1.42764 
 
 .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 
 
 .466 
 
 1.50416 
 
 .311 
 
 1.24070 
 
 .350 
 
 1.29997 
 
 .389 
 
 1.36425 
 
 .428 
 
 1.43309 
 
 .467 
 
 1.50608 
 
 .312 
 
 1.24216 
 
 .351 
 
 1.30156 
 
 .390 
 
 1.36596 
 
 .429 
 
 1.43491 
 
 .468 
 
 1.50800 
 
 .313 
 
 1.24361 
 
 .352 
 
 1.30315 
 
 .391 
 
 1.36767 
 
 .430 
 
 1.43673 
 
 .469 
 
 1.50992 
 
 .314 
 
 1.24507 
 
 .353 
 
 1.30474 
 
 .392 
 
 1.36939 
 
 .431 
 
 1.43856 
 
 .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 
 
 1.24948 
 
 .356 
 
 1.30954 
 
 .395 
 
 1.37455 
 
 .434 
 
 1.44405 
 
 .473 
 
 1.51764 
 
 .318 
 
 1.25095 
 
 .357 
 
 1.31115 
 
 .396 
 
 1.37623 
 
 .435 
 
 1.44539 
 
 .474 
 
 1.51958 
 
 .319 
 
 1.25243 
 
 .358 
 
 1.31276 
 
 .397 
 
 1.37801 
 
 .436 
 
 1.44773 
 
 .475 
 
 1.52152 
 
 .320 
 
 1.25391 
 
 .359 
 
 1.31437 
 
 .398 
 
 1.37974 
 
 .437 
 
 1.44957 
 
 .476 
 
 1.52346 
 
 .321 
 
 1.25540 
 
 .360 
 
 1.31599 
 
 .399 
 
 1.38148 
 
 .438 
 
 1.45142 
 
 .477 
 
 1.52541 
 
 .322 
 
 1.256S9 
 
 .361 
 
 1.31761 
 
 .400 
 
 1.38322 
 
 .439 
 
 1.45327 
 
 .478 
 
 1.52736 
 
 .323 
 
 1.25838 
 
 .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 
 
 .326 
 
 1.26288 
 
 .365 
 
 1.32413 
 
 .404 
 
 1.39021 
 
 .443 
 
 1.48069 
 
 .482 
 
 1.53518 
 
 .327 
 
 1.26437 
 
 .366 
 
 1.32577 
 
 .405 
 
 1.39196 
 
 .444 
 
 1.16255 
 
 .483 
 
 1.53714 
 
 .328 
 
 1.26588 
 
 .367 
 
 1.32741 
 
 .406 
 
 1.39372 
 
 .445 
 
 1.46441 
 
 .484 
 
 .53010 
 
 .329 
 
 1.26740 
 
 .368 
 
 1.32905 
 
 .407 
 
 1.39548 
 
 .446 
 
 1.46628 
 
 .485 
 
 .54106 
 
 .330 
 
 1.26892 
 
 .369 
 
 1.33069 
 
 .408 
 
 1.39724 
 
 .447 
 
 1.46815 
 
 .486 
 
 .54302 
 
 .331 
 
 1.27044 
 
 .370 
 
 1.33234 
 
 .409 
 
 1.39900 
 
 .448 
 
 1.47002 
 
 .487 
 
 1.54499 
 
 .332 
 
 1.27196 
 
 .371 
 
 1.33399 
 
 .410 
 
 1.40077 
 
 .449 
 
 1.471S9 
 
 .488 
 
 1.54696 
 
 .333 
 
 1.27349 
 
 .372 
 
 1.33564 
 
 .411 
 
 1.40254 
 
 .450 
 
 1.47377 
 
 .489 
 
 .54893 
 
 .334 
 
 1.27502 
 
 .373 
 
 1.33730 
 
 .412 
 
 1.40432 
 
 .451 
 
 1.47565 
 
 .490 
 
 .55091 
 
 .335 
 
 1.27656 
 
 .374 
 
 1.33896 
 
 .413 
 
 1.40310 
 
 .452 
 
 1.47753 
 
 .491 
 
 .55289 
 
 .336 
 
 1.27810 
 
 .375 
 
 1.34063 
 
 .414 
 
 1.40788 
 
 .453 
 
 1.47942 
 
 .492 
 
 .55487 
 
 .337 
 
 1.27964 
 
 .376 
 
 1.34229 
 
 .415 
 
 1.40966 
 
 .454 
 
 1.48131 
 
 .493 
 
 .55685 
 
 .338 
 
 1.28118 
 
 .377 
 
 1.34396 
 
 .416 
 
 1.41145 
 
 .455 
 
 1.48320 
 
 .494 
 
 .55884 
 
 .339 
 
 1.28273 
 
 .378 
 
 1.34563 
 
 .417 
 
 1.41324 
 
 .456 
 
 1.48509 
 
 .495 
 
 .56083 
 
 .340 
 
 1.28428 
 
 .379 
 
 1.34731 
 
 .418 
 
 1.41503 
 
 .457 
 
 1.48699 
 
 .496 
 
 56282 
 
 .341 
 
 1.28583 
 
 .380 
 
 1 .34899 
 
 .419 
 
 1.41682 
 
 .458 
 
 1.48889 
 
 .497 
 
 .56481 
 
 .342 
 
 1.PS739 
 
 .381 
 
 1.35068 
 
 .420 
 
 1.41861 
 
 .459 
 
 1.49079 
 
 .498 
 
 .56681 
 
 .343 
 
 1.28895 
 
 .382 
 
 1.35237 
 
 .421 
 
 1.42041 
 
 .460 
 
 1.49269 
 
 499 
 
 568S1 
 
 .344 
 
 1.29052 
 
 .383 
 
 1.35408 
 
 .422 
 
 1.42221 
 
 .461 
 
 1.49460 
 
 .500 
 
 .57080 
 
 Table of Lengths of Circular Arcs whose Radius 
 
 is 1. 
 
 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 of degrees, minutes, and seconds in 
 the arc, and multiply their sum by the radius of the circle. 
 
 EXAMPLE. What is the length of an arc subtending an angle 
 of 13 27' 8", with a radius of 8 feet. 
 
 Ans. Length for 13= 0.2268928 
 
 27' = 0.0078540 
 
 8"= 0.0000388 
 
 13 27' 8"= 0.2347856 
 
 8 
 
 Length of arc = 1 . 8782848 feet. 
 
MENSURATION. CIRCULAR ARCS. 
 
 59 
 
 Lengths of Circular Arcs; Radius=l. 
 
 Sec. 
 
 Length. 
 
 Min. 
 
 Length. 
 
 Deg. 
 
 Length. 
 
 Deg. 
 
 Length. 
 
 1 
 
 0.0000048 
 
 1 
 
 0.0002909 
 
 1 
 
 0.0174533 
 
 61 
 
 .0646508 
 
 2 
 
 . 0000097 
 
 2 
 
 0.0005818 
 
 2 
 
 0.0349066 
 
 62 
 
 .0821041 
 
 3 
 
 0.0000115 
 
 3 
 
 0.0008727 
 
 3 
 
 0.0523599 
 
 63 
 
 .0095574 
 
 4 
 
 0.0000194 
 
 4 
 
 0.0011036 
 
 4 
 
 0.0698132 
 
 64 
 
 .1170107 
 
 5 
 
 0.0000242 
 
 5 
 
 0.0014544 
 
 5 
 
 0.0872665 
 
 65 
 
 .1344640 
 
 6 
 
 0.0000291 
 
 6 
 
 0.0017453 
 
 6 
 
 0.1047198 
 
 66 
 
 .1519173 
 
 7 
 
 0.0000339 
 
 7 
 
 0.0020362 
 
 7 
 
 0.1221730 
 
 67 
 
 .1693706 
 
 8 
 
 0.0000388 
 
 8 
 
 0.0023271 
 
 8 
 
 0.1396263 
 
 68 
 
 . 1868239 
 
 9 
 
 . 0000436 
 
 9 
 
 0.0026180 
 
 9 
 
 0.1570796 
 
 69 
 
 .2042772 
 
 10 
 
 0.0000485 
 
 10 
 
 0.0029089 
 
 10 
 
 0.1745329 
 
 70 
 
 .2217305 
 
 11 
 
 0.0000533 
 
 11 
 
 0.0031998 
 
 11 
 
 0.1919862 
 
 71 
 
 .2391838 
 
 12 
 
 0.0000582 
 
 12 
 
 0.0034907 
 
 12 
 
 0.2094895 
 
 72 
 
 .2566371 
 
 13 
 
 . 0000030 
 
 13 
 
 0.0037815 
 
 13 
 
 0.2268928 
 
 73 
 
 .2740904 
 
 14 
 
 0.0000079 
 
 14 
 
 0.0040724 
 
 14 
 
 0.2443461 
 
 74 
 
 .2915436 
 
 15 
 
 0.0000727 
 
 15 
 
 0.0043033 
 
 15 
 
 0.2617994 
 
 75 
 
 .3089969 
 
 16 
 
 0.0000776 
 
 16 
 
 0.0046542 
 
 16 
 
 0.2792527 
 
 76 
 
 .3264502 
 
 17 
 
 . 0000^24 
 
 17 
 
 0.0049451 
 
 17 
 
 0.2967060 
 
 77 
 
 .3439035 
 
 18 
 
 0.0000873 
 
 18 
 
 0.0052360 
 
 18 
 
 0.3141593 
 
 78 
 
 .3613568 
 
 19 
 
 0.0000921 
 
 19 
 
 0.0055209 
 
 19 
 
 0.3316126 
 
 79 
 
 .3788101 
 
 20 
 
 0.0000970 
 
 20 
 
 0.0058178 
 
 20 
 
 0.3490G59 
 
 80 
 
 . 3962634 
 
 21 
 
 0.0001018 
 
 21 
 
 0.0061087 
 
 21 
 
 0.3665191 
 
 81 
 
 .4137167 
 
 22 
 
 0.0001067 
 
 22 
 
 0.0063995 
 
 22 
 
 0.3839724 
 
 . 82 
 
 .4311700 
 
 23 
 
 0.0001115 
 
 23 
 
 0.0066904 
 
 23 
 
 0.4014257 
 
 83 
 
 .4486233 
 
 24 
 
 0.0001164 
 
 24 
 
 0.0069813 
 
 24 
 
 0.4188790 
 
 84 
 
 .4660766 
 
 25 
 
 0.0001212 
 
 25 
 
 0.0072722 
 
 25 
 
 0.4363323 
 
 85 
 
 .4835299 
 
 26 
 
 0.0001261 
 
 20 
 
 0.0075031 
 
 26 
 
 0.4537856 
 
 86 
 
 .5009832 
 
 27 
 
 0.0001309 
 
 27 
 
 0.0078540 
 
 27 
 
 0.4712389 
 
 87 
 
 .5184364 
 
 28 
 
 0.0001357 
 
 28 
 
 0.0081449 
 
 28 
 
 0.4880922 
 
 88 
 
 .5358897 
 
 29 
 
 0.0001406 
 
 29 
 
 0.0084358 
 
 29 
 
 0.5061455 
 
 89 
 
 .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 
 
 0.0093084 
 
 32 
 
 0.5585054 
 
 92 
 
 1.6057029 
 
 33 
 
 0.0001600 
 
 33 
 
 0.0095993 
 
 33 
 
 0.5759587 
 
 93 
 
 1.6231562 
 
 34 
 
 0.0001648 
 
 34 
 
 0.0098902 
 
 34 
 
 0.5934119 
 
 94 
 
 1.6406095 
 
 35 
 
 0.0001697 
 
 35 
 
 0.0101811 
 
 35 
 
 0.6108052 
 
 95 
 
 1.6580628 
 
 36 
 
 0.0001745 
 
 36 
 
 0.0104720 
 
 36 
 
 0.6283185 
 
 96 
 
 1.6755161 
 
 37 
 
 0.0001794 
 
 37 
 
 0.0107629 
 
 37 
 
 0.6457718 
 
 97 
 
 1.6929694 
 
 38 
 
 0.0001842 
 
 38 
 
 0.0110538 
 
 38 
 
 0.6632251 
 
 98 
 
 .7104227 
 
 39 
 
 0.0001891 
 
 39 
 
 0.0113446 
 
 39 
 
 0.6806784 
 
 99 
 
 .7278760 
 
 40 
 
 0.0001939 
 
 40 
 
 0.0116355 
 
 40 
 
 0.6981317 
 
 100 
 
 .7453293 
 
 41 
 
 0.0001988 
 
 41 
 
 0.0119264 
 
 41 
 
 0.7155850 
 
 101 
 
 .7627825 
 
 42 
 
 . 0002036 
 
 42 
 
 0.0122173 
 
 42 
 
 0.7330383 
 
 102 
 
 .7802358 
 
 43 
 
 0.0002085 
 
 43 
 
 0.0125082 
 
 43 
 
 0.7504916 
 
 103 
 
 . 7970891 
 
 44 
 
 0.0002133 
 
 44 
 
 0.0127991 
 
 44 
 
 0.7679449 
 
 104 
 
 .8151424 
 
 45 
 
 0.0002182 
 
 45 
 
 0.0130000 
 
 45 
 
 0.7853982 
 
 105 
 
 . 8325957 
 
 46 
 
 0.0002230 
 
 46 
 
 0.0133809 
 
 46 
 
 0.802851 5 
 
 106 
 
 .8500490 
 
 47 
 
 0.0002279 
 
 47 
 
 0.0136717 
 
 47 
 
 O.S203047 
 
 107 
 
 .8675023 
 
 48 
 
 0.0002327 
 
 48 
 
 0.0139626 
 
 48 
 
 0.8377580 
 
 108 
 
 .8849556 
 
 49 
 
 0.0002376 
 
 49 
 
 0.0142535 
 
 49 
 
 0.8552113 
 
 109 
 
 .9024089 
 
 50 
 
 0.0002124 
 
 50 
 
 0.0145444 
 
 50 
 
 0.8726646 
 
 110 
 
 .9198622 
 
 51 
 
 0.0002473 
 
 51 
 
 0.0148353 
 
 51 
 
 0.8901179 
 
 111 
 
 .9373155 
 
 52 
 
 0.0002521 
 
 52 
 
 0.01512-32 
 
 52 
 
 0.9075712 
 
 112 
 
 .9547688 
 
 53 
 
 0.0002570 
 
 53 
 
 0.0154171 
 
 53 
 
 0.9250245 
 
 113 
 
 .9722221 
 
 54 
 
 0.0002618 
 
 54 
 
 0.0157080 
 
 54 
 
 0.9424778 
 
 114 
 
 .9890753 
 
 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 
 
 2.0591885 
 
 59 
 
 0.0002860 
 
 59 
 
 0.0171624 
 
 59 
 
 1.0297443 
 
 119 
 
 2.0769418 
 
 60 
 
 0.0002909 
 
 60 
 
 0.0174533 
 
 60 
 
 1.0471976 
 
 120 
 
 2.0943951 
 
60 MENSURATION. LENGTHS OF CHORDS. 
 
 To compute the chord of an arc when the chord of half the arc and 
 h the versed sine are given. (The versed 
 
 sine is the perpendicular bo, Fig. 31.) 
 RULE. From the square of the chord of 
 
 i p. ( 31 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 60, and the versed 
 sine 36, what is the length of the chord of the arc? 
 
 Ans. 60 2 ~36 2 =2304, and ^2304= 48, 
 and 48X2 = 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 re- 
 mainder. 
 
 EXAMPLE. The diameter of a circle is 100, and the versed 
 sine of an arc 36, what is the chord of the arc? 
 
 Ans. 30X2=72. 100-72=28. 100 2 -28 2 =9216. 
 V9216 = 96, the chord of the arc. 
 
 To compute the chord of half an arc 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? 
 
 Ans. V36 2 + 48 2 =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 1. 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. 
 
MENSURATION. ARCS AND VERSED SINES. 61 
 
 EXAMPLE. What is the radius of an arc whose chord is 96, and 
 whose versed sine is 36? 
 
 Ans. 48 2 + 36 2 =3600. 3600-^36=100, the diameter, 
 and 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 diame- 
 ter are given. 
 
 RULE. From the square of the diameter subtract the square 
 of the chord, and extract the square root of the remainder; sub- 
 tract this root from the diameter, 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 1. 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. 
 
 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 inches, what is the length of the arc in inches? 
 
 Ans. 10X3.1416x60=1884.96^-180=10.47 inches; 
 
 or, 10X0.01745X60=10.47 inches. * 
 
 To compute the length of the arc of a circle when the length is 
 given in degrees, minutes, and seconds. 
 
 RULE 1. Multiply the number of degrees by 0.01745329, and 
 the product by the radius. 
 
 RULE 2. Multiply the number of minutes by 0.00029, and 
 that product by the radius. 
 
 RULE 3. Multiply the number of seconds by 0.0000048 times 
 the radius. Add together these three results for the length of 
 the arc. 
 
 See also table, p. 59. 
 
 EXAMPLE. What is the length of an arc of 60 10' 5", the 
 radius being 4 feet? 
 
 Ans. 1. 60XO. 01745329X4=4. 188789 feet. 
 
 2. 10'XO. 00029 X4=0.0116 feet. 
 
 3. 5"X 0.0000048 X 4= 0.000096 feet. 
 
 4.200485 feet. 
 
62 MENSURATION. CIRCULAR SEGMENTS, ETC. 
 
 To compute the area of a sector of a circle when the degrees of the 
 
 arc and the radius are given (Fig. 32).* 
 RULE. Multiply the number of degrees in 
 the arc by the area of the whole circle, and di- 
 vide by 360. 
 
 EXAMPLE. What is the area of a sector of 
 a circle whose radius is 5, and the length of the 
 arc is 60? 
 Ans. Area of circle= 10X10X0.7854= 78.54. 
 
 Then area of sector= = 13 . 09. 
 
 ouO 
 
 // the length of the arc is given in degrees and minutes, reduce it 
 to minutes, and multiply by the area of the whole circle, and di- 
 vide by 21600. 
 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, and 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. 
 
 NOTE. The versed sine is the distance cd (Fig. 32). 
 
 RULE 1 (when the segment is less than a semicircle). Ascer- 
 tain the area of the sector having the same arc as the segment, 
 then ascertain the area of a triangle formed by the chord of the 
 segment and the radii of the sector, and take the difference of 
 these areas. 
 
 RULE 2 (when the segment is greater than a semircicle). As- 
 certain by the preceding rule the area of the lesser portion of the 
 circle, subtract it from the area of the whole circle, and the re- 
 mainder will give the area. 
 To compute the convex surface of a sphere. 
 
 RULE. Multiply the diameter by the circumference, and the 
 product will give the surface. 
 
 EXAMPLE. What is the convex surface of a sphere of 10 inches 
 diameter? 
 
 Ans. Circumference of sphere= 10X3 . 1416=31 .416 inches; 
 10 X 31 . 416 = 314 . 16 sq. in., the surface of sphere. 
 
 * The degrees of the arc are the same as of the angle aob. 
 
MENSURATION. SPHERES AND SPHEROIDS. 63 
 
 To compute the surface of a segment of a 
 
 RULE. Multiply the height (be, Fig. 33) 
 by the circumference of the sphere, and add 
 the product to the area of the base. 
 
 To find the area of the base, we have the 
 diameter of the sphere and the length of the 
 versed sine of the arc abd, and we can find 
 the length of the chord ad by the rule on 
 p. 60. Having, then, the length of the 
 chord ad for the diameter of the base, we 
 can easily find the area. 
 
 Fig. 33 
 
 EXAMPLE. The height, be, of a segment abd, is 36 inches, and 
 the diameter of the sphere is 100 inches. What is the convex sur- 
 face, and what the whole surface? 
 
 Ans. 100 X 3 . 1416 = 314 . 16 inches, the circumference of sphere. 
 36 X 314 . 16= 1 1309 . 76, the convex surface. 
 The length of ad= 100 -36X2 = 28. 
 \ / 100 2 -28 2 = 96, the chord ad. 
 96 2 X 0.7854= 2738. 2464, the area of base. 
 11309 . 76 + 7238 . 2464= 18548.0064, Fig. 34 
 
 the total area. 
 To compute the surface of a spherical 
 
 zone. 
 
 RULE. Multiply the height (cd, Fig. 34) a \ 
 by the circumference of the sphere for the 
 convex surface, and add to it the area of 
 the two ends for the whole area. 
 
 Spheroids, or Ellipsoids. 
 
 DEFINITION. Spheroids, or ellipsoids, are figures generated by 
 the revolution of a semi-ellipse about one of its diameters. 
 
 When the revolution is about the long diameter, they are pro- 
 late; and when it is about the short diameter, they are oblate. 
 
 A prolate spheroid is cigar-shaped, an oblate spheroid is like 
 a watch. 
 
 To compute the surface of a spheroid. 
 Let a= \ long axis; let 6=i short axis; 
 
 v |a 2 -& 2 
 
 let 
 
 then surface of oblate spheroid 
 
64 MENSURATION. CONES AND PYRAMIDS. 
 
 Surface of prolate spheroid 
 
 e 
 
 In the first formula, natural logarithms must be used. The 
 natural logarithm may be obtained by multiplying the common 
 logarithm by 2.302. 
 
 sin~ l e may be found, by finding the angle whose natural sine 
 is equal to e and dividing the angle so obtained by 57.3. 
 
 [Although the above formulae are complicated, no simpler rules 
 can be given that are at all reliable.] 
 To compute the surface of a cylinder. 
 
 RULE. Multiply the length by the circumference for the con- 
 vex surface, and add to the product the area 
 of the two ends for the whole surface. 
 To compute the sectional area of a circular 
 
 ring (Fig. 35). 
 
 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 
 Fig. 35 of the ring. 
 
 To compute the surface of a cone. 
 
 RULE. Multiply the perimeter or 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 inches, and 
 the slant height 15 inches, what is the area of the cone? 
 
 Ans. 3X3.1416= 9. 4248= circumference of base. 
 
 9 . 4248 X 7J= 70 . 686 square inches, the convex surface. 
 3X3X0.7854= 7. 068 square inches, the area of base. 
 Area of cone =77. 754 square inches. 
 
 To compute the area of the surface of the frus- 
 
 tum of a cone. 
 
 RULE. Multiply the sum of the perimeters 
 of the two ends by the slant height of the frus- 
 tum, and divide by 2, for the convex surface. 
 Add the area of the top and bottom surfaces. 
 To compute the surface of a pyramid. 
 
 RULE. Multiply the perimeter of the base 
 y one-half the slant height, and add to the 
 product the area of the base. 
 To compute the surface of the frustum of a 
 9" pyramid. 
 
MENSURATION. PRISMS. 
 
 65 
 
 Fig. 37 
 
 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 area of the two ends. 
 
 MENSURATION OP SOLIDS. 
 To compute the volume of a prism. 
 
 RULE. Multiply the area of the base by the height. 
 
 This rule applies to any prism of any shape on the base, as long 
 as the top and bottom surfaces are parallel. 
 To compute the volume of a prismoid. 
 
 DEFINITION. A prismoid is 
 a solid having parallel ends or 
 bases dissimilar in shape with 
 quadrilateral sides. 
 
 RULE. To the sum of the 
 areas of the two ends add four 
 times the area of the middle 
 section parallel to them, and m 
 multiply this sum by one-sixth 
 of the perpendicular height. ' 
 
 EXAMPLE. What is the vol- 
 ume of a quadrangular prismoid, as in Fig. 37, in which a&=6", 
 
 A ns. Area of top 
 
 Area of bottom 
 
 X 10=70. 
 
 Area of middle section = ^ X 10= 60. 
 
 [50 + 70+ (4X60)]Xf =480 cubic inches. 
 
 NOTE The length of the end of the middle section, as mn in Fig. 37 = 
 ed + ef 
 
 2 ' 
 
 To find the volume of a prism 
 truncated obliquely. 
 
 RULE. Multiply the area of ^-' 
 the base by the average height \ 
 of the edges. 
 
 EXAMPLE. What is the 
 volume of a truncated prisrn, 
 as in Fig. 38, where ef=Q 
 inches, fh=W inches, ea=10, 
 ci=12, dh=8, and /6=8? 
 
 Fig.38 
 
66 MENSURATION. POLYHEDRONS. 
 
 Ans. Area of base= 6X10 = 60 square inches. 
 
 1 I 1 2 I R I H 
 Average height of edges = - = 9J inches. 
 
 60X9^=970 cubic inches. 
 
 To compute the volume of a wedge 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; 
 multiply their sum by the perpen- 
 dicular height of the wedge, and 
 then by the breadth of the back, 
 and divide the product by 6. 
 
 Regular Polyhedrons. 
 
 DEFINITION. A regular body is a solid contained within a cer- 
 tain number of similar and equal plane faces, all of which are 
 equal regular polygons. 
 
 The whole number of regular bodies which can possibly be 
 found is five. They are : 
 
 1. 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 1 (when the radius of the circumscribing sphere is given) . 
 Multiply the cube of the radius of the sphere by the multiplier 
 opposite to the body 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 mul- 
 tiplier opposite to the body in column 3 of the following table. 
 
 RULE 3 (when the surface is given). Cube the surface given, 
 extract the square root, and multiply the root by the multiplier 
 opposite to the body in column 4 of the following table. 
 
MENSURATION. CONES, PYRAMIDS, ETC. 67 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 Figure. 
 
 
 Volume by 
 
 Volume by 
 
 
 
 No. of 
 
 radius of 
 
 radius of 
 
 Volume by 
 
 
 sides. 
 
 circumscribing 
 
 inscribed 
 
 surface. 
 
 
 
 sphere. 
 
 circle. 
 
 
 Tetrahedron 
 
 4 
 
 0.5132 
 
 13.85641 
 
 0.0517 
 
 Hexahedron. . . 
 
 6 
 
 1.539G 
 
 8 . 0000 
 
 . 06804 
 
 Oc^shedron 
 
 8 
 
 1 33333 
 
 6 9282 
 
 07311 
 
 Codecs hedron 
 
 12 
 
 2.78517 
 
 5 . 55029 
 
 0.08169 
 
 Icosahedron 
 
 20 
 
 2.53615 
 
 5 . 05406 
 
 . 0856 
 
 
 
 
 
 
 To compute the volume of a cylinder. 
 
 RULE. Multiply the area of the base by the height. 
 To compute the volume of a cone. 
 
 RULE. Multiply the area of the base by the perpendicular 
 height, and take one-third of the product. 
 To compute the volume of the frustum of a 
 cone. 
 
 RULE. Add together the squares of the 
 diameters of the two ends and the product 
 of the two diameters ; multiply this sum by 
 0.7854, and this product by the height, and 
 then divide this last product by 3. 
 
 EXAMPLE. What is the volume of a frus- 
 tum of a cone 9 inches high, 5 inches diame- 
 ter at the base, and 3 inches at the top? 
 
 Ans. 5 2 + 3 2 =34. 3X5=15. 15 + 34=49, 
 
 Fig. 40 
 
 the sum of the 
 
 squares and product of the diameters. 49 X 0.7854= 
 38 - 48 ; 16X9 =115.4538 cubic inches. 
 
 = 38.4846. 
 
 To compute the volume of a pyramid. 
 
 RULE. Multiply the area of the base by the perpendicular 
 height, and take one-third of the product. 
 To compute the volume of a pyramid. 
 
 RULE. Multiply the area of the base by the 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 the top 
 were put on, and then compute the volume of the completed pyra- 
 mid 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. 
 
68 MENSURATION. SPHEROIDS, PARABOLOIDS, ETC. 
 
 To compute the volume of a segment of a sphere. 
 
 RULE 1. To three times the square of the radius of its base 
 add the square of its height ; multiply this sum by the height, and 
 the product by 0.5236. 
 
 RULE 2. From three times the diameter of the sphere sub- 
 tract 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. 41), 
 of 7 inches for its base, and a height, cb, of 4 inches : what is its 
 volume? 
 
 Ans. (by Rule 1). 3X7 2 =147, and 147 + 42=163, three times 
 the square of the radius of the base plus the square of the height. 
 163X4X0.5236=341.3872 cubic inches vol- 
 
 SECOND SOLUTION. By the rule for find- 
 ing 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 
 inches; then, by Rule 2, (3X16.25) -(2X4) 
 = 40.75, and 40.75X42X0.5236=341.3872 
 cubic inches, the volume of the segment. 
 
 Fig 41. 
 
 To compute the volume of a spherical zone. 
 
 DEFINITION. The part of a sphere in- 
 cluded between two parallel planes (Fig. 
 42). 
 
 \b 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 
 Fig. 42 product by 1.5708. 
 
 To compute the volume of a prolate spheroid (see page 63). 
 
 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 revo- 
 
 lution (Fig. 43). 
 RULE. Multiply the area of the base by half the altitude. 
 
MENSURATION. EXCAVATIONS. 
 
 69 
 
 To compute the volume of a hyperboloid of revolutwn (Fig. 44). 
 
 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 prod- 
 uct by 0.5236. 
 
 To compute the volume of any figure of revo- 
 lutwn. 
 
 RULE. Multiply the area of the generating surface by the cir- 
 cumference described by its centre of gravity. 
 To compute the volume of an excavation, where the ground is irreg- 
 ular, and the bottom of the excavation is level (Fig. 45). 
 RULE. Divide the surface of the ground to be excavated into 
 equal squares of about 10 feet on a side, and ascertain by means 
 of a level the height of each corner, a, a, a, b, b, b, etc., above the 
 level to which the ground is to be excavated. Then add together 
 the heights of all the corners that only come into one square. 
 Next take twice the sum of the 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 be- 
 long to four squares, as 
 d, d, d, etc. Add to- 
 gether all these quan- 
 tities, 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 the excavation for a cellar be as in 
 the figure, 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 would be as follows, the area of each 
 square being 10X10=100 square feet: 
 
 Volume = i of 100 (a's + 2 Z>'s + 3 c's + 4 d's). 
 The a's in this case = 4 + 6 + 3 + 2 + 1 + 7 + 4=27 
 2X the sum of the 6's=2X (3 + 6 + 1+4 + 3 + 4) = 42 
 SXthe sum of the c's=3X (1 +3 + 4) =24 
 
 4Xthe sum of the <fs=4X (2 + 3 + 6 + 2) =52 
 
 c 
 
 6 
 
 3 i 
 
 a 
 
 & 5 
 
 3 
 
 i 
 
 d 
 
 2 
 
 d 
 
 3 
 
 d 
 
 8 i 
 1 
 
 4 
 2 
 
 3 
 3 
 
 6 
 1 
 
 2 
 1 1 
 
 
 
 a 
 
 * b b b 
 Fig.45 
 
 145 
 
70 
 
 GEOMETRICAL PROBLEMS. 
 
 Volume = 25 X 145= 3625 cubic feet, the quantity of earth to be 
 excavated. 
 
 GEOMETRICAL PROBLEMS. 
 
 PROBLEM 1. To bisect, or divide into equal parts, a given line, 
 ab (Fig. 46). 
 
 From a and b, with any radius greater 
 than half of ab, describe arcs intersecting 
 in c and d. The line cd, connecting these 
 ..intersections, will bisect ab, and be perpen- 
 
 Fig.46 
 
 ^dicular to it. 
 
 PROBLEM 2. To draw a perpendicular 
 to a given straight line from a point with- 
 out it. 
 
 IST METHOD (Fig. 47). From the point a describe an arc with 
 sufficient radius that it will cut 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 will be perpendicular to the line be. 
 
 2o METHOD (Fig. 
 48) . From any two 
 points, d and c, at some 
 distance apart in the 
 given line, and with 
 
 radii da and ca respectively, describe arcs cut- 
 ting at a and e. Draw ae, and it will be the- 
 perpendicular required. This method is use- 
 ful 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. IST METHOD (Fig. 49). With any 
 
 radius, from the given point a in the 
 line, describe arcs cutting the line in 
 the points b and c. Then with b and 
 c as centres, and with any radius 
 greater than ab or ac, describe arcs 
 cutting each other at d. The line da 
 will be the perpendicular desired. 
 
 d 
 
 Fig,48 
 
 d 
 
 a 
 
 Fig.49 
 
GEOMETRICAL PROBLEMS. 
 
 71 
 
 2o METHOD (Fig. 50, 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 line at d. Through b and d draw a 
 straight line intersecting the semicircle at e. 
 The line ea will then be perpendicular to the 
 line ac at the point a. 
 
 SD METHOD (Fig. 51) OR THE 3, 4, AND 5 
 METHOD. From the point a on the given 
 line measure off 4 inches, or 4 feet, or 4 of any other unit, and 
 with the same unit of measure describe an 
 arc, with a as a centre 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 will be the perpendicular. 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 laid 
 off by straight edges. 
 
 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 meas- 
 ure off, say 40 feet from a on the given line, then let one person 
 hold the end of the tape at 6, another hold the tape at the 80-foot 
 mark at a, and a third person take hold of the tape at the 50-foot 
 mark, with his thumb and finger, and pull the tape taut. The 
 50-foot mark will then be at the point c in the line of the per- 
 pendicular. 
 
 PROBLEM 4. To draw a straight line parallel to a given line 
 at a given distance apart (Fig. 52). 
 
 c d 
 
 Fig.52 b 
 
 From any two points near the ends of the given line describe 
 two arcs about opposite the line. Draw the line cd tangent to 
 these arcs, and it will be parallel tr ab. 
 
72 
 
 GEOMETRICAL PROBLEMS. 
 
 PROBLEM 5. To construct an angle equal to a given angle. 
 
 With the point A, at the apex of the given 
 angle, as a centre, and any radius, describe the 
 arc BC. Then with the point a, at the vertex 
 of the new angle, as a centre, and with the same 
 radius as before, describe an arc like BC. Then 
 with BC as a radius, and b as a centre, describe 
 an arc cutting the other 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. 54). 
 
 Take any distance, as ab, as a radius, and, with a as a centre, 
 describe the arc be. Then with b as a centre, and the same radius, 
 describe an arc cutting the first one at c. Draw from a a line 
 through c, and it will make with ab an angle of 60. 
 
 c 
 
 Fig.54 & Fig.55 I 
 
 PROBLEM 7. From a given point, A, on a given line, AE, to 
 draw a line making an angle of 45 with the given line (Fig. 55). 
 
 Measure off from A, on AE, any distance, A b, and at b draw a 
 line perpendicular to AE. Measure off on this perpendicular be 
 equal to A b, and draw a line from A through c, and it will make 
 an angle with AE of 45. 
 
 PROBLEM 8. From any point, A, on a given line, to draw a line 
 which shall make any desired angle with the given line (Fig. 56). 
 
 To perform this problem we must have a 
 table of chords at hand (such as is found 
 on pp. 88-96), which we use as follows. 
 Find in the table the length of chord to a 
 radius 1, for the given angle. Then take 
 ~Eany radius, as large as convenient, de- 
 scribe an arc of a circle be with A as a cen- 
 
 A Fig.56 
 
 tre. Multiply the chord of the angle, found in the table, by the 
 length of the radius A b, and with the product as a new radius, and 
 b as a centre, describe a short arc cutting be in d. Draw a line 
 from A through d, and it will make the desired angle with DE. 
 
GEOMETRICAL PROBLEMS. 
 
 73 
 
 EXAMPLE. Draw a line from A on DE, making an angle of 
 44 40' with DE. 
 
 SOLUTION. We find that the largest convenient radius for our 
 arc is 8 inches : so with A as a centre, and 8 inches as a radius, we 
 describe the arc be. Then, looking in the table of chords, we find 
 the chord for an angle or arc of 44 40' to a radius 1 is 0.76. Mul- 
 tiplying this by 8 inches, we have, for the length of our new ra- 
 dius, 6.08 inches, and with this as radius, and b as a centre, we 
 describe an arc cutting be in d. Ad will then be the line desired. 
 
 PROBLEM 8a.To lay off a given angle approximately by means 
 of an ordinary two-foot rule. 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 
 corresponds 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 approxima- 
 tion. 
 
 TABLES OF ANGLES CORRESPONDING TO OPENINGS 
 OF A TWO-FOOT RULE (TRAUTWTNE). 
 
 In. 
 
 Deg. Min. 
 
 In. 
 
 Deg. Min. 
 
 In. 
 
 Deg. Min. 
 
 In. 
 
 Deg. Min. 
 
 In. 
 
 Deg. Min. 
 
 M 
 
 1 12 
 
 
 11 22 
 
 4^ 
 
 21 37 
 
 
 32 3 
 
 m 
 
 42 46 
 
 
 1 48 
 
 2^ 
 
 11 58 
 
 
 22 13 
 
 6% 
 
 32 40 
 
 
 43 24 
 
 to 
 
 2 24 
 
 
 12 34 
 
 % 
 
 22 50 
 
 
 33 17 
 
 9 
 
 44 3 
 
 
 3 00 
 
 H 
 
 13 10 
 
 
 23 27 
 
 7 
 
 33 54 
 
 
 44 42 
 
 % 
 
 3 36 
 
 
 13 46 
 
 5 
 
 24 3 
 
 
 34 33 
 
 & 
 
 45 21 
 
 
 4 11 
 
 3 
 
 14 22 
 
 
 24 39 
 
 M 
 
 35 10 
 
 
 45 59 
 
 i 
 
 4 47 
 
 
 14 58 
 
 1 A 
 
 25 16 
 
 
 35 47 
 
 to 
 
 46 38 
 
 
 5 23 
 
 y* 
 
 15 34 
 
 
 25 53 
 
 H 
 
 36 25 
 
 
 47 17 
 
 H 
 
 5 58 
 
 
 16 10 
 
 y* 
 
 26 30 
 
 
 37 3 
 
 % 
 
 47 56 
 
 
 6 34 
 
 y% 
 
 16 46 
 
 
 27 7 
 
 H 
 
 37 41 
 
 
 48 35 
 
 H 
 
 7 10 
 
 
 17 22 
 
 H 
 
 27 44 
 
 
 38 19 
 
 10 
 
 49 15 
 
 
 7 46 
 
 % 
 
 17 59 
 
 
 28 21 
 
 8 
 
 38 57 
 
 
 49 54 
 
 % 
 
 8 22 
 
 
 18 35 
 
 Q 
 
 28 58 
 
 
 39 35 
 
 M 
 
 50 34 
 
 
 8 58 
 
 4 
 
 19 12 
 
 
 29 35 
 
 X 
 
 40 13 
 
 
 51 13 
 
 2 
 
 9 34 
 
 
 19 48 
 
 M 
 
 30 11 
 
 
 40 51 
 
 to 
 
 51 53 
 
 
 10 10 
 
 M 
 
 20 24 
 
 
 30 49 
 
 to 
 
 41 29 
 
 
 52 33 
 
 y* 
 
 10 46 
 
 
 21 00 
 
 to 
 
 31 26 
 
 
 42 7 
 
 
 
 PROBLEM 9. To bisect a given 
 angle, as BAG (Fig. 57). 
 
 With A as a centre, and any radius, 
 describe an arc, as cb. With c and b as 
 centres, and any radius greater than 
 one-half of cb } describe two arcs inter- 
 secting in d. Draw from A a line Fig. 57 
 through d, and it will bisect the angle BA C. 
 
 PROBLEM 10. To bisect the angle contained between two lines, 
 
74 
 
 GEOMETRICAL PROBLEMS. 
 
 as AB and CD, when the vertex of the angle is not on the drawing 
 (Fig. 58). 
 
 Fig.58 
 
 Fig.59 
 
 Draw fe parallel to A B, and cd parallel to CD, so that the two 
 lines will intersect each other, as at i. Bisect the angle eid, as in 
 the preceding problem, and draw a line through i and o 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. 59). 6 
 
 With B and C as centres, and a radius N 
 equal to the given radius, describe two arcs B 
 intersecting at A . With A as a centre, and 
 the same radius, describe the arc be, which 
 will be found to pass through the given points, B and C. 
 
 PROBLEM 12. To find the centre of a given circle (Fig. 60). 
 
 Draw any chord in the circle, as ab, and bisect this chord by 
 the perpendicular cd. This line will pass through the centre 
 of the circle, and ef will be a diameter of the circle. Bisect ef, and 
 the centre o will be the centre of the circle. 
 Fig. 60 
 
 K 
 
 PROBLEM 13. To draw a circular arc through three given 
 points, as A, B, and C (Fig. 61). 
 
GEOMETRICAL PROBLEMS. 
 
 75 
 
 Draw a line from A to B and from B to C. Bisect AB and BC 
 by the lines aa and cc, and prolong these lines until they intersect 
 at o, which will be the centre for the arc sought. With o as a 
 centre, and Ao as a radius, describe the arc ABC. 
 
 PROBLEM 14. To describe a circular arc passing through three 
 given points, when the centre is not available, by means of a tri- 
 angle (Fig. 62). 
 
 Let A, B, and C 
 be the given points. 
 Insert two stiff pins 
 or nails at A and C. 
 Place two strips of 
 wood, SS, as shown 
 in the figure; one 
 against A , the other 
 against C, and in- 
 clined so that their 
 intersection shall 
 come at the third 
 point, B. Fasten the strips together at their intersection, and 
 nail a third strip, T, to their other ends, so as to make a firm 
 triangle. Place the pencil-point at B, and, keeping the edges of 
 the triangle against A and B, move the triangle to the left and 
 right, and the pencil will describe the arc sought. 
 
 When the points A and C are at the same distance from B, if a 
 strip of wood be nailed to the triangle, so that its edge de shall be 
 at right angles to a line joining A and C as the triangle is moved 
 one way or the other, the edge de will always point to the centre 
 of the circle. This principle is used in the perspective lineard. 
 
 PROBLEM 15. To find a circular arc which shall be tangent to 
 a given point, A, on a straight line, and 
 pass through a given point, C, outside the 
 line (Fig. 63). 
 
 Draw from A a line perpendicular to 
 the given line. Connect A and C by a 
 straight line, and bisect it by the perpen- 
 dicular ac. The point where these two 
 perpendiculars intersect will be the cen- 
 tre of the circle. 
 
 PROBLEM 16. To connect two parallel lines by a reversed curve 
 composed of two circular arcs of equal radius, and tangent to the 
 lines at given points, as A and B (Fig. 64). 
 
76 
 
 GEOMETRICAL PROBLEMS. 
 
 Join A and B, and divide the line into two equal parts at C. 
 Bisect CA and CB by 
 perpendiculars. At A 
 and B erect perpen- 
 dicular's to the given 
 lines, and the intersec- 
 tions a and b will be 
 the centres of the arcs 
 composing the re- 
 
 quired curve. 
 
 PROBLEM 17. On a given line, as AB. to construct a com- 
 pound curve of three arcs of circles, the radii of the two side ones 
 being equal and of a 
 given length, and their 
 centres in the given 
 line; the central arc 
 to pass through a 
 given point, C, on the 
 perpendicular bisect- 
 ing the given line, and 
 tangent to the other 
 two arcs (Fig. 65). 
 
 Draw the perpen- 
 dicular CD. Lay off 
 Aa, Bb, and Cc, each equal to the given radius of the side arcs; 
 join ac] bisect ac by a perpendicular, The intersection of this 
 line with the perpendicular CD will be the required centre of the 
 central arc. Through a and b draw the lines De and De'', from 
 a and b, with the given radius, equal to A a, Bb, describe the arcs 
 Ae r and Be', from D as a centre, and CD as a radius, describe the 
 arc eCe' which completes the curve required. 
 
 PROBLEM 18. To construct a triangle upon a given straight 
 line or base, the length of the two sides being given (Fig. 66). 
 
 Fig.66a Fig.GGb 
 
 First (an equilateral triangle, Fig. 66a). With the extremities 
 
GEOMETRICAL PROBLEMS. 
 
 A and B of the given line as centres, and A B as a radius, describe 
 arcs cutting each other at C. Join AC and BC, 
 
 Second (when the sides are unequal, Fig. 666). Let AD be the 
 given base, and the other two sides be equal to C and B. With 
 D as a centre, and a radius equal to C, describe an indefinite arc. 
 With A as a centre, and -B as a radius, describe an arc cutting the 
 first at E. Join E with A and D, and it will give the required 
 triangle. 
 
 PROBLEM 19. To describe a circle about a triangle (Fig. 67). 
 
 Bisect two of 'the sides, as AC and CB, of the triangle, and at 
 their centres erect perpendicular lines, as ae and be, intersecting 
 at e. With e as a centre, and eC as a radius, describe a circle, and 
 it will be found to pass through A and B. 
 
 Fig. 67 
 
 PROBLEM 20. To inscribe a circle in a triangle (Fig. 68). 
 
 Bisect two of the angles, A and B } of the triangle by lines cut- 
 ting each other at o. With o as a centre, and oe as a radius, 
 describe a circle, which will be found to just touch the other two 
 sides. 
 
 PROBLEM 21. To inscribe a square in a circle, and to describe 
 a circle about a square (Fig. 69). 
 
 To inscribe the square. Draw two diameters, A B and CD, at 
 right angles to each other. Join the points A, D, B, C, and we 
 have the inscribed square! 
 
 To describe the circle. Draw the diagonals as before, intersect- 
 ing at E, and, with E' as a centre and AE as a radius, describe the 
 circle. 
 
 PROBLEM 22. To inscribe a circle in a square, and to describe 
 a square about a circle (Fig. 70). 
 
 To inscribe the circle. Draw the diagonals A B and CD, inter- 
 secting at E. Draw the perpendicular EG to one of the sides. 
 Then with E as a centre, and EG as a radius, describe a circle, 
 which will be found to touch all four sides of the square. 
 
78 
 
 GEOMETRICAL PROBLEMS. 
 
 To describe the square. Draw two diameters, AB and CD, at 
 right angles to each other, and prolonged beyond the circumfer- 
 
 \X^ 
 
 "\/ 
 
 /\ 
 
 /\ 
 
 ' \ 
 
 / \ 
 
 / 
 
 <x \ , 
 
 v/ 
 
 \y 
 
 
 
 /V^ 
 
 _^\ 
 
 F 
 
 Fig. 70 
 
 ence. Draw the diameter GF, bisecting the angle CEA or BED. 
 Draw lines through G and F perpendicular to GF, and terminat- 
 ing in the diagonals. Draw AD and CB to complete the square. 
 
 PROBLEM 23. To inscribe a penta- 
 gon in a circle (Fig. 71). 
 
 Draw two diameters, A B and CD, at 
 right angles to each other. Bisect AO 
 at E. With E as a centre, and EC as a 
 radius, cut OB at F. With C as a centre 
 and CF as a radius, cut the circle at G 
 and H. With these points as centres, 
 and the same radius, cut the circle at I 
 and*/. Join 7, /, H, G, and C, and we 
 then have inscribed in the circle a regular pentagon. 
 
 PROBLEM 24. To inscribe a regular hexagon in a circle (Fig. 72). 
 
 Fig.72 
 
 Fig.73 
 
 SOLUTION. Lay off on the circumference the radius of the 
 circle six times, and connect the points. 
 
GEOMETRICAL PROBLEMS. 
 
 79 
 
 PROBLEM 25. To construct a regular hexagon upon a given 
 straight line, AB (Fig. 73). 
 
 From A and B, with a radius equal to AB, describe arcs cut- 
 ing at 0. With as a centre, and a radius equal to AB t de- 
 scribe a circle, and from A and B lay off the length AB on the 
 circumference of the circle, and join the points thus obtained. 
 The result will be a regular hexagon. 
 
 PROBLEM 26. To construct a regular octagon upon a given 
 straight line, AB (Fig. 74). 
 
 Produce the line AB both ways, and draw the perpendiculars 
 Aa and Bb, of indefinite length. Bisect the external angles at A 
 and B, and make the length of the lines equal to AB. From H 
 and C draw lines parallel to Aa, and equal in length to AB; and 
 
 f 
 Fig. 74- Fig.75 
 
 from the centres G and D describe arcs, with a radius AB, cut- 
 ting the perpendiculars A a and Bb in F and E. Join G^, .F#, 
 and ED. 
 
 PROBLEM 27. To make a regular octagon from a square (Fig. 75). 
 
 A 
 
 Fig.77 
 
 Draw the diagonals AD and BC, and from the corners A, B, 
 C, and D, with a radius equal to AO, describe arcs cutting the 
 
80 
 
 GEOMETRICAL PROBLEMS. 
 
 sides of the square in a, b, c, d, e, f, h, and i. Join these points 
 to complete the octagon. ' 
 
 PROBLEM 28. To inscribe a regular octagon in a circle (Fig. 76). 
 
 Draw two diameters, A B and CD, at right angles to each other. 
 Bisect the angles AOD and AOC by the diameters EF and GH. 
 Join A, E, Dj H, B, etc., for the inscribed figure. 
 
 PROBLEM 29. To inscribe a circle within a regular polygon. 
 
 First (when the polygon has an even number of sides, as in Fig. 
 77). Bisect two opposite sides at A and B } and draw AB, and 
 bisect it at C by a diagonal, DE, drawn between two opposite 
 angles. With the radius CA describe the circle as required. 
 
 Second (when the number of sides is odd, as in Fig. 78). Bisect 
 two of the sides at A and B, and draw 
 lines, AE and BD, to the opposite an- 
 gles, intersecting at C. With C as a cen- 
 tre, and CA as a radius, describe thep 
 circle as required. 
 
 PROBLEM 30. To describe a circle 
 without a regular polygon. 
 
 When the number of sides is even, 
 draw two diagonals from opposite an- 
 gles, as ED and GH (Fig. 77), inter- 
 secting at C; and from C, with CD as a 
 radius, describe the circle required. 
 
 When the number of sides is odd, find the centre, C, as in last 
 problem; and with C as a centre, and CD (Fig. 78) as a radius, 
 describe the circle required. 
 
GEOMETRICAL PROBLEMS. 
 
 81 
 
 
 PBOBLEMS 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. 
 
 IST METHOD (Fig. 79, the two axes, AB and CD, being giv- 
 en). On AB 
 and CD as di- 
 ameters, and 
 from the same 
 centre, 0, de- 
 scribe the cir- 
 cles AGBH and 
 CLDK. Take 
 any convenient 
 number of 
 points on the 
 circumference 
 of the outer cir- 
 cle, as b, V, b", 
 etc., and from 
 them draw lines 
 to the centre, O, 
 
 Fig. 79 cutting the in- 
 
 ner circle at the points a, a', a" , etc., respectively. From the points 
 bj b', etc., draw -lines parallel to the shorter axis; and from the 
 points a, a', etc., draw 
 lines parallel to the 
 longer axis, and inter- 
 secting the first set of 
 lines at c, c', c", etc. 
 These last points will be 
 points in the ellipse, 
 and, by obtaining a suf- 
 ficient number of them, 
 the ellipse can easily be 
 drawn. 
 
 2D METHOD (Fig. 80). 
 Take the straight 
 edge of a stiff piece of paper, cardboard, or wood, and from some 
 point as a, mark off ab equal to half the shorter diameter, and ac 
 equal to half the longer diameter. Place the straight edge so 
 
82 
 
 GEOMETRICAL PROBLEMS. 
 
 G 
 
 that the point b shall be on the longer diameter, and the point c 
 on the shorter : then will the point a be over a point in the 
 ellipse. Make on the paper a dot at a, and move the slip around, 
 always keeping the points b and c over the major and minor axes. 
 In this way any number of points in the ellipse may be ob- 
 tained, which may be connected by a curve drawn freehand. 
 
 3o METHOD (Fig. 81, given the two axes AB and CD). From 
 the point D as a centre, 
 and a radius AO, equal 
 to one-half of AB, de- 
 scribe an arc cutting 
 AB at F and F'. 
 These two points are 
 called the foci of the 
 ellipse. [One property 
 of the ellipse is, that the 
 sum of the distances of 
 any two points on the 
 circumference from the 
 foci is the same. Thus Fig. 81 
 
 F'D + DF = F'E + EF or F'G + GF.] Fix a couple of pins into 
 the axis AB at F and F f , and loop a thread or cord upon them 
 equal in length, when fastened to the pins, to A B, so as, when 
 stretched as per dotted line FDF', just to reach the extremity D 
 of the short axis. Place a pencil-point inside the chord, as at 
 E, and move the pencil along, always keeping the cord stretched 
 tight. In this way the pencil will trace the outline of the ellipse. 
 PROBLEM 32. To draw a tangent to an ellipse at a given point 
 Q on the curve (Fig. 
 
 82). 
 
 Let it be re- 
 quired to draw 
 a tangent at the 
 point E on the 
 ellipse shown in 
 Fig. 82. First 
 find the foci F 
 and F', as in 
 the third method 
 for describing an 
 ellipse, then from 
 E draw lines EF and EF' . Prolong EF' to a, so that Ea shall 
 
GEOMETRICAL PROBLEMS. 
 
 83 
 
 equal EF. Bisect the angle aEF as at b, and through b draw a 
 line touching the curve at E. This line will be the tangent re- 
 quired. If it were desired to draw a line normal to the curve at 
 E, as, for instance, the joint of an elliptical arch, bisect the angle 
 FEF f , and draw the bisecting line through E, and it will be the 
 normal to the curve, and the proper line for the joint of an 
 elliptical arch at that point. 
 
 PROBLEM 33. To draw a tangent to an ellipse from a given 
 point without the curve (Fig. 83). 
 
 'Fig.83 
 
 From the point T as a centre, and a radius equal to the distance 
 to the nearer focus F, describe a circle. From F f as a centre, and 
 a radius equal to the length of the longer axis, describe arcs cut- 
 ting the circle just described at a and b. Draw lines from F f to 
 a and 6, cutting the circumference of the ellipse at E and G. 
 Draw lines from T through E and G, and they will be the tan- 
 gents required. 
 
 PROBLEM 34. To describe an ellipse approximately, by means 
 of circular arcs. 
 
 First (with arcs of two radii, Fig. 84) . Take half the difference 
 of the two axes AB and CD, and set it off from the centre to a 
 and c on OA and OC; draw ac, and set off half ac to d; draw di 
 parallel to ac; set off Oe equal to Od; join ei, and draw em and 
 dm parallels to di and ie. On m as a centre, with a radius mC, 
 describe an arc through C, terminating in 1 and 2 ; and with i as 
 a centre, and id as a radius, describe an arc through D, termin- 
 ating in points 3 and 4. On d and e as centres describe arcs 
 
84 
 
 GEOMETRICAL PROBLEMS. 
 
 through A and B, connecting the points 1 -and 4, 2 and 3. The 
 four arcs thus described form approximately an ellipse. This 
 method does not apply satisfactorily when the conjugate .axis is 
 less than two-thirds of the transverse axis. 
 Fig.84 
 C 
 
 Another method of approximating an ellipse by means of arcs 
 of two radii, is shown in Fig. 84a, the axis AB, and the semi- 
 
 Fig. 84a. 
 
 minor axis OC being given. Draw the rectangle AabB, and 
 the diagonal CB. Lay off Cc equal to the difference between 
 OB and OC. Bisect cB at M , and erect the perpendicular YD, 
 intersecting CO produced at Y and 01?, at x. Make Ox'=0x. 
 Then will x, x', and Y be the three centres required, the curves 
 becoming tangent at D. This method gives a slightly fuller 
 curve at the haunches than the preceding one. 
 
GEOMETRICAL PROBLEMS. 
 
 85 
 
 Second (with arcs of three radii, Fig. 85). On the transverse 
 axis A B draw the rectangle AGEB, equal in height to OC, half 
 
 the conjugate axis. Draw GD perpendicular to AC. Set off OK 
 equal to OC, and on A K as a diameter describe the semicircle 
 ANK. Draw a radius parallel to OC, intersecting the semicircle 
 at N, and the line GE at P. Extend OC to L and to D. Set off 
 OM , equal to PN, and on D as a centre, with a radius DM, de- 
 scribe an arc. From A and B as centres, with a radius OL, inter- 
 sect this arc at a and 6. The points H, a, D, 6, //', are the cen- 
 tres of the arcs required. Produce the lines aH, Da, Db, bH', 
 and the spaces enclosed determine the lengths of each arc. This 
 process works well for nearly all ellipses. It is employed in 
 striking out vaults, stone arches, and bridges. 
 
 NOTE. In this example the point H' happens to coincide with the point 
 K, but this need not necessarily be the case. 
 
 The Parabola. 
 
 PROBLEM 35. To construct a parabola when the vertex A, the 
 axis AB, and a point, M, of the curve, are given (Fig. 86). 
 
 Construct the rectangle A BMC. Divide MC into any number 
 of equal parts, four for instance. Divide AC in like manner. 
 Connect Al, A2, and A3. Through 1', 2', 3', draw parallels to 
 
86 
 
 GEOMETRICAL PROBLEMS. 
 
 the axis. The intersections I, II, and III, of these lines, are 
 points in the required curve. 
 
 PROBLEM 36. To draw a tangent to a given point, II, of the 
 parabola (Fig. 86). 
 C 
 
 d 
 Fig.86 
 
 From the given point II let fall a perpendicular on the axis 
 at b. Extend the axis to the left of A. Make A a equal to A b. 
 Draw all, and it is the tangent required. 
 
 The lines perpendicular to the tangent are called normals. To 
 find the normal to any point I, having the tangent to any other 
 point, II. Draw the normal He. From I let fall a perpendicular 
 Id, on the axis AB. Lay off de equal to be. Connect le, an we 
 have the normal required. The tangent may be drawn at I by 
 laying off a perpendicular to the normal le at I. 
 The Hyperbola. 
 
 The hyperbola possesses the characteristic that if, from any 
 point, P, two straight lines be drawn to two fixed points, F and 
 F', the foci, their differ- 
 ence shall always be the 
 same. 
 
 PROBLEM 37. To de- 
 scribe an hyperbola 
 through a given vertex, 
 a, with the given differ- 
 ence ab, and one of the 
 foci, F (Fig. 87). 
 
 Draw the axis of the 
 hyperbola AB, with the 
 given distance ab and 
 the focus F marked on 
 it. From b lay off bF t 
 equal to aF for the F ' 9 ' 87 
 
 other focus. Take any point, as 1 on AB 3 and with al as 
 
a radius, and F as a centre, describe two short arcs above and 
 below the axis. With 61 as a radius, and F' as a centre, describe 
 arcs cutting those just described at P and P' . Take several 
 points, as 2, 3, and 4, and obtain the corresponding points P 2 , 
 P 3 , and P 4 in the same way. Join 
 these points with a curved line, and 
 it will be 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 line will be the tangent re- 
 quired. 
 
 The Cycloid. 
 
 The cycloid is the curve described 
 by a point in the circumference of a 
 circle rolling in a straight line. 
 PROBLEM 38. To describe a cy- 
 
 (Fig. 88). 
 
 Draw the straight line AB as the 
 base. Describe the generating circle 
 tangent to this line at the centre, and 
 through the centre of the circle, C, 
 draw the line EE parallel to the base. 
 Let fall a perpendicular from C upon 
 the base . Divide the semi-circumfer- 
 ence into any number of equal parts, 
 for instance, six. Lay off on A B and 
 CE distances Cl', 1'2', etc., equal to 
 the divisions of the circumference. 
 Draw the chords Dl, D2, etc. From 
 the points 1', 2', 3', on the line CE, 
 with radii equal to the generating 
 circle, describe arcs. From the 
 
 / 
 
 points 1', 2', 3', 4', 5', on the line BA, and with radii equal 
 respectively to the chords Dl, D2, D3, D4, D5, describe arcs 
 cutting the preceding, and the intersections will be points of 
 the curve required. 
 
GEOMETRICAL PROBLEMS. 
 
 TABLE OF CHORDS; Radius =1.0000. 
 
 M. 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 M. 
 
 0' 
 
 .0000 
 
 .0175 
 
 .0349 
 
 .0524 
 
 .0698 
 
 .0872 
 
 .1047 
 
 .1221 
 
 .1395 
 
 .1569 
 
 1743 
 
 0' 
 
 1 
 
 .0003 
 
 .0177 
 
 .0352 
 
 .0526 
 
 .0701 
 
 .0875 
 
 .1050 
 
 .1224 
 
 .1398 
 
 .1572 
 
 .1746 
 
 1 
 
 2 
 
 .0008 
 
 .0180 
 
 .0355 
 
 .0529 
 
 .0704 
 
 .0878 
 
 .1053 
 
 .1227 
 
 .1401 
 
 .1575 
 
 1749 
 
 2 
 
 3 
 
 .0009 
 
 .0183 
 
 .0358 
 
 .0532 
 
 .0707 
 
 .0881 
 
 .1055 
 
 .1230 
 
 .1404 
 
 .1578 
 
 .1752 
 
 3 
 
 4 
 
 .0012 
 
 .0186 
 
 .0361 
 
 .0535 
 
 .0710 
 
 .0884 
 
 .1058 
 
 .1233 
 
 .1407 
 
 .1581 
 
 .1755 
 
 4 
 
 5 
 
 .0015 
 
 .0189 
 
 .0364 
 
 .0538 
 
 .0713 
 
 .0837 
 
 .1051 
 
 .1235 
 
 .1410 
 
 .1584 
 
 .1758 
 
 rj 
 
 a 
 
 .0017 
 
 .0192 
 
 .0366 
 
 .0541 
 
 .0715 
 
 .0890 
 
 .1064 
 
 .1238 
 
 .1413 
 
 .1587 
 
 .1761 
 
 e 
 
 7 
 
 .0020 
 
 .0195 
 
 .0369 
 
 .0544 
 
 .0718 
 
 .0893 
 
 .1067 
 
 .1241 
 
 .1415 
 
 .1589 
 
 .1763 
 
 7 
 
 8 
 
 .0023 
 
 .0198 
 
 .0372 
 
 .0547 
 
 .0721 
 
 .0896 
 
 .1070 
 
 .1244 
 
 .1418 
 
 .1592 
 
 .1766 
 
 8 
 
 9 
 
 .0026 
 
 .0201 
 
 .0375 
 
 .0550 
 
 .0724 
 
 .0899 
 
 .1073 
 
 .1247 
 
 .1421 
 
 .1595 
 
 .1769 
 
 9 
 
 10 
 
 .0029 
 
 .0204 
 
 .0378 
 
 .0553 
 
 .0727 
 
 .0901 
 
 .1076 
 
 .1250 
 
 .1424 
 
 .1598 
 
 .1772 
 
 10 
 
 11 
 
 .0032 
 
 .0207 
 
 .0381 
 
 .0556 
 
 .0730 
 
 .0904 
 
 .1079 
 
 .1253 
 
 .1427 
 
 .1601 
 
 .1775 
 
 11 
 
 12 
 
 .0035 
 
 .0209 
 
 .0384 
 
 .0558 
 
 .0733 
 
 .0907 
 
 .1082 
 
 .1256 
 
 .1430 
 
 .1604 
 
 .1778 
 
 12 
 
 13 
 
 .0038 
 
 .0212 
 
 .0387 
 
 .0561 
 
 .0736 
 
 .0910 
 
 .1084 
 
 .1259 
 
 .1433 
 
 .1607 
 
 .1781 
 
 13 
 
 14 
 
 .0041 
 
 .0215 
 
 .0390 
 
 .0564 
 
 .0739 
 
 .0913 
 
 .1087 
 
 .1262 
 
 .1436 
 
 .1610 
 
 .1784 
 
 14 
 
 15 
 
 .0044 
 
 .0218 
 
 .0393 
 
 .0567 
 
 .0742 
 
 .0916 
 
 .1090 
 
 .1265 
 
 .1439 
 
 .1613 
 
 .1787 
 
 15 
 
 16 
 
 .0047 
 
 .0221 
 
 .0396 
 
 .0570 
 
 .0745 
 
 .0919 
 
 .1093 
 
 .1267 
 
 .1442 
 
 .1616 
 
 .1789 
 
 16 
 
 17 
 
 .0049 
 
 .022-1 
 
 .0398 
 
 .0573 
 
 .0747 
 
 .0922 
 
 .1096 
 
 .1270 
 
 .1444 
 
 .1618 
 
 .1792 
 
 17 
 
 18 
 
 .0052 
 
 .0227 
 
 .0401 
 
 .0576 
 
 .0750 
 
 .0925 
 
 .1099 
 
 .1273 
 
 J447 
 
 .1621 
 
 .1795 
 
 18 
 
 19 
 
 .0055 
 
 .0230 
 
 .0404 
 
 .0579 
 
 .0753 
 
 .0928 
 
 .1102 
 
 .1276 
 
 .1450 
 
 .1624 
 
 .1798 
 
 19 
 
 20 
 
 .0058 
 
 .0233 
 
 .0407 
 
 .0582 
 
 .0756 
 
 .0931 
 
 .1105 
 
 .1279 
 
 .1453 
 
 .1627 
 
 .1801 
 
 20 
 
 21 
 
 .0061 
 
 .0236 
 
 .0410 
 
 .0585 
 
 .0759 
 
 .0933 
 
 .1108 
 
 .1282 
 
 .1456 
 
 .1630 
 
 .1804 
 
 21 
 
 22 
 
 .0064 
 
 .0239 
 
 .0413 
 
 .0588 
 
 .0762 
 
 .0936 
 
 .1111 
 
 .1285 
 
 .1459 
 
 .1633 
 
 .1807 
 
 22 
 
 23 
 
 .0067 
 
 .0241 
 
 .0410 
 
 .0590 
 
 .0765 
 
 .0939 
 
 .1114 
 
 .1288 
 
 .1462 
 
 .1636 
 
 .1810 
 
 23 
 
 24 
 
 .0070 
 
 .0244 
 
 .0419 
 
 .0593 
 
 .0768 
 
 .0942 
 
 .1116 
 
 .1291 
 
 .1465 
 
 .1639 
 
 .1813 
 
 24 
 
 25 
 
 .0073 
 
 .0247 
 
 .0422 
 
 .0596 
 
 .0771 
 
 .0945 
 
 .1119 
 
 .1294 
 
 .1468 
 
 .1642 
 
 .1816 
 
 25 
 
 26 
 
 .0076 
 
 .0250 
 
 .0425 
 
 .0599 
 
 .0774 
 
 .0948 
 
 .1122 
 
 .1296 
 
 .1471 
 
 .1645 
 
 .1818 
 
 26 
 
 27 
 
 .0079 
 
 .0253 
 
 .0428 
 
 .0602 
 
 .0776 
 
 .0951 
 
 .1125 
 
 .1299 
 
 .1473 
 
 .1647 
 
 .1821 
 
 27 
 
 28 
 
 .0081 
 
 .0258 
 
 .0430 
 
 .0605 
 
 .0779 
 
 .0954 
 
 .1128 
 
 .1302 
 
 .1476 
 
 .1650 
 
 .1824 
 
 28 
 
 29 
 
 .0084 
 
 .0259 
 
 .0433 
 
 .0608 
 
 .0782 
 
 .0957 
 
 .1131 
 
 .1305 
 
 .1479 
 
 .1653 
 
 .1827 
 
 29 
 
 30 
 
 .0087 
 
 .0262 
 
 .0436 
 
 .0611 
 
 .0785 
 
 .0960 
 
 .1134 
 
 .1308 
 
 .1482 
 
 .1656 
 
 .1830 
 
 30 
 
 31 
 
 .0090 
 
 .0265 
 
 .0439 
 
 .0614 
 
 .0788 
 
 .0962 
 
 .1137 
 
 .1311 
 
 .1485 
 
 .1659 
 
 .1833 
 
 31 
 
 32 
 
 .0093 
 
 .0268 
 
 .0442 
 
 .0617 
 
 .0791 
 
 .0965 
 
 .1140 
 
 .1314 
 
 .1488 
 
 .1662 
 
 .1836 
 
 32 
 
 33 
 
 .0096 
 
 .0271 
 
 .0445 
 
 .0619 
 
 .0794 
 
 .0968 
 
 .1143 
 
 .1317 
 
 .1491 
 
 .1665 
 
 .1839 
 
 33 
 
 34 
 
 .0099 
 
 .0273 
 
 .0448 
 
 .0522 
 
 .0797 
 
 .0971 
 
 .1145 
 
 .1320 
 
 .1494 
 
 .1068 
 
 .1842 
 
 34 
 
 35 
 
 .0102 
 
 .0276 
 
 .0451 
 
 .0625 
 
 .0800 
 
 .0974 
 
 .1148 
 
 .1323 
 
 .1497 
 
 .1671 
 
 .1845 
 
 35 
 
 36 
 
 .0105 
 
 .0279 
 
 .0454 
 
 .0628 
 
 .0803 
 
 .0977 
 
 .1151 
 
 .1325 
 
 .1500 
 
 .1674 
 
 .1847 
 
 36 
 
 37 
 
 .0108 
 
 .0282 
 
 .0457 
 
 .0631 
 
 .0806 
 
 .0980 
 
 .1154 
 
 .1328 
 
 .1502 
 
 .1676 
 
 .1850 
 
 37 
 
 38 
 
 .0111 
 
 .0285 
 
 .0460 
 
 .0634 
 
 .0808 
 
 .0983 
 
 .1157 
 
 .1331 
 
 .1505 
 
 .1679 
 
 .1853 
 
 38 
 
 39 
 
 .0113 
 
 .0288 
 
 .0462 
 
 .0637 
 
 .0811 
 
 .0986 
 
 .1160 
 
 .1334 
 
 .1508 
 
 .1682 
 
 .1856 
 
 39 
 
 40 
 
 .0116 
 
 .0291 
 
 .0465 
 
 .0640 
 
 .0814 
 
 .0989 
 
 .1163 
 
 .1337 
 
 .1511 
 
 .1685 
 
 .1859 
 
 40 
 
 41 
 
 .0119 
 
 .0294 
 
 .0468 
 
 .0643 
 
 .0817 
 
 .0992 
 
 .1166 
 
 .1340 
 
 .1514 
 
 .1688 
 
 .1862 
 
 41 
 
 42 
 
 .0122 
 
 .0297 
 
 .0471 
 
 .0646 
 
 .0820 
 
 .0994 
 
 .1169 
 
 .1343 
 
 .1517 
 
 .1691 
 
 1865 
 
 42 
 
 43 
 
 .0125 
 
 .0300 
 
 .0474 
 
 .0549 
 
 .0823 
 
 .0997 
 
 .1172 
 
 .1346 
 
 .1520 
 
 .1694 
 
 .1868 
 
 43 
 
 41 
 
 .0128 
 
 .0303 
 
 .0477 
 
 .0651 
 
 .0326 
 
 .1000 
 
 .1175 
 
 .1349 
 
 .1523 
 
 .1697 
 
 .1871 
 
 44 
 
 45 
 
 .0131 
 
 .0305 
 
 .0480 
 
 .0654 
 
 .0829 
 
 .1003 
 
 .1177 
 
 .1352 
 
 .1526 
 
 .1700 
 
 .1873 
 
 45 
 
 46 
 
 .0134 
 
 .0308 
 
 .0483 
 
 .0657 
 
 .0832 
 
 .1006 
 
 .1180 
 
 .1355 
 
 .1529 
 
 .1703 
 
 .1876 
 
 46 
 
 47 
 
 .0137 
 
 .0311 
 
 .0486 
 
 .0660 
 
 .0835 
 
 .1009 
 
 .1183 
 
 .1357 
 
 .1531 
 
 .1705 
 
 .1879 
 
 47 
 
 48 
 
 .0140 
 
 .0314 
 
 .0489 
 
 .0663 
 
 .0838 
 
 .1012 
 
 .1186 
 
 .1360 
 
 .1534 
 
 .1708 
 
 .1882 
 
 48 
 
 49 
 
 .0143 
 
 .0317 
 
 .0492 
 
 .0666 
 
 .0840 
 
 .1015 
 
 .1189 
 
 .1363 
 
 .1537 
 
 .1711 
 
 .1885 
 
 49 
 
 50 
 
 .0145 
 
 .0320 
 
 .0494 
 
 .0669 
 
 .0843 
 
 .1018 
 
 .1192 
 
 .1366 
 
 .1540 
 
 .1714 
 
 .1888 
 
 50 
 
 51 
 
 .0148 
 
 .0323 
 
 .0497 
 
 .0672 
 
 .0846 
 
 .1021 
 
 .1195 
 
 .1369 
 
 .1543 
 
 .1717 
 
 .1891 
 
 51 
 
 52 
 
 .0151 
 
 .0326 
 
 .0500 
 
 .0675 
 
 .0849 
 
 .1023 
 
 .1198 
 
 .1372 
 
 .1546 
 
 .1720 
 
 .1894 
 
 52 
 
 53 
 
 .0154 
 
 .0329 
 
 .0503 
 
 .0678 
 
 .0852 
 
 .1026 
 
 .1201 
 
 .1375 
 
 .1549 
 
 .1723 
 
 .1897 
 
 53 
 
 5J 
 
 .0157 
 
 .0332 
 
 .0506 
 
 .0681 
 
 .0855 
 
 .1029 
 
 .1204 
 
 .1378 
 
 .1552 
 
 .1726 
 
 .1900 
 
 54 
 
 55 
 
 .0160 
 
 .0335 
 
 .0509 
 
 .0683 
 
 .0858 
 
 .1032 
 
 .1206 
 
 .1381 
 
 .1555 
 
 .1729 
 
 .1902 
 
 55 
 
 55 
 
 .0163 
 
 .0337 
 
 .0512 
 
 .0686 
 
 .0861 
 
 .1035 
 
 .1209 
 
 .1384 
 
 .1558 
 
 .1732 
 
 .1905 
 
 56 
 
 57 
 
 .0166 
 
 .0340 
 
 .0515 
 
 .0689 
 
 .0864 
 
 .1038 
 
 .1212 
 
 .1386 
 
 .1560 
 
 .1734 
 
 .1908 
 
 57 
 
 53 
 
 .0169 
 
 .0343 
 
 .0518 
 
 .0092 
 
 .0867 
 
 .1041 
 
 .1215 
 
 .1389 
 
 .1563 
 
 .1737 
 
 .1911 
 
 58 
 
 59 
 
 .0172 
 
 .0346 
 
 .0521 
 
 .0695 
 
 .0*69 
 
 .1044 
 
 .1218 
 
 .1392 
 
 .1566 
 
 .1740 
 
 .1914 
 
 59 
 
 60 
 
 .0175 
 
 .0349 
 
 .0524 
 
 .0698 
 
 .0872 
 
 .1047 
 
 .1221 
 
 .1395 
 
 .1509 
 
 .1743 
 
 .1917 
 
 60 
 
GEOMETRICAL PROBLEMS. 
 
 Table of Chords; Radius =1.0000 (continued). 
 
 M, 
 
 11 
 
 13 
 
 13 
 
 14 
 
 15 
 
 16 
 
 17 
 
 18? 
 
 19 
 
 20 
 
 21 
 
 M. 
 
 
 
 .1917 
 
 .2091 
 
 .2264 
 
 .2437 
 
 .2611 
 
 .2783 
 
 .2956 
 
 .3129 
 
 .3301 
 
 .3473 
 
 .3645 
 
 
 
 1 
 
 .1920 
 
 .2093 
 
 .2207 
 
 .2440 
 
 .2613 
 
 .2786 
 
 .2959 
 
 .3132 
 
 .3304 
 
 .3476 
 
 .3648 
 
 1 
 
 2 
 
 .1923 
 
 .2096 
 
 .2270 
 
 .2443 
 
 .2616 
 
 .2789 
 
 .2962 
 
 .3134 
 
 .3307 
 
 .3479 
 
 .3650 
 
 2 
 
 3 
 
 .1926 
 
 .2099 
 
 .2273 
 
 .2446 
 
 .2619 
 
 .2792 
 
 .2965 
 
 .3137 
 
 .3310 
 
 .3482 
 
 .3653 
 
 3 
 
 4 
 
 .1928 
 
 .2102 
 
 .2276 
 
 .2449 
 
 .2622 
 
 .2795 
 
 .2968 
 
 .3140 
 
 .3312 
 
 .3484 
 
 .3056 
 
 4 
 
 5 
 
 .1931 
 
 .2105 
 
 ,22?9 
 
 .2452 
 
 .2625 
 
 .2798 
 
 .2971 
 
 .3143 
 
 .3315 
 
 .3487 
 
 .3659 
 
 5 
 
 6 
 
 .1934 
 
 .2108 
 
 .2281 
 
 .2455 
 
 .2628 
 
 .2801 
 
 .2973 
 
 .3146 
 
 .3318 
 
 .3490 
 
 .3662 
 
 6 
 
 7 
 
 .1937 
 
 .2111 
 
 .2284 
 
 .2458 
 
 .2631 
 
 .2804 
 
 .2976 
 
 .3149 
 
 .3321 
 
 .3493 
 
 .3665 
 
 7 
 
 8 
 
 .1940 
 
 .2114 
 
 .2287 
 
 .2460 
 
 .2634 
 
 .2807 
 
 .2979 
 
 .3152 
 
 .3324 
 
 .3496 
 
 .3668 
 
 8 
 
 9 
 
 .1943 
 
 .2117 
 
 ,2290 
 
 .2463 
 
 .2636 
 
 .2809 
 
 .2982 
 
 .3155 
 
 .3327 
 
 .3499 
 
 .3670 
 
 9 
 
 10 
 
 .1946 
 
 .2119 
 
 .2293 
 
 .2466 
 
 .2639 
 
 .2812 
 
 .2985 
 
 .3157 
 
 .3330 
 
 .3502 
 
 .3673 
 
 10 
 
 11 
 
 .1949 
 
 .2122 
 
 '.2296 
 
 .2169 
 
 .2642 
 
 .2815 
 
 .2988 
 
 .3160 
 
 .3333 
 
 .3504 
 
 .3676 
 
 11 
 
 12 
 
 .1952 
 
 .2125 
 
 .2299 
 
 .2472 
 
 .2645 
 
 .2818 
 
 .2991 
 
 .3163 
 
 .3335 
 
 .3507 
 
 .3679 
 
 12 
 
 13 
 
 1Q55 
 
 .2128 
 
 .2302 
 
 .2475 
 
 .2648 
 
 ,2821 
 
 .2994 
 
 .3166 
 
 .3338 
 
 .3510 
 
 3682 
 
 13 
 
 14 
 
 .1957 
 
 .2131 
 
 .2305 
 
 .2478 
 
 .2651 
 
 .2824 
 
 .2996 
 
 .3169 
 
 .3341 
 
 .3513 
 
 .3685 
 
 14 
 
 15 
 
 .1960 
 
 .2134 
 
 .2307 
 
 .2481 
 
 .2654 
 
 .2827 
 
 .2999 
 
 .3172 
 
 .3344 
 
 .3516 
 
 .3688 
 
 15 
 
 10 
 
 .1963 
 
 .2137 
 
 .2310 
 
 .2484 
 
 .2657 
 
 .2^30 
 
 .3002 
 
 .3175 
 
 .3347 
 
 .3519 
 
 .3690 
 
 M 
 
 17 
 
 .1966 
 
 .2140 
 
 .2313 
 
 .2486 
 
 .2660 
 
 .2832 
 
 .3005 
 
 .3178 
 
 .3350 
 
 .3522 
 
 .3693 
 
 17 
 
 18 
 
 .1969 
 
 .2143 
 
 .2316 
 
 .2489 
 
 .2662 
 
 .2835 
 
 .3008 
 
 .3180 
 
 .3353 
 
 .3525 
 
 .3696 
 
 18 
 
 19 
 
 .1972 
 
 ,2146 
 
 .2319 
 
 .2492 
 
 .2665 
 
 .2838 
 
 .3011 
 
 .3183 
 
 .3355 
 
 .?527 
 
 .3699 
 
 19 
 
 20 
 
 .1975 
 
 .2148 
 
 .2322 
 
 .2495 
 
 .2668 
 
 .2841 
 
 .3014 
 
 .3186 
 
 .3358 
 
 .3530 
 
 .3702 
 
 20 
 
 21 
 
 .1978 
 
 .2151 
 
 .2325 
 
 .2498 
 
 .2671 
 
 .2844 
 
 .3017 
 
 .3189 
 
 .3361 
 
 .3533 
 
 .3705 
 
 21 
 
 22 
 
 .1981 
 
 .2154 
 
 .2328 
 
 .2501 
 
 .2674 
 
 .2847 
 
 .3019 
 
 .3192 
 
 .3364 
 
 .3536 
 
 .3708 
 
 22 
 
 23 
 
 .1983 
 
 .2157 
 
 .2331 
 
 .2504 
 
 .2677 
 
 .2850 
 
 .3022 
 
 .3195 
 
 .3367 
 
 .3539 
 
 .3710 
 
 23 
 
 24 
 
 .1986 
 
 .2160 
 
 .2333 
 
 .2507 
 
 .2680 
 
 .2853 
 
 .3025 
 
 .3198 
 
 .3370 
 
 .3542 
 
 .3713 
 
 24 
 
 25 
 
 .1989 
 
 .2163 
 
 .2336 
 
 .2510 
 
 .2683 
 
 .2855 
 
 .3028 
 
 .3200 
 
 .3373 
 
 .3545 
 
 .3716 
 
 25 
 
 26 
 
 .1992 
 
 .2166 
 
 .2339 
 
 .2512 
 
 .2685 
 
 .2858 
 
 .3031 
 
 .3203 
 
 .3376 
 
 .3547 
 
 .3719 
 
 26 
 
 27 
 
 .1995 
 
 .2169 
 
 .2342 
 
 .2515 
 
 .2688 
 
 .2861 
 
 .3034 
 
 .3206 
 
 .3378 
 
 .3550 
 
 .3722 
 
 27 
 
 28 
 
 .1998 
 
 .2172 
 
 .2345 
 
 .2518 
 
 .2691 
 
 .2864 
 
 .3037 
 
 .3209 
 
 .3381 
 
 .3553 
 
 .3725 
 
 28 
 
 29 
 
 .2001 
 
 .2174 
 
 .2348 
 
 ,2521 
 
 .2694 
 
 .2%7 
 
 .3040 
 
 .3212 
 
 3384 
 
 3556 
 
 3728 
 
 29 
 
 30 
 
 .2004 
 
 .2177 
 
 .2351 
 
 .2524 
 
 .2697 
 
 .2870 
 
 .3042 
 
 .3215 
 
 .3387 
 
 .3559 
 
 .3730 
 
 30 
 
 31 
 
 .2007 
 
 .2180 
 
 .2354 
 
 .2527 
 
 .2700 
 
 .2873 
 
 .3045 
 
 .3218 
 
 .3390 
 
 .3562 
 
 .3733 
 
 31 
 
 32 
 
 .2010 
 
 .2183 
 
 .2357 
 
 .2530 
 
 .2703 
 
 .2876 
 
 .3048 
 
 .3221 
 
 .3393 
 
 .3565 
 
 .3736 
 
 32 
 
 33 
 
 .2012 
 
 .2186 
 
 .2359 
 
 .2533 
 
 .2706 
 
 .2878 
 
 .3051 
 
 .3223 
 
 .3396 
 
 .3567 
 
 .3739 
 
 33 
 
 34 
 
 .2015 
 
 .2189 
 
 .2362 
 
 .2536 
 
 .2709 
 
 .2881 
 
 .3054 
 
 .3226 
 
 .3398 
 
 .3570 
 
 .3742 
 
 34 
 
 35 
 
 .2018 
 
 .2192 
 
 .2365 
 
 .2538 
 
 .2711 
 
 .2884 
 
 .3057 
 
 .3229 
 
 .3401 
 
 .3573 
 
 .3745 
 
 35 
 
 36 
 
 .2021 
 
 .2195 
 
 .2368 
 
 .2541 
 
 .2714 
 
 .2887 
 
 .3060 
 
 .3232 
 
 .3404 
 
 .3576 
 
 .3748 
 
 36 
 
 37 
 
 .2024 
 
 .2198 
 
 .2371 
 
 .2544 
 
 .2717 
 
 .2890 
 
 .3063 
 
 .3235 
 
 .3407 
 
 .3579 
 
 .3750 
 
 37 
 
 38 
 
 .2027 
 
 .2200 
 
 .2374 
 
 .2547 
 
 .2720 
 
 .2893 
 
 .3065 
 
 .3238 
 
 .3410 
 
 .3582 
 
 .3753 
 
 38 
 
 39 
 
 .2030 
 
 .2203 
 
 .2377 
 
 .2550 
 
 .2723 
 
 .2896 
 
 .3068 
 
 .3241 
 
 .3413 
 
 .3585 
 
 .3756 
 
 39 
 
 40 
 
 .2033 
 
 .2206 
 
 .2380 
 
 .2553 
 
 .2726 
 
 .2899 
 
 .3071 
 
 .3244 
 
 .3416 
 
 .3587 
 
 .3759 
 
 40 
 
 41 
 
 .2036 
 
 .2209 
 
 .2383 
 
 .2556 
 
 .2729 
 
 .2902 
 
 .3074 
 
 .3246 
 
 .3419 
 
 .3590 
 
 .3762 
 
 41 
 
 42 
 
 .2038 
 
 .2212 
 
 .2385 
 
 .2559 
 
 .2732 
 
 .2904 
 
 .3077 
 
 .3249 
 
 .3421 
 
 .3593 
 
 .3765 
 
 42 
 
 43 
 
 .2041 
 
 .2215 
 
 .2388 
 
 .2561 
 
 .2734 
 
 .2907 
 
 .3080 
 
 .3252 
 
 .3424 
 
 .3596 
 
 .3768 
 
 43 
 
 44 
 
 .2044 
 
 .2218 
 
 .2391 
 
 .2564 
 
 .2737 
 
 .2910 
 
 .3083 
 
 .3255 
 
 .3427 
 
 .3599 
 
 .3770 
 
 44 
 
 45 
 
 .2047 
 
 .2221 
 
 .2391 
 
 .2567 
 
 .2740 
 
 .2913 
 
 .3086 
 
 .3258 
 
 .3430 
 
 .3602 
 
 .3773 
 
 45 
 
 46 
 
 .2050 
 
 .2224 
 
 .2397 
 
 .2570 
 
 .2743 
 
 .2916 
 
 .3088 
 
 .3261 
 
 .3433 
 
 .3605 
 
 3776 
 
 46 
 
 47 
 
 .2053 
 
 .2226 
 
 .2400 
 
 .2573 
 
 .2746 
 
 .2919 
 
 .3091 
 
 .3264 
 
 .3436 
 
 .3608 
 
 .3779 
 
 47 
 
 48 
 
 .2058 
 
 .2229 
 
 .2408 
 
 .2576 
 
 .2749 
 
 .2922 
 
 .3094 
 
 .3267 
 
 .3439 
 
 .3610 
 
 .3782 
 
 48 
 
 49 
 
 .2059 
 
 .2232 
 
 .2406 
 
 .2579 
 
 .2752 
 
 .2925 
 
 .3097 
 
 .3269 
 
 .3441 
 
 .3613 
 
 .3785 
 
 49 
 
 50 
 
 .2062 
 
 .2235 
 
 .2409 
 
 .2582 
 
 .2755 
 
 .2927 
 
 .3100 
 
 .3272 
 
 .3444 
 
 .3616 
 
 .3788 
 
 50 
 
 51 
 
 .2065 
 
 .2238 
 
 .2411 
 
 .2585 
 
 .275S 
 
 .2930 
 
 .3103 
 
 .3275 
 
 .3447 
 
 .3619 
 
 3790 
 
 51 
 
 52 
 
 .2067 
 
 .2241 
 
 .2414 
 
 .2587 
 
 .2760 
 
 .2933 
 
 .3106 
 
 .3278 
 
 .3450 
 
 .3622 
 
 .3793 
 
 52 
 
 53 
 
 .2070 
 
 .2244 
 
 .2417 
 
 .2590 
 
 .2763 
 
 .2936 
 
 .3109 
 
 .3281 
 
 .3453 
 
 .3625 
 
 .3796 
 
 53 
 
 54 
 
 .2073 
 
 .2247 
 
 .2420 
 
 .2593 
 
 .2766 
 
 .2939 
 
 .3111 
 
 .3284 
 
 .3456 
 
 .3628 
 
 .3799 
 
 54 
 
 55 
 
 .2076 
 
 .2250 
 
 .2423 
 
 .2596 
 
 .2769 
 
 .2942 
 
 .3114 
 
 .3287 
 
 .3459 
 
 .3630 
 
 .3802 
 
 55 
 
 56 
 
 .2079 
 
 .2253 
 
 .2426 
 
 .2599 
 
 .2772 
 
 .2045 
 
 .3117 
 
 .3289 
 
 .3462 
 
 .3633 
 
 .3805 
 
 56 
 
 57 
 
 .2082 
 
 .2255 
 
 .2429 
 
 .2602 
 
 .2775 
 
 .2948 
 
 .3120 
 
 .3292 
 
 .3464 
 
 .3636 
 
 .3808 
 
 57 
 
 58 
 
 .2085 
 
 .2258 
 
 .2432 
 
 .2605 
 
 .2778 
 
 .2950 
 
 .3123 
 
 .3295 
 
 .3467 
 
 .3639 
 
 .3810 
 
 58 
 
 59 
 
 .2088 
 
 .2261 
 
 .2434 
 
 .2608 
 
 .2781 
 
 .2953 
 
 .3126 
 
 .3298 
 
 .3470 
 
 .3642 
 
 .3813 
 
 59 
 
 60 
 
 .2091 
 
 .2264 
 
 .2437 
 
 .2611 
 
 .2783 
 
 .2956 
 
 .3129 
 
 .3301 
 
 .3473 
 
 .3645 
 
 .3816 
 
 60 
 
90 
 
 GEOMETRICAL PROBLEMS. 
 
 Table of Chords; Radius =1.0000 (continued) 
 
 M. 
 
 22 
 
 23 
 
 24 
 
 25 
 
 26 
 
 27 
 
 38 
 
 29 
 
 30 
 
 31 
 
 32 
 
 M. 
 
 0' 
 
 .3S16 
 
 .3087 
 
 .4158 
 
 .4329 
 
 .4499 
 
 .4669 
 
 .4838 
 
 .5008 
 
 .5176. 
 
 .5345 
 
 .5513 
 
 0' 
 
 1 
 
 .3819 
 
 .3990 
 
 .4161 
 
 .4332 
 
 .4502 
 
 .4672 
 
 .4841 
 
 .5010 
 
 .5179 
 
 .5348 
 
 .5516 
 
 1 
 
 2 
 
 3822 
 
 .3993 
 
 .4164 
 
 .4334 
 
 .4505 
 
 .4675 
 
 .4844 
 
 .5013 
 
 .5182 
 
 .5350 
 
 5518 
 
 2 
 
 3 
 
 .3825 
 
 .3996 
 
 .4167 
 
 .4337 
 
 .4508 
 
 .4677 
 
 .4847 
 
 .5016 
 
 .5185 
 
 .5353 
 
 .5521 
 
 3 
 
 4 
 
 .3828 
 
 .3999 
 
 .4170 
 
 .4340 
 
 .4510 
 
 .4680 
 
 .4850 
 
 .5019 
 
 .5188 
 
 .5350 
 
 .5524 
 
 4 
 
 5 
 
 .3830 
 
 .4002 
 
 .4172 
 
 .4343 
 
 .4513 
 
 .4683 
 
 .4853 
 
 .5022 
 
 .5190 
 
 .5359 
 
 .5527 
 
 5 
 
 6 
 
 3833 
 
 .4004 
 
 .4175 
 
 .4316 
 
 .4516 
 
 .4686 
 
 .4855 
 
 .5024 
 
 .5193 
 
 .5362 
 
 5530 
 
 6 
 
 7 
 
 .3836 
 
 .4007 
 
 .4178 
 
 .4349 
 
 .4519 
 
 .4689 
 
 .4858 
 
 .5027 
 
 .5196 
 
 .5364 
 
 .5532 
 
 7 
 
 8 
 
 .3839 
 
 .4010 
 
 .4181 
 
 .4352 
 
 .4522 
 
 .4692 
 
 .4361 
 
 .5030 
 
 .5199 
 
 .5367 
 
 .5535 
 
 8 
 
 9 
 
 .3842 
 
 .4013 
 
 .4184 
 
 .4354 
 
 .4525 
 
 .4694 
 
 .4864 
 
 .5033 
 
 .5202 
 
 .5370 
 
 .5538 
 
 9 
 
 10 
 
 .3845 
 
 .4016 
 
 .4187 
 
 .4357 
 
 .4527 
 
 .4697 
 
 .4867 
 
 .5036 
 
 .5204 
 
 .5373 
 
 .5541 
 
 10 
 
 11 
 
 .3848 
 
 .4019 
 
 .4190 
 
 .4360 
 
 .4530 
 
 .4700 
 
 .4869 
 
 .5039 
 
 .5207 
 
 .5376 
 
 .5543 
 
 11 
 
 12 
 
 .3850 
 
 .4022 
 
 .4192 
 
 .4363 
 
 .4533 
 
 .4703 
 
 .4872 
 
 .5041 
 
 .5210 
 
 .5378 
 
 .5546 
 
 12 
 
 13 
 
 .3853 
 
 .4024 
 
 .4195 
 
 .1369 
 
 .4536 
 
 .4708 
 
 .4875 
 
 .5044 
 
 .5213 
 
 .5381 
 
 .5549 
 
 13 
 
 14 
 
 .3856 
 
 .4027 
 
 .4193 
 
 .4369 
 
 .4539 
 
 .4703 
 
 .4878 
 
 .5047 
 
 .5216 
 
 .5384 
 
 .5552 
 
 14 
 
 15 
 
 .3859 
 
 .4030 
 
 .4201 
 
 .4371 
 
 .4542 
 
 .4711 
 
 .4881 
 
 .5050 
 
 .5219 
 
 .5387 
 
 .5555 
 
 15 
 
 16 
 
 .3862 
 
 .4033 
 
 .4201 
 
 .4374 
 
 .4514 
 
 .4714 
 
 .4884 
 
 .5053 
 
 .5221 
 
 .5390 
 
 .5557 
 
 16 
 
 17 
 
 .3865 
 
 .4035 
 
 .4207 
 
 .4377 
 
 .4517 
 
 .4717 
 
 .4886 
 
 .5055 
 
 .5224 
 
 .5392 
 
 .5560 
 
 17 
 
 18 
 
 .3868 
 
 .4039 
 
 .4203 
 
 .4330 
 
 .4550 
 
 .4720 
 
 .4889 
 
 .5058 
 
 .5227 
 
 .5395 
 
 .5563 
 
 18 
 
 19 
 
 .3870 
 
 .4042 
 
 .4212 
 
 .4383 
 
 .4553 
 
 .4723 
 
 .4892 
 
 .5061 
 
 .5230 
 
 .5398 
 
 .5566 
 
 19 
 
 20 
 
 .3873 
 
 .4044 
 
 .4215 
 
 .4386 
 
 .4556 
 
 .4725 
 
 .4895 
 
 .5064 
 
 .5233 
 
 .5401 
 
 .5569 
 
 20 
 
 21 
 
 .3876 
 
 .4047 
 
 .4218 
 
 .4388 
 
 .4559 
 
 .4728 
 
 .4898 
 
 .5067 
 
 .5235 
 
 .5404 
 
 5571 
 
 21 
 
 22 
 
 .3879 
 
 .4050 
 
 .4221 
 
 .4391 
 
 .4561 
 
 .4731 
 
 .4901 
 
 .5070 
 
 .5238 
 
 .5406 
 
 .5574 
 
 22 
 
 23 
 
 .3882 
 
 .4053 
 
 .4224 
 
 .4394 
 
 .4564 
 
 .4734 
 
 .4903 
 
 .5072 
 
 .5241 
 
 .5409 
 
 .5577 
 
 23 
 
 24 
 
 .3885 
 
 .4050 
 
 .4226 
 
 .4397 
 
 .4567 
 
 .4737 
 
 .4906 
 
 .5075 
 
 .5244 
 
 .5412 
 
 .5580 
 
 24 
 
 25 
 
 .3888 
 
 .4059 
 
 .4229 
 
 .4400 
 
 .4570 
 
 .4740 
 
 .4909 
 
 .5078 
 
 .5247 
 
 .5415 
 
 .5583 
 
 25 
 
 26 
 
 .3890 
 
 .4C61 
 
 .4232 
 
 .4403 
 
 .4573 
 
 .4742 
 
 .4912 
 
 .5081 
 
 .5249 
 
 .5418 
 
 .5585 
 
 26 
 
 27 
 
 .3893 
 
 .4064 
 
 .4235 
 
 .4105 
 
 .4576 
 
 .4745 
 
 .4915 
 
 .5084 
 
 .5252 
 
 .5420 
 
 .5588 
 
 27 
 
 23 
 
 .3396 
 
 .4067 
 
 .4233 
 
 .4408 
 
 .4578 
 
 .4748 
 
 .4917 
 
 .5080 
 
 .5255 
 
 .5423 
 
 .5591 
 
 28 
 
 29 
 
 .3899 
 
 .4070 
 
 .4241 
 
 .4411 
 
 .4581 
 
 .4751 
 
 .4920 
 
 .5089 
 
 .5258 
 
 .5426 
 
 .5594 
 
 29 
 
 30 
 
 .3902 
 
 .4073 
 
 .4244 
 
 .4414 
 
 .4584 
 
 .4754 
 
 .4923 
 
 .5092 
 
 .5261 
 
 .5429 
 
 .5597 
 
 30 
 
 31 
 
 .3905 
 
 .4076 
 
 .4246 
 
 .4417 
 
 .4587 
 
 .4757 
 
 .4926 
 
 .5095 
 
 .5263 
 
 .5432 
 
 .5599 
 
 31 
 
 32 
 
 .3908 
 
 .4079 
 
 .4249 
 
 .4420 
 
 .4590 
 
 .4759 
 
 .4929 
 
 .5098 
 
 .5266 
 
 .5434 
 
 .5602 
 
 32 
 
 33 
 
 .3910 
 
 .4081 
 
 .4252 
 
 .4422 
 
 .4593 
 
 .4762 
 
 .4932 
 
 .5100 
 
 .5269 
 
 .5437 
 
 .5605 
 
 33 
 
 34 
 
 .3913 
 
 .4084 
 
 .4255 
 
 .4425 
 
 .4595 
 
 .4765 
 
 .4934 
 
 .5103 
 
 .5272 
 
 .5440 
 
 .5608 
 
 34 
 
 35 
 
 .3916 
 
 .4087 
 
 .4258 
 
 .4428 
 
 .4598 
 
 .4768 
 
 .4937 
 
 .5106 
 
 .5275 
 
 .5443 
 
 .5611 
 
 35 
 
 36 
 
 .3919 
 
 .4090 
 
 .4261 
 
 .4431 
 
 .4601 
 
 .4771 
 
 .4940 
 
 .5109 
 
 .5277 
 
 .5446 
 
 .5613 
 
 36 
 
 37 
 
 .3922 
 
 .4093 
 
 .4263 
 
 .4134 
 
 .4601 
 
 .4773 
 
 .4943 
 
 .5112 
 
 .5280 
 
 .5448 
 
 .5616 
 
 37 
 
 38 
 
 .3925 
 
 .4096 
 
 .4268 
 
 .4137 
 
 .4607 
 
 .4776 
 
 .4946 
 
 .5115 
 
 .5283 
 
 .5451 
 
 .5619 
 
 38 
 
 39 
 
 .3927 
 
 .4093 
 
 .4269 
 
 .4439 
 
 .4309 
 
 .4779 
 
 .4948 
 
 .5117 
 
 .5286 
 
 .5454 
 
 .5622 
 
 39 
 
 40 
 
 .3930 
 
 .4101 
 
 .4272 
 
 .4442 
 
 .4612 
 
 .4782 
 
 .4951 
 
 .5120 
 
 .5289 
 
 .5457 
 
 .5625 
 
 40 
 
 41 
 
 .3933 
 
 .4104 
 
 .4275 
 
 .4445 
 
 .4615 
 
 .4785 
 
 .4954 
 
 .5123 
 
 .5291 
 
 .5460 
 
 .5627 
 
 41 
 
 42 
 
 .3936 
 
 .4107 
 
 .4278 
 
 .4418 
 
 .4613 
 
 .4788 
 
 .4957 
 
 .5126 
 
 .5294 
 
 .5402 
 
 .5630 
 
 42 
 
 43 
 
 .3939 
 
 .4110 
 
 .4230 
 
 .4451 
 
 .4621 
 
 .4790 
 
 .4960 
 
 .5129 
 
 .5297 
 
 .5465 
 
 .5633 
 
 43 
 
 44 
 
 .3942 
 
 .4113 
 
 .4283 
 
 .4454 
 
 .4624 
 
 .4793 
 
 .4963 
 
 .5131 
 
 .5300 
 
 .5468 
 
 .5636 
 
 41 
 
 45 
 
 .3945 
 
 .4116 
 
 .4286 
 
 .4456 
 
 .4626 
 
 .4796 
 
 .4965 
 
 .5134 
 
 .5303 
 
 .5471 
 
 .5638 
 
 45 
 
 46 
 
 .3947 
 
 .4118 
 
 .4289 
 
 .4459 
 
 .4629 
 
 .4799 
 
 .4968 
 
 .5137 
 
 .5303 
 
 .5474 
 
 .5641 
 
 46 
 
 47 
 
 .3950 
 
 .4121 
 
 .4292 
 
 .4462 
 
 .4632 
 
 .4802 
 
 .4971 
 
 .5140 
 
 .5308 
 
 .5476 
 
 .5644 
 
 -17 
 
 48 
 
 .3953 
 
 .4124 
 
 .4295 
 
 .4465 
 
 .4635 
 
 .4805 
 
 .4974 
 
 .5143 
 
 .5311 
 
 .5479 
 
 .5647 
 
 48 
 
 49 
 
 .3953 
 
 .4127 
 
 .4298 
 
 .4168 
 
 .4638 
 
 .4807 
 
 .4977 
 
 .5145 
 
 .5314 
 
 .5482 
 
 .5650 
 
 49 
 
 50 
 
 .3959 
 
 .4130 
 
 .4300 
 
 .4471 
 
 .4641 
 
 .4810 
 
 .4979 
 
 .5148 
 
 .5317 
 
 .5485 
 
 .5652 
 
 50 
 
 51 
 
 .3962 
 
 .4133 
 
 .4303 
 
 .4474 
 
 .4643 
 
 .4813 
 
 .4982 
 
 .5151 
 
 .5320 
 
 .5488 
 
 .5655 
 
 51 
 
 52 
 
 .3965 
 
 .4135 
 
 .4308 
 
 .4476 
 
 .4646 
 
 .4816 
 
 .4985 
 
 .5154 
 
 .5322 
 
 .5490 
 
 .5658 
 
 52 
 
 53 
 
 .3967 
 
 .4138 
 
 .4309 
 
 .4479 
 
 .1649 
 
 .48"19 
 
 .4988 
 
 .5157 
 
 .5325 
 
 .5493 
 
 .5661 
 
 53 
 
 54 
 
 .3970 
 
 .4141 
 
 .4312 
 
 .4182 
 
 .4652 
 
 .4822 
 
 .4991 
 
 .5160 
 
 .5328 
 
 .5490 
 
 .5664 
 
 54 
 
 55 
 
 .3973 
 
 .4144 
 
 .4315 
 
 .4485 
 
 .4655 
 
 .4824 
 
 .4994 
 
 .5162 
 
 .5331 
 
 .5499 
 
 .5666 
 
 55 
 
 56 
 
 .3976 
 
 .4147 
 
 .4317 
 
 .4488 
 
 .4658 
 
 .4827 
 
 .4996 
 
 .5165 
 
 .5334 
 
 .5502 
 
 .5669 
 
 56 
 
 57 
 
 .3979 
 
 .4150 
 
 .4320 
 
 .4491 
 
 .4660 
 
 .4830 
 
 .4999 
 
 .5168 
 
 .5336 
 
 .5504 
 
 .5672 
 
 57 
 
 58 
 
 .3982 
 
 .4153 
 
 .4323 
 
 .4193 
 
 .4663 
 
 .4833 
 
 .5002 
 
 .5171 
 
 .5339 
 
 .5507 
 
 .5675 
 
 58 
 
 59 
 
 .3985 
 
 .4155 
 
 .4326 
 
 .4496 
 
 .4666 
 
 .4836 
 
 .5005 
 
 .5174 
 
 .5342 
 
 .5510 
 
 .5678 
 
 59 
 
 60 
 
 .3987 
 
 .4158 
 
 .4329 
 
 .4499 
 
 .4669 
 
 .4838 
 
 .5008 
 
 .5176 
 
 .5345 
 
 .5513 
 
 .5680 
 
 60 
 
GEOMETRICAL PROBLEMS. 
 
 91 
 
 Table of Chords; Radius= 1.0000 (continued). 
 
 M. 
 
 33 
 
 34 
 
 35 
 
 36 
 
 37 
 
 38 
 
 39 
 
 40 
 
 41 
 
 43 
 
 43 
 
 M. 
 
 0' 
 
 .5680 
 
 .5847 
 
 .6014 
 
 .6180 
 
 .6346 
 
 .6511 
 
 .6676 
 
 .6840 
 
 .7004 
 
 .7167 
 
 .7330 
 
 0' 
 
 1 
 
 .5683 
 
 .5850 
 
 .6017 
 
 .6183 
 
 .6349 
 
 .6514 
 
 .6679 
 
 .6843 
 
 .7007 
 
 .7170 
 
 .7333 
 
 1 
 
 2 
 
 .5686 
 
 .5853 
 
 .6020 
 
 .6186 
 
 .6352 
 
 .6517 
 
 .6682 
 
 .6840 
 
 .7010 
 
 .7173 
 
 .7335 
 
 2 
 
 3 
 
 .5689 
 
 '.5856 
 
 .0022 
 
 .6189 
 
 .6354 
 
 .6520 
 
 .6684 
 
 .0849 
 
 .7012 
 
 .7176 
 
 .7338 
 
 3 
 
 4 
 
 .5691 
 
 .5859 
 
 .6025 
 
 .6191 
 
 .6357 
 
 .6522 
 
 .6687 
 
 .6851 
 
 .7015 
 
 .7178 
 
 .7341 
 
 4 
 
 5 
 
 .5694 
 
 .5861 
 
 .6028 
 
 .6194 
 
 .6360 
 
 .6525 
 
 .6090 
 
 .6854 
 
 .7018 
 
 .7181 
 
 .7344 
 
 5 
 
 6 
 
 .5697 
 
 .5864 
 
 .6031 
 
 .6197 
 
 .6363 
 
 .6528 
 
 .0093 
 
 .0857 
 
 .7020 
 
 .7184 
 
 .7346 
 
 6 
 
 7 
 
 .5700 
 
 .5867 
 
 .6034 
 
 .6200 
 
 .6365 
 
 .6531 
 
 .0095 
 
 .0800 
 
 .7023 
 
 .7186 
 
 .7349 
 
 7 
 
 8 
 
 .5703 
 
 .5870 
 
 .6036 
 
 .6202 
 
 .6368 
 
 .6533 
 
 .0098 
 
 .0802 
 
 .7026 
 
 .7189 
 
 7352 
 
 8 
 
 9 
 
 .5705 
 
 .5872 
 
 .6039 
 
 .6205 
 
 .6371 
 
 .6536 
 
 .6701 
 
 .6865 
 
 .7029 
 
 .7192 
 
 .7354 
 
 9 
 
 10 
 
 .5708 
 
 .5875 
 
 .6042 
 
 .6208 
 
 .6374 
 
 .6539 
 
 .6704 
 
 .6868 
 
 .7031 
 
 .7195 
 
 .7357 
 
 10 
 
 11 
 
 .5711 
 
 .5878 
 
 .6045 
 
 .6211 
 
 .6376 
 
 .6542 
 
 .6700 
 
 .6870 
 
 .7034 
 
 .7197 
 
 .7360 
 
 11 
 
 12 
 
 .5714 
 
 .5831 
 
 .6047 
 
 .6214 
 
 .6379 
 
 .C544 
 
 .6709 
 
 .6873 
 
 .7037 
 
 .7200 
 
 .7302 
 
 12 
 
 13 
 
 .5717 
 
 .5884 
 
 .6050 
 
 .6216 
 
 .6382 
 
 .6547 
 
 .6712 
 
 .0876 
 
 .7040 
 
 .7203 
 
 .7365 
 
 13 
 
 14 
 
 .5719 
 
 .5886 
 
 .6053 
 
 .6219 
 
 .6385 
 
 .6550 
 
 .6715 
 
 .6879 
 
 .7042 
 
 .7205 
 
 .7368 
 
 14 
 
 15 
 
 .5722 
 
 .5889 
 
 .6056 
 
 .6222 
 
 .6387 
 
 .6553 
 
 .6717 
 
 .6881 
 
 .7045 
 
 .7208 
 
 .7371 
 
 15 
 
 10 
 
 .5725 
 
 .5892 
 
 .6058 
 
 .6225 
 
 .0390 
 
 .6555 
 
 .6720 
 
 .6884 
 
 .7048 
 
 .7211 
 
 .7373 
 
 16 
 
 17 
 
 .5728 
 
 .5895 
 
 .6061 
 
 .6227 
 
 .0393 
 
 .6558 
 
 .6723 
 
 .6887 
 
 .7050 
 
 .7214 
 
 .7376 
 
 17 
 
 18 
 
 .5730 
 
 .5897 
 
 .6064 
 
 .6230 
 
 .6396 
 
 .6561 
 
 .6725 
 
 .6890 
 
 .7053 
 
 .7216 
 
 .7379 
 
 18 
 
 19 
 
 .5733 
 
 .5900 
 
 .6067 
 
 .6233 
 
 .6398 
 
 .6504 
 
 .6728 
 
 .6892 
 
 .7056 
 
 .7219 
 
 .7381 
 
 19 
 
 20 
 
 .5736 
 
 .5903 
 
 .6070 
 
 .6236 
 
 .6401 
 
 .6566 
 
 .6731 
 
 .6895 
 
 .7059 
 
 .7222 
 
 .7384 
 
 20 
 
 21 
 
 .5739 
 
 .5906 
 
 .6072 
 
 .6238 
 
 .6404 
 
 .6509 
 
 .6734 
 
 .6898 
 
 .7061 
 
 .7224 
 
 .7387 
 
 21 
 
 22 
 
 .5742 
 
 .5909 
 
 .6075 
 
 .6241 
 
 .6407 
 
 .6572 
 
 .0730 
 
 .6901 
 
 .7064 
 
 .7227 
 
 .7390 
 
 22 
 
 23 
 
 .5744 
 
 .5911 
 
 .6078 
 
 .6244 
 
 .6410 
 
 .6575 
 
 .^739 
 
 .6903 
 
 .7067 
 
 .7230 
 
 .7392 
 
 23 
 
 24 
 
 .5747 
 
 .5914 
 
 .6081 
 
 .6247 
 
 .6412 
 
 .0577 
 
 .0742 
 
 .6900 
 
 .7069 
 
 .7232 
 
 .7395 
 
 24 
 
 25 
 
 .5750 
 
 .5917 
 
 .G083 
 
 .6249 
 
 .6415 
 
 .6580 
 
 .6745 
 
 .0909 
 
 .7072 
 
 .7235 
 
 .7398 
 
 25 
 
 26 
 
 .5753 
 
 .5920 
 
 .6086 
 
 .0252 
 
 .6418 
 
 .6583 
 
 .0747 
 
 .6911 
 
 .7075 
 
 .7238 
 
 .7400 
 
 26 
 
 27 
 
 .5756 
 
 .5922 
 
 .6089 
 
 .6255 
 
 .6421 
 
 .6580 
 
 .0750 
 
 .6914 
 
 .7078 
 
 .7241 
 
 .7403 
 
 27 
 
 2S 
 
 .5758 
 
 .5925 
 
 .6092 
 
 .6258 
 
 .6423 
 
 .6588 
 
 .6753 
 
 .6917 
 
 .7080 
 
 .7243 
 
 .7406 
 
 28 
 
 29 
 
 .5761 
 
 .5928 
 
 .6095 
 
 .6260 
 
 .6420 
 
 .6591 
 
 .0750 
 
 .6920 
 
 .7083 
 
 .7246 
 
 .7408 
 
 29 
 
 30 
 
 .5764 
 
 .5931 
 
 .6097 
 
 .6263 
 
 .6429 
 
 .6594 
 
 .0758 
 
 .6922 
 
 .7086 
 
 .7249 
 
 .7411 
 
 30 
 
 31 
 
 .5767 
 
 .5934 
 
 .6100 
 
 .6266 
 
 .6432 
 
 .6597 
 
 .0701 
 
 .6925 
 
 .7089 
 
 .7251 
 
 .7414 
 
 31 
 
 32 
 
 .5769 
 
 .5936 
 
 .6103 
 
 .6269 
 
 .6434 
 
 .6599 
 
 .0704 
 
 .6928 
 
 .7091 
 
 .7254 
 
 .7417 
 
 32 
 
 33 
 
 .5772 
 
 .5939 
 
 .6106 
 
 .6272 
 
 .6437 
 
 .6602 
 
 .0707 
 
 .6931 
 
 .7094 
 
 .7257 
 
 .7419 
 
 33 
 
 34 
 
 .5775 
 
 .5942 
 
 .6108 
 
 .6274 
 
 .6440 
 
 .6605 
 
 .6769 
 
 .6933 
 
 .7097 
 
 .7260 
 
 .7422 
 
 34 
 
 35 
 
 .5778 
 
 .5945 
 
 .6111 
 
 .6277 
 
 .6443 
 
 .6608 
 
 .6772 
 
 .0930 
 
 .7099 
 
 .7262 
 
 .7425 
 
 35 
 
 36 
 
 .5781 
 
 .5947 
 
 .6114 
 
 .6280 
 
 .6445 
 
 .6610 
 
 .6775 
 
 .0939 
 
 .7102 
 
 .7265 
 
 .7427 
 
 36 
 
 37 
 
 .5783 
 
 .5950 
 
 .6117 
 
 .6283 
 
 .6448 
 
 .6613 
 
 .6777 
 
 .0941 
 
 .7105 
 
 .7208 
 
 .7430 
 
 37 
 
 38 
 
 .5786 
 
 .5953 
 
 .6119 
 
 .6285 
 
 .6451 
 
 .6010 
 
 .6780 
 
 .0944 
 
 .7108 
 
 .7270 
 
 .7433 
 
 38 
 
 39 
 
 .5789 
 
 .5956 
 
 .6122 
 
 .6288 
 
 .6454 
 
 .0019 
 
 .6783 
 
 .6947 
 
 .7110 
 
 .7273 
 
 .7435 
 
 39 
 
 40 
 
 .5792 
 
 .5959 
 
 .6125 
 
 .6291 
 
 .6456 
 
 .6621 
 
 .6786 
 
 .6950 
 
 .7113 
 
 .7276 
 
 .7438 
 
 40 
 
 41 
 
 .5795 
 
 .5961 
 
 .6128 
 
 .6294 
 
 .6459 
 
 .6624 
 
 .6788 
 
 .6952 
 
 .7116 
 
 .7279 
 
 .7441 
 
 41 
 
 42 
 
 .5797 
 
 .5964 
 
 .6130 
 
 .6296 
 
 .6402 
 
 .6627 
 
 .6791 
 
 .0955 
 
 .7118 
 
 .7281 
 
 .7443 
 
 42 
 
 43 
 
 .5800 
 
 .5967 
 
 .6133 
 
 .6299 
 
 .0405 
 
 .6630 
 
 .0794 
 
 .6958 
 
 .7121 
 
 .7284 
 
 .7446 
 
 43 
 
 44 
 
 .5803 
 
 .5970 
 
 .6136 
 
 .6302 
 
 .0407 
 
 .0032 
 
 .0797 
 
 .6961 
 
 .7124 
 
 .7287 
 
 .7449 
 
 44 
 
 45 
 
 .5806 
 
 .5972 
 
 .6139 
 
 .6205 
 
 .6470 
 
 .0635 
 
 .0799 
 
 .6963 
 
 .7127 
 
 .7289 
 
 .7452 
 
 45 
 
 46 
 
 .5808 
 
 .5975 
 
 .6142 
 
 .6307 
 
 .6473 
 
 .0038 
 
 .0802 
 
 .6966 
 
 .7129 
 
 .7292 
 
 .7454 
 
 46 
 
 47 
 
 .5811 
 
 .5978 
 
 .6144 
 
 .6310 
 
 .6476 
 
 .0040 
 
 .0805 
 
 .6969 
 
 .7132 
 
 .7295 
 
 7457 
 
 47 
 
 48 
 
 .5814 
 
 .5981 
 
 .6147 
 
 .6313 
 
 .6478 
 
 .0643 
 
 .0808 
 
 .6971 
 
 .7135 
 
 .7298 
 
 .7460 
 
 48 
 
 49 
 
 .5817 
 
 .5984 
 
 .6150 
 
 .6316 
 
 .6481 
 
 .0646 
 
 .0810 
 
 .6974 
 
 .7137 
 
 .7300 
 
 .7462 
 
 49 
 
 50 
 
 .5820 
 
 .5986 
 
 .6153 
 
 .6318 
 
 .6484 
 
 .6649 
 
 .6813 
 
 .0977 
 
 .7140 
 
 .7303 
 
 .7465 
 
 50 
 
 51 
 
 .5822 
 
 .5989 
 
 .6155 
 
 .6321 
 
 .6487 
 
 .6651 
 
 .0816 
 
 .0980 
 
 .7143 
 
 .7306 
 
 .7468 
 
 51 
 
 52 
 
 .5825 
 
 .5992 
 
 .6158 
 
 .6324 
 
 .0489 
 
 .6654 
 
 .0819 
 
 .6982 
 
 .7146 
 
 .7308 
 
 .7471 
 
 52 
 
 53 
 
 .5828 
 
 .5995 
 
 .6161 
 
 .6327 
 
 .6492 
 
 .6657 
 
 .0821 
 
 .6985 
 
 .7148 
 
 .7311 
 
 .7473 
 
 53 
 
 54 
 
 .5331 
 
 .5997 
 
 .0164 
 
 .6330 
 
 .6495 
 
 .6660 
 
 .0824 
 
 .6988 
 
 .7152 
 
 .7314 
 
 .7476 
 
 51 
 
 55 
 
 .5834 
 
 .6000 
 
 .6166 
 
 .6332 
 
 .6498 
 
 .6062 
 
 .6827 
 
 .6991 
 
 .7154 
 
 .7316 
 
 .7479 
 
 55 
 
 56 
 
 .5836 
 
 .6003 
 
 .0169 
 
 .6335 
 
 .6500 
 
 .6605 
 
 .6829 
 
 .6993 
 
 .7156 
 
 .7319 
 
 .7481 
 
 56 
 
 57 
 
 .5839 
 
 .6006 
 
 .6172 
 
 .6338 
 
 .6503 
 
 .6668 
 
 .6832 
 
 .6996 
 
 .7159 
 
 .7322 
 
 .7484 
 
 57 
 
 58 
 
 .5842 
 
 .6009 
 
 .6175 
 
 .6341 
 
 .6506 
 
 .6071 
 
 .6835 
 
 .6999 
 
 .7162 
 
 .7325 
 
 .7487 
 
 58 
 
 59 
 
 .5845 
 
 .0011 
 
 .6178 
 
 .6343 
 
 .6509 
 
 .6073 
 
 .6838 
 
 .7001 
 
 .7165 
 
 .7327 
 
 .7489 
 
 59 
 
 60 
 
 .5847 
 
 .6014 
 
 .6180 
 
 .6346 
 
 .6511 
 
 .6676 
 
 .6840 
 
 .7004 
 
 .7167 
 
 .7330 
 
 .7492 
 
 60 
 
O'J 
 
 rhonls; K.-ulius 1 0000 f/wnf). 
 
UEOMETIUUAL 
 
 Table of Chords; Radius =1.0000 (continued). 
 
 M. 
 
 55 
 
 56 
 
 57 
 
 58 
 
 59 
 
 60 
 
 61 
 
 63 
 
 63 
 
 64 
 
 M. 
 
 ()' 
 
 .0235 
 
 .9380 
 
 .9543 
 
 .9600 
 
 .9848 
 
 1 .0000 
 
 1.0151 
 
 1.0301 
 
 1.0450 
 
 1.0598 
 
 0' 
 
 1 
 
 .'.H.WX 
 
 ,9392 
 
 ,9546 
 
 .9009 
 
 ,9851 
 
 1.0003 
 
 1.0153 
 
 1.0303 
 
 .0452 
 
 1.0001 
 
 1 
 
 2 
 
 0210 
 
 9395 
 
 9 r rlX 
 
 .9701 
 
 .9X54 
 
 .0005 
 
 1.0150 
 
 1 .0300 
 
 0455 
 
 1 0003 
 
 2 
 
 3 
 
 ,9248 
 
 .0307 
 
 ,9551 
 
 .9704 
 
 ,9856 
 
 .0008 
 
 1.0158 
 
 1.0308 
 
 .0457 
 
 L0606 
 
 3 
 
 4 
 
 .9215 
 
 .010') 
 
 .0553 
 
 .970(1 
 
 .9S59 
 
 .0010 
 
 1.0101 
 
 1.0311 
 
 .0400 
 
 1.0608 
 
 4 
 
 5 
 
 ,9248 
 
 .0402 
 
 .9556 
 
 .9700 
 
 .9X01 
 
 .0013 
 
 1.0103 
 
 1.0313 
 
 .0462 
 
 1.0611 
 
 5 
 
 li 
 
 .0250 
 
 ,9405 
 
 .055!) 
 
 .9711 
 
 .9804 
 
 .0015 
 
 1.0106 
 
 1.0316 
 
 1.0465 
 
 1.0613 
 
 6 
 
 7 
 
 .0253 
 
 .0107 
 
 ,9561 
 
 .9714 
 
 .9860 
 
 .0018 
 
 1.0108 
 
 1.0318 
 
 1.0467 
 
 1.0616 
 
 7 
 
 8 
 
 ,9256 
 
 .0110 
 
 .0504 
 
 .9717 
 
 .9866 
 
 .0020 
 
 1.0171 
 
 1.0321 
 
 1.0470 
 
 1.0618 
 
 8 
 
 
 
 .0258 
 
 .0413 
 
 .05(J{i 
 
 .9719 
 
 .9871 
 
 .0023 
 
 .0173 
 
 .0323 
 
 .0472 
 
 1.0621 
 
 9 
 
 10 
 
 ,9201 
 
 .9415 
 
 .0500 
 
 .9722 
 
 .9874 
 
 .0025 
 
 .0176 
 
 .0326 
 
 1.0475 
 
 1.0623 
 
 10 
 
 1 ] 
 
 .0203 
 
 ,9418 
 
 .0571 
 
 .9724 
 
 .9X70 
 
 .0028 
 
 .0178 
 
 .0328 
 
 1.0477 
 
 1.0626 
 
 11 
 
 12 
 
 . ( .t:'(iii 
 
 .0120 
 
 ,9574 
 
 .0727 
 
 .9879 
 
 .0030 
 
 .0181 
 
 .0331 
 
 .0480 
 
 1.0628 
 
 12 
 
 18 
 
 .'.12' >S 
 
 .0423 
 
 .0570 
 
 .9729 
 
 .9881 
 
 .0033 
 
 .0183 
 
 .0333 
 
 1.0482 
 
 1.0630 
 
 13 
 
 li 
 
 .9271 
 
 .041'5 
 
 .0579 
 
 .9732 
 
 .0884 
 
 .0035 
 
 .0186 
 
 .0330 
 
 .0485 
 
 1.0633 
 
 14 
 
 ir> 
 
 ,9274 
 
 .OIL'S 
 
 .95X1 
 
 .0734 
 
 .0886 
 
 .0038 
 
 1.0188 
 
 .0338 
 
 1.0487 
 
 1.0635 
 
 15 
 
 in 
 
 .0270 
 
 .0130 
 
 ,9584 
 
 .9737 
 
 .9889 
 
 .0040 
 
 .0191 
 
 .0341 
 
 1.0490 
 
 1.0638 
 
 16 
 
 17 
 
 .0270 
 
 .0433 
 
 .9587 
 
 .0739 
 
 .9X91 
 
 .0043 
 
 .0193 
 
 .0343 
 
 .0492 
 
 1.0640 
 
 17 
 
 IS 
 
 .9281 
 
 ,9436 
 
 .05X0 
 
 .0742 
 
 .9894 
 
 1.0045 
 
 .0196 
 
 .0346 
 
 1.0495 
 
 1.0643 
 
 18 
 
 li) 
 
 ,9284 
 
 .9I3S 
 
 .0592 
 
 .0744 
 
 .9897 
 
 .0048 
 
 1.0108 
 
 .0348 
 
 1.0197 
 
 1.0645 
 
 19 
 
 20 
 
 ,9287 
 
 .0111 
 
 .0501 
 
 .9747 
 
 .9899 
 
 1.0050 
 
 1.0201 
 
 .0351 
 
 1.0500 
 
 1.0648 
 
 20 
 
 21 
 
 .02X0 
 
 .0443 
 
 .0507 
 
 .0750 
 
 .9902 
 
 1.0053 
 
 1.0203 
 
 .0353 
 
 1.0502 
 
 1.0050 
 
 21 
 
 22 
 
 .0202 
 
 ,9446 
 
 .0500 
 
 .9752 
 
 .9904 
 
 .0055 
 
 1.0206 
 
 .0356 
 
 .0504 
 
 1.0653 
 
 22 
 
 28 
 
 ,9294 
 
 .oils 
 
 .0002 
 
 .9755 
 
 .0907 
 
 1.0058 
 
 1.0208 
 
 .0358 
 
 .0507 
 
 1.0655 
 
 23 
 
 24 
 
 .0207 
 
 ,9451 
 
 .0004 
 
 .9757 
 
 .9909 
 
 1.0060 
 
 1.0211 
 
 .0301 
 
 .0509 
 
 1.0058 
 
 24 
 
 25 
 
 .0200 
 
 .0454 
 
 .9(107 
 
 .9700 
 
 .9912 
 
 .0003 
 
 1.0213 
 
 .0363 
 
 .0512 
 
 1.0600 
 
 25 
 
 26 
 
 .0302 
 
 .0150 
 
 .9010 
 
 .9702 
 
 .9914 
 
 1.0005 
 
 1.0216 
 
 .0360 
 
 .0514 
 
 1.0662 
 
 26 
 
 27 
 
 .0305 
 
 .0450 
 
 .9012 
 
 .9705 
 
 .9917 
 
 l.OOfW 
 
 1.0218 
 
 .0368 
 
 .0517 
 
 1.0665 
 
 27 
 
 28 
 
 .0307 
 
 .9101 
 
 .0(115 
 
 .0707 
 
 .9919 
 
 1.0070 
 
 1.0221 
 
 .0370 
 
 .0519 
 
 1.0667 
 
 28 
 
 L'O 
 
 .0310 
 
 .0404 
 
 .9617 
 
 .9770 
 
 .9922 
 
 1.0073 
 
 1.0223 
 
 .0373 
 
 .0522 
 
 1.0670 
 
 29 
 
 30 
 
 .9312 
 
 .9400 
 
 .0020 
 
 .9772 
 
 .9924 
 
 1.0075 
 
 1.0226 
 
 .0375 
 
 1.0524 
 
 1.0672 
 
 30 
 
 3! 
 
 .9315 
 
 .9409 
 
 .9622 
 
 .9775 
 
 .9927 
 
 1.0078 
 
 1.0228 
 
 .0378 
 
 .0527 
 
 1.0675 
 
 31 
 
 32 
 
 .0317 
 
 .9472 
 
 .0025 
 
 .9778 
 
 .9929 
 
 1.0080 
 
 1.0231 
 
 .0380 
 
 .0529 
 
 1.0677 
 
 32 
 
 33 
 
 .0320 
 
 .9474 
 
 .9627 
 
 .97X0 
 
 .9932 
 
 1.0083 
 
 1.0233 
 
 .0383 
 
 .0532 
 
 1.0680 
 
 33 
 
 34 
 
 .0323 
 
 .9477 
 
 .9630 
 
 .07X3 
 
 .9934 
 
 1.0086 
 
 1.0236 
 
 .0385 
 
 .0534 
 
 1.0682 
 
 34 
 
 3, r ) 
 
 .0325 
 
 .0170 
 
 .9033 
 
 .07X5 
 
 .9937 
 
 1.0088 
 
 1.0238 
 
 .0388 
 
 .0537 
 
 1.0685 
 
 35 
 
 30 
 
 .032X 
 
 94X1? 
 
 .0035 
 
 .9788 
 
 .9939 
 
 1.0091 
 
 1.0241 
 
 .0390 
 
 .0539 
 
 1.0687 
 
 36 
 
 37 
 
 .9330 
 
 .04X4 
 
 .003S 
 
 .0700 
 
 .9942 
 
 1.0093 
 
 1.0243 
 
 .0393 
 
 1.0542 
 
 1.0690 
 
 37 
 
 3S 
 
 .0333 
 
 .04X7 
 
 .0010 
 
 .9703 
 
 .9945 
 
 1.0096 
 
 1.0246 
 
 .0395 
 
 1.0544 
 
 1.0692 
 
 38 
 
 30 
 
 ,93811 
 
 .04X0 
 
 .0013 
 
 .9795 
 
 .9947 
 
 1.0098 
 
 1.0248 
 
 .0398 
 
 1.0547 
 
 1.0694 
 
 39 
 
 U) 
 
 ,9838 
 
 .9492 
 
 .9645 
 
 .9798 
 
 .9950 
 
 1.0101 
 
 1.0251 
 
 .0400 
 
 1.0549 
 
 1.0697 
 
 40 
 
 11 
 
 .9341 
 
 .9495 
 
 .9648 
 
 .9800 
 
 .9952 
 
 1.0103 
 
 1.0253 
 
 .0403 
 
 1.0551 
 
 1.0699 
 
 41 
 
 42 
 
 .0313 
 
 .0 107 
 
 .9650 
 
 .0X03 
 
 .9955 
 
 1.0106 
 
 1.0256 
 
 .0405 
 
 1.0554 
 
 1.0702 
 
 42 
 
 43 
 
 .9340 
 
 .0500 
 
 .9658 
 
 .9805 
 
 .9957 
 
 1.0108 
 
 1.0258 
 
 .0408 
 
 1.0556 
 
 1.07C4 
 
 43 
 
 M 
 
 .03 IS 
 
 0502 
 
 .9655 
 
 .osos 
 
 .9960 
 
 1.0111 
 
 1.0261 
 
 1.0410 
 
 1.0559 
 
 1.0707 
 
 44 
 
 15 
 
 .0351 
 
 .0505 
 
 .0658 
 
 .9810 
 
 .9062 
 
 1.0113 
 
 1.0203 
 
 1.0413 
 
 1.0561 
 
 1.0709 
 
 45 
 
 46 
 
 .9853 
 
 .0507 
 
 .0001 
 
 .0813 
 
 .9965 
 
 1.0116 
 
 1.0266 
 
 1.0415 
 
 1.0564 
 
 1.0712 
 
 46 
 
 47 
 
 .9858 
 
 .Of. 10 
 
 .0663 
 
 .OS 10 
 
 .9967 
 
 1.0118 
 
 1.0268 
 
 1.0418 
 
 1.0566 
 
 1.0714 
 
 47 
 
 4S 
 
 .0350 
 
 .051:> 
 
 .001)0 
 
 .OS IS 
 
 .9970 
 
 1.0121 
 
 1.0271 
 
 1.0420 
 
 1.0569 
 
 1.0717 
 
 48 
 
 49 
 
 ,9361 
 
 .9515 
 
 .9668 
 
 .OS 21 
 
 .9972 
 
 1.0123 
 
 1.0273 
 
 1.0423 
 
 1.0571 
 
 1.0719 
 
 49 
 
 50 
 
 .0304 
 
 .9518 
 
 .9671 
 
 .9823 
 
 .9975 
 
 1.0126 
 
 1.0276 
 
 1.0425 
 
 1.0574 
 
 1.0721 
 
 50 
 
 51 
 
 .0300 
 
 ,9520 
 
 .9673 
 
 .9826 
 
 .9977 
 
 1.0128 
 
 1.0278 
 
 1.0428 
 
 1.0576 
 
 1.0724 
 
 51 
 
 52 
 
 .0300 
 
 .0523 
 
 .9676 
 
 .OS2S 
 
 .9980 
 
 .0131 
 
 1.0281 
 
 1.0430 
 
 1.0579 
 
 1.0726 
 
 52 
 
 53 
 
 .0371 
 
 .0525 
 
 .007X 
 
 .0X31 
 
 .9982 
 
 .0133 
 
 1.0283 
 
 1.0433 
 
 1.0581 
 
 1.0729 
 
 53 
 
 54 
 
 ,9374 
 
 .052X 
 
 .00X1 
 
 .0X33 
 
 .9985 
 
 .0136 
 
 1.0286 
 
 1.0435 
 
 1.0584 
 
 1.0731 
 
 54 
 
 55 
 
 .9377 
 
 .9530 
 
 .00X3 
 
 .OS30 
 
 .9987 
 
 .0138 
 
 1.0288 
 
 1.0438 
 
 1.0586 
 
 1.0734 
 
 55 
 
 SO 
 
 .9379 
 
 9A33 
 
 .00X0 
 
 .OS3S 
 
 .9990 
 
 .0141 
 
 1.0291 
 
 1.0440 
 
 1.0589 
 
 1.0736 
 
 56 
 
 57 
 
 .03S2 
 
 .0530 
 
 ooxo 
 
 .OS 4 1 
 
 .9992 
 
 .0143 
 
 1.0293 
 
 1.0443 
 
 1.0591 
 
 1.0739 
 
 57 
 
 58 
 
 ,9394 
 
 .953S 
 
 0001 
 
 .0X43 
 
 .9995 
 
 1.0146 
 
 1.0296 
 
 1.0445 
 
 1.0593 
 
 1.0741 
 
 58 
 
 50 
 
 ,9887 
 
 .9541 
 
 .9694 
 
 .0X40 
 
 .900S 
 
 1.0148 
 
 1.0208 
 
 1.0447 
 
 1.0596 
 
 1.0744 
 
 59 
 
 00 
 
 .03SO 
 
 .9543 
 
 .9696 
 
 .9848 
 
 1.0000 
 
 1.0151 
 
 1.0301 
 
 1.0450 
 
 1.0598 
 
 1.0746 
 
 60 
 
94 
 
 GEOMETRICAL PROBLEMS. 
 
 Table of Chords; Radius =1.0000 (continued). 
 
 M 
 
 65 
 
 66 
 
 67 
 
 68 
 
 69 
 
 70 
 
 71 
 
 72 
 
 73 
 
 M. 
 
 
 
 1.0746 
 
 1.0893 
 
 1.1039 
 
 1.1184 
 
 1.1328 
 
 1.1472 
 
 1.1614 
 
 1.1756 
 
 1.1896 
 
 0' 
 
 1 
 
 1.0748 
 
 1.0395 
 
 1.1041 
 
 1.1186 
 
 1.1331 
 
 1.1474 
 
 1.1616 
 
 1.1758 
 
 1.1899 
 
 1 
 
 
 
 1.0751 
 
 1.0398 
 
 1.1044 
 
 1.1189 
 
 1.1333 
 
 1.1476 
 
 1.1C19 
 
 1.1760 
 
 1.1901 
 
 2 
 
 3 
 
 1.0753 
 
 1.0900 
 
 1.1046 
 
 1.1191 
 
 1.1335 
 
 1.1479 
 
 1.1621 
 
 1.1763 
 
 1.1903 
 
 j 
 
 4 
 
 1.0756 
 
 1.0903 
 
 1.1048 
 
 1.1194 
 
 1.1338 
 
 1.1481 
 
 1.1624 
 
 1.1765 
 
 1.1906 
 
 4 
 
 5 
 
 1.0758 
 
 1.0905 
 
 1.1051 
 
 1.1196 
 
 1.1340 
 
 1.1483 
 
 1.1626 
 
 1.1767 
 
 1.1908 
 
 i 
 
 6 
 
 1.0761 
 
 1.0907 
 
 1.1053 
 
 1.1198 
 
 1.1342 
 
 1.1486 
 
 1.1628 
 
 1.1770 
 
 1.1910 
 
 ( 
 
 7 
 
 1.0763 
 
 1.0910 
 
 1.1056 
 
 1.1201 
 
 1.1345 
 
 1.1488 
 
 1.1631 
 
 1.1772 
 
 1.1913 
 
 j 
 
 
 1.0766 
 
 1.0912 
 
 1.1058 
 
 1.1203 
 
 1.1347 
 
 1.1491 
 
 1.1633 
 
 1.1775 
 
 1.1915 
 
 
 
 S 
 
 1.0768 
 
 1.0915 
 
 1.1061 
 
 1.1206 
 
 1.1350 
 
 1.1493 
 
 1.1635 
 
 1.1777 
 
 1.1917 
 
 ( 
 
 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 
 
 1.1088 
 
 1.1213 
 
 1.1357 
 
 1.1500 
 
 1.1642 
 
 1.1784 
 
 1.1924 
 
 12 
 
 13 
 
 1.0778 
 
 1.0924 
 
 1.1070 
 
 1.1215 
 
 1.1359 
 
 1.1502 
 
 1.1645 
 
 1.1786 
 
 1.1927 
 
 13 
 
 14 
 
 1.0780 
 
 1.0927 
 
 1.1073 
 
 1.1218 
 
 1.1362 
 
 1.1505 
 
 1.1647 
 
 1.1789 
 
 1.1929 
 
 14 
 
 15 
 
 1.0783 
 
 1.0929 
 
 1.1075 
 
 1.1220 
 
 1.1364 
 
 1.1507 
 
 1.1650 
 
 1.1791 
 
 1.1931 
 
 15 
 
 16 
 
 1.0785 
 
 1.0932 
 
 1.1078 
 
 1.1222 
 
 1.1366 
 
 1.1510 
 
 1.1652 
 
 1.1793 
 
 1.1934 
 
 16 
 
 17 
 
 1.0788 
 
 1.0934 
 
 1.10SO 
 
 1.1225 
 
 1.1369 
 
 1.1512 
 
 1.1654 
 
 1.1796 
 
 1.1936 
 
 17 
 
 18 
 
 1.0790 
 
 1.0937 
 
 1.1032 
 
 1.1227 
 
 1.1371 
 
 1.1514 
 
 1.1657 
 
 1.1798 
 
 1.1938 
 
 18 
 
 19 
 
 1.0793 
 
 1.0939 
 
 1.1035 
 
 1.1230 
 
 1.1374 
 
 1.1517 
 
 1.1659 
 
 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 
 
 1.1666 
 
 1.1807 
 
 1.1948 
 
 22 
 
 23 
 
 1.0802 
 
 1.0949 
 
 1.1094 
 
 1.1239 
 
 1.1383 
 
 1.1526 
 
 1.1668 
 
 1.1810 
 
 1.1950 
 
 23 
 
 24 
 
 1.0805 
 
 1.0951 
 
 1.1097 
 
 1.1242 
 
 1.1386 
 
 1.1529 
 
 1.1671 
 
 1.1812 
 
 1.1952 
 
 24 
 
 25 
 
 1.0807 
 
 1.0954 
 
 1.1099 
 
 1.1244 
 
 1.1388 
 
 1.1531 
 
 1.1673 
 
 1.1814 
 
 1.1955 
 
 25 
 
 26 
 
 1.0810 
 
 1.0956 
 
 1.1102 
 
 1.1246 
 
 1.1390 
 
 1.1533 
 
 1.1676 
 
 1.1S17 
 
 1.1957 
 
 26 
 
 27 
 
 1.0812 
 
 1.0959 
 
 1.1104 
 
 1.1249 
 
 1.1393 
 
 1.1536 
 
 1.1678 
 
 1.1819 
 
 1.1959 
 
 27 
 
 23 
 
 1.0815 
 
 1.0961 
 
 1.1107 
 
 1.1251 
 
 1.1395 
 
 1.1538 
 
 1.1680 
 
 1.1821 
 
 1.1962 
 
 28 
 
 29 
 
 1.0817 
 
 1.0963 
 
 1.1109 
 
 1.1254 
 
 1.1398 
 
 1.1541 
 
 1.1683 
 
 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 
 
 1.1694 
 
 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 
 
 1.1699 
 
 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 
 
 33 
 
 1.0839 
 
 1.0985 
 
 1.1131 
 
 1.1275 
 
 1.1419 
 
 1.1502 
 
 1.1704 
 
 1.1845 
 
 1.1985 
 
 33 
 
 39 
 
 1.0841 
 
 1.0988 
 
 1.1133 
 
 1.1278 
 
 1.1421 
 
 1.1564 
 
 1.1706 
 
 1.1S47 
 
 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 
 
 41 
 
 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 
 
 1.1581 
 
 1.1723 
 
 1.1864 
 
 1.2004 
 
 46 
 
 47 
 
 1.0861 
 
 1.1007 
 
 1.1152 
 
 1.1297 
 
 1.1441 
 
 1.1583 
 
 1.1725 
 
 1.1866 
 
 1.2006 
 
 47 
 
 48 
 
 1.0863 
 
 1.1010 
 
 1.1155 
 
 1.1299 
 
 1.1443 
 
 1.1586 
 
 1.1727 
 
 1.1868 
 
 1.2008 
 
 48 
 
 49 
 
 1.0806 
 
 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 
 
 1J885 
 
 1.2025 
 
 55 
 
 56 
 
 1.0S83 
 
 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 
 
 1.1S96 
 
 1.2036 
 
 60 
 
Table of Chords; Radius =1.0000 (continued). 
 
 M 
 
 74 
 
 75 
 
 76 
 
 77 
 
 78 
 
 79 
 
 80 
 
 81 
 
 83 
 
 M. 
 
 
 
 1.2036 
 
 1.2175 
 
 1.2313 
 
 1.2450 
 
 1.2586 
 
 1.2722 
 
 1.2856 
 
 1.2989 
 
 1.3121 
 
 0' 
 
 
 1.2039 
 
 1.2178 
 
 1.2316 
 
 1.2453 
 
 1.2589 
 
 1.2724 
 
 1.2858 
 
 1.2991 
 
 1.3123 
 
 1 
 
 2 
 
 1.2041 
 
 1.21SO 
 
 1.2318 
 
 1.2455 
 
 1.2591 
 
 1.2726 
 
 1.2860 
 
 1.2993 
 
 1.3126 
 
 2 
 
 j 
 
 1.2043 
 
 1.2182 
 
 1.2320 
 
 1.2457 
 
 1.2593 
 
 1.2728 
 
 1.2862 
 
 1.2996 
 
 1.3128 
 
 3 
 
 i 
 
 1.2046 
 
 1.2184 
 
 1.2322 
 
 1.2459 
 
 1.2595 
 
 1.2731 
 
 1.2865 
 
 1.2998 
 
 1.3130 
 
 4 
 
 t 
 
 1.2048 
 
 1.2187 
 
 1.2325 
 
 1.2462 
 
 1.2598 
 
 1.2733 
 
 1.2867 
 
 1.3000 
 
 1.3132 
 
 5 
 
 ( 
 
 1.2050 
 
 1.2189 
 
 1.2327 
 
 1.2464 
 
 1.2600 
 
 1.2735 
 
 1.2869 
 
 1.3002 
 
 1.3134 
 
 6 
 
 f t 
 
 1.2053 
 
 1.2191 
 
 1.2329 
 
 1.2406 
 
 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 
 
 1.2062 
 
 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 
 
 1.3156 
 
 16 
 
 17 
 
 1.2076 
 
 1.2214 
 
 1.2352 
 
 1.2489 
 
 1.2625 
 
 1.2760 
 
 1.2894 
 
 1.3027 
 
 1.3158 
 
 17 
 
 18 
 
 1.207S 
 
 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 
 
 1.2304 
 
 1.2500 
 
 1.2636 
 
 1.2771 
 
 1.2905 
 
 1.3038 
 
 1.3169 
 
 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 
 
 1.3176 
 
 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 
 
 1.2G72 
 
 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 
 
 1.2423 
 
 1.2559 
 
 1.2695 
 
 1.2829 
 
 1.2962 
 
 1.3095 
 
 1.3226 
 
 48 
 
 49 
 
 1.2150 
 
 1.2288 
 
 1.2425 
 
 1.2562 
 
 1.2697 
 
 1.2831 
 
 1.2965 
 
 1.3097 
 
 1.3228 
 
 49 
 
 50 
 
 1.2152 
 
 1.2290 
 
 1.2428 
 
 1.2564 
 
 1.2699 
 
 1.2833 
 
 1.2967 
 
 1.3099 
 
 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 
 
 1.2434 
 
 1.2571 
 
 1.2700 
 
 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 
 
GEOMETRICAL PROBLEMS. 
 
 Table of Chords; Radius =1.0000 (concluded). 
 
 M. 
 
 83 
 
 84 
 
 85 
 
 86 
 
 87 
 
 88 
 
 89 
 
 M. 
 
 O 7 
 
 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 
 
 1.33S9 
 
 1.3518 
 
 1.3646 
 
 1.3773 
 
 1.3899 
 
 1.4024 
 
 3 
 
 4 
 
 1.3261 
 
 1.3391 
 
 1.3520 
 
 1.3648 
 
 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 
 
 1.37S2 
 
 1.3908 
 
 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 
 
 1.3916 
 
 1.4041 
 
 11 
 
 12 
 
 1.3279 
 
 1.3409 
 
 1.3538 
 
 1.3665 
 
 1.3792 
 
 1.3918 
 
 1.4043 
 
 12 
 
 13 
 
 1.3281 
 
 1.3411 
 
 1.3540 
 
 1.3668 
 
 1.3794 
 
 1.3920 
 
 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 
 
 1.3419 
 
 1.3548 
 
 1.3676 
 
 1.3303 
 
 1.3929 
 
 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 
 
 1.3933 
 
 1.4058 
 
 19 
 
 20 
 
 1.3296 
 
 1.3426 
 
 1.3555 
 
 1.36S2 
 
 1.3809 
 
 1.3935 
 
 1.4060 
 
 20 
 
 21 
 
 1.3298 
 
 1.3428 
 
 1.3557 
 
 1.3685 
 
 1.3811 
 
 1.3937 
 
 1.4062 
 
 21 
 
 22 
 
 1.3300 
 
 1.3430 
 
 1.3559 
 
 1.3687 
 
 1.3813 
 
 1.3939 
 
 1.4064 
 
 22 
 
 23 
 
 1.3302 
 
 1.3432 
 
 1.3561 
 
 1.3689 
 
 1.3816 
 
 1.3941 
 
 1.4066 
 
 23 
 
 24 
 
 1.3305 
 
 1.3434 
 
 1.3563 
 
 1.3691 
 
 1.3818 
 
 1.3943 
 
 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 
 
 1.3572 
 
 1.3699 
 
 1.3826 
 
 1.3952 
 
 1.4076 
 
 28 
 
 29 
 
 1.3315 
 
 1.3445 
 
 1.3574 
 
 1.3702 
 
 1.3828 
 
 1.2954 
 
 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 
 
 1.3322 
 
 1.3452 
 
 1.3580 
 
 1.3708 
 
 1.3834 
 
 1.3960 
 
 1.4084 
 
 32 
 
 33 
 
 1.3324 
 
 1.3454 
 
 1.3582 
 
 1.3710 
 
 1.3837 
 
 1.3962 
 
 1.40S6 
 
 33 
 
 34 
 
 1.3326 
 
 1.3456 
 
 1.3585 
 
 1.3712 
 
 .3839 
 
 1.3964 
 
 1.4089 
 
 34 
 
 35 
 
 1.3328 
 
 1.3458 
 
 1.3587 
 
 1.3714 
 
 .3841 
 
 1.3966 
 
 1.4091 
 
 35 
 
 36 
 
 1.3331 
 
 1.3460 
 
 1.3589 
 
 1.3716 
 
 .3843 
 
 1.3968 
 
 1.4093 
 
 36 
 
 37 
 
 1.3333 
 
 1.3462 
 
 1.3591 
 
 1.3718 
 
 .3845 
 
 1.3970 
 
 1.4095 
 
 37 
 
 38 
 
 1.3335 
 
 1.3465 
 
 1.3593 
 
 1.3721 
 
 .3847 
 
 1.3072 
 
 1.4097 
 
 38 
 
 39 
 
 1.3337 
 
 1.3467 
 
 1.3595 
 
 1.3723 
 
 .3849 
 
 1.3975 
 
 1.4099 
 
 39 
 
 40 
 
 1.3339 
 
 1.3469 
 
 1.3597 
 
 1.3725 
 
 .3851 
 
 1.3977 
 
 1.4101 
 
 40 
 
 41 
 
 1.3341 
 
 1.3471 
 
 1.3599 
 
 .3727 
 
 .385?, 
 
 1.3979 
 
 1.4103 
 
 41 
 
 42 
 
 1.3344 
 
 1.3473 
 
 1.3602 
 
 .3729 
 
 .3855 
 
 1.3981 
 
 1.4105 
 
 42 
 
 43 
 
 1.3346 
 
 1.3475 
 
 1.3604 
 
 .3731 
 
 .3858 
 
 1.3983 
 
 1.4107 
 
 43 
 
 44 
 
 1.3348 
 
 .3477 
 
 1.3606 
 
 .3733 
 
 .3860 
 
 1.39S5 
 
 1.4109 
 
 44 
 
 45 
 
 1.3350 
 
 .3480 
 
 1.3608 
 
 .3735 
 
 .3862 
 
 1.3987 
 
 1.4111 
 
 45 
 
 46 
 
 1.3352 
 
 1.3482 
 
 1.3610 
 
 .3738 
 
 .3864 
 
 1.3989 
 
 1.4113 
 
 46 
 
 47 
 
 1.3354 
 
 .3484 
 
 1.3612 
 
 .3740 
 
 .3866 
 
 1.3991 
 
 1.4115 
 
 47 
 
 48 
 
 1.3357 
 
 .3486 
 
 1.3614 
 
 1.3742 
 
 .3868 
 
 1.3993 
 
 1.4117 
 
 48 
 
 49 
 
 1.3359 
 
 .3488 
 
 1.3617 
 
 .3744 
 
 .3870 
 
 1.3995 
 
 1.4119 
 
 49 
 
 50 
 
 1.3361 
 
 1.3490 
 
 1.3619 
 
 .3746 
 
 1.3872 
 
 1.3997 
 
 1.4122 
 
 50 
 
 51 
 
 1.3363 
 
 1.3492 
 
 1.3621 
 
 .3748 
 
 1.3874 
 
 1.3999 
 
 1.4124 
 
 51 
 
 52 
 
 1.3365 
 
 1.3495 
 
 1.3623 
 
 .3750 
 
 1.3876 
 
 1.4002 
 
 1.4126 
 
 52 
 
 53 
 
 1.3367 
 
 1.3497 
 
 1.3625 
 
 1.3752 
 
 1.3879 
 
 1.4004 
 
 1.4128 
 
 53 
 
 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 
 
 1.3S85 
 
 1.4010 
 
 1.4134 
 
 56 
 
 57 
 
 1.3376 
 
 1.3505 
 
 1.3634 
 
 1.3761 
 
 1.3887 
 
 1.4012 
 
 1.4136 
 
 57 
 
 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 
 
HIP AND JACK RAFTERS. 97 
 
 Lengths and Bevels of Hip and Jack Rafters. 
 
 The lines ab and be in Fig. 89 represent 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 h, and hb will be the length of the hip- 
 rafter. Through e draw di at right angles to be. Upon 6, with 
 the radius bh y describe the arc hi, cutting di in i. Join b and i, 
 h 
 
 and extend gf to meet bi in / ; then gj will be 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 bi. From / draw 
 fk at right angles to fg, also fl at right angles to be. Make fk 
 equal to fl by the arc Ik, or make gk equal to gj by the arc jk; 
 then the angle at / will be the top bevel of the jack-rafters, and 
 the one at k the down bevel. 
 
 Backing of the hip-rafter. At any convenient place in be (Fig. 
 89), 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; then 
 these lines will form at s the proper angle for bevelling the top of 
 the hip-rafter. 
 
98 TRIGONOMETRY. 
 
 TRIGONOMETRY. 
 
 IT is not the purpose of the author to teach the use of trigonom- 
 etry, or what it is; but, for the benefit of those readers who have 
 already acquired a knowledge of this science, the following con- 
 venient formulas, and tables of natural sines and tangents, have 
 been inserted. To those who know how to apply these trigono- 
 metric functions, they will often be found of great convenience 
 and utility. 
 
 These tables are taken from Searle's "Field Engineering," John 
 Wiley & Sons, publishers, by permission. 
 
TRIGONOMETRIC FORMULAS. 
 
 TKIGONOMETRI 
 
 Let A (Fig. 107) = angle BAC = arc 
 AH=l. 
 We then have 
 
 sin A ^BC 
 cos A = AC 
 tan A = DF 
 cot A =-IIG 
 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 
 
 In the right-angled triangle ABC 
 Let AB = c, AC = b, and BC = a. 
 We then have: 
 
 1 . sin A = = cos B 
 
 2. cos A = =sin B 
 c 
 
 3. tan A = 2- =cot B 
 b 
 
 4. cot A = = tan B 
 a 
 
 5. sec A = - = cosec B 
 
 
 
 6. cosec A = =sec,B 
 a 
 
 c b 
 
 c FUNCTIONS. 
 5 BF, and let the radius AF = AB = 
 
 H K G 
 
 L ^^ 
 
 ^\ 
 J^*\ 
 A^ 6 P 
 
 A c F 
 
 / 
 
 FIG. 107. 
 (Fig. 107) 
 
 11. a = c sin A =6 tan A 
 12. 6 c cos A =a cot A 
 a b 
 
 sin A cos A 
 14. a = c cosB=-6 cot B 
 
 15. 6 = csin B = a tan 5 
 
 16 c a 6 
 
 cos B sin Z> 
 
 7. versA = = covers B 
 c 
 
 c b 
 
 17. a = V( c + 6)(c-6) 
 
 8. exsec A = r = coexsec B 
 b 
 
 18. & = ^( c + )(c-a) 
 
 9 covers A versin B 
 
 19. c =V a 2+6 2 
 20. C=90=A+ 
 
 a6 
 l= "2" 
 
 c 
 
 a 
 
 21. aret 
 
100 TRIGONOMETRIC FORMULAS. 
 
 SOLUTION OF OBLIQUE TRIANGLES. 
 B 
 
 FIG. 108. 
 
 A,B,a 
 
 A,a,b 
 
 C,a,b 
 
 a, b,c 
 
 A,B,C,a 
 
 C,b,C 
 
 B,C,c 
 
 A,B 
 
 area 
 A 
 
 FORMULAE. 
 
 -- 
 
 sm A 
 
 c = - - sin (A+B) 
 sin ^4 
 
 sin A 
 
 _ . sin C. 
 
 - tan J^(.4 +/?) 
 
 c = ( a + b\- 
 
 = (a-l 
 
 Lets = ^(a + & + d; sin \&A=\ 
 
 
 be ' 
 
 sin A = - 
 
 bo 
 
 vers A = 
 
 r . rf 2 sin ^.sin C 
 
 K. = : ~ A 
 
 2 sin A 
 
TRIGONOMETRIC FORMULAS. 101 
 
 GENERAL 
 i - cos 2 A = tan A cos A 
 
 35. sin A =2 sin $&A cos JA vers A co 
 
 39. cos A - cos 2 Yz A - sin 2 \& A = V J$ + y% cos 2A 
 
 40. tan A 
 
 41. tan A f A ~. 
 
 cos 2 A cos A 1+ cos 2A 
 
 1 cos 2 A vers 2.4 , , . 
 
 42. tan A - . OA - 9 , -exsec A cot ^A 
 
 43. cot A - . , r- 
 
 tan A sin A 
 
 sin 2 A sin 2A 1 4- cos 2A 
 
 l-cos2A ~^2~A sin2A 
 
 tan 
 45. cot A = 
 
 exsec A 
 
 46. vers A = 1 - cos A = sin A tan J^A = 2 sin 2 J^ A 
 
 47. vers A = exsec A cos A 
 
 48. exsec A = sec A 1 tan A tan J x J 
 
 49. 
 
 cos A 
 5 A A /'vers A 
 
 2 
 50. sin 2 A = 2 sin A cos A 
 
 51. CO.KX-V 1+C 2 OSA - 
 
 52. cos 2A = 2 cos 2 A - 1 = cos 2 A - sinM = 1-2 sinM 
 
TMCOXOMETR1C FORMITLAS. 
 
 c4-*JL' 
 
 1 -* A I/I- ---# <- 
 
 *A 1 
 
 
 ST.T 
 
 tt.nBC*4> 
 
 M. rim- 
 
 65. cJ 
 
 66. cn. 
 
 R 
 ^ 
 
 
SATTBAL SIXES AKD OOHKBBL 
 
 103 
 
104 
 
 NATURAL SINES AND COSINES. 
 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 
 
 Sine 
 
 Cosin 
 
 Sine 
 
 Cosin 
 
 Sine 
 
 Coain 
 
 Sine 
 
 Cosin 
 
 Sine 
 
 Cosin 
 
 
 
 
 .08716 
 
 .99619 
 
 .10453 
 
 .99452 
 
 .12187 
 
 .99255 
 
 .13917 
 
 .99027 
 
 .15643 
 
 .98769 
 
 60 
 
 1 
 
 .08745 
 
 .99617 
 
 .10482 
 
 .99449 
 
 .12216 
 
 .99251 
 
 .13946 
 
 .99023 
 
 .15672 
 
 .98764 
 
 59 
 
 2 
 
 .08774 
 
 .99614 
 
 .10511 
 
 .99446 
 
 .12245 
 
 .99248 
 
 .13975 
 
 .99010 
 
 .15701 
 
 .98760 
 
 58 
 
 3 
 
 .08803 
 
 .99612 
 
 .105-40 
 
 .99443 
 
 .12274 
 
 .99244 
 
 ,14004 
 
 .99015 
 
 .15730 
 
 .98755 
 
 57 
 
 4 
 
 .08831 
 
 .99609 
 
 .10569 
 
 .99440 
 
 .12302 
 
 .99240 
 
 .14033 
 
 .99011 
 
 .15758 
 
 .98751 
 
 56 
 
 5 
 
 .08860 
 
 .99607 
 
 .10597 
 
 .99437 
 
 .12331 
 
 .99237 
 
 .14061 
 
 .99000 
 
 .15787 
 
 .98746 
 
 55 
 
 6 
 
 .08889 
 
 .99604 
 
 .10626 
 
 .99434 
 
 .12360 
 
 .99233 
 
 .14090 
 
 .99002 
 
 .15816 
 
 .98741 
 
 54 
 
 7 
 
 .08918 
 
 .99602 
 
 .10655 
 
 .99431 
 
 .12389 
 
 .99230 
 
 .14119 
 
 .98098 
 
 .15845 
 
 .98737 
 
 53 
 
 8 
 
 .08947 
 
 .99599 
 
 .10684 
 
 .99428 
 
 .12418 
 
 .99220 
 
 .14148 
 
 .98994 
 
 .15873 
 
 .98732 
 
 52 
 
 
 
 .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 
 
 40771 
 
 .99418 
 
 .12504 
 
 .99215 
 
 .14234 
 
 .98982 
 
 .15959 
 
 .98718 
 
 49 
 
 12 
 
 .09063 
 
 .99588 
 
 .10800 
 
 .99415 
 
 .12533 
 
 .99211 
 
 .14263 
 
 .98978 
 
 .15988 
 
 .98714 
 
 48 
 
 13 
 
 .09092 
 
 .99586 
 
 .10829 
 
 .99412 
 
 .12562 
 
 .99208 
 
 .14292 
 
 .98973 
 
 .16017 
 
 .98709 
 
 47 
 
 14 
 
 .09121 
 
 .99583 
 
 .10858 
 
 .99409 
 
 .12591 
 
 .99204 
 
 .14320 
 
 .98969 
 
 .16046 
 
 .98704 
 
 46 
 
 15 
 
 .09150 
 
 .99580 
 
 .10887 
 
 .99406 
 
 .12620 
 
 .99200 
 
 .14349 
 
 .98965 
 
 .16074 
 
 .98700 
 
 45 
 
 16 
 
 .09179 
 
 .99578 
 
 .10916 
 
 .99402 
 
 .12649 
 
 .99197 
 
 .14378 
 
 .98961 
 
 .16103 
 
 .98695 
 
 44 
 
 17 
 
 .09208 
 
 .99575 
 
 .10945 
 
 .99399 
 
 .12678 
 
 .99193 
 
 .14407 
 
 .98957 
 
 .16132 
 
 .98690 
 
 43 
 
 18 
 
 .09237 
 
 .99572 
 
 .10973 
 
 .99396 
 
 .12706 
 
 .99189 
 
 .14436 
 
 .98953 
 
 .16160 
 
 .98686 
 
 42 
 
 19 
 
 .09266 
 
 .99570 
 
 .11002 
 
 .99393 
 
 .12735 
 
 .99186 
 
 .14464 
 
 .98948 
 
 .16189 
 
 .98681 
 
 41 
 
 20 
 
 .09295 
 
 .99567 
 
 .11031 
 
 .99390 
 
 .12764 
 
 .99182 
 
 .14493 
 
 .98944 
 
 .16218 
 
 .98676 
 
 40 
 
 21 
 
 .09324 
 
 .99564 
 
 .11060 
 
 .99386 
 
 .12793 
 
 .99178 
 
 .14522 
 
 .98940 
 
 .16246 
 
 .98671 
 
 39 
 
 22 
 
 .09353 
 
 .99562 
 
 .11089 
 
 .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 
 
 .99167 
 
 .14608 
 
 .98927 
 
 .16333 
 
 .98657 
 
 36 
 
 25 
 
 .09440 
 
 .99553 
 
 .11176 
 
 .99374 
 
 .12908 
 
 .99163 
 
 .14637 
 
 .98923 
 
 .16361 
 
 .98652 
 
 35 
 
 26 
 
 .09469 
 
 ,99551 
 
 .11205 
 
 .99370 
 
 .12937 
 
 .99160 
 
 .14660 
 
 .98919 
 
 .16390 
 
 .98648 
 
 34 
 
 27 
 
 .09498 
 
 .99548 
 
 .11234 
 
 .99367 
 
 .12966 
 
 .99156 
 
 .14695 
 
 .98914 
 
 .16419 
 
 .98643 
 
 33 
 
 28 
 
 .09527 
 
 .99545 
 
 .11263 
 
 .99364 
 
 .12995 
 
 .99152 
 
 .14723 
 
 .98910 
 
 .16447 
 
 .98638 
 
 32 
 
 29 
 
 .09556 
 
 .99542 
 
 .11291 
 
 .99360 
 
 .13024 
 
 .99148 
 
 .14752 
 
 .98900 
 
 .16476 
 
 .98633 
 
 31 
 
 30 
 
 .09585 
 
 .99540 
 
 .11320 
 
 .99357 
 
 .13053 
 
 .99144 
 
 .14781 
 
 .98902 
 
 .16505 
 
 .08629 
 
 30 
 
 31 
 
 .09614 
 
 .99537 
 
 .11349 
 
 .99354 
 
 .13081 
 
 .99141 
 
 .14810 
 
 .98897 
 
 .16533 
 
 .98624 
 
 29 
 
 32 
 
 .09642 
 
 .99534 
 
 .11378 
 
 .99351 
 
 .13110 
 
 .99137 
 
 .14838 
 
 .98893 
 
 .16562 
 
 .98610 
 
 28 
 
 33 
 
 .09671 
 
 .99531 
 
 .11407 
 
 .99347 
 
 .13139 
 
 .99133 
 
 .14867 
 
 .98889 
 
 .16591 
 
 .98614 
 
 27 
 
 34 
 
 .09700 
 
 .99528 
 
 .11431 
 
 .99344 
 
 .13168 
 
 .99129 
 
 .14896 
 
 .98884 
 
 .16620 
 
 .98609 
 
 26 
 
 35 
 
 .09729 
 
 .99526 
 
 .11465 
 
 .99341 
 
 .13197 
 
 .99125 
 
 .14925 
 
 .98880 
 
 .16648 
 
 .98604 
 
 25 
 
 36 
 
 .09758 
 
 .99523 
 
 ,11494 
 
 .99337 
 
 .13226 
 
 .99122 
 
 .14954 
 
 .98876 
 
 .16677 
 
 .98600 
 
 24 
 
 37 
 
 .09787 
 
 .99520 
 
 .11523 
 
 ,99334 
 
 .13254 
 
 .99118 
 
 .14982 
 
 .98871 
 
 .16706 
 
 .98595 
 
 23 
 
 38 
 
 .09816 
 
 .99517 
 
 .11552 
 
 .99331 
 
 .13283 
 
 .99114 
 
 .15011 
 
 .98867 
 
 .16734 
 
 .98590 
 
 22 
 
 39 
 
 .09845 
 
 .99514 
 
 .11580 
 
 .99327 
 
 .13312 
 
 .99110 
 
 .15040 
 
 .98863 
 
 .16763 
 
 .98585 
 
 21 
 
 40 
 
 .09874 
 
 ,99511 
 
 ,11609 
 
 ,99324 
 
 .13341 
 
 .99106 
 
 .15069 
 
 .98858 
 
 .16792 
 
 .98580 
 
 20 
 
 41 
 
 .09903 
 
 .99508 
 
 .11638 
 
 .99320 
 
 .13370 
 
 .99102 
 
 .15097 
 
 .98854 
 
 .16820 
 
 .98575 
 
 19 
 
 42 
 
 .09932 
 
 .99506 
 
 .11667 
 
 .99317 
 
 .13399 
 
 .99098 
 
 .15126 
 
 .98849 
 
 .16849 
 
 .98570 
 
 18 
 
 43 
 
 .09961 
 
 .99503 
 
 .11696 
 
 .99314 
 
 .13427 
 
 .99094 
 
 .15155 
 
 .98845 
 
 .16878 
 
 .98565 
 
 17 
 
 44 
 
 ,09990 
 
 ,99500 
 
 .11725 
 
 .99310 
 
 .13456 
 
 .99091 
 
 .15184 
 
 .98841 
 
 .16906 
 
 .98561 
 
 16 
 
 45 
 
 .10019 
 
 .99497 
 
 .11754 
 
 .99307 
 
 .13485 
 
 .99087 
 
 .15212 
 
 .98836 
 
 .16935 
 
 .98556 
 
 15 
 
 46 
 
 .10048 
 
 .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 
 
 .15299 
 
 .98823 
 
 .17021 
 
 .98541 
 
 12 
 
 49 
 
 .10135 
 
 ,99485 
 
 .11869 
 
 .99293 
 
 ,13600 
 
 .99071 
 
 .15327 
 
 .98818 
 
 .17050 
 
 .98536 
 
 11 
 
 50 
 
 ,10164 
 
 .99482 
 
 .11898 
 
 ,99290 
 
 .13629 
 
 .99067 
 
 .15356 
 
 .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 
 
 .$8521 
 
 8 
 
 53 
 
 .10250 
 
 .99473 
 
 .11985 
 
 .99279 
 
 .13716 
 
 .99055 
 
 .15442 
 
 .98800 
 
 .17164 
 
 .98516 
 
 7 
 
 54 
 
 .10279 
 
 .99470 
 
 .12014 
 
 .99276 
 
 .13744 
 
 .99051 
 
 .15471 
 
 .98790 
 
 .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 
 
 .99161 
 
 .12100 
 
 .90265 
 
 .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 
 
 rtosin 
 
 Sine 
 
 Cosin 
 
 Sine 
 
 Cosin 
 
 Sine 
 
 Cosin 
 
 Sine 
 
 Cosin 
 
 Sine 
 
 f 
 
 
 84 
 
 83 
 
 82 
 
 81 
 
 80 
 
 
NATURAL SINES AND COSINES. 
 
 105 
 
 
 1 
 
 
 
 1 
 
 1 
 
 1 
 
 2 
 
 1 
 
 3 
 
 1< 
 
 t 
 
 
 
 Sine 
 
 Cosin 
 
 Sine 
 
 Cosin 
 
 Sine 
 
 Cosin 
 
 Sine 
 
 Cosin 
 
 Sine 
 
 Cosin 
 
 
 
 
 .17365 
 
 .98481 
 
 .19081 
 
 .98163 
 
 .20791 
 
 .97815 
 
 .22495 
 
 .97437 
 
 .24192 
 
 97030 
 
 60 
 
 1 
 
 .17393 
 
 .98476 
 
 .19109 
 
 .98157 
 
 .20820 
 
 .97809 
 
 .22523 
 
 .97430 
 
 .24220 
 
 97023 
 
 59 
 
 2 
 
 .17422 
 
 .98471 
 
 .19138 
 
 .98152 
 
 .20848 
 
 .97803 
 
 .22552 
 
 .97424 
 
 .24249 
 
 .97015 
 
 58 
 
 3 
 
 .17451 
 
 .98466 
 
 .19167 
 
 .98146 
 
 .20877 
 
 .97797 
 
 .22580 
 
 97417 
 
 .24277 
 
 .97008 
 
 57 
 
 4 
 
 .17479 
 
 .98461 
 
 .19195 
 
 .98140 
 
 .20905 
 
 .97791 
 
 .22608 
 
 .97411 
 
 .24305 
 
 .97001 
 
 56 
 
 5 
 
 .17508 
 
 .98455 
 
 .19224 
 
 .98135 
 
 .20933 
 
 .97784 
 
 .22637 
 
 .97404 
 
 .24333 
 
 .96994 
 
 55 
 
 6 
 
 .17537 
 
 .98450 
 
 .19252 
 
 .98129 
 
 .20962 
 
 .97778 
 
 .22665 
 
 .97398 
 
 .24362 
 
 .96987 
 
 54 
 
 7 
 
 .17565 
 
 .98445 
 
 .19281 
 
 .98124 
 
 .20990 
 
 .97772 
 
 .22693 
 
 .97391 
 
 .24390 
 
 .96980 
 
 53 
 
 8 
 
 .17594 
 
 .98440 
 
 .19309 
 
 .98118 
 
 .21019 
 
 .97766 
 
 .22722 
 
 .97384 
 
 .24418 
 
 .96973 
 
 52 
 
 9 
 
 .17623 
 
 .98435 
 
 .19338 
 
 .98112 
 
 .21047 
 
 .97760 
 
 .22750 
 
 .97378 
 
 .24446 
 
 .96966 
 
 51 
 
 10 
 
 .17651 
 
 .98430 
 
 .19366 
 
 .98107 
 
 .21076 
 
 .97754 
 
 .22778 
 
 .97371 
 
 .24474 
 
 .96959 
 
 50 
 
 11 
 
 .17680 
 
 .98425 
 
 .19395 
 
 .98101 
 
 .21104 
 
 .97748 
 
 .22807 
 
 .97365 
 
 .24503 
 
 .96952 
 
 49 
 
 12 
 
 .17708 
 
 .98420 
 
 .19423 
 
 .98096 
 
 .21132 
 
 .97742 
 
 .22835 
 
 .97358 
 
 .24531 
 
 .96945 
 
 48 
 
 13 
 
 .17737 
 
 .98414 
 
 .19452 
 
 .98090 
 
 .21101 
 
 .97735 
 
 .22863 
 
 .97351 
 
 .24559 
 
 .96937 
 
 47 
 
 14 
 
 .17766 
 
 .98409 
 
 .19481 
 
 .98084 
 
 .21189 
 
 .97729 
 
 .22892 
 
 .97345 
 
 .24587 
 
 .96930 
 
 46 
 
 15 
 
 .17794 
 
 .98404 
 
 .19509 
 
 .98079 
 
 .21218 
 
 .97723 
 
 .22920 
 
 .97338 
 
 .24615 
 
 .96923 
 
 45 
 
 16 
 
 17823 
 
 .98399 
 
 .19538 
 
 .98073 
 
 .21246 
 
 .97717 
 
 .22948 
 
 .97331 
 
 .24644 
 
 .96916 
 
 44 
 
 17 
 
 .17852 
 
 .98394 
 
 .19566 
 
 .98067 
 
 .21275 
 
 .97711 
 
 .22977 
 
 .97325 
 
 .24672 
 
 .96909 
 
 43 
 
 18 
 
 17880 
 
 .98389 
 
 .19595 
 
 .98061 
 
 .21303 
 
 .97705 
 
 .23005 
 
 .97318 
 
 .24700 
 
 .96902 
 
 42 
 
 19 
 
 17909 
 
 .98383 
 
 .19623 
 
 .98056 
 
 .21331 
 
 .97698 
 
 .23033 
 
 .97311 
 
 .24728 
 
 .96894 
 
 41 
 
 20 
 
 .17937 
 
 .98378 
 
 .19652 
 
 .98050 
 
 .21360 
 
 .97692 
 
 .23062 
 
 .97304 
 
 .24756 
 
 .96887 
 
 40 
 
 21 
 
 .17966 
 
 .98373 
 
 .19680 
 
 .98044 
 
 .21388 
 
 .97686 
 
 .23090 
 
 .97298 
 
 .24784 
 
 .96880 
 
 39 
 
 22 
 
 .17995 
 
 .98368 
 
 .19709 
 
 .98039 
 
 .21417 
 
 .97680 
 
 .23118 
 
 .97291 
 
 .24813 
 
 .96873 
 
 38 
 
 23 
 
 .18023 
 
 .98362 
 
 .19737 
 
 .98033 
 
 .21445 
 
 .97673 
 
 .23146 
 
 .97284 
 
 .24841 
 
 .96866 
 
 37 
 
 24 
 
 .18052 
 
 .98357 
 
 .19766 
 
 .98027 
 
 .21474 
 
 .97667 
 
 .23175 
 
 .97278 
 
 .24869 
 
 .96858 
 
 36 
 
 25 
 
 .18081 
 
 .98352 
 
 .19794 
 
 .9S021 
 
 .21502 
 
 .97661 
 
 ,23203 
 
 .97271 
 
 .24897 
 
 .96851 
 
 35 
 
 2G 
 
 .18109 
 
 .98347 
 
 .19823 
 
 .98016 
 
 .21530 
 
 .97655 
 
 .23231 
 
 .97264 
 
 .24925 
 
 .96844 
 
 34 
 
 27 
 
 .18138 
 
 .98341 
 
 .19851 
 
 .98010 
 
 .21559 
 
 .97648 
 
 .23260 
 
 .97257 
 
 .24954 
 
 .96837 
 
 33 
 
 28 
 
 .18166 
 
 .98336 
 
 .19880 
 
 ,98004 
 
 .21587 
 
 .97642 
 
 .23288 
 
 .97251 
 
 .24982 
 
 .96829 
 
 32 
 
 29 
 
 .18195 
 
 .98331 
 
 .19908 
 
 .97998 
 
 .21616 
 
 .97636 
 
 .23316 
 
 .97244 
 
 .25010 
 
 .96822 
 
 31 
 
 30 
 
 .18224 
 
 .98325 
 
 .19937 
 
 .97992 
 
 .21644 
 
 .97630 
 
 .23345 
 
 .97237 
 
 .25038 
 
 .96815 
 
 30 
 
 31 
 
 .18252 
 
 .98320 
 
 .19965 
 
 .97987 
 
 .21072 
 
 .97623 
 
 .23373 
 
 .97230 
 
 .25066 
 
 .96807 
 
 29 
 
 32 
 
 .18281 
 
 .98315 
 
 .19994 
 
 .97981 
 
 .21701 
 
 .97617 
 
 .23401 
 
 .97223 
 
 .25094 
 
 .96800 
 
 28 
 
 33 
 
 .18309 
 
 .98310 
 
 .20022 
 
 .97975 
 
 .21729 
 
 .97611 
 
 .23429 
 
 .97217 
 
 .25122 
 
 .96793 
 
 27 
 
 34 
 
 .18338 
 
 .98304 
 
 .20051 
 
 .97969 
 
 .21758 
 
 .97604 
 
 .23458 
 
 .97210 
 
 .25151 
 
 .96786 
 
 26 
 
 35 
 
 .18367 
 
 .98299 
 
 .20079 
 
 .97963 
 
 .21786 
 
 .97598 
 
 .23486 
 
 .97203 
 
 .25179 
 
 .96778 
 
 25 
 
 36 
 
 .18395 
 
 .98294 
 
 .20108 
 
 .97958 
 
 .21814 
 
 .97592 
 
 .23514 
 
 .97196 
 
 .25207 
 
 .96771 
 
 24 
 
 37 
 
 .18424 
 
 .98288 
 
 .20136 
 
 .97952 
 
 .21843 
 
 .97585 
 
 .23542 
 
 .97189 
 
 .25235 
 
 .96764 
 
 23 
 
 38 
 
 .18152 
 
 .98283 
 
 .20165 
 
 .97946 
 
 .21871 
 
 .97579 
 
 .23571 
 
 .97182 
 
 .25263 
 
 .96756 
 
 22 
 
 39 
 
 .18481 
 
 .98277 
 
 .20193 
 
 .97940 
 
 .21899 
 
 .97573 
 
 .23599 
 
 .97176 
 
 .25291 
 
 .96749 
 
 21 
 
 40 
 
 .18509 
 
 .98272 
 
 .20222 
 
 .97934 
 
 .21928 
 
 .97566 
 
 .23627 
 
 .97169 
 
 .25320 
 
 .96742 
 
 20 
 
 41 
 
 .18538 
 
 .98267 
 
 .20250 
 
 .97928 
 
 .21956 
 
 .97560 
 
 .23656 
 
 .97162 
 
 .25348 
 
 .96734 
 
 19 
 
 42 
 
 .18567 
 
 .98261 
 
 .20279 
 
 .97922 
 
 .21985 
 
 .97553 
 
 .23684 
 
 .97155 
 
 .25376 
 
 .96727 
 
 18 
 
 43 
 
 .18595 
 
 .98256 
 
 .20307 
 
 .97916 
 
 .22013 
 
 .97547 
 
 .23712 
 
 .97148 
 
 .25404 
 
 .96719 
 
 17 
 
 44 
 
 .18624 
 
 .98250 
 
 .20336 
 
 .97910 
 
 .22041 
 
 .97541 
 
 .23740 
 
 .97141 
 
 .25432 
 
 .96712 
 
 16 
 
 45 
 
 .18652 
 
 .98245 
 
 .20364 
 
 .97905 
 
 .22070 
 
 .97534 
 
 .23769 
 
 .97134 
 
 .25460 
 
 .96705 
 
 15 
 
 46 
 
 .18681 
 
 .98240 
 
 .20393 
 
 .97899 
 
 .22098 
 
 .97528 
 
 .23797 
 
 .97127 
 
 .25488 
 
 .96697 
 
 14 
 
 47 
 
 .18710 
 
 .98234 
 
 .20421 
 
 .97893 
 
 .22126 
 
 .97521 
 
 .23825 
 
 .97120 
 
 .25516 
 
 .96690 
 
 13 
 
 48 
 
 .18738 
 
 .98229 
 
 .20450 
 
 .97887 
 
 .22155 
 
 .97515 
 
 .23853 
 
 .97113 
 
 .25545 
 
 .96682 
 
 12 
 
 49 
 
 .18767 
 
 .98223 
 
 .20478 
 
 .97881 
 
 .22183 
 
 .97508 
 
 .23882 
 
 .97106 
 
 .25573 
 
 .96675 
 
 11 
 
 50 
 
 .18795 
 
 .98218 
 
 .20507 
 
 .97875 
 
 .22212 
 
 .97502 
 
 .23910 
 
 .97100 
 
 .25001 
 
 .96607 
 
 10 
 
 51 
 
 .18824 
 
 .98212 
 
 .20535 
 
 .97869 
 
 .22240 
 
 .97496 
 
 .23938 
 
 .97093 
 
 .25629 
 
 .96660 
 
 9 
 
 52 
 
 .18852 
 
 .98207 
 
 .20563 
 
 .97863 
 
 .22268 
 
 .97489 
 
 .23966 
 
 .97086 
 
 .25657 
 
 96653 
 
 g 
 
 53 
 
 .18881 
 
 .98201 
 
 .20592 
 
 .97857 
 
 .22297 
 
 .97483 
 
 .23995 
 
 .97079 
 
 ,25685 
 
 .96645 
 
 7 
 
 54 
 
 .18910 
 
 .98196 
 
 .20620 
 
 .97851 
 
 .22325 
 
 .97476 
 
 .24023 
 
 .97072 
 
 .25713 
 
 .96638 
 
 6 
 
 55 
 
 .18938 
 
 .98190 
 
 .20649 
 
 .97845 
 
 .22353 
 
 .97470 
 
 .24051 
 
 .97065 
 
 .25741 
 
 ,96630 
 
 5 
 
 56 
 
 .18967 
 
 .98185 
 
 .20677 
 
 .97839 
 
 .22382 
 
 .97463 
 
 .24079 
 
 .97058 
 
 .25769 
 
 .96623 
 
 4 
 
 57 
 
 .18995 
 
 .98179 
 
 .20706 
 
 .97833 
 
 .22410 
 
 .97457 
 
 .24108 
 
 .97051 
 
 .25798 
 
 .96615 
 
 3 
 
 58 
 
 .19024 
 
 .98174 
 
 .20734 
 
 .97827 
 
 .22438 
 
 .97450 
 
 .24136 
 
 .97044 
 
 .25826 
 
 .96608 
 
 2 
 
 59 
 
 .19052 
 
 .98168 
 
 .20763 
 
 .97821 
 
 .22487 
 
 .97444 
 
 .24164 
 
 .97037 
 
 .25854 
 
 .96600 
 
 1 
 
 60 
 
 .19081 
 
 .98163 
 
 .20791 
 
 .97815 
 
 .22495 
 
 .97437 
 
 .24192 
 
 .97030 
 
 .25882 
 
 .96593 
 
 
 
 , 
 
 Cosin 
 
 Sine 
 
 iCosin 
 
 Sine 
 
 Cosin 
 
 Sine 
 
 Cosin 
 
 Sine 
 
 Cosin 
 
 Sine 
 
 / 
 
 
 7 
 
 9 
 
 7 
 
 8 
 
 7 
 
 7 
 
 7 
 
 6 
 
 7 
 
 5 
 
 
106 
 
 NATURAL SINES AND COSINES. 
 
 
 | 
 
 5 
 
 1 
 
 6 
 
 1 
 
 7 
 
 1 
 
 8 
 
 1 
 
 ? 
 
 
 
 Sine 
 
 Cosin 
 
 Sine 
 
 \>sin 
 
 Sine 
 
 .'osin 
 
 Sine 
 
 'osin 
 
 Sine 
 
 Cosin 
 
 
 
 
 25X82 
 
 96593 
 
 .27564 
 
 96126 
 
 .29237 
 
 95(530 
 
 .30902 
 
 9510(5 
 
 .32557 
 
 94552 
 
 00 
 
 1 
 
 25910 
 
 96585 
 
 .27592 
 
 5)01 18 
 
 .29205 
 
 95(522 
 
 .30929 
 
 95097 
 
 .32584 
 
 94512 
 
 59 
 
 2 
 
 2593X 
 
 96578 
 
 .27(520 
 
 901 10 
 
 .29293 
 
 95013 
 
 .30! 157 
 
 95088 
 
 32*512 
 
 94533 
 
 5X 
 
 3 
 
 25900 
 
 005 70 
 
 .2704N 
 
 90102 
 
 .29321 
 
 95005 
 
 .309X5 
 
 95079 
 
 .3203!) 
 
 94523 
 
 57 
 
 4 
 
 25991 
 
 90502 
 
 ,27676 
 
 9:5094 
 
 .2931X 
 
 95590 
 
 .31012 
 
 95070 
 
 .321 507 
 
 94514 
 
 5(5 
 
 5 
 
 20022 
 
 96555 
 
 .27704 
 
 5)00X0 
 
 .29370 
 
 955SX 
 
 :noio 
 
 95061 
 
 .32091 
 
 94504 
 
 55 
 
 6 
 
 20050 
 
 90547 
 
 .27731 
 
 90078 
 
 .29404 
 
 95579 
 
 31068 
 
 95052 
 
 32722 
 
 91495 
 
 54 
 
 7 
 
 20079 
 
 90510 
 
 .27759 
 
 90070 
 
 .29432 
 
 95571 
 
 .31095 
 
 950 I.'! 
 
 !32749 
 
 944X5 
 
 53 
 
 8 
 
 20107 
 
 90532 
 
 .27787 
 
 90002 
 
 .29400 
 
 955(52 
 
 .31123 
 
 95033 
 
 .32777 
 
 94476 
 
 52 
 
 9 
 
 20135 
 
 90524 
 
 27815 
 
 96054 
 
 .29487 
 
 95554 
 
 ;> 1 1 5 1 
 
 950' '4 
 
 3"X04 
 
 9440b 
 
 51 
 
 10 
 
 26163 
 
 90517 
 
 ,27848 
 
 90010 
 
 .29515 
 
 95545 
 
 .31178 
 
 95015 
 
 '.32832 
 
 94457 
 
 50 
 
 11 
 
 26191 
 
 90509 
 
 .27871 
 
 90037 
 
 .29513 
 
 95530 
 
 31200 
 
 95000 
 
 .32X59 
 
 9 I 147 
 
 49 
 
 12 
 
 26219 
 
 90502 
 
 .27X99 
 
 9002!) 
 
 .29571 
 
 9552X 
 
 .31233 
 
 94997 
 
 .32XX7 
 
 941 3X 
 
 48 
 
 13 
 
 26217 
 
 90194 
 
 .27927 
 
 90021 
 
 .29599 
 
 9551!) 
 
 31201 
 
 94 988 
 
 .32914 
 
 94 12X 
 
 47 
 
 14 
 
 20275 
 
 9(5480 
 
 .27955 
 
 90013 
 
 .29(520 
 
 955 1 1 
 
 312X9 
 
 94979 
 
 .32942 
 
 944 IX 
 
 40 
 
 15 
 
 26303 
 
 90479 
 
 .279X3 
 
 90005 
 
 .29054 
 
 95502 
 
 31310 
 
 94970 
 
 .329o!) 
 
 9140!) 
 
 45 
 
 16 
 
 26331 
 
 90471 
 
 .28011 
 
 95997 
 
 .29(5X2 
 
 95493 
 
 31344 
 
 949(51 
 
 .32997 
 
 91399 
 
 44 
 
 17 
 
 26359 
 
 96163 
 
 .2X03') 
 
 95989 
 
 .29710 
 
 954X5 
 
 31372 
 
 94952 
 
 .:',3021 
 
 94390 
 
 43 
 
 18 
 
 263S7 
 
 90150 
 
 .2X0(57 
 
 959X1 
 
 .29737 
 
 95476 
 
 3139!) 
 
 94943 
 
 .33051 
 
 943X0 
 
 42 
 
 19 
 
 20115 
 
 96448 
 
 2X095 
 
 95972 
 
 2970.") 
 
 95407 
 
 31427 
 
 94933 
 
 .33079 
 
 .94370 
 
 41 
 
 20 
 
 26443 
 
 96440 
 
 .28123 
 
 959(54 
 
 .29793 
 
 95459 
 
 .31454 
 
 94924 
 
 .33100 
 
 .94361 
 
 40 
 
 21 
 
 26471 
 
 96433 
 
 .28150 
 
 95956 
 
 .29821 
 
 95450 
 
 .31482 
 
 94915 
 
 .33131 
 
 94351 
 
 39 
 
 22 
 
 20500 
 
 90425 
 
 .2X17X 
 
 9594 X 
 
 .29X49 
 
 95441 
 
 .31510 
 
 94906 
 
 .33 1)51 
 
 94342 
 
 38 
 
 23 
 
 2052S 
 
 96417 
 
 .2X200 
 
 95940 
 
 .29X70 
 
 95433 
 
 .31537 
 
 94897 
 
 .33 IX!) 
 
 94332 
 
 37 
 
 24 
 
 20550 
 
 96410 
 
 .2X23 1 
 
 95931 
 
 .29904 
 
 95424 
 
 .31505 
 
 94XXX 
 
 .33210 
 
 94322 
 
 3(5 
 
 25 
 
 205S4 
 
 90402 
 
 .2X202 
 
 95923 
 
 .29932 
 
 95115 
 
 31593 
 
 94878 
 
 .33214 
 
 94313 
 
 35 
 
 26 
 
 26612 
 
 96394 
 
 2X290 
 
 95915 
 
 .29900 
 
 95407 
 
 31020 
 
 94869 
 
 .33271 
 
 94303 
 
 34 
 
 37 
 
 200 U) 
 
 90380 
 
 .2X3 IX 
 
 95907 
 
 .29987 
 
 95398 
 
 31648 
 
 94800 
 
 .33298 
 
 94293 
 
 33 
 
 28 
 
 2000S 
 
 90379 
 
 .2X34(5 
 
 95S9X 
 
 .30015 
 
 953X9 
 
 31(575 
 
 94851 
 
 .3332(5 
 
 942X4 
 
 32 
 
 29 
 
 26696 
 
 96371 
 
 .28374 
 
 95X90 
 
 .30043 
 
 95380 
 
 .31703 
 
 94812 
 
 .33353 
 
 94274 
 
 31 
 
 30 
 
 26724 
 
 .96363 
 
 .28402 
 
 95882 
 
 .30071 
 
 95372 
 
 .31730 
 
 94832 
 
 .33381 
 
 .942(54 
 
 30 
 
 31 
 
 26752 
 
 .96355 
 
 .28429 
 
 95874 
 
 .30098 
 
 953(53 
 
 .31758 
 
 94823 
 
 .33408 
 
 .94254 
 
 29 
 
 32 
 
 267SO 
 
 .9(5347 
 
 .28457 
 
 1)5X05 
 
 :ioi2o 
 
 95354 
 
 .317X0 
 
 948 1 4 
 
 .3343(5 
 
 .94245 
 
 28 
 
 33 
 
 20SOS 
 
 .903 10 
 
 .28485 
 
 95X57 
 
 .30154 
 
 95345 
 
 .31813 
 
 94X05 
 
 .33403 
 
 .94235 
 
 27 
 
 34 
 
 20X30 
 
 .90332 
 
 .28513 
 
 95X49 
 
 .30182 
 
 95337 
 
 .31X41 
 
 94795 
 
 .33490 
 
 .94225 
 
 2(5 
 
 35 
 
 20X04 
 
 .90324 
 
 .28541 
 
 95X4 1 
 
 .30209 
 
 9532X 
 
 .31808 
 
 94780 
 
 .335 IX 
 
 .94215 
 
 25 
 
 36 
 
 20S92 
 
 .9(5310 
 
 .2X5(59 
 
 95S32 
 
 .30237 
 
 95319 
 
 .31X9(5 
 
 94777 
 
 .33545 
 
 .94200 
 
 24 
 
 37 
 
 20920 
 
 .96308 
 
 .2X597 
 
 95X24 
 
 .30205 
 
 95310 
 
 .31923 
 
 .94768 
 
 .33573 
 
 .94196 
 
 23 
 
 38 
 
 20948 
 
 .90301 
 
 .28025 
 
 95X1(5 
 
 .30292 
 
 95301 
 
 .31951 
 
 94758 
 
 .33000 
 
 .94186 
 
 22 
 
 39 
 
 2007(1 
 
 .9(5293 
 
 .2X052 
 
 95X07 
 
 .30320 
 
 95293 
 
 .31979 
 
 .94749 
 
 .33027 
 
 .94176 
 
 21 
 
 40 
 
 .27004 
 
 .96285 
 
 .28680 
 
 .95799 
 
 .30348 
 
 95284 
 
 .32006 
 
 .94740 
 
 .33655 
 
 .94167 
 
 20 
 
 41 
 
 .27032 
 
 .96277 
 
 .2870X 
 
 95791 
 
 .30376 
 
 95275 
 
 .32034 
 
 .94730 
 
 .330X2 
 
 .94157 
 
 19 
 
 42 
 
 27000 
 
 .902(59 
 
 .28730 
 
 .957X2 
 
 .30103 
 
 95200 
 
 .32061 
 
 .94721 
 
 .33710 
 
 .94147 
 
 18 
 
 43 
 
 .27088 
 
 .9(5201 
 
 .28764 
 
 .95774 
 
 .30431 
 
 95257 
 
 .320X9 
 
 .94712 
 
 .23737 
 
 .91137 
 
 17 
 
 44 
 
 .27116 
 
 .9(5253 
 
 .28792 
 
 .95700 
 
 .3015!) 
 
 .9524X 
 
 .321 10 
 
 .94702 
 
 .337(54 
 
 .94127 
 
 16 
 
 45 
 
 .27144 
 
 .9(5240 
 
 .28X20 
 
 .95757 
 
 .30486 
 
 .95240 
 
 .32144 
 
 .94093 
 
 .33792 
 
 .941 IX 
 
 15 
 
 46 
 
 .27172 
 
 .90238 
 
 .28X47 
 
 .95749 
 
 .30514 
 
 .95231 
 
 .32171 
 
 .9 1(5X4 
 
 .33X1!) 
 
 .94108 
 
 14 
 
 47 
 
 .27200 
 
 .9(5230 
 
 .28X75 
 
 .95740 
 
 .30542 
 
 .95222 
 
 .32199 
 
 .94074 
 
 .33841 
 
 .94098 
 
 13 
 
 48 
 
 .27228 
 
 .90222 
 
 .2X903 
 
 .95732 
 
 .30570 
 
 .95213 
 
 .32227 
 
 .94665 
 
 .33X71 
 
 .!) 10XS 
 
 12 
 
 49 
 
 .2725C 
 
 .96214 
 
 .28931 
 
 .95724 
 
 .30597 
 
 .95204 
 
 .32254 
 
 .91050 
 
 .33901 
 
 .94078 
 
 11 
 
 50 
 
 .27284 
 
 .96206 
 
 .28959 
 
 .95715 
 
 .30625 
 
 .95195 
 
 .32282 
 
 .94646 
 
 .33929 
 
 .94068 
 
 10 
 
 51 
 
 .27312 
 
 .96198 
 
 .28987 
 
 .95707 
 
 .30653 
 
 .95186 
 
 .32309 
 
 .94637 
 
 .3395f 
 
 .94058 
 
 9 
 
 52 
 
 .27340 
 
 .9(5190 
 
 .29015 
 
 .95698 
 
 .30(5X0 
 
 .95177 
 
 .32337 
 
 .94627 
 
 .33983 
 
 .94049 
 
 8 
 
 53 
 
 .27308 
 
 .961.82 
 
 .29042 
 
 .95090 
 
 .3070X 
 
 .95168 
 
 .323(54 
 
 .94(5 IX 
 
 .34011 
 
 .9103! 
 
 7 
 
 54 
 
 .2739( 
 
 .96171 
 
 .29070 
 
 .950X1 
 
 .3073( 
 
 .95159 
 
 .32392 
 
 .94609 
 
 .3403X 
 
 .94021 
 
 6 
 
 55 
 
 .27424 
 
 .9(51(50 
 
 .29098 
 
 .95073 
 
 .3076? 
 
 .95150 
 
 .3241! 
 
 .94599 
 
 .34()6. p 
 
 .9401! 
 
 5 
 
 56 
 
 .27452 
 
 .9(5 158 
 
 .2912C 
 
 .95004 
 
 .30791 
 
 .95112 
 
 .32447 
 
 .94590 
 
 .340!).' 
 
 .9400! 
 
 4 
 
 57 
 
 .27480 
 
 .96150 
 
 .29154 
 
 .9505* 
 
 .30X1'. 
 
 .95133 
 
 .32474 
 
 .935X0 
 
 .34120 
 
 .9399? 
 
 3 
 
 58 
 
 .2750S 
 
 .96142 
 
 .291 XL 
 
 .95(547 
 
 .30841 
 
 .95124 
 
 .32502 
 
 .94571 
 
 .34147 
 
 .939X! 
 
 2 
 
 59 
 
 .27536 
 
 .96134 
 
 .2920'. 
 
 .06881 
 
 .30X74 
 
 .95115 
 
 .3252! 
 
 .94561 
 
 .34175 
 
 .9397! 
 
 1 
 
 60 
 
 .27564 
 
 .96126 
 
 .29237 
 
 .95630 
 
 .30902 
 
 .95106 
 
 .32557 
 
 .94552 
 
 .34202 
 
 .93969 
 
 
 
 9 
 
 Cosin 
 
 Sine 
 
 Cosin 
 
 Sine 
 
 Cosin 
 
 Sine 
 
 Cosin 
 
 Sinn 
 
 Cosin 
 
 Sine 
 
 t 
 
 
 3 
 
 4 
 
 7 
 
 3 
 
 7 
 
 2 
 
 7 
 
 1 
 
 7 
 
 
 
 
NATURAL SINES AND COSINES. 
 
 107 
 
 
 20 
 
 21 
 
 22 
 
 23 
 
 24 
 
 
 
 Sine 
 
 1 osin 
 
 Sine 
 
 'osin 
 
 Sine 
 
 'osin 
 
 Sine 
 
 Sown 
 
 Sine 
 
 'osin 
 
 
 
 
 34202 
 
 )3909 
 
 .35837 
 
 93358 
 
 37461 
 
 92718 
 
 39073 
 
 92050 
 
 40674 
 
 91355 
 
 oO 
 
 1 
 
 J4229 
 
 )395!) 
 
 .35804 
 
 9334XJ 
 
 37488 
 
 92707 
 
 39100 
 
 92039 
 
 40700 
 
 91343 
 
 59 
 
 2 
 
 34257 
 
 WM9 
 
 .35891 
 
 93337 
 
 37515 
 
 92697 
 
 39127 
 
 92028 
 
 40727 
 
 91331 
 
 58 
 
 3 
 
 54284 
 
 (3939 
 
 .35!) 18 
 
 93327 
 
 37542 
 
 92686 
 
 3!) 153 
 
 92016 
 
 .40753 
 
 91319 
 
 57 
 
 4 
 
 M3! 1 
 
 )39U9 
 
 .85915 
 
 93310 
 
 37509 
 
 92075 
 
 3!) ISO 
 
 92005 
 
 .40780 
 
 91307 
 
 56 
 
 5 
 
 ',4339 
 
 )39I9 
 
 .35973 
 
 93306 
 
 37595 
 
 92004 
 
 39207 
 
 91994 
 
 .40800 
 
 91295 
 
 55 
 
 ; 
 
 J4366 
 
 I3909 
 
 .36000 
 
 93295 
 
 37022 
 
 92053 
 
 39234 
 
 91982 
 
 .40833 
 
 91283 
 
 54 
 
 7 
 
 i 1393 
 
 (3X9!) 
 
 .36027 
 
 932X5! 
 
 37049 
 
 92042 
 
 39200 
 
 9197! 
 
 ,40860 
 
 91272 
 
 53 
 
 8 
 
 U421 
 
 )3SX9 
 
 .36054 
 
 93274 
 
 37070 
 
 92681 
 
 39287 
 
 91959 
 
 .40886 
 
 91200 
 
 52 
 
 9 
 
 14448 
 
 )3879 
 
 .30081 
 
 93264 
 
 37703 
 
 92020 
 
 39314 
 
 9 19 18 
 
 .40913 
 
 91248 
 
 51 
 
 JO 
 
 34475 
 
 MS 69 
 
 .30108 
 
 93253 
 
 37730 
 
 92009 
 
 39341 
 
 91930 
 
 .40939 
 
 91230 
 
 50 
 
 11 
 
 34503 
 
 9.W>9 
 
 ,86185 
 
 93213 
 
 37757 
 
 92598 
 
 39367 
 
 91925 
 
 .40906 
 
 91224 
 
 49 
 
 12 
 
 J4530 
 
 93S |9 
 
 .30102 
 
 932321 
 
 37784 
 
 925X7 
 
 39394 
 
 91914 
 
 .40992 
 
 91212 
 
 48 
 
 13 
 
 34557 
 
 93839 
 
 .30190 
 
 93222 
 
 37811 
 
 92576 
 
 39421 
 
 91902 
 
 .41019 
 
 91200 
 
 47 
 
 14 
 
 345S4 
 
 I3829 
 
 ,86217 
 
 93211 
 
 37838 
 
 92505 
 
 39448 
 
 91891 
 
 .41045 
 
 91188 
 
 46 
 
 15 
 
 34612 
 
 938 1 9 
 
 .36244 
 
 93201 
 
 37X05 
 
 92554 
 
 .39474 
 
 .91879 
 
 .41072 
 
 .91176 
 
 45 
 
 16 
 
 'Ml .39 
 
 <>3X09 
 
 .36271 
 
 93190 
 
 37X92 
 
 92543 
 
 .39501 
 
 .91808 
 
 .4109X 
 
 .91164 
 
 44 
 
 17 
 
 34666 
 
 9379!) 
 
 .3C-298 
 
 93180 
 
 37919 
 
 92532 
 
 .39528 
 
 .9l85(i 
 
 .41125 
 
 .91152 
 
 43 
 
 8 
 
 34694 
 
 93789 
 
 .30325 
 
 93109 
 
 37940 
 
 92521 
 
 .39555 
 
 .91845 
 
 .41151 
 
 .91140 
 
 42 
 
 19 
 
 34721 
 
 93779 
 
 .30352 
 
 93159 
 
 37973 
 
 92510 
 
 .395X1 
 
 .91833 
 
 .41178 
 
 .91128 
 
 41 
 
 20 
 
 34748 
 
 93709 
 
 .30379 
 
 93148 
 
 3799!) 
 
 92499 
 
 ,89608 
 
 .91822 
 
 .41204 
 
 .91116 
 
 40 
 
 21 
 
 34775 
 
 93759 
 
 .30400 
 
 93137 
 
 38026 
 
 92488 
 
 .39635 
 
 .91810 
 
 .41231 
 
 .91104 
 
 39 
 
 22 
 
 34803 
 
 9374S 
 
 .30434 
 
 93127 
 
 38053 
 
 92477 
 
 .89661 
 
 .91799 
 
 .41257 
 
 .9109L 
 
 38 
 
 23 
 
 34830 
 
 9373S 
 
 ,36461 
 
 93110 
 
 38080 
 
 92460 
 
 .39088 
 
 .91787 
 
 .41284 
 
 .9108( 
 
 37 
 
 24 
 
 84857 
 
 93728 
 
 .301X8 
 
 93100 
 
 38107 
 
 92455 
 
 .39715 
 
 .91775 
 
 .41310 
 
 .9 1 ()()> 
 
 36 
 
 25 
 
 3 1XS 1 
 
 937 IS 
 
 .30515 
 
 93095 
 
 38134 
 
 92444 
 
 .39741 
 
 .91764 
 
 .41337 
 
 .91051 
 
 35 
 
 20 
 
 34912 
 
 93708 
 
 .305.12 
 
 93084 
 
 38161 
 
 92432 
 
 .39708 
 
 .91752 
 
 .41363 
 
 .01044 
 
 34 
 
 27 
 
 3193!* 
 
 9309S 
 
 .30509 
 
 93074 
 
 38188 
 
 .92421 
 
 .39795 
 
 .91741 
 
 .41390 
 
 .91032 
 
 33 
 
 28 
 
 34966 
 
 93088 
 
 .30590 
 
 93003 
 
 38215 
 
 92410 
 
 .39822 
 
 .91729 
 
 .41416 
 
 .91020 
 
 32 
 
 20 
 
 34993 
 
 93077 
 
 ,36623 
 
 93052 
 
 28241 
 
 .92399 
 
 .39848 
 
 .91718 
 
 .41443 
 
 .91008 
 
 31 
 
 30 
 
 35021 
 
 93667 
 
 .36650 
 
 93042 
 
 38268 
 
 .92388 
 
 .39875 
 
 .91706 
 
 .41469 
 
 .90996 
 
 30 
 
 31 
 
 85048 
 
 93657 
 
 .36677 
 
 93031 
 
 38295 
 
 .92377 
 
 .39902 
 
 .916Q4 
 
 .41496 
 
 .90984 
 
 29 
 
 32 
 
 35075 
 
 93047 
 
 .36704 
 
 93020 
 
 38322 
 
 .92300 
 
 .39928 
 
 .91683 
 
 .41522 
 
 .90972 
 
 28 
 
 33 
 
 35102 
 
 93037 
 
 .30731 
 
 93010 
 
 38349 
 
 .92355 
 
 .3995f 
 
 .91671 
 
 .41549 
 
 .()%( 
 
 27 
 
 34 
 
 35130 
 
 93020 
 
 .30758 
 
 92999 
 
 38370 
 
 .92343 
 
 .39982 
 
 .91000 
 
 .41575 
 
 .90948 
 
 26 
 
 35 
 
 35157 
 
 930 1 
 
 ,36785 
 
 929XX 
 
 38403 
 
 .92332 
 
 .40008 
 
 .91648 
 
 .41602 
 
 .90931 
 
 25 
 
 30 
 
 35184 
 
 9300C 
 
 .3081'.' 
 
 9297S 
 
 .38430 
 
 .92321 
 
 .40035 
 
 .91030 
 
 .41628 
 
 .90924 
 
 24 
 
 37 
 
 352 1 1 
 
 9359" 
 
 .36839 
 
 92907 
 
 .38450 
 
 .92310 
 
 .40062 
 
 .91025 
 
 .41655 
 
 .9091 1 
 
 23 
 
 88 
 
 35239 
 
 93585 
 
 .30807 
 
 92950 
 
 .38483 
 
 .92299 
 
 .40088 
 
 .91613 
 
 .41681 
 
 .90X9! 
 
 22 
 
 39 
 
 3526fi 
 
 93575 
 
 .30891 
 
 92945 
 
 .385K 
 
 92287 
 
 ,40iia 
 
 .91001 
 
 .41707 
 
 .90887 
 
 21 
 
 40 
 
 35293 
 
 93505 
 
 .36921 
 
 .92935 
 
 .38537 
 
 .92276 
 
 .40141 
 
 .91590 
 
 .41734 
 
 .90875 
 
 20 
 
 41 
 
 35320 
 
 93555 
 
 .36948 
 
 .92924 
 
 .38564 
 
 .92265 
 
 .40168 
 
 .91578 
 
 .41760 
 
 .9086? 
 
 19 
 
 42 
 
 55347 
 
 93544 
 
 .36975 
 
 .92913 
 
 .3X5!)! 
 
 .92254 
 
 .40195 
 
 .91500 
 
 .41787 
 
 .9085 
 
 18 
 
 13 
 
 35375 
 
 93534 
 
 .37002 
 
 .92902 
 
 .38617 
 
 .92243 
 
 .40221 
 
 .91555 
 
 .41813 
 
 .9083! 
 
 17 
 
 44 
 
 3540!? 
 
 93521 
 
 .37029 
 
 .92892 
 
 .3864-1 
 
 .92231 
 
 .40248 
 
 .91543 
 
 .4140 
 
 .9082' 
 
 16 
 
 45 
 
 35429 
 
 93514 
 
 .37050 
 
 .92881 
 
 ,88671 
 
 .92220 
 
 .40275 
 
 .91531 
 
 .41866 
 
 .90814 
 
 15 
 
 46 
 
 35450 
 
 93503 
 
 .37083 
 
 .92870 
 
 .3809X 
 
 .92209 
 
 .40301 
 
 .91519 
 
 .41892 
 
 .90802 
 
 14 
 
 47 
 
 35484 
 
 931!):', 
 
 .37110 
 
 .92859 
 
 .38725 
 
 .92198 
 
 .40328 
 
 .91508 
 
 .41910 
 
 .90790 
 
 13 
 
 48 
 
 35511 
 
 93483 
 
 .37137 
 
 .92849 
 
 .3^752 
 
 .92180 
 
 .40855 
 
 .9149f 
 
 .41945 
 
 .90778 
 
 12 
 
 <0 
 
 .35538 
 
 .93472 
 
 .37164 
 
 .92838 
 
 .38778 
 
 .92175 
 
 .40381 
 
 .91484 
 
 .41972 
 
 .9070' 
 
 11 
 
 50 
 
 ,855611 
 
 .9340 
 
 .37191 
 
 .92827 
 
 .38805 
 
 .92164 
 
 .40408 
 
 .91472 
 
 .41998 
 
 .90753 
 
 10 
 
 51 
 
 .35592 
 
 .93452 
 
 .37218 
 
 .92810 
 
 .38832 
 
 .92152 
 
 .40434 
 
 .91461 
 
 .42024 
 
 .9074 
 
 9 
 
 52 
 
 .35511 
 
 .9344 
 
 .37245 
 
 .92805 
 
 .3885! 
 
 .92141 
 
 .40461 
 
 .91449 
 
 .4205 
 
 .9072' 
 
 8 
 
 5:5 
 
 .35047 
 
 .93431 
 
 .37272 
 
 .92794 
 
 .3888( 
 
 .92130 
 
 .40488 
 
 .91437 
 
 .42077 
 
 .907 P 
 
 7 
 
 54 
 
 .35074 
 
 .93420 
 
 .37299 
 
 .92784 
 
 .38912 
 
 .92119 
 
 .40514 
 
 .91425 
 
 .42104 
 
 .90704 
 
 6 
 
 55 
 
 .3570 
 
 .93410 
 
 .3732( 
 
 .92773 
 
 .38939 
 
 .92107 
 
 .40541 
 
 .91414 
 
 .42130 
 
 .900!). 
 
 5 
 
 50 
 
 .35728 
 
 .93400 
 
 .37353 
 
 .92762 
 
 .88961 
 
 .92090 
 
 .40567 
 
 .91402 
 
 .4215f 
 
 .900X( 
 
 4 
 
 57 
 
 .3575. 
 
 .9338' 
 
 .37380 
 
 .92751 
 
 .38993 
 
 .92085 
 
 .40594 
 
 .91390 
 
 .4218, 
 
 .90008 
 
 8 
 
 58 
 
 .3578: 
 
 .9337' 
 
 .37407 
 
 .92740 
 
 ,3902< 
 
 .92073 
 
 .40621 
 
 .9I.W 
 
 .4220 f 
 
 .9005. 
 
 2 
 
 59 
 
 .35810 
 
 .9330, 
 
 .37434 
 
 92729 
 
 .3904C 
 
 .92062 
 
 .40647 
 
 .91360 
 
 .4223. 
 
 .9004. 
 
 1 
 
 60 
 
 .3583 
 
 .93358 
 
 .3746 
 
 .92718 
 
 .39073 
 
 .92050 
 
 .40674 
 
 .91355 
 
 .42262 
 
 .9063 
 
 
 
 / 
 
 Oosin 
 
 Sine 
 
 CoRin 
 
 Sine 
 
 CoRm 
 
 Sine 
 
 Co sin 
 
 Sine 
 
 Oosin 
 
 Sine 
 
 / 
 
 
 69 
 
 8 
 
 7 
 
 
 
 65 
 
 
108 
 
 NATURAL SINES AND COSINES. 
 
 ' 
 
 25 
 
 36 
 
 . 27 
 
 28 
 
 29 
 
 ' 
 
 Sine 
 
 Cosin 
 
 Sine 
 
 Cosin 
 
 Sine 
 
 Cosin 
 
 Sine 
 
 Cosin 
 
 Sine 
 
 Cosin 
 
 
 
 .12262 
 
 .9063 
 
 .4383 
 
 .89879 
 
 .4539C 
 
 .89101 
 
 .4694 
 
 .8829 
 
 .4848 
 
 .87462 
 
 60 
 
 1 
 
 .4228* 
 
 .9061 
 
 .4386 
 
 .8986" 
 
 .4542 
 
 .89087 
 
 .4697 
 
 .8828 
 
 .4850t 
 
 .8744?; 
 
 59 
 
 2 
 
 .423 1 
 
 .9060 
 
 .4388 
 
 .89854 
 
 .4545] 
 
 .89074 
 
 .46999 
 
 .8826 
 
 .48532 
 
 .87434 
 
 58 
 
 3 
 
 .42341 
 
 .9059 
 
 .4391 
 
 .8984 
 
 .45477 
 
 .89061 
 
 .47024 
 
 .8825 
 
 .48557 
 
 .8742G 
 
 57 
 
 4 
 
 .42367 
 
 .90582 
 
 .43942 
 
 .89828 
 
 .4550? 
 
 .89048 
 
 .47050 
 
 .88240 
 
 .4858G 
 
 .87406 
 
 50 
 
 5 
 
 .12394 
 
 .90569 
 
 .43968 
 
 .89816 
 
 .4552S 
 
 .89035 
 
 .47076 
 
 .8822 
 
 .48608 
 
 .87391 
 
 55 
 
 6 
 
 ,42420 
 
 .90557 
 
 .43994 
 
 .89803 
 
 1.45554 
 
 .89021 
 
 .4710 
 
 .88213 
 
 .48634 
 
 .87377 
 
 54 
 
 7 
 
 .42446 
 
 .90545 
 
 .44020 
 
 .89790 
 
 .45580 
 
 .89008 
 
 .47127 
 
 .88199 
 
 .48659 
 
 .87363 
 
 53 
 
 8 
 
 .42473 
 
 .90532 
 
 .4104b 
 
 .89777 
 
 .45606 
 
 .88995 
 
 .47153 
 
 .8818o 
 
 .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 
 
 .89739 
 
 .45684 
 
 .88955 
 
 .47229 
 
 .88144 
 
 .48761 
 
 .87306 
 
 49 
 
 12 
 
 .42578 
 
 .90483 
 
 .44151 
 
 .89726 
 
 .45710 
 
 .88942 
 
 .47255 
 
 .88130 
 
 .48786 
 
 .87292 
 
 48 
 
 13 
 
 .42604 
 
 .90470 
 
 .44177 
 
 .89713 
 
 .45736 
 
 .88928 
 
 .47281 
 
 .88117 
 
 .48811 
 
 .87278 
 
 47 
 
 14 
 
 .42631 
 
 .90458 
 
 .41203 
 
 .89700 
 
 .45762 
 
 .88915 
 
 .47306 
 
 .88103 
 
 .18837 
 
 .87264 
 
 46 
 
 15 
 
 .42657 
 
 .90446 
 
 .44229 
 
 .89687 
 
 .45787 
 
 .88902 
 
 .47332 
 
 .88089 
 
 .48862 
 
 87250 
 
 45 
 
 16 
 
 .42683 
 
 .90433 
 
 .44255 
 
 .89674 
 
 .15813 
 
 .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 
 
 S8020 
 
 .48989 
 
 87178 
 
 40 
 
 21 
 
 42815 
 
 .90371 
 
 .44385 
 
 .89610 
 
 .45942 
 
 .88822 
 
 .47486 
 
 88006 
 
 .49014 
 
 87164 
 
 39 
 
 22 
 
 42841 
 
 .90358 
 
 .44411 
 
 89597 
 
 .45968 
 
 .88808 
 
 .47511 
 
 87993 
 
 .49040 
 
 87150 
 
 38 
 
 23 
 
 42867 
 
 .90346 
 
 .44437 
 
 89584 
 
 .45994 
 
 .88795 
 
 .47537 
 
 87979 
 
 .49065 
 
 87136 
 
 37 
 
 24 
 
 42S94 
 
 .90334 
 
 .44464 
 
 89571 
 
 .46020 
 
 .88782 
 
 .47562 
 
 87965 
 
 .49090 
 
 87121 
 
 36 
 
 25 
 
 42920 
 
 .90321 
 
 .44490 
 
 89558 
 
 .46046 
 
 .88768 
 
 .47588 
 
 87951 
 
 .49116 
 
 87107 
 
 35 
 
 26 
 
 42946 
 
 .90309 
 
 .44516 
 
 89545 
 
 .46072 
 
 .88755 
 
 .47614 
 
 87937 
 
 .49141 
 
 87093 
 
 34 
 
 27 
 
 42972 
 
 90296 
 
 .44542 
 
 89532 
 
 .46097 
 
 88741 
 
 .47639 
 
 87923 
 
 .49166 
 
 87079 
 
 33 
 
 28 
 
 42999 1 . 90284 
 
 .44568 
 
 89519 
 
 .46123 
 
 S8728 
 
 .47665 
 
 87909 
 
 .49192 
 
 87004 
 
 32 
 
 29 
 
 42025 
 
 .90271 
 
 .44594 
 
 89506 
 
 .46149 
 
 88715 
 
 .47690 
 
 87896 
 
 .49217 
 
 87050 
 
 31 
 
 30 
 
 43051 
 
 .90259 
 
 .44620 
 
 89493 
 
 .46175 
 
 88701 
 
 .47716 
 
 87882 
 
 .4924? 
 
 87036 
 
 30 
 
 31 
 
 43077 
 
 .90246 
 
 .44646 
 
 89480 
 
 .46201 
 
 88688 
 
 .47741 
 
 87868 
 
 .49268 
 
 87021 
 
 29 
 
 32 
 
 43104 
 
 .90233 
 
 .44672 
 
 89467 
 
 .46226 
 
 88674 
 
 .47767 
 
 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 
 
 26 
 
 35 
 
 13182 
 
 .90196 
 
 .44750 
 
 89428 
 
 .46304 
 
 .88634 
 
 47844 
 
 87812 
 
 .49369 
 
 86964 
 
 
 36 
 
 43209 
 
 .90183 
 
 .44776 
 
 89415 
 
 .46330 
 
 .88620 
 
 47869 
 
 87798 
 
 .49394 
 
 86949 
 
 24 
 
 37 
 
 43225 
 
 .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 
 
 .49470 
 
 86906 
 
 21 
 
 40 
 
 43313 
 
 .90133 
 
 44880 
 
 89363 
 
 .46433 
 
 .88566 
 
 47971 
 
 87743 
 
 .49495 
 
 86892 
 
 20 
 
 41 
 
 43310 
 
 .90120 
 
 44906 
 
 89350 
 
 .46458 
 
 .88553 
 
 47997 
 
 87729 
 
 .49521 
 
 86878 
 
 19 
 
 42 
 
 43366 
 
 .90108 
 
 44932 
 
 89337 
 
 .46484 
 
 .88539 
 
 48022 
 
 87715 
 
 .49546 
 
 86863 
 
 18 
 
 43 
 
 43392 
 
 .90095 
 
 44 958 
 
 89324 
 
 46510 
 
 .88526 
 
 48048 
 
 87701 
 
 .49571 
 
 86849 
 
 17 
 
 44 
 
 43418 
 
 .90032 
 
 44984 
 
 89311 
 
 16536 
 
 .88512 
 
 48073 
 
 87687 
 
 .49596 
 
 86834 
 
 16 
 
 45 
 
 43445 
 
 .90070 
 
 45010 
 
 89298 
 
 46561 
 
 .88499 
 
 18099 
 
 87673 
 
 .49622 
 
 86820 
 
 15 
 
 46 
 
 43471 
 
 .90057 
 
 45036 
 
 89285 
 
 46587 
 
 .88485 
 
 48124 
 
 87659 
 
 .49647 
 
 80805 
 
 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 
 
 15114 
 
 89245 
 
 46664 
 
 .88445 
 
 48201 
 
 87617 
 
 .49723 
 
 86762 
 
 11 
 
 50 
 
 43575 
 
 .90007 
 
 45140 
 
 89232 
 
 46690 
 
 .88431 
 
 48226 
 
 87603 
 
 .49748 
 
 86748 
 
 10 
 
 51 
 
 43602 
 
 .89994 
 
 45166 
 
 89219 
 
 46716 
 
 .88417 
 
 48252 
 
 87589 
 
 .49773 
 
 86733 
 
 9 
 
 52 
 
 13628 
 
 .89981 
 
 45192 
 
 89206 
 
 46742 
 
 .88404 
 
 48277 
 
 87575 
 
 .49798 
 
 86719 
 
 8 
 
 53 
 
 43654 
 
 .89968 
 
 45218 
 
 S9193 
 
 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 
 
 %675 
 
 5 
 
 56 
 
 43733 
 
 .89930 
 
 45295 
 
 S9153 
 
 46844 
 
 .88349 
 
 48379 
 
 87518 
 
 .49899 
 
 86601 
 
 4 
 
 57 
 
 43759 
 
 .89918 
 
 45321 
 
 89140 
 
 46870 
 
 .88336 
 
 48405 
 
 87504 
 
 .49924 
 
 86046 
 
 3 
 
 58 
 
 43785 
 
 .89905 
 
 45347 
 
 89127 
 
 46896 
 
 .88322 
 
 48430 
 
 .87490 
 
 .49950 
 
 86632 
 
 2 
 
 59 
 
 43811 
 
 .89892 
 
 45373 
 
 89114 
 
 46921 
 
 .88308 
 
 48456 
 
 .87476 
 
 .4997/5 
 
 %617 
 
 1 
 
 60 
 
 43837 
 
 .89879 
 
 45399 
 
 89101 
 
 46947 
 
 .88295 
 
 48481 
 
 .87462 
 
 .50000 
 
 86603 
 
 
 
 , 
 
 Dosin 
 
 Sine 
 
 Cosin 
 
 Sine 
 
 Cosin 
 
 cine 
 
 Cosin 
 
 Sine 
 
 Cosin 
 
 Sine 
 
 , 
 
 
 64 
 
 63 
 
 62 
 
 61 
 
 60 
 
 
NATURAL SINES AND COSINES. 
 
 109 
 
 
 30 
 
 31 
 
 33 
 
 33 
 
 34 
 
 
 
 Sine 
 
 Cosin 
 
 Sine 
 
 Cosin 
 
 Sine 
 
 Cosin 
 
 Sine 
 
 Cosin 
 
 Sine 
 
 Cosin 
 
 
 
 
 .50000 
 
 .86603 
 
 .51504 
 
 .85717 
 
 .52992 
 
 .84805 
 
 .54464 
 
 .83867 
 
 .55919 
 
 .82904 
 
 60 
 
 1 
 
 .50025 
 
 .86588 
 
 .51529 
 
 .85702 
 
 .53017 
 
 .84789 
 
 .54488 
 
 .83851 
 
 .55943 
 
 .82S87 
 
 59 
 
 2 
 
 .50050 
 
 .86573 
 
 .51554 
 
 .85687 
 
 .53041 
 
 .84774 
 
 .54513 
 
 .83835 
 
 .55968 
 
 .82871 
 
 58 
 
 3 
 
 .50076 
 
 .86559 
 
 .51579 
 
 .85672 
 
 .53066 
 
 .84759 
 
 .54537 
 
 .83819 
 
 .55992 
 
 .82855 
 
 57 
 
 4 
 
 .50101 
 
 .86544 
 
 .51604 
 
 .85657 
 
 .53091 
 
 .84743 
 
 .54561 
 
 .83804 
 
 .56016 
 
 .82839 
 
 56 
 
 5 
 
 .501 2f 
 
 .86530 
 
 .51628 
 
 .85642 
 
 .53115 
 
 .84728 
 
 .54586 
 
 .83788 
 
 .56040 
 
 82822 
 
 55 
 
 6 
 
 .50151 
 
 .86515 
 
 .51653 
 
 .85627 
 
 .53140 
 
 .84712 
 
 .54610 
 
 .83772 
 
 .56064 
 
 .82806 
 
 54 
 
 7 
 
 .5017* 
 
 .86501 
 
 .51678 
 
 .85612 
 
 .53164 
 
 .84697 
 
 .54635 
 
 .83756 
 
 .56088 
 
 .82790 
 
 53 
 
 8 
 
 .50201 
 
 .86486 
 
 .51703 
 
 .85597 
 
 .53189 
 
 .84681 
 
 .54659 
 
 .83740 
 
 .56112 
 
 .82773 
 
 52 
 
 9 
 
 .50227 
 
 .86471 
 
 .51728 
 
 .85582 
 
 .53214 
 
 .84666 
 
 .54683 
 
 .83724 
 
 .56136 
 
 .82757 
 
 51 
 
 10 
 
 .50252 
 
 .86457 
 
 .51753 
 
 .85567 
 
 .53238 
 
 .84650 
 
 .54708 
 
 .83708 
 
 .56160 
 
 .82741 
 
 50 
 
 11 
 
 .50277 
 
 .86442 
 
 .51778 
 
 .85551 
 
 .53263 
 
 .84635 
 
 .54732 
 
 .83692 
 
 .56184 
 
 .82724 
 
 49 
 
 12 
 
 .50302 
 
 .86427 
 
 .51803 
 
 .85536 
 
 .53288 
 
 .84619 
 
 .54756 
 
 .83676 
 
 .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 
 
 .83629 
 
 .56280 
 
 .82659 
 
 45 
 
 16 
 
 .50403 
 
 .86369 
 
 .51902 
 
 .85476 
 
 .53386 
 
 .84557 
 
 .54854 
 
 .83613 
 
 .56305 
 
 .82643 
 
 44 
 
 17 
 
 50428 
 
 .86354 
 
 .51927 
 
 .85461 
 
 .53411 
 
 .84542 
 
 .54878 
 
 .83597 
 
 .56329 
 
 .82626 
 
 43 
 
 18 
 
 50453 
 
 .86340 
 
 .51952 
 
 .85446 
 
 .53435 
 
 .84526 
 
 .54902 
 
 .83581 
 
 .56353 
 
 .82610 
 
 42 
 
 19 
 
 50478 
 
 .86325 
 
 .51977 
 
 .85431 
 
 .53460 
 
 .84511 
 
 .54927 
 
 .83555 
 
 .56377 
 
 .82593 
 
 41 
 
 20 
 
 50503 
 
 .86310 
 
 .52002 
 
 .85416 
 
 .53484 
 
 .84495 
 
 .54951 
 
 .83549 
 
 .56401 
 
 .82577 
 
 40 
 
 21 
 
 50528 
 
 .86295 
 
 .52026 
 
 .85401 
 
 .53509 
 
 .84480 
 
 .54975 
 
 .83533 
 
 .56425 
 
 .82501 
 
 39 
 
 22 
 
 50553 
 
 .86281 
 
 .52051 
 
 .85385 
 
 .53534 
 
 .84464 
 
 .54999 
 
 .83517 
 
 .56449 
 
 .82544 
 
 ?8 
 
 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 
 
 .83469 
 
 .56521 
 
 .82495 
 
 35 
 
 26 
 
 50654 
 
 .86222 
 
 .52151 
 
 .85325 
 
 .53632 
 
 .84402 
 
 .55097 
 
 .83453 
 
 .56545 
 
 .82478 
 
 34 
 
 27 
 
 50679 
 
 86207 
 
 .52175 
 
 .85310 
 
 .53656 
 
 .84386 
 
 .55121 
 
 .83437 
 
 .56569 
 
 .82462 
 
 33 
 
 28 
 
 50704 
 
 .86192 
 
 .62200 
 
 .85294 
 
 .53681 
 
 .84370 
 
 .55145 
 
 .83421 
 
 .56593 
 
 .82446 
 
 32 
 
 29 
 
 50729 
 
 86178 
 
 .52225 
 
 .85279 
 
 .53705 
 
 .84355 
 
 .55169 
 
 .83405 
 
 .56617 
 
 .82429 
 
 31 
 
 30 
 
 50754 
 
 86163 
 
 .52250 
 
 .85264 
 
 .53730 
 
 .84339 
 
 .55194 
 
 .83389 
 
 .56641 
 
 .82413 
 
 30 
 
 31 
 
 50779 
 
 86148 
 
 .52275 
 
 .85249 
 
 .53754 
 
 .84324 
 
 .55218 
 
 .83373 
 
 .56665 
 
 .82396 
 
 29 
 
 32 
 
 50804 
 
 86133 
 
 .52299 
 
 .85234 
 
 .53779 
 
 .84308 
 
 .55242 
 
 .83356 
 
 .56689 
 
 .82380 
 
 28 
 
 33 
 
 50829 
 
 86119 
 
 .52324 
 
 .85218 
 
 .53804 
 
 .84292 
 
 .55266 
 
 .83340 
 
 .56713 
 
 .82363 
 
 27 
 
 34 
 
 50854 
 
 86104 
 
 .52349 
 
 .85203 
 
 .53828 
 
 .84277 
 
 .55291 
 
 .83324 
 
 .56736 
 
 .82347 
 
 26 
 
 35 
 
 50*79 
 
 86089 
 
 .52374 
 
 .85188 
 
 .53853 
 
 .84261 
 
 .55315 
 
 .83308 
 
 .56760 
 
 .82330 
 
 25 
 
 36 
 
 50904 
 
 86074 
 
 .52399 
 
 .85173 
 
 .53877 
 
 .84245 
 
 .55339 
 
 .83292 
 
 .56784 
 
 .82314 
 
 24 
 
 37 
 
 50929 
 
 86059 
 
 .52423 
 
 .85157 
 
 .53902 
 
 .84230 
 
 .55363 
 
 .83276 
 
 .56808 
 
 .82297 
 
 23 
 
 38 
 
 50954 
 
 86045 
 
 .52448 
 
 .85142 
 
 .53926 
 
 .84214 
 
 .55388 
 
 .83260 
 
 .66832 
 
 82281 
 
 22 
 
 39 
 
 50979 
 
 86030 
 
 .52473 
 
 .85127 
 
 .53951 
 
 .84198 
 
 .55412 
 
 .83244 
 
 .56856 
 
 .82264 
 
 21 
 
 40 
 
 51004 
 
 86015 
 
 .52498 
 
 .85112 
 
 .53975 
 
 .84182 
 
 .55436 
 
 .83228 
 
 .56880 
 
 .82248 
 
 20 
 
 41 
 
 51029 
 
 86000 
 
 .52522 
 
 85096 
 
 .54000 
 
 .84167 
 
 .55460 
 
 .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 
 
 .56952 
 
 .82198 
 
 17 
 
 44 
 
 51104 
 
 85956 
 
 .52597 
 
 85051 
 
 .54073 
 
 .84120 
 
 .55533 
 
 .83163 
 
 .56976 
 
 .82181 
 
 16 
 
 45 
 
 51129 
 
 85941 
 
 52621 
 
 85035 
 
 .54097 
 
 .84104 
 
 .55557 
 
 .83147 
 
 .57000 
 
 .82165 
 
 15 
 
 46 
 
 51154 
 
 85926 
 
 52646 
 
 85020 
 
 .54122 
 
 .84088 
 
 .55581 
 
 .83131 
 
 .57024 
 
 .82148 
 
 14 
 
 47 
 
 51179 
 
 85911 
 
 52671 
 
 85005 
 
 .54146 
 
 .84072 
 
 .55605 
 
 .83115 
 
 .57047 
 
 .82132 
 
 13 
 
 48 
 
 51204 
 
 85896 
 
 52696 
 
 84989 
 
 .54171 
 
 .84057 
 
 .55630 
 
 .83098 
 
 .57071 
 
 .82115 
 
 12 
 
 49 
 
 51229 
 
 85881 
 
 52720 
 
 84974 
 
 .54165 
 
 .84041 
 
 .55654 
 
 .83082 
 
 .57095 
 
 .82098 
 
 11 
 
 50 
 
 51254 
 
 85866 
 
 52745 
 
 84959 
 
 .54220 
 
 .84025 
 
 .55678 
 
 .83066 
 
 .57119 
 
 .82082 
 
 10 
 
 51 
 
 51279 
 
 85851 
 
 52770 
 
 84943 
 
 .54244 
 
 84009 
 
 .55702 
 
 .83050 
 
 .57143 
 
 .82065 
 
 9 
 
 52 
 
 51304 
 
 85836 
 
 52794 
 
 84928 
 
 '.54269 
 
 83994 
 
 .55726 
 
 .83034 
 
 .57167 
 
 .82048 
 
 8 
 
 53 
 
 51329 
 
 85821 
 
 52819 
 
 84913 
 
 .54293 
 
 83978 
 
 .55750 
 
 .83017 
 
 .57191 
 
 .82032 
 
 7 
 
 54 
 
 51354 
 
 85800 
 
 52844 
 
 84897 
 
 .54317 
 
 83962 
 
 .55775 
 
 .83001 
 
 .57215 
 
 .82015 
 
 fi 
 
 55 
 
 51379 
 
 85792 
 
 52869 
 
 84882 
 
 .54342 
 
 83948 
 
 .55799 
 
 82985 
 
 .57238 
 
 .81999 
 
 5 
 
 56 
 
 51404 
 
 85777 
 
 52893 
 
 84866 
 
 .54366 
 
 83930 
 
 .55823 
 
 82969 
 
 .57262 
 
 81982 
 
 4 
 
 57 
 
 51429 
 
 85762 
 
 52918 
 
 84851 
 
 .54391 
 
 83915 
 
 .55847 
 
 82953 
 
 .57286 
 
 81965 
 
 3 
 
 58 
 
 51454 
 
 85747 
 
 52943 
 
 84836 
 
 .54415 
 
 83899 
 
 55871 
 
 82936 
 
 .57310 
 
 81949 
 
 2 
 
 59 
 
 51479 
 
 85732 
 
 52967 
 
 84820 
 
 .54440 
 
 83883 
 
 55895 
 
 82920 
 
 .57334 
 
 81932 
 
 1 
 
 60 
 
 51504 
 
 85717 
 
 52992 
 
 84805 
 
 .54464 
 
 83867 
 
 ^5919 
 
 82904 
 
 .57358 
 
 81915 
 
 
 
 , 
 
 Cosin 
 
 Sine 
 
 Cosin 
 
 Sine 
 
 Cosin 
 
 Sine 
 
 To sin 
 
 Sine 
 
 Cosin 
 
 Sine 
 
 , 
 
 
 59 
 
 58 
 
 57 1 
 
 50 1 
 
 55 
 
 
110 
 
 NATURAL SINES AND COSINES. 
 
 
 3 
 
 5 
 
 3 
 
 6 
 
 3 
 
 7 
 
 3 
 
 8 
 
 3 
 
 9 
 
 
 
 Sine 
 
 Cosin 
 
 Sine 
 
 Cosin 
 
 Sine 
 
 Cosin 
 
 Sine 
 
 Cosin 
 
 Sine 
 
 Cosin 
 
 
 
 
 57358 
 
 81915 
 
 58779 
 
 80902 
 
 60182 
 
 79864 
 
 .61560 
 
 78801 
 
 .62932 
 
 77715 
 
 60 
 
 1 
 
 57381 
 
 81899 
 
 58802 
 
 80885 
 
 60205 
 
 79846 
 
 .01589 
 
 78783 
 
 .02955 
 
 .77090 
 
 59 
 
 2 
 
 57405 
 
 81882 
 
 5S826 
 
 80867 
 
 60228 
 
 79829 
 
 .61612 
 
 78765 
 
 .62977 
 
 .77078 
 
 58 
 
 3 
 
 57429 
 
 818G5 
 
 58849 
 
 80850 
 
 60251 
 
 79811 
 
 .61035 
 
 78747 
 
 .63000 
 
 77000 
 
 57 
 
 4 
 
 57453 
 
 81848 
 
 58873 
 
 80S33 
 
 60274 
 
 79793 
 
 .61658 
 
 78729 
 
 .03022 
 
 77041 
 
 56 
 
 5 
 
 57477 
 
 81832 
 
 58896 
 
 80816 
 
 60298 
 
 79770 
 
 .61081 
 
 78711 
 
 .03045 
 
 77023 
 
 55 
 
 6 
 
 57501 
 
 81815 
 
 58920 
 
 80799 
 
 60321 
 
 79758 
 
 .61704 
 
 78694 
 
 .03008 
 
 77005 
 
 54 
 
 7 
 
 57524 
 
 81798 
 
 58943 
 
 80782 
 
 60344 
 
 79741 
 
 .61726 
 
 78670 
 
 .03090 
 
 77580 
 
 53 
 
 8 
 
 57548 
 
 81782 
 
 58967 
 
 80765 
 
 60367 
 
 79723 
 
 .61749 
 
 78658 
 
 .63113 
 
 77508 
 
 52 
 
 9 
 
 57572 
 
 81765 
 
 58990 
 
 80748 
 
 60390 
 
 79706 
 
 .61772 
 
 78640 
 
 .63135 
 
 77550 
 
 51 
 
 10 
 
 57596 
 
 81748 
 
 59014 
 
 80730 
 
 60414 
 
 79688 
 
 .01795 
 
 78622 
 
 .03158 
 
 77531 
 
 50 
 
 11 
 
 57619 
 
 81731 
 
 59037 
 
 80713 
 
 00437 
 
 79671 
 
 .01818 
 
 78604 
 
 .03180 
 
 77513 
 
 40 
 
 12 
 
 57643 
 
 81714 
 
 59061 
 
 80696 
 
 60460 
 
 79653 
 
 .61841 
 
 785S6 
 
 .03203 
 
 77494 
 
 48 
 
 13 
 
 57667 
 
 81698 
 
 59084 
 
 80679 
 
 00483 
 
 79635 
 
 .61864 
 
 7S5G8 
 
 .03225 
 
 77470 
 
 47 
 
 14 
 
 57691 
 
 816S1 
 
 59108 
 
 80662 
 
 00506 
 
 79618 
 
 .61887 
 
 78550 
 
 .03248 
 
 77458 
 
 46 
 
 15 
 
 57715 
 
 81664 
 
 59131 
 
 80644 
 
 00529 
 
 79600 
 
 .61909 
 
 78532 
 
 .03271 
 
 77439 
 
 45 
 
 16 
 
 57738 
 
 81647 
 
 59154 
 
 80627 
 
 00553 
 
 79583 
 
 .61932 
 
 78514 
 
 .03293 
 
 77421 
 
 44 
 
 17 
 
 57702 
 
 81631 
 
 59178 
 
 80010 
 
 60576 
 
 79565 
 
 .61955 
 
 78496 
 
 .03316 
 
 77402 
 
 43 
 
 18 
 
 57786 
 
 81614 
 
 59201 
 
 80593 
 
 60599 
 
 79547 
 
 .61978 
 
 78478 
 
 .03338 
 
 77384 
 
 42 
 
 19 
 
 57810 
 
 81597 
 
 59225 
 
 80576 
 
 60622 
 
 79530 
 
 .62001 
 
 784GO 
 
 .63301 
 
 77300 
 
 41 
 
 20 
 
 57833 
 
 81580 
 
 59248 
 
 80558 
 
 60645 
 
 79512 
 
 .62024 
 
 78442 
 
 .03383 
 
 77347 
 
 40 
 
 21 
 
 57857 
 
 81563 
 
 .59272 
 
 80541 
 
 60668 
 
 79494 
 
 .62046 
 
 78424 
 
 .03406 
 
 77329 
 
 39 
 
 22 
 
 57881 
 
 81546 
 
 .59295 
 
 80524 
 
 60691 
 
 79477 
 
 .62069 
 
 78405 
 
 .03428 
 
 77310 
 
 38 
 
 23 
 
 57904 
 
 81530 
 
 .59318 
 
 80507 
 
 60714 
 
 79459 
 
 .62092 
 
 78387 
 
 .63451 
 
 77292 
 
 37 
 
 24 
 
 57928 
 
 81513 
 
 .59342 
 
 80489 
 
 60738 
 
 79441 
 
 .62115 
 
 78309 
 
 .63473 
 
 77273 
 
 36 
 
 25 
 
 57952 
 
 81496 
 
 .59365 
 
 80472 
 
 60761 
 
 79424 
 
 .62138 
 
 78351 
 
 .63496 
 
 77255 
 
 35 
 
 26 
 
 57976 
 
 81479 
 
 .59389 
 
 80455 
 
 60784 
 
 79400 
 
 .62160 
 
 78333 
 
 .63518 
 
 77236 
 
 34 
 
 27 
 
 57999 
 
 81462 
 
 .59412 
 
 8043S 
 
 60807 
 
 79388 
 
 .62183 
 
 78315 
 
 .63540 
 
 77218 
 
 33 
 
 28 
 
 .58023 
 
 81445 
 
 .59436 
 
 80420 
 
 .60830 
 
 79371 
 
 .62206 
 
 78297 
 
 .03563 
 
 77199 
 
 32 
 
 29 
 
 .58047 
 
 81428 
 
 .59459 
 
 80403 
 
 .60853 
 
 79353 
 
 .62229 
 
 78279 
 
 .63585 
 
 77181 
 
 31 
 
 30 
 
 .58070 
 
 .81412 
 
 .59482 
 
 80386 
 
 .60876 
 
 79335 
 
 .62251 
 
 782G1 
 
 .63608 
 
 77102 
 
 30 
 
 31 
 
 .58094 
 
 81395 
 
 .59506 
 
 80368 
 
 .60899 
 
 79318 
 
 .62274 
 
 78243 
 
 .63630 
 
 77144 
 
 29 
 
 32 
 
 .58118 
 
 .81378 
 
 .59529 
 
 80351 
 
 .60922 
 
 79300 
 
 .62297 
 
 78225 
 
 .63653 
 
 77125 
 
 28 
 
 33 
 
 .58141 
 
 .81361 
 
 .59552 
 
 80334 
 
 .60945 
 
 79282 
 
 .62320 
 
 78206 
 
 .63675 
 
 77107 
 
 27 
 
 34 
 
 .58165 
 
 .81344 
 
 .59576 
 
 80316 
 
 .60968 
 
 79264 
 
 .62342 
 
 78188 
 
 .63698 
 
 770S8 
 
 26 
 
 35 
 
 .58189 
 
 .81327 
 
 .59599 
 
 80299 
 
 .60991 
 
 79247 
 
 .62365 
 
 78170 
 
 .63720 
 
 77070 
 
 25 
 
 36 
 
 .58212 
 
 .82310 
 
 .59622 
 
 80282 
 
 .61015 
 
 79229 
 
 .62388 
 
 78152 
 
 .03742 
 
 77051 
 
 24 
 
 37 
 
 .58236 
 
 .81293 
 
 .59646 
 
 .80264 
 
 .61038 
 
 79211 
 
 .62411 
 
 78134 
 
 .03765 
 
 77033 
 
 23 
 
 38 
 
 .58260 
 
 .81276 
 
 .59669 
 
 .80247 
 
 .61061 
 
 79193 
 
 .62433 
 
 78116 
 
 .63787 
 
 .77014 
 
 22 
 
 39 
 
 .58283 
 
 .81259 
 
 .59693 
 
 .80230 
 
 .61084 
 
 79176 
 
 .62456 
 
 78098 
 
 .03810 
 
 .70990 
 
 21 
 
 40 
 
 .58307 
 
 .81242 
 
 .59716 
 
 .80212 
 
 .61107 
 
 .79158 
 
 .62479 
 
 .78079 
 
 .03832 
 
 .70977 
 
 20 
 
 41 
 
 .58330 
 
 .81225 
 
 .59739 
 
 .80195 
 
 .61130 
 
 .79140 
 
 .62502 
 
 .78061 
 
 .03854 
 
 .70959 
 
 19 
 
 42 
 
 .58354 
 
 .81208 
 
 .59763 
 
 .80178 
 
 .61153 
 
 .79122 
 
 .62524 
 
 .78043 
 
 .03877 
 
 .70940 
 
 18 
 
 43 
 
 .58378 
 
 .81191 
 
 .59786 
 
 .80160 
 
 .61176 
 
 .79105 
 
 .02547 
 
 .78025 
 
 .03899 
 
 .70921 
 
 17 
 
 44 
 
 .58401 
 
 .81174 
 
 .59809 
 
 .80143 
 
 .61199 
 
 .79087 
 
 .02570 
 
 .78007 
 
 .03922 
 
 .70903 
 
 16 
 
 45 
 
 .58425 
 
 .81157 
 
 .59832 
 
 .80125 
 
 .61222 
 
 .79069 
 
 .02592 
 
 .77988 
 
 .63944 
 
 .70884 
 
 15 
 
 46 
 
 .58449 
 
 .81140 
 
 .59856 
 
 .80108 
 
 .61245 
 
 .79051 
 
 .02015 
 
 .77970 
 
 1.63966 
 
 .70800 
 
 14 
 
 47 
 
 .58472 
 
 .81123 
 
 .59879 
 
 .80091 
 
 .61268 
 
 .79033 
 
 .02638 
 
 .77952 
 
 .63989 
 
 .70847 
 
 13 
 
 48 
 
 .58496 
 
 .81106 
 
 .59902 
 
 .80073 
 
 .61291 
 
 .79010 
 
 .62660 
 
 .77934 
 
 .64011 
 
 .76828 
 
 12 
 
 49 
 
 .58519 
 
 .81089 
 
 .59926 
 
 .80056 
 
 .61314 
 
 .78998 
 
 .62683 
 
 .77916 
 
 .64033 
 
 .76810 
 
 11 
 
 50 
 
 .58543 
 
 .81072 
 
 .59949 
 
 .80038 
 
 .61337 
 
 .78980 
 
 .62706 
 
 .77897 
 
 .64056 
 
 .70791 
 
 10 
 
 51 
 
 .58567 
 
 .81055 
 
 .59972 
 
 .80021 
 
 .61360 
 
 .78902 
 
 .62728 
 
 .77879 
 
 .64078 
 
 .76772 
 
 9 
 
 52 
 
 .58590 
 
 .81038 
 
 .59995 
 
 .80003 
 
 .61383 
 
 .78944 
 
 .62751 
 
 .77861 
 
 .64100 
 
 .76754 
 
 8 
 
 53 
 
 .58614 
 
 .81021 
 
 .60019 
 
 .79986 
 
 .61406 
 
 .78920 
 
 .62774 
 
 .77843 
 
 .64123 
 
 .76735 
 
 7 
 
 54 
 
 .58637 
 
 .81004 
 
 .60042 
 
 .79968 
 
 .61429 
 
 .78908 
 
 .62796 
 
 .77824 
 
 .04145 
 
 .76717 
 
 6 
 
 55 
 
 .58661 
 
 .80987 
 
 .60065 
 
 .79951 
 
 .61451 
 
 .78891 
 
 .62819 
 
 .77806 
 
 .64167 
 
 .76698 
 
 5 
 
 56 
 
 .58684 
 
 .80970 
 
 .60089 
 
 .79934 
 
 .61474 
 
 .78973 
 
 1.62842 
 
 .77788 
 
 .64190 
 
 .76679 
 
 4 
 
 57 
 
 .58708 
 
 .80953 
 
 .60112 
 
 .79916 
 
 .61497 
 
 .78855 
 
 .62864 
 
 .77769 
 
 .64212 
 
 .76661 
 
 3 
 
 58 
 
 .58731 
 
 .80936 
 
 .60135 
 
 .79899 
 
 .61520 
 
 .78837 
 
 .62887 
 
 .77751 
 
 .64234 
 
 .7664? 
 
 2 
 
 59 
 
 .58755 
 
 .80919 
 
 .60158 
 
 .79881 
 
 .61543 
 
 .78819 
 
 .62909 
 
 .77733 
 
 .64256 
 
 .76623 
 
 1 
 
 60 
 
 .58779 
 
 .80902 
 
 .60182 
 
 .79864 
 
 .61566 
 
 .78801 
 
 .62932 
 
 .77715 
 
 .64279 
 
 .76604 
 
 
 
 , 
 
 Cosin 
 
 Sine 
 
 Cosin 
 
 Sine 
 
 Cosin 
 
 Sine 
 
 Cosin 
 
 Sine 
 
 Cosin 
 
 Sine 
 
 f 
 
 
 5 
 
 >4 
 
 I 
 
 ,3 
 
 I 
 
 2 
 
 
 
 >1 
 
 5 
 
 
 
 
NATURAL SINES AND COSINES. 
 
 Ill 
 
 
 
 40 
 
 41 
 
 42 
 
 43 
 
 44 
 
 ' 
 
 Sine 
 
 Cosin 
 
 Sine 
 
 Cosin 
 
 Sine 
 
 Cosin 
 
 Sine 
 
 Cosin 
 
 Sine 
 
 Cosin 
 
 
 
 64279 
 
 76604 
 
 65006 
 
 75471 
 
 66913 
 
 74314 
 
 68200 
 
 .73135 
 
 .69466 
 
 .71934 
 
 60 
 
 1 
 
 64301 
 
 76586 
 
 65628 
 
 75452 
 
 66935 
 
 74295 
 
 68221 
 
 .73116 
 
 .69487 
 
 .71914 
 
 59 
 
 2 
 
 64323 
 
 76567 
 
 65650 
 
 75433 
 
 66956 
 
 74276 
 
 .68242 
 
 .73096 
 
 .69508 
 
 .71894 
 
 58 
 
 3 
 
 64346 
 
 76548 
 
 65672 
 
 75414 
 
 66978 
 
 74256 
 
 .68264 
 
 .73076 
 
 .69529 
 
 .71873 
 
 57 
 
 4 
 
 64368 
 
 76530 
 
 65694 
 
 75395 
 
 66999 
 
 74237 
 
 .68285 
 
 .73056 
 
 .69549 
 
 .71853 
 
 56 
 
 5 
 
 64390 
 
 76511 
 
 65716 
 
 75375 
 
 67021 
 
 74217 
 
 .68306 
 
 .73036 
 
 .69570 
 
 .71833 
 
 55 
 
 6 
 
 64412 
 
 76492 
 
 65738 
 
 75356 
 
 67043 
 
 74198 
 
 .68327 
 
 .73016 
 
 .69591 
 
 .71813 
 
 54 
 
 7 
 
 64435 
 
 76473 
 
 65759 
 
 75337 
 
 .67064 
 
 74178 
 
 .68349 
 
 .72996 
 
 .69612 
 
 .7179? 
 
 53 
 
 8 
 
 64457 
 
 76455 
 
 65781 
 
 75318 
 
 .07086 
 
 74159 
 
 .68370 
 
 .72976 
 
 .69633 
 
 .71772 
 
 52 
 
 9 
 
 64479 
 
 76436 
 
 65803 
 
 7529.9 
 
 .67107 
 
 74139 
 
 .68391 
 
 .72957 
 
 .69654 
 
 .71752 
 
 51 
 
 10 
 
 64501 
 
 76417 
 
 65825 
 
 75230 
 
 .67129 
 
 74120 
 
 .68412 
 
 .72937 
 
 .69675 
 
 .71732 
 
 50 
 
 11 
 
 64524 
 
 76398 
 
 65847 
 
 75261 
 
 .67151 
 
 74100 
 
 .68434 
 
 .72917 
 
 .69696 
 
 .71711 
 
 49 
 
 12 
 
 64546 
 
 76380 
 
 65869 
 
 75241 
 
 .67172 
 
 74080 
 
 .68455 
 
 .72897 
 
 .69717 
 
 .71691 
 
 48 
 
 13 
 
 64568 
 
 76361 
 
 65891 
 
 75222 
 
 .67194 
 
 74061 
 
 .68476 
 
 .72877 
 
 .69737 
 
 .71671 
 
 47 
 
 14 
 
 64590 
 
 76342 
 
 65913 
 
 75203 
 
 .67215 
 
 74041 
 
 .68497 
 
 .72857 
 
 .69758 
 
 .71650 
 
 46 
 
 15 
 
 64612 
 
 76323 
 
 65935 
 
 75184 
 
 .67237 
 
 .74022 
 
 .68518 
 
 .72837 
 
 .69779 
 
 .71630 
 
 45 
 
 16 
 
 64635 
 
 76304 
 
 65956 
 
 75165 
 
 .67258 
 
 .74002 
 
 .68539 
 
 .72817 
 
 .69800 
 
 .71610 
 
 44 
 
 17 
 
 64657 
 
 76286 
 
 65978 
 
 75146 
 
 .67280 
 
 .73983 
 
 .68561 
 
 .72797 
 
 .69821. 
 
 .71590 
 
 43 
 
 18 
 
 64679 
 
 76267 
 
 06000 
 
 75126 
 
 .67301 
 
 .73963 
 
 .68582 
 
 .72777 
 
 .69842 
 
 .71569 
 
 42 
 
 19 
 
 64701 
 
 76248 
 
 66022 
 
 75107 
 
 .67323 
 
 .73944 
 
 .68603 
 
 .72757 
 
 .69862 
 
 .71549 
 
 41 
 
 20 
 
 64723 
 
 76229 
 
 66044 
 
 75088 
 
 .67344 
 
 .73924 
 
 .68624 
 
 .72737 
 
 .69883 
 
 .71529 
 
 40 
 
 21 
 
 64746 
 
 76210 
 
 66066 
 
 75069 
 
 .67366 
 
 .73904 
 
 .68645 
 
 .72717 
 
 .69904 
 
 .71508 
 
 39 
 
 22 
 
 64768 
 
 76192 
 
 66088 
 
 75050 
 
 .67387 
 
 .73885 
 
 .68666 
 
 .72697 
 
 .69925 
 
 .71488 
 
 38 
 
 23 
 
 64790 
 
 76173 
 
 66109 
 
 75030 
 
 .67409 
 
 .73865 
 
 .68688 
 
 .72677 
 
 .69946 
 
 .71468 
 
 37 
 
 24 
 
 64812 
 
 76154 
 
 66131 
 
 75011 
 
 .67430 
 
 .73846 
 
 .68709 
 
 .72657 
 
 .69966 
 
 .71447 
 
 36 
 
 25 
 
 64834 
 
 76135 
 
 .66153 
 
 74992 
 
 .67452 
 
 .73826 
 
 .68730 
 
 .72637 
 
 .69987 
 
 .71427 
 
 35 
 
 26 
 
 64856 
 
 76116 
 
 .66175 
 
 74973 
 
 .67473 
 
 .73806 
 
 .68751 
 
 .72617 
 
 .70008 
 
 .71407 
 
 34 
 
 27 
 
 64878 
 
 76097 
 
 .66197 
 
 74953 
 
 .67495 
 
 .73787 
 
 .68772 
 
 .725P7 
 
 .70029 
 
 .71386 
 
 33 
 
 28 
 
 64901 
 
 76078 
 
 .66218 
 
 74934 
 
 .67516 
 
 .73767 
 
 .68793 
 
 .72577 
 
 .70049 
 
 .71366 
 
 32 
 
 29 
 
 64923 
 
 76059 
 
 .66240 
 
 74915 
 
 .67538 
 
 .73747 
 
 .68814 
 
 .72557 
 
 .70070 
 
 .71345 
 
 31 
 
 30 
 
 64945 
 
 76041 
 
 66262 
 
 74896 
 
 .67559 
 
 .73728 
 
 .68835 
 
 .72537 
 
 .70091 
 
 .71325 
 
 30 
 
 31 
 
 64967 
 
 76022 
 
 66284 
 
 74876 
 
 .67580 
 
 .73708 
 
 .68857 
 
 .72517 
 
 .70112 
 
 .71305 
 
 29 
 
 32 
 
 64989 
 
 76003 
 
 66306 
 
 74857 
 
 .67602 
 
 .73688 
 
 .68878 
 
 .72497 
 
 .70132 
 
 .71284 
 
 28 
 
 33 
 
 65011 
 
 75984 
 
 66327 
 
 74838 
 
 .67623 
 
 .73669 
 
 .68899 
 
 .72477 
 
 .70153 
 
 .71264 
 
 27 
 
 34 
 
 65033 
 
 75965 
 
 .66349 
 
 7481S 
 
 .67645 
 
 .73649 
 
 .68920 
 
 .72457 
 
 .70174 
 
 .71243 
 
 26 
 
 35 
 
 65055 
 
 75946 
 
 66371 
 
 74799 
 
 .67666 
 
 .73629 
 
 .68941 
 
 .72437 
 
 .70195 
 
 .71223 
 
 25 
 
 36 
 
 65077 
 
 75927 
 
 66393 
 
 74780 
 
 .67688 
 
 .73610 
 
 .68962 
 
 .72417 
 
 .70215 
 
 .71203 
 
 24 
 
 37 
 
 65100 
 
 75908 
 
 .66414 
 
 74760 
 
 .67709 
 
 .73590 
 
 .68983 
 
 .72397 
 
 .70236 
 
 .71182 
 
 23 
 
 38 
 
 65122 
 
 75889 
 
 .66436 
 
 74741 
 
 .67730 
 
 .73570 
 
 .69004 
 
 .72377 
 
 .70257 
 
 .71162 
 
 22 
 
 39 
 
 65144 
 
 75870 
 
 .66458 
 
 74722 
 
 .67752 
 
 .73551 
 
 .69025 
 
 .72357 
 
 .70277 
 
 .71141 
 
 21 
 
 40 
 
 65166 
 
 75851 
 
 .66480 
 
 74703 
 
 .67773 
 
 73531 
 
 .69046 
 
 .72337 
 
 .70298 
 
 .71121 
 
 20 
 
 41 
 
 65188 
 
 75832 
 
 .66501 
 
 74683 
 
 .67795 
 
 .73511 
 
 .69067 
 
 .72317 
 
 .70319 
 
 .71100 
 
 19 
 
 42 
 
 65210 
 
 75813 
 
 .66523 
 
 74664 
 
 .67816 
 
 73491 
 
 .69088 
 
 .72297 
 
 .70339 
 
 .71080 
 
 18 
 
 43 
 
 65232 
 
 75794 
 
 .66545 
 
 74644 
 
 .67837 
 
 73472 
 
 .69109 
 
 .72277 
 
 .70360 
 
 .71059 
 
 17 
 
 44 
 
 65254 
 
 75775 
 
 .66566 
 
 74625 
 
 .67859 
 
 73452 
 
 .09130 
 
 .72257 
 
 .70381 
 
 .71039 
 
 16 
 
 45 
 
 65276 
 
 75756 
 
 .66588 
 
 74606 
 
 .67880 
 
 73132 
 
 .69151 
 
 .72236 
 
 .70401 
 
 .71019 
 
 15 
 
 46 
 
 65298 
 
 75738 
 
 .66610 
 
 74586 
 
 .67901 
 
 73413 
 
 .69172 
 
 .72216 
 
 .70422 
 
 .70998 
 
 14 
 
 47 
 
 65320 
 
 75719 
 
 .66632 
 
 74567 
 
 .67923 
 
 .73393 
 
 .69193 
 
 .72196 
 
 .70443 
 
 .70978 
 
 13 
 
 48 
 
 65342 
 
 75700 
 
 .66653 
 
 .74548 
 
 .67944 
 
 .73373 
 
 .69214 
 
 .72176 
 
 .70463 
 
 .70957 
 
 12 
 
 49 
 
 65364 
 
 75680 
 
 .66675 
 
 .74528 
 
 .67965 
 
 .73353 
 
 .69235 
 
 .72156 
 
 .70484 
 
 .70937 
 
 11 
 
 50 
 
 65386 
 
 .75661 
 
 .66697 
 
 .74509 
 
 .67987 
 
 .73333 
 
 .69256 
 
 .72136 
 
 .70505 
 
 .70916 
 
 10 
 
 51 
 
 65408 
 
 .75642 
 
 .66718 
 
 .74489 
 
 .68008 
 
 .73314 
 
 .69277 
 
 .72116 
 
 .70525 
 
 .70896 
 
 9 
 
 52 
 
 65430 
 
 .75623 
 
 .66740 
 
 .74470 
 
 .68029 
 
 .73294 
 
 .69298 
 
 .72095 
 
 .70546 
 
 .70875 
 
 8 
 
 53 
 
 65452 
 
 .75604 
 
 .66762 
 
 .74451 
 
 .68051 
 
 .73274 
 
 .69319 
 
 .72075 
 
 .70567 
 
 .70855 
 
 7 
 
 54 
 
 .65474 
 
 .75585 
 
 .66783 
 
 .74431 
 
 .68072 
 
 .73254 
 
 .69340 
 
 .72055 
 
 .70587 
 
 .70834 
 
 6 
 
 55 
 
 .65496 
 
 .75566 
 
 .66805 
 
 .74412 
 
 .68093 
 
 .73234 
 
 .69361 
 
 .72035 
 
 .70608 
 
 .70813 
 
 5 
 
 56 
 
 .65518 
 
 .75547 
 
 .66827 
 
 .74392 
 
 .68115 
 
 .73215 
 
 .69382 
 
 .72015 
 
 .70628 
 
 .70793 
 
 4 
 
 57 
 
 .65540 
 
 .75528 
 
 .66848 
 
 .74373 
 
 .68136 
 
 .73195 
 
 .69403 
 
 .71995 
 
 .70649 
 
 .70772 
 
 3 
 
 58 
 
 .65562 
 
 .75509 
 
 .66870 
 
 .74353 
 
 .68157 
 
 .73175 
 
 .69424 
 
 .71974 
 
 .70670 
 
 .70752 
 
 2 
 
 59 
 
 .65584 
 
 .75490 
 
 .66891 
 
 .74334 
 
 .68179 
 
 .73155 
 
 .69445 
 
 .71954 
 
 .70690 
 
 .70731 
 
 1 
 
 60 
 
 .65606 
 
 .75471 
 
 .66913 
 
 74314 
 
 .68200 
 
 .73135 
 
 .69466 
 
 .71934 
 
 .70711 
 
 .70711 
 
 
 
 , 
 
 Cosin 
 
 Sine 
 
 Cosin 
 
 Sine 
 
 Cosin 
 
 Sine 
 
 Cosin 
 
 Sine 
 
 Cosin 
 
 Sine 
 
 7" 
 
 
 4d 
 
 48 
 
 47 
 
 46 
 
 45 
 
 
112 NATURAL TANGENTS AND COTANGENTS. 
 
 
 
 
 1 
 
 2 
 
 3 
 
 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Ootang 
 
 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 
 
 27.9372 
 
 .05328 
 
 1&.7G7S 
 
 57 
 
 4 
 
 .00116 
 
 859.436 
 
 .01862 
 
 53.7086 
 
 .03609 
 
 27.7117 
 
 .05357 
 
 18.6656 
 
 50 
 
 5 
 
 .00145 
 
 687.549 
 
 .01891 
 
 52.8821 
 
 .03638 
 
 27.4899 
 
 .05387 
 
 18.5645 
 
 55 
 
 
 
 .00175 
 
 572.957 
 
 .01920 
 
 52.0SG7 
 
 .03667 
 
 27.2715 
 
 .05416 
 
 18.4645 
 
 54 
 
 7 
 
 .00204 
 
 401.106 
 
 .01949 
 
 51.3032 
 
 .03696 
 
 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 
 
 49.1039 
 
 .03783 
 
 26.4316 
 
 .05533 
 
 18.0750 
 
 50 
 
 11 
 
 .00320 
 
 312.521 
 
 .02066 
 
 48.4121 
 
 .03812 
 
 26.2296 
 
 .05562 
 
 17.9802 
 
 49 
 
 12 
 
 .00349 
 
 286.478 
 
 .02095 
 
 47.7395 
 
 .03842 
 
 26.0307 
 
 .05591 
 
 17.8863 
 
 48 
 
 13 
 
 .00378 
 
 264.441 
 
 .02124 
 
 47.0853 
 
 .03871 
 
 25.8348 
 
 .05620 
 
 17.7934 
 
 47 
 
 14 
 
 .00407 
 
 245.55? 
 
 .02153 
 
 46.4489 
 
 .03900 
 
 25.6418 
 
 .05649 
 
 17.7015 
 
 46 
 
 15 
 
 .00436 
 
 229.182 
 
 .02182 
 
 45.8294 
 
 .03929 
 
 25.4517 
 
 .05678 
 
 17.6106 
 
 45 
 
 16 
 
 .00465 
 
 214.858 
 
 .02211 
 
 45.2261 
 
 .03058 
 
 25.2644 
 
 .05708 
 
 17.5205 
 
 44 
 
 17 
 
 .00495 
 
 202.219 
 
 .02240 
 
 44.6386 
 
 .03987 
 
 25.0798 
 
 .05737 
 
 17.4314 
 
 43 
 
 18 
 
 .00524 
 
 190.984 
 
 .02269 
 
 44.0661 
 
 .04016 
 
 24.8978 
 
 .05766 
 
 17.3432 
 
 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 
 
 17.1093 
 
 40 
 
 21 
 
 .00611 
 
 163.700 
 
 I .02357 
 
 42.4335 
 
 .04104 
 
 24.3675 
 
 .05854 
 
 17.0837 
 
 39 
 
 22 
 
 .00040 
 
 156.259 
 
 .02386 
 
 41.9158 
 
 .04133 
 
 24.1957 
 
 .05883 
 
 16.0990 
 
 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 
 
 .05941 
 
 16.8319 
 
 36 
 
 25 
 
 .00727 
 
 137.507 
 
 .02473 
 
 40.4358 
 
 .04220 
 
 23.6945 
 
 .05970 
 
 16.7496 
 
 35 
 
 28 
 
 .-00756 
 
 132.219 
 
 .02502 
 
 39.9655 
 
 .04250 
 
 23.5321 
 
 .05999 
 
 16.6681 
 
 34 
 
 27 
 
 .00785 
 
 127.321 
 
 .02531 
 
 39.5059 
 
 .04279 
 
 23.3718 
 
 .06029 
 
 16.5874 
 
 33 
 
 28 
 
 .00815 
 
 122.774 
 
 .02560 
 
 39.0568 
 
 .0*308 
 
 23.2137 
 
 .06058 
 
 16.5075 
 
 32 
 
 29 
 
 ;00844 
 
 118.540 
 
 .02589 
 
 38.6177 
 
 .04337 
 
 23.0577 
 
 .06087 
 
 16.4283 
 
 31 
 
 30 
 
 .00873 
 
 114.589 
 
 .02619 
 
 38.1885 
 
 .04366 
 
 22.9038 
 
 .06116 
 
 16.3499 
 
 30 
 
 31 
 
 .00902 
 
 110.892 
 
 .02648 
 
 37.7686 
 
 .04305 
 
 22.7519 
 
 .06145 
 
 16.2722 
 
 29 
 
 32 
 
 .00931 
 
 107.42'^ 
 
 .02677 
 
 37.3579 
 
 .04424 
 
 22.6020 
 
 .06175 
 
 16.1952 
 
 28 
 
 33 
 
 .00960 
 
 104.171 
 
 .02706 
 
 36.9560 
 
 .04454 
 
 22.4541 
 
 .06204 
 
 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 
 
 05.4895 
 
 .02793 
 
 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 
 
 .06350 
 
 15.7483 
 
 22 
 
 39 
 
 .01135 
 
 88.1436 
 
 .02881 
 
 34.7151 
 
 .04628 
 
 21.6056 
 
 .06379 
 
 15.6762 
 
 21 
 
 40 
 
 .01164 
 
 85.9398 
 
 .02910 
 
 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 
 
 .04716 
 
 21.2049 
 
 .06467 
 
 15.4638 
 
 18 
 
 43 
 
 .01251 
 
 79.9434 
 
 .02997 
 
 33.3662 
 
 .04745 
 
 21.0747 
 
 .06496 
 
 15.3943 
 
 17 
 
 41 
 
 .01230 
 
 78.1263 
 
 .03026 
 
 33.0452 
 
 .04774 
 
 20.9460 
 
 .06525 
 
 15.3254 
 
 16 
 
 45 
 
 .01309 
 
 76.3900 
 
 .03055 
 
 32.7303 
 
 .04803 
 
 20.8188 
 
 .06554 
 
 15.2571 
 
 15 
 
 46 
 
 .01333 
 
 74.7292 
 
 .03084 
 
 32.4213 
 
 .04833 
 
 20.6932 
 
 .06584 
 
 15.1893 
 
 14 
 
 47 
 
 .01307 
 
 73.1390 
 
 .03114 
 
 32.1181 
 
 .04862 
 
 20.5691 
 
 .06613 
 
 15.1222 
 
 13 
 
 18 
 
 .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 
 
 31.2416 
 
 .04949 
 
 20.2056 
 
 .06700 
 
 14.9244 
 
 10 
 
 51 
 
 .01484 
 
 67.4019 
 
 .03230 
 
 30.9599 
 
 .04978 
 
 20.0872 
 
 .06730 
 
 14.8596' 
 
 9 
 
 52 
 
 .01513 
 
 66.1055 
 
 .03259 
 
 30.6833 . 
 
 .05007 
 
 19.9702 
 
 .06759 
 
 14.7954 
 
 8 
 
 53 
 
 .01542 
 
 64.8580 
 
 .03288 
 
 30.4116 
 
 .05037 
 
 19.8516 
 
 .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 
 
 .05095 
 
 19.6273 
 
 .06847 
 
 14.6059 
 
 5 
 
 56 
 
 .01629 
 
 61.3829 
 
 .03376 
 
 29.6245 
 
 .05124 
 
 19.5156 
 
 .06876 
 
 14.5438 
 
 4 
 
 57 
 
 .01658 
 
 60.3058 
 
 .03405 
 
 29.3711 
 
 .05153 
 
 19.1051 
 
 .06905 
 
 14,4823 
 
 3 
 
 58 
 
 .01687 
 
 59.2659 
 
 .03434 
 
 29.1220 
 
 .05182 
 
 19.2959 
 
 .00934 
 
 14.421? 
 
 2 
 
 59 
 
 .01716 
 
 58.2612 
 
 .03463 
 
 28.8771 
 
 .05212 
 
 19.1879 
 
 .06933 
 
 14.3607 
 
 1 
 
 60 
 
 .01746 
 
 57.2900 
 
 .03492 
 
 28.6363 
 
 .05241 
 
 19.0811 
 
 .06993 
 
 14.3007 
 
 
 
 / 
 
 Cotang 
 
 Tang 
 
 Cot an g 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 , 
 
 
 89 
 
 88 
 
 87 
 
 86 
 
 
NATURAL TANGENTS AND COTANGENTS. 113 
 
 
 1 
 
 5 
 
 
 
 7 
 
 
 
 lang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 ' 
 
 
 
 .06993 
 
 14.3007 
 
 .08749 
 
 11.4301 
 
 .10510 
 
 9.51436 
 
 .12278 
 
 8.14435 
 
 60 
 
 1 
 
 .07022 
 
 14.2111 
 
 .08778 
 
 11.3919 
 
 .10540 
 
 9.48781 
 
 .12308 
 
 8.12481 
 
 59 
 
 2 
 
 .0705! 
 
 14.1821 
 
 .08807 
 
 11.3540 
 
 .10569 
 
 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 
 
 .10687 
 
 9.35724 
 
 .12456 
 
 8.02848 
 
 54 
 
 7 
 
 .07197 
 
 13.8940 
 
 .08954 
 
 11.1681 
 
 .10716 
 
 9.33155 
 
 .12485 
 
 8.00948 
 
 53 
 
 8 
 
 .07227 
 
 13.8378 
 
 .08983 
 
 11.1316 
 
 .10746 
 
 9.30599 
 
 .12515 
 
 7.99058 
 
 52 
 
 9 
 
 .07256 
 
 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 
 
 10.9882 
 
 .10*63 
 
 9.20518 
 
 .12633 
 
 7.91582 
 
 48 
 
 13 
 
 .07373 
 
 13.5634 
 
 .09130 
 
 10.9529 
 
 .10893 
 
 9.18028 
 
 .12662 
 
 7.89734 
 
 47 
 
 14 
 
 .07402 
 
 13.5098 
 
 .09159 
 
 10.9178 
 
 .10922 
 
 9.15554 
 
 .12692 
 
 7.87895 
 
 46 
 
 15 
 
 .07431 
 
 13.4566 
 
 .09189 
 
 10.8829 
 
 .10952 
 
 9.13093 
 
 .12722 
 
 7.86064 
 
 45 
 
 16 
 
 .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.S0622 
 
 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 
 
 .07636 
 
 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' 
 
 .11246 
 
 8.89185 
 
 .13017 
 
 7.68208 
 
 35 
 
 26 
 
 .07753 
 
 12.8981 
 
 .09511 
 
 10.5136 
 
 .11276 
 
 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 
 
 .11364 
 
 8.79964 
 
 .13136 
 
 7.61287 
 
 31 
 
 30 
 
 .07870 
 
 12.7062 
 
 .09629 
 
 10.3854 
 
 .11394 
 
 8.77689 
 
 .13165 
 
 7.59575 
 
 30 
 
 31 
 
 .07899 
 
 12.6591 
 
 .09058 
 
 10.3538 
 
 .11423 
 
 8.75425 
 
 .13195 
 
 7.57872 
 
 29 
 
 32 
 
 .07929 
 
 12.6124 
 
 .09688 
 
 10.3224 
 
 .11452 
 
 S.73172 
 
 M3224 
 
 7.56176 
 
 23 
 
 33 
 
 .07958 
 
 12.5660 
 
 .09717 
 
 10.2913 
 
 .11482 
 
 8.70931 
 
 .13254 
 
 7.54487 
 
 27 
 
 34 
 
 .07987 
 
 12.5199 
 
 .09746 
 
 10.2602 
 
 .11511 
 
 8.6S701 
 
 .13284 
 
 7.52806 
 
 26 
 
 35 
 
 .08017 
 
 12.4742 
 
 .09776 
 
 10.2294 
 
 .11541 
 
 8.66482 
 
 .13313 
 
 7.51132 
 
 25 
 
 36 
 
 .08046 
 
 12.4288 
 
 .09805 
 
 10.1988 
 
 .11570 
 
 8.64275 
 
 .13343 
 
 7.49405 
 
 24 
 
 37 
 
 .08075 
 
 12.3838 
 
 .09834 
 
 10.1633 
 
 .11600 
 
 8.62078 
 
 .13372 
 
 7.47806 
 
 23 
 
 38 
 
 08104 
 
 12.3390 
 
 .09864 
 
 10.1381 
 
 .11629 
 
 8.59893 
 
 .13402 
 
 7.46154 
 
 22 
 
 39 
 
 .08134 
 
 12.2946 
 
 .09893 
 
 10.1080 
 
 .11659 
 
 8.57718 
 
 .13432 
 
 7.44509 
 
 ^\ 
 
 40 
 
 .08163 
 
 12.2505 
 
 .09923 
 
 10.0780 
 
 .11688 
 
 8.55555 
 
 .13461 
 
 7.42871 
 
 20 
 
 41 
 
 08192 
 
 12.2067 
 
 .09952 
 
 10.0483 
 
 .11713 
 
 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 
 
 8.44896 
 
 .13609 
 
 7.34780 
 
 15 
 
 46 
 
 08339 
 
 11.9923 
 
 .10099 
 
 9.90211 
 
 .11865 
 
 8.42795 
 
 .13639 
 
 7.33190 
 
 1-i 
 
 47 
 
 .08368 
 
 11.9504 
 
 .10128 
 
 9.87338 
 
 .11895 
 
 8.40705 
 
 .13669 
 
 7.31600 
 
 13 
 
 43 
 
 08397 
 
 11.9087 
 
 10158 
 
 9.84482 
 
 .11924 
 
 8.38625 
 
 .13698 
 
 7.30018 
 
 12 
 
 49 
 
 08427 
 
 11.8673 
 
 .10187 
 
 9.81641 
 
 .11954 
 
 8.36555 
 
 .13728 
 
 7.28442 
 
 11 
 
 50 
 
 08456 
 
 11.8262 
 
 .10216 
 
 9.78817 
 
 .11983 
 
 8.34496 
 
 .13758 
 
 7.26873 
 
 10 
 
 51 
 
 OS485 
 
 11.7853 
 
 .10246 
 
 9.76009 
 
 .12013 
 
 8.32446 
 
 .13787 
 
 7.25310 
 
 9 
 
 5? 
 
 08514 
 
 11.7448 
 
 .10275 
 
 9.73217 
 
 .12042 
 
 8.30406 
 
 .13817 
 
 7.23754 
 
 8 
 
 53 
 
 08544 
 
 11.7045 
 
 .10305 
 
 9.70441 
 
 .19072 
 
 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 
 
 8.16393 
 
 .14024 
 
 7.13042 
 
 1 
 
 60 
 
 08749 
 
 11.4301 
 
 .10510 
 
 9.51436 
 
 .12278 
 
 8.14435 
 
 .14054 
 
 7.11537 
 
 
 
 / 
 
 uotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 i 
 
 
 85 
 
 84 
 
 83 
 
 83 1 
 
 
114 NATURAL TANGENTS AND COTANGENTS. 
 
 f 
 
 8 
 
 9 
 
 10 
 
 11 
 
 / 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 
 
 .14054 
 
 7.11537 
 
 .15838 
 
 6.31375 
 
 .17633 
 
 5.671?8 
 
 .19438 
 
 5.14455 
 
 60 
 
 1 
 
 .14084 
 
 7.10038 
 
 .15868 
 
 6.30189 
 
 .17663 
 
 5.66165 
 
 .19468 
 
 5.13658 
 
 59 
 
 2 
 
 .14113 
 
 7.08546 
 
 .15898 
 
 6.29007 
 
 .17693 
 
 5.65205 
 
 .19498 
 
 5.12862 
 
 58 
 
 3 
 
 .14143 
 
 7.07059 
 
 .15928 
 
 6.27829 
 
 .17723 
 
 5.64248 
 
 .19529 
 
 5.12069 
 
 57 
 
 4 
 
 .14173 
 
 7.05579 
 
 .15958 
 
 6.26655 
 
 .17753 
 
 5.63295 
 
 .19559 
 
 5.11279 
 
 56 
 
 5 
 
 .14202 
 
 7.04105 
 
 .15988 
 
 6.25486 
 
 .17783 
 
 5.62344 
 
 .19589 
 
 5.10490 
 
 55 
 
 6 
 
 .14232 
 
 7.02637 
 
 .16017 
 
 6.24321 
 
 .17813 
 
 5.61397 
 
 .19619 
 
 5.09704 
 
 54 
 
 7 
 
 .14262 
 
 6.91174 
 
 .16047 
 
 6.23160 
 
 .17843 
 
 5.00452 
 
 .19649 
 
 5.08921 
 
 53 
 
 8 
 
 .14291 
 
 6.99718 
 
 .16077 
 
 6.22003 
 
 .17873 
 
 5.59511 
 
 .19680 
 
 5.08139 
 
 52 
 
 9 
 
 .14321 
 
 6.98268 
 
 .16107 
 
 6.20851 
 
 .17903 
 
 5.58573 
 
 .19710 
 
 5.07360 
 
 51 
 
 10 
 
 .14351 
 
 6.96823 
 
 .16137 
 
 6.19703 
 
 .17933 
 
 5.57638 
 
 .19740 
 
 5.08584 
 
 50 
 
 11 
 
 .14381 
 
 6.95385 
 
 .16167 
 
 6.18559 
 
 .17963 
 
 5.56706 
 
 .19770 
 
 5.05809 
 
 49 
 
 12 
 
 .14110 
 
 6.93952 
 
 .16196 
 
 6.17419 
 
 .17993 
 
 5.55777 
 
 .19801 
 
 5.05037 
 
 48 
 
 13 
 
 .14440 
 
 6.92525 
 
 .16226 
 
 6.16283 
 
 .18023 
 
 5.54851 
 
 .19831 
 
 5.04267 
 
 47 
 
 14 
 
 .14470 
 
 6.91104 
 
 .10256 
 
 6.15151 
 
 .18053 
 
 5.53927 
 
 .19861 
 
 5.03499 
 
 46 
 
 15 
 
 .14499 
 
 6.89688 
 
 .16286 
 
 6.14023 
 
 .18083 
 
 5.53007 
 
 .19891 
 
 5.02734 
 
 45 
 
 16 
 
 .14529 
 
 6.88278 
 
 .16316 
 
 6.12899 
 
 .18113 
 
 5.52090 
 
 .19921 
 
 5.01971 
 
 44 
 
 17 
 
 .14559 
 
 6.86874 
 
 .16346 
 
 6.11779 
 
 .18143 
 
 5.51176 
 
 .19952 
 
 5.01210 
 
 43 
 
 18 
 
 .14588 
 
 6.85475 
 
 .16376 
 
 6.10664 
 
 .18173 
 
 5.50264 
 
 .19982 
 
 5.00451 
 
 42 
 
 19 
 
 .14618 
 
 6.84082 
 
 .16405 
 
 6.09552 
 
 .18203 
 
 5.49356 
 
 .20012 
 
 4.99695 
 
 41 
 
 20 
 
 .14648 
 
 6.82694 
 
 .16435 
 
 6.0S444 
 
 .18233 
 
 5.48451 
 
 .20042 
 
 4.98940 
 
 40 
 
 21 
 
 .14678 
 
 6.81312 
 
 .16465 
 
 6.07340 
 
 .18263 
 
 5.47548 
 
 .20073 
 
 4.98188 
 
 39 
 
 22 
 
 .14707 
 
 6.79936 
 
 .16495 
 
 6.06240 
 
 .18293 
 
 5.46648 
 
 .20103 
 
 4.97438 
 
 38 
 
 23 
 
 .14737 
 
 6.78564 
 
 .16525 
 
 6.05143 
 
 .18323 
 
 5.45751 
 
 .20133 
 
 4.90690 
 
 37 
 
 24 
 
 .14767 
 
 6.77199 
 
 .16555 
 
 6.04051 
 
 .18353 
 
 5.44857 
 
 .20164 
 
 4.95945 
 
 36 
 
 25 
 
 .14796 
 
 6.75838 
 
 .16585 
 
 6.02962 
 
 .18384 
 
 5.43066 
 
 .20194 
 
 4.95201 
 
 35 
 
 26 
 
 .14826 
 
 6.74483 
 
 .16615 
 
 6.01878 
 
 .18414 
 
 5.43077 
 
 .20224 
 
 4.94460 
 
 34 
 
 27 
 
 .14856 
 
 6.73133 
 
 .16645 
 
 6.00797 
 
 .18444 
 
 5.42192 
 
 .20254 
 
 4.93721 
 
 33 
 
 28 
 
 .14886 
 
 6.71789 
 
 .16674 
 
 5.99720 
 
 .18474 
 
 5.41309 
 
 .20285 
 
 4.92984 
 
 32 
 
 29 
 
 .14915 
 
 6.70450 
 
 .16704 
 
 5.98646 
 
 .18504 
 
 5.40429 
 
 .20315 
 
 4.92249 
 
 31 
 
 30 
 
 .14945 
 
 6.69116 
 
 .16734 
 
 5.97576 
 
 .18534 
 
 5.39552 
 
 .20345 
 
 4.91516 
 
 30 
 
 31 
 
 .14975 
 
 6.67787 
 
 .16764 
 
 5.96510 
 
 .18564 
 
 5.38677 
 
 .20376 
 
 4.90785 
 
 29 
 
 32 
 
 .15005 
 
 6.66463 
 
 .16794 
 
 5.95448 
 
 .18594 
 
 5.37805 
 
 .20406 
 
 4.90056 
 
 28 
 
 33 
 
 .15034 
 
 6.65144 
 
 .16824 
 
 5.94390 
 
 .18624 
 
 5.36936 
 
 .20436 
 
 4.89330 
 
 27 
 
 34 
 
 .15064 
 
 6.63831 
 
 .16854 
 
 5.9333o 
 
 .18654 
 
 5.36070 
 
 .20466 
 
 4.88605 
 
 26 
 
 35 
 
 .15094 
 
 6.62523 
 
 .16884 
 
 5.92283 
 
 .18684 
 
 5.35206 
 
 .20497 
 
 4.87882 
 
 25 
 
 36 
 
 .15124 
 
 6.61219 
 
 .16914 
 
 5.91236 
 
 .18714 
 
 5.34345 
 
 .20527 
 
 4.87162 
 
 24 
 
 37 
 
 .15153 
 
 6.59921 
 
 .16944 
 
 5.90191 
 
 .18745 
 
 5.33487 
 
 .20557 
 
 4.86444 
 
 23 
 
 38 
 
 .15183 
 
 6.58627 
 
 .16974 
 
 5.89151 
 
 .18775 
 
 5.32631 
 
 .20588 
 
 4.85727 
 
 22 
 
 39 
 
 .15213 
 
 6.57339 
 
 .17004 
 
 5.88114 
 
 .18805 
 
 5.31778 
 
 .20618 
 
 4.85013 
 
 21 
 
 10 
 
 .15243 
 
 6.56055 
 
 .17033 
 
 5.87080 
 
 .18835 
 
 5.30928 
 
 .20648 
 
 4.84300 
 
 20 
 
 41 
 
 .15272 
 
 6.54777 
 
 .17063 
 
 5.86051 
 
 .18865 
 
 5.30080 
 
 .20679 
 
 4.83590 
 
 19 
 
 42 
 
 .15302 
 
 6.53503 
 
 .17093 
 
 5.85024 
 
 .18895 
 
 5.29235 
 
 .20709 
 
 4.82882 
 
 18 
 
 43 
 
 .15332 
 
 6.52234 
 
 .17123 
 
 5.84001 
 
 .18925 
 
 5.28393 
 
 .20739 
 
 4.82175 
 
 17 
 
 44 
 
 .15362 
 
 6.50970 
 
 .17153 
 
 5.82982 
 
 .18955 
 
 5.27553 
 
 .20770 
 
 4.81471 
 
 10 
 
 45 
 
 .15391 
 
 6.49710 
 
 .17183 
 
 5.81966 
 
 .18986 
 
 5.26715 
 
 .20800 
 
 4.80769 
 
 15 
 
 46 
 
 .15421 
 
 6.48456 
 
 .17213 
 
 5.80953 
 
 .19016 
 
 5.25880 
 
 .20830 
 
 4.80068 
 
 14 
 
 47 
 
 .15451 
 
 6.47206 
 
 .17243 
 
 5.79944 
 
 .19046 
 
 5.25048 
 
 .20861 
 
 4.79370 
 
 13 
 
 48 
 
 .15481 
 
 6.45961 
 
 .17273 
 
 5.78938 
 
 .19076 
 
 5.24218 
 
 .20891 
 
 4.78673 
 
 12 
 
 49 
 
 .15511 
 
 6.44720 
 
 .17303 
 
 5.77936 
 
 .19106 
 
 5.23391 
 
 .20921 
 
 4.77978 
 
 11 
 
 50 
 
 .15540 
 
 6.43484 
 
 .17333 
 
 5.7G937 
 
 .19136 
 
 5.22536 
 
 .20952 
 
 4.77286 
 
 10 
 
 51 
 
 .15570 
 
 6.42253 
 
 .17363 
 
 5.75941 
 
 .19166 
 
 5.21741 
 
 .20982 
 
 4.76595 
 
 9 
 
 52 
 
 .15600 
 
 6.41026 
 
 .17393 
 
 5.74949 
 
 .19197 
 
 5.20925 
 
 .21013 
 
 4.75906 
 
 Q 
 
 53 
 
 .15630 
 
 6.39804 
 
 .17423 
 
 5.73960 
 
 19227 
 
 5.20107 
 
 .21043 
 
 4.75219 
 
 7 
 
 54 
 
 .15660 
 
 6.38587 
 
 .17453 
 
 5.72974 
 
 J9257 
 
 5.19293 
 
 .21073 
 
 4.74534 
 
 6 
 
 55 
 
 .15689 
 
 6.37374 
 
 .17483 
 
 5.71992 
 
 .19287 
 
 5.18480 
 
 .21104 
 
 4.73851 
 
 5 
 
 56 
 
 .15719 
 
 6.36165 
 
 .17513 
 
 5.71013 
 
 .19317 
 
 5.17671 
 
 .21134 
 
 4.73170 
 
 4 
 
 57 
 
 .15749 
 
 6.34961 
 
 .17543 
 
 5.70037 
 
 .19347 
 
 5.16803 
 
 .21164 
 
 4.72490 
 
 3 
 
 58 
 
 .15779 
 
 6.33761 
 
 .17573 
 
 5.69064 
 
 .19378 
 
 5.16058 
 
 .21195 
 
 4.71813 
 
 2 
 
 59 
 
 .15809 
 
 6.32566 
 
 .17603 
 
 5.68094 
 
 .19408 
 
 5.15256 
 
 .21225 
 
 4.71137 
 
 1 
 
 60 
 
 .15838 
 
 6.31375 
 
 .17633 
 
 5.67128 
 
 .19438 
 
 5.14455 
 
 .21256 
 
 4.70463 
 
 
 
 f 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tan? 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 9 
 
 
 81 
 
 80 ' 
 
 79 
 
 78 
 
 
NATURAL TANGENTS AND COTANGENTS. 115 
 
 1 
 
 / 
 
 13 
 
 13 
 
 14 
 
 15 
 
 t 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Jotang 
 
 
 
 .21256 
 
 4.70463 
 
 .23087 
 
 4.33148 
 
 .24933 
 
 4.01078 
 
 .26795 
 
 3.73205 
 
 60 
 
 J 
 
 .21286 
 
 4.69791 
 
 .23117 
 
 4.32573 
 
 .24964 
 
 4.00582 
 
 .26826 
 
 3.72771 
 
 59 
 
 2 
 
 .21316 
 
 4.69121 
 
 .23148 
 
 4.32001 
 
 .24995 
 
 4.00086 
 
 .26857 
 
 3.72338 
 
 58 
 
 3 
 
 .21347 
 
 4.68452 
 
 .23179 
 
 4.31430 
 
 .25026 
 
 3.99592 
 
 .26888 
 
 3.71907 
 
 57 
 
 4 
 
 .21377 
 
 4.67786 
 
 .23209 
 
 4.30860 
 
 .25056 
 
 3.99099 
 
 .26920 
 
 3.71476 
 
 56 
 
 5 
 
 .21408 
 
 4.67121 
 
 .23240 
 
 4.30291 
 
 .25087 
 
 3.98607 
 
 .26951 
 
 3.71046 
 
 55 
 
 6 
 
 .21438 
 
 4.66458 
 
 .23271 
 
 4.29724 
 
 .25118 
 
 3.98117 
 
 .26982 
 
 3.70616 
 
 54 
 
 7 
 
 .21469 
 
 4.65797 
 
 .23301 
 
 4.20159 
 
 .25149 
 
 3.97627 
 
 .27013 
 
 3.70188 
 
 53 
 
 8 
 
 .21499 
 
 4.65138 
 
 .23332 
 
 4.28595 
 
 .25180 
 
 3.97139 
 
 .27044 
 
 3.69761 
 
 52 
 
 9 
 
 .21529 
 
 4.64480 
 
 .23363 
 
 4.28032 
 
 .25211 
 
 3.96651 
 
 .27076 
 
 3.69335 
 
 51 
 
 10 
 
 .21560 
 
 4.63825 
 
 .23393 
 
 4.27471 
 
 .25242 
 
 3.96165 
 
 .27107 
 
 3.8S909 
 
 50 
 
 11 
 
 .21590 
 
 4.63171- 
 
 .23424 
 
 4.26911 
 
 .25273 
 
 3.95680 
 
 .27138 
 
 3.68485 
 
 49 
 
 12 
 
 .21621 
 
 4.62518 
 
 .23455 
 
 4.26352 
 
 .25304 
 
 3.95196 
 
 .27169 
 
 3.68061 
 
 48 
 
 13 
 
 .21651 
 
 4.61868 
 
 .23485 
 
 4.25795 
 
 .25335 
 
 3.94713 
 
 .27201 
 
 3.67638 
 
 47 
 
 14 
 
 .21682 
 
 4.61219 
 
 .23516 
 
 4.25239 
 
 .25366 
 
 3 94232 
 
 .27232 
 
 3.67217 
 
 46 
 
 15 
 
 .21712 
 
 4.60572 
 
 .23547 
 
 4.24685 
 
 .25397 
 
 3.93751 
 
 .27263 
 
 3.66796 
 
 45 
 
 1G 
 
 .21743 
 
 4.59927 
 
 .23578 
 
 4.24132 
 
 .25428 
 
 3.93271 
 
 .27294 
 
 3.66376 
 
 44 
 
 17 
 
 .21773 
 
 4.59283 
 
 .23608 
 
 4.23580 
 
 .25459 
 
 3.92793 
 
 .27326 
 
 3.65957 
 
 43 
 
 18 
 
 .21804 
 
 4.58641 
 
 .23639 
 
 4.23030 
 
 .25490 
 
 3.92316 
 
 .27357 
 
 3.65538 
 
 42 
 
 19 
 
 .21834 
 
 4.58001 
 
 .23670 
 
 4.22481 
 
 .25521 
 
 3.91839 
 
 .27388 
 
 3.65121 
 
 41 
 
 20 
 
 .21864 
 
 4.57363 
 
 .23700 
 
 4.21933 
 
 .25552 
 
 3.91364 
 
 .27419 
 
 3.64705 
 
 40 
 
 21 
 
 .21895 
 
 4.56726 
 
 .23731 
 
 4.21387 
 
 .25583 
 
 3.90890 
 
 .27451 
 
 3.64289 
 
 39 
 
 22 
 
 .21925 
 
 4.56091 
 
 .23762 
 
 4.20842 
 
 .25614 
 
 3.90417 
 
 .27482 
 
 3.63874 
 
 38 
 
 23 
 
 .21956 
 
 4.55458 
 
 .23793 
 
 4.20298 
 
 .25645 
 
 3.89945 
 
 .27513 
 
 3.63461 
 
 37 
 
 24 
 
 .21986 
 
 4.54826 
 
 .23823 
 
 4.19756 
 
 .25676 
 
 3.89474 
 
 .27545 
 
 3.62048 
 
 36 
 
 25 
 
 .22017 
 
 4.54196 
 
 .23854 
 
 4.19215 
 
 .25707 
 
 3.SQ004 
 
 .27576 
 
 3.62636 
 
 35 
 
 26 
 
 .22047 
 
 4.53568 
 
 .23885 
 
 4.18675 
 
 .25738 
 
 3.88536 
 
 .27607 
 
 3.62224 
 
 34 
 
 27 
 
 .22078 
 
 4.52941 
 
 .23916 
 
 4.18137 
 
 .25769 
 
 3.88068 
 
 .27638 
 
 3.61814 
 
 33 
 
 28 
 
 .22108 
 
 4.52316 
 
 .23946 
 
 4.17600 
 
 .25800 
 
 3.87601 
 
 .27670 
 
 3.61405 
 
 32 
 
 29 
 
 .22139 
 
 4.51693 
 
 .23977 
 
 4.17064 
 
 .25831 
 
 3.87136 
 
 .27701 
 
 3.60996 
 
 31 
 
 30 
 
 .22169 
 
 4.51071 
 
 .24008 
 
 4.16530 
 
 .25862 
 
 3.86671 
 
 .27732 
 
 3.60588 
 
 30 
 
 31 
 
 .22200 
 
 4.50451 
 
 .24039 
 
 4.15997 
 
 .25893 
 
 3.86208 
 
 .27764 
 
 3.60181 
 
 29 
 
 32 
 
 .22231 
 
 4.49832 
 
 .24069 
 
 4.15465 
 
 .25924 
 
 3.85745 
 
 .27795 
 
 3.59775 
 
 28 
 
 33 
 
 .22261 
 
 4.49215 
 
 .24100 
 
 4.14934 
 
 .25955 
 
 3.85284 
 
 .27826 
 
 3.59370 
 
 27 
 
 34 
 
 .22292 
 
 4.48600 
 
 .24131 
 
 4.14405 
 
 .25986 
 
 3.84824 
 
 .27858 
 
 3.58966 
 
 26 
 
 35 
 
 .22322 
 
 4.47988 
 
 .24162 
 
 4.13877 
 
 .26017 
 
 3.84364 
 
 .27889 
 
 3.58562 
 
 25 
 
 36 
 
 .22353 
 
 4.47374 
 
 .24193 
 
 4.13350 
 
 .26048 
 
 3.83906 
 
 .27921 
 
 3.58160 
 
 24 
 
 37 
 
 .22383 
 
 4.46764 
 
 .24223 
 
 4.12825 
 
 .26079 
 
 3.83449 
 
 .27952 
 
 3.57758 
 
 23 
 
 38 
 
 .22414 
 
 4.46155 
 
 .24254 
 
 4.12301 
 
 .26110 
 
 3.82992 
 
 .27983 
 
 3.57357 
 
 22 
 
 39 
 
 .22444 
 
 4.45548 
 
 .24285 
 
 4.11778 
 
 .26141 
 
 3.82537 
 
 .28015 
 
 3.56957 
 
 21 
 
 40 
 
 .22475 
 
 4.44942 
 
 .24316 
 
 4.11256 
 
 .26172 
 
 3.82083 
 
 .28046 
 
 3.56557 
 
 20 
 
 41 
 
 .22505 
 
 4.44338 
 
 .24347 
 
 4.10736 
 
 .26203 
 
 3.81630 
 
 .28077 
 
 3.56159 
 
 19 
 
 42 
 
 .22530 
 
 4.43735 
 
 .24377 
 
 4.10216 
 
 .26235 
 
 3.81177 
 
 .28109 
 
 3.55761 
 
 18 
 
 43 
 
 .22567 
 
 4.43134 
 
 .24408 
 
 4.09699 
 
 .26266 
 
 3.80726 
 
 .28140 
 
 3.55364 
 
 17 
 
 44 
 
 .22597 
 
 4.42534 
 
 .24439 
 
 4.09182 
 
 .26297 
 
 3.80276 
 
 .28172 
 
 3.54968 
 
 16 
 
 45 
 
 .22628 
 
 4.41936 
 
 .24470 
 
 4.08666 
 
 .26328 
 
 3.79827 
 
 .28203 
 
 3.54573 
 
 15 
 
 40 
 
 .22658 
 
 4.41340 
 
 .24501 
 
 4.08152 
 
 .26359 
 
 3.79378 
 
 .28234 
 
 3.54179 
 
 14 
 
 47 
 
 .22089 
 
 4.40745 
 
 .24532 
 
 4.07639 
 
 .26390 
 
 3.78931 
 
 .28266 
 
 3.53785 
 
 13 
 
 18 
 
 .22719 
 
 4.40152 
 
 .24562 
 
 4.07127 
 
 .26421 
 
 3.78485 
 
 .28297 
 
 3.53393 
 
 12 
 
 49 
 
 .22750 
 
 4.39560 
 
 .24593 
 
 4.06616 
 
 .26452 
 
 3.78040 
 
 .28329 
 
 3.53001 
 
 11 
 
 50 
 
 .22781 
 
 4.38969 
 
 .24624 
 
 4.06107 
 
 .26483 
 
 3.77595 
 
 .28360 
 
 3.52609 
 
 10 
 
 51 
 
 .22811 
 
 4.38381 
 
 .24655 
 
 4.05599 
 
 .26515 
 
 3.77152 
 
 .28391 
 
 3.52219 
 
 9 
 
 52 
 
 .22842 
 
 4.37793 
 
 .24686 
 
 4.05092 
 
 .26546 
 
 3.76709 
 
 .28423 
 
 3.51829 
 
 8 
 
 53 
 
 .22872 
 
 4.37207 
 
 .24717 
 
 4.045S6 
 
 .26577 
 
 3.76268 
 
 .28454 
 
 3.51441 
 
 7 
 
 54 
 
 .22903 
 
 4.36623 
 
 .24747 
 
 4.04081 
 
 .26608 
 
 3.75828 
 
 .28486 
 
 3.51053 
 
 6 
 
 55 
 
 .22934 
 
 4.36040 
 
 .24778 
 
 4.03578 
 
 .26639 
 
 3.75388 
 
 .28517 
 
 3.50666 
 
 5 
 
 56 
 
 .22964 
 
 4.35459 
 
 .24809 
 
 4.03076 
 
 .26670 
 
 3.74950 
 
 .28549 
 
 3.50279 
 
 4 
 
 57 
 
 .22995 
 
 4.34879 
 
 .24840 
 
 4.02574 
 
 .26701 
 
 3.74512 
 
 .28580 
 
 3.49894 
 
 3 
 
 58 
 
 .23026 
 
 4.34300 
 
 .24871 
 
 4.02074 
 
 .26733 
 
 3.74075 
 
 .28612 
 
 3.49509 
 
 2 
 
 59 
 
 .23056 
 
 4.33723 
 
 .24902 
 
 4.01576 
 
 .26764 
 
 3.73640 
 
 .28643 
 
 3.49125 
 
 1 
 
 60 
 
 .23087 
 
 4.33148 
 
 .24933 
 
 4.01078 
 
 .26795 
 
 3.73205 
 
 .28675 
 
 3.48741 
 
 
 
 "7 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 / 
 
 
 77 
 
 76 
 
 75 
 
 74 
 
 
116 NATURAL TANGENTS AND COTANGENTS. 
 
 
 10 
 
 17 
 
 18 
 
 19 
 
 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 
 
 
 .28675 
 
 3.48741 
 
 .30573 
 
 3.27085 
 
 .32492 
 
 3.07768 
 
 .34433 
 
 2.90421 
 
 60 
 
 1 
 
 .28706 
 
 3.48359 
 
 .30005 
 
 3.26745 
 
 .32524 
 
 3.07464 
 
 .34465 
 
 2.90147 
 
 59 
 
 2 
 
 .28738 
 
 3.47977 
 
 .30637 
 
 8. 26406 
 
 .32556 
 
 3.07160 
 
 .34498 
 
 2.89873 
 
 58 
 
 3 
 
 .28769 
 
 3.47596 
 
 .30669 
 
 3.26067 
 
 .32588 
 
 3.06857 
 
 .34530 
 
 2.89600 
 
 57 
 
 4 
 
 .28800 
 
 3.47216 
 
 .30700 
 
 3.25729 
 
 .32621 
 
 3.06554 
 
 .34563 
 
 2.89327 
 
 56 
 
 5 
 
 .28832 
 
 3.4^837 
 
 .30732 
 
 3.25392 
 
 .32653 
 
 3.06252 
 
 .34596 
 
 2.89055 
 
 55 
 
 6 
 
 .28804 
 
 3.46458 
 
 .30764 
 
 3.25055 
 
 .32685 
 
 3.05950 
 
 .34628 
 
 2.88783 
 
 54 
 
 7 
 
 .28895 
 
 3.46080 
 
 .30796 
 
 3.24719 
 
 .32717 
 
 3.05649 
 
 .34661 
 
 2.88511 
 
 53 
 
 8 
 
 .28927 
 
 3.45703 
 
 .30828 
 
 3.24383 
 
 .32749 
 
 3.05349 
 
 .34693 
 
 2.88240 
 
 52 
 
 9 
 
 .28953 
 
 3.45327 
 
 .30360 
 
 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 
 
 .34856 
 
 2.86892 
 
 47 
 
 14 
 
 .29116 
 
 3.43456 
 
 .31019 
 
 3.22384 
 
 .32943 
 
 3.03556 
 
 .34889 
 
 2.86624 
 
 46 
 
 15 
 
 .29147 
 
 3.43084 
 
 .31051 
 
 3.22053 
 
 .32975 
 
 3.03260 
 
 .34922 
 
 2.36356 
 
 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 
 
 .34937 
 
 2.85822 
 
 43 
 
 18 
 
 .29242 
 
 3.41973 
 
 .31117 
 
 3.21063 
 
 .33072 
 
 3.02372 
 
 .35020 
 
 2.85555 
 
 42 
 
 19 
 
 .29274 
 
 3.41604 
 
 .31178 
 
 3.20734 
 
 .33104 
 
 3.02077 
 
 .35052 
 
 2.85289 
 
 41 
 
 20 
 
 .29305 
 
 3.41236 
 
 .31210 
 
 3.20406 
 
 .33136 
 
 3.01783 
 
 .35085 
 
 2.85023 
 
 40 
 
 21 
 
 .29337 
 
 3.40869 
 
 .31242 
 
 3.20079 
 
 .33169 
 
 3.01489 
 
 .35118 
 
 2.84758 
 
 39 
 
 22 
 
 .29368 
 
 3.40502 
 
 .31274 
 
 3.19752 
 
 .33201 
 
 3.01196 
 
 .35150 
 
 2.84494 
 
 38 
 
 23 
 
 .29400 
 
 3.40136 
 
 .31306 
 
 3.19426 
 
 .33233 
 
 3.00903 
 
 .35183 
 
 2.84229 
 
 37 
 
 24 
 
 .29432 
 
 3.39771 
 
 .31338 
 
 3.19100 
 
 .33266 
 
 3.00611 
 
 .35216 
 
 2^83965 
 
 36 
 
 25 
 
 .29463 
 
 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 
 
 .29526 
 
 3.38679 
 
 .31434 
 
 3.18127 
 
 .33363 
 
 2.99738 
 
 .35314 
 
 2.83176 
 
 33 
 
 28 
 
 .29558 
 
 3.38317 
 
 .31466 
 
 3.17804 
 
 .33395 
 
 2.99447 
 
 .35346 
 
 2.82914 
 
 32 
 
 29 
 
 .29590 
 
 3.37955 
 
 .31498 
 
 3.17481 
 
 .33427 
 
 2.99158 
 
 .35379 
 
 2.82653 
 
 31 
 
 30 
 
 .29621 
 
 3.37594 
 
 .31530 
 
 3.17159 
 
 .33460 
 
 2.98S68 
 
 .35412 
 
 2.82391 
 
 30 
 
 31 
 
 .29653 
 
 3.37234 . 
 
 .31562 
 
 3.16838 
 
 .33492 
 
 2.98580 
 
 .35445 
 
 2.82130 
 
 29 
 
 32 
 
 .29685 
 
 3.36875 
 
 .31594 
 
 3.16517 
 
 .33524 
 
 2.98292 
 
 .35477 
 
 2.81870 
 
 2^ 
 
 33 
 
 .29716 
 
 3.36516 
 
 .31626 
 
 3.16197 
 
 .33557 
 
 2.98004 
 
 .35510 
 
 2.81810 
 
 27 
 
 34 
 
 .29748 
 
 3.36158 
 
 .31658 
 
 3.15877 
 
 .33589 
 
 2.97717 
 
 .35543 
 
 2.81350 
 
 26 
 
 35 
 
 .29780 
 
 3.35800 
 
 .31690 
 
 3.15558 
 
 .33621 
 
 2.97430 
 
 .35576 
 
 2.81091 
 
 25 
 
 36 
 
 .29811 
 
 3.35443 
 
 .31722 
 
 3.15240 
 
 .33654 
 
 2.97144 
 
 .35608 
 
 2.80833 
 
 24 
 
 37 
 
 .29843 
 
 3.35087 
 
 .31754 
 
 3.14922 
 
 .33686 
 
 2.96858 
 
 .35641 
 
 2.80574 
 
 23 
 
 38 
 
 .29875 
 
 3.34732 
 
 .31786 
 
 3.14605 
 
 .33718 
 
 2.96573 
 
 .35674 
 
 2.80316 
 
 22 
 
 39 
 
 .29906 
 
 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 
 
 2.95437 
 
 .35805 
 
 2.79289 
 
 IS 
 
 43 
 
 .30033 
 
 3.32965 
 
 .31946 
 
 3.13027 
 
 .33881 
 
 2.95155 
 
 .35838 
 
 2.79033 
 
 17 
 
 44 
 
 .30065 
 
 3.32614 
 
 .31978 
 
 3.12713 
 
 .33913 
 
 2.94872 
 
 .35871 
 
 2.78778 
 
 16 
 
 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 
 
 2.78269 
 
 14 
 
 47 
 
 .30160 
 
 3.31565 
 
 .32074 
 
 3.11775 
 
 .34010 
 
 2.94028 
 
 .35969 
 
 2.78014 
 
 13 
 
 48 
 
 .30192 
 
 3.31216 
 
 .32106 
 
 3.11464 
 
 .34043 
 
 2.93748 
 
 .36002 
 
 2.77761 
 
 12 
 
 49 
 
 .30224 
 
 3.30868 
 
 .32139 
 
 3.11153 
 
 .34075 
 
 2.93468 
 
 .36035 
 
 2.77507 
 
 11 
 
 50 
 
 .30255 
 
 3.30521 
 
 .32171 
 
 3.10842 
 
 .34108 
 
 2.93189 
 
 .36068 
 
 2.77254 
 
 10 
 
 51 
 
 .30287 
 
 3.30174 
 
 .32203 
 
 3.10532 
 
 .34140 
 
 2.92910 
 
 .36101 
 
 2.77002 
 
 9 
 
 52 
 
 .30319 
 
 3.29829 
 
 .32235 
 
 3.10223 
 
 .34173 
 
 2.92632 
 
 .36134 
 
 2.76750 
 
 8 
 
 53 
 
 .30351 
 
 3.294S3 
 
 .32267 
 
 3.09914 
 
 .34205 
 
 2.92354 
 
 .36167 
 
 2.76498 
 
 7 
 
 54 
 
 303S2 
 
 3.29139 
 
 .32299 
 
 3.09606 
 
 .34238 
 
 2.92076 
 
 .36199 
 
 2.76247 
 
 6 
 
 55 
 
 .30414 
 
 3.28795 
 
 .32331 
 
 3.09298 
 
 .34270 
 
 2.91799 
 
 .36232 
 
 2.75996 
 
 5 
 
 56 
 
 .30446 
 
 3.28452 
 
 .32303 
 
 3.08991 
 
 .34303 
 
 2.91523 
 
 .36265 
 
 2.75746 
 
 4 
 
 57 
 
 .30478 
 
 3.28109 
 
 .32396 
 
 3.08685 
 
 .34335 
 
 2.91246 
 
 .36298 
 
 2.75496 
 
 3 
 
 58 
 
 .30509 
 
 3.27767 
 
 .32428 
 
 3.08379 
 
 .34368 
 
 2.90971 
 
 .36331 
 
 2.75246 
 
 1 
 
 59 
 
 .30541 
 
 3.27426 
 
 .32460 
 
 3.08073 
 
 .34400 
 
 2.90696 
 
 .36364 
 
 2.74997 
 
 
 
 60 
 
 .30573 
 
 3.27085 
 
 .32492 
 
 3.07768 
 
 .34433 
 
 2.90421 
 
 .36397 
 
 2.74748 
 
 2 
 
 t 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 , 
 
 
 73 
 
 72 
 
 71 
 
 70 
 
 
IMATUitALi TAIN U1WN 113 AJMJ <JUT AJN (jrliiJN IB. 
 
 
 20 
 
 21 
 
 22 
 
 23 
 
 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 (Jo tang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 
 
 
 .36397 
 
 2.74748 
 
 .38386 
 
 2.00509 
 
 .40403 
 
 2.47509 
 
 .42447 
 
 2.35585 
 
 60 
 
 1 
 
 .36430 
 
 2.74499 
 
 .38420 
 
 2.00283 
 
 .40436 
 
 2.47302 
 
 .42482 
 
 2.35395 
 
 59 
 
 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 
 
 2.40082 
 
 .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 
 
 54 
 
 7 
 
 .36628 
 
 2.73017 
 
 ,38020 
 
 2.58932 
 
 .40640 
 
 2.46065 
 
 .42688 
 
 2.34258 
 
 53 
 
 8 
 
 .36661 
 
 2.72771 
 
 .38654 
 
 2.58708 
 
 .40674 
 
 2.45S60 
 
 .42722 
 
 2.34069 
 
 52 
 
 9 
 
 .36694 
 
 2.72526 
 
 .38687 
 
 2.58484 
 
 .40707 
 
 2.45055 
 
 .42757 
 
 2.33881 
 
 51 
 
 10 
 
 .36727 
 
 2.72281 
 
 .38721 
 
 2.58201 
 
 .40741 
 
 2.45451 
 
 .42791 
 
 2.33693 
 
 50 
 
 11 
 
 .36760 
 
 2.72036 
 
 .38754 
 
 2.58038 
 
 .40775 
 
 2. -15240 
 
 .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 
 
 .42.894 
 
 2.33130 
 
 47 
 
 id 
 
 .36859 
 
 2.71305 
 
 .38854 
 
 2.57371 
 
 .40877 
 
 2.44630 
 
 .42929 
 
 2.32943 
 
 46 
 
 15 
 
 .36892 
 
 2.71002 
 
 .38888 
 
 2.57150 
 
 .40911 
 
 2.44433 
 
 .42903 
 
 2.32750 
 
 45 
 
 16 
 
 .36925 
 
 2.70819 
 
 .38921 
 
 2.56928 
 
 .40945 
 
 2.44230 
 
 .42998 
 
 2.32570 
 
 44 
 
 17 
 
 .36958 
 
 2.70577 
 
 .3S955 
 
 2. ,56707 
 
 .40979 
 
 2.44027 
 
 .43032 2.32383 
 
 43 
 
 18 
 
 .36991 
 
 2.70335 
 
 .38988 
 
 2.56487 
 
 .41013 
 
 2.43825 
 
 .43007 ; 2.32197 
 
 42 
 
 19 
 
 .37024 
 
 2.70094 
 
 .39022 
 
 2.56200 
 
 .41047 
 
 2.43623 
 
 .43101 
 
 2.32012 
 
 41 
 
 20 
 
 .37057 
 
 2.69853 
 
 .39055 
 
 2.50040 
 
 .41081 
 
 2.43422 
 
 .43130 
 
 2.31820 
 
 40 
 
 21 
 
 .37090 
 
 2.69612 
 
 .39089 
 
 2.55827 
 
 .41115 
 
 2.43220 
 
 .43170 
 
 2.31041 
 
 39 
 
 22 
 
 .37123 
 
 2.69371 
 
 .39122 
 
 2.55008 
 
 .41149 
 
 2.43019 
 
 .43205 
 
 2.31456 
 
 38 
 
 23 
 
 .37157 
 
 2.69131 
 
 .39156 
 
 2.553S9 
 
 .41183 
 
 2.42819 
 
 .43239 
 
 2.31271 
 
 37 
 
 24 
 
 .37190 
 
 2.68892 
 
 .39190 
 
 2.55170 
 
 .41217 
 
 2.42018 
 
 .43274 
 
 2.31080 
 
 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 
 
 .43378 
 
 2.30534 
 
 33 
 
 28 
 
 .37322 
 
 2.67937 
 
 .39324 
 
 2.54299 
 
 .41353 
 
 2.41819 
 
 .43412 
 
 2.30351 
 
 32 
 
 29 
 
 .37355 
 
 2.67700 
 
 .39357 
 
 2.54082 
 
 .41387 
 
 2.41020 
 
 .43447 
 
 2.30167 
 
 31 
 
 30 
 
 .37388 
 
 2.67462 
 
 .39391 
 
 2.53865 
 
 .41421 
 
 2.41421 
 
 .43481 
 
 2.29984 
 
 30 
 
 31 
 
 .37422 
 
 2.67225 
 
 .39425 
 
 2.53048 
 
 .41455 
 
 2.41223 
 
 .43510 
 
 2.29801 
 
 29 
 
 32 
 
 .37455 
 
 2.66989 
 
 .39458 
 
 2.53432 
 
 .41490 
 
 2.41025 
 
 .43550 
 
 2.29019 
 
 28 
 
 33 
 
 .37488 
 
 2.66752 
 
 .39492 
 
 2.53217 
 
 .41524 
 
 2.40827 
 
 .43585 
 
 2.29437 
 
 27 
 
 34 
 
 .375?! 
 
 2.66516 
 
 .39526 
 
 2.53001 
 
 .41558 
 
 2.40029 
 
 .43020 
 
 2.29254 
 
 26 
 
 35 
 
 .37554 
 
 2.66281 
 
 .39559 
 
 2.52780 
 
 .41592 
 
 2.40432 
 
 .43054 
 
 2.29073 
 
 25 
 
 36 
 
 .37588 
 
 2.66046 
 
 .39593 
 
 2.52571 
 
 .41020 
 
 2.40235 
 
 .43689 
 
 2.28891 
 
 24 
 
 37 
 
 .37621 
 
 2.65811 
 
 .39626 
 
 2.52357 
 
 .41000 
 
 2.40038 
 
 .43724 
 
 2.28710 
 
 23 
 
 38 
 
 .37654 
 
 2.65576 
 
 .39660 
 
 2.52142 
 
 .41694 
 
 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 
 
 .39701 
 
 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 
 
 2.51070 
 
 .41865 
 
 2.38863L 
 
 .43932 
 
 2.27626 
 
 17 
 
 44 
 
 .37853 
 
 2.64177 
 
 .39862 
 
 2.50804 
 
 .41899 
 
 2.38668 
 
 .43960 
 
 2.27447 
 
 10 
 
 45 
 
 .37887 
 
 2.63945 
 
 .39896 
 
 2:50052 
 
 .41933 
 
 2.38473 
 
 .44001 
 
 2.27267 
 
 15 
 
 40 
 
 .37920 
 
 2.63714 
 
 .39930 
 
 2.50440 
 
 .41968 
 
 2.38279 
 
 .44036 
 
 2.27088 
 
 14 
 
 47 
 
 .37953 
 
 2.63483 
 
 .39963 
 
 2.50229 
 
 .42002 
 
 2.38084 
 
 .44071 
 
 2.28909 
 
 13 
 
 48 
 
 .37986 
 
 2.63252 
 
 .39997 
 
 2.50018 
 
 .42036 
 
 2.37891 
 
 .44105 
 
 2.26730 
 
 12 
 
 49 
 
 .38020 
 
 2.63021 
 
 .40031 
 
 2.49807 
 
 .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 
 
 2.49380 
 
 .42139 
 
 2.37311 
 
 .44210 
 
 2.20196 
 
 9 
 
 52 
 
 .38120 
 
 2.62332 
 
 .40132 
 
 2.49177 
 
 .42173 
 
 2.37118 
 
 .44244 
 
 2.20018 
 
 8 
 
 53 
 
 .38153 
 
 2.62103 
 
 .40100 
 
 2.48907 
 
 .42207 
 
 2.36925 
 
 .44279 
 
 2.25840 
 
 7 
 
 54 
 
 .38186 
 
 2.61874 
 
 .40200 
 
 2.48758 
 
 .42242 
 
 2.36733 
 
 .44314 
 
 2.25063 
 
 
 
 55 
 
 .38220 
 
 2.61646 
 
 .40234 
 
 2.48549 
 
 .42276 
 
 2.36541 
 
 .44349 
 
 2.25486 
 
 5 
 
 56 
 
 .38253 
 
 2.61418 
 
 .40207 
 
 2.48340 
 
 .42310 
 
 2.36340 
 
 .44384 
 
 2.25309 
 
 4 
 
 57 
 
 .38286 
 
 2.01190 
 
 .40301 
 
 2.48132 
 
 .42345 
 
 2.36158 
 
 ,44418 
 
 2.25132 
 
 3 
 
 58 
 
 .38320 
 
 2.60963 
 
 .40335 
 
 2.47924 
 
 .42379 
 
 2.35967 
 
 .44453 
 
 2.24950 
 
 2 
 
 59 
 
 .38353 
 
 2.60730 
 
 .40309 
 
 2.47716 
 
 .42413 
 
 2.35770 
 
 .44488 
 
 2.24780 
 
 1 
 
 60 
 
 .38386 
 
 2.60509 
 
 .40403 
 
 2.47509 
 
 .42447 
 
 2.35585 
 
 .44523 
 
 2.24004 
 
 
 
 r 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 , 
 
 
 69 
 
 68 
 
 67 
 
 66 
 
 
118 NATURAL TANGENTS AND COTANGENTS. 
 
 
 A 
 
 J4 
 
 j 
 
 ,5 
 
 2 
 
 6 
 
 2 
 
 7 
 
 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 
 
 
 .44523 
 
 2.24604 
 
 .46631 
 
 2.14451 
 
 .48773 
 
 2.05030 
 
 .50953 
 
 1.96261 
 
 60 
 
 1 
 
 .44558 
 
 2.24428 
 
 .46666 
 
 2.14288 
 
 .48809 
 
 2.04879 
 
 .50989 
 
 1.96120 
 
 59 
 
 2 
 
 .44593 
 
 2.24252 
 
 .46702 
 
 2.14125 
 
 .48845 
 
 2.04728 
 
 .51026 
 
 1.95979 
 
 58 
 
 3 
 
 .44627 
 
 2.24077 
 
 .46737 
 
 2.13963 
 
 .48881 
 
 2.04577 
 
 .51063 
 
 1.95838 
 
 57 
 
 4 
 
 .44662 
 
 2.23902 
 
 .46772 
 
 2.13801 
 
 .48917 
 
 2.04426 
 
 .51099 
 
 1.95698 
 
 56 
 
 5 
 
 .44697 
 
 2.23727 
 
 .46308 
 
 2.13639 
 
 .48953 
 
 2.04276 
 
 .51136 
 
 1.95557 
 
 55 
 
 6 
 
 .44732 
 
 2.23553 
 
 .46843 
 
 2.13477 
 
 .48989 
 
 2.04125 
 
 .51173 
 
 1.95417 
 
 54 
 
 7 
 
 .44767 
 
 2.23378 
 
 .46879 
 
 2.13316 
 
 .49026 
 
 2.03975 
 
 .51209 
 
 1.95277 
 
 53 
 
 8 
 
 .44802 
 
 2.23204 
 
 .46914 
 
 2.13154 
 
 .49062 
 
 2.03825 
 
 .51246 
 
 1.95127 
 
 52 
 
 9 
 
 .44837 
 
 2.23030 
 
 .46950 
 
 2.12993 
 
 .49098 
 
 2.03675 
 
 .51283 
 
 1.94997 
 
 51 
 
 10 
 
 .44872 
 
 2.22857 
 
 .46985 
 
 2.12832 
 
 .49134 
 
 2.03526 
 
 .51319 
 
 1.94858 
 
 50 
 
 11 
 
 .44907 
 
 2.22683 
 
 .47021 
 
 2.12671 
 
 .49170 
 
 2.03376 
 
 .51356 
 
 1.94718 
 
 49 
 
 12 
 
 .44942 
 
 2.22510 
 
 .47056 
 
 2.12511 
 
 .49206 
 
 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 
 
 .51467 
 
 1.94301 
 
 46 
 
 15 
 
 .45047 
 
 2.21992 
 
 .47163 
 
 2.12030 
 
 .49315 
 
 2.02780 
 
 .51503 
 
 1.94162 
 
 45 
 
 16 
 
 .45082 
 
 2.21819 
 
 .47199 
 
 2.11871 
 
 .49351 
 
 2.02631 
 
 .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 
 
 .51614 
 
 1.93746 
 
 42 
 
 19 
 
 .45187 
 
 2.21304 
 
 .47305 
 
 2.11392 
 
 .48459 
 
 2.02187 
 
 .51651 
 
 1.93608 
 
 41 
 
 20 
 
 .45222 
 
 2.21132 
 
 .47341 
 
 2.11233 
 
 .49495 
 
 2.02039 
 
 51688 
 
 1.93470 
 
 40 
 
 21 
 
 .45257 
 
 2.20961 
 
 .47377 
 
 2.11075 
 
 .49532 
 
 2.01891 
 
 .51724 
 
 1.93332 
 
 39 
 
 22 
 
 .45292 
 
 2.20790 
 
 .47412 
 
 2.10916 
 
 .49568 
 
 2.01743 
 
 .51761 
 
 1.93195 
 
 38 
 
 23 
 
 .45327 
 
 2.20619 
 
 .47448 
 
 2.10758 
 
 .49604 
 
 2.01596 
 
 .51798 
 
 1.93057 
 
 37 
 
 24 
 
 .45362 
 
 2.20449 
 
 .47483 
 
 2.10BOO 
 
 .49640 
 
 2.01449 
 
 .51835 
 
 1.92920 
 
 36 
 
 25 
 
 .45397 
 
 2.20278 
 
 .47519 
 
 2.10442 
 
 .49677 
 
 2.01302 
 
 .51872 
 
 1.92782 
 
 35 
 
 26 
 
 .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 
 
 2.19769 
 
 .47626 
 
 2.099C9 
 
 .49786 
 
 2.00862 
 
 .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 
 
 2.00569 
 
 .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 
 
 .49931 
 
 2.00277 
 
 .52131 
 
 1.91826 
 
 28 
 
 33 
 
 .45678 
 
 2.18923 
 
 .47805 
 
 2.09184 
 
 .49967 
 
 2.00131 
 
 .52168 
 
 1.91690 
 
 2Z 
 
 34 
 35 
 
 .45713 
 .45748 
 
 2.18755 
 2.18587 
 
 .47840 
 
 .47876 
 
 2.09028 
 
 2.08872 
 
 .50004 
 .50040 
 
 1.99986 
 1.99841 
 
 .52205 
 
 .52242 
 
 1.91552 
 1.91414 
 
 26 
 25 
 
 36 
 
 .45784 
 
 2.18419 
 
 .47912 
 
 2.08716 
 
 .50076 
 
 1.99695 
 
 .52279 
 
 1.91288 
 
 24 
 
 37 
 
 .45819 
 
 2.18251 
 
 .47948 
 
 2.08560 
 
 .50113 
 
 1.99550 
 
 .52316 
 
 1.91142 
 
 23 
 
 38 
 
 .45854 
 
 2.18084 
 
 .47984 
 
 2.08405 
 
 .50149 
 
 1.99406 
 
 .52353 
 
 1.91017 
 
 22 
 
 39 
 
 .45889 
 
 2.17916 
 
 .48019 
 
 2.08250 
 
 .50185 
 
 1.99261 
 
 .52390 
 
 1.90876 
 
 21 
 
 40 
 
 .45924 
 
 2.17749 
 
 .48055 
 
 2.08094 
 
 .50222 
 
 1.99116 
 
 .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 
 
 .50295 
 
 1.98828 
 
 .52501 
 
 1.90472 
 
 18 
 
 43 
 
 .46030 
 
 2.17249 
 
 .48163 
 
 2.07630 
 
 .50331 
 
 1.98684 
 
 .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 
 
 1.98396 
 
 .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 
 
 1.97966 
 
 .52724 
 
 1.89667 
 
 12 
 
 49 
 
 .46242 
 
 2.16255 
 
 .48378 
 
 2.06706 
 
 .50550 
 
 1.97823 
 
 .52761 
 
 1.89533 
 
 11 
 
 50 
 
 .46277 
 
 2.16090 
 
 .48414 
 
 2.06553 
 
 .50587 
 
 1.97681 
 
 .52798 
 
 1.89400 
 
 10 
 
 51 
 
 .46312 
 
 2.15925 
 
 .48450 
 
 2.06400 
 
 .50623 
 
 1.97538 
 
 .52836 
 
 1.89266 
 
 9 
 
 52 
 
 .46348 
 
 2.15760 
 
 .48486 
 
 2.06247 
 
 .50660 
 
 1.97395 
 
 .52873 
 
 .89133 
 
 8 
 
 53 
 
 .46383 
 
 2.15596 
 
 .48521 
 
 2.06094 
 
 .50696 
 
 1.97253 
 
 .52910 
 
 .89000 
 
 7 
 
 54 
 
 .46418 
 
 2.15432 
 
 .48557 
 
 2.05942 
 
 .50733 
 
 1.97111 
 
 .52947 
 
 .88867 
 
 6 
 
 55 
 
 .46454 
 
 2.15268 
 
 .48593 
 
 2.05790 
 
 .50769 
 
 1.96969 
 
 .52985 
 
 .88734 
 
 5 
 
 56 
 
 .46489 
 
 2.15104 
 
 .48629 
 
 2.05637 
 
 .50806 
 
 1.96827 
 
 .53022 
 
 .88602 
 
 4 
 
 57 
 
 .46525 
 
 2.14940 
 
 .48665 
 
 2.05485 
 
 .50843 
 
 1.96685 
 
 .53059 
 
 1.88469 
 
 3 
 
 58 
 
 .46560 
 
 2.14777 
 
 .48701 
 
 2.05333 
 
 .50879 
 
 1.96544 
 
 .53096 
 
 1.88337 
 
 2 
 
 59 
 
 .46595 
 
 2.14614 
 
 .48737 
 
 2.05182 
 
 .50916 
 
 1.96402 
 
 .53134 
 
 1.88205 
 
 1 
 
 60 
 
 .46631 
 
 2.14451 
 
 .48773 
 
 2.05030 
 
 .50953 
 
 1.96261 
 
 .53171 
 
 1.88073 
 
 
 
 ~~7 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 t 
 
 
 ( 
 
 J5 
 
 e 
 
 >4 
 
 6 
 
 3 
 
 < 
 
 2 
 
 
NATURAL TANGENTS AND COTANGENTS. 119 
 
 t 
 
 28 
 
 29 
 
 30 
 
 31 
 
 ' 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 
 
 .53171 
 
 1.88073 
 
 .55431 
 
 1.80405 
 
 .57735 
 
 1.73205 
 
 .60086 
 
 1.66428 
 
 60 
 
 1 
 
 .53208 
 
 1.87941 
 
 .55469 
 
 1.80281 
 
 .57774 
 
 1.73089 
 
 .60126 
 
 1.66318 
 
 59 
 
 2 
 
 .53246 
 
 1.87809 
 
 .55507 
 
 1.80158 
 
 .57813 
 
 1.72973 
 
 .60165 
 
 1.66209 
 
 58 
 
 3 
 
 .53283 
 
 1.87677 
 
 .55545 
 
 1.80031 
 
 .57851 
 
 1 .72857 
 
 .60205 
 
 1.66099 
 
 57 
 
 4 
 
 .53320 
 
 1.87546 
 
 .55583 
 
 1.79911 
 
 .57890 
 
 1.72741 
 
 .60245 
 
 1.05990 
 
 56 
 
 5 
 
 .53358 
 
 1.87415 
 
 .55621 
 
 1.79788 
 
 .57929 
 
 1.72625 
 
 .60284 
 
 1.65881 
 
 55 
 
 6 
 
 .53395 
 
 1.87283 
 
 .55659 
 
 1 .79665 
 
 .57968 
 
 1.72509 
 
 .60324 
 
 1.65772 
 
 54 
 
 7 
 
 53432 
 
 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 
 
 1.86409 
 
 .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 
 
 .60642 
 
 1.64903 
 
 46 
 
 15 
 
 .53732 
 
 1.86109 
 
 .56003 
 
 1.78563 
 
 .58318 
 
 1.71473 
 
 .60681 
 
 1.64795 
 
 45 
 
 16 
 
 .53769 
 
 1.85979 
 
 .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 
 
 1.85720 
 
 .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 
 
 .60921 
 
 1.64148 
 
 39 
 
 22 
 
 .53995 
 
 1.85204 
 
 .56270 
 
 1.77713 
 
 .58591 
 
 1.70673 
 
 .60960 
 
 1.64041 
 
 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 
 
 .61080 
 
 1.63719 
 
 35 
 
 26 
 
 .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 
 
 .61230 
 
 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 
 
 .61360 
 
 1.62972 
 
 28 
 
 33 
 
 .54409 
 
 1.83794 
 
 .56693 
 
 1.76390 
 
 .59022 
 
 1 .69428 
 
 .61400 
 
 1.62866 
 
 27 
 
 34 
 
 .54446 
 
 1.83667 
 
 .56731 
 
 1.76271 
 
 .59061 
 
 1.69316 
 
 .61440 
 
 1.62760 
 
 26- 
 
 35 
 
 .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 
 
 1.6S754 
 
 .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 
 
 1.68531 
 
 .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 
 
 1.82276 
 
 .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 
 
 .59573 
 
 1.67863 
 
 .61962 
 
 1.61388 
 
 13 
 
 48 
 
 .54975 
 
 1.81899 
 
 .57271 
 
 1.74610 
 
 .59612 
 
 1.67752 
 
 .62003 
 
 1.61283 
 
 12 
 
 49 
 
 .55013 
 
 1.81774" 
 
 .57309 
 
 1.74492 
 
 .59651 
 
 1.67641 
 
 .62043 
 
 1.61179 
 
 11 
 
 50 
 
 .55051 
 
 1.81649 
 
 .57348 
 
 1.74375 
 
 .59691 
 
 1.67530 
 
 .62083 
 
 1.61074 
 
 10 
 
 51 
 
 .55089 
 
 1.81524 
 
 .57386 
 
 1.74257 
 
 .59730 
 
 1.67419 
 
 .62124 
 
 1.60970 
 
 9 
 
 52 
 
 .55127 
 
 1.81399 
 
 .57425 
 
 1.74140 
 
 .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 
 
 .600*46 
 
 1.66338 
 
 .62446 
 
 1.60137 
 
 r 
 
 60 
 
 .55431 
 
 1.S0405 
 
 .57735 
 
 1.73205 
 
 .60086 
 
 1.66428 
 
 .62187 
 
 1.60033 
 
 
 
 , 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tanar 
 
 / 
 
 
 61 
 
 60 
 
 59 
 
 58 
 
 
120 NATURAL TANGENTS AND COTANGENTS. 
 
 
 
 13 
 
 S 
 
 13 
 
 1 
 
 4 
 
 3 
 
 f> 
 
 
 
 Tang 
 
 (Jotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 ' 
 
 
 
 .62487 
 
 1.60033 
 
 .64941 
 
 1.53986 
 
 .67451 
 
 1.48256 
 
 .70021 
 
 .42815 
 
 00 
 
 1 
 
 .62527 
 
 1.59930 
 
 .64982 
 
 1.53888 
 
 .67493 
 
 1.48163 
 
 .70064 
 
 .42726 
 
 59 
 
 2 
 
 .62568 
 
 1.59826 
 
 .65024 
 
 1.53791 
 
 .67536 
 
 1.48070 
 
 .70170 
 
 .42638 
 
 5X 
 
 3 
 
 .62608 
 
 1.59723 
 
 .65065 
 
 .53693 
 
 .67578 
 
 1.47977 
 
 .70151 
 
 .42550 
 
 57 
 
 4 
 
 .021 i4 9 
 
 1.59620 
 
 .65106 
 
 .53595 
 
 .67620 
 
 1.47885 
 
 .70194 
 
 .42462 
 
 50 
 
 5 
 
 .62689 
 
 1.59517 
 
 .65148 
 
 .53497 
 
 .67663 
 
 1.47792 
 
 .70238 
 
 .42374 
 
 55 
 
 6 
 
 .62730 
 
 1.59414 
 
 .65189 
 
 .53400 
 
 .67705 
 
 1.47699 
 
 .70281 
 
 .42280 
 
 54 
 
 7 
 
 .62770 
 
 1.59311 
 
 .65231 
 
 .53302 
 
 .67748 
 
 1.47607 
 
 .70325 
 
 .42198 
 
 53 
 
 8 
 
 .62811 
 
 1.59208 
 
 .65272 
 
 .53205 
 
 .67790 
 
 1.47514 
 
 .70368 
 
 .42110 
 
 52 
 
 9 
 
 .62852 
 
 1.59105 
 
 .65314 
 
 .53107 
 
 .67832 
 
 1.47422 
 
 .70112 
 
 .42022 
 
 51 
 
 10 
 
 .62892 
 
 1.59002 
 
 .65355 
 
 .53010 
 
 .67875 
 
 1.47330 
 
 .70455 
 
 .41934 
 
 50 
 
 11 
 
 .62933 
 
 1.58900 
 
 .65397 
 
 .52913 
 
 .67917 
 
 1.47238 
 
 .70499 
 
 .41847 
 
 19 
 
 12 
 
 .62973 
 
 1.58797 
 
 .65438 
 
 .52816 
 
 .67960 
 
 1.47146 
 
 .70542 
 
 .41759 
 
 18 
 
 13 
 
 .63014 
 
 1.58695 
 
 .65480 
 
 .52719 
 
 .68002 
 
 1.47053 
 
 .70586 
 
 .41672 
 
 47 
 
 14 
 
 .63055 
 
 1.58593 
 
 .65521 
 
 .52622 
 
 .68015 
 
 1.4696? 
 
 .70029 
 
 .41584 
 
 46 
 
 15 
 
 .63095 
 
 1.58490 
 
 .65563 
 
 .52525 
 
 .68088 
 
 1.46870 
 
 .70073 
 
 .41497 
 
 15 
 
 16 
 
 .63136 
 
 1.58388 
 
 .65604 
 
 .52429 
 
 .68130 
 
 1.46778 
 
 .70717 
 
 .41409 
 
 44 
 
 17 
 
 .63177 
 
 1.58286 
 
 .65646 
 
 .52332 
 
 .68173 
 
 1.46686 
 
 .70760 
 
 .41322 
 
 43 
 
 18 
 
 .63217 
 
 1.58184 
 
 .65688 
 
 .52235 
 
 .68215 
 
 1.46595 
 
 .70804 
 
 1.41235 
 
 42 
 
 10 
 
 .63258 
 
 1.58083 
 
 .65729 
 
 .52139 
 
 .68258 
 
 1.46503 
 
 .70848 
 
 1.41148 
 
 41 
 
 20 
 
 .63299 
 
 1.57981 
 
 .65771 
 
 .52043 
 
 .68301 
 
 1.46411 
 
 .70891 
 
 1.41001 
 
 40 
 
 21 
 
 .63340 
 
 1.57879 
 
 .65813 
 
 .51946 
 
 .68343 
 
 1.46320 
 
 .70935 
 
 1.40974 
 
 39 
 
 22 
 
 .63380 
 
 1.57778 
 
 .65854 
 
 .51850 
 
 .68386 
 
 1.46229 
 
 .70979 
 
 1.40887 
 
 38 
 
 23 
 
 .63421 
 
 1.57676 
 
 .65896 
 
 .51751 
 
 .68429 
 
 1.46137 
 
 .71023 
 
 1.40800 
 
 37 
 
 24 
 
 .63462 
 
 1.57575 
 
 .65938 
 
 .51658 
 
 .68471 
 
 1.46046 
 
 .71066 
 
 1.40711 
 
 30 
 
 25 
 
 .63,503 
 
 1.57474 
 
 .65980 
 
 .51562 
 
 .68514 
 
 1.45955 
 
 .71110 
 
 1.40027 
 
 35 
 
 26 
 
 .63544 
 
 1.57372 
 
 .66021 
 
 .51466 
 
 .(>S. r )57 
 
 1.45864 
 
 .71154 
 
 .40540 
 
 34 
 
 27 
 
 .63584 
 
 1.57271 
 
 .66063 
 
 .51370 
 
 .68600 
 
 1.45773 
 
 .71198 
 
 .40454 
 
 33 
 
 28 
 
 .63625 
 
 1.57170 
 
 .66105 
 
 .51275 
 
 .68642 
 
 1.45682 
 
 .71242 
 
 .40367 
 
 32 
 
 29 
 
 :63666 
 
 1.57069 
 
 .66147 
 
 .51179 
 
 .68685 
 
 1.45592 
 
 .71285 
 
 .40281 
 
 31 
 
 30 
 
 .63707 
 
 1.56969 
 
 .66189 
 
 .51084 
 
 .68728 
 
 1.15501 
 
 .71329 
 
 .40195 
 
 30 
 
 31 
 
 .63748 
 
 1.56868 
 
 .60230 
 
 .50988 
 
 .68771 
 
 1.45410 
 
 .71373 
 
 .40109 
 
 29 
 
 32 
 
 .63789 
 
 1.56767 
 
 .66272 
 
 .50893 
 
 .68814 
 
 1.45320 
 
 .71417 
 
 .40022 
 
 28 
 
 33 
 
 .63830 
 
 1.56667 
 
 .63314 
 
 .50797 
 
 .68857 
 
 1 .45229 
 
 .71461 
 
 .39930 
 
 27 
 
 3i 
 
 .03871 
 
 1 .565% 
 
 .66356 
 
 .50702 
 
 .68900 
 
 1.45139 
 
 .71505 
 
 .30850 
 
 20 
 
 35 
 
 .63912 
 
 1.56466 
 
 .66398 
 
 .50607 
 
 .68942 
 
 1.45049 
 
 .71549 
 
 .39704 
 
 25 
 
 36 
 
 .63953 
 
 1.563*6 
 
 .66440 
 
 .50512 
 
 .68985 
 
 1.44958 
 
 .71593 
 
 .39079 
 
 24 
 
 37 
 
 .63994 
 
 1.56265 
 
 .66482 
 
 .50417 
 
 .69028 
 
 1 .44868 
 
 .71637 
 
 .39593 
 
 23 
 
 38 
 
 .64035 
 
 1.56165 
 
 .66524 
 
 .50322 
 
 .69071 
 
 1 .44778 
 
 .71681 
 
 .30507 
 
 99 
 
 39 
 
 .64076 
 
 1 .56065 
 
 .66566 
 
 .50228 
 
 .69114 
 
 1.44688 
 
 .71725 
 
 .39421 
 
 21 
 
 40 
 
 .64117 
 
 1.55966 
 
 .66608 
 
 .50133 
 
 .69157 
 
 1.44598 
 
 .71709 
 
 .39330 
 
 20 
 
 41 
 
 .64158 
 
 1.55866 
 
 .66650 
 
 .50038 
 
 .69200 
 
 1.44508 
 
 .71813 
 
 .39250 
 
 19 
 
 42 
 
 .64199 
 
 1.55766 
 
 .66692 
 
 .49944 
 
 .69243 
 
 1.44418 
 
 .71857 
 
 .39105 
 
 18 
 
 43 
 
 .64240 
 
 1.55666 
 
 .66734 
 
 .49849 
 
 .69286 
 
 1.44329 
 
 .71901 
 
 .39079 
 
 17 
 
 44 
 
 .64281 
 
 1.55567 
 
 .66776 
 
 .49755 
 
 .69329 
 
 1.44239 
 
 .71946 
 
 .38994 
 
 10 
 
 45 
 
 .64322 
 
 1.55467 
 
 .66818 
 
 .49661 
 
 .69372 
 
 1.44149 
 
 .71990 
 
 .38909 
 
 15 
 
 40 
 
 .64363 
 
 1.55368 
 
 .66860 
 
 .49566 
 
 .69416 
 
 1.44060 
 
 .7203 1 
 
 .38824 
 
 14 
 
 47 
 
 .64404 
 
 1.55269 
 
 .66902 
 
 .49472 
 
 .69459 
 
 1.43970 
 
 .72078 
 
 .38738 
 
 13 
 
 48 
 
 .64446 
 
 1.55170 
 
 .66944 
 
 .49378 
 
 .69502 
 
 1.43881 
 
 .72122 
 
 .38653 
 
 12 
 
 49 
 
 .64487 
 
 1.55071 
 
 .66986 
 
 .49284 
 
 .69545 
 
 1.43792 
 
 .72167 
 
 .38568 
 
 11 
 
 50 
 
 .64528 
 
 1.54972 
 
 .67028 
 
 .49190 
 
 .69588 
 
 1.43703 
 
 .72211 
 
 .38484 
 
 10 
 
 51 
 
 .64569 
 
 1.54873 
 
 .67071 
 
 .49097 
 
 .69631 
 
 1.43614 
 
 .72255 
 
 .38399 
 
 9 
 
 V2 
 
 .64610 
 
 1.51774 
 
 .67113 
 
 .49003 
 
 .69675 
 
 1.43525 
 
 .72299 
 
 .38314 
 
 8 
 
 53 
 
 .64652 
 
 1.54675 
 
 .67155 
 
 .48909 
 
 .69718 
 
 1.43436 
 
 .72344 
 
 .38229 
 
 7 
 
 54 
 
 .64693 
 
 1.54576 
 
 .67197 
 
 .48816 
 
 .69761 
 
 1.43347 
 
 72388 
 
 .38145 
 
 6 
 
 55 
 
 .64734 
 
 1.54478 
 
 .67239 
 
 .48722 
 
 .69804 
 
 1.43258 
 
 .72432 
 
 .38000 
 
 5 
 
 56 
 
 .64775 
 
 1.54379 
 
 .67282 
 
 .48629 
 
 .69847 
 
 1.43169 
 
 .72477 
 
 .37976 
 
 4 
 
 57 
 
 .64817 
 
 1.54281 
 
 .67324 
 
 .48536 
 
 .69891 
 
 1.43080 
 
 .72521 
 
 .37891 
 
 3 
 
 4 s 
 
 .64858 
 
 1.54183 
 
 .67366 
 
 1.48442 
 
 .69934 
 
 1.42992 
 
 .72565 
 
 .37807 
 
 2 
 
 & 
 
 .64899 
 
 1.54085 
 
 .67409 
 
 1.48349 
 
 .69977 
 
 1.42903 
 
 .72610 
 
 .37722 
 
 1 
 
 GO 
 
 .64941 
 
 1 .53986 
 
 .67451 
 
 1.48256 
 
 .70021 
 
 1.42815 
 
 .72651 
 
 .37038 
 
 
 
 , 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 ( 'ot;m<r 
 
 Tang 
 
 Cotang 
 
 Tang. 
 
 , 
 
 
 
 7 
 
 f 
 
 6 
 
 a 
 
 5 
 
 5 
 
 4 
 
 
NATURAL TAXGKXTS AXD COTAXGENTS. 121 
 
 
 36 
 
 37 
 
 38 
 
 311 
 
 
 
 Tang 
 
 Co tang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 ' 
 
 
 
 .72054 
 
 .37638 
 
 .75355 
 
 1.32704 
 
 .78120 
 
 1.27994 
 
 .80978 
 
 .23490 
 
 60 
 
 1 
 
 .72099 
 
 .37554 
 
 .75401 
 
 1.32024 
 
 .78175 
 
 1.27917 
 
 .81027 
 
 .23416 
 
 59 
 
 2 
 
 .72743 
 
 .37470 
 
 .75447 
 
 1 .32544 
 
 .78222 
 
 1.27841 
 
 .81075 
 
 .23343 
 
 58 
 
 3 
 
 .72788 
 
 .37386 
 
 .75492 
 
 1.32404 
 
 .78209 
 
 .27764 
 
 .81123 
 
 .23270 
 
 57 
 
 4 
 
 .72832 
 
 .37302 
 
 .75538 
 
 1.32384 
 
 .78316 
 
 .27688 
 
 .81171 
 
 .23196 
 
 56 
 
 5 
 
 .72877 
 
 .37218 
 
 .75584 
 
 1.32304 
 
 .78363 
 
 .27611 
 
 .81220 
 
 .23123 
 
 55 
 
 f\ 
 
 .72921 
 
 .37134 
 
 .7529 
 
 1.32224 
 
 .78410 
 
 .27535 
 
 .81268 
 
 .23050 
 
 54 
 
 7 
 
 .72900 
 
 .37050 
 
 .75075 
 
 1.32144 
 
 .78457 
 
 .27458 
 
 .8L316 
 
 .22977 
 
 53 
 
 8 
 
 .73010 
 
 .36967 
 
 .75721 
 
 1.32004 
 
 .78504 
 
 .27382 
 
 .81364 
 
 .22904 
 
 52 
 
 9 
 
 .73055 
 
 .30883 
 
 .75707 
 
 1.31984 
 
 .78551 
 
 .27306 
 
 .81413 
 
 .22831 
 
 51 
 
 10 
 
 .73100 
 
 .30800 
 
 .75812 
 
 1.31904 
 
 .78598 
 
 .27230 
 
 .81461 
 
 .22758 
 
 50 
 
 11 
 
 .73144 
 
 .36716' 
 
 .75858 
 
 1.31825 
 
 .78645 
 
 .27153 
 
 .81510 
 
 .22685 
 
 49 
 
 12 
 
 .73189 
 
 .36633 
 
 .75904 
 
 1.31745 
 
 .78692 
 
 .27077 
 
 .81558 
 
 .22612 
 
 48 
 
 13 
 
 .73234 
 
 .36549 
 
 .75950 
 
 1.31666 
 
 .78739 
 
 .27001 
 
 .81606 
 
 .22539 
 
 47 
 
 14 
 
 .73278 
 
 .36460 
 
 .75996 
 
 1.31586 
 
 .78786 
 
 .26925 
 
 .81655 
 
 .22167 
 
 46 
 
 15 
 
 .73323 
 
 .30383 
 
 .76042 
 
 1.31507 
 
 .78834 
 
 1.26849 
 
 .81703 
 
 .22394 
 
 45 
 
 16 
 
 .73308 
 
 .36300 
 
 .76088 
 
 1.31427 
 
 .78881 
 
 .26774 
 
 .81752 
 
 .22321 
 
 44 
 
 17 
 
 .73413 
 
 .30217 
 
 .76134 
 
 1.31348 
 
 .78928 
 
 .26698 
 
 .81800 
 
 .22249 
 
 43 
 
 18 
 
 .73457 
 
 .36134 
 
 .76180 
 
 1.31269 
 
 .78975 
 
 1.26622 
 
 .81849 
 
 .22176 
 
 42 
 
 19 
 
 .73502 
 
 .36051 
 
 .76226 
 
 1.31190 
 
 .79022 
 
 .26546 
 
 .81898 
 
 .22104 
 
 41 
 
 20 
 
 .73547 
 
 .35968 
 
 .76272 
 
 1.31110 
 
 .79070 
 
 .26471 
 
 .81946 
 
 .22031 
 
 40 
 
 21 
 
 .73592 
 
 .35885 
 
 .76318 
 
 1.31031 
 
 .79117 
 
 1.26395 
 
 .81995 
 
 .21959 
 
 39 
 
 22 
 
 .73637 
 
 .35802 
 
 .76304 
 
 .30952 
 
 .79164 
 
 .26319 
 
 .82044 
 
 .21886 
 
 38 
 
 23 
 
 .73681 
 
 .35719 
 
 .76410 
 
 .30873 
 
 .79212 
 
 .26244 
 
 .82092 
 
 .21814 
 
 37 
 
 24 
 
 .73726 
 
 .35637 
 
 .76456 
 
 .30795 
 
 .79259 
 
 .26169 
 
 .82141 
 
 .21742 
 
 36 
 
 25 
 
 .73771 
 
 .35554 
 
 .76502 
 
 .30716 
 
 .79306 
 
 .26093 
 
 .82190 
 
 .21670 
 
 35" 
 
 20 
 
 .73816 
 
 .35472 
 
 .76548 
 
 .30637 
 
 .79354 
 
 .26018 
 
 .82238 
 
 .21598 
 
 34 
 
 27 
 
 .73861 
 
 .35389 
 
 .76594 
 
 .30558 
 
 .79401 
 
 .25943 
 
 .82287 
 
 .21526 
 
 33 
 
 28 
 
 .73906 
 
 .35307 
 
 .76640 
 
 .30480 
 
 .79449 
 
 .25867 
 
 .82336 
 
 .21454 
 
 32 
 
 29 
 
 .73951 
 
 .35224 
 
 .76686 
 
 .30401 
 
 .79496 
 
 .25792 
 
 .82385 
 
 .21382 
 
 31 
 
 30 
 
 .73996 
 
 .35142 
 
 .76733 
 
 .30323 
 
 .79544 
 
 .25717 
 
 .82434 
 
 .21310 
 
 30 
 
 31 
 
 .74041 
 
 .35060 
 
 .76779 
 
 .30244 
 
 .79591 
 
 1.25042- 
 
 .82483 
 
 .21238 
 
 29 
 
 32 
 
 .74086 
 
 .34978 
 
 .76825 
 
 .30166 
 
 .79639 
 
 .25567 
 
 .82531 
 
 .21166 
 
 28 
 
 33 
 
 .74131 
 
 .34896 
 
 .76871 
 
 .30087 
 
 .79686 
 
 .25492 
 
 .82580 
 
 .21094 
 
 27 
 
 34 
 
 .74176 
 
 .34814 
 
 .76918 
 
 .30009 
 
 .79734 
 
 .25417 
 
 .82629 
 
 .21023 
 
 26 
 
 35 
 
 .7422] 
 
 .34732 
 
 .76964 
 
 .29931 
 
 .79781 
 
 .25343 
 
 .82678 
 
 .20951 
 
 25 
 
 36 
 
 .74267 
 
 .34050 
 
 .77010 
 
 .29853 
 
 .79829 
 
 .25268 
 
 .82727 
 
 .20879 
 
 24 
 
 37 
 
 .74312 
 
 .34508 
 
 .77057 
 
 .29775 
 
 .79877 
 
 .25193 
 
 .82776 
 
 .20808 
 
 23 
 
 38 
 
 .74357 
 
 .34187 
 
 .77103 
 
 .29696 
 
 .79924 
 
 .25118 
 
 .82825 
 
 .20736 
 
 22 
 
 39 
 
 .74402 
 
 .34105 
 
 .77149 
 
 .29618 
 
 .79972 
 
 .25044 
 
 .82874 
 
 .20665 
 
 21 
 
 40 
 
 .74447 
 
 .34323 
 
 .77196 
 
 .29541 
 
 .80020 
 
 .24969 
 
 .82923 
 
 .20593 
 
 20 
 
 41 
 
 .74492 
 
 .34242 
 
 .77242 
 
 1.29463 
 
 .80067 
 
 .24895 
 
 .82972 
 
 .20522 
 
 19 
 
 42 
 
 .74538 
 
 .34160 
 
 .77289 
 
 1.29385 
 
 .80115 
 
 .24820 
 
 .83022 
 
 .20451 
 
 18 
 
 43 
 
 .74583 
 
 .34079 
 
 .77335 
 
 1.29307 
 
 .80163 
 
 .24746 
 
 .83071 
 
 .20379 
 
 17 
 
 44 
 
 .74628 
 
 .33998 
 
 .77382 
 
 1.29229 
 
 :80211 
 
 .24672 
 
 .83120 
 
 .20308 
 
 16 
 
 45 
 
 .74674 
 
 .33916 
 
 .77428 
 
 1.29152 
 
 .80258 
 
 .24597 
 
 .83169 
 
 .20237 
 
 15 
 
 46 
 
 .74719 
 
 .33S35J 
 
 .77475 
 
 1.29074 
 
 .80306 
 
 .24523 
 
 .83218 
 
 .20166 
 
 14 
 
 47 
 
 .74764 
 
 .33754 
 
 .77521 
 
 1.28997 
 
 .80354 
 
 .24449 
 
 .83268 
 
 .20095 
 
 13 
 
 48 
 
 .74810 
 
 .33673 
 
 .77568 
 
 1.28919 
 
 .80402 
 
 .24375 
 
 .83317 
 
 .20024 
 
 12 
 
 49 
 
 .74855 
 
 .33592 
 
 .77615 
 
 1.28*42 
 
 .80450 
 
 .24301 
 
 .83366 
 
 .19953 
 
 11 
 
 50 
 
 .74900 
 
 .33511 
 
 .77061 
 
 1.28764 
 
 .80498 
 
 .24227 
 
 .83415 
 
 .19882 
 
 10 
 
 51 
 
 .74946 
 
 .33430 
 
 .7770S 
 
 1.28687 
 
 .80546 
 
 .2415?, 
 
 .83465 
 
 .19811 
 
 9 
 
 52 
 53 
 
 .74991 
 .75037 
 
 .33349 
 .33208, 
 
 .7775J* 
 ' .77801 
 
 1.28610 
 1.28533 
 
 .80594 
 .80642 
 
 .24079 
 .24005 
 
 .83514 
 .83564 
 
 .19740 
 .1966JL 
 
 8 
 
 1 
 
 54 
 
 .75082 
 
 .33187 
 
 .77848 
 
 1.28456 
 
 .80690 
 
 .23931 
 
 .83613 
 
 .19599 
 
 6 
 
 55 
 
 .75128 
 
 .33107 
 
 .77895 
 
 1.28379 
 
 .80738 
 
 .23858 
 
 .83662 
 
 .19528 
 
 5 
 
 56 
 
 .75173 
 
 .33026 
 
 .77941 
 
 1.28302 
 
 .80786 
 
 .23784 
 
 .83712 
 
 .19457 
 
 4 
 
 57 
 
 .75219 
 
 .32946 
 
 .77988 
 
 1 .28225 
 
 .80834 
 
 .23710 
 
 .83761 
 
 .19387 
 
 3 
 
 58 
 
 .75204 
 
 1.32805 
 
 .7803^ 
 
 1.28148 
 
 .80882 
 
 .23637 
 
 .83811 
 
 .19316 
 
 2 
 
 59 
 
 .75310 
 
 1.32785 
 
 .7808? 
 
 1.28071 
 
 .80930 
 
 .23563 
 
 .83860 
 
 .19246 
 
 1 
 
 60 
 
 .75355 
 
 1.32704 
 
 .78129 
 
 1.27994 
 
 .80978 
 
 1.23490 
 
 .83910 
 
 .19175 
 
 
 
 , 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 , 
 
 
 53 
 
 53 
 
 51 
 
 50 
 
 
122 NATURAL TANGENTS AND COTANGENTS. 
 
 
 40 
 
 41 
 
 42 
 
 43 
 
 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 
 
 
 .83910 
 
 1.19175 
 
 .86929 
 
 1.15037 
 
 .90040 
 
 1.110G1 
 
 .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 
 
 1.14834 
 
 .90199 
 
 1.10867 
 
 .93415 
 
 1.07049 
 
 57 
 
 4 
 
 .84108 
 
 1.18894 
 
 .S7133 
 
 1.14767 
 
 .90251 
 
 1.10802 
 
 .93469 
 
 1.06987 
 
 56 
 
 5 
 
 .84158 
 
 1.18S24 
 
 .87184 
 
 1.14699 
 
 .90301 
 
 1.10737 
 
 .93524 
 
 1.06925 
 
 55 
 
 
 
 .84208 
 
 1.18754 
 
 .87236 
 
 1.14632 
 
 .90357 
 
 1.10672 
 
 .93578 
 
 1.06862 
 
 54 
 
 7 
 
 .84258 
 
 1.18684 
 
 .87287 
 
 1.14565 
 
 .90410 
 
 1.10607 
 
 .93633 
 
 1.06800 
 
 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 
 
 .90674 
 
 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 
 
 1 .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 
 
 1.06056 
 
 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 
 
 1.17569 
 
 .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 
 
 26 
 
 .85207 
 
 1.17361 
 
 .88265 
 
 1.13295 
 
 .91419 
 
 1.09386 
 
 .94676 
 
 1.05G24 
 
 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 
 
 1.12831 
 
 .91794 
 
 1.08940 
 
 .95062 
 
 1.05194 
 
 27 
 
 34 
 
 .85609 
 
 1.16809 
 
 .88680 
 
 1.12765 
 
 .91847 
 
 1.08876 
 
 .95118 
 
 1.05133 
 
 26 
 
 35 
 
 .85660 
 
 1.16741 
 
 .88732 
 
 1.12699 
 
 .91901 
 
 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 
 
 1.08686 
 
 .95284 
 
 1.04949 
 
 23 
 
 38 
 
 .85811 
 
 1.16535 
 
 .88888 
 
 1.12501 
 
 .92062 
 
 1.08622 
 
 .95340 
 
 1.04888 
 
 22 
 
 39 
 
 .85862 
 
 1.16466 
 
 .88940 
 
 1.12435 
 
 .92116 
 
 1.08559 
 
 .95395 
 
 1.04827 
 
 21 
 
 40 
 
 .85912 
 
 1.16398 
 
 .88992 
 
 1.12369 
 
 .92170 
 
 1.08496 
 
 .95451 
 
 1.04766 
 
 20 
 
 41 
 
 .85963 
 
 1.16329 
 
 .89045 
 
 1.12303 
 
 .92224 
 
 1.08432 
 
 .95506 
 
 1.04705 
 
 19 
 
 42 
 
 .86014 
 
 1.16261 
 
 .89097 
 
 1.12228 
 
 .92277 
 
 1.08369 
 
 .95562 
 
 1.04644 
 
 18 
 
 43 
 
 .86064 
 
 1.16192 
 
 .89149 
 
 1.12172 
 
 .92331 
 
 1.08306 
 
 .95618 
 
 1.04583 
 
 17 
 
 44 
 
 .86115 
 
 1.16124 
 
 .89201 
 
 1.12106 
 
 .92385 
 
 1.08243 
 
 .95673 
 
 1.04522 
 
 16 
 
 45 
 
 .86166 
 
 1.16056 
 
 .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 
 
 1.15647 
 
 .89567 
 
 1.11648 
 
 .92763 
 
 1.07801 
 
 .96064 
 
 1.04097 
 
 9 
 
 52 
 
 .86521 
 
 1.15579 
 
 .89620 
 
 1.11582 
 
 .92817 
 
 1,07738 
 
 .96120 
 
 1.04036 
 
 8 
 
 53 
 
 .86572 
 
 1.15511 
 
 .89672 
 
 1.11517 
 
 .92872 
 
 1.07676 
 
 .96176 
 
 1.03976 
 
 7 
 
 54 
 
 .86623 
 
 1.15443 
 
 .89725 
 
 1.11452 
 
 .92926 
 
 1.07613 
 
 .96232 
 
 1.03915 
 
 6 
 
 55 
 
 .86674 
 
 1.15375 
 
 .89777 
 
 1.11387 
 
 .92980 
 
 1.07550 
 
 .96288 
 
 1.03855 
 
 5 
 
 56 
 
 .86725 
 
 1.15308 
 
 .89830 
 
 1.11321 
 
 .93034 
 
 1.07487 
 
 .96344 
 
 1.03794 
 
 4 
 
 57 
 
 .86776 
 
 1.15240 
 
 .89883 
 
 1.11256 
 
 .93088 
 
 1.07425 
 
 .96400 
 
 1.03734 
 
 3 
 
 58 
 
 .86827 
 
 1.15172 
 
 .89935 
 
 1.11191 
 
 .93143 
 
 1.07362 
 
 .96457 
 
 1.03674 
 
 2 
 
 59 
 
 .86878 
 
 1.15104 
 
 .89988 
 
 1.11126 
 
 .93197 
 
 1.07299 
 
 .96513 
 
 1.03613 
 
 1 
 
 60 
 
 .86929 
 
 1.15037 
 
 .90040 
 
 1.11061 
 
 .93252 
 
 1.07237 
 
 .96569 
 
 1.03553 
 
 
 
 / 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 e 
 
 
 49 
 
 48 
 
 47 
 
 46 
 
 
NATURAL TANGENTS AND COTANGENTS. 123 
 
 , 
 
 4 
 
 14 
 
 , 
 
 , 
 
 4 
 
 4 
 
 ; 
 
 , 
 
 4 
 
 4 
 
 , 
 
 
 Tang 
 
 Cotang 
 
 
 
 Tang 
 
 Cotang 
 
 
 
 Tang 
 
 Cotang 
 
 
 
 
 .96509 
 
 1.03553 
 
 60 
 
 20 
 
 .97700 
 
 .02355 
 
 40 
 
 40 
 
 .98843 
 
 1.01170 
 
 20 
 
 1 
 
 .96625 
 
 1.03493 
 
 59 
 
 21 
 
 .97756 
 
 1.02295 
 
 39 
 
 41 
 
 .98901 
 
 1.01112 
 
 19 
 
 2 
 
 .90681 
 
 1.03433 
 
 58 
 
 22 
 
 .97813 
 
 .02236 
 
 38 
 
 42 
 
 .98958 
 
 1.01053 
 
 18 
 
 3 
 
 .96738 
 
 1.03372 
 
 57 
 
 23 
 
 .97870 
 
 .02176 
 
 37 
 
 43 
 
 .99016 
 
 1.00994 
 
 17 
 
 4 
 
 .96791 
 
 1.03312 
 
 56 
 
 24 
 
 .97927 
 
 1.02117 
 
 36 
 
 44 
 
 .99073 
 
 1.00935 
 
 16 
 
 5 
 
 .96850 
 
 1.03252 
 
 55 
 
 25 
 
 .97984 
 
 1.02057 
 
 35 
 
 45 
 
 .99131 
 
 1.00876 
 
 15 
 
 6 
 
 .96907 
 
 1.03192 
 
 54 
 
 26 
 
 .98041 
 
 1.01998 
 
 34 
 
 46 
 
 .99189 
 
 1.00818 
 
 14 
 
 7 
 
 .96963 
 
 1.03132 
 
 53 
 
 27 
 
 .98098 
 
 1.01939 
 
 33 
 
 47 
 
 .99247 
 
 1.00759 
 
 13 
 
 8 
 
 .97020 
 
 1.03072 
 
 52 
 
 28 
 
 .98155 
 
 1.01879 
 
 32 
 
 48 
 
 .99304 
 
 1.00701 
 
 12 
 
 9 
 
 .97076 
 
 1.03012 
 
 51 
 
 29 
 
 .98213 
 
 1.01820 
 
 31 
 
 49 
 
 .99362 
 
 1.00642 
 
 11 
 
 10 
 
 .97133 
 
 1.02952 
 
 50 
 
 30 
 
 .98270 
 
 1.01761 
 
 30 
 
 50 
 
 .99420 
 
 1.00583 
 
 10 
 
 11 
 
 .97189 
 
 1.02892 
 
 49 
 
 31 
 
 .98327 
 
 1.01702 
 
 29 
 
 51 
 
 .99478 
 
 1.00525 
 
 9 
 
 12 
 
 .97246 
 
 1.02832 
 
 48 
 
 32 
 
 .98384 
 
 1.01642 
 
 28 
 
 52 
 
 .99536 
 
 1.00467 
 
 8 
 
 13 
 
 .97302 
 
 1.02772 
 
 47 
 
 33 
 
 .98441 
 
 1.01583 
 
 27 
 
 53 
 
 .99594 
 
 1.00408 
 
 7 
 
 14 
 
 .97359 
 
 1.02713 
 
 46 
 
 34 
 
 .98499 
 
 1.01524 
 
 26 
 
 54 
 
 .99652 
 
 1.00350 
 
 6 
 
 15 
 
 .97416 
 
 1.0205? 
 
 45 
 
 35 
 
 .98556 
 
 1.01465 
 
 25 
 
 55 
 
 .99710 
 
 1.00291 
 
 5 
 
 16 
 
 .97472 
 
 1.02593 
 
 44 
 
 36 
 
 .98613 
 
 1.01406 
 
 24 
 
 56 
 
 .99768 
 
 1.00233 
 
 4 
 
 17 
 
 .97529 
 
 1.02533 
 
 43 
 
 37 
 
 .98671 
 
 1.01347 
 
 23 
 
 57 
 
 .99826 
 
 1.00175 
 
 3 
 
 IS 
 
 .97586 
 
 1.02474 
 
 42 
 
 38 
 
 .98728 
 
 1.01288 
 
 22 
 
 58 
 
 .99.884 
 
 1.00116 
 
 2 
 
 19 
 
 .97643 
 
 1.02414 
 
 41 
 
 39 
 
 .98786 
 
 1.01229 
 
 21 
 
 59 
 
 .99942 
 
 1 .00058 
 
 1 
 
 20 
 
 .97700 
 
 1.02355 
 
 40 
 
 40 
 
 .98843 
 
 1.01170 
 
 20 
 
 60 
 
 1.00000 
 
 1.00000 
 
 
 
 
 Cotang 
 
 Tang 
 
 
 
 Cotang 
 
 Tang 
 
 
 
 Cotang 
 
 Tang 
 
 
 
 A 
 
 t5 
 
 
 
 4 
 
 5 
 
 
 
 4 
 
 5 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
123a NATURAL SECANTS AND COSECANTS. 
 NATURAL SECANTS AND COSECANTS. 
 
 I 
 
 
 
 1 
 
 2 
 3 
 4 
 
 Secants. 
 
 
 0' 
 
 10' 
 
 20' 
 
 30' 
 
 40' 
 
 50' 
 
 60' 
 
 1 . 00000 
 1.00015 
 1.00061 
 1.00137 
 1.00244 
 
 1 . 00001 
 1.00021 
 1 . 00072 
 1.00153 
 1.00205 
 
 1 . 00002 
 1.00027 
 1.00083 
 1.00169 
 1.00287 
 
 1.00004 
 1 . 00034 
 1.00095 
 1.00187 
 1.00309 
 
 1 . 00007 
 1 . 00042 
 1.00108 
 . 1 . 00205 
 1.00333 
 
 1.00011 
 1.00051 
 1.00122 
 1 . 00224 
 1.00357 
 
 1.00015 
 1.00061 
 1.00137 
 1.00244 
 1 . 00382 
 
 89 
 88 
 87 
 86 
 85 
 
 5 
 6 
 
 7 
 8 
 9 
 
 1.00382 
 1.00551 
 1.00751 
 1.00983 
 1.01247 
 
 1.00408 
 1 . 00582 
 1.00787 
 1.01024 
 1.01294 
 
 1.00435 
 1.00614 
 1.00825 
 1.01067 
 1.01342 
 
 1 . 00463 
 1.00647 
 1.00863 
 1.01111 
 1.01391 
 
 1.00491 
 1.00681 
 1.00902 
 1.01155 
 1.01440 
 
 1.00521 
 1.00715 
 1 . 00942 
 1.01200 
 1.01491 
 
 1 . 00551 
 1.00751 
 1 . 00983 
 1.01247 
 1.01543 
 
 84 
 83 
 82 
 81 
 80 
 
 10 
 11 
 12 
 13 
 14 
 
 1.01543 
 
 1.01872 
 1.02234 
 1.02630 
 1.03061 
 
 1.01595 
 1.01930 
 1.02298 
 1.02700 
 1.03137 
 
 1.01649 
 1.01989 
 1.02362 
 1.02770 
 1.03213 
 
 1.01703 
 1 . 02049 
 1 . 02428 
 1.02842 
 1.03290 
 
 1.01758 
 1.02110 
 1 . 02494 
 1.02914 
 1.03368 
 
 1.01815 
 1.02171 
 1.02562 
 1 . 02987 
 1.03447 
 
 1.01872 
 1 . 02234 
 1.02630 
 1.03061 
 1.03528 
 
 79 
 78 
 77 
 76 
 75 
 
 15 
 16 
 17 
 18 
 19 
 
 1.03528 
 1 . 04030 
 1.04569 
 1.05146 
 1.05762 
 
 1.03609 
 1.04117 
 1.04663 
 1.05246 
 1.05869 
 
 1.03691 
 1.04206 
 1.04757 
 1.05347 
 1.05976 
 
 1.03774 
 1.04295 
 1.04853 
 1.05449 
 1.06085 
 
 1.03858 
 1 . 04385 
 1.04950 
 1.05552 
 1.06195 
 
 1.03944 
 1.04477 
 1.05047 
 1.05657 
 1.06306 
 
 1. Q4030 
 1.04569 
 1.05146 
 1.05762 
 1.06418 
 
 74 
 73 
 
 72 
 71 
 70 
 
 20 
 21 
 22 
 23 
 24 
 
 1.06418 
 1.07115 
 1.07853 
 1.08636 
 1.09464 
 
 1.06531 
 1.07235 
 1.07981 
 1.08771 
 1.09606 
 
 1.06645 
 1.07356 
 1.08109 
 1.08907 
 1.09750 
 
 1.06761 
 1.07479 
 1.08239 
 1.09044 
 1.09895 
 
 1.06878 
 1.07602 
 1.08370 
 1.09183 
 1 . 10041 
 
 1.06995 
 1.07727 
 1.08503 
 1.09323 
 1.10189 
 
 1.07115 
 1.07853 
 1.08636 
 1.09464 
 1 . 10338 
 
 69 
 68 
 67 
 66 
 65 
 
 25 
 26 
 
 27 
 28 
 29 
 
 1 . 10338 
 1.11260 
 1 . 12233 
 1 . 13257 
 1 . 14335 
 
 1 . 10488 
 1.11419 
 1 . 12400 
 1 . 13433 
 1.14521 
 
 1 . 10640 
 1.11579 
 1.12568 
 1.13610 
 1 . 14707 
 
 1 . 10793 
 1.11740 
 1 . 12738 
 1.13789 
 1 . 14896 
 
 1 . 10947 
 1.11903 
 1.12910 
 1.13970 
 1.15085 
 
 1.11103 
 1 . 12067 
 1.13083 
 1.14152 
 1.15277 
 
 1.11260 
 1 . 12233 
 1.13257 
 1.14335 
 1 . 15470 
 
 64 
 63 
 62 
 61 
 60 
 
 30 
 31 
 32 
 33 
 34 
 
 1.15470 1.15665 
 1.16663 1.16868 
 1.17918 1.18133 
 1.19236; 1.19463 
 1.20622 1.20859 
 
 1.15861 
 1 . 17075 
 1 . 18350 
 1 . 19691 
 1.21099 
 
 1 . 16059 
 1.17283 
 1 . 18569 
 1 . 19920 
 1.21341 
 
 1 . 16259 
 1 . 17493 
 1 . 18790 
 1.20152 
 1.21584 
 
 1 . 16460 
 1.17704 
 1.19012 
 1.20386 
 1.21830 
 
 1.16663 
 1.17918 
 1 . 19236 
 1.20622 
 1.22077 
 
 59 
 58 
 57 
 56 
 55 
 
 35 
 36 
 37 
 38 
 39 
 
 1.22077 
 1.23607 
 1.25214 
 1.26902 
 1.28676 
 
 1.22327 
 1 . 23869 
 1.25489 
 1.27191 
 
 1.28980 
 
 1.22579 
 1.24134 
 1.25767 
 1.27483 
 1.29287 
 
 1.22833 
 1.24400 
 1.26047 
 1.27778 
 1.29597 
 
 1.23089 
 1.24669 
 1.26330 
 1.28075 
 1.29909 
 
 1.23347 
 1.24940 
 1.26615 
 1.28374 
 1.30223 
 
 1.23607 
 1.25214 
 1.26902 
 1.28676 
 1 . 30541 
 
 54 
 53 
 52 
 51 
 50 
 
 40 
 41 
 42 
 43 
 44 
 
 1 . 30541 
 1 . 32501 
 1 . 34563 
 1 . 36733 
 1.39016 
 
 1.30861 
 1 . 32838 
 1.34917 
 1.37105 
 1 . 39409 
 
 1.31183 
 1.33177 
 1.35274 
 1.37481 
 1 . 39804 
 
 1.31509 
 1.33519 
 1 . 35634 
 1 . 37860 
 1.40203 
 
 1.31837 
 1 . 33864 
 1 . 35997 
 1 . 38242 
 1.40606 
 
 1.32168 
 1.34212 
 1.36363 
 1 . 38628 
 1.41012 
 
 1.32501 
 1 . 34563 
 1 . 36733 
 1 . 39016 
 1.41421 
 
 49 
 48 
 47 
 46 
 45 
 
 $ 
 
 
 bt> 
 
 9 
 
 q 
 
 60' 
 
 50' 
 
 40' 
 
 30' 
 
 20' 
 
 10' 
 
 0' 
 
 Cosecants. 
 
IN A 1 U rUUU OEM AM 1 AiN JJ UUS&U A JN To . 
 
 NATURAL SECANTS AND COSECANTS~(Con*wwed). 
 
 1 
 
 
 
 1 
 
 2 
 3 
 
 4 
 
 Cosecants. 
 
 9 
 8 
 7 
 6 
 5 
 
 0' 
 
 10' 
 
 20' 
 
 30' 
 
 40' 
 
 50' 
 
 60' 
 
 57.29869 
 28.65371 
 19.10732 
 14.33559 
 11.47371 
 
 00 
 
 7.29869 
 8.65371 
 9.10732 
 4.33559 
 
 43.77516 
 49.11406 
 26.45051 
 18.10262 
 13.76312 
 
 171.88831 
 42.97571 
 24.56212 
 17.19843 
 13.23472 
 
 14.59301 
 38.20155 
 22.92559 
 16.38041 
 12.74550 
 
 35. 94561 
 34.38232 
 21.49368 
 15.63679 
 12.29125 
 
 8.75736 
 1.25758 
 . 23028 
 
 4.95788 
 1.86837 
 
 5 
 6 
 7 
 8 
 9 
 
 1.47371 
 9.56677 
 8.20551 
 7.18530 
 6.39245 
 
 11.10455 
 9.30917 
 8.01565 
 7.03962 
 6.27719 
 
 10.75849 
 9.06515 
 7.83443 
 6.89979 
 6.16607 
 
 10.43343 
 8.83367 
 7.66130 
 6.76547 
 6.05886 
 
 10.12752 
 8.61379 
 7.49571 
 6.63633 
 5.95536 
 
 9.83912 
 8.40466 
 7.33719 
 6.51208 
 5.85539 
 
 9.56677 
 
 8.20551 
 7.18530 
 6.39245 
 
 5.75877 
 
 34 
 
 S3 
 
 S2 
 SI 
 
 SO 
 
 10 
 11 
 12 
 13 
 
 14 
 
 5.75877 
 5.24084 
 4.80973 
 4.44541 
 4.13357 
 
 5.66533 
 5.16359 
 4.74482 
 4.39012 
 4.08591 
 
 5.57493 
 
 5.08863 
 4.68167 
 4.33622 
 4.03938 
 
 5.48740 
 5.01585 
 4.62023 
 4.28366 
 3.99393 
 
 5.40263 
 4.94517 
 4.56041 
 4.23239 
 3.94952 
 
 5.32049 
 4.87649 
 4.50216 
 4.18238 
 3.90613 
 
 5.24084 
 4.80973 
 4.44541 
 4.13357 
 3.86370 
 
 ~9 
 "8 
 ~7 
 76 
 75 
 
 15 
 16 
 
 17 
 
 18 
 19 
 
 3.86370 
 3.62796 
 3.42 30 
 3.23607 
 3.07155 
 
 3.82223 
 3.59154 
 3.38808 
 3.20737 
 3.04584 
 
 3.78166 
 3.55587 
 3.35649 
 3.17920 
 3.02057 
 
 3.74198 
 3.52094 
 3.32551 
 3.15155 
 2.99574 
 
 3.70315 
 3.48671 
 3.29512 
 3.12440 
 2.97135 
 
 3.66515 
 3.45317 
 3.26531 
 3.09774 
 2.94737 
 
 3.62796 
 3.42030 
 3 . 23607 
 3.07155 
 2 . 9238 
 
 74 
 
 73 
 
 72 
 71 
 -() 
 
 20 
 21 
 22 
 23 
 24 
 
 2.92380 
 2.79043 
 2.66947 
 2.55930 
 2.45859 
 
 2.90063 
 2.76945 
 2.65040 
 2.54190 
 2.44264 
 
 2.87785 
 2.74881 
 2.63162 
 2 . 52474 
 2.42692 
 
 2.85545 
 2.72850 
 2.61313 
 2.50784 
 2.41142 
 
 2.83342 
 2.70851 
 2.59491 
 2.49119 
 2.39614 
 
 2.81175 
 2 . 68884 
 2.57698 
 
 2.47477 
 2.38107 
 
 2.79043 
 2.66947 
 2.55930 
 2.45859 
 2.36620 
 
 69 
 $ 
 
 37 
 66 
 65 
 
 25 
 20 
 27 
 
 28 
 29 
 
 2.36620 
 2.28117 
 2.20269 
 2.13005 
 2.06267 
 
 2.35154 
 2.26766 
 2.19019 
 2.11847 
 2.05191 
 
 2.33708 
 2.25432 
 2.17786 
 2.107Q4 
 2.04128 
 
 2.32282 
 2.24116 
 2.16568 
 2. (,9574 
 2.03077 
 
 2 . 30875 
 2.22817 
 2.15366 
 2 . 08458 
 2.02039 
 
 2 . 29487 
 2.21535 
 2.14178 
 2.07356 
 2.01014 
 
 2.28117 
 2 . 20269 
 2.13005 
 2.06267 
 2.0 000 
 
 64 
 63 
 
 02 
 01 
 GO 
 
 30 
 
 31 
 32 
 33 
 34 
 
 2.00000 
 1.94160 
 1.88708 
 1.83608 
 1.78829 
 
 1.98998 
 1.93226 
 1.87834 
 1.82790 
 1.78062 
 
 1.98008 
 1.92302 
 1.86990 
 1.81981 
 1.77303 
 
 1.97029 
 1.91388 
 1.86116 
 1.81180 
 1.76552 
 
 1.96062 
 1.90485 
 1.85271 
 1.80388 
 1.75808 
 
 1.95106 
 1.89591 
 1.84435 
 1.79604 
 1.75073 
 
 1.94160 
 
 1.88708 
 1.83608 
 1.78829 
 1.74345 
 
 59 
 58 
 57 
 66 
 55 
 
 iOOt> GOO 
 
 co co co co co 
 
 1.74345 
 1.70130 
 1.66164 
 1.62427 
 1.58902 
 
 1.73624 
 1.69452 
 1.65526 
 1.61825 
 1.58333 
 
 1.72911 
 1.68782 
 1.64894 
 1.61229 
 1.5777 
 
 1.72205 
 1.68117 
 1.64268 
 1.60639 
 1.57213 
 
 1.71506 
 1.67460 
 1 . 63648 
 1.6005 
 1.5666 
 
 1.70815 
 1 . 66809 
 1.63035 
 1 . 59475 
 1.56114 
 
 1.70130 
 1.66164 
 1.62427 
 1.58902 
 1.55572 
 
 54 
 53 
 52 
 51 
 50 
 
 4 
 4 
 4 
 4 
 4 
 
 1.55572 
 1.52425 
 1 p 49448 
 1.4662 
 1.4395 
 
 1.55036 
 1.51918 
 1.48967 
 1.4617S 
 1.43524 
 
 1.54504 
 1.51415 
 1 . 4849 
 1.4572 
 1 . 4309 
 
 1.53977 
 1.50916 
 1.48019 
 1.45274 
 1.42672 
 
 1.5345 
 1 . 5042 
 1.4755 
 1.4483 
 1.4225 
 
 1 . 5293S 
 1.49932 
 1.4708" 
 1.44391 
 1.4183 
 
 1.52425 
 1 . 49448 
 1.46628 
 1.43956 
 1.41421 
 
 49 
 
 48 
 47 
 46 
 45 
 
 60' 
 
 50' 
 
 40' 
 
 30' 
 
 20' 
 
 10' 
 
 0' 
 
 8 
 
 ft 
 
 Secants. 
 
PART II. 
 
 STRENGTH OF MATERIALS, AND STABILITY OF 
 
 STRUCTURES. 
 
INTRODUCTION. 127 
 
 INTRODUCTION". 
 
 In the following chapters the author has endeavored to give 
 the necessary rules, formulas, and data for computing the 
 strength and stability of all ordinary forms of building con- 
 struction, whether of wood, steel, 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 trained engineer. 
 
 The rules and formulas have been reduced to their simplest 
 form or expression, and, in general, require only an elementary 
 knowledge of mathematics to understand them. Every pains 
 has also been taken to show the application of the formulas and 
 to preserve their accuracy, and it is believed that they repre- 
 sent the most intelligent practice of the present day. 
 
 In giving constants for the strength of materials, the author 
 has been guided by the practice of leading structural engineers, 
 by the available records of tests, and by his own experience of 
 many years as a practising and consulting architect. The vary- 
 ing conditions of building construction have* also 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 misapplica- 
 tion of rules and formulas and to insure absolute safety without 
 undue waste of materials. 
 
 Much' thought and labor has been given to the preparation 
 of the numerous tables contained in this portion of the book, 
 both to insure their accuracy and to arrange them in the most 
 convenient shape for instant use by architects and builders. 
 Nearly all of these tables were computed by the author, and all 
 have been carefully verified, and it is believed that they may 
 be used with perfect confidence. In all cases they give the same 
 values that would be obtained by using the formulas, while 
 affording a great saving of time and labor, as well as obviating 
 any chance for error in making the necessary computations. 
 
 Owing to the nature of the book, and the large number of 
 pages required to compass its scope as a book of reference, 
 some forms of construction, such as foundations, masonry and 
 
128 EXPLANATION OF SIGNS AND TERMS 
 
 fireproof construction, roof trusses, etc., have necessarily been 
 treated rather briefly, and more in the way of giving necessary 
 data than of going into an elaborate description or discussion 
 of the principles involved. Those persons who wish a more 
 complete treatise on foundations and masonry in general, the 
 author would refer to Part I. of his work on Building Construc- 
 tion and Superintendence, which supplements the rules and data 
 herein contained. References to various w r orks containing 
 more complete information on some subjects are also made in 
 the different chapters. 
 
 EXPLANATION" OP SIGNS AND TERMS USED 
 IN THE FOLLOWING- FORMULAS. 
 
 Besides the usual arithmetical signs and characters in general 
 use, the following characters and abbreviations will frequently 
 be used : 
 
 The sign V means square root of number behind. 
 ty means cube root of number behind. 
 () means that all the numbers between are to be 
 
 taken as one quantity. 
 
 means decimal parts; 2.5=2 T 5 Ty , or .46=^%. 
 ' denotes feet. 
 " denotes inches. 
 
 The letter A denotes the co-efficient of strength for beams one 
 
 inch square, and one foot between the supports. 
 
 C denotes resistance, in pounds, of a block of any 
 
 : material to crushing, per square inch of section. 
 
 E denotes the modulus of elasticity of any material, 
 
 in pounds per square inch. 
 e denotes .constant for stiffness of beams. 
 F denotes resistance of any material to shearing, 
 
 per square inch. 
 
 R denotes the modulus of rupture of any material. 
 S denotes a factor of safety. 
 T denotes resistance of any material to being pulled 
 
 apart, in pounds, per square inch of cioss- 
 
 section. 
 X between letters or words, denotes multiplication. 
 
EXPLANATION OF SIGNS AND TERMS. 129 
 
 [Note. In a few places in the book it has been necessary to 
 give a different meaning to one or more of the above letters but 
 in all such cases the new meaning has been very clearly 
 indicated.] 
 
 Breadth is used to denote the horizontal thickness of a beam 
 or the least side of a rectangular post or strut, and is always 
 measured in inches. 
 
 Depth denotes the vertical height of a beam or girder, and is 
 always to be taken in inches, unless expressly stated otherwise. 
 
 Length denotes, the -distance between supports and in jeet, unless 
 otherwise specified. 
 
 Abbreviations. In order to shorten the formulas, it has 
 often been found necessary to use certain abbreviations, such as 
 bet. for between, bot. for bottom, dist. for distance, diam. for 
 diameter, hor. for horizontal, sq. for square, etc., which, how- 
 ever, can in no case lead to uncertainty as to their meaning. 
 
 Where the word "ton" is used in this volume, it always means 
 2000 pounds. 
 
130 DEFINITIONS OF TERMS 
 
 CHAPTER I. 
 DEFINITIONS OF TEEMS USED IN MECHANICS. 
 
 THE following terms frequently occur in treating of mechani- 
 cal construction, and it is essential that their meaning be well 
 understood. 
 
 Mechanics is the science which treats of the action of forces. 
 
 Applied Mechanics treats of the laws of mechanics which 
 relate to works of human art; such as beams, trusses, arches, etc. 
 
 Best is the relation 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 between two points, when the straight 
 line joining them changes in length or direction, or in both. 
 
 A body moves relatively to a point, when any point in the 
 body moves relatively to the point first mentioned. 
 
 Force is that which changes, or tends to change, the state of a 
 body in reference to rest or motion. It is a cause regarding the 
 essential nature of which we are ignorant. We cannot deal with 
 forces properly, 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. 
 
 Statics is that part of Applied Mechanics which treats of the 
 conditions of equilibrium, and is divided into: 
 
 a. Statics of rigid bodies 
 
 b. Hydrostatics. 
 
 In building 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, as in the case of a 
 bridge or roof-truss. 
 
 They consist of two or more solid bodies, called pieces, 
 which are connected at portions of their surfaces called joints. 
 
 There are three conditions of equilibrium in a structure, viz. : 
 
 I. The forces exerted on the whole structure must balance 
 each other. These forces are; 
 
USED IN MECHANICS. 131 
 
 a. The weight of the structure. 
 
 b. The load it carries. 
 
 c. The supporting pressures, or resistance of the foundations, 
 called external forces. 
 
 II. The forces exerted on each piece must balance each other. 
 These forces are : 
 
 a. The weight of the piece. 
 
 6. The load it carries. 
 
 c. The resistance of its joints. 
 
 III. The forces exerted on each of the parts into which any 
 piece may be supposed to be divided must balance each other. 
 
 Stability consists in the fulfilment of conditions I. and II., 
 that is, tbe ability of the structure to resist displacement of its 
 parts. 
 
 Strength consists in the fulfilment of condition in., that is, 
 the ability of a piece to resist breaking. 
 
 Stiffness consists in the ability of a piece to resist bending. 
 
 The theory of structures is divided into two parts; viz.: 
 
 I. That which treats of strength and stiffness, dealing only 
 with single pieces, and generally known as strength of ma- 
 terials. 
 
 II. That which treats of stability, dealing with structures. 
 Stress. The load or system of forces acting on any piece 
 
 of material is often denoted by the term "stress," and the word 
 will be so used in the following pages. 
 
 The intensity of the stress per square inch on any normal sur- 
 face of a solid is the total stress divided by the area of the sec- 
 tion in square inches. Thus, if we had a bar ten feet long and 
 two inches square, with a load of 8000 pounds pulling in the 
 direction of its length, the stress on any normal section of the 
 rod would be 8000 pounds; and the intensity of the stress per 
 square inch would be 8000 -=-4, or 2000 pounds. 
 
 Strain. When a solid body is subjected to any kind of 
 
 stress, an alteration is produced in the volume and figure of the 
 
 body, and this alteration is called the "strain." In the case 
 
 of the bar given above, the strain would be the amount that 
 
 A the bar would stretch under its load. 
 
 The Ultimate Strength, or Breaking Load, of abody 
 is the load required to produce fracture in some specified way. 
 
 The Safe Load is the load that a piece can support without 
 impairing its strength. 
 
132 DEFINITIONS OF TERMS 
 
 Factors of Safety. When not otherwise specified, a 
 factor of safety means the ratio in which the breaking load ex- 
 ceeds the safe load. In designing a piece of material to sustain 
 a certain load, it is required that it shall be perfectly safe under 
 all circumstances; and hence it is necessary to make an allow- 
 ance for any defects in the material, workmanship, etc. It is 
 obvious, that, for materials of different composition, different 
 factors of safety will be required. Thus, steel being more homo- 
 geneous than wood, and less liable to defects, it does not require 
 so great a factor of safety. And, again, different kinds of strains 
 require different factors of safety. Thus, a long wooden column 
 or strut requires a greater factor of safety than a wooden beam. 
 As the factors thus vary for different kinds of strains and mate- 
 rials, we will give the proper factors of safety for the different 
 strains when considering the resistance of the material to those 
 strains. 
 
 Unit Stress is the allowed stress per unit of measurement; 
 generally the square inch, and corresponds to intensity. 
 
 Distinction between Dead and Live Load. The 
 term "dead load," as used in mechanics, means a load that is 
 applied by imperceptible degrees, and that remains steady; 
 such as the weight of the structure itself. 
 
 A "live load" is one that is applied suddenly, or accompanied 
 with vibrations; such as swift trains travelling over a railway- 
 bridge, or a force exerted in a moving machine. 
 
 It has been found by experience that the effect of a live load 
 on a beam or other piece of material is twice as severe as that 
 of a dead load of the same weight: 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 produced by a crowd of people walking on a floor is 
 usually considered to produce an effect which is a mean between 
 that of a dead and live load, and a factor of safety is adopted 
 accordingly. 
 
 In municipal ordinances and laws relating to the load 0:1 
 floors, the load to be supported by the floor, exclusive of its 
 inherent construction, and of stationary fixtures, is generally 
 referred to as the "live load," no matter of what it may consist; 
 but the term does not have the significance given to it by en- 
 gineers, and as defined in the paragraph above. 
 
 The Modulus of Rupture is a constant quantity found 
 
USED IN MECHANICS. 133 
 
 in the formulas for the strength of beams, and is eighteen times 
 the value of the constant "A" used for wooden beams. 
 
 In recent works the term fibre stress is more frequently used, 
 and represents the same quantity. 
 
 Modulus of Elasticity. If we take a bar of any elastic 
 material, one inch square, and of any length, secured at one end, 
 and to the other apply a force pulling in the direction of its 
 length, we shall find by careful measurement that the bar has 
 been stretched or elongated by the action of the force. 
 
 Now, if we divide the total elongation in inches by the original 
 length of the bar in inches, we shall have the elongation of the 
 bar per unit of length; and, if we divide the pulling force per 
 square inch by this latter quantity, we shall have what is known 
 as the modulus of elasticity. 
 
 Hence we may define the modulus of elasticity as the pulling 
 or compressing force per unit of section divided by the elongation 
 or compression per unit of length. 
 
 As an example of the method of determining the modulus of 
 elasticity of any material we will take the following: 
 ^/Suppose we have a bar of wrought iron, two inches square and 
 ten feet long, securely fastened at one end, and to the other end 
 we apply a pulling-force of 40,000 pounds. This force causes 
 the bar to stretch, and by careful measurement we find the 
 elongation to be 0.0414 of an inch. Now, as the bar is ten feet, 
 or 120 inches, long, if we divide 0.0414 by 120, we shall have the 
 elongation of the bar per unit of length. 
 
 Performing this operation, we have as the result 0.00034 of 
 an inch. As the bar is two inches square, the area of cross- 
 section is four square inches, and hence the pulling-force per 
 square inch is 10,000 pounds. Then, dividing 10,000 by 0.00034, 
 we have as the modulus of elasticity of the bar 29,400,000 
 pounds. 
 
 This is the method generally employed to determine the 
 modulus of elasticity of iron ties; but it can also be obtained 
 from the deflection of beams, and it is in that way that the 
 values of the modulus for most woods have been found. 
 
 Another definition of the modulus of elasticity, and which is 
 a natural consequence of the one just given, is the number of 
 pounds that would be required to stretch or shorten a bar one 
 inch square by an amount equal to its length, provided that the 
 law of perfect elasticity would hold good for so great a range 
 
134 CLASSIFICATION OF STRAINS. 
 
 The modulus of elasticity is generally denoted by E, and is used 
 in the determination of the stiffness of beams. 
 
 Moment. If we take any solid body, and pivot it at any 
 point, and apply a force to the body, acting in any direction 
 except in a line with the pivot, we shall produce rotation of the 
 body, provided the force is sufficiently strong. This rotation is 
 produced by what is called the moment of the force; and the 
 moment of a force about any given point or pivot is the product 
 of the force into the perpendicular distance from the pivot to 
 the line of action of the force, or, in common phrase, the product 
 of the force into the arm with which it acts. 
 
 The Centre of Gravity of a body is the point through 
 which the resultant of the weight of the body always acts, no 
 matter in what position the body be. If a body be suspended 
 at its centre of gravity, and revolved in any direction, it will 
 always be in equilibrium. 
 
 (For centre of gravity of surfaces, lines, and solids, see Chap. 
 V.) 
 
 CLASSIFICATION OP STRAINS WHICH MAY BE 
 PRODUCED IN A SOLID BODY. 
 
 The different strains to which building materials may be ex- 
 posed are: 
 
 I. Tension, as in the case of a weight suspended from one 
 end of a rod, rope, tie-bar, etc., the other end being fixed, tend- 
 ing to stretch or lengthen the fibres. 
 
 II. Shearing- Strain, as in the case of rivets, treenails, 
 pins in bridges, etc., where equal forces are applied on opposite 
 sides in such a manner as to tend to force one part over the 
 adjacent one. 
 
 III. Compression, as in the case of a weight resting on 
 top of a column or post, tending to compress the fibres. 
 
 IV. Transverse or Cross Strain, as in the case of a 
 load on a beam, tending to bend it. 
 
 V. Torsion, a twisting strain, which seldom occurs in 
 building construction, though quite frequently in machinery. 
 
 Combined Strains. The parts of structures are often 
 subjected to two or more of the above strains at the same time, 
 as in the case of "strut, beams" and "tie beams," and all beams 
 and girders are subjected to a shearing strain, as well as to 
 a transverse strain. 
 
FUUJNDAT1ON43 AND SPKEAJJ FOOTINGS. 
 
 CHAPTER II. 
 FOUNDATIONS AND SPREAD FOOTINGS. 
 
 THE term "foundation" is used to designate all that portion 
 of any structure which serves only as a basis on which to erect 
 the superstructure. 
 
 This term is sometimes applied to that portion of the solid 
 material of the earth upon which the structure rests, and also 
 to the artificial arrangements which may be made to support 
 the base. 
 
 In the following pages these will be designated by the term 
 " foundation-bed. " 
 
 Object of Foundations. The object to be obtained 
 in the construction of any foundation is to form such a solid base 
 for the superstructure that no movement shall take place after 
 its erection. But all structures built of coarse masonry, whether 
 of stone, or brick, will settle to a certain extent; and, with a few 
 exceptions, all soils will become compressed under the weight 
 of almost any building. 
 
 The main object of the architect or engineer, therefore, is not 
 to prevent settlement entirely, but to insure that it shall be 
 uniform; so that, after the structure is finished, it will have no 
 cracks or flaws, however irregularly it may be disposed over 
 the area of its site. 
 
 Nature and Bearing Power of Soils. The architect 
 should in all cases endeavor to discover the nature of the soil 
 upon which the building is to be built before commencing the 
 foundation plans, as a foundation that will prove satisfactory 
 in one soil or locality may not be sufficient for another. 
 
 For most buildings a sufficient idea of the soil may be ob- 
 tained from an inspection of adjoining excavations, or from 
 inquiry amongst builders who have erected buildings on ad- 
 joining lots. 
 
 Many soils, however, vary greatly within a comparatively 
 small area. This is especially true of soils composed of strata 
 of different materials, as sand or gravel and clay, and very often 
 
-LUU r vn .> i '.v i iv '.\ ^ . \.\i' rM UIVYI^ r v.;^/i irsvjo. 
 
 those strata have a divided dip, so that they aiv encountered 
 at different levels under different portions of the building. 
 For these reasons, therefore, the character and bearing power 
 of the soil under all large or heavy buildings should be deter- 
 mined at different points by borings or excavations, unless the 
 composition of the soil is homogenous and fully known. 
 
 Testing,' Soils. For ordinary buildings borings to the 
 depth of 6 feet below the bottom of 4he trenches will be suffi- 
 cient to determine the composition of the soil. These should 
 preferably be made by a 6-inch auger, but a 4-inch auger may 
 be used if a larger one cannot be had, and the borings examined 
 for every foot in depth and memoranda made of the same. 
 For very heavy and costly buildings the bearing power of the 
 soil, even when apparently of firm earth, is often determined 
 by testing. Clay soils, especially, vary much in their bearing 
 capacity, and are most frequently tested. Good sand or gravel 
 will seldom need to be tested. 
 
 Tests may be made with a platform resting on four legs, or 
 by a large pole or mast. The test should be made in several 
 places, and always at the proposed depth of the footings. 
 
 The ground under the Congressional Library at Washington, 
 D.C., was tested by means of a traveling car having four cast- 
 iron pedestals, each one foot square at the base and set 4 feet 
 apart each way. In testing the soil under the State Capitol at 
 Albany, N. Y., the load was placed on a mast 12 inches square, 
 held vertically by guys, with a cross-frame to hold the weights. 
 The bottom of the mast was set in a hole 3 feet deep, 18 inches 
 square at the top, and 14 at the bottom.* A permanent bench 
 mark should be established before loading, and accurate levels 
 taken by means of an engineer's level before the load is applied. 
 and frequent levels taken as the load is gradually increased 
 until a sinkage is shown. From one-fifth to one-half of the load 
 required to produce settlement is generally adopted for the 
 safe load according to circumstances. 
 
 Values for the Bearing Power of Soils. The 
 following values for the bearing power of soils, given by Prof. 
 Ira O. Baker,f of the University of Illinois, have been quite 
 generally accepted by engineers: 
 
 * For more complete descriptions of these tests see "Building Construc- 
 tion and Superintendence," Part I, p. 20. 
 
 t See "Treatise on Masonry Construction," p. 194. 
 
JL V^ U mArt. X JA^ O SL1MJ Dl'JLtJ^AJJ J?UU11JNUS. 
 
 TABLE I. BEARING POWER OF SOILS. 
 
 Kind of material. 
 
 Bearing power in tons 
 per square foot. 
 
 Min. 
 
 Max. 
 
 Rock the hardest in thick layers, in native bed . 
 Rock equal to best ashlar masonry 
 
 200 
 25 
 15 
 5 
 4 
 2 
 1 
 8 
 4 
 2 
 0.5 
 
 30 
 20 
 10 
 6 
 4 
 2 
 10 
 6 
 4 
 1 
 
 Rock equal to best brick masonry 
 
 Hock equal to poor brick masonry 
 
 Clay on thick beds, always dry 
 
 (May 011 thick beds, moderately dry 
 
 Tlav, soft 
 
 Gravel and coarse sand, well cemented 
 
 Sand, compact and well cemented 
 
 Sand, clean, dry 
 
 Quicksand, alluvial soils, etc 
 
 
 When deciding upon the pressure which may safely be put 
 upon the soil several practical considerations should be taken 
 into account. "For example, the pressure on the foundation 
 of a tall chimney should be considerably less than that of the 
 low massive foundation of a fire-proof vault. In the former case 
 a slight inequality of bearing power, and consequent unequal 
 settling, might endanger the stability of the structure; while 
 in the latter no serious harm would result. The pressure per 
 unit of area should be less for a light structure subject to the 
 passage of heavy loads as for example a railroad viaduct 
 than for a heavy structure, subject only to a quiescent load, 
 since the shock and jar of the moving load are far more serious 
 than the heavier quiescent load." * 
 
 The pressure under piers supporting a tier of columns should 
 also be a little greater than under a masonry wall, so that the 
 pier may settle a little more to allow for the compression in 
 the joints of the mason- work of the wall. Usually an increase 
 of pressure of about 10 per cent, may be allowed. 
 
 The following example of the known weight on different soils 
 will give a very good idea of what has been done in actual practice. 
 
 Rock. St. Rollox chimney, poorest kind of sandstone, 2 
 tons per sq. ft. 
 
 Clay. Chimney, McCormick Reaper Works, Chicago, If 
 tons per square foot on dry, hard clay. 
 
 Capitol at Albany, N. Y., rests on blue clay containing from 
 60 to 90 per cent, of alumina, the remainder being fine sand, 
 
 *Ira O. Baker, " American Architect," November 3, 1888. 
 
138 FOUNDATIONS AND SPREAD FOOTINGS. 
 
 and containing 40 per cent, of water on an average. The safe 
 load was taken at 2 tons per square foot. 
 
 In the case of the Congressional Library at Washington, which 
 rests on "yellow clay mixed with sand," 2\ tons per square foot 
 was taken for the safe load. "Experience in Central Illinois 
 shows that if the foundation is carried down below the action of 
 the frost the clay subsoil will bear 1J to 2 tons per square foot 
 without appreciable settling." * 
 
 Sand, and Gravel. ' In an experiment in France clean 
 river sand compacted in a trench supported 100 tons per square 
 foot. 
 
 "The piers of the Cincinnati Suspension Bridge are founded 
 on a bed of coarse gravel 12 feet below water; the maximum 
 pressure on the gravel is 4 tons per square foot. 
 
 "The piers of the Brooklyn Suspension Bridge are founded 44 
 feet below the bed of the river; upon a layer of sand 2 feet thick 
 resting upon bed-rock; the maximum pressure is about 5i tons 
 per square foot. 
 
 "At Chicago sand and gravel about 15 feet below the surface 
 are successfully loaded with 2 to 2 tons per square foot, 
 
 "At Berlin the safe load for sandy soil is generally taken at 2 
 to 2| tons per square foot. 
 
 "The Washington Monument, Washington, D. C,, rests upon 
 a bed of very fine sand 2 feet thick. The ordinary pressure on 
 certain parts of the foundation being not far from 11 tons per 
 square foot, which the wind may increase to nearly 14 tons per 
 square foot." * 
 
 The Home Insurance Building, La Salle and Adams St., 
 Chicago, was proportioned for a bottom pressure of 2 tons per 
 square foot. Settled 2\ inches. 
 
 "Probably none of the high buildings on spread footings 
 settled less than 6 inches. The amount of settlement generally 
 is between 6 and 12 inches. The Auditorium settled more 
 than 20 inches under the tower." f 
 
 Bearing 1 Power of Soils, as Fixed by Municipal 
 Laws. Many of the larger cities prescribe the maximum 
 pressure to be placed on the ground under the footings, although 
 as a rule the laws are somewhat indefinite as regards the 
 nature of the soil. 
 
 * Ira O. Baker, "American Architect," November 3, 1888. 
 t E. C. Shankland in "Inland Architect/' January, 1898. 
 
AJNJJ ISrKEAD *OOTIJNGS. loy 
 
 The building code of Greater New York specifies the follow- 
 ing as the maximum permissible loads for different soils ; 
 
 "Soft clay, one ton per square foot; 
 
 "Ordinary clay and sand together, in layers, wet and springy, 
 two tons per square foot; 
 
 "Loam, clay, or fine sand, firm and dry, three tons per square 
 foot; 
 
 * f Very firm coarse sand, stiff gravel, or hard clay, four tons 
 per square foot, or as otherwise determined by the Com- 
 missioner of Buildings having jurisdiction." 
 
 The requirements of the Chicago Building Ordinance is as 
 follows : 
 
 "If the soil is a layer of pure clay at least fifteen feet thick 
 without admixture of any foreign substance excepting gravel, 
 it shall not be loaded more than at the rate of 3,500 pounds per 
 square foot. If the soil is a layer of pure clay at least fifteen 
 feet thick and is dry and thoroughly compressed, it may be 
 loaded not to exceed 4,500 pounds per square foot. 
 
 "If the soil is a layer of dry sand fifteen feet or more in thick- 
 ness, and without admixture of clay, loam, or other foreign 
 substance, it shall not be loaded more than at the rate of 4,000 
 pounds per square foot. 
 
 "If the soil is a mixture of clay and sand, it shall not be 
 loaded more than at the rate of 3,000 pounds per square foot." 
 
 Proportioning- the Footing's. The footings under 
 dwellings and light buildings, when on firm soil, are usually 
 proportioned according to the thickness of the wall above, 
 rather than by the pressure on the soil, as the weight of such 
 buildings, when not more than three stories high, will seldom 
 exceed 1 J tons per square foot when distributed by the footings. 
 The width of the footings, however, even in light buildings, 
 should be proportioned so that the pressure on- the soil will be 
 approximately the same per square foot under all parts of the 
 building. It is owing largely to the unequal pressure on the 
 soil, as where wide openings occur, or where one wall is higher 
 than the adjacent, that cracks occur in brick and stone walls. 
 
 For high and heavily loaded buildings, the area of the foot- 
 ings should be carefully proportioned both to the load and to 
 the bearing power of the soil. 
 
 In computing the weight to be supported by the footings, all 
 of the dead or permanent load, such as the weight of the mate- 
 rials entering into and forming a part of the building should be 
 
140 FOUNDATIONS AND SPREAD FOOTINGS. 
 
 taken, and to this should be added only so much of the live or 
 movable load that the floors are to support as will probably be 
 upon the floor most of the time, as to secure uniform settlement, 
 it is necessary that the loads for which the footings are pro- 
 portioned shall be as near the actual weight of the building as 
 possible. 
 
 For warehouses, stores, etc., about 50 per cent, of the live load 
 for which the floor beams are proportioned should be added to 
 the dead load supported on the footings. 
 
 For office-buildings, hotels, etc., the weight of the people who 
 may occupy them should be neglected altogether in propor- 
 tioning the footings, and only about 15 Ibs. per square foot of 
 floor allowed to cover the weight of furniture, books, safes, etc. 
 
 For theatres and similar buildings some allowance should 
 probably be made for the weight of the people, the actual amount 
 depending upon the arrangement of the plan and the character 
 of the soil. Almost any soil, after it has been compacted by 
 the dead weight of the building, will carry a shifting load of 
 people without further settlement, while if the footings were 
 computed to carry the full live loads for which the floor beams 
 were designed, it would be found when the building was finished 
 that the actual loads on the footings under the walls would be 
 much greater than under the columns, and if the ground had 
 settled at all during the erection of the building, the probabili- 
 ties would be that the building would be higher in the centre 
 than at the walls.* 
 
 Municipal Requirements as to Proportioning 
 Footings to lave Loads. The Building Code of Greater 
 New York requires that footings shall be proportioned as follows : 
 
 " The load exerting pressure under the footings of founda- 
 tions in buildings more than three stories in height are to be 
 computed as follows: For warehouses and factories they are to 
 be the full dead load and the full live load established by this 
 code. In stores and buildings for light manufacturing pur- 
 poses, they are to be full dead load and 75 per cent, of the live 
 
 * It is the judgment of the best engineers that the areas of foundations 
 on compressible soil should be proportioned to the dead loads only, and 
 not to theoretical or occasional loads. When live loads have been 
 figured on both the interior columns and on the columns in the exterior 
 walls, the exterior columns have always been found to settle more, from 
 the fact that the live load forms a larger percentage of the interior column 
 loads than of the wall column loads. J. K. FREITAG. 
 
FOUNDATIONS AND SPREAD FOOTINGS 141 
 
 load established by this code. The same applies to churches, 
 schoolhouses, and places of public assembly. In office-build- 
 ings, hotels, dwellings, apartment houses, tenement houses, 
 lodging houses, and stables, they are to be the full dead load 
 and 60 per cent, of the live load established by this code." The 
 footings must be designed to distribute the loads as uniformly 
 as possible, so as not to exceed the safe bearing capacity of the 
 soil as established in this code." 
 
 The Chicago ordinance merely specifies that . "Foundations 
 shall be proportioned to the actual average loads they will have 
 to carry, and not to theoretical and occasional loads." 
 
 The Boston Building Laws make no specific requirements as 
 to how the loads shall be computed. 
 
 The following examples illustrate the proper method of pro- 
 portioning the area of footings: 
 
 EXAMPLE 1. To proportion the footings under a six-story 
 warehouse, with solid side walls of brick, and iron columns and 
 steel girders, spaced 16 ft. c. to c. across the building, and 
 the same distance longitudinally, the safe bearing capacity 
 of the soil being assumed at 3 tons per square foot. 
 
 Computation Walls. 
 
 Cubic feet of brickwork in one lineal foot of side 
 wall, from footing to top of fire-wall 164 ;. at 
 
 120 Ibs. per ft = 19.680 Ibs. 
 
 Floor area supported by 1 ft. of bearing wall, 8 ft. 
 
 in each story. 
 Actual weight of materials in 1 sq. ft. of floor, 
 
 75 Ibs. 75X8 ft.X6 floors = 3,600 Ibs. 
 
 Actual weight of 8 sq. ft. of roof, 60X 8 = 480 Ibs. 
 
 Probable constant load on first three floors, 50 Ibs. 
 
 per sq. ft., 50X8X3 = !> 200 lbs - 
 
 Probable constant load on 4th, 5th, and 6th floors, 
 
 40 lbs. per sq. ft, 8X40X3 
 
 Probable constant load on roof. ___ZZZL_ 
 
 Total load on 1 lineal foot of footing =25,920 lbs. 
 
 25,920 -J- 6,000 (3 tons) = 4 ft. 4 ins. width of footing. 
 
 Under Columns. 
 Weight of one tier of columns from footing to roof, 
 
 including fireproof covering and plaster = 12,000 lbs. 
 
 Floor area in each story supported by column 
 16X16 feet =256 sq. ft. 
 
142 FOUNDATIONS AND SPREAD FOOTINGS. 
 
 Load under columns from preceding page 12,000 Ibs. 
 Actual weight of 256 sq. ft. of floor for 6 stories 
 
 (256X75X6) =115,200 Ibs, 
 
 Actual weight of 256 sq. ft. of roof, at 60 Ibs = 15 ? 360 Ibs, 
 
 Probable constant load on first three floors, 50 Ibs. 
 
 X256X3 i = 38,400 Ibs. 
 
 Probable constant load on 4th, 5th, and 6th floors, 
 
 40lbs.X256X3 .. = 30,720 Ibs, 
 
 Probable constant load on roof . . 
 
 Total load on footings t =211,680 Ibs. 
 
 21 1,680 -J- 6,600 (3 tons increased 10%) = 32 sq. ft. = area of 
 footing. 
 
 The front and rear walls would probably be divided into 
 piers by large openings and should be proportioned in the same 
 way as the column footings, except that only the piers support- 
 ing ends of girders would be figured for floor loads. 
 
 Only warehouses for storage of heavy merchandise should 
 be figured for a probable constant load of 50 Ibs. For ordinary 
 merchandise 30 Ibs. would be more nearly correct.* 
 
 For an office-building or hotel, the calculation would be the 
 same for the dead load, but the probable constant load would 
 not exceed 15 Ibs. 
 
 EXAMPLE 2. To proportion the footings under the tower, 
 front and side walls of a church, built on ground capable of 
 sustaining 4 tons to the square foot, 
 
 Data. Tower walls, 82 ft. high above footings; 18 ft. of 
 wall 2 ft. thick, 13 ft. of wall 20" thick, 51 ft. of wall 16" thick. 
 
 Side wall adjacent to tower, 36 ft. high, 14 ft. of wall 20" 
 thick, balance of wall 16" thick. 
 
 The front wall is divided in the centre by a wide opening, 
 leaving piers 12 ft. wide at each side one pier being adjacent to 
 the tower. 
 
 Computation. It is proposed to make the footings under 
 the side wall 3 ft. wide and to proportion the other footings to 
 the same unit pressure. 
 
 Weight of masonry in one lineal foot of ciclo wall . . . 6,320 Ibs. 
 Weight of floor material and pews supported by one 
 
 lineal foot of side wall 200 Ibs. 
 
 * The floor beams, of course, should be computed for the full possible load. 
 
"Weight of roof and ceiling supported by one lineal 
 
 foot of side wall 200 Ibs. 
 
 Weight of snow on roof, and people on floors disregarded. 
 
 Total weight on one lineal foot of footing. . 6,720 Ibs. 
 6, 720 -i- 3 ft. (width of footing) =2, 240 Ibs. per sq. ft. on trenches, 
 which should be used as a basis for proportioning all other 
 footings. 
 
 Weight of masonry in one lineal foot of tower wall. . 15,080 Ibs. 
 Weight of floors supported by one lineal foot of tower 
 
 wall , 296 Ibs. 
 
 Weight of roof supported by one lineal foot of tower 
 
 wall 340 Ibs. 
 
 Total weight of one lineal foot of footing. . . 15,516 Ibs. 
 
 15,516^-2,240=7 ft.^width of footing. 
 Each of the 12-ft. piers of front wall contains and 
 
 supports masonry weighing 149, 040 Ibs. 
 
 Weight of gallery and pews supported by each pier. *3,876 Ibs. 
 
 Total weight on 12 ft. of footing , . 152,916 Ibs. 
 
 or 12,743 Ibs. per lineal ft. 
 
 12,743-5-2,240 lbs.=5.1 ft. width of footing. 
 
 As the pressure on the soil in this case is so slight, the width 
 of the tower footings could be reduced to 6 ft. and of the front- 
 wall footings to 4' 4" without causing cracks -where the walls 
 join, but the theoretical width should always be computed. 
 
 Where the unit pressure approaches closely to the safe bear- 
 ing of the soil no reduction should be made from the computed 
 widths. 
 
 Centre of Pressure Should Coincide with Centre 
 of Base. That the walls and piers of a building may settle 
 uniformly and without producing cracks in the superstructure 
 it is not only essential that the area of the footings shall be in 
 proportion to the load and the bearing power of the soil, but 
 also that the centre of pressure (a vertical line through the centre 
 of gravity of the wall or pier) shall pass through the centre of the 
 footing. 
 
 This condition is of the first importance, for if the centre of 
 pressure does not coincide with the centre of the footing, or 
 base, the ground will yield most on the side which is nearest 
 to the centre of pressure, and, as the ground yields, the base 
 assumes an inclined position, often tilting the lower portion of 
 
144 FOUNDATIONS AND SPREAD FOOTINGS. 
 
 the wall or pier, and producing unsightly cracks in the super- 
 structure. 
 
 Foundations on Rock. To prepare a rock foundation 
 for being built upon, all that is generally required is to cut away 
 the loose and decayed portions of the rock, and to dress the 
 rock to a plane surface as nearly perpendicular to the direction 
 of the pressure as is practicable; or, if the rock forms an in- 
 clined plane, to cut a series of plane surfaces, like those of steps, 
 for the wall to rest on. If there are any fissures in the rock 
 they should be filled with concrete. Concrete is better than 
 masonry for this purpose, as, when once set, it is nearly incom- 
 pressible under anything short of a crushing force; so that 
 it forms a base almost as solid as the rock itself, while the com- 
 pression of the mortar joints of masonry is certain to cause some 
 irregular settlement. 
 
 If it is unavoidably necessary that some parts of the founda- 
 tion shall start from a lower level than others, care should be 
 taken to keep the mortar joints as close as possible, or to execute 
 the lower portions of the work in cement, or some hard-setting 
 mortar; otherwise the foundations will settle unequally and 
 thus cause much injury to the superstructure. The load placed 
 on the rock should at no time exceed one-eighth of that neces- 
 sary to crush it. When building on a ledge much trouble is 
 often caused by the water which collects on top of the stone,, 
 and stands or runs on its surface. Some method of draining 
 the water is absolutely necessary if the basement is to be kept 
 dry. 
 
 Foundations on Clay. This soil is found in every con- 
 dition, varying from slate or shale, which will support almost 
 any load, to a soft, damp material, which will squeeze out in 
 every direction when a moderately heavy pressure is brought 
 upon it. 
 
 Ordinary clay soils, however, when they can be kept dry, 
 will carry any usual load without trouble, but as a rule clay 
 soils will give more trouble than either sand, gravel, or stone. 
 
 In the first place, the top of the footings must be carried 
 below the frost-line to prevent heaving, and for the same reason 
 the outside face of the wall should be built with a slight batter, 
 about f " to the foot, and perfectly smooth. The frost-line varies 
 with different localities, attaining a depth of six feet in some of 
 the very Northern States, although between three and four feet 
 is the usual depth in the so-called Northern States. The effect 
 
FOUNDATIONS AND SPREAD FOOTINGS. 145 
 
 of freezing and thawing on clay soils is very much greater than 
 on other soils. 
 
 The surface of the ground around the building should be 
 graded so that the rain-water will run away from the building, 
 and in most clays subsoil drains are necessary. When the 
 clay occurs in inclined layers great care must be exercised to 
 prevent it from sliding, and when building on a side hill the 
 utmost precautions must be taken to exclude water from 
 the soil, for if the clay becomes wet the pressure of the walls 
 may cause it to ooze from under the footings. The erection of 
 very heavy buildings in such locations must be considered 
 hazardous, even when every precaution is taken. 
 
 Should it be necessary to carry a portion of the foundations 
 to a greater depth than the rest, the lower portion of the walls 
 should be built as described under "Foundations on Rock," 
 and care must be taken to prevent the upper part of the bed 
 from slipping. Wherever possible the footings should be 
 carried all around the building at the same level. 
 
 If the clay contains coarse sand or gravel its supporting 
 power is increased, and it is less liable to slide or ooze away. 
 
 Foundations on Sand and Gravel. Gravel gives 
 less trouble than any other material as a foundation bed. It 
 does not settle under any ordinary load, and will safely carry 
 the heaviest of buildings if the footings are properly propor- 
 tioned. It is not affected by water, provided it is confined 
 laterally, so that the sand and fine gravel cannot wash out. 
 This soil is also not greatly affected by frost. 
 
 Sand also makes an excellent foundation bed when confined 
 laterally, and is practically incompressible, as clean river sand 
 compacted in a trench has been known to support 100 tons to 
 the square foot. 
 
 As long as the sand is confined on all sides, and the footings 
 are all on the same level, no trouble whatever will be encountered, 
 unless it be in the caving of the banks in making the excava- 
 tions. Should the cellar be excavated to different levels, how- 
 ever, sufficient retaining walls must be erected where the depth 
 changes to prevent the sand of the upper level from being forced 
 out from under the footings, and precautions should be taken 
 in such a case to keep water from penetrating under the upper 
 footings. 
 
 Foundations on Loam and Made Land. No 
 foundation should start on loam (soil containing vegetable 
 
146 FOUNDATIONS AND SPREAD FOOTINGS. 
 
 matter), or on land that has been made or filled in, unless, in- 
 deed, the filling consist of clean beach sand, which, when settled 
 with water, may be considered equal to the natural soil. 
 
 Loam should always be penetrated to the firm soil beneath, 
 and whe*n the made land or filling overlies a firm earth, the 
 footings should be carried to the natural soil. When the filled 
 land is always wet, as on the coast or the borders of a lake, 
 piles may be used, extending into the firm earth, and the tops 
 cut off below low- water mark; but piles should never be used 
 where it is not certain that they will be always wet. 
 
 Foundations for Chimneys. As examples of the 
 foundations required for very high chimneys we quote the 
 following from a treatise on foundations, in the latter part of a 
 work on "Foundations and Foundation Walls," by George T. 
 Powell. 
 
 Fig. 1 represents the base of a chimney erected in 1859 for 
 the Chicago Refining Company, 151 feet high, and 12 feet square 
 at the foot. The base, merely two courses of heavy dimension 
 
 ;tone, as shown, is bedded upon the surface-gravel near the 
 mouth of the river, there recently deposited by the lake. The 
 mortar employed in the joint between the stone is roofing-gravel 
 in cement. The area of the base is 256 square feet, the weight 
 of chimney, inclusive of base, 625 tons, giving a pressure of 
 2.44 tons to the square foot. This foundation proved to be 
 perfect. 
 
 Fig. 2 represents the base of a chimney erected in 1872 for the 
 McCormick Reaper Works, Chicago, which is 160 feet high, 14 
 feet square at the foot, with a round flue of 6 feet 8 inches 
 diameter. 
 
PILE FOUNDATIONS. 
 
 147 
 
 The base covers 025 square feet; the weight of the chimney 
 and base is approximately 1,100 tons; the pressure upon the 
 ground, (dry hard clay) is therefore 1.76 tons to the square foot. 
 This foundation also proved to be perfect in every respect. 
 
 , , [, 1 :. ... _] > ., | -l:'i ' . /I 
 
 j 
 
 Fig. 2. 
 
 Pile Foundations. When it is required to build upon 
 a compressible soil that is constantly saturated with water and 
 of considerable depth, the most practicable method of obtain- 
 ing a solid and enduring foundation for buildings of moderate 
 height is by driving piles. 
 
 A large proportion of the buildings in the city of Boston, Mass., 
 and several of the tall office-buildings of New York City and 
 Chicago, rest on piles, and piles are extensively used for sup- 
 porting buildings, grain elevators, etc., erected along the water 
 front of coast and lake cities. 
 
 The durability of piles in ground constantly saturated with 
 water is beyond question, as several instances exist where piles 
 have been found in a perfectly sound condition after the lapse 
 of from six to seventeen centuries. 
 
 Municipal Requirements. The laws of Boston re- 
 quire that piles ^hall be capped with granite, and that the 
 spacing shall not exceed 3 ft. between centres. The laws of 
 Chicago require that piles shall be driven to rock or hard pan 
 and be capped with an oak grillage; they also specify a maxi- 
 mum load of 25 tons per pile and a maximum fibre stress of 
 1,200 pounds per square inch for the oak grillage. 
 
 The laws of New York specify a minimum diameter of 5 inches, 
 a maximum spacing of 3 feet between centres, and a maximum 
 safe load of 20 tons per pile. 
 
148 PILE FOUNDATIONS. 
 
 The Piles are made from the trunks of trees; they should 
 be as straight as possible and not less than 5 ins. in diameter 
 at small end for light buildings, or 8 ins. for heavy buildings. 
 The woods generally used for piles in the Northern States are 
 the spruce, hemlock, white pine, Norway pine, Georgia pine, 
 and occasionally oak, hickory, elm, black gum, and basswood. 
 In the Southern States, Georgia or pitch pine, cypress and oak 
 are used. 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. 
 
 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 pene- 
 tration is less than 6 ins. at each blow the top of the pile should 
 be protected from " brooming" by putting on an iron ring about 
 1 inch less in diameter than the head of the pile, and from 2J 
 to 3 inches wide by f " thick. The head should be chamfered 
 to fit 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. 3, answers very well 
 for all but very hard soils, and for these a cast conical point about 
 5 inches 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 exposed to salt water should 
 be thoroughly impregnated with creosote, dead oil 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. The piles should always 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 
 is, by a successsion of blows given with a block of cast iron, or 
 steel, called the "hammer," which slides up and down between 
 the uprights of a machine called a "pile-driver." The ma- 
 chine is placed over the pile, so that the hammer descends fairly 
 on its head, the piles always being driven with the small end 
 
down. The hammer is generally raised by steam power, and 
 is dropped either automatically or by hand. The usual weight 
 of the hammers used for driving piles for building foundations 
 is from 1,500 to 2,500 pounds, and the fall varies from 5 to 20 
 feet, the last blows being given with a short fall. Occasionally, 
 hammers weighing up to 4,000 pounds and over are used. 
 
 Steam hammers are to a considerable extent taking the place 
 of the ordinary drop-hammer 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 60 to 70 
 
 Fig. 3. 
 
 to the minute, and seems to jar the piles down, the short interval 
 between the blows not giving time for the soil to settle around 
 the pile.* 
 
 In driving piles care should be taken to keep them plumb, 
 and when the penetration becomes small, the fall should be 
 
 * The 5,000 piles, averaging 48 ft. in net length, under the new Chicago 
 Post Office were driven with a steam hammer, weighing 4,400 Ibs. and making 
 60 blows per minute. 
 
150 PILE FOUNDATIONS. 
 
 reduced to* about 5 feet, the blows being given in rapid succes- 
 sion. 
 
 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 feet or 
 more and refuse to sink more than J inch under five blows of 
 a 1,200-pound hammer falling 15 feet, it is useless to try them 
 further, as the additional blows only result in brooming and 
 crushing the head and point of the pile, and splitting and crush- 
 ing the intermediate portions to an unknown extent. 
 
 Spacing 1 . Piles should not be spaced less than 2 feet on 
 centres, nor more than 3 feet, unless iron or wooden grillage is 
 used. 
 
 When long piles are driven nearer than 2 feet from centres 
 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 feet 6 inches from centres across the trench and 3 feet 
 from centres 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 feet apart from centres, unless driven by means of a water jet. 
 
 The number of piles under the different portions of the build- 
 ing should be proportioned to the weight which they are to 
 support, so that each pile will receive very nearly the same load. 
 
 Capping. 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, concrete or timber or steel grillage. 
 
 Granite Capping. In Boston it is obligatory to cap the piles 
 with blocks of granite, which rest directly on the tops of the 
 piles. If the stone does not fit the surface of the pile, or a pilo 
 is a little low, it is wedged up with oak or stone wedges. In 
 capping with stone a section of the foundation should be laid 
 out on the drawings showing the arrangement of the capping 
 stones. 
 
 A single stone may rest on one, two, or three piles, but not 
 on four, as it is practically impossible to make the stone bear 
 
evenly on four piles. 
 
 Fig. 4. 
 
 Fig. 4 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 one piece across the wall. 
 should be laid in cement mortar on 
 the capping. 
 
 Fig. 5 shows a partial piling plan, 
 with the arrangement of the cap 
 stones, of the Boston Chamber of 
 Commerce. It may seem that most 
 of the stones rest on three piles, and 
 a very few on two piles. 
 
 Concrete Capping. In New York 
 a very common method of capping 
 
 is to excavate to a depth of 1 foot below the top of the piles 
 and one foot outside of them, and fill the space thus excavated 
 solid with Portland cement concrete, deposited in layers and 
 well rammed. 
 
 After the concrete is brought level with the top of the piles 
 additional layers are deposited over the whole width of the 
 foundation until the concrete attains a depth of 18 inches above 
 the piles. On this foundation brick or stone footings are laid 
 as on solid earth. If long bars of twisted steel, about f " square 
 are imbedded in the concrete about 3 inches above the tops of 
 the piles, this makes, in the opinion of the author, the best 
 form of capping, the twisted bars giving great transverse strength 
 to the concrete. 
 
 Grillage. Most of the pile foundations of Chicago have 
 heavy timber grillage bolted to the tops of the piles, and on 
 these timbers are laid the stone or concrete footings. 
 
 The timbers for the grillage should be at least 10" X 10" in 
 cross-section, and should have sufficient transverse strength 
 to sustain the load from centre to centre of piles, using a low 
 fibre stress. They should be laid longitudinally on top of the 
 piles and be fastened to them by means of drift bolts, which are 
 plain bars of iron, either round or square, driven into a hole 
 about 20 per cent, smaller than the iron. One-inch round or 
 square bars are generally used, the hole being bored by a f- inch 
 
152 FOUNDATIONS AND SPREAD FOOTINGS. 
 
 auger for the round bolts or a J-inch auger for the square bolts. 
 The bolts should enter the pile at least 1 foot. 
 
 Fig. 5. 
 
 If heavy stone or concrete footings are used, and the space 
 between the piles and timbers is filled with concrete level with 
 
FOUNDATIONS AND SPREAD FOOTINGS. 153 
 
 the top of the timbers, no more timbering is required; but if 
 the footings are to be made of small stones, and no concrete is 
 used, a solid floor of cross timbers, at least 6 inches thick, for 
 heavy buildings, should be laid on top of the longitudinal cap- 
 ping and drift-bolted to them. 
 
 Where timber grillage is used it should, of course, be kept 
 entirely below the lowest recorded water line, otherwise it will 
 rot and allow the building to settle. It has been proved con- 
 clusively, however, that any kind of sound timber will last 
 practically forever if completely immersed in water. 
 
 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 evenly over the piles, as the transverse 
 strength of the timber will help to carry the load over a single 
 pile, which for some reason may not have the same bearing 
 capacity as the others. Steel beams, imbedded 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 Concrete Piles, see page 177. 
 
 Specifications for Pile Foundations. This con- 
 tractor is to furnish and drive the piles indicated on sheet No. 1. 
 
 The piles are to be of sound spruce (hemlock, Georgia pine) 
 perfectly straight from end to end, trimmed* close, and cut off 
 square to the axis at both ends. 
 
 They must be not less than six (6) inches in diameter, at the 
 small end, ten (10) inches at the large end, when cut off, and of 
 sufficient length to reach solid bottom, the necessary length of 
 piles to be determined by driving test piles in different parts of 
 the foundation. 
 
 All piles to be driven vertically, in the exact positions shown 
 by the plan, until they do not move more than five (5) inches under 
 the last five blows of a hammer weighing 2,000 Ibs. and falling 
 twenty (20) feet. All split or shattered piles are to be removed if 
 possible and a good one driven in place of each imperfect one. 
 In cases where such piles cannot be removed an additional one 
 must be driven for each imperfect one. If the piles show a ten- 
 dency to broom, they shall be bound with a wrought-iron ring, 
 2J ins. wide, and -J in. thick. 
 
 * For description of the pile foundations and capping of the Chicago 
 Post Office, see Freitag's "Architectural Engineering," pp. 350-352. 
 
154 PILE FOUNDATIONS. 
 
 All piles, when driven to the required depth shall be sawed ofi 
 square and horizontal at the grade indicated on the drawings. 
 
 Bearing Power of Files. As used for supporting build- 
 ings, piles may be divided into two classes: A. Those which are 
 driven to rock or "hard pan," i.e., firm gravel or clay, and (B) 
 those which do not reach hard pan. 
 
 Piles of Class A, 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 
 through 27 ft. of soft, plastic clay, 23 ft. of tough compact clay, 
 and 2 ft. into hard pan sustained a load of 50.7 tons per pile for 
 two weeks without apparent settlement. There are many in- 
 stances where piles driven to the depth of 20 ft. in hard clay sus- 
 tain from 20 to 40 tons, and 'a few instances up to 80 tons per pile. 
 
 Piles of Class B depend for their bearing power upon the 
 friction, cohesion, and buoyancy of the soil into which they are 
 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 load of piles of this class, but there are 
 so many elements that modify the penetration, or its exact de- 
 termination, as well as varying conditions in driving, and in the 
 soil, that it is regarded an impossibility to formulate any rule 
 that can be considered entirely satisfactory for all the conditions 
 under which such piles are driven. 
 
 The formula now most generally used by engineers was de- 
 rived by Mr. M. A. Wellington, and is often referred to as the 
 Engineering News formula. 
 
 The formula is 
 
 Safe load 2. w.h. 
 in tons S + 1 * 
 
 in which w= weight of hammer in tons, h= height of fall of hammer 
 in feet, S= penetration under last blow, or the average under the 
 last five blows. When loads are based on this formula the piles 
 should be driven until the penetration does not exceed the limit 
 assumed, or if this is found to be impracticable, new calculations 
 must be made based on the smallest average penetration that 
 
155 
 
 can be obtained, and a greater number of piles used. In locali- 
 ties where piling is commonly used for obtaining the foundation, 
 the least penetration that can be obtained within practical limits 
 of length of pile can generally be ascertained by observation, 
 or by consulting an experienced pile-driver. The longer the pile 
 the less will be the final set or penetration as a rule. 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 to an equal bearing. When the 
 piles are to be loaded to more than 50 per cent, of the assumed 
 safe load, the final set of each pile should be carefully meas- 
 ured by an inspector, the broom and splinters being removed 
 from the head of the pile for the last blow. 
 
 The following table, computed by the above formula, gives 
 the safe loads for different penetrations, under different falls, of 
 a hammer weighing one ton. For a hammer of different weight 
 multiply the safe load in table by the actual weight of hammer, 
 in tons. Thus for a hammer weighing 1,000 Ibs. the values in the 
 table should be multiplied by J or for a 1,500 Ib. hammer by J. 
 
 TABLE II. SAFE LOADS, IN TONS, FOR PILES. 
 
 (Hammer weighing 1 ton.) 
 
 Penetra- 
 tion of 
 
 Height of the fall of the hammer, in feet. 
 
 Pile, in 
 inches. 
 
 3 
 
 4 
 
 5 
 
 6 
 
 8 
 
 10 
 
 12 
 
 14 
 
 16 
 
 18 
 
 20 
 
 25 
 
 30 
 
 0.25 
 
 4 8 
 
 6,4 
 
 8,1 
 
 9.7 
 
 12.9 
 
 16.1 
 
 19.4 
 
 22.5 
 
 25.8 
 
 29.1 
 
 32.3 
 
 
 
 0.50 
 
 4.0 
 
 5.3 
 
 6.7 
 
 8.0 
 
 10.7 
 
 13.3 
 
 16.1 
 
 18.7 
 
 21.3 
 
 24.0 
 
 26.6 
 
 33.3 
 
 
 0.75 
 
 3 4 
 
 4,6 
 
 5.7 
 
 6.9 
 
 9.2 
 
 11. /> 
 
 13.8 
 
 16.1 
 
 18.4 
 
 20.7 
 
 23.0 
 
 28.8 
 
 34.5 
 
 1.00 
 
 3.0 
 
 4.0 
 
 5.0 
 
 6.0 
 
 8.0 
 
 10.0 
 
 12.0 
 
 14.0 
 
 16.0 
 
 18.0 
 
 20.0 
 
 25.0 
 
 30.0 
 
 1.25 
 
 
 3 6 
 
 4,5 
 
 54 
 
 7.1 
 
 8.9 
 
 10.7 
 
 12.5 
 
 14 3 
 
 16.1 
 
 17^9 
 
 22.3 
 
 26.7 
 
 1.50 
 
 
 3.2 
 
 4,0 
 
 4.8 
 
 6.4 
 
 8.0 
 
 9.6 
 
 11.2 
 
 12.8 
 
 14.4 
 
 16.0 
 
 20.0 
 
 24.0 
 
 1.75 
 
 
 
 3.6 
 
 4.4 
 
 5.8 
 
 7.3 
 
 8.8 
 
 10.2 
 
 11.7 
 
 13.1 
 
 14.6 
 
 18.2 
 
 21.9 
 
 2.00 
 
 
 
 3.3 
 
 4.0 
 
 5.3 
 
 6.7 
 
 8.0 
 
 9.3 
 
 10 7 
 
 12.0 
 
 13.3 
 
 16.7 
 
 20.0 
 
 2.50 
 
 
 
 
 3.4 
 
 4.6 
 
 5.7 
 
 6.9 
 
 8.0 
 
 9.1 
 
 10.3 
 
 11.4 
 
 14*3 
 
 17.1 
 
 3.00 
 
 
 
 
 3.0 
 
 4.0 
 
 5.0 
 
 6.0 
 
 7.0 
 
 8.0 
 
 9.0 
 
 10.0 
 
 12.5 
 
 15.0 
 
 3.50 
 
 
 
 
 
 3,6 
 
 4.4 
 
 5.3 
 
 6.2 
 
 7.1 
 
 8.0 
 
 8.9 
 
 11.1 
 
 13.3 
 
 4.00 
 
 
 
 
 
 3.2 
 
 4.0 
 
 4.8 
 
 5.6 
 
 6.4 
 
 7.2 
 
 8.0 
 
 10.0 
 
 12.0 
 
 5,00 
 
 
 
 
 
 
 3.3 
 
 4.0 
 
 4.7 
 
 5.3 
 
 6.0 
 
 6.7 
 
 8,3 
 
 10.0 
 
 6.00 
 
 
 
 
 
 
 
 3.4 
 
 4.0 
 
 4.6 
 
 5.1 
 
 5.7 
 
 7.1 
 
 8.6 
 
 Example of Pile Foundations. As an example of the 
 method of determining the necessary number of piles to support 
 a given building, we will determine the number of piles required 
 to support the side walls, and interior piers of the warehouse 
 
156 PILE FOUNDATIONS. 
 
 computed in Example 1. The method of computing the weights 
 being exactly the same in both cases, and the remarks regarding 
 the weight of people being applicable to pile foundations as well 
 as to foundations placed directly on the soil. 
 
 Data. From observation of the pile-driving for an adjacent 
 building it is found that piles driven from 20 to 30 feet, take a 
 set of 1 inch under a 1,200-lb. hammer falling 20 feet, and that 
 additional blows give about the same set. 
 
 Computation. From the above table we find that the safe load 
 for a fall of 20 ft. and penetration of 1 inch is 20 tons. Multi- 
 plying by the weight of our hammer in tons (.6), we have 12 tons 
 as the safe load per pile. 
 
 Referring to the computations on page 139, we see that the total 
 load on one lineal foot of footing is 25,920 Ibs., or about 13 tons. 
 As we must have at least two rows of piles, and the two piles will 
 support 24 tons, it follows that the spacing of the piles longitudi- 
 nally should be 24 -v- 13=1 ft. 10 ins. As this is too close, we 
 should use 3 rows of piles, spaced 2 ft. apart, and the longitudinal 
 spacing would then be 36-^-13=2 ft. 9 ins. The width of the 
 capping would be about five feet. 
 
 Under the Interior Piers. The load on the piles, under the in- 
 terior columns (p. 140) is 211,680 Ibs., or 105.8 tons. This di- 
 vided by 12, the safe load for one pile, gives 9 piles, or three rows 
 of three piles each, which should be spaced 2' 6" apart each way. 
 
 Some Instances of the Actual Load on Piles. The 
 following instances 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 design- 
 ing pile foundations. 
 
 Boston. At the new Southern R.R. Station three piles were 
 loaded with about 60* tons of pig iron (20 tons per pile), with- 
 out settlement. The allowed load was 10 tons per pile. 
 
 Piles 12 ins. in diameter at the butt, 6 ins. at the point, driven 
 31 ft. in hard blue clay, near Hay market Square, failed to show 
 movement under 30 tons. Ultimate load believed to be 60 
 tons.* Other piles driven 17.9 ft. sustained a load of 31 tons. 
 Average penetration under last ten blows of a 1,710-lb. hammer 
 falling from 9 to 12 feet varied from 0.4 to 0.95 ins. per blow for 
 fifteen piles. 
 
 Piles 25 ft. long under the Chamber of Commerce building 
 
 * Horace J. Howe, *' American Architect>" June 11. 1898. 
 
penetrated about 3 ins. under the last blow of a 2,000-lb. ram 
 falling about 15 feet. 
 
 Chicago. New Public Library building ; piles proportioned to 
 30 tons each. Tested to 50.7 tons without settlement. 
 
 Schiller Building; estimated load 55 tons per pile; building 
 settled from 1J to 2J ins. 
 
 Passenger Station, Northern Pacific Railroad, Harrison St.; 
 piles 50 ft. long carry 25 tons each without perceptible settlement. 
 
 The Art Institute and portions of the Stock Exchange rest 
 on piles, and also a large proportion of the warehouses and other 
 buildings on the banks of the river. 
 
 New York City. The Ivins (Park Row) Building is supported 
 by about 3,500 fourteen-inch 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 a refusal of 1 inch under a 20-foot blow 
 of a 2,000-lb. hammer. Material, fine dense sand to a depth of 
 over 90 feet. But few piles could be driven more than 15 or 20 
 feet. Average maximum load per pile, 9 tons.* 
 
 The American Tract Society Building is also supported by 
 piles. 
 
 Brooklyn, N. Y. Piles under the Government Graving Dock 
 driven 32 ft. on the average in fine sand mixed with fine mica 
 and a little vegetable loam are supposed to sustain from 10 to 
 15 tons each. 
 
 New Orleans. Piles driven from 25 to 40 ft. in a soft alluvial 
 soil carry safely from 15 to 25 tons with a factor of safety of 6 to 
 8. Patton. 
 
 Cost of Driving Piles. The cost of driving piles natu- 
 rally varies with the character of the soil, and the conditions 
 under which they are driven. 
 
 In 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. Piles were 70 ft. long, 8 
 ins. in diameter at the point, and 15 ins. at the head. 
 
 Average cost of driving 800 piles with the steam-hammer, 
 $2 each. 
 
 In New York Harbor 1,800 piles were driven by a steam-ham- 
 mer, 24 to 26 ft. into gravel and hard pan at a cost of 80 cents 
 each. 
 
 * For description of this foundation, see Engineering Record of July 23, 
 1898. 
 
158 SPREAD FOUNDATIONS. 
 
 In Chicago, 40 Norway pine piles were driven 45 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, 15 ft. deep into 
 hard sand each day at a cost of about 30 cts. each. In both 
 cases steam-hammers were used.* 
 
 In Boston, spruce piles from 30 to 45 ft. long cost from $3 to 
 $5 in place. Georgia pine piles as long as 70 ft. cost about $15 
 apiece for the piles themselves, and $2 or more each for the driv- 
 ing. Oak piles from 40 to 50 ft. long cost from $8 to $10 each 
 in place.*)* 
 
 References. A very valuable paper on " Some Instances 
 of Piles and Pile-driving, New and Old," by Horace J. Howe, 
 C.E., was published in the American Architect and Building News, 
 commencing June 11, 1898. The paper records a great many 
 tests and gives several formulas and many experiences of dis- 
 tinguished engineers. 
 
 Part I. of Building Construction and Superintendence also gives 
 much additional information in regard to pile foundations and 
 experiments on the bearing power of piles. 
 
 Much valuable information on piles is also given in " A Prac- 
 tical Treatise on Foundations," by W. M. Patton, C.E. John 
 Wiley & Sons, publishers. 
 
 SPREAD FOUNDATIONS. 
 
 Compressible soils are often met with that will bear from 1 
 to 2 tons per square foot with very little settlement, and with 
 a uniform settlement under the same unit pressure. 
 
 In such cases it is often cheaper to spread the foundations or 
 footings so as to reduce the unit pressure to the capacity of the 
 soil than to attempt to drive piles, or to go down to hard pan. 
 Spread footings may be built of concrete with iron tension bars, 
 of steel beams or girders, and concrete, or of timber. 
 
 Concrete with Iron Tension Bars. When the neces- 
 sary height can be obtained, spread footings composed of Port- 
 land cement concrete, with iron tension members, have many 
 qualities to recommend them. Such footings are easy of construc- 
 tion, they are cheap, and their durability is everlasting. The 
 iron being so completely imbedded in the concrete, it cannot 
 
 * American Architect, June 4, 1898, p. 78. 
 
 t George B. Francis, C.E., in American Architect, July 23, 1898. 
 
SPREAD FOUNDATIONS. 159 
 
 rust,* and hence there is no possibility of deterioration in the 
 lootings. 
 
 By the use of twisted iron or other forms of tension rods the 
 transverse strength of concrete footings may be made equal to 
 that of steel beams, but concrete footings require more height, f 
 
 Fig. 6 shows the most economical section for a concrete and 
 twisted iron footing. In building the footings with steel beams, 
 the strength of the concrete is practically wasted, while in this 
 method of construction it is all utilized. It has been proved that 
 the entire tensile strength of the twisted bars can be utilized, 
 and, being held continuously along their entire length by the con- 
 crete as a screw bolt is held by the nut, they neither draw nor 
 stretch, except as the concrete extends with them. 
 
 Fig. 6. 
 
 In building concrete footings, as shown in Fig. 6, a layer of 
 concrete from 3 to 6 inches thick, made in the proportion of 1 to 
 3 should first be laid, and the iron bars laid on and tamped down 
 into it. Another layer of 4 inches, mixed in the same propor- 
 tion, should then be laid, after which the concrete may be mixed 
 in the proportion of one to six. Each layer should be laid before 
 the preceding layer has had time to harden, otherwise they may 
 not adhere thoroughly. 
 
 The author has prepared Table III., giving the strength and 
 proportions of footings constructed in this way, which he be- 
 lieves to have a large margin of safety. Two sizes of bars are 
 
 * In cutting through a portion of a foundation built of concrete and iron, 
 and submerged in salt water, ten yeais after the work was done, no deterio- 
 ration to the iron whatever was found. Iron imbedded in concrete, with 
 the end projecting, has been found bright and clean after the projecting 
 end had completely rusted away. 
 
 t For description of tension bars see Chap. XXIII. 
 
160 
 
 SPREAD FOUNDATIONS. 
 
 given, with the corresponding safe loads for the footings, the other 
 measurements applying to both cases. The measurements in 
 the third column refer to the width of the brick or stone footing 
 resting on the concrete. The greater the width of this footing in 
 proportion to the width of the concrete, the less will be the strain 
 on the tension rods. 
 
 TABLE III. PROPORTIONS AND STRENGTH OF CON- 
 CRETE FOOTINGS WITH TWISTED IRON TENSION 
 BARS. 
 
 Width of 
 
 Thick- 
 
 Width of 
 
 Distance 
 
 Size of 
 
 Safe 
 
 Size of 
 
 Safe 
 
 Footing 
 in feet. 
 
 ness of 
 concrete. 
 
 Stone 
 footing. 
 
 between 
 centres 
 
 square 
 bar. 
 
 load per 
 lineal 
 
 square 
 bar. 
 
 load per 
 lineal 
 
 
 
 
 of bars. 
 
 
 foot. 
 
 
 foot. 
 
 
 Ft. In. 
 
 Ft. In. 
 
 Inches. 
 
 Inches. 
 
 Tons. 
 
 Inches. 
 
 Tons. 
 
 20 
 
 3 6 
 
 6 
 
 8 
 
 2 
 
 78 
 
 m 
 
 66 
 
 18 
 
 3 3 
 
 5 6 
 
 8 
 
 2 
 
 76 
 
 if! 
 
 56 
 
 16 
 
 2 10 
 
 5 
 
 
 m 
 
 73 
 
 \\^ 
 
 50 
 
 14 
 
 2 8 
 
 4 8 
 
 7 
 
 1% 
 
 70 
 
 1% 
 
 49 
 
 12 
 
 2 6 
 
 4 4 
 
 6 
 
 1% 
 
 65 
 
 1J4 
 
 48 
 
 10 
 
 2 3 
 
 4 
 
 6 
 
 ik 
 
 65 
 
 l 
 
 42 
 
 8 
 
 2 
 
 4 
 
 6 
 
 i 
 
 60 
 
 M 
 
 40 
 
 6 
 
 1 8 
 
 3 6 
 
 6 
 
 % 
 
 55 
 
 K 
 
 29 
 
 Piers. Footings for piers may be built in the same manner, 
 with two sets of bars laid crossways of each other, and also diag- 
 onally, as shown in Fig. 7. In the case of piers the pressure will 
 be more evenly distributed if the corners are cut off. The same 
 size of bars should be used for a pier as for a wall, whose footings 
 have the same projection beyond the masonry, and the depth 
 of the concrete should be the same. 
 
 Fig. 7 represents the construction of the pier footings under 
 the interior columns of a four-story factory for the Pacific Coast 
 Borax Co. at Bayonne, N. J. The footings are computed to 
 resist an upward pressure of the ground of 2,500 Ibs. per square 
 foot.* 
 
 This form of construction has been used to a considerable 
 extent in San Francisco and in the eastern States, and twisted 
 iron in connection with concrete is being more extensively used 
 every year. The right to use twisted iron in concrete is pro- 
 tected by letters patent, now owned by the Ransome Concrete 
 
 * For a description of this building and other illustrations, see Engineer- 
 ing Record of July 30, 1898. 
 
SPREAD FOUNDATIONS. 
 
 161 
 
 Machinery Co. of New York.* The corrugated bars controlled 
 by the St. Louis Expanded Metal Fireproofing Co. are also being 
 extensively used for spread footings. For detailed information 
 see 1903 catalogue of this company. 
 
 Steel Beam Footings. When it is necessary to make the 
 foundations from 8 to 15 feet wide, with a very small height to 
 the footings, as is the case in Chicago, steel beams must be used 
 to furnish the necessary transverse strength. Even when build- 
 
 Fig. 7. 
 
 ing on solid ground, it is claimed that iron and steel footings for 
 tall buildings, at the present price of steel, are cheaper than ma- 
 sonry footings. The author doubts, however, if steel footings 
 will prove as durable as those of masonry. 
 
 When used under walls, the beams are laid in one course at 
 right angles to the wall, and from 9 to 20 inches apart according 
 to the size of the beams, thickness of the concrete and estimated 
 
 * Twisted bars purchased from this company may be used, however, 
 without payment of further royalties. 
 
162 
 
 SPREAD FOUNDATIONS. 
 
 pressure per square foot. Over the centre of the platform of 
 beams is placed the brick or stone footings as 'shown in Fig. 8. 
 
 When used under piers, as is generally the case in the modern 
 tall building, the beams are usually arranged in two layers, as 
 shown in Fig. 9. The. bottom layer contains a sufficient number 
 of beams to cover the necessary bearing area. Above these is 
 laid a second layer of beams, at right angles to the first, and long 
 enough to reach the extreme outer edge of the outer beams of the 
 first layer. Upon the centre of the upper tier of beams is placed 
 
 TTT 
 
 r r 
 
 I . I 
 
 ilia 
 
 SIDE VIEW 
 
 CROSS SECTION. 
 Fig. 8. 
 
 the iron shoe of the column, or a heavy stone base. Frequently 
 the upper tier of beams is so wide that it cannot be well spanned 
 by a shoe, in which case a third layer of beams or a short riveted 
 girder or bolster is placed under the column. 
 
 When steel beam footings were first used, rails were employed 
 for the beams on account of their lesser cost, and they were built 
 up in five or six layers, but now that steel beams a"re so cheap it 
 is much better to use I-beams for the grillage and to build the 
 grillage in not more than two layers. When the upper layer is 
 composed of several beams, the author believes that, owing to 
 the bending of the beams in the lower layer, a greater strain is 
 
SPREAD FOUNDATIONS 
 
 163 
 
 brought on the two outer beams of the upper layer than on the 
 beams between, and that it is impossible to determine the 
 amount of this extra stress. For this reason the Author is 
 strongly of the opinion that it is better engineering to use but 
 two beams in the upper 
 course of a pier footing, or a 
 if sufficiently large beams 
 cannot be obtained, a 
 single riveted girder. , _ 
 
 In preparing the foot- 
 ings, the ground is first 
 carefully leveled and the 
 bottom of the pier loca- 
 ted. If the ground is not 
 compact enough to pej?- ( 
 mit of excavating for the 
 concrete bed without the 
 sides of the pit or trench 
 falling in, heavy planks a <- 
 or timbers should be set 
 up and fastened together 
 at the corners, and, if 
 necessary, tied between 
 with rods,to hold the con- 
 
 Slone 
 Footing 
 
 PLAN 
 
 
 III 
 
 Ifesasass: . ife^ 
 
 SECTION 
 Fig. 9. 
 
 crete in place and prevent 
 its spreading before it has 
 thoroughly set. A layer 
 of Portland cement con- 
 crete, made in the propor- 
 tion of 1 to 6, and from 6 to 12 inches thick, according to the 
 weight on the footings, should then be filled in between the tim- 
 bers and well rammed and leveled off. If the concrete is to be 
 12 inches thick it should be deposited in two layers. Upon this 
 concrete the beams should be carefully bedded in 1 to 2 Portland 
 cement mortar, so as to bring them nearly level and in line with 
 each other. 
 
 The distance apart of the beams, from centre to centre, must 
 not be so great that the beams will crush through the concrete, . 
 and on the other hand there must be a space of at least 2 inches 
 between the edges of flanges to permit the introduction of the 
 concrete filling. As soon as the beams are in place the spaces 
 between them should be filled with 1 to 6 concrete, the stone 
 
164 SPREAD FOUNDATIONS. 
 
 being broken to pass through a IJ-inch ring, and the concrete well 
 rammed into place, so that no cavities will be left in the centre. 
 The concrete must also be carried at least 3 inches beyond the 
 beams on sides and ends, and kept in place by planks or timbers. 
 
 If two or more layers of beams are used, the top of each layer 
 should be carefully leveled (after the concrete has been put in 
 place) with 1 to 2 Portland cement mortar, not more than J inch 
 thick over the highest beams, and in this the next layer of beams 
 should be bedded, and so on. 
 
 The stone or metal base plate or footing should also be bedded 
 in Portland cement mortar, not more than f inch thick, above 
 the upper tier of beams. 
 
 After the base plate or stone footing is in place at least 3 
 inches of concrete should be laid above the beams and at the 
 sides and ends, and when this is set the whole outside of the foot- 
 ings should be plastered with 1 to 2 Portland cement mortar. 
 
 Before the beams are laid they should be thoroughly cleaned 
 with wire brushes/and, while absolutely dry, either painted with 
 iron paint or else heated and coated with two coats of asphalt. 
 Before covering the beams with the concrete every portion of the 
 metal should be carefully examined, and wherever the paint or 
 asphaltum has been scraped off in handling the iron should be 
 thoroughly dried and the coating renewed. 
 
 Every pains should be taken to protect the beams from rust- 
 ing for, when unprotected, steel beams rust very quickly, and if 
 once the beams were subjected to the rusting process it would 
 probably not be long before the building commenced to settle.* 
 
 Calculations for the Size of the Steel Beams. 
 
 A. Beams under a wall, In determining the size of steel 
 beams to be placed under a wall, as in Fig. 8, the first step is to 
 determine the necessary width of the footing, which determines 
 the length of the beams, and then the projection P may be fixed. 
 The size of the beams depends upon the projection P and the 
 load to be supported. 
 
 The width of the footing is obtained by dividing the load per 
 lineal foot on the footing, by the safe resistance of the soil per 
 square foot. This also gives the length of the beams. 
 
 * Several engineers advocate placing the beams without paint, believing 
 that concrete is itself a better preservative than paint. The New York Build- 
 ing Code requires that the beams be painted, while the Chicago law does not. 
 
SPREAD FOUNDATIONS. 165 
 
 Knowing the length of the beams, the width of the masonry 
 footing may be decided upon. The wider the stone footing, or 
 the smaller the projection P, the less will be the transverse strain 
 on the beams. 
 
 The beams are computed only for the portion projecting be- 
 yond the stone footing, as the load on 'the beams directly under 
 the wall produces no transverse strain. 
 
 The beams are computed as if they resisted an upward pres- 
 sure of the ground, -or as if they were supported as in Fig. 10 and 
 
 Beam 
 
 Footing , ox . pj a te 
 
 Fig. 10. 
 
 loaded with a distributed load equal, per square foot, to the safe 
 resistance of the soil. 
 
 The formula for a beam loaded and supported in this way is 
 that for a beam fixed at one end and uniformly loaded over its 
 projection. The readiest method of computing the size of steel 
 beams thus loaded and supported is to determine the necessary 
 coefficient of strength for each beam, and then from the tables 
 giving the strength of steel beams, find the size of beam having a 
 coefficient equal to or next above the value determined. The 
 coefficient of strength is given in the tables in Chapter XV, in the 
 column headed C. 
 
 The necessary coefficient for the beams is found by the for- 
 mula 
 
 C=4XwXP 2 Xs . (1) 
 
 in which w represents the assumed bearing power of the soil in 
 tons per square foot, P the projection of the beam in feet, and 
 s the spacing or distance, centre to centre, of beams, also in feet. 
 X denotes multiplication. 
 
 Owing to the tendency of the beams, in bending, to concen- 
 trate the load on the outer edges of the masonry footing, and thus 
 
166 . SPREAD FOUNDATIONS. 
 
 crush them, which action would have the same effect on the beam 
 as lengthening the arm or projection, the author recommends 
 that when the course above the beams is of stone, brick, or con- 
 crete, at least one-third the width of the masonry footing be added 
 to the actual projection. 
 
 In determining the width of the footing, or the area of a pier 
 footing, the loads from the building should be computed as de- 
 scribed on page 139c The calculations above indicated will be 
 more clearty shown by the following example : 
 
 Example of Wall Footings. A building is to be erected on 
 a soil of which the safe bearing power is but 2 tons, and the 
 pressure on each lineal foot of the stone footing is 20 tons. It is 
 decided to build the footings as shown in Fig. 8. What should 
 be the dimensions and weight of the beams? 
 
 Answer. As the total pressure under each lineal foot of 
 wall is 20 tons, and the safe bearing power of the soil is 2 tons, the 
 footings must be 20-^2, or 10 feet wide. We will use 4-foot 
 granite blocks for the bottom course of the wall, which will give 
 an actual projection (P) of 3 feet for the beams. For making 
 the calculations we will add to the actual projection one-third of 
 4 feet or 16 inches, making the value of P 4 J feet. We will assume 
 1 foot for the spacing* of the beams, so that s will equal 1. The 
 beams must then have a coefficient of strength=4X^XP 2 Xs= 
 4 X 2 X (4 J) 2 X 1 = 150.22 tons. Examining the table giving the 
 strength of standard steel I-beams (Chapter XV) we find that a 
 10-inch 35-pound steel beam has a coefficient of 156. 2. tons, and 
 a 25-pound beam 130.2 tons; therefore we must use 35-pound 
 steel beams 10 feet long. If we spaced the beams 10 inches on 
 centres, s would equal f and C would equal 4x2X(4J) 2 Xi, or 
 125.1 tons, which would enable us to use 25-pound beams, thereby 
 effecting a saving of 50 pounds to the lineal foot of w r all. 
 
 To save making the above calculations in each case the Car- 
 negie Steel Company, Limited, publishes the following table 
 from which the size of the beams may be taken direct. 
 
 To apply the table, look down the column having a heading 
 equal to the resistance of the soil, and take the beam opposite 
 the number equal to, or just above, the projection of the beam. 
 
 Thus in the above example w=2 and the working projection 
 is 4.33. The nearest projection above 4.33 (in the column 
 headed 2, Table IV) is 4.90, which is opposite a 12-inch 31.5-lb. 
 beam, which would be cheaper than the 10-inch 35-lb. beam. 
 
 To use the table for other values of s than 1 foot, w should be 
 
SPREAD FOUNDATIONS. 
 
 IbV 
 
 TABLE IV, GIVING SAFE LENGTHS OF PROJECTIONS 
 "P" IN FEET (SEE FIG. 8), FOR "a" = l FOOT, AND 
 VALUES OF "w," RANGING FROM 1 TO 5 TONS. 
 
 Depth of beam. 
 
 Weight per foot. 
 
 w (Tons per square foot). 
 
 1 
 
 VA 
 
 * 
 
 2 
 
 2M 
 
 ^ 
 
 3 
 
 m 
 
 4 
 
 VA 
 
 5 
 
 In. 
 24 
 
 80.00 
 
 15.231 
 
 13.61 
 
 12.43 
 
 10.77 
 
 10.16 
 
 9.63 
 
 8.79 
 
 8.14 
 
 7,62 
 
 7.18 
 
 6.81 
 
 20 
 
 80.00 
 
 13.983 
 
 12.50 
 
 11.41 
 
 9.89 
 
 9.32 
 
 8.84 
 
 8.07 
 
 7.47 
 
 6.99 
 
 6.59 
 
 6.25 
 
 20 
 18 
 15 
 
 65.00 
 55.00 
 80.00 
 
 12.488 
 10.857 
 11.892 
 
 11.16 
 9.71 
 10.63 
 
 10.20 
 8.86 
 9.71 
 
 8.82 
 7.68 
 8.41 
 
 8.33 
 7.23 
 7.93 
 
 7.90 
 6.87 
 7.52 
 
 7.21 
 6.27 
 6.86 
 
 6.68 
 5.80 
 6.36 
 
 6.24 
 5.43 
 5.95 
 
 5.89 
 5.12 
 5.61 
 
 5.58 
 4.86 
 5.32 
 
 15 
 
 60.00 
 
 10.405 
 
 9.30 
 
 8.49 
 
 7.36 
 
 6.94 
 
 6.58 
 
 6.01 
 
 5.56 
 
 5.20 
 
 4.90 
 
 4.65 
 
 15 
 
 42.00 
 
 8.861 
 
 7.92 
 
 7.23 
 
 6.27 
 
 5.91 
 
 5.60 
 
 5.12 
 
 4.74 
 
 4.43 
 
 4.18 
 
 3.96 
 
 12 
 
 12 
 10 
 
 40.00 
 31.50 
 25.00 
 
 7.730 
 6.925 
 5.706 
 
 6.91 
 6.19 
 5.10 
 
 6.31 
 5.65 
 4.66 
 
 5.47 
 4.90 
 4.03 
 
 5.15 
 
 4.55 
 3.80 
 
 4.89 
 4.38 
 3.61 
 
 4.46 
 4.00 
 3.29 
 
 4.13 
 3.70 
 3.05 
 
 3.87 
 3.46 
 2.85 
 
 3.64 
 3.26 
 2.69 
 
 3.46 
 3.10 
 2.55 
 
 9 
 
 8 
 
 7 
 
 31.00 
 
 18.00 
 15.00 
 
 5.016 
 4.354 
 3.715 
 
 4.48 
 3.89 
 3.32 
 
 4.09 
 3.55 
 3.03 
 
 3.55 
 
 3.08 
 2.63 
 
 3.34 
 2.90 
 2.48 
 
 3.17 
 2.75 
 2.35 
 
 2.90 
 2.51 
 2.14 
 
 2.68 
 2.33 
 1.98 
 
 2.51 
 2.18 
 1.86 
 
 2.36 
 2.05 
 1.75 
 
 2.24 
 1.95 
 1.66 
 
 6 
 5 
 4 
 
 12.25 
 9.75 
 7.50 
 
 3.112 
 2.539 
 1.994 
 
 2.78 
 2.27 
 1.78 
 
 2.54 
 2.07 
 1.63 
 
 2.20 
 1.80 
 1.41 
 
 2.07 
 1.69 
 1.33 
 
 1.97 
 1.61 
 1.26 
 
 1.80 
 1.47 
 1.15 
 
 1.66 
 1.36 
 1.07 
 
 1.56 
 1.27 
 1.00 
 
 1.47 
 1.20 
 0.94 
 
 1.39 
 1.14 
 0.89 
 
 increased or decreased in the same ratio as s. Thus if &= 1 J ft. 
 w should be multiplied by 1J. Taking s=10", w=2X|=l. 
 The projection under 1J opposite a 10-inch 25-lb. beam is 4.66, 
 and as our projection was 4.33 it is evident that this beam would 
 answer for a spacing of 10 ins. 
 
 In general, however, it will be better to calculate the beams 
 by formula (1). 
 
 Beams under Piers. In this case the size of the lower beams 
 is determined in the same way as if under a wall, the length of P 
 being taken from the end of the beam to the centre of the outer 
 beam in upper tier. 
 
 I For the upper beams the load borne by each beam should be 
 computed and the coefficient of strength determined by the 
 formula 
 
 C=4X^XP (2) 
 
 w being in this case the total distributed load on either end of 
 
168 SPREAD FOUNDATIONS. 
 
 the beam in pounds, and P the distance from end of beam to the 
 base-plate above in feet. 
 
 Example. The basement columns of a ten-story building are 
 required to sustain a permanent load of 200 tons. 
 
 What should be the size of the beams in the footings, the sup- 
 porting power of the soil being but 2 tons? 
 
 Answer. Dividing the load by the bearing power of the soil 
 we have 100 square feet, or 10X10 feet, for the area of the foot- 
 ing. We will arrange the beams as shown in Fig. 9, using a cast- 
 iron bearing-plate 3 feet square under the column (instead of the 
 stone block shown). The distance between the centres of outer 
 beams in upper tier we will make 32 ins., thus making the value 
 
 jQ> 2' 8" 
 
 of P for the kwer beams = \ ' , or 3| ft. s we will make 
 
 2i 
 
 12 ins. or 1. 
 
 Then by formula 1, C=4X2X(3) 2 X 1=107.54 tons, which 
 is a little less than the coefficient for a 9-inch 25-lb. beam. As 
 the 10-inch 25-lb. beam will cost no more and will be stiffer we 
 should use that. 
 
 For the upper tier we will use five beams, spacing them 8 in. 
 on centres. From an inspection of the plan it is evident that 
 the five beams must support, or press down, an area equal to 
 abed, which in this case equals 3JX10 ft., or 35 sq. ft. As the 
 upward reaction is 2 tons per square foot, the five beams must 
 be figured to support 70 tons (2X35), or 14 tons each. The 
 projection will be 3* ft. Then by formula 2 ; C= 4 X 14 X 3J= 196 
 tons. The coefficient for a 12-inch 31i-lb. beam is 191.8, and 
 for a 12-inch 40-lb. beam 239. As it is well to use heavy beams 
 for the outer ones we will use two 12-inch 40-lb. beams and 
 three 12-inch, 31J-lb. beams in the upper tier. 
 
 If there were still another tier of beams the upper one would 
 be calculated in the same way. 
 
 If the cap is of stone, the value of P should be taken at least 
 6 inso greater than the actual projection, to allow of any crushing 
 of the stone or mortar. 
 
 The deepest beam for the weight should always be used, and 
 unless the beams in the upper tier have considerable excess of 
 strength the two outer beams should be heavy beams. 
 
 When the footings carry iron or steel columns in the basement, 
 as is generally the case, a cast-iron or steel base-plate should be 
 used, as shown in Fig. 11. This plate should be bedded in Port- 
 land cement directly above the beams, as previously described. 
 
SPREAD FOUNDATIONS. 16S 
 
 In placing the beams it is essential that they be arranged sym- 
 metrically under the base-plate, otherwise they will sink more 
 at one side than at the other. 
 
 Combined Footings. Two columns are often supported on one 
 footing, as shown in Fig. 11, and quite often four columns, one 
 near each corner. The computations for combined footings 
 are more complicated than for simple footings, especially when 
 the columns are unequally loaded, and require a considerable 
 knowledge of mechanics. The best presentation of the subject 
 with which the author is acquainted is in Freitag's Architectural 
 Engineering, second edition. 
 
 Description of Steel-beam Footing's, A very good 
 idea of what has been done in the way of supporting buildings 
 on spread footings of steel beams and girders, and of the various 
 arrangements that have been employed, may be obtained from 
 the descriptions of actual construction referred to below: 
 
 Surface Foundations, Engineering Record, July 2, 1898. 
 
 Fig. II. 
 
 Foundations of High Buildings, by W. B. Hutton, Engineer- 
 ing Record, September 23, 1893. 
 
 St. Paul Building, New York City, Engineering Record, June 
 25, 1898. 
 
 Harrison Building, Philadelphia, Engineering Record t Aug. 22, 
 1896. 
 
 Franklin Building (9 to 15 Murray Street), New York, Engi- 
 neering Record, May 28, 1898. 
 
 Buek Building, New York City, 25 ft. front, Engineering 
 Record, June 25, 1898. 
 
170 
 
 SPREAD FOUNDATIONS. 
 
 Masonic Temple, Chicago, Engineering Record, Aug. 13, 1898. 
 
 De Dino Building, New York City, Engineering Record, Aug. 
 13, 1898. 
 
 The Wilkes Building, New York City, Engineering Record, 
 June 7, 1890. 
 
 American Exchange Bank, New York City, Engineering 
 Record, Oct. 14, 1899. 
 
 Timber Footing's. For buildings of moderate height tim- 
 ber may be used for giving 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-inch plank laid close together and longitudinally 
 of the wall. Across these heavy timbers should be laid, spaced 
 about 12 inches from centres, the size of the timbers being pro- 
 portioned to the transverse strain. On top of these timbers 
 again should be spiked a floor of 3-inch plank of the same width 
 as the masonry footings which are laid upon it. A section of 
 such a footing is shown in Fig. 12. 
 
 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 foun- 
 dations are oak, Georgia pine, and Norway pine. Many of the 
 old buildings in Chicago rest on timber footings. 
 
 3 Inch plank 
 
 Heavy Timber 
 
 "HI 
 
 \2 inch plank 
 
 Fig. 12 
 
 Calculation for the Size of the Cross Timbers. The size of the 
 transverse timbers should be computed by the following formula : 
 
 Breadth in inches = 
 
 (3) 
 
 D 2 XA 
 w representing the bearing power in pounds per square foot, P 
 
SPREAD FOUNDATIONS. 171 
 
 the projection of the beam beyond the 3-inch plank in feet, 8 
 the distance between centres of beams in feet, and D the as- 
 sumed depth of the beam in inches. A is the constant for 
 strength, and should be taken at 90 for Georgia pine, 65 for oak, 
 60 for Norway pine, and 55 for common white pine or spruce. 
 
 Example. The side walls of a given building impose on the 
 foundation a pressure of 20,000 pounds per lineal foot; the soil 
 will only support, without excessive settlement, 2,000 pounds to 
 the square foot. It is decided for economy to build the footings 
 as shown in Fig. 12, using Georgia pine timber. What should 
 be the size of the transverse timbers? 
 
 Answer. Dividing the total pressure per lineal foot by 2,000 
 pounds, we have 10 feet for the width of the footings. The ma- 
 sonry footing we will make of granite or other hard stone, 4 feet 
 wide, and solidly bedded on the plank in Portland-cement mor- 
 tar. The projection P of the transverse beams would then be 3 
 feet. We will space the beams 12 inches from centres, so that 
 s=l, and will assume 10 inches for the depth of the beams. 
 
 rnu u f i /ON u ,uu i, 2X2000X9X1 ' 
 
 Then by formula (3), breadth in inches = = 4, 
 
 iuu x yu 
 
 or we should use 4"X1Q" timbers, 12 inches from centres. If 
 common pine timber were used we should substitute 55 for 90, 
 and the result would be 6J. 
 
 Foundations for Temporary Buildings. When 
 temporary buildings are to be built over a compressible soil, the 
 foundations may, as a rule, be constructed more cheaply of tim- 
 ber than of any other material, and in such cases the durability 
 of the timber need not be considered, as good sound lumber will 
 last two or three years in almost any place if thorough ventila- 
 tion is provided. 
 
 The World's Fair buildings at Chicago (1893) were, as a rule, 
 supported on timber platforms, proportioned so that the maxi- 
 mum load on the soil would not exceed 1J tons per square foot. 
 Only in a few places over "mud-holes" were pile foundations 
 used.* 
 
 Masonry Wells for Foundations. Where the site 
 of the building is composed of compressible soil overlaying bed- 
 rock or hard-pan, and especially where the site has been filled 
 or the conditions are not suitable for piling, wells of masonry 
 
 * A description of the foundations of these buildings may be found in 
 Part I, "Building Construction and Superintendence," p. 55. 
 
172 SPREAD FOUNDATIONS. 
 
 sunk to the bed-rock or hard-pan will generally prove as chesp 
 as any other equally good foundation. 
 
 The wells are formed by driving cylindrical tubes of from 4 to 
 6 ft. in diameter through the soil to the bearing stratum. The 
 tubes are usually made in short lengths and spliced as they are 
 sunk. After the tube has reached the firm stratum, it is exca- 
 vated and filled with brickwork or concrete, the masonry being 
 intended to support the weight, while the steel shell merely 
 forms a wall around the pier and enables it to be built. 
 
 The wells are arranged as isolated piers, with the walls of the 
 superstructure supported by steel girders resting on the piers. 
 
 A notable example of this type of foundation is that of the City 
 Hall of Kansas City, Mo.* 
 
 Such wells were also used under the new Stock Exchange in 
 Chicago. For the new Stock Exchange Building in New York 
 wooden cylinders were employed. 
 
 Caisson Foundations. In the case of the tall buildings 
 of New York City, which as a rule are built over a soil composed 
 of mud and quicksand, it has been found, in many cases, impos- 
 sible to safely support the building on the natural soil and cais- 
 sons sunk to the bed-rock by the pneumatic process have been 
 resorted to as the most satisfactory method of obtaining a foun- 
 dation. 
 
 Caissons have been used for many years in building the foun- 
 dations of bridges, but the first instance of their use for buildings 
 is believed to be in the foundations of the Manhattan Life In- 
 surance Company's building, New York City, in 1893. Since 
 that time caissons have been used in providing the foundation 
 for several buildings in that city. Caissons as used in building 
 foundations are made both cylindrical and rectangular in shape, 
 and they have been built both of wood and steel, the latter ma- 
 terial being more commonly used. Cylindrical caissons are the 
 most convenient and economical, but the positions of the col- 
 umns and the necessity of supporting two and often four col- 
 umns on the same caisson usually make it necessary to use rect- 
 angular caissons. 
 
 The size of the caissons vary according to the load and number 
 of columns to be supported. Caissons as small as 5 ft. in diame- 
 ter have been used, although from 8 to 10 ft. is a more common 
 
 * For illustrations, see Part I, "Building Construction and Superin- 
 tendence." 
 
SPREAD FOUNDATIONS. 173 
 
 size for cylindrical caissons. Rectangular caissons have been 
 used as large as 15JX25 ft. in plan. The usual height of the 
 caissons that have thus far been used is from 11 to 12 ft. 
 
 The caissons are sunk until they reach bed-rock (which lies 
 from 50 to 60 feet below the Broadway street-level in New York) ; 
 the surface of the rock is then cleaned and dressed to level sur- 
 faces and the caissons rammed full of concrete. On top of the 
 caissons, piers of hard-burned bricks are built to the proper 
 height to receive the superstructure, the piers being generally 
 built as the caissons descend, so that the top of the masonry will 
 always be above the water-line. The weight of the pier assists 
 in sinking the caisson. 
 
 "Although this process is costly, it has proved reliable and 
 applicable under the most troublesome conditions for carrying 
 masonry piers to solid rock at depths as great as 100 feet below 
 the water-line, although such great distances have not yet been 
 required for buildings. One of the greatest advantages claimed 
 for this method is the care and precision which can be exercised 
 in preventing the inflow of quicksand and outside materials and 
 thus avoiding any disturbance of the equilibrium in the sur- 
 rounding soils or settlements of adjacent loaded piers or the 
 undermining of walls. The pneumatic caisson consists of a steel 
 or wooden box with vertical sides and a flat top, but no bottom. 
 Its lower edges are provided with a cutting edge and it is made 
 air-tight and filled with air under any required pressure, which is 
 maintained by a powerful steam pump. Access is had to the 
 interior or working chamber through an extensible vertical shaft 
 in the roof surmounted by a small chamber or air lock with two 
 doors, the outer of which is closed whenever the inner one is 
 opened to give access to the shaft. As both doors are never 
 opened simultaneously, no direct communication is established 
 between the atmosphere and the interior air pressure, and only a 
 small quantity of compressed air is lost at each opening of the 
 outside door. 
 
 Two or more shafts and air locks are usually provided for 
 materials and for the workmen. The doors of the material lock 
 are successively opened and closed as quickly as possible, but in 
 the man lock the operation is a gradual one, because the pressure 
 in the lock must be slowly increased or diminished to avoid inju- 
 rious effects to the inmates. The men in the working chamber 
 excavate the earth underneath it and undermine its edges so that 
 it gradually sinks under the increasing load of the brick or stone 
 
174 SPREAD FOUNDATIONS. 
 
 masonry built up on the roof or heavy deck which forms the top 
 of the working chamber. The excavated material is hoisted to 
 the surface of the ground either in buckets through the material 
 locks, .or, when it is loose earth or mud, is blown up with water ! 
 through vertical pipes open on top and having their lower ends 
 sealed below the surface of the water in the interior of the caisson. 
 The caissons are lighted by electricity and often have telephone 
 communication with the superintendent's office above. Ex- 
 cavation is carried on by pick and shovel, and when necessary 
 by blasting with dynamite. Except at considerable depths 
 the men work the usual number of hours without experiencing 
 much evil effects from the increased pressure." * 
 
 A complete description of the foundation of the Manhattan 
 Life Insurance Building (N. Y.) may be found in the Engineer- 
 ing Record of Jan. 20, 1894, and an abstract of the same in 
 " Building Construction and Superintendence," Part I. 
 
 Descriptions of other caisson foundations may be found in the 
 following numbers of the Engineering Record, also in Freitag's 
 " Architectural Engineering." 
 
 July 13, 1896, American Surety Building, New York. 
 
 July 11, 1896, The Standard Block, (N. Y.). 
 
 Jan. 16, 1897, The Gillender Building (N. Y.), timber caisson. 
 
 Nov. 27, 1897, Five-foot cylindrical steel caissons. 
 
 Dec. 11, 1897, Empire Building (N. Y.) 
 
 Dec. 10, 1898, Residence (N. Y.) cylindrical wood caissons. 
 
 Oct. 28> 1898, McCready Building (N. Y.), cylindrical wood 
 caissons. 
 
 Sept. 28, 1901, Stock Exchange, N. Y., wood caissons, rec- 
 tangular and cylindrical. 
 
 Cantilever Foundations. 
 
 When buildings of skeleton construction are erected without 
 a party wall agreement, it is usually impossible to obtain a sym- 
 metrical foundation directly under the columns supporting the 
 side or party wall, and in such cases the foundation piers are 
 commonly built sufficiently inside of the wall line to give the 
 necessary spread to the footings, and at the same time have them 
 symmetrical with regard to the centre of pressure. Cantilever 
 girders resting on these piers as a fulcrum are then used to 
 
 * Engineering Record, July 30, 1898. 
 
SPREAD FOUNDATIONS. 
 
 175 
 
 carry the column next to the building line. By this method, 
 also, it is sometimes possible to build without undermining the 
 adjoining property. 
 
 Various arrangements of cantilevers have been used during 
 the past ten years, the particular arrangement being usually 
 determined by some peculiarity of the column groupings, or rela- 
 tion to adjoining building. 
 
 Figs. 13, 14, and 15 * show three different designs which illus- 
 trate fairly well the different types of cantilevers as used in 
 foundations. 
 
 Fig. 13. 
 
 Fig. 13 shows deep steel beams, used when the load on the 
 column resting on the cantilever produces such bending mo- 
 ments as can be taken up by the beams. In this type the long 
 end of the cantilever is connected to an interior column by means 
 of riveted connections. 
 
 Fig. 14 shows a method of cantilever construction where it is 
 not desirable to have a separate foundation under each column, 
 and a heavy box girder of suitable design is used to transmit the 
 various column loads to two independent foundations. Owing 
 to danger of unequal settlement in the supporting piers, which 
 would affect the stresses in the girder, this form of girder should 
 be avoided if possible. 
 
 Fig. 15 illustrates one of the latest types of cantilever founda- 
 tions, in which the objection to the continuous girder is over- 
 come. 
 
 * From the "Pocket Companion" of the Carnegie P-teel Co., Limited, by 
 permission. 
 
176 
 
 SPREAD FOUNDATIONS. 
 
 "An important feature in connection with cantilever construc- 
 tion is to adopt a pin support in place of resting the cantilever 
 
 Fig. 14. 
 
 beam directly on the top course of the foundation beams. For, 
 if the cantilever rests directly upon the upper course of founda- 
 tion beams, without a pin support, the outer beam nearest the 
 wall column will be strained more than any of the others, and 
 
 Fig. 15. 
 
 thus the centre of pressure will not be exactly in the middle of 
 the foundation, as it should be. 
 
 "The shoes for ordinary loads and conditions are made solid 
 of cast iron, and the pin of steel. 
 
 " The height of each shoe should not be less than 6 ins. and the 
 pin 2i ins. in diameter. Each individual case should be figured 
 by itself, the pin being figured for bearing, or crushing only. 
 
 "A clearance of J" to V is allowed between the cast shoes, 
 which are always faced, and the hole bored to suit the pin." * 
 
 * F. H. Hindi, C.E. 
 
Illustrated descriptions of cantilever foundations may be 
 found in the following numbers of the Engineering Record: 
 
 Cantilever Foundations for Small Buildings, Nov. 27, 1897. 
 
 Exchange Court Building, New York City, June 11, 1898. 
 
 Developments of Architectural Construction, July 30, 1898. 
 
 The calculations for cantilever foundations involve the deter- 
 mination of bending moment, shearing, and bucking in the girder 
 and the reaction on the fulcrum and at the long end of the girder. 
 
 The arrangements are so numerous that no special rules can be 
 given, but each case must be calculated by means of the general 
 principles relating 'to the strength of girders, and for determining 
 supporting forces, given elsewhere in this book. 
 
 Concrete Piles. Since the year 1902 concrete piles have 
 been introduced in this country, and for several years previous 
 they had been used to some extent in Europe. The practice of 
 French and German engineers has been to construct the piles on 
 the ground, casting them in a mould in which a steel skeleton 
 for reinforcement is first inserted and also a steel or cast-iron 
 shoe. After the piles have hardened a sufficient length of time 
 they are driven like timber piles, a cushioned cap being placed 
 on top of the pile to distribute the force of the blow evenly over 
 the concrete.* 
 
 In this country the practice thus far has been to construct the 
 piles in place by driving a hollow steel cylinder which retains 
 the walls of the hole in place until the concrete has been deposited 
 and rammed. As the filling-in of the concrete progresses, the 
 shell is drawn up, the lower end of the shell being always about 
 6 ins. below the top of the concrete. If desired, a reinforcing 
 skeleton can be placed in the shell before the concrete is poured, 
 but the piles are very strong without it. 
 
 Thus far two styles of shells have been successfully used, viz., 
 the " Simplex," controlled by the Simplex Concrete Piling Co. 
 of Philadelphia, and the Raymond Pile, controlled by the Ray- 
 mond Concrete Pile Co. of Chicago, from whom complete infor- 
 mation as to cost, carrying capacity, etc., may be obtained. 
 
 Concrete piles, although more expensive than timber piles, 
 possess many advantages over the latter, and can be used in 
 places where timber piles would not be durable. 
 
 They are capped with concrete or steel grillage in the same 
 manner as described for timber piles. 
 
 * For description of several types of cast piles, see the Engineering News 
 of March 10, 1904. 
 
178 MASONRY WALLS AND FOOTINGS. 
 
 CHAPTER III. 
 MASONRY WALLS AND FOOTINGS. 
 
 CEMENTS AND CONCRETES. 
 
 Footing Courses. Every foundation or bearing wall 
 overlaying anything except solid rock should rest on a footing or 
 base projecting beyond the wall on each side. On wet or com- 
 pressible soils these footings may be built of steel beams and 
 concrete, concrete and twisted iron, or timbers, as described in 
 Chapter II, but on firm soils the footings are almost invariably 
 either of concrete, stone, or brick. 
 
 Footings answer two important purposes : 
 
 1st. By distributing the weight of the structure over a larger 
 area of bearing surface, the pressure per square foot on the 
 ground is diminished and the liability to vertical settlement 
 correspondingly lessened. 
 
 2d. By increasing the area of the base of the wall they add 
 to its stability and form a protection against the danger of the 
 work being thrown out of plumb by any forces that may act 
 against it. Nearly every building law requires that every foun- 
 dation wall and every pier shall have a footing at least 12 inches 
 wider (6 ins. on each side) than the thickness of the wall or pier, 
 and this may be considered as the minimum projection, except 
 in rare instances where there may be a special reason for making 
 it less. On firm soils a projection of 6 ins. on each side of the 
 wall will generally reduce the unit pressure * to a point within 
 the safe resistance of the soil, but it is always wise to propor- 
 tion the footings to a uniform unit pressure, as explained on 
 pages 137-139. 
 
 To have any useful effect, footings must be well bedded and 
 have sufficient transverse strength to resist the upward reaction 
 on the projection. 
 
 Stone Footings. Stone foundation walls generally have 
 stone footings, although if the wall is heavily loaded a bottom 
 
 * Pressure per square foot. 
 
MASONRY WALLS AND FOOTINGS. 179 
 
 footing of concrete is advisable under the stone footing. If 
 practicable, stone footings should consist of stones having a 
 width equal to that of the footing. If impracticable to obtain 
 stones of this size, then two stones should be used, meeting under 
 the centre of the wall. In any event the footing courses should 
 extend inside of the course above, a distance equal to at least 
 1J times the projection, otherwise the stones will not be able 
 to transmit the necessary pressure, but will open at the joints 
 "as in Fig. 1. 
 
 Stone footings should be of hard, strong, and durable stone, 
 always laid on their natural bed 
 
 and be solidly bedded in mortar. 
 As a general rule, the thickness of 
 each course should be about equal 
 to its projection beyond the course 
 above. The most common defect 
 in large stone footings is that the 
 I J stones are not properly bedded, it 
 
 1jf t I being more difficult to bed a large 
 
 ' ^ "-' stone than a small one. The 
 F ' 9 ' ll stones should be laid in a thick bed 
 
 of mortar and worked with a bar sideways until firmly settled 
 into the mortar. 
 
 Offsets. The projection of the footings beyond the wall, or 
 the course above, is a point that must be 
 carefully considered, whatever be the 
 material of the footings. 
 
 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 will 
 depend upon the vertical pressure, the 
 transverse strength of the material, and the thickness of the 
 course. Each footing stone may be considered as a beam fixed 
 at one end and uniformly loaded, and in this way the safe pro- 
 jection may be calculated. 
 
 Table I gives the safe offset for masonry footing courses, in 
 terms of the thickness of the course, computed by a factor of safety 
 of 10. 
 
 It should be borne in mind that as each footing course trans- 
 mits the entire weight of the wall and its load, the pressure will 
 
180 MASONRY WALLS AND FOOTINGS. 
 
 TABLE I. 
 
 
 
 Offset for a pressure, in tons per 
 
 
 R. in 
 
 sq. ft. on the bottom of the course, of 
 
 Kind of footing. 
 
 Ibs. per 
 
 
 
 sq. in.* 
 
 
 
 
 
 
 
 
 
 0.5 
 
 1 
 
 2 
 
 3 
 
 5 
 
 10 
 
 Bluestone nagging 
 
 2700 
 
 3.6 
 
 2.6 
 
 1.8 
 
 1.5 
 
 1.2 
 
 .8 
 
 Granite 
 
 1800 
 
 2.9 
 
 2.1 
 
 1 5 
 
 1 2 
 
 1 
 
 7 
 
 Limestone 
 
 1500 
 
 2 7 
 
 1 9 
 
 1 3 
 
 1 i 
 
 9 
 
 6 
 
 Sandstone 
 
 1200 
 
 2 6 
 
 1.8 
 
 1 3 
 
 1.0 
 
 8 
 
 5 
 
 Slate 
 
 5400 
 
 5.0 
 
 3.6 
 
 2.5 
 
 2.2 
 
 1.5 
 
 1.2 
 
 Best hard brick 
 
 1200 
 
 2.6 
 
 1 8 
 
 1 3 
 
 1.0 
 
 .8 
 
 5 
 
 j 1 Portland 
 
 ) 
 
 
 
 
 
 
 
 Concrete ~\ 2 sand 
 
 > 150 
 
 8 
 
 6 
 
 4 
 
 
 
 
 (3 pebbles 
 
 f 
 
 
 
 
 
 
 
 ( 1 Rosendale. . . 
 
 ) 
 
 
 
 
 
 
 
 Concrete*! 2 sand 
 ( 3 pebbles 
 
 V 80 
 
 0.6 
 
 0.4 
 
 0.3 
 
 
 
 
 * Modulus of Rupture, values given by Prof. Baker in 
 Masonry Construction." 
 
 ; Treatise on 
 
 be greater per square foot on the upper courses, and the offsets 
 should be made proportionately less. 
 
 Concrete Footings. For all buildings of any great weight, 
 and especially if built on a clay soil, the author believes that ce- 
 ment concrete makes the best footing, and that it is even prefer- 
 able 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 being devoid of joints, it is like 
 a continuous beam, having sufficient strength to span any soft 
 spots that might happen to be in the foundation. When de- 
 posited in thin layers and well rammed the concrete also be- 
 comes firmly bedded on the bottom of the trenches, so that there 
 is no possible chance for settlement except that due to the com- 
 pression of the soil. 
 
 For footings, concrete should always be mixed with cement, 
 preferably Portland cement, and should have a thickness of at 
 least 8 ins., even under light buildings, and for buildings of more 
 than two stories, a thickness of at least 12 ins. In firm soils, such 
 as clay, the trenches should be accurately dug and trimmed to 
 the exact width of the footing, so that the concrete will fill the 
 trench. When the soil 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, 
 
MASONRY WALLS AND FOOTINGS. 
 
 181 
 
 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. 
 
 Concrete should be used as soon as mixed and should always 
 be deposited in layers, which as a rule should not exceed 6 ins. 
 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 trench. The 
 height from which the concrete is dumped, however, should not 
 exceed 4 feet above the bottom of the trench, as when falling 
 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 trench, it 
 should be levelled off and then tamped with a wooden rammer 
 weighing about 20 Ibs., 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 de- 
 positing the successive layers, the top of each layer should be 
 sprinkled before the next is deposited. 
 
 For buildings over five stories high, it is a good idea to place a 
 stone footing 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 either of brick or concrete. For interior 
 
 j BRICK 
 
 1$ BRICK 
 
 Fig. 3 
 
 Fig. 4 
 
 walls on dry ground, and in many 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 and 
 then be laid in single course for ordinary footings, the outside 
 
182 
 
 MASONRY WALLS AND FOOTINGS. 
 
 of the work being laid all headers, as in the accompanying illus- 
 trations, and no course projecting more than one fourth brick 
 beyond the one above it, except in the case of an 8- or 9-inch wall. 
 For brick footings under high or heavily loaded walls, each pro- 
 jecting course should be made double, the heading course above 
 and the stretching course below. Figs. 3, 4, 5, and 6 show foot- 
 ings for walls varying from one brick to three bricks in thickness. 
 
 2 BRICKS 
 
 Fig. 5 
 
 The bricks used for footings should be the hardest and sound- 
 est that can be obtained, and should be laid in cement or hy- 
 draulic lime mortar, either grouted or thoroughly slushed up, so 
 that every joint shall be entirely filled with mortar. The writer 
 favors grouting brick footings, that is, using thin mortar for 
 
 3 BRICKS 
 
 Fig. 6 
 
 filling the inside joints, as he has always found it to give very 
 satisfactory 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 
 
AINU JfUUllAlLBS. lOO 
 
 has been carefully levelled. All bricks laid in warm or dry 
 weather should be thoroughly wet before laying, for, if laid dry, 
 the bricks will rob the mortar of a large percentage of the moist- 
 ure it contains, greatly weakening the adhesion and strength of 
 the mortar. 
 
 Too much care canr^ot be bestowed upon the footing courses 
 of any building, as upon them depends much of the stability of 
 the work. If the bottom courses be not solidly bedded, if any 
 rents or vacuities are left in the beds of the masonry, or if the 
 materials themselves be unsound, or badly put together, the 
 effects of such carelessness are sure to show themselves sooner or 
 later, and almost always at a period when remedial efforts are 
 difficult and expensive. 
 
 Inverted Arches. When the external walls of a building 
 are divided into piers, with wide openings between, and the sup- 
 porting power of the soil is not more than two or three tons to the 
 square foot it may be desirable to connect the base of the piers 
 by means of inverted arches, for the purpose of distributing the 
 weight of the piers over the whole length of the footings, 
 
 Examples of inverted arch footings are shown by figures 7 and 
 8,* which represent respectively the construction employed in 
 the Drexel Building in Philadelphia and the World Building in 
 New York. 
 
 Unless the piers are about equally loaded,- however, it will be 
 difficult 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, other- 
 wise it may push out the corner pier. In the opinion of the 
 author, it is usually better to build the piers with separate foot- 
 ings, projecting equally on all four sides of the pier, and each pro- 
 portioned to the load supported. The intermediate wall may 
 be supported either by steel beams or arches as preferred. An 
 example showing the method of proportioning inverted arches is 
 given in Chapter III. of Part I., " Building Construction." 
 
 Foundation Walls. 
 
 This term is generally applied to those walls which are below 
 the surface of the ground, and which support the superstructure. 
 Walls whose chief office is to withhold a bank of earth, such as 
 around areas, are called retaining walls. 
 
 * From the Engineering Record of May, 1899, and Nov., 1890. 
 
184 
 
 MASONRY WALLS AND FOOTINGS. 
 
 Foundation walls may be built of brick, stone or concrete, the 
 former being the most common. Brick walls for foundations are 
 only suitable in very dry soils or in the case of party walls, where 
 there is a cellar or basement on each side of them. 
 
 Portland cement concrete is an excellent material for founda- 
 tion walls, and is being more extensively used for that purpose 
 
 Fig. 7 
 
 Fig. 8 
 
 every year. The concrete may be filled in between wooden 
 forms, which hold it in place until the cement has set, or concrete 
 blocks moulded so as to form a solid wall may be used. 
 
 If poured concrete is used the forms should be removed as soon 
 as the cement has set and the walls 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, not only makes 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. As 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 stone work and concrete varying in different 
 localities. A wall built of soft stone, or stone that is very irreg- 
 ular in shape, with no flat surfaces, is greatly inferior to a con- 
 crete wall, or even to a wall of good hard brick, and should be used 
 only for dwellings or light buildings. Stone walls should never 
 be less than 18 ins. thick, and should be well bonded, with full and 
 three quarter headers, and all spaces between the stones 
 filled solid with mortar and broken stone or spauls. 
 
The mortar for stone work should be made of hydraulic lime 
 or cement, and sharp and rather coarse sand. 
 
 The outside walls of cellars and basements should be plastered 
 smooth on the outside with 1 to 2, or 1 to 1 J cement mortar, 
 J inch to f inches thick. 
 
 In heavy clay soils it is a good idea to batter the walls on the 
 outside, making the wall from 6 ins. to a foot thicker at the bot- 
 tom than at the top. 
 
 The thickness of the foundation wall 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 foundation wail, to the depth of 12 ft. below the grade line, 
 shall be 4 ins. greater than the wall above for brick and 8 ins. for 
 stone, and for every additional 10 ft., or part thereof deeper, the 
 thickness shall be increased 4 ins. In all large cities the thick- 
 ness of the walls is controlled by law. For buildings where the 
 thickness is not so governed the following table will serve as a 
 fair guide : 
 
 TABLE II. THICKNESS FOR FOUNDATION WALLS. 
 
 Height of building. 
 
 Dwellings, Hotels, 
 etc. 
 
 Warehouses. 
 
 Brick. 
 
 Stone. 
 
 Brick. 
 
 Stone. 
 
 Two stories 
 
 Inches. 
 12 or 16 
 16 
 20 
 24 
 28 
 
 Inches. 
 
 20 
 20 
 24 
 
 28 
 32 
 
 Inches. 
 
 16 
 20 
 24 
 
 24 
 
 28 
 
 Inches. 
 20 
 24 
 28 
 28 
 32 
 
 Three stories 
 
 Four stories 
 
 Five stories . 
 
 Six stories 
 
 
 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 strain which comes upon any 
 horizontal section of such a wall, which can be ascertained, is 
 the direct weight of the wall above, and the pressure due to the 
 floors and roof. 
 
 In most walls, however, there is more or less tendency to 
 buckle, to overcome which it is necessary to make the walls 
 thicker than would be required to resist the direct crushing stress. 
 The resistance to fire should also be taken into account in de- 
 ciding on the thickness of any given wall. 
 
186 MASONRY WALLS AND FOOTINGS. 
 
 The strength of a wall also depends very much upon the qual- 
 ity of the materials used and upon the way in which the wall is 
 built. 
 
 A wall bonded every twelve inches in height, and with every 
 joint slushed full with good rich mortar, will be as strong as a 
 poorly built wall four inches 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 of the country the minimum thickness of the w r alls is pre- 
 scribed by law or ordinance, and as these requirements are gen- 
 erally ample they are commonly adhered to by architects when 
 designing brick buildings. Table III. gives a comparison of the 
 thickness of brick walls required for mercantile buildings in the 
 representative cities of the different sections of the United States, 
 and affords 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 are generally permitted to be 4 ins. 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, tenements, hotels, and office buildings in the city of 
 Chicago, which is as light as such walls should be built. Most 
 cities require 13-inch walls in the upper story of three-story build- 
 ings, and for large two-story dwellings. 
 
 In St. Louis the top two stories of dwellings are required to 
 be 13 ins. thick, the next two, below, 18 ins. thick, the next two 
 22 ins., and the next two 26 ins. 
 
 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 ins., including the thickness of the floor, as the New 
 York and Boston laws give the height of the walls in feet instead 
 of in stories. When the height of stories exceeds these measure- 
 ments the thickness of the walls in some cases will have to be 
 increased. 
 
 The maximum height of stories permitted by the Chicago 
 ordinance with these thicknesses of walls is 18 ft. in first story, 
 15 ft. in second story, 13 ft. 6 ins. in the third, and 12 ft. in the 
 stories above. 
 
MASONRY WALLS AND FOOTINGS. 
 
 187 
 
 TABLE III. THICKNESS OF WALLS IN INCHES, FOR 
 MERCANTILE BUILDINGS AND PUBLIC STABLES, 
 AND, EXCEPT IN CHICAGO, FOR ALL BUILDINGS 
 OVER FIVE STORIES IN HEIGHT. 
 
 TToicrVif rf 
 
 
 
 
 
 Sto 
 
 "ies. 
 
 
 
 
 Building. 
 
 
 1st, 
 
 2d. 
 
 3d. 
 
 4th. 
 
 5th. 
 
 6th. 
 
 7th. 
 
 8th. 
 
 
 'Boston . 
 
 16 
 
 I 9 
 
 
 
 
 
 
 
 
 New York 
 
 12 
 
 12 
 
 
 
 
 
 
 
 
 Chicago 
 
 12 
 
 12 
 
 
 
 
 
 
 
 Two j 
 
 Minneapolis. . . . 
 
 12 
 
 12 
 
 
 
 
 
 
 
 Stories. 
 
 St. Louis. . ' 
 
 18 
 
 13 
 
 
 
 
 
 
 
 
 Denver 
 
 13 
 
 13 
 
 
 
 
 
 
 
 
 San Francisco 
 ^ New Orleans 
 
 f Boston 4 . 
 
 17 
 13 
 
 20 
 
 13 
 13 
 
 16 
 
 16 
 
 
 
 
 
 
 
 New York. 
 
 16 
 
 16 
 
 12 
 
 
 
 
 
 
 
 Chicago 
 
 16 
 
 12 
 
 12 
 
 
 
 
 
 
 Three 
 
 ATinneapolis . 
 
 16 
 
 12 
 
 I 9 
 
 
 
 
 
 
 Stories. 
 
 St. Louis 
 
 18 
 
 18 
 
 13 
 
 
 
 
 
 
 
 Denver 
 
 17 
 
 17 
 
 13 
 
 
 
 
 
 
 
 Sari Francisco 
 New Orleans 
 
 17 
 13 
 
 17 
 13 
 
 13 
 13 
 
 
 
 
 
 
 
 f Boston 
 
 20 
 
 16 
 
 16 
 
 16 
 
 
 
 
 
 
 New York 
 Chicago 
 
 16 
 20 
 
 16 
 16 
 
 16 
 16 
 
 12 
 12 
 
 
 
 
 
 Four 
 
 Minneapolis. 
 
 16 
 
 16 
 
 12 
 
 12 
 
 
 
 
 
 Stories. 
 
 St. Louis 
 
 22 
 
 18 
 
 18 
 
 13 
 
 
 
 
 
 
 Denver 
 
 21 
 17 
 
 17 
 
 17 
 
 17 
 17 
 
 13 
 13 
 
 
 
 
 
 
 [New Orleans. . . . 
 
 18 
 
 18 
 
 13 
 
 13 
 
 
 
 
 
 
 fBoston. . . 
 
 20 
 
 20 
 
 9 
 
 20 
 
 16 
 
 
 
 
 
 New York 
 
 20 
 
 16 
 
 16 
 
 16 * 
 
 16 
 
 
 
 
 
 Chicago. . 
 
 20 
 
 *>0 
 
 16 
 
 16 
 
 16 
 
 
 
 
 Five , 
 Stories. 
 
 Minneapolis 
 St Louis. . 
 
 20 
 22 
 
 16 
 22 
 
 16 
 
 18 
 
 12 
 18 
 
 12 
 13 
 
 
 
 
 
 Denver . . . 
 
 21 
 
 21 
 
 17 
 
 17 
 
 13 
 
 
 
 
 
 San Francisco 
 
 21 
 
 17 
 
 17 
 
 J7 
 
 13 
 
 
 
 
 
 1. New Orleans. . . . 
 
 18 
 
 18 
 
 18 
 
 13 
 
 13 
 
 
 
 
 
 
 24 
 
 20 
 
 20 
 
 20 
 
 20 
 
 16 
 
 
 
 
 New York. 
 
 24 
 
 20 
 
 20 
 
 20 
 
 16 
 
 16 
 
 
 
 
 Chicago 
 
 20 
 
 20 
 
 20 
 
 16 
 
 16 
 
 16 
 
 
 
 feix 
 
 Minneapolis 
 
 20 
 
 20 
 
 16 
 
 16 
 
 16 
 
 12 
 
 
 
 Stories. 
 
 St. Louis 
 Denver 
 
 26 
 26 
 
 22 
 
 21 
 
 22 
 
 21 
 
 18 
 17 
 
 18 
 17 
 
 13 
 13 
 
 
 
 
 San Francisco 
 ^New Orleans. . * . . . 
 
 f Boston. 
 
 21 
 
 22 
 
 24 
 
 21 
 18 
 
 20 
 
 17 
 
 18 
 
 20 
 
 17 
 
 18 
 
 20 
 
 17 
 13 
 
 20 
 
 13 
 13 
 
 90 
 
 16 
 
 
 
 New York 
 
 28 
 
 24 
 
 24 
 
 20 
 
 20 
 
 16 
 
 16 
 
 
 
 Chicago 
 
 20 
 
 20 
 
 20 
 
 20 
 
 16 
 
 16 
 
 16 
 
 
 Seven , 
 
 Minneapolis 
 
 20 
 
 20 
 
 20 
 
 16 
 
 16 
 
 16 
 
 12 
 
 
 Storied. " 
 
 [St. Louis 
 
 26 
 
 26 
 
 22 
 
 22 
 
 18 
 
 18 
 
 13 
 
 
 
 Denver 
 
 26 
 
 21 
 
 21 
 
 21 
 
 17 
 
 17 
 
 17 
 
 
 
 New Orleans 
 f Boston 
 
 22 
 
 28 
 
 22 
 24 
 
 18 
 ?0 
 
 18 
 20 
 
 18 
 20 
 
 13 
 20 
 
 13 
 20 
 
 16 
 
 
 New York 
 
 32 
 
 28 
 
 24 
 
 24 
 
 20 
 
 20 
 
 16 
 
 16 
 
 
 Chicago 
 
 24 
 
 24 
 
 9 
 
 20 
 
 20 
 
 16 
 
 16 
 
 16 
 
 Eight 
 
 Minneapolis. 
 
 24 
 
 20 
 
 20 
 
 9Q 
 
 16 
 
 16 
 
 16 
 
 12 
 
 Stories. 
 
 St. Louis 
 
 30 
 
 26 
 
 26 
 
 9 2 
 
 22 
 
 13 
 
 18 
 
 13 
 
 
 Denver . . 
 
 30 
 
 26 
 
 21 
 
 21 
 
 21 
 
 17 
 
 17 
 
 17 
 
 
 
 22 
 
 2 9 
 
 22 
 
 18 
 
 18 
 
 18 
 
 13 
 
 13 
 
 
 
 
 
 
 
 
 
 
 
188 
 
 MASONRY WALLS AND FOOTINGS. 
 
 
 Stories. 
 
 Building. 
 
 
 
 
 43 
 
 43 
 
 43 
 
 
 
 
 
 
 
 
 " 
 
 3 
 
 CO 
 
 
 
 
 CO 
 
 K 
 
 oo 
 
 1 
 
 < 
 
 5 
 
 Cl 
 
 f Boston 
 
 28 
 
 24 
 
 24 
 
 20 
 
 20 
 
 20 
 
 20 
 
 20 
 
 16 
 
 
 
 
 1 New York.. . 
 
 32 
 
 32 
 
 28 
 
 24 
 
 24 
 
 20 
 
 20 
 
 16 
 
 16 
 
 
 
 
 Nine ! Chicago 
 
 24 
 
 24 
 
 24 
 
 20 
 
 20 
 
 20 
 
 16 
 
 16 
 
 16 
 
 
 
 
 Stories, j Minneapolis . 
 
 24 
 
 24 
 
 20 
 
 20 
 
 20 
 
 16 
 
 16 
 
 16 
 
 12 
 
 
 
 
 I St. Louis 
 
 30 
 
 30 
 
 26 
 
 26 
 
 22 
 
 22 
 
 18 
 
 18 
 
 13 
 
 
 
 
 1. Denver 
 
 30 
 
 26 
 
 26 
 
 21 
 
 21 
 
 21 
 
 17 
 
 17 
 
 17 
 
 
 
 
 f Boston 
 
 28 
 
 28 
 
 24 
 
 24 
 
 20 
 
 20 
 
 20 
 
 20 
 
 20 
 
 16 
 
 
 
 1 New York. . 
 
 36 
 
 32 
 
 32 
 
 28 
 
 24 
 
 24 
 
 20 
 
 20 
 
 16 
 
 16 
 
 
 
 Ten j Chicago 
 
 28 
 
 28 
 
 24 
 
 24 
 
 24 
 
 20 
 
 20 
 
 20 
 
 16 
 
 16 
 
 
 
 Stories. ] Minnea'polis. 
 
 24 
 
 24 
 
 24 
 
 20 
 
 20 
 
 20 
 
 16 
 
 16 
 
 16 
 
 12 
 
 
 
 St. Louis. .. . 
 
 34 
 
 30 
 
 30 
 
 26 
 
 26 
 
 22 
 
 22 
 
 IS 
 
 18 
 
 13 
 
 
 
 ^ Denver 
 
 30 
 
 30 
 
 
 26 
 
 21 
 
 21 
 
 21 
 
 17 
 
 17 
 
 17 
 
 
 
 1 Boston 
 
 36 
 
 32 
 
 32 
 
 28 
 
 28 
 
 24 
 
 20 
 
 20 
 
 20 
 
 20 
 
 16 
 
 
 New York... 
 Chicago. . . 
 
 36 
 28 
 34 
 
 33 
 28 
 34 
 
 32 
 24 
 30 
 
 28 
 24 
 30 
 
 28 
 24 
 26 
 
 24 
 
 20 
 26 
 
 24 
 
 20 
 
 22 
 
 20 
 20 
 22 
 
 20 
 16 
 
 18 
 
 16 
 
 18 
 18 
 
 16 
 16 
 13 
 
 
 Q, T = 
 
 St. Louis. .. . 
 
 Denver 
 
 30 
 
 30 
 
 26 
 
 26 
 
 26 
 
 21 
 
 21 
 
 21 
 
 17 
 
 17 
 
 17 
 
 
 1 Boston. . . 
 
 36 
 
 36 
 
 3 9 
 
 32 
 
 28 
 
 9 8 
 
 24 
 
 20 
 
 20 
 
 
 
 20 
 
 16 
 
 J\ ew I orj. . . 
 
 40 
 
 36 
 
 36 
 
 32 
 
 32 
 
 28 
 
 24 
 
 24 
 
 20 
 
 20 
 
 16 
 
 16 
 
 
 28 
 34 
 
 28 
 34 
 
 28 
 34 
 
 30 
 
 24 
 30 
 
 24 
 26 
 
 20 
 26 
 
 20 
 
 22 
 
 20 
 22 
 
 16 
 18 
 
 16 
 18 
 
 16 
 13 
 
 Q, ^^S?" " ' ' 
 
 ot. LOUIS. .. . 
 
 Denver . . 
 
 30 
 
 30 
 
 30 
 
 26 
 
 
 26 
 
 21 
 
 
 
 17 
 
 17 
 
 17 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 TABLE IV. THICKNESS OF ENCLOSING WALLS, FOR 
 RESIDENCES, TENEMENTS, HOTELS, AND OFFICE 
 BUILDINGS. CHICAGO BUILDING ORDINANCE. 
 
 
 -P 
 
 1 
 
 PQ 
 
 12 
 12 
 16 
 20 
 20 
 20 
 24 
 24 
 28 
 28 
 28 
 32 
 
 Stories. 
 
 2 
 
 
 
 i 
 
 8 
 12 
 16 
 16 
 20 
 20 
 20 
 24 
 24 
 24 
 
 43 
 -t 
 
 12 
 12 
 16 
 16 
 20 
 20 
 20 
 24 
 24 
 
 ^ 
 
 43 
 
 43 
 
 43 
 
 43 
 
 | 
 
 43 
 
 43" 
 
 s 
 
 10 
 
 12 
 
 12 
 16 
 16 
 20 
 20 
 20 
 24 
 
 CO 
 
 12 
 12 
 16 
 16 
 20 
 20 
 20 
 
 t^ 
 
 00 
 
 O 
 
 Basement and 
 Two-story 
 Three-story 
 Four-story. . 
 
 8 
 12 
 12 
 16 
 16 
 20 
 24 
 24 
 24 
 24 
 28 
 28 
 
 8 
 12 
 16 
 16 
 16 
 20 
 24 
 24 
 24 
 24 
 28 
 
 12 
 12 
 16 
 16 
 20 
 20 
 
 12 
 
 12 
 16 
 16 
 20 
 
 12 
 12 
 16 
 16 
 
 12 
 12 
 16 
 
 12 
 12 
 
 12 
 
 Five-story 
 Six-storv 
 
 Seven-story 
 
 Fjight-story . . . 
 
 Nine-story 
 Ten-story 
 
 
 Twelve-story. 
 
 
 General Rule for Thickness of Walls. Although 
 there is a great difference in the thicknesses given in Table III., 
 more indeed than there should be, yet a general rule might be de- 
 
MASONRY WALLS AND FOOTINGS. 189 
 
 duced from the table, for mercantile buildings over four stories 
 in height, which would be somewhat as follows : 
 
 For brick equal to those used in Boston or Chicago, make the 
 thickness of the three upper stories 16 ins., of the next three be- 
 low 20 ins., the next three 24 ins., and the next three 28 ins. 
 For a poorer quality of material make only the two upper stories 
 16 ins. thick, the next three 20 ins., and so on down. 
 
 In buildings less than five stories in height the top story may 
 be 12 ins. in thickness. 
 
 In determining the thickness of walls the following general 
 principles should be recognized : 
 
 First. That walls of warehouses and mercantile buildings 
 should be heavier than those used for living or office purposes. 
 
 Second. That high stories and clear spans exceeding 25 ft. 
 require thicker walls. 
 
 Third. That the length of the wall is a source of weakness, 
 and that the thickness should be increased 4 ins. for every 25 ft. 
 over 100 or 125 ft. in length. (In New York the thickness in the 
 table must be increased for buildings exceeding 105 ft. in depth. 
 In Western cities the tables are compiled for warehouses 125 ft. 
 in depth, as that is the usual depth of lots in those cities.) 
 
 Fourth. That walls containing over 33 per cent, of openings 
 should be increased in thickness. 
 
 Fifth. Partition walls may be 4 ins. less in "thickness than the 
 outside walls if not over 60 ft. long, but no partition to be less 
 than 8 ins. thick. 
 
 Walls Faced with Ashlar. " In reckoning the thickness 
 of walls, no allowance shall be made for ashlar, unless it is 8 
 ins. or more thick, in which case the excess over 4 ins. shall be 
 reckoned as part of the thickness of the wall. Ashlar shall be 
 at least 4 ins. thick and properly held by metal clamps to the 
 backing, or properly bonded to the same." Boston Building 
 law. 
 
 Stone Walls should generally be 4 ins. 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, except in 
 concrete construction. 
 
190 MASONRY WALLS AND FOOTINGS. 
 
 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 walls on either side of the air- 
 space shall be not less than 8 ins. thick, and shall be securely 
 tied together with ties not more than 2 ft. apart." 
 
 For a description of the construction of hollow brick walls, see 
 Part I of "Building Construction." 
 
 Walls of Cement Blocks* Blocks made of Portland- 
 cement concrete, and formed in moulds, are rapidly coming into 
 use for building walls and partitions. Within the past two years 
 several 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 or are now in process of con- 
 struction with walls built of these blocks. Most of the blocks 
 are moulded so as to form a hollow wall, and are made to imitate 
 natural stone. 
 
 Block construction 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. The 
 author believes that such walls are less liable to crack and will be 
 more uniform in color and texture. 
 
 Concrete walls in various forms will undoubtedly be more ex- 
 tensively used during the coming decade. 
 
 Party Walls. There is much diversity in building regu- 
 lations regarding the thickness of party walls, although they all 
 agree in that such walls should never be less than 12 ins. 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 ins. thicker 
 or thinner than for independent side walls. 
 
 When the walls are proportioned by the rule previously given 
 the author believes that the thickness of the party walls should 
 be increased 4 ins. on each story. The floor load on party walls 
 is obviously twice that on side walls, and the necessity for thor- 
 ough fire protection is greater in the case of party walls than in 
 other walls. 
 
 Curtain Walls. 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 ins. 
 thick for the whole height of a twelve- or fifteen-story building. 
 
"For skeleton construction, the Chicago ordinance allows 
 veneer walls of 12 ins. thickness for any height within the max- 
 imum limit of 130 ft. The New York City building law re- 
 quires the use of 12-in. curtain walls for 75 ft. of the uppermost 
 height thereof, and 4 ins. additional thickness for every lower 
 60 ft. section down to the sidewalk level. But, on account of the 
 severity of these requirements as applied to very high cage-con- 
 struction buildings, permission is frequently given by the Board 
 of Examiners, who are empowered to modify the building laws 
 within certain limits, to reduce the above-mentioned thickness 
 to 12 ins. and 16 ins. for buildings greatly exceeding 1QO ft. in 
 height. They have never, however, permitted a uniform thick- 
 ness of 12 ins. for buildings over twelve stories in height." * 
 
 A few of the earlier tall buildings were built with self-sustain- 
 ing walls, starting from the foundation, while columns were in- 
 troduced 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-sustain- 
 ing walls. The main roof is 191 ft. above the street level, mak- 
 ing 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-eotta, 
 the thickness increasing from 2 ft. at the top to as much as 11 
 ft. 4 ins. near the bottom, where the walls are offset to a con- 
 crete footing 15 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." "Architec- 
 tural Engineering," p. 148. 
 
 For a more extended discussion of curtain walls the reader is 
 referred to Freitag's "Architectural Engineering," and to Birk- 
 mire's " Planning and Construction of High Office Buildings." 
 
 Durability -of Iron Solidly Imbedded in Masonry. 
 
 I believe that, imbedded in lime-mortar at such depth as to 
 
 protect it from the air, hoop-iron bond is indestructible. 
 M. C. MEIGS, May 17, 1887. 
 
 Iron ties imbedded in cement concrete, even when under water, 
 will not rust, and may be considered as imperishable, provided 
 that the concrete does not crack so as to admit the water. 
 
 * Architectural Engineering, p. 164. 
 
192 HYDRAULIC CEMENTS. 
 
 Many of our most prominent engineers consider Portland ce- 
 ment a better preservative of iron or steel than any paint. 
 
 HYDRAULIC CEMENTS. 
 
 Two kinds of hydraulic cement are used in this country in 
 laying up mason work, and in making concrete, cement floors, 
 walks, etc., viz., natural-rock cement and Portland or artificial 
 cement. 
 
 Natural-rock Cement. These cements are made by 
 burning and finely grinding a natural rock whose principal in- 
 gredients are carbonate of lime, carbonate of magnesia, and 
 alumina (clay). 
 
 The principal localities in the United States where natural 
 cements are made for shipment are : Rosendale, N. Y. ; Akron, 
 N. Y.; Louisville, Ky.; Utica, 111.; La Salle, 111.; Milwaukee, 
 Wis. ; Fort Scott, Kan. ; Mankato, Minn. ; and Cement, Ga. 
 
 Brands. Natural cements are most generally known by the 
 name of the locality from which the material is obtained, as, for 
 instance, Rosendale Cement, Utica Cement, Louisville Cement, 
 etc. Each manufacturer, however, has a registered brand or 
 trade-mark for his product. The brands indicated below have 
 probably the largest sale amongst natural cements. 
 
 "Brooklyn Bridge," "Hoffman/' " Newark-Rosendale, " all 
 Rosendale cements. The "Utica," "Milwaukee," "Louisville," 
 and "Fort Scott" cements are also extensively used in the Mid- 
 dle West, and are good cements. 
 
 PKOPERTIES AND CHABACTERISTICS OF 
 NATURAL CEMENTS. 
 
 Color. Natural cements are not as uniform in color as the 
 Portland cements, but vary from a light to a dark brown, accord- 
 ing to the varying proportions of* oxide of iron and impurities 
 contained in the stone. "In Rosendale cement a light color 
 indicates an inferior underburnt rock." Utica cement is almost 
 a cream color. 
 
 Weight. The Rosendale cements vary in weight from 49 to 
 56 pounds per cu. ft. Every barrel of the Newark-Rosendale 
 and Brooklyn Bridge brands contains 300 Ibs., net. Akron, 
 Milwaukee, Utica, and Louisville cements weigh 265 Ibs. per 
 barrel, net. 
 
NATURAL CEMENTS. 193 
 
 Time of Setting 1 . The natural cements begin to set quicker 
 than the Portland cements, generally within thirty minutes and 
 always within an hour. Cement has set when it resists the im- 
 pression of the finger-nail. 
 
 Lime paste added to cement mortar will delay the setting and 
 make it work easier, but it also reduces its strength. 
 
 Lime should never be added when the mortar is to be used in 
 a wet or damp place. 
 
 Strength. A good natural cement should show a tensile 
 strength, neat, of at least 80 Ibs. per sq. in. when one week old, 
 and 120 Ibs. at the end of thirty days, or when mixed with one 
 part sand, 40 Ibs. at the end of one week and 70 Ibs. at the end 
 of a month. The best brands will give results 25% in excess of 
 these figures. 
 
 The strength of 1 to 2 natural-cement mortar is about equal 
 to Portland-cement mortar 1 to 4. 
 
 Proportions of Cement and Sand for Mortar 
 and Concrete. For mortar for stone rubble and ordinary 
 brickwork one part of natural cement may be mixed with three 
 parts of sand by measure. 
 
 For brick piers and first-class brickwork, not more than two 
 parts sand to one of cement, by measure, should be used, and one 
 or one and one -half parts of sand will make a still stronger 
 mortar. 
 
 Any admixture of sand with cement reduces the strength. 
 
 For cement plastering, use equal parts of sand and cement. 
 
 For concrete, natural cements may be used in the proportion 
 of one part cement to two parts of sand and four of gravel or 
 stone chips. 
 
 Mortar that has set should not be retempered, but should be 
 thrown away, as it will not take a true set a second time. 
 
 Natural-cement mortar possesses sufficient adhesion and 
 crushing strength for any ordinary masonry, and when mixed 
 in the proportion of 1 to 2 is probably just as good for masonry 
 above ground and for ordinary foundations as Portland cement, 
 but at the present price of Portland cement, it is not much, if any, 
 cheaper than 1 to 3 Portland-cement mortar. 
 
 Effects of Freezing on Natural Cement. It is com- 
 monly stated that natural cement should never be used in freez- 
 ing weather, but an elaborate series of tests on frozen briquettes, 
 published in the Engineering Record of Dec. 31, 1899, would 
 
194 ARTIFICIAL CEMENTS. 
 
 seem to show that Rosendale-cement mortar is not injured by 
 freezing in air, but that it is not safe to let it freeze in water in 
 less than two months. 
 
 ARTIFICIAL CEMENTS. 
 
 The artificial cements used in this country for laying up 
 masonry, or in making concrete, are of three varieties, viz., 
 true Portland cement, silica (sand) Portland cement, and Puz- 
 zolan (slag) cement. 
 
 Portland Cement. The true Portland cements are 
 made by thoroughly mixing together, in suitable proportions, 
 clay and finely pulverized carbonate of lime (either chalk, marl, 
 or compact limestone), burning the mixture in kilns at a high 
 heat and then grinding the burnt product to fine powder. 
 
 "Pure Portland cement as known to-day by architects and 
 engineers is strictly a mechanical mixture. Some manufac- 
 turers use as raw material clay and chalk, some marl and clay; 
 others use argillaceous limestone rock properly dosed, while the 
 first original Portland was made from mud dredged out of the 
 river-beds of the lower Thames and the Medway, together with 
 limestone." 
 
 True Portland cements are also now made which have slag 
 for their hydraulic base, the " Universal" brand of Portland 
 cement being a prominent example. Such cements differ in no 
 way from other standard Portland cements, and are accepted 
 in competition with them. 
 
 The chemical composition of a good Portland brand will oe 
 about as follows: Lime, 60.1; silica, 23.16; alumina, 8.5; ferric 
 oxide, 5.3; with less than five parts of magnesia and sulphides. 
 
 Previous to the year 1872, all of the Portland cement used in 
 this country was imported. In 1895, 2,300,000 Ibs. of Portland 
 cement was made in the United States, as compared with 
 13,500,000 in Germany and 8,300,000 in England. At the pres- 
 ent time more than 90% of the Portland cement used in this 
 country is of domestic production, and as American cements are 
 fully equal in strength and durability to the imported cements, it 
 will probably not be long before the importation of Portland 
 cement, except a few brands for special purposes, will practi- 
 cally cease. 
 
ARTIFICIAL CEMENTS. 195 
 
 Silica-Portland Cement is a mixture of true Portland 
 cement and siliceous sand ground together into an impalpable 
 powder in a tube-mill. 
 
 A mixture of equal parts of sand and cement thus ground to- 
 gether possesses about the same strength as ordinary Portland 
 cement alone. 
 
 A mixture of silica cement (one part cement and one part 
 sand) with three parts unground sand has the same composition 
 as one part cement and seven parts sand, but possessing the 
 strength of a mixture of one part cement and three parts sand.* 
 
 The silica-cement process was first introduced into Denmark 
 and has the special advantage of making mortar that is imper- 
 meable to moisture and able to resist the action of the elements. 
 
 During the years 1896-1902 a great many silica-Portland ce- 
 ment factories were erected abroad and several companies were 
 formed in New York, Pennsylvania, and Illinois to manufacture 
 it on a large scale. The author understands, however, that at 
 least some of the factories have been abandoned, and that this 
 material is now, 1905, used to a comparatively small extent* if at 
 all. 
 
 Eight thousand barrels of silica cement were used in the foun- 
 dations of the Cathedral of St. John the Divine, New York City. 
 
 Puzzolan Cement (sometimes called slag cement) is 
 made from granulated slag of a certain composition, both physi- 
 cal and chemical, ground to exceeding fineness with quicklime 
 which has been slaked with a solution of caustic soda. The* 
 product is a mechanical mixture of slag and slaked lime, no 
 clinker being first produced as in the manufacture of true Port- 
 land cement. " Steel Puzzolan cement" is ground to a fineness 
 of 96% through a 40,000-mesh sieve. 
 
 " Puzzolan cement made from slag is characterized physically 
 by its light lilac color ; the absence of grit attending fine grinding 
 and the extreme subdivision of its slaked-lime element; its low 
 specific gravity (2.6 to 2.8) compared with Portland (3 to 3.5) ; 
 and by the intense bluish-green color in the fresh fracture after 
 long submersion in water, due to the presence of sulphides, which 
 color fades after exposure to dry air. 
 
 " Puzzolan cement properly made contains no free or anhy- 
 drous lime, stands storage well, does not warp or swell, but is 
 
 * Addison IT. Clark, in Architects' Handbook of Cements. 
 
196 ARTIFICIAL CEMENTS. 
 
 liable to fail from cracking and shrinking (at the surface only) 
 in dry air. 
 
 "Mortars and concretes made from Puzzolan approximate 
 in tensile strength similar mixtures of Portland cement, but 
 their resistance to crushing is considerably less. On account of 
 its extreme fine grinding Puzzolan often gives nearly as great 
 tensile strength in 3 to 1 mixtures as neat. 
 
 "Puzzolan permanently assimilates but little water com- 
 pared with Portland, its lime being already hydrated. It 
 should be used in comparatively dry mixtures, well rammed, 
 
 "The cement is well adapted for use in sea-water, and gener- 
 ally in all positions where it will be constantly exposed to mois- 
 ture, such as in foundations, sewers and drains, and underground 
 works generally, and in the interior of heavy masses of masonry 
 or concrete." * 
 
 It should not be used for work exposed to dry air or mechan- 
 ical wear, as in floors and sidewalks, nor should it be used in con- 
 nection with iron or steel, unless the metal is well protected by 
 some coating. 
 
 Stainless Cements. Mortar mixed with natural-rock ce- 
 ments, or ordinary Portland cements, are likely to produce stains 
 in limestone and marble, and sometimes in granite. 
 
 There are a few Portland cements which do not cause stains, 
 and if any cement at all is to be used in the mortar for setting 
 or pointing, one of these brands should be specified. 
 
 Lime mortar does not stain the stones, but of course it does 
 not make as strong a job as cement mortar. 
 
 Leading Brands of Portland Cement. The follow- 
 ing are among the leading brands of Portland cement now 
 on the market. 
 
 American Portland : " Atlas," f " Alpha," " Dragon," " Le- 
 high," "Iron Clad," " Saylors," " Vulcanite" (lola, Colorado 
 Portland, Red Diamond J). 
 
 American Puzzolan: " Steel Puzzolan." 
 
 English Portland: " Brooks, Shoobridge & Co." 
 
 * Report of Board of Engineer Officers, U. S. Army, on Testing Hydraulic 
 Cements. 1901. 
 
 t The output of Atlas cement in 1901 was over 3,000,000 barrels. 
 
 J These cements are made in Kansas, Colorado, and Utah, respectively, 
 and are extensively used in those States. 
 
German Portland: "Alsen's," "Dyckerhoff," "Mann- 
 heimer," "Germania." 
 
 Stainless cements: "La Farge," French Portland; "Puzzo- 
 lan," H. H. Meier & Co., Bremen; "Rhinoceros," American. 
 
 Cost of Portland Cement. Portland cement can now be 
 purchased in this country at prices from $1 .25 to $2.50 per barrel, 
 the former price being for 5,000-barrel lots at the factory. For 
 a large order, in any of the Central States, cement can probably 
 be obtained at $2.00 per barrel, delivered. The retail price for 
 single barrels varies from about $2.25 to $2.75 per barrel. 
 
 In Germany the average price per barrel in the open market 
 appears to be about $1.25. 
 
 PROPERTIES AND CHARACTERISTICS OP 
 PORTLAND CEMENT. 
 
 Color. Portland cement should be of a greenish gray color. 
 Slag cements are of a light gray color. 
 
 Weight. The weight of Portland cement, loose, varies from 
 77 to 95 Ibs. per cu. ft., the average being from 85 to 90 Ibs. A 
 barrel of Portland cement is supposed to contain 3J cu. ft. 
 (packed), or about 380 Ibs. net of cement. When put up in 
 sacks, each sack is supposed to contain 95 Ibs., or four sacks to 
 the barrel.* 
 
 "Steel Puzzolan" (slag) cement weighs 330 Ibs. net to the 
 barrel, or 82 Ibs. per bag or sack. 
 
 Fineness. Fineness in cement is a very important quality, 
 as fine grinding increases the strength and sand-carrying capac- 
 ity. The fineness of Portland cement when ready for the mar- 
 ket should be such that not less than 95% will pass through a 
 
 *The actual weight per cubic foot and per bbl. of several brands of Port- 
 land cement, as tested by Chas, G. Reid, is shown by the following table: 
 
 Brand. 
 
 Volume 
 per barrel in 
 cubic feet 
 loose measure 
 
 Weight per barrel in pounds. 
 
 Weight 
 per cubic foot 
 loose 
 measure. 
 
 Gross. 
 
 Net. 
 
 Dyckerhoff 
 Atlas 
 Alpha 
 Meiers 
 
 4.47 
 4.45 
 4.37 
 4.84 
 4.96 
 4.64 
 
 395 
 401 
 400.5 
 375 
 35O 
 393 
 
 369.5 
 381 
 381 
 353.5 
 332.5 
 370.5 
 
 83 
 85.5 
 86.5 
 73.5 
 67.5 
 79.5 
 
 Steel. . 
 
 Hilton ... . 
 
 
198 PORTLAND CEMENT, 
 
 sieve of 2,500 meshes to the square inch. The U. S. Corps of 
 Engineers requires that 92% shall pass a sieve of 10,000 meshes 
 to the sq. inch. Some American cements will pass 99%. The 
 finer a cement is ground the more bulky it becomes, and the 
 less it weighs by measure. 
 
 Time of Setting". A true Portland cement is classed as 
 slow setting when a cake of neat cement takes over a half hour 
 to harden. Sand retards setting, so that cement which when 
 mixed neat would set in half an hour ma} r not set for one or twQ 
 days if mixed with large proportions of sand. 
 
 Strength. The best test for the strength of Portland cement 
 is the tensile strength of briquettes composed of 1 part cement 
 and 3 parts standard sand. 
 
 Such briquettes should show a strength at seven days of from 
 100 to 140 Ibs., at twenty-eight days of from 200 to 300 Ibs., and 
 at the end of one year of from 300 to 400 Ibs. 
 
 Briquettes mixed neat (without sand) should break at seven 
 days, at from 250 to 550 Ibs. ; at twenty-eight days, at from 400 
 to 800 Ibs., and at the end of a year, at from 500 to 1,000 Ibs. 
 The author has made briquettes which gave a breaking 
 strength of over 1,000 Ibs. when twenty-eight days old. The 
 briquettes should be kept in a damp box for the first twenty-four 
 hours, and then in water. 
 
 The crushing resistance of Portland cement varies from 8 to 
 12 times, the tensile strength, the average being 1Q times the 
 tensile strength. 
 
 The greater the increase per cent, between the seven-day and 
 twenty-eight-day tests, the stronger and harder the cement is 
 likely to become. This increase should be at least 25%. 
 
 Water Required in Mixing 1 . Good Portland cement 
 requires but little water to make a good mortar. Neat cement 
 will take 17% to 20% (by weight) of water, 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 lime. 
 
 When sand is mixed with cement, in the proportion of 3 to 1, 
 not more than 9% to 12J% (by weight) of water will be required. 
 
 Natural rock and slag cements require more water than do 
 Portland cements. 
 
 Too much water "drowns" the cement, retards the setting, and 
 weakens the mortar. 
 
 Cement can also be spoiled by a deficiency of water. 
 
PORTLAND CEMENT. 1UU 
 
 Portland-Cement Mortar. For first-class mortar not 
 more than 3 bbls of sand should be added to 1 bbl. of 
 cement. For rubble stonework under ordinary conditions a 
 mortar composed of 4 parts sand to 1 of cement will answer 
 every purpose, and be much stronger than lime mortar. 
 
 For the top surface of floors and walks, from 1 to 1J parts of 
 sand may be mixed with 1 part cement. 
 
 1 to 3 Portland-cement mortar has about the same strength at 
 the end of one year as 1 to 1 natural rock-cement mortar. 
 
 Mortar made with fi-ne sand requires twice the quantity of 
 cement to obtain 'a given strength as that made with coarse sand. 
 
 Effects of Freezing on Portland -Cement Mortar. Numerous 
 experiments and the experience of engineers bear out the 
 assertions, 
 
 1st, that the mortar is considerably injured, but not totally, 
 if frozen before it is set. 
 
 2d. That freezing only partially suspends chemical action in 
 the setting of cement. 
 
 3d. It is not safe to allow a slow-setting cement mortar to 
 freeze in less than four days after it has been placed, while a 
 very quick-setting mortar may freeze in twelve hours without 
 injury, provided the mortar is kept frozen until set. 
 
 4th. That Portland-cement mortar is injured more when it 
 alternately freezes and thaws than when it remains frozen before 
 it has set hard.* 
 
 5th. If salt is added to the water of mixture no bad effects 
 will result from freezing. The rule for the proportion of salt 
 used in the works at Woolwich Arsenal, is said to have been- 
 "Dissolve one pound of rock salt in eighteen gallons of water 
 when the temperature is at 32 degrees Fahr., and add three 
 ounces of salt for every three degrees of lower temperature." 
 
 6th. Hot water hastens the setting of Portland-cement mortar. 
 
 7th. 2 Ibs. carbonate of soda in 1 gal. of water boiled and 
 mixed in mortar hastens the setting and protects from freezing. 
 
 Quantity of Mortar required for Masonry and Plastering. f 
 
 "One barrel of Portland cement and three barrels of sand 
 thoroughly and properly mixed will make 3-| bbls., or 12 cu. ft., 
 of good strong mortar. This will be sufficient to lay up 1J cu. 
 
 * See Engineering Record for December 24 and 31, 1898. 
 f These figures can be considered as approximate only, as the amount of 
 oiortar will vary on different jobs. 
 
200 CONCRETE. 
 
 yds. of rough stone, or about 750 bricks, with \ to f-in. joints, 
 or cover 125 square feet of surface 1 in. thick, or 250 sq. ft. 
 } in. thick." 
 
 "One barrel of Rosendale cement and two barrels of lime, 
 mixed with about half a barrel of water, will make 8 cu. ft. of 
 mortar, sufficient to lay 522 common bricks, with J to f in. 
 joint, or about 1 cu. yd. of rough rubble." 
 
 For the top coat of walks or floors. 
 
 1 bbl. of Portland cement and 1 of sand will cover 75 to 80 
 sq. ft., | in. thick, or 50 to 56 sq. ft. J in. thick. 
 
 1 bbl. of Portland cement and. 1J bbls. of sand will cover 110 to 
 120 sq. ft. ot floor i in. thick, or 75 to 80 sq. ft. f in. thick. 
 
 CONCKETE. 
 
 There is probably no material that is so enduring or better 
 adapted for foundations, walks, and basement floors than cement 
 concrete, and for a certain class of buildings it may be used with 
 advantage for the walls, floors, and interior supports. In fact 
 there are now probably one hundred buildings in this country 
 in which all of the structural portions are formed of concrete, 
 and the use of Portland-cement concrete for a great variety of 
 purposes is rapidly extending, due largely to the reduced price of 
 Portland-cement, and also to a better appreciation of its merits. 
 
 Concrete may be defined as an artificial rock, made by unit- 
 ing sand, broken stone, gravel, fragments of brick, pottery, etc., 
 by means of lime or cement. 
 
 Concrete made with lirne, however, is not suitable for damp 
 situations, and even when used for walls above ground it is 
 much better to use either a "Portland" or "natural" cement 
 for the uniting material; in fact lime is no longer used for this 
 purpose. 
 
 Concrete made with good Portland cement, in proper propor- 
 tions, becomes so hard and strong that when pieces of the con- 
 crete are broken the line of fracture will often be found to pass 
 through the particles of stone, showing that the adhesion of the 
 cement to the stone is greater than the strength of the stone. 
 
 For the aggregates no material is better than clean, freshly 
 broken stone, in size about as large as a hen's egg. Granite 
 probably makes the best aggregates, but other hard stones will 
 answer for any ordinary concrete. Soft sandstones or "free- 
 
stones" are not desirable. Pieces of hard brick or dense terra- 
 cotta also make good aggregates. 
 
 Whatever material is used it is essential that it be free from 
 dirt and that the particles be clean.* 
 
 Good clean coarse gravel is also extensively used for the mass 
 of the concrete, and some architects and builders prefer it to 
 broken stone, but as all gravel has more or less rounded and 
 smooth surfaces, it would seem as though the cement must adhere 
 more firmly to angular and broken surfaces. f 
 
 A certain proportion of clean coarse sand is also required to 
 fill the voids between' the particles of stone or gravel. 
 
 The best proportion of cement, sand, and aggregates will de- 
 pend upon the kind and quality of the cement used, the character 
 of the aggregates, and of the work. 
 
 Proportions. The proportion of sand to aggregates should 
 be such that the sand will just fill the voids in the aggregates. 
 This will, of course, vary with the size of the aggregates and the 
 coarseness of the sand. For stone broken to go through a 2J- 
 inch ring about one-half as much sand as stone is required, on 
 an average, to fill the voids. After one batch of concrete has 
 been deposited and rammed the inspector can generally tell by 
 the appearance whether too much or too little sand has been used. 
 
 Natural-Cement Concrete. For concrete foundations 
 under buildings of moderate height, and for foundations for 
 cement pavements, natural cement makes as strong a concrete 
 as is required. 
 
 *Mr. G. J. Griesenauer, cement tester for the Chicago, Milwaukee & St. 
 Paul Ry., reports, in the Engineering News of April 16, 1903, a very interest- 
 ing series of tests on the comparative strength of cement mortar made from 
 Trorpedo sand and limestone and gravel screenings. These tests seem to 
 show that limestone screenings make very much stronger mortar than sand, 
 the increase in strength averaging about 115 per cent, for proportions of 1 
 to 3. Gravel screenings gave about the same strength as sand. 
 
 Mr. W. A. Rogers, formerly with the same railroad, in a very valuable 
 paper on concrete, reports tests which seem to show that "a small amount 
 of dirt in the sand is probably not seriously objectionable, if suitable in 
 other ways." 
 
 t From some experiments carried out under the direction of Captain Wm. 
 Black, of the United States Corps of Engineers, for the purpose of deter- 
 mining the influence of different aggregates on the strength of concrete, 
 it would seem that the gravel makes a much weaker concrete at the start 
 than stone, especially when natural cements are used, but that after a 
 period of one year it will probably attain the same strength as that made 
 of broken stone. (See Engineering Record for April 9, 1898.) 
 
202 CONCRETE. 
 
 For the" best brands of natural cements 1 part cement, 2 parts 
 sand, and 4 parts gravel or broken stone should be used. 
 
 (This proportion was used in the foundations of the Brooklyn 
 Bridge.) 
 
 Portland-Cement Concrete. For concrete to be used 
 under heavy buildings and under water Portland cement 
 should be used. 
 
 For the best brands of cement 2 parts of cement to 5 of sand 
 and 9 of broken stone will answer for almost any building con- 
 struction. Much larger proportions of sand and aggregates 
 than these are often used, but the author would not recommend 
 a greater proportion than the above unless the quality of the 
 cement is constantly tested and only the best used, and the con- 
 crete mixed under rigid inspection. 
 
 Manner of Mixing. The most satisfactory method of 
 mixing concrete by hand is to first prepare a tight floor of plank, 
 or, better still, of sheet iron with the edges turned up about 
 2 ins., for mixing the materials on. 
 
 Upon this platform should first be spread the sand, and upon 
 this the cement. The two should then be thoroughly and im- 
 mediately mixed by means of shovels or hoes, and the broken 
 stone or aggregates then dumped on top and the whole worked 
 over dry with shovels, and then again worked over while water 
 is added from a sprinkler on the end of a hose. After enough 
 water has been added the mass should be worked over at least 
 twice. Only as much water should be added as is necessary to 
 enable the mortar to completely coat and cause to adhere all 
 the particles of the aggregates, and so that when the concrete is 
 tamped the water will just flush to the surface without quaking. 
 
 The water should be clean and at about the temperature of 
 65 degrees. 
 
 There are many machines for mixing mortar which for large 
 quantities of concrete effect a material saving in the cost of mix- 
 ing, and probably do the work more thoroughly and evenly. 
 As soon as the concrete is mixed it should be wheeled to the 
 trenches in barrows and deposited in layers not over 6 ins. thick 
 and well tamped. After it is deposited concrete should be pro- 
 tected from drying too rapidly, as Portland cement reaches its 
 maximum strength only when kept damp.. If the concrete 
 dries quickly it is also liable to crack from contraction, which 
 in exposed work is likely to lead to its destruction by weathering. 
 
 Effect of Freezing on Concrete, It would seem that 
 
the general opinion among railway engineers is that when careful 
 precautions are taken in laying Portland-cement concrete, freez- 
 ing weather will not cause any trouble, w r hile the effect of frost 
 on concrete that has set either amounts to nothing or is confined 
 to surface cracks.* 
 
 Cost of Concrete and Materials Required per 
 Yard, The quantities of cement, sand, and gravel required 
 to make a yard (27 cu. ft.) of concrete will vary somewhat 
 on different jobs. The values given in the following tables may 
 be used as fair averages for making estimates. 
 
 QUANTITIES REQUIRED FOR 1 CUBIC YARD OF RAMMED CON- 
 CRETE. (Compiled by Edwin Thacher, C.E.) 
 
 Mixtures. 
 
 Stone, t 
 
 Gravel.} 
 
 
 
 
 Ce- 
 
 
 
 Ce- 
 
 
 
 Ce- 
 ment. 
 
 Sand. 
 
 Stone. 
 
 ment, 
 bbls. 
 
 Sand, 
 cu. yds. 
 
 Stone, 
 cu. yds. 
 
 ment, 
 bbls. 
 
 Sand, 
 cu. yds. 
 
 Gravel, 
 cu. yds. 
 
 
 1.0 
 
 2.0 
 
 2.63 
 
 0.40 
 
 0.80 
 
 2.30 
 
 0.35 
 
 0.74 
 
 
 1.0 
 
 3.0 
 
 2.10 
 
 0.32 
 
 0.96 
 
 1.89 
 
 0.29 
 
 0.86 
 
 
 1.5 
 
 3.0 
 
 1.90 
 
 0.43 
 
 0.87 
 
 1.71 
 
 0.39 
 
 0.78 
 
 
 1.5 
 
 4.0 
 
 1.61 
 
 0.37 
 
 0.98 
 
 1.46 
 
 0.33 
 
 0.88 
 
 
 2.0 
 
 3.0 
 
 1.73 
 
 0.53 
 
 0.79 
 
 .54 
 
 0.47 
 
 0.73 
 
 1 
 
 2.0 
 
 4.0 
 
 1.48 
 
 0.45 
 
 0.90 
 
 .34 
 
 0.41 
 
 0.81 
 
 1 
 
 2.0 
 
 5.0 
 
 1.29 
 
 0.39 
 
 0.98 
 
 .17 
 
 0.36 
 
 0.89 
 
 1 
 
 2.5 
 
 4.0 
 
 1.38 
 
 0.53 
 
 0.84 
 
 .24 
 
 0.47 
 
 0.75 
 
 1 
 
 2.5 
 
 5.0 
 
 1.21 
 
 0.46 
 
 0.92 
 
 .10 
 
 0.42 
 
 0.83 
 
 1 
 
 2.5 
 
 6.0 
 
 1.07 
 
 0.41 
 
 0.98 
 
 0.98 
 
 0.37 
 
 0.89 
 
 1 
 
 3.0 
 
 6.0 
 
 0.91 
 
 0.42 
 
 0.97 
 
 0.84 
 
 0.38 
 
 0.89 
 
 ACTUAL VOLUME OF RAMMED CONCRETE RESULTING FROM DIF- 
 FERENT PROPORTIONS OF INGREDIENTS. (As determined by 
 Messrs. A. W. Dow and W. J. Douglas. ) 
 
 Ingredients. 
 
 Propor- 
 tions. 
 
 Quantity 
 of Concrete. 
 
 Cement. 
 
 Sand. 
 
 Stone. 
 
 Gravel. 
 
 lbbl.= [ 
 4}cu. ft. 
 or ] 
 378ilbs. I 
 
 9 cu. ft. 
 
 iii " 
 iii " 
 
 13.5 " 
 
 20i cu. ft. 
 27 
 13} 
 
 
 
 13} cu. ft. 
 45 
 
 1:2:5 
 1 : 2} : 6 
 1 : 2} : 3 : 3 
 1 : 3 : 10 
 
 21.4 cu. ft. 
 27.66 " 
 27.66 " 
 45 
 
 For sand and gravel mixed as it comes from the pit 125 yds, 
 will make about 100 yds. of concrete. 
 
 At $2 a day for common labor the cost of mixing and deposit- 
 ing concrete, by hand, will vary from $1.25 to $1.50 a cu. yd. 
 
 On large jobs concrete can be mixed by machines, deposited 
 and tamped by hand at from .75 to .90 per cu. yd. 
 
 * Engineering Record, October 20, 1900, also December 7, 1901. 
 
 t 2} in. and under, dust screened out. 
 
 J f in. and under. 
 
 See Engineering News, March 10, 1904, p. 226. 
 
204 CONCRETE. 
 
 For small jobs where there are no special disadvantages $6 per 
 cu. yd. without forms is perhaps a fair average price at the pres- 
 ent time (1904), although with wages at $2 per day, and on large 
 jobs, the work can be done at from $4.00 to $5.00 a yard. 
 
 On the Boston subway the prices for labor and materials were 
 as follows, per cu. yd.* 
 
 Natural rock-cement concrete, $5.00 to $8.00. 
 
 Portland-cement concrete, $6.50 to $9.50. 
 
 The following exact figures, giving the cost per cu. yd. of con- 
 crete of an arched culvert of 26 ft. span, with wing walls and 
 parapet, built near Pittsburg, Pa., in 1901, should be of value 
 in estimating the cost of such work. The proportions were 1 to 
 8 and 1 to 10, and the mixing was done by hand. 
 
 For complete description of the work see the Engineering 
 Record for April 12, 1902. 
 
 The finished structure contained 1,439 cu. yds. of concrete 
 masonry, the total cost of which was $7,243.24. 
 
 The cost per cu. yd. of concrete for material and labor was 
 as follows: 
 
 Material. 
 Coarse gravel, 19 cts. per ton, 1.03 tons. . ..$0.19J 
 
 Fine gravel, 21 cts. per ton, 0.40 ton 08 J 
 
 Sand, 36 cts. per ton, 0.32 ton 11J 
 
 Cement, $1.60 per barrel 1.53J 
 
 Lumber 43 
 
 Tools and other storehouse accounts 07 J 
 
 $2.43f 
 
 Labor. 
 
 Preparing site and 'cleaning up after comple- 
 tion of structure, 15.5 cts. per hour $0 . 21 
 
 Forms, 23 cts. per hour 28 
 
 Platforms and buildings, 23 cts. per hour 05 
 
 Changing trestle, including service of work train 
 
 and steam-derrick car 08 J 
 
 Excavation, foundations, 15.5 cts. per hour 31 
 
 Handling material, 15.5 cts. per hour 03f 
 
 Mixing and laying concrete, 15.5 cts. per hour. ... 1.44 
 
 $2.41i 
 
 Total cost per cubic yard of concrete $4 . 85 
 
 Wages paid were as follows: Foreman mason in general 
 charge, 40 cents per hour; laborers, 15 cents per hour; foreman, 
 25 cents per hour; carpenters, 22.5 to 25 cents. 
 
 * Addison H. Clark, in " Architects' Handbook of Cement." 
 
EXAMPLES OF PORTLAND CEMENT CONCRETE. 205 
 
 DATA FOR ESTIMATING THE COST OF A CUBIC YARD OF CON- 
 CRETE OF VARIOUS PROPORTIONS. (As compiled by W. A. 
 
 Rogers, C.E.) 
 
 Proportion of 
 materials. 
 
 Cost of labor, 
 mixing and 
 placing per 
 cubic yard. 
 
 Cost of forms 
 per cubic yard 
 (where forms 
 are required). 
 
 Materials per 
 cubic yard. 
 
 -t-> 
 
 T3 
 d 
 
 o3 
 02 
 
 0.35 
 cu. yd. 
 
 Jls 
 
 
 
 pq "S 
 
 0.95 
 cu. yd. 
 
 1 part of natural ce- 
 ment to 1 parts 
 sand to 4 parts 
 broken stone 
 1 part Portland ce- 
 ment to 2 parts 
 sand to 5 parts 
 broken stone 
 1 part Portland ce- 
 ment to 3 parts 
 sand to 7 parts 
 broken stone .... 
 
 90 per cent of 
 the amount 
 paid per day 
 for labor. 
 
 From 35 cts. 
 to 85 cts. per 
 cubic yard. 
 
 M 
 
 H 
 bbls. 
 
 1.2 
 
 bbls. 
 
 0.9 
 bbls. 
 
 
 EXAMPLES OP PORTLAND CEMENT CONCRETE. 
 
 Foundation of U. S. Naval Observatory, Georgetown, D. C.: 
 1 part cement, 2J sand, 3 gravel, 5 broken stone. (1 barrel of 
 cement, 380 Ibs., made 1.18 yds. of concrete.) 
 
 Foundations of Cathedral of St. John the Divine, New York: 
 
 1 part Portland cement, 2 parts sand, 3 parts quartz gravel, 1J 
 to 2 ins. in diameter. (17,000 barrels of cement made 11,000 
 yards of concrete.) 
 
 Manhattan Life Insurance Building, New York, filling of 
 caissons: 1 part Alsen Portland cement, 2 parts sand, 4 parts 
 broken stone. 
 
 Filling of caissons, Johnston Building (15 stories), New York: 
 1 part Portland cement, 3 parts sand, 7 parts stone, finished on 
 top for brickwork with 1 part cement and 3 parts gravel. 
 
 Prof. Baker states that the concrete foundations under the 
 Washington Monument were made of 1 part Portland cement, 
 
 2 parts sand, 3 parts gravel, and 4 parts broken stone, and that 
 this mixture stood, at six months old, a load of 2,000 Ibs. per sq. 
 in., or 144 tons per sq. ft. For the strength of concrete see 
 Chapter V. 
 
 The weight of concrete varies from 130 to 140 Ibs. per cu. ft., 
 according to the material used, granite aggregates making natu- 
 rally the heaviest concrete. 
 
206 RETAINING WALLS VAULT WALLS. 
 
 CHAPTER IV. 
 RETAINING- WALLS VAULT WALLS. 
 
 A Retaining Wall is a wall for sustaining a pressure of 
 earth, sand, or other filling or backing deposited behind it after 
 It is built, in distinction to a brest or jace wall, which is a similar 
 structure for preventing the fall of earth which is in its undis- 
 turbed natural position, but in which a vertical or inclined face 
 has been excavated. 
 
 Fig. 1 gives an illustration of the two kinds of wall. 
 
 Fig. I 
 
 Retaining Walls. A great deal has been written upon the 
 theory of retaining walls, and many theories have been given for 
 computing the thrust which a bank of earth exerts against a re- 
 taining wall, and for determining the form of wall which affords 
 the greatest resistance with the least amount of material. 
 
 There are so many conditions, 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 therefore necessary, in designing retaining walls, to be 
 guided by experience rather than by theory. As the theory of 
 retaining walls is so vague and unsatisfactory, we shall not offer 
 any in this work, but rather give such rules and cautions as have 
 been established by practice and experience. 
 
 In designing a retaining wall there are two things to be con- 
 sidered, the backing and the wall. 
 
 The tendency of the backing to slip is very much less when it is 
 in a dry state than when it is filled with water, and hence every 
 
RETAINING WALLS VAULT WALLS. 
 
 ZUY 
 
 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 and run off. 
 The manner in which the material is filled against the wall also 
 affects the stability of the backing. If the ground be made irreg- 
 ular, as in Fig. 1, and the earth well rammed in layers inclined 
 from the wall, the pressure will be very trifling, provided that 
 attention be paid to drainage. If, on the other hand, the earth 
 be tipped, in the usual manner, in layers sloping towards the wall, 
 the full pressure of the earth will be exerted against it, and it 
 must be made of corresponding strength. 
 
 84 
 
 - 
 
 Fig.2 
 
 Fig. 3 
 
 The Wall. Retaining walls are generally built with a batter- 
 ing (sloping) face, as this is the strongest wall for a given 
 amount of material; and, if the courses are inclined towards the 
 back, the tendency to slide on each other will be overcome, and 
 it will not be necessary to depend upon the adhesion of the 
 mortar. 
 
 The importance of making the resistance independent of the 
 adhesion of the mortar is obviously very great, as it would other- 
 wise be necessary to delay backing up a wall until the mortar was 
 thoroughly set, which might require several months. 
 
 The Back of the Wall should be left Rough. In 
 brickwork it would be well to let every third or fourth course 
 below the frost-line proj ect an inch or two. This increases the fric- 
 tion of the earth against the back and thus causes the resultant of 
 the forces acting behind the wall to become more nearly vertical, 
 and to fall farther within the base, giving increased stability. 
 It also conduces to strength not to make each course of uniform 
 height throughout the thickness of the wall, but to have some of 
 the stones, especially near the back, sufficiently high to reach up 
 through two or three courses. By this means the whole masonry 
 becomes more effectually interlocked or bonded together as one 
 
208 
 
 RETAINING WALLS VAULT WALLS. 
 
 mass, and less liable to bulge. The courses of masonry are also 
 often laid with their beds sloping in, as in Fig. 6, to overcome 
 the tendency of the courses to slide on each other. 
 
 Where deep freezing occurs, the back of the wall should be 
 
 Fig.6 
 
 sloped forwards for three or four feet below its top, as at OC 
 (Fig. 2), which should be quite smooth, so as to lessen the hold 
 of the frost and prevent displacement. 
 
 Figs. 3, 4, 5, and 6 show the relative sectional areas of walls of 
 different shapes that would be required to resist the pressure of 
 a bank of earth twelve feet high ("Art of Building," E. Dobson, 
 p. 20) . The first three examples are calculated to resist the max- 
 imum thrust of wet earth, while the last shows the modified form 
 usually adopted in practice. 
 
 Fig.7 
 
 Rules for the Thickness of the Wall. As has been 
 stated, the only practical rules for retaining walls which we 
 have are empirical rules based upon experience and practice. 
 
RETAINING WALLS VAULT WALLS. 
 
 209 
 
 Trautwine, in his "Pocket-Book for Engineers," gives the 
 following table 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. 7) of 
 the earth as compared with the vertical height of the wall, AB] 
 which latter is assumed to be 1, so that the table begins with 
 backing of the same height as the wall. These vertical walls 
 may be battered to any extent not exceeding an inch and a half 
 to a foot, or 1 in 8, without affecting their stability, and without 
 increasing the base, 
 
 Proportion of Retaining Walls. 
 
 (Thickness of wall in terms of the height, A B, Fig. 7). 
 
 Total height of the earth com- 
 pared with the height of the 
 wall above ground. 
 
 Wall of 
 cut stone in 
 mortar. 
 
 Good mortar, 
 rubble, or 
 brick. 
 
 Wall of 
 good, dry 
 rubble. 
 
 1 
 
 0.35 
 
 0.40 
 
 0.50 
 
 1.1 
 
 0.42 
 
 0.47 
 
 0.57 
 
 1.2 
 
 0.46 
 
 0.51 
 
 0.61 
 
 1.3 
 
 0.49 
 
 0.54 
 
 0.64 
 
 1.4 
 
 0.51 
 
 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 
 
 o 
 
 0.58 
 
 0.63 
 
 0.73 
 
 2.5 
 
 0.60 
 
 0.65 
 
 0.75 
 
 3 
 
 0.62 
 
 0.67 
 
 0.77 
 
 4 
 
 0.63 
 
 0.68 
 
 0.78 
 
 6 
 
 0.64 
 
 0.69 
 
 0.79 
 
 If the wall is built as in Fig. 8, 
 with the ground practically level 
 with the top, the top of the wall 
 should be not less than 18 ins. thick, 
 and the thickness at a, a, just above 
 each step should be from one-third 
 to two-fifths of the height from the 
 top of the wall to that point. If 
 the earth is banked above the top 
 of the wall, the thicknesses should 
 be increased as indicated by the 
 table given above. 
 
 Fig. 8 
 
 If built upon ground that is affected by frost or surface water, 
 
210 RETAINING WALLS VAULT WALLS. 
 
 the footings should be carried sufficiently below the surface oi 
 the ground at the base to insure against heaving or settling. 
 
 Reinforced Concrete may be used to advantage in building 
 retaining walls, and often at less expense than stone. Fig. SA 
 shows a wall suggested by the St. Louis Expanded Metal Fire- 
 proofing Co. which reduces the masonry to a minimum. 
 
 Brest Walls (from Dobson's "Art of Building")- Where 
 the ground to be supported is firm, and the strata are horizontal, 
 the office of a brest wall is more to protect than to sustain the 
 earth. It should be borne in mind that a trifling force skilfully 
 applied to unbroken ground will keep in its place a mass of ma- 
 terial, which, if once allowed to move, would crush a heavy wall ; 
 and therefore great care should be taken not to expose the newly 
 opened ground to the influence of air and wet for a moment 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 brest wall must be proportionately in- 
 creased when the strata to be supported incline towards the wall; 
 where they incline from it, the wall need be little more than a 
 thin facing to protect the ground from disintegration. 
 
 The preservation of the natural drainage is one of the most 
 important points to be attended to in the erection of brest walls, 
 as upon this their stability in a great measure depends. No rule 
 can be given for the best manner of doing this: it must be a 
 matter for attentive consideration in each particular case. 
 
 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 sustain the street 
 and also the weight of the sidewalk. 
 
 Where practicable the space should be divided by partition 
 walls about every 10 ft., and when this is done the outer wall 
 may be advantageously built of hard brick in the form of arches, 
 as shown in Fig. 9. The thickness of the arch should be at least 
 16 ins. 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 practicable 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. 10 * shows a detail of the outer walls of the vault under 
 the sidewalk around the Singer Building, New York; Mr. Er- 
 
 * Fiom The Engineering Record of February 26, 1898. 
 
RETAINING WALLS VAULT WALLS. 
 
 211 
 
 nest Flagg, architect. These walls consisted of a core formed 
 by two-ring brick arches, with vertical axes built between the 
 flanges of 8-inch vertical steel I beams spaced about 5 ft. apart 
 and bedded at the bottom in a concrete footing. Their tops 
 
 Fig. 8A Fig. 9 
 
 were joined by 6-inch horizontal I beams and braced laterally 
 by the sidewalk beams 5 ft. apart. The arches themselves 
 
 Fig. 10 
 
 were segmental with a rise of about 6 ins., and were built up 
 solid against an 8-inch outside face walL A 4-inch plain cur- 
 tain wall was built inside against the flanges of the vertical 
 beams inclosing segmental air chambers in front of each arch. 
 
212 STRENGTH OF MASONRY AND CONCRETE. 
 
 CHAPTER V. 
 
 STRENGTH OP BRICK AND STONE MASONRY 
 AND CONCRETE. 
 
 CRUSHING RESISTANCE OF BRICK, BUILDING 
 STONES, MORTAR, CONCRETES, AND ARCHI- 
 TECTURAL TERRA-COTTA. 
 
 By the term "strength of masonry" is generally meant its 
 resistance to a direct crushing force or load, and this is the only 
 direct stress to which masonry should be subjected. Stone lin- 
 tels and footings may be subjected to a transverse stress, but 
 they can hardly be included in the term masonry, as they consist 
 of single pieces. There is also more or less of a tendency to 
 bend or split apart in brick walls and piers, as they are very high 
 in proportion to their thicknesss, but this is a stress which cannot 
 be accurately determined, and which should be avoided as much 
 as possible. It is impossible to fix values for the strength of 
 brick or stone work with anything like the exactness that w r e 
 do for wood or steel, for the reason that there is not only a great 
 variation in the strength of brick and stone, even when taken 
 from the same kiln or quarry, but the strength of walls and 
 piers is also very greatly affected by the kind and quality of the 
 mortar used, the way in which the work is built and bonded, and 
 whether the brick or stone is laid dry or wet. All that can be 
 done, therefore, is to give values which will be safe for the differ- 
 ent kinds of masonry built in the usual manner. 
 
 Working Strength of Masonry. The building laws of 
 most of the larger cities of this country specify the maximum 
 loads per sq. ft. which shall be placed upon different kinds of 
 masonry, which of course must govern the architect when build- 
 ing in those places. 
 
 When there is no restriction of this kind, Table I. will give a 
 pretty good idea of the maximum loads which it is safe to put 
 upon the different kinds of work indicated. Table II. gives the 
 maximum safe loads as specified in the building laws of seven dif- 
 ferent cities, and in the latter part of the chapter is given records 
 
of numerous tests made to determine the ultimate .or breaking 
 strength of various kinds of brick, building stones, mortars, and 
 concretes, which are of value in determining the safe load for 
 special cases. 
 
 In fixing the safe resistance of masonry from tests on the ulti- 
 mate strength of work of the same kind, a factor of safety of at 
 least 10 should be allowed for piers and 20 for arches. 
 
 The Chicago building ordinance fixes the maximum stress 
 for dimension stone piers at one-thirtieth of the ultimate strength 
 of the stone when the beds are dressed to a uniform bearing over 
 their entire surf ace, 'and at one-fiftieth of the ultimate strength 
 when the beds are not dressed. 
 
 When the stress exceeds one-seventieth of the ultimate 
 strength the stones must be bedded in Portland-cement mortar. 
 
 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 
 
 ' ' hydraulic lime mortar 6 
 
 natural cement mortar, 1 to 3 . 10 8 
 
 Arch or pressed brick in lime mortar 8 6 
 
 " " " natural cement. . .. 12 9 
 
 " " " Portland cement... 15 12 J 
 Piers exceeding in height six times their least dimensions should 
 be increased 4 ins. in size for each additional 6 ft. 
 
 Stonework. 
 (Tons per square foot.) 
 
 Rubble walls, irregular stones 3 
 
 ' t coursed, soft stone 2J 
 
 " " hard stone 5 to 16 
 
 Dimension stone, squared in cement : 
 
 Sandstone and limestone 10 to 20 
 
 Granite 20 to 40 
 
 Dressed stone, with f-inch dressed joints in cement: 
 
 Granite 60 
 
 Marble or limestone, best 40 
 
 Sandstone 30 
 
 Height of columns not to exceed eight times least diameter. 
 
214 STRENGTH OF MASONRY AND CONCRETE. 
 
 Concrete.* 
 
 Portland cement, 1 to 8, 6 months, 10 tons, 1 year, 15 to 20 tons. 
 Rosendale cement, 1 to 6, 6 months, 3 tons, 1 year, 5 to 8 tons. 
 
 Hollow Tile. 
 (Safe loads per square inch of effective bearing parts.) 
 
 Hard fire-clay tiles 80 Ibs.f 
 
 ' ' ordinary clay tiles 60 ' ' 
 
 Porous terra-cotta tiles 40 " 
 
 Mortars. 
 (In J-inch joints, 3 months old, tons per square foot.) 
 
 Portland cement, 1 to 4 40 
 
 Rosendale cement, 1 to 3 13 
 
 Lime mortar, best 8 to 10 
 
 Best Portland cement, 1 to 2, in J-ineh joints for bed- 
 ding iron plates 70 
 
 TABLE II. COMPARISON OF BUILDING LAWS. 
 
 Materials. 
 
 Ife 
 
 IS 
 
 2 
 
 *o3 IN 
 
 *; 
 B^ 1 
 
 i. 
 
 K*j O5 
 r* O5 
 
 *% 
 
 
 & 
 
 Chicago, 
 1893. 
 
 T 
 
 Si 
 
 -li 1 "" 1 
 yi 
 
 Philavlelphia, 
 1899. 
 
 Denver, 
 1898. 
 
 Granite, cut 
 
 Allo 
 
 60 
 40 
 30 
 
 'is' 
 
 12 
 
 8 
 
 wable pressures in tons 
 72-172 
 
 per sc 
 
 l.ft. 
 40 
 
 12 
 9 
 
 8 
 
 12 
 12 
 30 
 
 10 
 
 4 
 
 Marble and limestone, cut 
 
 "9' 
 
 "6 
 1.2 
 9 
 
 50-165 
 28-115 
 18 
 15 
 
 V 
 
 iii 
 
 "oi 
 
 'is' 
 
 "iii 
 11 
 
 15 
 12 
 
 8 
 
 Sandstone, hard, cut 
 
 Hard -burned brick in Port, cement 
 in nat. cement . 
 in cem't & lime. 
 1 in lime mortar . 
 Pressed brick in Portland cement. . 
 in natural cement. . . 
 
 Rubble stone in natural cement. . . 
 
 
 5 
 
 6 
 
 8 
 
 5-7 
 
 
 10 
 
 Dimension stone in foundations. . . 
 Portland cement concrete in foun- 
 dations 
 
 
 
 4 
 
 15 
 
 8 
 
 4 
 
 
 15 
 
 Natural cement concrete in foun- 
 dations. . 
 
 
 
 
 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 latter case but a few 
 
 * See pp. 226-228. 
 
 t These loads are those allowed by the Chicago BuilJing Ordinance. 
 
STRENGTH OF MASONRY AND CONCRETE. 215 
 
 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 quality of the work and materials the two 
 elements which most influence the strength of brick piers are 
 the proportions of height to least horizontal dimensions and the 
 method of bonding. When the height of a brick pier exceeds 
 six times its least 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 Prof. Ira O. Baker in 
 the Brickbuilder of April, 1898, and also from personal obser- 
 vation, the author has deduced the following formulas for the 
 maximum working loads of first-class brickwork in piers whose 
 height exceeds six times their least dimension. 
 Piers laid with rich lime mortar. 
 
 TT 
 
 Safe load per square inch = 110 5y^. . . . (1) 
 Piers laid with 1 to 2 natural-cement mortar. 
 
 TT 
 
 Safe load per square inch = 140 -5 Jyr-. ... (2) 
 Piers laid with 1 to 3 Portland-cement mortar. 
 
 TT 
 
 Safe load per square inch = 200 6yy (3) 
 
 H representing the heighi in feet, and D the least horizontal 
 dimension in feet.* 
 
 For a pier 20 ft. high and 2 ft. sq. 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 12"Xl2", and 
 when from 6 to 8 ft. in height they should be at least 8"X12". 
 
 Brick piers intended to carry more than 50 per cent, of the 
 safe loads given above should not be built in freezing weather 
 nor with dry bricks. Lime mortar should not be used for 
 
 * For piers faced with pressed brick, laid with *4" joint or less, and 
 backed with common brick in lime mortar, only the dimensions of the back- 
 ing should be considered in figuring the strength of the pier. If backing is 
 laid in cement mortar, and face brick well tied to backing, the full section 
 of pier may be considered. 
 
 For piers veneered with stone or terra-cotta, 4" thick, only the strength 
 of the backing should be considered. 
 
216 STRENGTH OF MASONRY AND CONCRETE. 
 
 building piers that will receive their full load within three 
 months. 
 Effect of Bond on the Strength of Brick Work. 
 
 Brick piers, loaded to the point of destruction, always fail by the 
 splitting and bulging out of the pier, and not by direct crushing 
 of the brick or mortar, showing that the pier is .weakest in the 
 bond and in the tensile or transverse strength of the brick. It is 
 very important therefore that the brickwork be well bonded, and 
 all joints filled with mortar or grouted. The strength of a brick 
 pier intended to carry an extreme load would probably be 
 increased by bonding frequently with hoop iron in addition 
 to the regular brick bond.* 
 
 Bond. Stones in Piers. Many competent architects and 
 builders consider that the strength of a brick pier is increased 
 by inserting bond stones r from 5 to 8 ins. in thickness and the 
 full size of the pier, every 3 or 4 ft. in height. 
 
 The Chicago Building Ordinance requires that for all piers 
 having a height four or more times their least dimension there 
 shall be a bond stone at least 8 ins. thick for each distance in 
 height equal to double that of the smallest dimension of such 
 pier. The Building Laws for the City of New York require 
 bond stones every thirty inches in height, and at least 4 ins. thick. 
 
 On the other hand, there are many first-class builders who 
 consider that bond stones in a pier do more harm than good, and 
 the author is of the opinion that this is generally the case. The 
 Boston Building Law does not require 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 ins., 
 for unless this is done the outer shell will take most of the load, 
 and will be likely to bulge away from the core. 
 
 Piers which support girders or columns should have a cap- 
 stone or iron plate of sufficient 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 or 
 cement and lime mortar unless the backing is very thick, say 
 30 ins. or more. The aggregate thickness of the mortar joints in 
 the backing is so much greater than in the facing, that any 
 shrinkage or compression of the mortar tends to throw undue 
 weight on the facing and to separate it from the backing. 
 
 * The manner in which brick piers fail is excellently shown by illustra- 
 tions on page 79 of the Brickbuilder for May, 1896. 
 
STRENGTH OF MASONRY AND CONCRETE. 217 
 
 Veneering of any kind should be tied to the tracking at least 
 every 18 ins. in height. 
 
 The New York Building Code requires (Sections 28 and 29) 
 that all bearing walls faced with brick laid in running bond, 
 and all walls faced with stone ashlar less than 8 ins. thick, shall 
 be of such thickness as to make the wall independent of the 
 facing conform to that required for unfaced walls. Ashlar 
 8 ins. thick and bonded into the backing may be counted as 
 part of the thickness of the wall. 
 
 Grouting 1 .* It is contended by persons having large ex- 
 perience in building that masonry carefully grouted, when the 
 temperature is not lower than 40 Fahr., 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 
 there is a tendency of the materials to separate and form layers. 
 
 Crushing Height of Brick and Stone. If we assume 
 the weight of brickwork to be 120 pounds per cubic foot, and that 
 it would commence to crush under 700 pounds per square inch, 
 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 pounds per cubic foot would require 
 a column 5,950 ft. high to crush the bottom stones; an average 
 granite at 165 pounds per cubic foot would require a column 
 10,470 ft. high. The Merchants' shot-tower at Baltimore is 
 246 ft. high, and its base sustains a pressure of six tons and a 
 half (of 2,240 pounds) per square foot. The base of the granite 
 pier of Salt ash 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 nine tons and a half per square foot. 
 
 Stone Piers. Piers of good strong building stone laid in 
 courses the full size of the pier, with the top and bottom courses 
 bedded true and even, may be used to support very heavy loads. 
 The height of such piers, however, should not exceed ten times 
 the least dimension, and when it exceeds eight times the thick- 
 ness, the safe load should be reduced. 
 
 The joints should not exceed f inch, and should be spread with 
 * See American Architect, July 21, 1887, p. 11. 
 
218 STRENGTH OF MASONRY AND CONCRETE. 
 
 1 to 2 Portlancfcement mortar, kept back 1 inch from the face 
 of the pier to prevent spalling of the edges. 
 
 A test of the strength of a limestone pier 12 ins. square is de- 
 scribed under Tests on the Crushing Resistance of Stone in this 
 chapter. 
 
 Rubble-work should not be used for piers whose height ex- 
 ceeds five times the least dimension, or in which the latter is 
 less than 20 ins. 
 
 Records of Tests on the Crushing Resistance of 
 Bricks. Table III gives the results of some tests on brick, 
 made under the direction of the author, in behalf of the Mas- 
 sachusetts Charrtable Mechanics' Association. 
 
 TABLE III. SHOWING THE ULTIMATE AND CRACK- 
 ING STRENGTH OF THE BRICK, THE SIZE AND 
 AREA OF FACE. 
 
 
 
 
 Corn- 
 
 
 Name of brick. 
 
 Size. 
 
 Area of 
 face in 
 
 men red 
 to crack 
 under 
 
 Net 
 strength 
 Ibs. per 
 
 
 
 sq. ins. 
 
 Ibs. per 
 
 sq. in. 
 
 
 
 
 sq. in. 
 
 
 Philadelphia Face Brick. . . . 
 
 Whole brick 
 
 33 7 
 
 4 303 
 
 6,062 
 
 
 Whole brick 
 
 32.2 
 
 3,400 
 
 5,831 
 
 * (i ti 
 
 Whole brick 
 
 34.03 
 
 2,879 
 
 5,862 
 
 Average. 
 
 
 
 3,527 
 
 5Q1 
 
 Cambridge Brick (Eastern).. . . 
 
 Half brick 
 
 10.89 
 
 3,670 
 
 ,yio 
 9,825 
 
 " " ** 
 
 Whole brick 
 
 25.77 
 
 7,760 
 
 12,941 
 
 " '* .... 
 
 Half brick 
 
 12 67 
 
 3,393 
 
 11,681 
 
 " " " 
 
 Half brick 
 
 13.43 
 
 3,797 
 
 14,296 
 
 Average 
 
 
 
 4,655 
 
 12,186 
 
 Boston Terra-Cotta Co.'s Brick 
 
 Half brick 
 
 11.46 
 
 11,518 
 
 13,839 
 
 " " " 
 
 Whole brick 
 
 25.60 
 
 8,593 
 
 11,406 
 
 " " " '* 
 
 Whole brick 
 
 28.88 
 
 3,530 
 
 9,766 
 
 Average. . . , 
 
 
 
 7,880 
 
 11,670 
 
 New England Pressed Brick. . . 
 
 Half brick 
 
 12.95 
 
 3,862 
 
 10,270 
 
 ** ... 
 
 Half brick- 
 
 13.2 
 
 8,180 
 
 13,530 
 
 '* "... 
 
 Half brick 
 
 13.30 
 
 2,480 
 
 13,082 
 
 *' ** 
 
 Half brick 
 
 13.45 
 
 4,535 
 
 13,085 
 
 Average 
 
 
 
 4., 764 
 
 12,490 
 
 
 
 
 
 
 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 brick and stone were crushed are fixed in one position, it is 
 necessary that the specimen tested should have perfectly parallel 
 faces. 
 
STRENGTH OF MASONRY AND CONCRETE. 219 
 
 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 Brick used in these tests were obtained from 
 a Boston dealer, and were fair samples of what is known in Bos- 
 ton as Philadelphia Face Brick. They were a very soft brick. 
 
 The Cambridge Brick were the common brick, such as is made 
 around Boston. They are about the same as the Eastern Brick, 
 
 The Boston Terra-Cotta Company's Brick were manufactured of 
 & rather fine clay, and were such as are often used for face brick. 
 
 The New England Pressed Brick were hydraulic-pressed brick, 
 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 brick was 13,925 pounds, and of 
 his common brick, 18,337 pounds per square inch, one brick 
 developing the enormous strength of 22,351 pounds per square 
 inch. This was a very hard-burnt brick. 
 
 Three brick of the Bay State (Mass.) manufacture showed an 
 average strength of 11,400 pounds per square inch. 
 
 The New England brick are among the hardest and strongest 
 brick in the country, those in many parts of the West not having 
 one-fourth of the strength given above, so that in heavy build- 
 ings, where the strength of the brick to be used is not known 
 by actual tests, it is advisable to have the brick tested. 
 
 Prof. Ira O. Baker, of the University of Illinois, reported some 
 tests on Illinois brick, made on the 100,000 pounds testing-ma- 
 chine at the university, in 1888-89, which give the crushing 
 strength of soft brick at 674 pounds per square inch, average of 
 three face brick, 3,070 pounds, and of four paving brick, 9,775 
 pounds. 
 
 In nearly all makes of brick it will be found that the face brick 
 are not as strong as the common brick. 
 
 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. 
 
 * Made under the direction of the author. 
 
220 STRENGTH OF MASONRY AND CONCRETE. 
 
 The brick used in the piers were procured at M. W. Sands's brick- 
 yard, Cambridge, Mass., and were good ordinary brick. They 
 were from the same lot as the samples of common brick de- 
 scribed above. 
 
 The piers were 8" by 12", and nine courses, or about 22 J" 
 high, excepting 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 
 about half an inch thick of pure Portland cement was put on the 
 top of each pier and the foot was grouted in the same cement. 
 
 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 re- 
 move it entirely and put on a layer of cement similar to that on 
 the top 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. 
 
 The piers were built by a skilled bricklayer, and the mortars 
 were mixed under his superintendence. The tests were made 
 with the government testing-machine at the Arsenal. 
 
 The following 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 brick were crushed. 
 
 
 A 
 
 sHI 
 
 IN 
 
 
 g 
 
 fc^- 
 
 ' 
 
 8" X 12" pier. 
 
 09 
 
 li* 
 
 it <& 
 
 Common bricks laid in 
 
 I'P, 
 
 \*\\ 
 
 i 
 
 
 5 
 
 lr^ 
 
 
 
 Lbs. 
 
 Lbs. 
 
 Lbs. 
 
 Lime mortar 
 
 150,000 
 
 833 
 
 1,562 
 
 Lime mortar, 3 parts; Portland cement, 1 
 
 
 
 
 part. . . 
 
 290,000 
 
 1,875 
 
 3,020 
 
 Lime mortar, 3 parts; Newark and Rosen- 
 
 
 
 
 dale cements, 1 part 
 
 245,000 
 
 1,354 
 
 2,552 
 
 Lime rnortar, 3 parts; Roman cement, 1 part 
 
 195,000 
 
 1,041 
 
 2,030 
 
 Portland cement, 1 part; sand, 2 parts 
 
 240,000 
 
 1,302 
 
 2,500 
 
 Newark and Rosendale cements, 1 part; 
 
 
 
 
 sand, 2 parts. ... . . 
 
 205,000 
 
 708 
 
 2,135 
 
 Roman cement 1 part * sand 2 parts 
 
 185,000 
 
 1,770 
 
 1,927 
 
 
 
 
 
STRENGTH OF MASONRY AND CONCRETE. 221 
 
 The Portland cement used in these tests was made by Brooks, 
 Shoobridge & Co., of England. 
 
 As the actual strength of brick piers is a very important con- 
 sideration 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 Government teoting- 
 machine for the year 1884, are given as being of much value. 
 
 Three kinds of brick were represented in the construction of 
 the piers, and mortars of different composition, ranging in 
 strength from lime mortar to neat Portland cement. The piers 
 ranged in cross-section dimensions from 8"X8" to 16"X16", 
 and in height from 16 ins. to 10 ft. 
 
 The piers were tested at the age of from 18 to 24 months. 
 
 Table IV gives the results obtained and memoranda regard- 
 ing the size and character of the piers. 
 
 Test of Mortar Cubes. Table V shows the crushing 
 strength of 6" cubes of mortar made by the United States 
 Government at Watertown, Mass., in the year 1884. 
 
 The mortar cubes were allowed to season in the open air a 
 period of fourteen and a half months, when they were tested. 
 
 The age of the plaster cube was four months. It should be 
 noticed that, while the cubes of Rosendale cement and lime 
 mortar showed a greater strength than when sand alone was 
 mixed with the cement, with the cubes of Portland cement and 
 lime mortar the reverse was the case, differing from the result 
 obtained by the author. This shows the necessity of a number 
 and variety of tests. 
 
 Tests of the Crushing Resistance of Various 
 Building Stones. 
 
 SANDSTONES. 
 
 Long Meadow (Mass.) Stone.* Reddish-brown sandstone, 
 two blocks about 4"X4" in cross-section and 8" high. 
 
 Block No. 1 commenced to crack at 10,333 Ibs. per square inch, 
 and flew from the machine in fragments at 13,596 Ibs. per square 
 inch. 
 
 Block No. 2 commenced to crack at 3,012 Ibs. per square [inch 
 and failed completely at 9,121 Ibs. per square inch. 
 
 * These tests made with U. S. testing-machine at Watertown Arsenal, 
 Mass. 
 
222 STRENGTH OF MASONRY AND CONCRETE. 
 
 
 
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224 STRENGTH OF MASONRY AND CONCRETE. 
 
 TABLE V. TABULATED RESULTS, 6" MORTAR CUBES. 
 
 CRUSHING STRENGTH. 
 
 No. 
 of 
 test. 
 
 Composition. 
 
 First 
 crack. 
 
 Ultimate 
 strength 
 per sq. in. 
 
 ll 
 g o 
 
 *i 
 
 3a 
 36 
 3c 
 
 1 part lime, 3 parts sand 
 1 3 
 1 " " 3 " 
 
 Lbs. 
 
 Lbs. 
 135 
 119 
 118 
 
 Lbs. 
 112 
 111 
 106 
 
 4a 
 
 1 part Portland cement 2 part j sand 
 
 
 560 
 
 116 
 
 46 
 
 1 " " 2 " " 
 
 
 696 
 
 120 
 
 4c 
 5a 
 
 1 " "2 " 
 
 1 part Rosendale cen.ent, 2 parts sand 
 
 11,500 
 
 383 
 156 
 
 115 
 
 111 
 
 56 
 5c 
 
 6a 
 66 
 Gc 
 
 1 " " " 2 " 
 l . "2 " 
 
 Neat Portland cement 
 <( 
 
 ' 4,500 
 95,666 
 
 186 
 143 
 
 2,673 
 3,548 
 4,227 
 
 109 
 107 
 
 126 
 129 
 135 
 
 7a 
 76 
 7c 
 
 8a 
 
 Neat Rosendale cement 
 1 part Portland cement, 2 pfirts lime mortar* 
 
 11,000 
 19,000 
 19,200 
 
 421 
 615 
 526 
 
 204 
 
 94 
 99 
 97 
 
 109 
 
 86 
 
 1 " 2 " 
 
 
 198 
 
 110 
 
 8c 
 
 1 " " 2 " " " 
 
 
 175 
 
 103 
 
 9a 
 
 1 part Rosendale cement 2 parts lime mortar* 
 
 
 194 
 
 105 
 
 96 
 9c 
 
 1 " " " 2 " " 
 1 " " " 2 " " 
 Plaster-of-Paris 
 
 
 193 
 162 
 1,981 
 
 106 
 105 
 
 74 
 
 1 Lime mortar, 1 part lime, 3 parts sand. 
 
 Sandstone from Norcross Bros., Quarries, East Long Meadow, 
 Mass. Soft Saulsbury* Block No. 1, 4"X4"X8" high, com- 
 menced to crack at 8,250 Ibs. and failed at 8,812 Ibs. per square 
 inch. 
 
 Block No. 2, 4"X4"X8" high, commenced to crack at 6,500 
 Ibs. and failed at 8,092 Ibs. per square inch. 
 
 Hard Saulsbury* Block No. 1, 4"X4"X8" high (about), 
 commenced to crack at 12,716 Ibs. and failed at 13,520 Ibs. per 
 square inch. 
 
 Block No. 2, same size as No. 1, commenced to crack at 13,953 
 Ibs. and failed at 14650 Ibs. per square inch. 
 
 Kibbe Stone* Block No. 1, 6"X6"X6", commenced to 
 crack at 12,590 Ibs. and failed at 12,619 Ibs. per square inch. 
 
 + These tests made with U. S. testing-machine at Watertown Arsenal, 
 
Block No. 2, same size as No. 1, commenced to crack at 12,185 
 Ibs. and failed at 12,874 Ibs. per square inch. 
 
 Brown Stone from the Shaler & Hall Quarry Co., Portland, 
 Conn.* 
 
 Dimensions. 
 
 Sectional 
 area, 
 sq. ins. 
 
 First 
 crack, 
 Ibs. 
 
 Ultimate 
 strength, 
 Ibs. per 
 sq. in. 
 
 Classification. 
 
 Height, 
 ins. 
 
 Compressed 
 surface, 
 ins. 
 
 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 
 2.95 
 2.97 
 2 . 53 
 2.52 
 
 6.13 
 6.13 
 8.85 
 8.85 
 6.45 
 6.25 
 
 84,800 
 81,700 
 123,200 
 122,000 
 63,850 
 58,340 
 
 13,980 
 13,330 
 13,920 
 15,020 
 9,900 
 9,330 
 
 1st quality 
 1st 
 2d 
 3d 
 Bridge 
 Bridge 
 
 Brown Stone from the Middlesex Quarry Co., Portland, Conn.f 
 Four nearly cubical blocks, about 1J" square. Pressure per 
 square inch at time of failure: No. 1, 10,928 Ibs.; No. 2, 10,322 
 Ibs. ; No. 3, 8,252 Ibs., and No. 4, 6,322 Ibs. 
 
 Red Sandstone f from Greenlee & Son's Quarries at Manitou, 
 Colo. One specimen failed at 11,000 Ibs. per sq. inch; weight 140 
 Ibs. per cu. ft. 
 
 Light-red Laminated Sandstone,^, from St. Vrain Canon, Colo. 
 (a very hard stone, excellent for walks and foundations) . Crush- 
 ing strength on bed 11,505 Ibs. per square inch; weight 150 Ibs. 
 per cubic foot. 
 
 Gray Sandstone { (free-working) from Trinidad, Colo. Crush- 
 ing strength 10,000 Ibs. per square inch; weight 145 Ibs. per cubic 
 foot. 
 
 Gray Sandstone J from Fort Collins, Colo, (laminated and simi- 
 lar in quality to the St. Vrain Stone). Crushing strength on 
 bed 11,700 Ibs. per square inch; weight 140 Ibs. per cubic foot 
 (one ton of this stone measures just a perch in the wall). 
 
 GRANITE. 
 
 Red Granite { from Platte Canon, Colo. Crushing strength 
 per square inch 14,600 Ibs. ; weight per cubic foot 164 Ibs. 
 
 * From tests made by Colt's Batent Fire-arms Manufacturing Co. 
 
 t These tests made with U. S. testing-machine 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 two-inch cubes. 
 
226 STRENGTH OF MASONRY ANDj CONCRETE. 
 
 Lava Stone from the Kerr Quarries, near Salida, Colo. Four 
 cubical blocks.* 
 
 Dimensions. 
 
 Sectional 
 area, 
 sq. ins. 
 
 First 
 crack, 
 Ibs. 
 
 Ultimate strength, 
 
 Height, 
 
 ins. 
 
 Compressed sur- 
 face, ins. 
 
 Lbs. 
 
 Lbs. 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 
 3.98 
 3.96 
 
 165,900 
 1 74, 100 
 36,400 
 38,200 
 
 165,000 
 174,100 
 37,100 
 38,200 
 
 10,369 
 10,881 
 9,322 
 9,646 
 
 Lava Stone, f Curry's Quarry, Douglas County. Crushing 
 strength, 10,675 Ibs. per square 'inch; weight, 119 Ibs. per 
 cubic foot. (Experience has shown that this stone is not suit- 
 able for piers, or where any great strength is required, as it 
 cracks very easily.) 
 
 MARBLE. 
 
 White marble quarried at Sutherland Falls, Vermont. Two 
 cubical blocks about 6 ins. square.* 
 
 Block No. 1 commenced to crack at 9,750 Ibs. per square inch 
 and failed suddenly at 11,250 Ibs. per square inch. 
 
 Block No. 2 did not crack until it suddenly gave way at 10,243 
 Ibs. per square inch. 
 
 Test of a Limestone Pier. A pier of Lemont limestone 1 ft. sq. 
 in cross-section and 9 ft. high, composed of 7 stones with bear- 
 ing surfaces planed perfectly true and parallel to natural bed 
 and the joints washed with a thin grout of the best English 
 Portland cement, was tested at the Watertown Arsenal for 
 Gen. Wm. Sooy Smith, and only commenced to crack when 'the 
 full power of the machine, 400 tons, was exerted. 
 
 Crushing Strength of Concrete. Tests for crushing 
 strength made on 6-in. cubes of concrete, made of one part silica 
 Portland cement (1.1), two parts sand, and three parts gravel. 
 The concrete was taken from the bucket just as it was ready to be 
 laid in the foundations of the Cathedral of St. John the Divine. 
 
 Each result is the average of the crushing strengths of four sep- 
 
 * Tested at U. S. Arsenal, Watertown, Mass. 
 
 + From tests made by Denver Society of Civil Engineers in 1884, also on 
 two-inch cubes. 
 
STRENGTH OF MASONRY AND CONCRETE. 227 
 
 arate cubes, made under exactly the same conditions at differ- 
 ent periods : 
 
 7 days old crushed at 77,162 Ibs. or 2,143 Ibs. per sq. in. 
 14 " " " " 83,225 " " 2,312 " " " " 
 30 " " " " 92,465 " " 2,568 " " " " 
 
 The following table gives the crushing strength of 12-in. 
 cubes of concrete prepared and tested by the Engineering De- 
 partment of the District of Columbia in the years 1896 and 1897, 
 the loads being in pounds per square foot. After the tests were 
 completed it was found that the machine used gave results 8% 
 too high, and the figures have not been corrected. 
 
 The figures for 1-year cubes are averages of 5 tests, all others 
 give the mean of two tests. 
 
 A more complete record of the tests may be found in the 
 Engineering Record for April 9, 1898.* 
 
 No. 
 
 Composition of concretes 
 by volume. 
 
 10 days. 
 
 45 days. 
 
 3 mos. 
 
 6 mos. 
 
 1 year. 
 
 
 1 part natural cement, 
 
 
 
 
 
 
 
 2 parts sand. 
 
 Lbs. 
 
 Lbs. 
 
 Lbs. 
 
 Lbs. 
 
 Lbs. 
 
 1 
 
 6 parts average concrete 
 
 
 
 . 
 
 
 
 
 stone . . 
 
 32,900 
 
 77,687 
 
 54,022 
 
 114,412 
 
 131,700 
 
 2 
 
 3 parts average concrete 
 stone, 3 parts gravel.. 
 
 15,500 
 
 52,362 
 
 85,315 
 
 90,965 
 
 121,100 
 
 3 
 
 4 parts average concrete 
 stone, 2 parts gravel. 
 
 
 
 
 
 131,700 
 
 4 
 
 6 parts OM average con- 
 
 
 
 
 
 
 
 crete stone, J4 grano- 
 
 
 
 
 
 
 
 lithic) 
 
 
 
 
 
 115,200 
 
 5 
 
 6 parts average gravel. . . 
 
 12,500 
 
 60,652 
 
 51,980 
 
 49,437 
 
 109,900 
 
 6 
 
 6 parts coarse concrete 
 
 
 
 
 
 
 
 stone (no fine) . 
 
 
 
 85,880 
 
 
 119,300 
 
 
 1 part (Atlas') Portland 
 
 
 
 
 
 
 
 cement, 2 parts sand. 
 
 
 
 
 
 
 7 
 
 6 parts average concrete 
 stone. . . . 
 
 130,750 
 
 t343,520 
 172,325 
 
 324,875 
 
 361,600 
 
 440,040 
 
 8 
 
 3 parts average concrete 
 stone 3 parts gravel.. 
 
 136,750 
 
 266,962 
 
 
 298,037 
 
 396,200 
 
 9 
 
 4 parts average concrete 
 
 
 
 
 
 
 
 stone, 2 parts gravel.. 
 
 
 
 
 
 408,300 
 
 10 
 
 6 parts (% average con- 
 
 
 
 
 
 
 
 crete stone, *4 grano- 
 
 
 
 
 
 
 
 lithic) 
 
 
 
 
 
 388,700 
 
 11 
 
 6 parts average gravel . . 
 
 99,900 
 
 234,475 
 
 385,612 
 
 265,550 
 
 406,700 
 
 12 
 
 6 parts coarse concrete 
 
 
 
 
 
 
 
 stone (no fine) 
 
 
 
 234,475 
 
 220,350 
 
 266,300 
 
 
 
 
 
 
 
 
 * Valuable data on the crushing strength of concretes of different propor- 
 tions may be found in the Engineering News of Feb. 4, 1904, p 114. 
 
 t Owing to the great variation in the strength of the two cubes, the 
 results for both are given. 
 
228 STRENGTH OF MASONRY AND CONCRETE. 
 
 The average crushing strength of four 12-inch cubes of con- 
 crete, tested at the U. S. Arsenal, Watertown, Mass., for the 
 city of Cleveland, Ohio, was 4,286 Ibs. per sq. inch. The cubes 
 were composed of 1 part Vulcanite Portland cement, 2 parts 
 lake sand and 4 parts of broken limestone, and were 85 days old 
 when tested. 
 
 Strength of " Hooped" Concrete Columns. In 
 1892, M. Considere conducted a series of experiments at the 
 laboratory of 1'Ecole des Fonts et Chaus- 
 se"es, which demonstrated conclusively that 
 the resistance -of concrete columns may 
 be very greatly increased by winding 
 spirally with wire and then plastering 
 with cement. Crushing resistances of 
 such columns as high as 9,150 Ibs. per 
 sq. inch on full section, and 12,700 Ibs. per 
 sq. inch on core section, were obtained. 
 M. Considere considers that working 
 values may be allowed for such columns of 
 from 950 to 2,150 Ibs. per sq. inch, accord- 
 ing to the way in which the columns are 
 made and reinforced. See the Engineer- 
 ing Record of Jan. 3, 10, 17 and 24, 1903. 
 
 The accompanying engraving shows 
 the method of reinforcing concrete col- 
 umns, employed by the Ransome Com- 
 panies. With this reinforcement it is customary to allow a safe 
 stress in the column of 800 to 1000 Ibs. to the square inch. 
 
 Architectural Terra-Cotta Weight and Strength. 
 
 The lightness of terra-cotta, combined with its enormous re- 
 sisting strength, and taken in connection also with its durability 
 and absolute indestructibility by fire, water, frost, etc., ren- 
 ders it specially desirable for use in the construction of all large 
 edifices. 
 
 Terra-cotta for building purposes, whether plain or ornamental, 
 is generally made of hollow blocks formed with webs inside, so as 
 to give extra strength and keep the work true while drying. This 
 is necessitated because good, well-burned terra-cotta cannot 
 safely be made more than about 1J inches in thickness, 
 whereas, when required to bond with brickwork, it must be 
 
 Re-inforcing Skeleton 
 for Concrete Columns. 
 
BT1UWNU111 U* MASUJNKY AJNJD UUJNUKETE. 
 
 at least four inches thick. When extra strength is needed, 
 these hollow spaces are filled with concrete or brickwork, which 
 greatly increases the crushing strength of terra-cotta, although 
 alone it is able to bear a very heavy weight. "A solid block of 
 terra-cotta of one foot cube has borne a crushing strain of 500 
 tons and over." 
 
 TABLE VI'. CRUSHING RESISTANCE OF BRICK, STONE, AND 
 CONCRETES. (PRESSURE AT RIGHT ANGLES TO BED.) * 
 
 Pounds 
 per sq. in. 
 
 Brick: Common, Massachusetts 10,000 
 
 Common, St. Louis 6,417 
 
 Common, Washington, D. C 7,370 
 
 Paving, Illinois 6,000 to 13,000 
 
 Granites: Blue, Fox Island, Me 14,875 
 
 Gray, Vinal Haven, Me 13,000 to 18,000 
 
 Westerly, R. I .' 15,000 
 
 Rockport and Quincy, Mass 17,750 
 
 Milford, Conn 22,600 
 
 Staten Island, N. Y 22,250 
 
 East St. Cloud, Minn 28,000 
 
 Gunnison, Colo 13,000 
 
 Red, Platte Canon, Colo 14,600 
 
 Limestones: Glens Falls, N. Y 11,475 
 
 Joliet, 111 . 12,775 
 
 Bedford, Ind 6,000 to 10,000 
 
 Salem, Ind 8,625 
 
 Red Wing, Minn 23,000 
 
 Stillwater, Minn 10,750 
 
 Sandstones: Dorchester, N. B. (brown) 9,150 
 
 Mary's Point, N. B. (fine grain, dark brown). . . . 7,700 
 
 Connecticut brown stone, f on bed .*. . . 7,000 to 13,000 
 
 Longmeadow, Mass, (reddish brown) 7,000 to 14,000 
 
 * ' " average, for good quality 12,000 
 
 Little Falls, N. Y 9,850 
 
 Medina, N. Y 17,000 
 
 Potsdam, N. Y. (red) 18,000 to 42,000 
 
 Cleveland, Ohio 6,800 
 
 North Amherst, Ohio 6,212 
 
 Berea, Ohio 8,000 to 10,000 
 
 Hummelstown, Pa 12,810 
 
 Fond du Lac, Minn 8,750 
 
 Fond du Lac, Wis 6,237 
 
 Manitou, Colo, (light red) 6,000 to 11,000 
 
 St. Vrain, Colo, (hard laminated) 11,505 
 
 Marbles: Lee, Mass 22,900 
 
 Rutland, Vt 10,746 
 
 Montgomery Co., Pa 10,000 
 
 Colton, Cal 17,783 
 
 Italy 12,156 
 
 Flagging: North River, N. Y 13,425 
 
 * For more complete tables of the strength, weight, and composition of 
 building stones, see Building Construction and Superintendence, Part I. 
 t This stone should not be set on edge. 
 
230 STRENGTH OF MASONRY AND CONCRETE. 
 
 Some exhaustive experiments made by the Royal Institute 
 of British Architects give the following results as the crushing 
 strength of terra-cotta blocks : 
 
 Crushing wt. 
 per cu. ft. 
 
 1. Solid block of terra-cotta 523 tons 
 
 2. Hollow block of terra-cotta, unfilled 186 tons 
 
 3. Hollow block of terra-cotta, slightly made and unfilled 80 ' ' 
 
 Tests of terra-cotta manufactured by a New ,York Com- 
 pany, which were made at the Stevens Institute of Technology 
 in April, 1888, gave the following results: 
 
 Crushing wt. Crushing wt. 
 ; :- ; ' per cu. in. per cu. ft. 
 
 Terra-cotta block, 2-inch square, red. . . . 6,840 Ibs. or 492 tons 
 
 Terra-cotta block, 2-inch square, buff 6,236 " " 449 " 
 
 Terra-cotta block, 2-inch square, gray 5,126*' ''369 " 
 
 From these results, the writer would place the safe working 
 strength of terra-cotta blocks in the wall at 5 tons per square 
 foot when unfilled, and 10 tons per square foot when fitted solid 
 with brickwork or concrete. 
 
 Strength of Terra-Cotta Brackets or Consoles. 
 A cornice modillion made by the Northwestern Terra-Cotta 
 Company, 11J- ins. high at the wall line, 8 ins. wide on face, with a 
 projection of 2 feet, was built into a wall and the upper sur- 
 face loaded with pig iron to the extent of two tons without 
 effect. 
 
 Another bracket, 5J ins. high, 6 ins. wide, and 14 ins. projec- 
 tion made in the East, broke at wall line under 2,650 Ibs., 
 while a duplicate of it sustained 2,400 Ibs. for one month with- 
 out breaking. (See "The Brickbuilder," Vol. 7, p. 142.) 
 
 The weight of terra-cotta in solid blocks is 122 pounds. When 
 made in hollow blocks 1J inches thick the weight varies from 
 65 to 85 pounds per cubic foot, the smaller pieces weighing the 
 most. For pieces 12" X 18" or larger on the face, 70 pounds per 
 cubic foot will probably be a fair average. 
 
 For the exterior facing of fireproof buildings, terra-cotta is 
 now considered as the most suitable material available. 
 
CHAPTER VI. 
 
 COMPOSITION AND RESOLUTION OP FORCES- 
 CENTRE OF GRAVITY. 
 
 LET us imagine a round ball placed on a plane surface at A 
 (Fig. 1), the surface being perfectly level/so that the ball will have 
 no tendency to move until some force is imparted to it. If, now, 
 we impart a force, P, to the ball in the direction indicated by the 
 arrow, the ball will move off in the same direction. If, instead 
 of imparting only one force, we impart two forces, P and P t to 
 the ball, it will not move in the direction 
 of either of the forces, but will move off 
 in the direction of the resultant of these 
 forces, or in the direction Ab in the figure. 
 If the magnitude of the forces P and PI 
 is indicated by the length of the lines, 
 then, if we complete the parallelogram 
 A BCD, the diagonal DA will represent the 
 direction and magnitude of a force which 
 will have the same effect on the ball as the 
 two forces P t and P. If, in addition to the two forces P l and P 
 we now apply a third force, P 2 , the ball will move in the direction 
 of the resultant of all three forces, which can be obtained by com- 
 pleting the parallelogram ADEF, formed by the resultant DA 
 and the third force P 2 . The diagonal R of this 
 second parallelogram will be the resultant of all 
 three of the forces, and the ball will move in the 
 direction Ae. In the same way we could find 
 the resultant of any number of forces. 
 
 Again, suppose we have a ball suspended in 
 the air whose weight is indicated by the line W 
 (Fig. 2). Now, we do not wish to suspend this 
 ball by a vertical line above it, but by two in- 
 clined lines or forces, P and P t . What shall be 
 the magnitude of these two forces to keep the ball suspended in 
 just this position? We have here just the opposite of our last 
 
232 COMPOSITION OF FORCES. 
 
 case; and, instead of finding the diagonal of the resultant, we 
 have the diagonal, which is the line W, and wish to find the sides 
 of the parallelogram. To do this, prolong P and P lt and from B 
 draw lines parallel to them to complete the parallelogram. Then 
 will CA be the required magnitude for P, and CB for P,. 
 
 Thus we see how one force can be made to have the same effect 
 as many, or many can be made to do the work of one. Bearing 
 the above in mind, we are now prepared to study the following 
 propositions : 
 
 I. A force may be represented by a straight line. 
 
 In considering the action of forces, either in relation to struc- 
 tures or by themselves, it is very convenient to represent the 
 force graphically, which can easily be done by a straight line hav- 
 ing an arrow-head, as in Fig. 3. The length 
 of the line, if drawn to a scale of pounds, 
 shows the value of the force in pounds; the 
 direction of the line indicates the direction 
 p. 3 of the force; the arrow-head shows which 
 
 way it acts; and the point A denotes the 
 point of application. Thus we have the direction, magnitude, 
 and point of application of the force represented, which is all 
 that we need to know. 
 
 Parallelogram of Forces. II. // two forces applied at 
 one point, and acting in the same plane, be represented by two 
 straight lines inclined to each other, their resultant will be equal to 
 the diagonal of the parallelogram formed on these lines. 
 
 Thus, if the lines A B and AC (Fig. 4) represent two forces act- 
 ing on one point, A, and in the same plane, / 
 then, to obtain the force which would have the 
 same effect as the two forces, we complete the 
 parallelogram ABDC, and draw the diagonal 
 AD. This line will then represent the result- 
 ant of the two forces. 
 
 When the two given forces are at right angles to each other, 
 the resultant will, by geometry, be equal to the square root of the 
 sum of the squares of the other two forces. 
 
 The Triangle of Forces. III. // three forces acting on 
 a point be represented in magnitude and direction by the sides 
 of a triangle taken in order, they will keep the point in equili- 
 brium. 
 
 Thus let P, Q, and R (Fig. 5) represent three forces acting on 
 the point 0. Now, if we can draw a triangle like that shown at 
 
the right of Fig. 5, whose sides shall be respectively parallel to 
 the forces, and shall have the same 'relation to each other as do 
 the forces, then the forces will keep the , 
 point in equilibrium. If such a triangle 
 cannot be drawn, the forces will be un- 
 balanced, and the point will not be in 
 equilibrium. 
 
 The Polygon of Forces. IV. // 
 any number of forces acting at a point can 
 be represented in magnitude and direction 
 by the sides of a polygon taken in order, 
 they will be in equilibrium. 
 
 This proposition is only the preceding 
 one carried to a greater extent. 
 
 Moments. In considering the stability of structures and 
 the strength of materials, we are often obliged to take into con- 
 sideration the moments of the forces acting on the structure or 
 piece ; and a knowledge of what a moment is, and the properties 
 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 about which the moment is taken. 
 
 The moment of a force about any given point may be defined as 
 the product of the force into the perpendicular distance from the 
 point to the line of action of the force; or, in other words, the 
 moment of a force is the product of the force by the arm with which 
 it acts. 
 
 Thus if we have a force F (Fig. 6), and wish to determine its 
 moment about a point P, we determine the perpen- 
 dicular distance Pa, between the point and the line 
 of action of the force, and multiply it by the force 
 in pounds. For example, if the force F were equal 
 Fm 6 ^ a we ight of 500 pounds, and the distance Pa 
 were 2 inches, then the moment of the force about 
 the point P would be 1,000 inch-pounds. 
 
 The following important propositions relating to forces and 
 moments should be borne in mind in calculating the strength or 
 stability of structures. 
 
 V. // any number of parallel forces act on a body, that the 
 body shall be in equilibrium, the sum of the forces acting in one 
 direction must equal the sum of the forces acting in the opposite 
 direction. 
 
T 
 
 234 COMPOSITION OF FORCES. 
 
 Thus if we have the parallel forces P 1 , P 2 , P 3 , and P 4 , acting 
 on the rod AB (Fig. 7), in the 
 p opposite direction to the forces 
 
 tp' IP' 3 | p 4 A, P 2 , P 3 , then, if the rod is in 
 
 J I I I B equilibrium, the sum of the forces 
 
 P 1 , P 2 , P 3 , and P 4 , must equal the 
 sum of the forces P lt P 2 , and P 3 . 
 
 VI. // any number of parallel 
 forces act on a body in opposite 
 directions, then, for the body to be 
 Fig. 7 in equilibrium, the sum of the 
 
 moments tending to turn the body 
 
 in one direction must equal the sum of the moments tending to turn 
 the body in the opposite direction about any given point. 
 
 Thus let Fig. 8 represent three par- 
 allel forces acting on a rod A B. Then 
 for the rod to be in equilibrium, the sum 
 of the forces F 2 and F 3 must be equal to 
 FI. Also, if we take the end of the rod, 
 A, for our axis, then must the moment 
 of FI be equal to the sum of the mo- 
 ments of F 2 and F 3 about that point, be- 
 cause the moment of F 1 tends to turn 
 the rod down to the right, and the moments of F 2 and F 3 tend to 
 turn the rod up to the left, and there should be no more tendency 
 to turn the rod one way than the other. For example, let the 
 forces F 3 , F 2 , each be represented by 5, and let the distance A a 
 be represented by 2, and the distance Ac by 4. The force 
 must equal the sum of the forces F s and F 2 , or 10; and its mo- 
 ment must equal the sum of the moments of F 3 and F 2 . If we take 
 the moments around A, then the moment of P 3 =5X2=10, and 
 of F 2 = 5 X 4 = 20. Their sum equals 30 : hence the moment of F 1 
 must be 30. Dividing the moment 30 by the force 10, we have 
 for the arm 3 ; or the force F l must act at a distance 3 from A to 
 keep the rod in equilibrium. 
 
 If we took our moments around b } then the force F^ would have 
 no moment, not having any arm, and so the moment of F 2 about 
 b must equal the moment of F 3 about the same point; or, as in 
 this case the forces are equal, they must both be applied at the 
 same distance from b, showing that b must be halfway between 
 a and c, as was proved before. 
 
COMPOSITION OF FORCES. 
 
 235 
 
 The Principle of the Lever. This principle is based 
 upon the two preceding propositions, 
 and is of great importance and conveni- 
 ence. 
 
 VII. // three parallel forces acting in 
 one plane balance each other, then each 
 force must be proportional to the distance A 
 between the other two. 
 
 B 
 
 Fig. 9 a 
 
 Thus, if we have a rod AB (Figs. 9a, 
 9b, and 9c), with three forces, P lt P 2J fi 
 P 3 , acting on it, that the rod shall be 
 balanced, we must have the following relation between the forces 
 and their points of application ; viz., 
 
 or 
 
 P l : 
 
 CB * AB ' AC' 
 \ :P 3 ::BC :AB :AC. 
 
 This is the case of the common lever, and gives the means of 
 determining how much a given lever will raise. 
 
 p Fig.9 b 
 C 
 
 
 ! 
 
 P 2 
 
 PI Fig. 9c 
 
 The proportion is also true for any arrangement of the forces 
 (as shown in Figs, a, b, and c), provided, of course, the forces are 
 lettered in the order shown in the figures. 
 
 EXAMPLE. Let the distance AC be 6 inches, and the distance 
 CB be 12 inches. If a weight of 500 pounds is applied at the 
 point B. how much will it raise at the other end, and what sup- 
 port will be required at C (Fig. 9b) ? 
 
 Ans. Applying the rule just given, we have the proportion: 
 
 P 3 : P l :: AC : CB, or 500 : (PO :: 6 : 12. 
 
 Hence P l = 1,000 pounds ; or 500 pounds applied at B will lift 1,000 
 suspended at A. The supporting force at C must, by proposi- 
 
236 CENTRE OF GRAVITY. 
 
 tion V., be equal to the sum of the forces P l and P 3 , or 1,500 
 pounds in this case. 
 
 Centre of Gravity. The lines of action of the force of 
 gravity converge towards the centre of the earth; but the dis- 
 tance of the centre 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 considered as equal to the number of particles compos- 
 ing the body. 
 
 The centre 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 in every position of the body. 
 
 If a body be supported at its centre of gravity, and be turned 
 about that point, it will remain in equilibrium in all positions. 
 The resultant of the parallel forces of gravity acting upon a body 
 is obviously equal to the weight of the body, and if an equal force 
 be applied, acting in a line passing through the centre of gravity 
 of the body, the body will be in equilibrium. 
 
 Examples of Centres of Gravity. Centre of Gravity 
 of Lines. Straight Lines. By a line is here meant a material line 
 whose transverse section is very small, such as a very fine wire. 
 
 The centre of gravity of a uniform straight line is at its middle 
 
 point. This proposition is too evident to require demonstration. 
 
 The centre of gravity of the perimeter of a triangle is at the 
 
 centre of the circle inscribed in the lines joining the centres of 
 
 the sides of the given triangle. 
 
 Thus, let ABC (Fig. 10) be the given 
 triangle. To find the centre of gravity 
 of its perimeter, find the middle points, 
 D, E, and F, and connect them by 
 straight lines. The centre of the circle 
 inscribed in the triangle formed by 
 these lines will be the centre of gravity 
 sought. 
 
 Symmetrical Lines. The centre of 
 
 gravity of lines which are symmetrical with reference to a point 
 will be at that point. Thus the centre of gravity of the circum- 
 ference of a circle or an ellipse is at the geometrical centre of 
 those figures. 
 
 The centre of gravity of the perimeter of an equilateral triangle, 
 or of a regular polygon, is at the centre of the inscribed circle. 
 
CENTRE OF GRAVITY. 237 
 
 The centre of gravity of the perimeter of a square, rectangle, or 
 parallelogram, is at the intersection of the diagonals of those 
 figures. 
 
 Centre of Gravity of Surfaces. Definition. A surface here 
 means a very thin plate or shell. i 
 
 Symmetrical Surfaces. If a surface can be divided into two 
 symmetrical halves by a line, the centre of gravity will be on that 
 line : if it can be divided by two lines, the centre of gravity will 
 be at their intersection. 
 
 The centre of gravity of the surface of a circle or an ellipse is 
 at the geometrical centre of the figure, of an equilateral triangle 
 or a regular polygon, it is at the centre of the inscribed circle; of 
 a parallelogram, at the intersection of the diagonals; of the sur- 
 face of a sphere, or an ellipsoid of revolution, at the geometrical 
 centre of the body; of the convex surface of a right cylinder at 
 the middle point of the axis of the cylinder. 
 
 Irregular Figures. Any figure may be divided into rectangles 
 and triangles, and, the centre of gravity of each being found, the 
 centre of gravity of the whole may be determined by treating the 
 centres of gravity of the separate parts as particles whose weights 
 are proportional to the areas of the parts they represent. 
 
 Triangle. To find the centre of gravity of a triangle, draw a 
 line from each of two angles to the middle of the side opposite: 
 the intersection of the two lines will give the centre of gravity. 
 
 Quadrilateral. To find the centre of gravity of any quadrilat- 
 eral, draw diagonals, and, from the end of each farthest from 
 their intersection, lay off, toward the intersection, its shorter 
 segment : the two points thus formed with the point of intersec- 
 tion will form a triangle whose centre of gravity is that of the 
 quadrilateral. 
 
 Thus, let Fig. 11 be a quadrilateral whose centre of gravity is 
 sought. Draw the diagonals AD 
 and BC, and from A lay off AF= 
 ED, and from B lay off BH=EC. 
 From E draw a line to the middle 
 of FH, and from F a line to the 
 middle of EH. The point of inter- 
 section of these two lines is the 
 centre of gravity of the quadri- A ^" p. 
 
 lateral. This is a method com- 
 monly used for finding the centre of gravity of the voussoirs of 
 an arch. 
 
238 CENTRE OF GRAVITY. 
 
 Table of Centres of Gravity. Let a denote 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 
 centre of gravity. Then 
 
 In an isosceles triangle . . . . D=%a 
 In a segment of a circle j _ chord 3 
 
 Vertex at centre of circle f 12 X are a 
 
 In a sector of a circle, the ver-) ^_ 2 x chord 
 tex being at the centre j J 3Xarc 
 
 In a semicircle, vertex being) _. 4R 
 
 \. 2j= = 42447? 
 
 at the centre ( 3n 
 
 In a quadrant of a circle . . . D=%R 
 
 In a semi-ellipse, vertex being ) 
 
 Sector. *H . >=0.425a 
 
 at the centre ( 
 
 In a parabola, vertex at intersection of) n_s 
 
 axis with curve ) 
 
 In a cone or pyramid D=|a 
 
 In a frustum of a cone or pyramid, let h = height of complete 
 cone or pyramid, 7^= height of frustum, and the vertex be at 
 
 Q/^4__Z, 4\ 
 
 apex of complete cone or pyramid; then D= ~ 
 
 
 
 Centre of Gravity of Heavy Particles. Centre o t 
 Gravity of Two Particles. Let P be the 
 weight of a particle at A (Fig. 12), and W 
 that at C. 
 
 The centre of gravity will be at some/^N 
 point, B, on the line joining A and C. \^7~ 
 The point B must be so situated, that if P W 
 
 the two particles were held together by a 
 
 stiff wire, and were supported at B by a force equal to the sum 
 of P and TF, the two particles would be in equilibrium. 
 
 The problem then comes under the principle of the lever, and 
 hence we must have the proportion (see proposition VII.). 
 
 P+W :P ::AC :BC, 
 or 
 
 PXAC 
 
 ' = ~p+W 
 
 If W=P, then BC=AB, or the centre of gravity will be half- 
 way between the two particles. This problem is of great im- 
 portance, for it presents itself in many practical examples. 
 
CENTRE OF GRAVITY. 
 
 239 
 
 Centre of Gravity of Several Heavy Particles. Let W if W 2 , W ZJ 
 W and W 5 (Fig. 13) be the weights of the particles. 
 
 Join W 1 and W 2 by a straight line, and 
 find their centre of gravity A , as in the pre- 
 ceding problem. Join A with W z , and find 
 the centre of gravity B, which will be the 
 centre of gravity of the three weights W lf 
 W 2 , and W 3 . Proceed in the same way with 
 each weight, and the last centre of gravity 
 found will be the centre of gravity of all the 
 particles. 
 
 In both of these cases the lines joining the particles are sup- 
 posed to be horizontal lines, or else the horizontal projection of 
 the real straight line which would join the points. 
 
 Centre of Gravity of Compound Sections Found 
 by Moments. To determine the strength of a beam having 
 an unsymmetrical section, it is first necessary to determine the 
 distance of the centre of gravity of the section from the bottom 
 of the beam. Various other computations also involve finding 
 the centre of gravity of an irregular figure, so that the problem 
 is one of practical importance. 
 
 If the figure of which the centre of gravity is sought can be 
 divided into regular figures the readiest and simplest method of 
 finding the distance of the centre of gravity from one edge is 
 by means of moments. 
 
 To explain this method we will assume a T-shape section of 
 uniform thickness pivoted on a wire, XX, as in Fig. 14. The T 
 
 Fig. 14 
 
 is made up of two rectangles, one forming what we will call the 
 flange, the other the web. The centre of gravity of each of 
 
240 
 
 CENTRE OF GRAVITY. 
 
 these rectangles will be at their centre, which can easily be 
 found. 
 
 Fig. 15 
 
 Now, if the T were placed horizontally, as in the figure, the 
 axis XX being fixed, it would immediately revolve about 
 the axis until it became vertical, and the moments causing the 
 revolution would be A.'df -\-A n d' f ^ A' representing the weight 
 of the web and A" the weight of the flange. To hold the T in 
 a horizontal position, there must be a moment acting in the 
 opposite direction just equal to the sum of the two moments 
 acting downwards, and if the force in this upward moment, rep- 
 resented by A, is equal to the weight of the entire T, then the 
 force must be applied at the centre of gravity of the entire figure 
 to make its moment just equal to the sum of the two moments. 
 
 But the moment of A will be A d, therefore d must denote the 
 distance from the end of the web to the centre of gravity of the 
 entire figure, and as Ad=A'd' + A"d", d must equal 
 
 (1) 
 
 and A is equal to A' +A". 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. 
 
 To reduce formula 1 to a rule we have : 
 
 VIII. The distance of the centre of gravity of a compound figure 
 from any line, taken as a base, is equal to the sum of the products, 
 found by multiplying the areas of the simple figures of which the 
 compound figure is composed by the distance of their centres of 
 gravity from the base line, divided by the area of the entire figure. 
 This rule applies to any compound figure. 
 
 EXAMPLE I. Assume that the T shown in Fig. 14 has the di- 
 mensions indicated in the figure. Then A' wih 1 equal 6, A", 8, 
 and A, 14. d' will equal 3 and d" 6J. 
 
 The sum of the products of A' by d' and A" by d' will be 
 18 + 52 or 70, and this divided by 14, the area of the entire figure, 
 gives 5 ins. for the distance d. 
 
 The distance d of the centre of gravity from the top of the 
 
CENTRE OF GRAVITY. 
 
 241 
 
 webs, in any of the figures shown in Fig. 15, may be found by 
 the following formula: 
 
 
 area of webs X -^ + area of flange 
 area of webs + area of flange 
 
 
 For a section like that shown in Fig. 16, in which A', A", A."' 
 represent the area of the respective rectangles, the distance d 
 of the centre of gravity from the top may be found by the 
 formula 
 
 d= 
 
 A'+A 
 
 (3) 
 
 EXAMPLE II. To show the application of proposition VIII. 
 to any compound figure, we will take that shown by Fig. 17 and 
 find the distance d of the centre gravity of the entire figure from 
 the vertex o. The area of the triangle is 36 sq. ins. and of the 
 semicircle 56.5. 
 
 Fig. 16 
 
 From the table on page 238 we find that the distance of the 
 centre of gravity of an isosceles triangle from the vertex is its 
 height, which gives 4 as the value for d'. The centre of gravity 
 for a semicircle is 0.4244 r from its base, so that d" equals 8.54. 
 Then 
 
 36X4 + 56.5X8.54 
 
 34 + 56.5 
 
 =6.77. 
 
 This method of finding the centre of gravity is the same as 
 that given in Chapter IX. for finding supporting forces, except 
 that in the latter case the problem is to find the balancing force 
 instead of the arm. 
 
242 STABILITY OF PIERS AND BUTTRESSES. 
 
 CHAPTER VII. 
 STABILITY OF PIERS AND BUTTRESSES. 
 
 A PIER or buttress may be considered stable when the forces 
 acting upon it do not cause it to rotate or "tip over/' or any 
 course of stones or brick to slide on its bed. When a pier has to 
 sustain only a vertical load, it is evident that the pier must be 
 stable, although it may not have sufficient strength. 
 
 It is only when the pier receives a thrust, such as that from a 
 rafter or an arch, that its stability must be considered. 
 
 In order to resist rotation, we must have the condition that the 
 moment of the thrust of the pier about any point in the outside of 
 the pier shall not exceed the moment of the weight of the pier 
 about the same point. 
 
 To illustrate let us take the pier shown in Fig. 1. 
 
 Let us suppose that this pier receives the foot of a rafter which 
 exerts a thrust T in the direction A B. The tendency of this 
 thrust will be to cause the pier to rotate about the outer edge 
 b lt and the moment of the thrust about this point will be T X a l b lf 
 aj&j being the arm. Now, that the pier shall be just in equilibrium, 
 the moment of the weight of the pier about the same edge must 
 just equal TXa 1 ^. The weight of the pier will, of course, act 
 through the centre of gravity of the pier (which in this case is at 
 the centre), and in a vertical direction; and its arm will be b^c, or 
 one-half the thickness of the pier. 
 
 Hence, to have equilibrium, we must have the equation 
 
 But under this condition the least additional thrust, or the 
 crushing off of the outer edge, would cause the pier to rotate; 
 hence, to have the pier in safe equilibrium, we must use some 
 factor of safety. 
 
 This is generally done by making the moment of the weight 
 equal to that of the thrust when referred to a point in the bottom 
 of the pier, a certain distance in from the outer edge. 
 
 This distance for piers or buttresses should not be less than one- 
 fourth of the thickness of the pier. 
 
STABILITY OF PIERS AND BUTTRESSES 243 
 
 Representing this point in the figure by b, we have the neces- 
 sary equation for the safe stability of the pier, 
 
 t denoting the width of the pier. 
 
 We cannot from this equation determine the dimensions of a 
 pier to resist a given thrust, because we have the distance ab, t, 
 and TF, all unknown quantities. Hence we must first guess at 
 the size of the pier, then find the length of the line ab, and see if 
 the moment of the pier is equal to that of the thrust. If it is not 
 we must guess again. 
 
 Fig. I. 
 
 Graphic Method of Determining the Stability of a 
 Pier or Buttress, When it is desired to determine if a given 
 pier or buttress is capable of resisting a given thrust, the prob- 
 lem can easily be solved graphically in the following manner. 
 
 Let ABCD (Fig. 2) represent a pier which sustains a given 
 thrust T at B. 
 
 To determine whether the pier will safely sustain this thrust, 
 we proceed as follows. 
 
 Draw the indefinite line BX in the direction of the thrust. 
 Through the centre of gravity of the pier (which in this case is at 
 the centre of the pier) draw a vertical line until it intersects the 
 line of the thrust at e. As a force may be considered to act any- 
 where in its line of direction, we may consider the thrust and the 
 weight to act at the point e, and the resultant of these two forces 
 can be obtained by laying off the thrust T from e on eX , and the 
 weight of the pier W, from e on the line eY, both to the same 
 scale (pounds to the inch), completing the parallelogram, and 
 drawing the diagonal. If this diagonal prolonged cuts the base 
 of the pier at less than one-fourth of the width of the base from 
 the outer edge, the pier will be unstable and its dimensions must 
 be changed. 
 
244 STABILITY OF PIERS AND BUTTRESSES. 
 
 The stability of a pier may be increased by adding to its weight 
 (by placing some heavy material on top) or by increasing its 
 width at the base by means of "off-sets," as in Fig. 3A. 
 
 Figs. 3 (A and B) show the method of determining the stability 
 of a buttress with offsets. 
 
 The first step is to find the vertical line passing through the 
 centre of gravity of the whole pier. This is best done by divid- 
 ing the buttress up into quadrilaterals, as A BCD, DEFG, and 
 GHIK (Fig. 3A), finding the centre of gravity of each quadri- 
 lateral by the method of diagonals explained in Chapter VI. and 
 then measuring the perpendicular distances X lt X 2) X 3 from the 
 different centres of gravity to the line KI. 
 
 Multiply the area of each quadrilateral by the distance of its 
 centre of gravity from the line KI and add together the areas 
 and the products. Divide the sum of the latter by the sum of 
 the former and the result will be the distance of the centre of 
 gravity of the whole buttress from KI. This distance we denote 
 
 Fifl.3B 
 
 EXAMPLE I. Let the buttress shown in Fig. 3A have the 
 dimensions given between the cross-marks. Then the area of 
 the quadrilaterals and the distances from their centres of gravity 
 to KI would be as follows: 
 
 1st area=35 sq. ft. 
 2d area=23 sq. ft. 
 3d area=ll sq. ft. 
 
 1st areaXXj=33.25 
 2d area X X 2 = 67. 85 
 3d 
 
 Total area, 69 sq. ft. Total moments, 155.55 
 
 The sum of the moments is 155.55, and, dividing this by the 
 total area, we have 2.25 as the distance X Q . Measuring this to 
 
STABILITY OF PIERS AND BUTTRESSES. 245 
 
 the scale of the drawing from KI, we have a point through which 
 the vertical line passing through the centre of gravity must pass. 
 After this line is found, the method of determining the stability of 
 the pier is the same as that given for the pier in Fig. 2. Fig. 3B 
 also illustrates the method. If the buttress is more than one foot 
 thick (at right angles to the plane of the paper), the cubic con> 
 tents of the buttress must be obtained to find the weight. It 
 is easier, however, to divide the real thrust by the thickness of the 
 buttress, which gives the thrust per foot of buttress. 
 
 Ldiie of Resistance. Definition. The line of resistance 
 or of pressures of -a pier or buttress is a line drawn through the 
 centre of pressure of each joint. 
 
 The centre of pressure of any joint is the point where the re- 
 sultant of the forces acting on that portion of the pier above the 
 joint cuts it. 
 
 The line of pressures, or of resistance, when drawn in a pier, 
 shows how near the greatest stress on any joint comes to the 
 edges of that joint. 
 
 It can be drawn by the following method : 
 
 Let ABCD (Fig. 4) be a pier 
 whose line of resistance we wish 
 to draw. First divide the pier in 
 height, into portions two or three 
 feet high, by drawing horizontal 
 lines. It is more convenient to 
 make the portions all of the same 
 size. 
 
 Prolong the line of the thrust, 
 and draw a vertical line through 
 the centre of gravity of the pier, 
 intersecting the line of thrust at 
 the point a. From a lay off to a 
 scale the thrust T and the weights 
 of the different portions of the pier, 
 commencing with the weight of the 
 upper portion. Thus w^ represents 
 the weight of the portion above the 
 first joint; w 2 represents the weight 
 of the second portion; and so on. 
 The sum of the w's will equal the F i g> 4 
 
 whole weight of the pier. 
 
 Having proceeded thus far, complete a parallelogram, with T 
 
246 STABILITY OF PIERS AND BUTTRESSES. 
 
 and WL for its two sides. Draw the diagonal, and prolong it. 
 Where it cuts the first joint will be a point in the line of resist- 
 ance. Draw another parallelogram, with T and Wi + w t for its 
 two sides. Draw the diagonal intersecting the second joint at 
 2. Proceed in this way, when the last diagonal will intersect the 
 base in 4. Join the points 1, 2, 3, and 4, and the resulting line 
 will be the line of resistance. 
 
 We have taken the simplest case as an example ; but the same 
 principle is true for any case. 
 
 Should the line of resistance of a pier at any point approach 
 the outside edge of the joint nearer than one-quarter the width 
 of the joint, the pier should be considered unsafe. 
 
 As an example embracing all the principles given above we will 
 take the following case. 
 
 EXAMPLE II. Let Fig. 5 represent the section of a side wall 
 of a church, with a buttress against it. Opposite the buttress, on 
 the inside of the wall, is a hammer-beam truss, which we will sup- 
 pose exerts an outward thrust on the walls of the church amount- 
 ing to about 9600 pounds. We will further consider that the 
 resultant of the thrust acts at P, and at an angle of 60 with a 
 horizontal. The dimensions of the wall and buttress are given in 
 Fig. 5A, and the buttress is two feet thick. 
 
 QUESTION. Is the buttress sufficient to enable the wall to 
 withstand the thrust of the truss? 
 
 The first point to decide is if the line of resistance cuts the 
 joint CD at a safe distance in from C. To ascertain this we 
 must find the centre of gravity of the wall and buttress above the 
 joint CD (Fig. 5). We can find this easiest by the method of 
 moments around KM (Fig. 5 A), as already explained. 
 
 The distance X t is, of course, half the thickness of the wall. 
 or one foot. W"e next find the centre of gravity of the portion 
 CEFG (Fig. 5A) by the method of diagonals, and, scaling the 
 distance- X 2 , we find it to be 2.95 feet. 
 
 The area of CEFG=A 2 =1Q square feet,; and of G1KL^A 1 
 = 26 square feet. 
 
 Then we have 
 
 36 36)55.5 
 
 .0=1.5 
 
STABILITY OF PIERS AND BUTTRESSES. 247 
 
 Or the centre of gravity is at a distance 1.5 feet from the line 
 ED (Fig. 5). Then on Fig. 5 measure the distance X Q = 1.5 feet, 
 and through the point a draw a vertical line intersecting the line 
 of the thrust prolonged at 0. Now, if the thrust is 9600 pounds 
 for a buttress two feet thick, it would be half that, or 4800 
 pounds, for a buttress one foot thick. We will call the weight of 
 the masonry of which the buttress and wall is built 150 pounds 
 per cubic foot. Then the thrust is equivalent to 4800 -f- 150, or 32 
 cubic feet of masonry. Laying this off to a scale from 0, in the 
 direction of the thrust and the area of the masonry, 36 square feet 
 from on the vertical line, completing the rectangle, and draw- 
 ing the diagonal, we find it cuts the joint CD at t, within the 
 limits of safety. 
 
 We must next find where the line of resistance cuts the base 
 AB. 
 
 First find the centre of gravity of the whole figure, which is 
 found by ascertaining the distances X 2 ', X 3 ', in Fig. 5A, and 
 making the following computation. 
 
 76 76)170.92 
 
 X '=2.25 
 
 Then from the line EB (Fig. 5) lay off the distance X '=2'.25, 
 and draw through d a vertical line intersecting the line of the 
 thrust at 0'. On this vertical from 0' measure down the whole 
 area 76, and from its extremity lay off the thrust T= 32 at the 
 proper angle. Draw the line O'e intersecting the base at c. This 
 is the point where the line of resistance cuts the base ; and, as it 
 is at a safe distance in from A, the buttress has sufficient stability. 
 
 If there were more offsets, we should proceed in the same way, 
 finding where the line of resistance cuts the joint at the top of 
 each offset. The reason for doing this is because the line of re- 
 sistance might cut the base at a safe distance from the outer edge, 
 while higher up it might come outside of the buttress, so that the 
 buttress would be unstable. 
 
 The method given in these examples is applicable to piers of 
 any shape or material. 
 
 Should the line of resistance make an angle less than 30 with 
 
248 STABILITY OF PIERS AND BUTTRESSES. 
 
 any joint, it might cause the stones above the joint to slide on 
 their bed. This can be prevented either by dowelling, or by 
 inclining the joint. 
 
 Fig.5 
 
 Fig.SA 
 
 It is very seldom in architectural construction that such a case 
 would occur, however. 
 
THE STABILITY OF ARCHES. 249 
 
 CHAPTER VIII. 
 THE STABILITY OP ARCHES. 
 
 THE arch is an arrangement for spanning large openings by 
 means of small blocks of stone, or other material, arranged in a 
 particular way. As, a rule, the arch answers the same purpose 
 as the beam, but it is widely different in its action and in the effect 
 that it has upon the appearance of an edifice. A beam exerts 
 merely a vertical force upon its supports, but the arch exerts both 
 a vertical load and an outward thrust. It is this thrust which 
 requires that the arch should be used with caution where the 
 abutments are not abundantly large. 
 
 Before taking up the principles of the 
 arch, we will define the many terms relat 
 ing to it. The distance ec (Fig. 1) is 
 called the span of the arch ; ai, its rise ; 6, 
 its crown; its lower boundary line, eac, its 
 soffit or intrados; the outer boundary line, 
 its back or extrados. The terms "soffit" 
 and "back" are also applied to the entire lower and upper curved 
 surfaces of the whole arch. The ends of the arch, or the sides 
 which are seen, are called its faces. The blocks of which the arch 
 itself is composed are called voussoirs: the centre one, K, is called 
 the keystone; and the lowest ones, SS, the springers. In seg- 
 mental arches, or those whose intrados is not a complete semi- 
 circle, the springers generally rest upon two stones, as RR, which 
 have their upper surface cut to receive them: these stones are 
 called skewbacks. The line connecting the lower edges of the 
 springers is called the springing-line; the sides of the arch are 
 called the haunches; and the load in the triangular space, between 
 the haunches and a horizontal line drawn from the crown, is 
 called the spandrel. 
 
 The blocks of masonry, or other material, which support two 
 successive arches, are called piers: the extreme blocks, which, in 
 the case of stone bridges, generally support on one side embank- 
 ments of earth, are called abutments. 
 
 A pier strong enough to withstand the thrust of either arch^ 
 should the other fall down, is sometimes called an abutment pier 
 
250 THE STABILITY OF ARCHES. 
 
 Besides their own weight, arches usually support a permanent 
 load or surcharge of masonry or of earth. 
 
 In using arches in architectural constructions, the form of the 
 arch is generally governed by the style of the edifice, or by a lim- 
 ited amount of space. The semicircular and segmental forms of 
 arches are the best as regards stabilty, and are the simplest to 
 construct. Elliptical and three-centred arches are not as strong 
 as circular arches, and should only be used where they can be 
 given all the strength desirable. 
 
 The strength of an arch depends very much upon the care with 
 which it is built and of the quality of the work. 
 
 In stone arches, special care should be taken to cut and lay 
 the beds of stones accurately, and to make the bed-joints thin 
 and close, in order that the arch may be strained as little as pos- 
 sible in settling. 
 
 To insure this, arches are sometimes built dry, grout or liquid 
 mortar being afterwards run into the joints; but the advantage 
 of this method is doubtful. 
 
 Brick Arches may be built either of wedge-shaped bricks, 
 moulded or rubbed so as to fit to the radius of the soffit, or of 
 bricks of common shape. The former method is undoubtedly 
 the best, as it enables the bricks to be thoroughly bonded, as in 
 a wall; but, as it involves considerable expense to make the 
 bricks of the proper shape, this method is very seldom employed. 
 Where bricks of the ordinary shape are used, they are accommo- 
 dated to the curved figure of the arch by making the bed- joints 
 thinner towards the intrados than towards the extrados; or, if 
 the curvature is sharp, by driving thin pieces of slate into the 
 outer edges of those joints; and different methods are followed 
 for bonding them. The most common way is to build the arch 
 in concentric rings, each half a brick thick; that is, to lay the 
 bricks all stretchers, and to depend upon the tenacity of the 
 mortar or cement for the connection of the several rings. This 
 method is deficient in strength, unless the bricks are laid in ce- 
 ment at least as tenacious as themselves. Another way is to 
 introduce courses of headers at intervals, so as to connect pairs 
 of half-brick rings together. 
 
 This may be done either by thickening the joints of the outer 
 of a pair of half-brick rings with pieces of slate, so that there shall 
 be the same number of courses of stretchers in each ring between 
 two courses of headers, or by placing the courses of headers at 
 such distances apart, that between each pair of them there shall 
 
THE STABILITY OF ARCHES. 
 
 251 
 
 be one course of stretchers more in the outer than in the inner 
 ring. 
 
 The former method is best suited to arches of long radius; the 
 latter, to those of short radius. Hoop iron laid round the arch, 
 between half-brick rings, as well as longitudinally and radially, 
 is very useful for strengthening brick arches. The bands of hoop 
 iron which traverse the arch racially may also be bent, and pro- 
 longed in the bed- joints of the backing and spandrels. 
 
 By the aid of hoop-iron bond, Sir Marc-Isarnbard Brunei built 
 a half-arch of bricks laid in strong cement, which stood, project- 
 ing from its abutment like a bracket, to the distance of sixty feet, 
 until it was destroyed by its foundation being undermined. 
 
 The New-York City Building Laws make the following re- 
 quirements regarding brick arches: 
 
 "All arches shall be at least four inches thick. Arches over 
 four-foot span shall be increased in thickness toward the haunches 
 by additions of four inches in thickness of brick. The first addi- 
 tional thickness shall commence at two* and a half feet from the 
 centre of the span, the second addition at six and a half feet 
 from the centre of the span; and the thickness shall be in- 
 creased thence four inches for every additional four feet of span 
 towards the haunches. 
 
 "The said brick arches shall be laid to a line on the centres with 
 a close joint, and the bricks shall be well wet, and the joints filled 
 with cement mortar in 
 proportions of not more 
 than two of sand to one 
 of cement by measure. 
 The arches shall be well 
 grouted and pinned, or 
 chinked with slate, and 
 keyed." * 
 
 Rule for Radius of Brick 
 Arches. A good rule for 
 the radius of segmental 
 brick arches over win- 
 dows, doors, and other 
 small openings is to make 
 
 Fig. 2 
 
 the radius equal to the width of the opening. This gives a good 
 rise to the arch and makes a pleasing proportion to the eye. 
 
 * For illustrations of the different ways of building brick arches, see 
 Chapter VII. of Part I., "Building Construction and Superintendence." 
 
252 THE STABILITY OF ARCHES. 
 
 Segmental Arches with Tie Rods. It is often desirable to span 
 openings in a wall by means of an arch when there is not suffi- 
 cient abutments to withstand the thrust or kick of the arch. In 
 such a case the arch can be formed on two cast-iron skewbacks, 
 which are held in place by iron rods, as is shown in Fig. 2. 
 
 When this is done, it is necessary to proportion the size of the 
 rods to the thrust of the arch. Xhe horizontal thrust of the arch 
 is very nearly represented by the following formula: 
 
 TT . , , ,, load on arch X span 
 
 Horizontal thrust = - : - c A-^-j -. 
 
 8 X nse ot arch in ieet 
 
 If the load is concentrated at the centre of the arch, the thrust 
 will be twice that given by above formula. 
 
 The stress in the rod or rods will equal the horizontal thrust 
 of the arch ; if there are two rods, the stress in each will be one- 
 half the thrust ; if there are three rods, then each must be capable 
 of resisting J of the thrust. Knowing the stress in the rods, theii 
 size may be readily determined from Table III. of Chapter XI. 
 
 Centres for Arches. A centre is a temporary structure, 
 generally of timber, by which the voussoirs of an arch are sup^ 
 ported while the arch is being built. It consists of parallel 
 frames or ribs, placed at convenient distances apart, curved on 
 the outside to a line parallel to that of the soffit of the arch, and 
 supporting a series of transverse blanks, upon which the arch 
 stones rest. 
 
 The most common kind of centre is one which can be lowered, 
 or struck all in one piece, by driving out wedges from below it, 
 so as to remove the support frorrj. every point of the arch at once. 
 
 The centre of an arch should not be struck until the solid part 
 of the backing has been built and the mortar has had time to set 
 and harden; and, when an arch forms one of a series of arches 
 with piers between them, no centre should be struck so as to 
 leave a pier with an arch abutting against one side of it only, un- 
 less the pier has sufficient stability to act as an abutment. 
 
 When possible, the centre of a large brick arch should not be 
 struck for two or three months after the arch is built. 
 
 Mechanical Principles of the Arch. In designing an 
 arch, the first question to be settled is the form of the arch ; and 
 in regard to this there is generally but little choice. Where the 
 abutments are abundantly large, the segmental arch is the strong- 
 est form; but where it is desired to make the abutments of the 
 
THE STABILITY OF ARCHES. 253 
 
 arch as light as possible, a pointed or semicircular arch should be 
 used. 
 
 Depth of Keystone. Having decided upon the form of the arch, 
 the depth of the arch-ring must next be decided. This is gen- 
 erally determined by computing the required depth of keystone, 
 and making the whole ring of the same or a little larger depth. 
 
 In considering the strength of an arch, the depth of the key- 
 stone is considered to be only the distance from the extrados to 
 the intrados of the arch; and if the keystone projects above the 
 arch-ring, as in Fig. 1, the projection is considered as a part of 
 the load on the arch. 
 
 There are several rules (or determining the depth of the key- 
 stone, but all are empirical ; and they differ so greatly that it is 
 difficult to recommend any particular one. Professor Rankine's 
 rule is often quoted, and is probably true enough for most arches. 
 It applies to both circular and elliptical arches, and is as fol- 
 lows : 
 
 Rankine's Rule. For the depth of the keystone, take a mean 
 proportional between the inside radius at the crown, and 0.12 
 of a foot for a single arch, and 0.17 of a foot for an arch forming 
 one of a series. Or, if represented by a formula, 
 
 Depth of keytsone for a single arch in feet 
 
 = V(0. 12 X radius at crown). 
 Depth of keystone for an arch of a series in feet 
 
 = V (0.17 X radius at crown). 
 
 This rule seems to agree very well with actual cases in arches 
 of a certain kind. By it, however, the depth of keystone is the 
 same for spans of any length, provided the radius is the same: 
 and in this particular, it seems to us, the rule is not satisfactory. 
 
 Trautwiiie's Rule. Mr. Trautwine, from calculations 
 made on a large number of arches, deduced an original rule for 
 the depth of keystone, which is more agreeable to theory than 
 Rankine's. His rule is, for cut stone, 
 
 Depth of key in feet- (^ radius + half span^ +Q 
 
 For second-class work this depth may be increased about one- 
 eighth part, or for brick or fair rubble, about one-fourth. 
 
 The following table gives a few examples of the depth of key- 
 stone of some existing bridges, together with the depth which 
 
254 
 
 THE STABILITY OF ARCHES. 
 
 would be required by Trautwine's or Rankine's Rule. From 
 this table it will be seen that both rules agree very well with 
 practice. 
 
 TABLE I. SHOWING DEPTH OF KEYSTONE OF SOME 
 EXISTING ARCHES. 
 
 Bridge (circiJar arc). 
 
 Span. 
 
 ~FtT~ 
 
 220.0 
 200.0 
 
 148.0 
 118 
 
 90.0 
 78.0 
 
 60.0 
 44.0 
 31.2 
 
 Rise. 
 
 Radius. 
 
 Actual depth of key. 
 
 Calculated 
 depth of 
 key. 
 
 Engi- 
 neer. 
 
 Trautwine's 
 Rule. 
 
 Rankine's 
 Rule. 
 
 Cabin John , Washing- 
 ton Aqueduct 
 Grosvenor Bridge, 
 Chester, Eng 
 Dora Riparia, Turin, 
 Italy 
 
 Ft. 
 57.25 
 42.00 
 
 18.00 
 38.00 
 
 30.00 
 25.00 
 
 1.8 00 
 8.00 
 5.00 
 
 Ft. 
 
 134.25 
 140.00 
 
 160.10 
 64.80 
 
 48.90 
 43.00 
 
 34.00 
 34.30 
 
 26.80 
 
 Ft. 
 4.60 
 4.00 
 
 4.92 
 3.50 
 
 3.00 
 3.00 
 
 2.50 
 
 2.50 
 1.66 
 
 Ft. 
 4.11 
 4.07 
 
 4.03 
 3.00 
 
 2.62 
 2.46 
 
 2.20 
 2.08 
 1.83 
 
 Ft. 
 
 4.00 
 4.10 
 
 4.38 
 2.79 
 
 2.88 
 2.27 
 
 2.00 
 2.02 
 1.79 
 
 Meigs. 
 Hartley. 
 
 Mosca. 
 Telford. 
 
 Telford. 
 Steele. 
 
 Kneass. 
 Steele. 
 Steele. 
 
 Tongueland, England . 
 Dean Bridge, Srotl'nd, 
 in a series 
 
 Falls Bridge, Phila- 
 delphia & Reading 
 Railroad 
 Chestnut St. Bridge, 
 Philadelphia, brick 
 in cement 
 
 Philadelphia & Read- 
 ing Railroad 
 Philadelphia & Read- 
 ing Railroad 
 
 
 Table II., taken from Trautwine's "Civil Engineers' Hand- 
 book," gives the depth of keystone for arches of first-class cut- 
 stone, according to Trautwine's Rule. For second-class cut- 
 stone add about one-eighth part and for good rubble or brick, 
 about one-fourth part. 
 
 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 determin- 
 ing this point : 
 
 EXAMPLE I. Unloaded semicircular arch of 20-foot span. 
 
 First, to find the depth of keystone, we will take Rankine's 
 Rule, and by it we have 
 
 Depth of key=Vo7l2xlO= VO= l l feet - 
 
THE STABILITY OF ARCHES. 
 
 255 
 
 TABLE II. TABLE OF KEYSTONES FOR ARCHES OF 
 FIRST-CLASS CUT-STONE. 
 
 Span 
 in 
 feet. 
 
 Rise in parts of the span. 
 
 K 
 
 Ys 
 
 M 
 
 % 
 
 VQ 
 
 K 
 
 He 
 
 
 key. ft. 
 
 key. ft. 
 
 key. ft. 
 
 key. ft. 
 
 key. ft. 
 
 key. ft. 
 
 key. ft. 
 
 2 
 
 0.55 
 
 0.56 
 
 0.58 
 
 0.60 
 
 0.61 
 
 64 
 
 0.68 
 
 4 
 
 0.70 
 
 0.72 
 
 0.74 
 
 0.76 
 
 0.79 
 
 0.83 
 
 88 
 
 6 
 
 0.81 
 
 0.83 
 
 0.86 
 
 0.89 
 
 92 
 
 0.97 
 
 1.03 
 
 8 
 
 0.91 
 
 0.93 
 
 90 
 
 1.00 
 
 .03 
 
 1.09 
 
 1.16 
 
 10 
 
 0.99 
 
 1.01 
 
 1.04 
 
 1.07 
 
 .11 
 
 1.18 
 
 1.26 
 
 15 
 
 .17 
 
 1.19 
 
 ' 1.22 
 
 1.26 
 
 .30 
 
 1.40 
 
 1.50 
 
 20 
 
 .32 
 
 1.35 
 
 1.38 
 
 1.43 
 
 .48 
 
 1.59 
 
 1.70 
 
 25 
 
 .45 
 
 1.48 
 
 1.53 
 
 1.58 
 
 .64 
 
 1.76 
 
 1.88 
 
 30 
 
 .57 
 
 1.60 
 
 1.65 
 
 1.71 
 
 .78 
 
 1.91 
 
 2.04 
 
 35 
 
 .68 
 
 1.70 
 
 1.76 
 
 1.83 
 
 1.90 
 
 2.04 
 
 2.19 
 
 40 
 
 .78 
 
 1.81 
 
 1.88 
 
 1.95 
 
 2.03 
 
 2.18 
 
 2.33 
 
 50 
 
 1.97 
 
 2.00 
 
 2.08 
 
 2.16 
 
 2.25 
 
 2.41 
 
 2.58 
 
 60 
 
 2.14 
 
 2.18 
 
 2.26 
 
 2.35 
 
 2.44 
 
 2.62 
 
 2.80 
 
 80 
 
 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 
 
 2.91 
 
 2.99 
 
 3.10 
 
 3.22 
 
 3.35 
 
 3.61 
 
 3.88 
 
 140 
 
 3.16 
 
 3.21 
 
 3.33 
 
 3.46 
 
 3.60 
 
 3.87 
 
 1.15 
 
 160 
 
 3.36 
 
 3.44 
 
 3.58 
 
 3.72 
 
 3.87 
 
 4.17 
 
 
 180 
 
 3.56 
 
 3.63 
 
 3.75 
 
 3.90 
 
 4.03 
 
 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 
 
 
 
 
 
 Trautwine's Rule would give nearly the same, or 
 
 -+0.2foot=1.3feet. 
 
 But if we should compute the stability of a semicircular arch 
 of 20-foot span and 1.3-foot depth of keystone, we should find 
 that the arch was very unstable; hence, in this case, we must 
 throw the rule aside and go by our own judgment. In the opin- 
 ion of the author, such an arch should have at least 2J feet depth 
 of arch-ring, and we will try the stability of the arch with that 
 thickness. 
 
 In all calculations on the arch, it is customary to consider the 
 arch to be one foot thick at right angles to its face; for it is evi- 
 dent that if an arch one foot thick is stable, any number of 
 arches of the same dimensions built alongside of it would be 
 stable. 
 
256 
 
 THE STABILITY OF ARCHES. 
 
 Graphic Solution of th<j Stability of the Arch. 
 
 The most convenient method of determining the stability of 
 the arch is by the graphic method, as it is called. 
 
 IST STEP. Draw one-half the arch to as large a scale as con- 
 venient and divide it up into voussoirs of equal size. In this 
 example, shown in Fig. 3, we have divided the arch-ring into ten 
 equal voussoirs. (It is not necessary that these should be the 
 actual voussoirs of which the arch is built.) The next step is to 
 find the area of each voussoir. Where the arch-ring is divided 
 into voussoirs of equal size, this is easiest done by computing 
 the area of the arch-ring and dividing by the number of voussoirs. 
 
 Fig.3 
 
 Rule for area of one-half of arch-ring is as follows : 
 
 Area in square feet= 0.7854 X (outside radius squared inside 
 radius squared). 
 
 In this example the whole area equals 0.7854X(12.5 2 10 2 ) 
 = 44.2 square feet. As there are ten equal voussoirs, the area of 
 each voussoir is 4.4 square feet. 
 
 Having drawn out one-half of the arch-ring, we divide each 
 joint into three equal parts; and from the point A (Fig.' 3) we 
 lay off to a scale the area of each voussoir, one below the other, 
 commencing with the top voussoir. The whole length of the 
 line AE will equal the whole area drawn to same scale. 
 
 The next step is to find the vertical line passing through the 
 centre of gravity of the whole arch-ring. To do this, it is first 
 necessary to draw vertical lines through the centre of gravity of 
 each voussoir. The centre of gravity of one voussoir may be 
 found by the method of diagonals, as in the second voussoir from 
 
THE STABILITY OF ARCHES. 257 
 
 the top (Fig. 3). Having the centre of gravity of one voussoir, 
 the centres of gravity of the others can easily be obtained from it. 
 
 Next, from A and E (Fig. 3) draw lines at 45 with AE, inter- 
 secting at 0. Draw 01, 02, 03, etc. Then, where AO intersects 
 the first vertical line at a, draw a line parallel to 01, intersecting 
 the second vertical at b. Draw be parallel to 02, cd parallel to 
 03, and so on to kn parallel to 010; prolong this, line downward 
 until it intersects AO, prolonged, at D. Then a vertical line 
 drawn through D will pass through the centre of gravity of the 
 arch-ring. 
 
 2o STEP. Draw a horizontal line through A (the upper part 
 of the middle third), and a vertical line through D, the two 
 lines intersecting at C (Fig. 3). 
 
 Now, that the arch shall be stable, it is considered necessary 
 that it shall be possible to draw a line of resistance of the arch 
 within the middle third. We will, then, first assume that the 
 line of resistance shall act at A and come out at B. 
 
 Then draw the line CB, and a horizontal line opposite the 
 point 10, between Q and p. This horizontal line represents the 
 horizontal thrust at the crown. 
 
 Draw AP equal to Qp, and the lines PI, P2, P3, etc. 
 
 Then, from the point where AC prolonged intersects the first 
 vertical, draw a line to the second vertical parallel to PI ; from 
 this point a line to the third vertical parallel to P2; and so 
 on. The last line should pass through B. If these lines, which 
 we will call the line of resistance, all lie within the middle third, 
 the arch may be considered to be stable. Should the line of re- 
 sistance pass outside of the arch-ring, the arch should be con- 
 sidered unstable. In Fig. 3 this line does not all lie in the middle 
 third, and we must see if a line of resistance can yet be drawn 
 within that limit. 
 
 2o TRIAL. The line of resistance in Fig. 3 passes farthest from 
 the middle third at the seventh joint from the top; and we will 
 next pass a line of resistance through A and where the lower line 
 of the middle third cuts the seventh joint, or at D (Fig. 4). 
 
 To do this we must prolong the line gh, parallel to 07 (Fig. 4), 
 until it intersects AO. In this case it intersects it at 0, but this 
 is merely a coincidence ; it would not always do so. Through 
 draw a vertical intersecting PA prolonged at C. Draw a line 
 through C and D, and the horizontal line pQ, opposite the point 
 7; this line represents the new horizontal thrust H^. Draw AP 
 = pQ, and the lines PI, P2, etc. ; then draw the line of resistance 
 
258 
 
 THE STABILITY OF ARCHES. 
 
 as before. It should pass through D if drawn correctly. This 
 time we see that the line of resistance lies within the middle third, 
 except for just a short distance at the springing; and hence we 
 may consider the arch stable. If it had gone outside the middle 
 third this time, to any great extent, we should have considered 
 the arch unstable. 
 
 The above is the method of determining the stability of an 
 unloaded semicircular arch. Such a case very seldom occurs in 
 practice ; but it is a good example to illustrate the method, which 
 applies to all other cases, with a little difference in the method 
 of determining the centre of gravity of loaded arches. 
 
 Fig.4 
 
 EXAMPLE II. Loaded or surcharged semicircular arch. 
 
 We will take the same arch as in Example I. and suppose 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 horizontal 
 surface of the wall being 3 feet 6 inches above the arch-ring at 
 the crown. 
 
 1st STEP. Find centre of gravity. 
 
 Commencing at the crown, divide the load and arch-ring into 
 strips two feet wide, making the last strip the width of the arch- 
 ring at the springing. Then draw the joints as shown in Fig. 5. 
 Measure with the scale the length of each vertical line, A a, Bb, 
 etc. ; then the area of AaBb is equal to the length of Aa + Bb, as 
 the distance between them is just two feet. The area of FjKk 
 is, of course, Ff X width of arch-ring. 
 
 In this case the areas of the slices are as shown by the figures 
 on their faces (Fig. 5). 
 
 Now divide the arch-ring into thirds, and from the top of the 
 
THE STABILITY OF ARCHES. 
 
 259 
 
 middle third, at R, lay off in succession, to a scale, the areas of 
 the slices, commencing with the first slice from the crown, AaBb. 
 These areas, when measured off, will be represented by the line 
 Rl, 2, 3 ... 6 (Fig. 5). From the extremities of this line, R 
 and 6, draw lines at 45 with a vertical, intersecting at 0. From 
 draw lines to 1, 2, 3, 4, 5, and 6. Next draw a vertical line 
 through the centre of each slice (these lines, in Fig. 5, are num- 
 bered 1, 2, 3, etc.). From the point in which the line RO inter- 
 sects vertical 1, draw a line parallel to 01, to the line 2. From 
 this point draw a line to vertical 3, parallel to 02, and so on. The 
 line parallel to 05 will intersect vertical 6 at Y. Then through 
 Y draw a line downwards at 45, intersecting OR at X. A ver- 
 tical line drawn through X will pass through the centre of 
 gravity of the arch-ring and its load. 
 
 E D B A 
 
 2D STEP. To find the thrust at the crown and at the springing. 
 
 To find the thrust at the crown, draw a vertical line through X, 
 and a horizontal line through R, intersecting at V. Now, the 
 weight of arch and load, and the resultant thrust of arch, must 
 act through this point. We will also make the condition that 
 the thrust shall pass through Q, the outer edge of the middle 
 third. Then the thrust of the arch must act in the line VQ. 
 Opposite 6, on the vertical line through 7?, draw a horizontal line 
 H, between VX and VQ. This horizontal line represents a hori- 
 
260 THE STABILITY OF ARCHES. 
 
 zontal thrust at R, which would cause the resultant thrust of the 
 arch to pass through Q. Now draw the horizontal line RP, equal 
 in length to H, and from P draw lines 1, 2, 3 . . . 6. The line 
 P6 represents the thrust of the arch at the springing. Its amount 
 in cubic feet of masonry can be determined by measuring its 
 length to the proper scale. 
 
 SD STEP. To draw the line of resistance. 
 
 The lines PI, P2, P3, etc., represent the magnitude and direction 
 of the thrust at each joint of the arch. Thus PI represents the 
 thrust of the first voussoir and its load, P2 that of the first two 
 voussoirs and their loads, and so on. Then from the point a', 
 where the line RP, prolonged, intersects the vertical line 1, draw 
 a line a' b' parallel to PI ; from b', on 2, draw a line 6V parallel 
 to P2, and so on. The last line should pass through Q and be 
 parallel to P6. 
 
 Now, if we connect the points where the lines a'6', 6V, etc., 
 cut the joints of the arch, we shall have a broken line, which is 
 known as the line of resistance of the arch. If this line lies within 
 the middle third of the arch, then we conclude that the arch is 
 stable. If the line of resistance goes far outside of the middle, 
 we must see if it be possible to draw another line of resistance 
 within the middle third; and if. after a trial, we find that it is 
 not possible, we must conclude that the arch is not safe, or un- 
 stable. 
 
 In the example which we have just been discussing, the line of 
 resistance goes a little outside of the middle third ; but it is very 
 probable that on a second trial we should find that a line of resist- 
 ance passed through R and Q' would lie almost entirely within 
 the middle third. 
 
 The method of drawing the second line of resistance was ex- 
 plained under Example I. ; and, as the same method applies to 
 all cases, we will not repeat it. 
 
 The method given for Example II. would apply equally well 
 for a semi-elliptical arch. 
 
 EXAMPLE III. Segmented arch, with load (Fig. 6). 
 
 IST STEP. To determine the centre of gravity. 
 
 In this case we proceed, the same as in the latter, to divide the 
 arch-ring and its load into vertical slices two feet wide, and com- 
 pute the area of the slices by measuring the length of the vertical 
 lines Aa, Bb, etc. Having computed the areas of the slices, we 
 lay them off in order from R to a convenient scale and then pro- 
 ceed exactly as in Example II., the remaining steps to determine 
 
THE STABILITY OF ARCHES. 
 
 261 
 
 the thrust and the lines of resistance are also the same as given 
 under Example IT. 
 
 In a flat segment al arch there is practically no need of dividing 
 the arch-ring into voussoirs by joints radiating from a centre, but 
 
 to consider the joints to be vertical. Of course, when built, they 
 must be made to radiate. 
 
 Fig. 6 shows the computation for an arch of 40-foot span and 
 with a load 13J feet high at the centre. The depth of the arch- 
 ring is 2 feet 6 inches. 
 
262 
 
 CAST-IRON ARCH-GIRDERS. 
 
 It will be seen that the curve of pressures lies entirely within 
 the middle third, and hence the arch is abundantly safe, or 
 stable. It should be remarked that the line of resistance in a 
 segments! arch should be drawn through the lower edge of the 
 middle third at the springing. 
 
 It will be noticed that the horizontal thrust, and the thrust T, 
 at the springing, are very great as compared with those in a semi- 
 circular arch; and hence, although the segmental arch is the 
 stronger of the two, it requires much heavier abutments. 
 
 These three examples serve to show the method of determining 
 the stability and thrust of any arch such as is used in building. 
 
 Concrete-Steel Arches. Many arches are now built of concrete 
 reinforced by steel ribs. A very comprehensive and practical 
 paper on such arches, by Mr. Edwin Thacher, C.E., was pub- 
 lished in the Engineering News of September 21, 1899. 
 
 Cast-iron Arch-girders with Wrought-iron 
 Tension-rods. 
 
 Cast-iron arch-girders were at one time quite extensively used 
 in some parts of this country for supporting brick walls over 
 store fronts or other wide openings, but now that structural steel 
 has become so cheap they are seldom used. Occasionally, how- 
 ever, the conditions are such as to make their use desirable. 
 
 Fig. 7 shows the usual form of such a girder, the section of the 
 casting and rod being shown in Fig. 8. 
 
 Fig.!7 
 
 Fig. 8 
 
 The casting is made in one piece with box ends, the latter hav- 
 ing grooves and seats to receive the wrought-iron tie-rod. 
 
 The tie-rod is made from one-eighth to three-eighths of an inch 
 shorter than the casting, and has square ends forming shoulders 
 so as to fit into the castings. The rod has usually one weld on 
 its length, and great care should be taken that this weld be perfect. 
 
CAST-IRON ARCH-GIRDERS. 263 
 
 The rod is expanded by heat, and then placed in position in the 
 casting, and allowed to contract in cooling; thus tying the two 
 ends of the casting together to form abutments for receiving the 
 horizontal thrust of the arch. If the rod is too long, it will not 
 receive the full proportion of the strain until the cast-iron has so 
 far deflected, that its lower edge is subjected to a severe tensile 
 strength, which cast-iron can feebly resist. If the tie-rod is made 
 too short, the casting is cambered up, and a severe initial strain 
 put upon both the cast and wrought iron, which enfeebles both 
 for carrying a load. The girders should have a rise of about two 
 feet six inches on a length of twenty-five feet.* 
 
 Rules for Calculating- Dimensions of Girder 
 and Rod. 
 
 A cast-iron arch-girder is considered as a long column, subject 
 to a certain amount of bending-strain; and the resistance will be 
 governed by the laws affecting the strength of beams, as well as 
 by those relating to the strength of columns. 
 
 If we regard the arch as flexible, or as possessing no inherent 
 stiffness, and the rod as a chord without weight, the horizontal 
 thrust or stress will be represented by the formula. 
 
 Hor. thrust _ load on girder in Ibs. Xspan in feet f . 
 or stress (Ibs.) ~~ 8 X rise of girder in feet 
 
 From this rule we can calculate the required diameter of the 
 tension-rod, which may be expressed thus 
 
 T. . . . , , t / load on girder X span in feet 
 
 Diameter m mches t = f- 8xrise infeetx7854 (2) 
 
 The rise should be measured from the centre of the rod to the 
 centre of the cast-iron arch; the load should be in pounds. 
 
 The rule generally used, however, in proportioning the 
 wrought-iron tie to the cast-iron arch is to allow one square inch 
 of cross-section of tie-rod for every ten net tons of load imposed upon 
 the span of the arch. 
 
 The following table, taken from Mr. Fryer's book on "Archi- 
 tectural Iron- Work," shows the section of the cast-iron arch re- 
 
 * "Architectural Iron-Work for Buildings," William J. Fryer, Jr., p. 38. 
 t For ft working stress of 10000 Ibs. per square inch. For rods of mild 
 steel, use 9800 in place of 7854. 
 
 't 
 
264 
 
 CAST-IRON ARCH-GIRDERS. 
 
 quired to support solid brick walls, and having a span of from 13 
 to 26 feet. 
 
 
 
 Dimensions of section. 
 
 Height of 
 
 Thickness of 
 
 
 wall. 
 
 wall. 
 
 
 
 
 
 
 Top flange. 
 
 Centre web. 
 
 Bulb. 
 
 40 feet 
 
 12 inches 
 
 12" XI" 
 
 12" X%" 
 
 3" X 2" 
 
 50 " 
 
 12 " 
 
 12" X 1J4" 
 
 12" X%" 
 
 3" X2" 
 
 40 " 
 
 16 " 
 
 12" x \y" 
 
 
 
 50 " 
 
 16' " 
 
 16" XW 
 
 12" XI" 
 
 4" X 1" 
 
 EXAMPLE I. It is desired to support a 12-inch brick wall 40 
 feet high over an opening 20 feet wide, with a cast-iron arch- 
 girder. What should be the dimensions of the girder? 
 
 For the casting, we find from the table that the cross-section 
 of the flange should be 12 inches by 1 inch; of the web, 12 
 inches by j inch; and of the bulb, 3 inches by 2 inches. We will 
 make the rise of the girder 2 feet and 6 inches, and from Formula 
 2 we find * 
 
 - i i i / weight of wall X span 
 
 Diam. of rod in inches = \f : ^-, r -. ; _ , .- 
 
 8 X rise of arch in feetX7854 
 
 ^ ./(20X 20X112) X 20 
 
 8X2JX7854 
 Figs. 9 and 10 show a cast-iron arched girder that was used to 
 
 Fig, 9 
 
 support a central tower over the crossing of the nave and transept 
 
 * Considering that the girder would only support about twenty feet of 
 the wall in height, the wall above that supporting itself. See " Beams Sup- 
 porting Brick Walls," Chapter XV. 
 
CAST-IRON ARCH-GIRDERS. 
 
 265 
 
 of St. John's Church, Stockton, California, 
 Mr. A. Page Brown, 
 architect. The clear 
 span is 29 J feet, and the 
 height of the wall above 
 the girder 18 feet. One 
 object in using such a 
 
 SECTION^ CENTER. ^^ ^ ^ ^ ^ 
 
 to get the height in the 
 centre without also raising the supports, 
 which could not be obtained with a steel 
 plate girder. The church has a vaulted 
 ceiling which comes just below the arch of 
 the girder, the tie-rod being exposed. 
 
 The rise of the casting in this case is rather 
 more than common, the usual rise being 
 from fa to J of the span. 
 
 Fig. 11 shows an arch girder, with the 
 casting in three sections, with pin joints, 
 the head of the suspending pieces A A , form- 
 ing the pin. The flexible bolt connections 
 serve to hold the sections in place laterally. 
 
 Mr. Peter H. Jackson, C.E., of San Fran- 
 cisco, who has had an extended experience 
 with this form of construction, says of it: 
 "The Franklin girder is unequaled for 
 strength in the application of the same 
 amount of metal in any other form. This 
 cast-iron arch is in effect a device for em- 
 ploying cast iron compressively, neutralizing 
 the tensile strain due to transverse strain. 
 It has been favorably commented on by 
 the scientific papers of the United States. 
 London and Paris." 
 
266 
 
 BENDING-MOMENTS. 
 
 CHAPTER IX. 
 
 BENDING-MOMENTS AND SUPPORTING 
 FORCES. 
 
 THE bending-moment of a beam or truss represents the de- 
 structive energy of the load on the beam or truss at any point for 
 which the bending-moment is computed. 
 
 The moment of a force around any given axis is the product 
 of the force into the perpendicular distance between the line of 
 action of the force and the axis, or the product of the force into 
 its arm. 
 
 In a beam the forces or loads are all vertical and the arms hori- 
 zontal. 
 
 The bending-moment at any cross-section of a beam is the alge- 
 braic sum of the moments of the forces tending to turn the beam 
 around the horizontal axis passing through the centre of gravity of 
 the section. 
 
 EXAMPLE. Suppose we have a beam with one end securely 
 fixed into a wall and the other end projecting from it, as in Fig. 1. 
 Let us now suppose we have a 
 weight which if placed at the end 
 ^. of the beam will cause it to break 
 ^Pat the point of support. 
 
 I Then, if we were to place the 
 
 weight on the beam at a point 
 " '"jnear the wall, the beam would 
 X Support the weight easily; but as 
 J we move the weight towards the 
 outer end of the beam, the beam 
 bends more and more, and when 
 the weight is at the end, the beam 
 breaks, as shown by the dotted lines, Fig. 1. 
 
 Now, it is evident that the destructive energy of the weight is 
 greater the farther the weight is removed from the wall-end of the 
 beam, although the weight itself remains the same all the time. 
 The reason for this is that the moment of the weight tends to 
 
 Fig.1 
 
BENDING-MOMENTS. 267 
 
 turn the beam about the point A, and thus produces a pull on the 
 upper fibres of the beam and compresses the lower fibres. As the 
 weight is moved out on the beam, its moment becomes greater, 
 and hence also the pull and compression on the fibres; and 
 when the moment of the weight produces a greater tension or 
 compression on the fibres than they are capable of resisting, they 
 fail and the beam breaks. Before the fibres break, however, 
 they commence to stretch, and this allows the beam to bend; 
 hence the name " bending-moment " has been given to the mo- 
 ment which causes a beam to bend, and perhaps ultimately to 
 break. 
 
 There may, of course, be several loads on a beam, and each one 
 having a different moment tending to bend the beam; and it 
 may also occur that some of the weights may tend to turn the 
 beam in different directions ; the algebraic sum of their moments 
 (calling those tending to turn the beam to the right + and the 
 others) would be the bending-moment of the beam. 
 
 Knowing the bending-moment of a beam, we have only to find 
 the section of the beam that is capable of resisting it, as is shown 
 in the general theory of beams, Chapter XV. 
 
 To determine the bending-moments of beams mathematically 
 requires considerable training in mechanics and mathematics; 
 but, as most beams may be placed under some one of the follow- 
 ing cases, we shall give the bending-moment for these cases and 
 then show how the bending-moment for any other methods of 
 loading may be easily obtained by a scale diagram. 
 
 Examples of Bending-Moments. 
 
 CASE I. 
 
 Beam fixed at one end and loaded 
 with concentrated load W. 
 
 Bending-moment = W X L. 
 may, or may not, be the whole length 
 of the beam according to where the 
 weight is located.) 
 
 Fig. 2 
 
268 
 
 BENDING-MOMENTS. 
 
 CASE II. 
 
 Beam fixed at one end, loaded with 
 a distributed load W. 
 
 Bending-moment = W X 
 
 2' 
 
 Fig. 3 
 
 NOTE. If L is in feet, the bending-mo- 
 ment will be foot-pounds ; if L is in inches, 
 the bending-momerit will be in inch-pounds. 
 See general formula for beams, Chapter XV. 
 
 CASE III. 
 
 Beam fixed at one end, loaded with 
 both a concentrated and a distributed 
 load. 
 
 Bending-moment = P X L 2 + W X -77. 
 
 CASE IV. 
 Beam supported at both ends, loaded with concentrated load at 
 
 centre. 
 
 W 
 
 g^JL^ Bending-moment 
 
 L 
 
 Fig. 5 
 
 CASE V. 
 Beam supported at both ends, loaded with a distributed load W. 
 
 Bending-moment 
 
 1 
 
 Fig. 6 
 
BENDING-MOMENTS. 
 
 269 
 
 CASE VI. 
 
 Beam supported at both ends, loaded with concentrated load not 
 at centre. 
 
 -m- 
 
 ilw 
 
 Bending-moment 
 f mXn 
 L ' 
 
 Fig. 7 
 
 CASE VII. 
 
 Beam- supported at both ends, loaded with two equal concen- 
 trated loads, equally distant from the centre. 
 
 Bending-moment 
 
 Wfl 
 
 IW 
 
 Fig. 8 
 
 From these examples it will be seen that all the.quantities which 
 enter into the bending-moment are the weight, the span, and the 
 distance of point of application of concentrated load from each 
 end. 
 
 CASE VIII. 
 
 Beam supported at both ends, loaded with a distributed load over 
 only a portion of the span. 
 
 Vt >>L nnn _____ 
 
 Bending-moment 
 _WXmXn 
 
 -L r 
 
 Fig. 9 
 
 TF X L W X Li 
 When m and n are equal, bending-moment = ^ . 
 
270 
 
 BEXDIXG-MOMENTS. 
 
 EXAMPLE. Let W= 800 Ibs.; n=8';w=12'; L=20'; 1^=8'. 
 Then bending-moment = 
 
 800X8X12 800X8 
 
 - . = 36,480 800 = 3040 foot-pounds or 
 Z(j o 
 
 36,480 inch-pounds. 
 
 EXAMPLE II. Let w=w=10ft; L=20ft.; 1/^4 ft.; TF= 
 600 Ibs. Then bending-moment = 
 
 600X20 _ 600X4 = 3000 _ 300 =2700 ft lbg or 32j400 in _ lbs 
 4 o 
 
 The bending-moment for any case other than the above may 
 easily be obtained by the graphic method, which will now be 
 explained. 
 
 Graphic Method of Determining Beiicling- 
 Momeiits. 
 
 The bending-moment of a beam supported at both ends and 
 loaded with one concentrated load may be shown graphically, as 
 follows : 
 
 Let W be the weight applied, as shown. Then, by rule under 
 Case VI., the bending-moment directly under 
 
 -P, _. raXra 
 
 Draw the beam, with the given span, accurately to scale, and 
 measure down the line AB (to a scale of pounds to the inch) 
 equal to the bending-moment. Connect B with each end of 
 the beam. If, then, we wished to find the bending-moment 
 at any other point of 
 the beam, as at o, 
 draw the vertical line 
 
 y to BC, and its, ' D .\ T A 
 
 length, measured to \ 
 the same scale as AB, 
 will give the bending 
 moment at o. 
 
 Beam with two 
 concentrated loads . 
 (Fig. 11.) 
 
 To draw the bending-moment for a beam with two connected 
 loads, first draw the dotted lines ABD and ABC, giving the out- 
 
 Fig. 10 
 
BENDING-MOMENTS. 
 
 271 
 
 line of the bending-moment for each load separately; EB being 
 equal to WX~^ and FC equal to PX -. 
 
 Fig. II 
 
 Now, the bending-moment at the point E equals EB, due to 
 the load W, and Eb, due to the load P; hence the bending- 
 moment at E should be drawn equal to EB + Eb = EB 1 ; and 
 at F the bending-moment should equal FC + Fc=FCi. The 
 outline for the bending-moment due to both loads, then, would 
 be the line AB^C^D and the greatest bending-moment would, 
 in this particular case, be FCj_. 
 
 Beam with three concentrated loads. (Fig. 12'.) 
 Proceed as in the last case, and draw the bending-moment 
 for each load separately. Then make AD=A1+A2 + A3, 
 
 Fig. 12 
 
 BE=Bl+B2 + B3, and CF=C1+C2 + C3. The line HDEFI 
 will then be the outline for the bending-moment due to all the 
 
272 
 
 BENDING-MOMENTS. 
 
 weights. The bending-moment for a beam loaded with any 
 number of concentrated weights may be drawn in the same way. 
 Beam with uniformly distributed load. (Fig. 13.) 
 
 Fig. 13 
 
 Draw the beam with the given span, accurately to a scale, as 
 before, and at the middle of the beam draw the vertical line AB 
 
 equal to WX-$-, W representing the whole distributed load. 
 
 o 
 
 Then connect the points C, B, D by a parabola and it will give 
 the outline of the bending-moments. If, now, we wanted the 
 bending-moment at the point a, we have only to draw the verti- 
 cal line ab, and measure it to the same scale as AB, and it will 
 be the moment desired. Methods for drawing the parabola 
 may be found in "Geometrical Problems/ 7 Part I. 
 
 Beam loaded with both distributed and concentrated loads. (Fig. 14.) 
 To determine the bending-moment in this case, we have 
 only to combine the methods for concentrated loads and for 
 the distributed 
 load, as shown in 
 the accompany- 
 ing figure. The 
 bending - moment 
 at any point on 
 the beam will 
 then be limited 
 by the line ABC 
 on top and 
 CDEFA on the 
 bottom; and the 
 greatest bending- 
 moment will be 
 the longest verti- 
 cal line that can be drawn between these two bounding lines. 
 
BENDING-MOMENTS. 
 
 273 
 
 For example, the bending-moment at X would be BE. The 
 position of the greatest bending-moment will depend upon the 
 position of the concentrated loads, and it may and may not 
 occur at the centre. 
 
 EXAMPLE. What is the greatest bending-moment in a beam 
 of 20 feet span, loaded with a distributed load of 800 pounds 
 and a concentrated load of 500 pounds 6 feet from one end, and 
 a concentrated load of 600 pounds 7 feet from the other end? 
 
 ,L 
 S 8' 
 
 -fe 
 
 T - - Tl 
 
 i 00 
 
 Ans. 1st. The moment due to the distributed load is 
 
 800 X 20 
 
 or 
 
 8 
 
 Fig. 15 
 
 2000 pounds. 
 We, therefore, 
 lay off to a 
 scale, say 4000 
 pounds to the 
 inch, 51 = 2000 
 pounds, and 
 draw a parabola 
 between the 
 points A t B, and 
 C. 
 
 2d. The bending-moment for the concentrated load of 500 
 
 pounds is 
 
 500X6X14 
 20 
 
 : , or 2100 pounds. Hence we draw E2= 2100 
 
 pounds to the same scale as Bl, and then draw the lines AE 
 and CE. 
 
 3d. The bending-moment for the concentrated load of 600 
 
 pounds is 600> < 7xl3 ? or 2730 pounds; and we draw D3=2730 
 20 
 
 pounds and connect D with A and C. 
 
 4th. Make ##=2-4, and D<7=3-5, and connect G and H 
 with C and A and with each other. 
 
 The greatest bending-moment will be represented by the 
 longest vertical line which can be drawn between the parabola 
 ABC and the broken line A HOC. In this example we find 
 the longest vertical line which can be drawn is xy; and by 
 scaling it we find the greatest bending-moment to be 5550 foot- 
 pounds, applied 10 feet 11 inches from the point A. 
 
 In this case the position of the line Xy was determined by 
 
274 SUPPORTING FORCES. 
 
 drawing the line T7\ parallel to HG, and tangent to ABC. The 
 line Xy is drawn through the point of tangency. 
 
 NOTE. If we wish the bending-moment in inch-pounds , multiply the 
 moment in foot-pounds by 12. 
 
 Supporting Forces. 
 
 It is a fundamental principle of mechanics that for a body to 
 be in equilibrium the forces acting upon it must balance each 
 other. When, therefore, a body, such as a beam, girder, or 
 truss, is subjected to loads acting downwards in a vertical direc- 
 tion, that the beam or truss shall keep its position there must 
 be an equal resistance in the opposite direction. This resistance 
 is furnished by the supports, which may be either of masonry, 
 columns, or another beam or truss. 
 
 From the above propositions it follows that the supports must 
 react against the beam or truss ivith a combined resistance equal to 
 the sum of the loads acting downwards. 
 
 It is often necessary to determine the amount of each reac- 
 tion, and in computing the shearing stress in a beam or girder, 
 or in drawing a strain diagram for a truss, this is the first step 
 of the problem. 
 
 The following rules will enable one to determine the support- 
 ing forces or reactions, for any manner of loading, when the 
 beam, girder, or truss is supported at both ends. 
 
 These rules apply either to a beam, girder, or truss, and to 
 any style of truss. 
 
 1. When the loads are symmetrically disposed between the sup- 
 ports, each supportinq force is equal to one-half of the total load. 
 
 2. For a single concentrated load applied at any point, as in 
 Fig. 16, 
 
 W OTff 
 
 A ------ ^ ---------- J 
 
 Fig. 16 
 
 ^ 2 . if 
 
 3. For a distributed load applied over only a portion of the span, 
 
SUPPORTING FORCES. 
 
 275 
 
 as in Fig. 17, assume the load to be concentrated at its centre, 
 and use formula (1). 
 
 Fig. 17 
 
 EXAMPLE. Let n=8, m=12, and TF=800; then P x = 
 
 800 V 12 
 ~~ = 480. When n and m are equal, then P l= P 2 = \W. 
 
 4. For any number of concentrated forces, indicate the distances 
 from the right-hand support, as in Fig. 18; then 
 
 W 1 m + W 2 n + W 3 o+ TF 4 r-f 
 
 - 
 
 (2) 
 
 The same result would be obtained by finding the reaction of 
 I for each load by formula (1) and adding the reactions. 
 
 
 Fig. 18 
 
 When a truss is loaded unsymmetrically, the supporting forces 
 will be found by formula (2), keeping the same notation, and 
 using the same number of terms in the formula as there are loads 
 on the truss. 
 
 It should always be borne in mind that the sum of the reactions 
 is equal to the sum of the loads. 
 
276 
 
 SUPPORTING FORCES 
 
 // the beam or girder supports <i distributt-il /<><*</ <im/ U/NO r<;/- 
 OtlUroM/ lihiJs. to eaeh of the reaetions obtained by formulas ^ H 
 OT (2) add one-half of the distributed load. 
 
 I \ vMj-i r I. A beam li ; it. long is supported at eaeh end b\ 
 tlu> t'u beam i>t' a truss, the di.Mamv lu'i>\-iMi the i-t'iitivs of the 
 trusses boing 1T> it. I ins.; at a point I It. I ins. from the eentre 
 of the left-hand support the beam sustains a eoneent rated load 
 of 12 tons. What part of the load is supported by eaeh truss? 
 
 Ans. Let P l denote the portion of the load borne by the truss 
 at l lie left, /*, that borne by the truss at the right, and /. the dis- 
 tance betNveen the eenires of the trusses; then, by formula (\\ 
 we have 
 
 ^ 8,6 tons and P t - 12 -8.6- 3,4 tons 
 
 EXAMPLE 2. A girder of 30 feet span is loaded \vith a dis- 
 tributed load of 15 tons and \\ith si\ eoneentrated loads of ">, 
 i>. 1. S, 3, and 'J tons, arranged consecutively from left to right. 
 
 Fig. 19 
 
 The distances from the right-hand support, corresponding to 
 those hi Fig. IS, are: m28, n22, o*16, r 12, 5-10, <6, 
 What will be the reaction at eaeh support? 
 
 .-liis. First End reactions for concentrated loads. By for* 
 rnula (2) 
 
 D 5X28 -f 6X22 -f 4 Xl6-f 8X12+3X10 + 2X6 
 P t = 3Q 
 
 Pt-5+6+4+8-f 3+2-15,8- 12.2 tona, 
 
 - 15.8 tons j 
 
SUPPORTING FORCES. 277 
 
 One-half of the distributed load is 7.5 tons; then P 4 for whole 
 load 15.8 + 7.5-= 23.3 tons and 7^=19.7 tons. 
 
 The reactions obtained for the concentrated loads may be 
 verified by multiplying each load by its distance from the other 
 support, and dividing the sum of the products by the span. 
 The result will be 7^. Thus in the above example 
 
 p 5X2 + 6X8 + 4X14 + 8X18 + 3X20 + 2X24 
 
 ~~30~ 12<Z ' 
 
 which proves the former calculation. 
 
 EXAMPLE 3. A truss is loaded in such a way that the loads 
 correspond to 3 tons for Wi (Fig. 19), 3 tons for W 2 , 5 tons for 
 Ws, 6 tons for W 4 , and 5 tons for TF 5 ; the distance L is 48 feet; 
 m, 40 feet; n, 32 feet; o, 24 feet; r, 16 feet, and s, 8 feet. What 
 is the reaction at each support? 
 
 r> 3X40 + 3X32 + 5X24 + 6X16 + 5X8 Q< 
 Ans. P t = = 9.83 tonsj 
 
 12.17 tons. 
 
278 MOMENTS OF INERTIA AND RESISTANCE. 
 
 CHAPTER X. 
 
 MOMENTS OP INERTIA AND RESISTANCE, AND 
 RADIUS OF GYRATION. 
 
 DIMENSIONS AND PROPERTIES OF STRUCTURAL 
 SHAPES. 
 
 MOMENT OF INERTIA. 
 
 THE strength of sections to resist strains, either as girders or as 
 posts, depends not only on the area, but also on the form of the 
 cross-section. The property of the section which represents the 
 effect of the form upon the strength of a beam or post is its 
 moment of inertia, usually denoted by 7. The moment of inertia 
 for any cross-section is the sum of the products obtained by multi- 
 plying the area of each particle in the cross-section by the square 
 of its distance from the neutral axis. 
 
 The neutral axis of a beam is the line on which there is neither 
 tension nor compression, and when the stresses are within the 
 elastic limit of the material, it can be shown that the neutral 
 axis passes through the centre of gravity of the cross-section. 
 
 For most forms of cross-section the moment of inertia is best 
 found by the aid of the calculus ; though it may be obtained by 
 dividing the figure into small squares or triangles, and multi- 
 plying their areas by the squares of the distance of their centres 
 of gravity from the neutral axis. The sum of all the products 
 will be the moment of inertia of the section. 
 
 MOMENT OF RESISTANCE. 
 
 The resistance of a beam to bending and cross-breaking at any 
 given cross-section is the moment of the two equal and opposite 
 forces, consisting of the thrust along the longitudinally com- 
 pressed layers, and the tension along the longitudinally stretched 
 layers. 
 
 This moment, called the "moment of resistance," is, for any 
 given cross-section of a beam, equal to 
 
 / moment of inertia \ 
 
 [ T TT-T 5 ) X modulus of rupture or fibre stress. 
 
 \extreme distance from axis/ 
 
RADIIS OF GYRATION. 270 
 
 The moment of resistance forms a part of all formulas for the 
 strength of beams. The portion of the above formula included 
 in parenthesis is sometimes erroneously designated the moment 
 of resistance ; in the handbooks published by the manufacturers 
 of structural steel shapes, it is now designated as the section 
 modulus, and for the sake of uniformity, the author has adopted 
 the same term. 
 
 RADIUS OF GYRATION. 
 
 The effect of the form or section of a column upon its strength 
 is determined by a property called the radius of gyration. The 
 value of the radius of gyration of any section is determined by 
 the formula, r=\/moment of inertia -4- section area. 
 
 The moment of inertia and radius of gyration of a section are 
 always taken about an axis passing through the centre of gravity 
 of the section. For all sections except circles there will be at 
 least two radii of gyration; the least of these will be that taken 
 about the axis around which the column, strut, or beam is most 
 likely to bend. 
 
 Formulas for the moment of inertia, radius of gyration, and 
 section modulus of the principal elementary sections are given 
 below. In the case of hollow or re-entering sections, the moment 
 of the hollow portion is to be subtracted from that of the 
 enclosing area. 
 
 Moments of inertia when referred to the same axis can be 
 added or subtracted like any other qualities which are of the 
 same kind. 
 
 Moments of Inertia, Section Modulus, and Radii 
 of Gyration. 
 
 I moment of inertia. 
 
 7 = section modulus. 
 
 r = radius of gyration. 
 
 A = area, of the section. 
 
 Position of neutral axis represented by broken line. 
 
 bd* 
 ~- 
 
 *. 
 12 
 
280 MOMENTS OF INERTIA AND RESISTANCE. 
 
 T 
 
 12 
 
 I 
 ~~bd-b,( 
 
 -IT /-. 
 
 ^ i 
 
 _ 37 6<P 
 
 * jK= 25 == 2- 
 ^ 2 I <* 2 
 
 m2 
 
 r ~A"18' 
 
 i 
 
 &d 3 
 
 / \4 = J- 
 
 /_ \i r*=? 
 
r 
 f 
 
 RADII OF GYRATION. 
 
 Xh 
 
 - u 
 
 7= 
 
 281 
 
 S\ 
 
 7=0 0491<2*. 
 
 - 0.0491 (D 4 -^ 1 )- 
 
 ,_ 1 D*-d* 
 ~ 
 
 - I ( a ver y close 
 
 ~ 5.64 i approximation). 
 
 L f^i 
 
 "*fcp- -^2/ 
 
 12 
 
 * To find the value of d, see page 240. 
 
282 MOMENTS OF INERTIA AND RESISTANCE. 
 
 
 A = bd-dt(b-t). 
 I = bd*-d(b-t) 
 
 To find x and x r see page 239. 
 
 ^_i/ 
 
 Moments of Inertia of Coinpound Shapes. 
 
 The moment of inertia of any combination of single shapes is 
 equal to the sum of the moments of inertia of the individual 
 shapes taken about an axis passing thrpugh the centre of gravity 
 of the combination. 
 
 The moment of inertia of the individual sections may be 
 obtained by the following rule: 
 
 The moment of inertia of any section about an axis other than 
 through its centre of gravity is equal to its moment of inertia about 
 a parallel axis passing through its centre of gravity plus the area of 
 the section multiplied by the square of the distance between the axes. 
 
 Thus, the moment of inertia of the angle (Fig. 1) about the 
 
RADII OF GYRATION. 
 
 283 
 
 FORMULAS USED FOR COMPUTING MOMENTS OF 
 INERTIA FOR STANDARD SECTIONS. 
 
 
 & 
 
 a- -> 
 
 Tan2a=-- 
 7, Axis 1-1 = 
 
 ' minimum , Axis 3 3 = 
 
 12 
 
 P CQS 2 a 7 sin 2 a 
 cos 2a 
 
 U 
 
 r 
 
 
 2-2=- 
 
 
 
 36 
 
 144 
 
 6-> 
 
 
 e=area of head. 
 
 2A 
 
 * 2 2s+)b 
 
 '.Axis 2-2 = -^- + 
 
 36 
 
284 MOMENTS OF INERTIA AND RESISTANCE. 
 
 FORMULAS USED FOR COMPUTING MOMENTS OF 
 INERTIA FOR STANDARD SECTIONS Continued. 
 
 
 2 .,* 
 
 A <d 1 2s(6 t) 1 ( & ~^ 2 
 
 1 
 
 1 
 
 r 
 
 
 r Axi3l i W W-l* 
 
 I , AXIS 1 1 1 . 
 1^ o 
 
 (,.% i(3 (,<_< 
 
 /'.Ax 1 s2-2 = -g-+ I 2 + ^-. 
 Slope of flange =0 = j: =>-= for standard sections. 
 h=d-2s. l = h-g(b-t). 
 
 
 
 i (i 
 
 . 
 
 -1- 
 
 
 lb 
 
 
 3 T 
 is 
 
 A tfl I c^?i t\ 1 V?,~P 
 
 r^i^ 2 1 < 6 -w 6 +>T. i 
 
 
 -.- - j 
 
 
 
 ^"L 65 ! 2 ' 18 J A ' 
 , 6d3 M_^4 
 
 1 
 
 (l 
 
 i c 
 
 i 
 
 ' 12 16 ' 
 /', Axis 2-2 = -![2s63 + fc3+^- 4 ]--4*2. 
 
 i 
 
 ft 
 
 Slope of flange g ~/ . _ j\ *** ~~ for standard sections. 
 fc=d-2s. l = h-2g(b-f). 
 
 \TT 
 
 | 
 
 i 
 
 fr- 
 
 J f 
 
 kl , 
 
 A = t(2a-t). 
 a?+at-t* 
 
 " 2(2a-0 ' 
 7Axkl 1 C-*> i + 8 -(-0(*-0 
 
 2^-2(a:-0 4 4-^[a- (2r |-)] 3 
 
 /// A f> O . 
 
 I \ 
 
 
 eg 
 
 | 
 
 
 
 \ 
 
 V 
 
 o 
 
 Hb 
 
 X 
 
 j, 
 
 ! t 
 
 tl 
 
 ITT' 
 
 <-fA-- 
 V - 
 
 ft 
 
 a^ 
 
 -2 
 
 -^ 
 
 A=<(a + 6-/)- 
 (2a' + 6)4a /2 , <(26' + a) + 6 / 2 
 
 2(^ + 6) 2(fe' + a) 
 m__ [(2a;-<)6(6-2a;') + (2sc'-0(a-0(a + <-2a;)] 
 
 2(/'-7) 
 I 4 ' 1 1 -*) 8 + ^-(6-0(*-0 
 
 r , . (6-a/)+a'-(a-0(x'-O s 
 
 1 \ 
 
 
 ; 
 
 4v- 
 
 
 -* 
 
 1,^^x182-2" g - -. 
 
 7" AuluT 1 ^cos2a~/'sin2a 
 
 1 * A **9> cos2a. 
 
RADII OF GYRATION. 
 
 285 
 
 axis AB is equal to its moment of inertia about the axis ab 
 plus the product of its area by x 2 . The mo- 
 ment of inertia for the standard merchant a j--^ ]-|" 
 shapes of structural steel may be found from 
 the tables given in this chapter. The dis- 
 tance d may be found from columns IX. and 
 X., "Properties of Angles." This distance 
 subtracted from D will give the distance x. 
 
 The method of finding the moment of inertia 
 for the most common combinations is indicated below. The 
 column numbers' refer to the columns in the table giving the 
 properties of the section under consideration. A period be- 
 tween letters denotes multiplication. 
 
 Fig 2. Moment of Inertia of Combination about Axis AB 
 
 = twice the moment of inertia for A. 
 beam a (col. II.) + that for " 
 beam b (col. III.). 
 
 Fig. 2 
 
 Fig. 3. Moment of Inertia of Combination about Axis CD 
 
 = twice the area of beam a (col. 
 I) Xd 2 + twice moment of in- 
 ertia for beam a (col. III.) + 
 that for beam 6 (col. II.). 
 
 Fig. 3 
 
 Fig. 4. Moment of Inertia of Combination about Axis AB 
 
 Xcdtlce 
 
 = twice the moment of single 
 channel in col. II. 
 
 Fig. 4 
 
286 MOMENTS OF INERTIA AND RESISTANCE. 
 
 Fig. 5. Moment of Inertia of Combination about Axis CD 
 
 = twice area of one channel 
 (col. I.)Xd 2 -ftwice moment 
 of inertia (col. III.). 
 d= distance of centre of gravity of 
 the channel from centre line 
 of the combination. 
 
 
 Fig. 5 
 
 Fig. 6. Moment of Inertia of Combination about Axis AB 
 
 C fb t s \ 
 
 \ I for plates = 21 - f- b . t . y^ ) * 
 = sum of < \ 12 / 
 
 (,1 for channels = twice the moment in col. II. 
 - C 
 
 J 
 
 k~-i- 
 
 o 
 
 I 
 
 
 u-i-B 
 
 ^__, 
 
 1 
 1 
 
 X 
 
 ^ 
 
 
 6 
 
 Fig. 6 
 
 
 Fig. 6. Moment of Inertia about Axis CD 
 
 ( Jf . 2.t.b 3 
 
 I for plates = r^ ; 
 
 = sum of { 
 
 i / for channel^ = 2 X (area of one channel X I 2 + mo- 
 
 t meht of inertia, col. III.). 
 
 r, coi. ix. 
 
 Fig. 7. Moment of Inertia of Combination about Axis AB 
 = sum of 
 
 "/for plates P= r-^+b.t.x*) X2; 
 
 / for four angles=4X i i i 
 
 \angie^ coi. j-j.^.. 
 
 B / for plate P 1 =-|^-. 
 
 y=\d-l, col. IX. 
 
 /moment of one , area of one angle\ 
 times y , ) J 
 
RADII OF GYRATION. 
 
 287 
 
 Fig. 7. Moment of Inertia about Axis CD 
 = sum of 
 
 /for plates P= 
 
 12 ' 
 
 /moment of one , area of one angleX 
 7 tor four angles^ X j ^^ ^ n + times p | 3 
 
 /for plate ^i~^- 
 
 l=d (col.: 
 
 Moment of inertia for Four Angles connected by Lattice and 
 without Cover-plates. Same as in middle line of above. 
 
 b 
 Fig. 7 
 
 Fig. 8. Moment of Inertia of Combination about Axis AB. 
 Same as for Fig. 7, letting ^ equal total thickness of web- 
 plates. 
 
 Fig. 8. Moment of Inertia about Axis CD 
 = sum of 
 
 / for flange-plates = J 
 
 /moment of one area of one angleN . 
 / for four angles= 1 X ^ angle ^ coL IL H times p / 
 
 /forweb-plates=2X 
 
288 MOMENTS OF INERTIA AND RESISTANCE. 
 
 Fig. 9. Moment of Inertia of Two Angles. 
 About axis AB :/= twice the moment of single angle, col. II. 
 
 AU , r ovx /moment of one , area of one angle\ 
 
 About axis CD: 7= 2X ( , , TTT -f 
 
 \angle, col. III. tiniest / 
 
 ol. IX.). 
 
 EXAMPLE I. Fig. 7, Let 6=12; <=}. d=30; ^=i. An- 
 gles 5X3iXj. Find moment of inertia of the girder about 
 axis AB. 
 
 From table of properties of standard angles, unequal legs, 
 we find area of one angle to be 4. Moment of inertia of angle 
 about axis parallel to long flange = 4. 05; distance from centre 
 of gravity to back of long flange =.91. 
 
 Then 
 
 2790.96 
 
 7 for four angles = 4X[4.05+4X(15-.91) 2 J <= 3192.20 
 
 7 for web-plate =^ = 1125.00 
 
 7 for whole section= 7108.16 
 
 It will be noticed that the moment of inertia of the flange- 
 plates and angles about their own axes is so small, compared 
 with the moment of the girder, that they might be omitted 
 without any appreciable error. 
 
 In calculating the moment of inertia of riveted girders it is 
 the custom with many engineers to let 7= area of flange-plates 
 
 (d\ 2 
 ~2 \ , which in this case would give 
 
 7=28X15 2 =6300. 
 
RADII OF GYRATION. 289 
 
 EXAMPLE II. Find the moment of inertia of two 6X4X| 
 inch angles, placed as in Fig. 9, d being made 1 inch. 
 
 Ans. Moment of inertia about axis AB= 2X13.47 (see col. 
 II., p. 303) = 26. 94 
 
 For moment about axis CD we have 
 
 Area of one angle from col. I., p. 303, =3.61 3 7=4.90.? 
 Z=.5 + .94 (col. IX.) = 1.44; then 
 
 / for both angles= 2 X[4.90 + 3.61 Xl.44 2 ]= 24.76. 
 
 Radius of Gyration of Compound Shapes. 
 
 A. By Moment of Inertia. 
 
 The radius of gyration of any combination is found by divid- 
 ing the moment of inertia of the shape by the total metal area 
 and taking the square root of the product. 
 
 Thus, the radius of gyration of the two angles in Example II., 
 
 about AB= A= 1.93; 
 7 <2i2i 
 
 about C>= -= 1.85. 
 
 7*22 
 
 B. Without Moment of Inertia. 
 
 In the case of a pair of any shape without a web the value of 
 the radius of gyration can always be readily found without con- 
 sidering the moment of inertia. 
 
 The radius of gyration for any section around an axis parallel 
 to another axis passing through its centre of gravity is found as 
 follows : 
 
 Let r= radius of gyration around axis through centre of 
 gravity; R = radius of gyration around another axis parallel to 
 above; d= distance between axes; then 
 
 Thus, in Example II., the radius of gyration about the axis 
 CD could have been obtained as follows: r= radius of one 
 
290 MOMENTS OF INERTIA AND RESISTANCE. 
 
 angle about its own axis parallel to CD=1.17 (Column III.), 
 d=x (Fig. 9) = .5 + .94 (Column IX.) = 1.44. 
 
 J2 = \/1.44 2 + 1.17 2 =1.85, the same result that we obtained 
 by using the moment of inertia. 
 
 The radius about A B, Fig. 9, is the same as for one angle 
 (Column II.). 
 
 When r is small compared with d } as is generally the case in 
 latticed girders and columns, R may be taken as equal to d 
 without material error. 
 
 EXAMPLE III. Two 9-inch, 15-pound standard channel-bars 
 are placed 4.6 inches apart, as in the figure; required the radius 
 of gyration around axis CD for combined 
 section. 
 
 Ans. Find r, in Column V., p. 298 = 
 0.665; and r 2 =.4422. 
 
 B Distance from base of channel to neutral 
 
 axis, Column IX., is 0.59. One-half of 
 4.6 = 2.3 + .59 = 2.89, the distance be- 
 tween neutral axis of single channel and 
 of combined section; hence 
 R= V8.3521 + .4422 = 2.96 ; or, for all practical purposes, R = d. 
 EXAMPLE IV. Four 3X3Xi-inch standard angles placed as 
 shown form a column 10 inches square; find the radius of gyra- 
 tion. 
 
 c 
 
 L. J 
 
 Ans. From Column TV., p. 310, we find r=0.93 and r z =.8649. 
 The distance from base of angle to neutral axis, Column IX., is 
 .84; hence, d=5-.84=4.16, or, d 2 = 17.3056, and 
 
 R= x/17.3056 + .8649= 4.26. 
 
 Table I. will be found of considerable assistance when com- 
 puting the moment of inertia of sections built with plates. 
 
RADII OF GYRATION. 
 
 291 
 
 TABLE I. 
 MOMENTS OF INERTIA OF I RECTANGLES. 
 
 .s 
 
 Width of rectangle in inches. 
 
 (S- s 
 
 i 
 
 
 
 ! 
 
 A 
 
 i 
 
 * 
 
 t 
 
 2 
 
 .17 
 
 .21 
 
 .25 
 
 .29 
 
 .33 
 
 .38 
 
 .42 
 
 3 
 
 .56 
 
 .70 
 
 .84 
 
 .98 
 
 1.13 
 
 1.27 
 
 1 4 
 
 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 
 
 4.50 
 
 5 6$ 
 
 6.75 
 
 7.88 
 
 9.00 
 
 10.13 
 
 11 25 
 
 7 
 
 7.15 
 
 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 
 
 15.19 
 
 18.98 
 
 22.78 
 
 26.58 
 
 30.38 
 
 34.17 
 
 87.97 
 
 10 
 
 20.83 
 
 26.04 
 
 31.25 
 
 36.46 
 
 41.67 
 
 46.8* 
 
 52.08 
 
 11 
 
 27.73 
 
 34.66 
 
 41.59 
 
 48.o3 
 
 55.46 
 
 62.39 
 
 69.32 
 
 12 
 
 36.00 
 
 45.00 
 
 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 
 
 85.75 
 
 100.04 
 
 114.33 
 
 128,63 
 
 142.92 
 
 15 
 
 70.31 
 
 87.89 
 
 105.47 
 
 123.05 
 
 140.63 
 
 158.20 
 
 175.78 
 
 16 
 
 85.33 
 
 106 . 67 
 
 128.00 
 
 149.33 
 
 170.67 
 
 192.00 
 
 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 
 
 303.75 
 
 19 
 
 142.90 
 
 178.62 
 
 214.34 
 
 250.07 
 
 285.79 
 
 321.52 
 
 357.24 
 
 20 
 
 166.67 
 
 208.33 
 
 250.00 
 
 291.67 
 
 333.33 
 
 375.00 
 
 416.67 
 
 21 
 
 192.94 
 
 241.17 
 
 289.41 
 
 337.64 
 
 385.88- 
 
 434.11 
 
 482.34 
 
 22 
 
 221.83 
 
 277 29 
 
 332.75 
 
 388.21 
 
 443.67 
 
 499.13 
 
 554 . 58 
 
 23 
 
 253.48 
 
 316.85 
 
 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 
 
 3h6 . 17 
 
 457 . 71 
 
 549.25 
 
 640.79 
 
 732 . 33 
 
 823.88 
 
 915.42 
 
 27 
 
 410.06 
 
 512.58 
 
 6i5.09 
 
 717.61 
 
 820.13 
 
 922.64 
 
 1025.16 
 
 28 
 
 457.33 
 
 571.67 
 
 6S6.00 
 
 800.33 
 
 9i4.67 
 
 1029.00 
 
 1143. S3 
 
 29 
 
 508.10 
 
 6d5.13 
 
 762.16 
 
 889.18 
 
 1016.21 
 
 1143.23 
 
 1270.26 
 
 30 
 
 562.50 
 
 703.13 
 
 843.75 
 
 984 . 38 
 
 1125.00 
 
 1265.63 
 
 1406.25 
 
 32 
 
 682.67 
 
 853.33 
 
 1024.00 
 
 194.67 
 
 1365.33 
 
 1536.00 
 
 1706.67 
 
 34 
 
 818.83 
 
 1023 . 54 
 
 1228.25 
 
 1432.96 
 
 637.67 
 
 1842.38 
 
 2047.08 
 
 36 
 
 972.00 
 
 1215.00 
 
 1458.00 
 
 1701.00 
 
 1944.00 
 
 2187.00 
 
 2430.00 
 
 38 
 
 1143.17 
 
 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 
 
 ^662.00 
 
 3105.67 
 
 3549.33 
 
 3993.00 
 
 4436.67 
 
 46 
 
 2027. S3 
 
 2534.79 
 
 3041.75 
 
 3548.71 
 
 4055.67 
 
 4562.63 
 
 5069.58 
 
 48 
 
 2304.00 
 
 2880.00 
 
 456.00 
 
 032 . 00 
 
 4608.00 
 
 5184.00 
 
 5760.00 
 
 50 
 
 2604.17 
 
 3255.21 
 
 906.25 
 
 557.29 
 
 208.33 
 
 5859.38 
 
 6510.42 
 
 52 
 
 2929 . 33 
 
 3661.67 
 
 394.00 
 
 126.33 
 
 591.00 
 
 5858.67 
 
 7323.33 
 
 54 
 
 S280.50 
 
 4100.63 
 
 920.75 
 
 740.88 
 
 561.00 
 
 7381.13 
 
 8201.25 
 
 56 
 
 3658.67 
 
 4573 . 33 
 
 488.00 
 
 402 . 67 
 
 317.33 
 
 8232.00 
 
 9146.67 
 
 58 
 
 1064.83 
 
 5081.04 
 
 U97 . 25 
 
 113.46 
 
 129.67 
 
 9145.87 
 
 10162.08 
 
 60 
 
 4500.00 
 
 5625 . 00 
 
 750.00 
 
 875.00 
 
 000.00 
 
 0125.00 
 
 11250.00 
 
292 MOMENTS OF INERTIA AND RESISTANCE. 
 
 TABLE I Continued. 
 MOMENTS OF INERTIA OF. 
 
 I 
 
 .RECTANGLES. 
 
 Width of rectangle in inches. 
 
 li 
 |j 
 
 H 
 
 i 
 
 1 3 
 IV 
 
 1 
 
 if 
 
 1 
 
 .46 
 
 .50 
 
 .54 
 
 .58 
 
 .63 
 
 .67 
 
 2 
 
 1.65 
 
 1.69 
 
 1.83 
 
 1.97 
 
 2.11 
 
 2.25 
 
 3 
 
 3.67 
 
 4.00 
 
 4.33 
 
 4.67 
 
 5.00 
 
 5.33 
 
 4 
 
 7.16 
 
 7.81 
 
 8.46 
 
 9.11 
 
 9.77 
 
 10.42 
 
 5 
 
 12.38 
 
 13.50 
 
 14.63 
 
 15.75 
 
 16.88 
 
 18.00 
 
 6 
 
 19.65 
 
 21.44 
 
 23.22 
 
 25.01 
 
 26.80 
 
 28.58 
 
 7 
 
 29.33 
 
 32.00 
 
 34.67 
 
 37.33 
 
 40.00 
 
 42.67 
 
 8 
 
 41.77 
 
 45.56 
 
 49.36 
 
 53.16 
 
 56.95 
 
 60.75 
 
 9 
 
 57.29 
 
 62.50 
 
 67.71 
 
 72.92 
 
 78.13 
 
 83.33 
 
 10 
 
 76.26 
 
 83.19 
 
 90.12 
 
 97.05 
 
 103.98 
 
 110.92 
 
 11 
 
 99.00 
 
 108.00 
 
 117.00 
 
 126.00 
 
 135.00 
 
 144.00 
 
 12 
 
 125.87 
 
 137.31 
 
 148.75 
 
 160.20 
 
 171.64 
 
 183.08 
 
 13 
 
 157.21 
 
 171.50 
 
 185.79 
 
 200.08 
 
 214.38 
 
 228.67 
 
 14 
 
 193.36 
 
 210.94 
 
 228.52 
 
 246.09 
 
 263.67 
 
 281.25 
 
 15 
 
 234.67 
 
 256.00 
 
 277.33 
 
 298.67 
 
 3?0.00 
 
 341.33 
 
 16 
 
 281.47 
 
 307.06 
 
 332.65 
 
 358.24 
 
 383.83 
 
 409.42 
 
 17 
 
 334.13 
 
 364.50 
 
 394.88 
 
 425.25 
 
 455.63 
 
 486.00 
 
 18 
 
 392.96 
 
 428.69 
 
 464.41 
 
 500.14 
 
 535.86 
 
 571.58 
 
 19 
 
 458.33 
 
 500.00 
 
 541.67 
 
 583.33 
 
 625.00 
 
 666.67 
 
 20 
 
 530.58 
 
 578.81 
 
 627.05 
 
 675.28 
 
 723.52 
 
 771.75 
 
 21 
 
 610.04 
 
 665.50 
 
 720.96 
 
 776.42 
 
 831.87 
 
 887.33 
 
 22 
 
 697.07 
 
 760.44 
 
 823.81 
 
 887.18 
 
 950.55 
 
 1013.92 
 
 23 
 
 792.00 
 
 864.00 
 
 936.00 
 
 1008.00 
 
 1080.00 
 
 1152.00 
 
 24 
 
 895.18 
 
 976.56 
 
 1057.94 
 
 1139.32 
 
 1220.70 
 
 1302.08 
 
 25 
 
 1006.96 
 
 1098.50 
 
 1190.04 
 
 1281.58 
 
 1373.13 
 
 1464.67 
 
 26 
 
 1127.67 
 
 1230.19 
 
 1332.70 
 
 1435.22 
 
 1537.73 
 
 1610.25 
 
 27 
 
 1257.67 
 
 1372.00 
 
 1486.33 
 
 1600.67 
 
 1715.00 
 
 1829.33 
 
 28 
 
 1397.29 
 
 1524.31 
 
 1651 . 34 
 
 1778.36 
 
 1905.39 
 
 2032.42 
 
 29 
 
 1546.88 
 
 1687.50 
 
 1828.13 
 
 1968.75 
 
 2100.38 
 
 2250.00 
 
 30 
 
 1877.33 
 
 2048.00 
 
 2218.67 
 
 2389 . 33 
 
 2560.00 
 
 2730.67 
 
 32 
 
 2251.79 
 
 2456.50 
 
 2661.21 
 
 2865 . 92 
 
 3070.63 
 
 3275.33 
 
 34 
 
 2673.00 
 
 2916.00 
 
 3159.00 
 
 3402.00 
 
 3645.00 
 
 3888.00 
 
 36 
 
 3143.71 
 
 3429.50 
 
 3715.29 
 
 4001.08 
 
 4286.88 
 
 4572.67 
 
 38 
 
 3666.67 
 
 4000.00 
 
 4333.33 
 
 4666.67 
 
 5000.00 
 
 5333.33 
 
 40 
 
 4244.63 
 
 4630.50 
 
 5016.38 
 
 5402.25 
 
 5788.13 
 
 6174.00 
 
 42 
 
 4880.33 
 
 5324.00 
 
 5767.67 
 
 6211.33 
 
 6655.00 
 
 7098.67 
 
 44 
 
 5576.54 
 
 6083.50 
 
 6590.46 
 
 7097.42 
 
 7604.38 
 
 8111.33 
 
 46 
 
 6336.00 
 
 6912.00 
 
 7488.00 
 
 8064.00 
 
 8640.00 
 
 9216.00 
 
 48 
 
 7161.46 
 
 7812.50 
 
 8463.54 
 
 9114.58 
 
 9765.63 
 
 10416.67 
 
 50 
 
 8055.67 
 
 8788.00 
 
 9520.33 
 
 10252.67 
 
 10985.00 
 
 11717.33 
 
 52 
 
 9021.38 
 
 9841 . 50 
 
 0661.03 
 
 1481.75 
 
 12301.88 
 
 .3122.00 
 
 54 
 
 10061.33 
 
 0976.00 
 
 1890.67 
 
 12805.33 
 
 13720.00 
 
 14634.67 
 
 56 
 
 11178. 2Q 
 
 2194.50 
 
 3210.71 
 
 14226.92 
 
 15243.12 
 
 16259.33 
 
 58 
 
 12375.00 
 
 3500.00 
 
 .4625.00 
 
 15750.00 
 
 16875.00 
 
 18000.00 
 
 00 
 
RADII OF GYRATION. 293 
 
 TABLE II. RADII OF GYRATION FOR ROUND COLUMNS 
 
 
 Thickness in inches varying by tenths. 
 
 Outside 
 diameter 
 Of column 
 
 .1 
 
 .3 
 
 .3 
 
 .4 
 
 .5 
 
 6 
 
 7 
 
 .8 
 
 9 
 
 1.0 
 
 
 Corresponding radius of gyration in inches. 
 
 2 
 
 .67 
 
 .64 
 
 .61 
 
 .58 
 
 .56 
 
 .54 
 
 .52 
 
 .51 
 
 .50 
 
 .50 
 
 3 
 
 1.03 
 
 .99 
 
 .96 
 
 .93 
 
 .90 
 
 .88 
 
 .85 
 
 .83 
 
 .81 
 
 .79 
 
 4 
 
 1.38 
 
 1.35 
 
 1.31 
 
 1.28 
 
 1.25 
 
 1.22 
 
 1.19 
 
 1.16 
 
 1.14 
 
 1.12 
 
 5 
 
 1.73 
 
 1.70 
 
 1.66 
 
 1.63 
 
 1.60 
 
 1.57 
 
 1.54 
 
 1.51 
 
 1.48 
 
 1.46 
 
 6 
 
 2.08 
 
 2.05 
 
 2.02 
 
 1.98 
 
 1.95 
 
 1.92 
 
 1.89 
 
 1.86 
 
 1.83 
 
 1.80 
 
 7 
 
 2.43 
 
 2.40 
 
 2.36 
 
 2.33 
 
 2.30 
 
 2.27 
 
 2.24 
 
 2.21 
 
 2.18 
 
 2.15 
 
 8 
 
 2.79 
 
 2.76 
 
 2.72 
 
 2.69 
 
 2.66 
 
 2.62 
 
 2.59 
 
 2.56 
 
 2.53 
 
 2.50 
 
 9 
 
 3.15 
 
 3.11 
 
 3.08 
 
 3.04 
 
 3.01 
 
 2.97 
 
 2.94 
 
 2.91 
 
 2.88 
 
 2.85 
 
 1O 
 
 3.51 
 
 3.47 
 
 3.44 
 
 3.40 
 
 3.37 
 
 3.33 
 
 3.30 
 
 3.27 
 
 3.23 
 
 3.20 
 
 11 
 
 3.86 
 
 3.82 
 
 3.79 
 
 3.75 
 
 3.72 
 
 3.68 
 
 3.65 
 
 3.62 
 
 3.58 
 
 3.55 
 
 2 
 
 4.21 
 
 4.18 
 
 4.15 
 
 4.11 
 
 4.08 
 
 4.04 
 
 4.01 
 
 3.97 
 
 3.94 
 
 3.90 
 
 TABLE III. RADII 
 
 OF GYRATION 
 COLUMNS. 
 
 FOR SQUARE 
 
 
 Thickness in inches varying by tenths. 
 
 Outside 
 of column 
 
 .1 
 
 -2 
 
 .3 
 
 4 
 
 .5 
 
 .6 
 
 7 
 
 8 
 
 .9 
 
 1.0 
 
 in inches. 
 
 
 
 
 
 
 
 
 
 
 
 
 Corresponding radius of gyration in inches. 
 
 2 
 
 .78 
 
 .74 
 
 .71 
 
 .68 
 
 .65 
 
 .63 
 
 .61 
 
 .59 
 
 .58 
 
 .58 
 
 3 
 
 1.18 
 
 1.14 
 
 1.11 
 
 1.08 
 
 1.04 
 
 1.01 
 
 .98 
 
 .96 
 
 .93 
 
 .91 
 
 4 
 
 1.59 
 
 1.55 
 
 1.51 
 
 1.47 
 
 1.44 
 
 1.41 
 
 1.38 
 
 1.35 
 
 1.32 
 
 1.29 
 
 5 
 
 2.00 
 
 1.96 
 
 1.92 
 
 1.89 
 
 1.85 
 
 1.81 
 
 1.78 
 
 1.75 
 
 1.71 
 
 1.68 
 
 6 
 
 2.41 
 
 2.37 
 
 2.33 
 
 2.29 
 
 2.25 
 
 2.21 
 
 2.18 
 
 2.15 
 
 2.11 
 
 2.08 
 
 7 
 
 2.82 
 
 2.78 
 
 2.74 
 
 2.70 
 
 2.66 
 
 2.62 
 
 2.58 
 
 2.55 
 
 2.51 
 
 2.48 
 
 8 
 
 3.23 
 
 3.19 
 
 3.15 
 
 3.11 
 
 3.07 
 
 3.03 
 
 2.99 
 
 2.96 
 
 2.92 
 
 2.89 
 
 9 
 
 3.63 
 
 3.59 
 
 3.55 
 
 3.51 
 
 3.48 
 
 3.44 
 
 3.40 
 
 3.36 
 
 3.32 
 
 3.29 
 
 10 
 
 4.04 
 
 4.00 
 
 3.96 
 
 3.92 
 
 3.88 
 
 3.84 
 
 3.80 
 
 3.77 
 
 3.73 
 
 3.70 
 
 11 
 2 
 
 4.45 
 4.86 
 
 4.41 
 4.82 
 
 4.37 
 
 4.78 
 
 4.33 
 4.74 
 
 4.29 
 4.70 
 
 4.25 
 4.66 
 
 4.21 
 4.62 
 
 4.17 
 4.58 
 
 4.13 
 4.54 
 
 4.10 
 4.51 
 
 Dimensions, Moments of Inertia, Radii of Gyra- 
 tion and Section Modulus of Standard Struc- 
 tural Shapes. 
 
 As in using steel in structural shapes one is practically con- 
 fined to the choice of such shapes as are rolled by the mills, it is 
 necessary to have at hand the dimensions and properties of 
 those shapes to be able to calculate the necessary size to meet 
 
294 MOMENTS OF INERTIA AND RESISTANCE. 
 
 special requirements for strength and the practical conditions 
 pf economy and framing. During the past fifteen years great 
 changes have been made both in the material and shape of 
 structural bars of steel and iron. At the present time the New 
 Jersey Steel and Iron Company is the only manufacturer of 
 wrought-iron beams in the country, to the writer's knowledge, 
 all other mills rolling steel shapes, only, except perhaps small 
 angles and bars. 
 
 The rolling mills which manufacture the most complete line 
 of structural shapes are those of the Carnegie Steel Co., Cambria 
 Iron Co., Jones & Laughlins, Passaic Rolling Mill Co., Pencoyd 
 Iron Works, and the Phcenix Iron Co. In general, the products 
 pf these mills agree in shape quite closely, especially for beams 
 and channels. This is particularly true of the shapes rolled 
 by the first three of the companies named above. 
 
 The standard steel beams and channels given in the following 
 pages are rolled by all six of the mills, with the exception of the 
 24-inch beams which are not rolled by the Passaic and Phcenix 
 mills. Some of the mills also roll additional weights. Thus 
 the Pencoycl Iron Works rolls 18-inch beams up to 90 Ibs., 
 and 6-inch beams up to 46 Ibs. per foot. Except for the 18-inch 
 beams, only the properties of the standard sizes are given in 
 this book. 
 
 The following tables of properties of structural shapes have 
 been compiled from the 1900 publication of the Carnegie Steel 
 Company, except in the case of shapes not rolled by them. It 
 may be well to state that the tables of properties for the various 
 structural shapes, published by the companies named above, 
 (lo not agree exactly, even for the same weights, but the differ- 
 ences are not of practical importance. The tables of the Cam- 
 bria Iron Company and of the Carnegie Steel Company agree the 
 closest, for beams and channels. As angles are very extensively 
 used for a great many purposes, the properties for all sizes rolled 
 are given, and also a table showing from which mills the different 
 sizes may be obtained. Naturally it will generally be advan- 
 tageous to use a size that is rolled by several mills. 
 
 The properties for grooved steel, given on p. 300, were com- 
 puted by the author from the dimensions given by the manu- 
 facturers. These small channels are quite extensively used in 
 connection with suspended ceilings, and other fireproof con- 
 structions, and it is believed that the table will be found useful 
 by many. The Tables A, B, C, and D will be found very con- 
 
RADII OF GYRATION. 
 
 295 
 
 venient when computing the strength of struts formed of a pair 
 of channels and angles. 
 
 Standard Steel Beams and Channels* 
 
 % . 
 
 The following data are common to all standard I beams and 
 channels, with the exceptions stated: 
 
 c= & minimum web ; 
 C= minimum web + ^ inch. 
 
 s= thickness of web = Z, minimum for all beams except 20'' 
 FS and 24" I's. 
 
 For 20" beam 5= .55", *= .50". 
 
 For 24" beams s= .60", *= .50". 
 
 For 20" beam, 80 Ibs., s= .65", t= .60". 
 
 The slope of flange of all beams and channels is 16 J per cent. 
 90 _ 27' 44" =2" per foot. 
 Weight per foot=areaX3.4. 
 
 When ordering I beams, channels, or angles, the weight or 
 thickness should be given, but not both. 
 
 
 
296 MOMENTS OF INERTIA AND RESISTANCE. 
 PROPERTIES OF STANDARD STEEL I BEAMS. 
 
 
 
 I. 
 
 
 
 II. III. 
 
 IV. V. 
 
 VII. 
 
 Depth 
 of 
 beam. 
 
 W'ght 
 per 
 foot, 
 Ibs. 
 
 Area, 
 sq. in. 
 
 Thick- 
 ness of 
 web, 
 in. 
 
 Width 
 of 
 flange 
 in. 
 
 Moment of 
 inertia. 
 
 Radius of 
 gyration. 
 
 Sec- 
 tion 
 mod- 
 ulus. 
 Axis 
 AB. 
 R. 
 
 Axis 
 AB. 
 /. 
 
 Axis 
 CD. 
 /'. 
 
 Axis 
 AB. 
 r. 
 
 Axis 
 CD. 
 r'. 
 
 24 
 
 80.00 
 85.00 
 90.00 
 95.00 
 100.00 
 
 65.00 
 70.00 
 75.00 
 
 80.00 
 85.00 
 90.00 
 95.00 
 100.00 
 
 55.00 
 60.00 
 65.00 
 70.00 
 
 75.00 
 80.00 
 85.00 
 90.00 
 
 42.00 
 45.00 
 50.00 
 55.00 
 
 60.00 
 65.00 
 70.00 
 75.00 
 
 80.00 
 85.00 
 90.00 
 95.00 
 100.00 
 
 31.50 
 35.00 
 
 23.32 
 25.00 
 26.47 
 27.94 
 29.41 
 
 19.08 
 20.59 
 '22.06 
 
 23.73 
 25.00 
 26.47 
 27.94 
 29.41 
 
 15.93 
 17.65 
 19.12 
 20.59 
 
 22.05 
 23.53 
 25.00 
 26.46 
 
 12.48 
 13.24 
 14.71 
 16.18 
 
 17.67 
 19.12 
 20.59 
 22.06 
 
 23.81 
 25.00 
 26.47 
 27.94 
 29.41 
 
 9.26 
 10.29 
 
 0.500 
 0.570 
 0.631 
 0.692 
 0.754 
 
 0.500 
 0.575 
 0.649 
 
 0.600 
 0.663 
 0.737 
 0.810 
 0.884 
 
 0.460 
 0.555 
 0.637 
 0.719 
 
 0.71 
 0.79 
 0.74 
 0.82 
 
 0.410 
 0.460 
 0.558 
 0.656 
 
 0.590 
 0.686 
 0.784 
 0.882 
 
 0.810 
 0.889 
 0.987 
 1.085 
 1 . 184 
 
 0.350 
 0.436 
 
 7.000 
 7.070 
 7.131 
 7.192 
 7.254 
 
 6.250 
 6.325 
 6.399 
 
 7.000 
 7.063 
 7.137 
 7.210 
 7.284 
 
 6.000 
 6.095 
 6.177 
 6.259 
 
 6.58 
 6.66 
 7.00 
 7.08 
 
 5.500 
 5.550 
 5.648 
 5.746 
 
 6.000 
 6.096 
 6.194 
 6.292 
 
 6.400 
 6.479 
 6.577 
 6.675 
 6.774 
 
 5.000 
 5.086 
 
 2087.9 
 2i68.6 
 2239.1 
 2309.6 
 2380.3 
 
 1169.6 
 1219.9 
 1268.9 
 
 1466.5 
 1508.7 
 1557.8 
 1606.8 
 1655.8 
 
 795.6 
 841.8 
 881.5 
 921.3 
 
 1023.5 
 1063.4 
 1149.6 
 1188.0 
 
 441.7 
 455.8 
 483.4 
 511.0 
 
 609.0 
 636.0 
 663.6 
 691.2 
 
 795.5 
 817.8 
 845.4 
 872.9 
 900.5 
 
 215.8 
 228.3 
 
 42.86 
 44.35 
 45.70 
 47.10 
 48.56 
 
 27.86 
 29.04 
 30.25 
 
 45.81 
 47.25 
 48.98 
 50.78 
 52.65 
 
 21.19 
 22.38 
 23.47 
 24.62 
 
 31.67 
 33.12 
 44.18 
 46.03 
 
 14.62 
 15.09 
 16.04 
 17.06 
 
 25.96 
 27.42 
 29.00 
 30.68 
 
 41.76 
 43.57 
 45.91 
 48.37 
 50.98 
 
 9.50 
 10.07 
 
 9.46 
 9.31 
 9.20 
 9.09 
 9.00 
 
 7.83 
 7.70 
 7.58 
 
 7.86 
 7.77 
 7.67 
 7.58 
 7.50 
 
 7.07 
 6.91 
 6.79 
 6.69 
 
 6.81 
 6.72 
 6.78 
 6.70 
 
 5.95 
 
 5.87 
 5.73 
 5.62 
 
 5.87 
 5.77 
 5.68 
 5.60 
 
 5.78 
 5.72 
 5.65 
 5.59 
 5.53 
 
 4.83 
 4.71 
 
 1.36 
 1.33 
 1.31 
 1.30 
 1.28 
 
 1.21 
 1.19 
 1.17 
 
 1.39 
 1.37 
 1.36 
 1.35 
 1.34 
 
 1.15 
 1.13 
 1.11 
 1.09 
 
 1.20 
 1.19 
 1.33 
 1.32 
 
 1.08 
 
 1.07 : 
 
 1.04 
 1.02 
 
 1.21 
 
 1.20 
 1.19 
 1.18 
 
 1.32 
 1.32 
 1.32 
 1.32 
 1.31 
 
 1.01 
 0.99 
 
 174.0 
 180.7 
 186.6 
 192.5 
 198.4 
 
 117.0 
 122.0 
 126.9 
 
 146.7 
 150.9 
 155.8 
 160.7 
 165.6 
 
 88.4 
 93.5 
 97.9 
 102.4 
 
 113.7 
 118.2 
 127.7 
 132.0 
 
 58.9 
 60.8 
 64.5 
 68.1 
 
 81.2 
 84.8 
 88.5 
 92.2 
 
 106.1 
 109.0 
 112.7 
 116.4 
 120.1 
 
 36.0 
 38.0 
 
 30 
 
 30 
 
 18 
 
 ! 18 * 
 
 15 
 
 15 
 
 15 
 
 12 
 
 
 * Rolled only by Pencoyd and Passaic Mills. 
 
RADII OF GYRATION. 
 
 297 
 
 PROPERTIES OF STANDARD STEEL I BEAMS. 
 
 (Continued.)* 
 
 
 
 I. 
 
 
 
 II. III. 
 
 IV. V. 
 
 VII. 
 
 Depth 
 of 
 beam. 
 
 W'ght 
 per 
 foot. 
 Ibs. 
 
 Area, 
 sq. in. 
 
 Thick- 
 ness of 
 web, 
 in. 
 
 Width 
 of 
 flange, 
 in. 
 
 Moment of 
 inertia. 
 
 Radius of 
 gyration. 
 
 Sec- 
 tion 
 mod- 
 ulus, 
 Axis 
 AB. 
 R. 
 
 Axis 
 AB. 
 
 Axis 
 CD. 
 /'. 
 
 Axis 
 AB. 
 r. 
 
 Axis 
 CD. 
 r'. 
 
 13 
 
 40.00 
 45.00 
 50.00 
 55.00 
 
 25.00 
 30.00 
 35.00 
 40.00 
 
 21.00 
 25.00 
 30.00 
 35.00 
 
 18.00 
 20.50 
 23.00 
 25.50 
 
 15.00 
 17.50 
 20.00 
 
 12.25 
 14.75 
 17.25 
 
 9.75 
 12.25 
 14.75 
 
 7.50 
 8.50 
 9.50 
 10.50 
 
 5.50 
 6.50 
 7.50 
 
 11.84 
 13.24 
 14.71 
 16.18 
 
 7.37 
 8.82 
 10.29 
 11.76 
 
 6.31 
 7.35 
 
 8.82 
 10.29 
 
 5.33 
 6.03 
 6.76 
 7.50 
 
 4.42 
 5.15 
 
 5.88 
 
 3.61 
 4.34 
 5.07 
 
 2.87 
 3.60 
 4.34 
 
 2.21 
 2.50 
 2.79 
 3.09 
 
 1.63 
 1.91 
 2.21 
 
 0,460 
 0.576 
 0.699 
 0.822 
 
 0.310 
 0.455 
 0.602 
 0.749 
 
 0.290 
 0.406 
 0.569 
 0.732 
 
 0.270 
 0.357 
 0.449 
 0.541 
 
 0.250 
 0.353 
 0.458 
 
 0.230 
 0.352 
 0.475 
 
 0.210 
 0.357 
 0.504 
 
 0.190 
 0.263 
 0.337 
 0.410 
 
 0.170 
 0.263 
 0.361 
 
 5.250 
 5.366 
 5.489 
 5.612 
 
 4.660 
 4.805 
 4.952 
 5.099 
 
 4.330 
 4.446 
 4.609 
 
 4.772 
 
 4.000 
 4.087 
 4.179 
 4.271 
 
 3.660 
 3.763 
 3.868 
 
 3.330 
 3.452 
 3.575 
 
 3.000 
 3.147 
 3.294 
 
 2.660 
 2.733 
 
 2.807 
 2.880 
 
 2.330 
 2.423 
 2.521 
 
 268.9 
 285.7 
 303.3 
 321.0 
 
 122.1 
 134.2 
 146.4 
 158.7 
 
 84.9 
 91.9 
 101.9 
 111.8 
 
 56.9 
 60.6 
 64.5 
 68.4 
 
 36.2 
 39.2 
 42.2 
 
 21.8 
 24.0 
 26.2 
 
 12.1 
 13.6 
 15.2 
 
 6.0 
 6.4 
 6.7 
 7.1 
 
 2.5 
 
 2.7 
 2.9 
 
 13.81 
 14.89 
 16.12 
 17.46 
 
 6.89 
 7.65 
 8.52 
 9.50 
 
 5.16 
 5.65 
 6.42 
 7.31 
 
 3.78 
 4.07 
 4.39 
 4.75 
 
 2.67 
 2.94 
 3.24 
 
 1.85 
 2.09 
 2.36 
 
 1.23 
 1.45 
 1.70 
 
 0.77 
 0.85 
 0.93 
 1.01 
 
 0.46 
 0.53 
 0.60 
 
 4.77 
 4.65 
 4.54 
 4.45 
 
 4.07 
 3.90 
 3.77 
 3.67 
 
 3.67 
 3.54 
 3.40 
 3.29 
 
 3.27 
 3.17 
 3.09 
 3.02 
 
 2.86 
 2.76 
 2.68 
 
 2.46 
 2.35 
 2.27 
 
 2.05 
 1.94 
 1.87 
 
 1.64 
 1.59 
 1.55 
 1.52 
 
 1.23 
 1.19 
 1.15 
 
 1.08 
 1.06 
 1.05 
 1.04 
 
 0.97 
 0.93 
 0.91 
 0.90 
 
 0.90 
 0.88 
 0.85 
 0.84 
 
 0.84 
 0.82 
 0.81 
 0.80 
 
 0.78 
 0.76 
 0.74 
 
 0.72 
 0.69 
 0.68 
 
 0.65 
 0.63 
 0.63 
 
 0.59 
 
 0.58 
 0.58 
 0.57 
 
 0.53 
 0.52 
 0.52 
 
 44.8 
 47.6 
 50.6 
 53.5 
 
 24.4 
 26.8 
 29.3 
 31.7 
 
 18.9 
 20.4 
 22.6 
 24.8 
 
 14.2 
 15.1 
 16.1 
 17.1 
 
 10.4 
 11.2 
 12.1 
 
 7.3 
 
 8.0 
 8.7 
 
 4.8 
 5.4 
 6.1 
 
 3.0 
 3.2 
 3.4 
 3.6 
 
 1.7 
 1.8 
 1.9 
 
 10 
 
 9 
 
 8 
 
 7 
 
 6 
 
 5 
 
 4 
 
 3 
 
298 MOMENTS OF INERTIA AND RESISTANCE. 
 
 s. 
 
 OQ 
 
 <J < + 
 
 Q 
 
 g r-TI 
 
 
 
 cj 
 
 <N rc M co cc co 
 OOt^-^iMO O5 
 
 CO T-< rH CO'<N 
 
 CO(NO5t>CO 
 
 <M-rf X-^OS 
 
 O 1C <M rH O 
 
 O5XO1CC 
 r-^OilO^ 
 
 
 
 N <N C^ (M C^J rH 
 
 OOC5C5O5 
 
 O5XXXX 
 
 oot^t> 
 
 
 
 
 
 
 
 
 -o 
 
 O CO 1C C<J r-i CO 
 O -^ >-i O5 t^ O 
 
 O5 O5 OS 00 00 00 
 
 I>COI>rHO 
 
 CDCOOXO 
 t^ 1> I> CO O 
 
 CO t^t^OI> 
 
 CCO5CO-*rH 
 
 COO^OtOO 
 
 COO5<M^ 
 CO^ rHOC 
 
 iOOiOr^' 
 
 MJ 
 
 "Sin J4 
 
 >> 
 
 2 O-.Q 
 
 G u, >-"KJ 
 88 +* c3 fl 1 ^ 
 
 O5 X X 00 O M 
 !> t^ t^ I s - X X 
 
 T^Xb-"* 1 (N 
 Ot^t>-di(M 
 
 O5OiO'-iO 
 
 co o cq to a 
 
 t^ooic 
 
 C5XrH 
 iCOCD 
 
 
 +-> C 2 S 
 
 gg-g 
 
 oooooo 
 
 ooooo 
 
 OOOOO 
 
 oooo 
 
 
 J|9 . 
 
 t>^COOI>'!t" 
 
 TH00505X 
 
 T^lXNCOrH 
 
 iOCOOt^ 
 
 > 
 
 Ill 03 
 
 ^ 
 
 rH (M CO O CO t^ 
 ^TtHT^lOlCHO 
 
 rH"tf COCifN 
 
 <N(M(N<MCO 
 
 cooxoco 
 
 i-MrlTH(M(M 
 
 OrHCOlO 
 
 > 
 
 d Q 
 .2 8 . 
 1 .S^ 
 
 (NXCO(NCOX 
 C5O5XXXOO 
 
 iOiOXl>i-H 
 
 oxcoio^o 
 
 Xl>t>I>l> 
 
 XCOO(M<N 
 
 rH Oi X t^- b* 
 
 i> CO CO CO CO 
 
 TJHIOCOI> 
 
 1>CO-*CO 
 CO CO CO CO 
 
 
 & $ 
 
 
 
 
 
 > 
 
 "0 pQ 
 I ^ 
 
 (NXCOINCOCD 
 
 CO IO Tt< CO <M rH 
 
 rHcoxi>a> 
 
 CO-*<NrHO 
 
 t^cO<M<NiO 
 
 xccto-^co 
 
 OSOrHO 
 -*^t(MrH 
 
 
 ^ .3 *" 
 
 4 
 
 10*0*0^0^010 
 
 ^^^^^ 
 
 CO CO CO CO CO 
 
 CO CO CO CO 
 
 i-4 
 
 .3 Q 
 B O v . 
 
 coxosqscqos 
 
 <M<tfCO&<MT-i 
 
 -HCOrHOCO 
 
 OO(NO5CO 
 
 O iO O O5 CO 
 
 cox-^oco 
 
 1>LOOX 
 
 t^os^os 
 
 *"^ 
 
 .s 1" 
 
 o 2 
 
 XXOiO<-H<N 
 
 co-^ioioco 
 
 (N<NCOCO^ 
 
 rHrH(MCQ 
 
 
 s 
 
 CO O O iH t> C<l 
 
 THOI^COO 
 
 OI>O<NIO 
 
 coosxt^ 
 
 rH 
 1 1 
 
 2 ^ . 
 I .S^ 
 
 *H X 
 
 S ^ 
 
 (N O I> O <M O 
 
 T-KM^t^OCO 
 CO CO CO CO -*^ 
 
 X"*rH Ol>. 
 
 (N^CO1>O5 
 iHrHr-lTHr-1 
 
 COXrH COO 
 COI>O5OrH 
 rHrH 
 
 1>OOO 
 T^ iOCOI> 
 
 
 5 
 
 '^'0 fl 
 
 tf)Tt<cqox 
 <M (N <N <N rH 
 Tt<iOOt^X 
 
 OOCOCOX 
 
 T^lOJ>O5rH 
 O5OrH(Mr}< 
 
 8 C^ OS CO CO 
 ^xcox 
 
 COt^XOrH 
 
 OXWiO 
 
 COX>OrH 
 
 r^^cOX 
 
 
 
 CO CO CO CO CO CO 
 
 W CO CO CO CO 
 
 C<I(N(MCOCO 
 
 C<J<N(M<N 
 
 
 Hi 
 
 8CO^(NOX 
 <N(M<M<M^n 
 
 T^T^lOCOt^X 
 
 XOir-ICOlO 
 
 <NCOiOcOl> 
 
 s^^?5 
 
 C^COiOCOX 
 
 OX(NO 
 
 COXtOrH 
 
 (NfN-^CO 
 
 
 |P 
 
 oooooo 
 
 OOOOO 
 
 OOOOO 
 
 OOOO 
 
 
 e 
 
 OO3CO 1 ^'-<X 
 
 O5 (N 1>(M t>- i-H 
 
 COiO(NOO 
 OCOX(Nl> 
 
 CO 00 1C (M OS 
 ^XCOXfN 
 
 OSr-lXlO 
 
 x-tf xco 
 
 rH 
 
 
 
 OSOrHCO^CO 
 
 OI>XOrH 
 
 TjHlOt^XO 
 
 COTjHOt>. 
 
 
 ^ 
 
 
 
 
 
 
 a 
 
 Ife-e 
 
 888838 
 
 OOOOO 
 lOOOOO 
 
 88888 
 
 oooo 
 
 (NOOO 
 
 
 sas 
 
 t ^ 
 
 COOOOOO 
 
 co co -tf * 10 o 
 
 OiCOiOO 
 (M (N CO CO r}< 
 
 XOOOO 5 
 
 rH(M<NCOCO 
 
 coico^o 
 
 rHrH(N<N 
 
 
 ^d ji . 
 
 f^l 
 
 P 
 
 W5 
 H 
 
 W 
 M 
 
 o 
 
 iH 
 
 OS 
 
RADII OF GYRATION. 
 
 299 
 
 ^ CO O CO I> l> O (N O C5 C5 t> rfi CM OJ GO CO *O O G5 00 <N T-I O 
 
 H 
 
 t>i>cococo COCDCOOIO loioioio ^^^ -<tcocQ cococo 
 
 ooooo* oodo'o do'od odd dod odd 
 Q ~ 
 
 a 2^PQ 
 
 OC500CO*O COOOOiO O 1 ^^ Oii-lCO ?HC 
 
 .5 O O5 O CO O CO >O GO Tt< O W rH O5 O5 OOCOCO 
 
 i-dHi-HC^W OiHr-lTHrH O O iH rH OOO OOO OOO 
 
 S W 
 
 O <t^ COOO5GOOO 
 
 S CQ*^ <Mcoo5coi> i-HTjHr>.oco coioi>o> b-oop 
 fl COCOCO-^T^ 
 
 ^ 
 
 Ol^C5O<N OGOCOGOCO 32^ ^^I 00O<N ^SS 
 
 _ r do'do'd o'dooo o'ooo ooo ooo oob 
 fi 
 
 OOCDCOOOO COOOO>O O5COCO lOCOr-l i-iT^t^. 
 
 C<| CO Tfl >O 1O W CO CO ^ tH C^ CO t IrHC^ fHtHiH 
 
 8S8SS 8S8S S8S S88 888 
 
 ^ ^"^"^ 5 "" 
 
 J 
 
 w 
 
 13 
 
 w 
 
 fe 
 
 O 
 
 S 
 
 
 e 
 
 
 o,*o ^"^3 
 
 O r3 d 
 
 Q 
 
300 MOMENTS OF INERTIA AND RESISTANCE. 
 
 DIMENSIONS AND PROPERTIES OF 
 
 GROOVED STEEL, OR SMALL 
 
 CHANNELS. 
 
 No. 
 of 
 Sec. 
 
 
 d 
 
 b 
 
 i 
 
 * 
 
 a 
 
 W'ght 
 per 
 foot. 
 
 Area. 
 
 Mo- 
 ment 
 of in- 
 ertia. 1 
 
 Sec- 
 tion 
 mod- 
 ulus. 1 
 
 Coeffi- 
 cient 
 of 
 str'th. 2 
 
 
 i 
 
 ns. 
 
 ins. 
 
 ins. 
 
 ins. 
 
 ins. 
 
 Ibs. 
 
 sq. ins. 
 
 
 
 Ibs. 
 
 1 
 
 * 
 
 ! 2*4 
 
 1.37 
 
 .25 
 
 .25 
 
 .25 
 
 3.80 
 
 1.12 
 
 0.80 
 
 0.71 
 
 7570 
 
 2 
 
 H 
 
 ! 2 
 
 1.09 
 
 .22 
 
 .31 
 
 .18 
 
 2.90 
 
 0.87 
 
 .48 
 
 .48 
 
 5120 
 
 3 
 
 =1 
 
 C 2 
 
 1.18 
 
 .31 
 
 
 
 3.60 
 
 1.06 
 
 .54 
 
 .54 
 
 5760 
 
 4 
 
 1 
 
 
 1.25 
 
 .25 
 
 .31 
 
 .25 
 
 3.60 
 
 1.062 
 
 .585 
 
 .585 
 
 6240 
 
 5 
 
 : 
 
 2 
 
 1.00 
 
 8 /16 
 
 .25 
 
 .22 
 
 2.6 
 
 0.756 
 
 .423 
 
 .423 
 
 4512 
 
 6 
 
 1 
 
 
 % 
 
 .25 
 
 .19 
 
 y& 
 
 2.0 
 
 0.619 
 
 .2665 
 
 .266 
 
 2836 
 
 7 
 
 H 
 
 <1% 
 
 0.59 
 
 .09 
 
 .25 
 
 .09 
 
 1.13 
 
 0.33 
 
 .15 
 
 .17 
 
 1815 
 
 8 
 
 1 
 
 l/^ 
 
 0.75 
 
 ^ 
 
 i^ 
 
 i^ 
 
 1.32 
 
 0.344 
 
 .1083 
 
 .144 
 
 1536 
 
 9 
 
 : 
 
 1^ 
 
 % 
 
 .19 
 
 .2 
 
 .14 
 
 1.46 
 
 0.433 
 
 .1194 
 
 .159 
 
 1736 
 
 10 
 
 : 
 
 1/4 
 
 0.5 
 
 ^ 
 
 %6 
 
 /^ 
 
 0.94 
 
 0.273 
 
 .0557 
 
 .089 
 
 950 
 
 11 
 
 : 
 
 -i/^ 
 
 0.56 
 
 .19 
 
 .19 
 
 i2 
 
 1.12 
 
 0.330 
 
 .0500 
 
 .088 
 
 939 
 
 12 
 
 1 
 
 1^ 
 
 % 
 
 ^ 
 
 & 
 
 j| 
 
 1.00 
 
 0.266 
 
 .0462 
 
 .082 
 
 874 
 
 13 
 
 
 l 
 
 0.5 
 
 H 
 
 %6 
 
 ^ 
 
 0.83 
 
 0.242 
 
 .0315 
 
 .063 
 
 672 
 
 14 
 
 
 :1 
 
 0.39 
 
 ^6 
 
 %6 
 
 /^ 
 
 0.68 
 
 0.208 
 
 .0253 
 
 .050 
 
 532 
 
 15 
 
 
 /f 
 
 %6 
 
 12 
 
 .16 
 
 .11 
 
 0.67 
 
 0.183 
 
 .0185 
 
 .042 
 
 448 
 
 16 
 
 
 % 
 
 0.42 
 
 . 11 
 
 
 ^ 
 
 0.69 
 
 0.193 
 
 .0189 
 
 .043 
 
 458 
 
 17 
 
 
 * 
 
 % 
 
 K 
 
 .16 6 
 
 .09 
 
 0.53 
 
 0.156 
 
 .0095 
 
 .025 
 
 266 
 
 1 Axis AB. 
 
 2 Computed for fibre stress of 16,000 Ibs. per square inch. 
 * Rolled by the Pencoyd Iron Works. 
 
 f *' " '* Illinois Steel Company. 
 % - - " Jones & Laughlins, Ltd. 
 
 DIMENSIONS OP CAR TRUCK CHANNELS. 
 
 (Rolled by Carnegie Steel Co. and Jones & Laughlins, Ltd.) 
 
 d 
 
 b 
 
 I 
 
 e 
 
 a 
 
 Weight. 
 
 Area. 
 
 13 
 
 4 
 
 0.375 
 
 0.88 
 
 0.34 
 
 32 
 
 9.41 
 
 12 
 
 2.64 
 
 0.31 
 
 0.75 
 
 0.34 
 
 21.33 
 
 6.27 
 
 ANGLES. 
 
 The following table has been compiled to show all the various 
 sizes of angles that are rolled, and also by what companies. 
 The abbreviations indicate the companies that roll that particu- 
 lar size. The word all shows that the size is rolled by all of the 
 five companies included in the list. The abbreviations refer 
 
RADII OF GYRATION. 
 
 301 
 
 to the following companies: Cam., Cambria Iron Co.; Car., 
 The Carnegie Steel Co.; J. & L., Jones & Laughlinsj Pas., 
 Passaic Rolling Mill Co. ; Pen., Pencoyd Iron Works. 
 
 ANGLES WITH UNEQUAL LEGS. 
 
 ANGLES WITH EQUAL LEGS. 
 
 Size. 
 
 Size. 
 
 8 X6 Pen. 
 
 8 X8 Car., Pen. 
 
 7 X3J Car., Pen. 
 
 6 X6 All. 
 
 6JX4 Pen. 
 
 5 X5 All. 
 
 6 X4 All. 
 
 4iX4J Cam. 
 
 6 X3J Cam., Car., J. & L., 
 
 4 X4 All. 
 
 Pen. 
 
 3JX3i All. 
 
 5fX5 Cam. 
 
 3iX3i J. &L. 
 
 5JX3J Pen. 
 
 3 X3 All. 
 
 5X4 Cam., Car., J. & L., 
 
 2fX2f Cam., Car., J. & L., 
 
 Pen. 
 
 Pen. 
 
 5 X3J All. 
 
 2JX2 All. 
 
 5 X3 All. 
 
 2JX2J All. 
 
 4J X 3 Cam., Car., Pas., Pen. 
 
 2 X2 All. 
 
 4 X3i All. 
 
 If Xlf All. 
 
 4 X3 All. 
 
 IJXli All. 
 
 3|X2| J. &L. 
 
 liXli All. 
 
 3iX3 All. 
 
 1 XI All. 
 
 3JX2J All. 
 
 f X J Car.-, Pas. 
 
 3JX2 Pen. 
 
 |X J Cam., Car., J. & L., 
 
 3JX2 Car.,J. &L. 
 
 Pas. 
 
 3 X2J All. 
 
 
 3 X2 All. 
 
 
 2iX2 All. 
 
 
 2JX1} Cam. 
 
 
 2^X1^ Cam. 
 
 
 2JXli Cam. 
 
 
 2JX1J Car., Pas., Pen. 
 
 
 2 Xlf Pas. 
 
 
 2 XlJ Cam., Pen. 
 
 
 2 Xlf Cam., Car. 
 
 
 2 Xli Pen. 
 
 
 IfXli Pas. 
 
 
 If XI Car. 
 
 
 1 X { J. & I>. 
 
 
I I i: I I \ \ .1. i;i 1.1 \ < i 
 
 l 
 
 
 
 
 Hi 
 
 ,'.':'; i' ."'v.;' 1 ..^ .-.!..; :,:,?; ';,;: ; 
 
 
 t *"-/"" /'" - -, 
 
 fkMS0RN ft* 
 
 ooooodbcod MO 
 
 fiflNMfiff^ 
 
 , 
 
 ssa* 
 
 oiw 
 
 N oooooe<o ee 
 
 N-;M 
 ooooooqpoo' ^^ 
 
 as 
 
 4N fJM 
 
 ',, ,: .:.':.-,:'":-. 
 9B55 ' 
 
 ,t , ; 
 
 - f i. 
 
 ** 
 
 sa 
 
 
 
 n 
 
 :J.:). >. 
 
 1 
 
 In, 
 
 XX 
 
i: \i>li oh' <;> i: \ TloN. 
 
 
 i* * ei O ffl * ft * !* iff f fl Q '^ "* ft *<',> 'P 3* -PW LTJ r-iew"<tt AN 
 HHHSGJ99O0350* JJlSJNR HHJHOOO t>O 0109 U<S(OlA4 Ks 
 
 ' ittWWuiWNHHH NNNfi' I i i i > i i HH iHM p^MMt-i fNiH 
 
 -** <( M03D*ab|*a' JSftl2SflSjfl5fi5ftCIC!P* 20! bl r**^fclfi *to 
 ^^^^ooojsoijiei o w oi oj 58 / w r-. HJW ojw c-<-joo eo 
 
 4M^M^^Hy-iddd i-<dddddo'dddo' *HH do VN^MMH IHH 
 
 ^HHHH 
 
 ;," 
 
 flM 
 
 i*p'l>fl>K5-f tMf* ")w' "tci 
 
 MgBKR!: 83 S5 
 
 eibciddclddcidd eboeiddddddd MIM die 
 
 1215- 
 
 o'dddd do 
 
 95j sis sasai st> 
 
 oddo'ddcdddd HH f*H HHHHH do 
 
 888B8888888 
 
 23 
 
 0*00 !>")<* 
 
 S$ Sj!2 ^8S*a US 
 
 gid us saas* aa 
 
 t;R asaan tsa 
 
 cin oko w H oo 1*1^1 
 
 MO l^' f *-J I t* >H Ij'- 1 
 frjM HH ei^HHH *i<7l 
 
 :'';;, 1 '; ,/,,/. ./,M'./,CI./. '/.' f J 
 
 . . I . nf', I ", "., i .. 
 
 X 
 <o 
 
 * 
 
 X 
 
 
 
 1 
 
304 MOMENTS OF INERTIA AND RESISTANCE. 
 
 \ 
 
 ^ 
 
 y 
 
 \\ 
 
 I 
 
 i 
 
 1 1 
 
 K I 
 
 I 
 
 PH 
 3 
 
 M 
 
 411 
 
 ||1 
 
 S8gS88S88S8SfcSSg8 
 
 
 |s|i 
 
 ?! 
 
 
 . 
 
 llfl 
 
 ||~: 
 
 O O5 Oi O5 Oi 00 00 00 00 00 00 00 1>- 1> 1> t> CC 
 
 1 1 
 
 IK 
 
 ^i 
 
 tHOOOOOOO OOOOOOOOO 
 
 K 
 
 1 
 
 -2Q 
 
 88888888 S838SS88S 
 
 ^ 
 
 TJ 
 O 
 
 So* 
 
 < u 
 
 
 A 
 
 1 
 
 R9 
 
 SSSS85iW32SSa3g3$ 
 
 > 
 
 <g 
 
 <<< 
 
 T^COCOCCC^C^KNTH ^'^ l COCCC 1 OC<lC'4C ; li-H 
 
 . 
 
 
 a-g; 
 
 MMWW ^MW 
 
 > 
 
 i 
 
 SP 
 
 OOOOOOOO OOOOOOOOO 
 
 . 
 
 1. 
 
 ro 
 
 O5O5OJOOOOO 00 00 00 00 X 00 OC 00 OC 
 
 
 O 
 
 <V 
 
 
 ^ 
 
 1 
 
 89 
 
 SSSSSSSSSSSfeSSSsiS 
 
 
 
 ^ 
 
 
 ,_ 
 
 .2 
 
 *RQ 
 
 88853888 fc38888l8SR 
 
 *"^ 
 
 r 1 
 
 <jo 
 
 O O * TJH T}< CO CO <N CO CC CO CO <M Cq C<J <N rH 
 
 
 1 
 
 2 * 
 
 S5i28g28^g 
 
 K 
 
 a 
 
 ^^ 
 
 COW<Mr-iOiOOl>CO CCCC(NrHOOSOOl>cO 
 
 
 O 
 
 
 
 
 *o fl 
 
 . 
 
 
 ^ 
 
 gl 
 
 .3 
 
 xccoj^oSo^o oo^oco2^cooo 
 
 
 g 
 
 
 
 u^^cocoo, to^^cocco^ 
 
 
 si 
 
 S 
 
 00 CO 00 C<1 CO O ^ l> O5 *O iH t N 00 CO 00 C^ 
 
 
 
 
 
 oooo>ocowooo osxt^io^c^r-iaioo 
 
 
 ^a 
 
 a 
 
 
 
 111 
 
 1! 
 
 cococococococococo 
 
 
 gj 
 
 53j 
 
 i 
 
 I 
 
 CO CO 
 
 X X 
 
RADII OF GYRATION. 
 
 305 
 
 3 CO O 00 CO TH TH O !> CO TH d OS l> *O CO TH 00 TH <M Ci 1> O CO O 00 CO I 
 COCOCD*O*O'OOTH''t l CO CO CO <N <N C^ C-1 CM iH H/iTjicOCOCOCOCOOlC^ ( 
 
 .i O5 00 00 00 OO l> i> l> t THOOOOOCJOiOJ C5CSCCOOOOOOOO>I> 00 
 
 ddddddddd iHiHi-HfHtHfH*ddd ddddddddd do odo'd 
 
 -O*O M CS1 C^ TH iH iH iH TH TH tHTHTHTHrHTHC 
 
 (NOOrHOJTt<t>OCOrH <NiOCOOtf5CO<MOcO I^XCiOOCiOOCOCO ( 
 
 COCOTHOOCOCOTHOOO OH>iOCOtHO5l>O(N OOcO^COOOOcO^CM <NC<1 C<IOO5J> 
 
 qiHiHiHTH (NC<J(N<M(NtHTHTHTH C^r-l (NC^iHTH 
 
 (>l>l>t>l co CO CO CO CO CO CO CO CO *O CO CC CO CO CO 
 
 ooooooooo oooodo'do'd ddddddddd do o'do'd 
 
 000000000000000000 OOOOOOOOO 000000000000000000 COl> 00000000 
 
 do'dddo'o'o'd iHTHfHTHrHTH^IrHTH o" o' o* o* o* o* o* do do o'ddd 
 
 CO5OiOTH<MCOH^T^ O5 O TH (N CO CO TH 1C CO THfNCqCOTHiOiOCOt*. OO THTHU5CO 
 OCOCOTHThTHThlTHTJH THC<J^1<M(N(NC<IC^C<1 O1C<IC^<MC^C<lC<IO4C^ iH iH OOOO 
 
 ^OO5005THiOOOCO OiOOcO(Nl>O5OO:a I^OOOO^cO<NOO<NiO IOOO COCOCO 
 tCOCCCMCXICMC^tHTH lOlCTHTHTHCOCOOKN COCOCOC^C<J<NC<|iHrH (NiH COCO(NC<I 
 
 COCOON tQTfOiOOS I>(N CO l> CO CQ CO 00 CO rH CO O5 CO O O d CO 00 I>D ( 
 COt>-THTHl>O(N>OcO 1>COOOCOOOCOI>THIO COO5T)HO>OOICO5CO T^TH ( 
 
 t>'ddo'oOT}Icoco' toco 
 
 iO lO "sf TH CO CO CO (N C^ lOO TH ^ CO CO CO (N d 1C TH ^ CO CO CO C^l d W ' 
 
 oo 
 
 (M O5 CO CO O5 iO TH t- U3(NO5cOCOO5iOTHl> tHOOOcOCOTHOOCTH COI> 1>.I>COO 
 
 .&p 
 
 & 
 
 CO 
 
 X 
 
 X 
 
 CO 
 
 X 
 
306 MOMENTS OP INERTIA AND RESISTANCE. 
 
 V 
 
 ? 
 
 oJ 
 
 W 
 
 I 
 
 $ 
 
 8 
 
 a 
 
 ^ 
 
 g 
 
 < 
 
 w 
 
 fr 
 
 O 
 
 i 
 
 PM 
 
 I 
 
 PH 
 
 M 
 
 ill 
 
 Jsi 
 
 ICCOOOCCO 
 
 rH rH rH C O 
 
 l> 1C CO O GC CO rt< rH 
 W (N (N (M rH rH H TH 
 
 8S 
 
 
 ^ 
 
 !|9 
 
 o^ g 
 
 fH4H ^ 
 
 
 
 
 K> 
 
 3jg 
 
 fi <n ^ 
 ftggo 
 
 ^S- 
 
 22 
 
 _o rt M 
 
 O OC' *O CO rH 
 
 ooooeocoo 
 
 t^iOCOOOOcO^rH 
 
 ss 
 
 U 
 
 &l* 
 ft 15 
 
 H'oqi! 
 
 ooooo 
 
 oooooooo 
 
 OO 
 
 P 1 
 
 ro 
 3 
 3 
 
 so 
 
 rH O 00 O (M 
 
 igsgsg5 
 
 THrH 
 
 * 
 
 - 
 
 s ^ 
 
 ^ 
 
 rHrHOOO 
 
 oooooooo 
 
 00 
 
 ^ 
 
 (3 
 
 .2 
 
 -g- 
 
 5^S2g 
 
 lOrHCOrHCOOSCOUt 
 
 GO I> tO Tt 1 (M O Ol t- 
 
 8S 
 
 
 1 
 
 
 
 rH rH TH rH rH rH 
 
 THO 
 
 g 
 
 
 ij 
 
 CO CO CO CO CO 
 
 ssssssss 
 
 00 OC 
 
 
 j 
 
 <w 
 
 OOOOO 
 
 cooooooo 
 
 OO 
 
 
 i 
 
 ^ 
 
 ro 
 
 r^oeooo 
 
 OOOOXO5Oi 
 
 gOOrHJCO^ 
 
 1-.CO 
 IO O 
 
 
 
 $5 
 
 ooooo 
 
 oooooooo 
 
 00 
 
 
 
 I 
 
 is 
 
 ooooS 
 
 OOOOOrH^rH* 
 
 coco 
 
 
 
 ^^ 
 
 
 
 
 M 
 
 a 
 1 
 
 Id 
 
 iowo8 
 
 <MrHO5COCOO5^00 
 
 S3 
 
 
 ? 
 
 <JO 
 
 
 
 00 
 
 I-H 
 
 M^ 
 
 1 
 
 |d 
 
 SS2KS 
 
 CO 1C 1C Tf rH CO Oi O 
 
 rH 00 iO (N CT) iO rH 00 
 
 iO CO 
 10CO 
 
 
 
 
 <:^ 
 
 CO CO CO (M (N 
 
 ^COCOCOW^^rH 
 
 C^rH 
 
 I-H 
 
 1| 
 
 02 
 
 COOCOCOO5 
 
 O CO CO *O CO rH 00 TH 
 
 O5rH 
 
 OCO 
 
 
 4 
 
 i 1 
 
 co co <N <n rH 
 
 COCOCOMW^THrH 
 
 THrH 
 
 
 12 -S 
 11 
 
 5 
 
 ^NrHOOCO 
 
 ^^^^eoN^o* 
 
 CO iO 
 
 
 .ss 
 
 fi 
 
 1 
 
 rHOOt-CO 
 
 Sr^S 0500 ^ ^ 
 
 CO-* 
 
 - 
 
 jj^ 
 
 y 
 
 CO CO CO 
 
 CO CO CO CO 
 
 
 
 if 
 
 
 pi rH 1> CO IQ 
 
 TH IO O5 rH I> CO 1C rH 
 
 CO T-I 
 
 
 i 
 
 a 
 
 ! 
 
 CO 
 
 X 
 
 1 
 
 i 
 
 X 
 
 I 
 
 XX 
 
RADII OF GYRATION. 
 
 307 
 
 K 
 
 rH O iO O (N O OC CO CO rH 
 (Mi i rH O O O O O O O 
 
 SSSS8 
 
 OO^OCOrHOCO 
 
 X 00 00 00 l> b- 
 
 COtH 
 
 oooo 
 
 ooo 
 
 00 
 
 OOOCt^b^ 
 
 
 HrHOOOO 
 
 M^^H^Q 
 
 000000 
 
 oo 
 
 oo 
 
 00 
 
 oooo 
 
 d 
 
 Ob~<NOO b-OCOrHOOcO OOCO-^MOS COpOOcO^HrH 
 
 10 CO 
 
 ?3S 
 
 z% 
 
 5 gs 
 
 oooo oooooo ooooo 
 
 oooooo 
 
 00 
 
 00 
 
 00 
 
 ooco 
 
 1 
 
 CO 00 b- CO <MTHcooCOO l><Nb-CNJiO 
 
 COr-< COrHIC O 
 
 rh rh CO CO <N (N 
 
 oio 
 
 (M TH 
 
 o = 
 
 2$ 
 
 COO-^TH 
 
 oooo oooooo ooooo 
 
 OOOOOO 
 
 00 
 
 CO 
 
 CO 
 
 coco 
 
 P 
 
 CO' TH O CO 
 
 H OO OOco'iO 
 
 8SSSS 
 
 b- CO 10 Tt< CO <N 
 
 CO 05 
 
 M oo 
 
 gs 
 
 1C rt CO CM 
 
 THrHOO 
 
 HrHOOOO 
 
 iHOCOO 
 
 oooooo 
 
 CO 
 
 CO 
 
 CO 
 
 oooo 
 
 P 
 
 333:3 
 
 3SSSSS 
 
 ^55? 
 
 C<> (M (M (M (M CO 
 
 %% 
 
 COCO <N<N 
 CO CO 
 
 O 
 
 oooo oooooo 
 
 ooooo 
 
 OOOOOO 
 
 00 
 
 > 
 
 n ^ s * ss g^K 
 
 iCiO>OiOiOCD 
 
 o g 
 
 OC1 
 
 %% 
 
 05^5 
 
 OOOO OOOOOO 
 
 ooooo 
 
 OOOOOO 
 
 00 
 
 CO 
 
 00 
 
 coco 
 
 5 
 
 OrH<M** 
 
 oooo 
 
 SSS8SS 
 
 gs 
 
 1C CO b- OOOOO 
 
 1>00 
 
 ooo 
 t> oo 
 
 Z 
 
 K8KS 
 
 THrHiHrH OOOOOO 
 
 ooooo 
 
 ooooco 
 
 00 
 
 00 
 
 oo 
 
 oooo 
 
 HH 
 
 joggo 
 
 38SS8S 
 
 CO CO OTt< CO 
 
 2%^% 
 
 oo 
 
 01 <N 
 
 fltl 
 
 COb- 
 
 rHO 
 
 SSS2 
 
 oooo 
 
 rHTHrHrHCO 
 
 ooooo 
 
 oooooo 
 
 00 
 
 oo 
 
 00 
 
 oooo 
 
 f-H 
 
 SS!S!S 
 
 %$$$^ 
 
 8SS88 
 
 rf CO rH O O TH 
 
 (NO (NCO 
 CD-* 00-* 
 
 {:? 
 
 00 COrf CO 
 
 
 
 
 
 00 
 
 00 
 
 CO 
 
 oooo 
 
 Cfl 
 
 CO CO 00 (M 
 
 ssaass 
 
 S;8^2 
 
 gOO>OTHCOrH 
 b-iOCOOOO 
 
 8 CO 
 b- 
 
 CDrH 
 
 COb- 
 
 s 
 
 COO! 00 CD 
 
 
 
 
 
 ' 
 
 OSOOcOTt* 
 
 225225 
 
 S-ooosod 
 
 OOTHCOOb-00 
 
 ** 
 
 5^. 
 
 CO(M 
 
 IOCOOCO 
 IO ^t 1 CO CS 
 
 
 CO 
 
 ^THCOTH 
 
 CO CD CD 
 
 rH (M rH 00 rH H^ 
 O5rHt>COlOrH 
 
 CO CD 
 
 THl>COlOTH 
 
 CD CO CO 
 
 (M^QO^T^rH 
 
 THb-coiOTHco 
 
 CO 
 
 T-lCO 
 
 oo2 
 
 coco 
 
 CD 
 OOrH 
 
 coco 
 
 co 
 
 THCOrHCO 
 
 
 (M 
 
 X 
 
 CO 
 
 X 
 
 CO 
 
 (M 
 
 X 
 
 CO 
 
 X 
 
 ] 2)4X1% 
 
 X 
 
 X 
 
 ;? 
 
 X 
 
 I 
 
308 MOMENTS OF INERTIA AND RESISTANCE. 
 
 
 AM 
 
 "O "5 cj 
 
 ^|^3 
 
 lift 
 
 100 
 
 COCO 
 
 O5rJ< 
 
 COCO 
 
 O^CO 
 coco 
 
 00 
 00 CO 
 
 i-HCN 
 * 
 
 co^ 
 ^* 
 
 t^cM 
 
 ^co 
 
 x" 
 
 - S- -J 
 ^0 v 
 
 3g^ M 
 o s >, CJ 
 
 o-af 
 
 HK-l ^ 
 o^ 
 
 OO 
 
 00 
 
 OO 
 
 OO 
 
 00 
 
 00 
 
 00 
 
 jj 
 
 1^ 
 S20 
 
 X %^ 
 
 8|j 
 
 (Nt>. 
 
 iOT}< 
 
 $% 
 
 8 
 
 CMrH 
 
 "tfCO 
 
 ooo 
 
 COOJ 
 
 OCO 
 <N<N 
 
 &Z 
 
 > ( 
 
 &l* 
 PnJ 
 
 'S^fl 
 
 r^ 8 
 
 H o^ 
 
 OO 
 
 00 
 
 00 
 
 00 
 
 00 
 
 00 
 
 OO 
 
 HH 
 
 
 
 .2X 
 
 SR 
 
 COiO 
 
 (NrH 
 
 l>l-l 
 
 iHrH 
 
 CMO5 
 
 rHO 
 
 ^^ 
 
 23 
 
 ^ 
 
 ^(N 
 
 * 
 
 'd 
 o . 
 
 See 
 
 < Q 
 
 00 
 
 00 
 
 00 
 
 00 
 
 00 
 
 00 
 
 00 
 
 I-H 
 (1 
 
 a 
 
 Ifj 
 
 OO5 
 
 COi-H 
 
 O500 
 <Nr-t 
 
 CO 00 
 
 CMiH 
 
 CO 00 
 
 COrH 
 
 1C CO 
 
 THO 
 
 8 
 
 too 
 
 ss 
 
 t> 
 
 1 
 
 ^^ 
 
 00 
 
 00 
 
 00 
 
 00 
 
 00 
 
 00 
 
 00 
 
 tf 
 
 
 8&' 
 
 COCO 
 COCO 
 
 %% 
 
 ccco 
 
 &% 
 
 iOTj< 
 
 <N<N 
 
 CM CM 
 cMCM 
 
 f-4lO 
 CM 1-4 
 
 > 
 
 1 
 
 <jW 
 
 OO 
 
 00 
 
 OO 
 
 00 
 
 OO 
 
 00 
 
 00 
 
 J> 
 
 1, 
 
 -M 
 
 ss 
 
 <NTJ< 
 
 *^ 
 
 8. 
 
 %% 
 
 %% 
 
 t^O 
 <N<N 
 
 Oh- 
 
 (MrH 
 
 
 
 
 <^ 
 
 00 
 
 OO 
 
 OO 
 
 00 
 
 OO 
 
 00 
 
 OO 
 
 j> 
 
 1 
 
 tf 
 
 l 
 
 <NiH 
 
 COO 
 
 (NCO 
 COCO 
 
 coco 
 
 coco 
 
 10** 
 COCO 
 
 coco 
 
 ^Tt< 
 
 THTj< 
 
 r^Tj( 
 
 O<M 
 
 TfCO 
 
 hH 
 
 
 <j^ 
 
 OO 
 
 OO 
 
 OO 
 
 OO 
 
 00 
 
 00 
 
 OO 
 
 I-H 
 
 "3 
 
 le 
 
 82 
 
 00(N 
 rHt-l 
 
 <NO> 
 
 rHO 
 
 fe& 
 
 
 
 s 
 
 si 
 
 t 1 
 
 *o^ 
 
 <JO 
 
 OO 
 
 OO 
 
 OO 
 
 OO 
 
 00 
 
 00 
 
 00 
 
 HH 
 
 1 
 
 ig 
 
 98 
 
 00 lO 
 CO(N 
 
 l>Tt< 
 
 CO<N 
 
 oco 
 
 C(N 
 
 coco 
 
 THO 
 
 s 
 
 (MO 
 
 3 
 
 
 o 
 
 1 
 
 <;<: 
 
 00 
 
 00 
 
 OO 
 
 OO 
 
 OO 
 
 OO 
 
 00 
 
 
 ll 
 
 1 
 
 t^l>. 
 
 OO 
 
 8 CM 
 CO 
 
 OOO 
 I>CO 
 
 Oit>. 
 
 THO 
 
 <NO 
 
 t^co 
 
 (TOGO 
 iO<N 
 
 too 
 
 CMrH 
 
 
 $1 
 
 7 
 
 1-1 
 
 HO 
 
 00 
 
 1HO 
 
 CO 
 
 OO 
 
 00 
 
 
 ^1 
 
 1 
 
 Tt<00 
 CO<N 
 
 %2 
 
 s 
 
 S8 
 
 >OcM 
 
 Tf 
 
 is 
 
 toco 
 
 OCCO 
 
 
 it 
 
 o 
 
 ft 
 
 CO(N 
 
 CO(N 
 
 dfr* 
 
 COiH 
 
 OiH 
 
 iHfH 
 
 OO 
 
 
 .iii 
 
 il 
 
 JOB ' 
 1 
 
 ij 
 
 COCO 
 \\ 
 
 oco 
 
 COCO 
 \\ 
 
 ioco 
 
 ^ 
 
 iHCO 
 
 CO 
 
 ^< 
 
 COCO 
 
 o 
 
 "^ 
 
 0i-i 
 
 5.00 
 
 
 
 0000 
 
 
 
 
 I 
 
 s 
 
 ^ 
 
 ^ 
 
 X 
 
 JS Y 
 
 3 
 
 
 3S 
 
 
 8J 
 
 j 
 
 j 
 
 J 
 
 X 
 
 CM 
 
 X 
 
 <N 
 
 X 
 
 <M 
 
 x .x 
 Jf 
 
 X 
 
 X 
 
 X 
 
 s 
 
 XX 
 
 ^^ 
 
RADII OF GYRATION. 
 
 309 
 
 PROPERTIES OF STANDARD AND SPECIAL ANGLES. 
 
 ANGLES WITH EQUAL LEGS. 
 
 
 
 
 I. 
 
 II. 
 
 IV. 
 
 VI. 
 
 VII. 
 
 IX. 
 
 
 
 
 
 
 
 
 
 Distance 
 
 
 
 
 
 Moment 
 
 Radii c 
 
 >f gyra- 
 
 Section 
 modu- 
 
 of centre 
 of 
 
 Size, in 
 inches. 
 
 Thick- 
 ness of 
 metal. 
 
 W'ght 
 per ft. 
 
 Area 
 in 
 sq. ins. 
 
 of 
 inertia. 
 
 ti 
 
 
 lus, 
 R. 
 
 gravity 
 from 
 back of 
 
 
 
 
 
 
 
 
 
 flange, 
 
 
 
 
 
 Axis 
 
 Axis 
 
 Axis 
 
 Axis 
 
 
 
 
 
 
 AB. 
 
 AB. 
 
 EF. 
 
 AB. 
 
 d. 
 
 
 1 1/8 
 
 56.9 
 
 16 . 73 
 
 97.97 
 
 2.42 
 
 1.55 
 
 17.53 
 
 2.41 
 
 
 11/16 
 
 54.0 
 
 15.87 
 
 93.53 
 
 2.43 
 
 1.56 
 
 16.67 
 
 2.39 
 
 
 1 
 
 51.0 
 
 15.00 
 
 88.98 
 
 2.44 
 
 1.56 
 
 15.80 
 
 2.37 
 
 
 15/16 
 
 48.0 
 
 14.12 
 
 84.33 
 
 2.44 
 
 1.56 
 
 14.91 
 
 2.34 
 
 
 7/8 
 
 45.0 
 
 13.23 
 
 79.58 
 
 2.45 
 
 1.57 
 
 14.01 
 
 2.32 
 
 8 X8 
 
 13/16 
 
 42.0 
 
 12.34 
 
 74.71 
 
 2.46 
 
 1.57 
 
 13.11 
 
 2.30 
 
 
 3/4 
 
 38.9 
 
 11.44 
 
 69.74 
 
 2.47 
 
 1.57- 
 
 12.18 
 
 2.28 
 
 
 11/16 
 
 35.8 
 
 10.53 
 
 64.64 
 
 2.48 
 
 1.58 
 
 11.25 
 
 2.25 
 
 
 5/8 
 
 32.7 
 
 9.61 
 
 59.42 
 
 2.49 
 
 1.58 
 
 10.30 
 
 2.23 
 
 
 9/16 
 
 29.5 
 
 8.68 
 
 54.09 
 
 2.50 
 
 1.58 
 
 9.34 
 
 2.21 
 
 
 1/2 
 
 26.4 
 
 7.75 
 
 48.63 
 
 2.50 
 
 1.58 
 
 8.37 
 
 2.19 
 
 
 1 
 
 37.4 
 
 11.00 
 
 35.46 
 
 1.80 
 
 1.16 
 
 8.57 
 
 1.86 
 
 
 15/16 
 
 35.3 
 
 10.37 
 
 33.72 
 
 1.80 
 
 1.16 
 
 8.11 
 
 1.84 
 
 
 7/8 
 
 33.1 
 
 9.74 
 
 31.92 
 
 1.81 
 
 1.17 
 
 7.64 
 
 1.82 
 
 
 13/16 
 
 30.9 
 
 9.09 
 
 30.06 
 
 1.82 
 
 1.17 
 
 7.15 
 
 1.80 
 
 
 3/4 
 
 28.7 
 
 8.44 
 
 28.15 
 
 .83 
 
 1.17 
 
 6.66 
 
 1.78 
 
 6 X6 
 
 11/16 
 
 26.5 
 
 7.78 
 
 26.19 
 
 .83 
 
 1.17 
 
 6.17 
 
 1.75 
 
 
 5/8 
 
 24.2 
 
 7.11 
 
 24.16 
 
 .84 
 
 1.18 
 
 5.66 
 
 1.73 
 
 
 9/16 
 
 21.9 
 
 6.43 
 
 22.07 
 
 .85 
 
 1.18 
 
 5.14 
 
 1.71 
 
 
 1/2 
 
 19.6 
 
 5.75 
 
 19.91 
 
 .86 
 
 1.18 
 
 4.61 
 
 1.68 
 
 
 7/16 
 
 17.2 
 
 5.06 
 
 17.68 
 
 .87 
 
 1.19 
 
 4.07 
 
 1.66 
 
 
 3/8 
 
 14,8 
 
 4.36 
 
 15.39 
 
 .88 
 
 1.19 
 
 3.53 
 
 1.64 
 
 
 1 
 
 30.6 
 
 9.00 
 
 19.64 
 
 1.48 
 
 0.96 
 
 5.80 
 
 1.61 
 
 
 15/16 
 
 28.9 
 
 8.50 
 
 18.71 
 
 1.48 
 
 0.96 
 
 5.49 
 
 1.59 
 
 
 7/8 
 
 27.2 
 
 7.99 
 
 17.75 
 
 1.49 
 
 0.96 
 
 5.17 
 
 1.57 
 
 
 13/16 
 
 25.4 
 
 7.46 
 
 16.77 
 
 1.50 
 
 0.97 
 
 4.85 
 
 1.55 
 
 
 3/4 
 
 23.6 
 
 6.94 
 
 15.74 
 
 1.51 
 
 0.97 
 
 4.53 
 
 1.52 
 
 5 X5 
 
 11/16 
 
 5/8 
 
 21.8 
 20.0 
 
 6.42 
 
 5.86 
 
 14.68 
 13.58 
 
 1.51 
 1.52 
 
 0.97 
 0.97 
 
 4.20 
 3.86 
 
 1.50 
 1.48 
 
 
 9/16 
 
 18.1 
 
 5.31 
 
 12.44 
 
 1.53 
 
 0.98 
 
 3.51 
 
 1.46 
 
 
 1/2 
 
 16.2 
 
 4.75 
 
 11.25 
 
 1.54 
 
 0.98 
 
 3.15 
 
 1.43 
 
 
 7/16 
 
 14.3 
 
 4.18 
 
 10.02 
 
 1.55 
 
 0.98 
 
 2.79 
 
 1.41 
 
 
 3/8 
 
 12.3 
 
 3.61 
 
 8.74 
 
 1 56 
 
 0.99 
 
 2.42 
 
 1.39 
 
310 MOMENTS OF INERTIA AND RESISTANCE. 
 
 PROPERTIES OF STANDARD AND SPECIAL ANGLES. 
 
 ANGLES WITH EQUAL LEGS (continued). 
 
 
 
 
 I. 
 
 II. 
 
 IV. 
 
 VI. 
 
 VII. 
 
 IX. 
 
 Size, in 
 inches. 
 
 Thick- 
 ness of 
 metal. 
 
 W'ght 
 per ft. 
 
 Area 
 in 
 sq. ins. 
 
 Moment 
 of 
 inertia. 
 
 Axis 
 AB. 
 
 Radii of gyra- 
 tion. 
 
 Section 
 modu- 
 lus, 
 R. 
 
 Axis 
 AB. 
 
 Distance 
 of center 
 of 
 gravity 
 from 
 baok of 
 flange. 
 
 d. 
 
 Axis 
 AB. 
 
 Axis 
 EF. 
 
 4^X4^ 
 
 5/8 
 9/16 
 1/2 
 7/16 
 3/8 
 5/16 
 
 13/16 
 3/4 
 
 11/16 
 5/8 
 9/16 
 1/2 
 7/16 
 3/8 
 5/16 
 
 13/16 
 3/4 
 11/16 
 
 5/8 
 9/16 
 1/2 
 7/16 
 3/8 
 5/16 
 
 3/4 
 
 3/8 
 
 5/8 
 9/16 
 1/2 
 7/16 
 3/8 
 5/16 
 1/4 
 
 1/2 
 7/16 
 3/8 
 5/16 
 1/4 
 
 1/2 
 7/16 
 3/8 
 5/16 
 1/4 
 3/16 
 
 17.8 
 16.1 
 14.5 
 12.7 
 11.0 
 9.2 
 
 19.9 
 18.5 
 17.1 
 15.7 
 14.3 
 12.8 
 11.3 
 9.8 
 8.2 
 
 17.1 
 16.0 
 14.8 
 13.6 
 12.3 
 11.1 
 9.8 
 8.5 
 7.1 
 
 14.7 
 7.8 
 
 11.4 
 10.4 
 9.4 
 8.3 
 7.2 
 6.1 
 4.9 
 
 8.5 
 7.6 
 6.6 
 5.5 
 4.5 
 
 7.7 
 6.8 
 5.9 
 5.0 
 4.1 
 3.1 
 
 5.23 
 4.75 
 4.25 
 3.75 
 3.23 
 2.71 
 
 5.84 
 5.44 
 5.03 
 4.61 
 4.18 
 3.75 
 3.31 
 2.86 
 2.40 
 
 5.03 
 4.69 
 4.34 
 3.98 
 3.62 
 3.25 
 2.87 
 2.48 
 2.09 
 
 4.32 
 2.29 
 
 3.36 
 3.06 
 2.75 
 2.43 
 2.11 
 1.78 
 1.44 
 
 2.50 
 2.22 
 1.92 
 1.62 
 1.31 
 
 2.25 
 2.00 
 1.73 
 1.47 
 1.19 
 0.90 
 
 9.71 
 8.91 
 8.07 
 7.20 
 6.30 
 5.36 
 
 8.14 
 7.67 
 7.17 
 6.66 
 6.12 
 5.56 
 4.97 
 4.36 
 3.71 
 
 5.25 
 4.96 
 4 65 
 4.33 
 3.99 
 3 64 
 3.26 
 2.87 
 2.45 
 
 2.96 
 
 2.27 
 
 2.62 
 2.43 
 2.22 
 .99 
 .76 
 .51 
 .24 
 
 .67 
 .51 
 .33 
 .15 
 0.93 
 
 1.23 
 1.11 
 0.98 
 0.85 
 0.70 
 0.55 
 
 1.36 
 1.37 
 1.38 
 1 . 39 
 1.40 
 1.40 
 
 1.18 
 1.19 
 1.19 
 1.20 
 1.21 
 1.22 
 1.23 
 .23 
 .24 
 
 .02 
 .03 
 .04 
 .04 
 .05 
 .06 
 .07 
 .07 
 .08 
 
 0.79 
 0.99 
 
 0.88 
 0.89 
 0.90 
 0.91 
 0.91 
 0.92 
 0.93 
 
 0.82 
 0.82 
 0.83 
 0.84 
 0.85 
 
 0.74 
 0.74 
 0.75 
 0.76 
 0.77 
 0.78 
 
 0.87 
 0.88 
 0.88 
 0.88 
 0.89 
 0.89 
 
 0.77 
 0.77 
 0.77 
 0.77 
 0.78 
 0.78 
 0.78 
 0.79 
 0.79 
 
 0.67 
 0.67 
 0.67 
 0.67 
 0.68 
 0.68 
 0.68 
 0.69 
 0.69 
 
 0.53 
 0.66 
 
 0.57 
 0.58 
 0.58 
 0.58 
 0.58 
 0.59 
 0.59 
 
 0.52 
 0.53 
 . 53 
 0.54 
 0.55 
 
 0.47 
 0.48 
 0.48 
 0.49 
 0.49 
 0.49 
 
 3.09 
 2.81 
 2.53 
 2.24 
 1.95 
 1.64 
 
 3.01 
 2.81 
 2.61 
 2.40 
 2.19 
 1.97 
 1.75 
 1.52 
 1.29 
 
 2.25 
 2.11 
 1.96 
 1.81 
 1.65 
 1.49 
 1.32 
 1.15 
 0.98 
 
 1.36 
 0.99 
 
 1.30 
 1.19 
 1.07 
 0.95 
 0.83 
 0.71 
 0.58 
 
 0.89 
 0.79 
 0.69 
 0.59 
 0.48 
 
 0.73 
 0.65 
 0.57 
 0.48 
 0.40 
 0.30 
 
 1.35 
 1.33 
 1.31 
 1.29 
 1026 
 1.24 
 
 .29 
 .27 
 .25 
 .23 
 .21 
 .18 
 1.16 
 1.14 
 1.12 
 
 1.17 
 1.15 
 1.12 
 1.10 
 1.08 
 1.06 
 1.04 
 1.01 
 0.99 
 
 1.08 
 0.95 
 
 0.98 
 0.95 
 0.93 
 0.91 
 0.89 
 0.87 
 0.84 
 
 0.87 
 0.85 
 0.82 
 0.80 
 0.78 
 
 0.81 
 0.78 
 0.76 
 0.74 
 0.72 
 0.69 
 
 4 X4 
 
 3^X3^ 
 
 3MX3M 
 
 3 X3 
 
 2MX2^ 
 
 2^X2^ 
 
RADII OF GYRATION. 
 
 311 
 
 PROPERTIES OF STANDARD AND SPECIAL ANGLES. 
 
 ANGLES WITH EQUAL LEGS 
 
 
 
 
 I. 
 
 II. 
 
 IV. 
 
 VI. 
 
 VII. 
 
 IX. 
 
 Size, in 
 inches. 
 
 Thick- 
 ness of 
 metal. 
 
 W'ght 
 per ft. 
 
 Area 
 in 
 
 sq.ins. 
 
 Moment 
 of 
 inertia. 
 
 Axis 
 AB. 
 
 Radii of gyra- 
 tion. 
 
 Section 
 modu- 
 lus, 
 R. 
 
 Axis 
 AB. 
 
 Distance 
 of centre 
 of 
 gravity 
 from 
 back of 
 flange, 
 
 d. 
 
 Axis 
 AB. 
 
 Axis 
 EF. 
 
 2MX2M 
 
 1/2 
 7/16 
 3/8 
 5/16 
 1/4 
 3/16 
 
 7/16 
 3/8 
 5/16 
 1/4 
 3/16 
 
 7/16 
 
 3/8 
 5/16 
 1/4 
 3/16 
 
 3/8 
 5/16 
 1/4 
 3/16 
 1/8 
 
 5/16 
 1/4 
 3/16 
 1/8 
 
 1/4 
 3/16 
 1/8 
 
 3/16 
 1/8 
 
 3/16 
 
 1/8 
 
 6.8 
 6.1 
 5.3 
 4.5 
 3.7 
 2.8 
 
 5.3 
 4.7 
 4.0 
 3.2 
 2.5 
 
 4.6 
 4.0 
 3.4 
 2.8 
 2.1 
 
 3.4 
 2.9 
 
 2.4 
 1.8 
 1.2 
 
 2.4 
 1.9 
 1.5 
 1.0 
 
 1.5 
 1.2 
 
 0.8 
 
 1.0 
 0.7 
 
 0.8 
 0.6 
 
 2.00 
 1.78 
 1.55 
 1.31 
 1.06 
 0.81 
 
 1.66 
 1.36 
 1.15 
 0.94 
 0.72 
 
 1.30 
 1.17 
 1.00 
 0.81 
 0.62 
 
 0.99 
 0.84 
 0.69 
 0.53 
 0.36 
 
 0.69 
 0.56 
 0.43 
 0.30 
 
 0.44 
 0.34 
 0.24 
 
 0.29 
 0.21 
 
 0.25 
 0.17 
 
 0.87 
 0.79 
 0.70 
 0.61 
 0.51 
 0.39 
 
 0.54 
 
 0.48 
 0.42 
 0.35 
 0.28 
 
 0.35 
 0.31 
 0.27 
 0.23 
 0.18 
 
 0.19 
 0.16 
 0.14 
 0.11 
 0.08 
 
 0.09 
 0.077 
 0.061 
 0.044 
 
 0.037 
 0.030 
 0.022 
 
 0.019 
 0.014 
 
 0.012 
 0.009 
 
 0.66 
 0.67 
 0.67 
 0.68 
 0.69 
 0.70 
 
 0.59 
 0.59 
 0.60 
 0.61 
 0.62 
 
 0.51 
 0.51 
 0.52 
 0.53 
 0.54 
 
 0.44 
 0.44 
 0.45 
 0.46 
 0.46 
 
 0.36 
 0.37 
 0.38 
 0.38 
 
 0.29 
 0.30 
 0.31 
 
 0.26 
 0.26 
 
 0.22 
 0.23 
 
 0.43 
 0.43 
 0.43 
 0.44 
 0.44 
 0.44 
 
 0.39 
 0.39 
 0.39 
 0.39 
 0.40 
 
 0.33 
 0.34 
 0.34 
 0.34 
 0.35 
 
 0.29 
 
 0.29 
 0.29 
 0.29 
 0.30 
 
 0.23 
 0.24 
 0.24 
 0.25 
 
 0.19 
 0.19 
 0.20 
 
 0.18 
 0.19 
 
 0.16 
 0.17 
 
 0.58 
 0.52 
 0.45 
 0.39 
 0.32 
 0.24 
 
 0.40 
 0.35 
 0.30 
 0.25 
 0.19 
 
 0.30 
 0.26 
 0.2S 
 0.19 
 0.14 
 
 0.19 
 0.162 
 0.134 
 0.104 
 0.070 
 
 0.109 
 0.091 
 0.071 
 0.049 
 
 0.056 
 0.044 
 0.031 
 
 0.033 
 0.023 
 
 0.024 
 0.017 
 
 0.74 
 0.72 
 0.70 
 0.68 
 0.66 
 0.63 
 
 0.66 
 0.64 
 0.61 
 0.59 
 0.57 
 
 0.59. 
 0.57 
 0.55 
 0.53 
 0.51 
 
 0.51 
 0.49 
 0.47 
 0.44 
 0.42 
 
 0.42 
 0.40 
 0.38 
 0.35 
 
 0.34 
 0.32 
 0.30 
 
 0.29 
 0.26 
 
 0.26 
 0.23 
 
 2 X2 
 
 mxm 
 
 1HX1J* 
 
 1MX1M 
 
 1 XI 
 
 %x% 
 
 IKxH 
 
312 MOMENTS OF INERTIA AND RESISTANCE. 
 
 PROPERTIES OF CARNEGIE DECK-BEAMS AND 
 BULB ANGLES. 
 
 DECK-BEAMS. STEEL. 
 
 Deck-beam. 
 
 Bulb angle. 
 
 
 1 
 
 .S 
 
 1 
 
 I. 
 
 II. 
 
 III. 
 
 IV. 
 
 Vo 
 
 VII. 
 
 1 
 
 f 
 
 1 
 
 1 
 
 a 
 .2 
 
 Moments of 
 
 Radii of 
 
 ^N 
 
 JO 
 
 PI 
 
 o 
 
 
 
 
 inertia, 
 
 gyration, 
 
 gs^ 
 
 
 a 
 
 1 
 
 tfc 
 
 M-S 
 
 /. 
 
 r. 
 
 d d ~ 
 
 JcA 
 
 60 
 
 1 
 
 | 
 
 13 s 1 
 
 
 
 1 si 
 
 
 
 
 
 o* 
 
 *1 
 
 lid 
 
 3| 
 
 2 
 
 Axis 
 
 Axis 
 
 Axis 
 
 Axis 
 
 <2T 
 
 q 
 
 ^ 
 
 H 
 
 $ 
 
 
 AB. 
 
 CD. 
 
 AB. 
 
 CD. 
 
 R. 
 
 11.5" 
 
 37.00 
 
 .55 
 
 5.30 
 
 10.9 
 
 194.7 
 
 6.60 
 
 4.23 
 
 0.78 
 
 30.6 
 
 11.5" 
 
 32.20 
 
 .42 
 
 5.17 
 
 9.5 
 
 178.7 
 
 6.06 
 
 4.34 
 
 0.80 
 
 27.6 
 
 10" 
 
 35.70 
 
 .63 
 
 5.50 
 
 10.5 
 
 139.9 
 
 7.41 
 
 3.64 
 
 0.84 
 
 25.7 
 
 10" 
 
 27.23 
 
 .38 
 
 5.25 
 
 8.0 
 
 118.4 
 
 6.12 
 
 3.83 
 
 0.87 
 
 21.2 
 
 9" 
 
 30.00 
 
 .57 
 
 5.07 
 
 8.8 
 
 93.2 
 
 5.18 
 
 3.25 
 
 75 
 
 19.6 
 
 9" 
 
 26.00 
 
 .44 
 
 4.94 
 
 7.6 
 
 85.2 
 
 4.61 
 
 3.35 
 
 0.76 
 
 17.7 
 
 8" 
 
 24.48 
 
 .47 
 
 5.16 
 
 7.2 
 
 62.8 
 
 4.45 
 
 2.97 
 
 0.79 
 
 14.1 
 
 8" 
 
 20.15 
 
 .31 
 
 5.00 
 
 5.9 
 
 55.6 
 
 3.90 
 
 3.08 
 
 0.82 
 
 12.2 
 
 7" 
 
 23.46 
 
 .54 
 
 5.10 
 
 6.9 
 
 45.5 
 
 4.30 
 
 2.57 
 
 0.79 
 
 11.7 
 
 7" 
 
 18.11 
 
 .31 
 
 4.87 
 
 5.3 
 
 38.8 
 
 3.55 
 
 2.70 
 
 0.82 
 
 9.7 
 
 6" 
 
 17.16 
 
 .43 
 
 4.53 
 
 5.0 
 
 24.4 
 
 2.66 
 
 2.20 
 
 0.73 
 
 7.2 
 
 6" 
 
 14.10 
 
 .28 
 
 4.38 
 
 4.1 
 
 21.6 
 
 2.22 
 
 2.28 
 
 0.72 
 
 6.1 
 
 BULB ANGLES. STEEL. 
 
 10" 
 
 32.00 
 
 .63 
 
 3.5 
 
 9.41 
 
 116.0 
 
 
 3.51 
 
 
 21.6 
 
 10" 
 
 26.50 
 
 .48 
 
 3.5 
 
 7.80 
 
 104.2 
 
 
 
 3.66 
 
 
 19.9 
 
 9" 
 
 21.80 
 
 .44 
 
 3.5 
 
 6.41 
 
 69.3 
 
 
 
 3.33 
 
 ..... 
 
 14.5 
 
 8" 
 
 19.23 
 
 .41 
 
 3.5 
 
 5.66 
 
 48.8 
 
 
 
 2.95 
 
 
 11.7 
 
 7" 
 
 18.25 
 
 .44 
 
 3.0 
 
 5.37 
 
 34.9 
 
 ..... 
 
 2.56 
 
 
 
 9.6 
 
 7" 
 
 16.00 
 
 .34 
 
 3.0 
 
 4.71 
 
 32.2 
 
 
 6.61 
 
 
 8.7 
 
 6" 
 
 17.20 
 
 .50 
 
 3.0 
 
 5.06 
 
 23.9 
 
 . . 
 
 2.16 
 
 . 
 
 7.6 
 
 6" 
 
 13.75 
 
 .38 
 
 3.0 
 
 4.04 
 
 20.1 
 
 
 
 2.21 
 
 
 6.6 
 
 6" 
 
 12.30 
 
 .31 
 
 3.0 
 
 3.62 
 
 18.6 
 
 . . . 
 
 2.28 
 
 . . . . . 
 
 5.7 
 
 5" 
 
 10.00 
 
 .31 
 
 2.5 
 
 2.94 
 
 10.2 
 
 
 
 1.86 
 
 
 
 4.1 
 
RADII OF GYRATION. 
 
 313 
 
 PROPERTIES OF CARNEGIE T SHAPES. STEEL. 
 
 Thickness varies slightly, that given being the minimum. 
 
 a 
 
 .9 
 
 
 I. 
 
 II. 
 
 III. 
 
 IV. 
 
 V. 
 
 VII. 
 
 VIII 
 
 IX. 
 
 1 
 
 a 
 
 pS 
 
 
 
 
 
 
 
 bC 
 Dj 
 
 *~^ 
 
 
 Moments of 
 
 Radii of 
 
 Section 
 
 Is 
 
 ,0 
 
 03 
 
 "o 
 
 
 inertia, 
 
 gyration, 
 
 modulus. 
 
 
 
 
 
 *-! 
 
 o 
 
 
 
 /. 
 
 r. 
 
 R. 
 
 S-> 
 
 bC 
 
 ti 
 
 o 
 
 QJ 
 
 a 
 
 
 
 
 c . 
 
 
 
 s, 
 
 
 
 
 
 
 
 
 1 
 
 1 
 
 
 
 
 
 
 
 
 
 
 C3 
 
 
 o 
 
 bC 
 
 g 
 
 Axis 
 
 Axis 
 
 Axis 
 
 Axis 
 
 Axis 
 
 Axis 
 
 S 
 
 i 
 
 ic 
 
 | 
 
 1 
 
 
 
 AB. 
 
 CD. 
 
 AB. 
 
 CD. 
 
 AB. 
 
 CD. 
 
 PQ 
 
 5 X3 
 
 1/2 
 
 13.6 
 
 3.99 
 
 2.6 
 
 5.6 
 
 0.82 
 
 1.19 
 
 1.18 
 
 2.22 
 
 0.75 
 
 5 X2^ 
 
 3/8 
 
 11.0 
 
 3.24 
 
 1.6 
 
 4.3 
 
 0.71 
 
 1.16 
 
 0.86 
 
 1.70 
 
 0.65 
 
 4/4 X 3^ 
 
 7/16 
 
 15.8 
 
 4.65 
 
 5.1 
 
 3.7 
 
 1.04 
 
 0.90 
 
 2.13 
 
 1.65 
 
 1.11 
 
 414 X 3 
 
 5/16 
 
 18.5 
 
 2.55 
 
 1.8 
 
 2.6 
 
 0.87 
 
 1.03 
 
 0.81 
 
 1.16 
 
 0.73 
 
 4^X3 
 
 3/8 
 
 10.0 
 
 3.00 
 
 2.1 
 
 3.1 
 
 0.86 
 
 1.04 
 
 0.94 
 
 1.38 
 
 0.75 
 
 4J4X214 
 
 5/16 
 
 8.0 
 
 2.40 
 
 1.1 
 
 2.6 
 
 0.69 
 
 1.07 
 
 0.56 
 
 1.16 
 
 0.58 
 
 434X234 
 
 3/8 
 
 9.3 
 
 2.79 
 
 1.2 
 
 3.1 
 
 0.68 
 
 1.08 
 
 0.65 
 
 1.38 
 
 0.60 
 
 4 X5 
 
 1/2 
 
 15.6 
 
 4.56 
 
 10.7 
 
 2.8 
 
 1.54 
 
 0.79 
 
 3.10 
 
 1.41 
 
 1.56 
 
 4 X5 
 
 3/8 
 
 12.0 
 
 3.54 
 
 8.5 
 
 2.1 
 
 1.56 
 
 0.78 
 
 2.43 
 
 1.06 
 
 1.51 
 
 4 X4J4 
 
 1/2 
 
 14.6 
 
 4.29 
 
 8.0 
 
 2.8 
 
 1.37 
 
 0.81 
 
 2.55 
 
 1.41 
 
 1.37 
 
 
 3/8 
 
 11.4 
 
 3.36 
 
 6.3 
 
 2.1 
 
 1.38 
 
 0.80 
 
 1.98 
 
 1.06 
 
 1.31 
 
 4 X4 
 
 1/2 
 
 13.7 
 
 4.02 
 
 5.7 
 
 2.8 
 
 1.20 
 
 0.84 
 
 2.02 
 
 1.40 
 
 1.18 
 
 4 X4 
 
 3/8 
 
 10.9 
 
 3.21 
 
 4.7 
 
 2.2 
 
 1.23 
 
 0.84 
 
 1.64 
 
 1.09 
 
 1.15 
 
 4 X3 
 
 3/8 
 
 9.3 
 
 2.73 
 
 2.0 
 
 2.1 
 
 0.86 
 
 0.88 
 
 0.88 
 
 1.05 
 
 0.78 
 
 4 X2J4 
 
 3/8 
 
 8.6 
 
 2.52 
 
 1.2 
 
 2.1 
 
 0.69 
 
 0.92 
 
 0.62 
 
 1.05 
 
 0.63 
 
 4 X2J4 
 
 5/16 
 
 7.3 
 
 2.16 
 
 1.0 
 
 1.8 
 
 0.70 
 
 0.91 
 
 0.55 
 
 0.88 
 
 0.60 
 
 4 X2 
 
 3/8 
 
 7.9 
 
 2.31 
 
 0.60 
 
 2.1 
 
 0.52 
 
 0.96 
 
 0.40 
 
 1.05 
 
 0.48 
 
 4 X2 
 
 5/16 
 
 6.6 
 
 1.95 
 
 0.54 
 
 1.8 
 
 0.51 
 
 0.95 
 
 0.34 
 
 0.88 
 
 0.51 
 
 334X4 
 
 1/2 
 
 12.8 
 
 3.75 
 
 5.5 
 
 1.89 
 
 1.21 
 
 0.72 
 
 1.98 
 
 1.08 
 
 1.25 
 
 334X4 
 
 3/8 
 
 9.9 
 
 2.91 
 
 4.3 
 
 1.42 
 
 1.22 
 
 0.70 
 
 1.55 
 
 0.81 
 
 1.19 
 
 314 x 3J4 
 
 1/2 
 
 11.7 
 
 3.45 
 
 3.7 
 
 1.89 
 
 1.04 
 
 0.74 
 
 1.52 
 
 1.08 
 
 1.06 
 
 3>6 X3H 
 
 3/8 
 
 9.2 
 
 2.70 
 
 3.0 
 
 1.42 
 
 1.05 
 
 0.73 
 
 1.19 
 
 0.81 
 
 1.01 
 
 3J4X3 
 
 1/2 
 
 10.9 
 
 3.21 
 
 2.4 
 
 1.88 
 
 0.87 
 
 0.77 
 
 1.13 
 
 1.08 
 
 0.88 
 
 334X3 
 
 3/8 
 
 8.5 
 
 2.49 
 
 1.9 
 
 1.41 
 
 0.88 
 
 0.75 
 
 0.88 
 
 0.81 
 
 0.83 
 
 334X3 
 
 5/16 
 
 7.8 
 
 2.28 
 
 1.6 
 
 1.18 
 
 0.89 
 
 0.76 
 
 0.72 
 
 0.68 
 
 0.78 
 
 3 X4 
 
 1/2 
 
 11.8 
 
 3.48 
 
 5.2 
 
 1.21 
 
 1.23 
 
 0.59 
 
 1.94 
 
 0.81 
 
 1.32 
 
 3 X4 
 
 7/16 
 
 10.6 
 
 3.12 
 
 4.8 
 
 1.09 
 
 1.25 
 
 0.60 
 
 1.78 
 
 0.72 
 
 1.32 
 
 3 X4 
 
 3/8 
 
 9.3 
 
 2.73 
 
 4.3 
 
 0.93 
 
 1.26 
 
 0.59 
 
 1.57 
 
 0.62 
 
 1.29 
 
 3 X3!4 
 3 X 3Vs 
 
 1/2 
 7/16 
 
 10.9 
 9.8 
 
 3.21 
 
 2.88 
 
 3.5 
 3.3 
 
 1.20 
 1.31 
 
 1.06 
 1.08 
 
 0.62 
 0.68 
 
 1.49 
 1.37 
 
 0.80 
 0.88 
 
 1.12 
 1.11 
 
314 MOMENTS OF KNKKTIA ANP 
 
 rr \VT. 
 
 PROPERTIES OF CARNKGIE T SHAPE 
 (concluded). 
 
 STEEL 
 
 
 1 
 
 jj 
 
 
 I. 
 
 II. 
 
 III. 
 
 IV. 
 
 V. 
 
 VII. 
 
 VIII. 
 
 IX. 
 
 
 1 
 
 i 
 
 1 
 
 
 Moments of 
 
 Radii of 
 
 Sect 
 
 "3 
 
 
 
 
 1 
 
 1 
 
 1 
 
 inert!*, 
 
 gyration, 
 
 modulus. 
 
 3 . 
 
 
 i 
 
 1 
 
 | 
 
 * 
 
 
 
 
 
 
 
 H 
 
 
 
 .* 
 
 "S 
 
 
 Axis 
 
 \\ - 
 
 Axis 
 
 Axis 
 
 V\ : .< 
 
 Axis 
 
 
 
 
 S 
 
 .s 
 
 j3 
 
 
 
 c 
 
 Alv 
 
 CD. 
 
 AB. 
 
 CD. 
 
 AH 
 
 
 (Q 
 
 
 x 
 
 S 
 
 fc 
 
 < 
 
 
 
 
 
 
 
 
 ;j 
 
 X ->w 
 
 3/8 
 
 S.o 
 
 2.49 
 
 2.9 
 
 0.93 
 
 1.09 
 
 0.61 
 
 1 2X 
 
 o . o-: 
 
 I 09 
 
 
 \ '* 
 
 1 -> 
 
 10.0 
 
 2.94 
 
 2.3 
 
 1.20 
 
 88 
 
 
 i!io 
 
 0.80 
 
 9.93 
 
 ;i 
 
 \3 
 
 7 lo 
 
 9.1 
 
 2.67 
 
 2.1 
 
 ' - 
 
 
 O.o I 
 
 1.01 
 
 0,72 
 
 0.9.' 
 
 
 
 ;> s 
 
 7.8 
 
 2.28 
 
 1.8 
 
 0.90 
 
 0.90 
 
 
 . So 
 
 O.IH 
 
 U.Ss 
 
 3 
 
 k| 
 
 5/16 
 
 6.6 
 
 1.95 
 
 1.6 
 
 0.75 
 
 0.90 
 
 0.^2 
 
 0.74 
 
 0,50 
 
 . So 
 
 ;> 
 
 
 ;> s 
 
 7,2 
 
 2.10 
 
 1.1 
 
 X> 
 
 0.72 
 
 O.oo 
 
 0.60 
 
 O.tH 
 
 . 7 1 
 
 
 X - H G 
 
 ;i lo 
 
 6.1 
 
 1.80 
 
 0.94 
 
 0.75 
 
 0.73 
 
 Q.tt 
 
 . ,-SL 1 
 
 O.oi 
 
 
 2MX2 
 
 5 lo 
 
 7.4 
 
 2.16 
 
 1.1 
 
 0.62 
 
 0.71 
 
 0.54 
 
 0.75 
 
 0.45 
 
 0.53 
 
 21 
 
 |X| 
 
 3/8 
 
 7.2 
 
 2.10 
 
 .8 
 
 0.54 
 
 0.92 
 
 0.51 
 
 0.87 
 
 0.43 
 
 0.97 
 
 a 
 
 \frt 
 
 5/16 
 
 6.1 
 
 
 .6 
 
 
 0.94 
 
 O..M 
 
 0.76 
 
 0.35 
 
 
 I 
 
 X - :i 4 
 
 :; S 
 
 6.7 
 
 1.98 
 
 .4 
 
 0.66 
 
 . S t 
 
 . ,> 
 
 0.73 
 
 0,53 
 
 0.87 
 
 a 
 
 ; x i >4 
 
 5/16 
 
 5.8 
 
 1.71 
 
 .2 
 
 0.44 
 
 0.83 
 
 0.51 
 
 0.60 
 
 o . ;>; 
 
 o . s;> 
 
 8 
 
 ; \ -ju 
 
 3/8 
 
 f> 4 
 
 1.89 
 
 .0 
 
 0.52 
 
 0.74 
 
 0.53 
 
 0.59 
 
 o.-r_ 
 
 0.7o 
 
 
 
 o lo 
 
 5.5 
 
 
 O.S7 
 
 0.44 
 
 0.74 
 
 0.52 
 
 0.50 
 
 0,35 
 
 0.7i 
 
 * 
 
 
 3/16 
 
 2.9 
 
 0.84 
 
 0.09 
 
 0.29 
 
 0.31 
 
 0.58 
 
 0.09 
 
 . L\ 
 
 0.29 
 
 2\ 
 
 4 X - n 4 
 
 5/16 
 
 4.9 
 
 1.44 
 
 0.66 
 
 0.33 
 
 (X 
 
 0.41 
 
 0.42 
 
 30 
 
 . t>9 
 
 2 
 
 4 \ * ? *-J 
 
 1/4 
 
 4.1 
 
 1.20 
 
 0.51 
 
 0.25 
 
 0.67 
 
 0.47 
 
 o . ;>i 
 
 (K 
 
 . (Hi 
 
 a 
 
 XI 
 
 5/16 
 
 4.3 
 
 1.26 
 
 0.45 
 
 0.23 
 
 6T 
 
 0.43 
 
 0.33 
 
 o.-j; 
 
 0.(>:^ 
 
 :? 
 
 \2 
 
 1/4 
 
 3.7 
 
 1 11^ 
 
 0.36 
 
 0.18 
 
 o'.eo 
 
 o. r_ 
 
 0.25 
 
 
 o r->9 
 
 i 
 
 
 1/4 
 
 3.1 
 
 0^90 
 
 0.16 
 
 0.18 
 
 0.42 
 
 0.45 
 
 0.15 
 
 oils 
 
 o.-u: 
 
 u 
 
 4X1H 
 
 1 4 
 
 3.1 
 
 0.90 
 
 0.23 
 
 0.12 
 
 0.51 
 
 0.37 
 
 0.19 
 
 0,14 
 
 0.54 
 
 
 4\ 1 1 4 
 
 ;; s 
 
 3.6 
 
 1.05 
 
 0.12 
 
 0.19 
 
 0.33 
 
 0.41 
 
 0.15 
 
 O.'Ji 
 
 0.91 
 
 ij 
 
 <X1M 
 
 1/4 
 
 2.4 
 
 0.75 
 
 0.15 
 
 0.08 
 
 0.49 
 
 0.34 
 
 0.14 
 
 0.10 
 
 0.42 
 
 
 g\Uo 
 
 3/16 
 
 1.84 
 
 0.54 
 
 0.11 
 
 0.06 
 
 0.45 
 
 0.31 
 
 0.11 
 
 0.07 
 
 0.44 
 
 i] 
 
 <X1^ 
 
 1/4 
 
 2.04 
 
 0.60 
 
 0.08 
 
 0.05 
 
 0.36 
 
 0.27 
 
 0.10 
 
 0.07 
 
 0.40 
 
 u 
 
 4\1 1 4 
 
 3/16 
 
 1.53 
 
 0.45 
 
 0.06 
 
 0.03 
 
 0.37 
 
 . L\ 
 
 0.07 
 
 0.05 
 
 6.1 
 
 I 
 
 XI 
 
 3/16 
 
 1.23 
 
 0.36 
 
 0.03 
 
 0.02 
 
 0.29 
 
 0.21 
 
 0.05 
 
 0.04 
 
 0.32 
 
 1 
 
 XI 
 
 1/8 
 
 0.87 
 
 0.26 
 
 0.02 
 
 0.01 
 
 0.29 
 
 0.21 
 
 0.03 
 
 0.02 
 
 . 1^9 
 
liADII OF 
 
 I;.\ 
 
 315 
 
 PROPERTIES OF CAMBRIA AND 
 CAKXhGIE STEEL Z-BARS. 
 
 s 
 
 
 v ' 
 
 ^r 
 
 
 
 6 
 
 .5 
 as 
 
 j, 
 
 Weight per foot, Ibs. 
 
 I. ."" 
 
 II. 
 
 III. 
 
 IV. 
 
 V. 
 
 VI. 
 
 ,J 
 *% a 
 
 T. -~ 
 
 Moments of 
 inertia. 
 
 Kadi i of gyration. 
 r. 
 
 Axis 
 AB. 
 
 Axis 
 CD. 
 
 Axis 
 AB. 
 
 Axis 
 CD. 
 
 Axis 
 EF. 
 
 il 
 
 7/16 
 
 1/2 
 
 15.6 
 18.3 
 21.0 
 
 4.59 
 5.39 
 6.19 
 
 25.32 
 29. 8( 
 
 9.11 
 
 10.95 
 12.87 
 
 2.35 
 2.35 
 2.36 
 
 .41 
 .43 
 .44 
 
 0.83 
 0.84 
 0.84 
 
 i? 
 
 gg 
 
 :$" 
 
 9/16 
 5/8 
 11/16 
 
 22.7 
 26.4 
 28.0 
 
 6.68 
 
 7. 10 
 
 34.64 
 38.86 
 43.18 
 
 12.59 
 14.42 
 16.34 
 
 2.28 
 2.28 
 2.29 
 
 .37 
 .39 
 .41 
 
 0.81 
 0.82 
 0.84 
 
 c> 
 
 i 
 
 3/4 
 
 isyw 
 
 7/8 
 
 29.3 
 32.0 
 
 :ii .0 
 
 8.63 
 
 9. JO 
 10.17 
 
 42.12 
 46.13 
 50.22 
 
 15.44 
 
 17.27 
 19.18 
 
 2.21 
 2.22 
 2.22 
 
 .34 
 
 .36 
 .37 
 
 0.81 
 0.82 
 0.83 
 
 .-, 
 
 | 
 
 7/16 
 
 11.6 
 
 ie!4 
 
 3.40 
 
 4.10 
 4.81 
 
 13.36 
 10. 18 
 19.07 
 
 6.18 
 7.65 
 9,20 
 
 1.98 
 1.99 
 4.99 
 
 .35 
 .37 
 .38 
 
 0.75 
 0.76 
 0.77 
 
 r. 
 
 :>K ; 
 
 1/2 
 9/16 
 5/8 
 
 17.8 
 20.2 
 22.6 
 
 5.25 
 5.94 
 6.64 
 
 19.19 
 
 21.83 
 24.53 
 
 9.05 
 
 to. si 
 
 12.06 
 
 1.91 
 1.91 
 1.92 
 
 .31 
 .33 
 .35 
 
 0.74 
 0.75 
 0.76 
 
 5 ' 
 
 i 
 
 11/16 
 13/16 
 
 23.7 
 26.0 
 28.3 
 
 6.96 
 7.64 
 8.33 
 
 23.68 
 
 20. 10 
 28.70 
 
 1 1 . '.',7 
 12.83 
 14.36 
 
 1.84 
 1.85 
 1.86 
 
 .28 
 .30 
 .31 
 
 0.73 
 
 . 7.-, 
 0.76 
 
 4 
 
 4J/16 
 
 1 
 
 1/4 
 5/16 
 
 3/8 
 
 S.2 
 10.3 
 12.4 
 
 2.41 
 3.03 
 3.66 
 
 6.28 
 7.94 
 9.63 
 
 4.23 
 5.40 
 6.77 
 
 1.62 
 1.62 
 1.62 
 
 1.33 
 1.34 
 1.36 
 
 0.67 
 0.68 
 0.69 
 
 4 
 
 l; 
 
 7/16 
 
 1/2 
 9/10 
 
 13.8 
 17^9 
 
 4.05 
 4.66 
 5.27 
 
 9.66 
 11.18 
 12.74 
 
 6.73 
 7.96 
 9.26 
 
 1.55 
 1.55 
 1.55 
 
 .29 
 .31 
 .33 
 
 0.66 
 0.67 
 0.69 
 
 4 
 
 1; 
 
 5/8 
 11/16 
 3/4 
 
 18.9 
 20.9 
 22.9 
 
 5.55 
 6.14 
 6.75 
 
 12.11 
 13.52 
 14.97 
 
 8.73 
 9.95 
 11.24 
 
 1.48 
 1.48 
 1.49 
 
 .25 
 .27 
 .29 
 
 0.66 
 0.67 
 0.69 
 
 3 
 
 i*" 
 
 1/4 
 5/16 
 
 6.7 
 8.4 
 
 1.97 
 
 2.48 
 
 2.87 
 3.64 
 
 2.81 
 3.64 
 
 1.21 
 1.21 
 
 1.19 
 1.21 
 
 0.55 
 0.56 
 
 3 
 
 Si 1 " 
 
 3/8 
 7/16 
 
 9.7 
 11.4 
 
 2.86 
 3.36 
 
 3.85 
 4.57 
 
 3.92 
 4.7o 
 
 1.16 
 1.17 
 
 1.17 
 1.19 
 
 0.55 
 0.56 
 
 3 
 
 si 10 
 
 1/2 
 9/16 
 
 12.5 
 14.2 
 
 3.69 
 4.18 
 
 4.59 
 5.26 
 
 4.85 
 5.70 
 
 1.12 
 1.12 
 
 1.15 
 1.17 
 
 0.55 
 0.56 
 
316 MOMENTS OF INERTIA AND RESISTANCE. 
 
 TABLE A. RADII OF GYRATION FOR A PAIR OF 
 ANGLES PLACED BACK TO BACK. 
 
 ANGLES WITH EQUAL LEGS. 
 
 Radii of gyration given correspond to directions indicated by arrow-heads. 
 
 Size, in 
 inches. 
 
 Weight per 
 foot of 
 single angle, 
 in Ibs. 
 
 *Area of 
 section, 
 in ins. 
 
 Radii of gyration. 
 
 r . 
 
 n- 
 
 "2. 
 
 7*3. 
 
 8 X8 Xi 
 
 26.4 
 
 15.50 
 
 2.50 
 
 3.32 
 
 3.49 
 
 3.58 
 
 8 X8 XH 
 
 56.9 
 
 33.46 
 
 2.42 
 
 3.42 
 
 3.60 
 
 3.69 
 
 6 X6 X f 
 
 14.8 
 
 8.72 
 
 1.88 
 
 2.49 
 
 2.67 
 
 2.76 
 
 6 X6 X 4 
 
 19.6 
 
 11.50 
 
 1.86 
 
 2.52 
 
 2.70 
 
 2.80 
 
 6 X6 X | 
 
 28.7 
 
 16.88 
 
 1.83 
 
 2.55 
 
 2.73 
 
 2.83 
 
 6 X6 Xl 
 
 37.4 
 
 22.00 
 
 1.80 
 
 2.59 
 
 2.77 
 
 2.87 
 
 5 X5 X f 
 
 12.3 
 
 7.22 
 
 1.56 
 
 2.09 
 
 2.26 
 
 2.35 
 
 5 X5 X 1 
 
 16.2 
 
 9.50 
 
 1.54 
 
 2.11 
 
 2.29 
 
 2.38 
 
 5 X5 X 1 
 
 23.6 
 
 13.88 
 
 1.51 
 
 2.15 
 
 2.33 
 
 2.43 
 
 5 X5 Xl 
 
 30.6 
 
 18.00 
 
 1.48 
 
 2.19 
 
 2.38 
 
 2.48 
 
 4 X4 X % 
 
 8*.2 
 
 4.80 
 
 1.24 
 
 1.67 
 
 1.85 
 
 1.94 
 
 4 X4 X | 
 
 9.8 
 
 5.72 
 
 1.23 
 
 1.69 
 
 1.88 
 
 1.97 
 
 4 X4 X f 
 
 15.7 
 
 9.22 
 
 1.20 
 
 1.72 
 
 1.91 
 
 2.00 
 
 4X 4 X % 
 
 19.9 
 
 11.68 
 
 1.18 
 
 1.75 
 
 1.94 
 
 2.04 
 
 31X3JX % 
 
 7.1 
 
 4.18 
 
 1.08 
 
 1.47 
 
 1.65 
 
 1.74 
 
 3iX3iX f 
 
 8.5 
 
 4.96 
 
 1.07 
 
 1.49 
 
 1.67 
 
 1.77 
 
 3iX3iX f 
 
 13.6 
 
 7.96 
 
 1.04 
 
 1.52 
 
 1.70 
 
 1.81 
 
 3JX3iX % 
 
 17.1 
 
 10.06 
 
 1.02 
 
 1.55 
 
 1.74 
 
 1.85 
 
 3 X3 X i 
 
 4.9 
 
 2.88 
 
 0.93 
 
 1.25 
 
 1.43 
 
 1.53 
 
 3 X3 X f 
 
 7.2 
 
 4.22 
 
 0.91 
 
 1.27 
 
 1.45 
 
 1.56 
 
 3 X3 X i 
 
 9.4 
 
 5.50 
 
 0.90 
 
 1.29 
 
 1.48 
 
 1.59 
 
 3 X3 X f 
 
 11.4 
 
 6.72 
 
 0.88 
 
 1.32 
 
 1.51 
 
 1.62 
 
 2fX2fX i 
 2fX2|X J 
 
 4.5 
 8.5 
 
 2.62 
 5.00 
 
 0.85 
 0.82 
 
 1.15 
 1.19 
 
 1.34 
 1.39 
 
 1.44 
 1.49 
 
 2iX2iX % 
 
 3.1 
 
 1.80 
 
 0.78 
 
 1.04 
 
 1.22 
 
 1.32 
 
 2JX2^X i 
 
 7.7 
 
 4.50 
 
 0.74 
 
 1.10 
 
 1.29 
 
 1.40 
 
 2iX2iX % 
 
 2.8 
 
 1.62 
 
 0.70 
 
 0.94 
 
 1.12 
 
 1.23 
 
 2JX2JX i 
 
 6.8 
 
 4.00 
 
 0.66 
 
 0.99 
 
 1.19 
 
 1.30 
 
 2 X2 X i 
 
 3.2 
 
 1.88 
 
 0.61 
 
 0.85 
 
 1.03 
 
 1.14 
 
 * The figures in this column give the area of both angles. 
 
RADII OF GYRATION. 
 
 317 
 
 TABLE B. RADII OF GYRATION FOR A PAIR OF 
 ANGLES PLACED BACK TO BACK. 
 
 ANGLES WITH UNEQUAL LEGS LONG LEG VERTICAL. 
 
 Radii of gyration given correspond to directions indicated by arrow-heads. 
 
 Size, in 
 inches. 
 
 Weight per 
 foot of 
 single angle, 
 in Ibs. 
 
 fArea of 
 section, 
 in ins. 
 
 Radii of gyration. 
 
 ro. 
 
 ri. 
 
 T2> 
 
 rs- 
 
 *8 X6 X i 
 
 23.0 
 
 13.52 
 
 2.56 
 
 2.32 
 
 2.49 
 
 2.57 
 
 *8 X6 XI 
 
 45.6 
 
 26.82 
 
 2.53 
 
 2.47 
 
 2.65 
 
 2.74 
 
 6 X4 X | 
 
 12.3 
 
 7.22 
 
 1.93 
 
 1.50 
 
 1.67 
 
 1.76 
 
 6 X4 X % 
 
 25.4 
 
 14.94 
 
 1.87 
 
 1.55 
 
 1.74 
 
 1.84 
 
 6 X3JX f 
 
 11.7 
 
 6.84 
 
 1.94 
 
 1.26 
 
 1.43 
 
 1.53 
 
 6 X3iX i 
 
 15.3 
 
 9.00 
 
 1.92 
 
 1.28 
 
 1.46 
 
 1.56 
 
 6 X3iX f 
 
 18.9 
 
 11.10 
 
 1.90 
 
 1.30 
 
 1.49 
 
 1.59 
 
 6 X3JX % 
 
 24.0 
 
 14.12 
 
 1.88 
 
 1.33 
 
 1.52 
 
 1.62 
 
 5 X4 X f 
 
 11.0 
 
 6.46 
 
 1.59 
 
 1.58 
 
 1.75 
 
 1.85 
 
 5 X4 X f 
 
 21.1 
 
 12.38 
 
 1.54 
 
 1.62 
 
 1.81 
 
 1.91 
 
 5 X3iX f 
 
 10.4 
 
 6.10 
 
 1.60 
 
 1.33 
 
 1.51 
 
 1.60 
 
 5 X3JX f 
 
 19.8 
 
 11.62 
 
 1.55 
 
 1.39 
 
 1.59 
 
 1.68 
 
 5 X3 X f 
 
 9.8 
 
 5.72 
 
 1.61 
 
 1.10 
 
 1.27 
 
 1.37 
 
 5 X3 X i 
 
 12.8 
 
 7.50 
 
 1.59 
 
 1.12 
 
 1.30 
 
 1.39 
 
 5 X3 X f 
 
 15.7 
 
 9.22 
 
 1.57 
 
 1.14 
 
 1.33 
 
 1. 42 
 
 5 X3 X i 
 
 18.5 
 
 10.88 
 
 1.55 
 
 1.17 
 
 1.36 
 
 1.46 
 
 4 X3JX f 
 
 9.1 
 
 5.34 
 
 1.25 
 
 1.43 
 
 1.60 
 
 1.70 
 
 4 X3iX f 
 
 17.2 
 
 10.12 
 
 1.20 
 
 1.44 
 
 1.62 
 
 1.72 
 
 4 X3 X f 
 
 8.5 
 
 4.96 
 
 1.26 
 
 1.46 
 
 1.64 
 
 1.74 
 
 4 X3 X J 
 
 16.0 
 
 9.38 
 
 1.22 
 
 1.48 
 
 1.67 
 
 1.77 
 
 3JX2JX i 
 
 4.9 
 
 2.88 
 
 1.12 
 
 0.96 
 
 1.13 
 
 1.23 
 
 3iX2iX * 
 
 7:2 
 
 4.22 
 
 1.10 
 
 0.98 
 
 1.16 
 
 1.26 
 
 3JX2JX i 
 
 9.4 
 
 5.50 
 
 1.09 
 
 1.00 
 
 1.19 
 
 1.29 
 
 3iX2iX % 
 
 12.4 
 
 7.30 
 
 1.06 
 
 1.03 
 
 1.23 
 
 1.33 
 
 3 X2 X i 
 
 4.0 
 
 2.38 
 
 0.95 
 
 0.75 
 
 0.93 
 
 1.03 
 
 3 X2 X i 
 
 7.7 
 
 4.50 
 
 0.92 
 
 0.80 
 
 1.00 
 
 1.10 
 
 2JX2 X % 
 
 2.8 
 
 1.62 
 
 0.79 
 
 0.79 
 
 0.97 
 
 1.07 
 
 2JX2 X i 
 
 6.8 
 
 4.00 
 
 0.75 
 
 0.84 
 
 1.04 
 
 1.15 
 
 * Rolled only by the Pencoyd Iron Co. Works. 
 
 t The figures in this column give the area of both angles. 
 
318 MOMENTS OF INERTIA AND RESISTANCE. 
 
 TABLE C. RADII OF GYRATION FOR A PAIR OF 
 ANGLES PLACED BACK TO BACK. 
 
 ANGLES WITH UNEQUAL LEGS. SHORT LEG VERTICAL. 
 
 Radii of gyration given correspond to directions indicated by arrow-heads. 
 
 Size in inches. 
 
 Weight 
 per foot 
 of single 
 angle, 
 in Ibs. 
 
 * Area of 
 
 section 
 in inches. 
 
 Radii of gjo-ation. 
 
 rg. 
 
 r\. 
 
 r 2 . 
 
 r s . 
 
 6 X4 X % 
 
 12.3 
 
 7.22 
 
 1.17 
 
 2.74 
 
 2.92 
 
 3.01 
 
 6 X4 X Y* 
 
 16.2 
 
 9.50 
 
 1.15 
 
 2.76 
 
 2.94 
 
 3.04 
 
 6 X4 X % 
 
 23.6 
 
 13.88 
 
 1.12 
 
 2.80 
 
 2.99 
 
 3.09 
 
 6 X4 XI 
 
 30.6 
 
 18.00 
 
 1.09 
 
 2.85 
 
 3.04 
 
 3.14 
 
 6 X3^X % 
 
 11.7 
 
 6.84 
 
 0.99 
 
 2.81 
 
 3.00 
 
 3.10 
 
 6 X 3 Ji> X 1 
 
 28.9 
 
 17.00 
 
 0.92 
 
 2.93 
 
 3.13 
 
 3.23 
 
 5 X4 X % 
 
 11.0 
 
 6.46 
 
 1.20 
 
 2.20 
 
 2.38 
 
 2.48 
 
 5 X4 X VB 
 
 24.2 
 
 14.22 
 
 1.14 
 
 2.29 
 
 2.48 
 
 2.58 
 
 5 X3^X % 6 
 
 8.7 
 
 5.12 
 
 1.03 
 
 2.26 
 
 2.44 
 
 2.54 
 
 5 X3/^X % 
 
 22.7 
 
 13.34 
 
 0.96 
 
 2.36 
 
 2.55 
 
 2.65 
 
 5 X3 X 3 /io 
 
 8.2 
 
 4.80 
 
 0.85 
 
 2.33 
 
 2.51 
 
 2.61 
 
 5 X3 X 13 /io 
 
 19.9 
 
 11.68 
 
 0.80 
 
 2.42 
 
 2.62 
 
 2.72 
 
 4 X3^X 5 /ie 
 
 7.7 
 
 4.50 
 
 1.07 
 
 1.73 
 
 1.91 
 
 2.00 
 
 4 X3VisX \k 
 
 11.9 
 
 7.00 
 
 1.04 
 
 1.76 
 
 1.95 
 
 2.04 
 
 4 X3^X % 
 
 14.6 
 
 8.60 
 
 1.03 
 
 1.78 
 
 1.98 
 
 2.07 
 
 4 XSj^X 13 Ae 
 
 18.5 
 
 10.86 
 
 1.01 
 
 i.si 
 
 2.01 
 
 2.11 
 
 4 X3 X 5 /i6 
 
 7.1 
 
 4.18 
 
 0.89 
 
 1.79 
 
 1.97 
 
 2.07 
 
 4 X3 X 13 A6 
 
 17.1 
 
 10.06 
 
 0.83 
 
 1.88 
 
 2.08 
 
 2.18 
 
 3^X3 X 5 /ie 
 
 6.6 
 
 3.86 
 
 0.90 
 
 1.52 
 
 1.71 
 
 1.80 
 
 
 15.7 
 
 9.24 
 
 0.85 
 
 1.61 
 
 1.81 
 
 1.91 
 
 3J/X2*^X M 
 
 4.9 
 
 2.88 
 
 0.74 
 
 1.58 
 
 1.76 
 
 1.86 
 
 3/^2 X 2^-6 X ^Vie 
 
 12.4 
 
 7.30 
 
 0.67 
 
 1.66 
 
 1.86 
 
 1.96 
 
 3 X2V^X M. 
 
 4.5 
 
 2.62 
 
 0.75 
 
 1.31 
 
 1.50 
 
 1.59 
 
 3 X2^X 9 /ic 
 
 9.5 
 
 5.56 
 
 0.72 
 
 1.37 
 
 1.56 
 
 1.66 
 
 3 X2 X H 
 
 4.0 
 
 2.38 
 
 0.57 
 
 1.38 
 
 1.56 
 
 1.66 
 
 3 X2 X Vz 
 
 7.7 
 
 4.50 
 
 0.55 
 
 1.42 
 
 1.62 
 
 1.73 
 
 2^X2 X 3 Ae 
 
 2.8 
 6.8 
 
 1.62 
 4.00 
 
 0.60 
 0.56 
 
 1.10 
 1.16 
 
 1.28 
 1.35 
 
 1.39 
 1.46 
 
 * The figures in this column give the area of both angles. 
 
RADII OF GYRATION. 
 
 319 
 
 TABLE P. RADII OF GYRATION FOR A PAIR OF 
 STANDARD CHANNELS PLACED BACK TO BACK. 
 
 Radii of gyration given correspond to directions indicated by arrow-heads. 
 
 Depth in 
 inches. 
 
 Thickness 
 of web. 
 
 Weight 
 per foot 
 of one 
 channel. 
 
 Area of 
 two 
 channels. 
 
 Radii of gyration. 
 
 ro. 
 
 n. 
 
 r 2 . 
 
 r 3 . 
 
 15 
 
 0.40 
 0.43 
 0.52 
 0.62 
 0.72 
 0.82 
 
 0.28 
 0.39 
 0.51 
 0.64 
 1.76 
 
 0.24 
 0.38 
 0.53 
 0.68 
 0.82 
 
 0.23 
 0.29 
 0.45 
 0.62 
 
 33.00 
 35.00 
 40.00 
 45.00 
 50.00 
 55.00 
 
 20.50 
 25.00 
 30.00 
 35.00 
 40.00 
 
 15.00 
 20.00 
 25.00 
 30.00 
 35.00 
 
 13.25 
 15.00 
 20.00 
 25.00 
 
 19.80 
 20.58 
 23.52 
 26.48 
 29.42 
 32.36 
 
 12.06 
 14.70 
 17.64 
 20.58 
 23.52 
 
 8.92 
 11.76 
 14.70 
 17.64 
 20.58 
 
 7.78 
 8.82 
 11.76 
 14.70 
 
 5.62 
 5.58 
 5.43 
 5.32 
 5.23 
 5.16 
 
 4.6X 
 4.43 
 
 4.28 
 4.17 
 ,.09 
 
 3.87 
 3.66 
 3.52 
 3.42 
 3.35 
 
 3.49 
 3.40 
 3.21 
 3.10 
 
 1.38 
 1.38 
 1.37 
 1.37 
 1.37 
 1.38 
 
 1.24 
 1.21 
 1.20 
 1.21 
 1.23* 
 
 1.14 
 1.10 
 1.10 
 1.12 
 1.16 
 
 1.09 
 1.07 
 1.05 
 1.07 
 
 1.48 
 1.47 
 1.46 
 1.45 
 1.46 
 1.47 
 
 1.34 
 1.31 
 1.30 
 1.31 
 1.32 
 
 1.24 
 1.20 
 1.20 
 1.22 
 1.26 
 
 1.19 
 1.17 
 1.15 
 1.17 
 
 1.58 
 1.57 
 1.56 
 1.56 
 1.56 
 1.58 
 
 1.44 
 1.41 
 1.40 
 1.41 
 1.43 
 
 1.34 
 1.31 
 1.31 
 1.33 
 1.37 
 
 1.29 
 1.28 
 1.26 
 1.28 
 
 12 
 
 10 
 
 9 
 
320 MOMENTS OP INERTIA AND RESISTANCE. 
 
 TABLE D. RADII OP GYRATION FOR A PAIR OP 
 STANDARD CHANNELS PLACED BACK TO BACK 
 
 (continued) . 
 
 
 L- _ 
 
 Radii of gyration given correspond to directions indicated by arrow-heads. 
 
 Depth in 
 inches. 
 
 Thickness 
 of web. 
 
 Weight 
 per foot 
 of one 
 channel. 
 
 Area 
 of two 
 channels. 
 
 Radii of gyration. 
 
 rfc. 
 
 TI. 
 
 r 2 . 
 
 r 3 - 
 
 8 
 
 0.22 
 
 11.25 
 
 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 
 
 16.25 
 
 9.56 
 
 2.89 
 
 1.03 
 
 1.14 
 
 1.24 
 
 8 
 
 0.49 
 
 18.75 
 
 11.02 
 
 2.82 
 
 1.03 
 
 1.14 
 
 1.24 
 
 8 
 
 0.58 
 
 21.25 
 
 12.50 
 
 2.77 
 
 1.03 
 
 1.14 
 
 1.24 
 
 7 
 
 0.21 
 
 9.75 
 
 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 
 
 14.75 
 
 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 
 
 19.75 
 
 11.62 
 
 2.39 
 
 1.00 
 
 1.10 
 
 1.22 
 
 6 
 
 0.20 
 
 8.00 
 
 4.76 
 
 2.34 
 
 0.94 
 
 1.05 
 
 1.15 
 
 6 
 
 0.32 
 
 10.50 
 
 6.18 
 
 2.21 
 
 0.94 
 
 1.05 
 
 1.16 
 
 6 
 
 0.44 
 
 13.00 
 
 7.64 
 
 2.13 
 
 0.95 
 
 1.06 
 
 1.16 
 
 6 
 
 0.56 
 
 15.50 
 
 9.12 
 
 2.07 
 
 0.95 
 
 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 
 
 1.11 
 
 5 
 
 0.48 
 
 11.50 
 
 6.76 
 
 1.75 
 
 0.91 
 
 1.01 
 
 1.12 
 
 4 
 
 0.18 
 
 5.25 
 
 3.10 
 
 1.56 
 
 0.84 
 
 0.95 
 
 1.06 
 
 4 
 
 0.25 
 
 6.25 
 
 3.68 
 
 1.51 
 
 0.84 
 
 0.95 
 
 1.06 
 
 4 
 
 0.32 
 
 7.25 
 
 4.26 
 
 1.46 
 
 0.84 
 
 0.95 
 
 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 
 
 3.52 
 
 1.08 
 
 0.83 
 
 0.93 
 
 1.05 
 

 RESISTANCE TO TENSION. 321 
 
 CHAPTER XL 
 RESISTANCE TO TENSION. 
 
 PHYSICAL PROPERTIES AND SPECIFICATIONS OF IRON 
 AND STEEL. 
 
 STRENGTH OF RODS, ROPES, AND CABLES. PROPORTIONS OF UPSET 
 SCREW ENDS, EYE-BARS, TURNBUCKLES, ETC. 
 
 THE resistance which any material offers to being pulled apart 
 is due to the tenacity of its fibres, or the cohesion of the "particles 
 of which it is composed. 
 
 It is evident that the amount of resistance to tension which any 
 cross-section of a body will exert depends only upon the tenacity 
 of its fibres, or the cohesion of its particles, and upon the number 
 of fibres or particles in the cross-section. 
 
 As the number of the fibres, or particles, in the section is pro- 
 portional to the area, the strength of any piece of material must 
 be as the area of its cross-section; and hence, if we know the 
 tenacity of the material per square inch of cross-section, we can 
 obtain the total strength by multiplying it by the area of the sec- 
 tion in inches. 
 
 The tenacity of different building materials per square inch has 
 been found by pulling apart a bar of the material of known 
 dimensions, and dividing the breaking force by the area of the 
 cross-section of the bar. 
 
 Table I. gives the allowable safe values for the tenacity of 
 building materials, as recommended by the best authorities. 
 
 Knowing the tenacity of one square inch of the material all 
 that is necessary to determine the tenacity of a piece of any uni- 
 form size is to multiply the area of its cross-section, in square 
 inches, by the number in the table opposite the name of the 
 material; or: 
 
 For a rectangular bar, 
 
 Safe load in Ibs. = breadth X depth X T. (1) 
 
 For a round bar, 
 
 Safe load in Ibs. = 0.7854 X diameter squared X T. (2) 
 
322 RESISTANCE TO TENSION. 
 
 If the size of the bar is desired we have 
 For a round bar, 
 
 Area of cross-section = ^T. (3) 
 
 (4) 
 
 5F= values for the material, given in Table I. 
 TABLE I. 
 
 Allowable Safe Tensile Stress per Square Inch for Building 
 Materials. 
 
 Safe Strength in 
 Material. Ibs. per sq. in. 
 
 T 
 Cement, natural, one week old .................... 60 to 100 
 
 Cement,* Portland, one week, fair average ....... ..... 350 
 
 METALS. 
 Cast iron . .................................... .... 3,000 
 
 Copper, cast ....................................... 2,000 
 
 " forged or rolled .............................. 5,500 
 
 " wire ....................................... 9,000 
 
 Wrought iron * ............................. 10,000 to 14,000 
 
 Wrought steel, soft ......................... 12,000 to 10,000 
 
 " " medium f .................... 12,500 to 18,000 
 
 Steel wire .......................... . ............. 20,000 
 
 WOODS. (Factor of safety of five to six.){ 
 
 Ash, white ........................................ 2,000 
 
 Ash, brown ____ . ................................... 1,500 
 
 Chestnut .......................................... 1,500 
 
 Hemlock. . .' ....................................... 1,200 
 
 Oak, white ......................................... 2,000 
 
 Pine, Georgia yeuW ....... . ................ . ........ 2,000 
 
 Pine, Oregon (Douglas Fir) ........................... 1,800 
 
 Pine, Norway ...................................... 1,600 
 
 Pine, white ...................................... . . 1,400 
 
 Redwood ........................................... 800 
 
 Spruce ............................................ 1,600 
 
 Whitewood ........................................ 1,200 
 
 * See page 324. t See page 331. 
 
 % The Building Law for Greater New York fixes the permissible unit 
 stress in yellow pine at 1200 Ibs. per sq. inch; in oak at 1000 Ibs.; in white 
 pine and spruce at 800 Ibs., and in hemlock at 600 Ibs. These values are 
 about one-tenth of the ultimate strength. 
 
RESISTANCE TO TENSION. 323 
 
 EXAMPLE I. The strain in the tie-beam of a truss has been 
 found to be 120,000 Ibs. What should be the size of the beam, 
 if made of white pine? 
 
 Ans. By formula (3) we have 
 
 120 000 
 Area of cross-section == -_ = 85. 7 sq. inches. 
 
 If we make the depth of the beam 12 inches then the thickness 
 
 85 7 
 must be -r^-, or 7.2 inches. As the beam is horizontal its own 
 
 weight would produce an additional strain in the fibres, for which 
 some allowance must be made. 
 
 Allowance must also be made for any cutting of the beam or 
 for holes for truss rods. If there is a two-inch hole through the 
 beam, we should use a 10X12 inch beam, which w r ill allow for 
 the hole, and for the weight of the beam. 
 
 For the calculation of tie-beams subject to a transverse load see 
 Chapter XV. 
 
 EXAMPLE II. What size angle bar should be used to resist a 
 tensile stress of 60,000 Ibs., the material being medium steel? 
 
 60,000 
 
 Ans. Sectional area= ~~ = 4 sq. in. 
 Ao,uuU 
 
 From the tables giving the properties of angles, Chapter X., we 
 find that a 4 X 4 X f angle has an area of 4.61 square inches. This 
 would be reduced by one f-inch hole, for a f-inch rivet, which 
 gives the net area 4.61 - -fX 1=4.06 square inches, or just above 
 that required. 
 
 [The tensile strength of the sizes of angles most commonly used 
 in trusses is given in Table X. For reduction in net area caused 
 by rivet-holes see Table XI., also Table I., Chapter XX.] 
 
 Wrought Iron. 
 
 Wrought iron is no longer used for the manufacture of struc- 
 tural shapes, such as angles, channels, beams, etc., except in case 
 of special orders, its use in structural work being practically 
 limited to rods, bars, and bolts. Nearly all bolts are made of 
 wrought iron, and truss rods are generally furnished in wrought 
 iron unless steel is specified. Flat tie-bars are made both of iron 
 and steel. The cost of bars and rods is about the same in 
 wrought iron or mild steel, but wrought iron is easier to work 
 than steel. 
 
324 RESISTANCE TO TENSION. 
 
 Tensile Strength and Quality. The best American rolled iron 
 has a breaking tensile strength of from fifty thousand to sixty 
 thousand pounds per square inch for specimens not exceeding 
 one square inch in section. Ordinary bar iron should not break 
 under a less strain than fifty thousand pounds per square inch, 
 and should not take a set under a stress less than twenty-five 
 thousand pounds per square inch. A bar one inch square and 
 one foot long should stretch fifteen per cent, of its length before 
 breaking, and should be capable of being bent, cold, 90 over the 
 edge of an anvil without sign of fracture, and should show a 
 fibrous texture when broken. 
 
 Iron that will not meet these requirements is not suitable for 
 structures ; but nothing is gained by specifying more severe tests, 
 because, in bars of the sizes and shapes usually required for such 
 work, nothing more can be attained with certainty, and conscien- 
 tious makers will be unwilling to agree to furnish that which it is 
 ' not practicable to produce. 
 
 The working strength of wrought-iron ties in trusses is gener- 
 ally taken at ten thousand pounds per square inch. In places 
 where the load is perfectly steady and constant twelve thousand 
 pounds may be used. 
 
 The extension of iron, for all practical purposes, is as follows : 
 
 Wrought iron, y^J^ of its length per ton per square inch. 
 
 Cast iron, -^^ of its length per ton per square inch. 
 
 Appearance of the Fractured Surface of Wrought 
 
 Iron. 
 
 At one time it was thought that a fibrous fracture was a sign of 
 good tough wrought iron, and that a crystalline fracture showed 
 that the iron was bad, hard, and brittle. Mr. Kirkaldy's experi- 
 ments, however, show conclusively that, whenever wrought iron 
 breaks suddenly, it invariably presents a crystalline appearance; 
 and, when it breaks gradually, it invariably presents a fibrous 
 appearance. From the same experiments it was also shown that 
 the appearance of the fractured surface of wrought iron is, to a 
 certain extent, an indication of its quality, provided it is known 
 how the stress was applied which produced the fracture. 
 
 Small, uniform crystals, of a uniform size and color, or fine, 
 close, silky fibres, indicate a good iron. 
 
 Coarse crystals, blotches of color caused by impurities, loose 
 and open fibres, are signs of bad iron; and flaws in the fractured 
 
RESISTANCE TO TENSION. 325 
 
 surface indicate that the piling and welding processes have been 
 imperfectly carried out. 
 
 Kirkaldy's Conclusions.* 
 
 Mr. David Kirkaldy of England, who made some of the most 
 valuable experiments on record on the strength of wrought iron, 
 came to some conclusions, many of which differed from what had 
 previously been supposed to be true. 
 
 The following are of special importance to the student of build- 
 ing constructio*n, and should be carefully studied : 
 
 "The breaking-strain does not indicate the quality, as hitherto 
 assumed. 
 
 "A high breaking-strain may be due to the iron being of supe- 
 rior quality, density, fine, and moderately soft, or simply to its 
 being very hard and unyielding. 
 
 "A low breaking-strain may be due to looseness and coarseness 
 in the texture; or to extreme softness, although very close and 
 fine in quality. 
 
 "The contraction of area at fracture, previously overlooked, 
 forms an essential element in estimating the quality of specimens. 
 
 "The respective merits of various specimens can be correctly 
 ascertained by comparing the breaking -strain jointly with the 
 contraction of area. 
 
 "Inferior qualities show a much greater variation in the break- 
 ing-strain than superior. 
 
 "Greater differences exist between small and large bars in 
 coarse than in fine varieties. 
 
 "The prevailing opinion of a rough bar being stronger than a 
 turned one is erroneous. 
 
 "Rolled bars are slightly hardened by being forged down. 
 
 "The breaking-strain and contraction of area of iron plates are 
 greater in the direction in which they are rolled than in a trans- 
 verse direction. 
 
 "Iron is less liable to snap the more it is worked and rolled. 
 
 "The ratio of ultimate elongation may be greater in short than 
 in long bars, in some descriptions of iron; whilst in others the 
 ratio is not affected by difference in the length. 
 
 "Iron, like steel, is softened, and the breaking-strain reduced, 
 by being heated, and allowed to cool slowly. 
 
 * Kirkaldy's Experiments on Wrought Iron and Steel. 
 
326 RESISTANCE TO TENSION. 
 
 "A great variation exists in the strength of iron bars which 
 have been cut and welded. Whilst some bear almost as much as 
 the uncut bar, the strength of others is reduced fully a third. 
 
 "The welding of steel bars, owing to their being so easily 
 burned by slightly overheating, is a difficult and uncertain opera- 
 tion. 
 
 "Iron is injured by being brought to a white or welding heat, if 
 not at the same time hammered or rolled. 
 
 "The breaking strain is considerably less when the strain is 
 applied suddenly instead of gradually, though some have imagined 
 that the reverse is the case. 
 
 "The specific gravity is found to generally indicate pretty cor- 
 rectly the quality of specimens. 
 
 "The density of iron is decreased by the process of wire-drawing 
 and by the similar process of cold rolling,* instead of increased, 
 as previously imagined. 
 
 "The density of iron is decreased by being drawn out under a 
 tensile strain, instead of increased, as believed by some. 
 
 "It must be abundantly evident, from the facts that have been 
 produced, that the breaking-strain, when taken alone, gives a 
 false impression of, instead of indicating, the real quality of 
 iron, as the experiments which have been instituted reveal the 
 somewhat startling fact, that frequently the inferior kinds of iron 
 actually yield a higher result than the superior. The reason of 
 this difference was shown to be due to the fact that, whilst the one 
 quality retained its original area only very slightly decreased by 
 the strain, the other was reduced to less than one-half. Now, 
 surely this variation, hitherto unaccountably completely over- 
 looked, is of importance as indicating the relative hardness or soft- 
 ness of the material, and thus, it is submitted, forms an essential 
 element in considering the safe load that can be practically applied 
 in various structures. It must be borne in mind that, although 
 the softness of the material has the effect of lessening the amount 
 of the breaking-strain, it has the very opposite effect as regards 
 the working-strain. This holds good for two reasons: first, the 
 softer the iron, the less liable it is to snap ; and, second, fine or soft 
 
 * The conclusion of Mr. Kirkaldy in respect to cold rolling is undoubtedly 
 true when the rolling amounts to wire-drawing; but, when the compression 
 of the surface by rolling diminishes the sectional area in greater proportion 
 than it extends the bar, the result, according to the experience of the 
 Pittsburgh manufacturers, is a slight increase in the density of the iron. 
 
RESISTANCE TO TENSION. 327 
 
 iron, being more uniform in quality, can be more depended upon 
 in practice. Hence the load which this description of iron can 
 suspend with safety may approach much more nearly the limit 
 of its breaking-strain than can be attempted with the harder or 
 coarser sorts, where a greater margin must necessarily be left. 
 
 "As a necessary corollary to what we have just endeavored to 
 establish, the writer now submits, in addition, that the working- 
 strain should be in proportion to the breaking-strain per square 
 inch of fractured area, and not to the breaking-strain per square 
 inch of original area, as heretofore. Some kinds of iron experi- 
 mented on by the writer will sustain with safety more than double 
 the load that others can suspend, especially in circumstances 
 where the load is unsteady, and the structure exposed to concus- 
 sions, as in a ship or railway bridge." 
 
 Cast Iron. 
 
 Cast iron has only about one-third the tensile strength of 
 Wrought iron ; and as it is liable to air-holes, internal strains from 
 unequal contraction in cooling, and other concealed defects, 
 reducing its effective area for tension, it should never be used 
 where it is subjected to any great tensile stress. 
 
 STANDARD SPECIFICATIONS FOR STRUCTURAL CAST IRON. 
 Except where chilled iron is specified, all castings shall be tough 
 gray iron, free from injurious cold-shuts or blow-holes, true to 
 pattern, and of a workmanlike finish. Sample pieces one inch 
 square, cast from the same heat of metal in sand moulds, shall 
 be capable of sustaining oil a clear span of 4 feet 8 inches a cen- 
 tral load of 500 pounds when tested in the rough bar. 
 
 Structural Steel.* 
 
 The strength of structural steel depends largely on the amount 
 of the constituent elements that are associated with the iron, and 
 each of which affect more or less the hardness and strength of the 
 metal. 
 
 The principal of these are carbon, manganese, silicon, phos- 
 phorus, and sulphur, the first-named being purposely retained as 
 useful or necessary, the others being rejected, as far as practi- 
 
 * Mr. James Christie in "Steel in Construction," published by the A.& P, 
 Roberts Company, proprietors of the Pencoyd Iron Works. 
 
328 RESISTANCE TO TENSION. 
 
 cable, as objectionable when in excess of certain minute pro- 
 portions. 
 
 The grade and character of steel is usually known by the 
 percentage of contained carbon. Steel used in structures usually 
 varies in tensile strength from 55,000 to 70,000 Ibs. per square 
 inch of section, or from .10 to .25 per cent, of carbon. 
 
 Table II. exhibits the physical characteristics of open-hearth 
 basic steel of the various grades, the results derived from an 
 extensive series of tests indicating the tendency of a total average 
 of the composition hereafter described to approximate to the 
 figures given in table. 
 
 The predominant elements other than carbon averaged 
 throughout the series as follows : manganese, .54 ; phosphorus, .05; 
 sulphur, .05 per cent. Any increase of these elements is attended 
 with an increase of tensile strength and reduced ductility, and 
 vice versa. The tensile strength of the steel is also affected to 
 some extent by the temperature at which it is finished, and the 
 rate of cooling, these influences being more apparent in the 
 grades containing highest carbon. Therefore the values given 
 have only a general significance, and individual tests may vary 
 widely above or below the figures in the table. 
 
 For Bessemer or open-hearth acid process steel the tensile 
 strength will ordinarily be greater for the same percentage of 
 carbon given in this table, for the reason that the proportions of 
 phosphorus and sulphur, and sometimes manganese, are usually 
 higher than in open-hearth basic steel, each of these elements 
 contributing to strength and hardness in the steel. 
 
 For convenient distinguishing terms*, it is customary to classify 
 steel in three grades, "mild or soft," "medium," and "hard"g 
 and although the different grades blend into each other, so that 
 no line of distinction exists, in a general sense the grades below 
 .15 carbon may be considered as "soft" steel, from .15 to .30 car- 
 bon as "medium," and above that "hard" steel. Each grade 
 has its own advantages for the particular purpose to which it is 
 adapted. The soft steel is well adapted for boiler-plate and simi- 
 lar uses, where its high ductility is advantageous. The medium 
 grades are used for general structural purposes, while harder steel 
 is especially adapted for axles and shafts, and any service where 
 good wearing surfaces are desired. Mild steel has superior weld- 
 ing property as compared to hard steel, and will endure higher 
 heat without injury. Steel below .10 carbon should be capable of 
 doubling flat without fracture, after being chilled from a red heat 
 
RESISTANCE TO TENSION. 329 
 
 TABLE II. OPEN-HEARTH BASIC STEEL. 
 
 Percentage 
 of carbon. 
 
 Tensile strength in pounds 
 per square inch. 
 
 Ductility. 
 
 Ultimate 
 strength. 
 
 Elastic 
 limit. 
 
 Stretch in 
 8 inches. 
 
 Reduction of 
 fractured area. 
 
 .08 
 
 54,000 
 
 32,500 
 
 32 per cent. 
 
 60 per cent. 
 
 .09 
 
 54,800 
 
 33,000 
 
 31 
 
 58 
 
 .10 
 
 55,700 
 
 33,500 
 
 31 
 
 57 
 
 .11 
 
 56,500 
 
 34,000 
 
 30 
 
 56 
 
 .12 
 
 57,400- 
 
 ' 34,500 
 
 30 
 
 55 
 
 .13 
 
 58,200 
 
 35,000 
 
 29 
 
 54 
 
 .14 
 
 59,100 
 
 35,500 
 
 29 
 
 53 
 
 .15 
 
 60,000 
 
 36,000 
 
 28 
 
 52 
 
 .16 
 
 60,800 
 
 36,500 
 
 28 
 
 51 
 
 .17 
 
 61,600 
 
 37,000 
 
 27 
 
 50 
 
 .18 
 
 62,500 
 
 37,500 
 
 27 
 
 49 
 
 .19 
 
 63,300 
 
 38,000 
 
 26 
 
 48 
 
 .20 
 
 64,200 
 
 38,500 
 
 26 
 
 47 
 
 .21 
 
 65,000 
 
 39,000 
 
 25 
 
 46 
 
 .22 
 
 65,800 
 
 39,500 
 
 25 
 
 45 
 
 .23 
 
 66,600 
 
 40,000 
 
 24 
 
 44 
 
 .24 
 
 67,400 
 
 40,500 
 
 24 
 
 43 
 
 .25 
 
 68,200 
 
 41,000 
 
 23 
 
 42 
 
 in cold water. Steel of .15 carbon will ocacsionally submit to the 
 same treatment, but will usually bend around a curve whose 
 radius is equal to the thickness of the specimen; about 90 per 
 cent, of specimens stand the latter bending test without fracture. 
 As the steel becomes harder, its ability to endure this bending 
 test becomes more exceptional, and when the carbon ratio 
 becomes .20, little over twenty-five per cent, of specimens will 
 stand the last-described bending test. Steel having about .40 
 per cent, carbon will usually harden sufficiently to cut soft iron 
 and maintain an edge. 
 
 Elasticity of Steel. 
 
 As the material elongates or shortens under stress, the change 
 of length is directly proportionate to the stress, and the material 
 recovers its original length after removal of the stress, until the 
 elastic limit is reached, when changes of length are no longer regu- 
 
330 RESISTANCE TO TENSION. 
 
 lar, and permanent set takes place, or the destruction of the 
 material has begun. 
 
 In good material the stress at elastic limit, for either tension or 
 compression, is usually about six-tenths of the ultimate tenacity. 
 
 The ductility under tensile strength is usually measured by the 
 total elongation in a given length, or by the percentage of reduc- 
 tion of the fractured area, or by both. 
 
 The elasticity is measured by the change of length under stress 
 below the elastic limit of the material. The elasticity of the 
 various grades of steel are practically uniform, that is, each 
 material will exhibit a uniform change of length under uniform 
 stress below the elastic limit; but, as the elastic limit of the 
 higher grades is greater than that of the lower or softer grades, 
 the former will elongate or shorten to a greater extent than the 
 latter before its elasticity is injured. This property is expressed 
 by a modulus, which for either material will average about 
 29,000,000 Ibs. That is, if the change of length could be extended 
 sufficiently, it would require 29,000,000 Ibs. per square inch of 
 section to double the original length under tensile strain, or to 
 shorten the length one-half under compression. Therefore, steel 
 will extend or shorten sTjr&WoiF P ar ^ of its normal length for 
 every pound per sectional inch in change of load. 
 
 Expansion by Heat. 
 
 Soft steel or iron will extend about rsihrtrG P art f i^ s length for 
 each degree F. of elevation of temperature. For a variation in 
 temperature of 100 degrees F., the change in length will be about 
 one inch in 125 feet. 
 
 Weight or Specific Gravity of Steel. 
 
 The specific gravity of steel varies according to the purity of 
 the metal, and also according to the degree of condensation 
 imparted by the process of rolling or forging. 
 
 As a rule, mild steel has a higher specific gravity than hard 
 steel, and both are lower than perfectly pure iron, but about two 
 per cent, higher than ordinary commercial iron. Structural steel 
 in comparatively small sections, having the composition denoted 
 in the previous table of tensile strength, has the following specific 
 gravity, corresponding to given carbon ratio: 
 
RESISTANCE TO TENSION. 
 
 331 
 
 Carbon, per cent. 
 
 Specific gravity. 
 
 Weight per cubic foot 
 in pounds. 
 
 .10 
 
 7.800 
 
 489.92 
 
 .20 
 
 7.858 
 
 489.80 
 
 .30 
 
 7.856 
 
 489.67 
 
 In the form of rolled beams and largest commercial sections the 
 weight will be slightly less than this. 
 
 The weights for steel sections given in this book are all calcu- 
 lated on a basis of 489.6 Ibs. per cubic foot, or the sectional area 
 in square inches multiplied by 3.4 equals the weight in pounds 
 per foot. 
 
 Working Strength of Steel. 
 
 In designing steel roof trusses engineers generally allow about 
 16,000 Ibs. per square inch for the working tensile strength of 
 steel shapes, such as angles or channels, and about 18,000 Ibs. for 
 round or flat bars, when the quality of the material is to be tested, 
 and it is known that the work will be first-class. For wind 
 bracing a stress of 20,000 Ibs. is often used. (See page 268 of 
 Freibag's " Architectural Engineering.") 
 
 Where the material is not to be tested, the author would not 
 recommend the use of greater unit strains than. 14,000 Ibs. for 
 shapes and 15,000 Ibs. for bars. For truss-rods obtained of an 
 ordinary blacksmith, and which have perhaps been welded, not 
 over 12,500 Ibs. should be used. 
 
 The New York and Chicago building laws fix the limit of tensile 
 stress in steel at 16,000 Ibs. 5 the Boston law at 15,000 Ibs. 
 
 MANUFACTURERS' SPECIFICATIONS GOVERN- 
 ING THE PHYSICAL PROPERTIES OF 
 STRUCTURAL STEEL. 
 
 Revised Oct. 23, 1896. 
 PROCESS OF MANUFACTURED 
 
 (1) Steel maybe made by either the open-hearth or Bessemer 
 process. 
 
 TEST-PIECES. 
 
 (2) All tests and inspections shall be made at place of manufac- 
 ture prior to shipment. 
 
332 
 
 RESISTANCE TO TENSION. 
 
 (3) The tensile strength, limit of elasticity, and ductility shall 
 be determined from a standard test-piece cut from the finished 
 material. The standard shape of the test-piece for sheared 
 plates shall be as shown by the following sketch : 
 
 ABOUT 3^ 
 
 / 
 
 c PARALLEL SECTION 
 
 
 
 NOT LESS THAN 9" 
 
 
 1-1 1 ' ' ' ? * ' 
 
 
 
 g 
 
 LUUU. , ; 
 
 ABOUT 18 . > 
 
 PIECE TO BE THE SAMETHICKNESS AS THE PLATE 
 
 On tests cut from other material the test-piece may be either 
 the same as for plates, or it may be planed or turned parallel 
 throughout its entire length. The elongation shall be measured 
 on an original length of 8 inches, except when the thickness of the 
 finished material is % inch or less, in which case the elongation 
 shall be measured in a length equal to sixteen times the thickness ; 
 and except in rounds of f inch or less in diameter, in w r hich case 
 the elongation shall be measured in a length equal to eight times 
 the diameter of section tested. Two test-pieces shall be taken 
 from each melt or blow of finished material, one for tension and 
 one for bending. 
 
 ANNEALED TEST PIECES. 
 
 (4) Material which is to be used without annealing or further 
 treatment is to be tested in the condition in which it comes from 
 the rolls. When material is to be annealed or otherwise treated 
 before use, the specimen representing such material is to be sim- 
 ilarly treated before testing. 
 
 MARKING. 
 
 (5) Every finished piece of steel shall be stamped with the 
 blow or melt number, and steel for pins shall have the blow or 
 melt number stamped on the ends. Rivet and lacing steel, and 
 small pieces for pin plates and stiffeners, may be shipped in 
 bundles securely wired together, with the blow or melt number 
 on a metal tag attached. 
 
 FINISH. 
 
 (6) Finished bars must be free from injurious seams, flaws, or 
 cracks, and have a workmanlike finish. fc 
 
RESISTANCE TO TENSION. 333 
 
 CHEMICAL PROPERTIES. 
 
 (7) Steel for buildings, train sheds, highway bridges and 
 similar structures shall not contain more than 0.10 per cent, of 
 phosphorus. Steel for railway bridges shall not contain more 
 than 0.08 per cent, of phosphorus. 
 
 GRADES OF STEEL. 
 
 (8) Structural steel shall be of three grades : RIVET, SOFT, and 
 MEDIUM. 
 
 RIVET STEEL. 
 
 (9) Ultimate strength, 48,000 to 58,000 pounds per square inch. 
 Elastic limit, not less than one-half the ultimate strength. 
 Elongation, 26 per cent. 
 
 Bending test, 180 degrees flat on itself, without fracture on out- 
 side of bent portion. 
 
 SOFT STEEL. 
 
 (10) Ultimate strength, 52,000 to 62,000 pounds per square 
 inch. 
 
 Elastic limit not less than one-half the ultimate strength. 
 Elongation, 25 per cent. 
 
 Bending test, 180 degrees flat on itself, without fracture on out- 
 side of bent portion. 
 
 MEDIUM STEEL, 
 
 (11) Ultimate strength, 60,000 to 70,000 pounds per square 
 inch. 
 
 Elastic limit, not less than one-half the ultimate strength. 
 Elongation, 22 per cent. 
 
 Bending test, 180 degrees to a diameter equal to thickness of 
 piece tested, without fracture on outside of bent portion. 
 
 PIN STEEL. 
 
 (12) Pins made from either of the above-mentioned grades of 
 steel shall, on specimen test-pieces cut at a depth of one inch from 
 surface of finished material, fill the physical requirements of the 
 grade of steel from which it is rolled for ultimate strength, elastic 
 limit, and bending, but the required elongation shall be decreased 
 5 per cent. 
 
334 RESISTANCE TO TENSION. 
 
 EYE-BAR STEEL. 
 
 (13) Eye-bar material, 1J inches and less m thickness, made of 
 either of the above-mentioned grades of steel, shall, on test- 
 pieces cut from finished material, fill the requirements of the 
 grade of steel from which it is rolled. For thicknesses greater than 
 1J inches there will be allowed a reduction in the percentage of 
 elongation of 1 per cent, for each -J of an inch increase of thick- 
 ness, to a minimum of 20 per cent, for medium steel and 22 per 
 cent, for soft steel. 
 
 FULL-SIZE TEST OF STEEL EYE-BARS. 
 
 (14) Full-size test of steel eye-bars shall be required to show 
 not less than 10 per cent, elongation in the body of the bar, and 
 tensile strength not more than 5,000 pounds below the minimum 
 tensile strength required in specimen tests of the grade of steel 
 from which they are rolled. The bars will be required to break 
 in the body, but should a bar break in the head, but develop 10 
 per cent, elongation and the ultimate strength specified it shall 
 not be cause for rejection, provided not more than one-third of 
 the total number of bars tested break in the head ; otherwise the 
 entire lot will be rejected. 
 
 VARIATION IN WEIGHT. 
 
 (15) The variation in cross-section of weight of more than 2J 
 per cent, from that specified will be sufficient cause for rejection, 
 except in the case of sheared plates which will be covered by the 
 following permissible variations: 
 
 a. Plates 12 J pounds per square foot, or heavier, when ordered 
 to weight, shall not average more than 2J per cent, variation 
 above, or 2^ per cent, below the theoretical weight. 
 
 b. Plates under 12J pounds per square foot, when ordered to 
 weight, shall not average a greater variation than the following : 
 
 Up to 75 inches wide, 2J per cent, above, or 2 J per cent, below 
 the theoretical weight. 
 
 75 inches and over, 5 per cent, above, or 5 per cent, below the 
 theoretical weight. 
 
 c. For all plates ordered to gauge, there will be permitted an 
 average excess of weight over that corresponding to the dimen- 
 sions on the order equal in amount to that specified in the fol- 
 lowing table. 
 
RESISTANCE TO TENSION. 
 
 335 
 
 TABLE OF ALLOWANCES FOR OVERWEIGHT FOR 
 RECTANGULAR PLATES WHEN ORDERED TO 
 GAUGE. 
 
 THE WEIGHT OF ONE CUBIC INCH OF ROLLED CTELL IS ASSUMED 
 TO BE .2833 POUND. 
 
 (Plates i" and over in thickness.) 
 
 
 Width of plate. 
 
 Thickness 
 of plate. 
 
 'Up to 57 inches. 
 
 75 in. to 100 in. 
 
 Over 100 inches. 
 
 i inch 
 
 10 per cent. 
 
 14 per cent. 
 
 18 per cent. 
 
 % 
 
 
 8 
 
 
 12 
 
 
 16 
 
 
 f 
 
 
 7 
 
 
 10 
 
 
 13 
 
 
 % 
 
 
 6 
 
 
 8 
 
 
 10 
 
 
 i 
 
 
 5 
 
 
 7 
 
 
 9 
 
 
 % 
 
 
 4J 
 
 
 61 
 
 
 8i 
 
 
 | 
 
 
 4 
 
 
 6 
 
 
 8 
 
 
 Over f 
 
 
 31 
 
 
 5 
 
 
 6i ' 
 
 
 For Ordinary Building Construction the following form of speci- 
 fication for the quality and testing of the steel work is recom- 
 mended : 
 
 Specifications for Structural Steel Work. 
 
 Material and Workmanship. The entire structural frame- 
 work as indicated by the framing plans, or as specified, is to be 
 of wrought steel, of quality hereinafter designated ; all material 
 to be provided and put in place by this contractor unless specific- 
 ally stated to the contrary. All work to be done in a neat and 
 skilful manner, as per detail or specified, and if not detailed or 
 specified, as directed by the superintendent. 
 
 Quality and Material. Steel may be made by either the 
 Bessemer or open-hearth process, but must be uniform in quality, 
 and in no case contain over ^ of one per cent, of phosphorus. 
 
 The grade of steel used (except for rivets) shall fill the following 
 requirements when tested in small specimens: 
 
 [Here should be inserted section (11) of the foregoing specifica- 
 tions.] - 
 
 Inspection. All steel work is to be inspected from the melt to 
 final delivery of finished material on board cars. The inspection 
 
336 RESISTANCE TO TENSION. 
 
 will include surface, mill, and shop inspection by an inspector 
 satisfactory to the architect or his engineer, to whom all reports 
 are to be made. No work shall be delivered until approved and 
 stamped by the inspector. All inspection shall be at the expense 
 of this contractor. 
 
 Tests. [Sections (3) and (4) hi preceding specification to be 
 inserted here.] 
 
 Eye-bars. To determine the strength of the eyes two full-size 
 eye-bars with eyes shall be tested to destruction. These tests 
 shall show [Section 14 in preceding specification to follow.] 
 
 Finish. Finished bars must be free from injurious seams, 
 flaws, or cracks, and have a workmanlike finish. 
 
 Rivet Steel. [Same as section (9), preceding specification.] 
 
 Rivets. The pitch of rivets shall never be less [than 1J" nor 
 more than 6", while the minimum distance from the centre of 
 any rivet to the edge of the shape shall be 1J". No rivets to be 
 used in tension. An excess of 25 per cent, shall be allowed in 
 proportioning field rivets. 
 
 Rivet-holes may be punched or drilled, but must not be 
 more than T y larger than diameter of rivet. 
 
 Rivet-holes must be accurately spaced, as drift-pins will be 
 allowed for assembling only. 
 
 The rivets shah 1 completely fill the holes, with full heads con- 
 centric with the rivets, and in full contact with the surface of 
 the metal. 
 
 Tie-bars, Eye-bars, Screw Ends, Clevises, Sleeve- 
 nuts, and Turn-buckles. 
 
 The best shape for an iron or steel tie is largely determined by 
 the manner in which the tie is to be secured at the ends. If the 
 tie is to be secured by rivets, either channels or angles are gen- 
 erally used, except where only a very small bar is required, in 
 which case a plain rectangular bar may be used. In figuring the 
 strength of such ties, it is customary to use the net sectional area 
 of the tie at the point where the area is most reduced by rivet- 
 holes. 
 
 For figuring the reduction in sectional area by rivet- or bolt- 
 holes, Table XI. of this chapter will be found very convenient. 
 
 Eye-bars. For pin-connected trusses, the ties almost invari- 
 ably consist of eye-bars, i.e., a rectangular bar with an eye at 
 each end. "Eye-bars are now generally made of mild steel, of 
 
RESISTANCE TO TENSION. 337 
 
 an ultimate strength of from 56,000 to 66,000 Ibs. per square 
 inch, the methods of manufacture securing a^more satisfactory 
 and reliable product from that metal than from iron. Steel eye- 
 bars are made by forging or upsetting the eye or head of the bar 
 in a die, and subsequently reheating and annealing the finished 
 bars previous to boring the pin-holes. Wrought-iron bars are 
 made by piling and welding, which is always an unreliable 
 process. 
 
 For economy in dies, the same head or eye is used for two or . 
 three different pin-holes, and for this reason it is often cheaper 
 to use a slightly larger head than would be really necessary for 
 strength, rather than to have a special die made to order. Table 
 V. gives the principal dimensions of the standard sizes of steel 
 eye-bars manufactured by the Edge Moor Bridge Works. Eye- 
 bars made by other companies vary slightly from those dimen- 
 sions and from each other, but not to any great extent. The 
 thickness of the bar for any given width should not be less than 
 the minimum thickness given in the table, because thinner bars 
 are difficult to manufacture, and are liable to buckle in the head 
 when under strain. "The thickness of the bar may be made 
 anything greater than this minimum, but a thickness of two 
 inches for bars six inches wide and under is rarely exceeded." 
 The thicker the bar the greater will be the bending moment on 
 the pin. 
 
 "It is always better to use an eye the diameter of which is 
 about two and one-quarter times the width of the bar. In 
 extreme cases the diameter of the eye may be made two and 
 one-half times the width of the bar, but it is never desirable to 
 exceed this, as the cost and difficulty of manufacture increase 
 rapidly if larger eyes are used. Eye-bars are now made as large 
 as 12X3 inches, with eyes 27 to 30 inches in diameter."* 
 
 Fig. l. Eye-bar with screw ends for sleeve-nut or turn-buckle. 
 
 Eye-bars are sometimes made with upset screw ends and 
 sleeve-nuts, or turn-buckles in the centre, as shown by Fig. 1. * 
 
 * C. W. Bryan, C.E., Engineer of the Edge Moor Bridge Works. 
 
338 
 
 RESISTANCE TO TENSION. 
 
 Light square rods, secured to large pins, are often made with loop 
 eyes, as shown by Figs. 2 and 3, as for such eyes the diameter of 
 the pin is not limited. 
 
 Loop eyes are made by welding, and as satisfactory welds can- 
 
 Fig. 2. Loop-eyes and sleeve-nuts. 
 
 not be generally secured with steel, loop-ended rods are usually 
 made of wrought iron. 
 
 When two single tie-rods balance each other on a pin, to avoid 
 eccentricity one of the rods must either have a clevis on the end, 
 
 Fig. 3. Forked loop. 
 
 as shown at the head of Table VI., or a forked loop, as in Fig. 3. 
 Clevises also afford means of adjusting the length of the tie. 
 
 Sleeve-nuts and Turn-buckles. For adjusting the length of the 
 tie-bars or rods, which pass over a pin, sleeve-nuts or turn- 
 buckles are used, and even when the end of the rod is held by a 
 nut, as in wooden trusses, it is often desirable to place the turn- 
 buckle in the centre of the rod, for adjusting after the truss has 
 seasoned, as it is then generally inconvenient if not impossible 
 to get at the nut. The open turn-buckle, Table VII., possesses 
 the advantages that the ends of the rod are visible, and it may be 
 easily inspected and the position of the rods noted; also, that 
 they may be adjusted by running a bar through the link. Tables 
 VII. and VIII. give dimensions of sleeve-nuts and turn-buckles 
 which, while not the same with all manufacturers, are very 
 ^nearly so. 
 
 Upset Screw Ends. When a screw thread is cut on a rod or 
 bolt, the strength of the rod or bolt is measured by the sectional 
 
RESISTANCE TO TENSION. 339 
 
 area at the root of the thread, and consequently there is a con- 
 siderable excess of metal in the body of the rod that is practically 
 wasted. For long rods, therefore, and especially where there 
 are many of a kind, the end of the rod is enlarged or upset by 
 forging, so that, when the screw is cut, the diameter of the screw 
 at the root of the thread is left a little larger than the body of the 
 rod. Frequent trials with such rods have proven that they will 
 pull apart in tension anywhere else but in the screw; the threads 
 remaining perfect, and the nut turning freely after having been 
 subjected to such a severe test. By this means the net section 
 required in tension is made available with the least excess of 
 material, and no more dead weight is put upon the structure 
 than is actually needed to carry the loads imposed. 
 
 Only the larger machine shops, however, are equipped for up- 
 setting, so that in small towns and cities it is often necessary to 
 send to a considerable distance for upset rods. For this reason 
 it is often cheaper to use a slightly larger rod without upsetting, 
 than to specify the theoretical size with upset ends. Upset rods 
 also require a larger hole to pass through. 
 
 Dimensions of upset screw ends are given in Table IV. 
 
 Tables. The following tables will be found useful when design- 
 ing ties of steel or iron, or for drawing turn-buckles, sleeve-nuts, 
 clevises, etc. The strength of the plain rods in Table III. are 
 based on the sectional area at the root of the thread. 
 
 j* 
 
340 
 
 RESISTANCE TO TENSION. 
 
 TABLE III. STRENGTH OF ROUND RODS OF IRON 
 AND STEEL. 
 
 Diameter in 
 inches. 
 
 NOT UPSET. 
 Allowed strain per sq. in.* 
 
 UPSET. 
 Allowed strain per sq. in.* 
 
 10,0001bs. 
 
 12,5001bs. 
 
 15,000 Ibs. 
 
 10, 000 Ibs. 
 
 12 ,500 Ibs. 
 
 15,000 Ibs. 
 
 1 
 
 268 
 
 335 
 
 402 
 
 491 
 
 613 
 
 736 
 
 % 
 
 452 
 
 565 
 
 678 
 
 767 
 
 958 
 
 1150 
 
 f 
 
 679 
 
 848 
 
 1,018 
 
 1,104 
 
 1,380 
 
 1,656 
 
 % 
 
 929 
 
 1,160 
 
 1,393 
 
 1,503 
 
 1,878 
 
 2,254 
 
 
 1,256 
 
 1,570 
 
 1,884 
 
 1,963 
 
 2,453 
 
 2,944 
 
 %> 
 
 1,618 
 
 2,022 
 
 2,427 
 
 2,485 
 
 3,106 
 
 3,727 
 
 | 
 
 1,963 
 
 2,453 
 
 2,944 
 
 3,068 
 
 3,835 
 
 4,600 
 
 
 3,000 
 
 3,750 
 
 4,500 
 
 4,418 
 
 5,520 
 
 6,627 
 
 I 
 
 4,200 
 
 5,250 
 
 6,300 
 
 6,013 
 
 7,516 
 
 9,020 
 
 
 5,430 
 
 6,780 
 
 8,140 
 
 7,854 
 
 9,815 
 
 11,780 
 
 H 
 
 6,860 
 
 8,570 
 
 10,290 
 
 9,940 
 
 12,425 
 
 14,900 
 
 U 
 
 8,850 
 
 11,060 
 
 13,270 
 
 12,270 
 
 15,330 
 
 18,400 
 
 if 
 
 10,700 
 
 13,370 
 
 16,050 
 
 14,840 
 
 18,550 
 
 22,260 
 
 i* 
 
 12,870 
 
 16,080 
 
 19,300 
 
 17,670 
 
 22,080 
 
 26,500 
 
 if 
 
 15,000 
 
 18,750 
 
 22,500 
 
 20,730 
 
 25,910 
 
 31,090 
 
 if 
 
 17,600 
 
 23,000 
 
 26,400 
 
 24,050 
 
 30,060 
 
 36,070 
 
 H 
 
 20,200 
 
 25,250 
 
 30,300 
 
 27,610 
 
 34,500 
 
 41,400 
 
 2 
 
 22,800 
 
 28,500 
 
 34,200 
 
 31,420 
 
 39,270 
 
 47,130 
 
 2i 
 
 26,400 
 
 33,000 
 
 39,600 
 
 35,460 
 
 44,320 
 
 53,190 
 
 21 
 
 30,000 
 
 37,500 
 
 45,000 
 
 39,760 
 
 49,700 
 
 59,680 
 
 2f 
 
 33,500 
 
 41,870 
 
 50,250 
 
 44,300 
 
 55,370 
 
 66,450 
 
 2J 
 
 37,200 
 
 46,500 
 
 55,800 
 
 49,080 
 
 61,350 
 
 73,620 
 
 2f 
 
 46,400 
 
 58,000 
 
 69,800 
 
 59,390 
 
 74,230 
 
 89,080 
 
 3 
 
 54,000 
 
 67,500 
 
 81,000 
 
 70,680 
 
 88,350 
 
 106,000 
 
 3i 
 
 65,000 
 
 81,250 
 
 97,500 
 
 82,950 
 
 103,690 
 
 124,400 
 
 3* 
 
 75,400 
 
 94,250 
 
 113,100 
 
 96,210 
 
 120,260 
 
 144,300 
 
 3f 
 
 85,600 
 
 107,000 
 
 128,400 
 
 110,450 
 
 138,060 
 
 165,600 
 
 4 
 
 99,000 
 
 123,750 
 
 148,500 
 
 125,660 
 
 157,000 
 
 188,490 
 
 4} 
 
 113,400 
 
 141,700 
 
 170,100 
 
 141,800 
 
 177,250 
 
 212,700 
 
 4-1 
 
 126,000 
 
 157,500 
 
 189,000 
 
 159,000 
 
 198,750 
 
 238,500 
 
 4J 
 
 141,800 
 
 177,250 
 
 212,700 
 
 177,200 
 
 221,500 
 
 265,800 
 
 5 
 
 157,600 
 
 197,000 
 
 236,400 
 
 196,300 
 
 245,370 
 
 298,400 
 
 51 
 
 175,900 
 
 219,870 
 
 263,850 
 
 216,400 
 
 270,500 
 
 324,000 
 
 5* 
 
 192,600 
 
 240,750 
 
 288,900 
 
 237,500 
 
 296,800 
 
 356,000 
 
 5f 
 
 212,300 
 
 265,370 
 
 318,400 
 
 259,600 
 
 324,500 
 
 389,000 
 
 6 
 
 231,000 
 
 288,750 
 
 346,500 
 
 282,700 
 
 353,300 
 
 424,000 
 
 * For first-class work and material 12,500 Ibs. may be allowed for iron 
 and 15,000 Ibs. for steel. If the rods are to be welded or are made by an 
 ordinary blacksmith use 10,000 Ibs. for iron and 12,500 Ibs. for steel. 
 
RESISTANCE TO TENSION. 
 
 341 
 
 TABLE IV. STANDARD PROPORTIONS OF UPSET 
 SCREW-ENDS FOR ROUND AND SQUARE BARS. 
 
 "2 
 
 'w 
 
 ROUND BARS. 
 
 SQUARE BARS. 
 
 la 
 
 042 
 
 o 
 
 tfl 
 
 "c8 
 
 -1 
 
 P 
 
 -1-3 
 
 -p 
 
 4 
 
 |, > 
 
 o * 
 
 a . 
 
 ^li 
 
 j 
 
 'fftsi 
 
 a . 
 
 ^^ 
 
 .s 
 
 "^ ra 
 
 f-l ri 
 
 4H fl 
 
 2 
 
 ft 
 
 a--2 
 
 <' 
 
 0) QJ 
 
 
 
 iG ^^ 
 
 *O Q< 
 
 5$ 
 
 03^ 
 
 S 
 
 OJ 02 *H 
 
 oo> 
 
 OQ 1 ^ 
 
 S 
 
 <U SQ SH 
 
 1^ 
 
 S^ 
 
 "0*0 
 
 m 
 
 'o 'o ^ 
 
 05 * 
 * 2 
 
 "o-g 
 
 02 
 
 "3*5 o 
 
 ~ 
 
 |i 
 
 S o 
 
 o3 
 
 111 
 
 1.1 
 
 
 J 
 
 1 i'S 
 
 1 
 
 c3 
 
 5 
 
 CS Or 
 
 s h 
 
 1 
 
 
 oj 
 
 3 
 
 6 S 
 
 H 
 
 I 03 ' 
 
 nches 
 
 nches 
 
 Inches. 
 
 No. 
 
 3 er cent 
 
 nches 
 
 Inches. 
 
 No. 
 
 5 er cent 
 
 jL 
 
 f 
 
 0.620 
 
 10 
 
 54 
 
 3. 
 4 
 
 0.620 
 
 10 
 
 21 
 
 % 
 
 i 
 
 0.620 
 
 10 
 
 21 
 
 
 0.731 
 
 9 
 
 33 
 
 5 
 
 7 
 
 0.731 
 
 9 
 
 37 
 
 1 
 
 0.837 
 
 8 
 
 41 
 
 % 
 
 Ij 
 
 0.837 
 
 8 
 
 48 
 
 1 
 
 0.837 
 
 8 
 
 17 
 
 3 
 
 1 
 
 0.837 
 
 8 
 
 25 
 
 H 
 
 0.940 
 
 7 
 
 23 
 
 % 
 
 H 
 
 0.940 
 
 7 
 
 34 
 
 
 1.065 
 
 7 
 
 35 
 
 
 IT 
 
 1.065 
 
 7 
 
 48 
 
 if 
 
 1.160 
 
 6 
 
 38 
 
 % 
 
 H 
 
 1.065 
 
 7 
 
 29 
 
 if 
 
 1.160 
 
 6 
 
 20 
 
 1 
 
 I 3 
 
 1 . 160 
 
 6 
 
 35 
 
 H 
 
 1.284 
 
 6 
 
 29 
 
 
 l| 
 
 1.160 
 
 6 
 
 19 
 
 If 
 
 1.389 
 
 5i 
 
 34 
 
 H 
 
 If 
 
 1.284 
 1.284 
 
 6 
 6 
 
 30 
 17 
 
 If 
 If' 
 
 1.389 
 
 1.490 
 
 5 2 
 
 20 
 24 
 
 H 
 
 If 
 If 
 
 1.389 
 1.490 
 
 5 2 
 
 23 
 
 29 
 
 l| 
 
 1.615 
 1.615 
 
 5 
 5 
 
 31 
 19 
 
 11 
 
 
 1.490 
 
 5 
 
 18 
 
 2 
 
 1.712 
 
 44- 
 
 22 
 
 * 8 
 
 l| 
 
 1.615 
 
 5 
 
 26 
 
 24 
 
 1.837 
 
 41 
 
 28 
 
 H 
 
 2 
 
 1.712 
 
 4-^ 
 
 30 
 
 2 i 
 
 1.837 
 
 4f 
 
 18 
 
 IX 
 
 2 
 
 1.712 
 
 4 I 
 
 20 
 
 2 i 
 
 1.962 
 
 4J 
 
 24 
 
 14 
 
 2* 
 
 1.837 
 
 41 
 
 28 
 
 2f 
 
 2.087 
 
 4J 
 
 30 
 
 --8 
 1% 
 
 ** 8 
 
 2| 
 
 1.837 
 
 4J 
 
 18 
 
 2f 
 
 2.087 
 
 4i 
 
 20 
 
 If 
 
 2i 
 
 1.962 
 1.962 
 
 4i 
 4i 
 
 26 
 17 
 
 2* 
 
 2| 
 
 2.175 
 2.300 
 
 4 
 4 
 
 21 
 26 
 
 & 
 
 If 
 
 2.087 
 2.175 
 
 4i 
 4 
 
 24 
 26 
 
 2f 
 2} 
 
 2.300 
 2.425 
 
 4 
 4 
 
 18 
 23 
 
 2 
 
 2| 
 
 2.17, 
 2.300 
 
 4 
 4 
 
 18 
 24 
 
 8 
 
 2.550 
 2.550 
 
 4 
 4 
 
 28 
 20 
 
 2J 
 2% 
 
 2| 
 2| 
 
 2.300 
 
 2.425 
 
 4 
 4 
 
 17 
 23 
 
 3 
 
 3i 
 
 2.629 
 2.754 
 
 g 
 
 20 
 24 
 
342 KESISTANCE TO TENSION. 
 
 TABLE IV. UPSET SCREW-ENDS (conceded). 
 
 1 
 
 ROUND RARS. 
 
 SQUARE BARS. 
 
 o . 
 
 11 
 
 1 
 
 " * 
 
 | 
 
 11 
 
 
 a^ 
 
 ri 
 
 |, . 
 
 O QJ 
 
 a 
 
 || 
 
 
 1 1 ^ 
 
 a 
 
 1 s 
 
 J3 
 
 1 1| 
 
 *s | 
 
 || 
 
 II 
 
 I 
 
 * 2, 
 
 "8 | 
 
 S-3 
 
 
 
 * fe 
 
 ij 
 
 
 "0*0 
 
 05 
 1 
 
 "8^1 
 
 1 2 
 
 "o'o 
 
 -3 
 
 "8*8 
 
 
 > '" 
 
 il 
 
 
 1 
 
 c3 
 0) 
 
 1 * 
 
 II 
 
 
 
 li 
 
 3 
 
 B 
 
 3* 
 
 H 
 
 
 3 
 
 
 1 
 
 .1" 
 
 Inches 
 
 Inches 
 
 Inches 
 
 No. 
 
 Per cent 
 
 Inches 
 
 Inches 
 
 No. 
 
 Per cent 
 
 2} 
 
 2} 
 
 2.550 
 
 4 
 
 28 
 
 34 
 
 2.754 
 
 34 
 
 18 
 
 
 2J 
 
 2.550 
 
 4 
 
 22 
 
 3i 
 
 2.879 
 
 34 
 
 22 
 
 2f 
 
 3 
 
 2.629 
 
 4 
 
 23 
 
 31 
 
 3.004 
 
 34 
 
 26 
 
 2% 
 
 31 
 
 2.754 
 
 34 
 
 28 
 
 3| 
 
 3.004 
 
 
 19 
 
 24. 
 
 31 
 
 2.754 
 
 3i 
 
 21 
 
 34 
 
 3.100 
 
 3J 
 
 21 
 
 2^6 
 
 3i 
 
 2.879 
 
 34 
 
 26 
 
 3f 
 
 3.225 
 
 3i 
 
 24 
 
 2f 
 
 3* 
 
 2.879 
 
 34 
 
 20 
 
 31 
 
 3 . 225 
 
 3i 
 
 19 
 
 2% 
 
 3f 
 
 3.004 
 
 34 
 
 25 
 
 3f 
 
 3.317 
 
 3 
 
 20 
 
 2f 
 
 3f 
 
 3.004 
 
 34 
 
 19 
 
 3f 
 
 3.442 
 
 3 
 
 23 
 
 2% 
 
 34 
 
 3.100 
 
 3i 
 
 22 
 
 3* 
 
 3.442 
 
 3 
 
 18 
 
 2J 
 
 3f 
 
 3.225 
 
 3J 
 
 26 
 
 4 
 
 3.567 
 
 3 
 
 21 
 
 2% 
 
 3f 
 
 3.225 
 
 3i 
 
 21 
 
 4i 
 
 3.692 
 
 3 
 
 24 
 
 3 
 
 3f 
 
 3.317 
 
 3 
 
 22 
 
 4J 
 
 3.692 
 
 3 
 
 19 
 
 3* 
 
 
 3.442 
 
 3 
 
 21 
 
 4f 
 
 3.923 
 
 2 1 
 
 24 
 
 3* 
 
 4 
 
 3.567 
 
 3 
 
 20 
 
 41 
 
 4.028 
 
 2$ 
 
 21 
 
 3f 
 
 41 
 
 3.692 
 
 3 
 
 20 
 
 4f 
 
 4.153 
 
 2J 
 
 19 
 
 3i 
 
 4i 
 
 3.798 
 
 21 
 
 18 
 
 
 
 
 
 3f 
 
 44 
 
 4.028 
 
 2f 
 
 23 
 
 
 
 
 
 3f 
 
 4f 
 
 4.153 
 
 2J 
 
 23 
 
 
 
 
 
 
 4J 
 
 4.255 
 
 
 21 
 
 
 
 
 
 REMARKS. As upsetting reduces the strength of iron, bars having the 
 same diameter at root of 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 metal in the upset screw-ends over that in the bar. 
 The above table is the result of numerous tests on finished bars made 
 
 at the Keystone Bridge Company's Works in Pittsburgh, and gives pro- 
 portions that will cause the bar to break in the body in preference to the 
 
 upset end. 
 
 The screw-threads in above table are the Franklin Institute standard. 
 
 To make one upset end for five inches length of thread allow six inches 
 length of rod additional. 
 
RESISTANCE TO TENSION. 
 
 343 
 
 TABLE V. STEEL EYE-BARS. 
 EDGE MOOR BRIDGE WORKS' STANDARD. 
 
 A 
 
 T 
 
 E 
 
 j) 
 
 Sectional 
 
 
 Width 
 of body 
 of bar. 
 
 Minimum 
 thickness 
 of bar. 
 
 Diameter 
 of head of 
 bar. 
 
 Diameter 
 of largest 
 pin-hole. 
 
 area of the 
 head on line 
 S-S in excess 
 of that in 
 
 Safe strength 
 at 15,000 
 Ibs. per 
 sq. in. 
 
 
 
 
 
 body of bar. 
 
 
 Inches. 
 
 Inches. 
 
 Inches. 
 
 Inches. 
 
 Per cent. 
 
 Pounds. 
 
 2 
 
 4 
 
 44 
 
 H 
 
 33 
 
 15,000 
 
 2 
 
 4 
 
 54 
 
 *f 
 
 33 
 
 15,000 
 
 21 
 
 f 
 
 54 
 
 2J 
 
 33 
 
 23,430 
 
 24 
 
 f 
 
 64 
 
 3J 
 
 33 
 
 23,430 
 
 3 
 
 I 
 
 64 
 
 24 
 
 33 
 
 33,750 
 
 3 
 
 | 
 
 8 
 
 4 
 
 33 
 
 33,750 
 
 3 
 
 
 9 
 
 5 
 
 33 
 
 33,750 
 
 4 
 
 I 
 
 94 
 
 4i 
 
 33 
 
 45,000 
 
 4 
 
 f 
 
 104 
 
 5i 
 
 33 
 
 45,000 
 
 4 
 
 f 
 
 114 
 
 6i 
 
 33' 
 
 45,000 
 
 5 
 
 | 
 
 114 
 
 4f 
 
 37 
 
 56,250 
 
 5 
 
 
 124 
 
 5| 
 
 37 
 
 56,250 
 
 5 
 
 l 
 
 13 
 
 6i 
 
 37 
 
 75,000 
 
 5 
 
 l 
 
 14 
 
 n 
 
 37 
 
 75,000 
 
 6 
 
 | 
 
 134 
 
 5i 
 
 37 
 
 78,750 
 
 6 
 
 f 
 
 144 
 
 6i 
 
 37 
 
 78,750 
 
 6 
 
 
 154 
 
 71 
 
 37 
 
 90,000 
 
 7 
 
 % 
 
 154 
 
 5f 
 
 40 
 
 98,400 
 
 7 
 
 % 
 
 17 
 
 7i 
 
 40 
 
 98,400 
 
 8 
 
 1 
 
 17 
 
 5f 
 
 40 
 
 120,000 
 
 8 
 
 1 
 
 18 
 
 6| 
 
 40 
 
 120,000 
 
 8 
 
 1 
 
 19 
 
 8 
 
 40 
 
 120,000 
 
 9 
 
 H 
 
 194 
 
 7 
 
 40 
 
 151,875 
 
 9 
 
 ij 
 
 2H 
 
 9 
 
 40 
 
 151,875 
 
 9 
 
 if 
 
 224 
 
 10 
 
 
 
 168,750 
 
 10 
 
 ~ 4 
 
 If 
 
 244 
 
 10| 
 
 
 206,250 
 
 The size of head given is the size of die. The size of finished head will 
 overrun this about J4" '. Eye-bars are hydraulic forged without the addi- 
 
 tion of extraneous metal and without buckles or welds. The heads on 
 
 eye-bars are finished of the same thickness "T" as body of bar. 
 
344 
 
 RESISTANCE TO TENSION. 
 
 TABLE VI. STANDARD CLEVIS NUTS. 
 THE CARNEGIE STEEL COMPANY, LIMITED. 
 
 (Distance H can be made to suit connections.) 
 
 Diam- 
 
 eter of 
 
 round 
 
 bar. 
 
 A 
 
 Upset 
 screw 
 end for 
 round 
 bar. 
 
 Side of 
 quare 
 bar. 
 
 A 
 
 Upset 
 screw 
 end for 
 square 
 bar. 
 
 Diam- 
 
 eter of 
 
 eye. 
 
 C 
 
 L'gth 
 
 of 
 fork. 
 
 L'gth 
 
 of 
 thread 
 
 Thick- 
 ness of 
 bar in 
 fork. 
 
 Width 
 of bar 
 
 fork. 
 
 It* 
 
 If 1 " 
 
 ! l 
 
 if 6 
 
 14 
 
 if 
 
 1% 
 if 
 
 2| 
 
 2.% 
 
 21 
 
 2% 
 
 2f 
 
 2J 6 
 2% 
 
 2157 
 
 2% 
 2J 
 2% 
 2} 
 
 I? 11 
 
 
 31 
 3| 
 
 3f 
 3| 
 
 64 
 
 64 
 
 7 
 7 
 7 
 8 
 8 
 8 
 8 
 8 
 8 
 
 84 
 
 84 
 
 9* 
 9 
 9 
 9 
 
 21 
 
 3% 
 3% 
 
 
 3* 
 
 3% 
 3% 
 3.V 
 
 3 
 
 35 
 
 4% 
 4% 
 4% 
 4% 
 4% 
 4% 
 
 51 
 51 
 
 21 
 
 2i; 
 
 2] 
 2i 
 
 2f 
 2f 
 2f 
 2f 
 3i 
 3i 
 
 3f 
 3f 
 3f 
 3f 
 3f 
 3f 
 3f 
 
 * This clevis used for all smaller bars. 
 
RESISTANCE TO TENSION. 
 TABLE VII. TURNBUCKLES. 
 
 345 
 
 D. Size = diameter of screw. 
 
 A. Length in clear between heads. 
 
 B. Length of tapped heads =1D. 
 
 C. Total length of buckle. 
 
 L. Total length of buckle and stub ends when open. 
 
 Size 
 D 
 
 A 
 
 B 
 
 C 
 
 L 
 
 Size 
 D 
 
 A 
 
 B 
 
 C 
 
 L 
 
 f 
 
 6 
 
 Q/ 
 % 
 
 n 
 
 22 
 
 1| 
 
 6 
 
 2f 
 
 lli 
 
 28 
 
 % 
 
 6 
 
 2 %2 
 
 7% 
 
 22 
 
 if 
 
 6 
 
 2% 
 
 HI 
 
 29 
 
 4 
 
 6 
 
 3 
 
 7. 
 
 7* 
 
 22 
 
 2 
 
 6 
 
 3 
 
 12 
 
 29 
 
 % 
 
 6 
 
 2 %2 
 
 7% 
 
 22 
 
 2* 
 
 6 
 
 3% 
 
 12f 
 
 29 
 
 ;t 
 
 6 
 
 % 
 
 71- 
 
 22 
 
 2J 
 
 6 
 
 3f 
 
 12} 
 
 30 
 
 i 
 
 6 
 
 H 
 
 Si 
 
 23 
 
 2f 
 
 6 
 
 3% 
 
 13i 
 
 31 
 
 1 
 
 6 
 
 1% 
 
 8f 
 
 24 
 
 2i 
 
 6 
 
 3f 
 
 13J 
 
 32 
 
 
 6 
 
 14 
 
 9 
 
 25 
 
 2f 
 
 6 
 
 3 
 
 ia| 
 
 32 
 
 n 
 
 6 
 
 1% 
 
 9f 
 
 25 
 
 2f 
 
 6 
 
 4* 
 
 14J 
 
 33 
 
 ii 
 
 6 
 
 if 
 
 9f 
 
 26 
 
 2| 
 
 6 ' 
 
 4* 
 
 141 
 
 33 
 
 it 
 
 6 
 
 2^6 
 
 ioi 
 
 27 
 
 3 
 
 6 
 
 4* 
 
 15 
 
 34 
 
 14 
 
 6 
 
 2i 
 
 104 
 
 27 
 
 si 
 
 6 
 
 4| 
 
 15| 
 
 36 
 
 If 
 
 6 
 
 2 
 
 W| 
 
 28 
 
 34 
 
 6 
 
 5-i- 
 
 16J 
 
 37 
 
 Lengths given above are standard for bridge, roof, and ordi- 
 nary truss buckles. 
 
 They have a guaranteed strength of 60,000 pounds per square 
 inch of section of bolt at bottom of thread. Stub bolt ends are 
 made of good bridge iron having tensile strength of 50,000 pounds 
 per square inch. 
 
 Open buckles of this form can be adjusted with a bar, hook, or 
 wrench, and have the great advantage of showing the ends of the 
 bolts, so that inspectors can see that they have a good hold of 
 thread and do not butt together. 
 
346 
 
 RESISTANCE TO TENSION. 
 
 TABLE VIII. RIGHT AND LEFT NUTS OR SLEEVE- 
 NUTS. 
 
 DIMENSIONS OF NUTS FROM EDGE MOOR BRIDGE WORKS' 
 STANDARD. 
 
 B 
 
 Diam. 
 of 
 screw. 
 
 G 
 
 L'gth 
 of 
 upset. 
 
 A 
 
 Diameter 
 of 
 bar. 
 
 A 
 
 Side of 
 square 
 bar. 
 
 L 
 Length 
 of 
 nut. 
 
 T 
 
 L'gth 
 of 
 thr'd. 
 
 W 
 Dia. 
 of 
 hex. 
 
 Weight of 
 
 One 
 
 nut. 
 
 One nut 
 and two 
 screw- 
 ends. 
 
 Ins. 
 
 Ins. 
 
 Ins. 
 
 Ins. 
 
 Ins. 
 
 Ins. 
 
 Ins. 
 
 Lbs. 
 
 Lbs. 
 
 
 
 
 
 ord.l'ths. 
 
 
 
 
 
 t 
 
 4} 
 
 i 
 
 % 
 
 6 
 
 1% 
 
 II 
 
 lf 
 
 4i 
 
 1 
 
 4i 
 
 %and f 
 
 | and% 
 
 6 
 
 1% 
 
 If 
 
 lf 
 
 41 
 
 H 
 
 41 
 
 % 
 
 f 
 
 6* 
 
 If 
 
 2 
 
 3 
 
 ?i 
 
 H 
 
 4f 
 
 t " % 
 
 % 
 
 6-1 
 
 If 
 
 2 
 
 3 
 
 74 
 
 if 
 
 5 
 
 1 " l.Ve 
 
 1 " % 
 
 7 
 
 H 
 
 2| 
 
 4f 
 
 111 
 
 H 
 
 5 
 
 H "1% 
 
 1 
 
 7 
 
 I* 
 
 2! 
 
 4f 
 
 llf 
 
 lf 
 
 si 
 
 H 
 
 1/Y 6 "H 
 
 ri 
 
 2,Y 6 
 
 2f 
 
 6f 
 
 16f 
 
 If 
 
 5} 
 
 1% "1! 
 
 1% 
 
 7i 
 
 2>tf, 
 
 2f 
 
 6f 
 
 m 
 
 H 
 
 5} 
 
 1% 
 
 1* "1 
 
 8 
 
 2^6 
 
 3i 
 
 9i 
 
 23} 
 
 2 
 
 51 
 
 H "1% 
 
 If 
 
 8 
 
 2% 
 
 34 
 
 0i 
 
 23-} 
 
 2* 
 
 5f 
 
 if " 1% 
 
 1% "1J 
 
 8* 
 
 24 
 
 3i- 
 
 12| 
 
 31} 
 
 2} 
 
 i 
 
 if "l% 
 
 1% 
 
 8i 
 
 2i 
 
 3i 
 
 12J 
 
 31* 
 
 2f 
 
 6 
 
 l| 
 
 If "1% 
 
 9 
 
 2f 
 
 3J 
 
 16| 
 
 41J 
 
 2} 
 
 6 
 
 IS "2 
 
 If 
 
 9 
 
 2| 
 
 3f 
 
 16f 
 
 41f 
 
 H 
 
 6* 
 
 2Yo "2i 
 
 1% "If 
 
 9i 
 
 2^6 
 
 41 
 
 21} 
 
 53i 
 
 2f 
 
 64 
 
 2 
 
 1% 
 
 01 
 
 2% 
 
 4i 
 
 2ii 
 
 53} 
 
 2 
 
 6* 
 
 2i "2% 
 
 2 "2tf 
 
 10 
 
 3% 
 
 4i 
 
 26} 
 
 66-} 
 
 3 
 
 6J 
 
 2-| 
 
 2J 
 
 10 
 
 3% 
 
 4f 
 
 26* 
 
 66} 
 
 3* 
 
 6f 
 
 2% "2| 
 
 2. 5 /6 
 
 10i 
 
 3f 
 
 5 
 
 32^ 
 
 81 
 
 3} 
 
 7 
 
 2% 
 
 2J 
 
 11 
 
 3f 
 
 P 
 
 3Si 
 
 97J 
 
 3J 
 
 7i 
 
 3 
 
 2% 
 
 11} 
 
 3% 
 
 Ml 
 
 45 
 
 116 
 
 4 
 
 74 
 
 3i 
 
 2| 
 
 12 
 
 4^6 
 
 6* 
 
 53J 
 
 138 
 
 
 
 
 
 ext. rths. 
 
 
 
 
 
 H 
 
 4f 
 
 1 " % 
 
 % 
 
 12 
 
 2| 
 
 2 
 
 
 
 ji 
 
 
 
 % 
 
 f 
 
 8i 
 
 If 
 
 2 
 
 4 
 
 9f 
 
 u 
 
 4f 
 
 1 " % 
 
 % 
 
 8i- 
 
 if 
 
 2 
 
 4 
 
 9f 
 
 if 
 
 5 
 
 1 " 1% 
 
 1 " % 
 
 9 
 
 if 
 
 2f 
 
 6i 
 
 15} 
 
 H 
 
 5 
 
 li "IX 
 
 1 
 
 9 
 
 *| 
 
 2f 
 
 
 
 151 
 
 it 
 
 51 
 
 H 
 
 IX "1-1- 
 
 9* 
 
 2% 
 
 2f 
 
 8f 
 
 21* 
 
 if 
 
 5} 
 
 IM "if 
 
 1% 
 
 9J 
 
 2% 
 
 2| 
 
 Sf 
 
 21} 
 
 w 
 
 5} 
 
 1% 
 
 H "l>f G 
 
 10 
 
 2^6 
 
 3i 
 
 12J 
 
 29} 
 
 2 
 
 5} 
 
 H " 1% 
 
 If 
 
 10 
 
 2% 
 
 3| 
 
 12} 
 
 29J 
 
 Length of upset ends for use with right and left 
 inch shorter than the dimensions given in column 
 
 nuts may be made one 
 G-' above. 
 
RESISTANCE TO TENSION. 
 
 347 
 
 TABLE IX. SAFE STRENGTH OF FLAT ROLLED BARS 
 
 (Computed at 10,000 Ibs. per square inch.) * 
 
 Thickness 
 in inches. 
 
 Width in inches. 
 
 \" 
 
 Ibs. 
 
 H" 
 
 Ibs. 
 
 11" 
 
 If" 
 
 2" 
 
 Ibs. 
 
 2i" 
 
 Ibs. 
 
 2J" 
 
 2|" 
 
 3" 
 
 3i" 
 
 
 ibs. 
 
 Ibs. 
 
 Ibs. 
 
 Ibs. 
 
 Ibs. 
 
 Ibs. 
 
 VlO 
 
 300 
 
 780 
 
 940 
 
 1,090 
 
 1,250 
 
 1,410 
 
 1,560 
 
 1,720 
 
 1,880 
 
 2,030 
 
 * 
 
 1,250 
 
 1,560 
 
 ' 1,880 
 
 2,190 
 
 2,500 
 
 2,810 
 
 3,130 
 
 3,440 
 
 3,750 
 
 4,060 
 
 3 /10 
 
 1,880 
 
 2,340 
 
 2,810 
 
 3,280 
 
 3,750 
 
 4,220 
 
 4,690 
 
 5,160 
 
 5,630 
 
 6,090 
 
 i 
 
 2,500 
 
 3,130 
 
 3,750 
 
 4,380 
 
 5,000 
 
 5,630 
 
 6,250 
 
 6,880 
 
 7,500 
 
 8,130 
 
 %<> 
 
 3,130 
 
 3,910 
 
 4,690 
 
 5,470 
 
 6,250 
 
 7,030 
 
 7,810 
 
 8,590 
 
 9,380 
 
 10,200 
 
 1 
 
 3,750 
 
 4,690 
 
 5,630 
 
 6,560 
 
 7,500 
 
 8,440 
 
 9,380 
 
 10,300 
 
 11,300 
 
 12,200 
 
 7 /16 
 
 4,380 
 
 5,470 
 
 6,560 
 
 7,660 
 
 8,750 
 
 9,840 
 
 10,900 
 
 12,000 
 
 13,100 
 
 14,200 
 
 i 
 
 5,000 
 
 6,250 
 
 7,500 
 
 8,750 
 
 10,000 
 
 11,300 
 
 12,500 
 
 13,800 
 
 15,000 
 
 16,300' 
 
 9 /10 
 
 5,630 
 
 7,030 
 
 8,440 
 
 9,840 
 
 11,300 
 
 12,700 
 
 14,100 
 
 15,500 
 
 16,900 
 
 18,300 
 
 1 
 
 6,250 
 
 7,810 
 
 9,380 
 
 10,900 
 
 12,500 
 
 14,100 
 
 15,600 
 
 17,200 
 
 18,800 
 
 20,300 
 
 iVlG 
 
 6,880 
 
 8,590 
 
 10,300 
 
 12,000 
 
 13.800 
 
 15,500 
 
 17,200 
 
 18,900 
 
 20,600 
 
 22,300 
 
 f 
 
 7,500 
 
 9,380 
 
 11,300 
 
 13,100 
 
 15,000 
 
 16,900 
 
 18,800 
 
 20,600 
 
 22,500 
 
 24,400 
 
 13 /16 
 
 8,130 
 
 10,200 
 
 12,200 
 
 14,200 
 
 16,300 
 
 18,300 
 
 20,300 
 
 "22,300 
 
 24,400 
 
 26,400 
 
 I 
 
 8,750 
 
 10,900 
 
 13,100 
 
 15,300 
 
 17,500 
 
 19,700 
 
 21,900 
 
 24,100 
 
 26,300 
 
 28,400 
 
 15 /16 
 
 9,380 
 
 11,700 
 
 14,100 
 
 16,400 
 
 18,800 
 
 21,100 
 
 23,400 
 
 25,800 
 
 28,100 
 
 30,500 
 
 1 
 
 10,000 
 
 12,500 
 
 15,000 
 
 17,500 
 
 20,000 
 
 22,500 
 
 25,000 
 
 27,500 
 
 30,000 
 
 32,500 
 
 1%6 
 
 10,600 
 
 13,300 
 
 15,900 
 
 18,600 
 
 21,300 
 
 23,900 
 
 26,600 
 
 29,200 
 
 31,900 
 
 34,500 
 
 14 
 
 11,300 
 
 14,100 
 
 16,900 
 
 19,700 
 
 22,500 
 
 25,300 
 
 28,100 
 
 30,900 
 
 33,800 
 
 36,600 
 
 Ww 
 
 11,900 
 
 14,800 
 
 17,800 
 
 20,800 
 
 23,800 
 
 26,700 
 
 29,700 
 
 32,700 
 
 35,600 
 
 38,600 
 
 u 
 
 12,500 
 
 15,600 
 
 18,800 
 
 21,900 
 
 25,000 
 
 28,100 
 
 31,300 
 
 34,400 
 
 37,500 
 
 40,600 
 
 11 
 
 13,800 
 
 17,200 
 
 20,600 
 
 24,100 
 
 27,500 
 
 30,900 
 
 34,400 
 
 37,800 
 
 41,300 
 
 44,700 
 
 n 
 
 15,000 
 
 18,800 
 
 22,500 
 
 26,300 
 
 30,000 
 
 33,800 
 
 37,500 
 
 41,300 
 
 45,000 
 
 48,800 
 
 n 
 
 16,300 
 
 20,300 
 
 24,400 
 
 28,400 
 
 32,500 
 
 36,600 
 
 40,600 
 
 44,700 
 
 48,800 
 
 52,800 
 
 H 
 
 17,500 
 
 21,900 
 
 26,300 
 
 30,600 
 
 35,000 
 
 39,400 
 
 43,800 
 
 48,100 
 
 52,500 
 
 56,900 
 
 H 
 
 18,800 
 
 23,400 
 
 28,100 
 
 32,800 
 
 37,500 
 
 42,200 
 
 46,900 
 
 51,600 
 
 56,300 
 
 60,900 
 
 2 
 
 20,000 
 
 25,000 
 
 30,000 
 
 35,000 
 
 40,000 
 
 45,000 
 
 50,000 
 
 55,000 
 
 60,000 
 
 65,000 
 
 * For unit stresses of 12,000, 12,500, and 15,000 Ibs. increase by , i, and \ 
 r working strength, of wrought iron and steel, see pages 324 and 331. 
 
348 
 
 RESISTANCE TO TENSION. 
 
 TABLE IX. SAFE STRENGTH OF FL AT ROLLED BARS 
 
 (concluded.) 
 (Computed at 10,000 Ibs. per square inch.) * 
 
 Thickness 
 in inches. 
 
 Width in inches. 
 
 3J" 
 
 3f" 
 
 4" 
 
 4i" 
 
 44" 
 Ibs. 
 
 43." 
 
 5" 
 
 5V' 
 
 6" 
 
 aj" 
 
 Ibs. 
 
 Ibs. 
 
 Ibs. 
 
 Ibs. 
 
 Ibs. 
 
 Ibs. 
 
 Ibs. 
 
 Ibs. 
 
 Ibs. 
 
 Me 
 
 2,190 
 
 2,340 
 
 2,500 
 
 2,660 
 
 2,810 
 
 2,970 
 
 3,130 
 
 3,440 
 
 3,750 
 
 4,060 
 
 * 
 
 4,380 
 
 4,690 
 
 5,000 
 
 5,310 
 
 5,630 
 
 5,940 
 
 6,250 
 
 6,880 
 
 7,500 
 
 8,130 
 
 %i 
 
 6,560 
 
 7,030 
 
 7,500 
 
 7,970 
 
 8,440 
 
 8,910 
 
 9,380 
 
 10,300 
 
 11,300 
 
 12,200 
 
 * 
 
 8,750 
 
 9,380 
 
 10,000 
 
 10,600 
 
 11,300 
 
 11,900 
 
 12,500 
 
 13,800 
 
 15,000 
 
 16,300 
 
 5 /4e 
 
 10,900 
 
 11,700 
 
 12,500 
 
 13,300 
 
 14,100 
 
 14,800 
 
 15,600 
 
 17,200 
 
 18,800 
 
 20,300 
 
 1 
 
 13,100 
 
 14,100 
 
 15,000 
 
 1"5,900 
 
 16,900 
 
 17,800 
 
 18,800 
 
 20,600 
 
 22,500 
 
 24,400 
 
 Tie 
 
 15,300 
 
 16,400 
 
 17,500 
 
 18,600 
 
 19,700 
 
 20,800 
 
 21,900 
 
 24,100 
 
 26,300 
 
 28,400 
 
 * 
 
 17,500 
 
 18,800 
 
 20,000 
 
 21,300 
 
 22,500 
 
 23,800 
 
 25,000 
 
 27,500 
 
 30,000 
 
 32,500 
 
 9 /16 
 
 19,700 
 
 21,100 
 
 22,500 
 
 23,900 
 
 25,300 
 
 26,700 
 
 28,100 
 
 30,900 
 
 33,800 
 
 36,600 
 
 1 
 
 21,900 
 
 23,400 
 
 25,000 
 
 26,600 
 
 28,100 
 
 29,700 
 
 31,300 
 
 34,400 
 
 37,500 
 
 40,600 
 
 % 
 
 24,100 
 
 25,800 
 
 27,500 
 
 29,200 
 
 30,900 
 
 32,700 
 
 34,400 
 
 37,800 
 
 41,300 
 
 44,700 
 
 5 
 
 26,300 
 
 28,100 
 
 30,000 
 
 31,900 
 
 33,800 
 
 35,600 
 
 37,500 
 
 41,300 
 
 45,000 
 
 48,800 
 
 18 /46 
 
 28,400 
 
 30,500 
 
 32,500 
 
 34,500 
 
 36,600 
 
 38,600 
 
 40,600 
 
 44,700 
 
 48,800 
 
 52,800 
 
 1 
 
 30,600 
 
 32,800 
 
 35,000 
 
 37,200 
 
 39,400 
 
 41,600 
 
 43,800 
 
 48,100 
 
 52,500 
 
 56,900 
 
 15 /ie 
 
 32,800 
 
 35,200 
 
 37,500 
 
 39,800 
 
 42,200 
 
 44,500 
 
 46,900 
 
 51,600 
 
 56,300 
 
 60,900 
 
 1 
 
 35,000 
 
 37,500 
 
 40,000 
 
 42,500 
 
 45,000 
 
 47,500 
 
 50,000 
 
 55,000 
 
 60,000 
 
 65,000 
 
 1%6 
 
 37,200 
 
 39,800 
 
 42,500 
 
 45,200 
 
 47,800 
 
 50,500 
 
 53,100 
 
 58,400 
 
 63,800 
 
 69,100 
 
 H 
 
 39,400 
 
 42,200 
 
 45,000 
 
 47,800 
 
 50,600 
 
 53,400 
 
 56,300 
 
 61,900 
 
 67,500 
 
 73,100 
 
 1%6 
 
 41,600 
 
 44,500 
 
 47,500 
 
 50,500 
 
 53,400 
 
 56,400 
 
 59,400 
 
 65,300 
 
 71,300 
 
 77,200 
 
 II 
 
 43,800 
 
 46,900 
 
 50,000 
 
 53,100 
 
 56,300 
 
 59,400 
 
 62,500 
 
 68,800 
 
 75,000 
 
 81,300 
 
 If 
 
 48,100 
 
 51,600 
 
 55,000 
 
 58,400 
 
 61,900 
 
 65,300 
 
 68,800 
 
 75,600 
 
 82,500 
 
 89,400 
 
 H 
 
 52,500 
 
 56,300 
 
 60,000 
 
 63,800 
 
 67,500 
 
 71,300 
 
 75,000 
 
 82,500 
 
 90,000 
 
 97,500 
 
 H 
 
 56,900 
 
 60,900 
 
 65,000 
 
 69,100 
 
 73,100 
 
 77,200 
 
 81,300 
 
 89,400 
 
 97,500 
 
 105,600 
 
 li 
 
 61,300 
 
 65,600 
 
 70,000 
 
 74,400 
 
 78,800 
 
 83,100 
 
 87,500 
 
 96,300 
 
 105,000 
 
 113,800 
 
 li 
 
 65,600 
 
 70,300 
 
 5,000 
 
 79,700 
 
 84,400 
 
 89,100 
 
 93,800 
 
 103,100 
 
 112,500 
 
 121,900 
 
 2 
 
 70,000 
 
 75,000 
 
 0,000 85,000 
 
 90,000 
 
 5,000 
 
 100,000 
 
 110,000 
 
 120,000 
 
 130,000 
 
 * See foot-note, preceding page. 
 
RESISTANCE TO TENSION. 
 
 349 
 
 TABLE X. SAFE TENSILE STRENGTH, IN TONS, OF 
 COMMON SIZES OF STEEL ANGLES WITH ONE 
 J-INCH HOLE FOR f-INCH RIVET DEDUCTED. 
 (Based on a working stress of 15,000 Ibs. per square inch.) 
 
 Size of Angle. 
 
 Tons. 
 
 Size of Angle. 
 
 Tons. 
 
 Size of Angle. 
 
 Tons. 
 
 6X4 XI 
 
 47.10 
 
 3X3*X| 
 
 30.21 
 
 3 X2jxi 
 
 15.45 
 
 f 
 
 39.82 
 
 f 
 
 25.72 
 
 J 
 
 11.92 
 
 i 
 
 32.22 
 
 
 21.07 
 
 
 10.12 
 
 
 
 * 
 
 16.12 
 
 r 
 
 8.17 
 
 5X3JX} 
 
 38.62 
 
 
 
 
 
 f 
 
 32.77 
 
 3JX3 Xf 
 
 23.40 
 
 3 X2 X% 
 
 12.15 
 
 
 26.70 
 
 i 
 
 19.20 
 
 t 
 
 10.50 
 
 
 
 f 
 
 14.77 
 
 %0 
 
 9.00 
 
 5X3 XI 
 
 35.85 
 
 
 
 i 
 
 7.27 
 
 f 
 
 30.45 
 
 3JX2JXf 
 
 21.07 
 
 
 
 4 
 
 24.82 
 
 /is 
 
 19.27 
 
 2JX2iXjlo 
 
 12.15 
 
 
 18.97 
 
 4 
 
 17.22 
 
 1 
 
 10.50 
 
 
 
 f 
 
 13.35 
 
 
 9.00 
 
 4X4 X| 
 
 35.85 
 
 
 9.15 
 
 i 
 
 7.27 
 
 2. 
 
 21.22 
 
 
 
 
 
 8 
 
 
 3 X3 Xf 
 
 21.07 
 
 2JX2 XX 
 
 10.50 
 
 4X3iX| 
 
 28.12 
 17.55 
 
 f 
 
 17.32 
 13.35 
 
 
 9.15 
 
 7.80 
 
 
 
 
 9.15 
 
 f 
 
 6.30 
 
 4X3 Xf 
 
 25.72 
 
 
 
 
 
 1 
 
 21.07 
 
 
 
 
 
 1 
 
 16.12 
 
 
 
 
 
350 
 
 RESISTANCE TO TENSION. 
 
 ffl I 
 p p 
 
 W -3 
 
 S 4 ? 
 0-8 
 
 I! 
 
 O 
 
 I 
 
 
 O 5 
 
 - 
 
 Diameter o 
 
 ! O CT> OOiOiOO 00 OC OC 1> I> I> t> CO 
 
 ICOCO TT< *C CO > 00 OS O rH CN CC "<t< 1C 
 
 35 
 
 < CO <N rH O O 00 1> CO *C rH 
 DcOt^ 00 C^ O O rH (N CO TT 
 
 g 
 
 CO CO 
 
 CO I> 00 00 CiOrHrH 
 
 Ol> COOCOCO O CO CO O CO CO O < 
 (M(M CO'^'^iC COCO1>00 OCOO< 
 
 O5C rHOO^O COCOOiC rH 00 '"t O 
 L >a xo CO CO t^ 00 00 OS O 
 
 rH (M CO CO " 
 
 00 CO OJiCr-t^ COOrhO CO (N ( 
 1C iC CO l> l> 00 C 
 
 !> CO 00 "^i Oi C O CO rH IXM C 
 <NCOCO^ TflCcOcO l>t>-OCC 
 
 ICO COcOrH COrHCOrH 
 rH(M C<<COCO^ r^iOiCcO 
 
 TfO5 COOOCOOO <Nt>-(McO rHCOO^C 
 rH rH (M CQ CO CO T^ rfi C C COOl>i> 
 
 CO !> rH CO O Tf< 
 
 rH rH (M (M CO CO 
 
 CO O ^f O5 
 
 1C CO CO CO 
 
 (NCO OC01>rH ICCTJCOI> rHlCOiCO 
 rHrH <NC^<NCO COCO^Tfri OiOCCO 
 
 rHrf OOrHlCOC (N^COiC^ 
 rHrH rH (N <N <N CO CO CO "tf 
 
 CO COOi(M-O OOrHTHOO rH-H^I>O 
 rH rH rH <M <N <N CO CO CO TtH TJH Tt 1C 
 
 O O rH rH rH rH <M 
 
 OCO 1C 00 
 CO CO CO CO 
 
 800 O<NTflCO OOOrHCO lCl>O5rH 
 O rH rH rH rH rH C^l C^ C^ C^ C^J O4 CO 
 
 8 32 
 
 \ 
 
RESISTANCE TO TENSION. 
 
 351 
 
 mow WIRE. 
 
 TABLE XII. SHOWING SIZE, WEIGHT, AND STRENGTH 
 OF CHARCOAL-IRON WIRE. 
 
 (Trenton Iron Cojs List.) 
 
 
 
 
 
 Area of 
 
 Actual 
 
 Tensile 
 
 No. by 
 wire 
 gauge. 
 
 Diameter 
 in deci- 
 mals of 
 1 inch. 
 
 Feet to 
 the 
 pound. 
 
 Weight of 
 1 mile, 
 in Ibs. 
 
 section, 
 in deci- 
 mals of 
 1 square 
 inch. 
 
 breaking 
 weight of 
 bright mar- 
 ket wire, 
 in Ibs. 
 
 strength of 
 bright mar- 
 ket wire 
 per sq. in. 
 of section, 
 in Ibs. 
 
 00000 
 
 .450 
 
 1.863 
 
 2833.248 
 
 .15904 
 
 12,598 
 
 79,217 
 
 0000 
 
 .400 
 
 2.358 
 
 2238.878 
 
 . 12566 
 
 9,955 
 
 79,220 
 
 000 
 
 .360 
 
 2.911 
 
 1813.574 
 
 .10179 
 
 8,124 
 
 79,811 
 
 00 
 
 .330 
 
 3.465 
 
 1523.861 
 
 .08553 
 
 6,880 
 
 80,437 
 
 
 
 .305 
 
 4.057 
 
 1301.678 
 
 .07306 
 
 5,926 
 
 81,110 
 
 1 
 
 .285 
 
 4.645 
 
 1136.678 
 
 .06379 
 
 5,226 
 
 81,925 
 
 2 
 
 .265 
 
 5.374 
 
 982.555 
 
 .05515 
 
 4,570 
 
 82,873 
 
 3 
 
 .245 
 
 6.286 
 
 839.942 
 
 .04714 
 
 3,948 
 
 83,756 
 
 4 
 
 .225 
 
 7.454 
 
 708.365 
 
 .03976 
 
 3,374 
 
 84,862 
 
 5 
 
 .205 
 
 8.976 
 
 588.139 
 
 .03301 
 
 2,839 
 
 86,000 
 
 6 
 
 .190 
 
 10.453 
 
 505 . 084 
 
 .02835 
 
 2,476 
 
 87,349 
 
 7 
 
 .175 
 
 12.322 
 
 428.472 
 
 .02405 
 
 2,136 
 
 88,802 
 
 8 
 
 .160 
 
 14.736 
 
 358.3008 
 
 .02011 
 
 1,813 
 
 90,153 
 
 9 
 
 .145 
 
 17.950 
 
 294.1488 
 
 .01651 
 
 1,507 
 
 91,276 
 
 10 
 
 .130 
 
 22.333 
 
 236.4384 
 
 .01327 
 
 1,233 
 
 92,916 
 
 11 
 
 .1175 
 
 27.340 
 
 193.1424 
 
 .01084 
 
 1,010 
 
 93,170 
 
 12 
 
 .105 
 
 34.219 
 
 154.2816 
 
 .00866 
 
 810 
 
 93,530 
 
 13 
 
 .0925 
 
 44.092 
 
 119.7504 
 
 .00672 
 
 631 
 
 93,900 
 
 14 
 
 .080 
 
 58.916 
 
 89.6016 
 
 .00503 
 
 474 
 
 94,234 
 
 15 
 
 .070 
 
 76.984 
 
 68.5872 
 
 .00385 
 
 372 
 
 96,701 
 
 16 
 
 .061 
 
 101.488 
 
 52.008 
 
 .00292 
 
 292 
 
 100,000 
 
 17 
 
 .0525 
 
 137.174 
 
 38.4912 
 
 .00216 
 
 ' 222 
 
 102,777 
 
 18 
 
 .045 
 
 186.335 
 
 28.3378 
 
 .00159 
 
 169 
 
 106,289 
 
 19 
 
 .040 
 
 235 . 084 
 
 22.3872 
 
 .0012566 
 
 137 
 
 109,024 
 
 20 
 
 .035 
 
 308.079 
 
 17.1389 
 
 .0009621 
 
 107 
 
 111,215 
 
 The gauge given is that adopted by the Trenton Iron Company. 
 
 The strengths given in the last column of the above table are 
 based upon tests made with bright (not annealed) charcoal- 
 iron wire. The strength of Swedish iron is about 10 per cent, 
 less, and that of mild bessemer and ordinary crucible cast steel 
 about 10 and 25 per cent., respectively, greater, than that of 
 charcoal iron. Special grades of crucible cast steel vary 
 between 30 and 100 per cent, over charcoal iron. 
 
 Annealing renders wire more pliable but less elastic, and redkices 
 its strength about 20 or 25 per cent. Galvanizing reduces the 
 tensile strength about 10 per cent., while tinning and coppering 
 exert no apparent influence upon the metal. Unannealed or hard 
 bmss wire has about three-fourths the strength of the above table, 
 and about one-ninth more weight. 
 
352 RESISTANCE TO TENSION. 
 
 Hard copper wire may be taken at two-thirds of the tabular 
 strengths, and full one-seventh more in weight. 
 
 WIRE HOPES. 
 
 Two kinds of wire rope are manufactured. The most pliable 
 variety is made of six strands of nineteen wires each, laid around 
 a hemp heart, and is generally used for hoisting and running rope. 
 It will wind on moderate-sized drums and pass over small 
 sheaves. 
 
 For standing rope, guys and rigging, ropes made of six strands 
 of twelve or seven wires each are better adapted, as they are 
 much stiff er than rope with 19 wires to the strand. From f-inch 
 diameter down to the smaller sizes this rope gives excellent 
 service for transmitting power. 
 
 Steel ropes are in many places superseding iron ropes. 
 
 In substituting steel rope for iron rope, however, the object 
 in view should be to gain an increased wear for the rope, rather 
 than to reduce the size. 
 
 To be serviceable, a steel rope should be of the best obtainable 
 quality, as ropes made from low grades of steel are inferior to 
 good iron ropes. The constant bending and vibration to which 
 they are subjected soon causes the poor steel to become brittle 
 and unsafe. 
 
 Ropes are made up to three inches in diameter, both of iron 
 and steel, upon special application. 
 
 For safe working load, allow one-fifth to one-seventh of the 
 ultimate strength, according to speed, so as to get good wear from 
 the rope. When substituting wire rope for hemp rope, it is good 
 economy to allow for the former the same weight per foot which 
 experience has approved for the latter. 
 
 Wire rope is as pliable as new hemp rope of the same strength"; 
 the. former will therefore run over the same sized sheaves and 
 pulleys as the latter. But the greater the diameter of the 
 sheaves, pulleys or drums, the longer wire rope will last. In the 
 construction of machinery for wire rope it will be found good 
 economy to make the drums and sheaves as large as possible. 
 The minimum size of drum is given in a column in Table XIII. 
 
 Experience has demonstrated that the wear increases with the 
 speed. It is, therefore, better to increase the load than the speed. 
 
 Wire rope is manufactured either with a wire or a hemp centre, 
 and the kind of centre wanted should be specified when placing 
 
RESISTANCE TO TENSION. 353 
 
 an order. The latter is more pliable than the former, and will 
 wear better where there is short bending. 
 
 Wire rope must not be coiled or uncoiled like hemp rope. When 
 mounted on a reel, the latter should be mounted on a spindle or 
 flat turn-table to pay off the rope. When forwarded in a small 
 coil, without reel, it should be rolled over the ground like a wheel, 
 and the rope run off in that way. All untwisting or kinking 
 must be avoided. 
 
 To preserve wire rope, apply raw linseed oil with a piece of 
 sheep-skin, wool inside, or mix the oil with equal parts of Spanish 
 brown or lamp-black. , 
 
 To preserve wire rope under water or under ground, take 
 mineral or vegetable tar, and add one bushel of fresh-slacked 
 lime to one barrel of tar, which will neutralize the acid. Boil it 
 well, and saturate the rope with the hot tar. To give the mixture 
 body, add some sawdust. 
 
 In no case should galvanized rope be used for running rope. 
 One day's use scrapes off the coating of zinc, and rusting pro- 
 ceeds with twice the rapidity. 
 
 The grooves of cast-iron pulleys and sheaves should be filled 
 with well-seasoned blocks of hard wood, set on end, to be renewed 
 when worn out. This end wood will save wear and increase 
 adhesion. The smaller pulleys or rollers which support the ropes 
 on inclined planes should be constructed on the same plan. 
 When large sheaves run with very great velocity, the grooves 
 should be lined with leather, set on end, or with India rubber. 
 This is done in the case of all sheaves used in the transmission 
 of power between distant points by means of rope, which fre- 
 quently run at the rate of 4,000 feet per minute. 
 
 The wire ropes described above are sold by the foot. 
 
 Ropes, Hawsers, and Cables. 
 
 (HAS WELL.) 
 
 Ropes of hemp fibres are laid with three or four strands of 
 twisted fibres and run up to a circumference of twelve inches. 
 
 Hawsers are laid with three strands of rope, or with four rope 
 strands. 
 
 Cables are laid with three strands of rope only. 
 
 Tarred ropes, hawsers, etc., have twenty-five per cent, less 
 strength than white ropes; this is in consequence of the injury 
 the fibres receive from the high temperature of the tar 290. 
 
354 
 
 RESISTANCE TO TENSION. 
 
 GALVANIZED STEEL WIRE STRAND, COMPOSED 
 OF 7 WIRES, TWISTED TOGETHER INTO A 
 SINGLE STRAND. 
 
 FOR SMOKESTACK GUYS, SIGNAL STRAND, TROLLEY LINE SPAN 
 WIRE AND SIMILAR PURPOSES. 
 
 Diameter. 
 
 Weight per 
 100 feet. 
 
 Estimated 
 breaking 
 strength. 
 
 Price per 
 100 feet. 
 
 Inch. 
 
 Pounds. 
 
 Pounds. 
 
 
 $ 
 
 51 
 
 8,320 
 
 S2.25 
 
 15 /32 
 
 48 
 
 7,500 
 
 2.05 
 
 % 
 
 37 
 
 6,000 
 
 1.65 
 
 i 
 
 30 
 
 4,700 
 
 1.40 
 
 % 
 
 21 
 
 3,300 
 
 1.05 
 
 %2 
 
 18 
 
 2,600 
 
 .90 
 
 17 /64 
 
 15 
 
 2,250 
 
 .75 
 
 i 
 
 Hi 
 
 1,750 
 
 .60 
 
 7 /82 
 
 8} 
 
 1,300 
 
 .50 
 
 & 
 
 6i 
 
 1,000 
 
 .45 
 
 %2 
 
 4i 
 
 700 
 
 .35 
 
 % 
 
 34 
 
 525 
 
 .28 
 
 i 
 
 2J 
 
 375 
 
 .22 
 
 %2 
 
 2 
 
 320 
 
 .20 
 
 Tarred hemp and manila ropes are of about equal strength. 
 Manila ropes have from twenty-five to thirty per cent, less 
 strength than white ropes. Hawsers and cables, from having 
 a less proportionate number of fibres, and from the increased 
 irregularity of the resistance of the fibres, have less strength than 
 ropes; the difference, varying from thirty-five to forty-five per 
 cent., being greatest with the least circumference. 
 
 Ropes of four strands, up to eight inches, are fully sixteen 
 per cent, stronger than those having but three strands. 
 
 Hawsers and cables of three strands, up to twelve inches, are 
 fully ten per cent, stronger than those having four strands. 
 
 The absorption of tar in weight by the several ropes is as fol- 
 lows: 
 
 Bolt-rope 18 per cent. 
 
 Shrouding. .15 to 18 per cent. 
 
 Cables 21 per cent. 
 
 Spun-yarn. .25 to 30 per cent. 
 
 White ropes are more durable than tarred. 
 
 The greater the degree of twisting given to the fibres of a rope, 
 etc., the less its strength, as the exterior alone resists the greater 
 portion of the strain. 
 
RESISTANCE TO TENSION. 
 
 355 
 
 TABLE XIII. STRENGTH OF IRON- AND STEEL- 
 
 WIRE ROPES. 
 
 MANUFACTURED BY THE JOHN A. ROEBLING'S SONS Co., 
 NEW YORK. 
 
 Trade 
 No. 
 
 Diam. 
 in 
 inches. 
 
 Weight 
 per foot 
 in Ibs. of 
 rope with 
 hemp 
 centre. 
 
 Iron. 
 
 Cast Steel. 
 
 Min. size of 
 drum or 
 sheave in feet. 
 
 Break- 
 ing 
 strain 
 in tons. 
 
 Proper 
 working 
 t load 
 in tons. 
 
 Break- 
 ing 
 strain 
 in tons. 
 
 Proper 
 
 working 
 < load 
 in tons. 
 
 Iron. 
 
 Cast 
 steel. 
 
 ' HOISTING ROPE. 
 
 WITH NINETEEN WIRES TO THE STRAND. 
 
 1 
 
 2J4 
 
 8.00 
 
 74.00 
 
 15.00 
 
 155 
 
 31 
 
 13 
 
 8.50 
 
 2 
 
 2 
 
 6.30 
 
 65.00 
 
 13.00 
 
 125 
 
 25 
 
 12 
 
 8 
 
 3 
 
 1% 
 
 5.25 
 
 54.00 
 
 11.00 
 
 106 
 
 21 
 
 10 
 
 7.25 
 
 4 
 
 1% 
 
 4.10 
 
 44.00 
 
 9.00 
 
 86 
 
 17 
 
 8 
 
 6.25 
 
 5 
 
 1% 
 
 3.65 
 
 39.00 
 
 8.00 
 
 77 
 
 15 
 
 7 
 
 5.75 
 
 5^ 
 
 1% 
 
 3.00 
 
 33.00 
 
 6.50 
 
 63 
 
 12 
 
 7 
 
 5.50 
 
 6 
 
 1/4 
 
 2.50 
 
 27.00 
 
 5.50 
 
 52 
 
 10 
 
 6 
 
 5 
 
 7 
 
 1//8 
 
 2.00 
 
 20.00 
 
 4.00 
 
 42 
 
 8 
 
 6 
 
 4.50 
 
 8 
 
 1 
 
 1.58 
 
 16.00 
 
 3.00 
 
 33 
 
 6 
 
 5.25 
 
 4 
 
 9 
 
 % 
 
 1.20 
 
 11.50 
 
 2.50 
 
 25 
 
 5 
 
 4 
 
 3.50 
 
 10 
 
 a^ 
 
 0.88 
 
 8.64 
 
 1.75 
 
 18 
 
 3.5 
 
 4 
 
 3 
 
 ioM 
 
 K/ 
 
 0.60 
 
 5.13 
 
 1.25 
 
 12 
 
 2.5 
 
 3 
 
 2.25 
 
 10M, 
 
 91 6 
 
 0.48 
 
 4.27 
 
 0.75 
 
 9 
 
 1.5 
 
 2.75 
 
 1.75 
 
 10% 
 
 K 
 
 0.39 
 
 3.48 
 
 0.50 
 
 7 
 
 1 
 
 2.25 
 
 1.50 
 
 10a 
 
 7 /16 
 
 0.29 
 
 3.00 
 
 0.37 
 
 5.5 
 
 0.75 
 
 2 
 
 1.25 
 
 1Q& 
 
 % 
 
 0.23 
 
 2.60 
 
 0.25 
 
 4.5 
 
 0.5 
 
 1.50 
 
 1 
 
 STANDING ROPE FOR GUYS AND RI'GGING. 
 
 WITH SEVEN WIRES TO THE STRAND. 
 
 11 
 
 IK 
 
 3.37 
 
 36.00 
 
 9.00 
 
 62 
 
 13 
 
 13 
 
 8.50 
 
 12 
 
 l&Z 
 
 2.77 
 
 30.00 
 
 7.50 
 
 52 
 
 10 
 
 12 
 
 8 
 
 13 
 
 1/4 
 
 2.28 
 
 25.00 
 
 6.25 
 
 44 
 
 9 
 
 10.75 
 
 7.25 
 
 14 
 
 1^6 
 
 1.82 
 
 20.00 
 
 5.00 
 
 36 
 
 7.50 
 
 9.50 
 
 6.25 
 
 15 
 
 j 
 
 1.50 
 
 16.00 
 
 4.00 
 
 30 
 
 6 
 
 8.50 
 
 5.75 
 
 16 
 
 % 
 
 1.12 
 
 12.30 
 
 3.00 
 
 22 
 
 4.50 
 
 7.50 
 
 5 
 
 17 
 
 % 
 
 0.92 
 
 8.80 
 
 2.25 
 
 17 
 
 3.50 
 
 6.75 
 
 4.50 
 
 18 
 
 Hie 
 
 0.70 
 
 7.60 
 
 2.00 
 
 14 
 
 3 
 
 6 
 
 4 
 
 19 
 
 Kx 
 
 % 
 
 0.57 
 
 5.80 
 
 1.50 
 
 11 
 
 2.25 
 
 5.25 
 
 3.50 
 
 20 
 
 9 /ie 
 
 0.41 
 
 4.10 
 
 1.00 
 
 8 
 
 1.75 
 
 4.50 
 
 3 
 
 21 
 
 H 
 
 0.31 
 
 2.83 
 
 0.75 
 
 6 
 
 1.50 
 
 4 
 
 2.50 
 
 22 
 
 
 0.23 
 
 2.13 
 
 0.50 
 
 4.50 
 
 1.25 
 
 3.50 
 
 2.25 
 
 
 
 091 
 
 1a K 
 
 
 4 
 
 1 
 
 2.75 
 
 2 
 
 23 
 
 C)A 
 
 
 . ^ L 
 01 A 
 
 . DO 
 
 100 
 
 
 3 
 
 75 
 
 2 '50 
 
 1 75 
 
 Z4 
 
 25 
 
 8 
 %2 
 
 . ID 
 
 0.125 
 
 . oo 
 
 1.03 
 
 
 
 2 
 
 0.'50 
 
 2^25 
 
 i!so 
 
 NOTE. A valuable pamphlet on wire rope for the transmission of power 
 may be obtained from the Trenton Iron Co., of Trenton, N. J. 
 
356 
 
 RESISTANCE TO TENSION. 
 
 To compute the Strain that can be borne with 
 Safety by ISTew Ropes, Hawsers, and Cables, 
 Deduced from the Experiments of the Russian 
 Government upon the Relative Strength of 
 Different Circumferences of Ropes, Hawsers, 
 etc. 
 
 The United States Navy test is 4,200 pounds for a white rope, of 
 three strands of best Riga hemp, of one and three-fourths inches in 
 circumference (i.e., 17,000 pounds per square inch); but in the fol- 
 lowing table 14,000 pounds is taken as the unit of strain that can 
 be borne with safety. 
 
 RULE. Square the circumference of the rope, hawser, etc., and 
 multiply it by the following units for ordinary ropes, etc. 
 
 TABLE XIV. SHOWING THE UNITS FOR COM- 
 PUTING THE SAFE STRAIN THAT MAY BE 
 BORNE BY ROPES, HAWSERS, AND CABLES. 
 
 
 Ropes. 
 
 Hawsers. 
 
 Cables. 
 
 
 White. 
 
 Tarred. 
 
 BB 
 
 1 
 
 4 
 
 a 
 
 Description. 
 
 
 
 X 
 
 8 
 
 %i 
 
 
 
 
 4 
 
 '4 
 
 4 
 
 02 
 
 o 
 
 CO 
 
 CO 
 
 i 
 
 CO 
 
 CO 
 
 CO 
 
 
 1 
 
 1 
 
 1 
 
 1 
 
 
 
 *d 
 
 f. 
 
 73 
 
 
 ,> 
 
 
 
 H 
 
 jjj 
 
 2 
 
 a 
 
 2 
 
 " 
 
 
 CO 
 
 If 
 
 CO 
 
 
 ft 
 
 H 
 
 ft 
 
 H 
 
 Circumference in inches. . . 
 
 Ibs. 
 
 Ibs. 
 
 Ibs. 
 
 Ibs. 
 
 Ibs. 
 
 Ibs. 
 
 Ibs. 
 
 Ibs. 
 
 White rope, 2.5 to 6 ins. 
 
 1,140 
 
 1,330 
 
 
 
 
 
 600 
 
 
 
 
 
 
 
 White rope, 6 to 8 ins . . 
 
 1,090 
 
 1,260 
 
 
 
 
 
 570 
 
 
 
 510 
 
 
 
 White rope, 8 to 12 ins. . 
 
 1,045 
 
 880 
 
 
 
 
 
 530 
 
 
 
 530 
 
 
 
 White rope, 12 to 18 ins. 
 
 
 
 
 
 
 
 
 
 550 
 
 
 
 550 
 
 
 
 White rope, 18 to 26 ins. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 560 
 
 
 
 Tarred rope, 2.5 to 5 ins. 
 
 
 
 
 
 855 
 
 1,005 
 
 
 
 460 
 
 
 
 
 
 Tarred rope, 5 to 8 ins. . . 
 
 
 
 
 
 825 
 
 940 
 
 
 
 48u 
 
 
 
 
 
 Tarred rope, 8 to 12 ins. . 
 
 
 
 
 
 780 
 
 820 
 
 
 
 50o 
 
 
 
 505 
 
 Tarred rope, 12 to 18 ins 
 
 
 
 
 
 
 
 
 
 - 
 
 
 
 
 
 525 
 
 Tarred rope, 18 to 26 ins. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 550 
 
 Manila rope, 2.5 to 6 ins. . 
 
 810 
 
 950 
 
 
 
 
 
 440 
 
 
 
 
 
 
 Manila rope, 6 to 12 ins. . 
 
 760 
 
 835 
 
 
 
 
 
 465 
 
 
 
 510 
 
 
 
 Manila rope, 12 to 18 ins. 
 
 
 
 
 
 
 
 
 
 
 
 535 
 
 
 
 Manila rope, 18 to 26 ins. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 560 
 
 
 
 When it is required to ascertain the weight or strain that can 
 be borne by ropes, etc., in general use, the above units should be 
 reduced one-third, in order to meet the reduction of their strength 
 by chafing and exposure to the weather. 
 
RESISTANCE TO TENSION. 
 
 357 
 
 TABLE XV. STRENGTH AND WEIGHT OF MANILA 
 ROPE. 
 
 
 1 
 
 1 
 
 
 
 <D 
 1 
 
 1 
 
 
 I 
 
 | 
 
 | 
 
 Breaking 
 load. 
 
 1 
 
 
 I 
 
 Breaking 
 load. 
 
 1 
 
 1 
 
 *" 
 
 
 1 
 
 1 
 
 sf 
 
 
 ft 
 
 *d 
 
 P 
 
 
 ft 
 
 
 
 & 
 
 
 ins. 
 
 ins. 
 
 Ibs. 
 
 Ibs. 
 
 tons. 
 
 ins. 
 
 ins. 
 
 Ibs. 
 
 Ibs. 
 
 tons. 
 
 0.239 
 
 3^ 
 
 .019 
 
 560 
 
 0.280 
 
 1.92 
 
 6^ 
 
 1.19 
 
 25,536 
 
 12.77 
 
 0.318 
 
 1 
 
 .033 
 
 784 
 
 0.39 
 
 2.07 
 
 
 1.39 
 
 29,120 
 
 14.56 
 
 0.477 
 
 1^5 
 
 .074, 
 
 1,568 
 
 0.78 
 
 2.23 
 
 7 2 
 
 1.62 
 
 32,704 
 
 16.35 
 
 0.636 
 
 2 
 
 .132 
 
 2,733 
 
 1.36 
 
 2.39 
 
 7% 
 
 1.86 
 
 36,288 
 
 18.14 
 
 0.795 
 
 2^5 
 
 .206 
 
 4,278 
 
 2.14 
 
 2.55 
 
 8 
 
 2.11 
 
 39,872 
 
 19.93 
 
 0.955 
 
 3 
 
 .297 
 
 6,115 
 
 3.06 
 
 2.86 
 
 9 
 
 2.67 
 
 47,040 
 
 23.52 
 
 1.11 
 
 3^5 
 
 .404 
 
 8,534 
 
 4.27 
 
 3.18 
 
 10 
 
 3.30 
 
 54,208 
 
 27.10 
 
 1.27 
 
 4 
 
 .528 
 
 11,558 
 
 5.78 
 
 3.50 
 
 11 
 
 3.99 
 
 61,376 
 
 30.69 
 
 1.43 
 
 4^2 
 
 .668 
 
 14,784 
 
 7.39 
 
 3.82 
 
 12 
 
 4.75 
 
 68,544 
 
 34.27 
 
 1 59 
 
 5 
 
 .825 
 
 18,368 
 
 9.18 
 
 4.14 
 
 13 
 
 5.58 
 
 75,712 
 
 37.86 
 
 1.75 
 
 5Y2 
 
 .998 
 
 21,952 
 
 10.97 
 
 4.45 
 
 14 
 
 6.47 
 
 82,880 
 
 41.44 
 
 Working Loads. For manila ropes from 1 to If ins. 
 diam., running at different speeds over sheaves of the diams. 
 stated, Mr. C. W. Hunt (Trans. Am. Soc. Mechl. Engrs., Vol. 
 XXIII, 1901) gives a table embodying approximately the 
 following results of experience. Working load = C X ultimate 
 strength of new rope, as given in above table. D = minimum 
 diam. of sheave in ins. 
 
 l"rope lM"rope 
 
 Speed ft. per min. as for work on ODD 
 
 Slow 50 to 100 derrick, crane, quarry 0.140 8 14 
 Medium 150 to 300 wharf, cargo 0.056 12 18 
 
 Rapid 400 to 800 0.028 40 70 
 
 Such ropes wear out rapidly. A rope 1| ins. diam. wears out 
 in lifting from 7,000 to 10,000 tons of coal. On the other hand, 
 1 J inch transmission ropes, running 5000 ft. per min. and carry- 
 ing 1000 H. P. oyer sheaves 5 ft. and 17 ft. in diam. last for 
 
 years. 
 
358 
 
 RESISTANCE TO TENSION. 
 
 TABLE XVI. WEIGHT AND PROOF STRENGTH OF 
 CHAIN. 
 
 MANUFACTURED BY THE NEW JERSEY STEEL AND IRON COMPANY. 
 
 
 
 ~K.K. 
 
 Stud chain. 
 
 Short-link chain. 
 
 crane 
 
 
 
 chain. 
 
 Size. 
 
 Average 
 weight 
 
 Proof. 
 
 Size. 
 
 Average 
 weight 
 
 Proof. 
 
 Proof. 
 
 
 per 
 
 
 
 per 
 
 
 
 
 fathom. 
 
 
 
 fathom. 
 
 
 
 inches. 
 
 Ibs. 
 
 tons. 
 
 inches. 
 
 Ibs. 
 
 tons. 
 
 tons. 
 
 1 
 
 33 
 
 10 
 
 3/ i6 
 
 2f 
 
 i 
 
 
 
 38 
 
 12 
 
 i_ 
 
 4 
 
 5 
 
 i 
 
 
 
 -J 
 
 43 
 
 14 
 
 ^io 
 
 7 
 
 
 
 
 Jg 
 
 50 
 
 16 
 
 3 
 
 s 
 
 9J 
 
 2 
 
 3 
 
 \ 
 
 58 
 
 18 
 
 
 12 
 
 2i 
 
 4 
 
 1/ie 
 
 65 
 
 20 
 
 i 
 
 15 
 
 3i 
 
 41 
 
 l| 
 
 72 
 
 23 
 
 
 19 
 
 4i 
 
 5j 
 
 l|f6 
 
 80 
 
 26 
 
 f 6 
 
 25 
 
 5* 
 
 7 
 
 l| 
 
 88 
 
 28 
 
 H> 
 
 30 
 
 7 
 
 gi 
 
 
 98 
 
 31 
 
 f 
 
 35 
 
 8 
 
 io 
 
 if 
 
 110 
 
 34 
 
 
 40 
 
 Q 1 
 
 ^2 
 
 114 
 
 1/1(5 
 
 114 
 
 37 
 
 i 
 
 47 
 
 11 
 
 13 
 
 l| x 
 
 127 
 
 41 
 
 
 54 
 
 121 
 
 14J 
 
 
 138 
 
 44 
 
 i /j 
 
 61 
 
 14 " 
 
 16 
 
 if 
 
 150 
 
 48 
 
 i i^t 
 
 69 
 
 16 
 
 19 
 
 1'Y- 
 
 157 
 
 52 
 
 11 
 
 76 
 
 18 
 
 21 
 
 i| 
 
 170 
 
 56 
 
 is,/ 
 
 85 
 
 20 
 
 23 
 
 1% 
 
 184 
 
 60 
 
 H. 
 
 95 
 
 22 
 
 25 
 
 ij 
 
 200 
 
 64 
 
 
 103 
 
 24 
 
 27 
 
 1/16 
 
 214 
 
 68 
 
 If 
 
 113 
 
 26 
 
 29 
 
 2 
 
 230 
 
 72 
 
 1/ia 
 
 123 
 
 28 
 
 31 
 
 2J 
 
 250 
 
 80 
 
 1J 
 
 133 
 
 30 
 
 33 
 
 21 
 
 290 
 
 . 88 
 
 
 
 
 
RESISTANCE TO TENSION. 
 
 359 
 
 Strength of Old Iron. A square link 12 inches broad, 1 
 inch thick, and about 12 feet long was taken from the Kieff 
 Bridge, then 40 years old, and tested in comparison with a similar 
 link which had been preserved in the stock-house since the bridge 
 was built. The following is a record of a mean of four longitu- 
 dinal test pieces, 1X1JX8 inches, taken from each link. 
 
 
 Old link 
 from bridge. 
 
 New link from 
 storehouse. 
 
 Tensile strength per square inch, tons. . . 
 Elastic limit per square inchj tons. . 
 
 21.8 
 11 1 
 
 22.2 
 11 9 
 
 
 14 05 
 
 18.42 
 
 
 17.35 
 
 18.75 
 
 
 
 
 (The Mechanical World, London.) 
 
360 
 
 RESISTANCE TO SHEARING. 
 
 CHAPTER XII. 
 
 EESISTANCE TO SHEARINGS-RIVETED 
 JOINTS. 
 
 STRENGTH OF PINS IN IRON AND STEEL TRUSSES. 
 STRENGTH OP BOLTS IN WOODEN TRUSSES AND 
 GIRDERS. 
 
 BY shearing is meant the pushing of one part of a piece by 
 the other. Thus in Fig. 1, let abed be a beam resting upon the 
 supports SS 9 which are very near together. If a sufficiently 
 
 Fig. I 
 
 heavy load were placed upon the beam, it would cause the beam 
 to break, not by bending, but by pushing the whole central part 
 of the beam through between the ends, as represented in the 
 figure. This mode of fracture is called "shearing." 
 
 Shearing stresses exist whenever two forces acting like a pair 
 of shears tend to cut a body between them. 
 
 When two bars of steel or iron are connected together by a 
 rivet, as in Fig. 2, the stresses in the bars acting as indicated by 
 the arrow-heads, the tendency is to shear the rivet at the joint 
 between the two bars, as though it were cut by a pair of shears. 
 When the shearing stresses tend to shear the piece only at one 
 place, as in Fig. 2, the piece is said to be in single shear; when 
 the stresses tend to shear the piece at two sections, as in Fig. 1, 
 the piece is in "double shear." 
 
RESISTANCE TO SHEARING. 
 
 361 
 
 The resistance of a body to shearing is, like its resistance to 
 tension, directly proportional to the area to be sheared. Hence, 
 if we denote the safe resistance of one square inch of the mate' 
 
 Fig. 2 
 
 rial to shearing by F, we shall have as the safe resistance to 
 shearing, 
 
 Safe shearing strength = area to be sheared X F t (1) 
 
 A piece of timber may be sheared either longitudinally or 
 transversely; and, as the resistance is not the same in both cases, 
 the value of F will be different in the two cases. Hence, in 
 substituting values for F, we must distinguish whether the force 
 tends to shear the piece longitudinally (lengthwise) or trans- 
 versely (across). 
 
 Table I. gives the average working values of F in building con- 
 struction as recommended by the best authorities, and as used 
 by structural engineers. 
 
 TABLE I. SAFE RESISTANCE TO SHEARING, IN LBS. 
 PER SQUARE INCH, FOR IRON, STEEL, AND WOOD. 
 
 Materials. 
 
 Values 
 
 forF. 
 
 Cast iron 
 
 
 6,000 
 
 Webs of rolled beams and riveted 
 girders. 
 
 Wrought iron. 
 6, 000 to 9 ,000 
 
 Rolled steel. 
 7, 000 to 10, 000 
 
 Bolts and field-driven rivets 
 
 6,000 
 
 7,500* 
 
 Rivets shop-driven. . . . 
 
 7,500 
 
 7, 500 to 10, 000 
 
 pins 
 
 7,500 
 
 7, 500 to 9,000 
 
 Woods. 
 Cedar 
 
 With grain. 
 
 Across grain 
 400 
 
 Chestnut. . 
 
 125 
 
 400 
 
 Hemlock 
 
 80 
 
 600 
 
 Oak white 
 
 150 
 
 1,000 
 
 Pine Georgia/ yellow .. 
 
 125 
 
 1,200 
 
 
 125 
 
 900 
 
 Pine, Norway. 
 
 90 
 
 750 
 
 Pine, white. . 
 
 80 
 
 500 
 
 Redwood (Califorina) 
 
 70 
 
 500 
 
 Spruce 
 
 90 
 
 750 
 
 Whitewood. 
 
 60 
 
 
 
 
 
 *For bolts in the connection-angles of beams, a shearing stress of 10,000 
 Ibs. is usually allowed, and the author believes that the same unit stress 
 may be used for bolts in the joints of wooden trusses. 
 
362 
 
 RESISTANCE TO SHEARING. 
 
 There are but few cases of architectural construction in which 
 the resistance of wood to shearing has to be provided for. The 
 one most frequently met with is at the end of the tie-beam in 
 wooden trusses. 
 
 Fig. 3 
 
 Fig. 3 shows the shearing of the end of the tie-beams due to 
 the thrust of the rafter, the drawing being made from a photo- 
 graph of an actual instance. 
 
 There is always a tendency for beams to shear vertically at 
 the points of support, as in Fig. 1, but it is very rare that wooden 
 beams are subject to dangerous stresses from shearing. It 
 could only happen in the case of a very short beam very heavily 
 loaded. The vertical shearing stresses in a beam are explained 
 hi Chapter XX. 
 
 A very long beam might also possibly fail by shearing longi- 
 tudinally, but such failure is not likely to occur under the safe 
 load given by either the formula for strength or the formula 
 for stiffness. Other common instances in which failure by shear- 
 
 Fig. 4 
 
 ing may take place, are in the case of rivets, pins, and bolts, 
 which are hereinafter more fully explained. 
 
RIVETED JOINTS. 363 
 
 Example of Shear at End of Tie-beam. In the case of the 
 truss joint, Fig. 4, the rafter exerts a thrust which tends to 
 push or shear off the piece ABCD, and the area of the section 
 along CD should offer enough resistance to keep the rafter in 
 place. This area is equal to CD times the breadth of the tie- 
 beam; and, as the breadth is fixed, we have to determine the 
 length, CD. If we let // denote the horizontal thrust of the 
 rafter, or the tension in the tie-beam, by a simple deduction 
 from formula (1), we have the rule, 
 
 TT 
 
 Length of CD in inches = : - rn j-. - == > (2) 
 
 breadth of beam X^ 
 
 F, in this case, being the resistance to shearing longitudinally. 
 
 EXAMPLE I. The horizontal thrust of a rafter is 20,000 
 pounds, the tie-beam is of Oregon pine, and is ten inches wide: 
 how far should the beam extend beyond the point D? 
 
 Ans. In this case H = 20,000 pounds, and from Table I. we 
 find that F= 125. Then 
 
 Practically a large part of the thrust is generally taken up 
 by an iron bolt or strap passed through or over the foot of the 
 rafter and tie-beam, in order to keep the rafter in place. As 
 the bolt and shoulder seldom act together, the length of the 
 tie-beam at CD should either be made long enough to resist 
 the entire thrust without help from the bolt, or else the bolt or 
 strap should be strong enough to resist the entire thrust. The 
 designing of such joints is more fully considered on pages 382 
 to 397. 
 
 RIVETED JOINTS. 
 
 The most common method of uniting pieces of wrought iron 
 or steel in framed structures is by means of -rivets, and that 
 the structures shall be equally strong in all its parts it is essential 
 that the joints shall be carefully designed. 
 
 A rivet is a piece of metal with a solid head at one end, and a 
 long circular shank. 
 
 Riveting consists of heating the rivet, passing it through the 
 holes in the plates to be united while hot, and then forging 
 another solid head out of the projecting end of the shank. 
 
364 
 
 RIVETED JOINTS. 
 
 The hammering causes the heated shank to fill all parts of the 
 holes, and the contraction of the metal, as it cools, draws the 
 heads together, thus firmly forcing and holding the pieces 
 together. 
 
 Rivets are generally made either of mild steel or the best 
 wrought iron, the latter being the most reliable. The rivet- 
 heads are made in four ways, as shown in Fig. 5. 
 
 > 
 
 
 Fig. 5. 
 
 The first shape is the one generally used. The second and 
 third are .used only for their appearance; and the fourth, or 
 counter-sunk head, is only used when a smooth surface is desir- 
 able, as over a bearing plate. 
 
 The exact sizes of heads, shapes ; etc., of rivets vary in differ- 
 ent mills. 
 
 When the size of rivet is specified the hole is always made ^ 
 inch larger; but the rivet is generally designated by the size of 
 the hole. 
 
 Pitch. The distance between the centres of the rivets, in 
 the line of riveting, is called the pitch. This (for practical 
 reasons) should never be less than 2} diameters ; nor should the 
 centre of the hole (if possible) be nearer to any edge than 1 J 
 diameters. In angle work, however, it is often necessary to 
 make the distance from the edge less than the above, but in thick 
 plates it should always be more. In drilled work the pitch 
 might be reduced to 2 diameters. If rivet-heads are counter- 
 sunk the pitch should.be increased according to the amount of 
 metal cut away, to make room for the rivet-head. 
 
 Rivet-holes are generally made by punching, by a powerful 
 steam-punch, as this is much the cheapest method. The best 
 
RIVETED JOINTS. 365 
 
 way to make the holes is to drill them after the pieces are bolted 
 or clamped together 
 
 Punching makes a ragged and irregular hole, and injures the 
 metal about the hole, causing a loss of strength to the remaining 
 portion of the metal of 15 per cent, in wrought-iron, and often 35 
 per cent, in steel. 
 
 Besides this, in punching there is liability of cracking the plate, 
 and of not having the holes in the two plates that are to be united 
 come exactly opposite each other. 
 
 The hardening of the metal by punching also decreases the duc- 
 tility of the pieces. , 
 
 The injury done by punching in steel plates may be almost en- 
 tirely removed, however, by annealing, and in first-class work 
 this should always be done. 
 
 In drilled work there is no loss, and the holes are not only 
 accurately located, but accurately cut, and the strength of the 
 remaining fibres is even increased from 12 to 25 per cent. 
 
 The cost of drilling, however, is very great, so that it is not 
 likely to be employed, except in making the joints in trusses and 
 connecting tie-bars, where the number of rivets is not great. 
 
 A medium course between punching and drilling is to punch 
 the holes a size smaller than desired, and then drill or ream them 
 to actual size, when partially secured together. The loss of 
 strength by this method will be very slight. 
 
 In most cases, however, the architect will have to be satisfied 
 with punched holes, and must, therefore, allow sufficient metal to 
 make good any damage done, or for any inaccuracies. 
 
 In driving and heading the rivet, however, machine riveting is 
 much better than hand riveting, as a greater pressure is used, 
 and the metal more completely fills the hole. 
 
 In designing riveted work, whether to be hand or machine 
 riveted, the architect must bear in mind the necessity of placing 
 the rivets so that they can be inserted in the holes from one side 
 and hammered from the other; and for machine work, that the 
 machine can reach them. Thus, the minimum distance from the 
 inside face of one leg of an angle iron to centre of nearest rivet- 
 hole in other leg should be at least 1| inch for J-inch rivets, 1 inch 
 for f-inch rivets, J inch for f-inch rivets, % inch for J-inch rivets ; 
 and, if possible, these distances should be increased. 
 
 Failure of Riveted Joints. Riveted joints may yield in any 
 one of five ways : 
 
 1st. By the crushing of the plate in front of the rivets (Fig. 6). 
 
366 
 
 RIVETED JOINTS. 
 
 2d. By the shearing of the rivets (Fig, 7). 
 
 3d. By the tearing of the plate between the rivet-holes (Fig. 8). 
 
 4th. By the rivet breaking through the plate (Fig. 9). 
 
 5th. By the rivet shearing out the plate in front of it. 
 
 Fig. 6 
 
 Fig. 7 
 
 Fig. 8 
 
 
 
 Fig. 9 
 
 The two latter cases are likely to occur only in the case of 
 single riveted lap-joint. 
 
 To design a riveted joint so that it will not break in either oJ 
 these ways, it is, therefore, necessary to calculate for the shearing 
 strength of the rivets, for the crushing strength of the plates joined 
 and to space the rivets far enough apart that the metal will nol 
 tear between the rivets. 
 
 The process of designing a riveted joint practically consists ir 
 first assuming the size of rivet to be used, and then catenating th< 
 number required to resist shearing and to prevent the crushing 
 of the plates joined, and then using the larger number. Thej 
 are then spaced by the rule that the pitch shall not be less thai 
 2J diameters, nor more than 16 times the thickness of the thin 
 nest plate at the joint, and the distance from the centre of th( 
 rivet to end of the plate should not be less than 1J diameters 
 The following table gives the sizes of rivets to be preferred fo] 
 different thicknesses of plates: 
 For plates from J inch to % inch thick, use rivet-holes f inch ir 
 
 diameter. 
 For plates from J inch to f inch thick, use rivet-holes f inch ir 
 
 diameter.* 
 
 For plates from % inch to % inch thick use rivet-holes f inch ir 
 diameter. 
 
 * In truss work f" rivets are generally used for thicknesses of plates anc 
 angles from %6-inch to i% 6 -inch. 
 
RIVETED JOINTS. 367 
 
 For plates from J inch to 1 inch thick, use rivet-holes 1 inch in 
 diameter. 
 
 The number of rivets required to resist shearing can be easily 
 ietermined by dividing the total amount of strain by the number 
 Dpposite the size of the rivet, in the fourth column of Tables II. 
 and III., pages 371 and 372, if the rivet is in single shear; and if in 
 double shear, take one-half the number of rivets. 
 
 To find the number of rivets required to prevent crushing, 
 divide the total amount of strain by the bearing value of the rivet 
 given in these tables. 
 
 Note. Table III. should only be used for the connections of steel 
 floor beams and roof trusses where the usual loads are to be sup- 
 ported; for riveted girders and live loads, or where only actual 
 loads have been provided for, Table II. should be used. The 
 heavy zigzag line in the tables indicates the limit at which the 
 bearing value exceeds single shear. All values above these lines 
 are in excess of single shear; all values below are less than single 
 shear. 
 
 The principal cases in which riveted joints occur in build- 
 ing construction are: 1. In the joints of wrought-iron trusses. 
 2. Splicing of tie-bars. 3. In the connecting angles of floor 
 beams. 4. In riveted girders. 
 
 Splicing of Tie-bars. 
 
 Tie-bars may be spliced in three ways. 
 1st. By a lap-joint, as shown in Fig. 10 
 
 I 
 
 _1 
 
 Fig. 10 
 
 2d. By a single cover plate, as shown in Fig. 11. 
 
 \ 
 
 
 II 
 
 
 .1 
 
 1 . 
 
 
 
 
 ZJ 
 
 Fig. II 
 
368 RIVETED JOINTS. 
 
 3d. By two cover plates, as in Fig. 12. 
 
 cz 
 
 Fig. 12 
 
 In Figs. 10 and 11 the rivets are in single shear; in Fig. 12 they 
 are in double shear. The last method is much the best, although 
 it is also the most expensive. The cover plates should always be 
 the full width of the bars connected, and ^ inch more in thickness 
 for the two plates, or for one single plate. 
 
 For lapped joints, which is the most common joint used, the 
 rivets should be arranged as in Fig. 13, in which case the plates 
 
 Fig. 13 
 
 are only weakened by the width of one rivet-hole, at A. At B, 
 two rivet-holes are lost, but the strain has been reduced by an 
 amount equal to the value of one rivet-hole and so on. 
 
 If the plates are narrow and thick, the rivets may be arranged 
 as in Figs. 14 or 15. 
 
 Fig. 14 
 
 Where cover plates are used, Fig. 15 is the best arrangement, 
 for by it the cover plates are weakened by only two rivet-holes 
 (the ones nearest the joint); while in Fig. 14 the cover plates 
 
RIVETED JOINTS. 369 
 
 are weakened by three holes nearest the joint, and, consequently, 
 must be made thicker. 
 
 Fig. 15 
 
 When rivets are arranged in rows, it is called chain riveting^ 
 when rivets are arranged to come opposite the space between the 
 preceding rivets, they are said to be staggered, as in Figs. 13 
 and 14. 
 
 In designing riveted joints care must be exercised not to 
 weaken the plates any more than is absolutely necessary. 
 
 EXAMPLE 2. A 12" X \" tie-bar is so long that it has to be 
 made in two pieces with a splice; the strain on the piece is 65,000 
 Ibs. How many rivets will be required ? 
 
 Ans. We will assume that the joint is to be a lapped joint, as in 
 Fig. 13, and that we will use j-inch rivets. 
 
 From Table II. we find that the resistance of a f-inch rivet to 
 single shear is 3,310 Ibs. and the bearing value for a half-inch 
 plate 5,630 Ibs. Dividing the strain, 65,000 Ibs., by the smaller 
 of these two quantities, 3,310, we find we shall require 20 rivets; 
 but as 20 rivets will not give us the arrangement we wish, we will 
 use 25, as in Fig. 13. The distance, P, between the centres of 
 rivets measured on the slant should be at least 2J diameters, or 
 2i X f inch = 1J inches, or, we will say, 2 inches. 
 
 Beam Connections. 
 
 EXAMPLE 3. A 10-inch, 30-lb. standard steel beam having a 
 span of 3J feet supports a load at the centre of 40,000 Ibs. and is 
 framed at one end to a 15-inch 50-lb. steel beam; how many l-inch 
 rivets will be required in the connection ? 
 
 Ans. From the table giving the properties of standard steel 
 I-beams, we find the web thickness of the 10-inch beam to be 
 0.455(%) inch, and of the 15-inch beam to be 0.558 inch. The 
 standard connection angle for a 10-inch beam (see Chap. XV.) is 
 Q X 4 x f". The number of rivets required in the 10-inch beam 
 
370 RIVETED JOINTS. 
 
 will therefore be determined either by the bearing resistance of 
 the web of the 10-inch beam, or by the resistance to shearing. 
 From Table III. we find the bearing value of a f-inch rivet on a 
 %-inch plate to be 5,890 Ibs. and the resistance to single shear 
 to be 4,420 Ibs. Dividing one half the load, or 20,000 Ibs., by 
 5,890, we find that 4 rivets will be required to sustain the load 
 without crushing the web. 
 
 As the rivets will be in double shear the resistance of each 
 rivet will be 8,836 Ibs., and of the 4 rivets 35,344 Ibs., which is 
 in excess of the load ; hence 4 rivets will be required in the 10-inch 
 beam. In the 15-inch beam the number of rivets will be deter- 
 mined by the shearing value, as here the rivets are in single shear. 
 20,000 Ibs. divided by 4,418 requires 5 rivets, or say 3 in each 
 angle. To accommodate the 4 rivets in the 10-inch beam, the 
 connection angle should be 6J inches long. 
 
 The standard connection for 10-inch beams shows 3 rivets 
 in each flange, but the load which we have assumed is greatly 
 in excess of that for which the standard connection is designed. 
 The maximum safe distributed load for this beam for a 10-ft. 
 span is 28,630 Ibs., or 14,315 Ibs. at each end, for which 3 rivets 
 are ample. 
 
 EXAMPLE 4. One end of a 10 X 12 wooden beam is supported 
 on a 4 X 4 X \-inc~h angle bracket, riveted to the web of an 18-inch 
 60-Z6. steel beam; the load on the wooden beam is 18,000 Ibs.; how 
 many \-inch rivets will be required in the bracket f 
 
 Ans. As the rivets are in single shear, and the web and angle 
 are each J-inch thick, the number of rivets will be determined by 
 the resistance to shearing, that being less than the bearing value. 
 The load to be supported by the bracket will be one-half the load 
 on the beam, or 9,000 Ibs. Dividing this by 4,420, we find that 
 two f-inch rivets are not quite sufficient, and we must therefore 
 use either three f-inch rivets, or two |-inch rivets. The f-inch 
 rivets should be placed 4 inches on centres, and the f-inch rivets 
 6 inches. 
 
 Rivets in Plate Girders. The methods for proportion- 
 ing the rivets to resist the various strains in plate girders are 
 explained in detail in Chapter XX. 
 
 Bending Moment in Rivets. While pins should always 
 be computed for resistance to cross breaking, it is not the custom 
 to consider the bending moment in rivets; as in a well-riveted 
 joint it is practically impossible to produce any bending of the 
 rivet, neither do the tests on riveted joints show any signs of the 
 
SHEARING AND BEARING VALUES OF RIVETS. 371 
 
 
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372 SHEARING AND BEARING VALUES OF RIVETS. 
 
 
 
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 TABLE IV. LENGTHS OF RIVETS LENGTH OF 
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 PLAIN RIVETS. 
 
 GRIP ^ 
 
 J<_ LENGTH " 
 
 COUNTERSUNK RIVETS. 
 
 K- GRIP- > 
 
 
 
 K- -LENGTH >J 
 
 Diameter in inches. 
 
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 Diameter in inches. 
 
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STRENGTH OF PINS. 375 
 
 rivets breaking in that way. Mr. C. W. Bryan, engineer for the 
 Edge Moor Bridge Works, says: " Rivets will fail by flexure 
 only in those cases of bad designing where the rivets are long and 
 it is impossible to drive them tight enough to have them upset 
 and completely fill the holes." He also adds: "Rivets are 
 never proportioned for flexure." * The only person that considers 
 the bending moment on rivets, so far as the author has been able 
 to learn, is Mr. Louis DeCoppet Berg, who has taken up the 
 subject of riveted joints most elaborately in Chapter IX. of Part 
 II. of his "Safe Building." 
 
 Strength of Pins in Steel Bridge and Roof 
 Trusses. Iron and steel trusses are now so generally used that 
 it is necessary for the architect who is at all advanced in his pro- 
 fession to know how to determine the strength of the joints and 
 especially of pin joints; and to facilitate the calculation of the 
 necessary size of pins, we give Table V., which shows the single 
 shearing strength and bearing value of pins, and Table VI., show- 
 ing the maximum bending moment allowed in pins. 
 
 Pins must be calculated for shearing, bending, and bearing 
 strains, but one of the latter two only (in almost every case) deter- 
 mines the size to be used. 
 
 By bearing strain is meant the force required to crush the edges 
 of the iron plates against which the pin bears. 
 
 The several strains per square inch usually allowed on pin con- 
 nections in bridges are: shearing, 7,500 pounds; crushing, 12,000 
 pounds; and bending, 15,000 pounds for iron, and 20,000 pounds 
 for steel. In roof trusses, 22,500 Ibs. fibre stress is commonly 
 allowed. 
 
 The shearing strain is measured on the area of cross-section ; the 
 crushing strain, on the area measured by the product of the diam- 
 eter of the pin by the thickness of the plate or web on which it 
 bears. 
 
 The bending moment is determined by the same rules as given 
 for determining the bending moment of beams. 
 
 When groups of bars are connected to the same pin, as in the 
 lower chords of trusses, the sizes of bars must be so chosen, and 
 the bars so placed, that at no point on the pin will there be an 
 excessive bending strain, on the presumption that all the bars are 
 strained equally per square inch. 
 
 * Modern Framed Structures, p. 261, 
 
376 SHEARING AND BEARING VALUES OF PINS. 
 
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BENDING MOMENT IN PINS. 
 
 377 
 
 TABLE VI. MAXIMUM BENDING MOMENTS IN INCH 
 POUNDS TO BE ALLOWED ON PINS FOR MAXI- 
 MUM FIBRE STRAINS OF 15,000, 20,000, AND 22,500 
 POUNDS PER SQUARE INCH.* 
 
 Diam- 
 eter of 
 pin. 
 
 Moment 
 15,000. 
 
 Moment 
 20^000. 
 
 Moment 
 22,500. 
 
 Diam- 
 eter of 
 pin. 
 
 Moment 
 15,000. 
 
 Moment 
 20,000. 
 
 Moment 
 for = 
 22,500. 
 
 In. 
 
 Lbs. in. 
 
 Lbs. in. 
 
 Lbs. in. 
 
 Inches 
 
 Lbs. in. 
 
 Lbs. in. 
 
 Lbs. in. 
 
 1 
 
 1,470 
 
 1,960 
 
 2,210 
 
 4 
 
 94,200 
 
 125,700 
 
 141,400 
 
 l/^ 
 
 2,100 
 
 2,800 
 
 3,140 
 
 4H 
 
 103,400 
 
 137,800 
 
 155,000 
 
 1^4 
 
 2,880 
 
 a,830 
 
 ' 4,310 
 
 44 
 
 113,000 
 
 150,700 
 
 169,600 
 
 WB 
 
 3,830 
 
 5,100 
 
 5,740 
 
 4% 
 
 123,300 
 
 164,400 
 
 185,000 
 
 1^ 
 
 4,970 
 
 6,630 
 
 7,460 
 
 4^ 
 
 134,200 
 
 178,900 
 
 201,300 
 
 1% 
 
 6,320 
 
 8,430 
 
 9,480 
 
 4% 
 
 145,700 
 
 194,300 
 
 218,500 
 
 I'M 
 
 7,890 
 
 10,500 
 
 11,800 
 
 4% 
 
 157,800 
 
 210,400 
 
 236,700 
 
 m 
 
 9,710 
 
 12,900 
 
 14,600 
 
 4% 
 
 170,600 
 
 227,500 
 
 255,900 
 
 2 
 
 11,800 
 
 15,700 
 
 17,700 
 
 5 
 
 184,100 
 
 245,400 
 
 276,100 
 
 2^ 
 
 14,100 
 
 18,800 
 
 21,200 
 
 5/^3 
 
 198,200 
 
 264,300 
 
 297,300 
 
 2/4 
 
 16,800 
 
 22,400 
 
 25,200 
 
 5J4 
 
 213,100 
 
 284,100 
 
 319,600 
 
 2% 
 
 19,700 
 
 26,300 
 
 29,600 
 
 5% 
 
 228,700 
 
 304,900 
 
 343,000 
 
 2^ 
 
 23,000 
 
 30,700 
 
 34,500 
 
 5 H 
 
 245,000 
 
 326,700 
 
 367,500 
 
 2% 
 
 26,600 
 
 35,500 
 
 40,000 
 
 5^8 
 
 262,100 
 
 349,500 
 
 393,100 
 
 2% 
 
 30,600 
 
 40,800 
 
 45,900 
 
 5M 
 
 280,000 
 
 373,300 
 
 419,900 
 
 2% 
 
 35,000 
 
 46,700 
 
 52,500 
 
 Wz . 
 
 298,600 
 
 398,200 
 
 447,900 
 
 3 
 
 39,800 
 
 53,000 
 
 59,600 
 
 6 
 
 318,100 
 
 424,100 
 
 477,100 
 
 3^ 
 
 44,900 
 
 59,900 
 
 67,400 
 
 6^ 
 
 338,400 
 
 451,200 
 
 507,600 
 
 3M 
 
 50,600 
 
 67,400 
 
 75,800 
 
 6^4 
 
 359,500 
 
 479,400 
 
 539,300 
 
 3M 
 
 56,600 
 
 75,500 
 
 84,900 
 
 6% 
 
 381,500 
 
 508,700 
 
 572,300 
 
 3 ix 
 
 63,100 
 
 84,200 
 
 94,700 
 
 672 
 
 404,400 
 
 539,200 
 
 606,600 
 
 3% 
 
 70,100 
 
 93,500 
 
 105,200 
 
 6% 
 
 428,200 
 
 570,900 
 
 642,300 
 
 3M 
 
 77,700 
 
 103,500 
 
 116,500 
 
 6% 
 
 452,900 
 
 603,900 
 
 679,400 
 
 3% 
 
 8570C 
 
 114,200 
 
 128,500 
 
 6% 
 
 478,500 
 
 638,000 
 
 717,800 
 
 REMARKS. The following is the formula for flexure applied to pins: 
 
 . 8*d* SAd 
 
 Af = __ or =-- 
 
 M = moment of forces for any section through pin. 
 
 S = strain per sq. in. in extreme fibres of pin at that section. 
 
 A = area of section. 
 
 d = 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 M max. is known, an inspection of the table will therefore show what 
 diameter of pin must be used in order that S may not exceed 15,000, 20,000, 
 or 22,500 Ibs., as the requirements of the case may be. 
 
 For railroad bridges proportioned to a factor of safety of 5, it is custom- 
 ary to make S max. = 15,000 Ibs. in iron and =20,000 Ibs. in steel. 
 
 
 * Carnegie Steel Company's Handbook. 
 
378 BENDING MOMENT IN PINS. 
 
 The following example will show the method of determining 
 the size of pin in a simple joint. , 
 
 EXAMPLE 5. Determine the size of pin for the joint shown by 
 Fig. 16, which is in the lower chord of a steel truss, the middle bar 
 being a vertical suspension rod merely to hold the chord in place. 
 
 ^ 40,000 
 
 IX 4" 
 
 
 
 
 1 
 
 \\W fer- 
 
 1 X 4 "-40,000 / 
 
 
 Es 
 
 s\s\N^ l-\ 
 
 IX 4'-40,000 ^ 
 
 . S 40,000 
 
 ~ 1 X 4" 
 
 i j 
 
 
 
 L 
 
 1 1 
 Fig. 16 
 
 
 Ans. The shearing and crushing strain in this case is 40,000 
 pounds. The bending moment will be the stress multiplied by 
 the distance between the centres of the two outer bars or 40,000 
 Xl" = 40,000 inch pounds. From Table VI., we find that to 
 sustain a bending moment of 40,000 pounds, with a fibre strain 
 of 20,000 pounds, will require a 2J" pin. From Table V. we find 
 that the bearing value of a 2f " pin is but 33,000 pounds, and that 
 we must increase the size of the pin to 3f inches. The shearing 
 strength of a 3f" pin is, from Table V., 67,000 pounds, so that the 
 size of pin we must use in this case is determined by the bearing 
 strain. To be sure of the correct size of the pin, one must 
 make the calculation for all three of the strains. 
 
 Bending Moment in Pins. 
 
 The only difficult part of the process of calculating the sizes of 
 pins will generally be found in determining the bending moment. 
 In cases where the strains all act in the same plane, the bending 
 moment can generally be determined by multiplying the outside 
 force by the distance from its centre to the centre of the next bar, 
 as in the foregoing example. When, however, the forces act in 
 several planes, as is generally the case, the process of determining 
 the bending moment is more difficult, and can be best determined 
 by a graphic process, first published by Prof. Chase Green, and 
 included in his lectures to the students in engineering at the 
 University of Michigan. 
 
 EXAMPLE 6. As the pieces acting on any well-designed joint 
 are symmetrically arranged, it is unnecessary to consider more 
 than one-half of their number. Fig. 17 shows a sketch of one- 
 half the members of a joint in the lower chord of a Howe truss. 
 
BENDING MOMENT IN PINS. 379 
 
 The pieces are parallel to the plane of the paper, and the pin is 
 perpendicular to the same, but drawn in cabinet perspective, at 
 an angle of 45 with a horizontal. 
 
 The bars are assumed to be each one inch thick and the channel 
 to have one-half -inch web. The centre of the hanger is J" from 
 the centre of the channel. 
 
 The method of obtaining the bending moment is as follows : 
 
 Draw the line A B (Fig. 18) at an angle of 45 with a horizontal, 
 and, commencing with c, lay off the distances between the centres 
 of the bars to a scale (1 J" or 3" to the foot will be found most con- 
 venient) ; then draw the lines 1-2, 2-3, etc., parallel to the pieces 
 which they represent in the truss, to a scale of pounds. Resolve 
 the oblique forces into their horizontal and vertical components 
 (in this example there is but one oblique force). 
 
 Next draw the stress diagram (Fig. 19) as follows : On a hori- 
 zontal line lay off 1-2, equal to the first or outer force ; 2-3, equal 
 to the next, then 3-4 ; and 4-1, being the horizontal component of 
 the brace, closes the figure. In the same way, lay off the vertical 
 forces 1-5, 5-6 and 6-1. If the forces are correct, the sum of the 
 forces acting in one direction will always equal those acting in 
 the opposite direction. From 1 draw the line 1-0 at 45, equal to, 
 say, 20,000 pounds, or any other convenient number at the same 
 scale. Draw 2, 3, 4, etc. Then, in Fig. 1$, starting at the 
 first horizontal force, draw c d parallel to 2, d e parallel to 
 3, e f parallel to 4, and / k parallel to 1. 
 
 In the same way, starting at the first vertical force, draw r s 
 parallel to 5, s t parallel to 6, and t v parallel to 1. Then the 
 line c d e f k will represent the boundary of the horizontal ordi- 
 nates, and r s t v the boundary of the vertical ordinates. And to 
 find the resultant of these ordinates at any point on the pin it is 
 only necessary to draw the diagonal from the ends of the ordinates 
 at that point. Thus, the resultant at X, Fig. 18, will be m-n, and 
 it is evident that this is the longest hypothenuse which' can be 
 drawn; and this hypothenuse, multiplied by 0-1 (20,000 pounds) 
 gives 52,500 pounds as the maximum bending moment on the 
 pin. 
 
 To obtain the maximum bending moment it is necessary to 
 take the longest hypothenuse that can be drawn, no matter at 
 what place it occurs. 
 
 If one desires to try the effect of changing the order of the bars 
 on the pin, it can readily be done. Suppose the diagonal tie to 
 change places with the next chord bar. The horizontal stress 
 
380 
 
 BENDING MOMENT IN PINS. 
 
 diagram then becomes 1-2, 2-3, 3-4', 4'-l. The equilibrium 
 polygons will now be (Fig. 20) c d e f k r and r' s' t r w and the 
 
 \\ 
 \\ 
 
 \\ 
 
 longest hypothenuse, w x, or 3f", which m^kes the bending 
 moment 75,000 pounds, showing that the arrangement in Fig. 17 
 is the best. 
 
BENDING MOMENT IN PINS. 
 
 381 
 
 As a rule, in arranging the bars on a pin, those forces which 
 counteract each other should be close together. 
 
 EXAMPLE 7. To further illustrate this method of determining 
 the bending moment on pins, we will determine the bending 
 
 FIG. 24 
 
 moment for the pin at the point A, Fig. 21. This is the same 
 truss as worked out in Example 7, Chapter XXVIII., the strains 
 given in Fig. 21 being J of the strains at the joint, as all the pieces 
 are doubled. Fig. 22 shows the size and arrangement of the ties 
 and strut. It is assumed that the web of the channel is re- 
 inforced to make it f" thick. Drawing the line AB, Fig. 24, we 
 lay off the outer force at a; then measuring off an inch, the dis- 
 tance between centres of the two outer bars, we lay off the next 
 force parallel to the direction in which it acts ; and in the same 
 way, the other two forces. The three inclined forces must be re- 
 solved into their horizontal and vertical components. We next 
 draw the stress diagram (Fig. 23) to the same scale of pounds, 
 making 1 equal to 20,000 pounds. The lines 4 and 6 happen, 
 in this case, to coincide. Then, in Fig. 24, we draw a b parallel 
 to 2, b c parallel to 3, c d= 4, and d e parallel to 1. In 
 
382' STRENGTH OF BOLTS. 
 
 the same way, we obtain the line hjkB. In this case, it will be 
 seen that the longest horizontal ordinate is h b, while at that 
 point there is no vertical ordinate; also, that no hypothenuse 
 can be drawn which will be as long as h b, so that w^e must take 
 h b as the greatest resultant; and this, multiplied by 20,000 
 pounds, gives 31,800 pounds as the maximum bending moment 
 on the pin. It will be seen that this is just the product of the 
 outer force by its arm to the centre of the next bar, so that the 
 greatest bending moment is at that point. 
 
 i o determine the size of the pin, we find, from Table VI., that 
 for a steel pin to sustain this moment, allowing a fibre strain of 
 20,000 pounds, we shall need a 2f" pin. This pin has a bearing 
 value of 31,500 pounds for a bar an inch thick. The outer bar in 
 this case is f " thick, and has a strain of 31,800 pounds, equivalent 
 to 42,400 pounds for a I" bar. And we see, from Table V., that 
 we shall need to use a 3J" pin to meet this strain. The shearing 
 strength of a 3J" pin is 36 tons, or more than double the strain. 
 Hence we must use a 3J" pin, or, by increasing the thickness of 
 the bars, we might reduce the pin to 3 inches. 
 
 Strength of Bolts in Wooden Trusses and Girders. 
 
 The strength of bolts in the joints of wooden structures is 
 something that has been given very little attention by writers and 
 engineers. The author knows of but one book which gives any 
 explanation of the way in which the size and number of the bolts 
 should be computed, or how to determine the stresses in them.* 
 The only actual knowledge that we have of the strength of bolt 
 joints in timber trusses is that derived from a series of tests 
 made at the Massachusetts Institute of Technology and described 
 in the Technology Quarterly for September, 1897. The results 
 of these tests were discussed by the author in the Engineering 
 Record of November 17, 1900. 
 
 The following rules and tables are entirely original with the 
 author; they are based upon the general principles of stresses, 
 upon the tests above referred to, and upon a very extended 
 experience with wooden trusses. The author believes that when 
 correctly used they will give perfectly safe results without an 
 undue excess of strength. 
 
 * The Design of Simple Roof Trusses in Wood and Steel by M. A. Howe, 
 C.E. John Wiley & Sons, Publishers. 
 
STRENGTH OP BOLTS. 
 
 383 
 
 TABLE VII. PERMISSIBLE BEARING VALUE (END 
 COMPRESSION) OF BOLTS IN TIMBER, PER INCH 
 OF LENGTH, AND DISTANCE* CENTRE OF BOLT 
 MUST BE FROM END OF TIMBER OR FROM THE 
 NEXT BOLT.* 
 
 Dia- 
 meter 
 
 Yellow pine. 
 
 Oregon pine 
 or oak. 
 
 Spruce. 
 
 White or 
 soft pine. 
 
 of 
 
 
 
 
 
 bolt 
 
 Bear- 
 
 Dis- - 
 
 Bear- 
 
 Dis- 
 
 Bear- 
 
 Dis- 
 
 Bear- 
 
 Dis- 
 
 . 
 
 ing, 
 
 tance, 
 
 ing, 
 
 tance, 
 
 ing, 
 
 tance, 
 
 ing, 
 
 tance, 
 
 
 Ibs. 
 
 ins. 
 
 Ibs. 
 
 ins. 
 
 Ibs. 
 
 ins. 
 
 Ibs. 
 
 ins. 
 
 | 
 
 1125 
 
 5 
 
 1012 
 
 44 
 
 900 
 
 5 
 
 750 
 
 5 
 
 4 
 
 1310 
 
 6 
 
 1183 
 
 5 
 
 1050 
 
 
 
 880 
 
 54 
 
 1 
 
 1500 
 
 6 
 
 1350 
 
 5} 
 
 1200 
 
 BJ 
 
 1000 
 
 6 
 
 14 
 
 1690 
 
 7 
 
 1520 
 
 6 
 
 1350 
 
 7 
 
 1125 
 
 7 
 
 i| 
 
 1870 
 
 74 
 
 1690 
 
 64 
 
 1500 
 
 74 
 
 1250 
 
 8 
 
 if 
 
 2060 
 
 8 
 
 1860 
 
 7* 
 
 1650 
 
 8 
 
 1375 
 
 9 
 
 tf 
 
 2250 
 
 9 
 
 2025 
 
 8 
 
 1800 
 
 9 
 
 1500 
 
 10 
 
 1J 
 
 2625 
 
 10 
 
 2360 
 
 9 
 
 2100 
 
 10 
 
 1750 
 
 11 
 
 2 
 
 3000 
 
 11 
 
 2700 
 
 10 
 
 2400 
 
 12 
 
 2000 
 
 12 
 
 2J 
 
 3375 
 
 12 
 
 3040 
 
 11 
 
 2700 
 
 13* 
 
 2250 
 
 13* 
 
 2* 
 
 3750 
 
 13 
 
 3375 
 
 12 
 
 3000 
 
 15 
 
 2500 
 
 15 - 
 
 2f 
 
 4125 
 
 14 
 
 3710 
 
 13 
 
 3300 
 
 16J 
 
 2750 
 
 164 
 
 3 
 
 4500 
 
 15 
 
 4050 
 
 14 
 
 3600 
 
 18 
 
 3000 
 
 18 
 
 * Based on a bearing resistance of 1500 Ibs. per sq. in. for Southern yellow 
 pine, 1350 Ibs. for oak and Oregon pine, 1200 Ibs. for spruce, and 1000 .Ibs. 
 for white pine. 
 
 TABLE VIII. PERMISSIBLE BEARING VALUE (ACROSS 
 THE GRAIN) OF BOLTS IN TIMBER, PER INCH 
 OF LENGTH.* 
 
 Diameter 
 of bolt 
 in ins. 
 
 Yellow 
 pine. 
 
 Oregon 
 pine. 
 
 Spruce. 
 
 White 
 pine. 
 
 Oak. 
 
 a 
 
 375 
 
 300 
 
 225 
 
 187 
 
 450 
 
 f 
 
 437 
 
 350 
 
 262 
 
 220 
 
 525 
 
 i 8 
 
 500 
 
 400 
 
 300 
 
 250 
 
 600 
 
 l| 
 
 562 
 
 450 
 
 337 
 
 280 
 
 675 
 
 1| 
 
 625 
 
 500 
 
 375 
 
 310 
 
 750 
 
 If 
 
 687 
 
 550 
 
 412 
 
 345 
 
 825 
 
 if 
 
 750 
 
 600 
 
 450 
 
 375 
 
 900 
 
 if 
 
 875 
 
 700 
 
 490 
 
 437 
 
 1000 
 
 2 
 
 1000 
 
 800 
 
 600 
 
 500 
 
 1200 
 
 * Based on unit stresses of 600 Ibs. per sq. in. for oak, 500 for Southern 
 yellow pine, 400 for Oregon pine, 300 for spruce, and 250 for white Dine. 
 
384 
 
 STRENGTH OF BOLTS. 
 
 TABLE IX. MAXIMUM PERMISSIBLE TENSION, 
 SHEAR, AND BENDING MOMENT (IN INCH- 
 POUNDS) FOR' WROUGHT-IRON BOLTS IN 
 TIMBER. 
 
 Diam. 
 
 
 
 
 Diam. 
 
 
 
 
 of 
 
 Ten- 
 
 Single 
 
 Bending 
 
 of 
 
 Ten- 
 
 Single 
 
 Bending 
 
 bolt 
 
 sion, 
 
 shear, 
 
 moment, 
 
 bolt 
 
 sion, 
 
 shear, 
 
 moment, 
 
 in 
 
 Ibs.* 
 
 Ibs. 
 
 inch-lbs. 
 
 in 
 
 Ibs.* 
 
 Ibs. 
 
 inch-lbs. 
 
 ins. 
 
 
 
 
 ins. 
 
 
 
 
 | 
 
 6,000 
 
 4,420 
 
 931 
 
 ii 
 
 35,000 
 
 24,050 
 
 11,800 
 
 |. 
 
 8,400 
 
 6,010 
 
 1,479 
 
 2 
 
 45,000 
 
 31,416 
 
 17,700 
 
 1 
 
 10,860 
 
 7,850 
 
 2,210 
 
 2i 
 
 60,000 
 
 39,760 
 
 25,200 
 
 11 
 
 13,720 
 
 9,940 
 
 3,140 
 
 2| 
 
 74,000 
 
 49,080 
 
 34,500 
 
 H 
 
 17,700 
 
 12,270 
 
 4,310 
 
 2f 
 
 92,000 
 
 59,400 
 
 45,900 
 
 if 
 
 21,400 
 
 14,480 
 
 5,740 
 
 3 
 
 108,000 
 
 70,700 
 
 59,600 
 
 li 
 
 25,740 
 
 17,670 
 
 7,460 
 
 3i 
 
 130,000 
 
 82,950 
 
 75,800 
 
 Unit stresses: Tension, 20,000 Ibs., shear, 10,000 Ibs., bending 22,500 Ibs. 
 * To be used only in truss joints. Not safe for rods. 
 
 General Principles. As a rule, bolts as used in wooden trusses 
 and girders are subject to the same kind of stresses as pins or 
 rivets in steel structures, although occasionally they are subject 
 only to direct tension. When the pieces joined are not more than 
 two inches thick, so that they can be drawn tightly together, 
 thereby producing a good deal of resistance from friction, the 
 bolts may be considered as rivets and proportioned for shearing 
 and bearing only, the bending moment being neglected. 
 
 When the pieces of wood joined are more than two inches thick, 
 the bolts should be proportioned for shearing, bearing, and 
 flexure. 
 
 Tables. To facilitate computing the number and size of the 
 bolts, the author has prepared Tables VII., VIII., and IX., giving 
 the safe resistance of bolts of different sizes to each kind of stress, 
 and also the length of wood required beyond or between the bolts 
 to prevent shearing of the wood. 
 
 The bearing resistance is determined by the resistance of the 
 wood to crushing, and not by the resistance of the bolt, but for 
 convenience it is considered as a property of the bolt. The 
 resistance of wood to crushing across the grain being very much 
 less than against end wood, the bearing resistance both ways is 
 given. With these tables it is only necessary to compute the 
 stress of each kind, and to select the bolt or number of bolts that 
 will resist all of the stresses. 
 
STRENGTH OF BOLTS. 385 
 
 The unit stresses allowed in computing the tables are some- 
 what larger than are recommended for struts or rods, but for the 
 conditions under which bolts are generally used the author 
 believes the tables may be used with perfect confidence. The 
 safe tension given in Table IX., however, should only be used 
 when the stress is computed as directed in Case V. 
 
 Special Cases. The various ways in which bolts are used in 
 wooden structures to transmit a load or stress from one piece to 
 another are illustrated by Figs. 25 to 35, which may be divided 
 into five cases,- each of which, to make the explanation more 
 readily understood, is treated separately. 
 
 Case 1. Bolts in Built-up Tie-beams. Figs. 25 and 26. Tie- 
 beams of wooden trusses, when more than 30 feet long, must 
 usually be built up of several pieces on account of the expense 
 of a single stick of timber of the full length. Such tie-beams 
 can generally be built to the best advantage of 2-inch plank, 
 breaking joint and bolted together side by side. 
 
 As the tensile stress in a tie-beam is often very considerable, 
 the placing of the joints and the size and number of the bolts 
 must be determined with much care, otherwise the beam may 
 be pulled apart longitudinally so as to permit the truss to sag, 
 or possibly to collapse. 
 
 EXAMPLE 8. Fig. 25 is given as a typical example of a built 
 tie-beam. It represents the tie-beam of a six-panel Howe Truss 
 of 50 feet span carrying two floors and a roof, the direct tension 
 in the different panels being as indicated on the lower line. The 
 thickness of the planks are drawn out of proportion to the 
 length in order to more clearly show the end-joints. The black 
 circles in the centre plank represent the vertical rods. The wood 
 is to be Oregon pine. 
 
 It will be seen that the rods practically cut the centre plank 
 in two, and for this reason it is better to build the tie-beam of an 
 uneven number of planks rather than of an even number, and the 
 centre course of planks should be jointed at the rods. 
 
 No dependence is placed upon the centre course of planks for 
 resisting the tension, although they count in resisting the trans- 
 verse strain. 
 
 The length of the planks that should be used for the outer 
 courses, and the way in which they should break joint, is a 
 matter that will vary for different trusses, and for which no 
 definite rule can be given. 
 
 In general the planks should be of such length and so arranged 
 
386 
 
 STRENGTH OF BOLTS. 
 
 that the distance between the joints in adjacent courses, as at 
 X and Y, will be as great as practicable, and so that not more than 
 two joints will come opposite each other. 
 
 For the tie-beam in question, the length and arrangement 
 shown is as good as can be devised. This gives a distance be- 
 tween X and Y of 12 feet ; which is about as little as would answer. 
 At the centre, where the stress is greatest, 
 only one joint occurs at any given cross 
 section. 
 
 In this beam, the two outer planks A' A. 
 must be capable of resisting the full tensile 
 strength in the centre panels of the truss, 
 and the planks B and C must transmit the 
 stress in the second panel to the end braces. 
 We must therefore place enough bolts be- 
 . tween the joints X-Y to transmit the stress 
 i from the outer planks to planks B and C. 
 
 The stress to be transmitted is the stress 
 * in the second panel, or 58,000 Ibs. We may 
 
 1 assume that A' will receive one half of 
 
 2 this, or 29,000 Ibs., and that if we provide 
 I enough bolts to transmit 29,000 Ibs. from 
 jj A.' to j3, the other side of the tie-beam will 
 
 carry a like strain. 
 
 These bolts must be computed for shear- 
 ^ ing and bearing. The bolts will be in single 
 shear between A' and B. We will now see 
 how many 1-inch bolts will be required to 
 resist a shearing and bearing stress of 
 29,000 Ibs. 
 
 From Table IX. we find the resistance 
 of a 1-inch bolt to single shear to be 7,850 
 Ibs.'; hence, to resist a stress of 29,000 Ibs. 
 will require four bolts. 
 
 The resistance of a 1-inch bolt in Oregon 
 pine (Table VII.) is 1,350 Ibs. per inch of 
 bearing. As the bearing in each plank is 2 inches, we have 
 2,700 Ibs. as the safe resistance to bearing of one bolt, conse- 
 quently it will require eleven 1-inch bolts to avoid crushing the 
 wood. As the number is larger than that required to resist 
 shearing, it is the number of bolts required, 
 
STRENGTH OF BOLTS. 
 
 387 
 
 These bolts must be placed between the points X and Y at 
 each side of the centre. From the distance column in Table VII. 
 we see that the bolts should be placed at least 5J inches from 
 the end of the planks. Calling it 6 inches and putting two bolts 
 &tX and two at F, we must divide the remaining space, 11 feet, 
 by the remaining 7 bolts. As there will be 8 spaces, the bolts will 
 be 16J inches apart, longitudinally. They should be staggered, 
 as shown in Fig. 26. 
 
 Joint 
 
 V 
 
 Vspike 
 
 | 
 
 ~ 6 "i 
 
 ll/' / ilir l'4 1 ^ X/ J 
 
 f 
 
 tzr 
 
 Fig. 26. Elevation of Beam opposite X. 
 
 These 11 bolts each side of the centre will be sufficient to 
 transmit the entire tensile stress to the supports, but bolts 
 should also be inserted between the points Y-Y f , and between 
 X-X' and the ends, to bind the planks together. These bolts, 
 however, need not be as large, nor as near together; j-inch 
 bolts will answer, spaced about 2 feet on -centres. Two bolts 
 should always be placed at the end of a built tie-beam. 
 
 The bolts should be of wrought iron or mild steel, driven 
 through holes of the same size as the bolt, provided with washers, 
 and the nuts screwed up tight. 
 
 Case II. Bolts in Girders, as in Figs. 27 and 28. The construc- 
 tion shown by Figs. 27 and 28 is very commonly used, where a 
 girder cannot project its entire depth below the floor joists. 
 The bolts in Fig. 27 should be computed for resistance to bearing 
 and shearing, and in Fig. 28 to bearing, shearing, and flexure. 
 In either case the resistance to single shear must equal S or S', 
 whichever is the larger. 
 
 , S+S' 
 Bearing on wood per mch= -g . 
 
 O 7 rr/ T 
 
 In case Fig. 28, Bending moment = o- or ~o~> whichever is 
 larger, B and L being measured in inches. 
 
388 
 
 STRENGTH OF BOLTS. 
 
 EXAMPLE 9. We will suppose that we wish to use the con- 
 struction shown in Fig. 27. The girder to be 8"Xl4", with a 
 span of 14 ft. The floor joists to be 3" X 12", with a span of 20 
 ft., measured from the centres of girders. Joists and girders to 
 be of Oregon pine. Angles to be 4"X3J"Xt". The floor load 
 to be figured at 60 Ibs. per sq. ft., including weight of floor. 
 
 How many and what size bolts should be used, S and $' being 
 equal? 
 
 Ans. The floor area supported by girder = 14 X 20= 280 sq. ft. 
 at 60 Ibs. persq. ft. S + S'= 280X60 =16,800 Ibs. or S= 8,4 00 Ibs. 
 Try |" bolts. Total single shear= 8,400 Ibs. Resistance of one 
 J" bolt to single shear, (see Table IX.) = 4,420 Ibs. Hence two 
 bolts will resist the shearing stress. 
 
 Bearing stress per inch= 
 
 16,800 _ 16,800 
 
 B 
 
 8 
 
 = 2,100 Ibs. 
 
 Bearing resistance of one f " bolt in Oregon pine, across the 
 grain, Table VIII, = 300 Ibs. Hence seven bolts will be required 
 to prevent crushing of the wood. As the span is 14 ft., this will 
 require a f -inch bolt every 2 feet. The centre of the bolts should 
 be at least 3" above the bottom of the girder. 
 
 EXAMPLE 10. Construction as shown in Fig. 28. Girder 
 6"X14", Oregon pine, 12 ft. span. Joists 2"X12", 18 ft. span 
 to centre of girder, on each side. Total floor load 65 Ibs. per sq. 
 ft. Strips on sides of girder 3"X4"j L=3". How many and 
 what size bolts should be used? 
 
 Ans. Load supported by girder = 12' X 18' X 65 = 14,040 Ibs. 
 $=7,020 Ibs. = shearing stress, 
 
 Bearing stress per inch= ^ = 2,340 Ibs. 
 
 7 020 V ^ 
 Bending moment= ' " A = 10,530 Ibs. 
 
STRENGTH OF BOLTS. 
 
 389 
 
 To resist the shearing stress will require two f" bolts. To 
 resist the bearing stress (use Table VIII.) will require eight J" 
 bolts, or seven J" bolts. 
 
 To resist the bending moment (use Table IX.) will require 
 eleven f " bolts, or seven " bolts. Eleven f " bolts would give a 
 spacing of only about 13", allowing for one bolt at each end, and 
 this would injure the girder, hence we must use seven f" bolts, 
 which would be spaced about 22" on centres. Practically the 
 strain on the bolts will be somewhat relieved by toe-nailing the 
 joists to the girder, but it is not safe to put much dependence 
 upon the spikes. 
 
 Caselll. Pin Bolts , as in Figs. 29-31. Whenever ties or struts 
 
 I 
 
 ELEVATION 
 
 B' 
 
 ~t \ \ l/ 2 S > 
 
 1 
 
 i 
 
 Hi ! 
 
 
 yy 
 
 
 B' 
 
 
 
 V2S -> 
 
 I 
 
 t. 
 
 t=r 
 
 Fig. 
 
 PLAN 
 29 
 
 are joined by bolts in the manner indicated by Figs. 29-31, and 
 the thickness B exceeds 2 inches, the diameter of the bolt OT 
 
 -y.s -T 
 
 Fig. 30 
 
390 STRENGTH OF BOLTS. 
 
 bolts should be computed for resistance to shearing, bearing and 
 flexure. 
 
 For any one of these joints the stresses will be as follows; 
 
 Single shear = - . 
 
 nr 
 
 Bearing pressure on pin per inch of length =* 
 
 T5 A' *J. 
 
 Bending moment j 
 
 i 
 
 If there should be more than one bolt, divide the stress obtained 
 by the above formulas by the number of bolts, to find the stress 
 in each bolt. 
 
 Fig. 31 
 
 In Fig. 29 S equals the horizontal component of the thrust T. 
 
 EXAMPLE 11. Construction as in Fig. 29. A6"XlO" rafter 
 is joined to two 3"X 10" tie-beams by a single bolt. The thrust 
 in the rafter is 30,000 Ibs., and the angle between the rafter and 
 tie-beams is 30 degrees. What should be the diameter of the 
 bolt, the timber being spruce? 
 
 Ans. The horizontal component of 30,000 Ibs. at an angle of 
 30 is practically 26,000 Ibs. Then =26,000, B= 6 inches, 
 L=9 inches. Single shear =13,000 Ibs. 
 
 2fi 000 
 Bearing pressure per inch of bolt= V. =4,333 Ibs. 
 
 -D j- 26,000X9 ,. ,, 
 
 Bending moment = ~^ =19,500 Ibs. 
 
 * This holds good only when B' in Figs. 29 and 30 is one half or more of 
 B, and for Fig. 31, when B' is two thirds or more of B. 
 
 t Based on the supposition that the bolt acts as a beam fixed at both ends 
 and uniformly loaded. 
 
STRENGTH OF BOLTS. 391 
 
 From Table IX. we find that to resist a shearing stress of 13,000 
 Ibs. will require a If" bolt, and to resist a bending moment of 
 19,500 Ibs. will require a 2J-inch bolt. 
 
 To resist a bearing pressure of 4,333 Ibs. on end wood in spruce 
 will require a larger bolt than is given in the table (Table VII.). 
 If we divide our stress of 4,333 Ibs. by 1,200, the allowed pressure 
 per sq. inch for spruce, we obtain 3| inches for the diameter 
 of the bolt; hence in this example the diameter of the bolt is 
 determined by the bearing pressure. This is a larger bolt than it 
 is desirable to use, and we will see what diameter will be required 
 if we make the strut 8"X8", and the tie-beams 4"X8", as the 
 strength of the timber would be about the same. 
 
 Using these dimensions, B=8 ins. and L, 12 ins. This will 
 
 give us 
 
 26 000 
 a bearing pressure of =3,250 Ibs. and a bending 
 
 8 
 
 moment of 26?OQ( 1 X 12 = 26,000 Ibs. The shear will be the same 
 
 as before, as it is not affected by the width of B. 
 
 To resist a bearing pressure of 3,250 Ibs. will require (see 
 Table VII.) a 2f " bolt, and to., resist a bending moment of 26,000 
 Ibs., a 2J" bolt. Hence if we make the strut 8"X8" we should 
 use a 2f" bolt, and D should be 16J" (from Table VIL). 
 
 EXAMPLE 12. Same construction as above, but with three 
 bolts, placed as shown by dotted circles, instead of one. Strut 
 to be 6" X 10" ; tie-beams, 3" X 10", spruce. Stress to be the same 
 as in the above example. The shearing, bearing, and bending 
 stresses will also be the same, but as we are using three bolts, each 
 stress should be divided by three. 
 
 This will give the stress on each bolt, and the corresponding 
 size of bolt, as follows : 
 
 Shearing stress =4,333 Ibs., requires a f-inch bolt. 
 Bearing pressure =1,444 Ibs., H-inch bolt. 
 
 Bending moment =6,500 Ibs., IJ-inch bolt. 
 
 In this case the bending moment requires the largest bolt, and 
 we must use three 1-J-inch bolts. 
 
 EXAMPLE 13. Construction as in Fig. 30. Centre beam to 
 be 6"X8", and outer beams 3"X8", all of Oregon pine. 
 
392 
 
 STRENGTH OF BOLTS. 
 
 Assume tension in centre beam to be 24,000 Ibs. What should be 
 the diameter of the bolt? 
 
 .4ns. S= 24,000; J5=6", and L=9". 
 
 Single shear= 12,000 Ibs. 
 
 24 000 
 Bearing pressure per inch= =4,000 Ibs. 
 
 Bending moment = 
 
 24,000X9 
 12 
 
 18,000 Ibs. 
 
 To resist the shear will require a 1J" bolt, to resist bearing 
 pressure a 3" bolt, and to resist the bending moment will re- 
 quire a 2J" bolt. For a 3" bolt the distance D should be 14". 
 
 EXAMPLE 14. Same conditions as in Example 13, except that 
 two bolts, one behind the other, will be used. With two bolts, 
 each stress will be one-half of that for a single bolt. Dividing 
 the stresses obtained in example 13 by 2, we have : 
 
 Single shear = 6,000 Ibs., requires a f-inch bolt. 
 Bearing pressure =2,000 Ibs., requires a IJ-inch bolt. 
 Bending moment =9,000 Ibs., requires a If -inch bolt. 
 
 Hence the size of the bolt is determined by the bending 
 moment, and we must use two If -inch bolts. For a If -inch bolt 
 D should be at least 8J inches, and the distance between the 
 bolts an inch or VII, more, say 10 inches. 
 
 Case IV. Strop and Bolt Joint, as in Fig. 32. The construc- 
 tion indicated by Fig. 32 is sometimes used to secure the foot of 
 
 b 
 
 Fjg. 32 
 
 the rafter in wooden trusses to the tie-beam. When the dis- 
 tance D is sufficient to resist the shearing stress, as explained 
 at the beginning of this chapter, the strap is only of value in 
 
STRENGTH OF BOLTS. 393 
 
 holding the rafter in place, and the bolt is not subject to any 
 great stress. When it is impossible to get the necessary 
 length for D, then the strap and bolt should be computed to 
 resist the full stress. 
 
 As the strap should not usually be more than J" to f " thick, 
 only the shear and bearing pressure on the bolt need be con- 
 sidered. These should be computed as follows: 
 
 S 
 Single shear = = tension in strap. 
 
 Zi 
 
 Of 
 
 Bearing pressure per inch on wood=^ where 5= breadth of 
 tie-beam in inches. 
 
 cr 
 
 Bearing pressure per inch on strap =--, where t equals thickness 
 
 b 
 
 of strap in inches. 
 
 To find the value of S, draw a line T, representing the thrust in 
 the rafter to a scale of pounds to the inch, and parallel with the 
 axis of the rafter. From the end a draw an indefinite line parallel 
 to the axis of the strap, and from the end b a line at right angles 
 to the seat of the rafter. These lines will intersect at C, and ac t 
 measured by the scale used in drawing T, will give the value of 
 S in pounds. If the rafter in Fig. 32 rests on the top of the tie- 
 beam, then be will be vertical, but if the tie-beam is notched out, 
 as shown by the dotted lines, then the line from b should be drawn 
 at right angles to the bottom of the notch, which will give the point 
 c'. It will be seen that notching the tie-beam increases the stress 
 in the strap. 
 
 EXAMPLE 15. In a king rod truss of 36 feet span the com- 
 pression in the rafter is 18,000 Ibs., and the inclination of the 
 rafter 45. The rafter is to be 6"X6" and the tie-beam 6"X8", 
 both of spruce. What size strap and pin-bolt will be required to 
 hold the foot of the rafter, without notching into the tie-beam? 
 
 Ans. The first step is to determine the stress S. As the in- 
 clination of the rafter is 45, and the seat of the rafter is hori- 
 zontal, the line ac (Fig. 32) must equal ab; hence S will equal 
 T, or 18,000 Ibs. 
 
 Then the single shear on bolt will be 9,000 Ibs. 
 Tension in each side of strap will be 9,000 Ibs. 
 
 18 000 
 Bearing pressure per inch on wood= ' = 3,000 Ibs. 
 
 9,000 
 
 Bearing pressure per inch on strap, -?. 
 
 t 
 
394 
 
 STRENGTH OF BOLTS. 
 
 That the strap may not crush the top of the rafter, it should 
 be at least 3 inches wide. At 10,000 Ibs. per sq. inch the sec- 
 tional area required in the strap will be .9 inch. If we divide this 
 by the width (3) we have .3 inch for the thickness. We will 
 therefore make the strap f inch thick and 3 inches wide. The 
 bearing pressure per inch on the strap will then be 
 
 Q nnn s 
 
 ^P^=| X 9,000= 24,000 Ibs. 
 f 3 
 
 The bolt must therefore be able to resist a single shear of 
 9,000 Ibs., a bearing pressure against spruce of 3,000 Ibs. per 
 inch, and a bearing pressure against the strap of 24,000 Ibs, 
 From Table IX. we find that it will require a IJ-inch bolt to 
 resist the shear; from Table VII we find that it will require a 
 2J-inch bolt to reduce the pressure on the wood to the proper 
 limit, and from Table V. of this chapter that we should use a 
 2-inch pin for a bearing of 24,000 Ibs. on the strap. The largest 
 bolt is that required for the bearing against the wood, or 2J 
 inches. If the width of the beam and rafter was increased to 
 
 gW^\^ Tie Beam 
 
 Fig. 33 
 
 Fig. 34 
 
 8 inches, the bearing on the wood per inch would be reduced to 
 2,250 Ibs., which would require only a 2-inch bolt; the same 
 diameter as required for bearing on the strap. As a rule this 
 form of joint is not desirable for trusses having a span of more 
 than 36 feet, or where the compression in the strut exceeds 
 18,000 Ibs. It has the advantage over the joint shown in Fig. 33, 
 however, in that there is no iron work to project below the 
 bottom of the tie-beam. 
 
STRENGTH OF BOLTS. 395 
 
 In the joint (Fig. 33) the bolt is subject to direct tension only, the 
 stress in the bolt being denoted by S. The value of S is found 
 in exactly the same way as explained under Case IV. The rafter 
 may be let into the tie-beam, or it may merely rest on top, the 
 stress in the bolt being least in the latter case, but it is easier to 
 fit the members of the truss together if the rafter is let into the 
 tie-beam say 1| or 1J inches. If the shoulder is 4 to 6 inches 
 long it will hold the rafter while the pieces are being fitted 
 together, and after they are fitted, the hole for the bolt can be 
 bored in the right position. 
 
 Whenever S exceeds 10,000 Ibs. a cast plate, as shown in 
 Fig. 34, made to fit the inclination of the bolt, should be let into 
 the bottom of the tie-beam for the head of the bolt to bear 
 against. The hole for the bolt should be -J inch larger than the 
 diameter of the bolt. The horizontal component of S should be 
 determined, and the distances D and D' made sufficient to resist 
 longitudinal shearing. 
 
 The horizontal component is found by drawing a vertical line 
 from c and a horizontal line from a, in the diagram, Fig. 33, in- 
 tersecting at d. ad, measured by the scale of the diagram, will 
 give the horizontal component. The distance D+D' should 
 equal the horizontal component divided by the breadth of the tie- 
 beam multiplied by the value of F, Table I. of this chapter. 
 
 EXAMPLE 16. Conditions the same as in Example 15. Deter- 
 mine the diameter of the bolt, and least distance for D. In this 
 example S will be greater than in Example 15, because the seat 
 of the rafter is not horizontal. Therefore draw T= 18,000 Ibs. 
 to a scale, and parallel to the axis of the rafter. (See diagram 
 Fig. 33.) From the lower end of T draw a line parallel to the 
 bolt, and from b a line at right angles to the seat of the 
 rafter. These two lines will meet at c, and ac will give the 
 value of 8, which we find to be 27,000 Ibs. From Table IX. we 
 find that it will require a 1 f-inch bolt to resist a direct tension 
 of 27,000 Ibs.; therefore the bolt must be If inches in diam- 
 eter. On the stress diagram draw a vertical line through c 
 and a horizontal line through a, then ad represents the shearing 
 force to be resisted at D. The line ad we find measures 19,000 
 Ibs. The breadth of the tie-beam is 6 inches, and F, for spruce, 
 
 s* i 1 Q 000 
 
 Table I., with the grain, is 90 Ibs. ; then D + D' must = ^-QQ or 35 
 
 inches, In Fig. 33, D= 20 inches, and D' 15J inches; therefore, 
 the distance is sufficient. 
 
396 
 
 STRENGTH OF BOLTS. 
 
 NOTE. The author believes that for computing the resistance 
 to longitudinal shearing, in a case like this, where there is a heavy 
 compression on the wood across the grain, it will be perfectly 
 safe to use values for F double those given in Table I. This 
 opinion is based on the tests made at the Massachusetts Institute 
 of Technology, and mentioned on page 382. 
 
 EXAMPLE 17. To determine the size of bolts for the joint 
 shown in Fig. 35, the thrust in the rafter being 65,500 Ibs. and 
 the timber being yellow pine. 
 
 8"x8" 
 Cast Washe] 
 
 Fig. 35 
 
 Ans. The first step is to determine the tension in the rods. 
 This is done by drawing the diagram, commencing with the line 
 ab, which represents the thrust in the rafter, ac is drawn 
 parallel to the bolts and b c at right angles to the seat of the 
 rafter. The line ac scales 96,500 Ibs., and assuming that the 
 strain will be equal in the two bolts, the tension in each bolt 
 will be 48,250 Ibs. From Table IX. we find that this will require 
 a 2}-inch bolt. Therefore we must use two bolts of 2J inches 
 diameter. 
 
 The horizontal component of ac is represented by the line ad, 
 which scales 68,350 Ibs. This will require a shearing area in 
 
 68 3^)0 
 hard pine of ^T^F~ or 547 sq. inches. As the tie-beam is 8 
 
 125 
 
 547 
 
 inches wide the length must*be ~ or 68i inches. In the draw- 
 
 o 
 
 ing we have much more than this, hence there will be no danger 
 of the bottom plates shearing the wood. 
 
STRENGTH OF BOLTS. 397 
 
 Theoretically, the size of the washers should be equal to the 
 stress in one bolt divided by the resistance of the wood to crushing 
 
 48 250 
 
 across the grain,* or ' or 96 sq. inches, but as a slight crush- 
 oUU 
 
 ing of the fibres in this case would do no particular harm, we 
 will reduce the area to 64 sq. inches or 8X 8 inches. 
 
 * For resistance of woods to crushing across the grain, see Chapter XIV. 
 
398 BEARING-PLATES FOR GIRDERS AND COLUMNS. 
 
 CHAPTER XIIL 
 
 PROPORTIONS OP CAST-IRON AND STEEI 
 BEARING - PLATES FOR COLUMNS, 
 BEAMS AND GIRDERS, AND FOR BRAC- 
 KETS ON CAST COLUMNS. 
 
 If a heavily loaded column or girder should rest directly upor 
 a wall or pier of masonry, the weight would be distributed ovei 
 such a small area that in most cases there would be danger o: 
 crushing the masonry, particularly if it were of brick or rubblf 
 work. To prevent this a bearing-plate should be placed betweer 
 
 T 
 
 VAY/ 
 
 
 
 mac 
 
 / 
 
 
 
 l \ 
 
 / 
 
 ; 
 
 --D- * 
 
 ^ p-X- 
 
 1 
 
 
 
 / 
 
 _L 
 
 J_ 
 
 SECTION 
 
 Fig. 2 
 
 Fig. 3 
 
 the end of the beam on column and the masonry, the size of the 
 plate being such that the load from the column or girder divided 
 by the area of the plate shall not exceed the safe crushing strength 
 of the masonry per unit of measurement. 
 
BEARING-PLATES FOR GIRDERS AND COLUMNS- 399 
 
 TABLE I. MAXIMUM LOAD PER SQUARE INCH ON 
 DIFFERENT KINDS OF MASONRY FROM BEAR- 
 ING PLATES. 
 
 For granite 1,000 Ibs. per sq. in. 
 
 " best grades of sandstone 700 " " " " 
 
 " soft sandstone 400 " " " " 
 
 " hard stone rubble 150 to 250 " " " " 
 
 " extra-hard brickwork in cement mor- 
 tar 150 to 200 " " " " 
 
 " good hard Eastern brickwork in lime 
 
 mortar 120 " " " " 
 
 " common brickwork .?,'??1^^W? 1 100 " " " " 
 
 " good Portland cement concrete. ..... 200 " " " " 
 
 " sand or gravel 60 " " " " 
 
 EXAMPLE 1. The basement columns of a six-story warehouse 
 support a possible load of 212,000 pounds each; under the column 
 is a base-plate of cast iron resting on a bed of Portland-cement 
 concrete two feet thick. What should be the dimensions of 
 the base-plate? 
 
 Answer. As the plate rests on concrete, the bottom of the 
 plate should have an area equal to 212,000-^-200=1060 square 
 inches, or 33 inches square. The column should be about 10 
 inches in diameter and 1 inch thick. The shape of the base-plate 
 should be as shown in Fig. 1. 
 
 Shape of Column Base-Plates. For small columns and wooden 
 posts with light loads, plain flat plates of cast iron are generally 
 used. They may have a raised ring or cross to fit inside the base 
 of a hollow column, or for a wooden post a raised dowel, 1| inches 
 or 2 inches in diameter. If the plate is very thick, a saving in 
 the weight of the plate may be made by bevelling the edge, as 
 shown in Fig. 2, without loss of strength. The outer edge, how- 
 ever, should not be less than -J inch thick. 
 
 When the bearing-plate is so large that the projection beyond 
 the column is more than six inches, a ribbed plate should be 
 used similar to that shown in Fig. 1, which is drawn for a round 
 column. Fig. 9, Chapter XIV., shows a similar base-plate for 
 an H-shaped column. With such plates no transverse strain 
 is developed, and if the column is bolted to the plate, it adds 
 greatly to the stability o f the column. 
 
 For base-plates similar to Fig. 1 the height H should be equal 
 to the projection P and D should be equal to the diameter of 
 
400 BEARING-PLATES FOR GIRDERS AND COLUMNS. 
 
 the column. The thickness of all portions of the plate should 
 be equal, or nearty so, to that of the column above the base, 
 This is not so much required for strength as to get a perfect 
 casting, as such castings are liable to crack by unequal cooling 
 when the parts are of different thickness. The projection of 
 the flange C should be at least 3 inches, to permit of bolting the 
 column to the plate. 
 
 For steel columns, base-plates of steel, such as are shown in 
 connection with the details of Z-bar and channel columns, 
 Chapter XIV, are commonly used, although for very heavy steel 
 columns cast-iron base-plates are also used, and where the cast 
 iron is entirely in compression, they are to be preferred to steel 
 bearing-plates. 
 
 Calculations for Bearing-Plates. For ribbed or bracketed 
 plates, such as Fig. 1, proportioned as above described, no other 
 calculation is necessary than that of finding the area of the base, 
 as illustrated by Example 1. With flat plates, however, a trans- 
 verse strain is developed in the metal, and it is necessary to 
 compute the thickness of the plate as well as its size. To find the 
 size and thickness of flat plates under columns and posts 
 
 First determine the size of the plate by dividing the load on 
 the column in pounds by the safe resistance of the material on 
 which the plate rests, as explained in Example 1. 
 
 Second. Knowing the size of the plate and the size of the 
 column, determine the projection of the plate beyond the column. 
 
 Let w = pressure under the plate in Ibs. per sq. in. 
 TF=Load on column in pounds; 
 A = Area of plate in sq. ins. ; 
 J5=one side of square plate in inches; 
 D= diameter of round column or side of square post in 
 
 inches : 
 A' = difference between area of plate and sectional area 
 
 of column; 
 
 P projection of edge of plate beyond column in inches; 
 t= thickness of plate in inches; 
 then 
 
 A-*, B^A, and P- 
 
 , , - 
 
 For cast-iron plates, 
 
 '- divided by 80. (1) 
 
BEARING-PLATES FOR GIRDERS AND COLUMNS. 401 
 For steel plates, 
 
 t= A/'^A^- divided by 220. 
 
 EXAMPLE 2. A yellow-pine post 12 ins. square supports a 
 probable load of 115,200 Ibs. The post will rest on a cast-iron 
 plate bedded on first-class brick work in cement mortar. What 
 should be the size and thickness of the plate? 
 
 Ans. TF= 115,200. .w=200. A = 115,200 ^-200= 576 sq. ins. 
 
 5=^576=24 ins. A'=576-144=432*sq. ins. 
 
 Then f -./200X6X432\ gn= 208 =9fi ^ 
 F 12 oO 
 
 208 
 For a steel plate ^=990 or ^ mc ^' 
 
 The cast-iron plate may be made 2.6 ins. thick under the post 
 and bevelled to 1} ins. at the edges. 
 
 For a rectangular post the plate should be proportioned so that 
 the projection will be the same on each side of the post. 
 
 When computing the area of bearing-plates under columns 
 the probable load on the column rather than the possible load 
 should be taken. 
 
 Bearing-plates Under Beams or Girders. 
 
 The ends of heavily loaded beams or girders should rest on 
 bearing-plates, either of iron, steel, or strong smooth stone. 
 
 The area of these bearing-plates should be computed in the 
 same way as the area of bearing-plates under columns. 
 
 The thickness of cast-iron plates may be computed by the fol- 
 lowing formula : 
 
 t=.Q 
 
 For steel plates 
 
 in which w=the safe bearing resistance of the masonry per sq. 
 inch, and P equals the projection of the plate beyond the beam, 
 (Fig. 3). 
 
402 BEARING-PLATES FOR GIRDERS AND COLUMNS. 
 
 EXAMPLE 3. A wooden beam 10 ins. wide supports a uniform 
 load of 24,000 Ibs. What size bearing-plate of cast iron should 
 be used on common brickwork? 
 
 Arcs. Load on bearing plate =24, 000-^2= 12, GOO Ibs. 
 
 Area of plate = 12,000-^-100=120 sq. ins. 
 
 Size of plate, 8" X 15". P= 15 ~ 10 = 2J". 
 
 
 
 =.024x2i\/100=.024x2JX 10= .6 ins. 
 
 When the theoretical thickness is less than an inch, the plate 
 had better be made 1 inch thick. 
 
 EXAMPLE 4. A 24-inch 80-lb. steel beam supports a distributed 
 load of 60,000 Ibs. What size of bearing-plate should be used 
 on brickwork capable of sustaining 150 Ibs. per square inch? 
 Ans. Load on plate = 60,000-^-2=30, 000 Ibs, 
 Area of plate =30, 000 -^150 =200. 
 Make size of plate 12x17 ins. Width of beam flange 
 is 7 ins. 
 
 17 7 
 
 Hence P= = = 5 ins. 
 2i 
 
 For cast iron *= .024x5\/ 150 =1.47 ins. 
 
 For steel t= .0137X 5^150= 0.84 ins. or J inch. 
 
 The load on the plate equals the end reaction of beam, which 
 is one-half of a distributed or centre load. When the load is 
 irregularly applied the reaction may be computed as explained 
 under supporting forces, Chapter IX. 
 
 The following table gives the standard sizes for steel bearing- 
 plates under I-beams and channels as recommended by the 
 Carnegie Steel Co. and Jones & Laughlins, and the bearing 
 values for three grades of masonry. When the reaction of the 
 beam exceeds the safe bearing value given in the table, the size 
 and thickness of the plate should be determined by the foregoing 
 rule. If the reaction is less than the bearing value, the size of 
 the plate can be reduced. 
 
 As the reactions vary with the span of the beam, such a table 
 as the following should be used with caution, and the reaction 
 always compared with the bearing value of the plate : 
 
BEARING-PLATES FOR GIRDERS AND COLUMNS. 403 
 
 TABLE II. STANDARD STEEL WALL BEARING-PLATES. 
 
 Depth of beam 
 or channel. 
 
 Bearing on wall. 
 
 Plates. 
 
 Safe bearing 
 values in tons 
 for plates rest- 
 ing on 
 
 1 
 o 
 ft 
 
 af 
 
 -a 
 
 1 
 
 4 
 5 
 9 
 
 14 
 14 
 20 
 20 
 31 
 41 
 54 
 46 
 61 
 73 
 
 Size. 
 
 1 
 1 
 
 1 
 
 aM 
 
 in 
 jii 
 
 92 ^ 
 
 115 
 
 ts 
 j=r 
 
 I'brc 
 
 
 'gag 
 
 o SN 
 
 3", 4", 5", and 6". . 
 3", 4", 5", and 6" 
 
 6" 
 
 6" 
 
 6"X 6" 
 6"X 6" 
 
 1 
 
 1.8 
 1.8 
 3.2 
 3.2 
 4.8 
 4.8 
 7.2 
 7.2 
 9.6 
 9.6 
 10.8 
 10.8 
 12.8 
 
 2.7 
 2.7 
 4.8 
 4.8 
 7.2 
 7.2 
 10.8 
 10.8 
 14.4 
 14.4 
 16.2 
 16.2 
 19.2 
 
 4.5 
 4.5 
 8.0 
 8.0 
 12.0 
 12.0 
 18.0 
 18.0 
 24.0 
 24.0 
 27.0 
 27.0 
 32.0 
 
 1" and 8" 
 1" arid 8" 
 
 8" 
 8" 
 8" 
 12" 
 12" 
 12" 
 12" 
 12" 
 12" 
 16" 
 
 8"X 8" 
 8"X 8" 
 8" X 12" 
 8" XI 2" 
 12"X12" 
 12"X12" 
 12" XI 6" 
 12"X16" 
 12"X18" 
 12" X 18" 
 16"X16" 
 
 i 
 
 w 
 
 1 
 
 $ 
 IK 
 
 i ' 
 
 9" and 10" . . . 
 
 9" and 10" 
 
 12' I 31 5 Ibs 
 
 12' I 31 5 Ibs. . 
 
 12' I 40 Ibs., 15" I 42 Ibs . 
 12' I 40 Ibs., 15" I 42 Ibs.. 
 15' I 60 and 80 Ibs. 
 
 15' I 60 and 80 Ibs 
 18' , 20", and 24" 
 
 
 * Use the thicker plate for bearing values exceeding those given under 
 common brickwork. 
 
 Bearing-plates on brickwork may be considerably reduced in 
 size by placing a strong flat stone under them/ The area of the 
 stone should be proportioned by the above rule, and the thick- 
 ness of the stone should be at least equal to its projection beyond 
 the iron plate. 
 
 BEDDING. 
 
 Base-plates should be bedded or grouted in cement from one- 
 half to three-quarters of an inch thick, the plate to be rammed 
 down solid, true and level. Web-plates should have holes in the 
 bottom, as shown in Fig. 1, to show if the cement is distributed 
 evenly under the plate. 
 
 Bearing-Brackets on Cast-iron Columns. 
 
 Fig. 4 shows the usual method of connecting iron floor-beams 
 and girders with cast-iron columns. The ends of the beam and 
 girder rest on plates P cast on the columns, and the plates are sup- 
 ported by cast brackets <7, so that no transverse strain .can come 
 upon the plate. For single beams one bracket is sufficient; for 
 double beams, or for wide beams or riveted girders, two brackets 
 should be used. The ends of the beams and girders are fastened 
 
404 BEARING-BRACKETS ON CAST-IRON COLUMNS. 
 
 to the column by bolting to the lugs L, which are also cast on the 
 column. (See also Fig. 8, Chapter XIV.) 
 
 As the plates can resist but little transverse strain, it is evident 
 that the strength of the support consists in the resistance of the 
 brackets and plate to being sheared or sliding down on the col- 
 umn, and also on the resistance of the bracket to crushing. The 
 
 Fig. 4. 
 
 thickness of the plate and brackets should not be less than the 
 thickness of the body of the column, and this simple rule will 
 generally insure sufficient strength for supporting the beams or 
 girders. In case of very heavily loaded beams or girders, it 
 would be well, however, to calculate the resistance of the support 
 both to shearing and crushing. 
 
 Both the plate and bracket would offer resistance to shearing, 
 but the author advocates considering only the resistance of the 
 bracket. The resistance of a single bracket to shearing is equal 
 to the height D multiplied by the thickness of the plate, and 
 the product by 7,000 pounds. Thus if the length D is six inches 
 (which should be about the minimum length), and the thickness 
 of the bracket one inch, the shearing area would be six inches, 
 
BEARING-BRACKETS ON CAST-IRON COLUMNS. 405 
 
 which, multiplied by 7,000, gives 42,000 pounds as the safe 
 strength of one bracket. 
 
 The resistance to crushing may be found by multiplying the 
 distance X by the thickness of the bracket and the product by 
 13,000. Thus, if X is four inches and the thickness one inch, the 
 resistance to crushing would be 52,000 pounds. Such a bracket 
 would support the end of a 20-inch light steel beam of 16 feet 
 span under its full load ; for heavier beams the thickness of the 
 bracket and also the length D should be increased. 
 
 Bevel of Brackets. If the plate P, on which the beam rests, is 
 cast square to the column, then, when the beam deflects, the load 
 will be brought on the extreme outer edge of the column. To 
 avoid this the shelf should be sloped downward, away from the 
 column, with a bevel of ^-inch per foot. 
 
 TABLE III. STANDARD CONNECTIONS TO CAST-IRON 
 
 COLUMNS. 
 
 The following table, published by the Passaic Rolling Mill Co. 
 will be found useful, when detailing cast-iron columns? 
 ALL DIMENSIONS ARE IN INCHES. 
 
 <M 
 
 o . 
 
 
 
 
 
 
 
 
 
 
 8 . 
 
 
 ^ a 
 II 
 
 A 
 
 B 
 
 C 
 
 D 
 
 E 
 
 F 
 
 G 
 
 H 
 
 K 
 
 O 1 "" 
 
 
 $r 
 
 
 
 
 
 
 
 
 
 
 
 
 Holes 
 
 
 
 
 
 
 
 
 
 
 
 
 cored 
 
 20 
 
 5 
 
 5 
 
 6 
 
 10* 
 
 1* 
 
 14 
 
 2 
 
 14 
 
 2 
 
 1 
 
 for 
 
 94" 
 
 18 
 
 4 
 
 5 
 
 6 
 
 104 
 
 14 
 
 H 
 
 2 
 
 H 
 
 2 
 
 1 
 
 bolts. 
 
 15 
 
 4 
 
 3* 
 
 5* 
 
 94 
 
 H 
 
 H 
 
 2 
 
 14 
 
 If 
 
 1 
 
 
 12 
 
 3 
 
 3 
 
 44 
 
 7| 
 
 H 
 
 ij 
 
 2 
 
 14 
 
 1* 
 
 1 
 
 
406 BEARING-BRACKETS ON CAST-IRON COLUMNS. 
 
 "8 . 
 
 
 
 
 
 
 
 
 
 
 I 
 
 
 | 
 
 0) o 
 
 A 
 
 B 
 
 C 
 
 D 
 
 E 
 
 F 
 
 G 
 
 H 
 
 K 
 
 C3 bC 
 >/) ^ 
 
 0^ 
 
 
 ft 
 
 
 
 
 
 
 
 
 
 
 go 
 
 Holes 
 
 
 
 
 
 
 
 
 
 
 
 
 cored 
 
 10 
 
 3} 
 
 3* 
 
 4 
 
 7 
 
 H 
 
 1 
 
 2 
 
 1* 
 
 11 
 
 1 
 
 for 
 
 W' 
 
 9 
 
 8 
 
 3 
 
 2* 
 
 3 
 3 
 
 4 
 4 
 
 7 
 
 7 
 
 1 
 1 
 
 1 
 1 
 
 2 
 2 
 
 1! 
 
 11 
 
 H 
 
 ,_4- 
 
 i 
 
 bolts. 
 
 7 
 
 2i 
 
 21 
 
 4 
 
 7 
 
 1 
 
 1 
 
 2 
 
 i| 
 
 H 
 
 t 
 
 
STRENGTH OF POSTS, STRUTS, AND COLUMNS. 407 
 
 CHAPTER XIV. 
 STRENGTH OF POSTS, STRUTS, AND COLUMNS. 
 
 DETAILS OF CONNECTIONS AND BASE-PLATES. 
 
 As the strength of a post, strut, or column, depends primarily 
 upon the resistance of the given material to crushing, we must 
 first determine the ultimate crushing strength of all materials 
 used for this purpose. 
 
 The following table gives the strength for all materials used 
 in building, excepting brick, stone, and masonry, which will be 
 found in Chapter V. 
 
 TABLE I. AVERAGE ULTIMATE CRUSHING LOADS, 
 IN POUNDS PER SQUARE INCH, FOR BUILDING- 
 MATERIALS. 
 
 Material. 
 
 Crushing 
 weight, in 
 Ibs/per 
 sq. inch. 
 
 Material. 
 
 Crushing 
 weight, in 
 Ibs. per 
 sq. inch. 
 
 For STONE, BRICK, and 
 MASONRY see Chap 
 
 C. 
 
 WOODS (continued). 
 
 C. 
 
 3,375 
 
 v 
 
 
 Hemlock . 
 
 3,000 
 
 
 
 Oak, white 
 
 4,000 
 
 METALS. 
 Cast iron 
 
 80000 
 
 Pine, Georgia yellow. .. . 
 Pine, Oregon 
 
 5,000 
 4,500 
 
 Wrought iron 
 
 36,000 
 
 Pine, Norway 
 
 3,800 
 
 Steel (rolled shapes) 
 
 48 000 
 
 Pine white ...... 
 
 3,500 
 
 WOODS (Endways).* 
 Cedar 
 
 3 500 
 
 Pine (Colorado) 
 Redwood (California). . . 
 
 3,150 
 3,000 
 4,000 
 
 Chestnut 
 
 4000 
 
 Whitewood 
 
 3,000 
 
 
 
 
 
 Table VI. 
 
 The values for cast iron, wrought iron, and steel are those gen- 
 erally used, although a great deal of iron is stronger than this. 
 The values for woods are those recommended by leading engineers, 
 and may be considered as a fair average of the results obtained by 
 experiment on full-size pieces of merchantable lumber. The 
 values for yellow pine, white pine, white oak, and cypress were 
 
408 STRENGTH OF WOODEN POSTS AND COLUMNS. 
 
 obtained from results of the tests conducted since 1890 by the 
 U. S. Forestry Division. The values for the other woods were 
 compiled from the best test data available, and are believed to 
 be as near the actual strength of ordinary full-size timbers as can 
 be determined. 
 
 The values for wood are for dry timber. Wet timber is only 
 .about one-half as strong to resist compression as dry timber, and 
 this fact should be taken into account when using green timber. 
 
 The strength of a column, post, or strut, depends, in a large 
 measure, upon the proportion of the length to the diameter 01 
 least thickness. Up to a certain length, failure occurs simply 
 by compression, and above that length by first bending and 
 then breaking. 
 
 "Wooden Columns. 
 
 For wooden columns, where the length is not more than twelve 
 times the least thickness, the strength of the column or strut may 
 be computed by the rule, 
 
 - , , area of cross-section X<7 /1N 
 
 Safe load = > f ^ (1) 
 
 factor of safety 
 
 where C denotes the strength of the given material as given in 
 Table I. 
 
 The factor of safety to be used depends upon the place where 
 the column or strut is used, the load which comes upon it, the 
 quality of the material, and, in a large measure, upon the value 
 taken for C. 
 
 For lumber of ordinary quality, and containing no very bad 
 knots, the author would recommend that a factor of safety of 
 five be used ; or, in other words, that the safe stress per square 
 inch of section area be made one-fifth of the values given in 
 Table I. 
 
 If the post 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 should also be taken into consideration in 
 determining the factor of safety. Thus the author would use a 
 larger factor for a post supporting a brick wall than for one 
 supporting a floor, as in the former case the full load is at all 
 times on the post, and the least reduction of its sectional area in 
 case of fire might cause it to give way. Columns supporting 
 
STRENGTH OF WOODEN POSTS AND COLUMNS. 409 
 
 machinery, or struts in railway bridges, should have a factor of 
 safety of from 6 to 8, if the values of C, given in Table. I., are used. 
 
 EXAMPLE 1. What is the safe load for a hard-pine post 10 X 10 
 inches, 12 feet long, using a factor of safety of 5? 
 
 Ans. Area of cross-section = 100 sq. ins. ; safe load per sq. in. 
 
 *= 5^5 =1000; 1000X100=100,000 Ibs. 
 o 
 
 EXAMPLE 2. It is required to support a brick wall weighing 
 80,000 Ibs. by an Oregon pine post 11 feet long. What should be 
 the size of the post? 
 
 Ans. We would recommend a factor of safety of 6. Then safe 
 
 4500 80 000 
 
 resistance per sq. in. of section area= = 750 ; -7=^ = 106 sq. 
 
 t) 7ou 
 
 ins. required in section of post, or say a 10 X 11 or 9 X 12 post. 
 
 Strength of Wooden Posts over Twelve Diameters 
 in Length. 
 
 When the length of a post exceeds twelve times its least thickness 
 or diameter, the post is liable to bend under the load, and hence 
 to break under a less load than would a shorter column of the 
 same cross-section. 
 
 To deduce a formula which would make the proper allowance 
 for the length of a column has been the aim of many engineers, 
 but their formula? have not been verified by actual results. 
 
 Until within two or three years the formulae of Mr. Lewis 
 Gordon and Mr. C. Shaler Smith have been generally used by 
 engineers, but the extensive series of tests made on the Govern- 
 ment testing machine at Watertown, Mass., on full-sized col- 
 umns, show that these formulae do not agree with the results 
 there obtained. 
 
 Mr. James H. Stanwood, Instructor in Civil Engineering, Mass. 
 Institute of Technology, in the year 1891 platted the values of all 
 the tests made at the Watertown Arsenal up to that time on full- 
 size posts. From the drawing thus obtained he deduced the fol- 
 lowing f orrmrla for yellow pine posts : 
 
 length in inches /ON 
 Safe load per square mch= 1000 - 10 X h dth inohes - ( 2 > 
 
 Uie<KJ.LIl 111 lULllcQ 
 
 The author has carefully compared this formula with the results 
 of actual tests,, and with other formulae, and believes that it meets 
 the actual conditions more nearly than any other formula, and 
 
410 STRENGTH OF WOODEN POSTS AND COLUMNS. 
 
 he has therefore discarded the tables of wooden posts given in the 
 earlier editions of this work and prepared the following tables 
 for the strength of round and square posts of sizes coming within 
 the range of actual practice. 
 
 For other sizes the loads can easily be computed by the 
 formula. 
 
 The loads for Texas pine, oak and white pine posts were com- 
 puted by the following formulae: 
 For Texas (yellow) pine : 
 
 Safe load per square inch=850~8.5X/ B "". ' ( 3 ) 
 
 breadth in ins. 
 
 For oak and Norway pine: 
 
 01 r i j T_ , length in ins. /y(x 
 
 Safe load per square mch= 750 7.5 X i , , . : . (4) 
 
 breadth in ins. 
 
 For white pine and spruce posts : 
 
 Safe load per sqnare inch= 625 6 X -, , , \ *. *"' , (5) 
 
 breadth in ins. ' 
 
 in which the breadth is the least side of a rectangular strut, or the 
 diameter of a round post. The round posts were computed for 
 the half-inch, to allow for being turned out of a square post, of 
 the size next larger. 
 
 The formulae were only used for posts exceeding 12 diameters 
 for yellow pine, and ten diameters for other woods. 
 
 For posts having bad knots, or other defects, or which are 
 known to be eccentrically loaded, a deduction of from 10 to 25 
 per cent, should be made from the values given in the tables. 
 
STRENGTH OF WOODEN POSTfe AND COLUMNS- 411 
 
 TABLE II. SAFE LOAD IN POUNDS FOR YELLOW PINE 
 AND OREGON PINE POSTS (ROUND AND SQUARE.)* 
 
 Size of 
 Post 
 in inches. 
 
 Length of Post in feet. 
 
 8 
 
 10 
 
 13 
 
 14 
 
 15 
 
 16 
 
 18 
 
 20 
 
 24 
 
 4X6 
 
 18,200 
 19,590 
 30,200 
 40,300 
 50,400 
 38,540 
 64,000 
 80,000 
 96,000 
 70,900 
 100,000 
 120,000 
 140,000 
 103,900 
 144,000 
 168,000 
 192,000 
 196,000 
 256,000 
 324,000 
 400,000 
 
 16,800 
 18,760 
 28,800 
 38,400 
 '48,000 
 37,130 
 54,400 
 68,000 
 81,600 
 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 
 17,550 
 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 
 196,000 
 256,000 
 324,000 
 400,000 
 
 16,500 
 25,900 
 34,600 
 43,200 
 34,300 
 50,600 
 63,200 
 76,800 
 58,350 
 83,200 
 99,800 
 116,500 
 88,730 
 123,800 
 144,500 
 165,100 
 196,000 
 256,000 
 324,000 
 400,000 
 
 25,200 
 33,600 
 42,000 
 33,590 
 49,600 
 62,000 
 74,400 
 57,429 
 82,000 
 98,400 
 114,800 
 87,690 
 122,400 
 142,800 
 163,200 
 170,900 
 229,100 
 324,000 
 400,000 
 
 24,500 
 32,600 
 40,800 
 32,890 
 48,600 
 60,800 
 73,000 
 56,580 
 80,800 
 97,000 
 113,100 
 86,550 
 121,000 
 141,100 
 161,300 
 169,100 
 225,300 
 289,400 
 400,000 
 
 46,700 
 53,400 
 70,100 
 54,800 
 78,400 
 94,100 
 109,800 
 84,160 
 118,100 
 137,800 
 157,400 
 165,800 
 221,400 
 285,100 
 356,800 
 
 76,000 
 91,200 
 106,400 
 82,290 
 115,200 
 134,400 
 153,600 
 162,400 
 217,600 
 280,800 
 352,000 
 
 109,440 
 127,680 
 145,920 
 155,800 
 209,900 
 272,160 
 342,400 
 
 5 round. . 
 
 6X6 . , 
 
 6X8 
 
 6X10 
 
 7i round. . 
 
 8X8 
 
 8X10 
 8X12 
 
 9 round. . 
 10X10 
 10X12 
 10X14 
 1H round 
 12X12 
 12X14 
 12 X 16 
 14X14 
 16X16 
 18 X 18 
 20X20 
 
 * These two woods appear to be of about equal strength for posts ex- 
 ceeding 12 diameters in height. 
 
 TABLE III. SAFE LOAD FOR TEXAS (YELLOW) PINE 
 POSTS (ROUND AND SQUARE). 
 
 Size of 
 post in 
 inches. 
 
 Length of post in feet. 
 
 8 
 
 10 
 
 13 
 
 14 
 
 15 
 
 16 
 
 18 
 
 20 
 
 24 
 
 4X6 . 
 
 15,500 
 
 14,280 
 
 13,050 
 
 
 
 
 
 
 
 5 round. . 
 
 16,650 
 
 15,790 
 
 14,900 
 
 14,030 
 
 
 
 
 
 
 6X6 
 
 25,704 
 
 24,480 
 
 23,256 
 
 22,032 
 
 21,420 
 
 20,808 
 
 
 
 
 6X8 . . . 
 
 34,272 
 
 32,640 
 
 31,008 
 
 29,376 
 
 28,560 
 
 27,744 
 
 
 
 
 6X10 
 
 42,840 
 
 40,800 
 
 37,760 
 
 36,720 
 
 35,700 
 
 34,680 
 
 
 
 
 7 round. . 
 
 32,740 
 
 31,540 
 
 30,340 
 
 29,140 
 
 28,540 
 
 27,940 
 
 26,740 
 
 
 
 8X8. . . . 
 
 47,870 
 
 46,240 
 
 44,600 
 
 42,970 
 
 42,160 
 
 41,340 
 
 39,710 
 
 
 
 8X10 
 
 59,840 
 
 57,800 
 
 55,760 
 
 53,720 
 
 52,700 
 
 51,680 
 
 49,640 
 
 
 
 8X12 
 
 71,808 
 
 69,360 
 
 66,910 
 
 64,460 
 
 63,240 
 
 62,000 
 
 59,560 
 
 
 
 9 round.. 
 
 54.150 
 
 52,650 
 
 51,150 
 
 49,580 
 
 48,820 
 
 48,070 
 
 46,570 
 
 
 
 10 X 10 
 
 85,000 
 
 78,800 
 
 72,760 
 
 70,720 
 
 69,700 
 
 68,680 
 
 66,640 
 
 64,600 
 
 
 10X12 
 
 102,000 
 
 89,760 
 
 87,300 
 
 84,860 
 
 83,640 
 
 82,400 
 
 80,000 
 
 77,500 
 
 
 10X14 
 
 119,000 
 
 104,700 
 
 101,860 
 
 99,000 
 
 97,580 
 
 96,150 
 
 93,300 
 
 90,400 
 
 
 Ui round 
 
 88,290 
 
 79,100 
 
 77,250 
 
 75,400 
 
 74,470 
 
 73,550 
 
 71,700 
 
 69,850 
 
 66,160 
 
 12X12 
 12X14 
 12X16 
 14X14 
 
 122,400 
 142,800 
 163,200 
 166,600 
 
 110,160 
 128,520 
 146,880 
 166,600 
 
 107,700 
 125,660 
 143,600 
 149,450 
 
 105,260 
 122,800 
 140,350 
 146,600 
 
 104,040 
 121,380 
 138,720 
 145,180 
 
 102,800 
 119,950 
 137,080 
 143,760 
 
 100,360 
 117,100 
 133,800 
 140,900 
 
 97,920 
 114,240 
 130,560 
 138,080 
 
 93,000 
 108,520 
 124,030 
 132,400 
 
 14X16 
 16X16 
 
 190,400 
 217,600 
 
 190,400 
 217,600 
 
 170,800 
 217,600 
 
 167,500 
 194,700 
 
 165,900 
 193,000 
 
 164,300 
 191,400 
 
 161,000 
 188,200 
 
 157,800 
 184,900 
 
 151,300 
 178,400 
 
412 STRENGTH OF WOODEN POSTS AND COLUMNS. 
 
 TABLE IV. SAFE LOAD IN POUNDS FOR OAK AND 
 NORWAY PINE POSTS (ROUND AND SQUARED 
 
 Size of 
 post in 
 inches. 
 
 Length of post in feet. 
 
 8 
 
 10 
 
 2 
 
 14 
 
 15 
 
 16 
 
 18 
 
 20 
 
 34 
 
 4X6 
 
 13,680 
 
 12,600 
 
 11,520 
 
 
 
 
 
 
 
 5 round. 
 
 14,700 
 
 13,900 
 
 13,160 
 
 12,370 
 
 
 
 
 
 
 6X6 
 
 22,680 
 
 21,600 
 
 20,520 
 
 19,440 
 
 18,900 
 
 18,360 
 
 
 
 
 6X8. ., 
 
 30,240 
 
 28,800 
 
 27,360 
 
 25,920 
 
 25,200 
 
 24,480 
 
 
 
 
 6X10... 
 
 37,800 
 
 36,000 
 
 34,200 
 
 32,400 
 
 31,500 
 
 30,600 
 
 
 
 
 7 round 
 
 28,900 
 
 27,850 
 
 26,780 
 
 25,720 
 
 25,190 
 
 24,660 
 
 
 
 
 8X8. . . . 
 
 42,240 
 
 40,768 
 
 39,360 
 
 37,880 
 
 37,120 
 
 36,480 
 
 35,000 
 
 
 
 8X10... 
 
 52,800 
 
 50,960 
 
 49,200 
 
 47,360 
 
 46,400 
 
 44,600 
 
 43,760 
 
 
 
 8X12... 
 
 63,360 
 
 61,152 
 
 59,040 
 
 56,830 
 
 55,680 
 
 54,720 
 
 52,500 
 
 
 
 9 round 
 
 47,960 
 
 46,440 
 
 45,160 
 
 43,740 
 
 43,100 
 
 42,400 
 
 41,120 
 
 
 
 10X10.. 
 
 75,000 
 
 66,000 
 
 64,200 
 
 62,400 
 
 61,500 
 
 60,600 
 
 58,800 
 
 57,000 
 
 
 10X12.. 
 
 90,000 
 
 79,200 
 
 77,040 
 
 74,880 
 
 73,800 
 
 72,720 
 
 70,560 
 
 68,400 
 
 
 10X14.. 
 
 105,000 
 
 92,400 
 
 89,880 
 
 87,360 
 
 86,100 
 
 84,840 
 
 82,320 
 
 79,800 
 
 
 1H round 
 
 77,925 
 
 69,820 
 
 68,160 
 
 66,490 
 
 65,770 
 
 64,833 
 
 63,170 
 
 61,600 
 
 
 12X12.. 
 
 108,000 
 
 108,000 
 
 95,040 
 
 92,880 
 
 91,700 
 
 90,700 
 
 88,560 
 
 86,400 
 
 82,080 
 
 12X14.. 
 
 126,000 
 
 126,000 
 
 110,800 
 
 108,300 
 
 107,000 
 
 105,840 
 
 103,300 
 
 100,802 
 
 95,760 
 
 12X16.. 
 
 144,000 
 
 144,000 
 
 126,700 
 
 123,800 
 
 122,300 
 
 120,900 
 
 118,000 
 
 115,200 
 
 109,400 
 
 14X14.. 
 16X16.. 
 
 147,000 
 192,000 
 
 147,000 
 192,000 
 
 147,000 
 192,000 
 
 129,300 
 192,000 
 
 128,100 
 170,500 
 
 127,000 
 168,900 
 
 124,400 
 166,100 
 
 121,900 
 163,000 
 
 116,800 
 157.400 
 
 18X18.. 
 
 243,000 
 
 243,000 
 
 243,000 
 
 243,000 
 
 243,000 
 
 217,000 
 
 213,800 
 
 210,600 
 
 204;iOO 
 
 20X20.. 
 
 300,000 
 
 300,000 
 
 300,000 
 
 300,000 
 
 300,000 
 
 300,000 
 
 267,600 
 
 264,000 
 
 256,000 
 
 TABLE V. SAFE LOAD IN POUNDS FOR WHITE PINE 
 AND SPRUCE POSTS (ROUND AND SQUARE). 
 
 Size of 
 
 Length of post in feet. 
 
 
 
 inches. 
 
 
 
 
 
 
 
 
 
 
 
 8 
 
 10 
 
 13 
 
 14 
 
 15 
 
 16 
 
 18 
 
 20 
 
 24 
 
 4X6 
 
 11,520 
 
 10,550 
 
 9,800 
 
 8,700 
 
 
 
 
 
 
 5 round.. 
 
 12,350 
 
 11,730 
 
 11,180 
 
 10,490 
 
 
 
 
 
 
 6X6. . . 
 
 19,080 
 
 18,216 
 
 17,352 
 
 16,490 
 
 16,050 
 
 15,620 
 
 
 
 
 6X8 
 
 25,440 
 
 24,290 
 
 23,140 
 
 21,980 
 
 21,400 
 
 20,830 
 
 
 
 
 6X10.... 
 
 31,800 
 
 30,360 
 
 28,920 
 
 27,480 
 
 26,760 
 
 26,040 
 
 
 
 
 7 round. 
 
 24,220 
 
 23,380 
 
 22,540 
 
 21,660 
 
 21,260 
 
 20,820 
 
 
 
 
 8X8 
 
 35,450 
 
 34,300 
 
 33,150 
 
 32,000 
 
 31,420 
 
 30,850 
 
 29,700 
 
 
 
 8X10... 
 
 44,320 
 
 42,480 
 
 41,440 
 
 40,000 
 
 39,280 
 
 38,560 
 
 37,120 
 
 
 
 8X12... 
 
 53,180 
 
 51,450 
 
 49,730 
 
 48,000 
 
 47,140 
 
 46,270 
 
 44,544 
 
 
 
 9 round 
 
 40,000 
 
 39,000 
 
 37,860 
 
 36,800 
 
 36,230 
 
 35,730 
 
 34,670 
 
 
 
 10X10. . 
 
 62,500 
 
 55,400 
 
 53,960 
 
 52,520 
 
 51,800 
 
 51,080 
 
 49,640 
 
 48,200 
 
 
 10X12. . 
 
 75,000 
 
 66,480 
 
 64,800 
 
 63,000 
 
 62,160 
 
 '61,300 
 
 59,570 
 
 57,840 
 
 
 10X14. . 
 
 87,500 
 
 77,560 
 
 75,600 
 
 73,500 
 
 72,520 
 
 71,510 
 
 69,500 
 
 67,480 
 
 
 11 round 
 
 64,930 
 
 58,390 
 
 57,140 
 
 55,800 
 
 55,170 
 
 54,550 
 
 53,100 
 
 51,950 
 
 
 12X12.. 
 
 90,000 
 
 90,000 
 
 79,780 
 
 78,000 
 
 77,180 
 
 76,320 
 
 74,590 
 
 72,860 
 
 69,400 
 
 12X14.. 
 
 105,000 
 
 105,000 
 
 93,170 
 
 91,050 
 
 90,050 
 
 89,000 
 
 87,020 
 
 85,000 
 
 80,900 
 
 12X16. . 
 
 120000 
 
 120,000 
 
 106,300 
 
 104,000 
 
 102,900 
 
 101,700 
 
 99,400 
 
 97,150 
 
 92,500 
 
 14X14/. 
 
 122,500 
 
 122,500 
 
 110,350 
 
 108,350 
 
 107,400 
 
 106,400 
 
 104,460 
 
 102,300 
 
 98,400 
 
 16X16.. 
 
 160,000 
 
 160,000 
 
 160,000 
 
 143,870 
 
 142,590 
 
 141,570 
 
 139,260 
 
 136,960 
 
 132,360 
 
 18X18. . 
 
 202,500 
 
 202,500 
 
 202,500 
 
 202,500 
 
 183,060 
 
 181,760 
 
 179,170 
 
 176,580 
 
 171,400 
 
 20X20.. 
 
 250,000 
 
 250,000 
 
 250,000 
 
 250,000 
 
 250,000 
 
 250,000 
 
 224,500 
 
 221,200 
 
 215,200 
 
STRENGTH OF WOODEN POSTS AND COLUMNS. 413 
 
 Eccentric Loading. 
 
 When the load on a post is applied in such a way that it is not 
 distributed uniformly over the end of the post the loading is 
 called eccentric, and the effect on the 
 post is much more injurious than if the 
 load were uniformly distributed. When 
 a post supports a girder on one side 
 only, or when the weight from one 
 girder is much more than from the 
 other, the load becomes eccentric, and 
 the sectional area of the post should be 
 increased, to resist the bending stress 
 due to the eccentricity. 
 
 When the eccentric load is applied 
 as in Fig. 1, the sectional area of. a 
 square or rectangular post should be 
 computed by the following formula: 
 Sectional area of post in square inches 
 
 ELEVATION 
 
 W 
 
 
 j X 4) 
 
 (6) 
 
 GfirderA 
 
 PLAN 
 
 Fig. 
 
 pXd ' 
 
 in which W= total load on post in Ibs.g 
 W^ eccentric load in Ibs.; 
 p=safe stress in Ibs. per sq. 
 
 inch. ; 
 
 d = distance from centre of 
 post to centre of bearing 
 in ins.; 
 d=side of post -parallel with girder. 
 
 In assuming the value of p, the probable ratio of the side of the 
 post to the length should be taken into account. Thus if it is 
 probable that the length will not exceed twelve times the side 
 (both being measured in inches) for yellow pine or Oregon pine 
 posts, or 10 diameters for other woods, then the value of p for 
 short posts may be taken. If the ratio will probably be greater 
 than this, then the probable ratio should be roughly calculated 
 and p computed for that ratio by the formula given for posts 
 more than 10 diameters in length. 
 
 EXAMPLE 3. The post P 1} Fig. 1, supports a total load on its 
 cap-plate of 60,000 Ibs., including the reaction from girder ^1 of 
 12,000 Ibs. What should be the size of the post for Oregon pine, 
 
414 CAST-IRON COLUMNS AND POSTS. 
 
 and length of 12 ft.? Ans. As it is probable that the post will 
 have to be at least 10 ins. square, we will assume 1,000 Ibs. for 
 p, and 10 ins. for d. W l will= 12,000 Ibs. and d Q 7 ins. 
 
 60,000 , 6X12,000X7 
 Then sectional area= T -^+ 1;OQ Q X1Q -60 + 50.4=110.4 
 
 sq. ins. Or the post should be 1 1 X 1 1 or 10 X 12 ins. 
 
 From Table I. we see that an 8X10 post, concentrically 
 loaded, would support 65,000 Ibs., hence the eccentric load from 
 the girder increases the size of the post from 8 X 10 to 10 X 12 ins. 
 
 Iron Caps and Bolsters for Wooden Posts. 
 
 Whenever wooden posts are used in tiers, one above another, 
 each post except the top one should have an iron cap-plate, and 
 the upper posts should set on the cap of the post below, and not 
 on the girder. Where a wooden post supports only a girder a 
 wooden bolster may be used in place of the cap. Details of post 
 caps and bolsters are shown in Chapter XXII. 
 
 Crushing of Timber Perpendicular to the Grain. 
 
 TABLE VI. 
 
 The bearing of wooden girders, the ends of posts resting on 
 a girder, and washers on truss rods, should be proportioned so 
 that the quotient obtained by dividing the load by the bearing 
 area will not exceed the following safe unit strains : 
 
 White oak 600 Ibs. 
 
 Yellow pine 500 " 
 
 Oregon pine 400 " 
 
 Norway pine 250 " 
 
 White pine 200 " 
 
 Colorado pine 200 Ibs. 
 
 Spruce 250 " 
 
 Hemlock 200 " 
 
 Cypress 200 " 
 
 Redwood.. . 175 " 
 
 Cast-iron Columns and Posts. 
 
 Advantages and Disadvantages. Although steel is being more 
 largely used every year for the upright supports in buildings, 
 it will probably never entirely supplant the cast-iron post, and, in 
 fact, it is still a disputed question whether a steel post is better 
 than one of cast iron for buildings of moderate height. 
 
 For skeleton construction, when the height of the building 
 exceeds twice its width, it seems unquestionable that the riveted 
 steel column, "breaking joint" in alternate stories, and with 
 riveted connections with the beams and girders, is much the best; 
 but for the larger proportion of the br/ldings in which iron posts 
 
CAST-IRON COLUMNS AND POSTS. 415 
 
 are used east iron possesses advantages which the author believes 
 are not exceeded by the riveted steel post. 
 
 The most important of these advantages are low cost, quick- 
 ness of production, adaptability to any desired shape, and ease 
 in making connections. 
 
 Cast-iron columns when unprotected will also resist the action 
 of fire better than unprotected steel columns, as has been quite 
 conclusively demonstrated by the experiments of Prof. Baus- 
 chinger, of Munich.* Cast iron three quarters of an inch or 
 more in thickness is also practically uninjured by rust, while it 
 is claimed that wrought iron or steel may be almost destroyed by 
 it, unless kept constantly protected by some coating impervious 
 to moisture. 
 
 For unprotected columns cast iron may be made in more 
 attractive shape than steel columns, without additional cost. 
 
 The disadvantages of cast-iron columns, as found in practice, 
 are lack of uniformity in the metal, the danger of shrinkage 
 strains, and the difficulty of making rigid connections. 
 
 There are many contingencies which may arise in the manu- 
 facture of cast-iron columns which preclude perfect uniformity 
 in the product. 
 
 Among these are unevenness in the thickness of the metal, 
 which has sometimes been found to be very xiifferent on one side 
 of a round column from that on the opposite side. The presence 
 of confined air, producing "blow-holes" and "honeycomb," and 
 the collection of impurities at the bottom of the mould, are also 
 frequent sources of weakness in cast iron. 
 
 By careful inspection and by boring, the columns these defects 
 can be discovered and imperfect columns rejected. 
 
 The most critical condition is that due to the unequal contrac- 
 tion of the metal during the process of cooling, thereby giving 
 rise to initial strains, at times of sufficient force to produce rup- 
 ture in the column or in its lugs on the slightest provocation. 
 
 In many cases the trouble is due to faulty designing or careless- 
 
 * Architect C. A. Ziegler, of Philadelphia, in commenting on the con- 
 flagration at Paterson, N, J., in Feb., 1902, says, in the Brickbuilder for 
 March of that year: "The manner in which cast-iron columns and girders 
 withstood the flames is most marvelous. The great majority that I saw 
 were not only intact but were as good as new, although some had appar- 
 ently fallen from great heights. 
 
 "The steel work , on the contrary [in modern fireproof buildings], wherever 
 it was reached by the heat, buckled and fell, heavy steel girders and posts 
 being twisted and knotted like whipcords." 
 
416 
 
 CAST-IRON COLUMNS AND POSTS. 
 
 ness in the execution of the work ; yet, even under favorable con- 
 ditions, it is so difficult to secure equal radiation from the moulds 
 in all directions that castings entirely exempt from inherent 
 shrinkage strains are probably seldom produced. 
 
 The most serious difficulties met with in using cast columns 
 in tall buildings are the difficulty of making true and rigid end 
 connections and the unreliability of the brackets which support 
 the beams and girders. By skilful designing and careful work- 
 manship these difficulties may to a considerable extent be over- 
 come, but cast columns can never in these respects be made to 
 equal the best forms of steel columns. 
 
 The length of cast-iron columns in inches should not exceed 
 thirty-six times their diameter, or least dimension. 
 
 Shapes of Cast Columns. -Cast-iron columns for buildings have 
 been made in all of the nine shapes shown in Fig. 2, although 
 solid columns are seldom made, and only for very small diameters. 
 
 No. 3 
 
 No. 4 
 
 For interior unprotected columns the hollow cylindrical shape 
 probably meets the usual requirements better than any other. 
 
 For exterior columns, as in store fronts, the rectangular shape, 
 No. 5, is more generally used, in order to give a good bearing for 
 the beams supporting the wall above. 
 
 For fire-proof buildings in which cast-iron columns are used 
 the author believes that the H-shaped No. 9 is the most desirable, 
 because of the following advantages: 
 
CAST-IRON COLUMNS AND POSTS. 
 
 417 
 
 1. Being entirely open, with both the interior and exterior sur- 
 faces exposed, any inequalities in thickness can be readily dis- 
 covered, and the thickness itself easily measured, thus obviating 
 any necessity for boring, and rendering the inspection of the 
 columns much less tedious. 
 
 2. The entire surface of the column can 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. 3, only the edge of 
 the column comes near the face of the wall. 
 
 4. Lugs and brackets can be cast on such 
 columns better than on circular columns, 
 especially for wide and heavy girders. 
 
 5. The end connections of the columns 
 
 do not require projecting rings, or flanges, which are often 
 objectionable in circular columns. 
 
 The cost of columns of this shape sliould not exceed that of cir- 
 cular columns of the same strength. 
 
 The column may be fire-proofed in the same way as the Z-bar 
 column, which it much resembles. The space occupied by the 
 column slightly exceeds that of both the 
 cylindrical and Z-bar column, but not 
 enough to be of any serious consequence. 
 Pilasters. Pilasters, . or columns with- 
 out a back, are often used as a facing to 
 the brick walls at the sides of store fronts. 
 If such pilasters are used to support a 
 girder, the inner side, A, Fig. 4, should be 
 wide enough to receive the girder, and the 
 back should be stiffened by cast ribs about 
 every thirty inches in height. If the load 
 on the girder is very great it will be much 
 better construction to build an H-shaped 
 column in the wall, to support the girder, 
 and put up a false front for appearance, 
 as shown in section by Fig. 5. To com- 
 pute the strength of a pilaster of the sec- 
 tion shown by Fig. 4, divide the length in 
 ' ELEVATION inches by the distance X, and from 
 
 OF BACK Table VII. find the ultimate strength per 
 
 F '9- 4 square inch of metal for that ratio. Then 
 
 multiply the sectional area of the front and two sides by this 
 
 PLAN 
 
 -f- 
 
418 
 
 CAST-IRON COLUMNS AND POSTS. 
 
 9* ** 
 
 value, and divide by 10 or 12 for a factor of safety. The pilaster 
 should be anchored to the brick wall by 
 long iron anchors hooked through a lug 
 cast on the inside of the face. The interior 
 of the pilaster should also be filled with 
 brickwork. 
 
 Connections of Cast-iron Columns. The 
 bearing of cast-iron columns should always 
 be turned true to the axis of the column. 
 Where only two stories of columns are used, and the joint is at 
 a floor level, it is not necessary to bolt the columns together. 
 For such cases a joint made as shown by Fig. 6 
 will generally be found satisfactory. If more 
 than the two stories of columns are used, or 
 the column is not well braced where the joint 
 occurs, the columns should be bolted together 
 by four f-inch bolts for columns 10 inches in 
 diameter or less, and six bolts for 12-inch and 
 larger columns. A desirable section for such joints is that shown 
 by Fig. 7. By keeping the lugs a quarter of 
 an inch from the end, less facing is required, 
 and a better bearing is ensured. Details of 
 end connections, brackets and base-plate for 
 H-shaped columns are shown by Figs. 8 and 
 9, and for round columns by Figs. 1, 2 and 
 4, Chap. XIII., also by Table III , of the same 
 chapter. For convenience in erecting columns, 
 the joint is generally placed just above the 
 beams or girder supported by the column. 
 Fig. 7 Projecting Caps and Bases. Columns with 
 
 ornamental caps and bases, should never be cast as shown by 
 the section Fig. 10, i. e., if the column is to support a load. In 
 all bearing columns, the core should extend in a straight line 
 from end to end. Plain moulded caps and bases may be cast 
 solid as in Fig. 11; if more ornamental caps are desired, or 
 heavy projecting bases, they should be cast separately and 
 attached to the straight column by screws. 
 
 Strength of Cast-Iron Columns. 
 
 The ultimate resistance of cast, iron to crushing is generally 
 taken at 80,000 Ibs. per square inch, and for posts, pintels, etc., 
 
CAST-IRON COLUMNS AND POSTS. 
 
 419 
 
 where the length is not more than six times the diameter, or 
 breadth, it will usually be safe to figure the working strength at 
 
 Fig. 10 
 
 six tons per square inch of metal. For longer posts, or columns, 
 the strength is affected by the ratio of length to diameter, but to 
 
420 CAST-IRON COLUMNS AND POSTS. 
 
 just what extent is not definitely known, hence all formulas for 
 columns must be more or less theoretical. The consequence is 
 that a great many formulas have been published, and there is 
 none that is universally accepted. The two following, however, 
 are now more commonly adopted than any others, and as they 
 appear to agree as well as any with actual tests, the author has 
 adopted them in place of those presented in the earlier editions 
 of this work. 
 
 Formulas.* 
 
 For hollow round cast-iron columns with square ends, 
 Ultimate ) r qn of lo-th in in*; H 
 
 i^r m ^^ 
 
 80,OOOA 
 
 z 2 * 
 
 For hollow rectangular cast-iron columns with square ends, 
 
 Ultimate ) r qn of Ifrth in irm T 
 
 strength { = metal area X fsO.OOO + 1 + f ' 5* J^' '" mS ; 1 , (8) 
 in pounds j l,067Xsq. of least I' 
 
 L e n nhe J 
 
 80,OOOA 
 
 72 ' 
 
 1,067<P 
 
 * The tables in the handbooks of the Cambria Iron Co., the Carnegie Steel 
 Co., Jones & Laughlins, and the Passaic Rolling Mill Co. are based on 
 formulas (7) and (8), and they have been adopted in the Boston building 
 laws. 
 
 The values obtained by these formulas will be slightly in excess of those 
 given in the Chicago building law, and considerably less than those per- 
 mitted by the building law of Greater New York ( p = 1 1 ,300 - -) . 
 
 In 1898 Prof. W. H. Burr made an analysis of the results of a number 
 of experiments on full-size, hollow, roun^. cast-iron columns made at the 
 Watertown Arsenal and Phoenixville, and by plotting the results found 
 
 that a straight-line formula having the equation p = 30,500 160-r repre- 
 
 a 
 
 sents the average of the plotted results. With a factor of safety of four 
 
 this would become p = 7,625 40 . 
 a 
 
 According to Prof. Burr's analysis the values for p given in the fourth 
 
CAST-IRON COLUMNS AND POSTS. 421 
 
 For solid cylindrical cast-iron columns, 
 
 (9) 
 266 X sq. of diam. J v 
 
 in pounds) 266 X sq. 
 
 For the star, T and H shape, use formula (7), taking d as 
 shown in Fig. 2 for the diameter. 
 
 The safe load is generally taken at one eighth of the ultimate 
 strength or breaking load. 
 
 Eccentric Reading. Cast-iron columns should not be 
 loaded with heavy eccentric loads, i.e., 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 strains. 
 
 Tables. 
 
 As the allowable pressure per square inch of metal depends 
 upon the ratio of length to diameter, without regard to actual 
 dimensions, i.e., it would be the same for a column 6 ins. in 
 diameter and 12 feet long, as for one 8 ins. in diameter and 16 
 feet long, it is practicable to prepare a table which will give the 
 value of the portions of formulas (7) and (8) inclosed in brackets 
 for all ratios of diameter to length, which will very much simplify 
 the computation for any particular column. " 
 
 Table VII. has been computed by means of the formulas 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 necessary to divide the length of the 
 column in inches by the least thickness or diameter also in inches, 
 and opposite the number in column 1 coming nearest to the 
 quotient find the safe strength per square inch for the column. 
 Multiply this load by the metal area in the cross-section of the 
 column, and the result will be the safe load for the column. 
 
 column of Table VII. represent a factor of safety of a little over four for 
 
 -T = 20, and nearly seven for = 36. 
 d d 
 
 A series of tests on full-size cast-iron columns and brackets was made 
 under the direction of Mr. Stevenson Constable, in December, 1897, a report 
 of which with illustrations may be found in the Engineering Record for 
 January 8 and 22, 1898. 
 
422 CAST-IRON COLUMNS AND POSTS. 
 
 EXAMPLE 4. What is the safe load for a 10-inch cylindrical 
 cast-iron column 15 feet long, the shell being one inch thick? 
 
 A ns. The length of the column divided by the diameter, both 
 in inches, is 18, and opposite 18 in Table VII. we find the safe load 
 per square inch for a round column to be 7,117 pounds. The 
 metal area of the column we find to be 28.27 inches; and multi- 
 plying these two numbers together, we have for the safe load of 
 the column 201,197 pounds, or about 100.5 tons. 
 
 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 com- 
 mon size and length. For lengths between those given in the 
 tables sufficiently accurate results may be obtained by interpola- 
 tion. For any other factor of safety multiply the safe load 
 given in the table by 8, and divide by the new factor of safety. 
 
CAST-IRON COLUMNS AND POSTS. 
 
 423 
 
 TABLE VII. STRENGTH PER SQUARE INCH OF HOL- 
 LOW, ROUND, AND RECTANGULAR CAST-IRON 
 COLUMNS. 
 
 (Calculated by Formulas (7) and (8).) 
 
 Length in 
 inches divided 
 by external 
 breadth or 
 
 Breaking weight in pounds 
 per square inch. 
 
 Safe load in pounds 
 per square inch. 
 Safety factor 8. 
 
 diameter. 
 
 
 
 
 
 
 Round. 
 
 Rectangular. 
 
 Round. 
 
 Rectangular. 
 
 8 
 
 74,074 
 
 75,470 
 
 9,259 
 
 9,433 
 
 9 
 
 72,661 
 
 74,350 
 
 9,082 
 
 9,293 
 
 10 
 
 71,110 
 
 73,126 
 
 8,888 
 
 9,140 
 
 11 
 
 69,505 
 
 71,870 
 
 8,688 
 
 8,983 
 
 12 
 
 67,800 
 
 70,487 
 
 8,475 
 
 8,811 
 
 13 
 
 66,060 
 
 69,084 
 
 8,257 
 
 8,635 
 
 14 
 
 64,257 
 
 67,567 
 
 8,032 
 
 8,446 
 
 15 
 
 62,450 
 
 66,060 
 
 7,806 
 
 8,257 
 
 16 
 
 60,606 
 
 64,516 
 
 7,576 
 
 8,064 
 
 17 
 
 58,780 
 
 62,942 
 
 7,347 
 
 7,867 
 
 18 
 
 56,940 
 
 61,360 
 
 7,117 
 
 7,670 
 
 19 
 
 55,134 
 
 59,745 
 
 6,892 
 
 7,468 
 
 20 
 
 53,333 
 
 58,180 
 
 6,666 
 
 7,272 
 
 21 
 
 51,580 
 
 56,610 
 
 6,447 
 
 7,076 
 
 22 
 
 49,843 
 
 55,020 
 
 6,230 
 
 6,877 
 
 23 
 
 48,163 
 
 53,470 
 
 6,020 
 
 6,684 
 
 24 
 
 46,512 
 
 51,950 
 
 5,814 
 
 6,494 
 
 25 
 
 44,918 
 
 50,440 
 
 5,614 
 
 6,305 
 
 26 
 
 43,360 
 
 48,960 
 
 5,420 
 
 6,120 
 
 27 
 
 41,862 
 
 47,530 
 
 5,233 
 
 5,940 
 
 28 
 
 40,404 
 
 46,110 
 
 5^50 
 
 5,764 
 
 29 
 
 39,000 
 
 44,742 
 
 4,875 
 
 5,592 
 
 30 
 
 37,647 
 
 43,390 
 
 4,706 
 
 5,424 
 
 31 
 
 36,347 
 
 42,080 
 
 4,543 
 
 5,260 
 
 32 
 
 35,090 
 
 40,816 
 
 4,386 
 
 5,102 
 
 33 
 
 33,884 
 
 39,580 
 
 4,235 
 
 4,947 
 
 34 
 
 32,720 
 
 38,380 
 
 4,090 
 
 4,797 
 
 35 
 
 31,608 
 
 37244 
 
 3,951 
 
 4,655 
 
 36 
 
 30,534 
 
 36,120 
 
 3,817 
 
 4,515 
 
424 
 
 CAST-IRON COLUMNS AND POSTS. 
 
 TABLE VIII. SAFE LOAD IN TONS OF 2,000 POUNDS 
 FOR HOLLOW ROUND CAST-IRON COLUMNS WITH 
 SQUARE ENDS. 
 
 (Based on formula (7). Safety factor 8.) 
 
 Ss 
 
 2 -a 
 
 a 
 
 H 
 
 11 
 
 2 
 
 Length of column in feet. 
 
 111 
 
 |J| 
 
 1 *, 
 
 Q.S 
 
 S3 
 
 6 
 
 8 
 
 10 
 
 12 
 
 14 
 
 16 
 
 18 
 
 20 
 
 22 
 
 24 
 
 
 *&s 
 
 5 
 
 M 
 
 39 
 
 34 
 
 29 
 
 24 
 
 
 
 
 
 
 
 10.0 
 
 31.3 
 
 
 % 
 
 45 
 
 38 
 
 32 
 
 27 
 
 
 
 
 
 
 
 11.3 
 
 35.3 
 
 61 
 
 H 
 
 46 
 
 40 
 
 35 
 
 30 
 
 26 
 
 
 
 
 
 
 11.2 
 
 35.0 
 
 
 7Z 
 
 52 
 
 46 
 
 40 
 
 34 
 
 29 
 
 
 
 
 
 
 12.7 
 
 39.7 
 
 6 
 
 r 
 
 52 
 
 47 
 
 41 
 
 36 
 
 31 
 
 27 
 
 24 
 
 
 
 
 12.4 
 
 38.7 
 
 
 7? 
 
 60 
 
 53 
 
 47 
 
 41 
 
 36 
 
 31 
 
 27 
 
 
 
 
 14.1 
 
 44.0 
 
 
 1 
 
 66 
 
 59 
 
 52 
 
 45 
 
 39 
 
 34 
 
 30 
 
 
 
 
 15.7 
 
 49.0 
 
 7 
 
 % 
 
 65 
 
 60 
 
 54 
 
 48 
 
 43 
 
 38 
 
 34 
 
 
 
 
 14.7 
 
 46.0 
 
 
 
 
 74 
 
 68 
 
 62 
 
 55 
 
 49 
 
 43 
 
 38 
 
 
 
 
 16.8 
 
 52.6 
 
 
 1 
 
 83 
 
 76 
 
 68 
 
 61 
 
 54 
 
 48 
 
 43 
 
 
 
 
 18.8 
 
 58.9 
 
 8 
 
 
 78 
 
 72 
 
 67 
 
 61 
 
 55 
 
 50 
 
 45 
 
 40 
 
 36 
 
 33 
 
 17.1 
 
 53.4 
 
 
 % 
 
 89 
 
 83 
 
 76 
 
 70 
 
 63 
 
 57 
 
 51 
 
 46 
 
 41 
 
 37 
 
 19.6 
 
 61.2 
 
 
 1 
 
 100 
 
 93 
 
 86 
 
 79 
 
 71 
 
 64 
 
 58 
 
 52 
 
 47 
 
 42 
 
 22.0 
 
 68.7 
 
 9 
 
 % 
 
 103 
 
 98 
 
 91 
 
 85 
 
 80 
 
 71 
 
 65 
 
 59 
 
 54 
 
 49 
 
 22.3 
 
 69.8 
 
 
 1 
 
 117 
 
 110 
 
 103 
 
 95 
 
 90 
 
 80 
 
 73 
 
 67 
 
 61 
 
 55 
 
 25.1 
 
 78.5 
 
 
 1^ 
 
 129 
 
 122 
 
 If 4 
 
 105 
 
 99 
 
 89 
 
 81 
 
 74 
 
 67 
 
 61 
 
 27.8 
 
 87.0 
 
 10 
 
 % 
 
 118 
 
 112 
 
 106 
 
 100 
 
 93 
 
 86 
 
 79 
 
 73 
 
 67 
 
 62 
 
 25.1 
 
 78.4 
 
 
 1 
 
 133 
 
 127 
 
 120 
 
 112 
 
 105 
 
 97 
 
 89 
 
 82 
 
 76 
 
 69 
 
 28.3 
 
 88.4 
 
 
 1/^c 
 
 147 
 
 141 
 
 133 
 
 125 
 
 116 
 
 107 
 
 99 
 
 91 
 
 84 
 
 77 
 
 31.4 
 
 98.0 
 
 
 1J4 
 
 161 
 
 154 
 
 146 
 
 136 
 
 127 
 
 118 
 
 109 
 
 100 
 
 92 
 
 84 
 
 34.4 
 
 107.4 
 
 11 
 
 1 
 
 149 
 
 143 
 
 137 
 
 129 
 
 122 
 
 114 
 
 106 
 
 98 
 
 91 
 
 85 
 
 31.4 
 
 98 .-2 
 
 
 i/^ 
 
 165 
 
 159 
 
 152 
 
 144 
 
 135 
 
 126 
 
 118 
 
 109 
 
 101 
 
 94 
 
 34.9 
 
 109.1 
 
 
 1^4 
 
 182 
 
 175 
 
 167 
 
 158 
 
 148 
 
 139 
 
 129 
 
 120 
 
 111 
 
 103 
 
 38.3 
 
 119.7 
 
 
 1% 
 
 197 
 
 190 
 
 181 
 
 171 
 
 161 
 
 151 
 
 140 
 
 130 
 
 121 
 
 112 
 
 41.6 
 
 129.9 
 
 12 
 
 1^ 
 
 184 
 
 178 
 
 171 
 
 163 
 
 154 
 
 146 
 
 137 
 
 128 
 
 120 
 
 112 
 
 38.4 
 
 120.1 
 
 
 1J4 
 
 202 
 
 195 
 
 188 
 
 179 
 
 170 
 
 160 
 
 150 
 
 141 
 
 132 
 
 123 
 
 42.2 
 
 131.9 
 
 
 1% 
 
 220 
 
 212 
 
 204 
 
 194 
 
 184 
 
 174 
 
 163 
 
 153 
 
 143 
 
 133 
 
 45.9 
 
 143 . 4 
 
 
 1J4 
 
 237 
 
 229 
 
 220 
 
 210 
 
 199 
 
 187 
 
 176 
 
 165 
 
 154 
 
 144 
 
 49.5 
 
 154.6 
 
 13 
 
 1^6 
 
 202 
 
 196 
 
 190 
 
 182 
 
 174 
 
 165 
 
 156 
 
 147 
 
 138 
 
 130 
 
 42.0 
 
 131.2 
 
 
 1/4 
 
 222 
 
 216 
 
 209 
 
 200 
 
 191 
 
 181 
 
 172 
 
 162 
 
 152 
 
 143 
 
 46.1 
 
 144.2 
 
 
 1% 
 
 242 
 
 235 
 
 227 
 
 218 
 
 208 
 
 197 
 
 187 
 
 176 
 
 166 
 
 156 
 
 50.2 
 
 156.9 
 
 
 1H 
 
 261 
 
 254 
 
 245 
 
 235 
 
 224 
 
 213 
 
 201 
 
 190 
 
 179 
 
 168 
 
 54.2 
 
 169.4 
 
 14 
 
 1J4 
 
 242 
 
 236 
 
 229 
 
 221 
 
 212 
 
 203 
 
 193 
 
 183 
 
 173 
 
 164 
 
 50.1 
 
 156.5 
 
 
 1^ 
 
 264 
 
 258 
 
 250 
 
 241 
 
 231 
 
 221 
 
 210 
 
 199 
 
 189 
 
 178 
 
 54.5 
 
 170.4 
 
 
 1V 
 
 285 
 
 278 
 
 270 
 
 260 
 
 250 
 
 238 
 
 227 
 
 215 
 
 204 
 
 193 
 
 58.9 
 
 184.1 
 
 
 i^ 
 
 306 
 
 298 
 
 289 
 
 279 
 
 268 
 
 256 
 
 243 
 
 231 
 
 219 
 
 207 
 
 63.2 
 
 197.4 
 
 15 
 
 1% 
 
 268 
 
 280 
 
 272 
 
 264 
 
 254 
 
 244 
 
 234 
 
 223 
 
 212 
 
 203 
 
 58.9 
 
 183.9 
 
 
 l\ 
 
 309 
 
 303 
 
 295 
 
 285 
 
 275 
 
 264 
 
 252 
 
 241 
 
 229 
 
 219 
 
 63.6 
 
 203.4 
 
 
 l^B 
 
 332 
 
 325 
 
 316 
 
 306 
 
 295 
 
 283 
 
 271 
 
 259 
 
 246 
 
 235 
 
 68.3 
 
 213.4 
 
 
 1M 
 
 354 
 
 346 
 
 337 
 
 327 
 
 315 
 
 302 
 
 288 
 
 276 
 
 263 
 
 251 
 
 72.8 
 
 227.6 
 
 16 
 
 1U 
 
 333 
 
 327 
 
 319 
 
 310 
 
 300 
 
 290 
 
 278 
 
 267 
 
 255 
 
 243 
 
 68.3 
 
 213.5 
 
 
 1% 
 
 358 
 
 351 
 
 343 
 
 333 
 
 322 
 
 311 
 
 299 
 
 286 
 
 273 
 
 261 
 
 73.4 
 
 229.3 
 
 
 1M 
 
 382 
 
 375 
 
 366 
 
 356 344 
 
 332 
 
 319 
 
 306 
 
 292 
 
 279 
 
 78.3 
 
 244.8 
 
 
 1% 
 
 455 
 
 446. 435 
 
 423 410 
 
 395 
 
 380 
 
 364 
 
 347 
 
 332 
 
 93.2 
 
 291.3 
 
 
 
 
 | 
 
 1 
 
 
 
 
 
 
 
 
CAST-IRON COLUMNS AND POSTS. 
 
 TABLE IX. SAFE LOAD 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 in 
 inches. 
 
 Thick- 
 ness in 
 inches. 
 
 Length of column in feet. 
 
 Area of 
 metal 
 in 
 inches. 
 
 Weight 
 per foot 
 of 
 length: 
 
 8 
 
 10 
 
 12 
 
 14 
 
 16 
 
 18 
 
 20 
 
 24 
 
 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 
 
 i* 
 i* 
 
 
 i 
 
 1* 
 
 1 
 
 1* 
 
 !' 
 i 
 
 ?! 
 
 i* 
 
 i* 
 
 x 
 f 
 
 1 4 
 
 1J4 
 
 i* 
 
 1M 
 
 41 
 51 
 56 
 60 
 70 
 
 64 
 81 
 69 
 89 
 75 
 96 
 86 
 111 
 
 63 
 80 
 75 
 96 
 81 
 104 
 
 87 
 112 
 99 
 129 
 117 
 153 
 
 80 
 102 
 92 
 119 
 111 
 144 
 
 95 
 
 124 
 148 
 109 
 141 
 170 
 
 122 
 158 
 192 
 
 34 
 42 
 46 
 50 
 59 
 
 55 
 
 71 
 60 
 78 
 65 
 84 
 74 
 97 
 
 57 
 
 72 
 68 
 87 
 73 
 94 
 
 79 
 101 
 90 
 116 
 106 
 138 
 
 73 
 94 
 85 
 109 
 102 
 133 
 
 90 
 115 
 140 
 103 
 132 
 161 
 
 115 
 
 148 
 181 
 
 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 
 167 
 
 
 
 
 
 
 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 
 26.25 
 34.00 
 
 21.75 
 28.00 
 33.75 
 24.75 
 32.00 
 38.75 
 
 27.75 
 36.00 
 43.75 
 
 39.8 
 49.2 
 53.9 
 58.6 
 68.0 
 
 53.9 
 
 68.8 
 58.6 
 75.0 
 63.3 
 81.3 
 72.7 
 93.8 
 
 49.2 
 62.5 
 58.6 
 75.0 
 63.3 
 81.3 
 
 68.0 
 87.5 
 77.3 
 100.0 
 91.4 
 118.8 
 
 58.6 
 75.0 
 68.0 
 87.5 
 82.0 
 106.3 
 
 68.0 
 87.5 
 105.5 
 77.3 
 100.0 
 121.1 
 
 86.7 
 112.5 
 136.7 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 41 
 53 
 45 
 58 
 49 
 63 
 56 
 72 
 
 45 
 57 
 54 
 69 
 
 58 
 75 
 
 62 
 80 
 71 
 92 
 84 
 109 
 
 61 
 78 
 70 
 91 
 85 
 110 
 
 77 
 99 
 119 
 87 
 113 
 137 
 
 98 
 127 
 154 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 40 
 51 
 47 
 61 
 51 
 66 
 
 55 
 71 
 63 
 81 
 74 
 97 
 
 55 
 70 
 63 
 
 82 
 77 
 99 
 
 70 
 91 
 109 
 80 
 104 
 125 
 
 90 
 116 
 142 
 
 35 
 
 45 
 42 
 54 
 45 
 
 58 
 
 49 
 63 
 55 
 72 
 66 
 85 
 
 49 
 63 
 57 
 74 
 69 
 89 
 
 64 
 83 
 100 
 73 
 95 
 115 
 
 82 
 107 
 130 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 44 
 57 
 51 
 66 
 62 
 80 
 
 59 
 76 
 91 
 67 
 86 
 105 
 
 75 
 97 
 118 
 
 49 
 63 
 76 
 55 
 
 72 
 87 
 
 62 
 
 81 
 98 
 
426 
 
 CAST-IRON COLUMNS AND POSTS. 
 
 TABLE IX. SAFE LOAD IN TONS OF 2,000 POUNDS FOR 
 HOLLOW SQUARE AND RECTANGULAR CAST-IRON 
 COLUMNS WITH SQUARE ENDS (continued). 
 (Based on formula (8). Safety factor 8.) 
 
 Size in 
 inches. 
 
 Thick- 
 ness in 
 inches. 
 
 Length of column in feet. 
 
 Area of 
 metal 
 in 
 inches. 
 
 Weight 
 per foot 
 of 
 length. 
 
 8 
 
 10 
 
 12 
 
 14 
 
 16 
 
 18 
 
 20 
 
 24 
 
 8X16 
 
 1 
 
 . 193 
 
 181 
 
 168 
 
 155 
 
 142 
 
 130 
 
 119 
 
 99 
 
 44.00 
 
 137.5 
 
 
 1*4 
 
 236 
 
 221 
 
 206 
 
 190 
 
 174 
 
 159 
 
 145 
 
 121 
 
 53.75 
 
 168.0 
 
 9X 9 
 
 
 111 
 
 106 
 
 99 
 
 93 
 
 86 
 
 80 
 
 74 
 
 63 
 
 24.75 
 
 77.3 
 
 
 1 4 
 
 144 
 
 137 
 
 129 
 
 120 
 
 112 
 
 103 
 
 96 
 
 85 
 
 32.00 
 
 100.0 
 
 9X12 
 
 1 
 
 171 
 
 162 
 
 153 
 
 143 
 
 133 
 
 123 
 
 114 
 
 97 
 
 38.00 
 
 118.8 
 
 
 1M 
 
 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 
 
 
 1*4 
 
 254 
 
 240 
 
 226 
 
 212 
 
 197 
 
 182 
 
 168 
 
 143 
 
 56.25 
 
 175.8 
 
 10X10 
 
 i 
 
 165 
 
 158 
 
 150 
 
 142 
 
 133 
 
 125 
 
 117 
 
 101 
 
 36.00 
 
 112.5 
 
 
 1*4 
 
 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 
 
 
 Hi 
 
 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 
 
 
 1*4 
 
 258 
 
 247 
 
 235 
 
 222 
 
 209 
 
 195 
 
 182 
 
 158 
 
 56 . 25 
 
 175.8 
 
 10X16 
 
 l 
 
 220 
 
 211 
 
 200 
 
 189 
 
 178! 167 
 
 155 
 
 135 
 
 48.00 
 
 150.0 
 
 
 1*4 
 
 270 
 
 258 
 
 245 
 
 232 
 
 218 204 
 
 190 
 
 165 
 
 58.75 
 
 183.6 
 
 10X18 
 
 l 
 
 239 
 
 228 
 
 217 
 
 205 
 
 193 
 
 181 
 
 168 
 
 146 
 
 52.00 
 
 162.5 
 
 
 1*4 
 
 293 
 
 280 
 
 266 
 
 251 
 
 236 
 
 221 
 
 207 
 
 179 
 
 63.75 
 
 199.2 
 
 10X20 
 
 1 
 
 257 
 
 246 
 
 234 
 
 221 
 
 208 
 
 194 
 
 181 
 
 157 
 
 56.00 
 
 175.0 
 
 
 1*4 
 
 316 
 
 302 
 
 287 
 
 271 
 
 255 
 
 239 
 
 223 
 
 193 
 
 68.75 
 
 214.9 
 
 10X24 
 
 l 
 
 294 
 
 281 
 
 267 
 
 252 
 
 237 
 
 222 
 
 207 
 
 180 
 
 64.00 
 
 200.0 
 
 
 1*4 
 
 362 
 
 346 
 
 329 
 
 311 
 
 292 
 
 274 
 
 255 
 
 221 
 
 78.75 
 
 246.1 
 
 12X12 
 
 % 
 
 183 
 
 177 
 
 171 
 
 164 
 
 156 
 
 149 
 
 141 
 
 126 
 
 38.9 
 
 121.7 
 
 
 i 
 
 207 
 
 201 
 
 193 
 
 185 
 
 177 
 
 168 
 
 159 
 
 142 
 
 44.00 
 
 137.5 
 
 
 1*4 
 
 253 
 
 245 
 
 236 
 
 223 
 
 216 
 
 206 
 
 195 
 
 174 
 
 53.75 
 
 168.0 
 
 
 l*iis 
 
 296 
 
 288 
 
 277 
 
 265 
 
 253 
 
 241 
 
 228 
 
 204 
 
 63.00 
 
 196.9 
 
 12X15 
 
 i 
 
 235 
 
 228 
 
 220 
 
 211 
 
 201 
 
 191 
 
 181 
 
 162 
 
 50.00 
 
 156.3 
 
 
 1*4 
 
 288 
 
 280 
 
 269 
 
 258 
 
 246 
 
 234 
 
 222 
 
 198 
 
 61.25 
 
 191.4 
 
 12X16 
 
 1 
 
 245 
 
 237 
 
 228 
 
 219 
 
 209 
 
 199 
 
 188 
 
 168 
 
 52.00 
 
 162.5 
 
 12X18 
 
 l 
 
 263 
 
 256 
 
 246 
 
 236 
 
 225 
 
 214 
 
 203 
 
 181 
 
 56.00 
 
 175.0 
 
 12X20 
 
 l 
 
 282 
 
 274 
 
 264 
 
 253 
 
 241 
 
 229 
 
 217 
 
 194 
 
 60.00 
 
 187.5 
 
 12X24 
 
 l 
 
 320 
 
 310 
 
 299 
 
 287 
 
 274 
 
 260 
 
 246 
 
 220 
 
 68.00 
 
 212.5 
 
 14X16 
 
 1 
 
 268 
 
 261 
 
 254 
 
 246 
 
 238 
 
 229 
 
 219 
 
 200 
 
 56.00 
 
 175.0 
 
 14X20 
 
 1 
 
 307 
 
 298 
 
 290 
 
 281 
 
 272 
 
 261 
 
 250 
 
 228 
 
 64.00 
 
 200.0 
 
 14X24 
 
 1 
 
 345 
 
 336 
 
 326 
 
 316 
 
 306 
 
 294 
 
 280 
 
 257 
 
 72.00 
 
 225.0 
 
 16X16 
 
 1 
 
 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 
 
CAST-IRON COLUMNS AND POSTS. 
 
 427 
 
 TABLE X. SAFE LOAD IN TONS OF 2,000 PC 
 H-SHAPED CAST-IRON POSTS. ^ ^ 
 
 (Based on formula (7). Safety factor 8.) 1 ^ 
 
 )UNDS FOR 
 
 'i 
 
 Size of post 
 in inches. 
 
 Area 
 
 A v% 
 Length of post in feet. , <0 
 
 m 
 
 
 YJk 
 
 
 in 
 
 '! 1 
 
 IP 
 
 
 inches. 
 
 
 
 
 
 ., 2% 
 
 |p 
 
 a. b. t. 
 
 
 10 
 
 12 
 
 13 
 
 14 
 
 K- 
 
 --l/-_,-> 
 
 6X 6X % 
 
 12% 
 
 41 
 
 36 
 
 33 
 
 31 
 
 
 
 1 
 
 16 
 
 53 
 
 46 
 
 43 
 
 40 
 
 
 16 
 
 
 
 1/4 
 
 193/ 
 
 64 
 
 56 
 
 52 
 
 48 
 
 15 
 
 18 
 
 20 
 
 6X 8X YA 
 
 137k 
 
 46 
 
 40 
 
 37 
 
 34 
 
 
 
 
 I 
 
 is 8 
 
 60 
 
 52 
 
 48 
 
 45 
 
 
 
 
 
 
 1J4 
 
 21% 
 
 73 
 
 63 
 
 59 
 
 54 
 
 
 
 
 
 
 7X 7X1 
 
 19 
 
 69 
 
 62 
 
 58 
 
 55 
 
 52 
 
 49 
 
 43 
 
 38 
 
 1/4 
 
 23% 
 
 84 
 
 75 
 
 71 
 
 67 
 
 63 
 
 5< 
 
 \ 
 
 53 
 
 46 
 
 7X 9X1 
 
 21 
 
 76 
 
 68 
 
 64 
 
 61 
 
 57 
 
 54 
 
 48 
 
 42 
 
 1M 
 
 25% 
 
 93 
 
 83 
 
 79 
 
 74 
 
 70 
 
 66 
 
 59 
 
 51 
 
 8X 8X H 
 
 16% 
 
 66 
 
 60 
 
 57 
 
 54 
 
 51 
 
 49 
 
 44 
 
 39 
 
 1 
 
 22 
 
 86 
 
 78 
 
 74 
 
 70 
 
 67 
 
 6^ 
 
 t 
 
 57 
 
 51 
 
 1/4 
 
 26% 
 
 105 
 
 95 
 
 91 
 
 86 
 
 82 
 
 7! 
 
 5 
 
 70 
 
 63 
 
 8X10X1 
 
 24 
 
 93 
 
 85 
 
 81 
 
 77 
 
 73 
 
 69 
 
 62 
 
 56 
 
 1M 
 
 29% 
 
 114 
 
 104 
 
 99 
 
 94 
 
 90 
 
 8, 
 
 
 76 
 
 69 
 
 1^ 
 
 34^ 
 
 134 
 
 122 
 
 117 
 
 111 
 
 105 
 
 100 
 
 89 
 
 81 
 
 9X 9X1 
 
 25 
 
 102 
 
 94 
 
 91 
 
 87 
 
 83 
 
 79 
 
 72 
 
 66 
 
 m 
 
 30% 
 
 125 
 
 116 
 
 111 
 
 106 
 
 102 
 
 97 
 
 89 
 
 81 
 
 ITS 
 
 36 
 
 147 
 
 136 
 
 130 
 
 125 
 
 120 
 
 11< 
 
 1 
 
 104 
 
 95 
 
 9X10X1 " 
 
 26 
 
 106 
 
 98 
 
 94 
 
 90 
 
 86 
 
 83 
 
 75 
 
 69 
 
 1/4 
 
 31% 
 
 130 
 
 120 
 
 115 
 
 111 
 
 106 
 
 101 
 
 92 
 
 84 
 
 1J4 
 
 37^ 
 
 153 
 
 142 
 
 136 
 
 130 
 
 125 
 
 119 
 
 108 
 
 99 
 
 10X10X1 
 
 28 
 
 118 
 
 111 
 
 107 
 
 103 
 
 99" 
 
 95 
 
 88 
 
 81 
 
 1/4 
 
 343/6 
 
 145 
 
 136 
 
 131 
 
 127 
 
 122 
 
 12' 
 
 \ 
 
 108 
 
 100 
 
 1J^2 
 
 40H$ 
 
 171 
 
 160 
 
 155 
 
 149 
 
 144 
 
 138 
 
 128 
 
 117 
 
 1% 
 
 46% 
 
 196 
 
 184 
 
 177 
 
 171 
 
 165 
 
 15* 
 
 \ 
 
 146 
 
 134 
 
 10X12X1 
 
 30 
 
 127 
 
 119 
 
 115 
 
 111 
 
 106 
 
 102 
 
 94 
 
 87 
 
 1/4 
 
 36% 
 
 156 
 
 146 
 
 141 
 
 136 
 
 131 
 
 12( 
 
 
 116 
 
 107 
 
 l/^ 
 
 43^ 
 
 184 
 
 172 
 
 166 
 
 160 
 
 154 
 
 148 
 
 137 
 
 126 
 
 l% 
 
 49% 
 
 211 
 
 198 
 
 191 
 
 184 
 
 177 
 
 17( 
 
 ) 
 
 157 
 
 144 
 
 2 
 
 56 
 
 236 
 
 222 
 
 214 
 
 207 
 
 199 
 
 191 
 
 176 
 
 162 
 
 12X12X1 
 
 34 
 
 151 
 
 144 
 
 140 
 
 136 
 
 132 
 
 128 
 
 121 
 
 113 
 
 1J4 
 
 41% 
 
 186 
 
 177 
 
 172 
 
 167 
 
 163 
 
 158 
 
 149 
 
 139 
 
 1^ 
 
 49^ 
 
 220 
 
 209 
 
 203 
 
 198 
 
 193 
 
 187 
 
 i 
 
 177 
 
 165 
 
 1% 
 
 56% 
 
 252 
 
 241 
 
 234 
 
 227 
 
 221 
 
 2H 
 
 
 202 
 
 189 
 
 2 
 
 64 
 
 284 
 
 271 
 
 263 
 
 256 
 
 249 
 
 242 
 
 227 
 
 213 
 
 12X14X114 
 
 44% 
 
 197 
 
 188 
 
 183 
 
 177 
 
 173 
 
 168 
 
 158 
 
 148 
 
 1J4 
 
 52^ 
 
 233 
 
 222 
 
 216 
 
 210 
 
 204 
 
 19? 
 
 ) 
 
 186 
 
 174 
 
 1% 
 
 60% 
 
 268 
 
 255 
 
 248 
 
 241 
 
 235 
 
 228 
 
 214 
 
 201 
 
 2 
 
 68 
 
 302 
 
 288 
 
 280 
 
 272 
 
 265 
 
 257 
 
 
 241 
 
 226 
 
 2M 
 
 75% 
 
 335 
 
 319 
 
 310 
 
 301 
 
 292 
 
 285 
 
 268 
 
 251 
 
428 STEEL COLUMNS AND STRUTS, 
 
 WROUGHT-mON AND STEEL, COLUMNS 
 AND STRUTS. 
 
 Owing to the many advantages of built steel columns over 
 cast-iron columns, especially for tall buildings, and the great re- 
 duction that has taken place during the past fifteen years in the 
 cost of steel construction, steel columns are now very extensively 
 used in buildings, even of moderate height, and for skeleton con- 
 struction, or buildings exceeding six stories in height, they are 
 certainly much to be preferred to cast columns. 
 
 Steel trusses are also much more commonly used in buildings 
 now than in former years, so that the architect must have at hand 
 data for designing the same and computing the strength. In 
 the following pages the author has endeavored to cover the 
 subject of columns and struts quite completely, and to furnish 
 such data as will enable one to decide upon the shape of column 
 or strut it is best to use, and to determine the size and section 
 with the least labor. 
 
 Forms of Steel Columns. 
 
 The forms of columns commonly used in current American 
 building practice are those shown by the following sections: 
 
 | A | Larimer column, 1 row of rivets. 
 
 r** ""i 
 
 Z-bar column, without [[ jj 4 angles and 
 
 covers, 2 rows. plate, 2 rows. 
 
 IL J 
 
 4-section Phoenix column, 4 rows. 
 
 iNurick column, 4 rows. 
 
 Channel column, with plates or lattice, 4 rows. 
 Gray column, 4 rows, 
 
STEEL COLUMNS AND STRUTS. 429 
 
 Z-bar column, with single covers, 6 rows. 
 Box column of plates and angles, 8 rows. 
 
 8-section Phoenix column, 8 rows. 
 
 Z-bar column, with double covers, 10 rows. 
 
 Each of these shapes has its advocates among experienced 
 engineers, and the choice of a section is generally governed by 
 some practical consideration, such as the cost, facility for making 
 connections, and promptness of delivery. 
 
 Relative Advantages and Disadvantages. 
 
 The relative advantages and disadvantages of the various 
 sections are set forth at considerable length by Mr. Joseph K. 
 Freitag, B.S., C.E., in his very practical work on "Architectural 
 Engineering." 
 
 In general it may be said that the factors which usually deter- 
 mine the choice of a section are one or more of the following 
 points, each of which should be carefully considered when 
 designing an important building: 
 
 1. Cost, including shop-work, availability. 
 
 2. Ability to transfer loads to centre of column, especially in 
 cases of heavy eccentric loads. 
 
 3. Convenient connection of floor system. 
 
 4. Relation of size of section to small columns. 
 
 5. Fireproofing capabilities of the section. "Point 1 is of the 
 greatest importance^ the owner and builder, and often governs 
 the selection of the column. Points 2, 3, and 4 are for the 
 engineer's consideration; while point 5 is of chief interest to the 
 architect and decorator." * 
 
 Cost, Availability. These vary more or less at different times, 
 the cost depending principally upon the market price of the 
 section used, and upon the amount of shop- work required. In 
 general it may be said that those forms which can be rolled or 
 
 * Freitag. 
 
430 STEEL COLUMNS AND STRUTS. 
 
 manufactured by any mill are likely to be the cheapest and mosl 
 available, although there may often be exceptions to this rule. 
 
 Plates and angles are generally the cheapest sections of roller 
 steel and the most available, and the Z-bar is now being rolled b} 
 several mills. The Phoenix column is rolled only by the Phcenh 
 Iron Company, and the Larimer column is manufactured only bj 
 Jones & Laughlins, Limited. The number of rivets required ir 
 putting the sections together, which comes under the head o: 
 "shop-work," is also an important factor in the cost of stee 
 columns. The Larimer column possesses an advantage in ihit 
 respect over all other shapes, and at the present price of stee 
 beams this column should be one of the cheapest shapes on the 
 market. 
 
 An objection has been found to the smaller sizes of this column 
 particularly the 6-inch size, that it is difficult to drive the rivets 
 which connect the angle brackets with the I-beam flanges without 
 interfering. 
 
 Next to the Larimer column in point of shop-work comes the 
 Z-bar column, without cover-plates, which has two rows of rivets. 
 For light loads this shape appears to have more advantages thar 
 any other, as it is an economical section, and the connections foi 
 floor beams and girders are quite simple, and the shape alsc 
 permits of bringing the weight well into the centre of the column. 
 
 In tall buildings, however, it has almost invariably been found 
 necessary to add cover-plates, and in some instances no less than 
 ten rows of rivets have been required, so that for tall buildings 
 this section does not appear to offer any advantage over col- 
 umns built of plates and channels, and in point of fact it is now 
 seldom used in high or heavy buildings. The Z-bar column, 
 however, has been more extensively used than any other shape 
 in the tall buildings erected during the past ten years in Chicago. 
 Its use in Eastern cities has been far more limited. Channel col- 
 umns and columns of plates and angles have also been quite ex- 
 tensively used both in Chicago and in the East. Although some- 
 what limited as to section, channel columns afford a very desir- 
 able shape, both as regards economy of material and facility for 
 making connections. Columns- built up of plates and angles 
 present a section that can be increased to any desired area, and 
 the area of the section can also be considerably varied without 
 increasing the exterior dimensions. 
 
 With heavy eccentric loads it is sometimes an advantage to use 
 
STEEL COLUMNS AND STRUTS. 
 
 431 
 
 a rectangular shape, with the long axis in the direction of the 
 eccentricity. 
 
 In practice, however, the choice of a section is generally gov- 
 erned more by the consideration of cost and connection facilities 
 than by the best theoretical shape. 
 
 Further description of the different columns, and also the 
 special advantages claimed for them, is given in the following 
 pages. 
 
 A new type of column which has recently been patented by 
 Mr. John Lanz, of Pittsburg, is shown by Fig. 12. The columns 
 
 Fig. 12 
 
 are formed of rolled channel beams, bent to the necessary form 
 and riveted together into a hollow column with projecting 
 flanges of a T-shape. It is proposed to bend the channels so as 
 to give columns of circular cross-section as well as the shapes 
 illustrated. Among the merits claimed for the hew column are 
 compactness, an unusually large radius of gyration for the 
 amount of material used, and three constant sizes of columns for 
 56 different sectional areas, making it very easy to get out details 
 of the framing. 
 
 Column Connections. 
 
 This feature in column construction is a very important one, 
 and often governs the selection of the shape to be used. Where 
 there are only two or four beams at the same level, and these are 
 symmetrically placed and loaded, satisfactory connections can be 
 made for almost any of the sections, but when irregular placing 
 of beams is necessitated, and eccentric loads must be provided 
 for, it is important that the character of the column affords as 
 great an opportunity as possible for the connection of plates and 
 
432 STEEL COLUMNS AND STRUTS. 
 
 angles, and for transferring eccentric loads to the centre of the 
 column. 
 
 When wrought-iron columns were first used it was customary 
 to use plates for connecting the tory lengths, and the beams or 
 girders often rested on these plates, as shown in Figs. 14 and 24. 
 In the best practice at the present time these plates are often 
 omitted, and the ends of the different lengths are closely fitted 
 together with milled ends, and splice plates are riveted to the 
 sides or flanges. 
 
 As it is impossible in these pages to cover the subject of 
 column connections in anything but a general way, the only 
 attempt that has been made in this line is to illustrate common 
 forms of connections that have been used with different forms of 
 columns. These will be found in the descriptions of different 
 columns contained in the following pages. 
 
 For a more complete consideration of the subject the reader is 
 referred to Mr. Freitag's "Architectural Engineering" and Mr. 
 Birkmire's "Skeleton Construction in Buildings." 
 
 Number and Spacing of Rivets. 
 
 Number of Rivets Required. ^No general rule can be given for 
 the number of rivets and size of the brackets required for col- 
 umn connections, as the loads to be supported vary in different 
 buildings and in different portions of the same building. The 
 number of rivets required in each connection must therefore be 
 determined by the rules given for designing riveted joints in 
 Chapter XII. Connections for single beams, however, will gen- 
 erally require the same number of rivets as are given for beam 
 connections, Chapter XV. The allowable strains for rivets in 
 column connections are generally taken at 10,000 Ibs. per sq. 
 inch for single shear and 18,000 Ibs. for bearing. 
 
 Spacing of Rivets. Steel and w r rought-iron 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 thick- 
 ness of the metal is insufficient. 
 
 The rule has been deduced from actual experiments upon 
 wrought-iron columns that the distance between centres of 
 rivets should not exceed, in the line of strain, sixteen times the 
 
STEEL COLUMNS AND STRUTS. 433 
 
 thickness of metal of the parts joined, and that the distance 
 between rivets or other points of support, at right angles to the 
 line of strain, should not exceed thirty-two times the thickness 
 of the metal. 
 
 Z-Bar Columns. 
 
 This column was designed by Mr. C. L. Strobel, C.E., about the 
 year 1887, and for a time the bars were rolled only by the Carnegie 
 Steel Company. ,At the present time they are rolled by nearly 
 all of the large mills, so that they can be obtained as readily as 
 channels or angles. For buildings of moderate height and load- 
 ing, no more advantageous section can be employed, while it is 
 probably as cheap as any. It has also been used quite exten- 
 sively in tall buildings, although at the present time columns 
 built of plates and angles appear to be more generally used. 
 
 For buildings of ordinary height, the column is formed of four 
 Z-bars and one web plate, with two rows of rivets. When un- 
 usually heavy loads must be provided for, as in the case of 
 columns for the lower stories of high buildings, the above- 
 mentioned section may be reinforced to the required strength 
 by using outside cover-plates, as shown on page 478, or cover- 
 plates and angles, forming a closed or box column. 
 
 Connections. The usual form of base plate, and the manner 
 of supporting single beams where the column is continuous, are 
 shown by Fig. 13. The beams should extend to within \ inch 
 of web plates, and should be also bolted or riveted to the sup- 
 porting angles. 
 
 The usual connection of one column to another is shown by 
 Fig. 14, which represents a plan of the cap plate, and vertical sec- 
 tion through centre of column. The ends of the two sections 
 should be carefully milled and connected to the cap plate by angle 
 brackets, the whole construction being firmly riveted together. 
 The cap plate is usually made from i to 1 inch in thickness, ac- 
 cording to the load to be supported. Where beams of different 
 depths rest on the cap plate, they may be brought to the same 
 level by means of cast-iron bolsters. 
 
 Fig. 15 shows a detail of one of the columns used in the Ameri- 
 can Surety Building in New York, the connections shown being 
 those of the sixteenth- and seventeenth-story floor beams. It 
 will be noticed that in this column the end connections do not 
 come at the floor level, but at some distance from it, and the 
 
434 
 
 STEEL COLUMNS AND STRUTS. 
 
 cap plate does not project beyond the Z-bars, the joint being 
 secured by means of splice plates. The object in giving such a 
 long bearing under the beams was to obtain stiffness to resist 
 
 . Fig. 13 
 
 Fig. 14 
 
 the horizontal wind pressure, four rivets being placed in each 
 side of the lower flange. 
 
 The connections shown in Fig. 15 are also applicable to channel 
 and plate and angle columns. 
 
 The standard connections for double I-beam girders and single 
 floor beams to Z-bar columns, detailed on page 436, were de- 
 signed by the Carnegie Steel Company to fairly cover the range 
 of ordinary practice. When the maximum loads in tons indi- 
 cated for each case, are exceeded, the connections may be corre- 
 spondingly strengthened by simply using longer vertical angles 
 for the brackets and increasing the number of rivets. In pro- 
 portioning these connections the shearing strain on rivets was 
 assumed of a maximum intensity of 10,000 pounds per square 
 inch. 
 
STEEL COLUMNS AND STRUTS. 
 
 SECTION ON LINE B.& 
 
 435 
 
 Fig. 15 
 
436 
 
 STEEL COLUMNS AND STRUTS. 
 
 DETAILS OF STANDABD CONNECTIONS 
 OF I BEAMS TO Z-BAR COLUMNS. 
 
 Connections of a single I Beam to Flanges of 2 Bars. 
 
 Fig. 4 
 
 2<?'I Beams, 
 44 Tons. 
 
 t5"and 12"! Beams 
 35 Tons. 
 
 ;'to,"9"and 8 7 f 'and 6" 
 I BeaiQ3 ' I Beams 
 17.6 Tons. - 8.8 Tons. 
 
 Connections of a double Beam girder to Flanges of Z Bars. 
 Fig. 5 
 
 V 
 
 20"! Beams 
 88 Tons. 
 
 Fig. 6 
 
 Fig. 7 
 
 Fig 
 
 *nr 
 
 .8 
 
 Q f 
 
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 Ji 
 
 I 
 
 |p 
 
 |0 
 
 i! 
 
 & 
 
 1 
 
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 1 3 
 
 6 
 
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 Tx 
 * 
 
 C-5 
 
 y 
 
 - -; 
 
 T 
 
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 fi B 
 
 '" ; 
 
 :-p, 
 
 Q i 
 Q 1 
 
 If a 
 
 ', 
 
 ^__ L g^ T 
 
 L 
 
 c 
 
 3 oj 
 
 n 
 
 1 
 
 2| c ! 
 
 x ':i' 
 
 ^ 
 
 i 
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 e | 
 
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 jl 
 
 Q ! 
 G j 
 
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 Q 
 
 
 j 
 
 i 
 
 
 
 xs".and 12" xo%,' xoj'Vamd^' 1 7" and 6" 
 I Beams I Beams I Beams 
 
 53 Tons. 35 Tons. 17.6 Tons, 
 
 The number of tons indicated, denote the loads on single beams or 
 firdersfor which the connections are proportioned. 
 
 Rivets and Bolts X dia .A II Bolts have beveled heads. 
 
STEEL COLUMNS AND STRUTS. 437 
 
 The standard sections of Z-bar columns as made by the Carnegie 
 Steel Co., together with the safe loads, are given on pages 474- 
 481. The properties of Carnegie Z-bars are given in Chapter X. 
 Constant Dimension Z-bar Columns. 
 
 On page 482 is shown a section of constant dimension Z-bar 
 columns designed by the Carnegie Steel Company, for the pur- 
 pose of keeping the same outside dimensions throughout the 
 successive stories of the structure. The advantage of this lies 
 in the quicker preparation of plans and subsequent shop details; 
 the convenience to the architect in dimensioning walls and pillars, 
 and the simplification of the fireproofing work. 
 
 For buildings of not more than six or eight stories, however, 
 these advantages are not sufficient to offset the disadvantage 
 of the extra space occupied by the column. ,4 
 
 Angle and Plate Columns. 
 
 Four angles and a plate riveted together as shown by Fig. 1 5a 
 are now being quite extensively used in building construction, 
 particularly for columns having an unsupported 
 
 length of less than 90 radii, also for the outer posts & gu 
 
 in steel mill buildings, and for light posts supporting *f 
 depot roofs, etc. Columns of this section are espe- Fi i5a 
 cially convenient for making beam and girder con- 
 nections, and for splicing, and are also well adapted to resisting 
 eccentric loads. The width of the plate is generally such that 
 the least radius of gyration is in the direction r 2 , which may be 
 obtained directly from the tables on pages 316 and 318. 
 Channel 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, 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, cover-plates may be riveted to the 
 flanges in place of the lattice, as in Fig. 18. Such columns are 
 very satisfactory, especially for making connections, provided 
 that only a single cover-plate on each side is required. Three 
 channels, riveted together, as in Fig. 16, also make a good column 
 for light loads ; in fact it was this combination which suggested 
 the Z-bar column. Three I-beams riveted together in the same 
 way have also been used for columns, but it is not an advan- 
 tageous shape. 
 
 Fig. 17 shows a light lattice column, with base-plate, and 
 Fig. 18 a typical channel column with single cover-plates, and 
 flip rrmnnpr of rrm.kino- snlices and connections. 
 
438 
 
 STEEL COLUMNS AXI) STRUTS. 
 
 Fig. 17 shows a light lattice column, with base-plate, and 
 Fig. 18 a typical channel column with single'cover-plates, and the 
 manner of making splices and connections. 
 
 Type 
 
 Sui 
 
 Fig. I5b 
 
 of Posts used for 
 Supporting the Bos- 
 ton Elevated Ry. 
 
 Fig. 16 
 
 (Q O 
 
 o 
 oi 
 
 00000 
 
 A 
 
 
 ^ 
 
 c^ 
 
 ^ o" 
 O 
 
 Fig. 17 
 
 H 
 IS 
 
 Fig. 18 
 
 Channel Column, with Cover-plates. 
 
STEEL COLUMNS AND STRUTS. 
 
 439 
 
 Rule for Latticing of Channels and Angles. When channels 
 are connected by latticework, as in Fig. 19, that 
 there may not be a tendency in the channels 
 to bend between the points of bracing, the dis- 
 tance I should be made to equal the total length 
 of 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, l=-n~ where the letters have the 
 
 following significance : 
 I length between bracing; 
 L= total length of strut; 
 
 r= least radius of gyration for a single chan- 
 nel; 
 
 R= least radius of gyration for the whole sec- 
 tion. 
 
 This same rule will also apply for angles, thougji with them 
 the latticework is generally doubled, as in Fig. 20. 
 
 TotariengthWL 
 
 Fig. 20 
 
 Generally it is found desirable to make the distance I less than 
 that obtained by the above formula, or so that the inclination of 
 lattice-bars will be about 45 with the axis of the column or strut. 
 
 The size of the lacing-bars should not be less than that given 
 in the following table : 
 
 Distance Z, Fig. 20, 
 or K I, Fig. 19. 
 
 Size of bar, 
 in inches. 
 
 Distance Z, Fig. 20, 
 or ^ Z, Fig. 19. 
 
 Size of bar, 
 in inches. 
 
 less than 6" 
 6" or less than 7" 
 7" or less than 9" 
 9" or less than 10" 
 
 Hxi 
 
 1|X| 
 
 2 v/ 5/ 
 
 10" or less than 16" 
 16" or less than 20" 
 20" or less than 24" 
 20" or above 
 
 2 X| 
 
 angles 
 
440 STEEL COLUMNS AND STRUTS. 
 
 The proper distance for d or D, Fig. 19, to give a pair of chan- 
 nels the same radius of gyration in both directions is given under 
 the properties of channels in Chapter X. 
 
 Plate and Angle Box Columns. 
 
 "For high buildings or heavy loads, where the required sec- 
 tional area is greater than can be obtained by using Z-bar col- 
 umns without cover-plates, the box column of plates and angles 
 will be found most satisfactory. This column form possesses 
 great advantages regarding connections, in that square surfaces 
 are always presented. Box columns were used in the Masonic 
 Temple, the highest building in Chicago, and in the Park Row 
 Building, one of the highest structures in New York City." * 
 - Fig. 21 shows a heavy column section, in the 
 Park Row Building, composed of 3 web-plates, 
 24" X%", 4 covers, 48" X%", and 8 angles, 
 6"X6"X%", and designed for a load of 1,450 
 tons. 
 
 A column composed of 10 web-plates, 4 covers, 
 and 12 angles, and weighing 46,980 Ibs., was 
 used in the Waldorf-Astoria Hotel to support 
 an estimated load of 2,700 tons. 
 
 - 21 The most common form of box column is that 
 
 shown by Fig. 22, the thickness and number of the web and 
 cover-plates varying with the load to be sup- ^ 
 ported. 
 
 Several examples of plate and angle columns 
 are given in Chapter XXVIII. 
 
 Ordinary connections for box columns are 
 made as shown in Figs. 15 and 18. More 
 elaborate connections are shown in Chapter 
 
 xxvm. F ' 922 
 
 The Phoenix Segmental Column. 
 
 This column has now been on the market for over thirty-eight 
 years and has been very extensively used in buildings, and also 
 for posts in bridges, and for piles and for wharfs and piers. 
 
 * J. K. Freitag. 
 
STEEL COLUMNS AND STRUTS. 
 
 441 
 
 In the anthracite coal regions of Pennsylvania it is very 
 extensively used as shafts for coal 
 screens. 
 
 The sections were first rolled of 
 wrought iron, and for a time in both 
 steel and iron, but are now made 
 only of steel. 
 
 The advantages claimed for this 
 column by the manufacturers are: 
 Economy of metal, simplicity of 
 construction, adaptability to the re- 
 quirements of building construction, 
 and its cheapness. 
 
 These columns are made up of 
 the rolled segments "C," Fig. 23, 
 which are riveted together through 
 the flanges with rivets about 6 
 inches apart. Between every two 
 segments an iron bar is frequently 
 inserted, through which the rivets 
 pass. These bars, or " fillers," as 
 they are called, increase the area 
 of the cross-section and contribute 
 much to the strength of the pillar. 
 Table XX. gives the sizes of the 
 columns rolled by the Phoenix Iron 
 Company, as published in their 
 book of sections, and also the 
 radius of gyrations and safe loads. 
 
 The largest standard size of this 
 column has a sectional area of 90.9 
 square inches, capable of sustain- 
 ing 615 tons with an unsupported 
 length of 36 feet. 
 
 The column can be made of almost any length desired. In 
 the Schiller Theatre Building, Chicago, there are Phoenix col- 
 umns 92 ft. 10 ins. long, while in the Chicago Board of Trade 
 12-section Phoenix columns, 3' 3" in diameter were employed 
 for an unsupported length of 90 ft. 
 
 Phoenix columns are in use in several prominent high buildings, 
 notably the " World," "Dun," and " Commercial Cable" build- 
 ings, New York; the Wainwright Building, St. Louis; Crocker 
 
442 
 
 STEEL COLUMNS AND STRUTS. 
 
 Building, San Francisco, and in a great number of buildings of 
 moderate height. Owing to the difficulty of making elaborate 
 connections, and possibly also to the fact that it is rolled only 
 by one company, it has not been much used in the later high 
 buildings, although it is still used to a considerable extent in 
 other buildings. The sections of the Phoenix column afford a 
 convenient means of " jacketing" cylindrical cast-iron columns 
 which need to be strengthened. 
 
 The interior surfaces of all Phoenix columns are thoroughly 
 painted before riveting the segments together. After twenty 
 
 Fig. 24 
 
 years of service in exposed situations columns have been cut 
 open and found uninjured by rust, and the paint still in good 
 condition. 
 
STEEL COLUMNS AND STRUTS. 
 
 443 
 
 Connections. For ordinary floor-beam connections, and for 
 joining the ends of the columns, a connection similar to that shown 
 in Fig. 24 has generally been used. The cap, which is usually a 
 single plate f inch to 1 inch in thickness, is made of sufficient size 
 to give the requisite bearing for the beams or girders, and is con- 
 nected to the column by means of brackets riveted to the shell 
 
 Fig. 25 
 
 and plate. The cap is also further supported by means of gusset- 
 plates, / and c, riveted either outside the flanges or directly to 
 the shell of the column. The upper column is set after the floor 
 
 Fig. 26 il; - 
 
 system is in place, and is secured to the cap-plate by angle brack- 
 ets. When columns with fillers are used the method shown in 
 Figs. 25 and 26 is generally followed. A cap-plate is used as in 
 
444 
 
 STEEL COLUMNS AND STRUTS. 
 
 the other connection, but is supported by angles riveted to the 
 extended fillers. 
 
 Fig. 26 shows a bracket formed beneath the cap-plate in a 
 similar manner, a trapezoidal plate being inserted between the 
 sections, in place of the filler, to support the bracket-plate. One 
 of the plates passes through the column and is riveted at both 
 sides ; the other plate is riveted to the first at the centre of the 
 column. 
 
 The latest and most perfect type of connection for this column, 
 especially where channel or riveted girders producing eccentric 
 loads are to be supported, is that shown in Fig. 27. A pintle, 
 
 
 
 
 J 
 
 
 
 o 
 
 ( 
 
 ( 
 
 > I 
 
 
 
 
 
 sfyca/Ja" 
 
 o o o 
 
 O 
 
 
 
 o 
 
 ( 
 
 
 d 
 
 O Q\Q O O O 
 
 Gfrder: 
 
 
 o 
 
 
 
 o 
 
 ^ 
 
 ( 
 
 am 
 
 L 
 
 o 
 
 
 
 w 
 
 I 
 | Girz/e* 
 
 .9**4** 
 
 O i 
 
 
 
 
 
 
 
 u 
 
 os 
 
 ( 
 
 ( 
 
 ) 
 i 
 
 o 
 
 o ! 
 o[ 
 
 O I 
 
 
 
 o o o 
 
 
 
 
 
 c 
 
 1 
 
 I 
 
 o 
 
 O O : O O O 
 
 3w3 
 
 
 
 o 
 o 
 
 
 i 
 
 > ! 
 
 o 
 
 r^. 
 
 \J 
 
 ^fyc&J Jo*fi 
 
 l TV 
 
 o| 1 V 
 
 H :1 
 
 IjJMI *J 
 
 
 
 
 
 
 
 
 Fig. 27 
 
 Continuous Column. 
 
 shown at a reduced scale, is inserted between the flanges, and the 
 girders and beams are riveted directly to the pintle. 
 
 This connection is probably as nearly perfect as any that could 
 be devised for any column, as the load is transmitted by the pintle 
 to all parts of the column, and the pintle also greatly stiffens the 
 column at the point of connection. 
 
THE LARIMER STEEL COLUMN. 
 
 445 
 
 The joint of the column occurs at the centre of the beams or 
 girders, and the column is thus made continuous from cellar to 
 roof, with no brackets either above or below the girder. 
 
 Larimer Column. 
 
 (Manufactured by Jones & Laughlins, Limited, Pittsburg.) 
 
 This column was patented June 2, 1891, its first use in building 
 construction being in the Newberry Library Building in Chicago,, 
 
 It is made by bending two I-beams at right angles in the middi 
 of the web and riveting them together with a small I-shaped 
 filler between. The column is very light and compact, and has 
 but one row of rivets. Table XXI. gives the strength and 
 dimensions of the standard sections. 
 
 The strength of the larger columns may be increased by rein- 
 forcing the flanges with steel plates, but the expense of doing this 
 is so great that it will be cheaper to use some other section. A 
 good many tons of this column are sold annually, but it is not 
 very extensively used in buildings. It is much used for the 
 
446 
 
 THE LARIMER STEEL COLUMN. 
 
 CONNECTIONS FOR LARIMER COLUMNS. 
 
THE LARIMER STEEL COLUMN. 
 
 447 
 
 CONNECTION^ FOR LARIMER COLUMNS. 
 
 lumber of rivets of'supporting brackets must b& 
 determined in accordance to load by using 
 
 i"fcivets for all columns made of 7'f 18, 3'lb I.E. and upward 
 t$" . > ... G < 12, 75 Ib. to 7 15, 25 lb, 
 
 A4" v v *' " o"x 16 lb. I. Bs. and 
 
 One privet. may be allowed for the bending of a&" 
 
 L.Bs. 
 
448 THE NURICK STEEL COLUMN. 
 
 support of windmills and water-tanks, where a light and in- 
 expensive column is desired. 
 
 Connections. The usual connections for this column are illus- 
 trated on the preceding pages. Generally a cap-plate is used to 
 support the floor system and to receive the upper column. The 
 flanges of the columns, both above and below, are secured to the 
 cap-plate by means of angle brackets, with two rivets in each leg 
 of the brackets. When a more rigid connection is desired, a 
 welded ring, in the shape of an angle, is made to fit around the 
 top of the column, the vertical flange being riveted to the flanges 
 of the column and the horizontal flange to the cap-plate, as shown 
 at A A, page 446. This connection is desirable when the 
 column is eccentrically loaded. 
 
 The Nurick Column. 
 
 This column, formed of four bent channels, riveted together as 
 in Fig. 28, was introduced by Jones & Laughlins, Limited, in 
 1898. It is not intended to be used in 
 ordinary skeleton buildings, but only in 
 places where a strong column is desired 
 with the least w r eight in the column itself. 
 It has been used to some extent in foundry 
 buildings. Where the column is exposed 
 it makes a better appearance than the 
 Z-bar column. 
 
 Table XXII gives the dimensions and 
 PI js sa f e loads for a few sections of this 
 
 column. Details of splices and connec- 
 tions are given in Jones & Laughlins' Manual. 
 
 The Gray Column. 
 
 This column was patented in December, 1892, by Mr. J. H. 
 Gray, C.E., and for a time was quite extensively used in build- 
 ings of skeleton construction.* 
 
 The column is made up of angle-bars, riveted together in pairs 
 
 * This column has been used in a number of prominent buildings, but 
 by many engineers it is not now regarded with favor, owing to the difficulty 
 of making satisfactory connections for eccentric loading. J. K. FREITAG. 
 
THE GRAY STEEL COLUMNS. 449 
 
 and braced about every two feet in length by tie-plates usually 8 
 or 9 inches wide, riveted to the angles as shown by the section 
 drawings, Figs. 29-32. 
 
 The special advantages claimed for this column are : 
 
 1. A strong economical section. As fully half of the metal is 
 at the extreme outer edge of the column, and practically none at 
 the centre, the radius of gyration is very large in proportion to 
 the weight of the metal. Moreover, as angles are the cheapest 
 shape of rolled steel that is manufactured, and are made by every 
 rolling-mill, they can 'be obtained at the lowest market price, and 
 the columns can be built by any bridge shop by paying a small 
 royalty to the patentee. (Gray columns were made by fourteen 
 different bridge companies in 1895.) 
 
 2. Size of column does not vary when section is increased or 
 diminished. This enables the architect to vary the section of the 
 column to suit differences in loading, without changing the out- 
 side dimensions, thus rendering the engineering work much 
 simpler, and enabling the use of uniform sizes of fire-proof 
 blocks. 
 
 3. Does away with "cap-plates" and joins sections of columns 
 firmly together, making a continuous column. In the Reliance 
 Building, Chicago, there is a Gray column 290 feet long, built in 
 one piece at the shop. 
 
 4. By varying the size or thickness of angles, and adding cover- 
 plates, any strength that may be required can be obtained. 
 
 5. Has four flat sides for connections. The usual connections 
 for single and double beams are shown by Fig. 32. 
 
 The joint in the column should be made above the floor system, 
 and the two portions connected by splice-plates. 
 
 Where eccentric loads are to be supported by this column it is 
 essential that the column be very rigidly bound together by out- 
 side plates or angles opposite or just below the connection, as 
 otherwise the load will be borne mainly by the pair of angles to 
 which the girder is connected, and not by the whole column. 
 
 6. Provides continuous air-space from basement to roof. 
 Tests made in the hydraulic machine of the Keystone Bridge 
 Works on 14-inch square columns, 11 feet long, developed a 
 resistance to crushing of from 38,000 to 40,000 pounds per 
 square inch of cross-section, and a modulus of elasticity of 
 from 24,030,000 to 27,750,000 pounds. 
 
 Table XXIII. of this chapter gives the safe loads in thousands 
 of pounds, as computed by Mr. Gray, for the sizes of columns 
 
450 
 
 STEEL STRUTS IN TRUSSES. 
 
 that have been most extensively used. Experience has shown 
 that these tables cover nearly any ordinary steel skeleton build- 
 ing and give all needed sections from basement to top of same. 
 
 Fig. 29 
 
 Fig. 32 
 
 Fid. 30 
 
 Fig. 31 
 
 Steel Struts in Trusses. 
 
 These are generally made of a pair of latticed channels, or 
 channels and plates for heavy trusses with pin connections, and 
 either of a pair of light channels or a pair of angles with uneven 
 legs for light trusses. For roof trusses having a span not ex- 
 ceeding 80 feet a pair of 4X6XJ inch angles is generally suffi- 
 cient for any of the compression members unless subject to trans- 
 verse strain, and the minor struts are very often made of a pair 
 of 2 X 2 J X i inch angles. The angles are placed from J to J inch 
 
STRENGTH OF STEEL COLUMNS AND STRUTS. 451 
 
 apart, to permit the filler-plate used in the joints to go between 
 them. 
 
 For compression members subject to transverse strain a pair 
 of channels generally offer the best section. If necessary the 
 channels can be reinforced by plates at top and bottom. 
 
 A pair of angles, with a deep web-plate riveted between, are 
 often used -for the principles of Fink trusses where they are 
 subject to a slight transverse strain. See Chapter XXV. 
 
 For very light compressive stresses and short members a single 
 angle is sometimes used. If the stress requires a greater section 
 than that of one 3 X 3 X J inch angle, it will be cheaper and better 
 to use a pair of smaller angles. 
 
 Where angles are used in pairs they should be connected by a 
 rivet and small filler-plate every two feet in length, to prevent 
 the angles from springing apart. 
 
 Maximum Length. It is good practice not to use a strut whose 
 unsupported length exceeds 150 times its least radius, of gyration, 
 or 50 times the least width of the member. For size of lattice- 
 bars see page 439. 
 
 Strength of Steel and Wrought-iron Columns 
 and Struts. 
 
 Prof. Wm. H. Burr, in his " Strength and Resistance of Mate- 
 rials," states that "The general principles which govern the re- 
 sistance of built 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 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 r." 
 
 The experiments quoted by Prof. Burr would seem to indicate 
 that a closed column is stronger than an open one, this being 
 apparently due to the fact that the edges of the segments are 
 mutually supporting when held in contact by a complete closure. 
 From a theoretical standpoint, therefore, the Phcenix or Nurick 
 shapes undoubtedly present the most favorable section for resist- 
 ing compression, as they form a closed column, and the metal is 
 
452 FORMULAS FOR STEEL COLUMNS AND STRUTS. 
 
 all at the outer line and equally disposed around the neutral axis. 
 With the pintel connection, shown in Fig. 27, it would seem that 
 these columns would have a greater ultimate resistance than open 
 forms, such as the open Z-bar, Gray, and Larimer, although the 
 latter column has developed a very high ultimate resistance. 
 
 It should also be remembered that any form of column having 
 a maximum and minimum radius of gyration, such as is the case 
 with a single I-beam, channel, or angle, is not economical for use 
 under a single concentric load, as the minimum radius must be 
 used in the calculation, and part of the material is to a certain 
 extent wasted, when we consider the ideal efficiency of the 
 column. 
 
 Formulas. 
 
 A great many different formulas have been published for the 
 strength of wrought-iron and steel posts, and scarcely any two 
 leading structural engineers use precisely the same formula. 
 Previous to the year 1888 a formula similar to formula (12), and 
 known as the Gordon formula, was generally used for all forms 
 of columns, although with more or less variation in the constants. 
 During the year 1888 Mr. C. L. Strobel deduced the following 
 formula for the ultimate strength of iron Z-bar columns : 
 
 Breaking loads in Ibs. per sq. in. of section area =46, 000 125 . 
 
 This formula appeared to agree a little more accurately than 
 the Gordon formula with the results of tests that had been made 
 on full-size columns, and as it was easier of application a modi- 
 fication of it was adopted by the Carnegie Steel Company for 
 computing the strength of their Z-bar columns. 
 
 This form of formula is now known as the straight-line formula, 
 and as it appears to give a satisfactory reduction of loads in pro- 
 portion to length of column, and is comparatively easy of applica- 
 tion, some form of the straight-line formula is now generally 
 used by structural engineers for steel columns and struts in 
 preference to Gordon's formula. For the constants used in the 
 " straight-line formula," however, there is no uniform practice, 
 except perhaps in the case of heavy columns, for which formula 
 (11) is quite generally used. 
 
 Gordon's formula is still used by many engineers, and as it is 
 the standard used in the Boston Building Law it is given below 
 as formula (12). A comparison of formulas recommended by 
 
FORMULAS FOR STEEL COLUMNS AND STRUTS. 453 
 
 different engineers, and contained in building laws vrill be found 
 at the end of this chapter. Those formulas which, in the opinion 
 of the author, most nearly represent the best current practice 
 are given below. 
 
 Formulas for Safe Loads, in Pounds, on Steel and 
 Wrought-iron Columns and Struts. 
 
 Safe load, W=pX sectional area (in sq. inches) of column or 
 strut. ' (10) 
 
 For steel columns in buildings: 
 
 p= 17. 100 -57-3 (11) 
 
 T 
 
 12,000 
 or p= - ' 2 - . (12) 
 
 36,000 r 2 
 For steel struts in trusses: 
 
 p= 13,500 -50-j% (13) 
 
 For wrought-iron columns: 
 
 36,000 r* 
 
 in which Z= length of column in inches, and r= least radius of 
 gyration (see Chapter X.) . The length of the column is measured 
 between the points where it is supported sideways, and usually 
 between the floor beams. 
 
 Maximum Safe Load for Columns and Struts. 
 
 For wrought-iron posts where the length in inches divided by 
 the least radius of gyration is less than 30, p may be taken at 
 9,000 Ibs. to the square inch. 
 
 For steel struts, in trusses, where is less than 50, p should be 
 
 taken at 11,000 Ibs. per square inch, unless the section is vf. y 
 large, when 12,000 Ibs. may be used. 
 
454 FORMULAS FOR STEjEL COLUMNS AND STRUTS. 
 
 For steel columns, such as are used in buildings, it is customary 
 to allow from 12,000 to 14,000 Ibs. per square inch of section when 
 the length is less than 90 radii. 
 
 When 14,000 Ibs. is used for p, however, an increase in area 
 should be made for any eccentricity in the loads. (See formula 
 (15).) 
 
 The tables for Carnegie Z-bar columns and for the Larimer 
 column are computed at 12,000 Ibs. per square inch for lengths 
 
 of 90 radii and under, and those for the Phcenix columns at 14,000 
 
 I 
 Ibs. for the same ratio of . The Chicago Building Ordinance 
 
 specifies 13,000 Ibs. for lengths of 60 radii and under. Formula 
 (11) was used in computing the strength given in the tables for 
 
 the Gray columns for all the values of , and for Phoenix, Z-bar, 
 
 Larimer, and channel columns exceeding 90 radii in length. 
 This formula also very nearly corresponds with that given in 
 the Chicago Building Ordinance. 
 
 Formula (13) is about an average of the constants used by lead- 
 ing structural engineers for angle and channel struts in trusses, 
 and w T as used by the Passaic Rolling Mill Company for computing 
 the safe loads for angle struts and I-beam struts published in 
 their handbook. It is believed that the stresses permitted by 
 this formula are such that it may be used for ordinary truss con- 
 struction without allowance for rivet-holes. It may be used for 
 either pin- or rivet-connected struts. 
 
 According to Prof. Wm. H. Burr, "the records of tests of 
 wrought-iron channel columns with both pin and flat ends, made 
 at the U. S. Arsenal at Watertown, Mass., have shown conclu- 
 sively that the ultimate resistance of columns with flat ends will 
 nearly invariably, if not always, fall below those of the same col- 
 umns with pin ends." This is accounted for by the fact that 
 with a pin-end column the centre of stress is practically at the 
 centre of the section of each end, and also that the very consider- 
 able friction of the pin against the pin-hole exerts a considerable 
 moment tending to hold the ends of the column in a "fixed" 
 condition in a plane normal to the axis of the pin. 
 
 On the other hand, with square ends, no matter how carefully 
 finished, it is almost impossible to apply the load so that the 
 centre of stress will coincide with the centre of the column. 
 
 The old classification of "square," "pin and square," and 
 "pin ' has therefore been abandoned. 
 
FORMULAS FOR STEEL COLUMNS AND STRUTS. 455 
 
 Application of Formulas. 
 
 EXAMPLE 1. What is the maximum load for a steel column 12 
 feet long, composed of two 6-inch 8-lb. channels placed back to 
 back, and secured by latticework? 
 
 Ans. To obtain the maximum resistance of the section the 
 channels should be placed 3J ins. apart (see col. d } page 299). 
 The least radius* of gyration (r) will then be the same as for a 
 single channel about axis AB, which is 2.34 (col. iv.). 
 
 To find the values of p } we will use formula (11): then 
 
 7 144 
 
 p=17 ; 100-57-= 17,100-57X^ji = 13,595 Ibs. Substitut- 
 
 ing this in formula (10), we have safe load for column = 13,595 X 
 4.76 (area of two channels) = 64,712 Ibs. 
 
 When the value of p obtained by formula (11) exceeds 12,000 
 Ibs. it is recommended that 12,000 Ibs. be used instead of the 
 value obtained by the formula, unless the loads assumed are 
 much in excess of the probable actual loads, or the column has 
 a large and closed section, when 14,000 Ibs. may be made the 
 maximum.* 
 
 EXAMPLE 2. What is the safe load for a column 16 feet long, 
 composed of two 12-inch 30-lb. channels, with J-inchx 12-inch 
 plates, riveted to channels, as shown in Fig. 33. 
 
 Ans. The first step will be to find the least radius of gyration, 
 by means of the methods explained 
 on page 286. 
 
 From the table of . properties of 
 channels we find that for a single 
 channel I^S.21, #=.677, width of 
 flange = 3. 17, and area = 8. 82. 
 
 The distance (d) between the backs 
 of channels would then be 12 (3.17 
 X 2) = 5.86. As this is less than d, 
 in the table of properties, the least 
 radius of gyration will be about the 
 
 K Q6 
 axis C - D. The distance, I (Fig. 33) = ~ + .677 = 3. 6. Then 
 
 >[ 
 
 
 
 A-- 
 
 i 
 
 K-z- 
 
 I 
 
 i 
 
 i 
 
 % 
 
 i 
 
 
 ; i 
 
 
 D I 
 
 Fig. 33 
 
 3 
 
 *See last pages of this chapter. 
 
456 STRENGTH OF STEEL COLUMNS AND STRUTS. 
 
 the moment of inertia about CD will be (see page 286), 
 
 for the channels, 2 X (8.82 X (3.6) 2 + 5.21) = 239.03 
 
 for the plates, gx|Xl2 3 = ^ 
 
 Z 
 
 Total moment =383.03. 
 
 Dividing this by the area of the section, which is 29.64, we have 
 12.92 for the square of the radius of gyration, and 
 
 r=Vl23~2= 3.6:-= ^=53.3. 
 r 3.6 
 
 As this is less than 90, we should not use formula (11), but mul- 
 tiply the area of the column by the allowable strain per sq. inch, 
 which for such a large section may safely be taken at 13,000 Ibs. 
 Then 29.64x13,000 = 385,320 Ibs. = safe 'load. 
 
 Eccentric Loads. 
 
 Where columns are used in tiers, one above another, the 
 beams and girders which they support must necessarily rest on 
 brackets or pintle-plates, beyond the centre of the column. 
 
 Such methods of connection necessarily produce a moment tend- 
 ing to bend the column. When the same load is applied to op- 
 posite sides of the column, the moments produced by the loads 
 will offset each other, and the centre of stress may be considered 
 as coinciding with the axis. Whenever a beam, however, is 
 attached to a column without a corresponding load on the oppo- 
 site side, the load will be "eccentric," and the area of the column 
 should be correspondingly increased, especially if strains as high 
 as 14,000 Ibs. per sq. inch are permitted. 
 
 The following formula, known as " Rankine's formula for eccen- 
 tric loads," is generally used for computing the additional area 
 required for eccentric loading : 
 
 Additional area for eccentric load= ^ xd i* d <> (15) 
 
 pXr 2 
 
 in which 
 
 W = eccentric load in Ibs. ; 
 
 d Q = distance from centre of column to point of application; 
 d= distance from centre of column to extreme fibre in direction 
 
 in which column would bend ; 
 r 2 = radius of gyration squared, for column used] 
 
 p = stress per square inch for , Table XI. 
 
STRENGTH OF STEEL COLUMNS AND STRUTS. 457 
 
 Note. In measuring the distance d very much depends upon the form 
 of the connection. Thus for single or double beams, where angle-brackets 
 are used, d should be measured to the centre of the bracket. In Figs. 13 
 and 24 it should be measured to the centre of the rivets in the beam flanges; 
 for connections, such as shown in Figs. 15 and 27, it is generally considered 
 sufficient to measure d to the outside of the column. 
 
 EXAMPLE 1. The total load on the top of a second-story 
 column is 194 ; 000 Ibs., of which 30,000 Ibs. comes from the end of 
 a girder, without a corresponding load on the opposite side of the 
 column It is proposed to use a 12-inch Gray square column. 
 What should be the section of the column, the distance to the cen- 
 tre of the bracket being 2\ in. and the length of the column 16 
 feet? 
 
 Ans. Looking iri the table giving the safe loads for a 12-inch 
 Gray column, we find that the section given in the second line has 
 a safe load of 195,000 Ibs. for 16 ft. length, and we will therefore 
 use that section as a basis. 
 
 Z 192 
 For this section, r=3.8 and = - = 50.5; and from col. I., 
 
 T o.o 
 
 Table XL, w y e find the value of p for that ratio to be 14,220. 
 
 Then TF=30,000; d =8i; ^=6; r 2 =3.8 2 = 14.44; and p= 
 14,220. 
 
 Substituting these values in formula (15) we have 
 
 The area of the section used is 13.84, and adding to this 7.23 we 
 have 21.07 as the required area, which corresponds with a section 
 composed of eight 3x3ixjie" angles; therefore this latter sec- 
 tion should be used. 
 
 EXAMPLE 2. What area w^ould be required for a 12-inch Z-bar 
 column under the same conditions as given in Example 1 ? 
 
 Ans. From the table on page 477 we find that the first section 
 has a safe resistance of 128.3 tons, or considerably more than the 
 
 load we wish to support, r for this section is 3.67 and = 52.3. 
 
 The corresponding value for p would then be (col. I, Table XL) 
 14,120. We will assume that the girder is supported as in Fig. 5, 
 p. 436, so that d t =B (page 476) =6.2 in., and d would be 
 about 8.5 in. 
 
458 STRENGTH OF STEEL COLUMNS AND STRUTS. 
 
 We would then have 
 
 , . , , 30,000X6.2X8.5 n . 
 Additional area for eccentric load= =9sq. in. 
 
 The area required for the total load, considered as acting through 
 centre of column= = ; - = 13.8 sq. in. Adding 13.8 and 
 
 9, we have 22.8 as the required area, which will necessitate using 
 the second section given in the table. 
 
 Tables for Strength of Columns. 
 
 To lessen the labor of calculating the strength of steel columns 
 and struts, of whatever shape, the author has computed Table XI., 
 which gives safe values of p for lengths varying from 30 to 130 
 
 radii. For values of which give a decimal remainder one can 
 
 readily interpolate between the values given. The values in this 
 table should correspond exactly with the results obtained by 
 using the corresponding formulas. 
 
 Table XII. gives the safe loads for gas or steam pipe used as 
 columns. These pipes are apt to vary somewhat from the thick- 
 ness published by the manufacturers, and when using them the 
 architect should see that they have a thickness equal to that given 
 in the table, if the full load is to be allowed. The ends of the pipe 
 should be turned true to the axis, and fitted with cast-iron or 
 steel plates, having the bearing planed or turned in a lath. 
 
 Tables XIII., XIV., and XVI. give the strength of standard 
 channels and angles used as struts. Only those sizes that are 
 most commonly used are given. 
 
 In Table XIII. the safe loads for both the minimum and maxi- 
 mum radius of gyration are given. If the strut is used also as a 
 beam, or is stayed so that it cannot bend sideways, the larger 
 value may be used; but if free to bend in either direction, then 
 the smaller value should be taken. If the struts are subjected 
 to a transverse strain they should be computed as explained 
 under the heading "Strut Beams," Chapter XV. 
 
 The tables giving the safe loads for Z-bar, Gray, Larimer, and 
 Nurick columns were not computed by the author; they are, 
 however, believed to be perfectly safe, provided that an increase 
 in area is made for eccentric loads. This is especially necessary 
 with the Gray columns, as the allowed value of p in many cases 
 exceeds 15,000 Ibs, 
 
STRENGTH OF STEEL COLUMNS AND STRUTS. 459 
 
 Application of Table XI. 
 
 This table will be found of most assistance in calculating the 
 strength of struts in trusses and in making calculations for eccen- 
 tric loading, as already illustrated. 
 
 EXAMPLE 1. What is the safe resistance for a strut composed 
 of two 5-inch 9-lb. standard steel channels, separated f inch, and 
 free to bend in either direction, the distance between joints being 
 7' 6"? 
 
 Ans. From Table D, Chapter X., we find the least radius of 
 
 gyration for this section to be 1; =90; and from column III., 
 
 Table XL, we find the value of p opposite 90 to be 9,000 Ibs.; 
 then the safe load = are a X??=5.3 (area of two channels) X 
 9 ; 000= 47,700 Ibs. 
 
 EXAMPLE 2. What is the safe resistance of a 7-inch 15-lb. 
 standard steel I-beam used as a strut, the length being 100 inches 
 and the strut free to bend in either direction? 
 
 Ans. From the table giving the properties of I-beams, 
 Chapter X., we find the least radius of gyration for this section to 
 
 be 0.78, and the area 4.42; = = 128.2; and from column 
 
 III., Table XL, we find, opposite 128, p= 7,100, for 128.2 p 
 would be about 10 Ibs. less, or 7,090. Multiplying this by the 
 area (4.42) we have 31,337 Ibs. as the safe resistance of the strut. 
 By means of the tables and rules given in Chapter X. the area 
 and radius of gyration of any standard section or any combina- 
 tion of sections may be found; and once these are obtained the 
 strength of a strut or column may be readily computed, as in the 
 above examples. 
 
 Proportion of Floor Loads Borne by Columns. 
 
 In tall buildings it is customary to reduce the column loads 
 somewhat from the loads used in calculating the floor beams. 
 This is done on the theory that it is quite impossible for the entire 
 floor area in every story to be loaded to the maximum limit at the 
 same time. For all buildings except warehouses it would seem 
 to be good practice to design the columns to carry all the dead 
 load and 75 per cent, of the assumed live load. 
 
 Thus f in an office building the dead load, or weight of the 
 
460 COLUMN LOADS. 
 
 floor construction, was taken at 80 Ibs. and the live load at 80 
 Ibs. per square foot, the load on the columns would be taken at 
 80 + 60=140 Ibs. per square foot times the floor area supported 
 by the column. In some cases the reduction might even be 
 greater, depending upon the live load assumed and the position 
 of the column in the building, the reductions being greater in the 
 lower stories than near the top. 
 
 The Building Law of Greater New York specifies that for build- 
 ings exceeding five stories in height the column loads shall be 
 made up as follows: "For the roof and top floor the full live 
 loads shall be used; for each succeeding lower floor it shall be 
 permissible to reduce the live load by 5 per cent, until 50 per 
 cent, of the live load is reached, when such reduced loads shall be 
 used for all remaining floors." Column loads and the practice 
 of leading architects in regard to proportioning columns to the 
 loads, especially in high buildings, is discussed at considerable 
 length by Mr. Freitag in his "Architectural Engineering." 
 
 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 will 
 include floor and roof loads, wind loads, spandrel and pier loads, 
 the weight of the columns themselves and their fire-proof cover- 
 ing, and in some cases special loads, such as tanks, vaults, safes, 
 and elevator loads. 
 
 In tabulating the floor loads it is a good idea to separate the 
 dead and live loads for convenience in proportioning the foot- 
 ings. See Chapter II. 
 
 Formulas for computing the wind loads on columns are given 
 in Chapter XXVIII. ; these loads are also considered as live loads. 
 
 In buildings not exceeding 100 feet in height wind loads are 
 generally disregarded. 
 
 Eccentric loads should always be tabulated separate from the 
 column loads. 
 
 On the opposite page is shown a form of column sheet which 
 combines all ordinary requirements. 
 
 The total load for each story will be the sum of all of the loads 
 above. 
 
 The table on page 462, taken from Freitag's "Architectural 
 Engineering," shows a very convenient form of schedule for 
 column lengths and column materials. 
 
COLUMN LOADS. 
 FORM OF COLUMN SHEET. 
 
 461 
 
 Story 
 
 
 Column No. 1. 
 
 Column 2. 
 
 Load on 
 column 
 concentric 
 
 Load on 
 column 
 eccentric 
 
 
 18th (top) Story. 
 
 Roof and ceiling, dead load . 
 
 
 
 
 live load . . 
 Masonry piers 
 
 Spandrels, cornice, -etc. . 
 
 Elevators. 
 
 Tanks 
 
 Column and casing. . . 
 
 Wind 
 
 
 Total 
 
 
 
 
 
 Sectional area required. 
 
 sq. ins. 
 
 sq. ins. 
 
 
 
 OQ 
 
 4d 
 
 From column above.* 
 Floor dead load. . . 
 
 
 
 
 
 Masonry piers 
 
 Spandrels 
 
 Safes, vaults, etc 
 
 Column and casing 
 
 Wind. . 
 
 
 Total . . 
 
 
 
 
 
 Sectional area required 
 
 sq. ins. 
 
 sq ins. 
 
 
 
 Basement. 
 
 From column above.* 
 Floor dead load . 
 
 
 
 
 
 Masonry piers . 
 
 Spandrels 
 
 Sidewalk 
 
 Column and casing . . . 
 
 Wind. . 
 
 
 Total. . . 
 
 
 
 
 
 Sectional area required 
 
 sq. ins. 
 
 sq. ins. 
 
 
 
 ! 
 Footings. 
 
 Deduct (^) live load .... 
 
 
 
 
 
 Total footing load 
 
 
 
 
 Area of footing required 
 
 sq. ft. 
 
 
 
 * In bringing down the loads from the column above the eccentric loads 
 may be added to the concentric loads and their sum placed in the first 
 column. 
 
462 COLUMN LENGTHS. 
 
 SCHEDULE OF COLUMN LENGTHS AND MATERIAL. 
 
 
 Column No.l 
 
 Column No,2 
 
 
 Roof Line 
 
 
 
 
 Top of Columns 
 
 CO 
 
 Jj 
 
 
 
 
 
 V 
 
 
 
 Jth S'TORY^ 
 
 
 J< b^ >> 
 
 
 
 7th Floor Line 
 
 
 
 tr W 5.^ 
 
 CO J> 
 
 
 
 6th STORY 
 
 
 1? 
 
 
 
 
 
 , 1 
 
 
 
 6th Floor Line 
 
 
 61 "^ x 
 
 
 
 
 
 
 ^CO^t- 
 
 
 
 
 *"o ^^ 
 
 
 
 5th STORY 
 
 _j- 5- 
 
 * 
 
 
 
 5th Floor Line 
 
 
 Y 
 
 
 - 
 
 
 
 
 
 
 
 ^ 
 
 
 
 1st Floor Line 
 
 
 I'M" 
 
 
 
 BASEMENT 
 Top of Stool 
 
 j 
 
 j 
 
 t 
 
 
 
 Grade 1~5.0 
 
 s 
 
 
 
 i 
 
 o TH 
 
 
 
 
 
 
 
 
STRENGTH OF COLUMNS PER SQ. INCH. 463 
 
 TABLE XL SAFE LOADS PER SQUARE INCH OF 
 METAL AREA FOR STEEL AND WROUGHT-IRON 
 COLUMNS AND STRUTS. 
 
 l_ 
 
 r 
 both in 
 inches. 
 
 Steel columns. 
 
 Steel struts. 
 13,500-50- 
 
 Wrought iron. 
 9,000 
 
 17,100-57- 
 r 
 
 12,000 
 
 J2 
 
 1+ l2 
 
 36,000r 2 
 
 36,000r2 
 
 
 I. 
 
 II. 
 
 III. 
 
 IV. 
 
 30 
 
 
 11,706 
 
 12,000 
 
 8 7Sn 
 
 36 
 
 
 11,581 
 
 11,700 
 
 O, I O\J 
 
 8 686 
 
 40 
 
 
 11,488 
 
 11,500 
 
 8^616 
 
 44 
 
 
 11,388 
 
 11,300 
 
 8*541 
 
 48 
 
 
 11,277 
 
 11,100 
 
 8*458 
 
 50 
 
 14,250 
 
 11,220 
 
 11,000 
 
 8^415 
 
 52 
 
 14,136 
 
 11,161 
 
 10,900 
 
 8,371 
 
 54 
 
 14,022 
 
 11,100 
 
 10,800 
 
 8,325 
 
 56 
 
 13,908 
 
 11,040 
 
 10,700 
 
 8,280 
 
 58 
 
 13,794 
 
 10,978 
 
 10,600 
 
 8,234 
 
 60 
 
 13,680 
 
 10,908 
 
 10,500 
 
 8,181 
 
 61 
 
 13^23 
 
 10,874 
 
 10,450 
 
 8,156 
 
 62 
 
 13,566 
 
 10,841 
 
 10,400 
 
 8,131 
 
 63 
 
 13,509 
 
 10,808 
 
 10,350 
 
 8,106" 
 
 64 
 
 13,452 
 
 10,772 
 
 10,300 
 
 8,079 
 
 65 
 
 13,395 
 
 10,740 
 
 10,250 
 
 8,055 
 
 66 
 
 13,338 
 
 10,704 
 
 10,200 
 
 8,028 
 
 67 
 
 13,281 
 
 10,666 
 
 10,150 
 
 8,000 
 
 68 
 
 13,224 
 
 10,633 
 
 10,100 
 
 7,975 
 
 69 
 
 13,167 
 
 10,597 
 
 10,050 
 
 7,948 
 
 70 
 
 13,110 
 
 10.561 
 
 10,000 
 
 7,921 
 
 71 
 
 13,053 
 
 10,525 
 
 9,950 
 
 7,894 
 
 72 
 
 12,996 
 
 10,489 
 
 9,900 
 
 7,867 
 
 73 
 
 12,939 
 
 10,452 
 
 9,850 
 
 7,839 
 
 74 
 
 12,882 
 
 10,416 
 
 9,800 
 
 7,812 
 
 75 
 
 12,825 
 
 10,380 
 
 9,750 
 
 7,785 
 
 76 
 
 12,768 
 
 10,341 
 
 9,700 
 
 7,756 
 
 77 
 
 12,711 
 
 10,302 
 
 9,650 
 
 7,727 
 
 78' 
 
 12,054 
 
 10,264 
 
 9,600 
 
 7,698 
 
 79 
 
 12,597 
 
 10,229 
 
 9,550 
 
 7,672 
 
 80 
 
 12,540 
 
 10,190 
 
 9,500 
 
 7,642 
 
 81 
 
 12,483 
 
 10,152 
 
 9^50 
 
 7,614 
 
 82 
 
 12,426 
 
 10,112 
 
 9^400 
 
 7,584 
 
 83 
 
 12,369 
 
 10,072 
 
 9,350 
 
 7,554 
 
 84 
 
 12,312 
 
 10,033 
 
 9,300 
 
 7,525 
 
 85 
 
 12,255 
 
 9.993 
 
 9,250 
 
 7,495 
 
 86 
 
 12,198 
 
 9,954 
 
 9,200 
 
 7,466 
 
 87 
 
 12,141 
 
 9,916 
 
 9,150 
 
 7,438 
 
 88 
 
 12,084 
 
 9,876 
 
 9,100 
 
 7,407 
 
 89 
 
 12,027 
 
 9,836 
 
 9,050 
 
 7,377 
 
464 STRENGTH OF COLUMNS PER SQ. INCH. 
 
 TABLE XI. (continued). 
 
 l_ 
 
 r 
 both in 
 inches. 
 
 Steel columns. 
 
 Steel struts. 
 13,500-50^ 
 
 Wrought iron. 
 9,000 
 
 17,100-57- 
 
 12,000 
 
 12 
 
 1+ l2 
 
 r 
 
 36,000r 2 
 
 ' 36,000r 2 
 
 
 I. 
 
 II. 
 
 III. 
 
 IV. 
 
 90 
 
 11,970 
 
 9,796 
 
 9,000 
 
 7,347 
 
 91 
 
 11,913 
 
 9,756 
 
 8,950 
 
 7,317 
 
 92 
 
 11,856 
 
 9,716 
 
 8,900 
 
 7,287 
 
 93 
 
 11,799 
 
 9,677 
 
 8,850 
 
 7,258 
 
 94 
 
 11,742 
 
 9,638 
 
 8,800 
 
 7,229 
 
 95 
 
 11,685 
 
 9,600 
 
 8,750 
 
 7,200 
 
 96 
 
 11,628 
 
 9,553 
 
 8,700 
 
 7,165 
 
 97 
 
 11,571 
 
 9,516 
 
 8,650 
 
 7,137 
 
 98 
 
 11,514 
 
 9,478 
 
 8,600 
 
 7,109 
 
 99 
 
 11,457 
 
 9,433 
 
 8,550 
 
 7,075 
 
 100 
 
 11,400 
 
 9,389 
 
 8,500 
 
 7,042 
 
 101 
 
 11,343 
 
 9,352 
 
 8,450 
 
 7,014 
 
 102 
 
 11,286 
 
 9,309 
 
 8,400 
 
 6,982 
 
 103 
 
 11,229 
 
 9,273 
 
 8,350 
 
 6,955 
 
 104 
 
 11,162 
 
 9,230 
 
 8,300 
 
 6,923 
 
 105 
 
 11,105 
 
 9,188 
 
 8,250 
 
 6,891 
 
 106 
 
 11,048 
 
 9,146 
 
 8,200 
 
 6,860 
 
 107 
 
 10,991 
 
 9,104 
 
 8,150 
 
 6,828 
 
 108 
 
 10,934 
 
 9,064 
 
 8,100 
 
 6,798 
 
 109 
 
 10,887 
 
 9,022 
 
 8,050 
 
 6,767 
 
 110 
 
 10,830 
 
 8,981 
 
 8,000 
 
 6,736 
 
 111 
 
 10,773 
 
 8,941 
 
 7,950 
 
 6,706 
 
 112 
 
 10,716 
 
 8,900 
 
 7,900 
 
 6,676 
 
 113 
 
 10,659 
 
 8,860 
 
 7,850 
 
 6,646 
 
 114 
 
 10,602 
 
 8,816 
 
 7,800 
 
 6,612 
 
 115 
 
 10,545 
 
 8,776 
 
 7,750 
 
 6,582 
 
 116 
 
 10,488 
 
 8,734 
 
 7,700 
 
 6,551 
 
 117 
 
 10,431 
 
 8,694 
 
 7,650 
 
 6,521 
 
 118 
 
 10,374 
 
 8,654 
 
 7,600 
 
 6,491 
 
 119 
 
 10,317 
 
 8,613 
 
 7,550 
 
 6,460 
 
 120 
 
 10,260 
 
 8,572 
 
 7,500 
 
 6,429 
 
 121 
 
 10,203 
 
 8,532 
 
 7,450 
 
 6,401 
 
 122 
 
 10,146 
 
 8,492 
 
 7,400 
 
 6,369 
 
 123 
 
 10,089 
 
 8,451 
 
 7,350 
 
 6,338 
 
 124 
 
 10,032 
 
 8,410 
 
 7,300 
 
 6,307 
 
 125 
 
 9,975 
 
 8,368 
 
 7,250 
 
 6,276 
 
 126 
 
 9,918 
 
 8,326 
 
 7,200 
 
 6,245 
 
 127 
 
 9,861 
 
 8,286 
 
 7,150 
 
 6,215 
 
 128 
 
 9,804 
 
 8,246 
 
 7,100 
 
 6,185 
 
 129 
 
 9,747 
 
 8,206 
 
 7,050 
 
 6,155 
 
 130 
 
 9,690 
 
 8,162 
 
 7,000 
 
 6,122 
 
STRENGTH OF PIPE COLUMNS. 
 
 465 
 
 TABLE XII. SAFE LOADS IN TONS FOR GAS OR 
 STEAM-PIPE COLUMNS. 
 
 Computed by formula : p = 1 1 ,000 - 35 * 
 
 |;. 
 
 11 
 
 1 
 
 Jd"o 
 
 bD O 
 
 *o d 
 
 a* 
 
 || 
 
 Length in feet. 
 
 11 
 
 ^ 3 
 
 
 < 
 
 ' 
 
 
 
 Jz; 
 
 wl 
 
 13 
 
 ^ ft 
 
 ^ ra 
 
 Qj ^ 
 
 
 
 
 
 
 
 
 ^ 
 
 
 
 
 8 
 
 9 
 
 10 
 
 12 
 
 14 
 
 inches. 
 
 inches. 
 
 inches. 
 
 Ibs. 
 
 
 
 
 
 
 
 
 
 2% 
 
 2.875 
 
 .204 
 
 5.74 
 
 1.59 
 
 .94 
 
 5.90 
 
 5.51 
 
 5.21 
 
 
 
 D 
 
 3 
 
 3.5 
 
 .217 
 
 7.54 
 
 2.26 
 
 1.16 
 
 9.14 
 
 8.75 
 
 8.35 
 
 7.52 
 
 
 'a 
 
 3* 
 
 4.0 
 
 .226 
 
 9.00 
 
 2.59 
 
 1.35 
 
 11.02 
 
 10.66 
 
 10.25 
 
 9.39 
 
 8.62 
 
 
 4 
 
 4.5 
 
 .237 
 
 10.66 
 
 3.33 
 
 1.50 
 
 14.45 
 
 14.11 
 
 13.65 
 
 12.72 
 
 11.78 
 
 t-H - 
 
 4* 
 
 5.0 
 
 .247 
 
 12.34 
 
 3.73 
 
 1.68 
 
 16.78 
 
 16.33 
 
 15.88 
 
 14.90 
 
 13.98 
 
 .2 
 
 5 
 
 5.563 
 
 .259 
 
 14.50 
 
 4.17 
 
 1.88 
 
 18.76 
 
 18.76 
 
 18.26 
 
 17.31 
 
 16.26 
 
 d 
 
 6 
 
 6.625 
 
 .280 
 
 18.76 
 
 5.57 
 
 2.25 
 
 25.06 
 
 25.06 
 
 25.06 
 
 24.39 
 
 23.32 
 
 J 
 
 7 
 
 7.625 
 
 .301 
 
 23.37 
 
 7.18 
 
 2.59 
 
 32.31 
 
 32.31 
 
 32.31 
 
 32.31 
 
 31.32 
 
 GO 
 
 18 
 
 8.625 
 
 .322 
 
 28.18 
 
 8.14 
 
 2.94 
 
 36.63 
 
 36.63 
 
 36.63 
 
 36.63 
 
 36.63 
 
 tf? 
 
 2.875 
 3.5 
 
 .56 
 .608 
 
 13.68 
 18.56 
 
 4.09 
 5.52 
 
 0.82 
 1.02 
 
 14.10 
 21.25 
 
 13.04 
 20.12 
 
 11.86 
 19.04 
 
 16.56 
 
 
 Jj3i 
 
 4.0 
 
 .642 
 
 22.75 
 
 6.63 
 
 1.20 
 
 27.18 
 
 26.02 
 
 24.86 
 
 22.54 
 
 19.89 
 
 02 )4 
 
 4.50 
 
 .682 
 
 27.48 
 
 8.33 
 
 1.35 
 
 35.31 
 
 34.15 
 
 32.84 
 
 30.19 
 
 27.57 
 
 K 15 
 
 5.563 
 
 .75 
 
 38.12 
 
 11.73 
 
 1.70 
 
 52.78 
 
 51.37 
 
 49.94 
 
 47.06 
 
 44.16 
 
 H 16 
 
 6.625 
 
 .875 
 
 53.11 
 
 15.80 
 
 2.04 
 
 71.10 
 
 71.10 
 
 70.58 
 
 66.99 
 
 64.22 
 
466 
 
 STRENGTH OF CHANNEL COLUMNS. 
 
 4 r- v 
 
 TABLE XIIL SAFE LOADS IN TONS FOR STRUTS 
 FORMED OF A PAIR OF CHANNELS. 
 
 Distance between webs, % inch. 
 If strut is free to bend in either direction use smaller value. 
 
 Strains per square inch: 
 
 12,000 Ibs. for lengths of 30 radii and under J 
 13,500-50 for lengths over 30 radii. 
 
 D'pth 
 in 
 
 Weight 
 per 
 
 Thick- 
 ness 
 
 Area 
 
 of two 
 i^ 
 
 ri 
 
 Length in feet. 
 
 ins. 
 
 foot , 
 Ibs.* 
 
 of web. 
 
 cnan- 
 nels. 
 
 r Q 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 14 
 
 
 33 
 
 0.40 
 
 19.80 } 
 
 1.48 
 5.62 
 
 101.57 
 118.80 
 
 97.56 
 118.80 
 
 93.55 
 
 118.80 
 
 89.54 
 118.80 
 
 85.48 
 118.80 
 
 77.44 
 118.80 
 
 
 35 
 
 0.43 
 
 20.5S~| 
 
 1.47 
 
 5.58 
 
 105.32 
 123.48 
 
 101.13 
 123.48 
 
 96.93 
 123.48 
 
 92.73 
 123.48 
 
 88.54 
 123.48 
 
 80.09 
 123.00 
 
 
 40 
 
 0.52 
 
 23.52 | 
 
 1.46 
 5.43 
 
 120.13 
 141.12 
 
 115.30 
 141.12 
 
 110.48 
 141.12 
 
 103.66 
 141.12 
 
 100.78 
 141.12 
 
 91.14 
 140.41 
 
 15 
 
 45 
 
 0.62 
 
 26.48 -j 
 
 1.45 
 5.32 
 
 134.91 
 
 158.88 
 
 129.48 
 
 158.88 
 
 123.99 
 
 158.88 
 
 118.50 
 
 158.88 
 
 113.00 
 
 158.88 
 
 102.08 
 157.82 
 
 
 50 
 
 0.72 
 
 29.42 { 
 
 1.46 
 5.23 
 
 150.36 
 176.52 
 
 144.23 
 176.52 
 
 138.20 
 176.52 
 
 132.17 
 176.52 
 
 126.06 
 176.52 
 
 114.00 
 174.75 
 
 
 55 
 
 0.82 
 
 32.36 \ 
 
 1.47 
 5.16 
 
 165.60 
 194.16 
 
 159.00 
 194.16 
 
 152.40 
 194.16 
 
 145.78 
 194.16 
 
 139.22 
 194.16 
 
 126.10 
 192.00 
 
 
 20^ 
 
 0.28 
 
 12.06 | 
 
 1.34 
 4.61 
 
 59.81 
 72.36 
 
 57.10 
 72.36 
 
 54.40 
 72.36 
 
 51.70 
 
 72.36 
 
 49.02 
 71.99 
 
 43.62 
 70.43 
 
 
 25 
 
 0.39 
 
 14.70 j 
 
 1.31 
 4.43 
 
 72.32 
 
 88.20 
 
 68.95 
 88.20 
 
 65.60 
 88.20 
 
 62.21 
 88.20 
 
 58.83 
 
 87.28 
 
 52.03 
 
 85.26 
 
 12 
 
 30 
 
 0.51 
 
 17.64 -j 
 
 1.30 
 
 4.28 
 
 86.52 
 105.84 
 
 82.46 
 105.84 
 
 78.36 
 105.84 
 
 74.30 
 105.48 
 
 70.25 
 104.25 
 
 62.09 
 101.78 
 
 
 35 
 
 0.64 
 
 20.58 j 
 
 1.31 
 4.17 
 
 101.25 
 123.48 
 
 96.52 
 123.48 
 
 91.78 
 123.48 
 
 87.10 
 122.65 
 
 82.37 72.90 
 121.16118.33 
 
 
 40 
 
 0.76 
 
 23.52 | 
 
 1.32 
 4.09 
 
 116.01 
 141.12 
 
 110.66 
 141.12 
 
 105.31 
 141.12 
 
 99.96 
 139.82 
 
 94.66 
 138.06 
 
 83.96 
 134.65 
 
 
 15 
 
 0.24 
 
 8.92] 
 
 1.24 
 3.87 
 
 42.94 
 53.52 
 
 40.78 
 53.52 
 
 38.64 
 53.29 
 
 36.48 
 52.62 
 
 34.32 
 51.91 
 
 30.01 
 50.43 
 
 
 20 
 
 0.38 
 
 11.76 j 
 
 1.20 
 3.66 
 
 55.86 
 70.56 
 
 52.92 
 70.56 
 
 49.98 
 69.73 
 
 47.04 
 68.79 
 
 44.10 
 
 67.82 
 
 38.22 
 65.85 
 
 10 
 
 25 
 
 0.53 
 
 14.70 j 
 
 1.20 
 3.52 
 
 69.82 
 88.20 
 
 66.15 
 87.94 
 
 62.47 
 86.69 
 
 58.80 
 85.44 
 
 55.12 
 84.19 
 
 47.77 
 81.69 
 
 
 30 
 
 0.68 
 
 17.64 j 
 
 1.22 
 3.42 
 
 84.40 
 105.84 
 
 80.04 
 105.13 
 
 75.71 
 103.63 
 
 71.35 
 102.04 
 
 67.03 
 100.20 
 
 58.34 
 97.41 
 
 
 35 
 
 0.82 
 
 20.58 j 
 
 1.26 
 3.35 
 
 99.76 
 123.48 
 
 94.82 
 122.34 
 
 89.93 
 120.49 
 
 85.04 
 118.64 
 
 80.16 
 116.79 
 
 70.33 
 113.13 
 
 
 13M 
 
 0.23 
 
 7.78-1 
 
 1.19 
 3.49 
 
 36.83 
 
 46.68 
 
 34.87 
 46.48 
 
 32.91 
 
 45.82 
 
 30.94 
 45.16 
 
 28.98 
 44.50 
 
 25.07 
 43.15 
 
 
 15 
 
 29 
 
 o 09 3 
 
 1.17 
 
 41.45 
 
 39.18 
 
 36.93 
 
 34.66 
 
 32.41 
 
 27.89 
 
 
 
 
 o.oa < 
 
 3.40 
 
 52.92 
 
 52.52 
 
 51.81 
 
 50.98 
 
 50.10 
 
 48.64 
 
 
 20 
 
 45 
 
 11 76 -< 
 
 1.15 
 
 54.85 
 
 51.77 
 
 48.71 
 
 45.65 
 
 42.57 
 
 36.42 
 
 
 
 
 j 
 
 3.21 
 
 70.56 
 
 69.50 
 
 68.38 
 
 67.29 
 
 66.20 
 
 64.00 
 
 
 25 
 
 0.62 
 
 14.70 -j 
 
 1.17 
 3.10 
 
 69.09 
 
 87.83 
 
 65.31 
 86.43 
 
 61.55 
 85.00 
 
 57.77 
 83.56 
 
 54.00 
 82.17 
 
 46.48 
 79.30 
 
 * Of single channel. 
 
STRENGTH OF CHANNEL COLUMNS. 
 
 467 
 
 TABLE XIII. SAFE LOADS IN TONS FOR STRUTS 
 FORMED OF A PAIR OF CHANNELS ._*> 
 (continued). 
 
 Distance between webs, ^ inch. 
 If strut is free to bend in either direction use smaller value. 
 
 Strains per square inch: 
 
 11,000 Ibs. for lengths of 50 radii and under; 
 13,500-50- for lengths over 50 radii. 
 
 D'pth 
 in 
 
 Weight 
 per 
 
 Thick- 
 ness 
 
 Area 
 of two 
 
 n 
 
 Length in feet. 
 
 ins. 
 
 Ibs.* 
 
 
 nels. 
 
 r 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 
 11.25 
 
 0.22 
 
 6.70 
 
 1.04 
 3.11 
 
 33.63 
 36.85 
 
 31.70 
 36.85 
 
 29.76 
 36.85 
 
 27.83 
 36.85 
 
 25.91 
 36.85 
 
 23.96 
 
 36.85 
 
 
 13.75 
 
 0.31 
 
 8.08 
 
 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 
 
 2.82 
 
 55.12 
 60.61 
 
 51.93 
 60.61 
 
 48.70 
 60.61 
 
 45.51 
 60.61 
 
 42.29 
 60.61 
 
 39.09 
 60.61 
 
 
 21.25 
 
 0.58 
 
 12.50 | 
 
 1.03 
 
 2.77 
 
 62.53 
 68.75 
 
 58.90 
 68.75 
 
 55.25 
 
 68.75 
 
 51.62 
 68.75 
 
 47.96 
 
 68.75 
 
 44.34 
 
 68.75 
 
 
 9.75 
 
 0.21 
 
 5.70 | 
 
 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 
 
 
 12.25 
 
 0.32 
 
 7.20 | 
 
 0.99 
 2.59 
 
 35.51 
 39.60 
 
 33.33 
 
 39.60 
 
 31.15 
 39. 6t) 
 
 28.98 
 39.60 
 
 26.78 
 39.60 
 
 24.60 
 39.42 
 
 7 
 
 14.75 
 
 0.42 
 
 8.68 j 
 
 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 
 
 
 19.75 
 
 0.63 
 
 11.62 | 
 
 1.00 
 2.39 
 
 57.52 
 63.91 
 
 54.03 
 63.91 
 
 50.54 
 63.91 
 
 47.06 
 63.91 
 
 43.57 
 63.91 
 
 40.08 
 62.39 
 
 
 8.00 
 
 0.20 
 
 4.76] 
 
 0.94 
 2.34 
 
 23.02 
 26.18 
 
 21.50 
 
 26.18 
 
 19.98 
 26.18 
 
 18.46 
 26.18 
 
 16.94 
 26.02 
 
 15.42 
 25.41 
 
 6 
 
 10.50 
 
 0.32 
 
 6.18 | 
 
 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 -j 
 
 0.95 
 2.13 
 
 37.11 
 42.02 
 
 34.68 
 42.02 
 
 32.27 
 42.02 
 
 29.87 
 41.88 
 
 27.44 
 40.81 
 
 25.04 
 39.72 
 
 
 15.50 
 
 0.56 
 
 9\12 j 
 
 0.95 
 2.07 
 
 44.30 
 50.16 
 
 41.40 
 50.16 
 
 38.53 
 50.16 
 
 35.66 
 49.68 
 
 32.78 
 48.33 
 
 29.89 
 47.03 
 
 
 6.50 
 
 0.19 
 
 3.90 -j 
 
 0.89 
 1.95 
 
 18.43 
 21.45 
 
 17.13 
 21.45 
 
 15.81 
 21.45 
 
 14.49 
 20.92 
 
 13.18 
 20.32 
 
 11.86 
 19.72 
 
 5 
 
 9.00 
 
 0.33 
 
 5.30 -j 
 
 0.90 
 1.83 
 
 25.17 
 29.15 
 
 23.41 
 29.15 
 
 21.65 
 
 28.83 
 
 19.87 
 27.97 
 
 18.11 
 27.10 
 
 16.35 
 26.22 
 
 
 11.50 
 
 0.48 
 
 6.76 | 
 
 0.91 
 1.75 
 
 32.26 
 37.18 
 
 30.03 
 37.18 
 
 27.81 
 36.36 
 
 25.58 
 35.20 
 
 23.35 
 34.03 
 
 21.12 
 
 32.88 
 
 
 5.25 
 
 0.18 
 
 3.10 
 
 0.84 
 1.56 
 
 14.28 
 1705 
 
 13.17 
 16.75 
 
 12.07 
 16.15 
 
 10.96 
 15.55 
 
 9.85 
 14.96 
 
 14.36 
 
 4 
 
 6.25 
 
 0.25 
 
 3.68 | 
 
 0.84 
 1.51 
 
 16.95 
 20.24 
 
 15.64 
 19.72 
 
 14.33 
 18.99 
 
 13.02 
 
 18.26 
 
 11.70 
 17.53 
 
 16.80 
 
 
 7.25 
 
 0.32 
 
 4.26 { 
 
 0.84 
 1.46 
 
 19.62 
 23.43 
 
 18.10 
 22.63 
 
 16.59 
 21.75 
 
 15.07 
 20.87 
 
 13.54 
 19.98 
 
 19.12 
 
 * Of single channel. 
 
468 
 
 STRENGTH OF ANGLE STRUTS. 
 
 TABLE XIV. SAFE LOADS IN TONS FOR SINGLE 
 
 ANGLE STRUTS (STEEL). 
 A. ANGLES WITH UNEQUAL LEGS. 
 
 Strains per square inch: 
 
 11,000 Ibs. for lengths of 50 radii and under; 
 en/ 
 
 13,500 for lengths over 50 radii. 
 
 Size. 
 
 Thick- 
 ness. 
 
 r 
 
 Axis. 
 EF* 
 
 Area. 
 
 Length in feet. 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 6 X4 
 
 3/8 
 
 7/8 
 
 0.88 
 0.86 
 
 3.61 
 7.99 
 
 42.78 
 
 40.00 
 
 37.21 
 
 34.44 
 
 31 64 
 
 28.86 
 
 26.07 
 
 5 X3H 
 
 3/8 
 3/4 
 
 5/16 
 3/4 
 
 0.76 
 0.75 
 
 3.05 
 5.81 
 
 
 
 
 
 
 
 
 5 X3 
 
 0.66 
 0.64 
 
 2.40 
 5.44 
 
 
 
 
 
 
 
 
 4^X3 
 
 5/16 
 3/4 
 
 0.66 
 0.64 
 
 2.25 
 5.06 
 
 24.66 
 
 22.29 
 
 19.92 
 
 17.55 
 
 15.18 
 
 
 
 4 X3^ 
 
 5/16 
 3/4 
 
 5/16 
 3/4 
 
 5/16 
 
 3/8 
 5/8 
 
 0.73 
 0.72 
 
 2.25 
 5.06 
 
 11.49 
 25.73 
 
 10.57 
 23.62 
 
 9.28 
 20.67 
 
 9.65 
 21.51 
 
 8.72 
 19.40 
 
 7.79 
 17.29 
 
 6.86 
 15.18 
 
 
 4 X3 
 
 0.65 
 0.64 
 
 2.09 
 4.69 
 
 10.25 
 
 22.86 
 
 8.32 
 18.47 
 
 7.51 
 
 8.84 
 14.12 
 
 4.92 
 7.21 
 9.22 
 
 7.36 
 16.27 
 
 6.59 
 7.74 
 12.35 
 
 6.39 
 14.07 
 
 
 
 3^X3 
 
 0.63 
 0.62 
 0.62 
 
 1.93 
 2.30 
 3.67 
 
 9.35 
 11.07 
 
 17.67 
 
 6.52 
 9.55 
 12.34 
 
 8.43 
 9.96 
 15.90 
 
 
 
 
 
 &AX2y 2 
 
 1/4 
 
 3/8 
 1/2 
 
 1/4 
 3/8 
 
 1/2 
 
 0.54 
 0.54 
 0.53 
 
 0.53 
 0.52 
 0.52 
 
 1.44 
 2.11 
 
 2.75 
 
 5.72 
 8.38 
 10.78 
 
 
 
 
 3 X2^ 
 
 1.31 
 1.92 
 2.50 
 
 5.88 
 8.52 
 11.10 
 
 5.13 
 
 742 
 9.66 
 
 4.39 
 6.31 
 8.22 
 
 
 
 
 
 3 X2 
 
 1/4 
 
 3/8 
 1/2 
 
 0.43 
 0.43 
 0.43 
 
 1.19 
 1.73 
 2.25 
 
 4.71 
 6.85 
 8.91 
 
 3.88 
 5.64 
 7.34 
 
 
 
 
 
 
 2^X2 
 
 1/4 
 
 3/8 
 1/2 
 
 0.42 
 0.42 
 0.42 
 
 1.06 
 1.55 
 2.00 
 
 4.13 
 6.03 
 
 7.79 
 
 3.37 
 4.93 
 6.36 
 
 
 
 
 
 
 * Axis diagonal, see p. 304. 
 
STRENGTH OF ANGLE STRUTS. 
 
 469 
 
 TABLE XIV. SAFE LOADS IN TONS FOR SINGLE 
 
 ANGLE STRUTS (continued). 
 
 B. ANGLES WITH EQUAL LEGS. 
 
 Strains per square inch: 
 
 11,000 Ibs. for lengths of 50 radii and under; 
 
 13,500 for lengths over 50 radii. 
 
 Size. 
 
 Thick- 
 ness. 
 
 r 
 Axis 
 EF* 
 
 Area. 
 
 Length in feet. 
 
 4 
 
 5 
 
 6 
 
 7 
 
 21.74 
 35.35 
 
 48.28 
 
 16.71 
 26.86 
 36.45 
 
 11.71 
 15.22 
 18.55 
 21.89 
 
 7.74 
 11.90 
 14.39 
 16.96 
 
 8 
 
 9 
 
 10 
 
 18.44 
 29.93 
 40.78 
 
 13.42 
 21.43 
 28.96 
 
 6 X6 
 
 3/8 
 5/8 
 "7/8 
 
 1.19 
 1.18 
 1.17 
 
 4.36 
 7.11 
 9.74 
 
 3.61 
 
 5.86 
 7.99 
 
 2.86 
 3.75 
 4.61 
 5.44 
 
 23.98 
 39.10 
 53.57 
 
 23.93 
 38.96 
 53.27 
 
 18.89 
 30.50 
 41.44 
 
 22.83 
 37.14 
 50.77 
 
 17.80 
 
 28.68 
 38.95 
 
 12.79 
 16.65 
 20.33 
 23.99 
 
 20.64 
 33.54 
 
 45.77 
 
 19.54 
 31.72 
 43.26 
 
 5 X5 
 
 3/8 
 5/8 
 7/8 
 
 0.99 
 0.97 
 0.96 
 
 0.79 
 0.78 
 0.77 
 0.77 
 
 19.85 
 32.23 
 43.94 
 
 14.96 
 19.54 
 23.93 
 28.24 
 
 15.64 
 25.06 
 33.95 
 
 10.61 
 13.78 
 16.75 
 19.77 
 
 6.83 
 10.47 
 12.61 
 14.86 
 
 14.53 
 23.24 
 31.46 
 
 9.53 
 12.33 
 14.95 
 17.65 
 
 4 X4 
 
 3/8 
 1/2 
 5/8 
 3/4 
 
 13.88 
 18.10 
 22.13 
 26.12 
 
 VAX&A 
 
 5/16 
 1/2 
 5/8 
 3/4 
 
 1/4 
 3/8 
 1/2 
 5/8 
 
 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 
 
 
 3 X3 
 
 0.59 
 0.58 
 0.58 
 0.57 
 
 1.44 
 2.11 
 2.75 
 3.36 
 
 0.90 
 1.19 
 1.73 
 2.25 
 
 6.79 
 
 9.88 
 12.87 
 15.60 
 
 6.06 
 8.78 
 11.45 
 13.84 
 
 5.32 
 7.69 
 10.03 
 12.07 
 
 4.59 
 6.60 
 8.60 
 10.30 
 
 
 
 2>X2^ 
 
 3/16 
 
 1/4 
 3/8 
 1/2 
 
 0.49 
 0.49 
 0.48 
 0.47 
 
 3.87 
 5.10 
 7.35 
 9.44 
 
 3.32 
 4.39 
 6.27 
 8.01 
 
 2.76 
 3.66 
 5.19 
 6.57 
 
 
 
 
 
 
 2MX2M 
 
 3/16 
 1/4 
 
 3/8 
 7/16 
 
 0.44 
 0.44 
 0.43 
 0.43 
 
 0.81 
 1.06 
 1.55 
 
 1.78 
 
 0.72 
 0.94 
 
 3.26 
 4.26 
 6.13 
 7.14 
 
 2.70 
 3.54 
 5.05 
 5.80 
 
 2.16 
 
 2.72 
 
 2.80 
 3.95 
 4.53 
 
 
 
 
 2 X2 
 
 3/16 
 
 1/4 
 
 0.40 
 0.39 
 
 2.70 
 3.45 
 
 2.00 
 
 
 
 
 
 * Axis diagonal, see p. 309. 
 
470 
 
 STRENGTH OF ANGLE STRUTS. 
 
 TABLE XV. SAFE LOADS IN TONS FOR TWO ANGLE 
 
 STRUTS. 
 LONG LEGS PAEALLEL AND J INCH APART. 
 
 Strains per square inch: 
 11,000 Ibs. for lengths of 50 radii and under; 
 
 rni 
 
 13,500- for lengths over 50 radii. 
 
 Size. 
 
 Thick- 
 ness. 
 
 Least 
 r 
 
 Area 
 of 
 two 
 an- 
 gles. 
 
 13.52 
 
 26.8$ 
 7.22 
 14.94 
 
 Length in feet. 
 
 5 
 
 74.36 
 147.51 
 39.71 
 82.17 
 
 6 
 
 74.36 
 147.51 
 39.71 
 82.17 
 
 7 
 
 74.36 
 147.51 
 39.65 
 
 82.17 
 
 8 
 
 74.36 
 147.51 
 38.35 
 80.26 
 
 10 
 
 11 
 
 12 
 
 8 X6 
 6 X4 
 
 1/2 
 
 3/8 
 13/16 
 
 2.49 
 2.65 
 1.67 
 1.74 
 
 .74.36 
 147.51 
 35.77 
 75.07 
 
 73.34 
 1*7.51 
 34.47 
 72.50 
 
 71.72 
 144.62 
 33.14 
 69.91 
 
 6 X3H 
 
 3/8 
 1/2 
 5/8 
 13/16 
 
 1.43 
 1.46 
 1.49 
 1.52 
 
 6.84 
 9.00 
 11. 1C 
 14.12 
 
 37.62 
 49.50 
 61.05 
 77.66 
 
 37.57 
 49.50 
 61.05 
 
 77.66 
 
 36.13 
 47.81 
 59.27 
 
 75.82 
 
 34.69 
 45.97 
 57.05 
 73.03 
 
 31.82 
 42.27 
 52.51 
 67.42 
 
 30.38 
 40.41 
 50.29 
 64.65 
 
 29.00 
 38.56 
 48.07 
 61.88 
 
 5 X4 
 5 X3K 
 
 3/8 
 3/4 
 V8 
 3/4 
 
 1.59 
 1.54 
 1.51 
 1.55 
 
 6.46 
 12.38 
 6.10 
 11.02 
 
 35.53 
 68.09 
 33.55 
 63.91 
 
 31.46 
 41.25 
 50.71 
 59.84 
 
 35.5c 
 68.09 
 33.55 
 63.91 
 
 30.50 
 40.2S 
 
 49.76 
 58.94 
 
 28.35 
 53.13 
 26.28 
 49.47 
 
 14.81 
 21.59 
 28.05 
 36.86 
 
 35.07 
 66.69 
 32.70 
 62.69 
 
 29.15 
 38.51 
 47.69 
 56.63 
 
 27.07 
 50.60 
 25.12 
 47.18 
 
 14.03 
 20.42 
 26.53 
 
 34.78 
 
 33.86 
 64.28 
 31.49 
 60.45 
 
 27.80 
 36.78 
 45.59 
 54.23 
 
 25.79 
 48.07 
 24.00 
 44.85 
 
 13.26 
 19.28 
 25.02 
 32.74 
 
 31.41 
 59.45 
 29.05 
 55.95 
 
 30.20 
 57.04 
 27.84 
 53.71 
 
 23.75 
 31.59 
 39.30 
 47.05 
 
 28.99 
 54.62 
 26.64 
 51.44 
 
 5 X3 
 
 3/8 
 1/2 
 5/8 
 3/4 
 
 1.27 
 1.30 
 1.33 
 1.36 
 
 5.72 
 7.50 
 9.22 
 10.88 
 
 25.00 
 33.32 
 41.40 
 49.42 
 
 22.39 
 29.85 
 37.29 
 44.66 
 
 4 X3H 
 4 X3 
 
 3/8 
 3/4 
 
 3/8 
 3/4 
 
 1.25 
 1.20 
 1.26 
 1.22 
 
 5.34 
 10.12 
 4.96 
 9.38 
 
 2.88 
 4.22 
 5.50 
 7.30 
 
 2.38 
 4.50 
 1.62 
 4.00 
 
 1.44 
 1.58 
 
 29.37 
 55.66 
 27.28 
 51.59 
 
 23.23 
 43.01 
 21.C4 
 40.24 
 
 21.94 
 40.48 
 20.49 
 37.94 
 
 20.66 
 39.95 
 19.50 
 35.64 
 
 33^X2^ 
 
 1/4 
 3/8 
 1/2 
 11/16 
 
 1.12 
 1.10 
 1.09 
 1.06 
 
 0.93 
 0.92 
 0.79 
 0.75 
 
 0.62 
 0.61 
 
 15.58 
 22.73 
 29.56 
 38.92 
 
 12.22 
 23.04 
 7.86 
 19.00 
 
 11.72 
 16.97 
 21.98 
 
 28.58 
 
 10.95 
 
 15.82 
 20.47 
 26.51 
 
 10.18 
 14.67 
 18.96 
 24.43 
 
 3 X2 
 2^X2 
 
 1/4 
 J/2 
 ?/16 
 1/2 
 
 11.45 
 21.58 
 7.24 
 17.40 
 
 5.54 
 7.14 
 
 10.60 
 20. IP 
 6.63 
 15.80 
 
 9.92 
 18.64 
 6.01 
 14.20 
 
 8.39 
 15.7C 
 
 7.02 
 14.23 
 
 
 2 X2 
 2 X2 
 
 3/16 
 
 1/4 
 
 6.22 
 8.08 
 
 4.S2 
 6.20 
 
 4.13 
 5.26 
 
 
 
 
 Two ANGLE STRUTS OF 'p SECTION, p. 471. 
 
 23^X23^ 
 
 3/16 
 
 1/4 
 
 1.07 
 1.11 
 
 1.80 
 2.38 
 
 9.63 
 
 12.85 
 
 9.13 
 12.19 
 
 8.64 
 1154 
 
 8.10 
 
 10.88 
 
 7.11 
 9.63 
 
 6.61 
 8.98 
 
 6.12 
 8.63 
 
 2MX2M 
 
 3/16 
 
 1/4 
 
 1.03 
 1.01 
 
 1.62 
 2.12 
 
 8.58 
 11.13 
 
 8.10 
 10.5i 
 
 7.65 
 9.91 
 
 7.16 
 9.27 
 
 6.23 
 8.CO 
 
 5.75 
 
 7.42 
 
 5.26 
 6.78 
 
 2 X2 
 
 3/16 
 
 0.93 
 
 1.44 
 
 7.37 
 
 6.91 
 
 6.48 
 
 6.01 
 
 5.0" 
 
 4. CO 
 
 4.13 
 
 
 1/4 
 
 0.94 
 
 1.S8 
 
 9.G3 
 
 9.07 
 
 8. 40 
 
 7.89 
 
 6.6/ 
 
 6.11 
 
 5.49 
 
STRENGTH OF I-BEAM STRUTS. 
 
 471 
 
 TABLE XVI. SAFE LOADS IN TONS FOR STANDARD 
 STEEL BEAMS USED AS COLUMNS OR STRUTS. 
 
 Strains per square inch: 13,500 50-. 
 BEAMS UNSUPPORTED SIDEWAYS. 
 
 Size, 
 ins. 
 
 Weight, 
 Ibs. 
 
 r 
 
 Area 
 of 
 
 section. 
 
 Length in feet. 
 
 9 
 
 10 
 
 11 
 
 12 
 
 13 
 
 14 
 
 5 
 
 12" -j 
 
 42.00 
 50.00 
 60.00 
 
 31.50 
 35.00 
 40.00 
 
 1.08 
 1.04 
 1.21 
 
 12.48 
 14.71 
 17.67 
 
 9.26 
 10.29 
 11.84 
 
 53.04 
 61.12 
 79.87 
 
 37.76 
 41.39 
 50.32 
 
 49.57 
 56.85 
 75.45 
 
 35.00 
 38.28 
 47.03 
 
 46.11 
 52.62 
 71.12 
 
 42.65 
 48.38 
 66.70 
 
 39.19 
 44.13 
 62.33 
 
 37.18 
 
 57.95 
 
 1.01 
 0.99 
 1.08 
 
 32.24 
 35.16 
 43.75 
 
 29.50 
 32.05 
 40.46 
 
 
 10" | 
 
 25.00 
 40.00 
 
 0.97 
 0.90 
 
 90 
 0.84 
 
 7 37 
 11.76 
 
 29.24 
 44.10 
 
 26.95 
 40.19 
 
 24.67 
 36.28 
 
 22.40 
 
 
 
 
 H 
 
 8"| 
 
 21.00 
 35.00 
 
 6.31 
 10.29 
 
 23.66 
 36.40 
 
 21.56 
 32.72 
 
 19.46 
 
 
 
 18.00 
 25.50 
 
 0.84 
 0.80 
 
 5.33 
 7.50 
 
 18.85 
 25.31 
 
 16.95 
 22.50 
 
 
 
 
 
 BEAMS SUPPORTED SIDEWAYS. 
 
 H 
 
 H 
 
 If 
 
 18.00 
 25.50 
 
 3.27 
 3.02 
 
 5.33 
 
 7.50 
 
 31.58 
 43.93 
 
 31.08 
 43.17 
 
 30.59 
 42.43 
 
 30.11 
 41.68 
 
 29.62 
 40.95 
 
 23.81 
 31.13 
 
 29.14 
 40.20 
 
 23.35 
 30.47 
 
 15.00 
 20.00 
 
 2.86 
 2.68 
 
 4.42 
 5.88 
 
 25.67 
 33.76 
 
 25.20 
 33.10 
 
 19.96 
 23.76 
 27.52 
 
 24.74 
 32.45 
 
 24.27 
 31.79 
 
 12.25 
 14.75 
 17.25 
 
 2.46 
 2.35 
 2.27 
 
 3.61 
 4.34 
 5.07 
 
 20.40 
 24.31 
 28.19 
 
 15.59 
 19.29 
 23.03 
 
 19.53 
 23.21 
 26.86 
 
 19.09 
 22.65 
 26.18 
 
 18.64 
 22.09 
 25,. 51 
 
 18.20 
 21.53 
 24.84 
 
 H 
 
 9.75 
 12.25 
 14.75 
 
 2.05 
 1.94 
 
 1.87 
 
 2.87 
 3.60 
 4.34 
 
 15.17 
 18.73 
 22.33 
 
 14.75 
 18.18 
 21.63 
 
 14.33 
 17.62 
 20.94 
 
 13.91 
 17.06 
 20.24 
 
 13.49 
 16.50 
 19.55 
 
 4 i 
 
 7.50 
 10.50 
 
 1.64 
 1.52 
 
 1.23 
 1.15 
 
 2.21 
 3.09 
 
 11.28 
 15.37 
 
 10.87 
 14.76 
 
 10.47 
 14.15 
 
 10.06 
 13.54 
 
 6.23 
 8.00 
 
 9.66 
 12.93 
 
 5.83 
 7.42 
 
 9.26 
 12.32 
 
 3 
 
 5.50 
 7.50 
 
 1.63 
 2.21 
 
 7.42 
 9.73 
 
 7.02 
 9.15 
 
 6.63 
 
 8.57 
 
 5.43 
 6.84 
 
 NOTE. The safe loads given on bottom of 
 p. 470 refer to two angles connected by 
 plates so as to form a cross- section, as in 
 accompanying figure. This form of strut is 
 frequently used in light steel trusses. 
 
472 
 
 STRENGTH OF CHANNEL COLUMNS. 
 
 TABLE XVII. SAFE LOADS IN TONS OF 2,000 LBS, 
 
 FOR CHANNEL COLUMNS. 
 
 I*- C--M 
 
 Allowed stresses per square inch; 
 12,000 Ibs. for lengths of 90 radii or under; 
 
 17,100 57- for lengths over 90 radii, and less than 125 radii, ad 
 
 Size of 
 plates, 
 ins. 
 
 Weight of 
 channels 
 and 
 plates. 
 
 r 
 
 Length in feet. 
 
 14 
 
 16 
 
 18 
 
 20 
 
 22 
 
 24 
 
 6" 8-LB. CHANNELS. B = 3J^". C = 5M". 
 
 Lattice. . 
 
 >MX8 
 7 ^X8 
 
 16.0 
 29.6 
 33.0 
 36.4 
 39.8 
 
 2.33 
 2.32 
 2.32 
 2.32 
 2.32 
 
 28.6 
 52.6 
 58.6 
 64.6 
 70.6 
 
 28.6 
 52.6 
 58.6 
 64.6 
 70.6 
 
 28.1 
 51.7 
 57.5 
 63.4 
 69.3 
 
 26.7 
 49.1 
 54.7 
 60.3 
 65.8 
 
 25.3 
 46.5 
 51.8 
 57.1 
 62.4 
 
 23.9 
 43.9 
 48.9 
 53.9 
 58.9 
 
 6" 15.5-LB. CHANNELS. B = 3J^". C = 5M". 
 
 Lattice. . 
 
 31.0 
 48.0 
 51.4 
 54.8 
 58.2 
 
 2.00 
 2.12 
 2.13 
 2.14 
 2.15 
 
 54.7 
 84.7 
 90.7 
 96.7 
 102.7 
 
 53.0 
 84.2 
 90.4 
 96.7 
 102.7 
 
 49.9 
 79.7 
 85.6 
 91.5 
 97.4 
 
 46.8 
 75.1 
 80.7 
 86.4 
 92.0 
 
 70.5 
 75.9 
 81.2 
 86.5 
 
 
 7" 9.75-LB. CHANNELS. B = 4^". C = 6%". 
 
 Lattice. . 
 
 19.5 
 34.8 
 38.6 
 42.5 
 46.3 
 
 2.72 
 2.67 
 2.67 
 2.66 
 2.66 
 
 34.2 
 61.2 
 67.9 
 
 74.7 
 81.5 
 
 34.2 
 61.2 
 67.9 
 74.7 
 81.5 
 
 34.2 
 61.2 
 67.9 
 
 74.7 
 81.5 
 
 34.2 
 61.2 
 67.9 
 74.4 
 81.1 
 
 32.8 
 58.5 
 65.0 
 71.2 
 77.6 
 
 31.4 
 55.9 
 62.0 
 68.0 
 74.1 
 
 7" 17.25-LB. CHANNELS. B = 4^". C = 6%". 
 
 Lattice. . 
 
 34.5 
 53.6 
 57.5 
 61.3 
 65.1 
 
 2.43 
 2.49 
 2.50 
 2.50 
 2.51 
 
 60.8 
 94.6 
 101.3 
 108.1 
 114.8 
 
 60.8 
 94.6 
 101.3 
 108.1 
 114.8 
 
 60.8 
 94.6 
 101.3 
 108.1 
 114.8 
 
 58.1 
 91.4 
 98.2 
 104.8 
 111.5 
 
 55.3 
 87.1 
 93.5 
 99.9 
 106.3 
 
 52.4 
 82.8 
 88.9 
 95.0 
 101.1 
 
 To weight of channels and plates add the weight of rivets and lattice- 
 bars. The size of lattice-bars should not be less than 1}^X%6 ins. for 
 6-inch channels, 1%X%6 inch for 7- and 8-inch channels, or 2X%e ins. 
 for 9- and 10-inch columns. See page 439. 
 
STRENGTH OF CHANNEL COLUMNS. 473 
 
 TABLE XVII. SAFE LOADS IN TONS OF 2,000 LBS. 
 FOR CHANNEL COLUMNS (continued). 
 
 Allowed stresses per square inch: 
 12,000 Ibs. for lengths of 90 radii or under; 
 
 17,100 57 for lengths over 90 radii, and less than 125 radii. 
 
 Size of 
 plates, 
 ins. 
 
 Weight of 
 channels 
 and 
 plates,. 
 
 r 
 
 Length in feet. 
 
 20 
 
 22 
 
 24 
 
 26 
 
 28 
 
 30 
 
 8" 11.25-LB. CHANNELS. B = 57/4 6 ". C = 7^". 
 
 Lattice. . 
 MX10 
 5 /4oXlO 
 
 ^xio 
 
 22.5 
 39.5 
 43.7 
 48.0 
 
 3.11 
 3.03 
 3.02 
 3.01 
 
 40.2 
 70.2 
 
 77.7 
 85.2 
 
 40.2 
 70.2 
 
 77.7 
 85.2 
 
 39.6 
 
 68.4 
 75.5 
 
 82.7 
 
 38.1 
 65.7 
 72.6 
 79.4 
 
 36.6 
 63.1 
 69.7 
 76.2 
 
 35.2 
 60.5 
 66.7 
 73.0 
 
 8" 16.25-LB. CHANNELS. 3 = 5^0". C=7^". 
 
 Lattice. . 
 
 ^xio 
 
 tteXlO 
 
 ^xio 
 
 32.5 
 58.0 
 62.3 
 66.5 
 
 2.89 
 2.92 
 2.91 
 2.91 
 
 57.4 
 102.4 
 109.9 
 117.4 
 
 56.8 
 101.9 
 109.3 
 116.7 
 
 54.6 
 97.9 
 105.0 
 112.1 
 
 52.3 
 93.9 
 
 100.7 
 107.5 
 
 50.1 
 89*9 
 96.4 
 102.9 
 
 47.8 
 85.9 
 92.1 
 98.3 
 
 9" 13.25-LB. CHANNELS. B = 6% 6 ". C=8H" 
 
 Lattice. . 
 #X11 
 fceXll 
 HX11 
 
 26.5 
 45.2 
 ' 49.9 
 54.6 
 
 3.49 
 3.40 
 3.38 
 3.36 
 
 46.7 
 79.7 
 88.0 
 96.2 
 
 46.7 
 79.7 
 88.0 
 96.2 
 
 46.7 
 79.7 
 88.0 
 96.2 
 
 46.7 
 
 78.8 
 86.7 
 94.6 
 
 45.2 
 76.1 
 
 83.8 
 91.4 
 
 43.6 
 73.4 
 
 80.8 
 88.1 
 
 9" 20-LB. CHANNELS. & = &%&" C = 8%". 
 
 Lattice. . 
 HX11 
 
 fteXH 
 
 8xn 
 
 40.0 
 68.1 
 
 72.7 
 77.4 
 
 3.21 
 3.25 
 3.25 
 3.24 
 
 70.6 
 120.1 
 128.3 
 136.6 
 
 70.6 
 120.1 
 128.3 
 136.6 
 
 70.6 
 120.1 
 128.3 
 136.6 
 
 68.0 
 116.3 
 124.2 
 132.1 
 
 65.5 
 112.1 
 119.7 
 127.3 
 
 63.0 
 107.9 
 115.2 
 122.5 
 
 10" 15-LB. CHANNELS. B = 7". C = 9^". 
 
 Lattice. . 
 % 6 X12 
 
 HX12 
 
 30.0 
 55.5 
 60.6 
 
 3.87 
 3.74 
 3.72 
 
 53.5 
 98.5 
 107.5 
 
 53.5 
 
 98.5 
 107.5 
 
 53.5 
 98.5 
 107.5 
 
 53.5 
 98.5 
 
 53.5 
 98.5 
 107.5 
 
 52.6 
 95.3 
 107.0 
 
 
 10" 25-LB. CHANNELS. B = 7". C = 9J^". 
 
 Lattice. . 
 9 /ie X 12 
 5 AX12 
 
 50.0 
 95.9 
 101.0 
 
 3.52 
 3.56 
 3.55 
 
 88.2 
 169.2 
 178.2 
 
 88.2 
 169.2 
 178.2 
 
 88.2 
 169.2 
 178.2 
 
 88.2 
 169.2 
 178.2 
 
 85.7 
 165.3 
 173.9 
 
 82.8 
 159.8 
 168.2 
 
474 
 
 DIMENSIONS OF Z-BAR COLUMNS. 
 
 DIMENSIONS OF Z-BAR COLUMNS. 
 CARNEGIE SECTIONS. 
 
 - -H- 
 
 rfffi 
 
 fcJ&L 
 
 * 
 
 4 Z-bars S-S 
 
 6" COLUMNS. 
 o" deep and 1 web-plate 5%"X thickness of Z-bars. 
 
 Thick- 
 ness of 
 metal. 
 
 1/4 
 5/16 
 
 3/8 
 7/16 
 1/2 
 9/16 
 
 12 
 
 12^6 
 
 5946 
 
 5Vi 
 
 D 
 
 2y s 
 
 in 
 
 2i% 
 
 2M 
 
 2M^ 
 
 tf 
 
 8" COLUMNS. 
 Z-bars 4-4K" deep and 1 web-plate Q%" X thickness of Z-bars. 
 
 || 
 
 Thick- 
 ness of 
 metal. 
 
 1/4 
 
 5/16 
 
 3/8 
 
 7/16 
 
 1/2 
 
 9/16 
 
 5/8 
 
 11/16 
 
 3/4 
 
 1411^, 
 141%, 
 
 6^6 
 6Vl6 
 
 6i%e 
 
 511^6 
 51^6 
 
 D 
 
 314 
 
 3M 
 3M 
 3M 
 
 1M 
 
 1M 
 1 3 4 
 
 3Vl6 
 33A 6 
 
 3Vi6 
 
 3%6 
 
 H 
 
 9 
 
 8% 
 
STRENGTH OF Z-BAR COLUMNS. 
 
 475 
 
 TABLE XVIII. SAFE LOADS IN TONS OF 2,000 LBS. FOR 
 Z-BAR COLUMNS WITH SQUARE ENDS. 
 
 { 12,000 Ibs. for lengths of 90 radii or under. 
 Allo wed stresses per square inch <. A e _ I . 
 
 | 17,100 57 for lengths oVer 90 radii. 
 
 6" Z-BAR COLUMNS. 
 Section: 4 Z-bars 3" deep and one web-plate 5^" X thickness of Z-bars. 
 
 
 d 
 
 oo a 
 
 <N d 
 
 W - Seo 
 
 ^ 
 
 os d 
 
 
 
 OS'^O 
 
 
 
 
 
 
 w i*2 
 
 CO _lOS 
 
 ^^ 
 
 f ^2 
 
 go-2 
 
 ^2 
 
 Length 
 
 " 1-1 II 
 
 ''b- II 
 
 JH & II 
 
 ^qjl^ 
 
 II CO II 
 
 *-SO' 1 
 
 of 
 
 'e5 PQ.'-N 
 
 -2 T-Hx s 
 
 "e3eo/~s 
 
 
 *c3 tx! / ~ N 
 
 -^O'^ 
 
 column 
 
 IB os' d 
 
 s7.s 
 
 "S 1 "" 1 d 
 
 "^ d 
 
 - 
 
 g^ 
 
 g<N d 
 
 in feet. 
 
 s !3 
 
 
 11! 
 
 II d 
 
 H S^ 
 
 8 HI 
 
 rJ! 
 
 12 and 
 under 
 14 
 
 55.9 
 55.7 
 
 70.3 
 70.3 
 
 81.6 
 81.6 
 
 95.8 
 
 95.8 
 
 105.7 
 105.7 
 
 119.8 
 119.8 
 
 16 
 
 52.3 
 
 66.5 
 
 76.6 
 
 91.3 
 
 99.9 
 
 114.8 
 
 18 
 
 48.8 
 
 62.3 
 
 71.7 
 
 85.6 
 
 93.6 
 
 107.8 
 
 20 
 
 45.4 
 
 58.1 
 
 66.7 
 
 79.9 
 
 87.2 
 
 100.8 
 
 22 
 
 42.0 
 
 53.9 
 
 61.8 
 
 74.3 
 
 80.9 
 
 93.8 
 
 24 
 
 38.6 
 
 49.7 
 
 56.9 
 
 68.6 
 
 74.6 
 
 86.8 
 
 26 
 
 35.2 
 
 45.5 
 
 51.9 
 
 63.0 
 
 68.2 
 
 79.8 
 
 28 
 
 31.7 
 
 41.3 
 
 47.0 
 
 57.3 
 
 61.9 
 
 72.8 
 
 30 
 
 28.3 
 
 37.1 
 
 42.0 
 
 51.7 
 
 55.5 
 
 65.8 
 
 8" Z-BAR COLUMNS. 
 Section: 4 Z-bars 4" deep and 1 web-plate 6V<j" X'thickness of Z-bars. 
 
 a 
 
 a 
 
 d 
 
 d 
 
 .5 
 
 d 
 
 .9 
 
 d 
 
 d 
 
 oq.S^ 
 
 .s 
 
 o 
 
 06 7 csj 
 
 06 cr^ 
 
 g"S 
 
 (N 
 
 ^ cr 1 ^ 
 
 oo C<M' 
 
 OS oc sj 
 
 ^ ^3 
 
 00 0* 
 O t(M 
 
 o 
 
 7 W . II 
 
 jl -1 II 
 
 IQ ] _ ( .. 
 
 II 9 II 
 
 7^ " 
 
 Jl 5 II 
 
 T ^ " 
 
 JLo ii 
 
 7 9 ii 
 
 -g 
 
 37 c> 
 
 3^"d 
 
 37 9 
 
 ifV ^ 
 
 'is^'d 
 
 J^'d' 
 
 37-S 
 
 **rf 
 
 a^? 
 
 |.s 
 
 
 1^ 
 
 " .3 
 
 I .'g 
 
 iii 
 
 i^ 
 
 
 !lS 
 
 ".'g 
 
 18 
 and 
 
 
 
 
 
 
 
 
 
 
 under 
 
 67.5 
 
 84.8 
 
 102.4 
 
 114.2 
 
 131.2 
 
 148.5 
 
 157.5 
 
 174.3 
 
 191.2 
 
 20 
 
 65.0 
 
 82.5 
 
 100.5 
 
 110.5 
 
 128.2 
 
 146.4 
 
 153.3 
 
 171.3 
 
 189.6 
 
 22 
 
 61.9 
 
 78.7 
 
 95.9 
 
 105.3 
 
 122.4 
 
 139.9 
 
 146.2 
 
 163.5 
 
 181.3 
 
 24 
 
 58.8 
 
 74.8 
 
 91.3 
 
 100.1 
 
 116.5 
 
 133.4 
 
 139.1 
 
 155.8 
 
 173.0 
 
 26 
 
 55.7 
 
 71.0 
 
 86.8 
 
 94.8 
 
 110.6 
 
 126.9 
 
 132.0 
 
 148.1 
 
 164.7 
 
 28 
 
 52.6 
 
 67.1 
 
 82.3 
 
 89.6 
 
 104.7 
 
 120.3 
 
 124.8 
 
 140.4 
 
 156.4 
 
 30 
 
 49.4 
 
 63.3 
 
 77.7 
 
 84.4 
 
 98.8 
 
 113.8 
 
 117.7 
 
 132.7 
 
 148.2 
 
 32 
 
 46.3 
 
 59.5 
 
 73.2 
 
 79.2 
 
 93.0 
 
 107.3 
 
 110.6 
 
 125.0 
 
 139.9 
 
 34 
 
 43.2 
 
 55.6 
 
 68.7 
 
 74.0 
 
 87.1 
 
 100.8 
 
 103.5 
 
 117.3 
 
 131.6 
 
 36 
 
 40.1 
 
 51.8 
 
 64.1 
 
 68.7 
 
 81.2 
 
 94.3 
 
 96.4 
 
 109.6 
 
 123.3 
 
 38 
 
 37.0 
 
 48.0 
 
 59.6 
 
 63.5 
 
 75.3 
 
 87.8 
 
 89.4 
 
 101.9 
 
 115.0 
 
 40 
 
 33.9 
 
 44.1 
 
 55.0 
 
 58.3 
 
 69.5 
 
 81.3 
 
 82.2 
 
 94.2 
 
 106.7 
 
 To the above weights of column shafts add the weight of rivets. 
 
476 
 
 DIMENSIONS OF Z-BAR COLUMNS. 
 
 DIMENSIONS OF Z-BAR COLUMNS. 
 CARNEGIE SECTIONS. 
 
 |^-G-^j f-D-W * : 
 
 |<- c-^ -<C - ^ 
 
 10" COLUMNS. 
 4 Z-bars 5-5H" deep and one web-plate 7" X thickness of Z-bars. 
 
 II 
 I" 
 
 a 
 
 Thick- 
 ness of 
 metal. 
 
 5/16 
 
 3/8 
 
 7/16 
 
 1/2 
 
 9/16 
 
 5/8 
 
 11/16 
 
 3/4 
 
 13/16 
 
 169,1 
 
 16% 
 
 16*4 
 
 1C5/1 
 
 5%2 
 
 5M 
 
 5}<C 
 
 5H 3 
 
 5~/l6 
 
 D 
 
 3^ 
 
 10 
 
 12" COLUMNS. 
 
 4 Z-bars 6-6>8 /r deep and one web-plate 8" X thickness of Z-bars. 
 
 Thick- 
 ness of 
 metal. 
 
 3/8 
 
 7/16 
 
 1/2 
 
 9/16 
 
 5/8 
 
 11/16 
 
 3/4 
 
 13/16 
 
 7/8 
 
 18i5/ i( 
 19 
 
 6i5/ 3: 
 
 sy$ 
 
 39/ie 
 
 H 
 
 11 
 
STRENGTH OF Z-BAR COLUMNS. 
 
 477 
 
 TABLE XVIII. SAFE LOADS IN TONS OF 2,000 LBS. FOR 
 Z-BAR COLUMNS WITH SQUARE ENDS (continued). 
 
 ( 12,000 Ibs. for lengths of 90 radii or under 
 Allowed stresses per square inch < I 
 
 I 17,100-57 for lengths of over 90 radii. 
 
 10" Z-BAR COLUMNS. 
 Section: 4 Z-bars 5" deep and one web-plate 7 // Xthickness of Z-bars. 
 
 d 
 
 d 
 
 .S 
 
 d 
 
 d 
 
 . 
 
 d t 
 
 q d ^ 
 
 d 
 
 ?c ' 
 
 
 t> <rH t oo 
 co crp 
 
 j>'^3 
 
 00'^ 00 
 
 o.\4.S 
 
 TJH o 11 "! 
 
 id O<M. 
 
 T 1 O""" 1 
 
 
 CO -^ 
 
 g 
 
 O cO 
 
 ^ co CO 
 
 b- co co 
 
 CO <KCO 
 
 
 O co co 
 
 || < CO 
 
 <N coco 
 
 II CO co' 
 
 o 
 
 jl II 
 
 ii . II 
 
 _!. ii 
 
 T 1 ^ " 
 
 l-^'l 
 
 7? ii 
 
 
 73 II 
 
 
 jalR 
 
 S^'J 
 
 3-?? 
 
 JS'3 
 
 "3^'d 
 
 3^^ 
 
 ^coG" 
 
 gw'J 
 
 r 3^'d~ 
 
 -^co"^ 
 
 i* O> 
 
 si's 
 
 1 p 
 
 Iji 
 
 " ".'d 
 S js^S- 
 
 in 
 
 " " '3 
 
 y- 
 
 a .!'s 
 
 "S ",'g 
 
 5 " -a 
 
 J' S 
 
 2?-^ 
 
 
 >~fc 
 
 
 c~ ** 
 
 
 H 
 
 ^ K 
 
 ?^^ 
 
 22 and 
 
 
 
 
 
 
 
 
 
 
 under 
 
 94.7 
 
 114.2 
 
 133.9 
 
 147.0 
 
 166.2 
 
 185.6 
 
 196.0 
 
 214.9 
 
 234 . 
 
 24 
 
 92.8 
 
 112.6 
 
 133.1 
 
 144.6 
 
 164.8 
 
 185.3 
 
 193.6 
 
 213.9 
 
 234 . 
 
 2Q 
 
 89.3 
 
 108.6 
 
 128.3 
 
 139.2 
 
 158.7 
 
 178.7 
 
 186.5 
 
 206.2 
 
 226.6 
 
 . 28 
 
 85.8 
 
 104.4 
 
 123.5 
 
 133.8 
 
 152.7 
 
 172.1 
 
 179.3 
 
 198.5 
 
 218.4 
 
 30 
 
 82.3 
 
 100.2 
 
 118.7 
 
 128.4 
 
 146.7 
 
 165.5 
 
 172.2 
 
 190.8 
 
 210.2 
 
 32 
 
 78.8 
 
 96.1 
 
 113.8 
 
 123.0 
 
 140.7 
 
 158.9 
 
 165.0 
 
 183.1 
 
 202.0 
 
 34 
 
 75.3 
 
 91.9 
 
 109.1 
 
 117.6 
 
 134.7 
 
 152.3 
 
 157.9 
 
 175.4 
 
 193.8 
 
 36 
 
 71.8 
 
 87.8 
 
 104.3 
 
 112.2 
 
 128.7 
 
 145.7 
 
 150.7 
 
 167.8 
 
 185.6 
 
 38 
 
 68.3 
 
 83.6 
 
 99.5 
 
 106.8 
 
 122.7 
 
 139.1 
 
 143.6 
 
 160.0 
 
 177.4 
 
 40 
 
 64.8 
 
 79.4 
 
 94.7 
 
 101.4 
 
 116.7 
 
 132.5 
 
 136.5 
 
 152.3 
 
 169.1 
 
 42 
 
 61.3 
 
 75.3 
 
 89.9 
 
 96.0 
 
 110.6 
 
 125.9 
 
 129.4 
 
 144.6 
 
 160.9 
 
 44 
 
 57.7 
 
 71.1 
 
 85.1 
 
 90.6 
 
 104.6 
 
 119.3 
 
 122.2 
 
 136.9 
 
 152.7 
 
 46 
 
 54.2 
 
 67.0 
 
 80.3 
 
 85.2 
 
 98.6 
 
 112.7 
 
 115.1 
 
 129.2 
 
 144.5 
 
 48 
 
 50.7 
 
 62.8 
 
 75.5 
 
 79.8 
 
 92.6 
 
 106.1 
 
 107.9 
 
 121 .5 
 
 136.3 
 
 50 
 
 47.2 
 
 58.6 
 
 70.7 
 
 74.4 
 
 86.6 
 
 99.5 
 
 100.8 
 
 113.8 
 
 128.1 
 
 12" Z-BAR COLUMNS. 
 Section: 4 Z-bars 6" deep and one web-plate 8" X thickness of Z-bars. 
 
 d 
 
 a 
 
 .2 
 
 d 
 
 d 
 
 .s' . 
 
 d 
 
 * 
 
 d 
 
 2-S 
 
 d 
 
 jj 
 
 ^ O<cO 
 
 id d* 1 ^ 
 
 9 QJ> 
 
 O D* 1 ^ 
 
 00 D 1 ^ 
 
 2 D* 1 ^ 
 
 *> D 1 ^ 
 
 ^H cr^o 
 
 <N cr 5 ^ 
 
 o 
 
 
 00 co co 
 
 
 
 ^ MOO 
 
 
 CO coco 
 
 
 
 
 
 
 
 
 ii II 
 
 
 7* ii 
 
 
 
 rd~ 
 
 isfe 
 
 3^i 
 
 I&! 
 
 3S^ 
 
 if? 
 
 'titX)^ 
 
 o ? d 
 
 a*d 
 
 2^$^ 
 
 3^7 
 
 is 
 
 ^il 
 
 Ijjl 
 
 Q> d 
 
 S^ 
 
 yi 
 
 
 a i/i 
 
 IjjS 
 
 ||| 
 
 iiS 
 
 s"* 
 
 ^^ ** 
 
 j,S-H fc. 
 
 N^^ *. 
 
 ^5^ K 
 
 usx""* 
 
 rH 
 
 M\^ *~ 
 
 rf ^ ^ 
 
 \oc^-< V. 
 
 26 and 
 
 
 
 
 
 
 
 
 
 
 under 
 
 128.3 
 
 150.3 
 
 172.6 
 
 187.3 
 
 209.1 
 
 231.0 
 
 243.0 
 
 264.5 
 
 286.1 
 
 28 
 
 127.0 
 
 149.7 
 
 172.5 
 
 186.0 
 
 208.9 
 
 230.3 
 
 240.8 
 
 261.4 
 
 282.1 
 
 30 
 
 123.0 
 
 145.1 
 
 167.6 
 
 180.2 
 
 202.5 
 
 223.3 
 
 233.2 
 
 253.2 
 
 273.2 
 
 32 
 
 119.0 
 
 140.5 
 
 162.4 
 
 174.5 
 
 196.1 
 
 216.3 
 
 225.7 
 
 245.0 
 
 264.2 
 
 34 
 
 115.1 
 
 135.9 
 
 157.2 
 
 168.7 
 
 189.8 
 
 209.2 
 
 218.2 
 
 236.7 
 
 255.2 
 
 36 
 
 111.1 
 
 131.3 
 
 152.0 
 
 162.9 
 
 183.4 
 
 202.1 
 
 210.6 
 
 228.4 
 
 246.3 
 
 38 
 
 107.1 
 
 126.7 
 
 146.8 
 
 157.1 
 
 177.0 
 
 195.1 
 
 203.1 
 
 220.2 
 
 237.3 
 
 40 
 
 103.1 
 
 122.1 
 
 141.5 
 
 151.4 
 
 170.7 
 
 188.0 
 
 195.6 
 
 211.9 
 
 228.3 
 
 42 
 
 99.1 
 
 117.5 
 
 136.3 
 
 145.5 
 
 164.4 
 
 180.9 
 
 188.0 
 
 203.7 
 
 219.4 
 
 44 
 
 95.1 
 
 112.9 
 
 131.1 
 
 139.8 
 
 158.0 
 
 173.9 
 
 180.5 
 
 195.5 
 
 210.4 
 
 46 
 
 91.2 
 
 108.3 
 
 126.2 
 
 134.0 
 
 151.6 
 
 166.8 
 
 172.9 
 
 187.2 
 
 201.4 
 
 48 
 
 87.2 
 
 103.6 
 
 120.7 
 
 128.2 
 
 145.3 
 
 159.8 
 
 165.4 
 
 179.0 
 
 192.4 
 
 50 
 
 83.2 
 
 99.1 
 
 115.5 
 
 122.4 
 
 138.9 
 
 152.7 
 
 157.9 
 
 170.7 
 
 183.5 
 
 To the above weights of column shafts add the weight of rivets. 
 
478 
 
 DIMENSIONS OF Z-BAR COLUMNS. 
 
 DIMENSIONS OP Z-BAR COLUMNS. 
 CARNEGIE SECTIONS. 
 
 j^H^^rffjJL 
 
 ~W I 
 
 /^ 
 
 ^1 
 
 F?^ 
 
 ^V 
 
 14" COLUMNS. 
 
 Section : 4 Z-bars 6H" X "/io". 1 web-plate 8" X HV- 2 side plates 14" wide. 
 
 
 Thickness 
 
 
 
 
 
 tj 
 
 of 
 
 A 
 
 B 
 
 C 
 
 D 
 
 O 
 
 side plates. 
 
 
 
 
 
 g 
 
 ,K* 
 
 3/8 
 
 19 9 /16 
 
 627/^6 
 
 !iy 16 
 
 lO^g 
 
 *O t^\ 
 
 7/16 
 
 19M/16 
 
 629/32 
 
 l-^^ie 
 
 lO^g 
 
 
 1/2 
 
 im 
 
 6*%i 
 
 l-^^io 
 
 lO/^ 
 
 Jf 
 
 9/16 
 
 19J1 
 
 
 ; II,^Q 
 
 105^ 
 
 t> > 
 
 1 : 
 
 5/8 
 11/16 
 3/4 
 
 1915A6 
 
 2Q 1 A 6 
 
 73/32 
 
 ;||i 
 
 10^ 
 10|g 
 
 s 
 
 13/16 
 
 20M 
 
 7%2 
 
 ly^Q 
 
 lO^g 
 
 
 7/8 
 
 205/16 
 
 71V 32 
 
 Hie 
 
 10^ 
 
 14" COLUMNS. 
 
 Section: 4 Z-bars 6" XM"- 1 web-plate 8" X%". 2 side plates 14" wide. 
 
 
 Thickness 
 
 
 
 
 
 ^, 
 
 of, , 
 
 A 
 
 B 
 
 C 
 
 D 
 
 o 
 
 side plates. 
 
 
 
 
 
 |- : 
 
 3/8 
 
 19 7 /ie 
 
 6M 
 
 1H 
 
 10^ 
 
 *o 
 
 7/16 
 
 19]^5 
 
 61% 6 
 
 Hi 
 
 lO!x> 
 
 
 1/2 
 
 19V 
 
 6J x s 
 
 IM 
 
 \Q]/2 
 
 -2 > 
 
 9/16 
 
 19^ 
 
 61%6 
 
 IM 
 
 \Q}/2 
 
 11 
 
 5/8 
 
 IQl^g 
 
 7, 
 
 
 \0^/2 
 
 
 11/16 
 
 19 7x s 
 
 7Vl6 
 
 1/4 
 
 ioj^ 
 
 a 
 
 3/4 
 13/16 
 
 20' 
 
 
 IM 
 
 ioj| 
 
 
 7/8 
 
 20H 6 
 
 7M 6 
 
 IM 
 
 |c8 
 
STRENGTH OF Z-BAR COLUMNS. 
 
 479 
 
 TABLE XVIII. SAFE LOADS IN TONS OF 2,000 LBS. FOR 
 STEEL Z-BAR COLUMNS, WITH SQUARE ENDS 
 
 (continued). 
 
 ( 12,000 Ibs. for lengths of 90 radii or under 
 Allowed strains per square inch -< I 
 
 I 17,100 57 for lengths over 90 radii. 
 
 14" Z-BAR COLUMNS. 
 Section: 4 Z-bars 6>s" X^ie". 1 web-plate 8" XHie". 2 side plates 14" wide. 
 
 
 
 co 
 
 
 M9 
 
 
 3 
 
 
 rh 
 
 
 .5 
 
 CO 
 
 
 10 
 
 
 TH 
 
 o 
 
 CO 
 
 00 
 
 <M 
 
 g 
 
 c fl ' 
 
 I-I rt< 
 
 00 g 
 
 s fl 
 
 g d 
 
 ^ d 
 
 O d . 
 
 N p 
 
 ^j fH 
 
 
 1-1 "~!o' 
 
 f'riaS 
 
 7'S^ 
 
 ll'^oq 
 
 || Q<00 
 
 I'd-oS 
 
 CN ""1 O 
 
 i'S^ 
 
 (N' rt O 
 
 || cro 
 
 JEj 
 
 32 M CO 
 
 cp ^ co' 
 
 02 M CO 
 
 a> ^co 
 
 co X 'CO 
 
 ^ 02 CO 
 
 02 W CO* 
 
 _2 co 
 
 
 o 
 
 .2. II 
 
 rtx " 
 
 
 
 
 ^. II 
 
 ^^ II 
 
 ^CO || 
 
 ^. II 
 
 
 
 lf.s 
 
 j^l'l 
 
 5T| 
 
 itl 
 
 -?3 
 
 s?l 
 
 "S-t'S 
 
 l?5 
 
 ffS 
 
 f | 
 
 x^T 
 
 X^ 
 
 xT 
 
 X^ 
 
 x^X 
 
 S*r 
 
 x^f 
 
 xjf 
 
 xj^ 
 
 J 
 
 * 
 
 rH 
 
 T? 
 
 ^ 
 
 ^ 
 
 
 T}H 
 
 ^ 
 
 ^^^ 
 
 
 
 
 
 
 
 
 
 
 
 28 and 
 
 
 
 
 
 
 
 
 
 
 under 
 
 294.0 
 
 304.5 
 
 315.0 
 
 325.5 
 
 336.0 
 
 346.5 
 
 357.0 
 
 367.5 
 
 378.0 
 
 30 
 
 286.6 
 
 297.2 
 
 307.7 
 
 318.3 
 
 328.9 
 
 339.5 
 
 350.0 
 
 360.4 
 
 370.9 
 
 32 
 
 277.8 
 
 288.1 
 
 298.3 
 
 308.6 
 
 318.9 
 
 329.2 
 
 339.4 
 
 349.5 
 
 359.7 
 
 34 
 
 269 . (j 
 
 278.9 
 
 288.9 
 
 298.9 
 
 308.9 
 
 318.9 
 
 328.8 
 
 338.6 
 
 348.6 
 
 36 
 
 260.1 
 
 269.8 
 
 279.5 
 
 289.2 
 
 298.9 
 
 308.6 
 
 318.2 
 
 327.7 
 
 337.4 
 
 38 
 
 251.3 
 
 260.7 
 
 270.1 
 
 279.5 
 
 289.0 
 
 298.3 
 
 307.6 
 
 316.8 
 
 326.2 
 
 40 
 
 242.5 
 
 251.6 
 
 260.7 
 
 269.7 
 
 278.9 
 
 288.0 
 
 297.0 
 
 306.0 
 
 315.0 
 
 42 
 
 233.7 
 
 242.5 
 
 251.3 
 
 260.1 
 
 269.0 
 
 277.8 
 
 286.4 
 
 295.1 
 
 303.8 
 
 44 
 
 224.9 
 
 233.3 
 
 241.9 
 
 250.4 
 
 258.9 
 
 267.4 
 
 275.8 
 
 284.2 
 
 292.6 
 
 46 
 
 216.0 
 
 224.3 
 
 232.4 
 
 240.7 
 
 249.0 
 
 257.2 
 
 265.2 
 
 273.3 
 
 281.5 
 
 48 
 
 207.2 
 
 215.1 
 
 223.0 
 
 230.9 
 
 238.9 
 
 246.9 
 
 254.6 
 
 262.4 
 
 270.3 
 
 50 
 
 198.4 
 
 206.0 
 
 213.6 
 
 221.3 
 
 229.0 
 
 236 . 5 
 
 244.0 
 
 251.5 
 
 259.1 
 
 14" Z-BAR COLUMNS. 
 Section: 4 Z-bars 6"X%". 1 web-plate 8"XM". 2 side plates 14^' wide. 
 
 fl 
 
 ^ 
 
 i 
 
 CO 
 
 CO 
 
 M 
 
 i 
 
 _, 
 
 2 
 
 q 
 
 *d 
 
 t3 d 
 
 t> a 
 
 0? d 
 
 0:1 d 
 
 O5 fl> 
 
 7-S 
 
 o & 
 
 ^ d . 
 
 N d . 
 
 g 
 
 l-H'^lO 
 
 ii '^-^ 
 
 rH >M .I^ 
 
 II '^hS 
 
 rH >rH .O5 
 
 CG '00 
 
 j !! 
 
 i'rroo 
 
 C jj > ' } 
 
 3 
 
 co m &i 
 
 J^co 
 
 " *co 
 
 00 S"^ 
 
 ^co 
 
 _<U KC yj 
 
 02 ^CO 
 
 _2 2co 
 
 00 "M 
 
 o 
 
 n>o || 
 
 ^oq || 
 
 0iO || 
 
 +^CO || 
 
 0)O || 
 
 ,* 9 II 
 
 ^^ II 
 
 ^ CO || 
 
 _^O || 
 
 <4H 
 O 
 
 ^^Hx-N 
 
 ftS'J 
 
 1^? 
 
 ^? 
 
 l^'d 
 
 e^'d 
 
 a^? 
 
 S^'d 
 
 "3-fS 
 
 U 
 
 ^I'g 
 
 ^I'g 
 
 ^'J/g 
 
 ^ll's 
 
 ^lf 
 
 3 s - iS 
 
 ^^5 
 
 SFjoS 
 
 ^^^S 
 
 ^S 
 
 X-^^ 
 
 X-Q^^ 
 
 XrJ^Y' 
 
 XjS^ 
 
 x^^f 
 
 x^2 ?~ 
 
 X j 
 
 X^ 5^ 
 
 X j^ 
 
 sr 
 
 ^ 
 
 5^ 
 
 S^ 
 
 2~ 
 
 !H 
 
 S 
 
 IH 
 
 s 
 
 s 
 
 28 and 
 under 
 30 
 
 306.0 
 296.7 
 
 316.5 
 307.2 
 
 327.0 
 317.8 
 
 337.5 
 328.3 
 
 348.0 
 338.9 
 
 358.5 
 349.4 
 
 369.0 
 359.9 
 
 379.5 
 370.5 
 
 390.0 
 381.1 
 
 32 
 34 
 36 
 38 
 40 
 
 287 .4 
 278.1 
 268.8 
 259.5 
 250 . 2 
 
 297.6 
 
 288.0 
 278.4 
 268.8 
 259.3 
 
 307.9 
 298.0 
 
 288.2 
 278.3 
 268.4 
 
 318.2 
 308.0 
 297.9 
 
 287.7 
 277.5 
 
 328.4 
 318.0 
 307.4 
 297.0 
 286.5 
 
 338 . 7 
 327.9 
 317.2 
 306.4 
 295.6 
 
 348.9 
 337.8 
 326.8 
 315.7 
 304.7 
 
 359 . 1 
 347.8 
 336.4 
 325 . 1 
 313.7 
 
 369.4 
 357.8 
 346.1 
 334.5 
 322.8 
 
 42 
 44 
 46 
 48 
 50 
 
 240.9 
 231.6 
 222.4 
 213.0 
 203.7 
 
 249.7 
 240.1 
 230.5 
 220.9 
 211.3 
 
 258.5 
 248.6 
 238.7 
 228.8 
 219.0 
 
 267.3 
 257.1 
 246.9 
 236.8 
 226.6 
 
 276.1 
 265.6 
 255 . 1 
 244.7 
 234.2 
 
 284.8 
 274.1 
 263.4 
 252.6 
 241.8 
 
 293.6 
 282.5 
 271.5 
 260.4 
 249.4 
 
 302.4 
 291.0 
 279.7 
 268.3 
 257.0 
 
 311.2 
 299.6 
 287.9 
 276.2 
 264.6 
 
 To the above weight of column shafts add the weight of rivets. 
 
480 
 
 DIMENSIONS OF Z-BAR COLUMNS. 
 
 DIMENSIONS OF Z-BAR COLUMNS. 
 
 CARNEGIE SECTIONS. 
 
 16" COLUMNS. 
 Section: 4 Z-bars 6V6" X K". 1 web-plate 10" X 1". 2 side plates 16" wide. 
 
 SfevSqsrtf _SJ 
 
 Thickness 
 of side 
 plates. 
 
 A 
 
 B 
 
 C 
 
 D 
 
 X 
 
 P 
 
 F.I 
 
 1 s 
 
 T 1 to 
 
 1/2 
 9/16 
 5/8 
 11/16 
 3/4 
 13/16 
 7/8 
 15/16 
 1 
 
 219/16 
 
 21-M 16 
 
 2113/16 
 2115/16 
 
 22 
 
 7|! 6 
 
 1H 
 
 iy s 
 
 1H 
 
 12j| 
 12 
 
 
 1x M 
 
 K^7 "^s" *zjtf~~** w . 
 
 ' l a 
 
 18" COLUMNS. 
 
 Section : 4 Z-bars 6 1 A" X V&". 1 web-plate 12" X 1". 
 2 side plates 18" wide. 
 
 j^c^^fi 5 
 
 Thickness 
 of side 
 plates. 
 
 A 
 
 B 
 
 7%6 
 
 7V2 6 
 
 C 
 
 D 
 
 <\!^ 
 ^ 
 
 Lk,^y 
 
 r ! 
 
 4 2 
 
 1/2 
 9/16 
 5/8 
 11/16 
 3/4 
 13/16 
 7/8 
 15/16 
 
 ^^c \-f J^S\w\o 
 co coco co co co^ob co" 
 
 <N CS (N <N <M <M (N (N <M 
 
 IK 
 
 V S 
 
 IK 
 IK 
 IK 
 
 14H 
 
 14M 
 14M 
 
 14M 
 14M 
 
 3 
 
 f -g 
 
 ^^ f 
 X i "Q 
 
 fc? X CTf"*" d 
 
STRENGTH OF Z-BAR COLUMNS. 
 
 481 
 
 TABLE XVIII. SAFE LOADS IN TONS OF 2,000 LBS. 
 FOR STEEL Z-BAR COLUMNS WITH SQUARE ENDS 
 
 (continued) 
 
 ( 12,000 Ibs. for lengths of 90 radii or under. 
 Allowed strains per square inch:-\ .,_ in _ c _ I f . ,, 
 
 / 17,100 57 for lengths *over 90 radii, 
 v ( 
 
 16" Z-BAR COLUMNS. 
 Section: 4 Z-bars 6H"XJi". 1 web-plate 10" X 1". 2 side plates 16" wide. 
 
 
 
 
 
 jS, 
 
 
 ^ 
 
 
 CO 
 
 
 d 
 
 i 
 
 10 
 
 CO 
 
 CO 
 
 aid 
 
 as 
 
 o' 
 
 CO . 
 CO pj 
 
 iO 
 
 d . 
 
 "d 
 
 i 
 
 3 
 
 (N"" 1 . O' 
 
 1^ 
 
 <N "~1 d 
 
 i'Ss 
 
 7 crlo 
 
 2 O 1 ^ 
 
 (N'^fN 
 
 ,i3 
 
 |i| 
 
 f'd-S 
 
 r o 
 
 o 
 
 ^ II 
 
 ^SA 
 
 h Ii 
 
 ISA 
 
 |^A 
 
 -ISA 
 
 15JI 
 
 ioA 
 
 ial 
 
 c 
 
 "H^ d 
 
 Q-<CO 
 
 "a 1 ^ d 
 
 ^^ii" ^ 
 
 13, || d 
 
 w^j* C 
 
 'H t n" d 
 
 d 
 
 ^2 d 
 
 rG . 
 
 \oi ll/p 
 
 JS .3 
 
 N* .3 
 
 ^ .3 
 
 \-f .'3 
 
 * . S 
 
 ^ -S 
 
 i^ .S 
 
 "s 
 
 fa & 
 
 v) S 1 ' 
 
 X.S^"' 
 
 xJS ^ 
 
 xJS^ 
 
 SX'Q V -' 
 
 X-D^^ 
 
 X-O^^ 
 
 y S^' 
 
 y 8*5 
 
 3^ 
 
 CD"" *" 
 
 co^ 
 
 co"" 
 
 CD"" 1 
 
 CD""* 
 
 co" ^ 
 
 co""" ' 
 
 CD""" ** 
 
 CD^ *" 
 
 32 and 
 
 
 
 
 
 
 
 
 
 
 under 
 
 400.1 
 
 412.1 
 
 424.1 
 
 436 . 1 
 
 448.1 
 
 460.1 
 
 472.1 
 
 1^4.1 
 
 496.1 
 
 34 
 
 397 . 7 
 
 409.8 
 
 421.9 
 
 433.9 
 
 446.0 
 
 458.1 
 
 470.2 
 
 482 . 2 
 
 494.2 
 
 36 
 
 387.6 
 
 399.3 
 
 411.1 
 
 422.9 
 
 434.7 
 
 446.5 
 
 458.2 
 
 470.0 
 
 481.8 
 
 38 
 
 377 . 5 
 
 388 . 9 
 
 400.4 
 
 411.8 
 
 423.4 
 
 434.8 
 
 446 . 3 
 
 457.9 
 
 469.3 
 
 40 
 
 367.3 
 
 378.5 
 
 389.6 
 
 400.9 
 
 412.1 
 
 423.2 
 
 434.4 
 
 445.6 
 
 456.7 
 
 42 
 
 357.1 
 
 368.0 
 
 378.9 
 
 389.8 
 
 400.7 
 
 411.6 
 
 422.5 
 
 433.4 
 
 444.2 
 
 44 
 
 347.0 
 
 357.6 
 
 368.2 
 
 378.8 
 
 389.4 
 
 400.0 
 
 410.5 
 
 421.1 
 
 431.7 
 
 46 
 
 336 . 9 
 
 347.1 
 
 357.4 
 
 367.7 
 
 378.1 
 
 388.4 
 
 398.6 
 
 409.0 
 
 419.2 
 
 48 
 
 326 . 7 
 
 336 . 7 
 
 346.7 
 
 356.7 
 
 366.7 
 
 376.8 
 
 386.7 
 
 396.7 
 
 406.7 
 
 50 
 
 316.6 
 
 326.3 
 
 336.0 
 
 345.7 
 
 355.4 
 
 365.1 
 
 ,374.8 
 
 384.5 
 
 394.2 
 
 
 
 
 
 
 
 
 
 
 
 IS" Z-BAR COLUMNS. 
 Section: 4 Z-bars 6V6" X>s". 1 web-plate 12" X I". 2 side plates 18" wide. 
 
 
 
 
 
 q 
 
 
 CO 
 
 
 O5 
 
 
 fl 
 
 * 
 
 o 
 06 
 
 b 
 
 CO 
 
 q 
 
 00 
 
 w 
 
 CO 
 
 co 
 
 rt 
 
 d 
 
 M ^ 
 
 iO ^ 
 
 (N (H 
 
 it d . 
 
 (N ff 
 
 X ^ 
 
 <N d 
 
 ^ d 
 
 
 
 7'S-ss 
 
 ll'd-00 
 
 <N Irt .o' 
 
 J'SS 
 
 (N^.CD 
 
 II erg 
 
 !"cr1 
 
 <N trH . (N 
 
 I'S^ 
 
 w'^g 
 
 'o 
 
 C5 
 
 1^7 
 
 1^1 
 
 l<^7 
 
 1*7 
 
 03N- || 
 
 |gt 
 
 B **3 
 
 IJ? 
 
 l^ll 
 
 *O 
 
 r^H^^ 
 
 ^^^ 
 
 --; t^ _; 
 
 p,r>-^ 
 
 r^^^ 
 
 00 3 
 
 ^'d" 
 
 00 G" 
 
 11 00^ 
 
 5^- 
 
 Sls'J, 
 
 
 |]l 
 
 1-1 
 
 5 ".'a 
 
 ^ II. -g 
 
 ^ ".'a 
 
 ? "' 
 
 3 "' 
 
 "S 
 
 
 X^^~^ 
 
 
 xir 
 
 x-^ v ^ 
 
 X-S"^ 
 
 x^T 
 
 X-^V 
 
 xJS^ 
 
 3^ 
 
 oo*^ K . 
 
 a" 1 " 
 
 00^ ^ 
 
 s 
 
 &o rt ' 
 
 00"^ 
 
 oo rt ' 
 
 &"* 
 
 00^ 
 
 34 and 
 
 
 
 
 
 
 
 
 
 
 under 
 
 424.1 
 
 437.6 
 
 451.1 
 
 464.6 
 
 478.1 
 
 491.6 
 
 505 . 1 
 
 518.6 
 
 532.1 
 
 36 
 
 419.7 
 
 436.8 
 
 451.1 
 
 464.6 
 
 478.1 
 
 491.6 
 
 505 . 1 
 
 518.6 
 
 532 . 1 
 
 38 
 
 409.4 
 
 426.4 
 
 443.2 
 
 456.2 
 
 476.8 
 
 491.6 
 
 505.1 
 
 518.6 
 
 532.1 
 
 40 
 
 399.2 
 
 416.0 
 
 432.7 
 
 449.5 
 
 466.0 
 
 482.6 
 
 499.1 
 
 514.2 
 
 527.5 
 
 42 
 
 388.9 
 
 405.6 
 
 422.3 
 
 438.8 
 
 455.3 
 
 471.7 
 
 488.1 
 
 503.0 
 
 516.0 
 
 44 
 
 378 . 7 
 
 395 . 2 
 
 411.7 
 
 428.2 
 
 444 . 5 
 
 460.8 
 
 477.0 
 
 491.8 
 
 504.5 
 
 46 
 
 368.4 
 
 384.9 
 
 401.2 
 
 417.5 
 
 433.8 
 
 449.9 
 
 466.0 
 
 480.5 
 
 493.0 
 
 48 
 
 358.1 
 
 374.5 
 
 390.7 
 
 406.9 
 
 423.0 
 
 439.0 
 
 454.9 
 
 469.3 
 
 481.4 
 
 50 
 
 347.9 
 
 364.1 
 
 380.2 
 
 396.2 
 
 412.2 
 
 428.1 
 
 443.9 
 
 458.1 
 
 469.9 
 
482 CONSTANT-DIMENSION Z-BAR COLUMNS. 
 
 DIMENSIONS OF CONSTANT-DIMENSION 
 Z-BAR COLUMNS. 
 
 (CARNEGIE SECTIONS.) 
 
 ,rvtS3 
 
 if 
 
 [j-T 
 
 li? 
 
 ! i 
 j] 
 
 \ 
 \ 
 
 Q 
 
 | 
 
 IAS & 
 
 1 
 
 J 
 
 ,- . 
 
 ^ :t^ j\ 
 
 P4 
 
 \, 
 
 i 
 
 i 
 \ 
 
 A 
 
 ^n^i u 
 
 
 X 
 
 X 
 
 i ! 
 
 1 
 
 IT 
 y.j^ 
 
 II { f- 
 
 ^^S^I t^^ x 
 
 p 3 
 
 I'^ji-^r-^ 1 ^! 
 
 p .-?c 
 
 --^-Q^ u 
 
 Constant dimensions are given on the sketch above for all columns. 
 
 Variable dimensions, see below. All rivets %" diameter. Open holes for 
 
 z /i" rivets or bolts. 
 
 pllLs9"5l:"x 0- 8 ll''f for a11 ~ lum - >- than metal. 
 For all columns %" metal and over, tie-plates are Y%" thick. 
 All tie-plates spaced about 3'-0" centre to centre. 
 
 Size of Z-bars. 
 
 X S 
 
 ",, x ty" 
 
 "XV\Q" 
 4H6"X3 1 ^ // X 1 A" 
 
 4 l /s" X 33/16^ X%" 
 
 4H" 
 
 41/16" 
 
 3^0," 
 
STRENGTH OF Z-BAR COLUMNS. 
 
 483 
 
 TABLE XIX. SAFE LOADS IN TONS OF 2,CCO LBS. FOR 
 CONSTANT-DIMENSION Z-BAR COLUMNS, SQUARE 
 ENDS. 
 
 12,000 Ibs. for lengths of 90 radii or under. 
 17,100-57 for lengths over 90 radii. 
 
 Allowed stresses per square inch: 
 
 Section: 4 Z-bars 4" deep with tie-plates. 
 
 
 V* 
 
 *Vfl w 
 
 l?j 
 
 * <" 
 
 ^5 
 
 * 
 
 Vis 
 
 ^w" 5 
 
 v 
 
 d 
 
 Xoo 
 
 #* 
 
 X&* 
 
 Xco 
 
 X^ 
 
 X^ 
 
 X^ 
 
 Xco 
 
 ^J 
 
 c2\ 
 Xco 
 
 E] 
 
 ^ <N<N 
 
 ^3 
 
 o oo 
 
 ^irjo' 
 
 ^\coc<i 
 
 ^THO 
 
 ^100 
 
 XeoO 
 
 vS^'od 
 
 1 
 
 <+-< . 
 
 d| 
 
 M^ 
 93 
 
 IP 
 
 co d5 
 
 ?dv2> 
 
 X'^.co 
 
 X'^.co 
 
 \ocOOjH 
 
 r-K .^ 
 
 co^floq 
 
 5^OI> 
 
 x^. 
 
 ^ .co 
 
 & o> 
 
 TH tcfl 
 
 $<" d 
 
 ^ M d 
 
 " ri 
 
 
 \ 02 
 
 ^ ^ d 
 
 S^ "d" 
 
 ^ ^''d 
 
 jp 
 
 Sa'9 
 
 ?s*i 
 
 
 3*1 
 
 S?1 
 
 fffi 
 
 ^' 
 
 ?S-| 
 
 
 
 28 and 
 
 
 
 
 
 
 
 
 
 
 under 
 
 
 
 
 97 2 
 
 111 8 
 
 126 5 
 
 133 2 
 
 147 4 
 
 162 
 
 30 
 
 57.8 
 
 72.7 
 
 87.8 
 
 96.9 
 
 111.2 
 
 125 '.5 
 
 131.3 
 
 144.9 
 
 158.9 
 
 32 
 
 56.7 
 
 71.1 
 
 85.6 
 
 94.1 
 
 108.0 
 
 121.8 
 
 127.4 
 
 140.6 
 
 154.1 
 
 34 
 
 55.0 
 
 69.0 
 
 83.1 
 
 91.4 
 
 104.8 
 
 118.2 
 
 123.5 
 
 136.2 
 
 149.3 
 
 36 
 
 53.4 
 
 67.0 
 
 80.6 
 
 88.6 
 
 101.6 
 
 114.5 
 
 119.6 
 
 131.9 
 
 144.5 
 
 40 
 
 50.2 
 
 62.9 
 
 75.7 
 
 83.0 
 
 95.2 
 
 107.2 
 
 111.8 
 
 123.2 
 
 134.9 
 
 Section: 4 Z-bars 4" deep; 4 // X3^je' / X;H?" with web-plates. 
 
 jj 
 
 . 
 
 J 
 
 4 
 
 4 
 
 4 
 
 J 
 
 J 
 
 j- 
 
 _g 
 
 "S 
 
 J% 
 
 *"J 
 
 00 
 
 v <N 
 
 CO 
 
 
 
 
 ,12 
 
 a 
 
 %oS * 
 
 *o* 
 
 
 ^S<X> 
 
 
 v CO 
 
 5 ^ . 
 
 Gi 
 
 ^t . 
 
 'o 
 
 x! 
 
 X^^ 
 
 x^5 
 
 x^S 
 
 X^ 
 
 x^i 
 
 x^S 
 
 xi 
 
 ^S 
 
 o 
 
 
 
 
 
 
 
 
 
 
 * 
 
 oo'^.co* 
 
 00*1 CO* 
 
 00'^ CO 
 
 oo'^.co 
 
 oo'^ co 
 
 oo.S co 
 
 oo.S co 
 
 oo.S co 
 
 oo.S co 
 
 II 
 
 ll| 
 
 JQ 1 -^^ 
 00 a 
 
 III 
 
 III 
 
 i^a 
 
 ^ 
 
 cr7 
 
 -g cc.w 
 
 ' D 1 *^? 
 
 "S 
 
 cS O* M 
 
 III 
 
 ^^ 
 
 <Nc5f 
 
 <N^T 
 
 <NCO 5. 
 
 <NW'T 
 
 & N^-' 
 (NCO ?. 
 
 (NCO !^ 
 
 WW Jv 
 
 tttt I* 
 
 (N rjn j> 
 
 26 and 
 
 
 
 
 
 
 
 
 
 
 under 
 
 169.2 
 
 175.2 
 
 181.2 
 
 187.2 
 
 193.2 
 
 205.2 
 
 217.2 
 
 229.2 
 
 241.2 
 
 28 
 
 166.4 
 
 171.5 
 
 176.6 
 
 181.7 
 
 186.7 
 
 196.7 
 
 206.7 
 
 216.6 
 
 226.4 
 
 30 
 
 161.1 
 
 166.0 
 
 170.8 
 
 175.6 
 
 180.4 
 
 189.9 
 
 199.3 
 
 208.7 
 
 218.0 
 
 32 
 
 155.8 
 
 160.4 
 
 165.0 
 
 169.5 
 
 174.1 
 
 183.1 
 
 192.0 
 
 200.9 
 
 209.6 
 
 34 
 
 150.4 
 
 154.8 
 
 159.1 
 
 163.5 
 
 167.7 
 
 176.2 
 
 184.7 
 
 193.0 
 
 201.3 
 
 36 
 
 145.1 
 
 149.2 
 
 153.3 
 
 157.4 
 
 161.4 
 
 169.4 
 
 177.3 
 
 185.1 
 
 192.9 
 
 40 
 
 134.4 
 
 138.1 
 
 141.7 
 
 145.2 
 
 148.8 
 
 155.7 
 
 162.6 
 
 169.4 
 
 176.1 
 
 Section: 4 Z-bars 4" deep; 
 
 X 3%$" X W with web-plates. 
 
 Length of column 
 in feet. 
 
 ill 
 
 1 
 
 2 plates 8" XW 
 45 sq. in. 153 Ibs. 
 r (min.) 3.3192. 
 
 oo ^ co 
 
 flJ 
 
 v ra 
 
 S^oJ 
 
 Jfl^ 
 '5.S 
 
 (N'O j^ 
 
 oo '"'co 
 
 li? 
 
 oo^.co 
 
 (NIC J* 
 
 oo^co 
 
 is 
 
 (NO * 
 
 22 and 
 under 
 
 
 
 
 
 
 
 318.0 
 
 330.0 
 
 342.0 
 
 24 
 26 
 28 
 30 
 32 
 34 
 36 
 40 
 
 246.0 
 243.4 
 235.1 
 226.9 
 218.7 
 210.4 
 202.2 
 185.7 
 
 258.0 
 253.8 
 245.1 
 236.3 
 227.5 
 218.8 
 210.0 
 192.5 
 
 270.0 
 264.2 
 254.9 
 245.7 
 236.4 
 227.1 
 217.8 
 199 . 3 
 
 282.0 
 274.5 
 264.7 
 254.9 
 245.2 
 235 . 4 
 225.6 
 206.0 
 
 294.0 
 284.8 
 274.5 
 264.2 
 253.9 
 243.6 
 233.2 
 212.6 
 
 306.0 
 295.1 
 284.2 
 273.4 
 262.6 
 251.7 
 240.9 
 219.2 
 
 316.7 
 305.3 
 293.9 
 282.6 
 271.2 
 259.8 
 248.4 
 225.7 
 
 327.4 
 315.5 
 303.6 
 291.7 
 279.8 
 -267.8 
 255.9 
 232.1 
 
 338.1 
 325.6 
 313.2 
 300.7 
 288.3 
 275.9 
 263 . 4 
 238.5 
 
484 STRENGTH OF PHOENIX STEEL COLUMNS. 
 
 TABLE XX. DIMENSIONS AND SAFE CONCENTRIC 
 LOADS FOR PHGENIX STEEL COLUMNS. 
 
 (For description of column, see page 440.) 
 The dimensions given in the following table are subject to 
 such slight variations as are unavoidable in the manufacture of 
 these shapes. 
 
 The weights given are those of the segments composing the 
 columns, and from 2 to 5 per cent, must be added for weight of 
 the rivet-heads. 
 
 The A, B 1 , B 2 , and C columns have each 4 segments, the E 
 have 6, and the G have 8 segments. 
 
 Any desired thickness between the minimum and maximum 
 can be furnished. 
 
 ( 14,000 Ibs. for lengths of 70 
 radii or under. 
 
 Allowed strains per sq. inch 
 
 17,100-57-, for lengths over 
 70 radii. 
 
 One segment. 
 
 Diameters in inches. 
 
 One column. 
 
 Safe load in 
 net tons for 
 
 Thickness in 
 inches. 
 
 li 
 fi 
 
 d 
 4 
 
 HH 
 
 D 
 
 O 
 
 
 
 6^6 
 
 6% 6 
 
 sif 
 
 Q) 02 CD 
 
 1*4 
 
 ill 
 
 05 
 
 ''S 2 S 
 
 SI 
 
 0) fl 
 
 1.45 
 1.50 
 1.55 
 1.59 
 
 1 
 
 21.7 
 27.9 
 34.2 
 40.5 
 
 41.2 
 50.7 
 59.8 
 69.5 
 84.0 
 93.8 
 103.6 
 
 OJ3 
 
 |> 
 
 18.1 
 23.9 
 29.0 
 34.7 
 
 1 
 1 
 1 
 
 % 
 
 9.7 
 
 12.2 
 14.8 
 17.3 
 
 16.3 
 19.9 
 23.5 
 27.0 
 30.6 
 34.2 
 37.7 
 
 A 
 
 4 
 
 3.8 
 4.8 
 5.8 
 6.8 
 
 12.9 
 16.3 
 19.7 
 23.1 
 
 B.1 
 
 5*f 
 
 5% 
 
 6 8 
 
 i 
 
 6.4 
 7.8 
 9.2 
 10.6 
 12.0 
 13.4 
 14.8 
 
 21.8 
 26.5 
 31.3 
 36.0 
 40.8 ' 
 45.6 
 50.3 
 
 1.95 
 2.00 
 2.04 
 2.09 
 2.13 
 2.18 
 2.23 
 
 36.6 
 45.3 
 54.0 
 62.8 
 71.7 
 80.9 
 90.2 
 
 18.9 
 22.9 
 27.0 
 31.1 
 35.2 
 39.3 
 43.3 
 
 B.2 
 
 61%6 
 
 7^6 
 
 75/^6 
 
 9.^ 
 
 7.4 
 9.0 
 10.6 
 12.2 
 13.8 
 15.4 
 17.0 
 
 25.2 
 30.6 
 36.0 
 41.5 
 46.9 
 52.4 
 57.8 
 
 2.39 
 2.43 
 2.48 
 2.52 
 2.57 
 2.61 
 2.66 
 
 51.8 
 63.0 
 74.2 
 85.4 
 96.6 
 107.8 
 119.0 
 
 46.3 
 56.7 
 67.2 
 77.8 
 88.6 
 99.4 
 110.4 
 
 Least radius of gyration equals D X .3636. 
 
STRENGTH OF PHCENIX STEEL COLUMNS. 485 
 
 TABLE XX. SAFE LOAD IN TONS OF 2,000 LBS. PHCENIX 
 
 STEEL COLUMNS (continued). 
 ALLOWED STRAINS PER SQUARE INCH, 14,000 LBS. 
 
 One segment. 
 
 Diameters in inches. 
 
 One column. 
 
 . 
 
 m 02 
 
 a 
 
 d 
 
 D 
 
 Z>i 
 
 a 
 
 
 9*'. 
 
 |fl 
 
 
 
 - o3 
 
 
 
 
 
 
 
 
 
 -M >> 
 
 
 
 
 
 
 
 
 18 
 
 
 4 
 
 0> 
 
 1 
 
 8 1"2 
 
 .*8g 
 
 O j_, O 
 
 *" S 
 
 < <n^ 
 
 ^2 g 
 
 ^ 
 
 'S3 
 
 
 
 > a 
 
 <| M ra 
 
 
 8 fcO'2 
 
 CQO 
 
 R 
 
 1 
 
 Or 
 
 1 1 
 
 'o 
 
 5 
 
 
 
 J 
 
 S^~ 
 
 
 H 
 
 25% 
 
 
 7 18 /4 6 
 
 l^Vie 
 
 10.0 
 
 34.0 
 
 2.84 
 
 70.0 
 
 %6 
 
 31 
 
 
 715/46 
 
 11^ 
 
 12.1 
 
 41.3 
 
 2.88 
 
 84.7 
 
 
 36 
 
 
 8% 6 
 
 111%6 
 
 14.1 
 
 48.0 
 
 2.93 
 
 98.7 
 
 %6 
 
 41 
 
 
 8% 6 
 
 11% 
 
 16.0 
 
 54.6 
 
 2.97 
 
 112.0 
 
 % 
 
 46 
 
 
 S 5 /IQ 
 
 1115^6 
 
 18.0 
 
 61.3 
 
 3.01 
 
 126.0 
 
 9 /16 
 
 51 
 
 
 8^46 
 
 12 
 
 19.9 
 
 68.0 
 
 3.06 
 
 139.3 
 
 % 
 
 56 
 
 
 8%6 
 
 12^6 
 
 21.9 
 
 74.6 
 
 3.11 
 
 153.3 
 
 i-Vio 
 
 62 
 
 71 
 
 81-W.e 
 
 
 24.3 
 
 82.6 
 
 3.16 
 
 170.1 
 
 M 
 
 68 
 
 
 
 813/4(5 
 
 125/40 
 
 26.6 
 
 90.6 
 
 3.20 
 
 186.2 
 
 J % 6 
 
 73 
 
 78 
 
 
 9^T 
 
 12% 6 
 
 12% 
 
 28.6 
 30.6 
 
 97.3 
 
 104.0 
 
 3.24 
 3.29 
 
 200.3 
 214.2 
 
 1 
 
 89 
 
 
 
 12% 
 
 34.8 
 
 118.6 
 
 3.34 
 
 243.6 
 
 
 99 
 
 
 9%6 
 
 
 38.8 
 
 132.0 
 
 3.48 
 
 271.7 
 
 IK 
 
 109 
 
 
 9iyi 6 
 
 13 
 
 42.7 
 
 145.3 
 
 3.57 
 
 298.9 
 
 y 
 
 28 
 
 
 H 9 /46 
 
 15% 
 
 16.5 
 
 56.0 
 
 4.20 
 
 115.3 
 
 5 A& 
 
 32^ 
 
 
 lll^g 
 
 15% 
 
 19.1 
 
 65.0 
 
 4.25 
 
 133.8 
 
 
 37 
 
 
 1113/16 
 
 15M 
 
 21.7 
 
 74.0 
 
 4.29 
 
 152.0 
 
 1J> 
 
 42 
 
 
 
 15% 
 
 24.7 
 
 84.0 
 
 4.34 
 
 173.0 
 
 I/ 
 
 47 
 
 
 12^4 6 6 
 
 
 27.6 
 
 94,0 
 
 4.38 
 
 193.2 
 
 %6 
 
 52 
 57 
 
 E 
 
 12% 6 
 
 16M6 6 
 
 163/46 
 
 30.6 
 33.5 
 
 104.0 
 114.0 
 
 4.43 
 4.48 
 
 214.1 
 234.7 
 
 1^ 
 
 62 
 
 1 1 \/ 
 
 127/46 
 
 16 B A6 
 
 36.4 
 
 124.0 
 
 4.52 
 
 255.0 
 
 *J 
 
 68 
 
 H/16 
 
 12/16 
 
 
 40.0 
 
 136.0 
 
 4.56 
 
 280.0 
 
 184 
 
 73 
 
 
 121^16 
 
 16%6 
 
 43.0 
 
 146.0 
 
 4.61 
 
 300.6 
 
 7/ 
 
 78 
 
 
 
 
 45.9 
 
 156.0 
 
 4.66 
 
 321.2 
 
 1 
 
 88 
 
 
 13Me 
 
 1613,46 
 
 51.7 
 
 176.0 
 
 4.73 
 
 362.0 
 
 ij| 
 
 98 
 108 
 
 
 135/16 
 
 17^6 
 175^6 
 
 57.6 
 63.5 
 
 196.0 
 216.0 
 
 4.84 
 4.93 
 
 403.2 
 444.7 
 
 ~~e/ 
 
 31 
 
 
 15K 
 
 19% 
 
 24.2 
 
 82.6 
 
 5.54 
 
 17.0 
 
 ^* 
 
 36 
 
 
 jga/ 
 
 
 28.1 
 
 96.0 
 
 5.59 
 
 190.7 
 
 74 
 
 41 
 
 
 1KI/ 
 
 19% 
 
 32.0 
 
 109.3 
 
 5.64 
 
 226.0 
 
 I/ 
 
 46 
 
 
 1 C5/ 
 
 191^6 
 
 36.0 
 
 122.6 
 
 5.68 
 
 254.0 
 
 9 /lQ 
 
 51 
 56 
 61 
 
 G 
 
 16 
 
 19M 
 19% 
 20 
 
 39.9 
 
 43.8 
 
 47.7 
 
 136.0 
 149.3 
 162.6 
 
 5.73 
 5.77 
 
 5.82 
 
 282.0 
 300.4 
 337.9 
 
 $ 
 
 66 
 71 
 
 14f 
 
 
 20% 
 20M 
 
 51.7 
 55.6 
 
 176.0 
 189.3 
 
 5.88 
 5.91 
 
 363.0 
 382.2 
 
 7/ 
 
 76 
 
 
 163/ 
 
 20% 
 
 59.6 
 
 202.6 
 
 5.95 
 
 419.3 
 
 1% 
 
 86 
 96 
 106 
 116 
 
 
 16% 
 16% 
 17% 
 17% 
 
 20% 
 20% 
 21 
 
 67.4 
 75.3 
 83.1 
 90.9 
 
 229.3 
 256.0 
 282.6 
 309.3 
 
 6.04 
 6.13 
 6.27 
 6.32 
 
 477.0 
 522.3 
 587.0 
 636.3 
 
 Least radius of gyration equals D X .3636. 
 
486 STRENGTH OF LARIMER STEEL COLUMNS. 
 
 TABLE XXI. SAFE LOADS IN TONS OF 2,000 LBS., LARI- 
 MER STEEL COLUMNS. 
 
 j 12,000 Ibs. for lengths of 90 radii or under. 
 Allowed strain per square inch, -j 17iloo _ 57 _l for lengths over 90 radii . 
 
 16" COLUMNS. 
 Made of 15" beams. Weight of filler bar 10.5 Ibs. per foot. 
 
 " rivets. 
 
 1 1 
 
 o-fl 
 
 *o 
 
 1 
 
 
 T. ;. : rj'J^rr" 
 
 rl 
 
 2-"S 
 
 
 1| 
 
 
 
 Qr3 
 
 <5 . 
 
 *d 
 
 
 Length of column 
 
 i s^'- I ' 
 
 ^ g> 
 
 ** S 
 
 a & 
 
 if 
 
 in feet. 
 
 
 S2 
 
 1?! 3 
 
 r3 
 
 ' 
 
 8 8> 
 
 
 j \ / ? 
 
 0) O 
 
 
 Jo 
 
 
 
 
 1 
 
 Pf 
 
 
 9 
 
 
 
 
 Lbs. 
 
 Lbs. 
 
 Sq.ins. 
 
 Inches. 
 
 32 and 
 under. 
 
 36 
 
 40 
 
 A 
 
 B 
 
 C 
 
 60 
 
 131.25 
 
 38.4 
 
 4.36 
 
 232 
 
 220 
 
 208 
 
 16" 
 
 17Ho" 
 
 6" 
 
 55 
 
 121.25 
 
 35.7 
 
 4.10 
 
 210 
 
 198 
 
 186 
 
 16*6 
 
 171/16 
 
 5% 
 
 50 
 
 111.25 
 
 32.8 
 
 4.18 
 
 195 
 
 184 
 
 173 
 
 16 
 
 17 
 
 521/82 
 
 45 
 
 101.25 
 
 29.8 
 
 4.28 
 
 179 
 
 169 
 
 160 
 
 1 529/30 
 
 16i^lo 
 
 5 9 /16 
 
 42 
 
 95.25 
 
 28.1 
 
 4.32 
 
 169 
 
 160 
 
 151 
 
 
 16% 
 
 
 13" COLUMNS. 
 
 Made of 12" beams. Weight of filler bar 10.5 Ibs. per foot. %" rivets. 
 
 Lbs. 
 
 Lbs. 
 
 Sq.ins. 
 
 Inches. 
 
 24 and 
 
 under. 
 
 28 
 
 32 
 
 A 
 
 B 
 
 C 
 
 45 
 
 101.25 
 
 29.7 
 
 3.40 
 
 178 
 
 170 
 
 158 
 
 13" 
 
 14^ e " 
 
 t$/tt 
 
 40 
 
 91.25 
 
 26.8 
 
 3.50 
 
 161 
 
 156 
 
 145 
 
 
 13iju 
 
 514 
 
 35 
 
 81.25 
 
 23.7 
 
 3.42 
 
 142 
 
 136 
 
 127 
 
 12% 
 
 131%6 
 
 5%2 
 
 31.5 
 
 74.25 
 
 21.6 
 
 3.51 
 
 130 
 
 126 
 
 118 
 
 121%6 
 
 13H 
 
 5 
 
 11" COLUMNS. 
 
 Made of 10" beams. Weight of filler bar 10.5 Ibs. per foot. %" rivets. 
 
 Lbs. 
 
 Lbs. 
 
 Sq.ins. 
 
 Inches. 
 
 22 and 
 under. 
 
 24 
 
 28 
 
 A 
 
 B 
 
 C 
 
 30 
 
 71.25 
 
 20.8 
 
 2.84 
 
 123 
 
 118 
 
 108 
 
 10%" 
 
 111%6* 
 
 413/ 16 " 
 
 25 
 
 61.25 
 
 17.8 
 
 2.94 
 
 107 
 
 103 
 
 94 
 
 1025/32 
 
 il-H 
 
 421/32 
 
 10" COLUMNS. 
 
 Made of 9" beams. Weight of filler bar 10.5 Ibs. per foot. %" rivets. 
 
 Lbs. 
 
 Lbs. 
 
 Sq.ins. 
 
 Inches. 
 
 20 and 
 under. 
 
 24 
 
 28 
 
 A 
 
 B 
 
 C 
 
 25 
 
 61.25 
 
 18.1 
 
 2.57 
 
 106 
 
 97 
 
 87 
 
 9H" 
 
 1013/16" 
 
 4i% 2 " 
 
 21 
 
 53.25 
 
 15.7 
 
 2.66 
 
 94 
 
 86 
 
 78 
 
 ^ 
 
 101*6 
 
 
STRENGTH OF LARIMER STEEL COLUMNS. 487 
 
 TABLE XXI. SAFE LOADS IN TONS OF 2,000 LBS., LARI- 
 MER STEEL COLUMNS (continued). 
 
 ( 12,000 Ibs. for lengths of 90 radii or under. 
 Allowed strain per square inch, < , _ ., _. __ I . 
 
 | 17,100 57 for lengths over 90 radii. 
 
 9" COLUMNS. 
 
 Made of 8" beams. Weight of filler bar 6 Ibs. per foot. %" rivets in 
 web. M" rivets in flange. 
 
 te'J 
 
 -Jf O 
 
 "8 
 
 ft 
 
 
 jljjjjj 
 
 
 IS 
 
 
 fj 
 
 
 f /' t ^\"*St 
 
 QJ <U 
 
 ^ 
 
 03 . 
 
 
 Length of column 
 
 i li Jc / / 
 
 fl 
 
 5a| 
 
 A g.J 
 
 ^ 
 C g 
 
 l| 
 
 in feet. 
 
 1 \ j 4 
 
 c 
 
 
 '-"0 
 
 'So 
 
 
 L^^^L^y' / 
 
 
 
 f 
 
 W 
 
 S 
 
 
 ^ 
 
 Lbs. 
 
 Lbs. 
 
 Sq.ins. 
 
 Inches. 
 
 18 and 
 under. 
 
 20 
 
 24 
 
 A 
 
 B 
 
 C 
 
 22.75 
 
 52.0 
 
 15.4 
 
 2.37 
 
 91 
 
 86 
 
 77 
 
 9 " 
 
 9 15 /16 // 
 
 4 3 /16 // 
 
 20.25 
 
 47.0 
 
 13.9 
 
 2.41 
 
 83 
 
 79 
 
 71 
 
 81%6 
 
 913/i 6 
 
 4% 2 
 
 17.75 
 
 42.0 
 
 12.4 
 
 2.47 
 
 75 
 
 72 
 
 65 
 
 m 
 
 
 4 
 
 8" COLUMNS. 
 
 Made of 7" beams. Weight of filler bar 6 Ibs. per foot. Y%' rivets. 
 
 Lbs. 
 
 Lbs. 
 
 Sq.ins. 
 
 Inches 
 
 16 and 
 under. 
 
 20 
 
 24 
 
 - A 
 
 B 
 
 C 
 
 20.0 
 
 46.5 
 
 13.6 
 
 2.10 
 
 81 
 
 72 
 
 63 
 
 8 " 
 
 & 7 /8," 
 
 3 7 A" 
 
 17.5 
 
 41.5 
 
 12.1 
 
 2.12 
 
 72 
 
 64 
 
 56 
 
 715/16 
 
 SM 
 
 3M 
 
 15.0 
 
 36.5 
 
 10.6 
 
 2.16 
 
 64 
 
 57 
 
 50 
 
 
 8Xs 
 
 32^32 
 
 1" COLUMNS. 
 
 Made of 6" beams. Weight of filler bar 6 Ibs. per foot. Y%' rivets. 
 
 Lbs. 
 
 Lbs. 
 
 Sq.ins. 
 
 Inches. 
 
 14 and 
 under. 
 
 16 
 
 20 
 
 A 
 
 B 
 
 C 
 
 14.75 
 
 36 
 
 10.5 
 
 1.85 
 
 62 
 
 58 
 
 50 
 
 61 5 /16" 
 
 7-M /7 
 
 3%e" 
 
 12.25 
 
 31 
 
 9.0 
 
 1.88 
 
 54 
 
 51 
 
 44 
 
 613/16 
 
 79/16 
 
 3H/32 
 
 6" COLUMNS. 
 
 Made of 5" beams. Weight of filler bar 6 Ibs. per foot. Y%" rivets in 
 
 web. 3^" rivets in flange. 
 
 Lbs. 
 
 Lias. 
 
 Sq.Ii* 
 
 Inches. 
 
 12 and 
 under. 
 
 16 
 
 20 
 
 A 
 
 B 
 
 C 
 
 12.25 
 
 31 
 
 9.0 
 
 1.56 
 
 53 
 
 45 
 
 37 
 
 5 1 %e" 
 
 6M" 
 
 ZH" 
 
 9.75 
 
 26 
 
 7.5 
 
 1.62 
 
 45 
 
 39 
 
 32 
 
 51% Q 
 
 6/16 
 
 3 
 
488 STRENGTH OF NURICK STEEL COLUMNS. 
 
 TABLE XXII. DIMENSIONS AND SAFE LOADS FOR 
 NURICK STEEL COLUMNS. 
 
 (JONES & LAUGHLINS, PROPRIETORS.) 
 
 p = 17,100 -57- for lengths over 90 radii, and 12,000 Ibs. for 90 radii 
 and under. 
 
 Inches 
 
 15 
 12 
 
 10 
 9 
 
 Lbs 
 
 45 
 40 
 33 
 35 
 30 
 25 
 
 20 
 15 
 20 
 15 
 
 14H 
 
 10% 
 8 
 9 
 
 -S*? 
 
 1M 
 
 Lbs. 
 
 183 
 163 
 135 
 143 
 123 
 103 
 85 
 
 83 
 63 
 83 
 63 
 53 
 
 68 
 58 
 48 
 62 
 52 
 42 
 
 44 
 34 
 38 
 
 28 
 
 o3 . 
 
 c S 
 .2-2 
 
 Sq.ins. 
 
 53.8 
 
 47.9 
 
 39.6 
 
 41.18 
 
 35.38 
 
 29.39 
 
 24.12 
 
 23.40 
 17.84 
 23.51 
 17.60 
 15.55 
 
 19.29 
 16.35 
 13.40 
 17.20 
 14.26 
 11.39 
 
 12.48 
 9.52 
 
 10.73 
 7.79 
 
 Sg 
 
 S 
 
 Inches 
 
 6.58 
 6.50 
 6.45 
 5.41 
 5.43 
 5.43 
 5.45 
 
 4.59 
 4.53 
 4.09 
 4.10 
 4.11 
 
 3.57 
 3.63 
 3.65 
 3.21 
 3.23 
 3.25 
 
 2.76 
 
 2.85 
 2.36 
 
 2.42 
 
 Tons. 
 
 323 
 287 
 237 
 247 
 212 
 176 
 145 
 
 140 
 107- 
 134 
 100 
 89 
 
 102 
 87 
 72 
 85 
 70 
 56 
 
 24ft. 
 
 69 
 54 
 54 
 40 
 
 Tons. 
 
 323 
 287 
 237 
 247 
 212 
 176 
 145 
 
 140 
 107 
 141 
 105 
 93 
 
 116 
 98 
 80 
 103 
 85 
 68 
 
 18ft. 
 
 and 
 
 under 
 
 75 
 
 57 
 
 63 
 
 46 
 
 125/4 6 
 12% 6 
 
 21 3 /8 
 
 21% 2 
 
 1^6 
 
 16i% 6 
 
 13i5/4 e 
 
 12 3 4 
 
 lift 
 
 11% 
 
 92% 2 
 
 9H4 6 
 
 22% 2 
 
 18% 
 18%e 
 
 16 
 1513/46 
 
 14% 
 
 13% 2 
 13*4 
 
 12V82 
 
 ll 13 /4 6 
 
 10/4 6 
 
 i" rivets in last four sections, %" rivets in all others. 
 
STRENGTH OF GRAY STEEL COLUMNS. 489 
 
 TABLE XXIII. SAFE LOADS FOR GRAY COLUMNS. 
 
 Computed by the formula PF = 17,100 57-. 
 12" SQUARE COLUMNS. 
 
 nieces. 
 
 Dimensions 
 of angles. 
 
 Properties. 
 
 Safe loads in thousands of 
 pounds. 
 
 *p 
 
 
 
 
 
 
 Column lengths. 
 
 d 
 fc 
 
 Length 
 of legs. 
 
 Thick. 
 
 Area, 
 square 
 ins. 
 
 7. 
 
 r. 
 
 
 12ft. 
 
 16ft. 
 
 20ft. 
 
 30ft. 
 
 fS 
 
 2^X2^ 
 
 5/16 
 
 11.76 
 
 172 
 
 3.8 
 
 175 
 
 165 
 
 160 
 
 140 
 
 
 8 
 
 2^X2^ 
 
 3/8 
 
 13.84 
 
 202 
 
 3.8 
 
 205 
 
 195 
 
 185 
 
 160 
 
 
 8 
 
 3 X2^ 
 
 5/16 
 
 12.96 
 
 198 
 
 3.9 
 
 195 
 
 185 
 
 175 
 
 150 
 
 
 8 
 
 3 X2y 2 
 
 3/8 
 
 15.36 
 
 234 
 
 3.9 
 
 230 
 
 220 
 
 205 
 
 180 
 
 
 8 
 
 3 X3 
 
 5/16 
 
 14.24 
 
 206 
 
 3.8 
 
 210 
 
 200 
 
 190 
 
 165 
 
 
 8 
 
 3 X3 
 
 3/8 
 
 16.88 
 
 241 
 
 3.8 
 
 250 
 
 240 
 
 225 
 
 195 
 
 
 8 
 
 3 X3 
 
 7/16 
 
 19.52 
 
 276 
 
 3.8 
 
 290 
 
 275 
 
 260 
 
 225 
 
 J8 
 
 3 X3^ 
 
 5/16 
 
 15.44 
 
 209 
 
 3.7 
 
 230 
 
 215 
 
 205 
 
 180 
 
 a |8 
 
 3 X3^ 
 
 3/8 
 
 18.40 
 
 245 
 
 3.7 
 
 270 
 
 260 
 
 245 
 
 210 
 
 
 8 
 
 3 X3^ 
 
 7/16 
 
 21.20 
 
 282 
 
 3.7 
 
 315 
 
 300 
 
 280 
 
 245 
 
 
 8 
 
 3 X3^ 
 
 1/2 
 
 24.00 
 
 318 
 
 3.7 
 
 355 
 
 340 
 
 320 
 
 275 
 
 
 8 
 
 3 X4 
 
 5/16 
 
 16.72 
 
 213 
 
 3.5 
 
 245 
 
 230 
 
 220 
 
 185 
 
 
 8 
 
 3 X4 
 
 3/8 
 
 19.84 
 
 249 
 
 3.5 
 
 290 
 
 275 
 
 260 
 
 220 
 
 
 8 
 
 3 X4 
 
 7/16 
 
 22.96 
 
 285 
 
 3.5 
 
 335 
 
 320 
 
 300 
 
 255 
 
 
 8 
 
 3 X4 
 
 1/2 
 
 26.00 
 
 321 
 
 3.5 
 
 380 
 
 360 
 
 340 
 
 290 
 
 18 
 
 3 X4 
 
 9/16 
 
 28.96 
 
 357 
 
 3.5 
 
 425 
 
 405 
 
 380 
 
 325 
 
 f8 
 
 3 X5 
 
 3/8 
 
 22.88 
 
 255 
 
 3.3 
 
 335 
 
 315 
 
 295 
 
 250 
 
 J8 
 
 3 X5 
 
 7/16 
 
 26.48 
 
 291 
 
 3 3 
 
 385 
 
 365 
 
 340 
 
 290 
 
 Ms 
 
 3 X5 
 
 1/2 
 
 30.00 
 
 327 
 
 3.3 
 
 435 
 
 410 
 
 385 
 
 325 
 
 18 
 
 3 X5 
 
 9/16 
 
 33.44 
 
 363 
 
 3.3 
 
 485 
 
 460 
 
 430 
 
 365 
 
 14" SQUARE COLUMNS. 
 
 
 8 
 
 214X2% 
 
 5/16 
 
 11.76 
 
 238 
 
 4.5 
 
 180 
 
 170 
 
 165 
 
 145 
 
 
 8 
 
 2^X2^ 
 
 3/8 
 
 13.84 
 
 280 
 
 4.5 
 
 210 
 
 200 
 
 195 
 
 170 
 
 
 8 
 
 3 X2^ 
 
 5/16 
 
 12.96 
 
 274 
 
 4.6 
 
 195 
 
 190 
 
 180 
 
 160 
 
 
 8 
 
 3 X2^ 
 
 3/8 
 
 15.36 
 
 325 
 
 4.6 
 
 235 
 
 225 
 
 215 
 
 190 
 
 8 
 
 3 X3 
 
 5/16 
 
 14.24 
 
 286 
 
 4.5 
 
 215 
 
 205 
 
 200 
 
 180 
 
 a\ 8 
 
 3 X3 
 
 3/8 
 
 16.88 
 
 336 
 
 4.5 
 
 255 
 
 245 
 
 235 
 
 210 
 
 18 
 
 3 X3 
 
 7/16 
 
 19.52 
 
 386 
 
 4.5 
 
 295 
 
 285 
 
 275 
 
 245 
 
 
 8 
 
 3 X3H 
 
 5/16 
 
 15.44 
 
 293 
 
 4.3 
 
 235 
 
 225 
 
 215 
 
 190 
 
 
 8 
 
 3X3^ 
 
 3/8 
 
 18.40 
 
 340 
 
 4.3 
 
 280 
 
 265 
 
 255 
 
 225 
 
 
 8 
 
 3 X&A 
 
 7/16 
 
 21.20 
 
 386 
 
 4.3 
 
 320 
 
 305 
 
 295 
 
 260 
 
 >8 
 
 3 X3^ 
 
 1/2 
 
 24.00 
 
 433 
 
 4.3 
 
 365 
 
 350 
 
 330 
 
 295 
 
 f8 
 
 3 X3V6 
 
 9/16 
 
 26.72 
 
 479 
 
 4.3 
 
 405 
 
 385 
 
 370 
 
 330 
 
 18 
 
 3 X3^ 
 
 5/8 
 
 29.36 
 
 526 
 
 4.3 
 
 445 
 
 425 
 
 405 
 
 360 
 
 6-18 
 
 3 X3^ 
 
 11/16 
 
 32.00 
 
 572 
 
 4.3 
 
 485 
 
 465 
 
 445 
 
 395 
 
 8 
 
 3 X 3V 
 
 3/4 
 
 34 . 48 
 
 619 
 
 4.3 
 
 520 
 
 500 
 
 480 
 
 425 
 
 18 
 
 3 X3^ 
 
 13/16 
 
 36.96 
 
 666 
 
 4.3 
 
 560 
 
 535 
 
 515 
 
 455 
 
 
 8 
 
 3 X4 
 
 5/16 
 
 16.72 
 
 300 
 
 4.2 
 
 250 
 
 240 
 
 230 
 
 205 
 
 
 8 
 
 3 X4 
 
 3/8 
 
 19.84 
 
 348 
 
 4.2 
 
 300 
 
 285 
 
 275 
 
 240 
 
 a 
 
 8 
 
 3 X4 
 
 7/16 
 
 22.96 
 
 396 
 
 4.2 
 
 345 
 
 330 
 
 315 
 
 280 
 
 
 8 
 
 3 X4 
 
 1/2 
 
 26.00 
 
 444 
 
 4.2 
 
 390 
 
 375 
 
 360 
 
 315 
 
 
 8 
 
 3 X4 
 
 9/16 
 
 28.96 
 
 491 
 
 4.2 
 
 435 
 
 420 
 
 400 
 
 350 
 
 
 8 
 
 3 X4 
 
 5/8 
 
 31.84 
 
 539 
 
 4.2 
 
 480 
 
 460 
 
 440 
 
 385 
 
 b 
 
 8 
 
 3 X4 
 
 11/16 
 
 34.72 
 
 587 
 
 4.2 
 
 525 
 
 500 
 
 480 
 
 420 
 
 
 8 
 
 3 X4 
 
 3/4 
 
 37.52 
 
 635 
 
 4.2 
 
 565 
 
 540 
 
 520 
 
 455 
 
 
 8 
 
 3 X4 
 
 13/16 
 
 40.24 
 
 683 
 
 4.2 
 
 605 
 
 580 
 
 555 
 
 490 
 
 a, tie-plates 8 inches wide, 2' 6" C. to C. 
 6, tie-plates 9 inches wide, 2' 6" C. to C. 
 
490 STRENGTH OF GRAY STEEL COLUMNS. 
 
 SAFE LOADS FOR GRAY COLUMNS. 
 14" SQUARE COLUMNS (continued). 
 
 s 
 1 
 
 Dimensions 
 of angles. 
 
 -Properties. 
 
 Safe loads. 
 
 8 
 
 
 
 Column lengths in thou- 
 
 6 
 
 
 
 
 
 
 sands of pounds. 
 
 
 Length 
 of legs. 
 
 Thick. 
 
 Area, 
 square 
 ins. 
 
 7. 
 
 r. 
 
 
 12 ft. 
 
 16ft. 
 
 20ft. 
 
 30ft. 
 
 (8 
 
 3 X5 
 
 3/8 
 
 22.88 
 
 365 
 
 4.0 
 
 345 
 
 325 
 
 310 
 
 370 
 
 iM8 
 
 3 X5 
 
 7/16 
 
 26.48 
 
 414 
 
 4.0 
 
 395 
 
 380 
 
 360 
 
 315 
 
 Is 
 
 3 X5 
 
 1/2 
 
 30.00 
 
 463 
 
 4.0 
 
 450 
 
 430 
 
 410 
 
 355 
 
 
 3 X5 
 
 9/16 
 
 33.44 
 
 512 
 
 4.0 
 
 500 
 
 480 
 
 455 
 
 400 
 
 18 
 
 3 X5 
 
 5/8 
 
 36.88 
 
 560 
 
 4.0 
 
 555 
 
 530 
 
 505 
 
 440 
 
 6-18 
 
 3 X5 
 
 11/16 
 
 40.24 
 
 609 
 
 4.0 
 
 605 
 
 575 
 
 550 
 
 480 
 
 I 8 
 
 3 X5 
 
 3/4 
 
 43.52 
 
 658 
 
 4.0 
 
 655 
 
 625 
 
 595 
 
 520 
 
 U 
 
 3 X5 
 
 13/16 
 
 46.72 
 
 706 
 
 4.0 
 
 700 
 
 670 
 
 635 
 
 560 
 
 f8 
 
 3^X3 
 
 5/16 
 
 15.44 
 
 320 
 
 4.5 
 
 235 
 
 225 
 
 215 
 
 190 
 
 fl !8 
 
 3jx^x 3 
 
 3/8 
 
 18.40 
 
 373 
 
 4.5 
 
 280 
 
 270 
 
 255 
 
 230 
 
 a ]s 
 
 3J 4 X 3 
 
 7/16 
 
 21.20 
 
 425 
 
 4.5 
 
 320 
 
 310 
 
 295 
 
 265 
 
 is 
 
 3HX3 
 
 1/2 
 
 24.00 
 
 477 
 
 4.5 
 
 365 
 
 350 
 
 335 
 
 300 
 
 8 
 
 3)^X3 
 
 9/16 
 
 26.72 
 
 529 
 
 4.5 
 
 405 
 
 ?90 
 
 375 
 
 335 
 
 8 
 
 3^ X 3 
 
 5/8 
 
 29.36 
 
 581 
 
 4.5 
 
 445 
 
 430 
 
 410 
 
 365 
 
 8 
 
 3^X3 
 
 11/16 
 
 32.00 
 
 633 
 
 4.5 
 
 485 
 
 470 
 
 450 
 
 400 
 
 8 
 
 3^X3 
 
 3/4 
 
 34.48 
 
 685 
 
 4.5 
 
 525 
 
 505 
 
 485 
 
 430 
 
 (8 
 
 3^X3H 
 
 3/8 
 
 19.84 
 
 389 
 
 4.4 
 
 300 
 
 290 
 
 275 
 
 245 
 
 a\s 
 
 3^X3^ 
 
 7/16 
 
 22.96 
 
 441 
 
 4.4 
 
 350 
 
 335 
 
 320 
 
 285 
 
 (8 
 
 3;Hi X 3J^ 
 
 1/2 
 
 26.00 
 
 493 
 
 4.4 
 
 395 
 
 380 
 
 360 
 
 320 
 
 f8 
 
 3^ X 3/^ 
 
 9/16 
 
 28.96 
 
 545 
 
 4.4 
 
 440 
 
 420 
 
 405 
 
 360 
 
 [8 
 
 3*/ X 3^ 
 
 5/8 
 
 31.92 
 
 597 
 
 4.4 
 
 485 
 
 465 
 
 445 
 
 395 
 
 6-{ 8 
 
 3/^X 3;Hj 
 
 11/16 
 
 34.72 
 
 649 
 
 4.4 
 
 525 
 
 505 
 
 485 
 
 430 
 
 18 
 
 3^X 3/^ 
 
 8/4 
 
 37.52 
 
 701 
 
 4.4 
 
 570 
 
 545 
 
 525 
 
 465 
 
 U 
 
 3^X3^ 
 
 13/16 
 
 40.24 
 
 753 
 
 4.4 
 
 610 
 
 585 
 
 560 
 
 500 
 
 (8 
 al.8 
 
 3HX5 
 3KX5 
 
 3/8 
 7/16 
 
 24.40 
 
 28.24 
 
 407 
 461 
 
 4.0 
 
 4.0 
 
 365 
 425 
 
 350 
 
 405 
 
 330 
 385 
 
 290 
 340 
 
 (8 
 
 3HX5 
 
 1/2 
 
 32.00 
 
 515 
 
 4.0 
 
 480 
 
 460 
 
 435 
 
 385 
 
 f 8 
 
 3^X5 
 
 9/16 
 
 35.76 
 
 570 
 
 4.0 
 
 535 
 
 510 
 
 490 
 
 425 
 
 !8 
 
 3^X5 
 
 5/8 
 
 39.36 
 
 624 
 
 4.0 
 
 590 
 
 565 
 
 535 
 
 470 
 
 / j 8 
 
 3^X5 
 
 11/16 
 
 42.96 
 
 678 
 
 4.0 
 
 645 
 
 615 
 
 585 
 
 515 
 
 | 8 
 
 3^X5 
 
 3/4 
 
 46.48 
 
 732 
 
 4.0 
 
 700 
 
 665 
 
 635 
 
 555 
 
 18 
 
 3^X5 
 
 13/16 
 
 50.00 
 
 786 
 
 4.0 
 
 750 
 
 715 
 
 680 
 
 600 
 
 18 
 
 33^X5 
 
 7/8 
 
 53.36 
 
 840 
 
 4.0 
 
 800 
 
 765 
 
 730 
 
 640 
 
 rg 
 
 3^X6 
 
 3/8 
 
 27.36 
 
 410 
 
 3.8 
 
 405 
 
 385 
 
 370 
 
 320 
 
 a 1 8 
 
 3^X6 
 
 7/16 
 
 31.76 
 
 468 
 
 3.8 
 
 475 
 
 450 
 
 430 
 
 370 
 
 f| 
 
 3^X6 
 3^X6 
 
 1/2 
 9/16 
 
 36.00 
 40.24 
 
 526 
 
 584 
 
 3.8 
 3.8 
 
 535 
 600 
 
 510 
 570 
 
 485 
 540 
 
 420 
 470 
 
 ) 8 
 
 3^X6 
 
 5/8 
 
 44.40 
 
 641 
 
 3.8 
 
 660 
 
 630 
 
 600 
 
 520 
 
 U 
 
 3^X6 
 
 11/16 
 
 48.48 
 
 698 
 
 3.8 
 
 725 
 
 690 
 
 655 
 
 565 
 
 a, tie-plates 8 inches wide, 2' 6" C. to C. 
 6, tie-plates 9 inches wide, 2' 6" C. to C. 
 
STRENGTH OF GRAY STEEL COLUMNS. 491 
 
 SAFE LOADS FOR GRAY COLUMNS. 
 
 16" SQUARE COLUMNS. 
 Tie-plates 9 inches wide, 2' 6" C. to C. 
 
 
 
 
 Safe loads in thousands of 
 
 
 
 
 pounds. 
 
 
 Dimensions of 
 
 
 
 sj 
 
 angles. 
 
 Properties. 
 
 
 'ft 
 
 
 
 
 tM 
 
 o 
 
 
 
 Column lengths. 
 
 1 
 
 
 
 Area, 
 
 
 
 
 
 
 
 
 
 Length 
 
 Thick. 
 
 square 
 
 /. 
 
 r. 
 
 
 
 
 
 
 of legs. 
 
 
 ins. 
 
 
 
 12ft. 
 
 16ft. 
 
 20ft. 
 
 30ft. 
 
 8 
 
 &AX2y 2 
 
 5/16 
 
 11.76 
 
 320 
 
 5.2 
 
 180 
 
 175 
 
 170 
 
 155 
 
 8 
 
 2y 2 x2y 2 
 
 3/8 
 
 13.84 
 
 374 
 
 5.2 
 
 215 
 
 205 
 
 200 
 
 180 
 
 8 
 
 2^X2y 2 
 
 7/16 
 
 16.00 
 
 427 
 
 5.2 
 
 245 
 
 240 
 
 230 
 
 210 
 
 8 
 
 2Y 2 X 2}4 
 
 1/2 
 
 18.00 
 
 481 
 
 5.2 
 
 280 
 
 270 
 
 260 
 
 235 
 
 8 
 
 3 X3 
 
 5/16 
 
 14.24 
 
 380 
 
 5.1 
 
 220 
 
 210 
 
 205 
 
 185 
 
 8 
 
 3 X3 
 
 3/8 
 
 16.88 
 
 443 
 
 5.1 
 
 260 
 
 250 
 
 240 
 
 220 
 
 8 
 
 3 X3 
 
 7/16 
 
 19.52 
 
 507 
 
 5 1 
 
 300 
 
 290 
 
 280 
 
 255 
 
 8 
 
 3 X3 
 
 1/2 
 
 22.00 
 
 570 
 
 5.1 
 
 340 
 
 325 
 
 315 
 
 285 
 
 8 
 
 3 X3 
 
 9/16 
 
 24.48 
 
 633 
 
 5.1 
 
 380 
 
 365 
 
 350 
 
 320 
 
 8 
 
 3 X3 
 
 5/8 
 
 26.88 
 
 696 
 
 5.1 
 
 415 
 
 400 
 
 385 
 
 350 
 
 8 
 
 3 l Ax3y 2 
 
 3/8 
 
 19.84 
 
 517 
 
 5.0 
 
 305 
 
 295 
 
 285 
 
 255 
 
 8 
 
 3A X 3y 2 
 
 7/16 
 
 22.96 
 
 588 
 
 5.0 
 
 355 
 
 " 340 
 
 330 
 
 300 
 
 8 
 
 3y 2 x3y 2 
 
 1/2 
 
 26.00 
 
 660 
 
 5.0 
 
 400 
 
 385 
 
 370 
 
 335 
 
 8 
 
 3 l AX3y 2 
 
 9/16 
 
 28.96 
 
 731 
 
 5.0 
 
 445 
 
 430 
 
 415 
 
 375 
 
 8 
 
 3%X3y 2 
 
 5/8 
 
 31.92 
 
 802 
 
 5.0 
 
 490 
 
 475 
 
 455 
 
 415 
 
 8 
 
 3% X 3y 
 
 11/16 
 
 34.72 
 
 873 
 
 5.0 
 
 535 
 
 515 
 
 500 
 
 450 
 
 8 
 
 3y 2 xsy 2 
 
 3/4 
 
 37.52 
 
 944 
 
 5.0 
 
 580 
 
 560 
 
 540 
 
 485 
 
 8 
 
 4 X4 
 
 3/8 
 
 22.88 
 
 588 
 
 5.0 
 
 350 
 
 340 
 
 325 
 
 300 
 
 8 
 
 4 X4 
 
 7/16 
 
 26.48 
 
 669 
 
 5.0 
 
 410 
 
 395 
 
 380 
 
 345 
 
 8 
 
 4 X4 
 
 1/2 
 
 30.00 
 
 750 
 
 5.0 
 
 460 
 
 445 
 
 430 
 
 390 
 
 8 
 
 4 X4 
 
 9/16 
 
 33.44 
 
 831 
 
 5.0 
 
 515 
 
 500 
 
 480 
 
 435 
 
 8 
 
 4 X4 
 
 5/8 
 
 36.88 
 
 912 
 
 5.0 
 
 570 
 
 550 
 
 530 
 
 480 
 
 8 
 
 4 X4 
 
 11/16 
 
 40.24 
 
 994 
 
 5.0 
 
 620 
 
 600 
 
 575 
 
 520 
 
 8 
 
 4 X4 
 
 3/4 
 
 43.52 
 
 1075 
 
 5.0 
 
 670 
 
 650 
 
 625 
 
 565 
 
 8 
 
 4 X4 
 
 13/16 
 
 46.72 
 
 1156 
 
 5.0 
 
 720 
 
 695 
 
 670 
 
 605 
 
 8 
 
 4 X6 
 
 7/16 
 
 33.44 
 
 730 
 
 4.6 
 
 510 
 
 490 
 
 470 
 
 420 
 
 8 
 
 4 X6 
 
 1/2 ' 
 
 38.00 
 
 810 
 
 4.6 
 
 580 
 
 560 
 
 535 
 
 480 
 
 8 
 
 4 X6 
 
 9/16 
 
 42.48 
 
 891 
 
 4.6 
 
 650 
 
 625 
 
 600 
 
 535 
 
 8 
 
 4 X6 
 
 5/8 
 
 46.88 
 
 972 
 
 4.6 
 
 715 
 
 690 
 
 660 
 
 590 
 
 8 
 
 4 X6 
 
 11/16 
 
 51.28 
 
 1053 
 
 4.6 
 
 785 
 
 755 
 
 720 
 
 645 
 
 8 
 
 4 X6 
 
 3/4 
 
 55 . 52 
 
 1134 
 
 4.6 
 
 850 
 
 815 
 
 780 
 
 700 
 
 8 
 
 4 X6 
 
 13/16 
 
 59 . 76 
 
 1215 
 
 4.6 
 
 915 
 
 880 
 
 840 
 
 755 
 
 8 
 
 4 X6 
 
 7/8 
 
 63.92 
 
 1296 
 
 4.6 
 
 975 
 
 940 
 
 900 
 
 805 
 
 
 
 
 
 
 
 
 
 l 
 
492 STRENGTH OF GRAY STEEL COLUMNS. 
 
 SAFE LOADS FOR GRAY COLUMNS. 
 
 16" WALL COLUMNS. 
 Tie-plates 9 inches wide, 2' 6" C. to C. 
 
 
 
 
 Safe loads in thousands of 
 
 
 
 
 pounds. 
 
 
 Dimensions of 
 
 
 
 Q) 
 
 .angles. 
 
 Properties. 
 
 
 i 
 
 
 
 
 'a 
 
 s 
 
 
 
 Column lengths. 
 
 1 
 
 Length 
 of legs. 
 
 Thick- 
 ness. 
 
 Area, 
 square 
 Ins. 
 
 7. 
 
 r. 
 
 
 12ft. 
 
 16ft. 
 
 20ft. 
 
 30ft. 
 
 6 
 
 2^X2y 2 
 
 5/16 
 
 8.82 
 
 Ill 
 
 3.6 
 
 130 
 
 12C 
 
 115 
 
 100 
 
 6 
 
 2%X2 1 A 
 
 3/8 
 
 10.38 
 
 120 
 
 3.6 
 
 150 
 
 145 
 
 135 
 
 115 
 
 6 
 
 2^X2y 2 
 
 7/16 
 
 12.00 
 
 139 
 
 3.6 
 
 175 
 
 165 
 
 160 
 
 135 
 
 6 
 
 2)4 X 2*4 
 
 1/2 
 
 13.50 
 
 167 
 
 3.6 
 
 200 
 
 185 
 
 180 
 
 150 
 
 6 
 
 3 X3 
 
 5/16 
 
 10.68 
 
 131 
 
 3.5 
 
 155 
 
 150 
 
 140 
 
 120 
 
 6 
 
 3 X3 
 
 3/8 
 
 12.66 
 
 157 
 
 3.5 
 
 185 
 
 175 
 
 165 
 
 140 
 
 6 
 
 3 X3 
 
 7/16 
 
 14.64 
 
 179 
 
 3.5 
 
 215 
 
 205 
 
 190 
 
 165 
 
 6 
 
 3 X3 
 
 1/2 
 
 16.50 
 
 200 
 
 3.5 
 
 240 
 
 230 
 
 215 
 
 185 
 
 6 
 
 3 X3 
 
 9/16 
 
 18.36 
 
 222 
 
 3.5 
 
 270 
 
 255 
 
 240 
 
 205 
 
 6 
 
 3 X3 
 
 5/8 
 
 20.16 
 
 244 
 
 3.5 
 
 295 
 
 280 
 
 265 
 
 225 
 
 6 
 
 3X3H 
 
 3/8 
 
 14.88 
 
 188 
 
 3.5 
 
 220 
 
 205 
 
 195 
 
 165 
 
 6 
 
 3^X3^ 
 
 7/16 
 
 17.22 
 
 215 
 
 3.5 
 
 255 
 
 240 
 
 225 
 
 190 
 
 6 
 
 3^X3K 
 
 1/2 
 
 19.50 
 
 241 
 
 3.5 
 
 285 
 
 270 
 
 255 
 
 220 
 
 6 
 
 33^X3^ 
 
 9/16 
 
 21.72 
 
 268 
 
 3.5 
 
 320 
 
 300 
 
 285 
 
 245 
 
 6 
 
 3^X3^ 
 
 5/8 
 
 23.94 
 
 294 
 
 3.5 
 
 350 
 
 335 
 
 315 
 
 270 
 
 6 
 
 3J|X3H 
 
 11/16 
 
 26.04 
 
 321 
 
 3.5 
 
 385 
 
 365 
 
 340 
 
 290 
 
 6 
 
 3>iX3K 
 
 3/4 
 
 28.14 
 
 347 
 
 3.5 
 
 415 
 
 395 
 
 370 
 
 315 
 
 6 
 
 4 X4 
 
 3/8 
 
 17.16 
 
 221 
 
 3.5 
 
 250 
 
 240 
 
 225 
 
 190 
 
 6 
 
 4 X4 
 
 7/16 
 
 19.86 
 
 252 
 
 3.5 
 
 290 
 
 275 
 
 260 
 
 225 
 
 6 
 
 4 X4 
 
 1/2 
 
 22.50 
 
 283 
 
 3.5 
 
 330 
 
 315 
 
 295 
 
 250 
 
 6 
 
 4 X4 
 
 9/16 
 
 25.08 
 
 314 
 
 3.5 
 
 370 
 
 350 
 
 330 
 
 280 
 
 6 
 
 4 X4 
 
 5/8 
 
 27.66 
 
 345 
 
 3.5 
 
 405 
 
 385 
 
 365 
 
 310 
 
 6 
 
 4 X4 
 
 11/16 
 
 30.18 
 
 376 
 
 3.5 
 
 445 
 
 420 
 
 400 
 
 340 
 
 6 
 
 4 X4 
 
 3/4 
 
 32.64 
 
 407 
 
 3.5 
 
 480 
 
 455 
 
 430 
 
 365 
 
 6 
 
 4 X4 
 
 13/16 
 
 35.04 
 
 439 
 
 3.5 
 
 515 
 
 490 
 
 460 
 
 395 
 
 6 
 
 4 X6 
 
 7/16 
 
 25.08 
 
 279 
 
 3.3 
 
 365 
 
 345 
 
 325 
 
 270 
 
 6 
 
 4 X6 
 
 1/2 
 
 28.50 
 
 311 
 
 3.3 
 
 415 
 
 390 
 
 370 
 
 310 
 
 6 
 
 4 X6 
 
 9/16 
 
 31.86 
 
 343 
 
 3.3 
 
 465 
 
 440 
 
 410 
 
 345 
 
 6 
 
 4 X6 
 
 5/8 
 
 35.16 
 
 375 
 
 3.3 
 
 510 
 
 485 
 
 455 
 
 380 
 
 6 
 
 4 X6 
 
 11/16 
 
 38.46 
 
 407 
 
 3.3 
 
 560 
 
 530 
 
 500 
 
 415 
 
 6 
 
 4 X6 
 
 3/4 
 
 41.64 
 
 440 
 
 3.3 
 
 605 
 
 570 
 
 540 
 
 450 
 
 6 
 
 4 X6 
 
 13/16 
 
 44.82 
 
 472 
 
 3.3 
 
 655 
 
 615 
 
 580 
 
 485 
 
 6 
 
 4 X6 
 
 7/8 
 
 47.94 
 
 504 
 
 3.3 
 
 700 
 
 660 
 
 ' 620 
 
 520 
 
STRENGTH OF GRAY STEEL COLUMNS. 493 
 
 SAFE LOADS FOR GRAY COLUMNS. 
 
 10J" CORNER COLUMNS. 
 
 8 
 
 8 
 
 Dimensions of 
 angles. 
 
 Properties. 
 
 Safe loads in thousands 
 of pounds. 
 
 IM 
 
 O 
 
 Length 
 
 Thick- 
 
 Area, 
 
 /. 
 
 
 Column lengths. 
 
 o 
 
 of legs. 
 
 ness. 
 
 square 
 
 . 
 
 T. 
 
 
 
 
 
 g 
 
 
 
 inches. 
 
 
 
 12ft. 
 
 16ft. 
 
 20ft. 
 
 30ft. 
 
 r 
 
 4 
 
 1 
 
 3 2 X3 
 
 5/16 
 
 3/8 
 
 [ 9.83 
 
 118 
 
 3.5 
 
 145 
 
 135 
 
 130 
 
 110 
 
 
 
 4 
 
 1 
 
 3^X3 
 3 X3 
 
 3/8 
 3/8, 
 
 HU.31 
 
 139 
 
 3.5 
 
 165 
 
 155 
 
 150 
 
 125 
 
 f 
 
 3^X3 
 3 X3 
 
 7/16 
 1/2 
 
 j-13.35 
 
 145 
 
 3.5 
 
 195 
 
 185 
 
 175 
 
 150 
 
 if 
 
 3^X3 
 3 X3 
 
 1/2 
 1/2 
 
 [l4.75 
 
 159 
 
 3.5 
 
 215 
 
 205 
 
 195 
 
 165 
 
 
 4 
 1 
 
 3^X3 
 3 X3 
 
 9/16 
 
 5/8 
 
 S16.72 
 
 172 
 
 3.5 
 
 245 
 
 230 
 
 220 
 
 185 
 
 6 
 
 
 
 4 
 
 1 
 
 3^X3 
 3 X3 
 
 5/8 
 5/8 
 
 18.04 
 
 186 
 
 3.5 
 
 265 
 
 250 
 
 235 
 
 200 
 
 
 4 
 
 3*^X3 
 3 X3 
 
 11/16 
 
 5/8 
 
 H 10.36 
 
 199 
 
 3.5 
 
 285 
 
 270 
 
 255 
 
 215 
 
 
 4 
 
 U 
 
 3 2 X3 
 
 3/4 
 5/8 
 
 [20.60 
 
 213 
 
 3.5 
 
 305 
 
 285 
 
 270 
 
 230 
 
 
 \ 
 
 3 2 X3 2 
 
 3/8 
 3/8 
 
 [l2. 03 
 
 139 
 
 3.4 
 
 175 
 
 165 
 
 155 
 
 130 
 
 a 
 
 4 
 1 
 
 3 2 X3 2 
 
 7/16 
 
 1/2 
 
 514.23 
 
 158 
 
 3.4 
 
 205 
 
 195 
 
 185 
 
 155 
 
 
 \ 
 
 33^X3^ 
 3 X3 
 
 1/2 
 1/2 
 
 j-15.75 
 
 177 
 
 3.4 
 
 230 
 
 215 
 
 205 
 
 175 
 
 
 4 
 
 1 
 
 3^X3^ 
 3 X3 
 
 9/16 
 
 5/8 
 
 j-17.84 
 
 196 
 
 3.4 
 
 260 
 
 245 
 
 230 
 
 195 
 
 
 \ 
 
 3 2 X3 2 
 
 5/8 
 5/8 
 
 119.32 
 
 215 
 
 3.4 
 
 280 
 
 265 
 
 250 
 
 210 
 
 6 
 
 \ 
 
 3 2 X3 2 
 
 11/16 
 5/8 
 
 [20.72 
 
 234 
 
 3.4 
 
 305 
 
 285 
 
 270 
 
 230 
 
 
 4 
 I 
 
 3 2 X3 2 
 
 3/4 
 
 5/8 
 
 [22.12 
 
 253 
 
 3.4 
 
 325 
 
 305 
 
 290 
 
 245 
 
 
 R 
 
 3 2 X3' 2 
 
 13/16 
 
 5/8 
 
 [23.48 
 
 272 
 
 3.4 
 
 345 
 
 325 
 
 305 
 
 260 
 
 ft 
 
 3^X4 
 3 X3 
 
 3/8 
 
 3/8 
 
 [l2.79 
 
 141 
 
 3.3 
 
 185 
 
 175 
 
 165 
 
 140 
 
 f 
 
 3^X4 
 3 X3 
 
 7/16 
 
 1/2 
 
 [l5.ll 
 
 160 
 
 3.3 
 
 220 
 
 205 
 
 195 
 
 165 
 
 14 
 
 U 
 
 3^X4 
 3 X3 
 
 1/2 
 1/2 
 
 [l6.75 
 
 180 
 
 3.3 
 
 245 
 
 230 
 
 215 
 
 180 
 
 
 f4 
 1 
 
 3^X4 
 3 X3 
 
 9/16 
 
 5/8 
 
 [l8.96 
 
 199 
 
 3.3 
 
 275 
 
 260 
 
 245 
 
 205 
 
 
 1 
 
 3^X4 
 3 X3 
 
 5/8 
 
 5/8 
 
 [20.56 
 
 219 
 
 3.3 
 
 300 
 
 280 
 
 265 
 
 220 
 
 Hf 
 
 3^X4 
 3 X3 
 
 11/16 
 
 5/8 
 
 [22.08 
 
 238 
 
 3.3 
 
 320 
 
 305 
 
 285 
 
 240 
 
 
 A 
 1 
 
 3^X4 
 
 a X3 
 
 3/4 
 
 5/8 
 
 [23.60 
 
 258 
 
 3.3 
 
 345 
 
 325 
 
 305 
 
 255 
 
 
 /- 
 
 U 
 
 3^X4 
 3 X3 
 
 13/16 
 
 5/8 
 
 [25.08 
 
 277 
 
 3.3 
 
 365 
 
 345 
 
 325 
 
 270 
 
 If 
 
 3^X5 
 3 X3 
 
 3/8 
 3/8 
 
 [14.31 
 
 145 
 
 3.2 
 
 205 
 
 195 
 
 180 
 
 150 
 
 H 
 
 3^X5 
 3 X3 
 
 7/16 
 3/8 
 
 [16.23 
 
 165 
 
 3.2 
 
 235 
 
 220 
 
 205 
 
 170 
 
 if 
 
 3^X5 
 3 X3 
 
 1/2 
 1/2 
 
 [18.75 
 
 185 
 
 3.2 
 
 270 
 
 255 
 
 240 
 
 200 
 
 a, tie-plates 8 i: 
 6, tie-plates 9 i 
 
 nches wide, 2' 6" C. to C. 
 nches wide, 2' 6" C. to C. 
 
494 COLUMN SHAPES, IN TALL BUILDINGS. 
 
 KINDS OF COLUMNS USED IN THE PRINCIPAL OFFICE 
 BUILDINGS OF CHICAGO AND NEW YORK. 
 
 Architect. 
 
 Building. 
 
 No. of 
 stories. 
 
 Kind 
 of column. 
 
 W. L. B. Jenney 
 
 Manhattan 
 
 16 
 
 Cast 
 
 
 "The Fair" 
 
 9 
 
 Z-bar 
 
 
 
 Y. M. C. A. 
 
 13 
 
 Z-bar 
 
 * 
 
 Isabella 
 
 10 
 
 Z-bar 
 
 Jenney & Mundie 
 
 New York Life 
 
 12 
 
 Steel; plates and 
 
 
 
 
 angles 
 
 
 
 Fort Dearborn 
 
 12 
 
 Channels and 
 
 
 
 
 plates 
 
 Holabird & Roche 
 
 Tacoma 
 
 13 
 
 Cast 
 
 
 Pontiac 
 
 14 
 
 Z-bar 
 
 
 
 Venetian 
 
 13 
 
 Z-bar 
 
 (4 
 
 Monadnoct Block, new 
 
 17 
 
 Z-bar 
 
 
 part 
 
 
 
 
 
 Old Colony 
 
 17 
 
 Z-bar and 
 
 
 
 
 Phoenix 
 
 
 
 Champlain 
 
 15 
 
 Z-bar 
 
 
 
 Marquette 
 
 16 
 
 Z-bar 
 
 Adler & Sullivan 
 
 Auditorium 
 
 10 & 17 
 
 Cast 
 
 
 Schiller Theatre 
 
 13 & 17 
 
 Z-bar and 
 
 
 
 
 Phoenix 
 
 
 
 Stock Exchange 
 
 13 
 
 Z-bar 
 
 Burnham & Root 
 
 Rookery 
 
 12 
 
 Cast 
 
 ** 
 
 Woman's Temple 
 
 13 
 
 Z-bar 
 
 
 
 Masonic Temple 
 
 20 
 
 Plates and angles 
 
 '* 
 
 Ashland 
 
 16 
 
 Z-bar 
 
 D. H. Burnham & Co. 
 
 Reliance 
 
 15 
 
 Gray 
 
 " 
 
 Fisher 
 
 18 
 
 Gray 
 
 H 
 
 Great Northern Theatre 
 
 16 
 
 Gray > 
 
 Henry Ives Cobb 
 
 Title & Trust 
 
 16 
 
 Phoenix 
 
 
 O wings 
 
 14 
 
 Cast 
 
 NEW YORK. 
 
 Bruce Price 
 
 American Surety 
 
 21 
 
 Angles and 
 
 
 
 
 plates Z-bar 
 
 Kimball & Thompson 
 
 Manhattan Life Ins. 
 
 18 
 
 Cast, 5 stories: 
 
 
 
 
 plates and an- 
 
 
 
 
 gles above 
 
 Geo. B. Post 
 
 Meyer, Jonasson 
 
 14 
 
 Plates and an- 
 
 <t 
 
 Havemeyer (Cortland 
 
 15 
 
 gles 
 Plates and an- 
 
 (< 
 
 St.) 
 St, Paul Building 
 
 26 
 
 gles 
 Plates and an- 
 
 ft 
 
 New York World 
 
 22 
 
 gles m 
 Phoenix 
 
 
 
 Union Trust 
 
 10 
 
 Phoenix 
 
 Harding & Gooch 
 
 Postal Telegraph 
 
 ' 14 
 
 Cast 
 
 
 
 Dunn Building 
 Park Row Building 
 
 15 
 29 
 
 Phoenix 
 Plates and an- 
 
 
 
 
 gles 
 
 
 
 Commercial Cable 
 
 20 
 
 Phoenix 
 
 R. H. Robertson 
 H. J. Harden berg 
 
 American Tract Society 
 Hotel Waldorf 
 
 20 
 12 
 
 Riveted 
 Cast 
 
COMPARISON OF FORMULAS. 495 
 
 FORMULAS FOR STEEL COLUMNS AND STRUTS, 
 
 GIVEN IN VARIOUS BUILDING LAWS, AND RECOMMENDED BY 
 LEADING ENGINEERS. 
 
 p= working stress in pounds per square inch of cross-section. 
 1= length in inches. r== least radius of gyration. 
 Chicago Building Law: 
 
 For columns more than 60 radii in length, p= 17,000 . 
 
 7" 
 
 For columns less than 60 radii in length, p= 13,500 Ibs. 
 Greater New York Law (1899) : 
 
 p= 15,200 -58-. 
 
 Boston Law: 
 
 p= 12,000 Ibs. reduced by approved modern formulae. 
 
 Buffalo Building Law (1896) : 
 
 For columns more than 90 radii in length, p 17,100 57 . 
 
 For columns less than 90 radii in length, p= 12,000 Ibs. 
 Denver Building Ordinance: 
 Same as Buffalo. 
 Carnegie Steel Co. ; Jones & Laughlins : 
 
 p= 17,100 - 57- for lengths over 90 radii. 
 p= 12,000 for lengths of 90 radii and under. 
 Passaic Rolling Mill Co. Geo. H. Blakeley, C.E. 
 
 C p= 12,000 for lengths up to 50 radii. 
 Z-bar and box j 7 
 
 columns. ") p= 15,000 -57- for lengths over 50 radii. 
 
 12,000 for lengths up to 30 radii. 
 Steel Struts. { 13 ^ 00 _ 50 1 for lengths OV er 30 radii. 
 
 Charles Evan Fowler, C.E. General specifications for steel 
 roofs and buildings: 
 For struts with flat and fixed ends, p= 12,500- 41 if-. 
 
496 COMPARISON OF FORMULAS. 
 
 Theodore Cooper, M. Am. Soc. C. E. General specifications for 
 iron and steel railroad bridges and viaducts: 
 
 p= 8,000-30- for live load stresses. 
 For chords. \ T 
 
 |^ p= 16,000 -60- for dead load stresses. 
 
 For posts. 
 
 p= 7;000 40- for live load stresses. 
 p= 14,000^80- for dead load stresses. 
 p= 10, 000 -60- for wind load stresses. 
 
 Formula proposed by Mr. Thomas H. Johnson, M. Am. Soc. 
 C. E. : 
 
 I Hinged ends, p= 13,125 - 55- . 
 
 For mild steel, -j -, 
 
 Flat ends, p= 13,125-45-. 
 
 Mr. Joseph K. Freitag, in commenting on the allowed working 
 stress for steel columns in buildings says : 
 
 "The writer believes that with the use of a mild steel of an 
 ultimate strength of from 65,000 to 68,000 Ibs. per square inch, 
 15,000 or 16,000 Ibs. per. square inch may safely be used for all 
 concentric dead, live, and wind loads combined (with an addi- 
 tional allowance for eccentric loading), provided that the wind 
 pressure is taken at not less than 30 Ibs. per square foot and that 
 the live loads on the floors are assumed as required by municipal 
 building laws." 
 
PRINCIPLES OF THE STRENGTH OF BEAMS. 497 
 
 CHAPTER XV. 
 
 GENERAL PRINCIPLES OF THE STRENGTH OF 
 BEAMS, AND STRENGTH OF STEEL BEAMS. 
 
 STEEL-BEAM BOX GIRDERSFRAMING AND CON- 
 NECTING OF STEEL BEAMS. 
 
 BY the term "beam" is meant any piece of material which 
 supports a load whose tendency is to break the piece across, or at 
 right angles to, the fibres, and which also causes the piece to bend 
 before breaking. A simple beam is one which rests upon sup- 
 ports at both ends. When a beam is supported at its centre it 
 is a cantilever beam, or if a part of a beam projects from a wall 
 or beyond a support, the projecting part is called a cantilever. 
 In a simple beam the lower part is in tension and the upper 
 part in compression; in a cantilever beam the reverse is the 
 case. 
 
 When a transverse load of any kind is applied to any beam it 
 will cause the beam to bend by a certain amount, and as it is im- 
 possible to bend a piece of any material without stretching the 
 fibres on the outer side, and compressing the fibres on the inner 
 side, the bending of the beam will produce tension in the stretched 
 side and compression of the fibres of the opposite side. Be- 
 tween the stretched and compressed fibres is a neutral surface 
 which is unchanged in length. From experiments it has been 
 found that the amount of elongation or shortening of any fibre 
 is directly proportional to its distance from 'the neutral surface ; 
 hence, if the elastic limit be not surpassed, the stresses are also 
 proportional to their distance from the neutral surface. The 
 line where the neutral surface would cut through the side or 
 cross-section of the beam is called the neutral axis. Within the 
 safe strength of the material the neutral axis passes through 
 the centre of gravity of the cross-section of the beam for all 
 materials. 
 
 To determine the strength of any beam to resist the effects of 
 any load, or series of loads, we must determine two things : first, 
 
498 PRINCIPLES OF THE STRENGTH OF BEAMS. 
 
 the destructive force tending to bend and break the beam, which 
 is called the "Pending-moment" ; and, second, the combined re- 
 sistance of all the fibres of the beam to being broken, which is 
 called the "moment of resistance" 
 
 The methods for finding the bending-moments for any load, or 
 series of loads, have been given in Chap. IX. The moment of 
 resistance is equal to the "moment of resistance area" or "sec- 
 tion modulus," multiplied by the strength of the material. 
 Formulas for finding the section modulus of common shapes are 
 given in Chap. X., and the value, R, for the section modulus of 
 merchant shapes of structural steel is given in the tables, pages 
 296 to 315. 
 
 The "coefficient of strength" usually given in tables of steel 
 beams is the maximum distributed load that a beam of one foot 
 span would support without producing a fibre stress exceeding 
 the safe limit, generally 16,000 Ibs. As the strength of a beam is 
 inversely as its span, the safe load for any span may be obtained 
 by dividing the coefficient by the span in feet. 
 
 Now, that a beam shall just be able to resist the load, and not 
 break, we must have a condition where the bending-moment in 
 the beam is equal to the section modulus multiplied by the 
 strength of the material. That the beam may be abundantly 
 safe to resist the given load, this product must be several times 
 as great as the bending-moment; and the ratio in which this 
 product exceeds the bending-moment, or in which the breaking- 
 load exceeds the safe load, is known as the "factor of safety." 
 
 By "the strength of the material" is meant a certain constant 
 quantity, which is determined by experiment, and which is known 
 as the "Modulus of Rupture." Of course this value is different 
 for each different material. The following table contains the 
 values of this constant divided by the factor of safety, for most 
 of the materials used in building construction. The section 
 modulus multiplied by these values will give the safe resisting- 
 power of the beam. 
 
 The term "Modulus of Rupture" is now seldom seen in the 
 various handbooks published by the rolling-mill companies, the 
 term "fibre stress" being used instead. The two terms, how- 
 ever, are synonymous. 
 
 The following values of S for wrought iron and steel are one- 
 fourth that for the breaking-loads; for cast iron, one-sixth; for 
 wood, one-third; and for stone, one-sixth. The constants for 
 wood are based upon tests made at the Massachusetts Institute of 
 
PRINCIPLES OF THE STRENGTH OF BEAMS. 499 
 
 MODULUS OF RUPTURE (S) FOR SAFE STRENGTH.* 
 
 Material. 
 
 Value of 
 
 . s > 
 in Ibs. 
 
 Material. 
 
 Value of 
 
 s, 
 
 in Ibs. 
 
 Cast iron 
 
 5,544 
 
 American White pine 
 
 1,080 
 
 \Vrought iron 
 
 12,000 
 
 American yellow pine 
 
 1,800 
 
 Steel . 
 
 16,000 
 
 American spruce 
 
 1,260 
 
 
 
 Oregon pine 
 
 1,620 
 
 American ash 
 
 2,000 
 
 
 
 American red beech 
 American yellow birch. . 
 
 1,800 
 1,620 
 
 Bluestone flagging (Hud- 
 son River) 
 
 450 
 
 American white cedar 
 
 1,000 
 
 Granite, average 
 
 300 
 
 American elm 
 
 1,400 
 
 Limestone 
 
 250 
 
 Chestnut 
 
 1,080 
 
 Marble 
 
 300 
 
 Hemlock 
 
 990 
 
 Sandstone. 
 
 150to200 
 
 American white oak 
 
 1,350 
 
 Slate 
 
 900 
 
 
 
 
 
 * For a comparison of values given in different Building Laws see last 
 pages of Chapter XVI. 
 
 Technology upon full-size timbers of the usual quality found in 
 buildings. The figures given in the above table are believed to 
 be amply safe for beams in floors of dwellings, public halls, roofs, 
 etc. ; but for floors in mills, and warehouse floors, the author 
 recommends that not more than two-thirds of the above values be 
 used. The safe loads for the steel sections given in the following 
 tables are all computed on the value of 16,000 Ibs for S. For 
 angles, tees, and deck-beams it was customary, previous to 1898, 
 to use a somewhat lower value for S, about 12,000 Ibs., on account 
 of the section not being symmetrical. All but one of the steel 
 companies now use 16,000 Ibs. for all shapes, and the author has 
 therefore revised the tables in this book to correspond ; but these 
 full loads should be used with caution, and reduced under the 
 conditions noted. For riveted steel girders the value of S is 
 generally taken at 13,000 Ibs. 
 
 There are certain cases of beams which most frequently occur 
 in building construction, for which formulas can be given by 
 which the safe loads of the beams may be determined directly; 
 but it often happens that we may have either a regularly shaped 
 beam irregularly loaded, or a beam of irregular shape but with 
 a common method of loading. For such cases it is impossible 
 to give tables for strength, as each case must be computed by 
 determining either the section modulus required to resist the 
 bending-moment, or the greatest bending-moment that may be 
 allowed for a given value of R (section modulus). 
 
 The general formula for any beam under any system of loading 
 is as follows; 
 
500 FORMULAS FOR THE STRENGTH OF BEAMS. 
 
 Greatest bending-moment (inch-lbs.) = section modulus XS, (a) 
 or 
 
 j i /E> N bending moment (inch-lbs.) 
 Section modulus (R = ) - 2 - - -. (b) 
 
 o 
 
 If the bending-moment is computed in foot-pounds, these 
 formulas become : 
 
 section modulus X S 
 Greatest bending-moment = -^ t ( c ) 
 
 or 
 
 a ,. , , /Ty . 12 X bending-moment 
 
 Section modulus (R) = - f . (d) 
 
 o 
 
 By substituting for the bending-moment its value in terms of 
 the load and span, the following formulse may readily be deduced 
 which apply to any shape of beam. 
 
 FORMULAE FOR STRENGTH OF BEAMS FOR DIFFERENT CONDITIONS 
 OF SUPPORT AND LOADING. 
 
 R= section modulus; $=safe modulus of rupture, or fibre 
 stress in pounds (p. 499). 
 
 W= total load on beam in pounds. 
 
 L=span in feet. 
 
 (7= coefficient of strength given in tables. 
 
 Values for R for the various shapes and sizes of structural steel 
 bars will be found in the tables on pages 296-315. 
 
 CASE 1. Beams fixed at one end and loaded at the other (Fig. 1). 
 
 Safe load in pounds = 
 
 or w w 
 
 w 
 
 Fig.1. 
 
 EXAMPLE. A steel T-bar is fixed at one end in a brick wall, 
 and loaded at the other end with 600 Ibs., the distance L being 
 4 ft. What size bar should be used to support the load with 
 safety? 
 
 * When C is given in tons, safe load will be tons. 
 
FORMULAS FOR THE STRENGTH OF BEAMS. 501 
 
 -4ns. We will allow 12,000 Ibs. for the value of 8} then R== 
 
 12x600X4 
 
 TrTflnA = 2.4. Now we must ascertain what size T-bar has 
 
 a section modulus equal to 2.4. Looking in the table giving 
 the properties of tees (p. 313, col. VII.), we find 2.43 opposite a 
 4X5XJ tee, and 2.55 opposite a 4X4JXJ tee; hence either 
 size will have sufficient strength, the first, however, being the 
 cheapest, as it weighs the least. 
 
 For an I-beam we could have used 16,000 Ibs. for S', then R 
 
 , 12X600X4 
 
 would equal =1.8, which would permit of using a 
 
 io,uuu 
 
 3-inch 6J-lb. beam. 
 
 CASE 2. Beams fixed at one end, loaded with uniformly dis- 
 tributed load (Fig. 2). 
 
 Safe load in pounds = 
 
 &** - E- 
 
 Fig. 2. 
 
 CASE 3. Beams supported at both ends, loaded at middle (Fig. 3). 
 
 (3) 
 
 r &J-* 
 
 3WXL 
 
 R C* 
 
 Safe load in pounds = ~y X 8, or ^T. 
 
 R=- 
 
 S 
 
 w 
 
 (3A) 
 
 L 
 
 . Fig. 3. 
 
 * When C is given in tons, safe load will be tons. 
 
502 FORMULAS FOR THE STRENGTH OF BEAMS. 
 
 CASE 4. Beams supported at both ends, load uniformly dis* 
 tributed (Fig. 4). 
 
 Fig. 4. 
 
 27? C 1 * 
 
 Safe load in pounds =- T xS, or - T -. 
 6L Li 
 
 3WXL 
 U ~ 2S ' 
 
 (4) 
 (4A) 
 
 CASE 4 A. Beams supported at both ends, with a distributed load 
 over only a portion of the span, as in Fig. 4a. 
 
 -L- 
 
 Fig, 4a. 
 
 In this case the load is generally given, and the problem will 
 be to determine the size of the beam. This can be accurately 
 done only by computing the bending-moment as explained in 
 Chapter IX., and substituting the value thus found in formulas 
 (b) or (d), page 500. If, however, the length L A is very short in 
 comparison with L, then the load may be considered as concen- 
 trated at its centre, and R may be found by formula (3 A) if the 
 load is at the centre of the beam, or by formula (5A ) if the load 
 is at one side of the centre. The error will be on the safe side. 
 
 * When C is given in tons, safe load will be tons. 
 
FORMULAS FOR THE STRENGTH OF BEAMS. 503 
 
 CASE 5. Beams supported at both ends, loaded with concentrated 
 load not at centre (Fig. 5). 
 
 -m- 
 
 fpW 
 
 L- 
 
 R-- 
 
 Fig. 5. 
 
 7? V T 
 Safe load in pounds = 77777^777, X S. 
 
 IZWXmXn 
 LXS 
 
 5) 
 
 'j m and n being measured in feet. 
 
 EXAMPLE. A steel I-beam of 20 feet span has to support a 
 concentrated load of 24,000 Ibs. at a distance of 6 feet from one 
 support. What must be the size and weight of the beam? 
 
 Ans. In this case W= 24,000, L=20, n=6, ra=14, and we 
 will allow 16,000 Ibs. for S. 
 
 Then 
 
 = 75.6. 
 
 12X24,000X6X14 
 20X16,000 
 
 Looking down column VIJ. of the Properties of Steel I-beams 
 (p. 296), we find that the nearest value (above) to 75.6 is 81.2 for 
 a 15-inch 60-lb, beam, and 117.0 for a 20-inch 65-lb. beam, or we 
 might use two 12-inch 35-lb. beams. The 15-inch 60-lb. beam 
 would, however, be the cheapest beam to use, although the 20- 
 inch beam would deflect much less under the load. 
 
 CASE 6. Beams supported at both ends, loaded with W pounds, 
 at the same distance m from each end (Fig. 6). 
 
 Iw 
 
 1 
 
 Fig. 6. 
 
 Safe load W, in pounds, at each point = 
 
 75 
 
 (6A) 
 
504 FORMULAS FOR THE STRENGTH OF BEAMS. 
 
 EXAMPLE. A 12-inch standard steel channel of 12 ft. span 
 supports the ends of two 10-inch beams 4 ft. from each support. 
 Each 10-inch beam is designed to carry 16,000 Ibs. What should 
 be the weight of the channel to support the beams? 
 
 Ans, The channel would have to support only one-half of the 
 load on the beams, whence W= 8,000; ra=4; S= 16,000; and 
 
 12X8,000X4 
 ^ = ifl nrtrt 24, which is the value of the section modulus 
 
 J-D,UUU 
 
 of a 12-inch 25-lb. channel. (Col. VII., p. 298.) 
 
 It will be noticed that in formulas (6) and (6,4) the span of the 
 beam is not taken into account, and if the beam itself had no 
 weight it would make no difference in the fibre strains how far 
 apart the loads W are placed. In reality, however, steel beams 
 do weigh considerable, and to be absolutely correct an example 
 such as the above should be calculated for the weight of the 
 beam, as well as for the weights W. The weight of the beam 
 would, of course, be a distributed load, and to be absolutely cor- 
 rect the maximum bending-moment on the beam should be found 
 graphically in a manner similar to that explained on the lower 
 half of page 272, and the value of R computed by formula (7). 
 Where the loads, however, 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 W with sufficient accuracy; 
 thus, the weight of the channel in the above example between 
 supports would be 12x25, or 300 Ibs., and W should be taken at 
 8,100 Ibs., which would give a value for R of 24.1. 
 
 Generally there is a sufficient factor of safety in the loads 
 allowed 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. **0 
 
 CASE 7. Beam loaded with several loads. In such a case as 
 this it will be necessary to compute the maximum bending- 
 moment on the beam and proportion the beam by the formula 
 
 _> max. bending-moment (ft.-lbs.)Xl2. 
 
 R= g- (7) 
 
 EXAMPLE. A steel beam girder is to be used to support a 
 brick wall, 16 inches thick and weighing 138,000 Ibs., over an 
 opening 22 ft. wide. The girder must also support the ends of 
 four 10-inch floor-beams spaced as in Fig. 7, each beam being 
 
FORMULAS FOR THE STRENGTH OF BEAMS. 505 
 
 assumed to carry 16,000 Ibs.; what should be the size of the 
 beams forming the girder? 
 
 Ans. The first step should be to determine on the allowance 
 for the weight of the girder. The total load on the girder = 
 138,000 + 4X8,000 (one-half the load on each beam) = 170,000 
 Ibs., or 85 tons. As we must use a pair of beams the load on 
 
 T) Un- 
 
 rig. 7. 
 
 each beam will be 42.5 tons. For our present purpose we may 
 consider the entire load as distributed, and from the table of 
 strength of I-beams, we find that to support 42.5 tons with 
 a span of 22 feet would require a 24-inch 85-lb. beam. Our 
 girder would then weigh between supports 2X85X22 = 3,740 
 Ibs., or say 4,000 Ibs. Adding this to the weight of the wall we 
 have for the total distributed load 142,000 Ibs. The next step 
 will be to determine the maximum bending-moment. 
 
 By the formulas given in Chapter IX. we find the bending- 
 moments for the various loads to be as follows : 
 
 For weight of wall, M = ^^H^ = 390,500 ft.-lbs. 
 For beam B 1? Mj = ^ =23,545 ft.-lbs. 
 
 _ _. O.UUU /\ O2 S\ --O'2' . ^ ^OT f4- TUvn 
 
 For beam B 2 , M 2 = ^ =41,727 tt.-lbs. 
 
 The beams being spaced symmetrically from the centre of the 
 span, the bending-moments for B 3 and B 4 will be equal to those 
 of B 2 and B t respectively. Platting the bending-moments to a 
 scale, in the manner explained on pages 272, 273, we obtain the 
 diagram shown in Fig. 8, the greatest bending-moment being the 
 line M , which scales 485,000 Ibs. Multiplying this moment by 
 12 and dividing by (= 16,000 Ibs.), we have 363.7 as the value 
 for R for both beams, or 181.8 for one beam. From column VII., 
 p. 296, Properties of I-beams, we find that a 24-inch 90-lb. 
 beam has a section modulus of 186.6, therefore two 90-lb. beams 
 will just answer. The maximum load for a single beam is 50.9 
 
506 
 
 THE STRENGTH OF STEEL BEAMS. 
 
 tons, which is greater than the load we wish to carry, so that 
 there is no danger of the web buckling. The two beams should 
 be securely bolted together with separators near each connection 
 of beams B lt B 2 , B 3 , B 4 , and at each end of the girder. 
 
 The method above indicated applies to any method of loading, 
 the only difference in the calculation being in determining the 
 beriding-moment. 
 
 INCLINED BEAMS. The strength of beams inclined to the 
 horizon may be computed, with sufficient accuracy for most pur- 
 poses, by using the formulas given for horizontal beams, and 
 taking the horizontal projection of the beam as its span. 
 
 Steel Beams. 
 
 Practically the only materials used in structural work for 
 beams, at the present day, are wood and steel. Wooden beams 
 being always rectangular in cross-section, the general formula can 
 be much simplified by substituting for R 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 is also occa- 
 sionally used for beams or lintels, but as this material is much 
 stronger to resist compression than tension, the beam must be of 
 a special shape in order to use the material to advantage. The 
 
THE STRENGTH OF STEEL BEAMS. 507 
 
 strength of cast-iron beams is therefore considered under a 
 special heading in Chapter XVI. Formulas for concrete-steel 
 beams are given in Chap. XXIII. 
 
 Since 1893, steel beams have practically superseded wrought- 
 iron beams, and the latter are now seldom, if ever, used. The 
 *ame formulas apply to wrought-iron as to steel beams, however, 
 n>j simply changing the value of S. 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, and angles and tees are the least economical of all shapes. 
 The following figures show the safe load per pound of steel, for 
 the various sections, for a 10-foot span; the same ratio would 
 hold for other spans. 
 
 10" I-beam 10" channel 10" deck-beam 4X6 angle 4X5 tee 
 104 94.6 83.0 28.7 21.6 
 
 Deepest Beams Stiffest and most Economical. 
 
 The strength of a wrought-iron, wooden, or steel beam of rectan- 
 gular shape varies as the square of the depth, and directly as the 
 breadth ; hence the deeper beam will have the greatest strength 
 in proportion to its sectional area. With I-beams this rule in 
 regard to the square of the depth does not hold strictly true, on ac- 
 count of the variation in the sections, but it is approximately true. 
 
 It therefore follows that, for any given span, it is more economi- 
 cal, where other conditions will permit, to use deep beams spaced 
 farther apart in floors, or to use one deep beam in place of two 
 shallower beams. Thus if we wished to support a distributed 
 load of 39 tons with a 16-ft. span, we might use one 20-inch 70-lb. 
 beam, two 15-inch 42-lb. beams, or three 12-inch 40-lb. beams, 
 but the 20-inch beam would weigh only 1,190 Ibs. (allowing for 
 6-inch bearings) as compared with 1,428 Ibs. for the 15-inch 
 beams and 2,040 Ibs. for the 12-inch beams, besides the saving 
 in bolts and separators. 
 
 Light beams are also more economical than heavy beams of the 
 same depth, 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 Load tor Steel Beams. All beams 
 are subject in a greater or less degree to three kinds of strains. 
 The most destructive of these is generally the beiiding-moment, 
 which has already been considered. The second kind is that 
 
508 THE STRENGTH OF STEEL BEAMS. 
 
 which tends to shear the beam, or make one part slide on the 
 other vertically. This strain, however, seldom needs to be con- 
 sidered except in the case of riveted girders, and short beams with 
 very thick webs. The third strain is that which tends to cause 
 the web of the beam to buckle, and for steel beams, where the 
 span is very short in proportion to the depth of the beam, the 
 resistance of the web to buckling generally determines the maxi- 
 mum load that the beam will support, without stiffening the 
 webs. 
 
 In the tables giving the safe loads for I-beams, channels, 
 and deck-beams, the column headed Max. Load gives the great- 
 est load that should be put on the beam, no matter how short the 
 span, unless the web is stiffened by riveting plates or angles to 
 the web. This load may be either distributed or concentrated 
 at the centre, provided it does not exceed the safe load as deter- 
 mined by the bending-moment. In the tables giving safe loads for 
 I-beams and channels the loads to the left of the dotted line 
 exceed the maximum distributed loads, and hence the beam 
 should not be used for those spans, unless stiffening is resorted 
 to. For concentrated loads very much shorter spans may be 
 ' used than for distributed loads. Thus for a 24-inch 80-lb. beam 
 the shortest span for a full distributed load is 25 feet, while for a 
 concentrated load at the centre 12 feet would be the shortest 
 span. In using the tables for safe loads, therefore, the maxi- 
 mum load should always be considered. The maximum loads 
 in the table are such that the greatest shear will not exceed 
 10,000 Ibs. per. sq. inch, nor the total load exceed that obtained 
 by the formula 
 
 Max. load in tons= 8X */ , (8) 
 
 14- 
 ^ 
 
 in which d= depth of beam and t= thickness of web, both in 
 inches. 
 
 This formula is that used by the engineers of the Pencoyd Iron 
 Works, and gives results considerably less than formulas used by 
 some of the other steel companies. 
 
 It is based on Gordon's formula for long columns, considering 
 the length of the column equal to the diagonal depth of the beam, 
 and using 8,000 Ibs. as the unit strength of the material instead 
 of ten or twelve thousand pounds, as used for columns and the 
 webs of riveted girders. 
 
THE STRENGTH OF STEEL BEAMS. 509 
 
 In comparing this formula with formulas giving the safe resist- 
 ance to buckling, it should be remembered that these formulas 
 give the maximum shear, and that the maximum shear is only 
 one-half of the safe load, when the load is either distributed or 
 concentrated at the centre. 
 
 For beams unsymmetrically loaded the maximum shear should 
 not exceed one-half of the maximum load. 
 
 Short lengths of beams used as blocking or bolsters should not 
 be loaded to more than one-half the maximum load, given in the 
 tables. 
 
 Lateral Strength. As has been stated, the effect of the 
 bending-moment on a beam is to produce compression in the top 
 flange and tension in the lower flange; the top flange therefore 
 becomes in effect a strut, and when its length exceeds 20 times its 
 width the compression tends to deflect the beam sideways. Pre- 
 vision should therefore be made for bracing the beam sideways 
 at intervals not exceeding 20 times the width of the flange. 
 Floor-beams are generally sufficiently braced by the filling be- 
 tween the beams and by the tie-rods. In the case of a pair of 
 beams bolted together the total width may be taken in determin- 
 ing the maximum length, 
 
 In cases where it is not practical to support the beams sideways, 
 the loads given in the tables should be reduced as indicated in the 
 following table: 
 
 BEAMS WITHOUT LATERAL SUPPORT. 
 
 Proportion of tabular load 
 Length of beam. forming greatest safe load. 
 
 20 times flange width Whole tabular load. 
 
 20 to 30 " " " 9/10 
 
 30 to 40 " " " 8/10 
 
 40 to 50 " " " 7/10 
 
 50 to 60 " " " 6/10 
 
 60 to 70 " V " 5/10 
 
 EXAMPLE. What is the maximum distributed load that should 
 be allowed for a 15-inch 42-lb. beam 25-foot clear span, the beam 
 being unsupported sideways? 
 
 Ans. The flange width of this beam (see table of properties of 
 standard beams) is 5J in. 25 ft. (300 in.) -s- 5}= 54. We should 
 therefore use only .65 of the load given in the table, or 8.12 tons. 
 From this the weight of the beam (1,050 Ibs.) should also be sub- 
 tracted, reducing the maximum safe load to 7.6 tons. 
 
510 
 
 DEFLECTION OF STEEL BEAMS. 
 
 Deflection of Steel Beams. The principles and gen- 
 eral formula for the deflections of beams are given in Chapter 
 XVIII., and the deflection of any beam under any load may be 
 found by the formula there given. A shorter and sufficiently 
 accurate method of finding the deflection of steel beams under 
 the safe loads given in the tables is afforded by the following 
 table, taken from the " Pocket Companion" of the Carnegie Steel 
 Company : 
 
 DEFLECTION COEFFICIENTS FOR SYMMETRICAL 
 SHAPES GIVEN IN 64THS OF AN INCH. 
 
 Coeffi- 
 cient 
 index. 
 
 ~~C 
 C' 
 
 C 
 
 C' 
 
 Distance between supports in feet. 
 
 6 
 
 38.0 
 30.0 
 
 8 
 
 10 
 
 12 
 
 14 
 
 16 
 
 271.0 
 212.0 
 
 18 
 
 20 
 
 22 
 
 68.0 
 53.0 
 
 106.0 
 83.0 
 
 152.5 
 119.0 
 
 208.0 
 162.0 
 
 343.0 
 268.0 
 
 424.0 
 331.0 
 
 513.0 
 400.5 
 
 Distance between supports in feet. 
 
 24 
 
 26 
 
 28 
 
 30 
 
 32 
 
 34 
 
 36 
 
 1373.0 
 1073.0 
 
 38 
 
 1530.0 
 1195.0 
 
 40 
 
 1695.0 
 1324.0 
 
 610.0 
 477.0 
 
 716.0 
 559.0 
 
 830.5 
 649.0 
 
 953.0 1085.0 
 748.0 847.0 
 
 1225.0 
 957.0 
 
 The figures given opposite C and C' are the Deflection Coeffi- 
 cients for steel shapes subject to transverse strain for varying 
 spans, under their maximum uniformly distributed safe loads, 
 derived from a fibre strain of 16,000 and 12,500 respectively, the 
 modulus of elasticity being taken at 29,000,000 Ibs. 
 
 To find the deflection of any symmetrical shape used as a beam, 
 under its corresponding safe load,* divide the coefficients given in 
 the above tables by the depth of the beam ; the result will be the 
 deflection in 64ths of an inch. This applies to such shapes as 
 beams, channels, etc. For those shapes having unsymmetrical 
 sections, such as tees, angles, etc., divide by twice the greatest 
 distance of the neutral axis from the outside fibre. 
 
 For a beam supported at both ends and loaded at the centre 
 
 * This applies only to the loads at the left of the heavy line in the tables 
 following; the loads to the right of this line being reduced by the rule for 
 stiffness, the deflections obtained by this rule would be excessive. 
 
STRENGTH OF STRUT BEAMS. 511 
 
 with one-half the distributed load the deflection will be .8 that 
 obtained by the above table. 
 
 EXAMPLE. Required the deflection of a 10-inch 25-lb. steel 
 beam, 10-foot span, under its maximum distributed load of 13 
 tons (16,000 Ibs. fibre strain). The above table gives 106 as the 
 deflection coefficient; dividing by the depth of the beam (10) we 
 
 i n f\ 
 have 77- for the deflection at the centre. This is equivalent to 
 
 .165 in. By formula 1, Chapter XVIII., we find the deflection for 
 
 - ' 
 
 in., the two results agreeing perfect^. For the same beam and 
 18-ft. span, with a load of 7.2 tons, we find the deflection by the 
 
 O/f O 
 
 above table to be -^i- r -536 in., and by formula 1, .532, or prac- 
 tically the same. 
 
 For a concentrated load of 6,500 Ibs. at centre of 18-ft. span the 
 deflection would be .8X.53 or .42 in. As a rule it is not desir- 
 able to subject any beam to a load which will produce a deflection 
 at the centre exceeding ^ - ff th of the span, or ^th of an inch per 
 foot of span. A greater deflection is liable to produce cracks in 
 plastered ceilings, and if the beam is exposed the deflection is 
 painful to the eye. 
 
 In the tables giving the safe loads for I-beams and channels all 
 of the loads given are within this limit, the loads to the right of 
 the heavy line having been reduced to conform with the rule for 
 stiffness.* 
 
 When the deflection is of no particular consequence these 
 loads may be increased to the value obtained by dividing the 
 coefficient, C, by the span, but as a general rule, the loads should 
 not exceed those given in the table. 
 
 Strut Beams. It cannot be considered as good engineering 
 to subject a strut to a cross-strain, as any such strain must pro- 
 duce a certain amount of flexure in the strut, which the compress- 
 ive stress tends to increase. 
 
 There are often cases, however, where practical considerations 
 make it desirable to use a strut as a beam also, as in the top chord 
 or principles of trusses. For determining the size of the section 
 in such cases the following method should be used : 
 
 *This rule is as follows: Multiply the load given immediately to the 
 left of the heavy line by the square of the corresponding span, and divide 
 by the square of the required span ; the result will be the required load. 
 
512 STRENGTH 'OF TIE BEAMS. 
 
 1st. Find the section modulus for the transverse load by for- 
 mulas 2 A to 6A, using 12,000 Ibs. as the value of S, and find the 
 area of a section corresponding to the value of R thus found. 
 
 2d. Find the section area required by a section of the size 
 found to resist the compression stress by dividing the stress by 
 
 the value opposite in column II., Table XL, Chapter XIV. 
 
 3d. Add the two areas thus found together and use the next 
 larger section having the required area. 
 
 EXAMPLE. The principal rafter in a truss, 8-| ft. long between 
 joints, supports the end of a purlin at the centre of the span; the 
 weight from the purlin is 2,800 Ibs. and the compressive stress is 
 30,000 Ibs. It is desired to use two angles, with long legs vertical 
 and J inch apart for the principal. What should be their size ? 
 
 Ans. By formula (3A), R = 
 
 As two angles will be used, R for each will be 2.98. From the 
 table of properties of angles (p. 304, col. VII.), we find that the 
 angle having a value next above 2.98 is a 5x3X9/16 inch. 
 The area of this angle is 4.18 in., and from the table on page 317 
 we find the least value of r for a pair to be about 1.58 (the strut 
 
 being braced sideways) ; then = - = 64.5, and p from column 
 
 T -L. Oo 
 
 II., Table XL, p. 463, =10,756 Ibs. 30,000-^10,756 = 2.79 
 sq. in., or 1.40 in. for each angle. The area of the angle found 
 for the beam was 4.18; adding to this 1.40, we have 5.58 as 
 the required area for each angle, which is found in the 
 5X3 X}|" size. 
 
 As the area in both steps considerably exceeds that required 
 by the calculation, we need not make further allowance for the 
 weight of the angles. 
 
 Tie Beams. Steel beams subject to both tensile and trans- 
 verse strain should be calculated in a similar way to that ex- 
 plained above for strut beams. The section necessary to resist 
 the transverse strain should first be found, and then the sectional 
 area necessary to resist the tensile strain, and the two added 
 together. 
 
 EXAMPLE. One span of a tie beam, 10 ft. between joints, has 
 to support a load at the centre of three tons, and a tensile stress of 
 84,000 Ibs. Two steel channels will be used for the tie. What 
 should be their size and weight? 
 
STRENGTH OF STEEL BEAMS. 513 
 
 Ans. A centre load of 3 tons corresponds with a distributed 
 load of 6 tons, or 3 tons for each channel. From the table giving 
 the strength of channels, we find that a light 7-inch channel will 
 be required, the sectional area being 2.85 sq. in. The area re- 
 
 84 000 
 
 quired to resist the tensile stress = - =6 sq. in., or 3 in. for 
 
 14,000 
 
 each channel, and the total area for each channel should be 
 2.85 + 3=5.85 sq. in. A 7-in. 19f-lb. channel has an area of 
 5.81 sq. in. which will answer, as we do not use the full strength 
 of the light channel. If a sufficiently heavy section could not be 
 found in the 7-inch channels, we should use the next size, or 
 8-inch. 
 
 Explanation of Tables for the Strength, of 
 Steel Beams. 
 
 The following tables give the greatest safe loads for all of the 
 standard sections of beams, channels, and angles, and for the 
 Carnegie deck-beams and tees, and also the limits for deflection 
 and buckling of the beams and channels. By following the ex- 
 planations given below these tables may be used with simple or 
 no computations (other than those required for determining the 
 load they will have to support) for the usual conditions of build- 
 ing construction. For several concentrated loads or for a con- 
 bination of distributed and concentrated loads it will be neces- 
 sary to use the methods previously explained under Case 7. 
 
 In using any of the following tables allowance should be made for 
 the weight of the beam itself. 
 
 I-beams and channels having loads and spans to the left of the 
 dotted line, should have the web stiffened. 
 
 The loads to the right of heavy line (I-beams and channels) 
 were computed by formula for deflection. "Max. Load" is the 
 greatest distributed load that should be used without stiffening 
 the web by plates or angles. (See page 508.) To find the safe 
 load for any other span than those given in the table, divide the 
 number in column headed C by the given span in feet and 
 decimals of a foot, and the answer will be the safe load for that 
 span, provided it is less than the max. load and within the limits 
 of deflection, and is stayed laterally. 
 
 To use any of the following tables for CONCENTRATED LOADS, 
 find the equivalent distributed load by multiplying the con- 
 
514 STRENGTH OF STEEL BEAMS. 
 
 centrated load by the factor given below, and then use the size 
 of beam having a safe load equal to the load thus found. 
 For concentrated load at centre, multiply by 2. 
 
 For load applied one-third the span from one end, m'ply by 1.78 
 
 " " " one-fourth " " " " " " ' " 1.5 
 
 " " " one-fifth " " " " " " " 1.28 
 
 " " " one-sixth " " " " " " " 1J 
 
 " " " one-seventh " " " " " " " .98 
 
 " " " one-eighth " " " " " " " f 
 
 " " " one-ninth " " " " " " " .79 
 
 " " " one-tenth " " " " " " " .72 
 
 For two equal loads applied one-third the span from each end, 
 
 multiply one load by 2. 
 For two equal loads applied one-fourth the span from each end 
 
 multiply one load by 2. 
 
 For beam fixed at one end, and loaded at the other, multiply by 8. 
 For beam fixed at one end, and uniformly loaded over entire 
 
 length, multiply by four. 
 
 Examples of Application. 
 
 EXAMPLE 1. A steel I-beam of 18-foot span has to support a 
 load of 4 tons at a point six feet from pne support. What should 
 be the size of the beam? 
 
 Ans. Six feet is one-third of the span. Multiplying the load 
 by 1.78, we have 7.12 tons. Looking in the following table for 
 the strength of steel I-beams, we find that a 10-inch 25-lb. beam 
 18-ft. span has a safe load of 7.2 tons, hence this beam will just 
 answer. 
 
 EXAMPLE 2. A steel I-beam of 18-ft. span supports two equal 
 loads of three tons each, applied 6 feet from each end. What 
 should be the size of the beam? 
 
 Ans. Six feet being one- third of the span, multiply one load 
 by 2|, which gives 8 tons as the equivalent distributed load. 
 This will require a 10-inch 35-lb. beam. 
 
 [NOTE. The same results should be obtained by using the 
 formula 6A, page 503.] 
 
 Following the tables giving the safe loads for channels is a table 
 computed by the author, giving the strength of small rectangular 
 steel bars. These bars are often used for supporting metal lath 
 in suspended ceilings, and the table will be found useful in deter- 
 mining the size of bar to use for any given span and spacing. 
 
STANDARD STEEL I-BEAMS. 
 
 515 
 
 
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 (M OOCOTt<| 
 
 ocot^o 
 
 TJHCOO5 
 
 
 1 
 
 Tfl 
 
 Tf<O 
 
 <M<M 
 
 O5 OTH<M 
 
 i> t-ooosj 
 
 lOiOiOCO 
 
 CO CO CO 
 
 
 
 
 Tfl CO 
 
 o ooo 
 
 l> rfiCO<M 
 
 00 <M COO| 
 
 OiCM O 
 
 COiOt> 
 
 
 2 
 
 COI> 
 (MM 
 
 O i-i (M CO 
 
 t^ 00050 
 
 iOCOcOi>| 
 
 CO"t "*i 
 
 <M(M(M 
 
 
 
 CO 05 
 
 oo aoi-< 
 
 "sf OOO 
 
 COl>i-i CO 
 
 co en co 
 
 I>O5(M 
 
 
 <M 
 
 00 O5 
 <M<M 
 
 O THCOTt< 
 
 00 O5OrH 
 
 COCOI>I> 
 
 T^-^ 1C 
 
 <M(MCO 
 
 
 
 r-HCO 
 
 00 O<MTT< 
 
 rH O1O5C 
 
 O5 CO 00 CO 
 
 0^*00 
 
 (MiOOO 
 
 
 - 
 
 8 
 
 ^H CO^iO 
 T-l 1-HrHrH 
 
 O5 O5O<M 
 
 COI>I>00 
 
 ioou: 
 
 CO CO CO 
 
 
 
 CO 00 
 
 c cocoes 
 
 O O5O<M 
 
 4OOcOt-i 
 
 OC5Tt< 
 
 00 (M CO 
 
 
 
 
 %$> 
 
 CO T^OCO 
 
 O O<MCO 
 
 t^000005 
 
 OiOcO 
 
 CO'*'* 
 
 
 
 1-HOO 
 
 Tfjcscooo 
 
 T-<',1-< ^ CO 
 
 Tj<05OTH 
 
 rHCO^i 
 
 COlN'-l 
 
 
 O5 
 
 00 O5 
 
 coco 
 
 Tf ;lOt^OO 
 
 i-H|<MCOCO 
 
 0000050 
 
 ?OCOI> 
 
 Tf<Tt<0 
 
 
 
 OCX 
 
 C<1 j'OJ^O'-* 
 
 tOjCOrHO 
 
 Tj<T-Hl>.Ttt 
 
 O5^O 
 
 CO CO 00 
 
 
 00 
 
 <Mrt< 
 
 cO;t^C5i-! 
 
 (MICOiOCO 
 
 0500^ 
 
 cot^oo 
 
 rf IOIO 
 
 
 
 
 
 
 
 
 
 
 
 
 <M<M 
 
 tO CO(Mrt^ 
 
 CO O5i-HO5 
 
 I>COO5-* 
 
 COi-H CO 
 
 O51OO5 
 
 03 
 5 
 
 3 
 
 Tj1t> 
 
 Oco 
 
 CO COCOC75 
 i-l (MIMCO 
 
 O O^CO 
 
 i-H (M CO-^H 
 
 C5COIMC5 
 
 rH(M<M 
 
 OCiOT-i 
 i-t(M 
 
 COCOO5 
 
 
 
 O5 t> 
 
 (M rH(M<M 
 
 CO O5 1> iO 
 
 OOOOOfM 
 
 (M t>CO 
 
 t^CO>C 
 
 $ 
 
 j 
 
 II 
 
 O (MCOO5 
 CO ^ IOCO 
 
 XC<M 
 O(MCO 
 
 ICOCO'-H 
 
 1>OOOCO5 
 
 >OC5-<f 
 tO iO CO 
 
 OOIMCO 
 
 COTjlTt 
 
 | 
 
 5 
 
 C 
 
 j= 
 bj 
 'a 
 
 .1 
 
 d 
 
 *jt 
 
 1 
 
 QiO 
 <OCO 
 
 iO O^OO 
 <M COCO^ 
 
 rH lOOO 
 
 M oicoco 
 
 8S8 
 
 oo'o'coio 
 
 rH(M^(M 
 
 00 
 too 
 
 25% 
 
 ooto 
 
 (Mt-tM 
 (M * t- 
 
 I 
 
 a 
 j: 
 
 *c 
 
 x 
 c 
 
 a 
 P 
 
 in inches. 
 
 CM 
 
 O 
 
 05 
 
 00 
 
 I> 
 
 
 
518 
 
 DECK-BEAMS. 
 
 SAFE DISTRIBUTED LOADS IN TONS FOR STANDARD 
 
 STEEL I-BEAMS (continued). 
 
 (See pages 513 and 515.) 
 
 Depth of 
 beam in 
 inches. 
 
 Jl 
 
 " 
 
 Jl 
 9.75 
 12.25 
 14.75 
 
 7.50 
 8.50 
 9.50 
 10.50 
 
 5.50 
 6.50 
 7.50 
 
 C. 
 
 "C 
 
 1 
 
 H 
 o3 
 
 Span in feet. 
 
 4 
 
 6.45 
 7726 
 
 8.07 
 
 3.97 
 4.24 
 
 4.50 
 4.76 
 
 2 20 
 2.39 
 
 2.58 
 
 5 
 
 6 
 
 e>y 2 
 
 3.68 
 4.15 
 4.61 
 
 2.27 
 2.42 
 2.57 
 2.72 
 
 1.08 
 1.17 
 1.27 
 
 8 
 
 3.22 
 3.63 
 4.03 
 
 OMOV 
 
 1.74 
 
 1.85 
 1.97 
 2.08 
 
 0.82 
 0.89 
 0.97 
 
 9 
 
 2.54 
 
 2.87 
 3.19 
 
 1.37 
 1.46 
 1.55 
 1.64 
 
 0.65 
 0.71 
 0.76 
 
 10 
 
 11 
 
 5 
 
 25.80 
 29.05 
 32 . 30 
 
 15.90 
 16.95 
 18.00 
 19.05 
 
 8.80 
 9.55 
 10.35 
 
 5.5 
 12.1 
 18.4 
 
 4.1 
 6.7 
 9.2 
 11.7 
 
 2.7 
 
 5.3 
 
 7.8 
 
 5.16 
 5.81 
 6.46 
 
 3.18 
 3.39 
 3.60 
 3.81 
 
 1.76 
 1.91 
 2.07 
 
 4.30 
 4.84 
 5.38 
 
 2.65 
 2.82 
 3.00 
 3.17 
 
 1.46 
 1.59 
 1.72 
 
 3.97 
 4.47 
 4.97 
 
 2.44 
 2.60 
 
 2 77 
 2^93 
 
 1.25 
 1.35 
 1.47 
 
 2.06 
 2.32 
 
 2.58 
 
 1.11 
 
 1.18 
 1.26 
 1.33 
 
 0.53 
 0.57 
 0.62 
 
 1.70 
 1.92 
 2.13 
 
 4 
 
 3 
 
 SAFE DISTRIBUTED LOADS IN TONS FOR CARNEGIE 
 
 DECK-BEAMS. 
 (For dead loads only.) 
 
 (See explanation, page 513.) 
 c = load to be added to C for each Ib. increase in weight of beam. 
 
 
 
 
 
 
 Maximum fibre strain, 16,000 Ibs. per square 
 
 si 
 
 o . 
 
 
 
 i 
 
 inch. 
 
 "^ a" 
 
 _ ~"^ 
 
 
 
 3 
 
 
 || 
 
 L^2 
 
 C. 
 
 c. 
 
 X 
 ca 
 
 Span in feet. 
 
 J 
 
 
 
 
 ^ 
 
 6 
 
 8 
 
 9 
 
 10 
 
 12 
 
 14 
 
 16 
 
 18 
 
 11J4 
 
 37.00 
 
 163.2 
 
 
 39.2 
 
 27.21 
 
 20.40 
 
 18.14 
 
 16.32 
 
 13.60 
 
 11.66 
 
 10.20 
 
 9.07 
 
 ll l /| 
 
 32.20 
 
 147.4 
 
 3.04 
 
 25.7 
 
 24.56 
 
 18.42 
 
 16.37 
 
 14.74 
 
 12.28 
 
 10.53 
 
 9.21 
 
 8.19 
 
 10 
 
 35.70 
 
 137.1 
 
 
 43.4 
 
 22.84 
 
 17.13 
 
 15.23 
 
 13.71 
 
 11.42 
 
 9.79 
 
 8.57 
 
 7.61 
 
 10 
 
 27.23 
 
 113.1 
 
 2.45 
 
 20.8 
 
 18.84 
 
 14.13 
 
 12.56 
 
 11.31 
 
 9.42 
 
 8.08 
 
 7.07 
 
 6.28 
 
 9 
 
 30.00 
 
 104.3 
 
 
 35.4 
 
 17.37 
 
 13.03 
 
 11.59 
 
 10.43 
 
 8.69 
 
 7.45 
 
 6.52 
 
 5.79 
 
 9 
 
 26.00 
 
 94.5 
 
 2.25 
 
 24.7 
 
 15.76 
 
 11.81 
 
 10.51 
 
 9.45 
 
 7.88 
 
 6.75 
 
 5.91 
 
 .5.25 
 
 8 
 
 24.48 
 
 75.1 
 
 
 25.3 
 
 12.51 
 
 9.39 
 
 8.35 
 
 7.51 
 
 6.25 
 
 5.36 
 
 4.69 
 
 3*70 
 
 8 
 
 20.15 
 
 64.9 
 
 2.00 
 
 13.7 
 
 10.82 
 
 8.11 
 
 7,21 
 
 6.49 
 
 5.41 
 
 4.64 
 
 4. on 
 
 3.20 
 
 7 
 
 23.46 
 
 62.3 
 
 
 27.2 
 
 10.38 
 
 7.79 
 
 6.92 
 
 6.23 
 
 5.19 
 
 4.4, r 
 
 3.40 
 
 2.69 
 
 7 
 
 18.11 
 
 51.5 
 
 i.Y" 
 
 13.0 
 
 8.58 
 
 6.44 
 
 5.72 
 
 5.15 
 
 4.29 
 
 3.6S 
 
 2.81 
 
 2.22 
 
 6 
 
 17.16 
 
 38.4 
 
 
 18.2 
 
 6.40 
 
 4.80 
 
 4.27 
 
 3.84 
 
 3.20 
 
 2.35 
 
 1.80 
 
 1.42 
 
 6 
 
 14.10 
 
 32.5 
 
 1.5 
 
 10.3 
 
 5.42 
 
 4.07 
 
 3.62 
 
 3.25 
 
 2.71 
 
 1.99 
 
 1.52 
 
 1.20 
 
STANDARD STEEL CHANNELS. 
 
 519 
 
 3' 
 
 iJ 
 W 
 
 S 
 
 S d : 
 
 Q -I 
 
 tf S . 
 
 <ri 
 
 -s 
 
 < "S 
 
 S M 
 
 02 'c ' 
 
 O J ^ 
 
 ^ o S 
 
 pa ^^: 
 
 QQ 
 
 Q 
 
 2 ^ d 
 | g.2 
 
 ^ll 
 
 
 Q 
 
 l|? 
 
 n 
 
 s s 
 
 
 CO 
 
 Ci O CO CO Gi iO 
 CO l> l> GO CO Oi 
 
 
 
 
 
 GO 
 CM 
 
 CO CM CM CM CM CM 
 
 OirH GO tO CM Oi 
 
 l> GO CO Oi' O OJ 
 
 IOi Oi CO t> rH 
 COCO^ti HH rfl 
 
 
 
 
 O 
 CM 
 
 ^ lOOCMrH CO 
 
 O t> tO CM O l> 
 
 CCGOOiOrHrH 
 
 IO CO t^ 00 O 
 M*"- 
 __,.."* 
 
 
 
 
 3 
 
 tO O O r-i CO rr 
 
 CM "tf CO rH Oi t> 
 
 oioiOrHrHCM 
 
 ItO CO Oi CO Oi 
 COGOT^OCO 
 lococo 
 
 
 
 
 CO 
 
 CO Oi b- CO -"tf CO 
 
 ICO CM GO CO CO 
 ixrocicocM 
 
 
 
 
 CM 
 
 OiOiOrHCMCO 
 
 
 
 
 
 CM 
 
 THCOCMrHOOi 
 
 00 CM CC rf CO 
 rHOOtOCMO 
 
 ItO CM O Oi GO 
 CO rH CO C tO 
 
 
 
 CM 
 
 OOrHCMCOCO 
 
 . 
 
 CM CO CO 't'* 
 
 
 
 
 to oo t> t^ co o 
 
 ^OGoScO 
 
 IrHCOCOOiCO 
 
 
 
 CM 
 
 O O rH OI CO Tf 
 
 iO CO CO l> CO 
 
 CM CO CO-* iO 
 
 
 <u 
 
 <M 
 
 o 
 
 rH CO CO CO CO CO 
 
 
 ICM r^ CO Oi to 
 
 rfrHCOlO 
 
 CM Tf CO CO 
 
 | 
 
 
 !>OOOOrH 
 
 
 
 
 a 
 
 02 
 
 ^ 
 
 rH CM CO ^ IO CO 
 
 COCOl>GOOi 
 
 
 
 co ^ T^ to co 
 
 CM CM CO CO 
 
 
 00 
 
 CO CO l> 00 OirH 
 
 COrHOiOO^ 
 
 cccOOiOCO 
 
 OiCOCMrHCO 
 
 
 
 
 ^^^^^2 
 
 cOt-b-COOJ 
 
 COrfHiOCOcO 
 
 CM CM CO * 
 
 
 
 O^^t^COOi 
 
 ^U5^^CO 
 
 Oi * O t^ -t 
 
 1 CCOXrf 
 
 
 1-1 
 
 CO CO rfi O CO l> 
 
 CO 1> CO Oi O 
 
 TjH^^COt- 
 
 CO CO CO -^ 
 
 
 CO 
 
 OiCN^COOirH 
 
 THOOiOiOi 
 
 lOiOcCcOO 
 Tf CM O CO t^ 
 
 lOt^tOCM 
 
 
 
 CO TJH iO CD CM Oi 
 
 I>COCOOiO 
 
 ^tocccoi- 
 
 COCO-ttO 
 
 
 IO 
 
 OOrH^H^OCO 
 
 o to to co co 
 
 t- CD'* CO CM 
 
 ^rHOOO 
 
 1>OOO to 
 
 
 
 
 t^COOiOrH 
 
 TMOCOt-CO 
 
 C0^rt<0 
 
 
 
 CO CM CO O -^ GO 
 
 rHrHCM^O 
 
 THOOiooco 
 
 CCOrHOi 
 
 
 r* 
 
 rH rH r-l rH CM CM 
 
 CO Oi O rH CM 
 
 lOCOCO^CO 
 
 ^H^^tO 
 
 
 
 iO Oi CO CM CO O 
 
 iO CO Oi CO CO 
 
 OiOOrHCM 
 
 cooooi 
 
 
 
 GO GO O CM CO 10 
 
 rH rH CM CM CM CM 
 
 ^SSJSS 
 
 !OI>COOiO 
 
 10 CO CO 
 
 
 
 
 CM CM rh CO COO 
 CM CM C\ CM CM CO 
 
 d2SI2^ 
 
 ^'cOoirH-CM- 
 
 IOCOI>00 
 
 |)U( 
 
 , 
 
 lO Tfl O rH O t> 
 
 1^ iO l> b- CO 
 
 CM CO 1 * to -^ 
 
 COrHCOrH 
 
 rannii 
 
 raw 
 
 CM CM ^ tO "O CO 
 
 r^ CM CO CO -t 
 
 OCOI^OCO 
 CJCM ^ to 
 
 I>CM OiCO 
 
 rH r-! CO 
 
 
 
 CM tOrH t^COOi 
 
 OiOt^-<* rH 
 
 COCO r-i CM 
 
 t-HCM OCO 
 
 * 
 
 
 CM N- 1> CO CO tO 
 
 CM CM -^ CO GOO 
 CM CM CM CM CM CO 
 
 CO GO CO Oi IO 
 
 rH CM Tf '0 l^ 
 
 i>COCir-CM 
 
 COO CM CO 
 iOCOt>GO 
 
 sq 
 
 [ 
 
 888888 
 
 8888 
 
 88888 
 
 CM888 
 
 !?q3ra 
 
 M 1 
 
 CO CO Th 'f tO tO 
 
 o too too 
 
 CM CM COCO-* 
 
 10 o to o >o 
 
 r-i CM CM CO CO 
 
 co too o 
 
 r-rHCMCM 
 
 J3 S 
 
 4-3 fl 
 
 CX-2 
 <B 
 
 QJ 
 
 Q 
 
 
 3 
 
 2 
 
 CM 
 
 
 
 Oi 
 
520 
 
 STANDARD STEEL CHANNELS. 
 
 1 
 
 a 
 a 
 
 a . 
 
 OJ 
 
 CO 
 
 IN rH TT CM 7C 
 
 N NCO COCO 
 
 S t^SSco 
 
 
 
 10 
 
 x NIO X<M 
 
 N COCO CO-* 
 
 1 . ..*.., 
 
 
 
 2 
 
 CO COCO -*Tt< 
 
 ^ IO CO r-i OS 
 O (NOXO 
 
 CO 
 
 1 rH OSOS OO 
 
 .CO COO OOS 
 
 s.ss* 
 
 1> OS N !"" 
 
 CO iOXO 
 
 rH rHrHlM 
 
 
 N 
 
 O OTF XCO 
 CO ^ ^ ^t 1 lO 
 
 'X 1-- IO CO r-l 
 
 IO CD ^t 1 rH 
 CO XrHTfl 
 
 
 (N COCOCOTJH 
 
 rH* rn'^W 
 
 - 
 
 rH CD CO rH O 
 
 OS COX COX 
 
 S iO CD X O 
 COI>rH CO 
 
 1OS N iOX ON 
 
 t 
 
 CO ^ rJ4 iO O 
 
 CO COCO^ 
 
 
 O 
 
 O O N 'f t- 
 
 CO XCO XCO 
 
 SSwS 
 
 N NCOCO rH rH 
 
 rn' 
 
 OS 
 
 X COOS OrH 
 
 rH OSOrH(M 
 l> OCOrH CO 
 
 t^ O5N CD CO b- 
 
 iO OS^X iO X 
 
 OS t^ CC*O 
 
 rH XOSO 
 
 N NCOCO rH rH 
 
 N rH 
 
 X 
 
 Tt< oco coos 
 
 rH COrH|>CO 
 
 N COCO'* rH C^ 
 
 -^ 1 O N CO 
 
 ^Jl^ 
 
 10 co CO t> I s - 
 
 ^ ^o^co 
 
 - 
 
 rH OSCO COrH 
 
 | NOTION 
 
 O T O CD iO O 
 CO X ^ OS N t> 
 
 M 3|ot2 
 
 co cob- xos 
 
 
 CO 
 
 rHJOOS t-co 
 
 CO -^ O CON 
 
 iO XCOOS CO COO XCOCO|OrH<N 
 
 00 r^rHt^ CO rHl> COXClXOSO 
 
 t^jXX OSO 
 
 10 cocoi>x 
 
 CO T^lOlO N COCO rHrHC^ll rH 
 
 
 CO ; ' CO CD t^b- 
 
 
 CO T*rHO> rS 
 
 ^ 0^23 ^co^ 
 
 XJOSO rH(M 
 
 CO I>XO5O 
 
 Tt< lOCOCD CO COTfH NNN rHrHrH 
 
 
 
 r-ioco oos 
 
 CO M CO O CO 
 
 x t-r-r- o h. 
 
 iO *O1>O r^cOX 
 
 O;(MCO rfiO 
 
 X OSOrHC^ 
 
 O COl-X CO ^ 
 
 O NNCO rHrHrH 
 
 co 
 
 co ot-i^N 
 
 rH COT^COX 
 
 r-osNco NJCO 
 
 COrH CO COXiO 
 * COl>O OSrHTtl 
 
 3 2^:2^ 
 
 rH (MCOlOCO 
 
 l> XOrH lOJCDI 
 
 >- COCO-* rHNN 
 
 I] 
 
 X <N-t> OO 
 
 O NOCOO3 
 
 ^ OlOOS CO rHl 
 
 ^ rHt^(M O^OO 
 
 CO CO>O <MX 
 
 CO CO CO N X 
 
 rH rH C<) N 
 
 rHrH(N rH rH 
 
 o 
 
 iO O O O O 
 O ON H/H> 
 
 O iO O O O 
 
 O OO*O O iO< 
 
 rH OSXt> X OSC 
 
 O COO O O O 
 
 M rHrHCN X O CO 
 
 CO X CO X CO 
 T^ rfiO lOCD 
 
 CO CO ^t Hj< LO 
 
 CO COO^ iO XN OrHiN OcOt^ 
 
 NNCOCO r-l rH W rHr-lrH 
 
 sq[ 
 
 '^OOJ J8d 
 
 ^q3t8yW 
 
 N t2^ {2c5 
 
 i2 ^^^{2 
 
 OOCO O OC 
 
 NNN 888 
 
 rH COCO XrH 
 
 05 ^^^2 
 
 X OCOO CO OSr 
 
 H u^co^ ^OCO 
 
 1 
 
 1 
 
 00 
 
 - 
 
 CO IO 
 
 ^ CO 
 
 I 
 
STANDARD STEEL CHANNELS. 
 
 521 
 
 SAFE DISTRIBUTED LOADS IN TONS FOR STANDARD 
 STEEL CHANNELS SET FLATWAYS 
 
 or with the load acting at right angles to the plane of the web. 
 
 (Computed by the Pencoyd Iron Works.) 
 (Fibre Stress 16,000 Ibs. per Square Inch.) 
 
 
 
 Length of span in feet. 
 
 
 Wt. 
 
 
 Size 
 
 in 
 
 
 
 
 
 
 
 
 
 
 
 in 
 
 Ibs. 
 
 4 
 
 ,5 
 
 ' 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 13 
 
 ins. 
 
 per 
 
 
 
 
 
 
 
 
 
 
 
 
 foot. 
 
 Safe load in net tons. 
 
 15 
 
 33.0 
 
 4.14 
 
 3.31 
 
 2.76 
 
 2.36 
 
 2.07 
 
 1.84 
 
 1.66 
 
 1.50 1.38 
 
 1.27 
 
 15 
 
 35.0 
 
 4.28 
 
 3.42 
 
 2.85 
 
 2.45 
 
 2.14 
 
 1.90 
 
 1.71 
 
 1.56 1.43 
 
 1.32 
 
 15 
 
 40.0 
 
 4.56 
 
 3.65 
 
 3.04 
 
 2.61 
 
 2.28 
 
 2.03 
 
 1.82 
 
 1.66 
 
 1.52 
 
 1.40 
 
 15 
 
 45.0 
 
 4.83 
 
 3.86 
 
 3.22 
 
 2.76 
 
 2.41 
 
 2.15 
 
 1.93 
 
 1.76 
 
 1.61 
 
 1.49 
 
 15 
 
 50.0 
 
 6.92 
 
 5.53 
 
 4.61 
 
 3.95 
 
 3.46 
 
 3.07 
 
 2.77 
 
 2.51 
 
 2.31 
 
 2.13 
 
 15 
 
 55.0 
 
 7.30 
 
 5.84 
 
 4.87 
 
 4.17 
 
 3.65 
 
 3.25 
 
 2.92 
 
 2.66 
 
 2.43 
 
 2.25 
 
 12 
 
 20.5 
 
 2.32 
 
 1.86 
 
 1.55 
 
 1.33 
 
 1.16 
 
 1.03 
 
 0.93 
 
 0.84 
 
 0.77 
 
 0.71 
 
 12 
 
 25.0 
 
 2.53 
 
 2.03 
 
 1.69 
 
 1.45 
 
 1.27 
 
 1.13 
 
 1.01 
 
 0.92 
 
 0.84 
 
 0.78 
 
 12 
 
 30.0 
 
 2.77 
 
 2.22 
 
 1.85 
 
 1.58 
 
 1.39 
 
 1.23 
 
 1.11 
 
 1.01 
 
 0.92 
 
 0.85 
 
 12 
 
 35.0 
 
 4.76 
 
 3.81 
 
 3.17 
 
 2.72 
 
 2.38 
 
 2.12 
 
 1.90 
 
 1.731 1.59 
 
 1.46 
 
 12 
 
 40.0 
 
 5.12 
 
 4.10 
 
 3.41 
 
 2.93 
 
 2.56 
 
 2.28 
 
 2.05 
 
 1.86 
 
 1.71 
 
 1.58 
 
 10 
 
 15.0 
 
 1.55 
 
 1.24 
 
 1.03 
 
 0.88 
 
 0.77 
 
 0.69 
 
 0.62 
 
 0.56 
 
 0.52 
 
 0.48 
 
 10 
 
 20.0 
 
 1.77 
 
 1.42 
 
 1.18 
 
 1.01 
 
 0.89 
 
 0.79 
 
 
 0.641 0.59 
 
 0.54 
 
 10 
 
 25.0 
 
 2.66 
 
 2.13 
 
 1.77 
 
 1.52 
 
 1.33 
 
 1.18 
 
 1 -OC 
 
 0.971 0.89 
 
 0.82 
 
 10 
 
 30.0 
 
 2.95 
 
 2.36 
 
 1.97 
 
 1.69 
 
 1.47 
 
 1.31 
 
 1.18 
 
 1.07 0.98 
 
 0.91 
 
 10 
 
 35.0 
 
 3.26 
 
 2.61 
 
 2.17 
 
 1.86 
 
 1.63 
 
 1.45 
 
 1.30 
 
 1.19 1.09 
 
 1.00 
 
 9 
 
 13 95 
 
 1.29 
 
 1.03 
 
 0.86 
 
 0.74 
 
 0.65 
 
 0.57 
 
 0.52 
 
 47 
 
 0.43 
 
 40 
 
 9 
 
 15.00 
 
 1.37 
 
 1.10 
 
 0.92 
 
 0.79 
 
 0.69 
 
 0.61 
 
 0.55 
 
 0.50 0.46 
 
 0.42 
 
 9 
 
 20.00 
 
 2.08 
 
 1.67 
 
 1.39 
 
 1.19 
 
 1.04 
 
 0.92 
 
 0.83 
 
 0.76 0.69 
 
 0.64 
 
 9 
 
 25.00 
 
 2.37 
 
 1.89 
 
 1.58 
 
 1.35 
 
 1.18 
 
 1.05 
 
 0.95 
 
 0.86 0.79 
 
 0.73 
 
 8 
 
 11.25 
 
 1.04 
 
 0.83 
 
 0.70 
 
 0.60 
 
 0.52 
 
 0.46 
 
 0.42 
 
 0.38 0.35 
 
 0.32 
 
 8 
 
 13.75 
 
 1.16 
 
 0.92 
 
 0.77 
 
 0.66 
 
 0.58 
 
 0.51 
 
 0.46 
 
 0.42 0.39 
 
 0.36 
 
 8 
 
 16.25 
 
 1.64 
 
 1.31 
 
 1.09 
 
 0.94 
 
 0.82 
 
 0.73 
 
 0.66 
 
 0.59' 0.55 
 
 0.50 
 
 8 
 
 18.75 
 
 1.77 
 
 1.42 
 
 1.18 
 
 1.01 
 
 0.89 
 
 0.79 
 
 0.71 
 
 0.64' 0.59 
 
 0.55 
 
 8 
 
 21.25 
 
 1.90 
 
 1.52 
 
 1.27 
 
 1.09 
 
 0.95 
 
 0.85 
 
 0.76 
 
 0.69 
 
 0.63 
 
 0.59 
 
 7 
 
 9.75 
 
 0.84 
 
 0.67 
 
 0.56 
 
 0.48 
 
 0.42 
 
 0.37 
 
 0.34 
 
 0.31 
 
 0.28 
 
 0.26 
 
 7 
 
 12.25 
 
 0.95 
 
 0.76 
 
 0.63 
 
 0.54 
 
 0.47 
 
 0.42 
 
 0.38 
 
 0.34 0.32 
 
 0.29 
 
 7 
 
 14.75 
 
 1.37 
 
 1 .10 
 
 0.91 
 
 0.78 
 
 0.69 
 
 0.61 
 
 0.55 
 
 0.50 0.46 
 
 0.42 
 
 7 
 
 17.25 
 
 1.51 
 
 1.20 
 
 1.00 
 
 0.86 
 
 0.75 
 
 0.67 
 
 0.60 
 
 0.55! 0.50 
 
 0.46 
 
 7 
 
 19.75 
 
 1.64 
 
 1.31 
 
 1.10 
 
 0.94 
 
 0.82 
 
 0.73 
 
 0.66 
 
 0.60 
 
 0.55 
 
 0.50 
 
 6 
 
 8.00 
 
 0.65 
 
 0.52 
 
 0.44 
 
 0.37 
 
 0.33 
 
 0.29 
 
 0.26 
 
 0.24 
 
 0.22 
 
 0.20 
 
 6 
 
 10.50 0.91 
 
 0.73 
 
 0.61 
 
 0.52 
 
 0.45 
 
 0.41 
 
 0.36 
 
 0.33 
 
 0.30 
 
 0.28 
 
 6 
 
 13.00 
 
 1.04 
 
 0.83 
 
 0.69 
 
 0.59 
 
 0.52 
 
 0.46 
 
 0.41 
 
 0.38 0.35 
 
 0.32 
 
 6 
 
 15.50 
 
 1.16 
 
 0.93 
 
 0.78 
 
 0.66 
 
 0.58 
 
 0.52 
 
 0.46 
 
 0.42 
 
 0.39 
 
 0.36 
 
 5 
 
 6.50 
 
 0.50 
 
 0.40 
 
 0.33 
 
 0.28 
 
 0.25 
 
 0.22 
 
 0.20 
 
 0.18 0.16 
 
 0.15 
 
 5 
 
 9.00 
 
 0.61 
 
 0.49 
 
 0.41 
 
 0.35 
 
 0.30 
 
 0.27 
 
 0.25 
 
 0.22 0.20 
 
 0.19 
 
 5 
 
 11.50 
 
 0.72 
 
 0.57 
 
 0.48 
 
 0.41 
 
 0.36 
 
 0.32 
 
 0.29 
 
 0.26 0.24| 0.22 
 
522 
 
 SMALL STEEL CHANNELS. 
 
 SAFE DISTRIBUTED LOADS IN POUNDS FOR SMALL 
 STEEL CHANNELS, OR GROOVED STEEL. 
 
 (Computed for fibre strain of 16,000 Ibs.) 
 (For dimensions of sections see page 300.) 
 
 Sec- 
 tion 
 
 D'pth 
 in 
 
 Wt. 
 
 per 
 foot, 
 
 C 
 Ibs. 
 
 Span in feet. 
 
 
 
 
 
 
 
 
 
 No. 
 
 ins. 
 
 Ibs. 
 
 
 2 
 
 2.5 
 
 3 
 
 3.5 
 
 4 
 
 4.5 
 
 5 
 
 6 
 
 1 
 
 y/ 
 
 3.80 
 
 7570 
 
 3785 
 
 3028 
 
 2523 
 
 2163 
 
 1892 
 
 1682 
 
 1514 
 
 1261 
 
 2 
 
 2 
 
 2.90 
 
 5120 
 
 2560 
 
 2048 
 
 1706 
 
 1463 
 
 1280 
 
 1138 
 
 1024 
 
 853 
 
 3 
 
 2 
 
 3.60 
 
 5760 
 
 2880 
 
 2304 
 
 1920 
 
 1643 
 
 1440 
 
 1280 
 
 1152 
 
 960 
 
 4 
 
 2 
 
 3.60 
 
 6240 
 
 3120 
 
 2496 
 
 2080 
 
 1783 
 
 1560 
 
 1386 
 
 1248 
 
 1040 
 
 5 
 
 2 
 
 2 . 60 
 
 4512 
 
 2256 
 
 1804 
 
 1504 
 
 1289 
 
 1128 
 
 1000 
 
 902 
 
 752 
 
 6 
 
 2 
 
 2.00 
 
 2836 
 
 1418 
 
 1134 
 
 945 
 
 810 
 
 709 
 
 630 
 
 567 
 
 472 
 
 7 
 
 1 3 4 
 
 1.13 
 
 1815 
 
 907 
 
 726 
 
 605 
 
 518 
 
 454 
 
 403 
 
 363 
 
 302 
 
 8 
 
 IX 
 
 1.32 
 
 1536 
 
 768 
 
 614 
 
 512 
 
 439 
 
 384 
 
 341 
 
 307 
 
 256 
 
 9 
 
 IK 
 
 1.46 
 
 1736 
 
 868 
 
 694 
 
 578 
 
 496 
 
 434 
 
 386 
 
 347 
 
 289 
 
 10 
 
 1 1 4 
 
 0.94 
 
 950 
 
 475 
 
 380 
 
 316 
 
 271 
 
 237 
 
 211 
 
 190 
 
 
 11 
 
 1H 
 
 1.12 
 
 939 
 
 469 
 
 375 
 
 313 
 
 268 
 
 234 
 
 208 
 
 188 
 
 
 12 
 
 IX 
 
 1.00 
 
 874 
 
 437 
 
 350 
 
 291 
 
 250 
 
 218 
 
 194 
 
 175 
 
 
 13 
 
 1 
 
 0.83 
 
 672 
 
 336 
 
 268 
 
 224 
 
 192 
 
 168 
 
 
 
 
 14 
 
 1 
 
 0.68 
 
 532 
 
 266 
 
 212 
 
 177 
 
 152 
 
 13? 
 
 
 
 
 15 
 
 & 
 
 0.67 
 
 448 
 
 224 
 
 180 
 
 149 
 
 128 
 
 lit 
 
 
 
 
 16 
 
 7 A 
 
 0.69 
 
 458 
 
 229 
 
 183 
 
 152 
 
 130 
 
 
 
 
 
 17 
 
 H 
 
 0.53 
 
 266 
 
 133 
 
 106 
 
 88 
 
 
 
 
 
 
RECTANGULAR STEEL BARS. 
 
 523 
 
 SAFE DISTRIBUTED LOADS IN POUNDS FOR RECTAN- 
 GULAR STEEL BARS, ON EDGE, USED AS BEAMS. 
 
 (Computed for a fibre stress of 16,200 Ibs.) 
 
 1 
 
 Depth 
 in ins. 
 
 Thick- 
 ness. 
 
 Span in Feet. 
 
 
 
 
 
 
 
 
 
 
 
 2 
 
 2H 
 
 3 
 
 3J/ 
 
 4 
 
 4te 
 
 5 
 
 5M 
 
 1 
 
 i 
 
 225 
 
 180 
 
 150 
 
 
 
 
 
 
 1 
 
 % 
 
 281 
 
 225 
 
 187 
 
 
 
 
 
 
 1 
 
 I 
 
 337 
 
 270 
 
 225 
 
 
 
 
 
 
 H 
 
 
 350 
 
 280 
 
 234 
 
 200 
 
 175 
 
 
 
 
 jj 
 
 % 
 
 438 
 
 350 
 
 292 
 
 250 
 
 219 
 
 
 
 
 If 
 
 
 52G 
 
 420 
 
 350 
 
 300 
 
 262 
 
 
 
 
 li 
 
 ! 
 
 506 
 
 405 
 
 338 
 
 289 
 
 253 
 
 225 
 
 
 
 li 
 
 % 
 
 632 
 
 506 
 
 422 
 
 361 
 
 316 
 
 281 
 
 ** 
 
 
 li 
 
 t 
 
 759 
 
 607 
 
 506 
 
 433 
 
 379 
 
 337 
 
 
 
 If 
 
 I 
 
 689 
 
 551 
 
 459 
 
 393 
 
 344 
 
 306 
 
 275 
 
 
 l! 
 
 %> 
 
 861 
 
 688 
 
 573 
 
 491 
 
 430 
 
 382 
 
 343 
 
 
 l! 
 
 
 
 1033 
 
 826 
 
 688 
 
 589 
 
 516 
 
 459 
 
 412 
 
 
 2 
 
 % 
 
 1125 
 
 900 
 
 750 
 
 642 
 
 562 
 
 500 
 
 450 
 
 409 
 
 2 
 
 f 
 
 1350 
 
 1080 
 
 900 
 
 781 
 
 675 
 
 600 
 
 540 
 
 490 
 
 2 
 
 
 
 1575 
 
 1260 
 
 1050 
 
 914 
 
 787 
 
 700 
 
 630 
 
 572 
 
 2i 
 
 % 
 
 1423 
 
 1138 
 
 948 
 
 813 
 
 711 
 
 632 
 
 569 
 
 517 
 
 |f 
 
 f 
 
 1708 
 
 1366 
 
 1138 
 
 976 
 
 853 
 
 759 
 
 683 
 
 621 
 
 II 
 
 Jio 
 
 1993 
 
 1594 
 
 1328 
 
 1139 
 
 996 
 
 885 
 
 797 
 
 724 
 
 2i 
 
 % 
 
 1757 
 
 1406 
 
 1171 
 
 1004 
 
 878 
 
 r 781 
 
 703 
 
 639 
 
 84 
 
 1 
 
 2109 
 
 1687 
 
 1406 
 
 1205 
 
 1054 
 
 937 
 
 843 
 
 747 
 
 |i 
 
 % 
 
 2460 
 
 1968 
 
 1540 
 
 1406 
 
 1230 
 
 1093 
 
 984 
 
 855 
 
 3 
 
 1 
 
 3037 
 
 2430 
 
 2025 
 
 L736 
 
 1518 
 
 1350 
 
 1215 
 
 1104 
 
 3 
 
 
 
 3543 
 
 2835 
 
 2362 
 
 2025 
 
 1771 
 
 1575 
 
 1417 
 
 1288 
 
 3 
 
 | 
 
 4050 
 
 3240 
 
 2700 
 
 2314 
 
 2025 
 
 1800 
 
 1620 
 
 1472 
 
524 
 
 COMMON SIZES OF STEEL ANGLES. 
 
 SAFE DISTRIBUTED LOADS IN TONS FOR COMMON 
 SIZES OF STEEL ANGLES. 
 
 Computed for fibre stress of 16,000 Ibs. For permanent and live loads 
 reduce 20 per cent. See further explanation on page 513. 
 
 ANGLES WITH EQUAL LEGS. 
 
 Size of angle. 
 
 c. 
 
 Span in feet. 
 
 2 
 
 3 
 
 4 
 
 5 
 
 8 X8 X14 
 
 93.49 
 
 46.74 
 
 31.16 
 
 23.37 
 
 18.70 
 
 8 X8 X I 
 
 44.64 
 
 22.32 
 
 14.88 
 
 11.16 
 
 8.93 
 
 6 X6 XI 
 
 45.72 
 
 22.86 
 
 15.24 
 
 11.43 
 
 9.14 
 
 6 X6 X f 
 
 18.82 
 
 9.41 
 
 6.27 
 
 4.70 
 
 3.76 
 
 5 X5 ^<1 
 
 30.91 
 
 15.45 
 
 10.30 
 
 7.73 
 
 6.18 
 
 5 X5 X f 
 
 12.91 
 
 6.45 
 
 4.30 
 
 3.23 
 
 2.58 
 
 4 X4 X% 
 
 16.05 
 
 8.03 
 
 5.35 
 
 4.01 
 
 3.21 
 
 4 X4 X% 
 
 6.88 
 
 3.44 
 
 2.29 
 
 1.72 
 
 1.38 
 
 3iX3iX!% 
 
 12.00 
 
 6.00 
 
 4.00 
 
 3.00 
 
 2.40 
 
 3iX3iX% 
 
 5.20 
 
 2.60 
 
 1.73 
 
 1.30 
 
 1.04 
 
 3 X3 X f 
 
 6.93 
 
 3.47 
 
 2.31 
 
 1.73 
 
 1.39 
 
 3 X3 X i 
 
 3.09 
 
 1.55 
 
 1.03 
 
 0.77 
 
 0.62 
 
 2}X2fX 1 
 
 4.75 
 
 2.37 
 
 1.58 
 
 1.19 
 
 0.95 
 
 2fX2fX i 
 
 2.56 
 
 1.28 
 
 0.85 
 
 0.64 
 
 0.51 
 
 2JX2JX J 
 
 3.89 
 
 1.95 
 
 1.29 
 
 0.97 
 
 0.78 
 
 2-|X2^X% 
 
 1.61 
 
 0.81 
 
 0.54 
 
 0.40 
 
 0.32 
 
 2iX2iX i 
 
 3.09 
 
 1.55 
 
 1.03 
 
 0.77 
 
 0.62 
 
 2JX2ix 
 
 1.30 
 
 0.65 
 
 0.43 
 
 0.32 
 
 0.26 
 
 2 X2 X% 
 
 2.13 
 
 1.07 
 
 0.71 
 
 0.53 
 
 0.43 
 
 2 X2 X% 
 
 1.01 
 
 0.51 
 
 0.34 
 
 0.25 
 
 0.20 
 
 IfXlfXjTe 
 
 1.60 
 
 0.80 
 
 0.53 
 
 0.40 
 
 0.32 
 
 liXl|X% 
 
 0.75 
 
 0.37 
 
 0.25 
 
 0.19 
 
 0.15 
 
 1JX1JX f 
 
 1.01 
 
 0.51 
 
 0.34 
 
 0.25 
 
 0.20 
 
 Hxijx 4 
 
 0.38 
 
 0.19 
 
 0.13 
 
 0.096 
 
 0.077 
 
 Hxiix^ 
 
 0.58 
 
 0.29 
 
 0.19 
 
 0.150 
 
 0.120 
 
 Hxijx J 
 
 0.26 
 
 0.13 
 
 0.087 
 
 0.065 
 
 0.052 
 
 1 XI X i 
 
 o.ao 
 
 0.15 
 
 0.100 
 
 0.075 
 
 0.060 
 
 1 XI X i 
 
 0.17 
 
 0.083 
 
 0.055 
 
 0.041 
 
 0.033 
 
 ix jxx 
 
 0.18 
 
 0.088 
 
 0.059 
 
 0.044 
 
 
 |x ix 4 
 
 0.12 
 
 0.061 
 
 0.041 
 
 0.031 
 
 
 ix f x 
 
 0.13 
 
 0.064 
 
 0.043 
 
 0.032 
 
 
 ix ix 4 
 
 0.091 
 
 0.045 
 
 0.030 
 
 0.023 
 
 
COMMON SIZES OF STEEL ANGLES. 
 
 525 
 
 SAFE DISTRIBUTED LOADS IN TONS FOR COMMON 
 SIZES OF STEEL ANGLES (continued). 
 
 Computed for fibre stress of 16,000 Ibs. For permanent and live loads 
 reduce 20 per cent. See further explanation on page 513. 
 
 ANGLES WITH EQUAL LEGS. 
 
 Size of angle. 
 
 Span in feet. 
 
 6 , 
 
 7 
 
 8 
 
 9 
 
 10 
 
 8 X8 Xlt 
 
 15.58 
 
 13.36 
 
 11.69 
 
 10.39 
 
 9.35 
 
 8 X8 X i 
 
 7.44 
 
 6.38 
 
 5.58 
 
 4.96 
 
 4.46 
 
 6 X6 XI 
 
 7.62 
 
 6.53 
 
 5.72 
 
 5.08 
 
 4.57 
 
 6 X6 X f 
 
 3.14 
 
 2.69 
 
 2.35 
 
 2.09 
 
 1.88 
 
 5 X5 XI 
 
 5.15 
 
 4.42 
 
 3.86 
 
 3.43 
 
 3.09 
 
 5 X5 X f 
 
 2.15 
 
 1.84 
 
 1.61 
 
 1.43 
 
 1.29 
 
 4 X4 x% 
 
 2.68 
 
 2.29 
 
 2.01 
 
 1.78 
 
 1.61 
 
 4 X4 X % 
 
 1.15 
 
 0.98 
 
 0.86 
 
 0.76 
 
 0.69 
 
 3iX3iX% 
 
 2.00 
 
 1.71 
 
 1.50 
 
 1.33 
 
 1.20 
 
 3JX3iX% 
 
 0.87 
 
 0.74 
 
 0.65 
 
 0.58 
 
 0.52 
 
 3 X3 X f 
 
 1.16 
 
 0.99 
 
 0.87 
 
 0.77 
 
 0.69 
 
 3 X3 X i 
 
 0.52 
 
 0.44 
 
 0.39 
 
 0.34 
 
 0.31 
 
 2fX2fX i 
 
 0.79 
 
 0.68 
 
 0.59 
 
 0.53 
 
 0.47 
 
 2fX2|X i 
 
 0.43 
 
 0.37 
 
 0.32 
 
 0.28 
 
 0.26 
 
 2JX2JX i 
 
 0.65 
 
 0.56 
 
 0.49 
 
 0.43 
 
 0.39 
 
 2iX2*X% 
 
 0.27 
 
 0.23 
 
 0.20 
 
 0.18 
 
 0.16 
 
 2JX2iX i 
 
 0.52 
 
 0.44 
 
 0.39 
 
 0.34 
 
 0.31 
 
 2iX2iX% 
 
 0.22 
 
 0.19 
 
 0.16 
 
 0.14 
 
 0.13 
 
 2 X2 X% 
 
 0.36 
 
 0.30 
 
 0.27 
 
 0.24 
 
 0.21 
 
 2 X2 X% 
 
 0.17 
 
 0.14 
 
 0.13 
 
 0.11 
 
 0.10 
 
 ifxiixjft 
 
 0.27 
 
 0.23 
 
 0.20 
 
 0.18 
 
 0.16 
 
 ijxijx# 
 
 0.12 
 
 0.11 
 
 0.093 
 
 0.083 
 
 0.075 
 
 ijxiix t 
 
 0.17 
 
 0.14 
 
 0.130 
 
 0.110 
 
 
 ilxijx i 
 
 0.064 
 
 0.055 
 
 0.048 
 
 0.043 
 
 
 Hxiix% 
 
 0.097 
 
 0.083 
 
 0.073 
 
 0.065 
 
 
 lixiix i 
 
 0.044 
 
 0.037 
 
 0.033 
 
 0.029 
 
 
 1 XI X i 
 
 0.050 
 
 
 
 
 
 1 XI X i 
 
 0.028 
 
 
 
 
 
526 
 
 COMMON SIZES OF STEEL ANGLES. 
 
 SAFE DISTRIBUTED LOADS IN TONS FOR COMMON 
 SIZES OF STEEL ANGLES. 
 
 Computed for fibre stress of 16,000 Ibs. For permanent and live loads 
 reduce 20 per cent. See further explanation on page 513. 
 
 ANGLES WITH UNEQUAL LEGS. LONG LEG VERTICAL. 
 
 Size of angle. 
 
 c. 
 
 Span in feet. 
 
 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 7 XS^Xl 
 
 56.43 
 
 28.21 
 
 18.81 
 
 14.11 
 
 11.29 
 
 9.40 
 
 8.06 
 
 7.05 
 
 6.27 
 
 5.64 
 
 7 X3^X Vie 
 
 26.72 
 
 13.36 
 
 8.91 
 
 6.68 
 
 5.34 
 
 4.45 
 
 3.82 
 
 3.34 
 
 2.97 
 
 2.67 
 
 5 X4 XI 
 
 42.77 
 
 21.39 
 
 14.26 
 
 10.69 
 
 8.55 
 
 7.13 
 
 6.11 
 
 5.35 
 
 4.75 
 
 4.28 
 
 6 X4 X Y& 
 
 17.71 
 
 8.85 
 
 5.90 
 
 4.43 
 
 3.54 
 
 2.95 
 
 2.53 
 
 2.21 
 
 1.97 
 
 1.77 
 
 6 X3HX1 
 
 41.76 
 
 20.88 
 
 13.92 
 
 10.44 
 
 8.35 
 
 6.96 
 
 5.97 
 
 5.22 
 
 4.64 
 
 4.18 
 
 6 X3^X YB 
 
 17.33 
 
 8.67 
 
 5.78 
 
 4.33 
 
 3.47 
 
 2.89 
 
 2,48 
 
 2.17 
 
 1.93 
 
 1.73 
 
 5 X4 X V% 
 
 26.61 
 
 13.31 
 
 8.87 
 
 6.65 
 
 5.32 
 
 4.44 
 
 3.80 
 
 3.33 
 
 2.96 
 
 2.66 
 
 5 X4 X % 
 
 12.48 
 
 6.24 
 
 4.16 
 
 3.12 
 
 2.50 
 
 2.08 
 
 1.78 
 
 1.56 
 
 1.39 
 
 1.25 
 
 5 X3^X V* 
 
 26.03 
 
 13.01 
 
 8.68 
 
 6.51 
 
 5.21 
 
 4.34 
 
 3.72 
 
 3.25 
 
 2.89 
 
 2.60 
 
 5 X3^X 5 /ie 
 
 10.35 
 
 5.18 
 
 3.45 
 
 2.59 
 
 2.07 
 
 1.73 
 
 1.48 
 
 1.29 
 
 1.15 
 
 1.04 
 
 5 X3 X 13 /i6 
 
 23.73 
 
 11.87 
 
 7.91 
 
 5.93 
 
 4.75 
 
 3.96 
 
 3.39 
 
 2.97 
 
 2.64 
 
 2.37 
 
 5 X3 X 5 /i6 
 
 10.08 
 
 5.04 
 
 3.36 
 
 2.52 
 
 2.02 
 
 1.68 
 
 1.44 
 
 1.26 
 
 1.12 
 
 1.01 
 
 4^X3 X is/16 
 
 19.31 
 
 9.65 
 
 6.44 
 
 4.83 
 
 3.86 
 
 3.22 
 
 2.76 
 
 2.41 
 
 2.15 
 
 1.93 
 
 4^X3 X Vie 
 
 8.21 
 
 4.11 
 
 2.74 
 
 2.05 
 
 1.64 
 
 1.37 
 
 1.17 
 
 1.03 
 
 0.91 
 
 0.82 
 
 4 X3>^X la /i6 
 
 15.57 
 
 7.79 
 
 5.19 
 
 3.89 
 
 3.11 
 
 2.60 
 
 2.22 
 
 1.95 
 
 1.73 
 
 1.56 
 
 4 X3>X 5 /ie 
 
 6.72 
 
 3.36 
 
 2.24 
 
 1.68 
 
 1.34 
 
 1.12 
 
 0.96 
 
 0.84 
 
 0.75 
 
 0.67 
 
 4 X3 X 13 /i6 
 
 15.31 
 
 7.65 
 
 5.10 
 
 3.83 
 
 3.06 
 
 2.55 
 
 2.19 
 
 1.91 
 
 1.70 
 
 1.53 
 
 4 X3 X &/16 
 
 6.56 
 
 3.28 
 
 2.19 
 
 1.64 
 
 1.31 
 
 1.10 
 
 0.94 
 
 0.82 
 
 0.73 
 
 0.66 
 
 3^X3 X 13 /ie 
 
 11.73 
 
 5.87 
 
 3.91 
 
 2.93 
 
 2.35 
 
 1.96 
 
 1.68 
 
 1.47 
 
 1.30 
 
 1.17 
 
 3^X3 X 5 /i6 
 
 5.12 
 
 2.56 
 
 1.71 
 
 1.28 
 
 1.02 
 
 0.85 
 
 0.73 
 
 0.64 
 
 0.57 
 
 0.51 
 
 3^X2^X Hie 
 
 9.87 
 
 4.93 
 
 3.29 
 
 2.47 
 
 1.97 
 
 1.64 
 
 1.41 
 
 1.23 
 
 1.10 
 
 0.99 
 
 3^X2VX H 
 
 4.00 
 
 2.00 
 
 1.33 
 
 1.00 
 
 0.80 
 
 0.67 
 
 0.57 
 
 0.50 
 
 0.44 
 
 0.40 
 
 3^X2 X 9 /ie 
 
 6.93 
 
 3.47 
 
 2.31 
 
 1.73 
 
 1.39 
 
 1.16 
 
 0.99 
 
 0.87 
 
 0.77 
 
 0.69 
 
 3MX2 X 1 A 
 
 3.36 
 
 1.68 
 
 1.12 
 
 0.84 
 
 0.67 
 
 0.56 
 
 0.48 
 
 0.42 
 
 0.37 
 
 0.34 
 
 3 X2^X 940 
 
 6.13 
 
 3.07 
 
 2.04 
 
 1.53 
 
 1.23 
 
 1.02 
 
 0.88 
 
 0.77 
 
 0.68 
 
 0.61 
 
 3 X2HX M 
 
 2.99 
 
 1.50 
 
 1.00 
 
 0.75 
 
 0.60 
 
 0.50 
 
 0.43 
 
 0.37 
 
 0.33 
 
 0.30 
 
 3 X2 X y, 
 
 5.33 
 
 2.67 
 
 1.78 
 
 1.33 
 
 1.07 
 
 0.89 
 
 0.76 
 
 0.67 
 
 0.59 
 
 0.53 
 
 3 X2 X M 
 
 2.88 
 
 1.44 
 
 0.96 
 
 0.72 
 
 0.58 
 
 0.48 
 
 0.41 
 
 0.36 
 
 0.32 
 
 0.29 
 
 3V^X2 X ^ 
 
 3.73 
 
 1.87 
 
 1.24 
 
 0.93 
 
 0.75 
 
 0.62 
 
 0.53 
 
 0.47 
 
 0.41 
 
 0.37 
 
 ^X2 X 8/16 
 
 1.55 
 
 0.77 
 
 0.52 
 
 0.39 
 
 0.31 
 
 0.26 
 
 0.22 
 
 0.19 
 
 0.17 
 
 0.16 
 
 2!4X1^X H 
 
 3.15 
 
 1.57 
 
 0.05 
 
 0.79 
 
 0.63 
 
 0.52 
 
 0.45 
 
 0.39 
 
 0.35 
 
 0.32 
 
 2MX1^X 3 /40 
 
 1.23 
 
 0.61 
 
 0.41 
 
 0.31 
 
 0.25 
 
 0.21 
 
 0.18 
 
 0.15 
 
 0.14 
 
 0.12 
 
 2 X1HX ^ 
 
 1.23 
 
 0.61 
 
 0.41 
 
 0.31 
 
 0.25 
 
 0.21 
 
 0.18 
 
 0.15 
 
 0.14 
 
 0.12 
 
 2 Xl^X 3/i6 
 
 0.96 
 
 0.48 
 
 0.32 
 
 0.24 
 
 0.19 
 
 0.16 
 
 0.14 
 
 0.12 
 
 0.11 
 
 0.10 
 
 1^X1 X M 
 
 0.48 
 
 0.24 
 
 0.16 
 
 0.12 
 
 0.10 
 
 0.08 
 
 0.07 
 
 0.06 
 
 0.05 
 
 0.05 
 
 1^X1 X K 
 
 0.32 
 
 0.16 
 
 0.11 
 
 0.08 
 
 0.06 
 
 0.05 
 
 0.05 
 
 0.04 
 
 0.04 
 
 0.03 
 
COMMON SIZES OF STEEL ANGLES. 
 
 527 
 
 SAFE DISTRIBUTED LOADS IN TONS FOR COMMON 
 SIZES OF STEEL ANGLES. 
 
 Computed for fibre stress of 16,000 Ibs. For permanent and live loada 
 reduce 20 per cent. See further explanation on page 513. 
 
 ANGLES WITH UNEQUAL LEGS. SHORT LEG VERTICAL. 
 
 Size of angle. 
 Inches. 
 
 c. 
 
 Span in feet. 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 7 X 3M X 1 
 
 15.79 
 
 7.89 
 
 5.26 
 
 3.95 
 
 3.16 
 
 2.63 
 
 2.26 
 
 1.97 
 
 1.75 
 
 1.58 
 
 7 X 3J/-2 X Vi e 
 
 7.84 
 
 3.92 
 
 2.61 
 
 1.96 
 
 1.57 
 
 1.31 
 
 1.12 
 
 0.98 
 
 0.87 
 
 0.78 
 
 6 X4 XI 
 
 20.21 
 
 10.11 
 
 6.74 
 
 5.05 
 
 4.04 
 
 3.37 
 
 2.89 
 
 2.53 
 
 2.25 
 
 2.02 
 
 6 X4 X % 
 
 8.53 
 
 4.27 
 
 2.84 
 
 2.13 
 
 1.71 
 
 1.42 
 
 1.22 
 
 1.07 
 
 0.95 
 
 0.85 
 
 6 X 3^ X 1 
 
 15.47 
 
 7.74 
 
 5.16 
 
 3.87 
 
 3.09 
 
 2.58 
 
 2.21 
 
 1.93 
 
 1.72 
 
 1.55 
 
 6 X3^X H 
 
 6.56 
 
 3.28 
 
 2.19 
 
 1.64 
 
 1.31 
 
 1.09 
 
 0.94 
 
 0.82 
 
 0.73 
 
 0.66 
 
 5 X4 X 7 A 
 
 17.65 
 
 8.83 
 
 5 .88 
 
 4.41 
 
 3.53 
 
 2.94 
 
 2.52 
 
 2.21 
 
 1.96 
 
 1.77 
 
 5 X4 X % 
 
 8.37 
 
 4.19 
 
 2.79 
 
 2.09 
 
 1.67 
 
 1.40 
 
 1.20 
 
 1.05 
 
 0.93 
 
 0.84 
 
 5 X3^X ^ 
 
 13.44 
 
 6.72 
 
 4.48 
 
 3.36 
 
 2.69 
 
 2.24 
 
 1.92 
 
 1.68 
 
 1.49 
 
 1.34 
 
 5 X 3J^j X 5/16 
 
 5.44 
 
 2.72 
 
 1.81 
 
 1.36 
 
 1.09 
 
 0.91 
 
 0.78 
 
 0.68 
 
 0.60 
 
 0.54 
 
 5 X3 X 13 /ie 
 
 9.28 
 
 4.64 
 
 3.09 
 
 2.32 
 
 1.86 
 
 1.55 
 
 1.33 
 
 1.16 
 
 1.03 
 
 0.93 
 
 5 X3 X 5 /io 
 
 4.00 
 
 2.00 
 
 1.33 
 
 1.00 
 
 0.80 
 
 0.67 
 
 0.57 
 
 0.50 
 
 0.44 
 
 0.40 
 
 4^X3 X 13 /i6 
 
 9.12 
 
 4.56 
 
 3.04 
 
 2.28 
 
 1.82 
 
 1.52 
 
 1.30 
 
 1.14 
 
 1.01 
 
 0.91 
 
 4JHj X 3 X % 6 
 
 4.05 
 
 2.03 
 
 1.35 
 
 1.01 
 
 0.81 
 
 0.68 
 
 0.58 
 
 0.51 
 
 0.45 
 
 0.41 
 
 4 X'3J^X 13 /i6 
 
 12.27 
 
 6.13 
 
 4.09 
 
 3.07 
 
 2.45 
 
 2.05 
 
 1.75 
 
 1.53 
 
 1.36 
 
 1.23 
 
 4 X3^X %e 
 
 5.39 
 
 2.69 
 
 1.80 
 
 1.35 
 
 1.08 
 
 0.90 
 
 0.77 
 
 0.67 
 
 0.60 
 
 0.54 
 
 4 X3 X 13 /i6 
 
 8.96 
 
 4.48 
 
 2.99 
 
 2.24 
 
 1.79 
 
 1.49 
 
 1.28 
 
 1.12 
 
 1.00 
 
 0.90 
 
 4 X3 X 5 /i6 
 
 3.95 
 
 1.97 
 
 1.32 
 
 0.99 
 
 0.79 
 
 0.66 
 
 0.56 
 
 0.49 
 
 0.44 
 
 0.39 
 
 3^X3 X 13 /i6 
 
 8.80 
 
 4.40 
 
 2.93 
 
 2.20 
 
 1.76 
 
 1.47 
 
 1.26 
 
 1.10 
 
 0.98 
 
 0.88 
 
 3^X3 X 5 /i6 
 
 3.84 
 
 1.92 
 
 1.28 
 
 0.96 
 
 0.77 
 
 0.64 
 
 0.55 
 
 0.48 
 
 0.43 
 
 0.38 
 
 3HX2^X 11 /i6 
 
 5.28 
 
 2.64 
 
 1.76 
 
 1.32 
 
 1.06 
 
 0.88 
 
 0.75 
 
 0.66 
 
 0.59 
 
 0.53 
 
 
 2.19 
 
 1.09 
 
 0.73 
 
 0.55 
 
 0.44,0.36 
 
 0.31 
 
 0.27 
 
 0.24 
 
 0.22 
 
 3}|x2' 2 X % 6 
 
 2.83 
 
 1.41 
 
 0.94 
 
 0.71 
 
 0.57|0.47 
 
 0.40 
 
 0.35 
 
 0.31 
 
 0.28 
 
 3MX2 X M 
 
 1.39 
 
 0.69 
 
 0.46 
 
 0.35 
 
 0.28 
 
 0.23 
 
 0.20 
 
 0.17 
 
 0.15 
 
 0.14 
 
 3 X214X 9 /i6 
 
 4.37 
 
 2.19 
 
 1.46 
 
 1.09 
 
 0.87 
 
 0.73 
 
 0.62 
 
 0.55 
 
 0.49 
 
 0.44 
 
 3 X 2^2 X 1 4 
 
 2.13 
 
 1.07 
 
 0.71 
 
 0.53 
 
 0.4310.36 
 
 0.30 
 
 0.27 
 
 0.24 
 
 0.21 
 
 3 X2 "X 1 A 
 
 2.51 
 
 1.25 
 
 0.84 
 
 0.63 
 
 0.50,0.42 
 
 0.36 
 
 0.31 
 
 0.28 
 
 0.25 
 
 3 X2 X M 
 
 1.33 
 
 0.67 
 
 0.44 
 
 0.33 
 
 0.27 
 
 0.22 
 
 0.19 
 
 0.17 
 
 0.15 
 
 0.13 
 
 2*^X2 X K 
 
 2.45 
 
 1.23 
 
 0.82 
 
 0.61 
 
 0.49 
 
 0.41 
 
 0.35 
 
 0.31 
 
 0.27 
 
 0.25 
 
 2*4X2 X 3 /{ 6 
 
 1.07 
 
 0.53 
 
 0.36 
 
 0.27 
 
 0.21 
 
 0.18 
 
 0.15 
 
 0.13 
 
 0.12 
 
 0.11 
 
 
 1.39 
 
 0.69 
 
 0.46 
 
 0.35 
 
 0.28 
 
 0.23 
 
 0.20 
 
 0.17 
 
 
 
 2MXl>|x 
 
 0.53 
 
 0.29 
 
 0.20 
 
 0.15 
 
 0.12 
 
 0.10 
 
 
 
 
 
 2 Xl^X K 
 
 0.64 
 
 0.32 
 
 0.21 
 
 0.16 
 
 0.13 
 
 
 
 
 
 
 2 Xl^X 3 /i6 
 
 0.48 
 
 0.24 
 
 0.16 
 
 0.12 
 
 
 
 
 
 
 
 1-HX1 X 34 
 
 0.27 
 
 0.13 
 
 0.09 
 
 
 
 
 
 
 
 
 1HX1 X H 
 
 0.16 
 
 0.08 
 
 0.05 
 
 
 
 
 
 
 
 
528 
 
 COEFFICIENT FOR STEEL ANGLES. 
 
 COEFFICIENT OF STRENGTH IN TONS FOR ALL SIZES 
 AND THICKNESSES OF STEEL ANGLES. 
 
 Computed for fibre stress of 16,000 Ibs. 
 
 For permanent or live loads reduce 20 per cent. 
 
 To find safe distributed load for any span, divide C by span in 
 feet : result will be load in tons ; or, to find size of angle for 
 any distributed load and span, multiply the load by the span, 
 and select an angle having a value for C equal or larger than 
 the product. 
 
 For load at centre of span multiply twice the load by the span. 
 
 For further explanation see page 513. 
 
 ANGLES WITH EQUAL LEGS. 
 
 Size in 
 inches. 
 
 Thick- 
 ness of 
 metal. 
 
 C. 
 
 Size in 
 inches. 
 
 Thick- 
 ness of 
 metal 
 
 C. 
 
 Size in 
 inches. 
 
 Thick- 
 ness of 
 metal. 
 
 C. 
 
 8X8 
 
 H 
 
 m 
 
 i 
 
 % 
 
 4 
 
 i 
 
 % 
 
 
 % 
 * 
 
 i 
 % 
 -i 
 % 
 i 
 % 
 i 
 % 
 
 ji 
 t 
 
 i 
 % 
 
 
 93.49 
 88.91 
 84.26 
 79.52 
 74.72 
 70.92 
 64.96 
 60.00 
 54.93 
 49.81 
 44.64 
 
 45.71 
 43.25 
 40.75 
 37.18 
 35.52 
 32.91 
 30.19 
 30.75 
 24.95 
 21.71 
 18.82 
 
 30.93 
 29.28 
 27.57 
 
 5X5 
 
 % 
 
 \% 
 I 
 
 % 
 
 4 
 
 1 
 
 \ 
 
 % 
 
 I 
 
 % 
 
 2. 
 
 % 
 f 
 96 
 
 K 
 
 i 
 
 25.87 
 24.16 
 22.40 
 20.58 
 18.72 
 16.80 
 14.88 
 12.91 
 
 16.48 
 14.98 
 13.49 
 11.95 
 10.40 
 8.75 
 
 16.05 
 15.18 
 13.92 
 12.80 
 11.68 
 10.51 
 9.33 
 8.11 
 6.88 
 
 3*X3i 
 
 % 
 
 !Ye 
 f 
 % 
 
 4 
 %, 
 
 I 
 % 
 
 I 
 1 
 
 f 
 % 
 
 \ 
 
 1 
 \ 
 
 % 
 
 A 
 
 12.00 
 11.25 
 10.45 
 9.65 
 8.80 
 7.95 
 7.04 
 6.13 
 5.22 
 
 7.25 
 
 5.28 
 
 6.93 
 6.35 
 5.71 
 5.07 
 4.43 
 3.78 
 3.09 
 
 4.75 
 4.21 
 3.68 
 3.15 
 2.56 
 
 4JX4J 
 
 3JX3} 
 
 6X6 
 
 3X3 
 
 4X4 
 
 2|-X2f 
 
 5X5 
 
 For Weight and Properties of these angles, see Tables Chapter XX. 
 
COEFFICIENT FOR STEEL ANGLES. 
 
 529 
 
 COEFFICIENT OF STRENGTH IN TONS FOR ALL SIZES 
 
 AND THICKNESSES OF STEEL ANGLES (continued). 
 
 Reduce 20 per cent, for permanent and live loads. 
 
 See explanation on opposite page. 
 
 ANGLES WITH EQUAL LEGS. 
 
 Size in 
 inches. 
 
 Thick- 
 ness of 
 metal. 
 
 C. 
 
 Size in 
 inches. 
 
 Thick- 
 ness of 
 metal. 
 
 C. 
 
 Size in 
 inches. 
 
 Thick- 
 ness of 
 metal. 
 
 C. 
 
 2JX2J 
 
 1 
 
 / \ 
 %> 
 
 \ 
 
 %> 
 
 \ 
 
 3.89 
 3.47 
 3.04 
 2.56 
 2.13 
 1.60 
 
 3.09 
 2.77 
 2.40 
 2.08 
 1.71 
 1.28 
 
 2X2 
 
 /16 
 3* 
 
 1 
 
 5/ 
 
 \ 
 
 2.13 
 
 1.87 
 1.60 
 1.33 
 1.01 
 
 1.60 
 1 ^Q 
 1.23 
 1.01 
 0.75 
 
 1.01 
 
 .864 
 .715 
 
 lixii 
 
 1 
 g i 
 
 '1 
 
 ! 
 
 0.555 
 .373 
 
 .581 
 
 .485 
 .378 
 .261 
 
 .298 
 .234 
 .165 
 
 .176 
 .123 
 
 .128 
 .091 
 
 nxn 
 
 ifxif 
 
 21x21 
 
 ixi 
 
 $* 
 
 Jxt 
 
 fxf 
 
 ANGLES WITH UNEQUAL LEGS. LONG LEG VERTICAL. 
 
 8X6 
 
 6X4 
 
 1 
 
 % 
 
 82.29 
 62.56 
 42.83 
 
 56.42 
 53.33 
 50.24 
 47.04 
 43.50 
 40.53 
 37.17 
 33.76 
 30.29 
 26.72 
 
 51.09 
 20.64 
 
 42.77 
 40.48 
 38.1 
 
 6X4 
 
 6X3J 
 
 35.73 
 33.33 
 30.62 
 
 28.32 
 25.76 
 23.04 
 20.43 
 17.71 
 
 41.76 
 
 39.52 
 
 37.22 
 
 34.9! 
 
 32.53 
 
 30.13 
 
 27.68 
 
 25.17 
 
 22.61 
 
 20.00 
 
 17.33 
 
 5|-X5 
 
 5fX3f 
 
 5X4 
 
 5X3J 
 
 I 
 % 
 
 4 
 
 f 
 
 % 
 i 
 
 28.21 
 18.72 
 
 24.85 
 14.72 
 
 26.61 
 23.31 
 19.89 
 16.26 
 12.48 
 
 26.02 
 24.42 
 22.82 
 21.17 
 19.46 
 17.70 
 15.94 
 14.08 
 12.21 
 
 For Weight and Properties of these angles, see Tables Chapter XX. 
 
COEFFICIENT FOR STEEL ANGLES. 
 
 COEFFICIENT OF STRENGTH IN TONS FOR ALL SIZES 
 
 AND THICKNESSES OF STEEL ANGLES (continued}. 
 
 Reduce 20 per cent, for permanent and live loads. 
 
 See explanation at beginning of table. 
 
 ANGLES WITH UNEQUAL LEGS. LONG LEG VERTICAL (conVd). 
 
 Size in 
 inchss. 
 
 Thick- 
 ness of 
 metal. 
 
 c. 
 
 Size in 
 inches. 
 
 Thick- 
 ness of 
 metal. 
 
 c. 
 
 Size in 
 inches. 
 
 Thick- 
 ness of 
 metal. 
 
 C. 
 
 5X3i 
 
 1 
 
 4 
 
 * 
 
 I 
 
 % 
 i 
 
 % 
 
 i 
 
 4 
 
 n 
 
 J 
 
 \ 
 \ 
 
 5 
 
 i 
 
 I 
 
 10.34 
 
 23.73 
 
 22.18 
 2D.58 
 18.93 
 17.22 
 15.92 
 13.76 
 11.94 
 10.08 
 
 19.31 
 18.02 
 16.74 
 15.41 
 14.08 
 12.64 
 11.20 
 9.76 
 8.21 
 
 15.57 
 14.66 
 13.65 
 12.53 
 11.46 
 10.29 
 9.17 
 8.00 
 6.72 
 
 15.30 
 14.29 
 13.28 
 12.26 
 11.14 
 10.08 
 8.96 
 7.78 
 6.56 
 
 3JX2| 
 
 I 
 t 
 
 J 
 9 I 
 
 I 
 
 g l 
 
 !. 
 
 5 t 
 1 
 i 
 
 | 
 
 I 
 i 
 J 
 
 5 I 
 
 12.21 
 6.72 
 
 11.73 
 10.93 
 10.58 
 9.38 
 8.58 
 7.73 
 6.88 
 6.02 
 5.12 
 
 9.86 
 9.12 
 8.32 
 7.52 
 6.72 
 5.81 
 4.96 
 4.00 
 
 3.84 
 
 6.93 
 6.24 
 4.85 
 3.36 
 
 6.13 
 -5.54 
 4 96 
 4.32 
 3.68 
 2.98 
 
 5.33 
 4.74 
 4.16 
 3.52 
 
 3X2 
 
 \ 
 1 
 
 1 
 
 \ 
 3 I 
 1 
 i 
 
 
 %> 
 \ 
 
 1 
 
 2.88 
 
 3.73 
 3.30 
 2.93 
 2.50 
 2.02 
 1.54 
 
 1.97 
 1.54 
 
 2.77 
 1.49 
 
 2.66 
 1.44 
 
 3.14 
 2.24 
 1.60 
 1.22 
 
 1.60 
 1.013 
 1.546 
 0.960 
 
 1.226 
 0.960 
 1.920 
 0.960 
 
 0.8 
 .320 
 .480 
 .320 
 
 .304 
 .149 
 
 5X3 
 
 2-|X2 
 
 3JX3 
 
 Ol \/ 1 3 
 "2 /\ J-^ 
 
 44X3 
 
 2JX11 
 
 3JX2J 
 
 21XH 
 
 p 
 
 4X3i 
 
 3|X2J 
 3JX2 
 
 2Xl| 
 
 3}X2 
 
 2X1J 
 
 2X1| 
 
 O 13 
 
 | 
 
 * L S 
 
 W 2X1-1- 6 
 
 ,X. 
 
 ifxit 
 
 ifxi 8 
 if xi 
 
 3X2 
 
 ifxl 
 ixf 
 
 For Weight and Properties of these angles, see Tables Chapter 
 
COEFFICIENT FOR STEEL ANGLES. 
 
 531 
 
 COEFFICIENT OF STRENGTH IN TONS FOR ALL SIZES 
 
 AND THICKNESSES OF STEEL ANGLES (continued). 
 
 Reduce 20 per cent, for permanent and live loads. 
 
 See explanation at beginning of table. 
 
 ANGLES WITH UNEQUAL LEGS. SHORT LEG VERTICAL. 
 
 Size in 
 inches. 
 
 Thick- 
 ness of 
 metal. 
 
 c. 
 
 Size in 
 inches. 
 
 Thick- 
 ness of 
 metal. 
 
 C. 
 
 Size in 
 inches. 
 
 Thick- 
 ness of 
 metal. 
 
 C. 
 
 glx^G- 1 - 
 
 1 
 
 3 
 
 49.06 
 
 07 QQ 
 
 5fX5 
 
 % 
 
 22.77 
 15 11 
 
 4JX3 
 
 & 
 
 4.05 
 
 Q v (\ 
 
 4 
 
 oc ftn 
 
 
 /16 
 
 
 
 is/ 
 
 1 9 9A 
 
 
 
 
 p;ay Q3 
 
 5 
 
 11 20 
 
 
 
 
 11 46 
 
 
 1 
 
 15.78 
 
 1 4 Q*3 
 
 ^4 AOj 
 
 5iX3-| 
 
 t 
 
 6.50 
 
 
 5 
 
 10.66 
 901 
 
 7X3% 
 
 1 
 
 * 
 
 I 
 
 14.08 
 13.22 
 12.32 
 11.41 
 10.50 
 Q fin 
 
 5X4 
 
 1- 
 1 
 f 
 
 t 
 
 17.65 
 15.46 
 13.22 
 
 10.88 
 8.37 
 
 4X3J 
 
 1 
 
 8.96 
 8.10 
 7.20 
 6.29 
 5.38 
 
 
 1 
 
 8.64 
 7.84 
 
 
 I 
 
 ' Ji 
 
 13.44 
 12.64 
 11 84 
 
 
 1 
 
 8.96 
 8.37 
 
 7 78 
 
 6IX4J 
 
 I 
 
 21.70 
 8.64 
 
 5X3J 
 
 4 
 
 /le 
 f 
 
 10.98 
 10.13 
 9 2 9 
 
 4X3 
 
 1 
 
 i 
 
 7.20 
 6.56 
 ^ Q7 
 
 
 1 
 
 20.21 
 19.14 
 
 18.08 
 
 1 f\ Oft 
 
 
 7 i 
 
 1 
 
 8.32 
 7.41 
 6.45 
 
 K A A 
 
 
 ^ 6 
 1 
 
 5.28 
 4.64 
 3.94 
 
 
 3 
 
 i K 04 
 
 
 /16 
 
 
 
 | 
 
 P 29 
 
 6X4 
 
 T 
 
 14,72 
 
 1 Q Pi A 
 
 
 x a 
 
 9.28 
 
 o ftQ 
 
 3|X2f 
 
 f 
 
 3.52 
 
 
 /M> 
 /i6 
 
 12.32 
 11.09 
 
 9.86 
 8.53 
 
 5X3 
 
 4 
 
 ? 
 1 
 
 8.05 
 7.41 
 6.77 
 6.13 
 544 
 
 3JX3 
 
 1 
 
 8.80 
 8.21 
 7.68 
 7.09 
 6 45 
 
 
 7 
 
 15.46 
 14.61 
 1, 81 
 
 
 1 
 
 4.74 
 4.00 
 
 
 i 
 
 
 
 5.86 
 5.22 
 4 53 
 
 
 8 
 3 
 
 12.96 
 1 9 1 n 
 
 
 !% 
 
 9.12 
 
 SCO 
 
 
 
 3.84 
 
 6X3J 
 
 4 
 
 g ! 
 
 
 11.25 
 10.34 
 9.44 
 
 8.48 
 7.52 
 6.5f 
 
 4JX3 
 
 I 
 
 I 
 
 794 
 7.30 
 6.66 
 6.02 
 5.38 
 4.69 
 
 aa 
 
 1 
 
 5.28 
 4.90 
 4.48 
 4.05 
 3.62 
 3.14 
 
 JOT Weight and Properties of these angles, see Tables Chapter XX. 
 
532 
 
 COEFFICIENT FOR STEEL ANGLES. 
 
 COEFFICIENT OF STRENGTH IN TONS FOR ALL SIZES 
 
 AND THICKNESSES OF STEEL ANGLES (continued). 
 
 Reduce 20 per cent, for permanent and live loads. 
 
 See explanation at beginning of table. 
 
 ANGLES WITH UNEQUAL LEGS. SHORT LEG VERTICAL (continued). 
 
 Size in 
 inches. 
 
 Thick- 
 ness of 
 metal. 
 
 c. 
 
 Size in 
 inches. 
 
 Thick- 
 ness of 
 metal. 
 
 c. 
 
 Size in 
 inches. 
 
 Thick- 
 ness of 
 metal. 
 
 C. 
 
 3JX2J 
 
 * 
 
 f 
 
 %, 
 t 
 
 % 
 
 7 2 
 i 
 
 i 
 
 A 
 1 
 
 2.66 
 2.18 
 
 2.18 
 1.12 
 
 2.82 
 2.56 
 1.97 
 1.38 
 
 4.37 
 3.94 
 3.52 
 3.09 
 2.61 
 2.13 
 
 2.50 
 2.24 
 1.97 
 1.70 
 1.33 
 
 2JX2 
 
 \ 
 A 
 4 
 
 '. 
 
 4 
 
 f 
 % 
 
 i 
 
 f 
 
 m 
 
 % 
 %> 
 
 2.45 
 2.18 
 1.92 
 1.65 
 1.33 
 1.06 
 
 1.06 
 .80 
 
 1.06 
 
 .586 
 
 .746 
 .426 
 
 1.386 
 1.066 
 .746 
 .586 
 
 1.226 
 .800 
 
 2X1J 
 
 % 
 
 
 S A 
 
 A 
 
 % 
 
 1 
 
 I 
 i 
 
 0.906 
 .586 
 
 .640 
 .480 
 
 .906 
 .373 
 
 .533 
 .213 
 
 .266 
 .160 
 
 .128 
 .064 
 
 3fX2J 
 
 3*X2 
 
 2X1| 
 
 3JX2 
 
 2xl% 
 2XH 
 
 2JX1J 
 
 ifxit 
 
 2JX1J 
 
 3X2J 
 
 ifxi 
 
 2JX1J 
 
 1 XJ 
 1 Xf 
 
 2iXli 
 
 3X2 
 
 2Xlf 
 
 For Weight and Properties of these angles, see Tables Chapter XIII. 
 
LOADS IN TONS FOR CARNEGIE TEES. 533 
 
 SAFE DISTRIBUTED LOADS IN TONS FOR CARNEGIE 
 TEES. 
 
 Computed for fibre stress of 16,000 Ibs. For permanent and live loads, 
 reduce 20 per cent. See further explanation page 513. 
 
 Size. 
 
 Wt. 
 
 
 Span in feet. 
 
 Flange 
 
 per 
 
 c. 
 
 
 by stem. 
 
 foot. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 5 X3 
 
 13.6 
 
 6.29 
 
 3. -15 
 
 2.10 
 
 1.57 
 
 1.26 
 
 1.05 
 
 0.90 
 
 0.79 
 
 0.70 
 
 0.63 
 
 5 X2% 
 
 11 
 
 4 59 
 
 2.29 
 
 1.53 
 
 1.15 
 
 0.92 
 
 0.76 
 
 0.66 
 
 0.57 
 
 0.51 
 
 46 
 
 ^AX&A 
 
 15.8 
 
 11.36 
 
 5.68 
 
 3.79 
 
 2.84 
 
 2.27 
 
 1.89 
 
 1.62 
 
 1.42 
 
 1.26 
 
 1.14 
 
 43^X3 
 
 8.5 
 
 4.32 
 
 2.16 
 
 1.44 
 
 1.08 
 
 0.86 
 
 0.72 
 
 0.62 
 
 0.54 
 
 0.48 
 
 0.43 
 
 4^X3 
 
 10.0 
 
 5.01 
 
 2.51 
 
 1.67 
 
 1.25 
 
 1.00 
 
 0.84 
 
 0.72 
 
 0.63 
 
 0.56 
 
 0.50 
 
 4^X2^ 
 
 8.0 
 
 2.99 
 
 1.49 
 
 0.96 
 
 0.75 
 
 0.60 
 
 0.48 
 
 0.43 
 
 0.37 
 
 0.32 
 
 0.30 
 
 4HX2^ 
 
 9.3 
 
 3.47 
 
 1.73 
 
 1.16 
 
 0.87 
 
 0.69 
 
 0.58 
 
 0.50 
 
 0.43 
 
 0.39 
 
 0.35 
 
 4 X5 
 
 15.6 
 
 16.53 
 
 8.27 
 
 5.51 
 
 4.13 
 
 3.31 
 
 2.76 
 
 2.36 
 
 2.07 
 
 1.84 
 
 1.65 
 
 4 X5 
 
 12.0 
 
 12.96 
 
 6.48 
 
 4.32 
 
 3.24 
 
 2.59 
 
 2.16 
 
 1.85 
 
 1.62 
 
 1.44 
 
 1.30 
 
 4 X4^ 
 
 14.6 
 
 13.60 
 
 6.80 
 
 4.53 
 
 3.40 
 
 2.72 
 
 2.27 
 
 1.94 
 
 1.70 
 
 1.51 
 
 1.36 
 
 4 X4H 
 
 11.4 
 
 10.56 
 
 5.28 
 
 3.52 
 
 2.64 
 
 2.11 
 
 1.76 
 
 1.51 
 
 1.32 
 
 1.17 
 
 1.06 
 
 4 X4 
 
 13.7 
 
 10.77 
 
 5.39 
 
 3.59 
 
 2.69 
 
 2.15 
 
 1.80 
 
 1.54 
 
 1.35 
 
 1.20 
 
 1.08 
 
 4 X4 
 
 10.9 
 
 8.75 
 
 4.37 
 
 2.92 
 
 2.19 
 
 1.75 
 
 1.46 
 
 1.25 
 
 1.09 
 
 0.97 
 
 0.87 
 
 4 X3 
 
 9.3 
 
 4.69 
 
 2.35 
 
 1.56 
 
 1.17 
 
 0.94 
 
 0.78 
 
 0.67 
 
 0.59 
 
 0.52 
 
 0.47 
 
 4 X2^ 
 
 8.6 
 
 3.31 
 
 1.65 
 
 1.10 
 
 0.83 
 
 0.66 
 
 0.55 
 
 0.47 
 
 0.41 
 
 0.37 
 
 0.33 
 
 4 X2^ 
 
 7.3 
 
 2.93 
 
 1.47 
 
 0.98 
 
 0.73 
 
 0.59 
 
 0.49 
 
 0.42 
 
 0.37 
 
 0.33 
 
 0.29 
 
 4 X2 
 
 7.9 
 
 2.13 
 
 1.07 
 
 0.71 
 
 0.53 
 
 0.43 
 
 0.36 
 
 0.30 
 
 0.27 
 
 0.24 
 
 0.21 
 
 4 X2 
 
 6.6 
 
 1.81 
 
 0.91 
 
 0.60 
 
 0.45 
 
 0.36 
 
 0.30 
 
 0.26 
 
 0.23 
 
 0.20 
 
 0.18 
 
 3^X4 
 
 12.8 
 
 10.56 
 
 5.28 
 
 3.52 
 
 2.64 
 
 2.11 
 
 1.76 
 
 .1.51 
 
 1.32 
 
 1.17 
 
 1.06 
 
 3^X4 
 
 9.9 
 
 8.27 
 
 4.13 
 
 2.76 
 
 2.07 
 
 1.65 
 
 1.38 
 
 1.18 
 
 1.03 
 
 0.92 
 
 0.83 
 
 3^X3^ 
 
 11.7 
 
 8.11 
 
 4.05 
 
 2.70 
 
 2.03 
 
 1.62 
 
 1.35 
 
 1.16 
 
 1.01 
 
 0.90 
 
 0.81 
 
 3^X3^ 
 
 9.2 
 
 6.35 
 
 3.17 
 
 2.12 
 
 1.59 
 
 1.27 
 
 1.06 
 
 0.91 
 
 0.79 
 
 0.71 
 
 0.63 
 
 3^X3 
 
 10.9 
 
 6.03 
 
 3.01 
 
 2.01 
 
 1.51 
 
 1.21 
 
 1.00 
 
 0.86 
 
 0.75 
 
 0.67 
 
 0.60 
 
 3^X3 
 
 8.5 
 
 4.69 
 
 2.35 
 
 1.56 
 
 1.17 
 
 0.94 
 
 0.78 
 
 0.67 
 
 0.59 
 
 0.52 
 
 0.47 
 
 3^X3 
 
 7.8 
 
 3.84 
 
 1.92 
 
 1.28 
 
 0.96 
 
 0.77 
 
 0.64 
 
 0.55 
 
 0,48 
 
 0.43 
 
 0.38 
 
 3 X4 
 
 11.8 
 
 10.35 
 
 5.17 
 
 3.45 
 
 2.59 
 
 2.07 
 
 1.72 
 
 1.48 
 
 1.29 
 
 1.15 
 
 1.03 
 
 3 X4 
 
 10.6 
 
 9.49 
 
 4.75 
 
 3.16 
 
 2.37 
 
 1.90 
 
 1.58 
 
 1.36 
 
 1.19 
 
 1.05 
 
 0.95 
 
 3 X4 
 
 9.3 
 
 8.37 
 
 4.19 
 
 2.79 
 
 2.09 
 
 1.67 
 
 1.40 
 
 1.20 
 
 1.05 
 
 0.93 
 
 0.84 
 
 3 X3J^ 
 
 10.9 
 
 7.95 
 
 3.97 
 
 2.65 
 
 1.99 
 
 1.59 
 
 1.32 
 
 1.14 
 
 0.99 
 
 0.88 
 
 0.79 
 
 3 X3^ 
 
 9.8 
 
 7.31 
 
 3.65 
 
 2.44 
 
 1.83 
 
 1.46 
 
 1.22 
 
 1.04 
 
 0.91 
 
 81 
 
 0.73 
 
 3 X3>1 
 
 8 5 
 
 6.45 
 
 3.23 
 
 2.15 
 
 1.61 
 
 1.29 
 
 1.08 
 
 0.92 
 
 0.81 
 
 0.72 
 
 0.65 
 
 3 X3 
 
 10.0 
 
 5.87 
 
 2.93 
 
 1.96 
 
 1.47 
 
 1.17 
 
 0.98 
 
 0.84 
 
 0.73 
 
 0.65 
 
 0.59 
 
534 LOADS IN TONS FOR CARNEGIE TEES. 
 
 SAFE DISTRIBUTED LOADS IN TONS FOR CARNEGIE 
 TEES (continued). 
 
 Computed for fibre stress of 16,000 Ibs. For permanent and live loads, 
 reduce 20 per cent. For further explanation see page 513. 
 
 Size. 
 Flange 
 by stem. 
 
 wt. 
 
 per 
 foot. 
 
 C. 
 
 Span in feet. 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 3 X3 
 
 9.1 
 
 5.39 
 
 2.69 
 
 1.80 
 
 1.35 
 
 1.08 
 
 0.90 
 
 0.77 
 
 0.67 ! 0.60 
 
 0.54 
 
 3 X3 
 
 7.8 
 
 4.59 
 
 2.29 
 
 1.53 
 
 1.15 
 
 0.92 
 
 0.7610.66 
 
 0.57 0.5110.46 
 
 3 X3 
 
 6.6 
 
 3.95 
 
 1.97 
 
 1.32 
 
 0.99 
 
 0.79 
 
 0.6610.56 
 
 0.490.440.39 
 
 3 X2K 
 
 7.2 
 
 3.20 
 
 1.60 
 
 1.07 
 
 0.80 
 
 0.64 
 
 0.53 
 
 0.46 
 
 0.40 
 
 0.36 
 
 0.32 
 
 3 X2^ 
 
 6.1 
 
 2.77 
 
 1.39 
 
 0.92 
 
 0.69 
 
 0.55 
 
 0.46 
 
 0.40 
 
 0.35 
 
 0.31 
 
 0.28 
 
 2*4X2 
 
 7.4 
 
 4.00 
 
 2.00 
 
 1.33 
 
 1.00 
 
 0.80 
 
 0.67 
 
 0.57 
 
 0.500.44:0.40 
 
 2VX3 
 
 7.2 
 
 4.64 
 
 2.32 
 
 1.55 
 
 1.16 
 
 0.93 
 
 0.77 
 
 0.66 
 
 0.580.5210.46 
 
 2^X3 
 
 6.1 
 
 4.05 
 
 2.03 
 
 1.35 
 
 1.01 
 
 0.81 
 
 0.68 
 
 0.58 
 
 0.51 
 
 0.45 
 
 0.41 
 
 2\4X2% 
 
 6.7 
 
 3.89 
 
 1.95 
 
 1.30 
 
 0.97 
 
 0.78 
 
 0.65 
 
 0.56 
 
 0.49 
 
 0.43 
 
 0.39 
 
 2^X2^ 
 
 5.8 
 
 3.20 
 
 1.60 
 
 1.07 
 
 0.80 
 
 0.64 
 
 0.53 
 
 0.46 
 
 0.400.360.32 
 
 2^X2!^ 
 
 6.4 
 
 3.15 
 
 1.57 
 
 1.05 
 
 0.79 
 
 0.63 
 
 0.52 
 
 0.45 
 
 0.39 
 
 0.350.31 
 
 2^X2^ 
 
 5.5 
 
 2.67 
 
 1.33 
 
 0.89 
 
 0.67 
 
 0.53 
 
 0.44 
 
 0.38 
 
 0.33 
 
 0.30 
 
 0.27 
 
 2^XH 
 
 2.9 
 
 0.48 
 
 0.24 
 
 0.16 
 
 0.12 
 
 0.10 
 
 
 
 
 
 
 2^X2 1 4 
 214x2*4 
 
 4.9 
 
 4.1 
 
 2.24 
 1.71 
 
 1.12 
 0.85 
 
 0.75 
 0.57 
 
 0.56 
 0.43 
 
 0.45 
 0.34 
 
 0.37 
 
 0.28 
 
 0.32 
 0.24 
 
 0.28 
 0.21 
 
 0.250.22 
 0.19)0.17 
 
 2 X2 
 
 4.3 
 
 1.76 
 
 0.88 
 
 0.59 
 
 0.44 
 
 0.35 
 
 0.29 
 
 0.25 
 
 0.22 
 
 0.20 
 
 0.18 
 
 2 X2 
 
 3.7 
 
 1.33 
 
 0.67 
 
 0.44 
 
 0.33 
 
 0.27 
 
 0.22 
 
 0.19 
 
 0.17 
 
 0.15 
 
 0.13 
 
 2 Xl l A 
 
 3.1 
 
 0.80 
 
 0.40 
 
 0.27 
 
 0.20 
 
 0.16 
 
 0.13 
 
 0.11 
 
 0.10 
 
 
 
 i*4xm 
 
 3.1 
 
 1.01 
 
 0.51 
 
 0.34 
 
 0.25 
 
 0.20 
 
 0.17 
 
 0.14 
 
 0.13 
 
 
 
 VAX m 
 
 3.6 
 
 0.80 
 
 0.40 
 
 0.27 
 
 0.20 
 
 0.16 
 
 0.13 
 
 0.11 
 
 0.10 
 
 
 
 l^Xl 1 ^ 
 
 2.4 
 
 0.75 
 
 0.37 
 
 0.25 
 
 0.19 
 
 0.15 
 
 0.12 
 
 
 
 
 
 l l AXl l A 
 
 1.84 
 
 0.59 
 
 0.29 
 
 0.20 
 
 0.15 
 
 0.12 
 
 
 
 
 
 
 1 1 4X1 1 4 
 
 2.04 
 
 0.53 
 
 0.27 
 
 0.18 
 
 0.13 
 
 0.11 
 
 
 
 
 
 
 WXlM 
 
 1.53 
 
 0.37 
 
 0.19 
 
 0.12 
 
 0.09 
 
 0.07 
 
 
 
 
 
 
 1 XI 
 
 1.23 
 
 0.27 
 
 0.13 
 
 0.09 
 
 0.07 
 
 . 05 
 
 
 
 
 
 
 1 XI 
 
 0.87 
 
 0.16 
 
 0.08 
 
 0.05 
 
 0.04 
 
 0.03 
 
 
 
 
 
 
LOADS IN TONS FOR Z-BARS. 
 
 535 
 
 SAFE DISTRIBUTED LOADS IN TONS FOR CAMBRIA 
 AND CARNEGIE Z-BARS. 
 
 For fibre stress of 16,000 Ibs. per square inch. 
 
 To use this table for other spans, or other methods of loading, see ex- 
 planation page 513. 
 
 Size, 
 ins. 
 
 Thick 
 ness 
 of 
 metal 
 
 c. 
 
 Span in feet. 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 12 
 
 14 
 
 6 
 
 6Vl6 
 
 7 /6 
 
 45.0 
 52.4 
 59.9 
 
 11.25 
 13.11 
 14.96 
 
 9.00 
 10.48 
 11.97 
 
 7.50 
 8.73 
 9.97 
 
 6.43 
 
 7.48 
 8.55 
 
 5.63 
 6.55 
 
 7.48 
 
 5.00 
 5.82 
 6.65 
 
 4.50 
 5.24 
 5.99 
 
 3.75 
 4.37 
 4.99 
 
 3.21 
 3.74 
 
 4.28 
 
 6 
 
 9 /16 
 
 61.6 
 68.4 
 75.2 
 
 15.40 
 17.09 
 
 18.80 
 
 12.32 
 13.67 
 15.04 
 
 10.27 
 11.40 
 12.53 
 
 8.80 
 9.76 
 10.74 
 
 7.70 
 8.55 
 9.40 
 
 6.84 
 7.60 
 8.36 
 
 6.16 
 6.84 
 7.52 
 
 5.13 
 5.70 
 6.27 
 
 4.40 
 4.88 
 5.37 
 
 6 
 
 6Vio 
 
 6J/8 
 
 1%6 
 
 74.9 
 
 81.2 
 87.5 
 
 18.72 
 20.29 
 21.86 
 
 14.98 
 16.23 
 17.49 
 
 12.48 
 13.53 
 14.57 
 
 10.70 
 11.59 
 12.49 
 
 9.36 
 10.15 
 10.93 
 
 8.32 
 9.02 
 9.72 
 
 7.49 
 8.12 
 8.75 
 
 6.24 
 
 6.76 
 7.29 
 
 5.35 
 5.80 
 6 . 25 
 
 5 
 
 ?/ 
 
 28.5 
 34.1 
 39.7 
 
 7.12 
 8.52 
 9.92 
 
 5.70 
 6.82 
 7.94 
 
 4.75 
 5.68 
 6.62 
 
 4.07 
 4.87 
 5.67 
 
 3.56 
 4.26 
 4.96 
 
 3.17 
 3.79 
 4.41 
 
 2.85 
 3.41 
 3.97 
 
 2.37 
 2.84 
 3.31 
 
 2.03 
 2.43 
 
 2.83 
 
 5 
 
 ^ 
 
 40.9 
 46.0 
 51.1 
 
 10.24 
 11.49 
 12.76 
 
 8.19 
 9.19 
 10.21 
 
 6.83 
 7.66 
 8.51 
 
 5.85 
 6.56 
 7.29 
 
 5.12 
 
 5 . 75 
 6.38 
 
 4.55 
 5.11 
 5.67 
 
 4.09 
 4.60 
 5.11 
 
 3.41 
 3.83 
 4.25 
 
 2.92 
 
 3.28 
 3.65 
 
 5 
 
 lfi6 
 
 50.5 
 55.2 
 59.7 
 
 12.63 
 13.79 
 14.94 
 
 10.10 
 11.03 
 11.95 
 
 8.42 
 9.19 
 9.96 
 
 7.21 
 7.88 
 8.54 
 
 6.32 
 6.89 
 7.47 
 
 5.61 
 6.13 
 -6.64 
 
 5.05 
 5.52 
 5.97 
 
 4.21 
 4.60 
 4.98 
 
 3.61 
 3.94 
 4.27 
 
 4 
 
 1 
 
 16.8 
 20.8 
 24.9 
 
 4.19 
 5.21 
 6.22 
 
 3.35 
 4.17 
 4.98 
 
 2.79 
 3.48 
 4.15 
 
 2.39 
 2.98 
 3.56 
 
 2.09 
 2.60 
 3.11 
 
 1.86 
 2.32 
 
 2.77 
 
 1.68 
 
 2.08 
 2.49 
 
 1.40 
 1.74 
 2.08 
 
 1.20 
 1.49 
 
 1.78 
 
 4 
 
 $* 
 
 25.7 
 29.3 
 32.9 
 
 6.44 
 7.33 
 8.24 
 
 5.15 
 5.87 
 6.59 
 
 4.29 
 4.89 
 5.49 
 
 3.68 
 4.19 
 4.71 
 
 3.22 
 3.67 
 4.12 
 
 2.86 
 3.26 
 3.66 
 
 2.57 
 
 2.93 
 3.29 
 
 2.15 
 2.44 
 2.75 
 
 1.84 
 2.09 
 2.35 
 
 4 
 
 M 
 
 32.3 
 35.5 
 38.7 
 
 8.06 
 8.86 
 9.68 
 
 6.45 
 7.09 
 
 7.74 
 
 5.37 
 5.91 
 6.45 
 
 4.61 
 5.06 
 5.53 
 
 4.03 
 
 4.43 
 4.84 
 
 3.58 
 3.95 
 4.30 
 
 3.23 
 3.55 
 
 3.87 
 
 2.69 
 2.96 
 3.23 
 
 2.31 
 2.53 
 2.76 
 
 3 
 
 3^6 
 
 %e 
 
 10.3 
 
 12.7 
 
 2.56 
 3.17 
 
 2.05 
 2.54 
 
 1.71 
 2.12 
 
 1.46 
 1.81 
 
 1.28 
 1.58 
 
 1.14 
 1.41 
 
 
 
 
 3 
 
 31^6 
 
 lie 
 
 13.7 
 15.9 
 
 3.44 
 3.97 
 
 2.74 
 3.18 
 
 2.28 
 2.65 
 
 1.96 
 2.27 
 
 1.72 
 1.98 
 
 1.52 
 1.77 
 
 
 
 
 3 
 
 He 
 
 16.3 
 18.3 
 
 4.08 
 4.57 
 
 3.26 
 3.66 
 
 2.72 
 3.05 
 
 2.33 
 2.62 
 
 2.04 
 2.28 
 
 1.81 
 2.03 
 
 
 
 
 Steel-beam Girders. 
 
 ' A box girder consisting of a pair of steel I-beams with top and 
 bottom flange-plates, furnishes an economical girder for short 
 
536 STEEL-BEAM BOX-GIRDEHS. 
 
 spans. The flange-plates are riveted to the beams with rivets 
 f" diameter, spaced from 6 to 9 inches on centres. In short 
 girders care must be taken to have a sufficient number of rivets 
 in each plate, between the end of the girder and the centre of the 
 span, to develop the full tensile or compressive strength of the 
 plate, figured at 13,000 Ibs. per square inch. 
 
 The following tables give the safe loads for the sizes of beams 
 most likely to be used in this way. 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 order to amply compensate for the deterioration 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 fibre stress was limited to 
 13,000 Ibs., although it is but right to state that most of the 
 latest handbooks of the steel manufacturers gi ye tables for such 
 girders based on 15,000 Ibs. fibre stress. The author advises 
 that for loads of masonry, which usually come very closely to 
 the estimated load, arid which are constantly exerted, the girders 
 be not loaded beyond the yalues given in the following tables, 
 while for ordinary floor loads, which seldom reach the estimated 
 load, an addition of Jth may be added to the values given in the 
 tables. 
 
 EXAMPLE. A 13" brick wall, 15 feet high, is to be built over an 
 opening of 24 feet. What will be the section of the girder re- 
 quired? 
 
 Ans. Assuming 25 feet as the distance, centre to centre of 
 bearings, the weight of the wall will be 25 X 15 X 121 = 45,375 Ibs., 
 or 22.68 tons. 
 
 From the tables we find that a girder composed of two 12" 
 steel beams, each weighing 31.5 Ibs. per foot, and two 14" X \ rf 
 flange-plates will carry safely, for a span of 25 feet, a uniformly 
 distributed load of 23.23 tons, including its own weight. Deduct- 
 ing the latter, 1.42 tons, given in the next column, we find 21.81 
 tons for the value of the safe net load, which is 1.07 tons less than 
 required. From the following column we find that by increasing 
 the thickness of the flange-plates %" we may add 1.52 tons to the 
 allowable load. This will more than cover the difference. Hence 
 the required section will be two 12" steel beams 31.5 Ibs. per foot, 
 and two 14" X%" steel cover-plates. 
 
STEEL-BEAM BOX-GIRDERS. 
 
 537 
 
 STEEL-BEAM BOX-GIRDERS. SAFE LOADS IN TONS, 
 UNIFORMLY DISTRIBUTED. 
 
 2-20" steel I-beams and 2 steel plates 16" 
 
 a 
 
 ? 
 
 ^_ 
 
 
 j-a 
 
 |<-7"-*j^ 
 
 
 "s 
 
 IM 
 
 O 
 
 O 
 ft 
 
 2 steel 
 plates, 
 16" XH" 
 
 
 
 u 
 
 20" steel 
 I-beams, 
 80.0 Ibs. 
 per foot. 
 
 2 steel 
 
 plates, 
 16" XM" 
 
 eg 
 
 il jl 
 
 20" steel 
 I-beams, 
 65.0 Ibs. 
 per foot . 
 
 girder for % 
 F flange-plat 
 
 d 
 
 OJ.^ 
 
 *5 
 
 ) ' 0- 
 
 
 
 
 
 o % 
 
 "g.S 
 
 s.s" 
 
 If" 
 
 05 03 
 
 fl*O*O 
 
 ^ g 
 
 l|" 
 
 < ' 02 
 
 co"- 1 fl DQ 
 
 
 "S 
 
 fffl 
 
 'Si'Sg 
 
 aVl! 
 
 
 >trj 
 
 
 fi^ 
 
 V 
 
 
 
 "~' "^3 r p < 
 
 ^ 3 H 
 
 *w hn 
 
 " H ^ 1 5"ft 
 
 "* .2 
 
 oT 
 o 
 
 -& '*jj 
 
 .S-Sj 
 
 _ j> jjj , 
 
 ^:2 ^-^^ 
 
 .S-^ t g 
 
 8-2-1! 
 
 0) 
 
 03 W 
 
 3 
 
 
 
 02 OJ C 
 
 ^-^ dl?^ 
 
 
 
 
 
 .SjS'S o 
 
 
 0373 03 C3 
 
 ^.S-i^ So 
 
 
 03 T3 03 03 
 
 
 "02 
 
 5 
 
 jplll 
 
 fill 
 
 * C 32 
 
 |S11I 
 
 fill 
 
 PI! 
 
 I.I 
 
 10 
 
 199.67 
 
 1.22 
 
 7.22 
 
 176.72 
 
 1.06 
 
 7.34 
 
 0.03 
 
 11 
 
 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 
 
 135.95 
 
 1.37 
 
 5.65 
 
 0.04 
 
 14 
 
 142.64 
 
 1.70 
 
 5.16 
 
 126.24 
 
 1.48 
 
 5.25 
 
 0.05 
 
 15 
 
 133.12 
 
 1.83 
 
 4.81 
 
 117.82 
 
 1.58 
 
 4.90 
 
 0.05 
 
 16 
 
 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 
 
 18 
 
 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 
 
 3.61 
 
 88.36 
 
 2.11 
 
 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 
 
 0.10 
 
 30 
 
 66.56 
 
 3.65 
 
 2.41 
 
 58.91 
 
 3.17 
 
 2.45 
 
 0.10 
 
 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 
 
 0.11 
 
 33 
 
 60.51 
 
 4.02 
 
 2.19 
 
 53.56 
 
 3.48 
 
 2.22 
 
 0.11 
 
 34 
 
 58.73 
 
 4.14 
 
 2.12 
 
 51.98 
 
 3.59' 
 
 2.16 
 
 0.11 
 
 35 
 
 57.05 
 
 4.26 
 
 2.06 
 
 50.50 
 
 3.70 
 
 2.10 
 
 0.1 
 
 36 
 
 55.46 
 
 4.38 
 
 2.01 
 
 49.09 
 
 3.80 
 
 2.04 
 
 0.1 
 
 37 
 
 53.96 
 
 4.50 
 
 1.95 
 
 47.77 
 
 3.91 
 
 1.98 
 
 0.1 
 
 38 
 
 52.54 
 
 4.62 
 
 1.90 
 
 46.51 
 
 4.01 
 
 1.93 
 
 0.1 
 
 39 
 
 51.20 
 
 4.75 
 
 1.85 
 
 45.32 
 
 4.12 
 
 1.88 
 
 0.1 
 
 Above values are based on maximum fibre strain of 13,000 Ibs. per 
 square inch, rivet-holes in both flanges deducted. Weights of girders 
 correspond to lengths, centre to centre of bearings. 
 
538 
 
 STEEL-BEAM BOX-GIRDERS 
 
 STEEL-BEAM BOX-GIRDERS. SAFE LOADS IN TONS, 
 UNIFORMLY DISTRIBUTED. 
 
 2-18" steel I-beams and 2 steel plates 16"Xf". 
 
 - 
 
 03 
 
 ,Q +=> 
 
 Js o> 
 
 
 
 1 
 
 o 
 
 e-7'-* 
 
 rS 
 
 ,, 
 
 1 
 
 rrj 
 
 
 
 H? ~ 
 
 tjj 
 
 8 
 
 
 
 , 
 
 K ~O 
 
 IP 1 
 
 "I 
 
 3 
 
 ^ . 
 
 
 
 
 to 
 
 
 
 
 
 S *- 
 
 
 5 
 
 J 
 
 rC*.Ja 
 
 9 
 
 c . 
 
 JI 
 
 2 <i 
 
 LI 
 
 fc X 
 
 ^b co 
 
 I 
 
 II 
 
 *! 
 
 1 ' r [ 1 
 
 i i 
 
 T3 v. 
 
 
 
 <M <M 
 
 (M (M 
 
 gW 
 
 Ol.S 
 
 t/^"*"* 
 
 
 
 
 
 
 
 sTi 
 
 _j 
 
 r--C 
 
 o 
 
 c3 to O 
 
 i5j2 
 
 CD 
 
 "S jH ^ 
 
 ^ P *o 
 
 Co 
 
 1 
 
 O.S> 
 ^g 
 
 B 
 
 
 II 
 
 
 J^.W) 
 
 Jl 
 
 i 
 
 
 
 .s ^ 
 
 bC *s 
 
 O> O a) 
 t(-i c rt 
 
 C ^ 
 
 bC-^j 
 
 ^"c ^ 
 
 CJ O CU 
 
 sS 
 
 V 
 
 o 
 
 ^ c 1 ^ 
 
 *0 3 
 
 11 . 
 
 - be .: 
 
 T3 C S 
 
 "o 3 
 
 03 .S fl 
 
 Ir^ 
 
 g- M 
 
 1 
 
 Jljis 
 
 g ft 
 
 
 oil 
 
 X^ 
 
 o a g S 
 
 S'3 tR 
 VT-X! J) 
 
 
 
 
 
 
 
 
 Wfl 
 
 
 
 
 s 
 
 08 - 
 
 1'" 
 
 I^.Sa 
 
 1'^ 
 
 | 
 
 |lfs 
 
 nS s-i o3 
 
 73 .S'E 
 
 1 
 
 12 
 
 132.2 
 
 2712 
 
 5.43 
 
 123.0 
 
 2352 
 
 2.81 
 
 5.43 
 
 82 
 
 13 
 
 122.0 
 
 2933 
 
 5.01 
 
 113.5 
 
 2548 
 
 2.61 
 
 5.01 
 
 88 
 
 14 
 
 113.3 
 
 3164 
 
 4.66 
 
 105.3 
 
 2744 
 
 2.43 
 
 4.66 
 
 95 
 
 15 
 
 105.7 
 
 3390 
 
 4.35 
 
 98.3 
 
 2940 
 
 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 
 
 4520 
 
 3.26 
 
 73.8 
 
 3920 
 
 1.70 
 
 3.26 
 
 136 
 
 21 
 
 75.5 
 
 4746 
 
 3 10 
 
 70.2 
 
 4116 
 
 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 
 
 4704 
 
 1.41 
 
 2.72 
 
 163 
 
 25 
 
 63.5 
 
 5650 
 
 2.61 
 
 59.0 
 
 4900 
 
 1.36 
 
 2.61 
 
 170 
 
 26 
 
 61.0 
 
 5876 
 
 2.51 
 
 56.7 
 
 5096 
 
 1.30 
 
 2.51 
 
 177 
 
 27 
 
 58.8 
 
 6102 
 
 2.41 
 
 54.6 
 
 5292 
 
 1.26 
 
 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 
 
 6076 
 
 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 
 
 .97 
 
 1.86 
 
 238 
 
 36 
 
 44.1 
 
 8136 
 
 1.81 
 
 41.0 
 
 7056 
 
 .94 
 
 1.81 
 
 245 
 
 37 
 
 42.9 
 
 8362 
 
 1.76 
 
 39.9 
 
 7252 
 
 .92 
 
 1.76 
 
 252 
 
 38 
 
 41.2 
 
 8588 
 
 1.72 
 
 38.8 
 
 7448 
 
 .90 
 
 1.72 
 
 258 
 
 Above values are based on maximum fibre strain of 13,000 Ibs. per sq. in., 
 rivet-holes in both flanges deducted. Weights correspond to lengths, centre 
 to centre of bearings. 
 
STEEL-BEAM BOX-GIRDERS. 
 
 539 
 
 STEEL-BEAM BOX-GIRDERS. SAFE LOADS IN TONS, 
 UNIFORMLY DISTRIBUTED. 
 
 2-15" steel I-beams and 2 steel plates 14"X^". 
 
 
 tp 
 
 
 /ft 
 
 
 
 
 
 
 
 
 
 a? 
 
 rrOJ* ~ V^ jpj/f 
 
 4TLjM ilr^ 15" 
 
 ^\C ^\\ steel I. 
 
 1 
 
 03 
 
 M 
 
 ^||P steel 1. 
 
 II II steel I. 
 
 
 a 
 
 ce +3 
 
 .3 
 
 
 60.0 
 
 1 1 lb<i 
 
 s- . 
 
 O M 
 
 '"^'5. 
 
 1 
 
 Ibs. 
 
 Ibs 
 
 " 
 
 2 Q 
 
 o i 
 
 J 
 
 II I L per 
 
 \ 1 1 1 per 
 
 foot 
 
 '* 
 
 ^ M 
 
 *0 
 
 dE=2==^!a foot. 
 
 ff ^ . ^> foot. 
 
 ^^^b^ 
 
 ^ a 
 
 a> 5 
 
 I 
 
 o ^ 
 
 03 03 
 
 Steel plates,' 
 
 14"X^s". 
 
 Steel plates, 
 14" XW. 
 
 Steel plates, 
 14" X%". 
 
 1 
 
 || 
 
 ^2 
 
 !>> i 
 
 > 
 
 !>. ' x-s 
 
 li /-v 
 
 - 
 
 i ^ 
 
 o^ 
 
 A d 
 
 -S d 
 
 03 * 
 
 d^ oj 
 
 "dS *" " 
 
 .2 M 02 
 
 ^"wCf 
 
 .5^2 03 
 
 11 m 
 
 .^ 
 
 1 
 
 l-S-SJa 
 
 ^ 
 
 g^ii 
 
 ^$ 
 
 ill| 
 
 TS^ 
 
 \ 
 
 P 
 
 "d 
 
 03 
 
 ^Jo 
 
 03 4>O 
 
 ?^ >a s 
 
 !"? 
 
 S-S'ag 
 
 -f^l 
 
 go 
 
 
 o 
 
 ''rrt '" 
 
 'So o>of 
 
 '"'"d <M~ 
 
 'Si) ^ci 
 
 P -0 * O " 
 
 Sb 5J e^f 
 
 '03^ 
 
 'fl3 
 
 oJ 
 
 
 ;> 
 
 
 
 
 tt-i T* **-* 
 
 
 
 
 
 3 
 
 1$ "Ej'bCG 
 
 *o'C o 
 
 'rf'S.M'o 
 
 c ^ o 
 
 ^ "3 bB^ 
 
 iS 
 
 03 d 
 
 QJ-r-l 
 
 S 
 
 3 
 
 ^O^D'03 2 
 
 n 
 
 p5"S ^ a 
 
 5 2 S 
 
 |||g 
 
 Cd 
 
 B 
 
 
 d ^ 
 
 0) 
 
 '_S ^ o 
 
 -g,-| o 
 
 *-> ^ o 
 
 fi^B 
 
 
 'S.^g o 
 
 d 
 
 M ^C 
 
 
 03 en bC^ 
 
 
 03 tc fafi-^ 
 
 
 03 "K hC"^ 
 
 
 
 
 fi 
 
 
 t> 2 
 
 ^^5.S.2 
 
 '3.9 
 
 ^^5.2.2 
 
 >'3.2 
 
 
 
 
 CO 
 
 [ .0 
 
 02 
 
 ^ 
 
 02 
 
 . ^ 
 
 
 
 10 
 
 122.33 
 
 1.05 
 
 111.01 
 
 0.91 
 
 90.29 
 
 0.72 
 
 4.63 
 
 0.03 
 
 11 
 
 111.21 
 
 1.17 
 
 100 . 92 
 
 .00 
 
 82.08 
 
 0.79 
 
 4.21 
 
 0.03 
 
 12 
 
 101.95 
 
 1.27 
 
 92.51 
 
 .09 
 
 75.24 
 
 0.86 
 
 3.86 
 
 0.03 
 
 13 
 
 94.10 
 
 1.38 
 
 85 . 40 
 
 .18 
 
 69.45 
 
 0.93 
 
 3.57 
 
 0.04 
 
 14 
 
 87.38 
 
 1.48 
 
 79.30 
 
 .27 
 
 64 . 50 
 
 1.00 
 
 3.31 
 
 0.04 
 
 15 
 
 81.55 
 
 1.59 
 
 74.01 
 
 .36 
 
 60.19 
 
 1.08 
 
 3.09 
 
 0.04 
 
 16 
 
 76.46 
 
 1.70 
 
 69.33 
 
 .45 
 
 56.43 
 
 , 1.15 
 
 2.90 
 
 0.05 
 
 17 
 
 71.95 
 
 1.80 
 
 65.30 
 
 1.54 
 
 53.11 ' 
 
 1.22 
 
 2.72 
 
 0.05 
 
 18 
 
 67.95 
 
 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 
 
 52.85 
 
 1.90 
 
 42.99 
 
 1.51 
 
 2 21 
 
 0.06 
 
 22 
 
 55.60 
 
 2.33 
 
 50.46 
 
 2.00 
 
 41.04 
 
 1.58 
 
 2.11 
 
 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 
 
 23 
 
 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 . 23- 
 
 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 
 
 0.10 
 
 34 
 
 35.98 
 
 3.60 
 
 32.65 
 
 3.08 
 
 26.55 
 
 2.44 
 
 1.37 
 
 0.10 
 
 35 
 
 34.95 
 
 3.70 
 
 31.72 
 
 3.17 
 
 25.80 
 
 2.51 
 
 1.33 
 
 0.10 
 
 36 
 
 33.98 
 
 3.81 
 
 30.84 
 
 3.27 
 
 25.08 
 
 2.58 
 
 1.29 
 
 0.10 
 
 37 
 
 33.06 
 
 3.91 
 
 30 . 00 
 
 3.36 
 
 24.40 
 
 2.66 
 
 1.25 
 
 0.11 
 
 38 
 
 32.20 
 
 4.02 
 
 29.21 
 
 3.45 
 
 23 . 76 
 
 2 73 
 
 1.22 
 
 0.11 
 
 39 
 
 31.37 
 
 4.13 
 
 28.47 
 
 3.54 
 
 23.15 
 
 2.80 
 
 1.19 
 
 0.11 
 
 Above values are based on maximum fibre strains of 13,000 Ibs. per. sq. in., 
 rivet-holes in both flanges deducted. Weights of girders correspond to 
 lengths, centre to centre of bearings. 
 
540 
 
 STEEL-BEAM BOX-GIRDERS. 
 
 STEEL BEAM BOX-GIRDERS. SAFE LOAD IN TONS, 
 UNIFORMLY DISTRIBUTED. 
 
 2-12" steel I-beams and 2 steel plates 14" X^". 
 
 bearings, 
 
 jS 
 
 2 steel 
 
 _f 6*\ ^ ^ 
 
 FT 
 
 12'steel 
 I-beams, 
 
 2 steel 
 plates. 
 
 .f-^o., 
 
 fr 
 
 12" steel 
 
 y 
 
 o a 
 
 O 
 
 u"x1*". 
 
 LL 
 
 per foot. 
 
 14"X^". 
 p. 
 
 LL 
 
 per foot. 
 
 ^S 
 d 
 
 . 
 
 ^ 
 
 ^ "--t)- ^_ 
 
 
 
 ^^\?* 
 
 
 t ^ 
 
 "" 
 
 
 
 
 
 
 
 *Su5 
 
 0> O> 
 
 
 
 
 
 
 
 
 sntre to c 
 ini 
 
 g 2*0*0 
 
 Ilil 
 
 arc ^ 
 
 QJ tn 
 
 c3 C! O . 
 
 s.s's's 
 
 1y 
 
 *c1 C 
 
 O m 
 
 *S o 
 
 5 
 
 ^3 | fl . 
 
 "Sgc 
 
 "V^'ft 
 
 ? jjj 1 3 
 
 "o Md . 
 
 ^^S"a 
 
 S? 
 
 oT 
 1 
 
 iiiio 
 
 
 &^'a d 
 
 lilts 
 
 ^^~ 
 
 |f || 
 
 m O 
 ci % 
 
 QJ 03 
 
 
 ^"Sco 
 
 s i 
 
 11 |^ 
 
 *^?Sq 
 
 s ^ i? 
 
 o c 
 
 | c 
 
 B 
 
 02~ M<N 
 
 ^<N 
 
 fl~ O 
 
 ^^-SbCW 
 
 ^0^(N 
 
 i3^ o O 
 
 ^.s 
 
 10 
 
 64.94 
 
 0.65 
 
 3.75 
 
 58.08 
 
 0.57 
 
 3.81 
 
 0.03 
 
 11 
 
 59.02 
 
 0.71 
 
 3.40 
 
 52.80 
 
 0.63 
 
 3.45 
 
 0.03 
 
 12 
 
 54.12 
 
 0.78 
 
 3.12 
 
 48.40 
 
 0.68 
 
 3.17 
 
 0.03 
 
 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 
 
 15 
 
 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 
 
 2.11 
 
 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 
 
 0.00 
 
 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 
 
 0.10 
 
 34 
 
 19.10 
 
 2.21 
 
 1 10 
 
 17.08 
 
 1.94 
 
 1.12 
 
 0.10 
 
 35 
 
 18.55 
 
 2.27 
 
 1.07 
 
 16.59 
 
 1.99 
 
 1.09 
 
 O.JO 
 
 36 
 
 18.04 
 
 2.34 
 
 1 04 
 
 16.13 
 
 2.05 
 
 1.06 
 
 0.10 
 
 37 
 
 17.55 
 
 2.40 
 
 1.01 
 
 15.70 
 
 2.11 
 
 1.03 
 
 0.11 
 
 38 
 
 17.09 
 
 2.47 
 
 0.99 
 
 15.28 
 
 2.17 
 
 1.00 
 
 0.11 
 
 39 
 
 16.65 
 
 2.53 
 
 0.96 
 
 14.89 
 
 2.22 
 
 0.98 
 
 0.11 
 
 Above values are based on maximum fibre strains of 13,000 lbs. per 
 sq. in., rivetholes in both flanges deducted. Weights of girders correspond 
 to lengths, centre to centre of bearings. 
 
STEEL-BEAM BOX-GIRDERS. 
 
 541 
 
 STEEL-BEAM BOX-GIRDERS. SAFE LOADS IN TONS, 
 UNIFORMLY DISTRIBUTED. 
 
 2-10" steel I-beams and 2 steel plates 
 
 a 
 
 a 
 
 ftS- 
 
 ^^_ 
 
 
 J0 
 
 
 
 
 "o 
 
 ^ 
 
 2 steel 
 plates, 
 12" XY 2 " 
 
 
 10" steel 
 I-beams, 
 35.0 Ibs. 
 per foot. 
 
 *i 
 
 2 steel 
 plates, 
 2" X V" 
 
 it 
 
 10" steel 
 I-beams, 
 25.0 Ibs. 
 per foot. 
 
 S 
 
 | 
 
 1 
 
 
 yk 
 
 
 
 
 jUJk. 
 
 t w i( 
 
 
 s 
 
 -2.S 
 
 4^ 
 
 1? b> rn 
 
 i.sl 
 
 I 1 tl_,<4_, 
 
 sirs 
 
 O 1 00 
 
 "ifL 
 
 O cc 
 
 8 
 
 a 
 
 fill 
 
 M-ll 9 
 
 a-cj 
 
 Ml 
 
 1||1 
 
 is! 
 
 C* o -+3 
 
 SJ 
 
 S 
 
 Ja .3 9? 
 
 "o SP.S 
 
 p^ ^ 
 
 ^ ^.2 ^ 
 
 "o SP.S 
 
 o ** 9- 
 
 .S.S 
 
 aT 
 
 l:.'^ bo - 
 
 JFH ..jS 
 
 ? O.S 3 
 
 *3'C M -pQ 
 
 -< $ 
 
 2 o.5 j 
 
 Ol 
 
 o 
 
 ^|.2|o 
 
 S^o 
 
 ClJ 
 
 -||?g 
 
 *> -0^ 
 
 *dlj 
 
 ii 
 
 VI 
 
 5 
 
 jpill 
 
 fill 
 
 si el 
 
 M 
 
 c^ > > | i> 7^ 'Sic^ 
 
 W '-^<N 
 
 HH 
 
 !- 
 
 10 
 
 44.35 
 
 0.55 
 
 2.59 
 
 39.23 
 
 0.47 
 
 2.64 
 
 0.02 
 
 11 
 
 40.32 
 
 0.60 
 
 2.36 
 
 35.66 
 
 0.52 
 
 2.40 
 
 0.03 
 
 12 
 
 36.96 
 
 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 
 
 16 
 
 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 
 
 18 
 
 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 
 
 1.15 
 
 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 
 
 16.35 
 
 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 
 
 .47 
 
 0.96 
 
 14.53 
 
 1.27 
 
 0.98 
 
 0.07 
 
 28 
 
 15.84 
 
 .53 
 
 0.93 
 
 14.01 
 
 1.32 
 
 0.94 
 
 0.07 
 
 29 
 
 15.29 
 
 .58 
 
 0.89 
 
 13.53 
 
 1.37 
 
 0.91 
 
 0.07 
 
 30 
 
 14.78 
 
 .64 
 
 0.86 
 
 13.08 
 
 1.41 
 
 0.88 
 
 0.07 
 
 31 
 
 14.31 
 
 .69 
 
 0.84 
 
 12.65 
 
 1.46 
 
 0.85 
 
 0.08 
 
 32 
 
 13.86 
 
 .75 
 
 0.81 
 
 12.26 
 
 1.51 
 
 0.82 
 
 0.08 
 
 33 
 
 13.44 
 
 .80 
 
 0.78 
 
 11.89 
 
 1.55 
 
 0.80 
 
 0.08 
 
 34 
 
 13.04 
 
 .86 
 
 0.76 
 
 11.54 
 
 1.60 
 
 0.78 
 
 0.08 
 
 35 
 
 12.67 
 
 .91 
 
 0.74 
 
 11.21 
 
 1.65. 
 
 0.75 
 
 0.09 
 
 36 
 
 12.32 
 
 .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 
 
 0.10 
 
 Above values are based on maximum fibre strains of 13,000 Ibs. per 
 square inch, rivet-holes in both flanges deducted. Weights of girders 
 correspond to lengths, centre to centre of bearings 
 
542 
 
 BEAMS SUPPORTING BRICK WALLS. 
 
 BEAMS SUPPORTING BRICK WALLS. 
 
 In calculating the size of a girder to support a brick wall, the 
 structure of the wall should be carefully considered. If the wall 
 is without openings, and does not support floor beams, only the 
 
 Fig. 10 
 
 portion 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 
 especially if there be a pier over the centre of the girder, as 
 shown in Fig. 11, then the manner in which the weight bears on 
 the girder should be carefully considered. In a case such as this 
 the entire dead weight included between the dotted lines A A 
 and B B should be considered as coming on the girder, and 
 proper allowance made for the load being mostly concentrated at 
 the centre. 
 
 When beams are used to support a wall entirely (that is, the 
 beams run under the whole length of the wall), and the wall is 
 more than sixteen or eighteen feet long, the whole weight of 
 the wall should be taken as coming upon the beams; for, if the 
 beams should bend, the wall would settle, and might push out 
 the supports, and thus cause the whole structure to fall 
 
FRAMING AND CONNECTING STEEL BEAMS. 543 
 
 FRAMING- AND CONNECTING STEEL BEAMS. 
 
 Separators. When beams are used to support walls, or as 
 girders to carry floor beams, they are often placed side by side ; 
 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, preventing side 
 
 A B 
 
 fTp 
 
 I 
 
 rrrn 
 
 /r n C==P\ 
 
 B 
 
 Fig. II 
 
 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 near the supports and at points where heavy 
 loads are imposed, otherwise at regular intervals of from 5 to 6 
 feet. 
 
 The illustrations on the following page show a pair of beams 
 connected by separators, and also the pattern of separators now 
 
514 CAST-IRON SEPARATORS FOR I-BEAMS. 
 
 CAST-IRON SEPARATORS FOR I-BEAMS. 
 
 -E- J d (g 
 
 Beams. 
 
 Separators. 
 
 Bolts, square heads 
 and hex nuts. 
 
 
 
 
 
 
 
 
 o cd 
 
 
 OD 
 
 
 
 a! 
 
 
 
 
 
 
 
 
 .s s 
 
 
 2Z 
 
 
 -2 
 
 1 S 
 
 
 
 
 1 
 
 
 
 
 
 
 & 
 
 
 C 
 
 
 
 
 6 
 
 a 
 
 2 
 
 
 
 ^-Q 
 
 
 O 
 
 
 
 Oi^D 
 
 Sec- 
 tion 
 
 1 
 
 
 
 L 
 
 I 
 B 
 
 out of fla 
 
 of beams. 
 
 tre to cent 
 )f beams. 
 
 Thickness. 
 
 .SP 
 
 f wt. for ei 
 I spread of 
 
 Diameter. 
 
 to centre < 
 
 a 
 
 
 
 I 
 
 of bolts f 01 
 1 spread of 
 
 No. 
 
 
 'S 
 
 
 fl 
 
 
 
 O cj 
 
 
 s 
 
 
 o 
 
 ^g 
 
 
 
 P 
 
 -g 
 
 6 
 
 
 
 $ o 
 
 
 
 
 
 
 ?! 
 
 
 
 
 O 
 
 
 
 
 si 
 
 
 
 
 
 '53 
 
 o^ 
 
 
 
 
 
 
 
 
 
 
 
 
 0-3 
 
 
 
 
 
 
 pi 
 
 1* 
 
 
 d 
 
 
 A 
 
 B 
 
 t 
 
 
 ^ 
 
 
 c 
 
 Z? 
 
 
 
 
 Ins. 
 
 Lbs. 
 
 Inches 
 
 Inches 
 
 In. 
 
 Lbs. 
 
 Lbs. 
 
 In. 
 
 Ins. 
 
 Ins. 
 
 Lbs. 
 
 Lbs. 
 
 SEPARATORS WITH ONE BOLT. 
 
 B 5 
 
 3 
 
 5.5 
 
 5Vl6 
 
 3 
 
 A 
 
 1.1 
 
 .29 
 
 y* 
 
 
 &/8 
 
 .94 
 
 .085 
 
 B 9 
 
 4 
 
 7.5 
 
 5% 
 
 3^4 
 
 iN? 
 
 1.6 
 
 .38 
 
 % 
 
 
 4J^ 
 
 .98 
 
 .123 
 
 B 13 
 
 5 
 
 9.75 
 
 gi^ 
 
 33^ 
 
 3^g 
 
 2.0 
 
 .49 
 
 % 
 
 
 43^ 
 
 1.01 
 
 .123 
 
 B 17 
 
 6 
 
 12.25 
 
 7% 6 
 
 4 
 
 M$ 
 
 3.3 
 
 .78 
 
 M 
 
 
 5 
 
 1.07 
 
 .123 
 
 B 21 
 
 7 
 
 15.0 
 
 7% 
 
 41^ 
 
 ^ 
 
 3.9 
 
 .92 
 
 % 
 
 
 5/^ 
 
 1.10 
 
 . 123 
 
 B 25 
 
 8 
 
 17.75 
 
 s/-^ 
 
 4]^2 
 
 i^ 
 
 4.7 
 
 1.08 
 
 
 
 5M 
 
 1.15 
 
 .123 
 
 B 29 
 
 9 
 
 21.0 
 
 96/ie 
 
 5 
 
 i^ 
 
 5.9 
 
 1.20 
 
 % 
 
 
 6Vg 
 
 1.21 
 
 .123 
 
 B 33 
 
 10 
 
 25.0 
 
 
 5M 
 
 ^ 
 
 6.8 
 
 1.33 
 
 % 
 
 
 Q'A 
 
 1.24 
 
 .123 
 
 B 41 
 B 105 
 
 12 
 12 
 
 31.5 
 40.0 
 
 11$ 
 
 6 4 
 
 % 
 
 8.8 
 8.9 
 
 1.61 
 1.58 
 
 % 
 
 % 
 
 
 Q% 
 
 1.30 
 1.35 
 
 .123 
 .123 
 
 SEPARATORS WITH Two BOLTS. 
 
 B 41 
 
 12 
 
 31.5 
 
 10M 
 
 5% 
 
 
 
 9.5 
 
 1.61 
 
 *4 
 
 6M 
 
 6% 
 
 2.61 
 
 .246 
 
 B 105 
 
 12 
 
 40.0 
 
 11M 
 
 6 
 
 H 
 
 9.5 
 
 1.58 
 
 % 
 
 VA 
 
 7K 
 
 2.70 
 
 .246 
 
 B 53 
 
 15 
 
 42.0 
 
 11M 
 
 6^ 
 
 \4 
 
 12.5 
 
 2.02 
 
 % 
 
 
 7^ 
 
 2.76 
 
 .246 
 
 B 109 
 
 15 
 
 60.0 
 
 12% 
 
 6% 
 
 H 
 
 13.0 
 
 1.97 
 
 % 
 
 7 
 
 m 
 
 2.92 
 
 .246 
 
 B113 
 
 15 
 
 80.0 
 
 13^ 
 
 7H 
 
 X 
 
 13.2 
 
 1.91 
 
 H 
 
 7 
 
 SH 
 
 3.10 
 
 .246 
 
 B 65 
 
 18 
 
 55.0 
 
 12% 
 
 6M 
 
 % 
 
 19.8 
 
 2.41 
 
 H 
 
 9 
 
 8 
 
 2.89 
 
 .246 
 
 B 73 
 
 20 
 
 65.0 
 
 13k 
 
 
 % 
 
 22.9 
 
 3.37 
 
 y% 
 
 10 
 
 8K 
 
 4.20 
 
 .334 
 
 B 121 
 
 20 
 
 80.0 
 
 14 3 4 
 
 7% 
 
 5 /8 
 
 24.6 
 
 3.34 
 
 y* 
 
 10 
 
 9% 
 
 4.49 
 
 .334 
 
 B 89 
 
 24 
 
 80.0 
 
 14% 
 
 7M 
 
 % 
 
 30.3 
 
 4.07 
 
 V* 
 
 12 
 
 9K 8 
 
 4.45 
 
 .334 
 
 Lengths and weights of separator bolts in above tables are for girders 
 composed of two beams of minimum section as shown. Lengths of bolts for 
 intermediate and maximum sizes of beams may be obtained by adding twice 
 the increase of web thickness to the lengths given. 
 
BEAM CONNECTIONS. 
 
 545 
 
 in common use. The table below the cuts gives the various 
 dimensions and weights as adopted by the Cambria Steel Co. 
 The weights vary slightly from those given by other manufac- 
 turers, but the table is probably as near an average of current 
 practice as any that could be given. 
 
 Separators formed of pieces of steam or gas pipe, cut to the 
 desired length and slipped over the bolts are often used by con- 
 tractors. 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 occurs 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. Separators with two bolts should be 
 used for beams over 12 ins. in depth. For 12-inch beams either 
 one or two separators may be used, according to the load; for 
 beams under 12 inches in height one bolt is sufficient. 
 
 Beam Connections. Steel beams and channels are 
 framed together by means of short pieces of angle-bars, which 
 
 Fig. 12 
 
 are usually riveted to the floor or tail beam and bolted to the 
 girder. The angles are always used in pairs, one on each side of 
 the floor beam. 
 
546 BEAM CONNECTIONS. 
 
 If the floor beam is framed flush, either with the top or bottom 
 of the girder, or where 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 end of beam and web 
 varies from % inch in the smaller beams to -J inch in the larger 
 ones. 
 
 Figs. 12 to 14 show beams of different depths framed in dif- 
 ferent positions, and Fig 15. shows a beam framed into a girder 
 of the same depth. 
 
 When a floor beam rests on top of another beam or girder, as 
 in Fig. 17, the beam should be secured by means of a pair of 
 wrought-iron clips, shown in Fig. 16, shaped so as to fit closely 
 
 Fig. 16 Fig. 17 
 
 the top flange of the girder, and either bolted or riveted to the 
 lower flange of the floor beam, on opposite sides of the same. 
 
 Fig. 18 shows the best method of framing the ends of wooden 
 floor joist to steel beams, a 4X3XJ inch angle being riveted 
 the whole length of the steel beam, 
 "^ by j-inch rivets, about 6 ins. apart. 
 The top of the beam is usually se- 
 cured by iron dogs or clamps. If the 
 floor beams are over 3 feet apart, 
 short lengths of angles may be placed 
 under each beam. 
 
 Standard Connection Angles 
 for I-Beams and Channels. 
 Fig. 18 The size of the angles and the 
 
 number of the rivets used for connecting steel beams, varies 
 somewhat with different shops and with different structural 
 engineers, so that there cannot be said to be a universal standard. 
 The variations in the different "standards," however, are not 
 very great, and as the connections adopted by the Carnegie 
 
BEAM CONNECTIONS. 
 
 547 
 
 Steel Co. are perhaps the most used, the author has selected 
 them for illustration on the following pages. 
 
 These connections are designed on the basis of an allowable 
 shearing stress of 10,000 Ibs. per square inch, and a bearing 
 stress of 20,000 Ibs. per square inch on rivets or bolts, correspond- 
 ing with extreme fibre stresses in the I-beams of 16,000 Ibs. per 
 square inch. The number of rivets or bolts required is found to 
 be dependent, in % most instances, on their bearing values. 
 
 The connections have been proportioned with a view to cover- 
 ing 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 % inch, 
 it may be found necessary to make provision for additional 
 strength in the connections. The limiting span lengths, at and 
 above which the standard connection angles may be used with 
 perfect safety, are given in the following table : 
 
 TABLE OF MINIMUM SPANS OF I-BEAMS, FOR WHICH 
 STANDARD CONNECTION ANGLES MAY BE SAFELY 
 USED WITH BEAMS LOADED TO THEIR FULL CA- 
 PACITY. 
 
 
 Mini- 
 
 
 Mini- 
 
 
 Mini- 
 
 Designation 
 of beam. 
 
 mum 
 safe 
 span, 
 
 Designation 
 of beam. 
 
 mum 
 safe 
 span, 
 
 Designation 
 of beam. 
 
 mum 
 safe 
 span, 
 
 
 in feet. 
 
 
 in feet. 
 
 
 in feet. 
 
 24" 80 Ibs. 
 
 21.0 
 
 15" 42 Ibs. 
 
 10.5 
 
 7" 15 Ibs. 
 
 
 20 80 
 
 18.0 
 
 12 40 " 
 
 9.0 
 
 6 12,25 Ibs. 
 
 
 20 65 
 
 17.0 
 
 12 31.5 Ibs. 
 
 7.5 
 
 5 9.75 Ibs. 
 
 
 18 55 
 
 14.0 
 
 10 25 Ibs. 
 
 9.5 
 
 4 7.5 Ibs. 
 
 
 15 80 
 
 16.0 
 
 9 21 " 
 
 8.0 
 
 3 55 " 
 
 
 15 60 
 
 12.5 
 
 8 18 " 
 
 6.5 
 
 
 
 For shorter spans and for heavier beams the number of rivets required 
 should be computed by the method explained in Chapter XII. 
 
548 
 
 STANDARD CONNECTION ANGLES. 
 
 STANDARD CONNECTION ANGLES FOR I-BEAMS AND 
 CHANNELS.* 
 
 o, p, 4"x 4"x %"L iVlff. Weight 38.4 Ibs. 
 
 -t -f > 
 
 Ifc* 
 
 4 x 4 x % L 1 3 Ig. Weight 32 Ibs. 
 
 
 
 i T ~ ~| for 18 an 
 
 for 5 and 6 I's 
 and. C's 
 
 6 x 4 x % L IK lg. 
 [p Weight 5.6 Ibs. 
 
 for 3 and 4 I's 
 and C's 
 
 All holes for ^Bolts or Rivets'. 
 
 The weights of connections include shop and field rivets. 
 Z/4 gauge on all 4 legs. 
 
 * As adopted by the Carnegie Steel Co., Ltd. 
 
BEAM CONNECTIONS. 
 
 549 
 
 CONNECTIONS FOR DIFFERENT DEPTHS OF BEAMS 
 FRAMING OPPOSITE.* 
 
 Standard connection angles 
 to be used on larger beams / 
 unless gauge exceeds 2%" L 
 on special angles of smaller^) 
 'beams. 
 
 Cut L's for.I's abo 
 
 .. 15," Land 7 "I 
 
 * As adopted by the Carnegie Steel Co., Ltd. 
 
CONNECTION ANOLE8 OJ? [-BEAMS, 
 
 STANDARD 8P ^CINGI AND DIM 3 OF RIVET AND 
 
 BOLT HOI ES THROUGH PLANQ] 
 
 'I ION AXGLI - OF MiK\ 
 
 
 r * 
 
 
 
 
 
 
 
 
 
 r 
 
 g- 
 
 ) 
 
 
 
 ii 
 
 Weight per 
 ifoot. 
 
 Max 
 bolt or rivet 
 in flange*. 
 
 t! 
 
 A 
 
 B 
 
 2 * 
 
 J 
 
 c 
 
 a 
 
 Depth in 
 inches. 
 
 Weight per 
 
 to : 
 
 Max. siae 
 bolt - 
 
 in tUic^vs. 
 
 ij 
 
 S* 
 B 
 
 8 SB 
 
 r 
 
 
 
 "J 
 
 c 
 
 dT 
 
 24 
 
 100 
 95 
 90 
 85 
 80 
 
 ' 
 
 4 
 
 ||" 
 
 4 
 
 | 
 
 ,, 
 
 
 
 45 
 4O 
 35 
 31.5 
 
 40 
 
 H 
 
 3 
 
 5^ 
 
 :' !'' 
 .-, 
 
 %o 
 
 t 
 
 20 
 
 100 
 95 
 90 
 85 
 80 
 75 
 70 
 65 
 
 ft 
 
 4 
 
 5 '^ 
 
 't/ 10 
 
 
 i 
 
 ,, 
 
 10 
 
 
 35 
 30 
 25 
 
 35 
 30 
 25 
 21 
 
 X 
 
 ,^ 
 
 55/1 a 
 
 M 
 K 
 
 j 
 
 i% 2 
 
 18 
 
 70 
 65 
 60 
 55 
 
 100 
 95 
 90 
 
 J^ 
 
 " 
 
 6 
 
 IL 
 
 * 
 
 8 
 
 25.5 
 23 
 20.5 
 18 
 
 20 
 17.5 
 15 
 
 % 
 
 5 
 
 I 
 
 *L 
 
 
 
 
 
 15 
 
 85 
 TO 
 
 n 
 
 60 
 
 65 
 
 50 
 
 A - 
 
 K 
 
 
 
 6*%i 
 
 r j y 
 
 fW 
 
 ,. 
 
 6 
 5 
 
 17.25 
 14.75 
 12 25 
 
 14.75 
 12.25 
 9-75 
 
 H 
 
 2 
 
 I 
 
 | 
 
 ft/ 
 
 ^7 
 
 
 42 
 
 M 
 
 3 
 
 
 
 -: 
 
 
 10.5 
 
 Q 
 
 i/ 
 
 r 
 
 57 x i fl 
 
 *y\ <\ 
 
 Wan 
 
 12 
 
 55 
 50 
 
 H 
 
 3 
 
 
 
 
 4 
 
 8.5 
 
 7.5 
 
 
 
 
 % 
 
 
 
 
 
 
 
 
 
 3 
 
 7.5 
 6.5 
 
 5.5 
 
 % 
 
 m* 
 
 Wo 
 
 vi 
 
 V. 
 
 Weights in heavy print are standard, othern are oeci 
 All li-il^s for connection* to bo for %" rivets of holts. 
 * From centre of through beam to end of tail beam. 
 
CONNECTION ANdLKS ()V CHANNELS. 
 
 551 
 
 STANDARD BPACINQ AND DIMENSIONS oi' IMVKT AND 
 lioLT lloLKS 'nili'.()ll<;il I'l.ANCiMS AND CO.NNKC- 
 TION AMJLKSOI' 1 (U1ANNEI.S.* 
 
 Depth in ins. ,' 
 
 Weight per ft. 
 
 Max. size bolt or 
 rivet in flanges. 
 
 jj 
 
 .g 
 
 1 
 3 
 
 A 
 
 2M 
 IK 
 
 tt Std. Conn. 
 *" spacing. 
 
 .g 
 
 4> 
 
 3,2 
 
 p 
 
 Q Grip in ins. 
 
 Depth in ins. 
 
 Weight per ft.5 
 
 03 
 
 dl 
 
 j-C 
 
 >Gauge in ins. 
 
 ' 
 
 5- 
 
 t3 , 
 * 
 H 
 
 ^Distance in 
 Q inches. | 
 
 ^ 1 oGrip in ins. 
 
 a I 
 
 ir> 
 
 1 
 
 55 
 50 
 i:> 
 40 
 35 
 33 
 
 % 
 
 6i% 
 
 : ."" ; 
 
 % 
 
 'Th. 
 
 Hid 
 
 % 
 
 *V>2 
 
 
 
 11.5 
 
 o.o 
 
 0-5 
 
 H 
 
 
 
 5H 
 
 r.y,o 
 
 r.y., 
 
 , 
 
 ' 
 
 8 /e 
 '. 
 
 Vui 
 
 | 
 
 1 
 B 
 
 7.25 
 i\ . 25 
 5.25 
 
 K_ 
 
 % 
 
 .i 
 
 "H 
 
 6%e 
 
 r ''i 
 
 r>y,, 
 
 %a 
 H 
 
 40 
 
 :',r, 
 :;<> 
 25 
 20.5 
 
 k 
 
 2 
 
 1% 
 
 &4 
 
 6He 
 
 "Km 
 
 'VlO 
 
 %l 
 
 V.u 
 
 N 
 Jj 
 
 i 
 
 jifl 
 
 % 
 
 1%2 
 
 6.0 
 5.0 
 4-0 
 
 5% 
 /Wo 
 
 
 
 HT\NI)AHI> ANt) HI'KCIAf, ANULKH. 
 
 10 
 <) 
 
 :>>r> 
 :;o 
 2fi 
 20 
 
 ir> 
 
 2* 
 
 2 
 1H 
 
 .',,; 
 
 r,"/,,, 
 
 5^ 
 5M 
 
 H 
 
 %e 
 
 Det>lli of 
 leg in iim. 
 
 M.'i.x. (!I:MM 
 of boll or 
 
 II Vd,. 
 
 GN.UKO in 
 
 IIM'llC., 1 ) 
 
 25 
 20 
 15 
 13-25 
 
 ^ 
 
 15i 
 W 
 
 1H 
 
 I'Y 
 
 5^4 
 
 /10 
 
 y,V. 
 
 N 
 
 %u 
 
 
 8 
 
 6 
 5 
 
 g 
 
 3 4 
 
 i 
 
 
 
 1.5! 
 
 M. 
 
 1 
 1 
 
 1 
 1 
 1 
 
 H 
 
 M 
 
 Variable 
 
 ii 
 
 2 
 
 ik 
 
 IK 
 1H 
 
 lM 
 
 1H 
 
 1' : 
 
 ' r /,o 
 
 '?''. 
 W 
 
 11/10 
 
 8 
 
 21.25 
 
 1 x . 7. r , 
 I <;.:;, 
 i:',.7. r , 
 11-25 
 
 H 
 
 5%e 
 5H 
 6H 
 Mia 
 
 5>i 
 
 /in 
 
 $!<> 
 
 N 
 
 
 7 
 6 
 
 19.75 
 17 . 25 
 
 II.',: 
 1 U . '25 
 
 9 75 
 
 M 
 
 1H 
 1H 
 
 1% 
 IMS 
 
 5H 
 
 5U 
 
 Ky!" 
 
 "/,. 
 71 
 
 J_ 
 
 H 
 H 
 H 
 
 M 
 
 N 
 
 ' '/:, 
 
 15.5 
 13.0 
 L0.fi 
 8.0 
 
 M 
 
 r> f Ki 
 5%a 
 fig 
 6ge 
 
 J %a 
 
 
 Weights in heavy print are ntandard, 
 
 Al! holes T'lf roniKM-l ioriM lo h" ['<>r ' \" 
 *A(ln|>lc(l hy tin- < '; ' 
 
 others are Hpecial. 
 
 rivH.s or holts. 
 
552 STANDARD RIVET GAUGES FOR ANGLES. 
 STANDARD GAUGES FOR ANGLES, TEES AND Z-BARS. 
 
 N 
 
 2K-3 
 
 2K-2K 
 2 
 
 IK 
 IK 
 
 IK 
 
 
 Korl' 
 
 ' 1 
 
 11 1 
 
 ' 1 
 
 ' 1 
 
 ' 1 
 
 Kor ^ 
 
 K 
 K 
 
 3 
 
 2K 
 
 l 5 /4 e 
 
 o 
 
 2" 
 
 IK 
 IK 
 
 <D O 
 tf 
 
 H 
 
 F. 
 
 5* 
 
 A. 
 
 2 
 
 IK 
 
 B. 
 
 3 
 
 2K 
 
 Rivet. 
 
 MINIMUM GAUGE FOR MACHINE RIVETING. 
 
 ;AH X 
 
 A must not be less than K /7 + KH. For size of 
 rivet-heads, see page 373. 
 
 * For 4 7/ and 5" legs rivet-holes should be staggered, so that the distance 
 between centres of rivets shall~not be less than 2" for %" rivets, or 2i" for 
 i/d' rivets. 
 
WALL ANCHORS. 553 
 
 WALL ANCHORS FOR BEAMS AND CHANNELS. 
 
 3 to 9 
 10 to 24 
 
 3 to 5 
 6 to 10 
 
 12 to : 
 
 H 
 
 3 to _ . _ 
 
 6 to 106X6X^s 
 
 12 to 24 6X6XH 
 
 li 
 
 15 
 
 18 
 
 6 
 
 6 
 
 12 
 
 2^ 
 3 
 3 
 
 ^3 
 
 6 
 
 8 
 11 
 
 
 6 
 
 All weights and dimensions 
 marked V are variable, as are also 
 other figures where not given. 
 
 All material for anchors steel, except Nos. 7 and 8, parts of which may be 
 cast or malleable iron. All anchors are shipped loose and riveted or bolted to 
 beams in the field ; and in order to avoid two size holes in the same piece 
 anchors should be so selected that holes for them and their connections may 
 be 13 /i6". The weights given above include the bolts or rivets for field con- 
 nections. 
 
 Anchors Nos. 1, 2,3,4, and 6 are common in building construction; the 
 split anchor bolts No. 5, with or without wedges are mostly used for bridge 
 work and column foundations; the washer for No. 7 on outside of wall may 
 be either a cast-iron star or a steel plate; expansion bolts No. 8 are of use in 
 repair work to fasten channels, etc., to brick walls. 
 
554 STRENGTH OF CAST-IRON BEAMS. 
 
 CHAPTER XVI. 
 
 STRENGTH OP CAST-IRON, WOODEN, AND 
 STONE BEAMS. 
 
 CAST-IRON BEAMS. 
 
 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 if made of cast-iron. The extreme brittleness of cast 
 iron, and its liability to flaws in casting, also render it an unde- 
 sirable material for resisting transverse strain. About the only 
 form in which cast-iron beams are now used in building construc- 
 tion in this country, is in the shape of lintels for supporting 
 brick or stone walls, in places where a flat soffit is desired, and 
 the walls are not to be plastered. Cast-iron lintels are also 
 occasionally used over store fronts, the face of the lintel being 
 panelled and moulded for architectural effect. 
 
 Before wrought-iron I-beams were manufactured, cast-iron 
 beams were frequently used as the only available material, other 
 than wood or stone. Early in the nineteenth century Mr. Eaton 
 Hodgkinson, an English engineer, made a series of experiments 
 with cast-iron beams from which he found that the form of 
 cross-section of a beam which will resist 
 
 Jthe greatest transverse strain is that 
 shown in Fig. 1, in which the bottom 
 flange contains six times as much metal 
 as the top flange. 
 When cast-iron beams are subjected to 
 very light strains, the areas of the two 
 flanges ought to be nearly equal. As in 
 _l_ practice it is usual to submit beams to 
 strains less than the ultimate load, and 
 yet beyond a slight strain, it is found that 
 
 when the flanges are as 1 to 4, we have a proportion which 
 approximates very nearly the requirements of practice. The 
 
STRENGTH OF CAST-IRON BEAMS. 
 
 555 
 
 thickness of the three parts web, top flange, and bottom flange 
 may with ad vantage be mad*- in proportion as 5, <">, arid 8. 
 
 If made in this proportion, the width of the top flange will be 
 equal to one-third of that of the bottom flange. As the result of 
 his experiments, Mr. Hodgkinson gave the following rule for the 
 breaking-weight at the centre for a cast-iron beam of the above 
 form : 
 
 /Area of bot. flange\ y /depth \ y 2 42f} 
 
 Breaking-load | ^ \ in square inches / \in iris./ ^. 
 
 in tons J clear span in feet 
 
 This rule, although largely empirical, agreed very well with the 
 few experiments that were made, and has been in general use 
 even to the present day. 
 
 Modern structural engineers, however, use the general for- 
 mula 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 used for the modulus of 
 rupture. 
 
 Thus the general formula for a beam supported at both ends, 
 and with the load uniformly distributed, as given on page 502, 
 Chapter XV., is: 
 
 27? 
 Safe load in pounds 7rP XS. As S, for cast iron, should be 
 
 taken at 3,000 Ibs., this formula becomes 
 Safe load in 
 
 and R for either section given below 
 
 Moment of Inertia 
 
 (2) 
 
 _ _/ _ j U_ 5. J U -- fr -- ^ k --- & -- >! J* --- b 
 
 I NEUTRAL AXIS' 
 
 The moment of inertia is computed by the formula 
 
 , 
 (3) 
 
556 
 
 STRENGTH OF CAST-IRON BEAMS. 
 
 in which b denotes the combined thickness of the webs, and the 
 distances d, d l} and d 2 are measured from the neutral axis, which 
 must pass through the centre of gravity of the section. The centre 
 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 single web it is well to make the thickness of 
 the web J or inch greater than the thickness of the flange. For 
 a beam of the shape shown in Fig. 1, formula (2) agrees very 
 closely with formula (1), using a factor of safety of six. 
 
 EXAMPLE. The following example will illustrate the applica- 
 tion of formula (2) : Compute the safe load for a cast-iron lintel 
 having a section as shown in Fig. 2 and a clear span of 10 feet. 
 The load to be uniformly distributed, and the thickness of the 
 
 metal to be one inch. The first step is to find the distance d that 
 the centre of gravity of the section is below the top of the beam. 
 This is found by taking the moments of the webs and flange 
 about the line x-y, and dividing their sum by the area of the 
 section (see page 240). Each web is 11 ins. deep and 1 in. thick, 
 hence the area is 11 sq. inches. The moments of the three webs 
 about x-y will then be 3X11X 5^ = 181.5 
 
 Moment of flange about x-y= 28 XlH= 322 
 
 503.5 
 
 Area of section =61. 
 
 503.5^61 = 8.25=d 
 
 Then 
 
 d =8.25 
 
 d 2 =2.75 
 
 d 5 =561.5 
 d, 3 = 52.7 
 d, 3 = 20.8 
 
 b =3 
 
 ^=28 
 
 Next find Moment of Inertia by formula (3) : 
 T 3X561.5 + 28X52.7-25X20.8 
 
 = 880. 
 
STRENGTH OF CAST-IRON BEAMS. 557 
 
 234.6. Safe load= 20 *f 4 - 6 =46,920 Iba. 
 1U 
 
 or 23.4 tons. 
 
 Ends and Brackets. When T-shaped lintels are used 
 over a single opening, the web may be tapered towards the ends, 
 as in Fig. 3, without affecting the strength. If the flange is more 
 than 8 ins. wide, brackets should be cast in the middle, as at A, 
 Fig. 3. 
 
 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 bolted together. 
 
 Fig. 4 
 
 All lintels with two or three webs should have solid ends con- 
 necting the webs. 
 
 Tables of Strength of Cast-iron Lintels. The tables 
 on the following pages have been computed in accordance with 
 formula (2) . The weight of the lintel itself should be deducted 
 from the safe load. In using these tables it should be remem- 
 
558 STRENGTH OF CAST-IRON BEAMS. 
 
 bered that the values are for loads uniformly distributed. If the 
 load is concentrated at the centre, it should be multiplied by 2. 
 If at some other point than the centre, multiply by the value on 
 page 514 which most nearly corresponds with the position of the 
 load. For other spans than those given multiply the distributed 
 load by the span, and use the lintel having a coefficient C just 
 above the product thus obtained. 
 
 EXAMPLE. It is desired to support a 12-inch brick wall, 10 ft. 
 high, over an opening 5 ft. 6 ins. wide, with a cast-iron lintel; 
 22 inches from one support a girder enters the wall, which may 
 bring a load of 9,600 Ibs. on the lintel. What should be the size 
 of the lintel? 
 
 Arts. At 110 Ibs. per cubic foot, the wall above the lintel will 
 weigh 10 X 5J X 1 10 = 6050 Ibs. As 22 ins. is one-third of the span, 
 we multiply the concentrated load by 1.78 (see page 514), which 
 gives 17,088 Ibs. The total equivalent distributed load is then 
 23,138 Ibs. Multiplying this by the span we have 127,259 Ibs. 
 or 63.6 tons as the least value for the coefficient C. Looking in 
 the table, we find that a 12 // XlO // lintel, I" thick, and one web, 
 has a coefficient of 72.2, and that a 12"X8"Xli" lintel with 
 two webs has a coefficient of 69.9. A lintel with two webs is 
 best for a 12" wall, and interpolating between the values of C 
 for I" and 1}" thickness of the 12" X 8" lintel, we have 65.4 as 
 the value of C for a thickness of 1 J". This exceeds the required 
 value by enough to more than compensate for the weight of the 
 lintel itself, hence we will use a 12"x8"XlJ" lintel with two 
 webs. 
 
 Owing to the liability of flaws in the castings, cast-iron beams 
 should always be tested for defects before being set in place, and 
 if there is any doubt at all as to their safety, they should be tested 
 up to the full load they may have to support. 
 
STRENGTH OF CAST-IRON LINTELS. 
 
 559 
 
 TABLE I. SAFE DISTRIBUTED LOADS IN TONS FOR 
 CAST-IRON LINTELS. 
 
 LINTELS OP 
 
 SHAPES. 
 
 Loads include weight of lintel. Maximum tensile stress 3,000 Ibs. per 
 square inch. See remarks page 558. 
 
 Size, 
 width 
 by 
 depth, 
 ins. 
 
 Thickness of 
 metal, ins. | 
 
 Wt. 
 
 per 
 foot, 
 Ibs. 
 
 c, 
 
 Tons 
 
 Span in feet. 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 
 S /4 
 
 26.3 
 
 15.9 
 
 3.18 
 
 2.65 
 
 2.27 
 
 1.98 
 
 1.76 
 
 1.59 
 
 1.44 
 
 1.32 
 
 6X6 
 
 I 
 
 34.4 
 
 19.0 
 
 3.80 
 
 3.16 
 
 2.71 
 
 2.37 
 
 2.11 
 
 1.90 
 
 1.72 
 
 1.58 
 
 
 1> 
 
 42.0 
 
 21.5 
 
 4.30 
 
 3.58 
 
 3.07 
 
 2.68 
 
 2.39 
 
 2.15 
 
 1.95 
 
 1.79 
 
 
 y 
 
 28.6 
 
 17.8 
 
 3.56 
 
 2.96 
 
 2.54 
 
 2.22 
 
 1.98 
 
 1.78 
 
 1.61 
 
 1.48 
 
 7X6 
 
 
 37.5 
 
 21.3 
 
 4.26 
 
 3.55 
 
 3.04 
 
 2.66 
 
 2.36 
 
 2.13 
 
 1.93 
 
 1.77 
 
 
 IK 
 
 45.9 
 
 24.0 
 
 4.80 
 
 4.00 
 
 3.43 
 
 3.00 
 
 2.66 
 
 2.40 
 
 2.18 
 
 2.00 
 
 
 3/ 
 
 31.0 
 
 22.6 
 
 4.52 
 
 3.76 
 
 3.23 
 
 2.82 
 
 2.51 
 
 2.26 
 
 2.05 
 
 1.88 
 
 7X7 
 
 1 
 
 40.6 
 
 27.5 
 
 5.50 
 
 4.58 
 
 3.93 
 
 3.43 
 
 3.05 
 
 2.75 
 
 2.50 
 
 2.29 
 
 
 IK 
 
 49.8 
 
 31.4 
 
 6.28 
 
 5.23 
 
 4.49 
 
 3.92 
 
 3.49 
 
 3.14 
 
 2.85 
 
 2.36 
 
 
 H 
 
 31.0 
 
 19.6 
 
 3.92 
 
 3.26 
 
 2.80 
 
 2.45 
 
 2.18 
 
 1.96 
 
 1.78 
 
 1.63 
 
 8X6 
 
 1 
 
 40.6 
 
 23.4 
 
 4.68 
 
 3.90 
 
 3.34 
 
 2.92 
 
 2.60 
 
 2.34 
 
 2.12 
 
 1.95 
 
 
 IX 
 
 49.8 
 
 26.4 
 
 5.28 
 
 4.40 
 
 3.77 
 
 3.30 
 
 2.93 
 
 2.64 
 
 2.40 
 
 2.20 
 
 
 % 
 
 33.3 
 
 25.0 
 
 5.00 
 
 4.16 
 
 3.57 
 
 3.12 
 
 2.77 
 
 2.50 
 
 2.27 
 
 2.08 
 
 8X7 
 
 1 
 
 43.7 
 
 30.3 
 
 6.06 
 
 5.05 
 
 4.33 
 
 3.79 
 
 3.36 
 
 3.03 
 
 2.75 
 
 2.52 
 
 
 IK 
 
 53.7 
 
 34.8 
 
 6.96 
 
 5.80 
 
 4.97 
 
 4.35 
 
 3.86 
 
 3.48 
 
 3.16 
 
 2.90 
 
 
 H 
 
 35.6 
 
 30.6 
 
 6.12 
 
 5.10 
 
 4.37 
 
 3.82 
 
 3.40 
 
 3.06 
 
 2.78 
 
 2.55 
 
 8X8 
 
 
 46.8 
 
 37.6 
 
 7.52 
 
 6.2C 
 
 5.37 
 
 4.70 
 
 4.18 
 
 3.76 
 
 -3.41 
 
 3.13 
 
 
 IK 
 
 57.6 
 
 43.4 
 
 8.68 
 
 7.23 
 
 6.20 
 
 5.42 
 
 4.82 
 
 4.34 
 
 3.94 
 
 3.61 
 
 
 % 
 
 38.0 
 
 36.5 
 
 7.30 
 
 6.08 
 
 5.21 
 
 4.56 
 
 4.05 
 
 3.65 
 
 3.31 
 
 3.04 
 
 8X9 
 
 
 50.0 
 
 45.2 
 
 9.04 
 
 7.53 
 
 6.45 
 
 5.65 
 
 5.02 
 
 4.52 
 
 4.11 
 
 3.76 
 
 
 IK 
 
 61.5 
 
 52.6 
 
 10.52 
 
 8.76 
 
 7.51 
 
 6.57 
 
 5.84 
 
 5.26 
 
 4.41 
 
 4.38 
 
 
 K 
 
 40.4 
 
 26.5 
 
 5.30 
 
 4.41 
 
 3.78 
 
 3.31 
 
 2.94 
 
 2.65 
 
 2.41 
 
 2.21 
 
 12X6 
 
 i 
 
 53.1 
 
 31.6 
 
 6.32 
 
 5.26 
 
 4.51 
 
 3.95 
 
 3.51 
 
 3.16 
 
 2.87 
 
 2.63 
 
 
 IK 
 
 65.4 
 
 34.8 
 
 6.96 
 
 5.80 
 
 4.97 
 
 4.35 
 
 3.86 
 
 3.48 
 
 3.16 
 
 2.90 
 
 
 K 
 
 45.0 
 
 41.7 
 
 8.34 
 
 6.95 
 
 5.95 
 
 5.21 
 
 4.63 
 
 4.17 
 
 3.79 
 
 3.48 
 
 12X8 
 
 1 
 
 59.4 
 
 51.2 
 
 10.24 
 
 8.53 
 
 7.31 
 
 6.40 
 
 5.69 
 
 5.12 
 
 4.65 
 
 4.26 
 
 
 IK 
 
 73.2 
 
 58.5 
 
 11.70 
 
 9.75 
 
 8.35 
 
 7.31 
 
 6.50 
 
 5.85 
 
 5.32 
 
 4.87 
 
 
 K 
 
 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 
 
 
 IK 
 
 81.0 
 
 83.8 
 
 16.76 
 
 13.96 
 
 11.97 
 
 10.47 
 
 9.31 
 
 8.38 
 
 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 
 
 1 
 
 71.9 
 
 94.8 
 
 18.96 
 
 15.80 
 
 13.54 
 
 11.85 
 
 10.53 
 
 9.48 
 
 8.62 
 
 7.90 
 
 
 IK 
 
 88.9 
 
 11.5 
 
 22.30 
 
 18.58 
 
 15.92 
 
 13.93 
 
 12.39 
 
 11.15 
 
 10.12 
 
 9.29 
 
560 
 
 STRENGTH OF CAST-IRON LINTELS. 
 
 TABLE I. SAFE DISTRIBUTED LOADS IN TONS FOR 
 CAST-IRON LINTELS (Continued). 
 
 LINTELS OF 
 
 SHAPES. 
 
 Loads include weight of lintel. Maximum tensile stress 3,000 Ibs. per 
 square inch. See remarks page 558. 
 
 Size, 
 width 
 by 
 depth, 
 ins. 
 
 H- H* I Thickness of I 
 & ^ | metal, ins. | 
 
 Wt. 
 per 
 foot, 
 Ibs. 
 
 c, 
 
 tons. 
 
 Span in feet. 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 12X6 
 
 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 
 
 12X8 
 
 i* 
 
 IX 
 
 62.1 
 81.3 
 99.6 
 
 49.5 
 60.9 
 69.9 
 
 9.90 
 
 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 
 
 14X6 
 
 1 4 
 IX 
 
 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 
 
 14X8 
 
 H 
 IX 
 
 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 
 8.51 
 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 
 
 16X6 
 
 1 4 
 IX 
 
 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 
 
 16X8 
 
 1 4 
 
 ,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 
 
 5.11 
 6.21 
 7.23 
 
 20X6 
 
 1 4 
 1M 
 
 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 
 
 20X8 
 
 1 4 
 IX 
 
 80.8 
 106.2 
 130.8 
 
 72.6 
 89.5 
 102.5 
 
 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 
 
 1 4 
 
 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 
 
 1 4 
 IX 
 
 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 
 
 24X8 
 
 1 4 
 
 1M 
 
 90.2 
 118.8 
 146.5 
 
 83.4 
 102.4 
 117.0 
 
 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 
 
STRENGTH OF CAST-IRON LINTELS. 
 
 561 
 
 TABLE I.- SAFE DISTRIBUTED LOADS IN TONS FOR 
 CAST-IRON LINTELS (Continued). 
 
 LINTELS OP 
 
 SHAPES. 
 
 Loads include weight of lintels. Maximum tensile stress 3,000 Ibs. per 
 square inch. See remarks page 558. 
 
 Size, 
 width 
 by 
 depth 
 ins. 
 
 Thickness of 
 metal, ins. 
 
 Wt. 
 per 
 foot, 
 Ibs. 
 
 c, 
 
 tons. 
 
 Span in feet. 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 24X10 
 
 1 4 
 
 99.6 
 131.3 
 162.1 
 
 116.0 
 144.4 
 167.6 
 
 23.20 
 28.88 
 33.52 
 
 19.33 
 24.06 
 27.93 
 
 16.57 
 20.63 
 23.94 
 
 14.50 
 18.05 
 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 4 
 
 1M 
 
 109.0 
 143.8 
 177.7 
 
 150.4 
 189.6 
 223.0 
 
 30.08 
 37.92 
 44.60 
 
 25.06 
 31.60 
 37.16 
 
 21.48 
 27.08 
 31.85 
 
 18.80 
 23.70 
 
 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 
 
 28X8 
 
 H 
 
 99.6 
 131.3 
 162.1 
 
 95.5 
 115.0 
 130.5 
 
 19.10 
 23.00 
 26.10 
 
 15.25 
 19.16 
 21.75 
 
 13.64 
 16.43 
 18.64 
 
 11.93 
 14.37 
 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 
 
 1 4 
 
 1M 
 
 109.0 
 143 8 
 
 177.7 
 
 140.5 
 164.8 
 192.0 
 
 28.10 
 32.96 
 38.40 
 
 23.41 
 27.46 
 32.00 
 
 20.07 
 23.54 
 27.43 
 
 17.56 
 20.60 
 24.00 
 
 15.61 
 18.31 
 21.33 
 
 14.05 
 16.48 
 19.20 
 
 12.77 
 14.98 
 17.45 
 
 11.70 
 13.73 
 16.00 
 
 28X12 
 
 M 
 i 
 
 118.3 
 156.3 
 193.3 
 
 171.4 
 216.1 
 256.7 
 
 34.28 
 43.22 
 51.34 
 
 28.56 
 36.01 
 
 42.78 
 
 24.48 
 30.87 
 36.67 
 
 21.82 
 27.01 
 32.08 
 
 19.04 
 24.01 
 28.52 
 
 17.14 
 21.61 
 25.67 
 
 15.58 
 19.64 
 23.33 
 
 14.28 
 18.00 
 21.39 
 
 LINTELS OF 
 
 
 
 DEPTH' 
 
 i! 
 
 
 SHAPES. 
 
 
 H 
 
 74.4 
 
 43.3 
 
 8.66 
 
 7.21 
 
 6.18 
 
 5.41 
 
 4.81 
 
 4.33 
 
 3.93 
 
 3.60 
 
 16X6 
 
 1 
 
 96.9 
 
 52.4 
 
 10.48 
 
 8.73 
 
 7.48 
 
 6.55 
 
 5.82 
 
 5.24 
 
 4.76 
 
 4.36 
 
 
 IK 
 
 118.1 
 
 59.3 
 
 11.86 
 
 9.88 
 
 8.47 
 
 7.41 
 
 6.59 
 
 5.93 
 
 5.39 
 
 4.86 
 
 
 H 
 
 88.5 
 
 68.1 
 
 13.62 
 
 11.35 
 
 9.73 
 
 8.51 
 
 7.56 
 
 6.81 
 
 6.19 
 
 5.67 
 
 16X8 
 
 1 
 
 115.6 
 
 83.9 
 
 16.75 
 
 13.98 
 
 11.98 
 
 10.48 
 
 9.32 
 
 8.39 
 
 7.62 
 
 6.99 
 
 
 1M 
 
 141.6 
 
 97.0 
 
 19.40 
 
 16.16 
 
 13.85 
 
 12.12 
 
 10.77 
 
 9.70 
 
 88.1 
 
 8.08 
 
 
 H 
 
 97.8 
 
 80.2 
 
 16.04 
 
 13.36 
 
 11.45 
 
 10.02 
 
 8.91 
 
 8.02 
 
 7.29 
 
 6.68 
 
 20X8 
 
 i 
 
 128.1 
 
 98.7 
 
 19.74 
 
 16.45 
 
 14.10 
 
 12.33 
 
 10.96 
 
 9.87 
 
 8.97 
 
 8.22 
 
 
 IK 
 
 157.2 
 
 113.9 
 
 22.78 
 
 18.98 
 
 16.27 
 
 14.23 
 
 12.65 
 
 11.39 
 
 10.35 
 
 9.49 
 
562 
 
 STRENGTH OF CAST-IRON LINTELS. 
 
 TABLE I. SAFE DISTRIBUTED LOADS IN TONS FOR 
 CAST-IRON LINTELS (Continued). 
 
 LINTELS OP 
 
 -i. 
 
 SHAPES. 
 
 Loads include weight of lintel. Maximum tensile stress 3,000 Ibs. pet 
 square inch. See remarks page 558. 
 
 Size, 
 width 
 by 
 depth, 
 ins. 
 
 20X10 
 
 3* 
 
 33 5 
 
 If 
 
 H 
 
 Wt, 
 per 
 foot, 
 Ibs. 
 
 c, 
 
 tons. 
 
 Span in feet. 
 
 5 
 
 22.40 
 27.94 
 32.70 
 
 6 
 
 7 
 
 8 
 
 14.00 
 17.46 
 20.43 
 
 9 
 
 12.44 
 15.52 
 18.16 
 
 10 
 
 11 
 
 12 
 
 111.9 
 146.9 
 180.7 
 
 112.0 
 139.7 
 163.5 
 
 18.66 
 23.28 
 27.25 
 
 16.00 
 19.95 
 23.35 
 
 11.20 
 13.97 
 16.35 
 
 10.18 
 12.70 
 14.86 
 
 9.33 
 
 11.64 
 13.62 
 
 20X12 
 
 1 4 
 
 IX 
 
 126.0 
 165.6 
 204.1 
 
 146.7 
 
 184.8 
 218.8 
 
 29.34 
 36.96 
 43.76 
 
 24.45 
 30.80 
 36.46 
 
 20.95 
 26.40 
 31.25 
 
 18.33 
 23.10 
 27.35 
 
 16.30 
 20 . 53 
 24.31 
 
 14.67 
 
 18.48 
 21.88 
 
 13.33 
 16.80 
 19.89 
 
 12.22 
 15.40 
 18.33 
 
 24X8 
 
 1 4 
 
 107.2 
 140.6 
 172.6 
 
 91.9 
 
 112.8 
 130.2 
 
 18.38 
 22.56 
 26.04 
 
 15.31 
 
 18.80 
 21.70 
 
 13.12 
 16.11 
 18.57 
 
 11.49 
 14.10 
 16.27 
 
 10.21 
 12.53 
 14.47 
 
 9.19 
 
 11.28 
 13.02 
 
 8.35 
 10.25 
 11.83 
 
 7.66 
 9.40 
 10.85 
 
 24X10 
 
 1 4 
 
 1M 
 
 121.3 
 159.4 
 196.3 
 
 127.8 
 159.5 
 183.6 
 
 25.56 
 31.90 
 36.72 
 
 21.30 
 26.58 
 30.60 
 
 18.25 
 22.78 
 26.23 
 
 15.97 
 19.94 
 22.95 
 
 14.20 
 17.72 
 20.40 
 
 12.78 
 15.95 
 18.36 
 
 11.61 
 14.50 
 16.69 
 
 10.65 
 13.29 
 15.30 
 
 24X12 
 
 i* 
 
 135.3 
 178.1 
 219.7 
 
 166.6 
 209.3 
 247.7 
 
 33.32 
 41.86 
 49.54 
 
 27.76 
 
 34.88 
 41 . 28 
 
 23.80 
 29.90 
 35.39 
 
 20.82 
 26.16 
 30.96 
 
 18.51 
 23.25 
 27.52 
 
 16.66 
 20.93 
 
 24.77 
 
 15.14 
 19.02 
 22.51 
 
 13.88 
 17.44 
 20.64 
 
 28X10 
 
 M 
 
 1M 
 
 130.7 
 171.9 
 211.9 
 
 141.4 
 
 177.4 
 207.8 
 
 28.28 
 35.48 
 41.56 
 
 23.57 
 29.57 
 34.63 
 
 20.20 
 25.34 
 29.68 
 
 17.67 
 22.17 
 25.97 
 
 15.71 
 19.71 
 23.09 
 
 14.14 
 17.74 
 20.78 
 
 12.85 
 16.12 
 18.89 
 
 11.78 
 14.78 
 17.31 
 
 28X12 
 
 
 
 1M 
 
 144.7 
 190.6 
 235.3 
 
 186.0 
 234.6 
 277.9 
 
 37.20 
 46.92 
 55.58 
 
 31.00 
 39.10 
 46.31 
 
 26.57 
 33.51 
 39.70 
 
 23.25 
 29.32 
 34.74 
 
 20.66 
 26.06 
 30.88 
 
 18.60 
 23.46 
 27.79 
 
 16.91 
 21.32 
 25.26 
 
 15.50 
 19 . 55 
 23.16 
 
 Strength of Wooden Beams. 
 
 Wooden beams are almost invariably square or rectangular 
 shaped timbers, and we shall therefore consider only that shape 
 in the following rules and formulas. 
 
 For beams with a rectangular cross-section, we can simplify 
 our formulas for strength by substituting for the moment of 
 
 inertia its value, viz., 
 its depth. 
 
 12 
 
 , where 6= breadth of beam and d 
 
STRENGTH OF WOODEN BEAMS. 
 
 563 
 
 Then, substituting this value in the general formulas for beams, 
 we have for rectangular beams of any material the following 
 formulas : 
 
 Beams fixed at one end, and loaded at the ether (Fig. 5). 
 
 L >! 
 
 Fig. 5 
 
 . , , . , bread thx square of depth X A* . . 
 
 Safe load in pounds = -. ? 1^~- F r ~> (4) 
 
 4 X length in feet 
 
 or 
 
 Breadth in inches = 
 
 4 X load X length in feet 
 square of depth X^. 
 
 (5) 
 
 Beams fixed at one end, and loaded with uniformly distributed 
 load (Fig. 6). 
 
 Fig, 6 
 
 _,.,,. , bread thx square of depth X A* ,.. 
 Safe load m pounds =- 2xl l ngthin ^ , (6) 
 
 or 
 
 Breadth in inches 
 
 2 X load X length in feet 
 square of depth X A 
 
 (7) 
 
 * For value of A , see Table II. 
 
564 
 
 STRENGTH OF WOODEN BEAMS. 
 
 Beams supported at both ends, loaded at middle (Fig. 7). 
 
 W 
 (HI 
 
 I 
 
 Fig. 7 
 
 . , , . , breadth X square of depth X A * 
 Safe load m pounds = - sp ' an in feet ' 
 
 (8) 
 (9) 
 
 T> 1,1 , span in feet X load 
 
 Breadth in inches = j-j .. . ,-. 
 
 square ot depth X A 
 
 Beams supported at both ends, load uniformly distributed 
 (Fig. 8). 
 
 Fig. 8 
 
 span m feet 
 
 , (10) 
 
 T> J.LI- i. span in feet X load 
 
 Breadth in inches =r-^ -- -r- -. (11) 
 
 2 X square of depth X A 
 
 Beams supported at both ends, load uniformly distributed over 
 only a portion of the span (Fig. 9). 
 
 -Li- 
 
 g. 9 
 
 * For value of A , see Table II. 
 
STRENGTH OF WOODEN BEAMS. 
 
 565 
 
 In this case the dimensions of the beam required to carry the 
 load can be accurately determined only by computing the bend- 
 ing-moment, as explained in Chapter IX. and substituting the 
 value thus found in formula (16), following. If, however, the 
 length L! is very short in comparison with L, then the load may 
 be considered as concentrated at its centre, and the breadth of the 
 beam may be found by formula (9), if the load is at the centre of 
 the span, or by formula (13), if it is at one side of the centre. The 
 error will be on the safe side. 
 
 Beams supported at both ends, loaded with concentrated load 
 NOT AT CENTRE (Fig. 10). 
 
 Fig. 10 
 
 d r. i j j breadth Xsq. of depth X span X A* __ x 
 
 Safe load in pounds = - * . -- -^-^ - , (12) 
 
 Breadth in inches = 
 
 square of depthXsparixA* 
 
 (13) 
 
 Beams supported at both ends, and loaded with W pounds at a 
 distance m from each end (Fig. 11). 
 
 Wfi 
 
 |W 
 
 Fig. II 
 
 Safe load W in pounds _ breadth X square of depth X A * 
 at each point 
 
 or 
 
 Breadth in inches = 
 
 4 X load at one point Xm 
 
 (14) 
 
 (15) 
 
 sq. of depth X A 
 
 NOTE. In the last two cases the lengths denoted by m and n should be 
 taken in feet, the same as the spans. 
 
 * For value of A , see Table II. 
 
566 STRENGTH OF WOODEN BEAMS. 
 
 Application of the foregoing formulas. 
 
 EXAMPLE 1. What load will an 8 inch by 12 inch hard pine 
 beam, securely fastened into a brick wall at one end. sustain 
 with safety, 6 feet out from the wall? 
 
 Ans. Safe load in pounds (Formula 4) equals 
 
 8X144X100 
 4X6 
 
 EXAMPLE 2. It is desired to suspend two loads of 10,000 
 pounds each, four feet from each end of an oak beam 20 feet long. 
 What should be the size of the beam? 
 
 Ans. Assume depth of beam to be 14 inches; then (Formula 
 
 irxu j^ 4X10,000X4 , 
 
 15) breadth = ' -=11 inches, nearly; therefore the 
 iyt) x / o 
 
 beam should be 11 X 14 inches. 
 
 To find the size of beam (supported at both ends) to support 
 several concentrated loads, or a distributed: load and one or more 
 concentrated loads. The correct method of finding the least size 
 of beam that will safely support a combination of loads, is to 
 first find the maximum bending-moment, as explained in Chapter 
 IX., and then substitute the value thus found for the bending- 
 moment in the following formula : 
 
 T> JJ.T- T_ 4 X max. bending moment, ft. Ibs. ,.,,. 
 
 Breadth in inches = 7% ^ . (16) 
 
 square of depth X^.. 
 
 An example of this kind for steel beams is worked on pages 
 504-506. 
 
 A shorter and easier method is to find the equivalent distrib- 
 uted load for each concentrated load, and then find the size of 
 beam required to support the total equivalent distributed load 
 thus found. The equivalent distributed load for concentrated 
 loads applied at different proportions of the span from either end, 
 may be obtained by multiplying the concentrated load by the 
 following f actoi's : 
 
STRENGTH OF WOODEN BEAMS. 
 
 567 
 
 For concentrated load applied at centre of span, multiply by 2 
 
 at l/3d the span, by 
 
 at l/4th ' 
 
 at l/5th " 
 
 at l/6th " 
 
 at l/7th " 
 
 at l/8th " 
 
 at l/9th " 
 
 at l/10th " 
 
 by 
 by 
 by 
 by 
 by 
 by 
 by 
 
 1.78 
 1.5 
 1.28 
 H 
 
 .79 
 
 .72 
 
 Thus a concentrated load of. 900 Ibs. applied at one-sixth of 
 the span from one support, will produce the same bending- 
 moment as a distributed load of 900 X 1J or 1,000 Ibs. 
 
 The above method of finding the size of beam for a combina- 
 tion of several loads, will give a larger beam than the correct 
 method, by formula (16), for the reason that the maximum bend- 
 ing-moment will not be equal to the sum of the individual bending- 
 moments, hence when there are several heavy loads to be sup- 
 ported, it will be economy to compute the maximum bending- 
 moment by the graphic method explained in Chapter IX. 
 
 EXAMPLE 3. The girder G, Fig. 12, supports the rafters of a 
 flat roof, and also three heavy beams, A, B, C, blocked up above 
 the roof and supporting a large 
 tank filled with water. The tim- 
 ber is to be longleaf yellow pine. 
 The weight of the roof and allow- 
 ance for snow will be 7,500 Ibs. 
 Each of the beams A, J5, and C 
 will impose a load on the girder 
 due to the weight of the tank 
 and its contents of 3,000 Ibs. 
 What should be the size of the 
 girder? 
 
 Ans. The roof load may be considered as uniformly dis- 
 tributed. The load from beam A is applied l/3d the span from 
 one end; the load from B 5/12ths the span from the other end, 
 and the load from C l/6th the span. The fraction 5/12ths is half 
 way between 1/2 and l/3d; hence the load from B should be 
 multiplied by 1.89. Multiplying the concentrated loads by their 
 proper factors, we find the equivalent distributed load to be as 
 follows : 
 
 Fig. 12 
 
568 STRUT BEAMS AND TIE BEAMS. 
 
 Roof load, distributed = 7,500 
 
 Load from A, 3,000 X 1.78 = 5,340 
 
 Load from 5,3,000X1.89 = 5,670 
 
 Load from C,3,OOOX1J = 3,333 
 
 Equivalent distributed load= 21,843 Ibs. 
 
 Assuming 14 ins. as the depth of the beam, and using formula 
 (11), we have 
 
 12X21,843 
 
 Assuming 12 ins. for the depth, we obtain 9.1 ins. for the 
 breadth, hence the girder must be 10"X12", or 7"X14". 
 
 Strut Beams and Tie Beams. 
 
 A " strut beam" is a beam that is subject both to a transverse 
 strain and to a comprossive stress. 
 
 A "tie beam" is one that is subject to direct tension in addition 
 to the transverse strain. 
 
 To find the strength of either, first find the size of beam 
 required to resist the transverse strain, and then the size of 
 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 feet long between joints 
 sustains a ceiling load of 2,000 Ibs. and a direct tensile stress of 
 40,000 Ibs, What should be the dimensions of the beam? 
 
 Ans. As a ceiling load is uniformly distributed we determine 
 the size of the beam by formula (11). Assuming the depth as 8 
 ins., the breadth should be 
 
 10X2,000 . 
 
 2X64X70 ] 
 
 The resistance of spruce to tension (see Table I., Chapter XI.) 
 is 1,600 Ibs. 40,000 divided by 1,600=25 sq. ins., which is 
 equivalent to 3J X 8 ins. ; therefore it will require a beam 5J" X 
 8" to resist both the transverse strain 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 feet long sup- 
 ports a distributed roof load of 6,000 Ibs., and is also subject to a 
 
STRUT BEAMS AND TIE BEAMS. 
 
 569 
 
 direct compression of 48,000 Ibs. What should be the size of the 
 beam? 
 
 Ans. Assuming 12 inches for the depth, we find the breadth 
 for the transverse load by formula 11 
 
 Breadth= 
 
 10X6,000 
 2X144X60 = 
 
 = 3J ins. nearly. 
 
 Looking in the table giving the strength of white pine posts, 
 Chapter XIV., we find that an 8 X 12 post 10 feet long will support 
 51,450 Ibs., or a little more than our compressive stress. Hence 
 it will require an 8 X 12 beam to resist the compressive stress and 
 a beam 3JX12 to resist the transverse load. We should there- 
 fore make the beam 12 X 12 ins. to resist them both. 
 
 VALUES OF THE CONSTANT A. 
 
 The letter A in formulas 4-16 denotes the safe load for a unit 
 beam one inch square and one foot span, loaded at the centre. 
 This is also one-eighteenth of the modulus of rupture or fibre 
 stress for safe loads. The following are the values of A, which are 
 obtained by dividing the moduli of rupture in Chap. XV. by 18. 
 
 TABLE II, VALUES OF A. CO-EFFICIENT FOR BEAMS. 
 
 Material. 
 
 Albs. 
 
 Material. 
 
 Albs. 
 
 Cast iron 
 
 308 
 
 Pine, white, Western. . . . 
 
 65 
 
 
 666 
 
 Texas yellow 
 
 90 
 
 Steel . . . 
 
 888 
 
 Spruce. 
 
 70 
 
 
 
 White wood (poplar) 
 Redwood (California) 
 
 65 
 60 
 
 Chestnut 
 
 60 
 
 Bluestone flagging (Hudson 
 
 
 Hemlock 
 
 55 
 
 River) 
 
 25 
 
 Oak, white . . 
 
 75 
 
 Granite, average 
 
 17 
 
 Pine, Georgia yellow 
 
 100 
 
 
 14 
 
 " Oregon 
 
 90 
 
 Marble 
 
 17 
 
 
 70 
 
 
 8 to 11 
 
 11 white Kastern 
 
 60 
 
 Slate 
 
 50 
 
 
 
 
 
 These values for the co-efficient A are one-third of the break- 
 ing-weight of timbers of the same size and quality as that used 
 in first-class buildings. This is a sufficient allowance for timbers 
 in roof trusses, and beams which do not have to carry a more 
 severe load than that of a dwelling-house floor, and small halls, 
 etc. Where there is likely to be very much vibration, as in the 
 floor of a mill, or a gymnasium floor, or floors of large public halls, 
 
570 STRENGTH OF WOODEN BEAMS. 
 
 the author recommends that only four-fifths of the above values 
 for A be used. 
 
 For beams supporting permanent loads, such as masonry, or 
 water-tanks, the safe load should be reduced ten per cent., as such 
 loads are not usually overestimated. 
 
 The values for stones are based on a factor of safety of six. 
 
 For comparative values of A, as given in Building Laws, see 
 page 573. 
 
 Relative Strength of Rectangular Beams. 
 
 From an inspection of the foregoing formulas it will be found 
 that the relative strength of rectangular beams in different cases 
 is as follows: 
 
 Beam supported at both ends, and loaded with a uniformly 
 
 distributed load 1 
 
 Beams supported at both ends: 
 
 Load uniformly distributed 1 
 
 Concentrated load at centre J 
 
 " " one-third the span $ 
 
 " " one-fourth " 
 
 " " one-fifth " f| 
 
 " " one-sixth " T % 
 
 " " one-seventh " |f 
 
 " one-eighth " f 
 
 " " one-ninth " fj 
 
 " " one-tenth " ff 
 
 Beam fixed at one end, and loaded with a uniformly dis- 
 tributed load i 
 
 Beam fixed at one end, and loaded at the other. 
 
 Also the following can be shown to be true: 
 Beam firmly fixed at both ends, and loaded at the centre. ... 1 
 Beam fixed at both ends, and loaded with distributed load. . .1J 
 
 These facts are also true of a uniform beam of any form of cross- 
 section. 
 
 When a square beam is supported on its edge, instead of on its 
 side that is, has its diagonal vertical it will bear about seven- 
 tenths as great a breaking-load. 
 
STRENGTH OF WOODEN BEAMS. 571 
 
 The strongest beam which can be cut out of a 
 round log is one in which the breadth is to the 
 depth as 5 to 7, very nearly, and can be found 
 graphically, as shown in margin. Draw any 
 diagonal, as ab, and divide it into three equal 
 parts by the points c and d ; from these points 
 draw perpendicular lines, and connect the 
 points e and / with a, and 6, as shown. 
 
 CYLINDRICAL BEAMS. A cylindrical beam is only Jf as 
 strong as a square beam whose side is equal to the diameter of the 
 circle. Hence, to find the load for a cylindrical beam, first find 
 the proper load for the corresponding square beam, and then 
 divide it by 1.7. 
 
 The bearing of the ends of a beam on a wall beyond a certain 
 amount does not strengthen the beam any. In general, a beam 
 should have a bearing of four inches, and if the beam be very 
 long, the bearing should be 6 ins. 
 
 Weight of the Beam itself to be taken into Account. The for- 
 mulas we have given for the strength of beams do not take into 
 account the weight of the beam itself, and hence the safe load of 
 the formulas includes both the external load and the weight of the 
 material in the beam. In small wooden beams, the weight of 
 the beam is generally so small, compared with the external load, 
 that it need not be taken into account. But in larger wooden 
 beams, and in 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 centre, one-half the weight of the 
 beam should be subtracted. 
 
 The weight per cubic foot for different kinds oT timber may be 
 found in the table giving the Weight of Substances, Part III. 
 
 Explanation of Tables III.-VII. 
 
 Tables for the strength of yellow and white pine, Oregon pine, 
 spruce, and oak beams, are given on the following pages for beams 
 one inch wide. These tables were computed by the author from 
 : the rules and coefficients given in this chapter, and are believed 
 to be perfectly reliable when used in accordance with the explana- 
 i tions. 
 
 To find the strength of a given beam of any other breadth, it is only 
 necessary to multiply the strength given in the table by the 
 breadth of the given beam. 
 
 EXAMPE 6. What is the safe distributed load for a yellow-pine 
 
572 STRENGTH OF WOODEN BEAMS. 
 
 beam, supported at both ends, 8 inches by 12 inches, 20 feet clear 
 span? 
 
 Ans. From Table III., safe load for one inch thickness is 
 1,440 pounds. 1,440 X 8= 11,520 pounds, safe load for beam. 
 
 To find the size of a beam that will support a given load with a 
 given span, find the safe load for a beam of an assumed depth one 
 inch wide, and divide the given load by this strength. 
 
 EXAMPLE 7. What size spruce beam will be required to carry 
 a distributed load of 8,640 pounds for a clear span of 18 feet? 
 
 Ans. From the table for spruce beams, we find that a beam 
 14 inches deep and 1 inch thick, 18 feet span, will support 1,524 
 pounds; and dividing the load, 8,640 pounds, by 1,524, we have 
 5i for the breadth of the beam in inches : hence the beam should 
 be 6X14 inches, to carry a distributed load of 8,640 pounds with 
 a span of 18 feet. 
 
 To find the safe centre load of a given beam, first find the safe 
 , distributed load as in Example 6, and divide by two. 
 
 To find the safe load when concentrated at some point other than 
 the centre, first find the safe distributed load for the given span, 
 and divide by the factors given on page 567. 
 
 To find the size of beam to support a given concentrated load, mul- 
 tiply the given load by the factor corresponding with the position 
 of the load as given on page 567, and then proceed as in Example 7. 
 
 If in doubt as to the application of the tables, in special cases, 
 it will be safer to use the appropriate formula, as given on pages 
 563 and 565. The formulas and tables should always give the 
 same result. 
 
 To use the tables for beams that run less than the nominal dimen- 
 sions. In many localities floor joists as carried in stock are more 
 or less scant of the nominal dimensions, and for such joists a 
 reduction in the safe load must be made to correspond to the 
 reduction in size. For beams \ inch scant in both dimensions 
 the safe load may be obtained by multiplying the safe load as 
 given in the table by the following factors : 
 For beams lf"X5|" by 1.6 For beams If'Xllf" by 1.67 
 
 2f"X5J" " 2.52 2}"Xlli" " 2.63 
 
 l}"X6f" " If !}"Xl3i" " 1.68 
 
 2J"X6f" 2.55 2f"Xl3}" " 2,65 
 
 l} // X7f // " 1.64 lf"Xl4f" " 1.69 
 
 2J"X71" " 2.58 2i"Xl4f" " 2.66 
 
 l-i"X9f" " 1.66 lt"Xl5f" " 1.7 
 
 2f"X9|" " 2.61 2f"Xl5f" " 2.66 
 
STRENGTH OF WOODEN BEAMS. 
 
 573 
 
 EXAMPLE. What is the safe load for a 2f "Xl3|" Oregon pine 
 beam, 20 feet span? 
 
 Ans. From Table IV. we find the safe load for a 1 X 14 beam 
 to be 1,764 Ibs. Multiplying this by 2.65 we have 4,674 Ibs. as the 
 safe distributed load for a beam 2|Xl3| ins. For a beam full 
 3X 14 ins. the safe load is 5,292 Ibs. 
 
 Stone Beams. The same formulas apply to stone as to wooden 
 beams, but the values of the co-efficient A are only from one- 
 sixth to one-tenth of breaking-loads. Sandstone beams should 
 never be subjected to any very heavy loads; but, where used as 
 lintels, the stone should be relieved by iron beams or brick arches 
 back of the stone. 
 
 Comparison of the values of A (for the transverse strength of 
 wooden beams) given in Building Laws with those of Table II. 
 (A as used by the author is T V f the fibre stress, and J of the 
 constant C, given in the Building Laws of Buffalo and Chicago). 
 
 Kind of wood. 
 
 Maximum working values for A . 
 
 Buf- 
 falo. 
 
 Bos- 
 ton. 
 
 Chi- 
 cago. 
 
 Den- 
 ver. 
 
 New 
 York. 
 
 * 
 
 Kid- 
 der. 
 
 Yellow Pine 
 Oregon Pine 
 
 100 
 
 69 
 
 80 
 
 100 
 90 
 75 
 
 66 
 
 44J' 
 44J 
 55| 
 44J 
 33J 
 
 66 
 61 
 40 
 40 
 55i 
 44J 
 33J 
 
 100 
 90 
 60-65 
 70 
 75 
 60 
 55 
 
 White Pine. . . 
 
 60 
 
 
 50 
 
 Spruce 
 
 42 
 55J 
 
 Oak (White) 
 Chestnut 
 
 75 
 
 60 
 
 90 
 
 Hemlock 
 
 60 
 
 
 
 
 
 
 
 
 * The values in this column were recommended by the Committee on 
 Strength of Bridge and Trestle Timbers of the Association of Railway 
 Superintendents of Bridges and Buildings, in 1895, and are supposed to 
 give a factor of safety of six. With a factor of safety of four they agree 
 very closely with the values recommended and used by the author for 
 ordinary floor beams and girders. 
 
574 STRENGTH OF HARD-PINE BEAMS. 
 
 42 
 
 ll 
 
 1 & 
 
 II 
 
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 53 8 
 
 2 1 
 s a s 
 
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 S -I 
 
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STRENGTH OF OREGON-PINE BEAMS. 575 
 
 s s 
 
 a 
 
 o o o o o 
 
 GO m ""* ^ OJ CQ 
 
 T-H" TH" r-T C<f 
 
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576 STRENGTH OF WHITE OAK BEAMS. 
 
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STRENGTH OF SPRUCE BEAMS. 
 
 577 
 
 
 S 
 
 1 1 
 
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 ! 
 
 
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578 STRENGTH OF WHITE-PINE BEAMS. 
 
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STRENGTH OF BUILT-UP WOODEN BEAMS. 579 
 
 CHAPTER XVII. 
 
 STRENGTH OP BUILT-UP WOODEN BEAMS, 
 FLITCH-PLATES, AND TRUSSED 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 a solid beam of the same 
 dimensions, because the planks will be better seasoned and more 
 free from check cracks and other defects. For beams or girders 
 10 ins. or less in depth spikes will usually be sufficient for binding 
 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 from the 
 others v v'' ! ' 
 
 Two bolts should be placed at each end of the beam and about 
 four feet apart between. 
 
 When beams are built up in this way each plank should be the 
 full length of the beam, or, in the case of a continuous beam, the 
 planks should break joint over the supports Built beams 
 should always be set with the planks on edge, and never flatways. 
 
 Compound Wooden Girders. It is often desirable to 
 use a wooden girder for a longer span or greater load than would 
 be 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. 
 
 By a compound wooden beam or girder is meant a beam built 
 up by placing two or more single beams one on top of the other, 
 with the view of having them act as a single beam having the 
 depth of the combined beams. 
 
 Thus if two 10 X 10-inch beams were placed one on top of the 
 other, and the upper one loaded at the centre, the beams would 
 act as two separate beams (Fig. 1) and their combined strength 
 would be no greater than if the two beams were placed side by 
 side. If, however, the two beams can be joined so that the fibres 
 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 
 
580 STRENGTH OF BUILT-UP WOODEN BEAMS. 
 
 two beams will not slip on each other, the compound beam will 
 have four times the strength of the single beam. 
 
 Various attempts have been made to join beams thus placed 
 BO as to prevent the two parts slipping on each other, but until 
 within a few years there has been no experimental data to show 
 how far such methods accomplish their object. 
 
 During the years 1896-7, however, Prof. Edgar Kidwell, of the 
 Michigan College of Mines, made quite an extended series of tests 
 
 Fig. I 
 
 of the efficiency of compound beams of different patterns, and 
 from these tests much valuable data has been obtained. A full 
 description of the tests accompanied by the conclusions of the 
 author, and rules arfd data for proportioning the bolts and keys, 
 of keyed beams, is published in Vol. XXVII., "Transactions of 
 the American Institute of Mining Engineers." 
 
 Probably the most common form of compound beam, as used 
 in American building construction, is that shown in Fig. 2, 
 
 Fig. 2 
 
 diagonal boards in opposite directions being nailed to each side 
 of the two timbers to prevent their slipping on each other. Mr. 
 T. M. Clark, in his "Building Superintendence/' advocates this 
 as one of the best forms of compound beams, and places its 
 efficiency at about 95 per cent, of a solid beam of the same depth. 
 Prof. Kidwell made nine tests of this style of beam, six having a 
 ratio of span to depth of beam as 12 to 1, and three as 24 to 1. 
 The shorter beams gave an average efficiency without much 
 
STRENGTH OF BUILT-UP WOODEN BEAMS. 581 
 
 variation, of 71.4 per cent., 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 drawn partly out, or bent 
 over in the wood, thereby per- 
 mitting the component beams 
 to slide on each other. It was 
 found that no amount of nailing 
 could prevent this." 
 
 When built with diagonal 
 boards 1 inches thick, nailed 
 with 10 d 's as in Fig. 2, the work- 
 ing strength of such a beam may 
 be taken at 65 per cent, of the 
 strength of a solid beam of the 
 same depth, and of a breadth 
 equal to the breadth of the tim- 
 bers. The deflection of the beam, 
 however, will be about double 
 that of a solid beam of the 
 same size, and on that account 
 this style of beam is not to be 
 recommended for supporting 
 floors with plastered ceilings or 
 carrying plastered partitions. 
 
 Keyed Beams. Prof. 
 Kidwell also tested several 
 styles of keyed beams, with the 
 result that a compound beam 
 keyed and bolted together, as 
 shown in Fig. 3, was found to be 
 the most efficient form that it 
 is practicable to build. 
 
 It was found that with oak 
 keys it was possible to obtain 
 an efficiency for spruce beams 
 
 
 
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582 STRENGTH OF BUILT-UP WOODEN BEAMS. 
 
 of 95 per cent., while the deflection varied from 20 to 25 per 
 cent, more than would be expected in a solid beam. 
 
 By using cast-iron keys the deflection was found to be but 
 little, if any more, than with a solid beam. The keys must be 
 wedge-shaped, as shown in Fig. 4, so that they can be driven 
 tightly against the end wood. 
 
 Prof. Kidwell recommends that for ordinary purposes an 
 efficiency of 75 per cent, be allowed when oak keys are used and 
 80 per cent, when the keys are of cast iron. The width of oak 
 keys should be twice the height of the key. Numerous small 
 keys closely spaced gave better results than fewer large keys. 
 In the centre of the span a space equal to about one-quarter of 
 the length of the beam should be left free of keys, bolts, etc. In 
 
 TABLE I SAFE DISTRIBUTED LOADS IN POUNDS FOR 
 COMPOUND KEYED BEAMS. 
 
 16 and 20-inch beams to have 1^ X 3-inch oak keys, %-inch bolts, 3-inch 
 washers. 
 
 24-inch beam to have 2 X 4-inch oak keys, %-inch bolts, 3>-inch washers. 
 
 28-inch beam to have 23^X4^-inch oak keys, Ji-inch bolts, 3^-inch 
 washers. 
 
 Size of beam. 
 
 Span of beam in feet. 
 
 20 
 
 24 
 
 28 
 
 30 
 
 32 
 
 36 
 
 
 1,152 
 1,344 
 
 960 
 1,120 
 1,440 
 1,600 
 
 1,500 
 1,750 
 2.250 
 
 823 
 960 
 1,234 
 1,371 
 
 1,285 
 1,500 
 1,928 
 2,142 
 
 1,851 
 2,160 
 
 2,777 
 3,085 
 
 2,520 
 
 768 
 896 
 1,152 
 1,280 
 
 1,200 
 1,400 
 1,800 
 2,000 
 
 1,728 
 2,016 
 2,592 
 
 2,880 
 
 2,352 
 2,744 
 3,528 
 3,920 
 
 720 
 840 
 1,080 
 1,200 
 
 1,125 
 1,312 
 1,687 
 1,875 
 
 1,620 
 1,890 
 2,430 
 2,700 
 
 2,205 
 2,572 
 3,307 
 3,675 
 
 1,500 
 1,666 
 
 1,440 
 1,680 
 2,160 
 2,400 
 
 1,960 
 2,286 
 2,940 
 3,266 
 
 1 1 J Spruce . 
 
 1 X lo-j Oregon pine 
 
 i Georgia pine. . . .... 
 
 
 r^tVhite pine ... 
 
 1,800 
 
 ., rt _ 1 Spruce 
 
 1X20 1 Oregon pine...:::.. 
 
 
 
 
 {White pine 
 
 
 2,160 
 2,520 
 
 
 
 Oregon pine 
 
 
 
 
 
 {White pine 
 
 
 
 Spruce 
 
 
 
 Oregon pine 
 
 
 
 
 Georgia pine 
 
 
 
 
 
 
 
 
 To find safe loads for any given thickness of beam, multiply the load in 
 the table by breadth of beam in inches. 
 
 For centre loads, take one-half those in table. For concentrated loads 
 at other points divide by the factors given on page 567. 
 
 Beams should not be used for shorter or longer spans than those for which 
 safe loads are given, except that 28-inch beams may be used up to 40 feet. 
 
STRENGTH OF BUILT-UP WOODEN BEAMS. 583 
 
 his report, Prof. Kidwell also gives formulas for the number and 
 spacing of the keys. 
 
 As compound beams, if used, would probably be built of 
 either 8, 10, 12, or 14-inch timbers, the author has prepared Tables 
 I. and II. , giving the maximum safe load that may be allowed 
 for keyed beams 16, 20, 24. and 28 inches in depth, put together 
 as in Figs. 3 and 4, and also the number of keys required on each 
 side of the centre. 
 
 TABLE II. NUMBER OF OAK KEYS REQUIRED EACH 
 SIDE OF CENTRE. 
 
 Size of keys. 
 
 White 
 pine. 
 
 Spruce. 
 
 Oregon 
 pine. 
 
 Georgia 
 pine. 
 
 16-inch beams IK X 3 -inch keys . 
 20- " " 1^X3 - " " . 
 24- " " 2 X4 - " " . 
 28- " " 2MX4K- " " . 
 Minimum spacing of Keys. 
 1^X3 -inch keys 
 
 7 
 9 
 8 - 
 9 
 
 lUiins. 
 
 8 
 11 
 9 
 10 
 
 11^ ins. 
 
 11 
 13 
 12 
 12 
 
 9 ins. 
 
 12 
 15 
 13 
 14 
 
 9 ins. 
 
 2 X4 - " " . . . . 
 
 15 " 
 
 15 " 
 
 11^ " 
 
 11^ " 
 
 2)^X4H- " " 
 
 17 " 
 
 17 " 
 
 13 " 
 
 13 " 
 
 
 
 
 
 
 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 (Fig. 4) they should not be closer than the 
 minimum spacing given in the table. For beams loaded at the 
 centre, the spacing of the keys should be uniform from X to Y , 
 Y being one-eighth of the span from the centre. If the distance 
 between the keys, centre to centre, works out less than the 
 minimum spacing, the safe load should be correspondingly re- 
 duced or the thickness of the beam increased. 
 
 For beams uniformly loaded, the first four or five keys from 
 the ends 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 1 to 16, the inner keys 
 may be a little more than one-eighth of span from centre for dis- 
 tributed loads. 
 
 Fig. 3 shows the proper spacing for a 20-inch spruce beam of 
 28 feet span and for a Georgia pine beam of 30 feet span, and the 
 following table gives the proper spacing for spruce beams (figured 
 from the end of the beam) of longer span. For other woods and 
 spans the spacing should be made as near like these as the fixed 
 
584 FLITCH PLATE GIRDERS. 
 
 conditions will permit. Four examples of spacing are given 
 below. 
 
 The sizes of bolts and washers to be used are given in the head- 
 ing of Table I. If the beam is not over 10 inches wide the bolts 
 
 A ELEVATION OF 20"BEAM 
 
 B PLAN OF 14" X 24" SPRUCE BEAM -36' SPAN 
 Fig. 4 
 
 may be arranged as for the spruce beam, Fig. 3; if 12 inches wide 
 or over the bolts should be staggered as shown for the hard pine 
 beam. v In a very wide beam the bolts might be spaced as in 
 detail B, Fig. 4. 
 
 Spacing of keys in inches (commencing at end) for distributed 
 load: 
 
 16-in. spruce beam, 32 feet span, 10, 12, 12, 16", 19, 24, 32. 
 20-" " i* 32 " " 10,11^,11^,11^,12,12,12,13,15,18,24. 
 24- " " " 36 " " 13, 15, 15, 15, 15, 16, 18, 20, 30. 
 28- " " " 36 " " 15, 17, 17, 17, 17, 17, 17, 17, 17, 17, 
 
 Flitch Plate Girders. 
 
 A Flitch plate girder is a beam composed of two wooden beams 
 of the same breadth and depth with a wrought-iron or steel plate 
 of the same length and depth as the wooden beams bolted be- 
 tween them, as in Fig. 5. Such beams are much stronger and 
 stiffer than a wooden beam of the same depth, and may often be 
 used in the place of steel beams, where the latter are difficult to 
 obtain. 
 
FLITCH PLATE GIRDERS. 585 
 
 Flitch plate beams were at one time much used, but with steel 
 at 3 or 3| cents a pound it is fully as cheap and better to use a 
 steel beam. 
 
 The following explanation and formulas are given, however, 
 for the benefit of any one who might have occasion to use a beam 
 of this kind. It has been found by practice that the thickness 
 of the iron plate should be about one-twelfth of the whole thick- 
 
 Fig. 5 
 
 ness of the beam, or the thickness of the wood should be eleven 
 times the thickness of the iron. As the elasticity of iron is 
 so much greater than that of wood, we must proportion the load 
 on the wood so that it shall bend the same amount as the iron 
 plate: otherwise the whole strain might be thrown on the iron 
 plate. The modulus of elasticity of wrought-iron is about 
 thirteen times that of hard pine ; or a beam of hard pine one inch 
 wide would bend thirteen times as much as a plate of iron of the 
 same size under the same load. Hence, if we want the hard-pine 
 beam to bend the same as the iron plate, we must put only one- 
 thirteenth as much load on it. If the wooden beam is eleven 
 times as thick as the iron one, we should put eleven- thirteenths 
 of its safe load on it, or, what amounts to the same thing, use a 
 constant only eleven-thirteenths of the strength of the wood. 
 On this basis the following formulas have been made up for the 
 strength of Flitch plate girders, in which the thickness of the 
 iron is one-twelfth of the breadth of the beam, approximately : 
 Let D= Depth of beam. 
 
 B= Total thickness of wood. 
 
 L= Clear span in feet. 
 t= Thickness of wrought-iron plate. 
 f 82 pounds for hard pine. 
 
 /= ] 75 pounds for Oregon pine. 
 ( 60 pounds for spruce. 
 
 W= Total load on girder. 
 
 Then, for beams supported at both ends, 
 
 7)2 
 
 Safe load at centre, in pounds = - 7 -(/ + 7000. (1) 
 
586 TRUSSED BEAMS, 
 
 27) 2 
 Safe distributed load, in pounds =-jr~(fB + 7000. (2) 
 
 For distributed load, D= A/ __ HJ^ _ (3) 
 
 V 2 + 1400* 
 
 For load at centre, D = A/ WL . (4) 
 
 B + 700t 
 
 The bolts should be f-inch in diameter, and spaced 2 feet on 
 centres. Each end should have two bolts, as in Fig. 5. 
 
 When steel plates are used, the thickness of the timbers should 
 be about 15 times the thickness of the steel plate. Thus with 
 two 6"X12" beams the steel plate should be I" thick. Instead 
 of using two beams each 6 ins. thick, three four-inch beams and 
 two J" plates will generally be better, as it reduces the bending 
 moment on the bolts. If two or three plates are used t should be 
 taken as the total thickness of the plates. 
 
 To use the above formulas for steel, multiply t, in formulas 1, 
 2, and 4 by 900 in place of 700, and in formula 3, by 1,800. 
 
 EXAMPLE. What is the safe load, uniformly distributed for a 
 girder composed of three 4"X 14" Georgia pine timbers and two 
 j"X!4" Flitch plates, with a span of 25 ft.? 
 
 Ans. By formula 2, safe load 
 
 O\/ 1 QA 
 
 = - (82X12+900X|) = 26,013 Ibs. 
 
 40Q 
 
 TRUSSED BEAMS. 
 
 Whenever we wish to support a 'floor upon girders having a 
 span of more than thirty feet, we must use either a trussed girder, 
 a riveted steel-plate girder, or two or more steel beams. The 
 cheapest and most convenient way is, probably, to use a large 
 wooden girder, and truss it, either as in Figs. 6 and 7, or Figs. 8 
 and 9. 
 
 In all these forms it is desirable to give the girders as much 
 depth as the conditions of the case will permit; as, the deeper 
 the girder, the less strain there is in the pieces. 
 
 In the belly-rod truss 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 of the 
 girder, if they can be obtained that length. The requisite dimen- 
 sions of the tie-rod, struts, and beam, in any given case, must be 
 determined by first finding the stresses which come upon these 
 
TRUSSED BEAMS. 
 
 587 
 
 pieces, and then the area of cross-section required to resist these 
 stresses. For SINGLE STRUT BELLY-ROD TRUSSES, such as is 
 represented by Fig. 6, the strain upon the pieces may be obtained 
 by the following formulas : 
 
 For DISTRIBUTED LOAD W over whole girder, 
 
 Tension in T = Jl 
 
 Compression in C = f T 
 Compression in B Jl 
 
 For CONCENTRATED LOAD W OVr C, 
 
 Tension in T = - x , r?> 
 2 length of C 
 
 Compression in C= W. 
 
 D T7 length of B 
 
 Compression in B= 7- x i ^rr FT?- 
 
 2 ^length of C 
 
 * length of C' 
 length of B 
 
 W 
 
 (6) 
 (7) 
 
 tttt 
 
 ' N length of C 
 / length of T 
 
 (9) 
 
 For girder trussed as represented in Fig, 7 under a DISTRIBUTED 
 LOAD W over whole girder, 
 
 Fig. 7 
 
 ^ o i TT7 v length of S 
 
 Compression in S= \W X lengthof ^ 
 
 Tension in R 
 Tension in B 
 
 =|TF.* 
 
 length of 
 
 (10) 
 
 (11) 
 
 *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 = %W. 
 
588 
 
 TRUSSED BEAMS. 
 
 Far CONCENTRATED LOAD, W at centre, 
 
 n o TF length 
 
 Compression m>S=X 
 
 Tension in R 
 Tension in B 
 
 = W. 
 
 W length of B 
 ~~ 2 X length of C* 
 
 (12) 
 
 (13) 
 
 For double strut belly-rod truss (Fig. 8), with DISTRIBUTED LOAD 
 W over whole girder (beam B divided into three equal spans), 
 
 Fig. 8 
 
 Tension in T 
 
 W length of T 
 = 3 length of C' 
 W 
 
 Compression in C= . 
 o 
 
 W length of B 
 
 Comp. inBorD =-^Xr- ' , n . 
 3 length of C 
 
 For CONCENTRATED LOAD W over each of the struts C, 
 
 length of T 
 
 Tension in T 
 Compression in C 
 
 --WX 
 --W. 
 
 Comp. in B or tension in D=WX 
 
 length of C' 
 length of B 
 
 (14) 
 
 (15) 
 
 (16) 
 
 (17) 
 
 length of C' 
 
 For girder trussed, as in Fig. 9, under a DISTRIBUTED LOAD W 
 over whole girder (beam B divided into three equal spans), 
 2 3 
 
 Fig. 9 
 
 Compression in S 
 Tension in R 
 
 W length of S 
 = 3 X length of R' 
 
 TF 
 = 3* 
 
 r> > ^ w length of B 
 
 Tension in B or comp. in D= Xi ^, -=-=>. 
 
 3 length of R 
 
 (18) 
 
 (19) 
 
TRUSSED BEAMS. 589 
 
 Under CONCENTRATED LOADS W applied at 2 and 3. 
 
 Compression in S =WX . (20) 
 
 length of R 
 
 Tension in R =T7. 
 
 Tension in B or comp. in D^Wx g. (21) 
 
 Trusses as shown in Figs. 8 and 9 should be divided so that 
 rods R, or the struts C, shall divide the lengths of the girder 
 to three equal or nearly equal parts. The lengths of the pieces 
 
 C, B, R, S, etc., should be measured on the centres of the 
 jces. Thus the length of R should be taken from the centre 
 the tie-beam B to the centre of the strut D ; and the length of 
 should be measured from the centre of the rod to the centre of 
 e strut-beam B. 
 After determining the strains in the pieces by these formulas, 
 
 may compute the area of the cross-sections by the following 
 les: 
 
 A r a.- c ^ comp. in strut /oox 
 
 Area of cross-section of short struts = - ^ ^ - . (22) 
 
 C 
 
 The size of the long strut D, Fig. 9, should be determined by 
 
 eans of the tables on pages 411, 412. 
 
 The diameter of the tie-rods may be obtained from the table 
 
 page 340. 
 
 For the beam B, when the load is distributed, we must compute 
 
 necessary area of cross-section as a tie or strut (according to 
 lich truss we use), and also the area of cross-section required 
 
 support its load acting as a beam, and give a section to the 
 am equal to the sum of the two sections thus obtained. 
 Area of cross-section of B to ) _ tension comp. f 
 
 resist tension or compression ) T C 
 
 In trusses 6 and 7, with distributed load, 
 
 Breadth of B (as a beam) = / . (24) 
 
 In trusses 8 and 9, with distributed load, 
 
 / 
 Breadth of B (as a beam) = g . (25) 
 
 denoting the full distributed load on the girder in pounds, and 
 the length of one section of the tie-beam in feet. When the 
 
590 TRUSSED BEAMS. 
 
 loads are concentrated over C, or at R, then there will be nc 
 transverse strain on the beam B, and it need be proportionec 
 only for the tensile or compressive stress, as the case may be. 
 In formulas 23, 24, and 25, 
 
 (7= 1,000 pounds per square inch for hard pine and Oregon pine 
 800 pounds per square inch for spruce and white oak, 
 700 pounds per square inch for w r hite pine, 
 13,000 pounds per square inch for cast-iron. 
 T= 2,000 pounds per square inch for hard pine and oak, 
 1,800 pounds per square inch for Oregon pine, 
 1,600 pounds per square inch for spruce, 
 1,400 pounds per square inch for white pine, 
 12,500 pounds per square inch for wrought-iron, 
 15,000 pounds per square inch for steel. 
 A = 100 pounds per square inch for hard pine, 
 
 90 pounds per square inch for Oregon pine, 
 70 pounds per square inch for spruce, 
 60 pounds per square inch for white pine. 
 
 EXAMPLES. To illustrate the method of computing the dimen 
 sions of the different parts of girders of this kind, we will tak< 
 two examples. 
 
 1. Computation for a girder such as is shown in Fig. 6, for a spar 
 of 30 feet, the trusses to be 12 feet on centres, and carrying I 
 floor for which we should allow 100 pounds per square foot 
 The girder will consist of three strut-beams and two rods. We 
 can allow the belly-rod T to come two feet below the beams B\ 
 and we will assume that the depth of the beams B will be 12 
 inches; then the length of C (which is measured from the centn 
 of the beam) would be 30 inches. The length of B would, oj 
 course, be 15 feet, and by computation, or by scaling, we find tht 
 length of T to be 15 feet 2J inches. 
 
 The total load on the girder equals the span multiplied by th 
 distance of girders on centres, times 100 pounds = SOX 12 XlOC 
 = 36,000 pounds. 
 
 Then, from formula 5, 
 
 36,000 182J inches m ,, 
 
 Tension in T= '- X r~ r =109,500 Ibs. 
 
 2 30 inches 
 
 or 54,750 Ibs. on each of two rods. For such a large stress it wil 
 be best to upset the ends of the rods, and allowing 15,000 Ibs 
 
TRUSSED BEAMS. 591 
 
 er square inch for steel rods, we find from the table on page 340 
 iat we must use two 2J-inch steel rods. 
 The strut-beam we will make of Oregon pine. From formula 
 
 36 000 180 
 we find the compressive stress in B= ' X -^- = 108,000 
 
 ounds. As we are to use three beams, this will give 36,000 Ibs. 
 i each beam. 
 
 To resist the compression will require ' or 36 square ins., 
 
 hich is equal to 3X12 inches. 
 From formula 24 w^e- find the total breadth required to resist 
 
 36,000X15 10 . 
 le transverse stram= =12 ins., or each beam must 
 
 4 x 144 x yo 
 
 e 4X12 inches to resist the transverse strain, and 3X12 ins. to 
 ;sist the compressive strain. Consequently each beam must 
 e 7X12 inches. 
 
 As this would make the girder very wide 25^ ins. we will 
 se beams 14 ins. deep, increasing the depth of the girder one 
 ich, so that the height on centres will still be 30 ins. 
 
 The area required to resist the compressive stress will be the 
 ime as before, 36 inches, but as our beam is 14 inches deep the 
 readth will be only 2-| inches. 
 
 The total breadth to resist the transverse strain will be 
 
 ins -> or 2 5 ins - for each beam ' The * otal breadth 
 )r each beam will therefore be 5J inches. A 6X14 beam 
 r hen dressed will run about 5iXl3f ins., which will just about 
 leet the requirements. The total width of the girder will then 
 e 21 inches. The load on C=f W= 22,500 Ibs., or 11,250 Ibs. 
 ver each rod. The sectional area necessary to resist this load 
 
 1 1 9 r A 1 1 2 50 
 
 for cast iron and L - 1 for oak. As the struts must 
 
 13,000 800 
 
 e the full width of the girder, however, it will be necessary to 
 take the sectional area much greater than the theoretical 
 equirements. If made of cast iron the strut should be of the 
 hape shown in Fig. 10, and if of oak, of the shape shown in Fig 11. 
 'he cast-iron strut will be the best, but an oak strut will answer. 
 EXAMPLE 2. It is desired to support a floor over a lecture- 
 oom forty feet wide, by means of a trussed girder; and as the 
 oom above is to be used for electrical purposes it is desired to 
 iave a truss with very little iron in it, and hence we use a truss 
 uch as is shown in Fig. 9. Where the girders rest on the wall 
 
592 
 
 TRUSSED BEAMS. 
 
 there will be brick pilasters having a projection of six inches 
 which will make the span of the truss 39 feet ; and we will spac< 
 the rods R R so as to divide the tie-beam into three equal spam 
 of 13 feet each. The tie-beam will consist of two hard-pine 
 beams, with the struts coming between them. We will hav< 
 two rods, instead of one, at R t coming down each side of the strut 
 and passing through an iron casting below the beams, forming 
 supports for them. The height of truss from centre to centre o 
 timbers we must limit to 18 inches, and we will space the trusses 
 8 feet on centres. Then the total floor-area supported by on< 
 
 Fig. 10 
 
 Fig. II 
 
 girder equals 8 feet by 39 feet, equal to 312 square feet. The 
 heaviest load to which the floor will be subjected will be the 
 weight of students, for which 75 pounds per square foot will be 
 ample allowance ; and the weight of the floor itself will be about 
 25 pounds ; so that the total weight of the floor and load will be 
 100 pounds per square foot. This makes the total weight liable 
 to come on one girder 31,200 pounds. 
 
 The compression in S will be, from formula 18, X 157 . ms .t =3 
 
 o 18 ins. 
 90,700 pounds. 
 
 W 
 Tension in one pair of rods= = 10,400 pounds. 
 
 Tension in B or compression in D= 
 
 X 
 
 156 ins. 
 18 ins. 
 
 = 90,130 Ibs. 
 
 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. From 
 Table III, page 411, we find that it will require a 10X12 
 
TRUSSED BEAMS. 593 
 
 3am 13 feet long to resist the compression in D, a 10X10 not 
 3ing quite strong enough. The tension in each rod will be only 
 200 Ibs., but as the rods must support a large washer at the 
 ottom we will make them 1 in. in diameter, not upset. The 
 :nsion in each of the beams B will be 45,065 Ibs. This divided 
 y 2,000=22.6 square ins., or say 2X12 ins. 
 The total breadth of the tie-beam to resist the transverse load 
 3 find from formula 25, assuming 12 inches as the depth 
 31,065X13 . _. , ^ _ . . 
 
 ms *' r a k ut 2 ? ins - * or eac k beam. 
 
 6X144X100 
 
 The breadth of each tie-beam must therefore be 2" X 2f "= 4f". 
 [ence the tie-beams must be 5X12 ins. Therefore our girder 
 tust be built with 10 X 12 in. strut beams, and two 5 X 12 in. tie- 
 earns, each 42 ft. long. The 1-in. rods may be cut J in. into the 
 /rut-beam, and J in. into the tie-beams, so that the latter will 
 ome close against the strut S. The "kick" of strut S will be 
 qual to its compressive stress, and we must design a connection 
 itween the tie-beams and strut that will be capable of resisting 
 .e kick, which in this case is 90,700 Ibs. As the inclination of 
 .e strut is very slight there will be ample room for bolts. It 
 ill be best to use bolts at least 1 J ins. in diameter. As the bolts 
 ill be in double shear, the resistance to shearing of one bolt will 
 3 (Table V, page 376) 26,500 Ibs. 
 
 The bearing area of a IJ-inch bolt in a timber 10 inches wide 
 ill be 15 inches. For bearing resistance in hard pine we may 
 low 1,500 Ibs. per square inch, which will give 22,500 Ibs. as the 
 earing resistance of one 1J" bolt. As the force to be resisted is 
 0,700 Ibs. it will require four IJ-inch bolts to sustain the bearing 
 ressure, the resistance to shearing being greater than the stress. 
 We must now see how many bolts it will require to resist the 
 ending moment. The total bending moment to be resisted (see 
 age 390) =90,700 times the distance between the centres of the 
 
 e-beams divided by 12, or 90,700 X = 113,375 inch-pounds. 
 
 12 
 
 From Table IX, Chapter X, we find that the maximum bending 
 oment for a IJ-inch pin is 7,460 Ibs. Hence it will require 
 fteen IJ-inch bolts to resist the thrust in S without bending the 
 olts. It would be impracticable to put in so many bolts, hence 
 r e must use larger bolts. For a 2f -inch bolt the maximum bend- 
 ig moment is 29,600 Ibs., and four times this gives 118,400 Ibs., 
 ence four 2|-inch bolts will be sufficient to resist the bending 
 Tain, and also the shearing and bearing stresses. It will be 
 
594 TRUSSED BEAMS. 
 
 seen from this example that it is much more difficult and expei 
 sive to make satisfactory end joints for girders trussed as i 
 Figs. 7 and 9 than it is for the belly-rod trusses. The bell] 
 rod trusses are to be preferred when the conditions will admit < 
 their use. 
 
 These four cases of trussed girders are but special example 
 trusses. The stresses in them may also be computed by 
 methods explained in Chapter XXVI, and where the division 
 the girder cannot be made uniform the stresses should be co 
 puted by the general method there explained. 
 
STIFFNESS AND DEFLECTION OF BEAMS. 595 
 
 CHAPTER XVIII. 
 STIFFNESS AND DEFLECTION OF BEAMS. 
 
 [N Chapters XV. and XVI. we have considered the strength of 
 ams to resist breaking only ; but in all first-class buildings it is 
 sired that those beams which show, or which support a ceiling, 
 mid not only have sufficient strength to carry the load with 
 ety, but should do so without bending enough to present a bad 
 pearance to the eye, or to crack the ceiling; hence, in calcu- 
 ing the dimensions of such beams, we should not only calculate 
 im with regard to their resistance to breaking, but also to bend- 
 Unfortunately we have at present no method of combining 
 two calculations in one operation. A beam apportioned by 
 rules for strength will not bend so as to strain the fibres 
 ond their elastic limit, but will, in many cases, bend more 
 in a due regard for appearance will justify. 
 The amount which a beam bends under a given load is called its 
 faction, and its resistance to bending is called its stiffness; 
 nee the stiffness is inversely as the deflection. 
 The rules for the stiffness of beams are derived from those for 
 deflection of beams; and the latter are derived partly from 
 thematical reasoning, and partly from experiments. 
 We can find the deflection at the centre of any beam not strained 
 d the elastic limit, by the following formula: 
 
 . . load in Ibs. Xcube of span in inches Xc ,+ ^ 
 
 = modulus of elasticity X moment of inertia" ? ' 
 
 The values of c are as follows: 
 
 Beam supported at both ends, loaded at centre . . 021 
 " " " uniformly loaded 0.013 
 
 " fixed at one end, loaded at the other . 333 
 
 " " " uniformly loaded . 125 
 
 3y making the proper substitutions in Formula 1, we derive 
 
596 STIFFNESS AND DEFLECTION OF BEAMS. 
 
 the following formula for a rectangular beam supported at hot} 
 ends, and loaded at the centre : 
 
 -T, . . load X cube of span in feet XI, 728 
 
 Def. m mches= 4xbreadthX( f ube of depthXjE . 
 
 From this formula the value of the modulus of elasticity, E 
 for different materials, has been calculated. Thus beams oj 
 known dimensions are supported at each end, and a knowr 
 weight applied at the centre of the beam. The deflection of the 
 beam is then carefully measured; and, substituting these knowi 
 quantities in Formula 2, the value of E is easily obtained. 
 
 1 72J 
 Formula 2 may be simplified somewhat by representing - = 
 
 by p, which gives us the formula 
 
 Def. in inches- ^g.^. <SJ 
 
 For a distributed load the deflection will be five-eighths of this 
 If we wish to find the load which shall cause a given deflection 
 we can transpose Formula 2 so that the load shall form the left- 
 hand member. Thus: 
 
 Load at centre _ 4 X breadth X cube of depth X def. in ins. X E 
 in pounds cube of span X 1,728 
 
 Now, that this formula may be of use in determining the load t( 
 put upon a beam, the value of the deflection must in some way be 
 fixed. This is generally done by making it a certain proportior 
 of the span. 
 
 Thus Tredgold and many other authorities say that if a floor- 
 beam deflects more than one-fortieth of an inch for every foot oi 
 span, it is liable to crack the ceiling on the under side ; and hence 
 this is the limit which is often given to the deflection of beams 
 in first-class buildings. 
 
 Then, if we substitute for "deflection" the value, length in feei 
 -T- 40, in the above formula, we have, 
 
 T , . bread thX cube of depth Xe ,_ N 
 
 Load at centre = 5 : ^ 7 t (5) 
 
 square of span in teet 
 
 Tjl 
 
 letting e= 
 
 17,280* 
 
 * The constant F corresponds to Hatfield's F, in his Transverse Strains. 
 
STIFFNESS AND DEFLECTION OF BEAMS. 597 
 
 Most engineers and architects think that one-thirtieth of an inch 
 per foot of 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. 
 
 If we adopt this ratio, we shall have as our constant for deflec- 
 
 tion, 
 
 E 
 
 12,960* 
 
 In either of the above cases it is evident that the values used 
 for E, F, e, or e lt should be derived from tests on timbers of the 
 same size and quality as those to be used. The values for the 
 various woods given in the table below have been adopted by the 
 author after careful comparison with the results of numerous 
 tests on large timbers and with values given by different authori- 
 ties. The author believes that they are perfectly reliable for 
 first-class merchantable timber. 
 
 TABLE I. VALUES OF CONSTANTS FOR STIFFNESS 
 
 OR DEFLECTION OF BEAMS. 
 E= Modulus of elasticity, pounds per square inch. 
 F= Constant for deflection of beam, supported at both ends, and 
 
 loaded at the centre. 
 e = Constant, allowing a deflection of one-fortieth of an inch per 
 
 foot of span. 
 i= Constant, allowing a deflection of one-thirtieth of an inch per 
 
 foot span. 
 
 
 ET 
 
 F E 
 
 E 
 
 E 
 
 
 
 432 
 
 '~ 17,280 
 
 ^"12,960 
 
 Cast iron 
 
 15 700 000 
 
 36 300 
 
 907 
 
 1 210 
 
 Wrought iron 
 
 26,000 000 
 
 60,000 
 
 1 500 
 
 2 000 
 
 Steel . 
 
 31,000,000 
 
 71,760 
 
 1,794 
 
 2,358 
 
 Long-leaf yellow pine. . . . 
 Oregon pine or Douglas fir 
 Spruce 
 
 1,780,000 
 1,425,000 
 1,294,000 
 
 4,120 
 3,300 
 3,000 
 
 103 
 82 
 75 
 
 137 
 110 
 100 
 
 White pine 
 
 1,073,000 
 
 2,480 
 
 62 
 
 82 
 
 Hemlock 
 
 1,045,000 
 
 2,420 
 
 60 
 
 80 
 
 White oak 
 
 1,240,000 
 
 2,870 
 
 72 
 
 95 
 
 Ash 
 
 1,482,000 
 
 3,430 
 
 86 
 
 114 
 
 Chestnut 
 
 944,000 
 
 2,180 
 
 54 
 
 72 
 
 Cypress 
 
 900,000 
 
 2,080 
 
 52 
 
 69 
 
 Maple 
 
 1,902,000 
 
 4,400 
 
 110 
 
 146 
 
 California red- wood 
 
 700,000 
 
 1,620 
 
 40 
 
 54 
 
 
 
 
 
 
598 STIFFNESS AND DEFLECTION OF BEAMS. 
 
 Rules for Stiffness of Beams. 
 
 Knowing the deflection caused by a weight at the centre of a 
 beam, and the ratio of other deflections, caused by different 
 modes of loading and supporting, we can easily deduce the for- 
 mulas for the different cases considered under the strength of 
 rectangular beams. These cases are: 
 
 BEAMS SUPPORTED AT BOTH ENDS.* 
 
 Loaded at the centre, 
 
 -. f , , breadth X cube of depth X e , c ^ 
 
 Safe load= , (6) 
 
 square of span 
 
 or, 
 
 o j^ load X square of span m . 
 
 Breadth= cubeofdepthxe ' (7) 
 
 Loaded at a point other than the centre, m and n being the seg- 
 ments into which the beam is divided, 
 
 breadth X cube of depth X square of span X e , . 
 Safeload= ______ p ( 8 ) 
 
 or, 
 
 Breadth- cube Q depthxsquare of spa nXe ' 
 
 Load uniformly distributed, 
 
 8 X breadth X cube of depth Xe /1 N 
 
 Safeload= 5 X square of span ** 
 
 or, 
 
 _ , , 5 X load X square of span nn 
 
 SXcubeofdepthX* 
 
 Inclined beam, loaded at the centre,^ 
 
 breadth X cube of depth X e ^ 
 
 = spanXhor. dist. between supports ' 
 
 * In formulas (6) to (17) the breadth and depth are to be taken in inches, 
 and the length or span in feet. The load is always in Ibs. 
 
 The values given in either of the last two columns of Table I. may be used 
 for e, according to the degree of stiffness desired, but the values in the last 
 column are ample under ordinary conditions. 
 
 t Tredgold's "Elements of Carpentry," p. 65. 
 
STIFFNESS AND DEFLECTION OF BEAMS. 599 
 
 or, 
 
 B , , _ load X span Xhor. dist. between supports ( . 
 cube of depth Xe 
 
 BEAMS FIXED AT ONE END. 
 Loaded at extreme end, 
 
 ~ c , -3 breadth X cube of depth X e ,., .. 
 
 Safe load = -7 - c , (14) 
 
 16 X square of span 
 
 or, 
 
 Breadth = 16 X load X square of span 
 cube of depth Xe 
 
 Load uniformly distributed, 
 
 a'Vi , bread thX cube of depth Xe /<I/SN 
 
 Safe load = T . . (16) 
 
 6 X square of span 
 
 or, 
 
 D j^u 6 X load X square of span , N 
 
 Breadth = r ~ , . (17) 
 
 cube of depth X e 
 
 NOTE. Beams whose span in feet is less than the depth in ins. 
 should not be calculated by formulas for stiffness, but by those 
 for strength, Chapter XVI. 
 
 Katio of the Stiffness of Beams. 
 
 If the stiffness of a beam supported at both ends and loaded 
 
 at the centre be called 1 
 
 Then that of the same beam with the same load uniformly 
 
 distributed will be. | 
 
 Firmly fixed at both ends and loaded at the centre, according 
 
 to Moseley 5 
 
 Firmly fixed at both ends and uniformly loaded 8 
 
 Fixed at one end and loaded at the other ^ 
 
 Fixed at one end and uniformly loaded J 
 
 The stiffest rectangular beam containing a given amount of 
 material is that in which the ratio of depth to breadth is as 10 to 
 6; hence, in designing beams, the depth and breadth should be 
 made to approach as near this ratio as is practicable. 
 
600 STIFFNESS AND DEFLECTION OF BEAMS. 
 
 EXAMPLE 1. What is the greatest distributed Lad that an 
 8 by 10 inch white-pine girder of 12 foot clear span will support, 
 without deflecting at the centre more than -^ of an inch per 
 foot of span? 
 
 Ans. This girder comes under the case of a beam supported 
 at both ends and loaded with a uniformly distributed load, and 
 hence should be calculated by Formula 10. Substituting the 
 given dimensions in Formula 10 we have, 
 
 -, , , , 8X8X1,000X82 
 
 Safe load= .', = 7,288 pounds. 
 
 O X 14:4: 
 
 EXAMPLE 2. What should be the dimensions of a yellow-pine 
 beam of 10-foot span to support a concentrated load of 4,250 
 pounds, without deflecting more than \ of an inch at the 
 centre? 
 
 Ans. A deflection of J of an inch in a span of 10 feet is in the 
 proportion of ^ of an inch per foot of span; and as the load is 
 concentrated and applied at the centre, we should use Formula 7, 
 employing for e the value given in the fourth column opposite 
 yellow pine. 
 
 Formula 7 gives the dimensions of the breadth, and to obtain 
 it we must assume a value for the depth. For this we will first 
 try 10 inches. 
 
 Substituting in Formula 7 we have, 
 
 4,250X100 
 Breadth- 1 ; OOQX137 - 3.1 inches. 
 
 Hence it will be necessary to use a 4"X10" beam. As the 
 span of this beam in feet is the same as the depth in ins., we 
 should see if it also meets the requirements for strength. From 
 Table III, Chapter XVI, we find that the safe distributed load 
 for a 1 X 10 beam 10 ft. span is 2,000 Ibs., and for a 4X 10 beam 
 the safe load would be four times as much, or 8,000 Ibs. The 
 load in this example, however, is applied at the centre ; hence we 
 must divide the safe distributed load by 2, which gives 4,000 Ibs. 
 for the safe centre load. As this is a little less than the load we 
 wish to support, we should increase the size of the beam to 
 5X 10 inches. As a general rule it is not safe to use the formulas 
 for stiffness when the span in feet does not exceed the depth in 
 inches. 
 
STIFFNESS AND DEFLECTION OF BEAMS. 601 
 
 EXAMPLE 3. What is the largest load that an inclined spruce 
 beam 8X12 inches, 16 feet long between supports, will carry at 
 the centre, consistent with stiffness, the horizontal distance be- 
 tween the supports being 14 feet? 
 
 Ans. Formula 12 is the one to be employed; and we will use 
 the value of e given in the last column opposite spruce. Making 
 the proper substitutions we have, 
 
 e i j 8X1,728X100 , 
 
 Safe load= ' ., =6,170 pounds. 
 
 lu X J-4 
 
 Cylindrical Beams. 
 
 For cylindrical beams the same formulas may be employed as 
 for rectangular beams, only instead of e use 1.7Xe; that is, a 
 cylindrical beam bends 1.7 times as much as the circumscribing 
 rectangle. 
 
 Deflection of Steel Beams. 
 
 For rolled steel beams the deflection is most accurately ob- 
 tained by Formula 1. 
 
 A shorter and sufficiently accurate method for determining the 
 deflection of the standard sections under their full safe load is 
 given on pages 510 and 511. 
 
 In using steel beams it should be remembered that for any 
 given span the deepest beam is always the most economical ; and 
 the stiffness of a floor is always greater when a suitable number 
 of deep beams are used. 
 
 Tables for Wooden Beams. 
 
 The following tables have been prepared so as to show at a 
 glance the greatest load that a beam one inch thick will support 
 without either exceeding the limit of deflection or the safe strength. 
 They give the same results as would be obtained by using the 
 above formulas, and the formulas for strength. 
 
 To find the corresponding load for thicker beams multiply the 
 load given in the table by the breadth of the beam in inches. The 
 loads thus obtained, however, are for beams that will run full to 
 the nominal dimensions. For beams that are J-inch scant in 
 
602 STIFFNESS AND DEFLECTION OF BEAMS. 
 
 both dimensions the correct load may be obtained by multiplying 
 the load given in the tables by the following factors: 
 
 For l|X5fby 1.5 For If X 9} by 1.6 
 
 2JX5J " 2.5 2|X 9| " 2.55 
 
 l}X7i " 1.6 IfXHf " 1.64 
 
 2-|X7| " 2.5 2iXH| " 2.6 
 
 IfXlSf " If 
 2|X13J " 2.6 
 
 Thus the maximum load consistent with stiffness for a 2f X 13 f- 
 inch Oregon pine beam of 20 f t.span will be 2.6 X 1,207= 3,138 Ibs. 
 
STIFFNESS AND DEFLECTION OF BEAMS. 603 
 
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604 STIFFNESS AND DEFLECTION OF BEAMS. 
 
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STIFFNESS AND DEFLECTION OF BEAMS, 605 
 
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606 STIFFNESS AND DEFLECTION OF BEAMS. 
 
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 ! 
 
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 tn^CpNOOOCMTHiO 
 
 .S H rH H i-H 
 
 
CONTINUOUS GIRDERS. 609 
 
 span I with W pounds, and at the centre of Zj with W^ pounds, 
 the re-action of the support RI will be represented by the formula 
 
 13W-3W, 
 Rl= ~"32 - ' 
 
 the re-action of the support R 2 by 
 
 (2) 
 
 and the re-action of the support R 3 by the formula 
 
 3 ~32 -- ' 
 
 If W=W lf then each of the end supports would have to sustain 
 T 5 ^ of one of the loads, and the centre support -V" f ^ Were the 
 girder cut so as to make two girders of one span each, then the end 
 supports would carry J or T \TF, and the centre support yfTF; 
 hence we see that, by having the girder continuous, we do not 
 require so much resistance from the end supports, but more from 
 the central support. 
 
 Fig. I 
 
 Girder of Two Spans, Uniformly Distributed Load Over Each 
 Span. Load over each span equals w pounds per unit of length. 
 Re-action of left support 
 
 w r 1 3 .73 n 
 
 *>=iL'-w^J- (4) 
 
 Re-action of central support, 
 Re-action of right support, 
 
 , 
 
 When both spans are equal to I, the re-action of each end support 
 is | if l^ and of the central support %wl; hence the girder, by being 
 continuous, reduces the re-action of the end supports, and in- 
 
608 CONTINUOUS GIRDERS. 
 
 CHAPTER XIX. 
 
 STRENGTH AND STIFFNESS OP CONTINUOUS 
 GIRDERS. 
 
 GIRDERS resting upon three or more supports are of quite fre- 
 quent occurrence in building construction; and a great variety 
 of opinions are held as to the relative strength and stiffness of 
 continuous and non-continuous girders ; very few persons, prob- 
 ably, having a correct knowledge of the subject. 
 
 In almost every building of importance it is necessary to 
 employ girders resting upon piers or columns placed from eight to 
 fifteen feet apart ; and in many cases beams can conveniently be 
 obtained which will span two and even three of the spaces be- 
 tween the piers or columns. When this is the case the question 
 arises, whether it will be better construction to use a long con- 
 tinuous girder, or to have each girder of only one span. 
 
 Most architects are probably aware that a girder of two or more 
 spans is stronger and stiffer than a girder of the same section of 
 only one span; but just how much stronger and stiffer is a ques- 
 tion they are Unable to answer. 
 
 As it is seldom that a girder of more than three spans is em- 
 ployed in ordinary buildings we shall consider only these two 
 cases. In all structures the first point which should be con- 
 sidered is the resistance required of the supports; and we will 
 first consider the resistance offered by the supports of a continu- 
 ous girder. 
 
 In this chapter we shall not go into the mathematical discussion 
 of the subject, but refer any readers interested in the derivation 
 of the formulas for continuous girders to an article on that sub- 
 ject, by the author, in the July (1881) number of Van Nostrand's 
 ' ' Engineering Magazine. ' ' 
 
 Supporting Forces. 
 
 Girders of Two Equal Spans, Loaded at the Centre of Each Span. 
 If a girder of two spans, I and l lt is loaded at the centre of the 
 
l -32 
 
 the re-action of the support R 2 by 
 
 CONTINUOUS GIRDERS. 609 
 
 span I with W pounds, and at the centre of Z t with W l pounds, 
 the re-action of the support R l will be represented by the formula 
 
 (2) 
 
 and the re-action of the support R 3 by the formula 
 
 13W.-3W 
 RS== ~32 -- * 
 
 If TF= W lt then each of the end supports would have to sustain 
 T \ of one of the loads, and the centre support -V 1 - of W. Were the 
 girder cut so as to make two girders of one span each, then the end 
 supports would carry J or T \TF, and the centre support j| TF; 
 hence we see that, by having the girder continuous, we do not 
 require so much resistance from the end supports, but more from 
 the central support. 
 
 B . G 
 
 Fig. I 
 
 Girder of Two Spans, Uniformly Distributed Load Over Each 
 Span. Load over each span equals w pounds per unit of length. 
 Re-action of left support 
 
 * ~ 
 
 Re-action of central support, 
 
 R 2 =w(l + l^-Ri-Rv (5) 
 
 Re-action of right support, 
 
 . - 
 
 When both spans are equal to Z, the re-action of each end support 
 is 1!^ and of the central support ^wl; hence the girder, by being 
 continuous, reduces the re-action of the end supports, and in- 
 
610 CONTINUOUS GIRDERS. 
 
 creases that of the central support by one-fourth, or twenty-five 
 per cent. 
 
 Continuous Girder of Three Equal Spans, Concentrated Load of 
 W Pounds at Centre of Each Span. 
 
 Re-action of either abutment, 
 
 (7) 
 
 Re-action of either central support, 
 
 R 2 =R 2 =UW; (8) 
 
 or the re-action of the end supports is lessened three-tenths, and 
 that of the central supports increased three- twentieths of that 
 which they would have been had three separate girders of the 
 same cross-section been used, instead of one continuous girder. 
 
 Ri 
 
 Continuous Girder of Three Equal Spans Uniformly Loaded with 
 w Pounds per Unit of Length. 
 Re-action of either end support, 
 
 R l =R,= lwl; (9) 
 
 Re-action of either central support, 
 
 (10) 
 
 hence the re-actions of the end supports are one-fifth less, and of 
 the central supports one-tenth more, than if the girder were not 
 continuous. 
 
 Strength of Continuous Girders. Having determined the re- 
 action of the supports we will now consider the strength of the 
 girder. 
 
 The strength of a beam depends upon the material and shape 
 of the beam, and upon the external conditions imposed upon the 
 beam. The latter give rise to the bending-moment of the beam, 
 or the amount by which the external forces (such as the load and 
 supporting forces) tend to bend and break the beam. 
 
 It is this bending-moment which causes the difference in the 
 
OONTIX 611 
 
 bearing-strength of continuous and non-continuous girders of 
 
 Continuous Girders of Two Spans. When a rectangular beam 
 is at the point of breaking we have the following conditions: 
 Bending- = Mod, of rupture XbrcadthXsq. of depth. 
 moment 6 
 
 and, that the beam may carry its load with perfect safety, we 
 must divide the load by a proper factor of safety. 
 
 Hence, if we can determine the bending-moment of a beam. 
 under any conditions, we can easily determine the required 
 dimensions of the beam from Formula 11. 
 
 The greatest bending-moment for a continuous girder of two 
 spans is almost always over the middle support, and is of the 
 opposite kind to that which tends to break an ordinary beam, 
 
 Distributed Load. The greatest bending-moment in a con- 
 tinuous girder of two spans, I and /^ loaded with a uniformly 
 distributed load of tr pounds per unit of length, is 
 
 Bending-moment = ^ j-~. 02) 
 
 When l=lit or both spams are equal 
 
 Z :. 1 ^ : r- : /. : r: -.1. ~. = . (12a) 
 
 o 
 
 which is the same as the bending-moment of a beam supported at 
 both ends, and uniformly loaded over its whole length: hence a 
 continuous girder of too spams uniformly loaded is no stronger than 
 if non-continuous. 
 
 Concentrated Load. The greatest bending-moment in a con- 
 tinuous girder of two equal spans, each of length 2, loaded with IT 
 pounds at centre of one span, and with !T t pounds at the centre of 
 the other span, is 
 
 Bending-moment = A* (IF-f IT,). 1 3 
 
 "When TT= TF L . or the two loads are equal, this becomes 
 
 Bending-moment=^Tn, (13a) 
 
 or one-fourth less than what it would be were the beam cut at the 
 middle support. 
 
 Continuous Girder of Tkne Spans. Distributed Load. The 
 greatest bending-moment in a continuous girder of three spans 
 loaded with a uniformly distributed load of r pounds per unit of 
 length, the length of each end span being ^ and of the i 
 
612 CONTINUOUS GIRDERS. 
 
 span I, is at either of the central supports, and is represented 
 by the formula, 
 
 T> j- 3 
 
 Bendmg-moment 
 
 When the three spans are equal, this becomes 
 
 wl 2 
 Bending-moment = , (14a) 
 
 or one-fifth less than what it would be were the beam not con- 
 tinuous. 
 
 Concentrated Loads. The greatest bending-moment in a con- 
 tinuous girder of three equal spans, each of a length I, and each 
 loaded at the centre with W pounds, is 
 
 Bending-moment = /$ Wl, (15) 
 
 or two-fifths less than that of a non-continuous girder. 
 
 Deflection of Continuous Girders. 
 
 Continuous Girder of Two Equal Spans. The greatest deflec- 
 tion of a continuous girder of two equal spans loaded with a 
 uniformly distributed load of w pounds per unit of length is 
 
 w n 
 Deflection = 0.005416^-. (16) 
 
 (E denotes modulus of elasticity; /, moment of inertia.) 
 
 The deflection of a similar beam supported at both ends and 
 uniformly loaded is 
 
 w u 
 
 Deflection= 0.013020^. 
 Oil 
 
 Hence the deflection of the continuous girder is only about two- 
 fifths that of a non-continuous girder. The greatest deflection 
 in a continuous girder is also not at the centre of either span, but 
 between the centre and the abutments. 
 
 The greatest deflection of a continuous girder of two equal 
 spans, loaded at the centre of one span with a load of W pounds, 
 and at the centre of the other span with W l pounds, is, for the 
 span with load W, 
 
 ^ . .. (23TF-9T70Z 3 
 
 Deflects ; (17) 
 
 for the span with load W lf 
 
 t* 1 - ,_ , 
 
 Deflection^ _JL__. (I 7a ) 
 
CONTINUOUS GIRDERS. 613 
 
 When both spans have the same load, 
 
 7 Wl 3 
 
 (176) 
 
 The deflection of a beam supported at both ends and loaded at 
 the centre with W pounds is 
 
 Wl 5 
 
 or the deflection of the continuous girder is only seven-sixteenths 
 of the non-continuous one. 
 
 Continuous Girder of Three Equal Spans. Uniformly dis- 
 tributed load of w pounds per unit of length 
 
 wl* 
 Deflection at centre of middle span =0.00052 ^7-. (18) 
 
 jl 
 
 wl* 
 
 Greatest deflection in end spans = 0.006884^. (19) 
 
 Mil 
 
 or the greatest deflection in the girder is only about one-half that 
 of a non-continuous girder. 
 
 Concentrated load of W pounds at centre of each span 
 
 JL Wl 3 
 Deflection at centre of middle span= - - -=-. (20) 
 
 11 Wl 3 
 
 Deflection at centre of end spans = r -== ; (21) 
 
 you CiL 
 
 or only eleven-twentieths of the non-continuous girder. 
 
 Several Observations and Formulas for Designing 
 Continuous Girders. 
 
 From the foregoing we can draw many observations and con- 
 clusions, which will be of great use in deciding whether it will 
 be best in any given case to use a continuous or non-continuous 
 girder. 
 
 First as to the Supports. We see from the formulas given for 
 the re-action of the supporting forces in the different cases that in 
 all cases the end supports do not have as much load brought upon 
 them when the girder is continuous as when it is not; but of 
 course the difference must be made up by the other supports 
 This might often be desirable in buildings where the girders run 
 across the building, the ends resting on the side-walls, and the 
 girders being supported at intermediate points by columns or 
 
614 CONTINUOUS GIRDERS. 
 
 piers. In such a case, by using a continuous girder, part of th 
 load could be taken from the walls, and transferred to th 
 columns or piers. 
 
 But there is another question to be considered in such a case 
 and that is vibration. Should the building be a mill or factor 
 in which the girders had to support machines, then any vibratio: 
 given to the middle span of the beam would be carried to the side 
 walls if the beam were continuous, while if separate girders wer 
 used, with their ends an inch or so apart, but little if any vibrs 
 tion would be carried to the side-walls from the middle span. 
 
 In all cases of important construction the supporting force 
 should be carefully looked after. 
 
 Strength. As the relative strength of continuous and nor 
 continuous girders of the same size and span, and loaded in th 
 same way, is as their bending-moments, we can easily calculat 
 the strength of a continuous girder, knowing the formula for it 
 bending-moment. From the values given for the bending 
 moments of the various cases considered, we see that the portio 
 of the girder most strained is that which comes over the middl 
 supports; also that, except in the single case of a girder of tw 
 spans uniformly loaded, the strength of a girder is greater if it i 
 continuous than if it is not. But the gain in strength in som 
 instances is not very great, although it is generally enough to pa 
 for making the girder continuous. 
 
 Stiffness. The stiffness of a girder is indirectly proportional t 
 its deflection ; that is, the less the deflection under a given loa 
 the stiffer the girder. 
 
 Now, from the values given for the deflection of continue 
 girders, we see that a girder is rendered very much stiffer by bein 
 made continuous; and this may be considered as the princip* 
 advantage in the use of such girders. 
 
 It is often the case in building construction that it is necessar 
 to use beams of much greater strength than is required to carr 
 the superimposed load, because the deflections would be to 
 great if the beam were made smaller. But, if we can use cor 
 tinuous girders, we may make the beams of just the size require 
 for strength, as the deflections will be lessened by the fact of th 
 girders being continuous. It should therefore be remembere 
 that, where great stiffness is required, continuous beams c 
 girders should be used if possible. 
 
CONTINUOUS GIRDERS. 615 
 
 Formulas for Strength and Stiffness. 
 
 For convenience we will give the proper formulas for calculat- 
 ing the strength and stiffness of continuous girders of rectangular 
 cross-section. The formulas for strength are deduced from the 
 formula 
 
 Bending-moment = -- - - , (22) 
 
 where R is a constant known as the modulus of rupture, and is 
 eighteen times what is generally known as the co-efficient of 
 strength. 
 
 STRENGTH. Continuous girder of TWO equal spans, loaded 
 uniformly over each span, 
 
 2XBXD 2 XA 
 Breakin g- weight *= j - , (23) 
 
 where B denotes the breadth of the girder, D the depth of the 
 girder (both in inches), and L the length of one span, in feet. The 
 values of the constant A are three times the values given in Table 
 II. of Chapter XVI. For yellow pine, 300 pounds; for Oregon 
 pine, 270 pounds; for spruce, 210 pounds; and for white pine, 
 180 pounds, may be taken as reliable values for A. 
 
 Continuous girder of TWO equal spans, loaded equally at the centre 
 of each span, 
 
 A 7? v D 2 v 4 
 Breaking-weight=|-x - L . (24) 
 
 Continuous girder of THREE equal spans, loaded uniformly over 
 each span, 
 
 Breaking-weight = X m (25 ) 
 
 Continuous girder of THREE equal spans, loaded equally at the 
 centre of each span, 
 
 Breaking-weight= X . (26) 
 
 o Ju 
 
 STIFFNESS. The following formulas give the loads which the 
 beams will support without deflecting more than one-thirtieth of 
 an inch per foot of span. 
 
 Continuous girder of TWO equal spans, loaded uniformly over 
 each span, 
 
 T -, BxD 3 Xe 
 
 Load on one span = Q 26xL2 . (27) 
 
 * Breaking weight in Ibs. in all cases, 
 
616 CONTINUOUS GIRDERS. 
 
 Continuous girder of TWO equal spans, loaded equally at cent 
 of each span, 
 
 Load on one span= y X BX ^' Xe . (2 
 
 Continuous girder of THREE equal spans, loaded uniformly ov 
 each span f 
 
 _0 
 Load on one span= Q33xL2 . (2 
 
 Continuous girder of THREE equal spans, loaded equally at t 
 centre of each span, 
 
 Load on one span=g- X e . (3< 
 
 The value of the constant e is obtained by dividing the moduli 
 of elasticity by 12,960; and, for the three woods most common 
 used as beams, the following values may be taken : 
 
 Yellow pine, 137; white pine, 82; spruce, 100; Oregon pin 
 110. (For other woods see table, page 597.) 
 
 For continuous steel beams the requisite size of beam may 1 
 found by first computing the bending-moment, by means 
 Formulas 12-15, and then selecting a beam whose section modul 
 
 3 X bending- moment (ft.-lbs.) Tr , . ,, 
 
 -- . Values for the section moduli 
 
 for the different shapes of rolled steel used as beams are giv( 
 in the tables in Chapter X. 
 
 EXAMPLE 1. What size steel beam should be used to suppo 
 two loads of 16,000 Ibs. each, concentrated at the centre of to 
 spans of 10 feet each, the beam being continuous? 
 
 Ans. Formula 13a gives the bending moment as -foWl, 
 30.000 ft.-lbs. We must therefore use a beam having a sectic 
 
 O vx OQ 000 
 
 modulus equal to ' or 22. From the table on paj 
 
 4,UUU 
 
 297 we find that a 9-inch 30-lb. beam has a section modulus 
 22.6, and a 10-inch 25-lb. beam a section modulus of 24. Eithi 
 of these beams will therefore answer, the 10-inch beam being tl 
 cheaper, however. 
 
 EXAMPLE 2. A steel beam continuous over three spans is n 
 quired to support a distributed load of 1,000 Ibs. per linear foo 
 The two end spans are 12 feet each, and the centre span is 10 fee 
 what size and weight of I-beam should be used? 
 
CONTINUOUS GIRDERS. 617 
 
 Ans. The bending-moment is found by Formula 14, and will 
 . 1,000X1,000 + 1,000X1,728 
 be - 4(30 + 24)" 
 
 3 X 12 630 
 
 The section modulus must equal ' =9.47, which will 
 
 4,UUU 
 
 require a 7-inch 15-lb. beam. 
 
 If the beam were not continuous an 8-inch 18-lb. beam would 
 be required for the 12-foot spans, and a 7-inch beam for the 
 10-foot span. 
 
 For beams of two equal spans, loaded uniformly, the strength 
 of the beam is the same as though the beam were not continuous. 
 
 The formulas given for the re-actions of the supports, and for 
 the deflections of continuous girders with concentrated loads, 
 were verified by the author by means of careful experiments on 
 small steel bars. The other formulas have been verified by 
 comparison with other authorities where it was possible to do so ; 
 though one or two of the cases given the author has never seen 
 discussed in any work on the subject. 
 
618 RIVETED PLATE AND BOX GIRDERS. 
 
 CHAPTER XX. 
 RIVETED STEEL PLATE AND BOX GIRDERS. 
 
 GIRDERS built up of plates and angles, in the manner shown in 
 Figs. 1 to 4, are coming more extensively into use every year. 
 This is undoubtedly owing to the simplicity of their construction, 
 comparatively low cost of the shapes of which they are composed, 
 and their adaptability to any arrangement of loads or to any 
 span for which girders are usually required. 
 
 Riveted girders, however, are seldom made of a greater span 
 than 60 feet, nor of a greater height than 5 feet. 
 
 The most common forms of these girders are those shown in 
 Figs. 2 and 4. 
 
 T 
 
 _JIU 
 
 Fig.l 
 
 Fig. 2 
 
 Fig. 3 
 
 Fig. 4 
 
 The sections with a single vertical plate (called the "web") 
 are usually designated as " plate-girders," and those with double 
 or triple webs as " box-girders." 
 
 Plate-girders are more economical than box-girders, and more 
 accessible for painting and inspection; but the box-girders are 
 stiffer laterally, and should always be used where great length of 
 span requires a wide top flange. 
 
 In general it may be said that plate-girders should be used for 
 supporting floor-beams and floor-arches, and walls not over 12 
 inches in thickness, and that box-girders should be used where a 
 greater flange width than 12 inches is required. 
 
 The section shown in Fig. 1, which has no flange-plates, should 
 only be used for comparatively light loads and short spans, and 
 never for. supporting masonry. 
 
RIVETED PLATE AND BOX GIRDERS. 619 
 
 The term "flange," as applied to riveted girders, embraces all 
 the metal in top or bottom of girder, exclusive of web-plate. 
 
 By the "depth" of a riveted girder is generally meant the dis- 
 tance between the centres of gravity of the flanges; in practice 
 this is taken as the height of the web-plate, and the word will be 
 so used in this chapter. The top and bottom of the flange angles 
 are always on a line with the top and bottom of the web-plate. 
 
 Stiffeners are short pieces of angles riveted to the web at inter- 
 vals, to keep the web from buckling. They should fit closely 
 against the horizontal flanges of the flange angles, and should 
 always be used at the supports. 
 
 Depth and Width of Girders. The depth of a riveted girder 
 may be from T V to T V of the span. The greatest economy of 
 materials is said to be obtained when the depth is ^ of the span. 
 Thus for a 36-ft. span a 3-ft. girder should be used if the con- 
 ditions will permit ; but the least depth should be T ^ of 36, or 2 ft. 
 3 in. 
 
 The width of the top flange should not be less than -fa of the 
 distance between lateral supports; or if there are no lateral 
 supports, then not less than ^V of the span. 
 
 Arches between girders or floor beams riveted to the sides of 
 girders may be considered as lateral supports. 
 
 DETAILS OF CONSTRUCTION.* 
 
 1. 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 con- 
 nections. 
 
 In members subject to tensile strain full allowance shall be 
 made for the reduction of section by rivet-holes. 
 
 2. The webs of plate girders, when they cannot be had in one 
 length, must be spliced at all joints by a plate on each side of the 
 web. 
 
 Tees must not be used for splices. 
 
 3. Stiffeners shall be used at the ends of all girders and wher- 
 ever concentrated loads occur, and elsewhere when the shearing 
 strain is greater than the resistance to buckling. 
 
 4. The pitch (distance between centres) of rivets shall not ex- 
 ceed 6 in., nor 16 times the thickness of the thinnest outside plate, 
 
 * The following twelve points are taken largely from Birkrnire's " Com- 
 pound Riveted Girders." 
 
620 RIVETED PLATE AND BOX GIRDERS. 
 
 nor be less than 2J in. for f-in. rivets, or 2| in. for f-in. rivets, in 
 a straight line. 
 
 5. The rivets used should be f in. in diameter for plates from 
 f in. to f in. thick, and f in. in diameter for greater thickness of 
 plates. 
 
 6. The distance between the edge of any piece and the centre 
 of a rivet-hole must never be less than 1 J in. 
 
 7. In punching plates or other iron, the diameter of the die 
 shall in no case exceed the diameter of the punch more than T ^ 
 of an inch. 
 
 8. All rivet-holes must be so accurately punched that when 
 the several parts forming one member are assembled together, a 
 rivet T V inch less in diameter than the hole can be entered, hot, 
 into any hole without reaming or straining the iron by " drifts." 
 
 9. The rivets when driven must completely fill the holes. 
 
 10. The rivet-heads must be hemispherical, except where flush 
 surfaces are required, and a uniform size for the same-sized 
 rivets throughout the work. They must be full and neatly 
 made, and be concentric to the rivet-holes. 
 
 11. Whenever possible, all rivets must be machine-driven. 
 
 12. The several pieces forming one built member must fit 
 closely together, and, when riveted, shall be free from twists, 
 bends, or open joints. 
 
 Splicing. "Girders 40 feet and less in length will not require 
 any splicing, as the plates and angles can be readily handled in 
 one length. 
 
 "In splicing 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 solidly. The rivets to be 
 closer near the joint. 
 
 "The plate covering the bottom flange must be of the same 
 area as the plates joined, and of sufficient length to take a num- 
 ber of rivets equal to the strength of the cover-plate." 
 
 CALCULATIONS FOR RIVETED GIRDERS. 
 
 In designing a riveted girder to sustain with safety a given 
 load, the following steps are necessary: 
 
 1. To determine the necessary flange area. 
 
 2. To determine the thickness of the web to resist (a) shearing, 
 (b) buckling. 
 
 This step also determines whether or not stiffeners are required. 
 
 3. To determine the number and pitch of the rivets. 
 
RIVETED PLATE AND BOX GIRDERS. 621 
 
 4. To determine the length of the outside flange-plates. When 
 but a single plate is used in the flanges this step is not required. 
 
 1 . Flange Area. For determining the flange area of riveted 
 girders, it is customary to assume that the bending-moment is 
 resisted entirely by the upper and lower flanges, the web-plate being 
 assumed to resist only the shearing strains. Some engineers 
 include J of the section of the web in the flange area, and some- 
 times the full moment of inertia of the section is taken. The 
 better practice, however, appears to be that based on the assump- 
 tion first given. The New York Building Law even goes further 
 than this, and requires that "No part of the web shall be esti- 
 mated as flange area, nor more than one-half of that portion of 
 the angle-iron which lies against the web." 
 
 As used in this chapter, the term "flange area" will include 
 the flange or cover-plates, and the full section area (less rivet- 
 holes) of the angles connecting the flange with the web. 
 
 In the flange plates and angles subjected to tensile strain full 
 allowance should be made for reduction of section by rivet-holes. 
 For the compression flange the gross sectional area may be taken 
 as making up the same, provided the riveting is well done, so as 
 to completely fill the holes. 
 
 The general formula for the strength of beams (see page 500) 
 is: Max. bending-moment = section modulus X& Assuming 
 that the flanges alone resist the bending-moment the section 
 modulus will be equal to the area of one flange multiplied by 
 the height of the girder and substituting this value in the above 
 equation we have 
 
 Max. bending-moment = area of one flange X height XS, 
 or 
 
 Area of one flange ) _ max, bending-moment (ft.-lbs.) 
 in square in. ) height of web in feetX& * 
 
 This applies to any condition of loading. 
 
 Rules for finding the maximum bending-moment for different 
 conditions of loading are given in Chapter IX. 
 
 For the upper or compression flange S should be taken at 
 12,000 Ibs. for steel and 9,000 Ibs. for iron. 
 
 For the bottom or tension flange S should be taken at 13,000 
 Ibs. for steel and 10,000 Ibs. for iron.* 
 
 *Most of the tables giving the strength of riveted girders, found in the 
 recent editions of the manuals issued by the rolling mills, are based on a 
 fibre stress of 15,000 Ibs. See pages 648-650. 
 
622 RIVETED PLATE AND BOX GIRDERS. 
 
 If it is desired to compute the safe distributed load for a girder 
 already constructed or designed, the following formula may be 
 used : 
 
 Safe load in Ibs. uniformly distributed = 
 
 SXnet area of bottom flange X height in ft.X$ 
 
 r T r . (la) 
 
 span in feet 
 
 From the result the weight of the girder itself should be sub- 
 tracted. 
 
 For safe centre load take one-half the result obtained by formula 
 (la) and subtract weight of girder. 
 
 1. Thickness of Web. The thickness of the web is deter- 
 mined by its resistance to shearing. Whether or not stiffeners 
 shall be used is determined by the resistance of the web to buck- 
 ling. 
 
 SHEARING. To resist shearing the net sectional area of web 
 must 
 
 maximum shear 
 F 
 
 F being taken at 6,000 Ibs. for iron and 7,000 Ibs. for steel.* 
 The maximum shear in any beam is at one or the other of the 
 
 supports, and in a girder supported at both ends is equal to 
 
 the greater of the supporting forces. 
 
 For a girder supported at both ends and uniformly loaded, 
 
 W 
 maximum shear -^- . 
 
 2 
 
 For a girder supported at both ends and loaded at the centre, max- 
 
 W 
 imum shear^, W representing the total load on the girder. 
 
 For a girder supported at both ends and loaded as in Fig. 7, 
 
 , WXm 
 
 maximum shear = -= =/i. 
 
 For a girder supported at both ends and loaded with two equal 
 concentrated loads W, W, equally distant from the centre, maxi- 
 mum shear ==W. 
 
 For combinations of loads the maximum shear will equal the 
 greater supporting force. The method of determining the sup- 
 porting forces in a beam is given on pages 274 and 275. The 
 shearing force at any given vertical section between the supports 
 
 * These are very conservative values. The Carnegie "Pocket Com.' 
 panion " and several building laws permit 10,000 Ibs. for steel. 
 
RIVETED PLATE AND BOX GIRDERS. 623 
 
 may be determined by the following rule: The shearing force at 
 any given cross-section of a beam is the algebraic sum of all the 
 forces acting on the beam from the origin to that cross-section, 
 
 j. m ^ 
 
 i : 
 
 1 - 1 | i 
 
 \ 
 
 y 
 
 W_ t -_z_ 
 
 1 C"! 
 
 : j-. Y 
 
 S-, _ pjg. 8 
 
 ft 
 
 ' ' 
 
 . / r '6- 
 P, 
 
 11 L H 
 
 T 
 
 
 P. 
 
 
 
 
 2 
 
 forces acting upwards being considered as minus, and those 
 acting downwards being considered as plus. 
 
624 RIVETED PLATE AND BOX GIRDERS. 
 
 Thus : In the case of the beam shown in Fig. 9 the reaction at 
 P l will be found, by the method explained on page 275, to be 
 150, and that at P 2 to be 140. 
 
 Taking our origin at P 1; we would have for the shearing force 
 at the section X, by the foregoing rule, 
 
 Shear at X = - 150+ 50 = - 100; 
 Shear at Y = - 150+ 50+ 80 = - 20 ; 
 Shear at Z = -150+50+ 80+100= + 80; 
 Shear at = - 150+ 50+ 80+ 100+ 60 =+ 140. 
 
 > The manner in which the shearing force varies between the 
 supports, under different methods of loading, is shown by the 
 etched areas in Figs. 5-9; in the first three cases W has the same 
 value. 
 
 When the load is distributed the shearing force can be found 
 by laying off P l and P 2 to a scale of pounds, and drawing the 
 line a&, Fig. 5. The shear at X will then be represented by the 
 ordinate X 1 and the shear at Y by Y t , which can be readily scaled. 
 
 The resistance of the web to buckling is determined by the for- 
 mula 
 
 . a f ., , , , v 10,000 X net area of section . 
 
 Safe resistance to buckling = - -- ^ - , (3) 
 
 14- 
 ^ 
 
 where /i=height, and t= thickness of web in inches. 
 
 When this resistance is less than the shearing force, at any 
 section, stiffeners must be used. 
 
 STIFFENERS. These should be made of angles, not less than 
 3X3X1 in. and seldom larger than 4X4XJ in. They should 
 always be tightly fitted between the flange angles, so as to sup- 
 port the horizontal flange. In order to bring the stiffeners in 
 contact with the web and vertical leg of angle, fillers are generally 
 used of the same thickness as the flange angle, as shown in Fig. 
 10. Where there are several girders exactly alike, something 
 may be saved by omitting the fillers and bending the stiffeners, 
 as shown in Fig. 11. This bending can only be properly done 
 by the use of special dies, and will cost more than the fillers unless 
 there are many stiffeners. 
 
 As to the spacing of stiffeners, they should in no case (where the 
 resistance to buckling is less than the shear) be spaced farther 
 apart than 1 \ times the height of the web, and it is safer to make 
 the distance from centres equal to the height of the web. 
 
RIVETED PLATE AND BOX GIRDERS. 625 
 
 On girders supporting distributed loads they are generally 
 placed nearer together at the ends than towards the centre. 
 
 Fig. 10 Fig. II 
 
 Stiffeners should always be placed at the ends and directly over 
 the edge of the support, as shown in Fig. 18, and wherever con- 
 centrated loads occur. 
 
 On plate girders the stiffeners are always placed on each side of 
 the web ; on box girders generally on the outside only. 
 
 Bearing of Girders. This depends somewhat upon the load, 
 but a safe general rule is to make the bearing of the girder beyond 
 the edge of the support equal to one-half the height of the girder. 
 
 Spacing of Rivets. 
 
 I. RIVETS IN WEB LEG OF ANGLES. 
 
 It will readily be seen that when a plate or box girder is loaded, 
 the tendency of the bending-moment 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 strain"), between any selected point of the flange and the 
 nearer end of the girder, is equal to the bending-moment at that 
 point divided by the depth of the web. 
 
 The total number of rivets between the selected point and the 
 nearer end must be such that their combined resistance to shear- 
 ing or bearing (whichever is the least) shall equal the "horizontal 
 flange strain" at the selected point; or number of rivets 
 
 horizontal flange strain 
 bearing or shearing of one rivet' 
 
 and the total number of rivets in web-angle from end to end 
 2Xmax. bending-moment (ft.-lbs.) 
 
 height of web (in ft.) X least resistance of one rivet ' 
 
 (4) 
 
626 RIVETED PLATE AND BOX GIRDERS. 
 
 If the number of rivets determined by formula (4) is such that 
 they would be more than 6 in. apart, then the number must be 
 increased, as in no case should they have a greater " pitch" than 
 6 in. 
 
 II. FLANGE LEG OF ANGLES. 
 
 a. With 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 feet, staggering the 
 rivets as in Fig. 15. Beyond that point to the centre, one-half 
 the number of rivets will be sufficient, provided this will not 
 give them a greater pitch than 6 in. 
 
 b. 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, between a and &, 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 centre the rivets can be spaced accord- 
 ing to the rule for greatest pitch. 
 
 III. 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. 
 
 Approximate Weight of Girder. 
 
 In determining the size of a riveted girder to support a given 
 load, it is desirable to be able to add to the superimposed load 
 the weight of the girder itself, as this often forms quite a con- 
 siderable portion of the load to be supported. 
 
 Mr. William H. Birkmire, in his book on "Compound Riveted 
 Girders," gives the following empirical rule for determining the 
 approximate weight of plate or box girders: 
 
 WXL ,~. 
 
 Weight of girder between support, in tons=- 70Q , 
 
 where W equals load to be supported in tons, and L equals span 
 in feet. 
 
 The constant 700 was determined for girders from 35 to 5C 
 long, but may be used without much excess for girders of shorter 
 span. 
 
RIVETED PLATE AND BOX GIRDERS. 627 
 
 Tables. 
 
 The calculations of riveted girders may be greatly facilitated 
 by Tables I., II., and III. Table I. gives the sectional area that 
 should be deducted for rivet-holes in plates of different thick- 
 nesses. In computing this table J inch was added to the diam- 
 eter of the rivet to allow for the injurious effect of punching. 
 
 Table II. gives the safe shearing value for web-plates for 
 various depths and thicknesses, and the deduction to be made 
 for each f-inch or f-inch rivet. 
 
 Table III. gives the safe resistance to buckling per square inch 
 of net section, and also the total resistance of the more common 
 sizes of web-plates, with two rivet-holes deducted. 
 
 It is very seldom that any vertical section between the stif- 
 feners contains more than two rivet-holes. Tables giving the 
 dimensions of angles will be found in Chapter X., and the shear- 
 ing and bearing value of rivets is given on page 371. 
 
 Examples. 
 
 EXAMPLE I. It is required to support the floor over a room 
 50X64 feet, by means of riveted steel plate girders, placed across 
 the room and 16 feet on centres. The floor above is to be used 
 for general assembly purposes. The floor joists are of wood, with 
 plastered ceiling below. Design the girder. 
 
 First Step: Load. The first step will be to determine the load 
 to be supported by each girder. The floor area supported by each 
 girder is 50'Xl6' or 800 sq. ft. The weight of the floor con- 
 struction between the girders will be not over 25 Ibs. per sq. foot, 
 and an allowance of 100 Ibs. per sq. foot for live load will be 
 ample. 800 X 125 gives 100,000 Ibs. or 50 tons as the load to be 
 carried by the girder. To this should be added the weight of 
 the girder itself. The rule for approximate weight of girder is 
 
 load in tons X span 50X50 
 = 70Q ~ = 7 Q Q = 3.57 tons, or about 7,000 Ibs., 
 
 making the total load 107,000 Ibs. This, of course, will be dis- 
 tributed. 
 
 Second Step: Flange Area. The next step will be to determine 
 the flange area. Before we can do this, however, we must de- 
 cide upon the width and depth of the girder. 
 
 As it is desirable to keep the girder as shallow as possible, con- 
 sistent with good engineering, we will make the depth, or height, 
 of the web-plate 36 inches, which is about }{ Q th of the span. 
 
628 RIVETED PLATE AND BOX GIRDERS. 
 
 As the girders are braced sideways by the floor joists we will 
 make the width of the flange-plates 12 inches. 
 
 The flange area is determined by formula (1), and equals 
 max. bending-moment in ft.-lbs. 
 
 height of web in ft. X S 
 
 The maximum bending-moment for a distributed load equals 
 WXL 
 
 or in this case 
 
 krinv/ Kn 
 
 668,750 ft.-lbs. 
 
 8 
 
 107,000X50 
 
 8 
 
 Substituting this in the above formula we have, 
 
 ~ 668,750 
 
 Gross area of upper flange= ^ = 18.57 sq. in. 
 
 668.750 
 
 Net area of lower flange = ' nn = 17.15 sq. in. 
 oX lo,UUU 
 
 We will first consider the upper flange. 
 
 For the angles we will use two 5"X3J"Xi" angles, with the 
 long leg horizontal.* The area of these two angles we find to be 
 8 sq. in., which leaves 10.57 sq. in. for the flange-plates. Divid- 
 ing this by the width of the plate, 12 in., we have .88, or say 
 in. as the required thickness of the plates. We will divide this 
 into two plates, one J inch thick, and the upper one f inch thick. 
 
 We will now see if these plates will have a net area, after de- 
 ducting the rivet-holes, sufficient for the lower flange. As we 
 shall stagger the rivets in the two legs of the angles, we will 
 have to deduct for only two rivets in flange legs of angles, and 
 two in the flange-plates. We will use f-inch rivets. From 
 Table I. we find that the area to be deducted for two f-inch rivets 
 in a J-inch plate is 1.53, and in a J-inch plate (thickness of angle) 
 .87. Adding these, we have 2.40 sq. in. to be deducted from 
 18.50 sq. in., the gross area of upper flange, which leaves 16.1 sq. 
 
 * For the flange-angles of plate coders the 5"X3W size is most com- 
 monly used, when the flange-plate' is from 10^ to 12 inches wide, and 
 6"X4" angles when the flange-plate is over 12 in. wide. For box girders 
 5X4,5X3^, 4X3J^, and 3^X3V are common sizes; while for very heavily 
 loaded girders, requiring two rows of rivets in the web leg, 6"X4" angles 
 are often used, with the long leg vertical. 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 centre of the girder as 
 possible. The minimum thickness of flange-angles should be %> of an inch, 
 and the maximum thickness for ordinary loads % inch. 
 
RIVETED PLATE AND BOX GIRDERS. 629 
 
 in. as the net area. As this is less than the net area required in 
 the lower flange, we will increase the thickness of outer plate 
 to J in., which will give us a little excess of area. 
 Our flanges will then be made up as follows: 
 
 Top flange = 2 angles 5" X 3J" X V = 8 sq. in. gross area 
 1 plate 12"X i" =6 " " " " 
 1 plate 12"X I" = 4.5 " " " " 
 
 Total, 18.5 " " " 
 
 Bottom flange =2 angles 5" X3i"Xi"B net area 7.13sq. in. 
 2 plates 12" Xi" " " 10.25 " 
 
 Total, 17.38 " 
 
 Third Step: Length of Flange-plates. We will now determine 
 the length of the outer plate in bottom flange. 
 
 To do this we must first determine the horizontal flange strain 
 at centre of girder. This is equal to the bending-moment 
 
 668 750 
 
 divided by the height of girder in feet, or '- = 222,910 Ibs. 
 
 o 
 
 The bending-moment in a beam or girder loaded with a uni- 
 formly distributed load is represented by the ordinates of a 
 parabola having its height equal to the bending-moment at the 
 centre. The horizontal flange strain is also represented by the 
 same curve. 
 
 If, therefore, we draw the parabola rht, Fig. 12 making ah= 
 horizontal flange strain, to a scale of pounds, any ordinate drawn 
 to this curve will represent the flatfge strain in the girder at the 
 corresponding point on the girder. 
 
 To find the theoretical length of the flange-plates, draw the 
 indefinite horizontal line AD, and from the point a lay off the 
 line ad equal to the total flange area, and at such an angle that 
 the end of the line d will come in the line AD. Then divide the 
 line ad into a6=area of two angles; 6c=area of first flange- 
 plate; cd=area of second flange-plate. 
 
 Draw horizontal lines through b and c] then the line ee'w'ill 
 represent the theoretical required length of the outer flange- 
 plate, and the line ff the length of the first flange-plate. 
 
 The plates must in practice, however, be extended beyond the 
 points e and / a distance sufficient to catch enough rivets to 
 transmit at least one-third of the resistance of the plate. 
 
 The first flange-plate we will make the full length of the 
 
630 RIVETED PLATE AND BOX GIRDERS. 
 
 girder, as it greatly strengthens the angles, and adds but a small 
 amount to the cost of the girder. We will also make the plates 
 in the upper flange of the same length as those in the lower flange. 
 Fourth Step: Web. The maximum shearing-stress in a beam 
 uniformly loaded is equal to one-half of the total load, or, in this 
 
 107 000 
 
 case, =53,500 Ibs. The web must be thick enough to 
 ft 
 
 resist the shear. From Table II. we find that the resistance to 
 shearing of a f"X36" web-plate is 94,500 Ibs. As this greatly 
 exceeds the total shear, we will use a f-inch web-plate. 
 
 Fifth Step: Stiff eners. As has been explained, stiffeners will 
 be required wherever the shear exceeds the safe resistance of the 
 
 web to buckling. In this case the maximum shear is 53,500 Ibs. 
 and the safe resistance of a f"X36" web with two f" rivets to 
 buckling (see Table III.) is 31,560 Ibs.; hence stiffeners will be 
 required at intervals of about 3 feet. 
 
 To determine how many stiffeners will be required, we draw 
 the horizontal line K-K, Fig. 12, and at each end lay off to a 
 scale of pounds the lines P lt P 2 , each equal to one-half the total 
 load on the girder. The shaded triangles will represent the 
 shearing-stress in the web. At 3 ft. from the end the shear will 
 equal S^ at6ft.,<8 2 ; at 9 ft., S 3 ; and so on. 
 
RIVETED PLATE AND BOX GIRDERS. 631 
 
 By measuring these lines with our scale we find the shear at m, 
 n, o, p, etc. In this case we find ^ = 46,200 Ibs., S 2 = 39,900 
 Ibs., $3 = 33,600 Ibs., and S 4 = 27,300 Ibs. As S 3 is greater than 
 the safe resistance to buckling, and S less, we might stop the 
 stiffeners at p; but as the floor-joists are framed flush, or nearly 
 so, with the top of the girder, and rest on angles riveted to the 
 web, we will put about 3 stiff eners between the point p and the 
 corresponding point on opposite end. 
 
 We will also put a stiffener at each end and directly over each 
 support, so that we will have 15 stiffeners on each side of the 
 girder. These we will make of 4"X4"Xt" angles. 
 
 Sixth Step: Rivets. We will first determine the number of 
 rivets in the web leg of the angles. As we should put a rivet in 
 the end of each stiffener, we will determine the number of rivets 
 required between each two adjacent stiffeners. The strain on 
 the rivets between the point m and the end of the girder is 
 equal to the line H l t , between m and nH 2 ', between n and 
 o=H 3 ; between o and p=# 4 ; and the strain between p and 
 the centre = H$. By scaling these lines we find ^ = 48,000 Ibs., 
 # 2 =44,500 Ibs., #3 = 38,000, 7/ 4 =28,500, and # 5 = 64,410. 
 
 In the web the rivets are in double shear; 'hence each rivet 
 will have a shearing resistance (see Table II., p. 371) = 6, 620 Ibs. 
 The resistance to bearing of a f-inch rivet on a j-inch plate (see 
 same table) = 4,220 Ibs., and the latter number will determine the 
 number of rivets. 
 
 48,000 Ibs. -4,220 = 11.4 rivets or 12 rivets, the number 
 required between m and the end of girder. We will put 1 rivet 
 through each of the two end stiffeners, 3 between the end stiffen- 
 ers, and 7 between the stiffeners at r and m, making 12 rivets to 
 
 the left of m. Between m and n we must have ~ ^ r= n rivets. 
 
 4,220 
 
 As this would make them closer together between m and n than 
 between r and m, we will space the 18 rivets evenly between r 
 and n, putting one in the end of the stiffener at n. This will 
 make the pitch just 4 in. 
 
 OQ f\r\c\ 
 
 The number of rivets between n and o must equal ' =9, 
 
 4,^^U 
 
 which gives the same pitch as before. Between'o and p we must 
 
 28 500 
 have ' n ft 7 rivets, which gives a pitch of 5j in. ; and between 
 
 p and the centre we must have ' , or 16 rivets. As the dis- 
 
 QjZZO 
 
632 RIVETED PLATE AND BOX GIRDERS. 
 
 tance is 13 ft., or 156 in., this would make the pitch nearly 10 in. 
 The maximum permissible pitch is 6 in., and we will therefore 
 use that pitch from t to the corresponding point on the other end. 
 
 The rivets in the flange leg we will space intermediate with 
 those in the web leg. To determine the length of the outer 
 plate, we have the net area of outer plate in lower flange =5. 13 
 sq. in. This multiplied by 13,000 = 66,690 Ibs., the resistance of 
 the plate. One-third of this, or 22,231 Ibs., must be transferred 
 by rivets placed beyond the points e, e' } Fig. 12. As the rivets 
 in the flange are in single shear, the shearing strength (3,310 Ibs. 
 for |-inch rivets) will determine the number 22,230-^3,310=7 
 rivets, or say 3 in each angle. 
 
 The point e, Fig. 12, comes at a, Fig. 15, and we will extend 
 the plate so as to take the next three rivets towards the end. 
 
 The rivets in the stiffeners we will space as near 6 in. as we 
 can, which gives five rivets between the ends. 
 
 The ends of the floor-joist we will support on 4"X4"Xi" 
 angles. The load on one lineal foot of this angle, on each side of 
 the girdei, = 8 ft. X 125 Ibs. = 1,000 Ibs. ; and as the same rivets 
 support both angles, the total load per running foot will be 2,000 
 Ibs., which is only about one-half of the resistance of a single 
 rivet. We will therefore pitch the rivets about 6 in. 
 
 Splices. 
 
 As the total length of the girder is 53 ft., it will probably be 
 necessary to splice the web and flange -plates. 
 
 The angles should not be^ spliced, as they can be obtained in 
 one length,* and it is difficult to make a good splice in the angles 
 If the web is spliced, the joint should be at the centre, as theoreti- 
 cally there is no strain on the web at that point when the load is 
 distributed. We will therefore use for the splice-plates (one on 
 each side of the web) \" plates, 8" wide, and of such length 
 that they will fit closely between the flange angles. These plates 
 will serve as fillers for the middle stiffener. If there was a shear- 
 ing stress at this point of the web the number of rivets on each 
 side of the joint should be sufficient to transfer the shear from 
 one side of the joint to the other. In this case we will use the 
 same number of rivets as we determined for the stiffener. 
 
 The outer flange-plates can easily be obtained in one length. 
 The first flange-plate it may be necessary to splice. 
 
 * Angles 3"X3" and less can be rolled up to 60 ft. in length. Angles 
 4" X4" to 6"X6'', up to 50 feet. 
 
RIVETED PLATE AND BOX GIRDERS. 
 
 633 
 
 Whenever a splice is required in a flange-plate, it should if 
 possible be at a point just beyond the end of the plate above it. 
 The joint must be made by rive ting- 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 shown by Fig. 
 13. Let e denote the theoretical end of outer plate, as deter- 
 mined by the strain diagram, and a the point to which the plate 
 must be extended to receive rivets equal to one-third the strength 
 of the plate. Then let the joint in inner plate be just under a and 
 extend the outer plate to 6, or such a distance that it can receive 
 a number of rivets equal to the strength of one plate. 
 
 In the girder in question we will use a separate splice-plate 
 J in. thick and 12 in. wide. The net area of the inner plate is 
 5.13 sq. in., and its safe strength, at 13.000 Ibs. to the inch, 
 
 0,0,00,00.0,0 
 
 Fig. 13 
 
 
 
 o 
 
 ooooojooooo 
 
 OO OOOjOOOOO 
 
 ooooo ooooo 
 ooooo'ooooo 
 
 
 
 ' 
 
 
 <t ---SPLICE PLATE--- > 
 
 
 Fig. 14 
 
 66,690 Ibs., which equals the resistance of 20 rivets. We must 
 therefore have 20 rivets through the splice-plate on each side of 
 
 
 -12V 
 
 -4 < 
 
 i 
 
 
 
 3 
 
 c 
 
 
 
 
 1 c 
 
 
 
 
 1-8- 
 
 i 3-0 
 
 I--*---; 
 
 < -3-0 
 
 <_ 3-V .- 
 
 <~5-0~ 
 
 
 
 
 '2-4:-'-.'--^--- 
 
 - 2 ^-"1 l 
 
 
 
 Fig. 15 
 
 the joint. These rivets we will space as shown in Fig. 14, which 
 shows the under side of the splice-plate. The splice-plate should 
 
634 RIVETED PLATE AND BOX GIRDERS. 
 
 be placed close to the end of the lower plate as shown in Fig. 13. 
 The joint in the upper flange we will make as shown by Fig. 15, 
 extending the outer plate 2' V beyond a. 
 
 Fig. 15 shows one end of the girder, drawn according to the 
 foregoing calculations, the joint in the upper flange being at the 
 other end. 
 
 For the construction of the girder we shall require the following 
 bill of quantities ; 
 
 DETAIL OF GIRDER. 
 
 Load 100,000 Ibs. uniformly distributed. Span 50'. Depth 3'. 
 Upper flange. Two angles 5"X3J"X 1" 53 ft. long. 
 
 One plate 12"X i" 40' 11 " long. 
 
 One plate 12"X \" 12' 1" long. 
 
 One plate 12" X I" 30' 6" long. 
 Lower flange. Two angles 5"X31"X4" 53 ft. long 
 
 One plate 12" X i" 43' 3" long. 
 
 One plate 12" X i" 9' 9" long. 
 
 One plate 12"X J" 28' 10" long. 
 Web Two plates 36"X f" 26' 6" long, spliced. 
 
 30 stiffeners 4"X4"X f" angles 2' 11" long. 
 
 28 filler-plates 4"Xi"X29" long. 
 
 92 ft. 8 in. of 4"X4"XJ" angles for supporting 
 floor- joist. 
 
 Two splice-plates for web 8"Xf" 29 in. long. 
 
 One splice-plate on bottom flange 12"Xi"> 4 ft. 
 
 8" long. 
 Rivets f in. in diameter. 
 
 EXAMPLE II, It is required to support the wall shown in Fig. 
 16 by a riveted steel box girder at the height indicated. Design 
 the girder. 
 
 First Step: Loads. The first step towards designing the girder 
 will be to determine the load. The space under the lower win- 
 dows is too shallow to permit of the weight from the piers being 
 distributed over the girder, so that the only safe calculation is to 
 assume that the weight of the wall between the lines A and B is 
 concentrated at W l} the weight of wall between lines B and C at 
 TF 2 , and so on. 
 
 We will assume that the floor- joists run across the building so 
 that only the weight of the wall will be supported by the girder. 
 
RIVETED PLATE AND BOX GIRDERS. 635 
 
 Allowing 200 Ibs. as the weight of one square foot of a 21-inch 
 wall plastered on the inside, and 165 Ibs. per sq. ft. for the 17-inch 
 wall, we shall have. 
 
 Load at W l 
 
 _ j [5' 3"X10'-7'X2' 3"]X200=.. 7,350 ) 33,145 
 
 " ([5'3"X40'-(2'3"X 14'+ 3' 2 // X7 / )]X 165=25,795 ) Ibs. 
 
 
 1 
 
 L 
 
 B 
 
 
 
 c 
 
 
 I 
 
 ) 
 
 f S 
 
 k 
 
 
 p 
 
 
 il 
 
 
 x-- 
 
 ir 
 
 I 
 
 X" 
 
 "X 
 
 
 
 
 
 
 
 
 
 
 
 
 M 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 ! 
 
 
 
 
 
 
 
 
 
 
 
 h 
 
 
 (-&- 
 
 'r- 
 
 ~ 
 
 -7- 
 
 '^ 
 
 _* 
 
 -74" 
 
 -- 
 
 -4 
 
 'H--> 
 
 \l 
 
 I 
 
 
 f'"' 
 
 
 
 
 r 2 
 
 
 WlO) 
 
 -T 
 
 fl-6 
 
 : 
 
 / 
 
 ^28^1 
 
 T 4 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 J 
 
 > 
 
 GIRC 
 
 >ER * 
 
 
 
 1 
 
 
 s 
 
 1 
 
 
 
 
 F 
 
 ! 
 'ig. 
 
 16 
 
 
 
 
 
 sy 
 2 
 
 Load at TF 3 
 
 _ J[7'4 // X10 / -4'6X7'0"]X200= 8,366) 40,720 
 
 " ([7'4 // X4d / -(4'6Xl4 / +4'9 // X70]X 165=32,354 \ Ibs. 
 
 Load at F 3 = that at W 2 = ^ 40 ; 720 Ibs. 
 
636 RIVETED PLATE AND BOX GIRDERS. 
 
 Load at TF 4 
 
 _ j [4' ll"X!0'-2' 3"X7']X200= 6,683 I 
 
 " } [4' ll"X40'-(2' 3"Xl4'+3' 2"X 7')]= 23,595 < 
 
 Total load on girder = 144,863 Ibs. 
 
 or 72.4 tons 
 
 Approximate weight of girder 
 
 About one-third of this, or say 1,600 Ibs., should be added to TF 2 
 and TF 3 , and 900 Ibs. to W l and TF 4 . This will give us the fol- 
 lowing loads applied as in Fig. 17 : 
 
 I 1 T,.i 
 
 < 75 =*- 7-4- -fc -7-3 &14>> t 
 
 '- I- [ 
 
 :__ :z 6 c d 
 
 I ^^-"r :::::: -"-- -"--"--" 
 
 rTOl 
 
 LJ \ \ *h>fe 
 
 Fig. 17 
 
 TF 1= = 34,000 Ibs. ; W 2 = 42,300 Ibs/; 
 TF 3 = 42,300 Ibs. ; TF 4 --= 31,200 Ibs. 
 
 Second Step: To Determine Maximum Bending-moment. By 
 means of the formula under Case VI., p. 269, we find the 
 bending-moment (in foot -Ibs.) for each of the loads to be as 
 follows : 
 
 Q4 fiflH V 1 f R x/ V 9Q' A** 
 
 Bending-moment f or W,= - 24^ 10^ -= 47,980 ft.-lbs. 
 
 1 1 
 
 Bending-moment for TF 2 = 
 Bending-moment for T7 3 = 
 
 / v s' 7" 
 
 242,000 ft. -Ibs 
 = 237,900 ft.-lbs. 
 
 ^ ,. .. _ 31,200Xl / 4 // X23 / 6 // __ . On .. ., 
 Bending-moment for TF 4 = 24/ 1Q// = 39,420 ft. -Ibs. 
 
 Platting these moments to a scale, as explained on page 271, we 
 
RIVETED PLATE AND BOX GIRDERS. 637 
 
 get the diagram shown in Fig. 17.* The maximum bending- 
 moment is at W 2 , and its amount equals the line 66, which scales 
 418,000 ft.-lbs. 
 
 Third Step: To Determine Flange Area and Length of Cover- 
 plates. Before we can determine the flange area we must decide 
 upon the height of the web-plate. As we have plenty of room 
 for our girder, we will make the height of the web-plate 30 in., 
 or about f^th of the span. 
 
 Then by formula (1), 
 
 418 000 
 Gross area of upper flange = o^rr-.! nn x r very nearly 14 sq. in/; 
 
 Net area of lower flange = gvx -! 9 nr>A or 13 sq. in. 
 
 As the thickness of the wall to be supported is 21 inches, we will 
 use flange-plates 20 in. wide. The least thickness of cover-plate 
 that we should use is f in. The area of a f X 20-inch plate is 7 J 
 sq. in., which leaves 6J sq. in. to be made up by the angles. The 
 area of two 5"X3J"X%" angles is 7.06, which gives a little 
 excess for the top flange. In the lower flange we must allow for 
 two j-inch rivet-holes in both the plate and angles. From 
 Table I., we find that the area to be deducted for two f" rivets, 
 in a f" plate, is 0.65, and in a %-inch plate 0.76 or 1.41 sq. in. in 
 all! The gross area of the plate and angles is 7 J+ 7. 06 =14. 56 
 sq. in. Deducting 1.41 sq. in., we have 13.15 sq. in. for net area 
 of bottom flange, which is just above what we require. 
 
 We will therefore use the same size of plate and angles in both 
 flanges. As the width of the flange is more than one-twentieth 
 of the span, the girder will not require lateral support. 
 
 Fourth Step: Web and Stiff eners. The least thickness that 
 should be used for the web-plates is f in. We will therefore first 
 determine if this thickness is sufficient to resist the shearing 
 stress. 
 
 The maximum shearing stress will be at the left-hand support, 
 and will equal the reaction of that support. This reaction we 
 must determine by formula (2), page 275, or 
 
 ( 34,000X23' 4"+42,300X 15' 11" \ 
 
 P 1= \ _ + 42,300 X8' 7"+ 31, 200 XI' 4" [ = 75,450 Ibs. 
 
 ( 24' 10" " ) 
 
 As there are two web-plates, the shearing force to be resisted 
 by each plate will be one-half of this, or 37,725 Ibs; From Table 
 
 * The bending-moments in this diagram are drawn to the scale of 400,000 
 ft.-lbs. to the inch. 
 
633 RIVETED PLATE AND BOX GIRDERS. 
 
 IL we find that the resistance of a steel plate }X30 in. to shear- 
 ing is 78.750 IbsL. or twice as great as the stream From Table 
 TTT. we find the safe resistance to buckling, deducting for two 
 i-inch rivets, is 33.830 Iba. As this is a little less? than the shear, 
 we wfll place 4X4 stiffeners. 2? 4" from each support, and 5 ' 
 between them, about 3' 4" on centres. 
 
 [XOTE. If OUT loads were really concentrated at the points IT, , 
 W& etc., as bj the action of column or girder, it would be neces- 
 sary to put stiffeners at each of those points, and two in each of 
 the 7-foot spaces. But as in this case the load is partially dis- 
 tributed it wiQ be better to space them as above indicated.] 
 
 There wifl also be two stiffeners over each support. 
 
 The only remaining point to determine is the 
 
 SPACING OF RIVETS. 
 
 We wfll first determine the number of rivets in the web leg of 
 angle, between IT, and left-hand end. The bending-moment at 
 IT, is found by scaling the tine aa, which gives 110,000 Ibs. 
 This divided by the height of the girder gives 44,000 Ibs., which 
 is the horizontal flange strain at that point. As there are two 
 webs, only one-half of tins strain, or 22,000 Ibs., will come on one 
 angle. The rivets in this case win be in angle shear. From 
 table on page 371 . we find that the resistance of a f rivet to single 
 shear is 3,310 Ibs., and the bearing value on a f" plate 4.220 Ibs. 
 The resistance to shearing win therefore determine the number of 
 rivets. 22,000-5-3,310 gives 7 as tiie number of rivets required 
 in tie web leg of each angle between TT t and the left-hand end 
 of girder. This distance is 40 in., which would make the pitch 
 about 5| in. 
 
 Over the bearings, however, the pitch ought not to exceed 
 4 in.; lie wfll therefore Increase the number of rivets to 12, 
 spacing the first six 3f in. on centres, and the next seven 4 in. 
 
 We wQl next determine the number of rivets between H^and 
 
 W+ The horizontal flange strain at TF 2 = 1*M9?= 167,200 Ibs., 
 
 *.& 
 
 and one-half of this is 83,600 Ibs. Dividing 83, 600 by 3,310, we 
 have 26 as the number of rivets required between W, and the 
 left-hand end of girder. As we have already pot in 12 rivets 
 we shaH only need 26-12 or 14 rivets between IT, and W 2 to 
 resist the horizontal strain. This distance is 89 in., which 
 divided by 14 gives 6 in. for the pitch. As for practical reasons 
 
RIVETED PLATE AND BOX GIRDERa 
 
 the pitch should not exceed 6 in., we will give the rivets that pitch 
 from W l to the corresponding distance from the other end, mak- 
 ing both ends of the girder alike. 
 
 Theoretically the number of rivets between IF, and the right- 
 hand end should be the same as on the other side of W^ and 
 most of these would be required at the right of IF* but in this 
 ease the number of rivets is determined by the maximum pitch, 
 
 The number of rivets theoretically lequired-in the flange leg 
 of angle equals the safe strength of plate divided by 3310- The 
 safe strength of a f X20 inch plate f 13,000 Iba unit stress*- 
 13,000X1X20=97,500 UK. This divided by 3,310 gives 30 
 rivets for both angles. As this number is so small, we must be 
 guided by the rule of maximum pitch, and will use the same 
 number of rivets, less one, as in the web leg, staggering the rivets. 
 
 The girder wffl then be detailed as below: 
 
 DETAIL OF Oi >_ 
 
 
 
 - 
 
 : 
 
 
 : 
 
 
 G 
 
 
 c 
 
 
 r 
 
 
 : 
 
 
 i 
 
 
 c 
 
 
 G 
 
 
 z 
 
 
 : 
 
 
 o 
 
 
 - 
 
 
 : 
 
 
 1 
 
 : : : 
 
 .: 
 
 _.--.. 
 
 ; 
 
 ~ . c 
 
 
 
 
 
 
 r ..';= 
 
 -~ :rc\r~=" 
 
 Loads 34,000 Ibs. 1' 6" from left support. Span 24' 10". 
 " 42,300 " & 11" from left support Depth 30". 
 " 42,300 " & 7" from right support, 
 " 31,200 " 1' 4" from right support 
 Both flanges: 4 angles, 5'X3J"X)", 2T 6" long. 
 
 One plate, 20"Xf, 2T 6" long; 
 Two webs, f"X30", 27' 6" long. 
 22 softeners, 4"X4"X|", W *< 
 22 filler-plate?. 4"X.V% 23" long. 
 Rivets, J inch diameter. 
 
 By the roles and examples above given it is possible to com- 
 pute the necessary dimensions and details for riveted girders 
 under any conditions of loading. If further examples are dewed, 
 the wader is referred to "Compound Riveted Girders/* by 
 William H. Birkmire, in which eight different yqipk of load- 
 ing are fully worked and explained. 
 
640 
 
 RIVETED PLATE AND BOX GIRDERS. 
 
 Detail drawings, with strain diagrams of one of the heaviest 
 plate girders ever used in building construction, are given in the 
 Engineering Record of Dec. 28, 1895. This girder is one of six 
 plate girders used in the construction of the Tremont Temple, 
 Boston, Mass., Messrs. Blackall & Newton, architects. The 
 girder is 75 ft. long between centres of columns 6 ft. 1 in. high, 
 with flanges 28 in. wide, and was calculated to support distributed 
 and concentrated loads aggregating 497.5 tons. The single web- 
 plate is 64 j in. high, and | in. thick at the ends; the flanges are 
 4i in. thick at centre; flange angles, .6"X8"X1". 
 
 TABLE I. SECTIONAL AREA TO BE DEDUCTED FROM 
 
 PLATES AND ANGLES FOR RIVET-HOLES. 
 
 (BIRKMIRE.) 
 
 Taken % inch in excess of diameter of rivet. 
 
 
 Number of rivets, 1 inch 
 
 Number of rivets, Kinch 
 
 Thickness of 
 
 diameter. 
 
 diameter. 
 
 plate. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 1 
 
 2 
 
 3 
 
 4 
 
 1 
 
 1.12 
 
 2 25 
 
 3.37 
 
 4.50 
 
 1.00 
 
 2.00 
 
 3.00 
 
 4.00 
 
 15/16 
 
 1.05 
 
 2!lO 
 
 3.16 
 
 4.21 
 
 0.94 
 
 1.87 
 
 2.81 
 
 3.75 
 
 7/8 
 
 0.98 
 
 1.97 
 
 2.95 
 
 3.93 
 
 0.87 
 
 1.75 
 
 2.62 
 
 3.50 
 
 13/16 
 
 0.91 
 
 1.83 
 
 2.74 
 
 3.65 
 
 0.81 
 
 .62 
 
 2.44 
 
 3.25 
 
 3/4 
 
 0.84 
 
 1.69 
 
 2.53 
 
 3.37 
 
 0.75 
 
 .50 
 
 2.25 
 
 3.00 
 
 il/16 
 
 0.77 
 
 1.55 
 
 2.32 
 
 3.09 
 
 0.69 
 
 .37 
 
 2.06 
 
 2.75 
 
 5/8 
 
 0.70 
 
 1.41 
 
 2.11 
 
 2.81 
 
 0.62 
 
 .25 
 
 .87 
 
 2.50 
 
 9/16 
 
 0.63 
 
 1.26 
 
 1.90 
 
 2.53 
 
 0.56 
 
 .12 
 
 .69 
 
 2.25 
 
 1/2 
 
 0.56 
 
 1.11 
 
 1.69 
 
 2.25 
 
 0.50 
 
 .00 
 
 .50 
 
 2.00 
 
 7/16 
 
 0.49 
 
 0.98 
 
 1.47 
 
 1.97 
 
 0.44 
 
 O.S7 
 
 .31 
 
 1.75 
 
 3/8 
 
 0.42 
 
 0.84 
 
 1.26 
 
 1.69 
 
 0.37 
 
 0.75 
 
 .12 
 
 1.50 
 
 Thickness of 
 
 Number of rivets, % inch 
 diameter. 
 
 Number of rivets, % inch 
 diameter. 
 
 plate. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 1 
 
 2 
 
 3 
 
 4 
 
 1 
 
 0.87 
 
 .75 
 
 2.62 
 
 3.50 
 
 0.75 
 
 1.50 
 
 2.25 
 
 3.00 
 
 15/16 
 
 0.82 
 
 .64 
 
 2.46 
 
 3.28 
 
 0.70 
 
 1.40 
 
 2.11 
 
 2.81 
 
 7/8 
 
 0.77 
 
 .53 
 
 2.30 
 
 3.06 
 
 0.65 
 
 1.31 
 
 1.96 
 
 2.62 
 
 13/16 
 
 0.71 
 
 .42 
 
 2.13 
 
 2.84 
 
 0.61 
 
 1.22 
 
 1.83 
 
 2.44 
 
 3/4 
 
 0.66 
 
 .31 
 
 1.96 
 
 2.62 
 
 0.56 
 
 1.12 
 
 1.69 
 
 2.25 
 
 11/16 
 
 0.60 
 
 1.20 
 
 1.80 
 
 2.40 
 
 51 
 
 1.03 
 
 1.54 
 
 2.06 
 
 5/8 
 
 0.55 
 
 1.09 
 
 1.64 
 
 2.19 
 
 0.47 
 
 0.94 
 
 1.41 
 
 1.88 
 
 9/16 
 
 0.49 
 
 0.98 
 
 1.48 
 
 1.96 
 
 0.42 
 
 0.84 
 
 1.26 
 
 1.69 
 
 1/2 
 
 0.43 
 
 0.87 
 
 1.31 
 
 1.75 
 
 0.37 
 
 0.75 
 
 1.12 
 
 1.50 
 
 7/16 
 
 0.38 
 
 0.76 
 
 1.15 
 
 1.53 
 
 0.33 
 
 0.66 
 
 0.98 
 
 1.31 
 
 3/8 
 
 0.32 
 
 0.65 
 
 0.98 
 
 1.31 
 
 0.28 
 
 0.56 
 
 0.84 
 
 1.12 
 
 5/16 
 
 0.27 
 
 0.55 
 
 0.82 
 
 1.09 
 
 0.23 
 
 0.47 
 
 0.70 
 
 0.94 
 
 1/4 
 
 0.22 
 
 0.44 
 
 0.66 
 
 0.87 
 
 0.18 
 
 0.37 
 
 0.56 
 
 0.75 
 
RIVETED PLATE AND BOX GIRDERS. 641 
 
 TABLE II. SHEARING VALUE OF WEB-PLATES IN 
 POUNDS. 
 
 Wrought Steel. Gross Area. Unit Stress 7 ,000 Ibs. 
 
 Depth in 
 inches. 
 
 Thickness in inches. 
 
 3/8 
 
 7/16 
 
 1/2 
 
 ' 9/16 
 
 5/8 
 
 3/4 
 
 7/8 
 
 28 
 30 
 32 
 36 
 40 
 42 
 46 
 48 
 
 73,500 
 78,750 
 84,000 
 94,500 
 105,000 
 110,250 
 120,750 
 126,000 
 
 85,750 
 91,87,5 
 98,000 
 110,250 
 122,500 
 128,625 
 140,875 
 147,000 
 
 98,000 
 105,000 
 112,000 
 126,000 
 140,000 
 147,000 
 161,000 
 168,000 
 
 110,250 
 118,125 
 126,000 
 141,750 
 157,500 
 165,375 
 181,125 
 189,000 
 
 122,500 
 131,250 
 140,000 
 157,500 
 175,000 
 183,750 
 201,250 
 210,000 
 
 147 ,000 
 157 ,5uO 
 168,000 
 189,000 
 210,000 
 220,500 
 241,500 
 252,000 
 
 171,500 
 183,750 
 196,000 
 220,500 
 245.000 
 257,250 
 281,750 
 294,000 
 
 
 Deduct for one M-inch rivet. 
 
 2,240 
 
 2,660 
 
 3,010 
 
 3,430 
 
 3,850 
 
 4,620 
 
 5,390 
 
 
 Deduct for one J^-inch rivet. 
 
 2,625 
 
 3,080 
 
 3,500 
 
 3,920 
 
 4,375 
 
 5,250 
 
 6,125 
 
 EXAMPLE. What is the safe shearing value of a 36"Xf" 
 web-plate with seven }-inch rivets in stiffeners? 
 
 Answer. Gross shearing value =94,500 Ibs. 
 Deduct for 7 rivets 7X2,240 =15,680 " 
 
 Safe resistance 
 
 = 78,820 Ibs. 
 
642 RIVETED PLATE AND BOX GIRDERS. 
 
 TABLE III. SAFE BUCKLING VALUE OF WEB-PLATES 
 IN POUNDS PER SQUARE INCH. 
 
 10000 
 
 Calculated by formula p = - 
 
 1-f 
 
 3000*2 
 
 d = depth in inches, t = thickness in inches. 
 
 d . 
 51 
 
 Thickness in inches. 
 
 &'~ 
 
 3/8 
 
 7/16 
 
 1/2 
 
 9/16 
 
 5/8 
 
 3/4 
 
 7/8 
 
 28 
 
 3,498 
 
 4,228 
 
 4,890 
 
 5,476 
 
 5,932 
 
 
 
 30 
 
 3,192 
 
 3,896 
 
 4,546 
 
 5,133 
 
 5,656 
 
 6,522 
 
 
 32 
 
 2,889 
 
 3,624 
 
 4,228 
 
 4,787 
 
 5,339 
 
 6,226 
 
 6,920 
 
 36 
 
 2,456 
 
 3,069 
 
 3,666 
 
 4,229 
 
 4,748 
 
 5,656 
 
 6,392 
 
 40 
 
 2,087 
 
 2,696 
 
 3,191 
 
 3,724 
 
 4,228 
 
 5,133 
 
 5,882 
 
 42 
 
 1,930 
 
 2,455 
 
 2,983 
 
 3,498 
 
 3,992 
 
 4,889 
 
 5,6-49 
 
 48 
 
 1,548 
 
 1,994 
 
 2,543 
 
 2,918 
 
 3,371 
 
 4,228 
 
 4,992 
 
 TOTAL RESISTANCE FOR PLATES WITH TWO f " RIVETS* 
 
 d . 
 
 fl'J 
 
 ft2 
 
 *1 
 
 28 
 30 
 36 
 42 
 48 
 
 Thickness in inches. 
 
 3/8 
 
 7/16 
 
 1/2 
 
 9/16 
 
 5/8 
 
 3/4 
 
 7/8 
 
 34,450 
 33,830 
 31,560 
 29,140 
 26,860 
 
 48,580 
 48,150 
 46,000 
 43,230 
 40,360 
 
 64,200 
 64,230 
 62,800 
 60,040 
 
 58,820 
 
 80,880 
 81,560 
 81,500 
 79,190 
 75,920 
 
 97,340 
 99,880 
 101,750 
 100,440 
 97,450 
 
 138,200 
 145,300 
 147,600 
 146,670 
 
 191,570 
 198,960 
 202,000 
 
 TOTAL RESISTANCE FOR PLATES WITH TWO f" RIVETS. 
 
 Depth in 
 inches. 
 
 Thickness in inches. 
 
 3/8 
 
 7/16 
 
 1/2 
 
 9/16 - 
 
 5/8 
 
 3/4 
 
 7/8 
 
 28 
 30 
 b6 
 2 
 
 ^8 
 
 34,100 
 33,510 
 31,310 
 ?8,950 
 26,700 
 
 48,110 
 47,720 
 45,660 
 42,960 
 40,140 
 
 63,570 
 63,640 
 62,320 
 59,660 
 58,490 
 
 80,100 
 80,840 
 80,900 
 78,700 
 75,520 
 
 96,390 
 98,980 
 100,690 
 99,800 
 96.910 
 
 136,960 
 144,230 
 146,690 
 145,860 
 
 190,170 
 197.710 
 200,930 
 
RIVETED PLATE AND BOX GIRDERS. 643 
 
 Tables of Riveted Steel Plate and Box Girders. 
 
 The tables on pages 644-647, giving the greatest safe dis- 
 tributed load that should be imposed on the girders were com- 
 puted by the author in accordance with formula (la), using 
 13,000 Ibs. fibre strain and deducting for two |-inch holes (for 
 J-inch rivets) in flange-plates and angles. 
 
 From the safe load given by the formula the weight of the girder 
 between supports has been subtracted. 
 
 The sizes given are those most commonly found in buildings. 
 
 The weight per foot should be considered as a close approxi- 
 mation only; it is intended to include rivets and stiffeners, 
 where required. 
 
 These tables should be used only for determining the size of 
 girder and thickness of the plates and angles. Rivet spacing 
 should be determined in each case by the rules previously given, 
 and also the number and position of stiffeners. For distributed 
 loads below the heavy cross-lines stiffeners will not be required. 
 It should, however, be remembered that stiffeners are always 
 required at the ends of the girders, as shown in Figs. 15 and 18. 
 
 These tables may also be used to serve as a. check on special 
 calculations for other girders. // more than two rivet-holes occur 
 in any given cross-section of the bottom flange, then the safe 
 load must be decreased accordingly. 
 
 The loads given in the second column of the tables are for the 
 least thickness of flange -plates that should be used. This thick- 
 ness may be increased as required to give the desired strength to 
 the girder, thus: If we wish to carry a distributed load of 47 
 tons, with a span of 35 feet, with a girder of the dimensions given 
 for girder A, we must increase the thickness of the flange-plates 
 sufficient to take difference between 47 and 38.12 tons or 8.88 
 tons. This will require an increase of T % or \ inch in both top 
 and bottom flange. 
 
 It is not desirable to use girders of these dimensions for greater 
 spans than those given in the table 
 
 The tables on pages 648-650 are from the manual of the 
 Passaic Rolling Mill Co., prepared by Geo. H. Blakeley, C.E. 
 It should be noted that they are based on a fibre stress of 15,000 
 Ibs. per sq. inch, and that they include weight of girders. 
 
644 RIVETED PLATE AND BOX GIRDERS. 
 
 STEEL PLATE GIRDERS. 
 SAFE LOADS IN TONS UNIFORMLY DISTRIBUTED. 
 
 See explanation, page 643. 
 
 4 
 
 <~\ 
 
 -TZTf 
 
 n 
 
 rrv- 
 
 ? . g g j 
 
 1 
 
 ,-= 
 
 ar-^- 
 $ T ~ 
 
 r iiil 
 
 
 
 
 ^ Ik' o" 
 A *Jx<2 
 
 
 
 
 B ^II'J 
 
 
 
 
 X^co+j 
 
 
 
 
 xl^S 
 
 d 
 
 -^ 
 =^= 
 
 *=^= 
 
 I hf 
 
 d 
 
 I 
 
 r> ,i 
 -<cr- 
 
 c. ^ 
 
 C7- 
 
 L g| 
 
 Span in 
 feet. 
 
 Safe 
 applied 
 load, in 
 
 Increase in 
 safe load for 
 l/io," increase 
 in thickness 
 
 Span in 
 feet. 
 
 Safe 
 applied 
 load, in 
 
 Increase in 
 safe load for 
 Me" increase 
 in thickness 
 
 
 
 tons. 
 
 of flange- 
 
 
 
 tons. 
 
 of flange- 
 
 
 
 
 
 plates. 
 
 
 
 
 
 plates. 
 
 20 
 
 
 6S 
 
 .80 
 
 4.16 
 
 20 
 
 
 76.81 
 
 4.57 
 
 21 
 
 
 66.33 
 
 3.96 
 
 21 
 
 
 73.00 
 
 4.36 
 
 22 
 
 
 63.17 
 
 3.78 
 
 22 
 
 
 69.52 
 
 4.16 
 
 23 
 
 24 
 
 
 60.27 
 
 57.82 
 
 3.61 
 3.46 
 
 23 
 24 
 
 
 66.34 
 63.42 
 
 3.98 
 
 3.81 
 
 25 
 
 
 55.16 
 
 3.33 
 
 25 
 
 
 60.72 
 
 3.66 
 
 26 
 
 
 51 
 
 >.90 
 
 3.20 
 
 26 
 
 
 58 
 
 .22 
 
 3.52 
 
 27 
 
 
 50.79 
 
 3.08 
 
 27 
 
 
 55.91 
 
 3.39 
 
 28 
 
 
 4* 
 
 S.83 
 
 2.97 
 
 28 
 
 
 53 
 
 .75 
 
 3.27 
 
 29 
 
 
 47.00 
 
 2.87 
 
 29 
 
 
 51 
 
 .74 
 
 3.15 
 
 30 
 
 
 45.28 
 
 2.77 
 
 30 
 
 
 49.86 
 
 3.05 
 
 31 
 
 
 4; 
 
 5.68 
 
 2.68 
 
 31 
 
 
 4 
 
 .09 
 
 2.95 
 
 32 
 
 
 42.17 
 
 2.60 
 
 32 
 
 
 . 46.43 
 
 2.86 
 
 33 
 
 
 4( 
 
 ).74 
 
 2.52 
 
 33 
 
 
 44 
 
 .86 
 
 2.77 
 
 34 
 
 
 39.40 
 
 2.44 
 
 34 
 
 
 43.38 
 
 2.69 
 
 35 
 
 
 3? 
 
 S.12 
 
 2.38 
 
 35 
 
 
 41 
 
 .98 
 
 2.61 
 
 36 
 
 
 36.92 
 
 2.31 
 
 36 
 
 
 40.66 
 
 2.54 
 
 37 
 
 
 35.77 
 
 2.25 
 
 37 
 
 
 39.12 
 
 2.46 
 
 38 
 
 
 3^ 
 
 L69 
 
 2.19 
 
 38 
 
 
 35 
 
 .20 
 
 2.41 
 
 39 
 
 
 3; 
 
 5.66 
 
 2.13 
 
 39 
 
 
 37 
 
 .06 
 
 2.35 
 
 40 
 
 
 32.66 
 
 2.08 
 
 40 
 
 
 35.97 
 
 2 29 
 
 Max. load for } 
 
 /" web, 86.94 tons. 
 
 Max. load for 
 
 K" web ,94.43 tons. 
 
 Loads above heavy cross -line require stiffeners. 
 
RIVETED PLATE AND BOX GIRDERS. 645 
 
 STEEL PLATE GIRDERS. 
 SAFE LOADS IN TONS UNIFORMLY DISTRIBUTED. 
 
 See explanation, page 643. 
 
 "E 
 
 =0= 
 
 XT- 
 
 *=^= 
 uLF^~ 
 
 r *i*i 
 
 r 
 
 _n.. 
 
 -i=rr< 
 I 
 
 <">_ 
 
 [K7- 
 1 
 
 w 
 
 
 
 1 
 
 ff 
 
 
 
 
 Illl 
 
 
 III 
 
 III! 
 
 
 
 
 D y*t 
 
 
 
 ^X^CO^N ft 
 
 
 
 
 ^K\c\^^7 
 
 d 
 
 JiL 
 
 " U U " 
 
 * fife| 
 
 pi 
 
 _J 
 =5f= 
 
 ILx 
 
 i =^= 
 
 - il 
 
 Span in 
 feet. 
 
 Safe 
 applied 
 load, in 
 
 Increase in 
 safe load for 
 yw" increase 
 in thickness 
 
 Span in 
 feet. 
 
 Safe 
 applied 
 load, in 
 
 Increase in 
 safe load for 
 yie" increase 
 in thickness 
 
 
 
 tons. 
 
 of flange- 
 
 
 
 tons. 
 
 of flange- 
 
 
 
 
 
 plates. 
 
 
 
 
 
 plates. 
 
 20 
 
 
 83 
 
 88 
 
 4.99 
 
 24 
 
 
 81. 
 
 02 
 
 4.85 
 
 24 
 
 
 69 
 
 28 
 
 4.16 
 
 26 
 
 
 74. 
 
 45 
 
 4.48 
 
 26 
 
 
 63 
 
 63 
 
 3.84 
 
 28 
 
 
 68. 
 
 78 
 
 4.16 
 
 28 
 30 
 31 
 
 
 58 
 54 
 52 
 
 76 
 52 
 60 
 
 3.56 
 3.33 
 3.22 
 
 30 
 31 
 32 
 
 
 63. 
 61. 
 59. 
 
 85 
 61 
 51 
 
 3.88 
 3.75 
 
 3.64 
 
 32 
 
 
 50 
 
 78 
 
 3.12 
 
 33 
 
 
 ^57" 
 
 53 
 
 3.53 
 
 33 
 
 
 49 
 
 08 
 
 3.02 
 
 34 
 
 
 55. 
 
 66 
 
 3.42 
 
 34 
 
 
 47 
 
 48 
 
 2.93 
 
 35 
 
 
 53. 
 
 89 
 
 3.32 
 
 35 
 
 
 45 
 
 95 
 
 2.85 
 
 36 
 
 
 52. 
 
 21 
 
 3.23 
 
 36 
 
 
 44 
 
 51 
 
 2.77 
 
 37 
 
 
 50. 
 
 63 
 
 3.15 
 
 37 
 
 
 43 
 
 14 
 
 2.70 
 
 38 
 
 
 49. 
 
 11 
 
 3.06 
 
 38 
 
 
 41 
 
 84 
 
 2.63 
 
 39 
 
 
 47. 
 
 68 
 
 2.98 
 
 39 
 
 
 40 
 
 59 
 
 2.56 
 
 40 
 
 
 46. 
 
 31 
 
 2.91 
 
 40 
 
 
 39 
 
 42 
 
 2.49 
 
 41 
 
 
 45. 
 
 00 
 
 2.84 
 
 41 
 
 
 38 
 
 29 
 
 2.43 
 
 42 
 
 
 43. 
 
 75 
 
 2.77 
 
 42 
 
 
 37 
 
 21 
 
 2 37 
 
 44 
 
 
 41. 
 
 41 
 
 2.64 
 
 44 
 
 
 35 
 
 19 
 
 2 27 
 
 46 
 
 
 39. 
 
 26 
 
 2.53 
 
 46 
 
 
 33 
 
 34 
 
 2 17 
 
 48 
 
 
 37. 
 
 27 
 
 2.42 
 
 48 
 
 
 31 
 
 83 
 
 2 '.08 
 
 50 
 
 
 35. 
 
 43 
 
 2.33 
 
 50 
 
 
 30 
 
 02 
 
 1.99 
 
 55 
 
 
 31. 
 
 35 
 
 2.11 
 
 Max. load for 
 
 Y 2 " web, 104 tons. 
 
 Max. 
 
 load for 
 
 Y^' web, 122 tons. 
 
 Max. load for 
 
 %6" web, 117 tons. 
 
 Max. 
 
 load for 
 
 Y%' web, 152 tons 
 
 Loads above heavy cross-line require stiffeners. 
 
646 
 
 RIVETED PLATE AND BOX GIRDERS. 
 
 STEEL BOX GIRDERS. 
 SAFE LOADS IN TONS UNIFORMLY DISTRIBUTED. 
 
 See explanation, page 643. 
 
 1 
 
 TJT 
 
 ( 
 
 _^rv- 
 
 1 ||1 
 
 - \ 
 
 -. jT> 
 
 .5 
 
 > c 
 
 r 
 
 ||l| 
 
 
 
 
 
 i1 
 
 13 G \2 
 
 
 
 
 
 F ijxj 
 
 
 
 ( 
 
 
 
 |x|| 
 
 
 < 
 
 c 
 
 L 
 
 pFf 
 
 1 
 
 
 o 
 
 1 "^ 
 
 i 
 
 ~^J " 
 
 *y- 
 
 |H (^ 
 
 Span in 
 feet. 
 
 
 
 
 Increase in 
 
 Span in 
 feet. 
 
 
 
 
 Increase in 
 
 Safe 
 
 safe load for 
 
 Safe 
 
 safe load for 
 
 applied 
 load, in 
 
 1$" increase 
 in thickness 
 
 applied 
 load, in 
 
 I/IQ" increase 
 in thickness 
 
 tons. 
 
 of flange- 
 
 tons. 
 
 
 of flange- 
 
 
 
 
 plates. 
 
 
 
 
 plates. 
 
 20 
 
 69.60 
 
 5.78 
 
 20 
 
 83.56 
 
 6.94 
 
 21 
 
 66.13 
 
 5.51 
 
 24 
 
 68.90 
 
 5.78 
 
 22 
 
 62.95 
 
 5.2^ 
 
 2 
 
 3 
 
 63.21 
 
 5 . 34 
 
 23 
 
 60.04 
 
 5.03 
 
 28 
 
 58.31 
 
 4.96 
 
 24 
 
 i 
 
 5' 
 
 r.s* 
 
 I 
 
 4.82 
 
 3( 
 
 ) 
 
 5 
 
 1.04 
 
 
 4.62 
 
 25 
 
 54.91 
 
 4.63 
 
 31 
 
 52.10 
 
 4.48 
 
 26 
 
 > 
 
 5 
 
 2.6- 
 
 i 
 
 4.45 
 
 31 
 
 2 
 
 5( 
 
 ).27 
 
 
 4.34 
 
 27 
 
 50.52 
 
 4.28 
 
 33 
 
 48.55 
 
 4.20 
 
 28 
 
 48 . 55 
 
 4.13 
 
 34 
 
 46.93 
 
 4.08 
 
 2 
 
 > 
 
 4 
 
 3.7( 
 
 ) 
 
 3.99 
 
 3, 
 
 5 
 
 4 
 
 5.39 
 
 
 3.96 
 
 30 
 
 44.98 
 
 3.85 
 
 36 
 
 43.93 
 
 
 3.85 
 
 31 
 
 
 4 
 
 3.3( 
 
 > 
 
 3.73 
 
 3" 
 
 r 
 
 4 
 
 2.55 
 
 
 3.75 
 
 32 
 
 41.84 
 
 3.61 
 
 38 
 
 41.23 
 
 3.65 
 
 3C 
 
 5 
 
 4 
 
 3.4( 
 
 ) 
 
 3.50 
 
 3< 
 
 ) 
 
 3 
 
 5.97 
 
 
 3.56 
 
 34 
 
 39.05 
 
 3.40 
 
 40 
 
 38.78 
 
 3.47 
 
 35 
 
 37.76 
 
 3.30 
 
 41 
 
 37.63 
 
 3.38 
 
 3f 
 
 i 
 
 3 
 
 5.5. 
 
 
 3.21 
 
 4 
 
 2 
 
 3 
 
 5.54 
 
 
 3.30 
 
 37 
 
 35.38 
 
 3.12 
 
 44 
 
 34.49 
 
 3.15 
 
 3? 
 
 J 
 
 3 
 
 1.3( 
 
 ) 
 
 3.04 
 
 4 
 
 B 
 
 3 
 
 2.60 
 
 
 3 02 
 
 39 
 
 33.25 
 
 2.96 
 
 48 
 
 31.06 
 
 2.89 
 
 40 
 
 32.25 
 
 2.89 
 
 . 50 
 
 29.22 
 
 2.77 
 
 Max. load for %' 
 
 ' webs, 130 tons. 
 
 Max. load for ?/g' 
 
 ' webs, 157 tons. 
 
 Loads above heavy cross-line require stiffeners. 
 
RIVETED PLATE AND BOX GIRDERS. 647 
 
 STEEL BOX GIRDERS. 
 SAFE LOADS IN TONS UNIFORMLY DISTRIBUTED. 
 
 See explanation, page 643. 
 
 
 r* ^_ 
 
 "$"0 c^ 
 
 r-4 P< rrt CK1 
 
 c 
 
 ^ -~\ 
 
 TT 
 
 ! jfif 
 
 
 IT 
 
 , IK| 
 
 
 
 " 111 
 
 
 'l r * J 
 
 r O \N Q> 
 
 
 it 
 
 coc^'S 
 
 w 
 
 
 -or- cr- 
 
 <N 
 
 
 
 
 
 Increase in 
 
 Span in 
 feet. 
 
 
 
 Increase in 
 
 
 
 Safe 
 
 safe load for 
 
 Safe 
 
 
 safe load for 
 
 Span in 
 feet. 
 
 applied 
 load, in 
 
 MV' increase 
 in thickness 
 
 applied 
 load, in 
 
 ^4e" increase 
 in thickness 
 
 
 
 tons. 
 
 of flange- 
 
 tons 
 
 
 of flange- 
 
 
 
 
 
 plates. 
 
 
 
 plates. 
 
 
 20 
 
 93. 
 
 75 
 
 7.41 
 
 20 
 
 120.49 
 
 8.89 
 
 
 21 
 
 89. 
 
 08 
 
 7.06 
 
 24 
 
 99.54 
 
 7.41 
 
 
 22 
 
 84. 
 
 83 
 
 6.73 
 
 2 
 
 6 
 
 91.4 
 
 3 
 
 6.84 
 
 
 23 
 
 80.93 
 
 6.44 
 
 28 
 
 84.45 
 
 6.35 
 
 
 24 
 
 77. 
 
 35 
 
 6.17 
 
 3 
 
 
 
 78.3 
 
 3 
 
 5.92 
 
 
 25 
 
 74. 
 
 05 
 
 5.95 
 
 31 
 
 75.60 
 
 5.73 
 
 
 26 
 
 70.99 
 
 5.70 
 
 32 
 
 73.00 
 
 5.55 
 
 
 27 
 
 68. 
 
 1.6 
 
 5.49 
 
 3 
 
 3 
 
 70. 5i 
 
 
 5.39 
 
 
 28 
 
 65 . 
 
 
 5.29 
 
 34 
 
 68.25 
 
 5.23 
 
 
 29 
 
 30 
 31 
 32 
 
 63 . 05 
 60.73 
 58 . 56 
 56.53 
 
 5.11 
 4.94 
 4.78 
 4.63 
 
 35 
 36 
 
 37 
 38 
 
 66.07 
 64.00 
 62.03 
 
 60.18 
 
 5.08 
 4.94 
 4.80 
 4.68 
 
 
 83 
 
 54.60 
 
 4.49 
 
 39 
 
 58.40 
 
 4.56 
 
 
 34 
 
 52.80 
 
 4.36 
 
 40 
 
 56.70 
 
 4.44 
 
 
 35 
 
 51. 
 
 07 
 
 4.23 
 
 4 
 
 1 
 
 55.0* 
 
 3 
 
 4.34 
 
 
 36 
 
 49. 
 
 44 
 
 4.11 
 
 4 
 
 2 
 
 53.5' 
 
 I 
 
 4.23 
 
 37 
 
 47.90 
 
 4.00 
 
 44 
 
 50.6^ 
 
 3 
 
 4.04 
 
 
 38 
 
 46. 
 
 43 
 
 3.90 
 
 46 
 
 47.98 
 
 3.86 
 
 
 39 
 
 45. 
 
 03 
 
 3.80 
 
 4 
 
 8 
 
 45.5! 
 
 > 
 
 3.70 
 
 40 
 
 43.69 
 
 3.70 
 
 50 
 
 -43.24 
 
 3.55 
 
 Max. load for %" webs, 130 tons. 
 
 Max. load for Yd 
 
 ' webs, 157 tons. 
 
 Loads above heavy cross-line require stiffeners. 
 
648 RIVETED PLATE AND BOX GIRDERS. 
 STEEL PLATE GIRDERS. 
 
 PASSAIC ROLLING MILL CO. 
 
 SAFE LOADS IN TONS OF 2,000 LBS. UNIFORMLY DISTRIBUTED. 
 
 No stiffeners required 
 
 except at ends, over 
 
 supports only. 
 
 Girders equivalent to 
 4 a 24" I beam. 
 
 Web 
 
 24" XH" 
 
 26" XH" 
 
 28" XW 
 
 30" X W 
 
 Angles 
 
 5 X3/ 2 X, 2 
 
 3 A X 
 
 5 X3A XA 
 
 5 X3 \/ 8 
 
 
 (B 
 
 V3.T 
 
 00 
 
 * -^ 
 
 tfl 
 
 
 V s * 5 
 
 
 V^ 
 
 
 3 
 
 SMS 
 
 O 
 
 *i-a 
 
 1 
 
 *sl 
 
 d 
 
 o 
 
 z^S'S 
 
 Span, centres 
 
 - 
 
 ,2 c c 
 
 ""O 
 
 
 
 *2 & S 
 
 
 S c nj 
 
 of bearings, 
 
 1 
 
 O ,,_ 
 
 Is 
 
 P C, 4 *" 1 
 
 
 C OJt4-l 
 
 i 
 
 V Qje*- 
 
 feet. 
 
 
 * m 
 
 * 
 
 s * 
 
 
 
 lie 
 
 ^0 
 
 * c C 
 
 
 1 
 
 I.P 
 
 1 
 
 IP 
 
 I 
 
 11^ 
 
 0) 
 
 1 
 
 ^ p 
 
 20 
 
 47.2 
 
 5.3 
 
 46.5 
 
 5.8 
 
 45.1 
 
 6.2 
 
 47.7 
 
 6.4 
 
 21 
 
 44.9 
 
 5.0 
 
 44.3 
 
 5.5 
 
 42.9 
 
 5.9 
 
 45.5 
 
 6.1 
 
 22 
 
 42.9 
 
 4.8 
 
 42.3 
 
 5.2 
 
 41.0 
 
 5.7 
 
 43.4 
 
 5.8 
 
 23 
 
 41.0 
 
 4.6 
 
 40.4 
 
 5.0 
 
 39.2 
 
 5.4 
 
 41.5 
 
 5.5 
 
 24 
 
 39.3 
 
 4.4 
 
 38.8 
 
 4.8 
 
 37.6 
 
 5.2 
 
 39.8 
 
 5.3 
 
 25 
 
 37.7 
 
 4.2 
 
 37.2 
 
 4.6 
 
 36.1 
 
 5.0 
 
 38.2 
 
 5.1 
 
 26 
 
 36.3 
 
 4.1 
 
 35.8 
 
 4.4 
 
 34.7 
 
 4.8 
 
 36.7 
 
 4.9 
 
 27 
 
 34.9 
 
 3.9 
 
 34.4 
 
 4.3 
 
 33.4 
 
 4.6 
 
 35.4 
 
 4.7 
 
 28 
 
 ?.3.7 
 
 3.8 
 
 33.2 
 
 4.1 
 
 32 2 
 
 4.5 
 
 34.1 
 
 4.5 
 
 29 
 
 32 . 5 
 
 3.6 
 
 32.1 
 
 4.0 
 
 31 . 1 
 
 4.3 
 
 32.9 
 
 4.4 
 
 30 
 
 31,4 
 
 3.5 
 
 31.0 
 
 3.8 
 
 30.0 
 
 4.2 
 
 31.8 
 
 4.2 
 
 31 
 
 30.4 
 
 3.4 
 
 30.0 
 
 3.7 
 
 29.1 
 
 4.0 
 
 30.8 
 
 4.1 
 
 32 
 
 29.4 
 
 3.3 
 
 29.1 
 
 3.6 
 
 28.2 
 
 3.9 
 
 29.8 
 
 4.0 
 
 33 
 
 28.6 
 
 3.2 
 
 28.2 
 
 3.5 
 
 27.3 
 
 3.8 
 
 28.9 
 
 3.9 
 
 34 
 
 27.7 
 
 3.1 
 
 27.4 
 
 3.4 
 
 26.5 
 
 3.7 
 
 28.1 
 
 3.7 
 
 35 
 
 26.9 
 
 3.0 
 
 26.6 
 
 3.3 
 
 25.8 
 
 3.6 
 
 27.3 
 
 3.6 
 
 36 
 
 26.2 
 
 2.9 
 
 25.8 
 
 3.2 
 
 25.0 
 
 3.5 
 
 26.5 
 
 3.5 
 
 37 
 
 25.5 
 
 2.8 
 
 25.1 
 
 3.1 
 
 24.4 
 
 34 
 
 25.8 
 
 3.4 
 
 38 
 
 24.8 
 
 2.8 
 
 24.5 
 
 3.0 
 
 23.7 
 
 3.3 
 
 25.1 
 
 3.3 
 
 39 
 
 24 2 
 
 2.7 
 
 23.8 
 
 2.9 
 
 23.1 
 
 3.2 
 
 24.5 
 
 3.3 
 
 40 
 
 23.6 
 
 2.6 
 
 23.3 
 
 2.9 
 
 22.5 
 
 3.1 
 
 23.9 
 
 3.2 
 
 Weight per 
 foot, Ibs. 
 
 88 
 
 7.2 
 
 84 
 
 7.2 
 
 79 
 
 7.2 
 
 79 
 
 6.8 
 
 Safe loads given include weight of girder. 
 
 Weights of girders given include weight of rivet heads, but not stif- 
 feners. 
 
 Maximum fibre strain, 15,000 Ibs. per square inch of net area, holes for 
 %" rivets being deducted. 
 
RIVETED PLATE AND BOX GIRDERS. 649 
 
 STEEL PLATE GIRDERS. 
 
 PASSAIC ROLLING MILL CO. 
 
 SAFE LOADS IN TONS OF 2,000 LBS. UNIFORMLY DISTRIBUTED. 
 
 No stiffeners required 
 
 except at ends, over 
 
 supports only. 
 
 Girders equivalent to 
 two 24" I beams. 
 
 Web 
 
 24" X 
 
 9 /ie" 
 
 26" 
 
 K%G" 
 
 28" 
 
 <y" 
 
 30" 
 
 xW 
 
 Angles . 
 
 5" X 5' 
 
 ' x y>" 
 
 5" X 5' 
 
 
 5"X5 
 
 
 5"X5 
 
 " x W 
 
 Plates 
 
 12" 
 
 
 12" 
 
 X 1 ^" 
 
 
 XM" 
 
 
 
 
 c 
 
 V|j B . 
 
 H 
 
 Vg.5 
 
 c 
 
 ksU 
 
 02 
 
 c 
 
 y ^ 
 
 
 3 
 
 'C'S ^ 
 
 O 
 
 ?T'S *" 
 
 c 
 
 ^'"2 ^ 
 
 5 
 
 f-< +* cS 
 
 Span, centres 
 
 T3 
 
 2 fl~?y 
 
 I-T 
 
 S S'X 
 
 "6 
 
 * S'E 
 
 
 S.S.fi 
 
 of bearings, 
 feet. 
 
 ig 
 
 il" 
 
 1 
 
 II" 
 
 1 
 
 ||o 
 
 KS 
 
 ^O 
 
 11^ 
 
 
 2 
 
 O o <1> 
 
 .a 
 
 o o o3 
 
 <D 
 
 O o 
 
 
 
 O o 3J 
 
 
 A 
 
 gjH 
 
 02 
 
 hlS s 
 
 1 
 
 ^.s e 
 
 A 
 
 11? 
 
 20 
 
 90.8 
 
 3.6 
 
 93.6 
 
 3.9 
 
 93.6 
 
 4.3 
 
 91.7 
 
 4.6 
 
 21 
 
 86.5 
 
 3.4 
 
 89.1 
 
 3.7 
 
 89.1 
 
 4.1 
 
 87.3 
 
 4.3 
 
 22 
 
 82.5 
 
 3.3 
 
 85.1 
 
 3.6 
 
 85.0 
 
 3.9 
 
 83.4 
 
 4.1 
 
 23 
 
 78.9 
 
 3.1 
 
 81.3 
 
 3.4 
 
 81.3 
 
 3.7 
 
 79.7 
 
 3.9 
 
 24 
 
 75.6 
 
 3.0 
 
 78.0 
 
 3.3 
 
 78.0 
 
 3.6 
 
 76.4 
 
 3.8 
 
 25 
 
 72.6 
 
 2.9 
 
 74.8 
 
 3.1 
 
 74.8 
 
 3.4 
 
 73.3 
 
 3.6 
 
 26 
 
 69.8 
 
 2.8 
 
 72.0 
 
 3.0 
 
 72.0 
 
 3.3 
 
 70.5 
 
 3.5 
 
 27 
 
 67.2 
 
 2.7 
 
 69.3 
 
 2.9 
 
 69.3 
 
 3.2 
 
 67.9 
 
 3.4 
 
 28 
 
 64.8 
 
 2.6 
 
 66.8 
 
 2.8 
 
 66.8 
 
 3.1 
 
 65.5 
 
 3.3 
 
 29 
 
 62.6 
 
 2.5 
 
 64.5 
 
 2.7 
 
 64.5 
 
 3.0 
 
 63.2 
 
 3.1 
 
 30 
 
 60.5 
 
 2.4 
 
 62.4 
 
 2.6 
 
 62.4 
 
 2.9 
 
 61.1 
 
 3.0 
 
 31 
 
 58.6 
 
 2.3 
 
 60.4 
 
 2.5 
 
 60.4 
 
 2.8 
 
 59.2 
 
 2.9 
 
 32 
 
 56.7 
 
 2.2 
 
 58.5 
 
 2.5 
 
 58 . 5 
 
 2.7 
 
 57.3 
 
 2.8 
 
 33 
 
 55.0 
 
 2.2 
 
 56.7 
 
 2.4 
 
 56.7 
 
 2.6 
 
 55.6 
 
 2.8 
 
 34 
 
 53.4 
 
 2.1 
 
 55.0 
 
 2.3 
 
 55.0 
 
 2.5 
 
 53.9 
 
 2.7 
 
 35 
 
 51.9 
 
 2.0 
 
 53.5 
 
 2.3 
 
 53.5 
 
 2.4 
 
 52.4 
 
 2.6 
 
 36 
 
 50.4 
 
 2.0 
 
 52.0 
 
 2.2 
 
 52.0 
 
 2.4 
 
 50.9 
 
 2.5 
 
 37 
 
 49.1 
 
 1.9 
 
 50.6 
 
 2.1 
 
 50.6 
 
 2.3 
 
 49.6 
 
 2.5 
 
 38 
 
 47.8 
 
 1.9 
 
 49.2 
 
 ^ . 1 
 
 49.2 
 
 2.3 
 
 48.3 
 
 2.4 
 
 39 
 
 46.6 
 
 1.8 
 
 48.0 
 
 2.0 
 
 48.0 
 
 2.2 
 
 47.0 
 
 2.3 
 
 40 
 
 45.4 
 
 1.8 
 
 46.8 
 
 2.0 
 
 46.8 
 
 2.1 
 
 45.8 
 
 2.3 
 
 Weight per 
 foot, Ibs. 
 
 158 
 
 5.1 
 
 153 
 
 5.1 
 
 143 
 
 5.1 
 
 136 
 
 5.1 
 
 Safe loads given include weight of girder. 
 
 Weights of girders given include weight of rivet heads, but not stif- 
 feners. 
 
 Maximum fibre strain, 15,000 Ibs. per square inch of net area, holes for 
 %" rivets being deducted. 
 
650 RIVETED PLATE AND BOX GIRDERS. 
 
 STEEL BOX GIRDERS. 
 
 PAS8AIC ROLLING MILL, CO. 
 
 SA.FE LOADS IN TONS OF 2,000 LBS. UNIFORMLY DISTRIBUTED. 
 
 No stiffeners required 
 
 except at ends, over 
 
 supports only. 
 
 Girders equivalent to 
 two 24" I beams. 
 
 Webs 
 
 24": 
 
 < z /s" 
 
 26" 
 
 X 3 /" 
 
 28" 
 
 *&(', 
 
 30" 
 
 yy 
 
 A.ngles. . . 
 
 5"X3' 
 
 ' X H" 
 
 5" X 3' 
 
 / V74 f. 1 ' 
 
 5" X 3' 
 
 
 5" X 3' 
 
 ' X ^/k ff 
 
 Plates 
 
 14" > 
 
 
 14" 
 
 j/'l/// 
 
 14": 
 
 K 7 4 " 
 
 14" 
 
 xy&" 
 
 
 
 
 
 
 
 
 
 
 
 <K 
 
 ^ K 
 
 m 
 
 \& 
 
 
 5^ 
 
 
 v* 
 
 
 
 
 a 
 
 
 d 
 
 
 
 
 
 O 
 
 fc ^ j 
 
 o 
 +i 
 
 S-i'S tj 
 
 p 
 
 C^^ 
 
 _o 
 
 s-<~ "03 
 
 Span, centres 
 
 - 
 
 *2.S*Oi 
 
 
 S "0. 
 
 
 
 
 
 2 S'S 
 
 of bearings, 
 
 1i 
 
 <U C>+-< 
 
 s 
 
 a. ajMH 
 
 <1 
 
 (D'atM 
 
 9 
 
 QJ 0)*- 
 
 feet. 
 
 o 
 
 o3 ^ 
 
 o 
 
 o3 o3 ^ 
 
 o 
 
 r* ^ 
 
 o 
 
 c3 cS ^ 
 
 
 2 
 
 S * 
 
 2 
 
 S ^ 
 
 o 
 
 egi 
 
 & 
 
 * 
 
 
 m 
 
 II s 
 
 03 
 DQ 
 
 ^.S c 
 
 *OJ 
 
 02 
 
 || S 
 
 o3 
 02 
 
 I| s 
 
 20 
 
 93.8 
 
 4.3 
 
 93.5 
 
 4.7 
 
 92 9 
 
 5.1 
 
 95.6 
 
 5.4 
 
 21 
 
 89.3 
 
 4.1 
 
 89.0 
 
 4.5 
 
 88.5 
 
 4.8 
 
 91.1 
 
 5.2 
 
 22 
 
 85.3 
 
 3.9 
 
 85.0 
 
 4.3 
 
 84.5 
 
 4.6 
 
 86.9 
 
 4.9 
 
 23 
 
 81.6 
 
 3.8 
 
 81.3 
 
 4.1 
 
 80.8 
 
 4.4 
 
 83.2 
 
 4.7 
 
 24 
 
 78.2 
 
 3.6 
 
 77.9 
 
 3.9 
 
 77.4 
 
 4 2 
 
 79.7 
 
 4.5 
 
 25 
 
 75.0 
 
 3.5 
 
 74.8 
 
 3.8 
 
 74.3 
 
 4.1 
 
 76.5 
 
 4.3 
 
 26 
 
 72.2 
 
 -3.3 
 
 71.9 
 
 3.6 
 
 71.5 
 
 3.9 
 
 73.6 
 
 4.2 
 
 27 
 
 69.5 
 
 3.2 
 
 69.2 
 
 3.5 
 
 68.8 
 
 3.8 
 
 70.8 
 
 4.0 
 
 28 
 
 67.1 
 
 3.1 
 
 66.8 
 
 3.4 
 
 66.3 
 
 3.6 
 
 68 . 3 
 
 3.9 
 
 29 
 
 64.7 
 
 3.0 
 
 64.4 
 
 3.2 
 
 64.0 
 
 3.5 
 
 66.0 
 
 3.7 
 
 30 
 
 62.5 
 
 2.9 
 
 62.3 
 
 3.1 
 
 61.9 
 
 3.4 
 
 63.8 
 
 3.6 
 
 31 
 
 60.5 
 
 2.8 
 
 60.3 
 
 3.0 
 
 60.0 
 
 3.3 
 
 61.7 
 
 3.5 
 
 32 
 
 58.6 
 
 2.7 
 
 58.4 
 
 2.9 
 
 58.1 
 
 3.2 
 
 59.8 
 
 3.4 
 
 33 
 
 56.9 
 
 2.6 
 
 56.6 
 
 2.8 
 
 56.3 
 
 3.1 
 
 58.0 
 
 3.3 
 
 34 
 
 55.2 
 
 2.5 
 
 55.0 
 
 2.7 
 
 54.6 
 
 3.0 
 
 56.3 
 
 3.2 
 
 35 
 
 53.6 
 
 2.5 
 
 53.4 
 
 2.7 
 
 53.1 
 
 2.9 
 
 54.7 
 
 3.1 
 
 36 
 
 52.1 
 
 2.4 
 
 51.9 
 
 2.6 
 
 51.6 
 
 2.8 
 
 53.1 
 
 3.0 
 
 37 
 
 50.7 
 
 2.3 
 
 50.5 
 
 2.5 
 
 50.2 
 
 2.7 
 
 51.7 
 
 2.9 
 
 38 
 
 49.4 
 
 2.3 
 
 49.2 
 
 2.5 
 
 48.9 
 
 2.7 
 
 50.3 
 
 2.9 
 
 39 
 
 48.1 
 
 2.2 
 
 47.9 
 
 2.4 
 
 47.6 
 
 2.6 
 
 49.0 
 
 2.8 
 
 40 
 
 46.9 
 
 2.2 
 
 46.7 
 
 2.4 
 
 46.4 
 
 2.6 
 
 48.0 
 
 2.8 
 
 Weight per 
 foot.lbs. 
 
 174 
 
 6.0 
 
 166 
 
 6.0 
 
 159 
 
 6.0 
 
 158 
 
 6.0 
 
 Safe loads given include weight of girder. 
 
 Weights of girders given include weight of rivet heads, but not stif- 
 
 Maximum fibre strain, 15,000 Ibs. per square inch of net area, holes for 
 %" rivets being deducted 
 
WOODEN FLOORS. 65) 
 
 CHAPTER XXI. 
 
 STRENGTH AND STIFFNESS OF WOODEN 
 FLOORS. 
 
 Two problems present themselves under this head; first, to 
 proportion the beams and girders forming the framework of the 
 floor to the greatest load likely to come upon it ; and second, to 
 determine the maximum safe load for a floor already built. 
 
 The former of these problems is the> one with which architects 
 and builders more commonly have to deal, and will therefore be 
 considered first. 
 
 Layout of the Floor Framing 1 . Before any calcula- 
 tions can be made for the size of the timbers it will be necessary 
 to know the span 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 beam, 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. For a detailed description of the manner 
 of framing wooden floors the reader is referred to Part II, of 
 " Building Construction and Superintendence." 
 
 Where the floor-beams are supported entirely by walls or par- 
 titions, the span of the beams will of course be fixed by the plan 
 of the building. When the distance between walls and parti- 
 tions is too great for a single span, there may be a question as to 
 the best location of the posts and girders. 
 
 When planning a building in which wooden floor-beams are to 
 be used, it is important to keep in mind how the floors are to be 
 framed, and particularly the span. Whenever practicable the 
 span of wooden beams should be kept under 25 feet. When the 
 distance between the supporting walls exceeds 30 feet, girders 
 should be placed so that the maximum span of the joists will not 
 exceed 24 feet for light buildings or 16 to 18 feet for warehouses. 
 
 In school buildings it is desirable to have the rooms at least 27 
 
652 WOODEN FLOORS. 
 
 feet wide, and hence in this class of buildings the joists usually 
 have a span of from 27 to 30 feet. For a span of 30 feet, however, 
 16-inch joists should be used, and as these are expensive, and 
 often difficult to obtain, it is much better and more economical 
 to make the schoolrooms 27 X 32 or 34 feet, than to make them 
 30 feet square. In the opinion of the writer a schoolroom 27 
 feet wide by 32 to 34 feet long, with windows on the long side of 
 the room only, is the most economical and satisfactory, as it 
 permits of using 3"Xl4" joists 28 feet long, and also gives the 
 most satisfactory lighting. 
 
 When floor-beams are supported by a girder placed so that a 
 24- or 26-foot beam will reach over the two spans, it is always 
 better to have the joists continuous over the girder, as it makes 
 a much stiffer floor, although the ultimate strength is not in- 
 creased (see Chapter XIX.). 
 
 Having decided on the arrangement of the joists, and drawn 
 a framing plan showing the span and location of all special 
 timbers, the next step will be to decide upon the loads for which 
 the joist and timbers shall be proportioned. 
 
 Floor loads are made up of two factors, first the weight of 
 materials composing the floor (and ceiling below, if there is one) ; 
 and second, an allowance for the load liable to come upon the 
 floor. The first is commonly designated as the "dead load/' and 
 the second as 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 beams, commonly called "joists,''' or 
 "floor- joists," one or two thicknesses of flooring boards, and, in a 
 finished building, of a ceiling underneath the beams. In figuring 
 the weight of f-inch flooring boards it will be sufficiently accurate 
 to estimate the weight of a single thickness at 3 pounds per square 
 foot. The joists may also be figured at 3 pounds per foot, board 
 measure, with the exception of hard pine and oak joists, which 
 should be figured at 4 pounds per foot 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 X 12-inch 
 joist is about 6 pounds per lineal foot. If the joists are spaced 
 12 inches on centres, this will be equal to 6 pounds per square foot; 
 but if the joists are 16 inches on centres there will be but one 
 lineal foot of joist to every 1J square fent, which will be equiva- 
 lent to 4J pounds per square foot, and if they are 20 inches on 
 eentres, the weight will be equal to 3J pounds per square foot; 
 
WOODEN FLOOHS. 
 
 653 
 
 spaced 24 inches on centres, the weight will be 3 pounds per 
 square foot. 
 
 The weight of a lath-and-plaster ceiling should be taken at 
 10 pounds per square foot, and of a J-inch wood ceiling at 2J 
 pounds per square foot. Corrugated iron ceiling weighs about 
 1 pound per square foot. For stamped steel ceilings 2 pounds 
 per square foot will cover the weight of the metal and furring. 
 
 The following table, giving the weight of joists, will be found 
 convenient in figuring the weight of floors: 
 
 TABLE I. WEIGHT OF FLOOR-JOISTS PER SQUARE 
 FOOT OF FLOOR. 
 
 
 Spruce, hemlock, white 
 pine. 
 
 Hard pine or oak. 
 
 Size of 
 joists in 
 inches. 
 
 Spacing in inches, centre 
 to centre. 
 
 Spacing in inches, centre 
 to centre. 
 
 
 12 
 
 16 
 
 12 
 
 16 
 
 
 Pounds. 
 
 Pounds. 
 
 Pounds. 
 
 Pounds. 
 
 2X3. .. 
 
 3 
 
 21 
 
 4 
 
 3 
 
 2X8.. .. 
 
 4 
 
 3 
 
 51 
 
 4 
 
 3X8.. .. 
 
 6 
 
 
 
 8 
 
 6 
 
 2X10. .. 
 
 5 
 
 3i 
 
 6| 
 
 5 
 
 3X10. .. 
 
 74 
 
 5f 
 
 10 
 
 71 
 
 2X12. .. 
 
 6 
 
 44 
 
 8 
 
 6 
 
 3X12. .. 
 
 9 
 
 6} 
 
 12 
 
 9 
 
 2X14. .. 
 
 7 
 
 5i 
 
 
 
 7 
 
 3X14. .. 
 
 10} 
 
 84 
 
 14 
 
 10| 
 
 Weight of Crowds. Prof. L. J. Johnson, of Harvard 
 Univ., reports in the Eng. News of Apr. 14, 1904, results of 
 some tests to ascertain the weight of crowds (of men) , in which 
 he obtained weights of 134.2, 143.9, 148.1, and 156.9 Ibs. per 
 sq. ft. The last weight was obtained by packing 67 men in a 
 room about ll'X6'. Prof. Johnson also found that with 50 
 men in the room, giving a weight of 122 Ibs. per sq. ft., the crowd 
 was compacted "so that a man could elbow his way through 
 it only with perseverance 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 dif- 
 ferent classes of buildings, as fixed by the building laws of the 
 cities mentioned: 
 
654 
 
 WOODEN FLOORS. 
 
 TABLE II. MINIMUM SAFE SUPERIMPOSED LOADS 
 FOR FLOORS REQUIRED BY VARIOUS BUILDING 
 LAWS. 
 
 Class of buildings. 
 
 Minimum live load per square foot 
 of floor. 
 
 Buffalo, 
 1896. 
 
 eT . 
 
 _OiO 
 
 Chicago, 
 1895. 
 
 
 
 Ji 
 
 NewYork, 
 1899. 
 
 A 
 
 Ol^ 
 
 W 
 
 
 40 
 
 70 
 70 
 100 
 120 
 
 50 
 
 50 
 100 
 150 
 250 
 
 70 
 
 70 
 70 
 70 
 150 
 
 40 
 
 50f 
 70 
 80} 
 150 
 
 60 
 
 60 
 75* 
 90 
 
 120 
 
 70 
 
 70 
 70* 
 120t 
 150 
 
 Hotels, tenements, and lodging- 
 
 Offices 
 
 Buildings for public assembly. . 
 
 Stores, warehouses, and mfg. bldgs. 
 
 * First floor, 150 Ibs. 
 t Also schoolhouses. 
 
 t With fixed desks. 
 And upwards. 
 
 It is the opinion of the author that the following allowances 
 for floor loads, taken in connection with the values given for the 
 safe strength of beams, will provide absolute safety with proper 
 allowance for economy. 
 
 For dwellings, sleeping and lodging rooms 40 Ibs. 
 
 For schoolrooms 50 " 
 
 For offices (upper stories) 60 " 
 
 EOF offices (first Story) 80 " 
 
 For stables and carriage-houses 65 " 
 
 For banking-rooms, churches, and theatres 80 " 
 
 For assembly halls, dancing halls, and the corridors of all 
 
 public buildings, including hotels 120 " 
 
 For drill-rooms 150 "' 
 
 Floors for ordinary stores, light manufacturing and light stor- 
 age should be computed for not less than 120 pounds per square 
 foot, and to sustain a concentrated load at any point of 4,000 Ibs. 
 
 It is rarely, if ever, that the floors of a dwelling, tenement, or 
 lodging-house, or the rooms in a hotel, are loaded to more than 
 twenty pounds per square foot, for the entire area, and a mini- 
 mum load of 40 pounds should provide for all possible con- 
 tingencies. 
 
 The floors of offices are as a rule not more heavily loaded than 
 dwellings, but the possibilities for increased loads, in the way of 
 safes and heavy furniture, and possibly of a more compact crowd 
 of people, are greater, so that the minimum floor load for offices 
 should be somewhat increased. Some years ago Messrs. Blackall 
 
WOODEN FLOORS. 655 
 
 & Everett, of Boston, found that the average live load in 210 
 offices, in three prominent office buildings in that city, was be- 
 tween 16 and 17 pounds, while the average load for the 10 
 heaviest offices was 33.3 pounds. As such loads, however, are 
 not usually evenly distributed, some portions of the floor being 
 generally much more heavily loaded than the others, it would 
 not appear to be safe to use the average above determined for 
 determining the strength of floor-beams and arches, although it 
 would probably answer for the columns. There seems to be 
 considerable difference of opinion among the leading architects 
 and structural engineers as to just what allowance should be 
 made for office floors. In the Mills Building in San Francisco 
 the live loads were assumed at 40 pounds per square foot for all 
 floors above the first; in the Venetian Building, Chicago, the 
 second, third, and fourth floors were calculated for 60 pounds, 
 and the upper floors for 35 pounds live load per square foot, 
 while in the Old Colony and Fort Dearborn Buildings in Chicago 
 the live loads on the floor-beams were assumed at 70 pounds 
 in accordance with the building ordinance. 
 
 An allowance of 120 Ibs. per square foot for the live load in 
 churches, theatres, and schoolhouses is, in the opinion of the 
 author, much greater than the actual conditions require. 
 
 The average size of a schoolroom is about 28X32 feet, and 
 such a room usually contains seats for fifty-six scholars and the 
 teacher. Assuming the average weight of each scholar at 120 
 pounds, we have for the average live load, including ten visiting 
 adults and the desks and furniture, 13 pounds per square foot. 
 Even supposing that the scholars of two rooms were united for 
 some special occasion, we would have but 21 pounds per square 
 foot, 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, a minimum load for the schoolrooms of 50 pounds per 
 square foot would appear abundant. 
 
 As a matter of fact, 3 X 14-inch Georgia pine beams, 16 inches 
 on centres and 28 feet span, have been used for schoolroom 
 floors for years, and no practical person would doubt their safety, 
 but such beams, if calculated by the formula for stiffness as 
 hereinafter recommended, would only support a live load of 
 56 pounds. 
 
 The minimum floor space allotted to a single seat in theatres 
 is 4 square feet, while the average is about 5 square feet. As- 
 
656 WOODEN FLOORS. 
 
 suming the weight of an opera-chair at 35 pounds and of the 
 average adult at 140 pounds (a liberal allowance), we have an 
 average of 44 pounds per square foot of floor. A minimum of 
 80 pounds would therefore seem to provide for any possible 
 crowding during a panic except in corridors. On the other hand 
 it has been shown * that a crowd of able-bodied men may pro- 
 duce a load of about 120 pounds per square foot, 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 vibra- 
 tion produced. 
 
 The average floor loads for stores has also been greatly over- 
 estimated. Mr. W. L. B. Jenney found that the average load 
 on the floors of the wholesale warehouse of Marshall, Field & Co., 
 in Chicago, was but 50 pounds per square foot, and very few 
 retail stores will average over 80 pounds. An allowance of 120 
 pounds is sufficient for any ordinary retail store, with the possible 
 exception of hardware stores. 
 
 Warehouses, on the other hand, may be very heavily loaded, 
 and the floors in buildings intended for the storage of merchan- 
 dise should be proportioned to the especial class of goods which 
 they are designed to support. 
 
 The following table, originally compiled by Mr. C. J. H. Wood- 
 bury,! and to which some additions have been made by the 
 Insurance Engineering Experiment Station and by the author, 
 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 consideration in fixing upon the 
 floor load. 
 
 In the following table "the measurements were always taken 
 to the outside of case or package, and gross weights of such 
 packages are given." 
 
 To find the size of joists, beams, and girders 
 required for any particular building. As already 
 explained, the first step should be to make a framing plan of the 
 floors or enough of it to show any special framing and the span 
 
 * See " Weight of Crowds," p. 653. 
 t The Fire Protection of Mills, p. 118. 
 
WOODEN FLOORS. 657 
 
 TABLE III. WEIGHTS OF MERCHANDISE. 
 
 Material. 
 
 Measurements. 
 
 Weights. 
 
 WOOL. 
 
 Floor 
 space. 
 3.0 
 5.8 
 ..7.0 
 
 Cubic 
 feet. 
 12.0 
 26.0 
 34.0 
 33.0 
 33.0 
 30.0 
 
 12.7 
 15.2 
 22.0 
 28.0 
 21.0 
 35.0 
 14.0 
 
 44.2 
 21.6 
 11.0 
 7.2 
 9.9 
 10.5 
 10.9 
 34.7 
 17.0 
 
 12.5 
 2.3 
 10.1 
 11.4 
 19.0 
 9.3- 
 13.4 
 8.8 
 
 5.3 
 
 39.5 
 
 40.0 
 30.0 
 34.0 
 65.0 
 30.0 
 11.1 
 
 i 
 
 Gross. 
 
 340 
 385 
 1000 
 
 482 
 550 
 200 
 
 220 
 330 
 460 
 550 
 350 
 450 
 250 
 
 ,515 
 550 
 263 
 254 
 300 
 450 
 '280 
 700 
 400 
 
 300 
 75 
 235 
 330 
 295 
 175 
 420 
 325 
 
 130 
 100 
 
 910 
 715 
 442 
 507 
 450 
 600 
 400 
 
 Per 
 
 sq. ft. 
 113 
 66 
 143 
 70 
 73 
 40 
 
 40 
 46 
 84 
 52 
 48 
 44 
 63 
 
 64 
 134 
 66 
 110 
 125 
 172 
 88 
 81 
 75 
 
 72 
 68 
 65 
 69 
 41 
 44 
 93 
 99 
 
 70 
 
 107 
 78 
 59 
 68 
 28 
 80 
 143 
 
 Per 
 cu. ft. 
 28 
 15 
 29 
 15 
 17 
 7 
 5 
 
 17 
 22 
 21 
 20 
 16 
 13 
 18 
 
 12 
 25 
 24 
 35 
 30 
 43 
 26 
 20 
 24 
 
 24 
 33 
 23 
 30 
 16 
 19 
 31 
 37 
 11 
 30 
 24 
 
 23 
 
 18 
 15 
 15 
 7 
 20 
 36 
 
 50 
 69 
 38 
 33 
 59 
 64 
 10 
 37 
 
 " Australia . . . . 
 
 *' South America . . . . : 
 
 " Oregon 
 
 6.9 
 7.5 
 5.0 
 
 5.5 
 7.1 
 5.5 
 10.5 
 7.3 
 10.3 
 4.0 
 
 8.1 
 4.1 
 4.0 
 2.3 
 2.4 
 2.6 
 3.2 
 8.7 
 5.3 
 
 4.0 
 1.1 
 3.6 
 4.8 
 7.2 
 4.0 
 4.5 
 3.3 
 
 1.4 
 
 8.5 
 9.2 
 7.6 
 7.5 
 16.0 
 7.5 
 2.8 
 
 " California 
 
 Bag wool 
 
 Stack of scoured wool 
 
 WOOLLEN GOODS. 
 Case flannels . 
 
 
 " dress goods 
 
 " cassimeres 
 
 ' underwear 
 
 " blankets . . . 
 
 " horse -blankets 
 
 COTTON, ETC. 
 Bale 
 
 " compressed 
 
 " American Cotton Co 
 
 " Planters' Compressed Co 
 
 " jute 
 
 " jute lashings . 
 
 *' manila 
 
 " hemp 
 
 " sisal . 
 
 COTTON GOODS. 
 Bale unbleached jeans 
 
 Piece duck 
 
 Bale brown sheetings 
 
 Case bleached sheetings 
 
 " quilts 
 
 Bale print cloth 
 
 
 Bale tickings 
 
 Skeins cotton yarn 
 
 
 Jute bagging 
 
 RAGS IN BALES. 
 White linen 
 
 
 Brown cotton . . 
 
 
 
 
 
 PAPER. 
 Calendered book 
 
 
 Newspaper . . . 
 
 Straw board 
 
 
 "Writing . 
 
 Wrapping. . . 
 
 Manila 
 
 
658 
 
 WOODEN FLOORS, 
 
 TABLE III. WEIGHTS OF MERCHANDISE (continued). 
 
 Material. 
 
 Measurements. 
 
 Weights. 
 
 GRAIN.* 
 Wheat in bags 
 
 Floor 
 space 
 4.2 
 
 4.1 
 3.1 
 3.6 
 3.7 
 3.3 
 5.0 
 1.75 
 1.75 
 1.75 
 1.75 
 
 11.8 
 10.8 
 3.0 
 4.0 
 1.6 
 4.3 
 3.0 
 3.0 
 1.06 
 3.6 
 3.8 
 3.8 
 3.7 
 3.0 
 4.3 
 
 2.7 
 
 9.9 
 13.4 
 7.3 
 11.2 
 6.0 
 6.0 
 12.6 
 
 3.0 
 3.0 
 
 Cubic 
 feet 
 4.2 
 
 5.4 
 7.1 
 3.6 
 5.9 
 3.6 
 20.0 
 5.25 
 5.25 
 5.25 
 5.25 
 
 39.2 
 29.2 
 9.0 
 3.3 
 4.1 
 6.8 
 10.5 
 10.5 
 .8 
 4.5 
 5.5 
 5.5 
 6.1 
 9.0 
 12.3 
 
 0.5 
 
 39.6 
 42.5 
 12.2 
 16.7 
 30.0 
 30.0 
 8.9 
 
 7.5 
 7.5 
 
 Gross. 
 165 
 
 218 
 218 
 112 
 218 
 96 
 284 
 125 
 100 
 150 
 100 
 
 1200 
 1800 
 385 
 150 
 160 
 600 
 250 
 350 
 55 
 225 
 325 
 400 
 325 
 430 
 422 
 
 139 
 
 1600 
 600 
 190 
 300 
 400 
 700 
 200 
 
 317 
 340 
 
 Per 
 sq. ft. 
 39 
 
 53 
 70 
 31 
 59 
 29 
 57 
 72 
 57 
 86 
 57 
 
 102 
 167 
 128 
 38 
 100 
 140 
 83 
 117 
 52 
 63 
 86 
 105 
 88 
 143 
 98 
 
 99 
 
 162 
 52 
 26 
 27 
 67 
 117 
 22 
 
 106 
 113 
 
 Per 
 cu. ft, 
 39 
 44 
 39 
 41 
 40 
 31 
 31 
 37 
 27 
 14 
 24 
 19 
 29 
 19 
 4 
 
 31 
 62 
 43 
 45 
 39 
 88 
 23 
 33 
 70 
 50 
 59 
 73 
 53 
 48 
 34 
 42 
 
 278 
 60 
 40 
 14 
 16 
 18 
 13 
 23 
 16 
 17 
 42 
 45 
 30 
 
 in bulk 
 
 
 " " "...... .mean 
 
 
 Corn in bags . ... 
 
 
 
 Bale of hay . 
 
 Hay, Dederick compressed 
 
 Straw " " 
 
 Tow " '* .... 
 
 
 
 DYESTUFFS, ETC. 
 Hogshead bleaching powder 
 
 
 
 
 * sumac 
 
 Caustic soda in iron drum 
 Barrel starch . 
 
 pearl alum 
 
 Box extract logwood 
 
 
 " cement, American. . ... 
 
 
 
 
 " lard oil 
 
 Rope 
 
 MISCELLANEOUS. 
 Box tin 
 
 " glass 
 
 
 
 
 
 * raw hides. . 
 
 ' " " compressed 
 
 
 
 Barrel granulated sugar 
 
 
 Cheese 
 
 
 and floor area supported by the different beams and girders. The 
 second step is to determine approximately the weight of the floor 
 and ceiling, and decide upon what superimposed load (per 
 square foot) the floor shall be proportioned to carry. 
 
 Having done this, the next step will be to compute the 
 required dimensions of the common floor joists. 
 
 1904 
 
 For pressure of grain in deep bins, see Engineering News of March 10, 
 1, pp. 224 and 336, ateo of Dec. 15, 1904. 
 
WOODEN FLOORS. 659 
 
 For most buildings the size of floor joist required can be 
 readily determined by reference to Tables VI.-X. of this chapter. 
 
 For other floor loads the size of the common joists may be 
 computed as follows : Compute the load to be supported by a single 
 joist and then, by the rules or tables in Chapter XVI. or XVIII. , 
 determine the dimensions of the -joists to support the load. (See 
 Example 1.) 
 
 For the floors of all buildings except stores and warehouses 
 the author recommends that the size of the common joists be 
 determined by the rules or tables in Chapter XVIII. For 
 stores and warehouses the size of the joists may be proportioned 
 by the formulas for strength, Chapter XVI. 
 
 The dimensions of all special beams, such as headers, trimmers, 
 beams supporting partitions, and also of the girders, should be 
 found in the same way, viz. , by computing the maximum load 
 which the beam may have to support, and then the dimensions 
 of a beam that will sustain the load with safety. 
 
 The manner of making the computations can be best ex- 
 plained by means of examples. 
 
 EXAMPLE 1. The simplest floor framing is that shown in 
 Fig. 1, in which all of the joists are of the same span and sustain 
 
 FSg. I. 
 
 Plan of Floor Beams. 
 
 equal floor areas. In such a floor, the floor area supported by 
 each joist is equal to the span L multiplied by the spacing S 
 (in feet). 
 
 The load on each joist is equal to the floor area multiplied by 
 the sum of the dead and superimposed loads. To show the 
 application of the above rules and directions we will assume that 
 Fig. 1 represents the framing of a floor in a dwelling- or lodging- 
 
660 WOODEN FLOORS. 
 
 house, that L = 18 ft., = 16 ins. or 1J ft., and that the timber is 
 to be common white pine. The joists are to sustain a plastered 
 ceiling and a double floor of -|-inch boards. What should be the 
 size of the joists? 
 
 Ans. The floor area supported by each joist will be 1JX18, 
 or 24 sq. feet. As the joists will probably have to be at least 
 2"X12", th^ir weight will be about 4J Ibs. per square foot (see 
 Table I.). The plastered ceiling will weigh about 10 Ibs. and 
 the flooring 6 Ibs., making the total weight of the floor 20 J Ibs, 
 per sq. ft. For the superimposed load we should allow 40 Ibs. 
 (see p. 654). The load on a single joist will therefore be 60 J 
 Ibs. X 24 sq. ft., or 1452 Ibs. 
 
 From Table V., Chapter XVIII., we find that the maximum 
 load for a 1 X 12 beam of 18 ft. span is 700 Ibs., hence to support 
 1452 Ibs. will require a breadth equal to 1452 -=-700 or 2 T *g ins. 
 Therefore, to comply with the requirements for stiffness, the 
 joists should be 2 T V / X12". 
 
 If we do not mind the deflection we can use the table for 
 strength (Table VII., Chapter XVI.), which gives 960 Ibs. for the 
 safe load of a 1X12 beam, and dividing 1452 by 960 we have 
 1.51 for the required breadth of the beam; therefore a If "X 12" 
 joist will be strong enough, but would bend more than is desirable 
 where the ceiling is to be plastered. Joists full 2"X 12", spaced 
 16 ins. on centres, would answer in this case, but if they come 
 J in. scant in one or both dimensions they should be spaced only 
 12 ins. on centres. From Table VI. we see that the maximum 
 span for 2" XI 2" joists, spaced 16 ins. on centres, in dwellings 
 is given as 17' 3". 
 
 EXAMPLE 2. Fig. 2 shows a partial section of a dwelling, in 
 which the second -floor joists support a plastered partition which 
 also supports an attic floor. What should be the size of the 
 second-floor joists to meet the requirements of strength, the 
 timber to be Eastern spruce? 
 
 NOTE. As the effect of a concentrated load in producing 
 deflection, compared with a distributed load, is not as great as 
 the comparative effect to produce rupture, whenever beams have 
 a considerable concentrated load they may be calculated by the 
 formula or tables for strength only. 
 
 Ans. The first step will be to determine the load on a single 
 floor joist. We will assume that the joists are to be 2"X10", 
 12 ins. on centres, that both the first- and second-story ceilings 
 are to be plastered, and that only single flooring will be used in 
 
WOODEN FLOORS. 
 
 661 
 
 the second story and attic. We will assume that the attic joists 
 are to be 2"X8", 16 ins. centre to centre, and that the width of 
 floor supported by the partition is 10 ft. 
 
 The second-floor area supported by a single joist will be 12"X 
 15 ft., or 15 sq. feet. The weight of the floor joists per sq. ft. 
 will be 5 Ibs., of the plastered ceiling 10 Ibs., and of the flooring 
 3 Ibs., making the dead load per sq. ft. 18 Ibs. For the live 
 or superimposed load we should allow 40 Ibs., hence the load 
 
 j Attic 
 
 -10- 
 
 -'39 
 
 Second Story 
 
 Fig. 2. 
 
 Section. 
 
 per sq. ft. on the second-floor joists due to the second floor and 
 its load will be 58 Ibs. As the floor area is 15 sq. ft. the load from 
 the second floor will be 15X58 or 871 Ibs. We must now find 
 what will be the load from the partition and attic floor. The 
 attic floor and ceiling will weigh about 16 Ibs. per sq. ft., and 24 
 Ibs. will be a sufficient allowance for the live load. The weight 
 per lineal foot on the partition will therefore be 400 Ibs. A 
 partition of 2X4 studding lathed and plastered both sides will 
 weigh about 20 Ibs. per sq. ft.; hence the partition itself will 
 
662 WOODEN FLOORS. 
 
 weigh 180 Ibs. per lineal ft. The partition and attic floor will 
 therefore bring a load of 580 Ibs. on each second-floor joist, 
 concentrated at a point one-fourth of the span from the inner end 
 of the joist. To combine this concentrated load with the load 
 from second floor, we must multiply the concentrated load by 
 1.5 (see page 565), which gives an equivalent distributed load 
 of 870 Ibs. Adding this to the second -floor load we have 1740 
 Ibs. as the total load for which each joist should be proportioned. 
 From Table VI., Chapter XVI., we find that the safe load for a 
 1X10 spruce beam of 15 ft. span is 933 Ibs.; hence the breadth 
 of the joists should be equal to 1740-^933 or 1J ins. If the 
 joists were spaced 16 ins. on centres the load on a single joist 
 would be increased one-third, or to 2320 Ibs., which would require 
 a 1|"X12" joist. 
 
 EXAMPLE 3. To determine the size of the girder and floor 
 timbers in the floor shown in Fig. 3, all of the timbers being of 
 Texas 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 feet. There 
 is to be a double floor and the ceilings and partitions are to be 
 plastered. The floor joists will be spaced 16 ins. centre to 
 centre. 
 
 Ans. 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 will be 24X1 J, or 
 32 sq. ft. 
 
 As it will probably require 2"X 14" joists, we will allow 7 Ibs. 
 per sq. ft. for the weight of joists and bridging, 10 Ibs. for the 
 ceiling, and 6 Ibs. for the flooring, making 23 Ibs. per sq. ft. for the 
 dead load. For the live load we will allow 40 Ibs. The load for 
 which the joists should be proportioned will therefore be 32X63, 
 or 2016 Ibs. As the stiffness of Texas pine is nearly the same as 
 that of Georgia yellow pine, we may use Table II., Chapter XVIII., 
 to find the maximum load for a 1"X14" beam of 24 ft. span. 
 The load given in the table is 1042 Ibs., hence the thickness of the 
 joists must equal 2016 -*- 1042 or 2 ins. Therefore 2"X 14" joists, 
 16 ins. on centres should be used, but they should run full 2 ins. 
 thick. 
 
 The joists at B have to support a partition, but as the 
 span is much less, and the partition is quite near the end of 
 the joists, it will be safe to make them of the same size as 
 at A. 
 
WOODEN FLOORS. 663 
 
 The joists at C have the same floor load to support as at A, 
 and in addition the weight of the partition, which is concentrated 
 one-third of the span from one support. As the partition is 10 
 ft. high, 13 J sq. ft. of partition will be supported by each joist 
 
 Fig. 3. 
 
 Plan of Floor Framing showing Partitions Above. 
 
 (the joists being 16 ins. on centres). Assuming 20 Ibs. per sq. 
 ft. as the weight of the partition, we have 267 Ibs. as the weight 
 from the partition to be borne by each joist. To reduce this to 
 
664 WOODEN FLOORS. 
 
 an equivalent distributed load, we should multiply by 1.78, 
 which gives 468 Ibs. The joist at C, therefore, should be pro- 
 portioned to a uniformly distributed load of 2016+468 or 2484 
 Ibs., which will require a 14-inch joist 2.4 ins. thick, or say 
 2JX14. 
 
 Header. We will next determine the required breadth 
 for the header H, the depth being necessarily 14 ins. (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 14X9, or 126 sq. ft. Multiplying 
 this area by 63, the weight per square foot, we have 7938 Ibs. as 
 the total floor load to be supported, to which must be added a 
 certain percentage of the partition. The portion of the partition 
 supported by the header is 12'-8" long (14'-0" l'-4') 10' high 
 and will weigh about 20 Ibs. per square foot, or a total of 2532 
 Ibs. As the partition is one-ninth of the span from the header, 
 eight-ninths of its weight will be supported by the header and 
 one-ninth by the wall. Eight-ninths of 2532 is 2251 Ibs., which 
 added to the floor load makes a total load for the header of 10,188 
 Ibs. From Table IV., Chapter XVI., we find that the safe load 
 for a 1"X 14" beam of Texas pine, 14 ft. span is 2520 Ibs., hence 
 it will require a breadth of 4 ins. to support 10,630 Ibs. If the 
 tail beams are framed into the header, additional thickness 
 should be given to the header to allow for the weakening effects 
 of the framing, so that the header should be at least 5"X 14". 
 
 Trimmers. We will next consider the trimmer T. This 
 beam has four loads: A distributed floor load; a distributed 
 load from the partition above; one-half the load on the header 
 H, and a small direct load from the longitudinal partition. The 
 strip of floor supported by the trimmer will be about 12 ins. wide 
 and 24 ft. long, and will weigh 1512 Ibs. 
 
 The partition above will weigh 10 X 24 X 20, or 4800 Ibs. One- 
 half of the load on H is 5094 Ibs. As this is concentrated one- 
 fourth of the span from the support, we must multiply it by 1.5 
 to obtain the equivalent distributed load, which gives 7641 Ibs. 
 About 8 inches of the longitudinal partition must be supported 
 by the trimmer, and this will weigh 133 Ibs. As it is concen- 
 trated one-third of the span from the support, we must multiply 
 by 1.78 to obtain the equivalent distributed load which gives 
 236 Ibs. 
 
 The total load for which the trimmer must be computed will 
 therefore be: 
 
WOODEN FLOORS. 665 
 
 From the floor 1512 
 
 From the partition above 4800 
 
 From the header 7641 
 
 From the longitudinal partition 236 
 
 Total 14,189 
 
 The trimmer should be of the same depth as the joists, 14 ins. 
 From Table IV., Chapter XVI,, we find that a 1X14 in. Texas 
 pine beam of 24 ft. span will safely support 1470 Ibs. ; hence the 
 breadth of the trimmer must = 14,189 -7-1470 =9.5 ins., and the 
 header should be hung in a stirrup or joist hanger. The load on 
 the trimmer R will be the same as on the trimmer T, except for 
 the cross partition. Deducting the weight of this partition, we 
 have 9389 pounds for the equivalent distributed load on R, 
 which will require a breadth =9389 -7-1470 =6. 4 ins. 
 
 Girders. The floor area supported by girder G is equal 
 to 12 X 24 ft., or 288 square feet. As a general rule, it will be safe 
 in estimating the live load on girders to take only 85 per cent, 
 of the load assumed for the floor beams, because there will 
 always be some portion of the floor supported by the girder that 
 is not loaded, and probably other portions that will not be loaded 
 up to the assumed load. 85 per cent, of 40 pounds is 34 pounds. 
 The dead load of the floor and ceiling will be about 23 Ibs., and 
 the girder itself will weigh at least 1 pound per sq. ft. of floor 
 more, so that we will use 58 Ibs. per square ft. for the total floor 
 load on girders. As girder G supports 288 sq. ft., this will be 
 equivalent to 16,704 Ibs. The girder also supports a partition, 
 9' high above, which will weigh 12 X 9X 20 =2160 Ibs. The total 
 load for which the girder should be proportioned is therefore 
 18,864 Ibs. Assuming 12 ins. for the depth of the girder, we find 
 from Table IV., Chapter XVI., that the safe load for a 1+ 12 beam 
 of 12 ft. span is 2160 Ibs., hence the breadth of the girder should 
 be 18,864-^2160 =9 ins. 
 
 The girder G' supports a floor area at the left of 12X12 = 144 
 sq. ft., which represents a distributed load of 8352 Ibs. On the 
 right side of the girder there is a strip of floor 40 ins. wide by 12 
 ft. long (8 ins. of the floor being included in the load on T) which 
 will weigh 2320 Ibs. This may be considered as a concentrated 
 load applied 20 ins. or one-seventh of 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. 
 
666 WOODEN FLOORS. 
 
 The load coming upon the girder from T will equal one-half 
 of the actual distributed load on T, plus f (J of f ) of the load 
 on#. 
 
 The load on H we found to be 10,188 Ibs., and three-eighths is 
 3820 Ibs. The actual distributed load on T we found to be 
 6312 Ibs., and one-half of this is 3156 Ibs. Hence the trimmer 
 T transmits a load of 6976 Ibs. to the girder, which must 
 be considered as a concentrated load applied at one-third of 
 the span from the support, and hence we must multiply it 
 by 1.78 to obtain the equivalent distributed load, which gives 
 12,417 Ibs. 
 
 The load for which the girder G f should be computed will there- 
 fore be 
 
 From the floor at the left 8,352 Ibs. 
 
 From the floor at the right. 2,320 " 
 
 From the trimmer T. 12,417 " 
 
 From the partition above 2,160 " 
 
 Total 25,249 " 
 
 This will require a beam 11.7 ins. wide. For this floor, there- 
 fore, we will require a 10"X 12" girder at G, a 12"X 12" at G' 9 a 
 9"X 14" beam for the trimmer T, 6i"X 14" for R, 5"X 14" for 
 H, and 2" X 14" joists at A-and B, and 2i"X 14" joists at C. This 
 example illustrates nearly all of the computations that are re- 
 quired to determine the size of the joists and special beams 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 propor- 
 tioned. 
 
 As will be seen, the most laborious computations are those for 
 beams which receive loads from different sources, and it will gen- 
 erally be found that the weakest portions of any particular floor 
 are the headers, trimmers, and girders, and the beams which sup- 
 port partitions. 
 
 Strength of Mill Floors. The beams and girders for mill 
 floors should be computed by the same process as exemplified in 
 the foregoing examples, viz., first determining the load on the 
 beam and then the size of timber required to support it. 
 
WOODEN FLOORS. 667 
 
 Required Thickness of Plank Flooring. The 
 
 thickness of the plank flooring in mill construction may be deter- 
 mined by formulas (a) and (p), following: 
 
 Thickness of plank in ins. ) _ . / weight per sq. ft. XL 2 
 required for strength | ~~ V ~ 24><Z 
 
 Thickness of plank in ins. ) = y weight per sq. ft. X~L*[ 
 required for stiffness ) V ~ 19. 2 X^ 
 
 L denotes span in feet, centre to centre of beams, A the con- 
 stants for strength, p. 567, and e i the constant for stiffness 
 (p. 595). 
 
 When the planks are connected by f-in. splines, and extend 
 over two spans, formula (a) may be used. If the planks are in 
 single lengths from beam to beam, or are not splined, then 
 formula (6) should be used. 
 
 Table IV. shows the safe loads for plank flooring of different 
 thicknesses and spans, as derived from the formulas for strength 
 and stiffness, the plain figures denoting the loads given by the 
 formula for strength and the figures in italics those given by the 
 formula for stiffness. 
 
 The span is supposed to be measured from centre to centre of 
 beams. The plain figures should be considered safe only for 
 splined floors and where the planks are continuous over at least 
 two spans. If the thickness of the plank falls short one-fourth or 
 even one-eighth inch from the dimensions given, the safe loads 
 must be materially reduced. 
 
 Tables for the Maximum Span of Floor Joists. 
 As the timbers commonly used for floor joists are sawn to regular 
 sizes, and are usually spaced either 12 or 16 ins. centre to centre 
 it is practicable to show by means of tables the size of joist 
 required to support a given load with a given span and spacing. 
 After having computed various tables the author has found that 
 tables giving the maximum safe span are the most convenient for 
 general use, and the following tables have accordingly been pre- 
 pared, which show at a glance the maximum span for which dif- 
 ferent sizes of floor and ceiling joists should be used for different 
 loads and spacings ; it is believed that they will be found appli- 
 cable to most buildings in which wooden floor joists are used. 
 
 By knowing the size of the room to be covered and the purpose 
 for which it is to be used, the size of joist required can be told at a 
 
668 
 
 WOODEN FLOORS. 
 
 TABLE IV. SAFE LIVE LOAD IN POUNDS PER 
 SQUARE FOOT FOR PLANK FLOORING.* 
 
 (See explanation on preceding page.) 
 LONG-LEAF YELLOW PINE. 
 
 
 Distance between centres of floor beams in feet. 
 
 Thickness of 
 
 
 plank in ins. 
 
 
 
 
 
 
 
 
 
 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 j 
 
 515 
 
 325 
 
 222 
 
 160 
 
 120 
 
 92 
 
 72 
 
 
 
 A/8 < 
 
 55 
 
 10 
 
 05 
 
 35 
 
 1 
 
 11 
 
 5 
 
 
 
 os/ 
 
 831 
 
 527 
 
 362 
 
 262 
 
 197 
 
 153 
 
 121 
 
 97 
 
 80 
 
 */8 
 
 530 
 
 05 
 
 143 
 
 55 
 
 
 34 
 
 4 
 
 1 
 
 
 OS/ 
 
 1118 
 
 710 
 
 488 
 
 354 
 
 267 
 
 208 
 
 165 
 
 134 
 
 110 
 
 */* 
 
 535 
 
 421 
 
 37 
 
 144 
 
 31 
 
 53 
 
 35 
 
 5 
 
 15 
 
 QJ> 
 
 
 1158 
 
 798 
 
 582 
 
 442 
 
 345 
 
 276 
 
 225 
 
 186 
 
 ' 
 
 
 554 
 
 504 
 
 310 
 
 202 
 
 130 
 
 34 
 
 07 
 
 47 
 
 4 J 
 
 
 
 1046 
 
 763 
 
 580 
 
 454 
 
 364 
 
 296 
 
 246 
 
 4 1 
 
 
 
 753 
 
 470 
 
 305 
 
 10 
 
 145 
 
 100 
 
 77 
 
 5 J 
 
 
 
 
 1200 
 
 913 
 
 716 
 
 576 
 
 471 
 
 392 
 
 5 1 
 
 
 
 
 334 
 
 015 
 
 47 
 
 304 
 
 
 100 
 
 6 J 
 
 
 
 
 
 1322 
 
 1038 
 
 836 
 
 686 
 
 572 
 
 1 
 
 
 
 
 
 1051 
 
 751 
 
 540 
 
 335 
 
 300 
 
 OREGON PINE OR SHORT-LEAF YELLOW PINE. 
 
 Thickness of 
 
 Distance centre to centre of floor beams in feet. 
 
 plank in ins. 
 
 
 
 
 
 
 
 
 
 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 7 J 
 
 462 
 
 291 
 
 199 
 
 143 
 
 106 
 
 81 
 
 64 
 
 
 
 1/8 j 
 
 05 
 
 33 
 
 5 
 
 5 
 
 15 
 
 7 
 
 
 
 
 OS/ 
 
 747 
 
 473 
 
 324 
 
 234 
 
 176 
 
 136 
 
 107 
 
 
 
 &/% 
 
 45 
 
 1 
 
 117 
 
 05 
 
 41 
 
 5 
 
 14 
 
 
 
 OS/ 
 
 1005 
 
 637 
 
 438 
 
 317 
 
 239 
 
 185 
 
 147 
 
 119 
 
 97 
 
 ^x4 
 
 070 
 
 335 
 
 157 
 
 11 
 
 03 
 
 44 
 
 5 
 
 17 
 
 9 
 
 _, 
 
 
 1040 
 
 717 
 
 522 
 
 395 
 
 308 
 
 246 
 
 200 
 
 165 
 
 0/^3 
 
 
 700 
 
 401 
 
 40 
 
 15.9 
 
 100 
 
 7 
 
 50 
 
 34 
 
 4! 
 
 
 1362 
 
 940 
 
 685 
 
 520 
 
 406 
 
 325 
 
 265 
 
 220 
 
 
 
 
 1001 
 
 000 
 
 374 
 
 #44 
 
 105 
 
 115 
 
 51 
 
 55 
 
 
 
 
 1476 
 
 1078 
 
 819 
 
 642 
 
 516 
 
 422 
 
 351 
 
 5 
 
 
 
 1135 
 
 745 
 
 431 
 
 335 
 
 40 
 
 174 
 
 15 
 
 
 
 
 
 1560 
 
 1187 
 
 932 
 
 749 
 
 614 
 
 512 
 
 1 
 
 
 
 
 130 
 
 503 
 
 537 
 
 
 314 
 
 30 
 
 * Weight of ceiling, if any, to be deducted. 
 
WOODEN FLOORS. 
 
 669 
 
 TABLE IV. SAFE LIVE LOAD IN POUNDS PER 
 SQUARE FOOT FOR PLANK FLOORING* 
 
 (continued). 
 
 (See explanation on page 667.) 
 SPRUCE. 
 
 
 Distance between centres of floor beams in feet. 
 
 Thickness of 
 
 
 plank in ins. 
 
 
 
 
 
 
 
 
 
 
 
 4 ' 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 j 
 
 360 
 
 227 
 
 155 
 
 111 
 
 83 
 
 64 
 
 50 
 
 
 
 A/8 "1 
 
 755 
 
 52 
 
 45 
 
 25 
 
 
 8 
 
 
 
 
 O3X J 
 
 581 
 
 368 
 
 252 
 
 182 
 
 137 
 
 105 
 
 83 
 
 67 
 
 54 
 
 ^/8 j 
 
 557 
 
 754 
 
 705 
 
 64 
 
 55 
 
 24 
 
 75 
 
 
 
 O3/ ^ 
 
 782 
 
 496 
 
 341 
 
 247 
 
 186 
 
 144 
 
 115 
 
 93 
 
 76 
 
 ^x* "j 
 
 072 
 
 507 
 
 775 
 
 704 
 
 66 
 
 42 
 
 25 
 
 75 
 
 
 3^ i 
 
 1228 
 
 781 
 
 548 
 
 391 
 
 296 
 
 231 
 
 184 
 
 150 
 
 124 
 
 
 7274 
 
 644 
 
 
 225 
 
 740 
 
 55 
 
 68 
 
 47 
 
 55 
 
 4 J 
 
 
 1060 
 
 731 
 
 533 
 
 405 
 
 317 
 
 253 
 
 207 
 
 171 
 
 
 
 505 
 
 554 
 
 545 
 
 225 
 
 755 
 
 705 
 
 77 
 
 50 
 
 m 
 
 
 
 1148 
 
 839 
 
 638 
 
 500 
 
 402 
 
 329 
 
 273 
 
 5 1 
 
 
 
 7055 
 
 682 
 
 450 
 
 577 
 
 272 
 
 702 
 
 720 
 
 R J 
 
 
 
 
 1213 
 
 924 
 
 725 
 
 583 
 
 478 
 
 400 
 
 6 1 
 
 
 
 
 7755 
 
 755 
 
 545 
 
 554 
 
 
 220 
 
 WHITE PINE. 
 
 
 Distance between centres of floor beams in feet. 
 
 Thickness of 
 
 
 plank in ins. 
 
 
 
 
 
 
 
 
 
 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 j 
 
 307 
 
 193 
 
 131 
 
 94 
 
 .70 
 
 53 
 
 41 
 
 
 
 l/s *j 
 
 755 
 
 74 
 
 55 
 
 
 77 
 
 5 
 
 
 
 
 O3/ J 
 
 496 
 
 314 
 
 114 
 
 154 
 
 116 
 
 89 
 
 70 
 
 56 
 
 
 ^/8 "1 
 
 575 
 
 757 
 
 50 
 
 50 
 
 40 
 
 75 
 
 70 
 
 
 
 2M \ 
 
 668 
 
 424 
 
 290 
 
 210 
 
 158 
 
 122 
 
 97 
 
 78 
 
 63 
 
 1 
 
 455 
 
 245 
 
 755 
 
 55 
 
 52 
 
 55 
 
 20 
 
 72 
 
 
 
 1088 
 
 691 
 
 476 
 
 346 
 
 261 
 
 203 
 
 162 
 
 131 
 
 108 
 
 **/2 i 
 
 7047 
 
 520 
 
 255 
 
 755 
 
 7/5 
 
 75 
 
 55 
 
 50 
 
 25 
 
 4 J 
 4 
 
 
 906 
 
 625 
 
 455 
 
 345 
 
 269 
 
 215 
 
 175 
 
 145 
 
 
 
 757 
 
 457 
 
 275 
 
 757 
 
 725 
 
 55 
 
 00 
 
 45 
 
 51 
 
 
 
 982 
 
 716 
 
 544 
 
 426 
 
 342 
 
 281 
 
 232 
 
 < 
 
 
 
 555 
 
 555 
 
 500 
 
 257 
 
 775 
 
 725 
 
 55 
 
 61 
 
 
 
 1419 
 
 1037 
 
 789 
 
 619 
 
 497 
 
 407 
 
 339 
 
 < 
 
 
 
 7555 
 
 570 
 
 045 
 
 445 
 
 575 
 
 254 
 
 775 
 
 * Weight of ceiling, if any, to be deducted. 
 
670 WOODEN FLOORS. 
 
 glance. Incidentally the tables also show which kind of wood 
 will be most economical. 
 
 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. 
 
 The only precautions to be exercised in using these tables are in 
 regard to the superimposed load and the actual size 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 (beams, flooring, plastering, and deafening, if any) 
 subtracted from the total load will give the superimposed load, 
 i.e., the load which the floor is expected to carry. 
 
 If the joists do not run full to dimensions, the span or spacing 
 must be reduced from that given in the tables, and as in certain 
 localities the stock sizes of joists often run from inch to f inch 
 scant of the nominal dimensions, this fact should always be 
 taken into account when determining upon the size of joists. 
 In this connection it will be convenient to remember that a 
 2-inch joist spaced 16 ins. c. to c. has the same strength as a 1 J' 
 inch joist 12 ins. centre to centre. 
 
 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 partition and joists. 
 
 Tables V. to IX. inclusive, were computed by the formula for 
 stiffness, on the assumption that the deflection should not exceed 
 $ of an inch per foot of span. Tables X. and XI. were computed 
 by the formula for strength. 
 
 The spans given in these tables come within the requirements 
 of the Buffalo and Denver building laws, and Tables V., VII., 
 VIII., IX., and X. 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 the spans 
 given. 
 
 By Georgia pine is meant the loiig-leaf yellow or hard pine. 
 
WOODEN FLOORS. 
 
 671 
 
 TABLE V. MAXIMUM SPAN FOR CEILING JOISTS. 
 
 Total load, 20 pounds per square foot. 
 
 Size of 
 Joist. 
 
 Dist. on 
 Centres. 
 
 Hemlock 
 
 White 
 Pine. 
 
 Spruce or 
 Norway 
 Pine. 
 
 Oregon or 
 Texas 
 Pine. 
 
 Georgia 
 Pine. 
 
 
 Ins. 
 
 Ft. Ins. 
 
 Ft. Ins. 
 
 Ft. Ins. 
 
 Ft. Ins. 
 
 Ft. Ins. 
 
 2X4 
 
 12 
 
 9 3 
 
 9 5 
 
 10 1 
 
 10 5 
 
 11 2 
 
 2X4 
 
 16 , 
 
 8 5 
 
 8 6 
 
 9 1 
 
 9 5 
 
 ID 1 
 
 2X6 
 
 12 
 
 14 
 
 14 1 
 
 15 1 
 
 15 7 
 
 16 8 
 
 2X6 
 
 16 
 
 12 8 
 
 12 10 
 
 13 8 
 
 14 2 
 
 15 2 
 
 2X8 
 
 12 
 
 18 8 
 
 18 10 
 
 20 1 
 
 20 9 
 
 22 4 
 
 2X8 
 
 16 
 
 17 
 
 17 2 
 
 18 4 
 
 18 11 
 
 20 5 
 
 2X8 
 
 20 
 
 15 9 
 
 15 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 
 
 2X12 
 
 12 
 
 26 5 
 
 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 
 
 See remarks, page 670. 
 
 TABLE VI. MAXIMUM SPAN FOR FLOOR JOISTS. 
 
 DWELLINGS, TENEMENTS, AND GRAMMAR-SCHOOL ROOMS WITH 
 
 FIXED DESKS. 
 Total load, 60 pounds per square foot. 
 
 Size of 
 
 Joists. 
 
 Dist. on 
 Centres. 
 
 Hemlock 
 
 White 
 Pine. 
 
 Spruce or 
 Norway 
 Pine. 
 
 Oregon or 
 Texas 
 Pine. 
 
 Georgia 
 Pine. 
 
 
 Ins. 
 
 Ft. Ins. 
 
 Ft. Ins. 
 
 Ft. Ins. 
 
 Ft. Ins. 
 
 Ft. Ins. , 
 
 2X6 
 
 12 
 
 9 9 
 
 9 10 
 
 10 5 
 
 10 10 
 
 11 7 
 
 2X6 
 
 16 
 
 8 9 
 
 8 10 
 
 9 6 
 
 9 10 
 
 10 6 
 
 3X6 
 
 12 
 
 11 1 
 
 11 2 
 
 12 
 
 12 5 
 
 13 4 
 
 3X6 
 
 16 
 
 10 1 
 
 10 2 
 
 10 10 
 
 11 2 
 
 12 1 
 
 2X8 
 
 12 
 
 12 11 
 
 13 1 
 
 13 11 
 
 14 5 
 
 15 6 
 
 2X8 
 
 16 
 
 11 9 
 
 11 10 
 
 12 8 
 
 13 1 
 
 14 1 
 
 3X8 
 
 12 
 
 Y 14 9 
 
 14 11 
 
 16 
 
 16 6 
 
 17 8 
 
 3X8 
 
 16 
 
 13 6 
 
 13 7 
 
 14 6 
 
 15 
 
 16 2 
 
 2X10 
 
 12 
 
 16 2 
 
 16 L 4 
 
 17 5 
 
 18 
 
 19 4 
 
 , 2X10 
 
 16 
 
 14 9 
 
 14 10 
 
 15 9 
 
 16 4 
 
 17 7 
 
 Total load, 66 pounds per square foot. 
 
 3X10 
 
 12 
 
 18 
 
 IS 1 
 
 19 3 
 
 20 
 
 21 6 
 
 3X10 
 
 16 
 
 16 3 
 
 16 5 
 
 17 7 
 
 18 2 
 
 19 6 
 
 2X12 
 
 12 
 
 18 10 
 
 19 
 
 20 3 
 
 20 10 
 
 22 6 
 
 2X12 
 
 16 
 
 17 2 
 
 17 3 
 
 18 4 
 
 19 
 
 20 6 
 
 3X12 
 
 12 
 
 21 6 
 
 21 8 
 
 23 2 
 
 24 
 
 25 9 
 
 3X12 
 
 16 
 
 19 7 
 
 19 8 
 
 21 1 
 
 21 9 
 
 23 5 
 
 2X14 
 
 12 
 
 22 
 
 22 2 
 
 23 8 
 
 24 4 
 
 26 3 
 
 2X14 
 
 16 
 
 20 
 
 20 1 
 
 21 6 
 
 22 2 
 
 23 10 
 
 2X14 
 
 12 
 
 23 8 
 
 23 10 
 
 25 6 
 
 26 3 
 
 28 3 
 
 2^X14 
 
 16 
 
 21 6 
 
 21 8 
 
 23 2 
 
 23 10 
 
 25 8 
 
 3X14 
 
 12 
 
 25 4 
 
 25 4 
 
 27 1 
 
 28 
 
 30 1 
 
 3X14 
 
 16 
 
 23 
 
 23 
 
 24 7 
 
 25 4 
 
 27 4 
 
672 WOODEN FLOORS. 
 
 TABLE ^11. MAXIMUM SPAN FOR FLOOR JOISTS. 
 
 OFFICE BUILDINGS. 
 Total load, 93 pounds per square foot. 
 
 Size of 
 Joists. 
 
 Dist. on 
 Centres. 
 
 White Pine 
 
 Spruce or 
 Norway 
 Pine. 
 
 Oregon or 
 Texas Pine 
 
 Georgia 
 Pine. 
 
 
 Ins. 
 
 Ft. Ins. 
 
 Ft. Ins. 
 
 Ft. Ins. 
 
 Ft. Ins. 
 
 3X8 
 
 12 
 
 12 10 
 
 13 9 
 
 14 2 
 
 15 4 
 
 3X8 
 
 16 
 
 11 8 
 
 12 6 
 
 12 10 
 
 13 10 
 
 2X10 
 
 12 
 
 14 1 
 
 15 1 
 
 15 6 
 
 16 7 
 
 2X10 
 
 16 
 
 12 9 
 
 13 8 
 
 14 1 
 
 15 2 
 
 3X10 
 
 12 
 
 16 1 
 
 17 3 
 
 17 9 
 
 19 2 
 
 3X10 
 
 16 
 
 14 8 
 
 15 8 
 
 16 2 
 
 17 5 
 
 2X12 
 
 12 
 
 16 10 
 
 18 1 
 
 18 8 
 
 20 1 
 
 2X12 
 
 16 
 
 15 4 
 
 16 5 
 
 17 
 
 18 3 
 
 Total load, 96 pounds per square foot. 
 
 3X12 
 
 12 
 
 19 2 
 
 20 6 
 
 21 2 
 
 22 9 
 
 3X12 
 
 16 
 
 17 5 
 
 18 7 
 
 19 3 
 
 20 8 
 
 2X14 
 
 12 
 
 19 6 
 
 20 10 
 
 21 7 
 
 23 2 
 
 2X14 
 
 16 
 
 17 9 
 
 19 
 
 19 7 
 
 21 2 
 
 2^X14 
 
 12 
 
 21 1 
 
 22 6 
 
 23 2 
 
 25 
 
 2X14 
 
 16 
 
 19 2 
 
 20 4 
 
 21 2 
 
 22 8 
 
 3X14 
 
 12 
 
 22 4 
 
 23 10 
 
 24 8 
 
 27 7 
 
 3X14 
 
 16 
 
 20 4 
 
 21 8 
 
 22 5 
 
 24 1 
 
 See remarks, page 670. 
 
 TABLE VIII. MAXIMUM SPAN FOR FLOOR JOISTS. 
 
 CHURCHES AND THEATRES WITH FIXED SEATS. 
 Total load, 102 pounds per square foot. 
 
 Size of 
 Joists. 
 
 Dist. on 
 
 Centres. 
 
 White Pine 
 
 Spruce or 
 Norway 
 Pine. 
 
 Oregon or 
 Texas Pine 
 
 Georgia 
 Pine. 
 
 
 Ins. 
 
 Ft. Ins. 
 
 Ft. Ins. 
 
 Ft. Ins. 
 
 Ft. Ins. 
 
 3X8 
 
 12 
 
 12 6 
 
 13 4 
 
 13 9 
 
 14 10 
 
 3X8 
 
 16 
 
 11 4 
 
 12 2 
 
 12 6 
 
 13 6 
 
 2X10 
 
 12 
 
 13 7 
 
 14 7 
 
 15 1 
 
 16 2 
 
 2X10 
 
 16 
 
 12 4 
 
 13 3 
 
 13 8 
 
 14 9 
 
 3X10 
 
 12 
 
 15 8 
 
 16 9 
 
 17 3 
 
 18 7 
 
 3X10 
 
 16 
 
 14 2 
 
 15 2 
 
 15 8 
 
 16 10 
 
 2X12 
 
 12 
 
 16 5 
 
 17 7 
 
 18 1 
 
 19 6 
 
 2X12 
 
 16 
 
 14 10 
 
 15 Tl 
 
 16 5 
 
 17 8 
 
 Total load, 105 pounds per square foot. 
 
 3X12 
 
 12 
 
 18 7 
 
 19 11 
 
 20 6 
 
 22 1 
 
 3X12 
 
 16 
 
 16 10 
 
 18 1 
 
 18 7 
 
 20 1 
 
 2X14 
 
 12 
 
 19 
 
 20 3 
 
 20 10 
 
 22 6 
 
 2X14 
 
 16 
 
 17 3 
 
 18 5 
 
 19 
 
 20 6 
 
 2^X14 
 
 12 
 
 20 4 
 
 21 9 
 
 22 6 
 
 24 3 
 
 2^X14 
 
 16 
 
 18 7 
 
 19 10 
 
 20 6 
 
 22 1 
 
 3X14 
 
 12 
 
 21 8 
 
 23 2 
 
 23 10 
 
 25 9 
 
 3X14 
 
 16 
 
 19 8 
 
 21 1 
 
 21 9 
 
 23 4 
 
WOODEN FLOORS. 673 
 
 TABLE IX. MAXIMUM SPAN FOR FLOOR JOISTS. 
 
 ASSEMBLY HALLS AND CORRIDORS. 
 Total load, 123 pounds per square foot. 
 
 Size of 
 
 Joists. 
 
 Dist. on 
 
 Centres. 
 
 White Pine 
 
 Spruce or 
 Norway 
 Pine. 
 
 Oregon or 
 Texas Pine 
 
 Georgia 
 Pine. 
 
 
 Ins. 
 
 Ft. Ins. 
 
 Ft. Ins. 
 
 Ft. Ins. 
 
 Ft. Ins. 
 
 3X8 
 
 12 \ 
 
 '11 7 
 
 12 7 
 
 13 
 
 14 
 
 3X8 
 
 16 
 
 10 8 
 
 11 4 
 
 11 9 
 
 12 8 
 
 2X10 
 
 12 
 
 12 10 
 
 13 9 
 
 14 2 
 
 15 2 
 
 2X10 
 
 16 
 
 11 7 
 
 12 6 
 
 12 10 
 
 13 10 
 
 3X10 
 
 12 
 
 14 8 
 
 15 8 
 
 16 2 
 
 17 5 
 
 3X11 
 
 16 
 
 13 4 
 
 14 3 
 
 14 9 
 
 15 10 
 
 2X12 
 
 12 
 
 15 4 
 
 16 6 
 
 17 
 
 18 3 
 
 2X12 
 
 16 
 
 14 
 
 15 
 
 15 5 
 
 16 7 
 
 Total load, 126 pounds per square foot. 
 
 3X12 
 
 12 
 
 17 6 
 
 18 8 
 
 19 3 
 
 20 9 
 
 3X12 
 
 16 
 
 15 10 
 
 17 
 
 17 7 
 
 18 11 
 
 2X14 
 
 12 
 
 17 10 
 
 19 1 
 
 19 8 
 
 21 2 
 
 2X14 
 
 16 
 
 16 2 
 
 17 4 
 
 17 11 
 
 19 3 
 
 2X14 
 
 12 
 
 19 3 
 
 20 6 
 
 21 2 
 
 22 9 
 
 2^X14 
 
 16 
 
 17 6 
 
 18 8 
 
 19 3 
 
 20 9 
 
 3 + 14 
 
 12 
 
 20 5 
 
 21 9 
 
 22 6 
 
 24 3 
 
 3X14 
 
 16 
 
 18 7 
 
 19 10 
 
 20 6 
 
 22 1 
 
 See remarks, page 670. 
 
 TABLE X. MAXIMUM SPAN FOR FLOOR JOISTS. 
 
 RETAIL STORES. 
 Total load, 174 pounds per square foot. 
 
 Size of 
 Joists. 
 
 Dist. on 
 Centres. 
 
 White 
 Pine. 
 
 Spruce or 
 Norway 
 Pine. 
 
 Oregon or 
 Texas Pine. 
 
 Georgia 
 Pine. 
 
 
 Ins. 
 
 Ft. Ins. 
 
 Ft. Ins. 
 
 Ft. Ins. 
 
 Ft. Ins. 
 
 3X8 
 
 12 
 
 11 6 
 
 12 v 5 
 
 14 1 
 
 14 9 
 
 3X8 
 
 16 
 
 9 11 
 
 10 2 
 
 12 2 
 
 12 9 
 
 2X10 
 
 12 
 
 11 8 
 
 12 8 
 
 14 5 
 
 15 1 
 
 2X10 
 
 16 
 
 10 2 
 
 10 11 
 
 12 5 
 
 13 1 
 
 3X10 
 
 12 
 
 14 4 
 
 15 6 
 
 17 7 
 
 18 7 
 
 3X10 
 
 16 
 
 12 5 
 
 13 5 
 
 15 2 
 
 16 
 
 2X12 
 
 12 
 
 14 1 
 
 15 2 
 
 17 2 
 
 18 2 
 
 2X12 
 
 16 
 
 12 2 
 
 13 1 
 
 14 11 
 
 15 8 
 
 Total load, 177 pounds per square foot. 
 
 3X12 
 
 12 
 
 17 2 
 
 18 5 
 
 20 11 
 
 22 1 
 
 3X12 
 
 16 
 
 14 10 
 
 16 
 
 18 2 
 
 19 1 
 
 2X14 
 
 12 
 
 16 3 
 
 17 7 
 
 19 11 
 
 21 1 
 
 2X14 
 
 16 
 
 14 2 
 
 15 2 
 
 17 3 
 
 18 2 
 
 2^X14 
 
 12 
 
 18 2 
 
 19 7 
 
 22 3 
 
 23 6 
 
 2X14 
 
 16 
 
 15 9 
 
 17 
 
 19 3 
 
 20 4 
 
 3X14 
 
 12 
 
 19 11 
 
 21 6 
 
 24 5 
 
 25 8 
 
 3X14 
 
 16 
 
 17 . 3 
 
 18 7 
 
 21 2 
 
 22 3 
 
674 
 
 WOODEN FLOORS. 
 
 TABLE XL MAXIMUM SPAN FOR RAFTERS. 
 
 A. SHINGLED ROOFS NOT PLASTERED.* 
 Total load, 48 pounds per square foot 
 
 Size of 
 Joists. 
 
 Dist. on 
 Centre. 
 
 Hemlock 
 
 White 
 Pine. 
 
 Spruce or 
 Norway 
 Pine. 
 
 Oregon or 
 Texas 
 Pine. 
 
 Georgia 
 Pine. 
 
 
 Ins. 
 
 Ft Ins. 
 
 Ft. Ins. 
 
 Ft. Ins. 
 
 Ft. Ins. 
 
 Ft. Ins. 
 
 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 
 
 11 1 
 
 11 7 
 
 12 6 
 
 14 2 
 
 15 
 
 2X6 
 
 20 
 
 9 11 
 
 10 4 
 
 11 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 11 
 
 20 
 
 2X8 
 
 20 
 
 13 3 
 
 13 10 
 
 14 11 
 
 16 11 
 
 17 10 
 
 2X8 
 
 24 
 
 12 1 
 
 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 
 
 15 1 
 
 15 9 
 
 17 
 
 19 3 
 
 20 4 
 
 B. SLATE ROOFS NOT PLASTERED, OR SHINGLE ROOFS 
 PLASTERED.* 
 
 ^ _ ,*, Total load, 57 pounds per square foot. 
 
 Size of 
 Joists. 
 
 Dist. on 
 Centres. 
 
 Hemlock 
 
 White 
 Pine. 
 
 Spruce. 
 
 Oregon 
 Pine. 
 
 Georgia 
 Pine. 
 
 
 Ins. 
 
 Ft. Ins. 
 
 Ft. Ins. 
 
 Ft. Ins. 
 
 Ft. Ins. 
 
 Ft. Ins. 
 
 2X4 
 
 16 
 
 6 9 
 
 7 1 
 
 7 7 
 
 8 8 
 
 9 2 
 
 2X4 
 
 20 
 
 6 
 
 6 4 
 
 6 9 
 
 7 9 
 
 8 2 
 
 2X6 
 
 16 
 
 10 2 
 
 10 7 
 
 11 6 
 
 13 
 
 13 8 
 
 2X6 
 
 20 
 
 9 1 
 
 9 6 
 
 10 2 
 
 11 7 
 
 12 3 
 
 3X6 
 
 16 
 
 12 6 
 
 13 
 
 14 1 
 
 15 11 
 
 16 9 
 
 3X6 
 
 20 
 
 11 1 
 
 11 8 
 
 12 7 
 
 14 3 
 
 15 
 
 2X8 
 
 16 
 
 13 7 
 
 14 2 
 
 15 3 
 
 17 4 
 
 18 3 
 
 2X8 
 
 20 
 
 12 2 
 
 12 8 
 
 13 8 
 
 15 6 
 
 16 4 
 
 2X8 
 
 24 
 
 11 1 
 
 11 7 
 
 12 6 
 
 14 2 
 
 14 11 
 
 3X8 
 
 16 
 
 16 7 
 
 17 4 
 
 13 9 
 
 21 3 
 
 22 5 
 
 3X8 
 
 20 
 
 14 10 
 
 15 6 
 
 16 9 
 
 19 
 
 20 1 
 
 3X8 
 
 24 
 
 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 1 
 
 19 4 
 
 20 6 
 
 2X10 
 
 24 
 
 13 10 
 
 14 6 
 
 15 7 
 
 17 8 
 
 18 8 
 
 * These tables allow for a snowfall of 2 feet. In the Southern States the 
 spans in section A will be safe for slate or gravel roofs, if the joists are full 
 to dimensions. 
 
WOODEN FLOOHS. 
 
 675 
 
 TABLE XI. MAXIMUM SPAN FOR RAFTERS (continued). 
 
 C. SLATE ROOFS PLASTERED, OR GRAVEL ROOFS NOT 
 
 PLASTERED.* 
 Total load, 66 pounds per square foot. 
 
 Size of 
 
 Joists. 
 
 Dist. on 
 Centres. 
 
 Hemlock 
 
 White 
 Pine. 
 
 Spruce or 
 Norway 
 Pine. 
 
 Oregon or 
 Texas 
 Pine. 
 
 Georgia 
 Pine. 
 
 
 Ins. 
 
 Ft. Ins. 
 
 Ft. Ins. 
 
 Ft. Ins. 
 
 Ft. Ins. 
 
 Ft. Ins. 
 
 2X6 
 
 16 
 
 9 5 
 
 9 10 
 
 10 8 
 
 12 1 
 
 12 9 
 
 2X6 
 
 20 
 
 8 6 
 
 8 10 
 
 9 6 
 
 10 9 
 
 11 5 
 
 3X6 
 
 16 
 
 11 7 
 
 12 1 
 
 13 1 
 
 14 10 
 
 15 7 
 
 3X6 
 
 20 
 
 10 4 
 
 10 10 
 
 11 8 
 
 13 3 
 
 14 
 
 2X8 
 
 16 
 
 12 7 
 
 13 2 
 
 14 2 
 
 16 2 
 
 17 
 
 2XC 
 
 20 
 
 11 3 
 
 11 9 
 
 12 9 
 
 14 5 
 
 15 2 
 
 2X8 
 
 24 
 
 10 3 
 
 10 9 
 
 11 7 
 
 13 2 
 
 13 10 
 
 3X8 
 
 16 
 
 15 5 
 
 16 1 
 
 17 5 
 
 19 9 
 
 20 10 
 
 3X8 
 
 20 
 
 13 9 
 
 14 5 
 
 15 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 1 
 
 14 8 
 
 15 11 
 
 18 
 
 19 
 
 2X10 
 
 24 
 
 12 10 
 
 13 5 
 
 14 6 
 
 16 6 
 
 17 5 
 
 2X12 
 
 16 
 
 18 10 
 
 19 9 
 
 21 4 
 
 24 2 
 
 25 6 
 
 2X12 
 
 20 
 
 16 10 
 
 17 8 
 
 19 1 
 
 21 8 
 
 22 10 
 
 2X12 
 
 24 
 
 15 5 
 
 16 1 
 
 17 5 
 
 19 9 
 
 20 10 
 
 * These tables are intended for climates where a snowfall of 2 feet maybe 
 expected. In the Southern States, where there is no snow to speak of, the 
 spans in the first sections will be safe for slate or gravel roofs if the joists are 
 sawn full to dimensions. 
 
 To Determine the Strength of an Existing Floor. 
 
 When a building is leased for mercantile or manufacturing 
 purposes the tenant will generally desire to know the greatest 
 load which it will be safe to put upon the floors, and some build- 
 ing laws require that the safe load for the floors in certain classes 
 of buildings shal 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, 
 including the weight of the construction, flooring, and ceiling, 
 while the "safe load" refers to the maximum load which may 
 safely be placed upon the floor. The safe load is found by first 
 computing the safe strength and then subtracting the weight 
 of the materials forming the floor, including the ceiling below, 
 
0/0 
 
 WOODEN FLOORS. 
 
 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 example will serve to show the process of 
 determining the safe load for an ordinary warehouse floor. 
 
 EXAMPLE 4. What is the safe load per square foot for a floor 
 framed as shown in Fig. 4, all 'of the timber being Eastern spruce, 
 
 it 
 
 ^ Stirrup 
 
 10 "x 14" 
 
 1 
 
 Load from Stairs 
 1800 Ibs. y 
 
 Stirrup 
 
 Fig. 4 
 
 the beams being covered with two thicknesses of f-inch flooring 
 and having a corrugated iron ceiling below ? 
 
 The first step will be to find the safe strength of the 22-ft. joists. 
 As this is a warehouse floor we will use the tables for strength 
 entirely. From Table VI. , Chapter XVI., we find the safe strength 
 of a 1X14 spruce beam of 22 ft. span to be 1,247 Ibs., hence the 
 strength of a 2J"X 14" beam will be 21 X 1,247, or 3,117 Ibs. As 
 the joists are 16 ins. on centres, each joist supports a floor area 
 of 1 JX 22 ft. =29 J sq. ft. The safe strength per square foot of this 
 portion of the floor will therefore be 3,117-^29.3 or, 106 Ibs. The 
 weight of the floor per square foot will be about 6J Ibs. for the 
 joists, 6 Ibs. for the flooring, and 1 Ib. for the corrugated iron 
 ceiling, or, say 14 Ibs. in all. Therefore the safe load per square 
 foot for the 22-ft. joists will be 106-14, or 92 Ibs. 
 
 We will next find the safe load for the 4X14 headers at each side 
 
WOODEN FLOORS. 677 
 
 of the stair well. As the tail beams are framed into the headers, 
 we should deduct one inch from the thickness of the beam for 
 the loss of strength in framing, leaving 3"X14" for the effective 
 dimensions of the headers. From Table VI., Chapter XVI., we 
 find the safe strength of a 1X14, 12-ft. span to be 2,286 Ibs. 
 Hence the strength of the 3 X 14 will be 6,858 Ibs. The floor area 
 supported by each header is 4JX12 ft. =54 sq. ft.; hence the 
 safe strength of the .header per square foot of floor =6, 858 ^54 = 
 127 Ibs. Deducting the weight of the floor per sq. ft. 14 Ibs., 
 we have 113 Ibs. per sq. ft. for the safe load. 
 
 Strength of Trimmer A. Trimmer A supports about the 
 same amount of flooring as one of the common joists, and also 
 the ends of the headers. Deducting 2J ins., the thicknesses of 
 the common joists, we have a 5" Xl 4" beam left to support 
 the headers. As the headers are supported in iron stirrups no 
 deduction in strength need be made for framing. 
 
 To find the safe strength of a beam loaded with two concen- 
 trated loads, equally distant from the supports, we must use 
 formula 14, Chapter XVI. In this case ra=8' 10" or 8f, and 
 A =70. 
 
 5X196X70 
 Applying the formula safe load at each point = - 5 =* 
 
 4XO(f 
 
 1,942 Ibs. The floor area supported by one stirrup is equal to 
 one-half of the area supported by the header, or 27 sq. ft. ; hence 
 the safe strength per square foot of the 5X 14 header is 1,942-7-27, 
 or 72 Ibs., and deducting 14 Ibs. for weight of the floor, we have 
 58 Ibs. per square foot as the safe load that the trimmer will sup- 
 port on the floor at each side of the stairs. Considering that the 
 safe load for the 2 J ins. which we deducted to take the place of a 
 common joist is 92 Ibs., we might place the safe load for the trim- 
 mer at an average of 92 and 58, or 75 Ibs. 
 
 Trimmer B. This timber has to support the same floor 
 loads as trimmer A, and also the bottom of a flight of stairs for 
 which an allowance of at least 1,800 Ibs. should be made. 
 
 This stair load being practically concentrated at the centre of 
 the trimmer is equivalent to a distributed load of 3,600 Ibs. As 
 the safe load for a IX 14-inch joist of 22 ft. span is 1,247 Ibs., it 
 will require a thickness = 3,600 -=-1, 247, or 2J ins., to support the 
 stairs, leaving 7J ins. to support the floor loads. As this is | 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 
 
WOODEN FLOORS. 
 
 given time, it would be safe to rate the strength of the floor at 
 each side of the stairway at 75 Ibs. per square foot, live load, and 
 beyond the stairway at 92 Ibs. 
 
 Partitions. When the floor supports partitions their weight 
 and any load resting upon them must be taken into account in 
 determining the safe load for the floor. If the 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 the 
 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 
 by Fig. 4 have to support a plastered partition 12 ft. high run- 
 ning across the joists half-way between the walls, what will be 
 the safe load for the floor? 
 
 Ans. A plastered partition with 2"X4" or 2"X6" studding 
 16 ins. on centres will weigh about 20 Ibs. per sq. ft. ; hence a 
 partition 12 ft. high will weigh 240 Ibs. per lineal foot. As the 
 joists are 16 ins. on centres, each joist will support 1 J lineal ft. 
 of partition weighing 320 Ibs. As this load is concentrated at the 
 centre of the joists it is equivalent to a distributed load of 640 
 Ibs. In Example 4, we found the safe distributed load for a 
 2J"xl4" spruce joist of 22ft. span to be 3,117. Subtracting 
 640 Ibs. from this we have 2,477 Ibs., which may be used for 
 the floor. As the floor area supported by one joist is 29 J sq. ft., 
 the safe strength of the floor per sq. ft. will be 2,477 -*- 29 J, or 
 84 Ibs., and the safe load 70 Ibs. Hence the partition decreases 
 the safe load by 22 Ibs. per square foot. 
 
 Whenever the upper-floor joists are supported by 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 care- 
 fully computed. 
 
 Bridging of Floor Beams. By "bridging" is meant 
 a system of bracing floor beams, either by means of small struts, 
 as in Fig. 5, or by means of single pieces of boards set at right 
 angles to the joists, and fitting in between them. 
 
 The effect of this bracing is decidedly beneficial in sustaining 
 any concentrated weight upon a floor; but it does not materially 
 strengthen a floor to resist a uniformly distributed load. The 
 bridging also stiffens the joists, and prevents them from turning 
 sideways. It is customary to insert rows of cross-bridging 
 at from every five to eight feet in the length of the beams; 
 and to be effective they should be in straight lines along the floor, 
 
WOODEN FLOORS. 
 
 679 
 
 so that each strut may abut directly opposite those adjacent to 
 it. The method of bridging shown in Fig. 1, and known as 
 "cross-bridging/' is considered 
 to be by far the best, as it al- 
 lows 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 board are used. 
 
 The bridging should be of 1 J 
 inch by 3-inch stock, for joists 
 2" X 10"and under, and 2" X 3" 
 stock for 12" and 14" joists. 
 
 Framing of Floor 
 Beams. In dwellings, tene- 
 ment and lodging houses, it 
 is a common practice to frame 
 the ends of the tail beams into Fig. 5 
 
 the headers, and very often the 
 
 ends of the headers are framed into the trimmers. For light 
 floors, with moderate spans, it is safe to frame the tail beams into 
 a header, provided the latter is strong enough to carry the load and 
 allow 1 inch in thickness for the mortising. Headers carrying not 
 
 Fig. 6 
 
 more than two tail beams may also be framed into the trimmers, 
 but all headers six feet long or over should be carried in 
 
680 
 
 WOODEN FLOORS. 
 
 joist hangers or stirrups, and in warehouses and all first-class 
 buildings all framing should be done by means of joist hangers. 
 As to the best shape and proportions for the tenon on the end 
 of the tail beam or header, that shown by Fig. 6 gives probably 
 as large a proportion of the strength of the timbers as it is pos- 
 sible to utilize, although for tail beams the author believes that 
 a single tenon like that shown in Fig. 7 is fully as strong, especially 
 when the header is built up of two-inch plank spiked together. 
 In either case, if the floor is loaded to its full strength, the tail 
 beam will split at the bottom of the tenon as shown in Fig. 8. 
 
 -XI 
 
 Fig. 7 
 
 Fig. 8 
 
 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, according to whether one or two beams are to 
 be supported. To prevent the floor from spreading and thus 
 permitting 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 figure the strength of a stirrup, multiply the sectional area 
 of the iron in square inches by 12,000 Ibs. 
 
 The following sizes of iron should in general be used for the 
 size of joist to be supported: 
 
 Size of Joist or Timber Section of 
 
 to be supported. Stirrup. 
 
 2X 8to3XlO i"X2J" 
 
 4X10 to 4X12 f"X2i" 
 
 6X12 to 3X14 f"X3 " 
 
 8X12 to 4X14 J"X3J" 
 
 6X14 J"X4 " 
 
 8X14 to 10X14 f"X4 " 
 
WOODEN FLOORS, 
 
 681 
 
 Joist Hangers. Aside from the matter of strength there 
 are objections to the use of stirrups, in that if the timber on 
 which they rest is not perfectly dry, the stirrup will settle by 
 an amount equal to the shrinkage of the beam on which it rests, 
 
 DOUBLE STIRRUP 
 
 .J ^ '1 
 
 SINGLE STIRRUP AND JOI.NT BOLT 
 
 Fig. 9 
 
 and let the header down with it; the projection of the iron above 
 the top of the timbers necessitates cutting out the flooring, and 
 where the stirrups are exposed they do not present a neat 
 appearance. 
 
 Fig. 10 
 
 Duplex Joist Hanger. 
 
 Fig. II 
 
 Goetz Joist Hanger. 
 
 Within the past fifteen years several patented hangers have 
 been placed upon the market, which are claimed to be superior 
 
682 
 
 WOODEN FLOORS. 
 
 to the wrought-iron stirrup. The first of these in point of time 
 was the Duplex hanger, shown in Fig. 10. This was quickly fol- 
 lowed by the Goetz hanger, shown in Fig. 11. Both styles have 
 been extensively used, and have proven perfectly satisfactory. 
 Both are made in sizes to fit all regular sizes of joists or timbers, 
 and have ample strength for the purpose for which they are 
 intended. As shown by the illustrations, they are made to be 
 inserted in round holes bored in the side of the carrying timbers, 
 at or a little above the centre line. With these hangers the effect 
 of shrinkage is reduced one-half, and the other two objections to 
 the stirrup, previously mentioned, are overcome. The duplex 
 hanger has ridges on the inside of the side brackets to hold the 
 beam. 
 
 When the timber to be supported exceeds 6 ins. in breadth, 
 the Duplex hanger is made in two parts, and is bolted to both 
 beams, an illustration of the larger size hangers being given in 
 Chapter XXII. Fig. 12 shows the Duplex I-beam hanger for 
 
 Fig. 12 
 
 Duplex I-Beam Hangers. 
 
 framing floor joists to I-beams. These hangers are made to 
 exactly fit into the flange of the I-beam, they have a rib in 
 bottom of hanger -J" high, which serves as a tie when the joist 
 is placed in the hanger, and they provide a bearing of 4J inches 
 for the joists. These hangers are made to carry all regular 
 sizes of joists from 2"X6" up to 6"X 16", and in the opinion of 
 the author offer the best device for framing wooden joists to 
 I-beams of the same depth. The hangers are all of uniform 
 height and a }" hole punched 6" from the bottom of the beam 
 will fit any of them. The hangers are bolted to the web of the 
 I-beam. 
 
 Fig. 13 shows a similar hanger made to support the wall end 
 
WOODEN FLOORS. 
 
 683 
 
 of a floor joist. The writer believes this to be much superior 
 to the method of building the joist 
 into the wall, as it absolutely pre- 
 vents dry-rot, and permits, the joist 
 to fall, in case of fire, without 
 throwing the wall. It also gives 
 the weight a good bearing on the 
 wall. 
 
 Other illustrations of wall hang- 
 ers are given in Chapter XXII. 
 
 The Van Dorn Hanger, illus- 
 trated by Fig. 14, IB essentially a 
 stirrup forged from high-grade F'9* ' 3 
 
 steel. The few tests that have been Bu P lex Brick Wal1 Han s er - 
 made would seem to indicate that it possesses a little more 
 resistance to bending than the ordinary stirrup, while it gives a 
 wider bearing for the joist, and presents a much neater appear- 
 ance. 
 
 Fig. 15 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. 16. 
 
 Fig. 14 
 
 Fig. 15 
 
 Although the author knows of no test of the strength of a Van 
 Dorn I-beam hanger, it would seem as though it must be much 
 stronger than the pattern made for wooden beams, on account 
 
684 
 
 WOODEN FLOORS. 
 
 of the clinch over the flange of the I-beam. The Van Dora 
 hangers have been used in many important buildings. 
 
 
 Fig. 16 
 
 National Hanger. 
 
 Figs. 17 and 18 show two other patented joist hangers of the 
 stirrup type, which are forged from plate steel. Both of these 
 
 hangers are also made 
 for building into brick 
 walls, and to go over 
 steel beams. The na- 
 tional hanger is a par- 
 ticularly good one on 
 account of the flange 
 on top, which should 
 help to a considerable 
 degree in distributing 
 the load over the top 
 of the beam. The 
 
 Fig. 18 larger hangers of this 
 
 Lane Hanger. style have holes in the 
 
 top for large spikes. The Lane hanger is made very light. 
 
 Comparative Strength of Different Styles of Joist 
 Hangers. Although the tests that have been made to deter- 
 mine the strength of different hangers are few in number, still 
 enough have been made to show that any one of the hangers 
 described, including the common stirrup, are abundantly strong 
 for any single floor beam not exceeding 4" X 14" in size. It is 
 only in the case of a header or trimmer which supports a con- 
 siderable floor area that the strength need be considered at all 
 
WOODEN FLOORS. 
 
 685 
 
 From tests made at the Massachusetts Institute of Technology, 
 and later at St. Louis, it would appear that the Duplex hangers 
 are affected the least of any under extreme loads. A two-part 
 hanger, carrying a 10 X 14 
 inch girder, sustained a 
 load of 38,000 Ibs. with- 
 out injury to the hanger 
 itself. A similar hanger 
 held until loaded to 
 39,550 Ibs., when one side 
 broke off short under the 
 nipple projecting into the 
 timber, the condition of 
 the hanger after failure 
 being shown by Fig. 19. 
 A common stirrup made 
 
 from f"X2J" wrought 
 
 Fig. 19 
 
 iron failed under a load of 13,750 Ibs. by bending and pulling 
 over the header, as shown in Fig. 20. A 6"X12" Van Dora 
 hanger "began to straighten out under a load of 13,300 Ibs., 
 and failed as in Fig. 21 at a load of 18,750 Ibs." * 
 
 Single hangers of the 
 stirrup type do not break, 
 but fail by the bending 
 up of the portion which 
 lays over the top of the 
 header, as in Figs. 20 and 
 21. They also appear to 
 crush the wood under 
 them, particularly at the 
 edge, to a very much 
 greater degree than does 
 the spool of the Duplex 
 hanger. 
 
 With a double stirrup 
 the ultimate strength is 
 measured by the strength 
 Fig- 20 O f the iron. Thus a 
 
 double stirrup made of f-"X2J" wrought iron was loaded 
 up to 57,650 Ibs. (28,825 Ibs. on each side), when' it broke 
 
 * Chas. E. Fuller, M.E.D., Dept. M.I.T. 
 
686 
 
 WOODEN FLOORS. 
 
 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 would to some degree 
 
 prevent the top of a stirrup 
 from springing up. The 
 tests that have been made 
 of the Duplex hangers 
 show conclusively that 
 where only a single hanger 
 is used the holes which are 
 bored in the header do not 
 affect its strength, at least 
 when the load is within the 
 safe limit, and a test made 
 at Baltimore, Md., Aug. 24, 
 1904, with 2"X12" joists, 
 spaced 12 ins. on centres 
 and suspended by duplex 
 hangers let into a header 
 formed of three 3"X12" 
 j oists , spik ed together , would 
 seem to prove that even 
 when the holes are 12 ins. 
 on centres they do not 
 
 weaken the header. The only record of the failure of any form 
 of hanger when in actual use in a building, of which the author is 
 aware, is that of a case in Minneapolis, where a portion of six 
 floors of a warehouse fell, on Nov. 7, 1902, through the failure of 
 a wall hanger made from a 4" X 2" Xi" structural steel angle, 
 sheared and bent as in Fig. 17, and riveted to a bearing-plate 
 8"Xl6"Xi". 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. The actual load on the hanger was 
 about 15,000 Ibs. See Engineering News of Nov. 20, 1902. 
 
 Fig. 21 
 
MILL AND WAREHOUSE CONSTRUCTION. 687 
 
 CHAPTER XXII. 
 MILL AND WAREHOUSE CONSTRUCTION'. 
 
 Mill Construction. This term is commonly used to des- 
 ignate a method of construction brought about largely through 
 the influence of the factory mutual insurance companies of New 
 England, and especially through the efforts of Mr. William B. 
 Whiting, whose mechanical judgment, experience, and skill as a 
 manufacturer were for many years devoted to the interests of 
 these 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 the past twenty years, is probably 
 due more to the influence of Mr. Edward Atkinson, president 
 of the Boston Manufacturers Mutual Insurance Co. and director 
 of the Insurance Engineering Experiment Station at Boston, than 
 to that of any other individual. 
 
 The motive of mill construction is to reduce the fire risk to 
 its lowest point, without going to the expense of fire-proof con- 
 struction. The mill construction recommended by the Factory 
 Mutual Companies has proved to be so safe as a whole, and 
 such factories have been covered by mutual insurance at so 
 little cost as to render it wholly inexpedient, or even unneces- 
 sary, for the owners of textile factories and workshops to take 
 any other method into consideration. 
 
 The entire subject of Slow-burning or Mill Construction, as 
 applied to factories, is most admirably described and illustrated 
 in Report No. 5, of the Insurance Engineering Station, No. 31 
 Milk St., Boston, Mass.,* from which the author has by permis- 
 sion taken the following illustrations and descriptions. 
 
 What Mill Construction Is. 
 
 [From Heport No. 5 of the Insurance Engineering Station.J 
 1. Mill construction consists in so disposing the timber and 
 plank in heavy solid masses as to expose the least number of 
 
 * This Report may be procured for 25 cents. 
 
688 MILL AND WAREHOUSE CONSTRUCTION. 
 
 corners or ignitable projections to fire, to the end also that 
 when fire occurs it may be most readily reached by water from 
 sprinklers or hose. 
 
 2. It consists in separating every floor from every other floor 
 by incombustible stops, by automatic hatchways, by encasing 
 stairways either in brick or other incombustible partitions, 
 so that a fire shall be retarded in passing from floor to floor to 
 the utmost that is consistent with the use of wood or any material 
 in construction that is not absolutely fire-proof. 
 
 3. It consists in guarding the ceilings over all specially haz- 
 ardous stock or processes with fire-retardent material such as 
 plastering laid on wire lath or expanded metal, or upon wooden 
 dovetailed lath, following the lines of the ceiling and of the 
 timbers without any interspaces between the plastering and 
 the wood; or else in protecting ceilings over hazardous places 
 with asbestos air-cell board, sheet metal, Sackett wall board, or 
 other fire-retardent. 
 
 4. It consists not only in so constructing the mill, workshop, 
 or warehouse that fire shall pass as slowly as possible from one 
 part of the building to another, but also in providing all suitable 
 safeguards against fire. 
 
 What Mill Construction is Not, 
 
 1. Mill construction does not consist in disposing a given 
 quantity of materials so that the whole interior of a building 
 becomes a series of wooden cells, being pervaded with concealed 
 spaces, either directly connected each with the other or by 
 cracks through which fire may freely pass where it cannot be 
 reached by water. 
 
 2. It does not consist in an open-timber construction of floors 
 and roof resembling mill construction, but of light and insuffi- 
 cient size in timbers and thin planks, without fire-stops or fire- 
 guards from floor to floor. 
 
 3. It does not consist in connecting floor with floor by com- 
 bustible wooden stairways encased in wood less than two inches 
 thick. 
 
 4. It does not consist in putting in very numerous divisions 
 or partitions of light wood. 
 
 5. It does not consist in sheathing brick walls with wood, espe- 
 cially when the wood is set off from the wall by furring, even 
 if there ctre stops behind the furring. 
 
MILL AND WAREHOUSE CONSTRUCTION. 689 
 
 6. It does not consist in permitting the use of varnish upon 
 woodwork over which a fire will pass rapidly. 
 
 7. It does not consist in leaving windows exposed to adjacent 
 buildings unguarded by fire-shutters or wired glass. 
 
 8. It is dangerous to paint, varnish, fill or encase heavy tim- 
 bers and thick plank as they are customarily delivered, lest what 
 is called dry-rot should be caused for lack of ventilation or oppor- 
 tunity to season. - 
 
 9. 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, pipos, and hydrants. 
 
 10. It does not consist in using any more wood in finishing the 
 building after the floors and roof are laid than is absolutely 
 necessary, there being now many safe methods available at low 
 cost for finishing walls and constructing partitions with slow- 
 burning or incombustible material. 
 
 It follows that if plastering is to be put upon a ceiling follow- 
 ing the line of the underside of the floor and the timber, it should 
 be plain lime-mortar plastering, which is sufficiently porous to 
 permit seasoning. The addition of the skim coat of lime putty 
 is hazardous, especially if the top floor is laid upon resin-sized 
 or asphalt paper. This rule applies to almost all timber as now 
 delivered. 
 
 All the faults above recited have been committed in buildings 
 purporting to be of mill construction, and all form a part of the 
 common practice in "combustible architecture." 
 
 Standard Mill Construction. 
 
 Fig. 1 shows a partial cross-section through a mill of the 
 customary or standard type as revised to Nov., 1902. 
 
 If additional stories are required the walls may be increased 
 in thickness according to the number of stories added, after a 
 computation of the loads which a standard factory may be 
 called upon to sustain. 
 
 Fig. 2 shows an enlarged view of the exterior of two bays, 
 with recessed panels between the piers. Fig. 3 shows the 
 common form of cast-iron pintle, which serves as a cap for the 
 lower column, and a support for the upper column. 
 
 These illustrations are only intended to give general directions 
 for slow-burning or mill construction. They should always be 
 
690 MILL AND WAREHOUSE CONSTRUCTION. 
 
 adapted to the special conditions of each site and of each art 
 for which the buildings are used. 
 
 When a span exceeds twenty-two feet it is judicious to add 
 to the support by hackmatack or iron knees projecting from 
 wall and posts. These knees or braces are not deemed neces- 
 sary even on spans of twenty-five feet when the timbers 
 are of ample dimension. They have sometimes been put into 
 old mills of high and narrow type and have stopped serious 
 vibration in the upper stories. If used, they must be kept 
 bolted closely to timbers and posts, and care should be taken 
 
 3" plank, 2 bays in length, - 
 Breaking Joints every 3 feet 
 
 Roofing;- 4 ply, Tar and Gravel, or Tin 
 
 ^p 
 $g 
 
 il 
 
 ~- K 
 ~~ ^10 "x 12" Rafter* 
 
 /l^To^-Roon Hard wood. 
 3 Thicknesses of Resin-giied paper^x 
 Each layer mopped with Tar; \ 
 
 ^9^"Wro't Iron Dogs 
 
 8"x S* 
 
 .^3" plank, 2 bays in length, 
 / Breaking Joints every 3 fee* 
 
 
 ^ 
 
 * 
 
 o K o o 
 
 
 
 i 
 
 ^-Caat Iroa Wafl Plate 
 ^22" aV 
 
 ^Double Floor Beams 6" x. 14" 
 
 
 IP 
 
 i 
 
 fi 
 
 -^50 
 
 Bays;- About 8 feet 
 
 9* x 9* 
 Iron Pintle-^ 
 
 
 
 
 
 
 
 1 
 
 
 1 
 
 ^10'xlO^ 
 
 
 Fig. I 
 Standard Construction. 
 
 that the load on each side should be practically the same. They 
 are necessary in the self-sustaining frame (Figs. 9 and 11). In 
 computing the size of the timbers in ratio to the working load, 
 regard must be given not only to the weight which is to be 
 carried, but also to the character of the mechanism which is 
 to be operated upon the floor. Beams of sufficient strength to 
 support the weight may be caused to vibrate or deflect under 
 the action of the machinery ; therefore the two factors of weight 
 and vibration must be considered in determining the size or 
 depth of the beams that may be made use of. 
 
 "We do not approve what has sometimes been miscalled mill 
 
MILL AND WAREHOUSE CONSTRUCTION. 691 
 
 Fig. 2 
 
 Detail of Side Walls. 
 
692 MILL AND WAREHOUSE CONSTRUCTION. 
 
 construction, i.e., longitudinal girders resting upon posts and 
 supporting floor-beams spaced four feet, more or less, on centres. 
 This mode of construction not only adds to the quantity of wood 
 used, but the disposal of the timbers obstructs the action of 
 sprinklers, prevents 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." 
 
 a Pintle, Cap and Base, 
 cast in one piece. 
 
 Fig, 3 
 
 The standard plan calls for but one thickness of boards laid over 
 the planks, with three layers of resin-sized paper mopped with 
 tar between. In the best mil]s lately built a board flooring has 
 been laid diagonally upon the plank, over that a top floor of 
 birch or maple, laid lengthwise. The diagonal floor gives great 
 resistance to the lateral strain or vibration; the top floor, espe- 
 cially in alleyways, can be more easily repaired or replaced 
 when worn. This intermediate diagonal flooring is well worth 
 the additional cost. 
 
 The following notes, pertaining to the details of mill construc- 
 tion, are the result of many years' study and observation, and 
 should be carefully noted when preparing plans and specifications 
 for mill construction. 
 
 Timbers, unless known to be absolutely and fully seasoned, 
 should not be encased in any kind of air-proof plastering, nor 
 should they be painted with oil-paints; whitewash, kalsomine, 
 and water-paints may be used as they are porous. Timbers or 
 plank may also be covered in with common lime mortar laid on 
 wire lathing, provided no skim coat of lime putty is added. 
 Ordinary plastering unskimmed is sufficiently porous to permit 
 seasoning. As a rule timbers may be left unprotected, except 
 in very dangerous places, since any fire which will seriously 
 impair and destroy a heavy timber will already have done its 
 work upon other parts of the structure. 
 
MILL AND WAREHOUSE CONSTRUCTION. 693 
 
 In many instances it may be preferable to substitute com- 
 pound beams for single timbers, made by securing two or more 
 beams or thick planks side by side; it being often easier to 
 obtain well-seasoned lumber in smaller dimensions; such com- 
 pound beams, of which the parts may be slightly separated by 
 spaces for ventilation when put together, are less subject to 
 decay. 
 
 Weaving mills can be made more rigid and more capable of 
 resisting the vibration caused by the motion of looms by laying 
 the top floor across the plank and parallel to the beams, nails 
 being driven in diagonal rows. This may brace the floor as 
 firmly as diagonal boarding, and it avoids the increased expense 
 in construction and repairs which ensues from the adoption of 
 that method. 
 
 The edges of the floor plank should be kept clear of the faces 
 of the brick walls by about half an inch, in order to obviate the 
 danger of cracking the walls, which sometimes occurs from the 
 swelling of the plank when laid close against them. These cracks 
 must be covered by strips or battens both above and below. 
 
 To protect the contents of floors below, three thicknesses of 
 tarred paper should be placed between the floor plank and top 
 floor, each layer to be mopped with tar, asphalt/ or similar 
 material, care being taken to break all joints. 
 
 Basement floors can be laid solid upon the natural soil if it 
 is dry, or upon rock or cinder filling, by covering either with a 
 suitable layer of coal-tar concrete. Upon this concrete place an 
 underfloor of two-inch plank. Then lay the top flooring across 
 the plank, and nail in the usual manner. Sills under the plank 
 are not thought to be necessary to the preservation of the 
 floor. If extra support is required to sustain machinery more 
 firmly than it can be upon a plank and board floor, independent 
 foundations of masonry are generally preferred. Cement con- 
 cretes may absorb moisture and promote the decay of timber 
 or plank laid upon them. 
 
 In view of the difficulties which have frequently occurred in 
 preserving basement floors of the ordinary timber construction 
 for 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, where they quickly become 
 saturated with moisture, artificial stone floors are being laid in 
 many of the modern plants. 
 
 If the mill is to be heated by conveying steam through pipes, 
 
694 MILL AND WAREHOUSE CONSTRUCTION. 
 
MILL AND, WAREHOUSE CONSTRUCTION 695 
 
696 MILL AND WAREHOUSE CONSTRUCTION. 
 
 such pipes should be hung overhead. If the modern method, 
 which is probably the best method, of conveying the heat 
 through ducts in the plastered walls should be adopted, provision 
 will be made thereto in the construction of the mill wall. 
 
 The carrying off from the walls of about one-half a roof 
 corresponding to this plan, in a hurricane, calls attention to 
 the necessity of tying, binding, or bolting the timbers of the roof 
 to the walls of the mill in a safe and suitable manner. This is 
 the common practice, but the necessity is sometimes overlooked. 
 
 Belt, Stairway, and Elevator Towers. 
 
 Stairways should always be located in towers or sections 
 of the building, cut off by incombustible walls from all the 
 rooms of the factory, the entrances to each room being guarded 
 with standard fire-doors. 
 
 In modern practice all belts or 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 or unguarded 
 openings in the inner walls of this belt chamber. 
 
 Elevator shafts and belt towers or chambers should be guarded 
 by fire-doors and covered overhead by skylights, glazed with 
 thin glass, protected underneath with wire netting. Hatchways 
 outside the fire-proof shafts should be well guarded by auto 
 matic or self-closing hatches, both to stop the passage of fire 
 and to assure safety to persons. The most important feature 
 in what is called slow-burning construction is to make each 
 and every floor continuous, avoiding belt holes and open ways to 
 the utmost possible extent, so that a fire originating in any 
 one room may be confined to that room or story, if possible. 
 
 Figs. 4 and 5 illustrate a partial section and plan of a cotton 
 mill, showing belt, stair, and elevator towers arranged on the 
 above principle. It should be noted that the water-closets 
 are located in the tower rather than in the manufacturing 
 rooms. 
 
 The boiler-house should be located beyond the engine-room, 
 and separated from the latter by a brick wall with doorway 
 protected by a standard automatic fire-door. 
 
MILL AND WAREHOUSE CONSTRUCTION. 697 
 
 Standard Storehouse Construction. 
 
 Figs. 6, 7, and 8 represent salient points in design for a mill 
 storehouse several stories in height, and include many fea- 
 tures found useful in practice for convenience in operation 
 and also securing the greatest measure of resistance to fire. 
 
 8x8 
 
 2 Thicknesses of Resin-sized paper under 
 Top Flooring. Floor Plank, 2 bays in length 
 breaking jointe every 3 feet 
 
 Fig. 6 
 
 One-half of Transverse Section. 
 
 The size of columns and beams is only for example, differ- 
 ing according to load and span, the drawings not being intended 
 to take the place of the services of any mill engineer, but rather 
 . to assist in such work. It is important that the floor beams 
 should be designed to sustain the greatest load ever to be 
 placed on them, and the stories^ should be made low enough 
 to prevent overloading, and also to prevent bales of material 
 from being piled to great height, the preferable method being 
 to place bales on end. 
 
593 MILL AND WAREHOUSE CONSTRUCTION. 
 
 These floors, with beams of 20 feet span, laid 8 feet on cen 
 tres, will sustain a load of ISO pounds per square foot, which 
 is as much as would be required for raw material or finished 
 goods of a textile or paper mill. The heavy drugs and dye- 
 stuffs would be placed on the ground floor. 
 
 For convenience, as well as to separate the different hazards 
 of raw material and finished goods, the building may be di- 
 vided into sections by fire-walls extending through the roof. 
 
 A storehouse one story in height is recommended in prefer- 
 ence to this design whenever there is sufficient quantity of 
 level land at disposal for this purpose, as being cheaper, more 
 convenient, and, when separated into small divisions by fire- 
 walls, the safest method of storehouse construction. 
 
 The floors in such a building should be continuous, without 
 openings, and of the standard slow-burning construction 
 a type which has not yet been burned through by any fire 
 starting under such a floor, unless there have been openings 
 in the floor. To reduce water damage the floors are not level, 
 but have a camber of two inches in the middle made by iron 
 plates inserted under the columns in the basement. If it 
 should become desirable to use the building for any purpose 
 requiring level floors, they can be reduced to a level by re- 
 moving these plates* Inclined iron tubes, with a light swing- 
 ing cap on the outside, laid in the wall at the level of the floors, 
 act as scuppers for the purpose of removing any water. 
 
 The floor-beams are preferably of Southern pine bolted to- 
 gether in pairs, leaving about one inch space between the 
 beams. At the columns the beams are joined by dogs made 
 of three-fourths inch round iron, driven in at the top, and they 
 are anchored to the walls by cast-iron wall-plates, to which 
 they are secured by means of a rib which fits into a groove 
 crossing the underside of the beam. It is important that 
 there should be a small space at each side and at the end of 
 the beam, in order to allow free ventilation, for the purpose 
 of preventing dry-rot. The Goetz box-anchor is a special form 
 of wall-plate which is especially adapted to such purposes. 
 
 The underfloor is made of spruce plank, generally three 
 inches thick, planed on the underside, and grooved at the 
 edges, and fitted with hardwood splines. These plank are 
 two bays in length, breaking joints at least every three feet. 
 
 The floor is smoother if laid across the line of plank, and 
 the travelling loads moved in or out of the storehouse are 
 
MILL AND WAREHOUSE CONSTRUCTION. 699 
 
 better distributed than when the top floor is laid parallel to 
 the plank. To protect the contents of floors below, three 
 thicknesses of tarred paper should be placed between the floor 
 plank and top floor, each layer to be mopped with tar, asphalt, 
 or similar material, care being taken to break all joints. The 
 floor pho'jW riot be secured to the walls, but a narrow strip 
 
 Fig. 7 
 
 Showing Stairway Tower Inside Walls of Building. 
 
 laid around the edges of the floor and fastened to the wall 
 covers any openings due to shrinkage. 
 
 Floors of storehouses may have a slight pitch toward the 
 centre, draining in the same method as the roof is drained; 
 or if the other type of roof is adopted, the floors of storehouses 
 may have a slight pitch from centre to walls, draining through 
 scupper-holes indicated in Fig. 6. Goods raised on low skids 
 may then be very free of water damage. 
 
 The columns should be square Southern pine or oak, with 
 iron cap, pintle, and base, preferably cast in one piece, and 
 secured to the under side of the beam by six-inch lag screws. 
 The caps should be large enough to give the beams ample 
 bearing surface. 
 
 In a warm storehouse it is preferable that the roof should 
 slope towards the centre one-half inch to the foot, and that 
 the gutter should slope towards the drain-pipe one-twentieth 
 of an inch to the foot. In a cold storehouse it is considered 
 necessary that the roof should slope one-half of an inch towards 
 the walls as in Fig. 1, and if there is a gutter, the conductors 
 should be carried outside of the building. 
 
 Access to the various stories is obtained by means of a tower 
 
700 MILL AND WAREHOUSE CONSTRUCTION. 
 
 outside the main building and extending above the roof, con 
 taining stairways, elevator, and water-pipes. At each story 
 of the tower open galleries communicate to the rooms on that 
 level. A doorway from the upper story of the tower affords 
 a ready means of reaching the roof. It is often a matter of 
 great convenience if the doorway at the first story of the tower 
 is made large enough, and at the outside grade, so that a wagon 
 can be backed directly to the elevator. It is unnecessary 
 to provide these elevators with automatic hatches, as guard- 
 gates serve every purpose. When it is necessary to construct 
 the elevator wells and stairway within the lines of the main 
 building it is best to arrange it as in Fig. 7. The omission 
 of the outer wall prevents the way becoming a flue. 
 
 The walls extend above the roof, and the parapet should 
 be laid in cement, because the moisture readily absorbed by 
 brick would otherwise pass downward a,nd render walls in the 
 top story damp. In some instances a course of brick dipped 
 in coal-tar is laid above the roof level 
 
 4 'Storage oOtew Material V///////////////7W////////////7ffl7fa Storage of GooflS. 
 
 Fig. 8 
 
 Showing Stairway Tower at Side of Storehouse. 
 
 In addition to yard hydrants near the buildings there should 
 be a six-inch standpipe in the tower, the supply to which 
 should be controlled by an out-of-door Post indicator valve 
 at a safe distance from the building, with tv/o 2J" hydrants 
 and hose at each story, and at the top story of the tower, the 
 standpipe branches to a Morse or Phillips monitor nozzle on 
 the roof, if there are any adjacent buildings which might be 
 reached by streams from this position. A set of plugs for the 
 roof drain-pipes will allow the roof to be covered with water 
 in case the property is endangered by sparks from burning 
 buildings. 
 
 Storehouses should be provided with automatic sprinklers. 
 
 
MILL AND WAREHOUSE CONSTRUCTION. 701 
 
 When so protected the water can be shut off in the winter; 
 or if an air system be adopted it may be applied only in the 
 winter; water being kept directly upon the sprinklers in warm 
 weather. 
 
 Mill Construction with Self-sustaining Frame. 
 
 glope of roof, one in twenty-four_ 
 
 p 
 
 ^ g ~~ 2 f 
 
 Double roof timbers, 5" x.12" 
 - s'x 8^y 
 
 
 
 DO o f o o .1 
 
 s 
 
 I * S3 
 
 7 Double .floor timbers, 6 " x 15 " 
 MQtzJCT 
 
 
 
 
 
 
 
 1 
 
 
 Rf Double floor timbers, 6" x 15-" ,J 
 
 'Rock filling covered with cement concrete, on which is a layer of Tar or Asphalt 
 
 Fig. 9 
 
 Partial Transverse Section, Showing Self-sustaining Frame. 
 
 Figs. 9, 10, and 11 show suggestions for mill construction 
 in which the interior framework is self-sustaining and inde- 
 pendent of the walls, except that the outer posts serve to brace 
 the walls. Regarding this construction the Boston Manu- 
 facturers Mutual Fire Insurance Co. says: 
 
 "It is suggested that the framework of a factory itself should 
 consist of two parts, first, of two outer lines of posts passing 
 around the whole building, joined and braced together either 
 with hackmatack knees, angle irons, or iron cross-ties; this 
 
702 MILL AND WAREHOUSE CONST1U CHON. 
 
 outer framework carrying the alleyways 1o be so constructed 
 that it may be put up separately from the outer walls and also 
 separately from the inner posts and floors on which the ma- 
 chinery is to be placed, so that this part of the frame bearing 
 the outer alleyways will stand alone. 
 
 "Second, The interior framework and the floors upon which 
 machinery is to rest may be adjusted and connect H! with 
 the outer lines of support already designated, so that in the 
 
 Fig. 10 
 
 Partial Plan, Showing Locations of Posts and Staircase Tower. 
 
 event of. the burning of any timber, the giving away of any 
 post, or accident to any part of the floor, any section of ma- 
 chine-bearing floor may fall out without bringing a severe 
 strain upon the outer line of posts or upon other parts of the 
 frame of the mill. 
 
 "The self-sustaining frame being established and covered in, 
 the question may follow rather than precede, as to what the 
 material of the outer walls should consist of. In very many 
 arts it is important that the outer walls should consist in large 
 
MILL AND WA! m. 703 
 
 of glass, especially since the adoption of double- 
 glazed windows arid the fc'jggestion of ribbed glass for glaz- 
 ing ha-, reived fte problem of the trar of light; while 
 Ujo double glazing in the same sash obstructs the passage of 
 heat and cold in a very efTeetual way, thus avoiding the 
 densation of the moisture within. 
 
 " These windows, are to be carried to the under side of the 
 roof, against the plate, and to the under side of each floor, 
 to the ceiling, therefore the only remaining part of the 
 outer wall to be dealt with will be the space between and be- 
 neath the windows. This part of the wall may be built of 
 brick, but as no dependence is to be placed upon the wall for 
 sustaining the building itself, the walls may be lighter or 
 thinner than the common practi 
 
 "It being premised that this building is planned for a de- 
 tached position, where it will be free from hazard of fire from 
 neighboring buildings, large windows may be put in which 
 cannot be guarded by fire-shutters, the consideration of danger 
 from fire being only given to the interior hazard. Upon such 
 conditions and in such a position other materials than brick 
 may be considered for the walls. For ins'tance, the timbers 
 may be so disposed as to show upon the outside. The entire 
 framework for the window to be placed between these tim- 
 bers may then be constructed so that it can be brought to the 
 factory ready to be put into its place, all window-frames being 
 interchangeable. This structure may then be protected both 
 and outside with incombustible materials. 
 
 " Where there is an outside hazard the windows must be di- 
 minished in width, with an equal or greater area of wall sur- 
 face between, in or upon which automatic shutters may be 
 placed for closing up the windows against fire. In such posi- 
 tions the outer wall can only safely consist of brick of such 
 thickness as may be suitable to each ca#?."* 
 
 Fig. 11 shows a detail of outside wall consisting prinripally 
 of windows, the frames filling the entire width between the 
 posts* The outside of the posts and the spaces under the 
 windows may be covered with plank, and then with metal 
 or sheathing lath and rough plaster; the entire wall being 
 carried by the posts. In this mill there is but a single line 
 of outer posts, Le., no alley. 
 
 * Hollow concrete walls should be even better than brick. Author. 
 
f04 MILL AND WAREHOUSE CONSTRUCTION. 
 
 Fig. II 
 
 Outside Walls of Wood and Plaster Supported by the Frame. 
 
 Example of One-story Slow-burning Machine- 
 shop, 
 
 "COVERING IMPROVEMENTS WHICH HAVE BEEN DEVELOPED BY 
 EXPERIENCE IN THE CONSTRUCTION AND USE OF ONE-STORY 
 FACTORY BUILDINGS UP TO THE PRESENT DATE." * 
 
 
 
 For workshops on cheap, level land, especially where the 
 stock is heavy, one-story buildings have proved to be more 
 
 * Edward Atkinson, President. November, 1902. 
 
MILL AND WAREHOUSE CONSTRUCTION. 705 
 
706 MILL AND WAREHOUSE CONSTRUCTION. 
 
 economical in cost of floor area, supervision, moving stock in 
 process of manufacture, and repairs to machinery many 
 kinds of which can be run at greater speeds than when in high 
 buildings. 
 
 Such buildings are readily warmed and ventilated, and 
 heavy plank roofs are free from condensation in cold weather; 
 the large window area reduces the hours of artificial illumi- 
 nation. 
 
 Forced circulation of heated air is a very desirable method 
 of heating a mill, being economical as to maintenance and 
 repairs, and thoroughly under control. Overhead steam- 
 pipes are very satisfactory, if used in the ratio of one foot of 
 l|-inch pipe to 70 cubic feet of air. 
 
 Floors. Floors over an air space or on cement are sub- 
 ject to dry-rot. Asphalt or coal-tar concrete is softened by 
 oil, and the dust will wear machinery, unless covered by floor- 
 ing. Floors made by laying sleepers on six inches of pebbles, 
 tarred when hot, then two inches tarred sand flush to top of 
 sleepers and covered by double flooring, have remained sound 
 since 1865; but double flooring at right angles can be laid 
 on the concrete without the use of sleepers, and nailed together. 
 It is usually preferable to secure nailing strips to stakes four 
 feet apart each way and driven to grade, concrete flush to 
 top of strips, and lay single IJ-inch flooring. 
 
 Walls. Piers reaching to roof timbers, and light walls to 
 window-sills are finished with slope on inside. To increase 
 the window area over that shown in the elevation, the brick 
 piers between the windows may be narrowed and made thicker 
 so as to give the requisite strength, leaving more space for 
 light. Large windows are placed high, and the sashes sepa- 
 rated by a mullion. Lower sashes should be stationary and 
 glazed with ribbed glass, with transom sash or window venti- 
 lators above. If the light is too strong, apply to glass white 
 zinc and turpentine. 
 
 Monitors may well be glazed with ribbed glass. 
 
 Columns. Wooden mill columns, Southern pine or oak, 
 safely sustain loads of 600 pounds per square inch; a square 
 column is stronger than a round one of the same diameter. 
 They should have a*lj-inch core bored from end to end, 
 and two half-inch holes through the column near to each 
 end. 
 
 The columns should be securely held at each end, the base 
 
MILL AND WAREHOUSE CONSTRUCTION. 707 
 
 resting on iron plates projecting above the floor level, and 
 the caps at the top bolted to the roof beams. 
 
 Roofs. Double or solid timbers of Southern pine sup- 
 port the roof plank, and the ends pass through the wall, and 
 are finished as brackets to the cornice; or another plan often 
 adopted is to make a projecting brick cornice covering the 
 ends of the roof timbers, thus avoiding the exposure to an 
 outside fire. The beams are anchored to plates in the walls 
 by means of tongues which project into grooves across the 
 lower side of the beams. Beams should not be painted or 
 varnished until thoroughly seasoned. 
 
 The roof plank should be two bays in length, breaking joints 
 every three feet. There is no need of gutters, but a concrete 
 walk at the ground level, sloping toward drains, will take the 
 water from the roof. Do not drive nails upward into the roof 
 plank, as moisture will condense and drop from the heads. 
 
 Monitors must be of solid construction. 
 
 The roof should be tied by binding or bolting the timbers 
 of the roof to the walls of the mill in a safe and suitable man- 
 ner. This is the common practice, but the necessity is some- 
 times overlooked. 
 
 The saw-tooth roof is taking the place of the monitor in 
 weaving and other buildings. We do not supply any plan 
 for this type because it requires, in each case, the service of 
 a competent mill engineer and constructor to plan the roof 
 so as to meet special conditions, and to supervise the work. 
 
 Roofing Material, Mill roofs are almost always flat, 
 as shown in the foregoing specifications, and are most com- 
 monly covered with coal-tar, pitch, and gravel, although as- 
 phaltic compositions are often used and occasionally tin roof- 
 ing is used. Cotton duck or canvas has been used for cover- 
 ing mill roofs to some extent, but does not appear to have 
 proved very satisfactory, except on small buildings and for 
 covering platforms, etc. Canvas roofing will stand harder 
 usage than any of the materials above mentioned, as is shown 
 by its continued use on the decks of vessels and steamers. 
 Duck or canvas for roofing purposes should be what is termed 
 "12 ounce," weighing 16 ounces to the square yard. It should 
 be tightly stretched, and tacked with seventeen-ounce tinned 
 carpet-tacks, the edges being lapped about an inch. If the 
 roof planks are rough, or not of an even thickness, a layer of 
 heavy roofing paper should be laid before the duck is put down. 
 
708 MILL AND WAREHOUSE CONSTRUCTION, 
 
 After the duck is laid, it should be thoroughly wet, and then 
 painted with white lead and boiled linseed-oil before it becomes 
 dry; which makes it water proof. To protect from fire, give 
 it two more coats of white lead, and over this a coat of iron- 
 clad paint. Instead of the four coats of white lead and oil, 
 the duck may be saturated with a hot application of pine-tar 
 thinned with boiled linseed-oil. This has been found to work 
 perfectly. The iron-clad paint should be applied, which- 
 ever method is used. 
 
 Partitions. Partitions used for dividing a mill into 
 sections should be built of brick, concrete or porous terra-cotta 
 tiling. Where a room is to be partitioned off the partitions 
 may be built of two-inch tongued and grooved plank set ver- 
 tically (so as to form a solid partition), and plastered both 
 sides, either on wire, or on dovetailed sheathing lath. Such 
 partitions have been found to work well after a trial of twelve 
 years, and offer effectual resistance to fire. 
 
 Two-inch solid partitions of plaster on metal lath wired 
 to light iron studs may also be used. 
 
 Mill Doors and Shutters should be built of two thick- 
 nesses of inch boards covered on all sides with tin as described 
 in Chapter XXIV. 
 
 For information relating to appliances for the fire protec- 
 tion of mills, the reader is referred to the Insurance Engineer- 
 ing Station, Boston. 
 
 Patented Systems of Mill Construction. 
 
 Mr. Chas. A. M. Praray, Mill Engineer of Providence, R. I., 
 has patented a system of mill construction which he has desig- 
 nated as the "Praray Improved Construction." The special 
 points in which this system differs from the regular mill con- 
 struction are, the construction of the walls, the shape of the 
 post caps, and the supporting of the floors and roof, independ- 
 ent of the walls. 
 
 The walls f are built as a continuous series of bay windows, 
 with a hollow brick pier between, and with a supporting col- 
 umn in the centre of each bay. Fig. 13 shows a plan of one 
 bay and of the column supporting the floor, while Fig. 14 
 shows a vertical section through the same. Fig. 15 shows 
 a detail of the post and girder connection. The posts are 
 cut down to a square where they pass through the girder 
 
MILL AND WAREHOUSE CONSTRUCTION. 709 
 
 Fig. 13 
 Plan of One Bay. 
 
 Fig. 14 
 
 Vertical Section through 
 One Bay. 
 
710 MILL AND WAREHOUSE CONSTRUCTION. 
 
 PLAN 
 
 Dog Bolt' 
 
 ^Dog Bolt 
 
 (Cast Iron 
 Post Cap 
 
 ^Fig. 15 
 
 Detail of Beam and Column Con- 
 nections for Intermediate Sup- 
 ports in all Stories. 
 
 and are dog-bolted to the girders. The advantages claimed 
 for this construction are a saving of about 33 per cent, in brick- 
 work, with an increase in light., 
 ing of about 33 per cent., and 
 also a saving of 10 per cent, in 
 the height of the building, and 
 a consequent saving in heat- 
 ing. The hollow piers between 
 the bays can be used as air ducts 
 for heating and ventilating. 
 Five large cotton mills have 
 been erected in the Southern 
 States on this system of con- 
 struction, which appear to verify 
 the claims of the inventor. . 
 
 Architects or owners can make 
 use of this system by paying a 
 royalty to Mr. Praray, which 
 will also include many practical 
 suggestions as to the carrying 
 out of the system. 
 
 Mr. S. E. Loring, Consulting Architect of . Syracuse, N. Y., 
 and one of the first in this country to advocate the use of por- 
 ous terra-cotta for fire-proofing, has also patented a system 
 of slow-burning construction, which is a form of skeleton con- 
 struction executed in wood instead of steel. The interior 
 construction is made entirely self-supporting, so that the walls 
 carry nothing but their own weight, and may consequently 
 be made very thin, or of wood veneered with brick. Both 
 the columns and the girders are built up of 2-inch plank; the 
 planks of the columns break joint so that the column is con- 
 tinuous from foundation to roof, and the horizontal and ver- 
 tical members are joined so as to make the entire skeleton 
 one piece of framework, and consequently very rigid. The 
 construction is rendered slow-burning by the size of the struc- 
 tural members, and by interlinings of felt, asbestos, or equiva- 
 lent fire-resisting materials, and also by the use of fire-proof 
 paints, tiles, metal sheathings, etc. 
 
 A large four-story factory, at Nashville, Tenn., for the Na- 
 tional Casket Co., was built in the fall of 1902, on this principle 
 of construction, and there are several examples of it in New 
 York State. Mr. Loring claims that the New England Fire 
 
MILL AND WAREHOUSE CONSTRUCTION. 711 
 
 Insurance Companies have granted steel structure ratings to 
 all buildings erected on this principle. 
 
 Mill Construction as applied to Warehouses. 
 
 The features of bad construction mentioned on page 688, are as 
 objectionable in warehouses as in factories, while the con- 
 struction advocated in mills may be used with almost equal 
 advantage in the erection of warehouses, although 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 fire has obtained 
 a good headway. 
 
 The main object of mill, or as it is often called, "slow-burn- 
 ing" construction, being to prevent a fire from readily getting 
 started, or from spreading in 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 all con- 
 cealed spaces, should be constantly kept in mind. 
 
 Warehouse floors, however, are generally required to sus- 
 tain heavier loads than are found in woollen and cotton mills 
 and hence require heavier construction. While warehouse floors 
 are quite often built with transverse girders, eight or ten feet 
 apart, with the space between spanned by flooring from four 
 to six inches thick, the more common method of construc- 
 tion is to use one or more lines of longitudinal girders, sup- 
 porting floor beams spaced from two to four feet apart. Where 
 very heavy loads are to be supported this is generally the 
 more economical construction, as it requires only a 2-inch 
 underfloor, while it is just about as slow-burning. 
 
 Steel and Iron not as Desirable as Wood. Wher- 
 ever wooden joists and flooring are to be used, it is more de- 
 sirable from the point of safety from fire to use wood for the 
 posts and girders also, than to use iron or steel for these por- 
 tions of the building, for the reason that steel beams will warp 
 and twist and pull down the building several minutes before 
 the wooden beams will be burnt to the breaking point, .i.e, 
 provided the wooden beams have a sectional area of at least 
 72 square inches and are spaced 4 feet or more from centres. 
 
712 MILL AND WAREHOUSE CONSTRUCTION. 
 
 Cast-iron columns will also generally fail in a fire sooner than 
 wooden posts. 
 
 By using Oregon fir, or long-leaf Southern pine for the 
 posts and girders and placing the posts close enough together, 
 it is practicable to obtain sufficient strength for a five-story 
 building with a live load of 300 pounds per square foot. 
 
 If it is thought necessary to place the posts so that the span 
 of the girders will be more than 12 feet, then it will be necessary 
 to use steel beams for the girders, but to obtain slow-burning 
 construction, all steel and also all cast-iron columns should 
 be protected to some degree from the heat. 
 
 Fire-proofing of Steel and Iron for Slow-burning 
 Construction. Absolute fire protection of the steel and iron is 
 hardly warranted in a building in which the larger portion 
 of the construction is of wood, but sufficient protection should 
 be given that the girders and columns will stand at least until 
 the floor timbers have fallen. Such protection for steel beam 
 girders can be most economically obtained by first enclosing 
 the girder with wood, then furring with J"Xl" corrugated 
 band iron, and then covering with metal lath and plaster. The 
 furring can be secured to the wood by a few staples, and the 
 metal lath by nails or staples according to the kind of lath- 
 ing that is used. Sheathing lath may also be used in place of 
 the metal furring. 
 
 Fig. 16 
 
 Fig. 16 shows a 20" steel beam girder protected in this way, 
 the floor beams being 6"X12" supported on malleable iron 
 brackets bolted to the I-beam. Such a covering would un- 
 doubtedly protect the steel until the floor beams had dropped, 
 and it is hardly to be expected that the columns and girders 
 would stand after all of the floors had fallen. 
 
MILL AND WAREHOUSE CONSTRUCTION. 713 
 
 The columns can be protected by metal furring and metal lath 
 and plaster as shown in Fig. 17. For round cast-iron columns, 
 
 Space 
 
 Fig. 17 
 
 Berger's economy stud, see Chapter XXIII., is probably the 
 
 cheapest form of furring that can be employed, as it is easily 
 
 applied and the lathing does not have to be wired to the furring. 
 
 Connection of Floor Beams and Girders. To 
 
 render the construction slow-burning, and particularly the 
 girders, it is important that there be no hollow space between 
 the top of the girders, and the flooring, or that the tops of the 
 floor beams shall be flush with the top of the girder. This, 
 of course, necessitates framing of the floor beams to the girder. 
 
 Fig. 18 
 
 For heavy construction the only kind of framing that is per- 
 missible, is by means of some form of joist hanger. The various 
 forms of joist hangers now in the market have been illustrated 
 and commented on in Chapter XXI. When the floor beams 
 are 6"X12" or larger, and the girders are of wood, the author 
 
714 MILL AND WAREHOUSE CONSTRUCTION. 
 
 would give the preference to the Duplex hanger shown in 
 Fig. 18. If the girder is of steel, the Van Dorn or National 
 double hanger will probably be more satisfactory, as these 
 hangers can be used with any depth of beam and girder, or 
 special malleable iron brackets may be riveted to the web 
 of the girder, as in Fig. 16. 
 
 Fig. 19 
 
 Fig. 19 shows a floor framed with Van Dorn hangers and 
 post caps. The same principle of construction is applicable 
 to larger joists spaced further apart. 
 
 Wall Supports and Anchors for Joists and 
 Girders. 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 burnt through, the ends may fall with- 
 out injuring the wall, and where large timbers are used, pro- 
 vision should be made against the possibility of dry-rot. 
 
 The method of supporting the beams in "Mill Construction," 
 as originally developed in the New England Mills, is shown by 
 Fig. 20. This fulfilled the requirements above mentioned, 
 but it weakened the wall to some extent. 
 
 The Goetz box anchors shown by Figs. 21, 22, and 23, are a 
 decided improvement upon the anchor shown in Fig. 20 as 
 they afford all of the advantages of the latter while they do 
 not weaken the wall, unless the floor beams are very wide. 
 
 These anchors are made wedge-shaped so that it is impossible 
 to pull them out of the wall, and the more weight there is upon 
 
MILL AND WAREHOUSE CONSTRUCTION. 715 
 
 the beam, the greater will be the bondage that holds beam to 
 box and box to wall. 
 
 In case of fire or accident, the joist can burn through or 
 break, and in falling they free the anchorage and leave the 
 
 Fig. 20 
 
 wall standing, not even weakened by the space left in the wall, 
 because the anchor remains, and the crushing strength of this 
 
 Fig. 21 
 
 Fig. 22 
 
 cast-iron box is much greater than that of the wall. No break 
 or breach is made in the wall, and the anchor that remains, 
 securely held, forms a space for the easy replacement of joist. 
 The anchor provides a perfect and secure foundation for each 
 
716 MILL AND WAREHOUSE CONSTRUCTION. 
 
 joist. Fire from a defective flue cannot ignite a joist end, 
 because it is protected by a ventilated cast-iron box. 
 
 The boxes, or anchors, also have air spaces in the sides, J inch 
 wide, which permit a circulation of air around the ends of the 
 joist, effectually preventing dry-rot in the ends of the timbers. 
 
 Fig. 23 
 
 If timber is wet or unseasoned it will have a chance to dry 
 out after it is put in the building. 
 
 The average weight of a box like Fig. 22 for 2X12 joists 
 is 10 pounds. 
 
 Another device for obtaining the same results in a different 
 
 Fig. 24 
 
 Duplex Wall Hanger. 
 
 way, is the wall hanger, of which two patterns are shown in' 
 Chapter XXI. Figs. 24 and 25 show Duplex wall hangers 
 for large timbers. The hanger shown in Fig. 25 is made extra 
 
 ' 
 
MILL AND WAREHOUSE CONSTRUCTION. 717 
 
 heavy and is provided with a plate which has eight inches 
 bearing on the wall, and the bearing of the timbers on the 
 hanger is also eight inches. 
 
 For beams not exceeding ten inches in breadth there is prob- 
 ably little choice between the box anchor, Fig. 23, and the 
 wall hangers, Figs. 24 and 25, except perhaps in the price 
 and appearance. When the wall hanger is used, no hole is 
 left in the wall, and -a saving of six inches in the length of the 
 beams is effected, which in some cases would be a consideration. 
 
 Fig. 25 
 
 Extra Heavy Duplex Hanger. 
 
 For girders 12"X14" and upwards the author believes the 
 hanger shown by Fig. 25 to be preferable to the box anchor. 
 Wall hangers made from stirrups should not be used for heavy 
 beams. Any one of these anchors or hangers is obviously 
 greatly superior to the ordinary method of anchoring beams 
 or girders to walls, and the use of such anchors will un- 
 doubtedly save much loss by the falling of the walls, which are 
 almost invariably pulled down by the ordinary iron anchors 
 when the beams fall. 
 
 A reduction in the rate of premiums for fire insurance can be 
 obtained when these anchors or hangers are used. 
 
 Weakness of Wrought Iroii Stirrups when Ex 7 
 posed to Fire. Referring to this subject, Prof. J. B. John- 
 son, of Washington University, says : 
 
 "The recent fire tests of steel stirrups and brick walls which 
 "Were made under my supervision in this city (St. Louis) show 
 
718 MILL AND WAREHOUSE CONSTRUCTION. 
 
 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 beam, and 
 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 stir- 
 rups, in that being of malleable iron they are not as quickly 
 affected 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., Feb. 9, 1902, some 
 Duplex wall hangers were subjected to a most severe test 
 without apparent injury. 
 
 It is undoubtedly desirable that all structural iron should 
 be protected from fire, but it is almost impracticable to effect- 
 ively protect the stirrups used in connection with wooden 
 beams without going to a greater expense than the character 
 of the construction will warrant. 
 
 Post and Girder Connections. Whenever a building 
 is constructed with wooden posts extending through several 
 stories, the upper posts should always rest on top of an iron cap 
 plate, fitted over the post below, as in Figs. 19 and 29, and 
 never on the girder or even on a wooden bolster. A bolster 
 would not be so objectionable but for the fact that the pressure 
 under the post will generally be sufficient to crush the fibres 
 of any kind of wood. Then, too, there would always be some 
 settlement 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 at least equal to one-half the load on the 
 girder divided by the safe resistance of the wood to crushing 
 across the grain, as given on page 414. For example, a 12"X 14" 
 yellow pine girder is designed to support a possible load of 
 38,000 pounds, what bearing should it have at the ends? 
 
 Ans. The safe resistance of yellow pine to crushing across 
 the grain is given at 500 pounds. One-half of the load on 
 the girder is 19,000 pounds, hence the bearing area should be 
 19,000-:-500 or 38 square inches. As the breadth of the beam 
 is 12 inches this would require a bearing lengthways of the 
 girder of 3J inches. A bearing of 4 or 5 inches, however, 
 
MILL AND WAREHOUSE CONSTRUCTION. 719 
 
 will be still better, but in no case should the bearing be less 
 than that required by the above rule. 
 
 Forms of Post Caps. A very common form of post 
 cap is shown by Fig. 26, the dimensions 
 given being for a 10 X 10 post. Fig. 27 
 shows a similar cap for a round post. 
 These caps fulfill all requirements for 
 strength and permit of the use of a 
 girder wider than the post. When 
 the girders and joists 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 great force to move them. 
 
 Fig. 26 
 
 Common Cast-iron Post Cap. 
 
 The 
 
 Fig. 27 
 
 girders should be tied together longitudinally by iron straps 
 spiked to their sides. 
 
 s' 
 Fig. 28 
 
 Goetz Post Cap. 
 
 Many persons, however, consider it important that in a 
 building of slow-burning construction the posts shall be tied 
 
720 MILL AND WAREHOUSE CONSTRUCTION. 
 
 together in vertical lines, and the girders secured in such a 
 way that they will be self-releasing without pulling down the 
 posts. Figs. 28 and 29 show two post caps which fulfill these 
 requirements. 
 
 Fig. 29 
 Duvinage Cap. 
 
 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 the 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. Pro- 
 vision is also made for bolting the cap to the upper post. The 
 author doubts very much, however, 
 if posts bolted together in this way 
 would stand after the girders had 
 fallen, as the planking would be 
 likely to pull the posts over, even 
 if they did not burn as quickly as 
 the beams. Both of the caps shown 
 by Figs. 28 and 29 are patented 
 and can not be used without pay- 
 ing a small royalty to the patentees. A cap like that shown 
 
 Fig. 30 
 
MILL AND WAREHOUSE CONSTRUCTION. 72i 
 
 by Fig. 30 without the lugs or pins can be made at any foundry 
 without infringing on the patents. 
 
 Figs. 31 and 32 show different styles of steel caps that are 
 largely taking the place of the cast-iron cap. The Duplex 
 
 Fig. 31 
 
 Van Dorn Post Caps. 
 
 post caps are also made so as to permit of the extension of the 
 post for two stories, thereby giving an extremely strong and 
 
 Fig. 32 
 
 Duplex Four-way Post Cap. 
 
 stiff connection. The tests that have been made of the Duplex 
 post caps show that they possess great strength. 
 
722 MILL AND WAREHOUSE CONSTRUCTION. 
 
 There is an objection to the use of four-way post caps where 
 the girders are of wood, in that the floor beams that are hung 
 from the girders will drop by an amount equal to the shrinkage 
 in the girder, if the beams are hung in stirrups, or by one-half 
 this amount if hung in Duplex hangers, while the beams sup- 
 ported on the post cap can not drop at all, consequently the 
 floor will be higher over the beam supported by the posts, 
 than over the intermediate beams. In one building where 
 deep beams were used, this unevenness in the floor amounted to 
 nearly an inch and was very noticeable. Wherever wooden 
 girders are used it is therefore much better construction to 
 support all of the floor beams from the girders, then the effect 
 of shrinkage will be uniform. With steel girders there is no 
 shrinkage, and a beam may be placed opposite the posts with 
 advantage. 
 
 Mill Construction with Concrete Flooring. 
 Fig. 33 shows a modification of mill or slow-burning construc- 
 
 Fig. 33 
 
 tion advocated by the Hinchman-Renton Fire-proofing Co, for 
 buildings in which first-class fire-proof construction cannot 
 be afforded. It differs from the standard slow-burning con- 
 struction only in the substitution of reinforced cinder concrete 
 
MILL AND WAREHOUSE CONSTRUCTION. 723 
 
 for the usual 2 or 3-inch plank between the beams. While 
 this construction has never been tested by a fire, it appeals to 
 the author as an improvement upon the standard wooden con- 
 struction, in that there is less wood to burn, while none whatever 
 (except the finished flooring) is exposed, and it is more sound 
 proof and more decorative than a floor ceiling without the 
 plaster. Were it not for the element of shrinkage which can 
 never be entirely overcome where wood is used for floor beams, 
 the author believes that this floor would stand fire fully as 
 long as many so called fire-proof floors with steel joists. This 
 floor can also be finished on top with cement. 
 
 Cost of Mills and Factories Built on the Slow- 
 Burning' Principle. 
 
 The cost per square foot of total floor area of mills and factories 
 <n the year 1884 was, according to Mr. Edward Atkinson, as 
 follows : 
 
 Mill with three stories for machinery, and a base- 
 ment for miscellaneous purposes 75 to 80 cts. 
 
 Mill with two stories for machinery, and no base- 
 ment 65 cts. 
 
 Mill with one story, of about one acre of floor, with 
 
 basement for heating and drainage only about 85 cts. 
 
 The above is for the total area of floors in the building, above 
 the basement. These figures, while perhaps a little low for 
 present prices, are a fair average taken through a number of 
 years. 
 
 The following data as to the cost of mill buildings built on 
 the "Praray Improved Construction" and also of mills built 
 on the modern " Slow- Burning Method of Construction" both 
 in the East and South, were kindly furnished the author by 
 Mr. Praray. 
 
 Mr. Praray also says: "The cost of building varies according 
 to the locality. Lumber, bricks, and labor cost 50 per cent, 
 more in New England than in the Carolinas, and therefore 
 the same building will cost much less in the South than in 
 the East." 
 
 EXAMPLES. The Dixie Cotton Mills at La Grange, Ga., 
 
724 MILL AND WAREHOUSE CONSTRUCTION. 
 
 built in 1895 and 1896 on what is called the "Praray Improved 
 Construction." 
 
 Total floor area of all buildings and steam plant, 87,100 square 
 feet. Cubical contents of all buildings, including the Smoke 
 Stack, which is 125 feet high, 52" core, 2,419,000 cubic feet. 
 
 Cost, per square foot floor space, 43 ^ cents. 
 
 The Whitman Cotton Mills, New Bedford, Mass., built in 
 1896 and 1897 on Modern Mill Construction, and approved 
 by the Mfrs. Mutual Ins. Companies. 
 
 Total floor area of all buildings and steam plant, 217,000 
 feet. Cubical contents of all buildings, including smoke stack, 
 which is 200 feet high, 10 feet core, is 6,494,000 cubic feet. 
 
 Cost per square foot floor space, 81^ cents. 
 
 The Moorhead Cotton Mills, Moorhead, Miss., built in 
 1900 on what is called the Modern or Slow-Burning Construc- 
 tion, and higher above grade than is usual on account of high- 
 water mark. 
 
 Total floor area of all buildings and steam plant, 31,000 feet. 
 Cubical contents of all buildings, including the smoke stack, 
 which is 125 feet high, 48" core, 532,640 cubic feet. 
 
 Cost per square foot floor space, 82 cents. 
 
 The above three mills were built for cotton mills, and are all 
 equipped with steam-power plants. 
 
 All are two-story buildings. It will be noticed that the 
 Mississippi mill cost more per foot floor space than the New 
 England mill. 
 
 The Georgia or Dixie mill cost about one-half per foot floor 
 space of the two other mills. 
 
 Five other mills on the "Praray Method" have been built in 
 the South, and the cost has been less than 50 cents per foot 
 floor space. 
 
 Mills built throughout the New England States cost from 
 75 cents to $1.10 per square foot floor surface 
 
 Mills built in the Carolinas, Georgia, and Alabama average 
 about 60 cents per square foot floor surface. 
 
 Mills oi less than 100,000 square feet floor surface will cost 
 from 80 cents to $1.25 per foot. 
 
 The greater amount of floor space will enable mills to be 
 built on the modern methods at the prices named above. 
 
 Labor in the South is much cheaper and surely 33 per cent, 
 slower. Lumber and materials in the South cost about 50 per 
 cent, of the price paid in New England. 
 
MILL AND WAREHOUSE CONSTRUCTION. 725 
 
 A mill built at Taunton, Mass., four stories high with a floor 
 area the same as the Whitman mills, cost 96 cents per square 
 foot floor space. This was also equipped with steam power. 
 
 The cost per square foot of floor space will generally be 
 greater for a small mill than for a large one for the reason that 
 a small mill that is to be run by steam power has to build boiler 
 and engine house, pump house, towers for tank purposes, etc., 
 large enough for doubling the size of the mill at some future 
 time. 
 
 The mills in the South are built for from 5,000 to 10,000 
 spindles to start with, and are planned to add that amount of 
 spindles at some future time. They must build boiler and 
 engine house, belt-ways, towers, etc., to accommodate future 
 extensions, which makes the first cost of the mill come very 
 high, and very often places the mill in an embarrassing position. 
 
 For example, the Moorhead Cotton Mills, Moorhead, Miss., 
 was built with the idea of adding double the amount of spindles 
 that they have installed, that is to say, the power house and 
 chimney were all large enough for the future extension, making 
 spare room in the boiler house, and spare room in the engine 
 house. 
 
726 FIRE-PROOFIXG OF BUILDINGS. 
 
 CHAPTER XXIII. 
 FIRE-PROOFING OF BUILDINGS. 
 
 Materials and Details of Construction. 
 
 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 incombustible mate- 
 rials, and any of these materials, such as steel or iron, which are 
 injuriously affected by heat or streams of w r ater must be effi- 
 ciently protected by other materials which are not so affected. 
 
 This precludes the use of wood, whether exposed or not ex- 
 posed, 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 fire-proof there are quite a large 
 number, however, that could not be destroyed by fire, and in 
 which the salvage would probably amount to from 60 to 80 
 per cent., and it is the latter class which is generally meant 
 when ,the term fire-proof is used. 
 
 Incombustible buildings, and buildings having wood con- 
 struction 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. 
 
 To build absolutely fire-proof is expensive to build so that 
 the building can be merely gutted by fire, is less expensive, and 
 for many classes of buildings all that is advisable. 
 
 A building should be designed, built, and finished to conform 
 to the purpose for which it is to be used a building that will 
 contain but little inflammable material, and that not of great 
 value need not be as thoroughly fire-proof as a building de- 
 signed for the storage of valuable goods, or where the safety 
 of human life is at stake. 
 
 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 as 
 to the best use of these materials he can then choose his 
 
FIRE-PROOFING DEFINED. 727 
 
 materials and use them to such an extent as the character of 
 the building and the interests of his client demand. It is this 
 sort of information that the author has tried to furnish in a 
 concise manner in this chapter. 
 
 Municipal Definitions. Municipal definitions as to 
 what constitutes " fire-proof construction" have a great bear- 
 ing on the construction - of buildings within their jurisdiction, 
 and those of the two largest cities *are therefore quoted. 
 
 Chicago Definition of Fire-proof Construction. 
 "The term 'Fire-proof Construction' shall apply to all build- 
 ings in which all parts that carry weights or resist strains, and 
 also all stairs and all elevator enclosures and their contents, 
 are made entirely of incombustible material, and in which all 
 metallic structural members are protected against the effects 
 of fire by coverings of a material which must be entirely in- 
 combustible and a slow heat conductor. The materials which 
 shall be considered as fulfilling the conditions of fire-proof cover- 
 ing are: First, brick; second, hollow tiles of burnt clay applied 
 to the metal in a bed of mortar and constructed in such a manner 
 that there shall be two air spaces of at least three-fourths of an 
 inch each by the width of the metal surface to be covered, 
 within the said clay covering; third, porous terra-cotta which 
 shall be at least two inches thick and shall also be applied direct 
 to the metal in a bed of mortar; fourth, two layers of plastering 
 on metal lath." 
 
 New York Definition. " Buildings required to be fire- 
 proof shall be constructed with walls of brick, stone, Port- 
 land cement concrete, iron or %teel, in which wood beams 
 or lintels shall not be placed, and in which the floors and roofs 
 shall be of materials provided for in Section 106 of this Code. 
 The stairs and staircase landings shall be built entirely of 
 brick, stone, Portland cement concrete, iron or steel. No 
 woodwork or other inflammable material shall be used in any 
 of the partitions, furrings, or ceilings in any such fire-proof 
 buildings, excepting, however, that when the height of the 
 building does not exceed twelve stories nor more than 150 
 feet, the doors and windows and their frames, the trims, the 
 casings, the interior finish when filled solid at the back with 
 fire-proof material, and the floor-boards and sleepers directly 
 thereunder, may be of wood, but the space between the sleepers 
 shall be solidly filled with fire-proof materials and extend up to 
 the underside of the floor-boards. 
 
728 FIRE-PROOFING OF BUILDINGS. 
 
 "When the height of a fire-proof building exceeds twelve 
 stories, or more than 150 feet, the floor surfaces shall be of stone 
 cement, rock asphalt, tiling, or similar incombustible material, 
 or the sleepers and floors may be of wood treated by some 
 process approved by the Board of Buildings, to render the same 
 fireproof. All outside window frames and sash shall be of 
 metal, or of wood covered with metal. The inside window- 
 frames and sash, doors, trim, and other interior finish may be 
 of wood covered with metal, or of wood treated by some process 
 approved by the Board of Buildings to render the same fire- 
 proof." 
 
 Section 106 refers to fire-proof floors. These may be con- 
 structed of brick, tile, cement concrete, and, in fact, of any 
 material that will successfully pass the tests prescribed by the 
 Code. Before any floor construction other than brick or tile 
 will be passed by the department, however, it must be tested 
 for strength and fire resistance under very rigid conditions, 
 and the construction must stand the test successfully. 
 
 Fire-resisting Design. A successful fire-proof building 
 must not only be of fire-proof construction, but it should 
 be provided with adequate equipment to cope with either 
 exterior or interior fire, and planned so that an interior fire 
 may be confined to limited portions of a building, and that 
 the occupants shall not be cut off from a safe exit. These 
 latter considerations cannot be properly treated in a "hand- 
 book," and the author therefore refers the reader to " The Fire- 
 proofing of Steel Buildings," by Mr. J. K. Freitag, for an able 
 discussion of these points, as/ well as of the whole subject of 
 fire-proofing. 
 
 Materials of Construction. 
 
 Brickwork. Common brickwork, when of a good quality, 
 w r ill stand exposure to fire for a considerable length of time, 
 but in a severe conflagration the heated side of the wall expands, 
 often to the point of throwing the wall, the bricks crack, shell, 
 and are sometimes melted. Experience has shown that thick 
 walls are less affected by heat than thin walls, and that hard- 
 burned bricks will stand better than soft, or under-burned 
 bricks. In buildings which are to contain large quantities of 
 inflammable material it is undoubtedly better to line the walls 
 with porous furring tile or hollow brick. 
 
MATERIALS OF CONSTRUCTION. 729 
 
 Stones. Very few stones will successfully stand the action 
 of severe heat, and consequently stone should be used very 
 sparingly in fire-proof buildings, and certain stones not at alL 
 
 Granite will explode and fly to pieces or disintegrate into 
 sand when exposed to flames. 
 
 Limestones and Marbles are usually ruined if not totally 
 destroyed by an ordinary fire. They are the least desirable 
 of all stones to use in a fire-proof building, and the granites 
 come next. 
 
 Sandstones, when fine-grained and compact will some times 
 stand fire without serious injury, but in the case of a severe 
 conflagration are generally so badly affected that they have to 
 be replaced. In general, it may be said that no building stone 
 will stand as well under fire and water as do brick and terra- 
 cotta. 
 
 Ornamental Terra-cotta. This is undoubtedly the 
 best material to use for the trimmings of a building that is in- 
 tended to be absolutely fire-proof, aud especially that which 
 has a glazed surface. "Terra-cotta will certainly require less 
 reconstruction after severe fire-and-water tests than any 
 building material, saving, possibly, the best qualities of fire- 
 brick." * 
 
 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 to temperatures of 1300 
 or 1500 degrees F. wiiile carrying very heavy loads even with 
 frequent applications of cold water while the metal is at a red 
 heat." * 
 
 The contents of most mercantile buildings, when burning 
 freely would probably generate a heat exceeding 2000 degrees. 
 Consequently cast-iron columns, when unprotected are almost 
 sure to fail in such a fire either by bending or breaking. 
 
 No building can be considered fire-proof in which unprotected 
 iron or steel columns are used, 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, cast-iron columns are unquestionably 
 preferable to steel columns, when unprotected (see pages 415 
 and 428). 
 
 Wrought-iron and steel will expand, bend, and twist under a 
 
 . - 
 
 * Freitag. 
 
730 FIRE-PROOFING OF BUILDINGS. 
 
 very moderate degree of heat, and are more quickly affected 
 by heat than large timbers. 
 
 Structural Terra-cotta. Terra-cotta, as used for 
 floor arches, column and girder protection, and for building 
 light hollow walls is made of three different compositions, the 
 material being known as "Porous," "Semi-porous," or " Dense," 
 according to the method of manufacture. 
 
 Porous Terra-cotta is made by mixing sawdust with 
 a tough plastic clay and submitting it to an intense heat, by 
 the action of which the sawdust is destroyed, leaving the mate- 
 rial light and porous like pumice-stone. 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 per cent, according to the toughness of the clay used. Care 
 is required in manufacture that the work of mixing, drying, 
 and burning be thoroughly done. The burning should be 
 done in down-draught kilns by a quick process. The product 
 should be compact, tough, and hard, ringing 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 may be easily driven into it for securing interior 
 finish, slates, tiles, etc. For the successful resistance of heat, 
 and as a non-conductor for the protection of other materials, 
 there is no building material superior and but few, if any, 
 equal to it. 
 
 Dense-tiling is made from a variety of clays. Most manu- 
 facturers, though not all, use more or less fire-clay, and com- 
 bine 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 semi- 
 glazed surface for outer walls of buildings; For such use it has 
 great durability, and effectually stops moisture. In using dense 
 tiling for fire-proof filling, care should be taken that the tiles 
 are free from cracks, and sound and hard burnt. 
 
 In the earlier days of fire-proof construction dense tiling was 
 almost exclusively used for fire-proof floor-arches, partitions, 
 etc., but of late years the superior advantages of the porous and 
 
FIRE-PROOFING MATERIALS. 731 
 
 semi-porous materials have practically limited the use of dense 
 tiling to exterior walls. 
 
 Semi-porous Tiling. This material was introduced by 
 those factories which use pure fire-clay in the manufacture of 
 their tile, to enable them to compete with the standard porous 
 material. 
 
 During the process of grinding the clay about twenty per cent 
 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. 
 
 Mr. 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/' 
 
 Comparative Advantages of Porous and Dense 
 Tiling. 
 
 A fire-proof filling and protecting material should be sub- 
 stantial as well as incombustible. In a building made of abso- 
 lutely incombustible materials it is of the first importance that 
 the fireproofing be able to withstand rough usage, for, in the 
 event of fire, damage to the structural parts wdll be serious 
 if the fireproofing is dislodged, falls apart, or yields to the action 
 of fire or of water when a fire is in progress, or if it collapses 
 under sudden loads, jars, or impact, although the material itself 
 may not burn at all. In such buildings enduring qualities, 
 both of the fire-proof material and its construction, are as vital 
 and important as the imcombustibility of the material. In 
 the event of fire the first danger is from the collapse of the 
 material and not from its combustion. Experience has shown 
 that fire-proof tiles of plastic clays, when porous, are more 
 enduring than dense tiles, even if the dense tiles be of part, or 
 all fire-clay. Porous tiles are tough and elastic. Dense tiles 
 are hard and brittle. The most essential requisites of a fire- 
 proof filling and protecting material are these: It should be 
 tough, not easily shattered by impact; non-expansive, not 
 easily cracked by heating or cooling; slightly elastic, yielding 
 gradually to excessive loads, but not breaking or collapsing; 
 compact and hard-burned, but not dense; strong enough, but 
 not of excessive crushing strength. Blocks should be light 
 weight by being porous, but not by having thin shell and webs; 
 
732 FIRE-PROOFING OF BUILDINGS. 
 
 should be built in between beams by such methods as bring all 
 parts of the tiles into position to do the greatest service, whereby 
 a structural efficiency equal to the efficiency of the material is 
 obtained. These requirements are quite fully met in properly 
 made and properly built-in porous tiling, and to a nearly equal 
 degree by semi-porous tiling. 
 
 Practically the same shapes of tile are made in all three 
 materials, but the webs with the porous material should be 
 thicker than with the semi-porous or dense. 
 
 Defects in Terra-cotta Tiling. 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." * 
 
 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 tem- 
 perature 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 con- 
 version into steam." 
 
 Porous terra-cotta absorbs water freely, and if allowed to 
 freeze when wet is more or less injured. If the process is per- 
 mitted to continue, the blocks become so weakened as to make 
 them unsafe for use. 
 
 Mortars, Plasters, and Plaster of Paris. Mortar 
 and plaster must necessarily enter into the composition of all 
 masonry buildings, whether built of brick, stone, t or terra- 
 cotta. That ordinary lime mortar, when well made, will endure 
 for unlimited periods of time, in dry situations, has been proven 
 by actual use. 
 
 Hydraulic cement mortars are equally durable in wet or 
 damp places. 
 
 For laying brick 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 
 
 * Freitag, p. 92. 
 
FIRE-PROOFING MATERIALS. 733 
 
 compositions there has been much controversy: the truth of 
 the matter seems to be that all such compositions will with- 
 stand 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 a large degree upon their body, and upon 
 the way in which they are used. 
 
 "As far as the actual resistance to heat is concerned, common 
 lime and sand mortar in small quantities, i.e., when used for 
 the joints between brickwork or as a plastering on a brick wall 
 has greater fire-resisting qualities than any other plastic mate- 
 rial. It is not uncommon for the surfaces of bricks to be melted 
 and the mortar joints to be left standing out from the wall like 
 a honeycomb." * 
 
 Lime plaster, applied on wire lath will also withstand a high 
 degree of heat without injury, but is liable to be washed away 
 in places by streams of water. 
 
 On the other hand, lime mortar used by itself, as in plaster 
 blocks, is practically worthless as a fire-proof material. 
 
 Hard wall plasters, or patent plasters, when applied to brick 
 work or metal lath, are, in all cases, equal in heat-resistance to 
 common lime, and many of the patent plasters will stand the 
 combined effects of fire and water longer than the common 
 mortars (see partitions, pp. 741-751). 
 
 Plaster of Paris. Compositions of plaster of Paris and 
 broken bricks, wood, chips, or sawdust are non-conductors of 
 heat and possess fire-resisting properties of considerable magni- 
 tude, and, on account of their lightness and cheapness, are used 
 to quite an extent in fire-proof or semi-fire-proof buildings. 
 
 In France such compositions have been used for generations 
 for forming ceilings between beams, and its durability and fire- 
 proofing qualities are there unquestioned. 
 
 Plaster-of-Paris compositions when subjected to a severe 
 heat are softened on the surface, and when water is thrown 
 upon it the plaster washes 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, which contains a large proportion of 
 asbestos. 
 
 "Claims of great fire-resisting properties are made for this 
 
 *P. B. Wright, in the Brickbuilder, Sept., 1896. 
 
734 FIRE-PROOFING OF BUILDINGS. 
 
 material, as well as resistance to the effects of water during firej 
 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 nails without chipping or crack- 
 ing. The weight is said to be about half that of ordinary cement 
 mortar." 
 
 Asbestic was subjected to a severe fire-and-water test in 
 the presence of the officials of the Supervising Architect's office 
 at Washington, " and the plaster did not crack or drop, but 
 remained intact." 
 
 "All of the walls, ceilings, and columns of the appraiser's 
 warehouse in New York City were covered with a coat of asbestic 
 applied from | to f of an inch thick, on the concrete or terra- 
 cotta surfaces. 
 
 "The great objection to the use of this material lies in its 
 slow drying, the time required for a thorough drying out being 
 usually very long." * 
 
 Cement Concretes. The principal competitor of terra- 
 cotta tiling for fire-proofing purposes is concrete composed of 
 Portland cement and various aggregates. Many tests have 
 been made to determine the fire-proofing qualities of cement 
 concretes, and volumes have been written pro and con; as a 
 result it is now generally recognized that for floor-construction 
 good cinder concrete is fully equal to porous terra-cotta and 
 that the gravel concretes are sufficiently fire-proof for many 
 classes of buildings. 
 
 Tests made by Thos. S. Johnson and J. S. Dobie to deter- 
 mine the loss of strength of cement briquettes, when subjected 
 to severe heat, showed conclusively that the strength and 
 cohesion of neat cement, and cement mortar, when in the form 
 of briquettes, is practically reduced to almost nothing, after 
 being heated to 1000 degrees F. and over.t 
 
 A great many tests on a large scale, and fires in buildings fire- 
 proofed with concrete, seem to show, how r ever, that the tests 
 above mentioned have practically no bearing on the fire-proof 
 qualities of concrete. 
 
 The most complete experiments ever made to determine the 
 fire-resisting qualities of different mixtures of concrete were 
 conducted by a commission appointed by the City of Hamburg, 
 Germany, in 1894. 
 
 * Freitag, p. 102. 
 
 t For summary of these tests, see Fire-proofing oj Steel Buildings, p. 96. 
 
FIRE-PROOFING MATERIALS. 735 
 
 "Tests were made on sixteen varieties of concrete mixtures. 
 These included cement and sand, cement and gravel; cement, 
 sand, and broken stone; cement and fine cinders; cement and 
 coarse cinders; and cement, sand, and broken basalt. The 
 tests consisted in exposing the samples to fire at a temperature 
 of 1880 degrees C. or 1976 degrees F. for a period of several 
 hours and then cooling slowly or very suddenly by the appli- 
 cation of cold water. 
 
 "The report shows that while all of the sand, gravel, and 
 stone mixtures, with one exception either crumbled or showed 
 greatly reduced coherence after the test, the cinder concretes, 
 especially the coarse mixtures, gave most excellent results. The 
 latter showed good coherence, and 'did not suffer' by wetting 
 while hot. 
 
 "The highest degree of coherence in the concretes, particu- 
 larly in the centre of the mass tested, was shown by a mixture 
 of one part cement to seven parts of coarse cinders. Fire 
 was applied 3f hours. One sample was cooled suddenly and 
 one slowly, but neither suffered under the test." * 
 
 Probably the most satisfactory tests on actual fire-proof floor- 
 construction that have ever been made, are those conducted 
 by the officials of the Building and Fire Departments of New 
 York City in 1896. A brief description of the various systems 
 tested and the results of the tests are given by Mr. Freitag in 
 his book on fireproofing. The cinder concrete in all of the tests 
 stood the action of the heat and water remarkably well, and 
 fully as good as porous terra-cotta tiling. 
 
 In one test, the cinder concrete became red-hot, but when 
 cooled by water its strength did not appear to be appreciably 
 affected. 
 
 A comparative test of semi-porous tiling, and cinder concrete, 
 made in Nov., 1897, under the most exact and impartial con- 
 ditions showed the cinder concrete to be superior in fire-resistance 
 to the terra-cotta tiling.-)- 
 
 The concrete in this test was composed of one part Aalborg 
 Danish Portland cement, two parts bay sand, and five parts 
 anthracite steam ashes (unscreened), and had been in place 
 thirty days at time of test. The temperature of the test-room 
 
 * Freitag. 
 
 t For full and complete description of this test, see "Tests," published 
 by the Roebling Construction Company. 
 
736 FIRE-PROOFING OF BUILDINGS. 
 
 was raised at a uniform rate during 1J hours to 2000 degrees 
 Fahr. and then maintained for 2 hours at between 2000 and 
 2300 degrees, when the hollow tile arch failed, and the fire was 
 quenched. Subsequent strength -tests showed that the con- 
 crete arch was uninjured at least for all practical purposes. 
 The cinder concrete also apparently gave better protection to 
 the steel beams than did the hollow tile, 
 
 As to concretes composed of broken stone or gravel, it is 
 quite generally considered that such concrete w r ill not stand 
 a very -high temperature as successfully as cinder concrete, 
 both on account of the presence of the stone, and because the 
 concrete is more dense. Nevertheless, stone concrete has stood 
 some very severe fire-tests with very satisfactory results, and 
 a building constructed entirely of stone or gravel concrete is 
 probably as nearly fire-proof as it is possible to attain. 
 
 Mr. G. L. Sutcliff, in his book "Concrete, its Nature and 
 Uses," states that "good (stone) concrete w r ill resist fire to a 
 very considerable extent. A thickness of 2 or 3 inches will 
 effectually prevent iron from being damaged, in at least moder- 
 ately severe conflagrations. The effect of fire on concrete 
 is scarcely perceptible in ordinary fires, especially when the 
 ceilings and floors are formed of that material; but in very large 
 fires the concrete would split into irregular forms, but not until 
 it became almost red-hot and was subjected to the action of 
 cold water thrown on it, and even then the result could not be 
 compared to that of ordinary stone." 
 
 Details of Fire-proof Construction. Floors. So 
 many forms of construction are used for the floors of fire-proof 
 and incombustible buildings, that the author has devoted the 
 following chapter to their consideration. 
 
 Girder and Column Protection. As the columns 
 and girders of a building form the " back-bone " of the structure, 
 it is of vital importance that they be very thoroughly pro- 
 tected from heat. As a rule, the manner of protecting these 
 structural elements depends quite largely upon the floor system 
 adopted. The concrete companies naturally prefer to use 
 concrete wherever possible, and hence where concrete is used for 
 the floor-construction it is generally employed for encasing the 
 columns and girders. Where hollow tile is used in the floors, 
 the same material is almost invariably employed for protecting 
 the steel frame. 
 
GIRDER AND COLUMN PROTECTION. 737 
 
 The usual methods of protecting girders are described and 
 illustrated in Chapter XXIV. 
 
 Columns. The destruction of iron columns by incipient 
 fires has been the common cause of the loss of vast amounts of 
 property ever since iron columns have been used. Their 
 destruction during fires, in buildings supposed to be fire-proof 
 and in which incombustible materials of construction have 
 been used, has shown the necessity for protecting them from 
 the effects of intense heat under all circumstances. These 
 disastrous effects have been intensified by the sudden throwing 
 of cold water upon the heated columns, causing them to bend 
 suddenly by contraction on the side upon which water is thrown, 
 and consequently to break with ordinary loads. The expan- 
 sion which occurs in iron columns before they have been mate- 
 rially weakened by heat is another element of weakness. The 
 first result in such cases is to raise the floors or walls; and, 
 inasmuch as the strain required to raise them is much greater 
 than that needed to hold them, the work to be done by the 
 columns is much greater under such circumstances. 
 
 In the earlier days of fireproofing, the columns were commonly 
 protected by surrounding them with hollow tiles of dense 
 terra-cotta, as in Fig. 1, the separate tiles being usually clamped 
 
 Fig. I 
 Earlier Forms of Fire-proof Column Covering. 
 
 or hooked together but not to the columns proper. The pro- 
 tection thus afforded was found to be very inefficient, as in 
 almost every large fire the column tiles were broken by the heat 
 and dislodged by the streams of water so that the iron or steel 
 was exposed to a very considerable degree. 
 
 It is now generally recognized that columns should be incased 
 with a solid mass of brick, tile, or concrete, with no air spaces, 
 except those contained in the tile themselves, and that where 
 tiles are used they should be of either the porous or semi-porous 
 material. 
 
738 
 
 FIRE-PROOFING OF BUILDINGS. 
 
 Fig. 2 shows the usual manner in which Z-bar columns are 
 now protected in the better class of fire-proof buildings, i.e., 
 
 Sheet Steel Guard\ N 
 /Mortar 
 
 Cement Gr.out> 
 2" Hollow Tile 
 
 Fig. 2 
 
 Sheet Steel. Guard 
 
 Fig. 3 
 
 where tile fireproofing is used, and Fig. 3, a common method 
 of protected round columns. 
 
 Fig. 4 
 
 The steel guard is employed only in mercantile or manu- 
 facturing buildings, and is usually only 4 to 5 feet high. 
 
 Fig. 4 shows the standard tile casing for Z-bar columns, 
 
GIRDER AND COLUMN PROTECTION. 
 
 739 
 
 finished circular. The circular blocks may be varied in size 
 to increase the diameter of the finished column. Although it 
 is not customary to do so, the efficiency of this construction is 
 greatly increased by warping the column with wire lath before 
 plastering. 
 
 To insure the protection of the metal, under the most trying 
 conditions, it is imperative that the protective covering shall 
 not be detached by the streams from the firemen's hose, so as 
 to 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. 5 shows a column protected in this way, the construc- 
 tion being essentially that adopted in the Fair Building in 
 
 Fig. 5 
 
 Chicago. The inner layer of tiles is wrapped with wire lath 
 imbedded in the mortar, and all spaces between the tiles and 
 metal filled solid with cement mortar. The protection afforded 
 by this construction should be perfect. 
 
 Where concrete is to be used for column protection, the most 
 efficient construction 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 to the 
 metal with a brush. The plank form should be set at least 2 ins. 
 outside of the metal. Concrete poured in this way, cannot 
 be dislodged by streams of water, and it also greatly strengthens 
 the column. 
 
740 
 
 FIRE-PROOFING OF BUILDINGS. 
 
 Blaster ff '"thick 
 
 Fig. 6 shows the method of protecting steel columns employed 
 
 by the Roebling Construction 
 Company. The column is first 
 furred by vertical rods held 
 in place by clamps, and then 
 by band iron laced to the 
 rods; stiffened wire lath is then 
 bent around and laced to the 
 furring. The space between 
 the lathing and the column is 
 then filled with a moderately 
 dry mixture of cinder concrete. 
 The lathing in this construction 
 is used principally as a form to 
 confine the concrete, in place 
 of a temporary wooden form, 
 
 Band Iron 
 \Rod 
 
 Clamp 
 
 Fig. 6 
 
 but it also serves to prevent the concrete from being washed 
 away during a fire. % Where wooden forms are used the con- 
 crete can be given much greater strength, so that lathing is 
 unnecessary although it forms an additional safeguard. 
 
 In many buildings having reinforced concrete floors, the 
 columns are protected simply by metal lath and plaster. When 
 but a single covering is provided, as in Fig. 17, Chapter XXII, 
 the protection cannot be considered as fire-proof, but when two 
 coverings are provided, as in Fig. 7, it is probably all that is 
 
 pace 
 
 Steel Fumng 
 Strips 
 
 Fig. 7 
 
 necessary for cast-iron columns, and as efficient for steel columns 
 as the terra-cotta covering, shown in Fig. 1. The greatest 
 defect in lath and plaster for fireproofing is that the plaster is 
 liable to be dislodged by the force of the water from the fireman's 
 hose. 
 
GIRDER AND COLUMN PROTECTION. 
 
 741 
 
 When there are two coverings, however, this danger is re- 
 duced to a minimum. 
 
 Probably the most defective part of the coverings of columns, 
 whatever the material used, is about the connections with the 
 beams and girders. Concrete undoubtedly is better adapted 
 for covering this portion of the column than any other material, 
 as, being plastic, it can be made to fit into any space and around 
 any form of connection. 
 
 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 run water-, waste-, and vent-pipes immediately 
 alongside the steel columns, and inside the fireproofing in- 
 closure." * This is undoubtedly bad construction, and in the 
 better types of fire-proof buildings the pipe space is separated 
 from the columns by the fireproofing. 
 
 Figs. 8 and 9 show the method of running the pipes in some 
 
 i 
 
 Girder 
 
 Blaster 
 
 Fig. 9 
 
 of the latest fire-proof buildings, and is probably as satisfactory 
 as any method where the pipes are to be run beside the columns. 
 
 Fig. 10 shows a somewhat similar method where concrete 
 and metal lath and plaster are employed for the fireproofing. 
 
 Partitions. A great many forms of construction, in- 
 volving various incombustible materials, have been used for 
 the partitions in fire-proof buildings, and there are several 
 which answer the purpose very satisfactorily, while others 
 have proved wholly inefficient. For bearing partitions (those 
 which support floor beams) there are probably no materials 
 
 * Freitag. 
 
742, 
 
 FIRE-PROOFING OF BUILDINGS. 
 
 more satisfactory than brick and concrete. The latter may 
 be used either in the form of blocks, or may be poured between 
 orms. Partitions of brick should be at least 12 ins. thick, 
 as thick walls are less affected by heat than thin walls. 
 
 As a rule the partitions in fire-proof buildings are not re- 
 quired to support any weight, but merely to serve the purpose 
 of dividing the space into rooms, and to confine a fire to the 
 compartment in which it originates. 
 
 The choice of construction should be influenced in some 
 degree by the character of the building, and by the openings 
 
 Space for Pipes and ~Wires N 
 Concrete^ 
 
 Wire Lath and Plaster/ 
 Fig. 10 
 
 in the partitions. If partitions are desired which shall abso- 
 lutely prevent the passage of fire and water, then porous terra- 
 cotta in blocks 6 ins. thick is undoubtedly the best material 
 to use, and all openings should be made absolutely fireproof 
 and closed by fire-proof doors or wire glass in metal frames. If 
 the partitions are to contain wooden frames with ordinary win- 
 dows and doors, the tile partitions offer no advantage over 
 plaster partitions, and on account of the less space which they 
 occupy, and their reduced weight, the solid partitions of metal 
 and plaster are often preferable to tile or block partitions. 
 
 Terra-cotta Partitions. These are usually built of 
 blocks either square or brick-shaped, according to the par- 
 ticular product used. The square blocks are usually 12"X12" 
 on the face, and the brick-shaped blocks are usually 12 ins. 
 long but of varying heights. Both shapes are made in thick- 
 nesses varying from 3 to 12 ins., the 3-, 4-, and 6-inch blocks 
 being most commonly used; the 4-inch blocks being the most 
 popular for ordinary work. Fig. 11 shows typical shapes of 
 both the square and brick-shaped blocks. 
 
 The blocks are commonly set with the voids horizontal, as 
 in Fig. 11, the blocks breaking joint like bricks, but at the ends, 
 and in filling small spaces they are sometimes set vertically. 
 
FIRE-PROOF PARTITIONS. 
 
 743 
 
 Fig. 12 shows round- and angle-cornered partition-blocks,, 
 which must be set vertically. 
 "Terra-cotta partitions of a 2-inch thickness have been 
 
 Fig. II 
 
 Terra-cotta Partition-blocks. 
 
 placed on the market, but have not been extensively used. A 
 
 2-inch terra-cotta partition of any strength or efficiency is 
 quite impracticable, and where floor area is so valuable that) 
 
744 
 
 FIRE-PROOFING OF BUILDINGS. 
 
 more space cannot be occupied, terra-cotta is not the material 
 to be employed." * Through the addition, however, of band- 
 iron laid between the courses and patented under the style 
 "Phoenix," the strength of a 2" tile partition is greatly increased. 
 Porous vs. Dense Material. For inside partitions 
 the porous material is preferable to the dense, while for out- 
 side walls the dense material should be used. With dense 
 
 Fig. 12. 
 Partition-blocks with Angular and Circular Corners, 
 
 tiling it is necessary to insert wooden nailing strips. With 
 porous tiling solid blocks of the same material should be in- 
 serted wherever necessary to provide nailings. 
 
 Mortar. Tile partition blocks should be set in mortar 
 made of one part lime-putty, two parts cement, and two to 
 three parts sand. The blocks should be well wet before setting 
 and the partition wet down before the plastering is applied. 
 
 Height and Length. "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-inch, 16 ft. for 4-inch, and 20 ft. for 6-inch 
 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 ceiling." * 
 
 * Freitag. 
 
FIRE-PROOF PARTITIONS. 745 
 
 Weight. The weights of either porous or dense terra- 
 cotta partitions will vary as follows: 
 
 3-inch partition, 12 to 16 Ibs. per sq. ft. 
 4-inch partition, 13 to 19 Ibs. per sq. ft. 
 5-inch partition, 20 to 22 Ibs. per sq. ft. 
 6-inch partition, 22 to 23 Ibs. per sq. ft. 
 8-inch partition, 28 to 33 Ibs. per sq. ft., 
 
 not including plastering, which will add about 10 Ibs per sq. ft. 
 for both sides. 
 Method of Setting and Details of Construction. 
 
 Tile partitions properly designed and built should stand intact 
 in almost any fire, but, as a matter of fact, there have been 
 few instances where they have passed through a severe fire 
 without suffering very material damage, owing to faulty design 
 or construction or both. For the best construction of tile 
 partitions the reader is referred to Mr. Freitag's work on " Fire- 
 proofing." 
 
 Plaster and Metal Partitions. Within the past 
 decade thin partitions of plaster applied to 'metal lath and 
 studding so as to make a solid partition finishing about 2 ins. 
 thick have been very extensively used in fire-proof buildings, 
 and while they will not stand as long in a severe fire as a first- 
 class terra-cotta partition, they are just about as effective 
 as the average tile partition containing doors and windows, 
 and on the whole have proved quite satisfactory for office 
 buildings, apartment houses, etc. 
 
 These partitions are remarkably stiff, owing to the adhesion 
 of the plaster to the steel, and they are lighter and occupy 
 less space than any other practical fire-proof partition of 
 equal strength. 
 
 Figs. 13 and 14 show the usual method of constructing 2-inch 
 partitions. The studs, usually f- or 1-inch channels, are 
 bent and punched at the ends, and at the bottom are nailed 
 I to wood strips, which are first secured to the floor-panels, or 
 to the top of the steel beams where the partitions come over 
 them. These wood strips have been found necessary as a sort 
 of cushion to permit of the expansion of the studding in case 
 of fire. 
 
 At the top, the studs are nailed to the under side of the 
 floor-panels, or in the case of a suspended ceiling, are wired 
 to the bars supporting the ceiling. At the openings 
 
746 
 
 FIRE-PROOFING OF BUILDINGS. 
 
 inch angles are used, and these are bored every 16 inches foi 
 No. 12 screws used in attaching the rough wood frame to the 
 angles. 
 
 After the studding is in position, metal lathing, of eithei 
 
 ^"'Nailing 
 Strip 
 
 i&?&$e^^ 
 
 Fig. 13 
 
 the stiffened wire, expanded metal or herring-bone pattern, 
 is laced to one side of the studding with No. 18 galvanized 
 
 %" Channel \ 
 IFurring for Basev 
 
 1" x l" x %j" L\ 
 
 Staple/ V 
 No. 18 Gal. Wire Lacingi- 
 
 Fig. 14 
 
 /Rough Frame 
 
 4 
 
 ,-i,. 
 
 wire. Fig. 13 shows the Roebling stiffened wire lath, having 
 a 1-inch solid steel rib woven in everv 7k inches, the rib running 
 
FIRE-PROOF PARTITIONS. , 747 
 
 crosswise over the studs. While stiffened wire lath undoubtedly 
 makes a stiffer partition and a firmer surface for the plaster 
 yet great quantities of expanded metal and perforated lath 
 are used for these partitions. 
 
 After the lathing is in place the carpenter should attach 
 wooden grounds for securing the base, chair-rail, picture- 
 moulding, etc. These are secured by staples and when the 
 partition is plastered become very rigid. 
 
 In plastering these partitions, five coats of plaster are re- 
 quired 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, Ada- 
 mant, Rock Wall, and many others. 
 
 The partitions acquire their stiffness largely from the solidity 
 of the plastering, hence the firmer and harder the plastering 
 the more substantial the walls. 
 
 J>ouble Partitions. Electric wires and |-inch gas-pipe 
 can be run in the 2-inch solid partition, but if it is desired to 
 run larger pipes, double partitions, i.e., partitions with lathing 
 on each side of the studding, must be used. For these parti- 
 
 }i .Steel Rodx 
 
 No. 18 Gal. Wire Lacing / 
 
 Fig. 15 
 
 tions, 2-, 3-, or 4-inch channels or flat bars set edgeways, may 
 be used, sheet steel channels being probably the most economi- 
 cal. When the space between the studding is not filled with 
 mortar or concrete, the double partition will not stand fire 
 and water as well as the solid partition, while it is much more 
 expensive. 
 
 Fig.. 15 shows a partial section through a solid partition 
 finishing 4 inches thick when plastered, which possesses great 
 strength and absolute resistance to fire and water, besides 
 affording convenient space for pipes and a thicker jamb for 
 door frames. This partition has a core of cinder concrete, 
 
748 , FIRE-PROOFING OF BUILDINGS. 
 
 with metal lath on both sides, and is plastered in the usual 
 way. As the concrete will receive nails, no wood furring is 
 necessary in order to attach the base-board, chair-rail, or 
 picture-moulding. 
 
 Berber's Economy Studding and Furring. 
 Fig. 16 illustrates a patent stud manufactured by the Berger 
 Manufacturing Company. It is made of 
 No. 18 or No. 20 sheet steel, and in five 
 sizes, varying from f to 1J inches. The 
 peculiar advantage 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, fastening 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 stud to permit of ex- 
 pansion. 
 
 Where partitions intersect or angles 
 occur, angle-irons with prongs are used 
 in place of the T. 
 
 By using this stud and expanded metal 
 lathing, a saving in cost can be effected 
 over the construction shown by Fig. 13. 
 p. These T's are also used for supporting 
 
 suspended ceilings under I beams, the T's 
 
 being secured to the flange of the beams by specially designed 
 clips. Furring strips and channels are also made on the same 
 principle. 
 
 Spacing of Studding. For 2-inch solid partitions with 
 f-inch rolled channels or 1-inch economy studs, the studs 
 should be placed 12 inches on centres when the height of the 
 story exceeds 10 feet. When the heights of the story is less 
 than 10 feet, a spacing of 16 inches will answer. For hollow 
 partitions with 2-inch studs, the studs can be spaced 16 inches 
 
FIRE-PROOF PARTITIONS. 
 
 749 
 
 on centres for story heights of 16 feet and less. For greater 
 heights they should be placed 12 inches on centres. 
 
 Weight. The weight of a 2-inch solid partition will be 
 about 20 Ibs. per sq. ft. when dry. The weight of partitions 
 of greater thickness may be estimated on a basis of 120 Ibs. 
 per cu. ft. for plaster and 96 Ibs. for cinder concrete, slightly 
 tamped. 
 
 Cost. The cost of 2-inch solid partitions will vary from 
 16 to 20 cts. per sq. ft. including plaster. 
 
 Plaster Block Partitions. Blocks made of plaster 
 of Paris combined with various substances such as cinders 
 wood chips, cocoanut fibre, asbestos, etc., have been used to 
 quite an extent for forming partitions in fire-proof buildings, 
 
 Fig. 17 
 
 Mackolite Partition Tile. 
 
 but while they are to be preferred to partitions built with 
 wooden studding, and will resist fire for a considerable period 
 of time, they cannot be considered as absolutely fire-proof, or 
 suitable for first-class fire-proof buildings. The principal 
 advantage claimed for these partitions is their great lightness 
 and reduced cost as compared with terra-cotta tile. Plaster 
 blocks can be readily cut with a saw, and will receive and hold 
 nails tolerably well. 
 
 The best known and most extensively used of the plaster 
 blocks are the Mackolite Hollow Blocks, made by Mackolite 
 Fire-proofing Company of Chicago. Mackolite partition tile are 
 made of the general shape shown by Fig. 17 and of 3, 3J, 4, 
 6, 8, and 12 ins. in thickness. The 3-, 3J-, and 4-inch tile 
 are made 48 inches long, and the others 30 inches long, all of the 
 
750 FIRE-PROOFING OF BUILDINGS. 
 
 fcile being made 12 inches high. The blocks are laid in regulaf 
 courses breaking joint as in cut-stone work. Lime mortar is 
 used for setting. In fitting around openings or at angles the 
 blocks are cut with a saw which effects a material saving in 
 time and material. It is claimed that the blocks make a very 
 strong partition. The composition of the blocks is plaster of 
 Paris mixed with certain chemicals, reeds, and fibre. Reeds 
 of the same length as the blocks are placed in the moulds, and 
 the plaster of Paris and fibre is then mixed with water to which 
 the chemical has been added and poured around the reeds so 
 that they shall be nowhere exposed. The reeds give longi- 
 tudinal strength to the blocks while the fibre makes them 
 tough and elastic. The material sets in about one half hour, 
 after which the blocks are kiln-dried for four days. 
 
 Boards of Mackolite, 12 ins. wide by 4 ft. long, and from 
 j ins. to 2 ins. thick are also made by the same company for use 
 with iron or wooden studding. 
 
 Weight. These blocks make the lightest practical parti- 
 tion known the weight' of the blocks per sq. ft. being as 
 follows: 
 
 Thickness of block, inches 3 3i 4 5 6 8 
 
 Weight in Ibs. per sq. ft 9i 10| 12 15 18 22 
 
 The plaster-boards, 1 in. thick, weigh 4 Ibs. per sq. ft. About 
 8 Ibs. per sq. ft. should be added to the weight of the partition 
 tile to obtain the weight of the partition when plastered both 
 sides. 
 
 Tests of the relative heat-conducting qualities of Mackolite 
 and fire-clay seem to show that the former is a much better 
 insulating material than the latter. The material also stands 
 well in fire, so long as water is not applied. While the author 
 does not consider any plaster-material equal to porous terra- 
 cotta for fire-proofing purposes, yet the Mackolite blocks make 
 a very good partition, and for many buildings all that can be 
 desired. All of the partitions in the newer portions of the 
 Monadnock block, Chicago, are built of Mackolite, and it has 
 been extensively used in Illinois and the surrounding States. 
 
 Sacket's Plaster Board. This is a composite board 
 of alternate layers of plaster and paper, the whole being about 
 J inch thick and designed to take the place of either wood or 
 metal lath with some advantages over both. 
 
FIRE-PROOF PARTITIONS. 751 
 
 It is claimed that this board will not warp, buckle, or shrink, 
 and that plastering applied to it will not fall off. As a fire 
 retardent, it is claimed to be equal to metal lath, and when 
 wired to metal studding may be considered as a fire-proof 
 partition. It has the advantage of being very light, and re- 
 quiring but little plastering material, with a consequent reduc- 
 tion in the amount of water used in plastering. 
 
 The boards are 32X36 ins., they may be nailed to wooden 
 studding or flat against solid beams, or plank, and can be cut. 
 with a saw. 
 
 For plastering the best results are obtained by applying 
 first a brown coat of hard wall-plaster \ to f inch thick; when 
 this is thoroughly set it should be finished with a thin coat of 
 regular hard finish (lime-putty and plaster). 
 
 This board has been extensively used in the Eastern States, 
 and in many prominent buildings. 
 
 Considering the saving effected in the plastering, the board 
 costs less than metal lath, and but a trifle more than wood 
 laths. 
 
 Deadening 1 Quality. The resistance to the passage of 
 sound through fire-proof partitions is an important considera- 
 tion in buildings used for apartments, and where the rooms 
 are to be used as music studios or for conservatory work, it 
 becomes a matter of great importance. 
 
 In Jan., 1895, some tests were made to determine the relative 
 deadening qualities of the different partitions shown by Fig. 18, 
 the object being to decide upon the construction that should 
 be used in Steinway Hall, Chicago. 
 
 The rank in sound-proof efficiency of the different partitions 
 tested is shown by the numbers at the right of Fig. 18. 
 
 The 4-inch porous partition was used, but was not a success. 
 In the Fine Arts Building, in the same city, double partitions, 
 similar to No. 1, were used, and the author is informed that 
 they have been a great success. 
 
 It is surprising to note that in the tests above mentioned, 
 the 2-inch solid-plaster partition (common mortar) ranked 
 higher than those with double studding. The relative cost 
 of partitions Nos. 1, 2, and 3, including plastering, is given 
 by- the Illinois Terra-cotta Lumber Company as $1.86, $1.16, 
 and SI. 14 respectively. 
 
 In 1892, Prof. Charles L. Norton tested the sound-deadening 
 qualities of several forms of partitions, with the purpose of 
 
752 
 
 FIRE-PROOFING OF BUILDING& 
 
 /Plaster 
 
 ' Plaster 
 
 ls^^j~^ 
 
 Angle Iron 
 12 "Centers 
 
 I \#"lronl 
 
 \Wirp filnth TJ 
 
 Rod Filled in solid 
 with Plasteu 
 
 Wire Cloth Laced to Rod 
 SOLID PLASTER PARTITION 
 
 " Studs 16" Centers 
 
 Wire Cloth. Laced to Rods 
 
 ^" Rod 12" Centers/ 
 
 Iron 16 "Centers 
 
 No Filling: 
 
 Plaster 
 
 ExpandedJVIe_tal/ 
 
 " Rod.12" Centers 
 
 ' |J> 
 
 " Iron Studs 16 "Centers 
 
 ^Wire Cloth Laced to Rod 
 
 Iron 16 "Centers 
 
 Tfl||f' 
 
 Expanded Metal/' Blaster * ^A" 
 
 Expanded Metalx 
 
 ii? oi I 
 
 ron 16" Centers 
 
 Piaster, ? ^ 
 
 Fig. 18 
 
 Sound carried through probably because of metal connections. 
 
FIRE-PROOF PARTITIONS. 
 
 753 
 
 selecting the best incombustible sound-proof partition for the 
 dormitories of the New England Conservatory of Music, in 
 which practically every room is a music studio. The results 
 of these tests, with a description of the partitions was pub- 
 lished in Insurance Engineering for August, 1902. 
 
 The various partitions were rated by Prof. Norton as follows: 
 
 No. 
 
 Room. 
 
 Side. 
 
 Scale. 
 
 Composition. 
 
 1 
 
 E 
 
 Left 
 
 100 
 
 Cabot's quilt ,3 thick + metal lath. 
 
 2 
 
 E 
 
 Right 
 
 95 
 
 .. 2 .. + .. .. 
 
 3 
 
 E 
 
 Rear 
 
 95 
 
 2 .. + ., 
 
 4 
 
 C 
 
 Rear 
 
 85 
 
 Sackett board, 2 felt on Ts. 
 
 5 
 
 C 
 
 Left 
 
 85 
 
 2 " " C. 
 
 6 
 
 C 
 
 Right 
 
 80 
 
 .. 2 .. 
 
 7 
 8 
 
 D 
 D 
 
 Rear 
 Right 
 
 75 
 
 75 
 
 Metal lath + paper. 
 " " +felt. 
 
 9 
 10 
 
 B 
 A 
 
 Right 
 Rear 
 
 60 
 50 
 
 Two 2-in. Keystone block with 2-in. airspace. 
 4-in. National terra-cotta blocks. 
 
 11 
 
 B 
 
 Rear 
 
 50 
 
 3-in. Keystone blocks. 
 
 12 
 
 A 
 
 Right 
 
 45 
 
 3-in. National terra-cotta blocks. 
 
 13 
 
 B 
 
 Left 
 
 40 
 
 2-in. Keystone blocks. 
 
 14 
 
 A 
 
 Left 
 
 40 
 
 2-in. National terra-cotta blocks. 
 
 15 
 
 D 
 
 Left 
 
 30 
 
 2-in. metal lath, solid plaster. 
 
 "Nothing more is to be inferred from the numerical effi- 
 ciencies (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 parti- 
 tions." 
 
 Professor Norton recommended a partition of Sackett board 
 and plaster with two thicknesses of Cabot's quilt between the 
 plaster board, and this construction was adopted. The stud- 
 ding was put up the same as for the 2-inch solid partition, the 
 quilt secured to each side of the studs, and the plaster board 
 was wired on to the studding through the quilt. This also 
 makes about as light a partition as it is possible to obtain. 
 
 Roof. Flat roofs are usually 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, for draining the water. As 
 the roof-loads are usually less than the floor-loads and 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 practically the same for both. 
 
 If terra-cotta is employed for the floor-panels, light side- 
 method arches, with raised skewbacks as shown by Fig. 5, 
 
754 FIRE-PROOFING OF BUILDINGS. 
 
 Chap. XXIV, are often employed when the beams are spaced 
 5 to 6 feet apart. The long-span reinforced tile systems, such 
 as the Johnson or Herculaneum, are also well adapted to roof- 
 construction, as they can be made to span from girder to girder, 
 without the use of intermediate beams. Where reinforced 
 concrete is used for the floors, the same construction, with a 
 less thickness of concrete, is generally used for the roof, except 
 that for the roof, the reinforcing material, generally some sort 
 of steel fabric, is usually placed on top of the beams. When 
 terra-cotta tiles are used, they should be levelled off with a 
 filling of cinder concrete to form a uniform surface for the 
 roofing. 
 
 When the roof is formed of reinforced concrete, the beams 
 should be set so that the concrete will give the desired incli- 
 nation to the roof, with a nearly uniform thickness, as this 
 reduces the amount of concrete required, and also the weight. 
 
 If the roof is to be covered with tin or copper, nailing-strips 
 should be imbedded in the concrete, the same 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 require no woodwork of any kind. 
 
 Whether terra-cotta or concrete is used for the roof panels, 
 the sides and bottoms of the steel beams and girders should 
 be efficiently protected, and all columns or other structural 
 metal in the roof space should also be well protected. In the 
 ordinary building, having stair 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 is often the poorest protected portion of the 
 building. 
 
 Pitched Koofs. Pitched roofs may be constructed in 
 various ways, according to the material that is to be used and 
 the kind of roofing that is to be employed. 
 
 When terra-cotta is to be used for the fireproofing, the most 
 common method of construction is to frame the roof with 
 I-beam rafters and T-iron purlins, set horizontally, and 16 
 or 18 ins. on centres. Between the tees, book or roofing 
 tiles are placed as in Fig. 19, and the roofing is applied directly 
 to the surface of the tile. If the roofing is to be of slate or 
 
 * Freitag, page 288. 
 
FIRE-PROOF ROOFS. 
 
 755 
 
 clay tiles, solid porous terra-cotta blocks should be used, be- 
 tween the tees, as the solid blocks hold the nails better than 
 the hollow tile. The same construction may be used for a 
 flat roof, bui 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. 19 it is impossible to efficiently protect the bottom of 
 the tees from the effects of heat by any economical method. 
 
 The author believes that reinforced cinder concrete, or 
 reinforced porous terra-cotta tile (Johnson System) afford 
 the best and also the most economical construction for fire- 
 proof pitched roofs. Either of these constructions may be 
 
 Fig. 19 
 
 filled between or on top of the rafters without the use of purlins 
 except about once in 6 to 10 feet, to prevent sliding and to 
 stiffen the roof. 
 
 "Three-inch plates of concrete with expanded metal im- 
 bedded have been successfully used up to spans of 6 to 7 feet 
 and in some cases even to 8 feet. 
 
 "The concrete is deposited on wooden centrings, as in the 
 floor-construction, and the upper side is smoothed off during 
 the setting and is then floated smooth and straight to receive 
 the roof -covering." * The roof - covering, usually slate, or 
 
 * Freitag. 
 
756 
 
 FIRE-PROOFING OF BUILDINGS. 
 
 clay tiles, may be nailed directly to the concrete, as cinder 
 concrete holds the nails nearly as well as does wood. (Note. 
 The above applies only to cinder concrete, as it is quite im- 
 possible to nail into rock or gravel concrete.) 
 
 With concrete roofs the rafters should also be surrounded 
 with concrete held in place by metal lath. With terra-cotta 
 roofs, the beams should be incased with terra-cotta blocks. 
 
 Fig. 20 shows the standard shapes of book tile and solid 
 roofing tile. These are made 2, 2J, and 3 ins. thick, and 15J, 
 
 BOOK TILE 
 
 GOVERNMENT ROOFING TILE 
 Fig. 20 
 
 17|, and 23J ins. long. Three-inch book tile weighs about 
 13 pounds per sq. ft. and the 2J-mch so lid tile about 16 pounds. 
 
 Both of these shapes are also used for ceilings and where a 
 light fire-proof filling is required. 
 
 Mansard Roofs are usually framed with 4-, 5-, or 6-inch 
 rafters, riveted or bolted to a wall-plate. The space between 
 the rafters may be filled with cinder concrete, hollow parti- 
 tion tile, or blocks extending from rafter to rafter as in Fig. 21 
 Slate or tiles may be nailed directly to cinder concrete or to 
 porous terra-cotta. 
 
 Probably the best provision for attaching slate or tiles, 
 however, is to nail 1J"X2" wood strips to the outer face of 
 the concrete or terra-cotta, the strips being set at the proper 
 distances apart to receive the slate or tile, and then plastering 
 between the strips with cement mortar. This gives a better 
 nailing for the roofing, and the wood strips would not be affected 
 by fire until the slate was practically destroyed. 
 
 With concrete or partition tile filling, the rafters may be 
 spaced 5 to 6 feet apart, while with single blocks, as in Fig. 21, 
 they cannot be spaced more than 2 feet on centres. 
 
 Roof Covering's. The materials ordinarily used for 
 the roof-covering of fire-proof buildings are: 1. Tar and gravel; 
 2. Asphalt and gravel or sand; 3. Vitrified tiles, brick or slate 
 
FIRE-PROOF ROOFS. 757 
 
 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 
 
 Fig. 21 
 
 Mansard Roof. 
 
 8 ins. square and 1J ins. thick, are made for this purpose, and 
 slate tiles 12 ins. sq. by 1 in. thick have been used. Flat 
 vitrified brick tiles are also used. 
 
 Gravel roofing should not be used on roofs having an incli- 
 nation exceeding f inch in 1 foot. For pitch roofs, either slate, 
 clay tiles, or metal tiles may be used. Clay tiles will stand 
 exposure to fire better than slate, and are to be preferred, 
 especially some of the patent interlocking tiles. 
 
 Suspended Ceilings. Office buildings, apartment 
 houses, etc., having a flat roof, require a ceiling below the roof 
 for appearance in the rooms, and also for heat insulation. 
 
 In office buildings the upper ceiling is often framed and 
 
758 
 
 FIRE-PROOFING OF BUILDINGS. 
 
 constructed similarly to the floors, but with lighter construc- 
 tion. More often the ceiling is suspended from the roof, as 
 this requires much less steel and is consequently much cheaper, 
 while it answers the purpose fully as well i.e., if the roof- 
 beams are efficiently protected. 
 
 Fig. 22 shows a common construction for such ceilings; 
 wrought-iron hangers about l"Xi", split at one end to hook 
 
 ki# Channel Bars v Metal Lath: Laced to Channel Bars 
 
 Fig. 22 
 
 over the lower flanges of the roof-beams, are used to support 
 flat steel bars, spaced about 4 feet on centres, and to the under 
 side of these are laced f-inch or J-inch channels, 12 or 16 ins. 
 on centres which receive the metal lathing. The bottom of 
 the hangers are 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 connections being made by lacing wire, or by 
 bending the iron. Where stiffened wire lath, such as the 
 Roebling or Clinton, is used, the channels may be spaced 16 ins. 
 on centres, but if the ordinary expanded laths are used, it is 
 better to place the channels 12 ins. on centres, and if ordi- 
 nary lime mortar is used for plastering, a 12-inch spacing is 
 really necessary. 
 
 Another system is to use only one set of horizontal bars, 
 which are spaced close enough to receive the lathing, and 
 every bar is supported by hangers. With stiffened wire lath- 
 ing, and roof-beams spaced not over 5 feet apart, and short 
 hangers, this may be the cheaper system, but without the 
 stiffened lathing, there is no stiffness to the ceiling at right 
 angles to the bars. Where the hangers are 3, 4, or 5 feet long, 
 and the spans between beams are more than 5 feet the two-bar 
 
SUSPENDED CEILINGS. 
 
 759 
 
 system shown by Fig. 22 will require less steel, for the reason 
 that the channels, having a span of only 4 feet may be made 
 very light, and only J or J as many hangers are required. 
 
 In place of the small channels, small tees, or flat bars may 
 be used, but where the bars are held by lacing, the channels 
 are to be preferred. 
 
 Figs. 23 and 24 (from Freitag's " Fireproofmg," p. 286) 
 show very satisfactory details for the construction of the two- 
 bar system. 
 
 Instead of the hook shown in Fig. 23, the hanger may be 
 
 Fig. 23 
 
 split at the top, and one half bent around one side of the beam 
 flange, and the other half bent around the other side. 
 
 Roof beams 5'(f et& 
 
 
 f, 
 
 
 XjtL 
 
 o 
 
 J- _!_ 
 
 Fig. 24 
 
 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 ins. long, 
 wrapped closely around the bars and hammered tight. 
 
760 
 
 FIRE-PROOFING OF BUILDINGS. 
 
 Trusses. Where 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 so that they will not expand sufficient to affect the vertical 
 position of the columns by which they are supported. 
 
 The following description of the covering of the trusses in 
 the new Tremont Temple, Boston, furnishes a good illustration 
 of the way in which this should be accomplished: 
 
 "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.' 7 
 
 Numerous shapes of terra-cotta tiles are made for casing the 
 structural shapes commonly used in steel trusses. Some of 
 these are shown by Fig. 25. The tiles should always be secured 
 
 -SECTION OF BRACING 
 SECTION OF STRUT 
 
 Fig. 25. 
 
 Tiles for Protecting Steel Trusses. 
 
 in place by metal clamps passing entirely around the envelope, 
 or better still, by wrapping with wire lath. The tiling should 
 then be plastered with hard wall plaster. 
 
 Furring of 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 
 
FIRE-PROOF WALL FURRING. 
 
 761 
 
 space between the plaster and the masonry to prevent the 
 passage of moisture. This fur- 
 ring should be either of terra- 
 cotta or metal, and never of wood. 
 Most, if not all, of the manufac- 
 turers of terra-cotta fireproofing 
 make furring tile, similar to that 
 shown by Fig. 26, for lining walls. 
 
 Burring lile 
 
 Fig. 26. 
 
 These tiles are set in mortar, and secured to the walls by spikes 
 driven in the joints. 
 
 Partition tile are also often used for the inner 4 ins. of brick 
 walls, the tile taking the place of a row of brick, as in Fig. 27. 
 
 Fig. 27. 
 
 By this means dampness is excluded without additional thick- 
 ness to the walls, and the only additional expense is the extra 
 cost of the hollow tile over common brick. When using either 
 furring blocks or hollow tile, the mason should be careful not 
 to drop mortar into the hollow spaces. Wire lathing, with 
 a 1-in. V-rib woven in every 7J ins. also makes a good furring 
 
762 FIRE-PROOFING OF BUILDINGS. 
 
 for brick walls, as it is easily applied, and affords an air-space 
 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. 
 
 Where walls are furred or lined with tile, solid porous terra- 
 cotta blocks should be built in wherever nailings are required 
 for base, picture moulding, etc. 
 
 Metal Furring. To produce architectural forms in the 
 interior decoration of fire-proof buildings, metal furring, and 
 lathing are now used almost universally. 
 
 The furring is always of a sham nature, and is never employed 
 to carry loais 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, clips, etc. The furring 
 pieces are bent or shaped to the approximate outline of the 
 finished plaster work, so that when the lathing is applied it 
 will not require more than 1J or 2 ins. of plaster to give the 
 desired outline. For plane surfaces the furring should be 
 brought to within f in. of the plaster line. Deep beams, etc., 
 should be braced by diagonal rods, to prevent distortion. 
 
 All structural steel members should always be fireproofed 
 back of the furring. 
 
 The lathing is secured to the furring by means of No. 18 
 galvanized lacing wire. 
 
 The spacing of the furring should be either 12 or 16 ins., 
 according to the kind of lath that is to be used. 
 
 Stairs. The stairs in the ordinary fire-proof building are 
 usually the most vulnerable part of the building, aside from 
 the wood finish, and in case of a severe fire, are usually unsafe 
 even for the use of the firemen. Unless inclosed with solid 
 brick walls, and shut off from the hallways by fire-proof doors, 
 the staircase forms a flue for the flames, so that the stairs are 
 exposed to intense heat. In such situations, even an absolutely 
 fire-proof stairway could not be used during a fire, and possibly 
 it is for this reason that greater pains have not been taken to 
 make the stairs fireproof. 
 
 A practical method of insulating the stairways from the hall- 
 
FIRE-PROOF STAIRS. 763 
 
 ways is given in Part II., of the author's " Building Construction," 
 p. 522e. 
 
 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 as fire-proof, but it is difficult to protect the iron 
 work of a stairway, as usually built, and at the same time pre- 
 serve 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. 
 
 Some excellent details for ornamental iron stairs were pub- 
 lished in the March, 1903, number of Fireproof, in an article 
 by Mr. J. K. Freitag. 
 
 Mr. Freitag calls attention to the fact that slate and marble 
 treads and platforms should never be used in stairs without a 
 support beneath. When subjected to heat, marble and slate 
 will crack and fall away, leaving the stairs impassable. 
 
 A fire department captain in New York -City recently lost 
 his life through the collapse of a marble platform. 
 
 If these materials are to be used, therefore, there should be 
 a sub-tread of iron, or concrete, beneath them. 
 
 A really fire-proof stair should be constructed with as little 
 iron work as possible, and that incased in fire-resisting mate- 
 rials. 
 
 It is possible and practicable to build stairs of clay tiles, 
 brick or reinforced concrete that are absolutely fire-proof. The 
 stairs in the Pension Building at Washington are built of brick 
 with slate treads, and in many of the earlier government 
 buildings the stairs are of stone. Stones suitable for stairs, 
 however, will not stand heat as well as cast iron. Part I. of 
 the author's "Building Construction" contains descriptions 
 with illustrations of some brick stairs. 
 
 The Guastavino Company have built several stairways on 
 their system, using flat clay tile imbedded in cement. No 
 iron work whatever is used in this construction, hence it is 
 eminentlv fire-proof. 
 
 Fig. 28 shows a partial section of a tile stairway 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 me- 
 
764 
 
 FIRE-PROOFING OF BUILDINGS. 
 
 chanics for carrying up material during the erection of the 
 building. 
 
 Reinforced concrete with slate or marble treads, also offers 
 a good material for the construction of stairs.* 
 
 Fig. 28. 
 
 Fig. 29 f shows the construction of the stairs in the new 
 Government Printing Office at Washington. 
 
 V '.':' 
 
 
 
 
 saaas 
 
 \ 
 
 
 ^<SJ 
 
 
 III 
 
 
 
 
 
 I>;:;^:'^"./-:N-.-O;-; ;: 
 
 
 W- 
 
 '' ''.-:'. '&,- 
 
 y^-i5:-;v^::V 
 
 
 
 r 
 
 '.'.''.."::^ 
 
 1 1 :i 
 
 ^^^ 
 
 Fig. 29, 
 
 These stairs have steel girders and strings which are inclosed 
 in the solid concrete which is moulded to form the steps and 
 risers as shown in the detail. The steel strings, however, are 
 hardly necessary, as the reinforcing bars will give sufficient 
 strength. 
 
 * An elaborate curved double stairway of reinforced concrete is described 
 in the Engineering Record for Dec. 12, 1903. 
 
 t From the Engineering Record of Dec. 6, 1902. 
 
FIRE-PROOF WINDOWS. 765 
 
 The corrugated sheet metal, known as Ferro-in-clave (see 
 Chapter XXIV.) offers a very convenient foundation for cement 
 stairs, when built between walls or partitions or with an open 
 
 Fig. 30 
 Stairs with Treads and Risers of Ferro-in-clave. 
 
 string. Fig. 30 shows one way in which the material has been 
 used, the stairs being finished with about 2 ins. of cement over 
 the metal and plastered underneath. The Ferro-in-clave is bolt- 
 ed to lugs or brackets screwed to or cast on the strings. Slate 
 or marble treads and risers may be bedded in the mortar if 
 desired. 
 
 Fire-proof Windows. Until within a very few years, it 
 was thought impossible to make windows fire-proof, and the 
 nearest approach to it was to provide fire-proof shutters. Shutters 
 even when really fire-proof, however, are unsightly on the front 
 of a building, and more likely to be open than closed when a 
 fire breaks out, and when closed and locked they prevent the 
 firemen from gaining admission to the building or from ascer- 
 taining the condition of the interior. 
 
 By means of wire glass and metal -sash and frames, it is now 
 practicable to provide windows which will resist the passage of 
 flames fully as well as any shutter, while at the same time they 
 have none of the disadvantages of the shutter, and possess 
 the great advantage of not hiding a fire. 
 
 Wire glass is either "ribbed," "rough," "maze," or polished 
 plate having wire imbedded in its centre during the process of 
 manufacture. 
 
 "The temperature at which the wire is imbedded in the glass 
 insures adhesion between the metallic netting and the glass, 
 and the two materials become one and inseparable, so that if 
 
766 FIRE-PROOFING OF BUILDINGS. 
 
 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, as although lire 
 and water may cause cracks to spread throughout the glass, 
 the wire holds the pieces so firmly that flames cannot pass 
 through. Many severe tests during actual fires have posi- 
 tively demonstrated the truth of the above claim. For ware- 
 houses and factories the "ribbed" or "maze" glass will gen- 
 erally be preferable, but for offices, or wherever clear trans- 
 parent 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 looking through a window with a 
 screen on the outside. 
 
 The wire netting used for this purpose is similar to the ordi- 
 nary "chicken netting" with about a 1-inch rnesh. The Missis- 
 sippi Glass Company of St. Louis is the chief manufacturer of 
 wire glass in this country, the material being handled by the 
 leading glass-merchants in all the large cities of the country. 
 
 Many tests and several fires seem to prove that prism <//</*,? 
 or ordinary plate glass in four-inch units, electro-glazed in copper 
 frames will also successfully resist heat to the melting-point 
 of glass or copper. 
 
 Slieet-iiietal Window Frames and Sash are now 
 made which are weather-tight and perfectly practicable hi all 
 respects, and should be used wherever fire-proof windows are 
 desired. The sash are made especially for holding wire glass. 
 
 These sheet-metal windows are made in a great variety of 
 forms to meet all purposes, the sashes may be stationary, 
 pivoted either horizontally or vertically, hinged, or double 
 hung with weights like an ordinary window. For factories, 
 warehouses, stairways, and elevator shafts a stationary lower 
 and pivoted upper sash is quite commonly used as this is the 
 cheapest type of window. 
 
 The double-hung windows are now made to work as smoothly 
 as wooden sash in ordinary box frames. For offices, hotels, 
 etc., a window having two sashes, glazed with wire glass, that 
 close and lock automatically in case of fire, and a third inner 
 sash glazed with clear glass gives all of the advantages of an 
 ordinary window with the additional advantage of fire-pro- 
 tection and a better diffusion of light. Metal fly-screens can 
 also be used with these windows. 
 
 All movable sash, glazed with wire glass, should be pro- 
 
FIRE-PROOF DOORS. 767 
 
 vided with a device by which the sash will close and lock auto- 
 matically in case of fire. 
 
 AY hen the contents of the building are inflammable and the 
 exposure severe, two tliicknesses of wire glass should be used 
 with a ventilated air-space of a least 1 in. between the lights. 
 
 Material. The frames and sash should be of at least 
 Xo. 24 gauge galvanized iron, or IS-oz. copper. No. 22 gal- 
 vanized iron and 20-oz. copper are sometimes used for large 
 frames. 
 
 The National Board of Fire Underwriters have adopted 
 rules governing the construction of metal frames and sash for 
 fire-proof windows which may be obtained from the Mississippi 
 Wire Glass Company. One of these rules provides that "The un- 
 supported surface of the glass shall in no case exceed 24x30 ins.*' 
 Hence metal sash with a glass opening more than 24 ins. in 
 width or 30 ins. in height must be divided by muntins. 
 
 The principal manufacturers of sheet-metal window-frames 
 and sash are the Smith- Warren Company of Boston, Mass. ; Ycigt- 
 maim & Co. of Chicago; George Hayes of New York; David 
 Lupton's Sons Co., Philadelphia; and W. H.'Mullins of Salem, 
 Oliio, from whom circulars may be obtained giving complete 
 information as to styles and details of construction. 
 
 Wire-glass Shutters. Whenever ordinary windows 
 are to be protected with shutters, wire glass set in angle-iron 
 frames makes a more desirable shutter than the solid shutter 
 of iron- or tin-clad wood, for the reason that they need not be 
 opened except for ventilation, and when closed they do not 
 conceal an internal fire, and may be more easily broken through 
 by the firemen. 
 
 Fire-proof Doors. Wherever appearance is not an im- 
 portant consideration, the most satisfactory fire-proof door is 
 one made of wood and covered with tin or sheet steeL Such 
 a door should be made of two thicknesses of |-inch boards, 
 tongue-and-grooved, laid diagonally across each other and 
 nailed with wrought-iron nails driven flush, and clinched on 
 the other side; the door then to be covered on the sides and 
 edges with sheets of IX tin locked together like a tin roof. 
 It is absolutely essential that the tin shall entirely encase the 
 wood, air-tight as far as possible. The hinges, fastenings, 
 or hangers must be bolted to the door, not nailed or screwed, 
 as the latter would pull out during a fire. If hung on hinges, 
 the hinge-hook should be built into the wall. This door 
 
768 
 
 FIRE-PROOFING OF BUILDINGS. 
 
 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 the appearance is not objectionable. 
 
 Fire-proof shutters are also made in the same way. 
 Panelled fire-proof doors suitable for offices, hotels, and 
 public buildings are made on the same principle, stamped 
 sheet-steel being used in place of tin. 
 
 The Fire-proof Door Company of Minneapolis manufacture a 
 very ornamental door having a core of three thicknesses of pine, 
 asbestos covered and the whole covered with two sheets of 
 steel which are joined on the edges by a patented joint. Panels 
 are sunk by hydraulic pressure. The doors are made with 
 solid and glass panels, and special panelling and moulding may 
 be made to detail. The doors are finished either duplex copper 
 or brass, any finish, solid copper or brass, or painted one coat 
 at factory for finishing at building to match wood. 
 
 All hardware is fitted to the doors at the factory without 
 charge. Aside from their fire-proof quality these doors have 
 the advantage that they do not swell or shrink. 
 
 Fire-proof Base and Trim. A building may have 
 all of its structural parts thoroughly fire-proof and yet if it 
 contains wooden doors, sash, flooring, and a considerable 
 amount of interior wood finish, and particularly around the 
 windows, a fire once started in the building may find sufficient 
 inflammable material to feed upon to seriously damage the 
 building and imperil the life of the occupants. 
 
 During the past ten years incombustible materials such as 
 Keene's cement, marble, tiles, and metals have been gradually 
 
 taking the place of wood for 
 interior finish, and in a few 
 buildings scarcely any wood has 
 been used. Keene's cement has 
 been used for many years for 
 running base mouldings, door 
 and window trim, etc., and in 
 many European buildings prac- 
 tically all of the interior finish is 
 of this material. Any moulding 
 can be "run" in it with good 
 
 Section ThrlughDoor Jamb. sllar P an S leS > and {i is sufficient- 
 
 ly hard to stand ordinary usage. 
 Fig. 31 shows a door opening with trim of Keene's cement. 
 
 Cement 
 
FIRE-PROOF BASE AND TRIM. 
 
 769 
 
 his detail can be further improved by covering the wooden 
 *ame and door with thin metal. The metal and cement can 
 e painted as desired. 
 
 Moulded Hollow Tiles are also being substituted for the 
 rdinary wood finish. The "Amelia Apartments" erected by 
 [. B. Camp at Akron, Ohio, in 1901,* is built almost entirely of 
 ollow tile. "The base, picture-mould, and architraves around 
 oors were made of special formed tile, as shown by Figs. 
 2 and 33. These tile were after- 
 r ard painted to harmonize with 
 le color-decoration scheme. All of 
 le floors throughout the building 
 re covered with a cement composi- 
 on composed of Sandusky cement 
 nd ground wood trowelled down 
 nooth and level." 
 
 Metal-covered Door Jambs 
 nd Trim are manufactured by the 
 ire-proof Door Company in a great 
 ariety of styles to match their doors. 
 
 Fig. 32 
 
 Fig. 33 
 
 laterials and Devices which Reduce Fire Risks. 
 -Metal Lath Wire Cloth. About the year 1878, 
 -hen the interest in fire-proof construction became more 
 sneral, wire netting came into use as a substitute for wood 
 ith. It was found that the strands of the netting became 
 Dmpletely imbedded in the plaster and held it so securely that 
 
 could not become detached by any ordinary accidents. The 
 laster also protects the wire from the heat, and the body of 
 le metal is so small that there is no appreciable expansion of 
 le metal when subjected to fire. 
 
 The author believes that heavy wire cloth tightly stretched 
 ver metal furrings forms the most fire-proof lath now on the 
 larket, and he has personally seen it demonstrated by severe 
 
 * Described in Fireproof ', for July, 1903. 
 
770 riKF. rKooriNv, OF m 11. PINGS. 
 
 imental tests nnd hy actual tiros in buildings. Hint plaster 
 on wire doth, and particularly hard plasters, will protect the 
 woodwork from a severe fire as long as the plaster remains 
 intact, provided there are no cracks or loopholes at the corners. 
 and around columns where the fire can get through. 
 
 The objection has boon found to ordinary wire cloth that it 
 is difficult to stretch it so tight that it will not yield to the 
 pressure exerted in applying the several coats. Another objec- 
 tion that is made to the wire lath, and also to the expanded 
 lath (Fig. :>tV> is that they take a great deal of plaster. I'Yom 
 the standpoint of first cost this is undoubtedly a valid objection, 
 but from a tire-proof standpoint the great amount of mortar 
 used is its principal value. It should be remembered that the 
 mortar is the fire-proof part of the wall or ceiling and not the 
 metal. No metallic lath, the author believes, should be con- 
 sidered as fire-proof which does not, in use, fccomc imbedded hi 
 the mortar, for if the thin coating of plaster peels off the metal 
 lath will resist the fire no better than the wood lath, and will 
 be more in the way of the fireman. 
 
 Furring for Wire Lath over Woodwork. In order 
 to properly protect wooden construction, such as beams, PO.MS, 
 studding, or plank, from fire by wire lath and plaster, it is 
 essential that the lath be kept at least inch away from the 
 woodwork by iron furring of some form, .and a 1-inch space 
 is much better. This setting off of the lath from the wood is 
 generally done either by means of bars woven into or attached 
 to the lathing, or by means of iron .furring put up bct'ore the 
 lathing. Probably the most common method of furring with 
 iron for metal lath is by menus of band-iron, cither straight 
 or corrugated, J inch, or J inch wide, set on edge and secured 
 to the under side of the joist or plank by narrow staples driven 
 so as to keep the iron in a vertical position. 
 
 On floor-beams and studding, unless heavy iron is used, it 
 is necessary to run the furring lengthways of the beams and 
 studding, and, as the latter are seldom less than 12 ins. on cenlres. 
 this does not give close enough bearings to secure a stiff sur- 
 face for the plastering, unless a stiff lath is used. 
 
 Under plank (mill) floors the hand-iron should be spaced 
 from 8 to 12 ins., according to the kind of lath, and, if corru- 
 gated iron is used, a very satisfactory surface is obtained. 
 After the furring is fixed in place the lath is laid over it and 
 Secured by staples nailed over the lath and the band-iron. 
 
MKTAL LATH IM:r:r;. 771 
 
 Hammond's MH;il Furring. A much better 
 of furring, ami, SO far as the, author is informed, the most. p<-r- 
 fec,t of jj.ll systems of ::< i,aral.f, furring over woodwork, is that 
 known as the "Hammond" furring and shown by Fig. 34. It 
 
 ,t.s of a eom!;in;ition of sheet. 
 metal hearings and steel rods. The 
 rod , form the furring for keeping the 
 wire, cloth away from the timber, arid 
 tin: ! orm the ofTsct for the 
 
 rods, hoth Leing secured to the joint 1 
 
 ding, or plank \>y means of staples, 
 as shown in the figure. The rods, 
 being only ahoiit J inch in diameter, 
 become completely imbedded in the 
 
 ' r when it is applied, and as the plaster hardens it unites 
 the rod arid cloth so as to make a much more rigid surface 
 than is possible where band-iron furring is used. The rods 
 also may, arid in fact should be, run across the beams or stud- 
 ding, and may therefore be spaced as close together as desired. 
 It is recommended that the spacing of the rods be made 7J ins. 
 when the joists are 12 iris, on centres, and 6 ins. when the 
 joists are 16 ins. on centres (being 5 arid 6 bars to each strip 
 of lathing). The bearings are \ in. and 1 in. deep, the latter 
 being recommended, '>: they give a greater air space between 
 the plaster and timber, which is especially desirable in lathing 
 around solid timbers or under pknking. The rods come in 
 lengths of about 10 ft. 
 
 This system of furring is applicable to wooden posts, parti- 
 tions, and any form of wood construction; it is readily put up, 
 and is but little or no more expensive than band-iron. After 
 the furring is in place the wire cloth (which should be No. 20 
 gauge, and painted or galvanized if hard plasters are to be 
 is stretched over it, preferably in the same direction as 
 the rods, and secured by staples driven over the wire and one 
 id< of the h'-M.ring, as shown in the figure. 
 
 Stylcw of Wire La tiling. Wire lathing is now made 
 eat vrmetv lo meet the requirements of the different plas- 
 tering compositions and the varying conditions of construction. 
 
 Plain lathing is plain wire cloth, usually 2}X2J meshes to 
 the inch, made from No. 17 to No. 20 wire. No. 20 is more 
 generally used than any other gauge. 
 
 The lathing is also sold plain, painted, and galvanized 
 
772 FIRE-PROOFING OF BUILDINGS. 
 
 Painted or galvanized lathing should be used in connection 
 with special hard-plaster compounds. Painted lathing costs 
 about one cent per square yard more than "bright" lathing. 
 
 Galvanizing the wire cloth after it is woven adds very much 
 to its stiffness, as the zinc solders the wires together where they 
 cross. Galvanized lathing is also less liable to corrosion before 
 the plastering is applied than the plain lathing. 
 
 The usual widths of plain lathing are 32 and 36 ins., although 
 the Roebling lath may be obtained of any width up to 8 feet. 
 
 All wire lathing should be stretched tight when applied, so 
 as to insure a firm surface for plastering. For this purpose 
 stretchers are supplied by the manufacturers. 
 
 Stiffened Wire L.atli. Owing to the difficulty of 
 stretching plain wire cloth tight enough to make a firm founda- 
 tion for plaster and the necessity for short spacings for the 
 bearings, three varieties of stiffened wire lath have been intro- 
 duced and extensively used with very satisfactory results. 
 All three varieties are applied so that the stiffening rib will 
 run at right angles to the bearings. 
 
 The Clinton stiffened lath has corrugated steel furring strips 
 attached every 8 ins. crosswise of the fabric by means of metal 
 clips. These strips constitute the furring, and the lath is 
 applied directly to the under side of the floor-joist, or to plank- 
 ing, furring, brick walls, etc. This lath is made in 32-in. and 
 36-in widths, and comes in 100-yard rolls. The manufacturers 
 of this lath also make a lath stiffened with round rods J in. to 
 J in. in diameter spaced from 8 ins. to 12 ins. apart. 
 
 The Roebling standard wire lath is made of plain wire cloth, 
 in which at intervals of 7J ins. stiffening ribs are woven. These 
 ribs have a V-shaped section and are made of No. 24 sheet- 
 steel J and 1 in. in depth. The J-in. rib is the standard size 
 for lathing on woodwork. This lathing requires no furring, 
 and is applied directly to woodwork or walls with steel nails 
 driven through the bottom of the V, as shown in Fig. 35. 
 
 The No. 20 V-rib stiffened lathing affords a satisfactory 
 surface for plastering, when attached to studs or beams spaced 
 16 ins. apart. 
 
 The 1-inch 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 
 T 8 g-or J-inch solid steel rod is substituted for the V-rib, and 
 the lathing is attached to light iron furring with lacing wire. 
 
METAL LATHS. 
 
 773 
 
 Fig. 35 
 
 This lath is distinguished by the term "solid rib stiffened 
 wire lath." 
 
 The lloebling lath, whether 
 plain or stiffened, is made with 
 2JX2J, 3X3, and 2JX4 mesh, 
 the latter being known as "close 
 warp." The 2 J X 2 J mesh should 
 be used for ordinary lime and 
 hair mortar, and the 3X3 or 
 2|X4 mesh for hard plasters 
 and thin partitions. This lath- 
 ing is also sold bright, painted, 
 and galvanized. 
 
 The No. 20 painted wire has 
 been extensively used and much of it has been in service for 
 from six to eight years and is now apparently as good and strong 
 as ever, so that there appears to be no necessity in ordinary 
 work of using heavier wire or galvanized netting. 
 
 The galvanized wire is stiff er than the painted, and would 
 possibly wear longer, but it is doubtful if the advantages are 
 at all proportionate with the cost. 
 
 Width. Wire lath can be furnished to order in any re- 
 quired width up to 10 feet. In widths less than 18 ins. there 
 is a small charge for "stripping." Before ordering, it is very 
 important to ascertain the proper width, especially in stiffened 
 lath, as it is desirable to have the edges of the lath joined at supports 
 when applied to woodwork; and lap at supports when laced to 
 iron furring. When the lath is not of the proper width the 
 results will not be so good and there is liable to be a waste of 
 material. 
 
 The standard width of plain and of V-rib stiffened lath is 
 36 ins. When beams or studs are spaced 16 ins. centre to 
 centre the lath should be 32 or 48 ins. wide. 
 
 Expanded Metal Lath. The first expanded lath was 
 invented by Mr. John F. Golding, and the patents on the lath 
 and the method of manufacture are controlled by the Expanded 
 Metal Company (see Chapter XXIV.). Very large quantities of 
 this lath have been used both for fire-proof work and for lathing 
 on wooden construction. It is made from strips of thin, soft, 
 and tough steel by a mechanical process which pushes out or 
 expands the metal into oblong meshes, and at the same time 
 reverses the direction of the edge, so that the flat surface of 
 
774 FIRE-PROOFING OF BUILDINGS. 
 
 the cut strand is at right angles with the general surface of the 
 sheet. 
 
 For plastering, two sizes of meshes are made, -f^ X 1 J ins. and 
 JXlJ ins., the former being best adapted for the hard mortars 
 and the latter for lime mortar. Both kinds are made in sheets 
 8 ft. long and from 14 to 20 ins. in width, 18 ins. being the 
 standard width. 
 
 This lath being flat and of considerable stiffness, does not 
 require to be stretched, and can be fastened directly to the 
 under side of floor-joist or to wood studding. If .used on plank 
 it should be fastened over metal furring strips. When applied 
 to studding the lath should be placed so that the long way of 
 
 the mesh will be at 
 right angles to the 
 studding, as shown 
 in Fig. 36, as this 
 insures the greatest 
 rigidity. The stud- 
 ding or furring strips 
 should be spaced 12 
 ins. on centres, and 
 the lathing secured 
 with Naples 1 in. 
 long, driven about 
 5 ins. apart on the 
 stud or joist. The 
 Fig. 36 lath, when applied, 
 
 is a scant i in. thick, and to obtain a good wall J-inch grounds 
 should be used. 
 
 Herringbone Lath. This is another form of expanded 
 metal lath that has been extensively used during the past three 
 or four years. It is made in four grades, A and AA, B and BR. 
 The B grades are made in wider sheets, and are more open and 
 consequently not as heavy or stiff as the A grades. The general 
 appearance of the A and B grades is shown by Fig. 37. 
 
 The A and A A grades and the B and BB grades differ only 
 in that the AA and BB grades have a smaller mesh and are 
 consequently stiffer than the A and B grades. The A A grade 
 is the stiffest of all and the most expensive, the A grade comes 
 next, the BB third, and the B grade is the lightest of all. 
 
 The A grade is probably most used. For ceilings "A flat" 
 or "AA flat" should be specified. The short cross ribs of the 
 
METAL LATHS. 
 
 775 
 
 "flat" lath are turned after being expanded, diminishing the 
 size of the key and presenting a larger surface to support the 
 plaster. The heavy longitudinal ribs are at an angle of about 
 
 A and AA 
 
 B and BB grades. 
 Fig. 37 
 
 Herringbone Lath. 
 
 45 degrees to the general surface of the lath and give much 
 stiffness to it. 
 
 In applying the lath the sheets should run at right angles 
 to the studding or joists and the longitudinal ribs should slope 
 down against the studding so as to hold ^the mortar. For 
 fastening to wood, a No. 12 or 14 "poultry" staple is used. 
 Except for the A A grade, it is best to space the studding 
 12 ins. on centres, although the A grade can be used with a 
 16-inch spacing. 
 
 Imperial or Spiral Lath. Fig. 38 shows still another 
 form of expanded metal lath recently placed on the market. 
 
 Fig. 38 
 Imperial Lath. 
 
 This lath is lighter than most of the laths made from sheet- 
 metal, and is also a little cheaper. It is furnished in sheets 
 48J ins. long, and 16 ins. wide, put up in bundles of 25 sheets. 
 Being so short the sheets nest and pack very closely and are 
 easily handled by one man. Large quantities of this lath 
 have been used, and it seems to be much liked by plasterers. 
 
 Perforated Sheet-metal Laths. There are some six 
 or more styles of metal lath made from sheet-iron or steel by 
 
776 FIRE-PROOFING OF BUILDINGS. 
 
 perforating the sheets so as to give a clinch to the mortar. 
 The sheets are generally corrugated or ribbed, also, in order 
 to stiffen them and keep them away from the wood. There is 
 not a great difference between these laths, although some styles 
 may possess certain advantages over the others. 
 
 In general, the author would prefer those styles which have 
 the greatest amount of perforations, or which approach the 
 nearest to the expanded lath. All of these laths come in flat 
 sheets about 8 ft. long and 15 to 24 ins. in width, and are readily 
 applied to woodwork by means of barbed-wire nails. The nails 
 should be driven every 3 ins. in each bearing, commencing at 
 the centre of the sheet and working toward the ends. These 
 laths work very nicely in forming round corners and coves. 
 Metal lath should never be cut at the angles of a room, but bent 
 to the shape of the angle and continued to the next stud beyond. 
 This strengthens the wall and prevents clacks at the angles. 
 
 Fig. 39 
 
 Bostwick Lath. 
 
 Of the various forms of sheet-metal lath in common use, the 
 Bostwick lath (Fig. 39) is perhaps the best known. It is made 
 of sheet-steel, with ribs every f of an inch in the width of the 
 sheet, and loops, fXlf ins., punched out between the ribs. 
 It has been extensively used, and is favored by plasterers be- 
 cause it is stiff and easy to apply and requires less plaster than 
 the more open laths. The lath should be applied with the 
 loop side out. 
 
 Fire-proof Wood. Section 105 of the building laws of 
 New York City require that all wood finish used in buildings 
 exceeding twelve stories, or 150 feet in height shall be "treated 
 by some process approved by the Bonrd of Buildings to render 
 the same fire-proof/* and all buildings erected in that city 
 during the past three years, and exceeding the height named, 
 
FIRE-PROOF WOOD. 777 
 
 have been finished with wood that has been treated by some 
 fire-proofing process. The U. S. Government has also used 
 fire-proof wood in the finishing of over seventy-five warships. 
 "There are to date five fire-proofing processes which have been 
 favorably passed upon by the New York Building Department 
 (during ihe preceding administration), the processes controlled 
 respectively by (1) The American Wood Fire-proofing Company. 
 (2) the Electric Fire-proofing Company, (3) the New York Fire- 
 proof Wood Company, (4) the Fire-proofine Company, and (5) the 
 Riscinate Wood Fire-proofing Company. Of these five processes 
 some were accepted upon the basis of results obtained from 
 rigid tests, while others were accepted upon very insufficient 
 evidence." * 
 
 Although the processes differ widely in character, the treat- 
 ment, in general, consists in thoroughly impregnating the wood 
 fibre with certain chemicals which render the wood inflammable 
 or at least slow-burning. After the fire-proofing process, the 
 lumber should be thoroughly kiln-dried before it is allowed 
 to enter into construction. The kiln-drying, to be done properly, 
 requires several weeks, the actual time varying in accordance 
 with the thickness of the stock, but to secure a first-class job 
 in fire-proofed wood it is essential that the stock be bone-dry. 
 
 The fire-proofing treatment does not affect the color of the 
 wood save that the hard woods are rendered much richer, and 
 altogether the product retains its strength and beauty and is 
 quite as workable as untreated wood. All kinds and thick- 
 nesses of lumber are treated by the different processes. 
 
 In regard to the fire-resisting quality of so-called fire-proofed 
 woods, Prof. Woolson, who has made over 400 tests to deter- 
 mine the relative merits of the different processes, says: "The 
 term 'fire-proof wood' is in a sense a misnomer; for such woods 
 will burn in all cases, if exposed for a sufficient length of time 
 to a high degree of heat. Strictly speaking, the processes of 
 treatment do not make the wood fire-proof, but they simply 
 render them fire retardants," i.e., they do not ignite as quickly 
 as untreated woods, and do not burn as freely. The fire-proof- 
 ing of woods is yet in its infancy, and just what may be fairly 
 expected of " fire-proof" wood has not yet been satisfactorily 
 determined. The fact that the leading powers of the world 
 
 * Ira H. Woolson, Instructor in Mechanical Engineering, Columbia 
 University, New York, in Engineering News of Feb. 20, 1902. 
 
778 FIRE-HIOOFIXG OF BUILDINGS. 
 
 arc Using "fire-proof" wood for the finishing of battle ships, 
 would indicate that it possesses some, merit. The incivnM'd 
 cost of lire-proofed woods, thoroughly kiln-dried, over Untreated 
 wood of the same kind and quality varies from $35 to $05 per 
 thousand feet, the hard woods costing the most. 
 
 Fire^proof Flooring. A wooden floor laid over hollow 
 tile or concrete with not more than a J-inch air space between 
 the wood and concrete, burns very slowly, and would have but 
 little effect in feeding a fire. Nevertheless, on the principle 
 that a fire-proof building should contain as little incombustible 
 material as possible, several materials have been used to lake 
 the place of wood for the finished floor surface. As a rule, 
 however, these materials have been introduced more on account 
 of their appearance, wearing, or sanitary qualities than to 
 reduce the fire risk. For warehouses and factories, floors 
 finished with Portland cement are about as satisfactory as j in y 
 flooring, and cement floors have been considerably used for 
 the guest rooms of hotels. In the latter rooms, the floor is 
 icovered by a carpet, which is secured to wood strips imbedded 
 n the cement around the borders of the room. This makes 
 a very sanitary floor, and is as easy to the feet as a carpeted 
 wood floor. 
 
 For public Corridors, banks, lobbies, toilet rooms, etc., either 
 encaustic, vitreous, ceramic, or marble tiling is generally Used. 
 In France and Germany large quantities of cement tile are 
 used. Cement tiles have also been introduced in this country, 
 but as yet they have not been able to compete with encaustic 
 tile. 
 
 Asbestolith* Marble, tile, or cement floors are trying 
 to the feet, when one has to stand on them for several hours 
 at a time, besides being rather expensive. Several attempts 
 have been made to obtain a flooring material which could be 
 spread over an entire floor without joints, and at the same 
 lime be elastic, wear well, and withstand water, acids, etc., 
 and not be too expensive. One of the most successful of these 
 materials is Asbcstolitk. This material is shipped in the form 
 of a dry powder to the poitit where it is to be used, there to 
 be mixed with a Specially prepared liquid. The resultant is a 
 plastic material which is laid upon the surface to be covered 
 much like ordinary cement or plaster. The material hardens 
 in from twelve to twenty-four hotirs in moderately dry weather, 
 when the floor is read for use. 
 
770 
 
 When properly laid it presents a smooth, fme-jrniincd, and 
 QOntinUrilU surface, F6flatnblihg linoleum. It will liohl taeks 
 or screws, and is claimed to be water- and fire-proof, and to 
 Withstand both acids and akalies and outwear a wood floor. 
 
 It is made in various colors, siifh as red, white, yellow, brown, 
 gray, black, blue, -and 'green, and can be laid on wood, stone, 
 concrete, asphalt, cement, or metals It has been used over 
 steel plates on three U. S. cruisers. Another advantage of 
 this material is that it can be carried up on UK; walls so as 
 to lorrn a coved base, without any cracks or joints. It makes 
 a perfect sanitary floor and is noiseless and very easy to the feet. 
 
 Monolith is a very similar material to asbestolith and 
 is applied in the same way, the base being sawdust. It can 
 be; l.'iid over almost any material, and at any season of the year 
 Its natural color is cream, but the color may be changed by 
 the addition of Venetian red, umber, or any earth-coloring 
 matter. Like asbestolith, it is fire- and water-proof, elastic, 
 and does not chip or crack (when properly laid). This material 
 has been extensively used in Milwaukee, Chicago, New York, 
 and Boston, and in hospitals throughout the country. It 
 would seem to be an ideal material for the floors of hospitals, 
 kitchens, public baths, etc., and also makes a very satisfactory 
 floor for offices. 
 
 Metallic Furniture and Fittings. In offices, banks, 
 libraries, and public buildings, the furniture and fixtures are 
 about the only articles on which a fire can feed if the building 
 itself is firo-proof and if these are made of incombustible 
 materials there is no chance for a fire to gain headway, or to 
 do much damage. l?or a number of years The Art Metal Con- 
 struction Company has been making metallic fixtures from rolled 
 steel plates finely finished in baked enamels relieved by brass 
 and bron/e trimmings. Almost anything in the way of furni- 
 ture arid fittings, even to roll-top desks and highly ornamental 
 cabinets, may now be obtained in metal, and many libraries, 
 banks, and court houses have been fitted up and furnished en* 
 tirely with incombustible cabinet work. 
 
 Precautionary Measures. No matter how thoroughly 
 a building may be fireproof ed, if it is filled with combustible 
 goods, an in warehouses, stores, and factories, there is always 
 the possibility of a fire, which if unchecked when first started 
 must necessarily entail a great lo;-:s and more or less damage 
 the building. If a fire is discovered ard checked in its incipient 
 
780 FIRE-PROOFING OF BUILDINGS. 
 
 stage this loss is avoided. There are now many valuable 
 devices for detecting and checking fires, which should be in- 
 stalled in every warehouse, and which may often be placed 
 with advantage in buildings used for other purposes. 
 
 The more important of these are: 
 Automatic alarms. 
 Automatic sprinklers. 
 Open sprinklers. 
 Standpipes, hose-reels, etc. 
 
 Automatic Alarms. By means of very sensitive 
 thermostats, a rise in temperature of 35 degrees above the 
 normal maximum temperature to be expected in the building 
 will cause an alarm to be sounded. 
 
 The Montauk Multiphase Cable Company make a fire-detecting 
 wire or cable which can be used in dwellings and other build- 
 ings in place of the ordinary bell wire, and, by judicious dis- 
 tribution and arrangement in elevator- and dumb-waiter shafts, 
 coal and wood cellars, closets, store-rooms, and other unoccupied 
 rooms, may be used to give timely warning of fire originating 
 in any of these places. 
 
 This fire-detecting wire consists of two conductors. The 
 central wire or core which forms one side of the circuit has a 
 thick coating or wall of fusible metal; over this is an insulating 
 coating. A number of fine wires are wound over this coating 
 to form a second conductor. The whole is then covered 
 with suitable insulation. 
 
 When flame or a dangerous degree of heat comes into con- 
 tact with this wire it will establish electrical connection be- 
 tween the two conductors and give a signal on the premises 
 equipped. 
 
 This wire was approved by the New York Board of Under- 
 writers, Feb. 20, 1901, and has been quite extensively used 
 in the Eastern States. 
 
 Automatic Sprinklers. "An automatic sprinkler is 
 a device for distributing 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 be- 
 yond the point of ignition. The distribution is also economi- 
 cal, as the water is more evenly applied than from a nozzle 
 
SPRINKLERS AND STAND-PIPESCOST. 781 
 
 attached to a fire-hose, and the source is directly above the fire. 
 
 "Whenever combustible merchandise constitutes the con- 
 tents of a building, automatic sprinklers are of great value, and 
 in 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." * 
 
 Information pertaining to the insulation of automatic sprink- 
 lers, their cost, where they may be obtained, etc., may be 
 obtained from the Insurance Engineering Station, Boston, 
 Mass. 
 
 Open Sprinklers are used principally to prevent the 
 passage of fire through window openings, by discharging a 
 sheet of water from an orifice just above and on the outside 
 of the window, sufficient to protect it from below. 
 
 Stand-pipes and Hose Reels. In office-buildings, 
 hotels, and apartment houses, where sprinkler systems are 
 hardly suitable, stand-pipes with hose reels on each floor and 
 the roof ready for instant use constitute the best means of 
 quickly controlling a fire. 
 
 The stand-pipe should be from 2J to 6 ins. in diameter, ac- 
 cording 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 depart- 
 ment. Check valves should be provided so that when the 
 fire-department engines are attached their force will be added 
 to tha,t of the buildings, pumps, or to that of the water system. 
 
 Cost of Fire-proof Construction. Mr. F. W. Fitz- 
 patrick, consulting architect, contributed to the March, June, 
 and July, 1903, numbers of Fireproof, some interesting papers 
 in which he gives the comparative cost per cubic foot of a large 
 number of buildings figured for both fire-proof and ordinary 
 construction. These figures seem to indicate that fire-proof 
 construction for office-buildings, hotels, etc., adds from 9 to 
 13 per cent over the cost of ordinary construction with wooden 
 joists. For stores and warehouses the difference will often be 
 less than 5 per cent. 
 
 See also, "Cost of Buildings per cubic foot," Part III. 
 
 * J. K. Freitag. 
 
782 FIRE-PROOF AND INCOMBUSTIBLE FLOORS. 
 
 CHAPTER XXIV. 
 
 FIRE-PROOF AND INCOMBUSTIBLE FLOORS 
 AND FLAT ROOFS. 
 
 THERE are now so many systems of fire-proof and incombusti- 
 ble floor constructions in use in this country and there is so 
 much that can be said as to the advantages of one system over 
 the other that to thoroughly consider the matter would require 
 more space than can be allotted to it in such a work as this. 
 The author has, therefore, confined himself to a brief descrip- 
 tion and illustration of those systems which are at present being 
 adopted in American buildings, with such data regarding their 
 weight, strength, and limitations as will be found useful by 
 architects in the preparation of plans and the computation for 
 the steel framing. A more thorough discussion of the subject 
 will be found in Chapter IX. of Part I. of the author's work on 
 " Building Construction and Superintendence." The most com- 
 plete presentation of fire-proof construction in all its details 
 will be found in Mr. Freitag's work, " The Fireproofing of Steel 
 Buildings." 1899. John Wiley & Sons, publishers. In this 
 work the term "Fire-proof" refers to those constructions which 
 are not only built of incombustible material, but which have 
 been found proof against the ravages of fire and the accompany- 
 ing deluge of water. This requires the thorough protection of all 
 structural iron and steel, and a very limited use of wood for 
 frames. In fact, it has been pretty well demonstrated that 
 absolute fire resistance does not depend so much upon the floor 
 slabs as upon the thoroughness with which all steel or iron has 
 been protected from both the penetration of heat and the 
 destructive effect of streams of water, and also upon the elimina- 
 tion of all combustible material about the windows and doors, 
 and for the flooring or finish. 
 
 As ordinarily used the word " fire-proof" is a relative term, 
 the degree of fire protection meant depending largely upon the 
 character and purpose of the building. Thus an isolated build- 
 ing intended to contain but little inflammable material might be 
 practically proof against any fire that could occur in or around 
 
BRICK ARCHES. 783 
 
 it under normal conditions, while for a warehouse, retail store 
 or tall office building the same protection would be entirely 
 inadequate. For this reason the selection of a fire-proofing sys- 
 tem for any particular building may wisely be governed by the 
 risk and exposure. 
 
 The general subject of fireproofing has been more particu- 
 larly discussed in Chapter XXIII., this chapter being confined 
 to floor and flat-roof constructions, as these must be considered 
 from the point of strength as well as from that of fire resistance. 
 
 As no floor in which wood is used as a structural element can 
 be considered fire-proof, only those systems of construction 
 will be described which are used in connection with steel beams, 
 or which are entirely supported by masonry walls, piers, and 
 partitions. 
 
 Divisions of the Subject. To consider the almost in- 
 numerable systems of floor construction which are advertised 
 as fire-proof in a concise and intelligent manner the author has 
 attempted to group them under the following classifications, each 
 system being described under the classification to which it most 
 properly belongs. 
 
 A. SYSTEMS USING BURNED CLAY PRODUCTS. 
 a. Brick arches. 
 6. Flat tile arches. 
 
 c. Segmental tile arches. 
 
 d. The serrated arch. 
 
 e. Reinforced tile arches (wide spans). 
 /. Guastavino constructions. 
 
 B. CONCRETE OR COMPOSITION SYSTEMS. 
 a. Reinforced monolithic floors, flat and panelled. 
 6. Concrete arches. 
 c. Sectional systems. 
 
 PIRE-PHOOP FLOORS OP BRICK ARCHES. 
 
 The first attempt at fire-proof floor construction between 
 wrought-iron beams was by using brick arches sprung between 
 the beams and resting on the bottom flange, as illustrated by 
 Fig. 1. 
 
 Above the arch the space was filled with cement concrete in 
 which wooden nailing strips were embedded to receive the floor- 
 ing. The bottom of the beams was left exposed. 
 
784 FIRE-PROOF AND INCOMBUSTIBLE FLOORS. 
 
 This formed a strong incombustible floor, but as the iron 
 beams were not protected it could not be considered as fire-proof, 
 
 Fig. I 
 
 while it was open to the practical objections of requiring a sus- 
 pended ceiling beneath to give a pleasing effect, and to the 
 great weight which is imposed upon the beams and columns, 
 although the latter did not exceed that of many of the latest 
 tile and concrete systems. 
 
 Brick arches were soon superseded by flat arches of hollow 
 tile, and the latter proved so much more desirable that brick 
 arches are now seldom used. 
 
 The main floors of the new building for the Government 
 Printing Office at Washington,* however, are formed of segmen- 
 tal solid porous brick arches set on heavy skewbacks of the 
 same material which have projecting lips 1J inches thick to pro- 
 tect the lower flanges of the floor beams. An independent 
 ceiling is placed about 14 inches below the bottom of the floor 
 beams, leaving a space between the floor and ceiling sufficient 
 
 Finished Floor. 
 
 Fig. 2 
 
 for a man to pass through, and in which all wires and cables are 
 placed. This space is accessible through man-holes. Fig. 2 
 
 * A description of the structural features of this building may be found 
 in the "Engineering Record" for Dec. 6. 1902. 
 
BRICK ARCHES. 785 
 
 shows a section through one of the floor arches; the floor beams 
 are 8 inches deep and 3 feet apart. 
 
 Span, Rise, and Strength of Brick Arches. Al- 
 though brick arches will probably never be used to any con- 
 siderable extent for floor construction, still there may occa- 
 sionally be circumstances which will lead to their adoption, so 
 that a few words as to how they should be built may not be out 
 of place. 
 
 The bricks used should be of good shape, and if the span of 
 the arch is more than 3 feet they should be hard burned. They 
 should be laid without mortar with their lower edges touching, 
 and all the joints should be filled with cement grout. 
 
 The arches need not be over 4 inches thick for spans between 
 6 and 8 feet, provided the haunches are filled with a good cement 
 and gravel concrete put in rather wet. The rise of the arch 
 should be about J of the span, or 1J inch to the foot, and the 
 most desirable span is between 4 and 6 feet. 
 
 To make the construction fire-proof the bottom flanges of 
 the beams should be protected by terra-cotta skewbacks, as in 
 Fig. 2. 
 
 A 4-inch brick arch of 6-foot span, well grouted and levelled 
 off with Portland cement concrete, should safely carry 300 or 
 400 Ibs. to the square foot. Experiments have shown that 
 brick arches will stand very severe pounding and a great amount 
 of deflection without failure. 
 
 The weight of a floor, such as shown in Fig. 1, will usually 
 vary from 70 to 75 Ibs. per square foot, depending upon the 
 amount of concrete required for levelling. 
 
 Tie Rods. As brick arches exert a considerable thrust, tie- 
 rods must be provided to prevent the beams from being pushed 
 apart, and especially to prevent the outer bays from spreading. 
 These rods are usually from J inch to 1 inch in diameter, and 
 are placed in parallel lines from 6 to 8 feet apart running 
 from beam to beam from one end of the building to the other. 
 If the outer arches spring from an angle, as in Fig. 1, the tie- 
 rods in this bay should be anchored into the wall with large 
 plate washers. The method of determining the necessary 
 diameter of the tie-rods is given on page 881 . 
 
786 FIRE-PROOF AND INCOMBUSTIBLE FLOORS. 
 
 Hollow-tile Arches. 
 
 Development.* Flat hollow-tile arches were first patented 
 and introduced in Chicago in 1872 by Mr. George H. Johnson, 
 the type of arch first used being shown in Fig. 3. At about the 
 same time Mr. Leonard F. Beckwith used a similar but heavier 
 construction in the corridors of the New York post-office. 
 
 Fig. 3 
 
 These arches, although very crude in materials and workman- 
 ship, proved substantial and answered the purpose of a light 
 and fire-resisting floor. They also aroused considerable interest 
 in fire-proof floor construction and led to further develop- 
 ments. 
 
 Previous to the year 1883, however, all of the tile arches used 
 in Chicago had been made of tiles without interior webs. In 
 1883, 9-inch flat arches, each tile having one vertical and one 
 horizontal web, were placed by a Chicago company in the build- 
 ing of the Mutual Life Insurance Co. of New York, in New York 
 City. 
 
 These arches were also the first in which soffit tiles were used 
 for the protection of the beam flanges. From 1883 to 1890 
 much improvement was made in the quality and shape of the 
 arched blocks, but nearly all floor arches made previous to 1890 
 were of what is known as the "side construction," that is, with the 
 vertical webs parallel to the sides of the arch, or to the I-beams. f 
 In the year 1890 Mr. Thomas A. Lee built some porous terra- 
 cotta arches for testing in connection with the contract for the 
 floors of the Equitable Building in Denver, in which all of the 
 voids in the blocks were at right angles to the beams from beam 
 web to beam web. These arches showed such great superiority 
 over the side-construction arches tested at the same time that 
 "end-construction" arches were very soon manufactured by 
 
 * The development of tile fireproofing is traced in a very interesting 
 manner by Mr. Freitag in his work above mentioned. 
 
 t The New York fire-Proof Building Co., controlled by Leonard F. Beck- 
 with and brother, used end-construction arches as early as 1877, but the 
 superiority of this construction was not generally recognized until demon- 
 strated by Mr. Lee. 
 
HOLLOW-TILE ARCHES. 787 
 
 nearly all of the hollow-tile fire-proofing companies, and the end 
 construction is now almost exclusively used for fiat-tile arches. 
 
 As the flat-tile arches were not adapted to spans between 
 beams greater than -6 to 7 feet, segmental arches built of hollow 
 tile were early introduced to effect a saving in the steel beams, 
 particularly in buildings where a level ceiling was not consid- 
 ered necessary. Segmental arches are still used to a considera- 
 ble extent, and for warehouses subject to very heavy loads prob- 
 ably give the cheapest construction, for the same strength, that 
 can be obtained by the use of hollow tile. 
 
 Besides these three types of construction, Mr. Henry L. Hin- 
 ton, engineer for the National Fire-proofing Company, has 
 invented a serrated floor arch which is in effect an end-con- 
 struction arch with a raised centre. These four types practi- 
 cally embrace all of the arched floor constructions formed of 
 hollow tile. 
 
 As each of these systems has peculiarities of its own, they will 
 now be considered separately. The fire-proofing qualities of 
 a floor, built on either system, of course, ' depends upon the 
 quality of the material of which the blocks are made, and upon 
 the thoroughness with which the steel is protected. These have 
 been fully considered in Chapter XXIH., and will not be further 
 considered here. 
 
 Manufacture and Commercial Status of Hollow- 
 tile Fireproofing". To manufacture hollow tile at a cost 
 that will enable the product to compete successfully with 
 that of other manufacturers, or with the concrete systems, 
 requires a good supply of the proper kinds of clay and a well- 
 equipped factory and consequently considerable capital. For 
 these reasons there are not near as many companies engaged 
 in the manufacture and erection of tile fire proofing as are 
 engaged in concrete fireproofing, but there are still a large 
 number of factories scattered throughout the States which 
 make hollow tile to a greater or less extent, and there are 
 several large companies which do a very extensive business, 
 and the variety in the shapes of the blocks manufactured is 
 almost endless.* 
 
 The largest company devoted to the manufacture and erec- 
 tion of hollow-tile fire-proofing material is the National Fire- 
 proofing Co., which owns what were formerly the Central Fire- 
 
 * See the recent Hand-Book of the National Fire-proofing Co, 
 
783 FIRE-PROOF AND INCOMBUSTIBLE FLOORS. 
 
 proofing Co., the Raritan Hollow & Porous Brick Co., the Empire 
 Fire-proofing Co., the E. V. Johnson Co., and several others. 
 Other large companies are Henry Maurer & Sons, New York; 
 the Haydenville Co., Haydenville, Ohio; Delaware Fire-proofing 
 Co., Delaware, Ohio; Pioneer Fire-proofing Co., Chicago, and 
 the Illinois Terra-Cotta Lumber Co., also of Chicago. Any 
 one of these companies can make any form of block desired 
 except such as are covered by letters patent, and as a rule in 
 either dense, porous or semi-porous material. 
 
 While more or less tile fireproofing is sold to contractors 
 who set it with their own men, yet most of the fire-proofing 
 companies prefer to set their material themselves, for the reason 
 that a contractor, as a rule, has little interest in the thorough- 
 ness with which the fireproofing is done, and any defective work 
 is liable to injure the reputation of the manufacturer. It is 
 undoubtedly better both for the owner and architect to give 
 the contract for the fireproofing, if hollow tile is to be used, 
 directly to the manufacturer, as he or they are more likely to 
 see that the work is thoroughly done. 
 
 The National Co. contracts for the manufacture, erection, and 
 setting in place complete of all fire-proofing material (of tile) 
 throughout the United States. 
 
 While reinforced concrete constructions have made great 
 inroads upon the business of the hollow-tile fire-proofing com- 
 panies, this is due very largely to the fact that concrete floors 
 could be had at less expense than tile floors, or to the concrete 
 systems effecting a saving in the structural steel. While the 
 author is a firm believer in reinforced concrete, he also believes 
 that there is no better fire-proofing material than porous terra- 
 cotta, and that the hollow-tile systems, when properly designed, 
 made of good material, and erected in a thorough and efficient 
 manner, afford as good fire-proof construction as can be had, 
 and for high office buildings is to be preferred to many, at least, 
 of the concrete systems. 
 
 In this connection the opinion of Mr. E. V. Johnson, who has 
 perhaps had as much experience with fire-proof construction as 
 any American, is of value. 
 
 "I am personally of the opinion that in first-class, standard 
 high-grade tall buildings the present system of steel construc- 
 tion with suitable girders and intermediate beams, spaced about 
 8 feet apart, thoroughly riveted together, is far preferable to 
 any method where the panels between the girders are filled with 
 
HOLLOW-TILE ARCHES. 789 
 
 any monolithic system of floors. My reasons for this are as 
 follows : 
 
 " (a) The intermediate beams between the girders act as a 
 great stiffener to a building, and in the case of high structures 
 greatly re-enforce the wind-resisting character of the edifice. 
 
 " (b) By the use of intermediate beams the tile arches can be 
 set in place much more rapidly than the large span systems of 
 monolithic floors on account of the facility with which the cen- 
 tring can be done. Again, time enters into the construction 
 of modern sky-scrapers to a large extent, and there is no sys- 
 tem that has yet been devised that can be so readily installed 
 in a building, during any season of the year, as the hollow-tile 
 method. It is for this reason that the tile arch has held its 
 own against all systems of construction. 
 
 " We have used the long-span system of tile construction in 
 large quantities for roof constructions, over car barns, factory 
 buildings, drying kilns, and such styles of structures. On 
 account, however, of the cumbersome centring, or false work, 
 necessary to be used for the installation of any system of mono- 
 lithic construction, whether of concrete or of tile bedded in 
 Portland cement, it is impossible to conduct the work at a rate 
 of speed that will permit the general introduction of this system 
 of construction in modern up-to-date, sky-scraper, fire-proof 
 buildings in the large cities." 
 
 It has been estimated that 900,000 tons of terra-cotta fire- 
 proofing material was manufactured and set in the United 
 States during the year 1902. 
 
 Disadvantages of Tile Arches. The principal disad- 
 vantage 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. 
 It is also more expensive to adapt the tile systems to a panel of 
 varying width than with the concrete systems. Tile arches, 
 especially of the end constructions, are weakened more by holes 
 for pipes than a monolithic floor. 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 remain- 
 ing tile 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 con- 
 siderable concrete filling over the arch the weight of the floor 
 
71;0 FIRE-PROOF AM) IXCOMiiUSTIBLE FLOORS. 
 
 construction will usually greatly cxccn-rl \.}\;\\, of UK- ro 
 systems, and this additional weight also means additional ox- 
 
 Side-construction Flat Arches. 
 
 Flat arches with the voids in the blocks running parallel with 
 the beams are now used to a Very limited extent, and only for 
 roofs and light floors. Before the end-construction arch came 
 into general use, side-construction arches formed as shown by 
 Fig. 4 were quite generally used, and such arches can still be 
 
 Fig. 4 
 
 had if desired, but the end construction is just as cheap and 
 much stronger for the same weight. 
 
 For a roof or light floor an arch such as is shown by Fig. 5 
 makes a very good construction, probably equal to any. Thia 
 
 T3* 1C,,'! 
 
 Fig. 5 
 
 arch is made by the Illinois Terra-Cotta Lumber Co., from 7 to 
 12 inches in depth, but the 7-inch arch, with a span of 5 feet, is 
 most commonly used. 
 
 The weight of the 7-inch arch, not including filling or flooring, 
 is 26 Ibs. per square foot. 
 
HOLLOW-TILBJ A.BCHEB, 
 
 701 
 
 Bad-construction Flat Arches. 
 
 In (bis construction the sides and voids of the individual 
 blocks run Mi right angles to (he beams, so that the pressure on 
 the blocks is endways of (he tile. It has been conclusi vely 
 demonstrated that hollow tile are much stronger in end com- 
 ])ressiou than transversely, consequently the end-construction 
 arch IIM.S almost superseded the side construction. 
 
 Two of the largest lire-proofing companies say that they now 
 use the end-construct ion intermediates exclusively. 
 
 The individual hln,-k* in the end construction are commonly 
 inMde rectangular in sliMpe and advancing by 1 incli from 6 to 15 
 inches in depth. Arches 1 and Hi inches deep MTC also occasion- 
 ally used. r fhe ItMigth a.nd width of the blocks may also be 
 varied, but the standard si/e is \'2 inches for both dimensions. 
 The number of partitions or webs in Hie blocks varies with the 
 si/e of the block and also with Hie strength desired. Tho 
 6-, 7-, and 8-inch blocks usually have two vertical and one hori- 
 zontal partitions, or one vertical and one hori/ontal for blocks 
 S inches wide. The 10- and iL'-inch arches may IIMVC either one 
 oi- two hori/ontal pM.rHl.ions. Arch blocks over 12 inches deep 
 should al\\ays have at least (.wo hori/ontal partitions. In the 
 strongest blocks the voids are about ;; inches square. 
 
 Thickness of \Veb. This should be at least } inch for 
 porous tiling and i inch for semi-porous. The thicker the 
 
 Fig. 6 
 
 Fig. 7 
 
 webs the j-realer will be the strength of the arch, and also it 
 lire resislanee. 
 
 The end joints are always bevelled as in Tig. C> ; (he ends being 
 
792 FIRE-PROOF AND INCOMBUSTIBLE FLOORS. 
 
 parallel, thus all the intermediate blocks are made with the same 
 die. 
 
 Bonding. It is desirable that the cross-joints in adjacent 
 parallel courses should break joint ; as in Fig. 8. This, however, 
 necessitates different lengths of skewbacks and keys and is 
 seldom done. Each course of blocks is always independent of 
 the adjacent courses except for the adhesion of the mortar. 
 
 Fig 8 
 
 Depth, Span, and Weight. The maximum spans for 
 different depths and the average weights per square foot of this 
 type of arch, set in place, are as follows: 
 
 Depth of Arch. 
 
 Maximum Span. 
 
 Weight per sq. ft. 
 
 6 ins. 
 
 4 ft. 6 ins. 
 
 29 Ibs. 
 
 8 ins. 
 
 5 ft. 6 ins. 
 
 31 Ibs. 
 
 9 ins. 
 
 6ft. 
 
 32 Ibs. 
 
 10 ins. 
 
 6 ft. 6 ins. 
 
 33 Ibs. 
 
 12 ins. 
 
 8 ft. 
 
 39 Ibs. 
 
 15 ins. 
 
 9ft. 
 
 46 Ibs. 
 
 16 ins. 
 
 10ft. 
 
 50 Ibs. 
 
 The depth of arch most frequently used is 10 inches, the gir- 
 ders being spaced to use 10-inch I-beams for joists spaced from 
 5 to 6 feet 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 tiling and less con- 
 crete filling. 
 
 The weights per square foot, as given by different manufac- 
 turers vary greatly, no doubt due to the character of the material 
 used and to the thickness of the webs. 
 
 Form of Skew-backs. An end-construction arch should 
 have skew-backs formed of the same blocks, with a notch in the 
 end of the block to fit over the bottom flange of the beam, as in 
 Fig. 9. It is generally considered that the end-construction skew 
 is much stronger than the side-construction skew, but on account 
 of the large amount of mortar lost in the voids and the difficulty 
 of obtaining an even bearing with end-construction skews, and 
 
HOLLOW-TILE ARCHES. 
 
 793 
 
 also because of the greater facility with which the side-construc- 
 tion skew-backs can be used, contractors generally prefer to use 
 
 Fig. 9 
 
 End-Construction Skew-backs. 
 
 the latter and this has given rise to the combination arch, shown 
 by Fig, 10. 
 
 " ' ; '," ' '. . . '".".' ''''' 
 
 .'... '"_' ] ~ . -'xJ 
 
 . . 
 2 s 4 Beveled Floor Strips lo" Centers 
 
 Fig. 10 
 
 Combination Arch. 
 
 Finished Floor Line^, 
 
 Fig. II 
 
 Longitudinal Section. 
 
 To develop the necessary strength side-construction skews 
 should have a large sectional area and a sufficient number of 
 partitions, following, approximately, the lines of thrust. 
 
794 FIRE-PROOF AND INCOMBUSTIBLE FLOORS. 
 
 With any form of skew the recess for the beam flange should 
 be wide enough so that when the tiles are set the protection 
 flange on the skew will not touch the bottom of the beam, but 
 will be at least J inch below it. 
 
 A great variety of side-construction skew-backs 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 length. If the span of the arch 
 is such that the standard intermediate blocks will require a key 
 6 inches wide or more then the end-method key is used, as jn 
 Fig. 6, but if the space for the key is small, a side-method key, 
 such as shown in Figs. 7 and 10, is used. As the key is almost 
 entirely in compression, a side-construction key 6 inches wide 
 or less will usually give all the strength required, provided that 
 the horizontal webs are in the same line with those in the inter- 
 mediate blocks. Mr. E. V. Johnson, Western manager of the 
 National Fire-proofing Co., says: " We prefer the use of an end- 
 construction key in all cases where possible. Our custom is to 
 use side-construction keys for spaces of 6 inches and under and 
 end-constructjen keys for larger spaces. When using the latter 
 keys we insert a J-inch fire-clay slab between the ends of the tile." 
 
 Raised Skew-backs. Where flat arches are sprung be- 
 tween 18-, 20- or 24-inch beams it is either necessary to use a raised 
 skew-back or else have a large space above the top of the tile 
 
 Fig. 12 
 
 Raised Skew-back. 
 
 arches which must be filled in some way. Raised skew-backs 
 are preferable to a hollow space above the tiles and cheaper than 
 concrete filling. They are often used for roof arches, because 
 
HOLLOW-TILE ARCHES. 
 
 795 
 
 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 skew-backs are almost always made on the side-con- 
 struction method, Figs. 12, 13, and 14 showing typical forms for 
 end-construction arches. 
 
 18 Steel Beam 
 
 Fig. 13 
 
 a D 
 a 
 
 a 
 
 Fig. 14 
 
 Flat vs. Panelled Ceilings. In connection with the 
 raising of the arches above the bottom of the beams or girders, 
 Mr. Freitag calls attention to the advantages of flat ceilings, as 
 follows ; 
 
/yo FIRE-PROOF AND 1NUOM13US1113.LU 1-LUUKb. 
 
 "Flat, unbroken ceilings are always to be preferred to any 
 type of terra-cotta arch which may require a panelled effect due 
 to the projection of the girders or beams below the main ceiling 
 line." A perfectly flat ceiling reflects more light and gives a 
 better-lighted room and also deflects heat. Panelling forms 
 pockets for the retention of heat and flame and greatly increases 
 the exposed area. 
 
 Arches should be of Same Depth as the Beams. 
 A deep block makes a much stronger floor than a shallower one, 
 and for the same depth of beams a lighter and cheaper floor. 
 A 12-inch arch will weigh less per square foot than a 10-inch 
 arch with 2 inches concrete filling and also costs less. 
 
 Setting of Tile Arches. Tile arches are always set on 
 wooden centres suspended by bolts hooked over the tops of the 
 I-beams. For all spans of 5 feet and over the centres should 
 be slightly cambered. Before any floor arches are set all girders 
 projecting before floor beams should be completely covered on 
 bottom and sides, independent of the floor construction. To 
 protect the steel from rust it should have a good coat of Port- 
 land-cement mortar before applying the tile. After the centres 
 are in place the beam tile should first be placed under bottom 
 of beams and mortar slushed on the sides. Then cover the 
 entire side of the skew-backs which rest against the floor beams' 
 with just enough mortar to give a perfect bearing and shove it 
 up against the beam. Then follow up with intermediate blocks, 
 covering the ribs on one end and one side with a full bed of 
 mortar, and shove in place. 
 
 The key should have mortar on both sides and one end (if 
 side-method key is used); it should fit snug, but not tight. 
 " Under no conditions 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 by a piece of 
 slate." (E. A. Hoeppner.) 
 
 " In setting tile arches it is very common to build the arches 
 in string courses, first fitting all the skews, then all the interme- 
 diates, and finally all the keys. This is bad practice, as it loads 
 the centre, both planks and stringers, to excess, causing too 
 great a deflection. In the end construction the arches should 
 be built one by one, each being complete before the next is 
 started. In side construction, where joints are broken longi- 
 tudinally, the arches should be keyed up or completed at the 
 first point where the intermediates meet the lines of the key, 
 
HOLLOW-TILE ARCHES. 797 
 
 thus completing the successive arches as rapidly as possible." 
 (Freitag). 
 
 All joints in the arches should be filled with mortar, especially 
 at the top. 
 
 Wetting the Tile. In warm weather all hollow tile, 
 whether dense or porous, should be well wet or water-soaked 
 before laying. In freezing weather they must be -kept dry. 
 
 Mortar for Setting'. "Mortar for setting porous hollow 
 tile should never be made of cement and sand alone, as such 
 mortar is too 'short' and rolls off the tile and does not insure 
 a full joint." (E. A. Hoeppner.) 
 
 One part Portland cement added to three parts rich cold lime 
 mortar makes a good mixture for either dense or porous tile. A 
 better mortar is made by mixing the cement and sand and 
 adding enough cold lime putty to make it work smooth. The 
 mortar should be thoroughly worked. Hot lime mortar should 
 never be used. 
 
 In dry weather the centres can be removed in 36 hours after 
 the tile are in place, but it is much better to allow 48 hours and 
 even longer in cold or wet weather. 
 
 Filling above Tile Arches. The strength of all tile 
 arches is greatly increased by wetting the tops of the arches and 
 covering with a rich cinder concrete (mixed with Portland 
 cement), well tamped and brought level with the tops of the 
 steel beams. 
 
 If the floors are to be finished in wood, nailing-strips are 
 required for securing the flooring. 
 
 These nailing-strips are usually of a dove-tail shape about 
 2J inches wide at the top, 3J inches at the bottom and If to 9 
 inches thick. It is preferable to lay them at right angles to the 
 steel beams, so that they may be secured to the top flange by a 
 metal clip, as in Fig. 10. 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 Portland cement and sand grout, applied with a brush. 
 The spaces between the nailing-strips should be filled with a 
 l-to-8- or 10-cinder concrete, finished about i inch below the top 
 of the strips. 
 
 Terra-cotta Filling-blocks. In cases where the tops of 
 the tile arches are 2 inches or more below the tops of the steel 
 beams hollow terra-cotta blocks are sometimes used for filling to 
 
798 FIRE-PROOF AND INCOMBUSTIBLE FLOORS. 
 
 the top of the beams, as in Fig. 15. These blocks are lighter than 
 good concrete, but they do not strengthen the arch unless they 
 are set in cement mortar and all the tiles and the tops of the 
 arches well wet just before laying the filling-blocks. 
 
 Cenient Floors. If the floors are to be finished with 
 cement, the cement and concrete should be at least 2J inches 
 and preferably 3 inches thick above the steel beams, and should 
 be blocked out in sections of not over 6 feet square, with joints 
 extending 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 from Stains in Ceiling. "If plastered 
 ceilings arc to be used, the terra-cotta work should be protected 
 against the smoke or soot from hoisting-engines. Stains are 
 also quite liable 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." (Freitag.) 
 
 To prevent these stains several hydraulic paints have been 
 used, some of which have proved very effective.* 
 
 Safe Loads for Flat Arches of Hollow Tile.f 
 
 The strength of flat arches of hollow tile depends upon the 
 crushing resistance of the material, the sectional area, per lineal 
 foot of arch, and upon the depth and span. For these reasons 
 it is impossible to give a table for strength which will apply to 
 all arches. The table on the following page is condensed from 
 two tables prepared by Mr. H. L. Hinton, who has gone very 
 elaborately into the strength of tile arches, in the handbook 
 prepared by him for the National Fire-proofing Co. 
 
 The values given for end-construction arches are based on 
 arch-blocks of the cross-sectional areas (per foot) given at the 
 head of the table and are intended to have a factor of safety of 
 7 with the weight of the tile only deducted. 
 
 Mr. Hinton says: "The safe loads as they stand in the table 
 afford a safe general statement of safe loads for all sections, since 
 
 * See Antihydrine, page 403. Building Construction; Part I. 
 
 t The variation in safe loads of hollow-tile arches as given by different 
 manufacturers is undoubtedly greater than it should be if all figured on the 
 same basis. The author believes that the safe loads given fertile arches are 
 as a rule more conservative than those given for the concrete constructions, 
 
HOLLOW-TILE AHCHES. 
 
 790 
 
 they represent specifically a light section in the case of each 
 arch." 
 
 The values for side-construction arches represent a factor of 
 safety of 5. No Account was taken of the density of the mate- 
 rial nor of the cross-sectional area of the blocks, hence the values 
 can only be considered as approximate safe loads. "They rep- 
 resent, however, the result of many tests with dense material 
 and with material more or less porous, and also the blocks hi 
 common use, and consequently in a way represent average cross- 
 sectional areas." 
 
 SAFE LOADS PER SQUARE FOOT OF FLOOR. 
 
 END-CONSTRUCTION FLAT ARCHES. 
 
 (H. L. HINTON). 
 Semi-porous material of sectional area per lineal foot as given in second line. 
 
 Depth of Arch. 
 
 6" 
 
 7" 
 
 8" 
 
 9" 
 
 10" 
 
 12" 
 
 15" 
 
 Areas, Sq. Ins. 
 
 310 
 
 340 
 
 370 
 
 400 
 
 430 
 
 490 
 
 580 
 
 Spans. 
 4' 6" . 
 
 Ibs. 
 196 
 
 Ibs. 
 254 
 
 Ibs. 
 319 
 
 Ibs. 
 391 
 
 Ibs. 
 470 
 
 Ibs. 
 648 
 
 Ibs. 
 968 
 
 5' 
 
 155 
 
 202 
 
 254 
 
 312 
 
 376 
 
 519 
 
 777 
 
 5' 6" . 
 
 
 163 
 
 205 
 
 254 
 
 306 
 
 424 
 
 636 
 
 6' 
 
 
 
 170 
 
 209 
 
 253 
 
 352 
 
 529 
 
 6' 6" 
 
 
 
 141 
 
 175 
 
 212 
 
 295 
 
 446 
 
 7' 
 
 
 
 
 147 
 
 179 
 
 251 
 
 380 
 
 7' 6" . . 
 
 
 
 
 
 153 
 
 215 
 
 326 
 
 8' 
 
 
 
 
 
 
 185 
 
 282 
 
 
 
 
 
 
 
 
 
 SIDE-CONSTRUCTION FLAT ARCHES. 
 
 Approximate loads for average arches. 
 Factor of safety of 5. 
 
 Spans. 
 
 Depth of Arch in Inches. 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 12 
 
 15 
 
 4' 
 
 Ibs. 
 149 
 114 
 
 Ibs. 
 257 
 198 
 157 
 126 
 
 Ibs. 
 382 
 297 
 236 
 191 
 157 
 
 Ibs. 
 518 
 404 
 322 
 262 
 216 
 180 
 152 
 
 Ibs. 
 663 
 518 
 415 
 338 
 280 
 234 
 199 
 170 
 
 Ibs. 
 953 
 747 
 599 
 490 
 407 
 343 
 291 
 250 
 
 Ibs. 
 1340 
 1051 
 845 
 692 
 575 
 485 
 413 
 355 
 
 4' 6" . . 
 
 5' 
 
 5' 6" . . 
 
 
 6' 
 
 
 6' 6" . . 
 
 
 
 7' 
 
 
 
 
 7' 6" 
 
 
 
 
 
 
 
 
 
 Patented End-method Arches. 
 
 > 
 
 Figs. 15 and 16 show two variations of a type of arcb invented 
 and patented by Mr, E. V. Johnson when manager of the Pioneer 
 
Company, of Chicago. The right to manufacture and use this 
 arch, in certain territory, was granted to the Pioneer Company; 
 also to Henry Maurer & Son, of New York, and to the Hayden- 
 ville (Ohio) Company. The original shape of the arch tile is 
 illustrated by Fig. 16, and this shape is still used by the Pioneer 
 Company. Henry Maurer & Son have modified the shape to 
 that shown by Fig. 15, considering that this shape gives a stronger 
 (arid also a slightly heavier) arch than the original shape. The 
 advantages of this arch are reduced weight, with equal strength 
 
 Fig. 15 
 
 and a clear space of 5 inches between the tile, which avoids cut- 
 ting of the blocks for the tie-rods. 
 
 This arch can be adapted to any span up to 10 feet by using 
 a suitable depth of block. 
 
 The limit of span, weight per square foot and safe load of the 
 "Excelsior" arch is given by Maurer & Son as follows: 
 
 Depth of Arch. 
 
 Limits of Span. 
 
 Weight per sq. ft. 
 
 Safe Load pei sq. ft. 
 
 8 ins. 
 9 ins. 
 10 ins. 
 12 ins. 
 
 5 ft. to 6 ft. 
 6 ft. to 7 ft. 
 7 ft. to 8 ft. 
 8 ft. to 9 ft. 
 
 27 Ibs. 
 29 Ibs. 
 33 Ibs. 
 38 Ibs. 
 
 300 Ibs. 
 350 Ibs. 
 300 Ibs. 
 350 Ibs. 
 
 The Pioneer Company have made arches as deep as 20 inches 
 and weighing 56 Ibs. per square foot. Both companies use 
 semi-porous material for the arch blocks. It should be noticed 
 that the arch made by the Pioneer Company has an end-con- 
 "struction skew, while Maurer & Son use a side-construction 
 skew. The Pioneer Company formerly used the side-construc- 
 tion skew, but found that when arches of this type were tested 
 
HOLLOW-TILE ARCHES. 
 
 801 
 
 to destruction the skew-backs were almost invariably the parts 
 which failed, hence their adoption of the end-construction skew. 
 Messrs. Maurer & Son, however, have tested the Excelsior arch, 
 
 Fig. 16 
 
 with spans of 8 and 10 feet, with loads of over 1000 Ibs. per 
 square foot without failure, with skew-backs as shown by them. 
 This arch has been very extensively used in both Eastern 
 and Western cities and is undoubtedly a very good type. 
 
 Segment Floor Arches. 
 
 For warehouses, manufacturing plants, printing establish- 
 ments, etc., where great strength is demanded and a flat ceiling 
 is not necessary a segmental arch will give the required strength 
 at less expense and with less dead weight than any other form 
 of tile arch. "A 6-inch segmental arch weighing 25 Ibs. to the 
 square foot (for the tile only) will easily carry 1000 Ibs. per 
 square foot up to a 16-foot span." (E. A. Hoeppner.) 
 
 These arches are usually formed of either 6" or 8" hollow tile, 
 set on the side-construction principle and bonded endways like 
 
 Floor Strip 
 
 16" Centers 
 
 Fig 17 
 
 a brick vault. They can be used for spans up to 20 feet, but 
 it is better to limit the span to about 16 feet. 
 
802 FIRE-PROOF AND INCOMBUSTIBLE FLOORS. 
 
 Figs. 17, 18, and 19 show typical forms of segment arches. 
 The weight of the arch tile will run about 26 Ibs. per square 
 foot for 6-inch tile and 32 Ibs. for 8-inch tile. To these weights 
 
 Fig. 18 
 
 should be added the weight of concrete filling, flooring, plaster, 
 
 etc. 
 
 Thickness of Webs. "For general use the webs of seg- 
 ment tile should be J inch thick for semi-porous tile and f inch 
 for porous tile. The skew-back web should be at least f inch thick 
 for the first-named material and 1 inch for the second. Fof 
 printing establishments or any other building where a large 
 
 19 
 
 amount of vibration occurs the webs of all tile must be designed 
 in proportionate thickness to the load they are required to carry." 
 (E. A. Hoeppner.) 
 
 Rise of Arch. The rise of the soffit of the arch above the 
 springing line should be from 1/10 to j of the span.* The greater 
 the rise the less will be the thrust of the arch. 
 
 Strength* "A 6-inch segment arch of 12 feet span made by 
 Henry Maurer & Son carried without any deflection a weight of 
 
 * Mr. E. A. Hoeppner gives f -inch per foot of span as a practical safe rise. 
 This is equivalent to 1/16 the span. 
 
HOLLOW-TILE ARCHES. 
 
 803 
 
 5200 Ibs. placed on 1 square foot of space over the centre." Henry 
 Maurer & Son give the safe load for a 6-inch arch of 12 feet span 
 or an 8-inch arch of 15 feet span with a rise of 1-10 the span at 
 from 400 to 500 Ibs. per square foot. 
 
 Skew-backs, Raised skew-backs are always used for seg- 
 mental arches, as shown by Figs. 17, 18, and 19. Wherever a 
 sprinkler system is to' be employed the lower edge of the skew- 
 back should be rounded as in Fig. 18. This will cause the 
 water to roll underneath the beam and not drip off on the side 
 of it, as will be the case where the skew-backs have a square 
 base. 
 
 Filling the Haunches, The haunches of segmental 
 arches should be filled with good cement concrete levelled up to 
 a point not less than 1 inch 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 strength of the 
 arch at the haunches depends largely upon the strength of the 
 concrete filling. Voids are sometimes formed in the haunches, 
 stiff pasteboard being used to form the core. 
 
 Double flooring 
 Cinder Concrete 
 
 
 k- Girder Tile 
 
 Fig. 20 
 
 Longitudinal sections. 
 
 Tie-rods. The thrust of segmental arches is very consid- 
 erable, so that it is important to provide plenty of tie-rods 
 between the beams. A formula for determining the stress in 
 the tie-rods and the diameter of the same is given on page 881. 
 
 To be most effective the tie-rods should be spaced within the 
 lower third of the beam, or preferably at the centre of the skew. 
 
 Placing the tie-rods within the lower third of the beam, how- 
 ever, will cause them to project below the soffit of the arch, 
 
 
804 FIRE-PROOF AND INCOMBUSTIBLE FLOORS. 
 
 giving an unsightly appearance to the ceiling and rendering 
 them difficult to protect. Occasionally the tie-rods are encased 
 with special tile, as in Fig. 20, but more often they are raised 
 so as to come about \\ inches above the soffit of the arch. For 
 the intermediate spans it is probably safe enough to raise the 
 tie-rods, but for all end spans they should either be dropped to 
 
 jTloorLine 
 
 1 
 
 xtOl 
 
 , / / 
 
 ck / 
 
 -Forged Ends 
 
 
 Fig. 21 
 
 near the centre of the skew-back and encased with special tile 
 or forked tie-rods should be used, as shown in Fig. 21. 
 
 The Serrated Arch. 
 
 Fig. 22 illustrates a new system of hollow terra-cotta floor, 
 arch construction devised by Mr. H. L. Hinton, engineer for 
 the National Fire-proofing Company. It may be considered 
 as an intermediate between the segmental arch and the com- 
 
 "Wood Flooring 
 
 Fig. 22 
 
 bination flat arch, with advantages over the former in the way 
 of economy and a more nearly level ceiling, while possessing 
 nearly the same strength. 
 
 The rise of this arch is invariably a 24th of the span or \ inch 
 to the foot (of the full span). This uniform rise is effected by 
 giving a batter to the skew-back of 2 inches to the foot of depth 
 of the section and a batter of but 1 inch of the same character to 
 the intermediate sections, the key having the same batter as 
 the skew-back. 
 
HOLLOW-TILE ARCHES. 
 
 805 
 
 '/hus regardless of the span a mortar joint of equal thickness 
 at the top and bottom of the block is secured and a change of 
 batter in the manufacture of each block obviated. 
 
 The advantages claimed for this arch over the ordinary flat 
 arches are greater strength, more stable (as it is better keyed), 
 saving in cost of niortar, also in the quantity of centring re- 
 quired, as the centring may be removed as soon as the keys 
 are set. 
 
 For very wide spans, however, this arch is not always practi- 
 cable, as the pointed crown, rising higher than the crown of a 
 segmental arch of the same span, causes greater thickness of 
 floor section at the I-beams. 
 
 Block sections for this form of arch are manufactured by the 
 National Fire-proofing Company. As yet, however, this form 
 of construction has been used to a very limited extent. 
 
 The safe live loads per square foot for standard sections of 
 this arch, of semi-porous material, with a factor of safety of 7, 
 are given as follows : 
 
 SAFE LIVE LOADS FOR SERRATED ARCHES. 
 
 Span in Feet. 
 
 Depth of Tile in Inches. 
 
 6 
 
 8 
 
 10 
 
 12 
 
 6 
 8 
 10 
 12 
 15 
 
 330 
 216 
 156 
 
 449 
 288 
 205 
 156 
 
 556 
 352 
 249 
 187 
 132 
 
 688 
 431 
 302 
 225 
 157 
 
 
 
 
 The weight per square foot of entire floor, including steel 
 beams, concrete, flooring, and plaster, will run about 57 Ibs. 
 for a 6-inch arch, 58 Ibs. for an 8-inch arch, 73 Ibs. for a 10-inch 
 arch, and 78 Ibs. for a 12-inch arch. 
 
 Single-block Flat Arches. There have been some at- 
 tempts to construct fire-proof floors by means of tile blocks or 
 lintels that would span from beam to beam in one piece, the 
 blocks acting as beams or lintels placed side by side and leveled 
 off on top with concrete. Owing, however, to the impractica- 
 bility of making tile that could be used for a greater span than 3 
 feet, this system requires so many steel beams for its support that 
 the cost of the steel framing practically prohibits its adoption. 
 The best floor ever built on this principle is the Fawcett Venti- 
 
806 FIRE-PROOF AND INCOMBUSTIBLE FLOORS. 
 
 lated Fire-proof Floor, which was at one time quite extensively 
 used in England, and to some extent in Philadelphia and Boston. 
 Being unable, however, to compete with other systems in cost 
 (considering both the fire-proofing and the steel), it is now 
 seldom, if ever, used. A description of the Fawcett system may 
 be found in Part I. of Building Construction. 
 
 The National Fire-proofing Company also makes a floor tile 
 which may be used to span from beam to beam, when the spac- 
 ing between beams does not exceed 3 feet, but the author believes 
 that they are not very extensively used. 
 
 Fig. 23 shows a type of arch introduced by Henry Maurer & 
 Son, which consists only of two skew-backs and one centre or 
 
 
 Fig. 23 
 " Eureka Arch." 
 
 "key-tile" set between them, that might be used to advantage 
 in dwellings and apartment houses where the loads to be sup- 
 ported are almost nominal and the spans do not usually exceed 
 16 feet. Under such conditions this arch has the advantages 
 of being very quickly and cheaply erected, as no centring is 
 required and no concrete filling except a little light filling between 
 the nailing-strips. This construction, however, requires a 
 uniform spacing of 30 inches between centres of I-beams and 
 cannot be advantageously used with beams deeper than 6 inches. 
 With 6-inch steel beams and single f-inch flooring the entire 
 floor construction will not weigh over 44 Ibs. per square foot. 
 
 Reinforced Tile Floors. 
 
 In order to obtain a wide-span flat arch of tile the manufac- 
 turers of terra-cotta tiling have resorted to the principle of rein- 
 forced concrete employed by the concrete fire-proofing com- 
 panies using steel tension members embedded in Portland 
 cement, but substituting hollow tile in place of concrete to 
 resist the compressive stress. While this construction is per- 
 
HOLLOW-TILE ARCHES. 
 
 807 
 
 fectly legitimate, it depends for its strength upon the adhesion 
 of the cement to both the steel and tiles, and its fire-resisting 
 qualities is gauged by the resistance of the cement. The prin- 
 ciple of construction is exactly the same as for the flat rein- 
 forced floors described in the latter portion of this chapter. 
 These reinforced tile floors have a greater depth or thickness 
 than solid concrete floors of the same span and strength, but as 
 the strength of a floor increases as the square of the depth this 
 additional depth is an advantage in giving greater strength, 
 while on account of the voids the weight is about the same or 
 somewhat less. 
 
 Aside from the question of cost (including the additional 
 height of building required by the greater thickness of floors), 
 the writer believes that there is little choice either way between 
 these floors and those of solid concrete. 
 
 The first person to use a reinforced flat-tile floor Was Mr. 
 Thomas A. Lee, who also introduced the end-arch construction. 
 
 In 1891 Mr. Lee used a construction of this kind with a span of 
 25 feet over a large room in the top story of the Equitable Build- 
 ing in Denver. Fig. 24 shows this construction as afterwards 
 perfected by him. It consists of hollow tile set end to end 
 
 . 24 
 
 from wall to girder or from girder to girder. In the sides of 
 each tile near the bottom are grooves to receive the steel-tension 
 member, which is embedded in soft cement. All joints between 
 tiles are also filled with cement, 
 
 For the tension member Mr. Lee Used twisted steel cables. 
 This special construction was patented by Mr. Lee, but owing 
 to financial difficulties brought about by the panic of '93 it has 
 been used to a very limited extent. It furnished a suggestion, 
 however, for two constructions based on the same principle 
 which have been very extensively introduced* 
 
808 FIRE-PROOF AND INCOMBUSTIBLE FLOORS. 
 
 The " Herculean " Arch,* This floor is built of semi- 
 porous terra-cotta blocks 12 inches by 12 inches on top and vary- 
 ing from 8 to 12 inches in depth, according to the span and load. 
 In the sides of the blocks are grooves to receive 1-| X 1J X 3/16-inch 
 T-bars. The blocks are laid end to end the entire length of the 
 span, with a bearing of 4 to 6 inches on walls or girders, present- 
 ing tv/o continuous grooves, which are filled with cement, and 
 the T-bars are then inserted. The T's must, of course, extend 
 the full length of the span. The grooves in the next course are 
 
 The 
 
 Fig. 25 
 1 Herculean" Arch. 
 
 then filled with cement and the blocks pushed into place, thus 
 thoroughly covering the steel with cement. 
 
 All joints between the blocks are filled with cement and the 
 blocks are laid to break joint endways, as in Fig. 25. 
 
 Span. This floor is adapted to spans up to 25 feet and has 
 been extensively used for spans varying from 19 to 23 feet. 
 
 Weight. The weight of the terra-cotta blocks and steel tees 
 per square foot is given at 33 Ibs. for- blocks 8 inches deep, 42 Ibs. 
 for 10-inch blocks and 51 Ibs. for 12-inch blocks. 
 
 Strength. A 12-inch arch of 20 feet clear span loaded with 
 510 Ibs. to the square foot (over about 7/10 of its area) showed 
 a deflection of but 9/16 of an inch in the middle after the load 
 
 * Patented and manufactured by Henry Maurer & Son, 1898 and 1900. 
 
HOLLOW-TILE ARCHES. 809 
 
 had been on for several months. On removal of the load the 
 arch sprung back to its original area. 
 
 Another test floor spanning 18 feet from wall to wall was loaded 
 with 600 Ibs. to the square foot, distributed over practically its 
 entire surface. This load remained on from May 21 to June 10, 
 "and during that time the floor showed no perceptible deflec- 
 tion." 
 
 The manufacturers estimate the safe load for this construction 
 as follows: 
 
 For 12-inch arch, 20-foot span, 400 Ibs. per square foot. 
 
 For 10-inch arch, 16-foot span, 400 Ibs. per square foot. 
 
 For 8-inch arch, 12-foot span, 150 Ibs. per square foot. 
 
 Fire-proofing Qualities. The steel tension members, being 
 buried in the terra-cotta blocks over 2 inches everywhere, are 
 unusually well protected, so that there can be no question of the 
 fire-proof quality of the floor. 
 
 Advantages. The chief advantage of this construction is its 
 low cost as compared with systems equally fire-proof and requir- 
 ing steel beams every 6 or 8 feet. 
 
 It is particularly well adapted to buildings having masonry 
 walls and partitions, as in such buildings little or no structural 
 steel is required. 
 
 The floor also affords an unusually smooth under surface 
 thereby reducing the cost of plastering. 
 
 No tie-rods are required for this floor. 
 
 Commercial Success. The author understands that this floor 
 has proved a success commercially as well as in other ways. 
 
 The Jolmsoii Long-span Flat Construction. The 
 other leading reinforced tile floor was invented by Mr. E. V 
 Johnson, and is now controlled and erected by the National 
 Fire-proofing Company. 
 
 The general construction of this floor is as follows: 
 
 A temporary flat centring is first erected and over this is 
 spread a layer of rich Portland cement mortar about f inch 
 thick. On top of this mortar is laid a woven fabric containing 
 steel rods varying from J inch to J inch in diameter, according 
 to the span and spaced from 2 inches to 8 inches centre to centre. 
 Another layer of the same mortar is then spread on top and hol- 
 low tiles from 3 to 12 inches in depth, according to the span, are 
 then set in the mortar and laid with "break joint," so as to form 
 continuous rows from one support to the other, ttfe same as in 
 end-construction flat arches, except that in the Johnson con'- 
 
810 FIRE-PROOF AND INCOMBUSTIBLE FLOORS. 
 
 struction the ends of the tile are square to the beds. A layer 
 of concrete about 2 inches thick is also usually spread on top of 
 the tile. 
 
 Fig. 26 shows the general method of construction of this sys- 
 tem, 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. 
 
 As already stated, this system differs from the flat concrete 
 systems only in the substitution of hollow tile for the concrete 
 
 Fig. 26 
 
 Johnson Arch. 
 
 in the upper portion of the slab, its strength depending upon 
 the reinforcement and the adhesion of the cement mortar to the 
 steel and tile. As the tile are covered both on the bottom and 
 top with concrete the fire-proofing quality is also measured by 
 the resistance of the concrete and not of the tile. 
 
 Many tests, however, have shown that the adhesion of the 
 mortar is perfect and that it will stand a high temperature with- 
 out injury. 
 
 Span. This construction can be used for any span up to 
 25 feet, the most advantageous span being about 16 feet. 
 
 Weight. The weight per square foot of this floor, includ- 
 ing the fabric and the cement on the bottom and in the joints, 
 but not on top of the tile, is as follows: 
 
 For depth of tile of 12 inches, 10 inches, 9 inches, 8 inches, 7 
 inches, 6 inches, 5 inches, 4 inches. 
 
HOLLOW-TILE ARCHES. 
 
 811 
 
 Weight per square foot, Ibs., 60, 55, 45, 42, 37, 34, 26, 24. 
 
 The concrete above the tile should be figured at 12 Ibs. per 
 square foot for each inch in thickness. 
 
 Strength. The proprietors of this system give the following 
 for the ultimate strength of the floors with 1 inch of 1 to 3 
 Portland-cement morlbar on top of the tile. 
 
 JOHNSON SYSTEM. 
 
 With 1" Portland-cement Floor Surface. 
 
 Spans 
 
 Ultimate Strength in Pounds per D Foot. 
 
 from 
 
 
 
 
 
 
 
 
 
 
 10 to 24 
 
 Thick- 
 
 Thick- 
 
 Thick- 
 
 Thick- 
 
 Thick- 
 
 Thick- 
 
 Thick- 
 
 Thick- 
 
 Thick- 
 
 Feet. 
 
 ness 
 
 ness 
 
 ness 
 
 ness 
 
 ness 
 
 ness 
 
 ness 
 
 ness 
 
 ness 
 
 
 of tile. 
 
 of tile. 
 
 of tile. 
 
 of tile. 
 
 of tile. 
 
 of tile. 
 
 of tile. 
 
 of tile. 
 
 of tile. 
 
 
 12" 
 
 10" 
 
 9" 
 
 8" 
 
 7" 
 
 6" 
 
 5" 
 
 4" 
 
 3" 
 
 
 Lbs. 
 
 Lbs. 
 
 Lbs. 
 
 Lbs. 
 
 Lbs. 
 
 Lbs. 
 
 Lbs. 
 
 Lbs. 
 
 Lbs. 
 
 10 feet 
 
 3375 
 
 2580 
 
 2140 
 
 1850 
 
 1525 
 
 1265 
 
 1000 
 
 775 
 
 560 
 
 11 feet 
 
 2800 
 
 2340 
 
 1780 
 
 1536 
 
 1264 
 
 1052 
 
 832 
 
 640 
 
 464 
 
 12 feet 
 
 2350 
 
 1800 
 
 1480 
 
 1280 
 
 1064 
 
 880 
 
 700 
 
 540 
 
 390 
 
 13 feet 
 
 2000 
 
 1540 
 
 1265 
 
 1100 
 
 910 
 
 752 
 
 595 
 
 460 
 
 334 
 
 14 feet 
 
 1730 
 
 1325 
 
 1100 
 
 950 
 
 780 
 
 650 
 
 510 
 
 400 
 
 290 
 
 15 feet 
 
 1500 
 
 1160 
 
 950 
 
 830 
 
 680 
 
 590 
 
 450 
 
 348 
 
 250 
 
 16 feet 
 
 1320 
 
 1010 
 
 840 
 
 720 
 
 600 
 
 500 
 
 395 
 
 305 
 
 220 
 
 17 feet 
 
 1180 
 
 900 
 
 740 
 
 640 
 
 578 
 
 440 
 
 350 
 
 . 270 
 
 194 
 
 18 feet 
 
 1020 
 
 795 
 
 664 
 
 570 
 
 473 
 
 392 
 
 310 
 
 242 
 
 174 
 
 20 feet 
 
 844 
 
 645 
 
 535 
 
 462 
 
 381 
 
 314 
 
 250 
 
 194 
 
 
 22 feet 
 
 700 
 
 536 
 
 445 
 
 384 
 
 316 
 
 263 
 
 208 
 
 
 
 24 feet 
 
 587 
 
 450 
 
 370 
 
 320 
 
 266 
 
 220 
 
 
 
 
 With this table the following factors of safety should be used: 
 
 Factor 4. Floors of offices, schoolrooms, hospital and asylum wards, 
 dwellings, and roofs. 
 
 Factor 5. Floors of stores, warehouses, theatres, public halls, and assem- 
 bly rooms. 
 
 Factor 6. Floors of buildings where vibration of machinery or loads, 
 ausing a sudden impact, occurs. 
 
 A section of this floor, 16 feet square, supported on walls 
 around the four edges, was loaded over its entire area with a 
 total uniformly distributed load of 187,680 Ibs. or 733 Ibs. to 
 each square foot. The deflection of the floor was as follows: 
 Under a load of 350 Ibs. per square foot, J inch scant; 733 Ibs. 
 per square foot, J inch full. 
 
 Advantages. The advantages of this system are the same as 
 noted for all long-span flat systems; the system can be used to 
 special advantage for roofs and for buildings divided by masonry 
 partitions, so that the spans do not exceed 25 feet. For such 
 buildings very little, if any, structural steel will be required. 
 
812 FIRE-PROOF AND INCOMBUSTIBLE FLOOR& 
 
 
 
 Fig. 37 
 
 Detail of Johnson Arch with Insulation Slabs* 
 
 Fig. 28 
 
 Partial Plan. 
 
HOLLOW-TILE ARCHES. 
 
 813 
 
 Commercial Success. This construction has been quite exten- 
 sively used in the Western and Northern States and can com- 
 pete commercially with other systems. Sixty thousand square 
 feet of this construction were used in the roof and floors of the 
 Chicago post-office. 
 
 Figs. 27 and 28 show a modification of this system as used in 
 a cold-storage warehouse built in Chicago in 1902. In this floor 
 a J-inch solid terra-cot ta slab tile was inserted in all end joints 
 to confine the air spaces and thus increase the insulation. 
 
 Protection of Girders and Beams around 
 Openings. 
 
 Girders where they project below the ceiling line, as is com- 
 monly the case, are much more exposed to the effects of fire 
 and water than the floor beams, and should, therefore, have the 
 most efficient protection. As a rule, such girders should be 
 provided with not less than 4 inches of terra-cotta protection 
 at the sides and 1J inches of solid tile under the bottom with a 
 space of i inch between the tile and the beam. 
 
 Fig. 29 
 
 Figs. 29 and 30 are typical of the latest methods of protect- 
 ing girders by means of hollow tile. The bottoms of the skews 
 (Fig. 29) are prevented from spreading by wire ties placed in 
 the end joints between the soffit tile and hooked into the round 
 holes in the skew-backs. Single-beam girders are usually pro- 
 tected as shown by Figs. 13 and 31, the latter figure showing 
 
814 FIRE-PROOF AND INCOMBUSTIBLE FLOORS. 
 
 more particularly the protection of a beam at the side of an 
 opening in the floor. 
 
 Inspection. Flat arches of hollow tile require close inspec- 
 tion during erection to see that broken or imperfect tile are not 
 used; that the ribs in end-construction tile abut opposite each 
 
 Fig. 30 
 
 Fig. 3f 
 
 other; that all joints are properly mortared, and that all of the 
 steel work is properly protected. Very much poor workman- 
 ship has been allowed to pass rather than to avoid delay, and 
 also because it cannot be discovered until the centring is 
 removed. A tile arch will generally look better on top than on 
 the bottom. The great carelessness which may obtain in the 
 setting of tile arches was well shown by an article in the Engi- 
 neering News of April 14, 1898. 
 
HOLLOW-TILE ARCHES COST. 815 
 
 Cost of Tile Arches. It is impossible to give more than 
 an approximate cost of hollow-tile arches, because the cost varies 
 with the depth and weight of the tile, the span between beams, 
 irregularity of framing, the quantity required, and also with 
 the locality and the condition of the labor market. 
 
 At the present time (summer of 1903) a flat arch of 10-inch 
 semi-porous tile, between 10-inch beams, will cost about 25 
 cents per square foot in Chicago or any of the large Eastern 
 cities. 
 
 A 12-inch arch, between 12-inch beams now costs about 27 
 cents per square foot, including beam and girder protection. 
 A 6-inch segmental arch between 15-inch beams, about 12 ft, 
 apart, can be furnished and set for about 23 cents per square 
 foot. 
 
 The Johnson long-span system costs about 30 cents per 
 square foot for a span of 16 ft., including the beam protection, 
 and 2 cents per square foot additional for each inch of cement 
 mortar on top of the arch. 
 
 The GUiastavino Tile Arch System. 
 
 This is a peculiar method of constructing floors, partitions, 
 staircases, etc., by means of thin tile 1 in. in thickness and 
 about 6 ins. wide and of lengths varying from 12 to 24 ins. 
 all bonded together in Portland cement so as to make one 
 solid mass. It was devised by R. Guastavino of New York and 
 Boston and is executed solely by the R. Guastavino Company. 
 It is essentially different in principle from all other methods 
 of fire-proofing construction with which the author is acquainted. 
 
 The floors in this system are built by spanning the space 
 between the girders with a single arch, vault, or dome, con- 
 structed of two or three or more thicknesses of these 1-inch 
 tile, depending upon the dimensions of the arch or vault. In 
 its best application, steel is used in tension only as tie-members, 
 and in place of steel girders tile girders are constructed of the 
 same material; wherever steel is used it is imbedded in the 
 masonry construction. 
 
 One of the earliest notable buildings in this system is that 
 of the Boston Public Library, built about fourteen years ago, 
 and some of the later important constructions are the Hall 
 of Fame and Library Building of the University of New York 
 and the Metropolitan Museum of Art, in New York, Massa- 
 chusetts Horticultural Building, American Type Foundry 
 
816 FIRE-PROOF AND INCOMBUSTIBLE FLOORS. 
 
 Building, and Massachusetts General Hospital, in Boston, 
 Minnesota State Capitol Building, St. Paul, Minn. 
 
 As indicating the spans which can be safely applied, the 
 floor above the crypt of the Cathedral of St. John the Divine, 
 in New York, measuring 56X60 ft. with no interior supports 
 and designed to carry a safe load of 400 pounds per square foot, 
 was constructed on this principle. 
 
 Wherever a vaulted ceiling is desired this seems to be the 
 best system of construction yet devised. 
 
 Strength. Floors built on this principle have been tested 
 under the supervision of the New York Building Department 
 up to 3700 pounds per square foot, with spans of 10 ft. 
 
 When used between I-beams the only steel beams required 
 are those spanning from column to column. 
 
 Architects contemplating the use of this system of construc- 
 tion are advised to consult the R. Guastavino Company before 
 letting any contracts. 
 
 Cost. Wherever vaulted ceilings are desired this construc- 
 tion should be as cheap, and generally is cheaper than any 
 other form of equally fire-proof construction a particular 
 advantage of the system being that frequently the soffit course 
 of tile is of pressed or glazed material making a most effective 
 and permanent finish as in the case of the City Hall Station 
 of the New York Subway, which was constructed for very 
 heavy loads without the use of steel 
 
 Reinforced Concrete Constructions. 
 
 History. In 1869 one Francois Coignet of Paris took 
 out letters patent on a combination of iron and concrete. In 
 1875 W. E. Ward constructed a building near Portchester, 
 New York, 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 light iron beams and rods." 
 
 Neither of these persons, however, appear to have realized 
 the importance of their invention or to have made any successful 
 effort toward a practical introduction of what is now com- 
 monly known as steel-concrete. 
 
 The general principle of reinforcing concrete with small 
 iron or steel for the purpose of supplying the necessary tensile 
 resistance required in beams or slabs, appears to have been 
 
REINFORCED CONCRETE CONSTRUCTIONS. 817 
 
 worked out independently by French and American inventors 
 and builders. 
 
 In 1876 Mr. Thaddeus Hyatt, a native of Maryland, but at 
 that time residing in London, England, while considering the 
 matter of fire-proof floor construction conceived the idea of 
 forming concrete beams by imbedding irpn in the bottom 
 of the concrete to afford the necessary tensile strength which 
 the concrete lacked. Mr. Hyatt made many experimental 
 beams, with the iron introduced in a great variety of ways, 
 as straight ties, with and without anchors and washers, truss 
 rods in various forms, flat pieces of iron set vertically and laid 
 flat, and 'anchored at intervals along the entire length. These 
 experimental beams were tested and broken by David Kirkaldy 
 of London. In the year 1877, Mr. Hyatt published a work 
 entitled "An account of some experiments with Portland 
 Cement combined with Iron as a Building Material," which 
 contains a description of these tests, and a discussion of the 
 results obtained. 
 
 A copy of this book may be found in the Patent Office Library 
 at Washington.* 
 
 On July 16, 1878, a U. S. patent, No. 206,112 was issued to 
 him on a combination of iron and concrete, similar to that 
 shown in Fig. 35, and on various other combinations of the two 
 materials. This patent virtually covered all combinations 
 of steel and concrete in which the steel is provided with ob- 
 structions to sliding, but as a principle cannot be patented, 
 Mr. Hyatt's patent included only the specific form of rein- 
 forcements described by him, leaving the field still open for 
 all other -shapes. 
 
 In his specifications Mr. Hyatt says : " 1 find it important 
 to use ties having the greatest friction surface." 
 
 He also realized that the combination of the two materials 
 would be unsuccessful for practical application, unless they 
 expanded uniformly when exposed to severe heat and cold. 
 To satisfy himself on this question he made very careful ex- 
 periments to determine the expansion of the two materials 
 separately, and when the iron wag imbedded in the concrete. 
 By these experiments he found the lineal expansion of con- 
 crete to be .00137 for 180 as compared with .00140 for wrought 
 
 * A brief resume" of Mr. Hyatt's experiments may be found in a communi- 
 cation by Mr. Edwin Thacher, in the Engineering News of March 26, 1903. 
 
818 FIRE-PROOF AND INCOMBUSTIBLE FLOORS. 
 
 iron. He also exposed blocks of concrete containing bars of 
 iron to the red heat of a furnace for six hours and found them 
 to be entirely sound and good when taken out, showing that 
 the relation of the two materials is not affected by expansion 
 or contraction. 
 
 The first person jn this country, so far as the author is aware, 
 to make practical application of Mr. Hyatt's invention and 
 researches, is Mr. P. H. Jackson, C.E., of San Francisco, who 
 iirst used concrete reinforced by steel in 1877, and in 1890 
 published a pamphlet entitled Improvement in Building Con- 
 struction, which gives a great amount of information on rein- 
 forced concrete, and on concrete in general construction. A 
 revised edition of this pamphlet was printed in 1897. 
 
 While Mr. Jackson was experimenting with the Hyatt tie 
 (Fig. 35), Mr. Ernest L. Ransome, a very successful worker of 
 concrete in San Francisco, conceived the idea of using square 
 bars of iron or steel twisted their entire length, for the rein- 
 forcing of concrete, and, finding by experiment that the twisted 
 bars were held perfectly by the concrete, he patented his im- 
 provement in 1884, and gradually succeeded in influencing 
 architects and owners in favor of his special forms of construc- 
 tion, until the Ransome system is now well known by all well- 
 informed architects. 
 
 While the Jackson and Ransome systems of reinforced con- 
 crete were being developed in this country, a system of rein- 
 forced concrete, invented in 1867 by P. A. J. Monier, a gardener 
 of Paris, was being introduced in Europe under the name of 
 Monier Construction, and the knowledge of what was being 
 done in Europe and in this country in the way of reinforced 
 concrete construction led Mr. John F. Golding, the inventor 
 of expanded metal to experiment with expanded metal as a 
 reinforcement for concrete slabs. His experiments were so 
 successful that expanded-metal constructions came rapidly 
 into great prominence, and their success and the great demand 
 for fire-proof floors has led to the introduction, during the past 
 three years, of almost innumerable forms of concrete floor 
 construction. 
 
 While developed mainly by practical persons, concrete-steel, 
 or ferro or armored concrete, as it is called in Europe, has 
 lately been made the subject of investigation by the leading 
 engineers of Europe and America, so that it may be designed 
 with a degree of confidence closely approaching that of steel 
 
REINFORCED CONCRETE BEAMS AND SLABS. 819 
 
 or timber construction. In the opinion of the author, it is the 
 greatest advancement that has been made in building con- 
 struction since the introduction of structural steel. 
 
 Mechanical Principle of Reinforced Concrete 
 Beams and Slabs.* 
 
 The art of concrete-steel construction is based upon the 
 adhesion of the concrete to the steel to such an extent that 
 the composite structure acts as a homogenous beam, the con- 
 crete extending with the steel. The following paragraph, 
 quoted from Mr. Considere, engineer of bridges and roads of 
 Paris, who has conducted elaborate and exhaustive investi- 
 gations into the properties of this material, is perhaps as satis- 
 factory a description of the action of concrete-steel under 
 transverse stress as can be given. 
 
 " Armored concrete submitted to tension acts in exactly 
 the same manner as ordinary concrete, so long as the tensile 
 stress does not exceed the usual breaking stress of ordinary 
 concrete. Under higher stresses it will support, without break- 
 ing, extensions which, in the case of specimens hardened under 
 water, have been as great as one five-hundredth of the total 
 length; and, in the case of air-hardened concrete, have ranged 
 between one eight-hundred-and-fiftieth, and one two-thou- 
 sandth of the total length. When ferro-concrete is stretched 
 beyond the usual elastic range of ordinary concrete, the tensile 
 stress on the concrete remains constant up to the ultimate 
 breaking point, the whole of the additional load being taken 
 up by the metal. " 
 
 To insure the above results, however, it is necessary, first, 
 that there be a perfect and permanent bond between the con- 
 crete and the metal reinforcement, and, second, that the latter 
 be well distributed through the stretching concrtee. 
 
 Durability and Fire- proofing- Qualities. The 
 successful application of concrete-steel to building and engineer- 
 ing construction also requires that the steel or iron shall be 
 perfectly protected by the concrete and its use for fire-proof 
 buildings demands that the material shall be able to success- 
 
 * Although many articles have been published on concrete-steel con- 
 structions the most comprehensive single paper on the subject that the 
 author has seen is an article by Edwin Thacher, C.E., entitled, Concrete- 
 steel Bridge Construction, published in the Engineering News of Sept. 21 r 
 1899, 
 
820 FIRE-PROOF AND INCOMBUSTIBLE FLOORS. 
 
 fully withstand the action of fire and water. The fire-proofing 
 qualities of concrete are considered in Chapter XXIII.; we will 
 merely state here that several of the concrete constructions 
 have most satisfactorily stood the rigid test required by the 
 department of buildings of the City of New York. 
 
 Regarding the durability of the imbedded steel, much has 
 been said pro and con on this subject. The elaborate investi- 
 gations of Prof. Chas. L. Norton have positively demonstrated 
 that neat Portland cement, even in thin layers, forms a perfect 
 protection from rust. When imbedded in concrete, the latter 
 should be dense and without voids and cracks, and should be 
 mixed quite wet where applied to the metal. 
 
 The most satisfactory evidence of the durability of reinforced 
 cinder concrete is the fact that although it has been exten- 
 sively used in building construction for a period of ten years, 
 no case of the serious corrosion of the metal has yet been 
 reported, and it is reasonable to assume that if the steel does 
 not rust within the first twelve months it will not rust at all. 
 
 The Pabst Building in New York City was removed early 
 in the present year to make way for improvements in connec- 
 tion with the Rapid Transit Subway. 
 
 This building was erected in the early part of 1899, and 
 had cinder concrete arches in the floors. The condition of the 
 steel work and reinforcing material was found to be very satis- 
 factory, and the paint well preserved. (See Engineering Record 
 of January 31, 1903.) 
 
 Applications of Concrete-steel. The scientific 
 application of reinforced concrete to building and engineering 
 construction has progressed much further in Europe than in 
 this country, but during the past five years it has made won- 
 derful strides in the United States owing partly, no doubt, to 
 the reduced cost of Portland cement, but more to a better 
 understanding of the merits and possibilities of the material. 
 Although first confined to beams and floor slabs, entire build- 
 ings are now built of concrete scientifically reinforced by small 
 steel members, and these embrace factories of all kinds, office- 
 buildings, hotels, and apartment houses, churches, and public 
 buildings, grain and cement bins, and several tall smokestacks. 
 In engineering constructions it has been used for bridges, some 
 of great span, culverts, sewers, walls, dams, tanks, etc. In fact, 
 the field for reinforced concrete appears to be almost unlimited. 
 In this chapter, however, the author has confined himself to 
 
REINFORCED CONCRETE FLOORS. 821 
 
 its application in floor and beam construction, and more par- 
 ticularly to those constructions now in actual use in this country. 
 
 Special Advantages of Reinforced Concrete for Floor Con- 
 struction. Although many advantages are claimed for rein- 
 forced 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 
 advantages are less weight per square foot of floor (usually but 
 not always), adaptability to irregular framing and rapidity 
 of construction. 
 
 Except in the immediate locality of the tile factories, fire- 
 proof floors of concrete can usually be placed at less expense 
 than those of hollow tile, and when the spans will permit of 
 the use of cinder concrete, the concrete floors will be 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. Concrete floors can be easily adapted to triangular or 
 any irregular framing, while tile arches cannot, and for build- 
 ings having a triangular or irregular plan, this is a very import- 
 ant advantage. 
 
 The materials entering into the construction of reinforced 
 concrete floors are readily obtained in almost any locality, 
 no special prepared material is required, except perhaps in a 
 few special forms of reinforcement, and the work can be done 
 almost entirely by unskilled labor. All of these considerations 
 are of advantage in preventing delays, and in executing the 
 work rapidly. Less capital is required for concrete work than 
 for the tile constructions, 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 sufficiently proven 
 by the immense amount of reinforced concrete now under 
 construction throughout the world. 
 
 Wherever a floor is to have a finished cement surface, rein- 
 forced concrete constructions will be considerably cheaper 
 than any tile system, because in the former construction, the 
 entire concrete is used to give strength, while with the flat- 
 tile arches it merely increases the dead weight. 
 
 The above advantages apply in a greater or less degree to 
 all of the concrete systems, while some systems have special 
 and economical advantages over the others. These are more 
 
822 FIRE-PROOF AND INCOMBUSTIBLE FLOORS. 
 
 particularly set forth in connection with the descriptions of 
 the different systems 
 
 Classification of Concrete-steel Floor Construc- 
 tions. 
 
 These constructions, although differing to a wide degree, 
 may be classified under four heads, viz.: 
 a. Flat or slab floors; 
 6. Paneled or beam and slab floors; 
 
 c. Arched systems; 
 
 d. Sectional systems. 
 
 Figs. 32, 33, and 34 show common types of slab floors of 
 
 Floor 
 
 Fig. 32 
 
 Gas Pipe\ Diagonal Sheafhing^ 
 
 
 Plaster Cornice 
 
 
 Fig. 33 
 
 imshed -Flboi; /Cement Tipeff ancl "Wires ^ 
 
 /Diagonal Sheathing 
 
 ffceam/^ x Metal Lath" "^"PlasteV . Barb Wire'^ 
 
 ft Span5'0to70' >| 
 
 Fig. 34 
 
 short spans; examples of the other forms of construction are 
 illustrated in the following pages. 
 The type of flat construction shown by Fig. 32 with the 
 
COMPOSITION OF THE CONCRETE. 823 
 
 fabric laid over the beams and running the full length of the 
 building is probably the most commonly used, and next to 
 this the type shown by Fig. 33. The type shown by Fig. 32 
 usually has the beams protected as in Fig. 33. 
 
 Composition of the Concrete. 
 
 For most reinforced concrete floors, having a span between 
 the steel beams of seven feet 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, and also 
 better resists the action of extreme heat, owing to its greater 
 porosity (see p. 735). The usual proportions of cinder con- 
 crete are one of cement to two of sand and five or six of cinders. 
 Quite often, 2J to 3 parts of sand to 1 of cement and 6 of cinders 
 are used. 
 
 To make a first-class concrete the cinders must be screened 
 through at least a f-inch mesh, and only hard coal cinders 
 should be used. Good cinders may sometimes be obtained 
 from power-plants using soft coal, but it must be well screened 
 to free from the ash. Concrete mixed with common ashes, 
 as is sometimes done, has little strength and is totally unre- 
 liable. 
 
 Cinder concrete is much inferior in crushing strength to 
 broken stone or gravel concrete and the author is decidedly 
 of the opinion that it should not be used for spans exceeding 
 7 ft. For spans of 5 ft. cinder concrete has ample strength for 
 almost any load, and it can safely be used up to a span of 7 ft. 
 for loads up to 150 Ibs. per square foot. Under such conditions 
 the author considers it preferable to gravel or broken-stone 
 concrete for ordinary fire-proof construction. 
 
 For all spans exceeding 7 ft., and for posts and girders 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 or 
 five of stone or gravel. 
 
 The comparative merits of gravel and broken stone for con- 
 crete are set forth on p. 201. 
 
 Concrete for slabs, beams, and posts should preferably be 
 mixed by machinery, as concrete thus mixed is much stronger 
 than that mixed by hand. 
 
 The weight of cinder concrete will vary from 80 to 100 Ibs. 
 per square foot, depending Upon the coarseness of the mate- 
 rial, quantity of sand, and the amount of tamping. 
 
824 FIRE-PROOF AND INCOMBUSTIBLE FLOORS. 
 
 For 1, 2J, and 5i concrete, not tamped, the weight may 
 be taken at 82 Ibs., but for all tamped cinder concrete it is not 
 safe to figure on less than 95 Ibs. per cubic foot. Rock or 
 gravel concrete will weigh from 140 to 145 Ibs. per cubic foot, 
 depending upon the aggregates, and the degree of wetness or 
 tamping. 
 
 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 metal employed. 
 
 For the flat syst ms some form of netting or fabric is most 
 commonly used, while for beams, bars or cables of various 
 sections are employed. 
 
 In a few instances plain round or square bars or wires are 
 used, but nearly all American engineers deem it important 
 that the shape of the reinforcement be such that it will offer 
 resistance to slipping in the concrete, independent of the ad- 
 hesion of the mortar.* 
 
 The theory that in concrete-steel beams both materials share 
 uniformly in the deformations and that all permanent changes 
 of length must be common to both, will hold actually true 
 only when the sliding resistance of the imbedded steel reaches 
 the required amount. Should the resistance fall below it, 
 sliding of the concrete will take place both materials will act 
 independently, and the total resistance of the member will be 
 materially reduced. In this connection Prof. Brik, an eminent 
 German engineer, says: "The consideration of the effect of 
 frequently repeated loads becomes of special importance be- 
 cause of the probability that the sliding resistance along the 
 imbedded steel will decrease in time under repeated loads. 
 This result may be particularly expected if these loads are ac- 
 companied by shocks and vibrations. 
 
 " The decrease of the sliding resistances again means a de- 
 crease of the carrying capacity and together with the same of 
 the factor of safety." (Engineering Record, Aug. 23, 1902.) If 
 the bar is disturbed in construction, as may frequently happen, 
 
 *" Although the natural adhesion between concrete and steel appears 
 to be very great, the writer does not consider it wise to place entire re- 
 liance upon this in concrete-steel construction, but provides mechanical 
 connection sufficient to insure its safety in case the adhesion from any 
 cause amounts to little or nothing." Edwin Thacher, C.E. 
 
FORMS OF REINFORCEMENT. 
 
 825 
 
 the sliding resistance of plain bars or even twisted bars, may 
 be insufficient to hold the concrete up to the full elastic limit 
 of the material. 
 
 Reinforcement of Flat Construction. As has 
 been stated, the first form of reinforcement used for flat floor 
 panels was the threaded bar (Fig. 35), patented by Mr. Hyatt 
 
 Fig. 35 
 
 and first used by Mr. P. H. Jackson. Next came the Ransome 
 twisted bar, then expanded metal followed by various woven 
 fabrics, strands of wire, twisted, barb wire, and various shapes 
 of bars. As the commercial success depends very largely upon 
 the kind of reinforcement used, the author has thought best 
 to describe in detail the various forms which have been found 
 successful from the standpoints of strength and economy. 
 
 Some of these forms are patented, or are sold only to licensed 
 companies, while others may be bought by any one and used 
 as desired. This point is indicated in connection with the 
 description of the different forms. 
 
 Expanded Metal. This material is now so well known 
 as to require but little description. The process by which it 
 is made, and the kinds used for lathing are described in Chap- 
 ter XXIII. Two styles of expanded metal lath are made (by 
 
 Fig. 36 
 
 the original process), but for floor construction, the diamond 
 mesh shown by Fig. 36 is used exclusively. This style is cut 
 in meshes from f in, to 6 ins. in width, and from 2 ins, to 12 ins. 
 
FIRE-PROOF AND INCOMBUSTIBLE FLOORS. 
 
 in length (the mesh being designated by the width of the dia- 
 monds) and comes in sheets 8 ft. long, and varying from 3 to 
 6 ft. in width according to the mesh. 
 
 It is made from a soft, tough steel of fine texture, varying 
 in thickness from No. 27 gauge (.017") to No. 4 gauge (.23"). 
 The meshes most commonly used for flat panels between floor 
 beams are 2^-inch mesh, No. 16 gauge, and 3-inch mesh No. 10 
 gauge. "The 2J-inch mesh, No. 16 gauge, gives the best 
 satisfaction on account of the strands being wider and, there- 
 fore, more effective in. the concrete." It also costs one cent 
 per square foot less than the 3-inch, No. 10. 
 
 When used between I-beams without other reinforcement, 
 the panels are usually formed by one of the systems shown by 
 Figs. 32 to. 34. The spans usually vary from 5 to 6 ft., although 
 panels 7 ft. wide between beams have been constructed. 
 
 Strength. Numerous tests have shown that expanded metal 
 and concrete floors when properly proportioned to the loads 
 and span and made with a good quality of cinder concrete have 
 sufficient strength for all ordinary purposes. 
 
 Use Limited to Licensed Companies. While expanded metal 
 lath can be purchased by any one, the larger meshes suitable 
 for floor construction cannot be purchased ; conesquently, 
 fire-proof floors with expanded metal reinforcement are con- 
 structed only by the licensed companies, of which there are 
 eleven in the United States and one in Toronto, Canada. 
 There is no competition between these companies. 
 
 Commercial Success. Expanded metal has probably been 
 more extensively used in concrete floor construction than any 
 other fabric, and, as a rule, has proven very satisfactory. 
 
 Lock-woven Fabric.* 
 
 This fabric is woven from high carbon steel wires, crossing each 
 other at right angles, and locked at the intersection by means 
 of No. 9 wire twisted around the strands as shown in Fig. 37. 
 
 The standard fabric is 56 ins. wide and is put up in rolls of 
 330 to 500 lineal feet, or of any shorter lengths desired. 
 
 The longitudinal strands are No. 10 wire, B. &. S gauge, 
 4 ins. on centres, and the cross strands No. 9 wire, 6 ins. on 
 centres. The standard fabric weighs two-tenths pounds per 
 square foot. 
 
 * Manufactured and for sale by W. N. Wight & Co., New York. 
 
LOCK-WOVEN FABRIC. 
 
 827 
 
 This fabric can be woven of any gauge wire and with any 
 larger mesh, either square or oblong, that may be required. 
 It can also be made up to 88 ins. wide. 
 
 It is sold either bright or galvanized the galvanized costs 
 but 1J cents per square yard more than the bright and is much 
 to be preferred. 
 
 This fabric has the same advantage as the welded, and tie- 
 
 * 9 Cross 
 
 Width 
 
 
 Wires 
 
 LOCK-WOVEN STEEL FABRIC 
 
 Fig. 37 
 
 lock fabrics, in that it can extend from wall to wall, thus mak- 
 ing a continuous tie. 
 
 It is used to best advantage in a construction like Fig. 38, 
 but may be used in any way suitable to an open mesh fabric. 
 
 For spans exceeding 8 ft., the fabric may u<ed in two thick- 
 nesses, one directly over the other, and with the strands stag- 
 gered," this arrangement, however, being covered by a patent 
 controlled by the manufacturers. 
 
 Fig. 38 
 
 Fig. 39 shows a system recommended by the manufacturers 
 for apartment houses, hotels, etc., or for any building where 
 the loads are not excessive. The special advantage of this 
 
828 FIRE-PROOF AND INCOMBUSTIBLE FLOORS. 
 
 system is that it gives a level ceiling combined with strength 
 and comparatively light weight. 
 
 Fig. 39 
 
 Fig. 40 
 
 The manufacturers issue a folder showing various forms of 
 floor arches that may be constructed with their fabric. Most 
 of these devices have been patented but all are free to those 
 who buy the fabric. 
 
 Strength. Systems 1, 2, and 3 have been approved by the 
 Bureau of Buildings of the City of New York for the spans and 
 live loads indicated. 
 
 In Sept., 1902, six floor arches, reinforced with lock-woven 
 fabric were tested for strength by the Bureau of Buildings, 
 Borough of Manhattan.* An arch like Fig. 38, 4i ins. thick 
 and 6-foot span, was loaded to 1452 pounds per square foot, 
 and one of 8 ft. span, 5 ins. thick, to 1412 pounds per square 
 foot. The latter arch had two layers of fabric. 
 
 An arch like Fig. 39, with concrete 4J ins. thick, and 6-foot 
 span slowly failed under 1165 pounds per square foot. 
 
 An arch like Fig. 40, 6-foot span, was loaded to 3018 pounds 
 per square foot without breaking. 
 
 * Complete details of these tests are published in Insurance Engineering 
 for Oct., 1902. 
 
METALLIC SHEETING. 
 
 829 
 
 Commercial Success. The manufacturers state that over 
 1,500,000 sq. ft. of lock- woven fabric were sold for concrete 
 floor construction in 1902, and that orders have thus far 
 (March 1) been received for 500,000 sq. ft. to be used this 
 year. Has been largely used for hotels and for manufacturing 
 plants. 
 
 The International Fence and Fire-proofing Co's.* 
 Metallic Sheeting. 
 
 arjrying- Wis 
 Fig. 41 
 
 The above company manufactures a tie-locked fabric which 
 has been extensively used in concrete 
 floors, and which may be purchased 
 by any responsible contractor. 
 
 An illustration of the fabric is shown 
 by Fig. 41, the detail at "A" show- 
 ing the lock. 
 
 It is made in sheets 200 ft. long and 
 4, 5, and 6 ft. wide, and put up in rolls 
 for shipment. Six styles of sheeting are carried in stock, viz.* 
 A-l. No. 9, carrying wire; No. 11, cross wire, 6"X'6' mesh. 
 
 A-2. No. 9, carrying wire; No 11, cross wire, 5"X6" mesh. 
 
 A-3. No. 9, carrying wire; No. 11, cross wire, 4"X6" mesh. 
 
 R-l. No 7, carrying wire; No. 9, cross wire, 6"X6" mesh. 
 
 B-2. No. 7, carrying wire; No. 9, cross wire, 5"X6" mesh. 
 
 B-3. No. 7, carrying wire; No. 9, cross wire, 4"X6" mesh. 
 
 v Carrying Wire 
 
 {Transverse "Wlre // 
 
 A, Detail of Lock. 
 
 * Of Columbus, Ohio. 
 
830 FIRE-PROOF AND INCOMBUSTIBLE FLOORS. 
 
 The cross wires are spaced 6 ins. on centres in all styles, the 
 variation in the mesh being in the spacing of the carrying 
 wires. All wires are well galvanized. The A-l sheeting is 
 most generally used. The weight of A-l 
 sheeting per 100 sq. ft. is 33 Ibs. and of 
 B-3 sheeting 48 Ibs. 
 
 Application. For spans between 
 beams not exceeding 6 ft., the sheeting 
 can be used for floor slabs without rein- 
 forcement. For spans exceeding 6 ft. the 
 manufacturers recommend that the sheet- 
 ing be laid over cables, as in Figs. 42 
 and 43, composed of seven strands of 
 No. 9 galvanized wire which they manu- 
 facture for this purpose. These cables 
 are placed from 12 tc 20 ins. apart, and 
 are made in lengths sufficiently long to 
 w run the full length of the building links 
 * are also furnished for splicing the 
 * cables. 
 
 Where the sheets meet at the sides they 
 are secured by wiring the looped ends 
 together, by simply passing a light wire 
 through the loops and giving it two or 
 three twists. The manufacturers claim 
 that the A sheeting, with No. 9 seven- 
 strand cables placed 12 ins. apart, will 
 carry successfully 300 Ibs. per square foot 
 on a 20-foot span, with concrete 6 ins. 
 thick, or it will carry the same load on 
 a 16-foot span with cables 16 ins. apart, 
 or on a 12-foot span with cables 20 ins. 
 apart. 
 
 ^ The sheeting is also made with J-, T V, 
 
 and f -inch longitudinal wires for the reinforcement of 
 concrete arches. When used in this way the segments are 
 formed to fit the span, and crated in sheets from 3 to 4 ft. 
 wide. 
 
 Commercial Success. This material has been used in a 
 number of large buildings in different portions of the United 
 States and Canada. The author is informed that more than 
 1,500,000 sq. ft. of floors were constructed with this fabric 
 
WELDED METAL FABRIC. 
 
 831 
 
 in 1902, and that over 800,000 sq. ft. of the sheeting was shipped 
 for buildings then under construc- 
 tion during the first two months of 
 1903. 
 
 /Wood Sleepers ^Wood Floor 
 
 The manufacturers publish a cata- Wire/ 
 
 Netting 
 
 Cables 
 12 "to 20" 
 C. to C. 
 
 Fig. 43 
 
 logue showing various ways in which 
 
 it may be used, and also furnish 
 
 tables giving the safe strength for 
 
 different spans with different spacings 
 
 of the cables. Fig. 43 shows a device 
 
 for holding the concrete below the I-beam by means of a clip, 
 
 which is somewhat of a novelty. 
 
 Welded Metal Fabric. 
 
 a a 1 a ft i 
 
 Fig. 44 
 
 The Clinton Wire Cloth Company manufacture a welded 
 fabric or mesh which has been extensively used in the United 
 States as a reinforcement for concrete construction of all kinds. 
 
 Fig. 44 shows the general style of the fabric, although the 
 meshes and wires can be varied to an almost endless extent, 
 the only limit being as to mesh, 1 in. being about the closest 
 that can be made. 
 
 From a theoretical standpoint, at least, this fabric would 
 appear to offer the ideal reinforcement for slab construction, 
 as the carrying wires may be varied, both in size and spacing, 
 to give the necessary area for any given weight and span, 
 and the distributing or cross wires may also be varied in the 
 same way The direction of the wires coincides with the line 
 
832 FIRE-PROOF AND INCOMBUSTIBLE FLOORS. 
 
 of stress, so that there is no tendency to distort the rectangle 
 of the mesh. 
 
 The cross wires, being welded to the carrying wires, .re rigidly 
 held in place and prevent the latter from slipping in the con- 
 crete. 
 
 In the meshes most commonly used the carrying wires vary 
 from No. 10 to No. 4,* and from 1 to 4 ins. on centres, while 
 the distributing wires vary from No. 11 to No. 6, and from 
 3 to 12 ins. on centres. 
 
 Welded metal is manufactured in long rolls, and by its use, 
 all joints and laps are avoided, and a floor can be made with 
 a continuous metallic bond from wall to wall (i.e., when the 
 mesh is laid over the top of the steel beams). 
 
 The standard width of rolls is 60 ins., but may be obtained 
 wider if desired. 
 
 This material can be used in all the ways in which other 
 meshes are used, and the author understands can be purchased 
 by any responsible party. Mr. E. Lee Heidenreich states that 
 he has obtained remarkable results with this material as to 
 strength and lightness. 
 
 Commercial Success. The manufacturers state that between 
 four and five million feet of this material has been used in 
 the construction of fire-proof floors, partitions, slabs, arch 
 forms, etc. 
 
 Truss Metal Lath.f 
 
 (Kuhne Patents,) 
 
 Fig 45. 
 
 This is an expanded-metal form intended for the reinforce* 
 ment of concrete floors and for thin partitions. The general 
 
 * Washburn & Moen gauge. 
 
 t Manufactured by the Truss Metal Lath Co., New York. 
 
BARB WIRE. 833 
 
 appearance of the lath is well shown by Fig. 45. The thickness 
 of the sheets or depth of the truss is about 1 inch. 
 
 It is at present manufactured in the form of sheets up to 
 30 ins. wide and to 9 ft, 4 ins. long. It is at present made 
 from soft steel, black and galvanized, of !k>. 24, 26, and 28 
 gauges. 
 
 It is much heavier and stiff er than anv other expanded-meta] 
 form, the No. 28 gauge weighing 0.67 Ibs. per square foot, with 
 a cross-section of 0.18 square inch per foot in width, the No. 26 
 gauge 0.8 Ibs. per square foot, with a cross-section of 0.216 
 square inch per foot in width, and the No. 24 gauge, 1.06 Ibs. 
 per square foot, with a cross-section of 0.3 square inch per foot 
 in width. 
 
 This lath is said to take mortar better than any other form. 
 It can be used as a centering for concrete arches, without wood 
 centres, and it would seem as though it might be advanta- 
 geously used for the reinforcement of concrete slabs, solid 
 partitions, sewers, tanks, etc. The price at present charged 
 for it per square foot, F. O. B. mill, is 3.60 cents for No. 28 
 gauge; 4 cents for No. 26 gauge, and 4.50 cents for No. 24 
 gauge; for galvanized sheets 1 cent extra per square foot. 
 
 Barb Wire. 
 
 The Hinchman-Renton Fireproofing Company of Denver use 
 barb wire as a reinforcement for floor slabs with spans of from 
 5 to 6| ft., and have secured letters patent for the use of barb 
 wire as a reinforcement of concrete. The wires are laid on 
 top of the centering, in both directions of the panels. Those 
 extending from beam to beam are placed from 1 in. to 2 ins. 
 apart, according to the load and span, and the longitudinal 
 wires from 3 to 6 ins, apart, and over the carrying wires. A 
 slab of cinder concrete, 4J ins. thick, 40 ins. wide, made in a 
 box and set on top of two I-beams. 6 ft. apart between flanges, 
 carried a distributed load of 13,000 Ibs. or 65C Ibs. per square 
 foot with a deflection of f in. The loading was stopped at 
 this point because the pig iron could not be safely piled higher. 
 Floors built by this company have been severely tested in 
 buildings by moving heavy machinery over them before the 
 finished floor was down. 
 
 This material is probably the cheapest form of reinforcement, 
 giving the same strength that can be used, and it possesses the 
 advantage that it is a stock article, readily obtainable in any 
 
834 FIRE-PROOF AND INCOMBUSTIBLE FLOORS. 
 
 quantity. This company has built many thousand square feet 
 of floors similar to Figs. 32 and 33 in Colorado and Utah. 
 
 liansomc Twisted Bars. 
 
 The Ransome twisted bars have also been extensively used 
 for floor slabs, not only by the Ransome people, but also by 
 many other contractors. 
 
 These bars are made from square bars of high-grade steel, 
 twisted cold. It has been found that twisting the bars increases 
 the tensile strength about 20 per cent. 
 
 For flat construction the carrying bars vary in size from 
 J in. to f in., according to the span and load. The spacing 
 of the bars is also varied according to the size, span, and load. 
 
 Tension. Bars 
 
 Auxiliary "B 
 
 Fig. 46 
 
 Thus for a slab of 16 ft. span intended to carry a superimposed 
 load of 125 Ibs. per square foot, the bars would be i in. square, 
 spaced 5 ins. C to C, and the thickness of the concrete 9| ins. 
 Two sets of bars are used, the carrying bars, or those which 
 run crossways of the span, are placed about \ in. from the 
 bottom of the slab, as in Fig. 46, and the second set, called 
 auxiliary bars, are placed on top of, and at right angles to them. 
 The auxiliary bars are spaced from 24 ins. to 36 ins. apart. 
 
 Necessity for Longitudinal Bars. Where wire 
 strands or bars are used for reinforcement it is essential that 
 there be longitudinal as well as transverse bars, for the reason 
 that under heavy concentrated loads, or when a heavy body 
 falls upon the slab the concrete will crack between the carrying 
 bars. The author has seen this very clearly demonstrated in 
 testing a floor slab without longitudinal wires under a drop test. 
 When the load is uniformly distributed the longitudinal wires 
 are not brought into play, but floor loads are more often con- 
 centrated than uniformly distributed. 
 
DE MAN TWISTED TENSION BAR. 835 
 
 The use of a twisted bar as a reinforcement for concrete 
 was patented by Mr. Ransome in 1884, and until the past year 
 twisted bars could not be used except by the parent or licensed 
 companies. As the patent has expired any one can now use 
 twisted bars. Owing to the fact that the Ransome Concrete 
 Machinery Co. have special machinery for twisting and have 
 the bars twisted in large quantities at the rolling mill, they can 
 furnish a better bar, and generally at less expense than it will 
 cost the contractor to buy the plain bar and do the twisting 
 himself. The price of the Ransome bars is from 2J to 3 cts. 
 a pound, F.O.B. New York. 
 
 Flat floors have been constructed with twisted tension bars 
 with spans up to 25 ft., using rock or gravel concrete, but the 
 beam or paneled system hereinafter described is more com- 
 monly used for spans exceeding 14 ft. 
 
 A section of a flat floor in the California Academy of Science 
 22 ft. span, and 15 ft. long, was tested in 1890 with a uniform 
 load of 415 Ibs. per square foot, and the load left in place for 
 one month. The deflection at the centre of the 22-ft. span 
 was only J in. 
 
 De Man Twisted Tension Bar. 
 
 Fig. 47 
 De Man Tension Bar. 
 
 Mr. Alphonse De Man, formerly of Detroit, Mich., but now 
 president of the American Fireproofmg and Cement Construction 
 Company of New York City has secured a patent on a rectangular 
 tension bar, twisted as shown in Fig. 47. It is designed to be 
 used in sizes of from T *g in. to J in. in thickness, and J in. to 1J 
 ins. in width. In practice, however, a f'Xi" bar has thus far 
 been used almost exclusively, the bars being spaced according 
 to the tensile strength required. 
 
 The twists in the f-inch bars occur every 3 ins. The bars 
 used up to this time have been twisted cold, but could be 
 twisted hot by an extra set of rollers if required in large quan- 
 tities. 
 
 These bars imbedded in cinder concrete have been used for 
 flat construction with spans up to S ft., and without cross ties,, 
 The author believes, however, that small transverse bars or 
 wires would strengthen the floor as noted on p. 834. 
 
836 FIRE-PROOF AND INCOMBUSTIBLE FLOORS. 
 
 A slab of cinder concrete, S'Xf/XS", with tension members 
 6" C to C, laid on steel rails 5 ft. 6 ins. apart, carried a load 
 of 14,000 Ibs. of pig iron with a deflection of f inch, the slab re- 
 turning to its original position on removal of the load. 
 
 The following table has been prepared by Prof. W. H. Burr 
 of the Engineering Department of Columbia College to show 
 the thickness of slab and number of bars required for different 
 spans and loads. It is useful for reference in connection with 
 other forms of tension bars: 
 
 TABLE OF LOADS AND SPANS FOR SOLID CONCRETE 
 FLOOR SLAB. 
 
 (REINFORCED WITH THE DE MAN TENSION BAR.) 
 
 
 Total Loads Carried in Pounds per Square Foot.* 
 
 Span 
 in 
 
 100 
 
 m 
 
 150 
 
 200 
 
 250 
 
 500 
 
 Feet. 
 
 
 
 
 
 
 
 3 
 
 2 
 
 2 
 
 2 
 
 2 
 
 3 
 
 3 
 
 
 1 
 
 1 
 
 1 
 
 3 
 
 1 
 
 3 
 
 4 
 
 2 
 
 3 
 
 3 ' 
 
 3 
 
 3 
 
 4 
 
 
 2 
 
 1 
 
 1 
 
 2 
 
 2 
 
 2 
 
 5 
 
 3 
 
 3 
 
 3 ' 
 
 3 
 
 4 
 
 5 
 
 
 1 
 
 1 
 
 2 
 
 4 
 
 2 
 
 3 
 
 6 
 
 3 
 
 3 
 
 3 
 
 4 
 
 4 
 
 6 
 
 
 2 
 
 3 
 
 5 
 
 2 
 
 3 
 
 3 
 
 7 
 
 3 
 
 4 
 
 4 
 
 4 
 
 5 
 
 
 
 3- 
 
 2 
 
 2 
 
 5 
 
 3 
 
 
 8 
 
 4 
 
 4 
 
 4 
 
 5 
 
 5 6 
 
 
 
 2 
 
 3 
 
 4 
 
 3 
 
 5 3 
 
 
 9 
 
 4 
 
 4 
 
 5 
 
 5 6 
 
 6 
 
 
 
 3 
 
 5 
 
 3 
 
 5 3 
 
 4 
 
 
 10 
 
 4 
 
 5 
 
 5 6 
 
 ' 6 
 
 6 
 
 
 
 5 
 
 3 
 
 4 3 
 
 4 
 
 6 
 
 
 * Including weight of floor. 
 
 NOTE. In these spaces the upper figure gives the total depth of concrete 
 in inches; the lower figure the number of steel bars in 12 
 inches of width. 
 
ROEBLING FLAT CONSTRUCTION 837 
 
 The De Man flat construction has been successfully used in 
 quite a number of buildings. The twisted bar can be used 
 only by licensed companies. 
 
 The Columbian Ribbed Bar. The Columbian Fire- 
 proofing Co. uses a special ribbed bar for flat floor construction 
 which is described in connection with their systems of con- 
 struction, pages 839-842. 
 
 PATENTED SYSTEMS OP FLAT FLOOR 
 CONSTRUCTION. 
 
 The following systems of floor construction, while based 
 upon the same general principles as those already described, 
 are patented and can be used only by the patentees: 
 
 Roebling Flat Construction. 
 
 This system was introduced by the Roebling Construction 
 Company to meet the demand for a light economical floor, with 
 greater spans between the I-beams than is practicable for their 
 arched system. 
 
 This flat construction is a reinforced concrete system, differ- 
 ing from other flat systems only in the reinforcing frame. The 
 details of construction are quite clearly shown in Fig. 48., The 
 main tension members consist of flat bars, usually 2 ins. in 
 width and varying from "J to J in. in thickness according to 
 the spacing of the beams and the load to be supported. These 
 bars stand on edge in the concrete, and are twisted at the ends 
 to lie flat on the I-beams, and are also bent around the flange. 
 The bars are held in position laterally by means of spacers, 
 formed from half-oval iron, with a hook at each end to fit over 
 the bars. 
 
 It was the original intention of the patentees to apply the 
 Roebling stiffened wire lath to the underside of the tension 
 bars by means of lacing wire, to serve as a centering for 
 the concrete, and under certain conditions the wire centering 
 is still used. When the building is to be erected in a large 
 city, it has been found more advantageous to use wood center- 
 ing for the reason that the concrete is not as easily damaged 
 by workmen walking over it before it has thoroughly set, as 
 when wire centering is used. 
 
 The latter, however, has important advantages when the 
 work is to be erected in cold weather, as it permits the moisture 
 
838 FIRE-PROOF AND INCOMBUSTIBLE FLOORS. 
 
 to drip away rapidly and prevents the concrete from being 
 injured by freezing. In isolated places where the lumber for 
 centering would have to be purchased new and then disposed 
 of at a sacrifice, the wire centering is also the more economical. 
 Besides the type of construction shown by Fig. 48 three 
 
 . -' : 
 
 X 2\ As Plat Bar, Imbedded 
 
 in Concrete 
 
 fx%l Steel Rod Spacer \*?* 
 
 ^-Kb. IS Gal. Lacing Wire 
 
 34 
 
 ,% Steel Rod Spacer 
 
 Fig. 48 
 
 Roebling Flat Construction. 
 
 other types, differing principally in the manner of supporting 
 the steel bars, are employed. 
 
 In Type 4 the tension bars are supported on the bottom 
 flange of the I-beams, so as to give a level ceiling between the 
 beams. This type, however, is not desirable when the I-beams 
 are more than 7 ins. deep. 
 
 When the distance between the steel beams is greater than 
 9 or 10 ft., the tension bars are bent downward so as to give a 
 sag of about 2 ins. or more at the centre of the span, as in Fig. 49, 
 the spacers being used as in Fig. 48. Type 5 has been success- 
 fully used in spans up to 22 ft. Under ordinary conditions, 
 however, considering both the steel work and the fireproofing, 
 the most economical results will be obtained when the girder, 
 
THE COLUMBIAN SYSTEM. 
 
 839 
 
 are spaced from 14 to 16 ft. apart. With this system a sus- 
 pended ceiling is not necessary or desirable. 
 
 Fig. 49 
 
 Long-span System. [Type 5.] 
 
 The concrete used with this system is composed of high-grade 
 Portland cement, sharp sand, and clean cinders, mixed ordi- 
 narily in the proportion of 1, 2J, and 6. 
 
 Adaptation. This floor system is particularly adapted to 
 public buildings, offices, theatres, schools, hospitals, hotels, 
 residences, etc., or w'lere there is no great weight to be sup- 
 ported, and the fire hazard is not as great as in stores, factories, 
 etc. 
 
 The system can be successfully adapted, however, to stores 
 and warehouses, but will require shorter spans and heavier 
 construction. 
 
 Tie Rods. This construction requires no tie-rods. 
 
 Weight. The weight of course is principally in the concrete, 
 which will weigh about 82 Ibs. per cubic foot when deposited 
 on wire centering, and about 96 Ibs. or 8 Ibs. per inch of thick- 
 ness when placed on wood centres, and tamped. 
 
 Strength. The Roebling Construction Company claims that 
 Type 1 has a safe carrying capacity with factor of safety of 4, 
 of 200 Ibs. per square foot with a span of 8 ft., and that Type 5, 
 with a span of 16 ft., will safely support a load of 100 Ibs. per 
 square foot. 
 
 A section of floor 4 ft. 5 ins. wide and 16 ft. span, carried 
 a total load of 17,250 Ibs. with a deflection of only T \ inch. 
 
 The Columbian System.* 
 
 This is a flat concrete system, with ribbed steel bar tension 
 members differing from the system previously described, 
 
 * Controlled 
 burgh, Pa. 
 
 by the Columbian Fireproofing Co., head office, Pitts- 
 
840 FIRE-PROOF AND INCOMBUSTIBLE FLOORS. 
 
 principally in the shape of the reinforcing bars, which are 
 entirely different in shape from those used in any other system, 
 and very much deeper. The general shape of the 1, 2, 2^, and 
 3J inch bars is shown by the hole in the stirrup, 
 Fig. 50; the larger sizes have more ribs as shown 
 by the reduced section at A . 
 
 The Columbian floors are made in two styles, 
 "long span" and " short span." 
 
 The short span consists of the 
 use of ribbed steel bars sus- 
 pended from the steel beams, 
 and supported on edge by 
 means of steel stirrups which 
 have the profile of the bar cut 
 
 A, Section of Fig. 50 n them, as shown by Fig. 50, 
 
 5-inch bar Stirrups for Bars. . , , . 
 
 (reduced). these bars being surrounded 
 
 by and completely imbedded in concrete. This type of paneled 
 construction is plainly shown by the sectional drawing Fig. 51. 
 
 Cinder filling 
 
 Z t 
 
 Fig. 51 
 
 If a level ceiling beneath the beam is required, it is con- 
 structed independently of the floor by means of solid con- 
 crete ceiling on lower flange of beams, wire lath, expanded 
 metal, or any other form of metallic iath upon which the plas- 
 tering is applied. 
 
 In this way all portions of the steel are completely imbedded 
 in solid concrete. The bottom flange of the beam, which is 
 the most vulnerable point, being protected by a concrete slab, 
 Fig. 52, with insulating air space. Three sizes of bars are 
 used for this floor construction, viz., 2J, 2, and 1 ins., the 
 
THE COLUMBIAN SYSTEM. 
 
 841 
 
 maximum spacing of the bars being 24 ins. The carrying 
 capacity of this floor is given by the table on following page. 
 The most economical spacing of floor beams for this type will 
 usually be 6 ft. for hotels, apartment-houses, and office-buildings, 
 using 1-inch bars, and from 6 to 9 ft. for greater floor loads, 
 using 2- and 2J-mch bars, depending upon the load required to 
 be carried. 
 
 Fig. 52 
 
 Showing protection of bottom flange. 
 
 This floor may be finished on top in the usual way by im- 
 bedding nailing strips in cinder filling, or the floor strips may 
 be nailed directly to the concrete floor, and the filling omitted. 
 The economy of this type of construction is that wall channels 
 and tie-rods are not required, and beams may be spaced up 
 to 9 ft. centre to centre. 
 
 Long-span Construction. In the second type of this con- 
 struction, or what is commonly known as " long span," the 
 rolled and ribbed steel bars are imbedded in the concrete, as 
 in the short span, and either hung in specially formed stirrups 
 or framed directly to the beam, as shown by Fig. 53, these 
 bars being anchored at intervals into the wall, and forming 
 a continuous tie across the entire floor of the building, thus 
 making of the entire floor a monolith of reinforced concrete. 
 This permits of the elimination of the floor beams between 
 girders, the monolithic slab of concrete and steel taking their 
 place. In this way a level ceiling is obtained between girders, 
 so that increased head room can be obtained with the same 
 amount of masonry, or the same head room with decreased 
 height of masonry. This is possible because of the fact that 
 the extreme thickness of this floor construction on a span of 
 20 ft. between beams, is but 6J ins., whereas for a span of 
 
842 FIRE-PROOF AND INCOMBUSTIBLE FLOORS. 
 
 15 ft., with lighter load, the thickness of concrete may be 
 reduced to 5 ins. The sizes of bars used in this type of con- 
 struction are 31, 4}, 5, and 6 ins., giving respectively 5; 5f, 
 6J, and 7J ins. of concrete. 
 
 Concrete. For the " long-span" type of construction the 
 Columbian Company recommends the use of either stone or 
 slag concrete in the proportion of 1, 2, 5. 
 
 Either cinder, slag, or stone concrete may be used with the 
 short span, the usual proportions being one part Portland cement 
 to two parts of sand and five parts of slag, stone, or cinders. 
 
 Carrying Capacity. The following table gives the loads that 
 the Columbian Company guarantees their various forms of 
 floors will carry safely. They call attention to the line of 
 deflection of their 1, 2, and 2J ins. bars, below which the loads 
 given for the respective spans should only be used for ceilings 
 or pitched roofs. 
 
 SAFE LOADS FOR COLUMBIAN FLOORS. 
 
 (In addition to the weight of floor construction.) 
 This table is compiled from actual tests on sections of floor, 
 using a safety factor of 4. Bars can be spaced down to 18 iris., 
 thereby increasing the strength of floor, but 2 ft. is the maxi- 
 mum spacing. 
 
 Distance 
 between 
 
 Floor Loads in Pounds, 
 Uniformly Distributed. 
 Bars 24" on Centres. 
 
 Distance 
 between 
 
 Floor Loads in 
 Pounds, Uniformly 
 Distributed. 
 Bars 24" on Centres. 
 
 
 
 
 
 uppor 
 
 6" 
 
 5" 
 
 4i" 
 
 3*" 
 
 ' 
 
 2" 
 
 1" 
 
 1" 
 
 
 Bar. 
 
 Bar. 
 
 Bar. 
 
 Bar. 
 
 
 Bar. 
 
 Bar. 
 
 Bar. 
 
 Feet. 
 
 
 
 
 
 Feet. 
 
 
 
 
 12 
 
 412 
 
 362 
 
 312 
 
 275 
 
 5 
 
 400 
 
 340 
 
 290 
 
 13 
 
 346 
 
 306 
 
 265 
 
 235 
 
 6 
 
 275 
 
 242 
 
 200 
 
 14 
 
 296 
 
 260 
 
 230 
 
 200 
 
 7 
 
 200 
 
 178 
 
 140 
 
 15 
 
 256 
 
 226 
 
 200 
 
 175 
 
 8 
 
 150 
 
 135 
 
 puT 
 
 16 
 
 225 
 
 200 
 
 175 
 
 
 9 
 
 125 
 
 100 
 
 70 
 
 17 
 
 200 
 
 175 
 
 125 
 
 
 10 
 
 100 
 
 70 
 
 
 18 
 
 177 
 
 150 
 
 
 
 11 
 
 ~80~ 
 
 
 
 19 
 
 140 
 
 100 
 
 
 
 
 
 
 
 20 
 
 100 
 
 80 
 
 
 
 
 
 
 
 Concrete 
 thickness 
 
 7i" 
 
 6J" 
 
 5f" 
 
 5" 
 
 
 4" 
 
 31" 
 
 3" 
 
THE COLUMBIAN SYSTEM. 
 
 843 
 
 This construction is especially strong in resisting drop or 
 jarring loads. A ram weighing 238 Ibs. was dropped from a 
 
 Fig. 53 
 
 Long-span System. 
 
 height of 8 ft. on the centre of a span several times and without 
 perceptible effect on the floor. In case of overloading the 
 floor will not fail suddenly, but the construction will gradually 
 bend, thus giving warning of danger. It also offers a great 
 resistance to concentrated loads, which occur at times in build- 
 ings, to an extent beyond what the floor is designed to carry. 
 
 After a fire- and water-test of three hours' duration made on 
 this system in Boston, published in the Engineering News of 
 Nov. 21, 1901, this floor on a span of 11 ft. 3 ins. carried 
 1650 Ibs. with deflection of only If inch. Before the floor slab 
 began to show any sign of failure, loading had to be stopped 
 on account of the fact that the walls of the test hut which car- 
 ried the floor began to crack. 
 
 The strength of the Columbian construction is derived from 
 combining steel and concrete in such a way that the ultimate 
 strength of the steel in tension and the concrete in compression 
 is fully developed. 
 
 In all concrete and steel construction where the steel re- 
 inforcement is placed entirely below the neutral axis of the 
 concrete slab, under overloads, the tendency is for the con- 
 crete to fail before the steel reinforcement. This weakness 
 is overcome in the Columbian system by using their ribbed 
 and roughened bars, which extend into the compression mem- 
 
844 FIREPROOF AM3 INCOMBUSTIBLE FLOORS. 
 
 her of the concrete-steel slab, thus reinforcing it against the 
 tendency to shear near the point of support or to fail suddenly 
 because of the ultimate limit of resistance to compression 
 being reached in the concrete before the ultimate limit of elas- 
 ticity is reached in the steel or before the steel is strained to 
 its ultimate limit in tension. 
 
 Economy. The Columbian system has one advantage over 
 most if not all of the other concrete systems in that no channels 
 are required against the wall, as the ribbed bars can be let into 
 the masonry like a small beam. 
 
 No tie-rods are required with this system. . 
 
 Holes may be cut in the floor for plumbing, wiring, etc., 
 at any point between the bars, and larger openings may be 
 framed out when the floor is being constructed. 
 
 Commercial Success. Both the short- and long-span types of 
 this system have been very extensively used in a great variety 
 of buildings, distributed throughout the territory east of the 
 Missouri River. The company is doing a large business through- 
 out the United States. 
 
 The Metropolitan Floor. 
 
 This floor, which was first introduced as the " Manhattan" 
 system, and is protected by letters patent, has now been in use 
 in this country for many years and is one of the leading fire- 
 proofing systems in vogue in the Eastern States, but until the 
 I^eaent year no attempt has been made to introduce it in the 
 Western States 
 
 This system is Mended for use between floor beams, placed 
 from 6 to 7 ft. apart, and is built in three standard forms, 
 Figs. 54 and 55, and a form similar to Fig. 54 but without 
 the blocks encasing the lower flange of the I-beams. 
 
 The construction of Form A is as follows: 
 
 Metal clips are first fastened to the bottom flanges on the 
 floor beams, which support l"X T y flat iron bars placed about 
 12 ins, on centres, running transversely with the floor beams, 
 the tops of the flats being about 1 in. below the bottom flanges. 
 
 Blocks \\ ins. thick of the Metropolitan composition, .com- 
 posed principally of plaster of Paris and wood chips are then 
 fastened securely to the bottom flanges, ana against the webs 
 of the floor beams covering the exposed portions. 
 
THE MEraOPOLTTAX FLOOR 
 
 To take the pfaater, 
 with firtfiirH""". TT wired to the 
 
 off the li 
 
 Rf.54 
 
 ^ _m A- 
 
 Efifcrl 
 
 I 
 
 RS.SS 
 
 To form the floor slab, cables, each composed of two No, 12 
 galvanized wire*, twisted are earned over the teas cf the flow- 
 beams as in Fig. 56 and aecwied to watts by anchors or bus. 
 
 or where they end on a beam they are secured to it by 
 hooks. These ctbtes are kid parallel and 
 
846 FIRE-PROOF AND INCOMBUSTIBLE FLOORS. 
 
 iron bars midway between the beams and about 2J ins. below 
 the top of the beam so as to cause the cables to deflect uni- 
 formly. The cables are laid at distances apart from each 
 other varying from 1 to 3 ins. according to spans. Forms 
 or centres are then put in place between the floor beams 1 in. 
 below the round iron bars, and the Metropolitan composition 
 poured in place and brought to a level about } in. above the 
 tops of the flanges of the floor beams, forming a floor-plate 
 about 4 ins. thick, ready for the laying of wood sleepers or 
 concrete. 
 
 The exposed portions of the girders carrying the floor beams 
 are covered with blocks of the same composition 1J ins. in 
 thickness, securely fastened in place. 
 
 Form B is constructed in the same manner as described above, 
 except that the ceiling construction is omitted and the composi- 
 tion covering of the web and bottom flanges of the I-beams 
 is cast in place by pouring into forms or moulds placed around 
 the beams. 
 
 Thickness and Span. The distance between centres of I-beams 
 for this system should be kept as near 6 ft. as practicable, and 
 should not exceed 8 ft. The thickness of the floor slab is 
 usually 4 ins., the bottom of the slab being 3J ins. below top of 
 I-beams. 
 
 Weight. Owing to the wood shavings mixed with the 
 plaster of Paris this is the lightest fire-proof floor system yet 
 introduced the weight of the composition being about 48 Ibs. 
 per cubic foot, or 16 Ibs. per square foot of 4-inch slab. 
 Exclusive of steel beams, wood flooring, and sleepers, and the 
 cinder filling between sleepers, Form A with 10-inch beams 
 and plaster ceiling will weigh not over 25 Ibs. per square foot. 
 
 Form B with 10-inch beams will weigh about 20 Ibs. per 
 square foot, including a thin coat of plaster on under side of 
 slab, and around the beams. 
 
 To these weights should be added weight of steel beams, 
 and whatever goes on top of the slab. 
 
 Strength. Some of the actual loads which have produced 
 failure when tested to destruction are as follows: 
 
 Span of 8 ft., ultimate load 861 Ibs. per square foot. 
 
 Span of 7 ft., ultimate load 1101 Ibs. per square foot. 
 
 Span of 6 ft., ultimate load 1350 Ibs. per square foot. 
 
 Span of 5 ft. 6 ins., ultimate load 1300 Ibs. per square foot. 
 
 Span of 5 ft. 5 ins., ultimate load 1920 Ibs. per square foot. 
 
BRUNER TRUSSED FLOOR. 847 
 
 With a span of 6 ft., 4-inch slab, and cables 1 in. apart, the 
 owners guarantee an ultimate load of 1800 Ibs. per square foot. 
 
 When tested to destruction, this floor most generally fails, 
 either by deflection and lifting of adjoining arches or by the 
 wires breaking where they bear on the beams. 
 
 Fire Resistance.-^- 11 When exposed to flame for a long time 
 the Metropolitan composition is attacked to a depth of from 
 three-sixteenths of an inch to an inch and a quarter, the 
 remainder being unaffected, and when water is thrown upon 
 it, the mass does not crack and fly. When made thoroughly 
 wet, the composition is not destroyed." 
 
 As a protection to the steel, the composition appears to be 
 superior to hard tile, and equal to porous tile. Has been 
 approved by the department of buildings, and used in more 
 than 120 large buildings, besides numerous residences. Has 
 been used in fifteen office-buildings, exceeding 100 ft. in 
 height. 
 
 Tie-rods. No tie-rods are required. 
 
 Special Advantages. The special advantages are saving in 
 weight and quickness with which the composition solidifies. 
 The slabs may be used for working purposes, thirty minutes 
 after the composition has been poured in place and the centers 
 can be removed at the end of four hours. No skilled labor 
 is required, save a competent foreman. It is also one of 
 the cleanest systems in use. 
 
 Criticism. The only criticisms that the author has seen of 
 this construction are possible discoloration of ceiling due to sap 
 in shavings, where the lumber from which the shavings are 
 made is not thoroughly kiln-dried, and to the dripping of water 
 through to the floors below. 
 
 Bruner Trussed Floor. 
 
 The P. M. Bruner Granitoid Company of St. Louis build 
 a flat floor up to 14 ft. span, in which they use trusses such as 
 is shown in Fig. 57 for the reinforcement. 
 
 These trusses consist of two square bars, A and B, held 
 apart at the centre by a small cast-iron strut and fastened 
 together at the ends by means of cast-iron heads. These 
 heads have openings into which the ends of the bars are in- 
 serted, and through another small opening in the top, melted 
 
848 FIRE-PROOF AND INCOMBUSTIBLE FLOORS. 
 
 zinc is poured, which fills the space around the bars and securely 
 fastens them in place. The cast-iron strut serves to hold the 
 bar B at proper elevation from the bottom of the slab. These 
 trusses are 6| ins. deep, for an 8-inch slab, and are spaced 
 from 12 to 16 ins. on centres, according to the load to be sup- 
 ported. 
 
 The advantage of the truss is that it will sustain the weight 
 of the floor independent of the adhesion of the concrete so that 
 
 B. & Sq. Bar 
 
 Fig. 57 
 
 the centers can be struck as soon as the concrete is hard enough 
 to hold together between the trusses. After the concrete has 
 fully set the upper bar is not required, but its cost is more 
 than offset by the strength it gives to the floor during con- 
 struction. 
 
 A section of floor, 8 ins. thick and 11 ft. 8 ins. span, rein- 
 forced with these trusses, was cut loose from the adjacent por- 
 tions and loaded up to 2000 Ibs. per square foot, when the 
 deflection at the centre was T 3 6 -inch. At the end of a week, 
 the load was removed and the floor returned to its first level. 
 
 When the span of the floor sections exceeds 12 ft., the trusses 
 are usually assembled in bunches of 3 or 5, forming deep ribs 
 about 5 ft. apart from centres with a 4-inch flat plate between. 
 Where two or more trusses come together, the cast heads are 
 made large enough to take all of the rods. 
 
 Dovetail Corrugated Sheets (Ferroiiiclave). 
 
 Sheets of thin steel corrugated so as to form dovetail grooves 
 have been used by several parties, as a reinforcement and cen- 
 tering for concrete steel, the dovetailing serving to unite the 
 sheets to the concrete. 
 
 Mr. P. H. Jackson of San Francisco still uses it for the 
 support of sidewalks, and for floors, and it may be used by 
 other parties. 
 
 The corrugations in the sheets used by Mr. Jackson measure 
 1J ins. deep by li ins. wide. With such large corrugations 
 
FERROINCLAVE. 
 
 849 
 
 it is impracticable to plaster the underside, and if a plastered 
 ceiling is deemed essential, the ceiling must be furred and 
 lathed. 
 
 The Brown Hoisting Machinery Company of Cleveland have 
 recently patented, under the name of ferroinclave, a tapered 
 corrugation which 'is small enough to hold hard mortar, and 
 hence can be plastered on the under side, which is a great 
 advantage. Fig. 58 shows a partial section of the ferroinclave 
 
 '' 'o o~"^~^^ o . o ^"""""*^- ^^-^^,-: i 
 / tt*!*'. " > .' o *o l 9 a M'?i a ? t ?* > "'*.** !*% cX '. ; o ' e '; < '.' <> *'*.'. \ 
 
 Fig. 58 
 
 Ferroinclave. 
 
 corrugated sheets, reduced a little more than one half, the 
 actual size of the corrugations being J in. in depth, and 2 ins. 
 centre to centre of corrugation, with an opening between the 
 edges of inch. 
 
 The tapering of the corrugations is also an advantage, espe- 
 cially for roofs as it enables the sheets to be lapped at the end 
 joints, so as to make a roof that will be absolutely tight, even 
 if water should penetrate the cement coating. 
 
 The principal advantage of corrugated sheets for floor con- 
 struction lies in their ability to sustain the concrete (with 
 moderate spans) before it has set, thus saving the cost of 
 centering and the time required in putting it in place. This 
 advantage, however, appears to be offset by the high cost of 
 the sheets when they have to be shipped, which brings the 
 cost of the completed floor fully as high as the average of the 
 reinforced concrete systems and higher than some. 
 
 For roofs, however, it makes the lightest and cheapest con- 
 struction with which the author is acquainted, as the total 
 thickness need not exceed 1} ins. for spans of 4 ft. 10 ins., 
 and it only requires a coat of asphaltic paint over the cement 
 to make the roof watertight. 
 
 With a good coat of hard plaster or gauged mortar on the 
 
850 FIRE-PROOF AND INCOMBUSTIBLE FLOORS. 
 
 underside, the iron will not be affected by heat until a con- 
 siderable 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, at a very slight expense. Another advan- 
 tage of ferroinclave for roofs is that the building can be covered 
 and made Watertight in the most severe winter weather and the 
 cement can be applied during the following spring, 
 
 Ferroinclave is made in sheets 20 ins. wide and up to 10 ft. 
 in length and usually of No. 24 gauge. 
 
 For roofs the ferroinclave is attached to purlins in the 
 same manner as iron roofing, the most economical spacing 
 of the purlins b'ein'g 4 ft. lOi ins. centre to centre, which 
 accommodates sheets 10 feet long with an end lap of 3 
 inches. 
 
 For the cement top coat, a mixture of one part Portland 
 cement to two parts sand, applied to a thickness of f-inch 
 above the top of the sheets is sufficient for roofs. For floors 
 a rich gravel or crushed stone 'Concrete should be used, the 
 thickness being governed by the span and 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 ins. wide and 4 ft. 10J ins. 
 span: 
 
 Thickness of 1 to 2 mortar above the metal. . 1" 2" 2" 3" 3" 4" 
 Ultimate strength in Ibs. per square foot 
 
 (span 4 feet 10^ inches) 615 915 1220 1560 1860 2120 
 
 A factor of safety of 6 should be ample for ordinary loads. 
 
 About a million square feet of ferroinclave has "thus far 
 been used for floors, roofing, and side walls. It is especially 
 adapted for the walls, roof, and floors of large manufacturing 
 plants, and may be used to advantage for partitions, gutters, 
 stair treads, vats, water-closet partitions, and fire-proof doors. 
 
 Berber's "Multiplex Steel Plate." 
 
 Fig. 59 shows a section of a corrugated steel plate manu- 
 factured by the Berger Manufacturing Company for floor and 
 roof Construction, the plate being an invention of G. Fugman, 
 architect. As shown by the illustration, it consists of a series 
 of vertical corrugations of sheet steel, painted or galvanized, 
 
BERGER'S MULTIPLEX STEEL PLATE, 851 
 
 ending at the top and bottom in three half circle arches, separat- 
 ing the vertical sides of the corrugations from each other, and 
 giving stiffness to the top and bottom of the plate. 
 
 This plate is made with depths, />, of 2, 2}, 3, and 4 ins., 
 and a uniform width of 2 ins. between manifolds. The sheets 
 are made at present in lengths up to 8 ft., but the company 
 expects to make greater lengths in the near future. 
 
 It can be made of any gauge of steel from No. 16 to No. 24, 
 but No. 18 is as heavy as would generally be required. 
 
 For floors and roof, the corrugated plate is laid on top of 
 the beams and the top portion filled with concrete and leveled 
 
 Fig. 59 
 
 off about 1 inch above the plate. For wood floors the nailing 
 strips may be imbedded in the concrete, the bottom of the 
 strips being raised only about J inch above the top of the plate. 
 
 This construction is very light and strong and requires no 
 centering, and no tie-rods between the beams. It cannot be 
 plastered underneath, however, and where a plaster ceiling 
 is required it must be constructed independently of the plate 
 by means of furring strips and metal lath. 
 
 The weight of the 4-inch plates, No. 18 gauge, with rock 
 concrete leveled 1 in. above top of plate is about 39 Ibs. per 
 square foot, and the safe load for an 8-foot span is given at 
 430 Ibs. per square foot. 
 
 While this floor has several practical advantages, the author 
 doubts if it can be considered as thoroughly fire-proof, on 
 account of the metal being exposed on the bottom. With a 
 plastered ceiling underneath, the iron would probably not be 
 affected by any ordinary fire before the latter could be con- 
 trolled. 
 
852 FIRE-PROOF AND INCOMBUSTIBLE FLOORS. 
 
 Arched Bib Constructions. 
 
 The Golding System (Fig. 60). This system was 
 designed by Mr. John F. Golding for spans of from 8 to 16 ft., 
 
 Fig. 60 
 
 and has been much used for these spans by the expanded- 
 metal companies, who control the patent. 
 
 It differs from the paneled constructions above described, 
 in that the ribs are in compression instead of in tension, thus 
 exerting a considerable thrust against the bottom of the I-beams. 
 
 The ribs are formed of steel channels, varying from 5 to 
 8 ins., curved to the required radius, with the flat side down, 
 and set in the angle formed by the web and bottom flange of 
 of the I-beams. The usual distance between centres of ribs 
 is about 4 ft. Above the channels the ribs are formed of con- 
 crete, deposited so as to be monolithic with the floor slab. 
 This construction has shown great strength, and so far as the 
 author can ascertain has proven satisfactory wherever it has 
 been used. The outer bays, at least, should be provided with 
 tie-rods to resist the thrust of the ribs. 
 
 Mr. P. H. Jackson, of San Francisco, has used a construc- 
 tion similar to the above, by forming the ribs of two small 
 
 Fig. 61 
 
 rails, weighing 6 Ibs. to the foot, and fastened together at 
 intervals by bolts and pipe separators. For reinforcing the 
 slabs, he uses dovetail corrugated sheets as described on p. 848. 
 
PANELED FLOOR SYSTEMS. 
 
 853 
 
 Suspension Ribs. Fig. 61 shows a rib for a paneled 
 floor, which is just the reverse of that shown in Fig. 60. The 
 ribs are usually spaced from three to four feet apart, with a 
 flat floor between as in Fig. 60. 
 
 This construction was used for a time by the expanded- 
 metal companies; but is not mentioned in their later catalogues. 
 
 Mr. P. H. Jackson has patented a construction which acts 
 on the same principle, the only difference being in the manner 
 of attaching the straps. 
 
 Paneled Systems \vith Concrete-steel Beams. 
 
 Concrete-steel beams, like those of wood or metal, require 
 depth to give them strength and stiffness, and when the span 
 between the girders or walls exceeds 11 ft., the thickness 
 required for a flat slab of concrete-steel, to give it the necessary 
 strength and stiffness, is so great that it makes quite a heavy 
 floor. To reduce this weight, concrete-steel beams from 4 
 to 6 ins. thick may be built between the girders, and these 
 beams utilized to support a thin floor slab, the concrete beams 
 being usually spaced about 3 ft. on centres. Fig. 62 shows 
 
 , Girder 
 
 Fig. 62 
 
 a floor built in this way. The first person in this country to 
 build a paneled concrete-steel floor, the writer believes to be 
 Mr. Ernest L. Ransome, who constructed a number of floors 
 paneled as shown in Fig. 63, the beams being usually 2J ft. 
 centre to centre. The floors in the works of the Pacific Coast 
 Borax Company at Alameda, Cal., were built in this manner, but 
 
854 FIRE-PROOF AND INCOMBUSTIBLE FLOORS. 
 
 with oblong instead of square panels. The floors in this build- 
 ing have a span between girders of 25 ft., and have frequently 
 
 Fig. 63 
 
 been loaded to 500 Ibs. per square foot. Paneled floors are 
 now built by several of the concrete construction companies, 
 and usually with only one set of beams, as in Fig. 62, the only 
 difference in the construction being in the form of the reinforce- 
 ment for the beams. For a given quantity of concrete this 
 construction undoubtedly gives the strongest and stiffest 
 concrete-steel floor that can be built, i.e., when the span exceeds 
 10 ft.; but when it is necessary to pay $3 or $4 a day for labor, 
 and where lumber (for centering) is expensive, it will probably 
 cost more to build than a flat suspended floor, such as is 
 shown by Figs. 38 and 42. Paneled or beam floors, however, 
 can be proportioned to any span up to 50 ft., and for any or- 
 dinary load.* The greatest economy will generally be obtained by 
 spacing the concrete-steel beams about 3 ft. centre to centre, 
 so that the slab between the beams will not be more than 2J 
 or 3 ins. thick. The beams should be designed as explained 
 under the formulas for strength, in the latter part of this chap- 
 ter. The top portion of the floor between the slabs should be 
 reinforced by expanded metal, metallic fabric, or light rods, 
 or barb wire. 
 
 For the reinforcement of the beams, the Ransome twisted 
 
 *The P. M. Bruner Granitoid Company of St. Louis has built a floor 
 87 ft. span by 60 ft. length, the ribs being reinforced by the truss 
 device de9cribed on p. 847. 
 
PANELED SYSTEMS. 
 
 855 
 
 bars, the Johnson corrugated bar (Fig. 64), the Thacher bar 
 (Fig. 65), channels, or even plain rods may be used.* 
 
 The St. Louis Expanded Metal Fireproofing Company have 
 adopted this system for panel spans, exceeding 14 ft., having 
 
 Fig. 64 
 
 Johnson Corrugated Bar. 
 
 found it the most economical of any system giving the same 
 strength and stiffness. For the reinforcement of the beams, 
 
 Fig. 65 
 Thacher Bar. 
 
 they employ corrugated bars, and for the top slab expanded 
 metal. They recommend this system for spans up to 30 feet. 
 
 The Heiuiebique System. Mr. Frangois Hennebique, 
 one of the most successful concrete-steel builders of Europe, 
 has developed a system of construction, using concrete-steel 
 beams and girders with thin slabs between, practically on the 
 principle of Fig. 62, except that he uses no steel beams or 
 girders whatever. The peculiar feature of the Hennebique 
 system is the reinforcement of the beams, which is illustrated 
 by Fig. 66. As will be seen, the reinforcement consists .of 
 two round rods with split ^ends, one of the rods being per- 
 fectly straight, while the other is bent upwards at about one 
 third of the span from the supports, with the idea of resisting 
 the shearing stresses at the ends. Stirrups of hoop iron are 
 also introduced at frequent intervals. The Hennebique en- 
 gineers claim that these stirrups materially strengthen the beams. 
 
 * For dimensions of Johnson and Thacher bars, 
 
856 FIRE-PROOF AND INCOMBUSTIBLE FLOORS. 
 
 As a rule two sets of reinforcing rods and stirrups are used 
 in each beam, as indicated by the dotted lines in the end sec- 
 tion, Fig. 66. Girders built as shown by Fig. 66 have been 
 
 
 ' 
 
 
 
 
 
 
 
 
 
 
 Center Line of Span >i 
 
 A 
 
 Fig. 66 
 
 constructed with spans up to 50 ft. and have shown great strength. 
 Fig. 67 shows three methods of providing for vertical shear 
 
 I in beams and 
 
 girders that 
 have been em- 
 ployed by the 
 companies us- 
 ing the Ran- 
 some twisted 
 ) (jTi t bars. Methods 
 ""N f A and C have 
 also been quite 
 generally used 
 in connection 
 with other 
 forms of bars. 
 The second 
 method the 
 author believes 
 to be the in- 
 vention of Mr. 
 E.L.Ransome 
 
 The question of stirrups in concrete-steel beams is discussed 
 under the head of "Formulas for strength and metal area," 
 in the latter part of this chapter. 
 
 Fig. 68 shows a beam construction with hollow-tile centering, 
 used to give a flat ceiling and also to cut down the expense 
 of the wood centering, which for a beam construction is neces- 
 sarily greater than for a flat construction. 
 
 This construction was invented by Mr. P. M. Bruner of 
 St. Louis, and has been used by him in a number of floors 
 with spans of from 14 to 18 ft. The tiles were 15 ins. wide 
 between the concrete beams and 11 and 13 ins. loner. No 
 
 Fig. 67 
 
ARCHED-FLOOR SYSTEMS. 
 
 857 
 
 dependence was placed upon the tile centering for strength. 
 At the present prices for labor and cement, this system, how- 
 
 Fig. 68 
 
 ever, is too expensive to successfully compete with many 
 others. 
 
 Arched-floor Systems. 
 
 For heavy warehouse floors the author believes that the 
 arched systems are preferable to the flat systems, as the con- 
 crete is thus used in its strongest form, and less reinforcement 
 is required. In warehouses, also a ceiling formed of a series 
 of arches is not objectionable. 
 
 For spans between floor beams of 5 ft. or less, a 1 to 6 gravel- 
 concrete arch, 3 ins. thick at crown and without any reinforce- 
 ment should sustain a distributed load of 1500 Ibs. per square 
 foot without cracking. 
 
 For spans exceeding 5 ft., the celebrated Austrian experi- 
 ments (1891-92) seem to show that reinforcing concrete with 
 small I-beams adds greatly to the strength of the arch, but 
 that small rods or netting are not of sufficient advantage to 
 warrant the additional expense.* Tests made on arches of 
 8-ft. span gave the following results: Concrete arch, 3f ins. 
 thick, 9J ins. rise, broke at 1130 Ibs. per square foot. A Monier 
 arch (wire ftetting), 1{ ins. thick, 10} ins. rise, or about half 
 the thickness of the concrete arch, failed at 1217 Ibs. per square 
 foot. Brick arch, 5J ins., thick, 9. e 5 ins. rise, failed at 885 Ibs. 
 
 *See Architecture and Building, Jan. 4, 1896. 
 
858 FIRE-PROOF AND INCOMBUSTIBLE FLOORS. 
 
 per square foot. A hollow brick arch, 3}f ins. thick, SJ-f ins. 
 rise, failed at 401 Ibs. per square foot. A 13-ft span, con- 
 crete arch, 3}f ins. thick, 15J ins. rise, failed at $12 Ibs. per 
 square foot. Melan arch ; 3J ins. thick, 11.4 ins. rise, broke 
 at 3360 Ibs. per square foot. The Melan arch had I-beams 
 3i ins. deep, spaced 40 ins. apart. The structure was one 
 year old when tested. 
 
 While there are several patented arched-floor systems, a 
 plain concrete arch can be built by any one, and if reinforcing 
 is desired for wide spans, plain rods or bars, small tees or chan- 
 nels, and various forms of netting may be used without in- 
 fringing on any patents. The principal advantages of the 
 patented arch systems lie in the matter of economy in putting 
 the arches in place. 
 
 All arched systems require tie-rods between the beams to 
 take up the thrust of the arches, the same as for tile arches, 
 see p. 880. 
 
 The Roebliiig Arch-floor System. 
 
 This system is now so widely known as to require but brief 
 description. It has been used in many of the best buildings 
 in the Eastern States, and has proven one of the strongest 
 
 I V Steel Rod woven into 
 7 s No. 20 Wire Lathing 
 
 Fig. 89 
 
 Type 1. For buildings requiring level ceilings. 
 
 floor systems in use, and when the bottoms of the steel beams 
 are protected as in Types 2 and 4, is unquestionably first-class 
 fireproof construction. The three principle types of floor con- 
 
THE ROEBLLNG ARCH-FLOOR SYSTEM. 859 
 
 struction are shown by Figs. 69, 70, and 71. Type 3 is similar 
 to Type 2, but has a suspended flat ceiling in addition, which 
 
 I 
 
 U #0 C. to G5-. ofBeams -, 
 
 Spruce Flooring, % Oak Flooring-^ 
 
 Fig. 70 
 Type 2. Warehouse construction. 
 
 50 C. to C. of Beams- 
 
 Steel Rod, woven 
 into Wire Lathing 
 
 Fig. 71 
 
 Type 2. Warehouse construction with sleepers depressed. 
 
 may be adjusted at any level below the floor beams to admit 
 piping, etc., as may be desired. The distinctive feature of 
 this system is the permanent wire centering which is always 
 erected in advance of the concreting, thus enabling the work 
 to progress continuously. The centering is made of the proper 
 size and form at the factory, so that it is readily placed in 
 position. 
 
 Concrete. The concrete used for the arches consists, usually, 
 of one part Portland cement to two and one-half parts of sharp 
 
860 FIRE-PROOF AND INCOMBUSTIBLE FLOORS. 
 
 sand and six parts of clean cinder, weighing on an average 
 82 Ibs. per cubic, foot when dry. It is never rammed, but is 
 spread in position and leveled with shovels. 
 
 Fig. 72 
 
 Typical girder section. 
 
 The Advantages of this centering, aside from the saving 
 over wood centres, and the rapidity with which it can be put 
 in place, are that it allows the superfluous water to drip out of 
 the concrete as soon as it is in position, and it also forms a 
 valuable safeguard against the falling of workmen, as it is suffi- 
 ciently strong to sustain a considerable load of itself. 
 
 Whether or not it increases the strength of the concrete 
 arch after the latter has set is an open question. 
 
 Strength. Sections of the Roebling arch floor have been 
 tested to from 1400 to 4100 Ibs. per square foot without failure. 
 
 With spans of from 5 to 6 ft., the author considers that they 
 will support 1000 Ibs. to the square foot with an ample factor 
 of safety. 
 
 Spans and Weight. The maximum spans that are desirable 
 for the different types are given in the illustrations. Type 4, 
 however, has been installed with success up to 18 ft. between 
 18-inch beams. 
 
 Wide spans require a corresponding depth at the haunches, 
 as the clear rise of the arch for Types 1, 2, and 3 should be 1J 
 ins. per square foot of span. In the 18-foot span, above-men- 
 tioned, the clear rise above beam-flange was 16 ins. For 14- 
 foot spans between 18-inch beams, the rise would be 14 ins. 
 
THE ROEBLING ARCH-FLOOR SYSTEM. 
 
 861 
 
 The following table, prepared by the Roebling Construction 
 Company, gives the weight per square foot for different spans: 
 
 When concrete is 
 to be leveled 
 above under side 
 of floor beams 
 to a height of 
 
 Maximum spacing 
 of iron floor 
 beams (independ- 
 ent of size of 
 beams) should 
 not exceed 
 
 Thickness of 
 crown at centre 
 of arch. 
 
 Weight per sq. 
 ft. including 
 only concrete 
 and wire. 
 
 8" 
 
 4' 0" 
 
 3" 
 
 33 Ibs. 
 
 9" 
 
 4' 6" 
 
 3" 
 
 34 Ibs. 
 
 10" 
 
 5' 0" 
 
 3" 
 
 36 Ibs. 
 
 12" 
 
 6' 0" 
 
 3" 
 
 41 Ibs. 
 
 15" 
 
 r 6" 
 
 3" 
 
 47 Ibs. 
 
 The weights given are for concrete to the level indicated in 
 the first column, with a 3-inch crown and for all wire con- 
 struction, including arch wire for floors and lathing for 
 ceiling. 
 
 Fig. 73 
 
 Type 4. For spans exceeding 10 feet. 
 
 Add for plaster 8 to 10 Ibs. per square foot; the weight of 
 the structural iron, of the wood or other finished floor, and 
 of the filling between sleepers, if any, must also be added for 
 the total dead load of floors. 
 
 Tie-rods. All floor beams should be tied together at 
 intervals of about eight times their depth and should be 
 framed level and flush on the underside where flat ceilings 
 are desired. 
 
862 FIRE-PROOF AND INCOMBUSTIBLE FLOORS. 
 
 Bromley Patent Fire-proof Floors. 
 
 (The Vulcanite Paving Company, Licensees for Eastern Penn. and 
 Southern N. J.) 
 
 S?^ ^7^7^ 
 
 Fig. 74 
 
 Fig. 75 
 
 This is essentially a concrete arch floor, but differing from 
 other arch systems in having a permanent centering of plaster 
 of Paris. The centering is made in sections, 1} ins. thick, 
 each reaching from the beam-flange to the centre of the span; 
 opposite sections abutting against each other. The usual 
 width of the sections (measured longitudinally) is 12 ins. 
 
 The bottom of the I-beam is protected by bending wire lath 
 around the flanges before the centres are set, and plastering 
 1 to 2 ins. thick with Portland cement or gauged mortar. 
 
 The concrete filling above the centres is preferably made of 
 cinder concrete with a thickness of 3 ins. at the crown. 
 
 Tie-rods. Tie-rods are required, the same as for brick or tile 
 arches, and temporary tie-rods are also attached to the bottom 
 flanges of beams, to prevent any possibility of spreading until the 
 arches are all in place. 
 
 Span and Rise. The span is only limited by the rise of the 
 arch, which must be at least one-twelfth, and preferably, one- 
 tenth of the span, measured from the bottom of the beam to 
 the top of plaster centre at the crown, and a minimum thickness 
 of 3 ins. for the concrete arch above the plaster centers. 
 
 The greatest economy, however, will usually be attained with 
 spans of about 6 ft., although 8-ft. spans have been constructed. 
 
SECTIONAL SYSTEMS. 863 
 
 Weight. The weight will vary with the span and is about the 
 same as for concrete. 
 
 With a 6-ft. span and 6 ins. rise, the weight of centering 
 and concrete arch, leveled 3 ins. above the centres will be about 
 65 Ibs. per square foot. 
 
 Strength. The main dependence for strength is upon the con- 
 crete arch. With a rise of one-twelfth, the floor should have 
 a safe load of 250 Ibs. per square foot for 6-ft. span, and 200 
 Ibs. for an 8-ft. span, with a factor of safety of 5. 
 
 Fire Resistance and Protection. Under an intense heat pro- 
 longed for a considerable time, the plaster centres are liable to 
 fall, but this does not affect either the strength or fire-proof 
 qualities of the concrete arch. In the official test at Philadelphia, 
 Jan. 15, 1902, this construction was most severely tetesd, and 
 according to the official report, the strength of the concrete 
 arch and the beam protection were unimpaired. 
 
 Special Advantages. The special advantages of -this system 
 
 are due to the plaster centering upon which the patent is based. 
 
 These centres can be moulded and fitted under cover, to meet 
 
 the spread of the beams, and then taken to the building ready 
 
 for placing in position. They are put in position without any 
 
 false work whatever, and if fitting is required to adjust them to 
 
 the supports they may be easily cut with an ordinary hand-saw. 
 
 The centres also give a smooth and even white ceiling, which 
 
 when pointed, should answer for all buildings in which a level 
 
 veiling is not thought necessary. 
 
 This construction was first used in 1900. At this time * there 
 have been constructed about 260,000 sq. ft. and contracts have 
 been made for some 214,000 sq. ft. to be placed during 1903. 
 
 Sectional Systems. 
 
 Several devices have been patented for building fire-proof 
 floors of reinforced concrete beams or slabs that could be made 
 in a factory taken to the building and set in place, between the 
 steel beams, without centering. Mr. Hyatt showed a design 
 for a construction of this kind in his application for the patent 
 referred to on p. 817, but the author is not aware that it was 
 ever used in actual construction. 
 
 Mr. John C. Pelton, an architect, also patented in the year 
 1900, a sectional system of floor construction, consisting of 
 reinforced beams, resting on the bottom flanges of I-beams, 
 * March, 1903. 
 
864 FIRE-PROOF AND INCOMBUSTIBLE FLOORS. 
 
 or on the walls and partitions, and set about 18 or 20 ins. apart. 
 These concrete beams support light arched blocks which form 
 the floor. To obtain a flat ceiling a suspended ceiling was 
 necessary. The author is not aware of this system having 
 been used in more than one building, although it was for a 
 time somewhat extensively advertised. 
 
 Mr. A. De Man, president of the American Fireproofing & 
 Cement Construction Company of New York secured a patent in 
 May, 1902, of a floor block construction which would seem to 
 to be both practicable and economical. The shape of the 
 block is fairly well represented by Fig. 76, a vertical section 
 
 Fig. 76 
 
 through the centre of the block being similar to a capital I. 
 It is proposed to make these blocks 10 ins. wide and 10 ins. 
 high, and for spans of from 5 ft. to 6 ft., 6 ins. centre to centre 
 of I-beams. They are intended to be set close together, so 
 as to form a continuous and level top-and-bottom surface with 
 the edges fitting into each other. The blocks are made at a 
 factory, and taken to the building ready to set in place. They 
 drop about 1J ins. below the steel beams, so that a beveled 
 flange-block may be slid in under the steel beam to protect 
 the flanges. The web and lugs of the blocks are reinforced 
 by the De Man tension bar, shown by Fig. 47. Although this 
 construction has not as yet been used in any building, a number 
 of blocks have been made and tested to over one ton per square 
 foot on spans of from 4 to 6 ft. The weight of the blocks is 
 about 30 Ibs. per square foot of floor area. The commercial 
 advantages claimed for this construction are that is it light, eco- 
 nomical, requiring no centering, and that it gives a flat ceiling. 
 
 The company above mentioned also has another sectional 
 floor system which has been used to some extent in dwellings. 
 
FORMULAS FOR REINFORCED CONCRETE BEAMS. 865 
 
 Formulas for Strength and Dimensions of Rein- 
 forced Concrete Beams and Slabs, 
 
 Although there is yet much to learn in regard to the resistance 
 of reinforced beams and slabs, yet enough tests have been made 
 of the strength of full-size beams to show that there is less 
 variation in the breaking strength of a large number of properly 
 designed concrete-steel beams of the same proportions and 
 dimensions than is likely to be found in the same number of 
 timber beams of uniform dimensions; also that variations in 
 manner of loading, span, and depth of beam have precisely 
 the same* effect as with beams of other material, or, in other 
 words, that the general theory of beams applies to concrete- 
 steel beams as well as to those of wood or steel. 
 
 Being constructed of two widely different materials, however, 
 there are more variables to be taken into account than in a 
 beam of homogeneous material such as steel. 
 
 Properties and Proportions ' Affecting- the 
 Strength of Reinforced Beams. In designing a con- 
 crete-steel beam or slab the following elements must be con- 
 sidered, viz.: 
 
 (a) The crushing strength of the concrete; 
 
 (6) The ratio of concrete to steel in sectional area; 
 
 (c) The elastic limit of the steel; and 
 
 (d) The position and distribution of the metal in the beam. 
 The coefficient of elasticity of the concrete and the shape of 
 
 the bar may also have some effect on the strength of the beam, 
 but there seem to be no data by which they can be satisfactorily 
 taken into account in the calculations. It is generally con- 
 ceded that considerations of safety require that the concrete 
 in compression shall be stronger than the steel, so that the beam 
 will fail gradually by excessive deflection and noticeable cracks 
 in the concrete, thus heralding the approach of danger. 
 
 If the reinforcement is relatively too strong for the concrete, 
 the latter will fail first by crushing without preliminary signs, 
 and the beam or floor is liable to collapse almost instantaneously. 
 
 It follows from the above that a rich concrete will take a 
 larger percentage of reinforcement than a poorer mixture. 
 
 A considerable ' number of carefully conducted tests have 
 shown conclusively that so long as the reinforcement is not 
 too great for the crushing strength of the concrete, the strength 
 
866 FIRE-PROOF AND INCOMBUSTIBLE FLOORS. 
 
 of the beam varies in a certain ratio with the percentage of 
 steel in tension, regardless of the richness of the concrete, and 
 also that, with a given percentage of metal, the higher the elastic 
 limit of the metal used, the greater will be the resistance of the 
 beam. 
 
 Medium vs. High Steel. Bars of ordinary merchant 
 steel and all structural shapes are commonly rolled from 
 medium steel having an ultimate strength of about 64,000 Ibs. 
 per square inch and an elastic limit varying from 33,000 to 
 36,000 Ibs. The Thacher and Kahn bars are rolled from this 
 grade of steel. The corrugated bars of the St. Louis Expanded 
 Metal Company are rolled from a much higher grade of steel 
 having an elastic limit of about 58,000 Ibs. The Rausome 
 twisted bars are made from medium steel, but the twisting of 
 the bar raises the elastic limit about 50 per cent, and the ultimate 
 strength about 35 per cent. The Ransome people give the 
 elastic limit of their bars at from 55,450 Ibs. for IJ-in. bars to 
 62,350 for ^-in. bars, and the ultimate strength at from 83,150 
 Ibs. to 86,700 Ibs. per square inch, the elastic limit and ultimate 
 strength decreasing as the size of the bar increases. 
 
 It would seem that there can be no question but that with the 
 same size of bars the high-grade steel will give a greater resistance 
 to the beam, although on the other hand, when the ultimate 
 strength of the beam is reached, failure will occur more suddenly 
 if the reinforcement is of high steel than if of medium steel. 
 There has been some contention as to whether or not it is wise 
 to use high-grade steel for reinforcement, but the actual facts 
 seem to be in its favor. "It may be stated that for an equal 
 moment of resistance a beam will absorb twice the kinetic energy 
 when reinforced by a high steel as when reinforced by iron or 
 soft steel, because it will be in a condition to sustain double 
 the deformation before breaking/' (Considere.) 
 
 Derivation of Formulas. Several theoretical formulas 
 have been published for computing the strength of concrete- 
 steel beams, and also several empirical formulas.* 
 
 As a rule the latter differ from the former in that they assume 
 
 * For the derivation of theoretical formulas, the reader is referred to 
 papers by Prof. W. K. Hatt, published in the Engineering Record of May 10 
 and June 28, 1902; to the catalogues of the St. Louis Expanded Metal 
 Company, for Johnson's formula; to a pamphlet published by the Concrete- 
 Steel Engineering Company, Park Row Building, New York, for Thacher's 
 formula; also to " Reinforced Concrete," by Buel & Hill for a general dis- 
 cussion of the subject, 
 
FORMULAS FOR REINFORCED CONCRETE BEAMS. 867 
 
 that the entire tensile stress is resisted by the reinforcement. 
 At or near the breaking-point this condition probably exists, 
 but when the load does not exceed one-third of the breaking 
 load a careful analysis of numerous tests would seem to indicate 
 that the concrete does materially assist in resisting the tensile 
 stress. Assuming that the entire tensile stress is resisted by 
 the steel, the moment of resistance of the beam, i.e., its ability 
 to resist the bending moment, is the moment of a couple formed 
 by the compression in the concrete at the top and the stress 
 in the reinforcing bar at the bottom acting with an arm whose 
 length is equal to the distance between the centre of the rein- 
 forcement and the centre of gravity of the compress! ve stresses. 
 The value of this moment, for any particular beam, will be 
 determined by the weaker of the two materials; thus if an 
 excessive amount of steel is used, the resistance moment will 
 be determined by the resistance of the concrete to crushing. 
 
 The preceding statement may be represented graphically by 
 Fig. 76a, which represents a vertical section through a rectan- 
 gular beam, the small squares in solid black representing the 
 steel bars, and the shaded portion 
 at the top the concrete in com- 
 pression. The line NN represents 
 the position of the neutral axis of 
 the beam, the line eg the centre of 
 gravity of compressive stresses, and 
 the distance xd the lever-arm of the 
 stresses. The area of concrete in 
 compression is assumed to extend 
 from the top of the beam to the neu- F ' 9 ' 76a 
 
 tral axis. The distance from the top of the beam to the line eg 
 is assumed by Prof. Turneaure to be %y lt by Mr. A. L. Johnson 
 as J2/ X , and by Prof. A. N. Talbot as -foUi- The variation 
 between these fractions is so small, however, that if the position 
 of the neutral axis could be determined with accuracy, the 
 actual resistance moment for any particular beam could be 
 determined very closely. The exact position of the neutral 
 axis, however, is very hard to determine, as it varies not only 
 with the percentage of reinforcement and the mixture of the 
 concrete, but also with varying loads, and it is practically 
 impossible to represent its position at all stages by any simple 
 formula, so that the author prefers to determine the length 
 of the arm xd directly from experimental data. 
 
 i W$y 
 
 N--4 ^^ -I r --N 
 
 * /v7 
 
 .11.. 
 
868 FIRE-PROOF AND INCOMBUSTIBLE FLOORS. 
 
 Employing the following notation and substituting the 
 proper values for the bending moment, we obtain by the above 
 analysis formula (1), which gives the breaking load for any 
 percentage of reinforcement below the maximum allowed for 
 a given mixture of concrete. 
 
 By substituting and combining the proper values for the 
 moduli of elasticity for steel and concrete, for the elastic 
 limit of the steel, and for the strength of the concrete in tension 
 and compression, in the formulas given by Prof. Hatt or Mr. A. L. 
 Johnson, and denoting the resultant coefficient by the letter F, 
 those formulas reduce to the form given by formula (2). By 
 taking the known breaking loads of beams containing different 
 percentages of both medium and high steel, we can obtain 
 the values for F which apply in those cases.* 
 
 It is obvious that with values for F obtained directly irom 
 experimental data, the results obtained by formula (2) will 
 agree with actual tests, whether or not the entire tensional 
 stress is resisted by the steel. 
 
 NOTATION USED IN FORMULAS. 
 
 A = sectional area of concrete above the centre of reinforce- 
 ment = b . d. 
 
 a = sectional area of reinforcement at the point of greatest 
 bending moment. 
 
 Both A and a are to be taken in square inches. 
 F = coefficient derived from experimental data. 
 
 F' = ratio of concrete to steel (in sectional area)= = - . 
 
 a a 
 L = clear span of beam or slab in feet. 
 
 M= bending moment in foot-pounds. 
 
 lOOa 
 
 p = per cent, of reinforcement = r- . 
 
 A. 
 
 s = stress in steel per square inch. 
 5 = total stress in steel =sXa. 
 b, d, xd, ?/! and ?/ 2 = dimensions in inches as indicated in Fig. 76a. 
 
 xd 
 x = , being always less than 1. 
 
 TF= breaking load uniformly distributed in pounds, including 
 
 the weight of the beam. 
 Periods between letters denote multiplication. 
 
 * Data for this purpose may bo found in the Engineering News of April 
 14 and Sept. 8, 1904, and in the Engineering Record of June 28, 1902. 
 
FORMULAS FOR REINFORCED CONCRETE BEAMS. 868a 
 
 FORMULAS FOR RECTANGULAR BEAMS SUPPORTED AT BOTH ENDS 
 AND NOT CONTINUOUS. 
 
 w J2s.a.x.d 
 
 3L ...... (1) 
 
 TT=^1 (2) 
 
 rwr 
 
 (3) 
 
 I- \ m 
 
 ~^w- 
 
 If the load instead of being distributed is concentrated at a 
 single point, the equivalent distributed load may be computed 
 by the factors given on page 514. For a combination of loads 
 compute the maximum bending moment in foot-pounds and 
 solve for d by formula (4). 
 
 'W 
 
 3Fb (4) 
 
 Limitations as to the Use of the Values for F 
 
 and x. The values given for F and x in the foregoing table 
 should be used only in connection with the corresponding 
 value for F' or p, and only for broken rock or gravel concrete 
 well mixed with a standard Portland cement. For short and 
 deep beams, or when the length in feet does not exceed d in 
 inches, stirrups or some form of vertical reinforcement should 
 be used. 
 
 The percentage of steel also should not exceed the following 
 limits : 
 
 T^ i o n i i , ( 1J% f r medium steel. 
 
 For 1:3: 6 broken-stone concrete 1 1% for corrugated or twisted 
 or 1 : 7 gravel concrete ) 
 
 For 1:2:5 trap-rock or hard] ~ , ,. , 
 
 limestone ' 2 % for medmm steel - 
 
 } 1 j% for corrugated or twisted 
 1:2: 4 ordinary broken stone, \ k ars 
 
 or 1 : 5 gravel concrete J 
 
 For 1 : 2 : 4 trap-rock or hard lime- ) 2^% for medium steel. 
 
 stone with vertical rein- [-2% for corrugated or twisted 
 forcement ) bars. 
 
 Breadth of beam b. The breadth of beam b should 
 be proportional to the diameter of the bars.. The Ransome 
 Concrete Machinery Company recommends that where a single 
 bar is used b be made three times the size of the bar. Where 
 
8686 FIRE-PROOF AND INCOMBUSTIBLE FLOORS. 
 
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FORMULAS FOR REINFORCED CONCRETE BEAMS. 868c 
 
 2, 3, or 4 bars are placed side by side the space between the 
 bars and the thickness of concrete outside of the outer bars 
 should be at least equal to the diameter or side of the bar. 
 
 The minimum thickness of beam for two Kahn bars is given 
 in the catalogue of the Trussed Concrete Steel Company. 
 
 Neither the St. Louis Expanded Metal Company nor Mr. 
 Thacher gives a limit for the value of b for rectangular beams. 
 By properly distributing the metal almost any value could 
 be given to b, but economical considerations will usually require 
 that b shall not exceed two thirds d. If b is too small, the beam 
 may fail by longitudinal shear in the concrete. 
 
 Depth of Concrete, d', Below the Centre of the 
 Bar. That the concrete may properly surround the bar and 
 protect it from heat, the depth d f should not be less than 1 in. 
 for J-in. bars or 3 ins. for 2-in. bars. 
 
 Factor of Safety. What factor of safety should be used 
 for concrete-steel beams seems to be as yet a matter^of personal 
 opinion. 
 
 Capt. John S. Sewell, U. S. Eng. Corps, in a paper read before 
 the International Engineering Congress at St. Louis, 1904, said: 
 "If the stresses in the extreme elements of the concrete and 
 steel be limited to 2,000 and 16,000 Ibs. per square inch respect- 
 ively, then beams, girders, etc., .will give a sufficient factor 
 of safety for all ordinary purposes, provided that the weakest 
 section is at the point of greatest bending moment. It would 
 require almost certainly four times the working load to cause 
 the beam to collapse." 
 
 Considere deems it wise to "adopt a factor of safety of 2,5 
 with respect to the breaking loads." 
 
 The Ransome people allow a stress of 20,000 Ibs. to the square 
 inch for safe loads, which gives a factor of safety of about 4. 
 In connection with the values for F given in the preceding 
 table, and for the stresses assumed, the author recommends 
 that a factor of safety of 3 be used for plain beams, 3.6 for 
 Thacher, Kahn-, and corrugated bars, and 4 for the Ransome 
 twisted bars. These factors correspond with a safe stress in 
 the steel of 16,000 Ibs. for plain bars, 16,110 Ibs. for Kahn bars, 
 17,360 Ibs. for Thacher bars, and 20,000 Ibs. for the corrugated 
 and twisted bars. 
 
 Application of Formulas to Rectangular Beams. 
 To ascertain the breaking strength of a given beam, the 
 values of A, a, and F' or p should first be computed, and the 
 
868d FIRE-PROOF AND INCOMBUSTIBLE FLOORS." 
 
 load may then be calculated directly by means of either formula 
 (1) or (2), using the value for F or x given in the table for the 
 corresponding value for F' or p. 
 
 If the value found for F' or p does not correspond with any 
 given in the table, the corresponding value for F or x may be 
 found with sufficient accuracy by interpolation. 
 
 To find the safe carrying load subtract the weight of the 
 beam from the breaking load and then divide by the factor of 
 safety recommended in preceding paragraph, or use the corre- 
 sponding safe stress and subtract one fourth or one third the 
 weight of the beam according to the factor of safety used. The 
 weight of the beam may be estimated with sufficient accuracy 
 by allowing 144 Ibs. to the cubic foot or 1 Ib. per lineal foot 
 for each square inch of sectional area. Thus the weight of an 
 8"X14" beam would be 112 Ibs. per lineal foot. 
 
 Example 1. What is the safe carrying load for a beam 
 8"X13J", 16ft. span, reinforced with three }-in. round rods 
 of medium steel, placed 1J ins. above the bottom of the beam, 
 using a factor of safety of 3? 
 
 Ans. The area of three |-in. round rods = 1.32 sq. ins., 6 = 
 
 8 ins., d = 12 ins., F' = = ^ = 72.7. The corresponding 
 
 d L .rj~i 
 
 value for F is about 285, and that for x, .645. Then by formula 
 (1), using 16,000 Ibs. for safe unit stress, 
 
 T[7 _2s.a.x.d_ 2X16,OOOX1.32X. 645X12 go11l ,, 
 
 ~~3ZT~ 3X16 
 
 The weight of the beam will be about 1,728 Ibs., and the safe 
 canying load 6,811-576 = 6,235 Ibs. 
 By formula (2), 
 
 TF== 285X^X144 = 2Q ^ 20 lbg (breaking load); 
 
 Subtracting the weight of the beam and dividing by the factor 
 of safety 3, we have 6,264 Ibs. for safe carrying load. 
 
 Example 2. What is the safe carrying load for a beam 
 5"X13J", 16 ft. span, reinforced with two f-in. twisted bars 
 1J ins. from the bottom, allowing a safe unit stress of 20,000 Ibs.? 
 
 fiO 
 Ans. Area of bars = .781 sq. in., 6 = 5, d = 12, F / = -^~ = 
 
 ,7ol 
 
 77, and a; = .535. Then 
 
 safe load = IXgOfflOX 781^ .535X12 
 
FORMULAS FOR REINFORCED CONCRETE BEAMS. 868e 
 
 Subtracting one fourth the weight of the beam, 270 Ibs., we 
 have for the safe carrying load 3,903 Ibs. For this beam we 
 should use 1:2:4 concrete, as the percentage is more than 1. 
 
 As a rule the problem will be to find the size of beam and 
 amount of steel to support a given load. In this case the 
 quickest solution is to assume some value for F and b and 
 solve for d in formula (3). 
 
 In assuming a value for F it will be more economical to take 
 the value corresponding to the largest percentage of steel which 
 it is advisable to use with the kind of concrete we wish to employ. 
 
 Example 3. We wish to design a girder to support 20,000 Ibs. 
 in addition to the weight of the girder, the span to be 14 ft., 
 the concrete to be mixed in the proportion of 1:2:4, and the 
 reinforcement to be of Ransome twisted bars. What should 
 be the dimensions of the girder and the size and number of the 
 bars? 
 
 Ans. For this proportion of concrete we will take -F = 405, 
 corresponding to 1| per cent, of reinforcement, and for the 
 safe load one fourth of this, or, say, 100. 
 
 For the weight of the beam we will allow, say, 3,000 Ibs., and 
 add one fourth of it to the given load, and for b we will assume 
 12 ins. 
 
 ),d= 2Q> 
 
 ^J l 
 
 Then, by formula (3),d= > W242 = 15.56 sq. ins. 
 
 The area of concrete above reinforcement would be 
 12X15.56 = 187 sq. ins., and the sectional area of the steel 
 
 must = = = -=- =2.79 sq. ins. For this area and a breadth of 
 
 12 ins. we can use three 1-in. bars or four f-in. bars, the area 
 
 in either case being slightly in excess of the required amount. 
 
 Application of'Formulas to Continuous Beams. 
 
 The values for F given in the table were obtained from the 
 breaking loads of beams resting on knife-edge supports. When 
 the beams are continuous over supports, as is the case in mono- 
 lithic buildings, or may occur when they rest on brick walls 
 or piers, the bending moment is decreased and consequently 
 the strength of the beam is increased. According to Thacher, 
 if a beam is continuous over two or more spans and the top 
 of the beam is reinforced by bars of the same size as in the 
 bottom, extending one quarter span each way from the sup- 
 port, the breaking load may be increased one fourth, or in 
 
868/ FIRE-PROOP AND INCOMBUSTIBLE FLOORS. 
 
 designing a beam to- support a given load we may compute d 
 for four fifths of the given load instead of for the full load. 
 Thus if the beam in Example 3 was to be continuous over two 
 or more spans, in place of using 20,750 Ibs. in the formula for d 
 we would use four fifths of 20,750, or 16,600 Ibs., and d would 
 
 e( l ual * n nn^o 4 =^194 = 13.93 ins.; or if we let 6 = 10 ins., 
 '^u lUUX -l^ 
 
 8., which would be a better propor- 
 
 tioned beam. 
 The area of steel required for the latter beam will be 
 
 153 
 
 = 2.29 sq. ins., or three f-in. bars. 
 o7 
 
 Application of Formulas to Beams of T Section. 
 
 When the system of floor construction shown by Figs. 62 
 and 77 is employed, and the joists and floor slab are truly 
 monolithic, the floor slab forms a part of the beam and mate- 
 rially increases the resistance to compression. This increase of 
 compression area has the effect of increasing the length of the 
 moment arm, xd, and consequently the resistance moment of 
 the beam. When the joists are spaced not less than 3 ft. on 
 centres the strength of the joist may be safely computed by 
 allowing A to equal the entire sectional area of the concrete 
 in the T beam above the centre of the bar, assuming the top 
 of the T to be 3 ft. wide and not more than 3 ins. thick, and then 
 using formula (1) as for a rectangular beam. 
 
 Example 4. Determine the breaking weight of the centre 
 beam shown in Fig. 78, the span being 14 ft. 6 in. and the other 
 dimensions as indicated in the figure. 
 
 In this example the area of concrete in the T above centre 
 of bar =3"X7" + 36"X 2^ = 111 sq. ins. Area of bar = .5625, 
 
 and F'=-^ = 197. The value of x for this value of F' , for 
 
 Ransome bars, we find by interpolation in the table to be .873. 
 Then, by formula (1), 
 
 If we neglect the flanges of the T, and consider the beam to 
 be 3 ins. wide and 9J ins. deep to centre of bar, A will equal 
 23.5 and F'=50. Using the corresponding value for x (.451), 
 
FORMULAS FOR REINFORCED CONCRETE SLABS. 86% 
 
 we obtain for W only 8,170 Ibs., and with so small a value for 
 F it would be necessary to use very rich concrete. 
 
 It will be seen that the actual load required to break the beam 
 was more than twice that obtained by the formula for T section. 
 This was probably due in part to the fact that the ends of the 
 beam were built into concrete-steel girders and the whole con- 
 struction was monolithic. 
 
 Caution in the Use of T Beams, or Paneled Floor 
 Construction. The above rule for computing the strength 
 of T beams is based on the supposition that the concrete for 
 the beam and slab is deposited at the same time so as to give 
 a truly monolithic construction. 
 
 Uis&j 
 
 i i 
 
 
 
 I 
 
 j 
 
 ^ Wires or Fabric 
 
 
 ! i 
 
 
 i 
 
 
 
 
 
 1 1 
 
 
 
 
 
 
 
 y y. 
 
 Tension Bau 
 
 
 y 
 
 
 Fig. 77 
 
 If the concrete in the beam and slab is not put in at the 
 same time so as to be perfectly united, then the slab will slip 
 on the joist, and the effective depth of the latter will only be 
 the distance from the bottom of the slab to the centre of the 
 bar. In making floors of a section like that shown in Fig. 77, 
 when stopping work, even for a few minutes, the concrete should 
 be continued to the farther side of the beam and stopped with 
 a bevel, as shown by the dotted lines B, B, supposing that 
 the work was commenced on the side towards A. 
 
 In building these floors, the forms or centering for the entire 
 floor, and also the reinforcement, should be put in place before 
 any concrete is deposited, and the work of placing the concrete 
 should be prosecuted day and night, without interruption, if 
 possible. The author also recommends that stirrups be used 
 in the beams, not only to assist in resisting the shearing stress, 
 but to tie the joist more securely to the slab. 
 
 Formulas for Floor Slabs. Formulas (1-4) can be 
 used for floor slabs by considering the slab as made up of rect- 
 angular beams, but as the load on floors is generally computed 
 at a certain amount per square foot, formulas (5) and C6) will 
 be found more convenient for computing the strength of a 
 
868/i FIRE-PROOF AND INCOMBUSTIBLE FLOORS. 
 
 given floor, or for finding the required value of d to support a 
 given load with a given span. 
 (5) 
 
 Spacing of bar j = oF' r , 
 . in ins. j d '" (7) 
 
 in which w denotes the breaking load per square foot, including 
 the weight of the slab; the other letters as given on page 868. 
 The value used for F should depend upon the percentage and 
 kind of steel, the same as for beams, and the same limitations 
 should be used in regard to the maximum percentage of steel 
 for different mixtures of concrete. 
 
 On account of the fact that floor slabs when tested in actual 
 construction usually develop a strength about twice that which 
 would be obtained by formula (5), using the value for F given 
 on page 8686, the author believes that the values for F given in 
 the table may be increased fully 50 per cent. When the slabs 
 are built between I beams with haunches resting on the lower 
 flange of the beam, and if the reinforcing bars or cables are 
 continuous over the top of the beams or are hooked over the 
 flanges and are bent down, so that the top of the slab is only 
 1 in. above the top of the I beam, as in Figs. 38, 42, and 49, with 
 haunches extending to the bottom flanges, then twice the 
 value of F given in the table may be used. In fact in no other 
 way can the loads which have actually been carried by such 
 constructions be accounted for. 
 
 If, on the other hand, the slab is merely laid on the beams, 
 as would be the case with a stone slab, then the values for 
 F given in the table should be used. 
 
 In making up the tables for the strength of floor slabs given 
 in their 1904 catalogue the St. Louis Expanded Metal Company 
 give the safe load at twice that which would be obtained by 
 their formulas. 
 
 Example 5. What is the safe carrying load per square foot 
 for a floor slab of 1:7 gravel concrete 5 ins. deep to centre of 
 bars, built between 15-in. I beams 12 ft. apart, the bottom of 
 the slab being haunched from the lower flanges of the beam 
 and the reinforcement consisting of J-in. Ransome twisted bars 
 spaced 8 ins. on centres? 
 
 Ans. In this example d = 5, a = .25 for every 40 sq. ins. of 
 
 40 
 concrete, and 1?' = = 160. For F' = 160 the value of F 
 
FORMULAS FOR REINFORCED CONCRETE SLABS. SSSi 
 
 in the table is 256. Increasing this one half we have 384. 
 
 12V ^84- V 2^ 
 Then w (formula 5) = - ^ =800 lbs.= breaking load 
 
 per square foot. Subtracting from this the weight of the 
 floor per square foot , (the total thickness of slab should be at 
 least 5f ins.), which would be about 70 Ibs., we have 730 Ibs. as 
 the breaking superimposed load. Using a factor of safety of 4, 
 we have 182 Ibs. per square foot for the safe carrying load of 
 the floor. 
 
 Example 6. The specifications for a certain building require 
 that the floors shall be formed of reinforced concrete slabs 
 built between 18-in. beams, 15 ft. 6 ins. on centres, and that 
 the said floors shall be capable of sustaining a superimposed 
 load of 200 Ibs. per square foot with a factor of safety of 4, 
 Using J-in. Ransome twisted bars for reinforcement, what 
 should be the thickness of the concrete and the spacing of 
 the bars to meet this requirement? 
 
 Ans. The breaking load per square fpot must evidently 
 be four times 200=800, plus the weight of the complete floor, 
 which we will assume at 70 Ibs., making 870 Ibs. 
 
 The most satisfactory percentage of reinforcement of floor 
 slabs for Ransome bars is between .6 and .8 per cent. In this 
 case we will assume a percentage of .71, corresponding to 
 F' = I40 and F = 270. Increasing F by 50 per cent, we have 
 405. For L we will use the distance between flanges of beams, 
 or 15 ft. Substituting these values of w, F, and L in formula (6), 
 
 The spacing of tne J-in. bars to give the assumed percentage 
 
 we find, from formula (7), =' = 5^ ins. 
 
 o.oTo 
 
 By using a rich concrete and making ^'=80 we can increase 
 F to 543, which will give d = 5J ins. For this percentage it will 
 
 be better to use f-in. rods, which must be spaced * =-= 
 
 o.o 
 
 = 5.7 ins. on centres. 
 
 The total thickness of the slab should be d + f ins. 
 
 Slabs of Cinder Concrete. For floor slabs of 1:2:5 
 cinder concrete the author would recommend the following 
 values for F and F', the value for F to be increased the same as 
 for gravel concrete under like conditions. 
 
868j FIRE-PROOF AND INCOMBUSTIBLE FLOORS. 
 
 For medium steel F' = should be in the neighborhood of 
 a 
 
 180, and F may be taken at 144. 
 
 For twisted or corrugated bars with high elastic limit F' 
 should be approximately 225, and F may be taken at 138. 
 
 In obtaining the value of F', b should be taken as the distance 
 between centres of bars in inches. Thus with J-in. square bars 
 spaced 3J ins. apart and set 4J ins. below the top of the slab, 
 
 QlV/41 
 
 a = .0625, 6=3i ins., d=4J ins., and F' = 4 Q ^ =234. 
 
 Test of Paneled Floors. On Sept. 23 and 24, 1902, 
 tests were made by the Turner Construction Company of New 
 York on two floor sections having a cross-section as shown in 
 Pig. 78 and a clear span between bearings of 14 ft. 6 ins. 
 
 YWW ,wWm/W 1 1 ,M 
 
 ytfb Bars, ^apart 
 
 =^tfj 
 
 Fig. 78 
 
 One section was constructed of gravel concrete consisting 
 of one part Lehigh Portland cement, two parts clean sharp 
 sand, and four parts clean gravel running in size from -J to 
 j in. diameter. The other section was constructed of the same 
 proportions of cement and sand with four parts f-in. screened 
 trap-rock. The metal reinforcement was the same in each. 
 
 The concrete was mixed by hand with sufficient water to 
 flush readily to the surface in tamping and would be termed 
 a "wet mixture." . 
 
 The load was applied by piling pig iron on two 12-in. planks 
 placed over the centre beam and extending the full length of 
 the span. 
 
 Assuming that the centre beam had a T section 3 ft. wide 
 at the top, the ratio of concrete to metal reinforcement, figuring 
 only the concrete above centre of bar, was as 111:. 5625, or 
 T J T , or for a beam 3"X9i" as ^. 
 
 The first observable cracks occurred in the gravel section 
 between loads 28,652 Ibs. and 30,952 Ibs., and in the stone 
 section at 25,477 Ibs., which would give 1606 and 1364 as values 
 
REINFORCING BARS. 
 
 869 
 
 for F respectively for the middle beam of the two sections, 
 taking b at 3 ins. and d at 9.5 iris. 
 
 At 32,784 Ibs. the shearing cracks in the stone section had 
 opened up \ to -J- in.; this load remained on the beam for four 
 days without further signs of failure. The sections were thirty- 
 five days old at the time of test. 
 
 Data for Estimating Area of Reinforcing 1 Bars. 
 
 The sectional area for round or square bars may be readily 
 obtained from the table on page 1350. 
 
 The sectional area for the standard gauge of wire is given on 
 page 1349, and the sectional area of small channels on page 300. 
 
 The following table gives the net sectional areas and weights 
 of the 
 
 JOHNSON CORRUGATED BARS. 
 
 Nominal Size of Bat. 
 
 Net Section. 
 
 Weight per Foot. 
 
 J inch 
 
 }t t 
 
 0.18 sq. in. 
 0.37 ** " 
 
 0.641bs. 
 1.35 *' 
 
 n 
 
 0.55 " " 
 
 1.95 " 
 
 i " 
 
 0.70 V " 
 
 2.70 " 
 
 H " 
 
 1.07 " " 
 
 4.00 " 
 
 DIMENSIONS AND WEIGHT OF THACHER BAR. 
 
 Nominal Size of Bar. 
 
 Net Section. 
 
 Weight per Foot. 
 
 J inch 
 
 .047 sq. in. 
 
 0.161bs. 
 
 f 
 
 
 .10 
 
 t 
 
 
 0.34 
 
 
 
 
 .18 
 
 
 
 0.61 
 
 
 J 
 
 
 .28 
 
 
 
 0.95 
 
 
 J 
 
 
 .41 
 
 
 
 1.39 
 
 
 J 
 
 
 .55 
 
 
 
 1.87 
 
 
 1 
 
 
 .71 
 
 
 
 2.42 
 
 
 H 
 
 
 1.10 
 
 
 
 3.74 
 
 
 ft 
 
 
 1.56 
 
 
 
 5.30 
 
 
 The Thacher bar was invented and patented by Mr. Edwin 
 Thacher of the Concrete-Steel Engineering Company. The bars 
 are manufactured hot from round steel, and are elongated from 
 8 per cent, to 10 per cent. The area and weight per foot are 
 therefore about 90 per cent, of the original bar. This bar can be 
 purchased from the Concrete Steel Engineering Company, Park 
 Row Building, New York, by parties desiring to use it. 
 
870 FIRE-PROOF AND INCOMBUSTIBLE FLOORS. 
 
 Stirrups in Concrete-steel Beams. 
 
 As mentioned on page 855, Mr. Hennebique, and the engineers 
 working under his patents, claim that the ultimate strength 
 of concrete-steel beams is materially increased by inserting 
 vertical stirrups, as shown in Fig. 66, and all beams and girders 
 built on the Hennebique system contain these girders. An 
 article by Capt. John S. Sewell, in the Engineering News of 
 Jan. 29, 1903, advocating the use of stirrups and somewhat 
 criticising American engineers in not recognizing their value 
 has led to quite a little discussion regarding the value or necessity 
 of stirrups.* 
 
 The advocates of stirrups (among whom are Engineers A. L. 
 Johnson, J. W. Schaub, and J. Kahn) claim that they are 
 necessary to resist the vertical shearing stress, and especially 
 near the ends of the beams. 
 
 Mr. Edwin Thacher, on the contrary, believes "that all 
 stirrups passing around the bars and leading upwards are 
 utterly useless, also all bends in bars, except to prevent slipping." 
 Unfortunately, there is not sufficient data from actual tests 
 to conclusively prove or disprove the theory that stirrups are 
 necessary. Mr. Schaub has probably stated the case about 
 right, in the following sentence: "It should be explained that 
 the use of stirrups is necessary only for short and deep beams, 
 and even then it is a question if the desired result cannot be 
 obtained in a much simpler way." 
 
 Stirrups, however, add but a trifle to the cost of the beams, 
 and, if not too large, can certainly do no harm. 
 The sectional area required for the stirrups (theoretically) 
 
 may be found by the following analysis 
 
 and formulas, published by Mr. J. W. 
 
 Schaub in the Engineering News of 
 
 April 16, 1903. 
 
 In Fig. 79, let A denote the sec- 
 
 tional area of the metal in a hori- 
 
 zontal plane, then the area of metal 
 Fig. 79 required in the stirrups at any point 
 
 becomes 
 
 * See Engineering News of March 12, 19, 26, April 16, 1903; also of Jan. 
 21 and Feb. 18, 1904. 
 
STIRRUPS IN CONCRETE-STEEL BEAMS. 871 
 
 The curve a c b is a parabola, with its vertex at c. 
 If the area is to be found at every foot of the beam (x 2 x l ) 
 = 1, equation (1) becomes 
 
 y 2 y 1 = ~-j-'\ 1 X * Xl [ =area required in stirrups. 
 Area in stirrups, 1 ft. from support = r- { 1 -y ! ; 
 
 Area in stirrups, 2 ft. from support = -y- -j 1 j M 
 
 4A f 71 
 Area in stirrups, 3 ft. from support =-y- j 1 j \ ; 
 
 and so forth. 
 
 In a recent example, the metal in the horizontal plane was 
 0.03655 sq. in. per 1-inch width of beam. As the beam was 
 7 ft. long, I was 7 ft. The metal required in the stirrups, 1 ft. 
 from the end was 
 
 4X0.03655 4 er 14nch width of beam. 
 
 =() Q12 gq 
 
 The metal required in the stirrups 2 ft. from the end was 
 found in a similar manner. 
 
 Buckled Plates. Steel plates, buckled as shown by 
 Fig. 80, are frequently used for the floors of bridges, and might 
 
 Fig. 80 
 Buckle Plate. 
 
 be used in buildings where great strength is required. These 
 plates, however, are much more expensive than any of the 
 fire-proof floors described on the preceding pages. When 
 used for the floors of bridges the plates are usually covered 
 with concrete and asphalt, or concrete and stone paving. 
 Buckle plates were formerly, and are yet, made with a single 
 buckle to a plate, but are now more commonly made in long 
 
872 FIRE-PROOF AND INCOMBUSTIBLE FLOORS. 
 
 lengths, 16 to 20 ft., having several buckles or domes in each 
 plate. 
 
 The width of the long plates varies from 3 ft. to 5 ft. and 
 the thickness from i to f inch. The thickness should never 
 be less than J in., while T 5 C in. is the usual thickness for bridge 
 floors. Plates such as is shown by Fig. 80 are usually supported 
 along the two longitudinal edges, and at the extreme ends, 
 and should be bolted or riveted to the supports, with f-inch or 
 J-inch bolts or rivets, spaced not over 6 ins. centres. If the 
 ends of the buckle plates do not rest on supports they should 
 be spliced with T-irons or a pair of angles riveted together. 
 
 There has not yet been devised a reliable formula by which 
 the strength of buckled plates may be computed. The follow- 
 ing table, taken from the manual of the Passaic Rolling Mill 
 Company, however, is believed to have an ample factor of 
 safety : 
 
 TOTAL SAFE UNIFORMLY DISTRIBUTED LOADS, IN 
 POUNDS, ON BUCKLE PLATES. 
 
 Size of 
 Plate. 
 
 30" 
 Square. 
 
 36" 
 Square. 
 
 42" 
 Square. 
 
 48" 
 Square. 
 
 54" 
 Square. 
 
 . 
 
 60" 
 Square. 
 
 Thickness 
 in Inches. 
 
 2 Inches, Depth of Buckle. 
 
 t 
 
 11,000 
 16,400 
 22,200 
 
 9,100 
 13,800 
 19,400 
 
 7,300 
 11,800 
 17,000 
 
 6,000 
 
 10,000 
 14,700 
 
 5,000 
 8,600 
 12,700 
 
 4,200 
 7,300 
 11,200 
 
 
 2 Inches, Depth of Buckle. 
 
 1 
 
 13,800 
 20,500 
 27,600 
 
 11,300 
 17,300 
 24,300 
 
 9,100 
 14,800 
 21,300 
 
 7,500 
 12,500 
 18,400 
 
 6,300 
 10,700 
 15,900 
 
 5,300 
 9,200 
 13,900 
 
 If the buckles are inverted, i.e., suspended, the safe loads will 
 be increased from 2 to 4 times that given in the above table, 
 depending upon the size of the plate. Buckled plates are 
 preferably made of soft steel. [For further information regard- 
 ing these plates, see the manuals of the Carnegie Steel Com- 
 pany, the Passaic Rolling Mill Company, and the Pencoyd Iron 
 Works.] 
 
FRAMING FOR FIRE-PROOF FLOORS. 
 
 873 
 
 Trough Plate or Corrugated Flooring. Trough 
 plates, riveted together, as in Fig. 81, are also used for the 
 
 Fig. 81 
 
 floors of bridges, and occasionally in heavy warehouse floors. 
 Several varieties of these plates are manufactured by the 
 Carnegie Steel Company, and the Pencoyd Iron Works. Safe 
 loads as high as 3700 Ibs. per square foot, with a 6-ft. span, 
 may be obtained by the use of these plates. 
 
 Fig. 82 shows a partial section of a trough floor made by the 
 
 , 
 
 Fig. 82 
 
 Youngstown Iron and Steel Roofing Company, from Nos. 16, 18, 
 and 20 sheet steel. With a span of 10 ft., the No. 16 gauge 
 will carry a safe load of 130 Ibs. per square foot in addition to the 
 weight of the floor, and with a factor of safety of about 6. 
 
 Steel Framing 1 for Fire-proof Floors. Before 
 the framing plans of a building can be made, it is necessary 
 to decide, in a general way, upon the system of floor construc- 
 tion or fireproofing that will be employed; thus if any of the 
 long-span systems such as the Hercularieum, Johnson, arid 
 many of the concrete systems is to be adopted the girders 
 should be spaced so that the floor construction will span be- 
 tween them, without floor beams, Avhile if an ordinary flat tile 
 
874 FIRE-PROOF AND INCOMBUSTIBLE FLOORS. 
 
 arch is to be used, floor beams will be required, spaced from 
 5J to 9 ft. apart, and these beams must be supported by girders. 
 If segmental tile arches are to be used deep beams or girders 
 should be provided, spaced from 12 to 18 ft. apart. Fig. 83 
 
 r- 111 
 
 T-Column f 
 
 1 Girder [ 
 
 1 r r 
 
 \ 
 
 
 C^ Tf 
 
 
 
 \ 
 
 
 1 
 
 
 ir* 
 
 u 
 
 
 s. 
 
 Tie Rod 
 
 
 
 1 
 
 4 i 
 
 
 
 
 - 
 
 I_ 6 V , 
 
 1 
 
 ._ 6 V- , 
 
 / 
 
 - 
 
 11 
 
 '1 J- 
 
 Girder 
 
 J pi 
 
 I 7 
 
 i 
 
 I ^ 
 
 J -t 
 
 i 1 
 
 f? 
 
 Fig. 83 
 
 Typical steel framing for short span arches. 
 
 shows a typical framing plan for a single-floor panel, where 
 end-construction flat arches are to be used, and Fig. 84 for a 
 long-span segmental arch. For long-span tension systems, the 
 framing would be as hi Fig. 84, without the tie-rods. 
 
 When there are no floor beams, a strut beam should be 
 riveted between the columns, as in Fig. 84, to hold the latter 
 in place during erection and to stiffen the building. 
 
 It should be remembered that with floor beams spaced not 
 over 7 ft. from centres, almost any system of floor construction 
 may be employed, while if the floor beams are omitted, one must 
 select from but a few systems. 
 
 Personally, the author favors the short-span systems for 
 
FRAMING FOR FIRE-PROOF FLOORS. 
 
 875 
 
 tall buildings or where heavy loads must be supported, for the 
 reasons set forth 011 p. 788. 
 
 With any form of filling between beams or girders, less steel 
 will be required for moderate spans of beams or girders than 
 when they are excessive. 
 
 Steel Clips for Fastening Angle- or Tee-bars to I-- 
 beams and Channels, Several years ago Mr. H. A. Streeter, 
 of Chicago, patented a steel clip for connecting angles and tees 
 
 r-F- 
 
 Column 
 
 9 Girder 
 
 !l 
 
 1 ^ 
 
 iii 
 
 T 
 
 T 
 
 Tie "Rod 
 
 
 
 i 
 
 a 
 
 1 
 
 , 1 
 
 S * 
 "S 
 
 u Ir 
 
 
 
 
 
 Girder 
 
 __, 
 
 T P 
 
 
 HIT 
 
 ' 
 
 
 lH= ' 
 
 IT 
 
 T^ 1 
 
 Fig. 84 
 
 Typical framing for long span constructions. 
 
 to I-beams without drilling or bolting, and they have been 
 extensively used, particularly in roof construction and for 
 suspended ceilings. Besides the saving effected in doing away 
 with the drilling and bolting required' by the old method, they 
 also enable the connections to be more quickly made and 
 afford an easy method of adjusting T-bars to any width of 
 tile. Several forms of clips with their application are illustrated 
 by Figs. 85 and 86. Other forms are also made on the same 
 principle. 
 
876 FIRE-PROOF AND INCOMBUSTIBLE FLOORS. 
 
 The safe load which may be supported by clips like N or NN, 
 1J ins. wide, is as follows: 
 
 No. 12 gauge=..OSOS in., 600 Ibs. 
 No. 14 gauge=.0641 in., 414 Ibs. 
 No. 16 gauge=.0508 in.', 215 Ibs. 
 
 No. 14 gauge is generally used, the material being specially 
 made for this purpose. The strength of the clip may be in- 
 creased by increasing the width. 
 
 As Furnished 
 
 The Outstanding Flanges 
 
 of Clip to be bent around 
 
 , Beam when applied 
 
 Clip as Furnished 
 Fig. 85 
 Clips for fastening tees and angles to beams and channels. 
 
 Computations for the Steel Framing. The com- 
 putations for the steel beams and girders of a fire-proof floor 
 are very much the same as for a wooden floor, viz., first esti- 
 mating the load or loads which any given beam will be required 
 to support and then finding the necessary size of beam to sup- 
 port the load. The dead load for any fire-proof floor may 
 
FRAMING FOR FIRE-PROOF FLOORS. 
 
 877 
 
 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 weight 
 of beams, weight of fireproofing, including all concrete filling, 
 weight of plastering, furring and lathing, nailing strips and 
 flooring. 
 
 The live loads may be estimated by means of the data given 
 in Chapter XXI. 
 
 Example. The best arrangement for the posts in a retail 
 store is 18 ft. on centres in one direction, and 18 ft. 6 ins. in 
 
 A's^Furnished 
 
 Clips' imposition, 
 
 N 
 
 Fig. 86 
 
 Clips for suspending tees, angles or channels below I-beams and channels. 
 Clip N may be used for suspending any kind of a section from a beam. 
 
 the other. It is decided to run the girders as shown by Fig. S3, 
 and to put a beam opposite each column and two between; 
 what size of beams and girders will be required, using an ordi- 
 nary end-arch construction between the beams? 
 
 Ans. From the table on page 792 we find that the least depth 
 of arch which it is desirable to use, is 10 in., but as we will prob- 
 ably have to use 12-inch beams it will be better to figure on a 
 12-inch arch, as this will give less filling on top. The weight of 
 the 12-inch arch will be about 39 Ibs. per square foot. We 
 shall probably require 2 ins. of concrete filling on top, which 
 will weigh 16 Ibs., arid 1J ins. of light filling between nailing 
 strips, weighing, say, 9 Ibs. The flooring and nailing strips will 
 
878 FIRE-PROOF AND INCOMBUSTIBLE FLOORS. 
 
 weigh about 4 Ibs., the plastering on ceiling 5 Ibs., and we must 
 allow at least 6 Ibs. per square foot for the weight of the beams 
 themselves. These make a total dead weight of 79 Ibs. per 
 square foot. The live load for a retail store should be taken 
 at 150 Ibs. per square foot making a total load per square foot 
 on the beams of 229 Ibs. The total load that each beam must 
 be capable of supporting wiU be 6J'X18'X229 Ibs. = 13.4 tons, 
 which is assumed to be uniformly distributed. From the 
 table, p. 516, we find that this load, with a span of 18 ft., will 
 require either a 12-inch, 50-lb. beam, or a 154nch, 42-lb. beam. 
 The latter will be both stronger and cheaper, but will increase 
 the thickness of the floor by 3 ins. and require additional filling. 
 
 The girder must support two concentrated loads of 13.4 tons 
 each. On p. 512 it is stated that when a beam supports two 
 equal loads applied one-third of the span from each end, the 
 equivalent uniformly distributed load may be found by multi- 
 plying one load by 2. Multiplying 13.4 by 2f we have 35.73 
 tons as the equivalent distributed load on the girder, which 
 slightly exceeds the strength of a 20-inch 65-lb. beam. As it 
 is allowable to make some reduction in the load on the girder 
 for necessary aisles, we will be perfectly safe in using this size 
 of beam. 
 
 If instead of using tile arches between beams, 6J ft. apart, 
 We conclude to use the Herculaneum or Johnson construction 
 spanning from girder to girder, we should frame our floor as in 
 Fig. 84. For this span we would require 10-in. tile, weighing 
 55 Ibs. per foot. Allowing 8 Ibs. for 1 in. of concrete, 9 Ibs. for 
 filling, 4 Ibs. for flooring and strips, and 5 Ibs. for plastering, 
 we have 81 Ibs. as the dead load per square foot (we have 
 added nothing for weight of girder, as this will be fully offset 
 by portions of floor not loaded). The live load per square foot 
 will be 150 Ibs. as before, and the total load to be supported 
 by the girder 18 / Xl9 / 6"X231 lbs.= 40.5 tons, which will re- 
 quire a 24-inch 80-lb. beam; hence by this arrangement we 
 increase the weight of our girder by only 15 Ibs. per lineal foot 
 and save the weight of the floor beams, except that a 6-inch 
 strut beam should be placed between the columns as in Fig. 84. 
 The calculations for any other floor construction are made 
 exactly as above, the variations being only in figuring the 
 dead weight of the construction. 
 
TABLES FOR FLOOR BEAMS. 
 
 879 
 
 Tables for Floor Beams. 
 
 It is a difficult matter to prepare tables showing the size of 
 steel beams required for fire-proof floors that may be generally 
 used, for the reason that such beams are often irregularly spaced, 
 and because of the wide variation in the dead loads. The 
 following tables, however, may be used in making approxi- 
 
 TABLE I. SIZE AND WEIGHT OF I-BEAMS FOR FLOORS 
 IN OFFICES, HOTELS, AND APARTMENT-HOUSES. 
 
 Total load, 120 pounds per square foot. 
 
 Span of 
 Beams 
 in Feet. 
 
 Distance between Centres of Beams. 
 
 4^ Feet. 
 
 5 Feet. 
 
 &A Feet. 
 
 6 Feet. 
 
 7 Feet. 
 
 
 ins. Ibs. 
 
 ins. Ibs. 
 
 ins. Ibs. 
 
 ins. Ibs. 
 
 ins. Ibsw 
 
 10 
 
 6 I2li 
 
 6 12^ 
 
 6 12^ 
 
 6 12^ 
 
 7 15 
 
 11 
 
 6 12^ 
 
 6 12M 
 
 7 15 
 
 7 15 
 
 7 15 
 
 12 
 
 6 1254 
 
 7 15 
 
 7 15 
 
 7 15 
 
 8 18 
 
 13 
 
 7 15 
 
 7 15 
 
 7 15 
 
 -8 18 
 
 8 18 
 
 14 
 
 7 15 
 
 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^ 
 
 19 
 
 9 21 
 
 10 25 
 
 10 25 
 
 10 25 
 
 12 313^ 
 
 20 
 
 10 25 
 
 10 25 
 
 12 31^ 
 
 12 31^ 
 
 12 3U 
 
 21 
 
 10 25 
 
 12 31K 
 
 12 31^ 
 
 12 3iy 2 
 
 12 31^ 
 
 22 
 
 10 25 
 
 12 3m 
 
 12 31^ 
 
 12 3iy 2 
 
 15 42 
 
 23 
 
 12 31V 
 
 12 31^ 
 
 12 3l}4 
 
 12 31^ 
 
 15 42 
 
 24 
 
 12 31H 
 
 12 31 ^ 
 
 12 31^ 
 
 15 42 
 
 15 42 
 
 25 
 
 12 3VA 
 
 12 3iy 2 
 
 15 42 
 
 15 42 
 
 15 42 
 
 TABLE II. SIZE AND WEIGHT OF I-BEAMS FOR 
 FLOORS IN RETAIL STORES AND ASSEMBLY 
 ROOMS. 
 
 Total load, 200 pounds per square foot. 
 
 Span of 
 
 Distance between Centres of Beams. 
 
 .Beams 
 in Feet. 
 
 4^ Feet. 
 
 5 Feet. 
 
 &A Feet. 
 
 6 Feet. 
 
 7 Feet. 
 
 
 ins. Ibs. 
 
 ins. Ibs. 
 
 ins. Ibs. 
 
 ins. Ibs. 
 
 ins. Ibs. 
 
 10 
 
 7 15 
 
 7 15 
 
 7 15 
 
 8 18 
 
 8 18 
 
 11 
 
 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 31M 
 
 15 
 
 9 21 
 
 10 25 
 
 10 25 
 
 12 31^ 
 
 12 31^ 
 
 16 
 
 10 25 
 
 10 25 
 
 12 31 1 A 
 
 12 31J^ 
 
 12 31}4 
 
 17 
 
 10 25 
 
 12 3U4 
 
 12 31^ 
 
 12 31^ 
 
 12 40 
 
 18 
 
 12 31^ 
 
 12 31^ 
 
 12 31% 
 
 12 40 
 
 12 40 
 
 19 
 
 12 31V4 
 
 12 31H 
 
 12 40 
 
 12 40 
 
 15 42 
 
 20 
 
 12 31^ 
 
 12 40 
 
 12 40 
 
 15 42 
 
 15 42 
 
880 FIRE-PROOF AND INCOMBUSTIBLE FLOORS. 
 
 TABLE III. SIZE AND WEIGHT OF I-BEAMS FOR 
 FLOORS IN WAREHOUSES. 
 
 Total load, 270 pounds per square foot. 
 
 Span of 
 Beams 
 
 Distance between Centres of Beams. 
 
 
 
 
 
 
 in Feet. 
 
 4% Feet. 
 
 5 Feet. 
 
 5% Feet. 
 
 6 Feet. 
 
 Q% Feet. 
 
 
 ins. Ibs. 
 
 ins. Ibs. 
 
 ins. Ibs. 
 
 ins. Ibs. 
 
 ins. Ibs. 
 
 10 
 
 8 18 
 
 8 18 
 
 8 18 
 
 9 21 
 
 9 21 
 
 11 
 
 8 18 
 
 9 21 
 
 9 21 
 
 9 21 
 
 10 25 
 
 12 
 
 9 21 
 
 9 21 
 
 10 25 
 
 10 25 
 
 10 30 
 
 13 
 
 10 25 
 
 10 25 
 
 10 25 
 
 12 31% 
 
 12 31% 
 
 14 
 
 10 25 
 
 10 30 
 
 12 31^ 
 
 12 31% 
 
 12 31% 
 
 15 
 
 12 31% 
 
 12 31^2 
 
 12 31^ 
 
 12 31% 
 
 12 40 
 
 16 
 
 12 31^ 
 
 12 31% 
 
 12 31^| 
 
 12 40 
 
 12 40 
 
 17 
 
 12 31% 
 
 12 40 
 
 12 40 
 
 12 40 
 
 15 42 
 
 18 
 
 12 40 
 
 12 40 
 
 15 42 
 
 15 42 
 
 15 42 
 
 19 
 
 12 40 
 
 15 42 
 
 15 42 
 
 15 42 
 
 15 42 
 
 20 
 
 15 42 
 
 15 42 
 
 15 42 
 
 15 45 
 
 15 55 
 
 mate 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 load does not exceed the 
 value given in the headings. The total load should include 
 sufficient allowance for the weight of any partitions that the 
 floor beams may be called upon to support. 
 
 Tie-rods for Brick, Tile or Concrete Arches. 
 
 As previously stated, tie-rods are required to prevent the 
 supporting beams, channels, or walls, from being pushed apart 
 whenever an arch construction of any kind is used. The 
 tie-rods should be located in the line of thrust of the arch, 
 which is ordinarily below the centre of the beam, and in some 
 cases near the bottom flange. 
 
 As a rule, tie-rods are proportioned and spaced by some 
 "thumb rule" 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 thrust of the arch should be computed and the rods pro- 
 portioned accordingly. For interior flat tile arches, the follow- 
 ing rule can usually be safely followed: 
 
 For spans of 6 ft. and under, use f-inch rods spaced about 
 5 ft. apart; for 7-ft. spans, use f-inch rods, 5 ft. centre to centre, 
 and for a 9-ft. span, f-inch rods, 4 ft. centre to centre. The 
 
TIE-RODS FOR FLOOR ARCHES. 881 
 
 spacing of the rods should not exceed twenty times the flange 
 width of the supporting beam or channel. The horizontal 
 thrust of an arch may be found by the following formula: 
 
 T= 
 
 in which T pressure or thrust in pounds per lineal foot of arch; 
 w=load on arch in pounds per square foot, uniformly 
 
 distributed; 
 
 L=span of arch in feet; 
 
 72= rise of segmental arch, or effective rise of flat arch 
 in inches. 
 
 The rise of a segmental arch is measured from the spring- 
 ing line to the soffit of the arch at the centre. For flat hollow- 
 tile arches, the effective rise may be figured from the top of 
 the beam flange to the top of the tile. As the tiles usually 
 project from 1J to 2 ins. below the bottom of the beam, the 
 effective rise will be from 2 to 2J ins. 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 load. 
 
 Having found the thrust of the arch, the spacing of the rods 
 (of any particular size) may readily be determined by dividing 
 the safe load given for that size of rod in the table on p. 340 
 (allowing 15,000 Ibs. 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 p. 877. 
 
 Ans. The depth of the tile arch is 12 ins., the dead load 
 79 Ibs., and the live load is assumed at 150 Ibs. The span 
 between beams is 6J ft. Then for the interior arches, w = 
 
 150 Ibs., B=12-2J=9i ins. and L=6J, and r= 
 
 = 1000 Ibs. The strength of a f-inch rod, not upset, at 15,000 Ibs. 
 is (from p. 340) 4500 Ibs. Dividing by 1000 we have 4J ft. 
 as the spacing. 
 
 The strength of a J-inch rod is given as 6300 Ibs., which would 
 admit of a spacing of 6.3 feet. 
 
 For the outer spans, w should be taken at 150 + 79=229 Ibs., 
 
 when T will equal 3X2 ^f 2 ' 25 =1526 Ibs. 
 
882 FIRE-PROOF AND INCOMBUSTIBLE FLOORS. 
 
 For this thrust we should use f-inch rods spaced about 4 ft. 
 2 ins. centre to centre. When channels are used to support the 
 outer edge of the floor the rule that the spacing of the rods 
 shall not exceed twenty times the flange width should be kept 
 in mind. 
 
 The formula for T applies to segmental arches of bflck or 
 concrete as well as to those of hollow tile. 
 The Kahn Trussed Bar. Since the foregoing chapter 
 was electrotyped the Kahn system of rein- 
 forced concrete construction has been placed 
 before the public, and as it is a system 
 possessing much merit, some mention of it 
 seems necessary. The system differs from 
 the ordinary tension-bar systems in provid 
 ing reinforcement in a vertical plane, as wel] 
 as in a horizontal one. It is in effect a 
 stirrup system, with the stirrups forming a 
 part of the bar. This is accomplished by 
 using a bar of the cross-section shown by the 
 marginal figure and shearing upwards into 
 an inclined position the web on both sides 
 of the main body, as shown in the per- 
 spective view. 
 
 It is claimed that hi all tests that have 
 b een ma de with this bar, the beam, or 
 slab, has failed by pulling the steel in two 
 at the centre of the slab, which is not 
 usually the case with plain or twisted 
 bars. 
 
 The deflection of beams reinforced with 
 this bar also appears to be less than where 
 plain bars are used. 
 
 The Kahn trussed bar is controlled by 
 the Trussed Concrete Steel Co. of Detroit, 
 Mich., who publish a catalogue explaining 
 its application and describing a number of 
 tests. 
 
 The bar is made in four sizes, with cross- 
 sectional areas of 0.38, 0.78, 1.42, and 2.0 
 square inches, and of any desired lengths. 
 It can be purchased by responsible parties. 
 
ROOF TRUSSES. 883 
 
 CHAPTER XXV. 
 ROOF TRUSSES. 
 
 TYPES OF WOODEN AND STEEL TRUSSES THEIR 
 LIMITATIONS AND REQUIREMENTS. 
 
 WHENEVER it is required to roof a.. hall, room, or building 
 with a clear span of more than thirty feet, it is generally neces- 
 sary to use one or more trusses to support the roof and ceiling. 
 
 Definitions. By the term "truss" as used in this and the 
 following chapters, the author means "a framework supported 
 only at the ends (or in the case of a cantilever, near the centre), 
 and so designed that it cannot suffer distortion without either 
 crushing or pulling apart one of the members of which it is 
 composed, and will exert only a vertical pressure on the walls." 
 A true truss does not depend upon the rigidity of the joints to 
 maintain its equilibrium. 
 
 A roof truss is a form of truss designed for the especial pur- 
 pose of supporting a roof, although it may also support the 
 ceiling below and perhaps a gallery or one or more floors. 
 
 Roof trusses are or should be designed upon the same prin- 
 ciple as other trusses, the difference between a roof truss and 
 a bridge truss being due to the difference in the shape of the 
 truss and the character of the load to be supported, rather than 
 in the mechanical principles involved. 
 
 By wooden trusses is meant trusses built principally of wood, 
 but having iron or steel rods for some of the tension members, 
 the term being used in distinction from trusses built wholly 
 of steel. The term " combination truss" is also sometimes 
 used to designate such trusses. 
 
 A member of a truss is any straight or curved piece of wood, 
 iron, or steel which connects two adjacent joints of a truss, and 
 which is essential to the. stability of the truss. The term 
 "piece" will also frequently be used to designate a particular 
 member. Every member of a true truss acts either as a strut 
 or a tie. 
 
884 
 
 WOODEN ROOF TRUSSES. 
 
 A tie is a member that is subject to tension; i.e., a pulling 
 stress. 
 
 A strut is a member that is subject to a compressive stress. 
 
 In wooden trusses, the struts are always made of wood, 
 but the ties may be of wood, wrought iron, or steel. 
 
 A tie-beam is a tie which is also subject to a transverse 
 strain; in wooden trusses the principal tie is usually called the 
 tie-beam, even when it has no transverse strain except that due 
 to its own weight. 
 
 A strut beam is a strut that is also subject to a transverse 
 strain. In wooden trusses, the horizontal struts are some- 
 times termed "straining beams." 
 
 The joints of a truss are the points where three or more mem- 
 bers meet, although two of the members may be formed of the 
 same piece of material. 
 
 Purlins are horizontal beams, sometimes trussed, extending 
 from truss to truss to support the rafters or ceiling joists. 
 
 Types of Wooden Trusses. 
 
 The simplest truss that can be built is that shown by Fig. 1, 
 
 which consists only of 
 two struts or rafters and 
 a tie-beam. 
 
 As the unsupported 
 length of a strut, on ac- 
 count of economy, should 
 not exceed 12 feet, such 
 a truss is not suitable 
 for spans exceeding 20 
 to 24 feet, and even for 
 
 Fig. I 
 
 a span of 20 feet there should be a centre rod, as shown by the 
 dotted line R, to support the tie-beam. To utilize this truss 
 for a greater span than 24 feet, it will be necessary to brace the 
 rafters from the foot of the centre rod as shown by Fig. 2, 
 This gives us the king-rod truss, the modern type of the old- 
 fashioned king-post truss shown by Fig. 3, which was built 
 wholly of wood except for the iron straps at S and P. 
 
 When the tie-beam supports a ceiling or attic floor, rods 
 should be inserted at R R, Fig. 2, 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 feet, and even for greater spans, but it is not an economical 
 
WOODEN ROOF TRUSSES. 
 
 885 
 
 type when the span exceeds 60 feet, on account of -the in- 
 creased length of the centre braces and rods. When there is no 
 
 Principal or 
 Rafter 
 
 Purlin 
 
 Fig. 2 
 
 King-rod Truss. For Spans up to 36 Feet. 
 
 load on the tie-beam the rods R R, Figs 4 and 5, may be 
 omitted. 
 
 Note. The names given to the trusses shown by Figs. 4 and 
 5 are original with the author. These trusses are sometimes 
 called queen trusses, but as the term queen truss commonly 
 means a truss such as is shown by Fig. 6, the author has pre- 
 
 FOR SPANS FROM 25 TO 35 FT. 
 Fig. 3 
 
 fixed the words "six-panel" and "eight-panel" to give a more 
 definite meaning to the name of the truss. 
 
 The rise of the rafter in any of the trusses, Figs. 1-5, should 
 never be less than 6 ins. in 12 ins., or 26^, and a J pitch, or a 
 
886 
 
 WOODEN ROOF TRUSSES. 
 
 rise of 8 ins. in 12 is generally the most economical. When the 
 span exceeds 36 feet, it is generally more economical to cut off 
 
 Fig. 4 
 
 Six-panel Queen Truss. For Spans from 36 to 50 Feet. 
 
 the top of the truss as in Fig. 6, which is the modern type of the 
 ancient queen-post truss. This truss is quite frequently used 
 
 Fig. 5 
 
 Eight panel Queen Truss. For Spans from 48 to 60 Feet. 
 
 for the support of deck roofs, although it may also be used for a 
 pitch roof with a ridge. When the top chord or straining beam 
 
 Fig. 6 
 
 Queen-rod Truss. For Spans from 30 to 45 Feet. 
 
WOODEN ROOF TRUSSES. 
 
 887 
 
 is more than 12 feet long, the size of the chords may be con- 
 siderably reduced by using a centre rod and a pair of braces as 
 shown in Fig. 7. The centre rod will be especially needed if 
 
 Fig. 7 
 
 For Spans from 40 to 52 Feet. 
 
 the bottom chord or tie-beam is subject to a transverse strain. 
 The centre rod should never be used, however, unless the braces, 
 B B are also added. 
 
 Counter Braces. The truss shown in Fig.' 6 differs from the 
 trusses shown in Figs. 1 to 5 in one very important respect. The 
 trusses 1 to 5 are composed of triangles, while the centre panel of 
 truss 6 is a rectangle. Now a triangle cannot be changed in 
 shape without lengthening or shortening one side, but a rect- 
 angle can be distorted without changing the length of the sides. 
 Thus in Figs. 8 and 9 
 the corresponding sides 
 have the same length in 
 both figures, hence a rect- 
 angle is not a rigid shape. F ' 9< 8 Fig * 9 
 For this reason a truss having a rectangle for the centre panel 
 and built with pin- joints would not be stable if one side of the 
 truss was more heavily loaded than the other. Thus if the 
 queen-rod truss shown in Fig. 6 was loaded with 6 tons at A, 
 and 3 tons at B } it would collapse as shown in Fig. 10 unless the 
 tie-beam was large enough to resist the pull from the rod. To 
 counteract this tendency to collapse a brace should be placed 
 in the centre panel inclined downwards from the side that is 
 most heavily loaded. 
 
 Thus, Fig. 11 shows the proper construction for a queen-rod 
 truss loaded at one side only, or more heavily loaded on the left- 
 hand side than on the right. It will be seen that this truss is 
 composed entirely of triangles. 
 
888 
 
 WOODEX ROOF TRUSSES. 
 
 In practice, the weight of a roof is generally uniform on both 
 sides, the only variation in the loading being that due to wind 
 and snow. For trusses not more than 36 feet span, and one- 
 third pitch, the tie-beam will generally possess sufficient stiffness 
 
 Fig. 10 
 
 to resist the tendency of the unequal pressure of wind or snow 
 to distort the truss; but for larger spans, and for a pitch of 45, 
 two braces should be inserted in the centre panel of queen-rod 
 trusses, as one side may receive the greater pressure at one time, 
 and the other side at another time. Braces put in to resist the 
 effect of unequal loading are called counter braces. Under a 
 
 Fig. II 
 
 uniform dead load counter braces receive no stress whatever. 
 Every truss with horizontal top and bottom chords should be pro- 
 vided with counter braces y whenever there is any possibility of a 
 material variation in the loading. 
 
 When such trusses support a floor, they should always have 
 counter braces, because a floor may be heavily loaded at one 
 point, while the rest of the floor may have no load at all. Thus, 
 
WOODEX ROOF 
 
 B86 
 
 if the truss shown by Fig. 7 supported a floor, counter braces 
 .should be inserted as shown by the dotted lines. 
 
 Fig. 12 shows an ornamental queen-post truss supporting a 
 portion of the roof of the Massachusetts Charitable Mechanics' 
 Association building in Boston (Mr. William G. Preston, archi- 
 
 tect). The members, which are of Georgia pine, were worked 
 from timbers of the dimensions given. In this truss posts are 
 used instead of rods, being bolted and tenoned to the tie-beam 
 and secured to the rafters by iron straps. 
 
 The curved ribs take the place of counter braces. 
 
890 
 
 WOODEN ROOF TRUSSES. 
 
 Fig. 13 shows 
 
 a queen truss from the Museum of Fine Arts, 
 St. Louis, Mo. (Messrs. Pea- 
 body & Stearns, architects), 
 which supports the floor below 
 by means of three rods. The 
 truss-rods have nuts and 
 washers below the tie-beam, 
 and the thread on the rods is 
 long enough to receive turn- 
 buckles which connect the 
 suspension rods with the 
 truss. This is generally the 
 best method of suspending 
 a floor from a truss. 
 Fig. 14 
 
 DETAIL OF JOINT "A" FIG 13 
 
 Fig. 14 shows the end joint of this truss. 
 
 Fig. 15 shows a combination of a queen-rod and a king-rod 
 truss, sometimes used where it is desired to keep the centre 
 of the attic free from obstructions. 
 
 In building this truss it will be more economical to form the 
 lower portion of the rafters of two timbers, as shown, than to make 
 it of one size for the full length. This construction also allows 
 of making a good joint at B. What has been said in regard to 
 counter braces in queen-rod trusses applies also to this truss, 
 although with this truss the continuous rafter aids very materi- 
 ally in resisting distortion from wind pressure, so that for ordi- 
 nary construction and for spans not exceeding 40 feet it will be 
 perfectly safe to omit counter braces. 
 
WOODEN ROOF TRUSSES. 
 
 891 
 
 Manner of Supporting the Common Rafters Purlins. Before 
 describing other types of trusses, it may be well to consider 
 the manner of supporting the common rafters by the trusses. 
 
 Fig. 15 
 
 For Spans up to 42. 
 
 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 span 
 from truss to truss, as shown by Fig. 16. 
 
 Fig. 16 
 
 The trusses can be designed so that the purlins need not be 
 more than 10 feet apart, and very often not more than 6 or 8 feet 
 apart, so that the common rafters need not be more than 2"X4" 
 or 2"X6" in cross-section while the trusses may be spaced 12, 
 14, or 16 feet on centres. As a rule a spacing of about 14 ft. for 
 the trusses, and of 9 ft. 6 in. for the purlins, will be found most 
 
892 WOODEN ROOF TRUSSES. 
 
 economical. Another advantage in the use of purlins is that 
 where the purlins are placed at the truss joints no cross-strain 
 is brought on the truss rafters or chords, and hence the latter 
 may be made much lighter than if they supported the common 
 .rafters. For wooden trusses of 60 feet span or more, purlins 
 should always be used. 
 
 The purlins should always "be located over or close to a "joint of 
 ':he truss, so as not to produce a bending-moment in the truss- 
 rafter or chord. Purlins may be placed with their sides either 
 vertical or at right angles to the plane of the roof, but the author 
 prefers placing them with the sides vertical, as shown in Figs. 2 
 and 4. The best method of supporting the ends of the purlins 
 is by means of duplex hangers, described in Chapter XXI ; they 
 may also be supported by double stirrups, or may rest on 3-inch 
 plank bolted and spiked to the sides of the trusses. The ceiling- 
 or floor-joists are usually supported by the tie-beams of the 
 trusses. They may be framed flush with the tie-beam, as at A , 
 Fig. 16, or they may rest on top of the tie-beam as at B. When 
 the joists are used to support an attic floor it will be better to 
 place them on top of the tie-beam. There is no particular 
 objection to imposing a transverse strain on a tie-beam, as the 
 tension in the beam tends to straighten it, and the cross-section 
 of a wooden tie-beam must always be made considerably larger 
 than would be required to resist the direct tension. In the case 
 of scissors trusses it is sometimes more economical to support the 
 ceiling-joists by purlins, but for all trusses with a horizontal tie- 
 beam it will be more economical to support the ceiling- or floor- 
 joists by the tie-beams. 
 
 Trusses with Horizontal Chords. For supporting flat roofs, 
 with or without a ceiling below, and for any place where a hori- 
 zontal truss is practicable, the type of truss shown by Figs. 17 to 19 
 is undoubtedly the most satisfactory of any that can be devised 
 for wooden construction, when the span does not exceed 80 feet, 
 and except in localities where iron rods are very expensive it 
 will be as economical as any. In this work the name "Howe 
 truss" will be given to trusses of this type, as the truss is an 
 adaptation to building construction of the Howe bridge truss. 
 The term " horizontal truss " is also sometimes applied to trusses 
 of this type. Trusses of this type can be made strong enough 
 for spans up to 150 feet, but when the span exceeds 100 feet it 
 will probably be cheaper to use some other truss. 
 
 When a Howe truss is placed longitudinally of a flat roof, 
 
WOODEN ROOF TRUSSES. 
 
 893 
 
 the top chord may be given the same inclination as the roof, 
 so as to support the rafters without blocking, as shown by 
 
 A TopChord 
 
 Bottom Chord 
 
 Purlins 
 
 Fig. 17 
 
 Five-panel Howe Truss. 
 
 *. ^Counter Braces* 
 
 \ I %fl ^ ^ 
 
 Fig. 18 
 
 Six-panel Howe Truss. 
 
 Fig. 19 
 
 Ten-panel Howe Truss. 
 
 Fig. 20. For deck roofs the top chord may be inclined upwards 
 toward the centre, to conform to the shape of the roof, as shown 
 by Fig. 21. For a deck and mansard roof the centre panels 
 
 Fig. 20 
 
 should have counter braces, as shown in Fig. 21, to resist the 
 wind pressure against the sides of the roof, and any unequal 
 distribution of snow. 
 
894 
 
 WOODEN ROOF TRUSSES. 
 
 Rules to be Observed When Designing a Howe Truss Height. 
 The height of the truss, always measured from centre to 
 centre of the chords, should never be less than one-ninth of 
 the span for spans up to 36 feet, or than one-tenth of the 
 span for spans from 40 to 80 feet. As a general rule a height 
 of from one-seventh to one-sixth of the span will be most eco- 
 nomical. When the top chord is inclined, as in Fig. 18, the 
 
 =-~~ 
 
 Fig. 21 
 
 height at X i.e., at the shortest rod should not be less than 
 the limit given above. 
 
 Number of Panels. A panel is the space between two ad- 
 jacent rods or between an outer rod and the end joint (see Fig. 
 17). As a rule, the number of panels should be such that the 
 braces will have an inclination of from 36 to 60, an inclina- 
 tion of about 45 being the most economical. It is not ma- 
 terial whether there be an even or an odd number of panels. 
 
 If the position of one or more of the purlins is fixed by some 
 special requirement, then the panels should be so arranged 
 that the upper end of a brace will come under the purlin, and 
 that the inclination of none of the braces will be less than 36. 
 
 Although it is generally better to have the truss symmetrical 
 about the centre, it is not absolutely necessary, nor is it neces- 
 sary that the panels be of uniform width. When the truss is 
 not symmetrically loaded, however, it may be necessary to 
 reverse the brace in one of the centre panels. This point is 
 considered in Chapter XXVI, under the heading of "Trusses 
 Unsymmetrically Loaded." 
 
 Counter Braces. If there is any chance of the truss being 
 more heavily loaded on one side of the centre than on the other, 
 counter braces that is, braces in the opposite direction from 
 the regular braces should be placed in the centre panels as 
 shown by dotted lines in Fig. 18. 
 
 When a load of much magnitude is placed on one side of a 
 truss having an odd number of panels, without a corresponding 
 load on the other side, a brace will always be required in the 
 
WOODEN ROOF TRUSSES. 895 
 
 centre panel, and the brace should incline downward from the 
 more heavily loaded side. Thus, if the truss shown by Fig. 17 
 were more heavily loaded to the left of the centre than to the 
 right, then a brace would be required from A to B. When 
 the load on the truss is practically uniform, counter braces are 
 not necessary, nor is it necessary to put a brace in the centre 
 panel of a truss having an odd number of panels. 
 
 Spacing of Trusses. The most economical spacing of the 
 trusses, all things considered, will usually be from 12 to 16 feet 
 for spans up to 60 feet, and from 14 to 20 feet for greater spans. 
 
 Spacing of Purlins. Purlins should always* be placed over 
 the end of the braces and close to the washers on the rods; they 
 should also be spaced so as to give the greatest economy in 
 the rafters, hence the spacing of the purlins will determine, to 
 a large extent, the number of panels. When the height of the 
 truss is not more than one-ninth or one-tenth of the span, it 
 will often be more economical to place a purlin over every other 
 joint, as in Fig. 19. 
 
 Bearing on Wall or Post. The point where the centre lines 
 of the end brace and of the tie-beam intersect should always 
 come over the support, and generally at least 6 ins. beyond 
 the inner face of the wall. 
 
 Stresses. The strain in the chords is always greatest at the 
 centre of the truss, diminishing towards the supports, while 
 the stress in the rods and braces is greatest at the ends. 
 
 Table of Dimensions for Howe Trusses. For 
 symmetrical trusses having panels of uniform width and uni- 
 formly loaded, the stresses in the different parts will be pro- 
 portional to the span, number of panels, height of truss, spacing 
 of trusses, and the load per square foot. It is therefore possible 
 to prepare tables giving the dimensions of the parts for such 
 trusses. Table I., computed by the author, gives the dimen- 
 sions for six-panel trusses for heights of one-sixth and one-eighth 
 of the span, and for three different spacings. 
 
 These dimensions are for a flat roof of tin, sheet iron or com- 
 position, and for a snow load of 16 pounds per square foot, which 
 is equivalent to about 24 ins. of light, dry snow; aho for a lath 
 and plaster ceiling supported by the tie-beam; the chords and 
 braces being of Norway pine and the rods of wrought iron. 
 
 These dimensions apply only when the rafters are supported 
 on purlins placed at the upper joints, as in Figs. 18 and 19. 
 When the rafters rest on the top chord, as in Fig. 20, the dimen- 
 
896 
 
 WOODEN ROOF TRUSSES. 
 
 sions of the latter must be greatly increased, and special cal- 
 culations should be made therefor. 
 
 The dimensions given in the table may be used for trusses 
 having a greater height than that given, but not for trusses with 
 
 TABLE I. DIMENSIONS FOR SIX-PANEL HOWE 
 TRUSSES, SYMMETRICALLY LOADED. 
 
 Timber, Norway pine, Oregon pine, or Eastern spruce. 
 
 d 
 
 oj 
 O. 
 
 |?3 
 
 11 
 
 frT^ 
 
 O o 
 
 | . 
 l 
 
 Braces. 
 
 Rods 
 (not upset). 
 
 02 
 
 :* oSO 
 
 ^^4 
 
 
 
 PQ-S 
 
 
 
 
 
 
 
 
 
 
 
 
 A. 
 
 B. 
 
 C. 
 
 D. 
 
 E. 
 
 F. 
 
 Ft. 
 
 Ft. 
 
 Ft. Ins. 
 
 Ins. 
 
 Ins. 
 
 Ins. 
 
 Ins. 
 
 Ins. 
 
 Ins. 
 
 Ins. 
 
 Tns 
 
 
 
 6 7 
 
 6X 6 
 
 6X 8 
 
 6X 6 
 
 6X 4 
 
 6X 3 
 
 1 V 
 
 g . 
 
 
 
 1 
 
 5 2 
 
 6X 8 
 
 6X 8 
 
 6X 6 
 
 6X 6 
 
 6X 4 
 
 
 / 
 
 y$ 
 
 36 
 
 15J 
 
 6 8 
 5 2 
 
 6X 8 
 8X 8 
 
 6X 8 
 
 8X 8 
 
 6X 6 
 
 SX 6 
 
 6X 4 
 6X 6 
 
 6X 3 
 6X 4 
 
 1M 
 
 K 
 
 y 8 
 
 
 !8] 
 
 6 8 
 5 2 
 
 6X 8 
 SX 8 
 
 6X 8 
 
 SX 8 
 
 6X 8 
 
 8X 8 
 
 6X 6 
 6X 6 
 
 6X 4 
 6X 4 
 
 IX 
 
 V, 
 
 N 
 
 f 
 
 19J 
 
 7 7 
 
 8X 6 
 
 8X 8 
 
 8X 6 
 
 8X 4 
 
 6X 4 
 
 i 
 
 7 
 
 
 
 12 1 
 
 5 11 
 
 SX 8 
 
 SX 8 
 
 8X 6 
 
 SX 5 
 
 8X 4 
 
 1/1 
 
 /8 
 
 /o 
 
 j 
 
 1ft j 
 
 7 8 
 
 SX 8 
 
 SX 8 
 
 8X 6 
 
 SX 5 
 
 6X 4 
 
 1 <?/ 
 
 . 
 
 
 1. { 
 
 15 i 
 
 5 11 
 
 8X 8 
 
 SX 8 
 
 8X 8 
 
 SX 6 
 
 SX 4 
 
 j" l/o 
 
 /8 
 
 Z A 
 
 [ 
 
 -i 
 
 7 8 
 6 1 
 
 8X 8 
 8X10 
 
 8X 8 
 8X10 
 
 SX 8 
 SX 8 
 
 SX 6 
 SX 6 
 
 SX 4 
 
 SX 4 
 
 [iM 
 
 1 
 
 Z A 
 
 
 1 9 J 
 
 8 8 
 
 SX 8 
 
 SX 8 
 
 8X 8 
 
 SX 6 
 
 SX 4 
 
 I 
 
 
 
 
 
 6 8 
 
 SX 8 
 
 8X 8 
 
 SX 8 
 
 8X 6 
 
 SX 4 
 
 f 1/8 
 
 /S 
 
 H 
 
 48 - 
 
 15] 
 
 8 8 
 6 10 
 
 SX 8 
 8X10 
 
 8X 8 
 8X10 
 
 SX 8 
 SX 8 
 
 8X 6 
 SX 6 
 
 SX 4 
 SX 4 
 
 [1*5 
 
 1 
 
 H 
 
 
 ( 
 
 8 8 
 
 SX 8 
 
 SX 8 
 
 SX 8 
 
 SX 6 
 
 SX 4 
 
 i 
 
 i 
 
 
 
 1 
 
 6 10 
 
 8X10 
 
 8X10 
 
 8X10 
 
 8X 6 
 
 SX 4 
 
 \i/2 
 
 
 /4 
 
 
 j 
 
 9 8 
 
 SX 8 
 
 8X 8 
 
 SX 8 
 
 sx e 
 
 SX 4 
 
 i 
 
 
 
 
 1 
 
 7 6 
 
 SX 8 
 
 8X10 
 
 SX 8 
 
 SX 6 
 
 SX 4 
 
 { 1/8 
 
 /B 
 
 /4 
 
 54- 
 
 16 
 
 9 8 
 
 7 7 
 
 8X 8 
 8X10 
 
 SX 8 
 8X10 
 
 SX 8 
 SX 8 
 
 SX 6 
 8X 6 
 
 SX 4 
 SX 4 
 
 VA 
 
 1 
 
 M 
 
 
 18] 
 
 9 10 
 
 7 7 
 
 8X10 
 10X10 
 
 8X10 
 10X10 
 
 8X10 
 10 X 8 
 
 8X 8 
 SX 8 
 
 SX 6 
 SX 4 
 
 iy 8 
 
 IK 
 
 M 
 
 (' 
 
 12] 
 
 10 9 
 
 8X 8 
 
 8X10 
 
 SX 8 
 
 SX 6 
 
 6X 6 
 
 i 
 
 
 
 
 
 8 4 
 
 8X10 
 
 8X10 
 
 8X10 
 
 SX 6 
 
 SX 4 
 
 1/8 
 
 
 /4 
 
 
 1 ^ j 
 
 10 10 
 
 8X1C 
 
 8X1C 
 
 8XK 
 
 SX 6 
 
 6X 6 
 
 ll/ 
 
 1 1/ 
 
 T/ 
 
 
 1 
 
 8 4 
 
 10X10 
 
 10X10 
 
 10 X S 
 
 10X 6 
 
 SX 4 
 
 1/2 
 
 1/8 
 
 >4 
 
 
 1C J 
 
 10 10 
 
 10 XH 
 
 10X10 
 
 10 X 8 
 
 10X 6 
 
 SX 6 
 
 _ 
 
 1 1/ 
 
 3/ 
 
 
 
 
 8 4 
 
 10X10 
 
 10X10 
 
 10x10 
 
 10X 6 
 
 SX 6 
 
 f ** 
 
 /S 
 
 M 
 
 
 12- 
 
 12 6 
 
 8X10 
 
 8X10 
 
 8X10 
 
 sx e 
 
 6X 6 
 
 J 
 
 
 3/ 
 
 
 
 9 7 
 
 10XK 
 
 10X10 
 
 10 X 8 
 
 10X 6 
 
 SX 6 
 
 1 1^2 
 
 
 % 
 
 70 
 
 15- 
 
 12 6 
 
 10X10 
 
 10X10 
 
 10X 8 
 
 10X 6 
 
 SX 6 
 
 1 
 
 
 
 
 
 9 9 
 
 10X12 
 
 10X12 
 
 10X10 
 
 10X 8 
 
 10X 6 
 
 j" 1x4 
 
 1/8 
 
 A 
 
 
 18- 
 
 12 6 
 
 10X1C 
 
 10X10 
 
 10XK 
 
 10X 6 
 
 8X 6 
 
 J _ 
 
 1 1/ 
 
 _ 
 
 
 
 
 9 9 
 
 10X12 
 
 10X12 
 
 10X12 
 
 10X 8 
 
 10X 6 
 
 f 1/i 
 
 1/4 
 
 Ji 
 
 j 
 
 12- 
 
 14 2 
 10 10 
 
 10X10 
 10X10 
 
 10X10 
 10X10 
 
 10X10 
 10X10 
 
 10X 6 
 10X 6 
 
 SX 6 
 SX 6 
 
 IK 
 
 IK 
 
 H 
 
 80^ 
 
 15 j 
 
 14 2 
 11 
 
 10X10 
 10X12 
 
 10X10 
 10X12 
 
 10X10 
 10 X 1C 
 
 10X 8 
 10X 8 
 
 SX 6 
 10X 6 
 
 \iy s 
 
 IX 
 
 Ji 
 
 
 18^ 
 
 14 4 
 
 10X12 
 
 10X12 
 
 10X12 
 
 10X 8 
 
 8.X 6 
 
 1 
 
 
 
 
 
 11 1 
 
 10X12 
 
 10X14 
 
 10X11 
 
 10X 8 
 
 10X 6 
 
 ^ 
 
 ,8 
 
 
WOODEN ROOF TRUSSES. 
 
 897 
 
 
 a less height, as the less the height the greater will be 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 parts of the truss 
 proportioned accordingly; but even in such cases the table will 
 serve somewhat as a check upon the computations. 
 
 Lattice Trusses. In localities where lumber is cheap, 
 and iron or steel rods quite expensive, the lattice truss (Fig. 22) 
 will often be the most economical for 
 supporting flat roofs. 
 
 This type of truss was designed 
 by Ithiel Towne for bridges long 
 before iron was used in this country 
 for such work. Several railroad 
 bridges were built on this principle, 
 and the truss has proved very 
 efficient in supporting loads. The 
 principal objection to the truss, from 
 a mechanical standpoint, is that the 
 truss cannot be tightened up, and 
 the joints are not as satisfactory as 
 in a Howe truss. 
 
 Proportions and Construction. The 
 height of a lattice truss, measured 
 between the centre lines of the chords, 
 should be from one-eighth to one- 
 sixth of the span, and the braces 
 should be placed at an angle of about 
 45 degrees. When laying out a lattice 
 truss, the first step should be to 
 determine the height, and then the 
 number of spaces between the joints 
 in the top and bottom chords. To 
 find the number of spaces, multiply 
 the span by two, and divide by 
 the height, using the nearest whole 
 number. Thus, if the span is 60 
 feet, and the height 8 feet, there 
 
 2X60 
 should be =15 spaces. 
 
 If the 
 
 height is 10 feet, there should be 12 spaces. The truss shown 
 in Fig. 22 has 16 spaces. 
 
898 
 
 WOODEN ROOF TRUSSES. 
 
 Having determined the height and number of spaces, fix the 
 centre of the end joints, and divide the distance between into 
 the number of spaces determined upon, thus fixing the position 
 of the braces. The chords should be built of four thicknesses of 
 plank, two on each side of the truss, and breaking joint opposite 
 their centres, using as long planks for the tie-beam as can be 
 obtained. At the ends, vertical planks should be cut between 
 the chords, on each side of the bracing, to act as posts. The 
 braces should be bolted to the chords and end-posts, and also to 
 each other where they cross. A goodly number of spikes should 
 also be used in the joints, as indicated in Fig. .24 
 
 Fig. 23 
 
 calf 
 
 Fig. 24 
 Detail of Joint B. 
 
 Vertical Section. 
 
 The bottom chord should also be bolted every two feet between 
 the joints, as this member is in tension. The top chord, being 
 in compression, will be tied sufficiently by the bolts at the joints, 
 and by a short bolt on each side of each butt-joint. The strain 
 on the joints near the ends of the truss will be much greater 
 than on the centre joints. The first three joints at each end 
 should have as many and as large bolts as are given in the last 
 column of Table II. The bolts in the next three joints may be 
 slightly reduced in size, and those in the centre joints still more. 
 When the span of the truss exceeds 40 feet, short pieces of plank 
 should be spiked to the end braces a a fitting tightly between 
 the other set of braces, to give them additional strength. It 
 
 should be kept in mind that the strength of a lattice truss is 
 
 usually measured by the strength of the joints. 
 
 Stresses in a Lattice Truss. The stresses in a lattice truss are 
 
 computed in about the same way as those in a riveted plate 
 
 girder; thus the chords are assumed to resist the bending- 
 
 moment, and the braces the shearing-stress. 
 
 The tension or compression in the chords is greatest at the 
 
 centre, while the stress in the braces is greatest at the ends. 
 
WOODEN ROOF TRUSSES. 
 
 899 
 
 Under a uniformly distributed load, the maximum "stress in 
 the chords may be found by multiplying the total load by the span 
 and dividing by 8 times the height, both in feet. 
 
 The stress in each of the end braces a a a when the angle of 
 inclination approximates 45, will be one- sixth of the total load, 
 multiplied by 1.4. 
 
 The following table gives the dimensions for lattice trusses, 
 
 TABLE II. DIMENSIONS FOR LATTICE TRUSSES OF 
 FIRST QUALITY WHITE PINE OR SPRUCE. 
 
 To support a gravel roof arid plastered ceiling, allowing 20 pounds per 
 square foot for snow. 
 
 d 
 
 MH 
 
 o M . 
 
 bC <B 
 fl 
 
 .So 
 
 *o | 
 
 ol-H 
 
 I* 
 
 ' g 
 
 9 
 
 o 
 
 sT 5 ! 
 
 OQ -H bC 
 
 i 
 
 II 
 
 || 
 
 41 
 
 III 
 
 o 
 
 q 
 
 J3 
 
 L 
 
 5 
 
 cc c o 
 
 
 02 
 
 o 
 
 
 
 CQ 
 
 W 
 
 
 
 si 
 
 Ft 
 
 Ft. 
 
 Ft. Ins. 
 
 
 
 
 
 
 Inch. 
 
 | 
 
 12 1 
 
 5 6 
 
 7 2 
 
 16 
 12 
 
 4 2X 6 
 4 2X 6 
 
 4 2X 6 
 4 2X 6 
 
 J2X 6 
 
 J2X 6 
 
 | 2 -! 
 
 40^ 
 
 14 1 
 
 5 7 
 7 3 
 
 16 
 12 
 
 4 2X 6 
 4 2X 6 
 
 4 2X 8 
 4 2X 8 
 
 -J2X 6 
 
 | 2X 6 
 
 1 3 y s 
 
 I 
 
 uj 
 
 5 8 
 
 7 4 
 
 16 
 12 
 
 4 2X 8 
 4 2X 8 
 
 4 2X 8 
 4 2X 8 
 
 J2X 8 
 
 J2X 6 
 
 |3-1 
 
 f 
 
 
 6 8 
 
 16 
 
 4 2X 8 
 
 4 2X 8 
 
 i 
 
 ( 2X 8 
 
 ( 
 
 
 12- 
 
 8 8 
 
 12 
 
 4 2X 8 
 
 4 2X 8 
 
 < 2X10 
 
 < and 
 |2X 6 
 
 i 3 - 1 
 
 50 -j 
 
 14- 
 
 6 8 
 8 8 
 
 16 
 12 
 
 4 2X 8 
 4 2X 8 
 
 4 2X 8 
 4 2X 8 
 
 J2X10 
 
 (2X8 
 < and 
 (2X 6 
 
 ja-^ 
 
 
 "1 
 
 6 9 
 
 8 8 
 
 16 
 12 
 
 4 2X 8 
 4 2X 8 
 
 42 X 10 
 4 2X 8 
 
 J2X10 
 
 ( 2X 8 
 < and 
 (2X 6 
 
 J3 VA 
 
 f 
 
 12 
 
 8 4 
 10 10 
 
 16 
 12 
 
 42 X 10 
 42 X 10 
 
 42X10 
 42X10 
 
 2X10 
 
 J2X 8 
 
 J3-1K 
 
 60 { 
 
 14 
 
 8 4 
 10 10 
 
 16 
 12 
 
 42X10 
 42 X 10 
 
 42 X 10 
 42 X 10 
 
 2X10 
 
 J2X 8 
 
 | 3 IK 
 
 [ 
 
 16- 
 
 8 4 
 10 10 
 
 16 
 12 
 
 42 X 10 
 42X10 
 
 42 X 10 
 42X10 
 
 2X10 
 
 J2X 8 
 
 J3-1K 
 
 
 14 
 
 9 5 
 
 12 4 
 
 16 
 12 
 
 42X10 
 42 X 10 
 
 42 X 12 
 42X10 
 
 2X10 
 
 J2X 8 
 
 1-2^ 
 
 70 - 
 
 16 
 
 9 5 
 
 12 4 
 
 16 
 12 
 
 42 X 10 
 42X10 
 
 42X12 
 42X10 
 
 2X10 
 
 -J2X 8 
 
 1 2 
 
 
 18 
 
 9 6 
 12 6 
 
 16 
 12 
 
 42 X 12 
 42X12 
 
 42 X 12 
 42 X 12 
 
 j 2X10 
 
 J2X 8 
 
 j 1V4 
 
 r 
 
 14J 
 
 11 
 14 
 
 16 
 12 
 
 42 X 12 
 42X12 
 
 42 X 12 
 42 X 12 
 
 2X10 
 
 j 2X 8 
 
 1-2M 
 
 
 i 
 
 11 2 
 
 16 
 
 42X14 
 
 42X14 
 
 
 \2X10 
 
 
 80 ( 
 
 16-j 
 
 14 
 
 T2 
 
 42X12 
 
 42X12 
 
 2X12 
 
 K and 
 (2X 8 
 
 13 
 
 
 ( 
 
 11 2 
 
 16 
 
 42X14 
 
 42 X 14 
 
 
 (2X10 
 
 
 1 
 
 18-] 
 
 
 
 
 
 2X12 
 
 < and 
 
 13 
 
 I 
 
 
 14 1 
 
 12 
 
 42X12 
 
 42 X 14 
 
 
 (2X 8 
 
 
 Uprights at end same size as end braces. 
 
900 
 
 WOODEN ROOF TRUSSES. 
 
 built as shown in Fig. 22, for five different spans, and different 
 spacings and heights, which will cover nearly all of the conditions 
 under which these trusses should be usefd. In localities where 
 a fall of snow two fe-et in depth is liable to occur, these dimen- 
 sions should be increased. 
 
 Referring to Fig. 22, it may be stated that each chord of the 
 truss is built of four 2X 10's in 10 and 20 foot lengths, the braces 
 a a a are 2 X 10 and the other braces 2X8. The joints at 1, 2, 3 ; 4 , 
 and 5 have three IJ-inch bolts, the joints between 6 and 8 and 
 7 and 9 have two |-inch bolts, while the other joints have two 
 1-inch bolts. There should also be two f-inch bolts in the tie- 
 beam, in each space between the joints, to assist in transmitting 
 the tension from one plank to the other. 
 
 Wooden Trusses with Raised Tie-beams. All of 
 the trusses thus far described have horizontal tie-beams, which 
 are the most desirable as well as the most economical, whenever 
 the conditions will permit. 
 
 In roofing churches, public halls, etc., a raised ceiling is often 
 desired in order to give greater height to the room, without in- 
 creasing the height of the walls. 
 
 Scissors Trusses. For such roofs some form of the scissors 
 truss (so named from its resemblance to a pair of scissors) is 
 most often used. When correctly designed, with members of 
 the proper size, and with the joints carefully proportioned to the 
 stresses, the scissors truss makes a very good truss for support- 
 ing the roof over halls and churches, up to a span of 48 feet, 
 
 but above that they 
 should be used with 
 much caution, as the 
 stresses become very 
 great, and the joints 
 difficult to make. 
 
 Figs. 25 to 30 show 
 different forms of the 
 truss adapted to dif- 
 ferent spans and roof 
 pitches.* None of 
 these trusses will ex- 
 ert a horizontal thrust 
 
 Fig. 25 
 
 * The dimensions given in these figures are for use in computing the 
 roof loads in the examples given in Chapter XXVI. 
 
WOODEN ROOF TRUSSES. 
 
 901 
 
 if the members are of ample size and the joints properly made. 
 The members having a + sign on or close to them are in com- 
 pression, while the others are in tension. 
 
 The members indicated by a single line should be rods (except 
 in the case of tie-beams). 
 
 F?g. 26 
 
 Fig. 25 shows the simplest form of the scissors truss, which 
 is suitable for spans up to 30 feet. When the span exceeds 
 
 Fig. 27 
 
 30 feet, it will be more economical to use two purlins on each 
 side, to support the common rafters, and additional supports 
 
902 
 
 WOODEN ROOF TRUSSES. 
 
 will generally be required by the tie-beams which will call for 
 the additional rods and braces shown in Fig. 26. 
 
 For a steep roof the arrangement shown by Fig. 27 is generally 
 befst adapted, and for a flatter roof that shown by Fig. 28. 
 Fig. 29 shows a finished truss, built on the same lines as 
 
 Fig. 29 
 
 Fig. 28, but with only one purlin. The truss shown by Fig. 30 
 is similar to that shown bv Fig. 27, with the peak cut off, and 
 
WOODEN ROOF TRUSSES. 
 
 903 
 
 a straining beam placed between the upper ends of the prin- 
 cipals, and the centre rod omitted. For spans exceeding 36 feet, 
 Fig. 30 gives a more economical truss than Fig. 27 ; this truss 
 can also be used where the roof is hipped. With this truss it 
 will be better to use ceiling purlins to support the ceiling joists 
 than to span them from truss to truss. 
 
 Common Rafters 
 
 Fig. 30 
 
 Fig. 31 shows the best way of making the joints at 5 and 7 of 
 Fig. 30. 
 
 2-iy 2 Rods 9M C. to C. 
 2 x lOSpiked Each Side 
 3"x %"stirrup 
 
 Fig. 31 
 
 Hammer-beam Trusses. One of the principal char- 
 acteristics of the Gothic style of architecture is that of making 
 the structural portions of the building ornamental, and exposing 
 the whole construction of the edifice to view. As the pointed 
 arch and steep roof were developed the roof truss became 
 an important feature in the ornamentation of Gothic halls 
 
904 
 
 WOODEN ROOF TRUSSES. 
 
 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 that of the " Hammer-beam 
 truss," which is still often used in Gothic churches. 
 
 Figs. 32 and 33 show early English forms of this truss, which 
 takes its name from the horizontal beam H, at the foot of the 
 principal, and which is called the "hammer-beam." 
 
 In the more ornamental trusses, the hammer-beam was 
 usually carved to represent kings 
 or angels. 
 
 These trusses differ in princi- 
 ple from all of the trusses thus 
 far described in that they have 
 no tie-beam, and no substitute 
 
 for one. In fact the trusses /ff/W/ff/ M 
 
 shown by Figs. 32 and 33 do not 
 
 SECTION OF SECTION OF 
 
 PRINCIPAL RAFTER COLLAR BEAM 
 
 Fig. 32 
 
 ROOF OVER NAVE 
 
 CHAPEL. SUFFOLK, ENG. 
 
 Span 18ft. 
 
 come within the scope of the definition for a truss given at 
 the beginning of the chapter. Although the rafters or prin- 
 
WOODEN ROOF TRUSSES. 
 
 905 
 
 cipals are connected near the top of the truss by a short collar 
 "beam, this would offer but little resistance to the rafters spread- 
 
 CHANCEL ROOF 
 
 BEDDINGTON CHURCH 
 
 SURREY 
 
 ing at their lower ends, 
 hence the truss must 
 depend either upon the 
 transverse strength of 
 the rafter or the resist- 
 ance of the walls to keep 
 it intact, and generally 
 upon both. 
 
 In the halls and 
 churches of the Gothic 
 period the walls were 
 generally very thick, and 
 usually re-enforced on the 
 outside by buttresses 
 built against the wall 
 directly opposite the roof- 
 trusses. In most cases such a wall possesses sufficient stabil- 
 ity to withstand the thrust of the truss, and hence the tie- 
 beam may be dispensed with; but in a wooden building the 
 walls offer no resistance whatever to being thrust out, unless 
 tied at the top, and hence no trass which exerts an out- 
 
906 
 
 WOODEN ROOF TRUSSES. 
 
 ward thrust on the walls should 
 be used in such a building. It 
 is therefore impracticable to use 
 a hammer-beam truss in a wooden 
 building. In roofs where this 
 form of truss is used, the ceiling 
 is generally formed of matched 
 sheathing nailed to the under 
 side of the jack-rafters between 
 the purlins, thus allowing the lat- 
 ter to be seen. The purlins are 
 generally decorated, and false 
 
 Fig. 34 
 
 Hammer -beam Truss. 
 First Church, Boston. 
 
 ribs are often placed 
 vertically between 
 them, so as to divide 
 the ceiling into panels. 
 The rafters should 
 be made very large 
 to prevent them from 
 breaking at the point 
 A. 
 
 An excellent exam- 
 ple of a hammer-beam truss adapted to mod- 
 ern conditions is shown by Fig. 34, which 
 represents half of one of the trusses in 
 the First Church, Boston, Mass. (Messrs. 
 Ware & Van Brunt, architects). The truss 
 is finished in black walnut, and has the 
 effect of being very strong and heavy. 
 Fig. 35 shows the framing of the same truss 
 without the casing and falsework. It should 
 
WOODEN ROOF TRUSSES. 
 
 907 
 
 be noticed that inside the turned column at the upper part 
 of the truss (Fig. 34) there is an iron rod (Fig. 35) which 
 holds up the joint A.* 
 
 In this form of truss the 
 outward thrust of the arch 
 enters the wall just above 
 the corbel, K' } and, as the 
 direction of the thrust is 
 inclined only about thirty 
 degrees from a vertical, the 
 tendency which it has to 
 overthrow the wall is not 
 
 FRAMING OF HAMMER 
 BEAM TRUSS 
 
 SCALE 
 5 10 
 
 15' 
 
 Span 61 feet 
 
 DISTANCE BETWEEN TRUSSES 
 ABOUT 15 feet 
 
 very great, and may be easily resisted by a 
 wall twenty inches or two feet thick, re- 
 enforced by a buttress on the outside. 
 
 In trusses of this kind, the pieces should be 
 securely fastened together wherever they cross 
 or touch each other, and the whole truss made 
 
 as rigid as possible. No dependence for extra strength should 
 
 be made on the casings and panel work. 
 
 Fig. 36 shows a form of truss used in Emmanuel Church at 
 
 Shelburne Falls, Mass. (Messrs. Van Brunt & Howe, architects). 
 
 * The main rafters of this truss are two five-inch by thirteenth-inch 
 hard-pine timbers. 
 
908 
 
 WOODEN ROOF TRUSSES. 
 
 This truss was probably derived from the hammer-beam truss, 
 and possesses an advantage over that truss in that it has in * 
 effect a trussed rafter, so that there is no danger of the rafter 
 being broken; and if the truss is securely bolted together 
 
 at 'all its joints it exerts but very little thrust on the walls. 
 The rafters and cross-tie are formed of two pieces of timber 
 bolted together, and the small upright pieces run in between 
 them. 
 
 The trusses in the church at Shelburne Falls have the hammer- 
 beams carved to represent angels. 
 
 The action of the stresses in hammer-beam trusses is ex- 
 plained in Chapter XXVJ. 
 
WOODEN ROOF TRUSSES. 
 
 909 
 
 Wooden Trasses 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, wrought-iron or steel rods may 
 be used for the ties, still retaining the wooden principals and 
 struts. Such trusses will be cheaper, for moderate spans, than 
 steel trusses, while they are just about as good, particularly 
 where the rafters and purlins are to be of wood. 
 
 Casting 
 
 Fig. 37 
 
 Spans up to 36'. 
 
 Figs. 37 and 40 show forms of trusses that are suitable for 
 many places. The dimensions given in Fig. 40 are for yellow 
 pine or Oregon pine timber and wrought-iron rods, and are 
 ample for a slate roof, the trusses to be spaced from 12 to 14 feet 
 on centres. Trusses like Fig. 37 are sometimes seen with the rods 
 C and D continuous. They 
 should not be made in this 
 way, however, as the stress in 
 C is greater than that in D. 
 The best way of making the con- 
 nection at joint B is shown by 
 Fig. 38, a cast-iron shoe being 
 fitted to the end of the strut to 
 receive the pin. For the truss 
 shown by Fig. 40, a shoe made 
 as shown in the detail drawing 
 will make a better connection for the rods, two of the rods 
 
 Pin Boll/ 
 JTear Rod G 
 
 Fig. 38 
 Detail of joint B. 
 
 RodE 
 
910 
 
 WOODEN ROOF TRUSSES. 
 
 being placed outside of the brackets, and three between the 
 
 brackets. 
 
 For a truss with a single strut, a turnbuckle on the rod E will 
 
 be sufficient to tighten the rods. When there are three struts, 
 
 there should be five turnbuckles, as in Fig. 40. 
 
 A cast-iron shoe should be made to receive the foot of the 
 
 rafter, and the rods secured to a pin passed through the shoe 
 
 and the rafter. At the apex of the truss shown by Fig. 40 there 
 
 should also be a casting to receive the ends of the rafters, and a 
 
 pin for the tie-bars. The apex 
 joint of the truss (Fig. 37) may 
 be made either by crossing the 
 rods through a cast washer, or 
 the joint may be made as in 
 Fig. 39. The pins at the joints 
 should be computed for shear- 
 ing, bearing and bending- 
 moment. 
 
 When it is desired to support 
 
 a hammer-beam truss on a clerestory wall without making the 
 
 Fig. 39 
 
 1 
 
 Fig. 40 
 
 wall very thick or bracing it from the outside, a form of truss 
 
WOODEN ROOF TRUSSES. 
 
 911 
 
 This 
 
 like that shown in Fig. 41 may be used to advantage. 
 
 truss has the appear- >x 
 
 ance of a hammer-beam 
 
 truss, and when placed 
 
 over a high nave the 
 
 effect of the rods is hot 
 
 objectionable. 
 
 The tie-rods should 
 
 extend through the 
 
 hammer beams to their 
 
 outer end. For a truss 
 
 of 32-feet span a 1J- 
 
 inch square bar will be 
 
 ample, and it may be 
 
 twisted to give a more 
 
 pleasing effect. 
 
 The curved ribs a, a, in this truss are not in tension but in com- 
 pression, and the braces under the hammer-beams are necessary 
 
 to resist the vertical component of the thrust in the curved ribs. 
 
 A truss similar to this was used in -the new Grace Chapel, New 
 
 York city. 
 
 Fig. 42 shows a form of truss used to support the roof of the 
 
 Metropolitan Con- 
 cert Hall, New 
 York city, George 
 B. Post, architect. 
 The span of the 
 truss in that build- 
 ing is about 54 feet, 
 and the propor- 
 tions are about as 
 shown in Fig. 42. 
 The arch be- 
 tween the rafter 
 and the raised rib 
 
 is ornamented with sawed work. The truss has a very light and 
 
 airy appearance, besides embodying all the strength that can be 
 
 desired in it. The tie-rod is kept from sagging by a vertical 
 
 rod from the centre of the arch. 
 Wooden Arched Ribs, with Iron or Steel Ties. 
 
 For roofing large halls or rooms a segmental timber arch, with an 
 
 iron or steel tie for taking up the horizontal thrust makes about 
 
912 
 
 WOODEN ROOF TRUSSES. 
 
 the cheapest truss that can be built, especially where there is 
 
 no ceiling to be sup- 
 ported. 
 
 Figs. 43 and 44 are 
 good examples of this 
 form of truss. The 
 arched ribs support all 
 the load that comes 
 upon the truss, and 
 the tie-rods prevent the 
 ends of the arch from 
 spreading, as would be 
 the case if there were 
 no tie-rods. 
 
 The bracing between 
 the arched ribs is sim- 
 ply to unite them, and 
 distribute the stresses 
 arising from the load 
 proportionately over the 
 two ribs. 
 
 The framework shown 
 above the arch in Fig. 
 43 is simply to support 
 the purlins and rafters, 
 and only carries the 
 load directly to the arch. 
 It does not assist the 
 truss in any way in 
 carrying the load. 
 
 The method of sup- 
 porting the roof of the 
 Fifth Avenue Riding- 
 School, New York city, 
 
 is slightly peculiar and very ingenious ; and, as it is an excellent 
 example of the' advantage of the arched form of truss, we 
 shall give a brief description of the construction of the roof and 
 its supports. A plan of the riding-room is represented by Fig. 
 45. The room is one hundred and six feet six inches long, 
 and seventy-three feet wide. This space is kept entirely clear 
 of posts or columns; and the entire roof is supported by two 
 large trusses, one of which is shown in Fig. 44. The roof be- 
 
WOODEN ROOF TRUSSES. 
 
 913 
 
 tween the trusses and on either side is supported by smaller 
 trusses resting on these 
 large trusses ; but each 
 of the large trusses 
 eventually carries a 
 roof area equal to 
 about2,930 square feet, 
 and a great amount 
 of extra framework. 
 It was desired to pro- 
 vide for the thrust 
 of these large arches 
 without having rods 
 showing in the room, 
 and the method adopt- 
 ed is very ingenious. 
 Opposite the upper 
 ends of the iron posts 
 which receive the 
 arched ribs are oak 31 
 struts, which are held *? 
 in place by iron tie- * 
 bars and heavy iron 
 beams, which together 
 form a horizontal truss 
 at each end. These two 
 trusses are prevented 
 from being pushed out 
 by two three-inch by 
 one-inch tie-bars in 
 each side-wall shown 
 in the plan (Fig. 45). 
 
 The bottoms of the 
 two iron posts are tied 
 together by iron rods 
 running under the floor 
 the whole length, of 
 the room. Altogether 
 this gives for the tie- 
 rods of each truss two 
 
 bars three inches by one inch, and an inch and a half iron rod, 
 which would be equivalent to two tie-bars three inches and 
 
914 
 
 WOODEN ROOF TRUSSES. 
 
 three-fourths by one inch. Enlarged sections of the ribs, up- 
 rights, and braces are shown in Fig. 44. It should be noticed 
 that the uprights act both as struts and ties, by having iron rods 
 through their centre holding the two ribs together. 
 
 SUVa 311 NOUI 
 
 unu is wvaa NOUI 
 
 J.S WV38 NOdl 
 
 'SiJVQ 311 NO.U.I 
 
 Fig. 46 shows a detail, or enlarged view, of the iron skewback 
 and post at each end of the truss shown in Fig. 44. 
 
 Fig. 47 shows the method adopted for supporting the roof and 
 gallery at the City Armory at Cleveland, O., the arch being of 
 wood. 
 
 Fig. 48 shows one-half of an arched wooden truss which, with 
 seventeen others, was designed for supporting the roof over the 
 
WOODEN ROOF TRUSSES. 
 
 915 
 
 15 BEAM 
 STRUT 
 
 Fig. 46 
 
 GROUND LINE 
 
 ~|H"lRON TIE TO OPPOSITE COLUMN 
 106 6 DISTANT 
 
 , 2* Pin- x 2-1% Rods upset' 
 
 Fig. 48 
 
916 
 
 WOODEN ROOF TRUSSES. 
 
 central bay of Saenger Hall, Philadelphia, Messrs. Hazelhurst 
 and Huckel, architects. This building was erected in 1897 for 
 the use of the Eighteenth National Saengerfest, and was intended 
 
 only for temporary use. With the dimensions slightly increased, 
 however, the truss would be suitable for permanent use. The 
 trusses were spaced 20 feet centre to centre. A description of 
 the building and trusses was published in the Engineering Record, 
 of Jan. 9, 1897. 
 
STEEL ROOF TRUSSES. 
 
 917 
 
 TYPES OF STEEL ROOF TRUSSES. 
 
 Trusses for Pitch Roofs. For ordinary conditions and 
 for spans under 100 feet, some one of the types shown by Figs. 
 49 to 60 will generally meet the requirements of strength and 
 economy. Trusses of these types are usually made with riveted 
 connections, this being the cheaper kind of construction for 
 short spans and small truss members. There are cases, how- 
 ever, when the pin connection may be the cheaper or more ad- 
 visable construction. 
 Pin-connected trusses 
 may be more con- 
 veniently shipped, and 
 where they are sup- 
 ported by brick walls 
 so as not to require 
 bracing, may often 
 be more economically 
 erected, especially if 
 
 Fig. 49 
 
 there is no other steel work about the building that requires 
 riveting during erection. When the trusses are supported by 
 steel columns, and where there is a good deal of steel work about 
 the building requiring the presence of iron-workers, riveted 
 trusses will always be more economical for spans up to 80 feet. 
 For a narrow shed or shop the shape of truss shown by Fig. 4$ 
 is the most economical, the truss proper being that portion 
 inclosed within the points A, B, C. This truss is practically 
 the same as that shown by Fig. 50. For spans of from 24 to 
 48 feet, and with an inclination not exceeding 6" to the foot, 
 types 51 and 52 are the most suitable. The truss types repre- 
 
 Fig. 50 
 
 Span 20' to 36'. 
 
 sented by these two figures has received the name of "Fan 
 truss." The truss shown by Fig. 50 is known as a "simple 
 
918 
 
 STEEL ROOF TRUSSES. 
 
 Fink truss." The truss shown by Fig. 52 differs from that 
 in 51 principally in the inclination of the braces, the braces 
 A and B in Fig. 52 being inserted to brace the truss from the 
 column to prevent racking under wind pressure. Fig. 52 
 
 Fig. 51 
 
 Span 36' to 50'. 
 
 Fig. 52 
 
 Span 40' to 60'. 
 
 should be used when the truss is supported by columns and 
 Fig. 51 when the truss rests on brick walls. A sag tie, as shown 
 by dotted line, is generally inserted. When the roof construc- 
 tion demands three purlins on each side of the truss, one of 
 
 Fig. 53 
 
 Span 40' to 80 7 . 
 
 the forms shown by Figs. 53, 54, 55, or 56 should be used. 
 The names given to these trusses are often confounded by 
 different writers; many engineers class the French and Fan 
 
STEEL ROOF TRUSSES. 
 
 919 
 
 trusses with the Fink truss. The term "French" appears to 
 be generally given to those trusses in which the tie-beam is 
 raised in the centre. The truss shown by Fig. 56 appears to 
 
 Fig. 54 
 
 French Truss. Span 40' to 80'. 
 
 have no generally recognized name. One writer refers to it 
 as an "English" truss. This truss is not as economical as the 
 Fink truss, except when the inclination of the rafter is less than 
 one-fourth pitch, on account of the great length of the inner 
 struts. 
 
 Although Fig. 56 somewhat resembles the queen truss, 
 Fig. 5, it will be seen that the diagonals run in the opposite 
 direction, the diagonals in Fig. 56 being in tension, and the 
 verticals in compres- 
 sion, the reverse of 
 the queen truss. In 
 designing steel trusses 
 it is desirable to have 
 as many members, and 
 especially of the long 
 members, in tension as 
 possible, as a given 
 
 weight of steel will _ _ _ _ 
 
 resist a much greater 
 stress when in tension than when in compression. The great 
 economy of Fink and Fan trusses lies in the fact that most of 
 the members are in tension and the struts are short. Com- 
 paring Figs. 55 and 56 it will be noticed that the inner strut 
 in Fig. 55 is only J as long as the strut in Fig. 56. Another 
 advantage of these trusses is that a partial load, as, for instance, 
 a wind or snow load, on one side of the truss never causes stresses 
 in excess of those produced by a uniform load of the same 
 
920 STEEL ROOF TRUSSES. 
 
 intensity over the whole truss. If the roof is hipped it is desir- 
 able to have vertical members in the hip trusses to receive 
 the short trusses or trussed purlins. 
 
 Depth of Fink and Fan Trusses. The depth of these 
 trusses at the centre is usually determined by the roofing mate- 
 rial that is to be used. Thus, slate should not be used on a 
 roof in which the rise is not equal to one-third of the span, for 
 wood shingles the rise should not be less than one-fourth the 
 span, and for corrugated iron not less than one-fifth of the span. 
 Steel-roll roofing may be laid on a slope of one-twelfth the span. 
 There are many kinds of so-called "ready roofing" put up in 
 rolls which may be used for any slope exceeding f " to the foot. 
 Tar and gravel roofing should never be used on a pitch exceed- 
 ing f" to the foot. Considering the construction of the roof 
 and the weight of the trusses the most economical pitch for a 
 
 Fig. 57 
 
 Span 68'. 
 
 roof is about one-fourth the span, or what is commonly called 
 a quarter piteh, the rise of the rafters being 6" in 12", or 26 degrees 
 and 34 minutes. When the rise is less than one-sixth the span 
 some other type of truss will generally be 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 
 inches in 12 inches. With Fink or Fan trusses having an 
 inclination for the rafter not exceeding 30 degrees it is more 
 economical to employ a horizontal chord or tie, since it obviates 
 bending of the laterals. A truss whose bottom chords has a 
 rise of two or three feet, as in Fig. 54, presents a better appear- 
 ance, however, than one with a horizontal chord. Raising 
 the bottom chord also materially increases the strains in the 
 truss members, hence it increases the cost. For steep roofs, 
 however, it will generally be fully as economical to raise the 
 bottom chord, because of the shortening of the members, 
 
STEEL ROOF TRUSSES. 
 
 921 
 
 Number of Struts. The number of struts that should 
 be used in each half of the truss will be determined in a great 
 measure by the construction of the roof. If Jack rafters and 
 purlins are used then the distance between the struts may be 
 as great as 12 feet, but if there are no Jack rafters and the 
 
 planking of the roof is nailed directly to the purlins, then the 
 latter will not be placed more than 8 feet apart, and if the roof 
 is covered with corrugated iron secured to the purlins, then the 
 purlins should not be more than 5 feet on centres. Whenever 
 the purlins are more than four feet apart they should come 
 over the end of a strut or brace, to avoid bending-moments, 
 consequently the spacing of the purlins will generally deter- 
 
STEEL ROOF TRUSSES. 
 
 mine the number of struts in each half of the truss. For this 
 reason the same form of truss may be required for a span of 
 40 feet as for a span of 80 feet, but of course the members will 
 not be as heavy in the 40-foot truss as in the one with greater 
 span. The trusses shown by Figs. 50 to 60 are mostly drawn 
 from actual cases, and give a pretty good idea of the most 
 economical division for different spans. 
 
 When the truss rafter is subject to a transverse strain, that 
 is when it is loaded between the joints, the distance between the 
 joints should not exceed 9 feet, and preferably 7 or 8 feet, depend- 
 ing somewhat on the distance the trusses are apart. The dia- 
 gram shown by Fig. 60 represents one-half of one of the steel 
 trusses used in roofing a car barn for the North Jersey Railway 
 Co. at Newark, N. J. There were 13 of these trusses spaced 
 19 feet 2J inches on centres, each having a span of 98i feet 
 between the centres of the supporting columns, to which the truss 
 is riveted by splice-plates engaging the end connection-plate and 
 the web of the column. The dimensions of the principal mem- 
 bers of these trusses are indicated in connection with the illus- 
 trations. A more complete description of the truss will be found 
 
 Main Tie 1-4-. 2-5"x 3K"x %" L's 
 
 " ' " 4-5. 2-3^"x2K"x 5 /i6"L's 
 
 Rafter, 1-2. 2-5 "x 3K"x V\S L's 
 
 " 2-3. 2-5" x SM"x%"L's 
 
 a, a, a, 2-2fc"x.2x x" L's 
 
 6,6,6, !-2^x2"xK" L's 
 
 C, 2-3 x 2M"x i" L's 
 
 Fig. 60 
 
 Truss over Car Barn, Newark, N. J. 
 
 in the Engineering Record of June 22, 1901. These trusses were 
 shipped in four sections, which were assembled in a horizontal 
 plane and riveted up complete at the surface of the ground. 
 The bottom chord was stiffened by lashing a rail on each side of 
 it for its entire length, and a sling being attached to the apex of 
 the top chord the truss was lifted and set on top of the columns 
 
STEEL ROOF TRUSSES. 923 
 
 by an 8X8 gin-pole 50 feet high. The roofing consists of corru- 
 gated iron supported by 5-inch I-beam purlins, weighing 10 Ibs. 
 to the foot, spanning from truss to truss and bolted to the 
 rafters with two bolts at each end; the general spacing of the 
 purlins being 4 feet 9| inches. This may be considered as an 
 example of an extremely light roof; the weight of each truss 
 being about 4,200 Ibs., and the entire weight of the truss, purlins, 
 bracing of the lower chord and the corrugated iron roofing being 
 only 8 Ibs. for each horizontal foot of surface covered. The 
 trusses shown by Fig. 59 were designed for the roof of a drill-hall 
 having a span of 80 feet, and with a spacing between the trusses 
 of 20 feet. The roof was to be constructed with 2"X8" rafters 
 supported by purlins at points A , B, C, D, E, and F. Sash were 
 to be placed in the rise E D, to light the interior of the building. 
 The joint at -X" was located with reference to the position of the 
 gallery rod ; if there had been no gallery it would have been more 
 economical to space the vertical struts uniformly as in Fig. 55. 
 The plus sign adjacent to a member in all the trusses illustrated 
 denotes that the member is in compression, while the minus sign 
 denotes tension. The members above the main rafter, as C D t 
 D E, and E F, in Fig. 59, and a and b in Fig. 60, do not form a 
 part of the truss proper, but are merely a framework to support 
 the elevated roof, and in drawing the stress diagram they would 
 be omitted. 
 
 Fink Trusses with Pin Joints. Fig. 61 shows one- 
 half of a Fink truss designed for pin connections. This truss has 
 a span of 55 feet 4 in. between the centres of end-pins, and the 
 distance between the centres of trusses is 6 feet. The roof is 
 covered with 12" X 20" slate, secured to ^"X2J" angle purlins 
 weighing 3 Ibs. to the foot and spaced 8J" on centres. The 
 angles span from truss to truss and are bolted to the deck-beam 
 with i-in. bolts. A 1J"X2J" nailing strip is fastened to every 
 third purlin for securing matched ceiling placed on the under 
 side of the roof. Complete details of this truss were published 
 in Architecture and Building for Jan. 18, 1890. Fig. 62 shows 
 details of the cast-iron struts. This truss, being put together 
 entirely with bolts and pins, could easily be erected with un- 
 skilled labor. 
 
 Trusses for Flat Roofs. For supporting flat roofs or 
 roofs having a fall not exceeding 1 inch to the foot, one of 
 the types shown by Figs. 63 to 67 will generally be found 
 economical, the choice of the particular type depending 
 
924 
 
 STEEL ROOF TRUSSES. 
 
 STRUT-D ! 
 
 Fig. 62 
 
 Detail of Struts, 
 Fig. 61. 
 
 ! STRUT-E 
 
STEEL ROOF TRUSSES. 
 
 925 
 
 somewhat on the span and whether the truss is supported 
 by columns or by brick or stone walls. For spans up to 50 
 feet either of the forms shown by Figs. 63 or 64 will answer 
 
 Fig. 63 
 
 Span 56'. 
 
 all practical requirements. The truss shown by Fig. 63 is in- 
 tended to be used where the fall of the roof is at right angles to 
 the truss; this truss can be built, however, with an inclination 
 to the top chord, as in Fig. 64. The end brace in Fig. 63 is in 
 
 Fig. 64 
 
 Spans SO'-SO*. 
 
 tension, while in Fig. 64 it is in compression. The portion of 
 the lower chord between the end joint and the wall, Fig. 63, has 
 
 Rafters 
 
 Fig. 65 
 
 no stress from the roof load, but is put in to brace the wall 
 and to stay the truss. In trusses supported by brick walls this 
 type is preferable to that shown by Fig. 64, while the latter is 
 
926 
 
 STEEL ROOF TRUSSES. 
 
 more suitable when the roof is supported by columns. The 
 vertical A, Fig. 64, is inserted to receive the tension or com- 
 pression from brace B, and would have no stress from the roof. 
 The truss shown by Fig. 65 is known as a "Double Warren 
 Truss," and is desirable where it is important to make the 
 trusses as shallow as practicable ; it can be built with light mem- 
 bers, and makes a very stiff roof, being especially suitable for 
 roofs supported by steel columns. Fig. 65 is drawn from an 
 actual truss. The strength under unsymmetrical loads, as for 
 example when there is more snow on one side than on the other, 
 would be materially increased by putting a vertical tie in the 
 centre as shown by the dotted line; without this member the 
 braces AA if subject to any stress whatever would produce a 
 bending in the bottom chord at the centre. Fig. 66 represents 
 an actual roof truss with span of 57 feet, supported by steel 
 columns. The entire load on the truss is transmitted to the 
 columns by the braces BE which are in tension. Fig. 67 shows 
 a truss of 96 feet span over a pier shed, New York city, the 
 trusses being spaced 20 feet apart. They are about 10 feet high 
 and weigh 1,300 Ibs. each; they were delivered complete from 
 the shops and were raised bodily by falls suspended from two 
 masts. The dimensions of these trusses are given in the En- 
 gineering Record of Jan. 18, 1896. 
 
 Fig. 66 
 Span 57'. 
 
 Fig. 67 
 Span 96'-' .0 
 
 The plus and minus signs in these illustrations indicate com- 
 pression and tension respectively under uniform dead load. 
 The plus and minus signs together indicate that the member may 
 
STEEL ROOF TRUSSES. 
 
 927 
 
 be subject to either tension or compression according to the 
 direction of the wind or to an uneven distribution of snow. In 
 most of these trusses an unsymmetrical load may change the 
 stress in the diagonals near the centre of the truss. This chang- 
 ing of stresses due ,to unequal loading will be considered in the 
 next chapter. Trusses shown by Figs. 63 to 67 are almost in- 
 variably built with riveted connections and with angle or 
 channel shapes for all members. 
 
 For horizontal steel trusses intended to support floor loads, 
 the Pratt truss, shown by Figs. 68 and 69, is the best adapted, * 
 the members indicated by double lines being in .compression and 
 those indicated by single lines in tension. When supporting 
 
 Fig. 68 
 
 Fig. 69 
 
 floors subject to moving loads, counter ties should be inserted 
 as indicated by dotted lines. For this truss, pin-connections 
 are generally employed and are preferable to riveted connec- 
 
 Fig 70. 
 
 Truss over Amphitheatre, Madison Square Garden. 
 
 tions. When properly proportioned this truss is capable of sus- 
 taining almost any load. 
 
928 
 
 STEEL ROOF TRUSSES. 
 
 The Quadrangular Truss. The truss shown by 
 Fig. 66 -is known as a quadrangular truss, although the more 
 common shape for this truss is that shown by Fig. 70, which 
 gives the proportions of the truss over the amphitheatre of 
 the Madison Square Garden, New York. Figs. 71 and 73 also 
 show variations of this truss, differing, however, from the 
 typical truss, in that the diagonals are all inclined in the same 
 direction, while in the typical truss they are usually reversed 
 in the centre in order to keep them in tension. 
 
 The plus and minus signs indicate the kind of stress in the 
 member produced by a uniform dead load. It should be 
 
 noticed that the centre 
 diagonals of trusses 71 and 
 73 are in compression. This 
 truss is well adapted to 
 steel construction for spans 
 up to 180 feet. When the 
 span exceeds 100 feet one * 
 end of the truss should be 
 supported on rollers to 
 allow for the expansion or 
 contraction in the steel. In 
 these trusses the load is 
 transmitted to the top of 
 the post by the end diagonal 
 which is always in tension 
 and subject to a very great 
 stress, the truss proper being 
 included within the points 
 A, B, C, D, and E, Figs. 71 
 and 72. The continuation 
 of the tie-beam to the post 
 is for the purpose of bracing 
 the roof from the columns, 
 there being no stress in this 
 member from a vertical 
 load only. In the truss 
 shown by Fig. 70 the post 
 P was made a part of the 
 truss ; the stress in this post 
 is equal to the reaction of 
 the truss. The brace B, Fig. 70, and the corresponding member 
 
STEEL ROOF TRUSSES. 
 
 929 
 
 in Figs. 71 and 72 should be so constructed as to resist both 
 tension and compression. For short spans the lower chord 
 
 may be made in the shape of a semi-circle or semi-ellipse so as 
 to give more of an arch effect. 
 
 There are numerous examples in this country of quadrangular 
 trusses having spans of from 100 to 180 feet. For the wider 
 
930 
 
 STEEL ROOF TRUSSES. 
 
 spans it is customary to build the truss with pin-connections, 
 eye-bars being used for the ties. When this is done it will 
 usually be necessary to insert counter braces in two panels on 
 each side of the truss as shown by the dotted lines, Fig. 70, 
 as under an unsymmetrical or wind load the stress in the diago- 
 
 xxxxxx 
 
 xxxxxx 
 
 s 
 
 I 
 I 
 
 nals is generally reversed. When the span is less than 100 
 feet, the truss may be built with riveted connections, in which 
 case the diagonals are generally made of angles capable of 
 resisting both tension and compression, and, therefore, counter 
 braces will not be required. For this type of truss the stresses 
 
STEEL ROOF TRUSSES. 931 
 
 due to wind and snow should be computed independently of 
 the dead load and the members computed for the maximum 
 stress that may be produced by any possible combination of 
 loading. 
 
 A description, with illustrations of the truss shown by 
 Fig. 73, 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. 
 
 ARCHED TRUSSES. 
 
 For roofing large rooms, such as railway stations, armories, 
 and exposition buildings, an arched truss is generally the most 
 economical. 
 
 Bowstring Trusses. Previous to the year 1880 wrought- 
 iron trusses of wide span were mostly built in the form of a 
 bow, from which the term " Bowstring" was derived. Trusses 
 of this type were built from 88 to 211 feet span and with a rise 
 in the centre of from one-fifth to one-fourth of the span. At 
 that time this style of truss was considered the most economi- 
 cal for spans exceeding 120 feet, but since the introduction of 
 the braced arch they have been comparatively little used. 
 
 Fig. 74 represents the diagram of a bowstring truss of 
 153-feet span. The trusses in this particular case are spaced 
 21 feet 6 inches apart. The arched rafter consists of a wrought- 
 iron deck-beam 9 inches deep, with a plate 10 inches by 1J 
 inches, riveted to its upper flange. Towards the springing 
 this rib was strengthened by plates 7 inches by J- inch, riveted 
 to the deck-beam on each side. 
 
 Fig. 74 
 
 The struts are wrought-iron I-beams 7 inches deep. The tie- 
 rods have a sectional area of 6J sq. ins., and the diagonal tension 
 braces are 1J inches in diameter. These trusses are fixed at 
 one end, and rest on rollers at the other, permitting free ex- 
 pansion and contraction of the iron under the varying heat of 
 the sun. 
 
932 
 
 STEEL ROOF TRUSSES. 
 
 Fig. 75 shows a similar truss having a span of 212 feet. It 
 consists of bowstring principals spaced 24 feet apart. The 
 
 Fig. 75 
 
 rise is one-fifth the span, the tie-rod rising 17 feet in the middle 
 above the springing, and the curved rafter rising 40 J feet. 
 The rafter is a 15-inch wrought-iron I-beam. The tie is a round 
 rod in short lengths, 4 inches diameter, thickened at the joints. 
 The tension bars of the bracing are of plate-iron, 5 inches to 
 3 inches in width, and inch thick. The struts are formed of 
 bars having the form of a cross. 
 
 Fig. 78 
 
 Braced Arches. Fig. 76 is a diagram of one of the 
 three arches used in roofing the train shed of the Sullivan 
 Square Station of the Boston Elevated Railway, a description of 
 
STEEL HOOF TRUSSES. 
 
 933 
 
 Fig. 76A 
 
 -Iftod 
 
 which may be found in the Engineering Record for June 15, 
 1 ( .)()1. These arches spring from steel columns and are provided 
 with tension rods which take up the thrust. The arch proper 
 rests on two 4J" pins a,t each 
 end as indicated in diagram, 
 the tie-rods being connected 
 to these pins. The bracing 
 below the pins is riveted to 
 the column and the arch 
 itself is built of angles and 
 plates with riveted connec- 
 tions. Fig. 76/1 shows the 
 joint at A where the tie-rods 
 are connected and are held 
 
 StfPin 
 
 2-l>6 Plates 
 
 up by a 1" suspension rod from the crown of the arch. This 
 construction is the same in principle as that of the wooden arch 
 shown by Fig. 48. It can hardly be considered as a truss in 
 the ordinary meaning of the word. 
 
 Three-Hinged, Braced Arches. The type of arched 
 truss most used at the present time for steel construction is that 
 shown by Figs. 78 and 79, which is commonly known as the 
 three-hinged, braced arch. This truss differs from all other types 
 of trusses in that it consists essentially of two separate parts, 
 each acting as a single piece and depending upon the opposing 
 force of its mate to keep it in position. As usually built, each 
 part is a semi-braced arch, the upper and lower members being 
 so connected by bracing as to form a stiff frame or curved rafter. 
 
 The first use of the braced arch appears to have been in 
 building railway bridges for French railroads, the earlier forms 
 being rigidly connected at the top. 
 
 The first suggestion for hinging the ribs at the crown was 
 made by M. Manton, a French engineer. 
 
 The application of this principle to roof trusses, at least on a 
 large scale, the author believes to have been in the train-sheds of 
 a Union Railway station at Frankfort-on-the-Main, Germany, 
 which was completed in the year 1888. These trusses have a 
 span of about 184 feet. The large roof of Machinery Hall, of 
 the Paris Exposition of 1899, was supported by this type of truss, 
 the span in this case being 368 feet, exceeding anything hitherto 
 attempted in a roof truss. Since then this truss has become 
 quite popular for roofing large exhibition buildings, train-sheds, 
 armories, etc. 
 
934 
 
 STEEL ROOF TRUSSES. 
 
 The three-hinged arch-truss proper is always supported on a 
 pin at the bottom and usually the two halves are pin-connected 
 at the top, thus allowing for expansion and contraction. The 
 bottom pins are usually placed below the ground floor level and 
 connected by tie-rods beneath the floor. These trusses can be 
 
 Fig. 77 
 
 Half Truss, Manufactures and Liberal Arts Building (Chicago). 
 
 built, however, and have been, without tie-rods, in which case it 
 is necessary that they rest on a foundation capable of resisting 
 the horizontal thrust, although the trusses can be so built that 
 the thrust will not be very great. 
 
 The special advantages of this type of truss for the class of 
 buildings above mentioned are economy, maximum clear space 
 beneath the truss and provision for expansion and contraction. 
 
STEEL ROOF TRUSSES. 
 
 935 
 
 Much of the economy of the truss lies in the fact that it re- 
 quires no columns to support it, and the base of the truss being 
 very near the ground level, it is well-proportioned to resist wind 
 pressure. 
 
 A great advantage of this truss is the free movement allowed 
 under temperature changes without strain to the structure, the 
 
 centre rising or falling freely with a slight rotation of the semi- 
 arches about the pivots. In the case of the trusses of the Paris 
 Exposition, it was estimated that a range of temperature of 100 
 degrees Fahr. would produce a change in level of 2J inches at 
 the centre pivot. 
 The arched ribs are always built of plates, angles or channels 
 
936 
 
 STEEL ROOF TRUSSES. 
 
 with riveted connections, and frequently with a solid plate web 
 at the bottom. 
 
 The determining of the stresses and detailing of the members 
 and joints will require the service of a competent structural 
 engineer, but the illustrations given will enable the architect to 
 
 -121-10- . 1 *{ 
 
 Fig. 79 
 
 Arched Truss, Machinery Hall, Chicago, 1890. 
 
 decide on the general shape of the truss for the purpose of making 
 preliminary drawings and the computations and detail draw- 
 ings can be made later. 
 
 For spans of from 80 to 120 feet this type is often put up 
 without the pin connections, as in Fig. 80, the mechanical prin- 
 ciple being essentially the same as in the three-hinged truss. 
 Complete drawings and details of the truss shown by Fig. 77 
 may be found in Vol. 26 of the Engineering Record, and of the 
 truss shown by Fig. 79 in Vol. 27. A description and details of 
 the truss shown by Fig. 78 may be found in the Engineering 
 Record for Dec. 3, 1899. Table VI, Chapter XXVI, gives the 
 dimensions and spacing of a number of trusses similar to Figs. 
 77, 78, and 80. 
 
 Other examples of three-hinged arched trusses are given in 
 Part III of the author's work on Building Construction. 
 
 Cantilever Trusses. The term "cantilever" was orig- 
 nally used to designate a projecting beam which served as a 
 
STEEL ROOF TRUSSES. 
 
 937 
 
 bracket; in mechanics it is used to denote a beam or girder fixed 
 at one end, either by being built into a wall or, most commonly, 
 by extending a sufficient distance beyond its support to form an 
 anchorage for the cantilever. Thus in Fig. 81 we have a beam 
 
 Fig. 80 
 
 resting on two supports ; the portion B is a cantilever, while the 
 part C forms the anchorage for it. 
 
 (In applying the cantilever to trusses it is customary to inter- 
 pret it as including both the projecting arm and the balancing 
 arm, as both portions form one piece of framework, and the term 
 will be so used in this work.) 
 
 It is obvious that if the entire beam (Fig. 81) were uniformly 
 loaded the post P would carry .the greater part of the weight, 
 and also that an additional load at W might produce an upward 
 pull on the post D, in which case the stress on P would exceed 
 the load on the beam. 
 
 Both conditions of loading occur in practice, although it 
 probably most often happens that the outer end of the truss 
 requires anchorage rather than a support. 
 
938 
 
 STEEL ROOF TRUSSES. 
 
 As applied to roof construction some such arrangement as is 
 shown in Fig. 82 is generally required to make this method of 
 support practicable; that is, a wide centre span, with shorter 
 spans or aisles on each side of it. 
 
 The projecting or inner arm of the cantilever is usually made 
 from one-quarter to one-third of the centre span, and a simple 
 truss, represented by /S, is used to support the rest of the roof, the 
 centre truss being supported by the arms of the cantilever. In 
 all such cases, therefore, cantilever trusses must be used in pairs, 
 one on each side of the building, and there must be rooms or pas- 
 sages outside of the principal span to permit of the outer or 
 balancing arm. Such an arrangement is generally found in 
 large halls, armories, exhibition buildings, etc., and it might 
 sometimes be provided in other classes of buildings. 
 
 Fig. 81 
 
 Of course, in a large building a simple beam such as is shown 
 in Fig. 82 could not be used, but the principle of construction 
 is the same whether the cantilever be a simple beam or a large 
 truss. 
 
 Fig. 83 shows the diagram for a truss to take the place of 
 the beam CB, Fig. 82, the single lines representing the tension 
 
STEEL ROOF TRUSSES. 
 
 939 
 
 members and the double lines compression members, and 
 Fig. 86 shows the complete arrangement of the trusses.* 
 
 The truss shown in these figures may be extended to almost 
 any extent, and the lower chord may be curved, but the general 
 outline of the truss will be found best adapted for all cases 
 where a wide central roof is to be supported by cantilevers. 
 
 For bridge trusses or floors the shape shown in Fig. 84 may 
 be used, and for -shed and platform roofs open on one side a 
 truss of the shape shown in Fig. 85 is about the only practicable 
 device. In this latter truss the proportions of the arms are 
 such that a slight support is required at W, thereby bringing 
 the lower portion of the rafter into compression. 
 
 It will be seen from Figs. 83, 84, and 85 that the strains in a 
 cantilever truss are directly the reverse of those in trusses sup- 
 ported at both ends, the upper chord or rafter in the cantilever 
 being in tension, while in all other trusses, except the hinged 
 arch, it is in compression. 
 
 Fig. 86 
 
 Suggestion for Wooden Cantilever Truss. 
 
 Advantages and Disadvantages of the Cantilever 
 Truss. The special advantages possessed by the cantilever 
 truss are: A greater clear height in the centre than can be ob- 
 tained with any other type excepting the three-hinged arch, 
 a light and graceful appearance, no horizontal thrust, and con- 
 sequently no tie-rods required. The particular advantage of 
 this truss for very great spans is that it can be erected with- 
 
 * Suggested by Mr. John Beverly Robinson for a simple trussed canti- 
 lever roof. 
 
940 
 
 STEEL ROOF TRUSSES. 
 
 out scaffolding under the centre, and in bridge work this is 
 considered as its only advantage. 
 
 It is claimed by prominent engineers that the cantilever is 
 not an economical type of truss, and not as desirable for spans 
 of 150 feet or more as the three-hinged arch. 
 
 It also does not permit of as readily overcoming expansion 
 and contraction as either the three-hinged arch, the bowstring 
 truss, or the quadrangular truss. For certain classes of buildings, 
 however, and especially where the central span does not exceed 
 150 feet, it can perhaps be used with better architectural effect 
 than is possible with other types, and with about the same 
 economy. For roofing platforms, grand-stands, etc., where an 
 outer support is not desired, it is the only type available. 
 
 Example of a Cantilever Truss. Fig. 87 is a dia- 
 gram of one of the cantilever trusses supporting the roof of 
 the grand-stand at the Monmouth Park (N. J.) racing-track, 
 the details of which were published in Architecture and Building 
 in February, 1890. This is an instance where the cantilever 
 was the only type of truss that could be used, and the form 
 adopted is both simple and economical. 
 
 Fig. 87 
 
 As will be seen from the drawing, the main supporting post 
 extends to the top of the truss, as is usually the case with canti- 
 lever trusses, and the truss is riveted to each side of it. The 
 upper and lower chords were made of two angles and a web- 
 plate, the upper chords or rafters acting as a tie-beam between 
 the bracing. The bracing consists of angle-bars used in pairs 
 and varying from 3X2Xi inches to 3X3X% inches, the whole 
 frame being connected by rivete. Other examples of canti- 
 lever roofs are given in Part III of " Building Construction." 
 
ROOF LOADS. 941 
 
 CHAPTER XXVI. 
 STRESSES IN ROOF-TRUSSES. 
 
 THE various steps to be pursued in designing a trussed roof 
 and proportioning its parts are as follows: 
 
 First. Deciding upon the roof covering and how it is to be 
 supported between the trusses. 
 
 Second Laying out the roof trusses on the plan and section. 
 
 Third. Computing the truss, loads and determining the 
 stresses produced thereby. 
 
 Fourth. Computing the size of the truss members. 
 
 Fifth. Detailing the joints. 
 
 The kind of roof covering to use, on a pitch roof, will be 
 determined largely by the external effect sought, and by the 
 Cost. For flat roofs, appearance usually cuts no figure, so that 
 the durability, cost, and adaptability to any peculiar requirements 
 of the building are the controlling elements. The matter of 
 incombustibility, or resistance to fire, is also generally a point to 
 be considered when steel trusses are to be used. 
 
 Roofing Materials for Pitch Roofs. The mate- 
 rials suitable for covering pitch roofs are slate, burnt clay tiles, 
 metal tiles or shingles, wood shingles, corrugated iron, tin with 
 standing seam, 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 is indicated by Table I. The cost, however, 
 can only be considered as approximate as it will vary for different 
 materials, according to the locality, and the scale of wages. 
 
 Flat roofs or roofs having a fall of J in. to f in. to the foot, 
 are usually covered with tar and gravel, asphalt, ready roofing, 
 or tin with lock-and-solder joint. A good tin roof costs about 
 $8 a square, besides the painting. The other kinds will vary 
 from $3.50 to $4.50 a square. 
 
942 
 
 STRESSES IN ROOF-TRUSSES. 
 
 TABLE I. COVERING MATERIALS FOR PITCH ROOFS. 
 
 Material 
 
 Least 
 Rise of 
 Rafter 
 in 12 
 ins. 
 
 Comparative 
 Cost per 
 Square. 
 
 Slates, black 
 
 8 
 
 $7 to $12 
 
 Slates, green 
 
 8 
 
 $7 to $10 
 
 Slates, red 
 
 8 
 
 $12 to $17 
 
 Burnt clay tiles, interlocking pattern 
 
 7 
 
 $15 to $25 
 
 Tin shingles, painted ... 
 
 6 
 
 $8 to $10 
 
 Galvanized iron tile, painted 
 
 6 
 
 $13 to $15 
 
 Cedar shingles, stained or painted 
 
 6 
 
 $3.80 to $7.20 
 
 Corrugated iron, painted ... 
 
 3 
 
 $4 00 to $4 50 
 
 Standing seam steel roofing, painted 
 
 2 
 
 $4 to $4.50 
 
 Ready roofing 
 
 1 
 
 $3.50 to $4.50 
 
 
 
 
 Manner of Supporting 1 the Roof from the Trusses. 
 
 Wooden roofs, supported by wooden trusses, require common 
 or jack rafters to support the sheathing 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, 
 see p. 891. 
 
 When slate or burnt clay tile are used on steel roofs, they 
 are usually secured to steel angles, running parallel with the 
 walls and spaced from 8 to 10J ins. apart, as may be necessary 
 to accommodate the size of the slate or tile. If the span is not 
 very great, the angles may be fastened to the truss rafters, 
 which will require that the trusses be not more than 6 or 7 ft. 
 apart. As a rule, however, when slate or tile are to be used, 
 it will be cheaper to space the trusses from 16 to 20 ft. apart, 
 and to use purlins and jack rafters for supporting 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, unless there is a wooden ceiling below, in which 
 case unprotected steel is little if any better than wood. 
 
 If corrugated iron is to be used for roofing, the most economi- 
 cal construction for steel roofs will be to space the trusses from 
 16 to 20 ft. apart, and to use light I-beams for purlins, spaced 
 about 4' 9" on centers, as in Fig. 60, Chapter XXV, the cor- 
 rugated iron being secured to the purlins by straps. If warm 
 air comes in contact with the underside of a corrugated roof 
 
ROOF LOADS. 943 
 
 the roofing should be laid on boards, or some kind of anti-con- 
 densation lining provided, otherwise the moisture in the air will 
 condense and fall on the floor or objects below. 
 
 Flat roofs will always require rafters and sheathing, or fire- * 
 proof filling between the rafters. 
 
 Spacing of Trusses. From the above it will be seen 
 that the economical spacing of the trusses will depend to a con- 
 siderable degree upon the kind of roofing that is to be used, 
 and also upon the span. As a general rule, however, the most 
 economical spacing will be about as follows: 
 
 For wooden trusses under 80 ft. span, 12 to 16 ft. C. to C. 
 
 For wooden trusses over 80 ft. span, 16 to 24 ft. C. to C. 
 
 For steel trusses under 80 ft. span, 16 to 20 ft. C. to C. 
 
 For steel trusses over 80 ft. span, 20 to 40 ft. C. to C. 
 
 The actual spacing of a number of steel trusses of wide span 
 is given in Table VI. 
 
 When the distance between the trusses exceeds 16 ft. for 
 wooden roofs or 20 ft. for steel roofs, it will generally be neces- 
 sary 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, and also the 
 manner of supporting the ceiling, if any, and any other loads 
 that are to be supported by the trusses. 
 
 The section and truss drawing with a knowledge of the weight 
 of materials, will afford the necessary data for computing the 
 loads at each joint of the truss. 
 
 Until the stresses have been determined, the size of the 
 members computed, and the joints detailed, an exact drawing 
 of the truss cannot, of course, be made, but to compute the 
 loads and stresses, it is necessary to know the position of the 
 joints, and these can be indicated with sufficient accuracy with- 
 out knowing the exact size of the members. Chapter XXV 
 gives sufficient information regarding the various types of 
 trusses, to enable one to decide on the height, and the number 
 and position of the struts and ties, and one can guess at the 
 size of the members for the preliminary drawings. 
 
944 
 
 STRESSES IN ROOF-TRUSSES. 
 
 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 transferred to the joints, 
 and that the members are free to move at the joints as if hinged, 
 even although the actual joint may be made with riveted con- 
 nections. The loads at the joints are, of course, equal to the 
 reaction of the purlins, 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 find the 
 roof or ceiling area contributory to the joint, and multiply 
 this area by the weight or load per square foot. 
 
 As a rule, the area contributory to any joint is equal to the 
 distance half way to the next joint on each side, multiplied 
 by the distance half way to the next truss or wall, on each side. 
 Thus if Fig. 1 represents truss 1, of Fig. 2, the roof area contribu- 
 tory to joint 2, is 2 -Xa. For truss 2, the area supported 
 by the same joint is ^ Xa, or if we let D represent the 
 
 --4 
 
 Rafters and Ceiling Joists 2 x * 
 16*C. to C. 
 
 Fig. 
 
 length of roof or ceiling supported at each joint, then the area 
 supported by joint 2=aXl> and the area supported by joint 
 3=2bxD. In the same way, the ceiling area supported at 
 joint 6=cXl>, the arrow-heads being half way between the 
 joints. 
 
 It makes no difference in the joint loads whether the common 
 rafters are supported on purlins or whether they rest on the 
 
ROOF LOADS. 
 
 945 
 
 rafter provided the purlins come at or close to the joints and 
 the load is uniformly distributed. 
 
 Thus the width of the ceilling contributory to joint 7, Fig. 3, 
 will be equal to c, just the same 
 as in Fig. 1, but it makes a con- 
 siderable difference in the strain 
 in the tie-beam. When the 
 trusses are spaced a uniform 
 distance apart, D, Fig. 2, will, 
 of course, be equal to the dis- 
 tance between centres of trusses. 
 When the trusses are not spaced 
 uniformly, D equals one half 
 the distance from the centre of 
 the truss on the left to the 
 centre of the truss on the right. 
 
 When the purlin comes more 
 than 12 ins. from a joint, or the 
 roof area is not symmetrical, as 
 is often the case at hips and 
 
 \ 
 
 T 
 
 ! Truss 3 
 
 
 I 'f 
 
 b 1 
 
 I 
 
 1" 
 
 di * Truss 2 
 
 V 
 
 ' \ 
 
 J 
 1 
 
 i 33!- 
 *P Truss 1 
 
 \ 
 
 r 
 
 J 
 
 F^ 
 
 
 JL 
 
 \ 
 
 : 1 
 
 Fig. 2 
 
 valleys, then the joint load must be determined by the principle 
 of the reaction of beams, as explained on pp. 274r-277. Ex- 
 
 JT 1?-^fl'a- ^ 122 "' ^ 
 
 2 x 6 Rafters 
 18 O.C. 
 
 Fig. 3 
 
 am pies showing the computation of joint loads are given a 
 little further on. 
 
946 STRESSES IN ROOF-TRUSSES. 
 
 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 snow and also an 
 allowance for wind pressure. The weight of the materials 
 compose what is called the dead load. Snow is generally con- 
 sidered as a live load, acting vertically. The pressure due to 
 the wind always acts normal, or at right angles to the surface 
 of the roof, but for trusses of less than 100 ft. span it is usually 
 combined with the wind and snow loads and treated as a ver- 
 tical load. 
 
 Data for Computing Dead Loads. The dead load of any roof 
 may be estimated quite closely from the following data: 
 
 TABLE II. WEIGHTS PER SQUARE FOOT OF ROOF 
 SURFACE. 
 
 Shingles, common, 2J Ibs.; 18 ins., 3 Ibs. 
 
 Slates, % in. thick, 7J Ibs. ; J in. thick, 9.6 Ibs. (the common 
 thickness is% in. for sizes up to 10"X20"). 
 
 Plain tiles or clay shingles, 11 to 14 Ibs. 
 
 Roman tiles, old style, two parts, 12 Ibs.; new style, one 
 part, 8 Ibs. 
 
 Spanish tiles, old style, two parts, 19 Ibs. 5 new style, one 
 part, 8 Ibs. 
 
 Improved Oriental tiles, 11 Ibs. 
 
 Ludowici tile, 8 Ibs. 
 
 For tiles laid in mortar add 10 Ibs. per square foot. 
 
 Copper roofing, sheets, 1J Ibs.; tiles, If Ibs. 
 
 Tin roofing, sheets or shingles, including one thickness of felt, 
 1 Ib. 
 
 Corrugated iron, painted or galvanized, No. 26, 1 Ib. ; No. 24, 
 1.3 Ibs.; No; 22, 1.6 Ibs.'; No 20, 1.9 Ibs.; No. 18, 2.6 Ibs.; and 
 No. 16, 3.3 Ibs. 
 
 Standing seam steel roofing, 1 Ib. 
 
 Five-ply felt and gravel roof, 6 Ibs. 
 
 Four-ply felt and gravel roof, 5J Ibs. 
 
 Three-ply ready roofing (elaterite, ruberoid, asphalt, etc.), 
 0.6 to 1 Ib. 
 
 Skylights with galvanized iron frame, -inch glass, 4J Ibs.; 
 %-in., 5 Ibs.; f-in., 6 Ibs. 
 
 Sheathing, 1 in. thick, 3 Ibs. per square foot for white pine, 
 spruce, or hemlock; 4 Ibs. for yellow or pitch pine. 
 
ROOF LOADS. 
 
 947 
 
 TABLE III. WEIGHT OF RAFTERS PER SQUARE FOOT. 
 
 Size of 
 Rafters, 
 
 Spruce, Hemlock, White Pine, 
 Spacing in Inches, Centre to 
 Centre. 
 
 Hard Pine, Spacing in Inches, 
 Centre to Centre. 
 
 
 16 
 
 20 
 
 24 
 
 16 
 
 20 
 
 24 
 
 
 Ibs. 
 
 Ibs. 
 
 Ibs. 
 
 Ibs. 
 
 Ibs. 
 
 Ibs. 
 
 2X4 
 
 I* 
 
 1.2 
 
 1 
 
 2 
 
 1.6 
 
 H 
 
 2X6 
 
 It 
 
 1.8 
 
 U 
 
 3 
 
 2.4 
 
 2 
 
 2X7 
 
 2f 
 
 2.1 
 
 If 
 
 3i 
 
 2.8 
 
 2J 
 
 2X8 
 
 3 
 
 2.4 
 
 2 
 
 4 
 
 3.2 
 
 2 
 
 2X10 
 
 3} 
 
 3 
 
 2i 
 
 5 
 
 1 4 
 
 3J 
 
 Wooden purlins will weigh about 2 Ibs. per square foot of roof 
 surface when the span is between 12 and 16 ft. 
 
 For steel roofs the size and weight of the purlins and rafters 
 should be computed for each particular case. 
 
 For a rough approximation the weight of steel trusses, purlins, 
 and bracing in a roof covered with corrugated iron with no ceiling 
 will run from 4 to 6 Ibs. per square foot of horizontal surface 
 covered. The steel work for slate roofs with suspended ceil- 
 ings below will run about 7J Ibs. per square foot when the span 
 does not exceed 50 ft. 
 
 Steel roofs supported by arched trusses will weigh from 8 to 12 
 Ibs. per square foor of roof surface. 
 
 Weight of Truss. To the weight of the roof construc- 
 tion proper should be added an allowance for the weight of the 
 trusses. 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 the trusses are completely designed. 
 Several tables for the weight 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 given for weight of steel trusses, 
 W being weight per horizontal square foot, 5 = span in feet. 
 Charles Evan Fowler, C.E., for Fink trusses: 
 
 W = .065 +.6 for heavy loads; 
 
 W=.Q4S + A for light loads. 
 H. G. Tyrrell, C.E.: 
 
 C.W.Bryan, C.E.: 
 
 dist. centre to centre- 
 
 w-- 
 
948 
 
 STRESSES IN ROOF-TRUSSES. 
 
 Tables IV and V compiled by the author, from a comparison 
 of other tables and formulas, and from the weight 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 the author prefers 
 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. 
 
 TABLE IV. WEIGHT PER SQUARE FOOT OF ROOF 
 SURFACE FOR WOODEN TRUSSES.* 
 
 Span. 
 
 H Pitch. 
 
 M Pitch. 
 
 M Pitch. 
 
 Flat. 
 
 
 Ibs. 
 
 Ibs. 
 
 Ibs. 
 
 Ibs. 
 
 Up to 36ft. 
 
 3 
 
 3* 
 
 3f 
 
 4 
 
 36 to 50ft. 
 
 3i 
 
 3| 
 
 4 
 
 4i 
 
 50 to 60ft. 
 
 3J 
 
 4 
 
 4* 
 
 4f 
 
 60 to 70ft. 
 
 3| 
 
 4J 
 
 4J 
 
 5i 
 
 70 to 80ft. 
 
 4i 
 
 5 
 
 5| 
 
 6 
 
 80 to 90ft. 
 
 5 
 
 6 
 
 <H 
 
 7 
 
 90 to 100 ft. 
 100 to 110 ft. 
 
 P 
 
 6J 
 T| 
 
 7 
 8 
 
 8 
 9 
 
 110 to 120 ft. 
 
 
 8} 
 
 9 
 
 10 
 
 * For scissors trusses increase one-third. 
 
 TABLE V. WEIGHT PER SQUARE FOOT OF ROOF 
 SURFACE FOR STEEL TRUSSES. 
 
 Span. 
 
 Y 2 Pitch. 
 
 Ys Pitch. 
 
 M Pitch. 
 
 Flat. 
 
 Up to 40 ft. 
 
 5.25 
 
 6.3 
 
 6.8 
 
 7.6 
 
 50ft. 
 
 5.75 
 
 6.6 
 
 7.2 
 
 8.0 
 
 60ft. 
 
 6.75 
 
 8.0 
 
 8.6 
 
 9.6 
 
 70ft. 
 
 7.25 
 
 8.5 
 
 9.2 
 
 10.2 
 
 80ft. 
 
 7.75 
 
 9.0 
 
 9.7 
 
 10.8 
 
 100 ft. 
 
 8.5 
 
 10.0 
 
 10.8 
 
 12.0 
 
 120 ft. 
 
 9.5 
 
 11.0 
 
 12.0 
 
 13.20 
 
 140 ft. 
 
 10.0 
 
 11.6 
 
 12.6 
 
 14.0 
 
 The data for the first seven buildings in Table VI were com- 
 piled by Mr. H. G. Tyrrell, C.E., who states that all of the seven 
 roofs were proportioned for slate and plank roofing resting on 
 wide rafters 2 ft. apart, supported by steel purlins about 
 10 ft. apart. Spans given are centre to centre of side bearings. 
 
SNOW LOAD. 
 
 949 
 
 Btr6fB60 computed for dead load of l>r> Ihs., snow load of |() Ihs. 
 per square fool, of sloping surface, liori/ont ;il wind 10 l|>s. per 
 s<|ii-ire fool, or !2<S Ihs. normal pressure. 
 
 Dal.a for compuliii!.!; Mir weight, of floors :IIM| floor loads 
 supported hy trusses, or for fireproof ronsl.rue! ion, may In- 
 found in Chapters \ \1 :uul XXIV. 
 
 TAKLK VL WEKJIIT AND SPACING OF SOME STEEL 
 
 K'OOFS OF Wll>l<; SPAN, INCLUDING TllUSSKS, 
 
 PURLINS, AND pd JACKS, BUT NOT HOOF COVER- 
 
 INO oli. IIAI'TKIJS. 
 
 Nniiic f Hnildititf. 
 
 Tvi>o of 
 
 TrUHH. 
 
 Sp.-iii, 
 ftft 
 
 S|i:irin>.' 
 
 c. fo c! 
 of 
 
 TriLSHitH. 
 
 \Vl, |,r, 
 
 S, ( M 
 SlopinK 
 Sin I'.-irr 
 
 U.S. 
 
 S.7 
 9.7 
 s.c, 
 8.0 
 II .S 
 
 P.5 
 
 12.4 
 
 \\i. ol 
 
 of 
 
 < >nr 
 Tl'UHH. 
 
 ':i\\l nrkrl Armory 
 'oil l.-i IM| , Mr. , A rmory . . . 
 
 Miu-nix H.-iii. Brockton . 
 
 Slorl li:ini|>lon Ai moi y . 
 ':il;irr Kink, 1 l:n 1 I'nnl . 
 'n>\ -iilrnrr \\\ . 1 l:ill 
 'lr\ rl:m<l Armory 
 '< > 1 ' >n A I'll ii )I'V - . . . 
 
 Fig. 80* 
 
 1-'i. 7Ii* 
 
 .'I liini'.r .-irrli 
 
 .: Mi .-iiri. 
 
 82 
 92 
 06 
 
 100 
 KM 
 1 IS 
 I'JO 
 122 
 17(1 
 
 I'.Hi 
 
 lS7';it 
 
 227 f 
 
 1 l'..,j 
 
 Fot 
 24 
 
 25 
 24 
 24 
 
 25 
 
 I'M 
 
 ; , 
 
 30 
 
 21 >(J 
 
 86 
 
 23-25 
 
 Tons 
 8.7 
 
 ) 
 
 10 
 
 11.5 
 12.5 
 
 21 
 
 :"M I.VKI,. (N. S'.) Armory . . . 
 Hr >< >k 1 \'ii \ i UK ii y .... 
 
 KMM.M.MS < 'it y < 'oiix'rnl inn 1 I/ill 
 7 Illi Kru'l AniKM-.v, |tulf:il<. 
 
 
 - 1 ( li:iplcr X XV. f ^ 'i-iil.rr lo crnl rr of -n<l [iiiM. 
 
 SllOW. --As :i l>:i.sis for m.-iKiii!-; :in :ill<.w;inee for snow, 
 T.-il.le VII is perlin,ps as good a pjuidn JIM any Mi;il, e;m he ^i\m. 
 When .smw <in<ir<lx ;in- lo IM- pl;i,eed on a. roof, |,he sarno allow- 
 ailC(^ should he innde for ;i h;il! pilch as for OIM- Uiird pitch. 
 
 TABLE VII. ALLOW ANOK Foil SNOW IN POUNDS 
 S(ii:.\IJ.K FOOT OF ROOF sm.'FACK. 
 
 
 
 l',l 
 
 1. pi Etg 
 
 ,r. 
 
 
 
 M 
 
 K 
 
 '. 
 
 '/r, 
 
 a? 
 
 Soilllirrn Slrilr;; :ui.| I'.'icilir Sl'.pc 
 (Vnt nil Sl.-itcs 
 
 * t 
 
 
 
 () fl 
 
 11 
 
 7- 10 
 
 * t 
 o 5 
 i.- 20 
 
 5 
 22 
 
 a 
 
 
 II) 
 
 10 l. r > 
 
 
 27 
 
 35 
 
 New l'!ii"l:!inl Sl;i|,OH 
 
 () ID 
 
 in I :> 
 
 20 2. r > 
 
 :',. r > 
 
 40 
 
 Norl li\\'r:-l Si :ilrn 
 
 
 1 ' IS 
 
 
 
 A* 
 
 
 
 
 
 
 
 in-:i.ir,i |, V :i.n .-i .-i.rii k (*) are r-.r islate, tile, or metal; thoie 
 
 hr:i,|,-(l |,y ;i , |:iKr'i ( | ) llfr I'or .iliin^lr roof. 
 
950 
 
 STRESSES IN ROOF-TRUSSES. 
 
 Wind Pressure. For roofs having a pitch of 5 ins. 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 author 
 recommends that the allowance for wind and snow combined 
 be not less than indicated in Table VIII. 
 
 TABLE VIII. ALLOWANCE FOR WIND AND SNOW 
 COMBINED IN POUNDS PER SQUARE FOOT OF 
 ROOF SURFACE. 
 
 Location. 
 
 Pitch of Roof. 
 
 60 
 
 45 
 
 H 
 
 1 A 
 
 % 
 
 H 
 
 Northwest States . 
 
 30 
 30 
 30 
 30 
 30 
 
 30 
 30 
 30 
 30 
 30 
 
 25 
 25 
 25 
 25 
 25 
 
 30 
 25 
 25 
 25 
 25 
 
 37 
 35 
 27 
 22 
 22 
 
 45 
 40 
 35 
 30 
 20 
 
 New England States 
 
 Rocky Mountain States 
 
 Central States 
 
 Southern and Pacific States 
 
 No roof truss should be proportioned for a total load of less 
 than 40 Ibs. per square foot, except flat roofs in warm climates. 
 
 For trusses having a span exceeding 100 ft. (except horizontal 
 trusses) and for trusses in which a partial load may produce 
 maximum stresses, or call for counter bracing, 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 to the maximum stress 
 to which it may be subject under any possible combination 
 of the load. 
 
 For determining the stresses due to wind pressure alone 
 the force of the wind is usually assumed to act in a direction 
 normal, i.e., at right angles to the slope of the roof. This 
 force is commonly based on a horizontal wind pressure of 30 Ibs. 
 
 * Mr. Bryan, the designing engineer of the Edgemoor Bridge Works, states 
 that " in Fink trusses a partial load due to wind or snow never causes any 
 maximum stresses, so that it is customary to calculate these trusses for a 
 uniform load over the entire truss, the wind and snow loads combined being 
 usually assumed at 30 Ibs. per sq . f t. of area covered ; i.e. , horizontal surface." 
 
WIND PRESSURE. 
 
 951 
 
 per square foot, although quite often it is taken* at 40 Ibs. per 
 square foot, depending somewhat upon the exposure and the 
 shape of construction of the roof and truss. 
 
 The normal and horizontal pressure per square foot of roof 
 surface corresponding to a horizontal pressure of 30 Ibs. against 
 a vertical surface is given in Table IX. 
 
 TABLE IX. NORMAL AND HORIZONTAL WIND PRES- 
 SURE ON ROOFS FOR 30 POUNDS HORIZONTAL 
 PRESSURE AGAINST A VERTICAL SURFACE. 
 
 Inclination. 
 
 Norm 
 
 Hor. 
 
 Inclination. 
 
 Norm. 
 
 Hor. 
 
 5.. 
 
 Ibs. 
 3 9 
 
 Ibs. 
 0.3 
 
 30. . 
 
 Ibs. 
 19.9 
 
 Ibs. 
 10.0 
 
 10 
 
 7.2 
 
 1.2 
 
 33-41' (K pitch) . . 
 
 22.0 
 
 12.0 
 
 15 
 
 10.5 
 
 
 35 . . 
 
 22 6 
 
 
 18-26' (K pitch) .... 
 
 13.0 
 
 4.0 
 
 40 
 
 25.1 
 
 15.9 
 
 20. . 
 
 13 7 
 
 4 5 
 
 45 (^ pitch). 
 
 27 1 
 
 19 
 
 21-48' (M> pitch) 
 
 15.0 
 
 6.0 
 
 50 .. . 
 
 28.6 
 
 21.9 
 
 25 
 
 16.9 
 
 
 55 
 
 29.7 
 
 
 26-34' (14 pitch) . . . 
 
 18.0 
 
 8.0 
 
 60 
 
 30.0 
 
 25.5 
 
 
 
 
 
 
 
 For horizontal wind pressure of 40 Ibs. per square foot the 
 pressure given above should be increased one- third. 
 
 Variations in Loading for which Stresses should 
 be Found. To determine the maximum stresses under 
 any possible condition of loading, stresses should be found for 
 the following cases: 
 
 (1) 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 cf truss nearer the fixed end. 
 
 It 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 combinations for maximum stress 
 will be either cases 1 and 3 or c ses 1, 2, and 4 or 5. 
 
 If the trusses are supported on iron columns instead of walls 
 the wind force is transferred to the foundations through the 
 columns, producing a bending moment in the columns. The 
 strains in the columns, trusses, and knee-braces should there- 
 fore be determined for the horizontal wind pressure against 
 the side of the building and roof. This pressure is obtained 
 by multiplying the area of the vertical surfaces by the full 
 
952 STRESSES IN ROOF-TRUSSES. 
 
 pressure per square foot and the elevation of the roof by the 
 horizontal component, given in Table IX. 
 
 For the trusses supporting the roof of the Kansas City Audi- 
 torium (see Fig. 73, Chapter XXV) 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 Ibs. and no load on roof- 
 garden floor; third, full dead load and 50 Ibs. 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 pp. 1023 and 1034. 
 
 Examples of the Computation of Roof Loads. 
 
 (All loads considered as acting vertically.) 
 
 1. For the first example we will take the roof and truss 
 shown by Fig. 1 (p. 944), which we will assume represents truss 
 2 of Fig. 2. We will assume that the timber is to be common 
 white pine and that the roof is to be covered with ^-inch slate 
 of medium size on J-inch sheathing. 
 
 The ceiling to consist of lath and plaster. 
 
 The dead load of roof and truss per square foot of roof sur- 
 face will be made up as follows: 
 
 For slate ?i Ibs. 
 
 For sheathing 3 " 
 
 For rafters 3 " 
 
 For purlins 2 " 
 
 For truss 3 " 
 
 Total 18J Ibs. 
 
 For wind and snow load combined we should allow about 
 28 Ibs. (the pitch being about 40 degrees) , which would make a 
 total roof load of 46J Ibs. To avoid fractions, however, we 
 will take 48 Ibs. per square foot. 
 
 As the distance to truss 1, Fig. 2, is 12 ft., and to truss 3 
 14 ft., the length of roof supported by the truss will be 13 ft. 
 The roof area supported by the purlins at joint 2 will be equal 
 to the distance a multiplied by 13 ft., and a will be one-half of 
 the distance from the wall plate to the next purlin, or 22' 8" 4- 2 
 
COMPUTATIONS OP HOOF- LOADS. 953 
 
 = 11' 4", or 11 J ft. Hence the roof area supported at joint 2 
 will be 11JX13, or 147J square feet. 
 
 The roof area supported by the purlins at joint 3 will be 
 26X13 ft., or 12' 4"X13'=160| square ft. 
 
 Multiplying the roof areas by the load per square foot (48), 
 we have 7,072 Ibs. for the load at joint 2 and 7,696 Ibs. for the 
 load at joint 3. The load at joint 4 will be equal to that at 2, 
 as the truss is symmetrical. 
 
 We must now compute the ceiling loads at joints 6 and 7. 
 The ceiling area supported at joint 6=cXl3 ft.,or8JX!3=107i 
 sq. ft. The area supported at joint 7=8f X13=114 sq. ft. 
 
 The actual weight of the ceiling per square foot will be 3 Ibs. 
 for the joists and 10 Ibs. for lath and plaster; but where there 
 is a large attic space it is liable to be used for storing odd articles, 
 so that it is always well to make a small allowance, say 5 Ibs. 
 per square foot, for any extra weight that might be placed in 
 the attic. We will, therefore, allow 18 Ibs. per square foot for 
 the weight of the ceiling, which would make the weight at 
 joints 6 and 8 107JX18, or 1,930 Ibs., and the weight at joint 7 
 114JX 18= 2,067 Ibs. 
 
 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 1 are transmitted directly to the wall and need 
 not be taken into account in determining the stresses. 
 
 EXAMPLE 2. To compute the joint loads for the truss shown 
 by Fig. 3, p. 945, all timber to be of spruce and the roof to be 
 covered with shingles on 1-inch sheathing; the ceiling to be 
 of lath and plaster. 
 
 For the dead load per square foot we have 
 
 Weight of shingles 2J Ibs. 
 
 Weight of sheathing 3 " 
 
 Weight of rafters 2J " 
 
 Weight of purlins 2 " 
 
 Weight of truss .'3 " 
 
 Total dead load per square foot . . . 12f Ibs. 
 
 Allowance for wind and snow 30 Ibs. 
 
 Total roof load per square foot .... 42J " 
 
 For the weight of the ceiling it will be well for a truss of 
 this kind to allow at least 20 Ibs. per square foot. 
 
 We will assume that the trusses are to be spaced uniformly 
 15 ft. centre to centre. 
 
954 
 
 STRESSES IX ROOF-TRUSSES. 
 
 Then the roof area supported at joint C will be 9' 10" XI 5', 
 or 147} square feet, and the load at this joint 0,300 Ibs. The purlin 
 at joint 3 supports the roof, from a point mid war to joint 2, 
 to the ridge, or b=4f ll"+8' 5", or 13' 4". The roof area 
 supported at this point is 13' 4" XI 5', or 200 sq. ft., and the 
 load 8,550 Ibs, 
 
 The loads at joints 4 and 5 will be equal respectively to those 
 at 3 and 2. 
 
 For the ceiling loads at joints 7 and S we have an area to be 
 supported=12 / 2"X15', or!S2J sq. ft., which multiplied by 20 
 gives 3,650 Ibs. 
 
 EXAMPLE 3. For this example we will take the church 
 roof shown in section by Fig. 4. In this roof the trusses take the 
 
 Fig, 4 
 
 place of the rafters and ceiling beams, the sheathing spanning 
 from truss to truss and the laths for the ceiling being nailed 
 to 1J"X2J" furring strips spaced 12 or 16 ins. on centres. 
 Assuming that the parts of the trusses will have the dimen- 
 sions indicated in the figure, and that the wood is to be white 
 pine, the actual weight of one truss will be about 1,200 Ibs. 
 The roof area supported by one truss is 170 sq. ft., hence the 
 weight of the trusses will be about 7 Ibs. per square foot of 
 
MPUTATIOXS Of R< "_'F LOADS. 955 
 
 roof surface. (Note. It will be seen that this weight is more 
 than twice that given in Table IV. owing principally to the 
 trusses b^ing so close together and the members of small di- 
 mensions.) The weight of the sheathing and shingles will 
 be about 5J Ibs., and we will allow 30 Ibs. for wind pressure. 
 (The roof is too steep for snow to lodge on it.) 
 
 This gives us a total roof load of 42 J Ibs. per square foot of 
 sloping surface. For the weight of the ceiling 12 Ibs. per square 
 foot will be ample, as no load other than its own weight is likely 
 to come upon it. 
 
 The roof area supported at joint 2 = 10f'x2J', or 27 sq. ft. 
 The area supported at joints 4 and 5 is equal to 12J'x2J'=31 
 sq. ft. for each. Ceiling area supported at joint 3 = 14J'X2J', 
 or 35^ sq. ft. Multiplying the joint areas by the correspond- 
 ing loads per square foot we have 1,148 Ibs. for the load at 
 joint 2, 1,318 Ibs. for the load at joints 4 and 5, and 426 Ibs. 
 for the load at joint 3. * 
 
 EXAMPLE 4. Roof corrugated iron, supported by a steel 
 truss of the shape shown by Fig. 60 of Chapter XXV. This 
 truss supports nothing but the corrugated iron and the purlins 
 and the pressure due to wind and snow, the purpose for which 
 the building is used being such that there, will be no occasion 
 for suspending any load from the tru?- - 
 
 In figuring the dead loads for such a roof, the size of the 
 purlins and the gauge of the iron should first be definitely fixed, 
 so that the weight per square foot of roof may be accurately 
 determined. In this instance the purlins are 5- inch I beams 
 spaced 4' 9" centre to centre and weighing 10 Ibs. per lineal 
 foot. 
 
 The weight of the purlins per square foot of roof is therefore 
 equal to 10 Ibs. divided by 4}, or 2.1 Ibs. 
 
 For a span of 4' 9" the corrugated iron should be No. 20 
 gauge (see Corrugated Iron, Part III), weighing 1.9 Ibs. per 
 square foot. 
 
 For the weight of the truss and bracing we will take the 
 weight given in Table V for a span of 100 ft. and 1 pitchy 10.8 
 Ibs.* This will give us a total dead load of 14.8 Ibs. per square 
 foot of sloping surface. 
 
 For wind and snow we should allow 22 Ibs. per square foot 
 
 * The actual weight of this truss and bracing was 4 Ibs. per square foot 
 of sloping surface, which is remarkably small. 
 
956 
 
 STRESSES IN ROOF-TRUSSES. 
 
 if the building is situated in the Central States, making the 
 total roof load 36.8 Ibs. per square foot. It is quite generally 
 recommended, however, that no roof should be designed for 
 a less load, all told, than 40 Ibs. per square foot; therefore the 
 joint loads should be computed on that basis. 
 
 The only loaded joints in this truss are under the purlins, and 
 as the trusses are spaced 19' 2J" centre to centre, and the 
 purlins 4' 9" centre to centre, the roof area supported at each 
 upper joint is 91 sq. ft. Hence the joint loads should be figured 
 at 3,640 Ibs. (Note. Even for the locality in which it was 
 built, this is a very light roof and would hardly be safe in the 
 more Northern or Western States.) 
 
 EXAMPLE 5. Flat roof (Fig. 5). Timber to be of spruce > 
 five-ply gravel roof and plastered ceiling. 
 
 Fig. 5 
 
 For the dead load we have 
 
 Weight of roofing 6 Ibs. 
 
 " sheathing 3 " 
 
 " - " rafters 2J " 
 
 " " purlins 2 " 
 
 " " truss, say 4J " 
 
 Total dead load 17J Ibs. per sq. f t. 
 
 No allowance will be required for wind pressure, but the 
 snow load will be a considerable item in any of the Northern 
 States, as indicated in Table VII. Assuming that the building 
 is located in one of the Central States, we should allow 30 Ibs. 
 per square foot for snow, making the total roof load 47i Ibs. 
 The plaster ceiling and the ceiling joists will weigh about 12J Ibs., 
 and as the roof space is not likely to be used for storage, 13 Ibs. 
 per square foot will be a sufficient allowance for the ceiling. 
 
COMPUTATIONS OF ROOF LOADS. 957 
 
 Assuming that the trusses are to be uniformly spaced, 14 ft. 
 centre to centre, the roof area supported at joint 2 will be 
 9J' X 14', or 133 sq. ft , and the area supported at joint 4, 9f X 14', 
 or 135J square feet. 
 
 The ceiling area supported at joint 3 will be 9J'X14', or 
 130 sq. ft., and at joint 5, 9 / Xl4 / , or 126 sq. ft. 
 
 Multiplying these areas by the corresponding loads per square 
 foot, we have 6,317 Ibs. for the load at joint 2, 6,428 Ibs. at 
 joint 4, 1,699 Ibs. at joint 3, and 1,638 Ibs. at joint 5. 
 
 In practice it is hardly worth while to try to compute the 
 stresses closer than 100 Ibs., so that the loads may as well be 
 put down at an even 50 or 100 Ibs. above the load 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 by Fig. 19, Chapter XXV, there would be no 
 loads on joints 2, 6, and 10. 
 
 The roof area supported at joint 4 (Fig. 19) is equal to one-half 
 the distance OB multiplied by the distance halfway to the truss 
 on each side. If the lower chord supports ceiling joists, then 
 there will be a load at each of the joints 3, 5, 7, 9, etc. Stress 
 diagrams can be drawn for any arrangement of loads, the im- 
 portant point being to compute the loads exactly as they will 
 be imposed on the truss. These five examples illustrate fairly 
 well the method of computing the loads on a truss. Special 
 cases of loading should be computed on the same principle. 
 
 Determining the Stresses. 
 
 To determine the stresses, a diagram of the truss, composed 
 of single lines representing the centre line 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 centre 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 centre lines of all members meeting 
 at any point intersect at a common point. 
 
 In wooden trusses it is not always practicable to place the 
 braces so that their centre line will pass through the centre of 
 the joints, but they should come as near to it as practicable, 
 and in steel trusses the joint connections should be made so that 
 the centre lines of all members meeting at a joint will intersect 
 at the same point. 
 
958 
 
 STRESSES IN ROOF-TRUSSES. 
 
 Stresses Obtained by Direct Computations. 
 
 As a general rule, the stresses in a roof truss can be deter- 
 mined much more readily by the graphic method than by 
 mathematical computations and with as close a degree of 
 accuracy as is necessary. There are a few forms of trusses, 
 however, for which the stresses can be quite easily determined 
 by computation provided the truss is perfectly symmetrical 
 
 TABLE X. COEFFICIENTS FOR DETERMINING THE 
 
 STRESSES IN SIMPLE FINK AND FAN TRUSSES 
 
 When panel loads are all equal. 
 
 |P=2.5 W. 
 
 To find the stress in any member multiply its factor by panel load W. 
 SIMPLE FINK TRUSS. 
 
 Member. 
 
 Kind of 
 Stress. 
 
 S -3 
 H~ 3 ' 
 
 | = 3.464 
 
 -30. 
 
 !- 
 
 cJ 
 
 H~ 5 ' 
 
 A 
 
 Comp. 
 
 2.71 
 
 3.00 
 
 3.35 
 
 4.04 
 
 B 
 
 u 
 
 2.15 
 
 2.50 
 
 2.91 
 
 3.66 
 
 D 
 
 (t 
 
 0.83 
 
 0.87 
 
 0.89 
 
 0.93 
 
 F 
 
 Tension 
 
 2.25 
 
 2.60 
 
 3.00 
 
 3.75 
 
 G 
 
 u 
 
 1.50 
 
 1.73 
 
 2.00 
 
 2.50 
 
 K 
 
 (( 
 
 0.75 
 
 0.87 
 
 1.00 
 
 1.25 
 
 SIMPLE FAN TRUSS. 
 
 A 
 
 Comp. 
 
 4.50 
 
 5.00 
 
 5.59 
 
 6.73 
 
 B 
 
 
 3.53 
 
 4.00 
 
 4.55 
 
 5.58 
 
 C 
 
 
 3.39 
 
 4.00 
 
 4.70 
 
 5.98 
 
 D 
 
 
 0.93 
 
 1.00 
 
 1.08 
 
 1.21 
 
 E 
 
 
 0.93 
 
 1.00 
 
 l.OS 
 
 1.21 
 
 F 
 
 Tension 
 
 3.75 
 
 4.33 
 
 5.00 
 
 6.25 
 
 G 
 
 
 2.25 
 
 2.60 
 
 3.00 
 
 3.75 
 
 K 
 
 
 1.50 
 
 1.73 
 
 2.00 
 
 2.50 
 
STRESSES IN FINK AND FAN TRUSSES. 959 
 
 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 mul- 
 tiplying the constant by the panel or joint load. These tables 
 only apply, however, when the rafter is divided by the struts 
 into uniform spaces, giving uniform panel loads. For any 
 
 TABLE XI. COEFFICIENTS FOR DETERMINING THE 
 STRESSES IN EIGHT-PANEL FINK TRUSS 
 
 When panel loads are all equal. * 
 
 w 
 
 S=Span 
 
 JP=3.5 W. 
 To find the stress in any member multiply its factor by panel load W. 
 
 Member. 
 
 Kind 
 of 
 
 Stress. 
 
 5 -3 
 H~ 3 ' 
 
 1 = 3.464 
 = 30. 
 
 S -4 
 H~ 
 
 !- 
 
 A 
 
 Comp. 
 
 6.31 
 
 7.00 
 
 7.83 
 
 9.42 
 
 B 
 
 
 5.75 
 
 6.50 
 
 7.38 
 
 9.05 
 
 C 
 
 
 5.20 
 
 6.00 
 
 6.93 
 
 8.68 
 
 D 
 
 
 4.65 
 
 5.50 
 
 6.48 
 
 8.31 
 
 E 
 
 
 0.83 
 
 0.87 
 
 0.89 
 
 0.93 
 
 F 
 
 
 1.66 
 
 1.73 
 
 1.79 
 
 1.86 
 
 G 
 
 
 0.83 
 
 0.87 
 
 0.89 
 
 0.93 
 
 I 
 
 Tension 
 
 0.75 
 
 0.87 
 
 1.00 
 
 1.25 
 
 K 
 
 
 0.75 
 
 0.87 
 
 1.00 
 
 1.25 
 
 L 
 
 
 1.50 
 
 1.73 
 
 2.00 
 
 2.50 
 
 M 
 
 
 2.25 
 
 2.60 
 
 3.00 
 
 3.75 
 
 N 
 
 
 5.25 
 
 6.06 
 
 7.00 
 
 8.75 
 
 O 
 
 
 4.50 
 
 5.19 
 
 6.00 
 
 7.50 
 
 P 
 
 
 3.00 
 
 3.46 
 
 4.00 
 
 5.00 
 
960 
 
 STRESSES IN ROOF-TRUSSES. 
 
 other conditions the stresses should be computed by the graph! < 
 method. Tables XIV and XV give formulas for computing 
 the stresses in Howe trusses. These formulas, unlike th< 
 
 TABLE XII. COEFFICIENTS FOR DETERMINING THI 
 
 STRESSES IN CAMBERED FINK AND FAN TRUSSES 
 
 When panel loads are all equal and the camber equals one 
 
 sixth the rise. 
 
 IH t 
 
 S v Spaa -Q H S=Span 
 
 JP=1.5W. lP=2.5W. 
 
 Fig. A Fig. B 
 
 To find the stress in any member multiply its factor by panel load W. 
 
 TRUSS LIKE FIG. A. 
 
 
 Kind 
 
 S 
 
 8 
 
 
 s 
 
 Member. 
 
 of 
 
 = 3. 
 
 ff 5.IO 
 
 = 4. 
 
 ~-. 
 
 
 Stress. 
 
 
 or 30. 
 
 H 
 
 H 
 
 A 
 
 Comp. 
 
 3.64 
 
 4.13 
 
 4.70 
 
 5.78 
 
 B 
 
 n 
 
 3.09 
 
 3.63 
 
 4.25 
 
 5.41 
 
 D 
 
 " 
 
 0.83 
 
 0.87 
 
 0.89 
 
 0.93 
 
 F 
 
 Tension 
 
 3.07 
 
 3.62 
 
 4.24 
 
 5.40 
 
 G 
 
 11 
 
 1.80 
 
 2.08 
 
 2.40 
 
 3.00 
 
 K 
 
 tt 
 
 1.43 
 
 1.69 
 
 1.98 
 
 2.52 
 
 TRUSS LIKE FIG. B. 
 
 A 
 
 Comp. 
 
 6.09 
 
 6.88 
 
 7.83 
 
 9.64 
 
 B 
 
 ii 
 
 4.89 
 
 5.63 
 
 6.48 
 
 8.10 
 
 C 
 
 (( 
 
 4.96 
 
 5.88 
 
 6.93 
 
 8.89 
 
 D 
 
 (t 
 
 1.04 
 
 1.15 
 
 1.26 
 
 1.49 
 
 E 
 
 (t 
 
 1.04 
 
 1.15 
 
 1.26 
 
 1.49 
 
 F 
 
 Tension 
 
 5.12 
 
 6.03 
 
 7.07 
 
 9.01 
 
 G 
 
 (i 
 
 2.70 
 
 3.12 
 
 3.60 
 
 4.50 
 
 K 
 
 tt 
 
 2.66 
 
 3,13 
 
 3.67 
 
 4.69 
 
STRESSES IN PINK TRUSSES. 
 
 661 
 
 constant in Tables X to XIII, may be used for unequal 
 panel loads provided that the truss is symmetrical about a 
 vertical line drawn half way between the supports. 
 
 For the young architect or engineer these tables will be found 
 useful in affording a check upon stresses determined by the 
 graphic method. 
 
 TABLE XIII. COEFFICIENTS FOR DETERMINING THE 
 STRESSES IN EIGHT-PANEL CAMBERED FINK 
 TRUSS. 
 
 When panel loads are all equal and camber - equals one-sixth 
 the total rise. 
 
 w 
 
 ^^___, ^ __, L 
 
 To find the stress in any member multiply its factor by panel load W. 
 
 Member. 
 
 Kind of 
 Stress. 
 
 I-- 
 
 |=3.464 
 
 or 30. 
 
 > 
 
 S -5 
 H [ 
 
 A 
 
 Comp, 
 
 8.49 
 
 9.63 
 
 10.96 
 
 13.49 
 
 B 
 
 tt 
 
 7.94 
 
 9.13 
 
 10.51 
 
 13.11 
 
 C 
 
 ft 
 
 7.39 
 
 8.63 
 
 10.06 
 
 12.74 
 
 D 
 
 ( 
 
 6.83 
 
 8.13 
 
 9.61 
 
 12.37 
 
 E 
 
 t 
 
 0.83 
 
 0.87 
 
 0.89 
 
 0.93 
 
 F 
 
 
 1.66 
 
 1.73 
 
 1.79 
 
 1.86 
 
 G 
 
 
 0.83 
 
 0.87 
 
 0.89 
 
 0.93 
 
 I 
 
 Tension 
 
 1.02 
 
 1.21 
 
 1.41 
 
 1.80 
 
 K 
 
 
 1.02 
 
 1.21 
 
 1.41 
 
 1.80 
 
 L 
 
 
 2.87 
 
 3.37 
 
 3.96 
 
 5.04 
 
 M 
 
 
 3.89 
 
 4.5S 
 
 5.37 
 
 6.85 
 
 N 
 
 
 7.17 
 
 8.44 
 
 9.90 
 
 12.61 
 
 
 
 
 6.15 
 
 7.23 
 
 8.48 
 
 10.81 
 
 P 
 
 
 3.60 
 
 4.16 
 
 4.80 
 
 6.00 
 
962 
 
 STRESSES IN ROOF-TRUSSES. 
 
 TABLE XIV. STRESSES IN TRUSS, FIG. C, DUE TO 
 ROOF LOADS ONLY. RAFTERS AND TIE-BEAMS 
 DIVIDED INTO FOUR EQUAL SPACES. 
 W = load at each upper joint. 
 
 Fig.C 
 
 COMPRESSION IN STRUTS. 
 Stress in FH= ~ X^. 
 
 Stress in.#/= W xj. 
 
 jl 
 
 3W DB 
 Stress in DB= X^. 
 
 TENSION IN VERTICAL TIES. 
 
 W 
 Stress in EH= ; Stress in DI=W; Stress in C = 3W. 
 
 COMPRESSION IN RAFTER. 
 CA 
 CB' 
 CA 
 CB' 
 CA 
 CB' 
 CA 
 CB' 
 TENSION IN HORIZONTAL TIE. 
 
 Stress from C to D = 2H 7 X 
 Stress from D to E = 2}TF X 
 Stress from E to F = 3TF X 
 Stress from F to A = 3J W X 
 
 Stress from B to 7=2iPFX . 
 
 Stress from / to H= 3W x . 
 
 C-D 
 
 Stress from H to A = 3 J W X 
 
 
STRESSES IN HOWE TRUSSES. 
 
 963 
 
 TABLE XV. STRESSES IN SIMPLE QUEEN ROD 
 TRUSS. TRUSS SYMMETRICAL AND SYMMETRIC- 
 ALLY LOADED. 
 
 w 
 
 Tension in R=w. 
 
 B 
 
 Compression in J5= (w+ W) X -77 * 
 Tension in N and M = (w + F) X -77- 
 
 12 
 
 Compression in D= tension in N. 
 
 NOTE. The distance a has no effect on the stresses, except 
 as it increases the loads w and W. 
 
 TABLE XVI. STRESSES IN FOUR-PANEL HOWE 
 TRUSS. TRUSS SYMMETRICAL AND SYMMETRIC- 
 ALLY LOADED. 
 
 Tension in R 1 
 " " R 
 
 n . 
 Comp. in A = 
 
 ^ 
 X -77. 
 
 4- 
 
 Tension in N = ( Ju> + W + w l + WJ X -77. 
 
 " " M = tension #+ 
 Compression in D= tension in N. 
 
 * Meaning length of B divided by height H, both in the same unit of 
 measurement. 
 
964 
 
 STRESSES IN ROOF-TRUSSES. 
 
 TABLE XVII. STRESSES IN FIVE-PANEL HOWE 
 TRUSS. TRUSS SYMMETRICAL AND SYMMETRIC- 
 ALLY LOADED. 
 
 fc 
 
 Tension in 
 " " " 
 
 Compression in A =* (w + W) X jr 
 
 B 
 
 Tension in N=(w+w l +W+W l )X-g. 
 
 " M and O=tension in N+ 
 
 Compresion in D= tension in. N. 
 " '* E= tension in M. 
 
 TABLE XVIII. STRESSES IN SIX-PANEL HOWE 
 TRUSS. TRUSS SYMMETRICAL AND SYMMETRIC- 
 ALLY LOADED. 
 
 Ti w w a \\fe 
 . . . I 1 I 
 
 Tension in 
 
 Compression in A = (Jw + JW) X^, 
 
 B 
 
STRESSES IN HOWE TRUSSES. 
 
 965 
 
 Tension in N= 
 
 " M=tension in N+ 
 
 ~. 
 
 Compression in D = tension in N, 
 lt " E= tension in M. 
 
 TABLE XIX. STRESSES IN SEVEN-PANEL HOWE 
 TRUSS. TRUSS SYMMETRICAL AND SYMMETRIC- 
 ALLY LOADED. 
 
 Compression in A = (w + W) X -. 
 
 Tension in N= (w +w 1 +w 2 + W + W l + TF 2 ) X 
 " "M= tension in N+ 
 
 . Compression in D = tension in AT". 
 " " E= tension in M. 
 
 " F= tension in 0. 
 
966 STRESSES IN ROOF-TRUSSES. 
 
 Examples Showing Application of Tables, 
 
 EXAMPLE I. Simple fan truss of 36 ft. span. Distance 
 
 o 
 
 between centres of trusses 12 ft. Height of truss 9 ft. or^r =4. 
 
 Total load per square foot of roof 40 Ibs.: 
 Length of rafter 20 ft., nearly. 
 
 on 
 
 Panel load W = =f X 12' X 40 =3,200 Ibs. 
 o 
 
 Then from Table X: 
 
 Stress in bottom of rafter =3,200X5.59 = 17,888 Ibs. 
 Stress in ends of main tie (F) =3,200X5.00 = 16,000 Ibs. 
 Stress in centre of main tie =3,200X3.00 =9,600 Ibs. 
 Stress in braces D and E =3,200X1.08 =3,456 Ibs. 
 Stress in tie #=3,200X2=6,400 Ibs. 
 
 EXAMPLE II. Truss shown in Fig. 5, p. 956 (four-panel 
 Howe truss). #=68 ins., a = 108 ins., 6=116 ins. Length 
 of inner braces (measured from centres of joints), 127J ins. 
 Length of outer braces, 134 ins. From p. 957, w = 1,640; 
 wjj = 1,700; W =6,430, and ^=.6,320^8. Then by means 
 of the formulas in Table XVI we find stress in centre rod = 
 1,640 Ibs. 
 
 Stress in outer rods=^p + ~- + 1,700=5,735 Ibs. 
 
 Q, . . 1640 + 6430 vx 127 _ KQA ,, 
 
 Stress in inner braces = - ~ - X -zr =7,536 Ibs. 
 
 ^ 08 
 
 Stress in / 1640 . 6430 , _\ x 134 =23?755 ^ 
 
 outer braces \ 2 2 F7 ~ 68 
 
 Tension in end panels of tie-beam 
 
 \ mo 
 
 Ibs. 
 
 Compression in top chord = 19,028 Ibs. 
 
 The Graphic Method of Determining the 
 Stresses in Roof Trusses. 
 
 The "Graphic Method" is the simplest and in mosfr cases 
 the quickest method (provided the tools are at hand) of deter- 
 mining the stresses in a roof truss, and, besides these, it has 
 the additional advantages that it can be used for any true 
 truss and for any arrangement of loads. There is also less 
 
PRINCIPLES OF GRAPHIC STATICS. 967 
 
 chance of making a mistake in the graphic method than by 
 numerical computations, as an error in the graphical analysis 
 almost always becomes manifest. 
 
 Stress diagrams can be very quickly drawn when once the 
 principle is understood, and 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 draw- 
 ing the diagrams should enable any architect, draughtsman, 
 or builder to grasp the principle. 
 
 Principles upon which the Graphic Method is based. To 
 thoroughly understand this method, a knowledge of the com- 
 position and resolution of forces as explained in Chapter VI 
 is essential, and before studying this subject the student 
 should read carefully pp. 231-233. Propositions I, III, and 
 IV on those pages form the basis of graphic statics. In the 
 graphic method all forces, including the loads, are repre- 
 sented by straight lines, and the direction of the force must 
 be constantly kept in mind, and often it is of assistance to indi- 
 cate the direction by an arrow-head as explained on p. 232. 
 The direction in which a force acts also tells whether it is a 
 pushing or pulling force, or whether the member in which the 
 force or stress acts is in compression or tension. This is more 
 fully explained on the following pages, and also in connection 
 with several of the stress diagrams. 
 
 Forces which Act In and On a Truss. Every stress diagram 
 represents three sets of forces, viz., the external loads, the sup- 
 porting forces, and the stresses in the truss members. 
 
 Supporting Forces. For a truss to stand in place, the supports 
 of the truss, taken together, must be capable of offering a 
 reaction equal to the total load on the truss, including the 
 weight of the truss itself. Each of these reactions must be 
 represented as one of the forces acting on the truss when drawing 
 the stress diagram; they will be hereinafter referred to as the 
 supporting forces. 
 
 When the loads are symmetrical on each side of the centre 
 of the span, the supporting forces will be equal, and each will 
 be equal to one-half of the total load on the truss. When 
 the loads are not symmetrical about the centre, either as regards 
 point of application or magnitude, the supporting forces will 
 be unequal and in most cases must be determined before 
 the stress diagram can be drawn. The supporting forces for 
 
STRESSES IN ROOF-TRUSSES. 
 
 unsymmetrically loaded trusses may be computed by the 
 method explained on pp. 275-277, 
 
 Application of Graphic Statics to Simple Trian- 
 gular Frames Having but One External Load. 
 
 The simple triangular frame is much used in building con- 
 struction, and many forms of roof trusses are simple combina- 
 tions 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. 
 
 In Diagram 1, Fig. 6, we have two struts abutting at the top 
 
 Fig. 6 
 
 and held both vertically and horizontally at the bottom by a 
 tie-beam. The vertical component of the thrust in the strut, 
 however, nearly passes through the tie-beam and is resisted by 
 the support below. 
 
 We will assume that a load of 100 Ibs. is applied at the apex 
 and disregard the weight of the frame itself. Now, if at 2 we 
 draw a vertical line w, 1 in. long (scale of 100 Ibs. to the inch) 
 and from the upper end draw a line parallel to A, and from the 
 lower end a line parallel to B, until the lines intersect, then 
 the length of the line a, measured to the scale of 100 Ibs. to 
 the inch, will give the compressive force in A and the line b 
 the compressive force in B. Further, if from the intersection 
 of a and b we draw a horizontal line (parallel with the tie-beam) 
 intersecting the line w, then the length of the line c will give 
 the horizontal stress in the tie-beam produced by the load of 
 100 Ibs. Moreover, the line c will divide the line w in the pro- 
 portion of the reactions of the supports. Thus the portion p 
 will be the amount of reaction at P and p' the reaction of P'. 
 
 All of these conditions remain true whatever the inclination 
 of the struts, whether equal or unequal, and also if the tie- 
 
PRINCIPLES OF GRAPHIC STATICS. 969 
 
 beam is inclined, provided that the lines a, 6, and c are drawn 
 parallel to the pieces A, B, and C of the frame. 
 
 Moreover, the stresses will be proportional to the load at the 
 apex. Thus for 200 Ibs. the stress in each part will be just 
 twice what it is for 100 Ibs. 
 
 In Fig. 7 we have a load supported by two ties instead of 
 two struts, the effect on the rod w 
 
 being the same as if the load m I c ^ 
 
 were suspended from the bottom. 
 
 If we let the vertical line 
 1-2 represent the load W, then 
 the lines a and 6, drawn parallel 
 to A and B respectively, will 
 represent the stress or tension 
 in the two parts of the rod, and 
 a horizontal line drawn from c 
 to the vertical line will represent 
 the compression in the strut C, F ' 9< 
 
 and p' will be the reaction at P' and p the reaction at P. The 
 stress in the post S will be equal to W. 
 
 The direction in which the forces act are determined as 
 follows: Dead loads always act downward (hence are repre- 
 sented by vertical lines), and consequently the arrow-head On 
 line 1-2 must point down. 
 
 The forces in b and a must also act in the direction of the arrow- 
 heads, i.e., around the figure, in order to preserve equilibrium. 
 Now the lines a, 6, and w represent the three forces acting at 
 o, and we see that the arrow-heads in a and b point away from 
 the joint, hence these pieces are in tension. The arrow-head 
 on w points towards the joint, hence $ is in compression. 
 
 In Fig. 8 we have a crane supporting a load W. 
 
 If we draw the vertical line dc to represent the load, and 
 from the lower end, or c, a line parallel to AC, and from the 
 upper end a line parallel to BC, the two lines intersecting at 0, 
 then a will represent the stress in AC and b the stress in BC. 
 
 Considering the forces as acting at C, the direction in Which 
 the forces act are as indicated by the arrow-heads. 
 
 The arrow-head on a points away from C, hence AC is in 
 tension; the head on 6 points towards C, hence BC is in com- 
 pression. 
 
 We will next consider the forces which act at the point A. 
 Of these three forces we have the force in AC represented 
 
970 
 
 STRESSES IN ROOF-TRUSSES. 
 
 by the line a. If from e we draw a line parallel to AE, inter- 
 secting w at o f then eo will represent the stress in AE, and oc 
 
 / 
 
 
 v 
 
 Piece intension 
 
 Piece in Compression, 
 Fig. 9 
 
 Fig. 8 
 
 the stress in AB. In the triangle eco, the arrow-heads will 
 point in the opposite direction from what they do in ecd, show- 
 ing that AE is in tension and AB in compression. 
 
 [NOTE. If two boys pull on the two ends of a rope so as 
 to just balance each other, the stress in the rope will be just 
 the force with which one boy 
 pulls, and each end of the rope 
 will pull away from the boy 
 holding it by the same force 
 that he exerts. Thus if each 
 boy exerts a force of 100 Ibs., 
 then the stress in the rope will be 100 Ibs., and each end of the 
 rope will be pulling away with a force of 100 Ibs. If the boys 
 were pushing against the two ends of a piece of timber with 
 a force of 100 Ibs., then the timber would push against each 
 boy with a force of 100 Ibs., although the entire stress in the 
 timber would be but 100 Ibs. 
 
 Consequently a stress line with arrow-heads pointing toward 
 each other, as at A, Fig. 9, denotes tension, and a stress line 
 with arrow-heads pointing in opposite directions, as at B, de- 
 notes compression. In other words, the stress in any member 
 of a truss acts in opposite directions at the two ends of the piece. 
 This is an important truth to remember in drawing stress 
 diagrams.] 
 
 Stress Diagrams for Vertical Loads. 
 
 Trusses Symmetrically Loaded. Before the stress diagram 
 for a truss can be drawn, it is necessary to make a skeleton 
 drawing of the truss, representing the centre lines of the 
 members as explained on p. 957. This diagram (which wiP 
 
LETTERING TRUSS DIAGRAMS. 971 
 
 be hereinafter designated as 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 Fig. 10, which is the truss diagram for 
 the truss represented by Fig. 1, and for which the loads were 
 computed on p. 953. 
 
 Combining the Ceiling Loads with the Roof Loads. It should 
 be noticed that in the truss diagram, Fig. 10, the ceiling loads 
 found on p. 953 are added to the roof loads. This is done 
 to simplify the stress diagram. As far as the stresses in the 
 struts and tie-beams are concerned it makes no difference 
 whether the ceiling loads are considered as applied at the top 
 or bottom of the truss, but the stresses in the rods will be in- 
 creased by just the amount of the ceiling load. The +2070 Ibs. 
 opposite the centre rod is put on the truss diagram as a re- 
 minder to add this load to the stress afterwards determined. 
 The rods from 2 to 6 and 4 to 8, Fig. 10, receive no stress from 
 the roof loads and are therefore omitted or dotted in the truss 
 diagram, the latter being lettered as though there were no rods 
 there. The stress on these rods is simply that of the ceiling 
 load at 6 and 8. 
 
 Whenever the ceiling loads are carried directly to the top by 
 vertical rods or ties it is much simpler to add them to the roof 
 loads, as above described, but when the ties are not vertical 
 the ceiling loads must be indicated at their point of application. 
 
 Supporting Forces. The supporting forces should also be 
 indicated on the truss diagram as in Fig. 10. These forces are 
 computed as explained on p. 967. 
 
 Lettering the Truss Diagram. After the truss diagram is 
 drawn, it should be lettered after a particular method known 
 as " Bow's Notation," which enables a ready comparison of 
 the truss and stress diagrams and also aids the student in 
 drawing the stress diagram and in tracing the stresses. The 
 essential principle of this method of lettering is to letter the 
 space each side of every force or piece of the truss so that 
 on the truss diagram a piece or 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 end of the corresponding 
 lines. 
 
 Fig. 10 shows the truss diagram of the truss represented in 
 Fig. 1, properly drawn, lettered, and figured, ready for drawing 
 
972 STRESSES IN ROOF-TRUSSES. 
 
 the stress diagram. The supporting force at the left is Ao, 
 the bottom of the main rafter AE, the left portion of the tie- 
 beam EO, etc. The loads acting at joints 2, 3, and 4 are 
 designated as AB, BC, and CD respectively. It makes no par- 
 ticular difference what letters are used, except that it is better 
 to letter the outside spaces consecutively and then the inside 
 spaces. 
 
 Stress Diagram. The stress diagram is drawn by taking the 
 forces acting on the joints in consecutive order, commencing 
 at one of the supports. The author considers it more natural 
 and convenient to start with the support at the left, or at joint 1. 
 
 [NOTE. In actual computations it is not necessary to number 
 the joints, but in order to refer to them in the description it is 
 necessary to number them in the illustrations.] 
 
 Commencing at joint 1, then, the first step of the stress dia- 
 gram is to draw a vertical line to a scale of pounds to the inch 
 to represent the supporting force OA This line is the line oa, 
 Fig. 10 A, which is here drawn to the scale of 16,000 Ibs. to the 
 inch.* It is best to use a scale as large as convenient and not 
 have the diagram too large. An engineer's scale, one divided 
 to lOths, 20ths, 30ths, etc., of an inch, will be found most con- 
 venient for these drawings. 
 
 The small letter o should be placed at the bottom of the line 
 and the letter a at the top. Next from a draw a line parallel 
 to the rafter AE and from o a line parallel to the tie-beam OE. 
 The two lines meet at e, and ae represents the stress in AE and 
 oe the stress in OE. As the supporting force acts up, the arrow- 
 head will be at the top of oa, and the others must follow in ro- 
 tation, showing that ae acts toward the joint and the piece is in 
 compression, and eo acts from the joint and the piece is in 
 tension. 
 
 We next consider the stresses at joint 2. Commencing at 
 the bottom of the joint and going around to the left the first 
 stress that we know is the stress in ae, which we have just 
 determined. As this stress acted downward at 1, it will act 
 upward at 2, as the stresses in the two ends of a strut or tie act 
 in opposite directions, as explained on p. 970. The stress ae we 
 determined in Diagram 10A, and for convenience in explana- 
 tion we will consider it redrawn in Fig. 10s. The next force 
 
 * The original of this drawing was at a scale of 8,000 pounds per inch, 
 the djr&wing being reduced one half in making the cut. 
 
STRESS DIAGRAMS VERTICAL LOADS. 
 
 6tof\ 
 73 
 
 is the load .4jF=9,000 Ibs., which we measure to our scale from 
 a downward (as the loads acts down), which gives us the point 
 6. ' The stresses in BF and EF we do not know, so from b 
 (Fig. 10, B) we draw a line parallel to BF, and from our starting- 
 point, e, a line parallel to EF, and we obtain the lines bf and fe, 
 which represent the stresses in BF and FE respectively. The 
 arrow-heads should follow as indicated, all of the parts being 
 
 ! Roof 7700 
 
 Ceiling 2070 
 Total 9770 
 
 4, 
 
 P=13,885 
 
 F!Q. 10, TRUSS DIAGRAM 
 
 in compression. At joint 7 we now know the stresses in OE 
 and EF, leaving three unknown forces and as we can only 
 determine two forces we must go to joint 3, where there are 
 but two unknown forces. The first force which we know at 3 
 is the stress fb, which now acts up; we then have the load BC 
 of 9,646 Ibs., which we measure off from b (Fig. 10, C) to our 
 scale, which gives us the point c. From c we draw a line parallel 
 to CO, and from / a line parallel to FG, and we have the lines 
 eg and /</, which represent the stresses in CG and FG respec- 
 tively. The arrow-heads follow as shown, gf acting downward 
 or from the joint 3, and hence indicating tension. As the truss 
 is symmetrical, we now have determined the stresses in all of 
 
974 
 
 STRESSES IN ROOF-TRUSSES. 
 
 the parts, but we can continue the process if we wish, when 
 we will obtain the stresses shown by the dotted lines, the dia- 
 gram being symmetrical about the line eo. The letter h will 
 
 Roof Load 18 IB*. 
 
 Fig. II 
 
 come opposite e, the stresses in the two parts of the tie-beam 
 being equal 
 
 In practice the stresses are all drawn on one diagram, as in 
 Fig. 10, C, the three diagrams being used here only to show the 
 different steps. 
 
 We now apply our scale to the different lines of the last dia- 
 gram and obtain the values indicated on the corresponding 
 lines of the truss diagram, Fig. 11. To }g should be added the 
 ceiling load of 2,070 Ibs. 
 
 By using the + sign before the figures we can show that the 
 piece is in compression, while the sign denotes tension.* 
 
 The truss diagram, as figured in 11, now gives all of the data 
 required to determine the size of the parts, and when these are 
 determined they should also be marked on the diagram so as 
 to have a complete record of the whole computation. 
 
 In practice diagrams Figs. 10 and 11 would be combined 
 in one drawing, they being shown separately merely to indicate 
 the progressive steps in lettering and figuring. 
 
 EXAMPLE 2. (Fig. 12). The upper diagram in Fig. 12 repre- 
 sents the centre lines of the truss shown by Fig. 3, and the 
 loads indicated are those found in Example 2, p. 953. The 
 counter braces in the centre panel are indicated by dotted lines 
 
 * There is no uniformity in the use of these signs by different writers, some 
 using + to denote tension ; hence the notation should be looked up in each 
 work. 
 
STRESS DIAGRAMS VERTICAL LOADS. 975 
 
 in the truss diagram, because under a symmetrical load there 
 is no stress in these members, and hence they cannot be 
 represented in the stress diagram. 
 
 As in the foregoing example, the ceiling loads are added to 
 the roof loads and treated as one load. 
 
 As the truss is symmetrically loaded each supporting force 
 will be equal to one-half of the total load, or 18,500 Ibs. 
 
 To draw the stress diagram, first draw a vertical line oa 
 equal to the supporting force, then from the upper end a line 
 parallel to AE, and from the lower end a line parallel to OE, 
 the two lines intersecting at e. We will thus have the triangle 
 oae representing the three forces acting at' the joint 1. As 
 the supporting force always acts up, the arrow-head on oa will 
 be at a, on ae at e, and on eo at o, showing that A E is in com- 
 
 8550 
 3650 
 
 pression and EO in tension. Next find the stresses acting at 
 joint 2. We already have the stress in AE, represented by the 
 line ea, and as the stress will act in the opposite direction at 
 joint 2 from what it does at joint 1, it will now act up. The 
 next forco is the load of 6,300 Ibs., which must act downward 
 from a. We obtain the point b by measuring from a a distance 
 =to 6,300 Ibs. (at the same scale as was used in drawing oa). 
 There now remain two stresses to be found, viz., the stresses in 
 BF and FE. From the point of beginning e, draw a line parallel 
 
976 STRESSES IN ROOF-TRUSSES. 
 
 to EF, and from b a line parallel to BF, the two lines intersecting 
 at /. Then the figure eabf will represent the four forces acting 
 at joint 2, and the stresses will act in the directions indicated 
 by the letters, or all act toward the joint. We may next 
 obtain the forces acting at either joints 3 or 7, as there are but 
 two unknown forces at either joint. 
 
 Considering the forces acting at joint 3, we already have the 
 force in FB, represented by the line fb, which acts up then the 
 load of 12,200 Ibs., which takes us to ^9, where we also put the 
 letter c to conform with the lettering on the truss diagram. 
 From c draw a horizontal line (parallel to CH), and from the point 
 of beginning, /, a line parallel to FH, the two lines intersecting 
 at h. ch will represent the stress in CH and fh the stress is 
 FH. 
 
 [NOTE. Although the line ch lays over the line oe, it should 
 be considered as a separate line representing a distinct stress.] 
 
 We have now determined the stresses in all of the truss members 
 except in the piece OH. This we find by considering the forces 
 acting at joint 7. At this joint we have the stress in OE, 
 represented by oe, next the stress ef, also fh, and the line ho 
 must complete the figure; hence ho denotes the stress in HO, 
 and as it acts from the joint, HO must be in tension. The line 
 ch acts toward joint 3, hence HC is in compression. Scaling 
 the lines in the stress diagram we obtain the figures shown by 
 the side of the lines, which represent pounds, the + sign 
 denoting compression and the sign tension. The line hf 
 scales 3,250 Ibs., but to this must be added the load at joint 7, 
 3,650 Ibs., which gives 6,900 Ibs. as the true stress in the rod. 
 
 Remark. The two foregoing examples illustrate as clearly 
 as can be shown in print the method of drawing the stress 
 diagram for simple symmetrical trusses symmetrically loaded. 
 The student should draw the truss diagrams in accordance 
 with the measurements given, but to a scale of not less than 
 J inch to the foot, and then draw the stress diagram, line by 
 line, in accordance with the foregoing directions and compare 
 the results obtained with those given in the figures. A varia- 
 tion of 100 or even 200 pounds may be expected, but a greater 
 variation will indicate either that sufficient care has not been 
 exercised in drawing the stress lines exactly parallel with the 
 corresponding lines of the truss diagram or that an error has 
 been made in drawing the truss diagram or in scaling the lines 
 of the stress diagram 
 
STRESS DIAGRAMS VERTICAL LOADS. 977 
 
 After these two examples have been worked, a number of 
 the following examples should be worked until the entire prin- 
 ciple is fully understood. 
 
 EXAMPLE 3. Fig. 13 represents the truss diagram of the 
 
 12,240 12,240 
 
 7,200 J F 
 
 6,000 
 
 Fig. 13 A 
 
 truss shown by Fig. 13, Chap. XXV, the loads indicated being 
 approximately those due to the roof and the suspended floor 
 below. 
 
 The loads being symmetrically disposed, each supporting 
 force will be equal to one-half of the total load, or 41,040 Ibs. 
 The counter braces CC, shown in Chap. XXV, are omitted from 
 the truss diagram because they have no stress when the truss 
 is uniformly loaded. 
 
 To draw the stress diagram, first draw the vertical line 
 oa =41,040 Ibs. = P, then ab and ob parallel to AB and OB 
 and representing the stresses acting at joint 1. At joint 2 
 we .have the line ba representing the stress in BA, and from 
 a measure down ac= 7,200 Ibs., then draw cd and bd, bacdb 
 representing the forces acting at joint 2. 
 
 At joint 3 we have three unknown forces, and as we cannot 
 find three unknown forces in one polygon, we must go next 
 to joint 4, where we already have dc and the load OF. 
 
978 STRESSES IN ROOF-TRUSSES. 
 
 [NOTE. In Fig. 13 the bottom loads are not shown added to 
 the top loads, but they should be so added before drawing 
 the stress diagram.] 
 
 Measuring off the force c/= 27,840 Ibs., we have only the 
 stresses in FE and DE to determine, which we obtain by draw- 
 ing a line from / parallel to FE, and a line from d parallel to 
 DE, the two lines intersecting at e. Now, going to joint 3, 
 we have ob, bd, and de (which we already know), and draw eg 
 and og to close the figure. In this case the point g happens 
 to come at the point 6, so that one lays over the other. At 
 joint 5 we have ge, ef, Ji (equal 12,000 Ibs.), and draw ih and 
 gh to close the figure. There would be no strain on the central 
 rod other than the direct pull of 12,000 Ibs., which it carries 
 from the floor below. It should also be remembered that the tie 
 de has, besides the stress shown in the diagram, a direct pull of 
 15,600 Ibs. from the weight of the floor suspended from it, so 
 that the two should be added to show the total pull in the rod. 
 The stresses in pounds, in the various pieces are given in numbers 
 on the corresponding lines in the stress diagram (Fig. 13 A). 
 
 EXAMPLE 4. Take the skeleton truss represented in Fig. 14, 
 loaded as there shown (by the weight of the roof above and a 
 ceiling below). 
 
 To draw the stress diagram, first draw the supporting force 
 oj (Fig. 14 A) =46,620 Ibs. Then for convenience measure off 
 from /, jk, equal to the sum of the weights at joints o and 1 
 (13,320 Ibs.), kl = 13,320, lm = 13,320, and mn = 13,320. Then 
 draw the lines ja and oa and we have the stresses at the support. 
 At joint 1 we know a/ and jk, and draw kc and ac to close the 
 figure. There wih 1 be no line in the stress diagram correspond- 
 ing to AB, for there is no stress in that tie excepting the direct 
 pull of 3,000 Ibs. At joint 2 we have oa and ac, and draw cd 
 and od to close the figure. At joint 3 we have dc } ck, and kl, 
 and draw le and de. At joint 4 we already, have od and de, 
 and find ef and of by drawing lines from e and o parallel to the 
 respective pieces in Fig. 14. At joint 5 we have fe, el, and Im, 
 and draw mg and fg. We must next go to joint 7; for at joint 
 fr we would have three stresses to find, and by the graphic method 
 we can find only two at a time. At joint 7 we have gm and 
 mn (13,320 Ibs.), and draw nh and gh to close the figure. This 
 completes the stresses in all the pieces for one-half of the truss, 
 and of course the stresses for each half are the same. 
 
 EXAMPLE 5 (Eight panel Howe Truss). For the next 
 
STRESS DIAGRAMS VERTICAL LOADS. 
 
 979 
 
 example we will take a Howe truss whose centre lines give the 
 diagram shown by Fig. 15. This truss is for a span of sixty- 
 four feet, and supports a flat roof and plaster ceiling below 
 
 the tie-beam, and also a gallery below on each side. The loads 
 at the different joints would be about as indicated in Fig. 15. 
 To draw the stress diagram (Fig. 15 A) lay off the loads on a 
 
980 
 
 STRESSES IN ROOF-TRUSSES. 
 
 vertical line, commencing first with the loads nearest the support. 
 Thus ab equals load at joints 1 and 2, be equals load at joints 
 3 and 4, cd equals load at joints 5 and 6, and do and oe each 
 equals one-half of loads at 7 and 8, because one-half of this 
 load is borne by each support. 
 
 Next, commencing at joint o, we have the supporting force oa, 
 the stress in the rafter ap, and the stress in the tie po t closing 
 the figure. At joint 1 we know pa and ab, and draw bn and pn, 
 closing the figure. At joint 2 we know op and pn already, and 
 draw nm and om. At joint 3 we know ran, nb, and 6c, and draw 
 
 4,800 4,800 
 
 4,800 4,800 
 
 2,00 3,00 2,00 2,400 j 
 
 
 A 
 
 34,200 
 
 62,200 
 
 63,000 
 
 / 
 
 66,600 
 
 63,000 
 
 cl and ml. The stresses at joints 5 and 6 are found in the same 
 way as those at 3 and 4; and at joint 7 we know the stresses hi, 
 id, and de, and draw ef and hf. The centre rod HH has no stress 
 excepting the direct pull of 2,400 Ibs., so it cannot be represented 
 in the stress diagram. 
 
 The stresses, in pounds, in the various members of the truss 
 are given on the stress diagram. These stresses can be checked 
 by means of the formulas given for a six-paael truss (Table 
 XVIII) carried one step further. 
 
STRESS DIAGRAMSVERTICAL LOADS. 681 
 
 EXAMPLE 6. Howe Truss loaded at alternate joints (Fig. 16). 
 This example has been selected to show how to proceed when 
 there is no load at one or more of the joints. Fig. 16 represents 
 the centre lines of a truss of 50 ft. span and only 5 ft. in height. 
 
 FIG. 16 
 
 10,000 
 
 fc / 
 
 bg = 20,000; "to'^= 25,000; oj cfc = 30,000 
 FIG. 1 6 A 
 
 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. 19 of Chap. XXV. The loads from 
 these purlins would "be about 5,000 Ibs. The stresses at joint 1 
 are found in the same manner as in the previous examples, 
 always starting with the supporting force. 
 
 At joint 2 we have the stress line da, and as there is no load 
 at this joint we draw from a a line parallel to AE (A covers 
 the entire space from joint 1 to joint 4), and from d a line parallel 
 to DE the two lines intersecting at e. At joint 3 the stress 
 lines are od, de ef, and fo: 
 Stresses at joint 4, fe, ea, ab, bg, and gf. 
 
 " " " 5, of, fg, gh, and ho. 
 
 " " " 6, kg, gb, bi, and ik. 
 
 " " " 7, ok, hi, ij, and jo 
 
 " '* " 8, ji, ib, be, and ck, the latter line bringing us 
 to the point of beginning, showing that 
 there is no stress in kj. 
 
 At joint 9 the only stresses are oj and lo, for as there is no stress 
 in JK there can be none in KL. 
 
982 
 
 STRESSES IN ROOF-TRUSSES. 
 
 There would also be no stress in the centre rod. Although 
 these members have no stress it is advisable to insert them in 
 the truss to stiffen the top and bottom chords, but they can 
 be made very light, say J inch for the rods and 3X6 for the 
 braces. 
 
 EXAMPLE 7. Howe Truss with slanting top chord. 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. 20, Chap. XXV. Fig. 17 
 shows the truss diagram for such a truss, and Fig. 17A the 
 
 Loads in Tonff 
 
 I P =6 Tons 
 
 O 
 FIG. 17 
 
 Ch, 
 
 I 
 
 FIG. f 7 A 
 
 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 will not be symmetrical. When the 
 stress diagram is not symmetrical it is necessary to complete 
 the entire diagram, so as to show the stress in every member of 
 the truss; the stress lines for joint 9 are om, mn, nr, and ro. 
 This leaves only the line rf to complete the diagram, and if 
 the diagram has been correctly drawn, a line joining r and / 
 will be exactly parallel to RF. There will be no stress in the 
 centre rod. 
 
 EXAMPLE 8. Truss with inclined ties (Fig. 18). This truss 
 has the same dimensions as the truss shown by Fig. 14, but the 
 
STRESS DIAGRAMS VERTICAL LOADS. 983 
 
 diagonals incline in the opposite direction and are in tension, 
 and the verticals, except at the centre, are in compression. 
 
 This form of truss is sometimes used in wooden construction 
 to avoid the long centre braces which occur in Fig. 14. Long 
 ties being, as a rule, more economical than long struts. 
 
 For this truss we cannot add the ceiling loads to the roof 
 loads, because the effect on the ties is greater than the amount 
 of the loads. 
 
 10,320 
 
 To draw the stress diagram (Fig. ISA), first draw oa=to 
 the supporting force (46,620 Ibs.) and from a and o draw lines 
 parallel to AF and OF, intersecting at /. The triangle oaf is 
 the same as in Fig. 14 A, showing that the maximum stresses 
 in rafter and tie-beam are the same as in the truss, Fig. 14. 
 Having found the forces at joint 1, we proceed to joint 2, where 
 we have fa acting up, ab= 10,320 Ibs., and draw bg and fg. 
 The arrow-head on gf points up, or towards the joint, showing 
 that FG is in compression. Next go to joint 3. The first 
 force which we know at this joint is the load of 3,000 Ibs. As 
 weights must always be represented by a vertical line acting 
 down, and as the bottom of the line in this case must be at o, 
 we measure upwards from o 3,000 Ibs. and mark the point 
 thus obtained p. Our polygon of forces for joint 3, then, com- 
 mences at p, and we have po, of, and fg. Then from p draw 
 a line parallel to PH, and from g a line parallel to GH, the two 
 intersecting at h. Then po, of, fg, gh, and hp represent the 
 
984 STRESSES IN ROOF-TRUSSES. 
 
 forces acting at joint 3. gh and hp both act from the joint, 
 and hence are in tension. 
 
 The stresses at joint 4 are hg, gb, be, ci, and ih. 
 " " " " 5 are qp, ph, hi, ij, and jq. 
 " " " " 6 are ji, ic, cd, dk, and kj. 
 " " " " 7 are rq, qj, jk, kl, and IT. 
 
 The stress in LM will be only that produced by the load 
 which it directly supports, viz., 3,000 Ibs., and it need not be 
 represented in the stress diagram, unless we wish to complete 
 the diagram so as to show the stresses in the other half of the 
 truss. To show the stress in LM draw sr= 3,000 Ibs.; we 
 have rl, and from I draw a vertical line, and from s a horizontal 
 line, the two intersecting at m. If we complete the stress diag- 
 gram for the entire truss, it will be symmetrical about a line 
 drawn half way between s and r. 
 
 The student should compare the stresses figured on Fig. ISA 
 with those on Fig. 14A and note the effect of changing the 
 direction of the braces. Fig 14 will require a very much larger 
 rod in the centre than is required for KL and MN in Fig. 18 
 while the centre rod in Fig. 18 may be made very light. 
 
 Fig. 18, however, requires special cast washers for the rods 
 to make a good job. 
 
 The manner of laying off the ceiling loads in Fig. ISA applies 
 to all trusses where the loads are not carried directly to the 
 top by means of vertical rods or ties. 
 
 EXAMPLE 9Simple Fan Truss (Fig. 19). In Fig. 19 we 
 have the skeleton of a simple fan truss with inclination of 30 
 and the rafters divided into three equal panels, so that the loads 
 are all alike. 
 
 The stress diagram is drawn on the same principle as those 
 previously explained and involves no unusual points. As 
 the loads are all alike, the stresses in this truss may be readily 
 figured by means of Table X, and the student should compare 
 the stresses thus obtained with those obtained by scaling the 
 stress diagram. 
 
 EXAMPLE 10. Cambered Fink Truss (Fig. 20). Inclination 
 of rafters 30. Distances between trusses 20 ft. Loads are 
 for slate roof on boards or angle-iron purlins. Commence the 
 stress diagram by drawing a vertical line equal to the supporting 
 force P, or 56,350 Ibs., and lettering the bottom o and the top a, 
 as these are the letters on each side of the supporting force at 
 joint o. Draw an and on parallel to AN and NO. At joint 1 
 
STRESS DIAGRAMS VERTICAL LOADS. 985 
 
 we have na acting up; measure off ab= 16,100 Ibs., draw bm 
 and nm parallel to BM and NM. At joint 2 we have on and 
 nm, and draw ml parallel to ML, the stress polygon being 
 on, nm, ml, and lo. 
 
 At joint 3 we meet a condition which we have not found in any 
 of the preceding examples, and which is peculiar to this truss, 
 
 FIG. 19 A 
 
 vijs., three unknown forces apparently. From a study of the 
 truss diagram, however, we see that ML and KI act as belly- 
 rods to take up the thrust in the struts at joints 2 and 5, and 
 as the loads at joints 1 and 6 are equal and NM and IH are 
 of the same length, the stress in KI must be the same as the 
 stress in ML, which we already know. This reduces the number 
 of unknown forces at joint 3 to two. 
 
 The first force which we know at this joint is Im, the next mb, 
 the next bc= 16,100 Ibs., and from c draw a line parallel to CI, 
 and from I, the point of beginning, a line parallel to LK. Now 
 between these two lines we must have a line, ik, parallel to IK 
 and equal in length to ml; this lin^ we obtain by means of the 
 dividers and a parallel ruler, or triangle. If correctly drawn, 
 the point i will be found in line with nm. The stress polygon 
 for joint 3, then, is Im, mb, be, ci, ik, and kl. 
 
 At joint 4 the stress lines are ol, Ik, kg, and go. 
 " " 5 " " " " gk, ki, ih, and hg. 
 " " 6 " " " " hi, ic, c 7 , and dh. 
 
 If the stress diagram is accurately drawn a line from c parallel 
 to the rafter will pass through the point h. The vertical tie GG, 
 
986 
 
 STRESSES IN ROOF-TRUSSES. 
 
 Fig. 20, has no stress and its only duty is to prevent the hori- 
 zontal tie from sagging. 
 
 EXAMPLE 11 (Fig. 21). Same Truss as in Fig. 20, carrying 
 two additional loads. Steel trusses of this shape are often 
 
 16,100 
 
 16,100 
 
 E 16,100 
 
 :i6,ioo 
 
 100 
 
 56350 
 
 m 
 
 63,600 
 
 EX 4& 
 
 Fig. 20 A 
 
 required to support loads from below. In Fig. 21 we have 
 two loads of 4 tons each, supported at joints 5 and 9, in addition 
 to the roof loads. 
 
 The stress diagram is drawn in exactly the same way as 
 Fig. 204, except that at joint 5 the first known force is RO, 
 
STRESS DIAGRAMS- VERTICAL LOADS. 987 
 
 4 tons, and we lay off above o a distance equal to 4 tons, which 
 gives us the point r. We then have at this joint ro, ol, Ik, 
 and draw kg and rg to close the figure. 
 
 It should be noticed that the stresses in NM, IH, ML, KI, 
 and LK are the same as the stresses in the corresponding mem- 
 
 bers of Fig. 20, as these are not affected by the ceiling load. All 
 of the other stresses, however, are increased because of the 
 increase in the supporting forces, the greatest increase, however, 
 being in KG and HG. 
 
 EXAMPLE 12. Simple Scissors Truss (Fig. 22). Fig, 22 is the 
 truss diagram of the truss shown by Fig. 25, Chap. XXV, 
 which is the simplest form of the scissors truss. The truss 
 diagram is drawn by commencing with the line oa equal to 
 the supporting force (9,600 Ibs.) and drawing ad and od parallel 
 to AD and OD. Next, at joint 2 we have da acting up; measure 
 off ab= 5,800 Ibs. and draw be and de parallel respectively to 
 BE and DE. Next go to joint 3. Here we have eb acting up; 
 measure off bc= 5,200 Ibs. and draw cf and ef parallel to CF 
 and EF. We now have the stresses in one half of the truss and 
 the stresses in the other half will be the same. If we wish 
 to complete the diagram, measure off above o, ro equal to 
 the load at joint 4, 2,400 Ibs., and draw rg and fg parallel to 
 RG and FG. The stress polygon for joint 4 is ro, od, de, ef, 
 
988 
 
 STRESSES IN ROOF-TRUSSES. 
 
 fg, and gr. For the stresses at joint 5, measure down from 
 c a distance =5,800 Ibs. and draw a line parallel to the rafter 
 which should pass through the point g. The completed figure 
 
 FIG. 22 A 
 
 should be symmetrical about a horizontal line, half way between 
 r and o. 
 
 EXAMPLE 13. Scissors Truss like Fig. 26, Chapter XXV. 
 Fig. 23 is the truss diagram of the truss shown in Fig. 26, Chap. 
 XXV, with the loads figured about as they would be for a 
 slate roof and wooden ceiling with trusses spaced 12 ft. on 
 centres. 
 
 Commence the stress diagram by drawing the line oa=to 
 the supporting force at joint 1 (14,750 Ibs.). The stress poly- 
 gons for the different joints are as follows: 
 
 At joint 1 : oa, ae, eo. 
 
 " " 2: ea, ab, bf, and fe. 
 
 " " 3: oe, ef, fh, and ho. 
 
 " " 4:hf,fb,bk,.andkh. 
 
 " " 5: ro- 1,100 Ibs., oh, hk, kl, and Ir. 
 
 " " 6: Ik, kb, bc= 5,400 Ibs., cm, and ml. 
 
 " " 7: me, cd= 5,700 Ibs., dn, and nm. 
 
 The student should notice how much the stresses in the prin- 
 cipal members of this truss exceed the supporting forces or 
 loads, and particularly the great stress in the centre rod. 
 
 For this reason this is not an economical type of truss for 
 spans exceeding 36 ft. 
 
STRESS DIAGRAMS VERTICAL LOADS. 986 
 
 EXAMPLE 14. Scissors Truss like Fig. 4. Fig. 24 is the 
 truss diagram of the truss shown by Fig. 4, p. 954, and for 
 which the roof and ceiling loads are computed in Example 3, 
 p. 954. The truss shown by Fig. 4 is built of planks spiked 
 and bolted together, but the stresses would be found in pre- 
 
 36 / 10 l 
 
 P 
 
 FIG. 23 
 
 FI.G. 23 A 
 
 j 
 
 ci&ly the same way if the truss were made of heavy timbers 
 and supported 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 1 and 2 are readily found commencing 
 with oa=P. At joints 3 and 4, however, We have three un- 
 known forces. We cannot obtain the stresses at joint 4 until 
 we have drawn those acting at joint 3. The known forces at 3 
 are the load OR=430 Ibs. and the stresses acting in OE and 
 EF, and the unknown forces those acting in FH, HK, and KR. 
 Now both HK and KR are in tension and both serve to hold 
 joint 3 from falling down and outwards. Either one (but not 
 both) could be omitted, and the greater the stress in one the 
 less will be the stress in the other. The only way in which we 
 can complete the stress polygon for joint 3 is to fix the amount 
 
990 
 
 STRESSES IN ROOF-TRUSSES. 
 
 of one of the unknown stresses arbitrarily. The most satis- 
 factory 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 o 430 Ibs.), next the 
 lines oe and ef. From / draw a line 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 line should be drawn so 
 that its length will be equal to kr, which can be done by means 
 of dividers. Lettering the ends of this line h and k we have the 
 completed stress polygon for joint 3, viz., ro, oe, ef, }h, hk, 
 and kr. Knowing the stress in FH, we have but two unknown 
 forces at the joint 4, which are readily found. 
 
 The stress polygon for joint 5 is Ic, cd, dm, and ml. Compar- 
 ing this stress diagram with Fig. 23 A, we see that the stress 
 in the centre rod is much less in proportion to the loads in 
 Fig. 24 A than it is in Fig. 23 A, this reduction being due to 
 the horizontal tie RK. For light trusses built of planks spiked 
 or bolted together the form of truss shown by Fig. 24 is prefer- 
 able to that shown in Fig. 23. 
 
 EXAMPLE 15. Scissors Truss like Fig. 30, Chap. XXV. 
 Fig. 25 is the truss diagram of the truss shown by Fig. 30 of 
 Chapter XXV. The line EF in Fig. 25 does not correspond 
 
STRESS DIAGRAMS VERTICAL LOADS. 991 
 
 with the centre line of the strut in Fig. 30, because the inner 
 end of the latter is dropped slightly on account of the detail 
 
 of the joint, but in the truss diagram all lines must go from joint 
 to joint, otherwise the stress diagram could not be drawn. 
 There is no stress in the upper portion of the tie-beams under 
 a symmetrical vertical load, hence they are shown by dotted 
 lines in Fig. 25. There are no complications in drawing the 
 stress diagram of this truss, therefore a detailed description 
 is unnecessary. 
 
 The stress polygons for the different joints are as follows: 
 For joint 1 : oa, ad, do. 
 11 "2: ro, od, de, er. 
 " "3: ed,da,db,bf,fe. 
 " "4: }b, be, ch, hf. 
 
 " 5: sr, re, ef,fh, and hs. 
 
 hs and he coincide, showing that the tension in HS is equal 
 to the compression in CH. The plus and minus signs on Fig. 25 
 denote compression and tension respectively. 
 
 EXAMPLE 16. The Hammer-beam Truss. As this truss is so 
 frequently used by architects for supporting the roofs of churches 
 and large halls, we have devoted considerable space to it. 
 
992 STRESSES IN ROOF-TRUSSES. 
 
 As generally constructed, hammer-beam roof trusses exert 
 a more or less horizontal pressure upon the walls supporting 
 them, requiring that the walls shall be heavy and re-enforced 
 by buttresses on the outside. In churches where the walls 
 are low, this horizontal thrust of the truss is easily taken care 
 of; but in many cases it is desirable to do away with it entirely 
 if possible. In order better to understand the action of the 
 stresses in this truss, we have presented first a truss (Fig. 26) 
 which has all the features of the hammer-beam truss, excepting 
 the lower braces, and yet exerts' no horizontal thrust against 
 the wall. 
 
 The truss is supposed to be built like the ordinary hammer- 
 beam truss, excepting the omission of the lower braces, and 
 putting in strong timber ties, HO and PO, in place of the orna- 
 mental curved pieces usually employed. In this particular 
 example we have assumed the span of the truss as 60 ft., the 
 rise as 35 ft., and the distance between centres of trusses 15 ft. 
 This would make the loads at different joints about as is in- 
 dicated in Fig. 26. 
 
 To draw the stress diagram, lay off the supporting force P 
 on a vertical line oa,= 42,000 Ibs. Now at joint 1 we have the 
 stresses oa, af, and /o; at joint 2, fa, ab, bg, and jg; at joint 3, 
 of, fg, gh, and oh, oh acting from h to g, and hence is a pulling 
 stress. At joint 4 we have hg, gb, be, ci, and hi to close the 
 figure; hi is also in tension. At joint 5 we have ic, cd, dk, and 
 ik. At the top joint 6 the stresses are kd, de, el, and kl, which 
 completes the stress diagram for one-half of the truss, which, 
 of course, is all that is needed. Examining, now, the diagram, 
 we find that the stresses are in general much larger than would 
 be the case if there were a horizontal tie across the truss; still, 
 if we make the pieces large enough to withstand these stresses, 
 the truss will be stable and exert no outward thrust on the walls. 
 
 Looking at Fig. 26 we see that OF, H, P, and R form a con- 
 tinuous tie, only it is pulled up in the centre in the form shown. 
 In Fig. 26 A we see tha the stress in the tie-rod KL is very great, 
 and this is because the rod has to hold up the inclined ties HO 
 and PO. If we imagine the tie KL to be cut in two just above 
 the joint, the main rafters would break at the joints 4 arid 9, 
 and the bottom portion immediately slide outwards, straightening 
 out the main tie and allowing the top of the truss to fall through. 
 
 Having seen that a hammer-beam truss could be built in which 
 there is no horizontal thrust, we will now consider the hammer- 
 
STRESS DIAGRAMS VERTICAL LOADS. 99* 
 
 Fig. 26 A 
 
994 STRESSES IN ROOF-TRUSSES. 
 
 beam truss as usually built, in which a horizontal thrust is 
 expected. The diagram of such a truss is shown in Fig. 27, in 
 which the curved braces usually built in the centre of the truss 
 are not shown, as they are considered to be purely ornamental 
 and have no stresses in them. The brace OM is drawn as 
 though it were straight; but a curved brace can be used as 
 well, without altering the diagram, for the reason that the 
 stress in the curved piece acts in a straight line connecting the 
 centres of each end of the brace. 
 
 To draw the stresses in this truss we must first find the hori- 
 zontal thrust of the truss against the wall. 
 
 To do this we have to consider that all the pieces from joints o 
 to joint 4 simply form a framed brace supporting the upper 
 portion of the truss at joint 4, or that a single- brace, shown 
 by the broken line 04, Fig. 27, would have the same effect 
 on the wall as all the pieces put together in the framed strut; 
 that is, we may consider the truss to have the same horizontal 
 thrust as the truss shown in Fig. 27 A. The load at joint 4 would 
 evidently be 12,000 Ibs. plus load at joint 5, plus half-load at 
 joint 6 and half-load at joint 2, making in all 36,000 Ibs. To 
 draw the horizontal thrust and stresses we proceed as follows: 
 
 Lay off ab (Fig. 27 5) = load at joint 2, 6c=load at joint 4, 
 cd=load at joint 5, and cfe=load at joint 6. Then the load at 
 joint 4 (Fig. 27A) = $ab + bc+cd + Jcfe; and if we draw from x 
 a horizontal line to the left, and from the centre of ab a line 
 parallel to 04 (Fig. 27.4), these two lines will intersect at m, 
 and mx will be the horizontal thrust exerted on the wall at the 
 point o. 
 
 Having obtained this thrust, it is easy to determine the 
 stresses in the pieces. 
 
 At joint o we have the thrust mx, the vertical supporting force 
 xa, and the stresses ao and mo closing the figure. At joint 1 
 we have oa, a/, and of, as the stresses in OA, AF, and FO. 
 
 At joint 3 the stresses are mo, of, fg, and mg\ at joint 2 they 
 are fa, ab, bg, and gf; at joint 4 the stresses are mg, gb] be 
 and ci closing the figure. It will be noticed that the figure 
 closes without allowing any line to be drawn parallel to MI} 
 hence there is no tensional stress in MI under purely vertical 
 loads. Under a wind stress there would be some compression 
 in MI, and in practice a tie-beam is necessary. 
 
 At joint 5 we have the stresses ic, cd t dk t and ki, and at joint 
 
STRESS DIAGRAMS-VERTICAL LOADS. 995 
 
 6 we have kd, de, el, and /;/, which completes the stresses for 
 one-half of the truss, which is all we need. 
 
 Fig. 27 A 
 
 Comparing, now, the diagram of stresses, Fig. 27#, with 
 Fig. 26 A, we find that in general the stresses in the truss, Fig. 27, 
 are much less than in the trus^, Fig. 26; while, on the other 
 hand, the latter truss exerts no outward thrust on the walls, 
 as is the case in Fig. 27. 
 
 By building a truss like Fig. 27, and putting in curved ties 
 from joints 3 and 11 to joint 12, we can relieve the brace OM 
 of part of- the load without straining the other timbers as much 
 as is the case in Fig. 26. 
 
996 
 
 STRESSES IN ROOF-TRUSSES. 
 
 The truss shown in Fig. 36, Chap. XXV, combines the ad- 
 vantages of both the forms of hammer-beam trusses which we 
 have considered, though it may not be quite so pleasing to 
 the eye. 
 
 EXAMPLE 17. Suspended Pratt Truss, Symmetrically Loaded. 
 Let Fig. 28 be the truss diagram of a suspended Pratt truss, 
 uniformly loaded at top and bottom, with 2 tons at each joint. 
 
 The stress diagram is drawn in exactly the same way as for 
 
 FIG. 28 A 
 
 a Howe truss, except that the diagonals run in the opposite 
 direction. The stresses should be drawn for the joints in the 
 order in which they are numbered. In this truss the verticals 
 are in compression and the diagonals in tension. 
 
 EXAMPLE 18. Truss like Fig. ' 63, Chap. XXV. Fig. 29 
 is the truss diagram of a light iron truss of 32 ft. span intended 
 to support a tar-and-gravel roof, the slope of the roof being 
 at right angles to the line of the trusses. 
 
 The stress diagram is drawn as in the previous examples, 
 taking the joints in the order in which they are numbered. 
 * EXAMPLE 19. Double Warren, or Lattice Truss. The truss 
 diagram shown by Fig. 30 is best analyzed by considering 
 it as built up of two Warren trusses, laid one over the other, 
 the full lines indicating a truss such as is shown in Fig. 31, 
 and the dotted lines a truss like Fig. 32. Three of the seven 
 
STRESS DIAGRAMS VERTICAL LOADS. 997 
 
 loads would come on the first truss and four on the second 
 The stresses are found for each truss separately and then 
 combined for the top and bottom chords. 
 
 Thus the stress In the top chord, from 1 to 3, Fig. 30, would 
 be that in AD, Fig. 31, or 3 tons; from 3 to 5 it would be equal 
 
 FIG. 29 A 
 
 to the stress in AD, Fig. 31, plus that in BE, Fig. 32, or 9 tons; 
 from 5 to 7 it would be equal to stress in BF, Fig. 31, plus 
 stress in BE, Fig. 32, or 13 tons, and so on, the stress in the 
 bottom chord being found in the same way. The diagonal 
 struts and ties act independently of each other, and the stresses 
 are those indicated on the stress diagrams. The plus signs 
 denote compression and the minus signs tension. 
 
 In Fig. 32 the stress polygon for joint 7 is fe, eb, be, and cf, 
 which closes without any room for a line parallel to FF, show- 
 ing that there is no stress in the two inner diagonals except 
 that due to the weight of the bottom chord. 
 
 This truss can be extended indefinitely by giving it sufficient 
 height for the span. It is usually built of steel angles with 
 riveted joints. 
 
 EXAMPLE 20. Truss like Fig. 66, Chapter XXV. Fig. 33 
 is the truss diagram of a truss similar to that shown by Fig. 66, 
 p. 926, the panel loads being taken at 2 tons each, the analysis 
 being the same for any other loads. The stress diagram is 
 drawn exactly as in the previous examples, commencing with 
 
998 
 
 STRESSES IN ROOF-TRUSSES. 
 
 the supporting force =oa and taking the joints in the order 
 in which they are numbered. In this truss the diagonal web 
 members are all in tension and the verticals in compression. 
 It will be noticed that the diagonals in the two panels nearest 
 
 T~ 
 
 -p = 4. Tons 
 
 I 
 
 d 
 FIG, 32 A 
 
 the centre incline in the opposite direction from those in the 
 outer panels. This is due to the inclination of the top chord, 
 which would cause the inner diagonals to be in compression 
 if they inclined the other way. The stress in LM t however, 
 
STRESS DIAGRAMS VERTICAL LOADS. 999 
 
 is so small that a single angle would resist either a compressive 
 or tensile stress. 
 
 FIG. 33 
 
 FIG. 33 A 
 
 Fig. 33 
 
 The truss shown by Fig. 34 is very similar to that shown in 
 Fig. 33, the principal difference being that the slope of the 
 top chord is less in the former than in the latter. In Fig. 34, 
 only the diagonals in the two centre panels incline from the 
 
 centre, and the stress in these diagonals is very small. With 
 
 a still less inclination to the top chord, the stress in NR would 
 
 | become o, and with a horizontal top chord the stress in NR 
 
 would become reversed, or to keep it in tension, the direction 
 
1000 
 
 STRESSES IN FxOOF-TRUSSKS. 
 
 should be changed, as in the Pratt truss, Fig. 28. Comparing 
 the stresses in these two trusses, it will be seen that while the 
 stresses in the end panels are less in Fig. 34.1 than in Fig. 33-4, 
 yet the stresses in the chords at the centre are considerably 
 greater. As a rule, the less the height of a truss in proportion 
 to the span the greater will be the stresses in the chords, espe- 
 cially at the centre of the truss. 
 
 EXAMPLE 21. Fig. 35 is a truss diagram similar to the truss 
 shown in Fig. 73, Chap. XXV. The truss diagram is drawn 
 as in the previous examples, except that in this case the bottom 
 chord, having different inclinations in the different panels, 
 the stress lines do not lie over each other, but all radiate from 
 o, the lines in the stress diagram being parallel to the corre- 
 sponding lines in the truss diagram. 
 
 Fio. 35 A 
 
 In this truss the stresses in the diagonal web-members re- 
 verse in the two panels nearest the centre. Thus the stress 
 polygon for joint 6 is nm, me, cd, dp, and pn, the stress pn 
 acting from the joint and hence denoting tension. At joint 8 
 the stress polygon is rp, pd, de, es, and sr, the latter line acting 
 towards the joint, and hence denoting compression. 
 
 Under irregular loading, the stress in SR would probably, 
 be reversed, so that the piece would be in tension instead of 
 compression. Trusses like Figs. 33, 34, and 35 should alwaj^s 
 be computed for snow on one half of the truss only, and also 
 for wind pressure. 
 
 EXAMPLE 22. In Fig. 30 we have the diagram of the truss 
 shown by Fig. 72, Chapter XXV. This truss is similar to 
 
STRESS DIAGRAMS VERTICAL LOADS. 1001 
 
 that shown by Fig. 34, except for the secondary bracing in 
 che panels and for the curved tie-beam. The stress diagram 
 presents no difficulties. In drawing the lines from o parallel 
 to the bottom chard the latter should be considered as made 
 up of straight lines joining the joints; thus om is drawn parallel 
 to an imaginary straight line connecting joints 4 and 8. As 
 there is no load over the centre of the panels next the centre, 
 there will be no stress in XX' and X'X". If the bottom chord 
 was straight, as in Fig. 34, there would be no stress in the tie 
 YZ, but as the chord is curved, it requires a- certain amount 
 
 2000 
 
 1000 
 
 1500 
 
 FiQ.^35 A. 
 
 of tension in YZ to hold it up, the stress being indicated by yz 
 (Fig. 36A). If the diagram were completed for the entire truss, 
 it would be symmetrical about a horizontal line drawn through o. 
 There is one. point in which this example differs from all 
 of the preceding, viz., in the load AB over the support. As 
 a matter of fact, there would be such a load over the support 
 for all of the trusses, but as the load does not act on the truss, 
 but only on the support, it has been neglected in the previous 
 examples. 
 
1002 
 
 STRESSES IN ROOF-TRUSSES. 
 
 When trusses are supported by columns this outer load 
 should be taken into account in computing the load on the 
 
 column. In representing the load AB, in the stress diagram, 
 we first measure off on a vertical line, oa, equal to the support- 
 
STRESS DIAGRAMS VERTICAL LOADS. 1003 
 
 ing force P, which acts up, then measure down ab, equal to 
 load AB; then draw bj and oj. The load AB has no effect on 
 the stresses in the truss, because if it is omitted the value of 
 P would be just that much less. 
 
 EXAMPLE 23. Iron Bowstring Truss. Span of truss, 90 ft.; 
 distance between trusses from centres, 20 ft.; rise of arched 
 rafter, 20 feet. 
 
 The form of truss, represented by Fig. 37, is one of the most 
 economical of trusses for very great spans. 
 
 In such cases as the present example, the rafter, or curved 
 principal, is the only piece that is in compression, and all the 
 others are in tension. Under a steady load only, such as the 
 weight of the roof itself, one set of braces placed as shown in 
 Fig. 37 would be all that would be needed; but under a severe 
 wind pressure blowing against one side of the roof only, it is 
 necessary to have another set of braces, as shown by the dotted 
 1'nes in the figure. 
 
 These "counter-braces," as they may be called, have no stress 
 on them at all when there is only a vertical load to be supported 
 by the trusses; so we must leave them out in drawing the 
 diagram of stresses. 
 
 To draw the stress diagram, lay off the loads on a vertical 
 line, as in all the previous examples, and remember that the 
 point o should be half-way between e and / (Fig. 37A); then oa 
 will be the supporting force at joint 1. In drawing the stresses 
 at the different joints, draw first those at joint 1 and then 
 those at joints 2, 3, 4, 5, etc., in the order in which they are 
 numbered (Fig. 37). 
 
 To commence the stress diagram, we have oa equal to the 
 supporting force at joint 1, and from a draw a line parallel to 
 AG, and from o a line parallel to OG. These two lines intersect 
 at g. (In drawing lines parallel to the curved lines of the truss, 
 draw the stress line parallel to a line connecting the two ends 
 of the curved chord. Thus ag should be drawn parallel to 1-3, 
 and og parallel to 1-2.) At joint 2 we already have og, and from 
 g draw a line parallel to GH, and from o a line parallel to 
 OH (2-4) : this gives the lines oh and gh. 
 
 At joint 3 we have hg, ga, and the load ab, and draw bi and 
 hi from b and h. 
 
 At joint 4 we now have oh and hi, and draw ik and ok. The 
 stress lines for joints 6 and 8 are drawn in a similar way, and 
 those for 5, 7, and 9 simila 'ly to those at joint 3. After drawing 
 
1004 STRESSES IN ROOF-TRUSSES, 
 
 the stresses at joint 9, go to joint 10; and after drawing the 
 lines for that joint all the stresses in the truss will have been 
 obtained. The stresses in this particular example are given 
 in pounds on the respective lines in the stress diagram. It 
 will be noticed that the stress is very severe on the top and 
 lower chords, but very slight on the bracing. It is in fact so 
 slight that it will be about as well to make all the diagonal 
 braces of the same size sufficient to resist the stress on IH, 
 where the stress is the greatest; or IH and KL might be the 
 same size and MN and PR a smaller size. 
 
 The vertical or radiating pieces might be all of a sectional 
 area capable of resisting the stress in NP. 
 
 The great advantage of this truss lies in the fact that all its- 
 parts are in tension excepting the upper chord, which, of course, 
 is in compression. We might analyze the way in which the 
 stresses act, by saying that the upper chord carries all the load, 
 like an arch, and is prevented from spreading out at the ends 
 by the lower tie. The object of the bracing and vertical pieces 
 is only to keep the tie in its curved position, and not permit it to 
 come down flat, and thus allow the ends of the arch to spread 
 out. 
 
 Trusses Unsymiiictrically Loaded. In all of the 
 preceding examples the loads have been symmetrically dis- 
 posed each side of the centre of the truss, so that each support- 
 ing force is equal to one half of the total load. It very often 
 happens, however, that the loads are not symmetrically dis- 
 posed, and in all such cases it is necessary to first compute the 
 supporting forces and then to draw the stress diagram for 
 the entire truss, as the diagram will not be symmetrical. Other- 
 wise the process is the same as described for the foregoing 
 examples. The following examples will illustrate sufficiently 
 the method of computing the supporting forces and drawing 
 the stress diagrams: 
 
 EXAMPLE 24. Fig. 38 represents the diagram of a truss 
 similar to that shown in Fig. 1, but of a greater span and having 
 a gallery supported from it at one side only. The approximate 
 roof and ceiling loads are indicated by the figures near the 
 arrows, and the weight coming on one truss from the gallery 
 would be about 9,000 Ibs. 
 
 The first step towards drawing the stress diagram is to com- 
 pute the reactions at the two ends of v the truss, which will give 
 the supporting forces. This is most readily done by the method 
 
VERTICAL LOADS NOT SYMMETRICAL. 1005 
 
 of moments explained on pages 274-277. in this example 
 we will take the moments about joint 1. 
 
 As the loads at joints 2 and 3 have the same arm, we will 
 add them together before multiplying by the arm, also the 
 loads at joints 4 and 5, and 6 and 7, The moments about 
 joint 1 will then be: 
 
 (8,000 + 4,500 + 9,000) =21 ,500 X 12 J = 268,750 ft.-lbs. 
 (8,000 + 4,500) --=12,500X25 = 312,500 " 
 
 (8,000 + 4,500) = 12,500X37i = 468,750 " 
 
 Total moments = 1 ,050,000 ft.-lbs. 
 
 This moment must be balanced by the supporting force P 2 , 
 which has an arm equal to the distance between P l and P 2 , 
 or 50 ft. Knowing the arm the force is obtained by dividing 
 the total moment of the loads by the span. Dividing 1,050,000 
 by 50 we have 21,000 Ibs. as the reaction or supporting force 
 at joint 8, and P t must equal the difference between the sum 
 of the loads and P 2 . The sum of the loads is 46,000 Ibs., and 
 subtracting 21,000 we have 25,500 as the value of P r We 
 are now ready to draw the stress diagram, Fig. 38 A. First 
 draw a vertical line oa=P ; = 25,500 Ibs. From a and o draw 
 lines parallel respectively to AE and OE, which gives the point 
 e. For the stress lines at joint 2 we measure up from o a 
 distance equal to the load at that joint, 13,500 Ibs., which 
 gives the point r, and from e and r draw lines parallel to EF 
 and RF, which intersect at /. At joint 3, the stress polygon 
 is fe, ea, ab, bg, and gf. Draw the stress polygons for joints 4, 
 5, and 6 in the order in which they are numbered. At joint 
 6 the stress polygon is ih, he, cd, dj, and ji. If the diagram 
 has been correctly drawn, the line i] will be just equal to the 
 load at joint. 7. The stress polygon for joint 7 is fc=4,500 
 Ibs., si, ij, and jt, the only line to be drawn being jt, which 
 must be parallel to JT, consequently j must be exactly oppo- 
 site t, or the polygon will not close. The distance dt should be 
 equal to P 2 . 
 
 In this example we have taken the ceiling and roof loads 
 separately, and hence the full stress in the vertical members 
 is shown by the stress diagram. It is simpler, however, to 
 add the ceiling loads (including the weight from the gallery 
 to the roof loads) and then draw the stress diagram as though 
 the toads were applied at joints 3, 4, and 6. 
 
1006 
 
 STRESSES IN ROOF-TRUSSES. 
 
 .The stress diagram, Fig. 385, is drawn in that way. In 
 this diagram the rods EF and IJ are not represented, be- 
 
 fe 
 
 FIG. 38 A. 
 
 VL g, /. > 
 
 16 8 r 12 ' 6 T aa-o 
 
 ^-21,000 
 
 FIG. 38 
 
 cause they have no stress when the loads are all at the top. 
 In drawing Fig. 385, the last line drawn is di, which must 
 
VERTICAL LOADS NOT SYMMETRICAL. 1007 
 
 start from d and be parallel to JD. If it does not pass through 
 the point i, previously found, then the diagram has not been 
 correctly drawn, or else an error has been made in computing 
 the supporting forces. 
 
 Comparing Figs. 38/1 and B, it will be seen that the inclined 
 lines and also the lines representing the stresses in different 
 parts of the tie-beam are of the same length in both diagrams, 
 but the line gh in r Fig. 385 is less in length than the corre- 
 sponding line in Fig. 38A. This difference should be just 
 equal to the load at joint 5, ^consequently if we draw the stress 
 diagram as in Fig. 385, we must add to the stress obtained 
 by scaling the line gh, the load at joint 5. The stresses in 
 the rods EF and IJ are just equal respectively to the loads 
 at joints 2 and 7, as the only purpose of these ro'ds is to transmit 
 the loads at 2 and 7 to the joints above. 
 
 When these rods are inclined from a vertical, the ceiling loads 
 must be treated separately as in Fig. 38A. 
 
 EXAMPLE 25. Fig. 39 is the diagram of a wooden roof truss 
 designed by the author for a certain building. The actual 
 
1008 
 
 STRESSES IN ROOF-TRUSSES. 
 
 loads were about as given on the diagram. Purlins occurred 
 at joints 3 and 5 only, and the ceiling below was suspended 
 by rods from joints 4 and 7, joint 4 being fixed by the framing 
 of the ceiling. 
 
 The moments of the loads about joint 1 are: 
 
 3,200 X 8i = 27,200 ft.-lbs. 
 
 5,500X15J = 85,250 " 
 
 4,100X19 = 77,900 " 
 
 5,500X24 =132,000 " 
 i 
 
 Sum of moments =322,350 ft.-lbs. 
 
 Dividing the sum of the moments by the distance between 
 supporting forces, we have 9,768 Ibs. as the value of P 2 . The 
 sum of the loads is 18,300 Ibs. Subtracting 9,768, we have 
 8,532 as the value of P r 
 
 To draw the stress diagram start with oa= 8,532 lbs.=Pj, 
 
 10,000 
 
 FIG. 40 
 
 and draw ae and oe. Assume that the load at 7 is transferred 
 to joint 2, then the stress polygon for joint 2 is ea, ab, bf, and 
 
HOWE TRUSSES UNSYMMETRICALLY LOADED. 1003 
 
 fe. At joint 3 we have fb, measure down 6c = 5,500 Ibs., and 
 draw eg and fg. At joint 4, start by measuring upwards from 
 o 4,100 Ibs., giving point o', and draw gh and o'h. At joint 5 
 we have Jig, gc, measure down cd = 5,500 Ibs., and a line from 
 d drawn parallel to DH should pass through h, which completes 
 the diagram. The stress in rod 2-7 will be the load at joint 7. 
 
 EXAMPLE 26. Fig. 40 is the truss diagram of another truss 
 used in the same building as the truss shown by Fig. 39. Taking 
 moments about joint 1, we have for the sum of the moments 
 406,050 ft .-Ibs., and dividing by 33 ft., we have 12,304 as the 
 value of P 2 . The sum of the loads is 28,600 Ibs., which leaves 
 16,296 Ibs. for the value of P x . 
 
 The stress diagram is drawn in the same manner as Fig. 39A, 
 starting with oa = P,. ab is drawn equal to 'the sum of the 
 loads at joints 2 and 3, and the actual stress in EF is 3,400 Ibs. 
 plus the length of the line ef. If the stress diagram is correctly 
 drawn a line through d parallel to KD will pass through the 
 point kj previously obtained. The character of the stresses 
 is indicated by the plus and minus signs on Fig. 40, + denoting 
 compression. 
 
 If we compare the stress diagrams in the last three examples 
 with those for symmetrically loaded trusses of similar shape 
 we shall find that while the stress diagrams, Figs. 38A, 39A, 
 and 40A, are unsymmetrical, they are of the same general 
 character, and the stresses are all of the same kind as when 
 the supporting forces are equal. This condition holds true 
 for most triangular trusses, but for trusses with horizontal 
 or curved chords, unsymmetrical loading will usually cause 
 a reversal of the stress in kind in one or more of the braces 
 or verticals, and if the truss contains any four-sided panels 
 an additional brace will generally be required. This is par- 
 ticularly true of the Howe truss, and as this truss is very ex- 
 tensively used by architects and builders, we will now con- 
 sider at some length the effect of unsymmetrical loading. 
 
 Howe Trusses TJnsyin metrically Loaded. 
 
 When a Plowe truss is loaded symmetrically each side of the 
 centre, all of the braces will incline downward from the centre, 
 as in Figs. 17-20, Chap. XXV, and if there are an odd number 
 of panels, the centre panel will need no brace. 
 
 When a load of much magnitude is placed on one side of a 
 truss having an odd number of panels without a corresponding 
 
1010 
 
 STRESSES IN ROOF-TRUSSES. 
 
 load on the other side, a brace will always be required in the 
 centre panel and the brace should incline downward from 
 the side which is most heavily loaded. 
 
 When the truss has an even number of panels, an unsym- 
 metrical load will cause a greater stress in the braces on one 
 side of the truss than on the other, and if there is a sufficient 
 difference between the loads on one side of the truss from those 
 on the other, it will cause a compression stress in one or more 
 of the rods and a tensile stress in one or more of the braces. 
 Now, as this truss is especially designed with the idea of having 
 the braces in compression and the verticals in tension, when- 
 ever the loading would cause tension in a brace, or a com- 
 pression in a rod, then the direction of the brace should be 
 reversed, which will cause it to be in compression again. 
 
 For instance, take the truss, Fig. 41, having 6 equal panels 
 
 FIG. 41 
 
 and loaded with 4 tons at each of the upper joints and 9 tons at 
 the second lower joint. Without the bottom load of 9 tons the 
 brace in the third panel should incline downward from the 
 centre joint, as shown by dotted line at B, but when the load 
 of 9 tons is added it will cause a tensile stress in B and a com- 
 pression stress in R. To avoid this, the direction of the brace 
 is reversed as shown by the full line, and the brace is then in 
 compression, and the vertical R has no stress except the direct 
 load of 9 tons. The same thing would occur if the load of 
 9 tons was applied at the joint directly above, instead of at 
 
 FIG. 42 
 
 the lower joint, although in that case there would be no stress 
 at all on R, except the weight of the tie-beam. If the load of 
 
HOWE ^TRUSSES UNSYMMETRICALLY LOADED. 1011 
 
 9 tons were reduced to 6 tons, then no brace at all would be 
 required in the third panel, and when the bottom load is less 
 than 6 tons, then a brace in the normal direction is required, 
 as shown in Fig. 42. 
 
 In the five-panel truss, shown by Fig. 43, a load of 7.5 tons 
 at A would require the arrangement of braces shown by the 
 full lines, and if the load at A were increased to more than 15 
 tons, then the bra'ce R would need to be reversed, as shown 
 by the dotted line. 
 
 FIG. 43 
 
 The stress diagram will, always show in which direction any 
 brace should be placed to be in compression, but it may also 
 be determined by the following: 
 
 Rule. When the sum of the loads to the left of any section 
 taken between Pj and the centre is greater than the reaction 
 at P lt then the direction of the brace cut by that section must 
 be reversed from its normal direction. When the sum of 
 the loads is less than P lt then the brace should be in its normal 
 position. When the sum of the loads (to the left of the section) 
 is just equal to P p then no brace at all will be required. For 
 example, take a section at X, Fig. 43; here the sum of the 
 loads to the left is 10.5, which is less than P v and consequently 
 the brace should be in its normal direction. 
 
 If we take a section at Y, the sum of the loads to the left 
 is 13.5 or greater than P t ; hence a brace will be required slant- 
 ing down ward- from the heavier loaded side. 
 
 Taking a section at X, Fig. 41, the load to the left is 4, which 
 Is less than P A ; hence the brace in that panel should be in its 
 normal position. Taking a section at Y, the sum of the loads 
 is greater than P lf and hence the brace in that panel must be 
 reversed. 
 
 Taking a section at F, Fig. 42, the sum of the loads to the 
 left is less than Pjj hence the brace should be hi its normal 
 position. By the rule above given, one can always tell in 
 which direction the brace in any panel should be placed, no 
 
1012 
 
 STRESSES IN ROOF-TRUSSES. 
 
 matter how complicated the loading, or whether or not the 
 panels are of equal width; but to apply the rule, it is first neces- 
 sary to determine the supporting forces, which can be done 
 by the method of moments explained in Example 24. 
 
 EXAMPLE 27. As an example of an un symmetrical Howe 
 truss unsymmetrically loaded, we will take the truss repre- 
 sented by the diagram, Fig. 44. This truss is supposed to 
 support a ceiling over a hall, a flat roof, and a wooden tower 
 located as shown. The position of the tower necessitates a 
 division of the panels as indicated, so that the truss is quite 
 unsymmetrical. 
 
 We will assume that the weight of the ceiling, roof, snow, 
 and tower will give the loads at the upper joints indicated by 
 the figures which are supposed to represent tons. Multiplying 
 each load by its distance from the support P 2 and adding 
 together the products we have 1,475 foot-tons as the total 
 moment. Dividing by the distance between P l and P 2 (62), 
 we obtain 23.8 as the value of P r The total load is 45.5 tons; 
 hence P 2 will equal 21.7 tons. 
 
 FIG. 44 A 
 
 The only panels of this truss in which there would be any 
 question as to the direction of the braces are the third and 
 
HOWE TRUSSES UNSYMMETR1CALLY LOADED. 1013 
 
 fourth. Taking a section at X, the sum of the loads to the 
 left is greater than P t ; hence the brace should be placed as 
 drawn. A section taken through C would give the sum of 
 the loads to the left less than P v and hence the brace should 
 be in its normal position. The stress diagram of this truss 
 is readily drawn, starting with oa=P l and going from joint 
 to joint as in previous examples. The completed stress dia- 
 gram is shown by Fig. 44^1. To the stresses on the verticals 
 obtained from the diagram 44^1 should be added the ceiling 
 loads which they support. 
 
 Counter Braces. These are extra braces that are put in a 
 truss to counteract the effect of a load which may be applied 
 for a time and then removed. For illustration, let us consider 
 the truss represented by Figs. 41 and 42. Here we have already 
 seen that when the load at A is less than 6, the brace in the 
 third panel should be in the position shown by Fig. 42, while 
 when the load is greater than 6, the brace should be in the 
 position shown by the full line, Fig. 41. Now, if the load at 
 A represented the weight of a gallery with people in it, or a 
 hoist for raising heavy loads, or in fact almost any live load, 
 it is evident that when the live load was absent the brace in 
 the third panel would need to be in its normal position, and 
 when the full load is present a brace is needed in the opposite 
 direction, and as it is not practical to move the brace to suit 
 the condition of loading, it is necessary to put in two braces, 
 only one of which, however, would come in action at any given 
 time. 
 
 The stresses in a Howe truss, therefore, that are subject to a 
 variable and unsymmetrical load should be computed for 
 at least two conditions of loading, viz.: a, when the maximum 
 load is applied; and, b, when the variable load is removed 
 and the truss proportioned to resist both conditions. Snow 
 is a variable load, to which such trusses are often subjected, 
 but as it is nearly uniformly distributed over the roof, it would 
 not change the stress (in kind) in any of the members; hence 
 if the truss is designed for the maximum snow load, it will 
 be more than strong enough when there is no snow. More- 
 over, the transverse strength of the chords is usually sufficient 
 to resist any slight inequality in the loading. 
 
 The principal variable loads, therefore, to which a roof truss 
 may be subjected that would require counter braces are those 
 due to the weight of people, merchandise, etc., these either 
 
1014 STRESSES IN ROOF-TRUSSES. 
 
 being suspended from the truss by rods or brought upon the 
 truss by a floor supported by the tie-beam. The truss shown 
 in Fig. 44 is also an instance of such loading. The weights 
 given by the figures indicate merely the combined dead and 
 snow loads. During a high wind the weight on the leeward 
 side of the tower would be much increased and lessened on 
 the windward side, so that with the wind blowing from the 
 right, the load at 4 would be much greater than indicated, 
 and less at 8, while with the wind in the opposite direction 
 the load would be increased at 8 and lessened at 4. This would 
 require counter braces in both the third and fourth panels. 
 
 As counter braces can do no harm, even if they are never 
 brought into action, it is always well to use them in the centre 
 panels wherever the loads are at all variable. 
 
 Simple Cantilever Trusses. 
 
 Cantilever trusses may be considered as unsymmetrically 
 loaded trusses, for although the loads may be symmetrical 
 in relation to the truss, they are usually unsymmetrical in 
 relation to the supports. 
 
 The method of computing the supporting forces and drawing 
 the stress diagram is quite clearly shown by the following 
 examples: 
 
 EXAMPLE 28. Fig. 45 is the diagram of a cantilever truss 
 such as might be used to support the roof over a grand-stand 
 or depot-platform, and could be constructed either of wood 
 or steel, although steel would be preferable. 
 
 The first step towards determining the stresses is to find 
 the supporting forces. 
 
 For this purpose we have taken the panel loads at 1,000 Ibs., 
 all of the panels being of equal width, as this illustrates the 
 method as well as actual loads and simplifies the problem. 
 
 In cantilever trusses the loads at the ends of the trusses 
 should be taken into account as well as the intermediate loads. 
 These end loads are each equal to one half of the panel loads. 
 
 To find the supporting forces, take moments about joint 13. 
 The sum of the moments will be found to be 147,000 ft. -Ibs. 
 This moment must be resisted by the force P v which acts with a 
 lever arm of 24'. Dividing 147,000 by 24, we have 6,125 as 
 the value of P v and as the total load is 7,000 Ibs., P 2 must be 
 875 Ibs. 
 
SIMPLE CANTILEVER TRUSSES. 
 
 1015 
 
 The stress diagram may be commenced either with the forces 
 at joint 1 or those at joint 13, but as we have commenced at 
 the left in all preceding examples we will continue in this order. 
 
 Commencing then with joint 1, we lay off on a vertical line 
 the load oa=500 Ibs., which acts down, and from o and a draw 
 lines parallel respectively to 01 and AI. The forces act from 
 o to a, a to i (from the joint), and from i to o (towards the joint), 
 showing that AI is in tension and 01 in compression, the re- 
 verse of a truss supported at both ends. 
 
 Next, at joint 2, we have the stress ia, and measure down 
 ab = 1,000 Ibs.; then draw ij and bj, IJ being in compression. 
 
 Next draw the forces for joint 3 
 and for the remaining joints in 
 the order in which they are num- 
 bered. At joint 6, the first force 
 which we know is the supporting 
 force P v which we represent by 
 measuring down from o, 6,125 Ibs. 
 (although the force acts up), giving 
 the point o' . The polygon of 
 forces will then be o'o, om, mn, 
 and no' . It will be noticed that 
 the stress in MN is equal to the 
 supposing orce, which is evident 
 from the truss diagram. In prac- 
 tice, P l wo Id probably be a 
 post, which would be continued 
 to the apex of the truss. 
 
 At joint 12 we have the stresses vu, uf, fg= 1,000 Ibs., and 
 
1016 
 
 STRESSES IN ROOF-TRUSSES. 
 
 gv must close the polygon. It will be noticed that yv acts 
 toward the joint; hence the rafter in the end panel is in com- 
 pression. If a line drawn from g parallel to the rafter passes 
 through v, then the stress diagram must be correct; if it does 
 not pass through v, then either the stress diagram has not been 
 drawn with sufficient accuracy or an error has been made 
 in computing the supporting forces. In drawing the stress 
 diagram for cantilever trusses, it is important to keep the 
 
 direction in which the 
 forces act in mind in 
 order to tell which 
 members are in com- 
 pression and which in 
 tension. 
 
 EXAMPLE 29. Fig. 
 46 is the diagram of 
 a truss similar in out- 
 line to Fig. 45, but 
 with the diagonal 
 braces inclined hi the 
 opposite direction, so 
 as to cause them to I e 
 'n compres ion and the 
 verticals in tension. 
 The supporting forces 
 are found in the same 
 way as in Example 
 28, and the stress dia- 
 gram is also drawn in 
 the same way as Fig. 45 A . 
 
 In this truss, however, the stress 
 
S1MPLK CANTILKYKR TRUSSES. 1017 
 
 in the vertical post MN is considerably less than the reaction P v 
 because a large portion of the loads is transmitted to joint 6 by 
 the struts LM and NK. It will also be noticed that in this truss 
 three sections of the rafter on the right side are in compression 
 and three sections of the tie-beam in tension, owing to the fact 
 that in this truss the projection of the overhang in proportion 
 to the anchor span is less than in Fig. 45. It may be noticed 
 that when the stress lines pass to the left of the load line (Fig. 
 46/1) the stresses are reversed in kind. 
 
 This truss is better adapted to wooden construction (with 
 vertical rods) than is the truss shown by Fig. 45. 
 
 EXAMPLE 30 (Fio. 47) . In this example we have a truss with 
 an anchorage at the outer end to hold it down, so that P l acts 
 downward. To obtain the value of the supporting forces 
 take moments about joint 6 as follows: 
 
 Moments of loads to the right of joint 7: 
 (5X8) + (5X 16) + (5X24) + (12.5X32) =640,000 * ft.-lbs. 
 Moments of loads to the left of joint 7: 
 
 (2.5X24) + (5X16) + (5X8) =180,000 ft.-lbs. 
 
 As these moments act in opposite directions, we must sub- 
 tract the smaller from the larger, and we have an unbalanced 
 moment of 640,000-180,000=460,000, tending to turn the 
 truss down on the right or to lift the left-hand end. This 
 moment must be resisted by the reaction P lt which has an 
 arm of 24 ft. Dividing 460,000 ft.-lbs. by 24 ft., we have 
 19,250 Ibs. as the reaction at P v or it will require a weight 
 of this amount to hold the truss in place. 
 
 As the support P 2 must resist this pull as well as the loads, 
 P 2 will equal the sum of the loads plus the pull at P v or 45,000 
 + 19,250=64,250 Ibs. 
 
 Having obtained the value of the supporting forces we pro- 
 ceed to draw the stress diagram by laying off on a vertical 
 line oa = 19,250 lbs.=P 1 , remembering that it acts down. The 
 next force is the load of 2,500 Ibs., which also acts down, and 
 which gives the point 6; then from b draw a line parallel to Bl 
 and from o a line parallel to 01, and we obtain the point i. 
 
 * Note that loads are in thousands of pounds. 
 
1018 
 
 STRESSES IN ROOF-TRUSSES. 
 
 bi acts from the joint and io towards it, showing that BI is 
 in tension and 10 in compression. The remainder of the stress 
 
 FIG. 47 A 
 
 diagram is drawn in the 
 same way as diagrams 
 Figs. 45A and 46A. At 
 joint 6 we must start with 
 the force P 2 , which acts 
 up, and the upper end of 
 which must be at o; conse- 
 quently we obtain o f by 
 measuring down from o, 
 
 W ^___ FM ^ 64,250 Ibs.; the stress poly- 
 
 gon for this joint being o'o, om, mn, and no' . After we have 
 measured off gh=lo&d at joint 13, the remaining distance ho' 
 should be just equal to the load at joint 14, or 12,500 Ibs. If 
 P l and P 2 have been correctly computed and the stress dia- 
 gram accurately drawn the points s, u, and w will, come in the 
 line o'n. 
 
THREE-HINGED ARCHED TRUSSES. 1019 
 
 In the last three examples we have considered vertical loads 
 only. Cantilever roof trusses, however, should always be 
 computed for wind loads as well as for vertical loads and should 
 be braced from the supports. 
 
 Three-hinged Arched Trusses. 
 
 Several examples of this type of truss are illustrated in 
 Chapter XXV. 
 
 For computing the stresses each half truss is considered as 
 an entire truss itself. Considering the half arch, Fig. 48, it 
 is evident that a horizontal pressure must be exerted at the 
 top to prevent the arch from falling down, and this horizontal 
 thrust takes the place of one supporting force, the other being 
 exerted on the bottom pin. In the actual 'truss this hori- 
 zontal thrust is provided by the opposite arch, each half arch 
 holding up the other. 
 
 In accordance with the mechanical principle that for a body 
 to be in equilibrium the algebraic sum of the forces acting 
 in any given direction on the body must equal zero, to main- 
 tain the half arch, Fig. 48, in equilibrium, a horizontal resistance 
 must be exerted on the bottom pin equal to the horizontal 
 reaction on the top pin, and the two horizontal forces must 
 act in opposite direct ons. In practice the horizontal re- 
 sistance at the bottom is usually provided by rods or eye-bars 
 connecting the pins of the two half arches, although the re- 
 sistance may be provided by an abutment as with a masonry 
 arch. 
 
 In Fig. 48 the horizontal reactions are represented by the 
 arrows H, H. 
 
 The vertical stress diagram for this truss is very readily 
 drawn after the reactions are determined. These reactions 
 consist of a vertical resistance, P v equal to the entire load on 
 the half arch, and a horizontal resistance H. To compute the 
 horizontal resistance, obtain the algebraic sum of the moments 
 of the loads about the bottom joint and divide by the vertical dis- 
 tance between the pins. In obtaining the sum of the moments, 
 those which tend to turn the truss to the right should be marked 
 plus, and those which tend to turn the truss to the left minus. 
 
 EXAMPLE 31. The moments of the loads in Fig. 48 about 
 the bottom pin are as follows, commencing with the load at 
 joint 5: 
 
1020 STRESSES IN ROOF-TRUSSES. 
 
 500 Ibs. X 3' 6" = -1,750 
 
 1,000 
 1,000 
 1,000 
 1,000 
 1,000 
 1,000 
 1,000 
 
 " x r 6"= + 7,500 
 
 " X18' 6"= 18,500 
 " X29' 6" = 29,500 
 " X40' 6" = 40,500 
 " X51' 6" = 51,500 
 " X62' 6" = 62,500 
 " X73' 6" = 73,500 
 
 Total moment = 283,500 - 1 ,750 = 281 ,750 
 H =281, 750 -T- 72.5=3,886, or say 3,890 Ibs. 
 P t =sum of the loads =7,500 Ibs. 
 
 Having obtained P l and H, commence the stress diagram 
 by drawing the vertical line oa=P i and a horizontal line from 
 0=3,890. The stress lines for the bottom joint will then be 
 so, oa, aj, and js. Both aj and js act towards the joint, hence 
 both of these members are in compression. At joint 1 the 
 stress lines are ja, ak, and kj, the point k being obtained by 
 drawing a line from j parallel to JK. At joint 2 the stress 
 lines are sj, jk, kl, and Is. jk and kl act from the joint and 
 Is towards the joint, hence JK and KL are in tension and LS 
 in compression. 
 
 At joint 3 the stress lines are Ik, ka, am, and ml, am acting 
 from the joint, showing that AM is in tension. At joint 4 
 the stress lines are si, Im, mn, and ns. At joint 5 we have 
 nm, ma, measure down ao=500 Ibs., and draw bp and np, 
 parallel respectively to lines BP and NP. Continue in the 
 same way at all of the joints in the order in which they are 
 numbered. In this example the point c happens to come very 
 close to the point k, but it is merely a coincidence. The line 
 xy is also very short, barely long enough to indicate the direc- 
 tion in which the stress acts. 
 
 At joint 20 the stress lines are sd' ', d'e', and e's. Now if 
 the horizontal resistance H was correctly computed and the 
 stress diagram has been drawn with great accuracy, a line 
 through o parallel to IE' will just pass through e'. Owing 
 to the fact that the lines of the truss are at so many different 
 angles, it is more than likely that when the stress diagram is 
 completed the line oef will not quite pass through ef, and it 
 may be necessary to go over the diagram a second time with 
 great accuracy to make it come out right. 
 
 In drawing the stress diagram for a truss of this kind it wil] 
 
THREE-HINGED ARCHED TRUSSES. 
 
 1021 
 
 be necessary to keep in mind the direction in which the stresses 
 act at each joint, in order to tell which members are in com- 
 pression and which in tension, as a slight change in the pro- 
 
 }t. 1-1-0 " Y i 
 
 i-o-^ft i-i-e^j< ii-e^k 1-1-0"' >jc H-O^-^ ^i-i'ol-d-s's'-^ 
 
 j i! i Q !U4^u 
 
 portions of the arch or the location of the joints may change 
 the character of the stress in the braces. 
 
 EXAMPLE 32. Fig. 49 represents the truss diagram of one 
 of the three-hinged arches used in the Liberal Arts Building 
 of the Columbian Exposition at Chicago, 1893, the diagram 
 being taken from one published in the Engineering Record of 
 July 9, 1892. The trusses were spaced 50 feet apart, with 
 trussed purlins supported at every other joint, as shown by 
 
1022 
 
 STRESSES IN ROOF-TRUSSES. 
 
 the arrows, Fig. 49. The horizontal roof area supported at 
 each of joints 11, 15, 19, etc., was therefore 50'X3S', or 1900 
 square feet. The dead load was assumed at 42 Ibs. per 
 horizontal square foot (snow 12 Ibs., steel and wood 30 Ibs.), 
 which multiplied by 950 gives the loads indicated for joints 11, 
 
 FiQ. 49 
 
 15, etc. The loads at joints 9 and 26 would obviously be one 
 half of the loads at intermediate joints. There are also dead 
 loads at joints 1 and 5, due to the weight of outside walls and 
 galleries. The total moments of the loads about the bottom 
 joint, remembering that the moments for the loads at joints 1, 
 5, and 7 are negative, is 35,158,500 Ibs. 
 
 Dividing this moment by the vertical distance between pins 
 (206' 4"), we have 170,400 Ibs., or say 171,000. 
 
 The sum of the loads is 457,750 lbs.=P r The stress dia- 
 
THREE-HINGED ARCHED TRUSSES. 
 
 1023 
 
 gram is drawn in the same way as explained for Fig. 48 A, and 
 presents no difficulties except in drawing the lines exactly 
 parallel to the corresponding rnembers of the truss. It will 
 be noticed that the line UU has no stress because there is no 
 load or other force to produce a stress where it joins the rafter. 
 It was doubtless inserted to stiffen the rafter between joints 9 
 and 11. The character. of the stress in the different members 
 is indicated by the plus and minus signs, + in all cases de- 
 noting compression. It will be noticed that the stress in AJ 
 and JK is very small under a dead load, due to the inclination 
 of A J and JS. In the stress diagram published in the Engineer- 
 ing News, the line aj comes on the other side of the load line, 
 the difference being due. either to the truss diagram, Fig. 49, 
 not being exactly right or possibly to what appears to be an 
 additional load at joint o. It will be noticed that if the line 
 JS was but a very little steeper it would bring the point / on 
 the other side of the load line. The stress diagram in Fig. 49 
 is correct for the truss as drawn and for the loads given. 
 
 Necessity for Determining Wind Stresses in Three-hinged 
 Arches. The stresses produced by the wind in trusses of this kind 
 will in many instances greatly exceed those due to the dead load, 
 and will also in many cases be of the opposite kind, so that it 
 is absolutely necessary to compute stresses for the wind ha 
 both directions (see pages 1024 and 1029). To show how the 
 stresses vary for dead and wind loads, we give below the stresses 
 for several members, as published in the Engineering Record: 
 
 Member. 
 
 Dead Load. 
 
 Wind Left. 
 
 Wind Right. 
 
 AJ 
 
 - 11,000 
 
 + 290,000 
 
 - 78,000 
 
 JS 
 
 + 498,000 
 
 -228,000 
 
 + 183,000 
 
 JK 
 
 + 2,500 
 
 - 86,000 
 
 + 24,000 
 
 BK 
 
 - 34,000 
 
 + 277,000 
 
 - 75,000 
 
 KL 
 
 -168,000 
 
 + 208,000 
 
 -r 97,000 
 
 LS 
 
 + 612,000 
 
 -389,000 
 
 + 254,000 
 
 LM 
 
 + 95,000 
 
 -119,000 
 
 + 55,000 
 
 With wind to the right, piece AJ would have a total tensile 
 stress of 89,000 Ibs., and with wind from the left a compressive 
 stress =290,000 -11, 000, or 279,000 Ibs. Piece LS would be sub- 
 ject to a compressive stress of 866,000 Ibs. when wind is from 
 the right and 223,000 Ibs. when wind is from the left. 
 
1024 STRESSES IN ROOF-TRUSSES. 
 
 Wind Load Stresses. 
 
 Thus far we have considered the stresses due to vertical 
 loads only, 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 the Fink 
 and fan types, it is not safe to consider wind pressure as acting 
 vertically, because the wind acts 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 causing 
 stresses of an opposite kind from those produced by a vertical 
 load. 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. 
 
 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 wind on the side of the truss nearer the ex- 
 pansion end, and for the wind on the side of the truss nearer 
 the fixed end. 
 
 Stresses due to permanent dead load. 
 
 Stresses due to snow covering the entire roof or only one 
 half, and even in special cases only a small area on one side. 
 
 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. Fig. 50 (from " Modern Framed Structures"), 
 which is a half diagram of the roof trusses of the St. Louis 
 Exposition Building,* shows the different stresses as figured 
 for those trusses. All loads and stresses are given in thousands 
 of pounds. The letters in connection with the stresses have , 
 the following significance: 
 
 D, permanent dead load at 20 Ibs. per square foot; S, uniform 
 
 * Erected several years ago. 
 
WIKD LOAD STRESSES. 
 
 1025 
 
1026 STRESSES IN .ROOF-TRUSSES. 
 
 snow load at 20 Ibs.; SL, snow load on left side only; SB, snow 
 load on right ride only; Wp, wind from fixed end; WR, wind 
 from roller end. The total maximum stresses are marked 
 M (for each kind). 
 
 In the table on p. 1023 is given the stresses in a few of the 
 members in the three-hinged arch, Fig. 49, due to vertical 
 load, and wind left and right. 
 
 For trusses with straight rafters it will generally be sufficient 
 to find the stresses due to permanent dead load, and to the 
 wind from both directions, disregarding 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 Ibs. per square foot of roof 
 surface to the dead load to alow for sleet. 
 
 In localities where heavy snowfalls may be expected the 
 stresses due to 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 
 trus; are fixed, the wind reactions are parallel to the resultant 
 wind load; if one end is free to move, i.e. on rollers or supported 
 on a rocker, the reaction at the roller end is vertical and that 
 at the fixed end will be 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 coefficient 
 of friction, which is about one-third." 
 
 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 feet the free end should be supported on rollers to 
 permit of expansion or contraction. 
 
 When steel trusses are supported by steel posts, as in steel 
 mill buildings, the trusses are rigidly attached to the columns 
 and no provision is made for expansion. In such buildings 
 the wind pressure produces a bending strain in the columns 
 which must be provided for. 
 
 EXAMPLE 33. To draw the wind-stress diagram for a truss 
 with fixed ends. Wind pressure is usually assumed to be applied 
 uniformly over one side of the roof and to act at right angles 
 
WIND LOAD STRESSES. 
 
 1027 
 
 to the surface of the roof. The joint, or panel, loads will therefore 
 be proportional to the roof areas supported. When the joints 
 d'vide the rafter into panels of equal length, then the joint 
 loads will be 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. 
 
 For this example we will take the triangular truss shown in 
 outline by Fig. 51 and a sume that the span and spacing of 
 the truss are such as will give a load of 1,000 Ibs. at joints 2 
 and 4. The loads at joints 1 and 5 would be only one half of 
 those at 2 and 4. 
 
 To find the supporting forces or reactions, draw a line repre- 
 senting the resultant of the loads, cutting the bottom chord 
 at X. As the loads are symmetrical the resultant must act 
 at the centre of the rafter and at right angles to it. 
 
 The reactions will be proportional to the two segments into 
 which a horizontal line joining the points of support is divided 
 by the resultant, or in this case to IX and X7, the larger re- 
 action being at joint 1. The sum of the reactions must be 
 equal to the sum of the loads. To find the reactions graph- 
 ically, draw a line from joint 1, at any angle, say from 30 to 
 45, and measure off a distance equal to the total load. 
 . In Fig. 51 the line 1-8 represents 3,000 Ibs. Join 7 and 8, 
 and from X draw a line parallel to 7-8, intersecting 1-8 at X'. 
 
 FIG. 51 A 
 
 Then X'-S will be the reaction at joint 1 and X'-l the reaction 
 at joint 7. 
 
 To draw the stress diagram, Fig. 51 A, first draw the load 
 line ae equal to the sum of the loads (in this case 3,000 Ibs.) 
 
1028 STRESSES IN ROOF-TRUSSES. 
 
 and perpendicular to the rafter 1-5, and divide it so that ao 
 =X / -8. Then at joint 1 we have oa equals the supporting 
 force, 6=500 Ibs., and from b and o daw lines parallel re- 
 spectively to BF and OF, intersecting at /. The stresses 
 act in the direction oa, ab, bf, and /o, showing that BF is in 
 compression and FO in tension. 
 
 At joint 2 the stress lines are fb, bc = 1,000 Ibs., eg, and gf. 
 The stress lines at joint 3 are of, fg, gh, and ho. At joint 4, 
 kg, gc, cd, di, and ih. At joint 5, id, de, ek, and ki. (Note. If 
 the load line has been correctly divided at o, and the stress 
 lines drawn exactly parallel to the lines of the truss, the point 
 k will be exactly above the point i.) 
 
 At joint 6 the stress lines are oh, hi, ik, and as the figure 
 must close by a horizontal line through o, it is evident that 
 the line KK 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 we have the reaction eo, acting up, 
 ok and ke must close the figure, showing that the line ke repre- 
 sents the stress in the entire length of the rafter to the right, 
 and that there is no stress in the bracing on that side of the 
 truss when the wind is from the left. If, however, either the 
 lower tie or the rafter were not straight, some of the braces on 
 that side would come into action. 
 
 By following the direction of the stresses in Fig. 51^4, it 
 will be found that the different members of the truss have 
 the same kind of stress as is produced by a vertical load. 
 
 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. 
 
 EXAMPLE 34. To draw the wind-stress diagrams for a truss 
 having one end fixed and the other end on rollers. 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 for wind from the left, marked WL, and one 
 for wind from the right, marked WR. It is customary with 
 authors when writing on this subject to consider that the rollers 
 are always under the right-hand support, and we shall follow 
 this custom. In practice the rollers may be placed under 
 
WIND LOAD STRESSES. 
 
 1029 
 
 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. 51, illustrating it again in Fig. 52, which is 
 drawn to show wind from the left. Lay off the load line 1-8 
 and divide it at X' t as in Example 33, and draw a line at ae, 
 
 perpendicular to the rafter and equal to 1-8, and divided in 
 the same proportions. Through ~K f on ae draw a horizontal 
 line, and through e a vertical line, the two intersecting at o. 
 Then eo will represent the vertical reactions at joint 7 and 
 oa the reaction at joint 1. 
 
 The stress lines at joint 1 are: oa, a&=500 Ibs., &/, and /o. 
 At joint 2: /&, be, eg, and gf. The remainder of the diagram 
 (WL) is completed exactly as described for Fig. 51 A, the only 
 difference in the two diagrams being in the location of point o, 
 which increases the stress in the tie-beam. 
 
1030 STRESSES IN ROOF-TRUSSES. 
 
 Fig. 53 represents the same truss with wind from the right. 
 To draw the stress diagram WR, start with td, perpendicular 
 to the rafter and equal to the total load (3,000 Ibs.). Divide 
 the line at X' in the same proportion as the line 1-8, Fig. 52, the 
 longer portion being at the top. To find the reactions draw a hori- 
 zontal line through X 1 and a ve ical line through t, the two lines 
 intersecting at o. Then ot is the reaction at joint 10, and od the 
 reaction at joint 1. For this diagram it will be better to start 
 with joint 10 and take the forces in the reverse order from that 
 in which we have taken them before. The stress lines for joint 10 
 are ot, is = 500 Ibs., 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 Td. 
 At joint 5, ke, ed, di, and ik. (Note that if the work has been 
 correctly done the point i will come exactly above the point k.) 
 
 Comparing the two figures WL and WR, we see that the 
 stress lines for the rafter and braces are of the same length 
 (and also of the same kind) in both diagrams, but that the 
 stress in the tie-beam is considerably less with wind from the 
 right. This condition does not apply to all trusses, however, 
 so that it is best to draw the stress diagrams for wind from both 
 directions. 
 
 EXAMPLE 35. Wind-stress diagram for wooden queen-rod 
 truss. Fig. 54 represents the outline of a queen-rod truss 
 for a roof having a rise of 14" in 12". As the truss is of wood 
 we will consider the supports fixed. Joint 2 divides the rafter 
 into two equal parts, consequently the wind load at this joint 
 will be twice that at joints 1 or 4. For convenience we will 
 assume that the wind load at joint 2 is 1,000 Ibs., and at joints 
 1 and 4, 500 Ibs. The resultant wLl be 2,000 Ibs. and will act 
 through joint 2 and intersect the tie-beam at X. To find the 
 supporting forces, draw the line 1-8=2,000 Ibs. and connect 7 
 and 8. From X draw a line para lei 7-8 intersecting 1-8 at 
 X'. Then X'-8 is the supporting force at joint 1 and \-X' 
 the supporting force at joint 7. 
 
 Begin the stress diagram (Fig. 54A) by drawing the line 
 ad at right angles to the rafter 1-4, and equal in length to 1-8. 
 By means of dividers locate the point o so that ao will equal 
 X'-8. Then the stress lines for joint 1 will be oa, db, be, and eo. 
 At joint 2, eb y be, cf, and fe. At joint 3, oe, ef, fh, and ho. At 
 joint 4, hf, fc, cd, dk, and kh. It wi.l be seen that we cannot 
 close the figure at joint 4 without the brace hk, because we 
 started at h, and a hor'zcntal line through d will not pass through 
 
WIND LOAD STRESSES. 
 
 1031 
 
 h. Therefore a queen-rod truss requires braces in the centre 
 panel to resist the wind stress. With the wind from the right, 
 a brace will be required from joint 3 to joint 6. 
 
 FIG. 54 
 
 At joint 5 the stress lines are oh, hk, kl, and lo. It 
 should be noticed that lo acts towards the joint, showing that 
 OL is in compression. At first it would seem as though this 
 could not be true, but if we glance at joint 7 we see that P l 
 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 rafters is exactly 45, there will be no stress 
 in OL, and when the inclination is less than 45, OL will be 
 in tension. 
 
 The stress lines for joint 6 are Ik, kd, and dl. If no errors 
 have been made, a line through d parallel to DL will just 
 pass through the point /, prev ously obtained. A very slight 
 inaccuracy in getting the point X f ', or in drawing the stress 
 diagram, however, w'll cause the line through d to pass to 
 one side or the other of point Z, and if this happens "t shows that 
 there has been some inaccuracy somewhere. In practice, a 
 slight divergence will not materially affect the stresses. At 
 joint 7 the stress polygon is ol, Id, and cZ0=P 1? the lines being 
 already drawn. 
 
 EXAMPLE 36. For the purpose of showing how the stresses 
 due to wind and vertical loads are combined we will take the 
 truss diagram shown by Figs. 55 and 56, being the same as 
 shown by Fig. 12, and representing the truss shown by Fig. 3. 
 
1032 
 
 STRESSES IN ROOF-TRUSSES. 
 
 We will first determine the stresses due to the weight of the 
 roof and ceiling and an allowance of 10 Ibs. per square foot 
 for sleet. 
 
 On page 954 the roof area supported at joint 2 was found 
 to be 147J sq. ft., and at joint 3, 200 sq. ft. On page 953 the 
 weight of the roof was estimated at 12f Ibs. per square foot, 
 and allowing 10 Ibs. for sleet, we have 22} Ibs. as greatest dead 
 load under a heavy wind, which gives 3,360 Ibs. for the load 
 at joint 2 and 4,550 Ibs. for the load at joint 3. The ceiling 
 loads would, of course, be the same as .in Fig. 12. 
 
 Fig. 55 shows the loads due to weight of materials and sleet 
 
 FIG. 55 A 
 
 as computed above, the ceiling loads being added to the roof 
 loads for convenience in drawing the stress diagram. Fig. 55A 
 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.) 
 
 Wind Stresses. The inclination of the roof is very close to 
 45, and from Table VIII we find the normal wind pressure 
 for that angle to be 27 Ibs. Multiplying the roof area at joints 
 2 and 3 by 27, we have the wind loads indicated in Fig. 56. 
 We must also figure the wind load at joint 1. The roof area 
 supported at this joint, allowing 17 ins. for eave projection (see 
 Fiff. 3) is 6J'X15'=95 sq. ft., which would make the wind load 
 2,565 Ibs. The next step will be to find the point at which 
 the resultant of these loads would cut the rafter. As the loads 
 
WIND LOAD STRESSES. 
 
 1033 
 
 are not symmetrical or uniform on the rafter, we must obtain 
 the point through which the resultant would act by means 
 of moments about joint 1. The arms of the loads at joints 2 
 and 4 are figured on the truss diagram (Fig. 56). The moments 
 are 
 
 3,990 X 9 T 5 2= 37,572 
 
 5,400 X18J = 98,550 
 
 Total moment = 136,122 ft.-lbs. 
 
 The resultant will be the sum of all the loads, or 11,955 Ibs., 
 and the distance of its point of application from 1 is found 
 by dividing the total moment by the resultant, 136,122 
 divided by 11,955 = 11.4 ft. Measuring off 11.4 ft. on the 
 rafter from joint 1 and drawing a line at right angles to it 
 intersecting the tie-beam we obtain the point X. From 1 
 draw the line 1-8 at any angle equal in length to the sum of 
 the loads, 11,955 Ibs., and connect 7 and 8. From X draw a 
 line parallel to 7-8, intersecting 1-8 at X'. Then X'-& will 
 be the supporting force at joint 1. 
 
 Supporting Forces Computed by Moments. The supporting 
 forces can also be computed by moments. The moments of 
 the loads about joint 1 tend to rotate the truss from left to 
 right. To prevent this rotation we have the supporting force 
 P t acting at joint 7. To just maintain equilibrium, the mo- 
 ment of P l about joint 1 must just equal the moments of the 
 loads about the same point, which we found above to be 
 
1034 
 
 STRESSES IN ROOF-TRUSSES. 
 
 136,122 ft.-lbs. The arm of P l is the perpendicular distance 
 between its line of action and joint 1. Continuing P l above 
 the truss we obtain the dotted line at p, and the distance from 
 1 to p is 26.5 ft. 
 
 Knowing the arm, the value of P l is obtained by dividing 
 the moments of the loads 136,122 by the arm, or 26.5 ft, which 
 gives 5,137 Ibs. As the sum of P and P must equal the total 
 load, P = 11,955 -5,137 =6,818. The distance l-X' and X'-8 
 should scale reasonably close to these figures. Knowing the 
 supporting forces, the stress diagram, Fig. 56 A, is drawn exactly 
 as described for Fig. 54 A . As the inclination of the rafters is 
 a little greater than 45, OL is in compression, but the stress 
 is very small. The figures on Fig. 56A indicate the stresses 
 in pounds. We are now prepared to tabulate the stresses, 
 which should be done 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. 
 
 STRESSES FOR TRUSS (Fias. 12, 55, AND 56). 
 
 Member.* 
 
 Dead Weight 
 and Sleet. 
 
 Wind 
 
 Stresses. 
 
 Total. 
 
 Stresses 
 (Fig. 12). 
 
 A-E 
 
 + 16,150 
 
 + 4,900 
 
 + 21,050 
 
 + 25,640 
 
 B-F 
 
 + 13,800 
 
 + 4,900 
 
 + 18,700 
 
 + 21,400 
 
 C-K 
 
 + 9,600 
 
 + 3,400 
 
 + 13,000 
 
 + 14,900 
 
 E-F 
 
 + 2,350 
 
 + 3,950 
 
 + 6,300 
 
 4,400 
 
 H-K 
 
 
 
 + 5,000 
 
 + 5,000 
 
 
 
 F-H 
 
 - 5,410 
 
 -3,550 
 
 - 8,960 
 
 - 6,900 
 
 E-O 
 
 -11,200 
 
 -5,900 
 
 -17,100 
 
 -17,800 
 
 H-0 
 
 - 9,600 
 
 -3,250 
 
 -12,850 
 
 -14,900 
 
 * Members are lettered according to Fig. 56. 
 
 Thus the stress in the rafter LC 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 4,900 Ibs. (the stress in LC). In the same way the stress 
 in the rod KL is greater than in FH; hence the stress n KL 
 should be tabulated. The stress in LO would slightly reduce 
 the tension due to dead load, but as the stress in EO increases 
 it, the stresses in EO and HO should be tabulated. 
 
 Both sides of the truss should of course be made alike, and 
 
WIND LOAD STRESSES. 1035 
 
 two braces should be inserted in the centre panel. In the 
 fifth column of the table we have given the stresses due to the 
 ceiling load and a vertical load on the roof of 42f Ibs. per square 
 foot, as obtained from the stress diagram, Fig. 12. Comparing 
 the stresses in the fourth and fifth columns, we see 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 the totals due to wind, dead weight, and sleet. 
 Vertical loads, of course, give no stress for the braces in centre 
 panel, and unless the wind stresses are drawn, it will be neces- 
 sary to guess at the sizes of these braces. The stress in these 
 braces, however, is so small that it will not require a very 
 large piece of timber. 
 
 The stresses given in the fourth column ara unquestionably 
 nearer what the real stresses are likely to be than those in 
 the fifth column. If the roof were to be erected in a warm 
 climate where there would be no sleet, then these stresses 
 could be further reduced by omitting the 10 Ibs. per square 
 foot added for sleet. 
 
 If, on the other hand, the inclination of the roof was less 
 than 30, the stresses produced by a heavy fall of snow with* 
 out wind will generally exceed the sum of those due to dead 
 weight, sleet, and wind, and for such roofs the stresses due 
 to maximum snow load should always be computed. 
 
 Reactions. It will be noticed that the reactions, or supporting 
 forces in Fig. 56, are very much inclined from a vertical. As 
 the dead load is always acting on the truss, however, the real 
 reaction would never have such an inclination, but would be 
 more nearly vertical, and when there- is no wind the reactions 
 will be exact y vertical. The theoretical reaction, due to 
 both wind and dead load, wi 1 be the diagonal of a parallelo- 
 gram formed with the reactions for dead and wind loads as 
 two of its sides. Thus if 7-a, Fig. 56, represents P t at a smaller 
 scale, and 7-& the vertical reaction to the same scale, then 
 PR will be the resultant reaction, which will be modified some- 
 what by friction. 
 
 Examples 33, 34, and 35 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 with 
 straight rafters. For trusses with curved rafters the diagrams 
 become more complicated, and the reader is referred to "Graph- 
 ical Analysis of Roof Trusses," by Prof. Charles E. Greene, 
 
1036 STRESSES IN ROOF-TRUSSES. 
 
 also to " Steel Mill Buildings," by Prof. Milo S. Ketchum, for 
 explanations regarding wind-stress diagrams for such trusses. 
 The latter work also takes up in detail stress diagrams for 
 trusses supported and braced from steel columns, and will 
 be found of valuable assistance in designing steel mill buildings. 
 
MEMBERS OF WOODEN TRUSSES 1037 
 
 CHAPTER XXVII. 
 HOOF-TRUSSES (Continued), 
 
 Proportioning the Members and Detailing the 
 Joints. 
 
 Proportioning the Members to the Stresses. The 
 size or sectional area of the different members of a truss cannot 
 be proportioned with any accuracy until the stresses which 
 the maximum loads will produce have been found. When the 
 stresses are known, however, the size of the truss members 
 can be readily computed by the rules and tables for the strength 
 of materials. 
 
 Every member of a truss must be either a tie or a strut. If 
 either is also subject to a transverse load, as is often the case 
 with rafters and tie-beams, then the member becomes a tie-beam 
 or strut-beam according as it is in tension or compression. We 
 therefore have four kinds of members (regardless of material) 
 to be considered in trusses, viz., simple ties, simple struts; 
 tie-beams and strut-beams. 
 
 Rules and data for computing the sectional area of simple 
 ties of any shape or material are given in Chapter XI. Struts 
 may be computed by the rules and tables given in Chapter XIV, 
 and directions for proportioning steel tie- and strut-beams 
 to the load and stress are given on pages 511 and 512, and for 
 wooden strut- and tie-beams on pages 568 and 569. 
 
 To more fully show the application of the rules, however, 
 we will compute the size of members for three or four trusses. 
 
 EXAMPLE 1. To compute the size of the members in the 
 truss shown by Fig. 1. 
 
 This is the same truss as is represented by Figs. 3, 12, 55, 
 and 56 of Chapter XXVI. 
 
 For the stresses we will use those given in the fourth column 
 of the table on p. 1034, and which are tabulated below. The 
 members RR are to be wrought-iron rods, not upset, and all 
 other members are to be of a good quality of white pine. 
 
1038 
 
 TRUSS MEMBERS AND JOINTS. 
 
 None of the members of this truss are subject to a trans- 
 verse strain, so that we have to consider only simple ties and 
 simple struts. 
 
 Rafters , 
 
 Fig. I 
 
 Rods. The tension in each of the two rods (see table below) 
 is 8,960 Ibs. As a considerable portion of the stress is due 
 to wind-pressure we can safely use a unit stress of 12,500 Ibs. 
 to the square inch. From the table on p. 340 we find that 
 the safe strength of a 1J" rod, not upset, at 12,500 Ibs. to the 
 square inch is 8,570 Ibs., and of a 1J" rod 11,060 Ibs. The 
 1J" rod is not quite strong enough and we will use a 1J" rod, 
 or we might use a 1J" steel rod. 
 
 STRESSES AND DIMENSIONS FOR TRUSS I. 
 
 Member. 
 
 Stress ; Lbs. 
 
 Dimensions. 
 
 A 
 
 + 21,050 
 
 6X8, white pine 
 
 B 
 
 + 18,700 
 
 6X8, white pine 
 
 C 
 
 + 13,000 
 
 6X8, white pine 
 
 D 
 
 + 6,300 
 
 4X6, white pine 
 
 E 
 
 + 5,000 
 
 4X6, white pine 
 
 N 
 
 -17,100 
 
 3 2"X8" I" bolts, 2' centre to centre 
 
 M 
 
 -12,850 
 
 3 2"X8" I" bolts, 2' centre to centre 
 
 R 
 
 - 8,360 
 
 1 i" rod, wrought iron, not upset 
 
MEMBERS OF WOODEN TRUSSES. 1039 
 
 Rafter. The stress in the rafter is 21,050 Ibs. at A and 18,700 
 Ibs. at B, but as it should be of the same size for its entire length 
 we will proportion it to the stress at A. The clear length 
 between joints is about 9 ft. From the table for white-pine 
 posts, p. 412, we see that a 6X8 timber is more than strong 
 enough, while a 6X6 is hardly sufficient. We will therefore 
 make the rafter 6X8. 
 
 Strut-beam (C). The stress in this member is 13,000 
 Ibs. and it is about 12 ft. long between bearings. From the 
 same table, p. 412, we see that a 6X6 timber would do for this 
 member, but on account of making a better joint we will make 
 it of the same size as the rafter, or 6X8. 
 
 Braces. The stress in the brace D is 6,300 Ibs. From 
 the table, p. 412, we see that a 4x6 timber will have ample 
 strength. The stress in the braces EE is 5,000 Ibs. and the 
 length about 17 ft. As the braces stiffen each other at the 
 intersection, however, we can safely make them 4" X 6", notch- 
 ing each brace 1 in. where they pass, so that the total thick- 
 ness at the intersection will be 6", and bolting them together 
 with a i" bolt in a f " hole to give a little play. Brace D had 
 better be set flatways and the braces E edgeways. 
 
 Tie-beam. The maximum tension in the tie-beam is 
 12,850 Ibs. The tensile strength of white pine is given on p. 322 
 at 1,400 Ibs. per square inch, therefore the tie-beam must have 
 a net sectional area at N 12,850-^1, 400 or 9.2 sq. ins. A 
 2" X 6" plank if continuous from end to end of the truss and 
 without holes would therefore resist the stress, but to make 
 good joints with the rafters and braces, the tie-beam must be 
 as wide as the rafters. 
 
 We must also allow for the holes where the rods pass through 
 and for a slight notch at joints 7 and 8. A 6X6 timber in 
 one length will have ample strength, but as this may be diffi- 
 cult to obtain, we can build it up of three 2"X8" planks bolted 
 together, using 24-ft. and 14-ft. lengths and lapping the long 
 pieces so that there will be 10 ft. between the joints. 
 
 The centre planks will be cut so nearly in two by the rods 
 that. they will have little strength, and the stress in the centre 
 will practically have to be borne by one plank. 
 
 The planks should be bolted together by f " bolts 2 ft. on centres. 
 We now have the dimensions for all members of the truss, and 
 they should be entered in the table opposite the stresses. 
 
 Note. In this example we have an excess of strength in the 
 
1010 
 
 TRUSS MEMBERS AND JOINTS. 
 
 timber, but as none of the timbers are large, nothing to speak 
 of would be gained by trying .to cut them down. When the 
 stresses are four or five times as great as in this truss, requiring 
 large timbers, then the size may be figured more closely, as the 
 cutting at the joints is not as much in proportion to the sec- 
 tional area in large timbers as in small ones. 
 
 EXAMPLE 2. For this example we will take the truss shown 
 by Fig. 2, which is the same truss as is shown by Figs. 4 and 
 24 of Chapter XXVI. The stresses produced by a vertical dead 
 load of 42J Ibs. per square foot of roof for wind and snow are 
 figured on the stress diagram, Fig. 24A, Chapter XXVI, and 
 reproduced in the following table. 
 
 The rafters and tie-beams of this truss also sustain a trans- 
 verse load which is uniformly distributed. In computing the 
 joint loads for this truss (see Example 3, Chapter XXVI), 
 we allowed 12 Ibs. per square foot for the weight of the ceiling, 
 which will give the transverse loads for S and B indicated in 
 the following table. 
 
 The transverse loads for the rafters A and B are figured at 
 42J Ibs. per square foot. 
 
 STRESSES AND DIMENSIONS FOR TRUSS 2. 
 
 Member. 
 
 Stress, Ibs. 
 
 Dimensions, Material 
 White Pine. 
 
 A 
 
 j Compression, 8,000 
 ( Transverse, 1,000 
 
 [2 ifxs" 
 
 B 
 
 j Compression, 6,600 
 (Transverse, 1,320 
 
 [2 ifxs" 
 
 D 
 
 Compression, 1,890 
 
 1 2X8 
 
 E 
 
 Compression, 750 
 
 1 2X8 or 2X10 
 
 F 
 
 Tension, 4,350 
 
 2 1X8 
 
 H 
 
 Tension, 2,530 
 
 2 1X6 
 
 S 
 
 j Tension, 1,875 
 / Transverse, 470 
 
 j-1 2X10 
 
 T 
 
 j Tension, 5,400 
 ( Transverse, 384 
 
 jl 2X8 
 
 T, 
 
 Tension, 1,875 
 
 1 2X8 
 
 We will assume that the truss is to be built of a good quality 
 of white pine, spiked and bolted at the joints. 
 
 Rafter. The compression in the bottom of the rafter A 
 is greater than at B, but as the length of B is considerably 
 greater than A, and the transverse load is also greater on B 
 
MEMBERS OF vVOODEN TRUSSES. 
 
 1041 
 
 if the rafter is strong enough to resist the strains at B, it will 
 be strong enough to resist those at A. 
 
 Fig. 2 
 
 We will first find the dimensions necessary to resist the trans- 
 verse load. As the rafter is inclined its strength as a beam 
 is considerably greater than if horizontal; we therefore will 
 use for the span 9 ft., which is about an average of the real length 
 and the horizontal projection. 
 
 To support 1,320 Ibs. with a span of 9 ft. wih 1 require a 
 lf"X8" joist (formula 11, p. 564). Considering the re- 
 sistance to compression, it should be remembered that the 
 sheathing is nailed to the rafters, and hence they cannot bend 
 sideways. The depth of the rafter can therefore be considered 
 as the breadth, so that the ratio of length to breadth will be 
 !*!=: 18 (the clear distance between the joints should be taken 
 for the length as a strut). 
 
 By formula (5), p. 410, we find that the safe resistance for a 
 white-pine strut with a ratio of length to breadth of 18 is 
 517 Ibs. per square inch, hence it will require 13 sq. ins. to 
 resist 6,600 Ibs. This is equivalent to If X8. Therefore two 
 pieces each lf"X8" will be strong enough for the rafters. 
 
1042 TRUSS MEMBERS AND JOINTS. 
 
 Tie-beams. These should preferably be of single planks 
 spiked between the rafters. 
 
 The transverse load on S is 470 Ibs. and the span, say, 15' 6". 
 Assuming a depth of 10 ins. the breadth, from formula (11), 
 p. 564, should be f in., or a }"X10" board would support the 
 transverse load. The sectional area required to resist the 
 tension equals ^f or less than 1J sq. ins.; hence a 1J"X10" 
 board will be strong enough for S, but it would not be stiff 
 enough to resist the compression at E, so we will make it 2" X 10". 
 
 For T we will try a depth of 8 ins., as the piece is inclined 
 and the span is not as great. The transverse load is 384 Ibs. 
 and we will call the span 12 ft. Then with a depth of 8 ins. 
 we shall require a breadth of f". 
 
 To resist the tension we shall require a sectional area = |, 
 or 3^ sq. ins., equivalent to about J"X8"; therefore a 2"X8" 
 plank will answer for T and T^ 
 
 We will now see if it will answer for D. As this piece is 
 free to bend in either direction we must divide the length, in 
 inches, by 2, to get the ratio of length to breadth. The length 
 
 is about 86 ins., therefore ^- = 43. The safe resistance per square 
 
 inch of a white-pine strut for this ratio is, formula (5), p. 410, 
 367 Ibs. ; hence we shall require a little more than 5 sq. ins. to 
 resist 1,890 Ibs. A 2X8 strict is therefore ample. 
 
 Ties F and H. For F we shall require a sectional area 
 fiS? or 3J sq. ins., and for H f g , or 1.8 sq. ins. As it would 
 be impossible to secure the ends of such small pieces, we will 
 make the tie F of two lX8's and HH of two lX6's, so as to 
 have plenty of room for nailing. 
 
 (Note. Wooden ties must always be much larger than the 
 sectional area required by the formula for tension, to provide 
 means for making a satisfactory joint.) We have now com_ 
 puted the dimensions for all parts of the truss, as indicated 
 in the table. By continuing the boards F to the tie S, so as 
 to shorten the span, we could reduce S to 2 / 'X8 // . 
 
 EXAMPLE 3. For this example we will take the Howe truss, 
 shown by Fig. 3. The trusses are supposed to be uniformly 
 spaced 15' 8" centre to centre and the rafters and ceiling joists 
 span from truss to truss and rest directly on the chords. 
 
 Allowing 30 Ibs. for snow and 6 Ibs. for tar and gravel roofing, 
 the dead load per square foot of roof will be 46 J Ibs., and for 
 the ceiling we will allow 16 Ibs. per square foot. This would 
 
MEMBERS OF WOODEN TRUSSES. 
 
 1043 
 
 make the roof load 5,885 Ibs. at joint 2 and 5,704 Ibs. at joints 
 4 and 6. The ceiling load at joint 3 would be 1,984 Ibs. and 
 at joints 5 and 7 1,968 Ibs. Fig. 4 shows the dimensions of 
 the truss on centre lines, the loads and the stresses that would 
 be produced thereby. 
 
 The figures above the chord lines preceded by the letter W 
 denote the transverse loads. All loads and stresses are in 
 pounds. 
 
 Rods. The diameter of the rods may be found directly by 
 means of Table III, p. 140. We will assume that they are to be 
 of wrought iron, not upset, and allow a unit stress of 12,500 Ibs. 
 per^ square inch. Then from the table (p. 140) we see that it 
 will require a If" rod at joint 2, a 1" rod at joint 4, and a T V' 
 rod at the centre. As the last, however, would look very light 
 we will make it f " in diameter. 
 
 * 2o"6.c. 
 
 Fig. 3 
 
 Top Chord. The load on one of the centre spans of the 
 top chord is 5,704 Ibs. and the span is about 7J ft. Assuming 
 a depth of 10 ins. we find the breadth required to resist this 
 load (by formula (11), p. 564, the wood being white pine) 
 
 =3.7 ins. The compression in the centre panels is 43,260 Ibs. 
 From Table V, p. 412, we see that a 10"XlO" post 8 ft. long 
 will support 62,500 Ibs. Therefore to support 43,260 Ibs. will re- 
 
1044 TRUSS MEMBERS AND JOINTS. 
 
 quire a 7"X 10" timber. Adding together the thickness required 
 for the transverse load and for the compressive stress, we have 
 10. 7" X 10" as the required size, which will require using a 
 12"X10" timber. As the timber will be stronger if placed ver- 
 tically, we will make the top chord 10 // X12", and build it of 
 five 2"X12" planks, bolted together. Between the end joints 
 and the wall the chord can be reduced to 6"X12 // . 
 
 Tie-beam. The transverse load on centre panel is 1,968 Ibs. 
 Assuming a depth of 10 ins., it will require a thickness of 1}" 
 to sustain the transverse load. To resist the direct tension will 
 
 require a net sectional area= r- r^- = 35 sq. ins., or 3|"XlO". 
 
 l,4u(J 
 
 Between the joints this must be increased by 1J" to resist the 
 transverse strain, so that a beam 4|"X10" is the least that 
 would answer for a solid tie-beam, i.e., a single stick of timber. 
 As it would be impracticable to obtain such a timber in most 
 localities, it will be best to build the beam of 2"X10" planks 
 bolted together, and on account of the reduction in net area 
 due to splicing, it will be necessary to use at least five planks 
 so that the tie-beam will be 10"X10". Even then it will be 
 necessary to lay out the beam with care, so as to get the re- 
 quired strength between the end joints of the planks. See 
 p. 1058. 
 
 Braces. As the chords are to be 10 ins. wide, the braces 
 1-2 and 3-4 should be of the same width. Brace 5-6 may 
 be reduced to 8 ins. wide. The length of the braces is about 
 9 ft, From Table V, p. 412, we see that a 6X10 is not quite 
 strong enough for the outer brace, and is a little stronger than 
 necessary for the second brace. Therefore we will use a 10" X 8" 
 timber for brace 1-2 and a 10X6 for brace 3-4. For the inner 
 braces a 3x6 would answer, except that it would not give 
 sufficient support to the fop chord, and it will therefore be 
 better to use either an 8X4 or au 8X3 timber. 
 
 Proportioning the Members of Steel Trusses. 
 
 EXAMPLE 4. Fig. 5 is the diagram of one half of a light steel 
 truss huilt some years ago for supporting the roof of a machine- 
 shop in New York State. The trusses were spaced 8 ft. centre 
 to centre. The roof consisted of 3" plank, spiked to a 3X6 
 bolted to the rafters of the truss, and covered with a patent 
 roofing similar to ruberoid. The actual weight of the roof 
 
MEMBERS OF STEEL TRUSSES. 
 
 1045 
 
 is therefore very small, but as it is quite steep it would be well 
 to allow 40 Ibs. per square foot of roof surface for obtaining 
 the stresses. As the roof area supported at each joint is 49J 
 sq, ft., this would make the panel loads 1 ,973 Ibs., or say 2,000 Ibs. 
 The stresses due to these loads are indicated on the diagram, 
 Fig. 5. For a roof construction such as this, it is more eco- 
 nomical to divide the rafter into uniform panel lengths, as in 
 Fig. 5. When this is done, the stresses in the four web-braces, 
 as BD and GL, are equal, also in the two ties DE and EL, so 
 that it is only necessary to compute the size for one strut and 
 one tie. 
 
 As the stresses in the rafters are comparatively small, it 
 will also be more economical to make the rafter of the same 
 section for its entire length. 
 
 The tie-beam we will make of one section from A to F, and 
 reduce it in the center panel. 
 
 For convenience in computing the size of the members we 
 will tabulate the maximum stresses for the different members, 
 omitting duplicates, also the length of the members. 
 
 (Note. In figuring length of struts, some reduction can be 
 made from the exact distance between joints, on account of 
 the riveting.) As the section of the ties is not affected by the 
 length, the latter is omitted for those members. 
 
 STRESSES AND SIZES (FiG. 5). 
 
 Member. 
 
 Stress, Lbs. 
 
 Ap. 
 Length, 
 Inches. 
 
 Net Area 
 of 
 Section 
 Re- 
 quired.* 
 
 Section Selected. 
 
 A-F 
 
 F-M 
 
 -16,900 
 8 200 
 
 
 Sq. Ins. 
 1.13 
 
 0.55 
 
 2, 2MX2XiL's. Netareal.76 
 sq. ins. 
 2, 2X2Xi L's Net area 1 52 
 
 F-K 
 
 7 700 
 
 
 52 
 
 sq. ins. 
 1 2X2Xi L Net area 76 
 
 D-E 
 
 3 070 
 
 
 0.21 
 
 sq. in. 
 
 1 2X2Xi L Net area 76 
 
 A-K 
 
 + 20 200 
 
 72 
 
 
 sq. in. 
 2 2X2X-J- L's 1 10" Xi" 
 
 
 2 000 t 1. 
 
 
 
 web-plate T 3 1 
 
 B-D 
 
 + 1 900 
 
 72 
 
 
 1 2X2Xi L r 39 Safe 
 
 E-F 
 
 + 5 000 
 
 144 
 
 
 strength 4,000 Ibs. 
 2, 2X2Xi L's. Cross section 
 
 
 
 
 
 r = 0.94. Safe stgth, 10,980 Ibs. 
 
 * At 15,000 Ibs. per square inch. 
 
1046 
 
 TRUSS MEMBERS AND JOINTS. 
 
 Dimensions of Tension Members. For these mem- 1 
 bers we can safely use a working strength of 15,000 Ibs. perj 
 square inch of net section. Dividing the stresses by 15,000 Ibs., | 
 we obtain the required net sectional areas given in the fourt' 
 column of our table. We must next select angles having 
 sectional area slightly in excess of these figures. 
 
 Fig. 5 
 
 For the main tie, AF, it is necessary to use two angles in 
 order to make satisfactory joints. For AF, then, we will us 
 two angles each having a sectional area slightly in excess o 
 1 13 
 ~~2~i or '^ sc l' m * ^ ne sec ti n al areas for angles of all size 
 
 are given on pp. 302-311. On p. 311 we find that a 2"X2"X T V 
 angle has a sectional area of .72, which would be large enoug] 
 for our purpose, but it is a good rule not to use anything les 
 than J" in thickness, and for the principal tie of a truss tw 
 2i"X2"Xi" angles are about the least that should be used 
 therefore we will use that joint for the tie from A to F. From 
 F to the corresponding joint on the other side we will use two 
 2"X2"X i" angles. 
 
 For the ties FK, DE, and EL we will use single 2"X2"Xi" 
 angles. (Note. A 2"X2" angle is the smallest size that it is 
 practicable to use in roof-trusses, although they are frequently 
 used only f s " thick.) 
 
 The sizes of angles selected and the net sectional areas should 
 be put in the table. The net sectional area is obtained by 
 
MEMBERS OF STEEL TRUSSES. 1047 
 
 ubtracting from the area given in the tables the amount cut 
 ut by one rivet-hole, which may be obtained from Table I, 
 n p. 640. For this truss, as the members are all small, we will 
 ise f " rivets. 
 
 Compression Members. For the main rafter we will use 
 wo angles and a web-plate, as in Fig. 6, as this is an economical 
 ection for a strut-beam, and a good section for making joint 
 onnections. 
 
 We will proportion' the section so that the plate will be 
 apable of resisting the transverse strength and the angles the 
 ompressive stress. 
 
 We will assume a depth for the plate of 10 ins. and find the 
 tecessary thickness. This may be computed by the same 
 ormula as given for wooden joists, formula (11), p. 564, using 
 Ibs. for A. The transverse load on each panel is 2,000 Ibs. 
 
 6' X 2,000 . 
 
 Then * = 2 X 100X888 m '' r TTr ' would 
 
 lot do to use a plate less than \ in. thick, therefore we will 
 nake the web-plate 10" Xi". 
 
 To find the size of angles required to resist the compressive 
 stress, we must assume some size, then find the radius of gyra- 
 tion of the entire section, and then the strength as a strut. 
 
 To find the radius of gyration, we must first find the centre 
 )f gravity of the section, then the moment 
 of inertia, and finally the radius of gyration. 
 
 The distance X of centre of gravity from axis C-j 1~ 4-sr- 
 AB (see p. 240) 
 
 area of plate X d" + area of both angles Xd' 
 area of entire section 
 
 As the stress in the rafter is comparatively F ' 9< 6 
 
 small we will try 2"X2"Xi" angles, having a total area of 
 1.88 sq. ins. 
 
 The distance d we find from the table, p. 311, to be .59, so 
 O that ^=10 -.59 = 9.41". d", of course, =5". Then x= 
 
 2.5X5+1.88X9.41 
 
 2 = 6.9. The moment of inertia of the section 
 
 about C g is found by the rule on p. 282, as follows: 
 
 C M' _ 
 Moment for plate ; 12 
 
 ( 2.5X1,9 2 =9.025 
 
1048 TRUSS MEMBERS AND JOINTS. 
 
 2X .35 (p. 311) = .70 
 
 Moment for angles I 
 
 .88X2.51 2 =11.84 
 
 Moment for entire section =42.36 
 
 The radius of gyration is found by dividing the moment of 
 
 inertia by the area of the section and taking the square root 
 
 of the quotient (see p. 289). 42.36 divided by the area of the 
 
 section=9.67, and the square root of this is 3.1 = r. As the 
 
 Z 72 
 length of each section of rafter may be taken as 6 ft., ~~ o~i = 
 
 23.2. From Table XI, p. 463, we see that when Z-nr is less than 
 30, we should use 12,000 Ibs. per square inch in computing the 
 strength of the strut. Multiplying the area of the two angles 
 (1.88) by 12,000, we have 22,560 Ibs. as the safe resistance to 
 compression, and as this is in excess of the stress, we will use 
 this section for the entire length of the rafter. 
 
 (Note. The above process for finding size of rafter seems 
 long and tedious, but there is no shorter way of finding the 
 strength of a strut of this section with any degree of accuracy.) 
 
 The other struts, being simply in compression, can be pro- 
 portioned directly by means of the tables in Chapter XIV. 
 Thus for the strut BD, which is 72 ins. long, we find from the 
 table, p. 469, that a single 2x2Xi-m. angle has a strength 
 greater than the stress, and we will therefore make the four 
 short struts of single 2X2 angles. For the strut EF, which 
 is long, but not very heavily strained, we will use two angle s 
 riveted together by plates, so that the cross-section will be 
 in the shape of a cross. At the bottom of p. 470, we find that 
 a strut of this section formed of two 2x2xi-in. angles has a 
 strength of 10,980 Ibs. for a length of 12 ft., or twice the stress 
 in the member; therefore we will use that section. For mem- 
 bers in compression it is not customary to deduct for rivet- 
 holes. We have now determined the sizes for all members 
 of the truss, as indicated in the table. 
 
 EXAMPLE 5. Fig. 7 is the diagram of one half of a steel 
 truss designed and built by the Berlin Iron Bridge Co. for 2 
 the Elerslie Coal and Coke Co., at Winifried Junction, W. Va. 
 The roof is covered with slates fastened to angle-iron purlins 
 running from truss to truss and spaced 10 J ins. c. to c. The \ 
 stresses indicated on the diagram are those that would be due 
 to a vertical load of 34 Ibs. per square foot of roof surface, with ] 
 trusses spaced 8 ft. on centres. The author does not know 
 
MEMBERS OF STEEL TRUSSES. 
 
 1049 
 
 or what loads the truss was actually computed, but they were 
 )robably somewhat in excess of those assumed. In the truss 
 as actually built all of the members are formed of pairs of 
 ingles, except ties CD and DF, which are single angles. 
 
 To facilitate determining the size of angles to be used for 
 -he different members, the stresses and length of struts are 
 riven, in the following table. The lengths, however, are not 
 the actual lengths, but are what may be termed the distance 
 >etween centres of bearings, considering each member as end- 
 ng at the joints. 
 
 The loads marked 1. 1. are the transverse loads on the rafter. 
 
 DATA FOR PROPORTIONING MEMBERS OF TRUSS 
 
 (FiG. 7). 
 
 Member. 
 
 Stress. 
 
 Length. 
 
 Net Sec- 
 tional 
 Area 
 Re- 
 quired.* 
 
 Angles Selected. 
 
 Net 
 Sec. 
 
 AC 
 
 -21,800 
 
 
 Sq. In. 
 1.46 
 
 2, 3 X2xi 
 
 Sq. In. 
 2.18 
 
 CE 
 
 - 18,700 
 
 
 1.25 
 
 2, 2JX2JXi 
 
 1.94 
 
 EH 
 
 - 12,500 
 
 
 0.84 
 
 2, 2JX2 Xi 
 
 1 68 
 
 EF 
 
 - 6,250 
 
 
 0.42 
 
 2, 2 X2 Xi 
 
 1 44 
 
 FG 
 
 - 9,300 
 
 
 0.62 
 
 2, 2 X2 Xi 
 
 1.44 
 
 CD 
 
 - 3,050 
 
 
 0.21 
 
 1, 2 X2 X% 
 
 0.56 
 
 AD 
 
 f+23,500 
 
 [ 8' 6" 
 
 
 2, 5 X3|X| 
 
 
 DG 
 
 \ 2,320 t.l. 
 j +21,600 
 
 ! 8' 6" 
 
 
 2, 5 X3JX% 
 
 
 BC 
 
 | 2,320 1. 1. 
 -f 2,325 
 
 1 
 3'0" 
 
 
 2, 2 X2 Xi 
 
 
 DE 
 
 -f 4,650 
 
 6' 6" 
 
 
 2, 2 X2 Xi 
 
 
 
 
 
 
 
 
 * At 15,000 Ibs. per sq. inch. 
 
 Tension Members. First find the nt sectional areas 
 required for these members by dividing the stresses by 15,000 
 
 ., the allowed stress per square inch, and put them in the 
 fourth column. Then, by means of the tables on pp. 306-311, 
 select the angles having sectional areas a little in excess of the 
 required area and put the sizes in the fifth column. It is also 
 a, good idea to put down the net areas of the angles selected 
 For the tension members, which are obtained by deducting 
 Tom the actual area the allowance for one f-inch rivet, p. 640. 
 
 Rafter. As the rafter has a transverse load, it will be 
 
1050 
 
 TRUSS MEMBERS AND JOINTS. 
 
 necessary to assume some section and then compute its strength 
 as a strut-beam, and if its strength is not equal to the combined 
 stress and load, we must try a larger section. 
 
 Fig. 7 
 
 For the rafter from A to D we will try two 5"X3i"Xf" 
 angles. From the table on p. 529 we find the coefficient for 
 one angle to be 12.21 tons, or 24,420 Ibs., and dividing by the 
 span 8.5 ft., we have 2,873 Ibs. as the safe transverse load, 
 with long leg vertical, and two angles would support 5,746 Ibs. 
 The actual load is 2,320 Ibs., or 44 per cent, of the strength of 
 the angles. 
 
 From the table on p. 470 we find the strength as a strut of 
 two angles of this size, 8' 6" long, to be about 30.9 tons, or 
 61,800 Ibs. The actual stress is 23,500 Ibs., or only 38 per cent, 
 of the strength of the section. As it requires 44 per cent, to 
 resist the transverse load, it will require 82 per cent, to resist 
 both, and as a smaller section would probably not be strong 
 enough we will use two 5X3JXf" angles for the rafter from 
 A to D. For the upper half of the rafter we will try the same 
 size of angles with a thickness of %". The coefficient for 
 this thickness is (p. 530) 10.34 tons, or 20,680 Ibs., and dividing 
 by the span we have 2,433 Ibs. as the safe strength of one angle. 
 Therefore it will require about 50 per cent, of the strength of 
 two angles to support the actual load. 
 
 The resistance to compression of two 5X3iX% /7 angles 
 is not given in the table, p. 470, but we find the difference 
 between the loads given for f and } thicknesses to be for 8 ft. \ 
 length 28.96 tons, which would be 4.83 tons for each ^ in. ! 
 in thickness, so if we subtract 5 tons from the safe load for 
 
JOINTS OF WOODEN TRUSSES. 1051 
 
 the f-in. thickness, we will have the safe load fqr % in. Mak- 
 ing the subtraction we have 26.66 tons as the safe load for 
 length of 8 ft., and to obtain the strength for 8' 6", we should 
 subtract about .62 ton, which would give the safe strength, 
 say 26 tons, or 52,000 Ibs., for a length of 8' 6". As the stress 
 is only 21,600 Ibs., we shall utilize only 42 per cent, of the 
 strength of the strut, and as we require 50 per cent, to resist 
 the transverse load, we 'require 92 per cent, in all; therefore 
 this section is strong enough for the upper portion of the rafter. 
 
 Struts. These we can find directly from the table on 
 p. 470. For all three of the struts we will use two 2x2Xi" 
 angles, which, while they have considerable excess strength, 
 are as light as should be used. 
 
 The actual size of angles used in this truss are indicated 
 on Fig. 28. 
 
 Joints of Wooden Trusses. 
 
 It is probably safe to say that the joints in wooden trusses, 
 taking them as they are found throughout the States, are the 
 weakest portion of the truss, and especially the joints at the ends 
 of wooden ties. For example, a 6"X6" timber of Georgia 
 pine would require a force of 288,000 Ibs. to pull it apart, but 
 it is practically impossible to secure the end of such a timber 
 so as to develop its full tensile strength. The splicing of tie- 
 beams also is often a weak place in many trusses. 
 
 The joints of any truss should be proportioned with as much 
 care as the size of the members, so that the truss will be equally 
 strong in all its parts. The principles by which the strength 
 of joints on which a pulling stress is exerted are explained at 
 length on pp. 382-397, and illustrated by a few examples. 
 To explain the subject still further, we will show how the joints 
 of the trusses illustrated by Figs. 1 and 3 (of this chapter) 
 should be made. 
 
 The first and most important joint of the truss shown by 
 Fig. 1 is joint 1, where the truss rests on the wall. There are 
 several ways in which this joint may be made, the simplest 
 being a bolt joint like that shown by Fig. 8. In trusses having 
 a horizontal wooden tie-beam, the tie-beam almost invariably 
 extends over the support, and the rafter or principal strut 
 bears on top of it. The correct method of properly portion- 
 ing a joint such as is shown by Fig 8 is explained on pp 392-395- 
 
1052 
 
 TRUSS MEMBERS AND JOINTS. 
 
 In this case tfre thrust in the rafter is 21,050 Ibs., and to find 
 the theoretical stress in the bolt, we should first make a drawing 
 of the joint at a scale of about 1 in. to the foot, giving the rafter 
 its correct inclination, and locating it on the tie-beam, so that 
 the point where the central lines of the tie-beam and rafter 
 intersect will be at least 6 ins. in on the wall. Then draw the 
 
 v Cast Iron PI. 16 x 1 
 p =~ ISuQO -+ 221 -= 82)a Ibs. 
 
 Fig 8 
 
 Joint 1 of Fig. 1. 
 
 notch so that the toe of the rafter will be about 2J ins. deep, 
 and a little to one side draw a line ab parallel and equal to 
 the stress in the rafter, to a scale of pounds, and from the upper 
 end a a line at right angles to the seat of the rafter, and from the 
 lower end b a line at right angles to the rafter, and parallel to the 
 bolt. Then the line be, measured by the scale with which ab is 
 drawn, gives the stress in the bolt. In this case the line be scales 
 31,250 ibs. To find the diameter of the bolt necessary to resist 
 this stress we should use table IX, p. 334. From that table we 
 find that to resist 31,250 Ibs, will require a If" bolt. The 
 bolt should be placed at right angles to the rafter, and should 
 have a good-sized washer at each end (see Washers, p. 1064). 
 It will not do to cut into the tie-beam sufficient to get a proper 
 bearing for so large a bolt therefore we must either put a wooden 
 block under the truss, as in Fig. 8, or use cast-iron washer, 
 as in Fig 33, p 394. For light trusses the wooden block 
 answers the purpose as well as the cast washer and will generally 
 be cheaper. To prevent the block from sliding, notches should 
 
JOINTS OF WOODEN TRUSSES. 
 
 1053 
 
 be cut in the top of 11 10 block and the bottom of the tie-beam 
 and V or -J" square iron bars driven in. The bolster should 
 also be well spiked to the tie-beam before the bolt is put in 
 place. 
 
 As a rule, it is a good idea to place the wall plate which re- 
 ceives the common rafters just above the tie-beam of the truss, 
 the wall being built around the truss. This affords an oppor- 
 tunity for getting at the nut on the bolt to tighten it in case 
 the wood shrinks. 
 
 The bearing of a truss on the wall should always be con- 
 sidered, and a plate or heavy stone provided which will reduce 
 the pressure to within the limits given on page 399. In this 
 case we will use a 16"Xl4"Xli" cast-iron plate, which reduces 
 the pressure on the brickwork to 82J Ibs. per square inch. 
 
 Joint 1 of Fig. 3. This joint might be made in the 
 manner shown by Fig. 35, p. 396, but if the tie-beam is to be 
 cased, the projection of the cast-iron washers below the tie- 
 beam is objectionable. Fig. 9 shows another method of making 
 
 Fig. 9 
 Detail of Joint 1, Fig. 3. 
 
 the bearing joint of a wooden truss which avoids the use of 
 large bolts and projecting bolt-heads. This is a strong joint, 
 especially serviceable for heavy stresses, and where the in- 
 clination of the rafter is less than 45 degrees. The points to 
 be computed in this truss are: Area of bent plate, height at 
 toe, and the distance X. The sectional area of the plate (which 
 should be of wrought iron) after deducting for the bolt-holes 
 
1054 TRUSS MEMBERS AND JOINTS. 
 
 at Y should be equal to the tension in the tie-beam divided 
 by 12,500 Ibs., and the thickness of the plate should never be 
 kss than I". 
 
 27 350 
 In this case we would require a net sectional area= '* =* 
 
 2.2 sq. ins., but as the plate must be 10" wide and f" thick 
 it will give a net area considerably in excess of this. The 
 height H for the toe of the rafter should be equal to the tension 
 in the tie-beam divided by the breadth of the rafter multiplied 
 by 1,000 for white pine, 1,200 for spruce, 1,350 for oak and 
 Oregon pine, and 1,500 for long-leaf yellow pine. 
 
 In this case the breadth of the rafter is 10 ins. and the wood 
 
 27 350 
 is white pine; therefore H should equal - J AA x=2f ins. 
 
 1U X 1,UUU 
 
 The distance X should be sufficient to resist the tendency of 
 the plate to shear off the top of the tie-beam, and is found by 
 dividing the tension in the tie-beam by the breadth of the 
 beam multiplied by the resistance to longitudinal shearing, 
 given on p. 361, increased by 20 per cent, on account of the 
 additional resistance to shearing caused by the vertical pressure 
 of the strut. The answer will be in inches. 
 
 27 350 
 
 In this case X should equal ^ ' =28| ins. In the draw- 
 ing X=30 ins. 
 
 Bolts. At least two bolts are always required for this 
 joint, one at Z and one at Y, and when the breadth of the tie- 
 plate exceeds 6 ins., there should be two bolts at Y. The bolt 
 at Z need not exceed V when the tension in the tie-beam is 
 less than 50,000. 
 
 The diameter of the bolts at Y should be in proportion to the 
 thickness of the plate, and the bolts should always be placed 
 against the lug on the plate. When a joint like Fig. 9 is under 
 pressure there is a decided tendency for the lug on the plate to 
 spring up out of the wood, and in an actual test the spring in 
 the plate was sufficient to break the head off of a V bolt. The 
 bolt, however, was placed about 2 ins. back from the notch. 
 The author knows of no way by which the stress in the bolts 
 at Y can be computed. In his judgment, however, two f" 
 bolts will be sufficient for a f " plate, two 1" bolts for a J" plate, 
 and two 1J" bolts for a f " plate 10 ins. wide. If the plate is | 
 12 ins. wide three bolts should be used. 
 
JOINTS OF WOODEN TRUSSES. 
 
 1055 
 
 Joint 2 of Fig. 1. Where a brace abuts against a rafter, 
 as in this joint, the end of the brace should be notched into 
 the rafter sufficient to give it 
 a good "hold." In this case 
 a notch of J" will be sufficient. 
 To support the purlin, a 3" 
 plank may be bolted to rafter 
 and brace, as in Fig. 1,0, or 
 the rafter may be hung in 
 duplex hangers let into the 
 rafter. For purlins larger than 
 8"X10" the duplex hangers 
 
 irace-^^vyO 
 
 Fig. 10 
 
 Detail of Joint 2 of Fig. 1. 
 
 are to be preferred. 
 
 In the truss shown by Fig. 1 , 
 there is no rod at joint 2, but as there very often is a rod at 
 this joint, one is shown in Fig. 10. If the rod does not exceed 
 1J" in diameter, a round hole may be bored in the top of the" 
 rafter to form a seat for a cast-iron washer. 
 
 % Wrought 
 Iron Plate 
 
 
 Fig. II 
 
 Joint at Apex of King-rod Truss. 
 
 Fig. 11 shows the joint at the top of a king-rod truss, with 
 a duplex hanger for supporting the purlin. For heavy trusses 
 
 a cast-iron cap-plate such as is 
 shown by Fig. 12 is preferable to 
 the bent plate, unless the latter is 
 made very heavy and lag-screwed 
 to the rafters. The rafters should 
 butt square against each other. 
 
 Joint 3 of Fig. 1. This 
 F| |2 should be made as shown by Fig. 
 
 13. In place of the cast washer a 
 bent plate of wrought iron is often used. 
 
1056 
 
 TRUSS MEMBERS AND JOINTS. 
 
 Fig. 14 shows how joint 2 of Fig. 3 should be made, this detail 
 applying also to any of the upper joints of a Howe truss, 
 except that at the centre of the truss, where two braces come 
 together, it is better to spike a block to the. bottom of the top 
 chord for the braces to butt against, as in Fig. 3, as this does 
 not weaken the truss, and also where counter-braces are re- 
 quired it is better to insert a hard- wood block as in Fig. 15, 
 so that each brace will bear against the chord independent of 
 the other. 
 
 -Ifc Rod 
 
 I 
 Fig. 13 
 
 Detail of Joint 3 of Fig. 1. 
 
 Fig. 14 
 
 Detail of Joint 2 of Fig. 3. 
 
 For joints such as that shown by Fig. 14 a double notch i 
 often made, as shown by the dotted lines. In the opinion 
 the author this does not make as strong a joint as the sing] 
 notch, for the reason that with a double notch it is very difficul 
 to fit the end of the brace so that it will bear evenly in bot 
 notches, while with a single notch the full bearing must neces- 
 sarily be brought on the toe. 
 
 As it is important not to cut into the chords of a Howe truss 
 for the braces more than is really necessary, the depth of tfu 
 notch should always be proportioned to tJie horizontal componen 
 of the stress in the brace. The latter can be readily measurec 
 from the stress diagram. Thus, Fig. 15 is the stress diagran 
 of the truss shown by Fig. 3, 0-2 is the horizontal componenl 
 of the stress in the end brace, 2-4 the horizontal component o 
 brace 3-4, and 4-6 the horizontal component of brace 5-6 
 the horizontal component of the stress in the end brace being; 
 always equal to the tension in the tie-beam of the end panel 
 To avoid splintering or crushing of the wood, the depth of th< 
 
JOINTS OF WOODEN TRUSSES. 
 
 1057 
 
 notch d (Fig. 14) multiplied by the breadth of the strut should 
 be equal to the horizontal component in pounds divided 
 by the values given on p. 1054 for finding the height H. For 
 
 27.350 
 
 Fig. 15 
 
 the truss shown by Fig. 3, this rule would require a depth d 
 for the outer brace of 2f", If" for the next brace, and }" for 
 the inner brace. A depth of -J inch, however, is about the 
 minimum that should be made. As the stress is the same at 
 both ends of a brace, the notch in the tie-beam should be of 
 same depth as is the top chord. 
 
 Fig. 16 is a detail of joint 7 of Fig. 1. The block between 
 the braces affords a bearing for the stirrup and also a good bear- 
 ing for the braces, and 
 does not weaken the tie- 
 beam as much as if the 
 block were omitted and 
 the braces notched into 
 the tie-beam beyond the 
 stirrup. When a block 
 is inserted between the 
 ends of two braces, and 
 especially when the braces 
 are not subject to the same 
 
 6 x 6 x & Washer 
 
 Fig. 16 
 
 Joint 7 of Fig. 1. 
 
 stress, the block should be notched into the tie-beam or chord 
 about 1 in., otherwise the brace having the greater stress might 
 push the other brace along. In the case of the two centre struts 
 of Fig. 3 the block between their upper ends need only be 
 spiked to the top chord, because the two braces would nearly 
 always have the stame stress and three or four good spikes 
 would be fully capable of resisting any difference in the stresses 
 that might arise through unequal loading of the truss. 
 
1058 
 
 TRUSS MEMBERS AND JOINTS. 
 
 Detail of Tie-beam, Fig. 3. 
 
 Fig. 17 shows a little more than 
 one half of the tie-beam as it should 
 be laid out in practice except that 
 the scale should be increased to 
 at least J inch to the foot. 
 
 In Fig. 17 the breadth of the 
 tie-beam in plan is drawn out of 
 scale in order to more clearly show 
 the different planks. 
 
 The first step in making such a 
 drawing is to locate the rods and 
 braces, with the proper notches for 
 the latter. It then remains to 
 show the splices. In this truss the 
 tie-beam is to be built up of 2" X 10" 
 planks five layers in thickness, and 
 the problem is how to break joints, 
 and how many bolts are required 
 to give the necessary tensile strength 
 to the chord. The correct method 
 of building up such a tie-beam is 
 fully explained under Case 1, p. 385; 
 therefore we will consider this ex- 
 ample as briefly as possible. For 
 convenience the tensile stress in the 
 tie-beam for each panel and the 
 net sectional area required is given 
 above the beam, Fig. 17. 
 
 Two planks will be amply strong 
 to resist the tensile stress even in 
 in the central panel. The centre 
 layer of the beam we will consider 
 merely as filling. The problem is 
 to bolt the other four layers together 
 so as to form a continuous tie hav- 
 ing the necessary tensile strength. 
 The two outer layers we will make 
 of two planks each two planks 
 A' 26' 0" long, and two A 23' 4" 
 long (the beam being 49' 6" long). 
 This will bring the joints in these 
 
JOINTS OF WOODEN TRUSSES. 1059 
 
 layers at Y and Z. (In the next layers we will use planks 
 28' long in the centre of the beam, with planks 10' 8" long 
 at each end, bringing the joints in the second and fourth 
 layers at X and the same distance from the other end. 
 
 As the planks B and B' reach beyond the centre panels on 
 each side, they will carry the entire stress in those panels, so 
 that we need only figure on transmitting the stress in the second 
 panel. 
 
 We can safely assume that the plank B will transmit one half 
 of the stress, or 21,630 Ibs. This stress must be transmitted to 
 A by bolts having a combined resistance of this amount and 
 these bolts must be located between the joints X and Y. From 
 Table VII, p. 383, we find that the resistance of a -in. bolt 
 in white pine is 880 Ibs. per inch of length, hence in a 2-in. 
 plank it is 1,760 Ibs. 21, 630^ 1,760= 12+. 
 
 As we will have four bolts between Y and Z, twelve bolts will 
 be ample between X and Y. Two of these bolts should be 
 placed 5J" from Y and two the same distance from X (see last 
 column of Table VII, p. 383), leaving eight to be spaced between, 
 which will make the distance c. to c. 15f ins. As the planks 
 A and A.' extend to the end of the tie-beam, it is only necessary 
 to use enough bolts from X to the end to hold the planks well 
 together; f" bolts, 2 ft. c. to c., will be ample for this purpose. 
 Wlierever an end joint comes in a tie-beam, two bolts should 
 be placed each side of the joint as at X, Y, and Z. 
 
 As the centre layer will offer some assistance in transmitting 
 the stress, the tie-beam will probably have some excess of 
 strength even with a good factor of safety; but, on the other 
 hand, some of the bolts may not fit perfectly and the planks 
 may not be full 2 ins. thick, so that it is well to be on the safe 
 side. 
 
 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 to the stress in the tie, 
 otherwise the joint is liable to open and allow 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 the same span, be- 
 cause 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 a J" bolt through the centre of each joint, with as 
 
1060 
 
 TRUSS MEMBERS AND JOINTS. 
 
 many spikes as can be driven, will ordinarily give sufficient 
 strength. 
 
 For trusses like those shown by Figs. 27-30 of Chapter XXV 
 the author has found that the best method of making the wall 
 joint, unless the roof is quite flat, is that shown by Fig. 18, 
 which is the detail of an actual joint used by the author where 
 the stress in the tie-beam was 25,000 Ibs. 
 
 It should be noticed that the wrought-iron strap is secured 
 to the tie by lag-screws instead of bolts. The author has found 
 
 .13, ^"-x 4K"'La& Screws 
 
 Dptted lines show scre.ws 
 
 on t other side. 
 
 Fig. 18 
 
 Wall Joint of Scissors Truss. 
 
 that 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 come opposite each other. 
 
 The net sectional area of the strap should at least be equal to 
 the stress in the tie-beam divided by 20,000 Ibs. 
 
 The number of lag-screws (for both side") 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 author 
 recommends the values given in Table I. 
 
JOINTS OF WOODEN TRUSSES. 
 
 1061 
 
 In the joint shown by Fig. 17 the stress in the tie-beam is 
 25,000 Ibs. and the wood is Oregon pine. 
 The above rules therefore require a sectional area in the 
 
 strap = OA ' nrtr> = li sq. ins. and twelve |" lag-screws. 
 20,000 
 
 TABLE I. SAFE RESISTANCE OF LAG-SCREWS WHEN 
 USED AS IN FIG. 17. 
 
 
 Safe Resistance in Pounds. 
 
 
 
 
 Minimum 
 
 Size of Screw. 
 
 Oak. 
 
 White 
 Pine. 
 
 Oregon 
 Pine. 
 
 Georgia 
 Pine. 
 
 Thickness 
 of Strap; 
 
 Dia. Length. 
 
 
 
 
 
 
 1 X 3J 
 
 800 
 
 600 
 
 700 
 
 800 
 
 i 
 
 J X 4 
 
 1400 
 
 1000 
 
 1100 
 
 1200 
 
 i 
 
 f X 4 
 
 2000 
 
 1500 
 
 1650 
 
 1800 
 
 A 
 
 1 X 4J 
 
 2500 
 
 1800 
 
 2100 
 
 2400 
 
 A 
 
 1 X 5 
 
 3000 
 
 2400 
 
 2800 
 
 3000 
 
 
 
 With a thickness of f in., the width of the strap necessary 
 
 1 25 
 
 to give a sectional area of 1.25 sq. ins. = ^r> = 3J ins. To 
 
 ,o7o 
 
 this should be added the diameter of one lag-screw to obtain 
 
 Casting 
 
 Fig. 19 
 
 Wall Joint of Scissors Truss. 
 
 the working width, 3 J+ = 4^ ins." The strap used was 4" X f ", 
 as some additional strength was obtained by the bolt at X, 
 
1062 TRUSS MEMBERS AND JOINTS 
 
 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 degrees. This joint has the advantage that if 
 the truss is erected one piece at a time the tie-beams may be 
 put up first and a seat is provided 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 using the value for 
 strength given in Table IX, p. 384. Fig. 20 shows a good form 
 of joint to use at joint 5 of Fig. 30, p. 903, when it is desired 
 to substitute a wooden tie for the rods shown in Fig. 30. 
 
 Oak Block 
 
 Fig. 20 
 
 The sectional area of the strap and number of lag-screws 
 should be proportioned by the rule given for Fig. 18. 
 
 Washers. When designing roof trusses it is important to 
 proportion the washers on the rods and large bolts so that they 
 will not crush the timber (see p. 414). As the soft woods crush 
 under a less pressure than the harder woods, washers cannot 
 be proportioned according to the size of the bolt or rod, but 
 must be proportioned according to the stress in the rod and 
 the kind of wood against which they bear. 
 
 Table II gives the maximum stress which round and rec- 
 tangular washers will resist without sinking into the wood. 
 
 The diameters of the round washers are those of the standard 
 sizes of cast-iron washers given in Table III. Comparing the 
 values given in Table II for round washers with the strength 
 of the rods for which they are intended, it will be seen that the 
 bearing resistance of the washers on white pine and spruce is 
 
JOINTS OF WOODEN TRUSSES. 
 
 1063 
 
 only about one half the working strength of the rod, conse- 
 quently for white pine and Oregon pine the standard size of 
 washers is not large enough for the strength of the rod. 
 
 TABLE II. SAFE BEARING RESISTANCE OF 
 WASHERS IN POUNDS. 
 
 ROUND WASHERS. 
 
 Diameter. 
 
 White Pine 
 and Spruce. 
 
 Oregon 
 Pine. 
 
 Georgia 
 Pine. 
 
 Oak. 
 
 2f 
 
 1,350 
 
 2,160 
 
 2,700 
 
 3,240 
 
 3 
 
 1,760 
 
 2,820 
 
 3,520 
 
 4,230 
 
 3} 
 
 2,070 
 
 3,300 
 
 4,140 
 
 4,970 
 
 3J 
 
 2,760 
 
 4,400 
 
 5,520 
 
 6,620 
 
 4 
 
 3,140 
 
 5,020 
 
 6,280 
 
 7,530 
 
 if 
 
 4,430 
 
 7,080 
 
 8,860 
 
 10,630 
 
 6 
 
 7,060 
 
 11,400 
 
 14,100 
 
 16,960 
 
 6-3 
 
 
 7,660 
 
 12,260 
 
 15,300 
 
 18,400 
 
 7: 
 
 
 10,300 
 
 16,500 
 
 20,600 
 
 24,700 
 
 81 
 
 
 12,900 
 
 20,700 
 
 25,800 
 
 31,100 
 
 9: 
 
 
 16,250 
 
 26,000 
 
 32,500 
 
 39,000 
 
 10^ 
 
 
 20,000 
 
 32,000 
 
 40,000 
 
 48,000 
 
 RECTANGULAR WASHERS. 
 
 Size. 
 
 
 
 
 
 4X6 
 
 6,000 
 
 9,600 
 
 12,000 
 
 14,400 
 
 4X8 
 
 8,000 
 
 12,800 
 
 16,000 
 
 19,200 
 
 6X6 
 
 9,000 
 
 14,400 
 
 18,000 
 
 21,600 
 
 6X7 ' 
 
 10,500 
 
 16,800 
 
 21,000 
 
 25,200 
 
 6X8 
 
 12,000 
 
 19,200 
 
 24,000 
 
 28,800 
 
 6X9 
 
 13,500 
 
 21,600 
 
 27,000 
 
 32,400 
 
 6X10 
 
 15,000 
 
 24,000 
 
 30,000 
 
 36,000 
 
 8X8 
 
 16,000 
 
 25,600 
 
 32,000 
 
 38,400 
 
 8X9 
 
 18,000 
 
 28,800 
 
 36,000 
 
 43,200 
 
 8X10 
 
 20,000 
 
 32,000 
 
 40,000 
 
 48,000 
 
 8X12 
 
 24,000 
 
 38,400 
 
 48,000 
 
 57,600 
 
 10X10 
 
 25,000 
 
 40,000 
 
 50,000 
 
 60,000 
 
 10X11 
 
 27,500 
 
 44,000 
 
 55,000 
 
 66,000 
 
 10X12 
 
 30,000 
 
 48,000 
 
 60,000 
 
 72,000 
 
 10X14 
 
 35,000 
 
 56,000 
 
 70,000 
 
 84,000 
 
 12X12 
 
 36,000 
 
 57,600 
 
 72,000 
 
 86,400 
 
 12X14 
 
 42,000 
 
 67,200 
 
 84,000 
 
 100,800 
 
 12X16 
 
 48,000 
 
 76,800 
 
 96,000 
 
 115,200 
 
 14X14 
 
 49,000 
 
 78,400 
 
 98,000 
 
 117,600 
 
 14X16 
 
 56,000 
 
 89,600 
 
 112,000 
 
 134,400 
 
 As a rule for the rods of wooden trusses it is best to use 
 rectangular washers cut from steel plates, cutting the washers 
 to the required size. It is, of course, not really dangerous to 
 
1064 
 
 TRUSS MEMBERS AND JOINTS. 
 
 use smaller washers than would be required by Table II, as a 
 little crushing of the timber will not en- 
 danger the safety of the truss, but it is best 
 to keep within the limits of Table II when 
 practicable. 
 
 Very large washers shouFd be made of cast 
 Fig. 21 iron with brackets, as in Fig. 21. The rod 
 
 in Fig. 15 has a stress of 8,960 Ibs., and as the wood is white 
 pine, we see from Table II that a 6" X 6" washer will be required. 
 
 TABLE III. PROPORTIONS OF 
 STANDARD CAST WASHERS. 
 
 For sizes not given below. 
 Diameter of bolt =d. 
 
 All dimensions in inches. 
 
 Standard Cast Washer. 
 
 Diameter 
 of 
 Bolt-rf. 
 
 A. 
 
 . 
 
 c. 
 
 JD. 
 
 Weight 
 in 
 Pounds. 
 
 
 2f 
 
 1| 
 
 %> 
 
 
 
 
 
 3 
 
 ll 
 
 % 
 
 
 
 
 
 3} 
 
 2J 
 
 % 
 
 
 j: 
 
 
 
 3* 
 
 2i 
 
 % 
 
 
 1^ 
 
 
 1 
 
 4 
 
 2J 
 
 1/ie 
 
 
 2< 
 
 
 1J 
 
 
 
 
 1J^ 
 
 If 
 
 3 
 
 
 il 
 
 6 
 
 6} 
 
 3 
 
 If 6 
 
 If 
 1} 
 
 i f 
 
 11 
 
 7} 
 
 3| 
 
 4 
 
 H 
 
 91 
 
 
 2 
 
 
 
 4i 
 
 2J 
 
 2 
 
 173 
 
 
 2} 
 
 9} 
 
 4| 
 
 2f 
 
 2i 
 
 20 
 
 
 2J 
 
 10} 
 
 5i 
 
 
 2J 
 
 27} 
 
 2} 
 
 Hi 
 
 5f 
 
 
 2J 
 
 36 
 
 
 3 
 
 12i 
 
 6i 
 
 
 3 
 
 46 
 
 
 Riveted Joints of Steel Trusses. 
 
 Trusses with riveted joints are invariably made with angle- 
 bars for the web members and generally for the chords, al- 
 though the latter are sometimes made of a pair of channels 
 
RIVETED JOINTS OF STEEL TRUSSES. 1065 
 
 DP of two angles and a web-plate. The members are connected 
 at the joints by means of gusset-plates, to which all of the mem- 
 bers are riveted. Typical examples of riveted joints in roof 
 trusses are shown by Figs. 24 to 34. When the rafter or chord 
 has a web-plate, as in Fig. 26, the web members are riveted 
 to this plate and a gusset-plate is not required except at the 
 3nd joint and apex. 
 
 In order that there shall be no twisting, it is necessary that 
 the principal members of the truss be double so that the gusset- 
 plate may 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 as 
 in Fig. 31. The thickness of the gusset-plates, as a rule, should 
 
 Fig. 22 
 
 be twice the thickness of the angles that are connected to it. 
 In laying out the joints, which should be done to a scale of not 
 less than 1 in. to the foot, the members should be arranged, 
 when practicable, so that the lines passing through their centre 
 of gravity will coincide with the lines of the truss diagram, and 
 thus meet at a single point, as in Fig. 22. This is not always 
 practicable, but the principle should be followed as closely as 
 possible. For small angles the rivet lines of the members may 
 be considered as passing through the centre of gravity of the 
 section without serious error. 
 
 The number of rivets required for each member must be 
 determined according to the stress in the members, the re- 
 sistance of the rivets being considered both for shearing and 
 bearing. 
 
 The method of determining the number of rivets in a joint 
 is explained on pp. 363-370, but to show more clearly the 
 application to truss joints we will illustrate by one example. 
 
1066 TRUSS MEMBERS AND JOINTS. 
 
 Fig. 23 
 
 Diagram of Light Steel Truss supported by Brick Walls. 
 
 -PI. S'xfc'-lVlong 
 
 - -0 - 0- i -0 \ 
 
 2^2" 
 
 -J- Bet. Angles 
 
 All Rivetefc" 
 
 Fig. 24 
 Detail of Joint A of Fig. 23, All Rivets | inch. 
 
RIVETED JOINTS OF STEEL TRUSSES. 1067 
 
 PLAN 
 
 Fig. 25 
 
 Detail of Joint D of Fig. 23. 
 
 -is'o 2 - 
 
 .**> l*J$ -! 
 
 PL 5"xX-10"lg. 
 8-X" Bolts IH'lg. 
 
 9'3*- 
 
 -2L 9 2' 
 
 t 3 3 = 9^4^3" 
 10" long I 
 
 -+'9'- 
 
 
 Fig. 26 
 Detail of Joint E of Fig. 23. All rivets ^ inch. 
 
1068 
 
 TRUSS MEMBERS AND JOINTS. 
 
 EXAMPLE. To find the number of rivets required in the joint 
 shown by Fig. 32, the stresses in the members being as follows: 
 A, -6,250 Ibs.; B, -3,050 Ibs.; C, +2,325 Ibs.; andZ>, -9,300 
 
 Fig. 27 
 Detail of Joint K of Fig. 23. 
 
 Fig. 28 
 
 Diagram of Light Steel Truss of 68 Feet Span. 
 
 Ibs. The dimensions of the members as previously determined 
 are given in the figure. 
 
 We will use a gusset-plate f " thick. 
 
RIVETED JOINTS OF STEEL TRUSSES. 1069 
 
 Number of Rivets Required for B. As there is but 
 one angle the rivets will be in single shear, and as the leg of 
 the angle is only 2" wide we must use f" rivets. From the 
 table on p. 372 we find the resistance of a f" rivet to single 
 shear to be 3,060 Ibs. The bearing resistance on a %" plate 
 (the thickness of the angle) is not given, but it is J" the re- 
 sistance for a %" plate, or 2,100 Ibs.; therefore the strength 
 of the rivet is governed by its resistance to bearing. As the 
 
 Fig. 29 
 
 Joint A of Fig. 28. 
 
 stress is 3,050 Ibs. it will require 1| or 2 rivets. Four rivets are 
 shown in the drawing, probably to give additional stiffness, as 
 but one leg of the angle is riveted. 
 
 Rivets in C. This member is composed of two angles, 
 consequently the rivets are in double shear, and their resistance 
 to shearing is 6,120 Ibs. each. The minimum bearing is on 
 the |" gusset-plate. The bearing resistance of a f " -rivet on a 
 " plate is 4,210 Ibs., which governs the strength of the rivet. 
 As the stress is only 2,325 Ibs. only one rivet would, theoretically, 
 
1070 TRUSS MEMBERS AND JOINTS. 
 
 be required to resist the stress, but two rivets is the least that 
 should ever be used in the end of a truss member, no matter 
 how small the stress. 
 
 Rivets in D. This member is also double, and as the 
 combined thickness of the angles is greater than the thickness 
 of the gusset-plates the strength of the rivets will be governed 
 by the resistance to bearing on a f " plate, or 4,210 Ibs. As the 
 stress is 9,300 Ibs., it will require three rivets to resist it and 
 two rivets for A. For such small stresses more rivets are 
 
 Fig. 30 
 
 Joint B of Fig. 28. 
 
 generally used than are theoretically required, but when the 
 stresses are large, only as many rivets as are theoretically re- 
 quired are generally used. 
 
 The above example illustrates the process to be pursued in 
 determining the number of rivets in any joint. 
 
 For Angles iii Tension, both legs should be connected 
 by rivets, as in Fig. 33, unless the sectional area of the angle is 
 very much greater than would theoretically be required, as is 
 the case with the brace B in the last example. 
 
 Cooper, in his " Specifications for Iron and Steel Bridges/' 
 requires that "Angles subject to direct tension must be con- 
 
RIVETED JOINTS OF STEEL TRUSSES. 1071 
 
 nected by both legs or the section of one leg only will be con- 
 sidered as effective." 
 
 When two rows of rivets are used in a tension member, the 
 rivets should be staggered as in Fig. 34, so that any cross- 
 section will be weakened by only one rivet-hole. 
 
 Stay-rivets. Struts composed of a pair of angles should- 
 be riveted together, with a washer between the angles, about 
 
 Fig. 31 
 
 Joint D of Fig. 28. 
 
 every eighteen inches for 2" angles, 24" for 2J" angles, and 30" 
 for 3J" angles, and from 30" to 3 ft. for tension members. Stay- 
 rivets are shown in Figs. 30 and 34. 
 
 For locating the rivet lines on angles, or the "pitch," as it 
 is called in bridge-shops, the distances given in the table on 
 p. 551 should be used. 
 
 Figs. 24-27 show the details of several of the joints in the 
 truss shown by the diagram, Fig. 23, and Figs. 29-33 several 
 of the joints of the truss shown in Fig. 28. The engravings 
 were made from the actual working drawings prepared by the 
 
1072 
 
 TRUSS MEMBERS AND JOINTS. 
 
 Berlin Iron Bridge Co., and are very good examples of riveted 
 joints in roof -trusses. 
 
 
 Fig. 32 
 Joint F of Fig. 28. 
 
 . A 1 *" 
 
 Fig 33. 
 
 Joint G of Fig. 28. 
 
 The solid black circles indicate holes for bolts to be put in 
 
PURLINS AND PURLIN CONNECTIONS. 1073 
 
 place in the field, the truss being shipped in four parts and 
 assembled at the building. 
 
 Fig. 34 was engraved from the working-drawing made by the 
 
 4,A.aa4B. 
 
 beoColuma.De.taiV 
 
 Fig. 34 
 
 New Jersey Steel and Iron Co. of Trenton, N. J., and represents 
 joint 1 of Fig. 60, p. 922. 
 
 Purlins and Purlin Connections. 
 
 Where the roofing is supported directly on the purlins, as 
 is generally the case in light steel roofs, the purlins and trusses 
 are generally spaced so close together that simple shapes may 
 be used for the former. 
 
 For spans between trusses of 8 or 10 feet, angles are com- 
 monly used, and for greater spans Z bars, channels, and I beams. 
 
 Wooden purlins are also frequently used with steel trusses. 
 
1074 
 
 TRUSS MEMBERS AND JOINTS. 
 
 If the purlins support wooden rafters or plank roofing, a strip 
 of wood is bolted to the I beam or channel purlin, as shown by 
 Figs. 36 and 37, to form nailings for the rafters or plank. 
 
 Fig. 35 
 
 Purlin-clips. 
 
 Fig. 36 
 
 Purlin Connections. 
 
 When the distance between trusses is more than about 15 ft., 
 a line of f " rods should be run from the ridge through the pur- 
 lins to prevent them from sagging in the plane of the roof. 
 Purlin Connections. Angle, channel, and Z-bar pur- 
 lins, and also wooden purlins, are fastened 
 to the rafters of the truss by angle-clips 
 
 aS in FigS< 35 ' 36j and 37 ' TheS dipS 
 should be riveted to the truss at the 
 
 shop, the purlins being secured to the 
 clips by bolts. 
 
 I-beam purlins are usually bolted di- 
 rectly to the rafter by a bolt in each 
 side of the flange. 12" XI 5" I beams 
 Fig. 37 and channels are sometimes braced as in 
 
 Fig. 37, the necessity for bracing depending largely upon the in- 
 clination of the roof. 
 
WIND BRACING OF BUILDINGS. 1075 
 
 CHAPTER XXVIII. 
 
 WIND STRESSES AND BRACING IN TOWERS 
 AND HIGH BUILDINGS. 
 
 THE stresses produced by the force of the wind acting against 
 high structures are often of great magnitude and must be 
 provided for as much as those produced by vertical loads. 
 
 Brick or stone structures, if the walls are well built and of 
 proper thickness, are able to withstand these stresses without 
 bracing, but framed structures require bracing and additional 
 sectional area in the posts; the amount of bracing and in- 
 crease in sectional area depending largely upon the height 
 and width of base, and the character of the construction. 
 
 The method of determining the wind stresses can best be 
 shown by means of examples. 
 
 EXAMPLE 1. We will assume that Fig. 1 is an elevation of 
 one side of a tower 48 ft. high, 12 ft. 8 ins. wide, and 25 ft. 4 ins. 
 long. The tower to be built with wooden posts and girts and 
 braced with rods, the latter being in the same plane as the 
 posts and girts. The spaces between the posts to be filled 
 with studding, and the entire tower to be sheathed and cov- 
 ered with some suitable material. In regard to its resistance 
 to wind pressure, such a frame is in effect a cantilever truss 
 fixed at one end, i.e., at the ground (either by bolts or by its 
 own weight), and uniformly loaded over [its entire length, and 
 the stresses may be found exactly in the same way as for a 
 cantilever truss. 
 
 The wind pressure is considered as acting horizontally and 
 applied at the joints the same as the loads on a truss. 
 
 In a tower, the two sides parallel with the direction of the 
 wind are assumed to resist the stress, so that the frame shown 
 by Fig. 1 has to resist only one half of the total pressure. 
 
 uming the wind to act from the left, the rods should be 
 placed as in the figure. 
 
 The wind load at joint o will equal half the height of the 
 
1076 WIND BRACING OF TOWERS. 
 
 panel multiplied by half the width of the structure, and the 
 product by the pressure per square foot. 
 
 For enclosed towers, the wind pressure should be taken equal 
 to 40 Ibs. per square foot of vertical elevation, at least, and 
 if the tower is in a very exposed situation, it will be safer to 
 assume a pressure of 50 Ibs.* 
 
 Assuming a pressure of 40 Ibs., we have for the loads at 
 joints o and 8, of Fig. 1, 6'X12' 8"X 40= 3,040 Ibs., or say 
 3,000 Ibs., and at joints 2, 4, and 6 twice this amount, or 6,000 
 Ibs. To draw the stress diagram, Fig. IA, we will commence 
 with joint 1, Fig. 1 being lettered as for a truss diagram (see 
 p. 971). The pressure exerted at o is transmitted by the top 
 girt directly to joint 1, and we may therefore consider the 
 force as acting at that joint. Then at joint 1 we have a hori- 
 zontal force of 3,000 Ibs., which is represented by the line ab 
 drawn to a scale, and the force acts in the direction indicated. 
 Besides this force we have the stresses in BF and FA, which 
 we obtain by drawing a vertical line from a, and a line from b, 
 parallel to the diagonal B'F, the two lines intersecting at /. 
 The triangle of forces for joint 1, then, is ab, bf, and fa. The 
 arrow-head on bf points from the joint, and on fa, towards the 
 joint; hence B'F is in tension and FA in compression. (Note. 
 It will be seen that the order of rotation is from right to left, 
 and this order must be followed at all of the joints.) 
 
 At joint 2 we have the stress in FB', which must act from 
 the joint, next the load of 2,000 Ibs., which we lay off from 
 b to c, to the same scale as ab (theoretically there will be no 
 stress in BB'}. Then draw eg and-/<7 to represent the stresses 
 in CG and FG respectively. The arrow-head on eg points from 
 the joint, hence CG is in tension. At joint 3 we have the 
 
 * In a paper read before the American Society of Civil Engineers, Mr. 
 Julius Baier stated that the St. Louis tornado of 1896 "gave evidence 
 that wind pressures existed at least equivalent to or greater than 20 Ibs. 
 60 Ibs., and 85 to 90 Ibs. per square foot over considerable areas, and that 
 the pressures at higher altitudes were more severe than those measured.' 
 
 After a thorough study of the effects of the wind pressure during this 
 tornado Mr. Baier recommended "that [the safety and interests of the 
 community and of the owner of the building require a recognition of a 
 wind pressure of at least 30 Ibs. per square foot against the exposed surface 
 of a building, with an additional local provision of 50 Ibs. for several stories 
 near the top ; and that this amount should be safely taken care of by some 
 positive and definite provision in the construction of the frame." 
 
 Railway structures and steel buildings are commonly designed to resist 
 a horizontal wind pressure of 30 Ibs. per square foot. 
 
WIND BRACING OP TOWERS. 
 
 1077 
 
 stresses af and fg, and draw gh and ha parallel respectively to 
 GH and HA. The stresses at joints 4 and 6 are found in the 
 same way as at joint 2, and those at joints 5 and 7 in the same 
 way as those at 3. At joint 8 we have the stresses Ik and ke, 
 and measure off the load of 3,000 Ibs. represented by em. 
 
 p & P i . ,c P 2~ \'d 
 
 P+Pi+P 2 +P 3 
 
 Fig. I 
 
 Fig. IA 
 
 Then, if from m we draw a vertical line, and from I a hori- 
 zontal line, the two intersecting at n, mn w r ill denote the an- 
 chorage required for the post EK, and In the stress in the girt 
 or sill, on the assumption that the entire horizontal thrust or 
 tendency to slide on the foundation is resisted by joint 9. In 
 practice it is customary to fasten the frame to each of the piers, 
 and to make the girt or sill strong enough to resist one half 
 of the thrust. 
 
 The stress denoted by mn will be offset to a considerable 
 degree, if not entirely overbalanced, by the weight of the frame 
 
1078 WIND BRACING OF TOWERS. . 
 
 and its load. In a light frame supporting no load, the tension 
 in the windward columns will be greater than the compression, 
 and the columns must be spliced to resist an upward pull and 
 be anchored to the foundation. 
 
 The uplift at joint 8 can also be obtained by taking moments 
 about joint 9. Thus the total wind pressure acting against 
 the windward side will be 4S / X25 / 4"X40 lbs.= 48,640 Ibs. 
 As each end resists one half of the pressure, the pressure for 
 one end will be 24,320 Ibs., or say 24,000 Ibs. This pressure 
 may be considered as acting at half the height of the frame. 
 Representing the pressure by PR, the moment about 9 tending 
 to overturn the tower=P#X-X\ To maintain stability there 
 must be a force, represented by the arrow, W, acting down. 
 Considering the tower as balanced on the pier at 9, the force W 
 tends to turn the tower to the left, and its moment =WxY. 
 To just maintain equilibrium WXY must just equal PRXX, 
 
 whence W= r- . Substituting the values of PR, X, and Y, 
 
 24 000x24 
 
 we have W= ' r-x = 48,000 Ibs., which is the same stress 
 
 \f> 
 
 as given by the stress diagram. To be perfectly safe against 
 gusts of wind or tornadoes, W should exceed the value given 
 by the above value by at least 25 per cent. 
 
 The difference between \\W and the weight on the post must 
 therefore be taken care of by a rod or strap extending into 
 the foundation, and there must be sufficient masonry provided 
 to balance this difference between \\W and the dead weight. 
 Thus we will assume that our tower weighs 80,000 Ibs., then 
 the load on each post will be one fourth of this, or 20,000 Ibs., 
 W= 48,000, and l\W= 60,000 Ibs. Therefore it will require 
 an anchorage of 40,000 Ibs. to secure absolute safety. As 
 the weight of stone masonry may be taken at 140 Ibs. per 
 
 40 000 
 
 cubic foot, it will require ' =286 cu. ft. to hold the tower 
 J.4U 
 
 down. 
 
 To the compression in the leeward columns due to wind pressure 
 must be added the compression due to the vertical loads. Thus 
 if the post 7-9 has to support a dead load of 20,000 Ibs., it 
 should be made large enough to sustain 20,000 + 48,000, or 
 68,000 Ibs. In computing the size of struts or ties to resist 
 wind pressure, however, a greater unit stress or a smaller 
 factor of safety is generally used than for other loads. 
 
WIND BRACING OF TOWERS. 1079 
 
 In Fig. 1 only one diagonal is shown for each panel, and if 
 we could be sure that the wind would always blow from the 
 left, that is all that would be required. 
 
 As the wind may blow from any direction, however, it is 
 necessary to insert diagonals in both directions, and in each 
 of the four sides of the tower, and if it is necessary to provide 
 any anchorage at all, all of the posts must be anchored, and 
 each post must be 'proportioned for the maximum net tension 
 and maximum compression. 
 
 Analysis of Stress Diagram. The stresses given on 
 Fig. 1A were obtained by scaling the lines by the scale used in 
 laying off the pressures P, P lt etc. Studying the diagram and 
 stresses, it will be seen that the compression (or shear, as it 
 is commonly called) in 2-3 = P+P r The shear in 4-5=. 
 P+P t + P 2 , and so on. Or the shear in any girt equals the panel 
 load at that point plus all of the panel loads above. 
 
 Also, the stress in the diagonals equals the shear in strut above 
 multiplied by the secant of the angle 0. 
 
 The compression in the leeward column from 1 to 3 equals 
 a/, or the vertical component of the stress in the diagonal. 
 The compression from 3 to 5 equals hf-\-fa, or the vertical 
 component of the diagonal hg-}- the compression in the panel 
 above, and this is true for every panel. 
 
 Now the line af^=P times tangent 6, and fh=fg*X. tangent 6. 
 If we denote the vertical component of the diagonals by the 
 term increment, then the increment for any panel is equal to the 
 shear in the strut at the top of the panel multiplied by the tan- 
 gent 0, and the compression in the leeward column in any panel 
 equals the increment for that panel plus the compression in the 
 panel above. It can also be seen that the tension in CG equals 
 the compression in AF , and the same relation is true for the 
 panels below, or the tension in the windward column in any panel 
 is equal to the compression in the leeward column in the panel 
 above. 
 
 These facts enable one to readily compute the stresses in a 
 simple frame like Fig. 1, without drawing the stress diagram, 
 and the wind stresses in the framework of high buildings are 
 usually computed directly by means of the above propositions, 
 as is shown on p. 1088. 
 
 If the tower is battering, however, the above propositions 
 do not hold true, and the stresses can be most easily obtained 
 by drawing a stress diagram. 
 
1080 WIND BRACING OF TOWERS. 
 
 EXAMPLE 2. To show the application of the graphic method 
 of finding the wind stresses when the columns are inclined, 
 we will determine the stresses for the water-tower shown by 
 Fig. 2. We will assume that the tower is square in plan and 
 open on the sides. The tank is supposed to be circular and 
 to weigh, when two thirds full of water, about 80,000 Ibs 
 The area of the tank exposed to the wind is its diameter mul- 
 tiplied by the average height, or 12X13=156 ft. For the 
 pressure per square foot of vertical surface we will assume 
 60 Ibs. to provide against any possible wind. This would 
 make the pressure on 156 sq. ft. 9,360 Ibs. For a circular 
 tower or chimney, however, it is customary to consider the 
 pressure as only two thirds what it would be on a flat surface, 
 which would make the pressure on the tank 6,240 Ibs., or 3,120 
 Ibs. on each side. For the pressure on the tower 20 Ibs. per 
 square foot of vertical elevation should be sufficient (consider- 
 ing that it is an open frame). This will give the panel loads 
 to be resisted by each side, as indicated in the figure, the load 
 at the top of the frame including both the pressure on the tank 
 and the pressure on the upper half of the frame. 
 
 The stress diagram (Fig. 2A) is drawn in exactly the same 
 way as Fig. 1A, commencing by drawing the line ab, equal 
 to the pressure at joint 1, and from a and b lines parallel re- 
 spectively to AF and B'F. At joint 2 we have fb, and draw be 
 equal to the pressure at that joint. Then from c draw a line 
 parallel to CG, and from / (the point of beginning) a horizon- 
 tal line, the two lines intersecting at g. At joint 3 the polygon 
 of forces is af, fg, gh, and ha. 
 
 The stresses at joints 4 and 6 are drawn in the same way as 
 those at joint 2, and the stresses at joints 5 and 7 in the same 
 way as those at joint 3. 
 
 At joint 8 we have Ik and ke, and draw em=to the pressure; 
 from m draw a vertical line, because the weight of the anchorage 
 will be vertical, and from I a horizontal line. Then mn will 
 represent the upward pull on the windward piers due to wind 
 pressure, and In the compression on the bottom girt, assuming 
 that the entire stress is transmitted to joint 9. 
 
 As all of the posts will be fixed, however, the girt need be 
 proportioned to resist only one half of the stress shown by In. 
 The stresses given in Fig. 2 A were obtained by scaling the 
 lines. It will be seen that all of the stresses are considerably 
 less than they would be if the tower were of the same width 
 
WIND BRACING OF TOWERS. 
 
 1081 
 
 at the base that it is at the top, or, in other words, the resistance 
 of the tower is materially increased by inclining the posts. 
 In proportioning the girts and diagonals, only the stress due 
 to wind pressure need be taken into account, as the vertical 
 load would produce no stress in the diagonals, and practical 
 requirements will cause the girts to be made greater than would 
 
 
 Wt 80,000 
 
 ii 
 
 
 
 T 
 
 
 , 
 
 i 
 
 f 8750 f 
 
 A 
 
 M- 
 
 Fig. 2 
 
 Fig. 2A 
 
 theoretically be necessary. The posts, however, must be pro- 
 portioned for both the dead load and wind stress. 
 
 Allowing 8,000 Ibs. for the weight of the frame, the dead load 
 on each post will be 22,000 Ibs., and as the wind stress on the 
 leeward posts between joints 7 and 9 is 12,800 Ibs., all four of 
 the posts should be proportioned to support 34,800 Ibs. com- 
 pression. 
 
 The tension in the windward posts is only 9,100 Ibs., and as 
 this is greatly exceeded by the dead load, it need not be taken 
 into account. The uplift on the windward piers is 12,700 Ibs., 
 but as the dead load is 22,000 Ibs , no anchorage will be re- 
 quired, although it would be well to bolt the posts to the piers 
 by I" or I" bolts 3 or 4 ft. long. 
 
 The diagonals should, of course, be run in both directions, 
 
1082 WIND BRACING OF BUILDINGS. 
 
 in all four sides of the tower, and should be provided with turn- 
 buckles, so that the rods may be well tightened after the frame 
 is erected. 
 
 In these two examples we have considered towers of only 
 moderate height, for convenience of illustration, but the analysis 
 is precisely the same for a frame of any number of panels or 
 stories. 
 
 A good example of a steel water-tower is described and illus- 
 trated in the Engineering Record of June 20, 1903, the stress 
 diagrams and details of construction being given. 
 
 Wind Bracing of Tall Buildings. When office and 
 other buildings of six to ten stories were built with solid masonry 
 walls no attention was paid to the lateral strains due to wind 
 pressure, except, perhaps, to make the walls and partitions a little 
 heavier. 
 
 And as such buildings were seldom built of a less width than 
 50 ft., no other precautions were really necessary, for whenever 
 buildings of ordinary construction with masonry walls have 
 been blown down, it has generally been due more to a poor 
 quality of work, especially in the walls, or to lack of sufficient 
 anchors, rather than to faulty design, although occasionally ; 
 as in the St. Louis tornado, a well-built building has been blown 
 down. 
 
 The modern steel buildings, however, are built to such great 
 heights, especially in proportion to their width, and are so desti- 
 tute of the ordinary means of resisting wind pressure, such as 
 solid walls and partitions, that some efficient means of bracing 
 the steel frame would seem to be a matter of necessity. As a 
 matter of fact, few if any skeleton steel buildings are now 
 erected without some provision for bracing the steel frame, in- 
 dependent of the partitions. 
 
 In some buildings these provisions consist merely in using 
 girders built of angles and plates of good depth, in the use of 
 riveted connections at the columns, and in breaking joints 
 of columns at the different floor-levels, while in others heavy 
 sway-bracing, knee or portal bracing, or both combined have 
 been employed. 
 
 In fact, the diversity of practice as regards the wind bracing 
 of buildings is much greater than in any other feature of con- 
 struction. 
 
 Buildings which Require Bracing-. It is generally 
 conceded that buildings of moderate height with solid masonry 
 
WIND BRACING OF BUILDINGS. 1083 
 
 construction, braced with permanent partitions, will require 
 no special wind bracing; also that all steel-frame buildings in 
 which the exterior walls are carried by the steel frame require 
 some provision in the frame itself to enable it to resist the wind 
 pressure. 
 
 The higher the building in proportion to its width, unless 
 protected by adjacent buildings, the greater will be the need 
 of efficient wind bracing. 
 
 The Chicago building ordinance makes the following require- 
 ments : 
 
 "In the case of all buildings the height of which is more 
 than one and one half times their horizontal dimension, allow- 
 ance shall be made for wind pressure, which shall not be 
 figured at less than thirty pounds for each square foot of ex-. 
 posed surface. In buildings of skeleton construction the 
 metal frame must be designed to withstand this wind pressure." 
 
 The building laws of Greater New York require that "All 
 structures exposed to wind shall be designed to resist a hori- 
 zontal wind pressure of thirty pounds for every square foot 
 of surface thus exposed, from the ground to the top of the same, 
 including, roof, in any direction." This is modified by the 
 following clause: "In buildings under one hundred feet in 
 height, provided the height does not exceed four times the 
 average width of the base, the wind pressure may be disre- 
 garded." 
 
 The building laws of Boston and Philadelphia contain no 
 reference to wind pressure. Mr. J. K. Freitag has a very 
 practical chapter on wind bracing in his excellent work "Archi- 
 tectural Engineering." 
 
 Methods of Wind Bracing. For buildings not exceed- 
 ing 120 ft. in height, and in which the least width is two thirds 
 the height, sufficient rigidity will be obtained by using con- 
 tinuous column splices as in Figs. 15 and 18 of Chapter XIV, 
 making the columns in two-story lengths, alternate columns 
 breaking joint in alternate floors, and riveting both flanges of 
 girders and beams to the columns by means of angles or brackets. 
 
 Exposed steel buildings in which the height exceeds one and 
 one half times the width, or which are more than 120 ft. in 
 height, should have some definite form of metallic bracing. 
 
 Fig. 3 shows in outline the different forms of wind bracing 
 that have been employed to which should be added the "portal 
 bracing" shown by Figs. 17 and 18. The form of bracing to 
 
1084 
 
 WIND BRACING OF BUILDINGS. 
 
 be employed in any given building will be governed by the 
 peculiar conditions which the building offers 
 
 "The height, width, slope, and exposure of the structure, 
 as well as the character of the enclosing walls, will determine 
 the amount of wind pressure to be cared for, while the details 
 of construction, the internal appearance, and the planning 
 of the various floors will largely influence the manner in which 
 the bracing is to be treated. The architectural planning of 
 the offices, rooms, and corridors often raises most serious ob- 
 
 xxxx 
 
 XXXX 
 
 Fig. 3 
 Types of Wind Bracing. 
 
 stacles to a proper arrangement of wind bracing, and the en- 
 gineer is frequently called upon to make most generous con- 
 cessions for doors, windows, passages, and even whole areas, 
 as is sometimes demanded in banking or assembly rooms and 
 the like." (Freitag.) 
 
 "The bracing, whatever system is used, must, of course, be 
 vertical, reaching down to some solid connection at the ground 
 level. It should also be arranged in some regular symmetrical 
 relation to the outlines of the building. For example, if the 
 building is narrow and is braced crosswise with one system of 
 bracing, that system should be midway between the ends of 
 1 the building, and if two systems are used they should be equi- 
 distant from the ends, the exact distance being unimportant, 
 because the floors when finished are extremely rigid. The 
 symmetrical arrangement is necessary to seeure an equal service 
 of the systems and prevent any tendency to twist." (C. T. 
 Purdy.) 
 
 Intensity of Wind Pressure. The intensity of wind 
 pressure which should be provided for in calculating the stresses 
 in the braces, columns, and struts is considered at considerable 
 length by Mr. Freitag. The building laws of New York and 
 
WIND BRACING OF BUILDINGS. 1085 
 
 Chicago specify a unit pressure of 30 Ibs. Mr. Freitag thinks 
 that 30 Ibs. should serve as a minimum in high buildings of 
 veneer construction. 
 
 It is seldom that the wind stresses are figured for a greater 
 unit stress than 30 Ibs. 
 
 Many engineers consider that fully 10 Ibs. of wind pressure 
 will be resisted by the connections between the columns and the 
 floor system, partitions, and dead weight, so that if the bracing 
 is computed to take care of 30 Ibs. the building will be safe to 
 resist an actual wind pressure of 40 Ibs.* 
 
 Computation of Stresses. As each different system 
 of wind bracing creates stresses unlike those created by the 
 other systems, each arrangement must be treated separately. 
 
 Diagonal Systems, or Sway-bracing-. The diagonal 
 system of bracing shown by a and b, Fig. 3, is the cheapest 
 and best when the division of the building by partitions will 
 admit of its use. 
 
 The arrangement of diagonals shown at a is to be preferred, 
 but the location of doors, etc., may sometimes be arranged to 
 better advantage by making the rods pass through two stories, 
 as shown at b. Sway-bracing was used in the Masonic Temple, 
 the Venetian Building, and 'the Ashland Block in Chicago. 
 
 Analysis. The wind stresses in a diagonal system are 
 computed exactly as in Example 1, although as the posts are 
 always vertical and the diagonals usually have the same incli- 
 nation the stresses can readily be computed mathematically, 
 as shown in the following example: 
 
 EXAMPLE 3. Let Fig. 5 be an outline elevation of one set 
 of bracing in a thirteen-story building having the same plan 
 and horizontal dimensions as the Venetian Building, Fig. 4, 
 and being protected on one side by an adjoining building which 
 reaches to the sixth floor. 
 
 From an examination of the plan it will be seen that the 
 exposed area contributory to each set of bracing for each story 
 
 * "The weight of the building affords some resistance, and in most cases 
 la worth taking into account. Most buildings are filled with tile or some 
 other sort of partitions, and when these are really constructed and their 
 continuance is assured, there is no good reason why we should not rely 
 also on them to some extent. There is also some resistance to lateral 
 strains in the connection of the beams to the columns where they are well 
 riveted. Some of these considerations will admit of calculation, but in 
 using them much must depend on the experience and judgment of the 
 engineer." (C. T. Purdy,) 
 
1086 
 
 WIND BRACING OF BUILDINGS. 
 
 is 21 T yX height of story, and as the stories are all 12 ft. from 
 floor to floor, the area contributory to each joint is 259 sq. ft. 
 
 Assuming a wind pressure of 30 
 Ibs., the wind loads at each floor 
 will be 7,770 Ibs., or say 7,800 
 Ibs., except that at the seventh 
 floor the load will be only one half 
 that at the floors above. 
 
 Note. There will, of course, be 
 a wind pressure on the stories 
 below the seventh, but it is safe 
 to assume that it will be resisted 
 by the buildings abutting on the 
 other side, particularly as the ex- 
 posed side will, in the business 
 portion of a city, be considerably 
 sheltered by the buildings on the 
 opposite side of the street. 
 
 In order to provide for door 
 openings next the columns it 
 will be necessary to connect the 
 diagonals with the struts, IS" 
 in from centre of columns, which 
 will make the angle between struts 
 and diagonals 42 42'. 
 
 (The tangent of the angle is r, or in this case .9230, and from 
 
 the table on natural tangents, p. 122, we find the angle whose 
 tangent is nearest to .9230 to be 42 42'.) 
 
 We are not prepared to compute the stresses which should 
 be entered in a table like that given below. As shown on 
 p. 1079, the shear at each floor is equal to the wind load at that 
 floor plus all of the loads above, which enables us to compute 
 the shears directly and enter them in the second column. It 
 was also shown that the stress in the diagonal for each story 
 is equal to the shear in the strut above multiplied by the secant 
 of the angle 0. From the table on p. 123a we find that the 
 secant of 42 42' is 1.36, and multiplying the shears by this 
 factor, we have the values given in the third column. 
 
 On p. 1079 it was shown that the stress in the leeward column 
 for any story is equal to the stress in the story above plus the 
 vertical component of the stress in the diagonal for that story, 
 
WIND BRACING OF BUILDINGS. 
 
 1087 
 
 and that the vertical component, to which we will give the 
 term increment, is equal to k the shear in 
 the strut above multiplied by the tangent 
 
 of the angle or by r which in this ex- 
 ample is .923. 
 
 Multiplying each shear by .923 we 
 obtain the increments given in the fourth 
 column of our table. 
 
 Tne compression in the leeward column 
 in the thirteenth story is the same as the 
 increment. In the twelfth story it is 
 equal to the compression in the thirteenth 
 story plus the increment for the twelfth 
 story and so on down to the basement. 
 
 It will be seen that the compression in 
 the columns increases very rapidly in the 
 lower stories and amounts to a very con- 
 siderable stress in the basement, first and 
 second stories. 
 
 The tension in the windward column in 
 any story is equal to the compression in 
 the leeward column in the story next 
 above, thus the tension in the windward 
 column will be 471,600 Ibs. in the first 
 story and 525,600 Ibs. in the basement. 
 
 The tensile stress exceeds the actual 
 dead load on the columns, including a 
 liberal allowance for weight of furniture, 
 etc. In this example, however, the dis- 
 tance between the columns is very short 
 in proportion to the height of the build- 
 ing, thus greatly increasing the column 
 stress. 
 
 It is extremely doubtful if the wind 
 blowing against a building such as we are 
 considering would actually produce an up- 
 lift on the windward columns. 
 
 Theoretically both columns should be 
 proportioned to the full dead load on the 
 columns, including a small allowance for 
 the weight of furniture, and also for the Fig. 5 
 
 7800 > 
 
 
 r 
 
 
 xx 
 
 
 
 
 13th 
 
 7800 
 
 .XX. 
 
 
 
 
 
 
 
 
 
 
 12th 
 
 
 Xx 
 
 
 A 
 
 
 
 
 
 
 
 
 llth 
 
 " ? 
 
 .X \ 
 
 
 
 ^/ 
 
 10th 
 
 > 
 
 x O" 
 
 
 
 X 
 
 9tb 
 
 
 51 
 
 8th 
 
 
 
 7th 
 
 3900 
 
 / ^ v 
 
 
 
 \ s / 
 
 Y 
 
 
 - : /^-- 
 
 6th 
 
 
 y^ 
 
 5th 
 
 
 ^ o- 
 
 
 
 \ ^f 
 
 
 
 x^ix. 
 
 1th 
 
 
 X' 
 
 j 
 
 
 
 
 
 
 3rd 
 
 
 
 
 
 \ x / 
 
 1 
 
 
 j*f 
 
 2nd 
 
 
 / \ 
 
 
 
 \ x X 
 
 
 
 ><^ 
 
 1st 
 
 
 x \ 
 
 
 Htk' 
 H 
 
 
 B 
 
1088 
 
 WIND BRACING OF BUILDINGS. 
 
 WIND STRESSES. 
 Unit pressure = 30 Ibs. 
 Tangent = 0.923. 
 
 EXAMPLE 3. 
 
 Angle 6 = 42 42'. 
 Secant 0=1.36. 
 
 Story. 
 
 Shear or 
 Com- 
 pression 
 in Strut. 
 
 Tension in 
 Diagonal 
 = shear 
 Xsec 6. 
 
 Increment 
 = shear 
 
 Xtan 6. 
 
 Compression 
 in Leeward 
 Col. 
 
 Attic 
 
 7,800 
 
 
 
 
 Thirteenth 
 
 15,600 
 
 10,600 
 
 7,200 
 
 7,200 
 
 Twelfth 
 
 22,400 
 
 21,220 
 
 14,400 
 
 21,600 
 
 Eleventh 
 
 31,200 
 
 31,820 
 
 21,600 
 
 43,200 
 
 Tenth 
 
 39,000 
 
 42,430 
 
 28,800 
 
 72,000 
 
 Ninth 
 
 46,800 
 
 53,040 
 
 36,000 
 
 108,000 
 
 Eighth 
 
 54,640 
 
 63,640 
 
 43,200 
 
 151,200 
 
 Seventh 
 
 58,500 
 
 74,250 
 
 50,400 
 
 201,600 
 
 Sixth 
 
 
 
 79,560 
 
 54,000 
 
 255,600 
 
 Fifth 
 
 ( 
 
 t 
 
 
 309,600 
 
 Fourth 
 
 t 
 
 t 
 
 t 
 
 363,600 
 
 Third 
 
 t 
 
 t 
 
 t 
 
 417,600 
 
 Second 
 
 t 
 
 t 
 
 ( 
 
 471,600 
 
 First 
 
 t 
 
 t 
 
 < 
 
 525,600 
 
 
 
 
 
 525,600 
 
 
 
 
 
 
 full wind stresses in the leeward column (as the wind may 
 blow against either side of the build- 
 ing), and if the frame stood by itself, 
 as in Fig. 5, this method should be 
 followed in practice, and the columns 
 should also be anchored to the 
 foundations sufficient to resist the 
 theoretical uplift minus the dead 
 load. 
 
 In the building under considera- 
 tion, however, there are three of 
 these panels in the width of the 
 building (see Fig. 4), and as the 
 floor connections would assist some- 
 what in relieving the braced system 
 from the full theoretical stresses, 
 most if not all structural engineers 
 would probably cut down the theo- 
 retical stresses in the columns con- 
 siderably, probably 50 per cent, in 
 
 ^he lower stories. 
 Partial Crojs^ecHon, Venetian The ^ ^ buildings { even 
 
WIND BRACING Of BUILDINGS. 1089 
 
 more than thirteen stories are standing with scarcely any pro- 
 vision for wind stress * would indicate that a considerable 
 cutting down of the column stresses is permissible. 
 
 Theoretically the columns should also be proportioned to 
 the eccentric loads due .to the increments being applied 18 ins. 
 from the centre of the columns. 
 
 Practically the columns should be made wide, in the direc- 
 tion of the wind, i.e., parallel to the end of the building, and 
 the braces should be applied as close to the centre of the columns 
 as practical conditions will admit. 
 
 All columns affected by the wind bracing should be made 
 continuous by means of splice plates from the foundation to 
 the top. 
 
 Where the rods come down to the first-floor level, the bottom 
 strut should be connected to the columns so as to take both 
 tension and compression horizontally, so that both columns 
 may assist in resisting the shear at that level. 
 
 The clearance spaces between all of the first-floor beams 
 and columns should be filled with metal wedges and the columns 
 wedged against the sidewalk walls, so that the entire floor 
 system will act as a strut, backed by the solid street. 
 
 For the diagonal braces, which should run in both directions, 
 square rods or flat bars should be used, and each should be 
 provided with a turnbuckle for adjustment after the frame is 
 erected. 
 
 It is customary to proportion the rods to the theoretical 
 wind stresses, allowing 20,000 Ibs. to the square inch. 
 
 The struts should be designed as strut beams if they also 
 assist in supporting the floor, and for the bending moment 
 produced by the bracing. 
 
 Fig. 7 shows the connection between column and strut recom- 
 mended by Mr. Purdy. "The strut need not be connected 
 to the column to resist horizontal forces, for there is no force 
 tending to tear the strut away from the columns in this direc- 
 tion. The force to be resisted here is vertical. The strut 
 should be made to butt the column squarely, instead of fastening 
 to the sides of the column by rivets passing through the two 
 members, or indirectly through connection plates, because 
 the forces producing stresses in the bracing at this point must 
 come into the strut by compression from without and not 
 
 * See Architectural Engineering, second edition p. 249. 
 
1090 
 
 WIND BRACING OF BUILDINGS. 
 
 through any possible tensile stress. When the strut butts the 
 column these forces are introduced into the strut without the 
 aid of rivets, and the full value of all the rivets can be used to 
 
 Fig. 7 
 
 Strut and Column Connections. 
 
 resist the vertical component of the rod stress. It serves also 
 to keep the arm at the end of the strut, or the distance from 
 the centre of pin to the bearing at the end, as short as possible, 
 all of which is important. The top angles may be placed 
 
WIND BRACING OF BUILDINGS. 1091 
 
 several inches above the strut and a cast filler block introduced 
 between them. 
 
 " Such an arrangement has several advantages. It generally 
 happens that these angles cannot be riveted to the column 
 directly above the channels of the strut, as shown in Fig. 7. 
 The consequence is that whatever intervenes must carry a 
 cross strain. The cast block will do this well. It is also im- 
 portant that there should be absolutely no clearance, other- 
 wise the whole system would lack in stiffness and efficiency. 
 The block can be cast a little large, and if necessary it can be 
 chipped at the building in order to crowd it into position. 
 
 " The block also has the further advantage of cheapness and 
 is always easily obtained. Every detail in wind bracing should 
 receive the most careful attention." * 
 
 Fig. 8 shows a detail of the channel struts used in the Vene- 
 tian Building up to and including the seventh floor. A lighter 
 section was used for the floors above. These struts were in- 
 dependent of the 'floor system. 
 
 Knee Braces. The system of wind bracing shown at c, 
 Fig. 3, is not an economical method of bracing a framed struc- 
 ture, because it produces heavy bending moments both in the 
 horizontal struts and in the columns. Nevertheless it is being 
 
 Fig. 8 
 
 Detail of Strut, Venetian Building. 
 
 used more largely in tall buildings than any other type of wind 
 bracing, particularly for bracing the outer columns. 
 
 In a personal letter to the author, Mr. C. T. Purdy, whose firm 
 (Purdy & Henderson) has been identified with the engineer- 
 ing work of a great many tall buildings built during the past 
 ten years, says: "While it is true that gusset-plate and knee- 
 brace construction is more expensive and not as desirable as 
 the diagonal system, yet it is also true that we have used that 
 
 * C. T. Purdy in Modern Framed Structures, p. 459. 
 
1092 
 
 WIND BRACING OF BUILDINGS. 
 
 construction a good deal, but almost always in exterior walls. 
 In all of these cases practical considerations have counted for 
 more than theoretical ones. These practical considerations 
 are: (1) On many buildings the arrangement or use of the 
 building prevents the direct treatment of the problem and the 
 owner or architect insists that the wind bracing shall be hidden 
 
 "Wolf Bracing 
 
 Intermediate Trans verse Bracing. 
 Fig. 9 Fig. 10 
 
 Wind Bracing in Flat-iron Building. 
 
 in the masonry regardless of cost. (2) When this construction 
 is used we can make the heavy girder do double duty. In 
 most cases the wall or floor construction also belonging to these 
 particular members would require considerable metal and depth 
 of brace. (3) Experience also shows that riveted construc- 
 tion in which all web members of a system can take either 
 tension or compression makes the stiffest structure and is more 
 satisfactory in every way than pin-connected work. In other 
 words, although it costs a little more, the gusset-plate work 
 
WIND BRACING OF BUILDINGS. 
 
 1093 
 
 in exterior walls accomplishes Us purpose and has proved 
 very satisfactory." 
 
 Gusset plates were used in the Fort Dearborn Building, 
 Chicago, by Jennie & Mundie, architects. 
 
 Figs. 9, 10, 11, and 12 * show details of the wind bracing 
 in the Flat-iron Building, New York, of which D. H. Burnham 
 & Co., were archi- 
 tects, Purdy & Hen- J9f . tc 
 derson,consulting en- 
 gineers. This build- ^ 
 ing is in plan a 
 right-angled triangle ^? Fk 
 with base and per- 
 pendicular 171 ft. |, 
 and 86 ft. respect- ^ 
 ively, the angles of $^ 
 the building being 
 curved, and the ^ 
 height is twenty-one 
 stories, or about 285 J 
 ft. above the curb. 
 
 In all the outer 
 walls of the building 
 the masonry is car- 
 ried on plate girders 
 in each floor from the 
 first to the twelfth 
 stories respectively, 
 and also at the 
 eighteenth floor. All ^ SsK 
 other stories, above 
 the twelfth have 
 
 Center Transverse Bracing. 
 
 Fig. U 
 
 wall girders made of a pair of 15-in. channels. 
 
 These wall girders are also utilized as wind struts and to 
 support the floor beams. In all cases they are connected to 
 the columns by solid web knee braces above and below the 
 girder as shown by Figs. 9 and 14. Besides the knee bracing 
 of the outside walls there are two systems of transverse bracing, 
 shown in part by Figs. 10 and 11, connecting the two sides 
 of the building. The system shown by Fig. 10 connects the 
 
 * These illustrations and the following description are from the Engineer- 
 ing Record of March 29, 1902. 
 
1094 WIND BRACING OF BUILDINGS. 
 
WIND BRACING OF BUILDINGS. 
 
 1095 
 
 
 X [ 
 
 th Floor _V 
 
 cth Floor 
 
 5th Floor 
 
 I 
 I 
 
 =i= 
 i 
 i 
 
 =s 
 
 third columns from the apex of the triangle, and chat shown 
 by Fig. 11 is 51 ft. or 3 panels beyond. "In addition to these 
 two general systems of transverse bracing there is intermediate 
 between them a supple- , 
 
 mental system parallel lothrElQg |-- I I i 
 
 with them, extending 
 from the second floor to 
 the foundation/' 
 
 Figs. 13 and 14 are 
 photographic views of the 
 bracing, and Fig. 12 
 shows the manner in 
 which the columns are 
 spliced. The lower sec- 
 tion of column 23 has a 
 sectional area of 226.6 
 sq. ins. 
 
 The Frick Building, 
 Pittsburg, a twenty-story 
 steel-cage office building, 
 is braced by plate gird- 
 ers and knee braces 
 similar to those in the 
 Flat-iron Building. A 
 description of this build- 
 ing is contained in the 
 Engineering Record of 
 Jan. 11, 1902. 
 
 The building of the 
 Bank of the State of 
 New York, New York 
 City,* which is about 
 85X100 ft. in plan and 
 twenty-five stories, or 
 about 340 ft. above the 
 
 i s t Floor 
 
 =F 
 
 Fig. 15 
 
 Partial Transverse Section, Bank of the 
 State of New York. 
 
 ; curb, has all four outside walls braced with long knee braces 
 ^and also two rows of interior columns. Fig. 15 shows the 
 [bracing in two of the five panels in a section parallel to the 
 pront. 
 
 Details giving sizes of girders, bracing of exterior walls, etc., 
 were published in the Engineering Record for Sept. 13, 1902. 
 
 * Clinton & Russell, architects; Purdy & Henderson, consulting engineers. 
 
1096 
 
 WIND BRACING OF BUILDINGS. 
 
 The Battery Place Building, New York,* has the two narrc 
 ends of the building braced by struts formed of pairs of channe 
 with solid web knee braces above and below, as in Fig. 9 (s 
 Engineering Record of July 19, 1902). 
 
 In the Land and Title Building, Philadelphia, twenty-to 
 stories, or about 317 ft. high above the curb, four differe: 
 systems of bracing are combined: (1) horizontal diagonals 
 every floor plane; (2) deep plate girders at floor levels in tl 
 plane of all wall columns; (3) solid web knee braces in tl 
 corners of all wall panels excepting in the two upper stories ; ai 
 (4) extra heavy beam and girder connections to interior colum: 
 (construction of the building illustrated and described 
 Engineering Record for Oct. 3, 1903). 
 
 The stresses for a system such as is shown in Fig. 16 mi 
 
 be computed with sufficient a 
 curacy as follows : f 
 Let P be the wind pressure 
 top floor, contrib 
 tory to the bent; 
 pressure 
 
 next floor below; 
 P 2 the wind pressure 
 second floor from to 
 and so on; 
 then max. compression in str 
 
 -EL-. 
 
 %_* 
 
 1 
 
 ^rt- 
 
 
 --f -i 
 
 Fig. 16 
 
 P 1 the wind 
 
 -* 
 
 i 
 
 max. compression in str 
 
 i=P+P,; 
 
 max. compression in str 
 
 Tension in col. A = compre 
 
 PXh 
 
 sion in A'= V=- 
 
 Increment for A and A i / =V l = 
 " A 2 andA/=7 2 = 
 
 * H. J. Hardenbergh, architect; Purdy & Henderson, consulting e 
 gineers. 
 
 t The best analysis of the stresses in braced portals and transvei 
 bents that the author has seen is in " Steel Mill Buildings," by Prof. M: 
 S. Ketchum.C.E. 
 
WIND BRACING OF BUILDINGS. 1097 
 
 Tension in A^ = compression in A 1 / =V+V r 
 
 11 A 2 = " " A/=7 + F 1 + F 2 . 
 
 " " brace B = compression in B'V sec 6. 
 " " B,= " "5/^sectf. 
 
 " " B 2 = " " JB/= V 2 sec 6. 
 
 Bending moment at b = j . 
 
 -L _ 
 
 j + j i + Jr 2 X d 2 
 
 The struts s, s u s 2 , etc., will be in tension at the leeward end; 
 therefore both ends of the strut should be riveted to the columns. 
 
 In the Isabella Building in Chicago, Mr. W. L. B. Jenney, 
 the architect, used the knee-brace system shown by Fig. 17. 
 When the braces meet at the centre of the strut, there is no 
 bending moment on the strut, and as the foot of the brace 
 naturally comes nearer the floor below, the bending moment" 
 on the column is materially reduced. 
 
 Portal Bracing*. This system can be used in the place 
 of sway-rods, where conditions as to corridors, doors, etc., prohibit 
 the crossing of such spaces. The system is not as economical 
 as sway-bracing, but is generally considered more effective and 
 cheaper than the knee-brace system, because it produces prac- 
 tically no bending moment on the columns and struts. The 
 portal system with a curved solid web was first used in the 
 Old Colony Building, Chicago, completed in 1894, a partial 
 cross-section of which is shown by Fig. 18 and a detail of one 
 of the portals by Fig. 19.* "This arrangement of wind bracing 
 proved very satisfactory in all respects." 
 
 It has since been used in a few panels in other buildings, 
 but the knee brace seems generally to be preferred. 
 
 Analysis of Stresses.! Fig. 20: 
 
 * From Architectural Engineering. 
 
 tThe following analysis by Mr. C. T. Purdy is taken by permission 
 from ' Modern Framed Structures." 
 
1098 
 
 WIND BRACING OF BUILDINGS. 
 
 Let A = accumulated force or horizontal shear from wind at the 
 floor next above floor M, applied half on one side 
 and half on the other; 
 
 3M7&&M72 
 
 B=the force of wind or shear directly tributary to floor M ; 
 Z)=the accumulated vertical wind load in the column next 
 
 above col. 2; 
 then 
 
 ~ C = vertical resistance due to A. and B, or the incre- 
 ment, as denoted in the preceding analyses; 
 and 
 
 A _i_ R 
 
 - = horizontal reactions due to A and B. 
 
WIND BRACING OF BUILDINGS. 
 
 1099 
 
 The actual wind load on col. 2 and the corresponding tension 
 
 in col. 1 will= 
 
 Ah + Bh~Bc 
 
 +D. 
 
 The horizontal shear along the line EE=A+B. 
 
 The horizontal shear in either leg below the line EE= %(A + ). 
 
 Ah + Bh-Bc 
 The vertical shear on .all vertical planes = , 
 
 The thickness of the web-plates must be determined by these 
 shears. It should be noted that the connection to the columns 
 must be equal to the 
 whole vertical shear. 
 The direct compression 
 in the flange s=%B. 
 
 Taking moments 
 about the point of 
 intersection of flange r 
 with the line ww, it 
 will be found that the 
 sum of the moments = 
 zero, that is, that there 
 is no bending moment 
 in the portal on the 
 line ww and that flange 
 t is not strained at 
 this point. 
 
 For maximum stress 
 in flange t take a 
 
 n 
 
 n 
 
 
 n 
 
 
 Fig. 18 
 
 Cross-section showing Portals, Old Colony 
 Building. 
 
 point p in flange r, distant x from the line ww and at right 
 angles to any given section of the flange /; then x times the 
 vertical shear divided by y = the stress at the section taken, 
 
 and this is maximum when - has its greatest value. 
 
 y 
 
 The leg of the portal, including col. 2, might be also taken 
 
 .. A+B A Ah+Bh-Bc 
 as a cantilever with two forces acting on it, ~ ancl ~~ 7 
 
 with flange t in compression and the column itself acting as a 
 tension cord. Take a point in the centre of the column, dis- 
 tant x l from the bottom of the leg and at right angles to any 
 
 A 4-B X* 
 given section in flange t t then - X~ = the strain in flange t, 
 
 and this is maximum when has its greatest value. There is 
 
1100 
 
 WIND BRACING OF BUILDINGS, 
 
 a slight error in this treatment, but it is on the side of safety. 
 If flange I has a section proportioned to these maximum stresses, 
 the requirements will be fulfilled. The stress and area re- 
 
 Fig. 19 
 Detail of Portal in Old Colony Building. 
 
 quired in 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 equal to }A at each leg. 
 
 Lattice G-irders. "In this type of bracing the wind 
 stresses are transferred to the ground on what is often called 
 the 'table- leg principle; 7 that is, each story is made rigid in 
 itself, the columns being figured as vertical beams to resist the 
 lateral flexure due to the wind forces." 
 
WIND BRACING OF BUILDINGS. 1101 
 
 er 
 
 KA 
 
 p Flange r^ 
 
 ' ------ 
 
 -v 
 
 / 
 
 A+B 
 2 
 
 D 
 
 fl 
 
 A\ 
 2 
 
 !r 
 
 Fig. 20 
 
 Analysis. Referring to Fig. 21: 
 Let A = accumulated 
 force or hori- 
 zontal shear 
 from wind at 
 thefloor next _B_ 
 above floor 2 
 M, applied 
 half on one 
 column and 
 half on the 
 other; 
 
 J5=the force of 
 wind or shear 
 directly trib- 
 tary to floor 
 
 MI 
 
 D=the accumu- 
 lated verti- 
 cal wind load 
 in the col- 
 umn next 
 above col. 2; 
 
 Floor M 
 
 *} J._L 
 
 J 
 
 AB 
 
 Fig. 21 
 
1102 WIND BRACING OF BUILDINGS. 
 
 then J5 may be considered as applied in a line with each chord 
 of the girder. The horizontal shear due to the force B must 
 then be resisted by the two columns at any and all points be- 
 tween the lower line of the girder and the top line of the girder 
 
 D 
 
 below. Hence the foot of each column must resist the shear . 
 
 2i 
 j^ 
 
 Also will equal the shear at the foot of the columns next 
 ft 
 
 above floor M , and as cols. 1 and 2 must resist this shear, as 
 well as that due to J3, the total shear at the foot of each of the 
 
 columns in the story under consideration = , the same as 
 
 Li 
 
 with portal bracing. 
 
 Considering the external forces applied as indicated in Fig. 21 , 
 and taking moments about joint e, we have the moment tending 
 
 7? 7? 
 
 to overturn the frame on e as a hinge, AXh l +Xh 2 +Xh 3 . 
 
 [Neglecting the forces D, D, because they act through the centre 
 of the columns and do not affect the stresses in the girder or 
 the bending moment in the column.] This moment must be 
 resisted by the tension in col. 1, which acts with an arm I', 
 therefore 
 
 . 
 
 To this must be added the load or tension D t from the column 
 above. 
 
 Taking moments about /, we will obtain the same value for 
 V in col. 2 that we obained above, col. 2 being in compression 
 and col. 1 in tension. 
 
 To find the compressive stress in the upper flange of the 
 girder ac, take moments about b and denote stress in ac by s. 
 The moments tending to revolve the column to the right are 
 
 f X (h,-h 3 ) + ~X (h.-h,). 
 
 These moments must be resisted by the stress in ac acting with 
 an arm db,^=h 2 h z , from which we obtain the equation 
 
 h,) B 
 
WIND BRACING OP BUILDINGS. 
 
 1103 
 
 Taking moments about a and denoting the stress in the bottom 
 flange of the girder by s^ we obtain 
 
 B 
 2' 
 
 Both struts are , principally in compression, although they 
 must be connected to the columns to resist an equal amount 
 of tension. Considering the columns as fixed at both ends the 
 maximum bending moments will be at the points 6 and d and 
 will be equal to* 
 
 The columns must be designed to resist this bending moment 
 as well as the vertical loads. From the above analysis it is 
 readily seen that the deeper the girder the less will be the stresses. 
 When used in outside walls they should be made the full depth 
 of the spandrel, reaching from just above the top of one window 
 to immediately below the sills of the windows in the next story 
 above. 
 
 * See Architectural Engineering, p. 277. 
 
PART in. 
 
 USEFUL INFORMATION 
 
 ARCHITECTS, BUILDERS, AND SUPERINTEND- 
 ENTS 
 
 AND ALL WHO HAVE TO DO WITH THE BUILDING TRADES. 
 
 NOTE. The Author has endeavored to arrange the information 
 herein contained in the following order: 
 Heating, Ventilation, Chimneys. 
 Hydraulics and Plumbing. 
 Illuminating-gas, Gas-piping, and Lighting. 
 Electrical Definitions, Rules, and Tables. 
 Weights, Quantities, and Data for Estimating Cost. 
 Dimensions and Data Useful in the Preparation of Plans. 
 Miscellaneous Information. 
 Glossary of Technical Terms. 
 Legal Definitions. 
 
 1105 
 
HEATING AND VENTILATION. 
 
 HEAT, FUEL, WATER, STEAM, AND AIR. 
 
 Heat is measured in two ways: 1st, by the thermometer, as 
 in ordinary practice, and, 2d, by the work which it performs. 
 
 The unit of heat (sometimes called the British, thermal unit) is 
 that quantity of heat which will raise the temperature of one 
 pound of water at or near the freezing-point, 1 Fahrenheit. 
 
 A French " calorie" is the heat required to raise one kilo- 
 gramme of water 1 Centigrade, and is equal to 3.96832 British 
 thermal units. 
 
 The equivalent in force of the unit of heat is the raising of 772 
 pounds avoirdupois one foot high, and is called the mechanical 
 equivalent of heat. 
 
 Various kinds of fuel contain a certain number of thermal 
 units per pound; and the method of heating which will convey 
 the largest number of units to the air to be warmed is the most 
 economical, so far as fuel and heating are concerned. But no 
 method has yet been devised which will utilize more than about 
 85 per cent, of the heat-units contained in the fuel. 
 
 Fuel.* The value of any fuel is measured by the number 
 of heat-units which its combustion will generate. The fuels 
 generally used in heating are composed of carbon and hydrogen, 
 and ash, with sometimes small quantities of other substances 
 not materially affecting its value. 
 
 "Combustible" is that portion which will burn, the ash or 
 residue varying from 2 to 36 per cent, in different fuels. 
 
 The following table gives, for the more common combustibles, 
 the air required for complete combustion, the temperature with 
 different proportions of air, the theoretical value, and the 
 highest attainable value under a steam-boiler, assuming that 
 the gases pass off at 320, the temperature of steam at 75 Ibs. 
 pressure, and the incoming draught to be at 60. 
 
 * From Steam, published by the Babcock & Wilcox Company, New 
 York and Glasgow, 
 
 1107 
 
1108 
 
 FUELS. 
 
 t) 
 o 
 
 3 
 
 13 
 
 II 
 
 s> 
 
 With Blast, Theoreti- 
 cal Supply of Air 
 at 60 Gas 320. 
 
 With Chimney Draft. 
 
 In Pounds of Water 
 Evaporated from and 
 at 212 withl Pound 
 Combustible. 
 
 O OJ COCO <N 00 <M 
 -' 
 
 tO O OOiOi-iOC<N 1-1 Tf< 00 
 to CO <NTfOt>O5 ^ CO O 
 
 OO CO -^TtiT^OOO CO CO T}< 
 
 O OOOtOO iO O O 
 OOOi-iO <N 10 00 
 
 IO IOCO0<NO|>I>IO 
 
 In Heat-units per 
 Pound of Combusti- 
 ble. 
 
 O|>OOO O O O 
 t^cCGO-^cO O -^ O 
 
 COM i-H r^i-HrHr 
 
 With Three Times the 
 Theoretical Supply of 
 Air. 
 
 With Twice the Theo- 
 retical Supply of Air. 
 
 With 1 1 A Times the 
 Theoretical Supply of 
 Air. 
 
 With Theoretical 
 Supply of Air. 
 
 O CO'-i(Nl>CO O CO O5 
 CO |>00|>COCO O iO -^ 
 
 o ooooo o o o 
 
 rj< lOOOTfOXN <* CO O 
 Tt< iOcOiOT^*t (N CM 1-1 
 
 iO OOOOO O O O 
 
 l-l CO<NCOi-H^ <M l-( l^ 
 
 Cfl COtOCOfNi-H 00 O5 CO 
 
 CO COCOCOCOCO (N (M (N 
 
 CO 
 
 In Pounds per Pound 
 of Combustible. 
 
 183 % %%%$ g 8 
 
 Kind of 
 
 The effective value of all kinds of wood per pound, when 
 dry, is substantially the same. The following are the weights 
 and comparative value of different woods by the cord: 
 
 Kind of Wood. 
 
 Weight. 
 
 Kind of Wood. 
 
 Weight. 
 
 Hickory shellbark 
 
 4469 
 
 Southern pine. . 
 
 3375 
 
 Hickory red-heart. . 
 
 3705 
 
 Virginia pine 
 
 2680 
 
 White oak 
 
 3821 
 
 Spruce. 
 
 2325 
 
 Red oak 
 
 3254 
 
 New Jersey pine 
 
 2137 
 
 Beech 
 
 3126 
 
 Yellow pine 
 
 1904 
 
 Hard maple . . 
 
 2878 
 
 White pine 
 
 1868 
 
 
 
 
 
 The following table of American coals has been compiled from 
 various sources: 
 
HEATING VALUE OF COALS. 
 AMERICAN COALS. 
 
 1109 
 
 Coal. 
 State. Kind of Coal. 
 
 Per Cent, 
 of Ash. 
 
 Theoretical Value. 
 
 In Heat- 
 units. 
 
 In Pounds 
 of Water 
 Evapo- 
 rated. 
 
 Pennsylvania, 
 
 Kentucky, 
 tt 
 
 tt 
 a 
 
 Illinois, 
 it 
 
 1C 
 
 Indiana, 
 
 a 
 
 (i 
 
 Maryland, 
 Arkansas, 
 Colorado, 
 
 u 
 
 Texas, 
 Washington, 
 Pennsylvania, 
 
 Anthracite 
 
 3.49 
 6.13 
 2.90 
 15.02 
 6.50 
 10.77 
 5.00 
 5.60 
 9.50 
 2.75 
 2.00 
 14.80 
 7.00 
 5.20 
 5.60 
 5.50 
 2.50 
 5.66 
 6.00. 
 13.98 
 5.00 
 9.25 
 4.50 
 4.50 
 3.40 
 
 14,199 
 13,535 
 14,221 
 13,143 
 13,368 
 13,155 
 14,021 
 14,265 
 12,324 
 14,391 
 15,198 
 13,360 
 9,326 
 13,025 
 13,123 
 12,659 
 13,588 
 14,146 
 13,097 
 12,226 
 9,215 
 13,562 
 13,866 
 12,962 . 
 11,551 
 20,746 
 
 14.70 
 14.01 
 14.72 
 13.60 
 13.84 
 13.62 
 14.51 
 14.76 
 12.75 
 14.89 
 16.76 
 13.84 
 9.65 
 13.48 
 13.58 
 13.10 
 14.38 
 14.64 
 13.56 
 12.65 
 9.54 
 14.04 
 14.35 
 13.41 
 11.96 
 21.47 
 
 u 
 
 n 
 
 Cannel 
 
 Connellsville. . . . 
 Semi-bituminous 
 Stone's gas 
 
 Youghiogheny. . . 
 Brown 
 
 Caking . . 
 
 Cannel 
 
 tt 
 
 Lignite 
 
 Bureau Co. . . 
 
 Mercer Co. . . . 
 
 Montauk 
 
 Block 
 
 Caking 
 
 Cannel. 
 
 Cumberland. . . . 
 Lignite 
 
 
 ii 
 
 (i 
 
 u 
 
 Petroleum 
 
 
 
 " Slack," or the screenings from coal, when properly mixed 
 anthracite and bituminous and burned by means of a blower 
 on a grate adapted to it, is nearly equal in value of combustible 
 to coal, but its percentage of refuse is greater. 
 
 One pound of pure carbon, when completely burned, yields 
 14,500 heat-units. 
 
 Temperature of Fire. 
 
 By, reference to the table of combustibles it will be seen that 
 the temperature of the fire is nearly the same for all kinds of 
 combustibles under similar conditions. If the temperature 
 
1110 
 
 WATER. 
 
 is known, the conditions of combustion may be inferred. The 
 following table, from M. Pouillet, will enable the temperature 
 to be judged by the appearance of the fire: 
 
 
 Appearance. 
 
 Tempera- 
 ture F. 
 
 Appearance. 
 
 Tempera- 
 ture F. 
 
 Red 
 
 just visible. . . 
 
 977 
 
 Orange deep 
 
 2010 
 
 
 dull 
 
 1290 
 
 clear 
 
 2190 
 
 
 
 cherry dull. . 
 
 1470 
 
 White heat . 
 
 2370 
 
 
 
 full 
 
 1650 
 
 bright. . 
 
 2550 
 
 
 
 ** clear. . . 
 
 1830 
 
 dazzling . 
 
 2730 
 
 
 
 
 
 
 To determine temperature by fusion of metals, etc. 
 
 The following figures for the melting-points of various sub- 
 stances are given by Clark (on the authority of Pouillet, Claudel, 
 and Wilson), except those marked f, which are given by Prof. 
 Roberts-Austen in his description of the Le Chatelier pyrometer. 
 These latter are probably the most reliable figures.* 
 
 Deg. F. 
 
 Mercury 39 
 
 Ice 32 
 
 Tallow 92 
 
 Stearine 109 to 120 
 
 Spermaceti. . , 120 
 
 Wax 142 to 154 
 
 Sodium 194 to 208 
 
 Alloy, 3 lead, 2 tin, 5 bismuth . . 199 
 
 Sulphur 239 
 
 Alloy, 1 1 A tin, 1 lead '. . . 334 
 
 Alloy, } tin, 1 lead. .... 370 to 466 
 
 Tin 442 to 446 
 
 Cadmium 442 
 
 Bismuth 504 to 507 
 
 Lead 608 to 618t 
 
 Zinc 680 to 779t 
 
 Deg. F. 
 
 Antimony 810 to 1150 
 
 Aluminium 1157t 
 
 Magnesium 1200 
 
 Calcium Full red heat 
 
 Bronze 1692 
 
 Silver 1733t to 1873 
 
 Potassium sulphate 1 859t 
 
 Gold 1913t to 2282 
 
 Copper 1929f to 1996 
 
 Cast iron, white 1922 to 2075f 
 
 " gray 2012 to 2786 2228t 
 
 Steel 2372 to 2532 
 
 " hard 2570f; mild, 2687f 
 
 Wrought iron 2732 to 2912 
 
 Palladium 2732t 
 
 Platinum 3227f 
 
 Water. The several conditions of water are usually stated 
 'as the solid, the liquid, and the gaseous. Two conditions are 
 covered by the last term, and water should be understood as 
 capable of existing in four different conditions the solid, the 
 liquid, the vaporous, and the gaseous. 
 
 At and below 32 F. water exists in the solid state, as ice; 
 at 39 F., it reaches its maximum density. Above 39 the 
 density diminishes. 
 
 The weight per cubic foot of water at different temperatures 
 and under pressure of one atmosphere is shown to two places 
 of decimals by the table on p. 1112 (calculated by Rankine's 
 formula) : 
 
 The boiling-point of water depends upon the pressure. Thus 
 
 * Kent, p. 455. 
 
STEAM. 1111 
 
 at one atmosphere (14-7 Ibs., 29.22" barometer) the tempera- 
 ture of ebullition is 212. With a partial vacuum, or absolute 
 pressure of 1 Ib. (2.037"of mercury), the boiling-point is 101.40 F. 
 
 On the other hand, if the pressure be 74.7 Ibs. absolute 
 (60 Ibs. by the gauge), the temperature of evaporation becomes 
 307 F. 
 
 When water is freed of air, it may be elevated in tempera- 
 ture to 270 before evaporation takes place. 
 
 Steam. 
 
 Dry steam is steam not containing any free moisture. It 
 may be either saturated or superheated. 
 
 Wet steam is steam containing free moisture in the form of 
 spray or mist, and has the same temperature as dry saturated 
 steam of the same pressure. 
 
 Saturated steam is steam in its normal state, that is, steam 
 whose temperature is that due its pressure; by which is meant 
 steam at the same temperature as that of the water from which 
 it was generated and upon which it rests. 
 
 Superheated Steam. Steam which has a higher tem- 
 perature than that normal to its pressure is termed "super- 
 heated," or "gaseous. " Dr. Siemens found that when steam 
 at 212 was heated separate from water it increased rapidly in 
 volume, up to 230, after which it expanded uniformly, as a 
 permanent gas. The use in any steam-boiler of superheating 
 surface exposed to the heated gases of combustion is highly 
 objectionable and is of doubtful efficiency. Steam cannot 
 be superheated when in contact with water. 
 
 Sensible and Latent Heat of Steam. The tempera- 
 ture of steam, as shown by the thermometer, is called its sensible 
 heat, and this varies with every different pressure; but it is 
 found that steam contains more heat than is shown by the 
 thermometer, and this extra heat is called the latent heat of 
 steam. 
 
 The following table gives the number of British thermal units 
 in a pound of water at different temperatures below the boiling- 
 point. They are reckoned above 32 F.; for, strictly speaking, 
 water does not exist below 32, and ice follows another law. 
 
 When a solid becomes a liquid or a liquid becomes a vapor 
 heat is absorbed, more than was necessary to raise it to the 
 temperature of conversion; and this latent heat does work in 
 
1112 
 
 HEAT-UNITS IN WATER. 
 
 HEAT-UNITS IN WATER, BETWEEN 32 AND 212 F., 
 AND WEIGHT OF WATER PER CUBIC FOOT. 
 
 Temp. 
 Deg. 
 Fahr. 
 
 Heat- 
 units. 
 
 Weight, 
 Lbs. per 
 Cu. Ft. 
 
 Temp. 
 Deg. 
 Fahr. 
 
 Heat- 
 units. 
 
 Weight, 
 Lbs. per 
 Cu Ft. 
 
 Temp 
 Deg. 
 Fahr. 
 
 Heat- 
 units. 
 
 Weight, 
 Lbs. per 
 Cu. Ft. 
 
 32 
 
 
 
 62.42 
 
 123 
 
 91.16 
 
 61.68 
 
 168 
 
 136.44 
 
 60.81 
 
 35 
 
 3 
 
 62.42 
 
 124 
 
 92.17 
 
 61.67 
 
 169 
 
 137.45 
 
 60.79 
 
 40 
 
 8 
 
 62.42 
 
 125 
 
 93.17 
 
 61.65 
 
 170 
 
 138.45 
 
 60.77 
 
 45 
 
 13 
 
 62.42 
 
 126 
 
 94.17 
 
 61.63 
 
 171 
 
 139.46 
 
 60.75 
 
 50 
 
 18 
 
 62.41 
 
 127 
 
 95.18 
 
 61.61 
 
 172 
 
 140.47 
 
 60.73 
 
 52 
 
 20 
 
 62.40 
 
 128 
 
 96.18 
 
 61.60 
 
 173 
 
 141.48 
 
 60.70 
 
 54 
 
 22.01 
 
 62.40 
 
 129 
 
 97.19 
 
 61.58 
 
 174 
 
 142.49 
 
 60.68 
 
 56 
 
 24.01 
 
 62.39 
 
 130 
 
 98.19 
 
 61.56 
 
 175 
 
 143.50 
 
 60.66 
 
 58 
 
 26.01 
 
 62.38 
 
 131 
 
 99.20 
 
 61.54 
 
 176 
 
 144.51 
 
 60.64 
 
 60 
 
 28.01 
 
 62.37 
 
 132 
 
 100.20 
 
 61.52 
 
 177 
 
 145.52 
 
 60.62 
 
 62 
 
 30.01 
 
 62.36 
 
 133 
 
 101.21 
 
 61.51 
 
 178 
 
 146.52 
 
 60.59 
 
 64 
 
 32.01 
 
 62.35 
 
 134 
 
 102.21 
 
 61.49 
 
 179 
 
 147.53 
 
 60.57 
 
 66 
 
 34.02 
 
 62.34 
 
 135 
 
 103.22 
 
 61.47 
 
 180 
 
 148.54 
 
 60.55 
 
 68 
 
 36.02 
 
 62.33 
 
 136 
 
 104.22 
 
 61.45 
 
 181 
 
 149.55 
 
 60.53 
 
 70 
 
 38.02 
 
 62.31 
 
 137 
 
 105.23 
 
 61.43 
 
 182 
 
 150.56 
 
 60.50 
 
 72 
 
 40.02 
 
 62.30 
 
 138 
 
 106.23 
 
 61.41 
 
 183 
 
 151.57 
 
 60.48 
 
 74 
 
 42.03 
 
 62.28 
 
 139 
 
 107 . 24 
 
 61.39 
 
 184 
 
 152.58 
 
 60.46 
 
 76 
 
 44.03 
 
 62.27 
 
 140 
 
 108.25 
 
 61.37 
 
 185 
 
 153.59 
 
 60.44 
 
 78 
 
 46.03 
 
 62.25 
 
 141 
 
 109.25 
 
 61.36 
 
 186 
 
 154.60 
 
 60.41 
 
 80 
 
 48.04 
 
 62.23 
 
 142 
 
 110.26 
 
 61.34 
 
 187 
 
 155.61 
 
 60.39 
 
 82 
 
 50.04 
 
 62.21 
 
 143 
 
 111.26 
 
 61.32 
 
 188 
 
 156.62 
 
 60.37 
 
 84 
 
 52.04 
 
 62.19 
 
 144 
 
 112.27 
 
 61.30 
 
 189 
 
 157.63 
 
 60.34 
 
 86 
 
 54.05 
 
 62.17 
 
 145 
 
 113.28 
 
 61.28 
 
 190 
 
 158.64 
 
 60.32 
 
 88 
 
 56.05 
 
 62.15 
 
 146 
 
 114.28 
 
 61.26 
 
 191 
 
 159.65 
 
 60.29 
 
 90 
 
 58.06 
 
 62.13 
 
 147 
 
 115.29 
 
 61.24 
 
 192 
 
 160.67 
 
 60.27 
 
 92 
 
 60.06 
 
 62.11 
 
 148 
 
 116.29 
 
 61.22 
 
 193 
 
 161.68 
 
 60.25 
 
 94 
 
 62.06 
 
 62.09 
 
 149 
 
 117.30 
 
 61.20 
 
 194 
 
 162.69 
 
 60.22 
 
 96 
 
 64.07 
 
 62.07 
 
 150 
 
 118.31 
 
 61.18 
 
 195 
 
 163.70 
 
 60.20 
 
 98 
 
 66.07 
 
 62.05 
 
 151 
 
 119.31 
 
 61.16 
 
 196 
 
 164.71 
 
 60.17 
 
 100 
 
 68.08 
 
 62.02 
 
 152 
 
 120.32 
 
 61.14 
 
 197 
 
 165.72 
 
 60.15 
 
 102 
 
 70.09 
 
 62.00 
 
 153 
 
 121.33 
 
 61.12 
 
 198 
 
 166.73 
 
 60.12 
 
 104 
 
 72.09 
 
 61.97 
 
 154 
 
 122.33 
 
 61.10 
 
 199 
 
 167.74 
 
 60.10 
 
 106 
 
 74.10 
 
 61.95 
 
 155 
 
 123.34 
 
 61.08 
 
 200 
 
 168.75 
 
 60.07 
 
 108 
 
 76.10 
 
 61.92 
 
 156 
 
 124.35 
 
 61.06 
 
 201 
 
 169.77 
 
 60.05 
 
 110 
 
 78.11 
 
 61.89 
 
 157 
 
 125.35 
 
 61.04 
 
 202 
 
 170.78 
 
 60.02 
 
 112 
 
 80.12 
 
 61.86 
 
 158 
 
 126.36 
 
 61.02 
 
 203 
 
 171.79 
 
 60.00 
 
 114 
 
 82.13 
 
 61.83 
 
 159 
 
 127.37 
 
 61.00 
 
 204 
 
 172.80 
 
 59.97 
 
 115 
 
 83.13 
 
 61.82 
 
 160 
 
 128.37 
 
 60.98 ! 
 
 205 
 
 173.81 
 
 59.95 
 
 116 
 
 84.13 
 
 61.80 
 
 161 
 
 129.38 
 
 60.96 j 
 
 206 
 
 174.83 
 
 59.92 
 
 117 
 
 85.14 
 
 61.78 
 
 162 
 
 130.39 
 
 60.94 
 
 207 
 
 175.84 
 
 59.89 
 
 118 
 
 86.14 
 
 61.77 
 
 163 
 
 131.40 
 
 60.92 
 
 208 
 
 176.85 
 
 59.87 
 
 119 
 
 87.15 
 
 61.75 
 
 164 
 
 132.41 
 
 60.90 
 
 209 
 
 177.86 
 
 59.84 
 
 120 
 
 88.15 
 
 61.74 
 
 165 
 
 133.41 
 
 60.87 
 
 210 
 
 178.87 
 
 59.82 
 
 121 
 
 89.15 
 
 61.72 
 
 166 
 
 134.42 
 
 60.85 
 
 211 
 
 179.89 
 
 59.79 
 
 122 
 
 90.16 
 
 61.70 
 
 167 
 
 135.48 
 
 60.83 
 
 212 
 
 180.90 
 
 59.76 
 
 the destruction of the force of cohesion and other changes 
 which take place, and must be absorbed from some other sub- 
 stance. In the case of steam in a boiler, it comes from the 
 fuel during combustion. When steam or vapor is condensed, 
 this same quantity of heat that was received, from whatever 
 source, is again given off to any substance within its influence 
 air, water, iron pipes, etc. colder than itself; and it is this 
 property, together with its great power of absorbing and re- 
 
PROPERTIES OF STEAM. 1113 
 
 taining heat, which makes water and its vapor such a valuable 
 medium for conveying heat from the furnace to the rooms to 
 be warmed. 
 
 The specific heat (or heat-absorbing capacity) of water is not 
 constant, but rises in an increasing ratio with the temperature; 
 so that it requires more heat the higher the temperature to 
 raise a given quantity of water from one temperature to another. 
 Thus, the specific heat at 32 being 1, at 212 it is 1.013, and 
 at 320 (the temperature of 75 Ibs. steam pressure) it is 1.0294. 
 The amount of heat rendered latent by each pound of water in 
 becoming steam varies at different pressures, decreasing as the 
 pressure increases. This latent heat, added to the sensible heat 
 (or thermometric temperature), constitutes the " total heat." 
 The " total heat" being greater as the pressure increases, it will 
 take more heat, and consequently more fuel, to make a pound 
 of steam the higher the pressure. 
 
 The table given on the following page shows the properties of 
 steam at different pressures, from 1 Ib. to 400 Ibs. "total pres- 
 sure"; i.e., above vacuum. 
 
 The gauge pressure is about 15 Ibs. less than the total pressure; 
 so that, in using this table, 15 must be added to the pressure 
 as given by the steam-gauge. 
 
 The column of "Temperatures" gives the thermometric tem- 
 perature of steam and boiling-point at each pressure. 
 
 The "Factor of Equivalent Evaporation" shows the propor- 
 tionate cost, in heat or fuel, of producing steam at the given 
 pressure, as compared with atmospheric pressure. To ascertain 
 the equivalent evaporation at any pressure, multiply the given 
 evaporation by the factor of its pressure and divide the quotient 
 by the factor of the desired pressure. 
 
 Each degree of difference in temperature of feed-water makes 
 a difference of 0.00104 in the amount of evaporation. Hence, 
 to ascertain the equivalent evaporation from any other tem- 
 perature of feed than 212, add to the factor given as many 
 times 0.00104 as the temperature of feed-water is degrees below 
 212. 
 
 For other pressures than those given in the table, it will be 
 practically correct to take the proportion of the difference 
 bet ween 'the nearest pressures given in the table. 
 
 Air. Air is a mechanical mixture of oxygen and nitrogen, 
 the proportion for pure air being 77 per cent, of nitrogen and 
 23 per cent, of oxygen by weight. It also contains about - 
 
1114 PROPERTIES OF STEAM. 
 
 TABLE OF PROPERTIES OF SATURATED STEAM.* 
 
 
 
 , 
 
 + 
 
 
 
 
 cS 
 
 Ll 
 
 
 "c3 0> 
 
 OJ 
 
 -g 
 
 
 o S*o 
 
 ,2g 
 
 1 
 
 .s 
 
 w| 
 
 fl 
 
 a 
 
 Ig 
 
 
 
 lie 
 
 r . 
 
 g c & 
 
 So 
 
 |.-fl 
 
 ""' _j 
 
 -u 
 
 i?*"! 
 
 OOQ 
 
 'o e *-' 
 
 iS'ocs 
 
 "3 3 
 
 fl 
 
 !S 
 
 !. 
 
 '55 r-4 
 
 11 
 
 >g 
 
 'if -el 
 
 -si* 
 
 ifl 
 
 H 50 
 
 JfiB 
 
 |h 
 
 11 
 
 5 
 
 |<8 
 
 i-S 3 O^ 
 
 &o& 
 
 !* 
 
 1 
 
 102 
 
 1113.05 
 
 1042.964 
 
 0.0030 
 
 330.36 
 
 20620 
 
 0.965 
 
 2 
 
 126.266 
 
 1120.45 
 
 1026.010 
 
 0.0058 
 
 172.08 
 
 10720 
 
 0.972 
 
 3 
 
 141.622 
 
 1125.131 
 
 1015.254 
 
 0.0085 
 
 117.52 
 
 7326 
 
 0.977 
 
 4 
 
 153.070 
 
 1128.625 
 
 1007.229 
 
 0.0112 
 
 89.62 
 
 5600 
 
 0.981 
 
 5 
 
 162.330 
 
 1131.449 
 
 1000.727 
 
 0.0137 
 
 72.66 
 
 4535 
 
 0.984 
 
 6 
 
 170.123 
 
 1133.826 
 
 995.249 
 
 0.0163 
 
 61.21 
 
 3814 
 
 0.986 
 
 7 
 
 176.910 
 
 1135.896 
 
 990.471 
 
 0.0189 
 
 52.94 
 
 3300 
 
 0.988 
 
 8 
 
 182.910 
 
 1137.726 
 
 986.245 
 
 0.0214 
 
 46.69 
 
 2910 
 
 0.990 
 
 9 
 
 188.316 
 
 1139.375 
 
 982.434 
 
 0.0239 
 
 41.79 
 
 2607 
 
 0.992 
 
 10 
 
 193.240 
 
 1140.877 
 
 978.958 
 
 0.0264 
 
 31.84 
 
 2360 
 
 0.994 
 
 15 
 
 213.025 
 
 1146.912 
 
 964.973 
 
 0.0387 
 
 25.85 
 
 1612 
 
 1.000 
 
 20 
 
 227.917 
 
 1151.454 
 
 954.415 
 
 0.0511 
 
 19.72 
 
 1220.3 
 
 1.005 
 
 25 
 
 240.000 
 
 1155.139 
 
 945.825 
 
 . 0634 
 
 15.99 
 
 984.8 
 
 1.008 
 
 30 
 
 250.245 
 
 1158.263 
 
 938.925 
 
 0.0755 
 
 13.46 
 
 826.8 
 
 1.012 
 
 35 
 
 259.176 
 
 1160.987 
 
 932.152 
 
 0.0875 
 
 11.65 
 
 713.4 
 
 1.015 
 
 40 
 
 267 . 120 
 
 1163.410 
 
 926.472 
 
 0.0994 
 
 10.27 
 
 628.2 
 
 1.017 
 
 45 
 
 274.296 
 
 1165.600 
 
 921 . 334 
 
 0.1111 
 
 9.18 
 
 561.8 
 
 1.017 
 
 50 
 
 280.854 
 
 1167.600 
 
 916.631 
 
 0.1227 
 
 8.31 
 
 508.5 
 
 1.021 
 
 55 
 
 286.897 
 
 1169.442 
 
 912.290 
 
 0.1343 
 
 7.61 
 
 464.7 
 
 1.023 
 
 60 
 
 292.520 
 
 1171.158 
 
 908.247 
 
 0.1457 
 
 7.01 
 
 428.5 
 
 .025 
 
 65 
 
 297.777 
 
 1172.762 
 
 904.462 
 
 0.1569 
 
 6.49 
 
 397.7 
 
 .027 
 
 70 
 
 302.718 
 
 1174.269 
 
 900.899 
 
 0.1681 
 
 6.07 
 
 371.2 
 
 .028 
 
 75 
 
 307.388 
 
 1175.692 
 
 897.526 
 
 0.1792 
 
 5.68 
 
 348.3 
 
 .030 
 
 80 
 
 311.812 
 
 1177.042 
 
 894.330 
 
 0.1901 
 
 5.35 
 
 328.3 
 
 .031 
 
 85 
 
 316.021 
 
 1178.326 
 
 891.286 
 
 0.2010 
 
 5.05 
 
 310.5 
 
 .033 
 
 90 
 
 320.039 
 
 1179.551 
 
 888.375 
 
 0.2118 
 
 4.79 
 
 294.7 
 
 .034 
 
 95 
 
 323.884 
 
 1180.724 
 
 885.588 
 
 . 2224 
 
 4.55 
 
 280.6 
 
 .035 
 
 100 
 
 327.571 
 
 1181.849 
 
 883.914 
 
 0.2330 
 
 4.33 
 
 267.9 
 
 .036 
 
 105 
 
 331.113 
 
 1182.929 
 
 880 . 342 
 
 . 2434 
 
 4.14 
 
 265.5 
 
 .037 
 
 110 
 
 334.523 
 
 1183.970 
 
 877.865 
 
 0.2537 
 
 3.97 
 
 246.0 
 
 .038 
 
 115 
 
 337.814 
 
 1184.974 
 
 875.472 
 
 0.2640 
 
 3.80 
 
 236.3 
 
 1.039 
 
 120 
 
 340.995 
 
 1185.944 
 
 873.155 
 
 0.2742 
 
 3.65 
 
 227.6 
 
 1.040 
 
 125 
 
 344.074 
 
 1186.883 
 
 870.911 
 
 0.2842 
 
 3.51 
 
 219.7 
 
 1.D41 
 
 130 
 
 347.059 
 
 1187.794 
 
 868.735 
 
 0.2942 
 
 3.38 
 
 212.3 
 
 1.042 
 
 140 
 
 352.757 
 
 1189.535 
 
 864.566 
 
 0.3138 
 
 3.16 
 
 199.0 
 
 1.044 
 
 150 
 
 358.161 
 
 1191.180 
 
 860.621 
 
 0.3340 
 
 2.96 
 
 187.5 
 
 1.046 
 
 160 
 
 363 . 277 
 
 1192.741 
 
 856.874 
 
 0.3520 
 
 2.79 
 
 177.3 
 
 1.047 
 
 170 
 
 368.158 
 
 1194.228 
 
 853.294 
 
 0.3709 
 
 2.63 
 
 168.4 
 
 1.049 
 
 180 
 
 372.822 
 
 1195.650 
 
 849.869 
 
 0.3889 
 
 2.49 
 
 160.4 
 
 1.051 
 
 190 
 
 377.291 
 
 1197.013 
 
 846.584 
 
 0.4072 
 
 2.37 
 
 153.4 
 
 1.052 
 
 200 
 
 381.573 
 
 1198.319 
 
 843.432 
 
 0.4249 
 
 2.26 
 
 147.1 
 
 1.053 
 
 250 
 
 401.072 
 
 1203.735 
 
 831.222 
 
 0.5464 
 
 1.83 
 
 114 
 
 1.059 
 
 300 
 
 418.225 
 
 1208.737 
 
 819.610 
 
 0.6486 
 
 1.54 
 
 96 
 
 1.064 
 
 350 
 
 431.956 
 
 1212.580 
 
 810.690 
 
 0.7498 
 
 1.33 
 
 83 
 
 1.068 
 
 400 
 
 444.919 
 
 1217.094 
 
 800.198 
 
 0.8502 
 
 1.18 
 
 73 
 
 1.073 
 
 of its volume of carbonic-acid gas and some watery vapor, and 
 is capable of absorbing any other gas or vapor to a certain 
 extent, distributing them through the whole atmosphere by 
 
 * Steam, 14th ed. Babcock & Wilcox Company, New York and Glasgow. 
 
PROPERTIES OF AIR. 1115 
 
 what is called the law of diffusion of gases, a property which 
 gases have of mixing and diluting, which prevents gases of 
 different specific gravities from stratifying for any considerable 
 time. This property is of the utmost importance to air; for, 
 if any noxious or poisonous gas were to remain separated in 
 the atmosphere, any one breathing it would be instantly killed. 
 
 Air at 60 F., and with the barometer at 30 ins., is taken as 
 the standard for the comparison of the weight of gases, itself 
 being considered as unity. 
 
 At the temperature of 32, 13J cu. ft. of air weigh a few 
 grains over 1 Ib. avoirdupois. 
 
 The expansion of air is nearly uniform at all temperatures, 
 expanding about Jo of its bulk at 32 and for. each increase oj: 
 one degree in temperature. 
 
 The table on the following page, giving the volume and weight 
 of dry air, tension and weight of vapor, etc., will be found use- 
 ful for reference. In this table 1,000 cu. ft. of dry air is taken 
 for a unit, and the coefficient of expansion is taken at ffo, the 
 air being under constant pressure of 30 ins. of mercury. 
 Column 5 is taken from Guyot's tables, Regnault's data. 
 
 Watery Vapor in the Atmosphere. Air is capable 
 of holding or absorbing a certain quantity of vapor of water, the 
 proportion depending on the temperature of the air. 
 
 The warmer it is the larger quantity it will hold, and as it 
 becomes cool again, it deposits it, or forms clouds or fogs which 
 condense on anything colder than the air, leaving the air, upon 
 raising its temperature, capable of taking up more moisture, 
 to be again deposited in dew or rain. It is this property of air 
 which gives it its drying qualities. 
 
 An absolutely dry atmosphere is almost an impossibility. 
 Air at 32 contains, when saturated with moisture, T J^ of its 
 weight of water; at 59 it contains /Q-; at 86 it contains ^; its 
 capacity for moisture being doubled by each increase of 27 F. 
 
 Air is said to be " saturated 1 ' when it has absorbed all the 
 water it will hold at that temperature. The tension of vapors 
 is the elastic force or pressure which they exert on the sides of 
 vessels in which they are contained. 
 
 Air, to be healthful, should contain about 75 per cent, of the 
 moisture required for saturation. 
 
 It requires more heat to raise the temperature of a given 
 quantity of moist air 1 than for dry air; but unless the air is 
 saturated this difference is not of much practical importance. 
 
1116 
 
 PROPERTIES OF AIR. 
 
 VOLUME AND WEIGHT OF AIR AND WEIGHT OF 
 VAPOR IN SATURATED AIR. 
 
 
 
 
 
 
 Weight of 
 
 W'ghtof 
 
 Tem- 
 pera- 
 ture. 
 
 Volume. 
 
 Number of 
 Cubic Feet 
 to 1 Pound. 
 
 Weight of 
 1,000 
 Cubic Feet 
 Dry Air. 
 
 Tension of 
 Vapor. 
 
 Vapor 
 Saturated 
 in 1,000 
 CubicFeet. 
 
 Air Dis- 
 placed 
 by 
 Vapor. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 
 
 0.9340 
 
 11.460 
 
 87 . 260 
 
 0.04379 
 
 0.07930 
 
 0.1264 
 
 5 
 
 0.9449 
 
 11.591 
 
 86.289 
 
 0.05747 
 
 0.10289 
 
 0.1646 
 
 10 
 
 0.9551 
 
 11.726 
 
 85.251 
 
 0.07116 
 
 0.12588 
 
 0.2014 
 
 15 
 
 0.9653 
 
 11.869 
 
 84.317 
 
 . 08535 
 
 0.14932 
 
 . 2389 
 
 20 
 
 0.9755 
 
 11.992 
 
 88.403 
 
 0.10748 
 
 0.18180 
 
 0.2909 
 
 25 
 
 0.9857 
 
 12.125 
 
 82.440 
 
 0.13367 
 
 0.22871 
 
 0.3661 
 
 30 
 
 0.9959 
 
 12.258 
 
 81.566 
 
 0.16581 
 
 0.27491 
 
 0.4398 
 
 r32 
 
 1.0000 
 
 12.311 
 
 81.235 
 
 0.17989 
 
 0.29633 
 
 0.4741 
 
 36 
 
 1.0082 
 
 12.417 
 
 80.515 
 
 0.21066 
 
 0.35201 
 
 0.5632 
 
 40 
 
 1.0163 
 
 12.523 
 
 79.872 
 
 0.24604 
 
 0.40770 
 
 0.6523 
 
 44 
 
 1.0244 
 
 12.629 
 
 79.176 
 
 0.28647 
 
 0.47070 
 
 . 0.7531 
 
 48 
 
 1.0326 
 
 12.735 
 
 78.493 
 
 0.33284 
 
 0.54204 
 
 0.8672 
 
 52 
 
 1.0408 
 
 12.841 
 
 77.825 
 
 0.38574 
 
 . 62282 
 
 0.9965 
 
 56 
 
 1.0489 
 
 12.947 
 
 77 . 220 
 
 0.44352 
 
 0.71063 
 
 1.1370 
 
 60 
 
 1.0571 
 
 13.053 
 
 76.628 
 
 0.51683 
 
 0.82173 
 
 1.3147 
 
 64 
 
 1.0652 
 
 13.159 
 
 75.988 
 
 . 59229 
 
 0.93390 
 
 1.4943 
 
 68 
 
 1.0734 
 
 13.265 
 
 75.357 
 
 0.67994 
 
 1.0631 
 
 1.7008 
 
 72 
 
 1.0816 
 
 13.371 
 
 74.794 
 
 0.78018 
 
 1.21050 
 
 1.9368 
 
 76 
 
 1.0897 
 
 13.477 
 
 74.184 
 
 0.89103 
 
 1.31715 
 
 2.1076 
 
 80 
 
 1.0979 
 
 13.583 
 
 73.638 
 
 1.01669 
 
 1.5540 
 
 2.4864 
 
 84 
 
 1.1060 
 
 13.689 
 
 73.046 
 
 1 . 15705 
 
 1.7536 
 
 2.8058 
 
 88 
 
 1.1142 
 
 13.795 
 
 72.464 
 
 1.31554 
 
 1.9772 
 
 3.1635 
 
 92 
 
 1 . 1223 
 
 13.901 
 
 71.942 
 
 1.49067 
 
 2.2257 
 
 3.5611 
 
 96 
 
 1 . 1305 
 
 14.007 
 
 71.377 
 
 1.69214 
 
 2:5060 
 
 4.0096 
 
 100 
 
 1 . 1387 
 
 .14.113 
 
 70.872 
 
 1.91937 
 
 2.8220 
 
 4.5152 
 
 104 
 
 1 . 1468 
 
 14.219 
 
 70.323 
 
 2.14669 
 
 3.133 
 
 5.0138 
 
 108 
 
 1 . 1550 
 
 14.325 
 
 69.784 
 
 2.43323 
 
 3.523 
 
 5.6368 
 
 112 
 
 1.1631 
 
 14.431 
 
 69 . 300 
 
 2.72984 
 
 3.926 
 
 6.2826 
 
 116 
 
 1.1713 
 
 14.537 
 
 68.776 
 
 3.05954 
 
 4.367 
 
 6.9882 
 
 120 
 
 1 . 1794 
 
 14.643 
 
 68.306 
 
 3.41728 
 
 4.843 
 
 7.7488 
 
 124 
 
 1 . 1876 
 
 14.749 
 
 67.797 
 
 3.81775 
 
 5.371 
 
 8.5940 
 
 128 
 
 1.1957 
 
 14.855 
 
 67.295 
 
 4.26073 
 
 6.088 
 
 9.7430 
 
 132 
 
 1 . 2039 
 
 14.961 
 
 66.845 
 
 4.72888 
 
 6.559 
 
 10.4950 
 
 136 
 
 1.2121 
 
 15.067 
 
 66.357 
 
 5.25807 
 
 7.240 
 
 11.584 
 
 140 
 
 1 . 2202 
 
 15.173 
 
 65.919 
 
 5.81736 
 
 7.957 
 
 12.731 
 
 144 
 
 1.2284 
 
 15.279 
 
 65.442 
 
 6.48029 
 
 8.800 
 
 14.048 
 
 148 
 
 1.2365 
 
 15.385 
 
 64.977 
 
 7 . 14323 
 
 9.630 
 
 15.408 
 
 152 
 
 1.2447 
 
 15.491 
 
 64.568 
 
 7.9104 
 
 10.595 
 
 16.952 
 
 156 
 
 1.2528 
 
 15.597 
 
 64.102 
 
 8.6923 
 
 11.566 
 
 18.506 
 
 160 
 
 1.2610 
 
 15.703 
 
 63.69 
 
 9 . 5948 
 
 12.681 
 
 20.290 
 
 164 
 
 .2691 
 
 15.809 
 
 63.251 
 
 10.5579 
 
 13.828 
 
 22.125 
 
 168 
 
 .2773 
 
 15.915 
 
 62.814 
 
 11.4673 
 
 14.950 
 
 23.920 
 
 172 
 
 .2855 
 
 16.021 
 
 62.422 
 
 12.7165 
 
 16.47 
 
 26.36 
 
 176 
 
 .2936 
 
 16.127 
 
 61.996 
 
 13.8657 
 
 17.43 
 
 27.89 
 
 180 
 
 .3018 
 
 16.233 
 
 61.614 
 
 15 . 2343 
 
 19.47 
 
 31.96 
 
 184 
 
 .3099 
 
 16.339 
 
 61 . 200 
 
 16.6030 
 
 21.08 
 
 33.73 
 
 188 
 
 1.3181 
 
 16.445 
 
 60.790 
 
 18.1447 
 
 22.89 
 
 36.63 
 
 192 
 
 1 . 3262 
 
 16.551 
 
 60.423 
 
 19.7441 
 
 24.75 
 
 39.60 
 
 196 
 
 1.3344 
 
 16.657 
 
 60.024 
 
 21.4297 
 
 26.69 
 
 42.71 
 
 200 
 
 1.3426 
 
 16.763 
 
 59.666 
 
 23 . 2962 
 
 28.85 
 
 46.16 
 
 Columns 6 and 7 of the above table give the weight of 
 vapor in 1,000 cu. ft. of saturated air, and the weight of dis- 
 placed air, for different temperatures from to 200. 
 
PROPERTIES OF AIR. 1117 
 
 The numbers in column 6 are obtained by multiplying the 
 corresponding numbers in column 4 by column 5 and the 
 product by -ff-. Column 7 is obtained from column 6 by 
 multiplying the values in column 6 by f . 
 
 Specific Heat of Air. The specific heat of any sub- 
 stance is the quantity of heat required to raise its temperature 
 1 compared with the quantity of heat required to raise the 
 temperature of 1 Ib. of water at the same temperature 1. 
 The specific heat of air, as determined by Regnault, is 0.2374. 
 Hence one thermal unit will raise the temperature of 1 Ib. of 
 water or 4J Ibs. of dry air (equals 51.7 cu. ft. at 32 F.) 1 F. 
 As all air contains more or less moisture, which must also be 
 warmed, 50 cu. ft. is generally considered as' the equivalent 
 of 1 Ib. of water in heating. 
 
 As 1 Ib. of steam at (gauge) pressure condensed to water 
 gives off 965 thermal units, it is therefore equivalent to warm- 
 ing about 48,000 cu. ft. of air 1. 
 
 Drying by Steam.* 
 
 There are three modes of drying by steam: 1st, by bringing 
 wet substances in direct contact with steam-heated surfaces, 
 as by passing cloth or paper over steam-heated cylinders, or 
 clamping veneers between steam-heated plates; 2d, by radiated 
 heat from steam-pipes, as in some lumber-kilns and laundry 
 drying-rooms; 3d, by causing steam-heated air to pass over 
 wet surfaces, as in glue- works, etc. 
 
 The second is rarely used except in combination with the 
 third. 
 
 The first is most economical, the second less so, and the third 
 least. Under favorable circumstances it may be estimated 
 that 1 horse-power of steam will evaporate 24 Ibs. of water 
 by the first method, 20 by the second ; and 15 by the third. 
 
 The philosophy of drying or evaporating moisture by heated 
 air rests upon the fact that the capacity of air for moisture is 
 rapidly increased by rise in temperature. If air at 52 is heated 
 to 72, its capacity for moisture is doubled, and is four times 
 what it was at 32. The following table gives the weight of a 
 saturated mixture of air and aqueous vapor at different tem- 
 peratures up to 160, the practical limit of heating air by steam, 
 together with the weight of vapor in pounds and percentage, 
 and total heat, with the portion thereof contained in the vapor: 
 
 * From Steam. Babcock & Wilcox Company, 
 
1118 PROPERTIES OF AIR. 
 
 SATURATED MIXTURES OF AIR AND AQUEOUS VAPOR, 
 
 
 
 *.* 
 
 P 
 
 * 
 
 
 
 
 S K 
 
 
 i 
 
 
 **" 
 
 n 
 
 fflS 09 
 
 1 
 
 II 
 
 1 
 
 * 
 
 o"". 
 
 fe as 
 
 "i 
 
 8| 
 
 <| 
 
 8"1 
 
 "0*0 &H 
 
 gj 
 
 *8S 
 
 II 
 
 w 
 
 % 
 
 |l 
 
 C-3 . 
 
 Jg| 
 
 . 
 
 . ^ 
 
 II 
 
 w 
 
 Sfe 
 
 -P c 
 
 .^ 3.5 
 
 i 
 
 *s ^ 
 
 sa 
 
 |w 
 
 ^^ 
 
 3 a 
 
 t< 
 
 : 3j 
 
 ^& 
 
 a 
 
 jlvg 
 
 Sj'jD 
 
 33 
 
 1^ 
 
 6^ 
 
 S l 
 
 i)^ 1 
 
 'ES'g 
 
 3S 
 
 I 
 
 cS^ 
 
 || 
 
 |5l 
 
 '*s ^ 
 
 j; 
 
 |3 
 
 s 
 
 || 
 
 | 
 
 |S5 
 
 M 
 
 pu,' M 
 
 1^ 
 
 IS* 
 
 35 
 40 
 
 8.004 
 7.92a 
 
 0.034 
 0.041 
 
 0.42 
 0.52 
 
 42.8 
 59.8 
 
 86.69 
 76.59 
 
 100 
 105 
 
 6.924 
 6.830 
 
 0.283 
 0.325 
 
 4.08 
 4.76 
 
 422.01 74. 58 
 474.7 76.22 
 
 45 
 
 7.834 
 
 0.049 0.62 
 
 77.7168.98 
 
 110 
 
 6.741 
 
 0.373 
 
 5.23 
 
 533.9 
 
 77.88 
 
 50 
 
 7.752 
 
 0.059 0.76 
 
 97.6J66.29 
 
 115 
 
 6.650 
 
 0.426 
 
 6.41 
 
 599.1 
 
 79.52 
 
 55 
 
 7.688 
 
 0.070 
 
 0.91 
 
 118.3 
 
 64.58 
 
 120 
 
 6.551 
 
 0.488 
 
 7.46 
 
 672.4 
 
 81.14 
 
 60 
 
 7.589 
 
 0.082 
 
 1.08 
 
 140.1 
 
 64.31 
 
 125 
 
 6.454 
 
 0.554 
 
 8.55 
 
 750.5 
 
 82.62 
 
 65 
 
 7.507 
 
 0.097 
 
 1.29 
 
 164.9 
 
 64.76 
 
 130 
 
 6.347 
 
 0.630 
 
 9.90 
 
 839.4 
 
 84.13 
 
 70 
 
 7.425 
 
 0.114 
 
 1.49 
 
 189.7 
 
 66.21 
 
 135 
 
 6.238 
 
 0.714 
 
 11.44 
 
 936.7 
 
 85.57 
 
 75 
 
 7.342 
 
 0.134 
 
 1.79 
 
 221.6 
 
 66.74 
 
 140 
 
 6.131 
 
 0.806 
 
 13.14 
 
 1042.7 
 
 86.89 
 
 80 
 
 7.262 
 
 0.156 
 
 2.15 
 
 253.6 
 
 68.02 
 
 145 
 
 6.015 
 
 0.909 
 
 15.11 
 
 1160.6 
 
 88.18 
 
 85 
 
 7.178 
 
 0.182 
 
 2.54 
 
 289.7 
 
 69.66 
 
 150 
 
 5.891 
 
 1.022 
 
 17.33 
 
 1288.4 
 
 89.39 
 
 90 
 
 7.108 
 
 0.212 
 
 2.98 
 
 330.2 
 
 71.19 
 
 155 
 
 5.764 
 
 1 . 145 
 
 19.88 
 
 1427.4 
 
 90.53 
 
 95 
 
 7.009 
 
 0.245 
 
 3.50 
 
 373.4 
 
 72.87 
 
 160 
 
 5.679 
 
 1.333 
 
 23.47 
 
 1638.7 
 
 91.93 
 
 By inspection of above table, it will be seen why it is more 
 economical to dry at the higher temperatures. The atmosphere 
 is seldom saturated with moisture, and in practice it will be 
 found generally necessary to heat the air about 30 above the 
 temr>erature of saturation. Drying on a large scale is now 
 accomplished almost entirely by the " hot-blast" system of 
 heating, details of which may be obtained from the American 
 Blower Company, Buffalo Forge Company, or the B. F. Sturte- 
 vant Company. 
 
 COMPARISON OP THERMOMETERS. 
 
 To convert the degrees of different thermometers from one into 
 the other, use the following formulas: 
 F stands for degrees of Fahrenheit, or 212 
 C " " " " Celsius,* " 100 boiling-point. 
 R " " " " Reaumur, " 80 
 
 +32, and 
 
 Q7? 
 
 Ei_32, and 
 
 4 
 
 ^= + 32 for degrees above freezing-point. 
 
 Qr' 
 
 = ~- 32 for degrees below freezing-point. 
 5 
 
 * Often called Centigrade. 
 
DIFFERENT COLORS OF IRON CAUSED BY HEAT. 1119 
 
 , and H= 
 
 , . , 
 
 for degrees above freezing-point. 
 
 ) 4(32-^), , , . , 
 
 , and R - - - ' for degrees below freezing-point. 
 
 Degrees Fahr. below zero should be given the sign. 
 Zero of Celsius or Reaumur =+32 Fahrenheit. Zero of 
 Fahrenheit = - 17 ; 77 -C, or -14.22 R. 
 
 Ex. 1. How much is 8 Celsius above zero,* in Fahrenheit? 
 
 +32 = 14.4 + 32 = 46.4 above. 
 o 
 
 Ex. 2. How much is 8 Celsius below zero, in Fahrenheit? 
 Q V8 
 
 ^=^p-32== 14.4-32 = 17.6 above. 
 o 
 
 IN CASES WHERE THE PRODUCT IS SMALLER THAN 32, IT INDI- 
 CATES THAT THE DEGREE IS ABOVE ZERO OF FAHRENHEIT; SEE 
 EXAMPLE 2. 
 
 Ex. 3. How much is 19 Celsius below zero, in Fahrenheit? 
 
 F =^i5 _ 32 = 34.2 -32 = 2.2 below Fahrenheit. 
 o 
 
 DIFFERENT COLORS OF IRON CAUSED BY HEAT. 
 
 [Pouillet.] 
 
 C. 
 
 Fahr. 
 
 Color. 
 
 210 
 
 221 
 
 256 
 
 261 
 370 
 
 500 
 
 525 
 
 700 
 
 800 
 
 900 
 
 1000 
 
 1100 
 
 1200 
 
 1300 
 
 1400 
 
 1500 
 
 1600 
 
 410 
 
 430 
 
 493 
 
 502) 
 680) 
 
 932 
 
 977 
 1292 
 1472 
 1657 
 1832 
 2012 
 2192 
 2372 
 2552 
 2732 
 2912 
 
 Pale yellow 
 Dull yellow 
 Crimson 
 
 {Violet, purple, and dull blue; between 261 and 
 370 C. it passes to bright blue, to sea-green, 
 and then disappears 
 
 Commences to be covered with a light coating 
 of oxide, loses a good deal of its hardness, 
 becomes a good deal more impressible to the 
 hammer, and can be twisted with ease 
 
 Becomes nascent red 
 
 Sombre red 
 
 Nascent cherry 
 
 Cherry 
 
 Bright cherry 
 
 Dull orange 
 
 Bright orange 
 
 White 
 
 Brilliant white, welding heat 
 
 { Dazzling white 
 
1120 
 
 EXPANSION BY HEAT. 
 
 LINEAL EXPANSION OF SOLIDS AT ORDINARY TEM- 
 PERATURES. 
 
 (British Board of Trade; from Clark.) 
 
 
 
 For 
 1 Fahr. 
 
 For 
 1 Cent. 
 
 Coef. 
 of 
 Expan- 
 sion 
 from 
 32 to 
 212 F. 
 
 Accord- 
 ing to 
 Other 
 Author- 
 ities. 
 
 Aluminium (cast) . 
 
 Length = 1 
 00001234 
 
 Length = 1 
 00002221 
 
 002221 
 
 
 
 00000627 
 
 .00001129 
 
 .001129 
 
 .001083 
 
 Brass, cast . 
 
 00000957 
 
 00001722 
 
 .001722 
 
 001868 
 
 " plate. . . 
 
 00001052 
 
 .00001894 
 
 .001894 
 
 
 Brick 
 
 00000306 
 
 00000550 
 
 . 000550 
 
 
 Bronze (Cu, 17; Sn,2>; Z, 1) 
 Bismuth 
 
 .00000986 
 . 00000975 
 
 .00001774 
 .00001755 
 
 .001774 
 .001755 
 
 .001392 
 
 Cement, Portland (mixed), pure. . 
 Concerte: cement, mortar, and 
 pebbles . 
 
 .00000594 
 00000795 
 
 .00001070 
 00001430 
 
 .001070 
 001430 
 
 
 Copper 
 
 00000887 
 
 00001596 
 
 .001596 
 
 .001718 
 
 Ebonite 
 
 . 00004278 
 
 . 00007700 
 
 .007700 
 
 
 Glass, English flint. . . 
 
 00000451 
 
 00000812 
 
 .000812 
 
 
 
 . 00000499 
 
 . 00000897 
 
 .000897 
 
 
 
 . 00000397 
 
 .00000714 
 
 .000714 
 
 
 
 00000438 
 
 . 00000789 
 
 .C00789 
 
 
 
 . 00000498 
 
 . 00000897 
 
 .000897 
 
 
 Gold, pure 
 
 00000786 
 
 00001415 
 
 .001415 
 
 
 
 . 00000356 
 
 .00000641 
 
 .000641 
 
 
 Iron, wrought 
 
 00000648 
 
 00001166 
 
 .001166 
 
 .001235 
 
 
 00000556 
 
 00001001 
 
 .001001 
 
 .001110 
 
 Lead 
 
 00001571 
 
 00002828 
 
 .002828 
 
 
 Magnesium 
 
 
 
 
 . 002694 
 
 tr i_i 1 from 
 
 00000308 
 
 00000554 
 
 000554 
 
 
 Marbles, vanous < , 
 
 00000786 
 
 00001415 
 
 .001415 
 
 
 ,_ , . . ( from . * 
 
 00000256 
 
 00000460 
 
 000460 
 
 
 Masonry, brick -j J. m 
 
 00000494 
 
 00000890 
 
 .000890 
 
 
 Mercury (cubic expansion) . . 
 
 00009984 
 
 00017971 
 
 .017971 
 
 .018018 
 
 Nickel 
 
 .00000695 
 
 .00001251 
 
 .001251 
 
 .001279 
 
 Pewter 
 
 .00001129 
 
 . 00002033 
 
 .002033 
 
 
 Plaster, white . . 
 
 00000922 
 
 00001660 
 
 .001660 
 
 
 Platinum 
 
 . 00000479 
 
 . 00000863 
 
 .000863 
 
 
 Platinum, 85 per cent. ? 
 
 00000453 
 
 00000815 
 
 .000815 
 
 . 000884 
 
 Iridium, 15 " f ' * 
 Porcelain 
 
 . 00000200 
 
 00000360 
 
 .000360 
 
 
 Quartz, parallel to major axis, t 
 to 40 C 
 
 00000434 
 
 00000781 
 
 .000781 
 
 
 Quartz, perpendicular to major 
 axis, t to 40 C 
 
 00000788 
 
 00001419 
 
 .001419 
 
 
 Silver pure 
 
 00001079 
 
 00001943 
 
 .001943 
 
 .001908 
 
 Slate. . . 
 
 00000577 
 
 00001038 
 
 .001038 
 
 
 Steel, cast . 
 
 00000636 
 
 00001144 
 
 .001144 
 
 .001079 
 
 tempered 
 
 00000689 
 
 00001240 
 
 .001240 
 
 
 Stone (sandstone), dry 
 
 00000652 
 
 00001174 
 
 .001174 
 
 
 " " Rauville 
 Tin 
 
 .00000417 
 00001163 
 
 .00000750 
 00002094 
 
 .000750 
 . 002094 
 
 .001938 
 
 
 . 00000489 
 
 00000881 
 
 .000881 
 
 
 Wood, pine. 
 
 00000276 
 
 00000496 
 
 .000496 
 
 
 Zinc 
 
 o 00001407 
 
 00002532 
 
 .002532 
 
 .002942 
 
 Zinc, 8 I 
 
 00001496 
 
 00002692 
 
 . 002692 
 
 
 Tin, 1 J 
 
 
 
 
 
 Note. Cubical expansion, or expansion of volume = linear expansion X 3. 
 
STEAM HEATING. 
 
 1121 
 
 Furnace heating . 
 
 Steam heating . 
 
 Hot-water heating. , 
 
 Systems of Heating.* 
 
 The various systems employed for the warming of buildings, 
 aside from the use of stoves and fireplaces, may be classified 
 as follows: 
 
 ( Gravity system. 
 ( Fan system. 
 Gravity, or lowpressure systems. 
 
 a. Direct radiation. 
 
 b. Direct-indirect radiation. 
 
 c. Indirect radiation. 
 
 d. Paul system. 
 
 Non-gravity, or high-pressure systems. 
 
 a. Gravity circulation with return trap 
 
 or pump. 
 
 b. Webster system. 
 
 c. Hot-blast systems. 
 Open system. 
 
 Direct or indirect radiation. 
 Closed system^ 
 
 Direct or indirect radiation. 
 
 These systems are briefly described in the following pages 
 and sufficient data given to enable an architect to specify or 
 design, in a general way, an ordinary heating plant. The limits 
 of the book preclude the going into many of the minor details, 
 which are usually left to the judgment of the contractor, or to 
 a discussion of the high-pressure systems, which are generally 
 employed only for very large buildings or for power plants, and 
 for which the plant should be designed by an expert. 
 
 For further information on this subject the reader is referred 
 to "Heating and Ventilating Buildings," by Prof. R. C. Car- 
 penter, which for architects and students is the best work on 
 the subject that the author has seen. 
 
 Gravity Systems of Steam Heating 1 . 
 
 A steam-heating plant may be divided into three distinct 
 parts: 1st, the boiler, or steam generator; 2d, the radiators; 
 and 3d, the supply and return pipes connecting the two. 
 
 * In the preparation of the article on Heating the author has had the 
 assistance o Mr. P. F. Monaghan, an experienced heating engineer. 
 
1122 STEAM HEATING. 
 
 Radiators. Radiators are generally made of iron, and 
 may be of any shape that will allow of a good circulation of 
 steam through them, and also permit the air to circulate freely 
 about the outside. It is also desirable that the thickness of 
 the metal shall be only enough to give sufficient strength. 
 
 Classes of Radiators. Radiators are divided into three classes: 
 those affording, 1st, direct radiation; 2d, direct-indirect radia- 
 tion; 3d, indirect radiation. 
 
 Direct radiating surfaces embrace all heaters placed within 
 a room or hall to warm the air already in the room. 
 
 Indirect radiating surfaces embrace heating surfaces placed 
 outside the rooms to be heated, and should only be used in con- 
 nection with some system of ventilation. 
 
 Direct-indirect radiation is a mean between the other two 
 methods. The radiators are placed in the rooms to be heated, 
 as in ths first method, and a supply of fresh air brought to them 
 through openings in the outside wall of the room or through a 
 space under the lower sash of a window. 
 
 Efficiency of Radiators. The condensation of one 
 pound of steam at 0, or pressure of one atmosphere to water at 
 212, gives out 965 thermal units. Hence to determine the 
 amount of heat given out by any radiator in a given time, it is 
 only necessary to determine the amount of water in pounds 
 which the radiator condenses in the same time and multiply 
 it by 965. 
 
 The radiator which, under the same conditions of steam 
 pressure and volume and temperature of surrounding air, will 
 condense the most water in a given time is the most efficient. 
 
 Measurement of Radiators. Radiators are rated, or 
 measured, not according to their size, but according to the amount 
 of heating surface coming in contact with the air. The size of 
 radiator for a given amount of heating surface will depend en- 
 tirely upon the form or shape of the radiator. 
 
 Heating by Direct Radiation. Direct radiation being 
 much more economical than indirect radiation, it will always 
 be much more commonly used for steam or hot-water heating; 
 and in buildings not requiring a great amount of ventilation it 
 offers a nearly perfect mode of heating. 
 
 Description of Direct Radiators. Pipe Radiators. 
 The cheapest direct radiator is one formed of wrought-iroti pipes 
 (1-inch pipes being generally preferred) placed against a wall one 
 above the other and connected with return bends or branch 
 
RADIATORS. 
 
 1123 
 
 fcees and elbows, to afford a circulation. The length of pipe re- 
 quired to make up a given 
 amount of heating surface 
 can easily be determined 
 by the use of the table on 
 p. 1205. For rooms in 
 which it is desirable that 
 the heating apparatus 
 shall present a neat ap- 
 pearance and occupy as 
 little space as possible 
 some form of upright 
 radiator is generally em- 
 ployed. Fig. 1 shows a 
 style of radiator, known as 
 a pipe radiator, which was 
 formerly largely used on 
 account of its cheapness; 
 it is now seldom seen, how- 
 ever. Pipe radiators are 
 formed of a number of 
 short upright 1-inch tubes 
 from 2 ft. 8 ins. to 2 ft. 10 
 ins. long, screwed into a hollow cast-iron base or box, and are 
 either connected together in pairs by return bends at their upper 
 ends or else each tube stands singly, with its upper end closed, 
 and having a hoop-iron partition extending up inside it from 
 the bottom to nearly the top. The radiators are also made 
 circular in form, either in one piece, or in halves for encircling 
 iron columns. 
 
 The table on next page shows the dimensions of 1-inch pipe 
 radiators for different heating surfaces. 
 
 Ca&t-iroii Direct Radiators. Direct radiators are 
 now made almost exclusively of cast iron.* Within the last 
 decade considerable improvement has been made in the design 
 and quality of cast radiators, so that the newer patterns have 
 very largely superseded those made previous to ten or twelve 
 years ago. 
 
 The principal manufacturers of radiators are the "American," 
 
 * Quite recently the Kinnear-Hood Steel Co. has placed on the market 
 a line of sheet-steel, brass, and copper radiators for direct and direct-indirect 
 radiation. The manufacturers claim that they are superior to cast radiators. 
 
 Fig. I 
 Direct Pipe Radiator. 
 
1124 STEAM HEATING. 
 
 TABLE OF VERTICAL PIPE RADIATORS. 
 
 No. of 
 Rows and 
 Width of 
 Ease. 
 
 Tubes 
 in Each 
 Row. 
 
 Surface , 
 in 
 Sq. Ft.* 
 
 Length. 
 Ft. in. 
 
 No. of 
 Rows and 
 Width of 
 Base. 
 
 Tubes 
 in Each 
 Row. 
 
 Surface, 
 in 
 Sq. Ft.* 
 
 Length. 
 Ft. In. 
 
 
 4 
 
 4 
 
 10M 
 
 
 8 
 
 16 
 
 1 6M 
 
 . 
 
 6 
 
 6 
 
 1 2J4 
 
 
 
 10 
 
 20 
 
 1 10M 
 
 
 8 
 
 8 
 
 1 6M 
 
 
 12 
 
 24 
 
 
 ^ 
 
 10 
 
 10 
 
 1 10M 
 
 g 
 
 14 
 
 28 
 
 2 63^ 
 
 tf-3.9 
 
 12 
 16 
 
 12 
 
 16 
 
 2 2M 
 2 10M 
 
 pfe.3 
 
 16 
 
 18 
 
 32 
 36 
 
 3 2j| 
 
 11- 
 
 20 
 24 
 
 20 
 24 
 
 3 6M 
 4 2M 
 
 i|^ 
 
 20 
 24 
 
 40 
 48 
 
 3 63-J 
 
 OQt^ 
 
 28 
 
 28 
 
 4 10M 
 
 '^ 
 
 28 
 
 56 
 
 4 10^ 
 
 ^* 
 
 32 
 
 32 
 
 5 6M 
 
 ^ 
 
 32 
 
 64 
 
 5 6/^ 
 
 
 38 
 
 38 
 
 6 6M 
 
 
 38 
 
 78 
 
 6 6M 
 
 ll- 
 
 8 
 12 
 
 24 
 36 
 
 2 2>f 
 
 .| 
 
 4 
 8 
 
 16 
 32 
 
 ?^ 
 
 
 16 
 
 48 
 
 2 10/4 
 
 o * 
 
 12 
 
 48 
 
 2 2)4 
 
 f^*o.S 
 
 20 
 
 60 
 
 3 6M 
 
 ^*o fl 
 
 16 
 
 64 
 
 2 10/^ 
 
 O> \* 
 
 24 
 
 72 
 
 4 2^ 
 
 f-rlO 
 
 20 
 
 80 
 
 3 6/4 
 
 "55o 
 
 28 
 
 84 
 
 4 10M 
 
 P^^ 
 
 24 
 
 96 
 
 4 234 
 
 -I 
 
 32 
 38 
 
 96 
 114 
 
 5 6M 
 
 ^ 
 
 28 
 32 
 
 112 
 128 
 
 5 6M 
 
 * For radiators 35 inches high. 
 
 the "National," the "United States," the "Penn," and the 
 "Holland" Radiator Companies, the A. A. Griffing Iron Co., the 
 J. L. Mott Iron Works, and the H. B. Smith Co., all of whom 
 make several complete lines. There are also a number of 
 smaller companies who make two or three styles. 
 
 The radiators made by the American Radiator Co., however, 
 are probably more extensively used than those of any other 
 make, particularly in the Western States, and it is for this 
 reason that they have been selected for illustration. Nearly 
 all of the patterns made by this company, however, are very 
 closely duplicated by the companies above named, the varia- 
 tion being principally in the ornamentation. 
 
 There are some types of radiators which are made for the 
 purpose of circulating steam and hot water in one construc- 
 tion, but the lines of goods made by the American Radiator 
 Co. for water and steam circulation are each made for its own 
 specific purpose. 
 
 Figs. 2, 3, and 4 illustrate three of the most popular styles of 
 radiators made by this company, -although a large variety of 
 radiators in one-, two-, three-, and four- column and in extended 
 single-column and flue construction are also made by them. 
 
 The National and Verona are "two-column radiators"; the 
 Rococo is a "three-column radiator." 
 
RADIATORS. 
 
 1125 
 
 Fig. 3 
 
 National Two-column Radiator. 
 
 Fig. 4 
 
 Verona Radiator. 
 
1126 
 
 STEAM HEATING. 
 
 Fig. 5 shows three sections of the Colonial wall radiator 
 made by this company, which is very convenient for use in 
 
 Fig. 5 
 Three Sections of Colonial Wall Radiator. 
 
 halls and bathrooms, as it projects only from 3J to 4J ins. 
 
 from the wall. 
 
 This radiator is made 
 in three sizes of sections, 
 29, 23, and 16f ins. long, 
 by 13J ins. wide and 2f 
 ins. thick, and contain- 
 ing 9, 7, and 5 sq. ft. 
 of heating surface re- 
 spectively. The sections 
 may be assembled 
 either horizontally or 
 vertically. 
 
 Corner, circular, curved, 
 and column radiators; 
 also dining-room, window, 
 stairway, box-base, and 
 direct-indirect radiators; 
 also such auxiliaries as 
 brackets, pedestals, tops, 
 dampers, and wall-boxes; 
 also special radiator sec- 
 tions with high, low, or 
 
 Fig. 6 
 
 Italian Flue Box- base Direct- indirect Radi- 
 ator. Made by Amer. Rad. Co. 
 
 single legs are also 
 
 made by the American 
 
 Radiator Co., and by all of the other companies above 
 
 mentioned. 
 
RADIATORS. 
 
 1127 
 
 HEATING SURFACE IN SQUARE FEET PER SECTION 
 OF SEVERAL STEAM- AND HOT-WATER RADIA- 
 TORS MADE BY THE AMERICAN RADIATOR CO. 
 
 Name of Radiaton 
 
 Length 
 per 
 
 Section. 
 
 Height of Radiator in Inches. 
 
 45 
 
 5 
 
 * 
 * 
 
 38 
 
 32 
 
 26 
 
 23 
 
 20 
 2 
 
 National 
 
 2 1 A 
 2^ 
 2^ 
 2^ 
 
 f 
 
 4 
 
 zy 2 
 
 2% 
 
 2y 2 
 
 Ideal 
 
 Peerless 
 
 7 
 
 5% 
 
 4y 2 
 
 * 
 
 * 
 
 3M 
 
 Perfection. 
 
 Verona. . 
 
 Italian flue 
 
 Rococo (ornamental or plain) .... 
 St. Louis standard, or Buffalo 
 standard 4 columns 
 
 
 44 
 
 38 - 
 
 32 
 
 26 
 
 22 
 
 18 
 
 2y 2 
 
 2 1 A 
 
 6 
 9 
 
 5 
 
 8 
 
 4^ 
 6% 
 
 3M 
 
 5^ 
 
 3 
 
 4 
 
 2M 
 3 
 
 ./Etna flue 
 
 
 20 
 
 18 
 
 16 
 
 14 
 
 13 
 
 
 
 3 
 3 
 
 6 
 6 
 
 sy 3 
 
 5 l /3 
 
 4^ 
 4% 
 
 4 
 4 
 
 3% 
 
 Zenith flue. . 
 
 
 * Not made in this height. 
 
 The width of base of the National, Ideal, and Peerless radia- 
 tors is 8J ins.; of the Perfection, 9^ ins.; Rococo, 10^ ins.; Buffalo, 
 12 ins.; St. Louis standard 4 col. and zenith flue, 12J ins.; 
 and of the JStna flue, 12J ins. 
 
 To find number of sections required, divide required heating 
 surface in feet by values given in above table. 
 To find length of radiator, multiply the number of sections 
 by length per section and add 1 inch for two bushings. 
 
 Radiators are generally put together at the factory as ordered. 
 The standard height, except for window radiators, is 38 ins. 
 Heights less than 38 ins. cost a little more. 
 
 Direct-indirect Radiation. 
 
 The only difference between this method of heating and the 
 direct method is that external air is introduced into the room in 
 such a way that it shall come in contact with the radiator and, 
 becoming heated, circulate through the room, and unless other 
 means are provided pass out through the cracks around the 
 doors and windows. By this arrangement sufficient ventilation 
 is afforded for living-rooms and offices. With direct radiation 
 
1128 
 
 STEAM HEATING. 
 
 no ventilation at all is afforded. Therj are several methods of 
 arranging the radiators and cold-air inlets, although nearly all 
 
 require that the radiator 
 shall be located against 
 an outside wall. 
 
 The simplest method 
 of providing direct-in- 
 direct radiation is by 
 using a radiator that 
 has the lower portion 
 encased so as to form a 
 box, as shown in Fig. 6. 
 Cold air can be con- 
 ducted from the outside 
 of the house through a 
 galvanized iron pipe and 
 admitted to the bottom 
 of the radiator, as in Fig. 
 7. It is then obliged to 
 pass upward between the 
 radiator flues their entire 
 length and is brought 
 into the room at an ex- 
 ceptionally high temper- 
 ature. A small damper 
 door is placed in the 
 front of the box, and a damper should also be put in the cold-air 
 supply, so that the radiator can be converted into the ordinary 
 direct type by simply closing the damper and opening the doors. 
 This would probably be required in very cold weather. The 
 outside of the radiator, of course, heats by direct radiation at 
 all times. If a large amount of ventilation is required, some 
 form of indirect radiator should be enclosed in an incombustible 
 casing and the outside air admitted below the radiator. A 
 very good arrangement to accomplish this purpose is shown 
 in Fig. 8. 
 
 It consists of a stack of pin or other indirect radiators en- 
 closed in a box of either iron, marble, or wood lined with tin 
 and provided with registers at the top for the escape of the 
 heated air. The cold air enters through a hollow iron sill placed 
 above the wooden-sill of a window and passes down back of the 
 
RADIATORS. 
 
 1129 
 
 radiator, through a galvanized iron pipe, to the space under the 
 radiator. 
 
 The cold-air inlet is provided with a damper so that it can 
 be closed, and registers are also placed at the base of the radia- 
 tor casing, so that in very cold weather the cold-air inlet may 
 be partially or wholly 
 closed and the , air ' 
 allowed to circulate 
 through the bottom reg- 
 ister, up through the 
 radiator, and out of the 
 top registers. 
 
 Indirect Radia- 
 tion. 
 
 Heating by indirect 
 radiation is accom- 
 plished by two methods, 
 the more general method 
 being to have separate 
 radiators for each room, 
 located in the cellar or 
 
 basement, incased^with metal or wood lined with tin and provided 
 with a fresh -air inlet and tin pipe to convey the hot air to the 
 room to be heated. 
 
 The other method is to provide one cold-air inlet for the whole 
 building arid place a large coil of steam-pipes behind it, so that 
 all the air entering the building must pass through this coil. 
 Such a method can only be used in connection with fan ven- 
 tilation. 
 
 Fig. 9 shows the usual method of casing indirect radiators. 
 The casing is generally of galvanized iron or of wood lined with 
 tin. The latter is best when the cellar is to be kept cool, as 
 there is a greater loss by radiation and conduction through 
 metal cases; otherwise metal is best, as it will not crack, and 
 when put together with small bolts can be removed to make 
 repairs without damage.* 
 
 The boxes should be fitted with a door in the bottom, and 
 the cold-air pipe should always be provided with a damper. 
 
 The vertical air-ducts are usually tin flues built into the wall 
 when the building is going up. Sometimes they are only plas- 
 
 VERTICAL SECTION THROUGH RADIATOR, 
 CASING AND WINDOW SILL. 
 
 Fig. 8 
 
STEAM HEATING. 
 
 tered; but round, smooth metal linings with close joints give 
 much the best results. The cross-section of the air-duct should 
 
 be comparatively 
 large, as a large 
 volume of warmed 
 air with a slow ve- 
 locity gives the best 
 results. 
 
 There should be 
 a separate vertical 
 air-duct for every 
 outlet or register. 
 In branched verti- 
 cal air-ducts one is 
 generally a failure. 
 The heated air 
 from one heater 
 may be taken to 
 two or more verti- 
 cal air-ducts when 
 they start directly 
 over it; the duct 
 to the lower room 
 being taken from 
 the top and that to 
 the upper room 
 
 Fig. 9 
 
 Section through Indirect Radiator Stack. 
 
 from the side, or both from the top. If both rooms are on the 
 same level, both ducts should be taken from the top of the box.. 
 
 Inlet or cold-air ducts are best when there is one for every 
 coil or heater. Sometimes only one large-branched cold-air 
 duct is used, but this system will give trouble unless all the 
 rooms are ventilated by forced ventilation. 
 
 The Radiators. For indirect radiation a form of radia- 
 tor is employed different from those used for direct heating. 
 In this method- the desideratum is to have as many feet of 
 heating surface in as little space as possible, appearance being of 
 no importance. The earliest form used, and which is still used 
 in the fan or hot-blast systems, is the*pipe-coil radiator, formed 
 of a coil of pipes connected at the ends with return bends. 
 
 For ordinary indirect heating cast-iron radiators of one of 
 the types shown by Figs. 10, 11, and 12* are now used almost 
 
 * From the catalogue of the American Radiator Co. 
 
INDIRECT RADIATORS. 
 
 1131 
 
 exclusively, as they are fully as cheap if not cheaper than pipe 
 radiators and more satisfactory. 
 
 The pin radiator is made by several manufacturers and is 
 one of the earliest types of indirect radiators. 
 
 The radiator shown by Fig. 10 is made in two types: for 
 
 
 Fig, 10 
 
 Perfection Pin, Extra Large, Flange and Bolt. 
 
 Fig. II 
 Excelsior Steam Indirect Radiator. 
 
 connecting by flange and bolt, and right and left threaded, 
 all tapped 2 ins. and bushed. The sections are made in two 
 sizes, viz., (1) standard size, 11 J ins. wide, 36 ins. long, and 
 occupying 2f ins. in the stack, the heating surface being 10 sq. 
 ft. per section; (2) the extra large size, which is 15J ins. wide, 
 36 ins. long, occupies 2J ins. in the stack and has a heating 
 
1132 STEAM HEATING. 
 
 surface of 15 sq. ft. per section. The Excelsior pattern, shown 
 by Fig. 11, is 36f ins. long, 8 ins. wide, occupies 3| ins. in the 
 stack, has a heating surface of 12 sq. ft. per section, and is 
 tapped 1J ins. The Sterling, Fig. 12, is 37 ins. long, 16 ins. 
 high, occupies 3J ins. in the stack, contains 20 sq. ft. per sec- 
 tion, and is tapped 2 ins. and bushed. 
 
 Cast-iron indirect radiators with plain surfaces are also made 
 by the "American" and by some of the other radiator com- 
 panies. 
 
 Nearly all indirect radiators may be used for either water or 
 
 Fig. 12 
 
 Sterling Indirect Radiator. 
 
 steam circulation, although the American Radiator Company 
 has slightly different patterns for steam than for water. 
 
 Indirect radiators are generally hung from the ceiling by 
 four iron hangers attached to the floor joists and having their 
 lower ends shaped so as to hold iron pipe or bar iron on which 
 the radiator rests. The front support should be J in. lower 
 than the rear, so that the upper pipe of each radiator will in- 
 cline to the rear and the lower pipe of each will incline to the 
 front. By this arrangement the water of condensation will 
 follow the course of steam throughout each section. The 
 outlet side of each stack should be from J to f of an inch lower 
 than the inlet side so as to allow the water free passage through 
 and out of the stack. 
 
 Each stack of radiators should have, in the warm-air cham- 
 
BOILERS. 
 
 1133 
 
 her, not less than 12 ins. clear space above them and not less 
 than 6 ins. below them. The supply and return pipes should 
 always be of ample size. 
 
 The space required for any quantity of heating surface of 
 any one of the three radiators described above may be readily 
 determined by means of the data given. The following table 
 will be found useful in proportioning size of air-ducts: 
 
 DATA FOR EXCELSIOR INDIRECT STEAM-RADIATORS. 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 *" 
 
 M 
 
 o 
 
 o 
 
 o 
 
 L 
 
 3 
 
 1 
 
 % 
 
 
 
 W 
 
 a 
 
 If 
 
 *? 
 
 
 CQ 
 
 GO 
 
 
 E 
 
 S 
 
 1 
 
 ^ 
 
 1-1 
 
 7-1 
 
 tc 
 S v 
 
 j 
 
 !?! 
 
 
 
 o^ 
 
 IH 
 
 *o 
 
 8 
 
 g 
 
 0+H 
 
 i 
 
 fl S C 
 
 SQtf 
 
 'cj3 
 
 ~o 
 
 ih 
 
 o^ 
 
 JP 
 
 It 
 
 i 
 
 |o 
 
 ^^ 
 
 t 1 
 
 8 
 
 5 
 
 ffi 
 
 OQ 
 
 OQ 
 
 & 
 
 i 
 
 a 
 
 Sq.Ft. 
 
 Sq.Tn. 
 
 Inches. 
 
 Sq. In. 
 
 Inches. 
 
 Inches. 
 
 Cu. Ft. 
 
 Cu. Ft. 
 
 Cu. Ft. 
 
 24 
 
 36 
 
 6.8 
 
 48 
 
 4X12 
 
 8X 8 
 
 720 
 
 840 
 
 960 
 
 36 
 
 54 
 
 8.3 
 
 72 
 
 8X12 
 
 9X12 
 
 10SO 
 
 1260 
 
 1440 
 
 48 
 
 72 
 
 9.6 
 
 96 
 
 8X12 
 
 10X14 
 
 1440 
 
 16SO 
 
 1920 
 
 60 
 
 90 
 
 10.0 
 
 120 12X12 
 
 12X15 
 
 1800 
 
 2100 
 
 2400 
 
 72 
 
 108 
 
 11.7 
 
 144 
 
 12X12 
 
 12X19 
 
 2160 
 
 2520 
 
 2880 
 
 84 
 
 126 
 
 12.7 
 
 168 
 
 12X16 
 
 14X22 
 
 2520 
 
 2940 
 
 3360 
 
 96 
 
 144 
 
 13.5 
 
 192 12X16 
 
 14X24 
 
 2880 
 
 3360 
 
 3840 
 
 108 
 
 162 
 
 14.4 
 
 226 12X20 
 
 16X20 
 
 3240 
 
 370 
 
 4320 
 
 120 
 
 ISO 
 
 15.2 
 
 240 
 
 12X20 
 
 16X24 
 
 3600 
 
 4200 
 
 4800 
 
 132 
 
 198 
 
 15.9 
 
 264 
 
 12X24 
 
 20X20 
 
 3960 
 
 4620 
 
 5280 
 
 144 
 
 216 
 
 16.6 
 
 288 
 
 12X24 
 
 20X24 
 
 4320 
 
 5040 
 
 5760 
 
 The Boiler. 
 
 Classes of Heating: Boilers. There are a great many 
 varieties of steam-boilers in use for generating steam for heating 
 purposes besides several types that were on the market some 
 twelve or fifteen years ago and are now practically obsolete. The 
 larger proportion of the boilers used at the present time may be 
 classed under the following heads, viz.: 
 
 (1) Horizontal tubular boilers. 
 
 (2) Fire-box boilers. 
 
 (3) Sectional boilers. 
 
 a. Boilers with vertical sections. 
 
 b. Boilers with horizontal sections. 
 Horizontal Tubular Boilers. This boiler has been 
 
 very extensively used both for heating and power and is still 
 
1134 STEAM HEATING. 
 
 preferred by many engineers for heating large buildings or 
 generating steam for hot-blast heating systems. It is an 
 efficient type of boiler, is easily cleaned, and is usually the most 
 economical type for a large amount of radiation, say over 2,500 
 sq. ft., and particularly when soft coal is used for fuel. 
 
 The chief objection to its use is that should an explosion 
 occur from any cause, it is liable to do a great amount of damage, 
 possibly demolish the building. The chance of an explosion, 
 however, is very small indeed.* 
 
 Tubular boilers are manufactured in nearly every city of 
 importance and can be purchased in every market at a reason- 
 able price. 
 
 The boiler should be provided with manholes with strongly 
 reinforced edges, so that a person can enter for cleaning. The 
 heads of the boiler above the tubes should be thoroughly braced 
 in order to sustain safely any pressure from the inside of the 
 boiler. 
 
 Domes. Domes are often placed above the horizontal 
 part of a boiler for the purpose of increasing the capacity for 
 the storage of steam and to afford a ready means of drawing 
 off dry steam. 
 
 The desirability of domes is a much disputed question. The 
 dome is always an element of weakness in a boiler, and many 
 engineers claim that the boiler is better without them. For 
 gravity heating, boilers without domes are probably most used, 
 while for power purposes the dome is generally provided. 
 There seems to be no standard proportions for tubular boilers, 
 as the practice of different makers and engineers varies some- 
 what. The proportions given in the following tables, however, 
 are fairly representative of most of the boilers made, those in 
 
 * "The claim for safety can also be made for the horizontal return tubu- 
 lar boiler. The fact is that when boilers of this type are properly con- 
 structed they do not explode. When one compares the few explosions 
 which occur with the great number of boilers of this type which are manu- 
 factured every year and the vastly greater number which are in use, a 
 large number of them carelessly constructed and carrying a greater pressure 
 than they were designed to carry, it is a strong argument in support of this 
 claim, that they are safety boilers when proper care and inspection are 
 given to their construction. 
 
 " Moreover, the horizontal return tubular boiler when well designed and 
 carefully constructed is not only a safety boiler, but when compared with 
 water-tube boilers we do not hesitate to say that it is more economical." 
 (Edward Kendall & Sons.) 
 
TUBULAR BOILERS. 
 
 1135 
 
 the first table being designed for hard coal and those in the 
 second table for soft coal. 
 
 HORIZONTAL TUBULAR BOILERS. 
 
 MANUFACTURED BY EDWARD KENDALL, & SONS, CAMBRIDGE, MASS.* 
 
 
 
 
 
 
 
 
 t-I 
 
 &J 
 
 *o g 
 
 "Si g-H- 
 
 *o 
 
 t-l . 
 
 
 "S 
 
 *o 
 
 *o . 
 
 *o 
 
 L 
 
 02 
 
 1 
 
 o 
 
 A 
 
 |Sa 
 
 "* 
 
 0) p 
 
 !ii! 
 
 S H 
 
 II 
 
 o C 
 
 (H r/' 
 
 JJJ! 
 
 -2 S 
 
 1 J3 
 
 m 
 
 is 
 
 u 
 
 C oJ 
 
 C ^ 
 
 sll 
 
 o 
 
 gS^J 1 
 
 S o 
 . gffl 
 
 ft 
 
 tc'o 
 
 r 
 
 F 
 
 IS 
 
 s 
 
 f 
 
 .! 
 
 r 
 
 1 
 
 fc 
 
 |i 
 
 e3 S 
 
 jit* 
 
 Ins. 
 
 Ft.Ins. 
 
 
 Ins. 
 
 Ft. 
 
 Ins. 
 
 Sq. Ft. 
 
 
 
 
 
 30 
 
 6 
 
 36 
 
 2 
 
 5 
 
 M 
 
 114 
 
 72^ 
 
 3,600 
 
 5 
 
 684 
 
 
 7 
 
 44 
 
 44 
 
 6 
 
 4 
 
 137 
 
 jgfe 
 
 3,750 
 
 5 
 
 822 
 
 
 8 
 
 " 
 
 44 
 
 7 
 
 
 160 
 
 
 3,900 
 
 6 
 
 990 
 
 
 9 
 
 44 
 
 44 
 
 8 
 
 
 182 
 
 12 3 
 
 4,050 
 
 8 
 
 1,092 
 
 36 
 
 8 
 
 34 
 
 2^2 
 
 7 
 
 
 189 
 
 
 4,390 
 
 8 
 
 1,124 
 
 
 9 
 
 44 
 
 44 
 
 8 
 
 
 216 
 
 14/^ 
 
 4,600 
 
 8 
 
 1,296 
 
 
 10 
 
 " 
 
 44 
 
 9 
 
 
 243 
 
 16 
 
 4,810 
 
 10 
 
 1,458 
 
 
 11 
 
 " 
 
 41 
 
 10 
 
 
 270 
 
 18 
 
 5,090 
 
 10 
 
 1,620 
 
 
 12 
 
 11 
 
 44 
 
 11 
 
 
 297 
 
 20 
 
 5,300 
 
 12 
 
 1,782 
 
 
 13 
 
 28 
 
 3 
 
 12 
 
 
 321 
 
 21 
 
 5,510 
 
 12 
 
 1,926 
 
 '2 
 
 10 
 
 45 
 
 2^2 
 
 9 
 
 
 315 
 
 21 
 
 6,610 
 
 12 
 
 1,890 
 
 
 11 
 
 44 
 
 44 
 
 10 
 
 
 350 
 
 23 
 
 7,030 
 
 12 
 
 2,100 
 
 
 12 
 
 " 
 
 11 
 
 11 
 
 
 384 
 
 26 
 
 7,300 
 
 14 
 
 2,304 
 
 
 13 
 
 41 
 
 44 
 
 12 
 
 
 420 
 
 28 
 
 7,660 
 
 14 
 
 2520 
 
 
 12 
 
 38 
 
 3 
 
 11 
 
 
 389 
 
 26 
 
 7,320 
 
 14 
 
 2,334 
 
 
 13 
 
 44 
 
 14 
 
 12 
 
 
 425 
 
 28 
 
 7,680 
 
 14 
 
 2,550 
 
 
 14 
 
 41 
 
 41 
 
 13 
 
 
 460 
 
 31 
 
 7,950 
 
 16 
 
 2,760 
 
 
 15 
 
 44 
 
 44 
 
 14 
 
 
 495 
 
 33 
 
 8,220 
 
 16 
 
 2,970 
 
 '8 
 
 12 2 
 
 69 
 
 2^2 
 
 11 
 
 & AQ 
 
 566 
 
 38 
 
 9,750 
 
 18 
 
 3,396 
 
 
 13 2 
 
 " 
 
 44 
 
 12 
 
 
 617 
 
 41 
 
 10,150 
 
 18 
 
 3,702 
 
 
 15 2 
 
 49 
 
 3 
 
 14 
 
 
 626 
 
 42 
 
 10,685 
 
 18 
 
 3,756 
 
 
 16 2 
 
 < 
 
 " 
 
 15 
 
 
 671 
 
 45 
 
 11,035 
 
 18 
 
 4,026 
 
 
 17 2 
 
 44 
 
 44 
 
 16 
 
 
 716 
 
 48 
 
 11,485 
 
 20 
 
 4,296 
 
 
 17 2 
 
 38 
 
 3^2 
 
 16 
 
 
 658 
 
 44 
 
 12,085 
 
 20 
 
 3,948 
 
 
 18 2 
 
 14 
 
 44 
 
 17 
 
 
 700 
 
 47 
 
 12,535 
 
 20 
 
 4,200 
 
 54 
 
 15 2 
 
 60 
 
 3 
 
 14 
 
 11,32 
 
 759 
 
 51 
 
 14,015 
 
 24 
 
 4,554 
 
 
 16 2 
 
 72 
 
 44 
 
 ,15 
 
 
 954 
 
 63 
 
 15,074 
 
 26 
 
 5,724 
 
 
 17 2 
 
 '* 
 
 44 
 
 16 
 
 
 1,018 
 
 68 
 
 15,584 
 
 28 
 
 6,108 
 
 
 18 2 
 
 44 
 
 14 
 
 17 
 
 
 1,082 
 
 72 
 
 16,094 
 
 28 
 
 6,492 
 
 
 17 2 
 
 54 
 
 3^2 
 
 16 
 
 
 905 
 
 60 
 
 15,458 
 
 26 
 
 5,430 
 
 
 18 2 
 
 44 
 
 41 
 
 17 
 
 
 961 
 
 64 
 
 15,960 
 
 26 
 
 5,766 
 
 
 19 2 
 
 44 
 
 44 
 
 18 
 
 
 1,018 
 
 68 
 
 16,552 
 
 28 
 
 6,108 
 
 60 
 
 18 2 
 
 92 
 
 3 
 
 17 
 
 ' ^ 
 
 1,364 
 
 91 
 
 19,000 
 
 34 
 
 8,284 
 
 1 
 
 18 2 
 
 64 
 
 3^2 
 
 17 
 
 
 1,133 
 
 76 
 
 18,468 
 
 30 
 
 6,798 
 
 4 
 
 19 2 
 
 44 
 
 " 
 
 18 
 
 
 1,200 
 
 80 
 
 19,227 
 
 32 
 
 7,210 
 
 66 
 
 18 2 
 
 110 
 
 3 
 
 17 
 
 
 1,615 
 
 108 
 
 22,430 
 
 40 
 
 9,690 
 
 44 
 
 18 2 
 
 82 
 
 3J^ 
 
 17 
 
 4 
 
 1,426 
 
 95 
 
 22,190 
 
 36 
 
 8,556 
 
 72 
 
 18 2 
 
 130 
 
 3 
 
 17 
 
 ^AG 
 
 1,900 
 
 127 
 
 26036 
 
 48 
 
 11,400 
 
 
 18 2 
 
 100 
 
 3y 2 
 
 17 
 
 
 1,721 
 
 115 
 
 25,980 
 
 44 
 
 10,326 
 
 * Selected from 156 sizes listed by this firm. These boilers are made 
 up to 96 ins. diam. and 21 ft. long, 
 t For hard coal or coke. 
 I Proportion 6 to 1. The last two columns added by the author. 
 
 When soft coal is used for fuel the efficiency of the boiler 
 may be increased by increasing the grate area about 20 per cent- 
 
1136 
 
 STEAM HEATING. 
 
 PROPORTIONS OF HORIZONTAL TUBULAR BOILERS. 
 
 Made by the Atlas Engineering Works, Indianapolis, Ind. 
 These are about the standard proportions as used in the Western States 
 for ordinary purposes. 
 
 
 Shell.t 
 
 Mean Thickness. 
 
 Tubes. 
 
 
 o 
 
 1 
 
 
 
 
 
 
 
 ^ 
 
 
 OQ 
 
 1 
 
 3K 
 
 t; 
 
 ^ 
 
 
 e 
 
 1 
 
 o> 
 
 -3 
 
 1 . 
 
 DQ 
 
 s . 
 
 1 
 
 "S 
 
 s 
 
 1 
 
 
 i 
 
 W> 
 
 "ce o 
 
 -2 
 
 * 
 
 S 
 
 a 
 
 1 
 
 
 1 
 
 i 
 
 M 
 
 |j! 
 
 O 
 
 
 Inches 
 
 Feet. 
 
 Inches. 
 
 Inches. 
 
 
 Ins. 
 
 Feet. 
 
 Sq. Ft. 
 
 Sq. Ft. 
 
 15 
 
 36 
 
 8 
 
 -J 
 
 | 
 
 26 
 
 3 
 
 8 
 
 214 
 
 5.8 
 
 20 
 
 36 
 
 10 
 
 ^ 
 
 | 
 
 26 
 
 3 
 
 10 
 
 266 
 
 8.3 
 
 25 
 
 36 
 
 12 
 
 i ' 
 
 I 
 
 26 
 
 3 
 
 12 
 
 318 
 
 9.5 
 
 30 
 
 40 
 
 12 
 
 
 1 
 
 34 
 
 3 
 
 12 
 
 404 
 
 12 
 
 35 
 
 42 
 
 12 
 
 i 
 
 
 40 
 
 3 
 
 12 
 
 464 
 
 12.8 
 
 40 
 
 46 
 
 12 
 
 If 
 
 /ie 
 
 42 
 
 3 
 
 12 
 
 491 
 
 14.6 
 
 45 
 
 48 
 
 12 
 
 ft 
 
 Jie 
 
 48 
 
 3 
 
 12 
 
 551 
 
 15.3 
 
 50 
 
 48 
 
 14 
 
 9 
 
 IT a" 
 
 Jie 
 
 40 
 
 3i 
 
 14 
 
 630 
 
 16 
 
 55 
 
 52 
 
 14 
 
 
 
 JTe 
 
 44 
 
 
 14 
 
 693 
 
 16.7 
 
 60 
 
 54 
 
 14 
 
 1 
 
 i 
 
 46 
 
 II 
 
 14 
 
 721 
 
 18 
 
 70 
 
 54 
 
 16 
 
 
 i 
 
 40 
 
 4 
 
 16 
 
 817 
 
 20.8 
 
 75 
 
 60 
 
 14 
 
 ft 
 
 
 62 
 
 3i 
 
 14 
 
 940 
 
 21.5 
 
 85 
 
 60 
 
 16 
 
 
 i 
 
 52 
 
 4 
 
 16 
 
 1045 
 
 22.2 
 
 100 
 
 66 
 
 16 
 
 f 
 
 
 64 
 
 4 
 
 16 
 
 1265 
 
 25 
 
 125 
 
 72- 
 
 16 
 
 
 | 
 
 82 
 
 4 
 
 16 
 
 1578 
 
 29.5 
 
 150 
 
 72 
 
 18 
 
 % 
 
 * 
 
 82 
 
 4 
 
 18 
 
 1775 
 
 36.5 
 
 * It will be noticed that these boilers are rated a little higher than the 
 usual standard of 15 sq. ft. of heating surface to 1 H.-P. ( 
 
 t In these boilers the smoke-box is made of a separate piece, so that 
 the actual length of boilers is 15 ins. more than length of shell. 
 
 Size of Tubes. In the Eastern States where hard coal is 
 used, 2J-inch tubes are commonly placed in boilers up to 12 ft. 
 long, but where soft coal is used for fuel, the tubes should not 
 be less than 3 ins. in diameter even for the smallest boiler, 
 while for boilers 16 ft. long and over 3J ins. or 4 ins. tubes 
 should be used. 
 
 Setting of Horizontal Tubular Boilers. Boilers are 
 set with half fronts and full fronts. With half-front setting, the 
 front end of the boiler projects 12 ins. or more beyond the 
 brickwork and is covered with a cast-iron frame containing 
 two doors for giving access to the flues. 
 
 With a full front, a cast-iron front is provided the full width 
 
FIRE-BOX BOILERS. 1137 
 
 of the boiler and extending from the floor to the top of the 
 brick setting. 
 
 Fig. 13 shows the proper method of setting a horizontal 
 tubular boiler with full front, and the table * opposite it gives 
 the dimensions indicated by the letters and the quantities of 
 bricks required. These will be found useful in showing the 
 boiler setting on the foundation plan of the building, and also 
 in estimating the cost of setting. 
 
 Fire-box Boilers. A fire-box boiler is a horizontal 
 tubular boiler with a fire-box formed in the front end, as in 
 Fig. 14. The fire-box has double walls, the space between 
 being filled with water, so that the fire is entirely surrounded 
 with water, the object being to utilize a greater percentage 
 of the heat generated by combustion than is possible with the 
 ordinary tubular boiler. 
 
 The American Radiator Co. and the Kewanee Boiler Co. 
 make a fire-box boiler intended especially for heating purposes, 
 which would seem to be a very efficient type of boiler for build- 
 ings having from 1,000 to 3,000 ft. of direct steam radiation or 
 1,500 to 6,000 ft. of hot- water radiation, and particularly where 
 hard coal or coke is used for fuel. 
 
 These boilers may be installed in very low cellars. The 
 danger from explosion with these boilers, however, when used 
 for' steam heating is about the same a# with plain tubular 
 boilers. 
 
 Fire-box boilers require a brick setting as shown by Fig. 14. 
 
 Sectional Cast-iron Boilers. This class of boiler has 
 been used for a great many years, but during the past ten 
 years they have become more popular than ever, and are now 
 very largely taking the place of tubular boilers for the heating 
 of quite large private and public buildings, principally on ac- 
 count of their safety from dangerous explosions. This, in fact, 
 is the chief advantage of the sectional boiler over a tubular 
 boiler. In a sectional boiler, should an explosion occur from 
 gross carelessness of the attendant, it would probably be con- 
 fined to not more than two sections, and do but little damage 
 to the building. Many improvements have been made in 
 these boilers during the past decade, so that some of the latest 
 patterns seem to be about perfect for the class of work for 
 which they are intended. 
 
 
 * Published by Kellog-Mackay-Cameron Co. 
 
1138 
 
 STEAM HEATING. 
 
 
 
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SECTIONAL BOILERS. 
 
 1139 
 
 Types of Sectional Boilers. There is such a great 
 variety of small sectional boilers for house heating that it is 
 
 impossible to describe them in a work of this character. Nearly 
 all are of a portable pattern and are generally made in horizontal 
 sections, i.e., the sections fitting one on top of the other* 
 
1140 
 
 STEAM HEATING. 
 
SECTIONAL BOILERS. 
 
 1141 
 
 For buildings having more than 400 ft. of direct radiation 
 in the radiators a vertical sectional boiler is to be preferred 
 to one with horizontal sections. 
 
 The vertical sectional boiler 
 is made up of a number of cast- 
 iron vertical sections ' set one 
 in front of the other on a cast- 
 iron base which forms the ash- 
 pit. The sections are connected 
 together either by means of 
 push nipples fitting tightly into 
 adjacent sections or by connect- 
 ing each section to three drums, 
 one above the boiler and one 
 on each side near the bottom. 
 The latter type of boiler is 
 designated as a " screw-nipple " 
 boiler and the former as a " push- 
 nipple " boiler. The push-nipple boiler is the later type and seems 
 to be most in favor with steam-fitters. It affords a freer eircu- 
 
 Fig. 15 
 
 ' Ideal " Sectional Steam Boiler. 
 
 Fig. 16 
 
 Gurney Bright Idea Boiler, 1200 Series Screw-nipple Type. 
 
 lation of steam and water than the screw-nipple type and is more 
 quickly erected. 
 
 On the other hand, if any section of a push-nipple boiler 
 
1142 STEAM HEATING. 
 
 becomes disabled, the entire boiler must be thrown out of use 
 until a new section can be put in, while with the screw-nipple 
 boiler, if an intermediate section is disabled it can be discon- 
 nected from the drums and the openings plugged, so that the 
 boiler can be run temporarily, or even permanently, if the 
 boiler is large enough, without taking out the disabled section. 
 
 Fig. 15 shows the general external appearance of push- 
 nipple boilers and Fig. 16 of the screw-nipple boilers. Fig. 17 
 is a sectional view of the Gurney Bright Idea sectional water- 
 tube hot-water boiler, "1200 series," adapted to from 5,000 
 to 11,000 ft, of radiation. Boilers constructed on the same prin- 
 ciple are also made for house heating. 
 
 Although the external appearance of nearly all vertical sec- 
 tional boilers is quite similar, the arrangement of the flues or 
 
 Fig. 17 
 Sectional View of Gurney Boiler. 
 
 passages for the gases of combustion differs somewhat in each 
 different line of boilers, and between some lines, as between 
 the Gurney " Bright Idea" and the " Ideal" line of the American 
 Radiator Co., is very great. In general, it may be said that 
 those heaters which have the greatest amount of heating surface 
 in proportion to the grate area are likely to prove the most 
 efficient in point of economy of coal consumption. 
 . As a rule, the intermediate sections of sectional boilers are 
 alike, so that the capacity of the boiler may be varied within 
 certain limits by increasing the number of sections. 
 
SECTIONAL BOILERS. 1143 
 
 The requirements of an economical and satisfactory working 
 boiler for house heating are as follows: 
 
 First. They should contain a quantity of water sufficiently 
 large to fill the pipes and radiators with steam to any required 
 pressure without lowering the water in the boiler to require an 
 addition when steam is up, for should the steam go down sud- 
 denly, there will be too' much water in the boiler This occurs 
 in boilers made with very small parts or pipes which have a 
 small capacity at the water-line; such boilers require great care 
 for should the boiler have an automatic water-feeder set for the 
 true water-line, it will fill up, but cannot discharge again when 
 the steam goes down, while if it has no feeder, there is danger 
 of spoiling the boiler, as the water is in the pipes in the form of 
 steam. 
 
 It is true that a boiler which contains a small amount of water 
 in proportion to its heating surface will get up steam quicker 
 than one containing a larger quantity of water, but the latter 
 will keep steam much better when the fire is renewed; and 
 boilers which contain small quantities of water are rapidly 
 chilled as well as rapidly heated and must be fired often and 
 regularly. 
 
 Second. The fire-box should be of iron, with a water space 
 around it, to prevent clinkering on the sides and the necessity 
 of repaid to brickwork, which are unavoidable in brick furnaces. 
 
 Third. 'i>o fire-box should be deep below the fire-door, to 
 admit of a thick fire to last all night and thus keep up steam. 
 For large boilers which require the services of an engineer it 
 is desirable to have a large grate area and a thin fire; but such 
 a fire requires to be renewed too often to be suitable for a house 
 boiler. 
 
 Fourth. The fire-box should be spacious, for the sake of 
 good combustion. 
 
 Fifth. The boiler should have few parts, and the flues 
 and tubes should be large and in a vertical position, so that they 
 will not foul easily, and that any deposit may fall to the bottom. 
 
 For dwellings the writer advises those forms of boilers which 
 are without tubes, or with but a very few, as the tubes will 
 invariably give out long before the shell, and if the tubes are 
 not kept clean they will transmit but a small percentage of heat. 
 
 Sixth. All parts should be readily accessible for cleaning and 
 repairs. This is a point of the greatest importance and economy. 
 When the heating surfaces become covered with soot and ashes, 
 
1144 STEAM HEATING. 
 
 the economy of the boiler greatly decreases, as the soot acts 
 as an insulator and prevents the heat reaching the boiler. It 
 is for this reason that boilers which work well when new are 
 found insufficient to do the work required of them when they 
 become dirty. 
 
 Seventh. The heating surface should be arranged as nearly 
 as possible at right angles to the currents of heated gases and 
 so break up the currents as to extract the entire available heat 
 therefrom. 
 
 Eighth. It should have, if possible, no joints exposed to the 
 direct action of the fire. 
 
 Ninth. It should have a great excess of strength over any 
 legitimate strain, and should be so constructed as not to be 
 liable to be strained by unequal expansion. 
 
 Tenth. It should be durable in construction and not liable 
 to require early repairs. 
 
 Eleventh. The water space should be divided into sections, so 
 arranged that should any section give out no general explosion 
 can occur and the destructive effects be confined to the simple 
 escape of the contents. 
 
 Twelfth. It should be proportioned for the work to be done, 
 and be capable of working to its full rated capacity with the 
 highest economy. 
 
 Thirteenth. It should be provided with the very best gauges, 
 safety-valves, and other fixtures. 
 
 The boiler should be set so that the water-line in the boiler 
 will be at least 2 ft. below the main horizontal supply-pipe. 
 
 The more prominent lines of sectional boilers for low-pressure 
 steam or hot- water heating are: The "Ideal" line, made by 
 the American Radiator Co ; the "International" and "Carton," 
 made by the International Heater Co.; the "Bright Idea," 
 made by the Gurney Heater Mfg. Co.; the "Mercer" and 
 "Gold," made by the H. B. Smith Co.; the "Furman," made 
 by the Herendeen Mfg. Co.; the "Sunray," made by the J. L. 
 Mott Iron Works; the "Burnham," made by Lord & Burnham 
 Co., and the " Florence," made by the Columbia Heating Co. 
 
 The "Ideal" boilers are very extensively used throughout 
 the Western States. Besides being a very efficient boiler they 
 also have the merit of being very low in stature, thus fitting 
 them for installation in buildings having very low cellars 
 without the necessity of constructing special pits. The American 
 Radiator Co. makes twenty different types of sectional boilers 
 
RATING OF STEAM-BOILERS. 1145 
 
 for steam and water, adapted to all kinds of fuel, and fifteen 
 different types of round boilers. 
 Setting and Covering of Sectional Boilers. The 
 
 only brickwork required for any of the boilers named above 
 is a suitable foundation with water-tight ash-pit about 12 ins. 
 deep. 
 
 The outside of the boilers, however, should be plastered with 
 a substantial covering, from 1 to 1J ins. thick, of plastic as- 
 bestos. 
 
 Rating of Steam-boilers. Tubular boilers are often 
 designated as so many " horse-power." 
 
 Strictly speaking, there is no such thing as " horse- power" 
 to a steam-boiler, as it is a measure applicable only to dynamic 
 effect. But as boilers are necessary to drive steam-engines, 
 the same measure applied to steam-engines has come to be 
 universally applied to the boiler and cannot well be discarded. 
 
 The standard established by the committee of judges of the 
 Centennial Exposition in 1876, and since adopted by the A, S. 
 M. E., is "the evaporation of 30 Ibs. of water per hour from 
 feed- water at 100 Fahr. into steam at 70 Ibs. gauge pressure." 
 This standard is equal to 33,305 thermal units per hour. As 
 the amount of water which any boiler will evaporate per hour 
 depends as much upon the management of the fire and the 
 kind of fuel used as upon the size, the above standard is a difficult 
 one to determine with accuracy, so that in practice the com- 
 mercial horse-power of a boiler has come to be measured by 
 the amount of its heating surface, i.e., the heating surface 
 available in generating steam. 
 
 It is the general practice to consider 15 sq. ft. of heating surface 
 in horizontal tubular boilers and 11.5 sq. ft. in water-tube boilers 
 as equivalent to one horse-power, and most manufacturers rate 
 their boilers by this standard. 
 
 The heating surface of horizontal tubular boilers is com- 
 puted as follows, all dimensions being taken in inches. Mul- 
 tiply two thirds the circumference of the shell by its length, 
 multiply the sum of the circumferences of all the tubes by 
 their common length; to the sum of these products add two 
 thirds of the area of both tube sheets less twice the combined 
 area of all the tubes and divide the sum by 144 to obtain the 
 result in square feet. Or, the heating surface is equal to the 
 surface area of all the tubes plus two thirds the surface of the 
 shell and both tube sheets minus the area of the holes. 
 
1146 STEAM HEATING. 
 
 Steam-heaters, i.e., boilers intended omy for the heating 
 of buildings, are generally rated by the manufacturers according 
 to the amount of direct radiating surface they will supply, 
 including all piping. These ratings are commonly made pretty 
 high, so that it is a safe rule to use a boiler having a rating 
 40 per cent, in excess of the actual direct radiation (radiators) 
 when the mains are covered and 50 per cent, when they are 
 not covered. 
 
 Each foot of indirect radiation should be figured as equal 
 to If ft. of direct radiation. 
 
 Proportioning Radiating Surface to Horizontal Tubular 
 Boilers. To determine the size of boiler necessary to supply 
 a given amount of direct radiation, allow 1 sq. ft. of heating 
 surface in the boiler to 6 to 7 sq. ft. of direct radiation when 
 all mains are covered and 1 to 5 or 6 sq. ft. when the mains are 
 not covered. A large boiler will usually supply a greater amount 
 of radiation in proportion to its heating surface than a small 
 one. 
 
 In these rules the piping is not to be included in the radiating 
 surface. 
 
 It should be borne in mind that no hard and fast rule can 
 be given for proportioning heating surfaces, hence in laying 
 out a heating plant the architect will do well to be guided to 
 some extent by the advice of an experienced steam-fitter. 
 
 Amount of Coal Burned per Hour. "The amount of coal 
 burned per square foot of grate surface per hour is rarely less 
 than 15 Ibs. with power boilers, and in some cases is very much 
 greater, but it is usually -less than 10 Ibs., and is sometimes as 
 small as 3 or 4 with heating boilers." * 
 
 Boiler Trimmings. Every steam-boiler should be pro- 
 vided with a brass-cased steam-gauge, safety-valve, and water- 
 column with gauge, water-gauge, and glass. An automatic 
 damper regulator with connections for operating draft door 
 and cold-air check is also desirable on house heaters. The best 
 safety-valve for low-pressure boilers is the single weighted type; 
 it should be connected at the top of the heater. 
 
 SYSTEMS OF PIPING FOR STEAM HEATING. 
 
 Distinction Between Gravity and Non-gravity 
 Systems. The various systems of steam heating are divided 
 
 * Prof. R. C. Carpenter. 
 
SYSTEMS OF STEAM HEATING. 1147 
 
 into two general classes, viz., gravity circulating systems and 
 non-gravity systems. The former embraces all systems in which 
 the water of condensation from the various radiators returns 
 to the boiler by its own weight, i.e., by gravity, without the 
 aid of any mechanical device. 
 
 Non-gravity systems require some special machinery, such 
 as a pump or return trap, to return the water to the boiler or 
 in some cases the water of condensation is wasted. 
 
 The kind of boiler used or the character of the radiation har> 
 nothing to do with the distinction between the two systems, 
 although with the non-gravity systems tubular or power boilers 
 are generally employed. Wherever high-pressure steam is 
 Carried on the boiler, the non-gravity system must be used, 
 hence this system is often designated as the high-pressure 
 system, but it is very seldom that high-pressure steam is carried 
 into the radiators. If high-pressure steam is generated for 
 power purposes, that portion of live steam which is used for 
 heating is generally passed through a reducing valve, so that 
 the pressure in the radiators does not exceed 10 Ibs., and if 
 exhaust steam is used it can be mixed with the reduced live 
 steam; otherwise the heating system is exactly the same as a 
 gravity system, except in returning the water of condensation 
 to the boiler. On the other hand, where low-pressure steam 
 is used and it is necessary to place radiators below the water- 
 line in the boiler, a non-gravity systerti must be used because 
 the water of condensation must be collected in a tank or re- 
 ceiver and returned to the boiler by a return trap or pump. 
 For gravity circulation the lowest radiation must be at least 
 4 ft. above the water-line in the boiler. 
 
 The same system of piping may be used for both systems, 
 except that with the non-gravity systems the return pipe 
 must terminate in a tank or receiver placed below the level 
 of the lowest radiator. 
 
 Definitions of Terms Used in Describing' Steam 
 and Hot-water Piping". There are certain terms used 
 in describing steam or hot-water piping with which an architect 
 or superintendent should be familiar. 
 
 The main or distributing pipe is the pipe leaving the boiler 
 and which conveys the steam or hot water to the risers or 
 branches which supply radiating surfaces. In steam heating 
 this pipe is termed the main steam-pipe, and in hot-water 
 heating the main flow pipe. The term supply pipe is some- 
 
 lie; 
 
1148 STEAM HEATING. 
 
 times applied to main steam-pipes, but it is not technically 
 correct. 
 
 The pipes in which the flow takes place from the radiator 
 are called return pipes. The main return is the pipe which 
 connects with the boiler below the water-line, or, in a non- 
 gravity system, connects with the receiver 
 
 Risers are those pipes which extend in a vertical direction 
 to supply radiators. The vertical pipes in which the flow is 
 downward are called return risers. 
 
 A relief or drip is a small pipe run from a steam-main to a 
 return. It must be used at all points where water is likely to 
 gather in the main. 
 
 Pitch is the inclination given to any pipe when running in a 
 ' nearly horizontal direction. 
 
 The term water-line is used to denote the height at which 
 the water will stand in the return pipes. In a gravity system 
 he water-line is practically the level of the water in the boiler. 
 
 " Water-hammer is a term applied to a very severe concussion 
 which often occurs in steam-heating pipes and radiators. It 
 is caused by cold water accumulating to such an extent as to 
 condense some of the steam in the pipe, thus forming a vacuum 
 which is filled by a very violent rush of steam and water. The 
 water strikes the side of the radiators or pipes with great force 
 and often so as to produce considerable damage. In general, 
 water-hammering may be prevented by arranging the piping 
 in size and pitch so that the water of condensation will imme- 
 diately drain out of the radiators or pipes." * 
 
 An air-trap is an upward bend in a pipe which accumulates 
 air to such an extent as to prevent circulation in the system. 
 When an air-trap cannot be avoided, a small pipe or air-valve 
 for the escape of air should be connected with the highest 
 portion of the bend and led to some pipe which will freely 
 discharge the entrapped air. 
 
 Systems of Steam Piping. Three systems of piping 
 are employed in gravity steam heating which may be briefly 
 described as follows: 
 
 First. The Mills, or Complete-circuit System (introduced into 
 this country by J. H. Mills and sometimes called the " overhead' 
 single-pipe system''). In this system the main pipe is led 
 directly to the highest part of the building, usually to the attic, 
 
 * Prof. Carpenter. 
 
SYSTEMS OF STEAM PIPING. 1149 
 
 from whence distributing pipes are run to the various return 
 risers, which extend to the basement and discharge into the 
 main return. The supply for the radiating surfaces is all 
 taken from the return risers, and in some cases the entire down- 
 ward circulation passes through the radiating system. 
 
 In this system the radiators in the top story receive steam 
 first, and the steam and water of condensation is always flow- 
 ing in the same direction except in the main steam riser. But 
 one connection is made to each radiator, the steam and water 
 of condensation flowing through the same opening and riser. 
 Below the first floor the piping carries only the return water 
 and steam. 
 
 "This system is equally well adapted for either steam or 
 hot-water heating, and on the score of positiveness of circula- 
 tion and ease of construction is no doubt to be commended as 
 superior to all others." * It is also the best system for com- 
 pensating for the expansion in the risers in tall buildings. The 
 principal objections to it are (1) the horizontal distribution 
 pipes having to be in the attic or top story instead of in the 
 basement, which may or may not be of serious importance; 
 and (2) the cost of piping is a little greater than with the usual 
 one-pipe system, but as a rule this will be more than offset by 
 the better working of the system. 
 
 This system is especially recommended for high buildings 
 and for mills and factories (see p. 1162). 
 
 Second. Ordinary One-pipe System, or tl One-pipe Basement 
 System" In this system one large steam-main runs around 
 the basement to a point where the last radiator or riser is taken 
 off and is then connected into a return main, which conveys 
 the water of condensation back to the boiler, or if there is no 
 occasion for dropping the return below the basement floor, 
 the steam main is continued around the basement and con- 
 nected to the return in the back of the boiler. 
 
 The steam-main when it leaves the boiler is elevated close 
 under the ceiling, and is graded down from the boiler about 
 J in. in 10 ft., so that the water of condensation will flow towards 
 the return. In this system as in the Mills system there is only one 
 connection made to each direct radiator, which is an advantage 
 over the double-pipe system, as there is only one valve to open 
 or close in turning on or shutting off a radiator. Unlike the 
 
 
 * Prof. Carpenter, 
 
1150 STEAM HEATING. 
 
 Mills system, however, the steam and water flow in opposite 
 directions in the risers. With this system a good automatic 
 air- valve should be placed on the extreme end of the horizontal 
 return main, above the water-line, to allow the escape of air 
 that cannot escape through the radiators. 
 
 This method of piping is the one now used most extensively 
 and when correctly installed gives good satisfaction. 
 
 Third. The Two-pipe System. This system consists in hav- 
 ing steam and return mains in the cellar and two connec- 
 tions to each radiator. The steam-main is' graded down from 
 the boiler about J in. in 10 ft., and is reduced in size as radiator 
 or riser connections are taken off; at the end it is connected 
 into the return main below the water-line. The return main 
 increases in size as it goes towards the boiler, as connections 
 are made to it from risers or radiators. Each radiator receives 
 steam from a riser or connection taken from the steam-main 
 and empties into the return through a return riser or connec- 
 tion, so that there is a complete circulation throughout the 
 entire system. 
 
 This system was used almost exclusively twenty or thirty , 
 years ago, but is now confined mainly to large buildings and 
 to buildings heated by indirect radiation. 
 
 Indirect Radiators must always have a flow and return f)ipe, 
 and When used in buildings heated by the one-pipe system the 
 return riser must be entered into a return main below the 
 water-line. 
 
 The two-pipe system is naturally much more expensive than 
 the one-pipe system, because twice as many radiator valves 
 are required for the former and 50 to 75 per cent, more piping. 
 
 The Paul System of Heating 1 .* This is a patented 
 system of exhausting all air from the radiators and piping, so 
 that the steam circulates below or a little above atmospheric 
 pressure. This is accomplished by attaching a patented air- 
 valve to each radiator, and at any points where air might 
 possibly connect on the returns, and connecting these valves 
 by means of small air-pipes with an exhausting apparatus 
 placed in the boiler-room. The valves are so constructed 
 that while they permit of the passage of air no water can escape 
 through them. The only difference between the Paul system 
 and the ordinary single-pipe gravity system lies in exhausting 
 
 * See foot-note p. 1152. 
 
EXHAUST SYSTEMS OF STEAM HEATING. 1151 
 
 the air so that the steam will be sucked through the pipes 
 rather than forced. 
 
 The exhausting apparatus may be operated by steam, elec- 
 tricity, gas, or water, water being usually employed with low- 
 pressure systems. 
 
 The cost of operating the exhausting apparatus when low- 
 pressure boilers are used need not exceed 3 cents per day for 
 a building containing 4,500 ft. of radiation. To install the 
 system the steam-fitter must purchase the valves and exhausting 
 apparatus from the Paul System Company and pay a small 
 royalty, the amount depending upon the amount of radiation 
 in the building. As by this system better cirgulation is pro- 
 vided than when the air discharges into the rooms through 
 ordinary automatic air-valves the radiators are made more 
 effective, consequently a little less radiation' and smaller piping 
 are required to do the same work. The cost of installation 
 under the Paul system is, therefore, but little if any more than 
 for the ordinary single-pipe gravity system, while it is claimed 
 that the system will effect an economy of at least 20 per cent, 
 in the amount of coal required for heating. 
 
 The system is in successful operation in a great many public 
 and private buildings, and the company has agents in most 
 of the larger cities from whom further information can be 
 obtained. -One great advantage of the system is that people 
 in the rooms cannot tamper with the air-valves and there is 
 no danger of their leaking. 
 
 Return of Water to Boiler in Non-gravity Sys- 
 tems of Steam Heating. As stated on p. 1147, whenever 
 the steam pressure in the radiators is less than that in the boiler, 
 or when a radiator is placed below the water-line, then the 
 water of condensation must be returned to a tank, called a 
 receiver, placed below the lowest radiator, and returned from 
 the receiver to the boiler by means of some mechanical device. 
 As a rule, either a pump or a return trap is used for this pur- 
 pose. For high-pressure systems, i.e., when stea/m is used 
 to run machinery or to run the fan in a hot-blast system, a steam- 
 pump running automatically is generally considered the most 
 satisfactory device for returning the water to the boiler. 
 
 Where there is no engineer in constant attendance, a return 
 trap will generally be preferable. The return trap works auto- 
 matically and will return the water as well as a pump, besides 
 less expensive. The greatest objection to a return trap 
 
1152 STEAM HEATING. 
 
 seems to be that if it gets out of order from any cause, it is 
 not as easify or quickly repaired as a pump. 
 
 A return trap should be placed upon or near the boiler and 
 the bottom of the trap should be at least 2 ft. above the water- 
 line of the boiler. A pump may be placed any distance below 
 the water-line of the boiler and at a considerable distance from 
 the boiler. In hot-blast heating the pump and receiver are 
 generally placed near the heating-stacks and fan. 
 
 The Webster System * (controlled by Warren Webster 
 & Co.). This, like the Paul system, is a vacuum system of steam 
 heating, but, unlike the Paul system, it exhausts all water of 
 condensation as well as air, so that the flow pipes are at all 
 times filled with dry steam. This system can also be applied 
 to all classes of non-gravity heating apparatus and where exhaust 
 steam is used. A Webster thermostatic water and air relief 
 valve is placed on the drip end of each radiator and a small 
 pipe connects each valve with the exhausting apparatus near 
 the boiler. The water of condensation is taken to a receiver, 
 from which it is fed back to the boiler. With this system com- 
 paratively small supply and return mains may be employed, 
 but the radiation should, if anything, be increased. 
 
 This system is especially adapted to large heating plants, 
 hot-blast systems, and dry kilns, and may be successfully and 
 economically applied to a great variety of manufacturing processes 
 by making slight modifications in its working details. 
 
 The patentees claim that the Webster system will give a 
 better circulation and effect greater economy in maintenance 
 than any other. 
 
 It has been successfully installed in a great many large build- 
 ings through the country and in many factories and manu- 
 "acturing plants. 
 
 * The vacuum system of heating was first introduced to the heating 
 trade in this country some time in the past seventies by N. Y. Williams, 
 a heating engineer of Philadelphia, Pa. His plan was to plug up all 
 air-verits and to attach a pump to the main return pipe and exhaust all 
 air and water from the steam -pipes, coils, and radiators in a system. The 
 plan was an improvement to the many poorly constructed plants in use 
 at the time, but it was not a complete success in itself. It would "short- 
 circuit," i.e., the pump would act only on a portion of the system. 
 
 The Warren Webster Co. bought the inventor's rights and some other 
 patents and in time introduced the Webster thermostatic valve, which 
 is now used in all their work on all radiators, and has had much to do in 
 making their system a success. The Paul and other vacuum systems have 
 been introduced since. 
 
HOT-BLAST SYSTEMS OF WARMING. 1153 
 
 Further information concerning this system may be obtained 
 at any of the offices of the company. 
 Hot-blast System of Warming and Ventilating-. 
 
 This system is used principally in buildings where a large 
 amount of ventilation is, required. The principle of the system 
 is the forcing of large volumes of air over or through a heater 
 and thence into the rooms to be warmed, and necessitates 
 a fan for driving the air. 
 
 It may be successfully operated in connection with hot-air 
 furnaces (see the author's work on " Churches and Chapels "), 
 but, as a rule, the heat is furnished by steam-coils. 
 
 An ordinary hot-blast heating and ventilating plant consists 
 of a steam-boiler, one or more stacks of steam-coils, a fan or 
 fans driven either by a small steam-engine or electric motor, 
 reducing- valve, receiver, and pump. The heating coils are 
 usually collected in a "stack," over which all of the air for 
 the building is passed, and from the stack the air is drawn or 
 forced through hot-air pipes to all parts of the building. Direct 
 radiation may also be employed in connection with this system 
 for warming the halls and corridors or any rooms which do 
 not require ventilation. 
 
 This system is especially adapted to the warming and ven- 
 tilating of schools, churches, hospitals, and public buildings, 
 and to many kinds of manufacturing plants. To insure suc- 
 cessful results, however, it must be laid out with much care. 
 Full information regarding it may be obtained from the Ameri- 
 can Blower Co., the Buffalo Forge Co., or the B. F. Sturtevant 
 Co. 
 
 Pipe, Fitting's, and Valves. The pipe used for con- 
 veying steam or hot water was formerly made exclusively of 
 wrought iron, but at the present time the term "wrought-iron 
 pipe" is used merely to distinguish wrought from cast pipe. 
 It is construed to mean merchant pipe, which is generally 
 made from soft steel. Persons desiring iron pipe should specify 
 " genuine wrought-iron pipe," for which an extra charge is 
 made. 
 
 Up to the present ftme the pipe made of steel has not been 
 as soft as that of wrought iron, and is often not so well welded 
 and is more likely to split. Nevertheless, steel pipe is much 
 more extensively used than the genuine wrought-iron pipe, 
 although the latter is unquestionably the best. 
 
 Steam-pipe is put on the market in three grades, or thick- 
 
1154 
 
 STEAM HEATING. 
 
 nesses standard, extra strong, and double extra strong (see tables 
 
 of Wrought-iron Pipe, pp. 1205, 1206). 
 
 Each length of pipe as sold is provided with a collar or coupling 
 (Fig. 18) on one end and has a thread cut 
 on the other. Connections are made- by 
 screwing the threaded end of one pipe iiito 
 the coupling on the other. Pipe is sold in 
 random lengths varying from 16 to 24 ft. 
 With the exception of couplings, the fittings 
 used for connecting pipes and for giving 
 them any desired direction with each other 
 are made of cast and malleable iron. 
 
 Fig. 18 
 
 Wrought-iron Coup- 
 ling. 
 
 For use on heating pipes, cast-iron fittings are generally 
 to be preferred to those of malleable iron, for several reasons 
 (see Carpenter, p. 92). 
 
 Fittings for Joining' Pipes. For joining pipes in the 
 same straight line, so as to make a continuous pipe from end 
 to end, the coupling, Fig. 18, with right-hand threads cut in 
 both ends is commonly used. With right-hand couplings it 
 is impossible to disconnect the pipe at any place without 
 commencing at the farther end and disconnecting the pipe 
 section by section. Reducing couplings are made for uniting 
 pipes of different sizes. 
 
 To connect two lengths of pipe, so that they can be discon- 
 nected at that point without interfering with other joints, 
 three kinds of connections are in use: 
 
 (1) Right and Left Couplings. The most common fitting for 
 joining pipes 2 ins. diameter and under. It requires, however, 
 that there shall be room for end motion 
 
 of one of the pipes sufficient to insert it. 
 
 (2) Lip Unions. These are generally 
 used on pipes up to 1J or 2 ins. in 
 diameter where it is desirable to have 
 a joint that may be readily disconnected. 
 The union consists of three pieces; two 
 of these parts screw on to the ends of 
 the pipe and are drawn together by a 
 revolving collar which engages with the 
 thread on one of the pieces, as shown by 
 Fig. 19. 
 
 With this connection no appreciable play is required in the 
 piping. 
 
 Fig. 19 
 Lip Union. 
 
FITTINGS AND VALVES. 
 
 1155 
 
 
 Unions are now commonly used in connecting radiators, 
 the union being attached to the radiator valve. 
 
 (3) Flange Unions (Fig. 20). These are used on pipes ex- 
 ceeding 2 ins. in diameter. The two parts of the union are 
 first screwed to the pipes and' 
 then bolted together. A ring of 
 packing must be placed between 
 the flanges to make a tight joint. 
 
 Nipples (Fig. 21) are frequently 
 used in steam fitting for connect- 
 ing pipes, radiators, and sectional 
 boilers. They are made with 
 right thread on both ends and 
 right thread on one end and a left 
 thread on the other. 
 
 Push nipples are made with ends bevelled and ground per- 
 fectly true, so as to make a tight joint by contact of the metal. 
 Their use is confined to radiators and sectional boilers. 
 
 Fig. 22 
 
 Fig. 20 
 
 Flange Union. 
 
 Fig. 21 
 
 Close Nipple. 
 
 Bushing. 
 
 Plug. 
 
 Bushings are used for reducing the size of opening in a fitting. 
 Plugs are used for closing the end of a fitting and caps for 
 covering the end of a pipe. 
 
 A great variety of cast-iron fittings are carried in stock, 
 such as elbows, tees,, crosses, branch tees, Y bends, return 
 bends, etc., each of these being made in a great variety of 
 sizes and shapes. 
 
 A description of them may be found in the catalogues of 
 dealers in steam-fitters' supplies. 
 
 Valves and Cocks. Three classes of valves are used 
 in steam-fitting, viz., globe valves, gate- valves, and check- 
 valves. 
 
 The valve shown by Fig. 26 is a globe valve, but is commonly 
 designated as an angle- valve, the term globe valve being com- 
 monly restricted to those valves which go on a straight line 
 of pipe. 
 
 In the gate-valve the disc which closes the opening is at 
 
1156 
 
 STEAM HEATING. 
 
 right angles to the pipe. The gate-valve when open offers 
 less obstruction to the flow of steam or water, and for this 
 reason is largely used on water-pipes. Some steam-fitters con- 
 
 Fig. 23 
 . Brass Globe Valve. 
 
 Fig. 24 
 Brass Gate-valve with Union. 
 
 tend that a gate-valve should not be used for steam, except 
 on the main return, near the boiler. 
 
 A disc valve is commonly a globe or angle valve with a com- 
 position disc or ring similar to the washer on a compression 
 cock, which fits against the "seat of the valve. A Jenkins disc 
 is a valve in which the disc or the entire valve is made by 
 
 Fig. 25 
 Section of Disc Globe Valve. 
 
 Fig. 26 
 
 Angle-valve with Union and Copper Disc. 
 
 Jenkins Bros. The common globe valve has no removable 
 disc or washer. (See Fig. 27.) 
 
 Disc valves should always be used on steam-radiators. 
 
STEAM- VALVES. 1 157 
 
 A union valve is a globe or angle valve with a union on one 
 side of the valve. 
 
 Globe valves are made for screw, union, or flange connections, 
 although the latter is commonly used only on large pipes. 
 
 Globe and angle valves for 2-inch pipes and under are com- 
 monly made with brass bodies and either iron or wood handles. 
 The larger sizes are commonly made with iron bodies. Radiator 
 valves should have brass bodies and wood wheels. 
 
 When it is desired- that radiators shall not be under the 
 control of the occupants of the room, valves operated by a 
 key may be used. Hot-water radiator valves may also be 
 had with pedal attachments so that they may be opened or 
 closed with the foot. 
 
 Special forms of quick-opening valves are largely used on 
 hot- water radiators. 
 
 Obstruction to Flow Offered by Globe Valves. 
 When globe valves are placed on horizontal steam-mains, the 
 stem should always* be placed in a horizontal position, for if set 
 vertically the seat of the valve forms an obstruction sufficient 
 to fill the pipe at least half full of water (as shown by Fig. 27). 
 Because of the obstructions which they offer to the flow of 
 water, globe valves should not be used on hot-water pipes. 
 
 Fig. 27 
 
 Check-valves. Where it is necessary that the flow shall 
 always take place in one direction and there is danger of a 
 reverse flow a check-valve must be employed. A check-valve 
 is always required on the water-supply to a steam-boiler and 
 on all connections to high-pressure boilers below water-line 
 except the blow-off pipes. 
 
 Check-valves are of three kinds, the more common form 
 
115S STEAM HEATING. 
 
 being that shown by Fig. 28, which has a valve which slides 
 up and down. The swinging check-valve, Fig. 29, is also com- 
 monly employed. The third kind utilizes a ball in place of 
 the sliding valve for closing the opening. The ball check-valve, 
 however, is not much used in steam fitting. 
 
 Fig. 28 Fig. 29 
 
 Common Type of Check-valve. Swing Check- valve. 
 
 A cock operates by means of a turned plug which has one 
 or two holes bored transversely to its axis. When the plug 
 is turned so that the hole is in line with the pipe the water 
 flows through, and when the plug is turned the water is shut 
 off. 
 
 Cocks are not much used in steam fitting, ^xeept on the 
 blo** r -off pipe. 
 
 RULES FOR PROPORTIONING RADIATING SUR- 
 FACE, AND SIZE OF STEAM AND HOT- WATER 
 MAINS AND RETURNS. 
 
 Direct Radiating Surface Steam Heating:. The 
 
 common practice of determining the direct radiating surface 
 required to warm a given room is to allow one square foot of 
 radiating surface to a certain number of cubic feet of space 
 contained in the room. The divisors given in the following 
 table fairly represent current practice. 
 
 To find square feet of direct radiation required divide the 
 cubic contents of room by the following factors: 
 
 For Dwellings Divide by 
 
 Living-rooms, one side exposed. 60 to 80 
 
 Living-rooms, two sides exposed 50 to 60 
 
 Living-rooms, three sides exposed 40 to 45 
 
 Sleeping-rooms 50 to 70 
 
 Halls and bathrooms . , .... 40 to 50 
 
 
RULES FOR RADIATING SURFACE. 1159 
 
 For Public Buildings Divide by 
 
 Offices 50 to 75 
 
 Schoolrooms 50 to 70 
 
 Factories and stores 80 to 125 
 
 Assembly halls and churches 100 to 150 
 
 In buildings of more than two stories the first and top 
 stories require the same amount of radiation if used for the 
 same purpose, but the radiation in intermediate stories may be 
 slightly reduced. 
 
 City houses require less heat than country houses and brick 
 houses less than wooden houses. 
 
 Baldwin's Rule. Mr. William J. Baldwin, in his excellent 
 work on " Steam-heating for Buildings," * recommends the fol- 
 owing rule, which he has used for several years, and which is not 
 wholly empirical: 
 
 "Divide the difference in temperature, between that at which 
 the room is to be kept and the., coldest outside atmosphere 
 by the difference between the temperature of the steam-pipes 
 and that at which you wish to keep the room and the quotient 
 will be the square feet, or fraction thereof, of plate or pipe 
 surface to each square foot of glass or its equivalent in wall 
 surface." f 
 
 The equivalent glass surface is found by multiplying the 
 superficial area of the walls in square feet by the number oppo- 
 site the substance in the following table and dividing by 1,000 
 (the value of glass). The result is the equivalent of so many 
 square feet of glass in cooling power and should be added to 
 the window surface. 
 
 TABLE OF POWER OF TRANSMITTING HEAT OF VARIOUS BUILD- 
 ING SUBSTANCES COMPARED WITH EACH OTHER. 
 
 Window glass 1,000 
 
 Oak and walnut : . . . . 66 
 
 White pine 80 
 
 Pitch pine 100 
 
 Lath and plaster 75 to 100 
 
 Common brick (rough) 200 to 250 
 
 Common brick (whitewashed) 200 
 
 Granite or slate 250 
 
 Sheet iron 1,030 to 1,110 
 
 * Published by John Wiley & Sons, of New York. 
 
 t It should be noticed that this proportion does not depend upon the dze 
 
1160 STEAM HEATING. 
 
 It must be distinctly understood that the extent of heating 
 surface found in this way offsets only the windows and other 
 cooling surfaces it is figured against, and does not provide for 
 cold air admitted around loose windows or between the board- 
 ing of poorly constructed wooden houses. These latter con- 
 ditions, when they exist, must be provided for by additional 
 heating surface. 
 
 EXAMPLE 1. What amount of heating surface should be sup- 
 plied to the sitting-room of a wooden dwelling with two out- 
 side walls, one 14 ft. by 9 ft. high and the other 15 ft. by 9 ft., 
 the total window area being 54 sq. ft., the external temperature 
 frequently being at F., and the steam never exceeding 5 Ibs. 
 pressure? 
 
 Ans. Temperature of room, 70 0=70; temperature of 
 steam-pipes at 5 Ibs., 228-70= 158; 70-- 158=. 443, or a 
 little less than one half a square foot of heating surface to each 
 square foot of glass or its equivalent. 
 
 Area of outside walls= 14X9+ 15X9= 126+ 135= 261. Sub- 
 tracting the glass area, 54, we have 207 sq. ft. of lath and 
 plaster. 
 
 207 X 100=20,700 
 54X1,000=54,000 
 
 1,000)74,700 
 
 Equivalent glass area =74. Multiplying this by .443, we 
 have 33 as the number of square feet of radiating surface re- 
 quired to warm the room, or 1 ft. of surface to 58 cu. ft. of air 
 space. 
 
 Ride of F. Schumann* "Divide the cubic feet of space 
 of the room to be heated, the square feet of wall surface, 
 and the square feet of the glass surface by the figures given 
 under these headings in the following table and add the quo- 
 tients together; the result will be the square feet of radiating 
 surface required. 
 
 For the above example with northwest and southeast ex- 
 posures and steam at 3 Ibs. pressure this rule would require 
 26.7 sq. ft. of radiating surface for a change of once per hour 
 and 45.1 sq. ft. for a change of twice per hour. 
 
 of the room, but only upon the climate, pressure of the steam, and desired 
 temperature of the room. 
 * Kent, p. 536. 
 
 j 
 
RULES FOR RADIATING SURFACE. 
 
 1161 
 
 SPACE, WALL, AND GLASS SURFACE WHICH ONE 
 SQUARE FOOT OF RADIATING SURFACE WILL 
 HEAT. 
 
 Air Change. 
 
 Steam Pressure 
 in Pounds. 
 
 o 
 'J3 
 
 3 
 O 
 
 .s 
 
 c6 4> 
 
 afe 
 
 02 
 
 Exposure of Rooms. 
 
 All Sides. 
 
 Northwest. 
 
 Southeast. 
 
 Wall 
 Surface. 
 Sq.Ft. 
 
 Glass 
 Surface. 
 Sq. Ft. 
 
 Wall 
 Surface. 
 Sq.Ft. 
 
 Glass 
 Surface. 
 Sq.Ft. 
 
 Wall 
 Surface. 
 Sq.Ft. 
 
 Glass 
 Surface. 
 Sq. Ft. 
 
 Once 
 per 
 hour 
 
 1 
 3 
 5 
 
 190 
 210 
 225 
 
 13.8 
 15.0 
 16.5 
 
 7 
 7.7 
 8.5 
 
 15.87 
 17.25 
 18.97 
 
 8.05 
 8.85 
 9.77' 
 
 16.56 
 18.00 
 19.80 
 
 8.4 
 9.24 
 10.20 
 
 Twice 
 per 
 hour 
 
 1 
 3 
 5 
 
 75 
 
 82 
 90 
 
 11.1 
 12.1 
 13.0 
 
 5.7 
 6.2 
 6.7 
 
 12.76 
 13.91 
 14.52 
 
 6.55 
 7.13 
 7.60 
 
 13.22 
 14.52 
 15.60 
 
 6.84 
 7.44 
 8.04 
 
 Prof. R. C. Carpenter says that for residences it is safe to 
 assume that the air of the principal living-rooms will change 
 twice in an hour, that of the halls three times, and that of the 
 other rooms once per hour under ordinary conditions. 
 
 Prof. Carpenter, in his work on "Heating and Ventilating 
 Buildings/' gives the following formula, which is convenient 
 and probably as accurate as any for general purposes, 
 
 in which TF=wall surface, G= glass or window surface, both 
 in square feet, C= contents of room in cubic feet, N= number 
 of times air will be changed per hour, and h= total heat-units 
 required per degree of difference of temperature between the 
 room and the surrounding space. 
 
 Under ordinary conditions of pressure and temperature 
 one square foot of steam-heating surface will supply 280 heat- 
 units per hour and 1 sq. ft. of hot-water heating surface 175 
 heat-units per hour. 
 
 To heat the room to 70 F. when the outside temperature 
 is at zero, the square feet of direct radiating surface required 
 will be i/i for steam heating and ^h for hot-water heating. 
 For churches and auditoriums N should be taken at least equal 
 |to3. 
 
 In Example I we have C= 1,890, TF=207, and (7=54. 
 Hence h= 140 when the air is changed once per hour and 174 
 
1162 STEAM HEATING. 
 
 when changed twice per hour. The steam radiating surface 
 required will be 35 and 43J sq. ft. respectively. 
 
 In practical work it is well to determine the heating surface 
 by two or more rules and then use the larger quantity. Dif- 
 ferent localities and different grades of buildings also affect 
 the amount of radiating surface required, so that practical 
 steam-fitters are usually governed to some extent by their 
 experience. There can never be any bad results from having 
 an excess of heating surface provided all rooms have their 
 proportionate amount, while a deficiency will always result 
 in cold rooms in extremely cold weather. 
 
 Overhead Steam-pipes (A. R. Wolff, Stevens Indicator, 
 1887). When the overhead system of steam heating is em- 
 ployed, in which system direct radiating pipes, usually 1J in. 
 in diameter, are placed in rows overhead suspended upon 
 horizontal racks, the pipes running horizontally and side by 
 side around the whole interior of the building, from 2 to 3 ft. 
 from the* wall and from 2 to 4 ft. from the ceiling, the amount 
 of 1^ -inch pipe required, according to Mr. C. J. H. Woodbury, 
 for heating mills (for which this system is deservedly much in 
 vogue) is about 1 ft. in length for every 90 cu. ft. of space. 
 Of course a great range of difference exists due to the special 
 character of the operating machinery in the mill, both in re- 
 spect to the amount of air circulated by the machinery and 
 also the aid to warming the room by the friction of the journals. 
 For this system of radiation the Mills system of piping should 
 be used. 
 
 Direct Radiation Hot -water Heating. Rule of 
 Thumb. Divide the cubic contents of room in cubic feet by 
 the following factors; the result will be the square feet of 
 radiation required: 
 
 For Dwellings Divide by 
 
 Living-rooms, one side exposed 40 to 50 
 
 Living-rooms, two sides exposed 30 to 40 
 
 Living-rooms, three sides exposed 20 to 25 
 
 Sleeping-rooms 30 to 50 
 
 Halls and bathrooms 20 to 30 
 
 For Public Buildings Divide by 
 
 Offices 30 to 40 
 
 Schoolrooms 30 to 40 
 
 Factories and stores - . 40 to 60 
 
 Assembly halls and churches 60 to 100 
 
RULES FOR INDIRECT RADIATION. 1163 
 
 Prof. Carpenter's rule for direct hot-water radiation is the 
 same as for steam (p. 1151), using 0.4 for a multiplier instead 
 ofi. 
 
 For Direct-indirect Radiation it is customary to allow 
 25 per cent, more surface for steam and 33 J per cent, for hot- 
 water than would be required for direct radiation. 
 
 Indirect Radiating- Surface (Prof. Carpenter's Rule). 
 The radiating surface for indirect heating may be found by 
 adding together the glass surface in the room to be warmed, 
 one fourth the exposed wall surface, both in square feet, and 
 multiplying by the following factors: 
 
 Steam Hot-water 
 
 Heating. Heating. 
 
 First story 0.7 1.05 
 
 Second story 0.6 0.9 
 
 Third story 0.5 0.8 
 
 The total amount of incoming air which this amount of 
 radiation will warm per hour in cubic feet may be found ap- 
 proximately by multiplying the radiating surface by the follow- 
 ing factors: 
 
 Steam Hot-water 
 
 Heating* Heating. 
 
 First story 200 125 
 
 Second story 250 160 
 
 Third story 300 200 
 
 If a greater quantity of air is required for ventilating purposes, 
 an additional foot of heating surface should be allowed for 
 each 250 cu. ft. of air heated by steam, or for each 150 cu. ft. 
 heated by hot water. 
 
 For rooms which are specially exposed these results should 
 be increased about 10 per cent., and 10 per cent, if the rooms 
 are heated during the daytime only. 
 
 Size of Air-ducts and Registers for Indirect 
 Radiator Stacks (Steam Heating-). 
 
 For computing the area of duct from stack to the room and 
 outlet pipe from the room the following data by Prof. Car- 
 penter will probably give as good results as can be obtained 
 by any rule, except where there is a very large glass area. 
 
1164 
 
 STEAk HEATIXG. 
 
 Rule. Multiply the sum of the glass surface and one quarter 
 the wall area by the appropriate factor given in the following 
 table: 
 
 TABLE OF FACTORS FOR AREA OF AIR-FLUES. 
 
 Story of Building. 
 
 Supply Duct. 
 
 Ventilating Duct. 
 
 1 
 II 
 
 fif 
 
 < 
 
 Velocity in 
 Feet per 
 Second. 
 
 f .3 
 
 O c3 l ~~' 
 
 Approximate 
 Distance to 
 Hoof. 
 
 Velocity in 
 Feet per 
 Second. 
 
 Factor for 
 Area. 
 Sq. Ins. 
 
 First floor 
 
 5 
 
 28 
 40 
 50 
 
 2.8 
 6.8 
 8.1 
 9.0 
 
 2.40 
 0.95 
 0.82 
 0.71 
 
 47 
 32 
 20 
 10 
 
 5.5 
 4.2 
 3.6 
 2.6 
 
 0.93 
 1.27 
 1.33 
 2.17 
 
 Second floor 
 
 Third floor 
 
 Fourth floor 
 
 
 The cold-air, or out-door, supply to the stack should have 
 a sectional area equal to about three fourths of that of the 
 warm-air flue. 
 
 The nominal size of registers should be about 50 per cent, 
 greater than the area of the warm-air flue. 
 
 The following sizes for air-ducts and registers for indirec 
 steam radiation are published by the International Heater Co 
 and a similar table is given on p. 1133. It is evident that som 
 judgment must be used with all three tables. 
 
 d 
 
 -*J O 
 
 Q)'r* 
 
 *-5 
 
 Cold-air Duct to 
 Stack. 
 
 Warm -air Duct. 
 
 Registers. 
 
 
 it 
 
 o* o 
 
 02 
 
 
 
 
 Tapping 
 
 For 
 First 
 Floor. 
 
 For 
 
 Upper 
 Floors. 
 
 For 
 
 First 
 Floor. 
 
 For 
 
 Upper 
 Floors. 
 
 First 
 Floor. 
 
 Upper 
 Floors. 
 
 
 Sq. Ins. 
 
 Sq. Ins. 
 
 Sq. Ins. 
 
 Sq. Ins. 
 
 Ins. 
 
 Ins. 
 
 Ins. 
 
 50 
 
 50 
 
 40 
 
 75 
 
 50 
 
 10X12 
 
 8X10 
 
 1 XJ 
 
 60 
 
 60 
 
 45 
 
 90 
 
 60 
 
 10X14 
 
 8X12 
 
 liXl 
 
 70 
 
 70 
 
 50 
 
 105 
 
 70 
 
 12X15 
 
 10X12 
 
 lixi 
 
 80 
 
 80 
 
 60 
 
 120 
 
 80 
 
 12X15 
 
 10X12 
 
 1JX.1 
 
 90 
 
 90 
 
 70 
 
 135 
 
 90 
 
 12X19 
 
 10X14 
 
 liXli 
 
 100 
 
 100 
 
 75 
 
 150 
 
 100 
 
 12X19 
 
 ' 12X15 
 
 ijxii 
 
RULES FOR SIZE OF PIPES. 
 
 1165 
 
 Size of Steam-mains and Return Pipes. 
 
 Mr. George H. Babcock gives the following rule for gravity 
 heating systems with separate returns (two-pipe system) : 
 
 "The diameter of the steam-mains leading from the boiler 
 should be equal in inches to one tenth the square root of radiating 
 surface, mains included, in square feet." 
 
 If the mains are covered they may be neglected in figuring 
 radiating surface. 
 
 For the one-pipe basement system it will be safe to use one 
 ninth instead of one tenth in the above rule, unless the pipes 
 are very long. It is always better to have the mains larger than 
 is necessary rather than too small. 
 
 Steam-mains should never be less than 1J ins. in diameter. 
 
 The sizes of returns that will prove satisfactory for given sizes 
 of steam-mains are given by Prof. Carpenter as follows, no re- 
 turn to be less than 1 in. diameter: 
 
 Diameter 
 Steam -pipe. 
 
 Diameter 
 Return Pipe. 
 
 Diameter 
 Steam-pipe. 
 
 Diameter 
 Return Pipe. 
 
 Inches. 
 
 Inches. 
 
 Inches. 
 
 Inches. 
 
 H 
 
 1 
 
 5 
 
 21 
 
 2 
 
 H 
 
 6 
 
 3 
 
 21 
 
 1? 
 
 8 
 
 3i 
 
 3 
 
 ll 
 
 9 
 
 4 
 
 3} 
 
 1J 
 
 10 
 
 4J 
 
 4 
 
 2 
 
 12 
 
 5 
 
 For connecting direct radiators with the single-pipe system, the 
 following sizes of pipes should be used: 
 
 For radiators containing 24 sq. ft. or under, 1-inch pipe; for 
 radiators containing 24 to 60 sq. ft., IJ-inch pipe; for radiators 
 containing 60 to 180 sq. ft., IJ-inch pipe; for radiators contain- 
 ing above 100 sq. ft., 2-inch pipe. 
 
 For Two-pipe Work. Radiators containing 48 sq. ft. and 
 under, 1-inch supply, J-inch return; 50 sq. ft. to 96 sq. ft, 
 IJ-inch supply, 1-inch return; above 96 sq. ft., IJ-inch supply, 
 IJ-inch return. 
 
 For Indirect Heating it will usually be sufficiently accurate 
 to use a pipe whose diameter is 1.4 times greater than that for 
 direct heating.* 
 
 * Prof. Carpenter. 
 
1166 STEAM HEATING. 
 
 For Hot-water Heating. Prof. Carpenter says: " We may 
 take as a practical rule, applicable when the pipes are less than 
 200 ft. in length: The diameter of main supply or main return 
 pipe in a system of direct hot-water heating should be one-pipe 
 size greater than the square root of the number of square feet 
 of radiating surface divided by 9 for the first story, by 10 for 
 the second story, and by 11 for the third story of a building; 
 for indirect hot-water heating multiply above results by 1.5." 
 
 In hot-water heating the return pipe must have the same diameter 
 as the supply pipe, and the capacity of both should be equal 
 to total capacity of risers. For equalizing hot-water pipes 
 the tables on p. 1203 will be found very convenient. 
 
 The standard tapping for hot-water radiators is as follows: 
 Radiators containing 40 sq. ft. and under, 1 in.; above 40 but 
 not exceeding 72 sq. ft., 1J ins.; above 72 sq. ft., 1J ins. 
 
 Boiler. To find the size of boiler necessary to supply any 
 given amount of radiation, see p. 1146. 
 
 Covering of Pipes. 
 
 Steam and hot-water mains radiate more heat in proportion 
 to their surface than do the radiators which they supply, and 
 unless this heat is needed for warming the space through which 
 the pipes pa,ss, it represents a very material loss in the con- 
 sumption of fuel. 
 
 To reduce this loss to a minimum, it is customary to cover 
 all pipes in unfinished basements with some insulating sub- , 
 stance. The saving in fuel effected by a good covering will 
 more than pay for its cost in a few seasons. 
 
 "The best insulating substance known is air confined in 
 minute particles or cells, So that heat cannot be removed by 
 convection. No covering can equal or surpass that of per- 
 fectly still and stagnant air; and the value of most insulating 
 substances depends upon the power of holding minute quan-/ 
 tities in such a manner that circulation cannot take place. 
 The best known insulating substance is a covering of hair-felt, 
 wool, or eiderdown, each of which, however, is open to the 
 objection that, if kept a long time in a confined atmosphere 
 and at a temperature of 150 or above, it becomes brittle a 
 partly loses its insulating power. 
 
 "A covering made by wrapping three or more layers of 
 asbestos paper, each about ^g in. thick, on the pipe, covering 
 with a layer of hair-felt f in. in thickness, and wrapping the 
 
COVERING OF PIPES. 1167 
 
 whole with canvas or paper is much used. This covering 
 has an effective life of about five years on high-pressure steam- 
 pipes and ten to fifteen years on low- temperature pipes. There 
 are a large number of coverings regularly manufactured for 
 use in such a form that they can be easily applied or removed 
 if desired. There is' a very great difference in the value of these 
 coverings; some of them are very heavy and contain a large 
 amount of mineral matter with little confined air and are very 
 poor insulators. Some are composed entirely of incombustible 
 matter and are nearly as good insulators as hair-felt. In general, 
 the value of a covering is inversely proportional to its weight, 
 the lighter the covering the better its insulating properties; 
 other things being equal, the incombustible mineral substances 
 are to be preferred to combustible material. The table on the 
 next page gives the results of some actual tests of different cover- 
 ings, which were conducted with great care and On a sufficiently 
 large scale to eliminate slight errors of observation. In general, 
 the thickness of the coverings tested was 1 in. Some tests 
 were made with the coverings of different thicknesses, from 
 which it would appear that the gain in insulating power ob- 
 tained by increasing the thickness is very slight compared with 
 the increase in cost. If the material is a good conductor its 
 heat-insulating power is lessened rather than diminished by 
 increasing the thickness beyond a certain point." * 
 
 Sectional Covering's. It may be seen from this 
 table that magnesia, asbestos, and mineral wool are the three 
 materials most valuable for the covering of steam-pipes, as 
 wool and hair, although being better non-conductors, are short- 
 lived on steam-pipes. Wool covering is extensively used, 
 however, on hot- water pipes. Sectional coverings, moulded 
 and formed to fit different sizes of pipes, are made by many 
 parties, and are used almost exclusively for covering steam, 
 and to a large extent for hot-water, pipes. After the sections 
 are applied they are commonly secured by brass lacquered 
 bands. The fittings, such as elbows and tees, are usually 
 plastered with plastic asbestos or magnesia and then covered 
 with canvas applied with flour paste. 
 
 The foregoing data, in connection with the following table, 
 will enable the reader to judge which kind of covering is likely 
 to be the most effective. 
 
 * Prof. Carpenter in "Heating and Ventilating Buildings." 
 
1168 STEAM HEATING. 
 
 TESTS OF VARIOUS PIPE-COVERINGS MADE AT SIBLEY 
 COLLEGE, CORNELL UNIVERSITY. 
 
 Relative 
 Kind of Covering. t^HeSt 
 
 Transmitted. 
 
 Naked pipe 100. 
 
 Two layers asbestos paper, 1 in. hair-felt, and canvas 
 
 cover 15.2 
 
 Two layers asbestos paper, 1 in. hair-felt, canvas 
 
 cover, wrapped with manilla paper . . . .^^.^ . 15.0 
 
 Two layers asbestos paper, 1 in. hair-felt. .......... 17.0 
 
 Hair-felt sectional covering, asbestos lined 18.6 
 
 One thickness asbestos board 59 . 4 
 
 Four thicknesses asbestos paper 50 . 3 
 
 Two layers asbestos paper 77 .7 
 
 Wool felt, asbestos lined 23 . 1 
 
 Wool felt with air spaces, asbestos lined 19.7 
 
 Wool felt, plaster-of-Paris lined . ;*>;- . . v . . . . : . ,... . 25.9 
 
 Asbestos moulded, mixed with plaster of Paris 31.8 
 
 Asbestos felted, pure long fibre 20 . 1 
 
 Asbestos and sponge 18.8 
 
 Asbestos and wool felt 20 . 8 
 
 Magnesia, moulded, applied in plastic condition 22.4 
 
 Magnesia, sectional 18.8 
 
 Mineral wool, sectional 19 .3 
 
 Rock wool, fibrous 20 . 3 
 
 Rock wool, felted %4^&4& '" *' * ' 20 ' 9 
 
 Fossil meal, moulded, f inch thick 29 . 7 
 
 Pipe painted with black asphaltum 105. 5 
 
 Pipe painted with light drab lead paint 108 . 7 
 
 Glossy white paint 95.0 
 
 Hot-water Heating". The system of heating by hot 
 water consists of circulating hot water in the radiators instead 
 of steam. The boiler, pipes, and radiators are completely filled 
 with water, the flow or circulation pipes being attached to 
 the top of the boiler and the return pipes to the bottom; the 
 water in the boiler when heated rises and circulates through 
 the pipes and radiators, parts with a portion of its heat, thus 
 becoming colder and heavier, and passes down through the 
 return pipes to the boiler, where it is again heated. 
 
 There are two general systems of hot- water heating, viz.,| 
 
HOT-WATER HEATING. 
 
 1169 
 
 (1) the open-tank system, and (2) the closed-tank, or pressure, 
 system. 
 
 With the open-tank system an open expansion tank is 
 connected to the heating system in such a way as to receive 
 the increase in the volume of the water due to expansion 
 by heat, and is connected with the outside air by a vent pipe, 
 so that there is no pressure on the tank. Fig. 30 shows the 
 common type of expansion tank, 
 although copper-lined wooden 
 tanks with automatic supply pipe, 
 similar to W. C. tanks, are some- 
 times used. 
 
 With the pressure system a 
 similar tank is used, but the 
 vent pipe is closed and a safety- 
 valve, which will open when the 
 pressure reaches a certain point, 
 is placed on the overflow pipe. 
 By increasing the pressure on the 
 system, the water may be heated 
 up to the temperature of low- 
 pressure steam, and hence less 
 radiatin surface and smaller pipes 
 may be used. 
 
 The open system is most gen- 
 erally used, although the closed 
 system is used occasionally. 
 
 The closed system is always 
 open to the danger of a serious 
 explosion from the safety-valve becoming inoperative or from 
 the giving away of any part of the apparatus. This system 
 cannot be recommended for house heating. 
 
 With the open expansion tank, about the only chance for an 
 explosion is by the stopping of the expansion pipe, either through 
 freezing or by the closing of a valve in the pipe. To avoid 
 this, no stop or valve should be placed on the expansion pipe, 
 and the expansion pipe should be well protected from frost. 
 
 The expansion pipe is usually taken off from the supply to 
 one of the radiators in the upper story and the tank should 
 always be on a level at least 2 or 3 .ft. above the highest radia- 
 tor. 
 
 The capacity of the tank should be somewhat greater than 
 
 I Expansion* 
 Pipe 
 
 Fig. 30 
 
 Expansion Tank. 
 
1170 HOT-WATER HEATING. 
 
 one twentieth of the total cubical contents of heater, pipes, and 
 radiators. 
 
 Boiler and Radiators. Hot-water radiators have the 
 same appearance as steam-radiators, but as a rule there is a 
 slight difference in the interior to improve the circulation. 
 
 Almost any boiler that is suitable for steam heating can be 
 used for hot-water heating, and most of the sectional boilers 
 mentioned on p. 1144 are used for both kinds of heating. For 
 hot water, the safety-valve and water-gauge are omitted. 
 For residence heating, a great variety of small boilers especially 
 designed for hot water have been placed on the market, notably 
 the "Ideal Portable," "Spence," "Gurney, 400 series/' "Palace 
 King/' 
 
 Nearly all of these heaters are made up of a number of hori- 
 zontal cast-iron sections, which are bolted together and the 
 joints packed or'push-nipples used to make them water-tight. 
 The flow pipes are taken from the top of the upper section, 
 and the return pipes are connected with the lowest section, 
 which generally forms either the fire-pot or the ash-pit. 
 
 The successful working of a hot-water heating apparatus 
 depends very largely upon the proper construction of the 
 boiler. It is generally admitted that in an efficient hot-water 
 heater the water must be cut up into small portions, so as to 
 heat quickly, and the whole arrangement of the heater should 
 be such that the least possible resistance is offered to free cir- 
 culation. 
 
 The boiler in which the most powerful circulation is main- 
 tained with the least consumption of fuel is the most satisfactory 
 as well as the cheapest. 
 
 The method employed in connecting the joints and the 
 facilities for cleaning fire surfaces are also points that should 
 be carefully examined. 
 
 For the capacity of the various sizes and styles of heaters the 
 architect or owner must depend largely upon the tables given 
 by the manufacturers. 
 
 A hot-water apparatus is generally filled by connecting the 
 house supply to return pipe at or near the heater. Sometimes 
 a supply is connected with the expansion tank and a ball cock 
 placed on it to insure that there shall always be three or four 
 inches of water in the tank. At the lowest point of apparatus 
 a draw-off, or emptying-cock, should be placed, to empty the 
 ey stem at any time. 
 
SYSTEMS OF HOT-WATER PIPING. 1171 
 
 The apparatus should bn kept full of water during the summer 
 months. This excludes the air and prevents corrosion or 
 oxidation of pipes. 
 
 System of Piping?. Three systems of 'hot-water piping 
 are in vogue, corresponding to the three systems described for 
 steam heating: 
 
 (1) The overhead system, in which the hot water is first 
 conducted to the highest part of the building, usually to the 
 attic, and from thence distributed to the radiators by return 
 pipes, exactly as in the Mills system, except that with hot 
 water a top and bottom connection is made with each radiator, 
 the water flowing into the radiator at the top and out at the 
 bottom. 
 
 An improvement on this system is to have a separate return 
 for the radiators as in the two-pipe system. 
 
 (2) Two-pipe System. This is the system most commonly 
 used. "In this system the mains and distributing pipe have 
 an inclination upward from the heater; the returns are parallel 
 to the main and have an inclination downward toward the 
 heater, connecting at its lower part. The flow pipes are taken 
 from the top of the main and supply one or more radiators. 
 The return risers from the radiators are connected with the 
 return pipe in a similar manner. In this system great care 
 must be taken to produce nearly equal resistance to flow in 
 all branches leading to the different radiators. It will be found 
 that invariably the principal current of heated water will take 
 the path of least resistance, and that a small obstruction, any 
 inequality in piping, etc., is sufficient to make very great differ- 
 ences in the amount of heat received in different parts of the 
 same system. For instance, two branch pipes connected at 
 opposite ends to a tee, which itself is connected by a centre 
 opening to a riser, are almost certain to have an irregular and 
 uncertain circulation." * 
 
 Where indirect radiation is used in hot-water heating, the 
 return pipe should be dropped below the floor and all return 
 risers should be separately connected with the main return. 
 
 (3) One-pipe System. In this system a single pipe is run 
 around the basement as in the one-pipe steam system, except 
 that the main hot-water pipe rises from the boiler; the flow 
 pipes are taken from the top of the main and the water after 
 
 * Prof. Carpenter. 
 
1172 HOT-WATER HEATING. 
 
 passing through the radiators is returned by a separate pipe 
 which is connected with the bottom of the main. With this 
 system the water in the main is chilled wherever the returns 
 are connected with it, so that the radiators at the far end of the 
 system cannot be heated to as high a temperature as those 
 which receive the water as it comes from the boiler. 
 
 A larger main is required for this system than for system 
 No. 2. For small jobs, and particularly with boilers with 
 horizontal sections, this system may be made to work satis- 
 factorily, but the two-pipe system is always to be preferred. 
 
 For hot-water heating, special fittings are made which insure 
 a more positive circulation than the ordinary fittings used in 
 steam piping. 
 
 Rules for computing radiating surface, diameter of pipes, etc., 
 are given on pp. 1162, 1163, and 1166 . 
 
 Comparative Advantages and Disadvantages of 
 Steam and Hot-water Heating. 
 
 (1) Safety. An open-tank hot-water system with no valve 
 on the expansion tank cannot possibly explode unless the 
 expansion pipe should freeze, which is quite unlikely. 
 
 With steam gross carelessness may cause an explosion, 
 although explosions of gravity heating plants are quite rare. 
 
 (2) Comfort. There is probably little difference in this 
 respect between steam and hot water, if both are well designed. 
 Hot- water radiators do not become as hot as steam- radiators, 
 and it is claimed that for this reason they do not dry, or "scotch," 
 the air as much as steam-radiators, and therefore hot-water 
 heating must be healthier. 
 
 The heat of a hot-water apparatus can be perfectly controlled 
 by either the fire in the heater .or the valve on the radiator, 
 by partly closing it; whereas with steam-radiators the valve 
 must be wide open or tightly closed. Also, with a hot- water 
 apparatus, some of the radiators may be run at their full capacity, 
 while others may be partly or entirely shut off without causing 
 noise or in any way interfering with the perfect working of the 
 system. 
 
 A hot-water apparatus is perfectly noiseless in operation, 
 there being none of the snapping or gurgling noises common 
 with steam. 
 
HOT WATER VS. STEAM HEATING. 1173 
 
 (3) First Cost. On an average, a hot- water apparatus 
 costs about one third more than a steam apparatus to do the 
 same work. This is because the hot- water apparatus requires 
 nearly twice as much radiating surface, larger piping, and more 
 expensive fittings. 
 
 (4) Economy in Running. With a steam-heating apparatus, 
 no heat is given off unless the water is kept boiling, while hot- 
 water radiators will give off heat with water in the boiler at a 
 temperature of 100, consequently in moderately warm weather 
 a hot-water plant will generally keep the rooms comfortable 
 with a less consumption of coal than a steam-heating plant. 
 In very cold weather, when the heating apparatus is worked 
 to its full capacity, there is but little difference, if any, in the 
 amount of coal consumed for either steam or hot-water heating. 
 
 In considering statements as to the economy of different 
 heating systems, it should be remembered that the economy 
 of any heating apparatus depends largely on the way in which 
 it is run or upon the party having charge of the plant. 
 
 Disadvantages of Hot-water Heating-. About the 
 only objections that can be urged against hot- water heating 
 are increased first cost, danger from freezing, extra space 
 occupied by radiators, and the fact that a building cannot be 
 as quickly warmed by hot water as by steam. 
 
 It is also more difficult to secure uniform circulation in a 
 large hot- water plant than in a large steam-plant. 
 
 While in large buildings and those that are not kept warm 
 all the time many of these objections are of considerable im- 
 portance, they do not, as a rule, hold good in residences, which 
 are kept at a uniform temperature and in which the extra 
 size of the radiators is of little consequence. 
 
 The danger of freezing is very much greater with hot-water 
 circulation than with steam, and on this account hot-water 
 indirect radiation must be used with much caution. 
 
 Summary. For a residence of eight, ten, or twelve rooms 
 probably 90 per cent, of those who are familiar with both steam 
 and hot-water heating would recommend hot water. 
 
 For larger residences and small apartment houses, about as 
 many would recommend steam as hot water, and for still larger 
 buildings, probably 90 per cent, of heating engineers would 
 recommend a gravity steam system or either the "Webster" 
 or "Paul" system. 
 
1174 RESIDENCE HEATING. 
 
 Hot-air, Steam, and Hot-water Heating in 
 Residences. 
 
 Much advancement has been made of late years in the methods 
 of heating residences and in the apparatus intended for that 
 purpose. While it is impossible in this book to treat the sub- 
 ject in detail, it is believed that the following information will 
 be of value in deciding upon the kind of heating to be used, and 
 in selecting an efficient apparatus and seeing that it is properly 
 put in. 
 
 In deciding upon a heating apparatus for a dwelling, the 
 governing conditions are, generally, (A) the size of the building, 
 and (B) the limit of first cost. When the latter condition is 
 not a controlling one, the cost of running the apparatus should 
 be given the first consideration. 
 
 For residences of eight or ten rooms and covering not more 
 than 1,200 sq. ft. of ground the author would recommend hot- 
 air heating by means of a good furnace. 
 
 For residences covering 1,400 sq. ft., a combination hot-air 
 and water system is recommended, or an entire hot-water 
 system. 
 
 For still larger residences, a steam or hot-water apparatus 
 should be used, 
 
 Furnace Heating. For warming residences not exceed- 
 ing 1,200 sq. ft. of ground area, the author believes a good 
 furnace, properly set and with hot-air pipes of proper size, 
 suitably located, will give the best satisfaction, as it is economical 
 in first cost, easy to manage, costs little for repairs, and furnishes 
 a pleasant and healthy heat at no greater expense of running 
 than with steam or hot water. 
 
 The most common defects observed in furnace-heating are 
 overheating of the air, vitiating of the air by the gases of 
 combustion, and imperfect distribution of the heat. 
 
 The first two defects may be entirely avoided if sufficient care 
 is exercised in the selection and setting up of the furnace and 
 in tending the fire, and the last defect may be reduced to a 
 minimum by a wise location and proper proportion of the flues 
 and registers. 
 
 The cause of the unsatisfactory heating of a great many 
 houses by furnaces is in the owner or builder refusing to pay 
 the necessary price for a first-class furnace and for the best 
 
HOT-AIR FURNACES. 1175 
 
 workmanship and materials. The same carelessness and 
 "skinning" that is sometimes permitted with furnace work, 
 if permitted on a steam or hot-water apparatus, would in most 
 cases prevent their working at all. 
 
 Furnace heating may be divided into two parts, the produc- 
 tion of heat and the distribution of the heat. 
 
 The former depends entirely upon the furnace, itc setting, 
 cold-air supply, draught, kind of fuel, and attendance. 
 
 The Furnace. In principle, a hot-air furnace is simply a 
 stove or heater incased with iron or brick, so as to form an air 
 chamber between the heater and casing. The air enters at the 
 bottom of the chamber, passes over the heated surfaces of the 
 heater, and is conducted by the hot-air pipes to the various 
 rooms. 
 
 The external surface of the fire-pot and all portions of the 
 heater which' receive heat from the fire or smoke are called the 
 radiating surface. 
 
 As a rule, the furnace which has the greatest radiating surface 
 in proportion to the size of the fire-pot will give off the most 
 heat for a given amount of fuel consumed. 
 
 As the amount of radiating surface largely affects the weight 
 of a furnace, and the latter in a great measure the selling price, 
 it is obvious that the best furnaces must cost the most. It is 
 true that one furnace may have its radiating surfaces better 
 arranged than another, so as to give off more heat for a less 
 quantity of metal, but it is seldom that a very light furnace, 
 particularly if of cast iron, is a good heater. 
 
 Furnaces should be so designed that the smoke, after leaving 
 the combustion-chamber, must travel around the radiator one 
 or more times before finding an exit to the chimney. With 
 a chimney-flue of proper size and topped out well above the 
 roof, it is possible to make the smoke travel a long distance 
 and thus obtain great economy of fuel. The best furnaces 
 are designed on this principle. 
 
 Besides having a large radiating surface, the furnace should 
 have as few joints as possible, and should be arranged so as 
 to be easily cleaned. 
 
 Furnaces are made of cast iron, wrought iron, and steel, either 
 used singly or combined. The radiating surface above the fire- 
 pot can be made more cheaply of wrought iron than of cast iron, 
 and in certain arrangements it is just as serviceable. 
 
 While there are excellent furnaces made of wrought iron and 
 
1176 
 
 RESIDENCE HEATING. 
 
 steel, the author believes that a heavy cast-iron furnace is the 
 most durable, and can be made as tight. Some furnaces are 
 made chiefly of cast iron, but with air or smoke flues of wrought 
 iron fitting into cast-iron sockets. This arrangement is not 
 generally approved, as the two metals expand and contract 
 unequally, thus tending to open the joint. 
 
 There are so many styles of furnaces manufactured that it is 
 quite impossible to go further into details. It may be said, 
 however, that the furnace shown in Fig. 31, made by the Richard- 
 
 Fig. 31 
 
 son & Boynton Company, is representative of the best type of 
 cast-iron furnace, and that shown in Fig. 32, made by Isaac A. 
 Sheppard & Co., of a modern steel-plate furnace. Fig. 33, of 
 which the Excelsior Steel Furnace Company are the makers, 
 shows a type of furnace which consists of a plain combustion- 
 chamber with a steel radiator. This radiator is divided with 
 a horizontal partition, so that smoke must ciculate entirely 
 around it before it enters the flue. This furnace is intended for 
 soft coal. The more modern furnaces, constructed for burning 
 
HOT-AIR FURNACES. 
 
 1177 
 
 soft coal, have provision for the introduction of superheated ail 
 into the fire-box, thereby preventing the formation of soot and 
 causing thorough combustion and intense heat. The one 
 shown in Fig. 31 is a hot-air blast-furnace, and is supplied with 
 oxygen at a high temperature for either hard or soft coal, acceler- 
 ating and intensifying combustion to a very high degree. 
 
 In the Twentieth Century furnace the fire-pot contains cells 
 and slots cast within the walls of the pot which admit air at 
 twenty points equally distrib- 
 uted around the circumfer- 
 ence of the same. By reason 
 of this admission of air the 
 fire burns from the top down 
 and from the circumference 
 toward the centre, causing an 
 intense heat around the out- 
 side of the bowl. This furnace 
 can be operated successfully 
 with steam coal. 
 
 The Thatcher Furnace Com- 
 pany are makers of a tubular 
 furnace that seems to possess 
 considerable merit. 
 
 The casing surrounding the ( 
 heater may be of brick or sheet 
 iron. If of brick, it should , 
 consist of two 4-inch walls with 
 a space between, the inner wall 
 being generally built on a cir- Fig. 32 
 
 cle and the outer one on a square. 
 
 "Brick set" furnaces are not as common as they formerly 
 were, as they can be cased as well with iron and without occupy- 
 ing so much space in the cellar. When cased with sheet iron, 
 the furnace is designated as " portable." Portable furnaces 
 should always have a double casing with an inch space between. 
 The inner casing may be of black iron, but the outer one should 
 be galvanized. The hot air is thrown into the pipes better if 
 the top of the casing is truncated, as in Fig. 32. 
 
 Cold-air Supply. In a house heated by a furnace, the 
 temperature of the rooms is maintained by a constant incoming 
 current of hot air, and it is absolutely necessary for satisfactory 
 heating that prouer provision be made for supplying this air 
 
1178 
 
 RESIDENCE HEATING. 
 
 to the furnace, and on no account should a hot-air furnace be 
 used without being provided with a direct supply of air from 
 outside the building. In dwellings this may be best accom- 
 plished by putting an opening in the external wall just beneath 
 the first-floor joist and as far above the ground as the elevation 
 of the building will permit. From this opening, which should 
 be covered with galvanized wire netting of about three eighths 
 of an inch mesh, a duct or flue should be carried to the air-pit 
 under the furnace, as shown in Fig. 33. 
 
 The duct may be either carried horizontally under the base- 
 ment ceiling until near the furnace and then dropped to the air- 
 
 HOT AIR 
 
 ^ r~ 
 
 s^^ru \ 
 
 INDIRECT DRAFT 1H / 
 V / 
 
 Fig. 33 
 
 pit, or it may be carried down against the cellar wall and thence 
 under the floor to the furnace. The portion of the duct above 
 the floor should be built of well-seasoned matched boards or 
 of galvanized iron. The portion below the floor should be con- 
 structed either of stone, brick, or glazed tile, and should be 
 
WARM- AIR PIPES AND REGISTERS. 1179 
 
 tightly cemented. If of brick or stone, the duct should be cov- 
 ered with stone slabs with the edges roughly dressed and the 
 joints cemented. The air-duct should not be carried under the 
 floor if the soil is at all damp, nor near any drain. 
 
 Fig. 34 shows the formation and construction of foundation 
 and pit of a portable -furnace. 
 
 Besides the external air supply, it is also a good idea to have 
 a smaller air-duct leading from a register in the front hall to 
 the base of the furnace. This duct may be of wood, tin, or 
 
 Fig. 34 
 
 Foundation and Pit of a Portable Furnace. 
 
 galvanized iron, and may be connected either with the base 
 of the furnace above the floor or teed into the outside duct, 
 but care should be taken to prevent the air from blowing from 
 the outside duct up through the inside one. 
 
 An inside duct will produce a better circulation of air through 
 the house, and on very cold nights the outside duct may be 
 shut off and the air taken entirely from the front hall, as the 
 air from this source, having nothing to contaminate it, will be 
 reasonably pure. 
 
 The Hot-air Pipes and Registers. The pipes which 
 convey the heated air from the furnace to the various rooms 
 ' should be of bright IX tin for sizes less than 14 ins. in diameter 
 and of No. 26 galvanized iron for larger sizes. 
 
 All pipes below the basement ceiling should be round, and for 
 the best work should be covered with asbestos paper, pasted 
 to the pipe with a specially prepared paste. 
 
 The vertical hot-air pipes, to rooms in second or third stories, 
 arc frequently termed "stacks." They usually pass up be- 
 tween the studding of the partitions in the lower stories, thus 
 necessitating a shallow pipe. 
 
1180 RESIDENCE HEATING. 
 
 For medium- and low-cost houses the stacks are usually made 
 3f ins. deep, of one thickness of tin, and wrapped with asbestos 
 paper pasted to the tin. For a better class of buildings double 
 pipes are, or should be, used for the stacks. These stacks have 
 an air space between the outside and inside pipes, affording 
 a circulation of air, which makes the stacks absolutely safe, 
 thus obviating the necessity of iron lath in front of the stack. 
 
 The table on p. 1197 gives the sizes and dimensions of safety 
 double hot-air stacks made by the Excelsior Steel Furnace 
 Company. 
 
 In providing for hot-air stacks, it should be remembered that 
 the friction against the sides of the pipe largely affects the 
 volume of air conveyed, and that consequently a round pipe 
 is always to be preferred to a square one, and a square pipe to 
 a shallow pipe. In large residences, 5- or 6-inch studding 
 should be used for partitions, so that thicker pipes may be used. 
 
 Brick flues should not be used for conveying hot air, as the 
 loss of heat by absorption is very great, and economical results 
 cannot be obtained. 
 
 The hot-air registers should be set in double register boxes 
 made of tin, and the bottom of the stacks should terminate in 
 a "boot" or "footing," arranged in such a way as will insure 
 the quick and easy flow of hot air from the feed-pipe into the 
 stacks. 
 
 Warm-air Radiators. In the use of warm-air furnaces 
 it is oftentimes extremely difficult to heat rooms located at a 
 distance from the furnace, rooms that are without any means 
 of ventilation, or rooms which are greatly exposed to outside 
 winds. This difficulty may sometimes be overcome by using 
 a warm-air radiator placed over the outlet of the furnace pipe, 
 which must be in the floor. These radiators are made of sheet 
 steel and are so constructed that they set up a circulation of 
 air in the room which tends to draw the air from the furnace. 
 They somewhat resemble a direct-indirect steam-radiator.* 
 
 Ventilation. A hot-air furnace plant, properly put in, j 
 will furnish a good supply of fresh air, and therefore afford fairly 
 good ventilation, if means are provided for carrying off the foul 
 air in the rooms. The warm air entering a room must of neces- 
 sity force out an equal quantity of the air already in the room; 
 
 * A very good pattern of warm-air radiator is made by the International 
 Heater Co. 
 
LOCATING THE FURNACE. 1181 
 
 exits are often found in the spaces around the doors and windows, 
 but these arc rarely sufficient to carry away the air as fast as it 
 would enter if unimpeded. Fireplaces, especially if kept in 
 use, afford excellent ventilation. A good arrangement for ob- 
 taining ventilation is by building a large flue in a central chim- 
 ney and using a galvanized-iron smoke-stack, placed in the 
 centre of it, for the furnace. The space surrounding the smoke- 
 pipe may then be used for ventilation and ducts from different 
 rooms connected with it. 
 
 L<o cation of Furnace, Upon the location of the fur- 
 nace the successful heating of the house often .depends, and it 
 is a matter that requires careful consideration. 
 
 As a general rule, the furnace should be located in the base- 
 ment, near the centre of the space occupied by the registers, 
 and a little nearer the side from which the prevailing winds 
 come in winter-time. The tendency, in hot-air heating, when 
 the wind is blowing strong in severe cold weather, is for 
 the rooms on the further side of the house from the wind to be 
 overheated, while those against the wind are poorly heated, 
 the registers on the windward side delivering almost no hot air. 
 Therefore, to counteract this tendency, the furnace should be 
 placed some few feet toward the windward side of the building, 
 provided this does not make the pipes to the general, or family, 
 living-rooms longer than the others. 
 
 The height of the basement should be such that the " leaders," 
 or horizontal hot-air pipes below basement ceiling, may have 
 a pitch of 1J ins. per running foot upward from the furnace. 
 If there is no inclination to these pipes, the first-story rooms 
 will be heated with difficulty. For a residence of ten rooms 
 the furnace-room should have a clear height of at least 7 ft. 
 6 ins. 
 
 Cold-air Opening'. If only one external cold-air supply 
 is used, it should be taken from the direction from which the 
 prevailing winds come. For buildings in exposed situations 
 it is desirable to have a cold-air supply from the opposite side 
 of the building also, the ducts connecting, and each being fur- 
 nished with a damper, so that either duct may be used, accord- 
 ing to the direction of the wind. Cases have been known where 
 the wind blowing from the opposite direction of the cold-air 
 supply has sucked the air from the house through the furnace 
 and cold-air duct, thus actually reversing the natural operation 
 of the furnace. Two supplies will obviate this possibility. 
 
1182 RESIDENCE HEATING. 
 
 Location of Stacks and Registers. To insure the 
 best results, the location of furnace, stacks, and registers should 
 be planned out before the work of construction begins, for while 
 the building need not be planned to suit the heating apparatus, 
 it almost always happens that the setting of the partitions, 
 swinging of doors, and placing of studs and joists can be 
 arranged so as to favor the placing of stacks and registers, 
 without seriously affecting any desired arrangement of the plan, 
 and this can be done much better on the plans than after the 
 house is started. 
 
 It is generally conceded that the hot-air stacks should be 
 placed in the partitions and as near to the furnace as practicable, 
 and that all horizontal branches should be as short as possible, 
 as the air travels much slower in the horizontal branches and 
 more heat is lost from radiation. The registers should be 
 placed as near the stack as possible; they should not be placed 
 near the windows, nor where the doors will swing over or 
 against them, nor in the floor near an open fireplace. 
 
 Whether the register shall be placed in the floor or partition 
 is a matter that should be decided by the owner. It is claimed 
 that the circulation from a wall register is not as good as from 
 one placed in the floor, and the wall above the register generally 
 becomes discolored after a time by the dust that is occasionally 
 blown up through the pipes. On the other hand, floor registers 
 catch much more dirt from sweeping the rooms, and many 
 ladies object to having their carpets cut. The author believes 
 that it is healthier to have the registers placed in the wall. 
 Convex registers are to be preferred for walls, as they deliver 
 more air than do the ordinary flat registers. It sometimes 
 happens that the stacks must be put in an outside wall. When 
 such is the case, the stack should be double and wrapped with 
 asbestos paper as well. Stacks should not be placed in out- 
 side walls, however, when it is possible to avoid it. 
 
 Calculations for Size of Furnace, Pipes, and 
 Registers. 
 
 There appears to be no rule by w T hich the architect can deter- 
 mine the size of the furnace that should be used to heat a given 
 building other than by using the tables given by the various 
 manufacturers. Rules have been given for determining the 
 necessary grate area of a furnace, but it is utterly impossible 
 to make such a rule that will apply to all furnaces, as the heating 
 
CAPACITY OF AIR PIPES AND REGISTERS. 1183 
 
 capacity depends almost as much upon the amount and char- 
 acter of the radiating surface, and these vary with the make 
 of the furnace. Some manufacturers give rules which take 
 into account not only the cubic space to be heated, but also the 
 outside wall and the glass area, both of which should be con- 
 sidered in deciding on the size of the heater. Most furnace- 
 makers, however, merely give the amount of cubic space that 
 the different sizes of their particular furnaces will heat, arid 
 as there is no way of telling how reliable these figures are, except 
 by experience, it is wise to have the contractor give a guarantee 
 that the furnace shall heat the building to 70 in zero weather 
 without forcing the furnace. 
 
 Pipes and Registers. The tables given in various books 
 and catalogues for the size of pipes and registers vary a great 
 deal and must be used with considerable judgment. The follow- 
 ing table appears to the author to be as reliable as any: 
 
 TABLE OF CAPACITY OF HOT-AIR PIPES AND 
 REGISTERS. 
 
 Size of 
 Register. 
 
 Equivalent 
 in Round or 
 Leader Pipe. 
 
 Equivalent 
 in Square or 
 Riser Pipe. 
 
 Cubic Feet 
 of Space on 
 First Floor 
 Same Will 
 Heat. 
 
 Cubic Feet 
 on Second 
 Floor. 
 
 Cubic Feet 
 on Third 
 Floor. 
 
 6X 8 
 
 6 in. 
 
 4X 8 
 
 400 
 
 450 
 
 500 
 
 *8X 8 
 
 7 
 
 4X10 
 
 450 
 
 500 
 
 560 
 
 *8X10 
 
 8 
 
 4X10 
 
 500 
 
 850 
 
 880 
 
 *8X12 
 
 8 
 
 4X11 
 
 800 
 
 1000 
 
 1050 
 
 *9X12 
 
 9 
 
 4X12 
 
 1050 
 
 1250 
 
 1320 
 
 *9X14 
 
 9 
 
 4X14 
 
 1050 
 
 1350 
 
 1450 
 
 * 10X12 
 
 10 
 
 4X14 
 
 1500 
 
 1650 
 
 1800 
 
 * 10X14 
 
 10 
 
 6X10 
 
 1800 
 
 2000 
 
 2200 
 
 10X16 
 
 10 
 
 6X10 
 
 1800 
 
 2000 
 
 2200 
 
 12X14 
 
 12 
 
 6X12 
 
 2200 
 
 2300 
 
 2500 
 
 *12X15 
 
 12 
 
 6X12 
 
 2250 
 
 2300 
 
 2500 
 
 *12X17 
 
 12 
 
 6X14 
 
 2300 
 
 2600 
 
 2800 
 
 12X19 
 
 12 
 
 6X14 
 
 2300 
 
 2600 
 
 2SOO 
 
 * 14X18 
 
 14 
 
 6X16 
 
 2800 
 
 3000 
 
 3200 
 
 * 14X20 
 
 14 
 
 6X16 
 
 2900 
 
 3000 
 
 3200 
 
 * 14X22 
 
 14 
 
 8X16 
 
 3000 
 
 3200 
 
 3400 
 
 * 16X20 
 
 16 
 
 8X18 
 
 3600 
 
 4000 
 
 4250 
 
 * 16X24 
 
 16 
 
 8X18 
 
 3700 
 
 4000 
 
 4250 
 
 * 20X24 
 
 18 ' 
 
 10X20 
 
 4800 
 
 5400 
 
 5750 
 
 * 20X26 
 
 20 
 
 10X24 
 
 6000 
 
 7000 
 
 7450 
 
1184 RESIDENCE HEATING. 
 
 This table gives different sizes of hot-air registers used in 
 furnace practice, together with the equivalents ' of the capacity 
 of the same in round leader pipes from furnace, with eleva- 
 tion of at least one inch to the foot; also equivalent in 
 riser pipes (or stacks), and also the cubic feet of space on 
 first, second, and third floors which said registers with their 
 proper round and square pipes will heat. The table is based 
 on normal conditions, with runs of pipe of usual length, and 
 is intended to show the size of registers and pipes neces- 
 sary to raise the temperature of air from zero outside to 70 
 on the inside, within reasonable time, without forcing. The 
 sizes that are marked with an asterisk are those recom- 
 mended for general use. The larger the register the less resist- 
 ance to the flow of the heated air, but sizes mentioned will 
 produce good results, and, being stock sizes, will always be 
 found in stock. In planning work arrange to use the sizes 
 referred to. 
 
 It should always be borne in mind, however, that uniform 
 heating does not depend so much upon the actual size of the 
 pipes as upon the relative sizes. For example, in a two-story 
 house of eight rooms of exactly the same size and the same amount 
 of wall and glass area the best heating results will be obtained 
 not by using the same size of pipes for all the rooms, even if the 
 pipes are of ample capacity, but by carefully proportioning 
 the sizes of the pipes according to the exposure, length of the 
 leaders, and whether the room is in the first or second story. 
 The registers in the rooms with north and west exposures should 
 be a little nearer the furnace, if possible, than the others, and 
 the pipes to the first story should be larger than those leading 
 to the second story. 
 
 The International Heater Company states that 1 sq. in. of 
 capacity of hot-air pipe will heat 50 cu. ft. in stores and 90 
 cu. ft. in churches when there is but one pipe directly over 
 the furnace. 
 
 Cold-air .Box. The sectional area of the cold-air box 
 should be equal to three-fourths of the aggregate sectional area 
 of the leaders. The box, or duct, should be 10 or 12 ins. deep 
 (for dwellings) and wide enough to give the required sectional 
 area. It should also always be provided with a damper, so 
 that the supply may be regulated to the heavy winds and ex- 
 treme cold weather. 
 
SPECIFICATIONS FOR FURNACE WORK. 1185 
 
 Specifications. 
 
 The following form is given as a guide to architects in pre- 
 paring the specifications for furnace work: 
 
 SPECIFICATIONS FOR -FURNACE WORK IN RESIDENCE FOR MR. 
 
 TO BE BUILT AT 
 
 Architect. 
 
 Furnace. Furnish and set up complete, where shown on base- 
 ment plan, one No. furnace, portable pattern, with 
 double casings. Connect the furnace with the chimney with 
 No. 24 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 ins. below the ceiling. 
 
 Air-pit. Excavate for and build a cold-air chamber under 
 the furnace not less than 18 ins. deep, with 8-inch brick walls, 
 laid and plastered with cement; also cement the bottom 
 of the chamber. Build the cold-air duct under cellar floor, 
 where shown on plan, to be ft. long, 14 ins. deep in the clear, 
 and ins. wide, with sides of hard brick in cement, and the sides 
 and bottom smoothly plastered with cement. Cover the duct 
 with 3-inch flag-stones with tight joints, leaving opening of 
 proper size 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 to be double 
 with air space between. All turns in leaders to be made by 
 three- or four-piece elbows, and the stacks to have boots or 
 starters of approved pattern. 
 
 SIZES OF PIPES AND REGISTERS. 
 
 Hall 12" leader No stack 12" X 15" register 
 
 Parlor 10" " 4"X 14" stack 10" X 12" " 
 
 Dining-room. ... 12" " 6"X12" " 12"X15" " 
 
 Library 10" " 4"X14" " 10"X12" " 
 
 Chamber No. 1... 9" " 4"X14" " 9"X14" " 
 
 u 2 ... 9" " 4"X12" " 9"X12" " 
 
 " " 3... 8" " 4"X10" " 8"X10" " 
 
 Registers. All registers are to be of sizes given in the fore- 
 going list, of the Tuttle and Bailey manufacture, japanned, 
 
RESIDENCE HEATING 
 
 except those in the first story, which are to be elect ro-bronze- 
 plated. All floor registers are to be set in iron borders corre- 
 sponding with the registers. 
 
 lit'tjixter Hows. All register boxes to be made double: for 
 first-floor boxes the joists arc to be lined irith tin and provided 
 with ceiling plates full size of register, with plaster collar an ached, 
 so that pipes and boxes can be removed without disturbing 
 the plastering or defacing the ceiling. 
 
 MisMRan&Hto. All horizontal pipes in the basement 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 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 all rubbish made by 
 him, clean up all ironwork, and leave the whole apparatus in 
 complete working order, and furnish a poker of proper size. 
 
 Guarantee. The contractor is to guarantee that the furnace 
 shall, under proper management, heat all rooms with registers 
 connected with the furnace to 70 Fahr. when temperature 
 outside indicates 10 Mow zero. In event of the failure of the 
 furnace to do this, the contractor is either to make the furnace 
 heat said rooms or substitute another furnace that will heat 
 the rooms at his own expense and without unnecessary delay. 
 
 Hot Air and Water Combination. 
 
 It is quite difficult, if not impossible, to heat throughout 
 dwellings covering more than l,400sq. 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 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 great variety of "combination" furnaces are now 
 made which contain provisions for heating water which- may 
 be carried by pipes to radiators located in the portions of the 
 house most difficult to heat by warm air. Such combination 
 as have been used with great success, and for heating 
 
COMIUN ATI<>\ SYSTKMS. 
 
 dwelling^ of (en average si/e rooms lli- author believes it to 
 be the most, successful system, as il guarantees the coiuforlal >le 
 warming of the house, and, if properly put in, thorough vmii- 
 lation, wliicli cannot he obtained by ;uiy system of direct hot- 
 water or ,st. -;iin radiation. Jt is claimed (hat nearly 200 sq. ft. 
 of hot water radiation' can l>e obtained by absorbing the surplus 
 heal \\hich would usually be wasted in a warm air furnace. 
 
 The construction of the parts for healini- the water varies 
 greatly with different makes of furnaces. Some furnaces have 
 a portion of the lire pot hollow, ami the water is heated there; 
 others have a .separate heater suspended over the lire-pot. It 
 is impossible here to consider the relative merits of the various 
 i he architect should examine the healers for himself 
 and look up their record before specifying any particular make. 
 
 As a rule, the portions of the house which should be heated 
 by the hot water are the halls, bathroom, and perhaps t he rooms 
 on the north or west side of the house. 
 
 The same rules govern the si/e of the radiators and piping 
 and tin' manner of installing as in an entire hot water plant. 
 
 Hot Air and Steam Combination.- -There are also 
 several furnaces which have a small steam-boiler placed above 
 the lire by means of which a few rooms may be heated by direct 
 steam radiation. Safety-valves are provided so that the steam 
 pressure cannot exceed 5 Ibs., and if the directions for running 
 the apparatus are followed, the apparatus is perfectly safe. 
 The steam combination possesses some advantages over the 
 ho! \\ater combination, and for a large residence the author 
 believes that it will give more satisfactory results with intelli- 
 gent manaL'vmenl . 
 
 Hot-water Heating in Residences. As stated on 
 p. 1 17;>. there is no better system of warming residences of ten 
 or twelve rooms than the hot-water system, and it is being 
 used to a greater extent every year. 
 
 The general principles of hot-water heating, as explained 
 on pp. 1 His to 1 172, apply to residences as to all other buildings. 
 The open tank svsteni should always be used for t his class of work. 
 The following A (I rice to Fit tern, published by the (Jurncy Heater 
 Manufacturing Company, contains many practical suggestions 
 that should be of almost cijual interest to the architect and 
 owner: 
 
 "When estimating upon a job, take well into consideration the 
 extent of all flow, return pipes, and risers, also their situation, 
 
1188 RESIDENCE HEATING. 
 
 and calculate them as radiating surface in addition to what 
 is placed in rooms, and allow heater power accordingly. 
 
 "Due care must be exercised to provide for any special con- 
 ditions, such as exposure of building, material of construction, 
 location, length and size of mains governing plant under con- 
 sideration. 
 
 . " Allowances should be made for loose construction of doors 
 and windows, which admit large volumes of cold air, and if 
 there are outside doors which are used frequently and open 
 directly into the room, a radiator should be placed near them. 
 
 "In estimating the radiating surface, it should be borne in 
 mind that a large surface at a comparatively low temperature 
 gives a much pleasanter atmosphere than a small surface at a 
 high temperature. 
 
 "Excess of surface is no discomfort, as is the case with steam, 
 since the temperature can easily be controlled by varying the 
 fire or by valve on radiator. 
 
 "All flow and return pipes in cellar should be properly covered 
 with hair-felt or some other good non-conducting material, to 
 obtain the best and most economical results. Doing this will 
 save one sixth of the heat. If no covering is used, paint all ex- 
 posed pipes in basement a black or maroon japan. The heater 
 should be neatly plastered with plastic asbestos." 
 
 Indirect Radiation. Every large residence heated, 
 either by hot- water or steam radiation, should have at least 
 two indirect radiators, to provide for some ventilation. These 
 should be placed in the cellar and connected with registers in 
 the front hall and principal living-room. The common method of 
 providing for indirect radiation is explained on pp. 1129 and 1130. 
 
 Direct radiation, as has been explained elsewhere, simply 
 heats the air in the room over and over, and not only does not 
 afford any ventilation, but tends to decrease the vitalizing 
 qualities of the air. 
 
 Specification. 
 
 The following may serve as a guide in specifying hot-water 
 heating for residences: 
 
 SPECIFICATION FOR HOT-WATER HEATING APPARATUS IN RESI- 
 DENCE FOR JOHN JONES, ESQ., BROOKLINE, MASS. 
 
 This specification contemplates a complete two-pipe circu- 
 lating system, guaranteed perfect in every respect. 
 
SPECIFICATIONS FOR HOT-WATER APPARATUS. 1189 
 
 Heater. Furnish and set up in cellar where shown on plan 
 one No. (55 Ideal portable) water-boiler, guaranteed free from 
 all flaws and defects. 
 
 The heater to 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 slice-bar, and one fine brush and handle. 
 
 Smoke-pipe. Connect the boiler to the chimney by means 
 of smoke-pipe made of No. 20 galvanized iron, the diameter of 
 the pipe to be equal to the outlet on the heater. 
 
 Trimmings. The boiler to be provided with one expansion 
 thermometer registering from 80 F. to 250 F. Attach to 
 main flow pipe, near the boiler, 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 j-inch cast-iron fitting for boiler con- 
 nection, which is to be made by this contractor, with suitable 
 cock. 
 
 Draw-off cock to be placed on lowest point of system and 
 to be fitted for hose-nipple attachment. 
 
 Pipes. Furnish and run all necessary flow and return pipes 
 of ample size, connecting them to radiators with pipes of ample 
 size to insure the free and rapid flow of hot water to the radiators 
 and easy flow of the cooler water back to the heater. 
 
 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 out and all obstructions 
 removed before pipes are placed in position. 
 
 All flow and return pipes in basement 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, floors, or 
 partitions, the pipes shall be encased in iron or tin tubes and 
 the holes protected with floor or ceiling plates. 
 
 Expansion Tank. The expansion tank to be made of No. 22 
 galvanized iron; 30 ins. high and 14 ins. in diameter, and is to 
 be furnished with a proper gauge-glass with brass mountings 
 complete. It is to be placed above all the radiators in some 
 suitable place and supported on a proper shelf. From this 
 tank an overflow pipe will be run to basement or other suitable 
 place with a vent pipe through the roof. 
 
 * 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. 
 
1190 RESIDENCE HEATING/ 
 
 Radiators. Furnish and set up the following radiators, viz.: 
 
 
 No. of Radiators. 
 
 Square Feet of 
 Radiating 
 Surface. 
 
 Main hall 
 
 1 indirect radiator 
 
 1 Jt 
 
 1 direct radiator 
 
 1 
 1 
 1 
 1 
 1 
 \ 
 
 lOSsc 
 120 
 40 
 60 
 40 
 44 
 36 
 32 
 32 
 
 M 
 
 t. 
 
 Sitting-room 
 
 Library. . . 
 
 Dining-room . 
 
 Sitting-room chamber 
 Library chamber 
 
 Dining-room chamber 
 Kitchen chamber 
 
 Bathroom 
 
 
 9 radiators 
 
 512 sq. ft. 
 
 In all 284 sq. ft. of direct surface and 223 sq. ft. of indirect; 
 total surface, 512 sq. ft. 
 
 The direct radiators to be (American Radiator Co.'s Rococo 
 hot-water pattern) 38 ins. high. 
 
 Air-valves. Each radiator will have properly connected to 
 it a nickel-plated air-valve to be opened and closed with a key. 
 
 Radiator Valves. All direct radiators will be promptly con- 
 necte<J to the system of piping with a (Gurney) quick-opening 
 nickel-plated radiator valve and union elbow. 
 
 Indirect Radiation. The indirect radiators shall consist of 
 two stacks of the (American Radiator Co.'s Excelsior hot- water 
 radiator) connected together with tight joints and firmly sus- 
 pended from the basement ceiling by suitable wrought-iron 
 hangers. 
 
 The stacks shall be so piped and hung as to permit a quick, 
 noiseless, and constant flow throughout of the heated water. 
 
 Each stack to be enclosed in galvanized iron chamber with 
 proper inlet for fresh air and a corresponding outlet for warm 
 air, connected by a galvanized pipe to the register in the room 
 which the stack is intended to heat. 
 
 The registers to be of the Tuttle & Bailey pattern, electro 
 bronzed plated, and of the following sizes: hall, 12X19; sitting- 
 room, 14X22. 
 
 To have floor borders and to be set in a register box. The 
 pipe connecting the stack and register is to be so arranged that 
 all fresh air coming in will be properly heated and conveyed 
 without 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; unless otherwise specified, this space is not to be less 
 than 12 ins. above and 10 ins. below the stack. 
 
 Covering of Pipe. All flow and return pipe and fittings in 
 cellar above the floor to be properly covered with 1-inch hair- 
 
STEAM HEATING FOR RESIDENCES. 1191 
 
 felt neatly sewed up in canvas and painted one coat of good 
 white lead, or to be covered with asbestos or magnesia sec- 
 tional covering with canvas cover and secured by brass lac- 
 quered bands. 
 
 Boiler Covering.- Cover all exposed parts of boiler, except 
 the front, with plastic asbestos (1^) inches thick, neatly applied 
 and trowelled smooth. 
 
 Workmanship. All work to be done in a neat, substantial, 
 and workmanlike manner, and the apparatus,' when completed, 
 to be thoroughly tested and left in good working order. 
 
 Guarantee. The contractor is to guarantee that the apparatus, 
 when completed in accordance with this specification, 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 and rapid circulation when in operation. 
 
 Steam Heating* for Residences. 
 
 Although hot water is perhaps more popular just now for resi- 
 dence heating, there can be no question that a building can be as 
 thoroughly warmed and ventilated by steam as by any other 
 system, and generally at a smaller first cost. In very cold weather, 
 it is doubtful if hot-water heating is as satisfactory as steam. 
 
 For indirect radiation, steam heat is generally considered 
 cheaper than hot- water heat, and in every way as satisfactory. 
 
 For very large residences, the author would recommend steam 
 heat, all' of the principal rooms to be heated by indirect radia- 
 tion, and only the bathroom, 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 regu- 
 lated according to the weather. 
 
 The same principles apply in heating a residence by steam 
 as in heating any other building, and there is no difference in 
 the piping and radiators. The boilers used in residence heating, 
 however, are generally of the cast-iron sectional type described 
 on pp. 1141 to 1144. 
 
 The single-pipe system is commonly used in dwellings, all 
 indirect radiators, however, being connected with a return 
 pipe dropped below the water-line. Two specifications are 
 appended for steam heating, one for all direct radiation and 
 one for all indirect radiation; the latter can be easily amended 
 to provide for some direct radiation. 
 
1192 RESIDENCE HEATING. 
 
 Typical Specification. 
 
 FOR A FIRST-CLASS LOW-PRESSURE STEAM-HEATING APPARATUS 
 FOR HEATING BY ALL DIRECT RADIATION. 
 
 Intention. This specification is intended to cover everything 
 necessary to fully finish and install in the above-mentioned 
 building a complete steam-heating system in strict accordance 
 with the plans and this specification, as prepared by T. Square, 
 architect. 
 
 Plans. The plans 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 Requirement. This contractor is to provide all 
 necessary tools and appliances for the erection and completion 
 of the work, and when completed must 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 
 ^hall be undertaken without consulting the architects. 
 
 This contractor shall be fully responsible for the safety and 
 good condition of the work and material embraced in this con- 
 tract until the completion and acceptance of the same. 
 
 All work must be of the best quality, and should at any 
 time improper, imperfect, or unsound material or faulty work- 
 manship be observed, whether before or after same has been 
 built into the structure, this contractor shall, upon notice from 
 the architect, remove same and good and proper material and 
 workmanship be substituted without delay in place thereof, 
 in default of which the architect will effect same by other means 
 as may be deemed best, and shall deduct the cost of such altera- 
 tions from the sum due the contractor under this contract. 
 
 System. The heating to be effected by direct radiation dis- 
 tributed throughout as shown on plans, and the circulation 
 of the steam shall be by the one-pipe basement system. 
 
 Boiler. This contractor is to build foundation for boiler, 
 where shown, 12" deep, of common hard brick laid in cement 
 mortar. Leave ash-pit for boiler of proper size, 12" deep, 
 cemented, and made water-tight. Furnish and set up one 
 ( Ideal C. I. sectional) boiler, provided with 6" low-pressure 
 brass-cased steam-gauge, water-gauge, and glass, gauge-cocks, 
 ombination column, safety- and blow-off valves, and all other 
 usual and necessary trimmings to complete the boiler,* and 
 full set of fire tools,^ consisting of one slicing-bar, one hoe, one 
 poker, and a cleaning brush. Cover boiler with \\" of asbestos 
 cement, neatly trowelled to a smooth finish. 
 
 Water Feed -The plumber will bring the water-supply to 
 
 * For house-heating plants it is well to specify also "one automatic 
 damper regulator of approved pattern, with connection for operating 
 draught door and cold-air check." 
 
SPECIFICATIONS: STEAM-HEATING APPARATUS. 1193 
 
 within 6 ft. of boiler, and this contractor is to make connection 
 with boiler with j" iron pipe, stop-cock, and check-valve. 
 
 Catch-basin. Furnish and set one cast-iron catch-basin, 
 28"X36", where shown on plans. Connect the boiler blow-off 
 pipe to catch-basin, connect same to sewer, and vent with 1-J" 
 pipe to roof. (Note.' Catch-basins are usually omitted in 
 house heating, a hose being attached to the blow-off valve for 
 blowing off.) 
 
 Smoke-pipe. Connect the boiler with the chimney with a 
 round smoke-pipe made of No. 16 black 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 main steam-pipe is to be of 
 ample size to carry all the risers and radiators attached to 
 the system, and is to be so graded that all water of condensa- 
 tion will flow freely back to the boiler without noise. 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, and when horizontal runs occur 
 they are to have a relief pipe to carry off all water of conden- 
 sation. 
 
 Eccentric fittings only to be used on heating mains where 
 reduced in size. 
 
 Sizes of supplies to radiators to be 1" to 24 sq. ft., 1" to 
 60 sq. ft., and \\" to all above. Radiators on first floor to 
 be connected direct to steam main. 
 
 All horizontal pipes to be one size larger than the vertical 
 pipes. 
 
 All steam connections from heating main to radiators and 
 risers to run on a 45 angle from heating main and to be one 
 size larger than risers and radiator feeds. 
 
 Pipe and Fittings. All pipe used throughout shall be of 
 the best quality wrought-iron pipe of standard weight and 
 thickness, smooth inside, free from imperfections, and true 
 to shape. All threads to be clean-cut, straight, and true. 
 All fittings to be of the best heavy gray iron, with taper threads 
 and heavy beaded. No inferior pipe or fittings will be allowed. 
 
 All couplings used must be of the best make, with recessed 
 ends, except reducers, which are to be offset. 
 
 Supports. All piping to be supported by approved expan- 
 sion hangers or rollers not to exceed 10 ft. apart. Use neat 
 cast-iron floor and ceiling plates where pipes pass through 
 floors, ceilings, and partitions. 
 
 Radiators. Furnish direct radiation to the amount as enu- 
 merated on plans of the American Radiator Co.'s make or equal, 
 all 33" radiators to be the (Perfection) pattern. All radiators 
 14" high to be "^Etna flue." 
 
 Radiator Valves. The radiators are to be furnished with 
 Jenkins disc union valves of the best metal nickel-plated and 
 have hard- wood handles. 
 
 Valves. All valves 2" and under to have brass bodies and 
 iron wheels, over 2" to be heavy cast iron with brass stem and 
 
1194 RESIDENCE HEATING.' 
 
 trimmings and iron wheels; all valves 4" and over to ha\6 
 heavy yokes. All gate-valves to be of (Crane Co.'s) make 
 or equal. 
 
 Air-valves. Each radiator throughout the entire building 
 shall be furnished with a Marsh automatic air- valve. 
 
 Painting and Bronzing. All radiators and exposed pipes 
 in rooms or halls are to be neatly painted two coats best 
 radiator enamel or bronzed in desired colors. 
 
 Finally. When completed, test the apparatus to 20 Ibs. 
 pressure and make tight at that pressure, said test to be con- 
 ducted under the supervision of the architect. Fuel for the 
 test to be furnished by the owner, and when accepted the 
 apparatus is to be turned over to the owner in complete working 
 order. 
 
 All valves and stuffing-boxes to be properly packed and the 
 plant to be 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 shall guarantee that when the 
 apparatus is completed in accordance with these specifications 
 and drawings it will be free from all mechanical defects and 
 of ample capacity to heat all rooms where radiation is placed 
 to a temperature of 70 when the outside temperature is 10 
 below zero. 
 
 Typical Specification. 
 
 FOR A SUPERIOR LOW-PRESSURE STEAM-HEATING APPARATUS 
 FOR HEATING BY THE INDIRECT SYSTEM, WITH A STEAM 
 PRESSURE OF FROM ONE TO FIVE POUNDS PER SQUARE INCH. 
 
 [NOTE. This specification should be accompanied by a heating plan 
 showing the position of all indirect radiation stacks in the basement, the 
 cold-air inlets to the same, and the size and general position of the main 
 steam and return pipes and the connections to the radiators. 
 
 The return main should be placed at or below the floor and the steam 
 main close under the ceiling. 
 
 The size and location of warm-air registers should be shown on the gen- 
 eral floor plans.} 
 
 General Requirements. Boiler, trimmings, and smoke and 
 feed connection same as in preceding specification. 
 
 System of Piping. The system of piping throughout will be 
 constructed on the double-pipe "gravity return" plan, and 
 all pipes erected will be of ample size to insure the active delivery 
 of dry steam to the radiators and easy flow of the water of 
 condensation back to the boiler. 
 
 Furnish and erect all eupply and steam mains and branch 
 connecting pipes of the sizes and located in the relative posi- 
 tions shown on the plans. All piping to be graded and properly 
 dripped and the steam mains to be hung in position by means 
 of expansion pipe-hangers. 
 
SPECIFICATIONS: INDIRECT STEAM HEATING. 1195 
 
 The main return to be run at or under basement floor and 
 protected from moisture.* 
 
 Pipe Covering. All pipes in the cellar above the floor to be 
 covered with asbestos (or magnesia) sectional covering with 
 canvas cover and secured by brass lacquered bands. 
 
 Stack Boxes and Flues. The heating of the several apart- 
 ments will be accomplished by means of indirect radiators 
 set in clusters of "stacks," each hung from the ceiling of the 
 cellar, and the heat from these "stacks" will be conveyed to 
 the room to be heated by means of tin hot-air pipes set in the 
 walls and leading from stack to the room to be heated; each 
 room heated to have an independent "stack" and to be con- 
 nected therewith by an independent tin hotTair pipe. Each 
 of the "stacks" of indirect radiators to be enclosed in a well- 
 made box or galvanizd iron chamber and from each "stack" 
 a galvanized-iron duct of proper size is to lead to the opening 
 in outside wall provided for the same. Place a damper in the 
 cold-air duct and a tight door in the stack casing below the 
 radiator. 
 
 The radiators shall be hung and the chambers made so that 
 there shall be a space of not less than (12) ins. above and (10) 
 ins. below the stack, and the cold-air duct shall connect with 
 the bottom of the chamber, at a point farthest from the warm- 
 air outlet. 
 
 Radiators. Furnish and erect in cellar, in the positions as 
 shown on plans, ten "stacks" of approved pattern indirect 
 radiators that in the aggregate will contain not less than (732) 
 sq. ft. of radiating surface, and divided up for the several rooms 
 to be heated as follows, viz.: 
 
 First Story: 
 
 Hall 1 "stack" to contain 108 sq. ft. 
 
 Parlor 1 " " " 96 "" 
 
 Dining-room 1 " " " 108 " " 
 
 Library 1 " " " 96 " " 
 
 Rear hall 1 " " " 48 " " 
 
 Second Story: 
 
 Chamber over parlor 1 "stack" to contain 72 sq. st. 
 
 Chamber over dining-room .1 " " " 72 "" 
 
 Chamber over library 1 " " " 72 " " 
 
 Hall bedroom 1 " " " 36 "" 
 
 Bathroom 1 " 24 " " 
 
 No valves are to be placed in either the supply or return to 
 radiating stack, but an improved automatic air-valve must 
 be placed on each stack. 
 
 Pipe Covering. All cellar pipes to be neatly covered with 
 asbestos sheathing, then 1-inch thick hair-felt and canvas 
 casing sewed on. 
 
 * In damp situations the return pipes, when necessary to drop below 
 floor, should be run in brick ducts laid in cement mortar and the pipe 
 packed with mineral wool or asbestos. 
 
1196 RESIDENCE HEATING. 
 
 Registers. Furnish and set in position in each room heated 
 a vertical wheel register of the size shown on plans. All registers 
 for first story to be bronze finish, and all others to be black or 
 white japanned finish, as shall be selected. 
 
 Tin and Galvanized-iron Work. Furnish to builder (and 
 by him to be set in position as shown on plans) all tin wall pipes 
 and register boxes for hot air to the rooms to be heated, all 
 to b'e made of IX tin and of the sizes shown on plan. 
 
 Furnish and erect the galvanized-iron casings for the ten 
 stacks as above specified, with galvanized-iron ducts to the 
 outside openings, to be constructed in a substantial and work- 
 manlike manner. 
 
 Guarantee. The contractor is to guarantee that the apparatus 
 when completed will be of ample capacity to maintain an even 
 temperature of 70 F. in the rooms heated when the outside 
 temperature is zero, and that the apparatus will afford free 
 circulation throughout and be noiseless in operation. 
 
 Books on Residence Heating 1 . Much valuable infor- 
 mation on residence heating may be obtained from pamphlets 
 published by different manufacturers, among whom are the 
 American Radiator Co., the International Heater Co., the 
 Gurney Heater Manufacturing Co., Gorton & Lidgerwood Co., 
 Isaac A. Sheppard & Co., and the Excelsior Steel Furnace Co., 
 of Chicago. The latter company publish a very complete book 
 on furnace heating and furnace fittings which every architect 
 should have. 
 
DATA FOR HOT-AIR STACKS. 
 
 1197 
 
 TABLES. 
 
 The following tables will be found useful in estimating the 
 size of registers, piping, and heating surface oi pipes and boiler 
 tubes: 
 
 TABLE OF SIZES AND DIMENSIONS OF SAFETY DOUBLE 
 HOT-AIR STACKS. 
 
 Made by the Excelsior Steel Furnace Company. 
 
1198 
 
 DIMENSIONS OF REGISTERS, 
 
 DIMENSIONS OF REGISTERS AND BORDERS.* 
 
 Made by the Tuttle & Bailey Manufacturing Co. 
 
 Size of 
 Body. 
 
 Register. 
 
 Extreme 
 Dimensions. 
 
 Depth 
 Open. 
 
 Border. 
 
 With Ribs. 
 Floor Opening. 
 
 Tin-box Size. 
 
 4X 6 
 
 4X 8 
 
 4X10 
 
 4X13 
 
 4X15 
 
 4X18 
 
 5X 8 
 
 5X11 
 
 5X13 
 
 5X16 
 
 6X 6 
 
 6X 8 
 
 6X 9 
 
 6X10 
 
 6X14 
 
 6X16 
 
 6X18 
 
 6X24 
 
 7X 7 
 
 7X10 
 
 8X 8f 
 
 8X10 
 
 8Xl2f 
 
 8X15 
 
 8X18 
 
 8X21 
 
 8X24 
 
 9X 9 
 
 9Xl2f 
 
 9X13 
 
 9Xl4f 
 
 9X16 
 
 9X18 
 
 9X20 
 
 10X10 
 
 10X12 
 
 10X14 
 
 10X16 
 
 10X18 
 
 10X20 
 
 12X12 
 
 12X14 
 
 12X15 
 
 5| X 7f 
 5i X 9J 
 5J Xlli 
 
 5j 
 
 5i X191" 
 
 6| X 9| 
 
 6f X12| 
 6| Xl4f 
 6f X17J 
 7%X 7% 
 7%X 9% 
 7%X10% 
 
 7%X19% 
 7%X25% 
 
 X 9} 
 Xll} 
 Xl3f 
 
 X16% 
 X19} 
 
 9f 
 9i 
 
 9 ; 
 95 
 9' 
 9; 
 
 m 
 
 10} XlOf 
 10} X13} 
 11 X15 
 10 1 X15J 
 10} X173 
 10} X19} 
 10} X21} 
 
 12 
 
 14^X14^6 
 
 If 
 
 2 
 
 2 
 
 2 
 
 2 
 
 2f 
 
 2| 
 
 2| 
 
 21 
 
 21 
 
 2| 
 
 2J 
 
 2| 
 
 2| 
 
 2f 
 
 3 
 
 3 
 
 3 
 
 3 
 
 3 
 
 3 
 
 3 
 
 3i 
 
 3i 
 
 3| 
 3f 
 3f 
 3| 
 3| 
 
 4 
 4 
 4 
 
 8} Xll} 
 8} X14J 
 8} X16} 
 8} X19J 
 
 9^X27% 
 
 10%X13% 
 11} Xll} 
 11} X13} 
 11} X15} 
 11} X1S} 
 11} X21} 
 11} X24} 
 11} X27} 
 
 13^X16^6 
 
 13%X20X 6 
 13^X22% 
 13^X24% 
 
 X 8 
 8f XlOf 
 8f X12|- 
 " X15{- 
 
 16^X19% 
 
 * For special side-wall registers, see p. 1201. 
 
 t These sizes are those most likely to be found in stock of local dealers. 
 
DIMENSIONS OF REGISTERS. 1199 
 
 DIMENSIONS OF REGISTERS AND BORDERS. Cont. 
 
 Size of 
 Body. 
 
 Register. 
 
 Border. 
 
 Extreme 
 Dimensions'. 
 
 Depth 
 Open. 
 
 With Ribs. 
 Floor Opening. 
 
 Tin-box Size. 
 
 12X16 
 
 14^X18 
 
 4 
 
 16X 6 X20X 6 
 
 12%X16% 
 
 12X17* 
 
 14X 6 X19 
 
 4 
 
 16X 6 X21X 6 
 
 12%X17% 
 
 12X18 
 12X19 
 
 14X 6 X20X 6 
 14Xe X 21)6 
 
 4 
 4 
 
 16X 6 X22X 6 
 16X 6 X23X6 
 
 12%X18% 
 12%X19% 
 
 12X20 
 
 14X 6 X22 
 
 4 
 
 16X 6 X24X 6 
 
 12%X20% 
 
 12X24 
 
 14^X26 
 
 4 
 
 16%X23X 6 ^ 
 
 12%X24% 
 
 12X30 
 
 14)2X32 
 
 4 
 
 
 
 12X36 
 
 14X6X38 
 
 4 
 
 
 
 14X14 
 
 16X 6 X16X 6 
 
 4 
 
 18%X18% 
 
 141 X141 
 
 14X16 
 
 16X 6 X18X 6 
 
 4 
 
 18%X20% 
 
 141 X161 
 
 14X18 
 
 16| X20Xe 
 
 4 
 
 18%X22% 
 
 141 X181 
 
 14X20 
 
 16X 6 X22X 6 
 
 4 
 
 18 1 X 6 X24% 
 
 141 X201 
 
 14X22 
 
 16| X24i 
 
 4 
 
 18 1 X 6 X26% 
 
 141 X221 
 
 15X25 
 
 17 1 X 6 X27 1 X 6 
 
 4i 
 
 19%X29% 
 
 16 J X26J 
 
 16X16 
 
 18^6X18% 
 
 4i 
 
 20 J X20J 
 
 161 X161 
 
 16X18 
 
 18X 6 X20X 6 
 
 4i 
 
 20 J X22J 
 
 161 X181 
 
 16X20 
 
 18X 6 X22X 6 
 
 4* 
 
 20 J X24J 
 
 161 X201 
 
 16X22 
 
 18%X24X 6 
 
 4i 
 
 20 J X26J 
 
 161 X22| 
 
 16X24 
 
 18X 6 X26% 
 
 4i 
 
 20J X-28J- 
 
 161 X25| 
 
 16X28 
 
 18X 6 X30X 8 
 
 4J 
 
 201 X32J 
 
 161 X2S1 
 
 16X32 
 
 18X 6 X34X 6 
 
 4i 
 
 20J X36J 
 
 161 X32| 
 
 18X18 
 
 20XeX20X 6 
 
 4| 
 
 22%X22 1 X 6 
 
 18| X18| 
 
 18X21 
 
 20X 6 X23X 6 
 
 4| 
 
 22%X25% 
 
 18| X2l| 
 
 18X24 
 
 20X 6 X26X 6 
 
 4f 
 
 22^6X2S% 
 
 181 X241 
 
 18X27 
 
 20XeX29X 6 
 
 4J 
 
 22%X31% 
 
 18| X27| 
 
 18X30 
 
 20X 6 X32i 
 
 4| 
 
 22%X34 1 X 6 
 
 181 X301 
 
 18X36 
 
 20%X38i 
 
 4| 
 
 22%X40% 
 
 181 X361 
 
 20X20 
 
 22| X22| 
 
 5} 
 
 25J X25J 
 
 20^X20% 
 
 20X24 
 
 22| X26f 
 
 5i 
 
 25J X29i 
 
 20%X24% 
 
 20X26* 
 
 22XeX2Sf 
 
 H 
 
 25J X31J 
 
 20%X26% 
 
 21X29 
 
 23f X31f 
 
 6* 
 
 26| X34J 
 
 21 1 XeX29% 
 
 24X24 
 
 26X 6 X26X 6 
 
 51 
 
 29 X29J 
 
 24%X24% 
 
 24X27 
 
 26X 6 X29| 
 
 51 
 
 29^ X32| 
 
 24%X27% 
 
 24X30 
 
 26X 6 X32f 
 
 5i 
 
 29J X35J 
 
 24^X30% 
 
 24X32 
 
 26X 6 X34| 
 
 5| 
 
 29^ X37i 
 
 24%X32% 
 
 24X36 
 
 26Ji^X38f 
 
 5f 
 
 29J X41J 
 
 241X6X36% 
 
 24X45 
 
 26X 6 X47| 
 
 5f 
 
 29^ X50^ 
 
 24%X45% 
 
 27X27 
 
 29X 6 X29X 6 
 
 6 
 
 32 J X32i 
 
 27!X6X27% 
 
 27X38 
 
 29X 6 X40| 
 
 6i 
 
 32^ X43i 
 
 27 1 X 6 X38% 
 
 30X30 
 
 32| X32f 
 
 7f 
 
 35^ X35^ 
 
 30%X30% 
 
 30X36 
 
 32f X38f 
 
 7| 
 
 35J X41J 
 
 30%X3G% 
 
 30X42 
 
 32f X44J 
 
 7| 
 
 35i X47i 
 
 30 1 X 6 X42iXe 
 
 * These sizes are those most likely to be found in stock of local dealers. 
 
1200 CAPACITY OF PIPES AND REGISTERS. 
 
 ESTIMATED CAPACITY OF PIPES AND REGISTERS. 
 
 ROUND PIPES. 
 
 Diameter 
 
 Area in 
 
 Diameter 
 
 Area in 
 
 Diameter 
 
 Area in 
 
 of Pipe. 
 
 Sq. Inches. 
 
 of Pipe. 
 
 Sq. Inches. 
 
 of Pipe. 
 
 Sq. Inches. 
 
 7 inches 
 
 38 
 
 12 inches 
 
 113 
 
 22 inches 
 
 380 
 
 8 " 
 
 50 
 
 14 " 
 
 154 
 
 24 " 
 
 452 
 
 9 " 
 
 63 
 
 16 " 
 
 201 
 
 26 " 
 
 531 
 
 10 " 
 
 78 
 
 18 " 
 
 254 
 
 28 " 
 
 616 
 
 11 " 
 
 95 
 
 20 " 
 
 314 
 
 30 " 
 
 707 
 
 RECTANGULAR PIPES. 
 
 Size 
 of Pipe. 
 
 Area in 
 Sq. Inches. 
 
 Size 
 of Pipe. 
 
 Area in 
 Sq. Inches. 
 
 Size 
 of Pipe. 
 
 Area in 
 Sq. Inches. 
 
 4X8 
 
 32 
 
 8X20 
 
 160 
 
 12X18 
 
 216 
 
 4X10 
 
 40 
 
 8X24 
 
 192 
 
 12X20 
 
 240 
 
 4X12 
 
 48 
 
 10X12 
 
 120 
 
 12X24 
 
 288 
 
 4X16 
 
 64 
 
 10X15 
 
 150 
 
 14X14 
 
 196 
 
 6X10 
 
 60 
 
 10X16 
 
 160 
 
 14X16 
 
 224 
 
 6X12 
 
 72 
 
 10X18 
 
 180 
 
 14X20 
 
 280 
 
 6-X16 
 
 96 
 
 10X20 
 
 200 
 
 16X16 
 
 256 
 
 8*X10 
 
 80 
 
 12X12 
 
 144 
 
 16X18 
 
 288 
 
 8X12 
 
 96 
 
 12X15 
 
 180 
 
 16X20 
 
 320 
 
 8X16 
 
 128 
 
 12X16 
 
 192 
 
 16X24 
 
 384 
 
 REGISTERS. 
 
 Size of 
 Opening. 
 
 Capacity in 
 Sq. Inches. 
 
 Size of 
 Opening. 
 
 Capacity in 
 Sq. Inches, 
 
 Size of 
 Opening. 
 
 Capacity in 
 Sq. Inches. 
 
 6X10 
 8X10 
 8X12 
 8X15 
 9X12 
 9X14 
 10X12 
 
 40 
 53 
 64 
 
 80 
 72 
 84 
 80 
 
 10X14 
 10X16 
 12X15 
 12X19 
 
 14X22 
 15X25 
 16X24 
 
 93 
 
 107 
 120 
 152 
 205 
 250 
 256 
 
 20X20 
 20X24 
 20X26 
 21X29 
 27X27 
 27X38 
 30X30 
 
 267 
 320 
 347 
 406 
 486 
 684 
 600 
 
 ROUND REGISTERS. 
 
 Size of 
 Opening. 
 
 Capacity in 
 Sq. Inches. 
 
 Size of 
 Opening. 
 
 Capacity in 
 Sq. Inches. 
 
 Size of 
 Opening. 
 
 Capacity in 
 Sq. Inches. 
 
 7 inches 
 
 26 
 
 12 inches 
 
 75 
 
 20 inches 
 
 209 
 
 8 " 
 
 33 
 
 14 
 
 103 
 
 24 " 
 
 301 
 
 9 " 
 
 42 
 
 16 " 
 
 134 
 
 30 " 
 
 471 
 
 10 
 
 52 
 
 18 " 
 
 169 
 
 36 " 
 
 679 
 
SIZES FOR HOT-WATER FLOW PIPES. 1201 
 
 T. & B. SPECIAL SIDE-WALL REGISTERS FOR SHALLOW 
 FLUES AND THIN PARTITIONS FOR USE IN BASE- 
 BOARDS. 
 
 This register has a single valve, and the front projects 2 inches into the 
 room; with it a 6"X13" flue can be used with 3" studding, i.e., in the 
 first-story rooms. 
 
 SIZES AND CAPACITY. 
 
 Register 
 
 Tin Flue. 
 
 Round Pipe. 
 
 
 Net Air 
 
 
 
 
 
 List 
 Size. 
 
 Opening in 
 Register 
 
 Size. 
 
 Capacity. 
 
 Size. 
 
 Capacity. 
 
 
 Face. 
 
 
 
 
 
 Inches. 
 
 Sq. inches. 
 
 Inches. 
 
 Sq. inches. 
 
 Inches. 
 
 Sq. inches. 
 
 7X10 
 
 47 
 
 4 X10 
 
 40 
 
 7 
 
 38 
 
 7X12 
 
 56 
 
 4 X12 
 
 48 
 
 8 
 
 48 
 
 8X13 
 
 70 
 
 5 X13 
 
 65 
 
 9 
 
 63 
 
 8X15 
 
 
 
 5 X15 
 
 75 
 
 10 
 
 78 
 
 10X13 
 
 86 
 
 6 X13 
 
 78 
 
 10 
 
 78 
 
 8X17 
 
 95 
 
 5iXl7 
 
 93 
 
 11 
 
 95 
 
 DIAMETER OF MAIN AND BRANCH PIPES AND SQUARE 
 FEET OF COIL SURFACE THEY WILL SUPPLY IN 
 AN OPEN HOT-WATER APPARATUS WHEN COILS 
 ARE AT DIFFERENT ALTITUDES FOR DIRECT 
 RADIATION OR IN THE LOWER STORY FOR IN- 
 DIRECT RADIATION.* 
 
 8 
 
 d 
 
 
 2* 
 
 .2 
 
 
 Pi 
 
 11 
 
 Direct Radiation. 
 
 J 
 
 |l 
 
 Height of Coil above Bottom of Boiler, in Feet. 
 
 cj 
 
 ^^ 
 
 
 1.2 
 
 3 
 
 
 
 10 
 
 20 
 
 30 
 
 40 
 
 50 
 
 60 
 
 70 
 
 80 
 
 100 
 
 
 Sq.ft. 
 
 Sq.ft. 
 
 Sq.ft. 
 
 Sq. ft. 
 
 Sq. ft. 
 
 Sq. ft. 
 
 Sq. ft. 
 
 Sq. ft. 
 
 Sq. ft 
 
 Sq. ft. 
 
 M 
 
 49 
 
 50 
 
 52 
 
 53 
 
 55 
 
 57 
 
 59 
 
 61 
 
 63 
 
 68 
 
 i 
 
 87 
 
 89 
 
 92 
 
 95 
 
 98 
 
 101 
 
 103 
 
 108 
 
 112 
 
 121 
 
 IM 
 
 136 
 
 140 
 
 144 
 
 149 
 
 153 
 
 158 
 
 161 
 
 169 
 
 175 
 
 189 
 
 i^l 
 
 196 
 
 202 
 
 209 
 
 214 
 
 222 
 
 228 
 
 235 
 
 243 
 
 252 
 
 271 
 
 2 
 
 349 
 
 359 
 
 370 
 
 380 
 
 393 
 
 405 
 
 413 
 
 433 
 
 449 
 
 483 
 
 2/^ 
 
 546 
 
 561 
 
 577 
 
 595 
 
 613 
 
 633 
 
 643 
 
 678 
 
 701 
 
 755 
 
 3 
 
 785 
 
 807 
 
 835 
 
 856 
 
 888 
 
 912 
 
 941 
 
 974 
 
 1,009 
 
 1,086 
 
 3/^ 
 
 1,069 
 
 1,099 
 
 1,132 
 
 1,166 
 
 1,202 
 
 1,241 
 
 1,283 
 
 1,327 
 
 1,374 
 
 1,480 
 
 4 
 
 1,395 
 
 1,436 
 
 1,478 
 
 1,520 
 
 1,571 
 
 1,621 
 
 1,654 
 
 1,733 
 
 1,795 
 
 1,933 
 
 4J^ 
 
 1,767 
 
 1,817 
 
 1,871 
 
 1,927 
 
 1,988 
 
 2,052 
 
 2,120 
 
 2,193 
 
 2,272 
 
 2,445 
 
 5 
 
 2,185 
 
 2,244 
 
 2,309 
 
 2,379 
 
 2,454 
 
 2,531 
 
 2,574 
 
 2,713 
 
 2,805 
 
 3,019 
 
 6 
 
 3,140 
 
 3,228 
 
 3,341 
 
 3,424 
 
 3,552 
 
 3,648 
 
 3,763 
 
 3,897 
 
 4,036 
 
 4,344 
 
 7 
 
 4,276 
 
 4,396 
 
 4,528 
 
 4 664 
 
 4,808 
 
 4,964 
 
 5,132 
 
 5,308 
 
 5,496 
 
 5,920 
 
 8 
 
 5,580 
 
 5,744 
 
 5,912 
 
 6^080 
 
 6,284 
 
 6,484 
 
 6,616 
 
 6,932 
 
 7,180 
 
 7,735 
 
 9 
 
 7,068 
 
 7,268 
 
 7,484 
 
 7,708 
 
 7,952 
 
 8,208 
 
 8,482 
 
 8,774 
 
 9,088 
 
 9,780 
 
 10 
 
 8,740 
 
 8,976 
 
 9,236 
 
 9,516 
 
 9,816 
 
 10,124 
 
 10,296 
 
 10,852 
 
 11,220 
 
 12,076 
 
 * F. Schumann, C.E. 
 
1202 
 
 SIZES FOR STEAM MAINS. 
 
 DIAMETER OF STEAM-SUPPLY PIPES AND SQUARE 
 FEET OF DIRECT RADIATION THEY WILL SUPPLY 
 WITH 3 POUNDS STEAM PRESSURE.* 
 
 Diam- 
 
 Distance of Radiator from Boiler, in Feet. 
 
 eter of 
 
 
 Pipe, 
 
 
 *^ ' 
 
 in 
 
 
 
 
 
 
 
 
 Inches 
 
 9 
 
 64 
 
 100 
 
 225 
 
 324 
 
 400 
 
 484 
 
 
 Sq. ft. 
 
 Sq. ft. 
 
 Sq. ft. 
 
 Sq. ft. 
 
 Sq. ft. 
 
 Sq. ft. 
 
 Sq. ft. 
 
 K 
 
 240 
 
 90 
 
 72 
 
 48 
 
 40 
 
 36 
 
 32 
 
 1 
 
 494 
 
 185 
 
 148 
 
 98 
 
 82 
 
 74 
 
 68 
 
 IK 
 
 863 
 
 324 
 
 259 
 
 172 
 
 144 
 
 129 
 
 118 
 
 1H 
 
 1,361 
 
 510 
 
 408 
 
 272 
 
 226 
 
 204 
 
 185 
 
 2 
 
 2,796 
 
 1,049 
 
 839 
 
 559 
 
 466 
 
 419 
 
 381 
 
 2H 
 
 4,884 
 
 1,831 
 
 1,465 
 
 977 
 
 814 
 
 732 
 
 666 
 
 3 
 
 7,700 
 
 2,887 
 
 2,310 
 
 1,540 
 
 1,283 
 
 1,155 
 
 1,050 
 
 3^ 
 
 11,323 
 
 4,246 
 
 3,097 
 
 2,264 
 
 1,887 
 
 1,698 
 
 1,544 
 
 4 
 
 15,819 
 
 5,932 
 
 4,745 
 
 3,164 
 
 2,636 
 
 2,372 
 
 2,157 
 
 4^ 
 
 21,226 
 
 7,959 
 
 6,368 
 
 4,245 
 
 3,537 
 
 3,184 
 
 2,894 
 
 5 
 
 27,997 
 
 10,361 
 
 8,289 
 
 5,599 
 
 4,666 
 
 4,144 
 
 3,768 
 
 6 
 
 44,230 
 
 16,586 
 
 13,269 
 
 8,846 
 
 7,372 
 
 6,634 
 
 6,031 
 
 7 
 
 64,013 
 
 24,005 
 
 19,204 
 
 12,802 
 
 10,668 
 
 9,602 
 
 8,729 
 
 8 
 
 89,615 
 
 33,605 
 
 26,884 
 
 17,923 
 
 14,936 
 
 13,442 
 
 12,220 
 
 9 
 
 120,275 
 
 45,103 
 
 36,082 
 
 24,055 
 
 20,046 
 
 18,041 
 
 16,401 
 
 10 
 
 156,277 
 
 58,604 
 
 46,883 
 
 31,255 
 
 26,046 
 
 23,441 
 
 21,310 
 
 * F. Schumann, C.E. 
 USEFUL MEMORANDA: HOT-WATER HEATING. 
 
 MEASUREMENT OF FLOW AND RETURN PIPES. 
 
 For the purpose of ascertaining the amount of heating surface 
 in flow, return pipes, and risers, the following table is used 
 
 
 Surface of Pipe Cover- 
 ing M Inch Hair-felt 
 and Canvas. 
 
 Table of Quantity of 
 Water contained in 100 
 Lineal Feet of Pip 3 of 
 Different Diameters. 
 
 Size of 
 Pipe. 
 
 Square Feet 
 in One Lin- 
 eal Foot. 
 
 Size of 
 Pipe. 
 
 Multiply 
 Length by 
 
 Diameter 
 of Pipa. 
 
 Contents ir 
 100 Feet ii 
 Length. 
 
 Inches. 
 
 
 Inches. 
 
 
 Inches. 
 
 Gallons. 
 
 3 
 
 .27 
 
 1 
 
 .79 
 
 1 
 
 4.50 
 
 1 
 
 .34 
 
 1J 
 
 .96 
 
 It 
 
 7.75 
 
 li 
 
 .43 
 
 1} 
 
 1.04 
 
 li 
 
 10.59 
 
 li 
 
 .50 
 
 2 
 
 1.09 
 
 2 
 
 17.43 
 
 2 
 
 .62 
 
 21 
 
 1.20 
 
 2} 
 
 24.80 
 
 21 
 
 .75 
 
 3 
 
 1.37 
 
 3 
 
 38.38 
 
 3 
 
 .92 
 
 31 
 
 1.49 
 
 31 
 
 51.36 
 
 31 
 
 1.05 
 
 4 
 
 1.64 
 
 4 
 
 66.13 
 
 4 
 
 1.17 
 
 
 
 
 
EQUALIZATION OF PIPE AREAS. 
 
 1203 
 
 To obtain the surface, multiply length of pipe by figures given 
 in the table, always pointing off two places. 
 
 Example: 500 lineal feet 1-inch pipe multiplied by .34 equals 
 170 sq. ft. 
 
 EQUALIZATION OF PIPE AREAS. 
 
 (R. C. Carpenter.) 
 
 Diam. 
 of 
 Pipes, 
 Inches. 
 
 Number of Small Pipes Required to Make Area Equivalent to 
 One Larger Pipe with Allowance for Friction. 
 
 T^ 
 In. 
 
 X 
 
 In. 
 
 1 
 In. 
 
 1M 
 In. 
 
 VA 
 In. 
 
 2 
 
 In. 
 
 2y 2 
 
 In. 
 
 3 
 In. 
 
 3^ 
 In. 
 
 4 
 In. 
 
 4^ 
 In. 
 
 5 
 In. 
 
 1 4 
 1# 
 
 u! 
 
 2 
 
 f 4 
 ft 
 
 f* 
 
 1 
 
 2.0 
 1 
 
 3.7 
 1.8 
 1 
 
 7.6 
 3.7 
 2.0 
 1 
 
 11.3 
 5.4 
 3.1. 
 1.5 
 1 
 
 19 
 9.2 
 5.1 
 2.6 
 1.7 
 1 
 
 37 
 16.7 
 9.3 
 4.5 
 3.1 
 1.83 
 1 
 
 55 
 25.5 
 14.7 
 7.3 
 4.7 
 2.9 
 1.7 
 1 
 
 80 
 39 
 27 
 10.6 
 7.1 
 4.1 
 2.5 
 1.5 
 1 
 
 108 
 53 
 30 
 14.7 
 9.8 
 5.8 
 3.5 
 2.4 
 1.4 
 1 
 
 146 
 70 
 39 
 19.5 
 13.4 
 7.8 
 4.7 
 2.7 
 1.8 
 1.3 
 1 
 
 188 
 90 
 53 
 25 
 16.8 
 9.9 
 5.9 
 3.5 
 2.5 
 1.7 
 1.25 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 EQUALIZATION OF PIPE AREAS. 
 
 (Babcock and Wilcox.) 
 
 Number of Smaller Pipes Equivalent to One Larger Pipe. 
 
 9s 
 
 5 S 
 
 1* 
 
 i H 
 r 
 
 4 
 6 
 6 
 
 7 
 8 
 
 H 
 
 In. 
 
 1 
 In. 
 
 V A 
 
 In. 
 
 2 
 In. 
 
 3 
 In. 
 
 4 
 In. 
 
 5 
 In. 
 
 6 
 In. 
 
 7 
 In. 
 
 8 
 In. 
 
 9 
 In. 
 
 10 
 In. 
 
 2.27 
 1 
 
 4.88 
 2.05 
 1 
 
 15.8 
 6.9 
 3.5 
 1 
 
 31.7 
 14 
 6.8 
 1.3 
 1 
 
 96.9 
 42.5 
 20.9 
 6.1 
 3.1 
 1.8 
 1 
 
 205 
 90.4 
 44.1 
 13 
 6.5 
 3.87 
 2.12 
 1 
 
 377 
 166 
 81.1 
 23.8 
 11.9 
 7.1 
 3.9 
 1.8 
 1 
 
 620 
 273 
 133 
 39.2 
 19.6 
 11.7 
 6.4 
 3 
 1.6 
 1 
 
 918 
 405 
 198 
 58.1 
 29.0 
 17.4 
 9.5 
 4.5 
 2.4 
 1.5 
 1 
 
 569 
 278 
 81.7 
 40.8 
 24.4 
 13.3 
 6.3 
 3.4 
 2,1 
 1.4 
 1 
 
 779 
 380 
 112 
 55.8 
 33.4 
 20.9 
 8.6 
 4.7 
 2.8 
 1.9 
 1.3 
 
 536 
 157 
 78.5 
 47.0 
 23.7 
 12.1 
 6.6 
 4.0 
 2.7 
 1.9 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1204 DIMENSIONS, ETC., OF BOILER TUBES. 
 
DIMENSIONS, ETC., OF STEAM PIPES. 1205 
 
 \N\N 
 
 5 "5 03 rH O5 !> *O GO ^ 00 O5 C5 CO rH 1C N <N rH t>. rH IO 
 
 S'S 1 s_,+ 3 ^ rt< <M iO CO rH CO TfH l^ OCOCO OCO-tf O CO t~~l> OCO 
 
 'rHrH(N M CO O 1> O5 O <N *' GO CO GO CO 1C OJ 
 
 ft&- rH rH rH rH CS <N CO <* TF TJ1 
 
 rCj^^Sr-, lOCOrH t^rH(MCO(NGOO5(NrH|> 
 
 Sft'SJEsSf-ta -M CO<N^ O5<N COO5rHiOiOCOO<NO5i>00<NOO*O<N 
 
 bCv- 1 ,2 G .Q O 
 
 C^fiyj^O 0>COCOrH<M OCOCO O<M OC>Tt<rHC5t^Tj<CO<N<NrHi-lrH 
 
 i-l'cu.S^^ jocol^^irH' 05 
 
 " S "- 1 "^ I> ^ O CO I> CO 00 lO <M O O5 00 l> CO IO TH ^ CO CO CO 
 
 
 
 rC! S i^ g -^HH{3^^COOQ rHOC^Osio?--^-^* 
 
 ^^_ ^__tg 
 
 (rHT^COO5(NiOGO l^T^GOCOOi^T^CO^COCO Tt< 
 
 ( O rH rH <M CO TjH CO 1> O tXN CO rH CO CO 1C C5 CO C O5 CO CO 
 
 O< * rH rH (M (N CO* CO Tj^' 1C CO 00 O rH CO -^ 
 
 02 
 
 CO r- H> 00 CO CO 
 
 oil>r^rHHHCOC^CO OOCO^OOt^ rH 0000 O 
 
 fl>OOO5 OCOCO 05 CO to 00 00 00 CO CO O5 GO CO Tt< CO CO CO 
 
 rH O rH rH CO lO 00 T^ O CO i> CO 00 t^ O5 Oi 00 t^ Ol> 00 O O 
 
 " O 1 T" 1 CNr r J T Ti>O^C s fliOO50000OC<100OCO 
 
 rX rHrHrH(NCOIOCOl>OSrH 
 
 _" . rowJWJ^Aj^rvwiJu^r ^O C^I'-HcOr^iCcOCQr^CO CO 
 
 H fe fl (N (M 1C iO CO iO CO COCOC5<N CO OCO OCO<NCOCO 
 
 -H rH C< CO >O 00 CO rH 00 ^ "^ CO *O O5 CO CO rj^ CO ^ t> t> ^f CO 
 
 oj 00 -^ <N l> O5 (M lO rH -HH CO CO CO 00 C<l O5 rJH CO CO CO b- 
 
 g rHrHrH(NCO^ O CO t- O> rH J ^JO O5 C^ O CO rH ^ t-, 
 
 .1 - ^(NCOrHOSOSrHlO OirHC<JCDCOl^OOI>COOCOOO(M 
 
 ^rHrH(N(M ) rHrHrHrHrHC^fNWCOCOCOTf 
 
 ScOOOOS OrHCO 1 ^ Tt< U3 O rH <N CO HH lO 00 O (N Tf CO t^ b- 
 
 O OOOrHrHrHrH rH rH C<1 C<l <N (N <N (N <N CO CO CO CO CO CO 
 
 -H . ^ r}H rjn CO -^ 00 rH 1> 00 l> 00 CO 00 O lO CO (N t^. O5 C 
 
 ^ fn o fl) l> CO O5 (N (N * OO rH CO CO CO * <N O ^t 1 CO (N 00 CO rH C 
 
 ,3 <N CO Tf CO 00 O CO CO O-* OO OIOOOOO5O5 OC 
 
 ^S 2 
 
 5COCOOCOCO O5 CO GO O O O O O 55 O CO CO ?- 1^ ?^ 
 
 ^p x s 9 ' 
 
 ill 
 
 r 
 
 ,-lrH rH (M <M CO CO Tf H- 1C CO t^- 00 O5 O rH C 
 
1206 DIMENSIONS, ETC., OF STEAM PIPES. 
 
 
 
 fc 
 
 S c 
 
 02^3 K! 
 
 T3 O l> 
 0M 2 
 
 3 fe^ 
 
 ^^ 
 
 r- GO GO "t Tf rH rH 
 <N TH rH TH rH TH TH 
 
 r^H^ 
 
 THi IQOOOGOOOGOOOOOOOOCGOOOGO 
 rHi-l 
 
 g 
 
 
 "3 
 
 . 
 
 11 
 
 rrt OS Tf< TJH OS OS l> O 
 
 g(NOl>CCOTH O 
 
 COC^t^iOt^t^C^-'tfGOl^OiOiOO 
 
 COOcD(N^O5(NiO>OCOO<NiMO 
 
 
 
 
 
 
 1 
 
 a 
 
 rHrHNCO 
 
 Pk 
 
 COiOI>O(N^GOOGOt^COGOTtH0 
 
 t| 
 
 I 
 
 Q 
 fl 
 
 |L| 
 0) 
 
 o' 8 
 
 i^S 
 
 isssssss 
 
 
 rf 
 H 
 
 6 
 
 si 
 
 
 ^GO^OSt-O^CO 
 
 <X^^^^^ 
 
 f 
 
 
 2 
 
 Q 
 
 fl 
 
 111 
 
 -gr^t^COiOrt^OO 
 
 OO5THt^t^THCOt^OOS 
 
 THTHeoosio^coGOi>o^Oiioos 
 
 OCDCOCO5GOI>COiOiO't l COCO<N 
 
 g 
 
 T3 
 
 
 r 
 
 1 
 
 hon ^ u? * MCTN 
 
 """^^ 
 
 PM 
 
 r^ 
 
 O 
 
 O 
 
 0> 
 
 
 3 
 
 gS2?53$ 
 
 ssssss^sgssss., 
 
 K 
 5 
 
 1 
 
 ra 
 
 j 
 
 1 
 
 d 1 
 02 
 
 THTHC^COCO'^OcOOO'HC^T^cOOS 
 
 
 
 1 
 
 jrj 
 
 * 
 
 s 
 
 QJ--4 
 
 ^ OOTHC4'Tl>C^ 
 
 
 * 
 
 SB 
 1 
 
 1 
 
 M 
 
 ^ 
 
 tH(M-^cOoOTHHHOOiOTt<iOOOr^OO 
 
 rH TH rH (N CO T}i IO 1> O 
 
 of 
 
 <J 
 
 1 
 
 J 
 
 tL 
 
 g^^|||^ 
 
 iOO<NTHCOTt<iOCO<MTt<cOCCO 
 COCOOS(McOCCOOt^CO(MCOcOOO 
 GO T t lT fcO>OOSCOCOHHcOTfi|>l^CO 
 
 
 I^f 
 
 1 
 
 
 P 
 
 02 
 
 "" !00>S22 -"" ?!g S 
 
 
 o3 
 S 
 
 oc 
 
 j 
 
 i. 
 
 *HH(N(M OTHQOOS 
 
 ^ co as co t> co os os 
 
 COOC^I OiOOS^r-1 OOOOSOCOOS 
 
 p 
 
 c3 
 
 a 
 
 o 
 
 2 
 
 fi fl 
 
 fl THrHC^(NCO 
 r 1 
 
 T}HCOI>OSOTHCO1OGOOCOI>OCO 
 
 rHTHTHTHTHCvJCNKNCOCO 
 
 Q 
 
 
 1 
 
 || 
 
 ^(McOTHCSCSTHio 
 
 OSTH(NCOCOl>OOt^COiOCOGO(NO 
 
 H 
 
 
 
 M ^ 
 
 r-irH (N (N CO * O 
 
 ot^asoc^iot>.ocob.ccoo 
 
 > 
 
 M 
 
 
 
 
 
 
 
 2 
 
 1 
 
 
 ii 
 
 ^OCOl>OSt^<Nr}< 
 ^J O(N(M^OOOOS 
 
 3SSSS5SSS?88888 
 
 tf 
 
 KH 
 
 
 i 
 
 3 fl 
 
 
 
 
 S 
 
 1 
 
 
 1 i^. 
 
 03lOrt<THC<JCOTHC<l 
 
 
 5 
 
 H 
 
 
 
 J T-i 
 
 ^-NNCCCO^^Offl^GOO-. 
 
 
 
 0) 
 
 1 
 
 18 i . 
 
 lilillsi 
 
 SiOiOOOOCCOiOiOiOiOOO 
 !>I>OOOCcOiMC^(MC^iOiO 
 
 cscoooooiooiococococoi>i> 
 
 
 
 1 
 
 -<w* 
 
 r-H 
 
 THC<JC^COrt*Tt<iO'OCOt > -OOOSOd 
 
 
 
 
 ^i 
 
 S "S fl 
 
 W^ y 
 
 \M ^ \N V^l 
 
 
 
 
 br^ 
 
 ^ p8pT9Ai-iantr 
 
 p8pT8AS.-dBT 
 
SMOKE PREVENTION. 
 
 1207 
 
 DIMENSIONS OF STANDARD DOUBLE EXTRA 
 STRONG PIPE. 
 
 Nominal. 
 
 Actual 
 External 
 Diameter. 
 
 , Actual 
 Internal 
 Diameter. 
 
 Thickness. 
 
 Metal 
 Area. 
 
 Nominal 
 Weight 
 per Foot, 
 Pounds. 
 
 4 
 
 .840 
 
 .244 
 
 .298 
 
 .507 
 
 1.7 
 
 f 
 
 1.050 
 
 .422 
 
 .314 
 
 .726 
 
 2.44 
 
 
 1.315 
 
 .587 
 
 .364 
 
 1.087 
 
 3.65 
 
 H 
 
 1.660 
 
 .885 
 
 .388 
 
 1.549 
 
 5.2 
 
 14 
 
 1.900 
 
 1.088 
 
 .406 
 
 1.905 
 
 6.4 
 
 2 
 
 2.375 
 
 1.491 
 
 .442 
 
 2.686 
 
 9.02 
 
 24 
 
 2.875 
 
 1.755 
 
 .560 
 
 4.073 
 
 13.68 
 
 3 
 
 3.500 
 
 2.284 
 
 .603 
 
 5.524 
 
 18.56 
 
 34 
 
 4.000 
 
 2.716 
 
 .642 
 
 6.772 
 
 22.75 
 
 4 
 
 4.500 
 
 3.136 
 
 .682 
 
 8.180 
 
 27.48 
 
 44 
 
 5.000 
 
 3.564 
 
 .718 
 
 9.659 
 
 32.53 
 
 5 
 
 5.563 
 
 4.063 
 
 .750 
 
 11.341 
 
 38.12 
 
 6 
 
 6.625 
 
 4.875 
 
 .875 
 
 15. 07 
 
 53.11 
 
 7 
 
 7.625 
 
 5.875 
 
 .875 
 
 18.555 
 
 62.35 
 
 8 
 
 8.625 
 
 6.875 
 
 .875 
 
 21.304 
 
 71.62 
 
 LAP-WELDED CASING. 
 
 
 
 8.625 
 
 8.265 
 
 .1*0 
 
 4.775 
 
 16.07 
 
 81 
 
 8.625 
 
 8.167 
 
 .229 
 
 6.040 
 
 20.10 
 
 W 
 
 8.625 
 
 8.0S2 
 
 .271 
 
 7.125 
 
 24.38 
 
 8f 
 
 9 
 
 8.640 
 
 .180 
 
 4.987 
 
 17.60 
 
 91 
 
 10 
 
 9.577 
 
 .211 
 
 6.504 
 
 21.90 
 
 10* 
 
 11 
 
 10.594 
 
 .203 
 
 6.886 
 
 26.72 
 
 111 
 
 12 
 
 11.594 
 
 .203 
 
 7.526 
 
 30.35 
 
 m 
 
 13 
 
 12.457 
 
 .271 
 
 10.852 
 
 33.78 
 
 13J 
 
 14 
 
 13.432 
 
 .284 
 
 12.24 
 
 42.02 
 
 144 
 
 15 
 
 14.416 
 
 .292 
 
 13.49 
 
 47.66 
 
 154 
 
 16 
 
 15.416 
 
 .292 
 
 14.41 
 
 51.47 
 
 Smoke Prevention. 
 
 Prof. O. H. Landreth, in a report to the State Board of Health 
 of Tennessee (published in Engineering News, June 8, 1893, 
 and quoted by Kent, p. 712) classifies the great number of 
 smoke-prevention devices which had been invented up to that 
 date as follows; 
 
 (a) Mechanical Stokers. They effect a material saving 
 in the labor of firing and are efficient smoke preventers when not 
 pushed above their capacity and when the coal does not cake 
 
1208 SMOKE PREVENTION. 
 
 badly. They are rarely susceptible to the sudden changes i 
 the rate of firing frequently demanded in service. 
 
 (6) Air-flues in side walls, bridge-wall, and grate-bar 
 through which air when passing is heated. The results ar 
 always beneficial, but the flues are difficult to keep clean and ii 
 order. 
 
 (c) Coking Arches, or spaces in front of the furnace arche 
 over in which the fresh coal is coked, both to prevent coolin 
 of the distilled gases and to force them to pass through th 
 hottest part of the furnace just beyond the arch The result 
 are good for normal conditions, but ineffective when the fire 
 are forced. The arches also are burned out and injured b 
 working the fire. 
 
 (d) Dead-plates, or a portion of the grate next the furnac 
 doors reserved for warming and coking the coal before it i 
 spread over the grate .v These give good results when the fur 
 nace is not forced above its normal capacity. This embodie 
 the method of " coke-firing" mentioned before. 
 
 (e) Down-draught Furnaces, or furnaces in which th 
 air is supplied to the coal above the grate and the products o 
 combustion are taken away from beneath the grate, thus caus 
 ing a, downward draught through the coal, carrying the dis 
 tilled gases down to the highly heated incandescent coal at th 
 bottom of the layer of coal on the grate. This is the mos 
 perfect manner of producing combustion and is absolute!; 
 smokeless. 
 
 (/) Steam-jets to draw air in or inject air into the furnac< 
 above the grate, and also to mix the air and the combust ibli 
 gases together. A very efficient smoke preventer, but on< 
 liable to be wasteful of fuel by inducing too rapid a draught. 
 
 (g) Baffle-plates placed in the furnace above the fire t< 
 aid in mixing the combustible gases with the air. 
 
 (h) Double Furnaces, of which there are two differen 
 styles, neither of which have proved practical. 
 
 Among the devices which seem to have proven both prac 
 tical and effective are those of the Smoke Prevention Compan} 
 of America and of the American Stoker Company. 
 
 Ventilation. 
 
 Ventilation as applied to a room or building consists in supply- 
 ing pure air to dilute and drive out that which has become 
 vitiated. 
 
VENTILATION. 1209 
 
 Perfect ventilation consists in supplying an adequate amount 
 of fresh air warmed or cooled to a comfortable temperature 
 in such a manner that the circulation shall be constant and 
 thorough in all parts of the room or building and at the same 
 time without the 'creation of draughts. 
 
 Ventilation may be broadly classified as Systematic and Non- 
 systematic. 
 
 Xoii-systematic Ventilation may be considered as in- 
 cluding all ventilation produced without systematic provision 
 for the admission and escape of the fresh air and power for 
 moving the air. 
 
 All rooms in a building of ordinary construction receive 
 some ventilation whenever the temperature of the room is 
 above or below that of the surrounding air. 
 
 Pettenkofer found that by diffusion through the walls the 
 air of a room in his house containing 2,650 cu. ft. was changed 
 once every hour when the difference of exterior temperatures 
 was 34. With the same difference of temperature, but with 
 the addition of a good fire in a stove, the change rose to 3,320 
 cu. ft. per hour. With all the crevices and openings about 
 doors and windows pasted up air-tight the change amounted 
 to 1,600 cu. ft. per hour.* 
 
 Prof. Carpenter says: "Even in the case of direct heating, 
 where no air is purposely supplied for ventilation, there will 
 be a change of air by diffusion of the air in the room which the 
 writer has found practically met by an allowance equal to 
 one to three changes in the cubic contents per hour." 
 
 Whenever air is introduced into a room as by ordinary in- 
 direct or hot-air heating, an equal amount of air must be driven 
 from the room, or if air is drawn from a room, as by the draught 
 in a fireplace, an equal amount of air must enter the room. 
 
 Heating by hot-air furnaces and by indirect steam or hot- 
 water radiation will generally provide sufficient ventilation for 
 private residences, especially if the principal rooms are pro- 
 vided with fireplaces or ventilation flue,5. 
 
 For Systematic Ventilation provision must be made 
 for the admission and expulsion of the air through flues or 
 definite openings and for power for moving the air. 
 
 The power for moving air for ventilating purposes is obtained 
 in two ways: (1) by expansion due to heating, and (2) by a 
 fan operated by an electric motor or by a steam- or gas-engine. 
 
 * Heating and Ventilating Buildings, p. 35. 
 
1210 VENTILATION. 
 
 Systematic ventilation also presupposes an attempt to admit 
 a definite amount of air, and the first step in any system of 
 ventilation would naturally be to decide upon the amount of 
 air required. 
 
 Amount of Air Required for Ventilation. 
 Authorities differ greatly on this point, except that for school 
 buildings it is generally agreed that 30 cu. ft. of air per minute 
 for each occupant or 1,800 cu. ft. per hour should be the 
 standard.* 
 
 For churches the same amount will give very fair ventila- 
 tion, but for theatres and auditoriums which are usually more 
 closely packed and occupied for a longer period, the air-supply 
 should be from 2,000 to 2,500 cu. ft. per sitting per hour. 
 
 Hospitals require the greatest air dilution, and for such 
 buildings an air-supply of from 4,000 to 6,000 cu. ft. per hour 
 for each bed should be provided, depending upon the character 
 of the cases treated, contagious diseases naturally requiring 
 the greater amount. 
 
 The quantity of air required is sometimes measured by the 
 number of times the air in a room will need to be changed, 
 but to determine this accurately it is necessary to fall back 
 to the supply per person. 
 
 Thus, if a schoolroom 27 / X32 / and 13" high contains fifty 
 pupils and a teacher and 1,800 cu. ft. per hour is required per 
 person, the total air-supply required per hour will be 1,800X51, 
 or 91,800 cu. ft. As the capacity of the room is 11,232 cu. ft., 
 the air in the room must be changed 8.26 times per hour to 
 supply 30 cu. ft. of air per minute to each person. 
 
 It is seldom that the air in a room is changed oftener than 
 four times per hour by natural ventilation. 
 
 Velocity of Entering" Air. The velocity of the air 
 through the inlet registers or grilles should not exceed 4 to 6 ft. 
 per second, the general allowance being 5 ft. per second when 
 the inlet is 7 ft. or more from the floor. 
 
 Estimating' Quantity of Air. The quantity of air 
 passing through a flue or opening is measured by multiplying 
 the sectional area of the flue, or the net area of opening, in 
 square feet by the velocity. 
 
 Thus with a velocity of 5 ft. per second the quantity of air 
 passing through an unobstructed opening 1 ft. square will 
 
 * This amount is required by law in Massachusetts. 
 
VENTILATION, 1211 
 
 equal 5 cu, ft. per second, 300 cu, ft. per minute, or 1,800 cu< ft, 
 per hour. 
 
 Velocities of air are measured by an instrument called an 
 anemometer. 
 
 Location of Inlet and Outlet. Mr. W. R. Briggs, of 
 Bridgeport, Conn., some years ago demonstrated quite conclu- 
 sively that in a rectangular room of moderate size the best 
 results are obtained when the inlet is in an inner wall near the 
 ceiling and the outlet is nearly under the inlet and close to 
 the floor. 
 
 This is now the general practice in well-designed schoolhouses, 
 and for churches and hospitals when warmed by indirect radia- 
 tion. 
 
 For cubical rooms not exceeding 50 ft. square the author 
 considers that one inlet is better than several. 
 
 In the ventilation of theatres the air is sometimes admitted 
 through the ceiling, but more often through the risers of the 
 floor or through specially designed seat ends. 
 
 Size of Flues. The size of the flues both for inlet and out- 
 let is determined by the quantity of air to be moved and the 
 velocity, or 
 Sectional area of ) _ j Quantity of air in cubic feet per minute 
 
 flue in sq. ft. f ~~ ( Velocity in feet per minute. 
 
 The actual velocity will depend upon the motive power, 
 the length, size, shape, and surface of the flue, the number of 
 turns or offsets, and whether the flue is vertical or horizontal 
 so that after the theoretical size of the flue has been deter- 
 mined, the actual size will oftentimes need to be increased by 
 an amount which must be determined largely by the judgment 
 of the designer. For this reason considerable practical experi- 
 ence with forced hot-air heating and ventilating is required to 
 lay out the system of flues to the best advantage, and the 
 architect when designing such a plant will do well to secure the 
 assistance of an expert. 
 
 With fan systems of ventilation the inlet openings should 
 be of such size that the required amount of air may be in- 
 troduced with a velocity not exceeding 500 ft. per minute 
 when the inlet is 5 ft. from the floor or 288 ft. per minute when 
 the inlet is in the floor or in the walls near the floor. 
 
 In figuring the size of ordinary registers the required area 
 should be increased about 50 per cent, to allow for the grilles 
 
1212 VENTILATION. 
 
 or pattern. With light grilles of y/'XiV' iron an "allowance 
 of 10 per cent, will ordinarily be sufficient. 
 
 The velocity in vertical flues supplying the inlets should not 
 exceed that through the opening by more than 50 per cent., 
 which gives a velocity in the vertical flues of from 500 to 800 ft. 
 per minute. The rate of flow through the connections to the 
 base of the flues should in turn be higher than that through 
 the flues, while the velocity in the main horizontal distributing 
 ducts should be still higher. "In fact, in schools and churches 
 the plan should be to gradually reduce velocities from the 
 point of leaving the fan to the point of discharge to the rooms. 
 Careful investigat ? on has shown that, everything considered, 
 the velocity in the main horizontal ducts from the fan should 
 not fall below 1,500 ft. per minute and preferably 2,000 ft. per 
 minute." * 
 
 The size of vent or eduction flues when air is forced into the 
 rooms by a fan should be two thirds to three fourths the sec- 
 tional area of the induction flues. 
 
 Velocity of Air in Vertical Flues Due to Expan- 
 sion by Heat. The velocity of air in heated flues is depend- 
 ent upon the excess of temperature of the air in the flue above 
 that of the room or space into which the flue empties, the 
 height of the flue, the loss by friction, and the pressure which 
 must be resisted by the entering air. Thus in a room heated 
 by indirect radiation or a warm-air furnace if no provision 
 is made for ventilation the heated air must force its way into 
 the room, pushing out an equal volume of air around doors or 
 windows, while if there is a good ventilating flue the movement 
 of air into the warm-air flue is assisted. The table on opposite 
 page, quoted by various writers, shows the velocities f of air that 
 may be expected in vent flues under the conditions noted. 
 
 To obtain the cubic feet of air discharged per hour per square 
 foot of cross-section of the flue, multiply the figures in the 
 table by 60. 
 
 While this table does not strictly apply to flues conveying 
 warm air into a room it is sufficiently accurate for practical 
 purposes. 
 
 Prof. Carpenter says that in residence heating the velocity 
 in flues is likely to be as follows, in feet per minute : First story, 
 
 * Ventilation and Heating. B. F. Sturtevant Co. 
 
 t The velocity in a flue 1 foot square being the same as the quantity of 
 air discharged. 
 
VENTILATION. 
 
 1213 
 
 TABLE SHOWING THE QUANTITY OF AIR, IN CUBIC 
 FEET, DISCHARGED PER MINUTE THROUGH A 
 FLUE OF WHICH THE CROSS-SECTIONAL AREA IS 
 ONE SQUARE FOOT. 
 
 (EXTERNAL TEMPERATURE OF THE AIR, 32 FAHR. ; ALLOWANCE 
 FOR FRICTION, 50 PER CENT.) 
 
 Height 
 of 
 Flue, in 
 Feet. 
 
 Excess of Temperature of Air in Flue above that of External Air. 
 
 10 
 
 15 6 
 
 20 
 
 25 
 
 20 
 
 50 
 
 100 
 
 150 
 
 1 
 
 34 
 
 42 
 
 48 
 
 54 
 
 59 
 
 76 
 
 108 
 
 133 
 
 5 
 
 76 
 
 94 
 
 10*9 
 
 121 
 
 134 
 
 167 
 
 242 
 
 298 
 
 10 
 
 19S 
 
 133 
 
 153 
 
 171 
 
 188 
 
 242 
 
 342 
 
 419 
 
 15 
 
 133 
 
 162 
 
 188 
 
 210 
 
 230 
 
 297 
 
 419 
 
 514 
 
 20 
 
 153 
 
 188, 
 
 217 
 
 242 
 
 265 
 
 342 
 
 484 
 
 593 
 
 25 
 
 171 
 
 210 
 
 242 
 
 271 
 
 297 
 
 383 
 
 541 
 
 663 
 
 30 
 
 188 
 
 230 
 
 265 
 
 297 
 
 325 
 
 419 
 
 593 
 
 726 
 
 35 
 
 203 
 
 248 
 
 286 
 
 320 
 
 351 
 
 453 
 
 640 
 
 784 
 
 40 
 
 217 
 
 265 
 
 306 
 
 342 
 
 375 
 
 484 
 
 684 
 
 838 
 
 45 
 
 230 
 
 282 
 
 325 
 
 363 
 
 398 
 
 514 
 
 724 
 
 889 
 
 50 
 
 242 
 
 297 
 
 342 
 
 383 
 
 419 
 
 541 
 
 765 
 
 937 
 
 60 
 
 264 
 
 325 
 
 373 
 
 420 
 
 461 
 
 594 
 
 835 
 
 1006 
 
 70 
 
 286 
 
 351 
 
 405 
 
 465 
 
 497 
 
 643 
 
 900 
 
 1115 
 
 80 
 
 306 
 
 375 
 
 453 
 
 485 
 
 530 
 
 688 
 
 965 
 
 1185 
 
 90 
 
 324 
 
 398 
 
 460 
 
 516 
 
 564 
 
 727 
 
 1027 
 
 1225 
 
 100 
 
 342 
 
 420 
 
 4*5 
 
 534 
 
 594 
 
 768 
 
 1080 
 
 1325 
 
 125 
 
 383 
 
 468 
 
 542 
 
 604 
 
 662 
 
 855 
 
 1210 
 
 1480 
 
 150 
 
 420 
 
 515 
 
 596 
 
 665 
 
 730 
 
 942 
 
 1330 
 
 1630 
 
 150 to 240; second story, 300; third story, 360; fourth story, 
 420. Also that in usual conditions of residence heating the 
 temperature of the air in the supply flues averages about 30 
 above the temperature of the air in the room. 
 
 Shape and Material of Air-ducts. The smoother 
 the surface of a flue the less will be the friction of the air against 
 it and the greater the velocity. Hot- or warm-air flues should 
 always be made of metal, preferably galvanized iron for flues 
 exceeding 12 ins. in diameter. Brick flues should be lined 
 with tin or galvanized iron when they convey warm air, not 
 only to reduce the fr'ction but also to lessen the cooling of the 
 air. When brick flues are used for ventilation lining is not 
 so necessary, although it will materially increase the draught. 
 
 Regarding the shape of the flue or duct, round pipes are 
 the best, square pipes next best, and rectangular pipes should 
 always be made as nearly square as possible. 
 
1214 VENTILATION. , 
 
 With indirect or natural systems of ventilation each inlet 
 register should be supplied by a separate pipe from the heater, 
 and but one pipe should be taken from a steam or hot-watei 
 stack. 
 
 With forced systems of warming and ventilation all of the 
 air from the heater often enters one large main, from which 
 distributing pipes are taken off to supply the risers to the 
 registers. With this system no branches should leave the 
 mains at right angles, but should branch off at an angle of 45 C 
 with easy radius curves in all cases. No 90 elbow should be 
 made with less than seven pieces or less inside radius than the 
 diameter of the pipe. No 45 elbow should be made of less 
 than four pieces. Each and every branch air-duct to flues 
 should have a damper near base of flue, and at every "Y" hi 
 the system there should be placed a regulating damper. Al] 
 of these dampers and fenders should be adjustable. Upon 
 completion of the system, these dampers should be adjusted 
 by trial so that each register will receive its proportionate 
 supply of air and then "set." 
 
 All warm-air pipes should be covered with one or more thick- 
 nesses of asbestos paper to reduce loss of heat. 
 
 Natural Systems of Heating and Ventilating. 
 All systems in which the air moves upwards, due to the ex- 
 pansion produced by its own heat, are commonly classified as 
 natural systems. 
 
 With such systems the ventilation is sometimes produced 
 by aspirating shafts or large flues containing a heater of some 
 sort at its base to increase the temperature of the air in the 
 flue and thus increase the velocity. Except where they can 
 be heated without additional cost, aspirating shafts are not 
 as economical, as a rule, as fans. 
 
 Buildings containing but one large room can generally be 
 fairly well ventilated by using a heavy galvanized-iron smoke- 
 flue for the furnace or boiler and locating the flue in the centre 
 of a large brick chimney, utilizing the space around the flue 
 for ventilation. The heat which escapes from the flue will 
 cause a good draught and without additional cost. 
 
 A draught may also be produced in a vent flue by means of 
 coils of steam-pipes placed in the flue just above the air-inlet, 
 or a gas heater may be employed for heating the flue. 
 
 The draught produced by aspiration is not usually sufficient 
 to draw air any distance through horizontal ducts. 
 
VENTILATION. 1215 
 
 Natural systems of ventilation are only effective when used 
 in connection with warming and afford no ventilation in warm 
 weather. 
 
 One of the most effective ways of warming and ventilating 
 without a fan system is by means of indirect steam radiation, 
 which may be supplemented, if the room is very large, by suffi- 
 cient direct radiation to offset the heat lost through the walls 
 and windows or a total direct radiating surface equal to one 
 fourth the sum of the glass area plus one fourth the exposed 
 wall surface. The indirect radiation surface required can be 
 estimated by the data given on p. 1163. A good arrangement 
 for the indirect radiation and flues in a church or schoolhouse 
 is illustrated in "Churches and Chapels," p. 133. 
 
 The author has obtained good results in warming and venti- 
 lating schoolrooms by hot-air furnaces, using a furnace for 
 every two rooms and vertical vent flues for each room extend- 
 ing straight up through the roof. There are but few furnaces 
 made, however, that will give satisfaction for this class of work; 
 they should be of the horizontal tubular pattern with large 
 radiating surface in proportion to the grate area and set in 
 brick with a large air-chamber. An excellent furnace of this 
 type is made by Lewis & Kitchen, of Kansas City and Chicago. 
 
 Fan Systems of Ventilation. Ventilation by means 
 of a fan may be effected by either of two systems, (a) The Plenum 
 System, in which the air is forced into the room to be warmed 
 and ventilated, and (6) The Exhaust System, in which the air 
 is exhausted from the room. 
 
 The Exhaust System. There are many objections to 
 the adoption of this system, and as a rule it should be avoided 
 when the plenum method can possibly be used. With the 
 exhaust system a partial vacuum is created within the room and 
 all currents and leaks are inward, so that air rushes around doors 
 and windows, forming unpleasant and sometimes dangerous 
 currents of air. The circulation of the air in the room is 
 also less thorough when exhausted than when forced in. The 
 exhaust system as a rule is used principally for affording venti- 
 lation in hot weather or for removing disagreeable odors, dust, 
 etc., for which purpose it is both economical and effective 
 when properly installed. 
 
 An exhaust fan can also be used to advantage for ventilating 
 churches in connection with hot-air furnaces or indirect steam 
 radiation, as it can be used both in winter and summer and 
 
1216 VENTILATION. 
 
 for as short a time as may be needed- The ventilation re- 
 quired in a church varies greatly at different times; a church 
 seating 500 persons cannot be sufficiently ventilated when 
 every seat is occupied without a fan, while when there are only 
 one or two hundred people present, a fan may not be required. 
 By this system the fan should be placed in the top of the main 
 ventilation shaft or in a tower or ventilating chamber under 
 the roof, with ducts leading to the outlet registers, and should 
 be operated by electricity. 
 
 The Plenum, or Hot-blast system, on the other hand, 
 maintains a slight pressure in the room or rooms ventilated 
 and the leakage is outward instead of inward. By this system 
 the temperature of the air and point of admission are com- 
 pletely under control. The denser the air also up to a certain 
 limit the better it is for comfort and good acoustics. 
 
 For heating and ventilating theatres, hospitals, and large 
 schools and churches this is undoubtedly the best system that 
 can be employed, and, with the possible exception of churches, 
 is as economical of fuel and maintenance as an indirect steam- 
 heating plant, while affording superior ventilation and greater 
 comfort. This system has also been applied to office buildings, 
 factories, and buildings used for various purposes. The system 
 may be used in summer as well as in winter, and by providing 
 a cooling chamber, the air may be cooled to any desired tem- 
 perature. 
 
 As ordinarily installed a forced-blast system consists of a 
 heater and fan with flues and ducts for conveying the air to 
 the various apartments as explained on p. 1153, and the entire 
 apparatus with the exception of the vertical flues is usually 
 located in the basement. 
 
 Two systems of ducts are commonly employed, viz., the 
 single-duct and double-duct system. A typical arrangement 
 of the single-duct system is shown by Fig. 35. The fan is 
 located at one side of the fresh-air chamber, so that air is drawn 
 into it at A and is forced through the heater into a warm-air 
 chamber from which one large duct with distributing branches 
 is taken off. A by-pass is provided so that a portion of the 
 air passes under the heater without being warmed, and by 
 means of a damper at the mouth of the duct more or less of 
 the cool air may be mixed with the heated air as desired. 
 
 With this system all of the air conveyed through the ducts 
 is of the same temperature. 
 
VENTILATION. 
 
 1217 
 
 With the double-duct system the upper duct conveys only 
 warm air and the under duct cool air, and the mixing damper 
 is placed at tjie bottom of the riser to each outlet. By this 
 system the temperature of the air to each room may be regu- 
 lated independently of the others. 
 
 A modification of the single-duct system is commonly used 
 in heating schools in which a large double chamber is located 
 near the heating stack, one portion being at all times filled 
 with warm air and the other portion with cool air. From this 
 double chamber -a single duct is led to each room, and the 
 connection is made with the chamber in such a way that either 
 
 s Warm *>. 
 *"" Air =-> 
 Chamber 
 
 Heater ' 
 Coil 
 
 Fig. 35 
 
 all warm or all cool air, or any proportion of both, may be ad- 
 mitted into the duct, the mixing being controlled by a damper 
 operated by a thermostat placed in the room with which the 
 duct connects. This arrangement saves the cost of running 
 two pipes, and when a thermostat regulating apparatus is 
 used to control the dampers is the most practical system. 
 
 When there are several rooms to be warmed and a thermo- 
 static regulating apparatus is not employed, so that the mixing 
 dampers must be operated by hand, the double-duct system 
 should be employed. 
 
 The system shown by Fig. 35 answers very well for warming 
 churches and auditoriums 
 
 The various systems of piping are fully described in the 
 catalogues- of the companies named on p. 1153. 
 
 When the fan is to be run in warm weather provision should 
 
1218 VENTILATION. 
 
 be made so that the entire capacity of the air may pass around 
 the heater. 
 
 By the arrangement illustrated in Fig 35 th^ fan is placed 
 between the heater and the cold-air chamber and forces the 
 air through the heater. The fan may, however, be placed on 
 the other side of the heater so as to pull the air through it by 
 exhaustion, at the same time forcing the heated air into the 
 ducts. Both arrangements are used, but the former is the 
 one more commonly employed. 
 
 With the forced-blast systems of warming and ventilating 
 a iresh-air chamber of ample size must be provided adjacent 
 to the fan or heater and communicating with the outside air 
 by a la^ge duct, the opening to which should be located as high 
 above the ground as practical conditions will admit. 
 
 Forced Blast in Connection with Warm-air Fur- 
 naces. Several schools and churches have been successfully 
 warmed and ventilated by utilizing warm-air furnaces of the long 
 tubular pattern to supply the heat and an electric motor for 
 power. For churches of moderate size this system would 
 appear to have some advantages, especially in economy, over 
 the steam systems. A description of such a system with 
 illustrations may be found in 'Churches and Chapels," p. 148. 
 
 Fans. Three types of fans are used in connection with the 
 heating and ventilating of buildings, viz., the disc fan, the 
 blower, or vadd^e^wheel fan, and the cone fan. 
 
 The disc fan receives the air at one side and delivers it at 
 the opposite side, the principal motion of the air being parallel 
 with the axis This type is only used for exhausting air, and 
 is commonly used for ventilating single rooms in warm weather. 
 Most of the electric fans used for ventilating kitchens, restau- 
 rants, etc., are of this type. 
 
 The paddle-wheel Jan is the type commonly used with the 
 forced-blast systems of heating. The fan in steel-plate blowers 
 is of the paddle-wheel type.* 
 
 The cone fan is a special type of the paddle-wheel fan which 
 has been used for maintaining a plenum in a large chamber 
 under an audience room. It is not adapted to high pressures. 
 
 Fans may be driven from a running countershaft, from an 
 engine directly connected, or from an electric or water motor. 
 
 Disc fans are commonly driven by an electric motor, and 
 this will be found the most convenient power for driving steel- 
 
 * The three types of fans are illustrated in ' Churches and Chapels," 
 
VENTILATION. 1219 
 
 plate blowers in churches and theatres, as in the summer-time 
 no heat is required. In schools, which are not used much in 
 warm weather, and in buildings where steam is kept up all the 
 year round, a small steam-engine will generally be most eco- 
 nomical. 
 
 All fans make some noise, hence they should be located 
 where they will be heard the least. 
 
 Capacity of Fans. The catalogued capacities of all 
 makes of fans are their capacities when running light in the 
 open air, not being attached to any ducts or heating coils. 
 These capacities will be reduced from 25 to 50 per cent, when 
 so attached, depending on the length of the ducts and the 
 method of distribution. 
 
 In figuring capacity of fans for forcing air through heating 
 coils and ducts it is customary to call the peripheral velocity 
 of the fan blades equal to the linear velocity of the air, and 
 to take one half of the theoretical delivery as the actual effi- 
 ciency. 
 
 The peripheral velocity is obtained by multiplying the revo- 
 lutions per minute by the circumference of the wheel. 
 
 Thus a fan 6 ft. in diameter running 200 revolutions per 
 minute has a peripheral velocity =200X18. 84 =3, 768 ft. per 
 minute. Deducting 50 per cent, for loss, the actual velocity 
 of the air would be 1,884 ft. per minute. The discharge opening 
 in a fan 6 ft. in diameter will have an area of at least 11.5 sq. ft 
 Multiplying this area by the working velocity we have 21,666 
 cu. ft. per minute as the probable actual discharge of the fan. 
 
 Mr. F. R. Still, of Detroit, who has had extensive engineering 
 experience with forced-blast systems, says that the maximum 
 limit of speed of a blower without making a serious noise is 
 250 revolutions per minute, and that except in rare cases the 
 blower should run at from 180 to 200 revolutions per minute. 
 
 With a disc fan, used for ventilation only, the velocity should 
 never exceed 900 ft. per minute. 
 
 As explained above, the actual capacity when connected 
 with a heating and ventilating system will be reduced from 
 25 to 50 per cent, from the values in the table on the next page, 
 while the horse-powers, on the other hand, are probably some- 
 what in excess of those actually required. 
 
 For further information on this subject the reader is referred 
 to the catalogues of the various manufacturers of blowers 
 and to " Heating and Ventilating Buildings." 
 
1220 
 
 CHIMNEYS. 
 
 TABLE OF CAPACITY AND POWER REQUIRED FOR 
 
 STEEL-PLATE BLOWERS OF VARIOUS SIZES. 
 
 WITH FREE INLET AND OUTLET. 
 
 
 
 M-ounce Pressure. 
 
 ^-ounce Pressure. 
 
 
 Diam- 
 
 
 
 Size, 
 
 eter of 
 
 
 
 
 
 
 
 Inches. 
 
 Wheel, 
 Inches. 
 
 Revo- 
 lutions. 
 
 Cubic 
 Feet per 
 Minute. 
 
 H.P. 
 
 Revo- 
 lutions. 
 
 Cubic 
 Feet per 
 Minute. 
 
 H.P. 
 
 70 
 
 42 
 
 214 
 
 10,336 
 
 .3 
 
 312 
 
 14,628 
 
 1.3 
 
 80 
 
 48 
 
 188 
 
 12,584 
 
 .5 
 
 265 
 
 17,809 
 
 1.6 
 
 90 
 
 54 
 
 167 
 
 16,150 
 
 .7 
 
 236 
 
 22,856 
 
 2.0 
 
 100 
 
 60 
 
 150 
 
 20723 
 
 .9 
 
 212 
 
 29,329 
 
 2.6 
 
 110 
 
 66 
 
 137 
 
 24,548 
 
 1.1 
 
 193 
 
 34,741 
 
 3.1 
 
 120 
 
 72 
 
 125 
 
 30,165 
 
 1.3 
 
 177 
 
 42,678 
 
 3.8 
 
 140 
 
 84 
 
 107 
 
 40,465 
 
 1.8 
 
 152 
 
 57,268 
 
 5.1 
 
 160 
 
 96 
 
 94 
 
 51,344 
 
 2.3 
 
 133 
 
 72,264 
 
 6.4 
 
 
 
 i^-ounce Pressure. 
 
 1-ounce Pressure. 
 
 
 Diam- 
 
 
 
 Size, 
 
 eter of 
 
 
 
 
 
 
 
 Inches. 
 
 Wheel, 
 Inches. 
 
 Revo- 
 lutions. 
 
 Cubic 
 Feet per 
 Minute. 
 
 H.P. 
 
 Revo- 
 lutions. 
 
 Cubic 
 Feet per 
 Minute. 
 
 H.P. 
 
 70 
 
 42 
 
 377 
 
 17,928 
 
 16 
 
 428 
 
 20,700 
 
 3.7 
 
 80 
 
 48 
 
 325 
 
 21,827 
 
 2.4 
 
 367 
 
 25202 
 
 4.5 
 
 90 
 
 54 
 
 289 
 
 28,012 
 
 3.7 
 
 333 
 
 32 343 
 
 5.7 
 
 100 
 
 60 
 
 260 
 
 35,945 
 
 4.8 
 
 300 
 
 41,503 
 
 7.4 
 
 110 
 
 66 
 
 236 
 
 42,579 
 
 5.7 
 
 273 
 
 49,162 
 
 8.8 
 
 120 
 
 72 
 
 217 
 
 52,304 
 
 7.0 
 
 250 
 
 60,392 
 
 10.7 
 
 140 
 
 84 
 
 186 
 
 70,188 
 
 9.4 
 
 214 
 
 81,040 
 
 14.4 
 
 160 
 
 96 
 
 163 
 
 89,057 
 
 11.5 
 
 152 
 
 102,807 
 
 18.3 
 
 Chimneys. 
 
 Object. A chimney is required for two purposes, (1) to 
 produce the draught necessary for the proper combustion of 
 the fuel, and (2) to furnish a means of discharging the noxious 
 products of combustion into the atmosphere at such a height 
 from the ground thr,t ' * ey may not prove a nuisance to people 
 living in the vicinity of the chimney. >: -~7 i 
 
 A good draught is absolutely essential to the satisfactory 
 and economical working of either a heating or power plant. It 
 is claimed by Kent that chimneys over 150 ft. in height are not 
 justified from the standpoint of economy, but where the gases 
 of combustion are poisonous, as in the case of smelters, or 
 
CHIMNEYS. 1221 
 
 (specially noxious, tall chimneys enhance the value of sur- 
 | rounding property, if in a town, far more than the cost of the 
 j chimney, and should be required by law. 
 
 Theory of Chimneys.* To produce an effective draught 
 I in the furnace a chimney requires size and height. 
 
 Each pound of coal burned yields from 13 to 30 Ibs. of gas 
 the volume of which varies with the temperature. 
 
 The Weight of Gas carried off by a chimney in a given time 
 depends upon three things size of chimney, velocity of flow, 
 and density of gas. But as the density decreases directly as 
 the absolute temperature, while the velocity increases, with a 
 given height, nearly as the square root of the temperature, it 
 follows that there is temperature at which the weight of gas 
 delivered is a maximum. This is about 550 above the sur- 
 rounding air. Temperature, however, makes so little differ- 
 ence that at 550 above, the quantity is only four per cent. 
 greater than at 300. Therefore height and area are the only 
 elements necessary to consider in an ordinary chimney. 
 
 The Intensity of Draught is, however, independent of the size, 
 and depends upon the difference in weight of the outside and 
 inside columns of air, which varies directly with the product 
 of the height into the difference of temperature. This is usually 
 stated in an equivalent column of water and may vary from 
 to possibly 2 ins. 
 
 To Fin (I the Maximum Draught for any given chimney, 
 the heated column being 612 F. and the external air 62: 
 Multiply the height above grate in feet by .GO 7 5 and the product 
 is the draught power in inches of water. 
 
 The intensity of draught required varies with the kind 
 and condition of the fuel and the thickness of the fires. Wood 
 requires the least and fine coal or slack the most. To burn 
 anthracite slack to advantage, a draught of 1 \ ins. of water is 
 necessary, which can be attained by a well-proportioned chim- 
 ney 175 ft. high. 
 
 A round chimney is better than square and a straight 
 flue better than tapering, though it may be either larger or 
 smaller at top without detriment. 
 
 * Babcock & Wileox Co. 
 
1222 CHIMNEYS FOR POWER PLANTS. 
 
 Size of Chimneys for Power Plants.* 
 
 The effective area of a chimney for a given power varies 
 inversely as the square root of the height. The actual area, in 
 practice, should be greater, because of retardation of velocity 
 due to friction against the walls. On the basis that this is equal 
 to a layer of air 2 ins. thick over the whole interior surface, and 
 that a commercial horse-power requires the consumption of an 
 average of 5 Ibs. of coal per hour, we have the following for- 
 mulae: 
 
 E^-^.^A-O.&VJ; (1) 
 
 Vh 
 
 S ,. r >; - (2) 
 
 . . . . : ~m . (3) 
 > = 13.54\/#+4; . . ;-^^. (4) 
 
 ;- =(^) 2 - -^Sir 
 
 In which #= horse-power; ft = height of chimney in feet; 
 E= effective area, and A = actual area in square feet; $ = side 
 of square chimney and D=dia. of round chimney in inches. 
 The first table on the next page was calculated by means of 
 these formulae. 
 
 High Chimneys Not Necessary. f "Chimneys above 
 150 ft. in height are very costly and their increased cost is 
 rarely justified by increased efficiency. In recent practice it 
 has become somewhat common to build two or more smaller 
 chimneys instead of one large one. A notable example is the 
 Spreckles sugar refinery in Philadelphia, where three separate 
 chimneys are used for one boiler plant of 7,500 H.P. The three 
 chimneys are said to have cost several thousand dollars less than 
 a single chimney of their combined capacity would have cost." 
 
 Size of Chimneys for House Heaters. Chimney- 
 flues for heating apparatus should be ample in size and carried 
 as nearly straight as possible from a point near the cellar floor 
 to above the highest projection of the roof. They should be 
 independent, having no connection with other flues or openings, 
 and always of the same area from top to bottom. A well- 
 
 * These formulae are those given by Kent, and are generally accepted 
 as reliable, 
 t Kent. 
 
CHIMNEYS FOR HOUSE HEATERS. 
 
 1223 
 
 SIZES OF CHIMNEYS WITH APPROPRIATE HORSE- 
 POWER OF BOILERS. 
 
 Diameter in 
 Inches. 
 
 Effective Area, 
 Square Feet. 
 
 V 
 
 il 
 
 <z 
 
 I 1 
 
 Height of Chimneys. 
 
 3 
 cr c 
 
 COt-" 
 
 " 
 
 -I s 
 
 w 
 
 16 
 19 
 22 
 24 
 27 
 30 
 32 
 35 
 38 
 43 
 48 
 54 
 59 
 64 
 70 
 75 
 80 
 86 
 
 50 
 Ft. 
 
 60 
 Ft. 
 
 70 
 
 Ft. 
 
 80 
 Ft. 
 
 90 
 Ft. 
 
 100 
 Ft. 
 
 110 
 Ft. 
 
 125 
 Ft. 
 
 150 
 Ft. 
 
 175 
 Ft. 
 
 200 
 Ft. 
 
 Commercial H.P. of Boiler. 
 
 18 
 21 
 24 
 27 
 30 
 33 
 36 
 39 
 42 
 48 
 54 
 60 
 66 
 72 
 78 
 84 
 90 
 96 
 
 0.97 
 1.47 
 2.08 
 2.78 
 3.58 
 4.48 
 5.47 
 6.57 
 7.76 
 10.44 
 -13.51 
 16.98 
 20.83 
 25.08 
 29.73 
 34.76 
 40.19 
 46.01 
 
 1.77 
 2.41 
 3.14 
 3.98 
 4.91 
 5.94 
 7.07 
 8.30 
 9.62 
 12.57 
 15.90 
 19.64 
 23.76 
 28.27 
 33.18 
 38.48 
 44.18 
 50.27 
 
 23 
 35 
 49 
 65 
 84 
 
 25 
 38 
 54 
 72 
 92 
 115 
 141 
 
 27 
 41 
 58 
 78 
 100 
 125 
 152 
 183 
 216 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 62 
 83 
 107 
 133 
 163 
 196 
 231 
 311 
 
 
 
 
 
 
 
 113 
 141 
 173 
 208 
 245 
 330 
 427 
 536 
 
 
 
 
 
 
 
 
 
 
 
 
 
 182 
 219 
 258 
 348 
 449 
 565 
 694 
 835 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 271 
 365 
 472 
 593 
 728 
 876 
 1038 
 1214 
 
 
 
 
 389 
 503 
 632 
 776 
 934 
 1107 
 1294 
 1496 
 
 
 
 
 551 
 692 
 
 849 
 1023 
 1212 
 1418 
 1639 
 1876 
 
 
 
 
 
 
 
 748 
 918 
 1105 
 1310 
 1531 
 1770 
 2027 
 
 981 
 1181 
 1400 
 1637 
 1893 
 2167 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 jointed tile flue, preferably round, is better than a square brick 
 flue of larger area. The chimney flue should be carried 3 or 
 4 ft. below the smoke-pipe entrance and provided with a clean- 
 out door at the base, tightly fitted, to facilitate the removal 
 of accumulated dust and soot. 
 
 The size of flues may be calculated from the following table: 
 
 
 
 Tile Flues, 
 
 Tile 
 
 
 
 
 Standard 
 
 Flues, 
 
 Brick 
 
 Total Contents of 
 Building, Cubic Feet 
 of Space. 
 
 Average of 
 Direct Radiation 
 Steam, Square 
 Feet. 
 
 Sizes, 
 Square or 
 Rectangu- 
 lar, Out- 
 
 Standard 
 Sizes, 
 Round, 
 Inside 
 
 Flues, 
 Inside 
 Dimen- 
 
 
 
 side Di- 
 
 Dimen- 
 
 "" 
 
 
 
 mensions. 
 
 sions. 
 
 
 
 
 Inches. 
 
 Inches. 
 
 Inches. 
 
 10,000 to 20,000 
 
 200 to 400 
 
 8JX8J 
 
 8 
 
 8X 8 
 
 25,000 to 50,000 
 
 450 to 900 
 
 8JX 13 
 
 10 
 
 8X12 
 
 60,000 to 100,000 
 
 1,000 to 1,600 
 
 13X13 
 
 12 
 
 12X12 
 
 100,000 to 150,000 
 
 1,600 to 3,000 
 
 18X18 
 
 16 
 
 16X16 
 
 Indirect radiation should be counted as 50 per cent, more 
 than direct and corresponding areas of flue be provided for. 
 
1224 CONSTRUCTION OF BRICK CHIMNEYS. 
 
 The amount of radiation determines the requisite size of boiler, 
 and therefore the area of the flue. 
 
 No chimney-flue should be less than 8 ins. in depth, nor of 
 a smaller size than the smqke-pipe from the heater. 
 
 For a kitchen range an 8X8 tile flue will generally answer, 
 but an 8X12 flue is better. 
 
 For -fireplaces the sectional area of the flue for burning wood 
 or bituminous coal should be one tenth to one eighth that of 
 the fireplace opening for a rectangular flue and one twelfth for 
 a circular flue For burning anthracite coal the above pro- 
 portions may be reduced to one twelfth and one sixteenth re- 
 spectively. 
 
 When practicable, chimneys should extend above the highest 
 surrounding roof, to prevent down-draught caused by eddies. 
 When this is impracticable a revolving chimney-top will often 
 prevent down-draughts. They may also often be avoided by 
 covering the top of the chimney with a stone flag and leaving 
 openings in two parallel sides of the chimney, the sides parallel 
 to the ridge of the adjoining roof or building being closed. 
 
 The walls of the flue should be as smooth as possible. Tile- 
 flue lining is preferable. Brick flues should be either smoothly 
 plastered on the inside with rich lime mortar or the joints 
 should be filled full and struck with the point of the trowel. 
 If the bricks are laid in cement mortar, the author recom- 
 mends striking the joints instead of plastering. 
 
 The walls of attached chimneys with flues not exceeding 
 8"X12" may be 4" thick for heights of 50 ft. Flues 12"X12" 
 and larger should have walls 8" thick to within 10 ft. of the 
 top. Aside from strength or stability, thick walls are preferable 
 to thin walls. 
 
 Stability of Chimneys. A general rule for diameter of 
 base of brick chimneys standing free, approved .by many years 
 of practice in England and the United States, is to make the di- 
 ameter of the base, or side of a square chimney, one tenth of the 
 height. 
 
 Construction of Brick Chimneys. "For chimneys 
 of 4 ft. in diameter and 100 ft. high and upwards, the best 
 form is circular with a straight batter on the outside. A cir- 
 cular chimney of this size, in addition to being cheaper than 
 any other form, is lighter, stronger, and looks much better and 
 more shapely. 
 
 "Chimneys of any considerable height are not built up of uni- 
 
CONSTRUCTION OF BRICK CHIMNEYS. 1225 
 
 form thickness from top to bottom nor with a uniformly varying 
 thickness of wall, but the wall, heaviest of course at the base, 
 is reduced by a series of steps. 
 
 " All boiler chimneys of any considerable size should consist 
 of an outer stack of sufficient strength to give stability to the 
 structure and an inner stack or core independent of the outer 
 one. This core is by many engineers extended up to a height 
 of but 50 or 60 ft. from the base of the chimney, but the better 
 practice is to run it up the whole height of the chimney; it 
 may be stopped off, say, a couple feet below the top and the 
 outer shell contracted to the area of the core, but the better 
 way is to run it up to about 8 or 12 ins. of the top and not 
 contract the outer shell. But under no circumstances should 
 the core at its upper end be built into or connected with the 
 outer stack. This has been done in several instances by brick- 
 layers, and the result has been the expansion of the inner core, 
 which lifted the top of the outer stack squarely up and cracked 
 the brickwork." * 
 
 Notwithstanding the above, a number of tall brick chimneys 
 have been built without an interior wall, an instance of which 
 is given on the next page. 
 
 Thickness of Walls. The following is considered as a 
 safe rule for the thickness of the outer wall of tall chimneys: 
 For the first 25 ft. from the top, one brick (8 or 9 ins); for the 
 second 25 ft., li bricks, and so on, increasing one half brick 
 for each 25 ft. from the top downwards. If the inside diam- 
 eter exceeds 5 ft. the top length should be 1 J bricks, the next two 
 bricks, etc.; if under 3 ft., the top may be one half brick for 10 ft. 
 
 The batter should be not less than 1 in 36 to give stability. 
 
 The inside core may be 4 ins. thick for 25 ft. from the top, 
 then 8 or 9 ins. for 50 ft. 
 
 Two chimneys of the Edison station, Brooklyn, each 150 ft. 
 high, have inner cores 80 ft. high and one brick thick for the 
 full height, the first 50 ft. being of fire-brick. 
 
 Fire-brick Lining 1 . If a chimney has but one wall it should 
 be lined with fire-brick for at least 30 ft., and if it has an inner 
 core, the latter is usually built of firebrick for 30 or 50 ft. from 
 the bottom. 
 
 The top of tall brick chimneys should be protected by a cast- 
 iron cap. 
 
 * From The Locomotive, 1884 and 1886. 
 
1226 CONSTRUCTION OF BRICK CHIMNEYS. 
 
 Examples of Tall Brick Chimneys. Several tall 
 brick chimneys are described in the thirteenth edition of this 
 book, also in Kent, p. 737. 
 
 Chimney-stacK at the West Cumberland Hem.i- 
 tite Iron Works. Designed by Professor J. Macquorn 
 Rankine, and considered as a model chimney. 
 
 Duty. The duty of this chimney is to carry off the gaseous 
 products of combustion from four blast-furnaces and from 
 various stoves and boilers. The total amount of fuel consumed 
 is estimated at about 10 \ tons per hour when all the furnaces 
 are at work. 
 
 The actual temperature inside the chimney when doing about 
 three fourths of its full duty is 490 F., and the pressure of the 
 draught is 1J ins. of water. 
 
 Figure and Dimensions. Above ground the chimney is a frus- 
 tum of a cone, with a straight batter. Underground there is a 
 plinth or basement, octagonal outside at the ground line and 
 square at the bottom; cylindrical inside and pierced with four 
 circular openings for flues. 
 
 Height of chimney above the ground, 250 ft. 
 
 Depth of foundation below the ground, 17 ft. 
 
 Total height from foundation to top, 267 ft. 
 
 Inside diameter at top of cone, 13 ft. 
 
 Inside diameter 2 ft. above bottom of cone, 21 ft. 10 ins. 
 
 Inside diameter in basement, 18 ft. 10 ins. 
 
 Inside diameter of archway for flues, 7 ft. 6 ins. 
 
 Outside diameter at top of cone, 15 ft. 3 ins. 
 
 Outside diameter 2 ft. above bottom of cone, 25 ft. 7 ins. 
 
 Outside dimensions of square basement, 30 ft.X30 ft. 
 
 Size of foundation course, 31 ft. 6 ins.X31 ft. 6 ins. 
 
 Size of concrete foundations, 34 ft. 6 ins. X 34 ft. 6 ins. and 
 3 ft. thick. 
 
 Thickness of Brickwork. First 2 ft. above foundation stepping 
 from four bricks to 2} bricks; next 88 ft.. 2J bricks; next 
 80 ft., 2 bricks; remaining 80 ft., 1J bricks. 
 
 The pressure on the ground below the concrete is 1.6 tons 
 on the square foot. 
 
 Fire-brick Lining. The thickness of brickwork given above 
 included the fire-brick lining, which was one brick in thickness 
 in the first 90 ft. and one half brick the remaining height, the 
 fire-brick being bonded in with the common brick, but being 
 
LIST OF TALL CHIMNEYS. 1227 
 
 laid in fire-clay. This method of construction was considered 
 better than that of the inner cone. 
 
 Strips of No. 15 hoop iron, tarred and sanded, were laid in the 
 bed- joints of the cone at intervals of 4 ft. in height, with their 
 ends turned down in the side- joints. The length of the iron 
 was twice the circumference of the chimney. 
 . Cap and Lightning Conductor. On the top of the chimney 
 is a pitch-coated, cast-iron curb 1 in. thick, coming down 
 3 ins. on the outside and inside. The lightning conductor is a 
 copper- wire rope f in. in diameter. It terminates in a covered 
 drain, in which there is always a sufficient run of water. 
 
 SOME OF THE TALLEST CHIMNEYS ON EARTH.* 
 
 Height 
 in Feet. 
 
 tFreiberg, Saxony, Germany, Halsbrucke Foundry 460 
 
 Glasgow, Port Dundas, Scotland, F. Townsend 454 
 
 Glasgow, St. Rollox, Scotland, Tenant & Co 436i 
 
 Creusot, France, Messrs. Musprath Chemical Works 406 
 
 Halifax, Dean Clough Mill, Scotland, Messrs. Crossley's. . . 381 
 
 Lancashire, Bolton, England, Dobson & Barlow 367 
 
 Boston, Mass., United States, Fall River Iron Co 350 
 
 Chicago, Illinois, United States 350 
 
 East Newark, N. J., United States, Clark Thread Co 335 
 
 Barmen, Prussia, Germany, Wessenfield & Co 331 
 
 Edinburgh, Scotland, Gas Works 329 
 
 Huddersfield, England, Brook & Son, Fire-clay Works. . . 315 
 
 Smethwick, England, Adams Soap W T orks 312 
 
 Carlisle, England, P. Dickon & Son 300 
 
 Bradford, England, Mitchell Brothers 300 
 
 Greenhithe, Kent, England, J. C. Johnson 297 
 
 Lowell, Mass., United States, Merrimack Mfg. Co 283 
 
 Dundee, Scotland, Camperdown, Linen Works, Cox Bros. . 282 
 
 Creusot, France, Schneider & Co 280 
 
 Darwin, North Lancashire, Darwin & Mostyn Iron Co. . . . 275 
 
 Pittsburg, Pennsylvania, United States 275 
 
 Lancashire, Eng., Barrow-in-Furness, Hematite Iron Co.. . 259 
 
 Bradford, England, Manningham Mills, Lester & Co 256J 
 
 Manchester, N. H., United States, Amoskeag Mfg. Co 255 
 
 West Cumberland, England, Hematite Iron Works 250 
 
 Lancaster, England, Story Brothers 250 
 
 Lawrence, Mass., Washington Mills 250 
 
 Cheshire, England, Connah's Quay, Chemical Co 245 
 
 * This is part of a list of chimneys compiled by W. Barnet Le Van and 
 published in Machinery, Sept., 1895. The order of the list has not 
 been changed except for the insertion by the author of several additional 
 chimneys. 
 
 t Built hv H. "R. Hfir>irtk*> nf np>rfnratfid ra.rlial hrip.lts. a.nH claimed to hft 
 
1228 LIST OF TALL CHIMNEYS. 
 
 Height 
 
 in Feet 
 
 Bradford, England, Newland's Mill ..................... 240 
 
 Boston Navy Yard, Mass., United States ............... 239 
 
 Providence, R. I., Narragansett E. L. Co ................ 238 
 
 Lawrence, Mass., United States, Pacific Mills ............ 233 
 
 Harwich, Dovercourt, England, Pattrie & Sons .......... 230 
 
 Lowell, Mass., United States, Fremont & Suffolk Co ...... 225 
 
 Woolwich Arsenal, England, Shell Foundry ............. 224 
 
 New York City, N. Y., U. S., New York Steam Heating Co. 221 
 
 Northfleet, England, F. C. Gostling & Co ............... 220 
 
 * Elizabethport, N. J., Plymouth Cordage Co ........... 220 
 
 Ivorydale, Ohio, United States, Procter & Gamble ....... 218 
 
 Lawrence, Mass., United States, The Tower Pacific Mills. . . 215 
 
 Philadelphia, Pa., The Fidelity Insurance Co ............ 212 
 
 Dewsbury, England, Olroyd & Sons .................... 210 
 
 Lanarkshire, England, Coltness Iron Works ............. 210 
 
 Wilmington, Delaware, United States, City Water Works. 204 
 
 Philadelphia, Penn., United States, Finley & Schlecter ____ 202 
 
 Camden, N. J., U. S., Highland Mill, S. B. Still & Co ...... 202 
 
 Ironton, Ohio, United States, Etna Iron Works .......... 200 
 
 Lamokin, Penn., United States, John M. Sharpless & Co. . . 200 
 
 Duluth, Minn., United States, Hartman Gen. Electric Co. . 200 
 
 Passaic, N. J., Passaic Print Works .................... 200 
 
 Creusot, France, Schneider & Co ....................... 197 
 
 East Newark, N. J., United States, Clark's Thread Mill. . . 192 
 
 Cleveland, Ohio, United States, Ohio Rolling Mill Co ...... 190 
 
 Nottingham, England, Stanton Iron Co ................. 190 
 
 Deepear, Sheffield, England, Fox & Co ................. 186 
 
 Philadelphia, Penn., United States, John Lang Paper Mills. 181 
 
 Bayonne, N. J., U. S., Lombard, Ayres & Co. Oil Refinery. 180 
 
 A few of the tall chimneys built by the Alphonse Custodis 
 Chimney Construction Co.: 
 
 Constable Hook, N. J., Oxford Copper Co ............ 365 10 ' 
 
 Providence, R. L, Rhode Island Suburban R'y Co ..... 308 16 
 
 New York City, Manhattan R'y Co ............ ..... 278 17 
 
 Philadelphia, Pa., Southern Elec. L't and Power Co. . . 275 18 
 
 Kansas City, Mo., Metropolitan St. R'y Co ........... 265 16 
 
 Kansas City, Mo., Armour Packing Co ......... . ---- 250 14 
 
 Boston, Mass., Edison Elec. 111. Co ................. 250 16 
 
 New York City, Jacob Ruppert Ice Plant ............ 250 10 
 
 Kansas City, Mo., ConsTd Elec. Light and Power Co. . 243 10 
 
 Cleveland, Ohio, Cleveland City R'y Co ............. 240 13 
 
 Miflinocket, Me., Great Northern Paper Co .......... 235 12 
 
 Weehawken, N. J., N. Y. Cen. and H. R. R, Co ...... 233 11 
 
 Edgewater, N. J. N. Y. Glucose Co ................ .225 12 
 
 Washington, D. C., St. Elizabeth's Insane Hospital. .. 225 10 
 
 * Reinforced concrete. 
 
CHIMNEYS OF REINFORCED CONCRETE. 1229 
 
 Radial Block Chimneys. Radial blocks for chimney 
 construction have been used extensively in England, Germany, 
 France, and Russia for many years, but their use in this country 
 has been quite limited. 
 
 Some thirty years ago, Alphonse Custodis, of Germany, origi- 
 nated a method of building tall chimneys of perforated radial 
 blocks, made from selected clays and burned at a very high 
 temperature, and a company * was formed for the purpose of 
 erecting chimneys by this method of construction. Since that 
 time the company through its various agencies has built over 
 4,000 chmineys in all parts of the world. 
 
 The blocks are formed to suit the circular and radial lines 
 of each section of the chimney, so that they can be laid with 
 thin even joints and regular smooth surfaces. The blocks 
 being much larger than common bricks there are only about 
 half as many joints. These chimneys are always circular in 
 plan above the base, and except for chemical works, metal 
 refineries, furnaces, etc., with a single-shell construction. They 
 are undoubtedly stronger and superior in every way to common 
 brick chimneys* 
 
 H. R. Heinicke, of Chemnitz, Germany, builder of the 460-ft. 
 stack at Halsbriicke and many tall chimneys in Europe and 
 America, also employs radial blocks made especially for each 
 chimney and very much resembling those described above. A 
 branch office is maintained at 160 Fifth Ave., New York. 
 
 The Steinl Improved Chimney Construction Company of 
 Birmingham, Ala., designs and erects an improved radial block 
 chimney in which every block is moulded for the position it is 
 to occupy and is tongued and grooved on the sides, so that 
 the blocks interlock, thereby forming a ring which it would 
 seem to be impossible to separate. The blocks are also per- 
 forated vertically so as to receive the cement when in place. 
 
 Chimneys of Reinforced Concrete. Within the past 
 ten years a number of tall chimneys have been built of rein- 
 forced concrete, and it seems more than probable that this 
 material will largely supersede brick for this purpose in the 
 future. A well-built steel-concrete chimney should be more 
 durable than either brick or steel, and in every respect as good, 
 while the cost of erection is less than for a brick chimney. 
 
 In July and August, 1902, a concrete-steel chimney 180 ft. 
 
 * Alphonse Custodis Chimney Construction Company, 517 Bennett Build- 
 ing, New York. 
 
1230 SELF-SUSTAINING STEEL CHIMNEYS. 
 
 high from bottom of footing and 165 ft. above floor of boiler- 
 room was built by Mr. Carl Leonardt for the Pacific Electric 
 Railway Company at Los Angeles, Cal., the Ransome system 
 of construction being employed. The inner diameter is 11 ft. 
 for the entire height. A detailed description of this chimney 
 was published in the Engineering Record of April 11, 1903. 
 
 A chimney built in 1903 for the Laclede Fire-brick Mfg. Com- 
 pany at St. Louis, Mo., has an inside diameter of 5 ft. and a 
 height of 130 ft. above foundation. The materials used in the 
 construction are river sand and T bars. 
 
 Up to the height of 65 ft. the chimney consists of two in- 
 dependent shells, the outer being 6 ins. thick and the inner 4 
 ins., separated by a 3-inch air space. 
 
 At the height of 65 ft. both shells join, the inner shell con 
 tinuing and tapering in proper intervals from 5 ins. to 4 ins., 
 and finally 3 ins. at the top. The air space is connected directly 
 above the grade, by means of four openings 4"X6", with the 
 outside air, which at the 65-foot height is allowed to enter from 
 the air space to the chimney proper through round holes. This 
 provision is to allow the inner shell which receives the direct 
 heat to expand and contract while being protected by the 
 outer shell against sudden cooling from the atmosphere.* 
 
 In 1900 a chimney was built on the Ransome system for the 
 Pacific Coast Borax Company at Bayonne, N. J., 6 ft. diameter 
 by 150 ft. high. It consists of one. outer and one inner shell 
 from grade to top, both shells being reinforced by means of 
 twisted square rods, vertically and horizontally. 
 
 A large number of these chimneys have been constructed 
 on the Ransome system, among which are two at South Bend, 
 Ind., and one for the Plymouth Cordage Company at Eliza- 
 bethport, N. J. The latter is 220 ft. high, witn an interior 
 diameter of 8 ft. 8 ins. It is built in two shells each having 
 vertical ribs running contiguously in the air space. 
 
 Self-sustaining Steel Chimneys are largely coming 
 into use, 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 per cent, as compared with brick chim- 
 neys; avoidance of infiltration of air and consequent checking 
 of the draught, common in brick chimneys. They are usually 
 
 * A more complete description of this chimney, with illustrations, may 
 be found in Cement and Engineering News for February, 1904. 
 
HYDRAULICS. 
 
 1231 
 
 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." * 
 
 The Philadelphia Engineering Works, which built a large 
 number of steel-plate chimneys, published, in 1894, a pamphlet 
 discussing the strength -and stability of such chimneys and con- 
 taining tables of dimensions for stacks of varying diameter and 
 height. This company has been succeeded by the Niles-Bement- 
 Pond Co., who confine themselves exclusively to the con- 
 struction of electric traveling cranes. The following table is 
 compiled from the pamphlet above mentioned: 
 
 SIZES OF FOUNDATIONS FOR SELF-SUSTAINING STEEL 
 CHIMNEYS, HALF LINED. 
 
 Diameter, clear, ft... 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 9 
 
 11 
 
 Height in feet 
 
 100 
 
 100 
 
 150 
 
 150 
 
 150 
 
 175 
 
 225 
 
 Least diam. of foun- 
 dation 
 
 15' 9" 
 
 15' 3" 
 
 20' 4" 
 
 21' 10" 
 
 22' 7" 
 
 25 ; 9" 
 
 29' 11" 
 
 Least depth of foun- 
 dation. . . 
 
 6' 6" 
 
 7' 
 
 9' 
 
 8' 
 
 9' 
 
 10' 
 
 13' 
 
 Height in feet 
 
 
 125 
 
 200 
 
 200 
 
 250 
 
 275 
 
 300 
 
 Least diam. of foun- 
 
 
 17' 6" 
 
 23' 8" 
 
 25' 0" 
 
 29' 8" 
 
 33' 6" 
 
 36' 0" 
 
 Least depth of foun- 
 dation 
 
 
 7' 6" 
 
 10' 
 
 10' 
 
 12' 
 
 12' 
 
 14' 
 
 
 
 
 
 
 
 
 
 The details of a self -sustained steel-plate stack 5 ft. inside 
 diameter and 120 ft. high above the base ring are published 
 in Engineering Record for February 15, 1902. 
 
 Hydraulics. 
 
 Water is practically an incompressible liquid, weighing, at 
 the average temperature of 62 F., 62.355 Ibs. to the cubic foot 
 and 8.335 Ibs. to the gallon. These figures change slightly with 
 changes in temperature and atmospheric pressure, and a slight 
 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 
 
 * Kent, p. 740. 
 
1232 
 
 FLOW OF WATER IN PIPES. 
 
 upon, and is equal to 0.433 Ib. per square inch for every foot 
 of head at 62 F. The fluid pressure per square inch is equal 
 in all directions. 
 
 To find the total pressure of quiet water against and per- 
 pendicular to any surface, whether vertical, horizontal, or in- 
 clined 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 centre 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 
 Z)=the vertical depth in feet of centre of gravity of 
 surface considered. 
 
 TABLE A. PRESSURE IN POUNDS PER SQUARE INCH 
 FOR DIFFERENT HEADS OF WATER. 
 
 Head, 
 Feet. 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 
 10 
 20 
 30 
 40 
 50 
 60 
 70 
 80 
 90 
 
 0.433 
 4.330 4.763 
 8.660 9.093 
 12.990 13.423 
 17.320 17.753 
 21.650 22.083 
 25.980 26.413 
 30.310 30.743 
 34.640 35-073 
 38.970 39.403 
 
 0.866 
 5.196 
 9.526 
 13.856 
 18.186 
 22.516 
 20.846 
 31.176 
 35.506 
 39.836 
 
 1.299 
 5.629 
 9.959 
 14.289 
 18.619 
 22.949 
 27.279 
 31.609 
 35.939 
 40.269 
 
 1.732 
 6.062 
 10.392 
 14.722 
 19.052 
 23.382 
 27.712 
 32.042 
 36.372 
 40.702 
 
 2.165 
 6.495 
 10.825 
 15.155 
 19.485 
 23.815 
 28.145 
 32.475 
 36.805 
 41.135 
 
 2.598 3.031 
 6.928 7.361 
 11.258 11.691 
 15.588 16.021 
 19.918 20.351 
 24.248 24.681 
 28.57829.011 
 32.908 33.341 
 37.238 37.671 
 41.568 42.001 
 
 3.464 
 7.794 
 12.124 
 16.454 
 20.784 
 25.114 
 29.444 
 33.774 
 38.104 
 42.436 
 
 3.897 
 8.227 
 12.557 
 16.887 
 21.217 
 25.547 
 29.877 
 34.207 
 38.537 
 42.867 
 
 The pressure for greater heads can be readily found by mul- 
 tiplication or addition, thus: the pressure for a head of 110 ft. 
 is ten times that for 11. The pressure for 118 ft. is equal to 
 the pressure for 110 ft. plus that for 8 ft. 
 
 Flow of Water in Pipes. 
 
 [NOTE. Owing to the many practical and variable conditions 
 which affect the flow of water in pipes, such as the smoothness 
 of the pipe, number and character of the joints, bends and 
 
FLOW OF WATER IN PIPES. 
 
 1233 
 
 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 in "Kent" and "Trautwine," 
 both of whom devote much space to this subject.] 
 
 The quantity of water passing 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. 
 
 Head is the vertical distance from the surface of the water 
 in the reservoir to the centre 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 in feet of water may be readily determined by the follow- 
 ing table: 
 
 TABLE B.* FOR CONVERTING PRESSURE PER 
 SQUARE INCH INTO FEET HEAD OF WATER. 
 
 
 10 
 20 
 30 
 40 
 50 
 60 
 70 
 80 
 90 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 r 
 
 8 
 
 9 
 
 
 2.309 
 25.404 
 48.499 
 71.594 
 94.688 
 117.78 
 140.88 
 163.97 
 187.07 
 210.16 
 
 4.619 
 27.714 
 50.808 
 73.903 
 96.998 
 120.09 
 143.19 
 166.28 
 189.38 
 212.47 
 
 6.928 
 30.023 
 53.118 
 76.213 
 99.307 
 122.40 
 145.50 
 168.59 
 191.69 
 214.78 
 
 9.238 
 32.333 
 55.427 
 78.522 
 101.62 
 124.71 
 147.81 
 170.90 
 194.00 
 217.09 
 
 11.547 
 34.642 
 57.737 
 80.831 
 103.93 
 126.02 
 150.12 
 173.21 
 196.31 
 219.40 
 
 13.85716.166 
 36.952 39.261 
 60.046 62.356 
 83.141 85.450 
 106.24 108.55 
 129.33 131.64 
 152.42 154.73 
 175.52 177.83 
 198.61 200.92 
 221.71 224.02 
 I 
 
 18.476 
 41.570 
 64.665 
 87.760 
 110.85 
 133.95 
 157.04 
 180.14 
 203.23 
 226.33 
 
 20.785 
 43.880 
 66.975 
 90.069 
 113.16 
 136.26 
 159.35 
 182.45 
 205.54 
 228.64 
 
 23.0947 
 46.1894 
 69.2841 
 92.3788 
 115.4735 
 138.5682 
 161.6629 
 184.7576 
 207.8523 
 
 * Tables A and B are exact for water at 62 F. and atmospheric pres- 
 sure =14.7 Ibs. 
 
 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, 
 
 hd~ 
 
1234 
 
 FLOW OF WATER IN PIPES. 
 
 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 line in feet. 
 
 VALUES OF COEFFICIENT m. 
 
 
 Diameter of Pipe in Feet. 
 
 I/ M 
 
 
 
 0.05 
 
 0.10 
 
 0.50 
 
 1 
 
 1.5 
 
 2 
 
 3 
 
 4 
 
 
 m 
 
 m 
 
 m 
 
 m 
 
 m 
 
 m 
 
 m 
 
 m 
 
 0.005 
 
 29 
 
 31 
 
 33 
 
 35 
 
 37 
 
 40 
 
 44 
 
 47 
 
 0.01 
 
 34 
 
 35 
 
 37 
 
 39 
 
 42 
 
 45 
 
 49 
 
 53 
 
 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 
 
 0.10 
 
 47 
 
 50 
 
 54 
 
 56 
 
 58 
 
 62 
 
 66 
 
 70 
 
 0.20 
 
 4 
 
 51 
 
 55 
 
 58 
 
 60 
 
 64 
 
 67 
 
 70 
 
 The above coefficients are averages deduced from a large 
 number of experiments. In most cases of pipes carefully laid 
 and in fair condition, they should give results from 5 to 10 per 
 cent, ot the truth. 
 
 EXAMPLE. Given the head, h = 50 ft. : the length, L = 5,280 ft. 
 and the diameter, d=2 ft.; to find the velocity and quantity 
 of discharge. 
 
 Substituting these values in above formula, we get 
 
 I dXh I 2X50 IjXX 
 
 \L+54d~~\j 5280+ 108 \J538 
 
 jpq 
 
 5388 = 
 
 =0.130. 
 
 In column headed 
 
 
 
 M 
 
 find 0.10, which is the value 
 
 nearest to O.136, and look along this line until column headed 
 "2" is reached, then read 62 as the value of coefficient m. 
 
 Then v = 62X0.136 = 8.432 ft. per sec., the required velocity. 
 
 To find the discharge in cubic feet per second, multiply 
 this velocity by area of cross-section of pipe in square feet. 
 
 Thus, 3.1416X(1)'X8.432 = 26.49 cu. ft. per second. 
 
 Since there are 7.48 gal. in a cubic foot, the discharge in 
 gallons per second = 26.49X7.48 = 198.2. 
 
 The above formula is only an approximation, since the flow 
 is modified by bends, joints, incrustations, etc. Wrought-irou 
 
FLOW OF WATER IN PIPES. 1235 
 
 and steel pipes are smoother than cast-iron Ones, thereby 
 presenting less friction and less encouragement for deposits; 
 and, being in longer lengths, the number of joints is reduced, 
 thus lessening the undesirable effects of eddy currents. 
 
 To find the head in feet necessary to give a stated 
 discharge in cubic feet, use the formula * 
 
 , 0.000704 Q 2 (L+ 54 d) 
 ~tf~ ~~' 
 
 in which h= total head in feet; 
 
 Z/= 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, 
 <?=3.07 cu. ft. per second; to find the necessary head. 
 Substituting these values in the above formula,* we get 
 
 , _ O.OQ0704X9.4X(20+27) 
 
 (0.5) 5 
 0.000704X9.4X47 
 
 0.03125 
 
 9.95 ft., the required head. 
 
 The following formula * is simpler and can be used when 
 54d in relation to L is so small as to be negligible: 
 
 i_ 0.000704 Q 2 XL 
 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, 
 
 0.234 
 
 - 
 
 The small 5 in these formulas denotes the fifth power or root, as the 
 may be. 
 
1236 FLOW OF WATER IN PIPES. 
 
 in which d= diameter of pipe in feet; 
 
 Q = cubic feet per second delivered; 
 L= length of line in feet; 
 ft = head in feet. 
 
 EXAMPLE. Given the head, h =700 ft.; the length of pipe, 
 L =3,000 ft.; the quantity to be delivered, Q = 4 cu. ft. per sec.; 
 required the diameter of pipe necessary. 
 
 Substituting these values in the above formula,* we get 
 
 d =0.234 s 16 00 =0.234 |/68^7=0.545 ft. =6.54 ins. 
 
 To find the diameter of pipe required to deliver a given quantity 
 of water with a given head. 
 
 RULE: 1st, Reduce the head to feet per 100 ft.; 
 then, 2d, From Table C, find the discharge for the head thus 
 obtained through a pipe 1 ft. in diameter; 
 
 then, 3d ; Divide the required discharge by that obtained from 
 Table C; then look for the quotient in the column of Table 
 D headed " Ratio of Discharge" and opposite it, in columns 
 1 and 2, will be found the required diameter. 
 
 NOTE. The use of Tables C and D is not sufficiently correct 
 for pipes less than 700 diameters long. 
 
 EXAMPLE. Given the head from a reservoir to point of 
 delivery as 20 it. in a distance of 1,860 ft., what is the diameter 
 01 a pipe to deliver 6 cu. ft. of water per second? 
 
 Oft 
 
 20 ft. head in 1,860 ft.--^ ft. in 100 ft., or 1.075 ft. in 100. 
 1. oU 
 
 From Table C we find the discharge per second with a head 
 of 1.136 is 3.989; for a head of 1.075 it would be about 3.8 cu. ft. 
 Dividing required discharge (6) by 3.8, we have 1.58. From 
 Table D the diameter ot pipe having ratio of discharge = 1.58 
 is found to be about 14J, therefore we must use a 15-inch pipe 
 to obtain the required discharge. If the required discharge 
 is in gallons divide bv 7.5. to reduce to cubic feet. If in cubic 
 feet per minute, divide by 60 to reduce to feet per .second. 
 
 * The small 5 in these formulas denotes the fifth power or root, as the 
 case may be. 
 
FLOW OF WATER IN PIPES. 
 
 1237 
 
 TABLE C. THE VELOCITIES AND DISCHARGES 
 THROUGH A STRAIGHT, SMOOTH PIPE ONE 
 FOOT IN DIAMETER AND ONE MILE, OR 5,280 
 DIAMETERS, IN LENGTH. 
 
 Head in 
 Feet per 
 100 Feet. 
 
 Head in 
 Feet per 
 Mile. 
 
 Velocity in 
 Feet per 
 Second. 
 
 Discharge in 
 Cubic Feet 
 per Second. 
 
 Discharge in 
 Cubic Feet 
 per 24 Hours. 
 
 .0568 
 
 3 . 
 
 1.13 
 
 .8914 
 
 76,982 
 
 .0758 
 
 '4 
 
 1.31 
 
 1.028 
 
 88,862 
 
 .0947 
 
 5 
 
 1.47 
 
 1.150 
 
 99,403 
 
 .1136 
 
 6 
 
 1.61 
 
 1.264 
 
 109,209 
 
 .1325 
 
 7 
 
 1.74 
 
 1.366 
 
 118,022 
 
 .1514 
 
 8 
 
 1.86 
 
 1.455 
 
 125,740 
 
 .1703 
 
 9 
 
 1.96 
 
 1.539 
 
 132,969 
 
 .1894 
 
 10 
 
 2.08 
 
 1.633 
 
 141,145 
 
 .2273 
 
 12 
 
 2.27 . 
 
 1.782 
 
 153,964 
 
 .2652 
 
 14 
 
 2.45 
 
 1.924 
 
 166,233 
 
 .3030 
 
 16 
 
 2.62 
 
 2.057 
 
 177,724 
 
 .3409 
 
 18 
 
 2.78 
 
 2.183 
 
 188,611 
 
 .3788 
 
 20 
 
 2.93 
 
 2.301 
 
 198,806 
 
 .4735 
 
 25 
 
 3.28 
 
 2.572 
 
 222,156 
 
 .5682 
 
 30 
 
 3.59 
 
 2.819 
 
 243,604 
 
 .6629 
 
 35 
 
 3.88 
 
 3.047 
 
 263,260 
 
 .7576 
 
 40 
 
 4.15 
 
 3.267 
 
 282,288 
 
 .8523 
 
 45 
 
 4.40 
 
 3.451 
 
 298,209 
 
 .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 
 
 110 
 
 6.87 
 
 5.395 
 
 466,128 
 
 2.272 
 
 120 
 
 7.18 
 
 5.639 
 
 487,209 
 
 2.462 
 
 130 
 
 7.47 
 
 5.866 
 
 506,822 
 
 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 
 
 3.408 
 
 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 
 
 664,848 
 
 4.735 
 
 250 
 
 10.4 
 
 8.168 
 
 705,728 
 
 5.208 
 
 275 
 
 10.8 
 
 8.482 
 
 732,844 
 
 5.682 
 
 300 
 
 11.3 
 
 8.914 
 
 769,824 
 
 6.629 
 
 350 
 
 12.3 
 
 9.621 
 
 831,168 
 
 7.576 
 
 400 
 
 13.1 
 
 10.28 
 
 888,624 
 
 8.532 
 
 450 
 
 13.9 
 
 10.91 
 
 943,056 
 
1238 
 
 FLOW OF WATER IN PIPES. 
 
 TABLE C. THE VELOCITIES AND DISCHARGES 
 THROUGH A STRAIGHT, SMOOTH PIPE ONE 
 FOOT IN DIAMETER AND ONE MILE, OR 5,280 
 DIAMETERS, IN LENGTH (Continued) . 
 
 Head in 
 Feet per 
 100 Feet. 
 
 Head in 
 Feet per 
 Mile. 
 
 Velocity in 
 Feet per 
 Second. 
 
 Discharge in 
 Cubic Feet 
 per Second. 
 
 Discharge in 
 Cubic Feet 
 per 24 Hours. 
 
 9.47 
 
 500 
 
 14.7 
 
 11.50 
 
 994,032 
 
 10.41 
 
 550 
 
 15.4 
 
 12.09 
 
 1,044,576 
 
 11.36 
 
 600 
 
 16.1 
 
 12.64 
 
 1,092,096 
 
 12.30 
 
 650 
 
 16.7 
 
 13.11 
 
 1,132,704 
 
 13.25 
 
 700 
 
 17.4 
 
 13.66 
 
 1,180,224 
 
 14.20 
 
 750 
 
 18.0 
 
 14.13 
 
 1,220,832 
 
 15.15 
 
 800 
 
 18.6 
 
 14.55 
 
 1,257,408 
 
 16.09 
 
 850 
 
 19.1 
 
 15.00 
 
 1,296,000 
 
 17.04 
 
 900 
 
 19.6 
 
 15.39 
 
 1,329,696 
 
 17.99 
 
 950 
 
 20.3 
 
 15.94 
 
 1,377,216 
 
 18.94 
 
 1000 
 
 20.8 
 
 16.33 
 
 1,411,456 
 
 22.73 
 
 1200 
 
 22.7 
 
 17.82 
 
 1,539,648 
 
 26.52 
 
 1400 
 
 24.5 
 
 19.24 
 
 1,662,336 
 
 30.30 
 
 1600 
 
 26.2 
 
 20.57 
 
 1,777,248 
 
 34.03 
 
 1800 
 
 27.8 
 
 21.83 
 
 1,886,112 
 
 37.87 
 
 2000 
 
 29.3 
 
 23.01 
 
 1,988,064 
 
 47.35 
 
 2500 
 
 32.8 
 
 25.72 
 
 2,221,560 
 
 56.81 
 
 3000 
 
 35.9 
 
 28.19 
 
 2,436,040 
 
FLOW OF WATE& IN PIPES. 
 TABLE D. 
 
 1239 
 
 
 
 Ratio of 
 
 
 
 Ratio of 
 
 Diam- 
 
 
 Discharge to 
 
 Diam- 
 
 
 Discharge to 
 
 eter of 
 
 Diameter 
 
 that through 
 
 eter of 
 
 Diameter 
 
 that through 
 
 Pipe in 
 Inches. 
 
 of Pipe in 
 Feet. 
 
 a 1-foot Pipe 
 with the 
 
 Pipe in 
 Inches. 
 
 of Pipe in 
 Feet. 
 
 a 1-foot Pipe 
 with the 
 
 
 
 Same Head 
 
 
 
 Same Head 
 
 
 
 per Mile. 
 
 
 
 per Mile. 
 
 1 
 
 .0833 
 
 .0020 
 
 12J 
 
 1.042 
 
 1.106 
 
 H 
 
 .1250 ' 
 
 .0055 
 
 13 
 
 1.083 
 
 1.221 
 
 2 
 
 .1667 
 
 .0113 
 
 14 
 
 1.167 
 
 1.470 
 
 2} 
 
 .20 Q 3 
 
 .0198 
 
 15 
 
 1.250 
 
 1.746 
 
 3 
 
 .2500 
 
 .0310 
 
 16 
 
 1.333 
 
 2.053 
 
 31 
 
 .2917 
 
 .0453 
 
 17 
 
 1.417 
 
 2.388 
 
 4 
 
 .3333 
 
 .0643 
 
 18 
 
 1.5 
 
 2.754 
 
 41 
 
 .3750 
 
 .0*57 
 
 19 
 
 1.53 
 
 3.153 
 
 5 
 
 .4167 
 
 .1119 
 
 20 
 
 1.667 
 
 3.585 
 
 51 
 
 .4583 
 
 .1422 
 
 21 
 
 l.?5 
 
 4.051 
 
 6 
 
 .5 
 
 .1767 
 
 22 
 
 1.833 
 
 4.551 
 
 61 
 
 .5417 
 
 .2159 
 
 23 
 
 1.917 
 
 5.084 
 
 7 
 
 .5333 
 
 .2600 
 
 24 
 
 2 
 
 5.649 
 
 7J 
 
 .6250 
 
 .3090 
 
 24f 
 
 2.052 
 
 6.000 
 
 8 
 
 .6667 
 
 .3631 
 
 26 
 
 2.167 
 
 6.912 
 
 81 
 
 .7083 
 
 .4220 
 
 28 
 
 2.333 
 
 8.319 
 
 9 
 
 .75 
 
 .4871 
 
 30 
 
 2.5 
 
 9.822 
 
 9| 
 
 .7917 
 
 ,5575 
 
 30i 
 
 2.521 
 
 10 
 
 10 
 
 .8333 
 
 .6337 
 
 32 
 
 2.667 
 
 11.6 
 
 10i 
 
 .8750 
 
 .7157 
 
 34 
 
 2.833 
 
 13.5 
 
 11 
 
 .9167 
 
 .8044 
 
 36 
 
 3 
 
 15.5 
 
 HI 
 
 .9583 
 
 .8987 
 
 38 
 
 3.167 
 
 17.8 
 
 12 
 
 1 
 
 1 
 
 40 
 
 3.333 
 
 2Q.2 
 
 This table also shows the relative discharging capacities of 
 long pipes. Thus, one 12-inch pipe = two 9-inch pipes, nearly 
 six 6-inch pipes, or thirty-three 3-inch pipes. 
 
1240 
 
 FLOW OF WATER IN PIPES. 
 
 TABLE E. FLOW OF WATER IN HOUSE-SERVICE 
 PIPES. 
 
 (Thomson Meter Co.) 
 To find discharge in gallons multiply by 7.47. 
 
 Condition 
 of Dis- 
 charge. 
 
 Pressure in Main, 
 Lbs. per Sq. Inch. 
 
 Discharge in Cubic Feet per Minute from the Pipe. 
 
 Nominal Diameters of Iron or Lead Service Pipe 
 in Inches. 
 
 
 
 y* 
 
 H 
 
 1 
 
 1$ 
 
 2 
 
 3 
 
 4 
 
 6 
 
 Through 35 
 feet of 
 service 
 Eipe, no 
 ack 
 pressure. 
 
 30 
 40 
 50 
 60 
 75 
 100 
 130 
 
 1.10 
 1.27 
 1.42 
 1.56 
 1.74 
 2.01 
 2.29 
 
 1.923.01 
 
 2.223.48 
 2.48,3.89 
 2.7i;4.26 
 3.034.77 
 3.505.50 
 3.996.28 
 
 6.13 
 7.08 
 7.92 
 8.67 
 9.70 
 11.20 
 12.77 
 
 16.58 
 19.14 
 21.40 
 23.44 
 26.21 
 30.27 
 34.51 
 
 33.34 
 38.50 
 43.04 
 47.15 
 52.71 
 60.87 
 69.40 
 
 88.16 
 101.80 
 113.82 
 124.68 
 139.39 
 160.96 
 183.52 
 
 173.85 
 200.75 
 224.44 
 245.87 
 274.89 
 317.41 
 361.91 
 
 444.63 
 513.42 
 574 . 02 
 628.81 
 703.03 
 811.79 
 925.58 
 
 Through 
 100 feet 
 of service 
 Eipe, no 
 ack 
 pressure. 
 
 3D 
 
 40 
 50 
 60 
 75 
 100 
 130 
 
 0.66 
 0.77 
 0.86 
 0.94 
 1.05 
 1.22 
 1.39 
 
 1.16 
 1.34 
 1.50 
 1.65 
 1.84 
 2.13 
 2.42 
 
 0.96 
 1.15 
 1.31 
 1.45 
 1.64 
 1.92 
 2.20 
 
 1.84 
 2.12 
 2.37 
 2.60 
 2.91 
 3.36 
 3.83 
 
 3.78 
 4.36 
 4.88 
 5.34 
 5.97 
 6.90 
 7.86 
 
 10.40 
 12.01 
 13.43 
 14.71 
 16.45 
 18.99 
 21.66 
 
 21.30 
 24.59 
 27.50 
 30.12 
 33.68 
 38.89 
 44.34 
 
 58.19 
 67.19 
 75.13 
 82.30 
 92.01 
 106.24 
 121.14 
 
 118.13 
 136.41 
 152.51 
 167.06 
 186.78 
 215.68 
 245.91 
 
 317.23 
 366.30 
 409.54 
 448.63 
 501.58 
 579.18 
 660.36 
 
 Through 
 100 feet 
 of service 
 pipe and 
 15 feet 
 vertical 
 rise. 
 
 30 
 40 
 50 
 60 
 75 
 100 
 130 
 
 0.55 
 0.66 
 0.75 
 0.83 
 0.94 
 1.10 
 1.26 
 
 1.52 
 1.81 
 2.06 
 2.29 
 2.59 
 3.02 
 3.48 
 
 3.11 
 3.72 
 4.24 
 4.70 
 5.32 
 6.21 
 7.14 
 
 8.57 
 10.24 
 11.67 
 12.94 
 14.64 
 17.10 
 19.66 
 
 17.55 
 20.95 
 23.87 
 26.48 
 29.96 
 35.00 
 40.23 
 
 47.90 
 57.20 
 65.18 
 72.28 
 81.79 
 95.55 
 109.82 
 
 97.17 
 116.01 
 132.20 
 146.61 
 165.90 
 193.82 
 222.75 
 
 260.56 
 311.09 
 354.49 
 393.13 
 444.85 
 519.72 
 597.31 
 
 Through 
 100 feet 
 of service 
 pipe and 
 30 feet 
 vertical 
 rise. 
 
 30 
 40 
 50 
 60 
 75 
 100 
 130 
 
 0.44 
 0.55 
 0.65 
 0.73 
 0.84 
 1.00 
 1.15 
 
 0.77 
 0.97 
 1.14 
 1.28 
 1.47 
 1.74 
 2.02 
 
 1.22 
 1.53 
 1.79 
 2.02 
 2.32 
 2.75 
 3.19 
 
 2.50 
 3.15 
 3.69 
 4.15 
 4.77 
 5.65 
 6.55 
 
 6.80 
 8.68 
 10.16 
 11.45 
 13.15 
 15.58 
 18.07 
 
 14.11 
 17.79 
 20.82 
 23.47 
 26.95 
 31.93 
 37.02 
 
 38.63 
 48.68 
 56.98 
 64.22 
 73.76 
 87.38 
 101.33 
 
 78.54 
 98.98 
 115.87 
 130.59 
 149.99 
 177.67 
 206.04 
 
 211.54 
 266.59 
 312.08 
 351.73 
 403.98 
 478.55 
 554.96 
 
 Table E may also be used when 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 f-inch 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 Ibs. 
 per square inch, and from Table E we find the discharge through 
 a f-inch pipe 100 ft. long with a pressure of 30 Ibs. to be 1.84 
 cu. ft. per minute. 
 
FLOW OF WATER IN PIPES. 
 
 1241 
 
 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 100 ft. of length in different size clean 
 iron pipes discharging given quantities of water per minute. 
 This friction loss is greatly increased by bends or irregularities 
 in the pipe. 
 
 To find " friction, head " in feet multiply figures by 2.3. 
 
 Gallons 
 per 
 Min- 
 ute. 
 
 Sizes of Pipes, Inside Diameter. 
 
 |-Inch. 
 
 1-Inch. 
 
 li-inch. 
 
 l^-inch. 
 
 2-inch. 
 
 2Hnch. 
 
 3-inch. 
 
 4-inch. 
 
 5 
 10 
 15 
 20 
 25 
 30 
 35 
 40 
 45 
 50 
 75 
 100 
 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 
 9.15 
 12.4 
 16.1 
 20.2 
 24.9 
 56.1 
 
 0.12 
 0.47 
 0.97 
 1.66 
 2.62 
 3.75 
 5.05 
 6.52 
 8.15 
 10.0 
 22.4 
 39.0 
 
 0.12 
 
 0.26 
 0.42 
 0.64 
 0.91 
 1.22 
 1.60 
 2.02 
 2.44 
 5.32 
 9.46 
 14.9 
 21.2 
 28.1 
 37.5 
 
 0.21 
 
 0.10 
 0.20 
 
 0.35 
 
 a. 74 
 
 1.31 
 1.99 
 2.85 
 3.85 
 5.02 
 7.76 
 11.2 
 15.2 
 19.5 
 25.0 
 30.8 
 
 0.27 
 
 0.09 
 0.23 
 0.33 
 0.49 
 0.69 
 0.94 
 1.22 
 1.89 
 2.66 
 3.65 
 4.73 
 6.01 
 7.43 
 9.54 
 14.32 
 
 
 
 
 0.81 
 1.80 
 3.20 
 4.89 
 7.00 
 9.46 
 12.47 
 19.66 
 28.06 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Water-pipe is usually tested to 300 Ibs. 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 
 12 ft. 4 ins. to 12 ft. 6 ins., depending upon the depth of the 
 socket, each length making approximately 12 ft. of pipe when 
 laid. Pipes 2 to 4 ins. diameter are sometimes made in 8 or 
 9 ft. lengths. 
 
1242 SAFE PRESSURES FOR CAST-IRON PIPES. 
 
 SAFE PRESSURES AND EQUIVALENT HEADS OF WATER 
 FOR CAST-IRON PIPE OF DIFFERENT SIZES AND 
 THICKNESSES. 
 
 (Calculated by F. H. Lewis from Tanning's Formula.) 
 
 1 
 s 
 
 0) 
 
 1 
 
 
 
 ? 
 
 %, 
 
 f. 
 
 Size of Pipe, Inches. 
 
 4 
 
 6 
 
 8 
 
 10 
 
 12 
 
 14 
 
 3J2 
 
 -S 
 
 112 
 224 
 336 
 
 J 
 
 S 
 
 258 
 516 
 
 774 
 
 3J2 
 
 1 
 
 (V 1 
 
 49 
 124 
 199 
 274 
 
 |i 
 
 * 
 
 3X> 
 IB. i 
 
 "* 
 
 a 
 
 1| 
 
 M* 
 
 0> . 
 
 p 
 
 fi; s 
 
 j 
 
 11 
 W^ 
 
 8 
 
 1 
 
 'A 
 
 11 
 w^ 
 
 rc 
 
 3& 
 8^ 
 
 c 
 (V~ 
 
 S . 
 11 
 & 
 
 97 
 170 
 244 
 316 
 392 
 465 
 538 
 612 
 
 112 
 
 280 
 458 
 631 
 
 18 
 74 
 130 
 186 
 
 42 
 171 
 
 300 
 429 
 
 44 
 89 
 132 
 177 
 224 
 
 101 
 205 
 304 
 408 
 516 
 
 24 
 62 
 99 
 137 
 174 
 212 
 249 
 
 55 
 143 
 
 228 
 316 
 401 
 488 
 574 
 
 42 
 74 
 106 
 138 
 170 
 202 
 234 
 266 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 ie 
 1* 
 
 H 
 H 
 
 
 if 
 if 
 
 16 
 
 18 
 
 20 
 
 24 
 
 30 
 
 36 
 
 56 
 84 
 112 
 140 
 168 
 196 
 224 
 
 129 
 194 
 258 
 323 
 387 
 452 
 516 
 
 41 
 66 
 91 
 116 
 141 
 166 
 191 
 216 
 
 95 
 152 
 210 
 267 
 325 
 382 
 440 
 497 
 
 51 
 74 
 96 
 119 
 141 
 164 
 209 
 256 
 
 118 
 
 170 
 221 
 274 
 325 
 
 378 
 481 
 589 
 
 30 
 
 49 
 68 
 86 
 105 
 124 
 161 
 199 
 237 
 
 69 
 113 
 157 
 198 
 242 
 286 
 371 
 458 
 546 
 
 24 
 39 
 54 
 69 
 84 
 114 
 144 
 174 
 204 
 234 
 
 55 
 90 
 124 
 159 
 194 
 263 
 332 
 401 
 470 
 538 
 
 32 
 44 
 57 
 
 82 
 107 
 132 
 157 
 
 182 
 207 
 
 74 
 
 101 
 131 
 189 
 247 
 304 
 362 
 419 
 477 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 WEIGHTS OF LEAD AND GASKET FOR PIPE JOINTS. 
 
 (Dennis Long & Co.) 
 
 Diameter 
 of Pipe. 
 
 Lead. 
 
 Gasket. 
 
 Diameter 
 of Pipe. 
 
 Lead. 
 
 Gasket. 
 
 Inches. 
 
 Lbs. 
 
 Lbs. 
 
 Inches. 
 
 Lbs. 
 
 Lbs. 
 
 2 
 
 2.5 
 
 0.125 
 
 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 
 
 9.0 
 
 0.200 
 
 20 
 
 33 
 
 0.625 
 
 10 
 
 13.0 
 
 0.250 
 
 
 
 
WEIGHT OF CAST-IRON WATER-PIPES. 1243 
 
 WEIGHTS, PER FOOT, OF CAST-IRON PIPES IN GEN- 
 ERAL USE INCLUDING SOCKET AND SPIGOT 
 
 ENDS. 
 
 (Dennis Long & Co., Inc., Louisville, Ky.) 
 
 Diam- 
 eter. 
 
 Thick- 
 ness. 
 
 Weight 
 per 
 Foot. 
 
 Diam- 
 eter. 
 
 Thick- 
 ness. 
 
 Weight 
 per 
 Foot. 
 
 Diam- 
 eter. 
 
 Thick- 
 ness. 
 
 Weight 
 per 
 Foot. 
 
 Ins. 
 
 In. 
 
 Lbs'. 
 
 Ins. 
 
 Ins. 
 
 Lbs. 
 
 Ins. 
 
 Ins. 
 
 Lbs. 
 
 3 
 
 | 
 
 12| 
 
 16 
 
 i 
 
 129 
 
 30 
 
 2 
 
 662 
 
 
 % 
 
 15 
 
 
 1 
 
 152 
 
 36 
 
 f 
 
 334 
 
 
 i 
 
 18 
 
 
 1 
 
 175 
 
 
 
 382 
 
 
 %, 
 
 20i 
 
 18 
 
 J 
 
 120 
 
 
 H 
 
 432 
 
 
 1 
 
 23 
 
 
 4 
 
 146 
 
 
 li 
 
 482 
 
 4 
 
 
 17 
 
 
 i 
 
 171 
 
 
 if 
 
 532 
 
 
 %: 
 
 20 
 
 
 1 
 
 197 
 
 
 if 
 
 587 
 
 
 4 
 
 23i 
 
 
 1J 
 
 223 
 
 
 if 
 
 632 
 
 
 % 
 
 26J 
 
 
 U 
 
 249 
 
 
 if 
 
 683 
 
 
 
 30 
 
 20 
 
 % 
 
 148 
 
 
 3 
 
 734 
 
 6 
 
 %+ 
 
 30 
 
 
 3. 
 
 4 
 
 161 
 
 
 2 
 
 786 
 
 
 4 
 
 34 
 
 
 1 
 
 190 
 
 42 
 
 i 
 
 445 
 
 
 %, 
 
 381 
 
 
 
 216 
 
 
 li 
 
 471 
 
 
 
 42J 
 
 
 11 
 
 247 
 
 
 li 
 
 560 
 
 
 j 
 
 52 
 
 
 if 
 
 276 
 
 
 If 
 
 629 
 
 8 
 
 % 
 
 40 
 
 
 H 
 
 305 
 
 
 li 
 
 675 
 
 
 4 
 
 43i 
 
 
 14 
 
 334 
 
 
 If 
 
 734 
 
 
 % 
 
 49f 
 
 24 
 
 
 191 
 
 
 1| 
 
 794 
 
 
 f 
 
 56 
 
 
 j 
 
 225 
 
 
 lj 
 
 853 
 
 
 
 68 
 
 
 1 
 
 258 
 
 
 2 
 
 912 
 
 10 
 
 & 
 
 50 
 
 
 11 
 
 293 
 
 48 
 
 H 
 
 572 
 
 
 4 
 
 54 
 
 
 l| 
 
 327 
 
 
 li 
 
 637 
 
 
 % 
 
 60 
 
 
 If 
 
 361 
 
 
 If 
 
 701 
 
 
 
 68 
 
 
 a 
 
 395 
 
 
 H 
 
 768 
 
 
 j 
 
 82 
 
 
 it 
 
 430 
 
 
 If 
 
 835 
 
 12 
 
 4 
 
 70 
 
 
 if 
 
 465 
 
 
 if 
 
 901 
 
 
 % 
 
 76 
 
 30 
 
 % 
 
 258 
 
 
 1J 
 
 967 
 
 
 f 
 
 82 
 
 
 i 
 
 278 
 
 
 2 
 
 1034 
 
 
 
 99 
 
 
 
 319 
 
 60 
 
 li 
 
 797 
 
 
 I 
 
 117 
 
 
 H 
 
 360 
 
 
 If 
 
 880 
 
 14 
 
 % 
 
 85 
 
 
 11 
 
 405 
 
 
 li 
 
 964 
 
 
 f 
 
 94 
 
 
 if 
 
 448 
 
 
 If 
 
 1049 
 
 
 
 113 
 
 
 li 
 
 489 
 
 
 1J 
 
 1133 
 
 
 I 
 
 137 
 
 
 if 
 
 532 
 
 
 If 
 
 1216 
 
 16 
 
 % 
 
 100 
 
 
 if 
 
 575 
 
 
 2 
 
 1300 
 
 
 f 
 
 108 
 
 
 1J 
 
 619 
 
 
 2i 
 
 1470 
 
 There is no standard weight of pipe for any given pressure. 
 
1244 
 
 THE HYDRAULIC RAM, 
 
 Private Water-supply: Pumps. 
 
 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 supplying water is requisite. 
 
 Power pumps are of so many kinds and so intricate in con- 
 struction that no attempt will be made to describe them. 
 
 The Hydraulic Ram. Where a small stream of water 
 having a fall of 5 ft. or more flows near the premises, an hydraulic 
 ram may be used to great advantage to furnish water for domestic 
 purposes, or even for irrigation. The ram is operated by the 
 pressure of the stream, and delivers water into an open tank. 
 Water can be conveyed by a ram 3,000 ft. and elevated 200 ft., 
 provided there is sufficient fall. The drive pipe supplying the 
 ram should be 30 or 40 ft. long to give the necessary pressure. 
 This is the most economical method of obtaining a water- 
 supply, as there is no expense for maintenance except for 
 repairs, and the cost of installation is also small. 
 
 TABLE OF ACTUAL TESTS WITH GOULD'S HYDRAULIC 
 RAMS.* 
 
 Size 
 of 
 Ram. 
 
 Length 
 of Drive 
 Pipe. 
 
 Head or 
 Fall of 
 Drive 
 Pipe. 
 
 Length 
 of Dis- 
 charge 
 Pipe. 
 
 Height 
 or Lift 
 of Dis- 
 charge 
 Pipe. 
 
 Water 
 Supplied 
 Ram per 
 Minute. 
 
 Water 
 Discharge 
 at Point of 
 Delivery 
 per 
 Minute. 
 
 List 
 Price. 
 
 
 Feet. 
 
 Feet. 
 
 Feet. 
 
 Feet. 
 
 Gallons. 
 
 Gallons. 
 
 
 2 
 
 70 
 
 12 
 
 100 
 
 50 
 
 2.1 
 
 .3 
 
 $9 
 
 3 
 
 70 
 
 10 
 
 200 
 
 100 
 
 2.4 
 
 .2 
 
 11 
 
 4 
 
 70 
 
 12 
 
 200 
 
 100 
 
 5.6 
 
 .5 
 
 14 
 
 5 
 
 70 
 
 13 
 
 200 
 
 100 
 
 7 
 
 .8 
 
 22 
 
 5 
 
 126 
 
 20 
 
 400 
 
 200 
 
 14 
 
 1.5 
 
 
 6 
 
 70 
 
 10 
 
 100 
 
 50 
 
 12.4 
 
 2.4 
 
 40 
 
 6 
 
 125 
 
 25 
 
 400 
 
 200 
 
 18 
 
 2 
 
 
 7 
 
 70 
 
 11 
 
 100 
 
 40 
 
 33 
 
 7.6 
 
 75 
 
 7 
 
 184 
 
 23 
 
 767 
 
 118 
 
 27 
 
 4.5 
 
 
 8 
 
 100 
 
 12 
 
 300 
 
 100 
 
 44 
 
 4 
 
 125 
 
 * Made by N. O. Nelson Mfg. Co. 
 
 Deep Wells and Plunger pumps. The most 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 
 
DEEP WELLS AND PUMPS. 
 
 1245 
 
 locality, and can only be determined by drilling. As the well 
 is driven, a large wrought-iron pipe is sunk to form the casing. 
 Casings are seldom less than 6" inside diameter or more than 
 10", 8" being the most 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, without lowering -the water, is practically unlimited. 
 
 The cost of drilling deep wells, per foot olf depth, including 
 the casing, is approximately as follows: 
 
 Well with 6f" casing $3.25 per ft. 
 
 " " 7f" " 3.75 " " 
 
 " " 8J" " 4.50 
 
 (f tl 
 
 5/25 " " 
 
 For raising the water into an open tank a single-acting pump 
 consisting of a working-head, which operates a 
 cylinder placed in a smaller pipe lowered into the 
 well through which the water is raised, is most 
 commonly employed. 
 
 The cylinder should preferably be placed below 
 the water-line in the well, and is usually con- 
 nected with the working-head by wooden sucker- 
 rods. 
 
 The working-head may be operated by hand, 
 or by a crank-rod attached to a pumping-jack, 
 windmill, or engine. 
 
 With a single-acting pump the plunger is 
 raised and lowered once with every revolution 
 of the driving-wheel, the principle of operation 
 being the same as in an ordinary handsuction- 
 pump. 
 
 The illustration on next page shows the 
 simplest arrangement for operating a working- 
 head by belt power (the trade term for the ap- 
 paratus being "pumping-jack"). 
 
 The "jack" is usually elevated some 10 or 12 
 ft. above the top of the well, so that a crank- 
 rod 8 or 9 ft. long may be used to connect with 
 the working-head which is set over the top of 
 the well. 
 
 A more substantial arrangement is an iron frame, containing 
 
 Working- 
 head. 
 
1246 
 
 DEEP WELLS AND PUMPS. 
 
 the entire operating gear, but such a pump costs three or four 
 times as much as a jack and working-head. 
 
 The jack shown will give- variations in stroke, viz., 8, 10, 
 12, 16, 18, or 20 ins., by changing the connection of the crank- 
 rod. The longer the stroke the greater will be the amount of 
 water pumped, but it will also require more power to operate. 
 
 The amount of water pumped in a minute by any single- 
 acting pump is determined by the diameter of the suction 
 
 Pumping-jack. 
 
 cylinder, the length of stroke, and the number of strokes per 
 minute. 
 
 The table on opposite page gives the capacity per stroke for 
 cylinders of different diameters, and for strokes of different 
 length. 
 
 To find the capacity per minute, multiply the figures given 
 in the table by the revolutions per minute. The usual speed 
 of single-acting working-heads and pumping- jacks is 25 to 30 
 revolutions per minute. 
 
 Cylinders over 2f ins. in diameter should have a substantial 
 iron working-head. 
 
 Hot-air Engines. These are very extensively used for 
 pumping water for country houses, as they are absolutely safe, 
 require little attention, and have no valves, springs, or gauges 
 to get out of order. They are also adapted to almost any 
 
HOT-AIR ENGINES. 
 
 124? 
 
 TABLE SHOWING CAPACITY OF SINGLE-ACTING 
 PUMPS OF GIVEN DIAMETER AND LENGTH OF 
 STROKE. 
 
 Diam. 
 of 
 Cylin- 
 der in 
 Inches. 
 
 Length of Stroke in Inches. 
 
 6 
 
 8 
 
 10 
 
 12 
 
 14 
 
 16 
 
 18 
 
 20 
 
 24 
 
 
 
 
 Capac 
 
 ity per 
 
 Stroke 
 
 in Gal 
 
 Ions. 
 
 
 
 l/^ 
 
 .0319 
 
 .0425 
 
 .0531 
 
 0637 
 
 .0743 
 
 .0848 
 
 .0955 
 
 .1062 
 
 .1274 
 
 m 
 
 .0385 
 
 .0513 
 
 .0642 
 
 .'077 
 
 .089 
 
 .1027 
 
 .1156 
 
 .1280 
 
 .1541 
 
 
 .0459 
 
 .0612 
 
 .0765 
 
 .0918 
 
 .1071 
 
 .1224 
 
 .1377 
 
 .1530 
 
 .1836 
 
 m 
 
 .0625 
 
 .0833 
 
 .1041 
 
 .1249 
 
 .1457 
 
 .1666 
 
 .1874 
 
 .2082 
 
 .2499 
 
 2 
 
 .0816 
 
 .1088 
 
 .136 
 
 .1632 
 
 .1904 
 
 .2176 
 
 .2448 
 
 .2720 
 
 .3264 
 
 2^ 
 
 . 1033 
 
 .1377 
 
 .1721 
 
 .2063 
 
 .241 
 
 .2754 
 
 .2096 
 
 .3442 
 
 .4128 
 
 2^1 
 
 .1275 
 
 .17 
 
 .2125 
 
 .255 
 
 .2975 
 
 .34 
 
 .3825 
 
 .425 
 
 .51 
 
 2M- 
 
 .1543 
 
 .2057 
 
 .2571 
 
 .3085 
 
 .3598 
 
 .4114 
 
 .4626 
 
 .5142 
 
 .617 
 
 3 
 
 .1836 
 
 .2448 
 
 .306 
 
 .3672 
 
 .4284 
 
 .4896 
 
 .5508 
 
 .612 
 
 .7344 
 
 3/^ 
 
 .2154 
 
 .2872 
 
 .3594 
 
 .4312 
 
 .503 
 
 .5748 
 
 .6466 
 
 .7182 
 
 .8624 
 
 3^2 
 
 .2499 
 
 .3332 
 
 .4165 
 
 .4998 
 
 .5831 
 
 .6664 
 
 .7497 
 
 .833 
 
 .9996 
 
 3M 
 
 .2868 
 
 .3824 
 
 .478 
 
 .5736 
 
 .6692 
 
 .7648 
 
 .8605 
 
 .9561 
 
 1.147 
 
 4 
 
 .3264 
 
 .4352 
 
 .544 
 
 .6528 
 
 .7616 
 
 .8704 
 
 .9792 
 
 1.088 
 
 1 . 3056 
 
 43^ 
 
 .3684 
 
 .4912 
 
 .6141 
 
 .7368 
 
 .8596 
 
 .9824 
 
 1.105 
 
 1.228 
 
 1.473 
 
 4^ 
 
 .4131 
 
 .5508 
 
 .6885 
 
 .8262 
 
 .9639 
 
 1.1016 
 
 1.2393 
 
 1.377 
 
 1 . 6524 
 
 # 
 
 .4602 
 
 .6136 
 
 .7671 
 
 .9204 
 
 1.073 
 
 1.227 
 
 1.380 
 
 1.534 
 
 1.84 
 
 kind of fuel, such as coal, coke, wood, gas, or kerosene oil. They 
 will pump from either a shallow or deep well, but are best 
 adapted to wells in which the surface of the water is within 
 20 ft. of the top of the well. 
 
 The best known hot-air engines are the Rider and Ericsson, 
 which have been in successful operation for over twenty-six 
 years. 
 
 These engines have capacities ranging from 150 to 3,500 
 gallons 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 attached varies from 
 $120 for the smallest size, having a capacity of 150 gals, per 
 hour raised 50 ft., to $540 for the largest size, having a capacity 
 of 3,500 gals, per hour raised 50 ft. The smaller size requires 
 about 1 quart of kerosene or 3 Ibs. of anthracite coal per hour. 
 
 Hot-air engines should be placed close to 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. 
 
1248 
 
 WINDMILLS. 
 
 It is not practical to draw water more than 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 catalogue of the Rider-Ericsson 
 Engine Co. 
 
 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. Prof. Thurston says, 
 regarding wind-mills: "In estimating the capacity, a working- 
 day of eight hours is assumed, but the 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 wind-mill 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. 
 
 * 
 
 Is 
 
 *o 
 
 Gallons of Water Raised per Minute to 
 
 1 
 
 i 
 
 *O m 
 
 
 an Elevation of 
 
 23][ 
 
 ? 
 
 Li 
 
 ,2^H 
 
 
 
 '5 JH 
 
 3-4 
 
 -^ 
 
 "3 $ S 
 
 
 
 "5 t 2'o5 
 
 p 
 
 'o^ 
 
 1^| 
 
 25 
 
 50 
 
 75 
 
 100 
 
 150 
 
 200 
 
 IP! 
 
 p 
 
 > 
 
 & 
 
 Feet. 
 
 Feet. 
 
 Feet. 
 
 Feet. 
 
 Feet. 
 
 Feet. 
 
 & 
 
 wheel 
 
 
 
 
 
 
 
 
 
 
 Feet. 
 
 
 
 ,, , ... ., , 
 
 
 
 
 
 
 
 8V 
 
 16 
 
 70 to 75 
 
 6.192 
 
 3.016 
 
 
 
 
 
 0.04 
 
 10 
 
 16 
 
 60 65 
 
 19.179 
 
 9.563 
 
 fi fi38 
 
 4.750 
 
 
 
 0.12 
 
 12 
 
 16 
 
 55 60 
 
 33.941 
 
 17.95211.851 
 
 8.435 
 
 5.680 
 
 
 0.21 
 
 14 
 
 16 
 
 50 55 
 
 45.139 22.569 
 
 15.304 
 
 11.246 
 
 7.807 
 
 4 998 
 
 0.28 
 
 16 
 
 16 
 
 45 50 
 
 64.600 31.654 
 
 19.542 16.150 
 
 9.771 
 
 8!075 
 
 0.41 
 
 18 
 
 16 
 
 40 45 
 
 97.682 52.16532.51324.421 
 
 17.485 
 
 12.211 
 
 0.61 
 
 20 
 
 16 
 
 35 40 
 
 124.950 63.750 
 
 40.800 31.248 
 
 19.284 
 
 15.938 
 
 0.78 
 
 25 
 
 16 
 
 30 35 
 
 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 
 
AIR-LIFT PROCESS. 1249 
 
 will develop 0.15 horse-power at 65 revolutions per minute; 
 and with the same breeze: 
 
 A 20-ft. mill 40 revolutions, 1 horse-power. 
 
 A 25-ft. " 35 " 1} " 
 
 A30-ft. " 28 " 3J " 
 
 A40-ft. " 22 " 74 " 
 
 A 50-ft. ." 18 " 12 " 
 
 The increase in power from increased velocity of the 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 4X1} =7 horse-power.* 
 
 A windmill "will run and produce work in a. 4-mile breeze." 
 
 Windmills have also been used successfully for the generating 
 and storage of electricity for small lighting plants, f 
 
 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 submerging a discharge 
 pipe in a closed well, with a smaller pipe inside delivering 
 compressed air into it at the bottom. The compressed air 
 by its inherent expansive 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 ma- 
 chinery required being an air-compressor and power for driving 
 it. 
 
 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 Co. 
 
 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. 
 
 * Kent, p. 497, quoted from the Iron Age. 
 TCent. n. 498. 
 
1250 HORSE-POWER REQUIRED TO RAISE WATER. 
 
 There is nothing outside the engine-room to look after or 
 wear out. Nothing but common pipe in the wells. 
 
 Water is cooled and purified by the thorough admixture and 
 expansion of air; iron, sulphur, and gases are thrown off. 
 
 Sand or gravel does no harm. 
 
 The cost of raising 1,000 gallons of water by this method, 
 including fuel, labor, oil, interest on cost of well, boiler, com- 
 pressor, foundations, pipes, real estate, and erection, taxes, 
 and fifteen per cent, for depreciation, runs from two and one- 
 half cents down to one fifth of one cent, 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 
 one and one half cents.* 
 
 The air-lift process is now extensively used in iceworks, 
 breweries, cold-storage houses, textile mills, dyeworks, 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 1,000,000 gallons daily, lifting water from 
 three 8-in. artesian wells. (Kent.) 
 
 Horse-power Required to Raise Water to 
 Different Heights. 
 
 The power required to raise a certain quantity of water to 
 a certain height varies directly with the quantity to be raised, 
 and also the height. 
 
 For instance, it requires twice as much power to raise 200 
 gallons per minute 10 ft. high as it does to raise 100 gallons 
 to the same height and in the same time; and to raise 100 
 gallons 20 ft. high requires twice as much power as it does to 
 raise 100 gallons 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 8.35, weight of one gallon, and this result by the 
 total number of feet the water is raised (that is, from the sur- I 
 face 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 theo- ! 
 retical power a liberal allowance must be made for the in- 
 efficiency of the pump. 
 
 * Ingersoll-Sergeant Drill Co. 
 
FlftE STREAMS. 1251 
 
 For a cylinder pump add 75 to 100 per cent. 
 
 To the actual height to which the water is to be raised add 
 the friction loss in feet, as given in Table F, when the discharge 
 is to be piped any distance. 
 
 EXAMPLE. Find the theoretical horse-power required to 
 raise 100 gallons per minute 120 ft. high, through a 3-in. pipe, 
 200 ft. long. 
 
 Ans. From Table F, the friction head for 100 gallons per 
 minute in 3-in. pipe, 100 ft. long, is 1.31X2.3 or 3 ft. For 
 200 ft. it will be 6 ft., which added to 120 gives 126 ft. for the 
 
 100X8.35X126 
 
 height. Then theoretical horse -power = 
 
 oo ,UUU 
 
 =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 gallons per minute 
 through 100 ft. of 2-in. pipe, the back pressure would be equiva- 
 lent 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 very materially increased, being 
 practically equal to the friction of 25 ft. of straight pipe. 
 
 Fire Streams. 
 
 The following is an extract from a paper read by Mr. John R. 
 Freeman at a meeting of the New England Waterworks Asso- 
 ciation, entitled "Some Experiments and Practical Tables 
 Relating to Fire Streams." 
 
 "When unlined linen hose is used the friction or pressure 
 loss is from 8 to 60 per cent., increasing with the pressure. 
 This kind of hose is best for inside use in short lengths. Mill 
 hose is better than unlined linen hose for long lengths, but 
 ordinarily the best quality of smooth rubber-lined hose is supe- 
 rior 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 I" ring nozzle discharges the same quantity of water as 
 a f " smooth, and a 1" ring nozzle the same as a f" smooth. 
 
 "Two hundred and fifty gallons per minute is a good standard 
 fire stream at 80 Ibs. pressure at the hydrant. 100 Ibs. pressure 
 
1252 
 
 CYLINDRICAL WOODEN TANKS. 
 
 should not be exceeded except for very high buildings or lengths 
 of hose exceeding 300 ft." 
 
 TABLE OF EFFECTIVE FIRE STREAMS, 
 
 Usin^ 100 ft. of 2J" ordinary best quality rubber-lined hose 
 between nozzle and hydrant or pump. 
 
 Smooth Nozzle, Size. . . . 
 
 M-inch. 
 
 %-inch. 
 
 Pressure at hydrant, Ibs. . 
 Pressure at nozzle, Ibs. . . 
 Vertical height feet 
 
 32 
 
 30 
 48 
 37 
 90 
 
 54 
 50 
 67 
 50 
 116 
 
 65 
 60 
 
 72 
 54 
 127 
 
 75 
 
 70 
 76 
 68 
 137 
 
 86 
 80 
 79 
 62 
 
 147 
 
 34 
 30 
 49 
 42 
 123 
 
 57 
 
 50 
 71 
 55 
 159 
 
 69 
 
 60 
 77 
 61 
 174 
 
 80 
 70 
 
 81 
 66 
 
 188 
 
 91 
 80 
 85 
 70 
 201 
 
 Horizontal distance, feet 
 Gals, discharged per min. 
 
 Smooth Nozzle, Size. . . . 
 
 1-inch. 
 
 IH-inch. 
 
 Pressure at hydrant, Ibs . 
 Pressure at nozzle, Ibs. . . 
 Vertical height, feet 
 Horizontal distance, feet 
 Gals, discharged per min . 
 
 37 62 
 30 : 50 
 
 51 73 
 471 61 
 161 208 
 
 75 
 
 60 
 79 
 67 
 
 228 
 
 87 
 70 
 85 
 72 
 246 
 
 100 
 80 
 89 
 76 
 263 
 
 42 
 30 
 52 
 50 
 206 
 
 70 
 50 
 75 
 66 
 266 
 
 84 
 60 
 83 
 72 
 291 
 
 98 
 
 70 
 88 
 77 
 314 
 
 112 
 80 
 92 
 81 
 336 
 
 Notes on the Construction of Cylindrical Wooden 
 Tanks.* 
 
 Material should be either cedar, cypress, or white pine, free 
 from imperfections and thoroughly air-dry. Where exposed to 
 freezing, Michigan pine free from sapwood is generally con- 
 sidered the most durable. 
 
 Staves and bottom to be made of 2J-inch (dressed to about 
 2J-inch) stock for tanks 12 ft. and not exceeding 16 ft. diam- 
 eter or 16 ft. deep. For larger tanks 3-in. (dressed to about 
 2}-in.) stock to be used. 
 
 Staves to be connected about one third the distance from 
 the top by a f-inch dowel to hold in position during erection. 
 
 The bottom planks to be dressed four sides, and the edges 
 of each plank to be bored with holes not over 3 feet apart for 
 f-inch dowels. 
 
 Taper. The batter to each side should not be less than \ in. 
 nor more than J in. per foot. 
 
 * These notes have been condensed from specifications published by the 
 Inspection Department of the Factory Mutual Fire Insurance Co , 31 
 Milk Street, Boston; a most excellent pamphlet. 
 
 
CYLINDRICAL WOODEN TANKS 
 
 1253 
 
 Hoops. All to be of round wrought iron or mild steel of good 
 quality. Wrought iron is preferable because it does not rust so 
 easily as steel. 
 
 There are to be no welds in any of the hoops. Where more 
 than one length of iron is necessary, lugs are to 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 pre- 
 paring for shipment. 
 
 Hoops to be chosen of such a size and spacing that the stress 
 in no hoop will exceed 12,500 Ibs. per square 
 inch when computed from the area at root of 
 thread. 
 
 On account of the swelling of the bottom 
 planks, the hoops near the bottom may be sub- 
 jected to a strain greater than that due to the 
 water pressure alone; therefore additional hoops 
 should be provided. For tanks up to 20 ft. in 
 diameter, one hoop of the size used next above 
 it should be placed around the bottom opposite 
 the croze and not counted upon as withstand- 
 ing 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 to be placed within 2 ins. of the 
 top of staves, so that overflow pipe may be in- 
 serted as high as possible. Hoops to be so placed 
 that the lugs will not come in a vertical line. No 
 hoop to be less than f in. diameter. All to be 
 cleaned of mill-scale and rust and painted one 
 coat 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 as quickly; a slight 
 amount of rust does not have the same weaken- 
 ing 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 to be spaced so that each hoop 
 will have the same stress per square inch, and no space to be 
 greater than 21 ins. 
 
 Fig. I 
 
1254 
 
 CYLINDRICAL WOODEN TANKS. 
 
 To meet this requirement the hoops must be spaced quite 
 close together at the bottom, the space between hoops gradually 
 increasing towards the top. Fig. 1 shows the proper spacing 
 of hoops for a tank 18 ins. 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 hoop in inches== - r~~ g - * e , u- 
 
 2. 6 X diameter in feetX# 
 
 For strength of a }-inch rod use 3,750; of a f-in. rod, 5,250; 
 of a 1-in. rod, 6,875; and of a 1 J-in. rod, 8,625. 
 
 H is the distance from top of water to centre of hoop in feet. 
 
 EXAMPLE. How far apart should 1-in. hoops be placed, at 
 15 ft. 2 ins. from top of tank, on a tank 20 ft. diameter? 
 
 6,875 , . 
 
 Lugs are to be as strong as the hoops. A lug similar to 
 
 Fig. 2 is simple and fulfils 
 the requirement for strength. 
 Malleable lugs are preferable. 
 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 and be not over 
 18 ins. apart, and of such thickness that the bottom of the staves 
 will be at least an inch from the floor (see Fig. 3). 
 
 Fig. 2 
 
 Lug for Hoops. 
 
 Fig. 3 
 
 Support for Bottom of Tank. 
 
 Discharge Pipe will preferably leave the bottom of the 
 tank at its centre and extend up inside of the tank 4 ins., to 
 allow for sediment collecting in the bottom of the tank. 
 . The Overflow Pipe should be placed as near the top of the 
 
CYLINDRICAL WOODEN TANKS. 
 
 1255 
 
 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 freezing. 
 
 When a tank is in an enclosed room, as in a mill tower, the 
 best method is to - keep the room wa.m 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 hi the 
 bottom of the tank. 
 
 With a tank located on a high trestle, or at a distance from 
 the steam-supply, it is often impracticable to arrange a return 
 pipe. In this case steam may be blown directly into the water 
 in the tank. A 1-inch pipe is generally sufficient for this pur- 
 pose. It should be carried to the top of the tank and there 
 bend over and dip downwards, so that its outlet is about 1 foot 
 below the high-water line. A check-valve is to be placed in this 
 steam-pipe, near its point of discharge, to prevent water being 
 drawn back by siphon action when the steam is shut off. 
 
 Frost -proofing for Pipes The discharge pipe from a 
 tank on a trestle, or one elevated above the roof, must be pro- 
 tected from freezing. The most common practice is to enclose 
 
 2 in. horizontal nailing strips 
 spaced about 3ft. apart.^ 
 
 fZ in. air space\ 
 
 // 2 in. air space \\ 
 
 2 in. air space \ 
 
 
 2'Thicknesses of tarred paper, % in. Tongued and 
 around each box except outside, grooved sheathing* 
 
 Fig. 4 
 Method of Frost-proofing Pipes. 
 
 the pipe in a double, triple, or quadruple box made of boards 
 and tarred paper as shown by Fig. 4. If steam is supplied 
 to the tank, the steam-pipe is carried inside the box. 
 
1256 
 
 CYLINDRICAL WOODEN TANKS. 
 
 In New England, New York, and Canada the quadruple 
 boxing is generally used, whereas in the milder regions to 
 the south triple or double boxing is used. 
 
 The boxing should always be carried down into the ground 
 below the frost-line, and a good tight joint made at the under- 
 side of the tank. 
 
 Covers. For economy in heating and to prevent birds, 
 leaves, etc., from getting into the water, all out-of-door tanks 
 should be covered. A double cover is recommended consist- 
 ing of a tight flat cover made of matched boards supported 
 by joists which span the top of the tank, and above this a 
 shingled, conical roof. To prevent the covering from being 
 blown off, it should be firmly fastened to the top of the tank 
 by straps of iron. 
 
 In order to keep out the wind particular attention should 
 be given to making a tight joint where the roof rests on the 
 top of the staves. 
 
 DIMENSIONS OF TANKS OF STANDARD SIZES. 
 
 
 Size 
 
 Thickness of 
 
 iy 
 
 
 Approx- 
 
 (Outside 
 Dimensions). 
 
 Lumber after 
 being Machined. 
 
 
 Hoops. 
 
 imate 
 
 
 
 
 
 Net 
 
 
 
 f i^$| 
 
 
 Capac- 
 
 
 
 
 
 i_HH 
 
 
 
 ity. 
 
 Average 
 Diam- 
 
 Length 
 of 
 
 Staves. 
 
 Bot- 
 
 
 Num- 
 ber 
 
 Size. 
 
 
 
 
 
 eter. 
 
 Stave. 
 
 
 tom. 
 
 A 
 
 B 
 
 c 
 
 of 
 
 
 Gallons. 
 
 Ft. Ins. 
 
 Ft. 
 
 Ins. 
 
 Ins. 
 
 Ins. 
 
 In. 
 
 Ins. 
 
 
 Ins. 
 
 10,000 
 
 13 4 
 
 12 
 
 21 
 
 21 
 
 31 
 
 1 
 
 2i 
 
 11 
 
 1 
 
 15,000 
 
 14 6 
 
 14 
 
 21 
 
 21 
 
 31 
 
 f 
 
 2i 
 
 14 
 
 1 
 
 20,000 
 
 15 6 
 
 16 
 
 21 
 
 21 
 
 31 
 
 i 
 
 2* 
 
 j 5 
 
 " 11 
 
 I 
 
 25,000 
 
 17 6 
 
 16 
 
 21 
 
 21 
 
 31 
 
 J 
 
 2f 
 
 j 4 
 
 i' 12 
 
 
 30,000 
 
 18 
 
 18 
 
 21 
 
 21 
 
 31 
 
 i 
 
 2| 
 
 4 
 
 \ 16 
 
 | 
 
 50,000 
 
 22 
 
 20 
 
 21 
 
 21 
 
 31 
 
 1 
 
 2f 
 
 4 
 
 t 
 
 75,000 
 
 24 6 
 
 24 
 
 21 
 
 21 
 
 31 
 
 I 
 
 2f 
 
 j 6 
 
 
 
 
 
 
 
 
 
 
 
 ( 21 
 
 i* 
 
 100,000 
 
 28 6 
 
 24 
 
 21 
 
 2} 
 
 31 
 
 1 
 
 2f 
 
 ( 5 
 129 
 
 i 
 ij 
 
NOTES ON STEEL TANKS. 1257 
 
 Scuttles should be arranged in both the conical and flat 
 covers to give access to the inside of the tank and a substantial, 
 permanent ladder erected to give easy access to the top of the 
 tank. 
 
 Xotes on Steel Tanks.* 
 
 Steel tanks of sizes commonly used for fire protection cost 
 from 40 to 100 per cent, more than do wooden tanks. The 
 additional cost for large tanks is relatively less than for small 
 tanks. A steel tank of about 40,000 gallons 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 sup- 
 ports 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 in (1) that 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 about fifteen years); (2) 
 that 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) that it will not be at all likely to 
 burst suddenly (if originally correctly designed) even if paint- 
 ing 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: (1) 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 freezing; (3) they give 
 more trouble by " sweating" when placed in a mill tower; (4) 
 they deteriorate rapidly if painting is neglected. 
 
 * Inspection Department of the Factory Mutual Insurance Co., Boston. 
 
1258 CAPACITY OF PIPES AND CYLINDERS. 
 
 CONTENTS IIN CUBIC FEET AND U. S. GALLONS OF 
 PIPES AND -CYLINDERS OF VARIOUS DIAMETERS 
 AND ONE FOOT IN LENGTH. 
 
 1 gallon = 231 cubic inches. 1 cubic foot = 7.4805 gallons. 
 
 
 For 1 Foot in 
 
 
 For 1 Foot in 
 
 
 For 1 Foot in 
 
 a * 
 
 Length. 
 
 .S 
 
 Length. 
 
 d 
 
 Length. 
 
 II 
 
 Cu.Ft., 
 
 U. S. 
 
 II 
 
 Cu. Ft., 
 
 U.S. 
 
 II 
 
 Cu. Ft., 
 
 U.S. 
 
 Jo 
 
 also Area 
 
 Gals., 
 
 
 also Area 
 
 Gals., 
 
 S 
 
 also Area 
 
 Gals., 
 
 fl 
 
 in Sq. Ft. 
 
 231 
 
 Si-H 
 
 in Sq. Ft. 
 
 231 
 
 C3hH 
 
 in Sq. Ft. 
 
 231 
 
 g 
 
 
 Cu.In. 
 
 3 
 
 
 Cu. In. 
 
 3 
 
 
 Cu. In. 
 
 IX 
 
 .0003 
 
 .0025 
 
 6M 
 
 .2485 
 
 1.859 
 
 19 
 
 1.969 
 
 14.73 
 
 Ha 
 
 .0005 
 
 .004 
 
 7 
 
 .2673 
 
 1.999 
 
 19H 
 
 2.074 
 
 15.51 
 
 
 .0008 
 
 .0057 
 
 7M 
 
 .2867 
 
 2.145 
 
 20 
 
 2.182 
 
 16 32 
 
 7 /ie 
 
 .001 
 
 .0078 
 
 7}/2 
 
 .3068 
 
 2.295 
 
 20^ 
 
 2.292 
 
 17.15 
 
 
 
 .0014 
 
 .0102 
 
 m 
 
 .3276 
 
 2.45 
 
 21 
 
 2.405 
 
 17.99 
 
 %e 
 
 .0017 
 
 .0129 
 
 8, 
 
 .3491 
 
 2.611 
 
 21/^ 
 
 2.521 
 
 18.86 
 
 
 .0021 
 
 .0159 
 
 
 .3712 
 
 2.777 
 
 22 
 
 2.640 
 
 19.75 
 
 l^g 
 
 .0026 
 
 .0193 
 
 8J^ 
 
 .3941 
 
 2.948 
 
 22^ 
 
 2.761 
 
 20.66 
 
 M 
 
 .0031 
 
 .0230 
 
 8M 
 
 .4176 
 
 3.125 
 
 23 
 
 2.885 
 
 21.58 
 
 
 .0036 
 
 .0269 
 
 9 
 
 .4418 
 
 3.305 
 
 23^ 
 
 3.012 
 
 22.53 
 
 ^8 
 
 .0042 
 
 .0312 
 
 9/^ 
 
 .4667 
 
 3.491 
 
 24 
 
 3.142 
 
 23.50 
 
 
 .0048 
 
 .0359 
 
 m 
 
 .4922 
 
 3.682 
 
 25 
 
 3.409 
 
 25.50 
 
 i , 
 
 .0055 
 
 .0408 
 
 9H 
 
 .5185 
 
 3.879 
 
 26 
 
 3.687 
 
 27.58 
 
 i/ 
 
 .0085 
 
 .0638 
 
 10 
 
 .5454 
 
 4.08 
 
 27 
 
 3.976 
 
 29.74 
 
 i/^ 
 
 .0123 
 
 .0918 
 
 lOM 
 
 .5730 
 
 4.286 
 
 28 
 
 4.276 
 
 31.99 
 
 1M 
 
 .0167 
 
 .1249 
 
 lO^Hz 
 
 .6013 
 
 4.498 
 
 29 
 
 4.587 
 
 34.31 
 
 2 
 
 .0218 
 
 .1632 
 
 10% 
 
 .6303 
 
 4.715 
 
 30 
 
 4.909 
 
 36.72 
 
 2/^ 
 
 .0276 
 
 .2066 
 
 11 
 
 .66 
 
 4.937 
 
 31 
 
 5.241 
 
 39.21 
 
 2J^ 
 
 .0341 
 
 .2550 
 
 HM 
 
 .6903 
 
 5.164 
 
 32 
 
 5.585 
 
 41.78 
 
 2% 
 
 .0412 
 
 . 3085 
 
 H/^} 
 
 .7213 
 
 5 . 396 
 
 33 
 
 5.940 
 
 44.43 
 
 3 
 
 .0491 
 
 . 3672 
 
 HM 
 
 .7530 
 
 5.633 
 
 34 
 
 6.305 
 
 47.16 
 
 3M 
 
 .0576 
 
 .4309 
 
 12 
 
 .7854 
 
 5.875 
 
 35 
 
 6.681 
 
 49.98 
 
 31^ 
 
 v .0668 
 
 .4998 
 
 12/^ 
 
 .8522 
 
 0.375 
 
 36 
 
 7.069 
 
 52.88 
 
 3 3 ^ 
 
 .0767 
 
 .5738 
 
 13 
 
 .9218 
 
 6.895 
 
 37 
 
 7.467 
 
 55.86 
 
 4 
 
 .0873 
 
 .6528 
 
 13 lx 
 
 .994 
 
 7.436 
 
 38 
 
 7.876 
 
 58.92 
 
 4M 
 
 .0985 
 
 .7369 
 
 14 
 
 1.069 
 
 7.997 
 
 39 
 
 8.296 
 
 62.06 
 
 
 .1134 
 
 .8263 
 
 l4^ 
 
 1.147 
 
 8.578 
 
 40 
 
 8.727 
 
 65.28 
 
 4f| 
 
 .1231 
 
 .9206 
 
 15 
 
 1.227 
 
 9.180 
 
 41 
 
 9.168 
 
 68.58 
 
 5 
 
 . 1364 
 
 1.020 
 
 15J^ 
 
 1.310 
 
 9.801 
 
 42 
 
 9.621 
 
 71.97 
 
 5/^ 
 
 .1503 
 
 1.125 
 
 16 
 
 1.396 
 
 10.44 
 
 43 
 
 10.085 
 
 75.44 
 
 51^ 
 
 .1650 
 
 1.234 
 
 ] 6/^ 
 
 1.485 
 
 11.11 
 
 44 
 
 10.559 
 
 78.99 
 
 5M 
 
 .1803 
 
 1.349 
 
 17 
 
 1.576 
 
 11.79 
 
 45 
 
 11.045 
 
 82.62 
 
 6 
 
 .1963 
 
 1.469 
 
 17x^ 
 
 1.070 
 
 12.49 
 
 46 
 
 11.541 
 
 86.33 
 
 
 .2131 
 
 1.594 
 
 18 
 
 1.768 
 
 13.22 
 
 47 
 
 12.048 
 
 90.13 
 
 6*1 
 
 .2304 
 
 1.724 
 
 
 1.867 
 
 13.96 
 
 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. 
 
 The 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. 
 
 
 
CAPACITY OF CYLINDRICAL TANKS. 1259 
 
 CYLINDRICAL VESSELS, TANKS, CISTERNS, ETC. 
 
 Diameter in feet and inches, area in square feet, and U. S. 
 
 gallons capacity for one foot in depth. 
 
 1 gallon-231 cubic inches = 0.1337 ,;ubic foot. 
 
 Diam. 
 
 Area. 
 
 Gals. 
 
 Diam. 
 
 Area. 
 
 Gals. 
 
 Diam. 
 
 Area. 
 
 Gals. 
 
 FtTiii 
 
 Sq. Ft. 
 
 1-Foot 
 
 Ft. In. 
 
 Sq. Ft. 
 
 1-Foot 
 
 Ft. In. 
 
 Sq. Ft. 
 
 1-Foot 
 
 
 * 
 
 Depth. 
 
 
 * 
 
 Depth. 
 
 
 *' 
 
 Depth. 
 
 i 
 
 .785 
 
 ' 5.87 
 
 5 8 
 
 25.22 
 
 188.66 
 
 19 
 
 283.53 
 
 2120.9 
 
 i i 
 
 .922 
 
 6.89 
 
 5 9 
 
 25.97 
 
 194.25 
 
 19 3 
 
 29.1.04 
 
 2177.1 
 
 1 2 
 
 1.069 
 
 8.00 
 
 5 10 
 
 26.73 
 
 199.92 
 
 19 6 
 
 298.65 
 
 2234.0 
 
 1 3 
 
 1.227 
 
 9.18 
 
 5 11 
 
 27.49 
 
 205.671 
 
 19 9 
 
 306 . 35 
 
 2291 7 
 
 1 4 
 
 1.396 
 
 10.44 
 
 6 
 
 28.27 
 
 211. 51 
 
 20 
 
 314.16 
 
 2350 . 1 
 
 \ 6 
 
 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 
 
 248 . 23 
 
 20 6 
 
 330.06 
 
 2469.1 
 
 1 7 
 
 1.969 
 
 14.73 
 
 6 9 
 
 35.78 
 
 267.69 
 
 20.9 
 
 338.16 
 
 2529.6 
 
 i 8 
 
 2.182 
 
 16.32 
 
 7 
 
 38.48 
 
 287.88 
 
 21 
 
 346 . 36 
 
 2591.0 
 
 1 9 
 
 2.405 
 
 17.99 
 
 7 3 
 
 41.28 
 
 308.81 
 
 21 3 
 
 354.66 
 
 2653.0 
 
 1 10 
 
 2.640 
 
 19.75 
 
 7 6 
 
 44.18 
 
 330.48 
 
 21 6 
 
 363.05 
 
 2715.8 
 
 i U 
 
 2.885 
 
 21.58 
 
 7 9 
 
 47.17 
 
 352.88 
 
 21 9 
 
 371.54 
 
 2779.3 
 
 2 
 
 3.142 
 
 23.50 
 
 8 
 
 50.27 
 
 370.01 
 
 22 
 
 380.13 
 
 2843.6 
 
 2 1 
 
 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 
 
 6.241 
 
 39.21 
 
 9 9 
 
 74.66 
 
 558.51 
 
 23 9 
 
 443.01 
 
 3314.0 
 
 2 8 
 
 6.585 
 
 41.78 
 
 10 
 
 78.54 
 
 587.52 
 
 24 
 
 452.39 
 
 3384.1 
 
 2 
 
 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 11 
 
 6.681 
 
 49.98 
 
 10 9 
 
 90.76 
 
 G78.05 
 
 24 9 
 
 481.11 
 
 3598.9 
 
 3 
 
 7.069 
 
 52.88 
 
 11 
 
 95.03 
 
 710.90 
 
 25 
 
 490.87 
 
 3G72.0 
 
 3 1 
 
 7.467 
 
 55.86 
 
 11 3 
 
 99.40 
 
 743.58 
 
 25 3 
 
 500.74 
 
 3745 .8 
 
 3 2 
 
 7.876 
 
 58.92 
 
 11 6 
 
 103.87 
 
 776.99 
 
 25 6 
 
 510.71 
 
 3820.3 
 
 3 3 
 
 8.296 
 
 62.06 
 
 11 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. uS 
 
 955.09 
 
 26 9 
 
 562.00 
 
 4204.1 
 
 3 8 
 
 10 . 559 
 
 78.99 
 
 13 
 
 132.73 
 
 992.91 
 
 27 
 
 672 .56 
 
 4283.0 
 
 3 9 
 
 11.045 
 
 82.62 
 
 13 3 
 
 137.89 
 
 1031.5 
 
 27 3 
 
 538.21 
 
 4362.7 
 
 3 10 
 
 11.541 
 
 86.33 
 
 13 6 
 
 143.14 
 
 1070.8 
 
 27 6 
 
 593.96 
 
 4443.1 
 
 3 11 
 
 12.048 
 
 90:13 
 
 13 9 
 
 148.49 
 
 1110.8 
 
 27 9 
 
 604.81 
 
 4524.3 
 
 4 
 
 12.566 
 
 94.00 
 
 14 
 
 153.94 
 
 1151.5 
 
 28 
 
 G15. 75 
 
 4606.2 
 
 4 1 
 
 13.095 
 
 97.96 
 
 14 3 
 
 159.48 
 
 1193.0 
 
 28 3 
 
 026.80 
 
 4688.8 
 
 4 2 
 
 13.635 
 
 1Q2.0Q 
 
 14 6 
 
 165.13 
 
 1235.3 
 
 28 G 
 
 637.94 
 
 4772.1 
 
 4 3 
 
 14.186 
 
 106.12 
 
 14 9 
 
 170.87 
 
 1278.2 
 
 28 
 
 649.18 
 
 4856.2 
 
 4 4 
 
 14.748 
 
 110.32, 
 
 15 
 
 176.71 
 
 1321.9 
 
 29 
 
 G60 .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 
 
 188.69 
 
 1411.5 
 
 29 6 
 
 683.1:9 
 
 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 1504.1 
 
 30 
 
 706.86 
 
 5287.7 
 
 4 9 
 
 17.72 
 
 132.56 
 
 16 3 
 
 207.39 1551.4 
 
 30 3 
 
 713.69 
 
 5376.2 
 
 4 10 
 
 18.35 
 
 137.25 
 
 16 6 
 
 213.82 
 
 1599.5 
 
 30 6 
 
 730.62 
 
 5465.4 
 
 4 11 
 
 18.99 
 
 142.02 
 
 16 9 
 
 220.35 
 
 1648.4 
 
 30 9 
 
 742.64 
 
 5555.4 
 
 5 
 
 19.63 
 
 146.88 
 
 17 
 
 226.98 
 
 1697.9 
 
 31 
 
 754.77 
 
 5646 . 1 
 
 5 1 
 
 20.29 
 
 151.82 
 
 17 3 
 
 233.71 
 
 1748.2 
 
 31 3 
 
 766 . 99 
 
 5737.5 
 
 $ 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 
 
 6 4 
 
 22.34 
 
 167.12 
 
 18 
 
 254 . 47 
 
 1S03.6 
 
 32 
 
 804.25 
 
 6016.2 
 
 5 5 
 
 23.04 
 
 172.38 
 
 18 3 
 
 261.59 
 
 1956.8 
 
 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 
 
 32 9 
 
 842.39 
 
 6301.5 
 
 * Also cubic feet for 1 foot in depth. 
 
1260 CAPACITY OF CYLINDRICAL TANKS. 
 
 CAPACITY OF CISTERNS AND TANKS. 
 NUMBER OF BARRELS (31J GALS.) IN CISTERNS AND TANKS. 
 
 
 Diameter, in Feet. 
 
 in Feet. 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 13 
 
 _ 
 
 23.3 
 
 33.6 
 
 
 45.7 
 
 59.7 
 
 75 
 
 .5 
 
 93.2 
 
 112.8 
 
 134.3 
 
 157.6 
 
 Q 
 
 28.0 
 
 40.3 
 
 
 54.8 
 
 7 
 
 1.7 
 
 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 
 
 g 
 
 37.3 
 
 53.7 
 
 
 73.1 
 
 9 
 
 5 . 5 
 
 120 
 
 .9 
 
 149.2 
 
 180.5 
 
 214.8 
 
 252.1 
 
 9 
 
 42.0 
 
 60.4 
 
 
 82.2 
 
 10 
 
 74 
 
 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 
 
 11 
 
 51.3 
 
 73.9 
 
 100.5 
 
 131.3 
 
 166 
 
 .2 
 
 205.1 
 
 248.2 
 
 295.4 
 
 346.7 
 
 12 
 
 56.0 
 
 80.6 
 
 1 
 
 09.7 
 
 14 
 
 3.2 
 
 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 
 
 1 
 
 27.9 
 
 16 
 
 -.1 
 
 211 
 
 .5 
 
 261.1 
 
 315.9 
 
 376.0 
 
 441.3 
 
 15 
 
 70.0 
 
 100.7 
 
 137.1 
 
 17^.0 
 
 226 
 
 .6 
 
 289.8 
 
 338.5 
 
 402.8 
 
 472.8 
 
 16 
 
 74.7 
 
 107.4 
 
 146.2 
 
 191.0 
 
 241 
 
 .7 
 
 298.4 
 
 361.1 
 
 429.7 
 
 504.3 
 
 17 
 
 79.3 
 
 114.1 
 
 1 
 
 55.4 
 
 
 
 2.9 
 
 256 
 
 .8 
 
 317.0 
 
 383.6 
 
 456.6 
 
 535.8 
 
 18 
 
 84.0 
 
 120.9 
 
 164.5 
 
 214.8 
 
 272 
 
 .0 
 
 335.7 
 
 406.2 
 
 483.4 
 
 567.3 
 
 19 
 
 88.7 
 
 127.6 
 
 1 
 
 73.6 
 
 22 
 
 6.8 
 
 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 
 
 Depth, 
 
 Diameter, 
 
 in Feet. 
 
 in Feet. 
 
 
 
 16 
 
 
 
 18 
 
 
 
 
 
 
 14 
 
 15 
 
 17 
 
 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 
 
 3 
 
 34.2 
 
 37 
 
 7.3 
 
 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 
 
 4 
 
 29.7 
 
 48 
 
 5.1 
 
 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 
 
 11 
 
 402.1 
 
 461.6 
 
 5 
 
 25.2 
 
 59 
 
 2.9 
 
 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 
 
 .6 
 
 875.2 
 
 969.8 
 
 1069.2 
 
 1173.5 
 
 14 
 
 511.8 
 
 587.5 
 
 6 
 
 68.2 
 
 75 
 
 4.6 
 
 846 
 
 .0 
 
 942.6 
 
 1044.4 
 
 1151.5 
 
 1263.7 
 
 15 
 
 548.3 
 
 629.4 
 
 716.2 
 
 80 
 
 8.5 
 
 906 
 
 .4 
 
 1009.9 
 
 1119.0 
 
 1233.7 
 
 1354.0 
 
 16 
 
 584.9 
 
 671.4 
 
 7 
 
 73.9 
 
 86 
 
 2.4 
 
 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 
 
 18 
 
 658.0 
 
 755.3 
 
 8 
 
 59.4 
 
 97 
 
 0.2 
 
 1087 
 
 .7 
 
 1211.9 
 
 1342.8 
 
 1480.4 
 
 1624.8 
 
 19 
 
 694.5 
 
 797.3 
 
 9 
 
 07.1 
 
 102 
 
 4.1 
 
 1148 
 
 .1 
 
 1279.2 
 
 1417.4 
 
 1562.7 
 
 1715.1 
 
 20 
 
 731.11 839.3 954.9 1078.0 
 
 1208 
 
 .5 
 
 1346.5 
 
 1492.0 
 
 1644.9 
 
 1805.3 
 
 Depth, 
 
 Diameter, 
 
 in Feet. 
 
 in Feet. 
 
 23 
 
 24 
 
 25 
 
 26 
 
 27 
 
 28 
 
 29 
 
 30 
 
 5 
 6 
 7 
 8 
 9 
 10 
 11 
 12 
 13 
 14 
 15 
 16 
 17 
 18 
 19 
 20 
 
 493.3 
 592.0 
 690.6 
 789.3 
 887.9 
 986.6 
 1085.2 
 1183.9 
 1282.6 
 1381.2 
 1479.9 
 1578.5 
 1677.2 
 1775.9 
 1874.5 
 1973.2 
 
 537.1 
 644.5 
 752.0 
 859.4 
 966.8 
 1074.2 
 1181.7 
 1289.1 
 1396.5 
 1503.9 
 1611.4 
 1718.8 
 1826.2 
 1933.6 
 2041 . 1 
 2148.5 
 
 582.8 
 699.4 
 815.9 
 932.5 
 1049.1 
 1165.6 
 1282.2 
 1398.7 
 1515.3 
 1631.9 
 1748.4 
 1865.0 
 1981.6 
 2098.1 
 2214.7 
 2321.2 
 
 630.4 
 756.5 
 882.5 
 1008.6 
 1134.7 
 1260.8 
 1386.8 
 1512.9 
 1639.0 
 1765.1 
 1891.1 
 2017.2 
 2143.3 
 2269.4 
 2305.4 
 2521.5 
 
 679.8 
 815.8 
 951.7 
 1087.7 
 1223.6 
 1359.6 
 1495.6 
 1631.5 
 1767.5 
 1903.4 
 2039.4 
 2175.4 
 2311.3 
 2447.3 
 2583.2 
 2719.2 
 
 731.1 
 877.3 
 1023.5 
 1169.7 
 1316.0 
 1462.2 
 1608.7 
 1754.6 
 1900.8 
 2047.1 
 2193.3- 
 2339.5 
 2485.7 
 2631.9 
 2778.1 
 2924.4 
 
 784.2 
 941.1 
 1097.9 
 1254.8 
 1411.6 
 1568.2 
 1723.0 
 1882.2 
 2039.0 
 2195.9 
 2352.7 
 2509.6 
 2666.4 
 2823.3 
 2980.1 
 3137.0 
 
 839.3 
 1007.1 
 1175.0 
 1342.8 
 1510.7 
 1678.5 
 1846.4 
 2014.2 
 2182.0 
 2343.9 
 2517.8 
 2685.6 
 2853.5 
 3021.3 
 3189.2 
 3357.0 
 
 For tanks that are tapering, measure the diameter four tenths from large end. 
 
CAPACITY OF RECTANGULAR TANKS. 1261 
 
 NUMBER OF U. S. GALLONS IN RECTANGULAR TANKS 
 FOR ONE FOOT IN DEPTH. 
 
 1 cu. ft. = 7.4805 gallons. 
 
 3 . 
 
 r*-** 
 
 11 
 
 
 Length of Tank, in Feet. 
 
 2 
 
 2.5 
 
 3 
 
 3.5 
 
 4 
 
 4.5 
 
 5 
 
 5.5 
 
 6 
 
 6.5 
 
 7 
 
 2 
 2.5 
 3 
 3.5 
 4 
 4.5 
 5 
 5.5 
 6 
 6.5 
 7 
 
 29.92 
 
 37.40 
 46.75 
 
 44.88 
 56.10 
 67.32 
 
 52.36 
 65.45 
 78.54 
 91.64 
 
 59.84 
 74.80 
 89.77 
 104.73 
 119.69 
 
 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 
 
 97.25 
 121.56 
 145.87 
 170.18 
 194.49 
 218.80 
 243.11 
 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 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^d 
 1 
 
 Length of Tank, in Feet. 
 
 3& 
 * 
 
 7.5 
 
 8 
 
 8.5 
 
 9 
 
 9.5 
 
 10 
 
 10.5 
 
 11 
 
 11.5 
 
 12 
 
 2 
 
 112.21 
 
 119.69 
 
 127.17 
 
 134.65 
 
 142.13 
 
 149.61 
 
 157.09 
 
 164.57 
 
 172.05 
 
 179.53 
 
 flft 
 
 140.26 
 
 149.61 
 
 158.96 
 
 168.31 
 
 177.66 
 
 187.01 
 
 196.36 
 
 205.71 
 
 215.06 
 
 22441 
 
 
 
 168.31 
 
 179.53 
 
 190.75 
 
 202.97 
 
 213.19 
 
 224.41 
 
 235.6c 
 
 246.86 
 
 258.07 
 
 269.30 
 
 35 
 
 196.36 
 
 209.45 
 
 222.54 
 
 235.63 
 
 248.73 
 
 261.82 
 
 274.9( 
 
 288.00 
 
 301.09 
 
 314.18 
 
 4 
 
 224.41 
 
 239.37 
 
 254.34 
 
 269.30 
 
 284.26 
 
 299.22 
 
 314.18 
 
 329.14 
 
 344.10 
 
 359.06 
 
 45 
 
 252.47 
 
 269.30 
 
 286.13 
 
 302.96 
 
 319.79 
 
 336.62 
 
 353.45 
 
 370.28 
 
 387.11 
 
 403.94 
 
 5 
 
 280.52 
 
 299.22 
 
 317.92 
 
 336.62 
 
 355.32 
 
 374.03 
 
 392.72 
 
 411.43 
 
 430.13 
 
 448.83 
 
 5.5 
 
 308.57 
 
 329.14 
 
 349.71 
 
 370.28 
 
 390.85 
 
 411.43 
 
 432. OC 
 
 452.57 
 
 473.14 
 
 493.71 
 
 6 
 
 336.62 
 
 359.06 
 
 381.50 
 
 403.94 
 
 426.39 
 
 448.83 
 
 471.27 
 
 493.71 
 
 516.15 
 
 538.59 
 
 6.5 
 
 36467 
 
 388.98 
 
 41330 
 
 437.60 
 
 461.92 
 
 486.23 
 
 510.54 
 
 534.85 
 
 550.16 
 
 583.47 
 
 7 
 
 392.72 
 
 418.91 
 
 445.09 
 
 471.27 
 
 497.4*) 
 
 523.64 
 
 549.81 
 
 575.00 
 
 602.18 
 
 628.36 
 
 7.5 
 
 420.78 
 
 448.83 
 
 476.88 
 
 504.93 
 
 532.98 
 
 561.04 
 
 589.08 
 
 617.14 
 
 645.19 
 
 673.24 
 
 8 
 
 ..... 
 
 478.75 
 
 508.67 
 
 538.59 
 
 568.51 
 
 598.44 
 
 628.36 
 
 658.28 
 
 688.20 
 
 718.12 
 
 Xft 
 
 
 
 540 46 
 
 572 25 
 
 604 05 
 
 635 84 
 
 667 63 
 
 690 42 
 
 731 21 
 
 703.00 
 
 9 
 
 
 
 
 605 92 
 
 639 58 
 
 673 25 
 
 706 90 
 
 740 56 
 
 774.23 
 
 807.89 
 
 9,5 
 
 
 
 
 
 675 11 
 
 710 65 
 
 746 17 
 
 781 71 
 
 817.24 
 
 852.77 
 
 10 
 
 
 
 
 
 
 748.05 
 
 785.45 
 
 822.86 
 
 860.26 
 
 897.66 
 
 10.5 
 
 
 
 
 
 
 
 824.73 
 
 864.00 
 
 903.26 
 
 942.56 
 
 11 
 
 
 
 
 
 
 
 
 905.14 
 
 946.27 
 
 987.43 
 
 11.5 
 
 
 
 
 
 
 
 
 
 989.29 
 
 1032.3 
 
 12 
 
 
 
 
 
 
 
 
 
 
 1077.2 
 
 
 
 
 
 
 
 
 
 
 To find weight of water in pounds at 62 F. multiply number 
 of gallons by 8J. 
 
 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 
 extreme left-hand column for 7.5 and opposite to this in 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. 
 
1262 PLUMBIKG DEFINITIONS. 
 
 Plumbing. 
 
 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 im- 
 portance. The following 
 
 EXTRACTS FROM THE RULES AND REGULATIONS OF THE DEPART- 
 MENT OF BUILDINGS OF THE CITY OF NEW YORK 
 may be used as a reliable guide in any locality. 
 
 Definition of Terms. 
 
 12.* The term " private sewer" is applied to main sewers that 
 are not constructed by and under the supervision of the Depart- 
 ment of Sewers. 
 
 13. The term "house sewer" is applied to that part of the 
 main drain or sewer extending from a point 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 extending 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 without 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- 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." 
 
 * Paragraph numbers are the same as those in the Official Regulations. 
 Missing numbers show where paragraphs have been omitted. 
 
PLUMBING REQUIREMENTS. 
 
 1263 
 
 20.* Pipe, including the hub, shall weigh not less than the 
 following average weights per lineal foot: 
 
 Diameters. 
 
 Weights per 
 Lineal Foot. 
 
 2 inc 
 3 
 4 
 5 
 6 
 7 
 8 
 10 
 12 
 
 hes r 
 
 5J pou 
 
 9* 
 
 13 
 17 
 20 
 27 
 33 J 
 45 
 54 
 
 nds 
 
 
 
 
 
 
 
 
 
 
 22. All joints must be made with picked oakum and molten 
 lead and be made gas-tight. Twelve (12) oz. of fine, soft pig 
 lead must be used at each joint for each inch in the diameter of 
 the pipe. 
 
 24. Wrought-iron and steel pipes must be galvanized, and 
 each length must have the weight and maker's name stamped 
 on it. 
 
 30. All brass pipe for soil-, waste-, and vent-pipes and solder 
 nipples must be thoroughly annealed, seamless, drawn, brass 
 tubing of standard iron-pipe gauge. 
 
 Lead Waste-pipes. 38. The use of lead pipes is restricted to 
 the short branches of the soil- and waste-pipes, bends and traps, 
 and roof connections of inside leaders. "Short branches " of 
 lead pipe shall be construed to mean not more than 
 
 5 feet of 1 \ inch pipe 
 
 A 
 O 
 2 
 
 39. All connections between lead pipes and between lead and 
 brass or copper pipes must be made by means of " wiped" 
 solder joint. 
 
 40. 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 lineal foot: 
 
 * See foot-note on page 1262. 
 
1264 PLUMBING REQUIREMENTS. 
 
 Diameters. 
 
 Weights per 
 Lineal Foot. 
 
 1 J inches (for flush-pipes only) 
 
 2i pounds 
 
 u " ; 
 
 3 " 
 
 2" " 
 
 4 " 
 
 3 " 
 
 6 " 
 
 4 and 4J inches 
 
 8 " 
 
 
 
 41. All lead traps and bends must be of the same weights and 
 thicknesses as their corresponding pipe branches. Sheet lead 
 for roof flashings must be 6-lb. lead and must extend not less 
 than 6 ins. from the pipe, and the joint made water-tight. 
 
 42. Copper tubing when used for inside leader roof connec- 
 tions 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. 
 
 57. All yards, areas, and courts must be drained. 
 
 58. Tenement-houses and lodging-houses must have their 
 yards, areas, and courts drained into the sewer. 
 
 59. These drains, when sewer connected, must have con- 
 nections not less than 3 ins. in diameter. They should be con- 
 trolled by one trap the leader trap if possible. 
 
 i 
 
 Leaders. 
 
 63. All buildings shall be kept provided with proper metallic 
 leaders for conducting water from the roofs in such manner 
 as shall protect the walls and foundations of said buildings from 
 injury. In no case shall the water from said leaders be allowed 
 to flow upon the sidewalk, but the same shall be conducted by 
 pipe or pipes to the sewer. If there be no sewer in the street 
 upon which such buildings front, then the water from said 
 leaders shall be conducted by proper pipe or pipes below the 
 surface of. the sidewalk to the street gutter. 
 
 64. Inside leaders must be made of cast iron, wrought iron, 
 or steel, with roof connections made gas- and water-tight by 
 means of a heavy lead or copper-drawn tubing wiped or soldered 
 to a brass ferrule or nipple calked or screwed into the pipe. 
 
 65. Outside leaders may be of sheet metal, but they must 
 connect with the house drain by means of a cast-iron pipe ex- 
 tending vertically 5 ft. above the grade level 
 
PLUMBING REQUIREMENTS. 
 
 1265 
 
 66. Leaders must be trapped with cast-iron running traps 
 BO placed as to prevent freezing. 
 
 67. Rain-water leaders must not be used as soil-, waste-, or 
 vent-pipes, nor shall any such pipe be used as a leader. 
 
 The House Sewer, House Drain, House Trap, and 
 Fresh-air Inlet. 
 
 72. 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. 
 
 73. If possible, the house drain must be above the cellar floor. 
 The house drain must be supported at intervals of 10 ft. by 
 8-inch brick piers or suspended from the floor-beams, or be 
 otherwise properly supported by heavy iron-pipe hangers at 
 intervals of not more than 10 ft. The use of pipe-hooks for 
 supporting drains is prohibited. 
 
 74. No steam-exhaust, boiler blow-off, or drip-pipe shall be 
 connected with the house drain or sewer. 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 pro- 
 vided. In low-pressure steam systems the condensing tank 
 may be omitted, but the waste connection must be otherwise 
 as above required. 
 
 75. The house and drain sewer must be run as direct as possi- 
 ble, with a fall of at least J in. per foot, all changes in direction 
 made with proper fittings, and all connections made with Y 
 branches and one eighth and one sixteenth bends. 
 
 Size of House Sewer.- 76. The house sewer and house drain 
 must be at least 4 ins. 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. 
 
 Fall Y Inch 
 per Foot. 
 
 Fall 3^ Inch per Foot. 
 
 6 ins 
 
 5,000 sq. ft. 
 
 7,500 sq. ft. of drainage of area 
 
 7 " 
 
 6,900 " 
 
 10,300 " " " " " 
 
 8 " 
 
 9,100 " 
 
 13,600 " " " " " 
 
 9 " 
 
 11,600 " 
 
 17,400 " " " " " 
 
 
 
 
1266 PLUMBING REQUIREMENTS. 
 
 77. Full size Y and T branch fittings for hand-hole clean- 
 outs must be provided where required on house drain and its 
 branches. 
 
 78. An iron running trap must be placed on the house drain 
 near the wall of the house, and on the sewer side of all connec- 
 tions, except 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 8 ins. 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; where under ground it will be 
 of extra heavy cast iron. Where possible it will extend to 
 the external air, and finish with an automatic device approved 
 by the Department of Buildings, at a point just outside the 
 front wall of building. The fresh-air inlet must be of the 
 same size as the drain up to 4 ins. For 5- and 6-in. drains it 
 must be not less than 4 ins. in diameter. For 7- and 8-in. drains 
 not less than 6 ins. in diameter or its equivalent, and for large 
 drains not less than 8 ins. in diameter or its equivalent. 
 
 [Note. The fresh-air inlet and running trap prescribed by 
 Sections 78 and 79 are not required in many cities, and it is a 
 disputed question whether or not they are desirable.] 
 
 Soil-, Waste-, and Vent-pipes. 
 
 80. All main, soil, waste, or vent pipes must be of iron, steel, 
 or brass. 
 
 89. The diameters of soil- and waste-pipes must not be less 
 than those given in the following table: 
 
 Main soil-pipes 4 inches 
 
 Main soil-pipes for water-closets on five or more floors . 5 ' 
 
 Branch soil-pipes 4 ' 
 
 Main waste-pipes 2 ' 
 
 Main waste-pipes for kitchen sinks on five or more floors 3 ' 
 
 Branch waste-pipes for laundry tubs . . 1J ' 
 
 When set in ranges of three or more 2 ' 
 
 Branch waste for kitchen sinks 2 ' 
 
 Branch waste for urinals 2 ' 
 
 Branch waste for other fixtures 1 J ' 
 
 96. The sizes of vent-pipes throughout must not be less than 
 the following: 
 
PLUMBING REQUIREMENTS. 1267 
 
 For main vents and long branches, 2 ins. in diameter; for 
 water-closets on three or more floors, 3 ins. in diameter; for 
 other fixtures on less than seven floors, 2 ins. in diameter; 3-in. 
 vent-pipe will be permitted for less than nine stories; for more 
 than eight and less than sixteen stories, 4 ins. in diameter; 
 for more than fifteen and less than twenty-two stories, 5 ins. in 
 diameter; for more than twenty-one stories 6 ins. in diameter; 
 branch vents for traps larger than 2 ins., 2 ins. in diameter; 
 branch vents for traps 2 ins. or less, 1J ins. in diameter. 
 
 For fixtures other than water-closets and slop-sinks and for 
 more than eight stories, vent-pipes may be 1 in. smaller than 
 above* stated. 
 
 Traps. 
 
 98. Every fixture must be separately trapped by a water- 
 sealing trap placed as close to the fixture outlet as possible. 
 
 99. A set of 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 the wash-trays must be branched in ~below the water seal. 
 
 100. The discharge from any fixture must not pass through 
 more than one trap before reaching the house drain. 
 
 106. All earthenware traps must have heavy brass floor plates 
 soldered to the lead bends and bolted to the trap flange and 
 the joint made- gas-tight with red or white lead. The use of 
 rubber washers for floor connections is prohibited. 
 
 107. No trap shall be placed at the foot of main soil- and 
 waste-pipe lines. 
 
 108. The sizes for traps must not be less than those given in 
 the following table: 
 
 Traps for water-closets 4 inches in diameter 
 
 Traps for slop-sinks. . 2 " " " 
 
 Traps for kitchen sinks 2 " " " 
 
 Traps for wash-trays ; . . 2 " " " 
 
 Traps for urinals 2 " " " 
 
 Traps for other fixtures 1J " " " 
 
 Traps for leaders, areas, floor and other drains must be at 
 least 3 ins. in diameter. 
 
1268 PLUMBING REQUIREMENTS. 
 
 Water-closets. 
 
 118. In tenement-houses, lodging-houses, factories, workshops, 
 and all public buildings the entire water-closet apartment and 
 side walls to a height of 16 ins. from the floor, except at the 
 door, must be made waterproof with asphalt, cement, tile, 
 metal, or other water-proof material as approved by the Board 
 of Buildings. 
 
 121. The general water-closet accommodations for a tene- 
 ment- or lodging-house cannot be placed in the cellar. 
 
 130. In all sewer-connected occupied buildings there must 
 be at least one w^ater-closet, and there must be additional 
 closets so that there will never be more than fifteen persons 
 per closet. 
 
 131. In tenement-houses and lodging-houses there must be 
 one water-closet on each floor, and when there is more than 
 one family on a floor, there will be one additional water-closet 
 for every two additional families. 
 
 132. In lodging-houses where there are more than fifteen 
 persons on any floor, there must be an additional water-closet 
 on that floor for every fifteen additional persons or fraction 
 thereof. 
 
 133. Water-closets and urinals must never be connected 
 directly with or flushed from the water-supply pipes. 
 
 136. Iron water-closets and urinal cisterns and automatic 
 water-closets and urinal cisterns are prohibited. 
 
 137. The copper lining of water-closets and urinal cisterns 
 must not be lighter than 10 oz. copper. 
 
 138. Water-closet flush-pipes must not be less than 1J ins. 
 and urinal flush-pipes 1 in. in diameter, and if of lead must not 
 weigh less than 2 J Ibs. and 2 Ibs. per lineal foot. Flush-couplings 
 must be of full size of the pipe. 
 
 Sinks and Wash-tubs. 
 
 143. In tenement-houses and lodging-houses sinks must be 
 entirely open, on iron legs or brackets, without any enclosing 
 woodwork. 
 
 144. Wooden wash-tubs are prohibited. Cement or arti- 
 ficial stone tubs will not be permitted unless approved by the 
 Board of Buildings. 
 
PLUMBING REQUIREMENTS. 1269 
 
 Testing the Plumbing System. 
 
 155. 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 or air test, as directed. 
 All pipes must remain uncovered in every part until they have 
 successfully 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 is prohibited. 
 
 156. 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 in- 
 clude 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 finished face of walls and partitions. 
 Deviation from the above rule will not be permitted, unless 
 upon written application to and approval by the Commissioner 
 of Buildings. 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. 
 
 157. The air test will be applied with a force-pump and 
 mercury columns under ten pounds pressure, equal to 20 ins. 
 of mercury. The use of spring gauges is prohibited. 
 
 158. After the completion of the work, when the water has 
 been turned on and the traps filled, the plumber must make 
 a peppermint or smoke test in the presence of a plumbing in- 
 spector and as directed by him. 
 
 159. The material and labor for the tests must be furnished 
 by the plumber. Where the peppermint test is used, 2 ozs. of 
 oil of peppermint must be provided for each line up to five 
 stories and basement in height, and for each additional five 
 stories or fraction thereof one additional ounce of peppermint 
 must be provided for each line. 
 
 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 
 
1270 
 
 PLUMBING TRAPS. 
 
 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 
 by Fig. A. 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, out 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 effect a passage is termed the ''water- 
 seal." The water-seal in the trap, Fig. A, is the distance S. 
 
 All plumbing pipes which connect with a sewerage system 
 require to be trapped to prevent sewer-gas from passing through 
 
 Fig. A 
 
 Fig. B 
 
 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 of sewer-gas as in Fig. B. By connect- 
 ing the upper bend of a trap wi.h the outside air by means of a 
 pipe, as at V, Fig. A, the suction will be stopped, and the water 
 in the pipe T will not fall below the level of the outlet at b. 
 
 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 traps, de- 
 
PLUMBING TRAPS. 
 
 1271 
 
 signed to prevent the sewage from flowing back into the 
 house drain. These are in the nature of check- valves, and 
 
 Bag 
 
 TRAP SCREW, 
 
 Fig. C 
 
 Different Shapes of Traps. 
 
 are used principally in seaport towns where tide-water might 
 possibly force the sewage back. 
 
 The more common shapes of lead traps used in plumbing, 
 with their trade names, are shown in Figure C. The same 
 shapes are also made in cast iron. 
 The pipes marked V are the vent 
 connections. The drum trap shown 
 by Fig. D has a deeper seal than those 
 shown in Fig. C, 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. 
 
 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. 
 
 Fig. D 
 
 Round Trap, 
 
1272 
 
 PLUMBING TRAPS. 
 
 In Colorado and many other places it is necessary to con- 
 nect the waste from kitchen sinks with a large grease trap, 
 which collects and holds the grease, but permits the water to 
 pass into the sewer system. After a tune 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-inch vitrified drain-tile or cement pipe, and should be 
 about 4 ft. deep. They may also be built of brick in cement 
 
 urTop of Ground 
 
 Fig. E 
 
 Outdoor Grease Trap. 
 
 mortar. Fig. E shows a section through such a grease trap 
 and the inlet and outlet pipes. 
 
 When the sink 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 ins. in diameter may be used, with a large trap screw 
 in the top for removing the grease. Fig. F shows a section 
 through such a trap and the way in which the connections 
 should be made. A better form of grease trap is made of cast 
 iron. Some city ordinances require that inside grease traps 
 
PLUMBING SUPPLY-PIPES. 
 
 1273 
 
 shall have a chilling jacket for the purpose of more perfectly 
 separating the grease and thus 
 preventing any of it from 
 entering the waste-pipes. 
 
 Supply - pipes. These 
 may be of lead, brass, galvan- 
 ized 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 gener- 
 ally considered more durable 
 underground than galvanized- 
 iron pipe. The grade known 
 
 Fig. F 
 
 Lead Grease Trap. 
 
 as 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 commonly 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 con- 
 veying hot water, and is largely used in the better class of build- 
 ings. 
 
 Tin-lined iron and lead pipes and pipes of block tin are 
 usually considered as offering the greatest resistance to cor- 
 rosion or chemical action, and should always be used for con- 
 veying 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 can not 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 bs drawn from them pure and free from poison or 
 rust. 
 
 Lead-lined pipe is made in the same way and insures deliver- 
 
1274 PLUMBING WATER-SUPPLY. 
 
 ing the water to the house just as it comes from the mains un- 
 changed by the chemical action which often results from contact 
 with wrought-iron pipe. 
 
 Seamless-drawn nickel-silver tubing is used to some extent for 
 the exposed plumbing pipes in high class residences, office and 
 public buildings. Being pure white metal throughout it can not 
 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 elevated 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 gradu- 
 ally 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 provided with art 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 tanks containing water for drinkinjg 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 char- 
 acter of the supply. Tanks supplied from the street main in 
 which the pressure is fairly constant need not have a capacity 
 exceeding 160 gallons. Where the water is pumped into the 
 tank by a windmill or hot-air engine, the tank should have a 
 capacity sufficient for a three or four days' supply at least. 
 
 Amount of Water Required, for Various Purr 
 poses. The amount of water required for household pur- 
 poses has been found to be about 25 gallons for each person, 
 large or small. 
 
 *For further information consult the Benedict & Burnham Mfg. Co.. 
 Waterbury, Conn. 
 
PLUMBING SIZE OF PIPES. 
 
 1275 
 
 A horse will drink about 7 gallons per day and a cow 5 to 
 6 gallons per day. 
 
 A carriage requires from 9 to 16 gallons 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 likely 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 Ibs. per square inch the system may be rated 
 as low pressure, and if above 20 Ibs. as high pressure. 
 
 Supply Branches. 
 
 Low 
 Pressure. 
 
 High 
 Pressure. 
 
 To Bath-cocks 
 
 Inch, 
 f to 1 
 
 Inch. 
 
 i tof 
 
 Basin-cocks 
 
 1 
 
 
 W C flush-tank 
 
 | 
 
 1 
 
 W C flush- valve. 
 
 1 to 1J 
 
 f to 1 
 
 Sitz or foot-bath 
 
 J tof 
 
 
 Kitchen sinks 
 
 tof 
 
 \ to * 
 
 Pantry sinks 
 
 I 
 
 
 Slop-sinks 
 
 | tof 
 
 itof 
 
 Urinals 
 
 I tof 
 
 to 
 
 
 
 
 With high-pressure systems, dwellings of five or six rooms 
 are sometimes, for economy, supplied entirely through -inch 
 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 p. 1264. 
 
 Bath and sink wastes, 1 J ins. 
 
 Basin and urinal wastes, 1 J ins. 
 
 Wash trays, 1J ins. from each compartment, entered into 
 4-inch round trap and 2-inch outlet from trap. 
 
 Water-closet trap, 3 j ins. 
 
1276 PLUMBING LEAD PIPES. 
 
 APPROXIMATE SPACING FOR TACKS ON LEAD PIPES. 
 
 
 Vertical Pipe. 
 
 
 
 Horizontal Pipe. 
 
 Size of Pipe, 
 Inches. 
 
 Distance Apart, Inches. 
 
 Distance Apart, Inches. 
 
 
 Hot. 
 
 Cold. 
 
 Hot. 
 
 Cold. 
 
 } 
 
 19 
 
 25 
 
 14 
 
 17 
 
 
 20 
 
 26 
 
 15 
 
 18 
 
 J 
 
 21 
 
 27 
 
 16 
 
 19 
 
 1 
 
 22 
 
 28 
 
 17 
 
 20 
 
 1J 
 
 23 
 
 29 
 
 18 
 
 21 
 
 li 
 
 24 
 
 30 
 
 18 
 
 22 
 
 Designation of Lead Pipe. The different thicknesses 
 of lead pipe were formerly designated by letters as in Table B, 
 but are now more commonly designated as in Table A, follow- 
 ing, which may be considered as generally accepted by dealers. 
 
 TABLE A. WEIGHTS AND SIZES OF LEAD PIPE. 
 
 Calibre. 
 
 Weight 
 per Foot. 
 
 Calibre. 
 
 Weight 
 per Foot. 
 
 Lbs. 
 
 Ozs. 
 
 Lbs. 
 
 Ozs. 
 
 ^-in Tubing 
 
 
 6 
 15 
 8 
 10 
 12 
 
 8 
 
 10 
 12 
 
 4 
 12 
 
 8 
 
 12 
 4 
 12 
 
 8 
 
 f-in. Ex. ex. Strong 
 f-in. Aqueduct 
 Ex. Light 
 Light 
 
 3 
 1 
 1 
 2 
 2 
 3 
 3 
 4 
 1 
 2 
 2 
 1 
 2 
 2 
 3 
 4 
 4 
 5 
 2 
 2 
 3 
 3 
 
 8 
 8 
 4 
 8 
 8 
 
 8 
 8 
 
 8 
 4 
 
 12 
 
 8 
 
 8 
 12 
 
 Fish Seine 
 f-in. Aqueduct 
 
 
 Ex Light. . . 
 
 
 Light 
 
 
 Medium 
 
 Medium 
 
 1 
 1 
 2 
 
 Strong 
 
 Strong 
 Ex. Strong. . . . 
 A-in Aqueduct 
 
 Ex. Strong. . . . 
 Ex. ex. Strong, 
 ^-in. Aqueduct 
 Ex. Light 
 Light 
 
 Ex. Light 
 Light 
 
 i' 
 
 1 
 1 
 2 
 2 
 3 
 
 Medium 
 
 1-in. Aqueduct 
 Ex. Light 
 Light 
 
 Strong. . 
 
 AA 
 
 Ex. Strong. . . . 
 Ex. ex. Strong. 
 f-in Aqueduct. 
 
 Medium 
 
 Strong 
 
 Ex. Strong. . . . 
 Ex. ex. Strong. 
 1 J-in. Aqueduct 
 Ex. Light 
 Light 
 
 Ex. Light 
 Light 
 Medium . . . 
 
 1 
 1 
 2 
 2 
 3 
 
 Strong 
 
 Ex. Strong. . . . 
 
 Medium 
 
 
PLUMBING LEAD PIPES. 
 
 1277 
 
 Calibre. 
 
 Weight 
 per Foot. 
 
 Calibre. 
 
 Weight 
 per Foot. 
 
 Lbs. 
 
 Ozs. 
 
 Lbs. 
 
 Ozs. 
 
 1 J-in. Strong. ...'.. 
 
 4 
 6 
 6 
 3 
 3 
 4 
 5 
 6 
 7 
 9 
 3 
 4 
 5 
 6 
 8 
 3 
 4 
 5 
 7 
 8 
 9 
 10 
 
 12 
 12 
 8 
 
 8 
 
 12 
 
 8 
 8 
 8 
 
 8 
 
 2 J-in. Waste 
 
 4 
 6 
 8 
 11 
 14 
 17 
 3 
 6 
 9 
 12 
 16 
 20 
 5 
 15 
 18 
 5 
 10 
 16 
 22 
 25 
 8 
 
 8 
 3 
 
 Ex. Strong. . 
 Ex. ex. Strong 
 IJ-in. Aqueduct. . : 
 Ex. Light. . . . 
 Light 
 Medium. .... 
 
 Light . 
 
 Medium, % thick 
 Strong, i 
 Ex. Strong, % " 
 Ex. ex. Strong, } " 
 3-in. Waste 
 
 Strong 
 Ex. Strong. . 
 Ex. ex. Strong 
 If -in. Ex. Light. . . 
 Light 
 
 Light 
 
 Medium, % thick 
 Strong, J 
 Ex. Strong, % " 
 Ex. ex. Strong, f " 
 3 J-in. Waste 
 
 Medium. 
 
 Strong 
 
 Strong, J thick 
 Ex. Strong, % " 
 4-in. Waste 
 
 Ex. Strong. . 
 2-in. Waste 
 Ex. Light. . . 
 Light . 
 
 Medium 
 
 Strong, J thick 
 Ex. Strong, % " 
 Ex. ex. Strong, f " 
 5-in. Waste 
 
 Medium 
 Strong 
 
 Ex. Strong. . 
 Ex. ex. Strong 
 
 
 Coils of supply-pipe weigh about 200 Ibs.; Aqueduct about 
 90 Ibs.; Suction-pipe, 100 to 180 Ibs. each. 
 
 Block-tin pipe is stronger for a given weight per foot than 
 lead- or tin-lined lead pipe. As compared with lead pipe its 
 strength is as 3 J to 1. 
 
 Tin-lined and lead-lined iron pipe is made with inside diame- 
 ters of J, f , 1, 1J, 1 J, and 2 ins., and in 10-ft. lengths, threaded 
 without couplings. Tin- and lead-lined fittings are also made 
 (see p. 1273). 
 
 WEIGHTS AND SIZES OF SHEET LEAD. 
 
 Thickness, inches 
 Pounds, per sq. ft 
 
 V24 
 
 zy 2 
 
 y 20 
 
 3 
 
 Ms 
 3K 
 
 M6 
 
 4 
 
 M4 
 
 4K 
 
 M 2 
 5 
 
 Mo 
 6 
 
 y 9 
 
 M 
 
 8 
 
 %4 
 
 9 
 
 % 
 10 
 
 %e 
 11 
 
 % 
 12 
 
1278 
 
 PLUMBING LEAD PIPES. 
 
 TABLE B. THICKNESS AND STRENGTH OF LEAD 
 PIPES. 
 
 Calibre. 
 
 jj 
 
 1 
 
 Weight per 
 Foot. 
 
 Thickness. 
 
 Mean Burst- 
 ing Pressure. 
 
 Safe Working 
 Pressure. 
 
 Calibre. 
 
 jj 
 
 B 
 
 ce 
 
 Lf 
 
 0> 
 
 a 
 
 &4J 
 
 MO 
 
 
 
 Thickness. 
 
 Mean Burst- 
 ing Pressure. 
 
 Safe Working 
 Pressure. 
 
 Ins. 
 
 % 
 
 \ 
 
 X 
 
 AAA 
 AA 
 A 
 B 
 C 
 
 Ib. O55. 
 
 1 12 
 1 5 
 1 2 
 1 
 14 
 10 
 
 ins. 
 0.18 
 0.15 
 0.13 
 0.125 
 0.11 
 0.087 
 
 Ibs. 
 1968 
 1627 
 1381 
 1342 
 1187 
 1085 
 
 Ibs. 
 492 
 406 
 347 
 335 
 296 
 271 
 
 ins. 
 1 
 1 
 1 
 1 
 1 
 1 
 
 A 
 B 
 
 C 
 D 
 
 E 
 
 Ib. oz. 
 4 -0 
 3 4 
 2 8 
 2 4 
 2 
 1 8 
 
 ins. 
 0.21 
 0.17 
 0.14 
 0.125 
 0.10 
 0.09 
 
 Ibs. 
 857 
 745 
 562 
 518 
 475 
 325 
 
 Ibs. 
 214 
 186 
 140 
 129 
 118 
 81 
 
 7 >i 6 
 
 'AAA' 
 
 9^ 
 3 
 
 2 8 
 
 0.08 
 0.25 
 0.225 
 
 775 
 1787 
 1655 
 
 193 
 446 
 413 
 
 1M 
 IK 
 1i/f 
 
 AAA 
 AA 
 A 
 
 6 12 
 5 12 
 4 11 
 
 0.275 
 0.25 
 0.21 
 
 962 
 823 
 685 
 
 240 
 205 
 171 
 
 I 
 
 AA 
 A 
 B 
 
 c 
 
 2 
 1 10 
 
 i 3 
 
 1 
 
 0.18 
 0.16 
 0.125 
 10 
 
 1393 
 1285 
 980 
 
 782 
 
 343 
 321 
 245 
 195 
 
 1M 
 
 1M 
 1M 
 l 1 ^ 
 
 B 
 
 C 
 D 
 
 3 11 
 3 
 2 8 
 2 
 
 0.17 
 0.135 
 0.125 
 095 
 
 546 
 420 
 350 
 322 
 
 136 
 105 
 
 87 
 80 
 
 y, 
 
 D 
 
 9 
 10 
 12 
 
 0.065 
 0.07 
 0.09 
 
 468 
 556 
 625 
 
 117 
 139 
 156 
 
 IK 
 
 1H 
 
 i>2 
 
 AAA 
 AA 
 
 A 
 
 8 
 
 7- 
 6 4 
 
 0.29 
 0.25 
 0.22 
 
 742 
 
 700 
 628 
 
 185 
 175 
 157 
 
 | 
 
 AAA 
 AA 
 A 
 B 
 
 3 8 
 2 12 
 2 8 
 2 
 
 0.23 
 0.21 
 0.18 
 
 o.ie 
 
 1548 
 1380 
 1152 
 
 987 
 
 387 
 345 
 288 
 246 
 
 i*J 
 fc 
 
 y 2 
 1% 
 
 B 
 C 
 D 
 
 5 
 4 4 
 3 8 
 3 
 
 0.18 
 0.15 
 0.14 
 0.12 
 
 506 
 430 
 315 
 245 
 
 126 
 107 
 
 78 
 61 
 
 
 I 
 
 X 
 
 % 
 
 H 
 
 M 
 
 1 
 
 C 
 D 
 AAA 
 AA 
 A 
 B 
 C 
 D 
 AAA 
 AA 
 
 1 7 
 1 4 
 4 14 
 3 8 
 3 
 2 3 
 1 12 
 1 3 
 6 
 4 8 
 
 0.117 
 0.10 
 0.29 
 0.225 
 0.19 
 0.15 
 0.125 
 0.09 
 0.30 
 0.23 
 
 795 
 708 
 1462 
 1225 
 1072 
 865 
 782 
 505 
 1230 
 910 
 
 198 
 177 
 365 
 306 
 268 
 216 
 195 
 126 
 307 
 227 
 
 m 
 
 m 
 
 1M 
 2 
 2 
 2 
 2 
 2 
 2 
 
 B 
 C 
 D 
 AAA 
 AA 
 A 
 B 
 C 
 D 
 
 5 
 4 
 3 10 
 10 11 
 8 14 
 7 
 6 
 5 
 4 
 
 6!i25 
 0.30 
 0.25 
 0.21 
 0.19 
 0.16 
 0.09 
 
 'sis' 
 
 611 
 511 
 405 
 360 
 260 
 200 
 
 116 
 93 
 79 
 152 
 127 
 101 
 90 
 65 
 50 
 
 WEIGHT AND SIZES OF PURE BLOCK-TIN PIPE. 
 
 Size Inside 
 Diameter in 
 Inches. 
 
 Weight per Foot, 
 Ounces. 
 
 Size Inside 
 Diameter in 
 Inches. 
 
 Weight per Foot, 
 Pounds. 
 
 % 
 
 4 
 
 I 
 
 9, 12, 16 
 
 J 
 
 4, 5, 6 
 
 1 
 
 12, 16 
 
 %0 
 
 4, 5, 6, 8 
 
 H 
 
 20,28 
 
 1 
 
 4, 5, 6, 8 
 ' 5, 6, 8, 10 
 
 if 
 
 2 
 
 24 and upwards 
 32 and upwards 
 
 S 
 
 9, 12, 16 
 
 
 
SEWER-PIPE. 1279 
 
 Sewer-pipe. 
 
 There are three kinds of sewer- or drain-pipe offered in the 
 market, viz., "Salt Glazed Vitrified Clay-pipe," "Slip Glazed 
 Clay-pipe/' and "Cement Pipe." The name of the latter suf- 
 ficiently indicates what it is without any description. 
 
 The "Slip Glazed Clay-pipe " is made of what is known as 
 "fire" (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, which, being a foreign sub- 
 stance to the body of the pipe, is liable to wear or scale off. 
 
 "Salt Glazed Clay-pipe" is made of a clay, which, when sub- 
 jected to an intense heat, becomes 'vitreous or glass-like; and 
 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 w T ith the clay in such a manner 
 as to form part of the body of the pipe, and is therefore inde- 
 structible. 
 
 Salt-glazed pipe can only be made from clay that will vitrify, 
 that is, when subjected to an intense heat will come to a hard, 
 compact body, not porous. And it should be borne in mind that 
 "slip glazing" is only resorted jbo when the clays are of such a 
 nature that they will not vitrify. 
 
 The material of drain-pipes should be a hard, vitreous sub- 
 stance; 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 constituents 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 
 proven sufficiently strong and durable to be used with confi- 
 dence in any important 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. 
 
1280 
 
 SEWER-PIPE. 
 
 CARRYING CAPACITY OF SEWER-PIPE. 
 
 (Gallons per minute.) 
 
 Size 
 of 
 Pipe. 
 
 Fall per 100 Feet. 
 
 1 Inch. 
 
 2 Inch. 
 
 3 Inch. 
 
 6 Inch. 
 
 9 Inch. 
 
 1 Foot. 
 
 2 Feet. 
 
 3 Feet. 
 
 Inch. 
 
 
 
 
 
 
 
 
 
 3 
 
 13 
 
 19 
 
 23 
 
 32 
 
 40 
 
 46 
 
 64 
 
 79 
 
 4 
 
 27 
 
 38 
 
 47 
 
 66 
 
 81 
 
 93 
 
 131 
 
 163 
 
 6 
 
 75 
 
 105 
 
 129 
 
 183 
 
 224 
 
 258 
 
 364 
 
 450 
 
 8 
 
 153 
 
 216 
 
 265 
 
 375 
 
 460 
 
 527 
 
 750 
 
 923 
 
 9 
 
 205 
 
 290 
 
 355 
 
 503 
 
 617 
 
 712 
 
 1,006 
 
 1,240 
 
 10 
 
 267 
 
 378 
 
 463 
 
 755 
 
 803 
 
 926 
 
 1,310 
 
 1,613 
 
 12 
 
 422 
 
 596 
 
 730 
 
 1,033 
 
 1,273 
 
 1,468 
 
 2,076 
 
 2,554 
 
 15 
 
 740 
 
 1,021 
 
 1,282 
 
 1,818 
 
 2,224 
 
 2,464 
 
 3,617 
 
 4,467 
 
 18 
 
 1,168 
 
 1,651 
 
 2,022 
 
 2,860 
 
 3,508 
 
 4,045 
 
 5,704 
 
 7,047 
 
 24 
 
 2,396 
 
 3,387 
 
 4,155 
 
 5,874 
 
 7,202 
 
 8,303 
 
 11,744 
 
 14,466 
 
 27 
 
 4,407 
 
 6,211 
 
 7,674 
 
 10,883 
 
 13,257 
 
 15,344 
 
 21,771 
 
 26,622 
 
 30 
 
 5,906 
 
 8,352 
 
 10,223 14,298 
 
 17,714 
 
 20,204 
 
 28,129 
 
 35,513 
 
 36 
 
 9,707 
 
 13,769 
 
 16,816 
 
 23,763 
 
 29,284 
 
 33,722 
 
 47,523 
 
 58,406 
 
 For determining the diameter of house sewers, the table on 
 p. 1265 will serve as a good guide. Storm sewers should be 
 proportioned to the area drained. 
 
 QUANTITIES OF CEMENT, SAND, AND OF CEMENT 
 MORTAR FOR SEWER-PIPE JOINTS. 
 
 (Prepared by J. N. Hazlehurst, C.E.) 
 For each 100 ft. of sewer (with Portland cement, 375 Ibs. net per bbl.) 
 
 
 
 
 Proportions: 1 Cement to 
 
 Size 
 
 
 Mortar 
 
 1 Sand. 
 
 2 Sand. 
 
 of 
 
 L'gth, 
 
 Cubic 
 
 
 
 Pipe, 
 
 Feet. 
 
 Yards. 
 
 
 
 
 
 
 
 Inch. 
 
 
 
 Cement, 
 Barrels. 
 
 Sand, 
 Cubic 
 Yards. 
 
 No. 
 Ft. to 
 Bbl. 
 Cem't. 
 
 Cement, 
 Barrels. 
 
 Sand, 
 Cubic 
 Yards. 
 
 No. 
 Ft. to 
 Bbl. 
 Cement. 
 
 6 
 
 2^ 
 
 0.003 
 
 0.01248 
 
 0.00201 
 
 803 
 
 0.00855 
 
 0.00252 
 
 1,168 
 
 8 
 
 23^ 
 
 0.038 
 
 0.15808 
 
 0.02546 
 
 633 
 
 0.10830 
 
 0.03192 
 
 923 
 
 10 
 
 2 1 A 
 
 0.058 
 
 0.24128 
 
 0.03886 
 
 410 
 
 0.16530 
 
 . 04872 
 
 605 
 
 12 
 
 2K 
 
 0.089 
 
 0.37024 
 
 0.05963 
 
 270 
 
 0.25365 
 
 0.07476 
 
 394 
 
 15 
 
 2^ 
 
 0.123 
 
 0.51268 
 
 0.08241 
 
 195 
 
 0.35055 
 
 0.10332 
 
 285 
 
 18 
 
 2^ 
 
 0.167 
 
 0.69472 
 
 0.11189 
 
 144 
 
 0.47595 
 
 0.14018 
 
 210 
 
 20 
 
 2 1 A 
 
 0.237 
 
 0.98592 
 
 0.15879 
 
 101 
 
 0.67545 
 
 0.19908 
 
 148 
 
 24 
 
 2 1 A 
 
 0.299 
 
 1 . 24384 
 
 0.20033 
 
 80 
 
 0.85215 
 
 0.25116 
 
 117 
 
 27 
 
 3 
 
 0.492 
 
 2 04672 
 
 0.32964 
 
 49 
 
 1.40220 
 
 0.41328 
 
 71 
 
 30 
 
 3 
 
 548 
 
 2 . 27968 
 
 0.36716 
 
 44 
 
 1.56180 
 
 0.46032 
 
 64 
 
 36 
 
 3 
 
 0.849 
 
 3.53184 
 
 0.56883 
 
 29 
 
 2.41965 
 
 0.71316 
 
 41 
 
PLUMBING SPECIALTIES. 1281 
 
 The maximum rainfall, as shown by statistics, is about an 
 inch per hour (except during very heavy storms), equal to 
 22,633 gallons per hour for each acre, or 377 gallons per minute 
 per acre. 
 
 Owing to various obstructions, not more than fifty to seventy- 
 five per cent, of the rainfall will reach the drain within the same 
 hour, and allowance should be made for this fact in determin- 
 ing size of pipe required. 
 
 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 flushometer. 
 
 The operation of the flushometer is to pull the handle for- 
 ward, which raises the main valve off its seat* making a direct 
 connection from the flushometer 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 of service, and yet so 
 simple in construction and operation that the same valve is 
 used for all requirements, the only difference being whether 
 it is to work on high or low pressure. 
 
 The flushometer is extensively used in the better class of 
 buildings in the Eastern States, including the largest 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 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 underground, the filtering 
 process being accomplished by beds of sand and gravel For 
 
1282 PLUMBING SPECIALTIES. 
 
 city buildings, however, a portable filter located in the basement 
 should be used. An excellent line of filters is made by Wm. B. 
 Scaife & Sons Co., of Pittsburg. These filters have capacities 
 ranging from 150 to 5,000 gallons per hour. The same com- 
 pany also manufactures a line of patent tripoli filters, espe- 
 cially for drinking and cooking purposes, and ranging in cost 
 from $15 to $200. 
 
 Those so-called niters 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 conve- 
 nience 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 10J ins. in diameter 
 and 30 ins. high will heat 20 gallons of water in eight minutes 
 at a cost of 1J to 2 cents with gas at $1 per 1,000 cu. ft. A 
 large line of these heaters are made by the Humphry Manufactur- 
 ing and Plating Co., Kalamazoo, Michigan, 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 temperature without attention, provided the 
 building has a supply of live steam, is made by James B. Clow & 
 Sons, the supply of steam being automatically regulated 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 1,500, 2,500, 4,000, and 
 6,500 gallons per hour. 
 
 The Climax Cellar Drainer * is a simple device for rais- 
 ing 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 the same 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 discharge 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, 
 
 * Manufactured by Jas. B. Clow & Sons. 
 
PLUNGE-BATHS. 1283 
 
 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 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 pressure of 
 15 Ibs. 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 economi- 
 cal 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 
 
 Pluiig'e-batlis. 
 
 As an example of the construction and details of a small 
 plunge- or swimming-bath, we give the following description 
 and 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 15X22 ft. and is 
 about 9 ft. in total depth. It was built in a pit about 19X26 ft. 
 and about 8 ft. deep below the main excavation, which was 
 blasted out of solid rock. A concrete invert a foot or more 
 in thickness was laid over the bottom, serving as a footing on 
 which the 12-inch walls of common red brick were laid in cement. 
 They were built close to the rough vertical faces of the excava- 
 tion, 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 bottom 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-inch inverted segmental flat floor arch of common brick was 
 laid, and on its skewbacks 4-inch vertical brick walls were 
 built against the water-proofed sides. The bottom was then 
 lined with vitrified w T hite tile and the sides were faced with 
 
 * The illustrations and accompanying descriptions are taken by per- 
 mission from the Engineering Record of Nov. 3, 1900. 
 
1284 
 
 PLUNGE-BATHS. 
 
 English white enamelled brick. The tops of the walls were 
 coped with bevelled and moulded 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 ornamental 
 posts, all of brass. A similar horizontal hand-rail is carried 
 
 1 
 
 
 p Overflows!! 
 
 =3CS 
 
 
 Mill 
 
 
 Floor Strainer 
 and Outlet \ 
 
 S 
 
 Inlet ' 
 ,Marble Coping. 
 
 
 Brass 
 Railing 
 
 
 
 s 
 
 
 
 
 PLAN 
 
 CROSS-SECTION 
 (P^^ _ Brass Railing 
 
 ELEVATION 
 
 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 swimming- 
 bath occupies one corner of the room and its elevated marble 
 platform 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 
 injecting steam into the delivery-pipe at the filter. The water 
 
ILLUMINATING-GAS. 1285 
 
 enters through the open upturned end of a 2-inch 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 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. Mr. C. L. W. Eid- 
 litz was the architect of the house and the waterproofing was 
 done by the T. New Construction Company." 
 
 Illuminating-gas. 
 
 \ 
 
 Varieties of Gas. Five varieties of gas are now commonly 
 used for lighting and cooking, viz. : 
 
 1. 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 
 consequently 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 injecting 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 
 
1286 ACETYLENE-GAS. 
 
 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 acety- 
 lene 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 satis- 
 factory production of acetylene-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 abso- 
 lute certainty. 
 
 Acetylene-gas to be pure must be thoroughly washed. Impure 
 acetylene, as with any other illuminating-gas, means a discolora- 
 tion of the flame, diminished illuminating power, clogging of pipes 
 and burners with carbon and other foreign matter, and smoky 
 burners, causing blackening of ceilings ancj tarnished and soiled 
 woodwork and upholstery. 
 
 It is now generally agreed that the requirements above out- 
 lined 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 lights 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 month. 
 
 To develop the full illuminating power of the gas it is neces- 
 sary to use a burner-tip having the thinnest slit obtainable, the 
 illuminating power of the gas being about 15 times that of coal- 
 gas, for the same consumption. 
 
GAS-FITTING. 1287 
 
 The light is a clear white, very nearly resembling sunlight in 
 color and diffusiveness, 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 quality, unique 
 among artificial illuminants, of reproducing even the most deli- 
 cate shades of color as faithfully as sunlight. Even when used 
 witli mantle burners, as it may be with great economy, acetylene 
 light presents a strong dissimilarity from ordinary gas under the 
 same conditions. Acetylene corrodes silver and copper, but 
 does not affect brass, iron, lead, tin, or zinc. 
 
 A government specification for a complete apparatus for acety- 
 lene gas was published in Engineering News of Jan. 14, 1904. 
 
 5. Gasolene-gas is a mixture of gasolene 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. 
 
 Gasolene changes from the liquid to the gaseous form under 
 ordinary atmospheric pressure, at temperatures above 40, the 
 evaporation being very slow at 40, quite rapid at 70, and furious 
 at 212. 
 
 If a tank containing liquid gasolene be left open to the air, 
 the liquid will all pass away in the form of gas. If a match 
 be lighted near an open can of gasolene, the escaping gas at once 
 takes fire and communicates the fire to the liquid, causing it to 
 explode with great violence. Although generally considered as 
 dangerous, it is only so when carelessly or ignorantly handled. 
 
 To produce 1,000 cu. ft. of gas of good quality requites about 
 4J gallons of the best grade of gasolene. 
 
 An ordinary burner consumes about 5 cu. ft. per minute. 
 
 PIPING A HOUSE FOR GAS. 
 
 [Circular issued by the Gilbert & Barker Manufacturing Company.] 
 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-holes, 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 
 infrequent that it is obstructed, and this precaution will save 
 much damage and annoyance. What is known as gas-fitters' 
 cement never should be used. It cracks off easily, in warm 
 
1288 GAS-FITTING. 
 
 places it will melt, and it can be dissolved by several different 
 kinds of gas. Nothing but solid metals is admissible for con- 
 fining 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, in distinction from being cut 
 in or near the centres of rooms. It is evident that a 10-inch 
 timber notched 2 ins. in the middle is no stronger than an 
 8-inch. All branch outlet-pipes should be taken from the sides 
 or tops of running lines. Bracket-pipes should run up from 
 below, in distinction from dropping from overhead. Never 
 drop a centre 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 centre of the building as is practicable. It is ob- 
 vious that where gas is distributed from the centre of a build- 
 ing, smaller running lines of pipe will be needed than when 
 the main pipe runs up on one end. Hence, timbers will not 
 require as deep cutting, and the flow of gas will be more regu- 
 lar 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 independent 
 rising pipe for each height of post, in distinction from dropping 
 a system of piping from a higher to a lower post, and grading 
 to a low point and establishing drip-pipes. Drip-pipes in 
 a building should always be avoided. The whole system of 
 piping should be so arranged that 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 possibility of their moving when 
 the gas-fixtures are attached. Centre pipes should rest on a 
 solid support fastened to the floor timbers near their tops. The 
 pips should be securely fastened to the support to prevent 
 lateral movement. The .drop-pipe must be perfectly plumb, 
 and pass through a guide fastened near the bottom of the tim- 
 bers, which will keep them in position despite the assaults 
 of lathers, masons, and others. In the absence of express 
 directions to the contrary, outlets for brackets should generally 
 be 5 ft. and 6 ins. high from the floor, excepting that it is 
 usual to put them 6 ft. in halls and bathrooms. The up- 
 right pipes should be plumb, so that the nipples that project 
 through the walls, will be level The nipples should project 
 
GAS-FITTINGS. 1289 
 
 not more than f in. from the face of the plastering. Laths 
 and plaster together are usually f in. thick; hence the nipples 
 should project 1J ins. from the face of the studding. Drop 
 centre pipes should project 1J ins. below the furring, or timbers 
 if there be no furring, where it is known that there will be no 
 stucco or centre-pieces used. Where centre-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 system 
 of piping should be proved to be air- and gas-tight under a 
 pressure of air that will raise a column of mercury 6 ins. 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 in- 
 spect 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 outlets to be loosened in different 
 parts of the building, first loosening one to let some air escape, 
 at the same time observing if the mercury falls, then tighten 
 it and repeat 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 atten- 
 tion: 
 
 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 
 
1290 GAS-FITTING. 
 
 pipe must be firmly supported at short intervals to prevent 
 sagging. 
 
 Rules and Table for Proportioning- Sizes of 
 House Pipes.* 
 
 The table on the opposite page 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 -^ 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. increas- 
 ing 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 
 designing the table, each f-in. outlet was assumed as requiring 
 a supply of 10 cu. ft. per hour. 
 
 In using the table observe the following rules: 
 
 1. No house riser shall be less than f 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 f in. An extension to 
 existing piping may be made of J-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 
 fin. 
 
 4. In figuring out the size of pipe, always start at the ex- 
 tremities 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 junc- 
 ture 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 " sec- 
 tion" therefore being made of but one size of pipe. 
 
 6. If any outlet is larger than f in. it must be counted 
 more than one, in accordance with the schedule below: 
 
 Size of outlet (inches) } J 1 1J 1 J 2 2J 
 
 Value in table 2 4 7 11 16 28 44 
 
 * The Denver Gas and Electric Company. 
 
GAS-FITTING. 
 
 1291 
 
 TABLE SHOWING THE CORRECT SIZES OF HOUSE 
 PIPES FOR DIFFERENT LENGTHS OF PIPES AND 
 NUMBER OF OUTLETS. 
 
 Number 
 of 
 Outlets. 
 
 Lengths of Pipes in Feet. 
 
 H-in. 
 
 Pipe. 
 
 J^-in, 
 Pipe. 
 
 %-in. 
 Pipe. 
 
 l-in. 
 Pipe. 
 
 l^-in. 
 Pipe. 
 
 IK-in. 
 Pipe. 
 
 2-in. 
 Pipe. 
 
 2^-in. 
 Pipe. 
 
 300 
 300 
 300 
 300 
 300 
 300 
 300 
 300 
 300 
 300 
 300 
 300 
 300 
 270 
 210 
 165 
 135 
 80 
 60 
 33 
 22 
 15 
 
 3-in, 
 Pipe. 
 
 400 
 400 
 400 
 400 
 400 
 400 
 400 
 400 
 400 
 400 
 400 
 400 
 400 
 400 
 400 
 400 
 330 
 200 
 150 
 80 
 50 
 35 
 28 
 21 
 17 
 14 
 
 1 
 2 
 3 
 4 
 5 
 6 
 8 
 10 
 13 
 15 
 20 
 25 
 30 
 35 
 40 
 45 
 50 
 65 
 75 
 100 
 125 
 150 
 175 
 200 
 225 
 250 
 
 20 
 
 30 
 
 27 
 12 
 
 50 
 50 
 50 
 50 
 33 
 24 
 13 
 
 70 
 70 
 
 70 
 70 
 70 
 70 
 50 
 35 
 21 
 16 
 
 100 
 100 
 100 
 100 
 100 
 100 
 100 
 100 
 60 
 45 
 27 
 17 
 12 
 
 150 
 150 
 150 
 150 
 150 
 150 
 150 
 150 
 150 
 120 
 65 
 42 
 30 
 22 
 17 
 13 
 
 200 
 200 
 200 
 200 
 200 
 200 
 200 
 200 
 200 
 200 
 200 
 175 
 120 
 90 
 70 
 55 
 45 
 27 
 20 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 7. If the exacji number of outlets given cannot be found in 
 the table, take the next larger number. For example, if seven- 
 teen outlets are required, work with the next larger number 
 in the table, which is 20. 
 
 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 corresponding to the outlets given 
 must be taken to determine the size of pipe required. 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 IJ-in. column, that size pipe would 
 
1292 GAS-FITTING. 
 
 be required. Under Rule 7 the same size pipe would be re- 
 quired for seven outlets. 
 
 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 1 in. may be used, no matter how short the " section" 
 may be. 
 
 10. In any piping plan, in any continuous run from an ex- 
 tremity to the metre, there may not be used a longer length 
 of any size pipe than found in the table for that size, as 50 ft. 
 for f in., 70 ft. for 1 in., etc. If any one "section " would exceed 
 the limit length, it must be made of larger pipe. Thus, 6 outlets 
 could not be fed through 75 ft. of 1-in. pipe, but 1 J in. would have 
 to be used. When two or more successive "sections^" work out to 
 the same size of pipe and their total length or sum exceeds the 
 longest length in the table for that size pipe, make the "section' 7 
 nearest the metre of the next larger size. For example, if we 
 have 5 outlets 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 
 1-in. pipe, and that 5 outlets through 45 ft. would also require 
 1-in. pipe, but as the sum of the two sections, 30 plus 45 equals 
 75 ft., is longer than the amount of 1 in. that may be used in 
 any continuous run. the 30-ft. section, being the one nearer the 
 metre, must be made of IJ-in. pipe. The application 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 f-in. pipe 
 in the section between the eighth and ninth outlet (counting from 
 the extremity of the system toward the metre), provided that 
 this 13 ft. added to the total length of f-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 f in. allowable in any one branch of the system. 
 Therefore, up to the eighth outlet, 37 ft. of f-in, pipe could 
 have been used, and yet allow 13 ft. of f 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 1-in. pipe. 
 
 11. Never supply gas from a smaller size 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 
 
GAS-FITTING. 
 
 1293 
 
 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. 
 ripe would be supplying a 2J-in., the 100 ft. section must be 
 made 2J in. 
 
 X-v^* 
 Mun.l&' ^x. 
 
 O 
 
 f 
 
 T> 
 
 The sizes of pipes in the above diagram are in accordance with 
 the foregoing rules and table. 
 
1296 
 
 LIGHTING AND ILLUMINATION. 
 
 candles per square inch. From this consideration it at once 
 follows that naked lights of the more modern type should be 
 kept carefully out of range of direct vision, or if necessity 
 requires that they should fall within the range of vision they 
 should be so screened as to reduce the intrinsic brilliancy to 
 within proper limits. 
 
 Another measurement of the intensity of illumination is the 
 "candle-foot," which is the illumination given by one candle 
 at a distance of 1 ft. 
 
 A candle-foot light is considered a good intensity for reading 
 purposes. The intensity of light varies inversely as the square 
 of the distance, or candle-feet= candle-power divided by square 
 of distance in feet. 
 
 Thus a 16-candle-power lamp has an intensity of 16 candle- 
 feet at a distance of 1 ft., 4 candle-feet at a distance of 2 ft., 
 and 1 candle-foot at a distance of 4 ft. 
 
 Quantity of Light Required.* The quantity of 
 light to be supplied is usually estimated in candle-power per 
 square feet of area, or per cubic foot of space. Fontaine showed 
 that the latter method is in the majority of instances more 
 nearly correct. In a drawing-room with medium-tinted walls, 
 for instance, 0.015 candle-power per cubic foot is about right 
 and in larger halls it is advisable to figure about 0.02 to 0.03 
 candle-power per cubic foot. The following table will give 
 some idea of tne values to be found in practice: 
 
 Apartment. 
 
 Volume. 
 Cubic 
 Feet. 
 
 Candle- 
 power. 
 
 Candle- 
 power 
 per Cubic 
 " Foot. 
 
 1. Museum 
 
 .330,000 
 
 8,000 
 
 .024 
 
 2. Public hall 
 
 12,425 
 
 1,000 
 
 .080 
 
 3. Town hall 
 
 48 000 
 
 1,376 
 
 028 
 
 4. Legislative hall 
 
 143,560 
 
 7,560 
 
 .052 
 
 5. Body opera-house 
 
 324,760 
 
 11,400 
 
 .034 
 
 6. Theatre 
 
 125 550 
 
 2,340 
 
 019 
 
 7. Colonial church 
 
 80,000 
 
 1,600 
 
 .020 
 
 
 
 
 
 In this list the second is wastefully bright, the others are all 
 about right. 
 
 It must be remembered that all globes and shades absorb a 
 
 * Wm. Lincoln Smith, engineer. 
 
LIGHTING AND ILLUMINATION. 1297 
 
 certain amount of light and that it is advisable to increase the 
 allowance as figured so as to correct for this loss. 
 
 "Assuming the 16-candle-power lamp as the standard, it is 
 generally found that two 16-candle-power lamps per 100 sq. ft. 
 of floor space give good illumination, three very bright, and four 
 brilliant. These general figures will be modified by the height 
 of ceiling, color of walls and ceiling, and other local conditions." * 
 
 SPACE ILLUMINATED BY ENCLOSED ARC LAMPS.f 
 
 Space to be Illuminated. 
 
 Square Yards 
 per 450-Watt 
 Lamp. 
 
 Outdoor areas. 
 
 2000-2500 
 
 Train sheds. . . .... 
 
 1400-1600 
 
 Foundries (general illumination) 
 
 600- 800 
 
 Machine shops 
 
 200- 250 
 
 Thread and cloth mills 
 
 200- 230 
 
 
 
 Means for Reducing Intrinsic Brilliancy 
 Globes. In practically all cases of interio illumination it is 
 necessary to reduce the intrinsic brilliancy by the use of some 
 type of diffusing shade or globe, and frequently to further alter 
 the direction of the rays of light by some type of reflector, etc. 
 There are on the market shades and globes which aim to accom- 
 plish each of these two results independently of the other, 
 one or two forms which aim to do both at once, and a great 
 number which accomplish neither result to any degree of satis- 
 faction are wasteful of light and many of them cannot even 
 claim to be ornamental. 
 
 Opal, opaline, or ground glasses are very good diffusers, 
 but they waste from 30 to 60 per cent, of the light. After 
 diffusing the light they cannot deflect or direct the rays in 
 such directions as they may be needed for use. Their only 
 use, therefore, is in softening the source of light so as to render 
 it less injurious to the eyesight, for they have no power to in- 
 crease the efficient illumination in any special direction. By 
 a properly calculated and worked-out system of prism glass 
 globes any light may be diffused over a large surface and its 
 intensity softened, while at the same time these diffused or 
 
 * H. C. Gushing, Jr., in "Practical Lessons in Electricity." 
 t International Library of Technology, Vol. 13. 
 
1296 
 
 LIGHTING AND ILLUMINATION. 
 
 candles per square inch. From this consideration it at once 
 follows that naked lights of the more modern type should be 
 kept carefully out of range of direct vision, or if necessity 
 requires that they should fall within the range of vision they 
 should be so screened as to reduce the intrinsic brilliancy to 
 within proper limits. 
 
 Another measurement of the intensity of illumination is the 
 "candle-foot/ 7 which is the illumination given by one candle 
 at a distance of 1 ft. 
 
 A candle-foot light is considered a good intensity for reading 
 purposes. The intensity of light varies inversely as the square 
 of the distance, or candle-feet = candle-power divided by square 
 of distance in feet. 
 
 Thus a 16-candle-power lamp has an intensity of 16 candle- 
 feet at a distance of 1 ft., 4 candle-feet at a distance of 2 ft., 
 and 1 candle-foot at a distance of 4 ft. 
 
 Quantity of Light Required.* The quantity of 
 light to be supplied is usually estimated in candle-power per 
 square feet of area, or per cubic foot of space. Fontaine showed 
 that the latter method is in the majority of instances more 
 nearly correct. In a drawing-room with medium-tinted walls, 
 for instance, 0.015 candle-power per cubic foot is about right 
 and in larger halls it is advisable to figure about 0.02 to 0.03 
 candle-power per cubic foot. The following table will give 
 some idea of the values to be found in practice : 
 
 Apartment. 
 
 Volume. 
 Cubic 
 Feet. 
 
 Candle- 
 power. 
 
 Candle- 
 power 
 per Cubic 
 " Foot. 
 
 
 330,000 
 
 8,000 
 
 .024 
 
 2 Public hall 
 
 12,425 
 
 1,000 
 
 .080 
 
 3 Town hall 
 
 48,000 
 
 1,376 
 
 .028 
 
 4 Legislative hall 
 
 143,560 
 
 7,560 
 
 .052 
 
 5 Body opera-house 
 
 324,760 
 
 11,400 
 
 .034 
 
 6 Theatre 
 
 125,550 
 
 2,340 
 
 .019 
 
 7 Colonial church . . 
 
 80,000 
 
 1,600 
 
 .020 
 
 
 
 
 
 In this list the second is wastefully bright, the others are all 
 about right. 
 
 It must be remembered that all globes and shades absorb a 
 
 * Wm. Lincoln Smith, engineer. 
 
LIGHTING AND ILLUMINATION. 1297 
 
 certain amount of light and that it is advisable to increase the 
 allowance as figured so as to correct for this loss. 
 
 "Assuming the 16-candle-power lamp as the standard, it is 
 generally found that two 16-candle-power lamps per 100 sq. ft. 
 of floor space give good illumination, three very bright, and four 
 brilliant. These general figures will be modified by the height 
 of ceiling, color of walls and ceiling, and other local conditions." * 
 
 SPACE ILLUMINATED BY ENCLOSED ARC LAMPS.f 
 
 Space to be Illuminated. 
 
 Squ'are Yards 
 per 450- Watt 
 Lamp. 
 
 Outdoor areas - .... 
 
 2000-2500 
 
 Train sheds. . . 
 
 1400-1600 
 
 Foundries (general illumination) 
 
 600- 800 
 
 Machine shops 
 
 200- 250 
 
 Thread and cloth mills 
 
 200- 230 
 
 
 
 Means for Reducing Intrinsic Brilliancy 
 Globes. In practically all cases of interio illumination it is 
 necessary to reduce the intrinsic brilliancy by the use of some 
 type of diffusing shade or globe, and frequently to further alter 
 the direction of the rays of light by some type of reflector, etc. 
 There are on the market shades and globes which aim to accom- 
 plish each of these two results independently of the other, 
 one or two forms which aim to do both at once, and a great 
 number which accomplish neither result to any degree of satis- 
 faction are wasteful of light and many of them cannot even 
 claim to be ornamental. 
 
 Opal, opaline, or ground glasses are very good diff users, 
 but they waste from 30 to 60 per cent, of the light. After 
 diffusing the light they cannot deflect or direct the rays in 
 such directions as they may be needed for use. Their only 
 use, therefore, is in softening the source of light so as to render 
 it less injurious to the eyesight, for they have no power to in- 
 crease the efficient illumination in any special direction. By 
 a properly calculated and worked-out system of prism glass 
 globes any light may be diffused over a large surface and its 
 intensity softened, while at the same time these diffused or 
 
 * H. C. Gushing, Jr., in "Practical Lessons in Electricity." 
 t International Library of Technology, Vol. 13. 
 
1298 
 
 LIGHTING A.ND ILLUMINATION. 
 
 softened rays are deflected into directions where they ar 
 needed for use, thereby increasing the efficient illumination. 
 
 At present there is only one system of prism glass globes 
 known to the author that carries out these purposes. This 
 is the invention of Messrs. Blondel and Psaroudaki of Paris 
 who have called it the Holophane system of compound prisir 
 glass. 
 
 Absolutely transparent glass is used. The inner surface oi 
 the glass is given over to carefully calculated flutings or prisms 
 used solely for diffusing or softening the light without loss oi 
 power. On the outside surface are prisms calculated for de- 
 flecting these diffused rays into directions where needed. 
 
 In practice, Holophane glass, made into globes and shades 5 
 when placed over a light, will render a dazzling light soft and 
 healthful, while increasing its effective illuminating power. 
 
 These globes are made of three classes, or of three different 
 shapes, each shape designed for a separate purpose, as for 
 desk, general, or large ulterior illumination. 
 
 The Meridian Lamp. The General Electric Company 
 has introduced a new lamp, which they have named the "Merid- 
 ian, Lamp," which is a specially designed incandescent lamp 
 
 ILLUMINATING DATA FOR MERIDIAN LAMPS. 
 
 Class 
 Service. 
 
 Light 
 Intensity 
 in Candle- 
 feet. 
 
 No. 1 Lamp (60 Watts). 
 
 No. 2 Lamp (120 Watts). 
 
 Height of 
 Lamp and 
 Diameter of 
 Uniformly 
 Lighted 
 Area. 
 
 Distance 
 between 
 Lamps 
 when Two 
 or More 
 are Used. 
 
 Height of 
 Lamp and 
 Diameter of 
 Uniformly 
 Lighted 
 Area. 
 
 Distance 
 between 
 Lamps 
 when Two 
 or More 
 are Used. 
 
 Desk or 
 reading- 
 table 
 
 J 3 
 
 I 2 
 i U 
 
 Feet. 
 2.9 
 3.5 
 4 
 
 Feet. 
 
 4.9 
 6 
 
 7 
 
 Feet. 
 4 
 5 
 5.75 
 
 Feet. 
 
 7 
 8.5 
 9.8 
 
 General 
 lighting 
 
 l'i 
 
 5 
 5.75 
 
 7 
 
 8.5 
 9.8 
 12 
 
 7 
 8.2 
 10 
 
 12 
 13.9 
 11 
 
 with a suitable reflector and ornamental collar detachable 
 from the lamp. The lamp bulb is spherical in shape, and 
 usually frosted. The light from the lamp is of high brilliancy, 
 rendered soft and white by the diffusing action of the sand- 
 
LIGHTING AND ILLUMINATION. 1299 
 
 blasted bulb and reflector. The illumination is uniform over 
 .in area having a, diameter equal to the height from the plane 
 on which the illumination is measured. The lamp is made 
 in two sizes, No. 1, ;$}"-bulb, 25 candle-power, consuming 
 60 watts, and No. 2, 5"-bulb, 50 candle-power, consuming 
 120 watts. The prices of the bulbs for renewal are 40 and 60 
 cents respectively. The lamps should always be suspended, 
 preferably from the ceiling. 
 
 The "Me rust Lamp. This is a new form of incandescent 
 lamp which derives its name from the inventor, Dr. Walther 
 Nernst, an eminent German scientist. The distinguishing 
 features of the Nernst lamp are its filament or glower, and 
 the means for making the glower conductive. The glower 
 operates in the open air, its removal and replacement may be 
 readily accomplished, and at ordinary temperatures it is a 
 non-conductor of electricity. A heater, separate therefrom, 
 is therefore; provided for giving it an initial temperature suffi- 
 cient to make it conductive. When it becomes conductive 
 by external In -Ml the current traversing the glower not only 
 causes it to emit light, but also to develop internally sufficient 
 heat to maintain it in a conductive condition, the action of 
 the preliminary heater being discontinued. For a given illu- 
 mination the Nernst lamp requires only about one half the 
 amount of electrical energy required by ordinary incandescent 
 lamps, and about the same as that of the enclosed arc lamp. 
 
 Nernst lamps are made in two types, viz.: the 110-volt type, 
 adjustable for any voltage from 100 to 120, and the 220-volt 
 type, adjustable for any even voltage from 200 to 240. The 
 former type is made in two sizes and the latter type in five sizes.* 
 
 Color of Illiiminants.t 
 
 The question of color plays an important part in the study of 
 illumination. For some purposes, where it is desired to produce 
 the effects of daylight as nearly as possible, the arc lamp, when the 
 violet rays are properly filtered out, plays an important part, 
 In general, however, the color of the arc is cold, and for a room 
 where the effect is to produce* a cheerful and warm appearance, 
 an illuminant with more of the red rays, such as the incandescent 
 
 * Additional data may bo obtained from the Nenwt k&mp Company, 
 Pittsburg, PA, 
 t Van ftrauelUw Unsingh, 
 
1300 LIGHTING AND ILLUMINATION. 
 
 lamp or ordinary gas, is very much to be preferred. The pre- 
 dominant color in a few of the most important illuminants is: 
 
 Sun at noon white. 
 
 Sun near sunset reddish. 
 
 Enclosed arc, low voltage white. 
 
 Open arc bluish white to violet. 
 
 Nernst lamp white. 
 
 Acetylene white . 
 
 Incandescent electric yellowish white. 
 
 Mantle burner -white with a tinge of green. 
 
 Open-flame gas orange- white. 
 
 Kerosene lamp orange-white. 
 
 Candle orange-yellow. 
 
 The amount of light reflected from surfaces is also largely 
 dependent on the condition and color of such surfaces. It is 
 very necessary hi calculations, where the walls or decorations 
 play any part, to know the character of the same; thus white 
 paper reflects from 70 to 80 per cent. ; yellow wall-paper gives 
 only about half that amount; emerald-green about 18 per cent. ; 
 black paper about 5 per cent., deep-blue paper about 3 per cent., 
 while black velvet gives only about -fa of 1 per cent. As these 
 coefficients of diffuse reflections play an important part in all 
 attempts at calculation, it is necessary, in order to do the best 
 work, to know rather closely the character of the decorations. 
 
 The Diffusion of Light through Windows. 
 
 Abstracts from report of Mr. Charles L. Norton, on an elaborate 
 series of tests made at the Mass. Institute of Technology.* 
 
 The results of the tests on a score or more of different glasses 
 may be stated briefly as follows: 
 
 We may increase the light in a room 30 ft. or more deep to 
 form three to fifteen times its present effect by using " Factory 
 Ribbed" glass instead of plane glass in the upper sash. By 
 using prisms we may, under certain conditions, increase the effect- 
 ive 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 js small, as in the case of win- 
 dows opening upon light shafts or narrow alleys. The increase in 
 the strength of the light directly opposite a window in which 
 
 * From Report No. Ill, Insurance Engineering Experiment Station t 
 Sept., 1902. 
 
DIFFUSION OF LIGHT. 1301 
 
 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 previously been 
 lighted. 
 
 The kinds of glass tested were as follows: 
 
 1. 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 Fig. A) 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, groove on one side being opposite the rib on the other, 
 giving a sinuous section (Fig. B). 
 
 7. "Ripple glass," with rippled surfaces on both sides; of 
 very beautiful appearance and a clear white color. 
 
 8. Glass ribbed on one side and figured on the other. 
 
 9. Ribbed 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. Ground 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 diffusing medium, giving no perceptible change in the effect- 
 ive 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 corrugation. 
 The "Ribbed Wire" glass is about twenty per cent, less effective 
 than the ordinary "Factory Ribbed" glass. The addition of a 
 second corrugation upon the back of the plate giving the "Sky- 
 light" 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," gives the widest diffusion, especially in 
 bright sunlight. A raised figure, when worked upon the back 
 
1302 
 
 LIGHTING AND ILLUMINATION. 
 
 of the " Ribbed" glass, renders it less offensive to the eye in 
 bright sunlight, but less effective in deep rooms. The only 
 
 Fig. A Fig. B Fig. C Fig. D 
 
 glasses of this group which it is worth while, then, to discuss 
 further are the " Factory Ribbed" and the "Maze" glass. 
 The second group comprises the following glasses : 
 
 1. 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 upon one side 
 and deeply notched upon the other (Fig. C) , the teeth or prisms 
 being of very fiat, smooth faces and 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 ins. 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 now being 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 Fig. D, The Daylight prisms 
 tested were made in large sheets and of approximately the game 
 croas-gection and general appearance, as, the Luxfer prisms for 
 factory use, No tiles of Daylight prisms were tested, as none 
 cam to hancj in time for th tent, The Mississippi prism glass ig 
 
DIFFUSION OF LIGHT. 
 
 1303 
 
 much like the other prisms in cross-section, but the ridges or prisms 
 do not run across the plate in a straight line, but in a wavy or 
 sinuous line. I cannot detect any advantage arising from this over 
 the straight-edge prism. 
 
 Conclusions. First. The conditions in a room less than 
 15 ft. deep are such that, except with a skylight 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 "liipple," is ordi- 
 narily preferable. 
 
 Second. When a room is from 20 ft. to 60 ft. deep, or even 
 more, and has a skylight of 60 or less, the ribbed and prismatic 
 glass gives a very great gain in effective light. The gain in 
 brilliancy 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 sky, where the available light is now 
 small, may have the light 20 ft. back from the window increased 
 
 \ 
 
 Fig. E 
 
 Fig. F 
 
 ten or twenty times by using prisms; and, by using canopies 
 of prisms, it is sometimes possible to strengthen the light from 
 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. 
 
1304 
 
 LIGHTING AND ILLUMINATION. 
 
 The refraction of the incident ray in a case of the ribbed glass 
 and prism is shown by Figs. E and F. 
 
 "Ribbed " and "Maze " glass are of very great value in soften- 
 ing the light, especially in the case of such windows as are exposed 
 to the direct sun, aside from their effectiveness in strengthening 
 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 photographer may have in 
 this way as well diffused a light as he now has with cloth screens 
 or shades, with a much greater intensity. To be efficient in 
 rooms 20 ft. deep or more, ribbed glass should be set with its 
 ribs horizontal, 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 com- 
 mon practice. If the lower sash is 
 to be glazed with diffusing glass as 
 well, a further increase of about 
 twenty-five per cent, may be ex- 
 pected. 
 
 Considering both expense and 
 efficiency, the following general sug- 
 gestions 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 30 to 50 ft. deep, with sky- 
 angles of 60 or more. 
 Use prisms or "Factory Ribbed" glass, in sheets, in all 
 vertical windows in rooms more than 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. G shows an effective method of lighting the basement and 
 first story where the light must come from a court. 
 
ELECTRICITY DEFINITIONS. 1305 
 
 ELECTRICITY.* 
 
 Definitions. Electricity is the name given to that invisible 
 agent which causes all electrical phenomena. Just what this 
 agent is, is unknown. It seems probable that all electrical 
 phenomena are due to a peculiar state or stress of a medium 
 called ether. 
 
 Electrical science is founded upon the effects produced by 
 the action of certain forces upon matter. 
 
 Electricity may appear either to reside upon the surface of 
 bodies as a charge under high pressure or to flow through their 
 substance as a current -under comparatively low pressure. 
 
 The former is called static electricity and the latter dynamic 
 electricity. 
 
 That branch of electrical science which treats of static elec- 
 tricity is termed electrostatics and that which treats of the 
 action of electric currents is termed electrodynamics. 
 
 Static electricity is produced by friction and is used prin- 
 cipally in medicine. 
 
 An electrostatic battery consists of a number of Ley den jars 
 whose inside coatings are all connected together and whose 
 outside coatings are all connected to the earth. 
 
 Voltaic electricity is a term applied to electricity developed 
 by chemical action in a voltaic cell, or battery. Such batteries 
 develop a continuous current of electricity, and hence voltaic 
 electricity is but a sub-branch of dynamic electricity. Electric 
 currents may be obtained by chemical action, heat, or induction. 
 
 The Electromagnet. When an electric current is passed 
 through a coil of wire, the coil becomes equivalent to a magnet 
 and possesses the same properties. 
 
 When a core of soft iron is inserted in such a coil it becomes 
 an electromagnet. The core is magnetized only when the 
 current is flowing in the coil, and it is to this fact that the prac- 
 tical value of the electromagnet is due. The principle of the 
 electromagnet is employed in the construction of telegraphic 
 instruments, dynamos, electric bells, etc. Electric clocks are 
 also governed by the action of electromagnets. 
 
 Dynamos generate current by the revolving of their arma- 
 
 * In the preparation of this subject the author has had the valued assist- 
 ance of Mr. Geo. A. Stiles, Electrical Engineer. Denver. 
 
1306 ELECTRICITY DEFINITIONS. 
 
 tures in a magnetic field. The armature is an electromagnet 
 with the wire wound parallel to its axis and so connected to 
 a commutator in direct -current machines and to col T ector 
 rings in alternators that the current may be taken off by 
 brushes applied to the commutator or collecter rings as the 
 case may be. 
 
 Types of dynamos may be divided into two divisions, being 
 distinguished by the nature of the current they are to supply 
 the one type continuous or direct current, the other alternating 
 or rapidly reversing the directions of current. 
 
 Flow of Electricity. Electricity, although commonly 
 described and referred to as flowing through a circuit, does not 
 actually flow. There is no transfer of matter along the circuit. 
 A wire carrying a current looks the same as one that is not, 
 and that electricity is present is only evident by the heating, 
 chemical, or magnetic effects produced. For practical pur- 
 poses, however, it is convenient to consider electricity as flow- 
 ing. 
 
 As water flows from a higher to a lower level, so electricity 
 flows from a high potential to a lower potential. 
 
 Potential is the electrical difference between the plates of a 
 battery or the poles of a dynamo or induction coil; it is analo- 
 gous to "head," or "pressure," in hydraulics. 
 
 Electromotive Force. As stated above, whenever a 
 difference of electrical potential exists between two points of a 
 circuit it causes a current to flow, and this difference of potential, 
 or the force to which it gives rise, is called electromotive force, 
 commonly designated by the letters E.M.F. or simply E. 
 
 The terms potential difference and electromotive force are 
 commonly used with the same meaning. 
 
 The unit of electromotive force is the volt, and the head, or 
 pressure, which produces the current is the voltage, high or low 
 voltage meaning that the E.M.F. is measured by a large or 
 small number of volts. In common language the terms pressure, 
 voltage, difference of potential, and electromotive force are 
 synonymous. 
 
 The strength of current in a conductor, corresponding 
 to rate of flow, for air or water is the quantity of electricity which 
 passes any point in the circuit in a second and is measured 
 in amperes. The quantity of electricity conveyed in a given 
 time is the product of the strength of the current by the time 
 it continues. 
 
ELECTRICAL UNITS, DEFINED. 1307 
 
 The quantity of electricity which passes any cross-section 
 of the conductor in one second when the current strength is 
 one ampere is called a coulomb. 
 
 The quantity or amount of electricity in coulombs is equal 
 to the current strength in amperes multiplied by the time in 
 seconds. Thus with a current of 4 amperes flowing for three 
 seconds the quantity delivered is 12 coulombs. 
 
 The coulomb is also called the ampere-second. 
 
 An ampere-hour represents an amount of electricity equal to 
 1 ampere flowing one hour, or 3,600 seconds, and is consequently 
 equal to 3,600 coulombs. 
 
 Load. The term load as used in electricity generally refers 
 to the current that is required either for supplying lamps or 
 motors. The load of a motor is the mechanical energy required 
 of it. 
 
 Resistance is that property of matter in virtue of which 
 bodies oppose or resist the free flow of electricity and is analo- 
 gous to friction or obstructions in water-pipes. 
 
 The specific resistance of a substance is the resistance of a 
 portion of that substance of unit length and cross-section at a 
 standard temperature, and is an inherent property of the sub- 
 stance or material. The specific resistance of any material 
 must first be determined by experiment. 
 
 The resistance of a conductor varies directly as the length, 
 inversely as the cross-sectional area or as the square of the 
 diameter, if the conductor is in the shape of a wire, and depends 
 upon the specific resistance of the material. 
 
 Thus the resistance of a wire 100 ft. long is twice as great 
 as another of the same cross-section and material 50 ft. long; 
 but if the sectional area of the first is twice that of the second, 
 then both wires will have the same resistance. 
 
 If a circuit is made up of several different materials joined 
 in series with each other, the resistance of the circuit is equal 
 o the sum of the resistances of its several parts. 
 
 The unit of resistance is the ohm, which is the resistance of 
 a uniform column of mercury 106.3 centimeters long and 14.4521 
 grams in mass at the temperature of melting ice. 
 
 The resistance of a piece of round copper wire ,001 in. in 
 diameter and 1 ft. long is 10.8 ohms. 
 
 All metals have their resistance increased by a rise of tem- 
 perature. 
 
1308 ELECTRICAL UNITS NOTATION. 
 
 Heating 1 Effects of Current. The passage of electricity 
 through a circuit raises the temperature of the circuit a certain 
 amount. 
 
 Joule's law is as follows: " The heating power of a current is 
 proportional to the product of the square of its strength and 
 the resistance of the circuit through which it passes." 
 
 The heating of a wire carrying a current is made use of for 
 lighting, for electric heaters, for exploding charges of powder, 
 dynamite, etc. The use of fuses for the protection of electric 
 circuits is also based on this principle. 
 
 Electric welding is accomplished by passing a powerful 
 current through two bars pressed together. The heating of 
 the junction fuses the metal and the rods become welded. 
 
 Energy. The unit of mechanical energy is the raising of 
 1 Ib. 1 ft. The unit of electrical work is the energy expended 
 by 1 ampere in 1 second in overcoming the resistance of 1 ohm 
 and is called the joule. The joule may also be denned as the 
 energy expended when 1 coulomb is carried through a distance 
 between which the difference of potential is 1 volt. 
 
 Electrical Power. The unit of mechanical work is the 
 foot-pound per minute. In electrical work the unit is the joule 
 per second = 1 watt. The watt is also sometimes called the 
 volt-ampere. One kilowatt = 1 ,000 watts. 
 
 The kilowatt-hour is a unit of energy and is the energy 
 expended in one hour when the power is 1 kilowatt. 
 
 746 watts = 1 electrical horse-power and is equivalent to 
 1 mechanical horse-power. 
 
 Notation of Electrical Units. The various electrical 
 units are commonly represented by the letters given in the 
 following table, those in parenthesis being sometimes used in- 
 stead of the letter which precedes : 
 Volt, the electro- ) _ T? M "FT Watt, the unit of power, W (P) . 
 
 motive force i 1 kilowatt = 1 ,000 watts = kw. 
 
 Ampere, unit of current or rate Joule, the unit of work, J (W). 
 
 of flow, C (/). H. P. = horse-power. 
 
 Ohm, unit of resistance, R. t = one second.] 
 
 Coulomb, unit of quantity, Q. T= one hour. 
 
 Ampere-hour = 3,600Q = Q'. 
 
 Electrical Equations. Using the above notation the 
 relation between the various units may be expressed by the 
 following equations, which may be transposed in the same 
 manner as any algebraic equation: 
 
ELECTRICAL EQUATIONS. 1309 
 
 QE 
 
 orCEt 
 or C 2 Rt H.P.= 
 
 EH 
 or -FT 
 
 W kw. 
 
 746 .746 
 
 746 
 
 EXAMPLES SHOWING APPLICATIONS OF ABOVE FORMULAS. 
 
 Example 1. What voltage is required to send a current 
 of 22 amperes through a wire having a resistance of 5 ohms? 
 
 Ans. #=22X5=110 volts. 
 
 Example 2. How many amperes will flow through a copper 
 wire having a resistance of 5 ohms, the voltage being 110? 
 
 Ans. C= r-=22 amperes. 
 o 
 
 Example 3. The pressure on a circuit is 110 volts, and it is 
 desired to supply current sufficient for twelve 16-c.p. lamps (6 
 amperes), what should be the resistance of the circuit? 
 
 Ans. R= ^= 18.33 ohms. 
 
 D 
 
 Example 4. The common 110- volt incandescent lamp has a 
 resistance of about 216 ohms. (1) What current is required 
 
 with a pressure of 110 volts? Ans. C=*7r=.51 ampere. 
 
 2i\\) 
 
 (2) How many watts does it consume? Ans. W= CE= .51 
 X 110= 56.1 watts. (3) How many such lamps can be sup- 
 plied by 1 electrical H.P.? Ans. 1 H.P.= 746 watts. If one 
 lamp requires 56.1 watts, the number of lamps that can be 
 
 746 
 supplied by 746 watts = = 13.3 lamps. (4) How many 
 
 OD. -L 
 
 such lamps will 10 kw. suffice? Ans. 10kw.= 10X1,000 watts 
 
 = 10,000 watts. 7rp= 178 lamps. 
 
 Example 5. How many H.P. will 10 kw. furnish? Ans. 
 H.P.= = 13.4 horse-power. 
 
 Dynamo-electric Machines. There are three classes 
 of dynamo-electric machines, viz. : 
 
 1. Generators for generating an electric current. 
 
 2. Motors for converting electrical into mechanical energy. 
 
 3. Rotary converters for changing the voltage of direct cur- 
 rents, or the voltage, phase, or frequency of alternating currents, 
 and also for changing alternating currents to direct or vice 
 versa, and 
 
 3a. Transformers for converting one voltage into a higher or 
 lower voltage. Converters and transformers belong to the same 
 class. 
 
1310 ELECTRICAL CURRENTS. 
 
 A motor is the same machine as a dynamo, but with the 
 nature of its operation reversed. 
 
 Generators are of two general classes, viz., continuous-cur- 
 rent and alternating-current machines ; the former are commonly 
 called dynamos and the latter alternators. 
 
 Generators and motors of all kinds vary in voltage ; current, 
 and speed, according to the purpose for which they are de- 
 
 A transformer consists essentially of two 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" trans- 
 former, -and if it raises it, it is known as a "step-up" trans- 
 former. 
 
 Kinds of Currents Produced. There may be said 
 to be four kinds of electrical currents, viz. : (1) Direct currents, 
 constant-potential, or pressure. (2) Direct currents, constant 
 current. (3) Alternating currents, constant-potential. (4) 
 Alternating currents, constant current. 
 
 Alternating currents may be single-phase, two-phase, three- 
 phase, five-phase, or any other number, depending upon the 
 number of poles and armature winding of the generator. 
 
 A current used for either lighting or power cannot be constant 
 in both pressure and rate. 
 
 Both for lighting and power a constant pressure is more de- 
 sirable than a constant current with varying pressure. 
 
 "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. The advantages of 
 alternating over direct currents are: 1. Greater simplicity of 
 dynamos and motors, no commutators being required; 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." (Kent, p. 1063.) 
 
ELECTRIC LIGHTING. .1311 
 
 Electric Lighting. 
 
 SYSTEMS COMMONLY USED FOR SUPPLYING THE ELECTRICAL 
 ENERGY TO LAMPS. 
 
 Direct-current, Constant-potential Systems. 
 
 a. Two-wire system largely used for incandescent lighting 
 from small plants, as for a large office building or factory; it 
 is usually operated at 110 volts. 
 
 b. Three-wire system used in small towns for the lighting of 
 buildings from the public mains, usually operated at 220 volts. 
 Also in large cities with underground conduit system. 
 
 The ordinary three-wire system requires two dynamos to 
 balance the load.' 
 
 Five-wire and seven-wire systems with high voltage have 
 been used in Europe, but very little in America. 
 
 Direct-current, Constant-current System. This 
 system is largely used for municipal and commercial arc lights, 
 but is rarely used for incandescent lighting. 
 
 Alternating-current, Constant-potential Sys- 
 tems. a. Single-phase System. Current transmitted to build- 
 ing at 1,000 to 2,000 volts and reduced to 50 to 110 volts by a 
 transformer. 
 
 b. Two-phase System. Two or three wires; most used for 
 lighting from public plants, principally because it enables 
 both lights and motors to be operated from the public dynamo. 
 
 c. Three-phase System. Three or four wires; used for same 
 purpose as the two-phase system. 
 
 All three of these systems are used both for incandescent 
 lighting and power from central stations. 
 
 An alternating current may be changed to direct 'current at a 
 sub-station by a rotary converter. 
 
 Alternating-current, Constant-current System, 
 practically if not wholly obsolete. 
 
 Fuses, Cut-outs, and Circuit-breakers. The fuse 
 consists of an easily fusible metal, generally a mixture of lead 
 and bismuth, which is inserted in the circuit. The passage of 
 an excesssive or dangerously large current from any cause melt 
 the fuse and breaks the circuit. The cause of the large currents 
 may then be removed and a new fuse inserted in place of the 
 old one. 
 
1312 ELECTRIC LIGHTING. 
 
 TABLE I. RELATIVE WEIGHT OF COPPER REQUIRED 
 IN DIFFERENT SYSTEMS FOR EQUAL EFFECTIVE 
 VOLTAGE (KENT). 
 
 Direct-current, ordinary two-wire system 1 . 000 
 
 Direct-current, three-wire system, all wires of same size. . .375 
 
 Direct-current, three wires, neutral, one-half size 313 
 
 Alternating-current, single-phase two-wire and two- 
 phase four-wire , 1 . 000 
 
 Two-phase three-wire, voltage between outer and middle 
 
 wire same as in single-phase two-wire 729 
 
 voltage between two outer wires same 1 . 457 
 
 Three-phase three-wire 750 
 
 Three-phase four-wire 333 
 
 Cut-outs and circuit-breakers are 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 cut-out consists of a porcelain base that has 
 suitable terminals for inserting a fuse between the ends of the 
 wire. It must be constructed so that the blowing out of a 
 fuse can do no damage, i.e., set anything on fire, and placed 
 where it can easily be reached to replace the fuse. 
 
 Formerly a piece of fuse wire was used in cut-outs, but the 
 underwriters now require enclosed fuses (Fig. 1) or fusible plugs 
 
 Fig. I 
 
 Enclosed Fuse. 
 
 which screw into a receptacle. Fuse 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 ex- 
 pensive than the link fuse, but are considered safer. A cut- 
 out or circuit-breaker is required at or near the place where 
 the wires enter a building, and every circuit of twelve 16-c.p. 
 lights must be protected by a cut-out. 
 
INCANDESCENT LAMPS. 1313 
 
 Circuit-breakers are automatic switches controlled by an 
 electromagnet and are made in a variety of styles. 
 
 They are more expensive than fusible cut-outs, and are 
 generally used only on switchboards for large installations 
 and where it is desirable to open the circuit instantly on cer- 
 tain loads, which a fuse cannot be depended on to do with any 
 degree of accuracy, owing to both time and surrounding tem- 
 perature factors. 
 
 Also used largely on installations where the variation in 
 load is large and often and the frequent burning out of fuse 
 would become expensive both for renewals and 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 above 
 the range of the eye, as in railway stations, stores, etc. 
 
 Incandescent lamps as commonly made consist of a glass 
 bulb containing a simple carbon conductor the ends of which 
 are connected to the source of the electric current. When 
 the current flows through the carbon filament it heats it to 
 such a degree that it becomes incandescent; hence the name 
 of the lamp. 
 
 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 carbon 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 per cent, lower reducing the candle- 
 power about one half. 
 
 The voltage most commonly used for 16-c.p. lamps is from 
 104 to 110. 
 
 Lamps are also made for voltages of 45 to 250, and 1-c.p. 
 lamps, for illuminating signs or decorative purposes, are made 
 for 12.5 and 15 volts, these lamps being commonly used in 
 series, eight lamps on a 110-volt circuit. Two 4-c.p. lamps, 
 52 volts, are also often used in series on a 110-volt circuit. 
 
 Candle-pouer. Incandescent lamps of 110 volts are commonly 
 made 4, 8, 10, 12, 16, 24, and 32 candle-power. Table II 
 
1314 
 
 ELECTRIC LIGHTING, 
 
 shows the standard candle-powers, voltages, and current re- 
 quired for incandescent lamps. 
 
 For data pertaining to the Meridian and Nernst lamps, see 
 pp. 1293, 1299. 
 
 TABLE II. INCANDESCENT-LAMP DATA.* 
 
 Volts. 
 
 Candle-power. 
 
 Current, 
 Amperes. 
 
 Watts 
 per Lamp. 
 
 52 
 
 4 
 
 .39 
 
 20 
 
 
 
 8 
 
 .61 
 
 32 
 
 t 
 
 10 
 
 .67 
 
 35 
 
 i 
 
 16 
 
 1.08 
 
 56 
 
 t 
 
 20 
 
 1.34 
 
 70 
 
 t 
 
 24 
 
 1.62 
 
 84 
 
 t 
 
 32 
 
 2.15 
 
 112 
 
 104 
 
 10 
 
 .34 
 
 35 
 
 a 
 
 16 
 
 .54 
 
 56 
 
 n 
 
 20 
 
 .67 
 
 70 
 
 tt 
 
 24 
 
 .81 
 
 84 
 
 ({ 
 
 32 
 
 1.08 
 
 112 
 
 110 
 
 8 
 
 .27 
 
 30 
 
 tt 
 
 10 
 
 .32 
 
 35 
 
 u 
 
 16 
 
 .51 
 
 56 
 
 { 
 
 20 
 
 .64 
 
 70 
 
 ( 
 
 24 
 
 .76 
 
 84 
 
 t 
 
 32 
 
 1.02 
 
 112 
 
 I 
 
 50 
 
 1.59 
 
 175 
 
 t 
 
 100 
 
 3.18 
 
 350 
 
 ( 
 
 150 
 
 4.77 
 
 525 
 
 220 
 
 16 
 
 .291 
 
 64 
 
 (i 
 
 32 
 
 .582 
 
 128 
 
 * H. C. Gushing, Jr., in Practical Lessons in Electricity. 
 
 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. 
 
 " Current for arc lighting is furnished either on the series 
 constant-current or on the parallel constant-potential system. 
 In the latter the voltage of the circuit is usually 110. In cur- 
 
ELECTRIC-LIGHT WIRING. 1315 
 
 rents with higher voltages lamps are used in series, for instance 
 5 to 10 with a 500-volt circuit. 
 
 "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 constant-current arcs. The most satis- 
 factory light is given by 45 to 47 volts. 
 
 "Alternating-current open arcs usually take about 15 amperes 
 at 30 to 35 volts, but are not much used. With the same 
 energy and carbons, the mean spherical candle-power is about 
 one half that of the continuous-current open arc. 
 
 "Direct-current enclosed arcs consume about 5 amperes at 
 80 volts, or 400 watts. Alternating-current enclosed arcs 
 usually take a current of 6 amperes at 70 or 75 volts." * 
 
 Arc lamps generally require a resistance in series with the 
 arc in order to regulate properly. This resistance is usually 
 placed within the structure of the lamp, and is adjustable so 
 that a single lamp can be made to burn well on any circuit 
 from 105 to 120 volts. 
 
 Methods of Connecting Lamps. 
 
 There are three ways of connecting lamps to the distribution 
 wires, viz.: (1) in series, (2) in parallel, and (3) in parallel 
 series. 
 
 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 lamps shown by Fig. 2 are in series. When conductors 
 are arranged in series the total resistance of the circuit is the 
 
 Fig. 2 
 
 Lamps in Series. 
 
 sum of the resistances of the several parts, and the pressure 
 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 4X52=208 volts. Arc lamps for street 
 
 * Kent, p. 1044. 
 
1316 
 
 ELECTRIC-LIGHT WIRING. 
 
 Distributing 
 -Wires- 
 
 lighting are often connected in series, but incandescent lamps 
 are almost never connected in series except for decorative 
 purposes and in electric signs. Where lamps of low voltage 
 are used on 110- volt systems it is necessary to connect them 
 in series. The underwriters do not approve connecting in- 
 candescent lamps in series. The series system requires a 
 constant current with varying pressure, 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 lamps. 
 
 Lamps in Parallel. This is the common method of con- 
 necting incandescent lamps. It is illustrated 
 by Fig. 3. With this system the pressure in 
 each lamp is the same as in the distributing 
 lines, and any lamp may be turned on or off 
 [ without affecting the other lamps. For this 
 system the pressure or voltage must be kept 
 constant, while the current or quantity of 
 electricity flowing in the lines will depend upon 
 the number of lamps that are burning. Thus 
 with twelve 16-c.p. lamps of 110 voltage on a 
 parallel circuit, each lamp requiring .51 ampere 
 (see Table II), when all the lamps are burning, 
 a current of 6.12 amperes, or 673. 2* watts, will 
 be required, but with but one lamp burning, a 
 current of only .51 ampere will flow. The 
 voltage, however, must be the same for one 
 lamp as for the twelve. For lamps in parallel, 
 therefore, a constant-potential system is required. 
 The current for lamps in 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 (S) as for the lower 
 lamp (Fig. 3). 
 
 Lamps in Parallel Series. This method is a combination 
 of the other two. Parallel lines are run as in the parallel 
 system, but two or more lamps are connected in series between 
 them as in Figs. 4 and 5. This method of connecting lamps 
 is used principally in places where it is desired to operate lamps 
 on a power system. Fig. 4 shows series of five lamps operated 
 on a 500- volt system, and Fig. 5 series of two lamps on a 110- 
 
 Fig. 3 
 
 
 * Watts being equal to amperes times voltage. 
 
ELECTRIC-LIGHT WIRING. 
 
 1317 
 
 or 220- volt system using 52- or 110- volt lamps respectively. 
 Any number of series may be connected across the mains, each 
 series being independent of the others. But in each series if 
 one light burns out, the others will go out, and one lamp cannot 
 
 ^220-VoltB 
 
 Fig. 4 Fig. 5 
 
 Lamps in Parallel Series. 
 
 be used without using the others. 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. 
 
 [Note. Although the lamps in Figs. 3, 4, and 5 are connected 
 directly across the wires, this is not necessary in practice so 
 long as the lamp wires are connected to the distributing wires 
 or mains. Thus five lamps in series on a 500-volt circuit may 
 be connected as in Fig. 6.] 
 
 fo\ 
 
 L k-ioo-Vr*-ioo-V-^l 
 ' ' ' 
 
 L 
 
 
 Fig. 6 
 
 The Edison Three-wire System. Figs. 3, 4, and 5 
 are examples of the two-wire system of distribution, which is 
 the system recommended for average sized office buildings, 
 apartment houses, theatres, and stores. 
 
 Where power is to be taken from the same plant and is not 
 
1318 ELECTRIC-LIGHT WIRING. 
 
 too great a portion of the capacity of the installation this sys- 
 tem may also be used, but separate mains should under all 
 circumstances be run for the motors, as the variation in. load 
 and consequently the current demand on the mains would 
 cause a very appreciable fluctuation in candle-power of the 
 lamps if on the same mains with the motors. 
 
 Where comparatively long lines are required and the amount 
 of current to be supplied is large the three-wire system is used. 
 
 By this system we can supply two voltages or pressures, 
 110 and 220 volts being those generally adopted, the 110-volt 
 circuit supplying the arc and incandescent lights and the 220- 
 volt circuit the motors. Fig. 7 shows how the wires are run 
 and connections made. 
 
 I*. 
 
 Fig. 7 
 
 The pressure between the two outside wires is the full voltage 
 transmitted from the dynamos or transformer, usually 220 
 volts for interior wiring. The current in these two wires flows 
 in opposite directions. The middle wire, called the neutral 
 wire, forms one side of two circuits, the current from one circuit 
 tending to flow in one direction and that from the other circuit 
 in the opposite 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 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 build- 
 
THREE-WIRE SYSTEM OF WIRING. 
 
 1319 
 
 ings carrying lamps only, the neutral wire should be of the 
 same size as the outer wires. 
 
 From Table I it will be seen that the three-wire system effects 
 a considerable saving in copper, amounting to fully 60 per cent, 
 of the ordinary two-wire 110-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 on the two-wire 
 system as in Fig. 8. 
 
 P v no v 
 
 D. denotes Dynamo 
 6.O. " Cut-out 
 T. " Lamp 
 M. " Motor, 
 
 
 
 
 
 
 
 
 
 
 
 li 6 - 220V - ri 1 
 
 -- 
 
 L 
 
 W 
 L 
 
 Fig. 8 
 
 Example of Three -wire System of Wiring. 
 
 When using the three-wire system for lighting only, the three 
 wires are usually run no farther within the building than to 
 the centres of distribution, and from these centres two wires 
 are run for each circuit, 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 current 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 incandescent-lighting systems 
 should be wound for 220 volts. 
 
1320 
 
 ELECTRIC-LIGHT WIRING. 
 
 WIRE CALCULATIONS. 
 
 \Vire Gnu pros. As the diameter of wires are ordinarily 
 designated by the numbefS of a wire gauce, and as there are 
 a number of wire gauges in common knowledge of 
 
 those used for copper wire is necessary. 
 
 The Brow* A Sharp, or B. & S.. srauge is almost exclusively 
 used in America in connection with electrical work, except 
 
 To Cut-ont Cabinet 
 .Second Story 
 
 Rg.9 
 
 where the size of the wire is designated in circular mils The 
 sizes of wire given by this gauge range from Xo. 0000 (.46 in.) 
 to Xo. 40 (.0031 in.), but Xo. 14 is the smallest size permitted 
 for interior wiring. The Xo. 10 wire has a diameter of very 
 nearly T ^ of an inch, and its resistance per 1,000 ft. is very nearly 
 1 ohm. For any given number of this gauge a wire three 
 numbers higher has very nearly half the cross-section, and one 
 three numbers lower has twice the cross-section; thus a Xo. 13 
 wire has very nearly one half the cross-section of a Xo. 10 wire, 
 and a Xo 7 has twice the axes-section of a Xo. 10, or four 
 times that of a Xo. 13. 
 
 The Circular-mil TV ire Gauge. This gauge was 
 designed by the engineering department of the Edisw Company 
 
WIRE CALCULATIONS. 
 
 lly for the designation of coppe. wire for electrical work, 
 and Lb now in universal ase in t:. y. In practice the 
 
 B. & S. gauge is commonly used for designating wires up 
 to No. or No. 00, and all wires above that size are designated 
 by circular mils (c.m.). 
 
 The size of wire required is often determined hi circular mils 
 and designated by the corresponding B. & S. gauge number, 
 which is readily done by means of Table III. 
 
 ->per wire is sold by the pound if bare or of the numerous 
 rier-proof varieties, but rubber-covered wire is sold by the 
 1,000 ft 
 
 The basis of the circular-mil gauge is the area of a wire 
 of an inch in diameter (1 mil=.001 in.), consequently 
 1 c.m. = .0000007854 sq. in. As the area of circles is directly 
 as the square of their diameter, it follows that the sectional 
 area of a wire 2 mils in diameter=4 c.m., of a wire 10 mils hi 
 diameter 100 c.m., and so on. 
 
 When wires are designated by circular mils, the sectional 
 area and not the diameter is generally given, c.m. always re- 
 ferring to sectional area. 
 
 The diameter of a wire in mils or in thousands of an inch= 
 square root of its area hi circular mils. 
 
 Thus the diameter of a wire of 3,600 c m.= 60 mils, or .060 in. 
 
 The diameter of a wire 14,400 c.m.= 120 mils= .12 in. 
 
 The area of a wire .162 in. in diameter, or 162 mils,= 162* 
 = 26,244. 
 
 To reduce circular mils to square inches multiply by 7,854 and 
 point off ten places of decimals.^ Thus, 5,000 c.m. = 7,854 
 X 5,000= .0039270000 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 6. What is the sectional area in circular mils of a 
 bar in. X \ in.? Ans. J in.= .125 in.= 125 mils, i in.= .250 in. 
 = 250 mils; 125X250X1.273=39,781.25 c.m. 
 
 The weight of bare copper wire per 1,000 ft.= c.m. X .003027 Ibs. 
 Thus the weight of 1,000 ft. of copper, wire having a sectional 
 area of 2,000 c.m.= .003027X2,000=6.054000 Ibs. 
 
 Table IV gives the dimensions and weights of bare copper 
 wire from No. ] 8 to No. 4-0 B. & S. gauge. 
 
 Carrying Capacity of Copper Wire. The safe cany- 
 ing: capacity of copper wire for interior wiring is practically 
 
1322 ELECTRIC-LIGHT WIRING. 
 
 fixed by the underwriters, and if the capacity limits given 
 by 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. 
 
 The lower ampere 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; i.e., the rubber covering makes necessary 
 a lower rate of heat development than is required for safety 
 from fire. 
 
 No smaller iho.n No. 14 wire may be used under insurance 
 rules, except that No. 16 may be used for flexible cord and 
 No. 18 for fixture wiring. Nos. 13, 11, 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 
 moulding 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, 110 volts, at the extreme end of the circuit it 
 will be somewhat less, depending upon the length and sectional 
 area of the wire. 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. 
 
 Mains and distributing wires may be capable of carrying 
 the number of amperes in accordance with Table III, and yet 
 cause a drop of potential of such magnitude that the most distant 
 lamps will burn only at a dull red. 
 
 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 per cent, drop, but where the current is 
 produced cheaply, as by a dynamo on the premises, a 3 per cent. 
 or 5 per cent, drop may be allowed. Not more than a 5 per cent, 
 drop on short distances should be permitted, even where very 
 cheap work is desired. 
 
WIRE CALCULATIONS. 
 
 1323 
 
 The drop in volts (not in percentage) = current in line X re- 
 sistance of line, or drop in volts = amperes X ohms. 
 
 Example. What will be the drop in a circuit of No. 14 copper 
 wire 280 ft. long, supplying nine lamps, requiring 4.5 amperes? 
 Ans. From Table V we find that the resistance of No. 14 wire 
 is 2.527 ohms per 1,000 ft., hence for 280 ft. it will be 2.527 X 
 .280=. 7075 ohm, and drop in volts=4.5X. 7075= 3.1837 volts. 
 The voltage for this current (.5 ampere per lamp) will be about 
 
 o i GQ'T 
 
 110, consequently the percentage of drop=^ =2 T 9 IF per 
 
 cent., nearly, 
 is 2.2 volts. 
 
 110 
 
 Two per cent, drop on a pressure of 110 volts 
 
 Centre of Distribution. The meaning of this term may 
 best be illustrated by a'n example. Let Fig. 10 represent a circuit 
 
 --40- 
 
 ~~L Jfc^HrA 
 ' -^ \ v 
 
 _^ i- 
 
 ~^- 
 L 
 
 plains; 
 
 Fig. 10 
 
 carrying six lamps, the first lamp being 40 ft. from the cut-out, or 
 source of supply. The whole of the current must be transmitted 
 through this! 40 ft., but from that point it will gradually fall 
 off, and the average current will only extend to the point CD, 
 half way between the extreme lamps. Or, in other words, the 
 centre of distribution is analogous to the centre of gravity of 
 the lamps on the circuit. 
 
 The centre of distribution determines the length of the line 
 in the rules for finding the necessary size of wire. 
 
 Distributing centres are the points in a building where 
 the cut-out cabinets are located and the branch circuits taken 
 off. 
 
 Calculations for Size of Wire for Incandescent 
 Lighting. The sizes of wires for interior lighting are or should 
 
 Ko dlw.va rlpfprrmnprl nn a. basis nf a. fivfiH rlrnn nf r>nt,fnt,ml 
 
1324 ELECTRIC-LIGHT WIRING. 
 
 usually 2 volts on the distributing circuit and 2 to 3 volts on 
 the feeders or mains.* The size of wire may be determined 
 either in terms of its sectional area in circular mils or in terms 
 of its resistance in ohms per 1,000 ft. 
 
 Knowing the sectional area in circular mils the corresponding 
 gauge number may be found from Table III, or if we have the 
 resistance in ohms per 1,000 ft., we may find the corresponding 
 gauge number from Table IV. 
 
 The formula for circular mils is as follows: 
 
 ., . 
 
 Circular mils= .... (A) 
 
 The formula for resistance per 1,000 ft. of wire is 
 
 l,000i; 
 
 In both these formulas d= distance in feet, one way, from 
 cut-out to centre of distribution (see p. 1323) for distributing 
 wires, or from entrance cut-out or source of current to dis- 
 tributing centre for main lines or feeders. c= current in am- 
 peres per lamp (Table II). N= number of lamps supplied. 
 i>= 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 of 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 (see top of p. 1319). 
 
 Example 7. The distance from the cut-out to centre of 
 distribution of a circuit carrying twelve 16-c.p. 110-volt lamps 
 is 50 ft. What size of wire should be used for a drop of 2 volts? 
 Ans. d=50; N=12; c (table II)=.51, and v=2. 
 
 By formula (A), 
 
 ., 10.8X100X12X.51 OOAC 
 Circular mils= - 2 - = 3,305. - 
 
 From Table III, we see that the next larger size of wire 
 is 4,107 c.m., equivalent to a No. 14 wire. 
 By formula (#), 
 
 Resistance per 1,000 ft. 
 
 * Many municipal lighting companies require that there shall be no 
 
 r\-ro fVan 9 ruvr rort. fnfal rJrrr ir> tViA wirinor for int.prinr litrht.infr- 
 
WIRE CALCULATIONS. 1325 
 
 which we see from Table IV is about the resistance of a No. 15 
 wire, but as No. 14 is the smallest wire permitted we must use 
 that size. 
 
 Example 8. The distance from the entrance cut-out (where 
 the wires enter the building) to the main distributing centre 
 of a building is 100 ft. The total number of 16-c.p. 110-volt 
 lamps supplied is ninety. What size mains should be used on 
 the two-wire system with a drop of two volts? 
 
 Ans. d=100; JV=90; c=.51j v=2. 
 
 By formula (A), 
 
 ., 10.8X200X90X.51 
 Circular mils= ^ * =49,572. 
 
 Looking in Table III, we see that we must use No. 3 wire. 
 If we allow a drop of 3 volts the sectional area required will be 
 33,048 c.m., which requires a No. 5 wire. The weight per 
 1,000 ft. of No. 3 weather-proof wire (Table IV) is 200 Ibs. and 
 of No. 5 wire 125 Ibs., consequently the saving in weight of wire 
 by using a drop of 3 volts instead of 2 is 75 Ibs., or 37 J per cent, 
 of 200, and as wire is sold by the pound, the saving in cost with 
 a 3 per cent, drop ranges from 30 to 40 per cent, of a 2 per cent, 
 drop. 
 
 Example 9. With the same conditions as given in Ex. 8, 
 what size of wire will be required for the ordinary three-wire 
 system with 2 per cent, drop? Ans. In this case we use one 
 half of N, or 45, and 2v instead of v; then 
 
 10.8X200X45X.51 
 Circular mils= -r -= 12,392, 
 
 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, we have two No. 3 wires weighing 400 Ibs. 
 per 1,000 ft., and with the three-wire system three No. 8 wires 
 weighing 207 Ibs., hence the saving in cost is nearly 50 per cent., 
 and if No. 9 wire were obtainable the saving would be 55 per cent. 
 
 With a drop of 3 per cent. (3.3 volts) the circular mils re- 
 quired for the three-wire system^ 1Q - 8 >< 20 ^ 45 X- 51 = 7> 5i 0> 
 
 requiring No. 10 wires. 
 
 The current in amperes in the two-wire system= A r Xc=45.9, 
 and in the three-wire system JA r Xc=22.95. 
 
 Referring to Table III, we see that the smallest size of 
 weather-proof wire permitted for 45.9 amperes is No. 8; con- 
 sequently we could use No. 8 wire with the two-wire system 
 
ELECTRIC-LIGHT WIRING. 
 
 and comply with the underwriters 7 rules, but the drop in poten- 
 tial would be 45.9 X. 2 X. 6285 (amperes X resistance of line) 
 = 5.77 volts; or over 5 per cent. 
 
 TABLE III. CARRYING CAPACITY OF WIRES AND 
 
 CABLES. 
 
 For interior conductors, all voltages. 
 (From the National Electrical Code.) 
 
 Wires, 
 No. B. & S. 
 Gauge. 
 
 Circular 
 Mils. 
 
 Capacity in Amperes. 
 
 Rubber- 
 covered. 
 
 Weather- 
 proof. 
 
 18 
 
 1,624 
 
 3 
 
 5 
 
 16 
 
 2,583 
 
 6 
 
 8 
 
 14 
 
 4,107 
 
 12 
 
 16 
 
 12 
 
 6,530 
 
 17 
 
 23 
 
 10 
 
 10,380 
 
 24 
 
 32 
 
 8 
 
 16,510 
 
 33 
 
 46 
 
 6 
 
 26,250 
 
 46 
 
 65 
 
 5 
 
 33,100 
 
 54 
 
 77 
 
 4 
 
 41,740 
 
 65 
 
 92 
 
 3 
 
 52,630 
 
 76 
 
 110 
 
 2 
 
 66,370 
 
 90 
 
 131 
 
 1 
 
 83,690 
 
 107 
 
 156 
 
 
 
 105,500 
 
 127 
 
 185 
 
 00 
 
 133,100 
 
 150 
 
 220 
 
 000 
 
 167,800 
 
 177 
 
 262 
 
 0000 
 
 211,600 
 
 210 
 
 312 
 
 Cables 
 
 200,000 
 
 200 
 
 300 
 
 " 
 
 300,000 
 
 270 
 
 400 
 
 ft 
 
 400,000 
 
 330 
 
 500 
 
 (i 
 
 500,000 
 
 390 
 
 590 
 
 <t 
 
 600,000 
 
 450 
 
 680 
 
 it 
 
 700,000 
 
 500 
 
 760 
 
 n 
 
 800,000 
 
 550 
 
 840 
 
 (t 
 
 900,000 
 
 600 
 
 920 
 
 ti 
 
 1,000,000 
 
 650 
 
 1,000 
 
 tt 
 
 1,100,000 
 
 690 
 
 1,080 
 
 n 
 
 1,200,000 
 
 730 
 
 1,150 
 
 < 
 
 1,300,000 
 
 770 
 
 1,220 
 
 n 
 
 1,400,000 
 
 810 
 
 1,290 
 
 ft 
 
 1,500,000 
 
 850 
 
 1,360 
 
 ( 
 
 1,600,000 
 
 890 
 
 1,430 
 
 t 
 
 1,700,000 
 
 930 
 
 1,190 
 
 t 
 
 1,800,000 
 
 970 
 
 1,550 
 
 t 
 
 1,900,000 
 
 1,010 
 
 1,610 
 
 t 
 
 2,000,000 
 
 1,050 
 
 1,670 
 
 A current of one ampere will supply two 16-c.p. lamps. 
 
WIRE CALCULATIONS. 
 
 1327 
 
 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| per cent, of the lamp voltage; Except 
 on very short lines a 2 per cent, drop will always demand larger 
 wires than required by the underwriters, and this is also usually 
 true of a 3 per cent. drop. 
 
 TABLE IV. DIMENSIONS, WEIGHT, AND RESISTANCE 
 OF COPPER WIRE. 
 
 Gauge 
 
 
 
 
 Weight ir 
 1,000 
 
 i Lbs. per 
 Feet. 
 
 Resistance 
 
 No 
 B. &S. 
 
 in Mils. 
 
 Cir. Mils. 
 
 Sq. Ins. 
 
 Bare 
 Wire. 
 
 Weather- 
 proof * 
 Wire. 
 
 per 
 1,000 Ft. 
 
 0000 
 000 
 00 
 
 
 1 
 
 2 
 3 
 
 4 
 5 
 
 6 
 
 7 
 8 
 9 
 
 460 
 410 
 365 
 325 
 289 
 258 
 229 
 204 
 182 
 162 
 144 
 128 
 114 
 
 211,600 
 167,800 
 133,100 
 105,500 
 83,690 
 66,370 
 52,630 
 41 ,740 
 33,100 
 26,250 
 20,820 
 16,510 
 13,090 
 
 .166190 
 .131790 
 .104520 
 .082887 
 .065732 
 .052128 
 .041339 
 .032784 
 .025999 
 .020518 
 .016351 
 012967 
 .010283 
 
 640.73 
 508.12 
 402.97 
 319.74 
 253.43 
 200.98 
 159.38 
 126.40 
 100.23 
 79.49 
 63.03 
 49.99 
 39.65 
 
 800 
 666 
 500 
 ' 363 
 313 
 250 
 200 
 144 
 125 
 105 
 87 
 69 
 
 .04904 
 .06184 
 .07797 
 .09827 
 .12398 
 .15633 
 .19714 
 .24858 
 .31346 
 .39528 
 .49845 
 .62849 
 79242 
 
 10 
 11 
 
 102 
 91 
 
 10,380 
 ,234 
 
 .008155 
 .006466 
 
 31.44 
 24 93 
 
 50 
 
 .99948 
 1 2602 
 
 12 
 13 
 14 
 15 
 
 81 
 72 
 64 
 57 
 
 6,530 
 5,178 
 4,107 
 3,257 
 
 .005129 
 .004067 
 .003225 
 
 .002558 
 
 19.77 
 15.68 
 12.44 
 9.86 
 
 31 
 "22" 
 
 1.5890 
 2.0037 
 2.5266 
 3 1860 
 
 16 
 17 
 
 18 
 
 51 
 45 
 40 
 
 2,583 
 2,048 
 1,624 
 
 .002028 
 .001608 
 .001275 
 
 7.82 
 6.20 
 4.92 
 
 14 
 
 "ii 
 
 4.0176 
 5.0660 
 6.3880 
 
 * Approximate weight of weather-proof line wire for outdoor work is 
 10 per cent, less than here given. 
 
 t Values given by H. C. Gushing, Jr., in Practical Lessons in Elec- 
 tricity. The author has been unable to find any two tables that give 
 exactly the same resistance. 
 
 To find the smallest size of wire that will comply with the 
 underwriters' rules it is only necessary to compute the total 
 current in amperes, and from Table III select the wire having 
 
1328 
 
 ELECTRIC-LIGHT WIRING. 
 
 a capacity equal to or next above the required number of 
 amperes. Table VI shows at a glance the maximum number of 
 16 c.p. 110 volt lamps permitted by the National Code. 
 
 TABLE V. MAXIMUM LENGTH OF LINE FOR GIVEN 
 NUMBER OF LAMPS THAT CAN BE USED WITH A 
 2 PER CENT. DROP. TWO-WIRE SYSTEM. 
 
 Based on J^ ampere per lamp. One 32-c.p. lamp = two 16-c.p. lamps 
 Two 24-c.p. lamps = three 16-c.p. lamps. 
 
 No. of 
 Wire, 
 B. &S. 
 Gauge. 
 
 Number of 16-c.p. 110- volt Lamps. 
 
 4 
 
 6 
 
 8 
 
 10 
 
 11 
 
 12 
 
 16 
 
 20 
 
 24 
 
 Maximum Length of Line, One Side, in Feet. 
 
 14 
 12 
 10 
 8 
 6 
 
 12 
 10 
 
 8 
 6 
 5 
 4 i 
 3 
 2 
 1 
 
 209 
 
 139 
 221 
 
 104 
 166 
 264 
 
 83 
 133 
 211 
 326 
 
 76 
 120 
 192 
 297 
 
 70 
 110 
 176 
 
 272 
 440 
 
 52 
 83 
 132 
 204 
 334 
 
 42 
 66 
 105 
 163 
 
 267 
 
 35 
 55 
 
 88 
 136 
 220 
 
 
 
 
 
 
 
 
 
 
 
 
 Number of 16-c.p. 110-volt Lamps. 
 
 30 
 
 36 
 
 40 
 
 50 
 
 60 
 
 70 
 
 80 
 
 90 
 
 100 
 
 Maximum Length of Line, One Side, in Feet. 
 
 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 num- 
 ber of lamps on each side length of wire may be increased four times. 
 
 Formulas (A) and (B) may also be used for motor wiring, if 
 the required current in amperes is known, by substituting the 
 given number of amperes for NXc. 
 
 Example 10. What size of wires should be run to a motor 
 that requires 30 amperes and 220 volts and is situated 200 ft. 
 
EXAMPLE OF LIGHT WIRING. 
 
 1329 
 
 from the distributing pole, the drop in volts not to exceed 2 per 
 cent.? Ans. Using formula (A), and substituting 30 for NXc, 
 we have 
 
 . , ., j!0.8X400X30 Oft/lr , 
 Circular mils = TT"^ =29,454, 
 
 which requires a No. 5 wire. 
 
 The current either in watts or 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, multiply by 1,000 and then divide by the voltage. 
 
 TABLE VI. MAXIMUM CARRYING CAPACITY OF WIRES 
 IN TERMS OF 1,6-C.P. 110-VOLT LAMPS, HOWEVER 
 SHORT THE WIRES MAY BE. 
 
 Based on ^ ampere per lamp. 
 
 No. of 
 
 Number of Lamps. 
 
 No. of 
 
 Number of Lamps. 
 
 Wire, 
 
 
 Wire, 
 
 
 B. &S. 
 
 
 
 B. &S. 
 
 
 
 Gauge. 
 
 Rubber- 
 
 Weather- 
 
 Gauge. 
 
 Rubber- 
 
 Weather- 
 
 
 covered. 
 
 proof. 
 
 
 covered. 
 
 proof. 
 
 14 
 
 24 
 
 32 
 
 4 
 
 130 
 
 184 
 
 12 
 
 34 
 
 46 
 
 3 
 
 152 
 
 220 
 
 10 
 
 48 
 
 64 
 
 2 
 
 180 
 
 262 
 
 8 
 
 66 
 
 92 
 
 1 
 
 214 
 
 312 
 
 6 
 
 92 
 
 130 
 
 
 
 254 
 
 370 
 
 5 
 
 108 
 
 154 
 
 00 
 
 300 
 
 440 
 
 Wiring Tables. Several forms of wiring tables are pub- 
 lished in various books on electricity which are very useful 
 to electricians. For ordinary interior wiring for 110- volt 
 16-c.p. lamps, Table V, computed by the author, 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 Centre of Distribution (p. 1323). 
 
 Simple Example of Wiring. To show the method of 
 wiring an ordinary building for incandescent lighting we will 
 take a two-story building having a floor plan as shown by 
 Fig. 11. The light outlets are all on the ceiling and are indi- 
 cated by a small circle and cross. The numbers 1 and 2 beside 
 the outlets denote the number of lamps to the outlet. 
 
 Current to be obtained from the wires of the public lighting 
 
 rnmTmnv. wliirl"i rrrv o. rvnrrpnt. nf 990 vnlf.s TVip fppH-wirps 
 
1330 
 
 KLECT RIG-LIGHT WIRING. 
 
 for the building should enter through the alley wall at about 
 the level of the second floor and should drop in the partition 
 
 ALLEY 
 
 f 
 
 D 
 
 --X 
 
 i 
 
 STKEET FRONT 
 SECOND FLOOR PLAN 
 Fig. II 
 
 Example of Wiring. 
 
 just inside the wall for the main fuse block and switch (M.S.), 
 
EXAMPLE OF LIGHT WIRING. 
 
 1331 
 
 should be located near the centre of the building, say at DC, 
 and there should be a cabinet in each story. From this cabi- 
 net we will run four circuits 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 of each of four rooms to control the 
 lights in those rooms. All of the lights on circuit C should be 
 controlled by a switch in the cabinet. 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 con- 
 trolled by knife switches in the cabinet, as shown by Fig. 12; 
 but this is not absolutely necessary. 
 
 fl fl 
 
 F.F, FUSE PLUGS 
 
 8.8, KNIFE SWITCHES 
 
 Fig. 12 
 
 Size of Wires. The centre of distribution of circuits A, C, 
 and D would be at about the points marked X. 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. The number of lamps and 
 length of wire, for each circuit are as follows: 
 Circuit A, 8 lights, 41 ft. one way to centre of distribution. 
 Circuit B, 12 lights, 52 ft. " " " " " 
 Circuit C, 4 lights, 37 ft. " " " " " " 
 
 Circuit D, 12 lights, 59 ft. " " '< M " " 
 
 Total number of lamps. 36. 
 
J632 ELECTRIC-LIGHT WIRING. 
 
 From Table V we see that the maximum length of line one 
 way for No. 14 wire carrying twelve lamps is 70 ft. , consequently 
 all of the lamp circuits can be No. 14 wire, which is the smallest 
 size permitted. 
 
 Feed-wires. These should be run on the three-wire system. 
 Allowing for seventy-two lamps in first and second stories 
 and eight in basement, the feed-wires must be capable of supply- 
 ing eighty lamps. The distance from outside the building 
 to distribution cabinet is about 72 ft., allowing for three drops. 
 
 Using formula (.4), and assuming that there will be forty 
 lamps on each side of the three-wire system, and doubling the 
 drop in volts, we have 
 
 10.8X144X40X.51 
 
 Circular mils= .- = 7,932 c.m., 
 
 4 
 
 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 
 we could use No. 12 wires. 
 
 For almost all buildings lighted from a central station the 
 lamp circuits will not usually require larger than No. 14 wire, 
 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 other than at the fixture. 
 
 In the better class of buildings most 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 (7, 
 Fig. 10, also by Fig. 3; one side of the loop must be connected 
 with one of the distributing 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, theatres, 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 off all of the lights. 
 
 As the underwriters do not permit more than twelve 16-c.p. 
 lamps on one circuit, not more than twelve lamps can be con- 
 trolled by one switch, except where the switch is placed on the 
 mains. 
 
SWITCHES AND SWITCH LOOPS. 
 
 1333 
 
 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 off 
 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 controlled 
 at will from either the first, second, 
 or third stories. Fig. 13 shows one 
 method of wiring for controlling a 
 hall light from first and second stories. 
 With the switches in the position 
 shown the circuit Is broken, 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.* 
 
 Fig. 13 
 
 Kinds of Switches. For controlling lamps from one point 
 three kinds of switches are used, viz., snap/ push-button, and 
 knife switches. When less than eight lamps are controlled by 
 the switch, a push-button switch is commonly used where a 
 neat appearance is desirable, 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 d.p. (double pole) knife 
 switch (Fig. 14) 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 d.p. knife switch necessarily opens both sides, and when 
 used on a three-wire system it must have three poles. 
 
 Double-pole snap and push-button switches are seldom used 
 for less than twelve lamps. 
 
 * For method of wiring for controlling lamps from three or more points 
 see p. 41, 27, vol. 13. International Library of Technology. 
 
 Fig. 14 
 
 Common Knife Switch. 
 
1334 ELECTRIC-LIGHT WIRING. 
 
 Duplex switches (sometimes called three-point switches) are 
 usually 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 fireproof buildings all of the lighting 
 wires are generally run in a system of conduits. 
 
 Kinds of Conduits. There are five kinds of interior conduits 
 now in common use, viz. : 
 
 1. Brass-covered conduit, which is made of paper wound to 
 form a tube, coated with tar on the inside, and covered with a 
 thin shell of brass on the outside. 
 
 2. Circular-loom tube, a flexible woven tube treated with 
 insulating material that makes it hold its shape. Although it . 
 has no metal covering, it is stronger than the brass-covered 
 conduit and is more convenient to use. 
 
 3. Unlined iron pipe. 
 
 4. Lined iron pipe. 
 
 5. Flexible armored conduit, made of metal ribbon wound 
 spirally. 
 
 For regular conduit systems only iron piping of the same 
 thickness as ordinary gas piping is approved by the under- 
 writers. 
 
 The circular-loom and flexible-steel conduit may be used 
 in dry places and for outlets through plaster if it extends back 
 to the nearest porcelain knob holding the wire which the con- 
 duit Covers. 
 
 The brass-covered conduit was at one time extensively 
 used, but its use is now confined principally to protecting 
 exposed risers on dry walls. 
 
 Unlined iron pipe must be galvanized, coated, or enamelled 
 on the inside; lined iron pipe must have an insulating lining 
 gV in. thick firmly secured to the pipe. : 
 
 Iron conduit whether lined or unlined is installed in the 
 same manner as a good job of gas fitting, except that for con- 
 duits the pipe may be bent to a curve and no elbow can 
 be used having less than 3J-iii. radius for the inner ed;e. 
 Wherever branches are taken off, junction boxes must be pro- 
 vided, and every outlet must have an approved outlet box or 
 plate. 
 
NATIONAL ELECTRICAL CODE. 1335 
 
 ^N atioiial Electrical Code. The National Board of Fire 
 Underwriters, in conjunction with committees from the national 
 associations of architects, 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. 
 
 The National Board of Underwriters also publish, 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 manufacturer. 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 Under- 
 writers' Inspection Bureau, or by writing to the Underwriters 
 Laboratories, 67 East 21st Street, Chicago. The following 
 requirements apply to almost every installation, and every 
 architect should be conversant with them. 
 
 EXTRACTS FROM THE NATIONAL 'ELECTRICAL CODE.* 
 
 1. 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. 
 
 2. Where wires are concealed and run parallel to joists they 
 must be supported on porcelain knobs which hold the wires 
 at least 1' in. from woodwork or surface wired over. Knobs 
 must be securely fastened and must be placed every 4J ft. apart. 
 Where wires are run throujh 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 ins. Where wires run down partitions, espe- 
 cially partitions formed by 2X4 studding, the wires must be 
 so supported as to run in centre of partition. If more than two 
 wires are run down partition between studs, they must be 
 separated by at least 5 ins. 
 
 * 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. 
 
1336 ELECTRIC-LIGHT WIRING. 
 
 4. Where wires pass through floors they must be bushed* 
 with porcelain tubes and have a floor tube or additional bush- 
 ing taped securely in place at floor. 
 
 5. All joints must be securely soldered and taped. A splice 
 to be approved must be the regular W. U. telegraph joint and 
 must have at least five turns of wire on each side where they 
 join. Joints to be properly taped require where rubber-covered 
 wire is used, first to be taped with rubber tape and then with 
 friction tape. 
 
 6. Where wires enter the building they must be provided 
 with a drip loop. 
 
 7. There must be a main cut-out and switch installed in an 
 easily accessible place, as near as possible to point where wires 
 enter building* (This will require that cut-out and switch 
 be placed where there is no need of a 12-ft. ladder to reach 
 them.) 
 
 8. Every lighting circuit of 660 watts must be protected by 
 a cut-out. This will limit the number to twelve 16-c.p. lights 
 on a two-wire 110-volt circuit, or twenty 16-c.p. lights on a 
 three-wire 220-volt circuit. 
 
 9. All cut-outs must be placed in an asbestos-lined cabinet. 
 Asbestos to be at least J-- in. in thickness and securely held in 
 place by shellac and tacks. Lumber of which cabinet is made 
 must be at least f 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 and car- 
 tridge 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. Cut-out to be placed in an asbestos-lined cabinet. 
 
 12. The practice of using fused rosettes w r ill not be approved. 
 
 13. Where wires run down side wall they must be protected 
 from mechanical injury. 
 
 14. All outlets must be made to conform to rule 22 e, p. 24, 
 National Electrical Code. 
 
 15. Fans or lights 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. 
 
GENERAL SUGGESTIONS 
 
 1337 
 
 General Suggestions. 
 
 Preface to the National Electrical Code. 
 
 In all electric work conductors, 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 conductor to conductor, 
 or between conductor and ground, may be reduced to the mini- 
 mum. 
 
 In all wiring special attention 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-current 
 systems, the work should, if possible, be started from a centre 
 of distribution, and the switches and cut-outs, .controlling and 
 connected with the several branches, be grouped together in a 
 
 Potential Wire 
 
 Main Fuse Block 
 Outside Wall 
 
 Fig. 15 
 
 safe and easily accessible place, where they can be readily got 
 at for attention or repairs. The load should be divided as 
 evenly 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. 
 
 Architects are urged, when drawing plans and specifications, 
 to make provision for the channelling 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. 
 
1338 ELECTRIC-LIGHT WIRING. 
 
 Fig. 15 shows a common arrangement of main cut-out, 
 switch, and metre, to comply with rule 1, p. 1336. The main 
 cut-out and switch should be as near as possible to the outside 
 wall, but the metre may be at some distance from the switch 
 if desirable for any reason. 
 
 Specifications for Interior Wiring. 
 
 Specifications for interior wiring should provide: 
 
 1. 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 1 and 2 are sufficient to insure a safe installa- 
 tion. 
 
 3. Contractor must obtain a satisfactory certificate of in- 
 spection 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 after the plastering is dry. 
 
 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 outlet shall not exceed 2% under 
 maximum load." 
 
 (Wiring specifications for buildings having their own generating 
 plant should be prepared by an expert.) 
 
 6. Cut-out cabinets and where they are to be placed; also 
 location of main-line cut-out and fuse. 
 
 (For buildings containing more than forty lights, one dis- 
 tributing point is generally sufficient, although in large houses 
 it is often convenient to have a cut-out cabinet on each floor.) 
 
SPECIFICATIONS AND COST. 1339 
 
 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 on Fig. 11. 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 number of pounds of wire 
 required, the kind and number of switches, character of cut-out 
 cabinets, etc., and the time required to do the work, so that 
 a close estimate cannot be made without plans and specifica- 
 tions. Again, wages and prices of material vary to a consider- 
 able extent in different portions of the country, so that an 
 estimate that would be about right for one locality would not 
 sufnceasfor another. 
 
 The following figures, however, will enable any one to form an 
 approximate idea of what any proposed wiring job will cost. 
 
 For 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, 25 to 100 lamps, allow $1.75 to $2.00 
 per outlet. 
 
 The extra labor involved in wiring old buildings will add 
 from 10 to 50 per cent, to the above figures. 
 
 For each switch loop with a single-pole snap switch add 
 $1.50 to $1.75. 
 
 For each switch loop with single-pole push-button switch 
 add $2.25 to $2.50. 
 
 For each lamp controlled by duplex switches add $5 to $6. 
 
 For each hardwood cut-out cabinet with door and lock add 
 from $7 up according 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 $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 $1250 to $1500, and a 
 similar plant with 600 lamps will cost from $2500 to $3000 
 
1340 ELECTRIC-LIGHT WIRING. 
 
 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 $2.00 upwards. Combination fixtures 
 cost about 25 per cent, more than straight electric fixtures. 
 
 The price of rubber-covered wire varies from $8.00 to $00.00 
 per 1,000 ft. according to size, and of weather-proof wire from 
 16 cts. to 25 cts. per pound. 
 
SPECIFIC GRAVITIES AND WEIGHTS. 1341 
 
 SPECIFIC GRAVITIES AND WEIGHTS OF VARIOUS 
 SUBSTANCES.* 
 
 The Basis for Specific Gravities is Pure Water at 
 
 62 Fahr., Barometer 30 Inches. 
 Weight of 1 Cubic Foot, 62.355 Pounds. 
 
 Average 
 
 Sp. Gr. 
 
 Water ==1. 
 
 Air, atmospheric at 60 F., under pressure 
 of one atmosphere, or 14.7 Ibs. per sq. 
 
 in. , weighs ^y-g-th as much as water 00123 
 
 Aluminum 2.6 
 
 Anthracite, 1.3 to 1.84; of Penn., 1.3 to 1.7 1.5 
 broken-, of any size, loose. . ....;. 
 
 " moderately shaken. . . . 
 
 " " heaped bushel, loose, 77 
 
 to 83 Ibs 
 
 " a ton loose occupies 40 
 
 to 43 cu. ft 
 
 Antimony, cast 6 . 70 
 
 native 6.67 
 
 Ash, perfectly dry (see note p. 1344) 752 
 
 " American white dry (see note p. 1344). . . 61 
 
 Ashes of soft coal, solidly packed 
 
 Asphaltum, 1 to 1 .8 1.4 
 
 Brass (copper and zinc), cast, 7.8 to 8.4. ... 8.1 
 
 " rolled 8.4 
 
 Brick, best pressed 
 
 " common and hard 
 
 " soft inferior 
 
 Brickwork, pressed brick, fine joints 
 
 medium quality 
 
 coarse, inferior, soft 
 
 " at 125 Ibs. per cubic foot, 1 cu. 
 
 yd. equals 1.507 tons and 
 
 17.92 cu. ft. equal 1 ton 
 
 Bronze, copper, 8, tin 1 (gun-metal) 
 
 Cement, hydraulic. American, Rosendale, 
 
 ground, and loose (see p. 192). . 
 
 " hydraulic. Portland, loose (see p. 
 
 197) 
 
 Charcoal of pines and oaks 
 
 Chalk , 2.5 
 
 Cherry, perfectly dry (see note p. 1344) 672 
 
 Chestnut, perfectly dry (see note p. 1344). . .660 
 
 Clay, potters', dry, 1.8 to 2.1 1.9 
 
 " dry in lump, loose 
 
 * The values in this table are taken largely from a table compiled by 
 the Cambria Iron Co. 
 
1342 SPECIFIC GRAVITIES AND WEIGHTS. 
 
 SPECIFIC GRAVITIES AND WEIGHTS OF VARIOUS 
 SUBSTANCES. Continued. 
 
 The Basis for Specific Gravities is Pure Water at 
 62 Fahr., Barometer 30 Inches. 
 Weight of 1 Cubic Foot, 62.355 Pounds. 
 
 Average 
 Sp. Gr. 
 Water = 1. 
 
 Average 
 Weight of 
 1 Cu. Ft., 
 Pounds. 
 
 Coal, anthracite; see Anthracite. 
 11 bituminous, solid, 1.2 to 1.5. 
 
 1.35 
 
 84 
 
 79 to 84 
 47 to 52 
 51 to 56 
 
 23 to 32 
 
 542 
 
 555 
 15 
 64 
 72 to SO 
 82 to 92 
 90 to 100 
 70 to 76 
 66 to 68 
 75 to 90 
 90 to 100 
 104 to 112 
 
 110 to 120 
 35 
 162 
 186 
 157 
 168 
 96 
 1204 
 1217 
 170 
 187 
 141.6 
 
 25 
 53 
 57.4 
 
 " bituminous, solid, Cambria Co., Pa., 
 1.27-1.34 
 
 " bituminous, broken, of any size, loose . 
 " bituminous, moderately shaken 
 
 
 
 " bituminous, a heaped bushel, loose, 
 70 to 78 
 
 
 " bituminous, 1 ton occupies 43 to 48 
 cubic feet. . 
 
 Coke loose, good quality 
 
 " loose, a heaped bushel, 35 to 42. . . . 
 
 3.9 
 8.7" 
 8.9 
 .24 
 .55 
 
 " 1 ton occupies 80 to 97 cu. ft. 
 
 Corundum pure 3.8 to 4 
 
 Copper, cast, 8.6 to 8.8 
 
 " rolled, 8.8 to 9 
 
 Cork dry (see note p. 1344) 
 
 Cypress, American (see note p. 1344). 
 
 Earth, common loam, perfectly dry, loose . . . 
 
 perfectly dry, shaken . 
 perfectly dry, rammed. 
 
 
 
 slightly moist, loose . . 
 
 
 more moist, loose. . . . 
 
 
 more moist, shaken . . 
 
 
 more moist, packed . . 
 
 
 as soft flowing mud . . 
 
 
 " as soft flowing mud 
 well pressed 
 
 
 Elm perfectly dry (see note p. 1344) 
 
 .56 
 2.6 
 2.98 
 2.52 
 2.69 
 
 Flint. . : 
 
 Glass 2 5 to 3.45 
 
 1 1 common window 
 
 Gneiss, common, 2.62 to 2.76 
 
 " in loose piles 
 
 Gold, cast, pure or 24 karat. ... 
 
 19 . 258 
 19.5 
 2.72 
 3.00 
 2.27 
 
 .4 
 
 .85 
 .92 
 
 " pure, hammered 
 
 Granite 2 56 to 2 88. . 
 
 Greenstone, trap, 2.8 to 3.2. . . . 
 
 Gypsum, plaster of Paris, 2.24 to 2.30 
 Hay loose 
 
 " in stacks, about 512 cu. ft. to ton. . . . 
 Hemlock, perfectly dry (see note p. 1344). . . 
 Hickory, " 
 Ice, .917 to .922 
 
SPECIFIC GRAVITIES AND WEIGHTS. 1343 
 
 SPECIFIC GRAVITIES AND WEIGHTS OF VARIOUS 
 SUBSTANCES. Continued. 
 
 The Basis for Specific Gravities is Pure Water at 
 
 62 Fahr., Barometer 30 Inches. 
 Weight of 1 Cubic Foot, 62.355 Pounds. 
 
 Iron, cast, 6.9 to 7.4 
 
 " gray foundry, cold 
 
 molten 
 
 " wrought 
 
 Lead, commercial 
 
 Lignum- vitse (dry) 
 
 Limestone and marbles. 
 
 Lime, quick 
 
 " quick, ground, well shaken, per struck 
 
 bushel, 80 Ibs. 
 
 " quick, ground, thoroughly shaken, 
 
 per struck bushel, 93| Ibs 
 
 Locust, dry (see note p. 1344) 
 
 Mahogany, Spanish, dry (see note p. 1344). , 
 Honduras, dry (see note p. 1344) 
 
 Maple, dry (see note p. 1344) 
 
 Marbles (see Limestone). 
 Masonry of granite or limestones, well- 
 dressed 
 
 of granite, well-scabbled mortar 
 rubble; about ^ of mass will be 
 
 mortar 
 
 of gr'nite, well-scabbl'd dry rubble 
 " of granite, roughly scabbled mor- 
 tar rubble ; about J to J of mass 
 
 will be mortar. 
 
 of granite, scabbled dry rubble . . . 
 of sandstone, J less than granite . . 
 Masonry of brickwork (see Brickwork). 
 
 Mercury at 32 Fahr 
 
 Mica, 2.75 to 3.1 
 
 Mortar, hardened, 1.4 to 1.9 
 
 Mud, dry, close 
 
 " wet, moderately pressed 
 
 " fluid 
 
 Oak, live, perfectly dry, .88-1.02 (see note 
 
 p. 1344) 
 
 " white, perfectly dry, .66 to .88 (see 
 
 note p. 1344) 
 
 " red, black, perfectly dry 
 
 Petroleum 
 
 Pine, white, perfectly dry, .35 to .45 (see 
 note p. 1344) 
 
 Average 
 
 Sp. Gr. 
 
 Water = 1. 
 
 7.15 
 
 7.21 
 
 6.94 
 
 7.69 
 
 11.38 
 
 65-1.33 
 
 2.6 
 
 1.5 
 
 .71 
 .85 
 '.56 
 .79 
 
 13.62 
 2.93 
 1.65 
 
 .95 
 
 .77 
 
 .878 
 .40 
 
 Average 
 Weight of 
 1 Cu. Ft., 
 Pounds. 
 
 446. 
 450 
 433 
 480 
 709.6 
 41 to 83 
 164.4 
 95 
 
 64 
 
 75 
 
 44 
 53 
 35 
 49 
 
 165 
 
 154 
 138 
 
 150 
 125 
 
 849 
 
 183 
 
 103 
 
 80 to 110 
 110 to 130 
 104 to 120 
 
 59.3 
 
 48 
 32 to 45 
 
 54.8 
 
 25 
 
1344 SPECIFIC GRAVITIES AND WEIGHTS. 
 
 SPECIFIC GRAVITIES AND WEIGHTS OF VARIOUS 
 SUBSTANCES. Continued. 
 
 The Basis for Specific Gravities is Pure Water at 
 62 Fahr., Barometer 30 Inches. 
 Weight of 1 Cubic Foot, 62.355 Pounds. 
 
 Average 
 Sp. Gr. 
 Water = 1. 
 
 Average 
 Weight of 
 1 Cu. Ft., 
 Pounds. 
 
 Pine, yellow, Northern,, perfectly dry, .48 
 to .62 (see foot-note) 
 
 .55 
 
 34 3 
 
 " yellow, Southern, perfectly dry, .64 
 to .8 (see foot-note) 
 
 72 
 
 45 
 
 Pitch 
 
 1.15 
 
 71 7 
 
 Poplar, dry (see foot-note) 
 
 .47 
 
 29 
 
 Platinum 
 
 21 5 
 
 1342 
 
 Quartz 
 
 2 65 
 
 165 
 
 Rosin 
 
 1.10 
 
 68 6 
 
 Salt, coarse (per struck bushel, Syracuse, 
 N. Y., 561bs.) :'."'. . 
 
 
 45 
 
 Sand, of pure quartz, perfectly dry and loose 
 
 
 90 to 106 
 
 " voids full of water. . . . 
 
 
 118 to 129 
 
 very large and small 
 grains, dry 
 
 
 117 
 
 Sandstone, 2.1 to 2 73, 131 to 171. . . 
 
 2 41 
 
 151 
 
 quarried and piled, 1 measure 
 solid makes If (about) piled. . 
 
 
 86 
 
 Snow, fresh fallen ; ; . 
 
 
 5 to 12 
 
 " moistened, compacted by rain 
 
 
 15 to 50 
 
 Sycamore, perfectly dry (see foot-note). . 1 , ! 1 
 
 59 
 
 37 
 
 Shales red or black, 2.4 to 2.8. 
 
 2 6 
 
 162 
 
 Silver 
 
 10 5 
 
 655 
 
 Slate, 2.7 to 2.9 : 
 
 2 8 
 
 175 
 
 Soapstone, 2.65 to 2.8 ". . . . 
 
 2 73 
 
 170 
 
 Spruce perfectly dry (see foot-note) . 
 
 4 
 
 25 
 
 Steel. . . 
 
 7 85 
 
 490 
 
 Sulphur 
 
 2 00 
 
 125 
 
 Tallow 
 
 .94 
 
 58.6 
 
 Tar 
 
 1 
 
 62 355 
 
 Tin cast, 7.2 to 7.5 . 
 
 7 35 
 
 459 
 
 Walnut, black, perfectly dry (see foot-note). . 
 Water, pure rain, distilled, at 32 F., bar. 
 30 ins 
 
 .61 
 
 38 
 62.417 
 
 " " " at 62 F.,bar. 
 30 ins. . 
 
 1 
 
 62 355 
 
 " " " at 212 F., bar. 
 30 ins 
 
 
 59.7 
 
 " sea 1.026 to 1 030. 
 
 1 028 
 
 64 08 
 
 Zinc or spelter, 6.8 to 7.2 
 
 7.00 
 
 437 .5 
 
 
 
 
 Note. Green timbers usually weigh from one fifth to nearly one half 
 than dry; ordinary building timbers, tolerably seasoned, one sixth n 
 
 more 
 more. 
 
WIRE GAUGES. 1345 
 
 Specific Gravity. 
 
 The specific gravity of a substance is the number which ex- 
 presses the ratio that the weight of a given volume of the sub- 
 stance bears to the weight of the same volume of distilled water 
 at a temperature of 62 Fahr. ; 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 Fahr. and at the 
 sea-level, is about 62.355 Ibs.* 
 
 The specific gravity of a solid substance " may be determined 
 by first weighing a portion 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 Ibs. in air; when 
 immersed in water it weighs 3.32 Ibs.. 
 
 Weight in air (5.32 Ibs. divided by loss of 'weight in water 
 (2 Ibs.) = 2. 66, the specific gravity. 
 
 2.66X 62.355 Ibs. = 165.84 Ibs. = weight per cubic foot. 
 
 Wire Gauges. 
 
 A "wire gauge" is a method of designating the diameter of 
 wires or the thickness of sheets of metal by the numbers of a 
 table arranged on a certain fixed basis. There are now nine or 
 ten different gauges, resulting in great confusion. The table on 
 the following page gives the diameter of the gauges in common 
 use. The only legal gauge in this country is the U. S. standard 
 gauge, described on p. 1438. It is used by most of the manu- 
 facturers of sheet iron and steel and tin-plate. The Brown & 
 Sharpe gauge is commonly used for designating size of copper 
 wires (see p. 1320) ; also for sheet copper and brass. 
 
 The American Steel and Wire Co. uses the old Washburn & 
 Moen gauge for all their steel and iron wire and also for wire 
 nails. The sectional areas for this gauge are given on p. 1349. 
 
 When placing orders for sheets and wire, it is always best to 
 specify the weight per square or lineal foot or the thickness or 
 diameter in thousands of an inch. 
 
 *The text-books differ slightly in regard to this value. 
 
1346 WIRE AND SHEET METAL GAUGES. 
 
 WIRE AND SHEET-METAL GAUGES COMPARED. 
 
 (In decimals of an inch.) 
 
 i 
 
 o| 
 
 II 
 
 If! 
 
 |tg a 
 
 6 
 
 g 
 
 ole S 
 
 
 
 03 d 
 
 CQ 
 
 o 
 
 ^ O CO <3 
 
 
 
 $r 
 
 '<S>-! r d 
 
 
 S| 
 
 flS 1 
 
 I3 
 
 fl r*fc*j2 o> 
 
 M| 
 
 C 
 
 "si 
 
 s-5* 
 
 1 
 
 a 
 
 "p!_Q ^ 
 
 pi 
 
 "t!i 
 
 
 f'8 
 
 
 Pit 
 
 fe 
 
 5^ 
 
 ^0 
 
 p 
 
 ^gtfoo 
 
 H^ 
 
 J 
 
 WrcO 
 
 7-0 
 
 
 
 .5 
 
 
 
 
 .500 
 
 6-0 
 
 
 
 . 46875 
 
 .4600 
 
 
 
 .464 
 
 5-0 
 
 
 
 4375 
 
 .4300 
 
 450 
 
 
 432 
 
 4-0 
 
 .454 
 
 .460000 
 
 .40625 
 
 .3938 
 
 .400 
 
 
 !400 
 
 3-0 
 
 .425 
 
 . 409642 
 
 .375 
 
 .3625 
 
 .360 
 
 .0315 
 
 372 
 
 2-0 
 
 .380 
 
 .364796 
 
 . 34375 
 
 .3310 
 
 .330 
 
 !0447 
 
 .348 
 
 
 
 .340 
 
 .324861 
 
 .3125 
 
 .3065 
 
 .305 
 
 .0578 
 
 .324 
 
 1 
 
 .300 
 
 .289297 
 
 .28125 
 
 .2830 
 
 .285 
 
 .0710 
 
 .308 
 
 2 
 
 .284 
 
 .257627 
 
 .265625 
 
 .2625 
 
 .265 
 
 .0842 
 
 .276 
 
 3 
 
 .259 
 
 .229423 
 
 .25 
 
 .2437 
 
 .245 
 
 .0973 
 
 .252 
 
 4 
 
 .238 
 
 . 204307 
 
 .234375 
 
 . 2253 
 
 .225 
 
 .1105 
 
 .232 
 
 5 
 
 .220 
 
 . 181940 
 
 .21875 
 
 .2070 
 
 .205 
 
 .1236 
 
 .212 
 
 6 
 
 .203 
 
 . 162023 
 
 .203125 
 
 .1920 
 
 .190 
 
 .1368 
 
 .192 
 
 7 
 
 .180 
 
 . 144285 
 
 .1875 
 
 .1770 
 
 .175 
 
 .1500 
 
 .176 
 
 8 
 
 .165 
 
 . 128490 
 
 .171875 
 
 .1620 
 
 .160 
 
 .1631 
 
 .160 
 
 9 
 
 .148 
 
 .114423 
 
 . 15625 
 
 .1483 
 
 .145 
 
 .1763 
 
 .144 
 
 10 
 
 .134 
 
 .101897 
 
 . 140625 
 
 .1350 
 
 .130 
 
 .1894 
 
 .128 
 
 11 
 
 .120 
 
 .090742 
 
 .125 
 
 .1205 
 
 .1175 
 
 .2026 
 
 .116 
 
 12 
 
 .109 
 
 .080808 
 
 . 109375 
 
 .1055 
 
 .105 
 
 .2158 
 
 .104 
 
 13 
 
 .095 
 
 .071962 
 
 .09375 
 
 .0915 
 
 .0925 
 
 .2289 
 
 .092 
 
 14 
 
 .083 
 
 .064084 
 
 .078125 
 
 .0800 
 
 .0806 
 
 .2421 
 
 .080 
 
 15 
 
 .072 
 
 .057068 
 
 .0703125 
 
 .0720 
 
 .070 
 
 .2552 
 
 .072 
 
 16 
 
 .065 
 
 .050821 
 
 .0625 
 
 .0625 
 
 .061 
 
 ,2684 
 
 .064 
 
 17 
 
 .058 
 
 .045257 
 
 .05625 
 
 .0540 
 
 .0525 
 
 .2816 
 
 .056 
 
 18 
 
 .049 
 
 .040303 
 
 .05 
 
 ,0475 
 
 .045 
 
 .2947 
 
 .048 
 
 19 
 
 .042 
 
 .035890 
 
 .04375 
 
 .0410 
 
 .040 
 
 .3079 
 
 .040 
 
 20 
 
 .035 
 
 .031961 
 
 .0375 
 
 .0348 
 
 .035 
 
 .3210 
 
 .036 
 
 21 
 
 .032 
 
 .028462 
 
 .034375 
 
 .03175 
 
 .031 
 
 .3342 
 
 .032 
 
 22 
 
 .028 
 
 .025346 
 
 .03125 
 
 .0286 
 
 .028 
 
 .3474 
 
 .028 
 
 23 
 
 .025 
 
 .022572 
 
 .028125 
 
 .0258 
 
 .025 
 
 .3605 
 
 .024 
 
 24 
 
 .022 
 
 .020101 
 
 .025 
 
 .0230 
 
 .0225 
 
 .3737 
 
 .022 
 
 25 
 
 .020 
 
 .017900 
 
 .021875 
 
 .0204 
 
 .020 
 
 .3868 
 
 .020 
 
 26 
 
 .018 
 
 .015941 
 
 .01875 
 
 .0181 
 
 .018 
 
 .4000 
 
 .018 
 
 27 
 
 ,016 
 
 .014195 
 
 .0171875 
 
 .0173, 
 
 .017 
 
 .4132 
 
 .0164 
 
 28 
 
 .014 
 
 .012641 
 
 .015625 
 
 .0162 
 
 .016 
 
 .4263 
 
 .0148 
 
 29 
 
 .013 
 
 .011257 
 
 .0140625 
 
 .0150 
 
 .015 
 
 .4395 
 
 .0136 
 
 30 
 
 .012 
 
 .010025 
 
 .0125 
 
 .0140 
 
 .014 
 
 .4526 
 
 .0124 
 
 31 
 
 .010 
 
 .008928 
 
 .0109375 
 
 .0132 
 
 .013 
 
 .4658 
 
 .0116 
 
 32 
 
 .009 
 
 .007950 
 
 .01015625 
 
 .0128 
 
 .012 
 
 .4790 
 
 .0108 
 
 33 
 
 .008 
 
 .007080 
 
 .009375 
 
 .0118 
 
 .011 
 
 .4921 
 
 .0100 
 
 34 
 
 .007 
 
 .006305 
 
 .00859375 
 
 .0104 
 
 .010 
 
 .5053 
 
 .0092 
 
 35 
 
 .005 
 
 .005615 
 
 .0078125 
 
 .0095 
 
 .0095 
 
 .5184 
 
 .0084 
 
 36 
 
 .004 
 
 .005000 
 
 .00703125 
 
 .0090 
 
 .009 
 
 .5316 
 
 .0076 
 
 37 
 
 
 .004453 
 
 .006640625 
 
 .0085 
 
 .0085 
 
 .5448 
 
 .0068 
 
 38 
 
 
 . 003^65 
 
 .00625 
 
 .0080 
 
 .008 
 
 .5579 
 
 .0060 
 
 39 
 
 
 .003531 
 
 
 .0075 
 
 .0075 
 
 .5711 
 
 .0052 
 
 40 
 
 
 .003144 
 
 
 0070 
 
 .007 
 
 .5842 
 
 .0048 
 
 
 
 
 
 
 
 
 
SHEETS OF STEEL, COPPER, AND BRASS. 1347 
 
 WEIGHT PER SQUARE FOOT OF SHEETS OF WROUGHT 
 IRON, STEEL, COPPER, AND BRASS. 
 
 (Thickness by American (B. & S.) Gauge.) 
 
 No. of 
 Gauge. 
 
 Thickness 
 in Inches. 
 
 Iron. 
 
 Steel. 
 
 Copper. 
 
 Brass. 
 
 0000 
 
 .46 
 
 18.46 
 
 18.70 
 
 20.84 
 
 19.69 
 
 000 
 
 .4096 
 
 16.44 
 
 16.66 
 
 18.56 
 
 17.53 
 
 00 
 
 .3648 
 
 14.64 
 
 14.83 
 
 16.53 
 
 15.61 
 
 
 
 .3249 
 
 13.04 
 
 13.21 
 
 14.72 
 
 13.90 
 
 1 
 
 .2893 
 
 11.61 
 
 11.76 
 
 13.11 
 
 12.38 
 
 2 
 
 .2576 
 
 10.34 
 
 10.48 
 
 11.67 
 
 11.03 
 
 3 
 
 .2294 
 
 ,9.21 
 
 9.33 
 
 10.39 
 
 9.82 
 
 4 
 
 .2043' 
 
 8.20 
 
 8.31 
 
 9.26 
 
 8.74 
 
 5 
 
 .1819 
 
 7.30 
 
 7.40 
 
 8.24 
 
 7.79 
 
 6 
 
 .1620 
 
 6.50 
 
 6.59 
 
 7.34 
 
 6.93 
 
 7 
 
 . 1443 
 
 5.79 
 
 5.87 
 
 6.54 
 
 6.18 
 
 8 
 
 .1285 
 
 5.16 
 
 5.22 
 
 5.82 
 
 5.50 
 
 9 
 
 .1144 
 
 4.59 
 
 4.65 
 
 5.18 
 
 4.90 
 
 10 
 
 .1019 
 
 4.09 
 
 4.14 
 
 4.62 
 
 4.36 
 
 11 
 
 .0907 
 
 3.64 
 
 3.69 
 
 4,11 
 
 3.88 
 
 12 
 
 .0808 
 
 3.24 . 
 
 3.29 
 
 3.66 
 
 3.46 
 
 13 
 
 .0720 
 
 2.89 
 
 2.93 
 
 3.26 
 
 3.08 
 
 14 
 
 .0641 
 
 2.57 
 
 2.61 
 
 2.90 
 
 2.74 
 
 15 
 
 .0571 
 
 2.29 
 
 2.32 
 
 2.59 
 
 2.44 
 
 16 
 
 .0503 
 
 2.04 
 
 2.07 
 
 2.30 
 
 2.18 
 
 17 
 
 .0453 
 
 1.82 
 
 1.84 
 
 2.05 
 
 1.94 
 
 18 
 
 .0403 
 
 1.62 
 
 1.64 
 
 1.83 
 
 1.73 
 
 19 
 
 .0359 
 
 1.44 
 
 1.46 
 
 1.63 
 
 1.54 
 
 20 
 
 .0320 
 
 1.28 
 
 1.30 
 
 1.45 
 
 1.37 
 
 21 
 
 .0255 
 
 1.14 
 
 1.16 
 
 1.29 
 
 1.22 
 
 22 
 
 .0253 
 
 1.02 
 
 1.03 
 
 1.15 
 
 1.08 
 
 23 
 
 .0226 
 
 .906 
 
 .918 
 
 1.02 
 
 .966 
 
 24 
 
 .0201 
 
 .807 
 
 .817 
 
 .911 
 
 .860 
 
 25 
 
 .0179 
 
 .718 
 
 .728 
 
 .811 
 
 .766 
 
 26 
 
 .0159 
 
 .640 
 
 .648 
 
 .722 
 
 .682 
 
 27 
 
 .0142 
 
 .570 
 
 .577 
 
 .643 
 
 .608 
 
 28 
 
 .0126 
 
 .507 
 
 .514 
 
 .573 
 
 .541 
 
 29 
 
 .0113 
 
 .452 
 
 .458 
 
 .510 
 
 .482 
 
 30 
 
 .0100 
 
 .402 
 
 .408 
 
 .454 
 
 .429 
 
 31 
 
 .0089 
 
 .358 
 
 .363 
 
 .404 
 
 .382 
 
 32 
 
 .0030 
 
 .319 
 
 .323 
 
 .360 
 
 .340 
 
 33 
 
 .0071 
 
 .284 
 
 .288 
 
 .321 
 
 .303 
 
 34 
 
 .0063 
 
 .253 
 
 .256 
 
 .286 
 
 .270 
 
 35 
 
 .0056 
 
 .225 
 
 .228 
 
 .254 
 
 .240 
 
 Specific gravity 
 Weight, cubic feet. . . 
 Weight, cubic ins. . . . 
 
 7.704 
 481 . 25 
 
 .2787 
 
 7.806 
 487.75 
 .2S23 
 
 8.698 
 543.6 
 .3146 
 
 8.218 
 513.6 
 .2972 
 
1348 WEIGHT OF LEAD, COPPER, AND BRASS. 
 
 
 p 
 
 4 
 w 
 
 t-3 
 - 
 
 O 
 
 s 
 
 5 
 
 PQ 
 
 Q 
 
 5 
 
 i 
 
 w 
 
 a 
 
 w 
 
 fe 
 
 O 
 H 
 
 I 
 
 H 
 fc 
 
 
 Or-!cO(MiOCCOOOOOOOO 
 :eOl>O'*l^'-iOCX)iOeCOt^COi-iO 
 
 OOCOOOOO 
 
 !Li 
 
 1 :7c 
 
 I rr 'O'- | CCCDO5COQOT 
 I J2OOOOO'-HTHC 
 
 T-Hr-d-HT-^(N(N(N<MCOCOCO't | T^T^iCOCOCDt^XGOO5 
 
 j g 
 
 PQ 9 Tf iO^THiCI>^^THXOr^OOOOOOOOOOOO 
 
 t-H I ,/Or-i.COCOaiCOCX)T^oOr^^l^CO(N^Oil^OO<MO(NOit^t^OOCO 
 
 73^> SoOOOOTH^-t(MCOOt^O5(NiOX'-iOOi-*OiO5OCOI>COC5l>CO 
 
 W o 
 
 M 
 
 t t^ (N t^ CO -i 00 Oi 
 
 ^oooooooooooooco 
 
 ^ 
 
 ^3 3 j 
 
 ___ 
 
 03 CQ CO C<1 <N CO C<1 CD CO O i i i i" 1 
 
 2 CO T-H CO X CO ^-i CO -^ i-i 00 I-H (N rH 00 \T}< \GO \ 00 ^ X C^ 00 ^ 00 
 
 'S \\\\\\\\\\\\\\I-H \co \io. \\\\\\\ 
 
 2 I r*r*COi-HOCOt^rHQCOt>'THa>*OTHCO!-<l>i-t rH i-l CO r-< O CO t>- 
 
SMOOTH STEEL WIRE. 
 
 1349 
 
 SIZE AND WEIGHT OF SMOOTH STEEL 
 WIRE. 
 
 (As Made by the American Steel and Wire Company). 
 
 A. S. & 
 W. Co. 
 Gauge. 
 
 Diam- 
 eter 
 in 
 Decimal 
 of an 
 Inch. 
 
 Sectional 
 Area, 
 Sq. Ins. 
 
 Approxi- 
 mate 
 Weight 
 of 
 100 Feet 
 (Lbs.). 
 
 A.S. & 
 W. Co. 
 Gauge. 
 
 Diam- 
 eter 
 in 
 Decimal 
 of an 
 Inch. 
 
 Sectional 
 Area, 
 Sq. Ins. 
 
 Approxi- 
 mate 
 Weight 
 of 
 100 Feet 
 (Lbs.). 
 
 000 
 
 .3625 
 
 . 1029 
 
 35.05 
 
 16 
 
 .0625 
 
 .00311 
 
 1.042 
 
 00 
 
 .3310 
 
 .0860 
 
 29.22 
 
 17 
 
 .0540 
 
 .00229 
 
 .7778 
 
 
 
 .3065 
 
 .0740 
 
 25.06 
 
 18 
 
 .0475 
 
 .00173 
 
 .6018 
 
 1 
 
 .2830 
 
 .0629 
 
 21.36 
 
 19 
 
 .0410 
 
 .00132 
 
 .4484 
 
 2 
 
 .2625 
 
 .0543 
 
 ' 18.38 
 
 20 
 
 .0348 
 
 .00096 
 
 .3230 
 
 3 
 
 .2437 
 
 .0467 
 
 15.84 
 
 21 
 
 .0317 
 
 .00080 
 
 .2680 
 
 4 
 
 .2253 
 
 .0398 
 
 13.54 
 
 22 
 
 .0286 
 
 .00061 
 
 .2182 
 
 5 
 
 .2070 
 
 .0336 
 
 11.43 
 
 23 
 
 .0258 
 
 .00049 
 
 .1775 
 
 6 
 
 .1920 
 
 .0289 
 
 9.832 
 
 24 
 
 .0230 
 
 .00041 
 
 .1411 
 
 7 
 
 .1770 
 
 .0246 
 
 8.356 
 
 25 
 
 .0204 
 
 .00031 
 
 .1110 
 
 8 
 
 .1620 
 
 .0206 
 
 7.000 
 
 26 
 
 .0181 
 
 .00025 
 
 .08738 
 
 9 
 
 .1483 
 
 .0172 
 
 5.866 
 
 27 
 
 .0173 
 
 .00022 
 
 .07983 
 
 10 
 
 .1350 
 
 .0143 
 
 4.861 
 
 28 
 
 .0162 
 
 ' .00020 
 
 .07 
 
 11 
 
 .1205 
 
 .0113 
 
 3.873 
 
 29 
 
 .0150 
 
 .00017 
 
 .06001 
 
 12 
 
 .1055 
 
 .0086 
 
 2.969 
 
 30 
 
 .0140 
 
 .00015 
 
 .05228 
 
 13 
 
 .0915 
 
 .0066 
 
 2.233 
 
 31 
 
 .0132 
 
 .00014 
 
 .04647 
 
 14 
 
 .0800 
 
 .0050 
 
 1.707 
 
 32 
 
 .0128 
 
 .00013 
 
 .04370 
 
 15 
 
 .0720 
 
 .0041 
 
 1.383 
 
 33 
 
 .0118 
 
 .00009 
 
 .03714 
 
 Kinds of Wire Manufactured by the American 
 Steel and Wire Company, 
 
 Market wire, Nos. 40 to 18. 
 
 Annealed stone or weaving wire, Nos. 16 to 47. 
 
 Tinned wire, Nos. to 18. 
 
 Tinned stone wire, Nos. 18 to 36. 
 
 Gun screw wire, finished with great care as regards round- 
 ness and exactness to gauge, Nos. 50 to 18. 
 
 Machinery wire, Nos. 00000 to 18. 
 
 Cast-steel wire, J-inch diameter, down to No. 20. 
 
 Drill and needle steel wire, Nos. 12 to 25. 
 
 The term " market wire" applies to the ordinary and most 
 used forms of Bessemer annealed, bright, galvanized, tinned, and 
 coppered wires. 
 
 Sectional area, weight, and strength of iron wire measured by 
 the Trenton Iron Company's gauge is given on page 351. 
 
1350 
 
 WEIGHTS, AREAS, ETC., OF BARS. 
 
 WEIGHTS AND AREAS OF SQUARE AND ROUND BARS 
 AND CIRCUMFERENCES OF ROUND BARS. 
 
 (Weights are for steel, at 489.6 Ibs. per cu. ft.) 
 
 Thickness 
 or 
 Diameter 
 in Inches. 
 
 Weight of 
 DBar 
 1 Foot 
 Long. 
 
 Weight of 
 QBar 
 1 Foot 
 Long. 
 
 Area of 
 D Bar 
 in Square 
 Inches. 
 
 Area of 
 t QBar 
 in Square 
 Inches. 
 
 Circumfer- 
 ence 
 of O Bar 
 in Inches. 
 
 1 A 
 
 .013 
 
 .010 
 
 .0039 
 
 .0031 
 
 .1963 
 
 %4 
 
 .021 
 
 .016 
 
 .0061 
 
 .0048 
 
 .2454 
 
 %2 
 
 .030 
 
 .023 
 
 .0088 
 
 .0069 
 
 .2945 
 
 T/64 
 
 .041 
 
 .032 
 
 .0120 
 
 .0094 
 
 .3436 
 
 1 
 
 .053 
 
 .042 
 
 .0156 
 
 .0123 
 
 .3927 
 
 %4 
 
 .067 
 
 .053 
 
 .0198 
 
 .0155 
 
 .4418 
 
 %2 
 
 .083 
 
 .065 
 
 .0244 
 
 .0192 
 
 .4909 
 
 H&A 
 
 .100 
 
 .079 
 
 .0295 
 
 .0232 
 
 .5400 
 
 % 
 
 .120 
 
 .094 
 
 .0352 
 
 .0276 
 
 .5890 
 
 13 /64 
 
 .140 
 
 .110 
 
 .0413 
 
 .0324 
 
 .6381 
 
 %2 
 
 .163 
 
 .128 
 
 .0479 
 
 .0376 
 
 .6872 
 
 *%4 
 
 .187 
 
 .147 
 
 .0549 
 
 .0431 
 
 .7363 
 
 1 
 
 .213 
 
 .167 
 
 .0625 
 
 .0491 
 
 .7854 
 
 17 /64 ' 
 
 .240 
 
 .188 
 
 .0706 
 
 .0554 
 
 .8345 
 
 %2 
 
 .269 
 
 .211 
 
 .0791 
 
 .0621 
 
 .8836 
 
 1%4 
 
 .300 
 
 .235 
 
 .0881 
 
 .0692 
 
 .9327 
 
 % 
 
 .332 
 
 .261 
 
 .0977 
 
 .0767 
 
 .9817 
 
 !%2 
 
 .402 
 
 .316 
 
 .1182 
 
 .0928 
 
 1.0799 
 
 f 
 
 .478 
 
 .376 
 
 .1406 
 
 .1104 
 
 1.1781 
 
 1%S 
 
 .561 
 
 .441 
 
 .1650 
 
 .1296 
 
 1.2763 
 
 % 
 
 .651 
 
 .511 
 
 .1914 
 
 .1503 
 
 1.3744 
 
 15 /32 
 
 .747 
 
 .587 
 
 .2197 
 
 .1726 
 
 1.4726 
 
 i 
 
 .850 
 
 .668 
 
 .2500 
 
 .1963 
 
 1 . 5708 
 
 17 /32 
 
 .960 
 
 .754 
 
 .2822 
 
 .2217 
 
 1.6690 
 
 % 
 
 1.076 
 
 .845 
 
 .3164 
 
 .24?5 
 
 1.7671 
 
 19 /32 
 
 1.199 
 
 941 
 
 .3525 
 
 .2769 
 
 1.S653 
 
 | 
 
 1.328 
 
 1.043 
 
 .3906 
 
 .3068 
 
 1.9635 
 
 % 
 
 1.607 
 
 1.262 
 
 .4727 
 
 .3712 
 
 2.1598 
 
 } 
 
 1.913 
 
 1.502 
 
 .5625 
 
 .4418 
 
 2.3562 
 
 % 
 
 2.245 
 
 1.763 
 
 .6602 
 
 .5185 
 
 2.5525 
 
 
 2.603 
 
 2.044 
 
 .7656 
 
 .6013 
 
 2.7489 
 
 * 
 
 2.989 
 
 2.347 
 
 .8789 
 
 .6903 
 
 2,9452 
 
WEIGHTS, AREAS, ETC., OF BARS. 
 
 1351 
 
 WEIGHTS AND AREAS OF SQUARE AND ROUND 
 STEEL BARS. 
 
 (Weights are for steel, at 489.6 Ibs. per cu. ft.) 
 
 Thickness, Ins. 
 
 n 
 
 O 
 
 Thickness, Ins. 
 
 a 
 
 O 
 
 Area. 
 
 Weight 
 per 
 Foot. 
 
 Area. 
 
 Weight 
 per 
 Foot. 
 
 Area. 
 
 Weight 
 per 
 
 Foot. 
 
 Area. 
 
 Wgt. 
 Foot. 
 
 1 1.000 
 
 3.400 
 
 .785 
 
 2.670 
 
 3 
 
 9.000 
 
 30.60 
 
 7.069 
 
 24.03 
 
 % 1.129 
 
 3.838 
 
 .887 
 
 3.014 
 
 X 6 | 9.379 
 
 31.89 7.366 
 
 25.04 
 
 
 1.266 
 
 4.303 
 
 .994 
 
 3.379 
 
 i 
 
 9.766 
 
 33.20 7.670 
 
 26.08 
 
 /ie 
 
 1.410 
 
 4.795 
 
 1 . 108 
 
 3.766 
 
 %, 
 
 10.16 
 
 34.55 
 
 7.980 
 
 27.13 
 
 i 
 
 1.563 
 
 5.312 
 
 1.227 
 
 4.173 
 
 * 
 
 10.56 
 
 35.92 
 
 8.296 
 
 28.20 
 
 k [ 1.723 
 
 5.857 
 
 1.353 
 
 4.600 
 
 %> 
 
 10.97 
 
 37.31 
 
 8.618 
 
 29.30 
 
 I 
 
 1.891 
 
 6.42-i 
 
 1.4'- 5 
 
 5.049 
 
 i 
 
 11.39 
 
 38.73 
 
 8.946 
 
 30.42 
 
 ^6 
 
 2.066 
 
 7.026 
 
 1.623 
 
 5.518 
 
 7 A 
 
 11.82 
 
 40.18 
 
 9.281 
 
 31.56 
 
 i 
 
 2.250 
 
 7.650 
 
 1.767 
 
 6.008 
 
 i 
 
 12.25 
 
 41.65 
 
 9.621 
 
 32.71 
 
 % 
 
 2.441 
 
 8.301 
 
 1.918 
 
 6.520 
 
 % 
 
 12.69 
 
 43l 14 
 
 9.968 
 
 33.90 
 
 ! 
 
 2.641 
 
 8.978 
 
 2.074 
 
 7.051 
 
 f 
 
 13.14 
 
 44.68 
 
 10.32 
 
 35.09 
 
 % 
 
 2.848 
 
 9.682 
 
 2.237 
 
 7.604 
 
 % 
 
 13.60 
 
 46.24 
 
 10.68 
 
 36.31 
 
 I 
 
 3.063 
 
 10.41 
 
 2.405 
 
 8.178 
 
 i 
 
 4 
 
 14.06 
 
 47.82 
 
 11.05 
 
 37.56 
 
 %3.285 
 
 11.17 
 
 2.580 
 
 8.773 
 
 % 
 
 14.54 
 
 49. 42; 11. 42 
 
 38.81 
 
 i |3.516 
 
 11.95 
 
 2.761 
 
 9.388 
 
 1 
 
 15.02 
 
 51.05 
 
 11.79 
 
 40.10 
 
 % 
 
 3.754 
 
 12.76 
 
 2.948 
 
 10.02 
 
 % 
 
 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 
 
 Ye 
 
 4.254 
 
 14.46 
 
 3.341 
 
 11.36 
 
 X 
 
 16.50 
 
 56.11 
 
 12.96 
 
 44.07 
 
 i 
 
 4.516 
 
 15.35 
 
 3.547 
 
 12.06 
 
 i 
 
 17.02 
 
 57.85 
 
 13.36 
 
 45.44 
 
 n 
 
 4.785 
 
 16.27 
 
 3.758 
 
 12.78 
 
 %> 
 
 17.54 
 
 59.62 
 
 13.77 
 
 46.83 
 
 \ 
 
 5.063 
 
 17.22 
 
 3.976 
 
 13 . 52 
 
 \ 
 
 18.06 
 
 61.41 
 
 14.19 
 
 48.24 
 
 % 
 
 5.348 
 
 18.19 
 
 4.200 
 
 14.28 
 
 % 
 
 18.60 
 
 63.23 
 
 14.61 
 
 49.66 
 
 I 
 
 5.641 
 
 19.18 
 
 4.430 
 
 15.07 
 
 
 19.14 
 
 65.08 
 
 15.03 
 
 51.11 
 
 % 
 
 5.941 
 
 20.20 
 
 4.666 
 
 15.86 
 
 k 
 
 19.69 
 
 66.95 
 
 15.47 
 
 52.58 
 
 1 
 
 6.250 
 
 21 . 25 
 
 4.909 
 
 16.69 
 
 i 
 
 20.25 
 
 68.85 
 
 15.90 
 
 54.07 
 
 % 
 
 6.566 
 
 22.33 
 
 5.157 
 
 17.53 
 
 % 
 
 20.82 
 
 70.78 
 
 16.35 
 
 55.59 
 
 t 
 
 6.891 
 
 23.43 
 
 5.412 
 
 18.40 
 
 t 
 
 21.39 
 
 72.73 
 
 16.80 
 
 57.12 
 
 % 
 
 7.223 
 
 24.56 
 
 5.673 
 
 19.29 
 
 % 
 
 21.97 
 
 74.70 
 
 17.26 
 
 58.67 
 
 i 
 
 7.563 
 
 25.71 
 
 5.940 
 
 20.20 
 
 -i 
 
 22.56 
 
 76.71 
 
 17.72 
 
 60.25 
 
 % 
 
 7.910 
 
 26.90 
 
 6.213 
 
 21.12 
 
 % 
 
 23.16 
 
 78.74 
 
 18.19 
 
 61.84 
 
 1 
 
 8.266 
 
 28.10 
 
 6.492 
 
 22.07 
 
 t 
 
 23.77 
 
 80.81 
 
 18.67 
 
 63.46 
 
 % 
 
 8.629 
 
 29.34 
 
 6.777 
 
 23 04 
 
 % 
 
 24.38 
 
 82.89 
 
 19.15 
 
 65.10 
 
 i 
 
 
 
 
 
 
 
 
 
1352 
 
 WEIGHTS, AREAS, ETC., OF BARS. 
 
 WEIGHTS AND AREAS OP SQUARE AND ROUND 
 STEEL BARS Continued. 
 
 (Weights are for steel, at 489.6 Ibs. per cu. ft.) 
 
 U 
 
 fl 
 
 D 
 
 
 
 a 
 
 a 
 
 
 
 1 
 
 
 Weight 
 
 
 Weight 
 
 1 
 
 
 Weight 
 
 
 Wgt. 
 
 1 
 
 Area. 
 
 per 
 Foot. 
 
 Area. 
 
 per 
 Foot 
 
 1 
 
 Area. 
 
 per 
 
 Foot. 
 
 Area. 
 
 per 
 
 Foot. 
 
 5 
 
 25.00 
 
 85.00 
 
 19.64 
 
 66.76 
 
 7 
 
 49.00 
 
 166.6 
 
 38.49 
 
 130.9 
 
 1 A 
 
 25.63 
 
 87.14 
 
 20.13 
 
 68.44 
 
 f 
 
 52.56 
 
 178.7 
 
 41.28 
 
 140.4 
 
 i 
 
 26.27 
 
 89.30 
 
 20.63 
 
 70.14 
 
 
 56.25 
 
 191.3 
 
 44 . 18 
 
 150.2 
 
 %> 
 
 26.91 
 
 91.49 
 
 21.14 
 
 71.86 
 
 f 
 
 60.06 
 
 204.2 
 
 47.17 
 
 160.3 
 
 i 
 
 27.56 
 
 93.72 
 
 21.65 
 
 73.60 
 
 8 
 
 64.00 
 
 217.6 
 
 50.27 
 
 171.0 
 
 5 A 
 
 28.22 
 
 95.96 
 
 22.17 
 
 75.37 
 
 1 
 
 68.06 
 
 231.4 
 
 53.46 
 
 181.8 
 
 1 
 
 28.89 
 
 98.23 
 
 22.69 
 
 77.15 
 
 i 
 
 72.25 
 
 245.6 
 
 56.75 
 
 193.0 
 
 7 A 
 
 29.57 
 
 100.5 
 
 23.22 
 
 78.95 
 
 f 
 
 76.56 
 
 260.3 
 
 60.13 
 
 204.4 
 
 j 
 
 30.25 
 
 102.8 
 
 23.76 
 
 80.77 
 
 9 
 
 81.00 
 
 275.4 
 
 63.62 
 
 216.3 
 
 % 
 
 30.94J 105. 2 
 
 24.30 
 
 82.62 
 
 i 
 
 85.56 
 
 290.9 
 
 67.20 
 
 228.5 
 
 f 
 
 31.64 
 
 107.6 
 
 24.85 
 
 84.49 
 
 i 
 
 90.25 
 
 306.8 
 
 70.88 
 
 241.0 
 
 % 
 
 32.35 
 
 110.0 
 
 25.41 
 
 86.38 
 
 t 
 
 95,06 
 
 323.2 
 
 74.66 
 
 253.9 
 
 f 
 
 33.06 
 
 112.4 
 
 25.97 
 
 88.29 
 
 10 
 
 100.0 
 
 340.0 
 
 78.54 
 
 267.0 
 
 % 
 
 33.79 
 
 114.9 
 
 26.54 
 
 90.22 
 
 i 
 
 105.1 
 
 ;57.2 
 
 82.52280.6 
 
 i 
 
 34.52 
 
 117.4 
 
 27.11 
 
 92.17 
 
 
 HO. 3 
 
 374.9 
 
 86.59294.4 
 
 % 
 
 35.25 
 
 119.9 
 
 27.69 
 
 94.14 
 
 I 
 
 115.6 
 
 392.9 
 
 90.76 
 
 308.6 
 
 6 
 
 36.00 
 
 122.4 
 
 28.27 
 
 96.14 
 
 11 
 
 121.0 
 
 411.4 
 
 95.03 
 
 323.1 
 
 i 
 
 37.52 
 
 127.6 
 
 29.47 
 
 100.2 
 
 I 
 
 126.6 
 
 430.3 
 
 99.40 
 
 337.9 
 
 
 39.06 
 
 132 8 
 
 30.68 
 
 104.3 
 
 i 
 
 132.3 
 
 449.6 
 
 103.9 
 
 353.1 
 
 f 
 
 40.64 
 
 138.2 
 
 31.92 
 
 108.5 
 
 
 138.1 
 
 469.4 
 
 108.4 
 
 368.6 
 
 i 
 
 42,25 
 
 143.6 
 
 33.18 
 
 112.8 
 
 12 
 
 144.0 
 
 489.6 
 
 113.1 
 
 384.5 
 
 f 
 
 43.89 
 
 149.2 
 
 34.47 
 
 117.2 
 
 
 
 
 
 
 
 45.56 
 
 154.9 
 
 35.79 
 
 121.7 
 
 
 
 
 
 
 1 
 
 47.27 
 
 160.8 
 
 37.12 
 
 126.2 
 
 
 
 
 
 
 Stock sizes of round and square bars vary by thirty sec- 
 onds of an inch from % in. to % in. diameter, by sixteenths 
 from f to 2 ins. diameter, by eighths from 2 to 3 ins. diameter, 
 and by quarters of an inch from 3 ins. diameter and upwards. 
 Round bars are also rolled by a few companies in sixty-fourths 
 of an inch up to 1 in. diameter. Below % in. rounds are com- 
 monly designated by wire-gauge numbers. 
 
WEIGHTS OF FLAT ROLLED STEEL BARS. 1353 
 
 WEIGHTS OF FLAT ROLLED STEEL BARS. 
 
 PER LINEAL FOOT. 
 
 (One cubic foot of steel weighs 489.6 Ibs.) 
 
 For thicknesses from Ho inch to Q /LQ inch and widths from }/ inch to % inch. 
 
 Thick- 
 ness, 
 in 
 Inches. 
 
 Width in Inches. 
 
 M" 
 
 5 /io" 
 
 %" 
 
 T/16" 
 
 W 
 
 9 /io" 
 
 *A" 
 
 Hie" 
 
 M" 
 
 -Via 
 
 .053 
 
 .066 
 
 .080 
 
 .093 
 
 .106 
 
 .120 
 
 .133 
 
 .146 
 
 .159 
 
 %4 
 
 .066 
 
 .083 
 
 .100 
 
 .116 
 
 .133 
 
 .149 
 
 .166 
 
 .183 
 
 .199 
 
 %2 
 
 .080 
 
 .100 
 
 .120 
 
 .139 
 
 .159 
 
 .179 
 
 .199 
 
 .219 
 
 .239 
 
 T/64 
 
 .093 
 
 .116 
 
 .139 
 
 .163 
 
 .186 
 
 .209 
 
 .232 
 
 .256 
 
 .279 
 
 % 
 
 .106 
 
 .133 
 
 .159 
 
 .186 
 
 .212 
 
 .239 
 
 .266 
 
 .292 
 
 .319 
 
 %4 
 
 .120 
 
 .149 
 
 .179 
 
 .209 
 
 .239 
 
 .269 
 
 .299 
 
 .329 
 
 .359 
 
 5 /32 
 
 .133 
 
 .166 
 
 .199 
 
 .232 
 
 .266 
 
 .299 
 
 .332 
 
 .365 
 
 .398 
 
 ^64 
 
 .146 
 
 .183 
 
 .219 
 
 .256 
 
 .292 
 
 .329 
 
 .365 
 
 .402 
 
 .438 
 
 %6 
 
 .159 
 
 .199 
 
 .239 
 
 .279 
 
 .319 
 
 .359 
 
 .398 
 
 .438 
 
 .478 
 
 13 /64 
 
 .173 
 
 .216 
 
 .259 
 
 .302 
 
 .345 
 
 .388 
 
 .432 
 
 .475 
 
 .518 
 
 7 /32 
 
 .186 
 
 .232 
 
 .279 
 
 .325 
 
 .372 
 
 .418 
 
 . .465 
 
 .511 
 
 .558 
 
 15 /64 
 
 .199 
 
 .249 
 
 .299 
 
 .349 
 
 .398 
 
 .448 
 
 .498 
 
 .548 
 
 .598 
 
 # 
 
 .213 
 
 .266 
 
 .319 
 
 .372 
 
 .425 
 
 .478 
 
 .531 
 
 .584 
 
 .638 
 
 17 /64 
 
 .226 
 
 .282 
 
 .339 
 
 .395 
 
 .452 
 
 .508 
 
 .564 
 
 .621 
 
 .677 
 
 %2 
 
 .239 
 
 .299 
 
 .359 
 
 .418 
 
 .478 
 
 .538 
 
 .598 
 
 .657 
 
 .717 
 
 19 /64 
 
 .252 
 
 .315 
 
 .379 
 
 .442 
 
 .505 
 
 .568 
 
 .631 
 
 .694 
 
 .757 
 
 9ie 
 
 .266 
 
 .332 
 
 .398 
 
 .465 
 
 .531 
 
 .598 
 
 .664 
 
 .730 
 
 .797 
 
 2 V64 
 
 .279 
 
 .349 
 
 .418 
 
 .488 
 
 .558 
 
 .628 
 
 .697 
 
 .767 
 
 .827 
 
 i&a 
 
 .292 
 
 .365 
 
 .438 
 
 .511 
 
 .584 
 
 .657 
 
 .730 
 
 .804 
 
 .877 
 
 2 %4 
 
 .305 
 
 .382 
 
 .458 
 
 .535 
 
 .611 
 
 .687 
 
 .764 
 
 .840 
 
 .916 
 
 N 
 
 .319 
 
 .398 
 
 .478 
 
 .558 
 
 .638 
 
 .717 
 
 .797 
 
 .877 
 
 .956 
 
 2 %4 
 
 .332 
 
 .415 
 
 .498 
 
 .581 
 
 .664 
 
 .747 
 
 .830 
 
 .913 
 
 .996 
 
 13 /32 
 
 .345 
 
 .432 
 
 ..518 
 
 .604 
 
 .691 
 
 .777 
 
 .863 
 
 .950 
 
 1.04 
 
 27 /64 
 
 .359 
 
 .448 
 
 .538 
 
 .628 
 
 .717 
 
 .807 
 
 .896 
 
 .986 
 
 1.03 
 
 7 /16 
 
 .372 
 
 .465 
 
 .558 
 
 .651 
 
 .744 
 
 .837 
 
 .930 
 
 1.02 
 
 1.12 
 
 2 %4 
 
 .385 
 
 .481 
 
 .578 
 
 .674 
 
 .770 
 
 .867 
 
 .963 
 
 1.06 
 
 1.16 
 
 1%2 
 
 .398 
 
 .498 
 
 .598 
 
 .697 
 
 .797 
 
 .896 
 
 .996 
 
 1.10 
 
 1.20 
 
 8 V64 
 
 .412 
 
 .515 
 
 .618 
 
 .721 
 
 .823 
 
 .926 
 
 1.03 
 
 1.13 
 
 1.24 
 
 H 
 
 .425 
 
 .531 
 
 .638 
 
 .744 
 
 .850 
 
 .956 
 
 1.06 
 
 1.17 
 
 1.28 
 
 8 %4 
 
 .438 
 
 .548 
 
 .657 
 
 .767 
 
 .877 
 
 .986 
 
 1.10 
 
 1.21 
 
 1.31 
 
 17 /32 
 
 .452 
 
 .564 
 
 .677 
 
 .790 
 
 .903 
 
 1.02 
 
 1.13 
 
 1.24 
 
 1.35 
 
 8 %4 
 
 .465 
 
 .5S1 
 
 .697 
 
 .813 
 
 .930 
 
 1.05 
 
 1.16 
 
 1.28 
 
 1.39 
 
 9 /16 
 
 .478 
 
 .595 
 
 .717 
 
 .837 
 
 .956 
 
 1.08 
 
 1.20 
 
 1.31 
 
 1 43 
 
1354 WEIGHTS OF FLAT ROLLED STEEL BARS. 
 
 WEIGHTS OF FLAT ROLLED STEEL BARS. Continued. 
 
 PER LINEAL FOOT. 
 (Me" to 2" in thickness, I" to 12" in width.) 
 
 Thick- 
 ness, 
 in 
 Inches. 
 
 1" 
 
 1M" 
 
 1 1 A" 
 
 1M" 
 
 2" 
 
 2M" 
 
 2H" 
 
 2M" 
 
 3" 
 
 
 
 .2l| .26 
 
 .32 
 
 .37 
 
 .43 
 
 .4$ 
 
 .53 
 
 .58 
 
 .63 
 
 
 .42 
 
 .53 
 
 .64 
 
 .75 
 
 .85 
 
 .96 
 
 1.06 
 
 1.17 
 
 1.28 
 
 %> 
 
 .63 
 
 .79 
 
 .96 
 
 1.11 
 
 1,23 
 
 1.44 
 
 1.59 
 
 1.75 
 
 1.91 
 
 \ 
 
 4 
 
 .85 
 
 1.06 
 
 1.2. 
 
 1.49 
 
 1.70 
 
 1.91 
 
 2.12 
 
 2.34 
 
 2.55 
 
 ^6 
 
 1.06 
 
 1.33 
 
 1.59 
 
 1.86 
 
 2.12 
 
 2 39 
 
 2.65 
 
 2.92 
 
 3.19 
 
 1 
 
 1.2 
 
 1.59 
 
 1.92 
 
 2.23 
 
 2.55 2.87 
 
 3.19 
 
 3.51 
 
 3.83 
 
 % 
 
 1.49 
 
 1.86 
 
 2.23 
 
 2.60 
 
 2.98| 3.35 
 
 3.72 
 
 4.09 
 
 4.46 
 
 i 
 
 1.70 
 
 2.12 
 
 2.55 
 
 2.9S 
 
 3.40 
 
 3.83 
 
 4.25 
 
 4.67 
 
 5.10 
 
 % 
 
 1.92 
 
 2.39 
 
 2.87 
 
 3.35 
 
 3.83 
 
 4.30 
 
 4.7^ 
 
 5.26 
 
 5.74 
 
 \ 
 
 2.12 
 
 2.65 
 
 3.19 
 
 3.72 
 
 4.25 
 
 4.78 
 
 5.31 
 
 5.84 
 
 6.38 
 
 % 
 
 2.34 
 
 2.92 
 
 3.51 
 
 4.09 
 
 4.67 
 
 5.26 
 
 5.84 
 
 6.43 
 
 7.02 
 
 
 2.55 
 
 3.19 
 
 3.83 
 
 4.47 
 
 5.10 
 
 5.75 
 
 6.38 
 
 7.02 
 
 7.65 
 
 % 
 
 2.76 
 
 3.45 
 
 4.14 
 
 4.P4 
 
 5.53 
 
 6.21 
 
 6.90 
 
 7.60 
 
 8.29 
 
 'I 
 
 2.93 
 
 3.72 
 
 4.47 
 
 5.20 
 
 5.95 
 
 6.69 
 
 7.44 
 
 8.18 
 
 8.93 
 
 % 
 
 3.19 
 
 3.99 
 
 4.78 
 
 5.58 
 
 6.38 
 
 7.18 
 
 7.97 
 
 8.77 
 
 9.57 
 
 
 3.40 
 
 4.25 
 
 5.10 
 
 5.95 
 
 6.80 
 
 7.65 
 
 8.50 
 
 9.35 
 
 10.20 
 
 1^6 
 
 3.61 
 
 4.52 
 
 5.42 
 
 6.32 
 
 7.22 
 
 8.13 
 
 9.03 
 
 9.93 
 
 10.84 
 
 Hr 
 
 3.83 
 
 4.78 
 
 5.74 
 
 6.70 
 
 7.65 
 
 8.61 
 
 9.57 
 
 10.52 
 
 11.48 
 
 1% 
 
 4.04 
 
 5.05 
 
 6.06 
 
 7.07 
 
 8.03 
 
 9.09 
 
 10.10 
 
 11.11 
 
 12.12 
 
 ii 
 
 4.25 
 
 5.31 
 
 6.38 
 
 7.44 
 
 8.50 
 
 9.57 
 
 10.63 
 
 11.69 
 
 12.75 
 
 1% 
 
 4.46 
 
 5.58 
 
 6.69 
 
 7.81 
 
 8.93 
 
 10.04 
 
 11.16 
 
 12.27 
 
 13.39 
 
 If 
 
 4.67 
 
 5.84 
 
 7.02 
 
 8.18 
 
 9.35 
 
 10.52 
 
 11.69 
 
 12.85 
 
 14.03 
 
 1% 
 
 4.89 
 
 6.11 
 
 7.34 
 
 8.56 
 
 9.78 
 
 11.00 
 
 12.22 
 
 13.44 
 
 14.66 
 
 li 
 
 5,10 
 
 6.38 
 
 7.65 
 
 8.93 
 
 10.20 
 
 11.48 
 
 12.75 
 
 14.03 
 
 15.30 
 
 1% 
 
 5.32 
 
 6.64 
 
 7.97 
 
 9.30 
 
 10.63 
 
 11.95 
 
 13.28 
 
 14.61 
 
 15.94 
 
 If 
 
 5.52 
 
 6.90 
 
 8.29 
 
 9.67 
 
 11.05 
 
 12.4313.81 
 
 15.19 
 
 16.58 
 
 1% 
 
 5.74 
 
 7.17 
 
 8.61 
 
 10.04 
 
 11.47 
 
 12.91 14.34 
 
 15.78 
 
 17.22 
 
 l! 
 
 5.95 
 
 7.44 
 
 8.93 
 
 10.42 
 
 11.90 
 
 13.40 
 
 14.88 
 
 16.37 
 
 17.85 
 
 1% 
 
 6.16 
 
 7.70 
 
 9.24 
 
 10.79 
 
 12.33 
 
 13.86 
 
 15.40 
 
 16.95 
 
 18.49 
 
 W 
 
 6.38 
 
 7.97 
 
 9.57 
 
 11.15 
 
 12.7514.34 
 
 15.94 
 
 17.53 
 
 19.13 
 
 1% 
 
 6.59 
 
 8.24 
 
 9.88 
 
 11.53 
 
 13.18 
 
 14.83 
 
 16.47 
 
 18.12 
 
 19.77 
 
 2 
 
 6.80 
 
 8.50 
 
 10.20 
 
 11.90 
 
 13.60 
 
 15.30 
 
 17.00 
 
 18.70 
 
 20.40 
 
WEIGHTS OF FLAT ROLLED STEEL BARS. 1355 
 
 WEIGHTS OF FLAT ROLLED STEEL BARS. Continued. 
 
 * PER LINEAL FOOT. . 
 
 (Vie" to 2" in thickness, 1" to 12" in width.) 
 
 Thick- 
 
 
 
 
 
 
 
 
 
 3 
 
 in 
 Inches. 
 
 3K 
 
 4" 
 
 4W 
 
 5" 
 
 58 
 
 6" 
 
 6^" 
 
 7" 
 
 >l6 
 
 .75 
 
 .85 
 
 .96 
 
 1.06 
 
 1.17 
 
 1.28 
 
 1.39 
 
 1.49 
 
 1.60 
 
 | 
 
 1.49 
 
 1.70 
 
 1.92 
 
 2.13 
 
 2.34 
 
 2.55 
 
 2.77 
 
 2.98 
 
 3.19 
 
 
 2.23 
 
 2.55 
 
 2.87 
 
 3.19 
 
 3.51 
 
 3.83 
 
 4.14 
 
 4.46 
 
 4.78 
 
 i 
 
 2.98 
 
 3.40 
 
 3.83 
 
 4.25 
 
 4.67 
 
 5.10 
 
 5.53 
 
 5.95 
 
 6.36 
 
 % 
 
 3.72 
 
 4.25 
 
 ' 4.78 
 
 5.31 
 
 5.84 
 
 6.38 
 
 6.90 
 
 7.44 
 
 7.97 
 
 i 
 
 4.47 
 
 5.10 
 
 5.74 
 
 6.38 
 
 7.02 
 
 7.65 
 
 8.29 
 
 8.93 
 
 9.57 
 
 
 5.20 
 
 5.95 
 
 6.70 
 
 7.44 
 
 8.18 
 
 8.93 
 
 9.67 
 
 10.41 
 
 11.16 
 
 i 6 
 
 5.95 
 
 6.80 
 
 7.65 
 
 8.50 
 
 9.35 
 
 10.20 
 
 11.05 
 
 11.90 
 
 12.75 
 
 % 
 
 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 
 
 
 8.18 
 
 9.35 
 
 10.52 
 
 11.69 
 
 12.85 
 
 14.03 
 
 15.2016.36 
 
 17.53 
 
 f 
 
 8.9310.20 
 
 11.48 
 
 12.75 
 
 14.03 
 
 15.30 
 
 16.58 
 
 17.85 
 
 19.13 
 
 %5 
 
 9.6711.05 
 
 12.43 
 
 13.81 
 
 15.19 
 
 16.58 
 
 17.9519.34 
 
 20.72 
 
 1 
 
 10.41 11.90 
 
 13.39 
 
 14.87 
 
 16.36 
 
 17.85 
 
 19.3420.83 
 
 22.32 
 
 
 11.1612.7514.34 
 
 15.94 
 
 17.53 
 
 19.13 
 
 20.7222.32 
 
 23.91 
 
 i i 
 
 11.9013.6015.30 
 
 17.00 
 
 18.70 
 
 20.40 
 
 22.10^3.80 
 
 25.50 
 
 iM 
 
 12.6514.45 
 
 16.26 
 
 18.06 
 
 19.87 
 
 21.68 
 
 23.48 
 
 25.29 
 
 27.10 
 
 i|- 
 
 13.3915.30 
 
 17.22 
 
 19.13 
 
 21 .04 
 
 22. 95 24.871 26. 78 
 
 28.68 
 
 
 14.1316.15 
 
 18.17 
 
 20.19 
 
 22.21 
 
 24.2326.2428.26 
 
 30.28 
 
 ii 6 
 
 14.8717.00 
 
 19.13 
 
 21.25 
 
 23.38 
 
 25.50 
 
 27.6229.75 
 
 31.88 
 
 IJie 
 
 15.6217.85 
 
 20.08 
 
 22.32 
 
 24.54 
 
 26.78 
 
 29.01 
 
 31.23 
 
 33.48 
 
 1| 
 
 16.3618.70 
 
 21.04 
 
 23.38 
 
 25.71 
 
 28.0530.3932.72 
 
 35.06 
 
 \i/ 
 
 17.1019.85 
 
 21.99 
 
 24.44 
 
 26.88 
 
 29.3331.7734.21 
 
 36.66 
 
 li 
 
 17.8520.40 
 
 22.95 
 
 25.50 
 
 28.05 
 
 30.6033.1535.70 
 
 38.26 
 
 1% 
 
 18.6021.25 
 
 23.91 
 
 26.57 
 
 29.22 
 
 31.8834.53 
 
 37.19 
 
 39.84 
 
 If 6 
 
 19.3422.10 
 
 24.87 
 
 27.63 
 
 30.39 
 
 33.1535.9138.67 
 
 41.44 
 
 
 20.0822.95 
 
 25.82 
 
 28.69 
 
 31.55 
 
 34.4337.3040.16 
 
 43.03 
 
 If 16 
 
 20.8323.80 
 
 26.78 
 
 29.75 
 
 32.73 
 
 35.70 
 
 38.68 
 
 41.65 
 
 44.63 
 
 1% 
 
 21.5724.65 
 
 27.73 
 
 30.81 
 
 33.89 
 
 36.98 
 
 40.05 
 
 43.14 
 
 46.22 
 
 1- 
 
 22.3125.50 
 
 2V 69 
 
 31.87 
 
 35.06 
 
 38.25 ! 41.44 
 
 44.63 
 
 47.82 
 
 1^6 
 
 23.0626.35 
 
 29.64 
 
 32.94 
 
 36.23 
 
 39.5342.8246.12 
 
 49.41 
 
 2 
 
 23.80 
 
 27.20 
 
 30.60 
 
 34.00 
 
 37.40 
 
 40.80 
 
 44.2047.60 
 
 51.00 
 
1356 WEIGHTS OF FLAT ROLLED STEEL BARS. 
 
 WEIGHTS OF FLAT ROLLED STEEL BARS. Continued. 
 
 PER LINEAL FOOT. < 
 
 (Vis" to 2" in thickness, 1" to 12" in width.) 
 
 Thick- 
 ness, 
 in 
 Inches. 
 
 8" 
 
 * 
 
 9" 
 
 * 
 
 10" 
 
 . 
 
 11" 
 
 2.34 
 4.68 
 7.02 
 9.34 
 
 U 
 
 12" 
 
 | 6 
 i 6 
 
 1.70 
 3.40 
 5.10 
 6.80 
 
 1.81 
 3.61 
 5.42 
 7.22 
 
 1.91 
 3.82 
 5.74 
 7.65 
 
 2.02 
 4.04 
 6.06 
 
 8.08 
 
 2.13 
 4.25 
 6.38 
 
 8.50 
 
 2.23 
 4.46 
 6.70 
 8.92 
 
 2.45 
 4.89 
 7.32 
 
 9.78 
 
 2.55 
 5.10 
 7.65 
 10.20 
 
 i 6 
 
 8.50 
 10.20 
 11.90 
 13.60 
 
 9.03 
 10.84 
 12.64 
 14.44 
 
 9.56 
 11.48 
 13.40 
 15.30 
 
 10.10 
 12.12 
 14.14 
 16.16 
 
 10.62 
 12.75 
 
 14.88 
 17.00 
 
 11.16 
 13.39 
 15.62 
 
 17.85 
 
 11.68 
 14.03 
 16.36 
 18.70 
 
 12.22 
 14.68 
 17.12 
 19.55 
 
 12.75 
 15.30 
 
 17.85 
 20.40 
 
 I 
 
 I 6 
 
 15.30 
 17.00 
 18.70 
 20.40 
 
 16.26 
 18.06 
 19.86 
 21.63 
 
 17.22 
 19.13 
 21.04 
 22.96 
 
 18.18 
 20.19 
 22.21 
 24.23 
 
 19.14 
 21.25 
 23.38 
 25.50 
 
 20.08 
 22.32 
 24.54 
 26.78 
 
 21.02 
 23.38 
 25.70 
 28.05 
 
 22.00 
 24.44 
 26.88 
 29.33 
 
 22.95 
 25.50 
 28.05 
 30.60 
 
 1 
 
 22.10 
 23.80 
 25.50 
 27.20 
 
 23.48 
 25.30 
 27.10 
 28.90 
 
 24.86 
 26.78 
 28.69 
 30.60 
 
 26.24 
 28.26 
 30.28 
 32.30 
 
 27.62 
 29.75 
 
 31.88 
 34.00 
 
 29.00 
 31.24 
 33.48 
 35.70 
 
 30.40 
 32 72 
 35.06 
 37.40 
 
 31.76 
 34.21 
 36.66 
 39.10 
 
 33.15 
 35.70 
 38.25 
 40.80 
 
 H 6 
 
 28.90 
 30.60 
 32.30 
 34.00 
 
 30.70 
 32.52 
 34.32 
 36.12 
 
 32.52 
 34.43 
 36.34 
 38.26 
 
 34.32 
 36.34 
 
 38.36 
 40.37 
 
 36.12 
 38.25 
 
 40.38 
 42.50 
 
 37.92 
 40.17 
 42.40 
 44.63 
 
 39.74 
 42.08 
 44.42 
 46.76 
 
 41.54 
 44.00 
 46.44 
 
 48.88 
 
 43.35 
 45.90 
 
 48.45 
 51.00 
 
 if 
 li 6 
 
 35.70 
 37.40 
 39.10 
 40.80 
 
 37.93 
 39.74 
 41.54 
 43.35 
 
 40.16 
 42.08 
 44.00 
 45.90 
 
 42.40 
 44.41 
 46.44 
 
 48.45 
 
 44.64 
 46.75 
 
 48.88 
 51.00 
 
 46.86 
 49.08 
 51.32 
 53.55 
 
 49.08 
 51.42 
 53.76 
 56.10 
 
 51.32 
 53.76 
 56.21 
 58.65 
 
 53.55 
 56.10 
 58.65 
 61.20 
 
 if 6 
 li 6 
 
 42.50 
 44.20 
 45.90 
 47.60 
 
 45.16 
 46.96 
 48.76 
 50.58 
 
 47.82 
 49.73 
 51.64 
 53.56 
 
 50.48 
 52.49 
 54.51 
 56.53 
 
 53.14 
 55.25 
 57.38 
 59.50 
 
 55.78 
 58.02 
 60.24 
 62.48 
 
 58.42 
 60.78 
 63.10 
 65.45 
 
 61.10 
 63.54 
 65.98 
 68.43 
 
 63.75 
 66.30 
 
 68.85 
 71.40 
 
 2 16 
 
 49.30 
 51.00 
 52.70 
 54.40 
 
 52.38 
 54.20 
 56.00 
 57.80 
 
 55.46 
 57.38 
 59.29 
 61.20 
 
 58.54 
 60.56 
 62.58 
 64.60 
 
 61.62 
 63.75 
 
 65.88 
 68.00 
 
 64.70 
 66.94 
 69.18 
 71.40 
 
 67.80 
 70.12 
 72.46 
 74.80 
 
 70.86 
 73.31 
 75.76 
 
 78.20 
 
 73.95 
 76.50 
 79.05 
 81.60 
 
ESTIMATING WEIGHT OF WROUGHT IRON, ETC. 1357 
 
 Rules for Estimating the Weight of any Piece of 
 Wrought Iron, Steel, or Cast Iron. 
 
 Wrought iron: 
 
 One cubic foot of wrought iron weighs . . . 480 Ibs. 
 One square foot, one inch thick, weighs. . 40 ' ' 
 One square inch, one foot long, weighs.. . 3J " 
 To find the weight per square foot of sheet iron, multiply 
 the thickness in inches by 40. 
 
 To find the weight per lineal foot of bars of any section, 
 multiply the cross-sectional area in square inches by 3J. 
 Steel : 
 
 One cubic foot <of steel weighs 489 . 6 Ibs. 
 
 (Or just 2 per cent, more than wrought iron.) 
 One square foot, one inch thick, weighs. .40.8 " 
 One square inch, one foot long, weighs. . 3.4 " 
 To find the weight per lineal 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 sectional area may be obtained 
 by dividing by 3.4. 
 Cast iron: 
 
 One cubic foot of cast iron weighs 450 Ibs. 
 
 One square foot, one inch thick, weighs . . 37J ' ' 
 One square inch, one foot long, weighs ... 3 J ' ' 
 
 One cubic inch weighs 26 ' ' 
 
 The weight of irregular castings must be estimated by the 
 cubic inch. 
 
 Rules for Weights of Castings. 
 
 Multiply the weight of the pattern by 12 for cast iron, 13 for 
 brass, 19 for lead, 12.2 for tin, 11.4 for zinc, and 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. 
 
 Cast iron, J 
 
 Pattern-makers' Rule. 
 
 Lead 
 
 Tin 
 
 Zinc 
 
 of an inch longer pel 
 lineal foot. 
 
1358 WEIGHT OF SQUARE CAST-IRON COLUMNS, 
 
 WEIGHT OF SQUARE CAST-IRON COLUMNS IN POUNDS 
 PER LINEAL FOOT. 
 
 (Birkmire.) 
 
 on 
 
 b 
 
 2a + 2b 
 
 Thickness of Metal in Inches. 
 
 K: 
 
 H 
 
 K . 
 
 1 
 
 IK 
 
 1M 
 
 IK 
 
 1M 
 
 2 
 
 * 
 
 
 
 
 
 
 
 
 
 
 12 
 
 18.6 
 
 21.1 
 
 23.3 
 
 25.0 
 
 26.4 
 
 27.3 
 
 28.1 
 
 
 
 14 
 
 22.5 
 
 25.8 
 
 28.7 
 
 31.3 
 
 33.4 
 
 35.1 
 
 37.5 
 
 
 
 16 
 
 26.4 
 
 30.5 
 
 34.2 
 
 37.5 
 
 40.4 
 
 43.0 
 
 46.9 
 
 49.2 
 
 50.0 
 
 18 
 
 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 
 
 93.0 
 
 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 
 
 30 
 
 53.7 
 
 63.3 
 
 72.5 
 
 81.3 
 
 89.6 
 
 97.7 
 
 112.5 
 
 125.8 
 
 137.5 
 
 32 
 
 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 
 
 100.0 
 
 110.7 
 
 121.1 
 
 140.6 
 
 158.6 
 
 175.0 
 
 38 
 
 69.3 
 
 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 
 
 77.1 
 
 91.4 
 
 105.3 
 
 118.8 
 
 131.8 
 
 144.5 
 
 168.8 
 
 191.4 
 
 212.5 
 
 44 
 
 81.0 
 
 96.1 
 
 110.8 
 
 125.0 
 
 138.8 
 
 152.3 
 
 178.1 
 
 202.3 
 
 225.0 
 
 46 
 
 84.9 
 
 100.8 
 
 116.2 
 
 131.3 
 
 145.9 
 
 160.2 
 
 187.5 
 
 213.3 
 
 237.5 
 
 48 
 
 88.8 
 
 105.5 
 
 121.7 
 
 137.5 
 
 152.9 
 
 168.0 
 
 196.9 
 
 224.2 
 
 250.0 
 
 50 
 
 92.8 
 
 110.2 
 
 127.2 
 
 143.8 
 
 159.9 
 
 175.8 
 
 206.3 
 
 235.2 
 
 262.5 
 
 52 
 
 96.7 
 
 114.3 
 
 132.6 
 
 150.0 
 
 167.0 
 
 183.6 
 
 215.6 
 
 246.1 
 
 275.0 
 
 54 
 
 100.6 
 
 11. .5 
 
 138.1 
 
 156.3 
 
 174.0 
 
 191.4 
 
 225.0 
 
 257.0 
 
 287.5 
 
 56 
 
 104.5 
 
 124.2 
 
 143.6 
 
 162.5 
 
 181.0 
 
 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 
 
 138.3 
 
 160.0 
 
 181.3 
 
 202.1 
 
 222.7 
 
 262.5 
 
 300.8 
 
 337.5 
 
 64 
 
 120.1 
 
 143.0 
 
 165.4 
 
 187.5 
 
 209.2 
 
 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 
 
 290.61 333.6 
 
 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 
 
 212.5 
 
 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 
 
 147.4 
 
 175.8 
 
 203.7 
 
 231.3 
 
 258.4 
 
 285-2 
 
 337.5 
 
 388.3 
 
 437.5 
 
 80 
 
 151.3 
 
 180.5 
 
 207.2 
 
 237.5 
 
 265.4 
 
 293.0 
 
 346.9 
 
 309.2 
 
 450.0 
 
 *a and 6 = either side (outside measurement). 2a + 26 = number. 
 Allowance has been made in this table for corners counted twice. 
 
 EXAMPLE. What is the weight per lineal foot of a 12 // Xl6 // 
 X 1" thick column? 
 
 Ans. 2a + 26 =24 + 32 =56. Opposite this number, under 
 1-inch thick metal, we find 162.5, or weight per lineal foot of a 
 12 // X16 // X1 // thick column. 
 
 NOTE. For flanges, brackets, etc., calculate the cubical con- 
 tents of same and multiply by .26; cast iron averaging 450 pounds 
 per cubic foot. 
 
WEIGHT OF CIRCULAR CAST-IRON COLUMNS. 1359 
 
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 ^S^^a8g^S^^28g^ .a 
 
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 i !O5COOOt>I>COCDiO^t i e'^t i COCO(NC^OrHOO -*-* 
 
 fl - -- .,-. I 
 
 eoooooopoqoooopooo p~o 
 
 ill 
 
 5^S.95P f 5i2^S?2'3l55S T ^ c ^ cc>ooc>c ^ lot ^ o: ' 
 
 C^ (M (M (N (M C^J 
 
 "S 
 
 
 
 I 
 
 S 
 
 .2 
 
 <u 
 2 
 
 OJ JP 
 
 ICOrHCOrHCQrHCOrHCOrHCOi <COO>OO>O rfl . 
 
 I % 
 
 >> 
 
 2^ 
 
 ^ S 
 
 3 
 
1360 
 
 WEIGHT OF CAST-IRON PLATES. 
 
 WEIGHT OF CAST-IRON PLATES. 
 
 WEIGHT, IN POUNDS, OF CAST-IRON PLATES ONE 
 INCH THICK. 
 
 (Calculated at 450 Ibs. per cubic foot.) 
 
 4 
 6 
 
 8 
 10 
 
 12 
 14 
 16 
 18 
 
 20 
 22 
 24 
 26 
 
 28 
 30 
 32 
 36 
 
 For larger plates take size of plate one half smaller and mul- 
 tiply by 2. Thus a plate 28"X32" will weigh twice as much 
 as one 14"X32". For plates more or less than one inch in 
 thickness multiply weight of plate by thickness in inches. 
 
 Width, in Inches. 
 
 6 
 
 8 
 
 10 
 
 12 
 
 14 
 
 16 
 
 18 
 
 18.7 
 28.1 
 37.4 
 46.8 
 
 20 
 
 20.8 
 31.2 
 41.6 
 52.0 
 
 24 
 
 25 
 38 
 50 
 63 
 
 30 
 
 3 
 4 
 6 
 
 7 
 
 6.25 
 9.37 
 12.50 
 15.60 
 
 8.3 
 12.5 
 16.6 
 20.8 
 
 10.4 
 15.6 
 20.8 
 26.0 
 
 12.5 
 18.7 
 25.0 
 31.2 
 
 14.6 
 21.8 
 29.1 
 36.4 
 
 16.6 
 25.0 
 33.3 
 41.6 
 
 18.70 
 21.80 
 24.90 
 28.10 
 
 25.0 
 29.2 
 33.3 
 37.5 
 
 31.2 
 36.4 
 41.6 
 46.8 
 
 37.5 
 43.7 
 50.0 
 56.2 
 
 43.7 
 51.0 
 58.2 
 65.5 
 
 49.9 
 58.2 
 66.6 
 74.9 
 
 56.2 
 65.5 
 74.9 
 84.2 
 
 62.4 
 72.8 
 83.2 
 93.6 
 
 75 
 88 
 100 
 113 
 
 9^ 
 10 
 12 
 14 
 
 31.20 
 34.30 
 37.50 
 40.60 
 
 41.6 
 45/8 
 50.0 
 54.0 
 
 52.0 
 57.2 
 62.4 
 67.6 
 
 62.3 
 68.6 
 75.0 
 81.2 
 
 72.8 
 80.1 
 87.4 
 94.6 
 
 83.2 
 91.5 
 99.8 
 108.2 
 
 93.6 
 103.0 
 112.3 
 121.7 
 
 104.0 
 114.4 
 124.8 
 135.2 
 
 125 
 
 138 
 150 
 163 
 
 15 
 17. 
 
 18 
 20 
 
 43.60 
 46.80 
 49.80 
 56.10 
 
 58.2 
 62.4 
 66.6 
 75.0 
 
 72.8 
 78.0 
 83.2 
 93.6 
 
 87.5 
 93.7 
 100.0 
 112.5 
 
 101.9 
 109.2 
 116.5 
 131.0 
 
 116.5 
 124.8 
 133.1 
 150.0 
 
 131.0 
 140.4 
 150.3 
 168.4 
 
 145.6 
 156.0 
 166.4 
 187.2 
 
 175 
 
 188 
 200 
 225 
 
 215 
 23' 
 25( 
 
 28 
 
 APPROXIMATE WEIGHT OF SQUARE-RIBBED CAST- 
 IRON COLUMN BASES. 
 
 The following table, giving the weight of cast-iron column 
 bas"es, is new and will be useful when estimating the steel and 
 iron in tall buildings : * 
 
 Size 
 
 of Square 
 Base. 
 
 Weight 
 
 in 
 Pounds. 
 
 22X22 600 
 
 24X24 750 
 
 26X26 880 
 
 28X28 1,020 
 
 30X30 1,180 
 
 Size 
 
 of Square 
 Base. 
 
 Weight 
 
 in 
 Pounds. 
 
 32X32 1,340 
 
 34X34 1,450 
 
 36X36 1,600 
 
 38X38 1,720 
 
 40X40.. .1,850 
 
 * H. G. Tyrrell, C.E., in Architects and Builders Magazine, Jan., 1903. 
 
SCREW-THREADS, NUTS, AND BOLT-HEADS. 1361 
 
 SCREW-THREADS, NUTS, AND BOLT-HEADS. 
 
 STANDARD SCREW-THREADS. 
 
 Recommended by Franklin Institute, Dec. 15, 1864, and adopted by 
 Navy Dept of the United States; by the R. R. Master Mechanics' and 
 Master Car-builders' Associations; "by Messrs. Jones & Laughlins, Limited; 
 and by many other of the prominent engineering and mechanical estab- 
 lishments tif the country. 
 
 Angle of thread 60 Flat at top and bottom K of pitch. 
 
 Diam. 
 of 
 Screw. 
 
 Threads 
 per Inch. 
 
 Diam. at 
 Root of 
 Thread. 
 
 Area at 
 Root of 
 Thread. 
 
 Diam. 
 of 
 Screw. 
 
 Threads 
 per Inch. 
 
 Diam. at 
 Root of 
 Thread. 
 
 Area at 
 Root of 
 Thread. 
 
 
 
 
 sq. in. 
 
 
 
 
 sq. in. 
 
 M 
 
 20 
 
 .185 
 
 .027 
 
 2 
 
 4^ 
 
 1.712 
 
 2.302 
 
 %6 
 
 18 
 
 .240 
 
 .045 
 
 2M 
 
 4^2 
 
 1.962 
 
 3.023 
 
 Y% 
 
 16 
 
 .294 
 
 .068 
 
 2^2 
 
 4 
 
 2.176 
 
 3.719 
 
 %6 
 
 14 
 
 .344 
 
 .093 
 
 2H 
 
 4 
 
 2.426 
 
 4.620 
 
 
 13 
 
 .400 
 
 .126 
 
 3 
 
 3^g 
 
 2.629 
 
 5.428 
 
 71.6 
 
 12 
 
 .454 
 
 .162 
 
 3^ 
 
 sy 2 
 
 2.879 
 
 6.510 
 
 
 11 
 
 .507 
 
 .202 
 
 3^ 
 
 3 
 
 3.100 
 
 7.548 
 
 % 
 
 10 
 
 .620 
 
 .302 
 
 3M 
 
 3 
 
 3.317 
 
 8.641 
 
 % 
 
 9 
 
 .731 
 
 .420 
 
 
 3 
 
 3.567 
 
 9.963 
 
 I 
 
 8 
 
 .837 
 
 .550 
 
 4K 
 
 2 
 
 3.798 
 
 11.329 
 
 IH 
 
 7 
 
 .940 
 
 .694 
 
 4^ 
 
 2 
 
 4.028 
 
 12.753 
 
 IH 
 
 7 
 
 1.065 
 
 .893 
 
 4M 
 
 2 
 
 4.256 
 
 14.226 
 
 itt 
 
 6 
 
 1.160 
 
 1.057 
 
 5 
 
 2 
 
 4.480 
 
 15.763 
 
 m 
 
 6 
 
 1.284 
 
 1.295 
 
 5^ 
 
 2 
 
 4.730 
 
 17.572 
 
 IH 
 
 &A 
 
 1.389 
 
 1.515 
 
 &/2 
 
 2 
 
 4.953 
 
 19.267 
 
 m 
 
 5 
 
 1.491 
 
 1.746 
 
 5M 
 
 2 
 
 5.203 
 
 21.262 
 
 IK 
 
 5 
 
 1.616 
 
 2.051 
 
 6 
 
 2 
 
 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 = 1HX diam. of bolt + H in. 
 
 Short diameter of finished nut = 1^X diam. of bolt + He in. 
 
 Thickness of rough nut = diam. of bolt. 
 
 Thickness of finished nut = diam. of bolt ^e in. 
 
 Short diameter of rough head = 1^ X diam. of bolt + H in. 
 
 Short diameter of finished head = 1H X diam. of bolt + ^le in. 
 
 Thickness of rough head = J^ short diam. of head. 
 
 Thickness of finished head = diam. of bolt ^6 in. 
 
 The long diameter of a hexagon nut may be obtained by multiplying 
 the short diameter by 1.155, and the long diameter of a square nut by 
 multiplying the short diameter by 1.414. 
 
1362 
 
 STANDARD NUTS AND BOLT-HEADS. 
 
 STANDARD DIMENSIONS OF NUTS AND 
 BOLT-HEADS. 
 
 Dia. 
 of 
 
 Short 
 Diam. 
 Rough. 
 
 Short 
 Diam. 
 Finish. 
 
 I^ong 
 Diam. 
 Rough. 
 
 Long 
 Diam. 
 Rough. 
 
 Thick- 
 ness, 
 Rough. 
 
 Nut. 
 
 Thick- 
 ness. 
 Rough. 
 Head. 
 
 Thick- 
 ness. 
 Finish. 
 Both. 
 
 Bolt. 
 
 9 
 
 8 
 
 
 
 <!> 
 
 on 
 
 sy 
 
 3 
 
 % 
 
 I 
 
 ? 
 
 87 /64 
 
 1/0 /12 
 6 %4 
 
 | 
 
 f 
 
 i 
 
 19 /64 
 ^32 
 
 | 6 
 
 7 A 
 
 2 %2 
 
 23 /32 
 
 %0 
 
 
 
 25 /04 
 
 I 16 
 
 
 X 
 
 /%5 
 
 1 
 
 I 15 {i4 
 
 | 6 
 
 Ji6 
 
 Jie 
 
 %> 
 
 3 y 32 
 
 29 /S2 
 
 11 
 
 l23/ 04 
 
 
 3 Vo4 
 
 J 
 
 f 
 
 1^6 
 
 l' 
 
 
 11 
 
 I' 
 
 1T 32 
 
 % 
 
 
 l| 
 
 1/ie 
 
 Sj 
 
 
 
 f 
 
 % 
 
 1 
 
 
 If 
 
 l21^ 
 
 2^r 
 
 8 
 
 23 /32 
 
 % 
 
 l 
 
 If 
 
 1% 
 
 1| 
 
 2io/ 64 
 
 1 
 
 %6 
 
 '% 
 
 tt 
 
 
 If 
 
 2% 2 
 
 2%Q 
 
 if 
 
 2 %2 
 
 1/ie 
 
 li 
 
 2 16 
 
 
 
 25% 4 
 
 if 
 
 1 
 
 1/ie 
 
 if 
 
 2% 
 
 2i 
 
 2i7/ 32 
 
 3%a 
 
 if 
 
 1%2 
 
 1/16 
 
 11 
 
 28 
 
 2/ie 
 
 " 
 
 3-%4 
 
 ii 
 
 1% 
 
 11 
 
 if 
 
 2% 
 
 21 
 
 
 3f 
 
 if 
 
 1%2 
 
 
 If 
 
 2f 
 
 2^ 6 
 
 3^ 32 
 
 
 if 
 
 If 
 
 1% 
 
 8 
 
 2% 
 
 
 
 4% 2 
 
 
 1 J %2 
 
 1% 
 
 2 
 
 31 
 
 3^6 
 
 3f 
 
 427/ 64 
 
 2 
 
 1/ie 
 
 2% 
 
 2J 
 
 31 
 
 3% 
 
 
 46^64 
 
 2i 
 
 If 
 
 2% 
 
 2| 
 
 3| 
 
 3% 
 
 41 6 
 
 
 21 
 
 
 2^6 
 
 
 4 
 
 4% 
 
 429/32 
 
 6 
 
 2f 
 
 2 i 
 
 2% 
 
 3 
 
 4 f 
 
 4% 
 
 51 
 
 617/^3 
 
 3 
 
 2^ 
 
 2% 
 
 
 5 
 
 4% 
 
 5% 
 
 7^6 
 
 3J 
 
 2i 
 
 3% 
 
 
 5| 
 
 5^6 
 
 
 
 31 
 
 2^ 6 
 
 
 3* 
 
 5f 
 
 5% 
 
 62y 32 
 
 8i 
 
 3f 
 
 
 3% 
 
 4 
 
 
 
 %. 
 
 7%, 
 
 8*%4 
 
 4 - 
 
 3^ 6 
 
 3% 
 
 4} 
 
 61 
 
 (j% 
 
 7% 
 
 9% 
 
 4i 
 
 
 4% 
 
 41 
 
 6J 
 
 6% 
 
 7 3 V3 2 
 
 
 41 
 
 3Jie 
 
 4^6 
 
 4f 
 
 7i 
 
 7% 
 
 8i% a 
 
 10 
 
 4, 
 
 31 
 
 4% 
 
 5 
 
 7f 
 
 7% 
 
 827/33 
 
 io/ 64 
 
 5 
 
 3 j3 io 
 
 4% 
 
 5} 
 
 8 
 
 7% 
 
 9^/32 
 
 Il2% 4 
 
 5J 
 
 4 
 
 5^ 
 
 51 
 
 81 
 
 8^6 
 
 9-'% 2 
 
 llj 
 
 51 
 
 4^6 
 
 
 5f 
 
 8j 
 
 8% 
 
 10% 2 
 
 121 
 
 5f 
 
 4| 
 
 5/fe 
 
 6 
 
 9i 
 
 9X 
 
 10i% 2 
 
 m 
 
 6 
 
 4% 
 
 5% 
 
WEIGH r OF BOLTS, NUTS, AND BOLT-HEADS. 1363 
 
 WEIGHT OF ONE HUNDRED BOLTS WITH SQUARE 
 HEADS AND NUTS. 
 
 INCLUDES WEIGHT OF NUT. 
 (Hoopes & Townsend's List.) 
 
 Length 
 under 
 Head 
 to Point. 
 
 Diameter of liolts, Inches. 
 
 M 
 
 5 /16 
 
 Ys 
 
 Vis 
 
 1 A 
 
 H 
 
 M 
 
 H 
 
 1 
 
 
 Ibs. 
 
 Ibs. 
 
 Ibs. 
 
 Ibs. 
 
 Ibs. 
 
 Ibs. 
 
 Ibs. 
 
 Ibs. 
 
 Ibs. 
 
 &t 
 
 4.00 
 
 7.00 
 
 10.50 
 
 15.20 
 
 22.50 
 
 39.50 
 
 63.00 
 
 ' 
 
 
 
 IM 
 
 4.35 
 
 7.50 
 
 11.25 
 
 16.30 
 
 23.82 
 
 41.62 
 
 66.00 
 
 
 
 
 
 2 
 
 4.75 
 
 8.00 
 
 12.00 
 
 17.40 
 
 25.15 
 
 43.75 
 
 69.00 
 
 109.00 
 
 163 
 
 2 1 A 
 
 5.15 
 
 8,50 
 
 12.75 
 
 18.50 
 
 26.47 
 
 45.88 
 
 72.00 
 
 113.25 
 
 169 
 
 2y 2 
 
 5.50 
 
 9.00 
 
 13.50 
 
 19.60 
 
 27.80 
 
 48.00 
 
 75.00 
 
 117.50 
 
 174 
 
 2% 
 
 5.75 
 
 9.50 
 
 14.25 
 
 20.70 
 
 29.12 
 
 50.12 
 
 78.00 
 
 121.75 
 
 180 
 
 3 
 
 6.25 
 
 10.00 
 
 15.00 
 
 21.80 
 
 30.45 
 
 52.25 
 
 81.00 
 
 126.00 
 
 185 
 
 &A 
 
 7.00 
 
 11.00 
 
 16.50 
 
 24.00 
 
 33.10 
 
 56.50 
 
 87.00 
 
 134.25 
 
 196 
 
 4 
 
 7.75 
 
 12.00 
 
 18.00 
 
 26.20 
 
 35.75 
 
 60.75 
 
 93! 10 
 
 142.50 
 
 207 
 
 4^ 
 
 8.50 
 
 13.00 
 
 19.50 
 
 28.40 
 
 38.40 
 
 65.00 
 
 99.05 
 
 151.00 
 
 218 
 
 5 
 
 9.25 
 
 14.00 
 
 21.00 
 
 30.60 
 
 41.05 
 
 69.25 
 
 105 . 20 
 
 159.55 
 
 229 
 
 5^ 
 
 10.00 
 
 15.00 
 
 22.50 
 
 32.80 
 
 43.70 
 
 73.50 
 
 111.25 
 
 168.00 
 
 240 
 
 6 
 
 10.75 
 
 16.00 
 
 24.00 
 
 35.00 
 
 46.35 
 
 77.75 
 
 117.30 
 
 176.60 
 
 251 
 
 &A 
 
 
 
 
 
 25.50 
 
 37.20 
 
 49.00 
 
 82.00 
 
 123.35 
 
 185.00 
 
 262 
 
 
 
 
 
 
 27.00 
 
 39.40 
 
 51.65 
 
 86.25 
 
 129.40 
 
 193.65 
 
 273 
 
 7 1 A 
 
 
 
 
 
 28.50 
 
 41.60 
 
 54.30 
 
 90.50 
 
 135.00 
 
 202.00 
 
 284 
 
 8 
 
 . . 
 
 
 
 30.00 
 
 43.80 
 
 59.60 
 
 94.75 
 
 141.50 
 
 210.70 
 
 295 
 
 9 
 
 
 
 
 
 
 
 46.00 
 
 64.90 
 
 103.25 
 
 153.60 
 
 227 . 75 
 
 317 
 
 10 
 
 
 
 
 
 
 
 48.20 
 
 70.20 
 
 111.75 
 
 165.70 
 
 224.80 
 
 339 
 
 11 
 
 
 
 
 
 
 
 50.40 
 
 75.150 
 
 120.25 
 
 177.80 
 
 261.85 
 
 360 
 
 12 
 
 
 
 
 
 
 
 52.60 
 
 80.80 
 
 128.75 
 
 189.90 
 
 278.90 
 
 382 
 
 13 
 
 
 
 
 
 
 
 
 
 86.10 
 
 137.25 
 
 202.00 
 
 295.95 
 
 404 
 
 14 
 
 
 
 
 
 
 
 
 
 91.40 
 
 145.75 
 
 214.10 
 
 313.00 
 
 426 
 
 15 
 
 
 
 
 
 
 
 
 
 96.70 
 
 154.25 
 
 226 . 20 
 
 330.05 
 
 448 
 
 16 
 
 
 
 
 
 
 
 __ 
 
 102.00 
 
 162.75 
 
 238 . 30 
 
 347.10 
 
 470 
 
 17 
 
 
 
 
 
 
 
 
 
 107.30 171.00 
 
 250.40 
 
 364.15 
 
 492 
 
 18 
 
 
 
 
 
 
 
 
 
 112.60 179.50 
 
 262.60 
 
 381.20 
 
 514 
 
 19 
 
 
 
 
 
 
 
 
 
 117.90 188.00 
 
 274 . 70 
 
 398.25 
 
 536 
 
 20 
 
 
 
 
 
 
 
 
 
 123.20206.50 
 
 286.80 
 
 415.30 
 
 558 
 
 Per inch 
 
 " addit'l 
 
 j- 1.37 
 
 2.13 
 
 3.07 
 
 4.18 
 
 5.45 
 
 8.52 
 
 12.27 
 
 16.70 
 
 21.82 
 
 WEIGHTS OF NUTS AND BOLT-HEADS, IN POUNDS. 
 
 (For calculating the weight of longer bolts.) 
 
 Diameter of Bolt, in Inches. 
 
 
 & 
 
 H 
 
 1 A 
 
 n 
 
 4 
 
 Ys 
 
 Weight of hexagon nut and 
 
 
 
 
 
 
 
 
 head / 
 
 
 017 
 
 057 
 
 128 
 
 267 
 
 43 
 
 73 
 
 Weight of square nut and 
 head 
 
 
 0.021 
 
 0.069 
 
 0.164 
 
 0.320 
 
 0.55 
 
 0.88 
 
 
 
 
 
 
 
 
 
 Diameter of Bolt, in Inches. 
 
 1 
 
 1M 
 
 W 
 
 m 
 
 2 
 
 2y 2 
 
 3 
 
 Weight of hexagon nut and 
 
 
 
 
 
 
 
 
 head 
 
 1.10 
 
 2.14 
 
 3.78 
 
 5.6 
 
 8.75 
 
 17 
 
 28.8 
 
 Weight of square nut and 
 
 
 
 
 
 
 
 
 head. 
 
 1.31 
 
 2.56 
 
 4.42 
 
 7.0 
 
 10.50 
 
 21 
 
 36.4 
 
1364 WEIGHT OF RIVETS. - 
 
 WEIGHT OF RIVETS AND ROUND-HEADED BOLTS 
 WITHOUT NUTS STEEL. 
 
 POUNDS PER HUNDRED. 
 
 Length, 
 Inches. 
 
 s Aln. 
 Diam. 
 
 ^In. 
 Diam. 
 
 & In ' 
 
 Diam. 
 
 ^In. 
 Diam. 
 
 Kin. 
 
 Diam. 
 
 lln. 
 Diam. 
 
 l^In. 
 Diam. 
 
 IK In. 
 Diam. 
 
 ii 
 
 5.5 
 
 12.8 
 
 22.0 
 
 29.3 
 
 43.9 
 
 66.6 
 
 93.3 
 
 127. 
 
 14 
 
 6.3 
 
 14.2 
 
 24.1 
 
 32.4 
 
 48.2 
 
 72.1 
 
 100. 
 
 136. 
 
 if 
 
 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. 
 
 2i 
 
 8.7 
 
 18.3 
 
 30.7 
 
 41.8 
 
 61.0 
 
 88.8 
 
 121. 
 
 162. 
 
 2J 
 
 9.4 
 
 19.7 
 
 32.8 
 
 44.9 
 
 65.2 
 
 94.4 
 
 128. 
 
 171. 
 
 2i 
 
 10.2 
 
 21.1 
 
 35.0 
 
 48.0 
 
 69.5 
 
 100. 
 
 136. 
 
 179. 
 
 3 
 
 11.0 
 
 22.5 
 
 37.2 
 
 51.1 
 
 73.7 
 
 105. 
 
 143. 
 
 188. 
 
 3} 
 
 11.7 
 
 23.9 
 
 39.3 
 
 54.3 
 
 78.0 
 
 111. 
 
 150. 
 
 197. 
 
 3| 
 
 12.6 
 
 25.3 
 
 41.5 
 
 57.4 
 
 82.3 
 
 116. 
 
 157. 
 
 205. 
 
 3j 
 
 13.4 
 
 26.7 
 
 43.7 
 
 60.5 
 
 86.5 
 
 122. 
 
 164. 
 
 214. 
 
 4 
 
 14.1 
 
 28.1 
 
 45.9 
 
 63.6 
 
 90.8 
 
 128. 
 
 170. 
 
 223. 
 
 4i 
 
 14.9 
 
 29.4 
 
 48.0 
 
 66.7 
 
 95.0 
 
 134. 
 
 177. 
 
 231. 
 
 4* 
 
 15.7 
 
 30.8 
 
 50.2 
 
 69.9 
 
 99.3 
 
 139. 
 
 185. 
 
 240. 
 
 4| 
 
 16.5 
 
 32.2 
 
 52.4 
 
 73.0 
 
 104. 
 
 145. 
 
 192. 
 
 249. 
 
 5 
 
 17.2 
 
 33.6 
 
 54.5 
 
 76.1 
 
 108. 
 
 150. 
 
 199. 
 
 258. 
 
 5J 
 
 18.1 
 
 35.0 
 
 56.7 
 
 79.2 
 
 112. 
 
 156. 
 
 206. 
 
 266. 
 
 5* 
 
 18.8 
 
 36.4 
 
 58.9 
 
 82.3 
 
 116. 
 
 161. 
 
 213. 
 
 275. 
 
 5J 
 
 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. 
 
 6i 
 
 21.9 
 
 42.0 
 
 67.6 
 
 95.1 
 
 133. 
 
 184. 
 
 241. 
 
 310. 
 
 7 
 
 23.5 
 
 44.7 
 
 71.9 
 
 101. 
 
 142. 
 
 195. 
 
 255. 
 
 327. 
 
 7J 
 
 25.1 
 
 47.5 
 
 76.1 
 
 108. 
 
 150. 
 
 206. 
 
 269. 
 
 345. 
 
 8 
 
 26.6 
 
 50.3 
 
 80.6 
 
 114. 
 
 159. 
 
 217. 
 
 284. 
 
 362. 
 
 8i 
 
 28.2 
 
 53.1 
 
 85.0 
 
 120. 
 
 167-. 
 
 227. 
 
 298. 
 
 379. 
 
 9 
 
 29.8 
 
 55.9 
 
 89.3 
 
 126. 
 
 176. 
 
 239. 
 
 312. 
 
 397. 
 
 9i 
 
 31.3 
 
 58.7 
 
 93.7 
 
 133. 
 
 185. 
 
 250. 
 
 325. 
 
 414. 
 
 10 
 
 32.8 
 
 61.4 
 
 98.0 
 
 139. 
 
 193. 
 
 261. 
 
 340. 
 
 431. 
 
 10* 
 
 34.5 
 
 64.2 
 
 103. 
 
 145. 
 
 202. 
 
 272. 
 
 354. 
 
 449. 
 
 11 
 
 36.0 
 
 67.0 
 
 107. 
 
 151. 
 
 210. 
 
 284. 
 
 368. 
 
 466. 
 
 Hi 
 
 37.6 
 
 69.8 
 
 111. 
 
 158. 
 
 218. 
 
 295. 
 
 382. 
 
 484. 
 
 12 
 
 39.2 
 
 72.5 
 
 115. 
 
 164. 
 
 227. 
 
 306. 
 
 396. 
 
 501. 
 
 Heads. 
 
 1.8 
 
 5.8 
 
 11.1 
 
 13.6 
 
 22.6 
 
 39.0 
 
 58.0 
 
 83.5 
 
 For length of shaft required to form rivet-head, see p. 374. 
 
NAILS. 1365 
 
 NAILS. 
 
 Kinds* The different kinds of nails may be classified as 
 follows : 
 
 Wrought nails, which are forged either by hand labor or 
 machine power* sometimes designated as clinch nails, on ac- 
 count of their property of bending without breaking. Seldom 
 used in connection with wood- work, although they are the best 
 clinch nail that can be had. 
 
 Cut nails, which are cut from a strip of rolled iron or steel of 
 the thickness that the nail is to be and a little wider than the 
 length of the nail. Cut nafls are now commonly made of steel. 
 
 Wire nails, which 'are made from steel wire of the same size 
 as the shank of the nail is to be. 
 
 Copper and brass nails are manufactured, and are sometimes 
 used in connection with marine and refrigerator work, and about 
 physical laboratories, to avoid the magnetic effects of iron or steel. 
 
 Composition nails are made of different alloys to avoid cor- 
 rosion, or to prevent galvanic action set up by iron when in 
 contact with zinc or other metals. 
 
 Varieties, Nails are also made in a variety of shapes and 
 sizes to adapt them to different classes of work; the principal 
 varieties are indicated by the tables on following pages. 
 
 Galvanized-wire nails may be obtained if desired. Wherever 
 exposed to constant or frequent moisture they are more durable 
 and satisfactory than uncoated nails, and are to be preferred for 
 securing shingles, slates, and all kinds of roofing. 
 
 Cement-coated Nails. J. C. Pearson Company, of Boston, 
 Mass., have obtained a patent on coating wire nails with an 
 asphaltum cement which greatly increases their holding power. 
 Most varieties are carried in stock in the larger cities. With this 
 coating slightly smaller nails may be used, with equal or greater 
 holding power. It is claimed that it is cheaper for contractors 
 to use cement-coated nails than ordinary wire nails. Most of 
 the wooden-box factories use these nails, and they are especially 
 desirable for nailing flooring, siding, etc. 
 
 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. 
 
 Twenty-penny 1593 703 Sixpenny 383 200 
 
 Tenpenny 908 315 Fourpenny 286 123 
 
 Eightpenny 597 227 
 
1366 
 
 NAILS. 
 
 The following table shows the result of tests made at the U. S. 
 Arsenal, Watertown, Mass., fn 1902, the wood being pine: 
 
 COMPARATIVE ADHESIVE RESISTANCE OF COMMON 
 SMOOTH WIRE NAILS AND CEMENT-COATED NAILS. 
 
 All nails driven into the same piece perpendicular to the grain. 
 
 Size and Name. 
 
 Diameter 
 in 
 Inches. 
 
 Length 
 Driven,* 
 Inches. 
 
 Adhesive 
 Retistance.t 
 Pounds. 
 
 Xenpenny, common, smooth. ... . . . . 
 
 .145 
 .117 
 .132 
 .114 
 .132 
 .112 
 .097 
 .092 
 
 2^ 
 
 ll 
 
 !* 
 
 2 
 1 5 A 
 
 w 
 
 167 
 418 
 182 
 327 
 189 
 316 
 106 
 226 
 
 coated . 
 
 Ninepenny common, smooth. 
 
 
 Eightpenny, common, smooth. . 
 
 coated 
 
 Sixpenny, common, smooth. . . . 
 
 coated 
 
 
 * All of the nails were left with their heads projecting from l /i to 
 t Average of three trials. 
 
 inch. 
 
 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 about as follows: White pine, 1; yellow 
 pine, 1.5; white oak, 3; chestnut, 1.6; beech, 3.2; sycamore, 
 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 nails 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 per cent., the 
 common nails showing an average superiority of '47.51 per. cent. 
 and the finishing nails an average of 72.22 per cent. 
 
 In eighteen series, comprising six sizes of box nails driven into 
 pine wood, in three ways the cut nails showed an average supe- 
 riority of 99.93 per cent. In no series of tests did the wire nails 
 hold as much as the cut nails. 
 
 QUANTITY OF NAILS -REQUIRED FOR DIFFERENT 
 KINDS OF WORK. 
 
 For 1,000 shingles allow 5 Ibs. fourpenny nails or 3J^ Ibs. threepenny. 
 
 1,000 laths, 7 Ibs. threepenny fine, or for 100 square yards of lathing, 
 
 10 Ibs. threepenny fine. 
 
 1,000 square feet of beveled siding, 18 Ibs. sixpenny. 
 1,000 " sheathing, 20 Ibs. eightpenny or 25 Ibs. tenpenny. 
 
 1,000 " flooring, 30 Ibs. eightpenny or 40 Ibs. tenpenny. 
 
 1,000 " studding, 15 Ibs. teripenny and 5 Ibs. twenty-penny. 
 
 1,000 " l"X2i/" furring, 12" centres, 9 Ibs. eightpenny or 
 
 14 Ibs. tenpenny. 
 1,000 ** l"X2J/" furring, 16" centres, 7 Ibs. eightpenny or 
 
 10 Ibs. tenpenny. 
 
CUT NAILS AND SPIKES. 
 
 1367 
 
 CUT STEEL NAILS AND SPIKES. 
 SIZE, LENGTH, AND NUMBER TO THE POUND. 
 
 (Cumberland Nail and Iron Company.) 
 
 ORDINARY. 
 
 CLINCH. 
 
 FINISHING. 
 
 Size. 
 
 Length, 
 in Ins. 
 
 No. to 
 Pound. 
 
 Length, 
 in Ins. 
 
 No. to 
 Pound. 
 
 Size. 
 
 Length, 
 in Ins. 
 
 No. to 
 Pound. 
 
 2d 
 3d fine 
 
 3d 
 4d 
 5d 
 Qd 
 Id 
 8d 
 lOd 
 I2d 
 20d 
 30d 
 4Qd 
 50d 
 60d 
 
 1 
 f 
 
 H 
 
 14 
 11 
 
 2 
 
 21 
 2f 
 
 3 
 
 31 
 
 4 
 
 4i 
 4f 
 
 5 
 
 5i 
 
 716 
 
 5S8 
 448 
 336 
 216 
 166 
 118 
 94 
 72 
 50 
 32 
 20 
 17 
 14 
 10 
 
 2 
 2i 
 2i 
 2f 
 3 
 3i 
 
 152 
 133 
 92 
 
 72 
 60 
 43 
 
 4d 
 5d 
 Qd 
 8d 
 Wd 
 12d 
 20d 
 
 if 
 
 2 S 
 2J 
 
 3 
 
 3f 
 3f 
 
 384 
 256 
 204 
 102 
 
 80 
 65 
 46 
 
 FENCE. 
 
 CORE. 
 
 2 
 
 2i 
 21 
 
 2| 
 3 
 
 96 
 66 
 56 
 50 
 40 
 
 Qd 
 
 $d 
 
 Wd 
 I2d 
 20d 
 30d 
 40d 
 
 WH 
 WHL 
 
 2 
 21 
 24 
 3* 
 
 3| 
 
 4i 
 41 
 
 2i 
 2i 
 
 143 
 68 
 60 
 42 
 25 
 18 
 14 
 
 69 
 
 72 
 
 LIGHT. 
 
 SPIKES. 
 
 4d 
 
 5d 
 
 Qd 
 
 If 
 If 
 
 2 
 
 373 
 
 272 
 196 
 
 3i 
 4 
 41 
 5 
 51 
 6 
 
 19 
 15 
 13 
 10 
 9 
 7 
 
 SLATE. 
 
 BRADS. 
 
 Qd 
 8d 
 IQd 
 I2d 
 
 2 
 
 2J 
 
 2| 
 
 31 
 
 163 
 96 
 
 74 
 50 
 
 BOAT. 
 
 3d 
 4d 
 5d 
 Qd 
 
 1% 
 
 1^6 
 
 If 
 2 
 
 288 
 244 
 187 
 146 
 
 H 
 
 206 
 
 TACKS. 
 
 
 
 Number 
 
 
 ^3 
 
 Number 
 
 
 
 Number 
 
 Size. 
 
 Length. 
 
 to 
 
 Size. 
 
 s 
 
 to 
 
 Size. 
 
 Length. 
 
 to 
 
 
 
 Pound. 
 
 
 j 
 
 Pound. 
 
 
 
 Pound. 
 
 1 oz. 
 
 i 
 
 16,000 
 
 4 oz. 
 
 % 
 
 4,000 
 
 14 oz. 
 
 % 
 
 1,143 
 
 H " 
 
 % 
 
 10,066 
 
 6 " 
 
 % 
 
 2,666 
 
 16 " 
 
 I 
 
 1,OCO 
 
 2 " 
 
 
 8,000 
 
 8 " 
 
 1 
 
 2,000 
 
 18 " 
 
 % 
 
 888 
 
 2J " 
 
 |j 
 
 6,400 
 
 10 " 
 
 Ye 
 
 1,600 
 
 20 " 
 
 1 
 
 800 
 
 
 I 
 
 5,333 
 
 12 <f 
 
 1 
 
 1,333 
 
 22 " 
 
 m 
 
 727 
 
1368 WIRE NAILS, SPIKES, AND TACKS. 
 
 STEEL-WIRE NAILS, SPIKES, AND TACKS. 
 
 SIZE, LENGTH, GAUGE, AND APPROXIMATE NUMBEK 
 
 TO THE POUND. 
 
 Compiled from Catalogue of American Steel and Wire Company, 1903. 
 Gauge is the A. S. and W. Co.'s Gauge, p. 1349. 
 
 Common Nails and Brads.* 
 
 Casing Nails. t 
 
 Finishing Nails.f 
 
 Size. 
 
 Length, 
 Inches. 
 
 Gauge. 
 
 No. to 
 Pound. 
 
 Gauge. 
 
 No. to 
 Pound. 
 
 Gauge. 
 
 No. to 
 Pound. 
 
 2d 
 
 1 
 
 15 
 
 876 
 
 15J 
 
 1,010 
 
 16} 
 
 1,351 
 
 3d 
 
 It 
 
 14 
 
 568 
 
 14} 
 
 635 
 
 15} 
 
 807 
 
 4d 
 
 11 
 
 121 
 
 316 
 
 14 
 
 473 
 
 15 
 
 584 
 
 5d 
 
 If 
 
 121 
 
 271 
 
 14 
 
 406 
 
 15 
 
 500 
 
 6d 
 
 2 
 
 111 
 
 181 
 
 121 
 
 236 
 
 13} 
 
 309 
 
 Id 
 
 2J 
 
 11} 
 
 161 
 
 
 210 
 
 13 
 
 238 
 
 Sd 
 
 2} 
 
 10i 
 
 106 
 
 Hi 
 
 145 
 
 12} 
 
 189 
 
 9d 
 
 21 
 
 
 96 
 
 11} 
 
 132 
 
 
 172 
 
 Wd 
 
 3 
 
 9 
 
 69 
 
 101 
 
 94 
 
 11} 
 
 121 
 
 12d 
 
 3t 
 
 9 
 
 63 
 
 10} 
 
 87 
 
 11} 
 
 113 
 
 IQd 
 
 3} 
 
 8 
 
 49 
 
 10. 
 
 71 
 
 11 
 
 90 
 
 20d 
 
 4 
 
 6 
 
 31 
 
 9 
 
 52 
 
 10 
 
 62 
 
 30d 
 
 4} 
 
 5 
 
 24 
 
 9 
 
 46 
 
 
 
 40d 
 
 5 
 
 4 
 
 18 
 
 8 
 
 35 
 
 
 
 60d 
 
 5} 
 6 
 
 3 
 2 
 
 14 
 11 
 
 Shingle Nails. 
 
 
 
 
 
 Size. 
 
 Length, 
 Inches. 
 
 i 
 
 Gauge. 
 
 No. to 
 Pound. 
 
 Spikes.* 
 
 
 OJ 
 
 11 
 
 1 Q 
 
 
 Size. 
 
 Length, 
 Inches. 
 
 Gauge. 
 
 No. to 
 Pound. 
 
 6a 
 5d 
 
 4 
 
 11 
 
 lo 
 
 12 
 12 
 
 274 
 235 
 
 lOd 
 
 3 
 
 6 
 
 41 
 
 7d 
 
 2 
 
 2} 
 
 12 
 11 
 
 204 
 139 
 
 I2d 
 
 3i 
 
 6 
 
 38 
 
 Sd 
 
 2} 
 
 11 
 
 125 
 
 I6d 
 
 3} 
 
 5 
 
 30 
 
 
 2} 
 
 11 
 
 114 
 
 Q/-V J 
 
 4 
 /i i 
 
 4 
 
 23 
 
 Wd 
 
 3 
 
 10 
 
 83 
 
 6Ud 
 
 4} 
 
 
 
 
 CA^-7 
 
 5 
 
 r 1 
 
 2 
 
 13 
 i n 
 
 Fine Nails. 
 
 50a 
 
 5} 
 6 
 
 , 
 1 
 
 1U 
 
 8 
 
 2d 
 
 1 
 
 16} 
 
 1,351 
 
 7" 
 
 7 
 
 
 
 7 
 
 3d 
 
 1J- 
 
 15 
 
 778 
 
 8" 
 
 8 
 
 00 
 
 6 
 
 4d 
 
 ii 
 
 14 
 
 473 
 
 9" 
 
 9 
 
 00 
 
 5 
 
 3d) 
 
 
 
 
 10" 
 
 10 
 
 f" 
 
 4 
 
 extra > 
 
 w 
 
 16 
 
 1,015 
 
 12" 
 
 12 
 
 f" 
 
 3 
 
 fine ) 
 
 
 
 
 * Common brads differ from common nails only in the head and point. 
 f Lengths are the same as common nails for corresponding size. 
 j Spikes are made with chisel points and diamond points; also with 
 convex heads and flat heads. 
 
WIRE NAILS, SPIKES, AND TACKS. 1369 
 
 STEEL-WIRE NAILS. Continued. 
 
 Clinch Nails. 
 
 Fence Nails.* 
 
 Slating Nails.* 
 
 Size. 
 
 Length, 
 Inches. 
 
 Gauge. 
 
 No. to 
 Pound. 
 
 Gauge. 
 
 No. to 
 Pound. 
 
 Gauge. 
 
 No. to 
 Pound. 
 
 2d 
 3d 
 4d 
 5d 
 Qd 
 Id 
 8d 
 9d 
 Wd 
 I2d 
 16d 
 20d 
 
 1 
 
 if 
 
 li 
 li 
 2 
 21 
 2J 
 2i 
 3 
 31 
 
 aj 
 
 4 
 
 14 
 13 
 12 
 12 
 11 
 11' 
 10 
 10 
 9 
 9 
 8 
 7 
 
 710 
 429 
 274 
 235 
 157 
 139 
 99 
 90 
 69 
 62 
 49 
 37 
 
 No. 5s 
 si 
 10 
 10 
 9 
 9 
 8 
 7 
 6 
 5 
 4 
 
 mallest 
 ze 
 142 
 124 
 92 
 82 
 62 
 50 
 40 
 30 
 23 
 
 12 
 104 
 
 104 
 10 
 9 
 
 411 
 225 
 
 187 
 142 
 103 
 
 Barbed Roofing Nails, f 
 
 f'XNo. 13 
 f'XNo. 12 
 l"XNo. 12 
 If'XNo. 12 
 li"XNo. 11 
 
 714 
 469 
 411 
 365 
 251 
 
 * Length same as clinch nails of corresponding size. 
 t Roofing nails are designated by the length, not by "penny." These 
 nails are made up to 2 ins. long. 
 
 WIRE TACKS. 
 
 
 
 m . 
 
 ^ 
 
 d 
 
 4 
 
 h ^ 
 
 d 
 
 J^B 
 
 6 
 
 2 
 
 P^ ^ 
 
 a! fl 
 
 o 
 
 [f ^ ^ 
 
 
 
 
 
 cj f3 
 
 *1 
 
 |1 
 
 "fl ^ o 
 
 aT 
 
 M 
 
 *fl o o 
 
 3 
 
 IS 
 
 'fl ^ O 
 
 S30 
 
 
 H &Pn 
 
 qsQ 
 
 g^ 
 
 H DtPn 
 
 ^3O 
 
 g^ 
 
 S p,fLj 
 
 B 
 
 iS 
 
 ^ 
 
 H 
 
 
 * 
 
 H. 
 
 H 
 
 K 
 
 l 
 
 i 
 
 16,000 
 
 4 
 
 % 
 
 4,000 
 
 14 
 
 is/ 
 
 /16 
 
 1.143 
 
 li 
 
 
 10,666 
 
 6 
 
 /ie 
 
 2,666 
 
 16 
 
 f 
 
 1,000 
 
 2 
 
 ^ 
 
 8,000 
 
 8 
 
 J 
 
 2,000 
 
 18 
 
 
 888 
 
 24 
 
 xl6 
 
 6,400 
 
 10 
 
 /le 
 
 1,600 
 
 20 
 
 1 ^ 
 
 800 
 
 3 
 
 f 
 
 5,333 
 
 12 
 
 J 
 
 1,333 
 
 22 
 
 l 1 ^ 
 
 727 
 
 
 
 
 
 
 
 24 
 
 li 
 
 666 
 
 Wire carpet tacks are made polished, blued, tinned, or cop- 
 pered; there are also upholsterers' and bill-posters' or railroad 
 tackso 
 
1370 SCREWS AND EXPANSION BOLTS. 
 
 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 expan- 
 sion bolt, which is also furnished with screw-head 
 bolts. There are two other forms of expansion bolts 
 on the market. 
 
 Screws. Screws are made of iron, steel, brass, 
 copper, bronze, and phosphor-bronze, the ordinary 
 X Bo?t? n screw being of iron. Iron screws are finished with 
 either a bright, blue, bronze, lacquered, tinned, or 
 galvanized surface, and are also plated in nickel, brass, bronze, 
 copper, and silver. 
 
 The size of screws is designated by the length in inches and 
 the number of gauge which denotes the diameter of the body 
 of the screw. Thus a 1-in. No. 12 screw denotes a screw 
 1 in. long and .2158 of an inch in diameter. 
 
 The gauge numbers range from No. to No. 30, and the 
 length from J in. to 6 ins. Lengths vary by eighths of an 
 inch up to 1 in., by -quarters of an inch up to 3 ins., by halves 
 up to 5 ins. 
 
 Screws from f in. to 4 ins. long are made in about sixteen 
 different gauge numbers. 
 
 The table on page 1346 shows the diameter to four places of 
 decimals of the American Screw Gauge. 
 
 It should be noticed that unlike the ordinary wire gauges, 
 the of the screw gauge is the smallest, and the diameter 
 increases with the number of the gauge. 
 
 Wood-screws are made with twenty-five different shapes of 
 heads for different purposes. The most common shapes, 
 however, are the ordinary flat head, round head, and oval 
 head. The latter is tapered for 
 counter-sinking, but is slightly 
 rounded on top. 
 
 Patent diamond - point steel 
 screws are made especially for 
 driving with a hammer. "^g-'^d Coach-screws. 
 
 Screws for metal have the same 
 diameter throughout and the threads are V shaped. 
 
 Lag- or coach-screws are large heavy screws used where great 
 
DATA ON EXCAVATING. 
 
 1371 
 
 strength is required, as in heavy framing, and for fixing iron- 
 work to timber. Lag-screws with conical point are made with 
 diameters of %j, f , %, J, %, f, i, and 1 in., and in lengths from 
 1 1 to 12 ins. ; coach-screws in diameters from %> to J in. and in 
 lengths from 1J to 12 ins. 
 
 HOLDING POWER OF LAG-SCREWS. 
 
 (Tests made by A. J. Cox, University of Iowa, 1891, quoted 
 by Kent, page 290.) 
 
 
 
 
 
 Max- 
 
 
 Kind of Wood. 
 
 Size 
 Screw. 
 
 Size 
 Hole 
 Bored. 
 
 Length 
 in 
 Wood. 
 
 imum 
 Resist- 
 ance, 
 
 No. 
 Tests. 
 
 
 
 
 
 Lbs. 
 
 
 
 Inch. 
 
 Inch. 
 
 Inches. 
 
 
 
 Seasoned white oak 
 
 f 
 
 J 
 
 4i 
 
 3 
 
 
 u a a 
 
 % 
 
 % 
 
 3 
 
 1 
 
 
 <( (i (( 
 
 i 
 
 I 
 
 41 
 
 2 
 
 
 Yellow-pine stick 
 
 | 
 
 \ 
 
 4 
 
 2 
 
 
 White cedar, unseasoned. . 
 
 f ' 
 
 \ 
 
 4 ' 
 
 2 
 
 
 (Hoopes & Townsend give the force at which screws were 
 drawn out of yellow pine as follows:) 
 
 Screw. . . . 
 
 1 A in. 
 
 % in. 
 
 Z A in. 
 
 Kin. 
 
 1 in. 
 
 Wood, depth 
 
 3* ins. 
 
 4 ins. 
 
 4 ins. 
 
 5 ins. 
 
 6 ins. 
 
 Force, pounds 
 
 4,960 
 
 6,000 
 
 7,685 
 
 11,500 
 
 12,620 
 
 
 
 
 
 
 
 Wood-screws are sold by the gross, lag- 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 p. 69. 
 
 For computing the" contents of wells and cesspools, the circu- 
 lar area in square feet may be obtained from the table on t 
 p. 53, and this multiplied by the depth in feet will give contents 
 in cubic feet. - 
 
 The cost of excavating and removing earth is ordinarily made 
 up of the following items: 
 
 a. Loosening the earth for the shovellers. 
 
1372 DATA ON EXCAVATING. 
 
 b. Loading by shovels into carts or barrows. 
 
 c. Hauling or wheeling it away, including emptying and 
 returning. 
 
 d. Spreading it out on the dump. 
 
 For every large job, such as railroad work, it is also neces- 
 sary to make an allowance for keeping the hauling road in 
 repair, sharpening and repair of tools, carts, harness, super- 
 intendence, and water-carriers. 
 
 Where the dirt excavated can be spread over the ground 
 immediately surrounding the excavation the loosened dirt 
 may be removed by scrapers without shovelling. 
 
 Data for Estimating Cost. For loosening: Two men with a 
 plough and team of horses will loosen from 20 to 30 cu. yds. of 
 strong, heavy soils per hour or from 40 to 60 cu. yds of ordinary 
 loam. One man with a pick will loosen 1J yds. per hour of 
 stiff clay or cemented gravel, 4 yds. of common loam, or 6 yds. 
 of light sand. 
 
 The average quantity of loosened earth which a man can 
 shovel into a cart per hour is: 
 
 Loam or sand 2.0 cu. yds. 
 
 Clay and heavy soils 1.7 " 
 
 Rock. 1.0 cu yd. 
 
 Average earth loosened swells to from 1J to 1J times its 
 original bulk in place. 
 
 The capacity of vehicles used for moving excavated materials 
 is about as follows: 
 
 Wheelbarrows 3 to 4 cu. ft. 
 
 1-horse dump-carts 18 " 22 " 
 
 2-horse dump-wagons 27 " 45 " * 
 
 Drag scrapers 3 " 7 " 
 
 Wheel scrapers 10 " 17 " 
 
 Dump-cars on rails 27 " 80 " 
 
 The economical length of haul with drag scrapers is about 
 150 ft.; with wheeled scrapers, 500 ft.; with wheelbarrows, 
 250 ft.; with 1-horse dump-carts, 600 ft.f 
 
 The average speed of horses is given as about 200 ft. per 
 minute. 
 
 *The ordinary load for 2-horse wagons- such as are commonly used 
 for hauling dirt* sand, and gravel is from IK to 1> cu, yds. 
 t Inspectors' Pocket-book, A. T. Byrne, C E. 
 
DATA ON STONEWORK 1373 
 
 Much valuable data for estimating the cost of excavating 
 may be fo'uiid in Trautwine's Engineer's Pocket-book, p. 800- 
 810. 
 
 Weight of Earth, Sand, and Gravel. For general calculations 
 the following average values may be taken: 
 
 19 cu. ft. of gravel weigh 1 ton 
 22 " " sand " 1 " 
 
 14 cu. ft. of chalk weigh 1 ton 
 18 " " clay " 1 " 
 21 " " earth " 1 " 
 
 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 1| cu. yds.; consequently the 
 cost of hauling or removal is about 50 per cent, more than 
 for dirt. 
 
 With labor at $1 per day, the actual cost for loosening hard 
 rock, including tools, drilling, powder, etc., will average about 
 45 cts. per cubic yard, in place, under all ordinary circumstances. 
 In practice it will generally range between 30 and 60 cts., 
 depending on the position of the strata, hajdness, 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 cts., while on the other hand shallow cuttings of 
 very tough rock with an unfavorable position of strata, 
 especially in the bottoms of excavations, may cost $1 per cubic 
 yard, or even considerably more. The quarrying of average 
 hard rock requires about i to J Ib. of powder per cubic yard, 
 in place, but the nature of the rock, the position of the strata, 
 etc., may increase it to j- Ib. 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 2J ft. deep and 2 ins. 
 diameter per day in average hard rock, at from 12 to 18 cts. 
 per foot.* 
 
 DATA ON STONEWORK. 
 
 (For description of various kinds of stonework, see Building 
 Construction and Superintendence, Part I Chapter VI.) 
 
 The commonest kind of stonework, v.e. 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 as coursed 
 rubble. 
 
 * Trautwine, p, 810. 
 
1374 DATA ON STONEWORK. 
 
 When the stones showing on the outside face of the wall are 
 squared, the work is designated as 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 desig- 
 nates work where the stones are roughly squared with a hammer. 
 This i,s a very cheap class of work. Good ashlar work should 
 be squared on the bench with chisels, and with beds and end 
 joints cut square 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- and dimension- 
 stone. Rubble includes the pieces of irregular size most easily 
 obtained from the quarry, and suitable for cutting into ashlar 
 12 ins. or less in height and about 2 ft. long. Stone ordered of 
 a certain size, or to square over 24 ins. each way, and of a par- 
 ticular thickness, is called dimension-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 founda- 
 tions 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. 
 
 Dimension-stone footings (that is, squared stone 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 16J cu. ft. The author has been unable to find any locality 
 where the legal perch of 24J cu. ft. is used by stone-masons. 
 In Philadelphia, St. Louis, and some portions of Illinois, 22 cu. ft. 
 are called a perch. 
 
 Railroad work is usually measured 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 also 
 whether or not openings are to be deducted. As a rule no 
 
DATA ON STONEWORK, 1375 
 
 deductions are made for openings of less than 70 superficial 
 feet. 
 
 Data for Estimating' Cost. The price of common rubble 
 as it comes from the quarry will vary from 50 cts. to $1.50 per 
 ton, f .o.b. at point of delivery, according to the cost of quarrying, 
 transportation, etc. $1.25 a perch is probably a fair average. 
 
 A ton of most stones will make from 1 to 1J perch. 
 
 The cost of laying one perch of stone may be estimated by 
 the following items: 
 
 Labor: mason 2f hrs., helper If hrs. (based on 2 helpers 
 to 3 masons); sand J load; lime f bu., or if laid in all cement 
 mortar, one perch- will' require from J to J bbl. cement. 
 
 At average wages, rubble cellar walls, 18 ins. to 2 ft. thick, 
 laid in lime mortar, vary in cost from $2.75 to $4 per perch, 
 $3.25 a perch being a fair average; in all cement mortar 
 from $3.25 to $4.25 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 point of delivery may vary 
 from 70 cts. to $1.25 per cubic foot for granite and 55 cts. to $1 
 for sandstones and limestones, depending largely upon cost of 
 transportation. 1 cu. ft. of stone should make 2 sq. ft. of 
 ashlar, at least. Some quarries get out stone especially suit- 
 able for ashlar and sell it at about 25 cts. per lineal foot for 
 courses 12 ins. high. 
 
 The cost of cutting ashlar, with stone-cutters' wages at $4 
 per day, will average about 15 cts. per square foot for soft 
 stones, 15 to 20 cts. per square foot for hard sandstones and lime- 
 stones, and 25 to 30 cts. for granite. The cost of setting ashlar 
 will vary from 10 cts. per square foot to 25 cts. for soft stones 
 or 30 cts. for granite, 15 cts. being an average price for sand- 
 stones and limestones. 
 
 The cost of cut-stone trimmings depends so largely upon the 
 kind of stone, that it is quite impossible to give prices that 
 would be of any serivce. 
 
 The following figures, however, quoted from The Building 
 Trades Pocket-book, may be of some guide in forming a 
 rough estimate, the prices if anything being probably a little 
 above the cost of the local stone in most localities. 
 
 Flagstones for sidewalks, ordinary stock, natural surface, 
 3 ins. thick, with joints pitched to line, in lengths (along walk) 
 from 3 to 5 ft., will cost, for 3-ft. walk, about 8 cts. per square 
 
1376 DATA ON BRICKS AND BRICKWORK. 
 
 foot (if 2 ins. thick, 6 cts.); for 4-ft. walk, 9 cts.; and for 5-ft. 
 walk, 10 cts. per square foot. The cost of laying all sizes 
 will average about 3 cts. per square foot. The above figures 
 do not include cost of hauling. 
 
 Curbing (4-in. X 24-in. granite) will cost at quarry from 25 
 to 30 cts. per lineal foot; digging and setting will cost from 
 10 to 12 cts. additional; and the cost of freight and hauling 
 must also be added. 
 
 The following figures show the approximate cost of cut blue- 
 stone for various uses: 
 
 Flagstone, 5 ins., size 8 ft.XlO ft., edges and top bush- 
 hammered, per square foot face measure $0 . 65 
 
 Flagstone, 4 ins., size 5 ft.X5 ft., select stock, edges clean- 
 cut, natural top, per square foot 30 
 
 Door-sills, 8 in. X 12 in., clean cut, per lineal foot 1 . 25 
 
 Window-sills, 5 in. X 12 in., clean-cut, per lineal foot 80 
 
 Window-sills, 4 in. X 8 in., clean-cut, per lineal foot 45 
 
 Window-sills, 5 in. X 8 in., clean-cut, per lineal foot .60 
 
 Lintels, 4 in. X 10 in., clean-cut, per lineal foot . .60 
 
 Lintels, 8 in. X 12 in., clean-cut, per lineal foot 1 . 10 
 
 Water-table, 8 in. X 12 in., clean-cut, per lineal foot 1 . 25 
 
 Coping, 4 in. X21 in., clean cut, per lineal foot 1 . 10 
 
 Coping, 4 in. X 21 in., rock-face edges and top, per lineal foot . 45 
 Coping, 3 in. X 15 in., rock-face edges and top, per lineal foot . 25 
 Coping, 3 in. X 18 in. , rock-face edges and top, per lineal foot . 30 
 
 Steps, sawed stock, 7 in. X 14 in., per lineal foot 90 
 
 Platform, 6 in. thick, per square foot 45 
 
 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 lineal foot, and for window-sills, etc., about 
 5 cts. per lineal foot. 
 
 DATA ON BRICKS AND BRICKWORK. 
 
 [For a complete description of clay bricks, their process of 
 manufacture, etc., also of all kinds of brickwork, see Chapter 
 VII, Part I, of Building Construction and Superintendence.] 
 
 The word brick as commonly used refers to blocks made 
 irom clay that have been moulded into the required shape 
 and burned in a kiln, and until quite recently practically all 
 bricks were made from clay; at the present time, however, 
 bricks are also made from sand and lime. 
 
 Clay Bricks. These may be broadly classified as common 
 brick, face-brick, fire-brick, and paving-brick. 
 
 As to the process of manufacture, bricks are classified as 
 
DATA ON BRICKS AND BRICKWORK. 1377 
 
 soft-mud bricks, stiff-mud bricks, dry-pressed bricks, and 
 re-pressed bricks. 
 
 Soft-mud bricks are made by tempering the clay with water 
 until it becomes soft and plastic, when it is pressed into the 
 moulds either by hand or by a machine. Practically all hand- 
 made bricks are soft-mud bricks. 
 
 Stiff-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; if 
 of the size of the side of the brick, they are side-cut. 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 strongest. 
 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 or hand- 
 made bricks. 
 
 Soft-mud bricks are often re-pressed to make face-bricks. 
 
 Dry-pressed bricks are made almost entirely for face-work, 
 although in some localities dry-pressed bricks are also used for 
 common bricks. Hydraulic-pressed bricks are dry-pressed. 
 Moulded bricks are always dry-pressed. Very fine bricks are 
 made by this process. 
 
 Bricks made by any of the above processes require to be burned 
 in a kiln. According to their position in the kiln, common 
 brick are designated as arch or hard-burned brick, red or well- 
 burned brick, and salmon or soft brick. As a rule, salmon 
 brick are not fit to use in an exterior or bearing wall. 
 
 Color. The color of brick depends principally upon the 
 presence of iron, lime, and 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 gives 
 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 
 
1378 DATA ON BRICKS AND BRICKWORK. 
 
 clay and plastic clay. They are usually white or-white mixed 
 with biown in color and are used for the lining of furnaces, 
 fireplaces, and tall chimneys. 
 
 Paviiig'-bricks are a very hard brick, usually vitrified or 
 annealed. They are much more expensive than common 
 brick 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 dimen- 
 sions vary with the maker and also with the locality. In the 
 New England States the common brick averages about 
 7f X3f X2J ins. In most of the Western States common bricks 
 measure about 8JX4JX2J ins., and the thickness of the walls 
 measures about 9, 13, 18, and 22 inches for thickness of 1, 1J, 
 2, and 2J bricks. The size of all common bricks varies con- 
 siderably in each lot, according to the degree to which they 
 are burnt; the hard bricks being from J- to % of an inch 
 smaller than the salmon bricks. 
 
 Pressed bricks or face-bricks are more uniform in size, as most 
 of the manufacturers use the same size of mould. The pre- 
 vailing size for pressed bricks is 8f X4-|X2f ins. Pressed bricks 
 are also made 1J ins. thick and 12X4X1J ins., the latter size 
 being generally termed Roman brick, or tile. 
 
 The weight of bricks varies considerably with the quality 
 of the clay from which they are made, and also, of course, with 
 their size. Common bricks average about 4J Ibs. each, and 
 pressed bricks vary from 5 to 5J Ibs. each. 
 
 For strength of bricks and brickwork, see pp. 213, 218, 229. 
 Fire-bricks are made in various forms to suit the required 
 work. A straight brick measures 9X4JX2J ins. and weighs 
 about 7 Ibs. 
 
 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. 
 
 Paving-bricks vary in size and weight according to the locality 
 and the requirements of the specifications. 
 
 The "standard" bricks are 2JX4X8 ins., requiring 61 bricks 
 to the square yard (on edge), and weigh 7 Ibs. each. "Re- 
 pressed" bricks are 2JX4X8J ins., requiring 58 to the square 
 yard and weigh 6J Ibs. each. " Metropolitan " are 3X4X9 ins., 
 requiring 45 to the square yard, and weigh 9J Ibs. each.* 
 
 * Building Inspectors' Pocket-book. 
 
DATA ON BRICKS AND BRICKWORK. 1379 
 
 Sand-lime Brick. Bricks made of sand and lime have 
 been made in Germany for fifty years or more and the industry 
 appears to be established on a successful basis. During the 
 past three or four years a number of plants have been equipped 
 in this country for the manufacture of these bricks. There 
 are three or four different processes of manufacture, the prin- 
 cipal ones being the "Huennekes" and "Schwarz" systems. 
 Parties who have personally inspected plants operated by each 
 system appear to be divided in their opinion as to which pro- 
 cess produces the best brick. The hardening process, by steam, 
 is common to all systems, as the practicability of sand-lime 
 bricks is due to the formation of silicate of lime ; brought about 
 by the heat and moisture. 
 
 Under the " Huennekes System" the process is briefly as 
 follows :* The sand is put through a dryer, and then passes to 
 a measuring-machine. The lime, previously burnt in a kiln, is 
 crushed very fine, and then passes to the measuring-machine, 
 and is mixed with the sand just after leaving ft. The mixture 
 is measured to contain 94 per cent, of sand and 6 per cent, of 
 lime. This mixture is then conveyed to a tube-mill, where 
 it is ground very fine, and then drops into the wet mixer, where 
 enough water is added so that the mixture will ball easily in 
 the hand. It is then conveyed to a large bin, where it is kept 
 about twelve hours to permit the lime to slake. From this 
 bin it goes to the press in which the bricks are formed under a 
 pressure of about 175 tons to the brick. They are then piled 
 on cars holding from 850 to 1000 bricks, and the cars are run 
 into a steel cylinder 62 ft. long and 6 ft. in diameter, fitted with 
 a track and a tank for holding chemicals. As soon as the cylin- 
 der is filled, the head is bolted on and steam is introduced. The 
 steam on entering goes through the chemical tank and becomes 
 supercharged with the chemical. Steam is kept at 120 Ibs. 
 pressure for eleven hours, when it is blown off, the head taken 
 off, and the bricks are taken out ready for the market. 
 
 The chemical combination is controlled exclusively by H. 
 Huennekes Company of New York City, who license and equip 
 factories for the manufacture of bricks under their process. 
 
 The Schwarz system f differs from the above in the prepara- 
 tion of the sand and lime for the press, which is done in a prepar- 
 
 * This information was furnished the author by Mr. D. P. De Long, Prest. 
 Granite Brick Company of Glens Falls, N. Y. 
 
 t Schwarz System Brick Co., 8 Bridge Street, New York. 
 
1380 DATA ON BRICKS AND BRICKWORK. 
 
 ing-machine invented by Dr. Schawrz of Zurich, Switzerland; 
 also no chemicals are used with this system nothing but lime 
 and sand. [It is claimed that not a single sand-lime brick 
 factory in Europe applies any kind of chemicals whatsoever.] 
 In tbie Schwarz preparing-machine all the moisture of the 
 sand is first removed by drying the same under vacuum; the 
 lime is then added and the materials thoroughly mixed by two 
 wing-shaped agitators revolving in the cylinder in opposite 
 directions Then follows a carefully measured and always con- 
 stant amount of water to slaken the lime, and the heat evolved 
 upon this reaction is immediately utilized for a second reaction, 
 i.e., the opening up of the silica of the sand and the formation 
 of silicate of lime, by which process the mass is rendered soft 
 and plastic, easy to mold, and causing little wear and tear to the 
 press. Finally, the mixing going on continually, again a 
 definite amount of water is added to moisten the mass for the 
 press, whereupon the apparatus is emptied and recharged. 
 
 The advocates of the Schwarz system claim that their pro- 
 cess produces a more uniform mixture, and consequently a 
 brick of more uniform quality. 
 
 The sand used should be a sharp silica sand free from clay * 
 and nearly free from loam. The lime should be a fat, quick- 
 slaking lime free from magnesia. 
 
 Qualities. The natural color of sand-lime brick is white or 
 a light gray ; the bricks are said to present a fine appearance. 
 They are very dense, and show a very small absorption of 
 moisture, usually under 10 per cent. 
 
 The average crushing strength seems to be about 3,000 Ibs. 
 per square inch, although tests have shown an ultimate strength 
 of 6,700 Ibs. per square inch. 
 
 The bricks made by the Granite Brick Company of Glens 
 Falls, N. Y., measure 8JX4X2J ins., and weigh 5 Ibs. each. 
 This company is selling its face brick at $10 per M., f.o.b. at 
 factory. 
 
 The author understands that sand-lime bricks are being used 
 to a considerable extent in different portions of the country. 
 
 Glazed aiid Enamelled Brick.f The terms "enam- 
 elled brick" and "glazed brick," as commonly used, refer practi- 
 
 * The presence of clay in the sand tends to prevent its standing freezing 
 weather. 
 
 t For description of process of manufacture, see p. 197 Building Con- 
 struction and Superintendence, Part I. 
 
DATA ON BRICKS AND BRICKWORK. 1381 
 
 cally to the same article, and neither include what is known 
 as a "salt-glazed" brick. The enamelled or glazed brick 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 
 enamelled brick are generally divided into two classes; true 
 enamelled brick, which has a glaze containing the coloring mat- 
 Jer applied to it without any intermediate slip; the other has a 
 transparent glaze placed over aVhite or colored slip, the slip com- 
 ing 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 brick, 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 highlg glazed 
 or satin (dull 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 tile. 
 
 An enamelled 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 brick; the 
 enamelled brick will show no line of demarcation between the 
 body of the brick and the enamel. 
 
 Enamelled bricks are made in two regular sizes, English size 
 (9"X3" enamelled surface, 4J' bed) and American size 
 (8f"X21" enamelled surface, 4J" bed). 
 
 The English size costs about $10 per M. more than the Ameri- 
 can, but on account of the saving in the number of bricks, 
 labor of laying, and mortar in joints, they really effect a saving 
 of about 7 cts. per square foot. 
 
 The Tiffany Enamelled Brick Company also make a ' ' Norman 
 flat" (12"X4t" enamelled surface, 2J" bed). 
 
 The selling price of enamelled brick in Chicago at the present 
 time (June, 1904), is as follows: 
 
 American size . . $75 per M. English size $85 per M. 
 
 Norman flat $100 
 
 At these prices the cost of the bricks per square foot will be: 
 
 American size, 7 bricks to the foot 52 J cts. 
 
 English size, 5 J bricks to the foot 45J " 
 
 English flat, 3| bricks to the foot 36 " 
 
 Norman flat, 3 bricks to the foot 30 " 
 
1382 DATA ON BRICKS AND BRICKWORK. 
 
 The standard colors carried in stock are white, cream, and 
 buff; other colors are made to order. 
 
 American enamelled and glazed bricks are now extensively 
 used for the exterior surfaces of buildings, particularly for street 
 fronts, light courts, and for interior side walls and partitions of 
 rooms or buildings used for a great variety of purposes. 
 
 Tjae principal manufacturers are the Tiffany Enamelled Brick 
 Company, Chicago; Blue Ridge Enamelled Brick Company, 
 Newark, N. J. ; Pennsylvania Enamelled Brick Company, New 
 York City. 
 Estimating Quantities and Cost of Brickwork. 
 
 The almost universal method of figuring the cost of brick- 
 work 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 in- 
 tended 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, the adjust- 
 ment for the more expensive portions of the work being made 
 in the manner of measuring. 
 
 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 compensa- 
 tion equal. 
 
 "To illustrate: If, in one day, a man can lay two thousand 
 bricks in a plain dead wall, and can lay only five hundred 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 
 compensate 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 different price for the execu- 
 tion of the various kinds of work."* 
 
 Wall Measure, How Figured. Plain walls are quite 
 universally figured at 15 bricks to the square foot of 8- or 9-in. 
 wall, 22 J bricks per square foot of 12- or 13-in. wall, 30 bricks 
 per square foot of 16- or 17-in. wall, and 7J bricks for each 
 additional 4 or 4J ins. in thickness of the wall. These figures 
 
 * From Rules of Measurement adopted by the Brick Contractors' Ex' 
 change of Denver, Col. 
 
MEASUREMENT OF BRICKWORK. 1383 
 
 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 superficial feet, 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 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 ins. on each side of the wall, 1 ft. is 
 added to the actual height of the wall. 
 
 Chimney-breasts and pilasters are measured by multiplying 
 the girth of the breast or pilaster from the intersections with 
 the wall by the height, and then by the number of bricks corre- 
 sponding 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 1 ft 4 ins. would 
 be measured as a 16- or 17-in. wall, 5 ft. 8 ins. long. 
 
 The rule for independent piers is to multiply the height of 
 the 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 super- 
 ficial feet are usually disregarded in estimating. If the arcli 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 thickness 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, accord- 
 ing to whatever the cost of plain brickwork may be. If the 
 building is to be faced with pressed brick, the actual cost of 
 the pressed brick, as nearly as it can be computed, is added 
 to the estimated price of the common brick work, nothing 
 
1384 DATA ON BRICKS AND BRICKWORK. 
 
 being added for laying the pressed brick, nor anything deducted 
 from the common-brick measurement, the measurement of the 
 common work displaced by the pressed brick being assumed to 
 offset the difference in the cost of laying the pressed and 
 common brickwork. 
 
 In arriving at the cost of the pressed brick, the external super- 
 ficial area of the walls faced with such brick is computed, and 
 all openings, belt courses, stone caps, etc., deducted. 5-in stone 
 sills are not usually deducted. If a portion of the wall is covered 
 by a porch, so that common brick may be used back of it, this 
 space is also deducted. The net pressed-brick surface is then 
 multiplied by 6, 6J, or 7 to obtain the number of bricks required, 
 6J giving about the number of pressed bricks required to the 
 square foot of the standard size. 
 
 The topping out of the chimneys, if of face-brick, is measured 
 by girting the chimney and multiplying by the height, and 
 adding the sum to the wall area. 
 
 EXAMPLE. As a simple example of this system of estimating 
 we will take a small brick house 28 by 32 ft. without cross- 
 walls, the basement walls to be 13 ins. thick, with footings 
 2 ft. 6 ins. wide; first-story walls, 13 ins. thick; second-story 
 walls, 9 ins. thick; height of basement walls from trench to 
 top of first-floor joists, 8 ft. 6 ins.; from first-floor joists to 
 top of second-floor joists, 10 ft. 6 ins.; from second-floor joists 
 to plate, 9 ft. 
 
 Wall Measurement. Basement walls, equal 120 ft. (girth of 
 building) X9 ft. 10 ins. (height and projection of footing) 
 X22J; equals 26,550 bricks. 
 
 First-story walls, 120 ft.XlO ft. 6 ins.X22J; equals 28,360 
 bricks. 
 
 Second-story walls, 120 ft.X9 ft.X 15; equals 16,200 
 bricks. 
 
 Topping out two chimneys, each 1 ft. 9 ins. XI ft. 5 ins., 14 
 ft. high above roof, equals 2X14 ft.X(l ft. 5 ins. + l ft. 9 ins. 
 + 1 ft. 5 ins.)X30; equals 3,600 bricks. 
 
 Total brickwork equals 74,710 bricks; at $9 per M. (present 
 price in Denver), equals $672.39. 
 
 Pressed Brick. From grade to the under side of plate the 
 wall measures 22 ft. 6 ins.; to be faced with $15 pressed brick 
 of the standard size. 
 
 The door and window openings measure 384 superficial 
 feet. 
 
ESTIMATING COST OF BRICKWORK. 1385 
 
 Surface of pressed brick equals 120 X22J, equals . . 2,700 sq. ft. 
 Deduct for openings 384 " 
 
 2,316 
 Add for two chimneys, 2 X 14 X 6 ft. 4 ins., equals. . . 177 " 
 
 2,493 " 
 
 2,493 X6J equals 16,204 pressed bricks, at $15 per M., equals 
 $243. 
 
 Total amount of bid, $672.39 + $243, equals $915.39. 
 
 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 of ironwork, as ties, thimbles, ash doors, 
 etc., are figured additional to the above. 
 
 Detailed Estimates. In estimating by the above 
 method, the price per thousand is to some extent a matter of 
 guesswork, and while an experienced 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 contractor 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 
 16J to 17f common bricks are required to the cubic foot after 
 deducting openings, and figuring the thickness of walls at 
 8, 12, 16, 20 ins., etc., or the actual number of bricks required 
 will run about two-thirds of the " wall measure " when the open- 
 ings are of about the average number and size. 
 
 The number of pressed bricks will be about 6 or 6J bricks 
 to the foot after deducting openings. 
 
 To lay 1,000 common bricks, kiln count, requires 2J bushels 
 or 200 Ibs. of white lime and f yd. of sand. For a good lime 
 and cement mortar allow 2 bushels lime, 1 bbl. cement, and 
 f yd. sand. For 1 to 3 cement and sand mortar allow 1J bbls. 
 cement and f yd. sand, or one half load. 
 
 To lay 1,000 pressed bricks with buttered joints will require 
 2 bushels of lime (160 Ibs.) and J yd. of sand; with spread joints 
 2 to 2J bushels of lime and f to J yd. of sand. 
 
 If colored mortar is used, about $1 per 1,000 bricks should be 
 added for the mortar color. 
 
1386 DATA ON BRICKS AND BRICKWORK. 
 
 A brick-mason, working on a city job under a good foreman, 
 will lay 60 pressed (face) bricks per hour, on an average, and 
 from 150 to 175 common bricks per hour, 160 being a fair 
 average. In country towns the average is nearer 120 an hour. 
 
 With wages at 62 J cts. per hour for masons, 31^ cts. for hod- 
 carriers, and 34f cts. for mortar-mixers and carriers, sand at 
 60 cts. a yard, and lime at 40 cts. per bushel of 80 Ibs., brick' 
 masons in Denver find that the average cost for laying common 
 brick in 12-in. walls is about $6 per M., kiln count, and for 
 laying pressed brick, about $10 per M. 
 
 For common brickwork, one helper will be required for every 
 mason, and on 9-in. walls faced with pressed brick, one helper 
 to every two masons. 
 
 In building common-brick fireplaces and chimneys one mason 
 and helper will lay about 600 bricks in a day of nine hours. 
 
 As a rule, chimneys of common brick 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. 
 
 One thousand old bricks, cleaned and loosely stacked, occupy 
 about 72 cu. ft. 
 
 A brick-layers' hod measures 21 ins. X 7 ins. X 7 ins., and will 
 hold 18 bricks. 
 
 A mortar hod measures 24 ins. X 12 ins. X 12 ins. X 12 ins. across 
 the top. 
 
 Mortar colors are usually in the form of a dry powder, put 
 up in barrels, the number of pounds to the barrel and price per 
 pound averaging about as follows: 
 
 Red, in 500-lb. barrels, dry 2 cts. per pound 
 
 Brown, in 450-lb. barrels, dry 2J " " 
 
 Buff, in 400-lb. barrels, dry 2J " " 
 
 Black, in 1,000-lb. barrels, dry 3J " " " 
 
 Red, brown, buff, or black, in pulp, J ct. per pound extra. 
 For lots of less than full barrels an extra charge is made for 
 packing and drayage.* 
 
 To color the mortar for laying 1,000 bricks with spread 
 joints will require about 50 Ibs. of red, brown, or buff, and from 
 40 to 45 Ibs. of black; with buttered joints, 40 Ibs. of red, 
 brown, or buff, or from 25 to 35 Ibs. of black. 
 
 The colors should first be mixed with dry sand, then the 
 
 * These figures are for Ricketson's mortar colors. 
 
LIME. 1387 
 
 cold slaked lime added and again mixed thorough/. It is very 
 important that the color be uniformly mixed. If it is not added 
 at first, but is 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. 
 
 LIME. 
 
 Definitions and Useful Data. Pure lime is a prot- 
 oxide of calcium, or, in other words, a metallic oxide. It has a 
 specific gravity of 2.3, is amorphous, somewhat spongy, highly 
 caustic, quite infusible, possesses great affinity for water, and if 
 brought in contact with it will rapidly absorb 22 to 23 per cent, 
 of its weight, passing into the condition of hydrate 01 lime. 
 
 Slaked lime is hydrate of lime. 
 
 Quicklime, or caustic lime, is the resulting lime left from the 
 calcination of limestone. It is chemically known as calcium 
 oxide. 
 
 Limestone, carbonate of lime. Crystallized lime, marble. 
 Fossil lime, chalk. Sulphate of lime, gypsum. Calcination is 
 heating to redness in air. 
 
 Slaking is the process of chemical combination of quicklime 
 with water. 
 
 Air-slaking. Hydration by the absorption of moisture from 
 the atmosphere. 
 
 Lime is shipped either in barrels or 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. 
 
 In most of the Eastern cities it is sold by the barrel, weighing 
 for Rockland (Me.) lime 220 Ibs. net. When shipped in bulk 
 it is generally sold by the bushel of 80 Ibs., 2J bushels, or 200 Ibs., 
 of lime being considered as equivalent to a barrel. 
 
 The average yield of lime paste from the best Eastern limes 
 has been found to be 2.62 times the bulk of unslaked lime. A 
 barrel of good quality well-burnt lime should make 8 cu. ft., 
 or 20 pails, of lime paste or putty. 
 
 Careful experiments conducted by U. S. engineers have 
 demonstrated that the best mortar is obtained by mixing 
 one part lime paste to two of sand. 
 
 "Popping" of Lime. The best qualities of lime should com- 
 pletely slake in forty-eight hours, but there are some limes in 
 which some of the particles will not slake with the bulk of the 
 lime, but continue to absorb moisture, and finally, after a long 
 
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1390 LATHING AND PLASTERING. 
 
 The third or finishing coat is designated by various terms, 
 such as skim coat, white coat, putty coat, sand-finish, etc. The 
 skim coat as used in the Eastern States is generally composed 
 of lime putty and washed beach-sand in equal proportions. 
 Sand-finish, which has a rough surface resembling coarse sand- 
 paper, 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 ndt be used. The skim coat or hard finish 
 should be finished with a steel trowel and wet brush. The 
 more the work is trowelled the harder it becomes. 
 
 A superior hard finish is obtained by mixing 4 parts Best's 
 Keene's cement to 1 part lime putty. 
 
 To make sure that the lime is well slaked, it is customary 
 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 contain one bushel of hair 
 when beaten up. Each package is supposed to weigh from 
 seven to eight pounds, but the weight often falls short. 
 
 Asbestos and manilla fibre 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, then run off the hot lime as soon as it is 
 slaked, and then to throw in the sand and mix the whole 
 together, when it is 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 
 
HARD WALL PLASTERS. 1391 
 
 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 an economical and satisfactory quality of walls 
 and ceilings by the use of the ordinary hand-mixed lime mortar, 
 other and more reliable plastering materials have been invented, 
 and are now being extensively employed, especially on the 
 largest and most costly structures, and are giving general 
 satisfaction. 
 
 Among the best-known of these improved plasters are the 
 Acme, Agatite, and Royal cement plasters, Adamant, Windsor 
 cement dry plaster, Rock wall plaster, and Best's Keene's 
 cement. The first three are natural products found in certain 
 parts of Kansas and Texas and simply calcined. Many other 
 brands of these cement plasters are made in the Western States 
 to supply the local markets* The other four plasters named 
 above are composed principally of plaster of Paris with certain 
 chemicals added. All appear to produce about the same 
 results. The Windsor dry plaster, Adamant, and Rock plaster 
 are mixed with the proper proportion of sand by the manu- 
 facturers, and only require being "wet up" before using. All 
 of these materials are sold by weight. They should be used 
 strictly in accordance with the directions furnished by the 
 manufacturers. 
 
 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 drying the plaster, minimum danger from frost, 
 less weight and moisture in the building, and greater resistance 
 to the action of fire and water. 
 
 Measuring 1 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 011 the laths. 
 
 Plastering on plain surfaces, as walls and ceilings, is always 
 measured by the square yard, whether it be one, two, or three- 
 coat work, or lime or hard plaster. 
 
 In regard to deducting for openings, custom varies some- 
 what in different portions of the country and also with different 
 
1392 LATHING AND PLASTERING. 
 
 contractors. Some plasterers allow one half the area of open- 
 ings for ordinary doors and windows, while others make no 
 allowance for openings less than 7 sq. yds. 
 
 Returns of chimney-breasts, pilasters, and all strips less 
 than 12 ins. in width should be measured as 12 ins. 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 also made. If the plastering cannot 
 be done from trestles an additional charge must be made for 
 staging. 
 
 Stucco cornices and moulded work are generally measured 
 by the superficial foot, measuring on the profile of the mould- 
 ing. When less than 12 ins. in girth they are usually rated as 
 1 ft. For each internal angle 1 lin. ft. should be added, and for 
 external angles, 2 ft. 
 
 For cornices on circular or elliptical work an additional price 
 should be charged. 
 
 Enriched mouldings are generally figured by the lineal foot, 
 the price depending upon the design and size of the mould. 
 
 Whenever plastering is done by measurement the contract 
 should definitely state whether or not openings are to be de- 
 ducted, and a special price should be made for the stucco-work, 
 based on the full-size details. 
 
 Quantities of Materials Required for Lathing 
 and Plastering. 
 
 To cover 100 sq. yds. requires from 1,400 to 1,500 laths, 
 or say 1,450 for an average job, and 10 Ibs. of 3d. nails. 
 
 Three-coat plastering on wood laths, plaster-of-Paris finish, 
 will require from 8 to 10 bu. of lime, 1J yds. of sand, 2 bu. of 
 hair, and 100 Ibs. of plaster of Paris per 100 sq. yds. 
 
 If finish coat is omitted, deduct 2 bu. of lime, and all of the 
 plaster of Paris. 
 
 If sand-finished, omit the plaster of Paris and add J yd. of 
 sand. 
 
 Two coats on brick or stone walls (brown coat and finishing 
 coat) will require 6 to 8 bu. of lime, 1 J yds. of sand r and 100 Ibs. 
 of plaster of Paris, to 100 sq. yds. 
 
 Using Best's Keene's cement for brown mortar and Keene's 
 on expanded metal lath will require, for brown mortar, 
 
COST OF PLASTERING. 1393 
 
 550 Ibs. cement, 5J bu. lime, 2 yds. sand, 2 bu. hair; for the 
 finish, 300 Ibs. cement and 1 bu. of lime per 100 yds. 
 
 Hard plasters on expanded metal lath, plaster-of-Paris finish, 
 require for brown mortar 2,000 Ibs. plaster and 2 yds. sand; 
 for the finish, 1 bu. lime and 100 Ibs. plaster of Paris per 100 yds. 
 Cost. The standard price for putting on wood laths (labor 
 only) in Denver (1904) is 3J cts. per yard. For expanded or 
 sheet-metal laths on wood studding, 5 cts.; on steel studding, 
 wired, 8 cts. 
 
 The cost of putting three coats on laths, plaster-of-Paris finish 
 (labor only), run about 15 cts. per yard for drawn work and 
 16 cts. for dry scratch. 
 
 With sand finish the cost is about the same as for white finish. 
 
 These figures are based on plasterers' wages at 62 J cts. per 
 
 hour, and 37 \ cts. per hour for hod-carriers and mortar-mixers. 
 
 The following table gives the average cost of different kinds 
 
 of plastering in Denver in 1904, based on Missouri lime at 
 
 40 cts. per bushel, sand at 75 cts. per load of 1J yds., hair at 
 
 40 cts. per bushel, and plaster of Paris at 50 cts. per 100 Ibs., 
 
 and wages as given above. 
 
 Scratch and brown coat (lime) on wood laths 25 cts. per yd. 
 
 3 coats (lime) on wood laths, plaster-of-Paris 
 
 finish 30 " " " 
 
 3 coats (lime) on wood laths, sand finish 30 " " " 
 
 Brown coat and finish on brick walls 23 " " " 
 
 For hard wall plaster instead of lime, add 3 " " " 
 
 3 coats (lime), plaster-of-Paris finish, metal lath 
 
 on wood studding 65 " " " 
 
 3 coats (lime) plaster-of-Paris finish, metal lath 
 
 on steel studding 68 " " " 
 
 For Keene's cement finish, add . . . . 10 " " " 
 
 For blocking in imitation of tile, add 50 " " " 
 
 2 coats hard wall plaster, plaster-of-Paris finish, 
 
 metal lath, wood studding 70 " " " 
 
 2 coats hard wall plaster, plaster-of-Paris finish, 
 
 metal lath on steel studs 73 " " " 
 
 For Keene's cement finish, add 10 " " " 
 
 Portland cement, brown coat, finished with 
 Keene's cement blocked in imitation of tile, 
 
 3"X 6" $2.80 per yd. 
 
 For running base, 9" high, in Best's Keene's ce- 
 ment 10 cts. per ft. 
 
1394 DATA ON LUMBER, 
 
 For running plain mouldings in plaster of Paris, 3 to 5 cts. per 
 
 inch of girth. 
 
 For finishing shafts of columns, 16 to 24 ins. diam., 12 to 14 ft. 
 high, $3 per column (labor only). 
 
 These prices are believed to be pretty near an average for 
 the entire country. In some localities prices for materials or 
 labor are less, in others higher. 
 
 i Staff is a composition of plaster of Paris and hemp fibre, cast 
 in moulds, and nailed or wired in place. All of the buildings 
 of the Columbian Exposition at Chicago (1893) were covered 
 with this material and all of the temporary buildings of the 
 St. Louis Exposition of 1904.* 
 
 It is not sufficiently durable for permanent work unless 
 kept well painted. 
 
 The cost of l( staff" as used on the buildings at Chicago in 
 1893 varied from $2 to $2.25 per square yard. 
 
 DATA ON LUMBER AND CARPENTERS' WORK.f 
 
 Framing Lumber may commonly be purchased in any 
 of the following sizes, except that common pine, spruce, and 
 hemlock cannot usually be obtained in larger sizes than 12 X 12 
 ins. 
 
 2 X4 3X6 4X12 8X12 
 
 2 X6 3X8 4X14 8X14 
 
 2 X8 3X10 6X6 10X10 
 
 2 XlO 3X12 6X8 10X12 
 
 2 X12 3X14 6X10 10X14 
 
 2 X14 3X16 6X12 10X16 
 
 2 X16 4X 4 6X14 12X12 
 
 2JX12 4X 6 6X16 12X14 
 
 2iXl4 4X 8 8X 8 12X16 
 
 2iXl6 4X10 8X10 14X14 
 
 14X16 
 
 In some of the New England mills, the following sizes are 
 also sawn: 2X3, 2X5, 2X7, 2X9, 3X4, and 3X5. 
 
 These sizes are not commonly carried in stock, and in most 
 localities would have to be obtained by ripping larger sizes. 
 
 * A description of the process of manufacture is given in Part I, Build- 
 ing Construction and Superintendence, p. 347. 
 
 t A comprehensive booklet giving the rules for the grading and classi- 
 fication of yellow-pine lumber and dressed stock may be obtained from the 
 Southern Lumber Manufacturers Association, Equitable Building, St. 
 Louis, Mo. 
 
DATA ON LUMBER. 1395 
 
 Most of the Southern yellow pine, Oregon pine, or Washing- 
 ton fir is shipped surfaced one side and edge the actual di- 
 mensions being from J in. to f in. scant of the nominal dimen- 
 sions, and sometimes J in. 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. 
 
 Length. 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 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 one foot wide, one foot long, and one inch thick. 
 
 To compute the board measure in any board, plank, or timber, 
 divide the nominal sectional area, in inches, by 12, and multiply 
 by the length in feet. Thus the number of. ''feet" in a 2X4 
 
 2X4 
 scantling 8 ft. long= -X8=5J ft. b. m. A 10 -inch board, 
 
 12 ft. long, contains X12=10 ft. b. m. 
 
 Extensive tables are published showing the feet, board measure, 
 in 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. 
 
 I . To use this table, multiply together, mentally, the dimen- 
 sions of the cross-section, and then in the column having a 
 heading equal to this product, and opposite the given length 
 will be found the feet, board measure. Thus, for a 3X4, 2X6, 
 or 1X12, look in column headed 12; for a 2X12, 4X6, or 3X8, 
 look in 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 that 
 for a single stick. 
 
1396 
 
 DATA ON LUMBER. 
 
 TABLE OF BOARD MEASURE. 
 
 For explanation, see p. 1395. 
 
 *! 
 
 Sectional Area in Square Inches. 
 
 1 s 
 
 4 
 
 6 
 
 8 
 
 10 
 
 12 
 
 14 
 
 16 
 
 18 
 
 20 
 
 
 ft. ins. 
 
 ft.* 
 
 ft. ins. 
 
 ft. ins 
 
 ft.* 
 
 ft. ins. 
 
 ft. ins. 
 
 ft.* 
 
 ft. ins. 
 
 6 
 
 2 
 
 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 
 
 11 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 
 
 16 
 
 5 4 
 
 8 
 
 10 8 
 
 13 4 
 
 16 
 
 18 8 
 
 21 4 
 
 24 
 
 26 8 
 
 18 
 
 6 
 
 9 
 
 12 
 
 15 '0 
 
 18 
 
 21 
 
 24 
 
 27 
 
 30 
 
 20 
 
 6 8 
 
 10 
 
 13 4 
 
 16 8 
 
 20 
 
 23 4 
 
 26 8 
 
 30 
 
 33 4 
 
 22 
 
 7 4 
 
 11 
 
 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 
 
 10 8 
 
 16 
 
 21 4 
 
 26 8 
 
 32 
 
 37 4 
 
 42 8 
 
 48 
 
 53 4 
 
 34 
 
 11 4 
 
 17 
 
 22 8 
 
 18 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 Area in Square Inches. 
 
 
 24 
 
 28 
 
 30 
 
 32 
 
 35 
 
 36 
 
 40 
 
 42 
 
 48 
 
 
 ft.* 
 
 ft. ins. 
 
 ft,* 
 
 ft. ins. 
 
 ft. ins. 
 
 ft.* 
 
 ft. ins. 
 
 ft.* 
 
 ft.* 
 
 6 
 
 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 10 
 
 42 
 
 46 8 
 
 49 
 
 56 
 
 16 
 
 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 10 
 
 78 
 
 86 8 
 
 91 
 
 104 
 
 28 
 
 56 
 
 65 4 
 
 70 
 
 74 8 
 
 81 8 
 
 84 
 
 93 4 
 
 98 
 
 112 
 
 30 
 
 60 
 
 70 
 
 75 
 
 80 b 
 
 87 6 
 
 90 
 
 100 
 
 105 
 
 120 
 
 32 
 
 64 
 
 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 
 
 101 4 
 
 110 10 
 
 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 measurements in these columns come out in even feet. 
 
TABLE OF BOARD MEASURE. 
 
 1397 
 
 TABLE OF BOARD MEASURE. Continued. 
 
 For explanation, see p. 1395. 
 
 ,J 
 
 0> 
 
 t! 
 
 Ss 
 I 
 
 Sectional Area in Square Inches. 
 
 56 
 
 60 
 
 64 
 
 72 
 
 80 
 
 84 
 
 96 
 
 100 
 
 112 
 
 
 ft. ins. 
 
 ft.* 
 
 ft. ins. 
 
 ft.* 
 
 ft. ins. 
 
 ft,* 
 
 ft.* 
 
 ft. iris. 
 
 ft. ins. 
 
 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 3 
 
 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 
 
 368 
 
 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 
 
 504 
 
 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 
 
 728 
 
 80 
 
 373 4 
 
 400 
 
 426 8 
 
 480 
 
 533 4 
 
 560 
 
 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 
 
 * The measurements in these columns come out in even feet. 
 
DATA ON LUMBER. 
 
 TABLE OF BOARD MEASURE. Continued. 
 
 For explanation, see p. 1395. 
 
 +s 
 
 0> 
 
 
 la 
 I 
 
 Size and Sectional Area in Inches. 
 
 120 
 10X12 
 
 140 
 10X14 
 
 144 
 12X12 
 
 160 
 10X16 
 
 168 
 12X14 
 
 192 
 12X16 
 
 196 
 14X14 
 
 224 
 14X16 
 
 
 ft.* 
 
 ft. ins. 
 
 ft.* 
 
 ft. ins. 
 
 ft.* 
 
 ft.* 
 
 ft. ins. 
 
 ft. ins. 
 
 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 
 
 296 
 
 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 
 
 336 
 
 384 
 
 392 
 
 448 
 
 26 
 
 260 
 
 303 4 
 
 312 
 
 346 8 
 
 364 
 
 416 
 
 424 8 
 
 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 
 
 506 8 
 
 532 i 608 
 
 620 8 
 
 709 4 
 
 40 
 
 400 
 
 466 8 
 
 480 
 
 33 4 
 
 560 1 640 
 
 653 4 
 
 746 8 
 
 42 
 
 420 
 
 490 
 
 504 
 
 560 
 
 588 
 
 672 
 
 686 
 
 784 
 
 44 
 
 440 
 
 513 4 
 
 528 
 
 586 8 
 
 616 
 
 704 
 
 7/18 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 
 
 50 
 
 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 
 
 1,008 
 
 56 
 
 560 
 
 653 4 
 
 672 
 
 746 8 
 
 784 
 
 896 
 
 914 8 
 
 1,045 4 
 
 58 
 
 580. 
 
 676 8 
 
 696 
 
 773 4 
 
 812 
 
 928 
 
 947 4 
 
 1,082 8 
 
 60 
 
 600 
 
 700 
 
 720 
 
 800 
 
 840 
 
 960 
 
 980 
 
 ,120 
 
 62 
 
 620 
 
 723 4 
 
 744 
 
 826 8 
 
 868 
 
 992 
 
 1,012 8 
 
 ,157 4 
 
 64 
 
 640 
 
 746 8 
 
 768 
 
 853 4 
 
 896 
 
 1,024 
 
 1,045 4 
 
 ,194 8 
 
 66 
 
 660 
 
 770 
 
 792 
 
 880 
 
 924 
 
 1,056 1,078 
 
 ,232 
 
 68 
 
 680 
 
 793 4 
 
 816 
 
 906 8 
 
 952 
 
 1,088 1,110 8 
 
 ,269 4 
 
 70 
 
 700 
 
 816 8 
 
 840 
 
 933 4 
 
 980 
 
 1,120 
 
 1,143 4 
 
 ,306 8 
 
 72 
 
 720 
 
 840 
 
 864 
 
 960 
 
 1,008 
 
 1,152 
 
 1,176 
 
 ,344 
 
 74 
 
 740 
 
 863 4 
 
 888 
 
 986 8 
 
 1,036 
 
 1,184 
 
 1,208 8 
 
 ,381 4 
 
 76 
 
 760 
 
 886 8 
 
 912 
 
 1,013 4 
 
 1,064 
 
 1,216 
 
 1,241 4 
 
 ,418 8 
 
 78 
 
 780 
 
 910 
 
 936 
 
 1,040 
 
 1,092 
 
 1,248 
 
 1,274 
 
 1,456 
 
 80 
 
 800 
 
 933 4 
 
 960 
 
 1,066 8 
 
 1,120 
 
 1,280 
 
 1,306 8 
 
 1,493 4 
 
 82 
 
 820 
 
 956 8 
 
 984 
 
 1,093 4 
 
 1,148 
 
 1,312 
 
 1,339 4 
 
 1,530 8 
 
 84 
 
 840 
 
 980 
 
 1,008 
 
 1,120 
 
 1,176 
 
 1,344 
 
 1,372 
 
 1,568 
 
 * The measurements in these columns come out in even feet. 
 
MEASUREMENT OF FLOORING, ETC. 139! 
 
 Measurement of Finishing Lumber, Flooring 
 Ceiling", etc. -Most, if not all, lumber for finishing is regular 
 sawn in thicknesses of 1 in., 1J in., 1 J in., and 2 ins., and in som 
 woods, such as white pine and poplar, is sawn 2J ins. and 3 ins 
 thick. 
 
 When surfaced both sides, the thickness is reduced to l % 
 1%, 1%, If, 2J, and 2% ins. 
 
 All dressed stock is measured and sold "strip count," i.e. 
 full size of rough material necessarily used in its manufacture 
 Thus l^-in. boards are measured as though 1J in. thick 
 The number of 'feet, board measure, for IJ-in. stock (1^ fin 
 ished) is 1J times that in a 1-in. board, and in the same wa^ 
 for IJ-in. and 2J-in. stock. If-in. plank is always measure< 
 2 ins. thick, and 2J-in. stock, 2J ins. thick. Boards less thai 
 1 in. thick are measured the same as inch boards, but for f 
 and f-in. stock a reduced price is generally made. 
 
 Matched Flooring* The standard sizes are 1X3, 1X4, an< 
 1X6, or HX3, 1JX4, and 1|X6. The thickness of 1-irj 
 flooring should be % in., and of IJ-in. flooring, l-^ in.; 3-irj 
 flooring should show 2J ins. on face, after it is laid, 4-in., 3J ins. 
 and 6-in., 5J ins. 
 
 Matched maple flooring is made in 2-in., 2J-in., and 3J-in. face 
 and in thicknesses of J, 1J, and If ins.. There are three grades 
 Clear, No. 1, and Factory. 
 
 Ceiling (matched and beaded boards) is regularly stuck in th 
 same widths as flooring. The standard (nominal) thicknesse 
 of yellow-pine ceiling are f , J, f , and f in., the actual thicknes 
 of each being %> in. less. The f-in. ceiling is dressed one sid 
 only, the other thicknesses both sides. 
 
 Yellow-pine Drop Siding, all patterns, measures f in.X5J ins 
 over all, and usually shows about 5-in. face. 
 
 Bevel Siding is resawed on a bevel from stock % m - X 5 J ins 
 after surfacing. 
 
 The New England Clapboards are 4 ft. long, 6 ins. wide 
 J in. thick at the butt, and about J in. thick at the other edge 
 They are put up in bunches and sold by the thousand. 
 
 Rules for Estimating Quantities of Sheathing 1 
 Flooring, etc. For common sheathing laid horizontally 01 
 a wall or roof without openings, add one tenth to the actua 
 superficial area to allow for waste. On the walls of dwellings 
 
 * Everywhere except in New England "flooring" is always understoo< 
 to be tongued and grooved. 
 
1400 COST OF CARPENTERS' AVORK. 
 
 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 10-in. 
 boards. If laid diagonally add one fourth for 6-in. boards, 
 one sixth for 8-in. boards, and one eighth for 10-in. boards. 
 
 For 3-in. matched flooring add one half to the actual super- 
 ficial 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 ins. to the weather, add one half to 
 the actual superficial area; if 4J ins. to the weather, add one 
 third. 
 
 Cost of Carpenters 1 Work. There are so many items and 
 conditions 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 estimating 
 carpenters' work. The best of these that the author has seen 
 is "Estimating Frame and Brick Houses," by Fred T. Hodgson. 
 
 The following figures of the cost (for labor and nails) of 
 framing and putting on sheathing and siding and laying floor- 
 ing are probably a fair average, with carpenters' wages at 
 $3 a day of eight hours (37 J cts. per hour). The cost of fram- 
 ing is almost always figured at a certain price per thousand 
 feet of lumber, board measure. The cost of laying flooring- 
 sheathing, etc., is always figured by the square of 100 sq. ft. 
 (10'XIO'). 
 
 For setting up studding and framing walls of wooden dwellings , $10 . 00 per M. 
 For framing and setting floor joists, 2X8 to 2X12. .. .$9 to $10 " " 
 Framing and setting heavy joists and girders, 6 X 12 to 10 X 14, $8 . 50 !i " 
 
 Framing gable roofs and setting in place $10.00 " 
 
 Framing hip roofs and setting in place $11 to $12 " 
 
 For putting in bridging, after it is cut, per 100 lin. ft. in the row, $1.25 
 For covering the sides or roofs of wooden buildings with 
 
 dressed sheathing, laid horizontally . 60 per square 
 
 If laid diagonally . 75 " 
 
 The cost of labor and nails for laying 6" flooring, blind 
 nailed to every joist without dressing after laying 
 
 is about 2 . 00 " " 
 
 For 4" flooring, not dressed, allow 2.25 " 
 
 For 3" flooring, not dressed, allow 2 . 50 " " 
 
 For 3" hard-pine flooring, hand smoothed or traversed. ... 3 . 75 " " 
 
 For 3" red-oak flooring, hand smoothed or traversed 6 . 00 ' 
 
 For 3" white-oak flooring, hand smoothed or traversed. ... 8 . 00 " " 
 For 3" maple flooring, hand smoothed or traversed. .$10 to $12 " " 
 
BUILDING PAPERS AND FELTS. 1401 
 
 BUILDING PAPERS, FELTS, QUILTS, ETC. 
 
 There is a great variety of papers and felts manufactured 
 for use on buildings. They may be broadly classified as follows : 
 
 Rosin-sized Building Papers,* These are about the 
 cheapest 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. Always put up in rolls 36 ins. wide and usually 
 containing 500 sq. ft. Weight varies from 18 to 40 Ibs. to the 
 roll of 500 sq. ft.; cost, from 50 cts. to $1.50 per roll.f 
 
 Water-proof Papers. Neponset Black Sheathing is 
 water- and air-proof, odorless and clean to handle. An excel- 
 lent paper under siding, shingles, slate, or tin. Rolls 36 ins. 
 wide, containing 250 and 500 sq. ft. ; cost, about $2.00 per roll 
 of 500 sq. ft. 
 
 Neponset Red Rope Sheathing and Roofing. Made of rope stock ; 
 has great strength and flexibility, absolutely water-proof and 
 air-tight. One of the best sheathing papers. Makes a good 
 cheap roofing for sheds, poultry-houses, etc. Rolls 36 ins. wide, 
 containing 250 and 500 sq. ft. Cost, about $5.00 per 500 sq. ft. 
 
 Parchment Water-proof Sheathing. -Semi-transparent, smooth 
 surface, odorless, water-, air-, and vermin-proof. Adapted for 
 general sheathing purposes and for use in concrete construction. 
 1-ply, 25 Ibs. to 900 sq. ft. ; 2-ply, 25 Ibs. to 500 sq. ft. ; 3- ply, 
 25 Ibs. to 275 sq. ft. All 36 ins. wide. 
 
 P. & B. Building Paper. Thoroughly coated with P. & B. 
 compound (principally paraffine), is water-, acid-, alkali-, and 
 gas-proof ; claimed not to decay. An excellent sheathing paper. 
 Black and glossy, but not sticky. Rolls 26 ins. wide, containing 
 1000 sq. ft. Made 1-ply (very thin), 30 Ibs.; 2-ply, 40 Ibs.; 
 3-ply, 65 Ibs. ; 4-ply, 80 Ibs. Cost, $3.00, $4.50, $6.00, and $8.00, 
 respectively. 
 
 Dry Felts. Common felts are composed of waste vege- 
 table fibres cemented together with rosin. Better grades are 
 made from wool stock. Felts are made in many different 
 thicknesses, and in 32-in. and 36-in. widths. They should be 
 specified by weight unless a particular brand is specified. Com- 
 mon dry felt weighs from 4J to 5 Ibs. per 100 sq. ft. 
 
 Barrett's Eureka Brand. All-wool stock, 32 ins. wide, and 
 weighs 1 Ib. to the square yard. 
 
 * The terms "building" and "sheathing" are indiscriminately applied 
 to all kinds of papers 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 heavier and better grades 
 are classed as sheathing papers. 
 
 t All prices are approximate ; they vary with locality and condition of 
 the market. 
 
1402 BUILDING PAPERS AND QUILTS. 
 
 Barrett's Excelsior Brand. All-wool stock, 32 ins. wide, and 
 weighs 1J Ibs. to the square yard. This is a very heavy felt. 
 
 A dry wool felt weighing 1 Ib. to the square yard will be 
 about | in. thick. Such felts are used principally for deadening 
 between floors and as carpet lining. Commonly sold by the 
 pound, 2J cts. a pound being perhaps an average price. 
 
 Saturated Felts. 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 Ibs. to the 
 100 sq. ft. Nothing lighter than 12 Ibs. should be used for 
 roofing. Usually sold by weight. Average price, 1J cts. a 
 pound. 
 
 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. Are especially adapted for 
 slaters' use, as they will carry a chalk line and are easy to handle. 
 Rolls 36 ins. wide contain 500 sq. ft. and weigh about 30 Ibs. 
 Cost, about 80 cts. per roll. 
 
 Asbestos Building' Felts are usually made about 6, 10, 
 14, and 16 Ibs. to the 100 sq. ft., although different manufac- 
 turers make different weights. Rolls 36 ins. wide. Sold by 
 weight. 
 
 Insulating- and Deadening Quilts. 
 
 Cabot's "Quilt" consists of a felted matting of eel-grass held 
 in place between two layers of tough manila paper by " quilt- 
 ing." ( Also made with a covering of asbestos. Single- ply 
 weighs 85 Ibs. per bale of 500 sq. ft. , width 36 ins. Double-ply 
 weighs 125 Ibs. per bale of 500 sq. ft., width 36 ins. 
 
 Keystone Hair Insulator. A quilt with hair filling. Four 
 brands, each packed in bales 3 ft. wide containing 500 sq. ft. 
 Acme, plain paper both sides, weight per bale 60 Ibs. Nep- 
 tune, water-proof paper one side, plain paper other side, weight 
 per bale 70 Ibs. Phcenix, asbestos paper one side, plain paper 
 other side, weight per bale 100 Ibs. Salamander, asbestos 
 paper both sides, weight per bale 130 Ibs. 
 
 The Union Fibre Company's Mineral-wool Deafener is made 
 of rock-fibre wool, quilted between sheets of rosin-sized, water- 
 proof or fire-proof paper. Put up in rolls 36 ins. wide, \ in. 
 thick, and containing 125 sq. ft. 
 
 The Union Fibre Company's Flax-fibre Floor Deadener is 
 made of degummed flax fibre, sewed between two thicknesses 
 of rosin-sized paper. Put up in rolls 36 ins. wide, J in. thick, 
 and containing 200 sq. ft. Also furnished with water-proof or 
 asbestos paper covering. 
 
 Cost of Building; and Sheathing Papers in Place. 
 
 The following, although necessarily restricted to a few lines, 
 will give a general idea of the cost of different kinds and grades 
 of sheathing papers, the price given being a fair average for 
 the material applied to an outside wall or roof: 
 
PAINTS AND PAINTING. 1403 
 
 Price per 100 
 Square Feet. 
 
 Common tarred felts (15 Ibs. per square)* $0 30 
 
 Red rosin-sized sheathing, best grades . 35 
 
 Manahan's parchment sheathing, single-ply . 26 
 
 double-ply . 40 
 
 ship-rigging tar sheathing, 2-ply . 75 
 
 "Neponset" black (water-proof) building paper 0.45 
 
 red rope roofing fabric 1 . 10 
 
 Sheathing papers with asphalt centre $0 .40 to . 50 
 
 Johns' asbestos building felt, 10 Ibs. per square 0.42 
 
 14 Ibs. per square . 55 
 
 Cabot's sheathing quilt, single-ply 1 .05 
 
 double-ply 1 . 25 
 
 Sawyer's century sheathing quilt (felt coated one side with a water- 
 
 and vermin-proof compound) 1 . 35 
 
 Painting*. 
 
 Materials Employed for Paints. A paint consists 
 of a base (usually a metallic oxide), a vehicle or carrier, and a 
 solvent. 
 
 Bases are those materials which give a body to the paint 
 and make it opaque. 
 
 Vehicles are water and drying-oils. 
 
 Solvents are spirits of turpentine. 
 
 Driers are red lead, litharge, acetate of lead, sulphate of zinc, 
 binoxide of manganese, etc.; they are used to make the vehicle 
 dry more rapidly. 
 
 Pigments. When the finished color is desired to be different 
 from that of the base, coloring-pigments are used. They 
 must be more or less finely ground, so as to be capable, when 
 mixed with the vehicle, of being spread out in a thin layer 
 or film over the surface to be painted. 
 
 Bases. The materials commonly used as a base for paints 
 are white lead, zinc white, red lead, yellow ochre, oxide of 
 iron, and graphite. 
 
 The last two are largely used for painting roofs, barns, etc., 
 and structural steel and iron. Yellow ochre with linseed-oil 
 is often used for priming outside woodwork and brick walls. 
 Red lead is used principally for painting metal- work. 
 
 For painting woodwork, pure white lead has generally been 
 considered as the best base that can be obtained, but it is now 
 recognized that for many purposes zinc white is superior to 
 white lead. For very dark colors, such as dark green, very 
 little white lead can be used, and no lead can be used in black 
 paints. 
 
 * A " square " is 100 sq. ft. 
 
1404 PAINTS AND PAINTING. 
 
 Pure white lead is produced by three processes: (1) The 
 Dutch process, by which thin sheets of pure lead are carbonated 
 and^then ground to a fine powder; (2) by grinding the metal 
 first and then carbonating, and (3) the sublimated lead process, 
 employed by the Pilcher Lead Company of Chicago, 111. 
 
 Adulterations. White lead is often mixed with sulphate 
 of baryta (a substance which verv..much resembles it in appear- 
 ance) in order to effect a saving in the amount of lead used 
 and thus reduce the cost of the paint. 
 
 Methods of testing for adulterations in white and red lead 
 and boiled linseed-oil are described in the Inspector's Pocket- 
 Book* 
 
 Zinc White vs. White Lead. (A) According to M. J. L. Bre- 
 ton, of the French Academy of Sciences, the idea of chemical 
 union between linseed-oil and white lead is an erroneous one. 
 Nothing but a mechanical mixture is or can be formed between 
 the two substances, and he says that the mixture of oxide of 
 zinc with linseed- oil is more homogeneous than that formed 
 with white lead. Zinc requires the addition of much more 
 drier to the oil, but this does not appear to injure its solidity; 
 and it is curious that, contrary to the common notion, oxide of 
 zinc has, weight for weight, nearly twice as much covering power 
 as lead when mixed with the same quantity of oil, and even 
 volume for volume the covering power of zinc is about a third 
 greater than that of lead. The oxide of zinc, however, when 
 mixed with oil gives a much less fluid paint than an equal 
 volume of white lead; so that the apparent deficiency in cover- 
 ing power of zinc paint, which every architect has observed, 
 does not come from any inherent quality of the material, but 
 from the fact that the painters, in mixing zinc, thin it to the 
 usual consistency of lead paint, thus forming a mixture which 
 is nearly all oil. With care to use zinc paint much thicker than 
 lead, and to put in plenty of drier, it will, according to M. Bre- 
 ton, cover as well as lead, and adhere even more strongly, 
 besides resisting the action of sulphurous gases, which soon 
 affect lead paint in interiors; and its advantage over lead in 
 not being poisonous is so great that humanity suggests its use 
 wherever practicable. 
 
 (B) According to Stanton Dudley, the consensus of en- 
 lightened opinion among paint authorities is that (1) where 
 pure white is required pure zinc white is absolutely necessary; 
 
 (2) where delicate tints are required they can be produced 
 only by using zinc white as the base, this condition being empha- 
 sized if the colors required for producing the tint be any of the 
 chemical or other artificial colors (excepting the carbons); 
 
 (3) for interiors pure zinc white or zinc white in combination 
 with one of the inert pigments (barytes, china clay, gypsum, 
 
 * See List of Books. 
 
PAINTS AND PAINTING. 1405 
 
 etc.) is the only permissible white base; if other white pig- 
 ment is used it should be protected with a surface coating of 
 pure zinc white. For the painting of exteriors pure zinc white is 
 preferable to anything else for permanence and economy, if the 
 material to be coated be absolutely dry and well seasoned, and 
 if the weather conditions be favorable, and if the paint be used 
 rather heavy for each coat; under other conditions it is gen- 
 erally thought advisable to use the zinc in combination with 
 lead or inert materials, a very 'desirable combination for this use 
 being 80 per cent, by weight of zinc and 20 per cent, of lead, 
 with or without from 1 to 5 per cent, of inert material. Zinc 
 having no reaction with linseed-oil, dries very slowly; it is, there- 
 fore, thought advisable on the under coats to substitute about 
 6 to 10 per cent, of spirits of turpentine for a like quantity of 
 the oil used as a menstruum, while for drier it is preferable to 
 use a purer manganese product than one prepared with lead 
 salts. The absolute purity of the linseed-oil used is a most 
 important factor in the results, and scarcely less essential to 
 satisfaction is it that each coat shall be thoroughly dry before 
 the succeeding one is applied. 
 
 Vehicles, or Carriers. While there is a great deal of dis- 
 pute as to the best material to use as a base for different paints, 
 there is none as to the superiority of linseed-oil over all other 
 commercial oils as a vehicle for all kinds of paints (not including 
 shingle stains). 
 
 Raw Linseed-oil is obtained by compressing flaxseed. The 
 raw oil when of good quality should be pale in color, perfectly 
 transparent, almost free from odor, and sweet in taste; the 
 quality improves with age. 
 
 Boiled Linseed-oil is prepared by heating raw oil either alone 
 or with driers, such as red lead, litharge, etc., or bypassing a cur 
 rent of air through raw oil. It is thicker and darker in color 
 than raw oil and dries much quicker. Because of the latter 
 quality it is much more extensively used for paints than the raw 
 oil. 
 
 Keady-mixed Paints. There are a great many brands 
 of these paints, some of which have considerable merit, but as a 
 rule mixed paints are looked upon with suspicion and architects 
 prefer to have all paints mixed on the job (except those 
 especially prepared for the protection of iron and steel). 
 
 Stains. A stain differs from a paint in that the former is 
 transparent while the latter is opaque. Stains are made by 
 mixing the coloring-pigment with the vehicle, and should not 
 be so thick as to -conceal the grain of the wood. 
 
 For staining outside woodwork, particularly shingles, either 
 
1406 PAINTS AND PAINTING. 
 
 boiled linseed-oil or creosote may be used for the vehicle; except 
 that the latter is cheaper, the author \s of the opinion that 
 there is very little choice between the two. As a preservative, 
 creosote is far superior to any other oil except linseed. Kero- 
 sene-oil should never be used. 
 
 For interior stains, oil stains are generally considered to be the 
 best, although turpentine stains and water stains are frequently 
 used. 
 
 Water Paints. Frescoing is commonly done with water- 
 colors, i.e., water is used as a vehicle. Kalsomine is composed 
 of glue, Paris white, and generally of some coloring-pigment, 
 mixed with water. Whitewash is pure white lime mixed with 
 water. (See Part 1, Building Construction and Superintendence, 
 p. 349.) 
 
 Weather-proof Water Paints. Contrary to the com- 
 mon opinion, weather-proof paints, at least for certain locations, 
 can be made with water as a vehicle. 
 
 Such paints are commonly designated as " cold- water paints." 
 One of the best of these is "Magnite," * which may be used 
 either for exterior or interior painting. It may be used as a 
 first coat on brick walls, and finished with oil paint, or for light 
 shafts, courtyards, etc., two coats without the oil paints may be 
 used with satisfactory results. It does not rub or scale and 
 is fire-resisting. ^ 
 
 "Petrol" * occupies a position between oil paint and kalso- 
 mine; it is applied with a kalsomine brush, but gives a surface 
 more like oil paint* 
 
 All cold-water paints are much more economical than oil 
 paints and for many purposes they are fully as satisfactory* 
 
 They are put up in the form of a dry powder, which can be 
 mixed with cold water to the desired consistency as wanted. 
 
 Damp-resisting Paints. Antihydrine, manufactured 
 by the Antihydrine Company of New Haven, Conn., is highly 
 recommended for making walls dampproof and stainproof. It 
 should be applied under the plaster* 
 
 The Zibell Damp Resisting Paint Company, New York, also 
 manufacture water-proof paints for protecting wood and iron 
 from moisture, and especially for applying to the inside of 
 brick walls to protect wall-paper, fabrics, and decorations from 
 being discolored by dampness. 
 
 * J. A. & W. Bird & Co., Boston, manufacturers. 
 
PAINTS AND PAINTING. 1407 
 
 Wood Preservatives. It is generally considered that 
 there is no better wood preservative than creosote provided 
 that the wood is thoroughly impregnated with it. 
 
 Carbolineum Avenarius* prepared from heavy coal-tar oils 
 to which are added chlorine and other powerful antiseptics 
 is highly recommended by Dr. B. E. Fernow and many engineers 
 as an effective, cheap, and simple means of increasing the dura- 
 bility of wood. 
 
 "This material can be applied with a brush, or better still 
 by immersing the wood in the hot liquid. It penetrates the 
 wood to sufficient depth to protect it against moisture and the 
 accompanying rot fungi in such places as architects are likely 
 to have to deal with."t 
 
 "Conservo" is a preparation prepared by Samuel Cabot for 
 the same purpose. 
 
 Notes on the Painting of Wood and Plaster. 
 
 By W. G. E. ROLAFF, Architect, Fort Worth, Texas. 
 
 Outside Woodwork. All outside woodwork should have at 
 least three coats of paint, of which the first coat should be 
 applied very thinly and contain nothing but pure linseed-oil 
 as a carrier. Being thin it will become a part of the wood and 
 the chances of it ever peeling off will be reduced to a minimum. 
 If white lead is used in the second and third coat, the last coat 
 should contain at least 15 per cent, of pure French zinc- white 
 (green seal), which will effectually prevent the crystallization of 
 white lead. Turpentine should be used very sparingly on all 
 outside work, as it does not possess the same weather-resisting 
 qualities as oil. 
 
 All nail holes should be filled with putty after the first coat 
 of paint is thoroughly dry, but the putty should not be smoothed 
 down at the time, but left projecting from the face of the wood. 
 When the putty is dry the surplus should be removed by a 
 sharp knife. By using this method putty will not show any 
 shrinkage . 
 
 Inside Work. Oil paints are used very extensively for interior 
 finishing of woodwork and give a handsome and lasting finish. 
 For fine interiors, the first two coats should contain nothing 
 
 * Prepared by the Carbolineum Wood-preserving Company, New York. 
 tDr. Fernow. 
 
1408 PAINTS AND PAINTING. 
 
 but oil as a carrier. The third coat should contain about half 
 oil and half turpentine and the last coat nothing but turpentine; 
 by this method an absolutely flat finish will be obtained. The 
 flat surface is the only one suitable for an inside finish, and 
 since it is not exposed to the weather the turpentine as a carrier 
 is not objectionable. After every coat the work should be 
 rubbed with No. sandpaper and made thoroughly smooth. 
 All paint to be used for inside work should be strained carefully. 
 Where the appearance of the paint is not of much consequence, 
 linseed-oil is preferable to turpentine as a carrier, as paints 
 mixed with oil will wear longer. 
 
 Enamels. There are a number of ready-for-use enamels on 
 the market, two of which, notably "Porcelite "* and Rinald 
 Bros.' Porcelain Enamel, have been extensively used with good 
 results. For enamel finish, poplar or some other fine-grained 
 and non-resinous wood should be used, since there is no danger 
 of raised grain and sweating of pitch, which will stain through 
 the enamel. The following method for obtaining an enamelled 
 surface has been used with unvarying success and better results 
 have been obtained with it than with ready-made enamels. 
 This is especially true with pure white and ivory enamels. For 
 the first two or three coats pure white lead and turpentine should 
 be used. All white lead to be used for enamels should first be 
 washed in gasoline and every particle of oil be extracted there- 
 from, as any oil remaining in the lead will eventually stain 
 the enamel. All work should be sandpapered with No. sand- 
 paper after each coat. After the third coat of white lead is 
 dry two or more coats of pure white damar varnish and pure 
 zinc-white should be carefully applied. *Rub between coats 
 with No. 3 steel wool or No. 00 sandpaper. The last coat should 
 contain very little zinc, and after drying it can be brought to 
 either a high gloss finish by rubbing gently with pumice and 
 water and polishing with rotten stone, or rubbed until it has 
 the egg-shell gloss. 
 
 For ivory enamel the third coat of white lead should be 
 colored with a slight tinge of yellow ochre and burnt umber. 
 By applying the damar varnish and zinc over this, one obtains 
 that transparency which is so desirable in ivory finish. If any 
 other color of enamel is desired the coloring-matter must be 
 added and refined as the work proceeds and the final color 
 
 * The Thompson Wood-finishing Company, manufacturers, Philadelphia, 
 
PAINTS AND PAINTING. 1409 
 
 be obtained by approaching it gradually in each successive coat 
 rather than by getting it in the last coat or two. 
 
 Stained Woodwork. The simplest and one of the best 
 methods of staining woodwork is to make the stain in a thick 
 paste of colors ground in oil (nothing but oil should be used 
 for a carrier). It should then be applied with a brush and 
 wiped off with rags as soon as it has thoroughly sunk into the 
 grain of the wood. 
 
 After this, the wood may be finished in several ways accord- 
 ing to the preference of the owner. It can be waxed in the 
 same manner that an ordinary hardwood floor is waxed or it 
 can be varnished, rubbed, and polished, the same as hard 
 woods. There are some finishes on the market, now, which 
 will accomplish the staining and waxing at the same time, 
 but for the best development of the grain of the wood each 
 operation should be performed separately. 
 
 Painting oil Plaster. All plaster should first be filled, 
 whether oil or water paint is to be used for the finish coats. 
 The best filler to use is a medium-grade varnish thinned with 
 turpentine or gasolene. This varnish size makes the plaster 
 almost if not quite impervious to moisture and is therefore far 
 superior to any filler that contains water. If water paint is 
 used and has to be removed at any time, it is necessary to 
 first clean the walls of all old paint, and if the varnish filler has 
 been used the paint can be sponged off without destroying the 
 size. 
 
 Oil Paints for Walls. The best wearing and appearing wall 
 finish is by all means that obtained with oil paints. Nothing but 
 white lead should be used for the body of the first two or three 
 coats, tinted to approach the desired color, and for these coats 
 nothing but linseed-oil should be used as the carrier with a very 
 small proportion of turpentine added as a drier. If the walls are 
 well filled, three coats should be sufficient for the groundwork. 
 The last coat should contain nothing but turpentine and the 
 color desired and this coat should be applied while the last 
 coat is still "tacky," and should be evenly stippled with a 
 stippling-brush as fast as it is applied. When dry, it will be 
 absolutely flat and present a beautiful velvet finish. It can 
 easily be washed with a damp rag at any time that dirt or dust 
 should accumulate. 
 
1410 PAINTS FOR STRUCTURAL STEEL. 
 
 Paints for Structural Steel. 
 
 The protection of structural steel from rust is of so great 
 importance, and such great quantities of steel are used, that 
 much attention has been given to the preparation of paints 
 for this especial purpose, and for painting structural steel and 
 iron it is generally safer to specify some particular brand or 
 brands than to leave the mixing of the paint to a painter. 
 
 The several kinds of paints made for this purpose may be 
 divided into oil paints, tar paints, asphalt paints, and var- 
 nishes. 
 
 The oil paints may be divided into lead paints, zinc paints, 
 iron paints, and carbon paints, according to the material used 
 for the base. All of the standard oil-paints have linseed-oil for 
 the vehicle. 
 
 Of the lead paints, red lead is considered as the best; white 
 lead does not make a good priming coat, and if used at all on 
 metal- work it should be used over another paint. 
 
 Zinc white alone does not make a good paint for metals, but 
 when mixed with red lead in the proportion of 1 of lead to 2 or 
 3 of zinc it is very durable. 
 
 Carbon paints are made either from lampblack or graphite, 
 both of which make excellent paints. There are two kinds of 
 graphite in common use for paints, the granular and the flake 
 graphite. 
 
 Very much has been written as to the comparative protecting 
 qualities of red lead, iron oxide, and graphite paints, and differ- 
 ent engineers have their preferences. Red lead is preferred as 
 a priming coat by many, while most of the prepared paints are 
 made from oxide of iron or graphite. 
 
 "The graphite and asphalt paints appear to withstand the 
 corroding action of smelter and engine gases better than red 
 lead or iron-oxide paints, while red lead is probably better 
 under these conditions than iron oxide."* 
 
 Asphalt Paint. "Many prepared paints are -sold under 
 the name of asphalt that are mixtures of coal-tar, or mineral 
 asphalt, alone, or combined with a metallic base or oils. The 
 exact compositions of the patent asphalt paints are hard to 
 determine. Black bridge paint made by Edward Smith & Co., 
 New York City, contains asphaltum. linseed-oil, turpentine, 
 
 *M. S. Ketchum, in Steel Mill Buildings, pp. 294 and 295. 
 
QUANTITIES AND COST OF PAINTING. 1411 
 
 and Kauri gum. The paint has a varnish-like finish and makes 
 a very satisfactory paint. The black shades of asphalt paint 
 are the only ones that should be used." * 
 
 A Portland-cement paint is described by Mr. Ketchum on 
 page 296 of " Steel-Mill Buildings," which after having been ap- 
 plied to a viaduct for a period of about two years ' ' was in almost 
 perfect condition and the metal under the coating was as clean 
 as when painted." 
 
 Of the prepared paints accepted by engineers for the protection 
 of structural steel the following are probably the most used: 
 
 Bessemer paint,- made by Rinald Bros.; Carbonizing Coating, 
 made by The Goheen Manufacturing Company, Canton, Ohio; 
 Dixon's Silica-graphite Paint, Dixon Graphite Company, Jer- 
 sey City ; Durable Metal Coating, Edward Smith & Co., New York ; 
 R. I. W. Damp-resisting Paint, Toch Bros., New York. 
 
 Measurement, Quantities, and Cost of Painting 1 . 
 
 Painters' work of all kinds is generally estimated by the square 
 yard, girting every part of the work that is covered with paint. 
 Windows, railings, etc., are usually measured solid. 
 
 Quantities. 1 gal. of lead and oil paint will cover about 
 55 sq. yds. of wood first coat, and from 70 to 90 yds. for each 
 additional coat. 
 
 On brickwork 1 gal. of paint will cover about 48 sq. yds. 
 first coat and 60 sq. yds. for each succeeding coat. 1 gal. of pre- 
 pared shingle stain will cover about 200 sq. ft. of surface when 
 applied with a brush, or will suffice for dipping 500 shingles. 
 
 Five pounds of cold-water paint will make 1 gal. and will 
 cover from 300 to 375 sq. ft. for first coat on smooth hard 
 boards, from 150 to 200 sq. ft. on rough boards, and from 150 
 to 200 sq. ft. on brick or stone walls. The paint costs about 
 45 cts. per gal. in white and 50 cts. in colors. 
 
 One gallon of varnish weighs from 8 to 9 Ibs., turpentine about 
 7 Ibs., and boiled or raw linseed-oil about 7J Ibs. 1 gal. Porcelite 
 (enamel) will cover about 225 sq. ft., two coats. For puttying, 
 about 5 Ibs. will be sufficient for 100 sq. yds. of interior or exterior 
 work. 
 
 The cost of materials to make 1 gal. of good paint, using 
 linseed-oil at 56 cts., will average about 55 cts. for oxide-of- 
 iron paint, $1.50 for pure lead paint, and 90 cts. for graphite. 
 
 The cost of painting (materials and labor) varies with the 
 
 * M. S. Ketchum, in Steel-Mill Buildings, pp. 294 and 295. 
 
1412 PAINTING STRUCTURAL STEEL. COST. 
 
 quality of paint used, the quality of the work and the materials 
 and character of the surface to be painted, also with the number 
 of coats applied. 
 
 The following prices may be taken as fair averages in making 
 approximate estimates. 
 
 1 coat paint, 1 color on interior woodwork . . 12 cts. per sq. yd. 
 
 2 coats paint, 2 colors 20 " " " 
 
 Q 05 " lt <l 
 
 1 coat shellac 10 " " " 
 
 Exterior work will run about the same or a little less than 
 interior work. 
 
 "A day's work in painting the outside of a two-story frame 
 building is 100 yds., including knotting, for priming coat, and 
 80 yds. for either second or third coat." * 
 
 For hard- wood or natural finish one coat paste filler and one 
 coat varnish are worth about 30 cts. a square yard if sandpapered, 
 and if liquid filler is used about 20 cts. Each additional coat 
 of varnish is worth about 10 cts. a square yard. 
 
 Floors filling, shellacking, varnishing, or waxing two coats, 
 35 cts. Painting brickwork, two coats, will cost about 18 cts. 
 a square yard or 25 cts. for three coats. 
 
 Tinting plaster walls in water-colors costs from 7 to 9 cts. 
 per square yard. 
 
 Miscellaneous. Dipping shingles costs about $3 per 1,000; 
 painting blinds, one coat, 8 cts. per square foot; tin roofs 
 per yard, 5 cts.; painting wooden fence 4 ft. high, one coat, 
 12 cts. per lineal foot. 
 
 Quantities and Cost of Paint on Structural 
 Steel.f The covering property of paint depends on the smooth- 
 ness or absorbing power of the surface painted; also on the 
 fluidity of the paint. Ordinarily 1 gal. of paint, consisting 
 of finely ground pigment and linseed-oil, covers about 600 sq. ft. 
 of metallic surface, one coat, or 350 sq. ft. with two coats. 
 
 If the surface is very smooth and non-absorbent, or the 
 paint is thinned with turpentine or naphtha, the paint may 
 spread over more surface to the extent of 50 per cent. If the 
 contrary conditions exist, the surface covered may be diminished 
 one half. The volume of the mixed paint usually exceeds the 
 volume of oil used from 20 to 75 per cent., according to the 
 kind of pigment used. 
 
 * Fred T. Hodgson, architect. 
 
 t Pencoyd Handbook, Eleventh Edition. 
 
PAINTING STRUCTURAL STEEL. 1413 
 
 AVERAGE SURFACE COVERED PER GALLON OF PAINT. 
 
 T> i 
 
 Volume 
 
 Lbs. 
 
 Volume 
 and 
 
 Sqi. 
 Fe 
 
 tare 
 et. 
 
 
 of Oil. 
 
 of Pig- 
 ment. 
 
 Weight 
 of Paint. 
 
 1 
 Coat. 
 
 2 
 Coats 
 
 Iron oxide (powdered). . . . 
 " (ground in oil). . 
 Red lead (powdered). . 
 
 gal. 
 
 8.00 
 24.75 
 22 40 
 
 Gals. Lbs. 
 1.2-16.00 
 2.6 = 32.75 
 1 4 30 40 
 
 600 
 630 
 630 
 
 350 
 375 
 375 
 
 White lead (ground in oil). . 
 Graphite (ground in oil). . . 
 Black asphalt 
 
 1 (turp.) 
 
 25.00 
 12.50 
 17 25 
 
 1.7 = 33.00 
 2.0 = 20.50 
 4 30 00 
 
 500 
 360 
 515 
 
 300 
 215 
 310 
 
 Linseed-oil (no pigment). . . 
 
 
 
 
 875 
 
 
 
 
 
 
 
 
 Light structural work will average about 250 sq. ft. and 
 heavy structural work about 150 sq. ft. of surface per net ton 
 of metal. 
 
 The cost of painting with oxide of iron or similar material, 
 based upon paint costing 50 cts. per gallon, labor at shops 
 $1.50 per day, and at erection $2.00 per day, will average 
 for one coat at the shop 45 cts. per net ton for light work and 
 30 cts. for heavy work. 
 
 For two coats after erection, $1.80 per ton for light work 
 and $1.20 for heavy work. 
 
 Specification for the Painting of Structural 
 Steel. 
 
 The following form was prepared by A. H. Sabin, M.S., 
 who is recognized as an expert on paints: 
 
 1. Shortly before riveting, all such parts of surfaces as are 
 to be brought permanently into contact shall be thoroughly 
 cleaned from dirt and rust, and from all scale which does not 
 perfectly adhere to the metal, by the use of scrapers, chisels, 
 and wire brushes; the latter alone shall not be considered suf- 
 ficient. Each such surface shall then receive one full coat of 
 (Durable Metal Coating), made by & Co. 
 
 [Note. The wire brush is an efficient means of getting rid of 
 loose scale and dirt ; but it is practically worthless for removing 
 thick rust or anything which adheres closely. Much of such 
 material may be removed by steel scrapers ; but deeply corroded 
 spots should be thoroughly cleaned out with a chisel and then 
 well brushed. These crevices are hereafter to be inaccessible, 
 and they are subject to the most dangerous corrosion, because 
 rusting at such places impairs not only the strength, but also 
 
1414 PAINTING STRUCTURAL STEEL. 
 
 the stiffness, of the structure a matter of much importance. 
 These joints therefore deserve more care than any other part.] 
 
 2. Shop-marks shall be compact and shall not cover more 
 surface than the inspector directs, the intent being to have the 
 surface occupied by such shop-marks as small as possible. 
 
 3. After assembling, the whole of the metal surfaces shall 
 be thoroughly cleaned in the manner described in the first 
 section, and shall then receive one full coat of said Durable 
 Metal Coating, except planed and turned surfaces and shop- 
 marks; and all planed and turned surfaces shall be coated with 
 Vacuum Flushing Oil * and shall be kept so coated until they are 
 erected in place; and all small cavities which will hereafter be 
 inaccessible shall be filled with a thick paste of litharge and 
 glycerine, freshly prepared, or with a melted mixture of three 
 or four parts of gilsonite or other equally hard asphaltum and 
 one part of linseed-oil. 
 
 4. The metal shall not be exposed to the weather nor loaded 
 for shipment until in the opinion of the inspector the paint 
 is sufficiently dry. At no time after the application of the 
 first coat of paint shall the pieces of iron or steel be laid on 
 the ground, but shall be laid on skids or trestles; and in all 
 handling and loading or unloading of the same care shall be 
 taken to avoid scraping off the preservative coating; and 
 in transportation care shall be taken to avoid nesting the pieces 
 except with packing material between them. 
 
 [This section calls for shop painting to be done under cover 
 and more careful handling of the steel than is customary. This 
 is probably the most radical reform called for in these specifica- 
 tons, and will be found difficult to enforce.] 
 
 5. After erection the work shall be carefully inspected, and 
 if there are any rusty spots these shall be thoroughly cleaned, 
 and all such places and also all places where the paint has been 
 rubbed off shall receive a coat of - - & Company's 
 (Durable Metal Coating); and all exposed edges and angles 
 shall receive an extra striping coat of the same, covering the 
 edge and the adjacent surface one or tw r o inches from the edge 
 on each side; all rivet- and bolt-heads and nuts shall also receive 
 an extra coat; after this has become dry, the whole surface, 
 having previously been thoroughly cleaned from dirt, shall 
 receive another full coat of said (Durable Metal Coating). 
 
 6. In no case shall a second or third coat of paint be applied 
 until the previous one is entirely dry. 
 
 [In order to distinguish successive coats some engineers 
 specify that they shall differ in color.] 
 
 7. During erection any small cavities which will hereafter be 
 inaccessible shall be filled as provided in Section 3. 
 
 * Vacuum flushing oil is a very heavy mineral oil, about as heavy as an oil 
 for wagon axles, and has been successfully used for a long time. 
 
PAINTING STRUCTURAL STEEL. 1415 
 
 8. All paint * and Durable Metal Coating used for this work 
 shall be purchased directly from the manufacturer or his 
 authorized agent, and each shipment shall be accompanied by 
 a signed certificate from the manufacturer or such agent, 
 stating that he has, at that time, shipped a specified amount of 
 the specified paint or (Durable Metal Coating) ; and all paint 
 and (Durable Metal Coating) shall be brought on to the premises 
 where it is to be used in the manufacturers' sealed packages, 
 which shall be opened in the presence of the inspector, who 
 may then, and at any subsequent time, take samples for examina- 
 tion or analysis; and in case any analysis made by direction 
 of the chief engineer shows impurity, adulteration, or substitu- 
 tion in these specified materials, the contractor shall pay all 
 the costs of such analysis, and shall moreover thoroughly clean 
 off all metal coated with such impure or unauthorized material 
 and shall repaint it to the satisfaction of the inspector. And 
 the contractor shall, upon demand, exhibit to the engineer 
 or inspector the bills from the manufacturers or their agents, 
 showing the amount of (Durable Metal Coating) purchased, and 
 also the certificates spoken of in this section; and the (Durable 
 Metal Coating) shall not be thinned with anything whatsoever, 
 nor shall any turpentine or benzine be allowed upon the premises 
 for any purpose, except by permission of the inspector and in 
 such quantity as he may allow. 
 
 9. The inspector shall be notified when any painting is to 
 be done, and no such work is to be done until the inspector 
 has approved tlie surface to which it is to be applied; and 
 the contractor shall furnish all facilties for inspection and for 
 necessary marking by the inspector, and all materials, such 
 as paint, brushes, etc., for such marking. No such inspection 
 or marking shall be done except by the engineer or his authorized 
 inspector. 
 
 10. In no case shall any paint be applied out of doors in 
 freezing, rainy, or misty weather, and all surfaces to which 
 paint is applied must be at the time dry and clean; and all work 
 must be done in a thorough, neat, and workmanlike manner. 
 If it is necessary, in cool weather, to thin the paint, this may 
 be done only by heating it; and this may be required by the 
 inspector. 
 
 11. The foregoing specifications shall be accepted and carried 
 out faithfully in every particular and shall not be construed 
 according to any prevalent practice not in full accord therewith. 
 
 GLASS -KINDS AND PRICE LISTS. 
 
 Sheet Glass or Common Window Glass. Com- 
 mon window glass is technically known as sheet or cylinder 
 
 glass because it is first blown into the form of a cylinder, then 
 cut longitudinally and flattened on a stone. Sheet glass can 
 readily be distinguished from plate glass, even at a distance, 
 because of its wavy appearance, Avhich cannot be wholly avoided* 
 
 * The word paint is inserted in case some other kind of paint, as, for in- 
 stance, a light colored paint, is specified for a third coat. 
 
1416 GLASS KINDS AND PRICE-LISTS. 
 
 Grades and Qualities of Sheet Glass. All common sheet glass, 
 without regard to quality, is graded according to thickness, 
 as "single strength" or " double strength." The double- 
 strength glass is supposed to have a nearly uniform thickness 
 of J in., while the single strength may be as thin as }{$ in. The 
 thickness of single-strength glass, however, is generally far 
 from uniform. 
 
 Both single- and double-strength glass are sorted into three 
 grades or qualities, the classification depending upon color, 
 brilliancy, and flaws. 
 
 In the common American glass the best quality is designated 
 as AA, the second as A, and the third as B. The A A quality 
 is supposed to be as good glass as can be made by the cylinder 
 process. As even this glass, however, is not entirely free from 
 defects, it is very difficult for any one but an expert to tell 
 exactly whether certain lights of glass are first or second quality. 
 The A quality is most used. The B quality is only suitable 
 for cellar windows, stables, factories, greenhouses, etc. 
 
 Sizes. The regular stock sizes vary by inches from 6 to 16 ins., 
 and above that by even inches up to 60 ins. in width and 
 70 ins. in height for double strength and 34 X 50 ins. for single 
 strength. 
 
 Cost. The price for sheet glass, as for all other clear glass, 
 varies with the size, strength, and quality. It is determined 
 by a schedule, or price-list, fixed from time to time by the 
 glass companies, from which a very large discount is made, 
 fluctuations in prices being regulated by the discount, which 
 at present is about 90 and 20 off for St. Louis, the discount vary- 
 ing with the freight rate. The list on common glass is changed 
 more frequently than that for plate glass ; the present list hav- 
 ing been adopted Oct. 1, 1893. The only way of ascertaining 
 the price of a light of glass of a given size is by means of the 
 price-list and discount. 
 
 The price per square foot increases rapidly as the size of 
 the glass increases, so that it is much cheaper to divide a large 
 window into eight or twelve lights than into two lights. 
 
 The table on page 1417 gives the present list price for single 
 lights of the sizes most commonly used. The net price is 
 obtained by deducting the discounts as illustrated by the 
 example under Plate Glass. 
 
 The price by the box is about 15 per cent, less than for single 
 lights. 
 
 Polished Plate Glass. Plate glass is the highest grade 
 of window glass, being cast in large sheets on a flat table and 
 then polished, while the common sheet glass is blown. It is 
 manufactured in sheets of various sizes, some as large as 12 ft. 
 wide by from 15 to 16 ft. long. The average thickness is from 
 i to % in. 
 
 The cost varies according to the size of the light. To as- 
 certain this cost a regular price-list is used, which is subject 
 to a large discount. This list is the standard list for the entire 
 trade and is maintained from year to year, rarely changing, 
 the present price-list having been established in 1894. The 
 
GLASS KINDS AND PRICE-LISTS. 
 
 1417 
 
 LIST PRICE OF COMMON WINDOW GLASS IN 1904. 
 
 Prices are for single lights, A quality; single strength up to and includ- 
 ing 15"X40'', double strength above. 
 
 Size in 
 
 Price 
 
 Size in 
 
 Price 
 
 Size in 
 
 Price 
 
 Size in 
 
 Price 
 
 Inches. 
 
 per 
 Light. 
 
 Inches. 
 
 per 
 Light. 
 
 Inches. 
 
 per 
 Light. 
 
 Inches. 
 
 per 
 Light. 
 
 6X8 
 
 $0.21 
 
 16X20 
 
 $2.28 
 
 24X32 
 
 $5.98 
 
 32X48 
 
 $14.15 
 
 7X9 
 
 0.27 
 
 16X24 
 
 2.76 
 
 24X34 
 
 6.65 
 
 32X60 
 
 19.55 
 
 8X10 
 
 0.35 
 
 16X28 
 
 3.56 
 
 24X36 
 
 6.65 
 
 32X72 
 
 33.26 
 
 8X12 0.42 
 
 16X30 
 
 3.80 
 
 24X40 
 
 8.05 
 
 36X36 
 
 11.79 
 
 9X12 
 
 0.46 
 
 16X32 
 
 4.07 
 
 24X44 
 
 9.20 
 
 36X40 
 
 14.15 
 
 9X15 
 
 0.59 
 
 16X36 
 
 ' 4.49 
 
 24X48 
 
 11.79 
 
 36X44 
 
 14.15 
 
 10X12 
 
 0.52 
 
 16X40 
 
 5.44 
 
 24X60 
 
 14.44 
 
 36X48 
 
 18.05 
 
 10X14 
 
 0.59 
 
 16X48 
 
 7.16 
 
 24X72 
 
 23.00 
 
 36X60 
 
 30.67 
 
 10X16 
 
 0.72 
 
 18X24 
 
 3.35 
 
 26X28 
 
 5.98 
 
 36X72 
 
 37.38 
 
 10X18 
 
 0.81 
 
 18X30 
 
 4.07 
 
 26X30 
 
 6.65 
 
 36X84 
 
 48.59 
 
 12X14 
 
 0.75 
 
 18X32 
 
 4.38 
 
 26X32 
 
 6.65 
 
 40X40 
 
 14.15 
 
 12X15 
 
 0.81 
 
 18X36 
 
 5.31 
 
 26X34 
 
 8.05 
 
 40X48 
 
 19.20 
 
 12X16 
 
 0.85 
 
 18X40 
 
 5.98 
 
 26X36 
 
 8.05 
 
 40X60 
 
 30.67 
 
 12X18 
 
 0.95 
 
 18X48 
 
 8.05 
 
 28X30 
 
 6.65 
 
 40X72 
 
 41.40 
 
 12X24 
 
 1.38 
 
 18X60 
 
 10.31 
 
 28X32 
 
 8.05 
 
 . 40X84 
 
 53.77 
 
 12X30 
 
 1.83 
 
 20X22 
 
 3.56 
 
 28X34 
 
 8.05 
 
 44X44 
 
 21.12 
 
 12X32 
 
 1.93 
 
 20X24 
 
 3.80 
 
 28X36 
 
 9.20 
 
 44X48 
 
 28.68 
 
 14X14 
 
 0.88 
 
 20X26 
 
 4.07 
 
 28X40 
 
 9.20 
 
 44X60 
 
 36.59 
 
 14X16 
 
 1.01 
 
 20X28 
 
 4.38 
 
 28X44 
 
 11.79 
 
 44X72 
 
 53.45 
 
 14X18 
 
 1.12 
 
 20X30 
 
 4.75 
 
 28X48 
 
 14.15 
 
 48X48 
 
 33.74 
 
 14X20 
 
 1.24 
 
 20X32 
 
 5.31 
 
 28X60 
 
 19.20 
 
 48X56 
 
 36.59 
 
 14X24 
 
 1.57 
 
 20X36 
 
 5.98 
 
 28X72 
 
 23.00 
 
 48X60 
 
 41.12 
 
 14X28 
 
 1.93 
 
 20X40 
 
 6.65 
 
 30X30 
 
 8.05 
 
 48X72 
 
 53.45 
 
 14X30 
 
 2.15 
 
 20X44 
 
 8.05 
 
 30X32 
 
 9.20 
 
 50X50 
 
 33.74 
 
 14X32 
 
 2.29 
 
 20X48 
 
 8.05 
 
 30X34 
 
 9.20 
 
 50X60 
 
 41.12 
 
 14X36 
 
 2.61 
 
 20X60 
 
 12.03 
 
 30X36 
 
 9.20 
 
 50X72 
 
 59.15 
 
 14X40 
 
 2.90 
 
 22X24 
 
 4.07 
 
 30X40 
 
 10.74 
 
 54X60 
 
 53.45 
 
 15X16 
 
 1.08 
 
 22X28 
 
 4.75 
 
 30X44 
 
 11.79 
 
 54X72 
 
 64.84 
 
 15X18 
 
 1.20 
 
 22X30 
 
 5.31 
 
 30X48 
 
 14.15 
 
 56X60 
 
 53.45 
 
 15X20 
 
 1.44 
 
 22X32 
 
 5.84 
 
 30X60 
 
 19.20 
 
 56X72 
 
 64.84 
 
 15X24 
 
 1.73 
 
 22X36 
 
 6.65 
 
 30X72 
 
 33.26 
 
 60X60 
 
 53.45 
 
 15X30 
 
 2.29 
 
 22X40 
 
 8.05 
 
 32X32 
 
 9.20 
 
 60X62 
 
 59.15 
 
 15X32 
 
 2.44 
 
 22X48 
 
 9.20 
 
 32X34 
 
 9.20 
 
 60X64 
 
 59.15 
 
 15X36 
 
 2.90 
 
 24X26 
 
 4.75 
 
 32X36 
 
 10.74 
 
 60X66 
 
 64.84 
 
 15X40 
 
 3.33 
 
 24X28 
 
 5.31 
 
 32X40 
 
 11.79 
 
 60X68 
 
 64.84 
 
 fluctuations in the selling price are arranged by means of a dis- 
 count which is the same for all sizes. At the present time 
 (July 1904) the discount to builders is about 80 and 5 off at 
 Denver. Nearer Pittsburgh the discount is greater on account 
 of lower freight charges. This discount is liable to sudden 
 changes. The price-list now in effect, slightly abridged, is 
 given on pp. 1420-1423. 
 
 Examples of Figuring Cost. What is the net cost of a light of 
 plate glass 72X96 ins., the discount being 80 and 5 per cent? 
 Ans. The list price, in table, is $173; 80 per cent =--$138. 40; 
 subtracting from $173 we have $34.60; 5 per cent off from 
 this leaves $32.87, the net price. 
 
 Odd and fractional parts of inches are charged at the price 
 of the next highest even inches. Thus 31X120J ins. costs 
 the same as 32X122 ins. 
 
 The average weight of plate glass is 3J Ibs. to the square foot. 
 
1418 
 
 GLASS KINDS AND PRICE-LISTS. 
 
 Cost of Bending 1 Plate and Window Glass. 
 
 Official scale, adopted March 1, 1900: 
 
 PLATE GLASS. 
 Plates where length and width are added, less than 76 inches. .$0.60 sq. ft. 
 
 of 76 c 
 41 90 
 " 100 
 
 >r more but less th 
 
 in 90 un 
 100 
 110 
 120 
 140 
 160 
 180 
 200 
 210 
 220 
 230 
 240 
 
 [DOW G] 
 ches 
 
 ted inches 0.75 
 
 .ft 
 
 , ., , 
 
 1.00 
 1.50 
 " 2 00 
 
 11 " " 120 
 " 140 
 
 
 * " 2.50 
 3.00 
 
 " 160 
 " 180 
 " " 200 
 
 
 
 " 3.50 
 " 4.00 
 4.50 
 
 " 210 
 " 220 
 
 
 
 5.00 
 5.50 
 
 " 230 
 
 Lights of less 
 " 60 
 " 70 
 " 80 
 " 90 
 " 100 
 
 WI]N 
 
 than 60 united in 
 or more but less th 
 
 6 . 00 
 
 LASS, 
 $0 25 s 
 
 ian 70 ur 
 
 1 80 
 90 
 1 100 
 ' 110 
 
 lited inches 0.30 
 
 1 0.40 
 
 " 
 
 ' . 50 
 " 0.60 
 " . . . 0.90 
 
 Figured Rolled Glass. The Mississippi Glass Com- 
 pany manufactures nine different patterns of figured rolled 
 glass for use in doors, transoms, and windows where an 
 obscure glass is desired, or for purely ornamental effects. The 
 Maze and Ondoyant patterns are especially valuable either 
 
 
 FULL-SIZE DETAIL OF FIGURED 
 ROLLED-GLASS, "FLORENTINE" 
 PATTERN. 
 
 Other popular patterns specified 
 are "Ondoyant," "Maze," "Vene- 
 tian," "Syenite," "Oceanic," and 
 "Figured No. 1," "Figured No. 2," 
 and "Figured No. 3." Thicknesses 
 i and 3/i 6 in. ; widths, 30, 40, and 42 
 ins.i lengths about 100 ins. 
 
 FULL-SIZE DETAIL OP ROLLED WIRE 
 GLASS, "ROUGH" or "HAMMERED'* 
 STYLE. 
 
 Other popular patterns specified 
 are "Maze" and "Ribbed" and 
 "Polished." ^ in. thick is standard 
 and is the only thickness "Polished." 
 "Maze," "Ribbed," "Rough," or 
 "Hammered" can be had in. 
 thick; widths up to 40 ins j lengths 
 up to 120 ins. 
 
GLASS KINDS AND PRICE-LISTS. 1419 
 
 in outside windows or skylights. For diffusing the light 
 see pp. 1300-1303. The Maze pattern may be had either with 
 or without embedded wire. Ondoyant glass is made J in. 
 thick and 30 ins. wide. The Maze and several other patterns 
 of rolled glass are made -J and ^ in. thick, and 42 ins. wide. 
 
 Maze wired glass is made in sheets J and f in. thick, up to 
 40 ins. wide and 100 ins. long. 
 
 Figured glass, on account of its greater cleanliness and dif- 
 fusing qualities, has almost entirely supplanted ground glass 
 and, to a considerable extent, chipped glass. 
 
 Wire Glass is described on p. 765. 
 
 Prismatic Glass, for glazing windows, skylights, and 
 sidewalk lights, is , now manufactured in a large number of 
 forms in both prisms and sheets, and by several companies, 
 the more important of which are as follows: 
 
 American Luxfer Prism Co Chicago, 111. 
 
 American Prismatic Light Co Philadelphia, Pa. 
 
 Cleveland Window Glass Co Cleveland, Ohio. 
 
 Daylight Glass Mfg. Co Philadelphia, Pa. 
 
 Daylight Prism Co .... Chicago, 111. 
 
 New York Prism Co New York, N. Y. 
 
 Solar Prism Co Cleveland. Ohio. 
 
 The diffusing properties of several types are described on 
 pp. 1300-1303. 
 
 Glass for Skylights. Where skylights are glazed with 
 clear or double thick glass, it may be used in lengths of from 
 16 to 30 ins. by a width of from 9 to. 15 ins. A lap of at least 
 an inch and a half is necessary for all joints. This is the cheapest 
 mode of glazing. The best glass, however, for skylight pur- 
 poses, next to prism or wire glass (see p. 1304), is fluted or rough 
 plate glass. The following thicknesses are recommended as 
 proportionate sizes: 
 
 12 inches by 48 inches is the extent for glass 8 /io inch thickness. 
 
 15 " " 60 " " ' y " 
 
 20 " " 100 " " " " " " % " 
 94 " " 156 " " " " " " % 
 
 WEIGHT OF ROUGH GLASS PER SQUARE FOOT. 
 
 Thickness 1 Ys WQ Yd H H % % 1 in. 
 
 Weight 2 23^ 3H 5 7 * 83^ 10 12^ Ibs. 
 
 The cost of skylights with galvanized-iron frame, glazed with 
 %-in. or J-in. ribbed glass, ranges from 40 to 60 cts. per square 
 foot of area covered. 
 
 Cost of Rolled Glass. In 1904, the different kinds of 
 glass were quoted for small quantities in St. Louis about as fol- 
 lows: 
 
 %6-in. ribbed skylight glass. . * 8 cts. per sq. ft. 
 
 M " 12 " 
 
 Ribbed wire glass, M in. thick 23 " 
 
 Maze. " " " " " 23 " 
 
 Factory ribbed glass, Vg in. thick . 9 " 
 
 Ondoyant glass, Ys in. thick 10 " 
 
 Maze glass (without wire), H in. thick 14 " 
 
 Maze glass, 3 /io in. thick 16 " 
 
 Prismatic glass in sheets from 25 to 50 " 
 
1420 GLASS KINDS AND PRICE-LISTS. 
 
 PRICE-LIST OF POLISHED PLATE GLASS. 
 
 IN EFFECT SINCE 1894. 
 Sizes in inches; prices in dollars and cents. 
 
 3 
 
 g 
 
 24 
 
 28 
 
 32 
 
 36 
 
 40 
 
 44 
 
 48 
 
 52 
 
 56 
 
 60 
 
 32 
 34 
 
 12.80 
 13.60 
 
 14.90 
 15.90 
 
 17.10 
 18.10 
 
 19.20 21.30 
 20.40 22.70 
 
 23.50 
 33.70 
 
 34.70 
 36.90 
 
 37.60 
 39.90 
 
 40.50 
 43.00 
 
 43 40 
 46.00 
 
 36 
 
 14.40 16.80 
 
 19.20 
 
 21.60 24.00 
 
 35.80 
 
 39.00 
 
 42.20 
 
 45.50 
 
 48.80 
 
 38 
 
 15.20 
 
 17.70 
 
 20.30 
 
 22.80 
 
 34.30 
 
 37.80 
 
 41.20 
 
 44.60 
 
 48.00 
 
 51.50 
 
 40 
 
 16.00 
 
 18.70 
 
 21.30 
 
 24.00 
 
 36.10 
 
 39.70 
 
 43.40 
 
 47.00 
 
 50.60 
 
 54.20 
 
 42 
 
 16.80 
 
 19.60 
 
 22.40 
 
 34.10 
 
 37.90 
 
 41.70 
 
 45.50 
 
 49.30 
 
 53.10 
 
 56.90 
 
 44 
 
 17.60 
 
 20.50 
 
 23.50 
 
 35.80 
 
 39.70 
 
 43.80 
 
 47.70 
 
 51.70 
 
 55.60 59.60 
 
 46 
 
 18.40 
 
 21.50 
 
 33.20 
 
 37.40 
 
 41.50 
 
 45.70 
 
 49.90 
 
 54.00 
 
 58.10 
 
 62.30 
 
 48 
 
 19.20 
 
 22.40 
 
 34.70 
 
 39.00 
 
 43.40 
 
 47.70 
 
 52.00 
 
 56.40 
 
 60.70 
 
 65.00 
 
 50 
 
 20.00 
 
 23.30 
 
 36.10 
 
 40.60 
 
 45.20 
 
 49.70 
 
 54.20 
 
 58.70 
 
 63.20 
 
 70.90 
 
 62 
 
 20.80 
 
 32.90 
 
 37.60 
 
 42.20 
 
 47.00 
 
 51.70 
 
 56.40 
 
 61.00 
 
 68.70 
 
 73.70 
 
 54 
 
 21.60 
 
 34.10 
 
 39.00 
 
 43.90 
 
 48.80 
 
 53.60 
 
 58.50 
 
 63.40 
 
 71.40 
 
 76.50 
 
 56 
 
 22.40 
 
 35.40 
 
 40.50 
 
 45.50 
 
 50.60 
 
 55.60 
 
 60.70 
 
 68.70 
 
 74.10 
 
 79.30 
 
 58 
 
 23.20 
 
 36.70 
 
 41.90 
 
 47.10 
 
 52.40 
 
 57.60 
 
 62.90 
 
 71.20 
 
 76.70 
 
 82.20 
 
 60 
 
 24.00 
 
 37.90 
 
 43.40 
 
 48.80 
 
 54.20 
 
 59.60 
 
 65.00 
 
 73.70 
 
 79.30 
 
 85.00 
 
 62 
 
 33.60 
 
 39.20 
 
 44.80 
 
 50.40 
 
 56.00 
 
 61.60 
 
 70.30 
 
 76.10 
 
 82.00 
 
 88 
 
 64 
 
 34.70 
 
 40.50 
 
 46.20 
 
 52.00 
 
 57.80 
 
 63.60 
 
 72.50 
 
 78.60 
 
 84.70 
 
 91 
 
 66 
 
 35.80 
 
 41.70 
 
 47.70 
 
 53.60 
 
 59.60 
 
 68.60 
 
 74.80 
 
 81.10 
 
 87.30 
 
 94 
 
 68 
 
 36.90 
 
 43.00 
 
 49.20 
 
 55.30 
 
 61.40 
 
 70.70 
 
 77.10 
 
 83.50 
 
 89.90 
 
 96 
 
 70 
 
 38.00 
 
 44.30 
 
 50.60 
 
 56.90 
 
 63.20 
 
 72.70 
 
 79.30 
 
 85.90 
 
 92.50 
 
 99 
 
 72 
 
 39.00 
 
 45.50 
 
 52.00 
 
 58.50 
 
 65.00 
 
 74.80 81.60 
 
 88.40 
 
 95.20 102 
 
 74 
 
 40.10 
 
 46.80 
 
 53.40 
 
 60.10 
 
 69.90 
 
 76.90 83.90 
 
 90.90 
 
 97.90105 
 
 76 
 
 41.20 
 
 48.10 
 
 54.90 
 
 61.80 
 
 71.80 
 
 79.00! 86.10 
 
 93.30 
 
 101 
 
 108 
 
 78 
 
 42.30 
 
 49.30 
 
 56.40 
 
 63.40 
 
 73.70 
 
 81.10 
 
 88.40 
 
 95.70 
 
 103 
 
 110 
 
 80 
 
 43.40 
 
 50.60 
 
 57.80 
 
 65.00 
 
 75.60 
 
 83.10 
 
 90.70 
 
 93.30 
 
 106 
 
 113 
 
 82 
 
 44.50 
 
 51.90 
 
 59.20 
 
 69.70 
 
 77.50 
 
 85.20 92.90 
 
 101 
 
 108 
 
 116 
 
 84 
 
 45.50 
 
 53.10 
 
 60.70 
 
 71.40 
 
 79.40 
 
 87.30 95.20 
 
 103 
 
 111 
 
 119 
 
 86 
 
 46.60 
 
 54.40 
 
 62.10 
 
 73.10 
 
 81.30 
 
 89.40 97.50 
 
 106 
 
 113 
 
 122 
 
 88 
 
 47.70 
 
 55.70 
 
 63.60 
 
 74.80 
 
 83.10 
 
 91.50 
 
 99.70 
 
 108 
 
 116 
 
 125 
 
 90 
 
 48.80 
 
 56.90 
 
 65.00 
 
 76.50 
 
 85.00 
 
 93.50 
 
 102 
 
 110 
 
 119 
 
 127 
 
 92 49.90 
 
 58.20 
 
 69.50 
 
 78.20 
 
 86.90 
 
 95.60 104 
 
 113 
 
 122 
 
 130 
 
 9451.00 
 
 59.50 
 
 71.00 79.90 
 
 88.80 97.70 107 
 
 115 
 
 124 
 
 133 
 
 9652.00 
 
 60.70 
 
 72.50 
 
 81.60 
 
 90. 70 1 99.70 109 
 
 118 
 
 127 
 
 136 
 
 98 
 
 53.10 
 
 62.00 
 
 74.10 
 
 83.30 
 
 92.60 
 
 102 
 
 111 
 
 120 
 
 130 
 
 139 
 
 100 
 
 54.20 
 
 63.30 
 
 75.60 
 
 85.00 
 
 94.50 
 
 104 , 
 
 113 
 
 123 
 
 132 
 
 142 
 
 10255.30 
 
 64.50 
 
 77.10 
 
 86.70 
 
 96.40 106 
 
 116 
 
 125 
 
 135 
 
 144 
 
 104 '56. 40 
 
 68.70 
 
 78.60 
 
 88.40 
 
 98.30 
 
 108 
 
 118 
 
 128 
 
 138 
 
 147 
 
 106 i 57. 50 
 
 70.10 
 
 80.10 
 
 90.10 
 
 100 
 
 110 
 
 120 
 
 130 
 
 140 
 
 150 
 
 108 
 
 58.50 
 
 71.40 
 
 81.60 
 
 91.80 
 
 102 
 
 112 
 
 122 
 
 133 
 
 143 
 
 153 
 
 110 
 
 59.60 
 
 72.70 
 
 83.10 
 
 93.50 
 
 104 
 
 114 
 
 125 
 
 135 
 
 145 
 
 165 
 
 11260.70 
 
 74.10 
 
 84.60 
 
 95.20 
 
 106 
 
 116 
 
 127 
 
 137 
 
 148 
 
 168 
 
 11461.80 
 
 75.40 
 
 86.10 
 
 96.90 
 
 108 
 
 118 
 
 129 
 
 140 
 
 151 
 
 171 
 
 11662.90 
 
 76.70 
 
 87.60 
 
 98.60 
 
 110 
 
 121 
 
 131 
 
 142 
 
 162 
 
 174 
 
 118 
 
 64.00 
 
 78.00 
 
 89.10 
 
 100 
 
 112 
 
 123 
 
 134 
 
 145 
 
 165 
 
 177 
 
 120 
 
 65.00 
 
 79.30 
 
 90.70 
 
 102 
 
 114 
 
 125 
 
 136 
 
 147 
 
 168 
 
 180 
 
 122169.10 
 
 80.70 
 
 92.20 104 
 
 115 
 
 127 
 
 138 
 
 150 
 
 171 
 
 183 
 
 124 
 
 70.30 
 
 82.00 
 
 93.70 105 
 
 117 
 
 129 
 
 141 
 
 152 
 
 174 
 
 186 
 
 126 
 
 71.40 
 
 83.30 
 
 95.20 107 
 
 119 
 
 131 
 
 143 
 
 164 
 
 176 
 
 189 
 
 128 
 
 72.50 
 
 84.70 
 
 96.70 
 
 109 
 
 121 
 
 133 
 
 145 
 
 166 
 
 179 
 
 192 
 
 130 
 
 73.70 
 
 86.00 
 
 98.20 
 
 110 
 
 123 
 
 135 
 
 147 
 
 169 
 
 182 
 
 195 
 
 132 
 
 74.80 
 
 87.30 
 
 99.70 
 
 112 
 
 125 
 
 137 
 
 150 
 
 172 
 
 185 
 
 198 
 
 134 
 
 76.00 
 
 88.60 
 
 101 
 
 114 
 
 126 
 
 139 
 
 152 
 
 174 
 
 188 
 
 201 
 
 136 
 
 77.10 
 
 89.90 
 
 103 
 
 116 
 
 128 
 
 141 
 
 163 
 
 177 
 
 190 1204 
 
 138 
 
 78.20 
 
 91.30 
 
 104 
 
 118 
 
 130 
 
 143 
 
 166 
 
 179 
 
 193 
 
 ?07 
 
GLASS KINDS AND PRICE-LISTS. 
 
 1421 
 
 PRICE-LIST OF POLISHED PLATE GLASS (Continued). 
 
 Sizes in inches; prices in dollars. 
 
 I 
 
 62 
 
 64 
 
 66 
 
 68 
 
 70 
 
 72 
 
 74 
 
 76 
 
 78 
 
 80 
 
 82 
 
 84 
 
 62 
 64 
 
 91 
 94 
 
 97 
 
 
 
 
 
 
 
 
 
 
 
 66 
 
 97 
 
 100 
 
 103 
 
 
 
 
 
 
 
 
 
 
 68 
 
 100 
 
 103 
 
 106 
 
 109 
 
 
 
 
 
 
 
 
 
 70 
 
 102 
 
 106 
 
 109 
 
 112 
 
 116 
 
 
 
 
 
 
 
 
 72 
 
 105 109 
 
 112 
 
 116 
 
 119 
 
 122 
 
 
 
 
 
 
 
 74 
 
 108 
 
 112 
 
 115 
 
 119 
 
 ,122 
 
 126 
 
 129 
 
 
 
 
 
 
 76 
 
 111 
 
 115 
 
 118 
 
 '122 
 
 126 
 
 129 
 
 133 
 
 136 
 
 
 
 
 
 78 
 
 114 
 
 118 
 
 121 
 
 125 
 
 129 
 
 133 
 
 136 
 
 140 
 
 144 
 
 
 
 
 80 
 
 117 
 
 121 
 
 125 
 
 128 
 
 132 
 
 136 
 
 139 
 
 144 
 
 147 
 
 151 
 
 
 
 82 
 
 120 
 
 124 
 
 128 
 
 132 
 
 136 
 
 139 
 
 143 
 
 147 
 
 151 
 
 164 
 
 168 
 
 
 84 
 
 123 
 
 127 
 
 131 
 
 135 
 
 139 
 
 143 
 
 147 
 
 151 
 
 164 
 
 168 
 
 172 
 
 176 
 
 86 
 
 126 
 
 130 
 
 134 
 
 138 
 
 142 
 
 146 
 
 150 
 
 163 
 
 168 
 
 172 
 
 176 
 
 181 
 
 88 
 
 129 
 
 133 
 
 137 
 
 141 
 
 145 
 
 150 
 
 163 
 
 167 
 
 172 
 
 176 
 
 180 
 
 185 
 
 90 
 
 132 
 
 136 
 
 140 
 
 144 
 
 149 
 
 153 
 
 166 
 
 171 
 
 175 
 
 180 
 
 184 
 
 189 
 
 92 
 
 135 
 
 139 
 
 143 
 
 148 
 
 152 
 
 166 
 
 170 
 
 175 
 
 179 
 
 184 
 
 189 
 
 193 
 
 94 
 
 138 
 
 142 
 
 146 
 
 151 
 
 165 
 
 169 
 
 174 
 
 179 
 
 183 
 
 188 
 
 193 
 
 197 
 
 96 
 
 141 
 
 145 
 
 150 
 
 163 
 
 168 
 
 173 
 
 178 
 
 182 
 
 187 
 
 192 
 
 197 
 
 202 
 
 98 
 
 143 
 
 148 
 
 153 
 
 167 
 
 171 
 
 176 
 
 181 
 
 186 
 
 191 
 
 196 
 
 201 
 
 206 
 
 100 
 
 146 
 
 151 
 
 165 
 
 170 
 
 175 
 
 180 
 
 185 
 
 190 
 
 195 
 
 200 
 
 205 
 
 210 
 
 102 
 
 149 
 
 163 
 
 168 
 
 173 
 
 178 
 
 184 
 
 189 
 
 194 
 
 199 
 
 204 
 
 209 
 
 214 
 
 104 
 
 152 
 
 166 
 
 172 
 
 177 
 
 182 
 
 187 
 
 192 
 
 198 
 
 203 
 
 208 
 
 213 
 
 218 
 
 106 
 
 164 
 
 170 
 
 175 
 
 180 
 
 185 
 
 191 
 
 196 
 
 201 
 
 207 
 
 212 
 
 217 
 
 223 
 
 108 
 
 167 
 
 173 
 
 178 
 
 184 
 
 189 
 
 194 
 
 200 
 
 205 
 
 210 
 
 216 
 
 221 
 
 227 
 
 110 
 
 170 
 
 176 
 
 181 
 
 187 
 
 192 
 
 198 
 
 203 
 
 209 
 
 214 
 
 220 
 
 225 
 
 231 
 
 112 
 
 174 
 
 179 
 
 185 
 
 190 
 
 196 
 
 202 
 
 207 
 
 213 
 
 218 
 
 224 
 
 230 
 
 235 
 
 114 
 
 177 
 
 182 
 
 188 
 
 194 
 
 199 
 
 206 
 
 211 
 
 217 
 
 222 
 
 228 
 
 234 
 
 239 
 
 116 
 
 180 
 
 185 
 
 191 
 
 197 
 
 203 
 
 209 
 
 215 
 
 220 
 
 226 
 
 232 
 
 238 
 
 244 
 
 118 
 
 183 
 
 189 
 
 195 
 
 201 
 
 206 
 
 212 
 
 218 
 
 224 
 
 230 
 
 236 
 
 242 
 
 248 
 
 120 
 
 186 
 
 192 
 
 198 
 
 204 
 
 210 
 
 216 
 
 222 
 
 228 
 
 234 
 
 240 
 
 246 
 
 252 
 
 122 
 
 189 
 
 195 
 
 201 
 
 207 
 
 213 
 
 220 
 
 226 
 
 232 
 
 238 
 
 244 
 
 250 
 
 256 
 
 124 
 
 192 
 
 198 
 
 205 
 
 211 
 
 217 
 
 223 
 
 230 
 
 236 
 
 242 
 
 248 
 
 254 
 
 260 
 
 126 
 
 195 
 
 202 
 
 208 
 
 214 
 
 220 
 
 227 
 
 233 
 
 239 
 
 246 
 
 252 
 
 258 
 
 265 
 
 128 
 
 198 
 
 205 
 
 211 
 
 218 
 
 224 
 
 230 
 
 237 
 
 243 
 
 250 
 
 256 
 
 262 
 
 269 
 
 130 
 
 201 
 
 208 
 
 214 
 
 221 
 
 227 
 
 234 
 
 240 
 
 247 
 
 253 
 
 260 
 
 266 
 
 273 
 
 132 
 
 205 
 
 211 
 
 218 
 
 224 
 
 231 
 
 238 
 
 244 
 
 251 
 
 257 
 
 264 
 
 271 
 
 277 
 
 134 
 
 208 
 
 214 
 
 221 
 
 228 
 
 234 
 
 241 
 
 248 
 
 255 
 
 261 
 
 268 
 
 275 
 
 281 
 
 136 
 
 211 
 
 218 
 
 224 
 
 231 
 
 238 
 
 245 
 
 251 
 
 258 
 
 265 
 
 272 
 
 279 
 
 286 
 
 138 
 
 214 
 
 221 
 
 228 
 
 234 
 
 241 
 
 248 
 
 255 
 
 262 
 
 269 
 
 276 
 
 283 
 
 290 
 
 140 
 
 217 
 
 224 
 
 231 
 
 238 
 
 245 
 
 252 
 
 259 
 
 266 
 
 273 
 
 280 
 
 287 
 
 294 
 
 142 
 
 220 
 
 227 
 
 234 
 
 241 
 
 248 
 
 256 
 
 263 
 
 270 
 
 277 
 
 284 
 
 291 
 
 298 
 
 144 
 
 223 
 
 230 
 
 238 
 
 245 
 
 252 
 
 259 
 
 266 
 
 274 
 
 281 
 
 288 
 
 295 
 
 302 
 
 146 
 
 226 
 
 234 
 
 241 
 
 248 
 
 255 
 
 263 
 
 270 
 
 277 
 
 285 
 
 292 
 
 299 
 
 307 
 
 148 
 
 229 
 
 237 
 
 244 
 
 252 
 
 259 
 
 266 
 
 274 
 
 281 
 
 289 
 
 296 
 
 303 
 
 311 
 
 150 
 
 232 
 
 240 
 
 247 
 
 255 
 
 262 
 
 270 
 
 277 
 
 285 
 
 292 
 
 300 
 
 307 
 
 315 
 
 152 
 
 236 
 
 243 
 
 251 
 
 258 
 
 266 
 
 274 
 
 281 
 
 289 
 
 296 
 
 304 
 
 312 
 
 319 
 
 154 
 
 239 
 
 246 
 
 254 
 
 262 
 
 269 
 
 277 
 
 285 
 
 293 
 
 300 
 
 308 
 
 316 
 
 323 
 
 156 
 
 242 
 
 250 
 
 257 
 
 265 
 
 273 
 
 281 
 
 288 
 
 296 
 
 304 
 
 312 
 
 320 
 
 328 
 
 158 
 
 245 
 
 253 
 
 261 
 
 269 
 
 276 
 
 284 
 
 292 
 
 300 
 
 308 
 
 316 
 
 324 
 
 332 
 
 160 
 
 248 
 
 256 
 
 264 
 
 272 
 
 280 
 
 288 
 
 296 
 
 304 
 
 312 
 
 320 
 
 328 
 
 336 
 
 162 
 
 251 
 
 259 
 
 267 
 
 275 
 
 283 
 
 292 
 
 300 
 
 308 
 
 316 
 
 324 
 
 332 
 
 340 
 
 164 
 
 254 
 
 262 
 
 271 
 
 279 
 
 287 
 
 295 
 
 303 
 
 312 
 
 320 
 
 328 
 
 336 
 
 344 
 
 166 
 
 257 
 
 266 
 
 274 
 
 282 
 
 290 
 
 299 
 
 307 
 
 315 
 
 324 
 
 332 
 
 340 
 
 349 
 
 168 
 
 260 
 
 269 
 
 277 
 
 286 
 
 294 
 
 302 
 
 311 
 
 319 
 
 328 
 
 336 
 
 344 
 
 353 
 
 
 
 
 
 
 
 
 
 
 
 
 
1422 
 
 GLASS KINDS AND PRICE-LISTS. 
 
 PRICE-LIST OF POLISHED PLATE GLASS (Continued). 
 
 Sizes in inches; prices in dollars. 
 
 A 
 
 86 
 
 88 
 
 90 
 
 92 
 
 94 
 
 96 
 
 98 
 
 100 
 
 102 
 
 104 
 
 106 
 
 108 
 
 90 
 92 
 
 193 
 
 198 
 
 198 
 202 
 
 202 
 207 
 
 212 
 
 
 
 
 
 
 
 
 
 94 
 
 202 
 
 207 
 
 211 
 
 216 
 
 221 
 
 
 
 
 
 
 
 
 96 
 
 206 
 
 211 
 
 216 
 
 221 
 
 226 
 
 230 
 
 
 
 
 
 
 
 98 
 
 211 
 
 216 
 
 220 
 
 225 
 
 230 
 
 235 
 
 240 
 
 
 
 
 
 
 100 
 
 215 
 
 220 
 
 225 
 
 230 
 
 235 
 
 240 
 
 245 
 
 250 
 
 
 
 
 
 102 
 
 219 
 
 224 
 
 229 
 
 235 
 
 240 
 
 245 
 
 250 
 
 255 
 
 260 
 
 
 
 
 104 
 
 224 
 
 229 
 
 234 
 
 239 
 
 244 
 
 250 
 
 255 
 
 260 
 
 265 
 
 ' 270 
 
 
 
 106 
 
 228 
 
 233 
 
 238 
 
 244 
 
 249 
 
 254 
 
 260 
 
 265 
 
 270 
 
 276 
 
 281 
 
 
 108 
 
 232 
 
 237 
 
 243 
 
 248 
 
 254 
 
 259 
 
 265 
 
 270 
 
 275 
 
 281 
 
 286 
 
 292 
 
 110 
 
 237 
 
 242 
 
 247 
 
 253 
 
 258 
 
 264 
 
 269 
 
 275 
 
 280 
 
 286 
 
 291 
 
 297 
 
 112 
 
 241 
 
 246 
 
 252 
 
 258 
 
 263 
 
 269 
 
 274 
 
 280 
 
 285 
 
 291 
 
 297 
 
 302 
 
 114 
 
 245 
 
 251 
 
 256 
 
 262 
 
 268 
 
 274 
 
 279 
 
 285 
 
 290 
 
 296 
 
 302 
 
 308 
 
 116 
 
 250 
 
 255 
 
 261 
 
 267 
 
 273 
 
 278 
 
 284 
 
 290 
 
 296 
 
 302 
 
 307 
 
 313 
 
 118 
 
 254 
 
 260 
 
 265 
 
 272 
 
 277 
 
 283 
 
 289 
 
 295 
 
 301 
 
 307 
 
 313 
 
 319 
 
 120 
 
 258 
 
 264 
 
 270 
 
 276 
 
 282 
 
 288 
 
 294 
 
 300 
 
 306 
 
 312 
 
 318 
 
 324 
 
 122 
 
 262 
 
 268 
 
 274 
 
 281 
 
 287 
 
 293 
 
 299 
 
 305 
 
 311 
 
 317 
 
 323 
 
 329 
 
 124 
 
 267 
 
 273 
 
 279 
 
 285 
 
 291 
 
 298 
 
 304 
 
 310 
 
 316 
 
 322 
 
 329 
 
 335 
 
 126 
 
 271 
 
 277 
 
 283 
 
 290 
 
 296 
 
 302 
 
 309 
 
 315 
 
 321 
 
 328 
 
 334 
 
 340 
 
 128 
 
 275 
 
 282 
 
 288 
 
 294 
 
 301 
 
 307 
 
 314 
 
 320 
 
 326 
 
 333 
 
 339 
 
 346 
 
 130 
 
 279 
 
 286 
 
 292 
 
 299 
 
 305 
 
 312 
 
 318 
 
 325 
 
 331 
 
 338 
 
 345 
 
 351 
 
 132 
 
 284 
 
 290 
 
 297 
 
 304 
 
 310 
 
 317 
 
 323 
 
 330 
 
 337 
 
 343 
 
 350 
 
 356 
 
 134 
 
 288 
 
 295 
 
 301 
 
 308 
 
 315 
 
 322 
 
 328 
 
 335 
 
 342 
 
 348 
 
 355 
 
 402 
 
 136 
 
 292 
 
 299 
 
 306 
 
 313 
 
 320 
 
 326 
 
 333 
 
 340 
 
 347 
 
 354 
 
 400 
 
 408 
 
 138 
 
 297 
 
 304 
 
 310 
 
 317 
 
 324 
 
 331 
 
 338 
 
 345 
 
 352 
 
 359 
 
 406 
 
 414 
 
 140 
 
 301 
 
 308 
 
 315 
 
 322 
 
 329 
 
 336 
 
 343 
 
 350 
 
 357 
 
 404 
 
 412 
 
 420 
 
 142 
 
 305 
 
 312 
 
 319 
 
 327 
 
 334 
 
 341 
 
 348 
 
 355 
 
 402 
 
 410 
 
 418 
 
 426 
 
 144 
 
 310 
 
 317 
 
 324 
 
 331 
 
 339 
 
 346 
 
 353 
 
 360 
 
 408 
 
 416 
 
 424 
 
 432 
 
 146 
 
 314 
 
 321 
 
 328 
 
 336 
 
 343 
 
 350 
 
 358 
 
 406 
 
 414 
 
 422 
 
 430 
 
 438 
 
 148 
 
 318 
 
 326 
 
 333 
 
 340 
 
 348 
 
 355 
 
 403 
 
 411 
 
 419 
 
 428 
 
 436 
 
 444 
 
 150 
 
 322 
 
 330 
 
 337 
 
 345 
 
 352 
 
 360 
 
 408 
 
 417 
 
 425 
 
 433 
 
 442 
 
 450 
 
 152 
 
 327 
 
 334 
 
 342 
 
 350 
 
 357 
 
 405 
 
 414 
 
 422 
 
 431 
 
 439 
 
 448 
 
 456 
 
 154 
 
 331 
 
 339 
 
 346 
 
 354 
 
 402 
 
 411 
 
 419 
 
 428 
 
 436 
 
 445 
 
 453 
 
 462 
 
 156 
 
 335 
 
 343 
 
 351 
 
 359 
 
 407 
 
 416 
 
 425 
 
 433 
 
 442 
 
 451 
 
 459 
 
 468 
 
 158 
 
 340 
 
 348 
 
 355 
 
 404 
 
 413 
 
 421 
 
 430 
 
 439 
 
 448 
 
 456 
 
 465 
 
 474 
 
 160 
 
 344 
 
 352 
 
 360 
 
 409 
 
 418 
 
 427 
 
 436 
 
 444 
 
 453 
 
 462 
 
 470 
 
 480 
 
 162 
 
 348 
 
 356 
 
 405 
 
 414 
 
 423 
 
 432 
 
 441 
 
 450 
 
 459 
 
 468 
 
 477 
 
 759 
 
 164 
 
 353 
 
 401 
 
 410 
 
 419 
 
 428 
 
 437 
 
 446 
 
 456 
 
 465 
 
 474 
 
 755 
 
 769 
 
 166 
 
 357 
 
 406 
 
 415 
 
 424 
 
 433 
 
 443 
 
 452 
 
 461 
 
 470 
 
 480 
 
 764 
 
 778 
 
 168 
 
 401 
 
 411 
 
 420 
 
 429 
 
 439 
 
 448 
 
 457 
 
 467 
 
 476 
 
 758 
 
 773 
 
 787 
 
 170 
 
 406 
 
 416 
 
 425 
 
 434 
 
 444 
 
 453 
 
 463 
 
 472 
 
 753 
 
 767 
 
 782 
 
 797 
 
 172 
 
 411 
 
 420 
 
 430 
 
 440 
 
 449 
 
 459 
 
 468 
 
 478 
 
 761 
 
 776 
 
 791 
 
 806 
 
 174 
 
 416 
 
 425 
 
 435 
 
 445 
 
 454 
 
 464 
 
 474 
 
 755 
 
 770 
 
 785 
 
 801 
 
 979 
 
 176 
 
 420 
 
 430 
 
 440 
 
 450 
 
 460 
 
 4C9 
 
 479 
 
 764 
 
 779 
 
 794 
 
 810 
 
 990 
 
 178 
 
 425 
 
 435 
 
 445 
 
 455 
 
 465 
 
 475 
 
 757 
 
 773 
 
 788 
 
 803 
 
 983 
 
 1001 
 
 180 
 
 430 
 
 440 
 
 450 
 
 460 
 
 470 
 
 480 
 
 766 
 
 781 
 
 797 
 
 812 
 
 994 
 
 1012 
 
 182 
 
 478 
 
 489 
 
 500 
 
 511 
 
 523 
 
 758 
 
 774 
 
 790 
 
 806 
 
 986 
 
 1005 1024 
 
 184 
 
 483 
 
 495 506 
 
 517 
 
 751 
 
 767 
 
 783 
 
 799 
 
 977 
 
 997 
 
 1016 1035 
 
 186 
 
 489 
 
 500 511 
 
 523 
 
 759 
 
 775 
 
 791 
 
 807 
 
 988 
 
 1007 
 
 1027 11046 
 
 188 
 
 494 
 
 506 
 
 517 
 
 751 
 
 767 
 
 783 
 
 800 
 
 979 
 
 999 
 
 1018 
 
 1038 
 
 1057 
 
 190 
 
 500 
 
 511 
 
 522 
 
 759 
 
 775 
 
 792 
 
 808 
 
 990 
 
 1009 
 
 1029 
 
 1049 
 
 1069 
 
 192 
 
 688 
 
 704 
 
 720 
 
 920 
 
 940 
 
 960 
 
 980 
 
 1000 
 
 1030 
 
 1040 
 
 1060 
 
 1080 
 
 194 
 
 695 
 
 711 
 
 909 
 
 930 
 
 950 
 
 970 
 
 990 
 
 1010 
 
 1031 
 
 1051 
 
 1071 
 
 1091 
 
 196 
 
 703 
 
 719 
 
 919 
 
 939 
 
 960 
 
 980 
 
 1000 
 
 1021 
 
 1041 
 
 1062 
 
 1082 
 
 1102 
 
GLASS KINDS AND PRICE-LISTS. 
 
 1423 
 
 PRICE-LIST OF POLISHED PLATE GLASS (Continued). 
 
 Size in inches; prices in dollars. 
 
 ,d 
 
 "& 
 
 1 
 
 110 
 
 112 
 
 114 
 
 116 
 
 118 
 
 120 
 
 124 
 
 128 
 
 132 
 
 136 
 
 140 
 
 144 
 
 no 
 
 302 
 
 308 
 
 314 
 
 319 
 
 324 
 
 330 
 
 341 
 
 352 
 
 403 
 
 415 
 
 428 
 
 440 
 
 112 
 
 308 
 
 348 
 
 355 
 
 361 
 
 367 
 
 373 
 
 386 
 
 398 
 
 411 
 
 423 
 
 436 
 
 448 
 
 114 
 
 314 
 
 355 
 
 361 
 
 367 
 
 374 
 
 380 
 
 393 
 
 405 
 
 418 
 
 431 
 
 443 
 
 456 
 
 116 
 
 319 
 
 361 
 
 367 
 
 374 
 
 380 
 
 387 
 
 400 
 
 412 
 
 425 
 
 438 
 
 451 
 
 464 
 
 118 
 
 324 
 
 367 
 
 374 
 
 380 
 
 387 
 
 393 
 
 406 
 
 42jO 
 
 433 
 
 446 
 
 459 
 
 472 
 
 120 
 
 330 
 
 373 
 
 380 
 
 387 
 
 393 
 
 400 
 
 413 
 
 427 
 
 440 
 
 453 
 
 467 
 
 480 
 
 122 
 
 335 
 
 380 
 
 386 
 
 393 
 
 400 
 
 407 
 
 462 
 
 478 
 
 493 
 
 507 
 
 522 
 
 762 
 
 124 
 
 341 
 
 386 
 
 393 
 
 400 
 
 406 
 
 413 
 
 470 
 
 485 
 
 501 
 
 516 
 
 753 
 
 775 
 
 126 
 
 346 
 
 392 
 
 399 
 
 406 
 
 413 
 
 420 
 
 477 
 
 493 
 
 508 
 
 524 
 
 766 
 
 787 
 
 128 
 
 352 
 
 398 
 
 405 
 
 412 
 
 420 
 
 427 
 
 485 
 
 501 
 
 516 
 
 756 
 
 778 
 
 800 
 
 130 
 
 357 
 
 404 
 
 412 
 
 419 
 
 426 
 
 433 
 
 493 
 
 509 
 
 525 
 
 767 
 
 790 
 
 812 
 
 132 
 
 403 
 
 411 
 
 418 
 
 425 
 
 433 
 
 440 
 
 501 
 
 516 
 
 847 
 
 873 
 
 898 
 
 990 
 
 134 
 
 409 
 
 417 
 
 424 
 
 432 
 
 439 
 
 447 
 
 509 
 
 524 
 
 860 
 
 886 
 
 977 
 
 1005 
 
 136 
 
 415 
 
 423 
 
 431 
 
 438 
 
 446 
 
 453 
 
 516 
 
 756 
 
 873 
 
 899 
 
 992 
 
 1020 
 
 138 
 
 422 
 
 429 
 
 437 
 
 445 
 
 452 
 
 460 
 
 523 
 
 767 
 
 886. 
 
 977 
 
 1006 
 
 1035 
 
 140 
 
 428 
 
 436 
 
 443 
 
 451 
 
 459 
 
 467 
 
 753 
 
 778 
 
 898 
 
 992 
 
 1021 
 
 1050 
 
 142 
 
 434 
 
 442 450 
 
 457 
 
 465 
 
 473 
 
 764 
 
 789 
 
 976 
 
 1006 
 
 1035 
 
 1420 
 
 144 
 
 440 
 
 448 456 
 
 464 
 
 472 
 
 480 
 
 775 
 
 800 
 
 990 
 
 1020 
 
 1050 
 
 1440 
 
 146 
 
 446 
 
 4541 462 
 
 470 
 
 479 
 
 760 
 
 786 
 
 811 
 
 1004 
 
 1034 
 
 1065 
 
 1460 
 
 148 
 
 452 
 
 460 
 
 469 
 
 477 
 
 758 
 
 771 
 
 796 
 
 987 
 
 1017 
 
 1048 
 
 1079 
 
 1480 
 
 150 
 
 458 
 
 467 
 
 475 
 
 755 
 
 768 
 
 781 
 
 807 
 
 1000 
 
 1031 
 
 1062 
 
 1094 
 
 1500 
 
 152 
 
 464 
 
 473 
 
 752 
 
 765 
 
 778 
 
 792 
 
 982 
 
 1013 
 
 1045 
 
 1077 
 
 1108 
 
 1520 
 
 154 
 
 471 
 
 479 
 
 762 
 
 775 
 
 789 
 
 802 
 
 995 
 
 1027 
 
 1059 
 
 1091 
 
 1123 
 
 1540 
 
 156 
 
 477 
 
 758 
 
 772 
 
 785 
 
 799 
 
 812 
 
 1007 
 
 1040 
 
 1072 
 
 1105 
 
 1327 
 
 1560 
 
 158 
 
 754 
 
 768 1 782 
 
 795 
 
 809 
 
 987 
 
 1020 
 
 1053 
 
 1086 
 
 1119 
 
 1344 
 
 1580 
 
 160 
 
 764 
 
 778 792 
 
 805 
 
 983 
 
 1000 
 
 1033 
 
 1067 
 
 1100 
 
 1322 
 
 1361 
 
 1600 
 
 162 
 
 773 
 
 787 802 
 
 975 
 
 996 
 
 1012 
 
 1046 
 
 1080 
 
 1114 
 
 1339 
 
 1378 
 
 1620 
 
 164 
 
 783 
 
 797i 812 
 
 991 
 
 1008 
 
 1025 
 
 1059 
 
 1093 
 
 1315 
 
 1355 
 
 1395 
 
 1640 
 
 166 
 
 793 
 
 807 i 986 
 
 1003 
 
 1020 
 
 1037 
 
 1072 
 
 1107 
 
 1331 
 
 1372 
 
 1412 
 
 1660 
 
 168 
 
 802 
 
 980 997 
 
 1015 
 
 1032 
 
 1050 
 
 1085 
 
 1120 
 
 1347 
 
 1388 
 
 1429 
 
 1680 
 
 170 
 
 812 
 
 992 1009 
 
 1027 
 
 1045 
 
 1062 
 
 1098 
 
 1322 
 
 1364 
 
 1405 
 
 1446 
 
 1700 
 
 172 
 174 
 
 985 
 997 
 
 1003 1021 1039 
 1015 1033 1051 
 
 1057 
 1069 
 
 1075 
 1087 
 
 1111 
 1124 
 
 1338 
 1353 
 
 1380 
 1396 
 
 1421 
 1438 
 
 1463 
 1480 
 
 1720 
 1740 
 
 176 
 
 1008 
 
 1027 1045 1063 
 
 1082 
 
 1100 
 
 1326 
 
 1369 
 
 1412 
 
 1454 
 
 1497 
 
 2200 
 
 178 
 
 1020 
 
 1038 1057 
 
 1075 
 
 1094 
 
 1112 
 
 1341 
 
 1384 
 
 1428 
 
 1471 
 
 1514 
 
 2225 
 
 180 
 
 1031 
 
 1050 1069 
 
 1087 
 
 1106 
 
 1125 
 
 1356 
 
 1400 
 
 1444 
 
 1487 
 
 1531 
 
 2250 
 
 182 
 
 1043 
 
 1062 108111100 
 
 1119 
 
 1327 
 
 1371 
 
 1416 
 
 1460 
 
 1504 
 
 2212 
 
 2275 
 
 184 
 
 1054 
 
 1073 1092 
 
 1112 
 
 1319 
 
 1342 
 
 1386 
 
 1431 
 
 1476 
 
 1521 
 
 2236 
 
 2300 
 
 186 
 
 1066 
 
 1085 1104 
 
 1124 
 
 1334 
 
 1356 
 
 1401 
 
 1447 
 
 1492 
 
 2196 
 
 2260 
 
 2325 
 
 188 
 
 1077 
 
 1097 
 
 1116 
 
 1325 
 
 1348 
 
 1371 
 
 1417 
 
 1462 
 
 1508 
 
 2219 
 
 2285 
 
 2350 
 
 190 
 
 1089 
 
 1108 
 
 1316 
 
 1339 
 
 1362 
 
 1385 
 
 1452 
 
 1478 
 
 1524 
 
 2243 
 
 2309 
 
 2375 
 
 192 
 
 1100 
 
 1120 1330 
 
 1353 
 
 1376 
 
 1400 
 
 1447 
 
 1493 
 
 2200 
 
 2267 
 
 2333 
 
 2400 
 
 194 
 
 1111 
 
 1320 1344 
 
 1367 
 
 1391 
 
 1415 
 
 1462 
 
 1,509 
 
 2223 
 
 2290 
 
 2358 
 
 2425 
 
 196 
 
 1123 
 
 1334 1358 
 
 1382 
 
 1405 
 
 1429 
 
 1477 
 
 1524 
 
 2246 
 
 2314 
 
 2382 
 
 2450 
 
 198 
 
 1323 
 
 1347 
 
 1372 
 
 1396 
 
 1419 
 
 1444 
 
 1492 
 
 2200 
 
 2269 
 
 2337 
 
 2406 
 
 2475 
 
 200 
 
 1337 
 
 1361 
 
 1385 
 
 1410 
 
 1434 
 
 1458 
 
 1507 
 
 2222 
 
 2292 
 
 2361 
 
 2431 
 
 2500 
 
 202 
 
 1350 
 
 1375 
 
 1399 
 
 1424 
 
 1448 
 
 1473 
 
 1522 
 
 2244 
 
 2315 
 
 2385 
 
 2455 
 
 
 204 
 
 1364 
 
 1388 
 
 1413 
 
 1438 
 
 1463 
 
 1487 
 
 2196 
 
 2267 
 
 2337 
 
 2408 
 
 2479 
 
 
 206 
 
 1377 
 
 1402 
 
 1427 
 
 1452 
 
 1477 
 
 1502 
 
 2217 
 
 2289 
 
 2360 
 
 2432 
 
 
 
 208 
 
 1390 
 
 1416 
 
 1441 
 
 1466 
 
 1491 
 
 1517 
 
 2239 
 
 2311 
 
 2383 
 
 2456 
 
 
 
 210 
 
 1404 
 
 1429 
 
 1455 
 
 1480 
 
 1506 
 
 1531 
 
 2260 
 
 2333 
 
 2406 
 
 2479 
 
 
 
 212 
 
 1417 
 
 1443 1469 
 
 1494 
 
 1520 
 
 2208 
 
 2282 
 
 2356 
 
 2429 
 
 
 
 
 214 
 
 1430 
 
 1456 
 
 1482 
 
 1508 
 
 2192 
 
 2229 
 
 2303 
 
 2378 
 
 2452 
 
 
 
 
 216 
 
 1444 
 
 1470 
 
 1496 
 
 1522 
 
 2212 
 
 2250 
 
 2325 
 
 2400 
 
 2475 
 
 
 
 
 
 
 I 
 
 
 
 
 
 
 
 
 
 
1424 TRANSLUCENT FABRIC MIHRORS. 
 
 Translucent Fabric.* During the past few years this 
 material has been introduced as a substitute for glass, particu- 
 larly for skylights of large area, and in all places where the 
 breakage of glass constitutes an element of trouble, expense, 
 or danger. It consists of wire cloth, embedded in a translucent 
 impervious material, which is strong and durable, flexible and 
 elastic, weather-proof and unbreakable. It is a non-conductor, 
 is easily cleaned, and is a better protection against fire than 
 glass. It transmits a large amount of light and diffuses it well. 
 
 The fabric is not damaged in the slightest by rain or snow, 
 cold or heat. The leaks that develop in glass skylights, due 
 to the expansion and contraction of the framework under the 
 action of the weather, do not trouble translucent fabric because 
 it is flexible and yielding. 
 
 The fabric is of a pale amber color, and the light it transmits 
 is of somewhat the same tint, being very soft and pleasant to 
 work under. The amount of light transmitted is not quite 
 equal to that transmitted by ordinary skylight glass, but, on 
 the other hand, it is better diffused. " Where one quarter of 
 the roof is covered with fabric the lighting is practically perfect/ 'f 
 The fabric is manufactured in sheets 3' 3" wide and in lengths 
 from 4' 6" to 9' 0". The cost is from 13 to 15 cts. per square 
 foot at the factory at Quincy, Mass. The framework for trans- 
 lucent fabric is best made of wood, to which the fabric is nailed. 
 Wooden skylights covered with this fabric cost complete from 25 
 to 30 cts. per square foot. 
 
 Translucent fabric was employed in the buildings of the 
 Tennessee Centennial Exposition held at Nashville in 1897, 
 and nearly 100,000 sq. ft. were used in the principal buildings 
 of the Trans-Mississippi and International Exposition held in 
 Omaha, Neb., in 1898. 
 
 Mirrors. 
 
 Mirrors are made by silvering the back of glass. Polished 
 plate glass is the only kind that is suitable for mirrors. The 
 price of mirrors is based on the price of the glass plus the cost 
 of silvering. 
 
 Kinds of Mirrors. " There are two kinds of mirrors on the 
 market, one the olcl 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 affinity 
 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 or patent-back mirror is produced by the 
 precipitation of a chemical solution of nitrate of silver and 
 
 * Manufactured by the Translucent Fabric Company, Quincy, Mass, 
 t M. S. Ketchum. 
 
MEMORANDA ON ROOFING, SHINGLES. 1425 
 
 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 manu- 
 facture 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, 
 redwood, or cedar, 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. 
 
 Cypress shingles are usually 18 ins. long and % in. thick 
 at the butt. Those from all -other woods are 16 ins. long, and 
 about % m - thick at the butt. 
 
 Ordinary roofing shingles are of random widths, varying 
 from 2J to 14 and sometimes 16 ins. They are put up in bundles, 
 usually four to the thousand. A " thousand" common shingles 
 means the equivalent of 1,000 shingles 4 ins. wide. 
 
 Dimension Shingles are sawn to uniform width, either 4, 5, 
 or 6 ins. Dimension shingles with the butt sawn to various 
 patterns are also carried in stock. 
 
 NUMBER OF SQUARE FEET 1000 SHINGLES WILL COVER, f 
 
 Laid. Area Covered. No. to a Square. 
 4" to the weather 100 sq. ft. 1,000 
 
 5" 
 
 110 
 120 
 133 
 145 
 157 
 
 910 
 833' 
 752 
 690 
 637 
 
 On hip roofs, or for four valleys, add 5 per cent, for cutting. 
 On irregular roofs with dormer windows, add 10 per cent. It 
 is claimed that redwood shingles will go farther than cedar 
 shingles. 
 
 With a rise to the roof of 8 to 10 ins. to the foot, cedar shingles 
 should be laid 4 to 4J ins. to the weather; with rise from 10 
 to 12 ins., 4J to 4f ins. to the weather; and on steeper roofs 
 they may be laid 4J to 5 ins. Redwood shingles may be laid 
 4 in. more to the weather. 
 
 On walls cedar shingles are commonly laid 5 ins. to the 
 weather, and redwood shingles 6 ins. 
 
 Labor. Ah average shin^ler should lay 1,500 shingles in 
 9 hours on plain work; on irregular roofs with dormers, 1,000 
 per 9 hours. 
 
 It requires about 5 Ibs. of threepenny or 7J Ibs. of fourpenny 
 nails to 1,000 shingles. 
 
 * For more complete information see Part II, Building Construction 
 and Superintendence, pp. 190-199. 
 
 t These figures are intended to allow for some waste. 
 
1426 MEMORANDA ON ROOFING. 
 
 Cost. Common cedar shingles of the best grade cost from 
 $2.25 to $3.50 per M, according to locality. Redwood shingles 
 cost from $4 to $5. In Denver, shingles are laid under con- 
 tract for from $1.25 to $2.00 per square, all materials furnished. 
 
 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 under 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 
 lustre and be free from all loose flakes or dull surfaces. 
 
 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. The red and dark colors are generally 
 considered the most effective, and the greens are generally used 
 only on factories, storehouses, and buildings where the appear- 
 ance is not of so much importance. 
 
 Some slates are marked with bands or patches of a different 
 color, and the dark-purple slates often have large' spots of light 
 green upon them. These spots do not as a rule affect the dura- 
 bility of the slate, but they greatly detract from its appearance. 
 
 Grading" of Slates. The Brownville, Maine, slates are 
 graded as follows: No. 1. Every sheet to be full %e" thick, both 
 sides smooth and all corners full and square. No pieces to be 
 winding or warped. 
 
 No. 2. Thickness may vary from J" to J", all corners square, 
 one side generally smooth, one side generally rough, no badly 
 warped slates. 
 
 The Bangor, Penn., slates are graded: 
 
 No. 1 Clear. A pure slate without any faults or blemishes. 
 
 No. 1 Ribbon. As well made as No. 1 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. 1 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. 
 
 * The best red slates are believed to be those quarried by the Algonquin 
 Red Slate Company of Worcester, Mass., and Mat hews' unfading bright 
 red, the Aldeii Speare's Sons Company of New York City selling agents. 
 
SLATE ROOFS. 1427 
 
 Hard Beds. A clear Bangor slate, not quite as smooth as 
 No. 1 Clear, but much better than a No. 2 Clear. 
 
 Ordinary Bent Slate. A smooth slate similar to No. 1 Clear, 
 .but bent at a radius of about 12 ft. 
 
 Punching. Formerly slates were punched for nail-holes 
 on the job; now, however, slates are bored and countersunk at 
 the quarry, when so ordered. Architects should always specify 
 that " slates be bored and countersunk," as punching badly 
 damages the slates. 
 
 Sizes. The sizes of slates range from 9" XT" to 24"X14", 
 there being some thirty-seven different sizes; the more common 
 sizes, however, are those given in the following table. 
 
 The sizes of slates best adapted for plain roofs are the large 
 wide slate, such as 12"X16" ; 18 // < X12 // , 20" X 12", or 24"X14"; 
 the large sizes make less joints in the roof, require less nails, 
 and avoid small pieces at hips and valleys. For roofs cut up 
 into small sections the smaller sizes, such as 14" X 7" or 16" X 8", 
 look the best. 
 
 Thickness. Slates vary in thickness from J to f in.; 3 /i 6 in. 
 is the usual thickness for ordinary sizes (see Grading of Slates) . 
 
 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 2 to 3 ins. wide and from 1 to 1J ins. 
 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 ins. 
 
 The slates are fastened with two threepenny or fourpenny 
 nails, one near each upper corner. For slates 20"X10" or 
 larger, fourpenny nails should be used. Copper, composition, 
 tinned, or galvanized nails should be used. Plain iron nails 
 are speedily weakened by rust, break, and allow the slates to 
 be blown off. 
 
 On iron roofs slates are often placed directly on small iron 
 purlins spaced at suitable distance 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 of the remainder obtained by sub- 
 tracting 3 ins. from the length of the slate. 
 
 Roofs to be covered with slate should have a rise of not less 
 than 6 ins. to the foot for 20- or 24-in. slates, or 8 ins. for smaller 
 sizes. 
 
 Elastic Cement. In first-class work, the top course of slate 
 on ridge, and the slate for 2 to 4 ft. from all gutters and 1 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. 
 
 Counter-flashings 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 counter-flashings. 
 
 Close and Open Valleys. A close valley is where the slates 
 
1428 
 
 MEMORANDA ON HOOFING. 
 
 are mitred 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 where the valley is formed of sheets of 
 copper or zinc 15 or 16 ins. wide, and the slates laid over these. 
 
 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 ins. 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 cuttings against walls or dormers 
 are measured extra 1 ft. wide by their whole length, the extra 
 charge being made for waste material and the increased labor 
 required 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. The cost of slates varies with the size, color, and 
 quality. The prices given in the following table are about the 
 average for blue-black slate, of No. 1 grade, at the quarry. 
 It will be seen that the medium sizes cost the most, and the 
 larger and smaller sizes the least. The larger sizes make the 
 cheapest roof. 
 
 Red slates cost from 60 to 150 per cent, more than black 
 slates. 
 
 NUMBER AND COST OF SLATES, AND POUNDS OF NAILS TO 
 100 SQUARE FEET OF ROOF. 
 
 (3-inch Lap.) 
 
 Sizes of 
 Slate. 
 
 Exposed 
 when Laid. 
 
 Number to 
 a Square* 
 
 Weight of 
 Galvanized 
 Nails. 
 
 Cost per 
 Square at 
 Quarry. 
 
 ins. 
 
 ins. 
 
 
 Ibs. oz. 
 
 
 14X24 
 
 Itt 
 
 98 
 
 
 1 6 
 
 $6.10 
 
 12X24 
 
 10* 
 
 115 
 
 f 
 
 1 10 
 
 6.60 
 
 12X22 
 
 9f 
 
 126 
 
 "d 
 
 1 12 
 
 6.50 
 
 11X22 
 
 M 
 
 138 
 
 5 
 
 1 15 
 
 6.90 
 
 12X20 
 10X20 
 
 I! 
 
 142 
 170 
 
 
 2 
 2 6 
 
 6.80 
 6.80 
 
 12X18 
 
 TV 
 
 160 
 
 
 1 13 
 
 6.80 
 
 10X18 
 
 7^ 
 
 
 192 
 
 
 2 3 
 
 7.20 
 
 9X18 
 
 7^ 
 
 
 214 
 
 
 2 7 
 
 7.10 
 
 12X16 
 
 & 
 
 
 185 
 
 
 2 2 
 
 6.80 
 
 10X16 
 
 6^ 
 
 
 222 
 
 
 2 8 
 
 7.10 
 
 9X16 
 
 6 
 
 
 247 
 
 
 3 
 
 7.00 
 
 8X16 
 
 6^ 
 
 
 277 
 
 3 V > 3 2 
 
 7.20 
 
 10X14 
 
 5J 
 
 
 262 
 
 
 3 
 
 6.60 
 
 8X14 
 
 5 
 
 
 328 
 
 
 3 12 
 
 6.60 
 
 7X14 
 
 5J 
 
 
 374 
 
 
 4 4 
 
 6.40 
 
 8X12 
 
 4J 
 
 
 400 
 
 
 4 9 
 
 5.50 
 
 7X12 
 
 4J 
 
 
 458 
 
 
 5 3 
 
 5.00 
 
 6X12 
 
 4J 
 
 
 533 
 
 I 6 1 
 
 4. 80 
 
 * The Building Trades Pocket-book 
 
ROOFING TILE. 1429 
 
 The cost of blue-black slate roofs, complete, varies from 
 $7 to $13 per square, depending on the class of work and re- 
 moteness from the quarries. 
 
 The additional cost of laying slate in elastic cement varies 
 from $1.50 to $2 per square. 
 
 An experienced roofer will lay on an average two squares 
 of slate in ten hours. 
 
 Weight. Slate roofing % in. thick will weigh on the roof 
 about 6 Ibs. per square foot, and \ in. slates 8f Ibs., the smaller 
 sizes weighing the most on account of the lap. The actual 
 weight of a square foot of slate \ in. thick is 3.63 Ibs. 
 
 Roofing Tile. 
 
 The term roofing tile is commonly understood to refer to 
 exterior roof covering made from clay 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 for half the prices prevailing twelve years ago, 
 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. 1 slate is a much-disputed question. The author is 
 of the opinion that, considering the quantities used, slates have 
 given better satisfaction than tile. 
 
 A tile roof, however, is certainly more attractive than a 
 slate roof, and the author believes that there are many roofing 
 tiles on the market which if properly laid will prove as tight 
 and durable as slate. 
 
 There are so many patterns of roofing tile that it is impos- 
 sible here to enter into a description of them. Of the various 
 patterns, those which interlock are considered to make the most 
 satisfactory roof from a practical standpoint. 
 
 Some manufacturers of roofing tile, notably the Ludowici 
 Roofing Tile Company, make glass tiles, of the same pattern as 
 the clay tiles, so that they may be worked in with them and 
 used in place of skylights. Many thousands of these glass tiles 
 have been used on the roofs of train-sheds, shops, and factories. 
 
 Roofing tile may be laid on felt or sheathing, or those with 
 a proper interlocking device may be laid direct on wood or steel 
 purlins without sheathing or inner roof of any kind. When so 
 laid, to prevent the entrance of dust or dry snow, the joints 
 should be pointed on the under side after laying. Most tiles, 
 particularly of the older patterns, are nailed to the sheathing, 
 but this is a defective principle of fastening and is superseded 
 by the modern practice of fastening with copper wires from a 
 pierced lug toward the lower end of the tile. 
 
 Roofing tiles weigh from 750 to 1,200 Ibs. per square (100 sq. 
 ft.). 
 
1430 MEMORANDA ON ROOFING. 
 
 The prices of tiles vary from $6 to $30 per square, according 
 to pattern and finish. 
 
 The cost of laying varies from $1.50 to $5 per square, accord- 
 ing to the pattern of tile used and the character and extent 
 of the roof. 
 
 The principal manufacturers of roofing tile in this country- 
 are the Akron Roofing Tile Company, Akron, Ohio; Celadon 
 Roofing Tile Company, New York, N. Y.; C. A. Conway & Co., 
 New Philadelphia, Ohio; Federal Roofing and Tile Company, 
 St. Louis, Mo.; Ludowici Roofing Tile Company, Chicago, 111.; 
 Mound City Roofing Tile Company, St=, Louis, Mo.; National 
 Tile Roofing Company, Lima, Ohio; Ohio Roofing Tile Com- 
 pany, Ottawa, Ohio from whom catalogues giving full infor- 
 mation may be obtained. 
 
 Sheet-metal Tiles. Roofing tiles stamped from sheet 
 steel, plain or galvanized, and also from sheet copper, in imita- 
 tion of clay tiles, are made by several parties, notably Merchant 
 & Company of Philadelphia and W.. H. Mullins of Salem, Ohio, 
 and have been extensively used. 
 
 The first cost of these tiles (except those of copper) is much 
 less than that of clay tiles and they do not require as heavy 
 roof framing. Tin or galvanized-iron tiles, however, must be 
 painted every few years, so that for a long period of years 
 they will probably cost as much as clay tiles and more than 
 slate. 
 
 Galvanized-iron tiles of the " Spanish" pattern cost from $13 
 to $15 per square laid and painted, and ordinary tin shingles 
 from $8 to $10. 
 
 Tin Roofs. 
 
 The Sheets. Roofing plates are made of soft steel or 
 wrought iron (more commonly of the former) and covered with 
 a mixture of lead and tin, and are designated as "terne plates," 
 in distinction from plates coated only with tin and therefore 
 called "bright tin." Roofing plates are, coated by two methods. 
 The original manner of coating the plates (commonly designated 
 "Old Process") was by dipping 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 several brands of roofing 
 tin are still made by this process. The other process, by which 
 the majority 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 which leaves on the iron or steel a thickness of coating which, 
 to a great extent, determines the value of the .plate. These 
 rolls can be so adjusted as to leave a good amount of coating 
 on the plate, an ordinary coating, or a very scant one; the 
 heavier the coating the more valuable the plate. 
 
 It is claimed that hand-dipped plates will last much longer 
 than those made by the new process, although the latter process 
 
TIN ROOFS. 1431 
 
 is much more extensively used and many good roofing sheets 
 are made by it. 
 
 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 "Old Style," Merchant's "Old 
 Method/' "M F," "Scott's Extra Coated," "Margaret," and 
 "Admiral." 
 
 Sizes. The common sizes of tin plates are 10x14 ins. and 
 multiples of that measure. The sizes more generally used are 
 14X20 ins. and '20x28 ins. The larger size is the more 
 economical to lay, and hence roofers prefer to use it, but for 
 flat roofs the 14X20 size makes the better roof. 
 
 Thicknesses. Terne plates are made in two thicknesses, viz., 
 I C, in which the iron body weighs about 50 Ibs. per 100 sq. ft., 
 and I X, in which it weighs 62^ Ibs. per 100 sq. ft. For roofing 
 the I C, or lighter weight, is to be preferred, because the seams 
 will not suffer as much from contraction and expansion as 
 with the thicker plates. 
 
 For spouts, valleys, and gutters, however, I X plates should 
 always be specified, and should preferably be used for flashings, 
 as they are stiff er 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. The standard weight of 14x20 in. I C terne 
 plates is 107 Ibs. to 112 sheets (the number usually packed 
 in one box), and of 14x20 in. I X sheets, 135 Ibs. 20X28 in. 
 sheets should weigh just twice as much. The black sheets 
 before coating should weigh, per 112 sheets, from 95 to 100 Ibs. 
 for I C, 14X20 ins., and from 125 to 130 Ibs. for I X, 14X20 ins. 
 The difference between the weight of the black sheets and of 
 the finished sheets shows the weight of the tin. A heavily 
 coated tin should weigh from 115 to 120 Ibs. per 112 sheets 
 for I C, 14X20 ins., and from 145 to 150 Ibs. for I X, 14X20 ins. 
 20X28 in. sheets should, of course, weigh twice as much. 
 
 The Roof. Roofs with less than one third pitch are made 
 with flat seams and should preferably be covered with sheets 
 14X20 ins., rather than from sheets 20X28 ins., because 
 the larger number of seams stiffen the surface and help to 
 prevent buckles and rattling in stormy weather. For a flat- 
 seam roof 1-in. barbed and tinned roofing nails should be used, 
 not over 6 ins. apart, well under the edge. They should be 
 well covered up and the seams should be pounded down over 
 the edge with a wooden mallet. Nails must never be exposed. 
 The seams should be made with great care; sufficient time must 
 be taken to properly "sweat" the solder into the seams. 
 
 Steep tin roofs should be made with standing seams and from 
 sheets 20X28 ins. The sheets are first double-seamed and 
 soldered together, preferably end to end, into long strips that 
 reach from eaves to ridge. The sloping seams are composed of 
 
1432 MEMORANDA ON ROOFING. 
 
 two "upstands," interlocked and held in place by cleats. The 
 standing seams are not soldered, but are simply locked together 
 with the cleats folded in from 15 to 18 ins. apart. Nails should 
 be driven into the cleats only. 
 
 The use of acid in soldering seams in a tin roof is to be care- 
 fully avoided; acid coming in contact with the bare iron on 
 the cut edges and corners where the sheets are folded and seamed 
 together will cause rusting. No other soldering flux but good 
 rosin should ever be used. 
 
 Durability. A tin roof of good material, properly put on, and 
 kept properly painted, will last from thirty to forty years. It 
 should not be painted for the first time until it has been well 
 washed by rain, to get the grease off the tin; and all lumps or 
 rosin left on the roof should be removed as soon as the tin is 
 laid and soldered. One or more layers of felt-paper should be 
 placed under the tin, to serve as a cushion, and also to deaden 
 the noise produced by rain striking the tin. 
 
 The durability of tin roofing, and especially of 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 Ibs. Venetian red, 1 Ib. red lead, 1 gallon pure 
 linseed-oil. 
 
 Number of Sheets Required to a Square. For 
 flat-seam roofing a sheet of tin 14X 20 ins. with J-:n. edges, 
 measures when edged or folded 13X19 ins., or 247 sq. ins.; 
 consequently the number of sheets required to a square equal 3 
 14,400-247, or 58J. 1,000 sq. ft. requires 583 sheets. A box 
 of 112 sheets 14X20 ins. will cover approximately 192 sq. ft. 
 
 Sheets 20X28 ins. measure when edged or folded 19X27 ins., 
 or 513 sq. ins. To cover 1,000 sq. ft. (10 squares) requires 288 
 sheets. 
 
 The standing seams and locks on a steep roof require 2f ins. 
 off the width and f in. off the length of the sheet. A sheet 
 20X28 ins. with the seams on the narrow edges will cover 
 486 sq, ins., and with the seams on the long edges 470 sq. ins. 
 The former requires 297 sheets to 1,000 sq. ft,, and the latter 
 307 sheets. 
 
 The cost of tin roofing varies from $8 to $11 per square 
 according to the grade of tin used and the scale of wages. 
 Standing-seam roofs cost about 50 cts. a square less than 
 seam roofs. 
 
 Slag or Gravel Roofing* (Composition Roofing)* 
 
 The ordinary gravel roofing is formed by first covering the 
 surface of the roof with dry felt (paper) and over this laying 
 three, four, or five layers of tarred or asphaltic felt, the layers 
 of felt lapping each other like shingles, so that only from 6 to 
 10 ins. of each layer are exposed. 
 
SLAG OR GRAVEL ROOFING. 1433 
 
 Flashing against walls, chimneys, curbs of skylights, etc., 
 is done by turning the felt up 4 ins. against the wall. 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 wall by nailing wooden strips or laths over the 
 felt and into the wall. 
 
 A better method is to lay two plys of tarred felt lapping 
 each other 17 ins. and then spreading a coat of pitch over the 
 entire roof. On this again three more layers of felt are laid, 
 then coated with pitch', into which the crushed slag or screened 
 gravel is embedded. Each layer of felt lapping another should 
 be mopped 2 ins. more than its exposed surface back from the 
 edge. 
 
 The following specification prepared by the Barrett Manu- 
 facturing Company describes the latter method, as also the 
 materials that should be used to secure a first-class job:* 
 
 Specification for Slag or Gravel Roofiiig.t 
 
 Over the entire roof shall be laid a five- (5) ply coal-tar pitch 
 felt and slag or gravel roof, to be constructed as follows: 
 
 The rosin-sized sheathing paper to be used shall weigh not 
 less than six (6) Ibs. per 100 sq. ft. 
 
 The felt shall weigh not less than fourteen (14) Ibs. per 100 
 sq. ft., single thickness. 
 
 The pitch shall be the best quality of straight-run coal-tar 
 pitch distilled direct from American coal-tar, and there shall be 
 used not less than one hundred and twenty (120) Ibs. (gross 
 weight) per 100 sq. ft. of completed roof. 
 
 The nailing shall be done with threepenny barbed-wire 
 roofing nails driven through tin discs. 
 
 The slag or gravel shall be of such a grade that no particles 
 shall exceed five eighths (|) of an inch or be less than one 
 fourth (J) of an inch in size. It shall be dry and free from 
 dust or dirt. In cold weather it must be heated immediately 
 before using. Not less than three hundred (300) Ibs. of slag or 
 four hundred (400) Ibs. of gravel shall be used per 100 sq. ft. 
 
 The materials shall be used as follows: 
 
 First lay one thickness of rosin-sized sheathing paper (A) , lap- 
 ping each sheet 1 in. over the preceding one, and nailing only so 
 often as may be necessary to hold in place until covered with 
 the tarred felt, and the nailing may be omitted entirely if 
 practicable. 
 
 * For specifications for ordinary gravel roofing, including flashing, 
 Part II, Building Construction and Superintendence, p. 498. 
 t Known as Barrett's specifications. 
 
1434 
 
 MEMORANDA ON ROOFING. 
 
 Over the rosin-sized sheathing lay two (2) full thicknesses of 
 
 tarred felt (B), lapping each 
 sheet seventeen (17) ins.* 
 over the preceding one, and 
 nailing along the exposed 
 edges of the sheets only so 
 often as may be necessary 
 to hold the sheets in place 
 until the remaining felt can 
 be applied. 
 
 Over the entire surface of 
 the felt thus laid spread a 
 uniform coating of pitch (C), 
 mopped on. Then lay three 
 (3) full thicknesses of felt 
 (D), lapping each sheet 
 twenty-two (22) ins. over 
 the preceding one, and nail- 
 ing, as laid, every three (3) 
 ft., not more than ten (10) 
 ins. from the upper edge. 
 
 When the felt is thus laid 
 and secured, mop with pitch 
 (E) the full width of twenty 
 (20) ins. under each lap. 
 Then spread over the entire 
 
 Gravel Roofing, showing Method SUrf * Ce f , the , r f uniform 
 
 of Laying. coating ot pitch, into which, 
 
 while hot, embed slag or 
 gravel (F). 
 
 Note. When this roof is to be laid over hydraulic cement 
 concrete, as in fire-proof construction, omit the rosin sheath- 
 ing paper, and in its place coat the concrete with hot pitch. 
 
 The only difference between slag and gravel roofing is that 
 for the former crushed slag is used instead of gravel. 
 
 As there are several different weights of tarred felt, the 
 specifications should either give the weight per 100 sq. ft. or 
 the number of some particular brand, as Barrett's No. 1, 2, or 3. 
 
 Temporary roofs may be made with three or even two thick- 
 nesses of tarred felt. 
 
 The object of laying dry felt or rosin-sized paper on the 
 sheathing is to prevent the pitch from dripping through the 
 cracks. The minimum weight of tarred felt that should ever 
 be used on temporary jobs is 12 Ibs. per 100 sq. ft. and the 
 
 * The width of roofing felts is 32 ins. A lap of 17 ins. gives a 2-in. 
 " head-cover." 
 
ASPHALT ROOFING. 1435 
 
 minimum amount of pitch 70 Ibs. for a 3-ply roof and 90 Ibs. 
 for a 5-ply (i.e., four layers of tarred felt.)* 
 
 Gravel roofs should not have a pitch of less than f nor more 
 than f in. to the foot in hot climates, or in the Mountain States. 
 In cold and damp climates the pitch may be as great as 4 ins. 
 to the foot, but is not as desirable as one of f in. to 1 in. 
 
 Fire-resisting Qualities. While it cannot be called fireproof, 
 it has been proved by carefully conducted tests that gravel roof- 
 ing will protect a wooden roof better than tin. 
 
 The effect of fire on gravel roofing is to soften the asphalt 
 and pitch in the roofing, to burn out the inflammable oil in the 
 same, and to cause the residue to swell and form a porous, incom- 
 bustible coke. 
 
 Durability. A 3-ply gravel roof of 12-lb. felt and 70 Ibs. 
 of straight-run distilled pitch should last for^ from four to 
 seven years; an ordinary 6-ply 15-lb. felt and 100 Ibs. pitch from 
 nine to ten years, and a roof put on as specified above, fifteen 
 to twenty years, and under favorable circumstances even longer. 
 
 Tar roofing is not readily attacked by corrosive gases and will 
 consequently last longer than metal on buildings exposed to 
 such gases. Creosote-oil is often added to coal-tar pitch, par- 
 ticularly in cold weather, to make it run well and to make the 
 slag or gravel stick. It is generally considered to lessen the life 
 of the pitch. 
 
 Roofers generally give a five-year guarantee with gravel roofs. 
 
 Cost. The cost of coal-tar gravel roofing varies with the 
 times and locality from $2.50 to $3.50 per square for 3-ply, 
 $3 to $5 for ordinary 5-ply, and about $7 for a roof as above 
 specified. 
 
 Asphalt Roofing differs from coal-tar roofing principally 
 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 tempera- 
 tures and that therefore the flexibility and life of asphaltic felts 
 and coatings- are not as quickly destroyed. As a matter of fact, 
 
 * In the Western States the number of "ply" is construed to mean the 
 total number of layers, including dry as well as saturated felt, and the 
 terms 3 ply, 5 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 
 felt. The total number of layers should always be specified. 
 
1436 MEMORANDA ON ROOFING. 
 
 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. 
 
 i The asphalt used for roofing is obtained principally from 
 
 the island of Trinidad. 
 
 The asphalt-roofing materials manufactured by the Warren 
 Chemical and Manufacturing Company of New York have been 
 used for many years and have given good satisfaction. 
 
 Specifications for Asphalt Roofing. The following 
 specification was prepared by the above-named company. The 
 manner of laying the felting differs from that ordinarily em- 
 ployed for coal-tar roofing: 
 
 Specifications. Cover the roof with two thicknesses of 
 Warren's Composite Roofing Felt, mamlla-paper side down, 
 lapping each sheet 17 ins. over the preceding one, and securing 
 with nails through tin discs about 2J ft. apart. Over the 
 entire surface of the composite felt thus laid mop an even 
 coating of Warren's Anchor Brand Natural Asphalt Roofing 
 Cement. Over this coating of cement lay one thickness of 
 Anchor-brand asphalt felt, lapping each sheet at least 2 ins. 
 over the preceding one, sticking these laps thoroughly with 
 the hot asphalt roofing cement, and securing with nails through 
 tin discs. Over this first sheet of Anchor-brand felt mop again 
 an even coating of cement, and over this lay a second sheet of 
 Anchor-brand felt, having the laps come in the middle of the 
 first sheet of Anchor-brand felt beneath, sticking the 2-in. laps 
 as before, and securing with nails through tin discs about 1 J ins. 
 from the upper edge of the sheet. Over the entire surface of 
 the felt thus laid spread an even coating of the Anchor-brand 
 cement, covering it immediately with a sufficient body of 
 well-screened dry gravel. If the roofing is applied in cold 
 weather the gravel must be heated. 
 
 Asphalt roofing costs a little more than coal-tar roofing of 
 the same grade. 
 
 An asphalt gravel roof should not have a slope exceeding 
 \ in. to the foot, on account of the liability to run in hot weather. 
 
 Ready Roofing. There are a large number of so-called "ready 
 roofings," which are prepared by cementing together two, 
 three, or more layers of saturated felt or felt and burlap and 
 then coating either with a hard solution of the same cementing 
 material, or with hot pitch or asphalt into w r hich is embedded 
 sand or fine gravel. 
 
 These roofings are commonly put up in rolls 36 ins. wide and 
 axe applied by lapping the strips 2 ins. with a coat of cementing 
 
READY ROOFING. 1437 
 
 material between, and nailing every 2 or 3 ins. with roofing 
 nails with tin caps. A sufficient quantity of cement, nails, 
 and tin caps is packed in the center of the rolls. 
 
 The particular advantage of these roofings is that no previous 
 experience 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 ready roofings are as durable -under ordinary 
 conditions as the light-weight gravel roefs. In Colorado, how- 
 ever, 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 1 inch or more to the foot, these 
 roofings make an economical and durable roof, and for some 
 buildings are to be preferred to other materials. 
 
 The best known and most extensively used of these ready 
 roofings are: 
 
 Brand. Name of Manufacturer. 
 
 The P. & B. Ruberoid Roofing Standard Paint Co., N. Y. 
 
 Malthoid Paraffine Paint Co., San Francisco. 
 
 Arrow Brands, Asphalt Roofing .... Asphalt Ready Roofing Co., N. Y. 
 
 Elaterite Roofing Western Elaterite RTg Co., N. Y. 
 
 Elaterite Roofing Elaterite R'f'g Co., San Francisco. 
 
 Standard Asbestos Roofing H. W. Johns-Man ville Co., N. Y. 
 
 Granite Roofing Eastern Granite R'f'g Co. , N. Y. 
 
 Carey's Magnesia Flexible Roofing. . Philip Carey M'f'g Co., Lockland, O. 
 Asphalt Sand-surfaced Roofing Warren Chemical & M'f'g Co., N. Y. 
 
 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.* 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 corrugation. It is claimed that the latter 
 
 * It is claimed that "the life of a genuine puddled-iron sheet when ex- 
 posed only to the pure air and natural elements is from five to eight times 
 longer, and when exposed to sulphurous and other gases ten to twenty 
 times longer, than that of steel or semi-steel of the same gauge, or a light 
 gauge of sheet made from pure puddled pig iron will wear longer than the 
 heaviest gauges of steel sheets, or than galvanized sheets of the same gauge." 
 
1438 
 
 CORRUGATED SHEETS. 
 
 method gives the more perfect and uniform corrugations. The 
 weight and thickness of the metal is represented 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, 1S93. 
 
 The following table gives the weight and thickness of the dif- 
 ferent gauges, from Nos. 7 to 30, for flat black sheets. [The 
 gauge extends from No. 7-0, J in. thick, up to No. 40, .005469 in. 
 in thickness, but sheet steel is not commonly made thinner than 
 No. 30, and above % in. the thickness is generally designated 
 by fractions of an inch.] 
 U. S. STANDARD GAUGE FOR SHEET IRON AND STEEL. 
 
 
 Thickness. 
 
 Weight. 
 
 No. of 
 Gauge. 
 
 Approximate 
 Thickness in 
 
 Approximate 
 Thickness in 
 
 Weight per 
 Square Foot 
 
 Weight per 
 Square Foot 
 
 
 Fractions of 
 
 Decimal Parts 
 
 in Ounces 
 
 in Pounds 
 
 
 an Inch. 
 
 of an Inch. 
 
 Avoirdupois, 
 
 Avoirdupois. 
 
 7 
 
 3/16 
 
 .1875 
 
 120 
 
 7.5 
 
 8 
 
 11/64 
 
 .171875 
 
 110 
 
 6.875 
 
 9 
 
 5/32 
 
 .15625 
 
 100 
 
 6.25 
 
 10 
 
 9/64 
 
 .140625 
 
 90 
 
 5.625 
 
 11 
 
 1/8 
 
 .125 
 
 80 
 
 5. 
 
 12 
 
 7/64 
 
 . 109375 
 
 70 
 
 4.375 
 
 13 
 
 3/32 
 
 .09375 
 
 60 
 
 3.75 
 
 14 
 
 5/64 
 
 .078125 
 
 50 
 
 3.125 
 
 15 
 
 9/128 
 
 .0703125 
 
 45 
 
 2.8125 
 
 16 
 
 1/16 
 
 .0625 
 
 40 
 
 2.5 
 
 17 
 
 9/160 
 
 ,05625 
 
 36 
 
 2.25 
 
 18 
 
 1/20 
 
 .05 
 
 32 
 
 2. 
 
 19 
 
 7/160 
 
 .04375 
 
 28 
 
 1.75 
 
 20 
 
 3/80 
 
 .0375 
 
 24 
 
 1.50 
 
 21 
 
 11/320 
 
 .034375 
 
 22 
 
 1.375 
 
 22 
 
 1/32 
 
 .03125 
 
 20 
 
 1.25 
 
 23 
 
 9/320 
 
 .028125 
 
 18 
 
 1.125 
 
 24 
 
 1/40 
 
 .025 
 
 16 
 
 1. 
 
 25 
 
 7/320 
 
 .021875 
 
 14 
 
 .875 
 
 26 
 
 3/160 
 
 .01875 
 
 12 
 
 .75 
 
 27 
 
 11/640 
 
 .0171875 
 
 11 
 
 .6875 
 
 28 
 
 1/64 
 
 .015625 
 
 10 
 
 .625 
 
 29 
 
 9/640 
 
 .0140625 
 
 9 
 
 .5625 
 
 30 
 
 1/80 
 
 .0125 
 
 8 
 
 .5 
 
 Section 3 of the act of Congress provides that in the practical 
 use and application of the above gauge a variation of 2 J per cent, 
 either way may be allowed. 
 
CORRUGATED ROOFING. 1439 
 
 Galvanizing the sheets adds approximately 2J ounces per 
 square foot to the above weights. 
 
 The regular sizes of the corrugations are 2J, 1 J, f , and % inch, 
 measured from centre to centre. 
 
 Besides these sizes, 5-in., 3-in., and 2-in. corrugations are 
 made by one or two corrugating companies. 
 
 Corrugated sheets are carried in stock in 6-, 7-, 8-, 9-, and 
 10-ft. lengths. The 8-ft. length, however, is most commonly 
 used. The width of the sheets, as a rule, is 24 ins. between 
 centres of the outer corrugations, so that the covering width is 
 24 ins. when one corrugate is used for side lap. This applies to 
 all sizes of corrugations, although one or two mills make wider 
 sheets. 
 
 The 2-, 2J-, and 3-in corrugated sheets are made in all gauges 
 from 16 to 28, the IJ-in. corrugated sheets are made from Nos. 
 22 to 28 gauge, the f-in corrugated sheets from Nos. 24 to 28, 
 and the %-in. corrugated sheets of Nos. 26, 27, and 28 gauges 
 only. No. 28 gauge is most used for all purposes. The sheets 
 are generally painted with a red mineral paint before shipping; 
 galvanized sheets can also be obtained if desired. 
 
 All corrugated sheets are sold by the square (100 sq. ft.), 
 measuring the actual width and length of the corrugated sheets. 
 
 Corrugated Roofing-.* 
 
 For covering roofs, either 3-, 2J-, or 2-in. corrugates should be 
 used, the 2J-in. being the most common size. The thickness 
 or gauge will depend on 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 1 to 2 ft. between centres. The maximum 
 distances between supports for other gauges should be as 
 follows : f 
 
 For No. 24 gauge, 2 to 2J ft. from centre to centre. 
 
 For Nos. 22 and 20 gauge, 2 to 3 ft. from centre to centre. 
 
 For No. 18 gauge, 4 to 5 ft. from centre to centre. 
 
 For No. 16 gauge, 5 to 6 ft. from centre to centre. 
 
 The least pitch which should be given to roofs that are to be 
 covered with corrugated sheets is 3 ins. to the foot, and for truss 
 
 * Much practical information regarding the use of corrugated sheets on 
 mill buildings, witn many details, is contained in Steel Mill Buildings, 
 by Milo S. Ketchum, C.E. 
 
 t For strength of corrugated sheets see Steel Mill Buildings, p. 190. 
 
1440 
 
 CORRUGATED ROOFING. 
 
 roofs it is not desirable to have less than a one fourth pitch (6 ins. 
 to the foot). 
 
 When laid on a roof, corrugated sheets should have a lap at 
 the lower end of from 3 to 6 ins., according to the pitch of the 
 roof. For a J pitch, a 3-in. lap; for a } pitch, a 4-in. lap; 
 and for a J 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 
 
 Fig. 1 
 
 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, how- 
 ever, is laid as in Fig. 2. 
 
 Fig. 2 
 
 In applying to sheathing or wood 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 ins. apart at the sides. 
 
 When applied to iron or steel purlins, the side laps should be 
 at least 1J corrugations, and the sheets should be riveted 
 together every 8 ins. on the sides and at every alternate corruga- 
 tion 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 the purlins, 
 which are usually of angles, a cleat of band iron f or f of an inch 
 wide may be passed around or under the purlins and riveted at 
 both ends to the sheet, as shown in Fig. 3. By contracting 
 or pressing this cleat toward the web a tight, secure fastening 
 
CORRUGATED ROOFING. 
 
 1441 
 
 is made, which allows for contraction and expansion of the 
 sheets. 
 
 Cleats, however, are generally used only with channel or 
 Z-bar purlins. For angle-iron purlins, the clinch-nail (of soft 
 iron wire) is most commonly used, as shown by Fig. 4; it makes 
 a very satisfactory fastening. 
 
 Fig. 3 
 
 Fig. 4 
 
 6 ins. 
 33 
 
 4X4^ ins. 
 
 7 ins. 
 
 27 
 
 Fig. 5 Fig. 6 
 
 The following table shows the size 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 2X2 ins. 2^ X 3 ins. 
 
 Length of nail 4 ins. 5 ins. 
 
 No. of nails per Ib 48 38 
 
 The nails should be placed through the top of every second 
 or third corrugation. 
 
 At the eaves of the building and along the edge of the venti- 
 lator especial pains should be taken in fastening the roofing, as 
 this is where the wind catches it and strips it from the purlins. 
 For these places the best method of fastening is shown by Fig. 5. 
 
 This consists of a strip of sheet iron about 2 inches wider than 
 the purlins, made of No. 12 iron, riveted to the purlins with |-in. 
 rivets spaced 10 ins. apart; to this strip the corrugated sheets 
 are riveted, at spaces of 5 ins. or two corrugates, with six-pound 
 rivets. The method of fastening shown by Fig. 6 also answers 
 very well and is less expensive. 
 
1442 
 
 CORRUGATED SIDING. 
 
 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 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 
 100 SQ. FT. OF ROOF. 
 
 End laps. . . . 
 
 1 in 
 
 2 ins 
 
 3 ins 
 
 . 
 
 s> 
 
 . 
 
 6 ins 
 
 
 
 
 
 
 
 
 
 Feet. 
 
 Feet. 
 
 Feet. 
 
 Feet. 
 
 Feet. 
 
 Feet. 
 
 Side lap, 1 corrugation . 
 " " H " 
 
 110 
 116 
 
 Ill 
 117 
 
 112 
 118 
 
 113 
 119 
 
 114 
 120 
 
 115 
 121 
 
 .. 2 
 
 123 
 
 124 
 
 125 
 
 126 
 
 127 
 
 128 
 
 APPROXIMATE WEIGHT IN POUNDS OF 100 SQ. FT. OF 2^-INCH 
 CORRUGATED SHEETS. 
 
 Gauge 
 
 No. 28 
 
 No. 27 
 
 No. 26 
 
 No. 24 
 
 No. 22 
 
 No. 20 
 
 No. 18'No. 16 
 
 
 Painted 
 
 69 
 86 
 
 77 
 93 
 
 84 
 99 
 
 111 
 127 
 
 138 
 ' 154 
 
 165 
 182 
 
 220 
 236 
 
 275 
 291 
 
 Galvanized. . . 
 
 Anti-condensation Lining. Wherever corrugated steel 
 is laid on purlins 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, consider- 
 able 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 
 corrugated steel may then be fastened to the purlins in the 
 usual way. The side laps may be secured by stove-bolts, with 
 1" X i" X 4" plate washers on the under side, to support the lining. 
 
 Corrugated Siding. 
 
 For siding, either the 2J-, 2-, or IJ-in. size corrugations are 
 used. The IJ-in. size, however, makes the best appearance. 
 For the lap, one inch at the bottom and one corrugation at the 
 sides is sufficient. 
 
 For sheds, etc., the sheets may be nailed to cross-piece's* cut in 
 between the studs horizontally and spaced from 2 to 3 ft. apart, 
 the studs being from 3 to 4 ft. on centres. For elevators, either 
 cross-corrugated sheets or sheets not more than 32 ins. long should 
 be used. The nails should be driven in the trough of each alter- 
 
FLOOR AND WALL TILING. 1443 
 
 nate corrugation 2 ins. above the lower end of the sheet, which 
 will be 1 in. above the top end of the under sheet. This will 
 allow the sheet to slide 1 in. in 32 ins. 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., %-in. or 
 f-in. corrugated sheets are much used; they make an excellent 
 material for this purpose. 
 
 The cost of corrugated sheets over sheathing is about $3.50 
 a square and on steel purlins $4 to $4.50. 
 
 Galvanized Iron. This term is commonly applied to all 
 galvanized sheet metal, although most, if not all, of the galvan- 
 ized sheets of the present day have a steel base. 
 
 The best quality of galvanized iron bears the trade-mark 
 "Appollo" or " Apollo Best Bloom." 
 
 Galvanized sheets come in Jengths of 6, 7, and 8 ft. in U. S. 
 Gauge Nos. 14, 16, 18, 20, 22, 24, 26, 27, 28, and 30, and in 
 widths of 24, 26, 28, 30, and 36 ins. for all gauges except No. 30, 
 which is made only in widths of 24, 26, and 28 ins. 
 
 Sheets of No. 28 gauge are also made in widths of 32 and 
 34 ins. The widths commonly carried in stock are 24, 28, and 
 30 ins. 
 
 Most of the galvanized iron used for cornices and ornamental 
 work is No. 27 gauge. No. 28 is sometimes used for gutters 
 and conductors. 
 
 Cost. The net price per 100 Ibs. of flat galvanized sheets, 
 in car-load lots at Pittsburg, June, 1904, is as follows: For Nos. 
 10 to 14, $2.35; Nos, 15 and 16, $2.50; Nos. 17 to 21, $2,60; 
 Nos. 22 to 24, $2.75; Nos. 25 and 26, $3.00; No. 27, $3.25; 
 No. 28, $3.50. The retail price in cities varies from 3 cts. 
 to 4J cts. per lb., depending largely upon the freight rate. 
 
 FLOOR AND WALL TILING, 
 
 Tile floors are extensively used in the better class of build- 
 ings, and particularly in those portions which are used by the 
 public, 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 sub- 
 ject to much wear. 
 
 The materials used for floors are tiles made from different 
 
1444 FLOOR AND WALL TILING. 
 
 grades of clay, marbles, slate, glass, and rubber. Of these the 
 most durable and sanitary are the vitreous clay tile. 
 
 For walls and wainscotings, glazed tiles, marbles, and glass 
 are extensively used. 
 
 Clay Tiles. The several grades of clay tile are known 
 under the following terms: 
 
 A. Floor Tile. 
 
 1. Common Encaustic Tile. The cheapest grade, made of 
 naturally colored clays red, buff, gray, chocolate, and black. 
 This tile is of a porous, absorbing character and is used for 
 common floors of no sanitary requirements. 
 
 2. Semi-vitreous Tile. A somewhat better grade of the 
 former article, having less porosity and absorption. 
 
 3. Vitreous Tile. The hardest tile known (cannot be scratched 
 by steel or sand), non-absorbent and thoroughly aseptic. It 
 is principally in use for floors requiring a perfect sanitary con- 
 dition; is manufactured in white, blue, gray, green, and pink 
 colors of great delicacy. 
 
 4. "Ceramic" Tile, or Ceramic Roman Mosaic. This material 
 is made of vitreous clay in tesseral pieces representing the 
 tesserse of the Roman mosaic. It is made in regular tile ranging 
 from j-in. to f-in. squares and also in hexagonal shapes from J 
 in. to 1 in. in size. A round " lozenge" is also manufactured to 
 be laid in tesseral paving. 
 
 The material itself is of great hardness and is well suited 
 for work of monumental or public character. The even and 
 regular texture of the tesserse admits the adoption of damask 
 designs which have become identified and associated with this 
 material. The minuteness of the tesserse admits great range , 
 in designing and can therefore follow each line of architecture. 
 The ceramic Roman mosaic is much preferred to mosaic con- 
 sisting of natural marbles on account of the great variety in 
 colors and also on account of its greater durability, the vitreous 
 clay tile being perfectly impervious to attacks of any acids 
 contained in the atmosphere, while marble especially is subject 
 to rapid disintegration caused by the sulphuric acid contained 
 in the smoke-laden atmosphere of our cities. 
 
 5. Florentine Mosaic and Flint Tile. This is the largest and 
 heaviest tile manufactured in this country. It is either plain or 
 inlaid and is in use especially in ecclesiastic work on account of 
 its relation to mediaeval application. The material is vitreous 
 
FLOOR AND WALL TILING. 1445 
 
 annealed and is more tough than brittle. It is also in use for 
 exterior polychrome work. 
 
 6. Aseptic Tile. A large and heavy thoroughly vitreous tile 
 for institute work. It is the only vitreous tile of large size made 
 in this country. As the tile is large and generally of hexagonal 
 shape, the joint space is reduced to a minimum, and it is, there- 
 fore, especially adapted for hospitals, operating-rooms, and 
 contagious wards in public institutions. 
 
 B. Enamelled or Wall and Mantel Tile. 
 
 1. White Wall Tile. A glazed tile for wainscots. This tile 
 has a white soft body and its surface is covered with a clear 
 glaze. The brilliancy of this glaze and its reflecting properties 
 makes the white wall tile especially desirable for dark passages. 
 
 2. Colored Glaze or Enamel Tile. This tile is about the same 
 as the former in quality; the "glaze," or "enamel," however, 
 is stained with metallic oxides, which produces a brilliant decora- 
 tive effect. 
 
 3. Dull Satin, etc., Finished Enamelled Tile. A glazed tile 
 with a "dull" or "blind" enamel. The dull finish is either pro- 
 duced by sandblasting or devitrifying enamels. It is princi- 
 pally used for quaint decorative effects in mantel work. 
 
 4. Glazed Roman Mosaic. The latest style of enamelled tiling 
 which has great decorative possibilities. It has the same tesseral 
 texture as the ceramic floor tile and finds ready application to 
 wainscots and mantel work. 
 
 Clay tile are set in Portland-cement mortar as a rule, and 
 floors should always be provided with a substantial concrete. 
 A new invention which has been placed on the market as "Pli- 
 caro" mosaic consists of the ceramic mosaic laid on a flexible 
 base. With this material wood floors can be provided with 
 tile floors, and owing to the elasticity and lightness of the mate- 
 rial, floors in elevators, boats, and other ambulant structures 
 can be safely tiled. 
 
 Marble Tiles from 9 to 12 ins. square have been extensively 
 used for floors, principally on account of their decorative effect. 
 None of the marbles, however, are as hard and consequently 
 as durable as the vitreous and ceramic tile, and from all prac- 
 tical standpoints do not make as good a floor. 
 
 When used, they should be 1J ins. thick and not over 12 ins. 
 square, and should be bedded in cement on a concrete base. 
 Marbles should not be used for floors in hospitals, as they yield 
 rapidly to the usual antiseptic floor washes. 
 
1446 FLOOR AND WALL TILING. 
 
 Slate, although non-absorbent and not affected even by 
 dilute mineral acids, is too cold and dingy to commend itself as a 
 floor tile, but because it is conveniently handled in large slabs 
 it is valuable as a cheap base and as a cover for wiring and 
 pipe trenches in the floor. 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 1 J ins. thick. 
 
 Marbleitliic Tile or Slabs are made of small pieces or 
 chips of marbles of irregular shapes, set in a backing of sand and 
 Portland cement, and after the cement has set, the top surface is 
 rubbed until it becomes flat and smooth. Marbleitliic resembles 
 mosaic or Terazzo, except that it is laid in the form of tiles in- 
 stead of being put down on the floor in a plastic condition. Much 
 objection has been made to Terazzo because of the cracks which 
 commonly occur in it, due to the slight settlements which are 
 unavoidable in a new building. With tile floors of any mate- 
 rial the joints allow for any slight movement of the floor, with- 
 out producing 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 now (1904) been in use for nine years and they have been 
 found to show but 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. r ,-,,,: 
 
 Sanitary coved base, stair treads, and wainscoting are also 
 made of it. 
 
 Cast Glass Tile, while quite resistant to a blow when the 
 polish is unbroken, will break very easily when the surface is 
 scratched. All glass tile 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 -i in. up to 2 ins. and in slabs 
 of all widths and lengths up to 100 ins. wide and 180 ins. long. 
 It is made in various colors and designs and in the following 
 finishes : natural fire finish, hone, semi-polished, and polished. 
 
 This material can be worked and handled the same as marble, 
 it is readily drilled and shaped to accommodate fixtures, etc. r 
 and is very handsome in appearance. It is impervious to 
 discoloration and is non-crazing. 
 
 * Made by the Perm-American Plate Glass Company, Pittsburg, Pa. 
 
FLOOR AND WALL TILING. 1447 
 
 These qualities make it especially desirable for floors, wain- 
 scoting, tables, shelves, etc., in all places where an absolute 
 sanitary condition is desired, combined with a handsome 
 appearance. 
 
 Interlocking Rubber Tiling. 
 
 Several years ago the New York Belting and Packing Company 
 introduced an interlocking rubber tile, which, because of its being 
 noiseless, non-slippery, and more comfortable to the feet than 
 inelastic substances, has met with great favor for floors in bank- 
 ing-rooms, counting-rooms, vestibules, elevators, stairs, cafes, 
 libraries, churches, etc. For elevators it is the most durable 
 and practical floor 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 secured, the tiles being made in a carefully selected 
 variety of colors. The tiles are laid directly over the original 
 floor, like a carpet (except that they are not fastened). Expe- 
 rience has shown that they are very durable. 
 
 Each tile is 2f ins. square and f in. thick; 25.5 tiles are 
 required to the square foot. Rubber nosing for stairs is made 
 to interlock with the tile. 
 
 Cost of Different Tiles. 
 
 The following prices are approximately the cost (to the trade) 
 at the factory at the present time (1904). To this should be 
 added freight and the dealers' profit. The cost of laying the tiles 
 on a cement base (in addition to the cost of the tiles) should not 
 exceed 25 cents per square foot. 
 
 FLOOR TILES. 
 
 Factory Price 
 per Sq. Ft, 
 
 Common encaustic tile, unglazed 15 cts. 
 
 Vitreous tile: white 22Vio ' ' 
 
 Colors (large sizes) from 23 to 26 ' ' 
 
 "Ceramic" tile, or ceramic Roman mosaic, from 20 to 35 " 
 WALL AND MANTEL TILE. 
 
 Factory Price 
 per Sq. Ft. 
 
 White glazed wall tile ^ 25 cts. 
 
 Colored glaze or enamel tile , 30 
 
 Enamel tile, dull satin finish 40 
 
 Marbleithic costs from 45 cts. per sq. ft., upwards, laid. 
 
1448 ASFHALTUM. 
 
 ASPHALTUM. 
 
 "Bitumen, Asphaltum, Asphalt. Bitumen is the name used to 
 denote a group of mineral substances, composed of different 
 hydrocarbons, found widely diffused throughout the world in a 
 variety of forms which grade from thin volatile liquids to thick 
 semi-fluids and solids, sometimes in a free or pure state, but 
 more frequently intermixed with or saturating different kinds 
 of inorganic or organic matter. 
 
 "To designate the condition under which bitumen is found, 
 different names are employed; thus the liquid varieties are 
 known as naphtha and petroleum, the semi-fluid or viscous as 
 maltha or mineral tar, and the solid or compact as asphaltum 
 or asphalt."* 
 
 Asphalt 11 m is found in extensive beds or lake-like deposits 
 on both continents ; the most notable of these are the pitch lakes 
 on the island of Trinidad, and at Bermundez, Venezuela. 
 
 It is also found saturating the limestone and sandstone 
 formations in certain localities. 
 
 Deposits of very nearly pure asphaltum are found in Utah, 
 Mexico, Cuba, and various parts of the United States. 
 
 Elaterite, gilsonite, and wurtzilite are varieties of very nearly 
 pure asphaltum. 
 
 Asphaltic roofing materials are manufactured principally 
 from Trinidad asphalt. These deposits have also been the 
 main source of supply for the asphaltum used in street-paving 
 in the United States. 
 
 The term rock asphalt is commonly used to designate the 
 material obtained from the bituminous limestone deposits at 
 Seyssel and Pyrimont, in the valley of the Rhone, France, and 
 in the Val-de-Travers, canton of Neuchatel, Switzerland, and 
 at Ragusa, on the island of Sicily. It is extensively employed 
 for paving purposes throughout Europe, and is considered 
 to make a much more durable pavement than can be made 
 with asphaltum. 
 
 Rock asphalt is prepared for shipment in two forms: (a) com- 
 pressed asphalt blocks, which are used for paving in much the 
 same way as stone blocks, and (6) mastic asphalt, which is put 
 up in cakes of varying shape, generally bearing the manu- 
 facturer's trade-mark. 
 
 * Byrne, Inspectors' Pocket Book. 
 
ROCK ASPHALT. 1449 
 
 In the Eastern States mastic asphalt is used for floors of 
 cellars, stores, breweries, malt-houses, hotel kitchens, stables, 
 laundries, conservatories, public buildings, carriage-factories, 
 sugar-refineries, mills, rinks, etc., and for any place where a 
 hard, smooth, clean, dry, fire- and water-proof, odorless, and 
 durable covering of a light color is required, either in basement 
 or upper stories. It can be laid either over cement concrete, 
 brick, or wood in one sheet without seams; also over cement 
 concrete for roots tor fire proof buildings. For dwelling-house 
 cellars, especially on moist or filled land, this material is especially 
 adapted, being water-tight, non-absorbent; free from mould or 
 dust, impervious to sewer-gases, and for sanitary purposes 
 invaluable. 
 
 Mastic asphalt is also valuable for damp courses over founda- 
 tions, and for covering vaults and arches under ground. 
 
 For floors of cellars, courtyards, etc., laid on the ground, a 
 base of cement concrete 3 ins. thick should first be laid; and over 
 this a layer of asphalt from f in. to 1J ins. thick, according 
 to the use to which it is to be put. For ordinary cellar floors, 
 the asphalt need not be more than f in. thick ; for yards on which 
 heavy teams are to drive, it should be 1J ins. thick. In specify- 
 ing asphalt pavement, both the thickness of the concrete and of 
 the asphalt should be given; it should also be remembered 
 that "asphalt pavement" does not include the concrete founda- 
 tion unless so specified. 
 
 In laying asphalt over plank or boards, a layer of stout, dry 
 (not tarred) sheathing-paper should first be put down and the 
 asphalt laid on this. Asphalt floors for stables should be at least 
 1 in. thick. The cost of rock asphalt in the large cities varies 
 from 12 tp 17 cents per square foot in jobs of 2,000 feet and over; 
 this does not include the concrete foundation. German and 
 other cheap asphalts are laid for somewhat less, while imitation 
 rock asphalts are furnished for considerably less. 
 
 Architects and owners desiring to employ rock asphalt for any 
 of the above purposes should be careful to secure the genuine 
 Val-de-Tr avers or Seyssel or Sicilian rock asphalt, as there are 
 imitations which are of but little value. 
 
 The bituminous sandstones of California have been exten- 
 sively used for paving streets in Western cities. They are pre- 
 pared for use as a paving material by crushing to powder. With 
 this powder a considerable proportion of sand or gravel is gen- 
 erally mixed and the mixture is then heated until it becomes 
 
1450 MINERAL WOOL. 
 
 plastic and then spread upon the street and compressed by roll- 
 ing. 
 
 MINERAL WOOL.* 
 
 There are at least two kinds of mineral wool made in this 
 country. The more common kind is made by converting the 
 slag f of blast-furnaces, mixed with certain rocks while in a 
 melted condition, to a fibro.us state. 
 
 Its appearance is much like that of wool, being soft and fibrous, 
 but in no other respect are the materials alike Mineral wool 
 made from slag appears in a variety of colors, principally white, 
 but often yellow or gray and occasionally quite dark. The 
 color, however, is said to be no indication of the quality, as all 
 of the peculiar properties of the material are present in equal 
 proportions in any of the shades. The other kind of mineral 
 wool is known as rock wool, and is made from granite rock raised 
 to 3,000 degrees of temperature. It is claimed to be absolutely 
 free from sulphur and the only odorless wool manufactured; it 
 has been approved by the U. S. War Department. Its color is 
 white and its general apparance is the same as that made from 
 slag. The peculiar nature of both kinds is that of a mass of 
 very fine, pliant, but inelastic, vitreous fibres interlacing each 
 other in every direction and forming an innumerable number 
 of minute air-cells. Its great value in the insulation and pro- 
 tection of buildings lies in the number of air-cells which it con- 
 tains, combined with its resistance to heat or fire. In common 
 slag wool 92 per cent, of the volume consists of air held in minute 
 cells, while in the best grade the proportion of air reaches as high 
 as 96 per cent. This confined air makes it one of the best, if 
 not the best, of the non-conductors of heat, and to a less degree of 
 sound. Aside from these qualities it is very durable, contains 
 nothing that can decay or become musty, and is almost a sure 
 protection against rats and vermin. 
 
 Ordinary mineral wool weighs about 12 pounds per cubic foot, 
 and is put up in bags containing from 40 to 60 pounds in each 
 bag. It costs at the works, in Stanhope, N. J., 1 cent per pound, 
 and at the store in New York City 1J cents per pound. 
 
 * For the uses of mineral wool in building construction see Part II, Build- 
 ing Construction and Superintendence, p. 208. 
 
 t The best being from slag that does not contain iron. 
 
ESTIMATING COST OF STRUCTURAL STEEL. 1451 
 
 Extra mineral wool weighs about 9 pounds per cubic foot, and 
 is put up in bags containing from 20 to 30 Ibs. in each bag. It 
 costs at the works 4 cents per pound, and at the store, New 
 York City, 4J cents per pound. 
 
 In estimating the quantity of wool required for filling, 1 pound 
 per square foot should be allowed for each inch in thickness for 
 ordinary wool and f pound for selected wool. 
 
 ESTIMATING THE COST OP 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 cost of the completed steel, work is made up 
 of the following items: 
 
 (1) Cost of the plain steel at the mill, plus freight and dealers' 
 profit. 
 
 (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 Pittsburg, plus 
 the freight to the point of delivery. 
 
 The base price at Pittsburg at the present time (July, 1904) 
 is $1.60 per 100 Ibs. for beams and channels 15 ins. and less, 
 and for angles and Z's, 3 to 6 ins. 
 
 Beams and channels over 15 ins. cost 10 cts. per 100 Ibs. 
 extra, and T's over 3 ins., 5 cts. extra. 
 
 For angles, channels, and T's under 3 ins. the base is $1.90 
 from Chicago stock (see page 1456). 
 
 For plates \ in. thick and over the base is $1.60 per 100 Ibs. 
 For plates % in. thick, add 10 cts. per 100 Ibs. 
 
 Freight Rate sat present are: Pittsburg to Chicago, 16 J cts. 
 per 100 Ibs.; to St. Louis, 22 cts.; to New York, 14 J cts.; to 
 Kansas City, 42J cts. ; to Denver, 92 J cts. ; and to San Francisco, 
 85 cts. 
 
 For Pacific coast points, a discount of about 18 per cent, is 
 
1452 ESTIMATING COST OF STRUCTURAL STEEL. 
 
 made from the base, at Pittsburg, on account of the high freight, 
 and to meet European competition. On account of the ex- 
 pense of carrying beams in stock, local dealers usually charge 
 from J to 1 ct. a pound extra on orders supplied from stock. 
 
 List of Extras to be Added to Price of Plain 
 Beams and Channels. If any kind of work whatever is 
 done on the plain steel, or if the same is cut to length with a 
 less variation than f in., an extra price is charged, which is 
 based on the following list, adopted in 1902, and still in force. 
 These charges are common to all shops if the order is of any 
 size, and are not likely to be changed for some time. 
 
 In Effect July 1, 1904. 
 
 EXTRAS TO BE ADDED TO BASE PRICE FOR EACH 100 LBS. 
 
 1. For cutting to length with less variation than plus 
 
 or minus f in 15 cts. 
 
 2. Plain punching one size hole in web only 15 " 
 
 3. Plain punching one size hole in one or both flanges.. 15 " 
 
 4. Plain punching one size hole in either web and one 
 
 flange or web and both flanges 25 " 
 
 5. Plain punching each additional size hole in either 
 
 web or flanges, web and one flange, or web and 
 
 both flanges 15 " 
 
 6. Plain punching one size hole in flange and another 
 
 size hole in web of the same beam or channel 40 " 
 
 7. Punching and assembling into girders 35 " 
 
 8. Coping, ordinary bevelling, including cutting to exact 
 
 length, with or without punching; including the 
 riveting or bolting of standard connection angles . . 35 " 
 
 9. For painting or oiling, one coat, with ordinary oil 
 
 or paint 10 " 
 
 10. Cambering, beams and channels, and other shapes 
 
 for ships or other purposes * 25 " 
 
 11. Bending, or oth^r unusual work Shop rates 
 
 12. For fittings, wb ether loose or attached, such as angle 
 
 connections, bolts, and separators, tie-rods, etc. . . $1 . 55 
 
 Tie-rods in all cases, where estimated upon in connection with 
 beams or channels, to be classified as fittings, 
 
 In making an estimate of the steel work from the framing 
 plans, the weight of all connection angles, gusset plates, sepa- 
 rators, tie-rods, etc., must be taken off separately, and the cost 
 figured at $1.55 per 100 Ibs. above the base price. 
 
ESTIMATING COST OF STRUCTURAL STEEL. 1453 
 
 The weights of standard connections are given on pages 548 
 and 549, and of standard separators on page 544. 
 
 In estimating cost of riveted columns and girders, the weight 
 of the plain bars and plates of which the column or girder is com- 
 posed may be taken, and an extra added to the price per pound 
 to cover cost of rivets and assembling. 
 
 This extra will be about as follows: 
 
 Light channel or Z-bar columns 1 J cts. per Ib. 
 
 Heavy channel or Z-bar- columns 1 " " " 
 
 Plate girders, 24 to 48 ins. deep 1J " " " 
 
 Box girders, 24 to 48 ins. deep 1J " " " 
 
 Box girders, 48 to 60 ins. deep 1 T \> " " " 
 
 Cost of Erecting 1 . For erecting ordinary beams and col- 
 umns in buildings having masonry walls the cost of erection 
 should not exceed $10 per ton with bolted connections, and 
 will sometimes be as low as $6 per ton. 
 
 For erecting the steel work of skeleton buildings having 
 riveted connections, it is common to allow $10 per ton. 
 
 Cost of Painting'. The common charge for shop painting 
 is $1 per ton, but if done in accordance with the specification 
 on page 1413 it would exceed this amount. 
 
 For painting one additional coat after erection, allow $2 per 
 ton. 
 
 Roof-trusses. In lots of at least six, the shop cost of ordi- 
 nary roof -trusses in which the ends of the members are cut off 
 at right angles was about as follows in 1902 : * Trusses weighing 
 1,000 Ibs. each, $1.15 to $1.25 per 100 Ibs.; trusses weighing 
 1,500 Ibs. each, $0.90 to $1.00 per 100 Ibs.; trusses weighing 
 2,500 Ibs. each, $0.75 to $0.85 per 100 Ibs. ; and trusses weighing 
 3,500 to 7,500 Ibs., $0.60 to $0.75 per 100 Ibs. Pin-connected 
 trusses cost from 10 to 20 cts. per 100 Ibs. more than riveted 
 trusses. (M. S. Ketchum, C.E. in Steel-Mill Buildings.) 
 
 Steel-mill Buildings. The average shop cost for the 
 frame of steel-mill buildings, including draughting is about $25.00 
 per ton, and the cost of erection from $15.00 oc $25.00 per ton. 
 
 (A great amount of data pertaining to the cost of steel-mill 
 buildings is given by Mr. Ketchum in the book above men- 
 tioned.) 
 
 * Under present conditions, July 1, 1904, these figures should be increased 
 25 per cent. 
 
1454 ESTIMATING COST OF STRUCTURAL STEEL. 
 
 Cost of Drafting. Details for church and court-house 
 roofs having hips and valleys cost from $6.00 to $8.00 per ton; 
 details for ordinary mill buildings cost from $2.00 to $4.00 per 
 ton. The details for all work fabricated by the Gillete-Herzog 
 Mfg. Co., with the exception of plain beams and complicated 
 tank-work, were made in 1896 by contract, by Mr. H. A. Fitch, 
 now structural engineer for the Minneapolis Steel and Machinery 
 Co., Minneapolis, for $2.60 per ton. This price netted the con- 
 tractor a fair profit.* 
 
 Approximate Estimates of the Weight of Steel 
 in Building's. According to H. G. Tyrrell, C.E.,f the weight 
 of steel in any proposed new building may be roughly estimated 
 by 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 Ibs. 
 
 Apartment houses without outside frame 9 ' ' 
 
 Office buildings, with outside frame 23 " 
 
 Office buildings, without outside frame 15 " 
 
 Warehouses, with outside frame 28 " 
 
 Warehouses, without outside frame 18 " 
 
 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 v the approximate weight of roof-trusses, see pages 947 
 and 949. 
 
 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 above the base. The base 
 price may fluctuate and be changed without notice, but the 
 extras remain constant, and are the same in all localities. Fol- 
 lowing is the 
 
 * M. S. Ketchum. 
 
 t Estimating Structural Steel, in Architects & Builders' Magazine, Jan., 
 1903. 
 
ESTIMATING COST OF STRUCTURAL STEEL. 1455 
 
 STANDARD STEEL CLASSIFICATION 
 
 In Effect July 1, 1904. 
 ROUNDS AND SQUARES. 
 
 to 3 ins. 
 
 Extra per 
 100 Ibs. 
 
 Base 
 
 
 to % in 
 
 . $0 10 
 
 3 9 ' 
 
 to J6 in 
 
 20 
 
 4/1 
 
 in 
 
 '. 0.40 
 
 4 9 i 
 
 in . 
 
 50 
 
 *>f 
 
 in . . 
 
 60 
 
 54 
 
 nd -g 9 ^- in . . . . 
 
 70 
 
 6t 
 
 in } 
 
 1.00 
 
 6| 
 
 in.. . 
 
 . 2.00 
 
 
 Extra per 
 100 Ibs. 
 
 to 3i ins 0.15 
 
 to 4 ins 0.25 
 
 to 4J ins 0.30 
 
 to 5 ins 0.40 
 
 to 5J ins 0.50 
 
 to 6 ins 0.75 
 
 to 6J iris 1.00 
 
 to 7i ins 1.25 
 
 FLAT BARS AND HEAVY BANDS. 
 
 1 to 
 
 1 to 
 
 !Ye to 
 
 % to 
 
 % and i 
 i 
 
 i 
 
 1J to 
 1J to 
 1} to 
 3J to 
 
 ins. 
 
 ins. 
 
 in. 
 
 in. 
 
 in. 
 
 in. 
 
 in. 
 
 in. 
 
 in. 
 
 in. 
 
 in. 
 
 ins. 
 
 ins. 
 
 ins. 
 
 ins. 
 
 I to 
 i- and 
 I to 
 i and 
 t to 
 i and 
 | and 
 i and 
 | 
 
 i and 
 and 
 
 1 in 
 
 %> in ......... $0.20 extra per 100 Ibs. 
 
 f in ......... 0.40 
 
 % in ......... 0.50 
 
 J in ......... 0.50 
 
 X 1)6 to 
 X H to 1J 
 X If to 2} ins. 
 X 3 to 4 ins. 
 
 n 
 in 
 in 
 in 
 in 
 in 
 
 ins 
 ins 
 
 0.70 
 0.90 
 1.10 
 1.00 
 1.20 
 1.50 
 0.10 
 0.20 
 0.30 
 0.40 
 
 LIGHT BARS AND BANDS. 
 
 1J to 6 
 
 in.xNos. 1,1 
 
 J, 9 and 56 in. 
 
 $0.40 extra per 100 Ibs. 
 
 if to 6 
 1 to 1J6 
 
 in. XNos. 10, 
 in.XNos. 7, i 
 
 11, 12 and Jin. 
 5, 9 and 56 in. . 
 
 . 0.60 " 
 0.50 " 
 
 \ "< 
 
 1 1 
 
 1 to 1J6 
 
 in. XNos.JLO, 
 
 11, 12 and J in. 
 
 . 0.70 " 
 
 i c t 
 
 ft 
 
 % to % 
 
 in. XNos. 7, 
 
 >, 9 and 56 in. 
 
 0.70 " 
 
 ( t( 
 
 1 1 
 
 % to % 
 
 in. XNos. 10, 
 
 11, 12 and J in 
 
 0.80 " 
 
 1 It 
 
 c c 
 
 %and | 
 
 in. XNos. 7, 
 
 J, 9 and 96 UL 
 
 1.00 " 
 
 t tt 
 
 11 
 
 
 in. XNos. 10, 
 
 11,12, and Jin. 
 
 1.20 " 
 
 * " 
 
 c e 
 
 ?6 an d I 
 
 in. XNos. 7, 
 
 J, 9 and 56 in. 
 
 1.20 " 
 
 t it tt 
 
 % and f 
 
 in. XNos. 10, 
 
 11, 12 and Jin. 
 
 1.30 " 
 
 t I It 
 
 i 
 
 in. XNos. 7, 
 
 , 9 and 5ie in. 
 
 1.30 " ' ' 
 
 ( 
 
 
 in. XNos. 10, 
 
 11, 12 and Jin. 
 
 1.56 " " ' 
 
 { 
 
 Jfs 
 
 in.XNos. 7, i 
 
 J, 9 and % in. . . 
 
 1.80 " " ' 
 
 t 
 
 J6 
 
 in. XNos. 10, 
 
 11. 12 and Jin. 
 
 2.10 " " ' 
 
 t 
 
 | 
 
 in.XNos. 7,8 
 
 , 9 and 56 i n - 
 
 1.90 " " " 
 
 t 
 
 I 
 
 in. XNos. 10, 
 
 11, 12 and Jin.. 
 
 2.40 " " " 
 
 t 
 
1456 ESTIMATING COST OF STRUCTURAL STEEL. 
 
 For intermediate sizes, the next higher extra to be charged in 
 all cases. 
 
 ANGLES. 
 
 li X %> ins. and heavier, but under 3 ins Base 
 
 1 to li X.% ins. and heavier $0 . 10 extra per 100 Ibs. 
 
 | X /le in . 20 
 
 JX% in 0.30 
 
 f X J in 2.00 
 
 |X I in 3.00 
 
 3X3 ins. Xless than in. thick 0.50 
 
 Angles J in. and larger, but smaller than 
 
 3 ins. J in. thick 0.10 per 100 Ibs over % in. 
 
 CHANNELS. 
 
 1 JX/ie ins. and heavier, but under 3 ins Base 
 
 1 to liX.% ins. and heavier $0. 10 extra per 100 Ibs. 
 
 |Xj^in 0.20 " " " " 
 
 fandfX^in 0.30 " " " " 
 
 fXiin 0.60 " " " " 
 
 jXi in. and thicker 1.00 " " " " 
 
 Channels } in. and wider, but under 3 ins. , 
 
 in. thick 0.10 per 100 Ibs. over % in, 
 
 TEES. 
 
 ins. and heavier, but under 3 ins Basq 
 
 , w ins. and heavier $0 . 10 extra per 100 Ibs. 
 
 1 "to 1 J X % ins. and heavier . 20 " " " " 
 
 }XJ in. and thicker 0.50 " " " " 
 
 f xi in. and thicker. 0.60 " " " " 
 
 fXj in. and thicker 2.00 " " " 
 
 Tees 1 in. and larger, but smaller than 3 
 
 ins., J in. thick . 10 cts. per 100 Ibs. over % in. 
 
 For intermediate sizes, the next higher extra to be charged in 
 all cases. 
 
 The base for all of the above, from stock in Chicago, on full 
 car-load lots, is $1.90 (July 1, 1904). For other principal points^ 
 the base may be obtained by adding the freight rates given on 
 page 1451. 
 
 Example. What is the probable cost at Kansas City of 
 11" X 1" flat steel bars. Am. Base = $1.90 per 100 Ibs. 
 
 Extra = 0.20 " (l " 
 Freight = 0.42 J " " " 
 
 Total = $2. 52i per 100 Ibs. 
 
 or about 2J cts. a pound in car-load lots. For small lots, about 
 3 cts. per pound might be charged. 
 
COST OF BUILDINGS PER CUBIC FOOT. 1457 
 
 COST OF BUILDINGS PER CUBIC FOOT. 
 
 The most accurate method of estimating the cost of any pro- 
 posed building, before the plans and specifications are sufficiently 
 complete for taking off the actual quantities, is by means of the 
 cubic contents. 
 
 Two buildings built in the same style, and for the same pur- 
 pose, of the same materials, and on the same scale of wages and 
 and prices of materials, should cost the same, or very nearly the 
 same, per cubic foot, although one building be somewhat larger 
 than the other and of different shape. 
 
 It therefore follows that if we know the cost per cubic foot of 
 different classes of buildings, in different localities, we can ap- 
 proximate quite closely the cost of any proposed building by 
 multiplying its cubic contents in feet by the known cost per cubic 
 foot of a similar building already built in that locality. 
 
 Conversely, if the cost of a proposed building must be kept 
 absolutely within a certain sum, the size of the building should 
 be proportioned so that the cubic contents shall not exceed the 
 quotient obtained by dividing the amount appropriated by the 
 average cost per cubic foot of similar buildings. Even then it 
 may be found, when the bids are opened, that they exceed the 
 appropriation, but the excess will probably not be so great but 
 that the necessary reductions can be made without altering the 
 main features of the building. 
 
 In estimating the cost by the cubic contents, it is of course 
 necessary that the contents be computed on the same basis, in 
 both the proposed building and the one already built. In the 
 following examples, the cubic contents are computed from the 
 basement or cellar floor, to the average height of a flat roof, or, 
 if a pitch roof, the finished portion of the attic is included, or 
 that part which might be finished, but mere air-spaces and open 
 porches are not included. Vaults and areas under sidewalks, 
 etc. , are included as part of the basement. All measurements are 
 to the outside of the walls and foundations. Cost does not, as a 
 rule, include the architect's fee. A few of the examples, that 
 were not compiled by the author, may not be computed closely 
 by the above rule, but it is to be presumed that they are. 
 
 It should be remembered in using this table, that wages and 
 building materials were considerablv higher during the years 
 1901-1903 than in the years from 1893-98, thereby increasing 
 the cost per cubic foot from 14 to 22 per cent. ; also that the cost 
 
1458 COST OF BUILDINGS PER CUBIC FOOT. 
 
 of first-class fire-proof buildings is greater in the Western and 
 Southern States than in the Eastern States, because of the dis- 
 tance from the great steel and material centres. 
 
 TABLE FOR ESTIMATING THE APPROXIMATE COST OF 
 A NEW BUILDING, OR THE VALUE OF AN EXISTING 
 BUILDING. 
 
 (Based on prices for labor and materials as they were in 1902.) 
 
 FARM AND COUNTRY PROPERTY.* 
 
 Cents 
 
 Dwellings, frame: Small box house, no cornice 4 
 
 Dwellings, frame: Shingle roof, small cornice, no sash 
 
 weights, plain 5 to 6 
 
 Dwellings, brick : Same class 7 to 8 
 
 Dwellings, frame: Shingle roof, good cornice, sash 
 
 weights, blinds (good house) 7 to 8 
 
 Dwellings, brick: Same class (good house) 9 to 10 
 
 Barns, frame: Shingle roof, not painted, plain finish. . 1J to 2J 
 Barns, frame: Shingle roof, painted, good foundation. 2J to 3 
 
 Stores, frame: Shingle roof, painted, plain finish 5 to 7 
 
 Stores, brick: Shingle roof, painted, good cornice, well 
 
 finished 7 to 9 
 
 Ordinary wood churches and schoolhouses : country . . 5 to 7 
 Brick churches and schoolhouses: country 8 to 10 
 
 If slate or metal roof, add J ct. per ft. to above. 
 
 CITY AND VILLAGE PROPERTY.* 
 Dwellings, frame: Shingle roof, pine floors and finish, 
 
 no bathroom or furnace, plain finish (good house) . 6 to 7 
 
 Dwellings, brick: Same class 8 to 9 
 
 Dwellings, frame: Shingle roof, hard-wood floor in hall 
 
 and parlor, bath, furnace, and fair plumbing 8 to 9 
 
 Dwellings, brick : Same class 8 to 10 
 
 Dwellings, frame : Shingle roof, hard wood in first floor, 
 good plumbing, furnace, artistic design, some inte- 
 rior ornamentation, well painted. .* 10 to 12 
 
 Dwelling brick: With good plumbing, bath, hot and 
 cold water, pine finish, well painted, no hard-wood 
 finish 11 to 12 
 
 MISCELLANEOUS BUILDINGS, f 
 
 Abattoirs and other slaughter-houses 14 to 16 
 
 Asylums lunatic per cubic foot, complete, including patients' 
 wards, administrative buildings, chapel, hospital, mortuary, 
 laundry, workshops, and all other accessories, 16 to 25 cts., 
 or from $1,350 to $1,600 per patient. 
 
 * These figures were compiled by James N. Brown of St. Louis, Mo., and 
 form part of instructions furnished by insurance companies to their ad- 
 justers. 
 
 t The following data is from an article by Fred T. Hodgson in the Archi- 
 tects and Builders' Magazine, May, 1902. 
 
COST OF BUILDINGS PER CUBIC FOOT. 1459 
 
 Bath-houses, complete, or for barracks, but not supplied with 
 hot water, per cubic foot, 45 to 50 cts., or per bath, $280 to 
 $320. 
 
 Baths, public, comprising swimming-baths, slipper-baths, laun- 
 dry, caretaker's quarters, machinery, etc., complete, per cubic 
 foot, 30 to 36 cts. 
 
 Breweries, complete, including buildings, cellarage, boilers, en- 
 gine, machinery, coppers, liquor-baths, mash-tubs, coolers, 
 refrigerator, ice storage, pumps, and all other requirements, 
 per cubic foot, 14 to 20 cts. 
 
 Churches, plain, per cubic foot, from 16 to 22 cts. 
 
 Per square foot, -from $4.50 to $6.50 
 
 Per sitting, from $40 to $55 
 
 Churches, ornamental, per cubic foot, from 22 to 39 cts. 
 
 Per square foot, from $7.00 to $12.50 
 
 Per sitting, from $65 to $120 
 
 Cotton mills, as generally constructed: 
 
 Per cubic foot 9 to 12 cts. 
 
 Per spindle 22 to 30 cts. 
 
 Cow-stables, complete, with iron finishings and'fittings: 
 
 Per cubic foot 14 to 16 cts. 
 
 Per square foot $2.20 to $2.80 
 
 Per cow $170 to $190 
 
 Second-class stable with common fittings: 
 
 Per cubic foot 11 to 13 cts 
 
 Per square foot $1.65 to $2.00 
 
 Per cow $130 to $145 
 
 Third class, for farm, wood fittings: 
 
 Per cubic foot 7 J to 10 cts. 
 
 Per square foot $1.45 to $1.50 
 
 Per cow $90 to $105 
 
 Drill-halls or sheds for infantry: 
 
 Per cubic foot 11 to 14 cts. 
 
 Per square foot $1.60 to $1.70 
 
 Electric stations of power-houses, buildings erected complete, 
 exclusive of machinery and plant, per cubic foot, 14 to 17 cts. 
 
 Flats, as constructed in New York, comprising ornamental brick- 
 work in front, elevators, fire-resisting floors, and the whole 
 well finished in ordinary wood throughout : 
 Per cubic foot 28 to 36 cts. 
 
 Hospitals, complete, including administrative buildings, etc. : 
 
 Per cubic foot 20 to 30 cts. 
 
 Per bed. $1,550 to $2,300 
 
 Cottage hospitals for small towns: 
 
 Per cubic foot 17 to 22 cts. 
 
 Per bed $1,050 to $1,550 
 
 Hospitals, isolated, including all nursery buildings: 
 
 Per cubic foot 17 to 22 cts. 
 
 Per bed ^ vl $1,800 to $2,300 
 
 Hotels, complete in every particular: 
 
 First-class, per cubic foot 31 to 41 cts. 
 
 Second-class, per cubic foot 23 to 31 cts. 
 
 Third-class, per cubic foot 20 to 24 cts. 
 
1460 COST OF BUILDINGS PER CUBIC FOOT. 
 
 Houses, complete, in brickwork and good substantial finishings: 
 
 First class Large mansion with elaborate finish: 
 Main building, 16-ft. ceiling, per cubic foot, 30 to 40 cts.; per 
 
 square foot, $5.50 to $6.50.* 
 
 Additions, 11-ft. ceilings, per cubic foot, 16 to 20 cts. : per square 
 foot, $2.50 to $3.00. 
 
 Second class Large mansion of ordinary character: 
 Main building, 14-ft. ceiling, per cubic foot, 22 to 30 cts. 5 per 
 
 square foot, $3.50 to $4.50. 
 
 Additions, per cubic foot, 15 to 20 cts.: per square foot, $1 65 
 to $2.15. 
 
 Third class Country houses: 
 
 Height of ceiling, 11 ft., per cubic foot, 15 to 20 cts.: per square 
 foot, $2.15 to $2.65. 
 Fourth class Speculative buildings: 
 
 Ceilings, 10 ft., per cubic foot, 13 to 15 cts.; per square foot 
 $1.30 to $1.55. 
 
 Fifth class Tenements and cottages to rent: 
 Ceilings, 9 ft., per cubic foot, 10 to 12 cts. ; per square foot, $1.10 
 
 to $1.35. 
 Libraries, public, complete in every particular: 
 
 Per cubic foot 16 to 22 cts. 
 
 Municipal lodging-houses for cities and large towns: 
 
 Per cubic foot 15 to 18 cts. 
 
 Per bed $300 to $375 
 
 Museums, public: 
 
 For large cities, per cubic foot 22 to 33 cts. 
 
 Towns 19 to 26 cts. 
 
 Music halls, complete, per head of accommodation: 
 
 For large cities $80 to $130 
 
 For small cities and towns $40 to $70 
 
 Town halls, complete: 
 
 Large cities, per cubic foot 31 to 36 cts. 
 
 Small cities and towns 22 to 30 cts. 
 
 Alternative prices: 
 
 Basement, per cubic foot . . . ^ 20 to 24 cts. 
 
 Superstructure, per cubic foot 27 to 35 cts. 
 
 Ornamental towers, per cubic foot 39 to 46 cts. 
 
 Theatres, complete, per head of accommodation: 
 
 In large cities $82 to $108 
 
 Small cities and towns $50 to $80 
 
 Per cubic foot 28 to 38 6ts. 
 
 Chimney shafts, plain, as for factories, etc., complete, including 
 foundations, iron cap, etc., height measured from surface of 
 ground to top of cap: 
 
 Per foot in heght. 
 
 Not exceeding 100 ft. in height $40 to $46 
 
 100 ft. to 180 ft. high $45 to $52 
 
 180 ft. to 250 ft. high $50 to $56 
 
 *The prices per square foot, in this and following paragraphs,areevidently 
 per sq. ft. of floor area, counting all of the floors above the basement. 
 Author. 
 
COST OF BUILDINGS PER CUBIC FOOT. 1461 
 
 EXAMPLES OF THE ACTUAL COST OF BUILDINGS PER 
 CUBIC FOOT. 
 
 COMPILED BY THE AUTHOR. 
 
 Office Buildings. 
 
 Name of Building. 
 
 Date. 
 
 Character of Construction and 
 Finish. 
 
 Cost 
 per 
 Cu. Ft. 
 Cts. 
 
 Chamber of Com- j 
 merce, Boston, V 
 
 1891-2 
 
 f Seven stories; pitch roof, iron and] 
 {slate; granite walls, pile founda- ( 
 tion ; fire-proof construction ; | 
 
 29 
 
 Mass. j 
 
 
 marble and oak finish. 
 
 
 "Ames Building," | 
 Boston. f 
 
 1889-91 
 
 {Thirteen stories ; granite and Ohiol 
 stone fronts ; flat roof ; fire-proof I 
 construction ; marble and oak f 
 
 53 
 
 
 
 finish. J 
 
 
 Exchange Building, ) 
 Boston. j 
 
 1889-91 
 
 j Nine stories ; granite front ; flat I 
 A roof ; fire-proof construction > 
 ( marble and oak finish. j 
 
 40 
 
 United States Trust ) 
 Co. Building, New V 
 
 1888 
 
 f Ten ^stories ; flat roof ; massive gran- "j 
 j ite front ; fire-proof construction ; ! 
 | extra foundation ; fixtures, rich j 
 
 60 
 
 York. ) 
 
 
 I. marble work and finish. j 
 
 
 Seven-story Office 1 
 
 
 ( Two massive stone fronts ; fire- 
 
 
 Building, New! 
 York (R. W. Gib- f 
 son). 
 
 1890 
 
 A proof construction; usual ma- - 
 ( chinery, fixtures, etc., complete.-) 
 
 37 
 
 Six-story Office ] 
 
 
 f Three brick and terra-cotta fronts; 
 
 
 Building, New! 
 
 
 j non-fire-proof, but with metal 
 
 9fi 
 
 York (R. W. Gib- [ 
 
 
 ! lathing; terra-cotta furring ; ma- 
 
 49 
 
 son). J 
 
 
 t chinery, elevators, etc. 
 
 
 
 
 fTwo stories and basement; tile' 
 
 
 Herald Building, } 
 New York City, f 
 
 1893 
 
 } and fire-proof roof, brick and 
 ', stone fronts ; fire-proof construc- 
 
 46 
 
 
 
 [ tion. 
 
 
 Auditorium Build- > 
 ing, Chicago. f 
 
 1887-9 
 
 (See description elsewhere.) 
 
 36 
 
 
 
 f Eleven stories ; flat roof; fire-proof] 
 
 
 Rookery Building, (_ 
 Chicago. j 
 
 1886 
 
 construction ; oak finish, marble i 
 ! floor and wainscot ; eleven -ele- f 
 
 32 
 
 
 
 I. vators. 
 
 
 
 
 f Twenty stories ; pitch roof ; gran-1 
 
 
 Masonic Temple, I 
 Chicago. f 
 
 1891 
 
 ite and terra-cotta fronts ; skele- 
 ton construction ; fire-proof ; rich \ 
 marble and metal work ; four- J 
 
 58 
 
 
 
 teen elevators. J 
 
 
 
 
 Seventeen stories ; flat roof ; Bed- ] 
 
 
 Old Colony Build- j 
 ing, Chicago. j 
 
 1893-4 
 
 ford stone, white brick, and ter- 
 ra-cotta fronts; skeleton con- \ 
 struction ; fire-proof ; rich marble 
 
 41 
 
 
 
 and metal work ; six elevators. J 
 
 
 
 
 'Twelve stories ; flat roof; first three] 
 
 
 N. Y. Life.Insur-] 
 
 
 stories dressed granite; terra- 
 
 
 ance Building, La ! 
 Salle and Monroe j 
 
 1893-4 
 
 cotta above; riveted skeleton 
 construction ; fire-proof ; machin- j 
 
 47 
 
 Streets, Chicago, j 
 
 
 ery ; rich marble work and finish; 
 
 
 
 
 [ small vaults ; five elevators. J 
 
 
 Stock Exchange! 
 Building, La Salle ! 
 and Washington [ 
 Streets, Chicago, j 
 
 1893-4 
 
 ( Thirteen stories ; flat roof ; skele- ) 
 < ton construction ; lire-proof ; rich V 
 ( terra-cotta facing. ) 
 
 35>i 
 
 Manhattan Build- 1 
 ing, Chicago.* f 
 
 1892 
 
 1 Sixteen stories ; five elevators ; two ) 
 -< fronts ; pressed brick, terra- > 
 ( cotta, and granite. ) 
 
 17H 
 
 * Jenney and Mundie, architects; see Inland Architect fox March, 1902. 
 
1462 COST OF BUILDINGS PER CUBIC FOOT. 
 
 ACTUAL COST OF BUILDINGS (Continued). 
 Office Building's. 
 
 Name of Building. 
 
 Date. 
 
 Character of Construction and 
 Finish. 
 
 Cost 
 per 
 Cu. Ft. 
 Cts. 
 
 Fort Dearborn) 
 Building, Chi- V 
 
 about 
 1893 
 
 j Twelve stories ; pressed brick and ) 
 
 %y 10 
 
 cago.* j 
 
 
 j terra-cotta. f 
 
 
 Isabella Building, ) 
 Chicago.* f 
 
 1893 
 
 ( Twelve stories ; granite and terra- ) 
 { cotta ; exposed on three sides ; > 
 ( tile roof. f 
 
 57M 
 
 Board of Trade ) 
 
 
 
 
 Building, Mon- v 
 
 1892-3 
 
 
 20 
 
 treal, Canada. j 
 
 
 
 
 Chamber of Com- ( 
 merce, Cincinnati, f 
 
 1887-8 
 
 1 Pitch roof ; seven stories ; granite ) 
 "I fronts ; fire-proof construction, f 
 
 26 
 
 
 
 f Ten stories ; flat roof ; stone facing' 
 
 
 Wain wright, Build-) 
 ing, St. Louis. f 
 
 1890 
 
 j first and second stories; rich 
 J terra-cotta above ; skeleton con- - 
 struction; fire-proof; four ele- 
 
 24% 
 
 
 
 t yators. 
 
 
 
 
 f Nine stories ; flat roof ; granite front 
 
 
 Equitable Building, ) 
 
 1891-2 
 
 two stories ; light brick and terra- | 
 -{ cotta above ; fire-proof construe- }- 
 
 42 
 
 Denver. j 
 
 
 tion; rich marble work; eight | 
 
 
 
 
 [ elevators. J 
 
 
 Ernest and Cramer ( 
 Building, Denver. }" 
 
 1890 
 
 j Eight stories ; flat roof ; brick ) 
 < front; mill construction; oak > 
 ( finish; three elevators. j 
 
 19 
 
 
 
 f Three stories ; flat roof ; one front 1 
 
 
 Bailey Block, Den-) 
 ver. f 
 
 1890 
 
 J store facing ; ordinary brick and ! 
 | timber construction ; plumbing f 
 L and steam heat ; pine finish. J 
 
 sy 2 
 
 
 
 f Ten stories ; flat roof ; brick and } 
 
 
 Crocker Building, ( 
 San Francisco. j 
 
 1890 
 
 1 terra-cotta fronts ; skeleton con- I 
 j struction ; fire-proof ; elaborate f 
 
 63 
 
 
 
 [ finish, marble, etc. 
 
 
 
 
 !Five stories; flat roof; buff brick) 
 
 
 Bradbury Building, ) 
 Los Angeles, Cal. J 
 
 1891 
 
 and terra-cotta walls ; fire-proof ( 
 construction; oak finish; two f 
 
 32 
 
 
 
 elevators. 
 
 
 
 
 Seven stories; flat roof; pressed- 1 
 
 
 Endicott Building, ) 
 St. Paul, Minn. f 
 
 1887-9 
 
 \ brick front ; fire-proof construe- ! 
 1 tion ; marble wainscot ; five f 
 
 29 
 
 
 
 I elevators. 
 
 
 
 
 f Three stories; two stone fronts;] 
 
 
 Office Building, ) 
 
 
 j fire-proof ; usual plumbing, heat- | 
 
 
 Connecticut (R. V 
 
 1891 
 
 -{ ing plant, fixtures, etc. ; rich J- 
 
 50 
 
 W. Gibson). j 
 
 
 | marble work ; stories of moder- | 
 
 
 
 
 t ate height. 
 
 
 Five Office Build- } 
 ings in Minnesota, j 
 
 1893-6 
 
 ( Eight- to twelve-story buildings ) 
 < about of the character of the |- 
 ( Rookery, Chicago. j 
 
 29i-35 
 
 Board of Trade) 
 Building, Duluth, V 
 
 1895 
 
 f Seven stories; two fronts; fire-1 
 (proof ; handsomely finished ; ! 
 equal to the Old Colony in j 
 
 38 
 
 Minn. ) 
 
 
 Chicago. J 
 
 
 Seven-story Office ) 
 Building, Mon- J- 
 
 1903 
 
 iOne front ; fire-proof ; about the ) 
 type of the Union Trust Build- c 
 
 36 
 
 treal. j 
 
 
 ing in St. Louis. 
 
 
 Ten - story O ffi c e ) 
 Building, Chicago, j 
 
 1903 
 
 5qual to Old Colony Building. 
 
 37f 
 
 * Jenney and Mundie, architects. 
 
COST OF BUILDINGS PER CUBIC FOOT. 1463 
 
 ACTUAL COST OF BUILDINGS (Continued). 
 Warehouses and Stores. 
 
 Name of Building. 
 
 Date. 
 
 Character of Construction and 
 Finish. 
 
 Cost 
 per 
 Cu. Ft. 
 Cts. 
 
 Eight-story Office ) 
 
 
 
 
 and Bank Build- > 
 
 1902 
 
 j One front ; fire-proof ; equal to the \ 
 
 39 
 
 ing, San Francisco ) 
 
 
 I Brown Hotel, Denver. j 
 
 
 Eight-story Bank 
 
 
 
 
 and Office Build- V 
 
 1904 
 
 Fire-proof; quite elaborate. 
 
 41 
 
 ing, Atlanta. ) 
 
 
 
 
 Warehouse, Minne- j_ 
 sota. f 
 
 1896 
 
 ( Five stories, fire-proof ; for very ) 
 < heavy goods ; good front ; steam V 
 ( heat ; plenty of elevators, etc. ) 
 
 w 
 
 Seven-story Ware- } 
 
 1 SQS 
 
 I Mill construction ; plain brick 1 
 
 
 house, Minnesota, f 
 
 ioyo 
 
 1 walls. 
 
 "713 
 
 Seven-story Ware- | 
 house, Cincinnati, j 
 
 1904 
 
 j Fire-proof ; cement floors ; no 1 
 ( finish. j 
 
 25% 
 
 Store Building, New J 
 
 1903 
 
 j Four stories; fire-proof; plain ( 
 
 ql 
 
 Orleans. 
 
 
 1 finish., \ 
 
 Ol 
 
 Department Store, ) 
 Chicago. J 
 
 1900 
 
 j Six stories ; fire-proof construction ; j 
 ) one front, modern. j 
 
 29 
 
 Leiter Building, Chi- ) 
 cago.* J 
 
 1892 
 
 (Wholesale and retail store; eight) 
 < stories ; granite three sides ; brick V 
 ( on alley. ) 
 
 1$ 
 
 Hotels and Apartment Buildings. 
 
 Hotel, New York ) 
 
 
 f Fourteen stories; brick and terra- ) 
 j cotta front ; skeleton construe- ! 
 
 (R. W. Gibson), f 
 
 
 , tion, riveted; fire-proof; usual; 
 
 
 
 I plumbing, machinery, etc. 
 
 
 
 j Triangular plan ; three stone 
 fronts; considerable carving; 
 
 
 
 nine stories ; flat roof ; all rooms 
 
 Brown Palace Hotel, ) 
 
 1892 
 
 face street; 350 guest rooms, 160 
 -{ private baths, 17 public toilet } 
 
 j^enver. ) 
 
 
 rooms, all tiled; steel construc- 
 
 
 
 tion; fire-proof; provided with 
 
 
 
 electric light, ice and refrigerator 
 L plant ; laundry ; 4 elevators. 
 
 Eight-story Apart- ) 
 
 
 
 ment House, New V 
 
 1901 
 
 Fireproof; elaborately finished. 
 
 York. \ 
 
 
 
 Two Apartment! 
 Houses, New York f 
 
 1903 
 
 ( Fire-proof, but no more elaborate 1 
 ( than above. f 
 
 Seven-story Apart- ) 
 ment House, Pitts- > 
 burg. ) 
 
 1903 
 
 1 Fire-proof ; hard -wood finish ; not ) 
 ( elegant; two elevators. j 
 
 The Lenox (Apart- j 
 ments), Cleveland, V 
 Ohio. \ 
 
 about 
 1889 
 
 ( Five stories ; flat roof ; pressed- ) 
 < brick front ; partly slow-burning v 
 ( construction. ) 
 
 Club Buildings, Y. M. C. A., Etc. 
 
 Athletic Club Build- j 
 ing, Denver, Colo, f 
 
 1890-1 
 
 fFour stories; flat roof; one front 1 
 
 I pressed brick ; thoroughly equip- 
 ped with swimming and Turk- | 
 
 \ ish baths, gymnasium, hand-ball } 
 room, billiard-room, social 
 rooms, etc. ; brick walls, wood | 
 
 ( construction. J 
 
 * Jenney and Mundie, architects. 
 
1464 COST OF BUILDINGS PER CUBIC FOOT. 
 ACTUAL COST OF BUILDINGS (Continued) 
 Club Buildings, Y. M. C. A., Etc. 
 
 Name of Building. 
 
 Date. 
 
 Character of Construction and 
 Finish. 
 
 Cost 
 per 
 Cu. Ft. 
 
 Cts. 
 
 Denver Club Build- ) 
 ing, Denver, Colo, f 
 
 Standard Club Ho., ) 
 Michigan Avenue / 
 
 1887-8 
 1887 
 
 I Three stories and high-pitch roof ;^| 
 ! stone ashlar, four sides ; slate ( 
 j roof; wood construction; oak f 
 [ and pine finish. J 
 
 24 
 
 12 9 /io 
 
 Chicago. ) 
 Y. M. C. A. Build- | 
 
 
 
 13 
 
 ing, Cleveland, O. j 
 
 
 
 
 School, College, and Seminary Building's. 
 
 
 
 f Three stories and basement ; recita- 1 
 
 
 Wingate Hall, State ) 
 
 
 tion- and drawing-rooms; brick j 
 
 
 College, Orono, V 
 
 1891-2 
 
 with granite trimmings; slate }- 
 
 10M 
 
 Me. | 
 
 
 roof; wood floors; brick par- 
 
 
 
 
 titions. J 
 
 
 
 
 JTwo stories and basement;! 
 
 
 Grammar-school) 
 Building, Denver, V 
 
 1891-2 
 
 pressed-brick walls; shingle and | 
 tin roof; wooden floors; brick ^ 
 
 93^ 
 
 Colo., 8 rooms. ) 
 
 
 partitions; cost, basement floor | 
 
 
 
 
 to second-story ceiling. 
 
 
 
 
 [Pressed brick; wooden-floor con-] 
 
 
 Smedley School,) 
 Denver, 4 rooms, j 
 
 1902 
 
 1 struction ; shingle roof ; slate ! 
 ] blackboard; janitor's rooms in f 
 
 10% 
 
 
 
 [ basement ; two large furnaces. J 
 
 
 Clayton School, ") 
 
 
 
 
 Denver, 15 rooms, | 
 2 lunchrrooms, 6 ' 
 
 1 OA1 
 
 f Light pressed brick ; wooden-floor"] 
 J construction; otherwise first- ( 
 
 
 rooms for janitor, [ 
 
 iyui 
 
 [ class building; fan system heat- [ 
 
 10 
 
 and large hall in | 
 
 
 1, ing and ventilation. J 
 
 
 attic. J 
 
 
 
 
 Ursuline Convent, I 
 Cleveland, O. f 
 
 1890 
 
 (Three stories ; pitch roof; brick) 
 with stone trimmings ; ordinary > 
 wood construction. \ 
 
 15 
 
 
 
 [Six buildings grouped around a] 
 
 
 Hill Theological) 
 Seminary, St. > 
 Paul, Minn. ) 
 
 
 quadrangle ; ordinary construe- | 
 tion; library, gymnasium, and 1 
 i staircases fire-proof; corridor ; 
 walls face brick; oak finish;] 
 
 11 
 
 
 
 L cost per cubic foot above grade, j 
 (This building, covering 21,000 feet] 
 
 
 Leland Stanford Jr. ) 
 Museum, PaloV 
 Alto, Cal. } 
 
 1891 
 
 1 and containing over 1,100,000 
 J cubic feet of space, is built en- ! 
 1 tirely of Portland-cement con- f 
 crete walls, floors, and roof 
 
 . 18 
 
 
 
 L and is fireproof throughout. J 
 f A large three-story building, most- 1 
 
 
 
 
 ly fire-proof construction. Cubi- 
 
 
 Newark High ) 
 
 
 cal contents from basement floor | 
 
 
 School, Newark, V 
 
 1897-8 
 
 { to mean point in roof, 1,803,000 
 
 10M 
 
 [ N. J. f 
 
 
 cu. ft. For description of build- 
 
 
 
 
 ing, list of contracts, etc., see 
 
 
 
 
 L American Architect, July 9, 1898. J 
 
 
COST OF BUILDINGS PER CUBIC FOOT. 1465 
 ACTUAL COST OF BUILDINGS (Continued) . 
 School-houses. 
 
 Name of Building. 
 
 Date. 
 
 Character of Construction and 
 Finish. 
 
 Cost 
 per 
 Cu. Ft. 
 
 Cts. 
 
 St. Louis. 
 Eugene Field School 
 Edward Wyman Sch. 
 Horace Mann School. 
 Ralph Waldo Emer- 
 son School. 
 Cote Brilliante School 
 Henry Blow School. 
 
 
 Cost per 
 Room. 
 1 f $5,600 
 5,600 
 I All first-class buildings, 6,007 
 } described in Brickbuilder -{ 
 for October, 1903. 5,636 
 6,758 
 J i. 6,243 
 
 15% 
 14 
 14Ao 
 
 14% 
 17 
 16 
 
 School-houses of entirely fire-proof construction, built in Boston, 1892- 
 1903, cost from 22.39 cts. per cu. ft. for the South Boston High School 
 to 24.98 cts. for the Heath Street School. The Dorchester High 
 School, which is fire-proof construction except for a plank roof, cost 
 16.33 cts. Schools of ordinary construction range from 16.58 to 24 
 cts. per cu. ft. Brickbuilder, August, 1903. 
 
 Public Library.New ) 
 London, Conn. j 
 
 Howard Memorial j 
 Library, New Or- v 
 leans, La. \ 
 
 Congressional, / 
 Washington, D.C. f 
 
 1889-90 
 
 1888 
 
 Hospital Building, ) 
 New York (R. W. V 
 Gibson). ) 
 
 Hospital Building, ) 
 New York (R. W. V 
 Gibson). j 
 
 1890-5 
 1890-5 
 
 Libraries. 
 
 j One-story stone building; ordi- ] 
 ( nary construction. j 
 
 Including some of its furnishings. 
 
 Hospitals. 
 
 f Seven stories ; pressed-brick front ; *| 
 
 stone trimmings; fireproof; 
 1 thorough heating and ventilat- Y 
 I ing plant; plumbing; much 
 
 marble and tiling. 
 Six stories; pressed-brick front ',} 
 stone trimmings ; part fireproof | 
 and part non-fireproof, but with }- 
 metal lathing and terra-cotta f ur- 
 ring ; plumbing, steam plant, etc. J 
 
 Churches. 
 
 44 
 
 40 
 
 32 
 
 Grace M.E. Church, ) 
 
 
 1 Two-story wooden building; tower^ 
 and spire; slate roof; copper | 
 
 
 Cambridgeport, V 
 Mass. ) 
 
 1886-7 
 
 metal- work; cost includes fur- } 
 naces, pews, frescoing, and gas- 
 
 8H 
 
 
 
 fixtures. 
 
 
 
 
 f Two-story stone thurch; stone] 
 
 / 
 
 
 
 j tower 71 feet high, with wood | 
 
 
 Christ M.E. Church, ) 
 Denver, Colo. f 
 
 1889-91 
 
 ; spire -108 feet high, above ; 1 
 | shingle roof ; steam heat ; oak fin- [ 
 
 21 
 
 
 
 ish in second story; pews, fres- 
 
 
 
 
 <_ coing, etc. J 
 
 
 Zion Temple, Syna- ) 
 
 
 
 
 gogue, Ogden Av., /- 
 
 1885 
 
 
 7/io 
 
 Chicago. \ 
 
 
 
 
1466 COST OF BUILDINGS PER CUBIC FOOT. 
 
 ACTUAL COST OF BUILDINGS. (Con tinned). 
 Theatres. 
 
 Name of Building. 
 
 Date. 
 
 Character of Construction and 
 Finish. 
 
 Cost 
 per 
 Cu. Ft. 
 Cts. 
 
 Theatre, Duluth, ) 
 Minn.* f 
 
 Schiller Building, or ) 
 German Theatre, V 
 Chicago. ) 
 
 Park pavilion 
 
 1893 
 1891 
 
 Mi 
 
 1898 
 1895 
 
 1893 
 
 1 Six stories; brick, stone, and teria-^) 
 cotta ; two fronts absolutely ! 
 fireproof and elegantly deco- f 
 rated and finished. 
 Seventeen stories; flat roof, faced) 
 j with terra cotta ; skeleton con- 1 
 | struction ; fireproof; rich marble j 
 I. work ; theatre in four stories. J 
 
 scellaneous. 
 
 i Built in middle West ; all wood and ) 
 glass; two stories, dining-room, V 
 dancing-hall, etc. ) 
 Exposed iron construction and ) 
 brick walls. f 
 I Steel construction, fire-proofed, I 
 | Sioux Falls, Jasper; first story, f 
 j pressed brick above ; tile arches ; i 
 | four stories and basement. { 
 
 
 American Express j 
 stables, Chicago, t f 
 
 * Traphagen & Fitspatrick, architects, t Jenney & Mundie, architects. 
 
 Dwellings. 
 
 (See also pages 1458, 1460.) 
 City dwellings in Chicago, designed by Adler & Sullivan, architects. 
 
 Cost per cubic foot from 17 to 20 cts. 
 
 Of dwellings designed by the author and built in Boston in 1886, 
 the average cost of eight- and ten-room wooden houses per 
 
 cubic foot of habitable space, including cellar, was about 11 cts. 
 
 In Denver, Colo., the cost of a first-class stone house (isolated), 
 with hard- wood finish, indirect steam heat, extra plumbing, dec- 
 orations, etc., complete, was in 1890 about. 
 
 Brick houses of ten rooms, pine finish, furnace heat, good plumb- 
 jllar floor, but not including unoccupied 
 
 27 cts. 
 
 , une finish, furnace heat, good plumb- 
 ing, etc., cost above cellar floor, but not including unoccupied 
 
 roof space, in 1892 14 cts 
 
 Cheap eight-room brick cottages of one and one-half or two stories; 
 bath-room and furnace ; cubic space reckoned from cellar floor, 
 but not including unoccupied roof space, were built in Den- 
 ver, in 1894, for about 10 cts. 
 
 Cost of Different Kinds of Work per Cubic Foot 
 of Building". 
 
 In Fireproof for March, 1903, Mr. F. W. Fitzpatrick gave some 
 figures showing the proportionate cost of the different branches 
 of work which go to make up the completed building. Believ- 
 ing that these data will be found useful in making up approxi- 
 mate estimates, the author obtained permission to use them 
 herein. 
 
 The following figures represent the actual cost of a prominent 
 ten-story of/ice building, 60' X 130', built in the middle West, 
 a No. 1 high grade fire-proof structure, with two street fronts 
 faced with granite; pile foundation. 
 
COST OF BUILDINGS PER SQUARE FOOT. 1467 
 
 (Figures are in cents per cubic foot of building.) 
 
 The foundation cost 1 
 
 Steel framing 2> 
 
 Granite and all masonry UK 
 
 C9rnice, roofs, and skylights. . . 
 
 Fire-proof floors % 
 
 Partitions (tile) % 
 
 All plastering and stucco 1>| 
 
 Elevator fronts and all orna- 
 mental metal- work 2 
 
 Heating 
 
 Plumbing 
 
 Elevators 1 
 
 Stairs, scenic structural fram- 
 ing, "making ends meet," 
 lamp fixtures, etc. What 
 might be called a fair amount 
 for ' 'contingencies " in such 
 a building, including lesser 
 items not mentioned here 
 but grouped together 423/ 12 , 
 
 Architect 's fee 1% 
 
 Total. 
 
 Plumbing 
 Heating 
 
 Marble-work . 
 
 Hardware %5 
 
 Joiner work \y 
 
 Glass. . '. . . 5/ 12 
 
 Painting and varnish 7 /6o 
 
 Electric wiring % 
 
 The Chicago post-office, a building of 12,000,000 cubic feet 
 and of monumental character and finish, cost, in some of its 
 items, as follows: 
 
 (Figures are in cents per cubic foot of entire building.) 
 
 Its foundation cost 1% Ornamental metal -work 
 
 The steel framing 2 ,V Marble 5% 
 
 Granite and masonry 13j/ 
 
 Fire-proof floors % 
 
 Plaster, plain and ornamental . 1% 
 
 It may be noticed that the relative cost of several of these 
 items was identically the same as in the office building. The 
 total cost of this building was 42J cts. per cubic foot. 
 
 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 
 as by the cubic foot, as there are few or no interior partitions, 
 and usually no plastering or interior finish. 
 
 Iron Building's. l ' Roughly speaking, the cost of one-story 
 iron buildings, complete, is, for sheds and storage-houses, 40 to 
 60 cts. per square foot of ground, and for such buildings as ma- 
 chine-shops, foundries, and electric-light plants, that are pro- 
 vided with travelling cranes, the cost is from 60 to 90 cts. per 
 square foot of ground covered." (H. G. Tyrrell.) 
 Textile Factories. See pages 723-725. 
 Exposition Buildings. The cost of the World's Fair 
 buildings (Chicago, 1893) per square foot of ground covered, in- 
 cluding sculpture and decoration, as given by E. C. Shankland, 
 chief engineer, was as follows: 
 
 Manufactures and Liberal Arts Building. . . .$1 .39 
 
 Transportation Building s 1 . 08 
 
 Electricity Building * 1 .69 
 
 Machinery Hall 2. 12 
 
 Agricultural Building 1 . 44 
 
 Administration Building 9 . 18 
 
 Horticultraul Building 1.41 
 
 Mines and Mining Building 1 . 04 
 
 Fisheries Building 2.35 
 
 Forestry Building 75 
 
1468 
 
 DEPRECIATION OF BUILDINGS. 
 
 Cost of Structures for the St. Louis Exposition 
 
 (1904). The following figures are issued by Isaac S. Taylor, 
 Director of Works, of the World's Fair, showing the area and 
 cost of the principal exhibition buildings. The total area of 
 twenty-two buildings is 123.51 acres, and the total cost $6,939,- 
 992.26. The cost is for the bare buildings, and does not include 
 sculptural or other decorations, or the architect's compensation. 
 
 
 Dimensions. 
 
 Area 
 in 
 Acres 
 
 Cost. 
 
 Cost 
 per 
 Sq. Ft. 
 
 Art Building. . . . 
 
 161' X 346' 
 144' X 423' 
 106' X 150' 
 200' X 736' 
 136' X 136' 
 525' X 750' 
 525' X 750' 
 525' X 758' 
 525' XI, 200' 
 525' X 758' 
 525' XI, 200' 
 525' XI, 000' 
 301'X326f 
 525' XI, 300' 
 374' X 782' 
 500' XI, 600' 
 300' X 600' 
 195' in diam- 
 eter, exclusive 
 of annex. 
 
 1.42 
 3.14 
 0.41 
 3.86 
 0.42 
 9.08 
 8.80 
 7.70 
 13.47 
 6.67 
 10.28 
 9.48 
 2.25 
 15.70 
 5.42 
 .18.62 
 4.07 
 
 V 1.09 
 
 [$967,833.90 
 
 39,388.99 
 328,980.00 
 45,000.00 
 488,848.50 
 471,820.95 
 323,950.75 
 711,510.00 
 408,531.57 
 704,067.96 
 509,110.50 
 135,480.00 
 674,853.42 
 225,342.27 
 520,491.07 
 168,883.38 
 
 215,899.00 
 
 $5.45 
 
 2.48 
 2.23 
 2.43 
 1.24 
 1.20 
 0.81 
 1.13 
 1.03 
 1.12 
 0.97 
 1.38 
 0.99 
 0.77 
 0.58 
 0.94 
 
 Two Art Pavilions, each 
 
 Art Building Annex 
 
 Government Building. . . 
 
 G9vernment Fisheries Building 
 Mines and Metallurgy 
 
 Liberal Arts. . . 
 
 Education and Social Economy.. 
 Manufactures. . 
 
 Electricity 
 
 Varied Industries. . . 
 
 Machinery 
 
 Steam, Gas, and Fuel Building. . 
 Transportation ... 
 
 Horticulture. 
 
 Agriculture. . . ... 
 
 Forestry, Fish, and Game 
 
 Festival Hall 4 
 
 
 Cost of United States Government Buildings. 
 
 There was published in 1900, by the Treasury Department, a 
 history of the public buildings, giving the cost, and in the 
 Architects and Builders' Magazine for Aug. 1902 and the Inland 
 Architect for April 1902, was published a list of 287 buildings, 
 giving the cost per cubic foot, material used for walls, and date 
 of erection. As a rule these buildings have cost more than 
 private buildings, so that their cost cannot be used as a guide, 
 except for government buildings. 
 
 DEPRECIATION OF BUILDINGS. 
 
 TIFFANY'S ESTIMATE OF DEPRECIATION. (Used by U. S. Gov't.) 
 The figures given on page 1458 are for NEW buildings. To 
 ascertain the present value, a discount between old and new 
 should be made as follows: 
 
 Per Cent per Year. 
 
 Brick, occupied by owner. 1 to 1 J 
 
 Brick, ' ' " tenant 1 J to 1 J 
 
 Frame, " " owner 2 to 2J 
 
 Frame, " " tenant 2J to 3 
 
DEPRECIATION OF BUILDINGS. 
 
 1469 
 
 If built of ' ' long-leaf " yellow pine, or of spruce, found in New 
 England States, add 20 to 30 per cent., or if of "short-leaf" yel- 
 low pine, add 40 to 50 per cent, to his figure. If, of redwood or 
 cedar, found on Pacific Coast, charge only about half his esti- 
 mates, which are for white pine or white pine with oak framing 
 timbers. 
 
 These figures for depreciation are to include buildings where 
 ordinary repairs have been made. If extraordinary repairs have 
 been made, the discount should not be so heavy. Exercise good 
 judgment as to depreciation. 
 
 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 ma- 
 terials and tabulated the result of his investigations in the fol- 
 lowing form: 
 
 Material in Building. 
 
 Frame 
 Dwelling. 
 
 Brick 
 Dwelling 
 (Shingle 
 Roof). 
 
 Frame 
 
 Store. 
 
 Brick 
 
 Store 
 (Shingle 
 Roof). 
 
 i 
 
 .'- 
 
 jit 
 
 oT 
 
 3 
 
 II 
 
 <i 
 
 & 
 
 3 
 
 o 
 
 ^2 a 
 g 1 ^ 
 
 1 
 
 p2 
 
 34 
 16 
 16 
 6 
 
 2 
 
 8 
 
 | 
 
 8 
 5 
 6 
 
 8 
 
 Brick 
 
 
 
 75 
 
 30 
 7 
 7 
 16 
 40 
 
 it 
 
 14 
 14 
 6 
 
 2} 
 
 
 
 66 
 30 
 6 
 6 
 16 
 40 
 
 50 
 13 
 30 
 30 
 20 
 30 
 30 
 13 
 20 
 16 
 30 
 66 
 
 Plastering 
 
 20 
 5 
 7 
 16 
 40 
 30 
 50 
 20 
 30 
 30 
 30 
 40 
 30 
 20 
 20 
 16 
 25 
 50 
 
 5 
 
 20 
 
 14 
 6 
 24 
 
 5 
 34 
 34 
 
 it 
 i 1 
 
 5 
 6 
 4 
 
 2 
 
 16 
 5 
 5 
 16 
 30 
 30 
 40 
 13 
 25 
 25 
 20 
 30 
 30 
 13 
 20 
 16 
 25 
 40 
 
 6 
 20 
 20 
 6 
 
 34 
 
 8 
 4 
 4 
 5 
 34 
 34 
 8 
 5 
 6 
 4 
 24 
 
 Painting, outside 
 
 Painting, inside 
 
 Cornice 
 
 Weather-boarding. . 
 
 Sheathing 
 
 50 
 20 
 30 
 30 
 30 
 40 
 30 
 20 
 20 
 16 
 40 
 75 
 
 2 
 5 
 
 34 
 
 24 
 34 
 5 
 5 
 6 
 
 Flooring. . 
 
 Doors, complete 
 
 Windows, complete 
 Stairs and newel. 
 
 Base. ... 
 
 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 companies in twenty-seven cities and towns of the 
 eleven Western States. 
 
1470 DIMENSIONS OF FURNITURE. 
 
 DIMENSIONS AND DATA USEFUL IN THE PRE- 
 PARATION OF PLANS. 
 
 Dimensions for Furniture. For the convenience of 
 draughtsmen when designing furniture or providing space for a 
 special article the following dimensions are given : * 
 
 Chairs and Seats. The average figures taken from a variety of 
 good chairs are: Height of the seat above the floor, 18"; depth 
 of the seat, 19"; the top of the back above the floor, 38". 
 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" above the seat. The slope of the back should not 
 be more than one fifth the depth of the seat. A lounge is 6' long 
 and about 30" wide. 
 
 Tables vary in shape and size almost as much as chairs. Writ- 
 ing- and dining-tables are made 2' 5" high, and the species oi 
 sideboard called a carving-table is made 3' high to the principal 
 shelf but tables for general use are 2' 6" high. 
 
 Dining-tables are made from 3' 6" to 4' wide and to extend 
 from 12' to 16' feet 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' clear 
 space between it and the floor. 
 
 The smallest size practicable for the knee-holes of desks and 
 library tables is 2' high by I/ 8" wide, the width to be in- 
 creased as much as possible. 
 
 Bedsteads are classed as single, three quarters, and double. A 
 single bed is 3' to 4' wide inside; a three-quarter bed, 4' to 
 4' 6"; a double bed, 5'. All bedsteads are 6' 6" to 6' 8" long 
 inside. Footboards are from 2' 6" to 3' 6" and headboards 
 from 5' to 6' 6" high. Single beds for dormitories are often made 
 only 2' 8" wide. 
 
 Bureaus vary in shape and size to such an extent that it is 
 impossible to say that any dimension is fixed. 
 
 Convenient sizes are: body, 3' 5" wide, 1' 6" deep, 2' 6" high; 
 or 4' wide, 1' 8" deep, 3' high. 
 
 * Many of these dimensions were first contri . 10 the American Archi- 
 tect of November 10, 1894, by Mr. Alvin C. Nye. 
 
DIMENSIONS OF PLUMBING FIXTURES. 1471 
 
 Commodes are 1' 6" square on the top and 2' 6" high. 
 
 Chiffoniers are about 3' wide, 1' 8" deep, 4' 4" high. 
 
 Cheval glasses are made, if large, 6' 4" high, 3' 2" wide. If 
 email, 5' high, I/ 8" wide. If medium, 5' 6" high, 2' wide. 
 
 TFas/i-s&mds of large sizes are 3' long, 1' 6" wide, and 2' 1" 
 high. Small sizes are 2' 4" to 2' 8" long. 
 
 Wardrobes may be 8' high, 2 / deep, and 4' 6" wide; or, 6' 9'' 
 high, 1' 5" deep, and 3' wide. 
 
 Sideboards may be 4' to 6' long and from 20" to 2' 2" deep. 
 
 Upright pianos vary from 4' 10" to 5' 6" in length, from 4 
 to 4' 9" in height, and are about 2' 4" deep over all. 
 
 Square pianos are about 6' 8" long by 3' 4" deep. 
 
 Billiard-tables (Collender), 4 / X8 / , 4' 2"X9', and 5'XlO'. 
 Size of room required 13'Xl7', 14'X18', and 15 / X20 / respec- 
 tively. 
 
 Dimensions of Plumbing Fixtures. Enamelled-iron 
 Bath-tubs. Standard sizes for roll-rim baths with sloping end 
 are: Nominal lengths, 4', 4J', 5', 5J', and 6'; width over all, 30" 
 to 34". Specially narrow tubs are made 25" to 29" wide. The 
 actual length over rim is usually 1" or 2" more than the nominal 
 length, and 2" will include ordinary overflow-pipe. 
 
 Wash-basins. Crockery basins, to go with marble slabs, are 
 made round and oval. Round bowls are made 10", 12", 13". 
 14", and 16" in diameter, measured from the outside of the rim. 
 Oval bowls, 14"X17 // , 15"X19", and 16"X21". The 12" and 
 14" round, and 15"Xl9" oval, are most commonly used. 
 
 Marble basin-slabs may be 20"X24", 20"X30", 22"X28", or 
 24"X30", the last being a very common size. Can be made any 
 size to order. They should be 1J" thick, countersunk on top, 
 and should have moulded edges where exposed. 
 
 Corner slabs are commonly made 21"X21" and 24"X24". 
 Marble backs are usually 8" or 10" high, and sometimes 12". 
 
 Enamelled-iron wash-basins or lavatories made in one piece: 
 Common sizes are 16"X20", 11"X14" basin; 18"X21", 11"X 
 15" basin; 18"X24", 12"X15" basin; back, 10i" high. The 
 smallest-size wash-basin is 13" wide at the back. 
 
 Corner basins, 12J"Xl2i", 12" round basin; 15"X15", 11"X 
 14" basin, 16"X16", 11"X14" basin, 19"X19", 11"X15" basin. 
 The standard height of wash-basins is 2' 6" from the floor. 
 
 Foot-baths, enamelled iron, roll rim, are 22J"X19"; width, in- 
 cluding fittings, V 11"; height 17"; depth inside 11". 
 
1472 DIMENSIONS OF PLUMBING FIXTURES. 
 
 Seat-baths, enamelled iron, average about 32" long over fittings, 
 and 27" wide. 
 
 Water-closets. The dimensions of water-closet bowls vary con- 
 siderably, the following being about an average: Width of bowl 
 over all, 13"; depth from wall to front of seat, 23"; height from 
 floor to seat, 17"; width of seat, 15" to 16". Closets with low- 
 down tanks measure about 28" from front of seat to wall. The 
 distance from centre of outlet opening to the walls, or the 
 "roughing in" dimensions, are given in manufacturers' cata- 
 logues, as they vary with different closets. The smallest space 
 permissible for water-closet compartments, where doors open 
 out, is 2' 4"X4' 0". If the door opens in, the compartment 
 should be 3'X5'. 
 
 Closet-ranges, used in schools and factories, are made 24", 27", 
 and 30", centre to centre of partitions. For grade schools, 24" 
 is ample, and for factories, 27", The range usually occupies a 
 space 28" in depth if set against a wall. 
 
 Urinal-stalls should be 24" to 27", centre to centre of parti- 
 tions, depth of partitions, 20" or 22"; of ends, 2'; of bottom 
 slab, 2'; height of partitions, 4' 6" to 5' 6". 
 
 Kitchen-sinks of cast iron are made in a great variety of sizes, 
 those most commonly used being 16"X24", 18"X30", 18"X36", 
 20"X30" and 20"X36" ; 24"X50" being the largest size for 
 enamelled sinks. The depth inside for the sizes given is 6". 
 Plain cast-iron sinks are made as large as 32" X 56" or 28" X 78". 
 Steel sinks are made in all of the above sizes up to 20" X 40". 
 
 Common sizes of Porcelain sinks are 20"X30", 23"X36", 24" 
 X42". 
 
 Cast-iron slop-sinks, common sizes, are 16"X16", 16"X20", 
 18"X22", 20''X24"; 12" deep. 
 
 Copper Pantry-sinks. Common sizes are 12"X18", 14"X20", 
 and 16"X24". 
 
 Laundry-tubs of slate or soapstone are commonly made 2' wide 
 over all, and 16" in depth. Lengths over all, two-part tubs, 
 4' 0" and 4' 6"; three-part tubs, 6' 0", 6' 6", and 7'. 
 
 Earthen and porcelain tubs come separately, and are connected 
 up as required. 
 
 The dimensions of each tub are 2' or 2' 7J" in length, 2' 1 J" 
 in width, and 15" in depth inside. 
 
 The length required for two 2' tubs is 4' l"[j for three tubs, 
 6' 2"; and for four tubs, 8' 3". 
 
DIMENSIONS OF CARRIAGES AND CARS. 1473 
 
 Wolff's roll-rim enamelled-iron wash-tubs are 55" over all, for 
 fcwo tubs, and 82" for three tubs. 
 
 Range-boilers are 12" diameter for 30-gallon boilers, 14" for 
 40-gallon, 16" for 52- and 63-gallon, 22" for 100- and 120-gallon. 
 
 Dimensions of Carriages. Covered Buggy (Goddard). 
 Length over all, 14'; width, 5'; height, 7' 4". Will turn in 
 space from 14' to 20' square, according to skill. 
 
 Coupe. Length over all, 18'; width, 6'; height, 6' 6". 
 
 Buggy (Piano Box). Length over all, 14'; width, 4' 10". 
 
 Landau. Length over all, 19' 6"; width, 6' 3"; height, 6' 3"; 
 length of pole, 8' 0". 
 
 Stanhope Gig (2 Wheels). Length over all, 10' 6"; width, 5' 
 8"; height, 7' 6". 
 
 Victoria. Length, without pole, 9' 6"; length of pole, 8'; 
 width over all, 5' 4". 
 
 Light Brougham. Length, without pole or shaft, 9' to 11'; 
 width over all, 5' 4"; height, 6' 4". 
 
 Dimensions and Weight of Fire-Engines. From 
 measurements of different fire-engines belonging to the city of 
 Boston, it was found that the greatest length, including pole, 
 was 22' 6". The widths varied from 5' to 5' 11", the average 
 height being 8' 8". 
 
 The average weight of 29 engines is 8,000 Ibs.; the greatest 
 weight being 9,420 Ibs., and the least 4,780 Ibs. 
 
 Dimensions and Weight of Hose Carriages. Ex- 
 treme length with horse, 19' 6", without horse, 17' 6"; .width, 
 5' 9" to 7' 0"; height, from 6' 8" to 7' 0"; average weight of 11 
 carriages, 2,943 Ibs. ; greatest weight, 3,500; least weight, 2,120. 
 
 Dimensions and Weight of Ladder Wagons. 
 Length of truck, 33'; total length, with ladders on, 45'; width, 
 6' 2"; average weight of 12 wagons, 6,660 Ibs.; greatest weight, 
 8,800; least, 4,350. 
 
 Dimensions of Locomotives and Cars, The dimen- 
 sions of locomotives and freight-cars vary considerably, but the 
 following will cover those in common use: 
 
 Locomotives. 15' 4" to 15' 10" to top of stack from top of 
 rail; extreme width of cab, 10' 2". Doors to admit locomo- 
 tives should be 12' to 13' wide arid 18' high. 
 
 Furniture-cars are 14' 1", top of track to top of brake-staff; 
 floor 3' 8" from track; extreme width, 9' 10". 
 
 Stock-cars, 13' 5", top of track to top of brake-staff; floor, 
 4' 0" from track; extreme width, 9' 8". 
 
1474 DIMENSIONS OF CARS, HORSE-STALLS, ETC. 
 
 Refrigerator-cars, 14' 6", top of track to top of brake-staff; 
 floor, 4' 0" from track; extreme width, 9' 7". 
 
 Ordinary freight-cars are about 13' 0" high to top of brake- 
 staff and 9' 4" in extreme width. 
 
 The height of floor of freight-cars varies from 3' 8" to 4' 0" 
 above top of track, for standard gauge, and 3' 0" to 3' 6" for 
 narrow-gauge cars. 
 
 Passenger-coaches vary from 14' to 16' in height and 10' to 11' 
 in width. Doors to admit cars should give at least 12" clearance 
 on each side, and 2' overhead. 
 
 Street trolley-cars are about 8' 6" wide for the car proper, and 
 the steps project about 8". Height from track to top of coach, 
 11' 6"; trolley-stand is 18" higher. Length up to 42'. Trucks 
 for a 41' 6" car are about 24' apart. Wheel-base, 4' 0" centre to 
 centre. Radius of shortest curve in Denver, 35' 0" to midway 
 between rails. 
 
 The gauge of a railroad track is the distance between the 
 inner sides of the heads of the two rails. 
 
 The standard or "broad" gauge is 4' 8J"; standard narrow 
 gauge, 3' 3J". 
 
 Capacity of Freight-cars. Car-loads. The capacity of 
 freight-cars, and the minimum car-load, varies so greatly that no 
 accurate general information can be given. For heavy freight, 
 25 tons is an average load; for light freight, 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 where special cars 
 are provided. 
 
 Miscellaneous Dimensions. Horse-stalls. Width, 3' 
 10" to 4', or else 5' or over in width, 9' long. Width should never 
 be between 4' and 5', as in such cases the horse is liable to cast 
 himself. 
 
 Dimensions of Drawings for Patents (United States). 10" X 15", 
 with border-line 1" inside all around. 
 
 Dimensions of a Barrel. Diameter of head, 17"; bung, 19"; 
 length, 28"; volume, 7,680 cu. ins. 
 
 Miscellaneous Memoranda. Weight of Men and 
 Women. The average weight of twenty thousand men and 
 women weighed at Boston, 1864, was, men, 141 Jibs.; women, 
 124J Ibs. 
 
DIMENSIONS OF SCHOOLROOMS, ETC. 1475 
 
 Avenues of City of New York run 28 50' 30" east of north. 
 
 Flag-poles. For a flagpole, extending from 30' to 60' above 
 the roof, the following proportions give satisfactory results: 
 The diameter at the roof should be ? V the height above the roof, 
 and the top diameter J the lower. To profile the pole, divide 
 the height into quarters ; make the diameter at the first quarter 
 above the roof, % of the lower diameter; at the second quarter, 
 -, and at the third quarter, f the lower diameter.* 
 
 Dimensions of Schoolrooms, Boston Schools. 
 The sizes of the rooms in the Boston schools, as adopted by the 
 School board, are, for grammar schools, 28 / X32 / Xl3 / 6" high; 
 for primary schools, 24 / X32 / Xl2 / . 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' is very satisfactory for schoolrooms, and is 
 commonly adopted because it permits of the use of 28' joists 
 without waste. 
 
 Height of Blackboards in Schoolroom. The height 
 from floor to top of chalk-rail should be about as follows: 
 
 3d and 4th grades, chalk-moulding 2' 1" from floor 
 
 5th grade, " 2' 2 \" " " 
 
 6th grade, " 2' 4" " " 
 
 7th and 8th grades, . " 2' 6" " " 
 
 Slate blackboards are made 3' 6", 4' 0", and 4' 6" high, 
 4' being a very common and satisfactory height. 
 
 SIZES OF CHAIRS AND DESKS FOR SCHOOLS AND 
 ACADEMIES. 
 
 Age of Scholar. 
 
 Height of Chair. 
 
 Height of Desk 
 (Next Scholar). 
 
 Space Occupied 
 by Desk and 
 Chair (Back to 
 Back of Desk). 
 
 16 to 18 ye, 
 14 to 16 
 12 to 14 
 10 to 12 
 8 to 10 
 7 to 8 
 6 to 7 
 5 to 6 
 4 to 5 
 
 irs. 
 
 16| inc 
 15* 
 15* 
 
 14* 
 13i 
 12* 
 
 ill 
 
 m 
 
 9| 
 
 lies. 
 
 29* inc 
 28 
 27* 
 26* 
 25* 
 24 
 22* 
 21 
 19 
 
 hes. 
 
 2fe 
 2 
 2 
 2 
 2 
 2 
 2 
 2 
 2 
 
 et 9 inc 
 9 
 8 
 7 
 5 
 4 
 3 
 2 
 
 
 hes. 
 
 Desks for two scholars are 3 ft. 10 ins. long, and for a single scholar, 2 ft. 
 long. 
 
 Aisles are 2 ft._to 2 ft. 4 ins. wide, according to age of scholars and size of 
 room. 
 
 
 * The Building Trades Pocket-book. 
 
1476 STAIRS. 
 
 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 dis- 
 tance from the face of one riser to the face of the next. "Risers" 
 are the upright boards forming the face of the steps, and the 
 "treads" are the horizontal boards on which the feet tread. 
 Treads are usually from 1J to If ins. wider than the run, on 
 account of the nosing. 
 
 The "rise" of any stairs is found by dividing the "total 
 rise" by the number of risers. The "run" of the stairs may 
 be fixed 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 Proportion of Treads and Risers. For ordinary 
 use a rise of 7 to 7J ins. makes a very comfortable stair. In 
 schools and for stairs used by children the rise should not exceed 
 6 ins. Stairs having a rise greater than 7} ins. 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, viz.: 
 
 (1) The sum of the rise and run should be equal to from 17 
 to 17J ins. 
 
 (2) The sum of two risers and a tread should not be less than 
 24 nor more than 25 ins. 
 
 (3) The product of the rise and run shall 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 to be com- 
 fortable for adults. 
 
 Height of Hand-rail. In dwellings, hotels, apartments, etc., 
 the height of the rail should be about 2 ft. 6 ins. above the tread, 
 on a line with the face of the riser. For grand staircases the 
 height may be reduced to 2 ft. 4 ins. On steep stairs the height 
 should be from 2 ft. 7 ins. to 2 ft. 9 ins. 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 
 centre of the tread, the usual height in residences being 2 ft. 
 8 ins. to 2 ft. 10 ins. 
 
 * This subject is quite fully treated in Part II, Building Construction and 
 Superintendence. 
 
SASH WEIGHTS. 
 
 1477 
 
 Sash-weights. The weights ordinarily used for balancing 
 windows are made of a cheap grade of cast iron, in the form of 
 a solid cylinder, with an eye cast in the upper end. On account 
 of the limited space in the weight-box, the weights should never 
 be of greater diameter than the thickness of the sash; conse- 
 quently for balancing heavy sash, the weights must be quite 
 long. For wide and low windows the ordinary sash-weight 
 may be too long to permit the sash to be raised or lowered its 
 entire height, and in special cases it is often necessary to use 
 square sash- weights, and frequently it is necessary to use lead 
 weights, lead being about 53 per cent, heavier than cast iron. 
 
 The length of sash-weight in inches required to balance a 
 given weight may readily be found by dividing the given weight 
 by the values in the following table. To the quotient thus 
 obtained 1 in. should be added to cover the eye. 
 
 WEIGHT OF IRON AND LEAD SASH-WEIGHTS PER LINEAL INCH. 
 
 Diameter, or 
 Side of Square. 
 
 Round 
 Cast Iron. 
 
 Square 
 Cast Iron. 
 
 Square 
 Lead. 
 
 Inches. 
 
 Pounds. 
 
 Pounds. 
 
 Pounds. 
 
 u 
 
 0.32 
 
 0.40 
 
 0.64 
 
 if 
 
 0.46 
 
 0.5S 
 
 0.92 
 
 if 
 
 0.62 
 
 0.79 
 
 1.25 
 
 2 
 
 0.81 
 
 1.04 
 
 1.64 
 
 2i 
 
 1.03 
 
 1.31 
 
 2.07 
 
 2J 
 
 1.27 
 
 1.62 
 
 2.56 
 
 2} 
 
 1.54 
 
 1.96 
 
 3.10 
 
 3 
 
 1.83 
 
 2.34 
 
 3.69 
 
 3i 
 
 2.50 
 
 3.18 
 
 5.02 
 
 4 
 
 3.26 
 
 4.16 
 
 6.56 
 
 The approximate diameters of the common stock cast-iron 
 sash- weights are: for weights of 8 Ibs. and under, 1J ins.; for 
 weights between 8 and 16 Ibs. inclusive, If ins.; for weights 
 between 16 and 20 Ibs.; 2 ins. and for weights between 20 and 30 
 Ibs. , 2 J ins. Weights above 30 Ibs. are usually square in cross- 
 section. 
 
 Weight of Sash and Glass. For approximating the weight 
 of windows, the weight of the glass may be taken at 3J Ibs. 
 per square foot for plate glass, 1J Ibs. for double-strength glass, 
 and 1 Ib. for single-strength glass. 
 
 For the weight of the wooden sash, add together the height 
 
1478 SEATING SPACE IN CHURCHES, ETC. 
 
 and width of each sash (in feet) and multiply by 2.1 for 2J-in. 
 sash, 1 for IJ-in. sash, and 1J for If-in. sash. 
 
 The exact weight, however, can only be obtained by weighing 
 each sash, as the glass varies considerably in weight. 
 
 In hanging sashes, the weights for the upper sash should 
 be about \ Ib. heavier than the sash, and for the lower sash 
 i Ib. lighter. 
 
 Seating- Space in Churches and Theatres. The 
 minimum spacing for pews, back to back, is 30 ins. This spacing 
 is fairly comfortable to occupants, but is a little cramped for 
 persons to pass by others into or out of the pew. A spacing 
 of 32 ins. is to be preferred, and if there is abundance of room > 
 the spacing may be made 33 ins.; anything over 33 ins. is a 
 waste of room. 18 ins. in the length of the pew is considered 
 as a " sitting." 
 
 For dimensions of pew bodies see p. 48 of "Churches and 
 Chapels." 
 
 Opera or Assembly Chairs are made 19, 20, 21, and 22 ins. 
 wide, centre to centre 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 ins. is the least that is desirable. 
 
 For theatres, 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 assembly chairs may 
 be comfortably spaced 30 ins. back to back, and this is the 
 usual spacing in halls and churches. 
 
 In theatres the chairs are usually set on steps. In the upper 
 gallery these steps should not be more than 30 ins. wide; in 
 the balcony they are usually made either 30 or 31 ins. wide, 
 and in the parquet 31 or 32 ins. wide. As a rule the higher- 
 priced seats are more commodious than the lower-priced. 
 
 Estimating Seating Capacity. The actual seating capacity 
 of theatres 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 lineal 
 feet of pews. 
 
 For approximate purposes the seating capacity or required 
 size of room may be determined by allowing from 7 to 8 sq. ft. 
 
CAPACITY OP CHURCHES AND THEATRES. 1479 
 
 to each seat, or sitting, when on a curve, and 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, 
 provided only the actual floor space utilized for seats and aisles 
 is considered. 
 
 CAPACITY OF SEVERAL CHURCHES, THEATRES, AND 
 OPERA-HOUSES. 
 
 CHURCHES. 
 (Estimating a person to occupy an area of 19.7 ins. square.) 
 
 St. Peter's 
 
 54,000 
 
 Notre Dame, Paris 
 
 21,000 
 
 Milan Cathedral 
 
 37,000 
 
 Pisa Cathedral. . 
 
 13,000 
 
 St Paul's Rome 
 
 32,000 
 
 St. Stephen's Vienna 
 
 12 400 
 
 St. Paul's, London 
 St Petronio's, Bologna .... 
 
 25,600 
 24,400 
 
 St. Dominic's, Bologna .... 
 
 12,000 
 11,400 
 
 Florence Cathedral 
 
 24,300 
 
 Cathedral of Sienna. . . . 
 
 11,000 
 
 Antwerp Cathedral 
 
 24,000 
 
 St. Mark's, Venice 
 
 7,000 
 
 St Sophia's Constantinople. 
 
 23,000 
 
 
 7,000 
 
 St John Lateran 's 
 
 22 900 
 
 
 
 
 
 
 
 THEATRES AND OPERA-HOUSES. 
 
 EUROPEAN. 
 
 Carlo Felice Genoa 
 
 2,560 
 
 Drury Lane, London. 
 
 1 948 
 
 Opera-house, Munich. 
 
 2,370 
 
 Co vent Garden, London . . . 
 
 3,000 
 
 Alexander St Petersburg. 
 
 2 332 
 
 
 1,636 
 
 
 2 240 
 
 Adelphi, London . . 
 
 2 300 
 
 Imperial St Petersburg 
 
 2 160 
 
 Lancaster, London 
 
 1,850 
 
 La Scala Milan. 
 
 2,113 
 
 Globe, London 
 
 1,100 
 
 
 2,092 
 
 
 
 
 
 
 
 AMERICAN. 
 
 The Auditorium, Chicago. . . 
 Metropolitan Theatre, N. Y.. 
 Philadelphia Academy 
 
 4,200 
 3,200 
 3,124 
 
 Abbey's Theatre, N. Y 
 
 Empire Theatre, N. Y 
 Fifth Ave. Theatre, N. Y. . 
 
 1,450 
 1,150 
 1,400 
 
 Boston Theatre, Boston. . . . 
 American Theatre N Y 
 
 3,000 
 2 500 
 
 Castle Square Theatre, I 
 Boston f 
 
 1,600 to 
 1,800 
 
 Proctor's Pleasure Palace, 
 
 NY . .. 
 
 2,100 
 
 Gaiety Theatre, Boston. . $ 
 
 nearly 
 3,000 
 
 Lyric Theater N. Y 
 
 1,543 
 
 Grand Opera-house, Cin- 
 
 
 
 
 cinnati, O . . 
 
 1,736 
 
 
 
 
 
1480 
 
 DIMENSIONS OF THEATRES. 
 
 DIMENSIONS OF THEATRES AND OPERA-HOUSES. 
 
 The following are the dimensions, in feet, of some of the 
 prominent theatres in this country and in Europe : 
 
 Name and Location. 
 
 Auditorium. 
 
 Prose i. 
 Opening. 
 
 Stage. 
 
 A 
 
 S 
 
 
 
 | 
 I 
 
 ^ 
 
 & 
 
 3 
 1 
 
 1 
 
 F 
 
 i 
 
 0> 
 
 w 
 
 A 
 
 T3 
 jfc 
 
 rd 
 Q, 
 
 P 
 
 Jd 
 
 bO 
 
 i 
 
 Alexander, St. Petersburg 
 Berlin 
 
 58 
 51 
 71 
 74 
 47 
 66 
 51 
 56 
 
 76 
 78 
 95 
 73 
 56 
 76 
 66 
 64 
 71 
 87 
 78 
 65 
 61 
 
 58 
 47 
 64 
 83 
 57 
 66 
 
 56 
 41 
 49 
 52 
 37 
 43 
 32 
 32 
 46 
 48 
 48 
 30 
 31 
 
 54 
 
 50 
 
 75 
 
 92 
 86 
 66 
 80 
 78 
 86 
 48 
 87 
 83 
 90 
 62 
 68 
 
 100 
 110 
 67 
 40 
 71* 
 80 
 77| 
 
 70 
 89 
 67* 
 
 67 
 
 68 
 60 
 
 84 
 76 
 78 
 74 
 69 
 82 
 55 
 80 
 68 
 71 
 72 
 38 
 46 
 
 73 
 
 70 
 30 
 65* 
 28* 
 35 
 43* 
 
 40 
 37 
 30$ 
 
 41 
 
 45* 
 
 42 
 
 88 
 95 
 65 
 
 73* 
 70 
 
 70 
 
 La Scala, Milan 
 
 San Carlo Naples. . 
 
 Grand Theatre, Bordeaux 
 Salle Lepelletier, Paris. . . 
 Covent Garden, London . 
 Drury Lane, London. . . . 
 Boston Theatre, Boston. . 
 
 
 58 
 
 Academy of Music, N. Y.. 
 Opera-house, Phila. . 
 
 62 
 66 
 60 
 68 
 
 74 
 
 Globe Theatre, Boston. . . 
 Museum, Boston 
 Metropolitan Theatre, 
 New York 4 
 
 
 
 The Auditorium, Chicago. 
 
 
 
 
 Empire Theatre, N. Y. 
 Abbey's Theatre, N. Y. . . 
 Harrigan's Theatre, N. Y. 
 Fifth Ave. Theatre, N. Y. 
 American, N. Y 
 Proctor's Pleasure Pal- 
 ace, N. Y. . 
 
 69 
 701 
 
 56* 
 
 66 
 79 
 52 
 
 
 34 
 35 
 
 27 
 
 34 
 34 
 
 473 2 
 
 74} 
 74* 
 
 74* 
 
 74* 
 
 
 39 
 
 34 
 35 
 32 
 
 36 
 40 
 
 39 
 
 34S 
 30 
 30 
 
 34 
 34 
 
 The Lyceum, N. Y 
 
 Hudson Theatre, N. Y. . . 
 Grand Opera-house, Cin- 
 cinnati 
 Castle Square Theatre, 
 Boston 6 
 
 67* 
 67 
 
 # 
 
 67 
 69 
 
 85* 
 80$ 
 
 70 2 
 
 Gaiety Theatre, Boston . . 
 
 
 
 
 1 From the curtain or back line of proscenium opening. 
 
 2 Measured from stage to centre of ceiling. 
 
 3 To the "gridiron" or rigging-loft. 
 
 4 As remodelled in 1893. 
 
 6 Can be enlarged to 40' X 40 . 
 
 6 The plan of this theatre is in the shape of a horseshoe. 
 
 Notes on Theatre Dimensions.* "The utmost dis- 
 tance 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 Theatre of San Carlos at 
 Naples is 73 ft.; at Bologna 74 ft. Of the London theatres, the 
 
 * From " The Planning and Construction of American Theatres," by 
 Wm. H. Birkmire 
 
GUTTERS AND CONDUCTORS. 1481 
 
 Adelphi is 74 ft., Covent Garden 80 ft., the Gaiety 53 ft. 6 ins., 
 Lancaster 58 ft. 4 ins., Marylebone 74 ft., and the Globe 47 ft. 
 6 ins." 
 
 The width of the ideal theatre, between inside walls, should be 
 from 70 to 75 ft., and "the ceiling should be 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 ins. to 
 4 ft. 3 ins. below the stage. A depth of 3 ft. 9 ins. is a good 
 height, as it fixes the eye of the spectator 5 ins. above the stage 
 level." 
 
 " The height of the stage, i.e., 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, 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 flymen to adjust their 
 ropes with facility. 
 
 Proportioning Gutters and Conductors to Roof 
 Surface. The size of gutters and down-spouts and their 
 distance apart for roofs (of Mill Buildings) with J pitch and of 
 different spans are shown by the following table : * 
 
 One half roof span, ft 10 20 30 40 50 60 70 80 
 
 Size of gutter, in 5 5 6 6 77 8 8 
 
 " " down-spouts, ins. ... 33445566 
 
 Spacing of down-spouts, ft.. . 50 50 50 50 40 40 40 40 
 
 The specifications of the American Bridge Company provide 
 as follows for the size of gutters and conductors :f 
 
 Span of Roof. 
 Up to 50ft. 
 50 to 70 " 
 70 to 100 " 
 
 Gutter. 
 6 ins. 
 
 7 " 
 8 " 
 
 Conductor. 
 4 ins. every 40 ft. 
 5 " " 40 " 
 5 " " 40 " 
 
 Hanging gutters should have a slope of about 1 in. to 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 of about 5 ins. diameter. The roof, which is paved 
 with fire-brick, is graded with slopes of perhaps one in fifty toward 
 
 * H. G. Tyrrell, C.E. 
 t M. S. Ketchum, C.E. 
 
1482 ELEVATORS. 
 
 the points at which the leader openings are placed, most of these 
 draining surfaces being about 40X 70 ft. each. The provision 
 here made is equivalent to about 1 sq. in. of leader opening to 
 140 sq. ft. of roof surface. On the Sloane Building, on 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 
 of about 6 ins. in diameter, and a third rectangular, 4X 6 ins. 
 This gives an allowance of 240 sq. ft. of surface to the square 
 inch of leader opening, while on the Massachusetts Hospital 
 Life Insurance Company's Building, and the Hemenway Build- 
 ing, in Boston, the proportion is only from 60 to 70 sq. ft to the 
 square inch of opening." * 
 
 ELEVATORS SPECIFICATIONS FOR.f 
 
 Conditions which should be Considered and made 
 Definite by the Architect, Preliminary to the 
 Elevator Specifications. 
 
 (a) The System: Electric or Hydraulic. If electric, whether 
 of the drum or friction-drive type. If hydraulic, whether of the 
 horizontal cylinder, the vertical cylinder, or the plunger type. 
 
 Where a reliable and sufficient direct-current supply is avail- 
 able for one or two elevators, the electric is unquestionably the 
 best system. For batteries of three or more the system must 
 be determined by the special conditions which exist in every 
 plant, and are relative to the other mechanical equipment, and 
 should be decided only after mature deliberation and consul- 
 tation with unprejudiced engineers and elevator builders. 
 
 (b) Location of Hoistways and Machinery Room. The location 
 of the hoist ways is rather a matter for the good judgment of the 
 architect, having reference to facility of ingress and egress of 
 passengers, so as to avoid crowding and confusion at the main 
 entrance. 
 
 The machinery-room should be immediately adjacent to the 
 hoistways, well ventilated, and protected from dust, large and 
 high enough to permit easy access to all parts of the machines 
 for inspection and repairs. 
 
 (c) Number and Sizes. The number and sizes will be deter- 
 mined, first, by the space available for hoistways; second, the 
 
 * Mr. D wight Potter in " The Technology Quarterly." 
 } Prepared by Sydney F. Weston. 
 
ELEVATORS. 1483 
 
 number of passengers to be carried during the rush hours; third, 
 the frequency of car departures from the ground floor, or 
 "schedule." 
 
 Having determined the square feet of cross-section to be used, 
 the next thing to determine is the number. Three cars, each 
 carrying one-third the passengers, is preferable to two, each 
 carrying one-half, because the car departures are more frequent, 
 reducing the time the passengers must wait at the ground-floor, 
 and therefore lessening the liability of over-congestion and 
 loss of patience by those waiting. 
 
 Every machine is likely to need repairs; therefore the more 
 units in the battery the less will the one out of commission be 
 missed. It is far greater economy to have an excess capacity 
 than even a slight under capacity, especially against the time 
 when it may be imperative to shut down one or more machines. 
 
 In determining the load for passenger service, allow 80 Ibs. 
 per sq. ft. of platform area, and 150 Ibs. per passenger. 
 
 (d) Loads and Speeds. The loads and speeds determine the 
 sizes of machines. The loads having been decided as above, 
 the question of speed is next, and is a most important factor. 
 
 Generally the local ordinances limit the car speed, as in New 
 York, to a maximum of 400 ft. per min. for cars that stop at 
 every floor; and to 500 ft. per min. for express cars, those that 
 go the first two-thirds of their travel without stop. 
 
 The best elevator insurance companies will not permit electric 
 drum elevators to travel over about 350 ft. per min., whereas 
 the electric friction-drive, or the hydraulic types, are safe and 
 under perfect control for the higher speeds. Four hundred feet 
 per minute is about as high a speed as the human system can 
 stand without unpleasant sensation, and is ample for the best 
 schedules. 
 
 In hydraulic systems it is necessary for figuring the pumps 
 and tanks that the maximum number of round trips per hour be 
 specified. 
 
 (e) Hoistways. The hoist ways 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. 
 
 Provide supports adjacent to the hoist way for the overhead 
 beams at a distance, if possible, of at least 6 ft. from the top of 
 the car frame when the car platform is flush with the top land- 
 ing, and more is better, in order to have ample "runby, " i.e., 
 the distance between the top of the car frame and the lowest 
 
ELEVATOR- 
 
 point of the overhead work, so thai should the ear elide h 
 top landing a Ihtle before the automatic limits shut off the mo- 
 tive power, there would be a minimum danger of running into 
 the overhead work, 
 
 For the same purpose there should be a pit at the bottom of 
 the shaft at least 5 ft. deep below the bottom landing. 
 
 The diftiTfM'** from the above-mentioned supports for overhead 
 beams, in the dear below the skylight, varies from 4 or 5 to 10 
 ft., and should be determined by the elevator-maker. 
 
 (f) Counterweight, Location of. In New York, the Building 
 Department requires that the "counterweights shall be run hi a 
 separate shaft from the car, or in a ehace separated from the 
 car shaft by a substantial screen or partition for the full height 
 of the hoist." These chaces should be at least 8 ins. de 
 
 36 ins. long. 
 
 (g) The Bureau of Buildings for the Borough of Manhattan on 
 April 24, 1902, issued regulations governing the construction, 
 inspection, and operation of passenger elevators, which were 
 published in the " Record and Guide/' Kay 10, 1902, and are 
 especially called to the attention of all architects, as not only 
 obligatory hi New York, but excellent practice at all times. 
 
 (h) The foregoing is intended to give an idea of what the archi- 
 tect most provide in the building for the reception of the elevator 
 apparatus, and what he must determine to enable the maker to 
 intelligently design and lay out his machines. 
 
 Above all things, avoid specifying apparatus of special con- 
 struction. Utilize standard design as much as possible, as, first, 
 it is more apt to be well designed, tested, and built; second, 
 repair parts can be easily and quickly obtained. 
 
 Specifications. These should state: 
 
 (1) Kinds of service and number of elevators for each ser 
 
 (2) Maximum load. (3) Speed with maximum load. (4) 
 Maximum speed. (5) Load with maximum speed. 
 
 (6) Maximum number of round trips per hour for each elevator. 
 
 (7) Method of car control. 
 
 -izes of hoistways and area of car platforms. 
 
 (9) Travel of car platform in feet; and the number of car 
 landings. 
 
 n ()) Syxtem. If electric, the current and voltage; if hydraulic, 
 the steam pressure for the pumps, or the water pressure if the 
 purchaser provides the pumps, tanks, or other source of water- 
 pressure supply. 
 
Kl KY ITORS 1 IS'* 
 
 (ID An elevation sketch showing landings, supports for over- 
 head beams, space for the overhead sheaves aiut runbvs at top 
 and bottom; a plan sketch showing si.-.o and shape of hoist wavs. 
 entrances, position of car anol counterweight sruido rails, and 
 U>( < ation of space available for machines, pumps, tanks, etc , 
 with ivtViviuv to the hoist wavs. 
 
 OL^ Car and counterweight iMiide rails. whether of wood or 
 stool. 
 
 (\:^ Posts or supports for fastening t ho rails, whether of wood 
 or iron, carried all the way up from the bottom; or iron brackets 
 bolted to the building frami'work at oaeh flov>r 
 
 (\ 1) rinishoo! rar or c;t;:\ value of; i e . the ^peeilied amount 
 to be allowed for eaeli. the design to be subjeel to the approval 
 of tlu x arehit(H't . 
 
 (\,~^ 1 \opes. the number and si/.e of. if not left t*> the judgment 
 of tho mak(M\ Abvavs require the la? -le. MS 
 
 this faetor d(^termiiu\s larj-ely the life of the rop *. 
 
 HO Signals, system of; i e.. v<^ annn: , ns \\ith 
 
 push billions nl the !an,lui",x; or (!>} "up" and "down" sigtmU 
 in (lie ears, \vilh " U{>" and "down" buttons at t he landings, 10 
 arranged that a ear oiu np rernxes onlv "up" signals, and A 
 ear :\oin ; ', down reeeives onlv "down" signals. <>aeh signal hoitlg 
 iuitomntu\Mlly reset by (ho liixt ear that passes that lhor in the 
 direetion for wh'u-h tho signal is ^iven. The latter -\ -inn iJ.U 
 :-,r,MllN to the ellieienev of a ba! terv of rlexalors. m (hat it ftVOidl 
 the eonfusion of more than one eai' an^werii\g H sigiml . or 
 
 m one duvet ion stoppin r !\oms % ; iu the oppo 
 
 site direelion. Mways speeify I he number of Moors at wlueU 
 (\-ieli ear is to land. 
 
 (17) //H//VU/O/-N, wluMher at the j^rotind Moor >nlv O'or the in 
 formation of tlu^ starter as to tle position of the ears) or at all 
 Moors. 
 
 ludieators are unneerssarv with the automatie -.I".IM! ; It t 
 doseribtnl, except at the jM-ound Moor, there beinjf ut OM'h Moor 
 MII "up" and a "ilowu" signal to show the tirst a\ailable e.n in 
 eilluM- direetion. 
 
 (IS") Source of power Spent \ \\ 'liet her I he connect ion will be 
 brought to the elevator MppMfMtus lv the purehaser or b\ the 
 rlevator rontraetor; if by the- latter, f*ivo .K.-t.-h .howin^ tl\o dw- 
 taneo, and for tlu^ eleetrie system .p< . n\ whether the wiring is 
 to be open (i i> . on eleats\ in mouldm.-.. or in eondmt . tlir i | ; 
 of wire, and the switch.- ;. eutoiits, ete . for an livdraui: 
 
1486 ELEVATORS. 
 
 the size of pipe for steam supply. Leave the sizes of watei -pip- 
 ing to the elevator contractor, and hold him responsible for them. 
 
 (19) Pumps and tanks in hydraulic plants to be furnished by 
 the contractor. Specify whether the capacity is to be just ample 
 to do the work, or whether there is to be a reserve capacity, with 
 reserve units, to provide against interfering with the service in 
 case of accident to a pump or tank, but leave the sizes and design 
 to the judgment of a responsible elevator maker. 
 
 (20) Foundations for the machine whether to be provided 
 by the purchaser or by the contractor. 
 
 (21) Miscellaneous. Gratings underneath the overhead work, 
 pit-pans, painting in addition to the standard factory finish, and 
 all items not above mentioned, are generally furnished by the 
 purchaser under separate contract, but by whom should be 
 specified in the elevator specifications. 
 
 Safety. Under the subject of " safety" must be considered the 
 most vital feature of the entire apparatus the mechanical de- 
 vice, or "car safety," for gripping the rails and stopping the car 
 in case the ropes break, or for other reason the car acquires a 
 falling speed in excess of that for which the mechanism is designed. 
 
 There are innumerable safeties on the market, but only one or 
 two fulfilling the ideal conditions of first "cushioning," or grad- 
 ually checking the fall, and then positively and mechanically 
 gripping the rails with a power that increases until the car stops. 
 
 Data as to Size and Number of Elevators Re- 
 quired.* An idea of the practice in elevator installations 
 may be obtained from Table No. 1, which gives the story heights, 
 the approximate area of office space above the first floor, the 
 number of cars, the office area per car, and the area of each car, 
 as actually installed. 
 
 To determine the number of trips and car-travel per hour, ob- 
 servations were made at four office buildings in Philadelphia: 
 Drexel Building, ten stories high; Stephen Girard Building, 
 thirteen stories high; Land Title and Trust Building, fifteen 
 stories high; Real Estate Trust Building, seventeen stories high. 
 
 In the Drexel Building, which has six elevators, one elevator 
 ran from the first to the fourth story; one elevator from the first 
 to the fifth story; two elevators from the first to the tenth story, 
 
 * Extract from a paper by Mr. Charles G. Darrach read before the Amer- 
 ican Society of Civil Engineers, October 2, 1901, and published in the Amer- 
 ican Architect, October, 1901, 
 
ELEVATORS. 
 
 1487 
 
 stopping, if required, at any of the floors ; and two elevators ran 
 to the fifth story " express/ 7 and served all the stories above. 
 
 TABLE NO. 1. 
 
 
 
 Office Area j^o. 
 
 Square 
 
 Area of 
 
 Building. 
 
 Stories. 
 
 above 
 First Floor, 
 Sq. Ft. 
 
 of 
 Cars. 
 
 Feet per 
 Car. 
 
 Car, 
 Sq. Ft. 
 
 St. Paul Building, New York 
 
 25 
 
 83,200 6 
 
 13,900 
 
 23.6 
 
 Empire Building, New York. 
 N. American Building, Phila- 
 
 21 
 
 150,000 10 
 
 15,000 
 
 42.0 
 
 delphia 
 
 18 
 
 90,500 5 
 
 18,100 
 
 27.6 
 
 Real Estate, Philadelphia . . . 
 
 17 
 
 155,650 10 
 
 15,560 
 
 23.7 
 
 Bowling Green, New York. . . 
 
 16 
 
 222,000 
 
 9 
 
 24,700 
 
 
 Land Title, Philadelphia. . . . 
 
 15 
 
 66,400 
 
 5 
 
 13,300 
 
 29.'6 
 
 Stephen Girard, Philadelphia 
 
 13 
 
 67,000 4 
 
 16,750 
 
 29.0 
 
 Drexel Building, Philadelphia 
 
 10 
 
 130,000 
 
 6 
 
 21,700 
 
 21.4 
 
 At the Stephen Girard Building there were four elevators, which 
 ran " accommodation " through. 
 
 At the Land Title and Trust Company's Building there were 
 five elevators which ran on schedule time, " accommodation" to 
 all floors except the second. 
 
 At the Real Estate Building all the cars ran " accommodation" 
 through. 
 
 Table No. 2 shows the results obtained. 
 
 TABLE NO. 2. 
 
 Building. 
 
 Stories. 
 
 Height, 
 Feet. 
 
 Travel 
 per Trip, 
 Feet. 
 
 Trips 
 per 
 Hour. 
 
 Average 
 Feet per 
 Minute. 
 
 Drexel Building. 
 
 4 
 
 40 
 
 80 
 
 60 
 
 80 
 
 
 5 
 
 50 
 
 106 
 
 52 
 
 87 
 
 41 14 
 
 10 1 
 
 108 
 
 216 
 
 35 
 
 126 
 
 i (I 
 
 10 1 
 
 108 
 
 216 
 
 35 
 
 126 
 
 Stephen Hirard Building 
 
 13 
 
 150 
 
 300 
 
 30 
 
 150 
 
 Land Title Trust Building. . . 
 
 15 
 
 180 
 
 360 
 
 27 1 
 
 162i 
 
 i i> i i < 
 
 15 
 
 180 
 
 360 
 
 242 
 
 144 2 
 
 Real Estate Trust Building, . . 
 
 17 
 
 200 
 
 400 
 
 25 
 
 167 
 
 1 Actual. 
 
 2 Estimated. 
 
 From observations at the Drexel Building in 1897, during the 
 noon hour, the up-travel from the first floor reached 00 passen- 
 gers, with a maximum of 12 to 13 passengers in the car. The 
 cars were also overtaxed all day, from 10 A.M. until 4 P.M. 
 
 At the Land Title Building, running twenty-four trips per hour, 
 the service was very satisfactory. There was a slight crowding 
 during the noon hour; this, however, can be remedied by the use 
 of the improved car-signalling apparatus. 
 
1488 
 
 ELEVATORS. 
 
 At the Stephen Girard Building, the cars are crowded during 
 the noon hour, and also between three and five in the afternoon. 
 
 All three of these buildings are well filled. 
 
 The Real Estate Building was not fully occupied, so that the 
 elevator service there could not be fairly judged. 
 
 Using the trips per hour as observed and estimated, and equat- 
 ing the car area by the formula: 
 
 a = 
 
 TX22' 
 
 in which a = square feet of car area; 
 A = square feet of office area; 
 T= total trips per hour. 
 
 we derive the following table: 
 
 TABLE NO. 3. EQUATED CAR AREAS. 
 
 Building. 
 
 Stories. 
 
 Num- 
 ber of 
 
 Cars. 
 
 Sq. Ft. of 
 Office Area 
 per Car. 
 
 Actual 
 Car Area 
 in Sq. Ft. 
 
 Equated 
 Car Area 
 in Sq. Ft. 
 
 Estimated 
 Trips per 
 Hour. 
 
 St. Paul 
 
 25 
 
 6 
 
 13,900 
 
 23 6 
 
 31 5 
 
 120 
 
 Empire 
 Real Estate. . . . 
 Bowling Green. 
 
 21 
 17 
 16 
 
 10 
 10 
 9 
 
 15,000 
 15,560 
 24,700 
 
 42.0 
 23.7 
 
 31.0 
 28.3 
 43.1 
 
 220 
 250 
 234 
 
 Land Title 
 
 15 
 
 5 
 
 13,300 
 
 
 22.4 
 
 135 
 
 Stephen Girard. 
 Drexel. 
 
 15 
 13 
 10 
 
 5 
 4 
 6 
 
 13,300 
 16,750 
 21,700 
 
 29.6 
 23 
 21.4 
 
 25 
 25.4 
 
 28.2 
 
 120 
 120 
 210 
 
 At the Drexel Building the two cars which ran "express" to 
 the fifth floor, and the two cars which ran "accommodation" 
 through, made the same number of trips, and carried practically 
 the same number of passengers. It would be interesting to know 
 whether similar results are obtained in any other buildings, and 
 the advantage gained in arranging the travel of the various cars 
 to serve "accommodation" through the entire trip, "express" 
 part way, or providing separate service to different heights in the 
 building. 
 
 Using the same formula, and equating to obtain the square 
 feet of office space per car, with given-sized cars, and the number 
 of through trips heretofore used, we have the folio whig results 
 with cars of 25 and 30 sq. ft. area: 
 
ELEVATORS. 
 
 1489 
 
 TABLE NO. 4. SQUARE FEET OF OFFICE AREA PER CAR. 
 
 Stories. 
 
 Car Area'=25 sq. ft. 
 
 Car Area = 30 sq. ft. 
 
 25. ., 
 
 11,000 sq. 
 12,100 
 13,750 
 14,300 
 14,850 
 16,500 
 19.-250 
 
 ft. p 
 
 er a 
 
 ir 
 
 13,200 sq. 
 14,500 
 16,500 
 17,160 
 17,820 
 19,800 
 23,100 
 
 4 ft. p 
 
 3F C< 
 
 ir 
 
 21 
 
 17... . 
 
 16. .. 
 
 15 
 
 13. . . 
 
 10. . 
 
 
 Additional data furnished by Mr. Kloman of the Otis Elevator 
 Co. 
 
 Name of Building, all in New 
 York City. 
 
 No. of 
 Eleva- 
 tors. 
 
 No. of 
 Floors. 
 
 Total 
 . Floor 
 Area. 
 
 Floor 
 Area per 
 Eleva- 
 tor. 
 
 
 18 
 
 20 
 
 465,540 
 
 25,864 
 
 Park Row (Ivins syndicate) 
 
 10 
 
 25 
 
 315,000 
 
 31,500 
 
 Atlantic Mutual 
 
 6 
 
 18 
 
 162,000 
 
 27,000 
 
 American Exchange Bank. 
 
 3 
 
 16 
 
 72,000 
 
 24-000 
 
 Bank of Commerce 
 
 7 
 
 19 
 
 172,000 
 
 24,571 
 
 S.E. cor. Broadway and Maiden Lane 
 Empire Building 
 
 6 
 10 
 
 18 
 20 
 
 129,000 
 170,000 
 
 21,500 
 17,000 
 
 
 
 
 
 
 The Empire Building is said to be noted for its quick service, 
 and the Park Row Building for slowness. 
 
 According to Mr. Kloman, the officers of the Otis Elevator 
 Co. have come to the conclusion that the best service is obtained 
 with a large number of small cars having a capacity of not over 
 15 passengers, rather than with fewer large cars. 
 
 Electric Elevator with Pusli-buttoii Control. 
 This is perhaps the most important of the latest improvements 
 in elevators, as it permits of the installation of elevators in resi- 
 dences and other buildings where a constant attendant would 
 be both expensive and undesirable. This type of elevator is 
 particularly adapted to private residences, apartment houses, 
 hospitals, and other places where the service is intermittent and 
 it is desired to do away with the expense of an attendant. 
 
 "The elevator is always ready for service, and it is equipped 
 with every safeguard which human ingenuity can devise against 
 the possibility of accident." 
 
 The operation of the elevator is as follows: A passenger desir- 
 ing to use the elevator presses a button placed near the elevator 
 shaft, and the car, if not in use, immediately travels to that floor 
 and stops automatically. When the car has come to rest at that 
 
1490 
 
 ELEVATORS. 
 
 floor, the door can be opened. The passenger then enters the 
 car and closes the door. The car will not leave that floor unless 
 the door is tightly closed. Inside the car there is a series of push- 
 buttons, numbered to correspond with the various floors. The 
 
 FIG. A, WOOD GUIDES. SIDE POST. 
 MACHINE AND COUNTERWEIGHT AT BACK 
 OR MACHINE OVERHEAD. /" 
 
 With machine and counter- 
 weight at side, the width of 
 hatch must be increased 3 ins., 
 and the depth may be 5 ins. 
 less. Steel guides effect a 
 saving in width of hatch of 
 1 to 2 ins. 
 
 With steel corner guides, 
 depth of hatch is same as in 
 Fig. B, but width is in. less. 
 
 F!G. B. WOOD GUfDES. CORNER POST. 
 
 MACHINE AT BACK OR OVER.HEAD. 
 
 COUNTERWEIGHT AT SIDE. 
 
 passenger pushes the proper button and the car proceeds to the 
 desired landing and stops automatically. Not until the passen- 
 ger has left the car and closed the door can the elevator be con- 
 trolled from any other floor. Should the passenger desire, for 
 any reason, to stop the car at any point of its travel, he can do 
 
MAIL CHUTES. 1491 
 
 so instantaneously, by merely pushing the safety button with 
 which the car is provided. 
 
 Standard Relations of Hatchway, Platform* and 
 Car Sizes. In their 1903 Catalogue the Otis Elevator Co. (which 
 furnishes a large proportion of the elevators for theJUnited States) 
 published sixteen engravings showing the required size of hatch- 
 way and car platforms under different conditions, taking the in- 
 side dimensions of the car as a base. 
 
 As these relative dimensions apply to all elevators electric, 
 hydraulic, steam, and belt-driven they will be found very use- 
 ful for reference in the preparation of plans, 
 
 The diagrams for two of the most common installations are re- 
 produced on opposite page. 
 
 MAIL CHUTES. 
 
 The Cutler patent system of mailing letters from each floor, 
 by means of a specially constructed chute connected with the 
 receiving-box at the bottom, has come into such general use in 
 public buildings, apartment houses, and. hotels that architects 
 should be informed in regard to the restrictions affecting the 
 same and what is required in the way of preparation. The 
 system is installed by the patentees, under regulations of the 
 Post Office Department governing its construction and location. 
 It may be placed in any building of more than one story used 
 by the public, where there is free delivery and collection service, 
 in the discretion of the local postmaster, subject to whose ap- 
 proval the contracts are made. 
 
 The chute must extend in a vertical line, must be exposed to 
 view, and accessible throughout its entire length. It is made in 
 removable sections, to facilitate clearing it in the event of acci- 
 dent. 
 
 The requirements for "preparatory work" are described in 
 Part II, Building Construction and Superintendence, p. 520. 
 Before the final completion of plans, however, architects or owners 
 should submit the same to the Cutler Mfg. Co., Rochester, N. Y., 
 with whom contracts for the installation must be made. 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. 
 
1492 
 
 REFRIGERATORS. 
 
 REFRIGERATORS. 
 
 The following information is given as a guide to architects in 
 providing for refrigerators in fine residences, hotels, club 
 buildings, etc. 
 
 A consultation with some reliable refrigerator builder,* how- 
 ever, is always wise before deciding in relation to space to be 
 occupied by refrigerators, refrigerating rooms, freezers, etc., as 
 a satisfactory refrigerator cannot be adapted to a badly proportioned 
 space. Care should be taken to select a refrigerator simple in its 
 working and easily cleansed, as modern sanitary science has 
 traced much sickness to poor refrigeration. Thorough insula- 
 tion is one of the most important features in a refrigerator, as 
 upon this depends economy in the use of ice, the keeping of the 
 cold air, and the consequent perfect preser- 
 vation of the food. 
 
 Fig. 1 is a kitchen refrigerator for use in 
 families of ordinary size, and has the ice 
 located in the centre. Depth should not be 
 over 3 ft. nor under 2 ft. Height may 
 ^ be 4 to 7 ft. Length of front largely de- 
 termines the capacity, and should be, say, 
 from 5 to 7 ft. 
 
 Fig. 2 shows greater capacity, and is better 
 
 adapted for use in large families, entertaining considerably, 
 and for small -clubs, boarding-houses, restaurants, private 
 hospitals, etc. This style is known as a "combination" re- 
 frigerator, from the fact that it 
 contains separate compartments 
 for the various kinds of food. 
 The large compartment at the 
 left is specially for large meats, 
 and packages in bulk, and is 
 fitted with shelves and meat- 
 hooks. The right end of the re- 
 frigerator is divided by a parti- 
 tion into two compartments, the 
 
 Fig. 1 
 
 Fig. 2 
 
 drawers being for steaks, chops, jellies, etc., and the door above 
 
 * The leading builders of high-class refrigerators are: The Lorillard Re- 
 frigerator Co., New York; McCray Refrigerator Co., Kendallville, Ind.; 
 Monroe Refrigerator Co., Lockland, Ohio; Wickes Refrigerator Co., 
 Chicago, 111. 
 
REFRIGERATORS. 
 
 1493 
 
 Fig. 3 
 
 for vegetables and sundries. The compartment to the right 
 of this is specially for milk and butter, and should be absolutely 
 separate from all other compartments. One ice-tank supplies 
 cold air to all compartments, and is filled through a door in 
 the front. 
 
 A convenient arrangement is a window in the wall at back of 
 
 refrigerator, through which ice may be passed into refrigerator. 
 
 Refrigerators over two feet in depth should be built in sections 
 
 bolted together, rendering them easy to transport and handle 
 
 in contracted space. 
 
 Fig. 3 is a refrigerator for use in butler's pantries, where 
 economy of space is important. The 
 ice-tank is arranged to come out on a 
 runway, for convenience in filling. When 
 the ice-tank is pushed back, this runway 
 folds up, and an outside door closes over 
 it. This does away with the necessity ' 
 of cutting through the counter-top, and 
 permits the ice-tank to be readily taken 
 out for cleansing purposes. The height should be about 2 ft. 
 8 ins., depth about 2 ft. Length of front determines capacity, 
 but should never be less than 2 ft. 10 ins. In every 3 ft or 
 3 ft. 6 ins. one ice-tank is allowed. The finish, wood, trim, and 
 hardware should correspond with other fittings. 
 
 Drainage. A short, accessible, well-trapped drain is im- 
 perative, and should be as nearly under the centre of the ice 
 compartment as possible. It is well to have 
 refrigerators on casters, so they can be easily 
 moved for cleaning about them. 
 
 Fig. 4 shows a good drainage arrange- 
 ment, permitting removal of refrigerator at 
 will. 
 
 Plumber's pan for reception of refrigerator 
 drip should be countersunk in floor. 
 
 Where a very low temperature is required, as for game or 
 fish carried in large quantities, or in medical colleges where the 
 object is to preserve bodies, it is absolutely necessary that ice 
 should go into the tanks from top. 
 
 Usual complement of refrigerators for use in ordinary families : 
 one in kitchen; one in butler's pantry. Large families same, 
 with greater capacity. Small clubs, small restaurants, etc., 
 one general storage; one wine; one in or near kitchen, for cook's 
 
 Fig. 4 
 
1494 LIBRARY STACKS. 
 
 use; one fish. Large hotels, clubs, restaurants, etc. : one storage 
 for large meat; one in or near kitchen, for cook's use; one fish; 
 one milk and butter ; one in storeroom ; one ice-cream (in hotels) ; 
 one wine. Private hospitals: one large storage; one for cook's 
 use, in or near kitchen; one for milk and butter; one iron-lined 
 box for broken ice. Large hospitals same, but increased capacity, 
 and a small refrigerator in each ward. Isolated hospitals should 
 have large storage ice-houses in addition. Medical colleges, for 
 preserving bodies, with accommodations for eight bodies: di- 
 mensions about 8 ft. 6 ins. front, 7 ft. 6 ins. deep, and 9 ft. 
 high. Ice going into tanks from top. 
 
 Revolving Doors. A great improvement over the ordi- 
 nary doors, or storm-doors, for many purposes. For description 
 see Part II, Building Construction and Superintendence, 
 
 Tower Clocks Dimensions of Clock Faces, For 
 description of requirements of installation of tower clocks, see 
 Churches and Chapels, p. 154. 
 
 Rule for Diameter of Dials.-^-"To look well and show plainly, 
 dials should be 1 ft. diameter for every 10 ft. of elevation and 
 should set out flush with or close to the line of the building or 
 tower." * 
 
 DIMENSIONS OF SOME LARGE CLOCK PACES. 
 
 Tower Clock, Depot of the Central Railroad of New Jersey, at 
 Communipaw. Diameter of single dial, 14 ft. 3 ins.; minute 
 hand is 7 ft, long, weighs 40 Ibs,; hour hand is 5 ft. long, weighs 
 28 Ibs. The motive power is furnished by a weight of 700 Ibs., 
 hung from a |4n. steel cable. 
 
 Four-dial Clock, New York Produce Exchange. Diameter of 
 each dial, 12 ft. 6 ins. 
 
 Four-dial Clock, Chronicle Tower, San Francisco. Diameter 
 of each dial, 16 ft. 6 ins.; length of minute hands, 8 ft.; length 
 of hour hands, 5 ft. 6 ins. The mechanism of the clock is 6 ft. 1 
 in. high and weighs 3,000 Ibs. 
 
 Pneumatic Clock, City PI all and Court House, Minneapolis. 
 Dials, 23 ft. 4 ins. in diam. 
 
 LIBRARY STACKS CAPACITY OF SHELVING. 
 
 General Description of the Library Stack Sys- 
 tem, using 1 Iron or Steel Stacks, The unit of the sys- 
 tem is the shelf compartment, or the space between two adjacent 
 
 * Seth Thomas Clock Co. 
 
CAPACITY OF LIBRARY SHELVING. 1495 
 
 partitions or shelf supports. A row of compartments, side by 
 side, constitutes a range. A number of ranges form a stack. 
 
 When the compartments are placed against walls, and are acces- 
 sible from only one side, they are called single- face'd; and when 
 placed free from walls, thus accessible on both sides, they are 
 double-faced. 
 
 A standard single-faced compartment is 3 ft. long, 8 or 10 ins. 
 wide, and 7 ft. high. A standard double-faced compartment is 
 16 or 20 ins. wide, other dimensions the same. Standard shelves 
 are 3 ft. long and 8 or 10 ins. wide. The aisles between the 
 ranges vary from 2 ft. 8 ins. to 3 ft. 4 ins. in width. 
 
 The shelf supports are made in various ways, differing with 
 each manufacturer. They should not seriously break the smooth 
 surface at the side, or expose the last book to damage. The 
 shelves are usually constructed of steel. The weight of stacks 
 and shelves (as made by the Snead & Co. Iron Works) with their 
 load of books is about 30 Ibn per cubic foot of stack. 
 
 When there are upper floors they are usually referred to as 
 docks; the height from deck to deck varies from 7 ft. to 7 ft. 6 ins., 
 7 ft. being the standard. The deck framing consists of steel tees, 
 angles, and bars, and the floor covering is of marble or rough plate 
 glass* The weight of deck framing and floor covering is about 
 24 Ibs. per sq. ft. for marble and 18 Ibs. for glass. 
 
 Capacity of Library Shelving. The capacity of a 
 library depends upon its character; for an ordinary circulating 
 library the capacity is about ten volumes per lineal foot of shelf; 
 for the Library of Congress it is about eight and a half volumes 
 per lineal foot, and this is about the average for an ordinary 
 collection of books. 
 
 The number of books a room will hold may be estimated as 
 follows ; 
 
 Let us suppose that the cases are 7 ft high, 16 ins. deep, and 
 have books on each side; that the width of passageway between 
 the cases is the minimum of 32 ins. ; and that each shelf is 36 ins. 
 in length, The floor-space that one division of one side of the 
 case will take is half the width of the case (8 ins.) plus half the 
 width Of passageway (16 ins.), multiplied by the length of the 
 shelf (36 ins.), which gives a result of 6 sq. ft, If the average 
 number of shelves in the division is 7, and there are 8J books 
 to the foot, the capacity of the division is 180 volumes, or an 
 average of 30 books to the square foot of floor area. In this 
 calculation no account has been taken of the stairs, windows, 
 
1496 CLASSICAL MOULDINGS. 
 
 doors, or cross gangway, and only a minimum width of passage- 
 way has been allowed. If space for these is taken into con- 
 sideration, a conservative estimate of shelving capacity of a 
 room will work out at about 22 volumes to the square foot, for 
 each deck or story 7 ft. high. 
 
 In the Congressional Library at Washington the double-faced 
 compartments are 24 ins. wide over all, and the aisles between 
 3 ft. 4 ins. wide, making 5 ft. 4 iris, between centres of compart- 
 ments. The stack rooms are nine stories high, each story being 
 7 ft. from floor to floor. The floors proper are thin white-marble 
 slabs, with polished side down for reflecting the light. 
 
 CLASSICAL MOULDINGS.* 
 
 Mouldings are so called because they are of the same shape ' 
 throughout their length as though the whole had been cast in the 
 same mould or form. The regular mouldings, as found in re- 
 mains of classic architecture, are eight in number, and are known 
 by the following names: 
 
 The last two are both called 
 
 Annulet, band, cincture, fillet, Astragal, or bead. "ro-AA " 
 
 listel, or square. OgCC. 
 
 Some of these terms are de- 
 rived thus: Fillet, from th& 
 
 Scotia, trochilus or mouth. -*-* i t /> T ee jt i 
 
 French word fil, "thread 
 
 ) f astragal, from astragalos , 
 
 OTolo, quarter-round, or echinus. Cavetto. cove, or hollow, bone of the heel," Or 
 
 *" I ~) curva t ure of the heel"; bead, 
 
 x~^ because this moulding, wher* 
 
 yma-reote. Inverted cymatium, or property Carved, resembles &, 
 
 string of beads; torus, or tore, 
 
 the Greek for rope, which it resembles when on the base of a 
 column; scotia, from skotia, "darkness," because of the strong 
 shadow which its depth produces, 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 kuma- 
 ton, "a wave." 
 
 Characteristics of Mouldings. Neither of these 
 mouldings is peculiar to any one of the orders of architecture ; 
 and although each has its appropriate use, yet it is by no means 
 confined to any certain position in an assemblage of mouldings. 
 
 * See also Glossary, under Moulding. 
 
THE CLASSICAL ORDERS. 1497 
 
 The use of the fillet is to bind the parts, as also that of the astra- 
 gal and torus, which resemble ropes. The ovolo and cyma- 
 reversa are strong at their upper extremities, and are therefore 
 used to support projecting parts above them. 
 
 The cyma-recta and cavetto, being weak at their upper ex- 
 tremities, 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 
 reasons for giving distinct names to them are that the torus, in 
 every order, is always considerably larger than the bead, and is 
 placed among the base mouldings, ^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, is 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.* 
 
 "In the classical styles several varieties of column and entab- 
 lature 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 in- 
 fluenced 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. 
 
 * The paragraphs in quotation-marks are taken from ' ' The American 
 Vlgnola" by Prof. Win. R. Ware, by permission of the owners of the copy- 
 right, the International Text-book Company, proprietors of the Interna- 
 tional Correspondence Schools. The engravings were made especially for 
 this book, and correspond with the original drawings prepared by Giacomo 
 Barozzi da Vignola. 
 
1498 
 
 THE CLASSICAL ORDERS. 
 
 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 ancient examples vary much among 
 
 IV Cymatium ' 
 
 ':_ 
 
 r ~-> 
 \ 
 
 
 
 
 Corona 1 *? g 
 
 T 1 
 
 
 j^->. Bed Mould ^ ^ 
 
 < 9 -|<-4~ 
 18 * 
 
 T 
 
 J N 
 
 '-**-*' SI 
 
 , h 
 
 ^ i <b . 
 
 r ~1 
 
 | Taenia o ^ f- ' 
 
 M^ 
 
 ..... fc'J J 
 
 ' 1 Abacus 
 
 ' ' I ....._._ J i "o 
 
 
 > V Echinus ) 9 '". 
 
 1- ^q 1 f/ 
 
 , 
 
 
 
 Necking f I i ! K 
 
 M 
 
 ' 
 
 tragaF 
 
 1 ! I !j 
 
 ii 
 
 s ^ 
 
 / I v it 
 
 T- 
 
 4- 
 >t 
 
 -^J 1 U^ ^ | 
 r Torus j 1 
 
 ^4 
 <; 16 J Plinh ' ( 
 
 Dimensions are in 2iths of Diameter. 
 
 Fig. I 
 
 The Tuscan Order. 
 
 themselves and differ in different places, and in modern times 
 still further varieties are found in Italy, Spain, France, Ger- 
 many, and England The best known and most admired forms 
 for the orders are those worked out by Giacomo Barozzi da 
 
THE CLASSICAL ORDERS. 
 
 1499 
 
 Vignola in the sixteenth century from the study of ancient 
 examples." 
 
 The Tuscan Order. "The distinguishing characteristic 
 of the Tuscan order is simplicity. Any forms of pedestal, 
 
 I 
 I 
 
 I 
 I 
 
 MM->N- is* 
 
 ! 
 
 u 
 
 1 1 
 
 1 
 
 
 
 
 1 f \ \ 
 
 1 1 
 
 
 
 71 ' iv 
 
 I 
 
 f f* 
 
 ^2>k-3 J 
 
 
 
 1 
 
 
 1 
 
 
 
 
 | 
 
 
 I A 
 
 
 
 
 
 
 Metope | 9 
 
 
 
 
 1 
 
 1 
 
 < 
 
 - Triglyph. f i 
 
 
 
 
 
 
 1 -S 
 
 
 
 
 ! 
 1 
 I 
 
 
 '^ 
 
 <- 12 ^ 
 
 Dimensions are in Siths Of Diameter 
 
 Fig. 2 
 The Doric Order. 
 
 column, and entablature that show but few mouldings, and 
 those plain, are considered to be Tuscan." 
 
1500 THE CLASSICAL ORDERS. 
 
 The Doric Order. "The distinguishing characteristics 
 of the Doric order are features in the frieze and in the bed-mould 
 above it called triglyphs and mutules, which are supposed to 
 be derived from the ends of beams and rafters in a primitive 
 wooden construction with large beams. Under each triglyph, 
 and beneath the tsenia which crowns the architrave, is a little 
 fillet called the regula. Under the regula are six long drops, 
 called guttae, which are sometimes conical, sometimes pyramidal. 
 There are also either eighteen or thirty-six short cylindrical 
 guttse under the soffit of each mutule. The guttse are supposed 
 to represent the heads of wooden pins, or treenails. 
 
 "Two different Doric cornices are in use the mutulary with 
 bracket and the denticulated with dentils, the principal difference 
 being in the bed-mould." The order shown by Fig. 2 has the 
 denticulated cornice. 
 
 The Ionic Order. "The prototypes of the Ionic order 
 are to be found in Persia, Assyria, and Asia Minor. 
 
 '"It is characterized by bands in the architrave and dentils 
 in the bed-mould, both of which are held to represent small 
 sticks laid together to form a beam cr a roof. But the most 
 conspicuous and distinctive feature is Che scrolls which deco- 
 rate the capital of the column. The,: 3 have no structural 
 significance, and are purely decorative forms derived from 
 Assyria and Egypt. Originally the Ion*; order had no frieze 
 and no echinus in the capital. These were borrowed from 
 the Doric order, and, in 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 Zoophorus, 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 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 the engraving. 
 
 "The Ionic frieze is plain, except for the sculpture upon it. 
 It sometimes has a curved outline, as if ready to be carved, and 
 
THE CLASSICAL ORDERS. 
 
 1501 
 
 -*- 
 
 f 
 
 i ! 
 
 X 
 
 -r-I 
 
 ^ o I 
 
 IDmpJULI I" f 
 
 %>'AI,kM,UJ,WA!U %' 
 
 .. Dimensions are in 2i"ths of Diai 
 
 Fig. 3 
 
 The Ionic Order. 
 
1502 THE CLASSICAL ORDERS. 
 
 Is then said to be pulvinated, from pulvinar, a bolster, which it 
 much resembles. 
 
 "The shaft of the column is ornamented with twenty-four 
 flutings, semicircular in section, which are separated not by an 
 arris, but by a fillet of about one fourth their width. This 
 makes the flutings only about two thirds as wide as the Doric 
 channels, or about one-ninth of a diameter, instead of one 
 sixth." 
 
 To Describe the Ionic Volute. There are several 
 methods of doing this, the simplest being by means of centres 
 found as shown by the diagram Fig. 3a. First locate the centre 
 of the eye \D vertically below the point A, Fig. 3. Then describe 
 a circle with a diameter equal to T \Z), to form the eye. Inside of 
 this circle inscribe a square at 45 degrees to a horizontal; then 
 draw the axes 1-3 and 2-4, and divide each of these into six equal 
 parts. Then with the point 1 as a centre, and a radius extending 
 to A, Fig. 3, draw a quarter-circle to line 1-2 produced, with 2 as a 
 
 centre, continue the curve 
 | until it intersects 2-3 pro- 
 
 duced, and so on. The 
 centres for the-outer curve of 
 the volute are at the points 
 1, 2, 3, 4, 5, 6, etc. For the 
 centres for the inner curve, 
 start with a point one third 
 the way from 1 to 5, then a 
 point one third the way from 
 2 to 6, and so on. 
 
 The Corinthian Or- 
 der. "The three distin- 
 I ', ' guishing characteristics of 
 
 Pig e 3 a the Corinthian order 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 by the use of the 
 acanthus leaf in both capitals and modillions. 
 
 "Here, again, the Attic base is commonly used, but some- 
 times, 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 is 
 fluted like the Ionic shaft, with twenty-four semicircular flut- 
 
THE CLASSICAL ORDERS. 
 
 1503 
 
 V, 
 
 ULTUUU1 " . 
 
 . 
 
 k ^r!2 - 9 
 
 1 
 
 
 .b 
 
 
 i 
 
 
 i 
 
 
 Dimensions are in 24ths of Diameter 
 
 THE CORINTHIAJlORJDEg. 
 
 Fig. 4 
 
1504 THE CLASSICAL ORDERS. ; ; 
 
 ings, but these are sometimes filled with a convex moulding or 
 cable 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 capi- 
 tal, 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 
 volutes are replaced by the large echinus, scrolls, and astragal of 
 a complete Ionic capital. 
 
 "Vignola's composite entablature differs from his Ionic 
 chiefly in the shape and size of the dentils. They are larger, 
 and are more nearly square in elevation, being a fifth of a diam- 
 eter high and one sixth wide, the interdentil being one twelfth, 
 and they are set one fourth of a diameter apart, on centres. 
 
 "The composite capital is employed 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 architecture of the ancient Egyp- 
 tians 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 enormous columns, very stout 
 in proportion to their height; the shaft sometimes polygonal, 
 having 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 1J diameters and seldom exceed- 
 ing 2J. 
 
 A great dissimilarity exists in the proportion, form, and gen- 
 eral feature of Egyptian columns. For practical use the colun 
 
 * From "The American House Carpenter," by R. G. Hatfield. 
 
LIGHTNING CONDUCTORS. 
 
 1505 
 
 shown in Fig. 5 may be taken as a standard of the Egyptian 
 style. 
 
 LIGHTNING CONDUCTORS. 
 
 The following rules for the erection of lightning conductors 
 were issued in 1882 by the Explosive Department of the English 
 Home Office to the occupiers of all factories and magazines for 
 
 FIG. 5. EGYPTIAN ARCHITECTURE. 
 (Diameter divided into 60 parts.) 
 
 explosives, and to those local and police authorities upon whom 
 devolves the inspection of stores of explosives : 
 
1506 LIGHTNING CONDUCTORS. 
 
 1. Material of Rod. Copper, weighing not less than 6 oz. per 
 foot run, the electrical conductivity of which is not less than 90 
 per cent, 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 
 B. W. G. (.109 in.). Iron may be used, but should not weigh 
 less than 2J Ibs. per foot 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 a sharper angle than 90. A foot 
 below the extreme point a copper 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 ins. 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 
 assumed 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 the conductor itself is composed 
 of. 
 
 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 Metal Work. All metallic spouts, gutters, iron doors, 
 and other masses of metal about the building should be elec- 
 trically connected with the conductor. 
 
 * The upper terminal is that portion of the conductor which is between 
 the top of the edifice and the point of the conductor. 
 
ADHESIVE STRENGTH OF SULPHUR, ETC. ISO? 
 
 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 of the lightning into the earth: (1) 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 pipe), if such exist near enough, 
 and be soldered to it; (2) a tape may be soldered to a sheet of 
 copper, 3 ft. X3 ft. X^ in. thick, buried in permanently wet 
 earth and surrounded by cinders or coke; (3) 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 in an iron gas-pipe, reaching 10 ft. 
 (if there is room) above ground and some distance into the 
 ground. 
 
 11. 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 eases 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 examination and testing, should opportunities 
 offer, are also very desirable, especially when iron earth con<- 
 nections are employed. 
 
 ADHESIVE STRENGTH OP SULPHUR, LEAD, AND 
 PORTLAND CEMENT FOR ANCHORING BOLTS. 
 
 The following test of these materials is reported in the Amer- 
 ican Architect, page 105, vol. xxiv. : 
 
 " Fourteen holes were drilled in a ledge of solid limestone, 
 seven of them being If ins. in diameter and seven of them If 
 ins. in diameter, all being 3J ft. deep. Seven |4n. and seven 
 1-in. bolts were prepared with thread and nut on one end and 
 plain at the other end but ragged for a length of 3J ft. from the 
 blank end. 
 
 "Four were anchored with sulphur, four with lead, and six 
 with cement, mixed neat. Half of each were f-in. and half 1-in. 
 
1508 EFFLORESCENCE ON BRICKWORK. 
 
 bolts, and all of them were allowed to stand till the cement was 
 two weeks old. At the expiration of this time a lever of suffi- 
 cient power was rigged and all the bolts were pulled with the 
 following result: 
 
 11 Sulphur. Three bolts out of four developed their full 
 strength, 16,000 and 31,000 Ibs. One 1-in. bolt failed by draw- 
 ing out under 12,000 Ibs. 
 
 11 Lead. Three bolts out of four developed their full strength, 
 as above; one 1-in. bolt pulled out under 13,000 Ibs. 
 
 "Cement. Five of the bolts out of six broke without pulling 
 out; one 1-in. bolt began to yield in the cement at 26,000 Ibs., 
 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, yet it did 
 not give the strength per square inch of area. To determine 
 this, four specimens of limestone were prepared, each 10 ins. 
 wide, 18 ins. long, and 12 ins. thick, two of them having IJ-in. 
 holes, and two of 'them 2|-in. holes drilled in them. Into the 
 small holes 1-in. bolts were cemented, one of them being per- 
 fectly plain round iron, and the other having a thread cut on 
 the portion which was imbedded 'in the cement. Into the 2- 
 in. holes were cemented 2-in. b'olts similarly treated, and the 
 four specimens were allowed to stand thirteen days before com- 
 pleting the experiment. At the end of this time they were put 
 into a standard testing-machine and pulled. The plain 1-in. 
 bolt began to yield at 20,000 Ibs., and the threaded one at 21,000 
 Ibs. The 2-in. plain bolt began to yield at 34,000 Ibs., and the 
 threaded one at 32,000 Ibs., the strain 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 Ibs. in the 
 case of the smooth one and at 50,000 Ibs. in the case of the 
 threaded one. 
 
 "It is thus seen that cement is more reliable, stronger, and 
 easier of application than either lead or sulphur, and that its re- 
 sistance is from 400 to 500 Ibs. per square inch of surface ex- 
 posed. It is also a well-ascertained fact that it preserves iron 
 rather than corrodes it. The cement used throughout the ex- 
 periment was an English Portland cement." 
 
 EFFLORESCENCE ON BRICKWORK. 
 
 There are at least three different substances which may cause 
 the white efflorescence often seen on the face of brickwork. 
 
RELATIVE HARDNESS OF WOODS. 
 
 1509 
 
 Of these, carbonate of soda is the most common upon new 
 work, after the lime stains have been removed. This is due to 
 the action of the lime mortar upon the silicate of soda in the 
 bricks. Silicate of soda seldom occurs in brick unless the clay 
 used is a salt clay. 
 
 The only other white efflorescence of importance is chiefly 
 composed of sulphate -of magnesia. This is due to pyrites in 
 the clay, which, when burned, gives rise to sulphuric acid, and 
 the latter unites with 'magnesia in the lime mortar. 
 
 The above are the results of actual examinations by Mr. 
 Samuel Cabot, chemist. The conclusions arrived at are these: 
 
 I. The efflorescence is never due to the bricks alone, and 
 seldom to the lime alone. 
 
 II. To avoid it, the bricks should be covered with an oily pre- 
 servative capable of keeping the salts from exuding. Linseed 
 oil cannot fill the requirements, as it is injured by the mortar. 
 
 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 OP ROUGH LUMBER PER 1,000 FEET. 
 
 BOARD MEASURE (APPROXIMATE). 
 (For weight of various woods see table, pp. 1341 to 1344.) 
 
 
 Dry. 
 
 Partly 
 Seasoned. 
 
 Greei-. 
 
 Pine and hemlock 
 
 2,500 Ibs. 
 
 2 700 Ibs. 
 
 3 000 Ibs. 
 
 Norway and yellow pine. . . . 
 Oak and walnut . . 
 
 3,000 " 
 4 000 " 
 
 4,000 " 
 5 000 " 
 
 5,000 " 
 
 Ash and maple 
 
 3,500 " 
 
 4000 " 
 
 
 
 
 
 
1510 
 
 FORCE OF THE WIND. 
 
 FORCE OF THE WIND. 
 
 According to experiments made in 1890 or thereabouts, by 
 Asst. Prof. C. F. Marvin, U. S. Signal Service, the relation be- 
 tween wind pressure and velocity is given very accurately by 
 the formula p = .004F 2 , where p = pressure in pounds per square 
 foot on a flat surface normal to the direction of the wind, and 
 V denotes velocity in miles per hour, Smeaton considered 
 the pressure as equal to .005 F 2 . 
 
 The following table based on Marvin's formula is quoted by 
 Profs. Turneaure and Ketchum. See also Trautwine's Pocket- 
 book, p. 321, note. 
 
 Miles 
 per 
 Hour. 
 
 Feet 
 per 
 Minute. 
 
 Feet 
 per 
 Second. 
 
 Force, in 
 Pounds, per 
 Square Foot. 
 
 Description. 
 
 1 
 
 88 
 
 1.47 
 
 0.004 
 
 Hardly perceptible 
 
 2 
 3 
 
 176 
 264 
 
 2.93 
 4.4 
 
 0.014 1 
 
 0.036 j 
 
 Just perceptible 
 
 4 
 5 
 
 352 
 440 
 
 5.87 
 7.33 
 
 0.064 I 
 0.1 \ 
 
 Gentle breeze 
 
 10 
 15 
 
 880 
 1,320 
 
 14.67 
 22 
 
 . 0.4 f 
 
 0.9 F 
 
 Pleasant breeze 
 
 20 
 25 
 
 1,760 
 2,200 
 
 29.3 
 26.6 
 
 1.6 j. 
 2.5 j 
 
 Brisk gale 
 
 30 
 35 
 
 2,640 
 3,080 
 
 44 
 
 51.3 
 
 3.6 ) 
 4.9 1 
 
 High wind 
 
 40 
 
 45 
 
 3,520 
 3,960 
 
 58.6 
 66 
 
 6.4 f 
 
 8.1 f 
 
 Very high wind 
 
 50 
 
 4,400 
 
 73.3 
 
 10.0 
 
 Storm 
 
 60 
 70 
 
 5,280 
 6,160 
 
 88 
 102.7 
 
 14.4 ) 
 19.6 f 
 
 Great storm 
 
 80 
 100 
 
 7,040 
 8,800 
 
 117.3 
 146.6 
 
 25.6 ) 
 40.0 \ 
 
 Hurricane 
 
 TO MAKE BLUE-PRINT COPIES OF TRACINGS. 
 
 The following directions, taken from The Locomotive, cover 
 the whole ground. The sensitized paper can be procured at 
 stores where artists' materials are sold, all prepared, so that 
 the process of preparing the paper by means of chemicals can 
 then be omitted, 
 
 The materials required are as follows: 
 
 1. A board a little larger than the tracing to be copied. The 
 drawing-board on which the drawing and tracing ar,3 made can 
 always be used. 
 
BLUE-PRINT COPIES OF TRACINGS. 1511 
 
 2. Two or three thicknesses of flannel or other soft white cloth, 
 which is to be smoothly tacked to the above board, to form a 
 good 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 which it is wished to 
 copy. 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. These can be obtained at any 
 drug-store. The price should not be over eight or ten cents 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 ordi- 
 nary glass bottle will do, and the solution made fresh 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 brush, a soft paste-brush about 4 ins. wide, is the best 
 thing we know of. 
 
 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. 
 If it is not, it would be better to make a water-tight box about 
 5 or 6 ins. deep, and 6 ins. wider and longer than the drawing 
 to be copied. 
 
 9. A good quality of white book-paper. 
 
 Dissolve the chemicals in cold water in the following propor- 
 tions: 1 oz. of citrate of iron and ammonia, 1 oz, of red prus- 
 siate of potash, 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 of 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 coating 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 
 
1512 HORSE-POWER, ETC. 
 
 for the drying; then place its sensitized side up, on the board 
 on which you have smoothly tacked the white flannel cloth; 
 lay your tracing which you wish to copy on top of it; on top of 
 all lay the glass plate, being careful that paper and tracing are 
 both smooth and in perfect contact with each other, and lay 
 the whole thing out hi the sunlight. Between eleven and two 
 o'clock in the summer-time, on a clear day, from six to ten min- 
 utes will be sufficiently long to expose it; at other seasons a 
 longer time will be required. If your location does not admit 
 of direct sunlight, the printing may be done in the shade, or 
 even on a cloudy day; but from one to two hours and a half 
 will be required for exposure. A little experience will soon 
 enable any one to judge of the proper time for exposure on 
 different days. After exposure, place your print in the sink or 
 trough of water before mentioned, and wash thoroughly, letting 
 it soak from three to five minutes. Upon immersion in the 
 water, the drawing, hardly visible before, will appear in clear 
 white lines on a dark-blue ground. After washing, tack up 
 against the wall, or other convenient place, bv the corners, to 
 dry. This finishes the operation, which is very simple and 
 thorough. 
 
 After the copy is dry, it can be written on with a common pen 
 and a solution of common soda, which gives a white line. 
 
 HORSE-POWER, PULLEYS, GEARS, BELTING, 
 AND SHAFTING. 
 
 Horse-power. A horse can travel 400 yds. at a walk in 
 4J minutes, at a trot in 2 minutes, and at a gallop in 1 minute; 
 he occupies at a picket 3 ft. by 9 ft.; and his average weight 
 equals 1,000 Ibs. 
 
 An average horse carrying 225 Ibs. can travel 25 miles in a day 
 of eight hours. 
 
 A draught-horse can draw 1,600 Ibs. 23 miles a day, weight of 
 carriage included. 
 
 In a horse-mill a horse moves at the rate of 3 ft. in a second. 
 The diameter of the track should not be less than 25 ft. 
 
 A horse-power, in machinery, is estimated at 33,000 Ibs., 
 raised 1 ft. in a minute; but as a horse can exert that force but 
 six hours a day, one machinery horse-power is equivalent to 
 that of 4 horses. 
 
PULLEYS, GEARS AND BELTING. 1513 
 
 Rules to Determine the Size and Speed of 
 Pulleys or Gears. The driving pulley is called the driver, 
 and the driven pulley the driven. 
 
 If the number of teeth in gears are used instead of diameter, 
 in these calculations, number of teeth must be substituted 
 wherever diameter occurs. 
 
 To find the diameter of driver, the diameter of the driven and 
 its revolutions, and also revolutions of driver, being given: 
 Multiply the diameter of driven by its revolutions, and divid 
 the product by the revolutions of the driver; the quotient 
 will give the diameter of the driver. 
 
 To find the diameter of driven, the revolutions of the driven, 
 also diameter and revolutions of the driver, being given: Mul- 
 tiply the diameter of driver by its revolutions, and divide the 
 product by the revolutions of the driven; the quotient will 
 give the diameter of the driven. 
 
 To find the revolutions of the driver, the diameter and revolu- 
 tions of the driven, also diameter of the driver, being given: 
 Multiply the diameter of driven by its revolutions, and divide 
 the product by the diameter of driver; the quotient will give 
 the revolutions of driver. 
 
 To find the revolutions of the driven, the diameter and revolu- 
 tions of the driver, also diameter of the driven, being given: 
 Multiply the diameter of driver by its revolutions, and divide 
 the product by the diameter of driven; the quotient will give 
 the revolutions of driven. 
 
 Horse-power Belting will Transmit. The ability 
 of belting to transmit power, or to turn a wheel or "pulley/ 1 
 depends upon the width and thickness of the belt, the arc con- 
 tact with the pulley, whether the belt is horizontal, vertical, or 
 at an angle, and upon ^Jie velocity. The greater the velocity 
 and the thicker the belt, the more power it will transmit. A 
 belt running vertically or inclined will transmit less power than 
 one running horizontally, but in figuring the horse-power ca- 
 pacity of belting only the velocity, width, and thickness of belt 
 are usually considered, it being assumed that the pulleys are 
 of proper size and located so that the belt will be nearly hor- 
 izontal. Belts are commonly assumed to be of leather, unless 
 otherwise designated. 
 
 The term single belt is used to designate a belt made of a 
 single thickness of cowhide leather. 
 
 A double belt is made by cementing and riveting together 
 
1514 NOTES ON BELTING. 
 
 two thicknesses of leather. There is no standard thickness for 
 either single or double belts. 
 
 RULES. Many rules have been given for determining the 
 horse-power belting will transmit.* Those most commonly 
 used are: 
 
 For Single Belts. Multiply the width (in inches) by the 
 velocity in feet per minute and divide by 1,000. 
 
 For Double Belts, Multiply the width by the velocity and 
 divide by 700. The answer is the number of horse-power. 
 
 Some authorities give divisors of 800 and 733 for single belts, 
 and 550 and 513 for double belts. 
 
 For the velocity of the belt multiply the number of revolu- 
 tions per minute of either pulley by the circumference of that 
 pulley, 
 
 Notes on Belting 1 . For continuous use a double belt is 
 the most economical, in the long run, except on very small pul- 
 leys or for very light duty. 
 
 Triplex and quadruple belts are sometimes used for very 
 heavy duty, but such belts are not commonly carried in stock. 
 
 Single belts should always be used with the hair side next 
 the pulley. 
 
 The belt speed for maximum economy should be from 4000 
 to 4500 ft. per minute. 
 
 Idler pulleys work most satisfactorily when located on the 
 slack side of the belt about one quarter way from the driving- 
 pulley. 
 
 Belts are more durable and work more satisfactorily made nar- 
 row and thick, rather than wide and thin. 
 
 As belts increase in width they should also be made thicker. 
 
 For dynamo work or electric motors the ends of the belt 
 should be fastened together by splicing and cementing, instead 
 of lacing. 
 
 For all other cases the ends are fastened by hooks or lacing. 
 
 Belts should be cleaned and greased every five to six months. 
 
 Distance Centre to Centre of Shafts.* In the 
 location of shafts that are to be connected with each other by 
 belts, care should be taken to secure a proper distance one 
 from the other. This distance should be such as to allow of 
 a gentle sag to the belt when in motion. 
 
 A general rule may be stated thus: Where narrow belts are 
 to be run over small pulleys 15 ft. is a good- average, the belt 
 * For discussion of belting, belt-dressings, care of, etc., see Kent, pp. 876-887. 
 
BELTS AND PULLEYS. 1515 
 
 having a sag of 1J to 2 ins. The minimum distance between 
 shafts is about 10 ft. 
 
 For larger belts, working on larger pulleys, a distance of 20 
 to 25 ft. does well, with a sag of 2J to 4 inches. 
 
 For main belts working on very large pulleys, the distance 
 should be 25 to 30 ft., the belts working well with a sag of 4 to 
 5 ins. 
 
 If too great a distance is attempted, the belt will have an 
 unsteady flapping motion, which will destroy both the belt 
 and machinery. 
 
 Arrangement of Belts and Pulleys.* If possible 
 to avoid it, connected shafts should never be placed one directly 
 over the other, as in such case the belt must be kept very 
 tight to do the work. For this purpose belts should be carefully 
 selected of well-stretched leather. 
 
 It is desirable that the angle of the belt with the floor should 
 not exceed 45. It is also desirable to locate the shafting and 
 machinery so that belts should run off from each shaft in opposite 
 directions, as this arrangement will relieve the bearings from 
 the friction that would result when the belts all pull one way 
 on the shaft. 
 
 If possible, machinery should be so placed that the direction 
 of the belt motion shall be from the top of the driving to the top 
 of the driven pulley, when the sag will increase the arc of con- 
 tact. 
 
 The pulley should be a little wider than the belt required for 
 the work, and should have a crowning face, except where the 
 belt is to be shifted. 
 
 The motion of driving should run with and not against the 
 laps of the belts. 
 
 Rubber belts are cheaper than leather belts and should 
 always be used in wet places, but for ordinary Use in dry places 
 they are not as durable as leather belts. 
 
 They should always be kept free from grease or animal oils. 
 If they slip, moisten the inside of the belt with boiled linseed 
 oil. Some fine chalk, sprinkled on over the oil, will help the 
 belt. 
 
 Rule for Finding the Length of Belts. Add the 
 diameter of the two pulleys togethef, multiply by 3^, divide 
 the product by 2, add to the quotient twice the distance 
 * 
 
 * Kent, p. 885. 
 
1516 
 
 SHAFTING CHAIN BLOCKS. 
 
 between the centre of the shafts, and the sum will be the 
 required length. 
 
 Horse-Power Shafting will Transmit. 
 
 Diameter of 
 
 Revolutions per Minute. 
 
 Shaft in 
 
 
 Inches. 
 
 
 
 
 
 
 
 
 
 100 
 
 150 
 
 200 
 
 250 
 
 300 
 
 350 
 
 400 
 
 ins. 
 
 16ths. 
 
 H.P. 
 
 H.P. 
 
 H.P. 
 
 H.P. 
 
 H.P. 
 
 H.P. 
 
 H.P. 
 
 
 
 15 
 
 1.2 
 
 1.7 
 
 2.4 
 
 3.1 
 
 3.6 
 
 4.3 
 
 5.0 
 
 1 
 
 3 
 
 2.4 
 
 3.7 
 
 4.9 
 
 6.1 
 
 7.3 
 
 8.5 
 
 9.7 
 
 1 
 
 7 
 
 4.3 
 
 6.4 
 
 8.5 
 
 10.5 
 
 12.7 
 
 14.8 
 
 16.9 
 
 1 
 
 11 
 
 6.7 
 
 10.1 
 
 13.4 
 
 16.7 
 
 20.1 
 
 23.4 
 
 26.8 
 
 1 
 
 15 
 
 10.0 
 
 15.0 
 
 20.0 
 
 25.0 
 
 30.0 
 
 35.0 
 
 40.0 
 
 2 
 
 3 
 
 14.3 
 
 21.4 
 
 28.5 
 
 35.6 
 
 42.7 
 
 49.8 
 
 57.0 
 
 2 
 
 7 
 
 19.5 
 
 29.3 
 
 39.0 
 
 48.7 
 
 58.5 
 
 68.2 
 
 78.0 
 
 2 
 
 11 
 
 26.0 
 
 39.0 
 
 52.0 
 
 65.0 
 
 78.0 
 
 87.0 
 
 104.0 
 
 2 
 
 15 
 
 33.8 
 
 50.6 
 
 67.5 
 
 84.4 
 
 101.3 
 
 118.2 
 
 135.0 
 
 3 
 
 3 
 
 43.0 
 
 64.4 
 
 85.8 
 
 107.3 
 
 128.7 
 
 150.3 
 
 171.6 
 
 3 
 
 7 
 
 53.6 
 
 79.4 
 
 107.2 
 
 134.0 
 
 158.8 
 
 187.6 
 
 214.4 
 
 3 
 
 11 
 
 65.9 
 
 97.9 
 
 121.8 
 
 164.8 
 
 195.7 
 
 230.7 
 
 243.6 
 
 3 
 
 15 
 
 80.0 
 
 120.0 
 
 160.0 
 
 200.0 
 
 240.0 
 
 280.0 
 
 320.0 
 
 4 
 
 7 
 
 113.9 
 
 170.8 
 
 227.8 
 
 284.7 
 
 341.7 
 
 398.6 
 
 455.6 
 
 4 
 
 15 
 
 156.3 
 
 234.4 
 
 312.5 
 
 390.6 
 
 468.7 
 
 546.8 
 
 625.0 
 
 CHAIN BLOCKS. 
 
 These are portable hoisting devices which enable one man 
 to raise a very heavy load and which will sustain the load at any 
 point. In general, they resemble pulleys operated by chains. 
 Since the invention of the differential pulley-block by' Thos. A. 
 Weston, about the year 1863, chain blocks have come into very 
 general use for economical hoisting, and particularly where it is 
 desired to hold the load at any point. 
 
 Chain blocks are of three general classes: 
 
 A. The differential block, which is the original and simplest 
 and cheapest form of self-sustaining pulley. 
 
 B. Screw- or worm-geared blocks, of which the Yale & Towne 
 duplex blocks are the most efficient type; and 
 
 C. Triplex blocks, spur-geared. > 
 Differential and worm-geared blocks of all kinds depend upon 
 
 friction to prevent the load from running down. In the triplex 
 block a separate device is introduced which automatically holds 
 the load safely, and yet enables it to be lowered with slight 
 effort and at high velocity but without acceleration or danger. 
 This is the most efficient of all chain blocks, and the most 
 economical wherever quick work is wanted and economy in 
 
CHAIN BLOCKS. 
 
 1517 
 
 time and labor >sought. For information as to the kind of block 
 best adapted to any particular service, the manufacturers 
 should be consulted. The following data on the power and 
 efficiency of chain blocks were supplied by the Yale & Tcwne 
 Manufacturing Company, i 
 
 Power and Efficiency of Chain Hoists. The table 
 below gives the work to be done by the operator at the hand- 
 pulling chain with each size of various kinds of chain blocks 
 in lifting the stated capacity* i. e. , the amount of work or pull- 
 ing required to lift this load one foot by stating the force exerted 
 in hounds and the distance in feet of operating chains to be 
 pulled. The product of these two factors determines the effici- 
 ency of the block and the ease and speed of hoisting. 
 
 Capacity 
 in Tons. 
 
 Triple?: 
 (Spur-geared). 
 
 Duplex 
 (Worm-geared). 
 
 Differential. 
 
 
 Lbs. Ft. 
 
 Lbs. Ft. 
 
 Lbs. Ft. 
 
 i 
 
 62 X 21 
 
 68 X 40 
 
 122X24 
 
 
 82 X 31 
 
 87 X 59 
 
 216X30 
 
 1* 
 
 110X 35 
 
 94 X 80 
 
 246X36 
 
 2 
 
 120 X 42 
 
 115X 93 
 
 308X42 
 
 3 
 
 114 X 69 
 
 132X126 
 
 557X38 
 
 4 
 
 124 X 84 
 
 142X155 
 
 
 5 
 
 110X126 
 
 145X195 
 
 
 6 
 
 130X126 
 
 145X252 
 
 
 8 
 
 135X168 
 
 160X310 
 
 
 10 
 
 140X210 
 
 160X390 
 
 
 12 
 
 130X126 
 
 
 
 16 
 
 135X168 
 
 
 
 20 
 
 140X210 
 
 
 
 These blocks have two hand chains. The figures give the 
 number of feet to be operated on each hand chain. 
 
 A man cannot pull more than his own weight on the operating 
 chains, and can pull faster in proportion as the pull required is 
 lighter. 82 Ibs. is maximum pull usually required of one man, 
 and he will do more work with less fatigue if the hand-chain 
 pull is not over 40 Ibs., because he can then pull the chain hand 
 over hand a little more than twice as fast as he could when pulling 
 twice as hard. When the hand-chain pull is less than 20 Ibs. 
 the speed of hoisting an equal load is diminished because the 
 man is tired by moving his arms too rapidly, and cannot do 
 as much work as with a heavier pull. 
 
1518 
 
 PROPORTIONS OF HOOKS. 
 
 The best result is obtained bv using a chain block having 
 a capacity double the usual load. 
 
 The operator then works to the best advantage with average 
 loads, and occasional heavy loads are easily handled without 
 overstraining either the operator or the chain block, which 
 should never be used beyond its capacity for fear of stretching 
 the chain so that it will not work smoothly. 
 
 Proportions of Hooks.* For economy of manufac- 
 ture each size of hook is made from some regular commercial 
 size of round iron. The basis, or initial point, in each case is, 
 therefore, the size of iron of which the hook is to be made, which 
 is indicated by the dimension A in the diagram. The dimen- 
 sion D is arbitrarily assumed. The other dimensions, as given 
 by the formulae, are those which, while preserving a proper 
 
 bearing-face* on the interior of 
 the hook for the ropes or chains 
 which may be passed through 
 it, give the greatest resistance to 
 spreading and to ultimate rup- 
 ture which the amount of mate- 
 rial in the original bar admits 
 of. The symbol A is used in 
 the formulae to indicate the 
 nominal capacity of the hook in 
 X. tons of 2,000 Ibs. The formulae 
 which determine the lines of the 
 other parts of the hooks of the 
 several sizes are as follows, the 
 measurements being all expressed 
 
 in inches : 
 
 =.5J +1.25 
 
 F=.33J+ .85 
 
 7=1.33A 
 
 G=.75 D 
 0=.363J+ .66 
 Q=.64J +1.60 
 
 M 
 
 .50 A 
 
 J=120A N= .85J3 -.16 
 
 #=1.13A C7= .866A 
 
 EXAMPLE. To find the dimension D for a 2-ton hook, 
 formula is: 
 
 The 
 
 * By Henry R. Towne, in his Treatise on Cranes, as the result of an 
 extensive experimental and mathematical investigation. 
 
THE LONGEST BRIDGES IN THE WORLD. 1519 
 
 and as J = 2, the dimension D by the formula is found to be 2J 
 ins. 
 
 The dimensions A are necessarily based upon the ordinary 
 merchant sizes of round iron. The sizes which it has been found 
 best to select are the following: 
 
 Capacity of hook i i * 1 H 2 34568 10 tons. 
 Dimension A H f IIB U H H 2 2* 2* 2f 3i inches 
 
 The formulae which give the sections of the hook at the sev- 
 eral points are all expressed in terms of A and can therefore 
 be readily ascertained by reference to the foregoing scale. 
 
 EXAMPLE. To find the dimension / in a 2-ton hook. The 
 formula is /= 1 33^4, and for a 2-ton hook A = If in. Therefore 
 /, in a 2-ton hook, is found to be 1% ins 
 
 Experiment has shown that hooks made according to the 
 above formulae will give way first by opening of the jaw, which, 
 however, will not occur except with a load much in excess of 
 the nominal capacity of the hook. This yielding ot the hook 
 when overloaded becomes a source of safety, as it constitute? a 
 signal of danger which cannot easily be overlooked, and which 
 must proceed to a considerable length before rupture will occur 
 and the load be dropped. A comparison of these hooks with 
 most of those in ordinary use will show that the latter are, as a 
 rule, badly proportioned, and frequently dangerously weak. 
 
 THE LONGEST BRIDGES IN THE WORLD. 
 
 Forth Bridge, 9,200 ft. 
 
 Montreal Bridge, over the St. Lawrence, 8,791 ft 
 
 The Baltimore & Ohio Bridge, at Havre de Grace, 6,000 ft. 
 
 Brooklyn Bridge, over the East River, N. Y. : 
 
 Length of river-span, 1,595 ft. 6 ins. 
 
 Length of each land-span, 930 ft. 
 
 Length of Brooklyn approach, 971 ft. 
 
 Length of New York approach, 1,562 ft. 6 ins. 
 
 Total length of bridge, 5,989 ft. Width of bridge, 86 ft. 
 
 Number of cables, 4; diameter of each, 15f ins. 
 
 Clear height of bridge in centre of river-span above high 
 water at 90 F., 135 ft. 
 
1520. THE LONGEST BRIDGES IN THE WORLD. 
 
 Williamsburg Bridge, crossing the East River at Grand St. 
 
 Ferry to Brooklyn: 
 
 Extreme length, 7,250 ft.; central span, 1,600 ft. 
 Estimated cost $21,000,000. 
 Manhattan Bridge, over East River,* 2,920 ft. long in three 
 
 spans. Length between terminals, 9,900 ft. Estimated 
 
 cost, $13,000,000. 
 Blackwell's Island Bridge,* extending over BlackwelPs Island, 
 
 N. Y.: 
 
 Total length, 7,449 ft. Estimated cost, $18,000,000. 
 Wooden bridge at Columbia, Pa., 5,366 ft. 
 Monongahela Bridge, near Homestead, 5,300 ft. 
 Louisville Railroad Bridge, over the Ohio, 5,218 ft. 
 Volga, over the Syzran, Russia, 4,947 ft. 
 Moerdyck, Holland, 4,927 ft. 
 Dnieper, near Jekaterinoslaw, Russia, 4,213 ft. 
 Cincinnati Southern Railroad, over the Ohio, 3,950 ft. 
 Kiev, over the Dnieper, 3,607 ft. 
 Dauphin Bridge, over the Susquehanna, 3,590 ft. 
 Barrage Bridge, Delta of the Nile, 3,353 ft. 
 Havre de Grace Bridge, over the Susquehanna, 3,271 ft. 
 Kronprinz Rudolph, over the Danube at Vienna, 3,266 ft. 
 Dnieper, near Krementchong, Russia, 3,250 ft. 
 Brommel, over the Meuse, Holland, 3,060 ft. 
 Plattsmouth Bridge, over the Missouri, 3,000 ft. 
 Two bridges of Rotterdam, over the Meuse, 2,833 ft. 
 Quincy Bridge, over the Mississippi, 2,847 ft. 
 St. Louis Bridge, over the Mississippi, 2,574 ft. 
 Omaha Bridge, over the Missouri, 2,750 ft. 
 Saint-Esprit, over the Rhone, France, 2,460 ft. 
 Kiulmbourg, over the Rhine, Holland, 2,347 ft. 
 Cincinnati, over the Ohio, 2,233 ft. 
 Keokuk, la., over the Mississippi, 2,008 ft. 
 Chaumont Viaduct, valley of the Suize, France, 2,000 ft. 
 Menai, England, 1,957 ft. 
 
 *In process of construction. 
 
OTHER NOTABLE BRIDGES. 
 
 OTHER NOTABLE BRIDGES. 
 
 The following bridges are notable either from their size or 
 historical connection. 
 
 The Lagong Bridge, , built over an arm of the China Sea, is 
 5 miles long, with' 300 arches of stone, 70 ft. high and 70 ft. 
 broad, and each pillar supporting a marble lion 21 ft. in length. 
 Its cost is unknown, but much exceeds that of the Forth Bridge. 
 
 The new London Bridge is constructed of granite, from the 
 designs of L. Rennie, and considered amongst the finest speci- 
 mens of bridge architecture. It was commenced in 1824, and 
 completed in seven years, at a cost of about $7,500,000. 
 
 The Bridge of Sighs, at Venice, over which the condemned 
 prisoners were transported from the Judgment Hall to the 
 place of their execution, was built in the Armada year, 1588. 
 
 The Bridge of the Holy Trinity, at Florence, consists of 
 three beautiful elliptical arches of white marble, and stands 
 unrivalled as a work of art. It is 322 ft. long, and was com- 
 pleted in 1569. 
 
 The Niagara Suspension Bridge was built in 1852-1855. It 
 is 245 ft. above high water, 821 ft. long, and the strength is 
 estimated at 12,000 tons. 
 
 The Rialto, at Venice, said to have been built from the designs 
 of Michael Angelo, consists of a single marble arch, 98 ft. 6 ins. 
 long, and was completed in 15S9. 
 
 The Britannia Bridge crosses the Menai Straits, Wales, at 
 an elevation of 103 ft. above high water. It is entirely of 
 wrought iron, 1,511 ft. long, and was finished in 1850. Cost, 
 $3,000,000. 
 
 The oldest bridge in England is a triangular bridge at Croy- 
 land, in Lincolnshire, which is said to have been erected about 
 A.D. 868. It is formed of three semi-arches, whose bases stand in 
 the circumference of a circle, equidistant from each other, and 
 uniting at the top. 
 
 Clifton Suspension Bridge, near Bristol, has a span of 703 ft., 
 and a height of 245 ft. above the water. The carriageway is 
 20 ft. wide, and footway 5J ft. wide. Cost, $500,000. 
 
 Coalbrookdale Bridge, over the Severn, has the reputation of 
 being the first cast-iron bridge built in England. It was erected 
 in 1779. It consists of one arch 100 ft. wide. Total weight, 
 378J tons. 
 
152 
 
 DIMENSIONS OF CHURCH BELLS. 
 
 DIMENSIONS AND WEIGHT OF CHURCH BELLS 
 
 MANUFACTURED BY BLAKE BELL Co., BOSTON. 
 
 Weight, 
 
 Tone. 
 
 Size of Frame 
 Diameter. jg^a. 
 Dimensions. 
 
 Diameter of 
 Vertical 
 Wheel. 
 
 Brands. 
 
 
 Inches. 
 
 Inches. 
 
 Inches. 
 
 200 
 
 
 21 
 
 42X32 
 
 34 
 
 250 
 
 
 22J 
 
 46X36 
 
 38 
 
 300 
 
 E 
 
 24 
 
 46X36 
 
 38 
 
 350 
 
 D* 
 
 26 
 
 46X36 
 
 38 
 
 400 
 
 D 
 
 27i 
 
 53X40 
 
 44 
 
 500 
 
 Cif 
 
 29 
 
 53X40 
 
 44 
 
 600 
 
 c 
 
 31 
 
 60X48 
 
 49 
 
 700 
 
 B 
 
 33 
 
 60X43 
 
 49 
 
 800 
 
 A 
 
 34i 
 
 60X48 
 
 49 
 
 900 
 
 
 36 
 
 70-X 54 
 
 58 
 
 1,000 
 
 A 
 
 37 
 
 70X54 
 
 58 
 
 1,100 
 
 GS 
 
 38i 
 
 76X57 
 
 64 
 
 1,200 
 
 
 39 
 
 76X57 
 
 64 
 
 1,300 
 
 
 40 
 
 76X57 
 
 64 
 
 1,400 
 
 G 
 
 41 
 
 76X57 
 
 64 
 
 1,500 
 
 
 42 
 
 76X57 
 
 64 
 
 1 7 600 
 
 
 43J 
 
 89X63 
 
 72 
 
 1,700 
 
 m 
 
 44?r 
 
 89X63 
 
 72 
 
 l,85t) 
 
 F 
 
 46 
 
 89X63 
 
 72 
 
 2,000 
 
 
 47 
 
 91X67 
 
 75 
 
 2,200 
 
 E 
 
 48 
 
 91X67 
 
 75 
 
 2,50D 
 
 r>3 
 
 51 
 
 100X70 
 
 84 
 
 3,000 
 
 
 53 
 
 112X73 
 
 96 
 
 3,200 
 
 L 
 
 55 
 
 112X73 
 
 96 
 
 4,000 
 
 Of 
 
 58 
 
 124X78 
 
 108 
 
 5,000 
 
 c 
 
 63 
 
 24X78 
 
 108 
 
 inch diameter 
 
 SIZE OF ROPE FOR BELLS. 
 
 For bells of less than 500 pounds J 
 
 " " " 500 to 800 pounds f 
 
 " " " 800 to 1,800 pounds j " " 
 
 " " above 1,800 pounds f to 1 " " 
 
 The actual weights usually exceed above from 2 to 3 per cent. 
 
LARGEST RINGING BELLS IN THE WORL 
 
 THE LARGEST RINGING BELLS IN THE WORLD.* 
 
 Names and Location 
 of Bells. 
 
 Date Cast. 
 
 Actual 
 Vibration, i 
 
 Key-note. 
 
 Diameter, 
 Inches. 
 
 Sound-bow. 
 
 || 
 ffi 
 
 Inches. 
 
 Stroke. 
 
 Moscow, Tzar Kolokol 
 
 1733 
 
 74 
 
 D 
 
 F 8 
 
 G 
 
 272 
 203? 
 185 
 156 
 155 
 151 
 136.3? 
 112 
 114.25 
 121 
 118 
 113.5 
 103.6 
 103 
 103 
 100 
 97.25 
 84 
 95 
 95.81 
 88 
 82.85 
 81 
 76 
 75.5 
 72 
 
 23 
 16? 
 14.75 
 
 12.5 
 12 
 10.6 
 
 0.84 
 0.80 
 6.80 
 
 0.80 
 0.80 
 0.80 
 
 443,772 
 201,600 
 127,350 
 120,000 
 95,000 
 69,664 
 60,736 
 45,000 
 42,000 
 40,320 
 40,200 
 35,620 
 30,800 
 28,670 
 28,560 
 24,080 
 18,000 
 17,024 
 16,016 
 15,848 
 13,000 
 12,096 
 11,500 
 10,080 
 0,856 
 8,960 
 
 Burmah, Mengoon 
 
 94 
 105 
 
 Moscow, St. Ivans 
 Pekin, Great Bell 
 
 1819 
 
 Burmah, Maha Ganda 
 
 
 125 
 125 
 141 
 
 B 
 B 
 
 C tt- 
 
 Nishni Novgorod 
 
 
 Moscow, Church Redeemer . . 
 Nankin, China 
 
 1879 
 
 London, St. Paul's. . ... 
 
 1881 
 
 157 
 
 157 
 157 
 166 
 176 
 166 
 176 
 187 
 187 
 210 
 198 
 210 
 198 
 210 
 222 
 210 
 249 
 249 
 
 E ? 
 
 E t> 
 
 E P 
 E 
 
 F 
 E 
 F 
 
 F tt 
 
 F 8 
 G tf 
 
 G 
 
 G S 
 
 G 
 
 G # 
 
 A 
 
 G 5 
 
 B 
 B 
 
 8.75 
 9.125 
 9.5. 
 9.375 
 9.75 
 7.5 
 7.8 
 8 
 7.5 
 6.125 
 7.2 
 7.75 
 6.375 
 6 
 6.08 
 5 
 5.94 
 5.75 
 
 0.76 
 0.75 
 0.80 
 0.83 
 0.75 
 0.73 
 0.76 
 0.80 
 0.77 
 0.73 
 0.76 
 0.71 
 0.73 
 0.73 
 0.75 
 0.66 
 0.78 
 C.79 
 
 Olmutz, Bohemia. . 
 
 Vienna, Austria. . . 
 
 1711 
 1856 
 1487 
 1680 
 1847 
 1845 
 1786 
 1680 
 1477 
 
 \Vestminster, London 
 
 
 
 Montreal, Canada 
 
 York, England 
 
 St. Peter, Rome 
 
 Great Tom, Oxford 
 
 Cologne, Germany 
 
 Brussels, Belgium ... 
 
 State-house, Philadelphia. . .. 
 Lincoln, England 
 
 1875 
 1834 
 1716 
 1675 
 1610 
 1857 
 
 St. Paul's, London " 
 
 
 Old Lincoln England 
 
 \Vesftninster London. 
 
 
 WEIGHT OF OTHER LARGE BELLS. 
 
 Rouen, France, 40,000 Ibs. 
 City Hall, New York, 22,300 Ibs. 
 Fire Alarm, 33d Street, New York, 21,612 Ibs. 
 
 * John W. Nystrom, in the Journal of the Franklin Institute. 
 
^YMBOLS FOR THE APOSTLES AND SAINTS. 
 
 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 sym- 
 bol of him, is never given. 
 
 St. Bartholomew. With a flay ing-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 aT. 
 
 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. 
 
HEIGHTS OF COLUMNS, TOWERS, AND DOMES. -SS2S 
 
 HEIGHTS OF COLUMNS, TOWERS, DOME S, SPIRES, 
 
 ETC. 
 
 COLUMNS. 
 
 Name. 
 
 Place. 
 
 Feet. 
 
 Alexander 
 
 St. Petersburg 
 
 175 
 
 Bunker Hill 
 
 Charlestown, Mass. . . . 
 
 221 1 
 
 Chimney (St. Rollox) 
 
 Glasgow 
 
 455J 
 
 Chimney (Musprat's) 
 
 Liverpool 
 
 406 
 
 City 
 
 London 
 
 202 
 
 July 
 
 Paris 
 
 157 
 
 Napoleon 
 
 Paris 
 
 132 
 
 Nelson's 
 
 Dublin 
 
 134 
 
 Nelson's 
 
 London 
 
 171 
 
 Place Vendome 
 
 Paris 
 
 136 
 
 Pompey's Pillar 
 
 Egypt 
 
 114 
 
 Trajan 
 
 Rome . 
 
 145 
 
 Washington 
 
 Washington 
 
 555 
 
 York 
 
 London 
 
 138 
 
 
 
 
 TOWERS AND DOMES* 
 
 Name. 
 
 Place. 
 
 Feet. 
 
 Eiffel Tower. . . 
 
 Paris 
 
 9P5 
 
 Tower 
 
 Babel 
 
 60 
 
 Tower 
 
 Baalbec. . 
 
 500 
 
 Cathedral (spire). . 
 
 Cologne 
 
 516| 
 
 Cathedral. 
 
 Rouen 
 
 491-| 
 
 Cathedral (spire) 
 
 Antwerp 
 
 476 
 
 St. Nicholas . 
 
 Hamburg. . ... 
 
 473 
 
 Cathedral. . . . 
 
 Anvers 
 
 472 
 
 St Peter's (cupola) 
 
 Rome 
 
 469J 
 
 Cathedral. 
 
 Cremona 
 
 392 
 
 Cathedral 
 
 Escurial 
 
 200 
 
 Cathedral 
 
 Florence. 
 
 384 
 
 Cathedral. 
 
 Milan. . 
 
 438 
 
 Cathedral. 
 
 St. Petersburg 
 
 363 
 
 Capitol (dome) 
 
 Washington 
 
 287i 
 
 Leaning Tower. , 
 
 Pisa. . . .... 
 
 188 
 
 Porcelain 
 
 China 
 
 200 
 
 St Paul's 
 
 London .... 
 
 366 
 
 St. Mark's 
 
 Venice . 
 
 328 
 
 City Hall 
 
 Philadelphia 
 
 537^ 
 
 
 
 
 * See also next page. 
 
1526- HEIGHT AND DIAMETER OF NOTED DOMES. 
 
 HEIGHT OF SPIRES. 
 
 Name. 
 
 Place. 
 
 Feet. 
 
 Cathedral 
 
 Strasburg 
 
 465J 
 
 Cathedral new 
 
 New York 
 
 325 
 
 Grace Church 
 
 New York 
 
 216 
 
 Cathedral 
 
 Salisbury 
 
 450 
 
 St John's 
 
 New York 
 
 210 
 
 St Paul's 
 
 New York 
 
 200 
 
 St Mary's 
 
 Liibeck. . . 
 
 404 
 
 St Peter's 
 
 Rome 
 
 391 
 
 St Stephen's 
 
 Vienna 
 
 465 
 
 Trinity Church 
 
 New York. . . 
 
 286 
 
 Balustrade of Notre Dame. . . . 
 
 Paris. . . . 
 
 216 
 
 Hotel des Invalides 
 
 Paris 
 
 344 
 
 Pyramid of Cheops 
 
 Egypt 
 
 520 
 
 Pyramid of Sakara . . 
 
 Egypt. . . 
 
 356 
 
 LIST OF THE PRINCIPAL DOMES IN THE WORLD. 
 
 Their diameter and height from the ground. 
 (Gwilt's Encyclopaedia.) 
 
 Place. 
 
 Diam., 
 Feet. 
 
 Height, 
 Feet. 
 
 Pantheon, at Rome 
 
 Duomo, or Sta. Maria del Fiore, at Florence . . . 
 
 St. Peter's, at Rome 
 
 Sta. Sophia, at Constantinople 
 
 Baths of Caracalla (ancient) 
 
 St. Paul's, London 
 
 Mosque of Achmet 
 
 Chapel of the Medici 
 
 Baptistery, at Florence 
 
 Church of the Invalids, at Paris 
 
 Minerva Medica, at Rome 
 
 Madonna della Salute, Venice 
 
 St. Genevieve, at Paris (Pantheon) 
 
 Duomo, at Sienna 
 
 Duomo, at Milan 
 
 St. Vitali's, at Ravenna 
 
 Val de Grace, at Paris 
 
 San Marco, Venice 
 
 United States Capitol, Washington 
 
 142 
 
 139 
 
 139 
 
 115 
 
 112 
 
 112 
 92 
 91 
 86 
 80 
 78 
 70 
 67 
 57 
 57 
 55 
 55 
 44 
 
 124f 
 
 143 
 310 
 330 
 201 
 116 
 215 
 120 
 199 
 110 
 173 
 
 97 
 133 
 190 
 148 
 254 
 
 94 
 133 
 
DIMENSION OF ENGLISH CATHEDRALS. 1527 
 
 I 
 
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1528 DIMENSIONS OF VARIOUS OBELISKS. 
 
 DIMENSIONS OF THE VARIOUS OBELISKS EXIST- 
 ING AT THE PRESENT TIME. 
 
 (Gwilt's Encyclopaedia.) 
 
 Situation. 
 
 Two large obelisks mentioned by Diodorus Sicu- 
 
 lus 158.2 7.9 
 
 Two obelisks of Nuncoreus, son of Sesostris, ac- 
 cording to Herodotus, Diodorus Siculus, and 
 
 Pliny 121 .8 
 
 Obelisk of Rhameses, removed to Rome by Con- 
 
 stantius 118.4 6.2 
 
 Two obelisks, attributed by Pliny to Smerres and 
 
 Eraphius 106.0 5.9 
 
 Obelisks of Nectanabis, erected near the Tomb of 
 
 Arsinoe by Ptolemy Philadelphus 105 . 5 5.3 
 
 Obelisk of Constantius, restored and erected in front 
 
 of S. Giovanni Laterano, at Rome 105.5 6.2 
 
 Part of one of the obelisks of the son of Sesostris, 
 
 in the centre of the piazza in front of St. Peter's . . 82 . 4 5.8 
 
 Two at Luxor 79.1 5.3 
 
 Obelisk of Augustus, from the Circus 
 
 Maximus, now in the Piazza, del Popola at Rome. . 78.2 4.5 
 
 Two in the ruins at Thebes, still remaining 72.8 5.0 
 
 Obelisk of Augustus, raised by Pius VI. in the 
 
 Piazza di Monte Citorio 71.9 4.9 
 
 Two obelisks: one at Alexandria, vulgarly called 
 
 Cleopatra's Needle, and the other at Heliopolis. . 67.1 5.1 
 
 Obelisk by Pliny, attributed to Sothis 63 . 3 4.5 
 
 Two obelisks in the ruins at Thebes 63.3 4.5 
 
 Great obelisk at Constantinople. 59.7 4.5 
 
 Obelisk in the Piazza, Navona, removed from the 
 
 Circus of Caracalla 54 . 9 2.9 
 
 Obelisk at Aries 50. 1 4.5 
 
 Obelisk from the Mausoleum of Augustus, now in 
 front of the Church of Sta. Maria Maggiore, at 
 
 Rome 48.3 2.9 
 
 Obelisk in the Gardens of Sallust, according to 
 
 Mercati 48 . 3 2.9 
 
 Obelisk at Bijije, in Egypt 42.9 2.6 
 
 Small obelisk at Constantinople, according to Gyl- 
 
 lius 34.2 3.9 
 
 The Barberini Obelisk -30.0 2.2 
 
 Obelisk of the Villa Mattel 26 . 4 2.2 
 
 Obelisk in the Piazza della Rotunda 20 . 1 2.1 
 
 Obelisk in the Piazza di Minerva 17 .6 2.0 
 
 Obelisk of the Villa Medici 16.1 1.9 
 
 Height 
 
 in 
 
 English 
 Feet. 
 
 Thickness, 
 in English Ft. 
 
 At 
 Top. 
 
SOME WELL-KNOWN EUROPEAN BUILDINGS. 1529 
 
 DIMENSIONS OF SOME WELL-KNOWN EUROPEAN 
 BUILDINGS.* 
 
 The body of Milan Cathedral, from the great doorway to the 
 end of the apse, measures 148 metres and 10 centimetres, with a 
 breadth of 57 metres. The total length of the transepts with the 
 chapels is 87 metres. The nave is 47 metres high by 19 in width, 
 and the total height, from the centre to the feet of the statue of 
 the Virgin which crowns the central tower, is 108.5 metres. 
 
 The Cathedral of York, burned in 1828, and which had already 
 been rebuilt in 1705, has a length of 142 English feet, a breadth 
 of 105 feet at the western extremity, and 109 feet at the opposite 
 end. The total height of the nave is 99 feet; the ceiling of the 
 central tower is 213 feet from the ground. A window which opens 
 at the extremity of the gallery, and which is entirely filled with 
 stained glass, is 65 English feet in height by 32 in width. 
 
 The Cathedral of Cordova, built in the year 792 by King 
 Abderame, is 134 feet long and 387 wide. This church contains 
 nine naves formed by 1,018 columns, the smallest of which are 
 7 feet and the largest 1 1 feet and 3 inches high. 
 
 The Escurial, begun in 1557, to which was given the form of a 
 gridiron, in honor of St. Lawrence, is 51 feet in height and 637 
 feet in length. 
 
 In the Alhambra at Granada, an ancient Moorish fortress, the 
 Lion Court is 100 feet square. 
 
 The Church of St. Denis, near Paris, is 335 feet long by 90 feet 
 high. It was built in 1152 by Suger. 
 
 The famous Column of the Grand Army on the Place Vendome, 
 Paris, is 136 feet high. 
 
 The Church of St. Genevieve, at Paris, to-day transformed into 
 the Pantheon, is one of the most remarkable structures by reason 
 of the vastness of its proportions. The diameter of the dome is 
 68 feet. The 32 columns which surround it are 34 feet in height, 
 and the highest point of the edifice is 237 feet from the sidewalk. 
 
 The Cathedral at Rheims, which Stendhal considers one of the 
 most beautiful churches in France, was built in 840, and measures 
 430 feet in length by 110 in height. 
 
 The Cathedral at Strasburg, which is perhaps the only purely 
 Gothic monument on the Continent of Europe, was finished in 
 1275. The first stone was laid in 1015. The tower, finished in 
 
 * Taken from an article on Milan Cathedral, published in the American 
 Architect, August 25, 1888. 
 
1530 DIMENSIONS GRAND OPERA HOUSE, PARIS. 
 
 1439, is, Vithout contradiction, the highest bit of masonry which 
 exists in Europe. Its height is 426 feet; width of nave, 43 feet; 
 length, 145 feet, inside measurements. 
 
 The tower of St. Etienne at Vienna is 414 feet high, 4 feet 
 less than that at Strasburg. 
 
 The tower of St. Michael at Hamburg is 390 feet. 
 
 The famous tower of Pisa measures 193 feet, but it leans toward 
 the south about 12 feet, which gives it a mean inclination of 6 
 feet in the hundred. 
 
 St. Sophia, at Constantinople, measures 270 feet in length by 
 240 feet in width, from north to south. The height of the dome 
 above the level of the ground is only 165 feet. 
 
 The towers of Notre Dame, at Paris, measure 240 feet in height. 
 The total length of this church is 409 feet. Its interior width at 
 the crossing is 150 feet; the width of the nave is 40 feet. 
 
 The Church of St. Paul, at London, is 500 feet in length by 169 
 feet in width. The height of the dome is 319 feet. 
 
 St. Peter's, at Rome; total length, including the portico and 
 thickness of the walls, is 660 feet. The foundation walls are 21 
 feet and 7 inches thick. The walls of the peristyle are 8 feet and 
 9 inches thick, and the peristyle is 39 feet and 3 inches in width. 
 The interior length of the crossing of St. Peter's is 98 feet. The 
 interior width of the nave, without the aisles and chapels, is 82 
 feet. The total height from the floor to the summit of the cross 
 which surmounts the dome is 408 feet. The height of the dome 
 under the key-stone is 249 feet. The interior height of the facade 
 is 259 feet. 
 
 DIMENSIONS OF THE GRAND OPERA-HOUSE, PARIS. 
 
 Superficial area, 37,317 square feet, and cubical contents, 
 428,660 metres. 
 
 The width of the fagade is 230 feet. 
 
 Greatest width of building, 408 feet. 
 
 Height above the ground level, 184 feet. 
 
 From foundation to summit, 266 feet. 
 
 No less than fifteen eminent painters, fifty-six eminent sculp- 
 tors, besides nineteen sculptors of ornament, were engaged on 
 the external and internal decorations. 
 
 M. Garhier, the architect, gave his entire and unremitting at- 
 tention to it, and, with the aid of his assistants, produced more 
 than 30,000 drawings. The building was in course of construc- 
 tion for thirteen years. 
 
TALLEST BUILDINGS IN UNITED STATES. 1531 
 
 HEIGHT OF SOME OP THE TALLEST BUILDINGS 
 IN THE UNITED STATES. 
 
 BUILDINGS IN NEW YORK CITY. 
 
 Height above 
 Sidewalk. 
 
 Ivins Syndicate (Park Row) Building l.. 29 stories 386 ft. 
 
 New Times Building 16 22 " 375* ' ' 
 
 Manhattan Life Building 2 18 " and tower 348 ' ' 
 
 International Bank Bld'g. 3 60 Wall St. .26 " Pine St. wing 345 " 
 
 Wall St. Exchange 3 25 " 340 '* 
 
 St. Paul Building * 26 " 313 " 
 
 American Surety Building 6 21 " 312 ' ' 
 
 Pulitzer (World) Building 5 16 " and dome 309 " 
 
 Hanover National Bank 10 22 ' 4 
 
 American Tract Society Building * 21 " 306 ' ' 
 
 Empire Building 2 20 " 304 ' ' 
 
 Commercial Cable Building 7 20 " . . 304 ' ' 
 
 Whitehall (Battery Place) Building 1 ?. .20 " 
 
 Forty-two Broadway Building 19 20 " 
 
 Madison Square Garden 8 to top of tower 300 ' * 
 
 Gillender Building 9 . . 19 stories and tower 300 " 
 
 Fuller (Flat Iron) Building 21 21 " 285 " 
 
 Trinity Church spire 284 ' ' 
 
 Standard Oil Building 2 (remodelled) . . 19 stories 280 " 
 
 Broad Exchange Building 3 20 " 276 ' ' 
 
 Bank of Commerce Building 10 19 " 264. ' " 
 
 Broadway-Maiden Lane Building 3 . ... 18 " 234 ' ' 
 
 Broadway Chambers 14 18 " 
 
 Home Life Insurance Building n 16 " and tower 257 " 
 
 Washington Building 12 13 " " " 250 ' * 
 
 New York Life Building 8 12 " " " 244 " 
 
 S. L. Mitchell Estate Building 15 " 230 " 
 
 Mutual Life Building 4 14 " 230 " 
 
 Manhattan Hotel 16 " 225 * 
 
 Produce Exchange Building 5 9 " and tower 225 " 
 
 Queens Insurance Co. Building 7 17 ' 
 
 Bowling Green Building 13 16 " 224 ' ' 
 
 St. James Building 6 16 " 
 
 American Exchange Bank 3 . 16 ' 
 
 New Netherlands Hotel 16 " 220 ' ' 
 
 Blair Building i 5 16 " 
 
 Bank of the Metropolis 6 16 ' 
 
 Beaver Building 3 15 ' 
 
 Dun Building 7 15 " 223 " 
 
 Central Bank Building 20 15 ' 219 " 
 
 Hudson Building ...16 " 218 " 
 
 Lords Court Building is 15 l 214 * 
 
 Johnston Building 15 " 212 ' ' 
 
 Syndicate Building 15 ' 207 " 
 
 * 430 ft. above footings. 
 
1532 TALLEST BUILDINGS IN UNITED STATES. 
 
 Height above 
 Sidewalk. 
 
 Continental Ins. Co. Building 14 stories 215 ft. 
 
 Union Trust Building 5 to top of tower 1 . 194 ' ' 
 
 Postal Telegraph Building ? 13 stories 192 " 
 
 Havemeyer Building 5 14 " 192 " 
 
 Mutual Reserve Building, 13 '*' 184 " 
 
 Times Building (old) 5 183 " 
 
 Silk Exchange Building- 13 stories 180 " 
 
 ARCHITECTS. * R. H. Robinson. 2 Kimball & Thompson. 3 Clinton & 
 Russell. 4 C. W. Clinton. 5 Geo. B. Post. 6 Bruce Price. 7 Geo. Edward 
 Harding & Gooch. 8 McKim, Mead & White. 9 Berg & Clark. 10 James B. 
 Baker. N. Le Brun & Sons. 12 E. H. Kendall. 13 Audsley Bros. 14 Cass 
 Gilbert. Carrere & Hastings. 16 Cyrus L. W. Eidlitz. 1? Henry J. Har- 
 denbergh. 18 John T. Williams. 19 Henry Ives Cobb. 20 Wm. H. Birkmire. 
 21 D. H. Burnham & Co. 
 
 CHICAGO. 
 
 Height above 
 Sidewalk. 
 
 Masonic Temple 22 . 20 stories Roof line 278 ft. 
 
 To top of skylight 303 " 
 
 Auditorium 23 17 stories and tower 265 ' 
 
 Fischer Building 21 18 " " attic 235 ' ' 
 
 Old Colony Building 24 17 " 213 " 
 
 Schiller Theatre 23 . 17 " 
 
 Katahdin & Wachusett Building 17 " 203 ' * 
 
 Unity Building 17 " 210 " 
 
 Railway Exchange Building 21 17 " 
 
 Marquette Building 2 * 16 " 207 
 
 Monadnock Building 16 " 215 ' ' 
 
 Ashland Block 16 " 200f ' ' 
 
 The New Great Northern Building 21. . . 16 " 200 ' 
 
 Manhattan Building a> 16 " 197 
 
 Reliance Building 21 , 14 " 200 ' 
 
 Security Building 14 " 200 ' 
 
 Title & Trust Building 16 " 198 ' 
 
 Woman 's Temple 22 13 " Ridge 198 ' 
 
 Champlain Building 2 * 15 " 189 ' 
 
 BOSTON. 
 
 Ames Building 25 Top of cornice 186 ft. 
 
 Chamber of Commerce 25 '. .Top of tower 172^ 4 ' 
 
 BUFFALO, N. Y. 
 Guaranty Building 23 13 stories 
 
 CINCINNATI. 
 
 Ingalls Building 27 15 stories (concrete-steel construct'n) 
 
DESCRIPTION OF AMERICAN BUILDINGS. 1533 
 
 PHILADELPHIA. 
 
 City Hall To top of tower 537 ft. 
 
 Land & Title Building 22 stories 317 ' ' 
 
 . PITTSBURG. 
 
 Allegheny County Court House 2G To top of finial 319 ft. 
 
 Farmers' Bank Building 28 25 stories 
 
 SAN FRANCISCO. 
 Spreckels Building 29 16 stories and tower 215 ft. 
 
 MISCELLANEOUS. 
 
 U. S. Capitol, Washington Top of dome 307 ft. 
 
 State Capitol, Hartford, Conn Top of figure on dome 256 ' ' 
 
 ARCHITECTS. 21 D. H. Burnham & Co. 22 Burnham & Root. 23 Adler 
 & Sullivan. 2 * Holabird & Roche. 25 Shepley, Rutan & Coolidge. 26 H. 
 H. Richardson and Shepley Rutan & Coolidge. ^ Elzner & Anderson. 
 28 Alden & Harlow. 29 Reid Bros. 3 Jenney & Mundie. 
 
 DESCRIPTION OF NOTABLE AMERICAN 
 BUILDINGS. 
 
 THE UNITED STATES CAPITOL. 
 
 [From "King's Hand-book of Washington. ' '] 
 
 The site of the building is 89 J ft. above ordinary low tide in 
 the Potomac. Entire length of building, 751 ft.; greatest 
 depth (breadth of wings), 324 ft.; area covered by building, 
 3J acres. The central building is 352 ft. long; corridors, 44 ft. 
 long; wings, 143 ft. front, 239 ft. deep, exclusive of porticos and 
 steps. Central building is freestone from quarries about 40 
 miles below Washington. This is painted white. 
 
 The wings are of white marble from Lee, Mass. Appropria- 
 tions made by Congress from 1800 to date for the erection and 
 remodelling of the Capitol amount to $15,000,000. 
 
 Dome designed by T. U. Walter, to replace a smaller one 
 removed in 1856. Exterior height crest of statue above base- 
 line, 307 } ft.; top of lantern above balustrade of building, 
 218 ft.; height of Statue of Freedom on the apex, 19 J ft.; 
 diameter of dome, 135J ft. 
 
 The dome rests on an octagonal base 93 ft. above the base- 
 ment floor, and as it leaves the top line of the building consists 
 of a peristyle, 124 ft. in diameter, of 36 iron-fluted columns 27 
 ft. high and weighing 6 tons each. 
 
1534 DESCRIPTION OF AMERICAN BUILDINGS. 
 
 The lantern is 15 ft. in diameter and 50 ft. high. 
 
 The weight of iron in the superstructure of the dome is 8,009,- 
 200 Ibs. This rests on a substructure of masonry and 40 interior 
 massive stone columns supporting heavy groined arches, upon 
 which also rests the pavement of the Rotunda. 
 
 Height from floor of Rotunda to canopy, 180 ft.; diameter 
 of Rotunda, 96 ft. 
 
 The canopy consists of an inner shell of iron ribs and lathing, 
 laid with plaster suitable for frescoing. It is 65J ft. in diameter, 
 and 21 ft. vertical height. 
 
 Supreme Court Room. Seventy-five ft. long, 45 ft. wide, and 
 45 ft. high. 
 
 Hall of Representatives. Length, 139 ft.; width, 93 ft.; 
 height, 36 ft.; floor, 115 ft. by 67 ft. Galleries will seat about 
 2,500 persons. 
 
 The ceiling of the hall is of cast iron, panelled, painted, and 
 gilded, and highly enriched with gilt mouldings. The panels 
 are filled with glass, with stained centre-pieces representing 
 the arms of the States. Above the ceiling is the illumination- 
 loft, with 1,500 gas-jets, for lighting the hall for night sessions. 
 
 Senate Chamber. Length, 113J ft.; width, 80J ft.; height, 
 39 ft. 
 
 Floor is 83 ft. long, 51 ft. wide. Galleries seat 1,200 persons. 
 The ceiling is of iron with glass panels, lighted same as Repre- 
 sentatives' Hall. 
 
 The Congressional Library. In response to an 
 invitation for competitive plans, 28 designs were submitted, 
 from among which that of Messrs. Smithmeyer & Pelz of Wash- 
 ington was selected as the best, and they were entrusted with 
 the work. Mr. Smithmeyer was early retired, and in 1892 Mr.' 
 Pelz was also retired, and after that Mr. Ed Ward P. Casey took 
 up the work. In many respects it is one of the most notable 
 buildings in this country. 
 
 The dimensions of the ground plan are: Length of frontage, 
 470 ft., depth, 340 ft. The reading-room is 100 ft. inscribed 
 diameter. The niches are 18 ft. additional, making the open 
 space between opposite walls 136 ft. The stair hall is 48'X 80', 
 but with adjoining corridors and between walls, is 94'X 136'. The 
 longest rooms, the north and south wings, are 210'X 35'. There 
 are three book repositories, with a total capacity of about 2,000,000 
 volumes.* 
 
 * The Architects' and Builders' Magazine, July, 1900. 
 
DESCRIPTION OF AMERICAN BUILDINGS. 1535 
 
 Treasury Building. Dimensions: 468 ft. north to 
 south, 264 ft. east to west; inclusive of porticos and steps, 
 582 ft. by 300 ft. Cost, $6,000,000. 
 
 Architects Robert Mills, T. U. Walter, Young, Rogers, and 
 A. B. Mullett. 
 
 State, War, and Nayy Building. A. B. Mullett, 
 architect. Extreme dimensions north to south, 567 ft.; east 
 to west, 342 ft.; exclusive of projection, 471 ft. north to south, 
 and 253 ft. east to west. Cost, $5,000,000. 
 
 New City Hall, Philadelphia; John McArthur, Jun., 
 architect. 
 
 Dimensions of Building 
 
 From north to south 486 ft. 6 ins. 
 
 " east to west 470 ft. 
 
 Area 4J acres 
 
 Number of rooms in building 520 
 
 Total amount of floor-room 14J acres 
 
 Height of main tower 537 ft. 4 ins. 
 
 Width at base. . .' 90 " 
 
 Centre of clock-face above pavement 361 " 
 
 Diameter of clock-face 20 " 
 
 State Capitol, Hartford, Conn.; R. M. Upjohn, archi- 
 tect, New York City. 
 
 Exterior is of marble; building is of fire-proof construction, 
 with brick and iron floors. 
 
 Length : 296 ft. 
 
 Depth 199 " 
 
 Height to top of roof 99 " 
 
 Height to top of figure on dome. . . . 256 " 
 
 Senate chamber 50 " X 40 ft., 35 ft. high 
 
 Representatives' hall 84 " X 56 " 48 " high 
 
 Supreme Court room 50 " X 31 " 35 " high 
 
 Cost of building, $2,500,000.00. 
 
 The Washington Monument, at Washington, D.C., is 
 555 ft. 5 ins. high, and has a base of 55 ft., with an entasis of 
 1 ft. in every 34 in height. The monument is faced with white 
 marble and backed with blue granite to the height of 452 ft.; 
 above that the walls are entirely of marble. The average settle- 
 ment of the structure at each corner is 1.7 ins. The monu- 
 
1533 DESCRIPTION OF AMERICAN BUILDINGS. 
 
 ment is a simple plain obelisk with no embellishments what- 
 ever. 
 
 The weight of the monument is 80,470 tons, or 3.6 tons per 
 square foot; the area covered by the foundation being 22,400 
 sq. ft. 
 
 The corner-stone of the monument was laid July 4, 1848, and 
 the cap-stone was set Dec. 6, 1884. 
 
 The Madison Square Garden, New York City. 
 Messrs. McKim, Mead & White, architects. This building covers 
 the block bounded by East Twenty-seventh Street, Fourth 
 Avenue, Twenty-sixth Street, and Madison Avenue. It was 
 opened to the public, June 16, 1S90, and cost $3,000,000. 
 
 It combines an immense amphitheatre, a restaurant (80'X 90'), 
 a ball-room, a concert hall, an open-air roof garden (80'X200') 
 and a theatre. 
 
 The amphitheatre is an enormous room, 310'X 194' and 80' high, 
 with an arena containing 30,000 sq. ft. The room is semi- 
 circular at each end, and is provided with permanent seats 
 for 7,800 people, with sufficient standing space left to give 
 room for a total of 15,000 persons. This vast arena, covered 
 by the immense roof without central support, is entirely open 
 and free from side to side and from end to end. For summer 
 performances the roof can be opened by machinery. 
 
 The theatre has a seating capacity of about 1,200, with stand- 
 ing room for 400 more. 
 
 The open-air garden extends over the roof along the Madison 
 Avenue front. It will hold from 3,000 to 5,000 people. 
 
 The building is surmounted by an immense tower 300 ft. high. 
 
 Auditorium Building, Chicago, 111, ; Adler & Sulli- 
 van, architects. 
 
 This building was built during the years 1887-89 and includes: 
 
 1. The Auditorium. Permanent seating capacity, over 4,000; 
 for conventions, etc. (for which the stage will be utilized), about 
 8,000. Contains the most complete and costly stage and organ 
 in the world. 
 
 2. Recital Hall Seats over 500. 
 
 3. Business Portion consists of stores and 136 offices, part of 
 which are in the tower. 
 
 4. Tower Observatory, to whir,h the public are admitted. 
 Above four departments of the building are managed by Chi- 
 cago Auditorium Association. 
 
 5. Auditorium Hotel has 400 guest rooms. The grand dining- 
 
ARCHITECTS OF NOTED PUBLIC BUILDINGS. 1537 
 
 room (175 feet long) and the kitchen are on the top floor. The 
 magnificent banquet hall is built of steel, on trusses, spanning 
 120 feet over the Auditorium. 
 
 Area covered by building, about one and one-half acres. 
 
 Cost of building, $3,200,000. 
 
 ARCHITECTS OF NOTED PUBLIC AND SEMI-PUBLIC 
 BUILDINGS IN THE UNITED STATES. 
 
 BUILDINGS ARRANGED ACCORDING TO LOCATION. 
 GOVERNMENT BUILDINGS IN WASHINGTON, D. C. 
 
 Architects. 
 United States Capitol Messrs. Hallet, Hadfield, Hoban, 
 
 Latrobe, Bulfinch, Walter, 
 
 and Clark. 
 
 National Museum Cluss & Schulye. 
 
 State, War and Navy Building. A. B. Mullett. 
 
 Treasury Building Robert Mills, T. U. Walter, 
 
 Young, Rogers, and A. B. 
 
 Mullett. 
 The Congressional Library Smithmeyer & Pelz, Edward P. 
 
 Casey.* 
 United States Post Offices and Court-houses: 
 
 Location. 
 
 Baltimore, Md James G. Hill. 
 
 Boston, Mass A. B. Mullett. 
 
 Chicago, 111. (old) A. B. Mullett. 
 
 Chicago, 111. (new) Henry Ives Cobb. 
 
 Cincinnati, O A. B. Mullett. 
 
 Detroit, Mich M. E. Bell. 
 
 Kansas City, Mo James G. Hill. 
 
 New York, N. Y A. B. Mullett. 
 
 St. Louis, Mo A. B. Mullett. 
 
 Other Government Buildings. 
 
 Immigrant Station, Ellis Island, 
 
 N, Y. Harbor Boring & Tilton. 
 
 New Naval Academy, Annapolis, 
 
 Md Ernest Flagg. 
 
 * See p. 1534. 
 
1538 ARCHITECTS OF NOTED PUBLIC BUILDINGS. 
 
 STATE CAPITOLS. 
 Capitol of: 
 
 Architects. 
 
 Colorado, at Denver E. E. Meyers & Son. 
 
 Connecticut, at Hartford R. M. Upjohn. 
 
 Illinois, at Springfield A. H. Piquenard. 
 
 Indiana, at Indianapolis Edwin May. 
 
 Iowa, at Des Moines A. H. Piquenard. 
 
 Georgia, at Atlanta W. J. Edbrook & F. P. Burn- 
 ham. 
 Louisiana, at Baton Rouge. . .W. A. Freret. 
 
 Maine, at Augusta Charles Bulfinch. 
 
 Massachusetts, at Boston,. . . .Charles Bulfinch; Brigham & 
 
 Spofford. 
 
 Michigan, at Lansing E. E. Meyers. 
 
 Minneapolis, at St. Paul Cass Gilbert. 
 
 Capitol of: 
 
 New York, at Albany Messrs. Fuller, Eidlitz, and 
 
 H. H. Richardson. 
 
 Ohio, at Columbus Henry & Wm. Walter. 
 
 Rhode Island, at Newport. . .James Munday. 
 
 Tennessee, at Nashville John Strickland. 
 
 Texas, at Austin E. E. Meyers & Son. 
 
 Virginia, at Richmond Thomas Jefferson. 
 
 COUNTY BUILDINGS. 
 
 Court-house, Baltimore Wyatt & Nolting. 
 
 Suffolk County Court-house, 
 
 Boston, Mass Geo. A. Clough. 
 
 Cook County Court-hquse, Chi- 
 cago, 111 J. J. Egan. 
 
 Arapahoe County Court-house, 
 
 Denver, Col E. E. Meyers & Son; F. Eberley. 
 
 Jefferson Market Court-house, 
 
 New York F. C. Withers. 
 
 The Appellate Division Court- 
 house, New York James Brown Lord. 
 
 Allegheny County Court-house 
 
 and Jail, Pittsburgh, Pa H. H. Richardson. 
 
 Court-house, Providence, R. I. .Stone & Carpenter. 
 
ARCHITECTS OF NOTED PUBLIC BUILDINGS. 1539 
 
 CITY AND TOWN HALLS. 
 
 City Hall: 
 
 Albany, N. Y H. H. Richardson. 
 
 Boston, Mass. -....'. Oilman & Bryant. 
 
 Detroit, Mich James Anderson. 
 
 New York, N. Y. (1803-12). .John McComb. 
 
 (New) Philadelphia, Pa John McArthur, Jr. 
 
 Worcester, Mass Peabody & Stearns. 
 
 Town Hall, North Easton, Mass. .H. H. Richardson. 
 
 LIBRARIES. 
 
 Name and Location. Architect. 
 
 Public Library, Boston, Mass. ..... McKim, Mead & White. 
 
 Public Library, Chicago, 111 Shepley, Rutan & Coolidge. 
 
 Newberry Library, Chicago Henry Ives Cobb. 
 
 Lenox Library, New York R. M. Hunt. 
 
 Free Circulating Library, N. Y. 
 
 Branch No. 1 * James Brown Lord. 
 
 Chatham Sq. Branch N. Y. Pub. 
 
 Library * McKim, Mead & White. 
 
 Blackstone Memorial Library, Bran- 
 ford, Conn S. S. Beman. 
 
 Public Library, Erie, Pa Alden & Harlow. 
 
 Public Library, Mankato, Minn.*. . Jardine, Kent & Jardine. 
 
 Public Library, Milton, Mass Shepley, Rutan & Coolidge. 
 
 Public Library, Tacoma, Wash. . . . Jardine, Kent & Jardine. 
 
 Public Library, Milwaukee, Wis. . . Ferry & Class. 
 
 Public Library, Newark, N. J Rankin & Kellogg. 
 
 Public Library, Schenectady, N. Y. M. T. Reynolds. 
 
 Carnegie Library, Syracuse, N. Y. . Jas. A. Randall. 
 
 Carnegie Library, Paducah, Ky. ... A. L. Lassiter. 
 
 Carnegie Library, East Orange, N. J. Jardine, Kent & Jardine. 
 Carnegie Library, Sandusky, O. . . . D'Oench & Yost 
 
 ART INSTITUTES AND MUSEUMS. 
 
 Museum of Fine Arts, Boston Sturgis & Brigham. 
 
 Academy of Fine Arts, Chicago. . . Burnham & Root. 
 
 Art Institute, Chicago Shepley, Rutan & Coolidge. 
 
 Art Museum, Detroit James Balfour. 
 
 Museum of Fine Arts, St. Louis . . . Peabody & Stearns. 
 
 * Carnegie Libraries. 
 
1540 
 
 LIST OF NOTED ARCHITECTS. 
 
 LIST OF NOTED ARCHITECTS. 
 
 (Gwilt.) 
 
 BEFORE CHRIST. 
 
 Name of Architect. 
 
 Century. 
 
 Principal Works. 
 
 Theodorus, of Samos. 
 
 Ictinus, of Athens. 
 
 Callicrates, of Athens. 
 
 Mnesicles, of Athens. 
 Dinocrates, of Macedonia 
 
 Andronicus, of Athens. 
 Callimachus, of Corinth. 
 
 Sostratus, of Cnidus. 
 Cossutius, of Rome. 
 
 Hermodorus, of Salamis. 
 
 Fussitius, of Rome. 
 
 Virtruvius Pollio, of Fano 
 Metrodorus, of Persia. 
 
 Aloisius, of Padua. 
 
 Anthemius, of Trales, of 
 Lydia. 
 
 Saxulphus, Abbot of 
 Peterborough, after- 
 wards made Bishop of 
 Lichfield, of England. 
 
 Egbert, Archbishop of 
 York, of England. 
 
 Romualdus, of France. 
 
 7th 
 
 6th 
 
 6th 
 
 6th 
 4th 
 
 4th 
 4th 
 
 4th 
 2d 
 
 2d 
 
 1st 
 
 Labyrinth at Lemnos, some buildings at 
 Sparta, and the Temple of Jupiter at 
 Samos. 
 
 Parthenon at Athens, Temple of Ceres 
 and Prosperpine at Eleusis, Temple of 
 Apollo Epicurius in Arcadia. 
 
 Assisted Ictinus in the erection of the 
 Parthenon. 
 
 Propylsea of the Parthenon. 
 
 Rebuilt the Temple of Diana at Ephesus, 
 engaged on works at Alexandria, was 
 the author of the proposition to trans- 
 form Mount Athos into a colossal 
 figure. 
 
 Tower of the Winds at Athens. 
 
 Reputed inventor of the Corinthian 
 order. 
 
 The Pharos of Alexandria. 
 
 Design for the Temple of Jupiter 
 Olympus at Athens. 
 
 Temple of Jupitor Stator in the Forum 
 at Rome, Temple of Mars in the Cir- 
 cus Flaminius. 
 
 Several buildings at Rome; the first 
 Roman who wrote on architecture. 
 
 AFTER CHRIST. 
 
 1st 
 
 I 
 
 4th 
 
 5th 
 
 6th 
 
 7th 
 
 8th 
 
 9th 
 
 great 
 
 Basilica Justitiae at Fano; 
 
 writer on architecture. 
 Many buildings in India and some 
 
 at Constantinople; the first-known 
 
 Christian architect. 
 Assisted in the erection of the cele- 
 
 brated rotunda at Ravenna, the cu- 
 
 pola of which is said to have been of 
 
 one stone, thirty-eight feet in diame- 
 
 ter and fifteen feet thick. 
 St. Sophia, at Constantinople. 
 
 Built the Monastery of Medeshamp- 
 stede, afterwards called Peterbor- 
 ough. 
 
 Rebuilt York Cathedral. 
 
 The Cathedral of Rheims, the earliest 
 
 OVQTYIT->IO /-.f n<-,fViin nrr>Viitprf iirfi. 
 
LIST OF NOTED ARCHITECTS. 
 
 1541 
 
 AFTER CHRIST 
 
 Name of Architect. 
 
 Century. 
 
 Principal Works. 
 
 Buschetto, of Dulichium. 
 
 10th 
 
 The Cathedral, or Duomo, of Pisa, the 
 
 
 
 earliest example of the Lombard 
 
 
 
 ecclesiastical style of architecture. 
 
 
 
 It was built in 1016. 
 
 Pietro di Ustamber, of 
 
 10th 
 
 Cathedral of Chartres. 
 
 Spain. 
 
 
 
 Lanfranc, Archbishop of 
 
 10th 
 
 Choir of Canterbury Cathedral, burnt in 
 
 Canterbury, of Eng- 
 
 
 1174. 
 
 land. 
 
 
 
 Remigius, Bishop of Lin- 
 
 llth 
 
 Part of Lincoln Cathedral. 
 
 coln, of England. 
 
 
 
 Walkelyn, Bishop of Win- 
 
 llth 
 
 Said to have erected the oldest part of 
 
 chester, of England. 
 
 
 Winchester Cathedral. 
 
 Mauritius, Bishop of Lon- 
 
 12th 
 
 Built old St. Paul's in 1033. 
 
 don, of England. 
 
 
 
 Alexander, Bishop of 
 
 12th 
 
 Rebuilt Lincoln Cathedral. 
 
 Lincoln, of England. 
 
 
 
 Dioti Salvi, of Italy. 
 
 12th 
 
 Baptistery of Pisa, near the Campo 
 
 
 
 Santo. His works were in the Lom- 
 
 
 
 bard style and were overloaded with 
 
 
 
 minute ornaments. 
 
 Buono, of Venice. 
 
 12th 
 
 The Tower of St. Mark at Venice, which 
 
 
 
 is three hundred and thirty feet high 
 
 
 
 and forty feet square, built in 1154; a 
 
 
 
 design for enlarging the Church of 
 
 
 
 Santa Maria Maggiore, at Florence, of 
 
 
 
 which the master-walls still exist; 
 
 
 
 the Vicaria and the Castello del' 
 
 
 
 Novo, at Naples; Church of St. An- 
 
 
 
 drew, at Pistola; la Casa della Citta; 
 
 
 
 Campanile at Arezzo. 
 
 Wilhelm, orGuglielmo,of 
 
 12th 
 
 The Leaning Tower of Pisa built in 
 
 Germany. 
 
 
 1174. Bonnano and Tomaso, two 
 
 
 
 sculptors of Pisa, were also engaged 
 
 
 
 upon it. 
 
 William, of Sens, of Eng- 
 
 12th 
 
 Canterbury Cathedral. 
 
 land. 
 
 
 
 Peter, of Colechurch, of 
 
 13th 
 
 Began London Bridge. 
 
 England. 
 
 
 
 Robert, of Lusarches, of 
 
 13th 
 
 Cathedral of Amiens, which was con- 
 
 France. 
 
 
 tinued by Thomas de Cormont and 
 
 
 
 finished by his son Renauld. 
 
 Poore, Bishop of Salis- 
 
 13th 
 
 Began Salisbury Cathedral. 
 
 bury, of England. 
 
 
 
 Pietro Perez, of Spain. 
 
 13th 
 
 The Cathedral of Toledo. 
 
 Robert de Courcy, of 
 
 13th 
 
 Rebuilt the Cathedral at Rheims. 
 
 France. 
 
 
 
 Juan Rari, of France. 
 
 14th 
 
 Finished the building of the Church of 
 
 
 
 Notre Dame, of Paris. 
 
1542 LIST OF NOTED ARCHITECTS. 
 
 AFTER CHRIST. 
 
 Name of Architect. 
 
 Century 
 
 Principal Works. 
 
 Rafaelle d'Urbino, of 
 
 16th 
 
 Continued the erection of St. Peter's at 
 
 Urbino. 
 
 
 Rome after the death of Bramante, 
 
 
 
 his master in architecture; engaged 
 
 
 
 on the buildings of the Farnese Pal- 
 
 
 
 ace; Church of Santa Maria, in Navi- 
 
 
 
 cella, repaired and altered; stables of 
 
 
 
 Agostino, near the Palazzo Farnese; 
 
 
 
 Palazzo Caffarelli, now Stoppani; 
 
 
 
 the gardens of the Vatican; the 
 
 
 
 facade of the Church of San Lorenzo, 
 
 
 
 and of the Palazzo Uggoccioni, now 
 
 
 
 Pandolfini, at Florence. 
 
 Bolton, W., Prior of 
 
 16th 
 
 Supposed to have designed Henry VII. 's 
 
 St. Bartholomew's, oi 
 
 
 Chapel, where he was master of the 
 
 England. 
 
 
 works. 
 
 Giovanni Gil de Honta- 
 
 16th 
 
 Plan of the Cathedral of Salamanca, 
 
 non, of Spain. 
 
 
 etc. 
 
 Michael Angelo di Buona- 
 
 16th 
 
 Library of the Medici, generally called 
 
 rotti, of Florence. 
 
 
 the Laurentian Library, at Florence; 
 
 
 
 model for the facade of the Church of 
 
 
 
 San Lorenzo, commonly called the 
 
 
 
 Capella dei Deposit! ; Church San 
 
 
 
 Giovanni, which he did not finish; 
 
 
 
 fortifications at Florence and at Monte 
 
 
 
 San Miniato; monument of Julius 
 
 
 
 II., in the Church of San Pietro in 
 
 
 
 Vincoli, at Rome; plan of the Cam- 
 
 
 
 pidoglio, Palace of the Conservatori, 
 
 
 
 building in the centre, and the flight 
 
 
 
 of steps in the Campidoglio, or Cap- 
 
 
 
 itol, at Rome; continuation of the 
 
 
 
 Palace Farnese and several gates at 
 
 
 
 Rome, particularly the Porta Nomen- 
 
 
 
 tana or Pia; steeple of St. Michaele, 
 
 
 
 at Ostia ; the gate to the Vineyard de 
 
 
 
 Patriarea Grimani; Tower of S. Lo- 
 
 
 
 renzo, at Ardea; Church of Santa 
 
 
 
 Maria, in the Certosa, at Rome; many 
 
 
 
 plans of palaces, churches, and chap- 
 
 
 
 els. He was employed on St. Peter's 
 
 
 
 after the death of San Sallo. 
 
 Martino de Gainza, of 
 
 16th 
 
 The Chapel Royal at Seville 
 
 Spain. 
 
 
 
 Machuca, of Spain. 
 
 16th 
 
 Royal Palace of Granada. 
 
 Theodore Havens, of 
 
 16th 
 
 Caius College, Cambridge. A good 
 
 England. 
 
 
 specimen of the architecture of the 
 
 
 
 day. 
 
LIST OF NOTED ARCHITECTS. 1543 
 
 AFTER CHRIST. 
 
 Name of Architect. 
 
 Century 
 
 Principal Works 
 
 Carlo Maderno, of Lom- 
 
 16th 
 
 Altered Michael Angelo's design for St. 
 
 bardy. 
 
 
 Peter's at Rome from a Greek to a 
 
 
 
 Latin cross; began the palace of 
 
 
 
 Urban VIII. 
 
 Sir H. Watton, of Eng- 
 
 17th 
 
 Author of "The Elements of Archi- 
 
 land. 
 
 
 tecture," published in London in 
 
 
 
 1624. \ :* 
 
 Inigo Jones, of England. 
 
 17th 
 
 Banqueting House; chapel, Lincoln's 
 
 
 
 Inn; Surgeon's Hall; arcade, Cov- 
 
 
 
 ent Garden, London; and a vast 
 
 
 
 number of other important works. 
 
 Claude Perrault, of 
 
 17th 
 
 Facade of the Louvre, Chapel of Sceaux, 
 
 France. 
 
 
 Chapel of Notre Dame in the Church 
 
 
 
 of the Petits Peres. 
 
 Sir Christopher Wren, of 
 
 17th 
 
 St. Paul's ; planned the city of London 
 
 England. 
 
 
 after the fire, nearly all the churches 
 
 
 
 therein, Hampton Court, etc. 
 
 Jules Hardouin Mansard, 
 
 17th 
 
 The dome of the Hotel des Invalides, 
 
 of France. 
 
 
 Gallerie du Palais Royal, the Place 
 
 
 
 de Louis de Grand, des Victoires, 
 
 
 
 etc. He was the nephew of Francois 
 
 
 
 Mansard, the reputed inventor of the 
 
 
 
 Mansard roof. 
 
 Alexander Jean Baptiste 
 
 18th 
 
 L'Hotel de Vendome, in the Rue d'En- 
 
 le Blond, of France. 
 
 
 fer, at Paris. He was employed much 
 
 
 
 in Russia by Peter the Great. 
 
 Galli da Bibbiena, of 
 
 18th 
 
 Theatre at Verona, theatre at Vienna; 
 
 Italy. 
 
 
 author of two books on architecture. 
 
 James Gibbs, of Scotland. 
 
 18th 
 
 Radcliffe's Library, Oxford; the new 
 
 
 
 church in the Strand; St.-Martin's-in- 
 
 
 
 the-Fields; King's College, Royal 
 
 
 
 
 Library, and Senate House, Cam- 
 
 
 
 bridge. 
 
 Sir William Chambers, of 
 
 18th 
 
 Somerset House and many other works ; 
 
 England. 
 
 
 author of a treatise on civil architec- 
 
 
 
 ture. 
 
 Robert Adam, of Scot- 
 
 18th 
 
 Architect to George III.'; author of a 
 
 land. 
 
 
 work on the ruins of Spalatro His 
 
 
 
 principal works are the Register Office 
 
 
 
 at Edinburgh, infirmary at Glasgow, 
 
 
 
 the Edinburgh University, Luton 
 
 
 
 House, Adelphi Terrace. 
 
 Sir John Soame, of Eng- 
 
 18th 
 
 Bank of England, Board of Trade, 
 
 land. 
 
 
 State-Paper Office. 
 
 Charles Percier, of France 
 
 18th 
 
 Architect of the Tuileries; restorations, 
 
 
 
 etc., at Louvre and Tuileries. 
 
1544 LIST OF NOTED . ARCHITECTS. 
 
 AFTER CHRIST. 
 
 Name of Architect. 
 
 Century. 
 
 Principal Works. 
 
 James Essex, of England. 
 
 18th 
 
 The earliest, in modern times, who prac- 
 
 
 
 tised solely mediaeval art ; restoration 
 
 
 
 of Ely and other cathedrals; altera- 
 
 
 
 tions at various colleges at Cambridge 
 
 
 
 and Oxford. 
 
 James Wyatt, of Eng- 
 
 18th 
 
 The Pantheon Assembly rooms, palace 
 
 land. 
 
 
 at Kew, Fonthill Abbey, Doddington 
 
 
 
 Hall, Ashridge House, and many res- 
 
 
 
 torations. 
 
 Augustus Pugin, of Eng- 
 
 18th 
 
 Published "Specimens of Gothic Ar- 
 
 land. 
 
 
 chitecture," "Examples of Gothic 
 
 
 
 Architecture," "Antiquities of Nor- 
 
 
 
 mandy," and other works. 
 
 John Nash, of England. 
 
 19th 
 
 Brighton Pavilion, Haymarket Theatre, 
 
 
 
 Buckingham Palace, Regent's Park 
 
 
 
 and its terraces of dwellings, Regent 
 
 
 
 Street and the Quadrant improve- 
 
 
 
 ments. 
 
 Thomas Rickman, of 
 
 19th 
 
 New court of St. John's College, Cam- 
 
 England. 
 
 
 bridge; restoration of the Bishop of 
 
 
 
 Carlisle's palace, Cumberland; up- 
 
 
 
 wards of twenty-five churches in the 
 
 
 
 midland counties, several private 
 
 
 
 dwellings. Published "Attempt to 
 
 
 
 Discriminate the Styles of Architec- 
 
 
 
 ture in England." 
 
 Carl Friedrich Schinkel, 
 
 19th 
 
 Hauptwache Theatre and Museum, 
 
 of Prussia. 
 
 
 Werder-Kirche (Gothic), Bauschule 
 
 
 
 and Observatory at Berlin, theatre 
 
 
 
 at Hamburg, Schloss Krzescowice, 
 
 
 
 Charlottenhof, and the Nicolai- 
 
 
 
 Kirche at Potsdam. Published his 
 
 
 
 designs, many of which were not 
 
 
 
 executed. 
 
 Guillaume Abel Blouet, 
 
 19th 
 
 Published supplement to Roudelet's 
 
 of France. 
 
 
 "L'Art de Batir," and revised the 
 
 
 
 tenth edition of that work. 
 
 Ernst Friedrich Zwirner, 
 
 19th 
 
 Restoration of Cologne Cathedral, 
 
 of Prussia. 
 
 
 church at Remagen. 
 
 David Hamilton, of Scot- 
 
 19th 
 
 The Nelson Monument, the Royal Ex- 
 
 land. 
 
 
 change, the Western Club-house, and 
 
 
 
 other buildings at Glasgow; Hamilton 
 
 
 
 Palace and Lennox Castle, Scotland. 
 
 Mr. Joseph Gwilt. 
 
 19th 
 
 Compiler of the "Encyclopedia of 
 
 
 
 Architecture." 
 
NOTED AMERICAN ARCHITECTS. 
 
 AFTER CHRIST. 
 
 1545 
 
 Name of Architect. 
 
 Century. 
 
 Principal Works. 
 
 James Fergusson, d. Jan., 
 
 19th 
 
 Author of the "History of Architec- 
 
 1886. 
 
 
 ture." 
 
 John Henry Parker, b. 
 
 19th 
 
 Author of the "Glossary of Architec- 
 
 in London, 1806; d. 
 
 
 ture," "The Domestic Architecture of 
 
 Jan. 31, 1884, 
 
 
 the Middle Ages," a revised edition 
 
 
 
 of Rickman's "Gothic Architecture." 
 
 George Edmund Street. 
 
 19th 
 
 The Law Courts, London. 
 
 William Burges. 
 
 19th 
 
 Cork Cathedral, restoration of Cardiff 
 
 
 
 Castle. 
 
 Sir Gilbert Scott. 
 
 19th 
 
 Hamburg Cathedral, Edinburgh Cathe- 
 
 
 
 dral, the Albert Memorial, Midland 
 
 
 
 Station and Hotel at St. Pancras, 
 
 
 
 England. 
 
 LIST OF NOTED AMERICAN ARCHITECTS. 
 
 CHARLES BULFINCH, the first New England architect, b. 1763, 
 d. 1844. Designed the first theatre in Boston, 1793; the Mass. 
 State House, 1795; the first Catholic church in Boston, 1803; 
 Faneuil Hall, enlarged, 1808; University Hall at Harvard Col- 
 lege, 1814; the McLean Asylum at Somerville, 1792-1817, and 
 the Mass. General Hospital, 1818. Architect of the Capitol at 
 Washington from 1797-1818. 
 
 JOHN HAVILAND, b. 1792, d. 1825. 
 
 Principal works: Pittsburgh Penitentiary; Eastern Peniten- 
 tiary at Cherry Hill; Hall of Justice, New York; Naval Asylum, 
 Norfolk; New Jersey State Penitentiary; and many other jails, 
 asylums, and public halls. 
 
 JONATHAN PRESTON, b. 1801, d. July, 1884; practised in Bos- 
 ton, Mass. 
 
 Principal works: The first building of the Massachusetts Insti- 
 tute of Technology, and the building of the Boston Society of 
 Natural History. 
 
 WILLIAM WASHBURN, b. in Lyme, N. H., 1808, d. in Boston, 
 November 8, 1890; practised in Boston. 
 
 Principal works : The Fifth Avenue and Victoria Hotels in New 
 York, and the Parker House, Tremont House, Revere House, 
 Adams House, Young's Hotel, and the American House in Bos- 
 ton; the Tremont Temple, Boston; Charlestown City Hall, and 
 many other public and private buildings. 
 
1546 NOTED AMERICAN ARCHITECTS. 
 
 THOMAS USTICK WALTER, LL.D., b. 1804, d. October 30, 1887; 
 practised in Philadelphia, Pa.; was one of the original mem- 
 bers of the American Institute of Architects, and president for 
 many years; received the degree of LL.D. from Harvard Uni- 
 versity, being the first architect to receive that degree in this 
 country. 
 
 Principal works: The five original buildings of Girard College, 
 designed in 1833 and completed in 1847. Extension of the Na- 
 tional Capitol, 1851-65; also the extensions of the Patent Office, 
 Treasury and Post-office buildings, the dome on the old Capitol, 
 the Congressional Library, and the Government Hospital for the 
 Insane; also numerous other buildings of lesser importance. Mr. 
 Walter was a member of the Franklin Institute and of many 
 literary and scientific associations. 
 
 ARTHUR GILMAN; practised in New York and Boston, in 
 partnership with Mr. Bryant. 
 
 Principal works : Boston City Hall; First Church, on Arlington 
 Street, Boston, and numerous dwelling-houses in New York and 
 Boston. In association with Mr. Edward Kendall, designed the 
 Equitable Life Assurance Company's building on Broadway, New 
 York. ; 
 
 R. G. HATFIELD, b. in Elizabeth, N. J., 1815, d. February, 1879; 
 author of the American House Carpenter and Transverse Strains; 
 associated for thirty-five years with his brother, Oliver P. Hatfield. 
 The firm became widely known as experts and consulting archi- 
 tects in matters pertaining to building construction. 
 
 Principal works: House of Refuge, Randall's Island, N. Y.; 
 Westchester County Buildings, White Plains, N. Y. ; New York 
 Institution for the Deaf and Dumb , Seaman's Bank for Savings, 
 City Bank building, Security Insurance Co. Building, all of New 
 York City. 
 
 OLIVER P. HATFIELD, d. April, 1891. 
 
 JOHN MCARTHUR, Jr., b. in Scotland in 1823, d. January, 1890; 
 practised in Philadelphia, Pa. 
 
 Principal works: House of Refuge, Continental Hotel, Girard 
 House, Public Ledger Building, First National Bank Building, the 
 Assembly Building, the Broad Street Presbyterian Church, and 
 the City Hall, all of Philadelphia. Also the Hospital for the 
 Insane, at Warren, Pa.; Lafayette College, Easton, Pa.; and 
 numerous other public and private buildings in Pennsylvania 
 and other States. Was twice tendered the position of Supervis- 
 ing Architect to the United States Government, but declined. 
 
NOTED AMERICAN ARCHITECTS. 1547 
 
 EBENEZER L. ROBERT, b. 1825; practised in New York City. 
 
 Principal works: Standard Oil Company's Building, on Broad- 
 way; the Ninth National Bank; the Baptist Church of the Epiph- 
 any, on Madison Avenue; St. Paul's Methodist Church, on Fourth 
 Avenue, all of New York City; and the Phoenix Insurance Com- 
 pany's Building, Brooklyn, N. Y. 
 
 ALEXANDER R. ESTY, b. 1827, d. July 2, 1881; practised in 
 Boston. 
 
 Principal works: Union Congregational Church, Boston; Har- 
 vard Street Baptist Church, Cambridge, Mass.; Grace Church, 
 Newton, Mass.; Emanuel Church, on Newbury Street, Boston; 
 Buildings of the Colby University, Waterville, Me. ; Massachu- 
 setts State Normal Schools, at Framingham and Worcester, and 
 the University of Rochester, N. Y. 
 
 CARL PFEIFFER, b. in Germany, d. May, 1888; practised in 
 New York City. 
 
 Principal works: Fifth Avenue Presbyterian Church, New 
 York; Fifth Avenue Riding School, New York; and many pri- 
 vate houses, apartment houses, hotels, etc. 
 
 CHARLES DEXTER GAMBRILL, b. 1832, d. September 13, 1880; 
 practised in New York, first in partnership with Mr. George B. 
 Post, later with H. H. Richardson. 
 
 JOHN H. STURGIS; practised in Boston, Mass., with Mr. 
 Charles Brigham as Sturgis & Brigham. 
 
 Principal works : Boston Museum of Fine Arts, building of the 
 Boston Young Men's Christian Association, Church of the Advent, 
 residence of Mr. F. L. Ames, and many other fine residences in 
 Boston and vicinity. 
 
 A. B. MULLETT, b. 1834, d. October 20, 1890; supervising archi- 
 tect to the Trea ury from 1865 to 1875. Also engineer of the 
 District of Columbia for several years. The Post-office build- 
 ings in New York, Boston, Cincinnati, St. Louis, and Chicago 
 were designed by him, and Iso the State, War, and Navy Build- 
 ings in Washingto . 
 
 HENRY HOBSON RICHARDSON, b. in Louisiana in 1838 or 1839, 
 d. in Brookline, Mass., April, 1886. Graduated at Harvard Uni- 
 versity in 1859, studied seven years at the Ecole des Beaux- Arts 
 in Paris. Was associated for a short time with Charles D. Gam- 
 brill of New York. 
 
 A complete list of the works executed by him, arranged in 
 chronological order, may be found in the thirteenth edition of 
 this book. 
 
1548 NOTED AMERICAN ARCHITECTS. 
 
 Perhaps the best-known examples of his work are: 
 
 Trinity Church and Brattle Street Church, Boston; City Hall, 
 Albany, and portions of the New York State Capitol; the Library 
 and Town Hall, at North Easton, Mass.; Sever Hall and New 
 Law School, Cambridge, Mass.; County Court House and Jail, 
 Pittsburgh, Pa.; wholesale warehouse for Marshall Field & Co., 
 Chicago; Chamber of Commerce, Cincinnati, Ohio. 
 
 THOMAS WISEDELL, b. in England in 1846, d. in New York, 
 July 31, 1884. Educated in the office of Mr. R. J. Withers of 
 London. Associated with Mr. Kimball of New York. Princi- 
 pal works: Madison Square Theatre, and the "Casino," both in 
 New York City 
 
 JOSEPH MORRILL WELLS, b 1853, d. in New York, February, 
 1890. Mr. Wells was a junior partner in the firm of McKim, 
 Mead & White, architects, of New York. The movement of 
 American architects towards the Italian Renaissance, which com- 
 menced about the year 1889, was undoubtedly caused more by 
 his influence than that of any other single individual. Among 
 the buildings of the firm, more especially designed by him, are: 
 the Villard houses on Madison Avenue, New York; the 
 "Memorial Building" in New Britain, Conn.; fayade of 
 the Century Club, New York, and a fountain in Portland, 
 Oregon. 
 
 HENRY O. AVERY, d. 1890; studied at the* School of Fine 
 Arts in Paris. Took an important part in designing the houses 
 of W. K. Vanderbilt and Henry G. Marquand; a prominent 
 member of the architectural League of New York, the Archaeo- 
 logical Institute, and the Society of American Artists. 
 
 JOHN WELLBORN ROOT, b. in Georgia, January 10, 1850, d. 
 in Chicago, 111., January 15, 1891. Entered into partnership 
 with Daniel H. Burnham in 1873, which continued until his 
 death. Mr. Root was the designer of the firm. They designed 
 and executed seventy-seven public buildings, many of them of 
 the first class, and one hundred and twenty residences. Of their 
 public buildings the following were perhaps the most important : 
 Calumet Club House, Art Institute, Academy of Fine Arts, 
 Montauk Block, Calumet Building, Rialto Office Building, 
 Insurance Exchange Building, Grannis Block, Phoenix Build- 
 ing, The Rookery, Masonic Building, Woman's Temple, First 
 Regiment Armory, all of Chicago; the Mills Block, San Fran- 
 cisco; Midland Hotel, Board of Trade Building, American 
 National Bank Building of Kansas City. Mr. Root was 
 
NOTED AMERICAN ARCHITECTS. 1549 
 
 secretary of the American Institute of Architects at the time of 
 his death. 
 
 HERBERT C. BURDETT, b. in Boston, 1855, d. in Buffalo, 
 April 10, 1891 ; associated with J. Herbert Marling, as Marling 
 & Burdette, and practised in Buffalo, N. Y. Principal works: 
 The Saturn Club House and numerous fine residences in 
 Buffalo. 
 
 GEORGE WASHINGTOR PERCY, A. A.I. A., b. at Bath, Me. July 5, 
 1847, d. during 1900. Practiced in San Francisco, California, 
 1876-1900; from 1879 associated with Mr. F. F. Hamilton. 
 The firm designed many important buildings in and about San 
 Francisco and Los Angeles, also at Honolulu, H. I. President 
 of the Technical Society of the Pacific Coast, 1898-1900. 
 
 DANKMARK ADLER, F.A.I. A., b. in Langsfeld, Saxe- Weimar, 
 July 3, 1844. Practised architecture in Chicago from 1869 
 until his death, April 16, 1900. Was for many years asso- 
 ciated with Louis H. Sullivan, Mr. Adler being the "practical 
 man" of the firm; secretary A.I. A. 1891-92; member Board of 
 Directors 1890-93. 
 
 EDWARD C. CABOT, F.A.I. A., b. in Boston April, 1818, d. 
 January, 1901. Practised in Boston. For a number of years 
 associated with Mr. F. W. Chandler. Designed the Boston 
 Athenseum in 1846, the Boston Theatre in 1852-53, and in 
 association with Mr. Chandler, the Johns Hopkins Hospital, 
 Baltimore. Became a member of the A.I.A. in 1857, and was 
 president of the Boston Chapter for thirty-three years. 
 
 EDWARD HALE KENDALL, F.A.I A., b. in Boston, July 30, 1842, 
 d. March 10, 1901. Practised in New York from about 1868 
 until his death. His chief works are perhaps the first plans of 
 the Equitable Building, the Field Building, No. 1 Broadway, 
 the Methodist Book Concern the Goelet houses, and the 
 Washington Bridge, of which he was the consulting architect. 
 Was vice-president A.I.A. in 1885, a director for many years, 
 and president in 1892 and 1893. Was president of the New 
 York Chapter from 1884-88. 
 
 NAPOLEON EUGENE, H. C. LE BRUN, F.A.I. A., b. in Phila- 
 delphia January 2, 1821, d. July 9, 1901. Practised in Phila- 
 delphia 1842-65, when he removed to New York. Among the 
 prominent buildings which he designed in Philadelphia are the 
 Cathedral, the Academy of Music, the old Tabernacle Presby- 
 terian Church, the Girard Estate Building, and several county 
 buildings and prisons. In New York Citv, in connection with 
 
1550 NOTED AMERICAN ARCHITECTS. 
 
 his son, he erected many dwellings and public buildings, 
 including the Masonic Temple, several large and beautiful 
 churches, the New York Foundling Asylum, the Metropolitan 
 Insurance Building on Madison Square, the Home Life Insur- 
 ance Building, and several municipal edifices Member A. I. A. 
 from 1868 until his death, twice president of the New York 
 Chapter, and also president of the Willard Architectural Com- 
 mission. 
 
 EDWIN CLARK, F.A.I.A., b. in Philadelphia August 15, 1822, 
 d. January 6, 1902. Architect of the United States Capitol 
 from 1865 until his death. 
 
 JAMES BROWN LORD, F.A.I. A., b. in New York 1859, d. June 
 1, 1902. Designed the Delmonico Building, New York; the 
 Bloomingdale Asylum at White Plains; the Carnegie Library 
 in East Seventy-sixth Street ; and the Appellate Court Building 
 on Madison Avenue and Twenty-fourth Street. 
 
 WALTER COPE, F.A.I.A., b. in Philadelphia October 30, 1860, 
 d. November 3, 1902. Associated with John Stewardson and 
 E. L Stewardson from 1885 until his death. 
 
 Among the notable buildings designed by this firm are Den- 
 bigh, Pembroke, and Rockefeller Halls, all dormitories of Bryn 
 Mawr College; the Dormitories, Law School, and Medical 
 Laboratories of the University of Pennsvlvania ; Blair Hah\ 
 Stafford-Little Hall, and Gymnasium of Princeton University, 
 the Pennsylvania Institution for the Instruction of the Blind, 
 at Overbrook, Pa. ; the Washington University of St. Louis, 
 Mo. ; the City Hall, at Atlantic City, N. J. ; the Harrison Office 
 Building and the Harrison stores in Philadelphia, and man} 
 fine residences. 
 
 HENRY VAN BRUNT, F.A.I.A., b. in Boston, Sept. 5, 1832, 
 d. April 6, 1903. Student of Richard M. Hunt, practised in 
 Boston, under the firm name of Ware & Van Brunt, until , 
 1882, when Mr. Ware accepted the chair of Architecture at 
 Columbia College, and Mr. Van Brunt formed a new partner- 
 ship with Mr. Frank M. Howe. The firm of Van Brunt & Howe 
 moved to Kansas City in 1387, and existed until the death of 
 Van Brunt. President of the American Institute of Architects, 
 1899, and a writer of great ability. 
 
 Notable buildings designed by Ware and Van Brunt: Memo- 
 rial Hall of Harvard College; First Church of Boston; St. 
 Stephens Church, Lynn, Mass.; buildings for Wellesley College 
 Of Van Brunt & Howe: New Coates House; the Gibraltar 
 
NOTED AMERICAN ARCHITECTS. 1551 
 
 Building; Emery - Bird - Thayer Building Kansas City Star 
 Building, all of Kansas City; the Union Depot, Denver. 
 
 BRUCE PRICE, F.A.I. A., b. in Cumberland, Md., 1845, d. in 
 Paris, May, 1903. An architect of great brilliance and origi- 
 nality. His chief works are the American Surety Company's 
 Building, N. Y.; St. James Building, N. Y.; the group of 
 buildings near Lake wood, N. J., which he designed for Mr. 
 George J. Gould ; Osborn Hall at Yale University, and a pic- 
 turesque hotel in Quebec known as the Chateau Frontenac. 
 Was for some years president of the N. Y. Architectural League. 
 
1552 SCHEDULE OF ARCHITECTS' CHARGES. 
 
 PROFESSIONAL PRACTICE OF ARCHITECTS, AND SCHEDULE OP 
 USUAL AND PROPER MINIMUM CHARGES. 
 
 (A. I. A. Schedule, revised October, 1903.) 
 
 The architect's professional services consist in making the 
 necessary preliminary studies, working drawings, specifications, 
 large scale and full-size details, and in the general direction and 
 supervision of the work, for which the minimum charge is five 
 per cent, upon the cost of the work. 
 
 For new buildings costing less than $10,000, and for furniture, 
 monuments, decorative and cabinet work, it is usual and proper 
 to charge a special fee in excess of the above. 
 
 For alterations and additions to existing buildings the fee is 
 ten per cent, upon the cost of the work. 
 
 Consultation fees for professional advice are to be paid in pro- 
 portion to the importance of the questions involved. 
 
 None of the charges above enumerated covers alterations and 
 additions in contracts, drawings, and specifications, nor profes- 
 sional or legal services incidental to negotiations for site, disputed 
 party walls, right of light, measurement of work, or failure of 
 contractors. When such services become necessary, they shall 
 be charged for according to the time and trouble involved. 
 
 Where heating, ventilating, mechanical, electrical, and sani- 
 tary problems in a building are of such a nature as to require the 
 assistance of a specialist, the owner is to pay for such assistance. 
 Chemical and mechanical tests, when required, are to be paid 
 for by the owner. 
 
 Necessary travelling expenses are to be paid by the owner. 
 
 Drawings and specifications, as instruments of service, are 
 the property of the architect. 
 
 The architect's payments are due as his work progresses in 
 the following order: Upon completion of the preliminary sketches 
 one-fifth of the entire fee; upon completion of working draw- 
 ings and specifications, two-fifths; the remaining two-fifths 
 being due from time to time in proportion to the amount of 
 work done by the architect in his office and at the building. 
 
 Until an actual estimate is received, the charges are based 
 upon the proposed cost of the work, and payments are received 
 as instalments of the entire fee, which is based upon the actual 
 cost to the owner of the building or other work, when completed, 
 including all fixtures necessary to render it fit for occupation. 
 
CONTRACT BETWEEN ARCHITECT AND OWNER. 1553 
 
 The architect is entitled to extra compensation for furniture or 
 other articles purchased under his direction. 
 
 If any material or work used in the construction of the build- 
 ing be already upon the ground or come into the owner's posses- 
 sion without expense to him, its value is to be added to the sum 
 actually expended upon the building before the architect's 
 commission is computed. 
 
 In case of the abandonment or suspension of the work, the 
 basis of settlement is as follows: Preliminary studies, a fee in 
 accordance with /the 'character and magnitude of the work; 
 preliminary studies, working drawings, and specifications, three- 
 fifths of the fee for complete services. 
 
 The supervision of an architect (as distinguished from the 
 continuous personal superintendence ' which may be secured by 
 the employment of a clerk of the works) means such inspection 
 by the architect or his deputy of work in studios and shops, or 
 of a building or other work in process of erection, completion, 
 or alteration, as he finds necessary to ascertain whether it is 
 being executed in conformity with the drawings and specifica- 
 tions or directions. He is to act in constructive emergencies, 
 to order necessary changes, and to define the true intent and 
 meaning of the drawings and specifications, and he has author- 
 ity to stop the progress of the work and order its removal when 
 not in accordance with them. 
 
 On buildings where the constant services of a superintendent 
 are required, a clerk of the works shall be employed by the ar- 
 chitect at the owner's expense. 
 
 CONTRACT BETWEEN ARCHITECT AND OWNER. 
 
 From , Architect, 
 
 to , Owner. 
 
 For a compensation of 
 
 the architect proposes to furnish preliminary sketches, contract 
 working drawings and specifications, detail drawings and general 
 superintendence of building operations, and, also, to audit all 
 
 accounts, for a 
 
 to be erected for 
 
 on 
 
 Terms of payment to be as follows: 
 
 One fifth when the preliminary sketches are completed; three 
 tenths when the drawings and specifications are ready for letting 
 
1554 CONTRACT BETWEEN ARCHITECT AND OWNER. 
 
 contracts; thereafter at the rate of per cent, upon each 
 
 certificate due to the contractor 
 
 If work upon the building is postponed or abandoned, the 
 compensation for the work done by the architect is to bear such 
 relation to the compensation for the entire work as determined 
 by the published schedule of fees of the American Institute of 
 Architects. 
 
 In all transactions between the owner and contractor, the 
 architect is to act as the owner's agent, and his duties and liabili- 
 ties in this connection are to be those of agent only. 
 
 A representative of the architect will make visits to the build- 
 ing for the purpose of general superintendence, of such frequency 
 and duration as, in the architect's judgment, will suffice, or may 
 be necessary to fully instruct contractors, pass upon the merits 
 of material and workmanship, and maintain an effective working 
 organization of the several contractors engaged upon the struc- 
 ture. 
 
 The architect will demand of the contractors proper correction 
 and remedy of all defects discovered in their work, and will assist 
 the owner in enforcing the terms of the contracts; but the archi- 
 tect's superintendence shall not include liability or responsibility 
 for any breach of contract by the contractors. 
 
 The amount of the architect's compensation is to be reckoned 
 upon the total cost of the building, including all stationary 
 fixtures. 
 
 Drawings and specifications are instruments of service, and as 
 such are to remain the property of the architect. 
 
 , Architect. 
 
 Approved and accepted , 190 
 
 , Owner. 
 
THE UNIFORM CONTRACT. 1555 
 
 THE UNIFORM CONTRACT.* 
 
 Form of Contract Adopted and Recommended for General Use by 
 the American Institute of Architects and the National Asso- 
 ciation of Builders. Revised 1902. 
 
 THIS AGREEMENT, made the 
 
 in the year one thousand nine hundred and 
 
 by and between 
 
 party of the first part 
 
 (hereinafter designated the Contractor ) , and 
 
 .-....' party of the second part 
 
 (hereinafter designated the Owner ), 
 
 WITNESSETH that the Contractor , in consideration of the 
 agreements herein made by the Owner , agree with the said 
 Owner as follows : 
 
 ARTICLE I. The Contractor shall and will provide all the 
 materials and perform all the work for the 
 
 as shown on the drawings and described in the specifications 
 
 prepared by Architect , 
 
 which drawings and specifications are identified by the signa- 
 tures of the parties hereto, and become hereby a part of this 
 contract. 
 
 ART. II. It is understood and agreed by and between the 
 parties hereto that the work included in this contract is to be 
 
 done under the direction of the said Architect , and that 
 
 decision as to the true construction and meaning of the draw- 
 ings and specifications shall be final. It is also understood and 
 agreed by and between the parties hereto that such additional 
 drawings and explanations as may be necessary to detail and 
 illustrate the work to be done are to be furnished by said Archi- 
 tect , and they agree to conform to and abide by the same so 
 far as they may be consistent with the purpose and intent of 
 the original drawings and specifications referred to in Art. I. 
 
 It is further understood and agreed by the parties hereto that 
 any and all drawings and specifications prepared for the purposes 
 
 of this contract by the said Architect are and remain 
 
 property, and that all charges for the use of the same, and for 
 the services of said Architect are to be paid by the said 
 Owner . 
 
 ART III. No alterations shall be made in the work except 
 upon written order of the Architect ; the amount to be paid by 
 the Owner or allowed by the Contractor by virtue of such alter- 
 ations to be stated in said order. Should the Owner and Con- 
 tractor not agree as to amount to be paid or allowed, the work 
 shall go on under the order required above, and in case of failure 
 
 * Printed here by permission of the Secretary of the Committee and the 
 Inland Publishing Company, the licensees for its exclusive publication and 
 sale, 
 
1556 THE UNIFORM CONTRACT. 
 
 to agree, the determination of said amount shall be referred to 
 arbitration, as provided for in Art. XII of this contract. 
 
 ART. IV. The Contractor shall provide sufficient, safe and 
 proper facilities at all times for the inspection of the work by 
 
 the Architect or authorized representatives; shall, 
 
 within twentv-four hours after receiving written notice from the 
 Architect to that effect, proceed to remove from the grounds 
 
 or buildings all materials condemned by whether 
 
 worked or unworked, and to take down all portions of the work 
 which the Architect shall by like written notice condemn as 
 unsound or improper, or as in any way failing to conform to 
 the drawings and specifications, and shall make good all work 
 damaged or destroyed thereby. 
 
 ART. V. Should the Contractor at any time refuse or neglect 
 to supply a sufficiency of properly skilled workmen, or of mate- 
 rials of the proper quality, or fail in any respect to prosecute 
 the work with promptness and diligence, or fail in the perform 
 ance of any of the agreements herein contained, such refusal, 
 neglect or failure being certified by the Architect , the Owner 
 
 shall be at liberty, after. . days' written notice to 
 
 the Contractor , to provide any such labor or materials, and to 
 deduct the cost thereof from any money then due or thereafter 
 to become due to the Contractor under this contract; and if 
 the Architect shall certify that such refusal, neglect or failure 
 is sufficient ground for such action, the Owner shall also be at 
 liberty to terminate the employment of the Contractor for the 
 said work and to enter upon the premises and take possession, 
 for the purpose of completing the work included under this 
 contract, of all materials, tools and appliances thereon, and 
 to employ any other person or persons to finish the work, and 
 to provide the materials therefor; and in case of such discon- 
 tinuance of the employment of the Contractor 
 
 shall not be entitled to receive any further payment under this 
 contract until the said work shall be Avholly finished, at which 
 time, if the unpaid balance of the amount to be paid under this 
 contract shall exceed the expense incurred by the Owner in 
 finishing the work, such excess shall be paid by the Owner to 
 the Contractor ; but if such expense shall exceed such unpaid 
 balance, the Contractor shall pay the difference to the Owner . 
 The expense incurred by the Owner as herein provided, either 
 for furnishing materials or for finishing the work, and any 
 damage incurred through such default, shall be audited and 
 certified by the Architect , whose certificate thereof shall be 
 conclusive upon the parties. 
 
 ART. VI. The Contractor shall complete the several portions, 
 and the whole of the work comprehended in this agreement by 
 and at the time or times hereinafter stated, to wit: 
 
 ART. VII. Should the Contractor be delayed in the prosecu- 
 tion or completion of the work by the act, neglect or default 
 of the Owner , of the Architect , or of any other contractor 
 
THE UNIFORM CONTRACT. 1557 
 
 employed by the Owner upon the work, or by any damage 
 caused by fire, lightning, earthquake, cyclone or other casualty 
 
 for which the Contractor not responsible, or by 
 
 strikes or lockouts caused by acts of employes, then the time 
 herein fixed for the completion of the work shall be extended 
 for a period equivalent to the time lost by reason of any or all 
 the causes aforesaid, which extended period shall be deter- 
 mined and fixed by the Architect ; but no such allowance 
 shall be made unless a claim therefor is presented in writing 
 to the Architect within forty-eight hours of the occurrence 
 of such delay. 
 
 ART. VIII. The Owner agree to provide all labor and 
 materials essential to the conduct of this work not included 
 in this contract in such manner as not to delay its progress, 
 and in the event of failure so to do, thereby causing loss to 
 the Contractor , agree that will reimburse the Con- 
 tractor for such loss; and the Contractor agree that if 
 
 shall delay the progress of the work so as to cause loss for 
 
 which the Owner shall become liable, then shall 
 
 reimburse the Owner for such loss. Should the Owner and 
 Contractor -fail to agree as to the amount of loss compre- 
 hended in this Article, the determination of the amount shall 
 be referred to arbitration as provided in Art. XII of this con- 
 tract. 
 
 ART. IX. It is hereby mutually agreed between the parties 
 hereto that the sum to be paid by the Owner to the Con- 
 tractor for said work and materials shall be 
 
 subject to additions and deductions as hereinbefore provided, 
 and that such sum shall be paid by the Owner to the Con- 
 tractor , in current funds, and only upon certificates of the 
 Architect , as follows: 
 
 The final payment shall be made within 
 
 days after the completion of the work included in this contract, 
 and all payments shall be due when certificates for the same 
 are issued. 
 
 If at any time there shall be evidence of any lien or claim for 
 which, if established, the Owner of the said premises might 
 become liable, and which is chargeable to the Contractor , 
 the Owner shall have the right to retain out of any payment 
 then due or thereafter to become due an amount sufficient to 
 
 completely indemnify against such lien or claim. 
 
 Should there prove to be any such claim after all payments 
 are made, the Contractor shall refund to the Owner all moneys 
 that the latter may be compelled to pay in discharging any 
 lien on said premises made obligatory in consequence of the 
 Contractor default. 
 
 ART X. It is further mutually agreed between the parties 
 hereto that no certificate given or payment made under this 
 contract, except the final certificate or final payment, shall be 
 conclusive evidence of the performance of this contract, either 
 
1558 ARCHITECTS' LICENSE LAW. 
 
 wholly or in part, and that no payment shall be construed to 
 be an acceptance of defective work or improper materials. 
 
 ART. XL The Owner shall during the progress of the work 
 
 maintain insurance on said work, in own name and in 
 
 the name of the Contractor , against loss or damage by fire, 
 lightning, earthquake, cyclone or other casualty. The policies 
 to cover all work incorporated in the building, and all materials 
 for the same in or about the premises, and shall be made pay- 
 able to the parties hereto, as their interest may appear. 
 
 ART. XII, In case the Owner and Contractor fail to agree 
 in relation to matters of payment, allowance or loss referred to 
 in Arts. Ill or VIII of this contract, or should either of them 
 dissent from the decision of the Architect referred to in Art. 
 VII of this contract, which dissent shall have been filed in 
 writing with the Architect within ten days of the announce- 
 ment of such decision, then the matter shall be referred to a 
 
 Board of Arbitration consisting of 
 
 in behalf of the Owner , 
 
 and in behalf of the Contractor , 
 
 these two to select a third. The decision of any two of this 
 Board shall be final and binding on both parties hereto. In 
 event of the death or inability to serve of the party named in 
 behalf of the Owner , then the Owner shall select a person in 
 his place; in event of the death or inability to serve of the 
 party named in behalf ot the Contractor , then the Contractor 
 shall select a person in his place; in event of the death or in- 
 ability to serve of the third party, then the remaining arbi- 
 trators shall choose a person in his place. Each party hereto 
 shall pay one-half of the expense of such reference. 
 
 ART. XIII. The said parties for themselves, their heirs, suc- 
 cessors, executors, administrators and assigns, do hereby agree 
 to the full performance of the covenants herein contained. 
 
 IN WITNESS WHEREOF, the parties to these presents have 
 hereunto set their hands and seals, the day and year first above 
 written. 
 
 In Presence of 
 
 ARCHITECTS' LICENSE LAW STATE OF ILLINOIS. 
 
 TO PROVIDE FOR THE LICENSING OF ARCHITECTS AND REGU- 
 LATING THE PRACTICE OF ARCHITECTURE AS A PROFESSION. 
 
 AN ACT 
 
 Enacted by the Fortieth General Assembly at the Regular Biennial 
 Session, Approved June 3, 1897, and in Force July 1, 1897; 
 with Amendments Adopted by the Forty- first General Assem- 
 bly and Approved April 19, 1899. In Force July 1, 1899. 
 
 APPOINTMENT OF A STATE BOARD OF EXAMINERS OF ARCHITECTS 
 
 SECTION 1. Be it enacted by the people of the State of Illinois, 
 represented in General Assembly: That within thirty days after 
 tbe passage ot this act the Governor of this State shall, by the 
 
ARCHITECTS' LICENSE LAW. 1559 
 
 advice and consent of the Senate, appoint a State Board of 
 Examiners of Architects, to be composed of five members, one 
 of whom shall be a member of the faculty of the Illinois State 
 University, and the other four shall be architects residing in the 
 State of Illinois, who have been engaged in the practice of 
 architecture at least ten years. Two of the said practicing 
 architects appointed as examiners shall be designated to hold 
 office for two years from the date of the passage of this act, and 
 the other two, together w r ith the member of the faculty afore- 
 said, shall hold office for four years from the passage of this 
 act; and thereafter upon the expiration of the term of office of 
 the person so appointed, the Governor of the State shall ap- 
 point a successor to each person whose term of office shall 
 expire, to hold office for four years, and said person so ap- 
 pointed shall have the above specified qualifications. In case 
 appointment of a successor is not made before the expira- 
 tion of the term of any member, such member shall hold office 
 until his successor is appointed and duly qualified. Any 
 vacancy occurring in membership of the bo&rd shall be filled 
 by the Governor of the State for the unexpired term of such 
 membership, 
 
 [Sections 2 and 3 relate to the organization of the board, 
 salaries, meetings, etc.] 
 
 EXAMINATIONS FEES. 
 
 SEC. 4. Provisions shall be made by the board hereby con- 
 stituted for holding examinations at least twice in each year, of 
 applicants for license to practice architecture, and any person 
 over twenty-one years of age, upon payment of a fee of fifteen 
 dollars to the secretary of the board, shall be entitled to an 
 examination for determining his or her qualifications. All ex- 
 aminations shall be made directly by said board, or a commit- 
 tee of two members delegated by the board, and due notice of 
 the time and place of the holding of such examinations shall be 
 published, as in the case provided for the publication of the 
 rules and regulations thereof. The examination shall have 
 special reference to the construction of buildings, and a test of 
 the knowledge of the candidate of the strength of materials, and 
 of his or her abilitv to make practical application of such knowl- 
 edge in the ordinary professional work of an architect, and in 
 the duties of a supervisor of mechanical work on buildings, and 
 should also seek to determine his or her knowledge of the laws 
 of sanitation as applied to buildings. If the result of the exam- 
 ination of any applicant shall be satisfactory to a majority of 
 the board, under its rules, the secretary shall upon an order of 
 the board, issue to the applicant a certificate to that effect, 
 and upon payment to the secretary of the board by the candi- 
 date of a fee of twenty-five dollars, he shall thereupon 
 issue to the person therein named a license to practice archi- 
 tecture in the State, in accordance with the provisions of this 
 act, which license shall contain the full name, birth-place and 
 age of the applicant, and be signed by the president and secre- 
 
1560 ARCHITECTS' LICENSE LAAY. 
 
 tary, and sealed with the seal of the hoard 1 1' an applicant fails 
 to pass saiil examination, h's or her fee shall he returned. 
 
 All papers received by the secretary in relation to applications 
 for license shall be kept on file in his office, and a proper index 
 and record thereof shall be kept by him. 
 
 ARCHITECTS WHO ARE ENTITLED TO LICENSE WITHOUT AN 
 
 EXAMINATION. 
 
 SEC. 5. Any person who shall, by affidavit, show to the 
 satisfaction of the State Board of Examiners of Architects that 
 he or she was engaged in the practice of the profession ot archi- 
 tecture on the date of the passage of this act shall be entitled 
 to a license without an examination, provided such application 
 shall bo made within six months after the passage of this act. 
 Such license, when granted, shall set forth the fact that the 
 person to whom the same was issued was practicing architecture 
 in this State at the time of the passage of this act, and is there- 
 fore entitled to a license to practice architecture without an 
 examination by the board of examiners, and the secretary of the 
 board shall, upon the payment to him of the fee of twenty- 
 live dollars, issue to the person named in said affidavit, 
 a license to practice architecture in this State, in accordance 
 with the provisions of this act. In the case of a co-partnership 
 of architects, each member whose name appears must be 
 licensed to practice architecture. No stock company or cor- 
 poration shall be licensed to practice architecture, but the 
 same may employ licensed architects. Each licensed archi- 
 tect shall have his or her license recorded in the office of the 
 county clerk in each and every county in this State in which 
 the holder thereof shall practice, and he or she shall pay to 
 the clerk the same fee that is charged for the recording of 
 notarial commissions. A failure to have his or her license so 
 ^corded shall be deemed sufficient cause for revocation of 
 such license. 
 
 COUNTY CLERKS TO KEEP RECORD OF LICENSES RECORDED. 
 
 SEC. 6. Each county clerk shall keep in a book, provided for 
 the purpose, a complete list of all licenses recorded by him 
 under the provisions of this act, together with the date of the 
 issuance of each license. 
 
 LICENSED ARCHITECTS TO HAVE A SEAL.*V~ 
 
 SEC. 7. Every licensed architect shall have a seal, the im- 
 pression of which must contain the name of the architect, his 
 or her place of business, and the words, "Licensed Architect," 
 "State of Illinois," with which he shall stamp all drawings 
 and specifications issued from his office, for use in this State. 
 
 PENALTY FOR PRACTICING ARCHITECTURE WITHOUT A LICENSE. 
 
 SEC. 8. After six months from the passage of this act it 
 shall be unlawful and it shall be a misdemeanor punishable by 
 a fine of not less than $50 nor more than $500 for each and 
 every week during which said offense shall continue, for any 
 
ARCHITECTS' IJCKXSI-: LAW. 1561 
 
 person to pmrticc architecture without a license in this State, 
 or to advertise, or put out any sign or card, or other device 
 which might indicate to the public that he or she is entitled to 
 practice as an architect. 
 
 PERSONS WHO ARE TO BE REGARDED AS ARCHITECTS. 
 
 SEC. 9. Any person who shall be engaged in the planning 
 or supervision of the erection, enlargement, or alteration of 
 buildings for others, and to be constructed by other persons 
 than himself, shall be regarded as an architect within the pro- 
 visions of this act, -and 'shall be held to comply with the same; 
 but nothing contained in this act shall prevent the draughts- 
 men, students, clerks of works or superintendents, and other 
 employes of those lawfully practicing as architects, under 
 license as herein provided for, from acting under the instruc- 
 tion, control or supervision of their employers; or shall prevent 
 the employment of superintendents of buildings paid by the 
 owners from acting, if under the control and direction of a 
 licensed architect who has prepared the drawing and specifica- 
 tions for the building. The term building in this act shall be 
 understood to be a structure, consisting of foundations, walls, 
 and roof, with or without the other parts; but nothing con- 
 tained in this act shall be construed to prevent any person, 
 mechanic or builder from making plans and specifications for, 
 or supervising the erection, enlargement, or alteration of any 
 building that is to be constructed by himself or employes; 
 nor shall a civil engineer be considered as an architect unless 
 he plans, designs and supervises the erection of buildings, in 
 which case he shall be subject to all the provisions of this act, 
 and be considered as an architect. 
 
 LICENSE REVOKED. 
 
 SEC. 10. Architects' licenses issued in accordance with the 
 provisions of this act shall remain in full force until revoked 
 for cause, as hereinafter provided. Any license so granted 
 may be revoked by unanimous vote of the State Board of 
 Examiners of Architects for gross incompetency, or reckless- 
 ness in the construction of buildings, or for dishonest practices 
 on the part of the holder thereof; but before any license shall 
 be revoked such holder shall be entitled to at least twenty 
 days' notice of the charge against him, and of the time and 
 place of the meeting of the board for the hearing and deter- 
 mining of such charge. And on the cancellation of such 
 license it shall be the duty of the secretary of the board to give 
 notice of such cancellation to the county clerk of each county 
 in the State in which the license has been recorded, whereupon 
 the clerks of the counties shall mark the license recorded in 
 his office cancelled. After the expiration of six months from 
 the revocation of a license, the person whose license was revoked 
 may have a new license issued to him by the secretary upon 
 certificate of the Board of Examiners, issued by them upon 
 satisfactory evidence of proper reasons for his reinstatement, 
 and upon payment to the secretary of the fee of five dollars. 
 
15G2 COLLEGES AND SCHOOLS OF ARCHITECTURE. 
 
 For the purpose of earn ing out the provisions of this act 
 relating to the revocation of licenses, the board shall have the 
 power of a court of record, sitting in the county in which their 
 meeting shall be held, and the power to issue subpoenas and 
 compel the attendance and testimony of witnesses. Witnesses 
 shall be entitled to the same fees as witnesses in a court of record, 
 to be paid in like manner. The accused shall be entitled to 
 the subpoena of the board for his witnesses and to be heard in 
 person or bv counsel in open public trial. 
 
 RENEWAL OF LICENSE. 
 
 SEC. 11. Every licensed architect in this State who desires 
 t ) continue the practice of his profession shall annually, during 
 the time he shall continue in such practice, pay to the secretary 
 of the board during the month of July a fee of live dollars and 
 the secretary shall thereupon issue to such licensed architect a 
 certificate of renewal of his license for the term of one vear. 
 Anv licensed architect who shall fail to have his license renewed 
 during the month of July in each and every year shall have his 
 license revoked; and it shall be the duty of the secretary of the 
 board to give notice of such revocation to the county clerk in 
 each county in the State, whereupon the clerks of the counties 
 shall make an entry of such revocation accordingly. 
 
 But the failure to renew said license in apt time shall not 
 deprive such architect of the jight to renewal thereafter; and 
 the secretary of the board shall give like notice of such renewal ; 
 but the fee to be paid upon the renewal of license after the 
 month of July shall be ten dollars, to cover the additional ex- 
 pense incurred by the board on account of such notices. 
 
 REPORT OF PROCEEDINGS TO BE FILED WITH THE AUDITOR 
 OF PUBLIC ACCOUNTS. 
 
 SEC. 12. Within the first week of December, after the 
 organization of the board, and annually thereafter, the secre- 
 tary of the board shall file with the Auditor .of State a full 
 report of the proceedings of the board, and a complete state- 
 ment of the receipts and expenditures of the board, attested 
 bv the affidavits of the president and secretary, subject to the 
 approval of the State Auditor. 
 
 COLLEGES AND SCHOOLS OP ARCHITECTURE IN 
 THE UNITED STATES. 
 
 Columbia University, New York. School of Archi- 
 tecture. Alfred D. F. Hamlin, Professor in charge. Offers: (1) Full 
 four-year course leading to degree of Bachelor of Science. In 
 the fourth year the student may elect a specialized course in 
 Advanced Architectural Engineering, in place of the usual 
 course in Advanced Design. (2) Advanced courses leading to 
 the degrees of Master of Arts, and Doctor of Philosophy. (3) 
 
COLLEGES AND SCHOOLS OF ARCHITECTURE. 1583 
 
 Special or elective courses for students not candidates for a 
 degree. Tuition, $200 per year. 
 
 Cornell University, Ithaca, N. Y. College of Architec- 
 ture. Prof. John V. Van Pelt in charge. Prof. Clarence A. Martin, 
 Secretary. Offers: (1) Three courses leading to the degree 
 Bachelor of Architecture as follows: First, the regular four-year 
 course; Second, a four-year course allowing specialization in 
 Architectural Design ; Third, a four-year course allowing special- 
 ization in Architectural Engineering. (2) A two-year special 
 course in Architecture, leading to a certificate. (3) A regular 
 two-year course in Painting, leading to a certificate. (4) Special 
 courses in Painting, arranged for individual cases but not lead- 
 ing to a certificate or degree. Tuition, $125 per year. 
 
 Harvard University, Lawrence Scientific 
 School. Department of Architecture. Herbert Langford 
 Warren, A.M., Nelson Robinson, Jr., Professor of Architecture, 
 in charge. Offers: (1) Full four-year programme of courses in 
 Architecture leading to the degree of Bachelor of Science in 
 Architecture. (2) Competent special students are admitted to 
 take a partial course. A certificate will be given to such stu- 
 dents. Tuition, $150 per year. 
 
 Lawrence Scientific School. Department of land- 
 scape Architecture. Prof. Frederick Law Olmstead, A.B., in 
 charge. Offers: (1) Full four-year programme of courses lead- 
 ing to the degree of Bachelor of Science in Landscape Architec- 
 ture. (2) Competent special students are admitted to take a 
 partial course, to whom a certificate will be given. Tuition, 
 $150 per year. 
 
 Massachusetts Institute of Technology, Boston, 
 Mass. Francis W. Chandler, Professor in charge. Offers: 
 (1) Three courses leading to the degree of Bachelor of Science : 
 First, the regular four-year course in Architecture; Second, 
 a four-year course allowing specialization in Architectural 
 Engineering; Third, a four-year course allowing specialization 
 in Landscape Architecture. (2) Special students are received 
 on the basis of office experience or college graduation and prepa- 
 ration in Geometry and Drawing. Graduate coui&es lead to the 
 Master's degree. Tuition, $250 per year. 
 
 University of Pennsylvania, Philadelphia, Pa. 
 Course in Architecture. Warren Powers Laird, Professor in 
 charge. Offers: (1) Full four-year course leading to the 
 degree of B.S in Architecture. (2) Two-year special course 
 
1564 COLLEGES AND SCHOOLS OF ARCHITECTURE. 
 
 leading to a certificate of proficiency. (3) Five-year or gradu- 
 ate course leading to the degree of M.S. in Architecture. (4) 
 Combined six-year course in Arts and Architecture leading to 
 the degree of A.B. at the end of the fourth year and B.S. in 
 Architecture at the end of the sixth year. (5) Course in Archi- 
 tectural Engineering leading to the degree of B.S. in Architecture 
 and differentiated from the regular four-year course in Archi- 
 tecture by the substitution in the last year of specialized work 
 in engineering subjects for Architectural Designing, Drawing, 
 etc. Tuition for all courses, SI 50 per year. 
 
 University of Illinois, Urbana, 111. Courses in 
 Architecture. Nathan Clifford Ricker, Professor in charge. 
 Offers: (1) Full four-year course, leading to degree of B.S. in 
 Architecture. (2) Full four-year course leading to degree of B.S. 
 in Architectural Engineering. Tuition is free to residents of the 
 State. There is an incidental fee of $24 a year. 
 
 Ohio State University, Columbus, Ohio. Course 
 in Architecture. J. N. Bradford, Professor in charge. Offers; 
 Full four-year course leading to degree. Tuition, free. 
 
 University of California, Oakland, Cal. Has re- 
 cently established a Department of Architecture with John 
 Galen Howard, Professor in charge. 
 
 Syracuse University, Syracuse, N. Y. College of 
 Fine Arts. F. W. Revels, Professor of Architecture. Offers: 
 (1) Full four-year course leading to degree. (2) Two-year 
 special course leading to certificate of proficiency. Tuition f 
 $120 per year. 
 
 Washington University, St. Louis, Mo. Course in 
 Architecture. Frederick M. Mann, Professor in charge. Offers: 
 (1) Four-year course leading to a degree. (2) Special course 
 lor draughtsmen. Tuition, $150 per year; special course, 
 $100 per year. 
 
 Rose Polytechnic Institute, Terre Haute, Ind. 
 Department of Architecture. Malverd A. Howe, C.E., director. 
 Offers a full four-year course, designed to give a thorough 
 training in Architectural Engineering together with systematic 
 instruction in Architectural Design. Tuition, $100 per year. 
 
 Drexel Institute, Philadelphia, Pa. School of 
 Architecture. Arthur Truscott, director. Offers a two-year 
 course in Architecture, a large share of the time being devoted 
 to purely Architectural work. Tuition, $60 a year. 
 
TRAVELLING SCHOLARSHIPS. 1565 
 
 Pratt Institute, Brooklyn, N. Y. Course in Archi- 
 tecture. Walter S. Perry, Director of Department of Fine Arts. 
 Offers: Full two-years' course leading to a certificate of pro- 
 ficiency. Tuition, $45 per year. 
 
 Academy of Architecture and Industrial Science, 
 1742 Chouteau Ave., St. Louis, Mo. H Maack 
 Principal. This is a private school founded by Mr. Maack in 
 1885, and designed more particularly to meet the wants of build- 
 ing tradesmen, offering them such instruction as is necessary 
 to attain the highest proficiency in their trade, and to fully 
 understand the plans and details of complicated buildings. 
 There is- also a special course for those desiring to fit them- 
 selves for positions as draughtsmen in architects' offices. Tui- 
 tion 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. 
 There are several special courses which may be commenced at any 
 time, and for which the tuition varies. 
 
 The Society of Beaux- Arts Architects of New 
 York has established a course of study for architectural draughts- 
 men, modelled on the system adopted by the ficole des Beaux- 
 Arts, Paris, France. The course is divided into two classes: 
 Class B, into which any one of either sex may enter without 
 any preliminary examination; Class A, which the student 
 reaches after having received certain awards in Class B. On 
 completing the course, which is not limited by time, the Society 
 awards a certificate of proficiency. 
 Address 
 
 CHAIRMAN, Committee on Education, 
 
 3 East 33d St., New York. 
 
 Instruction in Architecture, Architectural Engineering, and 
 Drawing is also given by the International Correspondence 
 Schools, Scranton, Pa., and by the American School of Corre- 
 spondence, at Armour Institute of Technology, Chicago, 111. 
 
 TRAVELLING FELLOWSHIPS AND SCHOLARSHIPS. 
 
 Itotch Travelling Scholarship. C. H. Blackall, Sec- 
 retary, 1 Somerset St., Boston, Mass. Candidates must be under 
 thirty years of age, must have worked during two years in 
 Massachusetts in the employ of an architect resident in Mas- 
 sachusetts, and will be required to pass preliminary examina- 
 tions upon the following subjects: 
 
1566 LIST OF VALUABLE BOOKS FOR ARCHITECTS. 
 
 I. Construction, Theory and Practice. (Written examina- 
 tion.) 
 
 II An Elementary Knowledge of the French Language. 
 (Written examination.) 
 
 III. History of Architecture. (Written examination.) 
 
 IV. Freehand Drawing from the Cast. 
 
 Candidates who pass in these preliminary examinations will 
 be asked to present themselves later for the competition in 
 Design. The successful candidate in each yearly examination 
 receives from the Trustees of the Scholarship annually, for two 
 years, $1,000 to be expended in foreign travel and study, pro- 
 vided always that the beneficiary shows such fitness and dili- 
 gence as may be required of him. 
 
 The Boston Society of Architects has offered the sum of $75 
 as a second prize. 
 
 The Society of Beaux- Arts Architects, Travel- 
 ling Scholarship. Lloyd Warren, Chairman Com. on Edu- 
 cation, 3 East 33d St., New York. A fund of $2,000 has been 
 provided to defray the expenses of this prize, which will be 
 awarded July, 1904, and the recipient will spend two years in 
 travel and study abroad. The award will be based on the 
 result of three competitive trials, to which all American 
 draughtsmen Under 28 years of age are eligible. The four 
 draughtsmen holding the best averages next to the final winner 
 of the scholarship will be awarded the sum of $100 each. 
 
 Columbia University Travelling- Fellowships. 
 Four travelling fellowships have been established, open to all 
 graduates of the School of Architecture under 30 years of age; 
 they are awarded in May of each year. 
 
 LIST OF VALUABLE BOOKS FOR ARCHITECTS, 
 DRAUGHTSMEN, AND BUILDERS. 
 
 [The author has carefully examined nearly all of the books named below, 
 and can recommend them as containing useful information on the subjects 
 under which they are listed. Name and address of publisher given at end of 
 the list.] 
 
 ARCHITECTURE. 
 
 Price 
 Handbook of Architectural Styles* By A. Rosengarten. . . . $2 . 50 
 
 History of Architecture. l By Prof. A. D. F. Hamlin 2 . 00 
 
 Vignola. The Five Orders of Architecture. 2 Edited by Ar- 
 thur Lyman Tuckerman 5.00 
 
LIST OF VALUABLE BOOKS FOR ARCHITECTS. 1567 
 
 Price 
 
 Vignola. American edition prepared for Bates & Guild 
 
 Co $5.00 
 
 The American Vignola. 3 By Prof. William R. Ware 3 .,00 
 
 Stepping-stone to Architecture.* By Thomas Mitchell . 50 
 
 A Discussion of Composition, especially as applied to Archi- 
 tecture. By John V. Van Pelt 2.00 
 
 Handbook of Ornament.* By Meyer *. 3 . 60 
 
 A Dictionary of Architecture and Building. 5 By Russell 
 
 Sturgis. In three volumes, per volume 18 . 00 
 
 BUILDING CONSTRUCTION, SUPERINTENDENCE, AND SPECIFI- 
 CATIONS. 
 
 (See also FOUNDATIONS and IRON AND STEEL CONSTRUCTION.) 
 
 Building Construction and Superintendence. 2 Part I. 
 Masonry and Plastering. Part II. Carpenters' Work. 
 Part III. (In press) Trussed Roofs and Roof-Trusses. 
 By F. E. Kidder. Each volume sold separately, per 
 volume 4 . 00 
 
 Building Superintendence. 5 By T. M. Clark 3 . 00 
 
 Safe Building. 5 By Louis De Coppert Berg. Two volumes, 
 
 each 5.00 
 
 Details of Building Construction. 4 By Prof. Clarence A. 
 
 Martin 2.00 
 
 Inspectors' Pocket-Book* for the use of Inspectors and Super- 
 intendents. By Austin T. Byrne 3 . 00 
 
 A Practical System for Writing Specifications for Buildings. 2 
 
 By W. Frank Bower 5.00 
 
 CONCRETE, PLAIN AND REINFORCED. 
 
 Experimental Researches on Reinforced Concrete. 13 By Ar- 
 mand Considere. Translated by Leon Moisseiff, C.E. Author- 
 ized American Edition. $2.00. 
 
 Materials, Construction and Design of Concrete and Reinforced 
 Concrete.* By Frederick W. Taylor, M.E., and Sanford E. 
 Thompson, Assoc. M. Am. Soc. C. E., with chapters by R. Feret, 
 Wm. B. Fuller, and Spencer B. Newberry. 8vo. 
 
 Reinforced Concrete. 14 By Chas. F. Marsh, Assoc. M. Inst. 
 C .E., Assoc. M. Inst. M. E. 4to, 7f X 11, 530 pp., 511 ill. $7.00. 
 
 Reinforced Concrete. 11 By A. W. Buel and C. S. Hill. $5.00. 
 
1568 LIST OF VALUABLE BOOKS FOR ARCHITECTS. 
 
 DRAWING. Price. 
 
 Architectural Draining. By C. Franklin Edminster $2.00 
 
 [The most practical and complete course in the ele- 
 ments of Architectural Drawing now published.] 
 Architectural Perspective for Beginners. 2 By F. A. Wright. 3.00 
 Pen Drawing.* By Charles D. Maginnis 1 . 00 
 
 ELECTRIC WIRING. 
 
 Vol. 13, International Library of Technology. 7 
 Practical Lessons in Electricity. 8 
 
 ESTIMATING. 
 
 Estimating Frame and Brick Houses. 9 .By Fred T. Hodg- 
 son 1 .00 
 
 FOUNDATIONS. 
 Building Construction and Superintendence. 2 Part I. By 
 
 F. E. Kidder 4.00 
 
 A Treatise on Masonry Construction. 6 By Ira O. Baker. ... 5 . 00 
 A Practical Treatise on Foundations.* By W. M. Patton, 
 
 C E <;.*viw ., ii .->* .-& , vv. 5.00 
 
 FURNITURE DESIGNING. 
 
 Furniture Designing and Drafting. 2 By Alvan Crocker 
 
 Nye ii-iii 2.00 
 
 HANDBOOKS. 
 
 The Civil Engineers' Pocket-Book.* By John C. Trautwine, 
 revised by John C. Trautwine, Jr., and John C. Traut- 
 wine, 3d r 5.00 
 
 The Mechanical Engineers' Pocket-Book. 6 By William 
 
 Kent 5 . 00 
 
 Carnegie Steel Company's Pocket Companion 2 . 00 
 
 Cambria Steel. Published by Cambria Iron Co 2 . 00 
 
 Manual of Structural Steel. Compiled by Geo. H. Blakeley 
 and published by the Passaic Steel Co. 
 
 Steel in Construction. Published by the Pencoyd Iron 
 Works. 
 
 Handbook. Published by the Dearborn Foundry Company, 
 Chicago. 
 
 Book of Standards. Edited by Prof. Reid T. Stewart, 
 
 and published by the National Tube Works 1 . 00 
 
 The Building Trades Pocket-Book. "By International 
 
 Correspondence Schools, Scranton, Pa 1 .50 
 
LIST OF VALUABLE BOOKS FOR ARCHITECTS. 1569 
 
 FlREPROOFING. Price. 
 
 The Fireproofing of Steel Buildings* By J. K. Freitag. . .$2.50 
 [A very practical and valuable work.] 
 
 HEATING AND VENTILATION. 
 
 Heating and Ventilation of Buildings* By Prof. Rolla 
 
 C. Carpenter 3 .00 
 
 Steam Heating for Buildings* By Wm. J. Baldwin 2.50 
 
 Vol. 32, International Library of Technology. 1 
 
 IRON AND STEEL CONSTRUCTION SKELETON CONSTRUCTION. 
 
 Architectural Iron and Steel* (many useful details). By 
 
 Wm. H. Birkmire 3 . 50 
 
 Compound Riveted Girders* By Wm. H. Birkmire 2.00 
 
 Skeleton Construction in Buildings* By Wm: H. Birk- 
 mire 3 . 00 
 
 Architectural Engineering* By Joseph Kendall Freitag. 2.50 
 [The best discussion of the engineering problems involved 
 in the construction of high buildings.] 
 
 PAINTING. 
 
 Rustless Coatings: * Corrosion and Electrolysis of Iron and 
 
 Steel. By M. P. Wood. 432 pp 4.00 
 
 The Industrial and Artistic Technology of Paints and Var- 
 nish.* By Alvah H. Sabin, 378 pp 3.00 
 
 PLANNING or CHURCHES 
 Churches and Chapels. 2 By F. E. Kidder 3.00 
 
 PLANNING OF OFFICE BUILDINGS. 
 The Planning and Construction of High Office Buildings.* 
 
 By William H. Birkmire 3.50 
 
 PLANNING OF SCHOOL BUILDINGS. 
 Modern American School Buildings.* By Warren R. 
 
 Briggs 4.00 
 
 School Architecture. 10 By Edmund M. Wheelwright 5.00 
 
 PLANNING OF THEATRES. 
 The Planning and Construction of American Theatres.* By 
 
 William H. Birkmire. . .3.00 
 
1570 LIST OF VALUABLE BOOKS FOIl ARCHITECTS. 
 
 PLUMBING AND SANITARY ENGINEERING. Price. 
 
 Sanitary Engineering of Buildings. Vol. I. By W. P. 
 
 Gerhard $5 . 00 
 
 ROOF-TRUSSES. 
 (See also Steel-Mill Buildings.) 
 
 Trussed Roofs and Roof-Trusses 2 (in press). Being the 
 third volume of Building Construction and Superin- 
 tendence. By F. E. Kidder. Sold separately 4.00 
 
 [A complete treatise on the subject, illustrated by many 
 
 examples of roof construction in wood and steel.] 
 The Design of Simple Roof-Trusses in Wood and Steel. Q By 
 
 Prof. Malverd A. Howe 2 . 00 
 
 Graphics for Engineers, Architects, and Builders. By 
 
 Prof. Chas. E. Greene. 
 Part I. Roof-Trusses. Diagrams for steady load, snow, 
 
 and wind 1.25 
 
 Part II. Bridge Trusses 2 . 50 
 
 Part III. Arches in Wood, Iron, and Stone 2. 50 
 
 [These books are among the best of those which show how 
 stresses may be determined by graphical solution ] 
 
 STEEL-MILL BUILDINGS. 
 
 The Design of Steel-Mill Buildings. 11 By Milo S. Ketchum. 4 . 00 
 [A practical and useful work, containing many details ] 
 
 STONES FOR BUILDING AND DECORATION. 
 
 Stones for Building and Decoration.^ By Geo. P. Merrill. . 5.00 
 [The most complete work published on building stones, 
 
 marbles, etc.] 
 Much practical information on building stones is contained in 
 
 Building Construction and Superintendence. Part I. 
 PUBLISHERS. * Published abroad. l Longmans, Green, & 
 Co., N. Y. 2 Wm. T. Comstock, N. Y. 3 The American Archi- 
 tect Co., Boston. 4 Bates & Guild Co., Boston. 5 The Macmil- 
 lan Co., N. Y. 6 John Wiley & Sons, N. Y. 'International 
 Text-Book Co., Scranton, Pa. 8 American School of Corre- 
 spondence at Armour Inst. of Technology, Chicago. 9 David 
 Williams Co., X. Y. 10 Rogers & Hanson, Boston. u Engineer- 
 ing News Publishing Co., N. Y. 12 Published by the Author. 
 "McGraw Publishing Co., X. Y. " D. Van Nostrand Co, 
 N. Y. 
 
TRADE REFERENCES. 1571 
 
 Trade References. 
 
 Because they are somewhat out of the ordinary line of building con- 
 struction and equipment, the following references are given that archi- 
 tects and builders may know whom to consult for information and prices. 
 All names have been inserted without the knowledge of the parties inter- 
 ested or any monetary consideration. Most of the manufacturers named 
 issue valuable publications along the line of their especial product, which 
 will be sent gratis on application. 
 Acetylene Gas Generators.* 
 
 Davis Acetylene Co., Elkhart, Ind. 
 
 General Acetylene Co., New York. 
 
 Niagara Falls Acetylene Gas Generator Co., Niagara Falls, N. Y. 
 Antifriction Drawer Slide. 
 
 Grant Pulley & Hardware Co. (Turner Slide), 25 Warren St., N. Y. 
 Artificial Marble. 
 
 Artificial Marble Co., St. James Building, N. Y. 
 
 Mycenian Marble Co., 524 W. 34th St., N. Y. 
 Automatic Fire Apparatus, Sprinklers, etc. 
 
 General Fire Extinguisher Co., Providence, R. I. 
 
 International Sprinkler Co., Philadelphia, Pa. 
 
 Niagara Fire Extinguisher Co., Akron, O. 
 Bells. 
 
 Merieely Bell Co., Troy, N. Y., and 177 Broadway, N. Y. City. 
 Blinds, Venetian, Rolling, Sliding, etc. 
 
 Burlington Venetian Blind Co., Burlington, Vt. 
 
 Jas. G. Wilson Mfg. Co., 3 W. 29th St., N. Y. 
 Chain Blocks. 
 
 The Yale & Towne Mfg. Co., 9 Murray St., N. Y. 
 Changeable Directories, for Office Buildings. 
 
 U. S. Changeable Sign Co., 150 Nassau St., N. Y. 
 Chimney Brick, Perforated Radial, Manufacturers. 
 
 National Pyrogranite Co., 17 Battery PI., N. Y. 
 Chimneys, Self-sustaining Steel. 
 
 The Wm. B. Pollock Co., Youngstown, O. 
 
 The Reeves Bros. Co., Alliance, O. 
 
 Walsh's Holyoke Steam Boiler Works, Holyoke, Mass. 
 Chimneys, Tall. Radial Brick Systems, see also p. 1229. 
 
 Alphonse Custodis Chimney Const. Co., Bennett Bldg., N. Y. 
 
 H. R. Heinicke, 160, 5th Ave., N. Y. 
 
 Steinl Improved Chimney Const. Co., Birmingham, Ala. 
 Chimneys, Tall. Of Reinforced Concrete (specialists). 
 
 Weber Steel-Concrete Chimney Co., Ashland Bl'k, Chicago, 111. 
 Clocks, Electric, Programme, and Tower. 
 
 Blodgett Clock Co., 141 Franklin St., Boston. 
 
 Johnson Service Co., 240 Fourth Ave., N. Y. 
 
 The Howard Clock Co., E. Boston and New York. 
 
 Prentiss Clock Improvement Co., 304 Hudson St., N. Y. 
 Clothes Dryers. 
 
 Chicago Clothes Dryer Works, 346 Wabash Ave., Chicago. 
 
 Peck, Williamson Co., Cincinnati, O. 
 
 The F. M. Watkins Co., Cincinnati, O. 
 Conservatories and Horticultural Buildings. 
 
 Hitchings & Co., 233 Mercer St. N. Y. 
 
 Lord and Burnham Co., 1133 Broadway, N. Y. 
 Conveyors. 
 
 Brown Hoisting Machinery Co., Cleveland, O. 
 
 C. W. Runt Co., West New Brighton, N. Y. 
 
 Lidgerwood Mfg. Co., New York. 
 
 Link-Belt Machinery Co., Chicago. 
 
 Robbins Conveying Belt Co., New York. 
 
 * See The Buyers' Reference for long list of Manufacturers. 
 
1572 TRADE REFERENCES. 
 
 Cranes and Hoists.* See also Derricks. 
 
 Brown Hoisting Machinery Co., Cleveland, O. 
 
 General Electric Co., Schenectady, N. Y. 
 
 Sprague Electric Co., New York. 
 
 Whiting Foundry Equipment Co., Harvey, 111. 
 
 Yale & Towne Mfg. Co., 9 Murray St., N. Y. 
 Creosoting Works. 
 
 American Creosote Works, New Orleans, La. 
 
 International Creosoting and Construction Co., Galveston, Tex. 
 Derricks. See also Cranes and Hoists. 
 
 American Hoist & Derrick Co., St. Paul, Minn. 
 Domestic Water and Light Plants. See also Pumps. 
 
 Fairbanks, Morse & Co., Monroe St., Chicago. 
 
 Electric Blue Printing Outfits, for making blue prints by means of 
 arc lamps. 
 
 General Electric Co., Schenectady, N. Y. 
 
 J. H. Wagenhorst & Co., Mansfield, O. 
 Electric Fans and Fan Motors. 
 
 General Electric Co., Schenectady, N. Y. 
 Elevators.* 
 
 Otis Elevator Co., principal office 17 Battery Place, N. Y. 
 
 Reedy Elevator Co., New York & Cincinnati, O. 
 
 Sprague Elevator Co., New York. 
 
 Standard Plunger Elevator Co., New York. 
 
 Warner Elevator Mfg. Co., Cincinnati, O. 
 
 Winslow Elevator and Machinery Co., Chicago. 
 Fibre, Hard, in Sheets. For insulating under columns, etc. 
 
 Delaware Hard Fibre Co., Wilmington, Del. 
 Filters.* 
 
 Albany Filter Co., New York. 
 
 Hygeia Filter Co., Detroit, Mich. 
 
 Wm. B. Scaife & Sons, Pittsburg, Pa. 
 
 Fireproof Doors and Shutters, and standard fixtures (underwriters' 
 requirements). 
 
 Coburn Trolley Track Mfg. Co., Holyoke, Mass. 
 Foundry Equipment. 
 
 Whiting Foundry Equipment Co., Harvey, 111. 
 Garbage Furnaces. 
 
 American Process Co., 62 William St., N. Y. 
 
 Morse-Boulger Destroyer Co., 39 Cortlandt St., N. Y. 
 
 Smith-Siemens Garb. Incin. Furnaces, 141 Broadway, N. Y. 
 Gasolene Engines. 
 
 Fairbanks, Morse & Co., Monroe St., Chicago. 
 Hoists (Pneumatic). See also Cranes and Derricks. 
 
 The General Pneumatic Tool Co., Montour Falls, N. Y. 
 Hot Air Pumping Engines. 
 
 Rider-Ericsson Mfg. Co., New York, Chicago, and Boston. 
 Hydraulic Rams. 
 
 N. O. Nelson Mfg. Co., St. Louis. 
 
 U. S. Wind Engine & Pump Co., Batavia, 111. 
 Ice Machines. 
 
 Remington Machine Co., Wilmington, Del. 
 
 The Singer Automatic Ice Machine Co., Bridgeport, Conn. 
 Industrial Railways and Equipment. 
 
 Arthur Koppel, 66 Broad St., N. Y. 
 
 C. W. Hunt Co., West New Brighton, N. Y. 
 
 Wonham-Magor Engineering Co., 29 Broadway, N. Y. 
 Insulating Materials for Cold Storage. 
 
 Samuel Cabot, Boston. 
 
 H. W. J9hns-Manville Co., 100 William St., N. Y. 
 
 Union Fibre Co., Winona, Minn. 
 
 Also manufacturers of Mineral Wool; see Buyers' Reference. 
 
 * See The Buyers' Reference for long list of Manufacturers. 
 
TRADE REFERENCES. 1573 
 
 Jails and Jail Cells. 
 
 L. Screiber & Sons Co., Cincinnati, O. 
 
 The Van Dorn Iron Works Co., Cleveland, O. 
 L,aundry Machinery. 
 
 American Laundry Machinery Co., 42 Cortlandt St., N. Y. 
 
 Chicago Clothes Dryer Works, 346 Wabash Avs., Chicago. 
 
 A. T. Hagen Co., Chicago, 111. 
 
 Steel Roll Mangle Co., Chicago, 111. 
 
 Troy Laundry Machinery Co., Troy, N. Y. 
 Library Stacks. 
 
 Art Metal Construction Co., Jamestown, N. Y. 
 
 Geo. Stykeman, 280 Broadway, N. Y. 
 
 J. B. & J. M. Cornell, 26th St. & llth Ave., N. Y. 
 
 Library Bureau, 530 Atlantic Ave., Boston. 
 
 Snead Architectural Iron Works, Louisville, Ky. 
 
 A. B. & W. T. Westervelt, 102 Chambers St., N. Y. 
 Ugh tiling Rods. 
 
 Bacon & Co., Cleveland, O. 
 
 Bajohr Lightning Rod Works, St. Louis, Mo. 
 
 Franklin Lightning Rod Works, St. Louis, Mo. 
 
 E. G. Washburn & Co., New York. 
 Metal Window Frames and Sash. See p. 767. 
 Parquet Floors and Borders.* 
 
 The Interior Hardwood Co., Indianapolis, Ind. 
 
 S. C. Johnson & Son, Racine, Wis. 
 Piling, Concrete. 
 
 Raymond Concrete Pile Co., 135 Adams St., Chicago, 111. 
 
 Simplex Concrete Piling Co., 915 Penn. Building, Philadelphia, Pa. 
 
 t Crawford Paving Co., Home Life Building, Washington, D. C. 
 
 t The Foundation Co., 35 Nassau St., N. Y. 
 
 t The Foundation Co., McCague Building, Omaha, Neb. 
 Piling, Sheet, Interlocking Steel. 
 
 U. S. Steel Piling Co., 135 Adams St., Chicago, 111. 
 
 Friestedt Interlocking Channel Bar Co., 1408 Tribune Bldg., Chicago, III 
 Pneumatic Tools. 
 
 Ingersoll-Sergeant Drill Co., The, 26 Cortlandt St., N. Y. 
 
 Philadelphia Pneumatic Tool Co., Philadelphia. 
 
 Thos. H. Dallett Co., Philadelphia, Pa. 
 Pumping by Compressed Air. 
 
 Ingersoll-Sergeant Drill Co., The, 26 Cortlandt St., New York. 
 
 Pneumatic Engineering Co., 85 Cedar-fit., N. Y. 
 Pumps for Domestic Purposes.* 
 
 The American Works, Aurora, 111. 
 
 The Deming Co., Salem, O. 
 
 Fairbanks, Morse & Co., Monroe St., Chicago. 
 
 The* Goulds Mfg. Co., Seneca Falls, N. Y. 
 
 Rider-Ericsson Mfg.Co. (Hot- Air), New York and Chicago. 
 Refrigerators. See p. 1492. 
 Revolving Doors. 
 
 Van Kannel Revolving Door Co., 524 E. 134th St., N. Y. 
 Rolling Shutters (Steel). 
 
 Columbus Steel Rolling-Shutter Co., Columbus, O. 
 
 Kinnear Mfg. Co., Columbus, O. 
 
 Rolling Steel Shutter Works, 162 W. 27th St., N. Y. 
 
 Jas. G. Wilson, Mfg. Co., 3 W. 29th St., N. Y. 
 Roofing Tiles.* See p. 1430. 
 Safes and Vaults.* 
 
 Diebold Safe and Lock Co., Canton, O. 
 
 Herring-Hall-Marvin Safe Co., Hamilton, O. 
 
 Victor Safe and Lock Co., Cincinnati, O. 
 
 * See The Buyers' Reference for long list of Manufacturers, 
 t Licensed by the Simplex Concrete Piling Co. 
 
1574 TRADE REFERENCES. 
 
 S ifety Treads. 
 
 American Mason Safety Tread Co., 40 Water St., Boston, Mass- 
 American Pressed Steel Co., Witherspoon Building, Philadelphia. 
 
 New York Belting and Packing Co., New York. 
 Sash-lifting Apparatus, for Monitor windows, greenhouses, etc. 
 
 The G. Drouve Co., Bridgeport, Conn. 
 
 Hitchings & Co., 233 Mercer St., N. Y. 
 
 Lord & Burnham Co., 1133 Broadway, N. Y. 
 Sasli Weights, compressed lead. 
 
 Raymond Lead Co., Lake & Clinton Sts., Chicago. 
 Sewerage Disposal Apparatus. 
 
 Newport Foundry and Machine Co., Newport, R. I. 
 Snow Guards. 
 
 Folsom Snow Guard Co., Roslindale (Boston), Mass. 
 Stand-pipes. 
 
 The Win. B. Pollock Co., Youngstown, O. 
 
 The Reeves Bros. Co., Alliance, O. 
 
 Walsh's Holyoke Steam Boiler Works, Holyoke, Mass. 
 Sun Dials. 
 
 E. B. Meyrowitz, 104 E. 23d St., N. Y. 
 r winging Hose Racks, for use in connection with stand-pipes. 
 
 H. J. M. Howard, 915 E. St., N. W., Washington, D. C. 
 
 Wirt & Knox Mfg. Co., 22 N. Fourth St., Philadelphia, Pa. 
 Tall Chimney Construction. See p. 1229. 
 Tanks, Large Wooden. 
 
 W. E. Caldwell Co., Louisville, Ky. 
 
 Flint & Walling Mfg. Co., Kendall ville, Ind. 
 
 U. S. Wind Engine & Pump Co., Batavia, 111. 
 Tanks, Steel, also towers for supporting same. 
 
 Flint & Walling Mfg. Co., Kendallville, Ind. 
 
 Chicago Bridge and Iron Works.. 105th & Troop Sts., Chicago. 
 Telephones,* for connecting portions of large buildings. 
 
 De Veau Telephone Mfg. Co., 27 Rose St., N. Y. 
 
 Electric Gas Lighting Co., 113 Purchase St., Boston. 
 
 The Simplex Interior Telephone Co., 19 E. Third St., Cincinnati. 
 Thermostats and Temperature Regulators.* 
 
 Davis & Roesch Temperature Controlling Co., 136 Liberty St., N. Y. 
 
 Howard Thermostat Co., Oswego, N. Y. 
 
 Johnson Electric Service Co., Milwaukee, Wis. 
 
 National Regulator Co., Chicago, 111. 
 Tiles, Roofing. See p. 1430. 
 Tiles, Rubber. 
 
 Goodyear Tire & Rubber Co., Akron, O. 
 
 Gutta Percha & Rubber Mfg. Co., New York. 
 
 Manhattan Rubber Mfg. Co., New York, N. Y. 
 
 Mechanical Rubber Co., Chicago, 111. 
 
 New York Belting & Packing Co., New York. 
 
 Peerless Rubber Mfg. Co., New York, N. Y. 
 Travelling Cranes. See Cranes. 
 Water Proofing for Brick and Stone. 
 
 Sze-elmey & Co., Home Life Building, Washington, D. C. 
 
 Toch Brothers, 470 West Broadway, N. Y. 
 Wind Mills. 
 
 U. S. Wind Engine & Pump Co., Batavia, 111. 
 
 Challenge Wind Mill Co., Batavia, 111. 
 
 Flint & Walling Mfg. Co., Kendallville, Ind. 
 Wire Rope, Wire Rope Tramways, Traiiemiss'oii < f Pow r by. 
 
 Bro 'erick & Bascom Rope Co., St. Louis, Mo. 
 
 A. Leschen & Sons Rope Co.,t St. Louis, Mo. 
 John A. Roebling Sons' Co.,t Trenton, N. J. 
 
 The Trenton Iron Co.,t Trenton, N. J. 
 
 * See The Buyers' Reference for long list of Manufacturer?, 
 t Publish valuable pamphlets on these subjects. 
 
GLOSSARY 
 
 CORINTHIAN DORIC 
 ABACUS. 
 
 or TECHNICAL TERMS, ANCIENT AND MODERN, USED BY ARCHITECTS, 
 BUILDERS, AND DRAUGHTSMEN. 
 
 (Compiled by the author from various sources.") 
 
 Aaron's-Rod. An ornamental figure representing a rod with a serpent 
 twined about it. It is sometimes confounded v.ith the caduceus of Mercury. 
 The distinction between the 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 orna- 
 ment in the centre, 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 moulded ; 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 bnild- 
 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 apiece of land on other land, street, river, etc. 
 
 Acanthus. A ptont found in the south of Europe, representations of whose 
 leaves are employed for decorating the Corinthian and 
 Composite capitals. Tho leaves of the acanthus are 
 used on the bell -.>? tLo capital, and distinguish the two 
 rich orders fron" .he three others. 
 
 Acrot' u,. The small pedestals placed on the ex- 
 treimi .cs and apex of a pediment. They are usually 
 without bases or plinths, and were originally intended 
 to receive statues. ACANTHUS. 
 
 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. 2. 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 sepa- 
 rated by an arch. 
 
 Alipterion. In ancient Roman architecture, a room used by bathers for 
 anointing themselves. 
 
 1575 
 
1576 GLOSSARY. 
 
 Almonry. The place or chamber where alms were distributed to the poor in 
 churches, or other ecclesiastical building. 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 distributed 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 Roman architecture, a place on which offerings or sacri- 
 fices were made to the gods. In Protestant churches, the 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 nicJies, 
 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 ob- 
 long enclosure in ancient churches, resembling in its uses and positions the mod- 
 ern 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. 
 
 Amphitheatre. A double theatre, 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 public. 
 
 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 par- 
 allel walls the vault of a corridor. Same as Barrel '^ , _ 
 Vault. 
 
 Annulet. A small square moulding used to sep- 
 arate others. The fillet which separates the flut- 
 ings of columns is sometimes known by this term. ANNUUJT. 
 
GLOSSARY. 
 
 1577 
 
 ANTEFIXA. 
 
 Anta, Antae. A name given to a pilaster when attached to a wall. Vitruvius 
 calls pilasters parastatce when insulated. They are not usually diminished, and 
 in all Greek examples their capitals are 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. 
 
 Anteohoir. 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 lions 1 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 
 applied 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 column, 
 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 moulded 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 ceilings. 
 
 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 Graeco-Roinan, Byzantine, and 
 Egyptian. It is supposed that they constructed many of their finest 
 buildings from the ruins of ancient cities. 
 
 Ar860Style. 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. 
 
 Arseosy stylos, That style of building in which four columns ARABESQUE. 
 are used in the space of eight diameters and a half ; the central 
 intercolumniation being three diameters and a half, and the others on each 
 side being only half a diameter, by which arrangement coupled columns are 
 introduced. 
 
 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. 
 
1378 
 
 GLOSSARY. 
 
 ARCADE. 
 
 Arcade. A range of arches, supported either 
 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 
 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 mouldings 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 amphitheatre 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 manufact- 
 ures 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. 2. 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 moulding, 
 sometimes plain and sometimes ornamented. 
 
 Asymptote. A straight line which continu- 
 ally approaches to a curve without touching it. 
 
 Atlases, or Atlantes Figures or half-figures 
 of men, used instead of columns or pilasters to 
 support an entablature ; called also Telamones. 
 
 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 ATLJLNTBS. 
 
GLOSSARY. 1579 
 
 evidently derived from the Greek, we find nothing exactly answering to it in 
 Greek architecture ; but it is very common in both Roman and Italian practice, 
 What are otherwise called tholobates in St. Peter's and St. Paul's Cathedrals 
 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 
 to 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 centre of any rotative motion. In a sphere, an imag- 
 inary line through the centre. 
 
 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 eittier 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 moulding above 
 and below, and is carved sometimes with foliages, but in BALDACHIN. 
 
 general with cusped circles, or quatrefoils, in which frequently are shields of 
 arms. 
 
 Band Of a Column. 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- 
 tifully carved with foliages, etc., as at Amiens. In several cathedrals there are 
 rings of 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. 
 They are frequent on the Continent ; that at Rome, near St. John Lateran, and 
 those at Florence, Pisa, Pavia, etc., are all well-known examples. The only ex- 
 amples in England are at Cranbrook and Canterbury ; the latter, however, is 
 supposed 10 have been originally part of the treasury. 
 
1580 
 
 GLOSSARY. 
 
 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, corbelled 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 oylets or arrow- 
 slits. 
 
 Basement. The lower part of a building, usu- 
 ally in part below the grade of the lot or street. 
 
 Base Mouldings. The mouldings immediately 
 above the plinth of a wall, pillar, or pedestal. 
 
 Base of a Column. That part which is between 
 the shaft and the pedestal, or, if there be no pedes- BARTIZAN. 
 
 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 ; Mczzo-rilievo, that in 
 which the figure projects one-half ; and Basso-rilievo, when ihe 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. 
 2. 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 clinched 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. 
 
 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- 
 cois 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 mouldings 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 mouldings were continued round the sides, as well aa 
 at top and bottom, mitriug at the angles, as over the doorway of Magdalene Col- 
 
 BATTLEMENT. 
 
GLOSSARY. 1581 
 
 lege, Oxford, England. The battlements of the Decorated and later periods are 
 often richly ornamented by panelling, as in the last example. In castellated 
 work the merlons are often pierced by narrow arrow-slits. (See Oylet.) In South. 
 Italy 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. 
 
 Baza&r. A kind of Eastern mart, of Arabic origin. 
 
 Bead. A circular moulding. When several are joined, it is called Heeding; 
 when flush with the surface, it is called Quirk-bead ; and when raised, Cock-bead. 
 
 Beam. A piece of timber, iron, etone, 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. 
 
 Beaufet, 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 Mouldings. Those mouldings 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. 
 
 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 
 sometimes double, /is at Northborough and Cozwell, 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 very curious and, it is believed, 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 moulded, 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 basilica, 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 
 
1582 GLOSSARY, 
 
 into the body of the church, that of the bishop hem? in the centre. The bemaia 
 generally ascended by steps, and railed off by cancelli. 
 
 Bench Table. The stone 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 solid body is said to 
 be bevelled 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 ornamented moulding much used in the Nor- 
 man period, resembling bezants, coins struck in Byzantium. 
 
 Billet. A species of ornamented moulding much used in Norman, and some* 
 times in Early English work, like short pieces of stick cut oft* and arranged alter- 
 nately. 
 
 Blocking 1 , 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 joints falling over 
 each other. In brickwork there .are several kinds of bond. In common brick 
 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 are clipped so as to 
 get in a diagonal course of headers behind. In Old English bond, every alternate 
 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 right 
 angles to its face, in order to bind it together. 
 
 Bond-timbers. Timbers placed in a horizontal direction in the walls of a 
 brick building in tiers, and to which the battens, laths, etc., are secured. In rub- 
 ble work, walls are better plugged for this purpose. 
 
 Border. Useful ornamental pieces around the edge of anything. 
 
 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 moulding, or torus. When it follows 
 a curve, as round a bench end, it is called a Roving Boutell. 
 
 BOTF. 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 timber, 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 Mould. [ { ] Two ressaunts 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. 
 
GLOSSARY. 
 
 1583 
 
 BrfiSSumnier.A lintel, beam, or iron tie, intended to carry an external 
 wall and itself supported by piers or posts ; used principally over shop win- 
 dows. This term is now seldom used, the word beam, or girder, taking its place. 
 
 Bridging. A method of stiffening floor joist and partition studs, by cutting 
 pieces in between. Cross bridging of floor joist is illus- 
 trated 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, I" 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 two pieces of timber 
 or moulding butt together. CROSS-BRIDGING. 
 
 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 which 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 little projection, and generally stop under a cornice 
 or corbel table. Early English buttresses project considerably, 
 sometimes with deep sloping weatherings in several stages, 
 and sometimes with gabled heads. Sometimes they are cham- 
 fered, and sometimes the angles have jamb shafts. At Wells 
 and Salisbury, England, they are richly ornamented with can- 
 opies and statues. In the Decorated period they became richly 
 panelled in stages, and often finish with niches and statues and 
 elegantly carved and crocketed gabelts, as at York, England. 
 In the Perpendicular period the weatherings became waved, 
 and they frequently terminate with niches and pinnacles. 
 
 Buttress, Flying. A detached buttress 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 
 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 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. 
 
 BUTTRESS. 
 
 FLYING BUTTRESS. 
 
 Cabinet, A highly ornamented kind of buffet or chest of drawers set apart 
 for the preservation of things of value. 
 
 Cabling. The flmtes 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. 
 
1584 GLOSSARY. 
 
 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- 3 
 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 concave 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, scat, or tomb. The word is supposed to be derived from cono- 
 pseum, the gauze covering over a bed to keep off the gnats ; a mosquito curtain. 
 Early English canopies are generally simple, with tref oiled 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 mouldings of the door, and form, as it were, the hood- 
 moulds to them, as at York. The former are above and independent of the door 
 mouldings, and frequently support an arch with a tympanum, above which is a 
 triangular canopy, as in the Duomo at Florence. 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. 
 
 Capital. 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 
 all 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, 
 ill its several stages, in Mayence Cathedral. But this form of capital was more 
 
GLOSSARY. 1585 
 
 folly 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 
 mouldings were always used, whether with or without foliage. 
 
 Caravansary. A huge, square building, or inn, in the East, for the recep- 
 tion of travellers 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 re- 
 ceive 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 materials, generally of a better 
 quality. 
 
 Casement. A glass frame which is made to open by turning on 
 hinges affixed to its vertical edges. 
 
 Cassoon, or Caisson. A deep panel or coffer in a soffit or ceil- 
 ing. This term is sometimes written in the French form, caisson; 
 sometimes derived directly from the Italian cassone, the augmenta- 
 tive 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. CARYATID. 
 
 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 moulding, opposed in effect to the ovolo 
 the quadrant of a circle. 
 
 Ceiling 1 . That covering of a room which hides the joists of the floor above, 
 or the rafters of the roof. Most European churches have either open roofs, or 
 are groined in stone. At Peterborough and St. Albans, England, there are verj 
 old flat ceilings of boards curiously painted. In later times the boarded ceilings, 
 and, in fact, some of those of plaster, have moulded 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 hoard, in exact imitation of stone groining. In the Elizabethan and 
 subsequent periods the ceilings are enriched with most elaborate ornaments in 
 stucco. 2. Matched and beaded boards, planed and smoothed, used for wain- 
 scoting. 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. 
 
1586 GLOSSABY 
 
 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, Champfer, or Chaumfer. 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 chambered ; if to a 
 large scale, it is said to be a canted corner. The chamfer is much used in mediae- 
 val work, and is sometimes plain, sometimes hollowed out, and sometimes 
 moulded. 
 
 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 founders tomb, and? are often endowed places where masses might 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 apartment in any large building, a palace, a nobleman's house, a 
 hospital or prison, used for public 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 re- 
 ceives an arch. 
 
 Charnel House. A place for depositing the bones which might be 
 thrown up in digging graves. Sometimes it was a portion of the 
 crypt: sometimes it was a separate building in the church-yard; 
 sometimes chantry chapels were attached to these buildings. M. 
 Viollet le-Duc has given two very cnrious 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. CHAPTEEL 
 
 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 "horse," is 
 chanted. x 
 
 Church. A building for the performance of 
 public worship. The first churches were built on . CHEVRON. 
 
 the plan of the ancient basilicae, 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. 
 
GLOSSARY. 
 
 1587 
 
 Ciborium. A tabernacle or vaulted canopy supported on shafts standing over 
 the high altar. 
 
 Cincture. A ring, list, or fillet at the top and bottom of a 
 column, serving to divide the shaft of the column from its 
 capital and base. 
 
 Cinque-foil. A sinking or perforation, like a 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 CINQUE-FOIL. 
 as honorary distinction among the Romans to such as had preserved the life 
 of a fellow-citizen. 
 
 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- 
 /oils, or spherical triangles. In large 
 building:*, 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 ; 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, eheds, etc. 
 
 Cloister. An enclosed square, like 
 the atrium of a Roman hmise, 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 
 or abbey. Sometimes the walls are 
 traceable, but now generally the 
 boundary is only known by tradi- 
 tion. 
 
 Close String, or Box String. A 
 
 Bath Abbey. 
 
 FLYING BUTTRESS AND CLERE-STORY. 
 
 A, buttress with pinnacle ; B, flying 
 
 sthod of finishing the outer edge of buttress supporting clere-story ; C, vaulted 
 + . ^ , -u- * i_ roof of aisle ; D D, pier dividing nave from 
 
 stairs, by building up a sort of curb aisle E< vau i ted roof of nave, 
 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. 
 
1588 
 
 GLOSSARY. 
 
 CLUSTERED 
 COLUMN. 
 
 OVOLO 
 
 FILLET:- 
 
 ,CAVETTO 
 
 _r 
 
 Clustered Column. Several slender pillars attached to each other so 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 covering of paint, plaster, or other work, 
 done at one time. 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, skim 
 coat, or white coat. It varies in composition in different localities. 
 
 Coffer. A deep panel in a ceiling. 
 
 Coffer Dam. A frame used in the building of a bridge in deep 
 water, similar to a caisson. 
 
 Collar Beam. A beam above the lower ends of the rafters, and 
 spiked to them. 
 
 Colonnade. A row of columns. The colonnade is termed, accord- 
 ing to the number of columns which support the entablature : Tetra- 
 style. when there are four , hexastyle, when six ; octostyle, when 
 eight, etc. When in front of a building they are termed porticos ; when surround- 
 ing a building, peristyle ; and when double or more, polystyle. 
 
 Colosseum, or Coliseum.- The immense amphitheatre built at Rome by Fla- 
 vius 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 larjje audience 
 building, generally of a temporary 
 nature. oj 
 
 Colossus. The name of a brazen j? 
 statue which was erected at the 3 
 entrance of the harbor at Rhodes, ^ 
 one hundred and five feet in height. 
 Vessels could sail between its legs. u 
 
 Column. A round pillar. The 
 parts are the base, on which it rests ; 
 its body, called 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- p 
 tached or engaged when they form o 
 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 
 beanTat bottom. Common joists are SECTION OP COLUMN AND ENTABLATURE. 
 the beams in naked flooring to which (Divided according to the Tuscar Order.) 
 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. 
 
 ABACUS 
 
 OVOLO "T 
 FILLETV r- 
 
 ILLET ::r^~ 
 
 APOPHYCE8 
 
 APOPHYCE3 
 FILLET J-. 
 TORUS 
 
GLOSSARY. 1589 
 
 Composite Order. The most elaborate of the orders of classical architecture. 
 
 Concrete. A mass composed of broken stone, sand, and hydraulic cement, 
 which makes a sort of artificial stone, much used for foundations ; a finer variety 
 is sometimes used in blocks for building houses. 
 
 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. 
 
 Confessional.- The seat where a priest or confessor sits to hear confessions. 
 
 Conge. Another name for the echinus or quarter round. 
 
 Conservatory. A building for the protection and rearing of tender plants, 
 often attached to a house as an apartment. Also, a public place of instruction, 
 designed to preserve and perfect the knowJedge of some Jbranch 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 scroJls or volutes at the 
 two ends, of unequal size and contrasted, but con- 
 nected 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. Jn 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 throating to form a drip. 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 apiece of stone iutting 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 Jn 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 trie foliage or ornaments resemble those 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 ormore 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 moulding, 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 top 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 period the cor- 
 bel table was nearly abandoned, and a large hollow,with one or two subordinate 
 mouldings, substituted ; this is sometimes filled with the ball flowers, and some- 
 times with, running foliages. In the Perpendicular style the parapet frequently 
 
1590 GLOSSARY. 
 
 did not project beyond the wall-line below ; the moulding then became a string 
 (though often improperly called a cornice), and was .ornamented by a quatre-foil, 
 or small rosettes, set at equal intervals immediately under the battlements. In 
 many French examples the moulded string is very bold, and enriched with foli- 
 age ornaments. 
 
 Corona. The brow of the cornice which projects over the bed mouldings 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 centre of a building and the 
 wings. Courts admit of the most elegant ornamentations, such as arcades, 
 etc, 
 
 Cove Coving. The moulding called the cavetto, or the scotia inverted, on a 
 large scale, and not as a mere moulding in the composition of a cornice, is called 
 a cove or a coving. 
 
 Cove-bracketing, The wooden skeleton mould or framing of a cove, applied 
 chiefly to the bracketing of a cove ceiling 
 
 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 iath 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 gabiets, hood -moulds, pinna- 
 cies spires: generally, a winding stem like a creeping plant, 
 with flowers or leaves projecting at intervals, and terminat- 
 ing ID a finiai 
 
 Cross -This religious symbol is almost always placed on 
 the ends of gables, the summit of spires, and other conspicu 
 ous piaces of old churches In early times it was generally 
 very pmm often a simple cross in a circle Sometimes they 
 take the tonn 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 
 by Edward I Of these a few yet remain, one of which has 
 recently been reerected at Charing Cross Preaching crosses were often setup 
 by the wayside as stations for preaching ; the most noted is that in front of St. 
 Pau> s, England The finest remaining sepulchral crosses are tne old elaborately 
 carved examples + ound in Ireland. 
 
 Cross-aisle. An old name tor a transept. 
 
 Cross-springer. The transverse ribs of a vault 
 
 Cross- vaulting -A common name eiven 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. 
 
GLOSSARY. 1591 
 
 Cupola. A small room, either circular or polygonal, standing on the top of a 
 dome By some it is called a Lantern. 
 
 Curb Root, or Mansard Roof. A roof formed of four contiguous planes, each 
 two having an external inclination. 
 
 Curtail Step, The first 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 ex- 
 ample in England of a plain cusp is probably that at Pythagoras School, at- Cam 
 bridge . of an ornamental cusp, at Ely Cathedral, where a small roll, witha rosette 
 at the end is formed at the termination of a cusp. In the later styles the termi- 
 nations of the cusps were more richly decorated ; they also sometimes terminate 
 not only in leaves or foliages, but in rosettes, heads, and other fanciful orna- 
 ments 
 
 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 Vitruvms monopterai 
 
 Cyma, - The name of a moulding of very frequent use It is a simple, waved 
 
 line, concave at one end and convex at the other, like an r- q 
 
 Italic /, When the concave part is uppermost it is called ^^ 
 
 a cyma recta , but if the convexity appear above and the \ .j 
 
 concavity below it is then a cyma reversa CYMA RECTA. 
 
 Cymatium,- When the crowning moulding of an en 
 tablature is of the cyma form, it is termed the Cyma 
 tiurn. 
 
 Cyrtostyle -A circular projecting portico Such are CYMA REVERSA. 
 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 ihe similar part of ail stereobates which 
 are arranged like 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 nails 
 there was generally a deep 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 probabiy 
 the name was given from the fact that the seats of great men were then sur 
 mounted by such an ornament 
 
 Darby, A nat toot used by plasterers in working, especially on ceilings it >a 
 generally about seven inches wide and forty two inches ^ong with two nandles on 
 the back. 
 
 Decastyle, A portico of ten columns in front 
 
 Decorated Style, -The second sta^e or ttie Pointed or Gothic style of archi- 
 tecture, considered the most complete and perfect development of Gothic archi 
 lecture, 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. 
 
 Dentil. The cogged or toothed member common in the bed-mouid of aOorin- 
 thian entablature, is said to be dentilled. and each cog or tooth is called a dentil. 
 
 Depressed Arches, or Drop Arches Those of less pitch than the equilateral 
 
 Design, The plans elevations, sections, and whatever other drawings may 
 be necessary for an edifice, exhibit the design, the term plan uavmg a restricted 
 application to a technical portion of the design 
 
 Detail, As used by architects, detail means the smaller parts into which a 
 
1592 GLOSSARY. 
 
 composition may be divided. It is applied generally to mouldings and other 
 enrichments, and again to their minutiae. 
 
 Diameter. The line in a circle passing through its centre, or thickest part, 
 which gives the measure proportioning the intercolumniation in some of the 
 orders. 
 
 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 resembling the pattern of a dia- 
 pered table-cloth, from which, iu fact, the name is supposed by some to have 
 been derived. 
 
 Diastyle. A spacious intercolumniation, to which three diameters are as- 
 signed. 
 
 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 dipterai 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 other 
 glutinous substance. All the cartoons of the ancients, previous to the year 3410, 
 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 
 antis. 
 
 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 Norman 
 period to the early part of the Decorated. It is in the form of a four leaved 
 flower, the centre of which projects, and probably was named from its resem- 
 blance 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 from the Italian custom of calling an archi- 
 episcopal 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 
 toge ther by morticesand tenons, and wrought, rebated, and beaded. 
 
 Doric Order, The oldest of the three orders of Grecian architecture. 
 
 Dormer Window. A 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 
 
GLOSSARY, 1593 
 
 of dormers, one above the other In Italian Gothic they are very rare in fact, 
 the former have an unusually steep roof, while ID 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. Jt 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, aud also for a 
 dormitory for the retainers of the nousehoJd, or those of visitors. 
 
 Double Vault. Formed by a duplicate wall , wine cellars are sometimes so 
 formed. 
 
 Dovetailing. "In carpentry and joinery, the method of fastening boards or 
 other timbers together, by Jetting one piece into another m the form of the 
 expanded tail of a dove. 
 
 Dowel. 1. A pin Jet into two pieces of wood or stone, where they are joined 
 together. 2. A piece of wood driven into a wan 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 forti- 
 fied 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 moulding which serves on a canopy for an opening, 
 and to throw off the rain. It is also called Weather Moulding. 
 
 Drop-scene. A curtain suspended by pulleys^ which descends or drops in 
 front of the stage in a theatre. 
 
 Drum. -The upright part of a cupola over a dome"; also, the solid part or vase 
 of the Corinthian and Composite capitals. 
 
 Dry-rot. A rapid decay of timber, by which its substance is converted into 
 a dry powder, which issues from minute cavities resembling the borings of 
 worms. 
 
 Dungeon. The prison in a castle keep, BO called because the Norman name 
 for the latter is donjon, and the dungeons, or prisons, are generally in its lowest 
 story. 
 
 Dwarf Wall. The walls enclosing courts above which are railings of iron ; 
 low walls, in general, receive this name. 
 
 Eaves. In slating and shingling, the margin or lower part of the slating 
 hanging over the wall, to throw the water off from the masonry or brickwork. 
 
 Echinus. A moulding of eccentric curve, gener- 
 ally cut (when it is carved) into the forms of eggs 
 and anchors alternating, whence the moulding is 
 called by the name of the more conspicuous, It is 
 the same as Ovolo. ECHINUS. 
 
1594 GLOSSARY. 
 
 Edifice. Is synonymous with the terms building, fabric, erection, but is 
 more strictly applicable to architecture 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 earli3st civilization and cultivation of the 
 arts was in Upper Egypt. The most remarkable and most ancient monuments 
 of the Egyptians, wiih the exception of the pyramids, are nearly all included in 
 Upper Egypt. The buildings of Egypt are characterized by solidity and mas- 
 siveness 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 generally 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 
 centres for the tracery are formed. These centres will all be found to fall on 
 points which, in some way or other, will be equimultiples of parts of the open- 
 ings. 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, applied to painting on 
 glass, porcelain, or tiles, where colors are fixed by heat ; hence, encaustic tiles, 
 brick, etc. 
 
 Engaged Columns. Are those attached to, or built into walls or piers, a por- 
 tion 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 con- 
 sists of three parts : the architrave, frieze, and cornice. 
 
 Entail. In Gothic architecture, delicate carving. 
 
 Entasis. The swelling of a column, etc. In mediaeval architecture, some 
 spires, particularlytho?e called "broach spires, 1 ' have a slight swelling in the 
 sides, but no more than to make them look straight ; for, from a particular 
 " deceptio visas," 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 
 
 
GLOSSARY. 1595 
 
 string-courses ; also, the ornamented plates from the centre of which door rings, 
 knockers, etc., are suspended, or which protect the wood of the key-hole from 
 the wear of the key. In mediaeval times these were often worked in a very 
 beautiful manner. 
 
 Etching. A mode of engraving on glass or metal (generally copper) by means 
 of lines, eaten in or corroded by means of some strong acid, 
 
 Eustyle. A species of intercolumniation to which a proportion of two diam- 
 eters and a quarter is assigned. This term, together with the others of similar 
 import pycnostyle, systyle, diastyle, and araeostyle referring to the distances 
 of columns from one another in composition, is from Vitruvius, who assigns to 
 each the space it is to express. It will be seen, however, by reference to them 
 individually, that the words themselves, though perhaps sufficiently applicable, 
 convey no idea of an exactly denned space, and, by reference to the columnar 
 structures of the ancients, that no attention was paid by them to such limita- 
 tions. It follows, then, that the proportions assigned to each are purely conven- 
 tional, and may or may not be attended to without vitiating the power of apply- 
 ing the terms. Eustyle means the best or most beautiful arrangement ; but, as 
 the effect of a columnar composition depends on many things besides the diam- 
 eter of the columns, the same proportioned intercolumniation would look well 
 or ill according to those other circumstances, so 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 
 stones ; 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 centre. 
 
 Facade, or Face. The whole exterior side of a building that can be seen at 
 one view ; strictly speaking, the principal front. 
 
 Face Mould. The pattern for marking the plank or board out of which orna- 
 mental hand-railings for stairs and other worSs are cut. 
 
 Fan Tracery. The very complicated mode of roofing used in the Perpendicu- 
 lar 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 
 buildings, but of small projection. The architraves in some of the orders are 
 composed of three bands, or fasciae ; the Tuscan and the Doric ought to have only 
 one. Ornamental projections from the walls of brick buildings over any of the 
 windows, except the uppermost, are called Fasciae. 
 
 Fenestral. A frame, or " chassis, 11 on which oiled paper or thin cloth was 
 strained to keep out wind and rain when the windows were not glazed. 
 
 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 mouldings, to sepa- 
 rate and combine them, and also to give breadth FESTOON. 
 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 fillet is a small, flat, projecting square, chiefly used to separate hollows 
 and rounds, and often found in the outer parts of shafts and bout/els. In this 
 situation the centre fillet has been termed a keel, and the two side ones, wings ; 
 but, apparently, this is not an ancient usage. 
 
1596 GLOSSABY. 
 
 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 FINIALS 
 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. (See Chapter XXIX.) 
 
 Flags. Flat stones, from 1 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 tbe 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. * The mouldings seem to be as much inferior to those of the preceding 
 period as tbe Perpendicular mouldings 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 or 
 bottom of iron columns, to fasten them to those above or below ; the top and 
 bottom of I-beama and channels are called the flange. 
 
 Flashings. Pieces of lead, tin, or copper, let into the joints of a wall BO 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 particu- 
 larly used for the small, slender erection rising from the intersection of the nave 
 and transepts in cathedrals and large churches, and carrying the sanctus bell. 
 
 Flight. A run of steps or stairs from one landing to another. 
 
 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. 
 
 Fleur-de-lis. The royal insignia of France, much used in decoration. 
 
 Flue. The space or passage in a chimney through which the smoke ascends. 
 Each passage is called a flue, while all together make the chimney. 
 
 Flush. The continued surface, in the same plane, of two contiguous masses. 
 
 Flute. A concave channel. Columns whose shafts are channelled are said 
 to be fluted, and the flutes are collectively called Flirtings. 
 
 Flying Buttress. An arched buttress used when extra strength was required 
 for the upper part of the wall of the nave, ei,c., 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 
 
GLOSSARY. 1597 
 
 to be that Hi wiiichConstantine is said to have been baptized ; mis is a porphyry 
 labrum from a Koman 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 have frequently 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 generally 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 joint firm and im- 
 movable. 
 
 Frame. The name given to the wood-work of windows, doors, etc. ; and in 
 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 mouldings, tracery, and other work 
 required to be executed with the chisel. The oolitic and sandstones are thoee 
 generally included by this term. 
 
 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 Kaffaelle 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- 
 richments either of foliage or figures which may be 
 relevant to the object of the sculpture. The frieze is also called the Zoophorus. 
 
 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. 
 
 Furr ings. Flat pieces of timber used to bring an irregular framing to an even 
 surface. 
 
1598 GLOSSARY. 
 
 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 panelled or perforated, sometimes very richly. 
 The gables in ecclesiastical buildings are mostly terminated with across; 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 moulded 
 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 panelling and 
 crockets. They are sometimes finished with small crosses, but oftener with 
 finials. 
 
 Gain. A bevelled 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 
 loft. In 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 GARGOYLE 
 porter, and guard-rooms for the soldiers ; and, gener- 
 ally, 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. 1. To mix plaster of Paris with common plaster to make it set quick, 
 called gauged mortar. 2. A tool used by carpenters, to strike a line parallel to the 
 edge of a board. 
 
GLOSSAKY. 1599 
 
 Girder. A large timber or iron beam, either single or built up, used to sap- 
 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^valls strongly buttressed. 
 In England the term was applied not only to the barns, but to the whole of the 
 buildings which formed the detached farms belonging to the monasteries; in 
 most cases there was a chapel either included among these or standing apart as a 
 separate edifice. 
 
 Grillage. A framework of beams laid longitudinally and crossed by similar 
 beams notched upon them, used to sustain walls to prevent irregular setting. 
 
 Grille. The iron-work forming the enclosure screen to a chapel, or the pro- 
 tecting railing to a tomb or shrine; more commonly found in France than in 
 England. They are of wrought iron, ornamented by the swage and punch, and 
 put together either by rivets or clips. In nudern times grilles are used exten- 
 sively for protecting the lower windows in city houses, also the glass opening in 
 outside doors. 
 
 Groin. By some described as the line of intersection of two vaults where they 
 cross each other, which others call the groin point ; by others the curved section 
 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 vau!t into bays or travees. 
 
 Groin Ceiling. A ceiling to a building com- 
 posed of oak ribs, the spandrels of which are filled 
 in with narrow, thin slips of wood. There are 
 several in England ; one at the Early English 
 church at Warmington, 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 
 
 stone ribs only are supported by timber ribs dur- GAINED VAULTING. 
 
 ing the progress of the work, any light stuff being used while filling in the span- 
 drels. 
 
 Groin Point. The name given by workmen to the arris or line of intersec- 
 tion 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 ribs, 
 
1600 GLOSSARY. 
 
 except occasionally a sort of wide band from wall to wall, to strengthen the con- 
 struction. In later Norman times ribs were added on the line of intersection of 
 the spandrels, crossing each other, and having a boss as a key common to both ; 
 these ribs the French authors call nerfs eti 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 possible material placed upon them, the 
 haunches only being loaded sufficiently to counterbalance the pressure from the 
 firown. Shortly after, half-ribs against the walls (formerets) were introduced to 
 carry the spandrels without cutting into the walling, and to add to the appearance. 
 The 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 horizontal, but rose from the level of the top of the formeret-rib 
 to the boss and fell again ; but this 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 required more 
 support . To give this, another set of ribs was introduced, passing from the spring- 
 ers 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 hexpartite, 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 unu- 
 sual width. The filling of the spandrels in this style is very peculiar, and, where 
 the different 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- 
 pendicular and parallel for some height, and the spandrels themselves are very 
 hollow. As styles progressed, and the desire for greater richness increased, 
 another series of ribs, called liernes, was introduced ; these passed crossways 
 from the ogives to the tiercerons, and thence to the doubleaux, dividing the 
 spandrels nearly horizontally. These various systems increased in the Perpen- 
 dicular period, so that the vaults were quite 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 
 Tibs are no part of the real construction, but are merely carved upon the vous- 
 eofrs, which form the actual vaulting. Fan Tracery is so called because the ribs 
 radiate from the springers, and spread out like the sticks of a fan. These later 
 methods are not strictly groins, for the pendentives are not square on plan, but 
 circular, and there is, therefore, no arris intersection or groin point. 
 
 Groins, Welsh, or TJnderpitch. 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 underpitch 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 moulding, stile, or rail, 
 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. 
 
GLOSSARY. 1601 
 
 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. Pieces of wood embedded in the plastering of walls to which 
 skirting and other joiner's work is attached. They are 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 are iraid 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, u,ed most frequently to enrich 
 the torus. 
 
 Guttae. The small cylindrical drops used to en- 
 rich the mutules and regulae of the Doric entabla- ' GUILLOCHE. 
 ture are so called. 
 
 Gutter. The channel for carrying off rain-water, m . i 
 
 The mediaeval 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- 
 nels in English, and cheneaux in French. 
 
 Gymnasium. A building classed in the first rank by the Greeks ; it was in 
 them they instructed the youth in all the arts of peace and war ; a building for 
 athletic exercises. 
 
 Hall. 1. 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' apartments ; 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. 2. A room or passage-way at the entrance 
 of a house, or suite of chambers. 3. A place of public 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 
 
1602 
 
 GLOSSARY. 
 
 walls of a chamber. Different materials were employed for this purpose, som* 
 of them exceedingly costly and beautifully worked in figures, gold and silk. 
 
 Hatching. Drawing parallel lines close together for the purpose of iudicat- 
 ing a section of anything. The lines are generally drawn at an angle of 45 C 
 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 afi 
 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 in- 
 trades. 
 
 Helix. A small volute or twist like a stalk, representing the twisted tops of 
 the acanthus, placed 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 in front of buildings. 
 
 Herring-bone Work. Bricks, tile, or other materials ar- 
 ranged 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 > 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-mould. A word used to signify the drip-stone for 
 label over a window or door opening, whether inside or HERMES. 
 
 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 calling 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 
 tnere 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 modem 
 days, the accommodation for the chaplain, medicine, nurses, stores, etc., being 
 Piuch the same in all ages, eacept that ia some of the earlier, instead of the sick 
 
GLOSSARY. 1G03 
 
 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 
 etatue. 
 
 Hypeethros. 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 mouldings of piers 
 or pilasters, from the top of which spring the archivoits or mouldings which go 
 round the arch. 
 
 In Antis. When there are two columns between the antae of the lateral walls 
 and the cella. 
 
 Incise. To cut in ; to carve : to engrave. 
 
 Indented. Toothed together. 
 
 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 insu- 
 lated. 
 
 Intaglio. A sculpture or carvingin which the figures are sunk below the gen- 
 era! surface, such as a seal the impression of which in wax is in bas-relief : 
 opposed to Cameo. 
 
 Inter COlumniation. Tfce 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, tne inner or concave curve of the arch stones. 
 
 Inverted Arches. Those whose key- stone or brick is the lowest in the 
 trch. 
 
 Ionic Order. One of the orders of Classical architecture. 
 
 Iron Work. In mediaeval architecture, as an ornament, is chiefly confined to 
 the hinges, etc., 01 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 ia 
 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 lat- 
 terly in fleurs-de-lis. Escutcheon and rins: handles, and the other furniture, par- 
 took 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 
 sometimes 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 
 g.v. 
 
1604 GLOSSARY. 
 
 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 Escon- 
 sons. 
 
 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- 
 dolf, 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 
 buildings, and passages and small chambers in the thickness of the walls. The 
 keep was intended for the last refuge, in case the outworks were scaled and the 
 other buildings stormed. There is generally a well in a mediaeval keep, ingen- 
 iously concealed in 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 centre 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 simple stone projecting beyond the rest ; in the Ionic it is adorned with 
 mouldings in 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 
 relieve 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-moulding^ 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 foliage. 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. 
 
GLOSSARY. 1605 
 
 lacunar, A panelled or coffered ceiling or soffit. The panels or cassoons of 
 a ceiling arc 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 jj 1 |lfflpf;^sl^' ) ^fi^ 
 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. 
 
 anj r 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 pmali 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. 2. A reticulated window, made of laths or slips of iron, 
 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 
 Viollet-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 Lodgement. 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 
 scaffolding 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 in England. 
 
 Light. A division or space in a sash for a single pane of glass ; also a pane 
 of glass. 
 
 Linen Scroll. An ornament formerly used for filling panels, and so called 
 from its resemblance to tue convolutions of a folded napkin. 
 
 Lining, Covering for the interior, as casing is covering 
 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. LINEN SCROLL. 
 
 Lip Mould. A moulding of the Perpendicular period like a hanging lip. 
 
 List, or ListeL A little square moulding, to crown a larger, also termed a fillet. 
 
1606 
 
 GLOSSARY. 
 
 Lithograph. A print from a drawing on stone. 
 
 Lobby, An open space surrounding a range of chambers, or seats in a theatre; 
 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. Jt reigned between the eighth and twelfth centuries, 
 during the time that the Saxon and Norman styles were in vogue in Eng- 
 land, and corresponded with them in its development into the Continental 
 Gothic. 
 
 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 Moulding. A kind of moulding used in Norman 
 architecture, of many different 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. 
 
 LOZENGE MOULDING. IiOUVER WINDOW. 
 
 Machicolation. A parapet 
 
 or gallery projecting from the upper part of the wall of a house or fortification, 
 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 Hoof. Curb roof, invented by Frai^ois 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 like. 
 
 Mausoleum. A magnificent tomb or sumptuous sepul- 
 chral monument. 
 
 Medallion. Any circular tablet on which are em- 
 bossed figures or busts. 
 
 Mediaeval Architecture, The architecture of Eng- MACHICOLATION. 
 
GLOSSARY. 
 
 1607 
 
 land, France, Germany, etc., during the Middle Ages, including the Norman and 
 Jiarly Gothic styles. It comprises also the Komanesque, Byzantine and Saracenic, 
 Bombard, and other styles. 
 
 Members. The different parts of a building, the different parts of an entab- 
 lature, the different mouldings of a cornice, etc. 
 
 Merlon. That part of a parapet which lies between two embrasures. 
 
 Metope. The square recess between the triglyphs 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-rilievo. Or mean relief, in comparison 
 with alto-rilievo, or high relief. 
 
 Minaret. Turkish : a circular turret rising by dif- 
 ferent stages or divisions, each of which has a balcony. 
 
 Minster. Probably a corruption of monasterium 
 the large church attached to any ecclesiastical fraternity. 
 If the latter be presided over by a bishop, it is generally METOPE. 
 
 called a Cathedral ; if by an abbot, an Abbey ; if by a 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 different 
 persons. 
 
 Mitre. A moulding returned upon itself at right angles is said to 
 mitre. 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 paid to mitre. 
 
 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 
 various 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 inter- 
 columniation of one triglyph. 
 
 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 
 etone, marble, or enamel of various colors. In Roman houses the floors are often 
 
 a 
 
 MINARET. 
 
 MODILLION. 
 
1608 
 
 GLOSSARY. 
 
 entirely of mosaic, the pieces being cubical. The best examples of mosaic work 
 are found in St. Mark's, at Venice. 
 
 Mosque. A Mahometan temple, or place of worship. 
 
 Moulding. When any work is wrought into long regular channels or projec- 
 tions, forming curves or rounds, hollows, etc., it is 
 said to be moulded, and each separate member is 
 called a moulding. In mediaeval architecture the 
 principal mouldings are those of the arches, doors, 
 windows, piers, etc. In the Early English style, the 
 mouldings, for some time, formed groups set back 
 in squares, and frequently very deeply undercut. 
 The scroll moulding is also common. Small fillets 
 now become very frequent in the keel moulding, MOULDINGS. 
 
 from its resemblance in section to the bottom of a a -> astragal ; b, ogee ; 
 ship ; sometimes, also, it has a peculiar hollow on to ; <?, scotia, or case- 
 each side, like two wings. Later in the Decorated ment ; /, apophyges ; 
 style the mouldings are more varied in design, ffj ?.}. ^orus^T 
 though hollows and rounds still prevail. The under- ree ding ; ,/,'band. ' 
 cutting is not so deep, fillets abound, ogees are more 
 
 frequent, and the wave mould, 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 mouldings in the later styles in some degree resem- 
 ble those of the Decorated, flattened and extended ; they run more into one 
 another, having fewer fillets, and bt-ing, as it were, less grouped. One of the 
 principal features of the change is the substitution of one, or perhaps two (sel- 
 dom more), very large hollows in the set of mouldings. These hollows are 
 neither circular nor elliptical, but obovate, like an egg cut across, so that one 
 half is larger than the other. The brace mould also has a small bead, where the 
 two ogees meet. Another sort of moulding, which has been called a lip mould, 
 is common in parapets, bases, and weatherings. 
 
 Mouldings, Ornamented. The Saxon and early Norman mouldings do not 
 eeem 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 mouldings ; and they are used in such 
 profusion as has been attempted in no other style. The decorations on Early 
 English mouldings 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 mouldings, the dark 
 shadow in the hollow contrasting in a very beautiful way with the light in these 
 mouldings. 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, are 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 rf windows ace often, found in Continental architecture. In the Perpeu- 
 
GLOSSARY. 1609 
 
 dicnlar period the mouldings are ornamented very frequently 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 stiff leaves, 
 generally called the Tudor leaf. On the Continent mouldings partook much of 
 the same character. 
 
 MuJlion, Munion. The perpendicular pieces of stone, sometimes like col- 
 umns, sometimes like slender piers, which divide the bays or lights of windows 
 or screen-work from each other. In all styles, in less important work, the mull- 
 ions are often simply plain chamfered, and more commonly have a very flat hol- 
 low on each side. Jn 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 guttae, or drops, depend. Mutule is equivalent to modillion, 
 but the latter term 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 
 basilica, 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, is the surface of a stone as it lies in the 
 quarry If not laid in walls in their natural bed the laminae separate. 
 
 fl ay e . -The central, part between the arches of a church, which formerly was 
 separated from a chancel or choir by a screen. It is so called from 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 mouldings, which 
 eeparates 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 rau upon. 
 
 Niche. A recess sunk in a wail generally for the reception of a statue. 
 Niches sometimes terminate by a simple label but more commonly by a can- 
 opy and with a bracket or corbel for the figure, in which eatse 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 smal* stones laid like brickwork. 
 
 Nosings. -The rounded and projecting edges of the treads of a stair, ortho 
 edge of a landing. 
 
1610 GLOSSARY. 
 
 Obelisk. Lofty pillars of stone, of a rectangular form, diminishing toward the 
 top, and generally ornamented with inscriptions and hieroglyphics among the 
 ancient Egyptians. 
 
 Observatory. A building erected on an derated spot of ground for making 
 astronomical observations. 
 
 Octostyle. A portico of eight columns in front. 
 
 Offsets. When the face of a wall is not one continued surface, but sets in by 
 horizontal jogs, as the wall grows higher and thinner, the jogs are called off- 
 sets. 
 
 Ogee. The name applied to a moulding, partly a hollow and partly a round, 
 and derived no doubt from its resemblance to an O placed over a G. It is rarely 
 found in Norman work, and is not very common in Early English. It is of fre- 
 quent use in Decorated work, where it becomes sometimes double, and is called a 
 wave moulding ; and later still, two waves are connected with a small bead, 
 which is then called a brace moulding. In ancient MSS. it is called a Ressaunt. 
 
 Orchestra. In ancient theatres, where the chorus used to dance ; in modern 
 theatres, 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 dwelling of a king, prince, or bishop. 
 
 Pale. A fence picket, sharpened at the upper end. 
 
 Pane. Probably a diminutive of panueau, 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 moulded into any desired shape. Much used for architect- 
 ural 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 panelled. 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 panelled, but oftener 
 
GLOSSARY. 1611 
 
 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. Panelled parapets are those ornamented by a series of panels, 
 either oblong or square, and more or less enriched, but are not perforated. These 
 are common in the Decorated and Perpendicular periods. 
 
 Pargeting. A species of plastering decorated by impressing patterns on it 
 when wet. These seem generally to have been made by sticking a number of 
 pins in aboard in certain lines or curves, and then pressing on the wet plaster in 
 various directions, so as to form geometrical figures. Sometimes these devices 
 are in relief, and in the time of Elizabeth represent figures, birds, foliages, etc. 
 2. 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. 2. 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 ad- 
 joining 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 ia 
 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 seg- 
 ment ; 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 moulded 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 ceilings, 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 
 
1612 GLOSSARY. 
 
 or a dome. In mediaeval architecture these arches, when under a spire in the 
 interior of a tower, are called Squinches. 
 
 Pendentive Bracketing, or Cove Bracketing. Springing from the rec- 
 tangular walls of an apartment upward to the ceiling, and forming the horizon- 
 tal part of the ceiling into 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 24f cu. ft. and 16 
 cu. ft., according to locality and custom. 
 
 Periptery. An edifice or temple surrounded by a peristyle. 
 
 Peristyle. A range of columns encircling an edifice, such as that which sur- 
 rounds 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 aa ob- 
 ject upon a plane surface as shall present precisely the same appearance Uat 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 nse 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 panelled with bold cappings ; in others the panels are orna> 
 mented with tracery or with the linen 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 tne same width at top as at bottom, but the 
 Romans gave them the same capitals as the columns, and made them of 
 diminished 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. 134.) 
 
 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, some- 
 times with other squares breaking out of them (this is more common in 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 English period 
 the pillars become loftier and lighter, and in most important buildings are a series 
 
GLOSSAKY. 1613 
 
 of clustered columns, frequently of marble, placed side by side, sometimes 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 other mouldings, 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 moulding. 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 afterward 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 slip 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 English 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, like 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 
 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 span by the 
 height ; 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. 
 
 Pitchmg-piece. A horizontal timber, with one of its ends wedged into the 
 wall at the top of a flight of stairs, to support the upper end of thorough 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, ona norizontal 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 in- 
 correctly used in the sense of Design. 
 
 Planceer. Is sometimes used in the same sense as soffit, but is more correctly 
 applied to the soffit of the corona in a cornice. 
 
 Plastering, A mixture of lime, hair, and sadd, to cover lath-work between 
 
1614 GLOSSARY. 
 
 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 cleanliness, 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 pcmpee : 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 projecting 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 PO PPY HEAD. 
 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 iron, 
 and sometimes entirely made of metal, hung so as to slide up and down in grooves 
 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 with columns. A"portico is distinguished as prostyle or in antis accord- 
 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 bressummers or 
 crossbeams under the walls. 
 
 Posticum, A portico behind a temple. 
 
 Presbytery, A wordapplied to various parts of large churches in a very am- 
 
GLOSSARY. 1615 
 
 biguous 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 apart, or the parts composing an order, 
 as of a base, cornice, etc. ; also, the perpendicular section. It is in the just pro- 
 portion of their profiles that the chief beauties of the different orders of archi- 
 tecture depend. The ancients were most careful of the profiles of their mould- 
 ings. 
 
 Proscenium. The front part of the stage of ancient theatres, on which the 
 ictors 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 
 eolid. 
 
 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 panelling, 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 then* 
 from sinking. 
 
 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 coat. 
 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. 
 
1616 GLOSSARY. 
 
 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. 
 
 Quatrefoil. Any small panel or perforation in the form of a 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 Mouldings. The convex part of Grecian mouldings when they recede 
 at the top, forming a reentrant angle, with the surface which covers the mould- 
 ings. 
 
 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. 
 
 Bail. A piece of timber or metal extending from one post to another, as in 
 fences, balustrades, staircases, etc. In framing and panelling, the horizontal 
 pieces are called rails, and the perpendicular, stiles. 
 
 Baking. Mouldings whose arrises are inclined to the horizon. 
 
 Ramp. A 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 
 inclined plane. 
 
 Random Work. A term used by stone-masons for stones fitted together at 
 rindom without any attempt at laying them in courses. Random Coursed Work 
 js a like term applied to work coursed in horizontal beds, but the stones are of 
 any height, and fitted to one another. 
 
 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 waH, as a niche, etc. 
 
 Refectory. The hall of a monastery, convent, etc., w r here the religious took 
 their chief meals together. It much resembled the great halls of mansions, cas- 
 tles, 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 moulding, 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 architect- 
 ure which sprang into existence in Italy as early as the beginning of the fifteenth 
 
GLOSSARY. 1617 
 
 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 
 known 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 same time by 
 John of Padua, architect to Henry VIII. This style in England is generally 
 known under the name of Elizabethan. 
 
 Rendering. In drawing, finishing a perspective drawing in ink or color, to 
 bring out the spirit and effect of the design. 2. The first coat of plaster on brick 
 or stone work. 
 
 Reredos, Dorsal, or Dossel. The screen or oftier ornamental work at the back 
 of an altar. In some large English 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 panellings behind 
 the alters ; 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 cibo- 
 rium, 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 moulding, projection, etc., in an opposite 
 direction. 
 
 Return Head. One that appears both on the face arid 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 moulding 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 with a smaller roll or a fillet between them, 
 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 mouldings 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 mouldings 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 roof, extending from top to 
 top of the several pairs of rafters of the trusses, for supporting the heads of the 
 jack rafters. 
 
1618 GLOSS ART. 
 
 Rilievo, or Belief. The projection of an architectural ornament. , 
 
 Rise, The distance through which anything rises, as the rise of a stair, Of 
 inclined 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 terra Romanesque embraces all tho^e styles of 
 architecture which prevailed between the destruction of the Roman Empire and 
 the beginning of Gothic architecture. In it are included the Early Roman Chris- 
 tian architecture, Byzantine, Mahometan, and the later Romanesque architect- 
 ure 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 architecture is known under the name of the Saxon, 
 Norman, and Lombard styles, according to the different political periods. 
 
 Rood. A name applied 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 saints 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 arrangement 
 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 transverse 
 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 panelling beneath, about 3 feet to 8 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, cre*tiii, r , 
 etc., and often painted in brilliant colors and gilded. These not only enclose the 
 chancels, but also chapels, chantries, and sometfmes even tombs. In English 
 mansions, and some private houses, the great haljs 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. 
 
 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 5 
 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. 2. 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 
 roughest irregularities are knocked off, it is called scabbled rubble, and wheii the 
 
GLOSSARY. 1619 
 
 stones in each conrse 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 ilutings, and serves to strengthen the edges. Sometimes, instead of a convex 
 shape, the flu tings are filled with a flat surface ; sometimes they are ornament- 
 ally carved, and sometimes on pilasters, etc. Ruderitures 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 rustle 
 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 bevelled to an 
 angle of one hundred and thirty-five degrees with the face so that two stones 
 coming together on the wall, the bevelling will form an internal right angle. 
 
 Sacristy. A small chamber attached to churches, where the chalices, vest- 
 ments, books, etc., were kept by the oflftcrr 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 
 eacrarium. 
 
 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 ihe 
 windows are wide, the lead lights are further strengthened by upright bars 
 passing through eyes forged on the saddle bars, and called stanchions. When 
 saddle bars pass right through the mullions in one piece, and are secured to the 
 jambs, they 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, os 
 for state purposes, or for the reception 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. 2. 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, ' r 
 etc., are read. This differs but little from the common bell cot, except that it in 
 generally on the top of the arch dividing the nave from the chancel. Sometimes, 
 
1620 GLOSSARY. 
 
 however, the bell seemg 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 email slender spire, called Jieche in 
 France, and guglio in Italy. 
 
 Saracenic 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 etone, and intended to contain the 
 body. 
 
 Sash. The framework which holds the glass in a window. 
 
 Scagliola. An imitation of colored marbles in plaster work, made by a com- 
 bination of gypsum, glue, isinglass, and coloring matter, and finished with a 
 high polish, invented between 1600 and 1649. 
 
 Scabble. To dress off the rougher projections of stones for rubble masonry 
 with a stone axe or scabbling hammer. 
 
 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 moulding, most commonly used in bases, which projects a 
 deep shadow on itself, and is thereby a most effective moulding under the eye, 
 as in a base. It is like a reversed ovolo t or, rather, what the mould 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 intervals 
 between them. 
 
 Screen. Any construction subdividing one part of a building from another, as 
 a choir, chantry, chapel, etc. The earliest screens are the low marble podia 
 shutting off the chorus cantantium in the Roman basilicas, and the perforated 
 cancelli enclosing the bema, altar, and seats of the bishops and presbyters. The 
 chief screens in a church are those which enclose the choir or the place where 
 the breviary services are recited. In Continental Europe this is done iiot only by 
 doors and screen work, but also, when these are of open work, by curtains, the 
 laity having no part in these services. In England screens were of two kinds: 
 one, of open wood-work, generally calied rood-screens or jubes, and which the 
 French call grilles, clotures du chceur ; 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 e^ ^tures, the heights of 
 the stories, thicknesses of the floors, etc. It is one of the ev^es 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 can- 
 opies, pinnacles, and other enrichments more or less elaborate. The piscina and 
 
GLOSSARY. 1621 
 
 ambry sometimes are attached to them. In Continental Europe the sedilia are 
 often movable Beat s ; 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 thin- 
 ner. 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 corbel 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 Hoof, 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 like 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 in 
 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 superstruct- 
 ure 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. 
 
 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 draw- 
 ings. 
 
 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 
 oblique 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 mouldings cont'nre down the pier. The 
 lowest stone of the gable is sometimes called ?i enrivper. 
 
 Squinches. Small arches or corbelled set off s running diagonally and, as it 
 
1622 GLOSSARY. 
 
 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 centre 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 fides 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 ttanfon, a wooden post, applied 
 to the upright iron bars which pass through the eyes of the saddle bars or hori- 
 zontal irons to steady the lead lights. The French call the latter traverses, 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. Tue upright piece in framing or panelling. 
 
 Stilted. Anything raised above its usual level. An arch is stilted when its 
 centre is raised above the line from which the arch appears to spring. 
 
 Stoop. A seat before the door ; often a porch with a balustrade and seats on 
 the sides. 
 
 Stoup. A basin for holy water at the entrance of Roman Catholic churches, 
 into which all who enter dip their fingers and cross themselves. 
 
 Straight Arch. A form of arch in which the intrados is straight, but with 
 Us 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-sills, or covers 
 a eet-off in the wall, it becomes a blocking-course. Also, horizontal mouldings 
 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 passing 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 mouldings, general out- 
 
GLOSSABT. 
 
 1625 
 
 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 ar.y nation at different times. 
 
 Stylobate. A basement to columns. Stylobate is synonymous with pedestal, 
 but is applied to a continued and unbroken substructure or basement to columns, 
 while the latter term is confined to insulated 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 mouldings on the top of the base of a pedes- 
 tal, podium, etc.; a moulding 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 also often used to denote the receptacle for relics, 
 which was often made in the form of a small h ntse 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 
 of 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. 
 
 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 o< 
 religious worship. 
 
 Templet, or Template. A mould used by masons for cutting or setting 
 work. 2. 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 parallelepiped, 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 quality. 
 Much used for bas-reliefs for adorning the friezes 
 of temples. In modern times employed for archi- 
 tectural ornaments, statues, vases, etc. 
 
 Tessellated Pavements. Those formed of 
 tesserae, or, as some write it, tessellce, or small 
 cubes from half an inch to an inch square, like 
 dice, 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 iwe, 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 desig- 
 
1624 GLOSSAKY. 
 
 nated the tholobate. A tholobate of a different description, and one to which 
 no other name can well be applied, is the circular substructure 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. 
 
 fie. 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. 2. Also, flat pieces of burned clay, either plain or ornamented, glazed 
 or unglazed, used for floors, wainscoting, and about fireplaces, etc. 3. 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 mouldings 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 moulding whose form is convex, 
 and generally nearly approaches a semicircle. It is 
 
 most frequently used in bases, and is generally the /f~T ~ "N 
 
 lowest moulding in a base. VJ ? J 
 
 Tower. An elevated building originally designed TORUS. 
 
 for purposes of defence. Those buildings are of the 
 
 remotest antiquity, and are, indeed, mentioned in the earliest Scriptures. In 
 mediaeval times they were generally attached to churches, to cemeteries, to cas- 
 tles, 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 intended to be de- 
 fended by archers. The upper windows, like those of the preceding 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 pro- 
 portions. 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 round. 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 VendSme, 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 colonnades. 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 
 
GLOSSARY. 1625 
 
 the fourteenth century. Like almost everything connected with mediaeval aichi- 
 tecture, this elegant and sometimes fairy-like decoration seems to have sprung 
 from the smallest beginnings. The circular-headed window of the Normans 
 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 
 assembled 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 mouldings 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 trans- 
 versely >s 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. 
 
 Trefoil. A cusping the outline of which is derived from a three-leaved flower 
 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 tres and 
 fores three doors, or openings that being a frequent number of arches in each 
 bay. 
 
 Triglyph. The vertically channelled 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 thicknc w of the 
 floor, between two trimmers. The bottom of the arch starting from the chimney 
 and the 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 Henry 
 VIIL 
 
 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 edifice in the tympana of temples, as at the 
 Parthenon and ^ 
 
1626 
 
 GLOSSARY. 
 
 Under-crof !. 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 early times it seems to have been 
 of various forms, as dragons, etc. ; but in the Tudor period the favorite design 
 was a beast or bird sitting on a slender pedestal, and carrying an upright rod. 
 on which a thin plate of metal is hung like a flag, ornamented in various 
 ways. 
 
 Vault. An arched ceiling or roof. A vault is, indeed, a laterally conjoined 
 series of arches. The arch of a bridge is, strictly speaking, a vault. Intersect- 
 ing vaults are said to be groined. See Groined Vaulting for fuller description of 
 vaults. 
 
 Verge. The edge of the tiling, slate or shingles, projecting over the gable of a 
 roof, that on the horizontal portion being called eaves. 
 
 Verge Board. Often corrupted into Barge Board ; the board under the verge 
 of gables, sometimes moulded, and often very richly carved, perforated, and 
 cusped, 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 catiliculus are used indifferently for 
 the angular horns of the Corinthian capital. 
 
 Voussoir. One of the wedge-like 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. 
 
 VERMICULATED. 
 
OLOSSABY. 1627 
 
 Wicket, A small door opening in a larger. They are common in mediaeval 
 doors, and were intended to admit single persons, and guard against sudden 
 surprises. 
 
 Wind. A tnrn, a bend. A wall is out of wind when it is a perfectly flat 
 surface. 
 
 "Wing". A side building less than the main building. 
 
 Witii.es. The partition between two chimney flues in the same stacfc, 
 
ARCHITECTURAL TERMS AS DEFINED Iff 
 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 
 mentioned in each case. The fact that other codes are not mentioned is not 
 necessarily a proof that the term is not also elsewhere in use as defined.} 
 
 Adjoining 1 Owner. The owner of the premises adjoining those on which 
 work is doing or to be done. [District of Columbia.'] 
 
 Alteration. Any change or addition except necessary repairs in, to, or upon 
 any building affecting an external, party, or partition wall, chimney, floor, or 
 stairway, and " to alter " means to make each change or addition. [Boston and 
 Denver.] 
 
 Appendages. Dormer-windows, cornices, mouldings, bay-windows, towers, 
 spires, ventilators, etc. [Chicago, Minneapolis.} 
 
 Areas. Sub-surface excavations adjacent to the building-line for lighting or 
 ventilation of cellars or basements. [District of Columbia.} 
 
 Attic Story. A story situated either in whole or in part in the roof. [Denver 
 and District of Columbia.} 
 
 Base." The base of a brick wall" means the course immediately above the 
 foundation wall. [Cincinnati and Cleveland.} 
 
 Basement- Story. One whose floor is 12" or more below the sidewalk, and 
 whose height does not exceed 12' in the clear ; all such stories that exceed 
 12' high shall be considered as first stories. [Chicago, 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 
 not exceed 11' in the clear ; all such stories that exceed 11' high shall be con- 
 sidered as first stories. [Minneapolis.} 
 
 A story suitable for habitation, partially below the level of the adjoining street 
 or ground. J [District of Columbia and Denver] 
 
 (See Cellar.) 
 
 Bay- window. A first-floor projection for a window other than a tower-pro- 
 jection or show-window. [District of Columbia.] 
 
 Any projection for a window other than a show-window. [Denver.] 
 
 i And below the first floor of joists. [District of Columbia.} 
 
 1628 
 
LEGAL DEFINITIONS OF ARCHITECTURAL TERMS. 1629 
 
 Bearing Walls. Those on which beams, trusses, or girders rest. [New York 
 and San Francisco.] 
 
 Brick Building. A building the walls of which are built of brick, stone, 
 iron, or other substantial and incombustible materials. [Boston, Denver, and 
 Kansas City.] 
 
 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, ihus including, among others, hotels, theatres, 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 5 
 adjoining. 2 [Boston, Denver, and Kansas City] 
 
 Portion of building below first floor of joists, if partially or entirely below 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 send 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 Bame 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 the 
 sidewalk or adjoining ground, the other stories to be numbered in regular suc- 
 cession, counting upward. [Denver and District of Columbia.] 
 
 Footing Course. A projecting course or courses under base of foundation 
 wall. [Cincinnati and Cleveland.] 
 
 Foundation. That portion of wall below level of street euro, 3 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. 
 [District of Columbia and Denver] 
 
 Foundation, Basement, or Cellar Walls. That part of walls of building that 
 are below the floor or joists, which are on or next above the grade line . \ Detroit.} 
 
 i Ground. [Providence] 
 
 * And not suitable for habitation. [Denver] 
 
 * " And serve as supports for piers, columns, girders, beams, or other walla." 
 
 York.] 
 
1G30 LEGAL 1>EFIK1TIONS OP ARC 
 
 Portion of the wall below the level of street curb, in fronf of the cor.tr -.1! lino ot 
 building. [San Francisco.] 
 
 Incombustible mantling partition. One plastered on bo: 
 lath or wire cloth, and filled in with brickwork 8" high from iloor, jnoviiled tl o 
 builduig is not over 8CK high. [Chicago.] 
 
 Incombustible Hoofing. Covered with not less than three (" 
 roofing-felt, and good coat of tar and gravel, or with tin, corrupted- ii on, or otlu r 
 fire-resisting material with standing-seam or lap-joint. [ZV /; <v . ] 
 
 Lengths. Walls are deemed to be divided into distinct knyths by return 
 walls, and the length of every wall is measured from the centre of one return 
 wall to the centre 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 be 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. [Minneajwlis.] 
 
 Lodging-house. A building in which persons are temporarily accommodated 
 with sleeping > apartments, and includes hotels. [Boston, and Kama* City.] 
 
 Any building or portion thereof in which persons are lodged for hire for leas 
 than a week at one time. [District of Colwnbia and Proridenc*] 
 
 Any building or portion thereof in which persons are lodged for hire tempo- 
 rarily, and includes hotels. [Denver.] 
 
 Mansard Boof. One formed with an upper and under set of rafters, the 
 upper set more inclined to the horizon than the lower set. [Denver Of id XHstrict 
 Of Columbia.] 
 
 Oriel Window. A projection for a window above the first floor. [District 
 tf 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 Proridentx.] 
 
 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 
 or more buildings.* [Boston* Cincinnati, Cleveland* Denver, Kansas 
 City^ and Provident*.} 
 
 A wall built upon dividing line between, adjoining premises for their common 
 use. [Districtqf Columbia*] 
 
 Parking. The space between the sidewalk and the building line. [District 
 of Columbia*] 
 
 Parking Line. The line separating parking and sidewalk. [District oj 
 Columbia.] 
 
 Public Building. .Every building used as church, chapel, or other place of 
 public worship ; also every building nsed as a college, school, public hall, 
 hospital, theatre, public concert-room, public ball-room, public lecture-room, or 
 for any public assemblage, [Cotton, Chicago, Cincinnati, Cleveland, Denver, 
 Kansas City, and Minneapolis.] 
 
 Such buildings as shall be owned and occupied for public purposes for this 
 
 Staying apartment*. [Kansas City.] 
 
 To be used jointly by separate buildings. [ Cincinnati and Cleveland.] 
 
LEGAL DKFl-NITIONS OF ARCHITECTURAL TERMS. 1(>:;1 
 
 State-, the United Stales, tin- corporation of the City of Brooklyn, or other 
 public, schools within said city. [ /Iraoklyn.] 
 
 Public Hall. Every theatre, oprm house, hull, church, school, or other build- 
 ing iniended lo he used 1'or public assemblage. | Milwaukee and Louisville.] 
 
 Return Wall. No wall subdividing any building shall \w doomed a return 
 wall, as before mentioned, unless ir is two-thirds the height of the external or 
 party -walls. [Cincinnati and Cleveland.} 
 
 Shed. A skeleton struct ure for storage or shelter. [District of Columbia.] 
 
 Open strueture, enclosed only on one side and end, and erected on tho 
 ground. [x<tn FrCinciscO.] 
 
 Open or closed board strueture. \l><ni\r.\ 
 
 Show-window. A. store window in which goods are displayed for sale or 
 advertisement . | Di*tri<'t of ( '<>hcnt.bia and Denver.] 
 
 Square thereof. The square or level of the walls before commencing the 
 pitch for roof. [ l)ixtri<-t of ( 'oltanbia.] 
 
 Standard Depth for Foundations. For brick and stone buildings, 14' 
 below curb line, [rtitii, JSrancixco. \ 
 
 Standard Depth of Cellars. 1C', measured down from sidewalk grade at 
 property line. [Memphis.] 
 
 Standard Iron Door. Made of No. 12 plate-iron, frame or continuous 
 1xJ ' \ ~" x a" an^le 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 f 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, 
 Btone or cement, in no .case wood. [Denver.] 
 
 Standard Skylight. Constructed of wrought-iron frames, with hammered 
 or desk-light glass not less than V thick ; not larger than 10' by 12', except by 
 special permission of the Inspector. [Denser] 
 
 Storehouse. -(Sec Warehouse Class.) 
 
 Street. All streets, avenues, and public 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 families 2 above the second floor, so living and cooking. 
 [Boston 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 
 sain building, or which building shall be intended for the separate accommoda- 
 tion of different families or occupants. [Charleston.] 
 
 Theatre. Public hall containing movable scenery or fixed scenery which 
 is not made of metal, plaster, or other incombustible material. [Chicago, Louis- 
 ville, and Milwaukee.] 
 
 Thickness of a Wall. The minimum thickness of such wall. 3 [Boston^ 
 Cincinnati, Cleveland, Kansas City, Milwaukee, and Providence] 
 
 1 Two instead of three. [District of Columbia and Minneapolis] 
 Upon one floor, but having a common right in the halls, stairways, yards, 
 etc. [Providence] 
 3 As applied to solid walls . [Minneapolis and Providence.] 
 
1632 LEGAL DEFINITIONS OF ARCHITECTURAL TERMS. 
 
 Tinned Covered Fire-door. -Wood doors or shutters, double thickness oi 
 wood, cross or diagonal construction, covered on both sides and all edges with 
 sheet-tin, joints securely clinched and nailed. [Denver.] 
 
 Tower Projection. A projection designed for an ornamental door-entrance, 
 for ornamental windows, or for buttresses . [District of Columbia.] 
 
 Vault, An underground construction beneath parking or sidewalk [District 
 of Columbia.'} 
 
 Veneered Building. Frame structure, the walls covered above the sill by a 
 4' wall of brick, instead of clapboards, f Common understanding in Chicago, 
 Milwaukee, and Minneapolis, but not defined by law. ] 
 
 Warehouse Class. Buildings used for the storage of merchandise, manufac 
 tories in which machinery is operated, breweries, and distilleries [Cincinnati 
 and St. Louis.'] 
 
 Width of buildings shall be computed by the way the beams are placed . the 
 lengthwise of the beams shall be considered and taken to be the widthwise of 
 the building [New York and San Francisco.] 
 
 Wholesale store, or storehouse, shall embrace all buildings used (or in- 
 tended to be used) exclusively for purpose of mercantile business or storage of 
 goods . f Chicago. Louisville, and Milwaukee.] 
 
 Wooden Building. A wooden or frame l building [Boston, Kansas City, 
 and Minneapolis.] 
 
 Any building of which an external or party wall is constructed in whole or in 
 part of wood. [Denver and District of Columbia.'] 
 
 Having more wood on the outside than that, required for the door and window 
 frames, doors, shutters, sash porticos, and wooden steps, and all frame buildings 
 or sheds, although the sides and ends are proposed to be covered with corrugated 
 iron or other metal, shall be deemed a wooden building under this law. [Charles- 
 ton and Nashville. J 
 
 i Or veneered. [Minneapolis. J 
 
INDEX. 
 
 The numbers refer to the pages. See also Glossary, pp. 1575, etc., and 
 Table of Contents. For address of Manufacturers, see Trade References, p. 
 1570. 
 
 A Batik-tubs. 
 
 A. I. A. Schedule of charges, 1552. 
 Acetylene gas, 1285. 
 Adamant, 1391. 
 
 Adhesive strength of sulphur, lead and 
 cement, for anchoring bolts, 1507. 
 Air, 
 
 composition and properties of, 1113. 
 
 saturated, 1115. 
 
 specific heat of, 1117. 
 
 weight and volume of , 1116. 
 Air-lift process of raising water, 1249. 
 Alhambra, the, 1529. 
 Ampere, definition of, 1306. 
 Anchoring bolts in stone, 1507. 
 Anchors, box, for wooden beams, 714. 
 
 wall, for steel beams, 553. 
 Ancient measures and weights, 36. 
 Angles, bulb, size and properties, 312. 
 
 measured by a 2-ft. rule, 73. 
 
 measured by chords, 72, 88. 
 
 steel, size and properties, 300. 
 strength of, as beams, 524, 528. 
 tensile strength of, tables, 349. 
 3" and under, list of extras, 1456. 
 Angular measure, 31. 
 Anticondensation lining for iron roofs, 
 
 1442. 
 
 Antihydrine, 1406. 
 Apostles, the, symbols for, 1524. 
 Arc lamps, 1314; space illuminated 
 
 by, 1297. 
 
 Arch girders of cast iron, 262. 
 Arched trusses, 932. 
 
 wooden ribs, with steel ties, 911. 
 Arches, 
 
 brick, 251. See also Brick arches. 
 
 centers for, 252. 
 
 concrete-steel, 262. 
 
 definition of terms, 249. 
 
 depth of keystone, 253. 
 
 for fire-proof floors, see Hollow 
 tile arches. 
 
 inverted, in foundations, 183. 
 
 stability of, how found, 256. 
 Architects' charges, A. I. A. schedule, 
 1552. 
 
 license law, State of Illinois, 1558. 
 Architects, noted, list of, 1540. 
 
 Architects' of noted public and semi- 
 public buildings, 1537 ; of tall 
 office buildings, 1531. 
 Architectural terra-cotta, weight and 
 
 strength, 228. 
 Architecture, 
 
 colleges and schools of, 1562. 
 
 the Five Orders of, 1497. 
 Arcs, circular, length of, 56. 
 Areas of circles, tables of, 44. 
 
 of square and round bars, 1350. 
 Arithmetic, 
 
 cube root, 5, 8. 
 
 signs and characters, 3. 
 
 square root, 4, 8. 
 
 table of squares, cubes, etc., 8. 
 Art Institutes, Architects of, 1539. 
 Asbestic plaster, 733. 
 Asbestolith, 778. 
 Asbestos building felts, 1402. 
 Asbestos pipe coverings, 1166. 
 Ashlar, 1374. 
 
 walls faced with, 189. 
 Asphalt, Asphaltum, 1448. 
 Asphalt roofing, specifications for, 
 
 etc., 1436. 
 
 Auditorium Building, Chicago, 1536. 
 Automatic alarms, 780. 
 Automatic sprinklers, 780. 
 Avenues of the city of New York, 
 1475. 
 
 Barb- wire, in concrete slabs, 833. 
 
 Barrell, dimensions of, 1474. 
 
 Bars, flat, tensile strength of, 347; 
 
 weight of, 1353. 
 
 Base price of structural steel, 1451. 
 Bath-tubs, dimensions of, 1471. 
 
 1633 
 
1634 
 
 INDEX. 
 
 Batlis Brickwork. 
 
 Baths, plunge, 1283. 
 
 Beam connections, to compute 
 
 strength of, 369; standard, 545. 
 Beam, definition of, 497. 
 Beams, 
 
 built-up wooden, 579. 
 compound wooden, 579. 
 continuous, 608. 
 cylindrical strength of, 571. 
 flitch-plate, 584. 
 inclined strength of, 506. 
 rectangular, relative strength of, 
 
 570. 
 
 stone, strength of, 573. 
 strength of, general principles, 497. 
 strut, of steel, 511 ; of wood, 568. 
 supporting brick walls, 542. 
 tie, of steel, 512; of wood, 569. 
 trussed, 586. 
 with concentrated loads, 503, 505 ( 
 
 514. 
 
 Beams, Cast Iron, strength of, for- 
 mulas, 555. 
 
 Beams, I-, see Beams, steel. 
 Beams, Steel (see also Steel beams), 
 buckling strength of, 508. 
 deepest beams most economical, 507. 
 deflection of, 510, 595, 601. 
 economical shapes, 507. 
 lateral strength of, 509. 
 maximum safe load for, 507. 
 size and properties of, 296. 
 strength of 
 
 formulas and examples, 500. 
 tables/515. 
 Beams, Wooden, 
 
 stiffness of, 595; tables, 603. 
 strength of, formulas, 533; tables, 
 
 574. 
 
 with concentrated loads, 567. 
 Bearing plates, proportions of, 398. 
 Bearing power of soils and rock, 137. 
 Bearing resistance of rivets, 371. 
 Bedsteads, dimensions of, 1470. 
 Bells, dimensions, tone and weight of, 
 
 1522. 
 
 the largest in the world, 1523. 
 Belly-rod trusses, 587. 
 Belting, Belts, notes on, 1514; trans- 
 mitting power of, 1513. 
 Bending, see Deflection. 
 Bending moments 
 
 in beams, rules for, 266. 
 
 determined graphically, 270. 
 in pins, 377, 379. 
 Bent glass, cost of, 1418. 
 Berger's economy studding and fur- 
 ring, 748. 
 
 Berger's multiplex steel floor-plate, 850. 
 Bevels of hip and jack rafters, 97. 
 Billiard-tables, dimensions of, 1471. 
 Bitumen, 1448. 
 Blackboards, height of, 1475. 
 Blocks, chain, 1516. 
 Blue-prints, directions for making, 
 
 1510. 
 
 Board measure, definition of, 1395; 
 tables of, 1396. 
 
 Boiler tubes,dimensions and data, 1204. 
 Boilers, hot-water, 1170. 
 Boilers, steam, 
 classes of, 1133. 
 fire-box, 1137. 
 horizontal tubular 1133; setting of, 
 
 1136. 
 
 rating (horse-power) of, 1145. 
 requirements of, 1143. 
 sectional cast iron, 1137; setting 
 
 and covering of, 1145. 
 size required to supply radiation, 
 
 1146. 
 
 trimmings for, 1146. 
 Boiling-point of water, 1110. 
 Bolsters, see Columns. 
 Bolt-heads, dimensions and propor- 
 tions of, 1361. 
 Bolts, expansion, 1370. 
 
 strength of, in wooden trusses and 
 
 girders, 382. 
 weight of, 1363. 
 Bond hoop iron, 216. 
 Bond-stones in piers, 216. 
 Books, for Architects, builders, and 
 
 draughtsmen, 1566. 
 Bostwick metal lath, 776 
 Bowstring truss, the, 
 
 description and examples, 931. 
 stress diagrams, 1003. 
 Box anchors, for wooden beams, 714. 
 Box girders, of steel beams, safe loads, 
 
 537. 
 of steel plates and angles, 618; 
 
 tables of, 644. 
 Braces, see Struts. 
 Bracing of tall buildings, 1082. See 
 
 also Wind bracing. 
 Breaking strain, 498. 
 Breast walls, 210. 
 Brick, Bricks (see also Brickwork), 
 crushing strength of, 218, 229. 
 fire-proof qualities of, 728. 
 glazed and enamelled, 1380. 
 kinds of, clay, 1376. 
 quantity required for setting boil- 
 ers, 1138. 
 sand-lime, 1379. 
 size and weight of, 1378. 
 space required for piling, 1386. 
 Brick arches, 250. 
 
 for fire-proof floors, 783; span, 
 
 rise, and strength, 785. 
 Brick chimneys (see also Chimneys), 
 construction of, thickness of walls, 
 
 etc., 1224. 
 
 tall, examples of, 1226. 
 Brick footings, 181. 
 Brick piers, 
 
 bond-stones in, 216. 
 effect of bond on strength of, 216. 
 strength by actual tests, 219, 222. 
 strength of, 213, 214. 
 Brick walls, 
 
 general rule for, 188, 
 thickness of, 186. 
 Brickwork, 
 cost of, 1385. , 
 
INDEX. 
 
 1635 
 
 Brickwork Centers. 
 
 Brickwork continued. 
 
 crushing height of, 217. 
 
 efflorescence on, 1508. 
 
 grouting of, 216. 
 
 measurement of, 1382. 
 
 municipal requirements, 214. 
 
 strength of, 213, 214, 216. 
 
 supported by girders, 542. 
 Bridges, longest in the world, 1519. 
 
 notable, 1521. 
 
 Bridging of floor beams, 678. 
 Bromley fire-proof floors, 862. 
 Brooklyn Bridge, the, 1519. 
 Bruner trussed, fire-proof floor, 847. 
 Buckle-plates, for floors, 871. 
 Buckling resistance of web plates, 624, 
 
 642. 
 Building Laws, relating to 
 
 fire-proofing, 727. 
 
 floor loads, minimum, 654. 
 
 footings, proportioning to live loads, 
 140. 
 
 masonry, maximum loads, 214. 
 
 pile foundations, 147. 
 
 plumbing, 1262. 
 
 soils, maximum load on, 138. 
 
 steel columns, 460. 
 
 wind bracing, 1083. 
 
 wooden beams, safe loads for, 573. 
 Building papers, kinds of, quantity in 
 
 a roll, weight, cost, etc., 1401. 
 Building stones, see Stones. 
 Buildings, 
 
 cost of, per cubic foot, 1457. 
 
 cost of, per square foot, 1467. 
 
 depreciation of, 1468. 
 
 exposition, cost of, 1467. 
 
 government, cost of, 1468. 
 
 iron, cost of, 1467. 
 
 notable American, description of, 
 1533. 
 
 noted, Architects of, 1537. a 
 
 noted European, dimensions of, 
 1530. 
 
 steel mill, shop cost of, 1453. 
 
 tallest, height of, 1531. 
 
 wear and tear of, 1469. 
 Built-up beams, wooden, 579. 
 Bulb angles, size and properties, 312. 
 Bureaus, dimensions of, 1470. 
 Buttresses, stability of, 242. 
 
 Cables, see Ropes. 
 Caisson foundations, 172. 
 Calendar, the old and new, 31 
 Candle foot, 1296. 
 
 Candle power, how measured, 1295. 
 
 of lamps, 1295, 1313. 
 Cantilever beam, definition, 497. 
 Cantilever foundations, 174. 
 Cantilever trusses, 
 
 advantages and disadvantages, 939. 
 
 example of, 940. 
 
 principle of, 936. 
 
 stress diagrams, 1014. 
 Canvas roofing, 707. 
 Capacity of 
 
 churches and theatres, to estimate, 
 1478; examples of, 1479. 
 
 freight cars, 1474. 
 
 hot-air pipes and registers, 1200. 
 
 library stacks, 1495. 
 
 pipes and cylinders, 1258 
 
 sewer-pipes, 1281. 
 
 single-acting cylinder pumps, 1247. 
 
 tanks, cylindrical, 1256, 1259. 
 
 tanks, rectangular, 1261. 
 
 wheelbarrows, wagons, and scrap- 
 ers, 1372. 
 
 Carbolineum Avenarius, 1407. 
 Carriages, dimensions of, 1473. 
 Cars, dimensions, of, 1473. 
 Castings, weight and shrinkage of, 
 
 1357. 
 Cast iron, 
 
 fire-proof qualities of, 729. 
 
 rules for estimating weight, 1357. 
 
 specifications for, 327 . 
 
 strength of, 327. 
 Cast-iron arch girders, 262. 
 Cast-iron columns, see Columns. 
 Cathedrals, the English, dimensions 
 of, 1527. 
 
 European, 1529. 
 
 Ceiling (wood), thicknesses and 
 widths, 1399; quantity re- 
 quired, 1400. 
 Ceiling joists, maximum span, table, 
 
 671. 
 Ceilings, suspended, in fire-proof 
 
 construction, 757. 
 Cellar drainer, Climax, 1282. 
 Cement, Cements, 
 
 cost of, 197. 
 
 leading brands of, 192, 196. 
 
 natural rock, 192. 
 
 Portland, 194, 197. 
 
 proportions of, for mortar, 193, 
 199. 
 
 Puzzolan, slag, 195. 
 
 quantities required for mortar, 
 
 " concrete, etc., 193, 199. 
 
 Silica-Portland, 194. 
 
 stainless, 196. 
 
 water required for mixing, 198. 
 Cement-block walls, 19-0. 
 Cement-coated nails, 1365. 
 Cement mortars, 
 
 freezing of, 193, 199. 
 
 proportions of, 193, 199. 
 
 quantities required for masonry 
 
 and plastering, 199. 
 Cement wall plaster, 1391. 
 Centers for arches, 253. 
 
1636 
 
 INDEX. 
 
 Centre Column, 
 
 Centre of gravity, 236. 
 
 examples of, 236. 
 
 of compound sections, 239. 
 
 to find, 237, 239. 
 Chain blocks, 1516. 
 Chains, weight and strength of, 358. 
 Chairs and desks for schools, sizes of, 
 
 1475. 
 
 Chairs and seats, dimensions of, 1470. 
 Channel columns, 
 
 details, 437. 
 
 strength of, tables, 466, 472. 
 Channels (standard steel), 
 
 size and properties of, 298. 
 
 strength of, as beams, 519, 521. 
 Channels, small, 
 
 extras, on (price), 1456. 
 
 size and properties of, 300. 
 
 strength of, 522. 
 Charges and professional practice of 
 
 Architects, 1552. 
 Check valves, 1157. 
 Chimneys, 1220. 
 
 brick, construction of, 1224. 
 
 draught in, 1221. 
 
 fire-brick lining, 1225. 
 
 foundations for, 146. 
 
 object of, 1220. 
 
 radial block, 1229. 
 
 reinforced concrete, 1229. 
 
 self -sustaining steel, 1230. 
 
 size of, for fire-places 1224; for 
 house heaters, 1222; for power 
 plants, 1222. 
 
 stability of. 1224. 
 
 tall, examples of, 1226; list of, 1227. 
 
 theory of, 1221. 
 
 thickness of walls, 1225. 
 Chords, table of, 88. 
 Churches, capacity of several large, 
 1479. 
 
 to estimate seating capacity of, 
 
 1478. 
 Cinder concrete, 735; proportions for, 
 
 823. 
 Circles, areas and circumferences of, 
 
 tables, 44. 
 
 Circuit-breakers, 1313. 
 Circular arcs, length of, etc., 56. 
 Circular measure, 31. 
 Circular sectors, area of, 62. 
 Circumferences of circles, tables, 44. 
 
 of round bars, 1350. 
 Cisterns and tanks, capacity of, 1259. 
 City Hall, Philadelphia, 1535. 
 Clapboards, dimensions of, 1399. 
 Classical mouldings, 1496. 
 Classical Orders, the, 1497. 
 Clay, 
 
 bearing power of, 137. 
 
 foundations on, 144. 
 Clevises, 336; dimensions of, 344. 
 Climax cellar drainer, 1282. 
 Clips, steel, for fastening angles and 
 
 tees, 875. 
 Clock dials, rules for, and dimensions 
 
 of some large, 1494. 
 Coach screws, 1370. 
 
 Coal, Coals, 
 
 value of, in heat units, 1109. 
 weight of, 1341, 1342. 
 Coal burned per hour in tubular boil- 
 ers, 1146. 
 Cocks, 1158. 
 
 Coefficient of strength, definition, 498. 
 Coin, weight of, 30. 
 Cold-air supply for furnace heating, 
 
 1177, 1181, 1184. 
 Colleges of Architecture, 1562. 
 Color of illuminants, 1299. 
 Colors of iron caused by heat, 1119. 
 Columbian fire-proof floors, 839. 
 Column, Columns, 
 Base plates, or stools, 
 bedding of, 403. 
 proportions for, 399. 
 weight of, 1360. 
 
 Cast iron; advantages and disad- 
 vantages, 414. 
 base plates for, 399. 
 brackets on, 403. 
 connections of, 418. 
 connections to, 405. 
 eccentric loading of, 421. 
 H-shaped, 427. 
 maximum length of, 416. 
 prominent buildings used in, 494. 
 shapes of, 416. 
 strength of, formulas, 420. 
 strength of (tables) round, 424; 
 
 square and rectangular, 425. 
 weight of, 1358. 
 Fire-proofing of, 736. 
 Gas- or steam-pipe columns, 465. 
 I-beam, strength of, as columns, 
 
 471. 
 
 Monumental, height of, 1525. 
 Schedule of, 462. 
 Sheets, 460. 
 Steel, 
 
 advantages and disadvantages, 
 
 429. 
 
 building laws, relating to, 460. 
 channel columns, 
 details of, 437. . 
 latticing of, 439. 
 strength of, tables, 466, 472. 
 connection of, 431. 
 cost of, 1453. 
 eccentric loads on, 456. 
 forms of, 428. 
 formulas for, 452. 
 formulas for, comparison of, 495. 
 Gray column, 448. 
 strength of, 489. 
 Larimer column, 445. 
 
 strength of, 486. 
 length of, maximum, 451. 
 loads, method of computing, 459. 
 number and spacing of rivets, 
 
 432. 
 Nurick columns, 448. 
 
 strength of, 488. 
 Phoenix column, 
 details, etc., 440. 
 strength of, 484. 
 
INDEX. 
 
 1637 
 
 Column Cost, 
 
 Columns continued. 
 
 plate and angle columns, 440. 
 strength of, formulas, 452. 
 strength of, tables, 463. 
 used in some prominent office 
 
 buildings, 494. 
 Z-bar columns and details, 433; 
 
 strength of, tables, 475. 
 Wooden, 
 
 caps and bolsters for, 414. 
 eccentric loading of, 413. 
 strength of, 408. 
 
 Comparison of the Metric and English 
 systems of weights and measures, 
 34. 
 
 Comparison of thermometers, 1118. 
 Composite Order, the, 1504. 
 Composition and resolution of forces, 
 
 231. 
 
 Compound wooden girders, 579. 
 Concentrated loads, factors for reduc- 
 ing to equivalent distributed 
 load, 567. 
 Concrete, Concretes, 200. 
 
 aggregates, relative merits, 201. 
 cinder, 735. 
 cost of, 203, 205. 
 examples of, 205. 
 fire-proofing qualities of, 734. 
 footings of, 180. 
 freezing of, 202. 
 hooped strength of, 222. 
 materials required for, 203, 205. 
 mixing of, 202. 
 natural cement, 201. 
 Portland cement, 202. 
 strength of, 214, 226. 
 weight of, 205. 
 Concrete piles, 177. 
 
 Concrete-steel, see Reinforced concrete. 
 Concrete-steel beams, 
 
 forms of bars for reinforcement; 
 
 corrugated bars, 855, 869. 
 grooved steel, 856. 
 Kahn trussed bar, 882. 
 Thacher bar, 855, 869. 
 twisted bars, 834. 
 formulas for strength and area of 
 
 metal, 865. 
 
 Hennebique system, the, 855. 
 Hinchman-Renton girder, 856. 
 stirrups in, 870. 
 Concrete-steel columns, 228. 
 Concrete- steel floors, see Reinforced 
 
 concrete floors. 
 
 Concrete- steel foundations, 158. 
 Concrete-steel slabs, formulas for 
 strength and area of metal, 865. 
 Conductors, proportion to roof sur- 
 face, 1481. 
 
 Conduit systems of electric wiring,! 334 
 Cones, surface of, 64; volume of, 67. 
 Congressional Library, the, descrip- 
 tion and capacity of, 1534; di- 
 mensions of stacks, 1496. 
 Connections between wooden posts and 
 
 girders, mill construction, 718. 
 for steel beams, 545. 
 
 Connections continued. 
 
 of steel columns, 431, 434, 436, 438, 
 442, 446. 
 
 to cast-iron columns, 405. 
 Consumption of water, 1274. 
 Continuous girders, strength and 
 
 stiffness of, 608. 
 Contract between Architect and 
 
 Owner, 1553. 
 Contract, the Uniform, between owner 
 
 and builder, 1555. 
 
 Conversion tables, metric -English, 34. 
 Corinthian Order, the, 1502. 
 Corrugated flooring, 873. 
 Corrugated iron and steel sheets, 1437. 
 Corrugated roofing, 1439. 
 Corrugated sheets for ceilings, 1443. 
 Corrugated siding, 1442. 
 Cosecants, table of, 123a. 
 Cosines, table of, 103. 
 Cost of 
 
 bending glass, 1418. 
 
 brickwork, how estimated, 1382. 
 
 builder's work, of different kinds, 
 per cubic foot of building, 1466. 
 
 building papers, felts, and quilts, 
 1401. 
 
 buildings per cubic foot, 1457. 
 per square foot, 1467. 
 
 carpenter's work, 1400. 
 
 concrete, 203, 205. 
 
 curbing, 1376. 
 
 drafting structural steel, 1454. 
 
 electric-light wiring and installa- 
 tions, 1339. 
 
 enamelled brick, 1381. 
 
 erecting structural steel, 1453. 
 
 excavating and quarrying, 1372. 
 
 Exposition buildings (Chicago and 
 St. Louis), 1467. 
 
 fire-proof floors, tile, 815. 
 
 fire-proof partitions, 2" solid plas- 
 ter, 749. 
 
 fire-proofing, 781. 
 
 floor and mantel tiles, 1447. 
 
 galvanized iron sheets, 1443. 
 
 glass, plate, 1420; rolled, 1419; 
 sheet, 1417. 
 
 gravel roofing, 1435. 
 
 lathing, 1393. 
 
 merchant steel, 1454. 
 
 mills and factories, 723. 
 
 mineral wool, 1450. 
 
 mortar colors, 1386. 
 
 paint and painting, 1411. 
 
 painting structural steel, 1413. 
 
 pile driving, 157. 
 
 piles, 158. 
 
 plasterers' work, 1393. 
 
 pumping by air-lift process, 1250. 
 
 rock asphalt, 1449. 
 
 roofing tile, 1429. 
 
 shingles and shingling, 1426. 
 
 slates and slate roofs, 1428. 
 
 steel roof trusses, 1453. 
 
 stonework, rough and'cut, 1375. 
 
 structural steel for buildings, data 
 for estimating, 1451. 
 
1638 
 
 INDEX. 
 
 Cost Durability. 
 
 Cost of continued, 
 tin roofing, 1432. 
 Translucent Fabric, 1424. 
 U. S. Government buildings, 1468. 
 Cotangents, table of, 112. 
 Counter-braces in wooden roof 
 
 trusses, 887,894. 
 Counter-flashings, 1427. 
 Courses in Architecture, 1562. 
 Covering of steam-pipes, 1166. 
 Cross bridging, 679. 
 Cross strain, see Beams. 
 Crushing height of brick and stone, 
 
 217. 
 Crushing loads for woods and metals, 
 
 407. See also Columns. 
 Crushing of timber perpendicular to 
 
 the grain, 414. 
 
 Crushing strength, see Strength. 
 Cube root, 5; table of, 8. 
 Cubes, table of, 8. 
 Cubic measure, 28. 
 Curbing, cost of, 1376. 
 Curtain walls, 190. 
 Cutler mail chutes, 1491. 
 Cycloid, to describe a, 87. 
 Cylinders, capacity of, 1258. 
 Cylindrical beams, strength of, 571; 
 
 stiffness of, 601. 
 
 Damp-resisting paints, 1406. 
 
 Data on, see Article in question. 
 
 De Mann sectional fire-proof floor, 
 
 864. 
 
 De Mann twisted tension bar, 835. 
 Dead load, definition of, 132. 
 Decimal equivalents for fractions of 
 
 an inch, 26. 
 
 Deck beams, size and properties of, 
 312. 
 
 strength of, table, 518. 
 Deep-well pumps, 1245. 
 Deep.wells, 1244. 
 Definition of, see Term in question, 
 
 also Glossary. 
 
 Definitions of terms used in mechan- 
 ics, 130. 
 
 Deflection to crack plastering, 596. 
 Deflection of steel beams, 510. 
 
 wooden beams, 595. 
 Depreciation of buildings, 1468. 
 Description of notable American 
 
 buildings, 1533. 
 Details of 
 
 columns, see Columns, 
 steel roof trusses, 1064. 
 wooden roof trusses, 1051. 
 
 Dials, clock, diameter of, 1494. 
 
 Differential pulleys, 1516. 
 
 Diffusion of light through windows, 
 
 1300. 
 
 Dimensions of (see also Article in 
 question), 
 
 barrels, 1474. 
 
 bells, 1522. 
 
 billiard -tables, 1471. 
 
 bricks, clay, 1378; enamelled, 1381. 
 
 carriages, 1473. 
 
 cars and locomotives, 1473. 
 
 chairs and desks for schools, 1475. 
 
 chimneys, for fire-places, 1224. 
 for house heaters, 1222. 
 for power plants, 1222. 
 for ranges, 1224. 
 
 clevis nuts, 344. 
 
 clock dials, 1494. 
 
 domes, principal in the world, 1526. 
 
 elevator hatchways, 1490. 
 
 elevators, 1486. 
 
 English cathedrals, the, 1527. 
 
 eye-bars, table, 343. 
 
 fire engines and wagons, 1473. 
 
 furniture, 1470. 
 
 Grand Opera House, Paris, 1530. 
 
 hods for brick and mortar, 1387. 
 
 horse stalls, 1474. 
 
 library stacks, 1495. 
 
 Madison Square Garden, 1536. 
 
 noted European buildings, 1529 . 
 
 nuts and bolt-heads, 1361. 
 
 obelisks, still existing, 1528. 
 
 opera chairs, 1478. 
 
 Patent Office drawings, 1474. 
 
 plumbing fixtures, 1471. 
 
 rivets, 373, 374. 
 
 schoolrooms, 1475. 
 
 sleeve-nuts, 346. 
 
 steel eye-bars, 343. 
 
 steel structural shapes, 296. 
 
 theatres and opera houses, 1480. 
 
 turnbuckles, 345. 
 
 U. S. Government buildings, 1533. 
 
 upset screw-ends, 341. 
 
 Washington Monument, the, 1535. 
 Disc values, 1156. 
 Discharge of water, 1234. 
 Domes, height of, 1525; diameter of, 
 
 1526. 
 
 Doors, fire-proof, 767. 
 Doric Order, the, 1499. 
 Down spouts, proportioning to roof 
 
 surface, 1481. 
 Drafting structural steel, cost of, 
 
 1454. 
 Drain-pipes, capacity and description 
 
 of, 1279. 
 Draught in aspirating flues, 1213. 
 
 in chimneys, 1221. 
 Drums and pulleys, 1513. 
 Drying by steam, 1117. 
 Duplex joist and wall hangers, 681, 
 
 713,716. 
 
 Duplex post caps, 721. 
 Durability of 
 
 asphalt roofing, 1436. 
 
INDEX. 
 
 1639 
 
 Durability of continued* 
 
 gravel roofing, 1435. 
 
 iron in masonry, 191. 
 
 ready roofings, 1437. 
 
 tin roofing, 1432. 
 Duvinage post caps, 720. 
 Dynamos, 1309. 
 
 Durability Factor. 
 
 Eccentric loads 
 
 on steel columns, 456. 
 
 on wooden columns, 413. 
 Edison 3- wire system of wiring, 1317. 
 Efflorescence on brickwork, 1508. 
 Egyptian style of Architecture, 1504. 
 Elastic cement, 1427. 
 Elasticity, modulus of, 133; table, 
 
 597. 
 
 Electric elevators, see Elevators. 
 Electric lighting, 1311. 
 
 circuit-breakers, 1313. ' 
 
 fuses and cut-outs, 1311. 
 
 lamps, arc, 1314; incandescent, 
 1313. 
 
 switches, 1332. 
 
 systems of, 1311; comparative cost 
 
 of, 1312. 
 Electric-light wiring, 
 
 carrying capacity of wire, 1321, 
 1326. 
 
 centre of distribution, 1323. 
 
 conduit system, 1334. 
 
 cost of, 1339. 
 
 distributing centres, 1323. 
 
 drop of potential, 1322. 
 
 Edison 3- wire system, 1317. 
 
 example of, 1329. 
 
 methods of connecting lamps, 1315. 
 
 National Electrical Code, 1335. 
 
 resistance of copper wire, 1327. 
 
 specifications for, 1338. 
 
 switches, 1332. 
 
 wire calculations, 1323. 
 
 wire gauges (for copper wire), 1320. 
 
 wiring tables, 1328. 
 Electricity, 1305. 
 
 definitions, 1305. 
 
 dynamo-electric machines, 1309. 
 
 electrical currents, kinds of, 1310. 
 
 electrical equations, 1308. 
 
 electrical units, 1308. 
 
 electromotive force, 1306. 
 
 flow of, 1306. 
 
 heating effects of, 1308. 
 
 resistance to, 1307. 
 Elevators, 
 
 data as to size and number re- 
 quired. 1486. 
 
 Elevators continued. 
 
 makers of (see Trade references), 
 1570. 
 
 notes on, 1482. 
 
 relation of hatchway to car plat- 
 form, 1490. 
 
 specifications for, 1484. 
 
 with push-button control, 1489. 
 Ellipse, to describe an, 81 
 Ellipsoids, 63. 
 Enamelled brick, 1380; cost and size 
 
 of, 1381. 
 
 Enamelled tiles, 1445. 
 Enamels (paint), 1408. 
 Engines, hot-air, 1246. 
 English cathedrals, the, dimensions 
 
 of, 1527. 
 
 Equalization of pipe areas, 1203. 
 Equilibrium, definition of, 130. 
 Erecting structural steel, cost of, 1453. 
 Escurial, the, 1529. 
 
 Estimating, see Cost or Measurement. 
 Examples of 
 
 arches, 254. 
 
 caisson foundations, 174. 
 
 concrete foundations, 205. 
 
 pile foundations, 156. 
 
 steel-beam footings, 169. 
 Excavating, Excavations, 
 
 data for estimating cost of, 1372. 
 
 measurement of, 1371. 
 
 to compute volume of irregular, 69. 
 Expanded metal for floor slabs, 825. 
 Expanded metal laths, 773. 
 Expansion bolts, 1370. 
 Expansion of solids for 1 tempera- 
 ture, 1120. 
 Expansion tank, for hot -water heating, 
 
 1169. 
 Exposition buildings, Chicago and St. 
 
 Louis, cost of, 1468. 
 Extras on merchant steel, 1455. 
 Extras, to be added to price of beams 
 
 and channels, 1452. 
 Eye-bars, 
 
 description and data, 336. 
 
 dimensions of (table), 343. 
 
 steel for, specifications, 334. 
 
 strength of, 331. 
 
 Eye-beams, see I-beams; also Beams, 
 steel. 
 
 Factor of safety for 
 beams, 498. 
 masonry, 213. 
 reinforced concrete, 866. 
 wood in compression, 408. 
 
1640 
 
 INDEX. 
 
 Factor Footings. 
 
 Factor of safety for continued. 
 
 wood in tension, 322. 
 Factors of safety defined, 132. 
 Fan and Fink trusses, 
 
 cambering of, 920. 
 
 depth of, 920. 
 
 description and examples, 918. 
 
 stress diagrams, 984. 
 
 stresses in, tables, 958. 
 
 with pin joints, 923. 
 
 with wooden rafters and struts, 910. 
 Fan systems of ventilation, 1215. 
 Fans, for moving air, 1218; capacity 
 
 of, 1219. 
 
 Feet converted into metres, 36a. 
 Fellowships, travelling, 1565. 
 Felts, dry, 1401 ; saturated, 1402. 
 Ferroinclave, 849. 
 Fibre stress, see Modulus of rupture, 
 
 498. 
 
 Filters, 1281. 
 Fink trusses, see Fan and Fink 
 
 trusses. 
 
 Fire, temperature of, 1109; to deter- 
 mine by fusion of metals, 1110. 
 Fire-box boilers, 1137. 
 Fire-bricks, 1377. 
 Fire engines, dimensions of, 1473. 
 Fire-proof, Fire-proofing, 
 
 definition of, 726. 
 
 definitions, municipal, 727. 
 
 materials, 728 See also Terra-cotta 
 tiling, Reinforced concrete, etc. 
 
 of steel and iron in slow-burning 
 
 construction, 712. 
 Fire-proof base and trim, 768. 
 Fire-proof construction, 726. See also 
 Fire-proof floors, roofs, etc. 
 
 automatic alarms and sprinklers, 7 80. 
 
 column protection, 736. 
 
 cost of, 781. 
 
 details of, 736. 
 
 furring of outside walls, 760. 
 
 girder protection, 813, 860. 
 
 metal furring for false work, 762. 
 
 metal lath, 769. 
 
 partitions, 741. 
 
 precautionary measures, 779. 
 
 protection of steel trusses, 760. 
 
 recesses for pipes, 741. 
 
 stairs, 762. 
 
 suspended ceilings, 757. 
 Fire-proof doors, 767. 
 Fire-proof flooring, 778. 
 Fire-proof floors, 782. See also Hol- 
 low tile arches, Reinforced con- 
 crete, etc. 
 
 cost of tile, 815. 
 
 girder protection, 813. 
 
 Guastavino constructions, 815. 
 
 of brick arches, 783. 
 
 of concrete arches, 857. 
 
 of flat tile arches, 786. See Hollow 
 tile arches. 
 
 of reinforced concrete beams and 
 slabs, 822. See Reinforced con- 
 crete floor constructions. 
 
 Fire-proof floors continued. 
 
 of reinforced tile, 806. 
 
 of segment arches, 801. 
 
 steel framing for, 873; computa- 
 tions for strength, 876. 
 Fire-proof furniture, 779. 
 Fire-proof partitions, 741. 
 
 Berger's studding for, 748. 
 
 deadening qualities of, 751. 
 
 of plaster and metal, 745; cost of, 
 749; weight of, 749. 
 
 of plaster blocks, 749; weight of, 
 750. 
 
 of terra-cotta tiling, 742 ; weight of, 
 745. 
 
 jacket's plaster board, 750. 
 Fire-proof roofs, 753. 
 
 coverings for, 756. 
 
 flat roofs, 753. 
 
 mansard, 756. 
 
 pitched roofs, 754. 
 Fire-proof windows, 765. 
 Fire-proof wood, 776. 
 Fire-resisting design, 728. 
 Fire streams, 1251. 
 Fitting for steam and hot-water piping, 
 
 1153. 
 
 Five Orders, the, 1497. 
 Flag-poles, rule for diameter of, 1475. 
 Flashings, 1427. 
 
 Flat arches, see Hollow tile arches. 
 Flat bars, 
 
 list of extras, steel, 1455. 
 
 strength of, as beams, table, 523. 
 
 tensile strength of, table, 347. 
 
 weight of, 1354. 
 Flitch-plate girders, 584. 
 Floor beams, steel, 
 
 computations for, 876. 
 
 tables for, 879. 
 Floor joists, wooden, 
 
 framing of, 679. 
 
 maximum span of. tables, 671. 
 
 weight of, 653. 
 Floor tiling, 1 443. 
 Flooring, fire-proof, 778. 
 Flooring, wood, 
 
 cost of laying, 1400. 
 
 dimensions of, 1399. 
 
 quantity required, 1400. 
 Floors, fire-proof, see Fire-proof 
 floors. 
 
 concrete, see Reinforced concrete 
 floors. 
 
 mill, 692. 
 
 minimum strength of, as required 
 by building laws, and as recom- 
 mended by author, 654. 
 
 solid or mill, strength of, 667. 
 
 wooden, see Wooden floors. 
 Flow of water hi pipes, 1232. 
 Flues, for ventilation, shapes and 
 
 materials of, 1213; size of, 1211. 
 Fluid measure, 28. 
 Footings, 
 
 brick, 181. 
 
 computing width of, example, 139, 
 
INDEX. 
 
 1641 
 
 Footings Globe*. 
 
 Footings continued. 
 
 concrete, 180. 
 
 concrete-steel, 158. 
 
 inverted arches, 183. 
 
 load on, method of computing, 139. 
 
 object of, 178. 
 
 offsets of, 179. 
 
 proportioning to soil and load, 139. 
 
 steel beam, 161. 
 
 timber, 170. 
 
 Force, definition of, 130. 
 Force of the wind, 1510. 
 Forces, 
 
 composition and resolution of, 231. 
 
 in and on a truss, 967. 
 
 moments of, 233. 
 
 polygon of, 233. 
 
 principle of the lever, 235. 
 
 supporting, how found, 274. 
 Formulas for strength of 
 
 steel beams, 500. 
 
 steel columns and struts, 452; com- 
 parison of, 495. 
 Foundations, 135. 
 
 actual loads on piles, 156. 
 
 bearing power of soils and rock, 135, 
 
 caisson, 172. 
 
 cantilever, 174. 
 
 example of footings, 141 
 
 for chimneys, 146. 
 
 for temporary buildings, 171. 
 
 masonry wells for, 171. 
 
 municipal laws, governing loads on 
 soils, 138. 
 
 municipal requirements as to foot- 
 ings, 140. 
 
 object of, 135. 
 
 on clay, 144. 
 
 on loam and made land, 145. 
 
 on rock, 144. 
 
 on sand and gravel, 145. 
 
 pile, 147. 
 
 proportioning the footings, 139. 
 
 spread with reinforced concrete, 
 158. 
 
 spread with steel beams, 161. 
 
 testing of soils, 136. 
 
 timber footings, 170. 
 Foundation walls, 183. 
 Fractions expressed in decimals, 26. 
 Fractured surface of wrought iron, 
 
 324. 
 Framing and connecting of steel 
 
 beams, 545. 
 
 Framing of wooden floor beams, 679. 
 Freezing of cement mortars, 193, 199. 
 
 of concrete, 203. 
 
 Freight cars, capacity of, 1474; di- 
 mensions of, 1473. 
 
 Freight rates on structural steel, 1451. 
 Fuels, value of, in heat units, 1107, 
 
 1108. 
 
 Furnaces, hot-air, 1175. 
 Furniture, dimensions of, 1470. 
 
 metallic, 779. 
 Furring of brick walls, with metal 
 
 lath, 761. 
 with terra-cotta blocks, 760. 
 
 Furring of woodwork for metal lath, 
 
 770. 
 Fuses, 1311. 
 
 Galvanized-iron sheets, size, thickness, 
 
 and cost, 1443. 
 Gas generators, 1286. 
 Gas, illuminating, varieties of, 1285. 
 
 piping a house for, 1287. 
 Gas-pipe columns, strength of, 465. 
 
 dimensions and data, 1205; rules 
 and table for proportioning size 
 of, 1291. 
 
 Gate valves, 1155. 
 Gauge of railroad tracks, 1474. 
 Gauge of rivet-holes 
 
 for angles, T's and Z-bars, 552. 
 
 for channels, 551. 
 
 in steel beams, 550. 
 Gauge, U. S. standard, 1438. 
 Gauges, wire, see Wire gauges. 
 Gears, rules to determine size and 
 
 speed of, 1513. 
 Geometrical problems, 70. 
 Geometrical terms, 37. 
 Geometry, definitions, 37. 
 Girders, 
 
 arched (cast iron), 262. 
 
 built-up wooden, 579. 
 
 compound wooden, 579. 
 
 continuous, strength and stiffness 
 of, 608. 
 
 fire-proofing of, 712, 736, 813, 860. 
 
 flitch-plate, 584. 
 
 for brick walls, 542. 
 
 riveted steel plate and box, 618; 
 tables, 644. 
 
 trussed, 586. 
 Glass 
 
 cost of bending, 1418. 
 of rolled glass, 1419. 
 
 discount on, 1416, 1417. 
 
 figured, rolled glass, 1418. 
 
 for skylights, 1419. 
 
 grades and qualities of sheet glass, 
 1416. 
 
 polished plate glass, 1416. 
 
 price-list of plate glass, 1420. 
 of sheet glass, 1417. 
 
 weight of plate glass, 1417. 
 
 of rough glass, 1419. 
 Glass tiles, 1446. 
 Glazed bricks, 1380. 
 Glazed tiles, 1445. 
 Globe valves, 1155. 
 Globes, 1297. 
 
1642 
 
 INDEX. 
 
 Goetz Horse-power. 
 
 Goetz box anchors, 714. 
 
 Golding system of fire- proof floors, 
 
 852. 
 Government buildings, architects of, 
 
 1537; description of, 1533. 
 Grading of slates, 1426. 
 Grand Opera House, Paris, dimensions 
 
 of, 1530. 
 Granite, 
 
 effect of fire on, 729. 
 strength of, 213, 225, 229. 
 weight of, 1342. 
 
 Graphic statics, application to sim- 
 ple triangular frames, 968; to 
 roof trusses, 970. 
 Gravel roofing, 1432. 
 cost of, 1435. 
 
 durability and fire-resisting qual- 
 ities, 1435. 
 
 method of applying, 1432. 
 specifications for, 1433. 
 weights of felt and pitch, 1434. 
 Gravity, Centre of, see Centre. 
 Gravity, specific, 1345. 
 Gray columns, description of, 448. 
 
 strength of, 489. 
 Grease traps, 1271. 
 Grillage over piles, 151. 
 Grooved steel, see Channels, small. 
 Grouting, 216. 
 
 Guastavino tile arch system, 815. 
 Gutters, proportioning to roof sur- 
 face, 1481. 
 
 Gyration, radius of, 279. 
 of angles in pairs, 316. 
 of channels in pairs, 319. 
 of compound shapes, 289. 
 of round columns, 293. 
 of structural shapes, 293, 296. 
 
 H 
 
 Hair, for plaster, 1390. 
 Hammer-beam truss, the, 
 
 description and examples, 903. 
 stress diagrams, 991. 
 Hand rail, height 9f, 1476. 
 Hangers, see Joist hangers, Wall 
 
 hangers, etc. 
 Hard-pine beams, table of stiffness, 
 
 603; table of strength, 574. 
 Hard wall plasters, 1391. 
 Hardness of woods, relative, 1509 
 Haunches, definition, 249. 
 Hawsers, see Ropes. 
 Headers, strength of, 664, 676. 
 
 Heat, 
 
 colors of iron caused by, 1119 
 how measured, 1107. 
 mechanical equivalent of, 1107 
 specific, 1117- 
 units in steam, 1114; in water, 
 
 1112. 
 Heating, 
 
 hot-air and steam, 1187. 
 and water, 1186. 
 heating, 1174, 1187. 
 hot-water heating, 1168. 
 Paul system, 1150. 
 specifications for, see Specifications, 
 steam, gravity systems, 1121. 
 non -gravity systems, 1151. 
 vs. hot water, 1172. 
 systems of, 1121. 
 Webster system, 1152. 
 Heating and Ventilation, see Ventila- 
 tion. 
 
 Heating effects of electricity, 1308. 
 Heights of 
 
 columns, domes, spires, and towers, 
 
 1525. 
 
 tallest buildings in the U. S., 531. 
 Herculean fire-proof floor, the, 808. 
 Hip and jack rafters, length and 
 
 bevels, 97. 
 Hoists, chain, 1516. 
 Holding power of lag screws, 1371. 
 
 of nails, 1365. 
 Hollow tile, 214. 
 Hollow tile arches, 
 bonding of, 792. 
 cost of, 815. 
 depths of, 792. 
 development of, 786. 
 disadvantages of, 789. 
 end construction, flat arches, 791. 
 . Excelsior arch, the, 800. 
 filling above, 797. 
 inspection of, 814. 
 keys for, 794 
 manufacture and commercial status, 
 
 787. 
 
 mortar for, 797. 
 protection from stains in ceiling, 
 
 798. 
 
 reinforced, 806. 
 safe loads for flat, 798, 800. 
 
 for segmental, 802. 
 segment arches, 801. 
 tie rods for, 803. 
 serrated arch, the, 804. 
 setting of, 796. 
 
 side construction, flat arches, 790. 
 single-block flat arches, 805. 
 skewbacks for, 792, 794. 
 spans of flat arches, 792. 
 weather protection, 798. 
 weight of flat arches, 792. 
 Hollow tiles, see Terra-cotta tiling. 
 Hollow walls, 189. 
 Hooks, proportions of, 1518. 
 Horse, the, strength of, 1512. 
 Horse-power, electrical, 1308. 
 in machinery, 1512. 
 
INDEX. 
 
 1643 
 
 Horse-power Joule. 
 
 Horse-power continued, 
 of boilers, 1145. 
 required to raise water, 1250. 
 Horse-stalls, dimensions of, 1474. 
 Hose-carriages, dimensions of, 1473. 
 Hose-reels, 781. 
 
 Hot-air and steam heating, 1187. 
 Hot-air and water heating, 1186. 
 Hot-air engines, 1246. 
 Hot-air (furnace) heating, 1174. 
 cold-air supply, 1177, 1181. 
 forced-blast system, 1218. 
 furnaces for, 1175. 
 location of furnace, 1181. 
 
 ^ of stacks and registers, 1182. 
 pipes and registers, 1179. 
 size of furnace, pipes, and registers 
 
 1182. 
 
 specifications for, 1185. 
 ventilation, 1180. 
 Hot-air pipes and registers, 1179, 1183 
 
 1197. 
 
 Hot-blast system of warming and ven- 
 tilation, 1153, 1216. 
 Hot-water heating, 1168, 1187. 
 boilers for, 1170. 
 disadvantages of, 1173. 
 expansion tank, 1169. 
 proportioning radiating surface, 
 
 rules for, 1162. 
 rules for size of air ducts, indirect 
 
 radiation, 1163. 
 size of pipes, rules for, 1166; tables 
 
 for, 1201. 
 
 specifications for, 1188. 
 systems of piping, 1171. 
 Howe trusses, 
 
 counter-braces in, 1013. 
 description of, 892. 
 stress diagrams, 977, 982. 
 stress in formulas, 963. 
 table of dimensions for, 896. 
 unsymmetr cally loaded, 1009. 
 H-shaped columns, details of, 1419; 
 
 strength of, 427. 
 Hyatt's experiments and inventions, 
 
 817. . 
 
 Hydraulic Cements, see Cement. 
 Hydraulic Ram, the, 1244. 
 Hydraulics, 
 
 discharges through pipes, 1234. 
 flow of water in house-service pipes, 
 
 1240. 
 
 flow of water in pipes, 1232. 
 friction of water in pipe's, 1241. 
 pressure of water, 1231. 
 private water-supply, 1244. 
 velocity of discharge, 1233. 
 Hyperbola, to describe an, 85. 
 
 I-beams, 
 
 size and properties of, 296. 
 
 strength of, as beams, table, 515. 
 
 strength of, as columns, 471. 
 Illuminants, color of, 1299. 
 Illuminating-gas, varieties of, 1285. 
 Illumination, notes on, 1294. 
 Incandescent lamps, 1313. 
 Inches converted into millimetres 
 366. 
 
 expressed in decimals of a foot, 25. 
 
 fractions of, expressed in decimal 
 
 26. 
 
 , . 
 imals. 
 
 ^u. 
 
 Inclined beams, strength of, 506. 
 Inertia, moment of, 278, 279. 
 for compound shapes, 282. 
 of rectangles, 291. 
 of round columns, 293. 
 of square columns, 293. 
 of structural shapes, 296. 
 Instantaneous water heaters, 1282. 
 Insulating quilts, 1402. 
 Insulation of sound, see Fire-proof 
 
 partitions, 751. 
 
 Interlocking rubber tiling, 1447. 
 International Fence and Fire-proof- 
 ing Co.'s system of floor con- 
 struction, 829. 
 Intrados, definition of, 249. 
 Introduction to Part II, 128 
 Inverted arches, 183. 
 Involution, 3. 
 Ionic Order, the, 1500. 
 Ionic Volute, to describe, 1502. 
 Iron (see also Wrought iron, Cast iron, 
 
 Steel, etc.). 
 
 Iron buildings, cost of, 1467. 
 Iron, colors of, caused by heat, 1119. 
 
 r ohnson long-span floor, 809. 
 r oints 
 
 in wooden construction, to deter- 
 mine the strength of, 338. 
 of steel trusses, 1064. 
 of wooden trusses, 1051. 
 pin, strength of, 375. 
 riveted, strength of, 363; failure of, 
 
 365; examples, 1066. 
 bist hangers, comparative strength 
 
 of, 684; description of, 681. 
 oule, definition of, 1308. 
 
1644 
 
 INDEX. 
 
 Kali ii Masonry, 
 
 K 
 
 Kahn trussed bar, 882. 
 
 Keene's cement, 1391. 
 
 Kenney flushometer, 1281. 
 
 Keyed beams, 581. 
 
 Keystone, definition of, 249. 
 
 Keystones, depth of, rule and table, 
 
 253. 
 King rod trusses, 885 ; stress diagrams, 
 
 970, 1027. 
 Kirkaldy's experiments on wrought 
 
 iron and steel, 325. 
 
 Ladder wagons, dimensions of, 1473. 
 
 Lafarge cement, 197. 
 
 Lag screws, sizes and holding power of, 
 
 1371. 
 Lamp, Lamps, 
 
 electric, 1313. 
 
 the Meridian, 1298. 
 
 the Nernst, 1299. 
 Larimer columns, 
 
 description and details, 445. 
 
 strength of, tables, 486. 
 Lateral strength of steel beams, 509. 
 Lath, Laths, 
 
 metal, 769. See also Metal lath. 
 
 wooden, size and quantity re- 
 quired, 1389. 
 Lathing, cost of, 1393. 
 Lattice trusses, 
 
 descriptiop of, 897. 
 
 stress diagrams, 996. 
 
 stresses in, 898. 
 
 table of dimensions for, 899. 
 Latticing of channel columns, 439. 
 Lead pipes, supply, 1275; waste, 1263; 
 
 weights and sizes, 1276. 
 Leaders, proportioning to roof surface, 
 
 1481 
 
 Length of bridges, 1519. 
 Lever, the, principle of, 235. 
 Libraries, Architects of, 1539. 
 Library stacks, 
 
 capacity of, 1495. 
 
 dimensions of, 1495. 
 
 weight of, 1495. 
 
 License Law, Architects' , State of Illi- 
 nois, 1558. 
 
 Light, diffusion of, through windows, 
 1300. 
 
 quantity of, required for illumina- 
 tion, 1296. 
 
 Lighting and illumination, notes on, 
 1294. * 
 
 Lightning Conductors, rules for, 1505. 
 Lights, artificial, color of, 1299; inten- 
 sity of, 1295. 
 Lime, kinds of, 1387. 
 popping of, 1387. 
 quantity required for mortar, 1375, 
 
 1385, 1389. 
 slaking of, 1387. 
 weight of, 1387. 
 
 Limestone^, strength of, 213, 226, 229 
 Line of Resistance in masonry, 245. 
 Linseed-oil, 1405. 
 Lintels, cast-iron, strength of, 555. 
 Liquid measure, 28. 
 List of books, 1566. 
 
 of foreign Architects, 1540. 
 of noted American Architects, 1545. 
 Live load, definition of, 132. 
 Load, distinction between dead and 
 
 live, 132. 
 
 Loads on columns, method of com- 
 puting, 459. 
 
 on floors, 654. See Floor loads. 
 on roof trusses, see Roof loads, 
 safe, for brick arches, 785. 
 for flat arches, 798. 
 for reinforced tile floors, 809, 811. 
 for segment arches, 801. 
 Lock -woven fabrics, 826. 
 Locomotives, dimensions of, 1473. 
 Longest bridges in the world, 1519. 
 Loop bars, 338. 
 Lumber, 
 
 finishing, measurement of, 1399. 
 rough, sizes of, 1394; measurement 
 
 of, 1395. 
 
 tables of board measure, 1396. 
 weight of, 1509. 
 Luxfer prisms, 1302 
 
 Madison 
 
 ison Squ 
 of, 1536. 
 
 M 
 
 are Garden, dimensions 
 
 Magnite, cold-water paint, 1406. 
 
 Mail-chutes, 1491. 
 
 Manufacturers of terra- cotta t ling for 
 
 fire-proofing, 787. 
 Marble, strength of, tests, 226, 229. 
 Marble tiles, 1445. 
 Marbleithic tile and slabs, 1446 
 Masonry (see also Brickwork, Stone- 
 
 work, Walls, etc.)- 
 bond-stones, 216. 
 brick piers, 214. 
 crushing height of brick and stones 
 
 217. 
 grouting of, 216. 
 
INDEX. 
 
 1645 
 
 Masonry Natural. 
 
 Masonry continued. 
 
 maximum loads on, from bearing 
 plates, 399. 
 
 strength of, 212. 
 
 weight of, 1343. 
 
 Masonry wells, for foundations, 171. 
 Maximum span of ceiling- joists, floor- 
 joists, and rafters, 671. 
 Maze glass, 1300, 1418. 
 Measure, Measures, 
 
 circular and angular, 31. 
 
 dry, 27. 
 
 liquid, 28. 
 
 metric system, the, 31* 
 
 miscellaneous, 28. 
 
 nautical, 27. 
 
 of length, 25. 
 
 of surface, 27. 
 
 of value, 30. 
 
 of volume, 27. 
 
 of weight, 28. 
 
 Scripture and ancient, 36. 
 Measurement of 
 
 brickwork, 1382. 
 
 excavations, 1371. 
 
 lumber, 1395. 
 
 painter's work, 1411. 
 
 plasterer's work, 1391. 
 
 slater's work, 1428. 
 
 stonework, 1374. 
 Mechanics, definition, 130. 
 Melting-point of metals, 1110. 
 Men, average height of, 1474. 
 Mensuration, 37. 
 
 areas, 40 ._ 
 
 areas of circles, tables, 44. 
 
 circular arcs, 56. 
 
 surface of solids, 62 
 
 volume of solids, 65. 
 Merchandise, weight of, 657. 
 Merchant steel, base price and extras, 
 
 1455. 
 
 Meridian lamp, the, 1298. 
 Metal-covered door-jambs and trim, 
 
 796. 
 
 Metal-covered doors, 768. 
 Metal furring, 762; Hammond's, 771. 
 Metal lath, 769. 
 
 furring for, 770. 
 
 kinds of 
 
 expanded metal, 773. 
 herringbone, 774. 
 Imperial, 775. 
 perforated sheet metal, 776. 
 plain wire lath, 769, 771. 
 stiffened wire lath, 772. 
 Metallic furniture and fittings, 779. 
 Metallic sheeting, tie-locked fabric, 
 
 829. 
 
 Metal studding, 748. 
 Metals, melting-point of, 1110. 
 Metric conversion tables, 34. 
 Metric system, the, 31. 
 Metropolitan fire-proof floor, the, 844. 
 Mill buildings, steel, shop cost of, 
 
 1453. 
 Mill construction, 
 
 arrangement of stairways, 699. 
 
 Mill construction continued. 
 
 belt, stairway, and elevator towers. 
 
 696. 
 
 columns in, 706. 
 
 connection of floor-beams and gird- 
 ers, 713; of girders and columns, 
 718. 
 
 cost of, 723. 
 description of, 687. 
 details of, 712. 
 doors and shutters in, 708. 
 one-story shops, 704. 
 partitions in, 708. 
 patented systems of, 708. 
 roofing materials for, 707. 
 standard, 689. 
 with concrete flooring, 722. 
 with self-sustaining frame, 701. 
 Mineral wool, 1450. 
 Mirrors, 1424. 
 Modulus of elasticity, defined, 133 J 
 
 values of table, 597. 
 of rupture, definition, 498; table of, 
 
 499. 
 
 Moments, 233. 
 bending, 236. 
 of inertia, 278/282, 296. 
 of resistance, definition, 498; tables 
 
 of, for structural shapes, 296. 
 Monolith, 779. 
 Mortar, Mortars, 
 for tile arches, 797. 
 quantity required for brickwork, 
 
 1385; for stonework, 1375. 
 strength of, 214, 221. 
 Mortar colors, cost of and quantity 
 
 required, 1386. 
 Mortise and tenon joints, 679. 
 Motion, definition of, 130. 
 Mouldings, classical, 1496. 
 Multiplex steel plate, Berger's, 850. 
 Municipal requirements, see Building 
 Laws, 
 
 'N 
 
 Nails, 
 
 cement-coated, 1365. 
 holding power of , 1365. 
 kinds and varieties of, 1365. 
 quantities of, required for different 
 
 kinds of work, 1366. 
 size, length, and number to the 
 
 pound, 1367. 
 
 National Electrical Code, 1335. 
 Natural rock cements, 192. 
 Natural sines, tangents, secants, etc., 
 103. 
 
1646 
 
 INDEX. 
 
 Nautical Pitch. 
 
 Nautical measure, 27. 
 Neponset building papers, 1401. 
 Nernst lamp, the, 1299. 
 Neutral axis, definition of, 497. 
 Notable buildings, American, descrip- 
 tion of, 1533; Architects of, 
 1537. 
 
 European, dimensions of, 1529. 
 Noted American Architects, list of, 
 
 1545. 
 
 Noted foreign Architects, list of, 1540. 
 Novus sanitary glass, 1446. 
 Nurick column, the, 448; strength of, 
 
 488. 
 Nuts, dimensions and proportions, 
 
 136. 
 
 Oak beams, table of stiffness, 607 ; ta- 
 ble of strength, 576. 
 
 Obelisks, dimensions of, 1528. 
 
 Office buildings, cost of per cubic 
 
 foot, 1461. 
 
 some of the tallest, and name of 
 the architect, 1531. 
 
 Ohm, definition of, 1307. 
 
 Old iron, strength of, 359. 
 
 Opera chairs, 1478. 
 
 Opera houses, see Theatres. 
 
 Orders, the Five, 1497. 
 
 Oregon pine beams, table of stiffness, 
 604; table of strength, 575. 
 
 P and B, building papers, 1401. 
 Paint, Paints, 
 
 adulterants, 1404. 
 
 cost of, 1411. 
 
 damp-resisting, 1406. 
 
 enamels, 1408. 
 
 for structural steel, 1410. 
 
 linseed-oil, 1405. 
 
 materials employed for, 1403. 
 
 stains, 1405, 1409. 
 
 water paints, 1406. 
 
 wood preservatives, 1407. 
 
 zinc white vs. white lead, 1404. 
 
 Pain tfer's work, measurements of, 1411. 
 Painting, cost of, and quantities re- 
 quired for, 1411. 
 
 of structural steel, cost of, 1453. 
 
 of wood and plaster, 1407. 
 Parabola, to describe a, 85. 
 Paris, Grand Opera House, 1530. 
 Partitions, fire-proof, 741. See also 
 Fire-proof. 
 
 solid, 745. See also Fire-proof. 
 Party walls, 190. 
 Patent-office drawings, dimensions of, 
 
 1474. 
 
 Paul system of heating, the, 1150. 
 Paving bricks, 1378. 
 People, average weight of, 1474. 
 Perch, number of cubic feet in, 1374. 
 Petrol, cold-water paint, 1406. 
 Philadelphia City Hall, 1535. 
 Phoenix columns, 
 
 details, etc., 440. 
 
 strength of, tables, 484. 
 Pianos, dimensions of, 1471. 
 Piers and buttresses, stability of, 242. 
 Piers, brick, 
 
 bond-stones for, 216. 
 
 bonding of, 2! 6. 
 
 strength of, 214. 
 Pile foundations, 147. 
 
 examples of, 155. 
 
 specifications for, 153. 
 Piles, concrete, 177. 
 Piles, timber, 
 
 bearing power of, 154. 
 
 capping of, 150. 
 
 cost of driving, 157. 
 
 driving of, 148. 
 
 loads on some, actual, 156. 
 
 materials for, 148. 
 
 spacing of, 150. 
 
 specifications for, 153. 
 Pine beams, 
 
 table of stiffness, yellow, 603; 
 white, 606. 
 
 table of strength, yellow, 574; 
 
 white, 578. 
 Pins, for bridge and truss joints, 
 
 bending moment in, how computed, 
 378. 
 
 bending moment in, table, 377. 
 
 shearing and bearing values of, 
 376! 
 
 strength of, 375. 
 
 Pipe (see also Gas-pipe, Steam-pipe, 
 etc.), 
 
 block tin, 1278. 
 
 gas and steam, 1153, 1205. 
 
 lead, 1276. 
 
 seamless drawn nickel silver, 1274. 
 
 tin-lined, 1273, 1277. 
 
 water, 1241. 
 
 Pipe areas, equalization of, 1203. 
 Pipe coverings, 1167. 
 Pipes, capacity of, 1258. 
 Pipes for hot air, 1179, 1183, 1197 
 Piping a house for gas, 1287. 
 Pitch of flat roofs, 1435. 
 
 of rivets, 364. 
 
INDEX. 
 
 1647 
 
 Plank- Quilt. 
 
 Plank flooring, thickness of, 667. i 
 Planks, measurement of, 1399. 
 Plaster, Plasters, 
 
 asbestic, 733. 
 
 fire-proofing qualities of, 732. 
 
 hard wall, 1391. 
 Plaster board, Sacket's, 750. 
 Plaster of Paris, 
 
 cost of, 1393. 
 
 fire-proofing qualities of, 733. 
 Plaster partitions, solid, 745. 
 Plastering, 
 
 cost of, 1393. 
 
 description of operations, terms 
 used, etc., 1389. 
 
 hair for, 1390. 
 
 improved wall plasters, 1391. 
 
 machine-made mortar, 1390. 
 
 measurement of, 1391. 
 
 quantities of materials required for, 
 
 1392. 
 
 Plate and angle columns, details, 440. 
 Plate girders, riveted steel, 618; ta- 
 bles of, 644. 
 
 Plate glass, 1416; price-list, 1420. 
 Plenum system of ventilation, 1216. 
 Plumbing, 1262. 
 
 definitions of terms, 1262. 
 
 drains, 1264. 
 
 lead waste-pipes, 1263, 1266. 
 
 leaders, 1264. 
 
 rules and regulations, City of New 
 York, 1262. 
 
 testing of, 1269. 
 
 traps, 1267, 1269. 
 Plumbing fixtures, dimensions of, 
 
 1471. 
 Plumbing specialties, 
 
 Climax cellar drainer, 1282. 
 
 filters, 1281. 
 
 Kenney flushometer, the, 1281. 
 
 water heaters, 1282. 
 Plunge baths, 1283. 
 Plunger pumps, 1245^ capacity of, 
 
 1247. 
 Polygons, 
 
 areas of, 40. 
 
 definitions, 37. 
 Porous terra-cotta, 730. See also 
 
 Terra-cotta. 
 
 Portal bracing of tall buildings, 1097. 
 Portland cement, 
 
 amount required for mortar, etc., 
 193, 199. 
 
 properties of, 197. 
 
 strength of, for anchoring bolts, 
 
 1507. 
 Portland-cement concrete, 202. See 
 
 also Concrete. 
 
 Portland -cement paint, 1411. 
 Post-caps, 719. 
 Posts, see Columns. 
 Prary improved mill construction, 
 
 708; cost of, 723. 
 
 Pratt truss, shape of, 9275 stress dia- 
 gram, 996. 
 
 Pressure of water, 1231. 
 Price, see Cost. 
 
 Principle of the lever, 235. 
 
 Principles of the arch, 252. 
 
 Prism glass, 1302. 
 
 Prismatic glass, list of Manufacturers, 
 
 1419. 
 
 Prisms, volume of, 65. 
 Private water-supply, 1244. 
 Problems, 
 
 geometrical, 70. 
 
 of the eclipse, parabola, hyperbola, 
 
 and cycloid, 81. 
 Professional practice of architects, 
 
 schedule of charges, 1552. 
 Properties of, see Article in question. 
 Properties of structural shapes, 296. 
 Proportioning gutters and conductors 
 
 to roof surface, 1481. 
 Proportions of concrete, 201, 203. 
 Proportions of mortar, cement, 199; 
 
 cement and lime, 200, 1375; lime 
 
 mortar, 1375, 1385, 1389. 
 Pulleys, rules to determine size and 
 
 speed of, 1513. 
 
 Public buildings, Architects of, 1537. 
 Pumps, 
 
 air-lift process, 1248. 
 Climax cellar drainer, 1282. 
 plunger, 1245; capacity of, 1247. 
 Purlin, Purlins, 891, 943. 
 
 connection to steel roof trusses, 
 
 1073. 
 
 Puzzolan, slag cement, 195. 
 Pyramids, surface, 64; volume of, 67. 
 
 Quadrangular truss, 
 
 description and examples, 928. 
 stress diagrams, 997. 
 Quantity, Quantities of, 
 
 materials for concrete, 203, 205. 
 for mortar, 199, 1375, 1385, 1389. 
 for top coat, cement walks and 
 
 floors, 200. 
 mortar for masonry and plastering, 
 
 199. 
 nails required for different kinds of 
 
 work, 1366. 
 
 Queen -rod trusses, 886; stress dia- 
 grams, 974, 1030. 
 Quilt, cabots, 1402. 
 
1648 
 
 INDEX. 
 
 Radial Roof. 
 
 R 
 
 Radial block chimneys, 1229. 
 Radiating surface, rules for, 1158, 
 
 1163. 
 Radiators for steam or hot water, see 
 
 Steam radiators. 
 Radiators, warm air, 1180. 
 Radius of gyration, see Gyration. 
 Rafters, hip and jack, length and 
 
 bevel, 97. 
 
 maximum span, table, 674. 
 Ram, hydraulic, 1244. 
 Range boilers, diameter of, 1473. 
 Ransome twisted bars, 834. 
 Ready roofings, 1436. v 
 
 Reciprocals, table of, 9. 
 Refrigerators, notes on, 1492. 
 Registers, 1183, 1198; capacity of, 
 
 1200. 
 
 Reinforced concrete, 
 applications of, 820. 
 beams and slabs, see Concrete-steel, 
 history of, 816. 
 theory of, 819, 824. m 
 Reinforced concrete chimneys, 1229. 
 Reinforced concrete floor construc- 
 tions, 
 
 advantages of, 821. 
 arched floor systems, 857. 
 Bromley, 862. 
 Roebling, 858. 
 corrugated flooring, 873. 
 durability of, 819. . 
 fire-proofing qualities of, 734. 
 flat or slab systems, 822, 825; forms 
 
 of reinforcement, 
 barb wire, 833. 
 Columbian ribbed bar, 839. 
 corrugated bar," 855. 
 De Mann twisted tension bar, 
 
 835. 
 
 dovetail corrugated sheets, 848. 
 expanded metal, 825. 
 Kahn trussed bar, 882. 
 lock woven fabric, 826. 
 metallic sheeting, 829. 
 Thacher bar, 855. 
 truss metal lath, 832. 
 twisted bars, 834. 
 welded metal fabric, 831. 
 formulas for strength and area of 
 
 metal, 865. 
 
 Hennebique system, 855. 
 Hinchman-Rentqn system, 833, 856. 
 mechanical principle of, 819, 824. 
 panelled systems, 853. 
 patented systems, 
 
 Berger's multiplex steel-plate 
 
 floor, 850. 
 
 Bruner trussed floor, 847. 
 Columbian system, 839. 
 Golding system, 852. 
 Metropolitan floor, 844. 
 Roebling flat construction, 837. 
 sectional systems, 863. 
 steel framing for, 873. 
 
 Reinforced tile arches, 
 the Herculean Arch, 808. 
 the Johnson long-span floor, 809. 
 Relative hardness of woods, 1509. 
 Relative strength of rectangular 
 
 beams, 570. 
 Residence heating, 1174, 1187, 1191] 
 
 books on, 1198. 
 Resistance, line of, in piers and but- 
 
 f tresses, 245. 
 Resistance, moments of, 278, 282; of 
 
 structural shapes, tables, 296. 
 Resistance (electrical) of copper wire, 
 
 1327. 
 
 Resolution of forces, 231. 
 Rest, definition, 130. 
 Retaining walls, 206. 
 
 of reinforced concrete, 210. ) 
 thickness of, 208. 
 Revolving doors, 1494. 
 Rivets, 
 
 bending moment in, 370. 
 
 dimensions of, 373. 
 
 in plate and box girders, 620, 
 
 625 . 
 
 in steel columns, 432. ^ 
 length of shank required to form 
 
 head, 374. 
 pitch of , 364. 
 shearing and bearing value, table, 
 
 371. 
 
 signs for, 373. 
 steel for, grade of, 333. 
 weight of, 1364. 
 
 Riveted joints, 363; failure of, 365. 
 in steel trusses, 1064. 
 splicing of tie-bars, 367. 
 Riveted girders, steel plate and box, 
 
 618. 
 
 calculations for, 620. 
 example of, 627. 
 splices, 632. 
 
 strength of web plates, 641. 
 tables of, 644. 
 
 weight of, approximate, 626. 
 Rock, 
 
 bearing power of, 137. 
 foundations on, 144. 
 Rock asphalt, 1448; cost of, 1449. 
 Rock- wall .plasters, 1391. 
 Rods, round, tensile strength of, 
 
 340. 
 
 size of head and nut, 1362. 
 upset, 340, 341. 
 Roebling fire-proof floors, arched, 858; 
 
 flat, 837.. 
 
 Roman measures and weights, 36. 
 Roof, Roofs (see also Roofing and 
 
 Roof trusses), 
 fire-proof, see Fire-proof, 
 method of supporting from trusses, 
 
 891, 942. 
 
 Roof loads on trusses, 
 data for computing, 946. 
 examples of computation of, 952. 
 method of computing, 944. 
 snow loads, 949. 
 wind pressure, 950. 
 
INDEX. 
 
 Roof Sand, 
 
 1649 
 
 Roof trusses, 
 
 definition of terms, 883. 
 
 details of steel trusses, 1064. 
 
 details of wooden trusses, 1051. 
 
 fire-proofing of, 760. 
 
 loading of, variations for which 
 
 stresses should be found, 951, 
 
 1024. 
 
 loads on, see Roof loads, 
 proportioning the members to the 
 
 stresses, 1037. 
 spacing of, 943. 
 stress diagrams, 970; for wind pres- 
 sure, 1026. 
 stresses in, determining the, 957, 
 
 970. t 
 
 supporting forces, 967. 
 unsymmetrically loaded, 1004. 
 weight of, 947. 
 wind stress diagrams, 1026. 
 Roof trusses, steel, 
 
 Arched trusses, 932. See also 
 
 Three-hinged arch. 
 Bowstring trusses, 
 
 description and examples, 931. 
 stress diagrams, 1003. 
 Cantilever trusses, 
 
 advantages and disadvantages, 
 
 939. 
 
 example of, 940. 
 principle of, 936. 
 stress diagram, 1014. 
 Cost of, 1453. 
 Fan and Fink trusses, 
 cambering of, 920, 
 depth of, 920. 
 description of, 918. 
 stress diagrams, 984. 
 stresses in, 958. 
 with pin joints, 923, 
 for flat roofs, 923. 
 for pitch roofs, 917. 
 joints of, 1064. 
 Lattice trusses, stress diagrams, 
 
 996. 
 Pratt truss, shape of, 927. 
 
 stress diagram, 996. 
 Proportioning the members of, 
 
 1044. 
 Quadrangular truss, 
 
 description and examples, 928. 
 stress diagrams, 997. 
 Three-hinged braced arches, 
 
 description arid examples of, 
 
 993. 
 
 horizontal resistance, 1019. 
 stress diagrams, 1021. 
 types of, 917. 
 weight and spacing of some steel 
 
 roofs with wide span, 949. 
 Roof trusses, wooden, 
 
 arched ribs, with iron or steel ties, 
 
 911. 
 cantilever trusses, 936. 
 
 stress diagrams, 1014. 
 counter-braces, object of, 887. 
 Fink trusses, with wooden rafters 
 and struts, 910. 
 
 Roof trusses, wooden continued. 
 Hammer-beam trusses, 
 
 description of, 903. 
 
 examples of, 905. 
 
 stress diagrams, 991. 
 Howe trussed, 
 
 counter -braces in, 1013. 
 
 description of, 892. 
 
 joints in, 1056. 
 
 stress diagrams, 977, 982. 
 
 stresses in, formulas, 963. 
 
 table of dimensions, 896. 
 
 unsymmetrically loaded, 1009. 
 joints of, 1051. 
 King and Queen trusses, 885. 
 
 stress diagrams, 970. 
 
 wind stress diagrams, 1027. 
 Lattice trusses, 
 
 description of, 897. 
 
 stresses in, 898. 
 
 table of dimensions, 899. 
 proportioning the members of, 1037. 
 Scissors trusses, 
 
 description of, 900. 
 
 joints in, 903. 
 
 stress diagrams, 989. 
 types of, 884. 
 
 Roofing, Roofing materials (see also 
 the Kind in question), 
 asphalt, 1435. 
 canvas, 707. 
 corrugated iron, 1439. 
 cost of, 942. 
 
 covering for fire-proof roofs, 756. 
 for flat roofs, 941. 
 for pitch roofs, 941. 
 gravel or slag, 1432. 
 least pitch for, 941, 942. 
 papers, 1401. 
 ready, 1436. 
 shingles, 1425. 
 slates, 1426. 
 tile, 1429. 
 tin, 1430. 
 weight of, 946. 
 Ropes, 
 
 hemp and Manila, 353, 356. 
 wire, 352, 355. 
 
 Rosin-sized building papers, 1401. 
 Rubber tiling, 1446. 
 Rubble stonework, 1373. 
 
 s 
 
 Jacket's plaster board, 750. 
 Saints, the, symbols for, 1524. 
 Salt in mortar, 199. 
 Sand and gravel, foundations on, 145. 
 Sand finish, 1390. 
 
 Sand, number of yards to a load, 
 screening weight, etc., 1388. 
 
1650 
 
 INDEX. 
 
 Sand-lime-Stability. 
 
 Sand-lime brick, 1379. 
 
 Sandstones, strength of, 213, 221, 229. 
 
 Sash, glazed, weight of, 1477. 
 
 Sash weights, 1477. 
 
 Scale of Architect's charges, 1552. 
 
 Scantlings reduced to board measure, 
 
 1396. 
 
 Scholarships, travelling, 1565. 
 Schoolrooms, dimensions of, 1475. 
 School seats, 1475. 
 Schools of Architecture, 1562. 
 Scissors trusses, 
 
 description and examples of, 900. 
 joints of, 903, 1059. 
 stress diagrams, 989. 
 Screw ends, upset, 338; dimensions of, 
 
 341. 
 
 Screw-geared blocks, 1516. 
 Screw threads, proportions of, 1361. 
 Screws, kinds, sizes, etc., 1370. 
 Scripture measure, 36. 
 Seating space in churches and the- 
 atres, 1478. 
 
 in schools, 1475. 
 Secants, table of natural, 123a. 
 Section modulus, denned, 498. 
 
 tables for structural shapes, 296. 
 Sectional area to be deducted from 
 
 plates and angles for round holes, 
 
 350, 640. 
 
 Sectional cast-iron boilers, 1137. 
 Sectional coverings for steam-pipes, 
 
 1167. 
 
 Segment arches, 801. 
 Self-sustaining steel chimneys, 1230. 
 Separators for steel beams, 543. 
 Sewer-pipe, 1279. 
 Shafting, horse-power capacity of, 
 
 1516. 
 Shearing, 
 
 examples of, 361, 363. 
 resistance to, 360, 361. 
 strength of rivets, 371. 
 Sheathing, cost of putting on, quan- 
 tity required, 1400. 
 Sheet lead, weights and thicknesses, 
 
 1277. 
 
 Sheet-metal laths, 775. 
 Sheet-metal tiles, 1430. 
 Sheet-metal window frames and sash, 
 
 766. 
 
 Shingles, wood, 
 C9st of, 1426. 
 
 kinds and dimensions of, 1425. 
 number to cover 100 sq. ft., 1425. 
 Shrinkage in castings, 1357. 
 Shutters with wire glass, 767; wood 
 
 covered with tin, 768. 
 Sideboards, dimensions of, 1471. 
 Siding, dimensions of, 1399; quan- 
 tity required, 1400. 
 Signs, arithmetical, 3. 
 Signs for rivets, 373. 
 Silica-Portland cement, 194. 
 Sines, table of natural, 103. 
 Sinks, dimensions of, 1472. 
 Size of, see Dimensions of (see also the 
 
 Article in question). & i 
 
 Skewback, definition, 249. 
 Skewbacks, for hollow tile arches, 792* 
 
 803. 
 Skylights, 
 
 cost of, glass for, 1419. 
 
 covered with translucent fabric, 
 1424. 
 
 in courts, 1304. 
 Slag roofing, 1432. 
 Slate tiles and slabs, 1446. 
 Slates, slater's work, etc., 
 
 characteristics and color, 1426. 
 
 cost of, 1428. 
 
 grading of, 1426. 
 
 laying of, 1427. 
 
 measurement of, 1428. 
 
 sizes of, 1427. 
 
 weight of, 1429. 
 Sleeve-nuts, 336, 338; dimensions of, 
 
 346. 
 Slow-burning construction, see Mill 
 
 construction. 
 Smoke prevention, 1207. 
 Snow, allowance for weight of, on 
 
 roofs, 949. 
 
 Soffit, definition of, 249. 
 Soil-pipe, 1262. 
 Soils, 
 
 bearing power of, 136. 
 
 maximum loads on, as fixed by 
 municipal laws, 139. 
 
 testing of, 136. 
 Solid built beams, 579. 
 Solid partitions, plaster, 745. 
 Span, definition of, 249. 
 Specific gravity of substances, 1341. 
 Specifications for 
 
 asphalt roofing, 1436. 
 
 electric-light wiring, 1338. 
 
 elevators, 1484. 
 
 furnace work, 1185. 
 
 gravel roofing, 1433. 
 
 hot-water heating, 1188. 
 
 painting structural steel, 1413. 
 
 steam heating, 1192, 1194. 
 
 structural steel work, 335. 
 Specifications governing physical 
 properties of structural steel, 331. 
 Speed of elevators, 1483. 
 Speed of gears and pulleys, 1513. 
 Spheres, 
 
 surface of, 62. 
 
 volume of, 65. 
 Spheroids, surface of, 63. 
 Spikes, sizes, number to a pound, etc., 
 
 1367. 
 
 Spires, height of, 1526. 
 Splices in riveted girders, 632. 
 Spread foundations, 158. 
 
 examples of, 169.^ 
 Sprinklers, automatic, 780. 
 Spruce beams, 
 
 table of stiffness, 605. 
 
 table of strength, 577. 
 Square root, 4; table of, 8. 
 Squares, table of, 8. 
 St. Peter's, Rome, 1530. 
 Stability, definition of, 131. 
 
INDEX. 
 
 1651 
 
 Stability Stonework. 
 
 Stability of arches, 256. 
 
 of piers and buttresses, 242. 
 Stacks, see Library. 
 Staff, 1394. 
 Stainless cement, 196. 
 Stains, 1405. 
 Stairs, 
 
 fire-proof, 762. 
 
 notes on, and rules for, 1476. 
 
 of reinforced concrete, 764. 
 
 with ferroinclave treads and risers, 
 
 765. 
 
 Standard building contract, 1555. 
 Standard connections for steel beams, 
 
 546. 
 
 Standard steel classification, 1455. 
 Standpipes, 781. 
 
 State Capitol, Hartford, Conn., 1535. 
 State Capitols, architects of, 1538. 
 Statics, definition of, 130. 
 Steam, 
 
 definitions, 1111. 
 
 drying by, 1117. 
 
 properties of, 1114. 
 
 sensible and latent heat of, 1111. 
 
 superheated, 1111. 
 Steam-boilers, see Boilers, steam. 
 Steam-hammers, for driving piles, 
 
 149. 
 Steam heating, gravity systems, 
 
 boilers for, 1133. See Boilers, 
 steam. 
 
 by direct-indirect radiation, 1127. 
 
 by direct radiation, 1122. 
 
 by indirect radiation, 1129. 
 
 for residences, 1191. 
 
 overhead systems of radiation, 
 1162. 
 
 rules for proportioning radiating 
 surface, 1158. 
 
 rules for size of air ducts, for indi- 
 rect radiation, 1163. 
 
 size of pipes, rules for, 1165. 
 tables for, 1202. 
 
 specifications for, 1192, 1194. 
 
 systems of piping, 1148. 
 
 the Paul system, 1150. 
 Steam heating, non-gravity systems, 
 
 distinction between gravity and 
 non-gravity systems, 1146. 
 
 hot-blast system, 1153. 
 
 return of water to boiler, 1151. 
 
 the Webster system, 1152. 
 Steam-pipe columns, strength of, 465. 
 Steam-pipes, 1153; dimensions and 
 
 data, 1205. 
 Steam-piping, in heating systems, 
 
 covering of, 1166. 
 
 definition of terms, 1147. 
 
 equalization of pipe areas, 1203. 
 
 fittings for, 1153. 
 
 systems of, for hot water, 1171. 
 for steam, 1148. 
 
 valves for, 1155. 
 Steam-radiators, 
 
 classes of, 1122. 
 
 direct, 1123; heating surface and 
 dimensions, 1127. 
 
 ^Steam-radiators continued. 
 
 direct-indirect, 1127. 
 
 efficiency of, 1122. 
 
 indirect, 1130. 
 
 measurement of, 1122. 
 
 pipe, 1124. 
 Steam-valves, 1155. 
 Steam vs. hot-water heating, 1172. 
 Steel, 
 
 chimneys, self-sustaining, 1230. 
 
 constituents of, 327. 
 
 crushing strength of, 407, 454. 
 
 elasticity of, 329. 
 
 expansion of, 330. 
 
 grades of, 328, 333. 
 
 rules for estimating weight of, 1357. 
 
 shearing strength of, 361. 
 
 specifications for, 331. 
 
 standard classification, 1455. 
 
 tensile strength of, 329. 
 
 transverse strength of, 569. 
 
 weight and specific gravity of, 330. 
 
 working strength of, 321. 
 Steel-beam box girders, safe loads, 
 
 537. 
 
 Steel-beam footings, 161; calcula- 
 tions for, 164. 
 
 Steel beams (see also Beams, I-beams, 
 etc.),, 
 
 connections for, 545. 
 
 framing and connecting of, 543. 
 
 in fire-proof floors, computations 
 for strength, 876; tables for, 879. 
 
 separators for, 543. 
 
 standard punching for connection 
 angles, 550. 
 
 strength of, formulas, 550; tables, 
 515. 
 
 wall anchors for, 553. 
 Steel clips, for fastening angles and 
 
 tees, 875. 
 
 Steel columns, see Columns. 
 Steel mill buildings, shop cost of, and 
 
 cost of erecting, 1453. 
 Steel plate and box girders, 618. See 
 
 also Riveted girders. 
 Steel trusses, see Roof trusses, steel. 
 Stiffness of beams, 595, 598; tables, 
 603. t 
 
 of continuous girders, 608. 
 
 of steel beams, 510. 
 Stirrups and joist hangers, 680, 713. 
 Stirrups- in concrete steel-beams, 870. 
 Stirrups, weakness of, when exposed 
 
 to fire, 717. 
 Stone arches, 255. 
 Stone beams, strength of, 573. 
 Stone footings, 178. 
 Stone piers, strength of, 217. 
 Stones, building, 
 
 cost of, 1375. 
 
 crushing strength of, 221, 224, 225. 
 
 fire-proof qualities of , 729. 
 Stone walls, thickness of, 189. 
 Stonework, 
 
 cost of, 1375. 
 
 crushing height of, 217. 
 
 data on, 1373. 
 
1652 
 
 INDEX. 
 
 Stonework Tension, 
 
 Stonework continued, 
 measurement of, 1374. 
 strength of, 213, 214. 
 Storehouse construction, 697. See 
 
 also Mill construction. 
 Strain, definition of, 131. 
 Strains, classification of, 134. 
 
 cross or breaking, see Beams. 
 Street cars, dimensions of, 1473. 
 Streeter's clips for fastening angles and 
 
 tees, 875. 
 Strength 
 
 of materials, defined, 131. 
 
 tensile, safe for building materials, 
 
 322. 
 transverse, for building materials, 
 
 499 569. 
 Strength, of (see also the Article in 
 
 question) 
 
 angles (tensile), 349. 
 bolts in trusses and girders, 382. 
 brick piers, 214, 215, 219. 
 bricks, actual tests, 218. 
 cast iron, 327. 
 
 cast-iron beams and lintels, 554 
 chain, 358. 
 
 columns, see Columns, 
 concrete, 214. 
 
 concrete-steel beams andgirders,866 
 concrete- steel columns, 228. 
 continuous girders, 608. 
 flat bars (tensile), 347. 
 flat bars as beams, 523. 
 hollow tile, 214. 
 hollow tile floor arches. 798, 800, 
 
 802. 
 
 inclined beams, 506. 
 lead pipe, 1278. 
 masonry, 213. 
 mortars, 214, 221, 224. 
 old iron, 359. 
 
 posts, struts, and columns (see Col- 
 umns), 407. 
 rods, 340. 
 
 ropes, hawsers, and cables, 356. 
 steel beams, formulas, 500. 
 tables, 515. 
 
 without lateral support, 509. 
 stones, actual tests, 221. 
 stonework, 213. 
 
 structural steel (as a metal), 327. 
 terra-cotta, architectural, 228, 230. 
 terra-cotta brackets and -consoles, 
 
 230. 
 
 water-pipes, 1242. 
 wire, 351. 
 
 wire ropes, 354, 355. 
 wooden beams, formulas, 562; ta- 
 bles, 574. 
 
 wooden floors, 651, 675. 
 wrought iron, 323. 
 Stress, definition of, 131. 
 Stress diagrams for roof trusses, 970. 
 Stresses in roof trusses, 957. See also 
 
 Roof trusses. 
 
 Structural shapes, properties of, 296. 
 See also I-beams, Channels, An- 
 gles, etc. 
 
 Structural steel (see also Steel), 
 cost of, base price, and extras, 1451. 
 cost of drafting, 1454. 
 of erecting, 1453. 
 of painting, 1413, 1453. 
 data for approximating weight of 
 
 in buildings, 1454. 
 paints for, 1410. 
 shapes of, 296. 
 specifications for, 335. 
 specifications for painting, 1413. 
 Structures, definition of, 130. 
 Strut-beams 
 
 of steel, rules for, 511. 
 of wood, rules for, 568. 
 Struts, steel, strength of, formula, 453; 
 
 tables, 466, 468. 
 Struts in steel trusses, 1047, 1050. 
 
 in wooden trusses, 1039. 
 Styles, see Orders. 
 Sulphur for anchoring bolts, 1507. 
 Supply-pipes, 1273; size of , 1275. 
 Supporting forces, how found, 274. 
 Suspended ceilings in fire-proof con- 
 struction, 757. 
 Switches, electric, 1332. 
 Symbols for the apostles and saints, 
 1524. 
 
 Table, Tables of, see] the Article in 
 
 question. 
 
 Tables, dimensions of, 1470. 
 Tacks, length, size and number to the 
 
 pound, 1367, 1369. 
 Tall buildings, 
 
 heights of, and name of Architect, 
 1531. 
 
 wind bracing of, 1082. 
 Tangents, table of natural, 112. 
 Tanks, 
 
 cylindrical, capacity of, 1259. 
 
 house, 1274. 
 
 rectangular, capacity of, 1261. 
 
 steel, notes on, 1257. 
 
 wooden, construction of, 1252. 
 Tees, T-bars, rolled steel, 
 
 size and properties of , 313. 
 
 small, base price and list of extras 
 on, 1456, 
 
 strength of, as beams, 533. 
 Temperature of fire, 1110. 
 
 of steam, 1114. 
 Tension, Tensile, see also Strength. 
 
 resistance to, 321. 
 
 safe tensile strength of materials, 
 322. 
 
 strength of rods, table, 340. 
 
INDEX. 
 
 1653 
 
 Terra-cotta U. S. 
 
 Terra-cotta arches, see Hollow tile 
 
 arches. 
 Terra-cotta, architectural, 
 
 brackets and consoles, strength of, 
 
 230. 
 
 fire-proof qualities of. 729. 
 weight and strength of, 228, 230. 
 Terra-cotta filling blocks, 797. t 
 Terra-cotta moulded tiles, for interior 
 
 finish, 769. 
 Terra-cotta partitions, 742 ; weight of, 
 
 745. 
 
 Terra-cotta stair-treads, 764. 
 Terra-cotta, structural, 
 dense tiling, 730. 
 porous tiling, 730. 
 semi-porous tiling, 731. 
 comparative advantages of above, 
 
 731. 
 Terra-cotta tiling for fire-proof floors 
 
 (see also Hollow tile arches), 
 cost of, 815. 
 defects in, 732. 
 nature of, 730. 
 setting of, 796. 
 weight of, 792. 
 
 Tests for structural steel, 332. 
 Theatres, 
 
 chairs for, 1478. 
 C9st of, per cubic foot, 1466. 
 dimensions of several, 1480. 
 notes on dimensions of, 1480. 
 seating capacity of several, 1479. 
 space required for seats, 1478. 
 Thermometers, comparison of, 1118. 
 Three-hinged braced arches, 
 description and examples, 933, 
 horizontal resistance of, 1019. 
 a stress diagrams, 1021. 
 Tie-bars, description and data, 336; 
 
 splicing of, 367. 
 Tie-beams, 
 
 built-up (wood), 385; detail of, 
 
 1058. 
 
 in wooden trusses, 1039, 1044. 
 of steel, strength of, 512. 
 of wood, strength of, 569. 
 Tie-rods for arches, formula for, 252, 
 
 263. 
 
 Tie-rods for floor arches, 
 formulas for, 881. 
 rule for, 880. 
 Ties, wooden^ 1042. 
 Tiffany's estimate of depreciation, 
 
 1468. 
 Tile, Tiles, 
 
 enamelled, 1445: cost of, 1447. 
 floor, kinds ot, 1444; cost of, 
 
 1447. 
 
 glass, 1446. 
 marble, 1445. 
 marbleithic, 1446. 
 moulded terra-cotta for interior 
 
 finish, 769. 
 roofing, 1429. 
 rubber, 1447. 
 
 terra-cotta, see Terra-cotta tiling; 
 also Hollow tile arches. 
 
 Timber, reduced to board measure, 
 
 1396. 
 
 Timber footings, 170. 
 Time, measure of, 30. 
 Tin, Tin roofs, 
 cost of, 1432. 
 durability of, 1432. 
 laying the sheets, 1431. 
 number of sheets required, 1432. 
 size, thickness, weight, methods of 
 manufacture, etc., of tin sheets, 
 1430. 
 
 Tin-covered doors and shutters, 767. 
 Tin-lined pipe, 1273, 1277. 
 Tower clocks, dimensions of dials, 
 
 1494. 
 
 Towers, heights of, 1525. 
 Trade references, 1570. 
 Translucent fabric, 1424. 
 Transverse strain or strength, see 
 
 Strength of beams. 
 Traps, for plumbing, 1267. 
 Travelling fellowships and scholar- 
 ships, 1565. 
 
 Treads and risers, rules for, 1476. 
 Triangle of forces, 232. 
 Triangles, defini^ns, 37 ; area of, 40. 
 Trigonometry, Trigonometrical, 
 formulas, 99. 
 
 table of secants and cosecants, 123a. 
 table of sines and cosines, 103. 
 table of tangents and cotangents, 
 
 112. 
 
 Trimmers, strength of, 664, 677. 
 Triplex blocks, 1516. 
 Trough plates, for floors, 873. 
 Truss metal lath, 832. 
 Trussed beams, 586. 
 Trusses, see Roof trusses. 
 
 fire-proofing of, 760. 
 Tubular boilers, 1133; setting of, 
 
 1136. 
 Turnbuckles, 336, 338; dimensions 
 
 of, 345. 
 
 Tuscan Order, the, 1498. 
 Twisted bars for concrete-steel beamf 
 
 and slabs, 834, 867. 
 Types of steel roof trusses, 917. 
 of wooden roof trusses, 884. 
 
 u 
 
 U. S. Capitol, the, description of, 1533. 
 
 U. S. Government buildings, archi- 
 tects of, 1537 ; cost of, 1468. 
 
 U. S. post-offices and court-houses, 
 architects of, 1537. 
 
 U. S. standard gauge for sheet metal, 
 1438. 
 
1654 
 
 INDEX. 
 
 Ultimate Weight. 
 
 Ultimate strength, see Strength. 
 
 definition of, 131. 
 Uniform contract, the, between owner 
 
 and builder, 1555. 
 Unit stress, definition of, 132. 
 Units, electrical, 1308. 
 Upset screw ends, 338, 341. 
 Urinals, dimensions of, 1472. 
 
 Valleys, distinction between open and 
 
 close, 1427. 
 
 Valves, for steam and hot water, 1155. 
 Vault walls, 210. 
 
 Velocity of air due to expansion by 
 heat, 1212. 
 
 of flow of water, 1232. 
 Ventilation, 
 
 amount of air required for, 1210. 
 
 defined, 1209. 
 
 diffusion of air through walls, 1209. 
 
 ducts, shape and material of, 1213. 
 
 fan systems of, 1215. 
 
 fans for, 1218. m 
 
 forced blast in connection with 
 warm-air furnaces , 1218. 
 
 location of inlet and outlet, 1211. 
 
 of traps, 1270. 
 
 plenum or hot-blast system, 1216. 
 
 size of flues, 1211. 
 
 velocity of air due to expansion by 
 heat, 1212. 
 
 velocity of entering air, 1210. 
 
 with furnace heating, 1180. 
 Vent-pipes, 1266, 1270. 
 Volt, definition of, 1306. 
 Volume of solids, 65. 
 Voussoirs, definition of, 249. 
 
 w 
 
 Wall anchors, box, for wooden beams, 
 
 714. 
 
 Wall anchors, for steel beams, 553. 
 Wall hangers, for floor joists, 716. 
 Walls, 
 
 breast, 210. 
 
 brick and stone, 185. 
 
 Walls continued. 
 
 cement block, 190. 
 
 curtain, 190. 
 
 faced with ashlar, 189. 
 
 foundation, 183. 
 
 general rule for thickness of, 188. 
 
 hollow, 189. 
 
 party, 190. 
 
 retaining, 206. 
 
 stone, thickness of, 189. 
 
 thickness of external, 186. 
 
 vault, 210. 
 
 Warehouse construction, see Mill con- 
 struction. 
 
 Washers, for roof trusses, 1062. 
 Washington Monument, the, 1535. 
 Waste-pipes, 1263; least diameter of, 
 
 1275. 
 Water, 
 
 amount of, required for various pur- 
 poses, 1274. 
 
 boiling-point of, 1110. 
 
 discharges through pipes, 1234. 
 
 flow of, in pipes, 1232. 
 
 friction of, in pipes, 1241. 
 
 pressure of, 1231. 
 
 several conditions of, 1110. 
 
 specific heat of, 1113. 
 
 weight of, at different temperatures, 
 
 1112. 
 Water-closets, N. Y. requirements, 
 
 1268. 
 
 Water-heaters, 1282. 
 Water-paints, 1406. 
 Water-pipe, 1241. 
 Water-proof papers, 1401. 
 Water-supply, private, 1244. 
 Wear and tear of building materials, 
 
 1469. 
 
 Webster system of heating, the, 1152. 
 Weight, measures of, 28. 
 Weight of (see also Article in question). 
 
 air, at different temperatures, 1116. 
 
 bars of brass, copper, and lead, 
 1348. 
 
 bells, 1522. 
 
 bolts, 1363. 
 
 bricks, 1378. 
 
 building papers, felts, and quilts, 
 1401, 1403. 
 
 cast-iron column bases, 1360. 
 
 cast-iron columns, 1358. 
 
 cast-iron plates, 1360. 
 
 cast-iron water-pipes, 1243. 
 
 coal, 1342. 
 
 coin, 30. 
 
 copper wire, 1327. 
 
 corrugated sheets, 1442. 
 
 crowds, 653. 
 
 earth, sand, and gravel, 1373, 1388. 
 
 flat-rolled steel bars, 1353. 
 
 glass, 1417, 1419.' 
 
 gravel roofing, 1433. 
 
 hay, 1342. 
 
 hollow tile arches, 792, 794. 
 
 lead pipes, 1276. 
 
 library stacks and books, 1495. 
 
 masonry, 1343. 
 
INDEX. 
 
 1655 
 
 Weight Zinc. 
 
 Weight of continued. 
 
 merchandise, 657 
 
 people, 1474 ; in crowds, 653. 
 
 rafters, table, 947. 
 
 rivets, 1364. 
 
 roofing materials, 946. 
 
 round and square steel bars, 1351. 
 
 sheet lead, 1277. 
 
 sheets of brass, copper, iron, lead, 
 and steel, 1347, 1358. 
 
 slates, for roofing, 1492. 
 
 square and round steel bars, 1350. 
 
 steel, 330, 1357. 
 
 steel in buildings, , approximate, 
 1454. 
 
 steel wire, 1349. 
 
 stones, 1341. 
 
 substances, table, 1341. 
 
 terra-cotta partition tiles, 745. 
 
 tin roofing sheets, 1431. 
 
 trusses, 947. f 
 
 water, at different temperatures, 
 
 1112. 
 
 Welded metal fabric, 831. 
 Wells, deep, 1244. 
 White lead, 1403. 
 Wind, 
 
 force of, 1510. 
 
 pressure against buildings and tow- 
 ers, 1076, 1084. 
 
 pressure on roofs, 950. 
 
 stress diagrams, 1026; for towers, 
 1075. . 
 
 stresses, in buildings, 1085 ; in tow> 
 
 ers, 1075. 
 Wind bracing of tall buildings, 1082. 
 
 buildings which require bracing, 
 1082. 
 
 computation of stresses, 1085. 
 
 examples of, 1085, 1092, 1100. 
 
 intensity of wind pressure, 1084. 
 
 methods of, 1083. 
 
 portal bracing, 1097. 
 Windmills, 1248. 
 Window glass, 1415. 
 Windows, fire-proof, 765. 
 Wire, copper, tables for, 1326. 
 
 iron, Trenton Iron Co.'s list, 351. 
 
 steel, kinds of, 1349. 
 
 steel, tables for, 351, 1349. 
 Wire gauges, 1345. 
 
 Amer. SteeJ and Wire Co.'s, 1349. 
 
 Brown and Sharp. 1320. 
 
 circular mil, 1320. 
 
 comparison of, 1346 
 
 Trenton Iron Co.'s, 351. 
 Wire glass, 765, 1418. 
 Wire laths, 769: 
 Wire nails, 1368. 
 Wire, ropes, 
 
 description of, 352. 
 
 strength of, 354. 
 
 Wiring for electric lighting, see Elec- 
 tric-light wiring. 
 Wiring tables, electrical, 1328. 
 Wood, Woods, 
 
 crushing resistance of, 407. 
 
 fire-proof, 776. 
 
 Wood continued. 
 
 hardness of, 1509. 
 
 preservatives for, 1407. 
 
 shearing strength of, 361. 
 
 stiffness of, 597. 
 
 tensile strength of, 322. 
 
 transverse strength of, 569. 
 Wooden beams, 
 
 built up, strength of, 579. 
 
 keyed beams, 581. 
 
 stiffness of, 595; tables, 603. 
 
 strength of, formulas, 562; tables 
 
 574. 
 
 Wooden columns, see Columns. 
 Wooden floors, 
 
 chapter on, 651. 
 
 framing of, 651, 679. 
 
 live loads, 654. 
 
 maximum span of joists, tables, 671. 
 
 plank flooring, formulas for thick- 
 ness of, 667. 
 
 stirrups and joist hangers, 680. 
 
 strength of, to determine, 675. 
 
 to find size of joists, girders, etc., 
 656. 
 
 weight of, 652. 
 Wooden girders, see Girders. 
 Wooden tanks, construction of, 1252. 
 Wooden trusses, see Roof trusses. 
 Working head, for pumps, 1245. 
 Working strength of, 
 
 Manila ropes, 357. 
 
 masonry, 213. 
 
 steel ties, 331. 
 
 terra-cotta, 230. 
 
 wrought-iron ties, 324. 
 Wrought iron, 
 
 appearance of fractured surface, 
 324. 
 
 Kirkaldy's experiment on, 325. 
 
 old, strength of, 359. 
 
 shearing strength of, 361. 
 
 tensile strength and quality, 323. 
 
 transverse strength of, 569. 
 
 weight of, rules, 1357. 
 
 working strength of, 324. 
 
 Z-bar columns, 
 
 constant dimension, 437, 483. 
 
 description and details, 433. 
 
 strength of, tables, 475. 
 Z-bars, 
 
 size and properties of, 315. 
 
 strength of, as beams, 535. 
 Zinc white vs. white lead, 1404. 
 
ALPHABETICAL INDEX TO ADVERTISEMENTS. 
 
 PAGE 
 
 American Bridge Co 3 
 
 American Luxfer Prism Co , 13 
 
 American Radiator Co 18 
 
 merican Sheet & Tin Plate Co 28 
 
 American Window Glass Co., The. 21 
 
 American Wood Fire Proofing Co., Ltd 16 
 
 \.rt Metal Construction Co 16 
 
 AUas Portland Cement Co 14 
 
 Barrett Manufacturing Co 17 
 
 Brown Hoisting Machinery Co.. The 7 
 
 ^xamberlain Metal Weather Strip Co 11 
 
 Clinton Wire Cloth Co 7 
 
 Columbian Fire-Proofing Co. 5 
 
 Columbus Steel Rolling Shutter Co., The 19 
 
 Crockett Co., The David B 24 
 
 Jutler Manufacturing Co , 22 
 
 DeVeau Telephone Manufacturing Co 25 
 
 Devoe & Co., F. W 26 
 
 )uplex Hanger Co 20 
 
 Gamewell Auxiliary Fire Alarm Co., The 19 
 
 General Fire-Proofing (. o 5 
 
 Globe Ventilator Co 9 
 
 }uastavino Co., R 11 
 
 linchman-Renton Fire-Proofing Co., The 8 
 
 lolophane Glass Co 13 
 
 nternational F. & Fire-Proofing Co., The 6 
 
 ves Co., The H. B 24 
 
 {euffel & Esser Co 28 
 
 liawrence Cement Co., The 15 
 
 d & Bnrnham Co 20 
 
 jorillard Refrigerator Co., The 12 
 
 Maurer & Son, Henry 3 
 
 Menzel & Son, William 20 
 
 Miller, James A. & Bro 11 
 
 Mississippi Wire Glass Co 10 
 
 Mosaic Tile Co., The , 26 
 
 National Fire-Proofing Co 2 
 
 few Jersey Zinc Co., The . 27 
 
 N"ew York Insulated Wire Co 22 
 
 landolph-Clowes Co 18 
 
 Ransome Concrete Machinery Co 4 
 
 iapp, John W 23 
 
 lider-Ericsson Engine Co 9 
 
 Roebling Construction Co., The 4 
 
 Roebuck Weather Strip & Wire Screen Co., The 20 
 
 Sackett Wall Board Co 14 
 
 Snead& Co. Ironworks, The 8 
 
 Standard Table Oil Cloth Co 23 
 
 Toch Brothers, "R.I. W." 24 
 
 Trenton Potteries Co., the 12 
 
 Truss Metal Lath Co 6 
 
 Trussed Concrete Steel Co 7 
 
 Voigtmann & Co 10 
 
 Waddell Manufacturing Co , 14 
 
 Sale & Towne Manufacturing Co., The 1 
 
 I 
 

 CLASSIFIED LIST OF ADVERTISEMENTS. 
 
 ARCHITECTS' REQUISITES. PAGE 
 
 Devoe& Co., F. W 26 
 
 Keuff el & Esser Co 28 
 
 ART METAL WORK. 
 
 Art Metal Construction Co 16 
 
 General Fire-Proofing Co., The 5 
 
 Snead & Co. Iron Works, The t 8 
 
 Yale & Towne Mfg. Co., The.... 1 
 
 ARTISTS' MATERIALS AND MATHEMATICAL INSTRUMENTS. 
 
 Devoe & Co., F. W 26 
 
 Keuff el & Esser Co 28 
 
 ARCHES, FIRE-PROOF. 
 
 Brown Hoist bag Machinery Co., The. 7 
 
 Clinton Wire Cloth Co 7 
 
 Columbian Fire-Proofing Co., The 5 
 
 General Fire-Proofing Co., The 5 
 
 Guastavino Co., R . 11 
 
 Hinchman-Renton Fire-Proofing Co 8 
 
 International F. & Fire-Proofing Co., The 6 
 
 Maurer & Son, Henry 3 
 
 National Fire-Proofing Co 2 
 
 Ransome Concrete Machinery Co ... 4 
 
 Roebling Construction Co., The 4 
 
 Truss Metal Lath Co 6 
 
 Trussed Concrete Steel Co 7 
 
 BATHS. Trenton Potteries Co., The 12 
 
 BOILERS, RANGE. Randolph-Clowes Co 18 
 
 CARVINGS, MOULDINGS, ETC. Waddell Mfg. Co 14 
 
 CEMENT. 
 
 (Portland) Atlas Portland Cement Co 14 
 
 (Portland and Rosendale) Lawrence Cement Co., The 15 
 
 CUTLER PATENT MAILING SYSTEM 22 
 
 DOMESTIC WATER SUPPLY. 
 
 Rider-Ericsson Engine Co 9 
 
 ENGINEERS AND CONTRACTORS. 
 
 American Bridge Company 3 
 
 Snead & Co. Iron Works, The 8 
 
 ENGINEERING INSTRUMENTS. Keuff el & Esser Co 28 
 
 EXPANDED METAL. General Fire-Proofing Co., The 5 
 
 FILING EQUIPMENT. 
 
 Art Metal Construction Co 16 
 
 General Fire-Proofing Co., The 5 
 
 Snead & Co. Iron Works, The 8 
 
 FIRE ALARMS. The Gamewell Fire Alarm Telegraph Co 19 
 
 FINE -PROOF MATERIALS AND CONSTRUCTION. 
 
 American Bridge Co 3 
 
 American Wood Fire-Proofing Co 16 
 
 Art Metal Construction Co 16 
 
 Brown Hoisting Machinery Co., The 7 
 
 Clinton Wire Cloth Co.. . 7 
 
 Columbian Fire-Proofing Co 5 
 
 Columbus Steel Rolling Shutter Co 19 
 
 General Fire-Proofing Co., The 5 
 
 Guastavino Co., R 11 
 
 Hinchman-Renton Fire-Proofing Co 8 
 
 International F. & Fire-Proofing Co 6 
 
 Maurer & Son, Henry 3 
 
 Miller, James A. & Bro 11 
 
 Mosaic Tile Co 2(1 
 
 National Fire-Proofing Co 8 
 
 Ransome Concrete Machinery Co 4 
 
 Rapp, John W 23 
 
 Roebling Construction Co 4 
 
 Sackett Wall Board Co 14 
 
 ii 
 
CLASSIFIED LIST OF ADVERTISEMENTS. 
 
 ATERIALS AND CONSTRUCTION Continued. PAGE 
 
 Sneact & Co. Iron Works, The 8 
 
 Truss Metal Lath Co 6 
 
 Trussed Concrete Steel Co 7 
 
 Voigtmann & Co 10 
 
 GLASS PRISM WINDOW LIGHTS, PRISM GLOBES AND SHADES. 
 
 American Luxfer Prism Co 13 
 
 Holophane Glass Co 13 
 
 GLASS WINDOW. 
 
 American Window Glass Co 21 
 
 Mississippi Wire Glass Co 10 
 
 GREENHOUSES. Lord & Burnham Co. 20 
 
 HANGERS, JOIST, WALL, BEAM. Duplex Hanger Co., The 20 
 
 HARDWARE, BUILDERS'. 
 
 H. B. Ives Co., The. 24 
 
 Yale&Towne Mfg. Co., The 1 
 
 HEATING AND VENTILATING. 
 
 American Radiator Co 18 
 
 Globe Ventilator Co 9 
 
 Lord & Burnham Co 20 
 
 INSULATED WIRES AND CABLES. New York Insulated Wire Co 22 
 
 LATH METAL, DIAMOND MESH, AND HEK RINGBONE. 
 
 General Fire-Proofing Co., The 5 
 
 LAUNDRY TUBS- Trenton Potteries Co., The 12 
 
 LAVATORIES. Trenton Potteries Co., The 12 
 
 LOCKS. Yale & Towne Mfsr. Co., The 1 
 
 MAILING SYSTEM. Cutler Mfg. Co., The 22 
 
 METAL COATINGS. 
 
 Menzel & Son, Wm 20 
 
 Toch Brothers, " R. I. W." 24 
 
 METAL-COVERED WOOD. Rapp John W 23 
 
 OIL CLOTH. Standard Table Oil Cloth Co 23 
 
 PLASTER BOARD. Sackett Wall Board Co 14 
 
 PAINTS, OILS, LEAD, ZINC, ETC. 
 
 Devoe&Co., F. W 26 
 
 Menzel & Son, Wm 20 
 
 New Jersey Zinc Co., The 27 
 
 Toch Brothers, "R.I. W." 24 
 
 PRESERVATIVE COATINGS. 
 
 David B. Crockett Co., The 24 
 
 Toch Brothers, " R. I. W." 24 
 
 PUMPING ENGINES. Rider-Ericsson Engine Co 9 
 
 RADIATORS. American Radiator Co 18 
 
 RANGE BOILERS. Randolph-Clowes Co 18 
 
 REFRIGERATORS. Lorillard Refrigerator Co., The. 12 
 
 ROOFING MATERIALS. 
 
 American Sheet and Tin Plate Co 28 
 
 Barrett Mfg. Co.. The 17 
 
 Brown Hoisting Machinery Co., The 7 
 
 SCREENS WIRE. Roebuck Weather Strip and Wire Screen Co 20 
 
 SHEET STEEL TIN PLATE. American Sheet and Tin Plate Co 28 
 
 SHUTTERS FIRE PROOF. Columbus Steel Rolling Shutter Co 19 
 
 STEAM AND HOT-WATER HEATING. 
 
 American Radiator Co 18 
 
 Lord & Burnham Co 20 
 
 STEEL AND IRON CONSTRUCTIONAL. 
 
 American Bridge Co 3 
 
 Art Metal Construction Co 16 
 
 Brown Hoisting Machinery Co., The 7 
 
 Clinton Wire Cloth Co 7 
 
 Columbian Fire- Proofing Co 5 
 
 Columbus Steel Rolling Shutter Co 19 
 
 General Fire-Proofing Co., The 5 
 
 International F. & Fire-Proofing Co 6 
 
 Ransome Concrete Machinery Co 4 
 
 Roebling Construction Co., The. 4 
 
 Snead & Co. Iron Works, The 8 
 
 Truss Metal Lath Co 6 
 
 Trussed Concrete Steel Co., The 1 
 
iv CLASSIFIED LIST OF ADVERTISEMENTS. 
 
 PAGE 
 
 TELEPHONES . DeVeau Telephone Mfg. Co ?? 25 
 
 TILES AND MOSAICS. Mosaic Tile Co , 26 
 
 TIN PLATE. American Sheet and Tin Plate Co 28 
 
 VARNISH. 
 
 David B. Crockett Co., The 24 
 
 Devoe&Co., F. W 26 
 
 Menzel & Son, Wm 20 
 
 VENTILATION. 
 
 Globe Ventilator Co 9 
 
 Lord & Burnham Co 20 
 
 WALL COVERINGS. Standard Table Oil Cloth Co 23 
 
 WATER-CLOSETS, URINALS, BASINS, ETC. Trenton Potteries Co., The 12 
 
 WATER-PROOF PAINT. 
 
 Menzel & Son, Wm 20 
 
 Toch Brothers, "R.I. W." 24 
 
 WEATHER STRIPS, 
 
 Chamberlain Metal Weather Strip Co 11 
 
 Roebuck Weather Strip and Wire Screen Co 20 
 
 WINDOWS FIRE-PROOF. Voigtmann & Co 10 
 
 WINDOW STOP ADJUSTERS. H. B. Ives Co., The...., 24 
 
 WIRE CLOTH, WIRE LATH, WELDED WIRE, ETC. 
 
 Clinton Wire Cloth Co 7 
 
 WIRE GLASS. Mississippi Wire Glass Co 10 
 
 WIRE INSULATED . New York Insulated Wire Co 22 
 
 WOOD CARVINGS, MOULDINGS, ETC. Waddell Mfg. Co 14 
 
 WOOD FIRE-PROOF. American Wood Fire-Proofing Co 16 
 
 WOOD PRESERVER. Menzel & Son, Wm 20 
 
 ZINC. New Jersey Zinc Co., The : 27 
 
The Yale & Towne 
 Mfg. Co. 
 
 The Yale Lock 
 
 in its originalform revolutionized the art of lock- 
 making ; in its latest 
 form, with Paracen- 
 tric Key, it marks the 
 highest standard of 
 security. It is made 
 in hundreds of styteS 
 and for every possi- 
 ble use. The Genuine all bear our Trefoil Trade Mark.* 
 
 Illustrating the Yale Pin 
 Tumbler Mechanism. 
 
 Builders' Hardware 
 
 embraces door and window trim of all kinds ; our 
 line covers every grade and is the largest in the 
 trade. It includes staple goods of all kinds and 
 numerous mechanical novelties and specialties.* 
 
 The Hardware of Ornament 
 
 comprises decorative metal-work for doors, win- 
 dows and cabinets ; our collection of designs and 
 patterns of this class is by far the largest in the 
 world, and of the highest technical excellence.* 
 
 *Technical literature on this subject furnished to Architect* 
 on request. 
 
 General Offices: 
 
 9-11-13 Murray St., New York City. 
 
National 
 
 Fire- Proof ing 
 
 Company 
 
 New York Boston Philadelphia 
 
 Pittsburg Baltimore Chicago 
 
 Owners of Patents for THE JOHNSON SYSTEM and NEW YORK 
 
 ARCH (Bevier Patent) FOR LONG SPAN CONSTRUCTION 
 
 2 
 
Engineers and Contractors* 
 
 Structural Steel a n d Iron. 
 
 Buildings, Bridges, Roofs, Trusses. 
 
 ompaity 
 
 of New York* ^^ 
 
 Of New York' 
 
 Branch Off ices: 
 
 Atlanta, Ga. 
 Baltimore, Md. 
 Boston, Mass. 
 Buffalo, N. Y. 
 Butte, Mont. 
 Charlestown, W. Va. 
 Chicago, III. 
 Cincinnati, O. 
 Cleveland >O. 
 
 Dallas, Tex. 
 Denver, Col. 
 Kansas City, Mo. 
 Lafayette, Ind. 
 Lansing, Mich. 
 Minneapolis, Minn. 
 New Haven, Conn. 
 New Orleans, La. 
 New York, N. Y. 
 Toledo, Ohio. 
 
 Philadelphia, Pa. 
 Pittsburg, Pa. 
 Portland, Me. 
 Rochester, N. Y. 
 San Francisco, Cal. 
 Salt Lake City, Utah. 
 Seattle, Wash. 
 St. Louis, Mo. 
 Syracuse, N. Y. 
 
 'Phoenix' 
 Hollow Wall Construction 
 
 (Patented) 
 
 Red Clay and Glass Roofing 
 Tiles 
 
 "Herculean" Flat Arch 
 
 (Patented) 
 
 Manufactured by 
 
 HENRY MAURER & SON 
 
 420 EAST TWENTY-THIRD STREET, NEW YORK, N* Y. 
 
 WORKS: MAURER, N. J. 
 
 PHILADELPHIA OFFICE, PENNSYLVANIA BUILDING 
 
 3 
 
The Roebling System 
 
 is now the recognized standard of fire=proof con- 
 struction. It has been used in over five hundred 
 buildings. It is the only system that has withstood 
 actual conflagrations without injury and without 
 the necessity of repairing the construction. It has 
 been adopted for the largest department stores, 
 offices and apartment hotels in the world. 
 
 72=PAGE ILLUSTRATED CATALOGUE 
 ON APPLICATION. 
 
 THE ROEBLING CONSTRUCTION CO. 
 
 FuHer Building, Broadway and 23d St., New York. 
 
 -BRANCHES- 
 
 Philadelphia. Boston. Buffalo. Cleveland. Pittsburg. Chicago. 
 St. Louis. San Francisco. Seattle. 
 
 RANSOME'S TWISTED STEEL 
 
 Is cheaper pound for pound than 
 any other reenforcing metal. 
 Weighs less per foot than any 
 other reenforcing metal of equal 
 strength. Over 2000 tons used 
 per year. Write for circulars. 
 
 RANSOME CONCRETE MACHINERY CO, 
 
 I Broadway, New York City. 
 
 4 
 
COLUMBIAN FIREPROOFING 
 COMPANY 
 
 HOLLOW TILE AND CONCRETE 
 
 FIREPROOFING 
 
 FOR ALL CLASSES OF CONSTRUCTION 
 
 Send for Catalogues 
 
 OFFICES 
 
 NEW YORK, N. Y. PITTSBURG, PA. 
 
 26 W. 26th St. Times Bldg. 
 
 BOSTON, MASS. CHICAGO ILL. 
 
 8 Beacon St. 324 Dearborn St. 
 
 BALTIMORE, MD. SAN FRANCISCO, CAL. 
 
 17 E Saratoga St. Rial to Bldg. 
 
 WASHINGTON, D. C. LONDON, ENG. 
 
 Savings Bank Bldg. 37 King William St. 
 
 MAKERS OP 
 
 EXPANDED METAL 
 
 \\\\\\\\\\\VV\V\\ 
 
 HERRINGBONE LATH. 
 
 THE GENERAL FIREPROOFING CO* 
 
 Main Offices: Youngstown, Ohio. 
 Branches: New York, Chicago, Washington. 
 
 ALSO CONSTRUCTORS OF 
 
 EXPANDED METAL=CONCRETE SYSTEM 
 
 AND 
 
 Designers and tdffidjfez^ Furniture and 
 
 Manufacturers of Wll*M*&t0> Filing Equipment. 
 
THE INTERNATIONAL SYSTEM 
 
 OF 
 
 CONTINUOUS REINFORCEMENT 
 
 FOR 
 
 CONCRETE CONSTRUCTION. 
 
 SCIENTIFIC, PRACTICAL 
 AND ECONOMICAL. 
 
 BOOKLET "D" 
 
 (SENT UPON REQUEST) 
 
 Contains valuable information, shows half-tones and official test! 
 in many prominent buildings. 
 
 THE INTERNATIONAL F. & FIREPROOFINQ CO. 
 
 COLUMBUS. OHIO. 
 
 Truss Metal Lath Co. me 
 
 MANUFACTURERS OP 
 
 Kuhne's Sheet Metal Structural Element 
 
 PATENTED 
 
 STEEL CONCRETE CONSTRUCTION 
 15-25 Whitehall St NEW YORK OH 
 
A REINFORCING MATERiAL 
 
 FOR CONCRETE ROOFS, FLOORS, WALLS, PARTITIONS, STAIRWAYS, ETC, 
 
 THE BROWN HOISTING MACHINERY CO, 
 
 NEW YORK CLEVELAND PITTSBURG 
 
 CLIfTON 
 
 WELDED [FABRICS 
 
 FR 
 
 CONCRETE ANJ> FIRE-PROOF 
 CONSTRUCTION, 
 
 1! 
 ife 
 
 AllSO 
 
 WIPE I LATH 
 PLAIN ANEJI STIFFENED. 
 
 CLINTON WIRE CLOTH CO. 
 
 CUNTOkMASS. 
 
 BOSTON, NEW YORK, CHIC AGO, SAN FRANCISCO 
 
 Do you employ in your reinforced=concrete structures 
 
 THE KAHN SYSTEM? 
 
 MADE FROM ONE PIECE. CATALOG D TELLS HOW 
 
 Contractors everywhere can increase their profits 
 
 Designs free. Write to 
 
 TRUSSED CONCRETE STEEL CO., 
 Detroit, Mich. Dept. I. 
 
 7 
 
THE SNEAD & CO. IRON WORKS, 
 
 MANUFACTURERS OF 
 
 Structural and Ornamental Iron and 
 Bronze Work for Buildings. 
 
 METAL BOOKSTACKS for LIBRARIES. 
 
 Office and Works : Pacific Avenue Station 
 Foot of Pine Street, C. R. R. of N. J. 
 
 JERSEY CITY, N. J. 
 
 THE HINCHMAN-RENTON 
 
 FIRE-PROOFING CO, 
 
 FIRE -PROOF CONSTRUCTION; CONCRETE 
 AND CEMENT WORK OF ALL DESCRIPTIONS 
 
 J8J5 Arapahoe Street 
 DENVER COLORADO 
 
 Our systems are universally used in the West in the 
 
 largest fire-proof buildings. Write for 
 
 Catalogue giving details. 
 
 ASSOCIATE OFFICES: 
 
 The Pacific Fire-Proofing Co,, 328 Crossley Bldg,, San Francisco, California, 
 The Hinchman-Renton Construction Co,, 925 Holland Bldg,, St, Louis, Mo, 
 TheHinchman-Renton Fire-Proofing Co,, 110 N, Main Street, Pueblo, Colorado, 
 The Utah Fire-Proofing Co,, 66 W, Second South St., Salt Lake City, Utah. 
 8 
 
DOMESTIC WATER SUPPLY, 
 
 Without depending on the Wind. 
 
 THE IMPROVED RIDER AND 
 
 IMPROVED ERICSSON HOT=AIR 
 
 PUMPING ENGINES. 
 
 In use lor Twenty-! ve years. 
 MORE THAN 20,000 SOLD. 
 
 Specified by the Leading Architects of 
 this Country 
 
 Catalogue on Application to nearest store. % 
 
 RIDER-ERICSSON ENGINE *CO M 
 
 ARR 
 >RA 
 
 THE 
 
 35 WARREN ST., NEW YORK 
 239 FRA Kl IN sT , BOSTON 
 
 40 DEARBORN ST., CHICAGO. 
 40 N 7th ST., PHILADELPHIA. 
 
 'GLOBE' VENTILATOR 
 
 ^USTHD 
 
 " Globe Ventilated Ridging" 
 
 msr 
 
 COPPER AND GALVANIZED IRON. 
 
 Symmetrical. 
 Efficient. 
 Stormproof. 
 Ornamental. 
 Extensively Specified. 
 Largely Used. 
 
 Send for Model, Catalogue, or 
 Blue Print. 
 
 MANUFACTURED BY 
 
 GLOBE YEHTILATBR Co., 
 
 TROY, N. Y. 
 
 PATENTED 
 
 Feb. 29, 1876. May 9, 1876. 
 May 29, 1888. Nov. 28, 1893 
 Deo. 6, 1893. Jaa.30.lS84. 
 
"flississippi Wire Glass" 
 
 The Approved Fire Stop 
 
 For Skylights, Elevator Doors, Shaft Openings, Fire Doors, Fire Windows 
 and all Roof, Floor and Wall Openings Exposed to Fire Hazard. 
 Recommended by the 
 
 NATIONAL BOARD OF FIRE UNDERWRITERS 
 NATIONAL FIRE PROTECTION ASSOCIATION 
 INSURANCE ENGINEERING EXPERIHRNT STATION 
 BRITISH FIRE PREVENTION COMA* r EE 
 INTERNATIONAL ASSOCIATION O* IRE ENGINEERS 
 and BUILDING, INSPECTION AND RAT1N BUREAUS 
 (From The Many Testimonials Addressed Us) 
 
 FIXED VALUES 
 
 " It retards fire withoutltiiding it permits the blaze to declare itself." 
 
 " It can be cracked, but it cannot be scattered. If fractured it retains 
 
 its place." EDWARD F. CROKER, 
 
 Chief, Fire Department, New York. 
 
 " The Most Satisfactory Fire Protection in Windows." 
 
 D. H. BURNHAM & CO., 
 
 Architects, Chicago, San Francisco, Philadelphia, Buffalo, New Orleans. 
 THICKNESSES-i-4, 3-8 and 1-2 inch 
 SIZES Up to 40 inches wide and 100 inches (and over) long 
 
 " The buildings found standing, after the fire, in which business could be 
 transacted, were the buildings in which wire glass had been employed to protect 
 openings in roofs and walls." 
 
 "Architect and Brtilders 1 Journal, Baltimore" 
 
 For additional information address 
 
 MISSISSIPPI WIRE GLASS CO., 
 ^ 277 Broadway, Itew York. 
 
 Increases 
 
 Rent 
 
 Values 
 
 Fire Barriers 
 Affording: Life 
 and Ventilation 
 
 Decreases 
 
 Fire 
 
 Premiums 
 
 The Voigtmann Adjustable Guide Window 
 Interior View Showing Sash Weights. 
 
 The Voigtmann Standard Automatic Clos- 
 ing and Locking Windows a Specialty 
 
 VOIGTMANN & COMPANY 
 
 Manufacturers under Patents of THEIR SPECIALTIES IN 
 
 IVl PT A I I If* WINDOW FRAMES 
 
 ITlC 1 /VlwlwlV AND SASHES & J, 
 
 For Carrying Wire and Plate Glass 
 
 In accordance with the requirements demanded by Fire Insurance Underwriters 
 and Building Departments. Generally acceptable in lieu of 
 ' common windows and fire shutters. 
 
 42-54 East Erie Street, CHICAGO 
 
 430 WEST i 4 TH STREET 
 427 WEST I3TH STREET 
 
 VODIf 
 IUKA 
 
 10 
 
 Telephone 
 
 771 Chelsea 
 
buildings in the Ui ited States are 
 equipped with 
 
 Ghamberlin Metal ffea'Jier Strips. 
 
 Permanently equipped, too. 
 Installed in over 400,000 Windows. 
 
 Highest Award Buffalo, 1901. 
 Gold Medal St. Louis, 1904. 
 
 SEND FOJR CATALOGUE. 
 OFFICES IN PRINCIPAL CITIES. 
 
 James A. Miller & Bro. 
 
 129-131 S. CLINTON ST., CHICAGO. 
 Manufacturers of 
 
 SHEET METAL WINDOW FRAMES AND SASH 
 
 (Galvanized Iron or Copper) 
 GLAZED WITH 
 
 JWIRE GLASS 
 
 (Rough, Ribbed or Polished) 
 
 Sliding or Pivoted 
 
 UNDER OUR OWN PATENTS 
 
 All under the Specifications and to the Approval of the National 
 Board of Fire Underwriters. 
 
 R. GUASTAVINO CO., 
 
 Fire = Proof Construction. 
 
 No. 49 EaLst 19th Street, New York. 
 No. 19 Milk Street. Boston, Mass. 
 
 SOflE PUBLIC WORK CONTAINING THIS SYSTEfl : 
 
 Metropolitan Museum of Art Union Club Hall of FameArt and 
 Science Building City Hall Station Subway, all of New York. Boston Pub- 
 lic Library Minnesota State Capitol, St. Paul. 
 
 u 
 
"LORILLARD" 
 
 \ REFRIGERA TOR 
 
 Is the Standard. Established 1877. 
 
 FOR FAfllLIES, HOTELS, 
 
 CLUBS, INSTITUTIONS, 
 STEAflSHIPS, ETC. 
 
 Drawings, Estimates and Specifications given on receipt of plans 
 and statement of requirements. 
 
 SEND FOR CATALOGUE AND INFORMATION. 
 
 THE LORILLARD REFRIGERATOR COMPANY, 
 23 West 34th Street, New York. 
 
 Solid Porcelain 
 
 Bath Tubs, 
 Laundry Tubs, 
 
 Sinks, 
 Lavatories, etc. ** 
 
 Siphon Jets, 
 Siphon Hoppers, 
 
 Washouts, 
 Urinals, Basins, 
 
 Made in Earthenware or 
 Vitrified China. 
 
 Special Designs for Decorated Bath Rooms. 
 
 All goods STANDARD make and guaranteed. 
 
 We are the largest manufacturers of Sanitary Wan 
 in the world, and employ the finest mechanical talent. 
 
 The Trenton Potteries Co. 
 
 TRENTON, V. J., U. S. A. 
 
AMERICAN 
 
 LUXFER PRISM 
 
 COMPANY 
 
 346-348 Wafaash Avenue, CHICAGO 
 
 LUXFER PRISMS 
 
 for lighting dark stores 
 
 LUXFER SHEET PRISMS 
 
 for office, school and factory buildings 
 
 LUXFER SIDEWALK PRISMS 
 
 for lighting dark basements 
 
 LUXFER PRISM SKYLIGHTS 
 
 Write for 
 descriptive booklet 
 
 LUXFER FIREPROOF 
 WINDOWS 
 
 DISTRIBUTING AGENCIES: 
 
 NEW YORK 160 Fifth Ave. BOSTON 15 Federal St. ST. PAUL 402 Drake Block. 
 
 KANSAS CITY 948 N. Y. Life Bldg. CLEVELAND 1022 Garfield Bldg. 
 
 SAN FRANCISCO 121 New Montgomery St. 
 
 ECONOMY IN LIGHTING, 
 
 DURABILITY, 
 ARTISTIC EFFECT, 
 
 MAXIMUM LIGHT-COMPLETE DIFFUSION-MINIMUM GLARE 
 
 GOLD MEDALS: Antwerp, Paris, Buffalo. 
 
 Compound Prism Globes and Shades Sri* 
 
 HOLOPHANE GLASS CO., 
 
 S East 32d Street, NEW YORK. 
 
 13 
 
A I LAS 
 
 PORTLAND 
 
 CEMENT 
 
 Is the Standard American Brand. 
 
 Used by all the leading Engineers and 
 Contractors throughout the United States, 
 and preferred by the U. S. Government 
 
 ATLAS PORTLAND CEMENT CO., 
 
 30 BROAD STREET, NEW YORK, 
 
 SACKETT PLASTER BOARD. 
 
 A FIRE RESISTANT SUPERIOR TO WOOD AND METAL LATH. 
 
 In the construction of plastered walls and ceilings 
 SAVES TIME IN CONSTRUCTION 
 
 Made in Boards, 32 x 36 inches, of INCOMBUSTI- 
 BLE MATERIALS. Nailed directly to the 
 studding and finished with plaster. Walls and 
 ceilings constructed on Sackett Plaster 
 Board will not fall are ^ re > heat, cold and 
 sound resisting. 
 
 Sample and Circular on Application 
 
 SACKETT WALL BOARD CO., 
 
 Whitehall Building, New York. 
 
 WADDELL MFGr. CO., 
 
 Cor. TAYLOR and COLDBROOK STS., GRAND RAPIDS, MICH., U. S. A. 
 
 MANUFACTURERS OF 
 
 Wood Carvings, 
 
 Hand and Machine Carvings, Carved 
 and Pressed Mouldings, Festoons, 
 Newel Posts, Head Blocks, Rope 
 and Twist Balusters, and Ornaments. 
 Over looo designs illustrated in 
 our catalogue and price-list No. 18. 
 Mailed for 8c. in stamps. 
 
15 
 
Metallic Furniture and Fixtures make 
 possible incombustible interiors. These 
 furnishings are artistic, durable, con- 
 venient and sanitary. We manufacture 
 in Steel and Bronze: Counters, Partitions, 
 Desks, Tables and Cases ; also Library 
 Shelving, Fixtures for Vaults and all kinds 
 of Metallic Filing Devices. Vertical Files 
 for Architectural Plates a specialty. Com- 
 plete Equipments furnished for Banks. 
 Our work is pure Cabinet Work in Metal, 
 and particular attention is paid to 
 architectural detail. Plans and estimates 
 furnished on request. 
 
 ART METAL CONSTRUCTION CO. 
 Jamestown, N. Y. 12 Branch Offices. 
 
 AMERICAN 
 
 WOOD FIREPROOFING 
 COMPANY, Ltd. 
 
 Process approved by 
 
 United States Navy, 
 
 Bureau of Buildings, N. Y. City, 
 
 Underwriters' Bureau 
 
 of Fire Protection Engineering. 
 
 This Company's process has attained the highest st dard of 
 tests required by the Bureau of Buildings. 
 
 LARGEST PLANT IN THE UNITED STATES, 
 
 16 
 
Architects, Builders and owners of manufac- 
 turing and commercial buildings everywhere 
 should send for " The Barrett Specification." 
 
 This Booklet is a most con- 
 cise and impartial treatise on 
 the roofing problem. In addi- 
 tion, it presents for your con- 
 sideration a Standard Roofing 
 Specification. 
 
 This Specification is not an 
 advertisement. Its treatment of 
 the subject is from the broad 
 standpoint of over fifty years' 
 actual experience. 
 
 It exploits no brands, it ex- 
 pounds no theories. The facts 
 only are there. 
 
 It is a little X-Ray on a 
 much discussed subject, and 
 should be in a handy place on 
 the desk of every Architect or 
 
 Builder. 
 
 Diagram fully explained in Specification. 
 
 Mailed free on application. 
 
 Barrett Manufacturing Co., 
 
 17 BATTERY PLACE, NEW YORK. 
 
 Chicago. Philadelphia. St. Louis. Cleveland. Cincinnati. Allegheny. 
 Minneapolis. Kansas City. New Orleans, 
 
 17 
 
AMERICANA ADIATOI^ COMPANY 
 
 Makers of the 
 
 AMERICANxlDEAL 
 
 /I RADIATORS ^ [BOILERS 
 
 14 Branch Offices and 20 Warehouses at prom- 
 inent shipping points throughout the 
 United States 
 
 General Offices 
 
 282-284 Michigan Ave., CHICAGO 
 
 RANDOLPH-CLOWES CO., 
 
 WATERBURY, CONNECTICUT, 
 SOLE MANUFACTURERS OF 
 
 nnnmmi nnnTurnon 
 
 SEAMLESS DRAWN COPPER 
 RANGE BOILER. 
 
 The only boiler which has no longitudinal seam. 
 
 18 
 
The Gamewell Auxiliary Fire Alarm Service 
 
 Furnishes any desired number of interior stations 
 from which Fire Alarms can be instantaneously 
 transmitted to Fire Department Headquarters. 
 
 This service is installed in thousands of Hotels, 
 Hospitals, Theatres, Office Buildings as well as in 
 Mercantile and Manufacturing concerns in New York 
 and many other cities. 
 
 For particulars address 
 
 THE GAMEWELL AUXILIARY FIRE ALARM CO., 
 19 Barclay Street, 
 
 New York City. 
 
 THE "COLUfiBUS" SSffSf 
 
 COLUMBLS, OHIO 
 
 The Best Door ever made for 
 
 Car Barns, Freight Houses, Warehouses, 
 Elevator Openings 
 
 FIRE PROOF AND CONVENIENT 
 
 Ask for Catalog and Sample 
 
 ii Broadway, New York. 
 ^. j^ 100 Lake St., Chicago. 
 
 3! *Qy 29 New Montgomery St., San Francisco. 
 
 222 Globe Building, Seattle. 
 66 Exchange St., Buffalo. 
 329 First Ave., Pittsburg. 
 
 315 Dwight Bldg., Kansas City. 
 8BCTH)N Odd Fellows Bldg., St. Louis. 
 
Is of a bright nut-brown color, which is very attract- 
 ive and brings out the grain or fibre of the wood to ad- 
 vantage, and this fact added to its acknowledged wood- 
 preserving- qualities, causes many of our most promi- 
 nent Architects to specify it regularly on Wooden 
 Buildings, Shingle Roofs, half timber Work, Verandahs, 
 Porches, beam ends and wherever woodwork is ex- 
 posed to moisture or climatic changes. Its disinfecting 
 qualities make it especially advantageous for Hospitals 
 and Stables, keeping them clean and healthy. 
 
 It soaks into the wood readily, destroys the albumi- 
 nous matter, which is the cause of rot or decay, leaves 
 the pores opon, permitting no Dry Rot to occur, and covers about 300 to 350 feet 
 of Dressed Lumber per gallon. For further particulars or samples apply to 
 
 WM. MENZEL & SOW, Sole Agents, 68 Broad Street, New York. 
 
 Eastern Agents for E, & S, Marble Enamel Paint and Compound Elastic Iron Paint. 
 
 Conservatories, Qreen= 
 houses, Vineries, etc., 
 
 ERECTED, HEATED, AND VENTILATED. 
 Catalogue upon application. 
 
 LORD & BURNHAM COMPANY, 
 
 New York Office: 
 1133 Broadway. 
 
 General Office and Works: 
 
 Irvington=on=Hudson, N. Y. 
 
 GEO, E, ROEBUCK, 
 President, 
 
 ESTABLISHED 1858 
 
 N. Y. TELEPHONE, CORTLANDT 215 
 BROOKLYN TELEPHONE, SOUTH 298 
 
 S, H, ROEBUCK, 
 Sec, & Treas, 
 
 The Roebuck Weather Strip & Wire Screen Co. 
 
 Wire Screens for Windows and Doors 
 made to Order in all Woods. 
 
 CABINET FINISH. 
 
 !72 Fulton Street, New York City. 
 
THE 
 
 AMERICAN 
 
 WINDOW GLASS 
 
 COMPANY 
 
 MANUFACTURERS OF 
 
 WINDOW GLASS 
 
 GROUND AND CRYSTALLIZED GLASS 
 
 We Guarantee our Product superior to any 
 Sheet Glass made 
 
 OFFICES 16th Floor Farmers Deposit National Bank Building, 
 Fifth Ave. & Wood Street, 
 
 PITTS3URQ, PA. 
 
 21 
 
THE CUTLER PATENT 
 
 MAILING SYSTEM 
 
 U. S. MAIL CHUTE 
 
 affords the only means of posting letters 
 in the upper stories of buildings. A let- 
 ter once in the chute is officially "mailed." 
 
 INSTALLED IN CONNECTION WITH 
 THE U. S. FREE COLLECTION SER- 
 VICE ONLY BY THE SOLE MAKERS, 
 
 THE CUTLER MFG. Co., 
 
 ROCHESTER, N. Y. 
 
 The Double Chute equipment, as installed in the more important 
 buildings, makes cleaning and repairs possible without interruption 
 of the Mail Service. 
 
 ALL OUR WIRES 
 
 NAT'L BOARD OF FIRE UNDERWRITERS 
 STANDARD. 
 
 NEW YORK INSULATED WIRE CO* 
 
 Main Office: I 14 Liberty Street, N. Y. 
 
 BRANCHES : 
 
 CHICAGO, 192 DESPLAINES STREET j BOSTON, 7 OT.S [STREET; 
 SAN FRANCISCO, 33 SECOND STREET. 
 
 9,9. 
 
THE HOUSE IMMACULATE, 
 
 Lotus Lodge at the St. Louis World's 
 Fair was built to demonstrate the beauty 
 and usefulness of SAN IT AS, the wash- 
 able Wall Covering SAMTAS iv- 
 ceived the highest award. It has a cloth 
 foundation, is decora led in cil colors, 
 applied to the wall like paper, is inex- 
 pensive, practical at d durable, ^old in 
 handsome plain colors, burlaps and 
 prints in dull finish. Glazed Tiles for 
 Kitchens and Bath-rooms. 
 
 Send for prices and Booklet No. 16. 
 
 Standard Table Oil Cloth Company, 
 
 320 BROADWAY, NEW YORK. 
 
 JOHN W.' RAPP, 
 
 Patent Metal Covered Doors, Windows, 
 and Interior Trim 
 
 FURNISHED AS CHEAP AS HARD WOOD. 
 
 Works: COLLEGE POINT, L. I. 
 Office : 156 FIFTH AVE., NEW YORK CITY. 
 
Architects 
 Who Know 
 
 specify " CROCKETT'S " a superior article 
 known by a trade-mark which is borne by 
 
 Wo. I. Preservative (for interior use). 
 Waterproof Floor Finish (for floors and floor 
 
 coverings). 
 Spar Composition (for all exterior work). 
 
 Liquid Pigment Filler (for all woodwork). 
 
 THE DAVID B. CROCKETT CO., BRIDGEPORT, CONN. 
 
 CROCKETT'S 
 
 IVES PAJEIMT 
 
 WINDOW STOP 
 ADJUSTERS 
 
 Prevents Drafts, Dust , Binding and 
 Rattling. The only stop adjuster made 
 from one piece of metal with a thick bed 
 that will not cup or bend in tightening 
 the screw. Working model with cata- 
 logue mailed free. 
 
 THE H. B. IVESICO 
 
 ., U. 8, A. 
 
 Whoever specifies or uses a corrosive oxide paint for the 
 protection of steel or iron commits a 
 
 tal 
 
 and if you want to know the reason why write to TOCH 
 BROTHERS, 468=472 West Broadway, New York, 
 who manufacture the " R. I. W." DAMP-RESISTING 
 
 PAINT and various other good paints, and they will send 
 you a scientific treatise on this subject which will interest 
 you, and which contains profitable information. Write to 
 us. We will send you free of charge a pamphlet entitled 
 < The Chemistry of Paint and Raw Materials/' 
 
 9A 
 
DeVeau Automatic Switchless Telephones 
 
 For Intercommunicating Systems. 
 Specified by Leading Architects and Engineers. 
 
 Catalogue 157 
 
 Send for our Seven Systems, containing Specifications, Com- 
 plete Information, and Wiring Diagrams for all 
 Intercommunicating Systems. 
 
 DEVEAU TELEPHONE MFU CO. 
 
 27 Rose Street NEW YORK CITY 
 
 25 
 
p. GU. DEVOE & CO. 
 
 (ESTABLISHED 1754.) 
 The Oldest and Largest Paint Manufacturing Concern in the United States. 
 
 PURE PAINTS, for all purposes. 
 FINE VARNISHES, for all purposes. 
 
 "ATRAMENT" RUST PREYE-NTATIYE PAINT, 
 
 HOUSE PAINTS, 
 
 FACTORY PAINTS, 
 
 BRIDGE PAINTS, 
 
 MACHINERY PAINTS. 
 
 ARTISTS' MATERIALS of all kinds. 
 
 MATHEMATICAL INSTRUMENTS, PAPERS, ETC. 
 
 CATALOGUES SENT. CORRESPONDENCE INVITED. 
 
 NEW YORK AND CHICAGO. 
 
 THE 
 
 MOSAIC TILE 
 COMPANY, 
 
 MANUFACTURERS OF 
 
 FLOOR TILE, 
 
 Glazed Ceramic, Plicaro Mosaic, 
 
 Floor Tiling applied directly to wood 
 floors without concrete foundation. 
 
 Special water-color designs furnished upon application accompanied 
 with floor plans. 
 
 Station A. Factory at ZANESVILLE, OHIO. 
 
 26 
 
The Elements 
 
 Are the only legitimate despoilers of 
 paint. Paint that chalks, cracks, 
 scales, darkens, or discolors from in- 
 herent weakness is not good paint, 
 and should be avoided in the speci- 
 fications of the careful architect. 
 
 Combination 
 
 4f * """ 
 
 Paints 
 
 Based on Zinc White have no inher- 
 ent defects. The elements wear 
 them out in time, but they do not 
 decay, nor darken, nor change color. 
 The careful architect, who values 
 permanence of color and material, 
 will specify a preponderating propor- 
 tion of Zinc White. 
 
 The New Jersey Zinc Company, 
 
 71 Broadway, New York. 
 
 See our terse practical treatises : 
 
 "The Paint Question," " Paints in Architecture/' 
 "Why, How and When." (French Government Decree.) 
 
 Mailed free. 
 87 
 
" The Best is the Cheapest" 
 
 The BEST ROOF is made of 
 
 MF Roofing Tin 
 
 It has held during the last sixty years 
 Trade Mark the flost Favored and leading place in 
 the race for superiority in Roofing Materials 
 
 '& 
 
 '* * 
 PITTSBURGH 
 
 The BEST METAL CORNICES 
 
 are made of 
 
 Apollo Best Bloom 
 Galvanized Sheets 
 
 The trade mark signifies the highest standard of reliability. The 
 easy working qualities of the,. Metal rthakgnti^hpfn r^nV of the Metal 
 Worker. When in. need of^galvani|id sheetjgJfSL^construction work, 
 don't be satisfied \vith substitutes, insisbon the genuine^.^-^ 
 
 .'" Our Products are for sale by all Metal Houses \- 
 
 American Sheet & Tin \plate CbTta piny 
 
 PITf SBURQH PA. ":" '- "" 
 
 KEUFFEL & ESSER CO,, 
 
 727 FULTON ST., NEW 
 
 BRANCHES: 
 
 111 Madison St., Chicago ; 708 Locust St., St. Louis ; V 
 303 Montgomery St., San Francisco. 
 
 Manufacturers and Importers of 
 
 DRAWING MATERIALS, 
 SURVEYING INSTRUMENTS. 
 
 Paragon, Key, and other Brands Drawing Instruments. 
 
 Paragon, Anvil, Universal, Normal, and Duplex Drawing Papers. 
 
 Standard Profile and Cross=section Papers, Cloths, and Books. 
 Helios, Columbia, and Parchmine Blue Print Papers. 
 
 Maduro Brown Print Paper. 
 Nigrosine and Umbra Positive Black Process Paper. 
 
 K. & E. Co.'s Patent Adjustable and Duplex Slide Rules. 
 Thacher's Calculating Instrument. 
 
 Paragon Scales, with White Edges. Patent Triangular Scales, 
 Triangles, T Squares, Drawing Boards and Tables. 
 Columbia and Kallos Indelible Drawing Ink. 
 
 TRANSITS, LEVELS. 
 
 SUPERIOR CONSTRUCTION; ACCURACY AND WEAR GUARANTEED. 
 
 Architects' Convertible Levels, Surveying and 
 
 Prismatic Compasses, Aneroid Barometers.etc. 
 
 Surveyors' Chains, Rods, Poles, etc. 
 
 We Warrant all our Goods ! 
 
 K.&E, Steel and Metallic Tapes. 
 
 Catalogue 500 Pages sent free on Application. Write for 
 our Pamphlet on " Photo, printing from tracings." 
 28 
 
Consulting Engineer 
 
 cCf 
 JMSON 8TS,, SAN ** K 
 
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 University of California Library 
 
 or to the 
 
 NORTHERN REGIONAL LIBRARY FACILITY 
 Bldg.40CX Richmond Field Station 
 University of California 
 Richmond, CA 94804-4698 
 
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 1-year loans may be recharged by bringing 
 books to NRLF 
 
 Renewals and recharges may be made 4 
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 DUE AS STAMPED BELOW 
 
 NOV 1 G 2001 
 
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 UNIVERSITY OF CALIFORNIA LIBRARY