THE DESIGN OF STEEL MILL BUILDINGS AND THE CALCULATION OF STRESSES IN FRAMED STRUCTURES BY MIL.O S. KETCHUM, C. E. ' Assistant Professor of Civil Engineering, University of Illinois: Associate Member American Society of Civil Engineers; Member Society for Promotion of Engineering Education. FIRST EDITION NEW YORK: THE ENGINEERING NEWS PUBLISHING CO. 1903. / A L GENERAL Copyright, 1903, by MILO S. KKTCHUM. PRESS OF BURT-TERRY-WILSON CO. LAFAYETTE, IND. PREFACE This book is intended to provide a short course in the calculation of stresses in framed structures and to give a brief discussion of mill building construction. The book is intended to supplement the elemen- tary books on stresses on the one hand, and the more elaborate treatises on bridge design on the other. While the book is concerned chiefly with mill buildings it is nevertheless true that much of the matter will apply equally well to all classes of steel frame construction. In the course in stresses an attempt has been made to give a concise, logical and systematic treatment. Both the algebraic and graphic methods of calculating stresses are fully described and illustrated. Each step in the solution is fully explained and analyzed so that the student will get a definite idea of the underlying principles. Attention is called to the graphic solutions of the transverse bent, the portal and the two-hinged arch, which are believed to be new, and have proved their worth by actual test in the class room. The diagram for finding the stress in eye-bars due to their own weight is new, and its use will save considerable time in designing bridges. In the discussion of mill building construction the aim has been to describe the methods of construction and the material used, together with a brief treatment of mill building design, and the making of esti- mates of weight and cost. The underlying idea has been to give methods, data and details not ordinarily available, and to discuss the matter presented in a way to assist the engineer in making his designs and the detailer in developing the designs in the drafting room. Every engineer should be familiar and be provided with one or more of th? standard handbooks, and therefore only such tables as are not ordinarily available are given. iv PREFACE The present book is a result of two years experience as designing engineer and contracting agent for the Gillette-Herzog Mfg. Co., Min- neapolis, Minn., and four years experience in teaching the subject at the University of Illinois. This book represents the course given by the author in elementary stresses and in the design of metal structures, pre- liminary to a course in bridge design. While written primarily for the author's students it is hoped that the book will be of interest to others, especially to the younger engineers. As far as practicable credit has been given in the body of the book for drawings and data. In addition the author wishes to ac- knowledge his indebtedness to various sources for drawings and in- formation to which it has not been practicable to give proper individ- ual credit. He wishes to thank Messrs. C. W. Malcolm, L. G. Parker and R. H. Gage, Instructors in Civil Engineering in the University of Illinois, for assistance in preparing the drawings, especially Mr. Malcolm who made a large part of the drawings. The author will consider it a favor to have errors brought to his notice. Champaign, 111., M. S. K. August 17, 1903. TABLE OF CONTENTS INTRODUCTION PAGE. Steel Frame Mill Buildings I Steel Mill Buildings with Masonry Filled Walls . 2 Mill Buildings with Masonry Walls 3 PART I. LOADS. CHAPTER I. DEAD LOADS. Weight of Roof Trusses 5 Weight of Purlins, Girts, etc 8 Weight of Covering 8 Weight of Structure 9 CHAPTER II. SNOW LOADS. Snow Loads 10 CHAPTER III. WIND LOADS. Wind Pressure 12 Wind Pressure on Inclined Surfaces 13 CHAPTER IV. MISCELLANEOUS LOADS. Live Loads on Floors 17 Weight of Hand Cranes 18 Weight of Electric Cranes 18 Weights of Miscellaneous Material 19 vi TABLE 01? CONTENTS PART II. STRESSES. CHAPTER V. GRAPHIC STATICS. Equilibrium 2O Representation of Forces 20 Force Triangle 20 Force Polygon . 22 Equilibrium of Concurrent Forces 22 Equilibrium of Non-concurrent Forces 23 Equilibrium Polygon 24 Reactions of a Simple Beam 27 Reactions of a Cantilever Truss 28 Equilibrium Polygon as a Framed Structure 29 Graphic Moments 44 Bending Moments in a Beam 31 To Draw an Equilibrium Polygon Through Three Points 31 Center of Gravity 32 Moment of Inertia of Forces , 33 Moment of Inertia of Areas 36 CHAPTER VI. STRESSES IN FRAMED STRUCTURES. Methods of Calculation 37 Algebraic Resolution 38 Graphic Resolution 40 Algebraic Moments 42 Graphic Moments 30 CHAPTER VII. STRESSES IN SIMPLE ROOF TRUSSES. Loads 45 Dead Load Stresses 45 Dead and Ceiling Load Stresses 46 Snow Load Stresses 47 Wind Load Stresses 47 Wind Load Stresses : No Rollers 48 Wind Load Stresses : Rollers 49 Concentrated Load Stresses 51 TABLE OF CONTENTS vii CHAPTER VIII. SIMPLE BEAMS. Reactions 53 Moment and Shear in Beams : Concentrated Loads 54 Moment and Shear in Beams : Uniform Loads 55 CHAPTER IX. MOVING LOADS ON BEAMS. Uniform Moving Loads 57 Concentrated Moving Loads 59 CHAPTER X. STRESSES IN BRIDGE TRUSSES. Method of Loading 63 Algebraic Resolution 63 Graphic Resolution 68 Algebraic Moments 70 Graphic Moments 71 Wheel Loads 74 CHAPTER XI. STRESSES IN A TRANSVERSE BENT. Dead and Snow Load Stresses 75 Wind Load Stresses 75 Algebraic Calculation of Stresses : Case I. Columns Hinged at the Base 76 Case II. Columns Fixed at the Base. . 79 Maximum Stresses 83 Stresses in End Framing 84 Bracing in the Upper Chord and Sides 84 Graphic Calculation of Stresses : Data 85 Case I. Permanent Dead and Snow Load Stresses 86 Case II. Wind Load Stresses ; Wind Horizontal ; Columns Hinged 88 Case III. Wind Load Stresses ; Wind Horizontal ; Columns Fixed at Base 90 Case. IV. Wind Load Stresses: Wind Normal; Columns Hinged 91 Case V. Wind Load Stresses : Wind Normal ; Columns Fixed at Base 93 Maximum Stresses 93 viii TABLE OF CONTENTS CHAPTER XII. STRESSES IN PORTALS. Introduction , 95 Case I. Stresses in Simple Portals : Columns Hinged. Algebraic Solution 96 Graphic Solution 98 Simple Portal as a Three-hinged Arch 100 Case II. Stresses in Simple Portals: Columns Fixed. Algebraic Solution 101 Anchorage of Columns 101 Graphic Solution 103 Stresses in Continuous Portals 103 Stresses in a Double Portal 104 CHAPTEB XIII. STRESSES IN THREE-HINGED ARCH. Introduction . 106 Calculation of Stresses 106 Calculation of Reactions : Algebraic Method 106 Calculation of Reactions : Graphic Method 107 Calculation of Dead Load Stresses 108 Calculation of Wind Load Stresses ....in CHAPTER XIV. STRESSES IN TWO-HINGED ARCH. Introduction 113 Calculation of Stresses 113 Calculation of the Reactions 114 Algebraic Calculation of Reactions 117 Graphic Calculation of Reactions 119 Calculation of Dead Load Stresses in Arch 121 Dead and Wind Load Stresses in Arch 123 Arch with Horizontal Tie 125 Temperature Stresses 126 Design of Two-hinged Arch 127 CHAPTER XV. COMBINED AND ECCENTRIC STRESSES. Combined Direct and Cross Bending Stresses 129 Combined Compression and Cross Bending 131 Combined Tension and Cross Bending 134 TABLE: OF CONTENTS ix Stress in a Bar Due to its Own Weight 135 Diagram for Stress in Bars Due to Their Own Weight 135 Eccentric Riveted Connections 138 PART III. DESIGN OF MILL BUILDINGS. CHAPTER XVI. GENERAL DESIGN. General Principles 141 CHAPTER XVII. FRAMEWORK. Arrangement 145 Trusses Types of Trusses 146 Saw Tooth Roof 149 Pitch of Roof 153 Pitch of Truss '. 154 Economic Spacing of Trusses 154 Transverse Bents 157 Truss Details / 159 Columns 164 Column Details 167 Struts and Bracing 171 Purlins and Girts 173 Design of Parts of the Structure 173 Design of Trusses 173 Design of Columns 177 Design of Girders 181 Crane Girders . 184 CHAPTER XVIII. CORRUGATED STEEL. Introduction 185 Fastening Corrugated Steel 187 Strength of Corrugated Steel 190 Corrugated Steel Details 192 Anti-condensation Roofing ' 201 Corrugated Steel Plans 204 Cost of Corrugated Steel 204 x TABLE OF CONTENTS CHAPTER XIX. ROOF COVERINGS. Introduction Corrugated Steel Roofing 206 Slate Roofing 207 Tile Roofing .210 Tin Roofs 211 Sheet Steel Roofing 213 Gravel Roofing 214 Slag Roofing 216 Asphalt Roofing 217 Shingle Roofs 218 Asbestos Roofing 218 Carey's Roofing 219 Granite Roofing '. 219 Ruberoid Roofing 219 Ferroinclave 220 Examples of Roofs 221 Roof Coverings for Railway Buildings 221 CHAPTER XX. SIDE WALLS AND MASONRY WALLS. Side Walls 223 Corrugated Steel 223 Expanded Metal and Plaster 223 Concrete Slabs 226 Masonry Walls 227 Concrete Buildings 228 CHAPTER XXI. FOUNDATIONS. Bearing Power of Soils 232 Bearing Power of Piles 233 Pressure of Wall on Foundation 235 Pressure of Pier on Foundation , 236 Design of Footings 238 Pressure of Column on Masonry 238 TABLE OF CONTENTS xi CHAPTER XXII. FLOORS. Ground Floors Types of Floors 239 Cement Floors 240 Tar Concrete Floors 242 Brick Floors 242 Wooden Floors 243 Examples of Floors 246 Floors above Ground 248 Timber Floors 248 Brick Arch 248 Corrugated Iron Arch 249 Expanded Metal 250 Roebling 251 "Buckeye" Fireproof 252 Multiplex Steel 253 Ferroinclave 253 Corrugated , 253 Buckled Plates 254 Steel Plate 255 CHAPTER XXIII. WINDOWS AND SKYLIGHTS. Glazing 256 Glass 256 Diffusion of Light . . . 257 Relative Value of Different Kinds of Glass 259 Kind of Glass to Use 259 Placing the Glass 260 Use of Window Shades 261 Size and Cost of Glass 262 Cost of Windows 263 Translucent Fabric 264 Cost of Translucent Fabric 265 Double Glazing 265 Details of Windows and Skylights ^ 265 Amount of Light Required , . 268 xii TABLE; OF CONTENTS CHAPTER XXIV. VENTILATORS. Ventilators 273 Monitor Ventilators 273 Cost of Monitor Ventilators 276 Circular Ventilators 276 CHAPTER XXV. DOORS. Paneled Doors 278 Wooden Doors 278 Steel Doors 279 Cost of Doors 281 CHAPTEB XXVI. SHOP DRAWINGS AND RULES. Shop Drawings 282 Erection Plan . . . : 283 Choice of Sections 284 CHAPTER XXVII. PAINTS AND PAINTING. Corrosion of Steel 286 Paint 286 Oil Paint 286 Linseed Oil 287 Lead 288 Zinc 289 Iron Oxide . 289 Carbon 289 Mixing the Paint 290 Proportions 290 Covering Capacity 290 Applying the Paint . 2QI Cleaning the Surface 292 Cost of Paint 292 Cost of Painting 293 Priming Coat 293 Finishing Coat 294 Asphalt Paint 295 Coal-Tar Paint 295 TABLE: of CONTENTS xiii Cement and Cement Paint 295 Portland Cement Paint 296 References on Paint and Painting 296 CHAPTER XXVIII. ESTIMATE: OF WEIGHT AND COST. Estimate of Weight 297 Estimate of Cost 305 Cost of Material '. 306 Cost of Mill Details 307 Shop Cost 309 Cost of Drafting 310 Actual Shop Costs 311 Cost of Erection 311 Cost of Miscellaneous Material 311 PART IV. MISCELLANEOUS STRUCTURES. Steel Dome for West Baden, Ind., Hotel 315 The St. Louis Coliseum 318 The Locomotive Shops of the Atchison, Topeka and Sant Fe R. R. 323 The Locomotive Erecting and Machine Shop, Philadelphia and Reading R. R 328 The New Steam Engineering Building for the Brooklyn Navy Yard 327 APPENDIX I. Specifications for Steel Frame Mill Buildings 341 STEEL MILL BUILDINGS . INTRODUCTION. Steel mill buildings may be divided into three classes as follows: (i) steel frame mill buildings; (2) steel mill buildings with masonry filled walls; and (3) mill buildings with masonry walls. i. Steel Frame Mill Buildings. A steel frame mill building is made by covering a self-supporting steel frame with a light covering, usually fireproof. The framework consists of transverse bents firmly braced by purlins, girts and diagonal braces. The usual methods of arranging the framework are as shown in Fig. I. (c) FIG. i. An intermediate transverse bent (c), Fig. i, consists of a steel roof truss with its ends supported on steel posts, and is made rigid by knee braces. The posts are either supported on the foundations or are anchored by them. The end bents are made either by running the end posts up to the end rafters as in (a), or by means of an end trussed bent as in (b) Fig. i. The end trussed bent (b) is usually preferred where extensions are contemplated, although the end post bent (a) is equally satisfactory and is usually somewhat cheaper. 2 INTRODUCTION The building is firmly braced transversely by means of bracing in the planes of the upper and lower chords and in the end bents, and longitudinally by means of bracing in the sides and in the planes of the upper and lower chords. The roof covering is supported on steel purlins placed at right angles to the trusses and rafters. The side covering is fastened to horizontal girts which are fastened to the side and end posts. Where warmth is desired the roof and sides are lined. Steel frame mill buildings are usually covered with corrugated iron or steel fastened to sheathing or directly to the purlins and girts. Expanded metal and plaster, or wire netting and plaster has been used to a limited extent for covering the sides and for sheathing the roof, and will certainly be much used in the future where permanent struct- ures are required. In the latter case slate or tile roofing is commonly used. The buildings are lighted by means of windows in the side walls and the clerestory of the monitor ventilator shown in Fig. I, or by means of windows in the side walls and skylights in the roof. Ventila- tion is effected by means of the monitor ventilator shown in Fig. I or by means of circular ventilators. Where glass is used in the clere- story of monitor ventilators the sash are made movable. The glass in the clerestory of monitor ventilators is often replaced by louvres which allow a free circulation of air and keep out the storm. In foundries and smelters the clerestory is often left entirely open or is slightly protected by simple swinging shutters. 2. Steel Mill Buildings with Masonry Filled Walls. In mill buildings of this type part of the bracing in the side walls is usually omitted and the space between the columns is filled with a light wall of brick, stone, concrete or hollow tile. The construction of the roof and other constructional details are essentially the same as for steel frame mill buildings. Buildings of this type are quite rigid and are usually somewhat cheaper than type (3). TYPES OF Miu, BUILDINGS 3 3. Mill Buildings with Masonry Walls. Buildings of this type are made by supporting the roof trusses directly on brick, stone or concrete walls. The construction of the roof is essentially the same as for types (i) and (2), except that the trusses are somewhat lighter on account of the smaller wind stresses. The discussion of -the simple steel frame mill building shown in Fig. I includes practically all the problems and details which are en- countered in the design of steel mill buildings of all types. The problems involved in the design of mill buildings will be di- vided into Part I, Loads; Part II, Stresses; Part III, Design of Mill Buildings ; and Part IV, Miscellaneous Structures. In general the discussion will relate to the design of mill buildings but in a few cases, particularly in stresses, quite a number of problems will be discussed that are only indirectly related to the subject. PART I. LOADS. The loads to be provided for in designing a mill building will de- pend to a large degree upon the .use to which the finished structure is to be put. The loads may be classed under (i) dead loads; (2) snow loads; (3) wind loads ; and (4) miscellaneous loads. Concentrated floor and roof loads, girder and jib crane, arid miscellaneous loads should receive special attention, and proper provision should be made in each case. No general solution can be given for providing for miscellaneous loads, but each problem must be. worked out to suit local conditions. CHAPTER I. DEAD LOADS. Dead loads may be divided into (a) weight of structure ; (b) con- centrated loads. The weight of the structure may be divided into (i) the weight of the roof trusses ; (2) the weight of the roof covering; (3) the weight of the purlins and bracing; (4) the weight of the side and end walls. The first three items, together with the concentrated roof loads, consti- tute the dead loads used in designing the trusses. The weights of mill buildings vary so much that it is not possible to give anything more than approximate values for the different items which go to make up the dead load. The following data will, however, materially assist the designer in arriving at approximately the proper WEIGHT OF ROOF TRUSSES 5 dead load to assume for computing stresses, and the approximate weight of metal to use as a basis for preliminary estimates. Weight of Roof Trusses. The weight of roof trusses varies with the span, the distance between trusses, the load carried or capacity of the truss, and the pitch. The empirical formula where H^weight of steel roof truss in pounds; F=capacity of truss in pounds per square foot of horizontal pro- jection of roof (30 to So Ibs.) ; A= distance center to center of trusses in feet (8 to 30 feet) ; Z, span of truss in feet; was deduced by the author from the computed and shipping weights of mill building trusses. The trusses were riveted Fink trusses with purlins placed at panel points, and were made up of angles with con- necting plates; minimum size of angles 2" x 2" x J4", minimum thick- ness of plates J4". The trusses whose weights were used in deducing this formula had a pitch of y.\ (6" in 12"), but the formula gives quite accurate results for trusses having a pitch , of % to ^. The trusses were designed for a tensile stress of 15000 Ibs. per square inch and a compressive stress of 15000 55 Ibs. per square inch, where / = length and r the radius of gyration of the member, both in inches. The weight of steel roof trusses for a capacity, P, of 40 Ibs. per square foot for different spacings is given in Fig. 2. The weights of trusses for other capacities can be obtained by multiplying the tabular values by the ratio of the capacities. Dividing (i) by A L we have the weight of roof truss, W s , per square foot of horizontal projection of the roof W ' = W( I +WVA) (2) DEAD LOADS lOOOQf | | | | | | | | i | ~7 * /^/~, eral Formula / J O" for A / Weiaht c / / I ri flnnd - - w ^ A ( fi+ ) ^ 2 -(''SKZJ ::: "7 ""/ % w II. / . 212 it of truss h Ibs " 2 Z / ~^" / y / y/ / / r j "1^7 y s ::^d; s tc nee between trusses n ft- ^ ^^ ^ / Q- L= spar > of truss in ft- 1 V / / 2 / Z y 2 . X / ^7 ^/^S&S ---- /^A/y\//\ ^ 7 - 3000 - - - - : : JjJ^22^i!^?!. Wetghtof Re )Of Trusses 40lbs-persqft ?flbs-persqin persq-in 12") n | o^vv^ tL ' ^ ^ ^ /^ ~* ^^ A Z_ // U(AJ ? ^7 X /^ ^ ^ ^3 "^- > ^ ^ > > x X ^ ^ * X < v^ ^ ^ Tension I5000lb c Rtch-^:(6"tn 9O 100 30 4-0 50 60 70 80 Length of Span of Truss /., Ft- B 4 ic. 2. WEIGHT OF ROOF TRUSSES FOR A CAPACITY OF 40 LBS. PER SQUARE FOOT. The weight of steel roof trusses per square foot of horizontal projection of roof for a capacity, P , of 40 Ibs. per square foot is given in Fig 3. It should be noted that W ^ is the dead load per square foot carried by an interior truss. The actual weight of trusses per square foot of horizontal projection for a building with n panels will be W, O 1) where end post bent (a), Fig. i, is used, and W s - - where end truss bent (b), Fig. I, is used, assuming that all trusses are made alike. Weight of Light Trusses. Formula (i) gives the weight of mill building trusses and will usually cover the weight of knee braces and ventilator framing. By reducing the minimum thickness of metal and WEIGHT OP ROOF TRUSSES - we iqhtot rtoot trusses p wt. per sq f r. nor proj. span of truss in ft. distance between t Sq-Tt t-MDP pr< 5J- " ^ |f. / _ A- ^^x^ 1 -- 6 - ii of roof russesinft^ S ^ i 11 I A/ x i?5 ^ s* x f 5 ^ ^ ^ ^ o *> - + ^'*/< r 3 * ^ '^^ *- ^s^ * & ***, *z 5 ^ ^ ' ^^^ *- *^ ^*^* S* ^ X X 1 ** x "^L^ 1 ^ ^ ? ^ ^ ^ -x rX x L! "^ x "^ ^ *** ^ ^x 1 . * < ^ J ' ^" ^ Q. ^ ^^ L *4<- ^ *"> ^" * 2 ^ 5^3 T F ompression = 15000-5511 Ibs per sq nsion= 15000 Ibs-persqin n - - , _ 20 3040 5060708090100 Length of Span of Truss, L, in feet- FIG. 3. WEIGHT OF ROOF TRUSSES PER SQUARE FOOT OF HORIZONTAL PROJECTION FOR A CAPACITY OF 40 LBS. PER SQUARE FOOT. by skinning the sections it is possible to materially reduce the weights. Weight of Simple Roof Trusses. Simple roof trusses supported TABLE I. WEIGHT OF FINK TRUSSES, SUPPORTED ON MASONRY WALLS, DE- SIGNED FOR A VERTICAL LOAD OF 40 POUNDS PER SQUARE FOOT OF HORIZONTAL PROJECTION OF ROOF. Span, L, in Feet Distance between Trusses, A. in Feet Weight of Truss, W, in Pounds Span, L, in Feet Distance between Trusses, A, in Feet Weight of Truss. W. in Pounds 30 16 741 65 20 3226 30 14 621 70 20 3951 35 16 910 75 20 4564 40 16 1211 75 14 3200 40 14 976 80 20 5160 45 16 1423 85 25 6730 50 16 1865 85 14 4000 50 14 1550 90 25 8010 55 16 2103 95 25 8600 60 20 2870 100 25 9392 60 14 2120 8 DEAD LOADS on walls will usually weigh somewhat less than the value given by Formula (i). The computed weights of Fink roof trusses without ven- tilators and with purlins spaced from 4 to 8 feet are given in Table I. These trusses were designed by two different bridge companies to serve as standards and represent minimum weights. The trusses with a spacing of 14 feet were designed with minimum thickness of metal 3-16'' and minimum size of angles 2" x i^i" x 3-16". In the remainder of the trusses the minimum thickness of plates was Y^" and minimum size of angles 2" x 2" x y^ . The trusses are all too light to give good service although their use in temporary structures may sometimes be allowable. Weight of Purlins, Girts, Bracing, and Columns. Steel purlins will weigh from i l /2 to 4 pounds per square foot of area covered, depending upon the spacing and the capacity of the trusses and the snow load. If possible the actual weight of the purlins should be cal- culated. Girts and window framing will weigh from 1*4 to 3 pounds per square foot of net surface. Bracing is quite a variable quantity. The bracing in the planes of the upper and lower chords will vary from y 2 to i pound per square foot of area. The side and end bracing, eave struts and columns will weigh about the same per square foot of sur- face as the trusses. Weight of Covering. The weight of corrugated iron or steel covering varies from i l / 2 to 3 pounds per square foot of area. WEIGHT OF FLAT AND CORRUGATED STEEL SHEETS WITH 2y 2 INCH CORRUGATIONS. Gaqe No. Thickness in inches Weight per Sq uare ( 100 sq-ft) Flat Sheets Corrugated Sheets Black Galvanized Black Painted Galvanized 16 .06^5 30 "66 Z75 a9i 18 .0500 EOO Z/6 ^^o 36 ^0 0375 150 166 165 Id2 ^Z 0315 l^5 /4I 13d 154 14 OE50 /oo / 16 III 127 ^6 0188 75 91 84- 99 ^8 0/56 65 79 69 06 WEIGHT OF ROOF COVERING 9 Ir estimating the weight of corrugated steel allow about 25 per cent for laps where two corrugations side lap and 6 inches end lap are re- quired, and about 15 per cent for laps where one corrugation side lap and 4 inches end lap are required. Nos. 20 and 22 corrugated steel are commonly used on the roof and Nos. 22 and 24 on the sides. Weight of Roof Covering. The approximate weight per square foot of various roof coverings is given in the following table : Corrugated iron, without sheathing I to 3 Ibs. Felt and asphalt, without sheathing 2 Felt and gravel, without sheathing 8 to 10 Slate, 3-16" to %", without sheathing 7 to 9 Tin, without sheathing I to i l / 2 " Skylight glass, 3-16" to y 2 " , including frames 4 to 10 White pine sheathing i" thick 3 Yellow pine sheathing i" thick 4 Tiles, flat 15 to 20 Tiles, corrugated 8 lo 10 Tiles, on concrete slabs . 30 to 35 Plastered ceiling % 10 For additional data on weight of roof coverings, see Chapter XIX. The actual weight of roof coverings should be calculated if possible. Weight of the Structure. The weight of the roof can now be found. The weight of the steel in the sides and ends is approximately the same per square foot as the steel work in the roof. A very close approximation to the weight of the steel in the en- tire structure where no sheathing is used and the same weight of cor- rugated iron is used on sides as on roof, may be found as follows : Take the sum of the horizontal projection of the roof and the net sur- face of the sides and ends, after subtracting one-half of the area of the windows, wooden doors and clear openings ; multiply the sum of these areas by the weight per square foot of the horizontal projection of the roof, and the product will be the approximate weight of the steel in the structure. CHAPTER II. SNOW LOADS. The annual snowfall in different localities is a function of the humidity and the latitude and is quite a variable quantity. The amount of snow on the ground at one time is still more variable. In the Lake Superior region very little of the snow melts as it falls, and almost the entire annual snowfall is frequently on the ground at one time; while on the other hand in the same latitude in the Rocky Mountains the dry \vinds evaporate the snow in even the coldest weather and a less pro- portion accumulates. In latitudes of 35 to 45 degrees the heavy snow- falls are often followed by a sleeting rain, and the snow and ice load on roofs sometimes nearly equals the weight of the annual snowfall. From the records of the snowfall for the past ten years as given in the reports of the U. S. Weather Bureau and data obtained by personal experience, in British Columbia, Montana, the Lake Superior region and central Illinois .the author presents the values given in Fig. 4 for snow loads for roofs of different inclinations in different latitudes. P'or the Pacific coast and localities with low humidity, take one-half of the values given. The weight of newly fallen snow was taken at 5 Ibs. and packed snow at 12 Ibs. per cubic foot. A high wind may follow a heavy sleet and in designing the trusses the author would recommend the use of a minimum snow and ice load as given in Fig. 4 for all slopes of roofs. The maximum stresses due to the sum of this snow load, the dead and wind loads ; the dead and the wind loads; or of the maximum snow load and the dead load be- ing used in designing the members. SNOW LOAD ON ROOFS ii I I M I I! Caast-ancf & Reg/ons use one- " ~' fabu/ar va/i/e 5 40 50 k 10 35 40 45 Latitude in Degrees 50 FlG. 4. SNOW LOAD ON ROOFS FOR DIFFERENT LATITUDES, IN LBS. PER SQUARE FOOT. Snow loads per square foot of horizontal projection of roof are specified in various localities as follows : Chicago and New York, 20 Ibs. ; Cincinnati and St. Louis, 10 Ibs. ; New England, 30 Ibs. The Baltimore and Ohio Railroad specifies 20 Ibs. per square foot of hori- zontal projection of roof. CHAPTER III. WIND LOADS. Wind Pressure. The wind pressure (P) in pounds. per square foot on a flat surface normal to the direction of the wind for any given velocity (F) in miles per hour is given quite accurately by the formula P = 0.004 F 2 (3) The following table gives the pressure per square foot on a flat surface normal to the direction of the wind for different velocities as calculated by formula (3). Vel. in miles Pressure, Ibs. per per hour. square foot. 10 0.4 , Fresh breeze. 20 1.6 30 3.6 Strong wind. 40 6.4 High wind. 50 10 . o Storm. 60 14.4 Violent storm. 80 25.6 Hurricane. 100 40.0 Violent hurricane. The pressure on other than flat surfaces may be taken in per cents of that given by formula (3) as follows: 80 per cent on a rectangular building; 60 per cent on the convex side of cylinders; 115 to 130 per WIND PRESSURE 13 cent on the concave side of cylinders, channels and flat cups; and 130 to 170 per cent on the concave sides of spheres and deep cups. The pressure on tne vertical sides of buildings is usually taken at 30 pounds per square foot, equivalent to P equals 37^/2 pounds in formula (3). This would give a \elocity of 96 miles per hour, which would seem to be sufficient for all except the most exposed positiona The velocity of the wind in the St. Louis tornado was about 120 miles per hour. The records of the U. S. Weather Bureau for the last ten years show only one instance where the velocity of the wind as recorded by the anemometer was more than 90 miles per hour. The actual pres- sure of wind gusts has been found to be about 60 per cent and the actual steady wind pressure only about 36 per cent of that registered by ordinary small anemometers, which further reduces the intensity of the observed pressures. The wind pressure has been found to increase as the distance above the ground increases. Recent German specifications for design of tall chimneys specify wind loads per square foot as follows: 26 pounds on rectangular chimneys ; 67 per cent of 26 pounds on circular chimneys ; and 7 1 per cent of 26 pounds on octagonal chimneys. The building laws of New York, Boston and Chicago require that steel buildings be designed for a horizontal wind pressure of 30 pounds per square foot. The Baltimore and Ohio Railroad specifies a horizon- tal wind pressure of 30 pounds per square foot. From the above discussion it would seem that 30 pounds per square foot on the sides and the normal component of a horizontal pressure of 30 pounds on the roof would be sufficient for all except exposed loca- tions. If the building is somewhat protected a horizontal pressure of 20 pounds per square foot on the sides is certainly ample for heights less than, say, 30 feet. Wind Pressure on Inclined Surfaces. The wind is usually taken as acting horizontally and the normal component on inclined sur- faces is calculated. 14 WIND LOADS The normal component of the wind pressure on inclined surfaces has usually been computed by Mutton's empirical formula Pn = Psi*A 1-842 cos ^-1 (4) where P equals the normal component of the wind pressure, P equals the pressure per square foot on a vertical surface, and A equals the angle of inclination of the surface with the horizontal, Fig. (5). The formula due to Duchemin 2 sin .4 (5) 1 + sin 2 A where P n , P and A are the same as in (4), gives results considerably larger for ordinary roofs than Hutton's formula, and is coming into quite general use. The formula P A (6) fn= ^A where P n and P are the same as in (4) and (5), arid A is the angle of inclination of the surface in degrees (A being equal to or less than 45), gives results which agree very closely with Hutton's formula, and is much more simple. FIG. 5. Hutton's formula (4) is based on experiments which were very crude and probably erroneous. Duchemin's formula (5) is based on very careful experiments and is now considered the most reliable form- ula in use. The Straight Line formula (6) agrees with experiments quite closely and is preferred by many engineers on account of its simplicity. The values of P n as determined by Hutton's, Duchemin's and the NORMAL WIND PRESSURE 15 Straight Line formulas are given in Fig. 6, for P equals 20, 30 and 40 pounds. It is interesting to note that Duchemin's formula with P equals 30 pounds gives practically the same values for roofs of ordinary inclina- tion as is given by Button's and the Straight Line formulas with P equals 40 pounds. Hutton Straight Line * Normal Pressure.lbs per sq ft P= Horizontal A =Angle of inclination of surface O 5 10 15 ^ 25 30 35 40 45 50 55 60 65 70 75 80 85 90 Angle Exposed Roof makes with Horizontal in Degrees. A. FIG. 6. NORMAL WIND LOAD ON ROOF ACCORDING TO DIFFERENT FORMULAS. Duchemin has also deduced the formula 2 sin 2 A Ph=P (7) sin 2 A where P h in (7) equals the pressure parallel to the direction of the wind, Fig. 5 ; and 2 sin A cos A (8) ' = 1 + sin 2 A 1 6 WIND LOADS where P l in (8) equals the pressure at right angles to the direction of the wind, Fig. 5. P t may be an uplifting, a depressing or a side pres- sure. With an open shed in exposed positions. the uplifting effect of the wind often requires attention. In that case the wind should be taken normal to the inner surface of the building on the leeward side, and the uplifting force determined by using formula (8). If the gables are closed a deep cup is formed, and the normal pressure should be in- creased 30 to 70 per cent. That the uplifting force of the wind is often considerable in exposed localities is made evident by the fact that highway bridges are occasion- ally wrecked by the wind. The most interesting example known to the author is that of a loo-foot span combination bridge in Northwestern Montana which was picked up bodily by the wind, turned about 90 degrees in azimuth and dropped into the middle of the river. The end bolsters were torn loose although drift-bolted to the abutments. The wind pressure is not a steady pressure, but varies in intensity, thus producing excessive vibrations which cause the structure to rock if the bracing is not rigid. The bracing in mill buildings should be designed for initial tension, so that the building will be rigid. Rigidity is of more importance than strength in mill buildings. For further information on this subject see a very elaborate and valuable monograph on "Wind Pressures in Engineering Construc- tion," by Capt. W. H. Bixby, M. Am. Soc. C. E., published in En- gineering News, Vol. XXXIIL, pp. 175-184, March, 1895. CHAPTER IV. MISCELLANEOUS LOADS. LIVE LOADS ON FLOORS. Live loads on floors for mill buildings are very hard to classify and should be calculated for each case. Floor loads as specified in the building laws of various cities are given in Table II, and the engineer should govern himself accordingly. TABLE II. FLOOR LOADS IN POUNDS PER SQUARE FOOT AS SPECIFIED IN VARIOUS CITIES'. \ New York Chicago Philadelphia Boston Dwelling's j Upper floors 75 100 100 100 Public Buildings. . Light Manufac- turing" . . 1 1st floor 150 90 120 100 100 120 100 150 Warehouses and Factories .... 150 and up 150 and up 250 and up Sidewalks 300 Without reference to building laws the live loads per square foot, exclusive of weight of floor materials, given below are about standard practice. Dwellings 70 Ibs. per sq. ft. Offices 70 to loo Ibs. per sq. ft. Assembly halls 120 to 150 Ibs. per sq. ft. Warehouses 250 and up, Ibs. per sq. ft. Factories 200 to 450 Ibs. per sq. ft. i8 MISCELLANEOUS LOADS The weight of floors above ground in mill buildings varies so much that it is useless to give weights. For a few data on weights of floors see Chapter on Floors. WEIGHT OF HAND CRANES. The approximate weight of a few of the common sizes of hand cranes made by Pawling and Har- TABLE III. WEIGHT OF TRAVELING HAND CRANES. Capacity of Crane in Tons Distance c to c of end wheels 20-FOOT SPAN 30 FOOT SPAN Weight of Crane Ibs. Maximum Load on each Wheel Ibs Weight of Crane Ibs. Maximum Load on each Wheel Ibs. 3 3' 0" 4500 4500 5000 5000 5 3' 0" 5500 7000 6000 7500 7 1 A 3' 8" 8000 10500 9000 11500 10 8' 0" 15000 18000 17000 20000 15 8' 0" 16000 .20000 18000 21000 20 8' 6" 20000 26000 22000 27000 nischfeger, Milwaukee, Wis., and the maximum load on each wheel when the loaded trolley' is at one end is given in Table III. 20 30 40 50 60 70 Span of Crane in Feet FIG. 7. WEIGHT OF ELECTRIC CRANES. The maximum load on each of the end wheels for common sizes, of electric cranes made by WEIGHTS OF MERCHANDISE Pawling and Harnischfeger is given in Fig. 7. Cranes made by different manufacturers differ considerably in weight. WEIGHTS OF MISCELLANEOUS MATERIAL. The weights of various kinds of merchandise are given in Table IV. For weights of other materials consult steel makers hand books. TABLE IV. WEIGHTS OF MERCHANDISE.* Commodity height in IDS. per cubic foot Commodity Weight in Ibs. per cubic foot Wool in Bales 5 to 28 Caustic Soda 88 Woolen Goods .... 13 to 22 iBarrel Starch 23 Baled Cotton 12 to 43 Barrel Lime 50 Cotton Goods 11 to 37 " Cement .... 73 Ka"s in Bale** 7 to 36 Plaster S3 Paper 10 to 69 * Lard Oil 34 Wheat 39 to 44 Rope . . . 42 Corn 31 Box Tin ' " 278 Oats 27 Box Glass 60 Baled Hav and Straw. 1 4 to 19 Crate Crockery 40 Bleaching" Powder.... 31 Bale Leather 16 to 23 Soda Ash 62 Susrar . 45 Box Indigo 43 Cheese 30 *From Report V. Insurance Engineering Experiment Station Kdward Atkinson, Director, Boston, Mass. PART II. STRESSES. CHAPTER V. GRAPHIC STATICS. Equilibrium. Statics considers forces as at rest and therefore in equilibrium. To have static equilibrium in any system of forces there must be neither translation nor rotation and the following conditions must be fulfilled for coplanar forces (forces in one plane). S horizontal components of forces = o (a) 2 vertical components of forces = o (b) S moments of forces about any point = o (c) Representation of Forces. A force is determined when its magnitude, line of action, and direction are known, and it may be rep- resented graphically in magnitude by the length of a line, in line of action by the position of the line, and in direction by an arrow placed on the line, pointing in the direction in which the force acts. A force may be considered as applied at any point in its line of action. Force Triangle. The resultant, R, of the two forces PI and P 2 meeting at the point a in Fig. 8 is represented in magnitude, and direc- tion by the diagonal, R, of the parallelogram abed. The combining of the two forces P l and P 2 into the force R is termed composition of forces. The reverse process is called resolution of forces. FORCE TRIANGLE 21 (c) The value of R may also be found from the equation R 2 = PS + P 2 2 + 2 P x P 2 cos e It is not necessary to construct the entire force parallelogram as in (a) Fig. 8, the force triangle (b) below or (c) above the resultant R being sufficient. If only one force together with the line of action of the two others be given in a system containing three forces in equilibrium, the magni- tude and direction of the two forces may be found by means of the force triangle. If the resultant R in Fig. 8 is replaced by a force equal in amount but opposite in direction, the system of forces will be in equi- librium, (a) or (b) Fig. 9. The force H is the equilibrant of the system of forces P and P 2 . FIG. 9. It is immaterial in what order the forces are taken in constructing the force triangle, as in Fig. 9, as long as the forces all act in the same direction around the triangle. The force triangle is the foundation of the science of graphic statics. 22 GRAPHIC STATICS Force Polygon. If more than three concurrent forces (forces which meet in a point) are in equilibrium as in (a) Fig. 10, R 1 in (b) will be the resultant of P^ and P 2 , R* will be the resultant of R^ and P 3 , (a) (b) FIG. 10. and will also be the equilibrant of P 4 and P 5 . The force polygon in (b) is therefore only a combination of force triangles. The force polygon for any system of forces may be constructed as follows: Beginning at any point draw in succession lines representing in magnitude and direction the given forces, each line beginning where the preceding one ends. If the polygon closes the system of forces is in equilibrium, if not the line joining the first and last points represents the resultant in magnitude and direction. As in the case of the force triangle, it is immaterial in what order the forces are applied as long as they all act in the same direction around the polygon. A force polygon is analogous to a traverse of a field in which the bearings and the distances are measured progressively around the field in either direction. The conditions for closure in the two cases are also identical. It will be seen that any side in the 'force polygon is the equilibrant of all the other sides and that any side reversed in direction is the re- sultant of all the other sides. Equilibrium of Concurrent Forces. The necessary condition for equilbrium of concurrent coplanar forces therefore is that the force polygon close. This is equivalent to the algebraic condition that 2 horizontal components of forces = o, and 5 vertical components of forces = o. If the system of concurrent forces is not in equilibrium the resultant can be found in magnitude and direction by completing EQUILIBRIUM OF FORCES the force polygon. The resultant of a system of concurrent forces is always a single force acting through their point of intersection. Equilibrium of Non-concurrent Forces. If the forces are non-concurrent (do not all meet in a common point), the condition that the force polygon close is a necessary, but not a sufficient condition for equilibrium. For example, take the three equal forces P lf P 2 and P 3 , making an angle of 120 with each other as in (a) Fig. n. Resultant Moment = -Rh (a) Positive Moment Moment=+Ph Negative Moment Moment = - Ph (c) FIG. ii. The force polygon (b) closes, but the system is not in equilibrium. The resultant, R, of F 2 and P 3 acts through their intersection and is parallel to P lt but is opposite in direction. The system of forces is in equilibrium for translation, but is not in equilibrium for rotation. The resultant of this system is a couple with a moment = F x h, moments clockwise being considered negative and counter clockwise positive, (c) Fig. n. The equilibrant of the system in (a) Fig. n is a couple with a moment -{- P r Ji. A couple. A couple consists of two parallel forces equal in amount, but opposite in direction. The arm of the couple is the per- pendicular distance between the forces. The moment of a couple is equal to one of the forces multiplied by the arm. The moment of a couple is constant about any point in the plane and may be represented 24 GRAPHIC STATICS graphically by twice the area of the triangle having one of the forces as a base and the arm of the couple as an altitude. The moment of a force about any point may be represented graphically by twice the area of a triangle as shown in (c) Fig. n. It will be seen from the preceding discussion that in order that a system of non-concurrent forces be in equilibrium it is necessary that the resultant of all the forces save one shall coincide with the one and be opposite in direction. Three non-concurrent forces can not be in equi- librium unless they are parallel. The resultant of a system of non- concurrent forces may be a single force or a couple. Equilibrium Polygon. First Method. In Fig. 12 the resultant, a, of P-L and P 2 acts through their intersection and is equal and parallel to a in the force polygon (a) ; the resultant, b, of a and P 3 acts through FIG. 12. their intersection and is equal and parallel to b in the force polygon ; the resultant, c, of b and F 4 acts through their intersection and is equal and parallel to c in the force polygon ; and finally the resultant, R, of c and P 5 acts through their intersection and is equal and parallel to R in the force polygon. R is therefore the resultant of the entire system of forces. If R is replaced by an equal and opposite force, H, the sys- tem of forces will be in equilibrium. Polygon (a) in Fig. 12 is called EQUILIBRIUM POLYGON 25 a force polygon and (b) is called a funicular or an equilibrium polygon. It will be seen that the magnitude and direction of the resultant of a system of forces is given by the closing line of the force polygon, and the line of action is given by the equilibrium polygon. The force polygon in (a) Fig. 13 closes and the resultant, R, of O (b) the forces P lf P 2 , P z , P 4 , P 5 is parallel and equal to P 6 , and is opposite in direction. The system is in equilibrium for translation, but is not in equilibrium for rotation. The resultant is a couple with a moment = P 6 h. The equilibrant of the system of forces will be a couple with a moment = + P G h. From the preceding discussion it will be seen that if the force polygon for any system of non-concurrent forces closes the resultant will be a couple. If there is perfect equilibrium the arm of the couple will be zero. Second Method. Where the forces do not intersect within the limits of the drawing board, or where the forces are parallel, it is not possible to draw the equilibrium polygon as shown in Fig. 12 and Fig. 13, and the following method is used. The point o, (a) Fig. 14, which is called the pole of the force poly- gon, is selected so that the strings a o, b o, c o, d o and e o in the equi- librium polygon (b), which are drawn parallel to the corresponding 26 GRAPHIC STATICS rays in the force polygon (a), will make good intersections with the forces which they replace or equilibrate. In the force polygon (a), F is equilibrated by the imaginary forces represented by the rays o a and b o acting as indicated by the arrows within the triangle; P 2 is equilibrated by the imaginary forces repre- FIG. 14. sented by the rays o b and c o acting as indicated by the arrows within the triangle; P s is equilibrated by the imaginary forces represented by the rays o.c and do acting as indicated by the arrows within the tri- angle; and P 4 is equilibrated by the imaginary forces o'd and e o acting as indicated by the arrows within the triangle. The imaginary forces are all neutralized except a o and o c, which are seen to be components of the resultant R. To construct the equilibrium polygon, take any point on the line of action of P- and draw strings o a and o b parallel to rays o a and o b, b o is the equilibrant of o a and F ; through the intersection of string o b and P 2 draw string c o parallel to ray c o, c o is the equilibrant of o b and P 2 ; through the intersection of string c o and P 3 draw string d o parallel to ray d o, d o is the equilibrant of c o and P 3 ; and through the intersection of string d o and P 4 draw string e o parallel to ray e o, e o is the equilibrant of d o and P 4 . Strings o a and e o acting as shown are components of .the resultant R, which will be parallel to R in the force polygon and acts through the intersections of strings o a and e o. REACTIONS OF A BEAM The imaginary forces represented by the rays in the force poly- gon may be considered as components of the forces and the analysis made on that assumption with equal ease. It is immaterial in what order the forces are taken in drawing the force polygon, as long as the forces all act in the same direction around the force polygon, and the strings meeting on the lines of the forces in the equilibrium polygon are parallel to the rays drawn to the ends of the same forces in the force polygon. The imaginary forces a o, b o, c o, d o, e o are represented in mag- nitude and in direction by the rays of the force polygon to the same scale as the forces P lt P 2 , P z , P. The strings of the equilibrium poly- gon represent the imaginary forces in line of action and direction, but not in magnitude. Reactions of a Simple Beam. The equilibrium polygon may be used to obtain the reactions of a beam loaded with a load P as in . 15- a Tt*. o (a) TtU (b) FIG. 15. The force polygon (b) is drawn with a pole o at any convenient point and rays o a and o c are drawn. Now from the fundamental con- ditions for equilibrium for translation we have P = R 1 + -^2- At any convenient point in the line of action of P draw the strings o a and o c parallel to the rays o a and o ^.respectively, in the force polygon. The imaginary forces a o and o c acting as shown equilibrate the force P. 28 GRAPHIC STATICS The imaginary force a o acting in a reverse direction as shown is an equilibrant of R lt and the imaginary force c o acting in a reverse direction is an eqnilibrant of R 2 . The remaining equilibrant of R 1 and of R 2 must coincide and be equal in amount, but opposite in direction. The string b o is the remaining equilibrant of R^ and of R 2 and is called the closing line of the equilibrium polygon. The ray b o drawn parallel to the string b o divides P in two parts which are equal to the reactions R^ and R 2 (for reactions of overhanging beam see Chapter VIII). Reactions of a Cantilever Truss. In the cantilever truss shown in Fig. 16, the direction and point of application B of the reaction R t (b) are known, while the point of application A of the reaction R 2 only is known. The direction of reaction R 2 may be found by applying the principle that if a body is in equilibrium under the action of three external forces which are not parallel, they must all meet in a common point, i. e., the forces must be concurrent. The resultant of all the loads acts through the point c, which is also the point of intersection of the reactions R^ and R 2 . Having the direction of the reaction R 2 , the values of the reactions may be found by means of a force polygon. The direction of reaction 7? 2 ,may be found by means of a force and equilibrium polygon as follows: Construct the force polygon (b) with pole o and draw equilibrium polygon (a) starting with point A, the EQUILIBRIUM POLYGON AS A FRAMED STRUCTURE 29 only known point on the reaction R 2 , and draw the polygon as prev- iously described. A line drawn through point o in the force polygon parallel to the closing line of the equilibrium polygon will meet R lt drawn parallel to reaction R lf in the point y, which is also a point on R. 2 . The reactions R t and R., are therefore completely determined in direc- tion and amount. The method just given is the one commonly used for finding the re- actions in a truss with one end on rollers, (see Chapter VII). Equilibrium Polygon as a Framed Structure. In (a) Fig. 17 the rigid triangle supports the load P^. Construct a force polygon R (a) FIG. 17. by drawing rays a i and c i in (b) parallel to sides a i and c i, respec- tively, in (a), and through pole i draw i b parallel to side I b in (a). The reactions R and R 2 will be given by the force polygon (b), and the rays i a, i c and i b represent the stresses in the members i a, i c and i b, respectively, in the triangular structure. The stresses in I a and i c are compression and the stress in i b is tension, forces acting toward the joint indicating compression and forces acting away from the joint indicating tension. Triangle (a) is therefore an equilibrium polygon and polygon (b) is a force polygon for the force P . From the preceding discussion it will be seen that the internal stresses at any point or in any section hold in equilibrium the external forces meeting at a point or on either side of the section. 30 GRAPHIC STATICS Graphic Moments. In Fig. 18 (b) is a force polygon and (a) is an equilibrium polygon for the system of forces P lt P 2J P z , P 4 . Draw FIG. 18. the line M N = Y parallel to the resultant R, and with ends on strings o e and o a produced. Let r equal the altitude of the triangle L M N and H equal the altitude of the similar triangle o e a, H is the pole distance of the resultant R. Now in the similar triangles L M N and o e a R :Y : :H :r and R r = H Y But R r = M = moment of resultant R about any point in the line M N and therefore M = H Y The statement of the principle just demonstrated is as follows: The moment of any system of coplanar forces about any point in the plane is equal to the intercept on a line drawn through the center of moments and parallel to the resultant of all the forces, cut off by the strings which meet on the resultant, multiplied by the pole distance of the resultant. It should be noted that in all cases the intercept is a distance and the pole distance is a force. This property of the equilibrium polygon is frequently used in finding the bending moment in beams and trusses which are loaded with vertical loads. BENDING MOMENTS IN A BEAM 31 Bending Moments in a Beam. It is required to find the mo- ment at the point M in the simple beam loaded as in (b) Fig. 19. The (Q) FIG. 19. moment at M will be the algebraic sum of the moments of the forces to the left of M. The moment of P t -- H x B C, the moment of P 2 H x C D and the moment of R = H x B A. The moment at M will therefore be M 1 = HxB C + HxC D HxB A H xAD H y The moment of the forces to the right of M' may 'in like manner be shown to be .!/, = + H y In like manner the bending moment at any point in the beam may be shown to be the ordinate of the equilibrium polygon multiplied by the pole distance. The ordinate is a distance and is measured by the same scale as the beam, while the pole distance is a force and is measured by the same scale as the loads. To Draw an Equilibrium Polygon Through Three Points. (liven a beam loaded as shown in Fig. 20, it is required to draw an equilibrium polygon through the three points a, b, c. Construct a force polygon (b) with pole o, and draw equilibrium polygon a b' c' in fa). Point b' is determined by drawing through b a line b b' parallel to bj_ b" which is the line of action of the resultants of the forces to the GRAPHIC STATICS v (b) FIG. 20. left of b, acting through points b and a. Through o draw o c" and o b" parallel to closing lines a c' and a b r , respectively. Point c" de- termines the reactions R 1 and R 2 , and point b" determines the reac- tions acting through a and b of the forces to the left of point b. Points c" and b" are common to all force polygons, and lines c" o' and b" o' drawn parallel to the closing lines of the required equi- librium polygon, a c and a b will meet in the new pole o'. With pole o' the required equilibrium polygon a b c can now be drawn. Center of Gravity. To find the center of gravity of the figure shown in (a) Fig. 21, proceed as follows: Divide the figure into elementary figures whose centers of gravity and areas are known. Assume that the areas act as the forces P lf P 2 , P.> through the centers of gravity of the respective figures. Bring the line of action of these forces into the plane of the paper by turning them downward as in (b) and to the right as in (c). Find the resultant of the forces for case (b) and for case (c) by means of force and equilibrium polygons. The intersection of the Resultants R will be the center of gravity of the figure. The two sets of forces may be assumed to act at any angle, however, maximum accuracy is given when the forces are assumed to act at right angles. If the figure has an axis of symmetry but one force and equilibrium polygon is required. MOMENT OF INERTIA OF FORCES 33 FIG. 21. Moment of Inertia of Forces. The determination of the moment of inertia of forces and areas by graphics is interesting. There are two methods in common use: (i) Culmann's method, in which the moment of inertia of forces is determined by finding the moment of the moment of forces by means of force and equilibrium polygons; and (2) Mohr's method, in which the moment of inertia of forces is determined from the area of the equilibrium polygon. The moment of inertia of a force about a parallel axis is equal to the force multiplied by the square of the distance between the force and the axis. Culmann's Method. It is required to find the moment of inertia, /, of tfce system of forces P lf P 2 , P 3 , P, Fig. 22, about the axis M N. Construct the force polygon (a) with a pole distance H, draw the equilibrium polygon a b c d e, and produce the strings until they intersect the axis M N. Now the moment of P about axis M N equals E D x H; moment of P 2 equals D C x H; moment of P s equals C B x H; moment of P 4 equals B A x H; and moment of resultant R equals E A x H. With intercepts H D, D C, C B, B A, as forces acting in place of P lf P 2 , P 3f P 4 / respectively, construct force polygon (b) with pole distance H', and draw equilibrium polygon (c). As before the moments of the forces will be equal to the products of the intercepts and pole distance ,and the moment of the system of forces represented by the 34 GRAPHIC STATICS Culmonn's Method I of Forces a bout axis M-N (a) FIG. 22. intercepts will be equal to the intercept G F multiplied by pole distance H'. But the intercepts D, D C, C B } B A, multiplied by the pole distance H equal moments of the forces P 1 , P 2 , P 3 , P 4 , respectively, about the axis M N, and the moment of inertia of the system of forces P lf P Zf P 3} P 4 , about the axis M N will be equal to the intercept G F multiplied by the product of the two pole distances H and H' , and I = F G xH x H' . Mohr's Method. It is required to find the moment of inertia, I, of the system of forces P lf P 2 , P s , P 4 , Fig. 23, about the axis M N. Construct the force polygon (a) with a pole distance H, and dr*w the equilibrium polygon (b). Now the moment of P about the axis M N equals intercept F G multiplied by the pole distance H, and the moment of inertia of P x about the axis M N equals the moment of the moment of P! about the axis, = F G x H x d. But F G x d equals twice the area of the triangle F G A,, and we have the moment of inertia of P equal to the area of the triangle F G A x 2 H. In like manner the moment of inertia of P 2 may be shown equal to area of the triangle G H B x 2 H; moment of inertia of P 3 equal to area of the triangle H I C x 2 H ; and moment of inertia of P 4 equal to. area of the triangle 7 / D x 2 H. Summing up these values we have the moment of inertia of the sys- MOHR'S METHOD FOR MOMENT OF INERTIA 35 (a). Mohrs Method I of Forces about axis M-N =Area (b) FIG. 23. tern of forces equal to the area of the equilibrium polygon multiplied by twice the pole distance, H, and / = area F AB C D B J Fx 2 H To find the radius of gyration, r, we use the formula / = R r- In Fig. 23 the moment of inertia, I 1 , of the resultant of the sys- tem of forces about the axis M N, can in like manner be shown to be equal to area of the triangle F E J x 2 H. If the axis M N is made to coincide with the resultant R the mo- ment of inertia I c g of the system will be equal to the area of equi- librium polygon ABCDEx2H. This furnishes a graphic proof for the proposition that the moment of inertia, I, of any system of parallel forces about an axis parallel to the resultant of the system is equal to the moment of inertia, 7 , of the forces about an axis through their centeroid plus the moment of inertia, I rf of their resultant about the given axis. I=I c .g. + Rr* = Ic.g. + IT It will be seen from the foregoing discussion thst the moment of inertia of a system of forces about an axis through the centeroid of the system is a minimum. 36 GRAPHIC STATICS Moment of Inertia of Areas. The moment of inertia of an area about an axis in the same plane is equal to the summation of the products of the differential areas which compose the area and the squares of the distances of the differential areas from the axis. The moment of inertia of an area about a neutral axis (axis through center of gravity of the area) is less than that about any parallel axis, and is the moment of inertia used in the fundamental formula for flexure in beams where M = bending moment at point of inch-pounds ; S = extreme fibre stress in pounds ; / =. moment of inertia of section in inches to thvi fourth power; c = distance from neutral axis to extreme fibre in inches. An approximate value of the moment of inertia of an area may be obtained by either of the preceding methods by dividing the area into laminae and assuming each area to be a force acting through the center of gravity of the lamina, the smaller the laminae the greater the accuracy. The true value may be obtained by either of the above methods if each one of the forces is assumed to act at a distance from the given axis equal to the radius of gyration of the area with reference to the axis, d = i/a 2 + r 2 , where a is the distance from the given axis to the center of gravity of the lamina and r is the radius of gyration of the lamina about an axis through its center of gravity. If A is the area of each lamina the moment of inertia of the lamina will be / == A d 2 = A a 2 + A r 2 = A a 2 + / ^ which is the fundamental equation for transferring moments of inertia to parallel axes. CHAPTER VI. STRESSES IN FRAMED STRUCTURES. Methods of Calculation. The determination of the reactions of simple framed structures usually requires the use of the three funda- mental equations of equilibrium 3 horizontal components of forces = (a) 3 vertical components of forces = (b) 2 moments of forces about any point = (c) Having completely determined the external forces, the internal stresses may be obtained by either equations (a) and (b) (resolution), or equation (c) (moments). These equations may be solved by graphics or by algebra. There are, therefore, four methods of calcu- lating stresses: ( Algebraic Method Resolution of Forces < ~ . A/ r^ii { Graphic Method . -^ I Algebraic Method Moments of Forces { & , . , { Graphic Method The stresses in any simple framed structure can be calculated by using any one of the four methods. However, all the methods are not equally well suited to all problems, and there is in general one method that is best suited to each particular problem. The common practice of dividing methods of calculation of stresses into analytic and graphic methods is meaningless and mis- leading for the reason that both algebraic and graphic methods are analytical, i. c. capable cf analysis. The loads on trusses are usually considered as concentrated at the joints in the plane of the loaded chord. 38 STRESSES IN FRAMED STRUCTURES Algebraic Resolution. In calculating the stresses in a truss by algebraic resolution, the fundamental equations for equilibrium for translation 2 horizontal components of forces = (a) 2 vertical components of forces = (b) are applied (a) to each joint, or (b) to the members and forces on one side of a section cut through the truss. (a) Forces at a Joint. The reactions having been found, the stresses in the members of the truss shown in Fig. 24 are calculated as (a; (b) (c) FIG. 24. follows : Beginning at the left reaction, R 1} we have by applying equa- tions (a) and (b) \-x sin 6 \-y sin a = (9) \-x cos 9 l-y cos or R = (10) The stresses in members i-x and i-y may be obtained by solving equations (9) and (10). The direction of the forces which rep- resent the stresses in amount will be determined by the signs of the results, plus signs indicating compression and minus signs indicating tension. Arrows pointing toward the joint indicate that the member is in compression; arrows pointing away from the joint indicate that the member is in tension. The stresses in the members of the truss at the remaining joints in the truss are calculated in the same way. The direction of the forces and the kind of stress can always be determined by sketching in the force polygon for the forces meeting at the joint as in (c) Fig. 24. ALGEBRAIC RESOLUTION 39 It will be seen from the foregoing that the method of algebraic resolution consists in applying the principle of the force polygon to the external forces and internal stresses at each joint. Since we have only two fundamental equations for translation (resolution) we can not solve a joint if there are more than two forces or stresses unknown. \Yhere the lower chord of the truss is horizontal as in Fig. 25, we (C) FIG. 25. have by applying fundamental equations (a) and (b) to the joint at the left reaction l-x= + R, sec 6 (11) l-i/ = R l tan 9 (12) the plus sign indicating compression and the minus sign tension. Equa- tions (n) and (12) may be obtained directly from force triangle (c). Equations (n) and (12) are used in calculating the stresses in trusses with parallel chords and lead to the method of coefficients (Chapter X). (b) Forces on One Side of a Section. The principle of resolu- tion of forces may be applied to the structure as a whole or to a por- tion of the structure. If the truss shown in Fig. 26 is cut by the plane A A, the internal stresses and external forces acting on either segment, as in (b) will be in equilibrium. The external forces acting on the cut members as shown in (b) are equal to the internal stresses in the cut members and are opposite in direction. 4 o STRESSES IN FRAMED STRUCTURES Applying equations (a) and (b) to the cut section 3_ ?/ _|_ 2-3 cos oc 1-x sin 9 =0 (13) 2-3 sin oc 2-^cos9 + R r P, =0 (14) Now, if all but two of the external forces are known, the un- knowns may be found by solving equations (13) and (14). If more (a) (b) FIG. 26. than two external forces are unknown the problem is indeterminate as far as equations (13) and (14) are concerned. Graphic Resolution. In Fig. 27 the reactions R^ and R 2 are found by means of the force and equilibrium polygons as shown in (b) and (a). The principle of the force polygon is then applied to each joint of the structure in turn. Beginning at the joint L the forces are shown in (c), and the force triangle in (d). The reaction R^ is known and acts up, the upper chord stress i-.v acts downward to the left, and the lower chord stress i-;y acts to the right closing the polygon. Stress i-x is compression and stress i-y is tension, as can be seen by applying the arrows to the members in (c). The force polygon at joint U is then constructed as in (f). Stress i-.v acting toward joint U and load /\ acting downward are known, and stresses 1-2 and 2-x are found by completing the polygon. Stresses 2-x and 1-2 are compression. The force polygons at joints L x and f/ 2 are constructed, in the order given, in the same manner. The known forces at any joint are indicated in direction in the force poly- GRAPHIC RESOLUTION 20' 3O' Scale of Lengths P, *- ' L. At a distance x from the left support, the bending moment is which is the equation of a parabola. The parabola may be constructed by means of the force and equi- librium polygons by assuming that the uniform load is concentrated at points in the beam, as is assumed in a bridge truss, and drawing the force and equilibrium polygons in the usual way, as in Fig. 38. The greater the number of segments into which the uniform load is divided the more nearly will the equilibrium polygon approach the bending moment parabola. The parabola may be constructed without drawing the force and equilibrium polygons as follows : Lay off ordinate m n n p = bend- ing moment at center of beam = l / w L 2 . Divide a p and b p into the same number of equal parts and number them as shown in (b). Join the points with like numbers by lines, which will be tangents to the BEAMS Load = w Ibs per lin- ft- L r \** i x ^ x Ri >- V *** i Y "* ~"~ "" ^ ^ ^ x > k s |-H I RZ *~-^*H- "^90 / i - ->i 1 s / i-J r'/ (a) Force Polygon (c) Shear Diagram FiG. 38. required parabola. It will be seen in Fig. 38 that points on the parabola are also obtained. The shear at any point x, will be S=R^ wx = -^wL wx = w (- x} which is the equation of the inclined line shown in (c) Fig. 38. The shear at any point is therefore represented by the ordinate to the shear diagram at the given point. Property of the Shear Diagram. Integrating the equation for shear between the limits, x = o and x = x we have which is the equation for the bending moment at any point, x, in the beam, and is also the area of the shear diagram between the limits given. From this we see that the bending moment at any point in a simple beam uniformly loaded is equal to the area of the shear dia- gram to tne left of the point in question. The bending moment is also equal to the algebraic sum of the shear areas on either side of the point. CHAPTER IX. MOVING LOADS ON BEAMS. Uniform Moving Loads. Let the beam in Fig. 39 be loaded with a uniform load of p Ibs. per lineal foot, which can be moved on or off the beam. x Uniform Moving Load = p Ibs- per lin- ft- (a) Maximum Positive Shear Load moving off TO The right (b) Maximum Negative Shear Load moving off to the left FIG. 39. To find the position of the moving load that will produce a max- imum moment at a point a distance a from the left support, proceed as follows: Let the end of the uniform load be at a distance x from the left reaction. Then taking moments about R 2 we have and the moment at the point whose abscissa is a will be 58 MOVING LOADS ON BEAMS Differentiating (16) and placing derivative of M with respect to x equal to zero, we have after solving x=o (17) Therefore the maximum moment at any point in a beam will occur when the beam is fully loaded. The bending moment diagram for a beam loaded with a uniform moving load is constructed as in Fig. 38. To find the position of the moving load for maximum shear at any point in a beam loaded with a moving uniform load, proceed as fol- lows : The left reaction when the end of the moving load is at a dis- tance x from the left reaction, will be A- (/:)3 P (15) and the shear at a point at a distance a from the left reaction will be S=R,-(a-^p=^-^L p-(a-- X }p (18) which is the equation of a parabola. By inspection it can be seen that S will be a maximum when a = x. The maximum shear at any point in a beam will therefore occur at the end of the uniform moving load, the beam being fully loaded to the right of the point as in (a) Fig. 39 for maximum positive shear, and fully loaded to the left of the point as in (b) Fig. 39 for maximum negative shear. If the beam is assumed to be a cantilever beam fixed at A, and loaded with a stationary uniform load equal to /> Ibs. per lineal foot, and an equilibrium polygon be drawn with a force polygon having a pole distance equal to length of span, L, the parabola drawn through the points in % the equilibrium polygon will be the maximum positive shear diagram, (a) Fig. 39. The ordinate at any point to this shear diagram will represent the maximum positive shear at the point to the same scale as the loads (for the application of this principal to bridge trusses see Fig. 50, Chapter X). CONCENTRATED MOVING LOADS 59 Concentrated Moving Loads. Let a beam be loaded with con- centrated moving loads at fixed distances apart as shown in Fig. 40. A 1 fc __ a _._>).- b--*- c - ^ u -- -"^- FIG. 40. To find the position of the loads for maximum moment and the amount of the maximum moment, proceed as follows: The load P 2 will be considered first. Let x be the distance of the load P 2 from the left support when the loads produce a maximum moment un- d-r load P 2 . Taking momenta about R 2 we have ia P*bPt(b + c) L and the bending moment under load P 2 will be (2 l Differentiating (20) we have d M (L 2 x} (P, + P 2 + P 3 + P.) + P, aP, b P^b+c) = Q d x L and solving (21) for x we have JL P^-P*b-P<(b+c) (22) '- 2 ~ 2(P l + P 2 +P 3 + P<) Now Pj_ a P n & F 4 (& + c) , is the static moment of the loads about P 2 and 60 MOVING LOADS ON BEAMS = dlst ance from P to P i P . /? _LP f l I ~'$ I -* 3 ~T~ * 4 center of the gravity of all the loads. Therefore, for a maximum moment under load /%, it must be as far from one end as the center of gravity of all the loads is from the other end of the beam, Fig. 40. The above criterion holds for all the loads on the beam. The only way to find which load produces the greatest maximum is to try each one, however, it is usually possible to determine by inspection which load will produce a maximum bending moment. For example the maximum moment in the beam in Fig. 40 will certainly come under the heavy load P 2 . The above proof may be generalized without diffi- culty and the criterion above shown to be of general application. For two equal loads P = P at a fixed distance, a, apart as in the case of a traveling crane, Fig. 41, the maximum moment will occur under one of the loads when L a i "C-G-of Loads ^r-2. >, t< -2-5"" L L *K-, L H ^ f L H FIG. 41. Taking moments about the right reaction we have -- L (23) and the maximum bending moment is (24) 2L CONCENTRATED MOVING LOADS 61 There will be a maximum moment when either of the loads satis- fies the above criterion, the beilding moments being equal. By equating the maximum moment above to the moment due to a single load at the center of the beam, it will be found that the above criterion holds only when a < 0.586 L Where two unequal moving loads are at a fixed distance apart the greater maximum bending moment will always come under the heavier load. The maximum end shear at the left support for a system of con- centrated loads on a simple beam, as in Fig. 40, will occur when the left reaction, R lf is a maximum. This will occur when one of the wheels is infinitely near the left abutment (usually said to be over the left abutment). The load which produces maximum end shear can be easily found by trial. The maximum shear at any point in the beam will occur when one of the loads is over the point. The criterion for determining: which load will cause a maximum shear at any point, x, in a beam will now be determined. In Fig. 40, let the total load on the beam, P v + P 2 + P s -\- F 4 = W, and let x be the distance from the left support to the point at which we wish to determine the maximum shear. When load P x is at the point, the shear will be equal to the left reaction, which is found by substituting x + a for x in (19) to be (L-x-a] W+ P ia -P z b- P 4 (6 + c) 3i /fi - L and when P 2 is at the point the shear will be (L x) : Subtracting S, from S we have 62 MOVING LOADS ON BEAMS Now $! will be greater than S 2 if P x L is greater than PF a, or if The criterion for maximum shear at any point therefore is as follows : The maximum positive shear in any section of a beam occurs when P / the foremost load is at the section, provided W is not greater than - P T If W 7 is greater than - , the greatest shear will occur when some succeeding load is at the point. Having determined the position of the moving loads for maxi- mum moment and maximum shear, the amount of the moment and shear can be obtained as in the case of beams loaded with stationary loads. // , - * CHAPTER X. STRESSES IN BRIDGE TRUSSES. Method of Loading. The loads on highway bridges, and in many cases on railway bridges as well, are assumed to be concent-rated at the joints of the loaded chord, and if the panels of the truss are equal the joint loads are equal. The assumption of joint loads simplifies the solution and gives values for the stresses that are on the safe side. Equal joint loads will be assumed in this discussion. Algebraic Resolution.* Let the Warren truss in Fig. 42 have dead loads applied at the joints as shown. From the fundamental equations for equilibrium for translation, reaction R^ = R 2 = 3 W. WSecG -, WtanS Dead Load Coefficients FIG. 42. The stresses in the members are calculated as follows: Resolving at the left reaction, stress in i-.i- = + 3 W sec 0, and stress in i-y = - 3 W tan 0. Resolving at first joint in upper chord, stress in 1-2 = - 3 W sec , and stress in 2-.r = + 6 W tan . Resolving at second joint in lower chord, stress 2-3 = 4-2 W sec0, and stress 3-3; = 8 / r tan . And in like manner the stresses in the remaining members arc found as shown. The coefficients shown in Fig. 42 for the chords are to be multiplied by W tan 0; while those for the webs are to be multiplied by W sec . *Also called "Method of Sections." 64 STRESSES IN BRIDGE TRUSSES It will be seen that the coefficients for the web stresses are equal to the shear in the respective panels. Having found the shears in the different panels of the truss, the remaining coefficients may be found by resolution. Pass a section through any panel and the algebraic sum of the coefficients will be equal to zero. Therefore, if two coefficients are known, the third may be found by addition. Beginning with member i-x, which is known and equals 3 ; coefficient of z-x = ( 3 3) = + 6 ; coefficient of 3-3; = (+ 6 + 2) = - - 8 ; coefficient of ^-x = ( 8 2) = + 10; coefficient of 5-37 = (+ 10 + i) = n ; coefficient of 6-x = ( n i) = + 12 ; coefficient of y-y = (+ 12-}-) = I2 > Loading for Maximum Stresses. The effect of different positions of the loads on a Warren truss will now be investigated. Let the truss in Fig. 43 be loaded with a single load P as shown. Chord Stresses - Coefficients x PtanG + t '9 ** +$ ** ^ Web Stresses < Coefficients for One Load FIG. 43. r p The left reaction, R^ = -y-P, and the right reaction, R 2 = -y . The 6 6 stress in i-y = y- P tan 6 , and stress in i-x = + "7" -P sec * The stress in 1-2 = -=- p sec and stress in 2-3 =. - -y- P sec 0, etc. The remaining coefficients are found as in the case of dead loads by adding coefficients algebraically and changing the sign of the result. In Fig. 44 the coefficients for a load applied at each joint in turn are shown. for the different members; the coefficients for the load on left being given in the top line. MAXIMUM AND MINIMUM STRESSES PsecG Maximum and Minimum Coefficients FIG. 44. The following conclusions may be drawn from Fig. 44. (1) All loads produce a compressive stress in the top chord and a tensile stress in the bottom chord. (2) All the loads on one side of a "panel produce the same kind of stress in the web members that are inclined in the same direction on that side. For maximum stresses in the chords, therefore, the truss should be fully loaded. For maximum stresses in the web members the longer segment into which the panel divides the truss should be fully loaded ; while for minimum stresses in the web members the shorter segment of the truss should be fully loaded. The conditions for maximum loading of a truss with equal join! loads are therefore seen to be essentially the same as the maximum load- ing of a beam with a uniform live load. Stresses in Warren Truss. The coefficients for maximum and minimum stresses in aWarren truss due to live load are shown in Fig. 45. These coefficients are seen to be the algebraic sum of the co- efficients for the individual loads given in Fig. 44. The live load chord coefficients are the same as for dead load, and if found directly are found in the same manner. The maximum web coefficients may be found directly by taking off one load at a time beginning at the left. The left reaction, which may be found by algebraic moments, will in each case be the coefficient of 66 STRESSES IN BRIDGE TRUSSES the maximum stress in the panel to the left of the first load. A rule for finding the coefficient of left reaction for any loading is as follows : Multiply the number of loads on the truss by the number of loads plus unity, and divide the product by twice the number of panels in the truss and the result will be the coefficient of the left reaction. -8 in Webs Minimum In Webs Live Load Coefficients FIG. 45. If the second differences of the maximum coefficients in the web members are calculated, they will be found to be constant, which shows that the coefficients are equal to the ordinates of a parabola. 6 1 10 4 1 15 5 1 21 6 SECOND DIFFERENCES OF NUMERATORS OF WEB COEFFICIENTS. This relation gives an easy method for checking up the maximum web coefficients, since the numerators of the. coefficients are always the same beginning with unity in the first panel on the right and progressing in order I, 3, 6, 10, etc.; the denominators always being the number of panels in the truss. It should be noted that in the Warren truss the members meeting on the unloaded chord always have stresses equal in amount, but op- posite in sign. Stresses in Pratt Truss.-- In the Pratt truss the diagonal members are tension members and counters (see dotted members in (c) Fig. 46) must be supplied where there is a reversal of stress. The coefficients for the dead and live load stresses in the Pratt truss shown in (a) and (b) STRESSES IN PRATT TRUSS 67 Fig. 46, are found in the same manner as for a Warren truss. The member U 1 L acts as a hanger and carries only the load at its lower end. The stresses in the chords are found by multiplying the coeffi- cients by W tan 0, and in the inclined webs by multiplying the co- efficients by W sec $ The stresses in the posts are equal to the ver- tical components of the stresses in the inclined web members meeting them on the unloaded chord. U! Dead Load Coefficients Detd Load Stresses Dead Load =8Tbns per Joint- Sec 6 = 1-28- Tan 6 =0-80 (a) R L. -2z Li -^ L 3 Live Load Coefficients and Stresses Live Load =l67bns per Joint- Sec0 = 1-28- "Tan 0=0-80 (b) Rl -E| ' > Li - ^8-0 U -76-8 L3 -25-6 L 2 '16-0 L ; - Maximum Stresses Minimum Stresses (C) FIG. 46. 68 STRESSES IN BRIDGE TRUSSES / The maximum chord stresses shown on the left of (c) are equal to the sum of the live and dead load chord stresses. The minimum chord stresses shown on the right of (c) are equal to the dead load chord stresses. The maximum and minimum web stresses are found by adding algebraically the stresses in the members due to dead and live loads. Since the diagonal web members in a Pratt truss can take tension only, counters must be supplied as U 3 Z/ 1 a in panel Iy 1 2 L 3 . The tensile stress in a counter in a panel of a Pratt truss is always equal to the compressive stress that would occur in the main diagonal web member in the panel if it were possible for it to take compression. Care must always be used to calculate the corresponding stresses in the vertical posts. Graphic Resolution. The stresses in a Warren truss due to dead loads are calculated by graphic resolution in Fig. 47. The solution is the same as for ceiling loads in a roof truss. The loads beginning with the first load on the left are laid off from the bottom upwards. The analysis of the solution is shown on the stress diagram and truss and needs no explanation. From the stresses in the members it is seen (a) that web members meeting on the unloaded chord have stresses equal in amount but op- posite in sign, and (b) that the lower chord stresses are the arithmetical means of the upper chord stresses on each side. The live load chord stresses may be obtained from the stress dia- gram in Fig. 47 by changing the scale or by multiplying the dead load stresses by a constant. The live load web stresses may be obtained by calculating the left reactions for the loading that gives a maximum shear in the panel (no loads occurring between the panel and the left reaction), and then con- structing the stress diagram up to the member whose stress is required. In a truss with parallel chords it is only necessary to calculate the stress in the first web member for any given reaction since the shear is con- stant between the left reaction and the panel in question. GRAPHIC RESOLUTION 69 The live load web stresses may all be obtained from a single dia- gram as follows: With an assumed left reaction of, say, 100,000 Ibs. construct a stress diagram on the assumption that the truss is a canti- lever fixed at the right abutment and that there are no loads on the 2O-O .j -v 17.60 Warren Truss. Span \ZO'-0* Pi 7 Tons. FIG. 47. tni. c s. Then the maximum stress in any web member will be equal to the stress scaled from the diagram, mutilplied by 100,000, divided by the left reaction that produces the maximum stress. This method is a very convenient one for finding the stresses in a truss with inclined chords. 70 STRESSES IN BRIDGE TRUSSES Algebraic Moments. The dead and live load stresses in a truss with inclined chords are calculated by algebraic moments in Fig. 48. The conditions for maximum loading are the same in this truss as in a truss with parallel chords, and are as follows: Maximum chord stresses occur when all loads are on; minimum chord stresses occur when no live load is on ; maximum web stresses in main members occur when the longer segment of the truss is loaded ; and minimum stresses in main members and maximum stresses in counters occur when the shorter segment of the truss is loaded. An apparent exception to the kilter rule occurs in post. U 2 L 2 which has a maximum stress when the truss is fully loaded with dead and live loads. -' 60.00 MAXIMUM AND MINIMUM STRESSES IN CAMELS BACK TRUSS BY ALGEBRAIC MOMENTS Dead Load L'ive Load 3 Tons per Joi fl " > FIG. 48. To find the stress in member C7 L 2 take moments about point A, the intersection of the upper and lower chords produced. The dead load stress is then given by the equation /! L 2 x 70. 7 + RI x 60 W x 80 = o C7j_ L 2 x 70 . 7 = 6 x 60 + 3 x 80 = 120 foot-tons C/ L 2 i . 70 tons ALGEBRAIC MOMENTS 71 The maximum live load stress occurs when all loads are on except L lf and U-i L 2 x 70 7 + RI x 60 r= o Uj_ L 2 x 70. 7 = | F x 60 = 576 foot-tons 7 Z, 2 = 8. 14 tons The maximum live load stress in counter U 2 Z, x occurs with a load a^ L!, and is given by the equation U 2 L l x 62.43 + RI x 60 P x 80 = o 7 2 L! X 62.43 n : _A P X 60 8x80 7 2 L! = 4.10 tons The dead load stress in counter U 2 L^ when main member t/ L 2 is not acting will be U 2 Lj x 62.43 = + 120 foot-tons U 2 L! = + !-9 2 tons The maximum stress in C7 L 2 is therefore 1.70 8.14 = - 9.84 tons, and the minimum stress is zero. The maximum stress in counter U 2 L is + 1.92 4.10 = 2.18 tons, and the minimum stress is zero. The stresses in the remaining members may be found in the same manner. To obtain stresses in upper chords U^ U 2 and U 2 U 2 , take mo- ments about Lo as a center ; to obtain stress in lower chord L b L take moments about U-^ as a center. The dead load and maximum live load stress in post U 2 L 2 is equal to the vertical component of the dead and live loads, respectively, in upper chord U 1 U. 2 . The stresses in L U lf L L lf L. 2 ZA, U 2 U 1 2 and U 2 L 1 ? are most easily found by algebraic resolution. Graphic Moments. The dead load stresses in the chords of a Warren truss are calculated by graphic moments in Fig. 49. Bending Moment Polygon. The upper chord stresses are given by the ordinates to th| / * FIG. 49. ber of panels in the truss were odd the mid-ordinate would not be equal to any chord stress. The parabola is then constructed as shown in Fig. 49. The live load chord stresses may be found from Fig. 49 by chang- ing the scale or by multiplying the dead load chord stresses by a con- stant. Shear Polygon. In Chapter IX it was shown that the maximum shear in a beam at any point could be represented by the.ordinate to a parabola at any point. The same principle holds for a bridge truss loaded with equal joint loads, as will now be proved. In Fig. 50 assume that the simple Warren truss is fixed at the left end as shown, and that right reaction R^ is not acting. Then with all joints fully loaded with a live load P, construct a force polygon as shown, with pole o and pole distance H = span L, and beginning at point a in the. load line of the force polygon construcl the equilibrium polygon a g h for the cantilever truss. Now the bending moment at the left support will be equal to GRAPHIC MOMENTS X 73 Y /. \/ 3 \/ 5 \ / FIG. 50. ordinate F multiplied by the pole distance H. But the truss is a sim- ple truss and the moment of the right reaction will be equal to the moment at the left abutment and F t H = R, L and since H = L -Y L = RL and Now, with the loads remaining stationary, move the truss one panel to the right as shown by the dotted truss. With the same force polygon draw a new equilibrium polygon as above. This equilibrium polygon will be identical with a part of the first equilibrium polygon as shown. As above, the bending moment at left reaction is F 3 H = Y z L 7?n L, and F 3 = R^. In like manner F 5 can be shown to be the right reaction with three loads on, etc. Since the bridge is symmetrical with reference to the center line, the ordinates to the shear polygon in Fig. 50, are equal to the maximum shears in the panel to the right of the or- dinate as the load moves off the bridge to the right. 74 STRESSES IN BRIDGE TRUSSES To draw the shear parabola direct, without the use of the force and equilibrium polygons proceed as follows : At a distance of a panel length to the left of the left abutment lay off to scale a lond line equal to one-half the total load on the truss, divide this load line into as many parts as there are panels in the truss, and beginning at the top, which call I, number the points of division of the load line I, 2, 3, etc., as in Fig. 49. Drop vertical lines from the panel points and number them i, 2, 3, etc., beginning with the load line, which will be numbered I, the left reaction numbered 2, etc. Now connect the numbered points in the load line with the point f, which is under the first panel to the left of the right abutment; and the intersection of like numbered lines will give points on the shear parabola. It should be noted that the line h g is a secant to the parabola and not a tangent as might be expected. The dead load shear is laid off positive downward in Fig. 50 to the same scale as the live load shears, and the maximum and minimum shears due to dead and live loads are added graphically. The stresses in the web members are calculated graphically in Fig. 50. Wheel Loads. The criteria for maximum moments and shears in bridge trusses loaded with wheel loads are as follows : (1) Maximum Moment at any joint in a bridge loaded with wheel loads will occur when the average load on the left of the section is the same as the average load on the whole span. (2) Maximum Shear in any panel in a bridge loaded with wheel loads will occur when the load on the panel is equal to the load on the bridge divided by the number of panels. For the proof of these criteria and for a more complete discus- sion of the subject, see the various standard text books on bridges. CHAPTER XL STRESSES IN A TRANSVERSE BENT. Dead and Snow Load Stresses. The stresses due to the dead load in the trusses of a transverse bent are the same as if the trusses were supported on solid walls. The stresses in the supporting columns are due to the dead load of the roof and the part of the side walls supported by the columns, and are direct compressive stresses if the columns are not fixed at the top. If the columns are fixed at the top the deflection of the truss will cause bending stress in the columns. The dead load produces no stress in the knee braces of a bent of the type shown in Fig. I except that due to deflection of the truss, which may usually be omitted The stresses may be computed by algebraic or graphic methods. The stresses due to snow load are found in the same way as the dead load stresses. In localities having a heavy fall of snow the freez- ing and thawing often cause icicles to form on the eaves of sufficient weight to tear off the cornice, unless particular care has been exercised in the design of this detail. Wind Load Stresses. The analysis of the stresses in a bent due to wind loads is similar to the analysis of the stresses in the portal of a bridge. The external wind force is taken (i) as horizontal or (2) as normal to all surfaces. The first is the more common assumption, although the second is more nearly correct. For a comparison of the stresses in a bent due to the wind acting horizontal and normal, see Figs. 54, 55, 56 and 57, and Table V. In the discussion which immed- iately follows, the wind force will be assumed to act horizontally. The magnitude of the wind stresses in the trusses, knee braces and 76 STRESSES IN A TRANSVERSE BENT columns will depend (a) upon whether the bases of the columns arc fixed or free to turn, (b) upon whether the columns are rigidly fixed to the truss at the top, and (c) upon the knee brace and truss con- nections. Of the numerous assumptions that might be made, only two, the most probable, will be considered, viz.: (I) columns pin connected (free to turn) at the base and top, and (II) columns fixed at the base and pin connected at the top. Columns in mill buildings are usually fixed by means of heavy bases and anchor bolts. Where the columns support heavy loads the dead load stress in the columns will assist somewhat in fixing them. Where the dead load stress plus algebraically the vertical component of the wind stress in the column, multiplied by one-half the width of the base of the column parallel to the direction of the wind, is greater than the bending moment developed at the base of the leeward column when the columns are considered as fixed, the columns will be fixed without anchor bolts (see Chapter XII, Fig. 61). In any case the resultant moment is all that will be taken by the anchor bolts. The dead load stresses in mill buildings are seldom sufficient to give material assistance in fixing the columns. Unless care is used in anchoring columns it is best to design mill buildings for columns hinged at the base. The general problem of stresses in a transverse bent for Case 1 and Case II, in which the stresses and forces are determined by alge- braic methods, will now be considered. The application of the general problem will be further explained by the graphic solution of a par- ticular problem. ALGEBRAIC CALCULATION OF STRESSES: Case I. Columns Free to Turn at Base and Top. In Fig. 51, H H 1 W = horizontal reaction at the base of the column due to external wind force, W . IV I = vertical reaction at base of column due to 2 s the wind force, W . The wind produces bending in the columns, and also the direct COLUMNS HINGED AT THE; BASE 77 stresses V and F 1 . Maximum bending occurs at the foot of the knee brace and is equal to (H - - W^} d on the windward side, and H 1 d on the leeward side. These bending moments are the same as the bend- ing moments in a simple beam supported at both ends and loaded with a concentrated load at the point of maximum moment. Since the max- MK 1 H v (a) External Forces H' H 1 v'(b) (c) Leeward Col- Beam H 1 (d) Shear (e) Moment FIG. 51. imum moment occurs at the foot of the knee brace in the leeward column, we will consider only that side. We will assume that the lee- ward column (b), Fig. 51, acts as a simple beam with reactions H 1 and C and a concentrated load B, as in (c). The reaction C and load B will now be calculated. From the fundamental equation, of equilibrium, summation hori- zontal forces equal zero, we have B = //' + C (25) Taking moments about &, we have C (h d) = H 1 d r= //1 d (26) h d The stresses K, U and L can be computed by means of the follow- ing formulas : K = B cosecant in (27) where m = angle knee brace makes with column; U (F 1 K cos m) cosecant n (28) where n = angle of pitch of roof; and 78 STRESSES IN A TRANSVERSE BENT L = C U cos n / (29) In calculating the corresponding stresses on the windward side, the wind components acting at the points (a), (b) and (c) must be subtracted from H, B and C. The shear in the leeward column is equal to J/ 1 below and C above the foot of the knee brace, (d) Fig. 51. The moment in the column is shown in (e), Fig. 51, and is a max- imum at the foot of the knee brace and is, M = 7/ 1 d. The maximum fibre stress due to wind moment and direct loading in the columns will occur at the foot of the knee brace in the leeward column, and will be compression on the inside and tension on the out- side fibres, and is given by the formula* f f - p + M y r * +A ~~A~~ Ph- ' (30) WE where / = maximum fibre stress due to flexure ; f 2 = fibre stress due to direct load P; A = area of cross-section of column in square inches ; M = bending moment in inch-pounds = /f 1 d; y =: distance from neutral axis to extreme fibre of column in inches ; / = Moment of Inertia of column about an axis at right angles to the direction of the wind ; P direct compression in the column in pounds ; h = length of the column in inches ; = the modulus of elasticity of steel = 28,000,000 ; Ph* IQ is minus when P is compression and plus when P is tension. The maximum compressive wind stress is added to the direct dead and minimum snow load compression and governs the design of the column. "This formula was first deduced by Prof. J. B. Johnson. For deduction of the formula see Chapter XV, or "Modern Framed Structures" by Johnson, Bryan and Turneaure. COLUMNS FIXED AT THE BASE 79 Having the stresses K, U , and L, the remaining stresses in the truss can be obtained by ordinary algebraic or graphic methods. For a simple graphic solution of the stresses in a bent for Case I, in which these stresses are computed graphically, see Fig. 54 for wind horizontal, and Fig. 56 for wind normal to all surfaces. Case II. Columns Fixed at the Base. With columns fixed at the base the columns may be (i) hinged at the top, or (2) rigidly fixed to the truss. (i) Columns fixed at the base and hinged at the top. It will be further assumed that the deflections at the foot of the knee brace and the top of the column, Fig. 52, are equal. zw 3- Pr M b (d) (e) Shear Moment *r' I -H f H' t H H' J (a) i J/W 'cl External Forces Leeward Col. Beam FIG. 52. In Fig. 52 we have as in Case I V and V 1 are not as easily found as in Case I, but will be cal- culated presently. The leeward column will be considered and will have horizontal external forces acting on it as shown in (c) Fig. 52. For convenience we will consider the leeward column as a beam fixed at a and acted upon by the horizontal forces B and C as shown in (c) Fig. 52, the de- llcction of the points b and c being equal by hypothesis. From the fundamental condition of equilibrium, summation hori- zontal forces equal zero, we have B = W + C (31) 8o STRESSES IN A TRANSVERSE; BENT To obtain B and C a second equation is necessary. From the theory of flexure we have for the bending moment in the column at any point y, where the origin is taken at the base of the column, when y^d y^ (32) Integrating (32) between the limits 3> = and y = d, we have dy L 2 2 J y = o Bd* (33) 2 Now (33) equals E I times the angular change in the direction of the neutral axis of the column from y = o to y = d. When y ^ d, we nave M = E I ^!_5 = _ C(hy) (34) d y 2 Integrating (34) we have E I--= _*> + + F 2 (35) dy 2 Now (35) equals H I times the change in direction of the neutral axis of the column at any point from y = d to y = h. To determine the constant F 2 in (35) we have the condition that the angle at y = d must be the same whether determined from equation (33) or equation (35). Equating (33) and (35) and making y =_ d f we have * = (36: Substituting this value of F 2 in (35) we have Integrating (37) between the limits y = d and y = h, we have Chy2 4- c - v * ~~ 2 _ 2 ^ ^ 3 \ ~ / COLUMNS FIXED AT THE BASE 81 Now (38) equals / times the deflection of the column from y = d to y = h, which equals zero by hypothesis. Solving (38) we have C 3^ 2 A- 3d 3 B 3 h d 2 -. = 2^+yj*- rf ' (39) In a beam fixed at one end there is a point of inflection at some point, between y = o and y = d, where the bending moment equals zero. Now if y equals the value of y for the point of inflection, we have from (32) B (d 3' ) = C (h y ) and C_ d y Q , 4Q , B h-y Q Equating the second members of equations (39) and (40) and solving for y , we have To find the relations between y and d, we will substitute h in terms of d in (41) and solve for ;y . For d= h = d Solving (31) and (39) for C, we have ~~2~'(A-ASK 83 The maxiinuni fibre stress occurs at the foot of the knee brace, and is given by the formula f f - P + My ~ ( 30a ) ~ WE The nomenclature being the same as for (30) except h, which is the distance in inches from the point of contra-flexure to the top of the column. (2) Columns fixed at the base and top. In this case it can be seen by inspection that the point of inflection is at a point y = and we have for this case B == H- + C ( 3 ia) t , = 2L* =Mk (32a) It is difficult to realize the exact conditions in either (i) or (2), in Case II, and it is probable that when an attempt is made to fix columns at the base, the actual conditions lie some place between (i) and (2). It would therefore seem reasonable to assume the minimum value, TO = as the best value to use in practice. This assumption is commonly made and will be made in the problems which follow. Having the external forces H l f B, C and F 1 the stresses K, U and L are computed by formulas (27), (28) and (29). The remaining stresses in the truss can then be computed by the ordinary algebraic or graphic methods. IJpr a simple graphic solution of this problem, where the ex ternal forces B and C are not computed, see Fig. 55 and Fig. 57. Maximum Stresses. It is not probable that the maximum snow and wind loads will ever come on the building at the same time, and it is therefore not necessary to design the structure for the sum of the maximum stresses due to dead load, snow load and wind load. A 84 STRESSES IN A TRANSVERSE BENT common method is to combine the dead load stresses with the snow or the wind load stresses that will produce maximum stresses in the members. It is, however, the practice of the author to consider that a heavy sleet may be on the roof at the time of a heavy wind, and to design the structure for the maximum stresses caused by dead and snow load ; dead load, minimum snow load and wind load ; or dead load and wind load. It should be noted that the maximum reversals occur when the dead and wind load are acting. For a comparison of the stresses due to the different combinations see Table VI. A common method of computing the stresses in a truss of the Fink type for small steel frame mill buildings is to use an equivalent uni- form vertical dead load ; the knee braces and the members affected directly by the knee braces being designed according to the judgment of the engineer. This method is satisfactory and expeditious when used by an experienced man, but like other short cuts is dangerous when used by the inexperienced. For a comparison of the stresses in a 6o-foot Fink truss by the exact and the approximate method above, see Table VI. Stresses in End Framing. The external wind force on an end bent will be one-half what it would be on an intermediate trans- verse bent, and the shear in the columns may be taken as equal to the to- tal external wind force divided by the number of columns in the braced panels. The stresses in the diagonal rods in the end framing, as in Fig, i, will then be equal to the external wind force H, divided by the number of braced panels, multiplied by the secant of the angle the diagonal rod makes with a vertical line, (For analysis of Portal Bracing see Chapter XII). Bracing in the Upper Chord and Sides. The intensity of the wind pressure is taken the same on the ends as on the sides, and the wind loads are applied at the bracing connection points along the end rafters and the corner columns. The shear transferred by each braced panel is equal to the total shear divided by the number of braced panels. The stresses in the diagonals in each braced panel are com- GRAPHIC CALCULATION OF STRESSES 85 puted by applying wind loads at the points above referred to, the wind loads being equal to the total wind loads divided by the number of panels. The stresses are computed as in a cantilever truss. The brac- ing in the plane of the lower chord is designed to prevent undue de- flection of the end columns and to brace the lower chords of the trusses. All wind braces should be designed for, say, 5,000 pounds initial stress in each member, and the struts and connections should be proportioned to take the resulting stresses. It should be noted that a mill building can be braced so as to be rigid without knee braces if the bracing be made sufficiently strong. GRAPHIC CALCULATION OF STRESSES. Data. To il- lustrate the method of calculating the stresses in a transverse bent by graphic methods, the following data for a transformer building similar to one designed by the author will be taken. The building will consist of a rigid steel frame covered with cor- rugated steel and will have the following dimensions: Length of building, 80' o"; width of building, 60' o" ; height of columns, 20' o"; pitch of truss, ]/\ (6" in 12"); total height of building, 35' o"; the trusses will be spaced 16' o" center to center. The trusses will be riveted Fink trusses. Purlins will be placed at the panel points of the trusses and will be spaced for a normal roof load of 30 Ibs. per square foot. The roof covering will consist of No. 20 corrugated steel with 2^-inch corrugations, laid with 6-inch end laps and two cor- rugations side lap, with anti-condensation lining (see Chapter XVIII). The side covering will consist of an outside covering of No. 22 corru- gated steel with 2^ -inch corrugations, laid with 4-inch end laps and one corrugation side lap; and an inside lining of No. 24 corrugated steel with 1^4 -inch corrugations, laid with 4-inch end laps and one corrugation side lap. For additional warmth two layers of tar paper will be put inside of the lining. Three 36-inch Star ventilators placed on the ridge of the roof will be used for ventilation. The general ar- angement of the framing and bracing will be as in Fig. I and Fig. 81. 86 STRESSES IN A TRANSVERSE BENT The approximate weight of the roof per square foot of horizontal projection will be as follows: Trusses 3.6 Ibs. per sq. ft. Purlins and Bracing 3.0 " Corrugated Steel 2.4 " Roof Lining I .o " " " " Total 10. o " " " " The maximum snow load will be taken at 20 pounds, and the minimum snow load at 10 pounds per square foot of horizontal pro- jection of roof. The wind load will be taken at 20 pounds per square foot on a vertical projection for the sides and ends of the building, 20 pounds per square foot on a vertical surface when the wind is considered as acting horizontally on the vertical projection of the roof, and 30 pounds per square foot on a vertical surface when the wind is consid- ered as acting normal to the roof. The stresses in an intermediate transverse bent will be calculated for the following: CASE i. Permanent dead and snow loads. CASE 2. A horizontal wind load of 20 pounds per square foot on the sides and vertical projections of the roof, with the columns hinged ar the base. CASE 3. Same wind load as in Case 2, with columns fixed at the base. CASE 4. A horizontal wind load of 20 pounds per square foot on the sides, and the normal component of a horizontal wind load of 30 pounds per square foot on the roof, with columns hinged at the base. CASE 5. Same wind load as in Case 4, with columns fixed at the base. Case i. Permanent Dead and Snow Load Stresses. On ac- count of the limited size of the stress diagram the secondary members have been omitted and the loads applied as shown in Fig. 53. The DEAD AND SNOW LOAD STRESSES loads producing stresses in the truss are laid off to the prescribed scale, .i^-y being the left, and y-.r s the right reaction.. The stresses are cal- culated as follows: Beginning with the left reaction, x^-y, draw lines through .\\ and y, parallel to the upper and lower chords of the truss, respectively, and the line x^-2, will represent the compressive stress in the member .\\-2 and v-2 will represent the tensile stress in the member y-2 to the scale of the stress diagram. Data Span ,L, 60-0" c toe Length of Buiding,80-0"c-to c- Distance c-to c Trusses ,16-0" Height of Columns 20'-0" Pitch of Roof i(6"m 12") Le 60 CASE I Dead Load lOlbs persq-ft nor projection Dead Load Stress Dioqram 3000 4000 6000 Compression Tension Snow Load 20 IbS per 59 ft horproj * Snow Load Stress Diagram 4000 8000 I200O FIG. 53. DEAD AND SNOW LOAD STRESS DIAGRAM. Calculate the stresses in the remaining members in like manner, being careful to take the members in order around a joint in com- pleting any polygon. The indeterminate case at the joint U 2 , can be '88 STRESSES IN A TRANSVERSE BENT solved by calculating the stress in 5-6 and substituting it in the diagram, or by substituting an auxiliary member as shown. Compression and tension in the truss and stress diagram in Fig. 53 are indicated by heavy and light lines respectively. The stress in each column is equal to one-half the sum of the ver- tical loads, plus the load carried directly by the column. Case 2. Wind Load Stresses: Wind Horizontal; Columns Hinged. The wind will be considered as acting at the joints, as shown in Fig. 54. Replace the columns with trusses as indicated by the dotted lines. This makes the bent a two-hinged arch (see Chapter XIV), and the stresses will be statically determinate as soon as the horizontal reac- tions H and H 1 at the bases of the columns, have been determined. The usual assumption in mill buildings and portals of bridges is that H = H * = -^- where W = the horizontal component of the external wind force (see Chapter XII). To calculate V and F 1 graphically, pro- duce the line of resultant wind until it inersects a vertical line through the center of the truss, and connect the intersection A with the bases of the columns B and C. From A lay off H = H 1 = , as shown in Fig. 54, and complete the triangles by drawing vertical lines through the ends of these lines. The vertical closing lines will be V = F 1 , as shown in Fig. 54. The stresses are calculated as follows : Beginning with the foot of the column B, lay off the dotted line A-B R. At B, lay off the load a-B 2240 Ibs. ; through a draw a line parallel to auxiliary truss member a-b, and through A draw a line parallel to the column b-A, completing the polygon A-B-a-b. The line a-b in the stress diagram w r ill be the compression in the auxiliary member a-b, and A-b will be the tension in the column A-b. It should be noted that V is equal to the algebraic sum of the vertical components of the stresses in a-b and A-b. Next lay off x-a =. 3200 Ibs. and complete the polygon a-x-c-b by drawing lines through x and b par- allel to the auxiliary truss members x-c and b-c respectively. In like manner determine the stresses at the foot of the knee brace bv con- WIND LOAD STRESSES, CASE 2 89 structing the polygon A-b-c-i ; and at the top of the column by con- structing the polygon c-;r-;r-2-i, etc., until the diagram is cnecked up at C with C-A = R 1 . The indeterminate case at the joint U 2 , can be solved 600 U* CASE 2 Columns Pin Connected Maximum Mom- in Col =940800 in IDS Wind Load Stress Diagram Wind Horizontal, 20 Ibs persq-ft- O 4000 8000 12 84. FIG. 54. WIND LOAD STRESS DIAGRAM, CASE 2. by computing the stress in 5-6 (component due to stress in 6-7), and substituting it in the diagram, or by substituting an auxiliary member. The stresses in the auxiliary members are represented by dotted lines and are of no value in designing the bent. It should be noted that the auxiliary members do not affect the stresses in the trusses and knee braces, which are correctly given in the stress diagram. The maximum stress in the knee brace A-i$ is compression, and occurs on the leeward side. go STRE The maximum shear in the leeward column below the knee brace is J/ 1 5600 Ibs. ; the maximum shear above the knee brace Is 13,100 Ibs. The maximum moment occurs at the foot of the knee brace and is H 1 x 14*. 12 = 940,800 inch-lbs. Case 3. Wind Load Stresses: Wind Horizontal; Columns Fixed at Base. This is Case 2 with the base of the column hinged at the point of contra-flexure. In calculating H and V , Fig." 55, the wind 600 U 5 10 15 20 Wind =8^60 Ibs 208C) 560 L Columns Fixed at Base Max-Mom- in Col- = 376320 in- Ibs. 13 Wind Load Stress Diagram Wind Horizontal 20 Ibs per sq-ft- 4-000 8000 Compression Tension 12 8 4 A FIG. 55. WIND LOAD STRESS DIAGRAM, CASE 3. above the point of contra-flexure only (see formula (45)) produces stresses in the bent. The value of fixing the columns at the base is seen by comparing the stresses in Case 2 with those in Case 3, both being drawn to the same scale. Maximum shear in the leeward column below the knee brace is H 1 -- 4480 Ibs. ; above the knee brace is 5230 Ibs. The maximum positive moment occurs at the foot of the knee brace and negative moment at the foot of the column, and is H* x 7 x 12 = 376,320 inch-lbs. \YiNi> LOAD STRESSES, CASE 4 9 1 Case 4. Wind Load Stresses : Wind Normal ; Columns Hinged. In Fig. 56 the resultant of the external wind forces on the sides and the roof acts through their intersection, and is parallel to C B in the stress diagram (line C B is not drawn). To calculate V and F 1 con- nect the point of intersection, A, of the resultant wind and the vertical line through the center of truss, with the bases of the columns B and C & , \o." ?....? ? '? ? VVmd 6400 \ Ibs > v a \ i Columns Pin Connected Max- Mom- in Col 324000 in-lbs CASE 4 Wind Load Stress Diagram Wind Normal, Roof 18 Ibs- Sides 20 Ibs sqfr- 4OOO 8OOO IMG. V. \\ ) STRESS DIAGRAM, CASE 4. 9 2 STRESSES IN A TRANSVERSE BENT From A lay off one-half of resultant wind on each side, and from the extreme ends drop vertical lines V and F 1 to the dotted lines A B and A C. The vertical lines V and F 1 will be the vertical reactions, the horizontal lines will be H and H 1 , and R and R l will be the resultants of the horizontal and vertical reactions at B and C respectively. The stresses are calculated by beginning at the base of the column B as in Case 2. In the polygon a-B-A-b at B, A-B = R, a-B = 2240 Ibs., and a-b and A-b are the stresses in a-b and A-b respectively. 4. 5 10 15 20 2080 \I5 Columns Fixed at Base\ Max Mom in Co\- 3GI200 in- Ibs rt 16 " CASE 5 Wind Load Stress Diaqram Wind Normal, Roof 18 Ibs Sides 20 Ibs- sq-fr- 4000 8000 Compression Tension FIG. 57. WIND LOAD STRT,;S DTAHRAM, CASE 5. \YIXD LOAD STRESSES, CASE 5 93 The maximum shear in the leeward column below the knee brace is H 1 5500 Ibs., above the knee brace is 12,800 Ibs. ; the maximum moment occurs at the foot of the knee brace and is H 1 x 14 x 12 = 924,000 inch-lbs. Case 5. Wind Load Stresses: Wind Normal; Columns Fixed at Base. This is Case 4 with the base of the column moved up to the point of contra-flexure The maximum shear in the leeward column below the knee brace is 4300 Ibs., above the knee brace is 5000 Ibs. ; the maximum positive moment occurs at the foot of the knee brace and negative moment at the foot of the column and is H 1 x 7 x 12 = 361,200 inch-lbs. For analysis see Fig. 57. Maximum Stresses. The stresses in the different members of the bent for the different cases are given in Table V. The maximum TABLE V. Name of Piece Stresses in a Bent For Dead Load Snow Load Wind Load* Case 2 Case3 Case 4 Case 5 X-2 +93OO i-18900 +3700 +29OO +/54OO +I49OO X-3 +8800 +/76OO +4900 +4OOO +I540O +I49OO X-6" + 8200 +/640O + 4OO + /4OO +/O2OO +IIZ OO X-7 -hi 700 +I54OO + 1400 +3400 +102OO' +//20O X-9 +7700 -H54OO -6/00 -1900 - 14 OO + 2dCO X-13 +9300 +I360O -19600 -3600 -14600 -3600 1-2 -6500 -I660O + 5700 +2600 - 5100 -80OO 2-3 +//OO + 2200 + 50O + 300 + 2400 +2400 3-4- -/ZOO -2400 -6800 -4900 -6500 -6700 4-5 +2200 + 4400 +380O +3000 + 7300 + 6600 5-6 -1200 -2400 - 60O - 600 -2600 -2600 6-7 +1/00, + 2200 + 500 + 50O +2400 +24OO 5-8 -2400 -480O -4300 -33 OO -820O -7400 7-8 -3600 - 7100 -4900 -390O -IO800 -10000 8-9 -3600 - 7200 +75 OO +360O 1-7400 + 35OO 9-12 &ZOO +4-4OO -5700 -32 OO -670O -3200 12-13 -/2oo -2400 +/5200 + 7400 +/4SOO + 7000 Y-4 -7 IOO -14200 +2400 + 800 -6000 -7700 Y-8 -47OO - 7400 +6dOO +4OOO + 22OO - 4OO y-\a -7/00 -14200 +/4200 9 +7700 9700 +2IOO 13-15 -dioo -16600 +4600 +3000 + 5OO -/300 Arl -9000 -6200 -8500 -6700 A-15 +22300 +IIOOO i- 2. 15 00 +/0400 A-b +4-8OO + 3600 -3200 -2 WO + 340O +4500 c-i +46OO + 9600 + 1700 +/3OO + 8000 + 7600 A-17 +4 GOO + 9600 +3100 +2IOO +3300 + 4IOO 15-16 +4300 + 9600 -8600 -3800 -6400 -24CO 94 STKKSSUS IN 'A TRANSVERSE BENT stresses in the different members of the bent for ( I ) dead load plus max- imum snow load; (2) dead load plus wind load, Case 4; (3) dead load plus minimum snow load plus wind load, Case 4; and (4) a vertical dead load of 40 Ibs. per sq. ft. horizontal projection of the roof are given in Table VI. The stresses which control the design of the members may be seen in Table VI. B> comparing these values with the stresses given in the last column the accuracy of the equivalent load method can be seen. TABLE VI. Maximum Stresses ina Bent For Name of Piece Dead Load + fMax-Snow Lo'dd Dead Load + Wind Load Case A- DeadLoad+Min- Snow Load-f Wind Load- Case 4- Vert- Dead Load of 40 Ibs- per Sq- FT- of HonProj- x-2 +28200 +247OO +3430O + 372 OO x-3 +26400 +24200 ' +33OOO + 352 OO X-6 +26400 +/84OO +266OO +32800 X-7 ' +23100 +I79OO +256OO +3OdOO X-9 +23100 + 6300 +/4OOO +30800 X-13 +28200 - 5300 + 4000 +372OO 1-2 -24900 -13400 -21700 -33200 2-3 1-3300 + 350O + 46OO + 4400 3-4 -3600 - 9700 -/O9OO - 4-8OO 4-5 + 6600 + 3500 + 1 17 OO + 8800 5-6 - 3600 -3800 - 5OOO - 4-8OO 6-7 + 3300 + 35OO + 4600 + 44OO 5-8 - 7200 -/O600 -/3000 -9600 7-8 -10800 -14^00 -/8000 -14-400 8-9 -/O800 + 3800 + 200 -/4400 9-/2 + 6600 - 450O -2300 + 88OO 12-13 -3600 +/360O +/24OO -4800 Y-4- -21300 -/3/OO -20200 -28400 Y-8 -141 OO - 25OO - 52OO -I48OO Y-12 -23100 + 2600 - 45OO -284OO 13-15 -24300 - 78OO ~/6lOO -32400 A-l -85OO - 8500 A-15 +Z/5OO -2/300 A-b +/4400 + 820O +/3OOO + /92OO C-l +14400 +/28OO +/7600 + /92OO A- 17 +14400 +/0/OO +/490O +/92OO 15-16 +/44OO - 1600 + 32OO + /92OO CHAPTER XII. STRESSES IN PORTALS. Introduction. Portal bracing is frequently used for bracing the sides of mill buildings and open sheds. There are many forms of portal bracing in use, a few of the most common of which are shown in Fig. 58. *- (<3I I H G F fd) H 6 F, F? - Cb) " F, R 7i AJ " (e) FIG. 58. 6 f e d r^HG^lF R ^7- -^ C l 1 ! 1 h d i --h- 5 --> i I l ;B -* -^ A- (f) Portal bracing may be in separate panels or may be continuous. The columns may be hinged or fixed at the base in either case. 96 STRESSES IN PORTALS CASE I. STRESSES IN SIMPLE PORTALS: Columns Hinged. The deflections of the columns m the portals shown in Fig. 58 are assumed to be equal and H = H * = ~ Taking moments about the foot of the windward column F 1 = V R h s Having found the external forces, the stresses in the members may be found by either algebraic or graphic methods. Algebraic Solution. Portal (a). To obtain the stress in member G C, (a) Fig. 58, pass a section cutting G F, H F and G C, and take moments of the external forces to the right of the section about point F as a center. G C = _ Hh . - (46) (h d) sin e D ^ But H = -L, and (hd) sin 6 = cos 9. Substituting- these values in (46) we have G C = Rh = V sec 9 (47) s cose Resolving at C and F we have, stress in H F = o, and also stresses E & and H H' = o. To obtain stress in G D, pass section cutting H G, HE' and G D, and take moments of the external forces to the left of Ihe section about point H as a center. G D= . = + Fsec e (48) (h d) sin To obtain stress in G F, pass a section cutting G F, H F and G C, and take moments of the external forces to the right of the section about point C as a center. GF= , R(h-d}+ Hd h d (49 ALGEBRAIC SOLUTION 97 To obtain stress in H G f pass a section cutting H G, H B' and G D f and take moments of the external forces to the left of the section about the point D as a center. The stress in the windward post, A P , is zero above and V below the foot of the knee brace C; the stress in the leeward post is zero above and F 1 below the foot of the knee brace D. The shear in the posts is H below the foot of the knee brace, and above the foot of the knee brace is given by the formula ' s = Hd - = stress in H G (51) h a The maximum moment in the posts occurs at the foot of the knee braces C and D and is M = Hd (52) For the actual stresses, moments and shears in a portal of this type, see Fig. 59. Portal (b). The stresses in portal (b) Fig. 58, are found in the same manner as in portal (a). The graphic solution of a similar portal with one more panel is given in Fig. 60, which see. It should be noted that all members are stressed in portals (b) and (d). Portal (c). The stresses in portal (c) Fig. 58, may be obtained (i) by separating the portal into two separate portals with simple bracing, the stresses found by calculating the separate simple portals with a load = y 2 R being combined algebraically, to give the stresses in the portal ; or (2) by assuming that the stresses are all taken by the system of bracing in which the diagonal ties are in tension. The latter method is the one usually employed and is the simpler. Maximum moment, shear, and stresses in the columns are given by the same formulas as in (a) Fig. 58. Portal 0). In portal (e) Fig. 58, the flanges G F and D C are assumed to take all the bending moment, and the lattice web bracing 7 98 STRESSES IN PORTALS is assumed to take all the shear. The maximum compression in the upper flange G F occurs at F, and is (53) h d The maximum stress in the lower flange D C is Hd (54) // d The maximum stress. in the lower flange D C is DC=-^JL^ (55) n d maximum tension occurring at C, and maximum compression occurring at D. The maximum shear in the portal strut is V , which is assumed as taken equally by the lattice members cut by a section, as a a. Maximum moment, shear, and stresses in the columns are given by the same formulas as in (a) Fig. 58. Portal (/). The maximum moment in the portal strut / F in (f) Fig. 58, occurs at H and G, and is M= + Hh Va (56) The maximum direct stress in H G is -|- R, and in / H is The maximum stress in G F is given by formula '(49). The maximum shear in girder I F is equal to V . The stress in G C \s V sec and in H D is + V sec 0, as in (a) Fig. 58. Portal strut / F designed as a girder to take the maximum mo- ment, shear and direct stress. Maximum moment, shear, and stresses in the columns are given by the same formulas as in (a) Fig. 58. Graphic Solution. To make the solution of the stresses statically determinate, replace the columns in the portal with trussed framework GRAPHIC SOLUTION 99 as in Fig. 59. The stresses in the interior members are not affected bv ** * the change and will be correctly given by graphic resolution. -Md =20 00 G -2000 F +4000 h-d I i V= 3000 : T N I 2 \! ' -C 10 I ^ i. V=3000 Moment Shear Portal 7 * *i & \ / n / \ / V j \ / \ f \ / \ / \ 1 \ / \ 1 \ f \ I \ t f \ 1 \ \ 1 -7 \ / .. V ! !>^ tf *y CASE I Columns Hinqed Stress Diagram O 1000 ZOOO 3OOO Compression Tension FIG. 59. As before H = + H* = and F=- Having the calculated H, H 1 ^ F^ and F 1 , the stresses are calculated by graphic resolution as follows : Beginning at the base of the column A, lay off A-4 = V = 3000 Ibs. acting downward, and A-a = H = 1000 Ibs. acting to the right. Then a-i and 4-1 are the stresses in members a- 1 and 4-1, respectively, heavy lines indicating compression and light lines tension. At joint in auxiliary truss to right of C the stress in i-a is known and stresses in 1-2 and 2-a are found by closing the polygon. IOO STRESSES IN PORTALS The stresses in the remaining members are found in like manner, taking joints C , H, F, etc. in order, and finally checking up at the base of the column B. The full lines in the stress diagram represent stresses in the portal ; the dotted lines represent stresses in the auxiliary members or stresses in members due to auxiliary members, and are of no con- sequence. The shears and moments are shown in the diagram. Moment Shear v'i /R, Portal pA !v CASE I Columns Hinged Stress Diagram O 1000 2000 3000 Compression Tension FIG. 60. Simple Portal as a Three-Hinged Arch. In a simple portal the resultant reactions and the external load R meet in a point at the mid- dle of the top strut, and the portal then becomes a three-hinged arch COLUMNS FIXRD, ALGEBRAIC SOLUTION 101 (see Chapter XIII), provided there is a joint at that point (point b, Fig. 60). In Fig. 60 the reactions were calculated graphically and the stresses in the portal were calculated by graphic resolution. Full lines in the stress diagram represent required stresses in the members. Stresses 3-2 and 11-12 were determined by dropping verticals from points 3 and ii to the load line 4-10. CASE II. STRESSES IN SIMPLE PORTALS: Columns Fixed. The calculation of the stresses in a portal with columns fixed at the base is similar to the calculation of stresses in a transverse bent with columns fixed at the base. The point of contra-flexure is at the point ' measured up from the base of the column. The point of contra-flexure is usually taken at a point a distance above the bases of the columns. The stresses in a portal with columns fixed may be calculated by considering the columns hinged at the point of contra-flexure and solv- ing as in Case I. Algebraic Solution. In Fig. 61 we have and , V = V 1 = R ( h ~~ 7 Z ) Having found the reactions H and H 1 , V and V*, the stresses in the members are found by taking moments as in (a) Fig. 58, consider- ing the columns as hinged at the point of contra-flexure. The shear diagram for the columns is as shown in (a) and the mo- ment diagram as in (c) Fig. 61. Anchorage of Columns. In order that the columns be fixed, the anchorage of each column must be capable of developing a resisting T r j moment greater than the overturning moment M = - = , shown in IO2 STRESSES IN PORTALS (c) Fig. 61. The anchorage required on the windward side is a max- imum and may be calculated as follows : Let T be the tension in the windward anchor bolt, 2a be the distance center to center of anchor NHd j-IOOO O D H'=IOOO B' | * F snt ) 2(h-c \XXcX" i i i i b T3N I r - J- > o ? 8 g 1 + T3IN ^ H = IOOO v'=zooo v=zooo < 5 = 16- 0" i i A y Mom< (c Shear (a) ^ ^ Portal Columns Fixed (b) FIG. 61 = 96000 in-lbs- -Hd 2. - 2 a - -*; Base of Column (d) bolts, and P be the direct load on the column. Taking moments about the leeward anchor bolt we have = - Hd - '~ ~ V (58) If the nuts on the anchor bolts are not screwed down tight, there will be a tendency for the column to rotate about the leeward edge of the base plate, and both anchor bolts will resist overturning. The maximum pressure on the masonry will occur under the leeward edge of the base plate and will be = + ^f A ~T COLUMNS FIXED, GRAPHIC SOLUTION 103 where W = direct stress in post; A = area of base of column in sq. ins. ; M = bending moment = y 2 Hd; c = one-half the length of the base plate; / =: moment of inertia of the base plate about an axis at right angles to the direction of the wind. Graphic Solution. The stresses in the portal in Fig. 62 have been calculated by graphic resolution. This problem is solved in the same manner as the simple portal with hinged columns in Fig. 59. b -HOOP + 3500 R = 2000 /a < \ 9 \ b \ JH looo ~, / a o Moment Shear T3 5 = 16'- .y. Portal CASE -a Columns Fixed Stress Diagram O 1000 2000 3OOO Compression Tension FIG. 62. STRESSES IN CONTINUOUS PORTALS. The portal with five bays shown in Fig. 63 will be considered. The columns will all be assumed alike and the deformation of the framework will be neglected. The shears in the columns at the base will be equal, and will IO4 STRESSES IN PORTALS be H= ^ To find the vertical reactions proceed as follows: Determine the center of gravity of the columns by taking moments about the base of one of the columns. Now there will be tension in each one of the columns on the windward side and compression in each one of the columns on the leeward side of the center of gravity of the columns. The sum of the moments of the reactions must be equal to the moment H -^v : \> tCiva hi* 4.-*t*-d3->* ds >K da >i d 6 ^ di -- FIG. 63. of the external wind load, R. The reactions at the bases of the columns will vary as the distance from the center of gravity and their moments will vary as the square oi the distance from the center of gravity. Now, if a equals the reaction of a column at a units distance from the center of gravity, we will have V^ = a d 1} V 2 = a d 2 , V 3 = a d z , V = + a d, V\ = + a d 5 , and F 6 and the moment a d f = a (d, 2 + d* + di- + d* + 5 d 2 R h a = R JL + = R h (59) Having found a, the vertical reactions may be found. Now having found the external forces H and V, the stresses can be calculated by either algebraic or graphic methods. Stresses in a Double Portal. To illustrate the general problem the stresses in a double portal are calculated by graphic resolution in Fig. 64. In this case DOUBLE PORTAL 105 H '= H = H= = 1000 Ibs. and V = V^ = - 2s = 2250 Ibs. The vertical reaction of the middle column is zero. By substitut- ing the dotted members as shown, the stresses can be calculated as in the case of the simple portal. The full lines represent stresses in the portal U J members. The shear in the columns is equal and is H below, and above the foot of the knee brace. h d CASE I Columns Hinged Stress Diagram o 1000 ^ooo 3000 Compression Tension c e~ 10 FIG. 64. The maximum bending moment occurs at the foot of the knee brace and is M = H d 192,000 inch-lbs. CHAPTER XIII. STRESSES IN THREE-HINGED ARCH. Introduction. An arch is a structure in which the reactions are inclined for vertical loads. Arches are divided, according to the num- ber of hinges, into three-hinged arches, two-hinged arches, one-hinged arches, and arches without hinges or continuous arches. Three-hinged arches are in common use for exposition buildings, train sheds and other similar structures. Two-hinged arches are rarely used in this country ; continuous arches are used only in dome construction. A three-hinged arch is made up of two simple beams or trusses. Trussed three-hinged arches, only, will be considered in this chapter, and trussed two-hinged arches in the next. CALCULATION OF STRESSES. The reactions for a three- hinged arch can be calculated by means of simple statics with slightly more work than that necessary to obtain the reactions in simple trusses. Having determined the reactions the stresses may be calculated by the ordinary algebraic and graphic methods used in the solution of the stresses in simple roof trusses. Calculation of Reactions: Algebraic Method. Let H and V, H 1 and F 1 be the horizontal and vertical reactions at the left and right supports for a concentrated load P, placed at a distance x from the center hinge C in the three-hinged arch in Fig. 65. From the three fundamental equations of equilibrium 3 horizontal components of forces = o (a) 2 vertical components of forces = o (b) S moments of forces about any point = o (c) CALCULATION OF REACTIONS 107 FIG. 65. we have H = H 1 and V + V^ = P Taking moments about B, we have + * ) = and taking moments about center hinge C, we have y f ^. Hh Px -0 Solving (60) we have and (60) (61) (62) (63) Substituting (61) in (62), we have The horizontal reactions at the crown are the same as at the sup- ports. Reactions for an inclined load may- be found by substituting the proper moment arms. Calculation of Reactions : Graphic Method. Let P, Fig. 66, be the resultant of all the loads on the left segment. Since there is no io8 STRESSES IN THREE-HINGED ARCH bending moment at hinge C, the line of action of the reaction R 2 must pass through the hinge at the crown. This determines the direction of reaction R 2 , and since the three external forces R 1} R 2 arid P produce equilibrium in the structure they must meet in a point. Therefore to find the direction of R 1 produce B C to d and join d and A. FIG. 66. The values of R^ and R z may then be obtained from the force poly- gon. The reactions due to loads on the right segment may be found in the same manner. The two operations may be combined in one as il- lustrated in the solution of the dead load stresses in a three-hinged arch, Fig. 67. Calculation of Dead Load Stresses. To find the reactions for the dead loads in Fig. 67, the loads are laid off on the load line of the force polygon in order, beginning at the left reaction A, and two equi- librium polygons, one for each segment, are drawn using the same force polygon. The vertical reactions at the crown, P c , and at abut- ments, P R and P Bt are found by drawing a line through pole o of the force polygon parallel to the closing lines of the equilibrium polygons. The load P C at the crown causes reactions R^ and R 2 l < and combining DEAD LOAD STRESSES 109 reactions R^ and P R at A, and R^ and P B at B, we have the true reactions R and R 2 . PR R Diagram Force Polygon / A FlG. 67. Having obtained the reactions, the stresses in the members are found in the same manner as in simple trusses. In Fig. 67 the stresses in the left segment are calculated by graphic resolution. The diagram no STRESSES IN THREE-HINGED ARCH is begun with the left reaction x-y R lf Where the dead load is sym- metrical a stress diagram need only be drawn for one segment. WIND LOAD STRE-55 DIAGRAM FOR WINDWARD SIDE FIG. 68. WIND LOAD STRESSES in Calculation of Wind Load Stresses. The reactions for wind lead in Fig. 68 are found as follo\\s : The reactions F a and P c for the windward segment, considering it a simple truss supported at the hinges, are found by means of force 13 WIND LOAD STRESS DIAGRAM FOR LEEWARD SIDE 1000 2000 5000 4000 I i i I I 10 ii2 STRESSES IN THREE-HINGED ARCH and equilibrium polygons. The lines of action of P a and P c are par- allel to each other and to the resultant R. The line of action of the right reaction, R 2 , must pass through the center hinge C, and the reac- tion P will be replaced by two reactions R 2 and R^ parallel to R 2 * and Rj* in the arch respectively, and the force triangle will be closed by drawing R^ in the force polygon. The intersection of force R and reactions R^ and R 2 falls outside the limit of the diagram. Having obtained the reactions, the stresses in the members are calculated in the same manner as in a simple truss. The wind load stresses must be calculated in both the windward and leeward segments. The wind load stress diagram for the wind- ward segment is shown in Fig. 68, and for the leeward segment in Fig. 69, compression being indicated in the stress diagrams by heavy lines and tension by light lines. Both wind load stress diagrams and the dead load stress diagram are usually constructed for the same segment of the arch. By comparing wind load stress diagrams in Fig, 68 and Fig. 69, it will be seen that there are many reversals in stress. The maximum stresses found by combining the dead, snow and wind load stresses as in the case of simple trusses and transverse bents, are used in designing the members. CHAPTER XIV. STRESSES IN TWO-HINGED ARCH. Introduction. A two-hinged arch is a frame-work or beam with hinged ends which has inclined reactions for vertical loads. The bot- tom chords of two-hinged arches are usually cambered, however, a simple truss becomes a two-hinged arch if the ends are fixed to the abutments so that deformation in the direction of the length of the truss is prevented. The horizontal components of the reactions may be supplied either by the abutments or by a tie .connecting the hinges. In the latter case the deformation of the tie must be considered in determining the hori- zontal reactions. Two-hinged arches are statically indeterminate struc- tures and their design is subject to the same uncertainties as continuous and swing bridges. Two-hinged roof arches are rigid and economical, but have been used to a very limited extent on account of the difficulties experienced in their design. The methods outlined in this chapter are quite simple in principle, although they necessarily require quite extended calcula- tions. Two-hinged roof arches with open framework, only, will be considered in this chapter. CALCULATION OF STRESSES. The vertical reactions in a two-hinged arch are the same as in a simple truss or a three-hinged arch having the same loads and span. The horizontal reactions, however, de- pend upon the deformation of the framework and cannot be determined by simple statics alone. Before the deformations can be calculated, the sizes of the members must be known, and conversely, before the sizes 8 H4 STRESSES IN TWO-HINGED ARCH of the members can be calculated, the stresses which depend upon the deformations must be known. Any method for the calculation of the stresses in a two-hinged arch is, therefore, necessarily a method of successive approximations. With a skilled computer, however, it is rarely necessary to make more than two or three trials before obtain- ing satisfactory results in designing roof arches. Two-hinged bridge arches require somewhat more work to design than roof arches on account of the greater number of conditions for maximum stresses in the members. Having determined the correct value of the horizontal thrust, H, the stresses in a two-hinged arch may be calculated by the ordinary algebraic or graphic methods used in the solution of the stresses in simple trusses. Calculation of the Reactions. In Fig. 70 the vertical reactions, V^ and V z , are the same as for a simple truss. The horizontal reactions, H f will be equal and will be the forces which would prevent change in length of span if the ends of the arch were free to move. The horizon- tal thrust, H, will therefore be the force which, applied at the roller end of a simple truss, will prevent deformation and make the truss a two- hinged arch. An expression for H may be determined as follows : In Fig. 70 assume that all members are rigid except the member 1-3;, which is increased in length 8, under the action of the external load, W. The w FIG. 70. CALCULATION OF THE REACTIONS 115 movement of the truss A' at the hinge Z/ will then be due to the change in length, g, of the member i-y. Let h 1 be the horizontal reaction necessary to bring L 1 back to its original position, and let U /i 1 be the stress in the member i-y due to the horizontal thrust h l . Now the internal work, ^ g h l U, in short- ening the member i-r to its original length will be equal to the external work, y 2 h l A', required to bring the hinge L^ back to its original position, y 2 h l A' = % d h l U and * A' = 8 U (65) p r but 5 = , where P is the unit stress in the member i-y due to the E external load W, L is the length of the member i-y, and H is the mod- ulus of elasticity of the material of which the member is composed. Substituting this value of 8 in (65) we have where U is the stress in i-y due to a load unity at L 1 Now if each one of the remaining members of the arch is assumed to be distorted in turn, the others meanwhile remaining rigid, the dis- tortion in each case at L\ will be represented by the general equation (66) and the total deformation, A , at L? Q will be Let P 1 h 1 be the unit stress in the member i-y due to a horizontal thrust /i 1 , then by the same reasoning A' = 5 U (65a) but s = P^VL and A , _^/" UL E and the total deformation, A, will be n6 STRESSES IN TWO-HINGED ARCH h l P 1 U L P l U L A - 2 ^ = /f 3 -- (68) Now for equilibrium, the values of A as given in equations (67) and (68) must be equal, and we have, after solving for H P 2 H = - (69) which is an expression for computing the horizontal thrust in any two- hinged arch due to external loads. This formula holds for any system of loading as long as P is the unit stress due to that loading, U is the stress in the member and P 1 is the unit stress in the member due to a unit load acting at the point at which the deformation is desired, and parallel to the direction in which the deformation is to be measured. The method of finding the correct value of the horizontal reaction, H, is as follows : ( I ) calculate the stresses in the arch for the given loading on the assumption that it is a simple truss with one end sup- ported on frictionless rollers ; (2) calculate the stresses in the arch for an assumed horizontal reaction, H 1 =, say, 20000 Ibs. on the assumption that it is a simple truss on frictionless rollers; (3) calculate the defor- mation, A, of the free end of the truss for the given loads by means of formula (67) ; (4) calculate the deformation, A' of the free end of the truss for the assumed horizontal reaction H 1 = 20000 Ibs. by means of formula (68). The true value of H is then by formula (69) given by the proportion H\ H 1 :: A: A' _ H 1 A 20000 A (70) A' A' The calculation of the horizontal reaction, H, and the stresses can be made by algebraic methods alone or by a combination of graphic and algebraic methods. The first requires less work, while the second ALGEBRAIC CALCULATION OF REACTIONS 117 is probably easier to understand. The algebraic solution will be given first. Algebraic Calculation of Reactions. In Table VII the values of the unit stress, P, in each member due to the external loads are given P L in column 5 ; values of -^- are given in column 6 ; values of the stress, U, in each member due to a unit horizontal thrust are given in column P U L 8 ; and values of are given in column 9. The algebraic sum of the quantities in column 9 gives the total deformation, A = .956 inches at the point where the unit horizontal thrust was applied meas- ured parallel to the line of action of the thrust. In Table VIII similar values are given for the arch as a truss with an assumed horizontal reaction of H l = 20000 Ibs. The algebraic TABLE VII. Simple Truss with Vertical Loads "lember 2 Area 5q-in- 3 Length,L inches 'A- Stress Ibs- 5 Unit5tress P Ibs. 6 PL 7 No- of Mem- 8 U 9 PUL E E i-x 5-3 252. +6000O + //32O +095 9 -0-90 -086 o ^\s 53 /92 +4IOOO + 774O +050 6 -0-80 -O40 4~X 53 180 +67000 +/Z650 +076 1 -/45 -no Ol v/" 5-3 /92. 1-41000 + 774O +050 IZ -0-80 -040 I'-X 5-5 252 i-60000 +//320 +095 15 -O-90 -086 I _\y/ 5-5 216 -25000 - 472O -034 8 +/-60 -054 3-Y 5-3 192 -57000 -10760 -069 4 i-2-05 --I4I 3'~Y 53 192 -57OOO -10760 -069 IO +205 -141 1 '_ v 53 2/6 -25OOO - 4720 -034 14 +/-60 -054 j-2 20 150 -30000 -/5000 -075 7 +075 -056 2-3 40 204 +32000 + 8000 +054 5 -045 -024 ^ A. 4-0 150 -22000 - 5500 -023 a +0-80 -022 3*4 40 150 -22000 - 5500 -028 3 +0-00 -022 2 '-3' 4-O ^04 +320OO 1- 600O + 054 II -045 -024 I' J 2' 2-0 150 -30OOO -/5000 --O75 13 +075 -056 Total Deformation =2EL!k = -9J6 m of the quantities in column 9 gives the total deformation, A' = 74 inches at the point where the horizontal thrust was applied. STRESSES IN TWO-HINGED ARCH TABLE VIII. Simple Truss with H -20000 Ibs. Member 2 Area Sq-in- 3 Length J_ inches 4 Stress ibs- 5 Unit Stress P Ibs- E 7 No-of Mem- 8 U ,9 PUL I-X 53 252 -18000 -3400 -<028 9 -0-90 -.025 2-X 53 192 -/6000 -3000 -0/9 6 -0-80 -.0/5 4-X 53 IdO -29000 - 5500 -035 I -1-45 -048 2'-X 53 /92 -16000 -3000 -019 12 -0-80 -0/5 r-x 53 252 -18000 -3400 -028 15 -090 -.025 I-Y 53 216 +32000 + 6000 +045 ' 8 +/-60 -.069 3-Y 53 192 Ml 000 + 7500 +050 4 +2-05 -.102 3 L Y 53 192 +41000 + 7800 + 050 10 +2-05 -102 I'-Y 53 2/6 +32000 + 6000 +.043 14 +1-60 -.069 1-2 2-0 150 +15000 + 7500 +038 7 +075 -.029 2-3 4.0 204 -9000 -2250 -015 5 -0-45 -.007 3-4 40 150 +16000 + 4000 +.020 2 +0-80 -.016 3 L 4 4-0 150 +16000 + 4000 +.020 5 +0-80 -016 2-3' 4-0 204 -9000 -2250 -.015 U -0-45 -007 1'- 2' 2-0 /50 +15000 + 7500 +.05d 13 +075 -029 Total Deformation = f!uL = ^574 TABLE IX. Simple Truss with Dead and Wind Loads 1 Member 2 Area Sq-in- 3 LenqthJ_ inches 4 ' Stress Ibs. 5 Unit Stress Plbs. 6 PL ~E~ 7 No-of Mem- Q U 9 PUL E l-X 5-3 252 +870OO +I640O +-I38 9 -090 -.124 2-X 5-3 192 + 720OO +/3600 f-087 6 -0-80 -.069 4-X 5-5 180 +95OOO +/7800 +107 i -145 -.155 2'-X 5-3 /92 +52OOO + 98 OO +065 12 -0-80 --O50 I'-X 5-3 252 +72000 +/3600 +.114 15 -090 -103 I-Y 5-3 216 -38000 -/O900 -.078 8 -1-60 -.125 3-Y 5-3 /92 -870OO -I640O -.105 4 i-2-05 -.2/5 3'-Y 53 /92 -74OOO -I4OOO -.090 IO +2-05 -.185 r-Y 5-3 216 -30OOO -5650 -.041 14 -/60 -.064 1-2 2.0 /50 -36000 -/80OO -.090 7 +0,75 -067 2-3 40 204 +28OOO + 7000 +.048 5 -0.45 -D2Z 3-4 4-0 /50 -220OO -5500 -028 2 +0-80 -.022 3-4 4-0 150 -42OOO -10500 -.055 3 +0-50 -.042 2'-3' 4-0 204 146OOO +II5OO +078 // -045 -.035 r-2 1 2-0 /50 -4 2O 00 -21000 -.105 13 +075 -.079 Total Deformation = 2^- = 1357 GRAPHIC CALCULATION OF REACTIONS 119 The correct value of H is given by the proportion H : 7/ 1 :: A : A' H = 20000 X .956 = 33400 Ibs. In Table IX the deformation, A, for the same arch considered as a simple truss and acted upon by dead and wind loads is 1 . 357 inches, and 20000 X 1.357 H = .574 = 47300 Ibs. Graphic Calculation of Reactions. In the graphic solution of the horizontal reactions the total amount of the deformations, A and A' are found by means of deformation diagrams. Before con- structing the deformation diagrams the quantities in the first seven columns in Tables VII and VIII or VIII and IX must be 20 30 Vertical Loads (a) Dead Load Stress I Simple Truss (b) Simple Truss H ^0000 Ibs (c) Stress Diagram , H=20000 Ibs. (d) FIG. 71. i2o STRESSES IN TWO-HINGED ARCH calculated. The stresses given in column 4 are calculated as shown in Fig. 71. Column 6, giving deformations of each member, and col- umn 7, giving the order in which these deformations are used, are, how- ever, the only values used in constructing the deformation diagrams. Deformation Diagram. The principle upon which the construc- tion of the deformation diagram is based is as follows : Take the two members a-c and c-b in (d) Fig. 72, meeting at the point c. Assume that a-c is shortened and b-c is lengthened the amounts indicated. It is required to find the new position, c', of the point c. With center at a and a radius equal to the new length of a-c = a-c r , describe an arc. The new position of c must be some place on this arc. Then with a center at b and a radius equal to the new length of b-c = b-c', describe an arc cutting the first arc in c'. The new position of c must be some place on this arc and will therefore be at the intersection of the two arcs, c r . Since the deformations of the members are always very small as compared with the lengths of the members, the arcs may be replaced by perpendiculars, and the members themselves need not be drawn, (e) Fig. 72. To draw the deformation diagram, (b) Fig. 72, for the arch as a truss with one end on frictionless rollers and loaded with vertical loads, proceed as follows : Begin with the member marked i, lay off its deformation = -f- .076 inches (Table VII., column 6) to scale and parallel to member i. Now lay off the deformation of 2 = - - .028 inches away, from the joint U 2 and parallel to the member 2, and lay off deformation of 3 = -- .028 inches, away from the joint U' 2 and parallel to the member 3. Perpendiculars erected at the ends of de- formations 2 and 3 will meet in the new position of L 2 . The vertical distance between the deformation i and point L 2 represents to scale the change in position of L 2 relative to the member U 2 U 1 2 . At L 2 in the deformation diagram lay off deformation of 4 = -- .069 inches, away from the joint and parallel to the member 4, and at U 2 lay off deforma- tion of 5 = -f .054 inches, toward the joint and parallel to the member 5. The perpendiculars erected at the ends of the deformations 4 and 5 DEFORMATION DIAGRAM 121 (b) ^'-'' / Deformation Diagram for Simple Truss H = 20000 Ibs. (C) Deformation Diagram for Simple Truss \t Vertical Loads ^ ^^-^^ \ 55 ^^20 ?Xv *- 0< t~'-' FIG. 72. determine the new position of joint L t relative to the other points. In like manner perpendiculars erected at the ends of deformations 6 and 7 determine U lt and finally perpendiculars erected at the ends of deformations 8 and 9 determine L . The deformation diagram for the right half of the truss is constructed in the same manner. The horizon- tal line joining L and I/ represents to scale the movement of the joint L\. In drawing the deformation diagram it is immaterial whether plus deformations are laid off toward the joints and minus deformations away from the joints as was done in the preceding problem, or the reverse. The former method is more common, but the latter is prob- ably more consistent. The deformation diagram (b) if drawn in the latter way would be turned upside down and inside out. Calculation of Dead Load Stresses in Arch. In Fig. 71, (b) is the stress diagram for the arch as a simple truss with vertical loads as shown in (a) ; and (d) is the stress diagram for the arch as a simple 122 STRESSES IN TWO-HINGED ARCH truss with a horizontal thrust, H 1 , of 20000 Ibs. as shown in (c). The quantities for calculating the deformations of the simple truss with vertical loads are given in Table VII, and the deformation diagram is shown in (b) Fig. 72. The quantities for calculating the deforma- tions of the simple truss with a horizontal thrust of 20000 Ibs. are given in Table VIII, and the deformation diagram is shown in (c) Fig. 72. The true value of H is found by the proportion H : 20000 : : .956 : .574 H = 33400 Ibs. The stress diagram for the two-hinged arch with V = V = 42000 Ibs., and H H 33400 Ibs. is shown in (b) Fig. 73. The difference in the stresses in the members of a simple truss and a two-hinged arch may be seen by comparing stress diagram (b) Fig. 71, and stress diagram (b) Fig. 73, both diagrams being drawn 2000 Two Hinqed Arch (a) I H =33400 Ibs. X, Stress Diagram Two Hinqed Arch (b) FIG. 73. to the same scale. The stresses in the arch may be found from the stresses given in Tables VII and VIII by adding the stresses in column 4, Table VII, to the corresponding stresses in column 4, Table VIII, multiplied by 1.67, the ratio between the actual and as- DEAD AND WIND LOAD STRESSES 123 sumed horizontal reactions. For example, the stress in \-x in the arch equals + 60000 18000 x 1 .67 = + 29800 Ibs. Stress in i-y equals - 25000 -f 32000 x i . 67 = + 28440 Ibs. Dead and Wind Load Stresses in Arch. In Fig. 74, (b) is the stress diagram for the arch as a simple truss loaded with dead and wind loads as shown in (a). Table IX gives the same data for this case as 0' 10' 20' 50' \ Simple Truss Dead and Wind Loads (a) Simple Truss N Dead and Wind Load Stress Diaqrar (b) O 20000 40000 Simple Truss H- 20000 Ibs- (c) Stress Diagram , H=20000lbs. (d) FIG. 74. are given in Table VII for the simple truss with vertical loads. The deformation diagram for the deformations given in column 6, Table IX, is shown in (b) Fig. 75. In drawing the deformation diagram for this case the member marked I w r as assumed to be fixed in position and the other members were assumed free to move. The horizontal dis- tance between L and L' will be the total deformation required. 124 STRESSES IN TWO-HINGED ARCH The deformation diagram for the simple truss with a horizontal 1-357 inches o" o.i" o-a" 0.3" 04" ^ffP^ "X c ^ Vv/// ^ efo 0.574 inches Deformation Diagram for Simple Truss H=20000lbs- (CJ */ Deformation Diagram ?% Simple Truss Dead and Wind Loads ( b ) FIG. 75. thrust, H 1 , of 20000 Ibs. is given in (c) Fig. 75 and is the same as that given in (c) Fig. 72. The true value of H is found by the proportion H : 20000 : : 1.357 -574 H 47300 Ibs. The stress diagram for the two-hinged arch with dead and wind loads and a horizontal thrust, H, of 47300 Ibs. is given in (b) Fig. 76. The stresses in the arch for this case may be found from the stresses in Tables IX and VIII by adding the stresses in column 4, Table IX, to the corresponding stresses in column 4, Table VIII, multiplied by 2.865, the ratio between the actual and assumed horizontal reactions. ARCH WITH HORIZONTAL TIE 125 Two Hinged Arch (a) 20000 40000 Stress Diagram Two Hinged Arch tb) FIG. 76. As a check on the accuracy of the calculations the movement at L ' in the arch was calculated in Table X and was found to be zero as it should be. Arch With Horizontal Tie. If a horizontal tie is used the final deformation of the arch will be equal to the deformation of the tie. TABLE X. Two Hinged Arch with Dead and Wind Loads 1 Member 2 Area 5q-in- 3 Length,L inches 4 Stress Ibs- D UnOress P Ibs- 6 PL 8 U 9 PUL E E I-X 3-3 E5 +43500 + Q220 +069 -090 -063 a-x 53 192 +34200 + 6450 +041 -O.QO -033 4-X 5-3 '180 i-26500 +5000 +.030 -1-45 -045 2-X 3-3 192 +14200 +2660 +017 -0-80 -0/4 r-x 5-5 252 +29500 +5550 +.047 -0.90 -^042 I-Y 3-3 216 +/8OOO +3400 +324 + /-60 +-038 3-Y 3-3 192 +10000 + 1890 +-OI2 +2-05 +.025 3 L Y 5-5 192 i-25000 +4350 +028 +205 +.057 r-Y 5-5 216 +46000 + 6700 +061 +/-60 +.093 \- 2-0 ISO - 500 - 250 -.001 +0-75 -.001 Z~S 4-0 204 + 6500 + 1625 +011 -0-45 -005 3-4 40 150 +/5800 +5950 +-OEO +0-80 +016 5-4 4-0 150 -4200 -/05O -.005 +0-80 -.004 2'-3' 40 204 +22dOO +5700 +.039 -0.45 -0/8 !'-' 20 150 -5000 -2300 -013 +075 -0/0 Total Deformation = ^ p V L = .000 126 STRESSES IN TWO-HINGED ARCH Assume that the joints L and Z, ' in (a) Fig. 73 are connected by a tie having 3 sq. in. cross-section. A force of a 1000 Ibs. will stretch the tie 1000 X 720" " 3X29,000,000 = - 0083 inches ' 574 The movement for 1000 Ibs. applied as H is equal to ^- = .0287 inches. The value of H therefore which will produce equilibrium for the arch with vertical loads will be + .0083 H + .0287 H = .956 x 1000 Ibs. n .956X 1000 .0370 - 2584 lbs ' The stresses in the arch for this case may be found from the stresses in Table VII and Table VIII as previously described. Temperature Stresses. Where a horizontal tie is used and all parts of the structure are exposed to the same conditions and range of temperature, the entire arch will contract and expand freely and tem- perature stresses will not enter into the calculations. Where the tie is protected and where rigid abutments are used the temperature stresses must receive careful attention. The deformation A' due to a uniform change of temperature of t degrees Fahr. when the arch is assumed to be a truss supported on frictionless rollers, will be etL, where e is the coefficient of expansion of steel per degree Fahr. = . 00000665 ; t equals change in temperature in degrees Fahr. ; and L equals the length of the span. For a change of 75 degrees Fahr. from the mean, the deformation will be A' = .00000665 X 75 Z = -4- L (71) ~ 2000 DESIGN OF TWO-HINGED ARCH 127 For the arch in Fig. 73 720" A' = . . . ., v = db .36 inches This will be equivalent to a change in H of x 20000 = . r^ / T" 12540 Ibs. The stresses clue to temperature in the two-hinged arch will be equal to the stresses in column 4, Table VIII, multiplied by .627. The maximum stresses due to external loads and temperature will be found by adding algebraically the temperature stresses to the stresses due to the external loads. If the arch is not erected at a mean temperature this fact must be taken into account in setting the pedestals. Design of Two-Hinged Arch. In designing a two-hinged roof arch proceed as follows: (i) With one end free to move, calculate the stresses in the arch as a simple truss ; (2) with an assumed horizon- tal reaction, H 1 , of, say, 20000 Ibs., calculate the stresses in the arch as a simple truss; (3) calculate the Stresses in the arch for some assumed value of H, this value of H may be guessed at or often may be estimated with considerable accuracy; (4) design the members for approximate stresses in the arch 5(5) calculate the deformation of the arch as a truss for the approximate sections and stresses ; (6) calculate the deforma- tion of the arch as a truss for an assumed horizontal reaction of 20000 Ibs.; (7) determine a more accurate value of H from the deformations as previously described ; (8) recalculate the stresses m the arch, re- design the members, recalculate the deformations, recalculate a new value of H, etc., until satisfactory sections are obtained. The second approximation is usually sufficient. Corrections for horizontal tie and temperature should be applied in making the approximations. The gross area of the sections of all members should be used in determining the deformation of the members. If riveted tension members are much weakened, a somewhat smaller value of H, say, 26,000,000, may be used than the 29,000,000 commonly used for the compression members. The method just described is much more expeditious than the usual method of designing the members for the stresses found by con- 128 STRESSES IN TWO-HINGIS ARCH sidering the arch a simple truss with allowable stresses, say, twice those to be finally allowed. In the latter case the first approximation is usually worthless on account of the reversal of stresses in the members which have been designed as tension members. If the value of H in tht first method is taken large enough to make members in compression that the designer's judgment or experience says should be in compres- sion, the second approximation is usually final. CHAPTER XV. COMBINED AND ECCENTRIC STRESSES. Combined Direct and Cross Bending Stresses. Thus far members of trusses and frameworks have been considered as acted on by direct forces, parallel to the axis of the member. While this is the more common case, it often becomes necessary to design members which support loads as in (a), (b), (c), or (d), Fig. 77, or in which the line of action of the external force does not coincide with the *. neutral axis of the member, (e), (f), (g), or (h), Fig. 77. / u, / TV [w (a) (b.) (d) (e) FIG. 77. 130 COMBINED AND ECCENTRIC STRESSES The following nomenclature will be used : L,et P = total direct loading on member in pounds ; / = length of member in inches ; L = length of member in feet; / = moment of inertia of member; y\ = distance from neutral axis to remote fibre on side for which stress is desired ; = modulus of elasticity of the material ; e eccentricity of P, i.e. distance from line of action of P to neutral axis of member in inches ; u' = deflection of member in inches ; A = area of member in square inches ; f^ fibre stress due to cross bending; p / 2 - - = direct fibre stress ; si M = total bending moment; M 2 = bending moment due to deflection, = P v; Mj = bending moment due to external forces and is equal to y 4 W.1 in (a) and (b) ; % w I 2 in (c) and (d) ; and P e in (e), (f), (g) and (h) Fig. 77 . Now M=MIMI=PVMI= (72) y\ ' ' in which c is a constant depending upon the condition of the ends, and the manner in which the beam is loaded. Substituting this value of v in (72) we have COMPRESSION AND CROSS BENDING 131 and reducing, the stress due to cross bending is l ~ P / 2 (73) 7 ~~^E~ where the minus sign is to be used when P is compression and the plus sign is to be used when P is tension. The factor c may be taken equal to 10 for columns, beams and bars with hinged ends as in Fig. 77 ; equal to 24 where one end is hinged and the other end is fixed ; and equal to 32 where both ends are fixed. The total stress in the member due to direct stress and cross bend- ing will therefore be for columns with hinged ends l* + ~A (74 WE Formula (74) is general, and applies to all forms of sections and all forms of loading. The second term in the denominator is minus when P is compression, and plus when P is tension In finding the stress due to weight of member and direct loading, the value for f^ given by formula (73) must be multiplied by the sine )f the angle that the member makes with a vertical line. Combined Compression and Cross Bending. The method of calculating direct and cross bending stresses will be illustrated by cal- ilating the stresses in the end post of a bridge due to direct compres- sion, weight, eccentricity of loading, and wind moment. The end post is composed of two lo-inch channels weighing 15 Ibs. per foot with a 14" x y\" plate riveted on the upper side and laced on the lower side with single lacing. The pins are placed the center of the channels giving an eccentricity of e -- i .44 inches. ic compressive stress P produces a uniform compression on all fibres )f the section jweight of the member causes tension on the lower andcom- >ssion on the upper fibres ; eccentricity of the load P causes compres- on lower and tension on upper fibres ; and wind moment causes com- 132 COMBINED AND ECCENTRIC STRESSES Ui K -y/ /4"*4" .-'2 - 10 @/5# 95300 | --e = 1.44 ins. Area I4"x;fp|. =3.50 sq-in- " 2-IO"ll@i5*=8.92 Total Area = 1242 " " Ib locate neutral axisAA take moments about lower edqe of channels 8 ' 92 Yo Eccentricity.e = 6.44 -5-OO = 1.44" Moment of Inertia, IA, about AA Let IB =1 of 1 about axis I- 1 = 133.8 IpUlof Pl-aboutaxis 2-2 = .02 An=Areaof S = 8-92 sq-in- Api.=Area of PI- -3- 50 5q-in- ThenT A =lB t Age 2 1 1 pi. +A P Ld 2 = I33.-8 1 3-92 X(I.44) 2 -K02 + 3-5 (3.685^ = 199.8 Radius of gyration , r A =y 199.8- = 4 Hd * 2 J" - or (95500-6520) & > 36|600 but 347120 < 361600 and the end post will not be fixed. ("While this is The usual solution ,the resisting moment certainly reduces the bending moment and the bending stress is less Than computed below-) The maximum moment will Then occur at the foot of the portal knee brace and will be M =3200x226 =723200 in Ibs- Stress due to wind moment is a maximum in The leeward post and is f - M Vi 725ZOOX7 I -.EL 2 % , , (95500 1 1 2 500) 553 2 IOE 10X28000000 f w = 22480 Ibs. Stress.fw.is compression on the windward side and tension on the lee- ward side of the member- pression on the windward and tension on the leeward fibres. The maximum fibre stress will come at the foot of the kneq. in. Problem 2. Required the stress in a 5" x ^4" eye-bar, 30 feet long, which has a direct tension of 60,000 Ibs., and is inclined so that it makes an angle of 45 with a vertical line. In this case, h = 5", L 30 feet, f 2 16,000 Ibs., and =45. From the diagram as in Problem i, y. 2 =1.8 tens of thousandths, and Y! = 6.5 tens of thousandths, and /. = - - - sin 9 = 1200 X sin = 850 Ibs. per sq. in. Relations between h, f lt f and L. For any values of / 2 and L, f t will be a maximum for that value of h which will make 3^ -j- y z a min- 138 COMBINED AND ECCENTRIC STRESSES imum. This value of h will now be determined. Differentiating equa- tion (76) with reference to f 1 and h, we have after solving for h after placing the first derivation equal to zero ~ 480oV /s in which h is the depth of bar which will have a maximum fibre stress for any given values of / and f z . Now if we substitute the value of h in (78) back in equation (76), we find that / will be a maximum when y y z . Now in the diagram the values of y and y z for any given values of / 2 and L will be equal for the depth of bar, h f corresponding to the intersection of the / 2 and L lines. It is therefore seen that every intersection of the inclined f 2 and L lines in the diagram, has for an abscissa a value of h, which will have a maximum fibre stress f lf for the given values of f z and L. For example, for L = 30 feet and f z = 12,000 Ibs. we find h = 8.3 inches and / == 1700 Ibs. For the given length L and direct fibre stress f z , a bar deeper or shallower than 8.3 inches will give a smaller value of /! than 1700 Ibs. Eccentric Riveted Connections. The actual shearing stresses in riveted connections are often very much in excess of the direct shearing stresses. This will be illustrated by the calculation of the shearing stresses in the rivets in the standard connection shown in Fig. 79 and Fig. 80. The eccentric force, P, may be replaced by a direct force, P, acting through the center of gravity of the rivets and parallel to its original direction, and a couple with a moment M = P x 3" 60,000 inch-lbs. Each rivet in the connection will then take a direct shear equal to P divided by n, where n is the total number of rivets in the connection, and a shear due to bending moment M. The shear in any rivet due to moment will vary as the distance, ECCENTRIC RIVETED CONNECTIONS 139 and the resisting moment exerted by each rivet will vary as the square of the distance of the rivet from the center of gravity of all the rivets. Xow, if a is taken as the resultant shear due to bending moment in a rivet at a unit's distance from the center of gravity, we will have the relation M = a d d rf 2 A d 2 and M a = (79) The remainder of the calculations are shown in Fig. 79. The re- sultant shears on the rivets are given in the last column of the table Direct Shear 5 = 20000 -r 5 = 4000 Ibs- Moment = aoooo x 3 = 600OO in Ibs Where a = Moment shear on rivet 3 = ZG30 Ibs- Rivet d d 2 Moment M S R 1 Z 3 4 5 ^.7o 1.90 1.00 1 90 Z.7C 7.29 561 1-00 5.61 7.29 19/85 9500 2650 9500 19185 7100 5000 630 5000 7100 4000 4000 4000 4000 4000 9300 3ZOO 6G30 3200 9300 a Zd 2 = <^.SOa=60000 in. Ibs 20000 a = 630 Ibs- = moment shear on rivet 3 M = Shear due to Moment . S = Shear due to Direct Load , P R - Resultant Shear - O 40OO 8OOO 12000 FIG. 79. and are much larger than would be expected. The force and equilibrium polygons for the resultant shears and load P, drawn in Fig. 80, close, which shows that the connection' is in equilibrium. 140 COMBINED AND ECCENTRIC STRESSES Equilibrium Polygon O 400O 8OOO IOOO Standard Connection Force Polygon FIG. 80. PART III. DESIGN OF MILL BUILDINGS. CHAPTER XVI. DESIGN. General Principles. The general dimensions and outline of a mill building will be governed by local conditions and requirements. The questions of light, heat, ventilation, foundations for machinery, hand- ling of materials, future extensions, first cost and cost of maintenance should receive proper attention in designing the different classes of structures. One or two of tire above items often determines the type and general design of the structure. Where real estate is high, the first cost, including the cost of both land and structure, causes the adoption in many cases of the multiple story building, while on the other hand where the site is not too expensive the single story shop "or mill is usually preferred. In coal tipples and shaft houses the handling of materials is the prime object; in railway shops and factories turning out heavy machinery or a similar product, foundations for the ma- chinery required, and convenience in handling materials are most im- portant ; while in many other classes of structures such as weaving sheds, textile mills, and factories which turn out a less bulky product with light machinery, and which employ a large number of men, the principle items to be considered in designing are light, heat, ventilation and ease of superintendence. 142 GENERAL, DESIGN Shops and factories are preferably located where transportation facilities are good, land is cheap and labor plentiful. Too much care cannot be used in the design of shops and factories for the reason that defects in design that cause inconvenience in handling materials and workmen, increased cost of operation and maintenance are permanent and cannot be removed. The best modern practice inclines toward single floor shops with as few dividing walls and partitions as possible. The advantages of this type over multiple story buildings are (i) the light is better, (2) ventilation is better, (3) buildings are more easily heated, (4) founda- tions for machinery are cheaper, (5) machinery being set directly on the ground causes no vibrations in the building, (6) floors are cheaper, (7) workmen are more directly under the eye of the superintendent, (8) materials are more easily and cheaply handled, (9) buildings admit of indefinite extension in any direction, (10) the cost of construction is less, and (n) there is less danger from damage due to fire. The walls of shops and factories are made (i) of brick, stone, or concrete; (2) of brick, hollow tile or concrete curtain walls between steel columns ; (3) of expanded metal and plaster curtain walls and glass; (4) of concrete slabs fastened to the steel frame; and (5) of corrugated iron fastened to the steel frame. The roof is commonly supported by steel trusses and framework, and the roofing may be slate, tile, tar and gravel or other composition, tin or.she^t steel, laid on board sheathing or on concrete slabs, tile or slate supported directly on the purlins, or corrugated steel supported on board sheathing or directly on the purlins. Where the slope of the roof is flat a first grade tar and gravel roof, or some one of the patent com- position roofs is used in preference to tin, and on a steep slope slate is commonly used in preference to tin or tile. Corrugated steel roofing is much used on boiler houses, smelters, forge shops, coal tipples, and similar structures. Floors in boiler houses, forge shops and in similar structures are generally made of cinders ; in round houses brick floors on a gravel or DETAILS op DE'SIC.X 143 concrete foundation are quite common ; while in buildings where men have to work at machines the favorite floor is a wooden floor on a foun- dation of cinders, gravel, or tar concrete. Where concrete is used for the foundation of a wooden floor it should be either a tar or an asphalt concrete, or a layer of tar should be put on top of the cement concrete to prevent decay. Concrete or cement floors are used in many cases with good results, but they are not satisfactory where men have to stand at benches or machines. Wooden racks on cement floors remove the above objection somewhat. Where rough work is done, the upper or wearing surface of wooden floors is often made of yellow pine or oak plank, while in the better classes of structures, the top layer is com- monly made of maple. For upper floors some one of the common types of fireproof floors, or as is more common a heavy plank floor supported on beams may be used. Care should be used to obtain an ample amount of light in build- ings in which men are to work. It is now the common practice to make as much of the roof and side walls of a transparent or translucent ma- terial as practicable ; in many cases fifty per cent of the roof surface is made of glass, while skylights equal to twenty-five to thirty per cent of the roof surface are very common. Direct sunlight causes a glare, and is also objectionable in the summer on account of the heat. Where windows and skylights are directly exposed to the sunlight they may best be curtained with white muslin cloth which admits much of the light and shades perfectly. The "saw tooth" type of roof with the shorter and glazed tooth facing the north, gives the best light and is now coming into quite general use. Plane glass, wire glass, factory ribbed glass, and translucent fabric are used for glazing windows and skylights. Factory ribbed glass should be placed with the ribs vertical for the reason that with the ribs horizontal, the glass emits a glare which is very trying on the eyes of the workmen. Wire netting should always be stretched under sky- lights to prevent the broken glass from falling down, where ^ire glass is not used. 144 GENERAL DESIGN Heating in large buildings is generally done by the hot blast sys- tem in which fans draw the air across heated coils, which are heated by exhaust steam, and the heated air is conveyed by ducts suspended from the roof or placed under the ground. In smaller buildings, direct radiation from steam or hot water pipes is commonly used. The proper unit stresses, minimum size of sections and thickness of metal will depend upon whether the building is to be permanent or temporary, and upon whether or not the metal is liable to be subjected ; to the action of corrosive gases. For permanent buildings the author : would recommend 16,000 Ibs. per square inch for allowable tensile, and 16,000 70 -bs. per square inch for allowable compressive stress for direct dead, snow and wind stresses in trusses and columns ; / being the center to center length and r the radius of gyration of the member, both in inches. For wind bracing and flexural stresses in columns due to wind, add 25 per cent to the allowable stresses for dead, snow and wind loads. For temporary structures the above allowable stresses may be increased 20 to 25 per cent. The minimum size of angles should be 2" x 2" x %", and the minimum thickness of plates %", for both permanent and temporary structures. Where the metal will be subjected to corrosive gases as in smelters and train sheds, the allowable stresses should be decreased 20 to 25 per cent, and the minimum thickness of metal increased 25 per cent, unless the metal is fully protected by an acid-proof coating (at present the best paints do little more in any case than delay and retard the corrosion). The minimum thickness of corrugated steel should be No. 20 gage for the roof and No. 22 for the sides ; where there is certain to be no corrosion Nos. 22 and 24 may be used for the roof and sides respectively. The different parts of mill buildings will be taken up and discussed at some length in the following chapters. CHAPTER XVII. FRAMEWORK. Arrangement. The common methods of arranging the frame- work in simple mill buildings are shown in Fig. I, Fig. 81 and Fig. 82. The different terms which are used in the discussion that follows will be made clear by an inspection of Fig. i and Fig. 81. ?*pteP'' ' Purkn - ' 5__ ; -, s - ~0o ^^ ^,-' \p- ^ 5 .-Do \ -: -' ^^ ^-J*,-' 4 ^ (!; .'Do ~-^ ,-" " ,'' > "-^^ ^ ?c7vr5fri. ' / s \ V ; 1 &rt ^^ V / (i^C ^ ':\ - / v ,V v s ' v J G,r> - / v ^ Transverse Bent Side Elevation End Framing ^ Plan Lower Chord Plan Upper Chord FIG. 81. \ The three types of mill buildings steel frame mill buildings, mill buildings with masonry filled walls, and mill buildings with masonry walls have been discussed in the Introduction. FIG. 82. A. T. & S. F. R. R. BLACKSMITH SHOP, TOPEKA, KAS. The end post bent, shown in (a) Fig. I and in Fig. 81, usually requires 10 146 FRAMEWORK less material than the end trussed bent shown in (b) Fig. I and in Fig. 82, and is commonly used for simple mill buildings. Extensions can be made with about equal ease in either case, and .the choice of methods will usually be determined by the local conditions of the problem and , 1 - --) ii czzi ttfa.----- -*- the fancy of the designer. In train sheds and similar structures the end trussed bent (b), Fig. i, is used. Where the truss span is quite long, as in train sheds, the end trusses are often designed for lighter loads than are the intermediate trusses, thus saving considerable ma- terial. In the case of simple mill buildings of moderate size all trusses are, however, commonly made alike, the extra cost of detailing being usually more than the amount saved in material. In train sheds, coliseums, and similar structures requiring a large floor space, the three-hinged arch is very often used in place of the typical transverse bent system. The various parts of the framework of mill buildings will be taken up and discussed in order. TRUSSES. Types of Trusses. The proper type of roof truss to use in any particular case will depend upon the span, clear headroom, style of truss preferred, and other conditions. For spans up to about 100 feet, the Fink type of truss is commonly used. This type of truss has the advantage of short struts, simplicity of details and economy. The stresses that control the design are with but a very few exceptions TYPES OF TRUSSES 147 those caused by an equivalent uniform dead load, thus simplifying the calculation of stresses (see Table VI). The outline of the truss will depend upon the spacing of the pur- lins, and upon whether or not the purlins are placed at the panel points of the truss. The most economical and pleasing arrangement is to make a panel point in the truss under each purlin. Taking the normal wind load on the roof at from 25 to 30 Ibs. per sq. ft., it will be seen in Fig. 112 that for Nos.2O and 22 corrugated steel, when used without sheathing, the purlins should be spaced from 4 to 5 feet. If this spac- ing is exceeded corrugated steel roofing supported directly on the pur- lins is almost certain to leak. Where sheathing is used the purlin spac- ing can be made greater. Many designers, however, pay no attention to the matter of placing the purlins at the panel points, the upper chord of the truss being stiffened to take the flexural stress. In Fig. 83, (a) shows the form of a Fink truss for a span of 30 feet; (b) for a span of 40 feet; (c) for a span of 50 feet; (d) for a span of 60 feet ; and (e) for a span of 80 feet, on the assumption that the purlins are spaced from 4 to 5 feet, and come at the panel points of the truss. If trusses with vertical posts are desired the triangular trusses (h) and (j), or Fink truss (f) may be used. The truss shown in (i) is occasionally used for long spans, although it has little to rec- ommend it except novelty. The truss shown in (k) is used where there is ample headroom. The quadrangular truss shown in (1) and the camels back truss shown in (m), are used for long spans where the appearance of the truss is an important feature, as in convention halls and train sheds. The lower chords of mill building trusses are usually made horizontal, but by giving the lower chord a camber, as in (g), the appearance from the side is greatly improved. The "saw tooth" or "weaving shed" roof shown in (a) Fig. 84, has been used abroad for many years and is now coming into quite general use in this country for shops and factories as well as for weav- ing sheds, as indicated by the name. The short leg of the roof is made inclined as in (a), or vertical as in (b), and is glazed with glass or 148 FRAMEWORK translucent fabric. The glazed leg of the roof is made to face the north, thus giving a constant and agreeable light and doing away with the use of window shades. The principal difficulty in saw tooth roof construction is in obtain- ,30 Ft. Span (b) 40 Ft- Span (c) 50 Ft- Spa (d ) 60 FT Span (e) 80 FT Spar (f) Modified Fink (g) Cambered Fink FINK TRUSSES ( h ) Howe (i ) Hybrid ( I ) Quadranqulor (m) Camels Back FIG. 83. TYPES OF* ROOF TRUSSES. SAW TOOTH ROOF 149 ing satisfactory and efficient gutters, and in preventing condensation on the inner surface of the glass and gutters. Another objection to the use of saw tooth roofs in localities having a heavy snowfall is that the snow drifts the roof nearly full and shuts off the light. The common method of preventing the snow from collecting, and for taking care of the roof water, is that given in the description of the Conkey plant, which see. The modified saw tooth roof shown in (b), Fig. 84, is pro- posed by the author as a substitute for the usual type of saw tooth roof shown in (a). This modified saw tooth roof allows the use of ordinary valley gutters, and gives an opportunity to take care of the condensation on the inner surface of the glass by suspending a gutter at the bottom of the monitor leg. Snow will cause very little trouble South End North End Cd) Saw Tooth (Weaving Shed) South End North End -qlass .x^U-qlass ^X|<-qlass * .XTvSw * .X^N^ J m \ \ m (b) Modified Saw Tooth FIG. 84. with this roof on account of the increased depth of gutter. The mod- fied saw tooth roof has a greater pitch, and has a more economical truss "or long spans than the common fofm shown in (a). Condensation on the inner surface of the glazed leg can be practically prevented by us- ng double glazing with an air space between the sheets of glass. Double 1 50 FRAMEWORK glazing in windows and skylights makes the building much easier to heat, the air space making an almost perfect non-conductor. Brown & Sharp Foundry. In the Brown & Sharp Mfg. Com- pany's Foundry, a modification of the saw tooth roof was adopted in which glass was used on both surfaces of the roof. The skylights ex- tend east and west and have a pitch of 45 degrees. The southerly pitch is glazed with opaque glass, the other with ordinary rough glass. The ventilator monitor, which surmounts the skylights, is glazed with opaque, glass on the southerly side, and extends high enough so that no light up to an angle of 70 degrees reaches the glass below. By this arrange- ment no direct sunlight is admitted to the shop from above excepting for a few minutes at noon during the longest days of the year. The result of this overhead light, combined with the almost wholly glass walls of the room is that the floor below is as light as out of doors, to all intents and purposes, yet diffused light only is admitted. A rod placed upright on the floor of one of these rooms casts no shadow. Conkey Printing Plant*. The printing plant of the W. B. Conkey Co., Hammond, Ind., consists of a single story building, 540 x 450 ft. The roof is of the weaving shed or saw tooth type and all windows are glazed with frosted glass and are placed at an angle, looking toward the north. Every 29 feet of roof space provides 1 1 feet of light. Ow- ing to the angle' of the roof the direct rays of light are kept out of the building, which is thus lighted by the soft reflected rays from the northern sky. The entire roof is built up out of light structural steel- work resting on cast iron columns spaced 29 ft. c. to c. one way, and 16 ft. c. to c. in the other direction. The height of the trusses above the floor is 12 ft. To prevent the snow collecting in the valleys between the skylights, the bottom of the gutter and the glass are kept heated so that the snow melts as it falls. This method produces condensation on the inner surface of the glass, which is collected in a system of con- densation gutters and carried outside the building. The heating and ventilating of the building is 'accomplished by a blast system, with the heating ducts under the floor, which supply reg- isters throughout the plant, arranged on the side walls of each depart- ment. The heating system can be made to produce a mild heat for the seasons of spring and fall, and can also be turned into a cooling sys- tem in the summer, by running cold water through the steam pipes at *Engineering News, Dec. 8, 1898. SAW TOOTH ROOFS 151 the fan and changing the air every 15 minutes with cool air in hot weather. The floor is built of heavy plank and finished maple laid on sleep- ers which are bedded in cinders. The walls are made of heavy tile and the openings are closed with iron fire doors. The building is practically fireproof and takes a very low rate of insurance. Boycr Plant. The Boyer Plant of the Chicago Pneumatic Tool Co., at Detroit, Mich., is 325 x 185 ft., with the longer dimension ex- tending north and south. The roof of the building is divided into two sections, having spans of about 92 ft. each, a pitch of about l /t an d is covered with Patent Asbestos Roofing manufactured by W. H. Johns- Manville Co., Milwaukee, Wis. laid on i*/-in. plank sheathing. The building is lighted by means of saw tooth skylights facing north and extending from the ridge of the roof to within about 6 ft. of the eaves on the outside and the valley gutter on the inside. The trusses are spaced 16 ft. apart, and there are three saw tooth skylights between each pair of trusses, making 240 skylights in the roof. The north leg of the saw tooth is vertical and is glazed with double corrugated glass, the south leg is covered with asbestos roofing. The building is venti- lated by means of circular ventilators placed in the ridge of the roof and spaced 16 ft. apart. The lighting in this building is almost perfect. The roofing has given satisfaction with the exception of the large val- ley gutters, which will be covered with copper or lead in the near future. There has been a little trouble with condensation, but not enough to make it necessary to go to the expense of putting in con- densation gutters. This building is described in the Railway and Engineering Review, March 9, 1901. For additional details of saw tooth roofs see Fig. 97. The cross-section of a locomotive shop for the Eastern Railway of France is shown in Fig. 85. The entire building is made of fireproof materials, the framework is of iron and the roof of sheet metal and. glass. The building extends from east to west and has a saw tooth roof, with the shorter leg facing north, and glazed with crinkled glass. The floor is made of treated oak cubes measuring 3.94 in. on the edge, set with the grain vertical, on a bed of river sand about 8 in. thick. The saw tooth roof is well suited to structures of this class. FRAMEWORK ^ \s \s \/ \ ^ \/ \/ \/ 773 r~~ 56-5" ^ - 56-5 - -- *< .- --, V 1 t '//% FIG. 85. LOCOMOTIVE SHOP, EASTERN RAILWAY OF FRANCE. A few of the forms of trusses in common use where ventilation and light are provided for are shown in Fig. 86. The Fink truss with gloss or louvres glass qbss or louvres (a) (b) glass glass glass (C) glass or louvre' glass (d) glass->- gloss glass ^riglass glass-- c.ircutar ventilator --qlass ( f ) glass (h) Silk Mill FIG. 86. glass PITCH OF ROOF 153 monitor ventilator and skylights in the roof shown in (a), is a favorite type for shops; truss (b) with double monitor ventilator is especially adapted to round house construction; trusses (c) and (e) are adapted to shop and factory construction where a large amount of light is de- sired, ventilation being obtained by means of circular ventilators ; truss (d) is similar to (c) and (e), but allows of better ventilation; truss (f) has skylights in the roof and has circular ventilators placed along the ridge of the roof; truss (g) is the type in common use for blacksmith shops, boiler houses, and roofs of small span. The "silk mill'' roof shown in (h) was used by the Klots Throwing Co. in their silk mill at Carbondale, Pa. The spans of the three trusses are 48' 8" each, with a clerestory of 13' 9" in the monitor ventilators, which are glazed with glass n' o" high. The monitors face east and west, al- lowing a maximum amount of direct sunlight in the morning and evening, and none at midday. This roof has given very satisfactory results, however, it would seem to the author that it would be necessary to use shades, and that there would be shadows in the building. The trusses in this building are spaced 10' 6" apart and support the plank sheathing which carries the roof, no purlins being used. The shafting to run the machinery in this building is placed in a sub-base- ment; a method much more economical and convenient than the com- mon one of suspending the shafting from the trusses. Pitch of Roof. The pitch of a roof is given in terms of the center height divided by the span; for example a 6o-ft. span truss w r ith % pitch will have a center height of 15 ft. The minimum pitch allow- able in a roof will depend upon the character of the roof covering, and upon the kind of sheathing used. For corrugated steel laid directly on purlins, the pitch should preferably be not less than % (6" in 12"), and the minimum pitch, unless the joints are cemented, not less than ^5. Slate and tile should not be used on a less slope than J4 an( l preferably not less than 1/3. The lap of the slate and tile should b. \\ ^_r~; &'/"/*?' Truss !* ; u ~ "7i jrt~i~n 3 i f &HQ-^&/IQ Part FraminqPlan FIG. 87. Section A-B ROOF COVERED WITH i^uowici TILE. Calculations of a series of simple Fink trusses resting on walls and having a uniform span of 60 feet, and different spacings gave the. least weight per square foot of horizontal projection of the roof for a spacing of 18 feet, and the least weight of trusses and purlins com- bined for a spacing of 10 feet. The weight of trusses per square foot was, however, more for the lo-ft. spacing than for the i8-ft. spacing, so that the actual cost of the steel in the roof was a minimum for a 156 FRAMEWORK spacing of about 16 feet ; the shop cost of the trusses per pound being several times that of the purlins. Local conditions and requirements Glass or Louvres (a) (e) -Glass -Glass or Louvres ^f\/ r Travel inqCrane\ (Si r^ J <-Glass V^, || 1 (b) :>J -Glass y 1 *- Glass or Louvres CZSZSZSt v\y\7\7 / \ (0 (f) Trusses Spaced 18 400 'Long Locomotive 5hop- Oregon Short Line FIG. 89. be put. A number of the common types of transverse bents are shown in Fig. 88. Transverse bents (a), (b), (d) and (h) are commonly used for boiler houses, shops and small train sheds. Where a travel- ing crane is desired, the crane girders are commonly suspended from the trusses in the bents referred to, although the crane may be made to span the entire building as in (h). Transverse bent (d) was used for a round house with excellent results. Transverse bents (f ) and (g) are quite commonly used where it is desired that the main part of the building be open and be provided with a traveling crane that will sweep 158 FRAMEWORK the building, while the side rooms are used for lighter tools and mis- cellaneous work. Transverse bent (c) may be used in the same way as (g), by supplying a traveling crane. Transverse bent (e) is very often used for shops. Cross-sections of the locomotive shops of several of the leading railways are shown in Figs. 89 to 92, inclusive, and the locomotive shops of the A. T. & S. F., and the Philadelphia and Reading Railroads are described in detail in Part IV. For the most part these buildings ' Long Locomotive Shop -5T-L-.I-M-&5. FIG. 90. are built with self-supporting frames, and have brick walls built out side the framing. The arrangement of the cranes, provisions for light 5kylic|ht 496~0 Long Locomotive Shop -Union Pacific FIG. 91. TRUSS DETAILS 159 ing and ventilating, and the main dimensions are shown in the cuts and *- need no explanation. Skylig U 39 : 9 f * XJJt Locomotive Shop -A-T& 5-F- FIG. 92. A cross-section and end view of the train shed of the Richmond L'nion Passenger Station are shown in Fig. 93. Riveted trusses are Hcrtiou, Lmikiny .\orth. Klrration, .\'',rth End. Train Shed Richmond Union Passenger Station. FIG. 93. quite b nerally used in train sheds ; a notable exception to this state- ment, however, being the trusses for the new train shed of the C. R. I. & P., and'L. S. & M. S. Railways in Chicago. The trusses in this struc- ture have a length of span of 207 ft., a rise of the bottom chord of 40 ft. and a depth of truss at the center of 25 ft. The trusses are pin con- nected, the compression members being built up channels and the ten- sion members eye-bars. The building is described in detail in Engineer- ing News, August 6, 1903. Truss Details. Riveted trusses are commonly used for mill build- ings and similar structures. For ordinary loads, the upper and lower i6o FRAMEWORK chords, and the main struts and ties are commonly made of two angles placed back to back, forming a T-section, the connections being made by means of plates. The upper chord should preferably be made of unequal legged angles with the short legs turned out. Sub-struts and ties are usually made of one angle. Flats should not be used. Where a truss member is made of two angles placed back to back, the angles should always be riveted together at intervals of 2 to 4 feet. Trusses that carry heavy loads or that support a traveling crane or hoist, are very often made with a lower chord composed of two chan- nels placed back to back and laced or battened, and are sometimes made with channel chord sections throughout (see Fig. 175). When the purlins are not placed at the panel points of the truss the upper chord must be designed for flexure as well as for direct stress. The section in most common use for the upper chord, 'where the purlins are not placed at the panel points, is one composed of two angles and a plate as shown in (c) Fig. 96. (a) (b) FIG. 94. Trusses may be fastened to the columns by means of a plate as shown in (a) Fig. 94, or by means of connection angles as shown in (b) and (c). The first method is to be preferred on account of the rigidity of the connection, and the ease with which the field connection can be made. DETAILS OF A STEEL ROOF TRUSS 161 FlG. 95. SHOP DRAWINGS FOR A STEEL ROOF TRUSS. 1 62 FRAMEWORK Trusses supported directly on masonry walls have one end sup- ported on sliding plates for spans up to about 70 feet; for greater lengths of span one end should be placed on rollers, or should be hung on a rocker. Trusses for mill buildings should be made with riveted rather than with pin connections, on account of the greater rigidity of the riveted structure. The complete shop drawings of a truss for the machine shop at the University of Illinois, are shown in Fig. 95. This truss is more completely detailed than is customary in most bridge shops. The practice in many shops is to sketch the truss, giving main dimensions, number of rivets and lengths of members, depending on the '-0- ---- P' tch 50 --- FIG. 96. TRUSS DETAILS 163 templet maker for the rest. In Fig. 95 the rivet gage lines are taken as the center lines. This is the most common practice, although many use one leg of the angle as the center line in secondary members. The latter method has the advantage of reducing the length of connection plates without introducing secondary stresses that are liable to be troublesome. The detail drawings of a transverse bent are shown in Fig. 96. The common methods of attaching purlins and girts, and of making lateral connections are also shown. The fan type of Fink Truss shown in Fig. 96 is quite commonly used where an odd number of panels is desired, and makes a very satisfactory design. The details of the end connection of a 60- ft. span truss are shown in (a), and of a 45-ft. span truss with a reinforced top chord are shown in (c), Fig. 96. The method of reinforcing the top chord shown (c) is the one most com- monly employed where purlins are not placed at the panel points. The method of making lateral connections for the lateral rods shown in (c) is not good, for the reason that it brings bending stresses in a plate which is already badly cut up. The detail drawings of a saw tooth roof bent for the Mathiessen & Hegeler Zinc Works, LaSalle, 111., are shown in Fig. 97. This building was erected in 1899 along the lines suggested by an experience with a similar saw tooth roof building erected in 1874. The building was de- signed by Mr. August Ziesing, Vice President American Bridge Co., and was erected by the American Bridge Co. The following description is from a personal letter from Mr. Julius Hegeler of the firm of Mathiessen & Hegeler, to the author in reply to a request for plans: "The cast iron gutters are fastened to the pur- lins and roof boards by spikes through holes in the gutters (holes are not shown in the drawing) ; on account of their slope, however, hardly any fastening is necessary. These gutters are so placed that the gal- vanized iron down spouts are next to the posts, there being two down spouts at each post. The condensation gutters are fastened to the gut- ters and empty into the down spouts. Ice has never caused any trouble by forming in the gutters." 164 FRAMEWORK s-r i *# J. ** 58J& Details of Cast Iron GuTter FIG. 97. CROSS-SECTION OF THE SHOPS OF THE MATHIESSEN & HEGELER ZINC WORKS, LASAU.E, Iix. The original saw tooth roof shop built by this firm in 1874 is still in use, and is one of the first, if not the first, saw tooth roofs built in America. COLUMNS. The common forms of columns used in mill build- ings are shown in Fig. 98. For side columns where the loads are not excessive, column (g) composed of four angles laced is probably the best. In this column a large radius of gyration about an axis at right angles to the direction of the wind is obtained with a small amount TYPES OF MILL BUILDING COLUMNS 165 of metal. The lacing should be designed to take the shear, and should be replaced by a plate, (f) Fig. 98, where the shear is excessive, or where the bending moment developed at the base of the column requires the use of excessive flanges. The I beam column (h) makes a good side column where proper connections are made, and is commonly used for end columns (see Fig. 81). The best corner column is made of an equal legged angle with 4, 5 or 6-in. legs, (i) Fig. 98. Details for the bases of the three columns above described are shown in Fig. 99. Z Channels Laced (a) ^Channels Laced (b) a n ZChannels Z Plates CO 2 Channels I I Beam (d) X 4 Z Bars I Plate fe) 4Anqles I Plate ffj 1 1 Beam (h) I Angle (i) H Special I Beam Larimer (k) Gray (I) 4 Angles Box Laced (m) a 4 Angles Box Laced (n) I 4 Angles Starred (O) FlG. 98. TYPES OF MIU, BUILDING COLUMNS. 1 66 FRAMEWORK Columns made of two channels laced, or two channels and two plates, are used where moderately heavy loads are to be carried. Chan- nel column (a), with channels turned back to back and laced, is the form most commonly used; column (b), with the backs of the channels turned out and laced, gives a better chance to make connections and can be made to enter an opening without chipping the legs of the channel ; column (c) is a closed section and is seldom used on that account. The cost of the shop work on column (b) was formerly considerably more than for column (a), for the reason that it was impossible to use a power riveter for driving all the rivets. A pneumatic riveter is now made, however, that will drive all the rivets in column (b), and the shop cost for columns (a) and (b) are practically the same. Where very heavy loads are to be carried, columns (d) or (e) are often used. Column (d), composed of two channels and one I beam, is a very economical column and is quite often used as a substitute for the Z-bar column shown in (e), for the reason that it can be built up out of the material that is in stock or that can be easily obtained. Con- nections for beams are easily and effectively made with either columns (d) or (e). The special I beam column (j), with flanges equal to the depth of the beam, is now being rolled in Germany by the use of a process patented by an American, Mr. Henry Grey. This column makes an almost ideal column for heavy loads, since it has all the advantages of the Z-bar column with a very much smaller shop cost. The Larimer column (k) is a painted column manufactured by Jones & Laughlins, and is used by their patrons quite extensively. The Gray column (1) is a patented column and is but little used. Columns made of four angles box-laced, are used where extremely light loads are carried by very long columns. The shop cost of column (m) is somewhat less than that of column (n), although with small angles there is no dif- ficulty in riveting (n) with a machine riveter. Column (o) is a very poorly designed column, for the reason that the radius of gyration is very small for the area of a cross-section of the column. Columns made of two angles "starred" and fastened at intervals of two or three COLUMN DETAILS. 167 feet by means of batten plates, are quite frequently used for light loads. Column Details. The details of a 4-angle laced column attached to a truss are shown in Fig. 96 ; and the details of a 4-angle plate column are shown in Fig. 97. The details of bases for 4-angle, I beam and angle columns are shown in Fig. 99. (a) (CJ Shop details of a 4-angle column are shown in Fig. 100. This column was designed for a mill building with a span of 60 feet, trusses spaced 16 feet apart. The long legs of the angles are placed out, to give a larger radius of gyration about an axis at right angles to the direc- tion of the wind. The details of a 4-angle and plate column, designed to carry a crane girder as well as the roof, are shown in Fig. 101. The details of a heavy column composed of two channels placed back to back and laced, are shown in Fig. 102 ; the lacing is heavy and is well riveted. The bent plate connections for the anchor bolts on this column are very satisfactory. This is one of the columns used in the A. T. & S. F. R. R. shops at Topeka, Kas., to carry the crane girders. The shop details of a light channel column are shown in Fig. 103. The single lacing alternates on the two sides of the column. The various details of the columns can be seen, and require no explanation. i68 . FRAMEWORK Center Roof Truss. KnceBmcz Jflii*r Q. * FIG. 100. THE ENO.NEERINO RECORC FIG. 101. COLUMN DETAILS 169 >3->-r*i\ -y ~ ypitf ^^a i : -; M 1 *"- FIG. 102. FIG. 103. 170 FRAMEWORK The American Bridge Company's specifications for lattice bars for single and double lacing are shown in Fig. 104. Maximum Distance C for given thlckr SINGLE .AGING t- DOUBLE l.ACI H| t C C f * 10 1-3 I 4 fa 1 04- 1 63- * i 1 3 1 1CH I I 1 5ir 2 2i I 1 1 8 2 6 i 1 10* 2 95- I 1 2 1 3- li 1 Rivet i R " t Rivet r - -"? ^N 3 ) -f-f- "<^| ! .._*_.]. (9 "H M UJ FIG. i j*j 34. Q4 Single lacing should make an angle of not less than 60 degrees, and double lacing, riveted at the center, not less than 45 degrees with the axis of the member, These specifications are standard. The properties of angles, I beams and channels, and of Z-bar, Larimer and Gray columns are given in the manufacturers handbooks. The moment of inertia of two channels placed back to back and laced, as in (a) or (b) Fig. 98, about an axis parallel to the webs and through the center of gravity of the section, is given by the formula I = 2 T + 2 Ad 2 where /' = moment of inertia of one channel about an axis through its center of gravity and parallel to the given axis, A = the area of one channel, and d distance from the center of gravity of one channel to the center of gravity of the column. The lacing is omitted in find- ing the moment of inertia and the area of the section. The moment of inertia of the column about an axis perpendicular to the webs is equal STRUTS AND BRACING 171 to twice the moment of inertia of one channel, which may be found in the table of properties of channels given in the handbooks. Having the moment of inertia I, the radius of gyration of the column is given by the formula \\ith channels placed back to back and laced, the radii of gyra- tion about the two axes are equal when the clear distance is equal to about 3 inches for 5-in. channels, and 10 inches for I5~in. channels. A common rule is to space the channels about eight-tenths the depth. \Yith channels placed with backs out and laced, the radii of gyration about the two axes are equal when the clear distance is about equal to 5 inches for 5-in. channels, and 13 inches for i5-in. channels (see Cambria Steel, 1903 Edition, p. 217). The moment of inertia of a 4-angle laced column, about an axis perpendicular to the lacing and through the center of the post, is given by the formula / == 4/' + 4Ad 2 where /' = moment of inertia of one angle about an axis through its cen- ter of gravity and parallel to the given axis, A =. the area of one angle and d = the distance from the center of gravity of the separate angles to the center of gravity of the column. The moment of inertia about the other axis is found in a similar manner. STRUTS AND BRACING. Eave struts are very commonly made of four angles laced, made in the same way as the 4-angle posts, Fig. 100. Eave struts made of single channels are more economical, and are equally as good as the laced struts for most cases. End rafters are commonly made of channels. The sides, ends, upper and lower chords are commonly braced as shown in Fig. 81. The bracing in the plane of the lower chords should preferably be made of members cap- able of taking compression as well as tension. The diagonal bracing in the plane of sides, ends, and upper chords is commonly composed of rods. Initial tension should always be thrown into diagonal rods by 172 FRAMEWORK screwing up the turnbuckles or adjustable ends. Stiff bracing should be made short, and should be brought into position for riveting by using drift pins ; to accomplish this there should be not less than three rivet holes in each lateral connection. A connection for lateral rods to the chords of trusses is shown in Fig. 105. Lateral Connection FIG. 105. Cast lateral lugs for connecting lateral rods to the webs of I beams and to heavy plates are shown in (a) and (b), Fig. 106. I" *i' (2) Cast Lateral Luq (a) Cast Lateral Lug (b) FIG. 1 06. Where rod bracing in the ends and sides of buildings interferes with windows and doors, or where the building is to be left open, portal bracing is used. In the latter case the bents are usually braced in pairs, DESIGN OF PARTS OF THE: STRUCTURE 173 although the portal bracing is sometimes made continuous. Stiff brac- ing is often placed between the trusses in the plane of the center of the building and materially stiffens the structure (see Fig. 17 $J. PURLINS AND GIRTS. Purlins are made of channels, angles, Z-bars and I beams, Fig. in, where simple shapes are used. Channel and angle purlins should be fastened by means of angle lugs as shown in Fig. 107. I beam purlins are very often fastened as shown in the A. T. & S. F. R. R. shops, Fig. 175. Z-bar purlins are bolted direct- ly to the upper chords of the trusses. The channel purlin is the most economical, and the I beam purlin is the most rigid. Girts are made of channels, angles, and Z-bars, and are fastened as shown in Fig. in. \Yhere the distance between trusses is more than 15 or 16 feet the pur- lins and girts should be kept from sagging by running y% or */2-inch rods through the centers to act as sag rods, the ends of the rods being fastened to the eaves and ridge (see Fig. 81). .-F'ur/in Where the columns and trusses are placed so far apart that the use of simple rolled shapes is no longer economical, purlins and girts are trussed. DESIGN OF PARTS OF THE STRUCTURE. The methods of determining the sizes of the various members in a mill building will be illustrated by a few examples. For a more detailed treatment of this subject, see "Modern Framed Structures" by Johnson, Bryan and Turneaure ; "Roofs and Bridges" by Merriman and Jacoby ; and other standard works on bridge design. Manufacturers of structural material issue handbooks which con- i^4 FRAMEWORK tain tables that give weights, areas of sections, positions of centers^of gravity, moments of inertia, radii of gyration, etc., for the shapes manufactured by the different companies. Tables are also given for the resisting moments on pins, the shearing and bearing values of rivets, standard bolts, eye-bars, bridge pins, standard connection angles, bear- ing plates, minimum size of rivets, spacing of rivets, and many other useful tables. The handbooks best known are as follows, the popular name being given in brackets : Cambria Steel (Cambria), issued by the Cambria Steel Company, Johnstown, Pa. ; Pocket Companion (Car- negie), issued by the Carnegie Steel Company, Pittsburg, Pa.; Stand- ard Steel Construction (Jones & Laughlins), issued by Jones & Laugh- 1ms, Limited, Pittsburg, Pa.; Steel in Construction (Pencoyd), issued by A. and P. Roberts Company, Philadelphia ; and Structural Steel and Iron (Passaic), issued by the Passaic Rolling Mill Company, Pater- son, N. J. These books can be obtained for from 50 cts. to $2.00. The American Bridge Company issued, in 1901, a book entitled Standards for Structural Details, for use at its various plants. The Carnegie handbook was formerly very generally used in de- signing offices, but recently the supply has been limited so that the Cam- bria handbook has taken its place in schools and in many offices, and for this reason references will be made to Cambria in obtaining weights, properties of sections, etc. All references to Cambria will be to the 1903 edition. Design of Trusses. The method of determining the proper sizes of the truss members will be illustrated by designing a few of the members of the truss in the transverse bent of the mill building shown in Fig. 53 ; the stresses in which are given in Table VI. The secondary members will be omitted from the truss in the design, as they were in obtaining the stresses. The material will be assumed to be medium steel and the allow- able stresses as given in Appendix I, will be taken. The allowable stresses are as follows: Tension 16,000 Ibs. per sq. in. Compression 16,000 70 / -i- r Ibs. per sq. in. DESIGN OF TRUSSES 175 where / = the length of the member in inches, and r radius of gyra- tion of member in inches. Rivets and Pins, bearing 22,000 Ibs. per sq. in. Rivets and Pins, shear 1 1,000 " " " " Pins, bending on extreme fibre 24,000 " " " " Plate Girder webs, shear on net section 10,000 " " " " Compression Members. Piece .v-2. Maximum stress + 34,300 Ibs. The upper chord will be made of two angles with unequal legs placed back to back, with the shorter legs turned out, and separated by i-inch gusset or connection plates. Try two 4" x 3" x 5-16" angles. From table on page 187 Cambria, the least radius of gyration, r, is 1.27 inches. The unsupported length of the member is 8.5 feet, and l-i-r = 102 -f^ 127 = So. The allow- able stress per square inch = 16,000 70 / -r- r = 16,000 5,600 =. 10,400 Ibs. The area required will be 34,300 -5- 10,400 ==3.3 sq. in. The combined area of the two angles is 4.18 sq. ins. (page 170 Cam- bria), which is somewhat large. Try two 3^4" x 3" x 5-16" angles. From the table on page 186 Cambria, r = 1 . 10 inches ; then / -i- r = 93, and allowable stress is 16,000 70 x 93 = 9,490 Ibs. per sq. in. Required area = 3.62 sq. in. The area of the two angles is 3.88 sq. in., so the section is sufficient. To make the two angles act together as one piece it is necessary to rivet them together at intervals, such that the two angles acting singly will be stronger than the two angles acting together. On page 170 Cambria, the least radius of gyration of a 3^" x 3" x 5-16" angle about a diagonal axis is 0.63 inches. The angles must therefore be riveted at least every 0.63 x 93 = 58.6 inches. It is the common practice to rivet angles in compression about every 2^4 to 3 feet. The truss will be shipped in two parts and in order to avoid a splice, and because the difference in the stresses is small, the entire top chord will be made of two 3^" x 3" x 5-16" angles. 176 FRAMEWORK Tension Members. Member 1-2. Maximum stress = 24,900 Ibs. The net area required is 24,900 -f- 16,000 = 1 . 56 sq. in. The gross area of the section must be such, that there will be a net area of not less than 1 .56 sq. in. after the area of the rivet holes in any section has been deducted. Try two 3" x 3" x y\" angles. It will be necessary to deduct the area of one rivet hole from each angle. \The diameter of the rivet hole deducted is taken J/ inch larger than the diameter of the rivet before driving! Assuming the rivets as fy& inch, it will be necessary to deduct o. 19 sq. in. from each angle (page 310 Cambria). The net area of two 3" x 3" x /4" angles is 2.88 0.38 = 2.50 sq. in. The section is somewhat large, but will be used, for the reason that angles much smaller than these will be deficient in rigidity. The angles will be riveted together about every 3 feet to make them act as one member. Member 5-6. Maximum stress = 5>ooo Ibs. The net area required is 5,000 -f- 16,000 = 0.32 sq. in. The gross area of the section must be such that there will be a net area of at least 0.32 sq. in. after the area of the rivet holes in any section has been deducted. Try two 2" x 2" x J4" angles the minimum angles that can be used under the specifications. Deducting the area of one rivet the net area is 1.88 0.38 = 1.50 sq. in. The section appears to be exces- sively large and one 2" x 2" x y^" angle will be tried. Where angles m tension are fastened by one leg the specifications require that (para- graph 35) only one leg shall be counted as effective, or the eccentric stress shall be calculated. The net area of the one 2" x 2" x J4 " angle when fastened by one leg, will then be ^2 0.94 o. 19 = 0.28 sq. ins., which ib insufficient. One 2^/2" x 2y>" x y\" angle will have a net area of 0.40 sq. in., which will be sufficient. However, since it is preferable to make tension members of symmetrical sections, the member will be made of two 2" x 2" x J4" angles. DESIGN OF COLUMNS 177 Alternate Tension and Compression. Where members are subject to alternate tension and compression the specifications require that they be designed to take each kind of stress, (paragraph 32). Member 4-3-. Maximum stresses = ( 21,300 and + 2600 Ibs). Try two 3" x 3" x y 4 " angles the same as member 1-2. The net area required for tension is 21,300 -r- 16,000 = 1 .34 sq. in. The net area of two 3" x 3" x %" angles is 2.88 0.38 = 2.50 sq. in. which is ample for tension. The least radius of gyration is r = 0.93 inches (page 185 Cam- bria). Length = 108 inches, and / -f- r = 117. The allowable stress per square inch = 16,000 70 x 117 := 8,810 Ibs. Required area = 0.30 sq. in. The section appears to be large, but it can not be made much smaller without exceeding the maximum limit of 125 for / -=- r. Two 3" x 2^2 " x 1/4" angles will be found by a similar calculation to be sufficiently large, and will be used. Member 3-4. Maximum stresses ( 10,900 and + 13,600 Ibs). Try two 2" x 2" x l / 4 " angles. The area required to take the ten- sion is 10,900 -7- 16,000 = 0.69 sq. in. The net area of the twb angles is 1 .88 0.38 = 1 .50 sq in., which is ample for tension. The least radius of gyration is r = 0.61 inches (page 185 Cambria). The length is 108 inches, and l-^-r = 177. This is greater than the max- imum allowed of 125, and a larger section must be used. Try two 3" x 2" x y 4 " angles, with short legs out. In this case i __ r equals 108 -f- 0.89 = 120. The allowable stress per sq. in. is 16,000 70 x 1 20 = 7,600 Ibs. The required area for compression is 13,000 -i- 7,600 = i .79 sq. in. The area of the two angles is 2.38 sq. in., which is ample. The section is sufficiently large to take both ten- sion and compression, and will be used. Design of Columns. Columns must be designed to take the stress due to direct loading, to eccentric loading, and to wind moment. The method of column design will be illustrated by the design of the leeward column in the transverse bent shown in Fig. 56 ; the stresses for which are given in Table VI. 12 178 FRAMEWORK Direct stress in A-ij = 14,900 Ibs.; and bending moment = 924,000 inch-lbs. A 4-angle laced column will be used. Try four 4" x 3" x 5-16" angles, long legs out, and a depth of 1.8" out to out of angles ; y%' lacing and connection plates will be used. The radius of gyration of two 4" x 3" x 5-16" angles with the long legs out, is found on page 189 Cambria to be 1.93 inches. The moment of inertia of a section of the post about the shorter axis is / = 4 /' + 4 Ad 2 4 x i . 65 + 4 x 2 . 09 (9 . oo o . 76) 2 = 574.24 and the radius of gyration is / 574.24 ' r= *u r> oft =8. 3 inches. The maximum fibre stress will occur on the windward side of the post and will be found by substituting in formula (300) to be 14,900 924,000 X 9 /-A+/i = -QT + 14.9000 X240 280,000,000 = 1780 + 14,560 = 16,340 Ibs. per square inch. The allowable stress per square inch for direct loads is 16,000 - 70 / -r- r = 16,000 ( 70 x 29 14,000 Ibs. ; and since the wind mo- ment comes only occasionally we will increase the allowable stress for direct loads by 25 per cent when wind loads are considered, making an allowable stress of 14,000 x 1.25 = 17,500 Ibs. per square inch. The section chosen is therefore sufficiently large. The direct load will have to be carried by the column, and it will be necessary to investigate the column about its longer axis. For this case / -r- r = 240 -^- 1 .93 = 125, which is allowable under the specifica- tions, and the section is ample. The lacing will be designed to take the shear, which is 5,500 Ibs. below and 12,800 Ibs. above the- foot of the knee brace. The maximum stress in the lacing will be 12,800 x sec 30 14,700 Ibs. The al- lowable tensile stress per square inch will be 16,000 x 1.25 = 20,000 TABLES 179 TABLE XL RlVET SPACING IN ANGLES. Cr - iffL F" Leg. Inches. 8 7 6 5 4 3 2 2 Inches. Max. Rivets. Inches. Leg. Inches. Inches. Inches. Max. Rivets. Inches. 4 2 3 2 s MS M (i M M 8 7 6 5 3 3 3 M Where 6" Angle Exceeds %". 6 * 2M * TABLE XII. MAXIMUM SIZE OF RIVETS IN BEAMS, CHANNELS, AND ANGLES. I-BEAMS. CHANNELS. ANGLES. Depth Weight Size Depth Weight Size Depth Weight Size Length Size Length Size c! per ol of per of of per of of of . of of Bete. Foot. Rivet. Beam. Pcot. Rivet. Channel Foot. Rivet. Leg. Rivet. Leg. Ri76t. Insh's. Pounds. Inelus. laches . Pounds. Inches. Inches. Pounds. Inches. Icobes. Inches. Inches. Inches. 3 5.5 H 15 42.0 # 3 4.0 H X X 2^ /< 4 7.5 >/2 15 60.0 # 4 5.25 /2 1 H 2# /& 5 9.75 # J5 80.0 H 5 6.5 /2 IV /2 3 6 12.25 H 18 55.0 y* 6 8.0 H li A a # S/2 1 7 15.0 H 20 65.0 i 7 9.75 y* Itt % 4 1 8 18.0 y* 20 80.0 i 8 11.25 x 1/2 % 4^ 1 9 21.0 x 24 80.0 i Q 13.25 # IX tt 5 1 10 25.0 x 10 15.0 ^ 2 H 6 1 12 31.5 x 12 20.50 X 2X X 7 1 12 40.0 x 15 33.0 % 2A X i8o FRAMEWORK TABLE XIII. RIVET SPACING. Size Minimum Maximum Pitch at Minimum Pitflh in Distance from Edge of Piece to of Bivet. Pitch. Ends of Compression Flanges of Chords and Qird's. Center of Rivet Hole. Members. Inches. Inches. Inehes. Inehes. Minimum. Usual. Inches. Inches. I X % . . . 1 ll 2K 4 JJL 1 6 'iii ^A- 2/4^ 3 4 i/^ % 2^ 3% 4 I /5 " iK i 3 4 4 IV 2 TABLE XIV. SHEARING AND BEARING VALUE OF RIVETS IN POUNDS. Diameter of Rivet Inches Area in Square Inches. Single Shear at 11000 Lbs. Bearing Value for Different Thicknesses of Plate in Inches, at 22,000 Pounds per Square Inch. X _5._ 1 6 ^ & /^ a. 1 6 5 /8 JLJL 16 X Frac- tion Deci- mal X % .375 .500 .1104 .1963 1210 2160 2060 2750 2580 3090 4820 5500 3440 4130 % .625 .3068 3370 3440 4300 5160 6020 6880 7740 8600 X .750 .4418 4860 4130 5160 * 6190 7220 8250 9280 10320 11340 12380 k .875 .6013 6610 4810 6020 7220 8430 9630 10840 12040 13240 14440 1 1. 00 .7854 8640 5500 6880 8250 9630 11000 12380 13750 15130 16500J All bearing values above or to right of upper zizgag lines are greater than double shear. Values below or to left of lower zigzag lines are less than single shear. Ibs. The required net area for tension will be 14,700 -;- 20,000 = 0.74 square inches. The gross area of a 3" x ^/g" bar is i . 125 square inches (page 388 Cambria) and the net area after deducting for one Y^' rivet is 0.895 square inches (page 310 Cambria) which is sufficient for tension. DESIGN OF PLATE GIRDERS 181 The allowable stress for compression is (16,000 7O/-=-r) 1.25. The moment of inertia of a 3" * ft" bar is 0.0135, and the radius of gyration is o.n inches. The ends of the lacing bars are practically fixed, and it will be assumed that the length c. to c. of rivets will as a result be shortened by one-half. Then l-r-r = 75, the allowable stress will be 13,340 Ibs. and the required area i.io square inches. The lac- ing bars are therefore sufficient to take either the tension or compression. Lacing bars 2y 2 " x ft," will be found sufficient below the foot of the knee brace. The allowable shear on each rivet in the lacing will be (Table XIV) 4860 x 1.25 = 6,075 Ibs.; and the allowable bearing will be 6,190 x i . 25 = 7,740 Ibs. The stress in the lacing bars below the foot of the knee brace is 5,500 x sec 30 = 6,300 Ibs. ; the ft -rivets are all right for bearing but are not quite large enough for shear, however it is so near, that they will be used. Above the foot of the knee brace it will be necessary to increase the thickness of the lacing bars and put two rivets in each connection as shown in Fig. 102, or use a solid plate. In designing the bases of columns hinged at the base, part of the stresses may be assumed to pass directly to the base plate if the abutting surfaces have been milled; but in columns fixed at the base all of the stresses must be transferred by the rivets. The rivets must be designed to take the direct stress and the stress due to bending moment ; the so- lution is similar to that for anchorage (Fig. 61) and will not be given. Design of Plate Girders. The maximum moments and shears are found as described in Chapter X. If the plate girder were de- signed by means of its moment of inertia, as in the case of rolled sec- tions, about Y(, of the web would be effective as flange area to take the bending moment ; or deducting rivets about ft would be found ef- fective. It is, however, the common practice to assume that all the moment is taken by the flanges, and that all the shear is taken by the web ; and this assumption will be made in the discussion which follows. Flange Stress. The stress, F, in the flanges at any point in a plate girder is F = M -*- h (80) 182 FRAMEWORK where M = bending moment in inch-pounds, and h = the distance between centers of gravity of the flange areas (effective depth), (a) Fig. 108. The net flange area, A, will be A = F -f- / where / = the allow- able unit stress. The tension flanges of plate girders are designed as above, and the compression flanges are made with the same gross area. ooo oooooo O Or o Flange Anqles j I Web Plate Flange Angles ooooooooo (bl ? ^"T" 1 ! i ' i . i i J i L U^ i H- 10 I I I I 'I , ' in * 5 ' (d FIG. 108. I i i i, t't.f 6 6^-0 re) Web. The web plate should not be less than 5-16 of an inch in thickness although ^4 -inch plates may be used if provided with suf- ficient stiffeners. The shear in the web is commonly assumed as uni- formly distributed over the entire cross-section of the plate. Stiffeners. There -is no rational method for the design of stif- feners. If they are placed at distances apart not exceeding the depth of the girder, nor more than 5 feet, where the shearing stress is greater DESIGN OF PLATE GIRDERS 183 than given by the formula allowed shearing stress 12,500 90 H, where H = ratio of depth to thickness of web plate, the stiffeners will be near enough together. Where the shearing stress is less than given by the above formula, stiffeners may be omitted or spaced as desired. Stiffeners are commonly designed as columns, free to move in a di- rection at right angles to the web, with an allowed stress P = 12,000 55 / -r- r. Stiffeners should be provided at all points of support and un- der all concentrated loads, and should contain enough rivets to traansfer the vertical shear. Web Splice. In the plain web splice shown in Fig. 108, the rivets take a uniform shear equal to S -r- n, where S is total shear, and n is number of rivets on one side of splice, and a shear due to the shearing stress not being applied at the center of gravity of the rivets. This is the problem of the eccentric riveted connection, which has been dis- cussed in Chapter XV. If the web is assumed to take part of the bending moment there will be an additional shear due to bending moment. Rivets in the Flanges. In Fig. 108, let S = the shear in the girder at the given section, h f = distance between rivet lines, p = the pitch of the rivets, and r = the resistance of one rivet (r is usually the safe bearing on the rivet in the web) . Then taking moments about the lower right hand rivet, we have Sp = rh', and p = rh' -f- S (81) Where the rivets are in double rows as shown in (d), the distance h r is taken as a mean of the distances for the two lines. The crane loads produce an additional shear in the rivets, (e) Fig. 108, which will now be investigated. We will assume that the rail dis- tributes the load over a distance of 25 inches ; this distance will be less for light rails and more for heavy rails. The maximum vertical shear on one rivet will be Pp -f- 25 = 0.04 Pp. The horizontal stress due to bending moment is r = Sp -f- h', and the resultant stress from the two sources will be 184 FRAMEWORK r> = and solving for p I r> (82) (0.04/>) 3 +(^ Crane Girders. The maximum moments and shears in crane gir- ders are found as explained in Chapter X. For small cranes I beam girders are commonly used, and are designed by the use of their mo- ments of inertia. Plate girders are designed as previously described. In designing both rolled and plate girders care must be used to proper- ly support the girder laterally. CHAPTER XVIII. CORRUGATE STEEL. Introduction. Corrugated steel is made from sheet steel of stand- ard gages, and is either galvanized at the mill or is left black. The black corrugated steel is usually painted at the mill and is always paint- ed after erection. Paint will not adhere well to the galvanized steel until after it has weathered unless a portion of the coating is removed by the application of an acid. The common standard for the gage of sheet steel in the United States is the United States Standard Gage, and this should be used in specifying the weight and thickness. The thickness and weights per square of 100 square feet, for black and gal- vanized sheet and corrugated steel are given in Table XV. The weights of the corrugated steel given in the table are for standard corrugations, approximately 2^2 inches wide and j^j of an inch deep. If black sheet steel is painted, add about 2 Ibs. per square. TABLE XV. \YEIGHT OF FLAT, AND CORRUGATED STEEL SHEETS WITH 2^ -INCH CORRUGATIONS. Gaqe No. Thickness in inches Weight per Sq uare ( 100 sq-ft-) Flat Sheets Corrugated Sheets Black Galvanized Black Fbinted Galvanized 16 .0625 250 266 275 291 Id .0500 200 216 220 236 10 .0375 150 166 163 Id2 22 .0313 125 /4I 13d 154 4 0250 too //6 III 127 26 0/88 75 SI 84- 99 28 0156 65 79 69 86 Corrugated steel is also made with corrugations 5, 3 and inches wide approximately. Corrugated steel with corrugations 1 86 CORRUGATED inches wide and y% of an inch deep is frequently used for lining build- ings. Corrugated steel with i^J-inch corrugations weighs about 4 per cent more than steel of the same gage with 2^-inch corrugations. Cor- rugated sheets are commonly made from flat bessemer steel sheets, by rolling one corrugation at a time. Iron and open hearth steel corrugated sheets can be obtained, but are very hard to get and cost extra. The standard sheets of corrugated steel with 2^/2 -inch corrugations, are 28 inches wide before, and 26 inches wide after corrugating, and will cover a width of 24 inches with one corrugation side lap, and ap- proximately 2iJ/2 inches with two corrugations side lap, (c) and (a) Fig. 109. Special corrugated steel can usually be obtained that will cover a width of 24 inches with \y 2 corrugations side lap, (b). Cor- rugated steel should be laid with 6 inches end lap on the roof and 4 inches end lap on the sides of buildings. Corrugated Roof Steel Side Lap 2 Corrugations *- -*t*- Cowers /*- 2d t "w/afe before c&rrug&r/ng r-/?6" n after (a) Special Cor- Roof Steel Side Lap \i Corrugations Covers 24"- H< - Covers 24" --- * 2% "->) \< -30 "w/tfe before corrug&f/'ng " End Lap for Roof 6" (b) Corrugated Siding Steel Side Lap I Corrugation - Covers 24 "- *** - Covers 24 " - -~ I* d "w/tfe before cerrugaf/ng ^26" " affer End Lap for 5 ides 4 " (C) FIG. 109. FASTENING CORRUGATED STEEL Stock lengths of corrugated steel sheets can be obtained from 5 to 10 feet, varying by one-half foot. Sheets of any length between 4 and 10 feet can usually be obtained directly from the mill without extra charge. Sheets from 48 to 5 inches long, cost from i-io to y 2 cents per pound extra. Sheets from 10 to 12 feet long are very hard to obtain and cost extra. Sheets cannot be obtained longer than 12 feet. Stock lengths of sheets should be used whenever possible as odd lengths often delay the filling of the order. Bevel sheets should preferably be ordered in multiple lengths and should be cut in the field. Sheets to fit around windows and doors should be cut in the field; no part of a sheet less than l /4 the width of a full sheet should ever be used. >GEAR WHEELS SECTION A-A FIG. no. For cutting and splitting corrugated sheets in the field the rotary shear shown in Fig. no is invaluable. It will make square or bevel cuts, or will split sheets without denting the corrugations. The shear shown in Fig. no is one made by the Gillete-Herzog Mfg. Co., Min- neapolis, Minn., and was used by the author in the erection of a steel stamp mill in Northern Michigan, while in the employ of the above named company. The shear is not on the market, but can be made in any ordinary machine shop at a comparatively small cost. Fastening Corrugated Steel. Where spiking strips are used, the corrugated steel is fastened with 8d barbed roofing nails J4 to 2^/2 inches long, spaced 6 to 8 inches apart. The 2^/2 -inch barbed nails should be used for nailing to spiking strips and to sheathing whenever possible. For weight of barbed roofing nails see Table XVI. i88 CORRUGATED TABLE XVI. NUMBER OF BARBED ROOFING NAILS IN ONE POUND. Size Length inches Gage No. No. in one Ib. Size Length inches, Gage No. No. in one Ib. 4d IK 13 339 20d 4 6 30 6d 2 12 205 30d 4# 5 23 8d 2X 10. 96 40d 5 4 17 lOd 3 9 63 50d 5M 3 13 12d 3X 8 52 60d 6 2 10 16d 3X 7 38 The common methods of fastening corrugated steel directly to the purlins and girts are shown in Fig. 1 1 1. Nailing pieces should pref- erably be used where anti-condensation roofing, Fig. 127, is used, or where the sides are lined with corrugated steel. The clinch nail is prob- r ft/vefs ancfc/inch na/b go fop of corrugations Methods of Fastening Corrugated Steel to Purlins Table of Clinch Nails FIG. in. L Purlin leq Lenqth No- per Ib. J" ( 3Z 4' 6" ^9 5" 7" 23 6" 8" ^l 7" 9" Id C Purlin leg Length No- per Ib. 3" 6" 29 4" 7"or8' 21 5" 9" 18 6" /O" Ib 7" II" 14- METHODS OF FASTENING CORRUGATED AND GIRTS. TO PURLINS ably the most satisfactory fastening for the usual conditions. The side laps are fastened together by means of copper or galvanized iron clos- WEIGHT OF COPPER RIVETS i8 9 ing- rivets, spaced about 8 to 12 inches apart on the roof and about 2 feet apart on the sides. Clinch nails are made of J /s inch or No. 10 soft iron wire and are clinched around the purlin. The usual sizes and weights of clinch nails for different lengths of angle and channel purlins are given in Fig. in. Care should be used in punching the holes in the corrugated steel for clinch nails and rivets to get them in the top of the corrugations and to avoid making the hole unnecessarily large. Clinch nails are spaced from 8 to 12 inches apart. Two clinch nails are usually furnished for each lineal foot of purlin and girt. Straps are made of No. 18 gage steel, 24 inches wide, and are TABLE XVII. NUMBER OF COPPER RIVETS IN ONE POUND. Diam- eter. Gage No. Length of Rivets in inches. B * __ 16 % .1. I 6 Ys TV % X % i IK ix 1% 3 70 4 78 5 85 64 60 53 48 46 44 39 36 32 6 180 105 100 96 90 74 68 61 56 54 50 46 7 368 211 180 171 160 150 140 132 110 97 91 79 72 63 8 417 266 248 227 200 172 157 147 136 116 100 93 88 71 9 600 365 336 261 248 228 220 184 169 156 133 124 113 99 10 820 411 376 336 305 257 249 223 206 180 162 11 944 416 400 360 338 320 n 1167 545 475 400 342 325 308 292 257 221 190 13 1442 799 640 547 502 448 400 392 316 14 1620 1040 995 816 784 616 550 528 15 3512 fastened with two 3-1 6-inch stove bolts ^ inches long. Straps are spaced 8 to 12 inches apart. One strap and two bolts are usually fur- nished for each lineal foot of purlin and girt: One bundle of hoop steel for making straps contains 400 lineal feet and weighs 50 Ibs. Clips are made of No. 16 gage steel, i l / 2 " x 2^/2", and are fastened with two 3- 1 6-inch stove bolts l / 2 inches long. Clips are spaced from 8 to 12 inches apart. One clip and two bolts are usually furnished for each lineal foot of purlin and girt. 190 CORRUGATED STEEL Copper rivets weighing about 6 pounds per 1000 rivets have com- monly been used for closing rivets ; but galvanized iron rivets made of very soft wire and weighing about 7 pounds per 1000 rivets are fully as good, and cost 7 cents per pound in 1903 as compared with about 25 cents per pound for copper rivets. The weight of copper rivets is given in Table XVII. Strength of Corrugated Steel. The safe load per square foot for corrugated steel supported as a simple beam, for sheets with 2^ -inch corrugations and of various gages is given in Fig. 112. This diagram is based on Rankine's formula *-%*& where W = safe load in Ibs. ; S working stress in Ibs. ; h = depth of the corrugations in inches ; b = width of the sheet in inches; t = thickness of the sheet in inches ; / = clear span in inches. 3 '4 5 6 5 pan,/., in Feet. FIG. 112. SAFE UNIFORM LOAD IN POUNDS FOR CORRUGATED STEEI, FOR DIFFERENT SPANS IN FEET. A summary of experiments to determine the strength of corrugated steel made by the author's assistant, Mr. Ralph H. Gage, is given in STRENGTH OF CORRUGATED 191 Table XVIII. The coefficient C in column 8 depends on the angle that the metal makes with the horizontal axis and varies as follows: angle of 30, C = 0.278; 45, C = 0.293 ; 60, C = 0.312, and for 90, C = 0.393- TABLE XVIII. SUMMARY OF EXPERIMENTS TO DETERMINE THE STRENGTH OF COR- RUGATED STEEL.* 1 2 3 4 5 6 7 8 9 1O Width Thick- Angle Tensile Gage's Actual Rankine's No. of Depth ness of Span Strength Formula Brkng Formula. Corru- fffltiODS h t Metal with / Ibs. per so in \\r CShbt. Load W W ___Skbt Ins. Ins. Ins. Axis Ins. I Ibs. Ibs. i 7 Ibs. 1 2.50 0.6025 .0588 39" 11' 44.0 58,000 643 630 597 2 2.50 0.612 .05683910' 44.0 58,000 632 630 587 3 2.50 0.625 .066 39 30' 44.0 58,000 745 720 692 4 2.50 0.606 ! ,0655!4042' 44.0 58,000 725 700 670 5 | 2.88 0.650 .036736 0' 43.25 67,000 505 500 475 6 2.88 0.650 .036636 0' 44.0 67,000 494 490 465 7 2.50 0.630 .036636 0' 44.0 50,000 358 350 335 8 2.50 0.61 .036536 0' 44.0 50,000 344 340 324 9 1.25 0.27 .036536 0' 24.0 50,000 281 300 262 10 1.25 0.27 .036536 0' 24.0 50,000 281 295 262 11 1.25 0.27 .029336 0' 24.0 50,000 225 200 211 12 1.25 0.27 .029336 0' 24.0 50,000 225 195 211 13 1.00 0.18 .029136 0' 24.0 50,000 298 310 279 14 1.00 0.18 .029136 0' 24.0 50,000 298 300 279 15 1.00 0.18 .026 36 0' 24.0 50,000 266 280 250 16 1.00 0.18 .026 36" 0' 24.0 50,000 266 260 250 i The actual breaking load agrees in most cases more closely with Gage's formula than with Rankine's, although the latter is more often on the safe side. Purlins are commonly spaced for a safe load of 30 Ibs. per square foot as given in Fig. 112; if the purlins are spaced farther apart than this, the steel will deflect a dangerous amount when walked on, and will leak snow and rain. Girts should be spaced for a safe load of about 25 Ibs. per square foot. From an inspection of Fig. 112, it is evident that corrugated steel lighter than No. 24 is of little use for mill buildings. *For details of experiments see article by Ralph H. Gage, in the Technograph, No. 17. 192 CORRUGATED Corrugated steel of No. 26 or 28 gage is so thin that it soon rusts out and should never be used unless for lining cheap buildings. Corrugated Steel Details. Ridge Roll The ridge roll most commonly used is made from No. 24 flat steel, and has a 2 l / 2 -inch roll and 6-inch aprons. It comes in 96-inch lengths and should be laid with 3 inches end lap. Plain and corrugated ridge roll are used (see Fig. PLAIN RIDGE CAP. CORRUGATED RIDGE ROLL. Gable Cornice Fove Cornice PLAIN RIDGE ROLL. Flashing for Stack CORRUGATED END WALL FLASHING. Flashing Outside Corner Finish CORRUGATED SIDE FLASHING. FIG. 113. FLASHING 193 113). Ridge roll is fastened with rivets or nails spaced 6 to 8 inches apart. Flashing. Flashing is used where the roof changes slope, around chimneys and openings in the roof, and over windows and doors, and should be of sufficient dimensions and so arranged that at least 3 inches vertical height is obtained between the edge of the flashing and the end of the corrugated steel roofing. Vertical and horizontal seams of all flashing should be closely riveted. Flashing is made from flat sheets HALF-ROUND GUTTER; LAP JOINT OR SLIP JOINT. EAVES TROUGH HANGERS FIG. 114. 13 194 CORRUGATED of the same gage as the corrugated steel, and can be obtained up to 96 inches in length. Flashing is made both plain and corrugated (see Fig. 113)- Corner Finish. Corner finish is made in various ways, three of which are shown in Fig. 113. Other methods are shown on the suc- ceeding pages. /' every 4--0". Hanging Gutter FIG. 115. Hanging Gutter y^P/fc/? B/ock /n Gutter Hanging Gutter Box Gutter FIG. 116. Gutters and Conductors. Gutters for eaves are ordinarily made from No. 24, and valley gutters from No. 20 galvanized steel. Gutters may be obtained in even foot lengths up to 10 feet, and should have 4-inch end laps. Special flat sheets up to 42 inches in width can be obtained for making gutters and details. CONDUCTORS AND GUTTERS 195 The common sizes of half round gutters made by the Garry Iron and Steel Roofing Co., Cleveland, Ohio, are shown in Fig. 114. Two common forms of adjustable hangers are shown in (a) and (b) in Fig. 114. Two forms of hanging gutters are shown in Fig. 115 and one form of a hanging, and a box gutter used with brick walls are shown in Fig. 116. A standard form of valley gutter is shown in Fig. 117. Extreme care should be used in making valley gutters to see that the sides are carried well up, and that the laps are well soldered. Volley Gutter FIG. 117. Conductors are made plain round or square, and corrugated round or square. Corrugated conductors are to be preferred to plain conduc- tors for the reason that they will give when the ice freezes inside of them, and will not burst as the others often do. Common sizes of round pipe are 2", 3", 4", 5", and 6" diameter. Common sizes of square pipe are i#" x 2}4", 2^" x 3^ ", 2#" x 4 M" and 3 #" x 5", equal to 2", 3" and 4" round pipe, respectively. Conductor pipes are fastened with hooks or by means of wire. Design of Gutters and Conductors. The specifications of the American Bridge Company for the design of gutters and conductors are as follows: 196 CORRUGATED Span of roof. Gutter. Conductor, up to 50' 6" 4" every 40' 50' to 70' 7" 5" " 40' 70' to 100' 8" 5" " 40' Hanging gutters should have a slope of at least i inch to 15 feet. The diagram in Fig. 118 for the design of gutters and conductors was described in Engineering News, April 17, 1902, by Mr. Emmett Steece, Assoc. M. A. Soc. C. E., City Engineer of Burlington, Iowa, as follows : FIG. 118. "The curves are for 54 pitch or flat roofs, to full pitch or domes. The areas are reduced to plan as shown.. The minimum sizes of circu- lar and commercial rectangular conductors are given on the left side of the diagram and the sizes and the minimum cross-sectional areas of square gutters are given on the right hand side. To use the diagram: Assume an area of roof, say 30 x 100 ft., or 3000 sq. ft., Y-2 pitch and one conductor for the whole area. Note the intersection of the vertical over area 3000 and the curve of ^ pitch ; following thence the horizontal line to the left it strikes a diameter of 5 ins. for circular, or over 3^ x 4^ ins. for commercial size. The next larger size would be used. The minimum cross-sectional area of gut- ters is shown on the right to be about 30 sq. ins., and the side of a square conductor about 4 . 5 ins." This diagram was based on a maximum rainfall of i . 98 inches per hour. CORNICE 197 English practice is as follows: Rain-water or down-pipes should have a bore or internal area of x at least one square inch for every 60 square feet of roof surface in temperate climates, and about 35 square feet in tropical climates. They should be placed not more than 20 feet apart, and should have gutters not less in width than twice the diameter of the pipe. The practice among American architects is to provide about one square inch of conductor area for each 75 square feet of roof surface; no conductor less than 2 inches in diameter being used in any case. Cornice. There are many methods of finishing the gables and eaves of buildings. A gable finish for a steel end, and for a brick end Ffoof 5tee/ C/mch Roof 5ree/ - , Clinch R/vet-* fin/sh Ang/e- Goble Finish for Sfeel End Gable Finish with Bnck Wall FIG. 119. Flashed Finish FIG. 120. 198 CORRUGATED as used by the American Bridge Company, are shown in Fig. 119. The steel end may have a cornice made by bending the corrugated steel as shown, or a molded cornice. The flashed finish shown in Fg. 120, is used by the American Bridge Company ; it is quite effective and gives a very neat appearance. The corrugated steel siding should preferably be carried up to the roof steel. The cornice and ridge finish shown in Fig. 121, designed by Mr. H. A. Fitch, Minneapolis, Minn., is very neat, efficient and economical. Section at Ridge Section at Gables Section at Eaves, FIG. 121. The galvanized rivets are much cheaper than copper rivets, and are preferred by many to the copper rivets. The detail shown was for a small dry house in which the eave strut was omitted. Nat/ing strip on^ eavejfrut^ Section /Va/ting stnp on end rafter orc/7a f frujs through Gable Corner Finish FIG. 122. CORNICE: 199 In Fig. 122, the eave cornice is made by simply extending the roof- ing steel, while the gable cornice is made by bending a sheet of cor- rugated steel over the ends of the purlins and nailing to wooden strips as shown. Section through Gable Corner Finish Section through Eaves FIG. 123. The Sheets heavier than No. 22 should not be bent in the field, corner finish is made by bending a sheet of corrugated steel. In Fig. 123, the eave and gable cornice are made'of plain flat steel bent in the shop as shown. The eave cornice is made to mitre with the gable cornice, thus giving a neat finish at the corner. The corner finish is made by using sheets at the corners in which one-half is left plain. -Na/7/ng 5tnp on end rafter Section Through Gable Corner Finish Section through Eaves FIG. 124. 2OO CORRUGATED In Fig. 124, the eave strut and gable cornice are molded. The two cornices are so made as to mitre at the corners, the mitres being made in the field. A plain corner cap is put on as shown, after bending the corrugated steel around the corner. I Section through Gable Brae kefs /8c-c /$"*' iron Cern/Ce of "^4crimpeaf v cja/'Steel -Crimps+ */'& Gvffer o/ *Z4 gar/ sfee/ fasfeneaf To cornice an& roofing Cor- wood f///er - - - 5/C3f/r>g of steel , /j '"b OOOOOOOOO/ , 4 1 ojjo ojjo J Ojj O j q o is <5T o Section throuqh Corn! JJ [_ , # 10 6a/ cor s fee/ Z4 crimped 'ga/- 5 feel. Clip to 5"*2z "L s \ Purlin > \-n-a-4 i Truss L s s Section throuqh Gable FIG. 126. ANTI-COXDENSATION ROOFING 201 In Fig. 125, an eave purlin is used and a channel is placed along the ends of the purlins. Spiking strips should always be used as shown, and the eave purlin should be fastened to the rafter by means of angle clips. The finish shown in Fig. 126, was used by the U. S. Government and needs no explanation. Anti-condensation Roofing. To prevent the condensation of moisture on the inner surface of a steel roof, and the resulting dripping, the anti-condensation roofing shown in Fig. 127 and in Fig. 129 is fre- quently used. The usual method of constructing this roofing is as follows : Galvanized wire poultry netting is fastened to one eave purlin 7&r Ffrper- Pov/fry Netting Anti-Condensation Roofing FIG. 127. and is passed over the ridge, stretched tight and fastened to the other eave purlin. The edges of the wire are woven together, and the net- ting is fastened to the spiking strips, where used, by means of small staples. On the netting are laid one or two layers of asbestos paper i-i6-inch thick, and sometimes one or two layers of tar paper. The corrugated steel "is then fastened to the purlins in the usual way. Stove bolts, 3-16" diameter, with ix j /frx 4-inch plate washers on lower side, are used for fastening the side laps together and for support- ing the lining (see Fig. 129). The author would recommend that pur- lins be spaced one-half the usual distance where anti-condensation lin- ing is used ; the stove bolts could then be omitted. Asbestos paper 1-16- inch thick comes in rolls, and weighs about 32 pounds per square of 100 square feet. Galvanized poultry netting comes in rolls 60 inches wide and weighs about 10 pounds per square. The corrugated steel used with anti-condensation roofing should never be less than No. 22, and the purlins should be spaced for not less 202 CORRUGATED i< ------------ 60-0" ----------- End Elevation .i -"-I Louvres ! ; .___j ^ii:~^^::"j^j^/jz@^^^i::""^:iiii:^ 1 I \A7 (S> Q'-f>" , . 6-0" K7tL6 47i@5'-0" Wi Y'-l04@4'-9 4@ b'-O' 4i@4'-9' ...I 4@6'-o" i^ T3 v 4@4'0" 4@4'-9 4@4'-O' -7 -if "I J r~- i_ JT j< /6'-O" >k I6'-0" >K I6'-O" >4< Ib'-O" >K /6-O" >\ Side Elevation FIG. 128. CORRUGATED STEEL PLANS FOR A TRANSFORMER BUILDING. CORRUGATED STEEL PLANS 203 CorruqaTed Steel List for Building Rectanqular Sheets N'O 35 93 9? M 40 190 61 a? r - II 81 enqrh 4-/O" 3-0" 6'-Z" $% 9-6" 4 '-IO' 5'-Z' s'-y 5-4- 6-0- Beveled Sheets os per Sketch m enaih 7-, Is' 4' 9 /2 r-9i" 6-0" I0 ':". 7-4- UO! Wm L 2 52 * 4*8 2*10 Z* It ' l - ons 2? " Corrupted 5fee/ on 5/ae5, A/o.Z4B/ack, /Corrugation 5/<&e /ay? &/7& 1 4 "nd /&p. Corrugate? J fart on FfovfA/a Z Bf&cA; Ffr/nrea, 5/are /a/? ant? <5 " e 'Fbi//try Netting Method of Fastening Steel and Lining on Rooi Method of Fastening Steel on the Sides 1 V rs 1^ 3| , >.. PC "^ V Gable ^ ^ Cornice ^ S ^ Finish at Corner -Asbestos -Wire Netting Louvers A/o 20 Eave Cornice Detail of Louvres FIG. 129. CORRUGATED STEEL LIST AND DETAILS FOR TRANSFORMER BUILDING. 2O4 CORRUGATED than 30 pounds per square foot. A less substantial roof will not usually be satisfactory. An engine house with anti-condensation lining on the roof and sides has been in use in the Lake Superior copper country for several years, and has been altogether satisfactory under trying conditions. The covering and lining of roof and sides are fastened by clinch nails to angle purlins and girts spaced about two feet apart. A transformer building designed by the author and built by the Gillelle-Herzog Mfg., Co., at East Helena, Montana, has anti-condensa- tion lining on the roof as shown in Fig. 129, and is lined on the sides with one layer of asbestos paper, and i54-inch No. 26 corrugated steel. The black framework, the red side lining, and white roof lining made a very pleasing interior. This building after several years is giving en- tire satisfaction. Corrugated Steel Plans. The shop plans, list of steel and details of the corrugated steel for a mill building are shown in Fig. 128 and Fig. 129 (for the general plans and a detailed estimate of this build- ing see Chapter XXVIII). Corrugated steel sheets should be ordered to cover two purlins or girts if possible. Bevel sheets should be ordered by number, and sheets should be split and reentrant cuts should be made in the field. All sheets should be plainly marked with the number or length. Sheets No. 22 or lighter can be bent in the field, heavier metal should always be bent at the mill. In preliminary estimates of corrug- ated steel allow 25 per cent for laps where two corrugations side lap and 6 inches end lap are required, and 15 per cent for laps where one corrugation side lap and 4 inches end lap are required. Cost of Corrugated Steel. Galvanized steel in 1903 is quoted at about 75 per cent off the standard list, f . o. b. Pittsburg ; list price of flat galvanized steel being as follows : No. 10 to 16 inclusive I2c. per Ib. No. 17 to 21 inclusive I3C. " " No. 23 to 24 inclusive I4c. " " No. 25 to 26 inclusive I5c. " " No. 27 i6c. " " Cost OF CORRUGATED STEEL 205 The net cost of corrugated galvanized steel is found by adding .O5c. per pound to the net cost of flat galvanized sheets. The standard card of extras used in 1903 is given below. These extras are to be added to the net price of flat black or galvanized sheets to obtain the cost. These extras are not subject to discount. CARD OF EXTRAS FOR BLACK OR GALVANIZED SHEETS. For corrugating Q5c. per Ib. For painting with red oxide loc. " " For painting with Dixon's graphite 2Oc. " " For painting with Goheen's carbonizing coating -3Oc.> " " For all trimmings, etc., flashings, ridge caps, and louvres I . ooc. " " For flat sheets rolled from reworked muck bar .500. " " For sheets rolled from iron scrap mixture 25c. " " For arches . 2$c. " " Black corrugated steel in 1903 is quoted about as follows, f. o. b. Pittsburg : Xo. 16 to 18 inclusive . . .2.2C. per Ib. No. 20 to 22 inclusive 2.6c. " " No. 24 to 26 inclusive 2,/c. " " CHAPTER XIX. ROOF COVERINGS. Introduction. Mill buildings are covered with corrugated steel supported directly on the purlins ; by slate or tile supported by sub- purlins; or by corrugated steel, slate, tile, shingles, gravel or other composition roof, or some one of the various patented roofings sup- ported on sheathing. The sheathing is commonly made of a single thickness of planks, I to 3 inches thick. The planks are sometimes laid in two thicknesses with a layer of lime mortar between the layers as a protection against fire. In fireproof buildings the sheathing is com- monly made of reinforced concrete constructed as described in Chapter XX. Concrete slabs are sometimes used for a roof covering, being in that case supported directly by the purlins, and sometimes as a sheath- ing for a slate or tile roof. The roofs of smelters, foundries, steel mills, mine structures and similar structures are commonly covered with corrugated steel. Where the buildings are to be heated or where a more substantial roof cov- ering is desired slate, tile, tin or a good grade of composition roofing is used, or the roof is made of reinforced concrete. For very cheap and for temporary roofs a cheap composition roofing is commonly used. The following coverings will be described in the order given ; corrug- ated steel, sla"te, tile, tin, sheet steel, gravel, slag, asphalt, shingle, and also the patent roofings ; asbestos, Carey's, Granite, Ruberoid and Fer- roinclave. The construction of reinforced concrete roofing is de- scribed in Chapter XX. Corrugated Steel Roofing. Corrugated steel roofing is laid on plank sheathing or is supported directly on the purlins as described in Chapter XVIII. For the cost of erecting corrugated steel roofing see Chapter XXVIII. SLATE ROOFING 207 Corrugated steel roofing should be kept well painted with a good paint. Where the roofing is exposed to the action of corrosive gases as in the roof of a smelter reducing sulphur ores, ordinary red lead or iron oxide paint is practically worthless as a protective coating; better results being obtained with graphite and asphalt paints. Graphite paint has been quite extensively used for painting corrugated steel in the Butte, Mont., district. The corrosion of corrugated steel is sometimes very rapid. In 1898 the author saw at the Trail Smelter, Trail, B. C., a corrugated steel roof made of No. 22 corrugated steel and painted with oxide of iron paint that had corroded so badly in one year that one could stick his finger through it as easily as through brown paper. The climate in that locality is moist and the smelter was used for re- ducing sulphur ores. Galvanized corrugated steel is quite extensively used in the Lake Superior district. Slate Roofing. There are many varieties of roofing slate, among which the Brownville and Monson slates of Maine, and the Bangor and Peach Bottom slates of Pennsylvania are well known and are of Gage. ^ LJUUULJ FIG. 130. excellent quality. Besides the characteristic slaty color, green, purple, red and variegated roofing slates may be obtained. The best quality of slate has a glistening semi-metallic appearance. Slate with a dull 208 ROOF COVERINGS earthy appearance will absorb water and is liable to be destroyed by the frost. Roofing slates are usually made from ^s to % inches thick; 3-16- inch being a very common thickness^ Slates vary in size from 6" x 12" to 24" x 44" ; the sizes varying from 6" x 12" to 12" X 18" being the most common. Slates are laid like shingles as shown in Fig. 130. The lap most commonly used is 3 inches ; where less than the minimum pitch of *4 is used the lap should be increased. The number of slates of different sizes required for one square of 100 square feet of roof for a 3-inch lap are given in Table XIX. The weight of slates of the various lengths and thicknesses required for one square of roofing, using a 3-inch lap is given in Table XX. The weight of slate is about 174 pounds per cubic foot, The weight of slate per superficial square foot for different thick- nesses is given in Table XXL The minimum pitch recommended for a slate roof is l /\ ; but even with steeper slopes the rain and snow may be driven under the edges of the slates by the wind. This can be prevented by laying the slates in slater's cement. Cemented joints should always be used around eaves, ridges and chimneys. Slates are commonly laid on plank sheathing. The sheathing should be strong enough to prevent deflections that will break" the elate, and should be tongued and grooved, or shiplapped, and dressed on the upper surface. Concrete sheathing -reinforced with wire lath or expanded metal is now being used. quite extensively for slate and tile roofs, and makes a fireproof roof. Tar roofing felt laid between the dates and the sheathing assists materially in making the roof waterproof, and prevents breakage when the roof is walked on. The use of rubber- soled shoes by the workmen will materially reduce the breakage caused by walking on the roof. . Roofing slates may also be supported directly on laths or sub-purlins. The details of this method are practically the same as for tile roofing, which see. 209 TABLE XIX. NUMBER OF ROOFING SLATES REQUIRED TO LAY ONE SQUARE OF ROOF WITH 3-INCH LAP. Size in Inches. No. of Slate in Square. Size in Inches. No of Slate in Square. Size in Inches. No. of Slate in Square. 6x12 533 8x16 277 12x20 141 7 12 457 9 16 246 14 20 121 8 12 400 10 16 221 11 22 137 9 12 355 12 16 184 12 22 126 10 12 320 9 18 213 14 22 108 12 12 266 10 18 192 12 24 114 7 14 374 11 18 174 14 24 98 8 14 327 12 18 160 16 24. 86 9 14 291 14 18 137 14 26 89 10 14 261 10 20 169 16 26 78 12 14 218 11 20 154 TABLE XX. THE WEIGHT OF SLATE REQUIRED FOR ONE SQUARE OF ROOF. Weight in pounds, per square, for the thickness. J_>CLll.ll Inches. X' A" y %' w %* X' 1" 12 483 724 967 1450 1936 2419 2902 3872 14 460 688 920 1370 1842 2301 2760 3683 16 445 667 890 1336 1784 2229 2670 3567 18 434 650 869 1303 1740 2174 2607 3480 20 425 637 851 1276 i 1704 2129 2553 3408 22 418 626 836 1254 1675 2093 2508 3350 24 412 617 825 1238 1653 2066 2478 3306 26 407 610 815 \ 1222 1631 2039 2445 3263 TABLE XXL WEIGHT OF SLATE PER SQUARE FOOT. Thickness-in U vV U % K % 3 1 \V eight -Ibs I 81 2 71 3 62 5.43 7.25 9 06 10 87 14 5 14 210 ROOF COVERINGS When roofing slates are laid on sheathing they are fastened by two nails, one in each upper corner. When supported directly on sub- purlins the slates are fastened by copper or composition wire. Gal- vanized and tinned steel nails, copper, composition and zinc slate roofing nails are used. Where the roof is to be exposed to corrosive gases cop- per, composition or zinc nails should be used. Slate roofs when made from first class slates well laid have been known to last 50 years. When poorly put on or when an inferior qual- ity of slate is used slate roofs are comparatively short-lived. Slates are easily broken by walking over the roof and are sometimes broken by hailstones. Slate roofing is fireproof as far as sparks are concerned, but the slates will crack and disintegrate when exposed to heat. Local conditions have much to do with the life of slate roofs ; an ordinary life being from 25 to 30 years. First class slate 3-16 to ^ inches thick may ordinarily be obtained f . o. b. at the quarry for from $5 . oo to $7 . oo per square ; common slate for from $2.00 to $4.00 per square ; while extra fine slate may cost from $10.00 to $12.00 per square. An experienced roofer can lay from ij/2 to 2 squares of slate in a day of 10 hours. In 1903 slater's supplies were quoted as follows : Galvanized iron nails, 2^ to 3 cents per Ib. ; copper nails, 20 cents per I'o. ; zinc nails, 10 cents per Ib. ; slater's felt, 70 to 75 cents per roll of 500 square feet ; two-ply tar roofing felt, 75 cents per square ; slater's cement in lo-lb. kegs, lot cents per Ib. Trautwine gives the cost of slate roofs as $7.00 per square and upwards. The costs of slate, roofs per square is given in the reports of the Association of Railway Superintendents of Bridges and Buildings, as follows: New England, $9.00 to $12.00; New York, $9.00 to $10.00; Virginia $4.10 to $5.00; California, $10.00 to $10.50. Tile Roofing. Baked clay or terra-cotta roofing tiles are made in many forms and sizes. Plain roofing tiles are usually ioj/^> inches long, 6j4 inches wide and ^ inches thick ; weigh from 2 to 2^2 pounds each and lay one-half to the weather. There are many other forms of TIN ROOFS 211 tile among- which book tile, Spanish tile, pan tile and Liidowici tile are well known. Tiles are also^made of glass and are used in the place of skylights. Tiles may be laid (i) on plank sheathing, (2) on concrete and ex- panded metal or wire lath sheathing, or (3) may be supported directly on angle sub-purlins as shown in Fig. 87. Tiles are laid on sheathing in the same manner as slates. The roof shown in Fig. 87 was constructed as follows: Terra- cotta tiles, manufactured by the Ludowici Roofing Tile Co., Chicago, 111., w r ere laid directly on the angle sub-purlins, every fourth tile being se- cured to the angle sub-purlins by a piece of copper wire. The tiles were interlocking, requiring no cement except in exceptional cases. The tiles were 9 x 16 inches in size; 135 being sufficient to lay a square of 100 square feet of roof. These tiles weigh from 750 to 800 Ibs. per square, and cost about $6.00 per square at the factory. Skylights in this roof were made by substituting glass tiles for the terra-cotta tiles. This and similar tile has been used in this manner on a large number of mills and train sheds with excellent results. Tile roofs laid without sheathing do not ordinarily condense the steam on the inner surface of the roof unless the tiles are glazed, al- though several cases have been brought to the author's attention where the condensation has caused trouble with tile roofs made- of porous tiles. Anti-condensation roof lining should be used where there is dan- ger of excessive sweating, or a porous tile should be used that is known to be non-sweating. The cost of tile roofing varies so much that general costs are practically worthless. The reports of the Association of Rail- way Superintendents of Bridges and Buildings give the cost in New England as from $30.00 to $33.00 per square. Tin Roofs. Tin plates are made by coating flat iron or steel sheets with tin, or with a mixture of lead and tin. The former is called "bright" tin plate and the latter "terne" plate. Terne plates should not be used where the roof will be subjected to the action of corrosive gases for the reason that the lead coating is rapidly destroyed. Plates are 212 ROOF COVERINGS covered with tin ( I ) by the dipping process in which the plates are pickled in dilute sulphuric acid, annealed, again pickled, dipped in palm oil and then in a bath of molten tin or tin and lead ; or ^2) by the roller process in which the plates are run through rolls working in a large vessel containing oil, immediately after being dipped. The latter method gives the better results. Two sizes of tin plates are in common use, 14" x 20" and 20" x 2&" ', the latter size being most used. Tin sheets are made in several thicknesses, the 1C, or No. 29 gage weighing 8 ounces to the square foot, and the IX, or No. 27 gage weighing 10 ounces to the square foot, being the most used. The standard weight of a box of 112 sheets, 14 x 20 size is 108 pounds for 1C plate, and 136 pounds for IX plate. Boxes containing imperfect sheets or "wasters" are marked ICW or ICX. Every sheet should be stamped with the name of the brand and the thickness. The value of tin roofing depends upon the amount of tin used in coating and the uniformity with which the iron has been coated. The amount of tin used varies from 8 to 47 pounds for a box of 20 x 28 size containing 112 sheets. Tin roofing is laid (i) with a flat seam, or (2) with a standing seam. In the former method the sheets of tin are locked into each other at the edges, the seam is flattened and fastened with tin cleats or is nailed firmly and is soldered water tight. Rosin is the best flux for soldering, although some tinners recommend the use of diluted chloride of zinc. For flat roofs the tin should be locked and soldered at all joints, and should be secured by tin cleats and not by nails. For steep roofs the tin is commonly put on with standing seams, not soldered, running with the pitch of the roof, and with cross-seams double locked and soldered. One or two layers of tar paper should be placed betwen the sheathing and the tin. In painting tin all traces of grease and rosin should be removed, benzine or gasoline being excellent for this purpose. A paint composed of 10 pounds Venetian red and one pound red lead to one gallon of SHEET STEEX ROOFING 213 pure linseed oil is recommended. The under side of the sheets should be painted before laying. Tin roofs should be painted every two or three years. If kept well painted a tin roof should last 25 to 30 years. For flat seam roofing, using y 2 -inch locks, a box of 14 x 20 tin will cover 192 square feet, and for standing seam, using ^-inch locks and turning 1^4 and I ]/?. -inch edges, making i-inch standing seams, it will lay 168 square feet. For flat seam roofing, using ^-inch locks, a box of 20 x 28 tin will lay about 399 square feet, and for standing seam, using ^-inch locks and turning i 1 /^. and 1^2 -inch edges, making i -inch standing seams, it will lay about 365 square feet. Current prices in 1903 for tin in small quantities were about as follows : American Charcoal Plates: 1C, 14 x 20 $5 . 50 to $6 . 50 per box of 1 12 sheets ; IX, 14 x 20 $6. 60 to $8. 25 per box of 112 sheets. American Coke Plates, Bessemer : 1C, 14 x 20 $4. 70 to $4.80 per box of 1 12 sheets ; IX, 14x20 $6. 60 to $8. 25 per box of 112 sheets. American Terne Plates: 1C, 20x28 $ 9.50; IX, 20x28 $11.50. Two good workmen can put on and paint from 2 l / 2 to 3 squares of tin roofing in 8 hours. Tin roofs cost from $7.00 to $11.00 or $12.00 per square depending upon the specifications and the cost of labor. Sheet Steel Roofing. Sheet steel roofing is sold in sheets 28 inches wide and from 4 to 12 feet long, or in rolls 26 inches wide and about 50 feet long. It is commonly laid with vertical standing seams and horizontal flat seams; tin cleats from 12 to 15 inches apart being nailed to the plank sheathing and locked into the seams. Sheet steel plates are also made with standing crimped seams near the edges, which are nailed to V-shaped sticks; the horizontal seams being made by lapping about 6 inches. 214 ROOF COVERINGS Care should be used in laying sheet steel roofing to see that it does not come in contact with materials containing acids, and it should be kept well painted. The weight of flat steel of different gages is given in Table XV. Nos. 26 and 28 gage sheets are commonly used for sheet steel roofing. No. 26 black sheet steel was quoted in 1903 at about $3.20 per 100 pounds, and No. 26 galvanized sheet steel at about $4.00 per 100 pounds in small lots. Sheet steel roofing can be laid at a somewhat less cost than tin roofing. Gravel Roofing. Gravel roofing is made by laying and firmly nailing several layers of roofing felt on sheathing so as to break joints from 9 to 12 inches ; the laps are mopped and cemented together with roofing cement or tar, and finally the entire surface is covered with a good coating of hot cement or tar. The cement or tar should not be hot enough to injure the fibre of the felt. While the cement or tar is still hot the surface of the roof is covered with a layer of clean gravel that has been screened through a ^s-inch mesh. It requires from 8 to 10 gallons of tar or cement and about ^ of a yard of gravel per square of 100 square feet of roof. When the roof is to be subjected to the action of corrosive gases it should be flashed with copper or composi- tion, or the flashing may be made of felt. The number of layers of felt varies with the conditions, but should never be less than four (4-ply). The details of laying gravel roofs differ and it is impossible to do more than give a few standard specifications. The following specifi- cations are about standard in the W T est. In writing specifications for four-ply gravel roofing omit one layer of roofing felt in the specifications for five-ply gravel roofing. Three-ply roofing is sometimes used for temporary structures. Five (5) Ply Wool Pelt, Composition and Gravel Roof. First cover the sheathing boards with one (i) layer of dry felt and over this put four (4) thicknesses of wool roofing felt, weighing not less than fifteen (15) pounds (single thickness) to the square of one hundred (100) feet. This felt to be smoothly and evenly laid and well cemented together the full width of the lap, not less than nine (9) inches between each layer, with best roofing cement or refined tar, using not less than GRAVED ROOFING 215 one hundred (100) pounds of roofing cement or. tar to the square of one hundred (100) feet. All joinings along walls and around openings to be carefully made. The roof to be then covered with a heavy coating of roofing cement or tar and screened gravel, not less than one (i) cubic yard of gravel to six hundred (600) square feet, gravel to be screened through j^j-inch mesh and free from sand and loam. All walls and openings to be flashed. All roofing cement and tar is to be applied hot. Six (6) Ply Cap Sheet Wool Felt, Composition and Gravel Roof. First cover the sheathing boards with one (i) layer of dry felt and over this put four (4) thicknesses of \vool roofing felt, weighing not less than fifteen (15) pounds (single thickness) to the square of one hundred ( 100) feet. This felt to be smoothly and evenly laid and well cemented together the full width of the lap, not less than nine (9) inches between each layer, with best roofing cement or refined tar, using not less than one hundred and twenty (120) pounds of roofing cement or tar to the square of one hundred ( 100) feet,. The entire surface then to be mopped over with roofing cement or tar and a cap sheet of wool felt applied. All joinings along the walls and around the openings to be carefully made. The roof to be then covered with a heavy coating of roofing cement or tar and screened gravel, not less than one (i) cubic yard of gravel to six hundred (600) square feet, gravel to be screened through ^6 -inch mesh and free from sand and loam. All walls and openings to be flashed. All roofing cement and tar shall be ap- plied hot. Six (6) Ply Combined Flax and Wool Felt, Composition and Gravel Roof. First cover the sheathing boards with one (i) layer of dry felt and over this put one ( i ) layer of flax felt and three thicknesses of wool roofing felt, weighing not less than fifteen (15) pounds (single thickness) to the square of one hundred (100)' feet. This felt to be smoothly and evenly laid and well cemented together the full width of the lap, not less than eleven ( 1 1 ) inches between each layer, with best roofing cement or refined tar, using not less than one hundred and twenty (120) pounds of roofing cement or tar to the square of one hundred (100) feet. The entire surface then to be mopped over with roofing cement or tar and a cap sheet of wool felt applied. All joinings along walls and around openings to be carefully made. The roof to be then covered with a heavy coating of roofing cement or tar and screened gravel, not less than one (i) cubic yard of gravel to six hun- dred (600) square feet, gravel to be screened through ^-inch mesh and 216 ROOF COVERINGS free from sand and loam. All walls and openings to be flashed. All roofing cement and tar shall be applied hot. In Building Construction and Superintendence, Part II, Kidder gives the following specifications for flashing a gravel roof: "Flashing. Finish the roofing against fire walls, chimneys, scuttle and skylight by turning the felt up 4 inches against the wall. Over this lay an 8-inch strip of felt with half its width on the roof. Fasten the upper edge of the strip and the several layers of felt to the wall by laths or wooden strips securely nailed, and press the strip of felt into the angle of the wall and cement to the roof with hot pitch. Nail the lower edge of the strip to the roof every 4 or 5 inches. Take spe- cial care in fitting around chimneys and skylights. Extend the felt up 6 inches on the pitch of the roof, and secure every 4 inches with 30 nails with tin washers." The pitch should not be more than % and should preferably be about 24 to I inch to the foot. Gravel is sometimes used on roofs nearly flat. Gravel roofing under ordinary conditions will last for from 10 to 15 years. With careful attention it can be made to last longer and has been known to last 30 years. The cost of gravel roofing varies with local conditions and speci- fications. In various reports of the Association of Railway Superintend- ents of Bridges and Buildings costs of gravel roofs, not including the sheathing, per square are given as follows: Three-ply gravel roof in California, costs $3.75 ; four-ply (4) gravel roof in Kansas, costs $3.00 ; in Chicago, costs from $3.00 to $4.00; and in New England, costs from $4.00 to $5.00. The cost varies greatly with the specifications. Prepared Gravel Roofing. Prepared gravel roofings may be bought in the market. Prepared gravel roofing manufactured by the Armitage Manufacturing Company, Richmond, Va., was quoted at $2.50 per roll of 1 08 square feet and including nails and cement, delivered in cen- tral Illinois. This company has discontinued the manufacture of pre- pared slag roofing. Slag Roofing. Slag is sometimes used in the place of gravel in making roofs. The method of constructing the roof and the specifica- ASPHAI/T ROOFING 217 tions are essentially the same as for a gravel roof. For detailed specifi- cations for laying slag roofing see description of the Locomotive Erect- -ng and Machine Shop, Philadelphia & Reading R. R., given in Pr.rfr IV. Asphalt Roofing. Asphalt roofing is laid like tar and gravel roof- ing except that asphalt is used in the place of tar or cement. For dis- cussion of the composition and properties of asphalt see Baker's Roads and Pavements, Chapter XIII. The following specifications will give a good roof: Five (5) Ply Wool Felt, Trinidad Asphalt and Gravel Roof. First cover the sheathing boards with one ( I ) thickness of dry felt, and over this put four (4) thicknesses of No. I wool roofing felt, weighing not less than fifteen (15) pounds (single thickness) to the square of one hundred (100) square feet. The felt to be smoothly and evening laid, and well cemented together the full width of the lap, rot less than nine (9) inches between each layer, with Trinidad asphalt roofing cement, using not less than one hundred (100) pounds of asphalt to one square of one hundred (100) square feet. All joinings along the wall and around openings to be carefully made. The roof is then to be cov- ered with a coating of asphalt and screened gravel, not less than one (i) cubic yard of gravel to six hundred (600) square feet of roof, gravel to be screened through a ^g-inch mesh and to be free from loam. All walls to be flashed with old style tin or galvanized iron, or a 2 x 4 is to be built into the walls to make roof connections to. Five (5) Ply Combined Flax and Wool Felt, Trinidad Asphalt and Gravel Roof. First cover the sheathing boards with one thickness of dry felt, over this put one (i) thickness of flax felt and three (3) thick- nesses of No. i wool roofing felt, weighing not less than fifteen (15) pounds (single thickness) to the square of one hundred (100) square feet. The felt to be smoothly and evenly laid, and well cemented to- gether the full width of the lap, not less than eleven (n) inches be- tween each layer, with Trinidad asphalt roofing cement, using not less than one hundred (100) pounds of asphalt to the square of one hun- dred (100) square feet. All joinings along the walls and around open- ings to be carefully made. The roof is then to be covered with a coat- ing of Trinidad asphalt roofing cement and screened gravel, not less than one (i) cubic yard of gravel to six hundred (600) square feet 218 ROOF COVERINGS of roof, gravel to be screened through a ^5 -inch mesh and to be free from loam. All walls to be flashed with old style tin or galvanized iron, or a 2 x 4 is to be built into the wall to make connections to. Prepared asphalt roofing can be bought in the market. It is sold in rolls 36 inches wide and is laid in courses. The Arrow Brand Ready Asphalt Roofing, manufactured by the Asphalt Ready Roofing Company, New York, was quoted in 1903 de- livered in central Illinois as follows : Arrow Brand No. I, sand sur- faced, per roll $2.75; rolls contain no square feet which will cover 100 square feet of roof and weigh 80 pounds. Arrow Brand No. 2, gravel surfaced, per roll $2.75 ; rolls contain no square feet which will cover 100 square feet of roof and weigh 140 pounds. The necessary nails and asphalt required in laying the roofing are included in the above prices. This roofing is in use by a number of railways. Shingle Roofs. Shingle roofs are now very seldom used for mill buildings. Shingles have an average width of 4 inches and with 4 inches laid to the weather 900 are required to lay one square of roof. One thousand shingles require about 5 Ibs. of nails. One man can lay from 1500 to 2000 shingles in a day of 8 hours. The cost of shingle roofs varies with the locality from, say, $3.25 to $6.25 per square. Asbestos Roofing. The "Standard" Asbestos Roofing, manufac- tured by the H. W. Johns-Manville Co., New York, is composed of a strong canvas foundation with asbestos felt on the under side, and sat- turated asbestos felt on the upper side finished with a sheet of plain asbestos ; the whole being cemented together with a special cement and compressed together into a flexible roofing. It does not require paint- ing, although it is commonly painted with a special paint, one gallon of which will cover about 150 square feet. The roofing is laid with a lap of 2 inches, beginning at the lower edge of the roof and running parallel to the eaves. The laps are cemented and are nailed with special roofing nails and caps. The roofing is laid on sheathing and is very easily and cheaply laid. It is quite flexible and may be used for flash- ing and for gutters. It is practically fireproof and makes a very satis- factory roof. Asbestos roofing comes in rolls and weighs about 75 PATENT ROOFINGS 219 pounds per square. It costs about $3.00 per square laid on the roof. The above named company makes several other brands of asbestos roofing the cost of which is about the same as the "Standard." Asbestos roofing felts may be purchased which are used for roof- ing in one, two or three-ply, and are laid in the same way as for gravel roofing. Carey's Roofing. Carey's Magnesia Flexible Cement Roofing, manufactured by the Philip Carey Manufacturing Company, Lockland, Ohio, is made by putting a layer of asphalt cement composition on a foundation of woolen felt and imbedding a strong burlap in the upper surface of the cement. After laying, the burlap is covered with a tough elastic paint which when it dries gives a surface similar to slate. The roof is practically acid proof and burns very slowly. It comes in rolls 29 inches wide and containing sufficient material to lay one square of roof. The roofing is made in two weights, standard weighing 90 pounds per square, and extra heavy weighing about 115 pounds per square. A special flap is provided on one side to cover the nail heads. The roofing is very pliable and can be used for flashing and for gutters. It should be laid on sheathing and is very easily and cheaply applied. It may be laid over an old shingle or corrugated iron roof. It costs about $2 . 75 to $3 . 25 per square laid on the roof. Granite Roofing. Granite Roofing, manufactured by the Eastern Granite Roofing Company, New York, is a ready-to-lay composition roofing with manufactured quartz pebbles imbedded in its upper sur- face. It is a very satisfactory roofing and is quite extensively used. It costs about $2 . 75 to $3 . 75 per square laid on the roof. Ruberoid Roofing. P. & B. Ruberoid Roofing, manufactured by the Standard Paint Co., New York, is quite extensively used and has given good satisfaction. The following description is taken from the maker's catalog: "No paper whatever is used in the manufacture of Ruberoid Roofing. It has a foundation of the best wool felt, except in the case of the >^-ply grade which is a combination of wool and hair. This is first saturated with the P. & B. water and acid proof compound, 22o ROOF COVERINGS and afterwards coated with a hard solution of the same material, there- by making the roofing at once light in weight as well as strong, dur- able and elastic. It is thoroughly acid and alkali proof, is not affected by coal gas or smoke and can be laid on either pitched or flat roofs, proving equally effectual in both cases. Inasmuch as it contains no tar or asphalt the roofing is not affected by extremes in temperature." Ruberoid is made jA-ply weighing 22 pounds per square; i-ply weighing 30 pounds per square ; 2-ply weighing 43 pounds per square ; and 3-ply weighing 51 pounds per square. The 2-ply and the 3-ply roofing are commonly used for factories and mills. The roofing is put up in rolls 36 inches wide, containing two squares (200 square feet), with an additional allowance of 16 square feet for two-inch laps at the seams ; sufficient tacks, tin caps and cement are included with each roll. Ruberoid roofing costs from $2.75 to $3.75 per square laid on the roof. Ferroinclave. This is a patented roofing made by the Brown Hoisting Machinery Co., Cleveland, Ohio, and is described in a letter to the author as follows: "Ferroinclave roofing is made by coating a special crimped or corrugated iron or steel on both sides with a mixture of Portland cement and sand, after which it is painted on the upper side. The sheets are made of No. 22 or No. 24 sheet steel, and full sized sheets are 20 inches wide and 10 feet long. The steel is crimped or corrugated with corrugations about 2 inches wide and J/ inch deep, the width of the corrugation on the outer side being less than on the inner side, thus forming a key to hold the cement mortar in place. The sheets are laid in the same manner as corrugated steel, and a coating of Portland cement mortar, composed of I part Portland cement and 2. parts sand, is plastered on the upper and lower surfaces to a thick- ness of y% of an inch above and below the corrugattans, making the total thickness of the roofing 1^4 inches. The weight of No. 24 sheet steel Ferroinclave is about 15 Ibs. per square foot when filled with cem- ent mortar as above. A test of a sheet of Ferroinclave made as above, showed failure with a uniformly distributed load of 300 Ibs. per square foot with supports 4' 10" apart, the cement having set ten days. The EXAMPLES OF ROOFS 221 cost of this roofing is about $21 .00 per square complete in place on the roof." The Brown Hoisting Machinery Co. has also used Ferroinclave quite extensively for floors and side walls of buildings. Examples of Roofs. The Boston Manufacturer's Mutual Fire Insurance Co., recommend the following roof for mill buildings : "Roofs of ordinary type may be only of plank covered with composition or other suitable roofing material. In special cases the roof should consist of a 3-inch plank, I inch of mortar, a i-inch top board and a 5-ply com- position roof. Such a roof is impervious to heat and cold." The roof of the machine shop of the Chicago City Railway is com- posed of 2 x 6-in. tongued and grooved sheathing overlaid with 5 layers of "Cincinnati" wool felt, having 100 pounds of cement to 100 square feet, and is covered with tar and gravel. The roof of the Lehigh Valley R. R. Shops at Sayre, Pa., is a slag roofing on armored concrete. The roof of the Great Northern R. R. shops at St. Paul, Minn., has double sheathing with I x 3-in. strips between the layers to provide an air pace and prevent sweating. Monarch roofing is laid on the sheathing. The roof of the Philadelphia & Reading shops, at Reading, Pa., is felt on plank sheathing covered with tar and slag. The roof of the A. T. & S. F. R. R. machine shops at Topeka, Kas., is Ludowici tile laid on 2 x 2-in. timber strips. The roof of the Union Train Shed at Peoria, 111., is Ludowici tile laid on angle sub-purlins as shown in Fig. 87. Roof Coverings for Railway Buildings. The following abstract of the report of the committee on roof coverings presented at the an- nual meeting of the Association of Railway Superintendents of Bridges and Buildings, 1902, will give a very good idea of the. present practice in covering railroad buildings. "Slate is much used for station buildings where there is not much climbing for repair of skylights or telegraph wires. It has a life of from 35 to 40 years, and the roof should have a pitch of not less than 6 inches per foot. Vitrified tile is very durable where rightly made and laid on steep roofs, but is not adapted for ordinary railroad build- ings. Shingle roofs last as long as 28 years, and should be laid with 222 ROOF COVERINGS 6 inches pitch per foot; they are very satisfactory where slate is too expensive. For flat roofs a tar and gravel composition is preferred and will last 12 to 1 8, and even 20 years. Slag or broken stone of the size of peas is sometimes used in the place of gravel. In such roofs, much depends upon the paper used, the pitch, and the thoroughness of the work ; 3-ply is too light, 4-ply is good, but 5-ply is better. Asphalt pitch is sometimes preferred to coal-tar, but the latter is sufficiently dur- able. An asphalt-gravel roof must slope not more than */ inch to the foot, on account of the liability to run in hot weather ; but tar-gravel roofs may have a pitch of I inch per foot. With such very flat roofs as are required for asphalt, any settlement will form hollows that will hold water. "Sheet metal roofs, corrugated or flat are not durable. Steel is less durable than iron and will last only about one year, where exposed to engine gases. Tin shingles of good quality give good results. Painted shingles have a short life unless frequently painted. "Of patented roof coverings, Sparham is pulverized talcose lime rock, mixed with coal-tar pitch and applied hot to the roof with a trowel. This may be used for a flat roof or for a roof with a pitch of 3 or 4 inches per foot. Ruberoid is a wool felt saturated with a parafme preparation. Perfected Granite Roofing is 2-ply tarred paper with sea grit on one side. Both of these last may be used on any roof with a pitch of not less than 2 inches per foot. Cheap roofs made from roofing papers require mopping with tar, and if thus treated every two years (before the paper is bare) will last almost indefinitely. In railway work, however, roofs are generally left without attention until leaks are reported, when it is .too late for mopping to do any good. "Roofs requiring treatment every two years can hardly be consid- ered as permanent. Slate for pitched roofs and tar and gravel for flat roofs are as nearly permanent as can be obtained for railway buildings. "The cost per square of 100 square feet for roofs of different kinds in New England is as follows : Slate $ 9.00 to $12.00 Tar and gravel. . . .$4.00 to $5.00 Tile 30.00 to 33.00 Sparham 5.00 to 5.50 Shingles Ruberoid 2.75 to 3.75 Sawed cedar... 4.50 to 5.00 Prefected Granite.. 2.75 to 3.25 Tinned 5.00 to 6.50 Paroid t . 3.00 to 3.50 Sheet tin, standing 2-ply double... 2.00 to 2.25 seam 6.50 to 8.00 3~ply single . 1.50 to 2.00" CHAPTER XX. SIDE WALLS AND CONCRETE BUILDINGS. SIDE WALLS. The sides of steel frame mill buildings are cov- ered with corrugated steel, expanded metal and plaster, wire lath and plaster, or with Ferroinclave a patent covering made of special corrug- ated steel and plaster, manufactured by the Brown Hoisting Co., Cleve- land, Ohio. Corrugated Steel. The methods of fastening corrugated steel to the sides of buildings are the same as on the roof and are described in detail in Chapter XVIII. Where warmth is desired, buildings cov- ered with corrugated steel are often lined with No. 26 corrugated steel with 1 54 -i ncn corrugations . Where this lining is used spiking pieces should be bolted to the girts and intermediate spiking pieces should be placed between the girts to which to nail the lining. If this is not done the corrugated steel will gape open for the reason that it is impossible to rivet the side laps of the lining. Where anti-condensation lining is used on the sides it is made the same as on the roof except that the girts should always be placed not more than one-half the usual distance. The clinch-nail fastening is the best method for fastening the corrug- ated steel where the anti-condensation lining is used. Expanded Metal and Plaster. The methods of making walls of expanded metal and plaster are shown in Fig. 131 and Fig. 132, which show details of the construction of the soap factory buildings of W. H. Walker, Pittsburg, Pa. These buildings were constructed as follows: The buildings were made with a self-supporting steel frame, all con- nections except those for the purlins and girts being riveted. Inacces- sible surfaces were painted with red lead and linseed oil before erection and the entire framework was painted two coats of graphite paint after 224 SIDE WALLS AND CONCRETE BUILDINGS erection. The trusses are spaced from 14 to 18 feet and carry 6, 7 and 8-inch channel purlins. The purlins are spaced from 6 to 7 feet apart and carry roof slabs 2^2 to 3 inches thick made of expanded metal and concrete. The expanded metal is made from No. 16 B. W. G. steel plate with 4-inch mesh, and the concrete is composed of I part Port- land cement, 2 parts sand and 4 parts screened furnace cinders. The roof slabs are covered with 10 x 1 2-inch slate nailed directly to the Slate - N "" Concrete Expanded Metaf PI aster- Ex ponded ' Metal 3 5tiffener --Plaster Expanded "Metal Section through Plaster Expanded " Metal Channel Iron L d"l Beam ^-Exp-Meta! Window Box Stone !8"xl8"*l2" Brick Concrete Column Grade k 37 6 * FIG. 131. CROSS-SECTION OF STEEL BUILDING COVERED WITH EXPANDED METAL AND PLASTER. concrete, and are plastered smooth on the under side. The side walls were made by fastening 24 -inch channels at 1 2-inch centers to the steel framing, and covering this framework with expanded metal wired on. The expanded metal was then covered on the outside with a coating of cement mortar composed of I part Portland cement and 2 parts sand and on the inside with a gypsum plaster, making a wall about 2 inches thick. The ground floors were made by covering the' surface with a 6-inch layer of cinders in which were imbedded 2 x 4-in. white pine nail- EXPANDED METAL AND PLASTER 225 ing- strips 1 6 inches apart, and on these strips was laid a floor of tongued and grooved maple boards i% inches thick and 2^/2 inches wide. The upper floors are made of concrete slabs reinforced with ex- panded metal, and supported on beams spaced 4 to 1 5 feet apart. Where the spans exceed 7 feet suspension bars \" were placed 3 feet apart and were bent around the flanges of the beams. The concrete filling was composed of I part Portland cement, 2 parts sand and 6 parts cinders. (For another description of this building see Engineer- ing Record, August 25, 1900.) 1 f - 7"! Beam i -7"I Beam ,-7" I Beam CS I'O t* H % 2i" L 6-, l< |5-o" FIG. 132. SIDE ELEVATION OF STEEL BUILDING COVERED WITH EX- PANDED METAL AND PLASTER. The Northwestern Expanded Metal Co. now recommends that the first coat of the plaster used for curtain walls be composed of two parts lime paste, i part Portland cement and 3 parts sand, and that the wall be finished with a smooth coat composed of I part Portland cement and 2 parts sand. For coating on wire lath the following has been found to give satisfactory results in Chicago and vicinity: For the first coat use a 15 226 SIDE: WALLS AND CONCRETE BUILDINGS mortar composed of I part Portland cement and 2 parts ordinary lime mortar. The lime should be very thoroughly slaked before using as the presence of any free lime will injure the wall. After the first coat has hardened it is thoroughly soaked and a finishing coat composed of 1 part Portland cement, 2 parts sand and a small quantity of slaked lime is applied and rubbed smooth. A method of plastering curtain walls is described by Mr. George Hill in the Transactions of the American Society of Civil Engineers, Vol. 29, as follows : "The external curtain walls were composed of hard plaster, Portland cement and sand in equal parts, the scratch coat being applied to uncoated metallic lath, making the thickness of the scratch coat about I inch; then a surfacing of Portland cement ^-inch thick was applied on each side making the curtain walls a total thickness of 2 inches. Good results were obtained in every case except one, where the scratch coat was alternately frozen and thawed several times, and the outer surfacing of the wall peeled off in patches.'^ The Northwestern Expanded Metal Co. does not recommend the use of hard or patent plasters for curtain walls. Expanded metal and plaster curtain walls are light, strong and efficient. They do not require the heavy foundations required by brick and stone walls and are fireproof. They can be used to advantage where it is desirable to have a large glass area in the sides of buildings. This type of construction is almost ideal for factory construction and will be much used in the future. There are quite a number of different systems but the methods of construction are essentially the same in all. Curtain walls are made of wire lath and plaster in the same wav as expanded metal and plaster and have all the advantages of the latter. The cost of curtain walls made as described above is about $1.50 to $1.80 per square yard. For a detailed description of the construction of small cement and steel buildings see Engineering Record, March 26, 1898. Concrete Slabs. The construction of reinforced concrete slabs patented by Milliken Brothers, New York, is described in Engineering MASONRY WALLS 227 Record, December 22, 1900, as follows: "The slabs used on the roof of the concrete stable built for the Anglo-Swiss Condensed Milk v Com- pany, Brooklyn, N. Y., were 4 feet wide and about 15 feet long and were constructed as follows : Each slab has a steel frame with three 2 x y$ -inch transverse strips set edgewise at the ends and middle, and connected by longitudinal % -inch rods about 3^ inches apart so as to form a gridiron. The rods are set in staggered holes in the edge of the bars and form a framework over and under which No. 14 trans- verse wires are woven 6 inches apart. The lower surface of the frame is covered with open mesh fine- wire netting, wired around the edges, and the frame is filled with 1:2:4 Portland cement concrete made with very fine broken stone. The slab is 2 inches thick and has. offset edges to make scarfed joints which are set with cement mortar. Voids are left in the concrete at the edges of the slabs to permit thin flat steel bars or angle clips to be bolted to the frames, and to be bolted to or locked around the framework. Then the holes are flushed with cement mortar and a ^J-inch surface coat is plastered over the slabs for the final finish. These slabs have been used for side and partition walls as well as for roof sheathing." Masonry Walls. Walls for filling in between the columns of mill buildings are commonly made very light, being usually determined by the clearance and the height. For buildings with 20 to 25 ft. posts, 8-inch walls are very commonly used. Where the columns are placed inside of the line of the walls, a greater thickness of wall is used than above; 13 and 17-inch walls being quite common. The thickness of factory and warehouse walls which support roof trusses is about as given in Table XXII. The thickness of the wall may be decreased when pilasters are used to assist in supporting the trusses. For detailed information on the construction of brick and stone walls see Baker's Masonry Construction and Kidder's Building Con- struction and Superintendence, Part I. 228 SIDE WALLS AND CONCRETE BUILDINGS TABLE XXII. THICKNESS OF WAREHOUSE WALLS. Height of Wall. Feet. Thickness of Wall. Brick. Inches. Stone. Inches. 25 50 75 16 20 24 20 24 36 CONCRETE BUILDINGS. Within the last few years quite a number of factory buildings have been constructed of concrete. Most of these buildings are monolithic, although recently quite a number patents have been issued for concrete building blocks. The walls are usually made hollow when made monolithic or made of concrete blocks ; the air space prevents the passage of dampness through the walls, makes the building warmer and is less expensive than to make the wall solid. In monolithk concrete construction the roof, floors and the angles in the walls are reinforced with metal put in according to some one of the many systems now in use. The following abstract of the description of the construction of a monolithic concrete building, printed in the Engineering Record, July 3Oth, and August 2Oth., 1898, will give the reader an idea of the methods employed. "The factory of the Pacific Coast Borax Company, at Constable Hook, Bayonne, N. ]., is about 200 x 250 feet in extreme dimensions, and is partly one story and partly four stories in height. All the floors, floor beams, walls, columns, etc. are constructed of reinforced concrete on the Ransome system, built in molds so as to form a monolithic struc- ture continuous throughout, except for the shrinkage joints dividing it into separate panels. "The columns are supported on concrete footings reinforced with twisted steel bars. The walls of the building were built solid at the ends of the floor beams and the intermediate portions were made hoi- CONCRETE BUILDINGS ' 229 low by inserting wooden fillers, which were afterwards removed. The walls of the four story portion are 16 inches in extreme thickness up to the third floor, and are 15 inches above that point. The hollow walls have 3 to 4 inches of concrete on each side of the air space. Both the walls and the columns were bonded by vertical bars of twisted steel y^- inch square, extending through them continuously from top to bottom, and similar rods were carried through the buildings from side to side transverse to the beams imbedded in the different floors about 12 feet apart so as to provide a certain transmission of the strain across the building and assure the resistance of the structure as a whole under the action of eccentric loads and pressures. "At about every 25 feet in the length of the walls a vertical space of ys of an inch was made, extending from top to bottom and separat- ing the wall into distinct sections. At each of these joints a twisted 24-inch rod was imbedded from top to bottom on each side of the space. Similar rods were also placed at the corners of the building. Where the vertical shrinkage joints occur in the outside walls the continuity of the structure is preserved by "carry ing through them horizontal lon- gitudinal pieces of twisted ^4-inch square rods about 2 feet long and set about 2 feet apart throughout the height of the wall. "The columns were built in 1 6-foot sections, each section being one story in height, and were constructed by ramming the concrete inside of forms. The vertical boards composing these forms were made in short lengths, breaking joints over the cross pieces, and were placed in position as the concrete was placed in position. The forms were al- lowed to stand until required for another story, often remaining in po- sition for several weeks, although it was considered that the concrete was strong enough to permit their removal when 48 hours old. The walls were laid up between vertical surfaces of plain i l / 2 -inch plank, laid horizontally and secured by tie bolts running through the molds. The wall was built up in sections about four feet in height and the concrete was laid in continuous 6-inch layers, extending en- tirely around the circumference of the wall, and was thoroughly rammed as deposited. After the concrete had set sufficiently, the bolts were loosened and the boards forming the sides of the mold were pulled up and set in position for building another zone of wall. About 35 men were at work building the walls and constructed an average of 2000 square feet a day. 230 SIDE WALLS AND CONCRETE BUILDINGS "The partitions in the building are 2 inches thick and are made of solid concrete reinforced by a framework of twisted ^4 -inch bars about 2 feet apart, both vertically and horizontally. The partitions were built in molds, and set so that the face comes exactly eve# with the edge of a shrinkage joint in the floor, and always set over a floor beam. "The concrete was made of Atlas cement and broken basaltic rock, all of which will pass through a 2-inch ring and most of which will pass through a i-inch ring. The unscreened rock was mixed with cement in the following proportions: For foundations, I to 10; for the walls, floors and most of the work, I to 6 l / 2 ; for the columns, I to 5 ; and for the lower chords of the floor beams, I to 6, using very fine stone." In constructing the Ingalls office building in Cincinnati, Ohio, described in Engineering News, July 30, 1903, and Engineering Record, scribed above with a few exceptions which will be noted. "The broken stone included the total product of the crusher and was fine enough to pass through a i-inch screen. The concrete was mixed rather wet to insure complete filling of all interstices around the bars. Enough water was used to always give a semi-fluid consistency which allowed puddling rather than ramming. It was made wetter for the columns than for the floors and girders because the bars interferred with the ramming in the molds for the columns. The columns were built in one-story lengths and the concrete was rammed in the molds in layers not more than 12 inches deep. The concrete was dumped from the floor above into the bottom of the mold. The steel rods were placed in position before the concreting was commenced, and were wired in position. A force of 28 men working with hoisting machines and wheelbarrows placed about 100 cubic yards of concrete in a day." The present tendency in concrete building construction is toward the use of a concrete made of Portland cement and finely crushed stone, mixed very wet and deposited in the molds practically without ram- ming. The concrete must be rich in cement to make a good wall un- der these conditions. CONCRETE BUILDINGS 231 Surface Finish. Where it is desired to imitate stonework, imita- tion joints are formed in the face of the wall and the surface is either picked while the concrete is yet tender or is tooled after the concrete has hardened. Bush hammering of concrete walls can be done by an ordinary workman for from i l / 2 to 2 cts. per sq. ft. Where the con- crete is coarse a coating of cement mortar may be applied as the con- crete is placed in the molds by means of a piece of sheet steel placed from I to 2 inches from the forms; the cement mortar, usually made of I part Portland cement and 2 parts sand, is then rammed into the vacant space, after the main body of the concrete has been rammed in place, and the piece of sheet steel is removed. The preparation of the forms requires considerable study to obtain a smooth surface and unbroken corners. The use of matched or tongued-and-grooved stuff is not desirable as the concrete fills the open- ings made by shrinkage and there is no room to expand. Unmatched boards dry apart and let the water in the concrete leak out, carrying with it some of the cement. The best way to build the forms is to use narrow stuff and bevel one edge of the boards ; the sharp edge of the bevel lying against the square edge of the adjoining board allows the edge to crush when swelling and closes up the joint. A coat of soft soap applied to the forms before filling, prevents the concrete from ad- hering. The soap should be scraped and brushed off with a steel brush as the forms are removed. CHAPTER XXI. FOUNDATIONS. Introduction. The design of the foundations for mill buildings is ordinarily a simple matter for the reason that the buildings are usu- ally located on solid ground and the loads on the columns are small. Where the soil is treacherous or when an attempt is made to fix the columns at the base the problem may, however, become quite com- plicated. Bearing Power of Soils. The bearing power of a soil depends upon the character of the soil, its freedom from water, and its lateral support. The downward pressure of the surrounding soil prevents lat- eral displacement of the material under the foundation and adds ma- terially to the bearing power of treacherous soils. The safe bearing power of soils given in Table XXIII may be used as an aid to the judgment in determining on a safe load for a foundation. However no important foundations should be built with- out making careful soundings and bearing tests. A soil incapable of supporting the required loads may have its supporting power increased (i) by increasing the depth of the foun- dation; (2) by draining the site; (3) by compacting the soil; (4) by adding a layer of sand or gravel; (5) by using timber grillage to in- crease the bearing area ; (6) by driving piles through the soft stratum, or far enough into it to support the loads. A method used in France for compacting foundations is to drive holes with a heavy metal plunger and then fill these holes with closely rammed sand or gravel. Several kinds of patented concrete piles are now in use to a limited extent in this country for building foundations. BEARING POWER OF SOILS 233 TABLE XXIII. SAFE BEARING POWER OF SOILS.* Kind of Material Safe Bearing per g Power in Tons q. Ft. Min. Max. Rock-hardest in thick layers in bed " equal to best ashler masonry " " " brick 200 25 15 30 20 " " poor brick 15 10 Clay in thick beds, always dry 4 6 " " " moderately dry 2 4 ' Soft 1 2 Gravel and coarse sand, well cemented Sand compact and well cemented 8 4 10 6 " clean, dry 2 4 Quicksand alluvial soils etc 5 1 When foundations are placed on solid rock, the surface of the rock should be carefully cleaned of loose and rotten rock and roughly brought to a surface as nearly perpendicular to the direction of the pressure as practicable. A layer of cement mortar placed directly on the rock surface will assist in bonding the foundations and the footing together. When foundations are placed on sand, gravel or clay it is usually only necessary to dig a trench and start the foundation below frost. If the soil is somewhat yielding or if the load is heavy the foundation should be carried to a greater depth or the footings should be made wider than for greater depths. Bearing Power of Piles^ Probably no subject has been more freely discussed and with more conflicting views and opinions than has the safe bearing power of piles. The safe load to put on a pile in any par- ticular case is dependent upon so many conditions that any formula for the safe bearing power is necessarily simply an aid to the judgment of the engineer, and not an infallible rule to be blindly followed. All *Treatise on Masonry Construction, by Ira O. Baker, John Wiley & Soas, Publishers, New York. 234 FOUNDATIONS formulas for the bearing power of piles determine the safe bearing power from the weight of the hammer, the length of free fall of the hammer, and the penetration of the pile. The penetration of the pile for any blow of the hammer depends on the condition of the head of the pile, upon whether the pile is driving straight, and upon the rigidity of the pile. The penetration of a slim, limber pile with a broomed head is very misleading, and any formula will give values too large. The Engineering News formula for the safe bearing power of piles is most used and is certainly the most reliable. It is p= 2 Wh ' s + l where P = safe load on pile in tons; W = weight of hammer in tons ; h = distance of free fall of the hammer in feet ; s = penetration of the pile for the last blow in inches. If the pile is driven with a steam hammer the factor unity in the denominator is changed to one-tenth. This formula is supposed to give a factor of safety of about 6, and has been shown by actual use to give values that are safe. Where piles are to be driven through gravel or very hard ground the lower ends are often protected with cast iron or steel points. The value of these points is questionable and most engineers now prefer to drive piles without their use, simply making a very blunt point on the pile. In driving piles, care must be used where small penetrations are obtained not to smash or shiver the pile. Piles driven to a good refusal with a penetration of, say, I inch for the last blow, with a fall of 20 ft. and a 2ooo-lb. hammer will safely support almost any load that can be put on them. Piles are usually driven at about 3-ft. centers over the bottom of the foundation. After the piles are driven they are sawed off below the water level and ( i ) concrete is deposited around the heads of the piles, or (2) a grillage or platform is built on top of the piles to support the walls PRESSURE OF WALLS ON FOUNDATIONS 235 or piers. The first method is now the most common one for mill build- ing foundations. Pressure of Walls on Foundations. In Fig. 133, let W = re- sultant weight of the wall, the footing and the load on the wall, / = length of the footing and b = distance from center of gravity of footing to point of application of load W, and let the wall be of unit w w A o B a R length. The pressure on the footing will be that due to direct load W, and a couple with an arm b and a moment =. + Wb. The pressure due to the direct W will be F = W 7 -r- / as shown in (a), 236 FOUNDATIONS and the maximum pressure due to the bending moment, M = + Wb, will be p Me _ 6 W b ~ 7 7^ The pressure at A will be and at B will be P = P i P 2 = - - 6 W ^ b (84) as shown in (c). Now if P is made equal to P 2 the pressure at B will be zero and at A will be twice the average pressure. Placing P = P 2 in (84) and solving for b, we have b l /6 I. This leads to the theory of the middle third or kern of a section. If the point of application of the load never falls outside of the middle third there will be no tension in the ma- sonry or between the masonry and foundation, and the maximum com- pression will never be more than twice the average shown in (a). If the point of application of the load falls outside the middle third (b greater than % /) there will be tension at B, and the compres- sion at A will be more than twice the average. But since neither the masonry nor foundation can take tension, formulas (83) and (84) will give erroneous results. In (d) Fig. 133, assume that b is greater than % I, and then as above, the load W will pass through the center of pressures which will vary from zero at the right to P at A. If 3 a is the length of the foundation which is under pressure, then from the fundamental con- dition for equilibrium for translation, summation vertical forces equals zero, we will have W y 2 P 3 a and P = *^ (85) PRESSURE; OF PIER ON FOUNDATIONS 237 Pressure of a Pier on Foundation. In Fig. 134, let W = resul- tant of the stresses in the column- and the weight of the pier, / = length, c = depth and n = the breadth of the footing of the pier in feet. The bending moment at the top of the pier is M = l / 2 H d and at the base of the pier is M = H .( l / 2 d -\- c). Now the pier must be designed so the maximum pressure on the foundation due to W and the bending moment Af x will not exceed the allowable pressure. The maximum pressure on the foundation will be w __ W 3 H (d + 'Z c} (86) It will be seen from (86) that a shallow pier with a long base is most economical. To find the relations between / and c when the maximum pressure is twice the average, place W = 3 H (d + 2 c) In n / 3 and / = 3 H (d ^~ 2 ^ (87) For any given conditions the value of / that will be a minimum may be found by substituting in the second member of (87;. To illustrate the method of calculating the size of a pier we will calculate the pier required to fix the leeward column in Fig. 57. The sum of the stresses in column A-\*j is a minimum for dead and wind load and will be (Table V) equal to 4800 + 4500 = 9300 Ibs. Try a pier 3' o" x 3' o" on top, 6' o" x 6' o" on the base and 6 feet deep, weighing about 16,700 Ibs. Substituting in (86) we have 26.000 H 3 X 4300 (14 + 12) 36 6 X 36 238 FOUNDATIONS This gives tension on the windward side which will not do, and so we will reinforce the footing with beams and make / = 10 ft., and then P = 722 559 = 1281 or 163 Ibs. per square foot, which is safe for ordinary soils. If it had been necessary to drive piles for this pier, a small amount of tension might have been allowed on the windward side if the tops of the piles had been enclosed in concrete. Design of Footings. The thickness and length of the offsets in a concrete or masonry footing are commonly calculated as for a beam fixed at one end and loaded with a uniform load over the projecting part equal to the maximum pressure on the footing. If p = projection of the footing in inches ; t the thickness of the footing in inches ; P =: pressure on foundation in pounds per sq. ft. ; and S = safe working load of the material of which the footing is made in pounds per square inch, by substituting in the fundamental formula for flexure and solving for p, P -- 2 ' - (88) The values of 6* in common use are: first class Portland cement concrete 50 Ibs.; ordinary concrete 30 Ibs.; limestone 150 Ibs.; granite 1 80 Ibs. ; brickwork in cement 50 Ibs. The projection and thickness of the footing course is sometimes calculated on the assumption that the footing course is a beam fixed at the center, in place of as above. This solution hardly appears to be justified. Pressure of Column on Masonry. The following pressures in pounds per square inch are allowed by the building laws of New York. Portland cement concrete 230 Ibs. ; Rosendale cement concrete 125 Ibs. ; Rubble stonework laid in Portland mortar cement 140 Ibs. ; brickwork laid in Portland cement mortar 250 Ibs. ; brickwork laid in lime mortar no Ibs. ; granite 1000 Ibs. ; limestone 700 Ibs. It is very com- mon to specify 250 Ibs. per square inch for bearing on good Portland cement pedestals, and 300 Ibs. per square inch is not uncommon. CHAPTER XXII. FLOORS. Introduction. The requirements and the local conditions govern- ing the design of floors for shops and mills are so varied and diversified that the subject of floor design can be treated only in a general way. Floors will be discussed under the head of (i) ground floors and (2) floors above ground. GROUND FLOORS. Types of Floors. There are three gen- eral types of ground floors in use in mills and shops: (i) solid heat conducting floors as stone, brick or concrete; (2) semi-elastic, semi- heat conducting floors as earth, macadam or asphalt; (3) elastic non- heat conducting floors of wood or with a wooden wearing surface. (1) Floors of the first class have been used in Europe and form- erly in this country to quite an extent in shops and mills, and at pres- ent are much used in round houses, smelters, foundries and in other buildings where the wear and tear are considerable or where men are not required to stand alongside a machine. Floors of this class are cold and damp and make workmen uncomfortable. The wooden shoes of the continental workmen or the wooden platforms in use in many of our shops which have floors of this class, overcome the above objec- tions to some extent. The gritty dust arising from most concrete floors is very objectionable where delicate machinery is used. The noise and danger from breakage and first cost are additional objections to floors of this class. (2) Floors of this class have many of the objections and defects of floors of the first class. These floors are liable to be cold and damp unless properly drained, and give rise to a gritty dust that is often in- tolerable in a machine shop. 240 FLOORS Earth and cinder floors are very cheap and are adapted to forge shops and many other places where concrete and brick floors are now put down. Floors of this class should be well tamped in layers and should be carefully drained. Tar-concrete and asphalt floors are more elastic and conduct less heat than any of the floors above mentioned, but the surface is not sufficiently stable to support machinery directly, and floors of this class are very much improved by the addition of a contin- uous wooden wearing surface. (3) Floors of wood or with a wooden wearing surface appear to be the most desirable for shops, mills and factories. Wooden floors are elastic, non-heat conducting and are pleasant to work on. They are cheap, easily laid, repaired and renewed. They are easily kept clean and do not give rise to grit and dust. The most satisfactory wearing surface on a wooden floor is rock maple % to i% inches thick and 2.^/2 to 4 inches wide, matched or not as desired. The matched flooring makes a somewhat smoother floor and is on the whole the most satisfactory. The wearing floor should be laid to break joints and should be nailed to planking or stringers laid at right angles to the surface layer. The thickness of the planking will depend upon the foundation and upon the use to which the floor is to be put. The different classes of floors will now be briefly discussed and illus- trated by examples of floors in use. Cement Floors. The construction of cement or concrete floors is similar to the construction of cement sidewalks, the only difference being that the floor usually requires the better foundation. The foun- dation will depend upon the use to which the floor is to be put, and upon the character of the material upon which the foundation is to rest. The excavation should be made to solid ground or until there is depth enough to allow a sub- foundation of gravel or cinders. Upon this base a layer of cinders or gravel 6 to 8 inches thick is placed and thoroughly rammed. The cement concrete base, made of i part Portland cement, 3 parts sand and 5 to 6 parts broken stone or gravel, is then placed on CEMENT FLOORS 241 the sub-foundation and thoroughly rammed. The cement and sand should be mixed dry until the mixture is of a uniform color, the gravel or broken stone is then added, having previously been wet down, and the concrete is thoroughly mixed, sufficient water being added during the process of mixing to make a moderately wet concrete. The con- crete is of the proper consistency if the moisture will just flush to the top when the concrete is thoroughly rammed. The concrete should be mixed until the ingredients are thoroughly incorporated and each par- ticle of the aggregate is thoroughly coated with mortar. The wearing coat is usually made of I part Portland cement and one or two parts of clean sharp sand or granite screenings that will pass through a ^J-inch screen. The thickness of the wearing coat will de- pend upon the wear, and varies from y 2 to 2 inches thick, I inch being a very common thickness. The mortar for the wearing surface should be rather dry and should be applied before the cement in the concrete base has begun to set. Care should be used to see that there is not a layer of water on the upper surface of the base or that a film of clay washed out of the sand or gravel has not been deposited on the sur- face, for either will make a line of separation between the base and the wearing surface. The mortar is brought to a uniform surface with a straight edge, and is rubbed and compressed with a float to expel the water and air bubbles. As the cement sets it is rubbed smooth with a plastering trowel. Joints should be formed in the floor making it into blocks about 4 to 8 feet square. Cement floors are said to be a failure for railway round houses for the reason that they flake and crack after they have been used a short time, on account of the varying changes to which they are subjected. Cement floors vary in cost, depending upon the thickness of the floor and upon local conditions. In central Illinois a cement floor hav- ing a i -inch surface coat and 3 inches of concrete laid on a cinder foundation 6 to 8 inches thick can be obtained (1903) for about 12 cents per square foot. A very substantial concrete floor can usually be obtained for about 20 cents per square foot. 16 242 FLOORS Tar Concrete Floors. The following specifications for tar con- crete floors are given in circulars Nos. 54 and 55 of the Boston Man- ufacturer's Mutual Fire Insurance Co., and are reprinted in Engineer- ing News, March 21, 1895. "The floor to be 6 inches thick, and to be put down as follows : The lower 5 inches to be of clean coarse gravel or broken stone, with sufficient fine gravel to nearly fill the voids, thoroughly coated with coal-tar and well rammed into place. On this place a layer I inch thick of clean, fine gravel and sand heated and thoroughly coated with a mixture of coal-tar and coal-tar pitch in the proportions of I part of pitch and 2 parts of tar. This layer is to be rolled with a heavy roller and brought to a true and level surface ready to receive the floor plank. No sand or gravel to be used while wet. "A floor of the kind above specified should always be protected by a floor of wood over it, and the plank should be laid and bedded in the top surface while it is warm and before it becomes hard. "For light work the thickness of the lower layer of concrete may be reduced one or more inches if upon a dry gravelly or sandy soil. For storage purposes where the articles stored are light and trucks are little used, the following specification has been found to give a satis- factory floor: "The lower layer being mixed and put down as above specified, the top layer will be of fine gravel and sand, heated and thoroughly mixed with a mixture of equal parts of coal-tar, coal-tar pitch and paving cement, so that each particle of sand and gravel is completely coated with the mixture, using not less than one gallon of the mix- ture to each cubic foot. of sand and gravel. This layer should be well rolled with a heavy roller and allowed to harden several days before be- ing used." Brick Floors. Brick floors are recommended as the most satis- factory floors for round houses. Round house floors on the Boston & Maine R. R. are made as follows : *Brick is laid flat on a 2-inch layer of bedding sand on well compacted earth, gravel or cinders. Joints are left open y% of an inch and are swept full of cement grout. Round house floors are made on the Chicago, Milwaukee & St. Paul R. R., as follows : * Vitrified brick is laid on edge on a layer of sand I *Eighth Annual Report of the Association of Railway Superintendents of Bridges and Buildings. WOODEN FLOORS 243 to 2 inches thick on a cinder foundation 6 inches thick. Fine sand is broomed into the cracks after the brick are in place. The cost of this floor per square yard is about as follows : Material. Firebox cinders cost nothing $00.00 Paving brick o . 50 Labor. Preparing the foundation o . 20 Laying the brick 0.15 Total cost per square yard $o . 85 Total cost per square foot 9^ cents. The cost of brick floors as given in the reports of the Association of Railway Superintendents of Bridges and Buildings varies from 9^2 to 13 cents per square foot. The Southern & Southwestern Railway Club Eng. News, Jan. 16, 1896 recommends that round house floors be made of vitrified brick laid as follows : Make a bed surface of slag or chert about 18 inches thick, then put a coat of sand over slag, lay brick on edge and level them up by tamping. After this is done a coat of hot tar is applied which enters the space between the bricks and cements them together. Wooden Floors. Coal-tar or asphalt concrete makes the best foundation for a shop floor. If Portland cement is used, the planking will decay very rapidly unless the top of the concrete is mopped with coal-tar or asphalt. A floor laid by Pratt & Whitney Co., of Hartford, Conn., is described as follows: "In laying a basement floor about 18 years since of 10,000 square feet, 8,000 square feet were laid over coal- tar and pitch concrete in about equal proportions, and about 2,000 square feet were laid over cement concrete. The latter portion of the floor was removed in about ten years, the timbers and the plank being com- pletely rotted out; while the other was in a perfect state of preserva- toin and has continued so until the present time." The floor with tar concrete foundations was constructed as follows: "Excavation was made about one foot below the floor and six inches of coarse stone 244 FLOORS was filled in, then five inches of concrete made of coarse gravel, coal- tar and pitch, and finally about one inch of fine gravel tar concrete. Before the concrete was laid, heavy stakes were driven about three feet apart to which the 4" x 4" floor timbers were nailed and leveled up. The concrete was then filled in around the floor timbers and thoroughly tamped. A layer of hot coal-tar was then spread on top of the concrete and the flooring was laid and nailed to the timbers. It is very es- sential that the gravel be perfectly dry before mixing; and this is ac- complished by mixing it with hot coal-tar. What is known as dis- tilled or refined coal-tar must be used as that which comes from the gas house without being refined does not work in a very satisfactory manner." The following paragraph is abstracted from Report No. V., Insur- ance Engineering Experiment Station, Boston, Mass : "Floors over an air space or on cement are subject to a dry rot. Asphalt or coal-tar concrete is softened by oil, and the dust will wear machinery unless the concrete is covered by plank flooring. Floors made by laying sleepers on 6 inches of pebbles, tarred when hot, then 2. inches tarred sand packed flush with the top of the sleepers, and cov- ered with a double flooring, have remained sound for 37 years. Double flooring at right angles can be laid on concrete without the use of sleepers. It is usually preferable to secure nailing strips to stakes 4 feet apart each way and driven to grade, concrete flush to top of strips, and lay i^-inch flooring." The floor shown in Fig. 135 was laid in an extensive shop on the Boston & Maine Railway. The earth was well compacted and brought to a proper surface and a 4-inch bed of coal-tar concrete put down in ^ ver Louvres made of * 4 5 tee I \ Max- Length 4 '-/* " End Lap T"*,;^ * "to z " Order steel for loi/v- **! JL // "wide % "holes in uprights, z ,1'^u for* "oval screw head bolts \"long- Hashing ~~^ Hoof 5 tee/ -~ Useang/e uprights at splice joints of louvres ~* -(M --*- -_~*jLouvre Block '? I 'j" Long ...*. FIG. 159. BERLIN LOUVRES. The details of the Shiffler louvres shown in Fig. 158, and of the Berlin louvres shown in Fig. 159 are those adopted by the American Bridge Company. The details of the louvres are shown in the cuts and need no further explanation. MONITOR VENRILATORS 275 i . ' i *V1 , ; * * N NJ i. _: 1: 14" 'Flash i nq Jfecl 5pnna fo opposite s/afe FIG. 160. HINGED MONITOR SHUTTER. Details of a hinged shutter are shown in Fig. 160. The angle iron frame is covered with a corrugated iron covering. The shutters are made from 6 to 10 feet long, with two hinges for shutters 8 feet long and three hinges for shutters more than 8 feet long. Where shutters are to be glazed they are hung as in Fig. 156. The lever gear shown by the dotted lines is used in the better class of structures. This device can be used where the shutters are glazed if care is used in operating. In smelters the clerestory of the monitor is often left entirely open or is slightly protected by self acting shutters. In the latter case the shutters are hinged at the bottom and are connected at the top with each other and with a counter-weight so that the shutter will ordinarily make 276 VENTILATORS an angle of about 30 degrees with the vertical. A wind or a storm will close the windward shutter and open the leeward shutter wider. The eaves of the monitor are made to project, so that very little of the storm enters. Cost. The shop^ cost for louvres is ordinarily about I cent per pound. To this must be added the cost of the sheet steel and the cost of the framework and details. In 1900 louvres without frames cost about 25 cents per square foot. Circular Ventilators. Circular ventilators are often used for ven- tilating mill buildings in place of the monitors, and on buildings requir- ing a small area for ventilation. They are made of galvanized iron, copper or other sheet metal, and are usually placed along the ridge line of the roof. STAR" VENTILATOR Globe Ventilator GARRY VENTILATOR Acorn Ventilator. BUCKEYE VENTILATOR. FIG. 161. CIRCULAR VENTILATORS. CIRCULAR VENTILATORS 277 There are many styles of circular ventilators on the market, a feu of which are shown in Fig. 161. The Star ventilator made by Mer- chant & Co., Chicago, is quite often used and is quite efficient. It is made in sizes varying from 2 to 60 inches. In 1903 Star ventilators made of galvanized iron were quoted about as follows: 12-in., $2.00; i8-in., $6.75; 24-in., $10.00; 4O-in., $45.00. The Globe ventilator made by the Cincinnati Corrugating Com- pany, Cincinnati, Ohio; the Garry ventilator made by the Garry Iron & Steel Roofing Co., Cleveland, Ohio ; and the Acorn and Buckeye ven- tilators made by the Youngstown Iron & Steel Roofing Co., Youngs- town, Ohio, are quite efficient and all cost about the same as the Star except the Garry ventilator, which is cheaper. Home-made circular ventilators can be made that are quite as sat- isfactory as the patented ventilators and are much less expensive. In 1900, ten 36-inch circular ventilators cost $12.25 each, and two 24- inch circular ventilators cost $9.25 each in Minneapolis, Minn. The cost of the 24-inch ventilators was large on account of the small number made. CHAPTER XXV. DOORS. Paneled Doors. For openings from 2' o" x 6' o" to 3' o" x 9' o" ordinary stock paneled doors are commonly used. The stock doors vary in width from 2' o" to 3' o" by even inches and in length by 4" to 6" up to 7' o" for 2! o" doors, and 9' o" for 3' o" doors. Stock doors are made i^ and ify inches thick, and are made in three grades, A, B and C ; the A grade being first class, B grade fair and C grade very poor. Paneled doors up to 7 feet wide and 2^ inches thick can be obtained from most mills by a special order. Wooden Doors. Wooden doors are usually constructed of matched pine sheathing nailed to a wooden frame as shown in Fig. 162 and Fig. 163. Section A- A U from 3' to 6 Swing Wooden Doors FIG. 162. Sliding Wooden Door FIG. 163. DETAILS OF DOORS 279 Designs for wooden swing doors are shown in Fig. 162, and for a wooden sliding door in Fig. ,163. These doors are made of white pine. Doors up to four feet in width should be swung on hinges ; wider doors should be made to slide on an overhead track or should be counter- balanced and raise vertically. Sliding doors should be at least 4 inches wider and 2 inches higher than the clear opening. "Sandwich" doors are made by covering a wooden frame with flat or corrugated steel. The wooden framework of these doors is com- monly made of two or more thicknesses of %-inch dressed and matched white pine sheathing not over 4 inches wide, laid diagonally and nailed with clinch nails. Care must be used in handling sandwich doors made as above or they will warp out of shape. Corrugated steel with i^- inch corrugations makes the neatest covering for sandwich doors. For swing doors use hinges about as follows : For doors 3' x 6' or less use lo-inch strap or lo-inch T hinges; for doors 3' x 6' to 3' x 8' use i6-inch strap or i6-inch T hinges ; for doors 3' x 8' to 4' x 10' use 24-inch strap hinges. Steel Doors. Details of a steel lift door are shown in Fig. 164. This door is counterbalanced by weights and lifts upward between ver- t ' fia/e for 4 "stee/ cable for /K sting - ~ >. . ***&&&- I'T- -~--r- 7 - -*- -i'-r- !& Steel Lift Door FIG. 164. 280 DOORS tical guides. This door was covered with corrugated steel with ij^- inch corrugations as described in the cut. Details of a steel sliding door are shown in Fig. 165. This door is made to slide inside the building and swing clear of the columns. Where the columns are so close together that there is not room enough for the door to slide the entire length of the opening, it should be placed on the outside of the building. The track and hangers shown '>/>j'- O/rf- ^ ^^ ^ere from 0vte/afe Steel Sliding Door FIG. 165. make a very satisfactory arrangement ; however there is a tendency for the wheels to jump the track unless the grooves in the wheels are made very deep. There are quite a number of patented devices on the market for hanging sliding doors. The Wilcox trolley door hanger, track and COST OF DOORS 281 bolt latch shown in Fig. 166, are efficient and are quite, generally used. The prices of the door fixtures srjown in Fig. 166 are about as follows : door hangers, $2.25 to $3.00 per pair ; steel track, 10 to 25 cts. per ft. ; clips, 15 to 25 cts. each; door latch, $1.00, f. o. b. the factory at Aurora, 111. Discounts for this and several other well known makes of door fixtures are given each week in the Iron Age, New York, and the list prices are given in the manufacturer's catalogs. Wilcox Trolley Door Hanger Wilcox Gravity Door Bolt and Latch FIG. 166. Cost of Doors. Stock panel doors cost $1.50 to $5.00 each, depend- ing upon the grade, size and conditions. The details of steel doors vary so much that it is necessary to make detailed estimates in each case. The shop cost of the framework is often quite high and may run as high as 3 or 4 cts. per pound. The wooden frames for sandwich doors cost from 20 to 25 cts. per square foot. The cost of hinges, bolts, etc., required for doors can be found by applying the discounts given in the Iron Age to the list prices given in the standard lists (see Chapter XXVIII). CHAPTER XXVI. SHOP DRAWINGS AND SHOP DRAWINGS. The rules for making shop drawings in use by the American Bridge Company are given in their Standards for Structural Details, and are reprinted in part, in Roofs and Bridges, Part III, by Merriman and Jacoby. The following rules are essentially those in common use by bridge companies, for mill buildings and ware- houses. Make sheets for shop details 24 by 36 inches, with two border lines, y* and I inch from the edge, respectively. For mill details use special beam sheets. The title should come in the lower right hand corner, and should contain the name of the job, the contract number, and the initials of the draftsman and checker. Detail drawings should be made to a scale of $4 to I inch to the foot. Members should be detailed as nearly as practicable in the po- sitions in which they occur in the structure. Show all elevations, sec- tions, and views in their proper positions. Holes for field connections should always be blackened. Members that have been cut away to show a section, may be either blackened or cross-hatched. Members, the ends of which are shown in elevation or plan, should be neither black- ened nor cross-hatched. Holes for field connections should be located independently, and should be tied to a gage line of the member. When metal is to be planed, the ordered and finished thickness should be given. In making shop drawings for mill buildings two methods are in use. The first method is to make the drawing so complete that templets can be made for each individual piece, separately on the bench. The second method is to give on the drawings only sufficient di- mensions to locate the interior of the members and the position of the ERECTION PLAN 283 pieces, leaving the templet-maker to work out the details on the laying- out floor. The first method is illustrated in Fig. 96, and the second in Fig. 95. In the second method sufficient figures should be given to proper- ly locate the main points in the truss ; the interior pieces should be lo- cated by center-lines corresponding to the gage lines of the rivets, the centers of gravity lines or the outside edges of the pieces, as the case may be. The drawings should always indicate the number of rivets to be used in each connection, the size of rivets, the usual rivet pitch, and the minimum pitch allowed. Erection Plan. The erection plan should be made very complete. All the notes that it is necessary for the erecter to have, should be put on the erection plans ; how much of the structure is to be riveted and how much bolted, whether it is to be painted after erection or not, whether the windows and doors are to be erected or not, etc. Center line drawings are usually sufficient for the erection plans. The name and the size of the piece should be given and every piece should have a name. The following method was used by the Gillete-Herzog Mfg. Co., for mill buildings, and was very satisfactory: If the points of the compass are known, mark all pieces on the north side with the letter "N", those on the south side with the letter "S", etc. Mark girts N. G. I ; N. G. 2 ; etc. Mark all posts with a different number, thus : N. P. i ; N. P. 2 ; etc. Mark small pieces which are alike with the same mark; this would usually include everything except posts, trusses and girders, but in order to follow the general marking scheme, where pieces are alike on both sides of a building, change the general letter; e. g. N. G. 7 would be a girt on the north side and S. G. 7 the same girt on south side. Then in case the north and south sides are alike, only an elevation of one side need be shown, and under it a note thus: "Pieces on south side of building, in cor- responding positions have the same number as on this side, but prefixed by the letter "S" instead of the letter "N." Mark trusses T. I ; T. 2 ; etc. Mark roof pieces R. I ; R. 2 ; etc. 284 SHOP DRAWINGS AND The above scheme will necessarily have to be modified more or less according to circumstances ; for example, where a building has dif- ferent sections or divisions applying on the same order number, in which case each section or division should have a distinguishing letter which should prefix the mark of every piece. In such cases it will per- haps be well to omit other letters, such as N., S., etc., so that the mark will not be too long, for easy marking on the piece. In general, how- ever, the scheme should be followed of marking all the large pieces, whether alike or not, with a different mark. This would refer to pieces which are liable to be hauled immediately to their places from the cars. But for all smaller pieces which are alike, give the same mark. For architectural buildings adopt the following general scheme of marking: The basement "A"; first floor "B" ; second floor "C" ; then mark all the pieces on the first floor B. i ; B. 2; etc. ; columns between first and second floors B. C. I ; B. C. 2 ; etc. It will greatly aid the detailing, checking and erection if small sec- tions are made showing the principal connections, such as girt connec- tions, purlin connections, etc. The erection plans of a mill building drawn in accordance with these rules are shown in Fig. 167 and Fig. 168. CHOICE OF SECTIONS. In designing, it will be found eco- nomical to use minimum weights of sections, and to use sections that can be most easily obtained. As small a number of sizes should be used as is practicable where material is to be ordered from the mill, if good delivery is to be expected. The ease with which any section can be obtained in a mill order, depends upon the call that that particular mill is having for the given section. If there is a large demand for the section, it will be rolled at frequent intervals, while if there is little or no demand for the section, the rollings are very infrequent and a small order may have to wait for a long time before enough orders for the section will accumulate that will warrant a special rolling. The ease with which sections can be obtained will, therefore, depend upon the mill and the conditions of the market. The standard and permissible CHOICE: OF SECTIONS 28= sizes of. sections in use by the American Bridge Company, are given in the following table. Standard Angles. Permissible Angles. 6" x 6" 6" x 4" 8" x 8" 6" x $y 2 " 4" x 4" 5" ' x 3^" 5" x 5" 4" - ~ T/ " 3/2" x 3/2" 3" x 3" 2y 2 " x 2y 2 " 4 x 3 3>^" x 3" 3" x 2 1 / 2 y 2 " x 2" Standard Channels. 15" 8" 12" 6" 10" Standard I Beams. 20" 10" 18" 15" 6" 2" 254" 2/ 2 " 8" 6" 3/2" X 2} 2" X 2" 3 " X 2 Permissible Channels 9" Permissible I Beams. 24" Permissible Tees. 3" x y%' 2" x 2" x 5-16" Permissible Zee Bars. 5" 4" Standard Flats. 3" 6" 3/2" 7" 4" 8" 4/2" 9" 5" 10" Standard Rounds. 12' 14' I/' 1 v" y& i Standard Squares. w Other sizes than those specified may be obtained, but the time of delivery will be very uncertain unless the -order is large enough to war- rant a rolling. Deck beams, bulb angles and special section Z-bars are hard to get unless ordered in large quantities. Flats J^" thick and under are very hard to get. Flats under 4" should.be ordered by y 2 " variation in width; flats and universal plates over 4" should be ordered by i" variation in width. CHAPTER XXVII. PAINTS AND PAINTING. Corrosion of Steel. If iron or steel is left exposed to the atmos- phere it unites with oxygen and water to form rust. Where the metal is further exposed to the action of corrosive gases the rate of rusting is accelerated, but the action is similar to that of ordinary rusting. Rust is a hydrated oxide of iron, and forms a porous coating on the surface of the metal that acts as a carrier of oxygen and moisture, thus pro- moting the action of corrosion. If nothing is done to prevent or retard the corrosion of the iron and steel used in metal structures, the metal rapidly rusts away and the structure is short lived. Wrought iron is affected by corrosion more than cast iron, and steel is affected more than wrought iron. The corrosion of iron and steel may be prevented or retarded by covering it with a coating that is not affected by the corroding agents. This is very effectually accomplished by galvanizing; but on account of the cost it is impracticable to use the process for coating anything but sheet steel and small pieces of structural steel. The most common methods of protecting iron and steel are by means of a coating of paint, or by imbedding it in concrete. PAINT. The paints in use for protecting structural steel may be divided into oil paints, tar paints, asphalt paints, varnishes, lacquers, and enamel paints. The last two mentioned are too expensive for use on a large scale and will not be considered. OIL PAINTS. An oil paint consists of a drying oil or varnish and a pigment, thoroughly mixed together to form a workable mixture. "A good paint is one that is readily applied, has good covering powers, LINSEED OIL 287 adheres well to the metal, and is durable." The pigment should be inert to the metal to which it is applied and also to the oil with which it is mixed. Linseed oil is commonly used as the varnish or vehicle in oil paints, and is unsurpassed in durability by any other drying oil. Pure linseed oil will, when applied to a metal surface, form a trans- parent coating that offers considerable protection for a time, but is soon destroyed by abrasion and the action of the elements. To make the coating thicker, harder and more dense, a pigment is added to the oil. An oil paint is analogous to concrete, the linseed oil and pigment in the paint corresponding to the cement and the aggregate in the concrete. The pigments used in making oil paints for protecting metal may be divided into four groups as follows: (i) lead; (2) zinc; (3) iron; (4) carbon. Linseed Oil. Linseed oil is made by crushing and pressing flax- seed. The oil contains some vegetable impurities when made, and should be allowed to stand for two or three months to purify and settle before being used. In this form the oil is known as raw linseed oil, and is ready for use. Raw linseed oil dries (oxidizes) very slowly and for that reason is not often used in a pure state for structural iron paint. The rate of drying of raw linseed oil increases with age ; an ol'd oil be- ing very much better for paint than that which has been but recently extracted. Raw linseed oil can be made to dry more rapidly by the addition of a drier or by boiling. Linseed oil dries by oxidation and not by evaporation, and therefore any material that will make it take up oxygen more rapidly is a drier. A common method of making a drier for linseed oil is to put the linseed oil in a kettle, heat it to a tem- perature of 400 to 500 degrees Fahr., and stir in about four pounds of red lead or litharge, or a mixture of the two, to each gallon of oil. This mixture is then thinned down by adding enough linseed oil to make four gallons for each gallon of raw oil first put in the kettle. The addition of four gallons of this drier to forty gallons of raw oil will reduce the time of drying from about five days to twenty- four hours. A drier made in this way costs more than the pure linseed oil, so that driers are verv often made by mixing lead or manganese oxide with 288 PAINTS AND PAINTING rosin and turpentine, benzine, or rosin oil. These driers can be made for very much less than the price of good linseed oil, and are used as adulterants ; the more of the drier that is put into the paint, the quicker it will dry and the poorer it becomes. Japan drier is often used with raw oil, and when this or any other drier is added to raw oil in barrels, the oil is said to be "boiled through the bung hole." Boiled linseed oil is made by heating raw oil, to which a quantity of red lead, litharge, sugar of lead, etc., has been added, to a temper- ature of 400 to 500 degrees Fahr., or by passing a current of heated air through the oil. Heating linseed oil to a temperature at which merely a few bubbles rise to the surface makes it dry more rapidly than the unheated oil ; however, if the boiling is continued for more than a few hours the rate of drying is decreased by the boiling. Boiled linseed oil is darker in color than raw oil, and is much used for outside paints. It should dry in from 12 to 24 hours when spread out in a thin film on glass. Raw oil makes a stronger and better film than boiled oil, but it dries so slowly that it is seldom used for outside work without the addition of a drier. Lead. White Lead (hydrated carbonate of lead specific grav- ity 6.4) is used for interior and exterior wood work. White lead forms an excellent pigment on account of its high adhesion and covering power, but it is easily darkened by exposure to corrosive gases and rapidly disintegrates under these conditions,, requiring frequent re- newal. It does not make a good bottom coat for other paints, and if it is to be used at all for metal work it should be used over another paint. Red Lead (minium; lead tetroxide specific gravity 8.3) is a heavy, red powder approximating in shade to orange ; is affected by acids, but when used as a paint is very stable in light and under ex- posure to the weather. Red lead is seldom adulterated, about the only substance used for the purpose being red oxide. Red lead is prepared by changing metallic lead into monoxide litharge, and converting this product into minium in calcining ovens. Red lead intended for paints must be free from metallic lead. One ounce of lampblack added to one pound of red lead changes the color to a deep chocolate and increases the PIGMENTS 289 time of drying. This compound when mixed in a thick paste will keep 30 days without hardening. Zinc. Zinc white (zinc oxide specific gravity 5.3) is a white loose powder, devoid of smell or taste and has a good covering power. Zinc paint has a tendency to peel, and when exposed there is a tendency to form a zinc soap with the oil which is easily washed off, and it therefore does not make a good paint. However, when mixed with red oxide of lead in the proportions of I lead to 3 zinc, or 2 lead to I zinc, and ground w r ith linseed oil, it makes a very durable paint for metal surfaces. This paint dries very slowly, the zinc acting to delay harden- ing about the same as lampblack. Iron Oxide. Iron oxide (specific gravity 5) is composed of anhydrous sesquioxide (hematite) and hydrated sesquioxide of iron (iron rust). The anhydrous oxide is the characteristic ingredient of this pigment and 'very little of the hydrated oxide should be present. Hydrated sesquioxide of iron is simply iron rust, and it probably acts as a carrier of oxygen and accelerates corrosion when it is present in considerable quantities. Mixed with the iron ore are various other in- gredients, such as clay, ocher and earthy materials, which often form 50 to 75 per cent of the mass. Brown and dark red colors indicate the anhydrous oxide and are considered the best. Bright red, bright purple, and maroon tints are characteristic of hydrated oxide and make less durable paints than the darker tints. Care should be used in buying iron oxide to see that it is finely ground and is free from clay and ocher. Carbon. The most common forms of carbon in use for paints are lampblack and graphite. Lampblack (specific gravity 2.6) is a great absorbent of linseed oil and makes an excellent pigment. Graphite (blacklead or plumbago specific gravity 2.4) is a more or less im- pure form of carbon, and when pure is not affected by acids. Graphite does not absorb nor act chemically on linseed oil, so that the varnish simply holds the particles of pigment together in the same manner as the cement in a concrete. There are two kinds of graphite in common use for paints the granular and the flake graphite. The Dixon Graphite Co., of Jersey City, uses a flake graphite combined with silica, 19 290 PAINT AND PAINTING while the Detroit Graphite Manufacturing Co., uses a mineral ore with a large percentage of graphitic carbon in granulated form. On account of the small specific gravity of the pigment, carbon and gra- phite paints have a very large covering capacity. The thickness of the coat is, however, correspondingly reduced. Boiled linseed oil should always be used with carbon pigments. Mixing the Paint. The pigment should be finely ground and should preferably be ground with the oil. The materials should be bought from reliable dealers, and should be mixed as wanted. If it is not possible to grind the paint, better results will usually be obtained from hand mixed paints made of first class materials than from the ordinary run of prepared paints that are supposed to have been ground. Many ready mixed paints are sold for less than the price of linseed oil, which makes it evident that little if any oil has been used in the paint. The paint should be thinned with oil, or if necessary a small amount of turpentine may be added ; however turpentine is an adulterant and hsould be used sparingly. Benzine, gasoline, etc., should never be used in paints, as the paint dries without oxidizing and then rubs off like chalk. Proportions. The proper proportions of pigment and oil required to make a good paint varies with the different pigments, and the methods of preparing the paint ; the heavier and the more finely ground pigments require less oil than the lighter or coarsely ground while ground paints require less oil than ordinary mixed paints. A common rule for mixing paints ground in oil is to mix with each gallon of lin- seed oil, dry pigment equal to three to four times the specific gravity of the pigment, the weight of the pigment being given in pounds. This rule gives the following weights of pigment per gallon of linseed oil : white lead, 19 to 26 Ibs. ; red lead, 25 to 33 Ibs. ; zinc, 15 to 21 Ibs. ; iron oxide, 15 to 20 Ibs. ; lampblack, 8 to 10 Ibs. ; graphite, 8 to 10 Ibs. The weights of pigment used per gallon of oil varies about as follows : red lead, 20 to 33 Ibs. ; iron oxide, 8 to 25 Ibs. ; graphite, 3 to 12 Ibs. Covering Capacity. The covering capacity of a paint depends upon the uniformity and thickness of the coating ; the thinner the coat- COVERING CAPACITY 291 ing the larger the surface covered per unit of paint. To obtain any given thickness of paint therefore requires practically the same amount of paint whatever its pigment may be. The claims often urged in favor of a particular paint that it has a large covering capacity may mean nothing but that an excess of oil has been used in its fabrication. An idea of the relative amounts of oil and pigment required, and the cov- ering capacity of different paints may be obtained from the following table. AVERAGE SURFACE COVERED PER GALLON OF PAINT.* Volume of Lbs. Volume and Square Feet. Paint. oil. of Tig- ment. Weight of Paint. 1 Coat. 2 Coats. Iron Oxide (powdered) " " (ground in oil) . Red Lead (powdered). . White 1 ead(g'rdin oil). Graphite (ground in oil). Black Asphalt I gal 1 1 ' 1 1 ' 1 '(turp ) 8.00 24.75 22.40 25.00 12.50 17 25 Gals. Lbs. 1.2=16.00 2.6=32.75 1.4=30.40 1.7=33.00 2. 0=20. 50 4 030.00 600 630 630 500 360 515 350 375 375 300 215 310 .Linseed oil (no pigment) i 875 Light structural work will average about 250 square feet, and heavy structural work about 150 square feet of surface per net ton of metal. It is the common practice to estimate J^ gallon of paint for the first coat and % gallon for the second coat per ton of structural steel, for average conditions. Applying the Paint. The paint should be thoroughly brushed out with a round brush to remove all the air. The paint should be mixed only as wanted, and should be kept well stirred. When it is necessary to apply paint in cold weather, it should be heated to a tem- perature of 1 30 to 1 50 degrees Fahr. ; paint should not be put on in freezing weather. Paint should not be applied when the surface is damp, or during foggy weather. The first coat Should be allowed to stand for three or four days, or until thoroughly dry, before applying *Pencoyd Handbook page 293. 292 PAINTS AND PAINTING the second coat. If the second coat is applied before the first coat has dried, the drying of the first coat will be very much retarded. Cleaning the Surface. Before applying the paint all scale, rust, dirt, grease and dead paint should be removed. The metal may be cleaned by pickling in an acid bath, by scraping and brushing with wire brushes, or by means of the sand blast. In the process of pickling the metal is dipped in an acid bath, which is followed by a bath of milk lime, and afterwards the metal is washed clean in hot water. The method is expensive and not satisfactory unless extreme care is used in removing all traces of the acid. Another objection to the process is that it leaves the metal wet and allows rusting to begin before the paint can be applied. The most common method of cleaning is by scraping with wire brushes and chisels. This method is slow and laborious. The method of cleaning by means of a sand blast has been used to a limited extent and promises much for the future. The average cost of cleaning five bridges in Columbus, Ohio, in 1902, was 3 cts. per square foot of surface cleaned.* The bridges were old and some were badly rusted. The painters followed the sand blast and covered the newly cleaned surface with paint before the rust had time to form. Mr. Lilly estimates the cost of cleaning light bridge work at the shop with the sand blast at $1.75 per ton, and the cost of heavy bridge work at $1.00 per ton. In order to remove the mill scale it has been recommended that rusting be allowed to start before the sand blast is used. One of the advantages of the sand blast is that it leaves the sur- face perfectly dry, so that the paint can be applied before any rust has formed. Cost of Paint. The following costs of paints will give an idea of costs and proportions used :** Oxide of Iron (Prince's Metallic Brown). One gallon of paint. 6^4 Ibs. mineral at I cent 6 cts. 6^4 Ibs. raw linseed oil 5-6 gallon at 56 cents 47 ' Cost of materials per gallon of paint 53 cts. *Sand Blast Cleaning of Structural Steel, by G. W. Lilly, Transactions A. Soc. C. E., Feb., 1903. **Walter G. Berg, Engineering !N"ews, June 6, 1895. COST OF PAINTING 293 Red Lead (National Paint Co.). One gallon of paint. 20 Ibs. red lead at 5 cents $i .00 5^ Ibs. raw linseed oil y^ gallon at 56 cents 42 Cost of materials per gallon of paint $i .42 Graphite Paint (Dixon's Graphite). Five pounds of graphite paste and i gallon of oil make i^ gallons of paint. 3^4 Ibs. graphite paste at 12 cents 45 cts. 24 gallon boiled linseed oil at 59 cents 44 " Cost of materials per gallon of paint 89 cts. Mr. A. H. Sabin in a paper read before the American Society of Civil Engineers, June, 1895, gives the following as the minimum costs of paints: Iron Oxide paint, 6}4 Ibs. of oxide worth 9^2 cents; 6^4 Ibs. of oil worth 46^ cents; mixing in a mill, barrels, etc., 5 cents; making the actual cost of the paint 55 cents per gallon. The cost of a gallon of pure lead paint using 20 Ibs. of red lead per gallon and oil at 56 cents per gallon will cost not less than $1.50 per gallon. Cost of Painting. The cost of applying the paint depends upon the condition of the surface to be painted, and upon other conditions. A common rule for ordinary work is that the cost of painting is about two to three times the cost of a good quality of paint required for the job. The cost of labor may not be more than the cost of the paint, and may be four or five times as much. The cost of painting light struc- tural work in which considerable climbing has to be done is very dif- ficult to estimate. The average cost of painting four bridges in Den- ver, Col., with a finishing coat of Goheen's Carbonizing, in 1899, was 51 cents for paint and 80 cents for labor, per ton of metal painted. Priming Coat. Engineers are very much divided as to what makes the best priming coat; some specify a first coat of pure linseed oil and others a priming coat of paint. Linseed oil makes a transparent coating that allows imperfections in the workmanship and rusted spots to be easily seen ; it is not permanent however, and if the metal is ex- posed for a long time the oil will often be entirely removed before the second coat is applied. It is also claimed that the paint will not adhere 294 PAINTS AND PAINTING AS well to linseed oil that has weathered as to a good paint. Unseed oil gives better results if applied hot to the metal. Another advantage of using oil as a priming coat is that the erection marks can be painted over with the oil without fear of covering them up. Red lead paint toned down with lampblack is probably used more for a priming coat than any other paint; the B. & O. R. R., uses 10 ozs. of lampblack to every 12 Ibs. of red lead. Without going further into the controversy it would seem that there is very little choice between linseed oil and a good red lead paint for a priming coat. Finishing Coat. From a careful study of the question of paints, it would seem that for ordinary conditions, the quality of the materials and workmanship is of more importance in painting metal structures than the particular pigment used. If the priming coat has been prop- erly applied there is no reason why any good grade of paint composed of pure linseed oil and a very finely ground, stable and chemically non- injurious pigment will not make a very satisfactory finishing coat. Where the paint is to be subjected to the action of corrosive gases or blasts, however, there is certainly quite a difference in the results ob- tained with the different pigments. 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. Portland cement paint is the only paint that will withstand the action of engine blasts, and its use is now entirely in the experimental stage. Conclusion. It is urged against red lead paint, that the oil and the lead form a lead soap which is unstable ; against iron oxide paint, that since the paint contains more or less iron rust it is necessarily a promoter of rust ; against graphite paint, that there is not enough body in the pigment to make a substantial paint; etc. There is more or less truth -in all the accusations made against the different kinds of paint, if the paint be bought ready mixed, or if made out of poor materials ; however, with a good pigment and pure linseed oil, none of the above objections are of weight. MISCELLANEOUS PAINTS 295 To obtain the best results in painting metal structures therefore, proceed as follows: (i) prepare the surface of the metal by carefully removing all dirt, grease, mill scale, rust, etc., and give it a priming coat of pure linseed oil or a good paint red lead seems to be the most used for this purpose; (2) after the metal is in place carefully remove all dirt, grease, etc., and apply the finishing coats preferably not less than two coats giving ample time for each coat to dry before applying the next. Painting should not be done in rainy weather, or when the metal is damp, nor in cold weather unless special precautions, are taken to warm the paint. The best results will usually be obtained if the materials are purchased in bulk from a responsible dealer and the paint ground as wanted. Good results are obtained with many of the patent or ready mixed paints, but it is not possible in this place to go into a discussion of their respective merits. 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 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. COAL-TAR PAINT. Coal-tar used for painting iron work should be purified from all constituents of an acid nature ; for this rea- son it is preferable to employ coal-tar pitch and convert it into paint by solution in benzine or petroleum. Tar paint should preferably be applied while hot. Oil paint will not stick to tar, and when repainting a surface that has been painted with tar it is necessary to scrape the surface if a good job is desired. Tar paint does not become hard and will run in hot weather ; it is therefore not a desirable paint to use for many purposes. CEMENT AND CEMENT PAINT. Experiments have shown that a thin coating of Portland cement is effective in preventing rust ; that a concrete to be effective in preventing rust must be dense and made very wet. The steel must be clean when imbedded in the concrete. There is quite a difference of opinion as to whether the metal should be painted before being imbedded or not. It is probably best to paint the 296 PAINTS AND PAINTING metal if it is not to be imbedded at once, or is not to be used in con- crete-steel construction where the adhesion of the cement to the metal is an essential element. When the metal is to be imbedded immediately it is better not to paint it. Portland Cement Paint. A Portland cement paint has been used on the High St. viaduct in Columbus, Ohio, with good results. The viaduct was exposed to the fumes and blasts from locomotives, so that an ordinary paint did not last more than six months even on the least exposed portions. The method of mixing and applying the paint is described in Engineering News, April 24th and June 5th, 1902, as follows : "The surface of the metal was thoroughly cleaned with wire brushes and files the bridge had been cleaned with a sand blast the previous year. A thick coat of Japan drier was then applied and before it had time to dry a coating was applied as follows : Apply with a trowel to the minimum thickness of 1-16 inch and a maximum thick- ness of y\. inch (in extreme cases y 2 inch) a mixture of 32 Ibs. Portland cement, 12 Ibs. dry finely ground lead, 4 to 6 Ibs. boiled linseed oil, 2 to 3 Ibs. Japan drier." After a period of about two years the coating was in almost perfect condition and the metal under the coating was as clean as when painted. The cost of the coating including the hand cleaning, materials and labor was 8 cents per square foot. While this method of protecting metal is somewhat expensive it will certainly pay for itself in many places around smelters and shops. References on Paint and Painting. For a more complete dis- cussion of the subject of paints the reader should consult the following: Iron Corrosion by Louis E. Andes. The Painting and Sand Blast Cleaning of Steel Bridges and Via- ducts, by George W. Lilly, Engineering News, April 24th, 1902. Rustless Coatings of Iron and Steel, by M. P. Wood, Transactions American Society of Mechanical Engineers, Vols. 15 and 16. Preservation of Iron Structures Exposed to the Weather, by E. Gerber, Transactions American Society of Civil Engineers, May, 1895. Painting Iron Railway Bridges, by Walter G. Berg, Engineering News, June 6, 1895. Paints and Varnishes, by A. H. Sabin, Association of Engineering Societies, February, 1900. Application of Paints, Varnishes, and Enamels for the Protection of Iron and Steel Structures and Hydraulic Work a pamphlet for free distribution by Edward Smith & Company, New York. CHAPTER XXVIII. ESTIMATE OF WEIGHT AND COST. ESTIMATE OF WEIGHT. The contract drawings for mill buildings are usually general drawings about like those in Fig. 167 and Fig. 168, in which the main members and the outline of the building are shown, together with enough sketch details to enable the detailer to properly detail the work. In making an estimate of weight from general drawings it is necessary that the estimater be familiar with the style of the details in use at the shop, and with the per cent of the main members that it is necessary to add, to provide for details and get the total shipping weight of the structure. There are two methods of al- lowing for details : ( I ) to add the proper per cent for details to the weight of each main member in the structure, and (2) to add a per cent for details to the total weight of the main members in the structure. The first method is the safest one to follow, although the second gives good results when used by an experienced man. The best way to obtain data on the per cents of details of different members in buildings and other structures is to make detailed estimates from the shop drawings. By checking these data with the actual shipping weights, the engineer will soon have information that will be invaluable to him. Second hand data on estimating are of comparatively little value for the rea- son that the conditions under which they hold good are rarely noted, and it is better that the novice work out his own data and depend on his own resources, at least until he has developed his estimating sense. In short the only way to learn to estimate, is to estimate. The method of making estimates will be illustrated by making an estimate from the working drawings of a steel transformer building, the general plans of which are shown in Figs. 167 and 168. The 2 9 8 ESTIMATE OF WEIGHT AND COST members marked "Main Members" are those given on the general drawing, and the "Details" are those members whose sizes are supplied by the detailer. The building is a steel frame building, 60' o" wide, 80' o" long, 20' o" posts, pitch of roof y$, and is covered with corrugated SE1CTION 4-1 7"II5 7 IS Bracing in Plane of Bottom Chord Bracing in Plane of Top Chord FIG. 167. CROSS-SECTION AND PLAN OF STEEL TRANSFORMER BUILDING. ESTIMATE OF WEIGHT 299 steel. The general plans of the framework are shown in Figs. 167 and 168, and the plans and details oLthe corrugated steel are shown in Figs. 128 and 129. The weights of the different sections were obtained from Cam- bria Steel. The estimate is self explanatory. 80--0- SIDE ELEVATION * END ELEVATION FIG. 168. SIDE AND END ELEVATIONS OF STEEL TRANSFORMER BUILDING. 300 ESTIMATE OF WEIGHT AND COST ESTIMATE OF WEIGHT Steel Frame Transformer Building , 60-0" Wide , 80'-0"Lonq ,20-0" Posts- Pitch of Roof 5 - Covered with Corruqated Iron dumber Of Pieces Shape Section Length Weight per Foot Weiqht Details RerCent of Ma in Members Total Weight Feet nches Main Members Details 4 Trusses each thus=- 4 L 4x2*4 19 5i 6.0 463 4 Iff 18 j 2 4-9 353 4 3 x 2 2 x | 1 1 1 5-0 222 ^ 1^5 3 x 2 x^ 6 10 IO 4-0 173 t is 3x 2 x i 16 2 4.0 259 8 .L? 2X 2x4- 2 9 3-2 7O A Lf 5 IO 3-6 84 8 LS 2 x 2 x 5 1 32 130 A L? 3x2x4 10 5z 4.0 167 A [S 2z x x 4. 1 1 IO 3-6 170 8 LS 2x2x4 10 9 3.2 271 1 L 3x2x4: 19 Z 4-0 77 4 2 X 2 x ^ 6 3.2 77 5 2 x 2x4. 5 7^ 32 90 2 |_S 2x2x4 4 3-2 29 4 L? 3x 2 x4 II ~U 3-2 186 2 PI 3. i**| 2 9/3 89 2 PIS ti 5-95 1 2 Pis 44x4 9* 3-61 6 6 Pis 7x -! 1 5-95 36 II PIS 7^ x - 34. 6-16 42 4 Pis 8g x - 1 722 29 2 Pis 85x4 1 2 722 1 7 4 PIS 12x4 I 10 10.2 73 2 Pis 1 8 1381 46 1 Pis 24x^ 3 2 204- 65 4 Pis *| 1 5z 255 15 12 PIS 7 553 42 2 Pis 95x4 7 6-18 9 2 Pis 9+xi 1 4.46 9 2 [S 2^x2 f x "i. 9! 4.0 6 16 L 5 3i*i* i 7 4.9 45 2 I? 3g x 2| x i 3 4.9 3 1348 5 Rivet Heads Per 100 3.95 134 36 8 Washers Per IOO 30.0 2821 684- 24.6 Total Weiqht of 4 Trusses - 35O5 X4 = 140 2O 8 Posts each thus.-- A L? 3f *2i x 4 19 Hi 4-9 391 \ PI 104x4 2 871 16 4 L 5 3i*2i *4 Ti 5-9 15 1 PI 13X4; 1 11.05 13 1 PI I0x| r ii 21-25 41 2 L s 6x3^ x J 10 11-6 19 2 I s 6x4 x r 92 12-3 21 17 Bar5 2 x - i 7^ 1-7 47 160 f Rivet Heads Per 100 9-95 16 39l 188 48.1 Tota 1 Weiqht of 8 Posts = 579 x 8 = 463E 18652 ESTIMATE OF WEIGHT 301 Number of Pieces Shape Section Length Weiqht per Foot Weiqht Details in Per Cent of Main Members Total Weight Feet Inches Mam Member Details A Posts ,each thus-.- Brought Forward 18652 i I 9"@ 21 * 35 21 21 740 8 LS 3i * 3$. * \ 7-1 26 2 LS 6X4X1 6 12.3 13 2 LS 6 x 3|xJ 9 11-6 17 PI i 5 19-13 27 88 |" Rivet Heads per 100 9.95 9 Total Weight A- PC )StS = 837 X 740 h = 92 12.5 3328 4 Posts ,e ach thus . i I 9"@ 21* 27 10^ 21 586 6 is 32 X 3l X || $i 7.1 20 1 L 6 x 6 x i 9 14.8 1 1 2 [5 6x^x3 6| 12.3 13 2 LS 6X3^*1 9 11.6 17 I R 9x| S I 5 19.13 27 SO |" Rivet Heads per 100 9.95 8 586 96 16.4 Total Weight 4 Posts = 682 x 4 = Z728 A- Posts, each thus;- I L 6x6x| 20 8 i 14.8 306 10 Rs 7*i 6i 595 33 1 PI 5x^ 4.25 3 1 PI 10 x| 10 21.25 18 1 L 5 x 3^ x 5 1 1 87 9 3 L? 5 x 3j x 'A 8 87 17 r L 32x3jx!a 3 71 3 2 j_S 6 x 3 x f 94 116 18 100 1" Rivet Heads per lOO 995 IO | 306 1 1 1 36.3 Total Weight 4 Posts =417*4 = 1668 4 End Rafters .each thus ;- i C 7 <> 94* 37 s| 9.75 365 Con L? and Rs 19 365 79 220 Total Weight 4 End Rafters = 4 44X4 = 1776 2 Eave Struts, each thus- 5 s. 9 e 134 16 O 13.25 1060 Total Weight 2 Eave Struts = 1060 x 2 ZI20 Bottom Chord Bracing.- 8 19 3x3 x^ 18 A-.9 706 10 is 7"@;5* 15 2. 15.0 2275 36 e 6 x-4 x J 5 12.3 164 4 15 3x3 x^ 5 4.9 8 128 f'Rivet Heads per IOO 995 2981 205 7.0 Total Weight Bottom Chord Bracing = 3186 Purlins '- 30 B 5@ 6 i# 32 74 6.5 6355 14- 15 "i 6-5 (452 6 5 16 65 650 6 L 5 5x3x5 32 7^ 8-2. /604- 2 1! 15 tii 8-Z 26Z 2 L? " 16 7j 82 111 IO595 Total Weigl it of Purlins = 44O53 3 02 ESTIMATE OF WEIGHT AND COST Number of Pieces Shape Section L-enqtV-, Weiqht Per Foot Weight details m Percent Of Main Members Total Weiqht Feet Inches Mam Members DetcuU, Sid's:*- Brouqht For ware 4-4053 L> A" @ 5%* 1664 Imft. 525 8736 |_s 3"x -SVjr ' 96 4.9 470 L* 2i"*2i"*i" 96 - A O 384 Total Weiqht 0590 Rods. 8 Rods "i" ^ 28 2.0 448 16 Rods s" ^ 18 2.0 576 16 Rods "S 23 2.0 736 32 Bolts Anchor g l 6 2.0 96 4 .. .. I 20 8 18 Rods Louvre f"0 3 1.0 54 18 Bolts u I" 1.5 9 18 S>prmq Cotchee 0.5 9 36 Pis Anchor A"X ^" 4 1-4 5O 56 Pms Cotter l|"xZ|" Tol ol w ;.o 1 3 ht 1760 ~300 17.0 2060 Total Weiqht Steel Framework 55703 C orr uga-ted Iron.-* 84 Sqoores No 22 OS pe- lis+, per sq. 138 11592 70 24 ..... .Ill 7770 Ridae Roll 22 Black 250 Fto*hinc| 22 414 Cornice 20 1500 Louvres 20 and No 16 2100 19362 4264 Total Weiqht Corruqated \ron 23626 Total Weight 51 eel 79329 Trusses. I28A 2736 Z4-.6 14020 4L_ Posts 3IZ8 1504 48.1 4632 IB 5304 75Z 14.1 6056 L, I 224 444 36.3 1668 ELnd Rafters 1460 316 22.0 1776 ETave Struts 2I2O 2I2O Bottorn Chord Braonq 298I ^OS 70 3186 Rod s I 760 300 17.0 2060 Weiqht Excluding Purlins ond 6ir+& 2926 1 6257 220 35518 Purl.ns 105^5 IO595 & irts, 9590 9590 Total Prom e work 49446 6257 13.0 55703 Corruqated Iron 23626 Total Weiqht 79329 The weights and per cents of three other buildings, are shown in Table XXVI. The estimates for these buildings were made from the shop drawings, and were checked with the shipping weights. These buildings are of light construction with end post bents, (a) Fig. i. ESTIMATE OF COST OF MILL BUILDING 303 ESTIMATE OF CO5T Classification of Material Cost of Material Cost of Labor Weight Price Amount Price Amount Riveted Trusses 14020 ^1.60 *224.32 *MX> 9 , 4a?0 ' Latticed Columns 463 (.60 74.1 I I.OO 4632 I Beam 6O56 1-65 99-92 50 30.Z8 L " 1668 1-60 2669 5O 8.34 C Struts 3896 1-60 62-34 -26 9-14 I Beam Bracing 2480 1-65 40.9Z 25 6-20 L Bracing 706 1-60 11-30 -25 1-77 C Purlins 10595 1-60 169-52 -15 15-90 C Girts 9590 1-60 15344 -15 14-39 Rods 2060 1-80 37.08 1-00 20-6O Corrugated Iron No- 22 II 592 2-60 301.39 n 24- 7770 2-70 209-79 Ridge Roll , Louvres , Etc 4264 2-50 106-60 1-00 4.fe4 Asbestos Mill Board 1760 2-50 44.00 Poultry Netting 400 32-50 6-d Barbed Roofing Nails 32 5.00 .96 40-d Wire Noils 5 2-50 .13 540 Stove Bolts -2."x r(perlOC >) 5 36-00 1-94 540 Washers rx"x4' 76 6-00 4-56 540 Cut Washers 5" 2 7.00 .14 80O Wire Staples 5 4.0O 20 Copper Rivets *8 -J'long 1200 Carnage Bolts f*2i"(per 6 100) 210 25.00 *I-IO 1-50 13-20 Zoo z"x3i" " 46 * (-5O 3-00 260 Wood Screws *I4-J" 10 * 60 1-56 54 Steel Butts 3i"x3z' 60 * &OO 4.32 4 Mortise Door Locks 10 7500 3.00 18 IO 1 T Hinges 40 IZ.OO 2.16 2-to- Foof Bolts 5 50.00 1.00 2- Chain Bolts 5 50.00 1-00 96 Window Weights I44O 2.00 28-60 24 > LocKs 16 /5.00 3-60 24 " Lifts 10 10.00 2.40 675 Lin- Ft- Sash Cord 30 15^)0 4.50 2-8 Light Windows V Frame 80 * 4.00 8-00 12 "24 " *' * ./600 * <3-00 96-00 Z Doors 8OO *I5-00 30.00 2 Doors 200 *4-.00 8-00 Total Weic ht 872/2 Cost Mat'1,181 3.89 Cost Labor *336.38 SUMMARY Cost of Material f 1813.89 Cost of Shop Labor f 336-38 Cost of Details 30 tons @ 3-6O 108-00 Cost of Shop Pointing 4O-OO Total Shop Cost 2398-27 Freight, Mill -t-oShop 30 tons @ *5.00 150.00 Freight, Shop to Site E rect ion .Structure 1 JJ Corrugated 44 " @*I6.00 30 tons %25 75U70 ?*-75 45.00 Miscellaneous 5O.OO ( 76 galS- Paint 76-OO Pointing) Lo , r 75-00 Total Cost *38I3.27 34 ESTIMATE OF WEIGHT AND COST TABLE XXVI. WEIGHTS AND PER CENTS OF DETAILS OF MILL BUILDINGS. 5>feel Mill Buildings with Self Supporting Frames covered on Roof and Sides with one thickness of Corruqated Iron Part of Structure A0'-o"x40-o'xl4'-0' 2 Trusses 40-0" Pitch End Framing cH*s : ~ 2 CircularVenlilator 40 1 0"x48-o"x 14-0" 2Trusses40-0" Pi ten End Framing <*HE? SCircularVenlilotor 60-0"* 75-0" x t&'-O* 4 Trusses 60'-0 Pitch -^ End Framinq . T (Roo^*22 Cor ' Tron |5ides*E4 3CircularVentilator 60-0'x 80-0" x 20-0" 4 Trusses 60 -0" Pitch -5 End Framinq (Roof* 22 Cor lron |sicles*24 Monitor Ventilators Weiqht Details in per cent of Main Members Weiqht Details in per cent of Main Members Weight Detail sin per cent of Main Members Weiqht details in percent of Main Members Ibs percent Ibs. percent Ibs. percent Ibs percent Trusses A- \- Columns I Beam V_ C olumns End Rafters Eave Struts LowerChord Bracing Rods Purlins G\rts 2848 1428 1 148 9ia 1036 900 930 900 2281 3170 25 70 15 36 17 22 15 5 2 2848 1428 1143 952 1076 1080 1049 920 3516 3252 25 70 15 36 22 20 17 7 2 13940 3476 4Z5I 1470 3314 3117 3763 1737 6713 9895 344 52.5 33.0 14.0 1 1.6 33.2 9.7 6.2 47 10.0 14020 4632 6056 1668 1776 2120 3186 2060 10595 9590 24.6 48 i 14. 1 36.3 200 00 7.0 \2.0 0.0 00 Weight of Framework Weiqht perSq.Ft 15553 9.8 19 17269 9.0 20 50676 n.z 24.0 55703 11.7 3j5 Corrugated Iron 5880 6892 \7000 23626 Total of Steel Weight perSq.Ft. ZI453 \3.4 Z4I6I 12.6 67676 15.\ 79329 16.5 Channel eave struts were used in all except the third building in which 4-angle laced struts were used. A very good idea of the per cent of details in the different parts of the structures can be obtained from Table XXVI. The details of riveted mill building trusses will commonly vary between the limits of 25 and 35 per cent as given in the table; being more often near 25 than 35 per cent. The per cent of details in trusses is practically independent of the length of span, arid is larger for being more often near 25 than 35 per cent. The per cents of details in columns is mostly due to the bases and connections the per cents of details will therefore decrease as the length of the column increases. The weights of the other parts are so variable that no general rules can be given. Where a uniform per cent is added to the total weight of main members to provide for details, it is common to add about 30 ESTIMATE OF COST 305 per cent to the weight of the framework exclusive of the purlins and girts where end bent (b) Fig. i, is used.' In the estimate given it will be seen that the per cent is only 22, the small value being due in part to the use of channel eave struts and the end post framing. In estimating the weight of corrugated steel add 25 per cent for laps where two corrugations side lap and 6 inches end lap are required, and 15 per cent where one corrugation side lap and 4 inches end lap are required. The weights of the sections, rods, bolts, turnbuckles, etc., are ob- tained from Cambria Steel, or other handbook. The engineer should use every care to check his work in making estimates, the material should be checked off the drawings, and the cal- culations should be carefully checked and rechecked. Slide rules and adding machines are invaluable in this work. No results should, how- ever, be allowed to pass until they have been roughly checked by the engineer by aliquot parts, or by making a mental estimate of each quantity. The engineer can soon develop a sense of estimate, so to speak, and will often detect blunders intuitively. Accuracy is of more value in estimating than precision. While the method outlined may seem somewhat crude at first glance, it is nevertheless true that a pre- liminary estimate made by a skilled man will commonly be within I or 2 per cent of the shipping weight, and if off more than 2^ per cent it is pretty certain that there was something wrong either with the estimate or with the estimater. The estimated weight should be a little heavy rather than light, say I to 2 per cent. ESTIMATE OF COST. The cost of the different parts of a mill building varies with the local conditions, cost of labor, and cost of materials. The discussion of this subject will be divided into (i) cost of material, (2) cost of shop work, and (3) cost of erection. The cost of transportation must also be included in arriving at the total cost. The subject of costs is a very difficult one to handle and the author would caution the reader to use the data given on the following pages with care, for the reason that costs are always relative and what may 20 306 ESTIMATE OF WEIGHT AND COST be a fair cost in one case may be sadly in error in another case which appears an exact parallel. The price of labor will be given in each case, or the costs will be based on a charge of 40 cents per hour which in- cludes labor, cost of management, tools, etc. Cost of Material. The cost of structural steel can be obtained from the current numbers of the Iron Age, Engineering News, etc., or may be obtained direct from the manufacturers or dealers. In 1903 beams, channels, angles, plates, and bars were quoted at about i . 60 cents per pound f. o. b. Pittsburg. Beams 18, 20 and 24 inches deep take o.io cents per pound higher price than the base price for beams. The mills at present quote a delivered price only, equal to the mill price plus the usual freight charge. This price is often more than the cus- tomer could obtain by paying the freight himself, on account of the freight rebates that are often allowed. Cost of Mill Details. Mills are allowed a variation in length of sections of 4 of an inch; which means that beams, channels, etc., may come y% of an inch shorter or ^ of an inch longer than the length called for. When a less variation than this is required a special price is charged for cutting to exact length. The following list of mill ex- tras adopted January, 1902, is now in force : LIST OF EXTRAS TO BE ADDED TO PRICE OF PLAIN BEAMS AND CHANNELS. 1. For cutting to length with less variation than plus or minus ^ inch $0.15 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 flange, web and one flange or web and both flanges .25 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 COST OF Miu, DETAILS 307 8. Coping, ordinary beveling, including cut- ting 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 1 1 . Bending or other unusual work Shop rates 12. For fittings, whether loose or attached, such as angle connections, bolts and sepa- rators, tie-rods, etc 1 . 55 The above prices are per 100 Ibs. of steel. In ordering material from the mill the following items should be borne in mind. Where beams butt at each end against some other member, order the beams ^ inch shorter than the figured lengths ; this will allow a clearance of ^4 inch if all beams come y% of an inch too long. Where beams are to be built into the wall, order them in full lengths making no allowance for clearance. Order small plates in mul- tiple lengths. Irregular plates on which there will be considerable waste should be ordered cut to templet. Mills will not make reentrant cuts in plates. Allow *4 of an inch for each milling for members that have to be faced. Order web plates for girders *4 to ^2 inch narrower than the distance back to back of angles. Order as nearly as possible every thing cut to required length, except where there is liable to be changes made, in which case order long lengths. It is often possible to reduce the cost of mill details by having the mills do only part of the work, the rest being done in the field, or by sending out from the shop to be riveted on in the field connection angle? and other small details that would cause the work to take a very much higher price. Standard connections should be used wherever possible, and special work should be avoided. The classification of iron and steel bars is given in Table XXVII. The full extra charges for sizes other than those taking the base rate are seldom enforced ; one-half card extras being very common. 308 ESTIMATE OF WEIGHT AND COST TABLE XXVII. Iron Classification. Adopted Dec 3, 1895, by National Bar Iron Association. Adopted March 16, 1899, by Eastern Bar Iron Manufacturers' Association. Rounds and Squares. V to A. A'toH Htoif Jo * l * to A # to A y^ to A - & toH If to A X to A Half ^tO ! tftO ! > to 1 # to ^ to Vto - I to i I tO I i# to i T. l /2 tO 4 iX to 4 iH to 4 2 to 4 2 tO 4. Extra. itox Extra. Base sizes no extra I \! 2 to 2% A - A 3 to 3*4 - ' A 3^5 to 4 A 5 1C. 4 4^ to 5 i A 3 5^ to 6 lA 2 6^ to 6y z . ' *Tff - --- 2 A 1 6% to 7V -- 2 A Oval Extra. Iron. ^ to ! x >^ V to If . Extra, i A T 8 c A j c A A [ Half Round. # to|^ . Extra. A Half Oval anc Extra. . .. 4A X to }| ... ' 2 2^ ^ to 2 2 j T / ' 5 ova 1 s less than -Vx Vto A % x V to A -.% 3.68 4.40 5.68 8.24 11.20 16.10 22.30 * ? 2.42 2.50 2.r,s MIS 5.20 ;.;;,' 3.844.60 4.004.80 4.165.00 5.94 6.20 6.46 8.62 9.00 9.38 11.70 12.20 12.70 16.80 17.50 18.20 2:i.20 24.10 25.00 71 2.(i(i 5.4.1 4.325.20 6.72 9.76 13.20 18.90 25.90 8* 2.74 i.r.t; 4.485.40 6.98 10.14 13.70 19.60 20.80 9 J.SH i.NI 4.805.80 7.50 10.90 14.70 21.00 28.60 10 i.Oli 1.114 5.126.20 8.02 11.66 15.70 22.40 30.40 11 5.22 J.2S 5.44 li.fid 8.54 12.42 16.70 23.80 32.20 13 3.3S 4.52 r ).7(i ; ,is 7.00 7 40 9.06 9 58 13.18 13.94 17.70 18.70 J,->.20 26.60 34.00 35.80 14 ;.4u 7.80 10.10 14.70 19.70 28.00 37.60 15 J.72 9.20 10.62 15.46 20.70 29.40 39.40 18 ~.04 8. CO 11.14 16.22 21.70 30.80 41.20 17 11.66 16.98 22.70 32.20 43.00 18 2 18 7.74 23.70 33.60 44.80 19 12.70 18.50 24.70 35.00 46.60 20 13.22 19.26 25.70 36.40 48.40 21 26.70 37.80 50.20 22 27.70 39.20 52.00 23 28.70 40.60 53.80 24 29.70 42.00 55.60 25 30.70 43.40 57.40 26 31 .70 44.80 59.20 27 !2 70 46 20 61 00 28 33.70 47.60 62.80 29 34.70 49.00 64.60 30 3"). 70 50.40l66.40 vmg extras are to be understood as a part of the Machine Bolt List: Bolts with Hexagon Heads or Hexagon Nuts, 10 per cent extra. If both Hexagon Heads and Hexagon Nuts, 20 per cent extra. Joint Bolts with Oblong Nuts, Bolts with Tee Heads, Askew Heads, and Eccentric Heads, 10 per cent extra. Special Bolts with irregular Threads and unusual dimensions of Heads or Nuts will be charged extra at the discretion of the manufacturer. AVERAGE WEIGHT OF SQUARE HEAD MACHINE BOLTS PER 100. D AMI: FEB. Length. & A 5, & A % X X 1 1H 4.0 6.8 10.6 15.0 23.9 40.5 tS 4.4 7.3 11.3 16.1 25.1 42.7 73. 2 M 7.8 8.4 12. 12 17.2 18.2 26.3 27.7 44.8 47.0 76. 79. 2/4 13 i 19. 29.0 49.2 120 5 20. 30.4 51.4 85. 124.7 3 6.1 10.0 14.' 21 31.8 53.5 88.' 185 ?: 8 S 8.2 III 13.2 16 17. 18. 25^ 27 34 7 37.5 40.2 57.9 62.3 667 95. 01. 07. 137.4 145.8 159.2 196.0 207.0 218.0 5 8.9 14.3 20. 29. 43 7.1.0 13. 167.7 229.0 6 10.3 16.5 22 33. 48.4 79.8 26. 184.6 Saio In 11.0 11.7 17.6 18 6 4. 25 85. 37. 51.2 54.0 84 1 88.5 32. 38. 193.0 201.4 262 278.0 Pi 12.4 197 27. 39.1 56.7 92.9 45. 209.9 284.0 18.1 33 45.0 64.8 1060 aV 940? 317.0 10 36. 49.0 114.7 176. 257.1 389.0 11 40. 53.0 V5.8 123.5 188.' 273.9 360.0 12 13 44. 51.0 81.3 86.7 182.2 201. 213.4 290.0 307.7 3-8 92.2 225.9 426.0 15 16 97.7 103.1 157.6 166.1 238.3 250.8 358:3 JS-8 I 108.6 114.1 174.6 183.1 263 2 275.6 375.2 392.0 ffl-8 19 119.5 191.5 288 1 408 9 536 20 125.0 200.0 300.5 425.8 558.0 Per Inch M. 1.4 2.2 3.6 4.0 5.5 8.5 18.4 16.9 22.0 APPROXIMATE WEIGHT OF NUTS AND BOLT HEADS, IN POUNDS. Diam. of Bolt In Inches, Diam of Bolt In inches. PART IV. MISCELLANEOUS STRUCTURES. The descriptions of the different structures given in this part have been abstracted from descriptions published in the Engineering News, Engineering Record, etc. Figs. 171 and 172 are from the Railroad Gazette; and Fig. 169 and Figs. 172 to 181, inclusive, are reproduced from originals kindly loaned by the Engineering News. STEEL DOME FOR THE WEST BADEN, IND V HOTEL.* .... The dome of the new hotel at West Baden, Ind., is remarkable for its size. This dome has a steel framework and is larger than any other ever built, its span exceeding by about 15 feet that of the Horticultural Building of the Chicago Exposition of 1893. The dome is about 200 feet in outside diameter and rises about 50 feet above the bed plates. Its frame consists of 24 steel ribs, all con- nected at the center or crown to a circular plate drum, and tied together at the bottom by a circular plate girder tie. Each rib foots at its out- side end on a built up steel shoe, resting on a masonry pier. The rib is connected to the shoe by a steel pin, and the outside plate girder toe is attached to the gusset plate at this point, just above the shoe. The shoes of all the girders are constructed as expansion bearings, being provided with rollers in the usual manner. The dome is therefore virtually an aggregation of two-hinged arches with the drum at the center forming their common connection. Their thrust at the foot goes into the circular tie-girder, and only ver- tical loads (and wind loads) come upon the shoes and the bearing piers. At the same time any temperature stresses are avoided, since the ex- pansion rollers under the shoes permit a uniform outward motion of the lower ends of all the ribs. The outline of the dome and part of the dome framing are shown *Engineering News, Sept, 4, 1902. 3 i6 MISCELLANEOUS STRUCTURES DOME FOR WEST BADEN HOTEL 317 it, Fig. 169. The rise is between }4 and ^5 of the span. The outline of the top chord approximates, an elliptical curve, and the bottom chord is parallel to the top chord throughout its length, except in the three end panels on either side ; the depth of the arch being 10 ft. back to back of chord angles. The web members are arranged as a single system of the Pratt type, with substruts to the top chord as purlin supports. In the end sections the arrangement is necessarily modified, the sharper curvature of the chords being allowed for by more frequent strutting. The maximum stresses in the different members of the arch are given on the right half of the rib in Fig. 169. They are obtained by properly combining the dead load stresses with the stresses due to wind blowing successively in opposite directions in the plane of the rib in question. The loads used in the calculation were a dead load separate !y estimated for each panel point, a variable snow load, heaviest at the center of the roof, a wind load of 30 Ibs. per sq. ft. on a normal surface reduced for inclination of the roof to the vertical. The makeup of the members is given on the left half of the rib in Fig. 169. In the plan part of the dome the method of bracing the ribs is fully shown. Suc- cessive pairs of ribs are connected by bays of bracing in both upper and lower chords. In the upper chord the I beam purlins are made use of as struts, angle struts being used in the lower chord. The bracing consists throughout of crossed adjustable rods. At the center, these rods are carried over to a tangential attachment to the central drum, so as to give more rigidity against twisting at the center. The central drum, 16 ft. in diameter by 10 ft. deep, has a web of ^8 inch plate, with stiffener angles to which the ribs are attached. At top and bottom the drum carries a flange plate 24 ins. x 3-16 ins. for lateral stiff eners. In addition it is cross braced internally by four diametrical frames intersecting at the center. The outer tie-girder, which takes the thrust of the arch ribs, is a simple channel-shaped plate girder, 24 ins. deep, as shown on the plan. The weight of the dome complete, including framework and covering was 475,000 Ibs. This makes the dead load about 15 Ibs. per square foot of horizontal projec- tion of roof surface. Mr. Harrison Albright, of Charleston, W. Va., was the architect of the building and the design of the steel dome was worked out by Mr. Oliver T. Westcott, while in charge of the estimating department of the Illinois Steel Company. The structural steel was furnished by the Illinois Steel Co. THE ST. Louis COUSEUM.* The St. Louis Coliseum Building is a rectangular brick building 186' 2" x 322' 3". The steel framework is made entirely independent of the masonry walls and consists of three-hinged arches properly braced. The Coliseum has an area of 222 x 112 feet clear of the curb wall. Ordinarily there are seats for 7,000 persons on the main floor and the galleries, but for convention purposes with seats in the arena trie num- ber can be increased to 12,000 persons. The steel framework consists of a central arched section adjoined at each end by a half dome formed by six radial arched trusses. The main arches forming the central section have a span 178' 6" c. to c. of shoe pins, are spaced 36' 8" apart, and are connected by lateral bracing in pairs. The pins at the foot of the arches are 4 7-16" diameter, and at the crown the pin is 2 5-16" diameter. The rise of the arches is 80' o", the lower chord points being in the curve of a true ellipse. The end radial trusses correspond essentially to the semi-trusses of the main arches except for their top connection, where their top chords are attached to a semicircular frame supported by the end main trusses and designed to receive thrust, but no vertical reaction, as shown in Fig. 170. The roof covering of asphalt composition is laid on i^-inch boards, resting on 2^/2 x i6-inch wood joists, 3 feet apart and ceiled underneath. These, in turn, are carried by the steel purlins of the structure, which are spaced about 16 feet apart. The gallery floor beams are carried on stringers of 8-inch channels spaced 3' 8" center to center, carried by girders running between, and supported by the arches. The rear string- er is a plate girder ; the front one is a latticed girder, the gallery beams running through the latter and cantilevering out 5' 4". The main floor beams, supporting the lower tier of seats, consist of Q-inch I beams, spaced 3' 8" center to center, which are similarly carried on girders, and their lower ends rest on a brick wall. *Engineering News, Aug. 10, 1899, and Engineering Record, 1899. THE ST. Louis COUSEUM Sectional Plan Rgure I. General Plan of Trusses* Framing Ran of Half Ring Connecting Radial Trusses to Main Trusses Main Arches Figure 2 - Cross Section Showing Construction of Main Arches FIG. 170. The loads, in accordance with which the trusses were figured, are as follows: CASE I. Wooden deck and gravel of roof 17.5 Ibs. per sq. ft., vertically Steel 12.5 ' Snow and wind 25.0 Total 320 MISCELLANEOUS STRUCTURES Add for floors, viz. : Main floors, banks and galleries 105.0 " " " " Attic floors 60 . o " " " " CASE II. Wooden deck and gravel of roof 17.5 Ibs. per sq. ft, vertically Steel 12.5 " " " " Snow . .10.0 " " " " Total 40.0 ' Wind pressure over entire elevation of wall and roof of 30.0 Ibs. per sq. ft., horizontally LOADS ON PURLINS. Wooden deck and gravel of roof I 7-S I DS - P er sq. ft., vertically Steel 3.5 Snow and wind 25 . o " Total .....46.0 ' LOADS ON FLOOR BEAMS, GIRDERS AND COLUMNS OF MAIN FLOORS. Banks and galleries,- beams 140 Ibs. per sq. ft. Banks and galleries, girders 112 " " " " Banks and galleries, columns 105 " " " " Attic floors beams, columns and girders 60 ' For the main trusses, in addition to the stresses of Case II., there was added the stress due to the wind bracing between these trusses. For the radial trusses, in addition to loading of Case II., there was assumed an additional load of 50,000 pounds supposed to act up or down at the upper point of truss ; this load being what was assumed probable in case there was slight unequal settlement of the footings. For the half ring connecting the tops of the radial trusses there was another case assumed, beside Cases I. and II. viz., a tKrust of 50,000 pounds at any point of the half ring; this being the thrust of a radial truss under its full live and wind load. All the material used was of medium steel, excepting the rivets, which were made of soft steel. Both material and workmanship con- form to manufacturer's standard specifications. THE; ST. Louis COUSICUM 321 UNIT STRAINS. ] 16,000 Ibs. per sq. in. Compression, for lengths of 90 radii or under. . . . 12,000 " " " " Compression, for lengths of over 90 radii 17,100 57 I -f- r Combined stress due to tension or compression and transverse loading 16,000 " " " " Shear on web plates 7.500 " " " " Shear on pins ....... 1 1,000 " " " " Shear on rivets 10,000 " " " " Bearing on pins 22,000 " " " " Bearing on rivets 20,000 " " " " Bending, extreme fibre of pins 25,000 " " " " Bending, extreme fibre of beams 16,000 " " " " Lateral connections have 25 per cent greater unit strains than the above. In Case II of trusses, the above unit strains were increased one- third. The main and radial arch trusses are built a^ shown in Fig. 170, except that above the haunches the ribs of the radial arches are T-shaped instead of I-shaped, i. e., they have no inside flanges. The purlins are triangular trusses 4^2 feet deep, made of angles. The brac- ing between main arch trusses terminates at the bottom with heavy portal struts of triangular box section. The lateral rods are not car- ried to the ground on account of the obstruction they would make. The radial trusses are coupled together in pairs with lateral rods down to the ceiling line. The thrust due to wind is transmitted from them into the line of girders around the structure at this point, and into the ad- joining floor systems. The compression ribs of the main and radial arches are stayed laterally by angle iron ties, connecting to the first panel-point in the bottom chord of the purlins. In the planes of the first diagonal braces of the trusses above the haunches, diagonal rods connect the bottom ribs of the trusses to the upper ribs of the next trusses. Xo struts were used between the bottom chords, as they would have been directly in the line of vision from the rear gallery seats to the farther end of. the arena. The front and rear girders supporting the gallery and main floor beams are tied together with a triangular system of angle iron bracing. To provide for expansion, the radial purlins and all the girders be- tween the arches have slotted hole connections in every alternate bay. The diagonal rods between the two lines of ridge purlins were tightly 21 322 MISCELLANEOUS STRUCTURES adjusted on a hot day. To prevent secondary strains in the half ring to which the radial trusses are connected at their tops, there is i-i6-inch clearance in all the pin holes. There is also clearance between the pin plates, so that the trusses and the ring can slide a little sideways on their pins. The lines of the arch trusses were laid out full size and the principal points checked by independent measurements in the template shop, and the work was accurately assembled. In order to avoid the handling of large, heavy pieces before the drill press, the foot of the arch, through which the pin hole was bored, was made separately and afterward riveted on. The total weight of the iron in the entire structure was 1,905,000 pounds, as follows: Main arches, 64,000 pounds, each; radial arches 21,000 pounds, each; purlins between main trusses 1,450 pounds, each; main floor stringers 810 pounds, each; balcony floor stringers, 280 pounds, each; cast shoes 3,000 pounds, each. There were 4,188 days labor spent on the work in the shop and 3,550 days labor during erec- tion, the average number of men in the erecting force being about 50. The stress diagrams and detail plans of the steel frame were made un- der the supervision of Mr. Stern, in the office of the Koken Iron Works, who were contractors for the ironwork, and were submitted for approv- al to the consulting engineer, Mr. Julius Baier, Assoc. M. Am. Soc. C. E. Mr. C. K. Ramsey was the architect of the Coliseum, and Mr'. L. H. Sullivan was the consulting architect. Mr. A. H. Zeller was consulting engineer for the Board of Public Improvements ; Mr. J. D. McKee, C. E., was shop inspector, and the Hill-O'Meara Construction Company was the general contractor. THE LOCOMOTIVE SHOPS OF THE; ATCHISON, TOPEKA AND SANTA FE R. R., TOPEKA, KAS.* This building is intended for all the locomotive work, including boilers and tenders. It is of particular note for its great size and the peculiar features of its design. In general plan it is 852 ft. long and 153 ft. 10 ins. wide, the width being divided into a center span of 74 ft. 3 ins. and two side spans of 39 ft. 9 ins. It is of self-supporting steel frame construction, with concrete foundations and floor, 13-in. brick walls, and Ludowici tile roof. There is no sheathing under the tiles, which thus constitute the sole covering. The tiles are laid on 2 x 2-in. timber strips to which every fourth tile is fastened by copper wire. The most striking feature of the design is that the saw tooth or weaving shed type of roof is adopted for the side spans, the glazed vertical sides of the ridges facing northward. This feature was intro- duced with the view of making the shop as light as possible. The ar- rangement could not well be used where heavy snows are frequently experienced, as the snow would pack between the ridges, but there are comparatively few heavy snow storms in the vicinity of Topeka. In addition to this arrangement, the greater proportion of the area of the side walls is composed of windows, while the exposed parts of the sides of the central span (between the ridges of the side spans) are also glazed. There are also several windows in the end walls. The roof of the central span has on each side of the ridge a skylight 12 ft. wide, extending the full length of the building. These skylights are fitted with translucent fabric instead of glass. By these various means an exceptionally good lighting effect and diffusion of light are obtained and the shop is in fact remarkably light even on a gloomy day. There is no monitor roof, but ventilation is provided for by Star ventilators 25 ft. apart along the ridge of the main roof. The columns are built up of pairs of 15-in. channels, and independ- ent columns of similar construction carry the double-web box girde* runways for the electric traveling cranes which run the entire length of the central span. Fig. 173 shows the elevations, sections and plans *Engineering News, Jan. 3, 1903: and Eaihyay Gazette, Nov. 7, 1902. MISCELLANEOUS STRUCTURES ; FIG. 171. LOCOMOTIVE SHOP. FIG, 172. CROSS-SECTION LOCOMOTIVE SHOP. of the steel structural framework, and Fig. 174 is a partial elevation on the east side. Fig. 175 shows the design of the central roof trusses and the lattice girders which form longitudinal bracing between the trusses. This longitudinal bracing is not continuous but is fitted only between LOCOMOTIVE SHOPS, A. T. & S. F. R. R. 32.5 alternate pairs of trusses. End trusses are built into the walls> as these walls are pierced by numerous windows and dcors and are not relied upon in any way to support the roof. Portal bracing is fitted between the side or wall columns at intervals. No metal less than -in. Elevation A-B'. Eieva-Mon C-D, Cross Section of Machine Shop. Plan Rivtting Towtr Elevation G-H. Cross Section of Boiler Shot>. FIG. 173. PART ELEVATIONS AND PLANS OF STEEL STRUCTURAL WORK OF NEW LOCOMOTIVE SHOPS. thick is used in the structural work. The roof trusses are proportioned for a load of 15 Ibs. per sq. ft. for the weight of the roofing, 10 Ibs. per sq. ft. for snow, and 25 Ibs. per sq. ft. for wind pressure, or 50 Ibs. per sq. ft. in all. The members ~ '.\ _ jfrrrn- [rn-nrnrfrTrfTir rrrrfi nrrn-BBaTrirn- irfrrr nrrrrr rrrnr rrrrfr rrfrrr [7rrfr rrirfr n-irmririL i iPimij P r irirfTTn'rir[rfrttPiiriTwririTirHn'FrirtiririirirmM[r.friF FIG. 174. HALF EAST ELEVATION OF NEW LOCOMOTIVE SHOP. (SHOWING RIVETING TOWER AND WEAVING SHED ROOF.) 326 MISCELLANEOUS STRUCTURES were calculated on a basis of 16,000 Ibs. per sq. in. for tension and 14,000 Ibs. per sq. in. for compression. Provision for expansion and contraction is made at intervals of 100 ft. The structural work for this shop was built at the Toledo Works of the American Bridge Co. The steel is painted a light grey, and the brick is whitewashed, a pneumatic machine being used for the latter work. 12' I SL ffi S,8*L* 16,25 Ibs. Half -K'O'C.tvC.of Trusses NEWS. Half Transverse Section. FIG. 175. The arrangements for lighting the shop by day have already been referred to. For night work there will be arc lights for general light- ing and incandescent lamps convenient to the tools, etc. The building is heated by the Sturtevant hot blast system. On each side are two fan rooms, each containing a steam-driven blower fan and a heating LOCOMOTIVE SHOPS, A. T. & S. F. R. R. 327 chamber filled with coils of pipe through which passes the exhaust steam. The hot air is delivered into two longitudinal underground con- duits parallel with the lines of columns, with a duct leading to the sur- face at each column. Each duct is fitted with a vertical sheet iron pipe 7 ft. high, with a flaring head to deliver the air horizontally. The plant is guaranteed to maintain a temperature of 70 F. throughout the shop in zero weather. The floor foundation is formed of 6 inches of concrete resting on the natural soil well tamped. The concrete is composed of I part Louis- ville cement, 2 parts sand and 4 parts stone. On the concrete are laid vellow pine nailing strips, 3" x 4", 18 ins. c. to c., to which is spiked the 1 24 -in. splined hard-maple flooring. All tracks in the shop are laid with 75-lb. rails on ties of New Mexico pine treated by the zinc-chlor- ide process, the floor concrete being laid only to the ends of the ties, so that adjustment of the track can be made without tearing up the floor. At the engine pits (which are of concrete) the rails are laid on longitudinal timbers. The concrete for column foundations is com- posed of I part lola Portland cement, 3 parts sand and 5 parts stone. These foundations are 8 to 15 ft. deep, extending to solid clay. They are built up with gas pipe sleeves to form holes for the anchor bolts, and the holes in the bed plates of the columns are slotted longitudinally so as to allow of adjustment for any slight variation. The foundations for the tools, etc., are also of Portland cement concrete, and these are built by the mechanical department to suit its own requirements as to arrangement of tools. This arrangement was only arrived at after careful study, and of course no changes can be made without expen- sive work in cutting out and replacing concrete. One suggestion for the floor construction was to use a brick floor with no conrete, so as to allow for future changes and putting in new foundations. THE LOCOMOTIVE ERECTING AND MACHINE SHOP, PHILADELPHIA & READING R. R., READING, PA.* The combined machine and erecting shop is 204 ft. 4^ ins. wide and 749 ft. 10 ins. long, with provision made for its extension to a total length of 1,000 ft. At its present length it has repair pits for 70 locomotives, and the proposed extension will provide for 30 pits more. Fig. 176 shows the general arrangement of the shop in plan, an(,l Fig. 177 is a transverse section showing the general character of the con- struction. The building, it will be observed, is divided transversely into three bays by means of two rows of intermediate columns running lengthwise of the building. These intermediate columns and the side wall columns carry the roof trusses and the overhead cranes, and are spaced 20 ft. apart longitudinally. The walls of the building are entirely indepen- dent of the steelwork. Considering the building transversely it will be observed that the two side bays contain the repair pits ; one pit be- SftjBS oqa'.n^ ar J \ f J ' ...i. i \ -K 5'>i i 'i 1 if 1 "T "[ & / ? j A j SL i ff < Lj'-'ern steps fifn' i i I '^1 T TT 1 4'-^ ] * | ; ..j i .4 i t - T;-' ll! 1 _ _ - , i | -T ! i a J - IJ rj 4- rd J g*j S ~j "^ ! 'lantern Stops here ^~ iton cranes. It will also be observed from Fig. 181 that the lower portion of the clerestory roof has a concrete and expanded mefal cov- ering with roofing slate nailed direct to the concrete. The concrete i. c composed of Portland cement and cinder, and is 3^2 ins. thick. The floor construction throughout will be 10 ins. of concrete covered with i in. of granolithic or Kosmocrete. In the tool and testing rooms off the machine shop, and between the boiler and erecting shops, an effort has been made to secure a dust-proof construction, and a roof which will be free from drippings due to condensed moisture. Over these rooms the skylight roofs consist of double-glazed Paradigm skylights, with a I -in. air space betwen them. PART SIDE ELEVATION. . ^r ,-;,i CROSS-SECTION OF BOILEU HOUSL-. THt ENC.NllRJ-,0 BICOHO FIG. GENERAL CROSS-SECTION OF ROLLING MILL. z * STEEL ROLLING MILL BUILDING FOR THE AMERICAN ROLLING MILL COMPANY, MIDDLETOWN, OHIO. *Engineering Record, July 20, 1901. APPENDIX I. GENERAL SPECIFICATIONS FOR STEEL FRAME MILL BUILDINGS MILO S. KETCHUM, Assoc. M. AM. Soc. C. E. 1903 GENERAL DESCRIPTION 1. The height of the building shall be the distance from the top of the masonry to the under side of the bottom chord of the truss. 2. The width and length of the building shall be the extreme distance out to out of framing or sheathing. 3. The length of trusses and girders in calculating stresses shall be considered as the distance from center to cen- ter of end bearings when supported, and from end to end when fastened between columns by connection angies. 4. The pitch of roof for corrugated steel shall preferably be not less than y (6" in 12"), and in no case less than J /$. For a pitch less than ^ some other covering than corrugated steel shall be used. 5. Trusses shall be spaced so that simple shapes may \ be used for purlins. The spacing should be about 16 feet for spans of, say, 50 feet and about 20 to 22 feet for spans of, say, loo feet. For longer spans than 100 feet the purlins may bo trussed and the spacing may be increased. Height of Building. Dimensions Building. of Longth of Span. Pitch of Roof. Spacing of Trusses. 342 APPENDIX Spacing of Purlins. Form of Trusses. Bracing. Proposals. Detail Plans. Approval of Plans. Dead Loads. 6. Purlins shall be spaced not to exceed 4' 9" where cor- rugated steel is used, and shall be placed at panel points of the trusses. 7. The trusses shall preferably be of the Fink type with panels so subdivided that panel points will come under the purlins. If it is not practicable to place the purlins at panel points, the upper chords of the trusses shall be designed to take both the flexural and direct stresses. Trusses shall preferably be riveted trusses. 8. Bracing in the plane of the lower chord shall be stiff ; bracing in the planes of the top chords, the sides and the ends may be made adjustable. 9. Contractors in submitting proposals shall furnish com- plete stress sheets, general plans of the proposed structures giving sizes of material, and such detail plans as will clearly .show the dimensions of the parts, modes of construction and ^sectional areas. 10. The successful contractor shall furnish all work- ing drawings required by the engineer free of cost. Working drawings will, as far as possible, be made on standard size sheets 24" x 36" out to out, 22" x 34" inside the inner border lines. 11. No work shall be commenced or materials ordered until the working drawings are approved in writing by the en- gineer. The contractor shall be responsible fo r dimensions and details on the working plans, and the approval of the de- tail plans by the engineer will not relieve the contractor of this responsibility. LOADS. 12. The trusses shall be designed to carry the following loads : 13. DEAD LOADS. Weight of Trusses The weight of trusses per square foot of horizontal projection, up to 150 feet span shall be calculated by the formula L W = P_ 45 where W = weight of trusses per square foot of horizontal projection ; SPECIFICATIONS 343 P = capacity of truss in pounds per square foot of hor- izontal projection ; L = span of the truss in feet ; A = distance between trusses in feet. 14. Weight of Covering. The weight of corrugated corrugated steel, steel shall be taken from Table I. TABLE I. Gaqe No. Thickness m inches Weight per Sc uare ( 100 sq-ft) Flat Sheets Corrugated Sheets Black Galvanized Black Painted Galvanized 16 .0625 ISO 166 275 291 18 .0500 too 2/6 220 256 20 0575 150 166 165 152 22 -0315 115 /4I 13d 154 14 0250 too 116 111 127 16 0188 75 SI 84 99 ^^ 0156 65 79 69 Q6 \Yhen two corrugations side lap and six inches end lap are used add 25 per cent to the above weights ; when one cor- rugation side lap and four inches end lap are used add 15 per cent to the above weights to obtain weight of corrugated steel laid. For paint add 2 pounds per square. The weight of cov- ering shall be reduced to weight per square foot of horizontal projection before combining with weight of trusses. 15. Slate laid with 3-inch lap shall be taken at a weight of 7*^ pounds per square foot of inclined roof surface for 3-16" slate 6" x 12", and 6V 2 pounds per square foot of inclined roof surface for 3-16" slate 12" x 24", and proportionately for other sizes. 1 6. Terra-cotta tile roofing weighs about 6 pounds per : square foot for tile i inch thick; the actual weight of tile and other roof coverings not named shall be used. 17. Sheathing of dry pine lumber shall be assumed to weigh 3 pounds per foot and dry oak purlins 4 pounds per foot board measure. slate Ti]e Sheathng and Purlins 1 8. The exact weight of sheathing, purlins, bracing, ven- Miscellaneous tilators. cranes, etc., shall be calculated. Loads. 344 APPENDIX Snow Loads. Wind Loads. Mine Buildings. Concentrated Loads. Purlins. Roof Covering. Minimum Loads. 19. SNOW LOADS. Snow loads shall be taken from the diagram in Fig. I. | ^ x^ F Q_ 40 jz / / / ^or \r,c ia/, H 1 / f'fi 7C/t ^ec he fc ?/<9/ /in Co 15 &// 75 ^ ^ ^ ; Z ^ fe ^ ^ !iS^ ^^ V^ _ I ) J 2 ^ ^ ^ 30 a 20 ^ ,o -> c JO f^ 1 " ^ _X^ ^xH ' I 1 3 r- ^^ 1 ^> ^x"^ ^/r,/ ^^* "^ ^ ^ J (^- -p" -^? ** ^=- * - ^=- He -^ .X /ce and s/eef for a// slopes ^ J -^ FIG. 30 35 40 45 50 Latitude in Degrees I. SNOW I.OAD ON ROOFS FOR DIFFERENT LATITUDES, IN LBS. PDR SQUARE FOOT. 20. WIND LOADS. The nofmal wind pressure on trusses shall be computed by Duchemin's formula, Fig. 2, with P = 30 pounds per square foot, except for buildings in ex- posed locations, where P 40 pounds per square foot shall be used. 21. The sides and ends of buildings shall be computed for a normal wind load of 20 pounds per square foot of ex- posed surface for buildings 30 feet and less to the eaves ; 30 pounds per square foot of exposed surface for buildings 60 feet to the eaves, and in proportion for intermediate heights. 22. Mine, smelter and other buildings exposed to the action of corrosive gases shall have their dead loads increased 25 per cent. 23. Concentrated loads and crane girders shall be con- sidered in determining dead loads. 24. Purlins shall be designed for a normal load of not less than 30 Ibs. per square foot. 25. Roof covering shall be designed for a normal load of not less than 30 Ibs. per square foot. 26. No roof shall, however, be designed for an equiva- lent load of less than 30 pounds per square foot of horizontal projection. SPECIFICATIONS 345 Norrrol FY^essure.lbs per sq ft P= Horizontal" A =Anqle of inclination of surface 75 80 85 90 5 10 15 20 25 X 35 4O 45 5O 55 60 65 70 Angle Exposed Roof mokes with Horizontal in Degrees. A- IG. 2. NORMAL WIND LOAD ON ROOF ACCORDING TO DIFFERENT FORMULAS. PROPORTION OF PARTS. 27. In proportioning the different parts of the structure the maximum stresses due to the combinations of the dead and wind load ; dead and snow load ; or dead, minimum snow and wind load are to be provided for. Concentrated loads where they occur must be provided for. 28. Allowable Unit Tensile Stresses for Medium Steel. Pounds per square inch Shapes, main members, net section 16,000 Bars 16,000 Bottom flanges of rolled beams 16,000 Shapes, laterals, net section , . 20,000 Iron rods for laterals 20,000 Plate girder webs, shearing on net section .... 10,000 Stresses. Tensile Stress. 346 APPENDIX Compressive Stress. Plate Girders. Alternate Stress. Combined Stress. Shapes liable to sudden loading as when used for crane girders 10,000 Expansion rollers per lineal inch ooo x D where D = diameter of roller in inches. Laterals shall be designed for the maximum stresses due to 5,000 pounds initial tension and the maximum stress due to wind. 29. Allowable Unit Compressive Stress for Medium Steel. For direct dead, snow and wind loads 5* 16,000 70 where $ = allowabl unit stress in pounds per square inch / = length of member in inches c. to c. of end con- nections ; r = least radius of gyration of the member in inches. 30. Top flanges of plate girders shall have the same gross area as the tension flanges. 31. Shear in webs of plate girders shall not exceed 1 0,000 ' pounds per square inch. 32. Members and connections subject to aTternate stresses shall be designed to take each kind of stress. 33. Members subject to combined direct and bending stresses shall be proportioned according to the following formula : c _ P M y l = A ' -TW where 5 = stress per square inch in extreme fibre; P direct load ; A = area of member ; M = bending moment in inch-pounds ; 3' t = distance from neutral axis to extreme fibre ; / = moment of inertia of member ; / length member, or distance from point of zero moment to end of member in inches ; modulus of elasticity = 28,000,000. SPECIFICATIONS 347 When combined direct and flexural stress due to wind is considered add 25 per cent to- the above allowable ten- sile and compressive stresses. 34. Soft steel may be used in mill buildings with unit stresses ten per cent less than those allowed for medium steel. 35. Where the stress due to the weight of the member or ue to an eccentric load exceeds the allowable stress for direct oads by more than ten per cent, the section shall be increased mtil the total stress does not exceed the above allowable stress or direct loads by more than ten per cent. The eccentric stress caused by connecting angles by one eg when used as ties or struts shall be calculated, or only one eg will be considered effective. 36. Rivets shall be so spaced that the shearing stress shall lot exceed 1 1 ,000 pounds per square inch ; nor the pressure on he bearing surface (diameter x thickness of piece) of the ivet hole exceed 22,000 pounds per square inch. Rivets in lateral connections may have stresses 25 per ent in excess of the above. Field rivets shall be spaced for stresses two-thirds those llowed for shop rivets. Field bolts, when allowed, shall be spaced for stresses wo-thirds those allowed for field rivets. Rivets and bolts must not be used in direct tension. 37. Pins shall be proportioned so that the shearing stress hall not exceed 11,000 pounds per square inch; nor the pres- ure on the bearing surface (diameter x thickness of piece) of he pin hole exceed 22,000 pounds per square inch ; nor the ex- reme fibre stress due to cross bending exceed 24,000 pounds >er square inch when the applied forces are assumed as act- ng at the center of the members. 38. Rolled beams shall be proportioned by their moments )f inertia. 39. Plate girders shall be proportioned on the assump- ion that the flanges take all the bending moment, and that the hear is resisted by the web. The distance between centers of gravity of the flange areas hall be considered as the effective depth of all girders. 40. The webs of plate girders shall be stiffened at bear- ngs and at all points of concentrated loading, and at inter- soft Steel. Stress due to Weight of Member. Rivets. Pins. Rolled Beams. Plate fiirders. Stiffeners. 348 APPE NDIX Timber. mediate points, wherever the shearing per square inch exceeds the stress allowed by the following formula : Allowed shearing stress = 12,500 90 d -i- t where d = depth, and t = thickness of web plate. 41. Compression flanges of plate girders shall be stayed transversely when their length is more than thirty times their width. 42. The allowable stresses in timber purlins and other timbers shall be taken from Table II. TABLE II. WORKING UNIT STRESSES, IN POUNDS, PER SQUARE INCH. Kind of Timber. Tension. Compression. Transverse. Shearing-. 1 With Srain. 2 Across drain. Ten. With rain. 6 Extreme Fibre Strass. 7 Modulus of Elasticity. 8 With S'ain. 9 Aoross Siain. 3 End Bear- in?. 4 Columns Ur.der 15 Biams. 5 Asross Srain. Faetor of SafeU. Ten. Five. Five. Four. Six. TWO. Four. Four White Oak 1000 700 1200 1200 I 000 900 900 800 10 1(00 800 600 6 800 900 700 200 50 60 50 50 1400 1100 1600 160J 1200 1200 r<>oj 1266 9CO 700 1000 1200 "s'oo" 800 800 1000 1000 800 800 800 800 lOOu 800 800 500 200 350 300 250 200 200 20 J 150 . 200 200 250 200 1000 700 120J 1100 800 1000 810 700 ' 's'oo' 700 600 800 800 800 750 800 550000 5000CO 850000 70,OOJ 600COO 600000 601)000 '766660' 600 00 450000 45000J 3500uO 500000 35 000 6 0000 200 100 150 150 . . 1000 500 1250 White Pine South. Long-leaf or Georgia Yellow Pine Douglas. Oregon and Yellow Fir Washington Fir or Pine (Red Fir) Northern or Short-leaf Yellow Pine . . . Red Pine iouo ' Norway Pine Canadian (Ottawa) White Pine Canadian (Ontario) Red Pine "56" 10J 100 JOO 100 150 " 100 '"756 " 600 '"460" 4UO Spruce and Eastern Fir Hemlock Cvpress . 12iO V200 Cedar Chestnut Calif orni a Redwood California Spruce Corrugated Steel. The allowable stress, P, in timber columns longer than 15 diameters shall be obtained by means of the formula p - c - eams or 4 angles laced. Corner columns shall preferably be composed of one angle. The cross-bending stress due to eccentric loading in col- umns carrying cranes shall be calculated. 71. Laced compression numbers shall be stayed at the ends by batten plates placed as near the end of the member as >racticable and having a length not less than the greatest width of the member. The thickness of batten plates must not be ess than 1-40 of the distance between rivet lines at right angles o axis of member. 72. Single lattice bars shall have a thickness of not less han 1-40, and double bars connected by a rivet at the intersec- ion of not less than 1-60 of the distance between the rivets connecting them to the member ; they shall make an angle not ess than 45 with the axis of the member; their width shall >e in accordance with the following standards, generally : SIZE OF MEMBER. 15-inch channels, or built sections with 3^ and 4- inch angles. 12, 10 and Q-inch chan- nels, or built sections with 3-inch angles. WIDTH OF LACING BARS. inches (%-inch rivets). inches (3/4 -inch rivets). Upset Rods. Upper Chords. Compression Members. Columns. Crane Posts. Lacing. 3 354 APPENDIX Pin Platea. Maximum Length. Splices. Splices. Tension Members. Eye- Bars. Pins. For 8 and 7-inch channels, or built sections with 2^/2 -inch angles. For 6 and 5-inch channels, or built sections with 2-inch angles. 2 inches (^-inch rivets). inches (^2 -inch rivets). Where laced members are subjected to bending, the size of lacing bars or angles shall be calculated or a solid web plate shall be Used. 73. All pin holes shall be reenforced by additional mater- ial when necessary, so as not to exceed the allowable pressure on the pins. These reenforcing plates must contain enough rivets to transfer the proportion of pressure which comes upon i them, and at least one plate on each side shall extend not less ; than 6 inches beyond the edge of the tie plate. 74. No compression member shall have a length exceed- ing 125 times its least radius of gyration for main members, nor 150 times its least radius of gyration for laterals and sub- members. 75. In compression members joints with abutting faces planed shall be placed as near the panel points as possible, and must be spliced on all sides with at least two rows of rivets on each side of the joint. Joints with abutting faces not planed 1 must be fully spliced. 76. Joints in tension members shall be fully spliced. 77. Tension members shall preferably be composed o angles or shapes capable of taking compression as well as tension. Flats riveted at the ends shall not be used. 78. Main tension members shall preferably be made of 2 angles, 2 angles and a plate, or 2 channels laced. Secondary tension members may be made of a single shape. 79. Heads of eye-bars shall be so proportioned as to de- velop the full strength of the bar. The heads shall be forged and not welded. 80. Pins must be turned true to size and straight, and must be driven to place by means of pilot nuts. The diameter of pin shall not be less than % of the depth of the widest bar attached to it. SPECIFICATIONS 355 The several members attached to a pin shall be packed so as to produce the least bending moment on the pin, and all vacant spaces must be filled with steel fillers. 81. Long laterals may be made of rods with clevis or sKvve nut adjustment. Bent loops shall not be used. 82. Trusses shall preferably be spaced ao as to allow the use of single pieces of rolled sections for purlins. Trussed purlins shall be avoided if possible. 83. Purlins and girts shall preferably be composed of single sections channels, angles or Z-bars placed with web at right angles to the trusses and posts and legs turned down. 84. Purlins and girts shall be attached to the top chord of trusses and to columns by means of angle clips with two rivets in each leg. 85. Purlins shall be spaced at distances apart not to exceed the span as given for a safe load of 30 pounds, and girts for a safe load of 25 pounds in Fig. 3. 86. Timber purlins shall be attached and spaced the same as steel purlins. ^ 87. Base plates shall never be less than y Inch in thick- ness, and shall be of sufficient thickness and size so that the pressure on the masonry shall not exceed 250 pounds per square inch. 88. Columns shall be anchored to the foundations by means of two anchor bolts not less than i" in diameter upset, placed as wide apart as practicable in the plane of the wind. The anchorage shall be calculated to resist the bending moment at the base of the columns. 89. Lateral bracing shall be provided in the plane of the top and bottom chords, side and ends ; knee braces in the transverse bents ; and sway bracing wherever necessary. Later- al bracing shall be designed for an initial stress of 5,000 pounds in each member, and provision must be made for putting this initial stress into the members in erecting. 90. Variations in temperature to the extent of 1 50 degrees F. shall be provided for. Rods. Spacing Trusses. Purlins and Girts. Fastening. Spacing. Timber Purlins, Base Plates. Anchors. Lateral Bracing. Temperature. 356 APPENDIX WORKMANSHIP. Workmanship. Riveted Work Punching. Holes for Field Rivets. Planing and Reaming. Rivets. Riveters. Bolts. Neat Finish. Contact Surfaces. 91. All workmanship shall be first-class in every partic- ular. Due regard must be had for the neat and attractive ap- pearance of the finished structure, and details of an unsightly character will not be allowed. 92. All riveted work shall be punched accurately with holes 1-16 of an inch larger than the size of the rivet, and when the pieces forming one built member are put together, the holes must be truly opposite; no drifting to distort the metal will be allowed; if the hole must be enlarged to admit! the rivet, it must be reamed. 93. All holes for field rivets in splices in tension mem- bers shall be accurately drilled to an iron templet or reamed while the connecting parts are temporarily put together. 94. In medium steel over y% of an inch thick, all sheared! edges shall be planed, and all holes shall be drilled or reamed to a diameter of y% of an inch larger than the punched holes, so as to remove all the sheared surface of the metal. Steel which does not satisfy the drifting test must have holes drilled. 95. The rivet heads must be of. approved hemispherical shape, and of a uniform size for the same size rivets through- out the work. They must be full and neatly finished through- out the work and concentric with the rivet hole. 96. All rivets when driven must completely fill the holes, the heads be in full contact with the surface, or countersunk when so required. 97. Rivets shall be machine driven wherever possible., Power riveters shall be direct-acting machines, worked by steam, hydraulic pressure, or compressed air. 98. When members are connected by bolts which trans- mit shearing strains, such bolts must have a driving fit. 99. The several pieces forming one built member must' fit closely together, and when riveted shall be free from twists, bends, or open joints. 100. All portions of the work exposed to view shall be neatly finished. 101. All surfaces in contact shall be painted before they are put together. SPECIFICATIONS 357 102. The heads of eye-bars shall be made by upsetting, rolling, or forging into shape. Weids in the body of the bar will not be allowed. 103. The bars must be perfectly straight before boring. 104. The holes shall be in the center of the head and on the center line of the bar. 105. All eye-bars shall be annealed. 1 06. All abutting surfaces in compression members shall i be truly faced to even bearings, so that they shall be in such contact throughout as may be obtained by such means. 107. Pin holes shall be bored truly parallel with one an- other and at right angles to the axis of the member unless otherwise shown in drawings ; and in pieces not adjustable for I length, no variation of more than 1-64 of an inch for every 20 feet will be allowed in the length between centers of pin holes. 1 08. Bars which are to be placed side by side in the structure shall be bored at the same temperature, and shall be of such equal length that, upon being piled on each other, the pins shall pass through the holes a^both ends at the same time I without driving. 109. All pins shall be accurately turned to a gage, and shall be straight and smooth. no. The clearance between pin and pin hole shall be 1-50 of an inch for pins up to 3^2 inches in diameter, and 1-32 for larger pins. in. All pins shall be supplied with steel pilot nuts, for use during erection. Forged Work Eye-Bare. Machine Work Facing. Pin Holes. Pins. Play in Pin Holes. Pilot Nuts. QUALITY OF MATERIAL. STEEL. 112. All steel must be made by the open hearth process, and if by acid process, shall contain not more tlian 0.08 per cent of phosphorus, and if by basic process, not more than 0.06 per cent of phosphorus, nor more than 0.05 per cent of sul- phur, and must be uniform in character for each specified kind. 113. The finished bars, plates and shapes must be free from injurious seams, flaws, or cracks, and have a clean smooth finish. Process of Manufacture Finish. 358 APPENDIX Test Pieces. Annealed Test Pieces. Marking. Physical Properties. Rivet Steel. Soft Steel. Medium Steel. Full Size Test of Steel Eye-Bars. No work shall be done on any steel between the tempera- ture of boiling water and of ignition of hard wood saw dust. 1 14. The tensile strength, limit of elasticity and ductility, shall be determined from a standard test-piece, cut from the finished material, of at least y^ square inch section. All brok- en samples must show a silky fracture of uniform color. 115. 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 matrial is to be similarly treated before testing. 1 1 6. Every finished piece of steel shall be stamped with the blow number identifying the melt. 117. Steel shall be of three grades: Rivet, Soft and Medium. 118. Rivet steel shall have: Ultimate strength, 50,000 to 58,000 pounds per square inch. Elastic limit, not less than one-half the ultimate strength. Elongation, 26 per cent in 8 inches. Bending test, after or before heating to a light cherry red and cooling in water, 180 degrees flat on itself, without fracture on outside of bent portion. 119. Soft steel shall have: Ultimate strength, 54,000 to 62,000 pounds per square inch. Elastic limit, not less than one-half the -ultimate strength. Elongation, 25 per cent in 8 inches. Bending test, after or before heating to a light cherry red and cooling in water, 180 degrees flat on itself, without fracture on outside of bent portion. 1 20. Medium steel shall have : Ultimate strength, 60,000 to 68,000 pounds per square inch. Elastic limit, not less than one-half the ultimate strength. Elongation, 22 per cent in 8^ inches. Bending test, 180 degrees to a diameter equal to thickness of piece tested, without fracture on outside of bent portion. 121. 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 SPECIFICATIONS 359 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. 122. Pins made of either of the above mentioned grades of steel shall, on specimen test pieces cut from finished mate- rial, fill the requirements of the grade of steel from which they are rolled, excepting the elongation, which shall be decreased 5 per cent from that specified. 123. In steel */% inch or less in thickness punched rivet holes, pitched two diameters from a sheared edge, must stand drifting until the diameter is one-third larger than the original hole, without cracking the metal. 124. The slabs for rolling plates shall be rolled from ingots of at least twice their cross-section. 125. Pins up to 7 inches diamater shall be rolled. 126. A variation in cross-section or weight of rolled material of more than 2^ per cent from that specified, may be cause for rejection, except in the case of plates which will be covered by the manufacturer's standard specifications (Cambria Steel, page 345). STEEI, CASTINGS. 127. Steel castings shall be made of open hearth steel containing from 0.25 to 0.40 per cent, and not over 0.08 per cent of phosphorus nor 0.05 per cent sulphur, and shall be practically free from blow holes. CAST IRON. 128. Except where chilled iron is specified, all castings shall be of tough, gray iron, free from injurious cold shuts or blow holes, true to pattern, and of workmanlike finish. Test bars one inch square, loaded in middle between supports 12 inches apart, shall bear 2,500 pounds or over, and deflect 0.15 of an inch before rupture. WROUGHT IRON. 129. All wrought iron must be tough, ductile, fibrous and of uniform quality. Finished bars must be thoroughly welded Pin Steel. Drifting. Slabs for Plates. Pins. Variation in Weight. Steel Castings. Cast Iron. Character and Finish. APPENDIX Manufacture. Standard Test Piece. Elastic Limit. Tension. Bending Test. Timber. Painting. during the rolling, and be straight, smooth and free from in- jurious seams, blisters, buckles, cracks or imperfect edges. 130. No specific process or provision of manufacture will be demanded, provided the material fulfills the requirements of these specifications. 131. The tensile strength, limit of elasticity and ductility, shall be determined from a standard test piece of as near square inch sectional area as possible. The elongation shall be measured on an original length of 8 inches. 132. Iron of all grades shall have an elastic limit of not less than 26,000 pounds per square inch. 133. When tested in specimens of uniform sectional area of at least y 2 square inch the iron shall show a minimum ulti- mate strength of 50,000 pounds per square inch, and a mini- mum elongation of 18 per cent in 8 inches. 134. All iron for tension members must bend cold through 90 degrees to a curve whose diameter is not over twice the thickness of the piece, without cracking. When nicked on one side and bent by a blow from a sledge, the fracture must be mostly fibrous. TIMBER. 135. The timber shall be strictly first-class spruce, white pine, Douglas fir, Southern yellow pine, or white oak timber ; sawed true and out of wind, full size, free from wind shakes, large or loose knots, decayed or sapwood, wormholes or other defects impairing its strength or durability. PAINTING. 136. All iron work before leaving the shop shall be thoroughly cleaned from all loose scale and rust, and be given one good coating of pure boiled linseed oil or paint as speci- fied, well worked into all joints and open spaces. 137. In riveted work, the surfaces coming in contact shall each be painted before being riveted togetlier. 138. Pieces and parts which are not accessible for paint- ing after erection shall have two coats of paint. ' SPECIFICATIONS 139. The paint shall be a good quality of red lead or graphite paint, ground with pure -linseed oil, or such paint as may be specified in the contract. 140. After the structure is erected, the iron work shall be thoroughly and evenly painted with two additional coats of paint, mixed with pure linseed oil, of such quality and color as may be selected. Painting shall be done only when the surface of the metal is perfectly dry. No painting shall be done in wet or freezing weather unless special precautions are taken. 141. Pins, pin holes, screw threads and other finished surfaces shall be coated with white lead and tallow before being shipped from the shop. INSPECTION. 142. All facilities for inspection of material and work- manship shall be furnished by the contractor to competent in- spectors, and the engineer and his inspectors shall be allowed free access to any part of the works in which any portion of the material is made. 143. The contractor shall furnish, without charge, such specimens (prepared) of the several kinds of material to be used as may be required to determine their character. 144. Full sized parts of the structure may be tested at the option of the purchaser; but, if tested to destruction, such material shall be paid for at cost, less its scrap value, if it proves satisfactory. 145. If it does not stand the specified tests, it will be con- sidered rejected material, and be solely at the cost of the con- tractor. ERECTION. 146. The contractor shall furnish at his own expense all necessary tools, staging and material of every description re- quired for the erection of the work, and remove the same when the work is completed. 147. The contractor shall assume all risks from storms or accidents, unless caused by the negligence of the owner, 361 Inspection. Testing. Tool?. Risks. 362 APPENDIX and all damage to adjoining property and to persons until the work is completed and accepted. The contractor shall comply with all ordinances or reg- ulations appertaining to the work. The erection must be carried forward with diligence and must be completed promptly. INDEX Page. Aglebraic calcuation of stresses see Stresses. Allowable sections 285 Anchorage of columns 101 Anti-condensation roofing 201 Arch see Two-hinged and three- hinged arches. Asbestos roofing 218 Asphalt paint 295 Asphalt roofing 217 A. T. & S. F. Locomotive Shops.. 323 Bearing power of piles 233 Bearing power of soils 232 Bending moment in beams 31, 54, 55, 57. Boyer plant 151 Bracing 84 Brick arch floors 248 Brick floors 248 Bridge trusses, stresses in ^ Camel Back 70 Pratt 67 Warren 65 Also, see Stresses. Brown & Sharp foundry 150 "Buckeye" flooring 252 Buckled plates 254 Carbon paint 289 Carey's roofing 219 Center of gravity 32 Cement floors 240 Choice of sections 284 Circular ventilators 276 Cleaning the surface of steel.... 292 Coal-tar paint 295 Columns Design of 177 Details 167, 168, 169, 336 Pressure on masonry 238 Types of 165 Combined stresses 129 Compression and cross bending 131 Tension and crossbending 134 Stress in bars due to weight.. 135 Diagram for stress in bars due to weight 135 Concentrated moving loads 5) Concentrated load shear 54 Concentrated load stresses 51 Concrete buildings 228 Concrete slabs 220 Conkey printing plant 150 Corrosion of steel 286 Corrugated floor 253 Corrugated steel Anti-condensation lining 201 Corner finish 194 Cornice 197-201 Cost of 204 Details 192 Diagram for safe loads 190 Flashing 193 Fastening 187 Gutters and Conductors 194 Design of 195 Plans 204 Plans for transformer 205 Roofing ' 206 Rotary shear for cutting 187 Ridge roll 192 Standard sheets 186 Steel lists for transformer building Strength of 190 Tests of r!91 Weight of 8, 185 Cost see estimate of cost, and cost under different items. Estimate of 302, 305 Of miscellaneous materials 311 Standard hardware lists 313 Of material 307 Of mill details shop work 309 Crane girders 184 Details of 336, 338 Deformation diagram /120 Details see Article for which de sign is wanted. Details seeArticle for which de- tails are wanted. Diagram for stress in bars due to their own weight 135 364 INDEX Diffusion of light 257 Doors. Paneled .278 Wooden 278 Sandwich 279 Steel 279 Details for 281 Cost of 281 Fastening Corrugated Steel 187 Ferrohiclave 220, 253 Finishing cost of paint .294 Floors '....'.239 Brick 242 Brick arch 248 Buckled plates 254 "Buckeye" fireproof 252 Cement 240 Corrugated 253 Corrugated iron arch 240 F/xpanded metal 250 Ferroinclave 253 Roebling 251 Multiplex steel 253 Steel plates 254 Tar concrete 242 Wooden 240 Foundations Bearing power of piles. 233 Bearing power of soils 232 Design of footings 238 Pressure of walls on foundation 235 Pressure of pier on foundation 23C Pressure of column on masonry 238 Hardware lists 313, 314 Girders, crane 184 Girders, design of 181 Glass Amount of light required 268 Cost of 262 Details of windows 265 Diffusion of light 257 Double glazing 265 Kinds of 256 Factory ribbed 257 Maze 257 Plane 256 Plate 256 Prisms 257 Ribbed 257 Wire 257 Window . .256 Relative value of different kinds 257 Placing the glass 260 Size of 262 Window shades 261 Granite roofing 219 Gravel roofing 214 Ground floors 239 Iron oxide 289 Iron, classification 308 Iron, corrugated see Corrugated steel. Lead 287 Linseed oil 287 Lists, standard hardware. . . .313, 314 Loads Dead loads 4 Weight of covering 8 Weight of cranes 18 Weight of girts 8 Miscellaneous material 19 Weight of purlins S Weight of structure 9 Loads on simple roof trusses. 45 Snow loads 10 Wind loads 12 Miscellaneous loads 17 Live loads on floors 17 Locomotive shops A. T. & S. F 159, 323 Oregon Short Line 157 Philadelphia & Reading 328 St. L. I. M. & S 158 Union Pacific 158 Methods of calculations Algebraic moments 42, 70 Algebraic resolution 38, 63 Graphic moments 44, 71 Graphic resolution 40, 68 Also see Stresses. Mill buildings General design of 141 Specifications for 341 Types 1 Masonry walls 3 Masonry filled walls 2 Steel frame I Miscellaneous loads Live loads on floors. . .17 INDEX 365 Wright of electric cranes 18 \\ Vi^'lit of hand cranes , . . 18 Weight of miscellaneous ma- terial 19 Miscellaneous structures. A. T. & S. F. shops 159, 323 Philadelphia & Reading shops 328 St. Louis Coliseum 319 Steam Engineering Buildings Brooklyn Navy Yard 337 su-el Dome West Faden Hotel 315 Mixing paint 290 Moment or inertia of areas 3C Moment of inertia of forces 33 Oulmann's method I 33 Mohr's method 34 Moments Algebraic 42, 54, 55, 70 Graphic 30, 44, 54, 55, 71 Moments in beams. Concentrated loads 54 Concentrated moving loads.... 57 Uniform loads 55 Uniform moving loads 57 Monitor ventilators 273 Multiplex steel floor ^. . 253 Oil, linseed ,. 287 CHI, paint 286 Paint. Applying the 291 Aspahlt 295 Carbon 289 Cement paint 295 Cleaning the surface 292 Coal-tar paint 295 Cost of 292 Covering capacity 290 Finishing coat 294 Iron oxide 289 Lead 288 Linseed oil 287 Mixing the 290 Oil paints . 286 Priming coat 293 Proportions 290 References on paint .296 Zinc 289 Painting Applying the paint 291 Cost of 293 Cleaning the surface 292 Paneled doors 278 Philadelphia & Reading shops 328 Pitch of roof 153 Pitch of trusses 154 Plate girders 181 Polygon. Equilibrium 24 Force 22 Moment 71, S4, 55, 57, 59 Shear 72, 54, 55, 57, 59 PoYtals Anchorage of columns 101 Stresses in Continuous portals 103 Double portal 104 Simple portals, columns hinged Algebraic solution 96,98 Graphic solution 98 Simple portals, columns fixed. Algebraic solution 101 Graphic solution 103 Portland cement paint 296 Pressure of columns on masonry 238 Pressure of pier on foundation. . .235 Pressure of wall on foundation. .23C Proportions of paint and oil.... 290 Purlins 173 Reactions of Beams 27, 53 Cantilever truss 28 Overhanging beam 53 , Three-hinged arch 106, 107 Two-hinged arch 114, 117, 119 Resolution Algebraic 38, 63 Graphic 40, 68 Red lead 288 References on paint and painting 296 Roebling floor 251 Roof, pitch of 153 Roof trusses, see Trusses. Stress in see Stresses. Roof coverings for railway build- ings 221 Roofing. Asbestos 131, 218 Asphalt 217 Carey's 219 Corrugated steel 206 Cost of 206, 222 3 66 INDEX Examples of 221 Ferroinclave 220 Granite 219, 222 Gravel 214, 222 Paroid 222 Ruberoid 219, 222 Slag 216, 331 Sheet steel 213, 222 Slate ....207, 221, 222 Sparham 222 Tile 210, 221, 222 Ruberoid roofing 219 Saw tooth roofs 143, 149, 150, 151, 151, 152, 164, 324, 325. Boyer plant 151 Brown & Sharp foundry 150 Conkey prntiing plant 150 Locomotive shop 152 Matthessen & Hegeler shops . . . 164 Sections, choice of 284 Shear in beams, for Concentrated loads 54 Concentrated moving loads .... 59 Uniform moving loads 57 Shear polygon, see Polygon. Sheet steel roofing 213 Shingle roofs 218 Shop cost 309 Shop costs, actual 311 Side walls Concrete slabs 226 Corrugated steel ..223 Expanded metal and plaster. . . .223 Masonry walls 227 Thickness of 227 Skylights ....> 261 Details of 265 Slate roofing 210 Slag roofing 216^ 331 Snow loads 10 Sparham roofing 221 Specifications for Steel Frame Mill Buildings Appendix I.. 341 Standard hardware lists 313, 314 Steam engineering buildings for Brooklyn Navy Yard 337 Stress in bars due to weight. .. .135 Stresses, allowable 144, 174 Also see Appendix 1 341 Stresses in Bracing 84 Bridge trusses see Trusses. Portals see Portals. Roof trusses see Roof trusses. Transverse bent see Transverse bent. Three-hinged arch see Three- hinged arch. Two-hinged arch see Two- hinged arch. Stresses. Calculation of 20 Combined 138 Eccentric 129 Struts and bracing . 173 Tar concrete floors 242 Three-hinged arch Calculation of stresses 106 Dead load 108 Reactions Algebraic method 106 Graphic method 107 Wind load stresses Ill Timber floors 248, 243 Tile roofing 210 Tin roofs 211 Translucent fabric 264 Cost of 265 Transverse bent Details 162, 164 Transverse bent, stresses in Dead load 75, 86 Maximum 83, 93 Snow load 75 Wind load Algebraic calculation 76 Columns fixed 79 Columns hinged 76 Graphic colculation Case 2 88 Case 3 90 Case 4 91 Case 5 96 Trusses. Economic spacing of 154 Design of 174 Details of 159, 161, 334 Pitch of 152, 164 Saw tooth see Saiw tooth roofs. Types 146, 152 Trusses, stresses. Bridge trusses. Algebraic moments 70 INDEX 367 Algebraic resolutions 63 Graphic moments 71 Graphic resolutions 68 Roof trusses. Algebraic moments 42 Algebraic resolution 38 t.rnphic moments 44 (Graphic resolution 40 Concentrated load 51 Dead load . 45 Dead and ceiling load 46 Snow load 47 Wind load 47, 48, 49 Two-hinged arch. Design of 127 Two-hinged arch, stresses. Calculation of reaction 114 Algebraic solution 117 Graphic solution 119 Dead load 121 Dead and wind load 123 Temperature stresses 126 With horizontal tie . ..125 Ventilators 173 Ventilators 273 Monitor 273 Cost of 273 Circular 276 Cost of 277 Walls, masonry 227 Walls, side 223 Weight, estimate of 297 West Baden dome 315 Window shades 261 \v r indows. Amount of light 268 Cost of 263 Details of 265, 268 Double glazing 265 Glass see Glass. Wooden doors 278 Wooden floors . . .243 Zinc paint 3ITV THIS BOOK IS DUE ON THE LAST BATE STAMPED BELOW AN INITIAL FINE OF 25 CENTS WILL. BE ASSESSED FOR FAILURE TO RETURN THIS BOOK ON THE DATE DUE. THE PENALTY WILL INCREASE TO SO CENTS ON THE FOURTH DAY AND TO $1.OO ON THE SEVENTH DAY OVERDUE. NOV 17 1932 FB 4 IN STACKS APR 61978 IN STACKS OCT 6 1977 BEG. CIR. SEP 12 78 LD 21-50nt-8,'32 UNIVERSITY OF CALIFORNIA LIBRARY