FORT DEARBORN HOTEL, CHICAGO Holabird & Roche, Architects STEEL CONSTRUCTION A TEXT AND REFERENCE BOOK COVERING THE DESIGN OF STEEL FRAME- WORK FOR BUILDINGS By HENRY JACKSON BURT, C.E. MEMBER AMERICAN SOCIETY OP CIVIL ENGINEERS MEMBER WESTERN SOCIETY OF ENGINEERS MEMBER SOCIETY FOR THE PROMOTION OF ENGINEERING EDUCATION STRUCTURAL ENGINEER FOR HOLABIRD AND ROCHE, ARCHITECTS ILLUSTRATED AMERICAN TECHNICAL SOCIETY CHICAGO 1914 I COPYRIGHT, .1914, BY AMERICAN TECHNICAL SOCIETY COPYRIGHTED IX GREAT BRITAIN ALL BIGHTS RESERVED CONTENTS PAGE Introduction 1 Method of manufacture 9 Steel sections adaptability and use 23 Properties of sections 35 General information 40 Quality of material 42 Standard specifications 42 Discussion of important features 44 Unit stresses 49 Rivets and bolts 52 Beams 75 Review of theory of beam design 76 Calculation of load effects 80 Calculation of resistance 97 Practical applications 113 Details of construction 120 Riveted girders 134 Theory of design 135 Design of plate girder 137 Other forms of riveted girders . . . . 158 Practical applications 162 Details of construction 165 Compression members columns 173 Steel columns 173 Loads and their effects 173 Strength of columns formulas 179 Column sections * 181 Tables 188 Details of construction 216 Cast-iron columns 225 Characteristics 225 Strength formula 228 CONTENTS PAGE Compression members columns Cast-iron columns Tables 230 Details of construction 232 Tension members 233 Loads and their effects 233 Sections 235 Details of connections 23? Wind bracing 239 General conditions 239 Systems of framework , . . 243 Design of wind-bracing girders 255 Combined wind and gravity stresses in girders .262 Effect of wind stresses on columns , 266 Practical design a sixteen-story fireproof hotel 269 Fireproof specifications 294 Loads 295 Type of floor construction 301 Framing specifications 306 Design of steel members 309 Column pedestals 319 Wind bracing 322 Miscellaneous features 327 Dimensioning drawings 329 Protection of steel 333 Protection from rust 333 Rust formation 333 Paint 335 Protection from fire -. 339 Specifications , 349 General characteristics 350 Example of specifications 353 Index... ..373 INTRODUCTION A GREAT part of the satisfaction derived from the practice of engineering comes from seeing the "dreams come true". The engineer is commonly assumed to deal with facts and to be guided by mathematical relations. While this is true, he must at times be a dreamer, a man with an active imagination. Before a line is drawn or a figure placed on paper, the engineer must have some conception of the structure he is to create. The more definite this conception, the more readily it can be committed to paper in the form of drawings. The mention of a building of a certain dze or for a certain purpose brings a vision of the skeleton to support it; the architect's perspective or elevation suggests the columns concealed within the piers and the girders behind the spandrels; the floor plans indicate the location of columns, girders, and joists which will be required to support the floors, partitions, and walls. From these mental pictures, the design drawings can be evolved by applying the mathematical relations to deter- mine the sizes of members required. Part8 of converter it has become Charged during the Ope- Courtesy McGraw-Hill Publishing Company \. ,N 14 STEEL CONSTRUCTION ration and which would render the steel unfit for use. The silicon is added to get rid of the gases which are contained in the bath. After adding these materials, or "recarburizing" as it is called, the metal is poured into ingots which are allowed to solidify, and then rolled, while hot, into the desired sizes and forms. The character- istics of the Bessemer process are: (a) great rapidity of purification, say ten minutes per "heat"; (b) no extraneous fuel is used; and Fig- 7. Section Through Bessemer Converter While Blowing From Stoughton's "Metallurgy of Iron and Steel" Courtesy McGraw-Hill Publishing Company (c) the metal is not melted in the furnace where the purification takes place. " Acid Open- Hearth Process. The acid open-hearth furnace is heated by burning within it gas and air, each of which has been highly preheated before it enters the combustion chamber. A sec- tion of the furnace is shown in Fig. 9. The metal lies in a shallow pool on the long hearth, composed of silicious material, and is STEEL CONSTRUCTION 15 heated by radiation from the intense flame produced as described. The impurities are oxidized by an excess of oxygen in the furnace gases over that necessary to burn the gas. This action is so slow, however, that the 3 to 4 per cent of carbon in the pig iron takes a Fig. 8 A Bessemer Blow From Stoughton's "Metallurgy of Iron and Sieel" Courtety McGra\c~H\U Publishing Company long time for combustion. The operation is therefore hastened iu two ways: (a) iron ore is added to the bath, and (b) the carbon is diluted by adding varying amounts of cold steel scrap. The steel 16 STEEL CONSTRUCTION scrap is added to the furnace charge at the beginning of the process, and it takes from 6 to 10 hours to purify a charge, after which we recarburize and cast the metal into ingots. The characteristics of the open-hearth process are: (a) long time occupied in purifica- tion; (b) large charges treated in the furnace (modern practice is usually 30 to 70 tons to a furnace) ; (c) at least part of the charge melted in the purification furnace; and (d) furnace heated with preheated gas and air, Fig. 10. "Basic Open- Hearth Process. The basic open-hearth operation is similar to the acid open-hearth process, with the difference that we Fig. 9. Section of Regenerative Open-Hearth Furnace From Stoughton's "Metallurgy of Iron and Steel" Courtesy McGraw-Hill Publishing Company add to the bath a sufficient amount of lime to form a very basic slag. This slag will dissolve all the phosphorus that is oxidized, which an acid slag will not do. We can oxidize the phosphorus in any of these processes, but in the acid Bessemer and the acid open- hearth furnaces the highly silicious slag rejects the phosphorus, and it is immediately deoxidized again and returns to the iron. The characteristics of the basic- open-hearth process are the same as those of the acid open-hearth with the addition of: (e) lime added to 18 STEEL CONSTRUCTION produce a basic slag; (f) hearth lined with basic, instead of silicious, material, in order that it may not be eaten away by this slag; and (g) impure iron and scrap may be used, because phosphorus, and, to a limited extent, sulphur can be removed in the operation. " Rolling the Ingots. The steel in the ingot is in its final condi- tion as to chemical composition, Figs. 11 and 12, and must now be Fig. 11. Steel Ingots Incased in the Molds and Resting on Car From Stoughton's Metallurgy of Iron and Stee Courlrxy MrGm w-llill Publish iinj Company worked into the shapes required for structural uses. This is done by passing the steel between rolls. Rolls are used in pairs, called a "two-high mill", as shown in Fig. 13, or in sets of three, called a ''three-high mill", as shown in Fig. 14. As the piece goes through the same mill se-seral times, the two-high mill must be reversed for each pass or else the piece must be taken over or around the mill between the successive passes. These disadvantages are eliminated by the use of the three-high STEEL CONSTRUCTION 19 mill, in which the rolls rotate continuously and work is done on the piece as it passes back and forth. Blooming. Before going to the rolls, the ingot is placed in a furnace, called the ''soaking pit", in which it is heated to a high temperature. In passing between the rolls, Fig. 13, a heavy pres- sure is exerted on the metal, which reduces it in thickness, in-. creases it in width to some ex- tent, and extends it greatly in, length. If the material is des- tined to be made into plates, it is rolled into a slab in the first set of rolls; if it is for structural shapes, the ingot will be turned alternately from side to edge in passing through the rolls so that it will be kept approximately square in section until it is reduced to the proper size for beginning to form the shape. At this stage it is called a "bloom" and the rolls are called "blooming rolls", Fig. 15. Fig. 12. Stripping the Ingots Courtesy McGraw-Hill Publishing Company Fig. 13. Action on Steel in "Two-High" Mill Fig. 14. Action on Steel in "Three-High" Mill Courtesy McGraw-Hill Publishing Company Courtesy McGraw-Hill Publishing Company Roughing and Finishing Holls. The next step is to pass the steel through the roughing rolls. These rolls are grooved in such .20 STEEL CONSTRUCTION Fig 15. "Two-High" Blooming Rolls Courtesy Ufa man. Slccth Cum pony a way that the successive passes gradually develop the metal toward the required shape. Finally it goes through the finishing rolls which bring the section to the required shape and size. This process is clearly illustrated by Figs. *16, 17, 18, 19, and 20. Fig. 16. "Three-High" I-Beam Roughing Rolls Courtesy Seaman, Sleeth Company *Catalogue of Phoenix Roll Works, by permission. STEEL CONSTRUCTION Fig. 17 'Three-High" I-Beam Finishing Rolls Courlesy Seaman, Sleeth Company "HO I iff II Fig. 18. "Three-High" Equal Angle Roughing Rolls Courtesy Seaman, Sleeth Company 22 STEEL CONSTRUCTION Fig. 19. "Three-High" Equal Angle Finishing Rolls Courtesy Seaman, Sleeth Company Plate Rolls. A three-high set of plate rolls is shown in Fig. 21. There is nothing to control the width of the plates, therefore the edges -of plates rolled in this mill will be uneven and must be sheared to the correct width after the rolling is completed. Such plates are known as ' 'sheared plates." Vertical rolls can be placed in front of the horizontal rolls to Fig. 20. "Three-High" Z-Bar Rolls Courtesy Seaman, Sleeth Com pa MM STEEL CONSTRUCTION 23 control the width, as shown in the left-hand view, Fig. 22. Such a mill is called a "Universal Mill" and the plates produced by it are Fig. 21. "Three-High" Chill Plate Rolls Courtesy Seaman, Sleeth Company called "Universal Mill plates," or edged plates. Fig. 22 is a special form known as the Grey mill and is used by the Bethlehem Steel Company for making I-beams and column sections. Fig. 23 is a 3-high Universal Mill manufactured by the United Engineering and Foundry Company, Pittsburgh. H P V P P P I IK L'2. Vnivorsul Mill for Rolling Bethlehem Beams STEEL SECTIONS ADAPTABILITY AND USE Classification of Sections. Structural steel members are gener- ally designated by the shapes of their cross sections. Thus a member whose cross section has the shape of a capital letter I is called an I-beam. The other important sections are channels, angles, zees, STEEL CONSTRUCTION 25 tees, and H-sections, whose shapes are indicated by the names. Round and square members are called "rods" and "bars". Flat members six inches wide and less are usually designated as "bars" or "flats". Flat members wider than six inches are designated as "plates". Structural sections are frequently designated as "plates" and "shapes". In general, the structural shapes are standard. Standard Sections. The shapes in common use conform to the standards of the Association of American Steel Manufacturers. These standard shapes as made by the various manufacturers are identical in dimensions and weights; therefore, in designing it is only necessary to specify the sections and not the name of the manufacturer. Special Sections. In addition to the standard sections, most manufacturers make some special sections. Some of these are now so common that they are as available as standard sections, but generally it is advisable for the designer to give the name of the manu- facturer in specifying them. The handbooks indicate which sections are standard and which are special.* The designer should generally use only standard sections. This matter is given full consideration elsewhere in this text. Use the handbook for con- stant reference in the following discussion of the sections. I -Beams. Standard Sections. An I-beam, Fig. 24, is designated by the depth and the weight per lineal foot, thus: 12" I 31 J# Fig. 24. Details of Standard The standard depths are 3, 4, 5, 6, 7, 8, 9, 10, 12, 15, 18, 20, and 24 inches, respectively. For each depth there are several standard weights. Most of the mills also make some special weights, viz: 12" deep weighing 40 to 55 # 15" deep weighing 60 to 80 # 15" deep weighing 80 to 100# 20" deep weighing 80 to 100 # *The 1903 edition of the "Carnegie Handbook" used the term standard in relation to beams and channels to apply to the minimum weight of each size. It is preferable to limit the use of the term to the sections adopted by the Association of American Steel Manufacturers. 26 STEEL CONSTRUCTION Carnegie Sections. The Carnegie Steel Company rolls some additional sizes of special beams which are similar to the standard beams, as follows: 24" deep weighing 105 to 115# 18" deep weighing 75 id 100 # It also rolls special sizes of certain depths which are lighter than the minimum weight standard beams. They are as follows: *10" I 22 # 18" I 46 # 12" I 27| # 21" I 57J # 15" I 36 ^ 24" I 69| # 27" I 83 # A distinctive feature of these beams is that the fillets connecting flange to web form a compound curve instead of a simple curve as in the standard beams. Bethlehem Sections. The Bethlehem Steel Companyt makes a series of special I-beams ranging in depth from 8 to 30 inches. The minimum weights of these beams are about V*?^Uy 10 P er cen t l ess than the minimum weights of the corresponding standard beams. The section is so designed that the theoretical strength of the minimum section is about the same as that of the standard section. This is accomplished by putting less metal in the web and more in the flanges. Fig. 25 gives the dimensions of the Bethlehem 15" I 38 #. Comparison with the corresponding standard beam shows: 15"I38# 15"I42# Web thickness .28" .41* Flange width 6.66* 5.50* Moment of inertia 442 .60 441 . 80 The Bethlehem Company also makes a series of girder beams ranging in depth from 8 to 30 inches. These beams are much * Apply to the nearest office of the Carnegie Steel Company or the Illinois Steel Company, for a circular giving the properties of these beams, or see "Pocket Companion/' Carnegie Steei Company, 1913. t Complete data are fciven in the^Corapany's handbook. STEEL CONSTRUCTION 27 heavier than either the standard beams or the Bethlehem special beams and the flanges are also much wider. Fig. 26 gives the dimensions of the Bethlehem girder 15"X73#. Efficiency of Minimum Sections. Note in the handbook that the weights of beams of a given depth _ I05& . _ are grouped. The beams in a group are rolled with the same rolls, the min- imum section being produced when the rolls are set close together, and the heavier sections being made by spread- ing the rolls. In this change the depth remains constant, while the web is thick- ened and the flanges widened. In Fig. 27, the shaded portion represents the Fig 26 ' Brthw * Girder 15 ' X73 # minimum section, and the unshaded portion represents the metal added to produce the heavier section. From this it is clear that most of the added metal is in the web, and is not placed to such good advan- tage as the metal in the minimum section. The increased strength is not nearly so great as the increased weight. For example, compare 15" I 42 # with 15" I 60# of the same group. The increase 1 R /| BB2^HH 8' SLOPE C4T sff/HDiUS 7^"7^T-~ ^ in weight is 18 pounds, or =43%. The increase in strength as indicated by the change in the moment of iner- tia from 441.8 to 538.6 is 96.8, or Fig. 27. Showing Method of In- creasing Section of I-Beama ence is 70.4, or Thus it appears that the minimum weight of each group is the most efficient. As a consequence the range in weight from a given set of rolls is limited to about 20 pounds. When a greater range is required for a given depth of beam, more than one set of rolls is used. Now compare the standard 15" I 60$ and the special 15" I 60 #. Their respective mo- ments of inertia are 538.6 and 609.0. The differ- 70.4 . = 13%. This illustrates the -advantage of 538.6 having the additional set of rolls. More than one set of rolls is provided for 12-inch, 15-inch, 18-inch, 20-inch and 24-inch beams. STEEL CONSTRUCTION PROBLEM Make full-size drawings on tracing paper of the following sections: Standard 15" I 42# Standard 15* I 55# Special 15" I 60# Special 15" I 80# Special 15" I 100# Carnegie 15" I 36# Bethlehem 15" I 38# Bethlehem 15" GB 73# L Superimpose these tracings and note the difference in thickness of web, width of flange, and shape of fillets. Characteristics and Uses. An inspection of an I-beam section shows it is much stiffer in one direction than in the other. The section is designed to resist bending in one direction only, i. e., in the plane of the web of the beam. The I-beam is used almost exclusively for this purpose, though to a limited extent it is used in built-up columns. When used in a column, it is economical only when com- bined with other sections to give stiffness in both directions. It is sometimes used alone as a column when the limitations of space offset the lack of economy in weight. Beams less than 6 inches deep are not Fig. 28. Details of Channel of ten used in the framework for buildings. On many jobs the minimum is 8 inches. Channels. Standard and Special Sections. A channel, Fig. 28, is designated by the depth and the weight per lineal foot, thus: 15" C33# The standard depths are 3, 4, 5, 6, 7, 8, 9, 10, 12, and 15 inches, respectively. For each depth there are several weights. A number ' of special sizes and weights are made but they are not much used for structural purposes. The Cambria Steel Company makes a group of channels 18 inches deep, weighing from 45 to 60 pounds. The weights of channels are increased in the same manner as the weights of beams, Fig. 29, and the comments regarding beams in this respect apply to them. Characteristics and Uses. Channels, like beams, are much stronger in one direction than in the other. This makes them suit- STEEL CONSTRUCTION 29 Fig. 29. Show- ing Method of Increasing Sec- tion of Chan- able for use as beams when the loads are applied in the plane of the web. However, they are not so economical as I-beams and require more lateral support to keep them from buckling. Hence, they are not used for this ' purpose except when there is some condition which makes them specially suitable. This occurs around wellholes in floors, against walls, where nailing strips are to be bolted on, in wall spandrels or lintels, etc. The most important use of channels is in the construction of columns and truss members. For this purpose they are used in pairs connected to- gether with lacing, tie plates, or cover plates. They are also used to some extent for girder flanges and for many miscellaneous purposes. , Angles. Standard and Special Sections. There are two styles of angles: angles with equal legs and angles with unequal legs, Fig. 30. An angle is designated by the lengths of the legs and the thickness or the weight per lineal foot, thus: L 4" X 4" X I" or L4"X4"X 15.7 #. L 6" X 3i" X f or L6"X3f Xll.7# The standard sizes of angles with equal legs are 1J, 2, 2J, 3, 3J, 4, 6, and 8 inches, respectively. There are a number of special sizes, the most important of which is 5 inches. The If -inch angle is seldom used in structural work. The standard sizes of angles with unequal legs are 1\" X 2", 3" X 2J*, 3J" X2i", 3|"X3", 4"X3", 5*X3', 5'X3i", 6"X3i", 6" X 4". The important special sizes usually obtain- able are 3' X 2", 1" X 3i", 8" X 6". Each size of angle is furnished in several thicknesses varying by tV inch. Although some of the smaller sizes of angles are made -THICKNESS SHORT LG f Fig. 30. Details of Angle Sections 30 STEEL CONSTRUCTION in less thickness than J inch, this is the minimum that should be used for structural purposes. On important work the minimum should be f inch. The minimum and maximum thickness, for the several sizes are given in the handbook and need not be repeated here. Angles are increased from the minimum thickness by spreading the rolls. In Fig. 31 the minimum thickness is shaded and the added metal unshaded. As the thickness is increased, a correspond- ing amount is added to the length of each leg. In the case of larger sizes, some mills use two sets of rolls, as has been described for I-beams. This additional length of the legs of angles must be taken into account in allowing for clearance. The Fig. 31. showing actual length of legs for any angle is easily com- Sc^n'oTA^- puted, thus: L 3" X 3" X f ; minimum thickness for this size J", increase over minimum f", length of leg 3" + f = 3|". PROBLEM Compute the actual lengths of legs for the maximum thickness of all the standard and special angles listed in the handbook. Assume a second set of rolls is used on the following sizes: S'X^XiV'; 4"X4"Xi"; Sfc'XSi'X**; 5"xsrxr; 5"x3"xr; 4"xsrxr; 4"x3"xr; 6"x3rxiV; 6*X4"XiV'; 5"X5"XjV'; 6"X6"XH"; 7"X3rxf; S"XQ"X%": 8"X8"Xi". Record the results in the handbook in the tables of "Properties." The results in the above problem may not agree with the sizes of angles furnished by the various mills but will be sufficiently exact for the uses of the designer. Characteristics and Uses. Angles are the most adaptable of the structural sections. They are used with plates or other shapes in built-up mem- bers, such as columns, plate girders, etc.; for connecting members together, as beams and girders to columns; as beams for special conditions of loading, as lintels; Fig - 32 - Details of Zee Bar singly or in pairs as struts; singly or in pairs as tension members. Zees. Standard Sections. A Zee, Fig. 32, is designated by its nominal depth and thickness, thus: Z3"X|" The sizes listed by the Carnegie Steel Company are 3, 4, 5, and 6 STEEL CONSTRUCTION 31 inches, respectively. The thicknesses vary by T V inch. The mini- mum and maximum thicknesses are: for 3" Z, r and ft' for 4' Z, fand f for 5" Z, A" and * for 6" Z, f * and }' Zees are increased in thickness by spreading the rolls. In Fig. 33 the shaded portion indicates the minimum section, and the unshaded part the additional section. The thickness of its web and flanges are increased equally, and thereby the depth of web and width of flange are increased by the same amount. Three sets of rolls are used . Fig. 33 Showing for each depth, so that the overrun is yV inch for "JJjSng Section 3-inch zees and J inch for larger sizes. of Zee3 Uses. Zee bars have been used extensively for columns, but they are rapidly becoming obsolete and should not be used unless there is some special reason for so doing. Tees. Standard Sections. A Tee, Fig. 34, is designated by the width of flange, length of stem, and weight per lineal foot, thus: T4" X 3"X9.3# T3" X 4"X9.3# always giving the width of flange first. Some recent handbooks do not list tees. The sizes that have been available range from T X 1" X 1.0# to 5" X 3" X 13.6# with more than* 50 intermediates. These are listed and their properties given in the Carnegie Steel Company's "Pocket Companion", 1913. edition. Characteristics and Uses. As indicated above tees are going out of use, and as the demand decreases they will become more Fig. 34. Typical Tee Sections difficult to obtain. The section is not an economical one for the common uses of structural steel. It is not efficient as a beam or as a strut, and is not suited for use in built-up sections. 32 STEEL CONSTRUCTION It is well adapted for supporting book tile in ceiling and roof construction, Fig. 35. In cases where the T-section is needed to Fig. 35. Section Showing Tees Supporting Book Tile meet any special condition it can be made up of two angles placed back to back. In this manner a large variety of tees can be made. Plates. Standard Sizes. A Plate, Fig. 36, is designated by its width and thickness, thus: PL 48" X T V or by its width and weight per square foot, thus:' PL 36" X 10.2 # The former method is used on design drawings for structural steel work, and the latter on mill orders and shop details, also on design drawings for tank work. Plates are made in thicknesses varying by iV inch from y\ inch up to 2 inches. Steel plates thinner than i\ inch are called "sheets'* and are not used for structural work. The minimum thickness com- monly used is \ inch, and on many jobs nothing less than f inch is per- mitted. Plates thicker than 1 inch are seldom used on account of - THICKNESS Fig. 36. Rolled Steel Plate difficulty in punching. When a greater thickness is needed, it is made up of two or more plates. Styles. There are two styles of plates: the Universal Mill Plate, or Edged Plate, and the Sheared Plate. STEEL CONSTRUCTION 33 The Universal Mill Plate is rolled to exact width, the width being controlled by a pair of vertical rolls as previously described and illustrated, Fig. 22. They vary in width by intervals of 1 inch from 6 inches to 48 inches. Sheared plates, as the name indicates, are sheared to required width after rolling. The stock sizes range in width from 24 inches to 132 inches in intervals of 6 inches, but they can be furnished in any intermediate width, even in fractions of an inch. The extreme lengths of plates that can be furnished are given in the handbooks. This data should be consulted to determine r ** i i_ J^ RADIUS 0.31' (Cf.745- CARNEGIE -H-SXJ4 O BETHLEHEM- H- 14X98.6 Fig. 37. Typical H-Sections whether the required lengths can be obtained. In many cases the web plates of girders must be spliced on this account. Plates alone are not used for structural members. They are used in built-up members, such as columns and girders; for web and cover plates; and to connect members together. H-Sections. The H-section, Fig. 37, is designated by the name of the maker, the depth, and the weight per lineal foot, thus: Carnegie 8" H 34.0 # Bethlehem 14" H 98.8 # The H-section is not standard. At this time it is made only by the Carnegie Steel Company and the Bethlehem Steel Company. The Carnegie H's* are 8"H34.0# 5"H 18.7 # 6" H 23.8# 4" H 13.6# There is but one weight for each size. *Apply to the nearest office of the Carnegie Steel Company, or the Illinois Steel Company, lor circular giving properties, or see Carnegie Steel Company's Pocket Companion, 1913 edition. 34 STEEL CONSTRUCTION The nominal sizes of the Bethlehem H-sections are 8, 9, 10, 11, 12, 13, and 14 inches, respectively. The actual sizes range from 7J inches to 16J inches in intervals of J inch. The extreme weights are 34.6 pounds and 291.2 pounds per lineal foot. The H-sections are designed for use as columns and struts. They are not intended to be used in built-up members, except a special section which is designed to be increased by adding flange plates. Fig. 38. Miscellaneous Special Sections Miscellaneous Sections. In addition to the regular structural sections just described there are a number of special sections, Fig. 38, with which the designer should be familiar, viz: (a) Railroad Rails (e) Steel Sheet Piling (b) Wide-Flanged Channels (f) Steel Railroad Ties (c) Bulb Beams (g) Square Root Angles (d) Bulb Angles (h) Hand Rail Tees (i) Checkered Floor Plates These sections are not often used in steel construction for buildings, but occasionally conditions have to be met to which some of them are specially suited. STEEL CONSTRUCTION PROPERTIES OF SECTIONS 35 Under the heading "Properties of Sections" the handbooks give tables of the numerical values of the various functions of the sec- tions. Referring to these tables, certain items need no explanation, viz: dimensions; thickness of metal; area; weight per lineal foot. Other items are not self-evident and will be explained in detail. Center of Gravity (C.G.). See "Strength of Materials" for definition. The I-beam, H-section, and Z, Fig. 39, being symmetrical e 3= V Fig. 39. Location of Center of Gravity of Sections. Values of x, x'. and x' to be taken from Tables in Handbook about both axes, the center of gravity is in the center of the web and no values are given in the handbook tables. The C-section, Fig. 39, is symmetrical only about the axis which is perpendicular to the web; the center of gravity must, therefore, lie on this axis. The table gives the distance of the center of gravity from the back of the channel. Angles not being symmetrical about either axis, the center of gravity must be located by dimensions from the backs of both legs. If the legs are equal, both dimensions are the same; if the legs are unequal, the dimensions are unequal, the distance from the short leg x' being greater than that from the long leg x, Fig. 39. 36 STEEL CONSTRUCTION The position of the center of gravity must be known in order to compute the moment of inertia of the section and the moments of inertia of built-up members. The former values are given in the tables; the latter must usually be computed by the designer. Illustrative Example. Compute the position of the center of gravity of L4" X 4" X > disregarding fillets and rounded corners, Fig. 40. Divide the angle into two rectangles (1) and (2) as shown. Their centers of gravity are at c t and c 2 . Area of (1) 4 ;/ X V * 2.00 sq. in. Area of (2) 3 J" X |" = 1.75 sq. in. Total area 3.75 sq. in. Moments about a' a' for (1) = 2.00 X \ = 0.50 Moments about a' a' for (2) =1,75 X 2J = 3.94 Total moment 4.44 TV * 4 - 4 4 Distance x = - = 1.18 Similar computations apply about the axis b'b' and give the same result. Compute the position of the center of gravity of the following: 15"C33# Moment of Inertia (7). Refer to "Strength of Materials" for defi- j^ nition and method of computing Fig. 4o a ' Diagram showing computation moment of inertia. Moment of of Position o^cen^r of Gravity inertia j s designated by the letter 7. When a subscript is added it indicates which axis is used. Thus 7 means the moment of inertia about the axis a. Note that this symbol is the same as is used for the beam. Care must be taken to avoid confusion. The meaning can be determined in each case by the context. The tables in the handbook give the value of 7 about both of the rec- tangular axes of the section and, in the case of angles, about a diagonal axis also. The position of this diagonal axis is so chosen STEEL CONSTRUCTION 37 as to give the minimum value of 7. For I-beams and channels the minimum value is about the axis parallel to the web. The moment of inertia enters into the formulas for bending and for deflection. It is also used in computing the radius of gyra- tion of columns. Its values are given in the handbooks for the structural shapes and for plates, but it must be computed for most built-up sections, espe- cially for plate girders. The factors entering into the computation of the moments of inertia are always in inches. Illustrative Examples. 1. Compute I a and /6 for the plate shown in Fig. 41. 1 / a= :_X8Xl X X 1 X 8X8X8 = 42 Fig. 41. Diagram for Moment of Inertia of Rectangular Plate 2. Compute I a for the plate girder section in Fig. 42 made of 1 PI. 42" X 1* and i- 4Ls 6" X 6" X y. for 1 PI. 42" X y I a (from tables) =3087 for 4 Ls 6" X 6" X i" l c (from tables) 4 X 19.91 = 80 for4 Ls6*X6* X \' f / 4 X 5.75 X 19.57 X 19.57 = 8809 Deductions for rivet holes at m Area of 2 holes = 2 X 1J* X F = 2.625 sq. in. For 1 hole I d = T 'i X 11* X V X V X |" = -08 (a value so small that it is neglected) / = 2.625 X 18.75 X 18.75 = 11.976 11 rvRO Fig. 42. Diagram for Moment 11 ,053 of Inertia of Plate Girder 38 STEEL CONSTRUCTION PROBLEMS 1. Compute the values of / for the section in Fig. 43. Deduct rivet holes. The section is made up of 4 Ls G"X4"X iV connected with lacing bars (lacing not figured). 2. Compute the values of / for the section shown in Fig. 44. 1 C 12' 7 X20J# 1 L 4"X3"X|" The axes a a and b b are through the center of gravity The section not being symmetrical, the position of the center of gravity must be computed. Radius of Gyration (r). The radius of gyration is a value de- rived from the moment of inertia, but as its definition involves higher mathematical relations it need not be given here. It is reoresented by r, and is expressed in inches. The radius of gyration is derived from the moment of inertia by dividing by the area A in square inches and taking the square root of the result. This is expressed by the formulas 7 Fig, 43. Diagram for Moment of Inertia of Four Angles Illustrative Examples. 1. Referring to Fig. 41, the value of I b = 42f ; and A = 8X1=8 sq in. Therefore r 2 = 42-fS = 5j, or r=^5J = 2.31". .2. Referring to Fig. 42, the value of 7 a = Fig. 44. Diagram for 1 1,976 (disregarding rivet holes). To find the Moment of Inertia of j* j.' Channel and Angle TadlUS OT gyration /I PL 42" X |" =-21 sq. : 44 *Refer to the textbook on Arithmetic for method of extracting the square root. Tables are given in the handbooks from which the values can be taken. STEEL CONSTRUCTION 39 PROBLEMS 1. Compute the values of r for the sections given in Figs. 43 and 44. 2. Check the values given in the handbook for r fora 12* I 31 f#. The radius of gyration is used in the column formula as explained later in the text. , Section Modulus I 1. In the formula for the resisting mo- ment of sections subjected to bending occurs the expression -, in c which I is the moment of inertia and c is the distance from the neutral axis to the extreme fiber of the section. - has a definite c value for each section, and is called the section modulus. It saves one operation in arithmetic to have these values given for the various sections and they are given in the handbooks. As indicated by the fraction -, the value of the section modulus is determined by divid- c ing the moment of inertia by the value of c. Illustrative Examples. 1. Compute -for an 8" I 18 # about the axis perpendicular to the web. From the table, 7 = 56.9. The distance c is half the depth = 4" c" 4 2. Compute - for a channel 1 2"X 20. 5 # about the axis par- allel to the web. Not being a symmetrical section it has two values; From handbook, 7 = 3.91; c= (2.94 -.70) =2.24, and c = 0.70. 7 3.91 - -, ,7 3.91 PROBLEM Compute the values of - for 15" I 42# about axis parallel to web 9' I 21# about axis perpendicular to web 15* I 33# about axis perpendicular to web L S'XS'Xt* about axis at 45 to legs L 6*X4 ir X 3* about axis parallel to short leg Miscellaneous Properties. The handbooks include in the tables values of other properties of sections such as Coefficient of Strength, Coefficient of Deflection, and Resisting Moment. 40 STEEL CONSTRUCTION Strictly speaking, these are not properties of the sections, as they depend upon the value of the unit stress. They will be discussed in the text relating to beams. GENERAL INFORMATION Price Basis. The designer needs to be posted on the basis of prices for structural steel. For a number of years Pittsburgh, which has been the recognized center of steel production, has been the basing point for steel prices. Given a certain price for steel at Pittsburgh, the price at any other point is determined by adding to the base price the freight from Pittsburgh. Thus, if the price of steel at Pittsburgh is SL50 per hundred pounds, the price in Chi- cago is SI. 68 per hundred pounds, the freight rate being (at the time of writing) 18 cents per hundred pounds. Certain sizes of material are called "base" sizes. They are usually sold at a uniform price. The base sizes are: I-beams, 3 inches to 15 inches, inclusive; angles, 3 inches to 6 inches inclusive; channels, 3 inches to 15 inches inclusive; tees, 3 inches and over; zees, all sizes. I-beams over 15 inches, angles over 6 inches, and angles and tees under 3 inches are charged for at a higher rate, usually 10 cents per hundred pounds,- above base price. Special -ections and sections rolled exclusively by one manufacturer are sold at prices varying from the base price according to market conditions. The base price itself varies from time to time, usually from SI. 25 per hundred pounds to SI. 50 per hundred pounds; occa- sionally it goes beyond these limits. Mill and Stock Orders. Structural steel orders are handled on two bases: (a) based on securing the plain material for the job from the rolling mills; (b) based on securing it from stock. Of course there may be a combination of the two. The mill basis is cheaper, as it eliminates waste, saves expense of handling, saves interest cost on the value of material, and may save a profit or premium demanded by the dealer for quick service. Consequently all work is carried out on the mill basis, if the time allowed for completion permits it to be done. When the material is to be furnished on the mill basis, the engineer who makes the detail drawings or the engineering depart- ment of the fabricating company makes a list of the individual STEEL CONSTRUCTION 41 pieces required. These pieces are then ordered from the rolling mills, cut to the lengths required (a small variation in length is usually allowed; short pieces are usually ordered in multiple lengths). Thus there is practically no waste of material. Material carried in stock is ordered from the rolling mills in lengths as long as can be handled conveniently. The lighter sec- tions are ordered in lengths of 30 feet and 36 feet, and the heavier sections in lengths of 60 feet. In cutting this stock material there is necessarily considerable waste. This stock material is not usually available direct from the rolling mills. The dealers in stock are usually fabricating companies," jobbers, or brokers. They charge an advance in price over the mill price to cover waste, handling, cutting, and other expenses incidental to the business, and to cover such profit as the market condition may permit. This advance in price varies from 10 cents to 50 cents per hundred pounds. Stocks of plain material are carried in all the larger cities. Printed lists of the material on hand are issued at frequent intervals. These lists should be consulted and used as a guide -in selecting the sections that are to be used in all cases where stock is required. Whether mill or stock material will be used depends upon the size of the job and the time service required. Small jobs, say less than 100 tons, will usually be taken from stock unless only one. or two sections are required. If delivery of fabricated material is required within 60 days, it will usually have to be taken from stock. Even for much more extended deliveries, all or part of the material must be taken from stock,* if there is a great demand. Variation in Weight. Attention is called to the provision in the specifications, p. 360, which permits a slight variation in the weight of the finished steel as compared with its theoretical weight. This variation in the case of sections other than plates is 2.5 per cent above or below the theoretical weight. This represents the prac- ticable limits in adjusting the rolls of the mill. The variation applies to individual pieces and not to a bill of steel as a whole; some pieces will be overweight and some underweight, so that the average on a bill of considerable size should agree very closely with the theoretical weight. In the case of plates, *Apply to the nearest dealer for a copy of his stock list. Use it in solving the problems in this book. 42 STEEL CONSTRUCTION a much larger variation is allowed, amounting in some cases to as much as 18 per cent. It will be noticed that this variation is greater when plates are ordered to be of a certain gage or thickness than it is when they are ordered to be of a certain weight. The reason for this is that plates are slightly thicker in the middle than they are along the edges and, therefore, as the thickness must necessarily be measured near the edge, there is an excess of metal near the middle of the plate w r hich is not counted. This excess is due to the springing of the rolls. Plates can be ordered by weight, that is, to have a certain weight per square foot of surface, and when so ordered the allowable variation is less because the rolls can be adjusted to give the average weight. The result is that the fabri- cating shop usually orders large plates by w r eight per square foot. In a job involving a large amount of plate \vork, as for chimneys, tanks, etc., this may become a matter of importance, but for build- ing work a relatively small number of plates are required and it is not customary to specify them by weight, but by thickness. QUALITY OF MATERIAL Reliability of Structural Steel. Structural steel is the most reliable material used in building construction. Its manufacture has been a continuous development to the extent that the quality of material produced is under almost absolute control. The ingredi- ents are tested and measured before being put into the furnace, and the product is analyzed and tested physically to make sure that it fulfills the required standards; so that, with a reasonable amount of inspection and test, the purchaser can have definite assurance that he is securing the quality of material which he needs. The manufacturers and users of structural steel have co-oper- ated in developing the material in order to attain the most prac- ticable results. On the one hand, the manufacturers have insisted on keeping the quality such as to make its manufacture commercially satisfactory. On the other hand, the users of steel have demanded the best material that it is possible to make and still keep within reasonable limitation of cost of manufacture. STANDARD SPECIFICATIONS As a result of the efforts of the manufacturers and users, Standard Specifications ha.ve been formulated covering the quality STEEL CONSTRUCTION 43 of structural steel. There are three sets of specifications that may safely be used, viz:* (a) Manufacturers' Standard Specifications for Structural Steel Class Bt (b) Standard Specifications for Structural Steel for Build- ings, adopted by the American Society for Testing Materials (Given in full p. 359) (c) Specifications for Structural Steel, adopted by the American Railway Engineering Association Comparison of Specifications. A brief comparison of the pro- visions of these three sets of specifications is of interest. Range of Application. The specifications (a) and (b) are intended primarily to apply to steel for building work, whereas (c) is for railway bridges. In buildings, the greater part of the load to be supported is permanent or dead load. The variable or live load usually is applied gradually, without shock or vibration. In railway bridges the conditions are quite different. The permanent load for a short span is the smaller part of its capacity. The live load, being much larger than the dead load and being applied quickly, produces great shocks and vibration. Because of these conditions, specifica- tion (c) is more rigorous in its requirements than are (a) and (b). Process of Manufacture. Specification (c) requires the open- hearth process of manufacture; (a) and (b) permit either open- hearth or Bessemer. Chemical Analysis. Specification (c) requires the chemical analysis to report the percentages of sulphur, phosphorus, carbon, and manganese, and limits the amount of sulphur; (a) and (b) limit the phosphorus. Tensile Strength. Specification (c) places the desired ultimate tensile strength of steel sections at 60,000 pounds per square inch, allowing a variation of 4000 pounds, thus making the range of strength 56,000 to 64,000 pounds; (b) allows a range from 55,000 to 65,000 pounds; (a) allows the same range as (b) and in addition * (a) Published in the handbooks issued by the Steel Manufacturers; (b> Published by American Society for Testing Materials. Edgar Marburg, Secretary, University of Pennsylvania, Philadelphia, Pa.; published in full in Carnegie Steel Company's Pocket Companion, 1913 edition; -(e) Published by American Railway Engineering Association, 910 South Michigan Boule- vard, Chicago, III. t Class A is for railroad bridges. 44 STEEL CONSTRUCTION permits a maximum of 70,000 pounds if the percentage of elongation is the same as for steel having a tensile strength of 65,000 pounds. Rivet Steel Strength. Specification (c) specifies the desired strength of rivet steel at 50,000 pounds, allowing 4000 pounds vari- ation, thus making the range of strength from 46,000 to 54,000 pounds; (a) allows a range from 46,000 to 56,000 pounds; and (b) allows a range from 48,000 to 58,000 pounds. Elongation and Fracture. The three specifications are in close agreement as to their requirements for elongation of the test speci- men and the character of fracture. Bending Requirements. Specification (c) is somewhat more rigorous than the others in the bending requirements. Either of these specifications will give satisfactory results, but specification (b) of the American Society for Testing Materials is recommended as being most suitable for building work. It is given in full on p. 359. DISCUSSION OF IMPORTANT FEATURES Method of Manufacture. A brief description has been given of the two methods of manufacture of steel. The Bessemer process is more rapid and, as a result, is less subject to accurate control than the open hearth. In the Bessemer process the operator is governed by the character and color of the flame issuing from the converter. He must learn by experience to do this, as the whole matter depends upon his judgment. The open-hearth process, being slower, gives an opportunity to take samples and make analyses, and thus control the operation. The Bessemer process, as ordinarily conducted, does not remove sulphur and phosphorus, so that whatever quantities of these unde- sirable elements are in the iron ore remain in the finished steel, On the other hand, the usual open-hearth practice reduces the amount of sulphur and phosphorus, these elements being removed in the slag. For the above reasons, the product of the open-hearth furnace is considered more desirable than that of the Bessemer, when steel is to be subjected to severe use, as in the case of railway bridges. Heretofore the question has been an economic one. The Bes- semer process being the cheaper, most of the producing capacity was of that type, and a higher price was charged for open-hearth STEEL CONSTRUCTION 45 steel. Recently the situation has changed. Most of the new furnaces are open-hearth and no extra charge is demanded for steel made by this process. There is now no difficulty in securing it. Chemical Composition. Carbon. The essential elements of steel are iron and carbon. All of the other elements found may be considered as impurities. The iron, of course, constitutes all but a small percentage of the total. The function of the carbon is to make the steel hard and strong. Within certain limits the tensile strength of steel increases, while the ductility decreases, with the increase in the amount of carbon used. The amount of carbon in structural steel varies from 0.10 per cent to 0.40 per cent. The smaller amount occurs in rivet steel. For structural shapes, the usual limits are 0.15 per cent to 0.25 per cent. A larger amount makes steel too hard for structural purposes. Steel to be forged or welded needs to be low in carbon. Steel to be tempered must be high in carbon. These features do not con- cern structural steel. Phosphorus. Phosphorus occurs as an impurity in the iron ore. It is not practicable or necessary to remove all of it. It increases the strength of the steel but produces brittleness. The amount of phosphorus allowed is about 0.10 per cent. Sulphur. Sulphur is also found as an impurity in the iron ore. Its presence in the steel causes trouble in rolling. It usually amounts to less than 0.05 per cent. Silicon. Silicon may be in the pig iron or may be absorbed from the material used in lining the steel furnace. It increases the hardness of the steel and has a beneficial effect in the process of manufacture, so that the presence of a limited quantity, about 0.20 per cent, is not objectionable. Manganese. Manganese also may be found in the iron ore, but if not, it is added during the process of manufacture to assist in the chemical transformations. Its presence in the finished steel to the extent of about 1.0 per cent is an advantage, as it adds to the strength and improves the forging qualities. However, some authorities believe that it promotes corrosion of steel and on this account is objectionable. Alloys of Steel. A much larger quantity of manganese is sometimes used as an alloy, but such a steel is not used for structural 46 STEEL CONSTRUCTION purposes. There are many alloys of steel, developed for special purposes. The only one used for structural work is nickel steel, and up to the present time its use has been limited to a few large bridges. Probably nickel steel will not be economical for building work for some time. Physical Properties. The determination of the physical prop- erties most suitable for structural steel has been a gradual develop- ment. It has been influenced by the cost of manufacture and ease of fabrication on the one hand, and uniformity and economy to the consumer on the other. The manufacturers have required that such limits be set as would permit them to operate economically. Expensive refinements of small importance have been eliminated. The allowable range in strength has been made large enough so that it can easily be attained. The fabricating shops have encouraged the use of a material that can easily be punched and sheared. The designing engineers representing the consumers have de- manded a small range in strength and uniformity in physical proper- ties, and at the same time as great strength as is consistent with relia- bility of material, with economy of manufacture, and with ease of fabrication. As the physical properties are closely related to the uses of the steel, their requirements are much more explicit than are those relating to chemical composition. The chemical tests are of inter- est only to the extent that they indicate physical properties. Thus, high carbon and high phosphorus indicate high tensile strength and brittleness, but these properties can be determined more directly by the tension test, with the attendant observations of elongation and character of fracture. Railway Bridge Grade Steel. It has been noted that the Manu- facturers' Standard Specifications (a) provide for steel, which has a maximum strength five thousand pounds greater than the strength provided by specifications (b) and (c). This grade of steel was formerly very much used for building work, but now steel having the lower strength is generally used. The reason for using the lower strength steel is that it is more reliable and more uniform in quality. The higher the strength the more brittle the material, hence the greater danger of injury from careless handling and from the shop STEEL CONSTRUCTION 47 operations of fabricating. This latter condition makes the fabricating shops prefer to use the softer grade. It seems probable that this harder grade of steel will be used less and less and, therefore, more difficult to get; so it is wise to specify the railway bridge grade, which is Class A, in case Manufacturers' Standard Specifications are used. Yield Point. The yield point indicates one of the most import- ant properties of structural steel. When a piece of steel is subjected to a tensile stress, it elongates, the amount of the elongation within certain limits being proportional to the load applied ; .thus, if a piece of steel of one square inch cross section is subjected to a load of 5000 pounds, and then to a load of 10,000 pounds, the elongation in the second case will be twice as inuch as that in the first case. The test for the strength of the steel specimen, as described in the specifica- tions, is made in a tension or pulling machine, to which is attached a lever arm carrying a weight, corresponding to the beam of an ordinary scale. If the load is increased at a uniform rate, the weight on the scale beam, by being moved at a certain uniform rate, will kee'p the beam exactly balanced until about one-half the ultimate strength of the material is reached; then the scale beam will drop, which indicates that the specimen has begun to elongate at a more rapid rate. The stress in the steel at which this occurs is called the "yield point" of the steel. Breaking Load. If the load which produced the above effect were applied continuously for a long time, the specimen would finally break; but usually in testing, additional load is applied at the same rate as before until the specimen breaks. The breaking load, according to the specifications, should be about 60,000 pounds per square inch. This represents the load which will break the steel if applied within a relatively brief period of time, but a much smaller load will break it if applied over a long period of time. Elastic Limit. The change in the rate of elongation does not occur just at the point where it becomes manifest by the action of the scale beam, but at a somewhat lower stress. The point where the change actually occurs is called the "elastic limit". This term formerly was used in specifications and, in fact, still is used in the Manufacturers' Standard Specifications, but as the commercial methods of testing structural steel do not clearly show the exact point of the elastic limit, the yield point is ued. 48 STEEL CONSTRUCTION Yield Point and Factor of Safety. The Standard Specifications require that the yield point shall be not less than one-half the ulti- mate strength. The value of the yield point is usually several thousand pounds above this amount. When the yield point is reached, the material has begun to fail. This value, therefore, in- stead of that for the ultimate strength, is the one which should be used in computing the factor of safety. If the yield point is at 32,000 pounds and the unit stress 16,000 pounds, the factor of safety is 2 instead of 4, as commonly stated. Refer to the discussion of factor of safety, p. 7. Reduction of Area. The provision in the specifications re- garding the reduction of area of the test piece at the point of fracture is of importance, as it indicates the ductility of the metal. If the piece breaks without much reduction in area, it indicates that the material is hard and probably brittle. Such material is likely to break, if subjected to shock, and may /" *7 J d ~ ZZ? fracture in punching and shearing The y j \ character of the fracture is indicative of the FOP STRUCTURAL STCLL same condition. If cup-shaped and silky in (^ ^ appearance, it indicates toughness; but if the roR PH/CT STEEL fracture is irregular, it indicates brittleness. Fig. 45. Biding Tests for The bending test also is importantTor deter- mining whether the steel is tough or brittle. Inspection and Tests. In order to check the quality of the steel as it is made, tests are made of each melt. The chemical analysis is made from a sample taken from the molten metal as it comes from the furnace or converter. Sometimes a check analysis is made from drillings taken from the rolled sections. Physical tests are made in accordance with the requirements of the standard specifications. The test specimens are cut from the finished structural steel. The bend test is made by bending the specimen around a pin whose diameter equals the thickness of the specimen, Fig. 45. Rivet rods must bend flat on themselves. These tests are made with cold steel. The work is done either by blows or by pressure. To pass the test, the specimens must show no fracture on the outside of the bent portion. The tension-test specimen is shaped as shown in Fig. 46. It is put in a tension-testing machine and pulled until it breaks. From STEEL CONSTRUCTION 49 this are determined the total strength, yield point, elongation, and character of fracture, Fig. 47. Records of these tests are furnished to customers if desired. / "TO j "/?/? HOT LSS THfJH 9" (4 > } \ ABOUT 1 i / r TC. ABOUT /8 ~ Fig. 46. Tension Test Piece Customers may, and on important jobs do, employ inspectors to supervise the tests. These inspectors also make a surface inspection to see that the finished sections are straight and free from cracks, blisters, buckles, and slivers. Fig. 48 is a specimen report of tests. Fig. 47. Test Piece Before and After Being Broken by Tension UNIT STRESSES General Discussion. The unit stress, or working stress, is the stress or load that is allowed on each square inch of cross section of the metal and is expressed in pounds per square inch. There is I o 3 S. W. o; Oi M i- i 5 S Iii. *|l,| fe 1 II m S * I MI a S3 H a> to eo 00 ^^Tj'^-tftOtOTj' I oooooooo / i o f- IO ^ SSSS^^SS *Y z ^,^^1 8 5 1 00 H H O H H tO 10 H Jj OOOOOOOO ^1 CD 1 to 1 O CMH ^SSS^nS^ 5^ 5 3 Bd ^ S 1 H ^ 1 0) O o {* f ft H " 5 o cS l a M Jjp o g II o } m H treets, ! H | oo tf (VJ OX H bO bO bO U)tJ bO bfl bO /^^ CO if? t- a> OOl^-tOCOHc^H i o 1*1 co to COHHOtOlOCOO H ^ IO IO CO iii t" C-C\jCMt-lOOf.0 i (A m M CD CO CMCVJ Cv2C\2CN]C\2c\2c\2c\]C\2 P4 Buren 8 ill H o o c\2 co IO O OH CO CO OOOOOOOO tOOCOc^OOO^ cacoO'tcooococM cocoocococococo "8 1 H 1! H 10 IO to to totototototototo CVJ CO fc o ort Dearborn H< O H U) S ^ 8 XX co to XX CO 10 (0 CO CO jr 1 Htoioto.iotto " XXXX" XXX H H H CM H H & 15 H cvj a> CO t*. tO xf if 1 | I o o IO t>- H IO OC-COOOHHH ^OOOHHHHW * 1 * C\2 cv2 SO O O H H H H CM CM CM CQ CVJ CM OJ STEEL CONSTRUCTION 51 practical agreement on the values used for the various kinds of stress. The following values can be used with assurance that they will give safe results. Note that these values are for building work; they may also be used for highway bridges but not for railroad bridges. Structural Steel. Structural steel is so dependable and of such uniform quality that the values for unit stress are well established. The values given follow standard practice. Maximum Allowable Stresses on Structural Steel in Pounds per Square Inch: Axial tension net section 16,000 Bending on extreme fiber, tension 16,000 Bending. on extreme fiber, compression 16,000 Bending on extreme fiber, of pins... 25,000 Shear on shop-driven rivets 12,000 Shear on field-driven rivets and turned bolts 10,000 Shear on rolled-steel shapes 12,000 Shear on plate-girder webs 10,000 Bearing on shop-driven rivets and pins 25,000 Bearing on field-driven rivets and turned bolts 20,000 Axial compression on columns 16,000 70 In the above, / is the length of the column in inches from center to center of bearing, and r is the least radius of gyration. The maxi- mum value allowed is 14,000 pounds per square inch. For wind pressure alone or combined with gravity loads, the unit stresses may be 50 per cent in excess of those given above, but the section must not be less than required for the gravity loads alone. The discussion under "Columns" should be consulted regarding limitations of the use of the compression formula and the conditions under which higher and lower values are used. Cast Iron. There is not such close agreement among engineers as to the unit stresses allowable on cast iron. The following values represent fairly well the current practice; they are in pounds per square inch. Axial tension not allowed Bending on extreme fiber, tension 3,000 Bending on extreme fiber, compression 10,000 Shear 2,000 Compression 10,000-6o| 52 STEEL CONSTRUCTION The discussion of cast-iron columns should be consulted for limitations of values used and length of columns. These values are taken from the Building Ordinances of the City of Chicago. Masonry. As the ultimate bearing of steel work is on masonry, and as the bearing values are necessary in designing the bearing plates and column bases, the values are given for the usual forms of masonry. The values below, expressed in pounds per square inch, are taken from the Building Ordinances of the City of Chicago. Coursed rubble, Portland cement mortar 200 Ordinary rubble, Portland cement mortar 100 Coursed rubble, lime mortar 120 Ordinary rubble, lime mortar GO First-class granite masonry, Portland cement mortar 600 First-class lime and sandstone masonry, Portland cement mortar 400 Portland cement concrete, -2-4 mixture, machine mixed 400 Portland cement concrete, -2-4 mixture, hand mixed 350 Portland cement concrete, -2^-5 mixture, machine mixed. . . 350 Portland cement concrete, -2J/2-5 mixture, hand mixed 300 Portland cement concrete, -3-6 mixture, machine mixed 300 Portland cement concrete, 1-3-6 mixture, hand mixed 250 Natural cement concrete, 1-2-5 mixture ; 150 Paving brick, mortar 1 part Portland cement, 3 parts torpedo sand 350 Pressed brick and sewer brick, mortar same as above 250 Hard common select brick, same as above 200 Hard common select brick, mortar, 1 part Portland cement, 1 part lime, 3 parts sand 175 Common brick, all grades, Portland cement mortar 175 Common brick, all grades, good lime and cement mortar . . . 125 Common brick, all grades, natural cement mortar 1,50 Common brick, all grades, good lime mortar 100 The American Railway Engineering Association permits a bearing of 800 pounds per square inch on concrete, provided the area of the pier is twice the area of the base plate. The writer would allow this high stress only when the concrete is properly reinforced with hooping, similar to that used in hooped columns. RIVETS AND BOLTS Ordinary Sizes. The sizes of rivets vary in a general way with the thickness of steel which they connect. In structural steel work the sizes commonly used are | inch, \ inch, and J inch, the f-inch STEEL CONSTRUCTION 53 size being used much more than any other. In very light work s-inch rivets are sometimes used and, in very heavy work, rivets 1 inch, 1J inches, and 1J inches are used. Rivets smaller than J inch are used when the size of the mem- bers connected requires it, or when the thickness of metal used is chiefly J inch. |-inch rivets must be used in the flanges of 6-inch and 7-inch I-beams; 6-inch and 7-inch channels; and 2-inch angles, f-inch rivets can be used in all of the beams, channels, and angles larger than the above' sizes, {-inch rivets may be used in beams 18 inches and larger, and angles 3 inches and larger. Another consideration that sometimes affects the sizes of rivets used, and concerns particularly the sizes larger than J inch, is the thickness of metal to be joined together. It is the general experi- ence in shops that satisfactory punching cannot be done when the thickness of metal is greater than the diameter of the hole to be punched. Of course, it is possible to punch thicker material than this, but it is troublesome to do so because of the frequent breakage of punches. Consequently if most of the material to be punched is J inch in thickness, J-inch rivets will be used. Another approximate rule governing the size of rivets is that in general the diameter of the rivet shall be not less than one-fourth of the total thickness of metal. The use of more than one size of rivet on a job is to be avoided as much as practicable on account of the trouble and expense of frequently changing the punches. It is especially inconvenient to punch more than one size of hole or drive more than one size of rivet in a structural member. Spacing. There are a number of conditions that control the spacing of rivets. These have been developed into practical rules which are quite uniform among the various fabricating shops. Rivets spaced too close together would cut out too large a percentage of the cross section of members. Rivets spaced too far apart cause a waste of material in connecting pieces. The specifications relating to rivet spacing,* p. 365, items 57 to 63, are in accord with usual practice and should be followed. *Frora "Specifications for Structural Work of Buildings" by C. C. Schneider, M. Am. Soc. C. E., published in Transactions of the American Society of Civil Engineers, Vol. LIV (June, 1905), p. 498. 54 STEEL CONSTRUCTION TABLE I Gages for Angles p\ Leg 3 i t s, i g ] G, ; 3* 3" CO tO 4^ to toco 3" 2 ' 2f 2" If . * T* T Max. Rivet lf 1" i" i 1 i 5 | Leg 2f 2" If if if if i" f G t G 2 if If 1" 8 i" i" i" f G, Max. Rivet i ; I f 1" I" t" i" i" Gage. The term "gage" is used to designate the spacing of rivet lines parallel to the axis of the member. For example, Fig. 49 illustrates the gage lines of beams, channels, and angles. Standard values are assigned in the hand-books to the gage lines in the flanges of I-beams and channels, and in angles. However, as manufacturers do not agree as to the gage lines of angles, values used by the American Bridge Company are given, Table I. Gage lines in webs of beams and channels and in plates are not standard and are located according to requirements. GAGE LINES Fig. 49. Diagrams Showing Gage and Pitch Lines Pitch. By the pitch of rivets is meant the spacing along the gage lines, Fig. 49. Some of the rules for this spacing are given in Schneider's Specifications previously referred to. Note carefully STEEL CONSTRUCTION 55 the provisions there given. The rule usually followed for the mini- mum pitch is three times the diameter of the rivet. But this mini- mum should be used only when necessary, it being preferable to use a larger spacing of rivets under ordinary conditions. Three inches is desirable for f-inch rivets, where this spacing does not involve the use of an excess of material in the connected pieces. Where no definite stress occurs in the rivet, as in built-up columns, or where the stress is small, as in certain portions of flanges of plate girders, six inches has been established as the maximum. In case there are two gage lines closer together than the minimum spacing allowed, the rivets in the adjacent rows must alternate so that the diagonal dis- tance between them will exceed the minimum by 40 per cent or more. Edge Distance. If holes are punched too close to the edge of the metal, the tendency is to bulge out the metal and perhaps to crack the edge. This necessitates maintaining a certain distance fpom the edge to the center of the rivet holes. This distance must be greater in the case of a sheared edge, as of a plate, than is required for a rolled edge, as the flange of a beam, an angle, or a universal mill plate. The values commonly used are given in Schneider's Specifications quoted above. In the smaller sizes of beams and channels, the gage distances do not comply with these specifications. The width of flange is not sufficient to permit the use of the full edge distance and still allow necessary clearance from web to permit driving. On account of the danger that the metal will bulge out or crack along the edge, designers should try to avoid using smaller than 10-inch I-beams and channels in a way that will require flange punching. Instead, web connections or clips and clamps can generally be used. Clearance, A hole cannot be punched close against the web of an I-beam or close to the leg of an angle. A certain amount of space is required for the die. Of course holes can be drilled in any position, but this is not resorted to unless there is some particular reason for so doing. However, the punching of holes is not the limiting feature in the matter of rivet clearance. The required clearance is governed by the size of the die used in forming the rivet head. The usual rule for clearance is one-half the diameter of the rivet head plus three-eighth of an inch. The clearances required for 56 STEEL CONSTRUCTION various conditions for several sizes of rivets are given in Fig. 50, which represents the practice of the American Bridge Company. Closely associated with the amount of clearance is the ac- cessibility for driving the rivets, Fig. 51. For power driving, the rivet must be so situated that it can be brought between the jaws of the riveting machine. For riveting with the percussion ham- mer (air hammer), it must be possible to hold on to one head of the rivet with a die while the other head is formed by the riv- eter. For hand riveting it is necessary to be able to hold on to one head of the rivet and that the other end of it be accessible for driving with a maul. It is sometimes necessary to cut away flanges of I-beams or cut holes in the webs of box girders to make the rivets accessible for driving, Fig. 51. This matter is generally looked after in making shop drawings, but needs some attention in designing. H ^ 1^ L. . V J J .-_ i M1N, STD. r. >*;. FOK / f KJVZTS i /3 " 4 " *l *t I " " *4 1 1 " / " >t 'i~ 'i" " //' " Fig. 50. Clearance Allowed for Riveting 9 a USUAL METHOD IMPOSSIBLE: TO DRIVC BY USUAL METHODS rLAHGE Or BEAMS CUT AWAY TO PERMIT DRIVIHG f> RIVETS CAfiHOT - BE DRIVEM AFTER BEAMS ARE ASSEMBLED Fig. 51. Difficult Situations for Riveting Rivet Heads. Manufacture. Rivets are made with one head. This is done by heating a length of rivet rod to the proper tempera- ture and running it into the rivet machine. The machine upsets the end of the rod, making a head, and then cuts" off the rivet to the desired length. It is necessary that the dies in which the heads are formed be of proper size and be kept in perfect condition in order to make good rivets. If the two halves of the die which grip the sides of the rivet do not fit closely, some of the metal will be forced STEEL CONSTRUCTION 57 between them, forming fins on the sides of the rivets, Fig. 52. If the corners of the die become rounded, a shoulder wiU be formed at the junction of the shank with the head. Either of these de- fects will prevent the rivet head from fitting up tight against the plate, thus causing unsatisfac- tory results when driven. This Fig . 62 . Defective Rivets point is especially important in tank work where the rivets must be water-tight. Button Head. The shapes of the rivet heads vary among different makers, although these variations are slight. The type of head used in structural work is called the "button head" to dis- tinguish it from the cone head which is used in tank and boiler work. Flattened and Countersunk Heads. It is sometimes necessary to flatten rivet heads for special situations in order to provide the required clearance for an adjacent member. This flattening may vary from a slight reduction from the full thickness of the head down to a flush or countersunk head. The different thicknesses ordinarily used are f inch, J inch and | inch. A countersunk rivet is one in which the head is made in the form of a truncated cone and is formed by driving in a hole which has been tapered by reaming FORMULAE -dXt5+ a-DiAM. OF HEAD -a* 4ZS b -HEIGHT -i> X I f e.-i- ONO RADIUS -b c 'SHORT RADIUS Diam. of Rivets Diam. of Holes FULL DRIVEN HEAD Height COUNTERSUNK Depth H 15 I If Fig. 53. Proportions of Rivets in Inches Prom American Bridge Company 58 STEEL CONSTRUCTION so that the diameter at the outside is greater than at the inside of the plate. The sizes of rivet heads are shown in Fig. 53. The conventional signs for riveting are given in the handbooks. It is to be noted that countersunk rivets are not as strong as rivets with button heads and are much more expensive, conse- quently they are not used unless absolutely required by the condi- Fig. 54. 100-Ton Hydraulic Riveter, 120-inch Gap Courtesy Mackintosh, Hemphill & Company tions. A flattened rivet should be used in preference to a counter- sunk rivet; but when a smooth surface is to be obtained, the head must be countersunk and chipped flush with the plate. Driving. Before rivets can be driven, the pieces to be joined must be assembled accurately in position and be held together with bolts. The number of bolts used for this purpose will depend to STEEL CONSTRUCTION 59 some extent on the accuracy of the punching and the straightness of the pieces. If the several pieces are not held together, the metal of the rivet will be forced out between them, or the driving of adjacent Fig. 55. Hanna Pneumatic Riveter, 24-inch Gap Courtesy Vulcan Engineering Sales Company rivets may draw the plates closer together previously driven. Rivet holes are punched A inch larger of the rivet for when the rivet is heated, making it necessary to have the larger size the rivet must be done in such a way as to shank so that it fills the rivet hole solidly, filling out any irregularities in the hole, and and loosen the rivets than the nominal size it expands somewhat, hole. The driving of upset the metal of the even to the extent of then the button head 60 STEEL CONSTRUCTION must be formed on the driving side. As the rivet cools, it shrinks and thus grips the steel more tightly. than when first driven. Fig. 56. Rivet Ready for Driving Courtesy Vulcan Engineering Sales Company Riveting Machines in Shop. In the shop, rivets are driven with an hydraulic riveter, Fig. 54, or a pneumatic riveter, Fig. 55. The Fig. 57. Three Stages in Process of Riveting machine consists essentially of a yoke which spans the members to be riveted, Fig. 56. On the outer arm of the yoke is a die which STEEL CONSTRUCTION Gl fits over the head of the rivet; the other arm carries a similar die, or rivet set, which pushes against the end of the rivet, upsetting the shank of the rivet and thus forming a head, Fig. 57 The power is applied by means of hydraulic or pneumatic pressure. The pressure Fig. 58. Pneumatic Riveting Hammer Courtesy Chicago Pneumatic Tool Comjtany is held on until the rivet is partly cooled and has acquired enough strength so that the spring of the plates will not stretch it. Pneumatic Hammer. Whenever the rivet is in such position that it cannot be reached by means of the power riveter, it is driven Fig. 59. Light Motor-Driven Punch Ctmrteay Mackintosh. Hemphill & Company with a pneumatic hammer. The rivet is inserted in the hole and held in place by means of a die pressed against the head, the die being -held in position by hand or by a suitable arrangement of levers. The pneumatic riveter, or air gun, Fig. 58, carries a die, 62 STEEL CONSTRUCTION or set, for upsetting the rivet and forming the head. When the power is turned on, this machine delivers very rapid blows and thus performs the required work. Riveting in the field on the assembled structure is usually done by means of the pneumatic hammer. Hand Riveting. Hand riveting is now used only on small jobs, the air gun being replaced by the sledge hammer. The rivet is first hammered down by blows from the sledges, then the- rivet set is applied and sledged to form the head to its proper shape. Perfect rivets can be driven by either of the above methods. Fig. GO. Heavy Motor-Driven Multiple Punch Courtesy of Mackintosh, Hemphill & Company Punching and Reaming. Rivet holes in structural steel work are ordinarily punched in the metal by means of a powerful punching machine, Figs. 59 and GO showing examples of the single and multi- ple types, respectively. The essential features of the machine for doing this work are a punch and a die. The die is usually about A inch larger in diameter than the punch. The two are placed STEEL CONSTRUCTION 63 in the machine so that their axes are exactly in line. The plate is placed over the die and the punch is forced through, thus shearing out a round piece. This resulting hole is not perfectly smooth. The degree of roughness will depend on the condition of the punch and die, and the amount of difference in their diam- eters. The metal around the hole is to some extent torn and distorted. For ordinary structural purposes the holes are accurate enough and the damage to the metal so slight that no further treatment is needed, but in railroad structures and sometimes for special cases of building work it is required that the holes be reamed. In such cases the hole is punched smaller than the size of the rivet called "sub-punching" and it is then enlarged to the proper size by means of a drill or reamer. In railroad bridge construction, it is customary to ream all metal over f inch in thickness and to ream all holes for field connections. In structural work for buildings, reaming is rot required to such a great extent. Sometimes it is required on metal thicker than f inch and on field connections of very heavy members where a slight inaccuracy would occasion serious inconvenience in erecting. Where the several pieces assembled together have a thickness of more than four times the diameter of the rivet, or where through any inaccuracy of punching the holes do not match accurately, the holes should be reamed to true them up ; but in such cases they need not be sub-punched and the. reaming only serves the purpose of trimming up the irregularities. As previously stated, the diameter of the rivet hole as punched is A inch larger than the diameter of the rivet ; but in order to take account of the injured metal in computing the net section, the hole is figured J inch larger than the rivet. Functions of Rivets and Bolts. Rivets and bolts are used for fastening together the several sections used in building up the structural steel members and for connecting the members together in the finished structure. Rivets are always used for this purpose unless there is some special reason for using bolts. Generally speaking, rivets are cheaper than bolts and for most purposes more effective. They fill the holes full even though the holes may be slightly irregular in shape, and if driven tight will remain so; whereas 64 STEEL CONSTRUCTION bolts, unless they are turned and driven tight into reamed holes, are apt to become loose after a time. The function of rivets is to hold one piece of steel to another and to transmit stress from one to the other. In so doing they must resist a bearing pressure and a shearing stress. In many cases the rivets are not subjected to any definite shear- ing or bearing stress, but simply serve to hold the steel sections together in built-up members. They are unquestionably subjected to some stresses, but it is not possible to determine just what these are. In such 'situations the spacing of rivets is governed by rules resulting from practical experience. It sometimes happens that the direction of the stress applied to the rivet is along its axis, that is, the rivet is subjected to tension. It was formerly the custom to specify that rivets should not be 9? Fig. 61. Diagrams Showing Stresses in Rivets subjected to tension, but that bolts should be used in such situations. This provision was necessary when wrought-iron rivets were in use, as their heads could be easily broken off. Steel rivets are much more reliable in this respect and, if properly driven, can be sub- jected to tension as safely as bolts. Bearing. Fig. 61-a represents two pieces, m and n, riveted together, so that the stress (4000 pounds) in m is transmitted to n. Fig. 61-b represents three pieces riveted together so that the stress (8000 pounds) in the center piece m is transmitted to the two out- side pieces I and n. The bearing on the rivet is the pressure exerted on it by the plate through which it passes. In Fig. 61-a the bearing from plate m is on the right half of the rivet and from plate n on. the left half of the rivet. Although the actual bearing is on the curved surface, STEEL CONSTRUCTION 65 i. e., one-half the circumference of the rivet, the area used in figuring is the projected area of this surface, i. e., the thickness of the plate multiplied by the diameter of the rivet. For the plate ra, the area is J" X J* or .375 sq. in., and for plate n, f'X J" or .281 sq. in. The unit stress allowed in bearing is 25,000 pounds per square inch for shop-driven rivets; thus the allowed values in bearing are for m 0.375 X 25,000 = 9375 # for n 0.281 X 25,000 = 7025 # The stress actually transmitted is 4000 pounds, and each bearing must be good for at least this amount, hence the bearings are sufficient. The actual bearings per square inch are form 4000 ^0.375 = 10,600 # for n 4000-^0.281 = 14,200 # PROBLEM Compute from the above data the allowable bearing values for m and n and the actual bearing per square inch on m and n for field-driven rivets. In Fig. 61-b the stress is transmitted from the plate m to the plates / and n and divided equally between them. The bearing areas are form x = 0.375 sq. in. for I and n combined 2 Xf Xf = 0.5625 s<|. in. , The allowed bearing values on shop-driven rivets are form 0.375 X 25,000= 9375 # for I and n combined 0.5625 X 25,000 = 14,065 # The stress actually transmitted is 8000 pounds, so that the bearing for m is 8000 pounds and for I and n 4000 pounds each; hence, the bearings are sufficient. The actual bearings per square inch are form 8000^0.375 =21,300# for / and n combined 8000^ 0.5625 = 14,200# PROBLEM Compute from the above data the allowable bearings for I, m, and n for field-driven rivets. Shear. Referring again to Fig. 61-a, the forces acting on the two plates tend to cut, or shear, the rivet along the plane between the plates. This shearing action is resisted by the cross-section area of the rivets. This sectional area is -, which in this case is 66 STEEL CONSTRUCTION - I -T X|Xf or 0.4418 sq. in. The unit stress allowed fn shear on shop-driven rivets is 12,000 pounds per square inch. Then the allowable value for one f-inch rivet is 12,000x0.4418 or 5302. This is greater than the actual stress applied and is sufficient. The actual shear on the rivet per square inch of cross section is 4000-4-0. 4418 = 9054$ PROBLEM Compute the shearing value of a f-inch rivet, field driven. In Fig. 61-b there is a tendency to shear the rivet along two planes, i. e., on each side of the plate m. Consequently the shearing value of one rivet in this case is twice the value computed above, or 2X5302 or 10,604 pounds, and is sufficient to carry the actual load, which is 8000 pounds. The actual shear per square inch is the same as before, because both the actual load and the total cross- section area resisting it are twice as much as before, giving 8000^(2X0.4418) = 9054# In the first case the rivet is in single shear, in the second case i&.-is in double shear. It is clear that rivets should be used in cldtible shear wherever possible, provided the middle plate has a bearing value more than that of a rivet in single shear. PROBLEMS 1. Compute the shear value for shop-driven rivets of the following sizes: i, If f > s, and 1 inch, respectively, for (a) single shear and (b) double shear. 2. Compute similar values for field-driven livets. Illustrative Example. In the case illustrated in Fig. 61-a, what thickness of plate n is required to make the bearing value equal the shearing value? The shearing value is 5302 pounds. The bearing 5302 area required is . nnn or 0.212 sq. in. The diameter of rivet being 0.75 in., tne thickness required to give the required area is 0.212 sq. in. -5- 0.75 or 0.283 in. The next higher commercial size is 0.3125 in. or ft in. thick. PROBLEMS 1. In the case illustrated in Fig. 61-b compute the thickness of plate in required to make the bearing value equal the shearing value. 2. Compute the thickness of plates whose bearing values correspond to the single shear values of Hn., |-in., g-in., and 1-in. 'rivets. Compute the same for double shear values. STEEL CONSTRUCTION 67 3. How many J-in. rivets, field driven, single shear are required to trans- mit 175,000 pounds? 4. How many 1-in rivets, field driven, double shear, are required to transmit 100,000 pounds? 5 Assume shop rivets in double shear, middle plate $-in thick How imny f-in. rivets are required to transmit 235,000 pounds? How thick must be the outside plates? The designer can readily fix in mind the thickness of plates which give bearing values corresponding to the shear values of the rivets, then it will be necessary to compute only the shearing values. Friction. If the plates are held together when the rivet is driven, the shrinkage in length as the rivet cools will exert consid- erable pressure This makes the riveted joint develop a frictional resistance, which is additional to the shear and the bearing resist- ance, The amount of this friction has not been accurately deter- mined. Furthermore, it may have no value if the rivets are not tight. Consequently, no account is taken of the friction in figuring the strength of riveted joints Tension Specifications do not usually assign any value to rivets in tension. While their use in this manner is to be avoided, they may be so used when conditions require it The unit stress allowable is the same as for shear (See p 51) Rivet Tables. The handbooks contain tables giving the shear- ing and bearing values of rivets These tables cover several values of unit shearing stress and unit bearing stress They give the diameter of rivet, area of cross section, single shear, double shear, and the bearing for various thicknesses of plates. PROBLEM Refer to tne rivet tables and check all the examples and problems that have been given. If the handbook does not contain tables based on the unit stresses given herein, prepare such tables and keep them for future use. Most handbooks have blank pages in the ^ack part of the book for such use.* * f Investigation of Riveted Joints. The theoretical strength of a riveted joint involves three elements: the bearing value of the rivets; the shearing value of the rivets; and the area of the section of metal after deducting rivet, holes.- *The student should become familiar with all the tables given in the handbook relating to rivets and bolts. 68 STEEL CONSTRUCTION In a perfect design these three elements would be equal in value, but this ideal is rarely reached. Most frequently it is the shearing value which determines the strength of the joint, next the bearing value, and least frequently the section of the metal. Illustrative Example. Fig. 62 illustrates a splice of two plates, each 7"Xf". Rivets f" diameter, field driven. (a) Using all of the ten rivets, Shear value 10 X4418 =44,180# Bearing value 10 X5625 = 56,250# Tension value at (1) '6|Xf X 16,000 = 36,750 # Tension value at (2) 5JXf X 16,000 = 31, 500 # Loss of tension value between (1) and (2) = 5,250 # As this loss is more than the amount transmitted from m to n by the m 1 1 V iFf 1 / z 3 4 J e 7 Fig. 62. Diagrammatic Views of a Riveted Joint rivet at (1), the entire tension value at (1) is not available and the strength of the joint is the tension value at (2) plus the shear value of the rivet at (1), or 31, 500+4418 = 35,918#. (b) Now consider that the rivets at (1) and (7) are omitted. Shear value 8 X4418 = 35,344# Bearing value 8 X 5625 = 45,000 # Tension value at (2) 5iXf X 16,000 = 31, 500# The strength of the joint is the tension value at (2), i. e., 31,500#. (c) Next consider that the rivets (4) are omitted. Shear value 8 X 441 8 = 35,344 # Tension value at (2) plus shear value of rivet at (1) as above = 35,918 # STEEL CONSTRUCTION G9 The strength of the joint is the shear value 35,344 #. 7000 X 4. 375 = 30,625 ft.-lb. M = 30,625 ft.-lb. = 367,500 in.-lb. The formula for this bending moment is M = J W L = lX 14,000X17.5 = 30,625 ft.-lb. Cantilever Beam. Fig. 74. represents a cantilever beam support- ing a uniformly distributed load. Assume the length L of cantilever to be 8'-9", and the load, 800 pounds per lineal foot; then PF = 8. 75X800 = 7000$ The maximum bending moment is at Fi g . 74. Diagram of Cantilever Uniformly Loaded the support, and therefore M = W X ^ = 7000 X 4 . 375 = 30,625 ft.-lb. Compare these results with those obtained for the simple span 82 STEEL CONSTRUCTION having the same load per lineal foot. The span is one-half as much, while the shear and the bending moment are the same. Combination Simple and Cantilever Beam. A beam resting on two supports, projecting beyond one of them, and supporting a uni- formly distributed load is represented in Fig. 75. Assume the span L between supports to be 17'-6", the length L' of the canti- lever to be 8'-9", and the load 800 pounds per lineal foot; then TT=(800X17.5) + (800X8.75)=21,000# The reactions must be determined by the method of moments. Take the moments about R v . For the positive moment the lever arm is the distance from R l to the center of gravity of the entire beam, viz, 13.125 feet; therefore Positive moment = 21,OOOX!3.125 = 275,625 ft.-lb. Fig. 75. An Overhanging Beam with Shear and Moment Diagrams The negative moment must equal the positive moment; then R 2 XL = 275,625 and the value of R 2 is found by dividing the positive moment by the distance L between supports.' 275,625 Therefore R 2 = = STEEL CONSTRUCTION 83 Now since the sum of the reactions must equal the total load, the value of R< can be determined by subtracting R 2 from W; then R, = 21,000- 15,750 = 5250# This value of R t can- be checked by taking moments about R 2 . The position of the maximum shear is not self-evident so the shear values must be computed. F t =5250. Proceeding toward the right, 800 pounds is deducted for each foot, so the shear becomes zero at 6.5625 feet from R lf * continuing to a point just to the left of 7? a , the value of the shear is F 2 =5250-(800X17.5) = -8750# Continuing, to the right, add the value of R 2 , then the value of the shear is F 3 = -8750+15,750 = +7000 # Continuing, the shear reduces at the rate of 800 pounds per lineal foot, becoming zero at the end of the cantilever. The above values are shown graphically on the shear diagram. The maximum positive bending moment is between /?, and R 2 at the same position as the zero shear. Its value is f-f 5250X6.5625 4-34,448) U +17,224 ft.-lb. 1-800X6. 5625X^~^ -17,224 J The maximum negative bending moment is at R v Its value computed on the right is -800X8. 75X^p= -30,625 ft.-lb. or computed on the left is f +5250X17. 5 =+ 91,875) I = -30,625 ft.-lb. U 800X17. 5X^= -122,500 J The moment diagram can be constructed by computing the values at points one foot apart and plotting the results. From this dia- gram it will be noted that the bending moment changes from positive to negative at the point x. This is called the "point of contra- flexure" and in this case it is located 13.125 feet from R t . 84 STEEL CONSTRUCTION It is usually easier to compute the bending moment for simple spans uniformly loaded from the formula and for cantilevers from the formula For the combination span illustrated above, the maximum negative moment may be computed from the cantilever formula. But the maximum positive moment cannot be expressed in a simple formula and must be computed by means of the summation of moments as illustrated. EXAMPLES FOR PRACTICE 1. A joist has a span of 21 feet. It supports a floor area 5| feet wide. The floor construction weighs 115 pounds per square 5-O f- 15 -O ' H 4-O Fig. 76. Uniformly Loaded Beam Overhanging at Both Ends. foot and the live load to be supported is 50 pounds per square foot. Compute the shear and bending moment. 2. What are the maximum shear and bending moment for a total load of 80,000 pounds uniformly distributed on a span of 8 feet; 10 feet; 12 feet; 14 feet; 16 feet? What is the ratio of the bending moments for the 8-foot, and the 16-foot spans? 3. Compute the maximum shears and bending moments for a beam supporting a uniformly distributed load of 1,000 pounds per lineal foot on a span of 8 feet; 10 feet; 12 feet; 14 feet; 16 feet. What is the ratio of the bending moments for the 8-foot and 16-foot spans? 4. Compute the maximum shears and bending moments for cantilevers from the data given for the preceding problem. Com- pare the results with those for the simple beam. 5. Fig. 76 represents a beam extending beyond both supports. Its load is 600 pounds per lineal foot. What is the maximum shear? ^ What are the bending moments at 7?, and 7? 2 ? What is the maximum positive bending moment? STEEL CONSTRUCTION , 85 6. Construct the shear and moment diagrams for the preced- ing problems. 7. Given a span of 20 feet and a bending moment of 50,000 foot-pounds, what is the total uniformly distributed load? 50,000X8 20 8. Given a span of 18 feet and a bending moment of 72,000 foot-pounds, what is the load per lineal foot? Concentrated Loads. Girders in floor construction usually receive their loads at points where joists connect. P I* f* ' P Simple Beam. Fig. 77 rep- j~j-- 4-0'-^ ^o'^z-o^ resents a simple beam supporting C the concentrated loads P v P 5 , P 3 , and P 4 . The loads are P t = 60,000 # P 2 = 80,000 # P 3 = 80,000 # ^4 = 50>QQQflr Fig. 77. Simple Beam with Concentrated Loads. Total load = 270,000 # To determine the reaction R 2 , take moments about R t : 3X60,000 = 180,000 7X80,000 = 560,000 11X80,000 = 880,000 15X50,000 = 750,000 2,370,000 ft.-lb. 2 Similarly, to determine the reaction R lt take moments about R 2 : 2X50,000 = 100,000 6X80,000 = 480,000 10X80,000 = 800,000 14X60,000 = 840,000 2,220,000 ft.-lb. Therefore R t +R 2 = 130,588+1 39,412 = 270,OCO# which checks with the total load. 86 STEEL CONSTRUCTION The maximum shear occurs at the left of # 2 and is 139,412 pounds. By constructing the shear diagram, it is found that the shear passes from positive to negative at P 2 . This position of zero shear establishes the point of maximum moment. Computing the moment from the loads and reaction on the left gives i +7X130,588 = +914,116 -4X 60,000 =-240,000 Fig. 78. Cantilever Beam with ^ncentrated Loads +674,116 ft.-lb. Computing on the right gives + 10X139,412= +1,394,120 - 4X 80,000 = 320,000 - 8X 50,000 = 400,000 - 720,000 + 674,120 ft.-lb. Cantilever Beam. Fig. 78 represents a cantilever supporting the concentrated loads P 1 and P 2 . R = P, + P 2 = 30,000+40,000 = 70,000 # The maximum shear is 70,000 at the right of R. Zero shear is at the right of P 2 . ' The maximum bending moment is at R. It is -4X30,000 =-120,000 -9X40,000= -360,000 -"480^000 ft.-lK Simple Beams on Two Supports and Projecting at Both Ends. Fig. 79 represents a beam resting on two supports and projecting beyond both of them. Jt supports concentrated loads as shown. The loads are P t = 15,000# P 2 = 15,000 # P 8 = 15,000# P 4 = 15,000 # P 6 = 15,000# P= 30,OOQ# Total load - 105,000 # STEEL CONSTRUCTION To determine the reaction R 2 , take moments about R t : 0X15,000 (P 2 ) = 00,000 4X15,000 (P 8 ) = 60,000 8X15,000 (P 4 ) =120,000 12X15,000 (P 6 ) =180,000 16X30,000 (P tt ) =480,000 840,000 ft.-lb. - 4X15,000 (P t ) = " - 60,000 Moment of reaction /?,= 780,000 ft.-lb. y *t & *t \ *k L 4\ L , _L j. '- 4- t'-o" 4" ' t r g't ^ "^d 20 r p ** t> i"- iL *^ j< 21 r - r i P P t** fr* BENDING MOMENT CONSTANT BETWEEN LOADS *\ r \ 4 te f j p -f ' t' t"f trL. t L je 25 X ,P D S n-tn r^f) p, rf H POSITION Of TWO conceriTRA JED L OADS FOX MAXIMUM BE H DING MOMENT I &m ?( WL 24 w V O 25 9 I w WL , 3 /./ 1- A 26 i gw^ w WL, L^-J 27 in pi ~rrr> 1 w jf W L o 28 ^^^_ w iwu o b-^i^/. 29 1 r p r.L o i 30 mtt m LI , i ^ r P Ir! o i 96 STEEL CONSTRUCTION The point of zero shear is important only as the easiest means of locating the place of maximum bending moment. For a cantilever beam, irrespective of the manner of loading, the maximum bending moment and maximum shear occur at the sup- port. Illustrative Examples. To illustrate the use of Table II, assume a beam 18 feet long to be loaded from the left support to the middle at 320 pounds per lineal foot. W =9X320 = 2880# ^ = ^ = 1^ = 1x2880 = 2160# 7 2 = j R, = ifF = iX2880 = 720 # M = WL = X28SOX 18 = 7290 ft.-lb. Moving Loads. It is sometimes necessary to know what posi- tion of a moving load will produce the maximum bending moment in a beam. If it is a single concentrated load, the maximum occurs when the load is at the center of the span, as in item 16. Compare items 16, 17, and 19. If there are two concentrated loads, as the wheels of a traveling crane, the position producing the maximum is shown in item 23. As there indicated, one load is j D distant on one side of the center of the span and the other is f D distant on the other side. The maximum bending moment is at the load nearer to the center. Illustrative Example. Assume two crane wheels spaced 8 feet centers, each loaded with 10,000 pounds, span- 20 feet, to find maxi- mum bending moment. From the formulas # 1 = 8,000# and fl 2 =12,000#; Z = 8 ft. Max. M = 8X8000 = 64,000 ft.-lb. Beam with Two or More Loadings. A beam may have two or more of the loadings illustrated. The respective reactions for the combined loads are the sums of the corresponding reactions for the separate loadings. This applies in all cases. The maximum bend- ing moment for the combined loads is the sum of the moments for the separate loadings, provided the positions of the maximums for the separate loadings are the same. Generally this condition occurs only when all the loads are symmetrical about the center of the span, or for cantilever beams. STEEL CONSTRUCTION 97 EXAMPLES FOR PRACTICE 1. What is the bending moment of a concentrated load of 89,000 pounds at the center of a span 21'-G" long? 2. What are the shear and bending moment of a load of 21,000 pounds at the quarter point of a span 19 feet long? 3. A beam is loaded at 750 pounds per lineal foot on the two end-thirds. What is the bending moment? 4. A beam carries a uniformly distributed load of 18,000 pounds and a center load of 9000 pounds. Span 16 feet. What arc the reactions and maximum bending moment? 5. A crane girder has a span of 20 feet. The wheel load is [ 30,000 pounds. The wheel base is 10 feet. What is the position of loads for maximum bending moment? What is the amount of the maximum bending moment? CALCULATION OF RESISTANCE Factors Considered. Having determined the shear and bending ^moment to which a beam is subjected, the next step, logically, is to 'determine the dimensions of the section w T hich will resist them. I The resistance to bending is first provided for, as this usually governs in the design of the rolled beam section. Then the shearing resist- ance is compared with the shearing stress to make sure that it is sufficient. To investigate the resisting moment in complete detail would require the following operations: (1) Assume maximum unit stress on extreme fiber (2) Assume section of beam, and compute its moment of inertia (3) From these values compute the resisting moment of the assumed section (4) Compare this resisting moment with the bending moment (5) Repeat the operation until a resisting moment is found which equals or slightly exceeds the bending moment This procedure, with some additional steps, is followed in the case of riveted beams, but for rolled beams the tables in the hand- books and elsewhere give resisting moments and various other properties of the sections so that the operations are much simplified. Resisting Moment. The resisting moment of any beam is determined from the formula 98 STEEL CONSTRUCTION as stated on p. 78 and demonstrated under Resisting Moment in "Strength of Materials" Part I. This formula may be changed to the form I^M c S which stated in words is moment of inertia _ resisting moment one-Mf the depth unit stress Section Modulus. In the expression just given - is called the c "section modulus," (p. 39). Its values for I-beams, channels, and angles are given in the handbook. Since the resisting moment must be equal to or greater than the bending moment and, since the value of the unit stress has been established, the value of the section modulus can be computed and the section selected from the tables. For example, the allowable unit stress in bending on the extreme fiber is 16,000 pounds per square inch; assume a beam subjected to a bending moment of 100,000 foot-pounds; since the section modulus is in terms of inches, the bending moment must be expressed in inch-pounds and for this case becomes 1,200,000 inch-pounds; then the section modulus required is I_M_ 1,200,000 ^ eA c~~ S~ 16,000 = Referring to the tables for I-beams it is found that the section having the nearest higher value of the section modulus is* 15" I 60 # Expressed In simple words the operations are: (1) Multiply the bending moment of the beam by 12 to reduce it to inch-pounds. (2) Divide this by 16,000 to determine the required section modulus. (3) From the tables select a section whose section modulus is equal to or greater than the required value. Tabular Values for Resisting Moments. For a given unit stress each section has a definite resisting moment which is computed from the formula M=S~ c The values of the resisting moment are not given in all of the hand- STEEL CONSTRUCTION 99 books. They are given in Table III, based on a unit stress of 16,000 pounds per square inch, and expressed in foot-pounds. This shortens the operation of selecting a section, it being necessary only to choose a section whose resisting moment is equal to or greater than the bending moment produced by the load on the beam. For example, assume a bending moment of 30,625 foot-pounds. Referring to Table III, the beam having the nearest higher resisting moment is 10" I 25 #, whose resisting moment is 32,500 foot-pounds. If the load on the beam is uniformly distributed, the compu- tations may be still further shortened by means of tables given in the handbooks. These tables give the safe loads uniformly dis- tributed for various lengths of spans. The Carnegie handbook has formerly given these values for I-beams, channels, angles, tees, and zees in tons but in the 1913 edition they are given in thousands of pounds. The Cambria handbook gives the values for I-beams and channels only and expresses them in pounds. For example, a beam 20 feet long supports a load of 700 pounds per lineal foot. The total load is 20 X 700= 14,000 #. From the tables the size of beam is found to be 10" I 30 #. EXAMPLES FOR PRACTICE 1. Two angles are required to support a load of 4200 pounds uniformly distributed on a span of 6 feet. Determine the section, by means of the section modulus. 2. A channel having a span 12'-6" long is required to support a concentrated load of 17,900 pounds at the middle point. What section is required? 3. Determine the sizes of beams required for the conditions given in the problems on p. 97. Use the simplest of the three methods given above, and check the results by one of the other methods. Application of Tables to Concentrated Loads. By careful study of the moment factors given in Table II, the designer can adapt the tables in the handbooks for uniformly distributed loads to other forms of loading. Thus a concentrated load at the center of a span produces the same bending moment as a uniformly dis- tributed load of twice the amount; then to use the table select a beam whose capacity is twice the amount of the concentrated load. 100 STKICL CONSTRUCTION TABLE III Strength of Beams I-Beams; H-Sections; Channels; Angles; and Tees Moment of Section Modulus Resisting Moment Based on Shearing Resistance of Web Strength of Standard End Con- Extreme Length for Deflection for Plastered Ceilings Limit 1-360 .Span Extreme Length for Beams without Lateral Support I I_ G erf 18,000 Lb. per Sq. Inch at 10.000 Lb. per Sq. Inch nections American Bridge For Uniformly Distrib- For Center Load When Loaded to Full When Loaded to Half Co.. 1911 uted Load Capacity Capacity (In.)* (In.)' Ft.-Lb. Pounds Pounds Ft. In. Ft. In. Ft. In. Ft In 27"! S3# 2888.6 214.0 285,300 114,500 54-0 36-0 12- 6 37-6 24' I 115# 2955.5 2463 328,400 180,000 f>3,000 48-0 32-0 13- 4 40-0 110 2883.5 240.3 320,400 165,100 ' 13- 3 39-0 105 2811.5 234.3 312,400 150,000 1 13- 1 39-4 100 2380.3 198.4 264,500 181,000 1 12- 1 36-3 95 2309.6 192.5 256,700 166,100 1 12- 36-0 90 2239.1 186.5 248,800 151,400 ' 11-11 35-8 85 2168.6 180.7 240,900 136,800 1 11- 9 35-4 80 2087.9 174.0 232,000 120,000 ' 11- 8 35-0 69* 1928.0 160.7 214,300 93,600 43,900 11- 8 35-0 21'l57i# 1227.5 116.9 155,900 75,000 33,400 42-0 28-0 10-10 32-6 20* I 100# 1655.8 165.6 220,800 176,800 44,200 40-0 26-8 12- 2 36-5 95 1606.8 160.7 214,300 162,000 " " 12- 36-1 90 1557.8 158.5 207,700 147,400 " 11 11 11-11 35-8 85 1508.7 150.9 201,200 132,600 " " 11- 9 35-4 80 1466.5 146.7 195,600 120,000 " " " 11- 8 35-0 75 1268.9 126.9 169,200 129,800 " " " 10- 8 32-0 70 1219.9 122.0 162,700 115,000 . " 11 . 10- 7 31-8 65 1169.6 117.0 156,000 100,000 " " " 10- 5 31-3 IS* I 90# 1260.4 140.0 186,700 145,300 43,100 36-0 24-0 12- 1 36- 3 85 1220.7 135.6 180,800 130,500 " " " 11-11 35-10 80 1181.0 131.2 175,000 115,900 " M M 11-10 35- 5 75 1141.3 126.8 169,100 101,200 " " " 11- 8 35- 70 921.3 102.4 ' 136,500 129,400 " " " 10- 5 31- 4 65 881.5 97.9 130,500 114,700' " " " 10- 4 30-11 60 841.8 93.5 124,700 99,900 " 11 " 10- 2 30- 6 55 795.6 88.4 117,900 82,800 " " " 10- 30- 46 733.2 81.5 108,700 58,000 30,200 " 11- 8 35- 15" I 100# 900.5 120.1 160,100 177,600 35,400 30-0 20-0 11- 3 33-10 95 872.9 116.4 155,200 162,800 " " 11- 1 33- 4 90 845.4 112.7 150,300 148,000 " " 11 11- 32-11 85 817.8 109.0 145,300 133,400 " " 10- 9 32- 4 80 795.5 106.1 141,500 121,500 " " " 10- 8 32- 75 691.2 92.2 122,900 132,300 " " " 10- 6 31- 5 70 663.6 88.5 118,000 117,600 " " " 10- 4 31- 65 636.0 84.8 113,100 102,900 11 11 " 10- 2 30- 6 60 609.0 81.2 108,300 88,500 M . " " 10- 30- 55 511.0 68.1 90,800 98,400 " " " 9- 7 28-9 50 483.4 64.5 86,000 83,700 " " " 9- 5 28- 3 45 455.8 60.8 81,100 69,000 " " " 9- 3 27- 9 42 441.7 58.9 78,500 61,500 " " " 9- 2 27- 6 3S 405.1 54.1 72,000 43,400 32,500 " " 9- 2 27- 6 STKK1. TABLED III (Cpr.tinueJt Strength of Beams I -Beams; H -Sections; Channels; Angles; and Te< SECTION Moment of Inertia Section Modulus I c Resisting Moment Based on Unit Str.-ss of 16.000 Lh. per Sq. Inch Shearing Resistance of Web at 10.000 Lb. per Sq. Inch Strength Standard End Con- nections American Bridge Co.. 1911 Extreme Length for Deflection for Plastered Ceilings Limit 1-360 Span Extreme Length for Beams without Lateral Support For Uniformly Distrib- uted Load For Center Load When Loaded to Full Capacity When Loaded to Half Capacity (In.)< (In.) 3 Ft.-Lb. Pounds Pounds Ft. In. Ft. In. Ft. In. Ft. In. 12* I 55# 50 45 40 35 311 27* 321.0 303.3 285.7 268.9 228.3 215.8 199.6 53.5 50.6 47.6 44.8 38.0 36.0 33.3 71,300 67,500 63,500 59,700 50,700 48,000 44,400 98,600 83,900 69,100 55,200 52,300 42,000 38,200 26,500 23,900 24-0 16^0 9- 4 9- 2 8-11 8- 9 8-6 8- 4 8-4 28- 1 27- 5 26-10 26- 3 25-5 25- 25- 10" I 40# 35 30 25 22 158.7 146.4 134.2 122.1 113.9 31.7 29.3 26.8 24.4 22.8 42,300 39,100 35,700 32,500 30,400 74,900 60,200 45,500 31,000 23,200 17,700 17,400 20-0 \3r-4 8-6 8-3 8-0 7-9 7-9 25-6 24-9 24-0 23-4 23-4 9"I35# 30 25 21 111.8 101.9 91.9 84.9 24.8 22.6 20.4 18.9 33,100 30,100 27,200 25,200 65,900 51,200 36,500 26,100 17,700 18^0 12-0 7-11 7- 8 7- 5 7- 3 23-10 23- 22- 3 21- 8 8' I 25J# 23 20J 18 17* 68.4 64.5 60.6 56.9 58.3 17.1 16.1 15.1 14.2 14.6 22,800 21,400 20,100 18,900 19,500 43,300 35,900 28,600 21,600 16,800 17,700 15,800 16K) 10j8 7- 1 7-0 6-10 6- 8 7- 3 21- 4 20-11 20- 5 20- 21- 8 7"I20# 17} 15 42.2 39.2 36.2 12.1 11.2 10.4 16,100 14,900 13,900 32,100 24,700 17,500 17,700 14-0 9-4 6-5 6-3 6-1 19- 4 18-10 18- 4 6'117i# 14! 124 26.2 24.0 21.8 8.7 8.0 7.3 11,600 10,700 9,700 28,500 21,100 13,800 8,800 8,600 12-0 8-0 7-2 5-9 5-7 21-5 17-3 16-8 5' I 14i# 12} 91 15.2 13.6 12.1 6.1 5.4 4.8 8,100 7,200 6,400 25,200 17,800 10,500 8,800 7,900 10-0 6-8 5-6 5-3 5-0 16-6 15-9 15-0 4"I10J# 9* 11 7.1 6.7 6.4 6.0 3.6 3.4 3.2 3.0 4,800 4,500 4,300 4,000 16,400 13,500 10,500 7,600 8,800 7,100 8yO 5r-4 4-10 4- 8 4- 7 4- 5 14-5 14-0 13-8 13-4 3'I 7*# 2.9 2.7 2.5 1.9 1.8 1.7 2,500 2,400 2,270 10,800 7,900 5,100 8,800 6,400 6jO 4^0 4- T 4-0 3-11 12-7 12-1 11-8 H-8'-34.0# 6'-23.8 5M8.7 4M3-6 115.4 45.1 23.8 10.7 28.9 15.0 9.5 5.3 38,500 20,000 12,700 7.100 30,000 18,800 15,600 12,500 | 13-4 12-0 10-0 8-0 10-8 8-0 6-8 5-4 - 102 STHKL roXSTRTCTlON TABLE III. (Continued) Strength of Beams I -Beams; H -Sect ions; Channels; Angles; and Tees SECTION Moment cf Inertia I Section Modulus _L c Resisting Moment Based ou Unit Stress of 16.000 Lb. per Sq. Inch Shearing Resistance of Web at 10,000 Lb. per .Sq. Inch Strength of Ftandard End Con- nections American Bridge Co., 1911 Extreme Length for Deflection for Plastered Ceilings Limit 1-360 Span Extreme Length for Beams without Lateral Support For Uniformly Distrib- uted Load Center Load When Loaded to Full Capacity When Loaded to Half Capacity (In.)* (In.)' Ft.-Lb. Pounds Pounds Ft. In. Ft. In. Ft. In. Ft In. 15* C 55# 40 45 40 35 33 430.2 402.7 375.1 347.5 320.0 312.6 57.4 53.7 50.0 46.3 42.7 41.7 76,500 71,600 66,700 61,700 56,900 55,600 122,700 108,000 93,300 78,600 63,900 60,000 35^400 - uted Load For Center Load For Uniformly Distrib- uted Load For Center Load (In.)* (In.) Ft.-Lb. Ft. In. Ft. In. (In.) 4 (In.)' Ft.-Lb. Ft. In. Ft. In. L-4x3x 1 t 5.05 4.52 3.96 3.38 1.89 1.68 1.46 1.23 2,500 2,200 1,940 1,640 8^0 5-4 2.42 2.18 .1.92 1.65 1.12 0.99 0.87 0.74 1,490 1,320 1,160 9CO 6^6 4-4 X co X rt Jl 4.98 4.70 4.41 4.11 3.79 3.45 3.10 2.72 2.33 2.20 2.05 1.91 1.76 1.61 1.45 1.29 1.13 0.96 2,900 2,700 2,500 2,300 2,100 1,930 1,720 1,510 1,280 7-0 4-9 3.33 3.15 2.96 2.76 2.55 2.33 2.09 1.85 1.58 1.65 1,54 1.44 1.33 1.21 1.10 0.98 0.85 0.72 2,200 2,100 1,920 1,770 1,610 1,470 1,310 1,130 960 C-4 4-3 L-3Jx2Jx|* & f 4.13 3.85 3.55 3.24 2.91 2.56 2.19 1.80 1.85 1.71 1.56 1.41 1.26 1.09 0.93 0.75 2,500 2,300 2,100 1,880 1,680 1,450 1,240 1,000 6^4 4-6 1.72 1.61 1.49 1.36 1.23 1.09 0.94 0.78 0.99 0.92 0.84 0.76 0.68 0.59 0.50 0.41 1,320 1,230 1,120 1,010 910 790 670 550 fr-4 3-6 L-3Jx2x A p f 2.64 2.42 2.18 1.92 1.65 1.36 1.30 1.17 1.05 0.91 0.77 0.63 1,730 1,560 1,400 1,210 1,030 840 6-4 4-3 0.75 0.69 062 0.55 0.48 0.40 0.53 ~0.48 0.43 0.37 0.32 0.26. 710 640 570 490 430 350 4-4 3-0 L-3x2x A f 2.28 2.08 188 1.66 1.42 1.17 1.15 1.04 0.93 0.81 0.69 0.56 . 1,530 1,390 1,240 1,080 920 750 6^0 4-0 1 42 1.30 1.18 1.04 0.90 0.74 0.82 0.74 066 0.58 0.49 0.40 1,090 990 880 770 650 530 4-4 3-6 L-3x2x IT f 1.92 1.73 1.53 1.32 1.09 1.00 0.89 0.78 0.66 0.54 1,330 1,190 1,040 880 720 5-9 3-9 0.67 0.61 0.54 0.47 0.39 0.47 0.42 0.37 0.32 0.25 630 560 490 430 330 4 _4 3-0 L-2|x2x * T IT s 1.14 1.03 0.91 0.79 0.65 0.51 0.70 0.62 0.55 0.47 0.38 0.29 930 830 730 630 510 390 5-0 3-4 0.64 0.58 0.51 0.45 0.37 0.29 0.46 0.41 0.36 0.31 0.25 0.20 610 550 480 410 330 270 4-3 2-9 STKKL CONSTRUCTION TABLE III (Continued) Strength of Beams I-Beams; H-Sections; Channels; Angles; and Tees 107 SECTION Mom- ent of Inertia I Section Modu- lus "c~ Resisting Moment Based on Unit Stress of 16,000 Lb.per Sq.In. Extreme Length for Deflection for Plastered Ceilings Limit 1-180 Span SECTION Mom- ent for Inertia I Section Modu- lus J_ c Resisting Moment Based on Unit Stress of 16.000 Lb.per Sq.K. Extreme Length for Deflection for Plastered Ceilings Limit 1-480 Span For Uni- formly Distrib- uted Load For Cen- & For Uni- formly Distrib- uted Load For Cen- ter Load Flange X Stem X Weight (In.) (In.) Foot- pounds Ft. In. Ft. Flange X Stem X Weiht (In.) (In.) 3 Foot- pounds Ft. In. Ft. In. T-5 x3 -13.6 2.6 1.18 1,570 6-9 4-6 T-3 x3 -10.1 9.0 7.9 6.8 2.3 2.1 1.8 1.6 1.10 1.01 0.86 0.74 1,470 1,350 1,150 990 6-3 4-3 T-5 x2i-11.0 1.6 0.86 1,150 5-6 3-8 4-? 4-6 3-10 T-4^x3H5.9 5.1 2.13 2,840 7 2 T-3 x2|- 7.2 6.2 1.1 0.94 0.60 0.52 800 690 5-4 3-6 T-4jx3 - 8.6 -10.0 1.8 2.1 0.81 0.94 1,080 1,250 6-9 T-2fx2 - 7.4 14 0.75 1,000 4-6 3-0 T-4*x2- 8.0 9.3 1.1 1.2 0.56 0.65 750 870 5^9 T-2*x3 - 7.2 6.2 -1.8 1.6 0.87 0.76 1,160 1,010 6yX) 4-0 T-4 x5 -15.7 12.3 10.7 8.5 3.10 2.43 4,140 3,240 10^6 7^0 6^3 T-2x2|- 6.8 5.9 1.4 1.2 0.73 0.60 970 800 5^8 3-9 5^3 T-4 x4^-14.8 11.6 8.0 6.3 2.55 1.98 3,400 2,640 9-6 T-2^x2- 6.5 5.6 1.0 0.87 0.59 0.50. 790 670 3-6 T-4 x4 -13.9 10.9 5.7 4.7 2.02 1.64 2,690 2,190 8 T 6 5-8 T-2|xH- 3.0 0.094 0.09 120 3-0 2-0 T-4 x3 - 9.3 2.0 0.88 1,170 6-8 4-6 3-9 3-0 T-2ix2i- 5.0 4.2 0.66 0.51 0.42 0.32 560 430 4-9 3-^0 T-4 x2|- 8.7 7.4 1.2 1.0 0.62 0.55 830 730 5-8 T-2 x2 - 4.4 3.7 0.45 0.36 0.33 0.25 440 330 4-0 2-9 T-4 x2 - 7.9 6.7 0.6 0.54 0.40 0.34 530 450 4-6 T-2 xlj- 3.2 0.16 0.15 200 3-3 2-2 T-3^x4 -12.8 10.0 5.5 4.3 1.98 1.55 2,640 2,070 8-4 5-6 T-Hxlf- 3.2 0.23 0.19 250 3-8 2-6 T-Uxli- 2.6 2.0 0.15 0.11 0.14 0.11 190 150 3^3 2-2 T-3|x3Hl-9 9.3 3.7 3.0 1.52 1.19 2,030 1,590 7-6 5-0 T-Hxih 2.1 0.08 0.06 0.10 0.07 130 93 2-6 1-9 T-3x3 -11.0 8.7 7.7 2.4 1.9 1.6 1.13 0.88 0.72 1,510 1,170 960 6^6 4-4 5-4 T-l xl - 1.3 1.0 .0.03 0.02 0.05 0.03 67 40 2-0 1-4 T-3 x4 -11.9 10.6 9.3 5.2 4.8 4.3 1.94 1.78 1.57 2,590 2,370 2,100 8-0 T-3 x3 11.0 9.8 8.6 3.5 3.3 2.9 1.49 1.37 1.21 1,990 1,830 1.610 7-2 4-9 108 STEEL CONSTRUCTION This can be applied to designing girders for floor panels. Fig. 86 shows a section of floor with several arrangements of joists. When the girder length is divided by the joists into an even number of spaces as 2, 4, and 6 in (a), (b), and (c), respectively, Fig. 86, the bending moment on the girder is the same as if the entire panel load were uniformly distributed over the length of the girder. When the girder length is divided by the joists into an odd number of spaces as 3, 5, and 7 in (d), (e), and (f), respectively, the bending moment is less than if the entire panel load were uniformly distributed over the length of the girder. PROBLEM To prove the foregoing statements, assume panels 20 feet square and a load of 100 pounds per square foot. Compute the bending moments on the girder for all the cases illustrated in Fig. 86. (a) fr ! ^ (H ^ L (f) v* - I I I I I I Fig. 86. Diagrams of Girders Showing Types of Joist Spacing Shearing Resistance. It has been stated, p. 79, that the maxi- mum shear in a beam section can be determined approximately by assuming that the entire shear is resisted by the web of the beam. For this purpose the area of the web may be taken as the total depth of the beam multiplied by the thickness of the web. Then the total resistance V is the area of the web A multiplied by the allowable unit shear S a and is expressed by the formula The unit stress allowed is 10,000 pounds per square inch. For example, to determine the shearing resistance of a 12" I 40 #: A= 12X0.46 = 5.52sq. in. then F=5.52X10,000 = 55,200# PROBLEM Refer to the problems given under bending resistance. Compute the! -shearing resistance of the beams and compare with the maximum shearing stress.. STEEL CONSTRUCTION 109 The shearing resistance is usually much in excess of the amount required. It need not be investigated unless the span is short or unless a heavy load is applied near a support so that it produces a small bending moment and high shear. The values of the shearing resistance of beams are given in Table III. By the use of this table the shearing resistance of the beam which has been selected can be compared with the computed maximum shear on the beam. Of more importance is the strength of the standard end connec- tions for beams. These are discussed in a later section of this text. Their values are given in Table III. In all cases the strength of the connection is less than the shearing strength of the beam. Hence, the strength of the connection must be compared with the maximum shear on beams. If the standard connection is not strong enough, a special one must be devised and the strength of the web investi- gated. Deflection. The deflection of a beam may be of as much importance as its strength. If its amount is noticeable, it gives the impression of weakness. This is especially true when it shows a definite change under the application and removal of live load. If the beam deflects unduly, it will cause cracks in the supported material. The most common results of too much deflection are cracks in plaster under the middle of joist spans and cracks in tile or concrete floors over the ends of joists where they connect to girders. This is shown in an exaggerated way in Fig. 70. It is not uncommon to find such unsightly cracks in the tile or marble floors of high-grade buildings. It has been determined experimentally that plaster will crack when the deflection is - of the span, i. e., obO 1 inch in 30 feet; but a much lower value should be used for masonry and for marble floors and ceilings. Deflection Formulas. Deflection formulas (p. 80) are as follows : 5 Wl 3 for uniformly distributed load d = -=-= Oo4 LJ I 1 W I 3 for load concentrated at center d = - 48 LJ I in which d is deflection in inches; W is total load; / is length in inches; E is modulus of elasticity; and / is moment of inertia. 110 STEEL CONSTRUCTION To illustrate their use, assume a 12" 131 2 #, span 15 feet, or 180 inches, load u. d. 25,000 pounds. The value of I for this beam is 215.8. Then , = 5 25,000X180X180X180 384 30,000,000X215 8 If we change the load from u. d. to concentrated . 1 25,000X180X180X180 48 30,000,000X215.8 A comparison of the results shows that the deflection is l.G times as much for the concentrated load as for the uniformly dis- tributed load. If both the above loads are applied at the same time, the total deflection is the sum of the two amounts computed above, i. e., <* = 0.29"-f0.47" = 0.76" Formulas are given in the handbooks for other forms of loading, but as they are not used often they are not given here. Concentrated loads within the middle third may be treated as if at the center, and if outside the middle third, as if uniformly distributed. The results from this approximate method will be reasonably close to the cor- rect values. Safe Span Length. Based on a maximum deflection of - of ouO the span, and on a unit stress of 10,000 pounds per square inch, the permissible span is 25 times the depth for a uniformly distributed load and 15.6 times the depth for a center load. These relations are correct for sections symmetrical about the neutral axis, as I-beams and channels. They err on the safe side for unsymmetrical sections, as angles and tees, and may be used for them. These values should be considered the extreme lengths for beams loaded to their full capacity. It is preferred that shorter lengths be used for several reasons: viz, noticeable deflection is objectionable; the greatest practicable stiffness is desired; deflection causes secondary stresses in the connections. The handbooks, in their tables of "Safe Loads Uniformly Dis- tributed for I -beams", limit the span length for deflection to 24 times the depth. The designer must use his judgment in this matter, giving consideration to the conditions of loading. A con- STEEL CONSTRUCTION 111 vonient rule for a u. d. load is 2 feet of length for each inch of depth (24 times the depth); and for a center load 1 feet of length for oac-h inch of depth (16 times the depth). Table III gives the max- imum allowable spans for these ratios, based on a unit stress of 16,000 pounds per square inch. If, however, the unit stress is less than 16,000 pounds, longer spans may be used. In most cases the beam section required to resist the bending moment comes well within the limiting length for deflection. It is only when a long span has a relatively light load 'that deflection must be considered. This condition occurs most frequently in joists. Girders rarely have excessive deflection. To illustrate such a case, assume a beam of 30-foot span sup- porting a load of 8000 pounds u. d. The bending moment is 30,000 foot-pounds, which requires 10" I 25$. The length of this beam is 36 times its depth, therefore the deflection will be excessive. If it is decided arbitrarily to make the depth of beam -of the span, the sec- tion required is 15" I 42 #. This beam, if loaded to full capacity, would deflect just to the allowed limit. But the resisting moment of 15" I 42$ is 79,000 foot-pounds, more than twice the bending moment computed above, hence its deflection being in direct pro- portion to the load is less than half that allowed. Assume that the deflection must not exceed 1 inch, i. e., --- of the span. Then try .; ouO -^ 12" I 3H# and compute the deflection from the formula A w /3 - 5 SOQQX 360X360X360 384 El 384 30,000,000X215.8 _ As the computed deflection is less than the allowed amount, the 12-inch I-beam is satisfactory. The problem can be solved directly instead of by trial. Trans- form the equation to the form 5 IF/ 3 ^5 8000 X 360 X 360 X 360 384 Ed 384 30,000,000 X 1 The beam having a value 7 next higher than 162 is 12" I 31 \ #. The handbooks give explanations and tables for aiding the solution of this problem. 112 STEEL CONSTRUCTION Attention is called to the fact that usually a joist receives a considerable percentage of its load (the floor construction) before the plastering is done. It has already deflected in proportion to the load it has received. It is only the subsequent loading and the resulting deflection that may crack the plaster. Consequently, the total deflection might be much greater than - times the span and - oOU still not cause trouble. Nevertheless it is best to keep within this limit . The situation regarding marble or concrete floors is quite different. Fig. 70 illustrates in an exaggerated way the joists in two panels, connecting to a cross girder. It takes but little deflection to cause cracks in the floor over the girder. No definite limit of deflection has been determined for this case. The writer has ob- served an instance where the deflection appeared to be less than | inch in a span of 24 feet (about r r). No definite suggestion can oOO be made for taking care of this difficulty other than to make the joists as stiff as practicable within a reasonable cost. Probably this trouble can best be eliminated by the use of elastic joints in the floor over the girder. PROBLEM What I -beam is required to support a u. d. load of 4500 pounds on a span of 24 feet the permissible deflection being 3/2 inch? Lateral Support. If the top flange of a beam is not supported laterally, it is in much the same condition as a column. It is then not capable of supporting the full load given by the beam formula. In many cases where the lateral support is not furnished by the floor construction, connecting beams, or otherwise, it can be supplied by means of tie rods or struts inserted for that purpose. When no such lateral support can be provided, the allowable load must be reduced. The handbooks contain tables which give the proportion of the total load that may be used for various ratios of length to width of flange. They permit the full load when the unsupported length is less than 20 times the width. To illustrate the use of these tables assume a 12" I 31 }# 20 feet long, supported laterally at the center. The unsupported length is STEEL CONSTRUCTION 113 10 feet, or 120 inches. The width of flange is 5 inches. Then the 120 ratio of length to width of flange is - = 24. In the Cambria o handbook, the allowable load is 94 per cent of that given by the beam formula. In Table III, the extreme' lengths are given for beams without lateral support when loaded to full capacity and when loaded to half capacity. Intermediate values can be interpolated. The lengths given are, respectively, 20 and 60 times the flange width. In all cases beams must have lateral support at the end bearings. PROBLEMS 1. What is the safe resisting moment of an 8* I 18# on a 12-foot span when the top flange has no lateral support? 2. The required resisting moment of. a beam is 42,000 foot-pounds; its unsupported length is 12 feet. What I T beam is required? PRACTICAL APPLICATIONS Panel of Floor Framing. Fig. 87 illustrates a typical floor panel in a building. It is desired to investigate the various possible arrangements of framing for this panel. Assume that the dead load on the joists is 80 pounds per square foot including the weight of joists (but not the weight of the girders and their fireproofing); assume that the live load is 100 pounds per square foot on joists, and 85 pounds per square foot on girders. Scheme (a). Scheme (a) places the girders on the longer span and divides the panel into 4 parts. The joists are spaced 5'-4|" c. c. Area supported by one joist 16 X 5f = 86 sq. ft. dead load on one joist 86 X 80 = 6880 # live load on one joist 86X100 = 8600 # Total load 15,480 # This total load, 15,480 pounds, is uniformly distributed on a span 16 feet. The table of safe loads in the handbook indicates 10" I25#. The girder carries the reaction of the joists on each side and the weight of itself and of its fireproofing (assumed at 200 pounds per lineal foot). On the theory that the whole floor will not be loaded at one time, the live load on the girder is taken at 85 pounds per ^t *0 / ec -V 65* X , / o 1 d z?a cs c. ' '< \ J 1 * r ^ ' 1 o DO ^l'-6' , M } - 775 1- .1 t 1 ! | ' . 86K8<. 6X-*--J \ ^ '- .-g-t$ . - hi - e'-o" ' \ i 3 I r: -IP'-O" Fig. 88. Types of Lintels EXAMPLES FOR PRACTICE 1. Design lintel for case a, span 4 feet, wall thickness 9 inches. Use 2 Ls. The horizontal legs of the angles should be 3 1 or 4 inches wide to support the brickwork properly. See Table II for formula for bending moment for this condition of loading. 2. Design the lintel required for conditions given for case b. Assume that the channels carry the entire load. 118 STEEL CONSTRUCTION 3. What section of I-beam is required for the lintel in case c? Neglect the value of the plate on the bottom of the beam. 4. In case d assume a load of 20,000 pounds from the girder in addition to the weight of brickwork. What section of I-beam and channel are required? Neglect the value of the angle. 5. In case e assume a load of 2000 pounds per lineal foot in addition to the weight of the wall. What section of I-beam and channel are required? The span is the same as for case c. 6. Determine the angle required to support the face 'brick across a 5-foot opening. (Case /). (The back is supported by brick arches.) Cantilevers. Fig. 89 snows a beam projecting beyond the wall of a building, that is, a cantilever beam. The projection is 6 feet Fl !J i6-o' T^r Fig. 89. Cantilever Construction from the face of the wall. The load to be suspended from the end of the cantilever is 10,000 pounds. Within the building the beam serves as a girder on a span of 16 feet. As such it supports a dead load of 1600 pounds per lineal foot and a live load of 1700 pounds per lineal foot. PROBLEM Compute, from the data given above, the reactions and construct the moment and shear diagrams for each of the three following combinations of loading and determine the I-beam required: (1) Dead load and live load (2) Dead load and suspended load (3) Dead load, live load, and suspended load Tank Support. Fig. 90 illustrates the framework for supporting a wood _ water tank. The tank rests on 4"X6* wood sub-joists STEEL CONSTRUCTION 119 spaced about 18 inches center to center. These- in turn rest on steel joists. The load on the steel joists may be considered as uniformly distributed. Fig. 00. Plan and Elevation of Tank Support To compute the volume and weight, use the outside dimensions of the tank. (Assume the weight of water to be 62.5 pounds per cubic foot.) This will give some excess which will be sufficient to cover the weight of the steel beams. On this basis 3.1416X13X13, volume -Xl6 = 2125cu. ft. weight =2125X62.5 = 132,800# 120 STEEL CONSTRUCTION This can be used as a check on the sum of the partial loads. The load per square foot for 16 feet of water is 16X62.5 or 1000 pounds. PROBLEMS 1. Lay out an assumed plan of the framework and the outline of the tank accurately to scale. Determine the area supported by each beam by measure- ments from the scale drawings as indicated by the shaded areas in the figure. 2. Compute the bending moment and shear for the several joists and the girders, and select the required I-beams. Check for strength of end connections. DETAILS OF CONSTRUCTION Connection of Beams to Beams. When one beam bears on top of another, the only connection required is rivets or bolts through the flange, as shown in Fig. Ql. No stress is transmitted by these Fig. 91. Riveted Con- nection of Beam to Beam Fig. 92. Beam Connections by Means of Sheet Steel Clips rivets or bolts. They serve simply to hold the beams in position. Steel clips are sometimes used for this purpose, Fig. 92, but as they are not positive in holding the beams in position they are not as good, especially when lateral support is required. When this is not important, the clips can be used and may effect a saving in cost. These clips are most useful for attaching tees and angles to beams in ceiling and roof construction. Angle Connections. The most common method of connecting one beam to another is by means of angles riveted to the web. There are several sets of standard connections, various concerns having their own standards. Those of the American Bridge Company are STEEL CONSTRUCTION 121 given in Fig. 93.* The values given in Table III are based on these. The two-angle connection is generally used, but when beams are used in pairs or iwhen for any reason the two-angle con- TWO ANGLE: CONNECTIONS OfiC ANGLE CONNECTIONS 24" WT. JO* I ANGLE 6"X6"Xi 6 Xl'-5?" WT. 25 ^ ANGLES 4 15" I?* 2 AH6L CS 6'X 4"X 'WT. 2 AHGLTS 6"X 4" X R X 5" I ANGLE 6"* 6'Xfc'x 5" 3f*4 ff( 5"& 6" ^ ANGLES 6"x J"& 4' ^ ANGLES 6x f^"& 6"WT. 5* '& 4'WT. 4 3"& 4" I ANGLE 6"* 6"X X ^' i Fig. 93. Beam Connection Angles Used by American Bridge Company nection cannot be used, the one-angle connection is used. The rivets used in the standard connections are J inch in diameter. "Subsequently a different set of standarda has been adopted. See Carnegie Pocket Com- panion, 1913 edition. 122 STEEL CONSTRUCTION The strength of the two-angle connection may be limited by (1) Shop rivets in double shear (2) Field rivets in single shear (3) Shop rivets in bearing in web of joist (4) Field rivets in bearing in web of girder For example, take the connection for a 15" I 42$: (1) 6 shop rivets in double shear 6X10,300 =61,800# (2) 8 field rivets in single shear 8X 4420 = 35,360 # (3) 6 shop rivets in bearing in web of joist 6 X. 41 X. 75 X 25,000 = 46,125 # (4) 8 field rivets in web of girder; the thickness of the web is not given. It must be at least 0.30 inch for a connection on one side only, or of twice this thickness if an equal connectioh is on the opposite side, in order to have the same strength as the field rivets in shear. Jif COPE TO I8"l 35* Fig. 94. Plate Riveted to Web of I-Beam to give Additional Bearing / ) ( ) ( ) ( ) ( r iff 00 O O O O O O O \ i oo i I o i oo i i \ f7=3 ^> o o ) O O Tt~4^ Fig. 96. Types of Beam Connections 124 STEEL CONSTRUCTION quent. If it does happen, however, angles with 6-inch legs may be used to provide space for more rivets, or a reinforcing plate may be riveted to the web of the girder, Fig. 94. Special Connections. When beams on the two sides of a girder do not come opposite or are of different sizes so that the standard connections do not match, it is necessary to devise a special connec- tion. If a beam is flush on the top or on the bottom with the one to which it connects, the flange must be coped, Fig. 95. A number of special connections are shown in Fig. 96 and need no explanation. Connections of Beams to Columns. A beam may connect to a column by means of a seat or by means of angles on the web. The great variety of conditions that may be encountered make it im- k I ^ practicable to have standards for == \ T s f a T B these connections, though the work of each shop is standard- ized to some extent. Seat Connections. The seat connection is shown in Fig. 97. This seat or bracket is made up of a shelf angle, one or two stiffener angles, and a filler plate. The load is transmitted by the rivets, acting in single shear, which connect the bracket to the column. The number of rivets used is proportioned to the actual load instead of being standardized for the size of the beam. The stiffener angles support the horizontal leg of the shelf angle and carry the load to the lower rivets of the connection. Shelf angles are 6 inches, 7 inches, or 8 inches vertical and 4 inches or 6 inches horizontal, having a thickness of ft inch to f inch, depending on the size of beam and the load. The leg of the stiffener angle parallel to the web of the beam is usually \ inch or 1 inch less than the horizontal leg of the shelf. The leg against the column is governed by the gage line of the rivets in the column. The filler is the same thickness as the shelf angle. An angle connecting the top flange of the beam to the column is generally used. It is not counted ^ 4 -o <> -o g <> -(> Fig. 97. Seated Connection of Beam tor Column STEEL CONSTRUCTION 125 as carrying any of the load, but serves to hold the top of the beam in position and stiffens the connection. The rivets connecting the bottom flange of the beam to the shelf serve only to hold the mem- >-^ Fig. 98. Types of Scat Connections bers together and make a stiff connection. Usually there are only* two rivets in each flange but sometimes larger angles and more 126 STEEL CONSTRUCTION rivets are used to develop resistance to wind stresses. Fig. 98 gives .a. number of examples of seat connections. The advantages of the seat connection are ^1) All shop riveting is on the column which is a riveted member. No shop riveting is required on the beam which thus needs only to be punched (2) The seat is a convenience in erecting (3) The rivets which carry shear are shop driven (4) The number of field rivets is small Web Connections. The web connection is made by means of two angles, Fig. 99. The legs parallel to the beam rivet to the w r eb and the outstanding legs to the columns. The connection to the web of the beam is governed by the same conditions as the standard beam connection. The length of the outstanding leg is governed by the gage lines of the rivets in the column or the space available for them. Usually the angles are shop riveted to the beam and field riveted to the column. If the angles were shop riveted to the column, it would be difficult or impossible to erect the beam. However, one angle may be shop riveted to the column and the other furnished loose. In this case the number of field rivets generally will be the same as if the Fig. 99. Web ConncctioB of Beam to Column ) y f L/HE Of FIREPROOFIING Fig. 100. Diagrams Showing Disadvantage of Seat Connection for Fireproofing angles were shop riveted to the beam, but the shop riveting on the beam will be eliminated, which is an advantage. When this connec- STEEL CONSTRUCTION 127 tion is used, a small seat angle is provided for convenience in erecting. The advantage of the web connection is the compactness of the parts, keeping within the limits of the fireproofing and plaster, whereas the seat connection may necessitate special architectural treatment to fireproof it or conceal it, Fig. 100. Combination Connections. A combination of web and seat connections may be used to meet special conditions. For example, the load may be too great for a web connection, and at the same time a seat connection may be objectionable. The combination will reduce the seat connection to a minimum, perhaps eliminating the stiffener angles. Another case is where top and bottom angles are required for wind bracing but stiffener angles are not permitted ; there the combination can be used. The objection to the combination is that there are two groups of rivets for supporting the load. If the connection is not accurately made, the entire load may be carried by one group of rivets. A number of miscellaneous connections are illustrated later in the text under column details. Separators. When beams are used in pairs or groups, some connection is usually made between them at short intervals. The connecting piece is called a "sep- arator". If the purpose to be served is merely to tie the beams together and keep them properly spaced, the gas-pipe separator is used, Fig. 101. This consists of a piece of gas pipe with a bolt running through it. This form Fig. 101. Gas-Pipe Separators is used in lintels and in grillage beams. For beams 6 inches or less in depth, one separator and bolt may be used; for greater depth, two should be used. The separator most commonly used is made of cast iron, Fig. 102. It not only serves as a spacer but it stiffens the webs of the beams and, to a limited extent, transmits the load from one beam to the other in case one is loaded more heavily. It seldom fits exactly to the beam so it cannot be relied upon to transmit much load. One bolt is used for beams less than 12 inches deep and two 128 STEEL CONSTRUCTION bolts for 12-inch and deeper beams. The dimensions and weights of separators and the bolts for them are given in the handbooks. They can be made for any spacing of beams and special shapes can I Fig. 103. Special Type of Cast-Iron Separators Fig. 102. Cast-iron Separators be made for beams of different sizes, Fig. 103. The individual beams of a pair or group should be designed for the actual loads which they carry, if it is practicable to do so. If it is necessary to transfer some load from one to the other, a steel separator or diaphragm should be used. This may be made of a 91 ioi o! CM OJ o: Fig. 104. Steel Separator or Diaphragm plate and four angles or of a short piece of I-beam or channel, Fig. 104. If the beams are set close together, the holes must be reamed and turned bolts must be used in order to get an efficient con- STEEL CONSTRUCTION 129 nection. If the beams are set with four inches or more clearance between the flanges, the separator can be riveted to the beams. Specifications usually require that separators be spaced not further than five feet apart. They should be placed at points of concentrated loads and over bearings. Fig. 105. Layout Showing Tie-Rod Connections Between Joists Tie=Rods. A common form of fireproof floor* construction is the hollow tile arch between steel joists spaced from 5 feet to 7 feet apart. The arch exerts a thrust sidewise on the beams and would spread the beams apart and cause the arch to fall, if they were not tied together. Rods f inch in diameter are used for these ties. They are spaced about 6 feet apart and placed 3 or 4 inches above the bottom of the beams. After the arch construction is in place, the thrusts on the two sides of a beam would balance if equally 5EGMENTAL TERRA COTTA ARCH COHSTRUCTIOn Fig. 106. Tie- Rod Connections for Segmental Arches loaded so that under these conditions the rods would be needed only in the outside panels. However, they are needed in all panels 130 STEEL CONSTRUCTION during construction and as the loads on the several panels may be unequal, they are retained throughout the floor construction, Fig. 105. If long span segmental arches are used, the thrust is much greater. Its amount must be computed and the tie-rods propor- tioned for the actual stress, Fig. 106. Bearings. :. Dimensions of Bearing Plates. Under Unit Stresses ate given the safe bearing values on masonry. The end of a beam testing on masonry' usually does not have sufficient bearing area, and a bearing plate is required. The area of the plate is determined by dividing the load (the end reaction of the beam) by the allowed unit pressure on the masonry. For example, assume a 15" I 42$ bearing on a wall of hard brick in cement mortar, the reaction at the bearing being 18,000 pounds. The allowable pressure is 200 pounds per square inch. Then the required 18,000 r 03 L area of the plate is 200 or 90 square inches. Fig. 107. Diagram Show ing Bearing Plata./ A plate S"X12" or one 1.0"XlO" would be used. The required thickness of the bearing plate depends on the pressure per square inch on the masonry and the projection of the plate beyond the flange of the beam. , ( This projecting portion of the plate acts as an inverted cantilever with a u. d. load. Thus in Fig. 107 the beam is a 15" I 42 #, the plate 8"X 12". The projection of the plate is 3^ inches and the upward pressure per square inch is 200 pounds. To determine the thickness, assume a strip 1 inch wide; then there is a cantilever 3| inches long with a load of 200 pounds per inch. ^ The bending moment is > 3.25X200X = 105Gin.-lb. / From the bending moment the required section modulus can be c obtained by the formula given on p. -98; and from it the thickness t of the plate can be obtained by the formula given on p.- 37, thus I = M = J 050 c X 10,000 ~' Ub STEEL CONSTRUCTION 131 From the section modulus the thickness t can be computed by the reverse of the method previously given for computing /, thus 1 t I = bt a o = 1 c 19 9 i i A _L = -L ^ = 1*2 c 12 _*_ 6 2 * 2 = 6X- = 6X.066=.396 c * = V7396 = 0.63", or |" thick The square root can be figured by the usual rules but can be obtained more easily from tables in the handbook. Graphical Diagram for Designing Bearing Plates. Fig. 108 is a graphical diagram for designing bearing plates. Along the left side ?;n m Tzwr y&rS THICKNE 35 Of PLA TE Ifi IrtCHES (Mult iplu by Z} for Caar Jron) Fig. 108. Diagram for Determining Thickness of Steel Bearing Plates is given the projection of the plate in inches; along the bottom is the" thickness in inches; the diagonal lines represent the several allowable pressures for different classes of masonry. Having com- puted the size of plate needed for bearing, find the amount of its projection beyond the flange of the beam. Enter the diagram at the left on the horizontal line corresponding to the projection; trace 132 STEEL CONSTRUCTION to the right to the diagonal line representing the pressure; then vertically downward to the bottom of the diagram and read the thickness. For example, assume a projection of 3J inches and an allowable bearing of 200 pounds per square inch ; the required thick- ness is | inch. Standard Bearing Plates. In the handbooks are given standard bearing plates for the various sizes of beams. One size of plate is given for each size of beam, hence these standard plates are designed for the heaviest loads likely to be carried by the heaviest beam section and, consequently, are larger than needed for most cases. In the example given above, the Cambria standard plate is 12" X 15" Xf". It is larger than re- quired, thus showing that it is economical to design the plates for the actual loads and the allowable bearing pressures. In this same example, if the bearing is on concrete at 400 pounds per square inch, no plate is required as the beam flange alone gives the necessary area. Penetration into Wall. The penetration of beams into the wall, if the thickness of wall permits, should be not less than Fig. 109. I-Beams Used For Bearing the f ollowing : for 3-inch, 4-inch, 5-inch, and 6-inch beams and channels 6 inches for 7-inch, and 8-inch beams and channels 8 inches for 9-inch, and 10-inch beams and channels 10 inches for 12-inch, and 15-inch beams and channels 12 inches for 18-inch, 20-inch, 21-inch, and 24-inch beams and channels 15 inches When the thickness of the wall does not permit the penetration recommended above, the allowable bearing stress should be reduced. The reduction should be 50 per cent for heavy beams on an 8-inch STEEL CONSTRUCTION 133 bearing. A penetration less than S inches should never be used for beams 8 inches or more in. depth. Because all beams deflect under load their bearing plates should be set with a slight slope downward toward the face of the wall, J inch per foot being a satisfactory slope. This prevents the whole load from being concentrated on the front edge of the plate. Plates thicker than 1 inch are difficult to get. When this thickness is not enough for the projection desired, one or more Fig. 110. Anchors for Beams I-beams or channels should be used for the bearing, Fig. 109. These are designed as inverted cantilevers in the regular way. Cast-Iron Plates. The foregoing discussion relates to steel plates. Cast-iron plates may be used. The method of designing them is the same as for steel plates, except that the allowable fiber stress is 3000 pounds per square inch. On account of this differ- ence in. the allowable stress, the thickness of the cast-iron plate is 2| times the thickness of the steel plate. The diagram, Fig. 108, may be used for cast iron by first determining the thickness for 134 STEEL CONSTRUCTION steel and multiplying the result by 2}. In most localities the cast iron costs more than steel on account of the additional weight. Anchors. Beams bearing on masonry are usually anchored to it to give greater stability to the structure as a whole. Fig. 110 shows the common forms of anchors used for this purpose. The bent rod a is the cheapest. The angle lugs b are the most efficient. The other forms are used for the special conditions indicated. The thickness of metal used is arbitrary, usually J inch for rods and f inch for angles and plates. Miscellaneous Details. Almost every structure presents some conditions requiring special details of the beams. The relative position of the steel members may require a special form of con- nection, or the other materials of construction may necessitate special details for their support. A number of such details will be shown in connection with the practical designs later in this text. RIVETED GIRDERS Definition. The term "riveted girder" is here used to apply to all riveted beams, i. e., beams made of two or more steel sections r\ r\... (<*) (c) Fig. 111. Types of Riveted Girders riveted together. The most common forms of riveted girders are illustrated in Fig. Ill as follows: (a) I-beam with flange plates (c) Plate box girder (b) Plate girder (d) Beam box girder STEEL CONSTRUCTION 135 THEORY OF DESIGN Determination of Resisting Moment. All that was stated under Review of Theory of Beam Design applies as well to riveted girders as to rolled beams, provided the sections are so riveted together that they act as a single piece. However, there are two methods of determining the resisting moment, viz, by moment of inertia and by chord stress, Fig. 112. Moment of Inertia Method. The procedure for determining the resisting moment of a beam, or girder, by means of the moment of inertia has been fully explained. The value of / for the single Fig. 112. Diagram of Bending Stresses in a Riveted Girder, (a) Moment of Inertia Method: -(b) Chord Method rolled section, such as the I-beam, is taken from the tables in the handbook, but for the riveted girder it must be computed. Chord Stress Method. The second method of designing riveted girders assumes that the tensile stresses are resisted by the tendon flange and the compressive stresses by the compression flange. It is assumed that the stress is uniformly distributed over the entire area, of the flange. Then the moment of resistance is the same as if the whole stress were acting at the center of gravity of the flange area. The resisting moment determined from the moment of inertia is n/ The resisting moment by the chord method is as follows : In Fig. 112, t and c represent, respectively, the total tension and total compression values of the flanges, applied at the centers of gravity of the flange sections. The distance d between them is called the "effective depth of the girder". In order to have equilibrium, / must equal c. Each must equal the area A of the flange multiplied by 136 STEEL CONSTRUCTION the unit stress S. Then t c == A X S, and the resisting moment is Having determined the bending moment in inch-pounds from the loads on a girder, the procedure by the chord method is as follows : Assume the total depth of girder and from this approximate the effective depth d in inches. This can be taken at 2 to 4 inches less than the total depth, depending on the size of flange angles. By dividing the bending moment M by the effective depth d, the flange stress t or c is obtained; and dividing the flange stress by the average unit stress, say 14,500 pounds per square inch, the result is the net area in square inches required for the flange. The sections required to make up this net area can then be determined. The foregoing computations are expressed by the formula A-& ~Sd The average value of the unit stress to be used is proportioned from the extreme fiber stress, 16,000 pounds per square inch. Thus if the effective depth is yV of the extreme depth, the average unit stress to be used is yV of 16,000, or 14,400 pounds per square inch. The result of the first trial is only approximate. From the section thus determined the value of d can be computed and the above operations repeated. This result, which is also approximate if any change is made in the section, is usually accurate enough to be accepted as final. Most specifications permit J of the v/eb to be counted in each flange section. Illustrative Example. Assume M equals 420,000 foot-pounds; total depth of girder 36 inches; approximate value of d equals 33 inches. To find the required section . = 420,000X12 = 5,040,000 in.-lb. A 5,040,000 {J web 36" X T Y' = 1.41sq. in. 2Ls6"X3|"Xf" = 11.10 less 1 rivet hole= 1.10 =10.00 ^ = 11.41sq. in. As the area of the chosen section is greater than the calculated value, it is satisfactory. STEEL CONSTRUCTION 137 PROBLEM Fig. 113 illustrates 1he plate girder described in the above example. Com- pute the correct value of d. (Note: No. account is taken of the part of web plate which is counted as flange section, in computing the position of the c. g. of the flange. Also no account is taken of the rivet H ,. . SH holes in the web.) Compute the net flange area re- quired and, if necessary, correct the size of angles. The two methods of designing lead to about the same results. No further consid- eration will be given to the chord method, as the moment of inertia method is preferred. Calculation of Load Effects. The bend- ing moments and shears are computed in just the same manner for girders as for beams. However, in making a complete design of a riveted girder the bending moment is required for all points along the girder for computing rivet spacing and for deter- mining the length of cover plates, if they are used. Consequently the moment diagram is needed in most cases. (It can be constructed Fig. 113. Section and Details . . .11. ,1 A - of Plate Girder by the methods given in the sections on Bending Moments and Moment Diagrams in "Strength of Mate- rials".) DESIGN OF PLATE GIRDER Having computed the bending moments and shears and con- structed the diagrams for them, the steps in the design are: Determine allowable depth \y Compute thickness of web y. Compute required moment of inertia Compute flange section which will give required mo- ment of inertia Determine length of flange plates Design stiffeners Design end connection Compute spacing of rivets for flanges For illustrating the operations, assume a plate girder as shown in Fig. 114. The span is 45'-0"; load 4000 pounds per lineal foot equals total load of 180,000 pounds; end shear 90,000 pounds; 138 STEEL CONSTRUCTION maximum bending moment 12,150,000 inch-pounds. The shear and moment diagrams are given. Depth. Economy. For any set of conditions governing the design of a plate girder there is a depth which gives the greatest economy of metal. But there are so many conditions entering into the problem that no simple formula can be given for computing it. /8O.OOO U.D, 1 S-o , t 4-C\ s'-"> ,4-0 4-0 4-0 4-O 4-0 4-0 4-6 '90,000* MOMENT PI A GRAM Fig. 114. Plate Girder Design The effects of some of these conditions can be stated in general terms as follows: The greater the shear the greater the depth required The greater the bending moment the greater the depth required The longer the span the greater the depth required The thicker the web plate the less the depth For lateral stiffness shallow depth is better The smaller the deflection allowed the greater the depth needed STEEL CONSTRUCTION 139 If it is desired to determine the most economical depth for a given case, several depths must be assumed, the designs made, and the cross sections or weights computed. A few trials will lead to the desired result. The depth of the girder may be as small as -fa of the span and may be as great as J the span, but the usual range is A to J. In the absence of any governing feature J of the span may be assumed as a suitable depth. Other Consideration*. Usually other considerations than econ- omy will determine the depth. In building construction it is gener- ally desirable to make the girders as shallow as practicable, then the depth may be governed by deflection, by practicable thickness of web or section of flanges, or by details of connections. The final result must be determined by trial designs. In the example, Fig. 114, assume the depth of web plate to be 48 inches. On account of the fact that the edges of the plate will not be exactly straight (unless they have been planed), it is custom- ary to set the flange angles J inch beyond the edge of the plate, making the depth in this case 48J inches back to back of angles. Thickness of Web. In building work, ^ inch is a suitable thickness to adopt as the minimum. For exceptional cases when the loads are light J inch may be used. Under Unit Stresses, p. 51, the allowable shear on girder webs is given, i. e., 10,000 pounds per square inch. This is the .average shear on the net cross section of the wet). In the example, Fig. 114, the maximum 90 000 shear is 90,000 pounds; then the net area of the web must be '^^ .LUjUUU or 9.0 square inches. The depth of the web is 48 inches, from which must be deducted 2 rivet holes J inch in diameter, making the net depth 46J inches. The thickness required to give the net cross 9 section-is ' or 0.19 inches. Hence a plate 0.19 inch thick fulfills 4u . ^O the requirements for shear on the web. This is less than the mim% mum adopted, so the thickness is made A inch. PROBLEM What thickness of web is required for a shear of 220,000 pounds, depth 44 inches? Before the thickness of web can be accepted as being satisfac- tory, it must be known to provide ample bearing for the rivets which 140 STEEL CONSTRUCTION connect the flanges to the web. The design of this riveting is ex- plained later. For the present purpose the method used is this: Assume that an amount of stress equal to the maximum vertical shear must be. transmitted from the web to each flange within a distance equal to the depth of the web. Applying this to the exam- ple, the maximum vertical shear is 90,000 pounds and this amount must be transmitted from web to flange in a distance of 48 inches, which equals the depth of the web. The bearing value of a J-inch rivet in a ^-inch web is 5860 pounds. The number required is 90000 ^- or 16. This number of rivets in a distance of 48 inches gives OobO a spacing of 3 inches, which is satisfactory and requires only one row of rivets. (Two rows could be used, giving space for twice as many rivets as are needed.) Therefore, the web thickness is satisfactory. Shearing Value of Web Plates. A study of the shearing value of web plates compared with the bearing value of rivets in the web will show that sufficient bearing value can be developed to equal the shearing value. Consequently, the bearing test need not be applied. For a unit shear of 10,000 pounds per square inch and a unit bearing of 25,000 pounds per square inch, it can be shown that two rows of f-inch rivets, spaced 3f inches center to center in each' row, will have the same bearing value as the shearing value of the plate (no reduc- tion being made in shearing value on account of rivet holes). PROBLEM Assume a plate 64 inches deep and i inch thick. Prove the foregoing statement, Moment of Inertia Required. Having the bending moment and the depth of the girder, the value of the required moment of inertia can be computed from the formula, (see p. 78). , Me . " S In the example, Fig. 114, M = 12,150,000 in.-lb.; S = 16,000 #. If no flange plates are used, the distance c is measured to the back of the angle, i. e., 24J inches. Then If it develops that flange plates must be used, the value of the moment of inertia must be increased to correspond to the increased depth. STEEL CONSTRUCTION 141 Flange Section. Having determined the moment of inertia required, it is next necessary to find by trial the section which has this moment of inertia. To avoid tedious figuring, a rough approxi- mation is first made. The web plate being determined, its moment of inertia may be computed or be taken from the handbook. 7 for PL 48" X A" = 2880 This amount deducted from 18,415 leaves 15,535 as the net value of 7 to be supplied by the flanges. The general formula for moment of inertia, p 38, is 15 535 ' oUo In this case r is about 22.5 inches, then r 2 = 506, and A= or 30.7 square inches. This is the net area of the two flanges. The gross section must be larger to allow for rivet holes; for this add 2.3 square inches, making 33.0 square inches, or 16.5 square inches for each flange. This area may be made up of 2 angles without a plate or of 2 angles with a plate. Both cases are given. Case A Without Flange Plates. With- out flange plates, use 2Ls 6"X6*Xf", having an area of 2X8.44 or 16.88 square inches. For this case the total depth is 48J inches, as previously determined, and no correc- tion is needed for the required value of 7, viz, 18,415. Now compute its value for the approximate section, Fig. 115, making Fig. 115. Section of Plate Girder Without Flange Plates the necessary corrections for rivet holes. 1 PI. 8" X T V (from tables) .............. 2,880 Deduct for holes 2X1 X ft X21 .75x21 .75 260 2,620 4 Ls 6X6Xf (from tables) about axis a-a 113 about axis 6-64x8.44x22.47x22.47 17,045 17,158 Deduct for holes 4XIX|X21.75X21. 75 1,241 15,917 Total net value of / 18,537 142 STEEL CONSTRUCTION In deducting for rivet holes, the diameter of hole deducted is | inch for a f-inch rivet. The distance to the holes is taken at the outer of the two rows of holes. The moment of inertia of the section is somewhat larger than the required amount, therefore the section is satisfactory. Case B With Flange Plates. With flange plates it is usually specified that not less than one-half the flange area shall be in .the angles, or the largest size, of angle shall be used. In this example it has been found that only one row of rivets is necessary for connecting flange to web. For the first trial use 2Ls6"X4"Xf" and 1 PI. 14" X A*. Then the gross area of one flange equals for2Ls6"X4*Xf" for 1 PL 14' X A" Total area 2X5.86 = 11.72 = 6.12 = 17.84 The section is shown in Fig. 116. For this section the value of c is 24.25+0.44 or 24.69. The required value of / must be corrected to correspond: 12,150,000X24.69 16,000 = 18,750 Fig<11 with Se F C bnge 0f pSes Girder The value of I computed for the assumed section is 1 PL 48' X ft* = 2880 Deduct for holes 2XIX ft X21 .75X21 .75= 260 2,620 4 Ls6"X4"Xf" about axis a-a = 30 about axis b-b 4X5. 86X23. 22X23. 22 =12,637 12,667 2,296 10,371 = 6,418 = 19,409 Deduct for holes 4X|X|X21.75X21.75 = 1 4X1X1X23.94X23.94 = 1260 2 PL 14"XTV less 2 rivet holes 2X12JXAX24.47X24.47 Total net value of I STEEL CONSTRUCTION 143 This value of 7 is in excess of the required value, the latter being 18,750, hence the section may be reduced. The correction can be made without going through the calculations in detail. The angles need not be changed, but the flange plates may be reduced in thick- ness. By inspection it can be seen that a reduction of ^ inch in thickness reduces / by 4 of 6418, or 917. The resulting net value of / is 19,409-917 or 18,492. This reduction in the thickness of the flange plate also reduces the required value of 7. It now becomes 7 12,150,000X24.63 1Q7nn 16,000 These results are sufficiently close and the reduced section is used although it is somewhat scant. The revised section is x web plate 48"X T V /2Ls6"X4"Xf" each flange ( lVLl * xr * The sectional areas of the two designs are Case A. 1 PI. 48 X A 15.00 sq. in. 4Ls6x6Xf 33.76sq. in. 48.76sq. in. CaseB. 1 PL 48 X A 15. 00 sq. in. 4Ls6X4Xf 23.44sq. in. 2 PL 14 X f 10. 50 sq. in. 48. 94 sq. in. This showing is slightly in favor of Case A, but it is more favor- able to Case B when it is considered that the flange plates do not extend the full length of the girder. Case B also has the advantage of greater lateral stiffness due to its greater width. On the other hand the cost of the additional riveting may amount to more than the saving in weight. Also the use of the flange plates, taking into account the rivet heads, increases the over-all depth about two inches, which may be objectionable in some cases. In general, the design without flange plates is preferred. Width of Flange Plates. The width of a flange plate is limited by the permissible projection beyond the outer row of rivets. The limits are eight times the thickness of the plate, or a maximum of 144 STEEL CONSTRUCTION six inches. In the above example this limit is 8Xf" or 3". This permits a distance of 8 inches between the gage lines, which is satisfactory. The customary widths of flange plates vary by 2 inches, thus, 10-inch, 12-inch, 14-inch, etc. For 6-inch flange angles the maxi- Fig. 117. Graphical Method of Determining Length of Flange Plates, (a) For Uniformly Distributed Loads; (b) For Concentrated Loada mum width is 20 inches, and for 8-inch angles, 24 inches, but 18 and 20 inches, respectively, are preferable, and 14 inches and 18 inches are most used. When more than one plate is used on a flange, usually the outer one is made less in thickness than the inner one. Length of Flange Plates. The flange section which has just been computed is the section required at the place of maximum bending moment. The bending moment decreases toward the ends, as shown in the moment diagram Fig. 114, and, if it were STEEL CONSTRUCTION 145 practicable to do so, the flanges might be decreased correspondingly. It is necessary for practical reasons to extend the flange angles the ull length of the girder but the flange plates can be stopped at the points where they are no longer needed. The plate ceases to be needed at the point where the bending moment equals the resisting moment of the web plate and flange angles. This can be computed by the methods and from the data already given, but the process is tedious and the results can be obtained more easily by graphical methods with sufficient accuracy. Graphical Solution for Uniformly Distributed Loads. Let Fig. 117-a represent the moment diagram for any uniformly distributed load. The lines at 1, 2, 3, etc., represent the amount of the bending moment at the several points along the girder. The maximum bending moment is at 5. The resisting moment is represented by the line o c'. This line is divided into three parts, o a representing the resisting moment of the web plate, a b the resisting moment of the flange angles, and 6 c' the resisting moment of the flange plates. Then the distance a 1 a! equals the theoretical length of the flange angles, but practically they are made the full length of the girder, and b'b' equals the theoretical length of the flange plates. If more than one plate is used on each flange, additional divisions may be made of the line oc', and the lengths determined in the same manner. If the resisting moments of the several parts of the flanges have not been computed, their moments of inertia may be used for this purpose in the following manner. On the edge of a sheet of paper or on a scale lay off at any convenient scale o a t , aj) lt and 6 t Cj equal, respectively, to the values of I for the web plate, flange angles, and flange plates. Hold the zero point at o and swing the paper or scale to the position where c v falls on the horizontal line through the apex of the moment diagram c'. Then the horizontal lines through a l and b l will cut the diagram at a' d and b r b' and give the lengths of flange plates required. Graphical Solution for Concentrated Loads. Fig. 117-b repre- sents a moment diagram for concentrated loads. The same explan- ations and procedure apply as for uniformly distributed loads. Taking the girder section determined for Case B, p. 142, the length of its flange plates can be determined by the method just 146 STEEL CONSTRUCTION described, using the moment diagram in Fig. 114. The values of 7, as computed on p. 143, are for web plate 2,620 for flange angles 10,371 for flange plates 5,501 18,492 Using a convenient scale lay off o c l equals 18,492, so that c t falls on the horizontal line through c'. Then divide o c t at a l and b l so that 0^ = 2620, 04^-10,371, and 6,^=5501. Draw horizontal lines through a l and b lt cutting the moment diagram at a' a' and 6 '6'. Then a' a' and b' b' represent the theoretical lengths of the flange angles and the flange plates, respectively. As previously stated, the flange angles always extend the full length of the girder. The flange plates are usually made two or three feet longer than theo- retically required. In this case the length b' b' is 23'-6" (approx.); the plates are made 26'-0" long. This extra length is used so that some stress can be developed in the plate at the points &' &'. Web Stiff eners. Schneider's Specifications* provide "The web shall have stiffeners at the ends and inner edges of bearing plates, and at all points of concentrated loads, and also at intermediate points, when the thickness of the web is less than one-sixtieth of the unsupported distance between flange angles, generally not farther apart than the depth of the full web plate, with a minimum limit of 5 feet." The theory of stresses concerned in the design of stiffeners is too complicated for consideration in this text, but some simple rules can be established which will lead to safe construction. Web stiffeners may be divided into two distinct classes: (1) stiffeners at loaded points and (2) intermediate stiffeners. Stiffeners at Loaded Points. The chief purpose of stiffeners at loaded points is to transmit the loads to the girder web. According to the theory of stresses in girders, the load must be applied to the web and produce shear therein from which tension and compression are produced in the flanges. It is, therefore, necessary to carry the applied loads into the web plate as directly as possible. If the load is uniformly distributed on either the top or bottom flange, it is *"The Structural Design of Buildings" by C. C. Schneider, M. Am. Soc. C. E., Transactions American Society. of Civil Engineers, Vol. LIV, p. 495. STEEL CONSTRUCTION 147 transmitted to the web by the rivets connecting the flange angles to the web. The effect of this load on the number of rivets required is considered later in the text. When concentrated loads are applied, enough rivets cannot be placed in the flanges to transmit the load to the web, and also it is desirable that the load be applied throughout the depth of the web plate. To meet these conditions stiff ener angles are used. These /6QOOO LBS Fig. 118. Details of Girder Showing Use of Stiffeners Under Concentrated Load stiffeners may be designed as short compression members using a unit stress of 12,000 pounds per square inch. They must be at- tached to the web plate with enough rivets to transmit the load. Generally the bearing value of rivets in the web plate will govern. As an example, assume that a girder supports a concentrated load of 160,000 pounds, Fig. 118. On account of the width of bearing of the load, it is desirable to use two pairs of stiffeners. The 148 STEEL CONSTRUCTION 160 000 area required is ' -- or 13.33 square inches. 4 Ls5 r X3i*X ft" area 4X3.53 or 14.12 square inches provide the necessary sectional area. The thickness of the girder web being f inch, the bearing value of .a f-inch rivet is 7030 pounds. Then the number 160,000 7030 or 23. There is ample space for this of rivets required is number of rivets. The condition at the end bearing of a plate girder is analogous to that described for a concentrated load and is treated in the same manner. If the end of the girder connects to a column or another girder by means. of web angles, the design is made in the same manner as for the web connection of I-beams. Intermediate Stiff eners. Intermediate stiff eners are used to prevent buckling of the web plate. Ac- cording to the specifications quoted above, stiffeners must be used if the unsupported depth of plate is more than 60 times its thickness. Such stiffeners are to be spaced not farther than the depth of the girder, or for deep girders not more than 5 feet. Applying this to the girder illustrated in Fig. 118, it is found that stiffeners are required, for the unsup- ported depth is 36 inches, while 60 times the thick- ness | inch is 22J inches. The depth of the girder is 4 feet, so the stiffeners are spaced 4 feet. Stiff eners, at loaded points serve incidentally to stiffen the web and are taken into account in spacing the intermediate stiffeners. Intermediate stiffeners are usually angles- in pairs. The leg of the angle parallel to the web plate need be only wide enough for rivet- ing, say 3 inches, as it adds but little to the lateral stiffness. The outstanding leg must be determined arbitrarily. For a 30-inch girder, 3 inches may be used; and for a 90-inch girder, 6 inches; and others in proportion. The thickness should be consistent with the size of the angle and not less than the thickness of the web plate; and the width of the outstanding leg should be somewhat less than the outstanding leg of the flange angles Stiffeners at loaded points must be ground to fit accurately against the loaded flange; intermediate stiffeners need not be so Fig. 119. Crimped Stiffeners STEEL CONSTRUCTION 149 carefully fitted. The use of fillers under stiff ener angles is not necessary, but a better fit can be obtained when they are used. This makes it desirable to use them at loaded points and end bear- ings. Where fillers are not used, the stiffener angles must be crimped to fit the flange angles, Fig. 119. There is little difference in cost, as the expense of crimping offsets the cost of the filler plates. Refer to the girder in Fig. 114. There being no concentrated loads, stiffeners at loaded points are required only at the end bearings, The reaction at each end is 90,000 pounds. The area of stiffener angles required is O r 7.5 square inch. 4 Ls 3J' X 3" X A" have sufficient area, but it is desirable to have them approximately as wide as the flange angles, so 4 Ls 5*X3"X ft* are used. Sixteen rivets are required. There is ample space for them. The web plate is ft inch thick and has an unsupported depth of 36 inches, hence it requires intermediate stiffeners. These are spaced about 4 feet apart (equal to the depth of the girder). Angles 4"X3"X ft* may be used for these stiffeners. Rivets Connecting Flange Angles to Web. In order to make the several pieces of the plate girder act as a unit, they must be rigidly connected. It is evident that if the angles and plates were simply placed in their relative positions without being riveted, they would not co-operate but would tend to act independently. This is explained under Horizontal Shear in "Strength of Materials," Part II. Number of Rivets. The loads on the girder are applied either directly or indirectly to the web, producing vertical shear. By flexure, the vertical shear produces horizontal shear, which becomes tension and compression in fibers below and above the neutral axis, respectively. Most of these stresses occur in the flange plates and angles and must be transmitted to them from the web by the rivets which connect the angles to the web plate. There must be enough rivets to transmit the whole amount of the stress and they must be located at the points where the stress should pass from the web to the flanges. Then in each flange there must be such a number of rivets between the point of maximum flange stress (maximum moment) and each end to transmit the total flange stress; or, stated in other terms, the resisting moment of the rivets between the point 150 STEEL CONSTRUCTION of maximum bending moment and each end must equal the maxi- mum bending moment, and this equals the resisting moment of the girder section, In Fig. 118, let d be the average distance between the rivets in the top and bottom flanges; k the bearing value of one rivet (usually bear- ing in the web plate) ; M the bending moment in inch-pounds; and N the number of rivets in one end of one flange. Then k Xd equals the resisting moment of one pair of rivets in inch-pounds and N equals the number of pairs or the number of rivets in each flange from the center or point of maximum bending moment to either end. For example, assume the following data: M =450,000 ft.-lb. = 5,400,000 in.-lb. k =7030$, bearing value of a f-inch rivet in a f-inch web d -41" Ar 5,400,000 then * Rivet Spacing in Flanges. If the rivets, Fig. 117-a and -b, were spaced uniformly, their resisting moment would be represented by the moment diagram o' c' o', whereas, the bending moment diagram is o' a' b' c' b' a' o'. From this it is clear that the resisting moment of the rivets is less than the bending moment at all points except at the maximum. But these rivets can be so spaced that the two moment diagrams will coincide. To determine this spacing proceed as follows: Lay off oN equal to the total value of the number of rivets, say 19, and divide it into 19 spaces at the points s. Through the points s, draw horizontal lines intersecting the moment diagram at p'oints t . Through the points t, draw vertical lines intersecting the base line at the points r. Then the points r are the locations of the rivets. It is important to note that the rivets are closer together near the ends, i. e., where the bending moment is changing rapidly. On the left side of Fig. 117-b, the spaces are nearly equal because this side of the moment diagram is nearly a straight line. There is a change of spacing wherever there is a change in direction of the moment diagram. For the uniform load, Fig. 117-a, there is a change in each space. Of course it is not practicable to space the rivets strictly in accordance with the theory. The practical method STEEL CONSTRUCTION is to divide the girder into sections, usually taking the divisions formed by the stiffeners, and space the rivets equally in each division. In the problem, Fig. 114. use the following data: , M = 12,150,000 in.-lb. k =5800 #, bearing value of a f-inch rivet in a &-inch web d =41.26" (Case A, Fig. 115) Ar 12,150,000 , n . thcn ^ "5860X41. 26^ nVetS Lay off oN equals 50. Along oo f lay off the points /, 2 9 3, etc., marking the positions of the stiffeners. Through these points draw verticals intersecting the moment diagram at t v t 2 , etc.; thence draw horizontals intersectinjg o N at s v s 2 , s s , etc. Then o s l repre- sents the number of rivets between o and 1 ; s t s 2 , the number between 1 and 2\ s 2 s 3 the number between 2 and 5; etc. o s l represents 17 rivets; the distance o'-l is 64 inches; space the rivets 3 inches center to center. $j s 2 represents 14 rivets; the distance 1-2 is 48 inches; space the rivets 3J inches center to center, s 2 s d represents 10 rivets; the distance $-$ia 48 inches; space the rivets 4 inches'center to center. s 3 s 4 represents 7 rivets; the distance 3-4 is 48 inches; space the rivets 6 inches center to center, and this being the maximum spacing allowed, continue it to the center of the span. If Case B be used, the procedure is just the same. The value of d would be larger (Fig. 116) and, consequently, the number of rivets smaller. Riveting for Cover Plates. In Case 'B there must also be deter- mined the necessary riveting for attaching the cover plates to the flange angles. The procedure is similar to that just given. In Fig. 114, p c' represents the resisting moment of the cover plates and, therefore, the required resisting moment of the rivets. The rivets are in single shear, and the moment arm is the distance back to back of flange angles. Use the following data: A/ = 3,600,000 in.-lb. (approx.). k =4420#, single shearing value of a ^-inch rivet d =481" (Fig. 116) A r 3,600,000 152 STEEL CONSTRUCTION Lay off p A 7 ! equals 17. Along 6' &' lay off the points 10, 11, etc., at intervals of say 4 feet. Draw verticals to JO , , etc., and horizontals to # 10 , s n , etc. ps lo represents 9 rivets; the distance b'-W is 48 inches. There are two rows of rivets in the flange plate, so there are 4| rivets required in one row in 48 inches, i. e., spaced about 10 inches, center to center. But the maximum allowable spacing is 6 inches, center to center, and this is used throughout the length of the cover plates except at the ends where a spacing of 4 inches for a distance of two feet is adopted arbitrarily. Rivet Spacing Computed from Web Bearing. The method, p. 140, for checking the thickness of the web plate for rivet bearing may be used for determining the rivet spacing; for example, assume that an amount of stress equal to the vertical shear must be transmitted from the web to each flange within a distance equal to the depth of the web. Then the number of rivets required in this distance is determined by dividing the vertical shear by the bearing value of one rivet. Referring to Fig. 114 and applying this method: Shear at 0' = 90,000 # 90,000 =10, spacing about 3" No. of rivets in 48 5860 Shear at 1 = 72,000 # 72,000 XT e - A AO* * 13, spacing about 3 J* No. of rivets in 48 5800 Shear at 2 = 56,000 # 56,000 XT t AO* =10, spacing about 4 J No. of rivets in 48* 5860 Shear at 3 =40,000 # 40,000 XT . A . ' = 7, spacing about 6" No. of rivets in 48 5860 Spacing when Load Transmitted through Flange Rivets into Web. If the load on the girder is applied in such a way that it must be transmitted through the flange rivets into the web, then the rivet spacing must take this into account. The exact method of doing so is difficult to apply, but safe results can be obtained by simply adding enough rivets to transmit the load to the web. Thus in Fig. 114 it has been determined that 17 rivets are required between o'-l. The load on this space is 18,000 pounds, which requires 4 rivets to transmit it into the web plate. Then the total number of rivets is 21 and the spacing 2\ inches. STEEL CONSTRUCTION 153 Assuming that the load is applied on the top flange, the extra rivets are required only in. that flange. But in practice the riveting is usually made the same in both flanges. Where stiffeners are used at loaded points, the extra rivets are not required. The actual location and spacing of the rivets must be worked out in making the shop details in order to afford neces- sary clearances from stiff- eners and to suit any other conditions that may apply to the case. It is sufficient for the de- signer to indicate the spacing as it has been computed above. Fig. 120 shows the design drawing for the girder developed in the preceding pages, using Case B, that is, a girder with flange plates. PROBLEMS 1 . Design a plate girder from the data given in Fig. 121. Make the design draw- ing at f-inch scale. 2. Design a plate girder having the same span as the one in Fig. 121, but support- ing only one-half the load there specified. 154 STEEL CONSTRUCTION Tables and Diagrams. A number of tables have been pub- lished giving strength and properties of plate girders. These tables BJ?ICK WALL 'LAID in CEMEHT MORTAR Fig. 121. Data for a Plate Girder Design are of much assistance in arriving at the approximate section of the required girder, but usually the final design must be computed in detail, as in the foregoing example. MOMENT OF INERTIA Fig. 122. Diagram for Determining Moments After Deducting Rivet Holes. 2 Holes, H" (%" Rivets) for %" The large number of plate girder sections that it is possible to make up from the available sizes of web plates, flange angles, and flange plates makes it impracticable to have complete tables of them. The Carnegie Pocket Companion, 1913 edition, contains a valuable STEEL CONSTRUCTION 155 table giving the section modulus for a large number of riveted girders. The handbooks give tables of the moment of inertia of rectangles from which can be taken the value of 7 for the web plate (from this value must be deducted the value of / for rivet holes). Other reference books give the values of 7 for web plates with rivet holes deducted and for many sizes of flange angles placed at various depths; similar tables are given for flange plates. By the use of these tables, the value of 7 for the complete girder section can be found by adding together the values for the web plate, flange angles, and flange plates.* The diagrams, Figs. 122, 123, and 124, give respectively, the values of 7 for web plates, flange angles, and flange plates.' They give the moments of inertia for the sizes of plates and angles most Enter diagram at left margin with depth of- we opiate Trace horizontally to trie diagonal line representing the assumed thickness of the plate, thence vert/ca/ly to the bottom margin and read the moment of inertia MOMENT OF INERTIA of Inertia of Web Plates of Plate Girders to i'' Plates; 2 liolea, 1" d" Rivets) for \" to 1" Plates commonly used for plate girders. Values for intermediate sizes of plates and thicknesses of angles can be interpolated. Although not ""Godfrey's Tables" by Edward Godfrey, M. Am. Soc. C. E. "Civil Engineer's Pocketbook" by Albert I. Frye, S. B., M. Am. Soc. C. E. 156 STEEL CONSTRUCTION ill! iill = OOOI 006 008 001 009 00? OOt STEEL CONSTRUCTION 157 158 STEEL CONSTRUCTION mathematically exact, the results obtained from these diagrams are accurate enough for designing, and will lead to the selection of the same sections as would be determined by computation. The tables and diagrams give only the sections to be used for the girder. The flange plate length, stiffeners, end connections, and rivet spacing must still be designed by the methods heretofore explained. In many .cases, these latter items are left to the de- tailers; but they are properly a part of the design and should be worked out at the same time the girder section is determined, as the detailer i& not likely to have as clear an understanding of the conditions as the designer. PROBLEM Check the girder sections in Figs. 115 and 116 by means of the diagrams in Figs. 122, 123, and 124. OTHER FORMS OF RIVETED GIRDERS The discussion and examples thus far have dealt with the plate girder. The principles and the methods involved are the same for all forms of riveted girders. I=Beams with Flange Plates. A form of girder, Fig. 111-a, is used when shallow girders are required and the I-beams are not strong enough. This often occurs in joists and girders of a floor when it is desired to maintain approximately the same depth for members w r hich carry heavy and light loads. Moment of Inertia. To determine the moment of inertia of the girder, take from the handbook the value of / for the beam and deduct therefrom the value of / for the holes in the flanges; add to this net value for the beam, the value of 7 for the net section of the flange plates. For example compute the moment of inertia for 15"I42#and2P1.8"Xf. /for 15" I 42 # 442 deduct for 4 rivet holes 4XJX|X7.2X7.2 114 328 for 2 PI. 8"Xf" after deducting rivet holes 2x6iXfX7.9x7.9 585 Total value of I 913 Note that two rivet holes are deducted from each flange and from each plate. If the rivet holes are carefully staggered, only one-half STKKL CONSTRUCTION 159 TABLE IV Moments of Inertia of I-Beams with Holes in Flanges (Hol<-s for 3 .i '" rivets computed J/* diam.) SECTION MOMENTS OF INERTIA Grip, or Thick t.esa of Metal at Hole Whole 1 Hole Out of Each Flange 2 Holes Out ot Each Flange 27"! 83# 2888.6 2623.0 2357.4 .89 24*1 100 # 2380.3 2149.0 1917.7 1.00 24'I 80# 2087.9 1884.9 1681.9 .87 2i"I 1028.0 1734.3 1540.6 .82 21"! 1227.5 1090.0 952.5 .74 20"! 14G6.5 1320.0 1173.5 .92 20"! 65# 1169.6 1042.4 915.2 .79 is-I 1141.3 1026.8 011.3 .90 is'T 705.6 704.9 614.2 .69 18*1 733.2 645.2 557.2 .67 15"! 80 r 795.5 706.6 617.7 1.03 i.y'I 609.0 536.6 464.2 .82 151 441.7 385.3 328.9 .62 15"! 3d-- 405.1 351.8 298.5 .59 12"! 40 # 268.9 231.3 193.7 .66 121 31 i- 215.8 184/5 153.2 .545 12"! L'7!. - 199.6 169.9 140.2 .51 10"! 2fi# 122. 1 102.7 83.3 .49 9"! 21 84.9 70.2 55.5 .46 S"I iv-. 56.9 46.1 35.3 .425 of this number need be deducted. The shearing value of the web must be investigated and the length of flange plates and rivet spac- ing computed in the same manner as for plate girders: PROBLEMS 1 What is the resisting moment of a girder made of one IS" I 53$ and two flange, plates 8" XT? -^ * 2. A beam has a span of 24 feet and supports a u. d. load of 80,000 pounds. Design the beam using a 18* I 55# with flange plates. Determine length of plates and rivet spacing. 3. What is the resisting moment of a 20" I 65$ with two |-inch holes in each flange? (Note the great loss of strength due to punching holes in the flanges.) The moments of inertia of I-beams with holes in the flanges are given in Table IV and of flange plates in the diagram, Fig. 123. Beam Box Girders. Beam box girders, Fig. 1 1 1-d, are designed in just the same way as single I-beams with flange plates. They are not economical and should be u^ed onlv when the available 160 STEEL CONSTRUCTION depth prevents the use of a deeper girder. The handbooks give tables of strength of this form of riveted girders. PROBLEMS 1. Compute the moment of inertia of a girder made of two I-beams 24*X80# and two plates 18* Xf'. 2. Design a beam box girder to support a load of 300,000 pounds at the middle of a 30-foot span. Use 24-inch beams. 3. What is the resisting moment of a girder made of two 15* Cs 33# and two plates 14' Plate Box Girders. The plate box girder, Fig. 111-c, needs no explanation as to the method of design, requiring the same procedure as the plate girder. It is used for very heavy loads when the depth allowed is greater than the deepest I-beam but not sufficient to per- mit the use cf a girder with a single web. It is to be noted that the rivets connecting the flange angles to the webs are in single shear, hence the shearing value rather than the bearing value of the rivets will be used in computing rivet spacing. PROBLEM Compute the moment of inertia of a girder made of two web plates 36* X %*> four angles 6' X6* X !', two flange plates 22* X !*, and two flange plates 22* X H*- Unsymmetrica! Sections. Thus far in the discussion of riveted girders the sections considered have been symmetrical about the neutral axis and, therefore, the neutral axis has been at mid-depth. It sometimes happens that the two flanges cannot be the same. This makes the computation of the moment of inertia more difficult. Having made the first approximation of the section, it is necessary to find the center of gravity of the assumed section, p. 35, and then the moment of inertia about the neutral axis (through the center of gravity), p. 36. The common examples of unsymmetrical sections are crane girders, I-beam lintels with one flange plate, girders requiring extra lateral stiffness on account of unsupported top flange, and I-beams with rivet holes in the tension flange at the place of maximum bending moment. In designing such girders the flanges are made as nearly equal as practicable, so that the neutral axis may be near mid-depth. Of course this cannot be done when a single flange plate is used on an I-beam. With the exception noted above, viz, locating the .fot-.i 162 STEEL CONSTRUCTION 'V0O-TJ aOOM II O3J. VNIUV 7 PXf-fr 3NH ~U -3NINVZZ3 5? kWjtfjWriy*- 8 s> *^*, f*f? Sl8 ^ i , ^ ?i ^ (Vj -J. << "\ \ . a 6 % ^* 'VET 5 PA GERED n K | 1 1 ** E| ?! T- ** g j % ^ i ^ s Si \ | V l IT Va *J i P - $ i 8 p 1 1 5 s 5 ? 54 i E Ig B I o Ml |l Ci * , 1- ^ * 5 V ^ .1 >' & t VD L. KT ^ 01 isg o (P (o . r? ^ S 7; ^ _J j i-H ..( -----I neutral axis, the procedure in designing is the same as for symmetrical girders. PROBLEMS 1. A lintel is made of a 12* I 31 1 /2# and a plate on .the top flange 12" X A". What is the moment of inertia of the section? 2. What is the resisting mo- ment of a 15" I 42# which has two holes for f-inch rivets in the bottom flange? PRACTICAL APPLICATIONS Girder Supporting a Col= umn. In order to get the rooms in the lower part of a building arranged satisfacto- rily, it is sometimes desirable to space the columns differ- ently than they are placed above. This makes it neces- sary to carry the upper col- umns on girders. Such a case is shown in Plate O, p. 285. As is usual in such cases, the amount of vertical space avail- able is limited and the depth of the girder is fixed by other considerations than economy of design. The top is limited by the floor level above, it being necessary to have room for fireproofing and for the fin- ished flooring. The bottom is limited by the clearance re- quired for the floor below. The actual depth of web is de- termined after making a pre- STEEL CONSTRUCTION 163 liminary design of the flanges and finding the approximate thickness of flange plates. _ V I \ ) iff- 0" - lO'-O- * lO'-O" 4- lO'-O'- [ IO'-O" * 10-0" * PAH CL LOAD 10* I9> 80*- 15,200 ^ ii P^ T i A 1! j. j i '*-! Fig. 127. Girder for Garage Roof The vertical shear is so large that a single web plate would have greater thickness than is desirable and, furthermore, the shape and posi- tion of the supporting columns would make the connection of a single girder somewhat difficult to design. This leads to the adoption of two web plates. At the supporting columns it is desired to connect one web plate to each flange of the col- umn as shown. If a box girder were used, it would be difficult to erect it, hence two girders best fulfill the conditions. Having settled the above points, the girder is designed by the meth- ods which have been given. Plate O shows the design drawing of the girder and Fig. 125 is the shop detail drawing. PROBLEM In the first story of a building it is necessary to omit a column and support the upper part of the column on a Fig. 128. Section of Typical Craae Girder 164 STEEL CONSTRUCTION .girder. The span of the girder is 36 feet. The load is 540,000 pounds applied at the center of the span, and in addition to this there is a u. d. load from the second floor, the weight of girder with its firoproofing amounting to 4200 pounds per lineal foot. The depth available is 50 inches. Design the cross section of the girder. Plate Girder Lintel. Fig. 12G shows a plate girder used as a lintel over a driveway into a building. It supports the wall above and the floor loads which bear on the wall. Roof Girder. A garage roof is to be built with no supporting columns, so it must be carried from wall to wall on girders. The roof slab rests on I-beams which 0000 0000 00 1 5 T IFF E HER ANGL CS 4 "" FILLER -A PLATE ^K f $ 1 {^ O FITTED TO FLANGE \ T ^K ^K- Q- &\ O e !, t 8 SOLE PLATE: -~^ _ti> ci uHij BEAMING PLATE Fig 129. Plate Girder Bearing on Masonry Fig. 130 Diagram Showing Web Connection of are connected to the girders. The dimensions and loads -are given in Fig. 127. There is no limitation of depth, the most economical section being desired. PROBLEM Design the girder for the conditions given above and make design drawing at f-inch scale. ( Crane Girders. Crane girders do not belong to the class of buildings now under consideration. Fig. 128 represents a typical crane girder and is given to illustrate the use of an unsymmetrical STEEL CONSTRUCTION 165 FITTED ANCLC SEAT ANCLE FF EWE ft ANCLES- FILLER MN WEB section of girder. The stresses in a crane girder and the design are explained under Runway Girders in "Roof Trusses". The channel on the top flange is required to give lateral stillness to the girder in order to resist the lateral thrust of the crane when the carriage is moving crosswise of the build- ing. It also serves incidentally as a guard rail. PROBLEM Locate the neutral axis of the girder illustrated in Fig. 128. DETAILS OF CONSTRUCTION* End Bearings. When the end of a girder bears on ma- sonry, Fig. 129, the bearing plate is designed in the same manner as for beams. With riveted girders it is much more fre- quently necessary to replace the plain bearing plate by I- beams to spread the bearing along walls, than when the girder is an I-beam. A sole plate should be riveted to the bottom of the girder. It stiffens the flange angles and furnishes a more even bearing surface than the angles. In high-grade work, the bottom of the girder may be faced before the sole plate is attached. A very heavy load may require a bearing plate thicker than it is practicable to obtain. Then, if it is not desired to use I-beam grill- age, a cast-iron pedestal may be used similar to those used for columns. The method of designing them is given under columns, p. 220. PROBLEM Design the end bearing for the girder specified in Fig 114. *The details of stiffener angles, filler plates, flange plates, and i cussed and illustrated in the preceding pages. SECTION Fig. 131. of Girder to Column tet spacing have been dia- 166 STEEL CONSTRUCTION Connections to Columns. Web Angle Connection. The con- nection of a girder to a column is usually made with web angles. The connection is designed in the same manner as for I-beams. The angle legs connecting to the girder web should be wide enough to Fig. 132. Diagram Showing Connection of Girder to Face of Column take two rows of rivets and, if the construction is heavy, the filler plate should be wide enough to take a row of rivets beyond the edge of the angles, Fig. 130. The end angles must be set accurately to the correct length and at right angles to the axis of the girder. In railroad bridge construction the end angles ere required to be faced and, to allow for it, the angles used are inch thicker than STEEL CONSTRUCTION 167 otherwise would be required. This should be done on heavy work in building construction. F.LAHGC PL, I4"xi~ / SPLICE PL. 14* f 0- O- SPLICE in FLANGE: PLATE. (6) SPL /C Iff rL AHGE ^fiGL US 0000 0000 WCBPL. (c; SPLICE IN WEB PLATE. Fig. 133. Diagrams of Splices in the Members of a Plate Girder Section Bracket Connection. " The bracket connection, Fig. 131, may be used. It does not make as stiff a joint as the web connection and should not be used unless there is some special reason for it. This 168 STEEL CONSTRUCTION type of connection is specially applicable to box columns on which the brackets must be riveted before the column is assembled. Other forms of connection may be used to meet special conditions. Fig. 132 shows a connection of the web directly to the face of the column. Splices. It is self-evident that there should be no splice in a girder section or in any of its members unless such a splice is abso- lutely necessary. If the splicing is of individual members rather than the whole girder section, the extra work is done at the shop instead of in the field and, therefore, is not so serious. Splicing Due to Transportation Difficulties. The splicing of an entire girder section may be occasioned by transportation condi- tions but it is expensive on account of extra material and field riveting required, and cannot be considered as good as the unspliced section. A girder of any length likely to occur in building construc- tion can be shipped by rail, so that the matter involves only the comparison of the extra freight cost with the cost of the splice. But transportation by boat involves not only the extra charge for long members but an absolute limit to the length that can be stowed. The designer, if not familiar with freight rates and rules, must inves- tigate them, if girder? longer than 36 feet are to be shipped. Splicing Due to Members Longer than Stock Sizes. The individual members of a girder may need splicing, due to inability to secure material of sufficient length, which often happens when material is ordered from stock. ^ This indicates the desirability of consulting stock lists while designing, so that the available sections may be used. The rolling mills regularly furnish angles 60 feet long and by special arrangement will furnish longer lengths. All usual sizes of cover plates are furnished in lengths up to 85 feet. Web plates are most likely to require splicing. Lists of extreme sizes are given in the handbooks. Greater lengths than there listed can be secured from some mills, but it is safer to be governed by these lists unless definite arrangements can be made for the longer plates. Full Strength Splices for Flanges. Both tension and compres- sion flanges must be fully spliced, i. e., the entire tension or com- pression must go through the splice plates and angles and the rivets by which they are attached. In this case no reliance is placed on abutting ends of compression members as is done in columns. STEEL CONSTRUCTION 169 Figs. 133-a, -b, and -c show, respectively, splices in a flange plate, in flange angles, and in web plate. Splice for Flange Plate. Fig. 133-a. The flange plate is 14" X \". The stress must be carried across the gap by a single plate (assum- ing that there is no unused capacity in the flange angles), which must not be less than 14"Xi". The net area of this plate after deducting rivet holes is 12J*X|" or 6.125 square inches. Its tensile value is 6.125 X 16,000 or 98,000 pounds. The splice rivets are in single shear, 98 000 hence the number required on each side of the joint is Use 20 rivets. Splice jor Flange Angles. Fig. 133-b. The flange angles are 2 Ls 6*X6"xr. Their area is 2x7 11 or 14.22 square inches, which, after deducting one rivet hole from each angle, becomes a net area of 13. 12 square inches. The splice plates must have this net area. It is desired to splice both legs of each angle as directly as possible, so the splice plates are arranged as shown. Their sizes and net areas are m 2 PI. 5" Xf, net area 6 18 n 1 PL 13" Xf, net area 7. 03 Total 13.21 sq. in. From these values the number of rivets can be computed in the usual way, noting that the rivets through m are in double shear and through n in single shear. The plates m must extend beyond n at each end far enough to take two additional rivets. The purpose of this is to relieve the angles of a portion of their stress before the first holes in n are reached. Otherwise, in designing the main girder section one hole additional would be deducted from each angle. Splice for Web Plate. Fig. 133-c. The web plate must be spliced to transmit shear and bending according to the amount of these stresses where the splice occurs; if at the place of maximum bending moment, only the bending stresses need be considered, shear being zero; if near the end where the flange angles will take care of all the bending stresses, then only the shear need be provided for. Resistance to Bending. The necessary resistance to bending can be furnished by a flange plate, as in Fig. 133-a; by splice plates on the angles, as plates m in Fig. 133-b; or by splice plates o in Fig. 170 STEEL CONSTRUCTION 133-c; or by any combination of them. In either case the moment of inertia of the net section of the splice plate must equal that of the web plate, or such portion of it as is needed at the place where the splice occurs. It must be noted that a web plate which must be spliced loses some of its moment of inertia because of the holes for attaching the splice plates; consequently, it is better, if practicable, to use a form of splice which will add no rivet holes. If a flange plate is used as a part of the girder section, then an additional flange plate may be used for. splicing the web. If there is no flange plate in the girder section, then plates such as ra, Fig. 133-b, may be used to advantage for all or part of the web splice. Taking for example the girder in Fig. 116, the web plate is 48" Fig 134. Splice in Plate Girder Fig. 135. Bracket tor Bracing Top Flange of Girder X ft*. Its net moment of inertia is 2620, p. 141. Two flange plates 14" X J" after deducting 2 rivet holes from each, have a net value of_/ 7 = 2Xl2JxiX24. 9X24. 9 = 3800 which is more than required. Taking the girder shown in Fig. 115, if a flange plate should be used for splicing, the angles would be weakened by the rivet holes for attaching the plate. If plates such as m, Fig. 133-b, are used, no additional rivets are needed. Try four plates 5"Xf". Their net value of I after deducting one rivet hole for each is which is near enough to be satisfactory. STEEL CONSTRUCTION 171 In a similar manner, plates o, Fig. 133-c, are found to be G"X ft* '. The strength of the splice plate must be developed by rivet bearing in the web plate requiring 10 on each side of the joint. Although this is the most direct method of splicing for bend- ing, it is not as economical as either of the other methods given above. Resistance to Shear. For resisting shear, the splice plates are in the form of Q{ the plates;?, Fig. 133-c. On each side of <3 the joint there must be enough rivets to transmit the total shear. They may be in one or more rows. The thickness of each plate must be at least half that of the web plate and is sub- ject to the same minimum. Hence, in this case the thickness is made ft inch. Fig. 13G. Brace for Plate Girder Fig. 137. Brace for End Girder Position of Splices. Girders completed in the shop will have splices arranged to come at different places; thus the web may be spliced at the center and the angles near one end ; still better, one angle may be spliced on one side of the center and the other on the opposite side. Of course, in a field splice all the elements are joined at one place. The method of computing is the same as has been given for the individual parts of the girder (bearing in mind that the rivets are 172 STEEL CONSTRUCTION field driven). Fig. 134 illustrates such a splice made up from the several splices shown in Fig. 133. PROBLEM Design field splice for plate girder shown in Fig 115. Lateral Support. Girders, like beams, must be supported later- ally to prevent the compression flange from buckling. Schneider's Specifications provide that "the unsupported length of flange shall not exceed 16 times its width. In plate girders used as crane run- ways, if the unsupported length of the compression flange exceeds 12 times its width, the flange shall be figured as a column between the points of support."* In most cases the lateral support is provided by the joists or floor construction. Where this is not the case, the supports can be provided in a number of different ways. For lengths up to 25 feet, the necessary stiffness can be provided by the use of wide flange plates. For greater lengths, box girders may be used, if the load warrants their use. Fig. 135 shows a plate girder to which a joist connects near the bottom. From this joist a bracket extends up to and supports the top flange. The corner brace indicated in Fig. 136 sometimes may be used to advantage. As provided in Schneider's Specifications, crane girders whose length exceeds 12 times the width must be designed as columns. The method is the same as given hereinafter for columns. The ends of the girders must be especially well secured against overturning. When connected to columns or other girders, the desired result is easily attained by the use of web angles or top con- nection angles. If the end rests upon and is built into masonry', the required support is thus provided. Fig. 137 shows one girder rest- ing on another and braced thereto. *Transactions American Society of .Civil Engineers, Vol. LIV, p. 495 MONROE BUILDING, CHICAGO Holabird & Roche, Architects CONSTRUCTION PART III COMPRESSION MEMBERS COLUMNS STEEL COLUMNS Definitions. A column (or strut) is a member subjected to compression in the direction of its longitudinal axis, i. e., subjected to axial compression. The term "column" is usually applied to a vertical member subjected directly to a gravity load. The com- pression members of trusses, and also small isolated members, and members in other than the vertical position, are called "struts" A series of columns in a vertical line is called a "stack". The columns in any one story of a building constitute a "tier". Loads and their Effects. Computation of Loads. The loads on a column are applied to it by the column section above and through the connections of other members or other materials. Most com- monly this is through beams and girders. The amounts of these loads may be taken from those, previously computed for the beams and girders, or may be computed directly from the floor and wall areas tributary to the column. The former method is easier when the loads and areas are irregular, and the latter when the loads are uniform and the arrangement of beams regular. Practical exam- ples of computing the loads are given later in this book. The ideal condition of loading of a column is had when the load is applied uniformly over the top of a column, and when the bottom of the column bears evenly on its support or foundation. In a stack of columns, the load on any column which comes from the column above is usually applied in this ideal way. But the other loads are generally applied to the sides of the column through beam connections, in many cases with greater loads on one side than on the other. 174 STEEL CONSTRUCTION } () (*>) "'ig. 138. Diagram Showir Examples of (a) Concentric Loads and (b) Eccentric Loads Loads applied centrally, or which are equally balanced on oppo- site sides, are called "concentric loads", Fig. 138-a. Loads applied t I to the sides of the column and not balanced, or those which bear on top but are not cen- trally placed, are called "eccentric loads", Fig. 138-b. These terms apply to the bear- ing at the bottom of the column as well as to the loading at the top, but usually the bearing at the bottom is made uniform, i. e., concentric. Concentric Loads. Concentric loads, Fig. 139, produce direct or axial compres- sion in the column. This compression may be considered as evenly distributed over the entire cross section, even if the loads be balanced loads connected to opposite sides of the column. Then the unit stress P on the column is the load W divided by the area A : which is expressed by the formula "5 Conversely the capacity of a column or its total permis- sible load is the allowable unit stress multiplied by the area: W=PA For example, assume the load on a column to be 190,000 pounds and the area of the assumed column 16.4 square inches. Then the unit stress, or average compres- . . 190,000 sion, is or 11.585 pounds per square inch. Eccentric Loads. Eccentric loads, Fig. 140, produce axial compression and in addition cause bending stresses. The axial compression is determined in the same way as for concentric loads, and the bending stresses in the same manner as for beams, p. 81. The bending, or eccentric, moment of the load is the centric Loads amount of the load multiplied by its distance from the neutral axis of Fig. 139. Dia- STEEL CONSTRUCTION 175 the column. The sum of the axial compression per square inch and the maximum compression fiber stress per square inch is the maxi- mum combined stress resulting from the eccentric load. (See Flex- ure and Compression for Beams, in "Strength of Materials", Part II.) This is illustrated in Fig. 140. W is an eccentric load. The direct stress in the column is, represented by the area abed and equals W. (This area may represent the total load on the column if there are other loads than W.) The bending moment produces the com- pression 066' and the tension o c c' . Then the maximum fiber stress in the column is a &', being the sum of a 6 and b b'. On the side opposite to the eccentric load, the tension due to bending overcomes part or all of the compression due ta direct stress. The result in this case is dc r ', but the stress in this side of the column rarely needs consideration. Of course, the eccentricity may be so great that the opposite side of the column is in tension, but even this does not require attention unless the column is spliced. The total stress produced by all the loads equals the sum of the stresses produced by the loads separately*. Some authorities allow three- fourths of the bending moment to be used hi computing the effect on the column. This prac- tice is satisfactory and is followed in the illus- tration used later in this book. Typical Cases. The entire load on the col- umn, including its own weight and the weight of the fireproofing, must be determined (making no distinction between concentric and eccentric loads). Then compute the bending moments due to the eccentric loads, dividing these moments between the respective axes of the column. (a) As an example, refer to Figs. 139 and 140, letting them represent the same column. Assume W a concentric load of 100,000 7 1 lit i ^xj tr . 140. Diagram of *Thia statement is not exactly correct but represents usual practice. 176 , STEEL CONSTRUCTION pounds; W an eccentric load of 50,000 pounds; and e an eccen- tricity, or lever arm of W, of 10 inches. Then Total load = 100,000+50,000= 150,000 # The bending moment due to the eccentric load is M = 50,000X10 = 500,000 in.-lb. As a trial section, take a column made of 1 PI. 12"X|" and 4Ls 6"X3J"Xf" from which c, the distance from the neutral axis to the extreme fiber, is 6.125 inches; r, the radius of gyration about the same axis as the bending moment, is 5.00 inches; -, the section c modulus, is 74.7 inches 3 ; and A, the area, is 18.2 square inches. The average stress resulting from the total load is 150,000 co/ , n j, - 18 2 =8240ff persq. in. This is represented by a b in Fig. 140. The maximum fiber stress resulting from the bending moment, taking three-fourths of the computed moment, is fX500,000 CAOn i, - ^ = 5020# per sq. in. This is represented in Fig. 140 by b b' and c c' in compression and tension, respectively. Then the total maximum fiber stress in the column is 8240+5020 = 13,260 # per sq. in. This is represented by a b'. The method of determining the allowable stress has not yet been given so it cannot be decided whether the trial section given above is satisfactory. (b) Fig. 141 illustrates cases of concentric and eccentric load- ing. In each of them there may be a concentric load from the column section above. In Fig. 141-a, the loads are concentric, pro- vided those on opposite sides are equal and balance each other. If m be omitted, o becomes eccentric, but as it connects to the web of the column the^ eccentricity is small and usually is neglected. If n be omitted, p becomes eccentric with a moment arm e and a bending moment pXe. If n- is less than p, the difference is the eccentric load and the bending moment is (pn) Xe. In Fig. 141-b, the load u is eccentric about the axis 2-2, and the bending moment STEEL CONSTRUCTION 177 is uXe r The resulting fiber stress must be computed from the moment of inertia about the same axis. The load v is eccentric about the axis 1-1, and the bend- ing moment is tXe r The result- ing fiber stress must be com- puted from the moment of inertia about the same axis. Both eccentric loads produce compres- sion at the corner d, hence the effects of both must be added to the axial stress produced by the total load, in order to determine the maximum fiber stress in the column. As an example, take Fig. 141-b and assume the following data, taking for the trial section, a column made of 1 PL 12" Xf and 4 Ls 6"X3"Xf from Which Fig. Ml Diagrams Showing (a) Concentric Load and (b) Eccentric Loads on Columns 7 1 is 213; 7 2 is 721; c, is 6f; c 2 is 6J"; e t is 7"; e 2 is 9i"; and A is 29.7 sq. in. Concentric load from column section above = 150,000 t>= 30,000 u = 45,000 Total load Unit stress from total load = 225,000 # 225,000 , 29.7 = 7575 # per sq. in. M i = 30,000X7 = 210,000 in.-lb. f of this = 157,500 in.-lb. TT -*u * A 157,500X6| , 7on /i Unit fiber stress due to v = - - - =4720# per sq. in. .- lt> 3/ 2 = 45,OOOx9i = 416,000 in.-lb. f of this = 312,000 in.-lb. Unit fiber stress due to u = 2650 # per sq. in. Total fiber stress at d = 7575 +4720 +2650= 14,945 # per sq. in. 178 STEEL CONSTRUCTION PROBLEM Assume a heavier column section for the example given above'and compute the total maximum fiber stress. Eccentric Load In Terms of Equivalent Concentric Load. The effect of the eccentricity of the load can be expressed in terms of an equivalent concentric load, which can be added to the actual load and the resulting total be applied as a concentric load, giving the same maximum stress as if computed by means of the bending moment. The proportion to be added, if the full eccentricity is used, is given by the expression wt-wi& Or, if the reduction in eccentricity is made in accordance with the rule on p. 175, the expression is In these formulas W is the eccentric load and W e ' is the equivalent concentric load. Before this method can be applied, it is necessary to select the trial column section, and from it compute the values of c and r. As the values of c and r for the trial section will vary but little from those for the final section, it usually will be unnecessary to correct the equivalent concentric load computed by this method. Referring now to the example illustrated in Figs. 139 and 140 and explamed on p. 176, the eccentric effect is t 5X5 Then the total equivalent concentric load on the column is W =100,000 W'= 50,000 HY= 91,875 241, 875 # and the resulting stress in the column is This result agrees closely with the results obtained by Use of the bending moment. It would agree exactly if all the computations STEEL CONSTRUCTION 179 and the values of the properties were given in more exact figures. Note that the equivalent concentric load is not- carried down into the next lower section of column but disappears at the bottom of column section under consideration. PROBLEM Compute the equivalent concentric load and the resulting unit stress for the eccentric loads u and v in Fig. 141-b from the data given on p. 177. Strength of Columns. The ideal column is perfectly straight, symmetrical, and homogeneous, but these conditions are never fully attained. The material may not be exactly straight, then inaccur- ate workmanship, the punching of rivet holes, driving of rivets, abuse in handling, and internal defects of the steel, all cp-operate to produce results somewhat short of ideal. These imperfections are of more importance with long than with short columns, and like- wise with small columns than with large ones. The fo'regoing conditions make it necessary to use lower stresses in columns than are used for beams; also to vary the stresses accord- ing to the length and size of the column. The relations cannot be expressed in a rational formula, that is, a formula deduced, from theory, as is the case with beams; hence empirical formulas are used, i. e., formulas based on experimental data. A large number of tests have been made to determine the effect of the length and size on the strength of columns. Several formulas have been derived giving results agreeing closely with the tests. Formula for Unit Stress. The simplest of these formulas and the one now most generally used is P = 16,000-70- r in which P is the permissible compression per square inch of cross section; / is. the unsupported length of column in inches; and r is the least radius of gyration in inches. The radius of gyration rather than the side or the diameter is used as the measure of the size of the column as it relates more directly to the stiffness. From the above formula the allowable stress per square inch can be determined for any column having known values of I and r. Thus if/ = 180" and r = 2.4" i&n P = 16,000-70 = 16,000-5250- 10,750# per sq. in. 180 STEEL CONSTRUCTION Then the total capacity W equals PxA (p.174); and assuming A = l2.0sq. in. \V =10,750X12.0 = 129,000 # The end condition of the column has some effect on the strength. A column which has ends resting on pins or pivots will not support as great a load as one which has flat or fixed bearings. The formula given above applies to columns with flat or fixed ends and as these are used almost universally in building construction, the other formulas need not be considered in this text. Pivoted and pin ends for columns occur in bridge construction and the necessary formulas for them are given in books on that subject. The values given by the formula .do not apply to very long or very short columns. The maximum value of P allowed (see Unit Stresses, p. 51) is 14,000 pounds. This corresponds to a value of = 30, so 14,000 must be used when is equal to, or less than, 30. r r' . In the other direction the limiting value of is 120, according to most specifications. However, larger values may be used with safety if particular care is taken to avoid eccentricity. Schneider's Specifications provide that "No compression member shall have a length exceeding 125 times its least radius of gyration, except those for wind and lateral bracing, which may have a, length not exceeding 150 times the least radius of gyration/'* The formula takes into account only the average imperfections in columns, and makes no allowance for the different styles of columns. Nevertheless, It is known that columns with solid web plates are more efficient than laced columns, and laced columns in turn are more efficient than columns w r ith batten plates. There is no w r ell-established practice in reference to this but a rea- sonable allowance is to deduct from the values given by the formula 25 per cent for laced columns and 50 per cent for battened columns. Having adopted a formula by which the allowable unit stress can be computed, the example given on p. 17G can be completed. *Transactions American Society Civil Engineers, Vol. LIV, p. 495. ; STEEL CONSTRUCTION 181 The trial section there used was a column made of 1 PL 12"X|" and 4 Ls 6"X3i"Xf , from which r (least value) is 2.56"; and A is 18.2 sq. in. Assume /=102". The allowable unit stress is P = 16,000-70 - = 16,000-70 4- = 13,200# per sq. in. r 2. on The maximum fiber stress computed from the assumed loading is 13,260 pounds per square inch,, hence the trial section is satis- factory. Taking the example on p. 177, the trial section of column is made of 1 PI. 12"Xf" and 4 Ls 6" X3i"Xf, from which r (least value) is 2.6S"; and A is 29.7 sq. in. Assume /= 138". -The allowable unit stress is TOO P =16,000-70 ~- = 12,400# per sq. in. The maximum fiber stress computed from the assumed loading is 14,945 pounds per square inch, hence the trial section is not large enough and a heavier section must be tried. Properties of Column Sections. In the foregoing discussion of the formulas, it appears that certain properties of the column must be known before the formula can be applied. The formula for allowable unit stress requires the radius of gyration r and the unsupported length / of the column section. If the column sup- ports an eccentric load, the moment of inertia 7, or the radius of gyration r, and the distance to the extreme fiber c must also be known in order to compute the maximum fiber stress due to bending. Area. The area A is computed by adding together the areas of the several pieces which make up the column section. The areas of the individual pieces are given in the handbooks. No deduction is made for rivet holes. Distance from Neutral Axis to Extreme Fiber. The distance to the extreme fiber from the neutral axis is readily computed from the dimensions of the column section. It must be taken from the axis about which the bending moment is computed. Thus, in Fig. 182 STEEL CONSTRUCTION 141-b, C 2 must be used in connection with the load u, and c, in con- nection with the load v. Moment of Inertia. The moment of inertia is computed by the method explained and illustrated on p. 37. It also must be taken in reference to the neutral axis about which the bending moment is computed. Thus in Fig. 141-b, 7 must be calculated in reference to axis 2-2 for the load -M, and to axis 1-1 for the load v. Radius of Gyration. The radius of gyration is computed about each axis by the method explained and illustrated on p. 38. The lesser value is usually required for computing the unit stress, but either or both may be required for computing eccentric effects. Thus, in Fig. 141-b, both radii of gyration are used. There are conditions under which the larger radius of gyration is used. One such case is that of a column built into a masonry wall in such a way that it is supported by the masonry in its weaker direction, Fig. 142. Then the larger radius is used, but designers are cautioned against using this unless the wall is so substantial that it gives real support to the col- umn. A casing of brick or con- crete or a poorly built brick wall is not sufficient. It sometimes happens that a column is supported in one direction at closer intervals than in the other direction. The weaker way of the column should be turned, if practicable, in the direction of the closer supports. Then the design may be governed by the lesser radius combined with the shorter length; or by the greater radius combined with the longer length. Unsupported Length. The length / is needed for solving the allowable unit stress. It is expressed in inches and is the unsup- ported length of column. This unsupported length is usually measured from floor to floor, but if there are deep girders with rigid connections, the clear distance between girders may be taken as the length. PROBLEM Compute the values of A, / 7 2 , c,, c 2 , r w and r 2 for the column sections, which are shown in Fig. 143. Fig. 142. Section Showing Column Supported by Masonry in Its Weaker Direction STEEL CONSTRUCTION 183 Column Sections. Practically all rolled sections of steel may be used as columns or struts, but only a few of them are economical when used alone. Most columns are built up of several pieces. Fig. 144 shows a number of sections. Section a. The tingle angle is not economical but may be used for a light load. When used, its radius of gyration must be taken about the diagonal axis. Section b. Two angles make a satisfactory strut for short lengths and light loads. Usually angles with unequal legs are used, with the long legs parallel. The radii about both axes are nearly the same for most sizes. The value about the axis 2-2 can be varied somewhat by the use of fillers between the angles. Such fillers should be Spaced two to three feet apart. Fie. 143. Diagrams for Estimating Properties of Column Sections Section c. The star strut is made of two angles with batten plates. The batten plates in each direction are spaced from two to four feet apart. They must be wide enough for two rivets in each end. The least radius is about the diagonal axis 3-3. In accord- ance with the rule, p. 180, this being a battened section, the unit stress should be only one-half that given by the formula. Conse- quently, the section is not economical but is suitable to use when the load is light. It is quite useful as a brace between trusses .and other similar situations. Section d. Four angles placed at the corners of a square and joined together with lacing bars can be made to have a large radius of gyration with a small area. This makes a column suitable for supporting light loads on .a long length. It is not suitable for eccentric loads. The spacing of the angles may be made as great J/ IN j i (C) fe=_l_<=5j 5S__| ^"/ji Fig. 144. Typical Column Sections STEEL CONSTRUCTION 185 as required by the conditions. The allowable unit stress on this section must be reduced on account of the lacing in accordance with the rule, p. 180. However, if the column is filled and encased in concrete, the full unit stress may be used. It is well adapted to use in this way. On account of the weight of the lacing and the cost of shop labor, this section is more expensive than most others for a given area, hence it is used only for conditions described above. Section e. When the angles are placed in this form, the cost of shop work is somewhat reduced, but otherwise the above comments apply. Section f. The Gray column* is made of eight angles joined together in pairs and these pairs are assembled into a column by means of batten or tie plates. The batten plates are usually made 8" X I" and spaced 2'-6", center to center The advantages of this sec- tion are its large radius of gyration and ease of making connections for beams and girders. Its disadvantages are that it is a battened column and, therefore, not capable of carrying the full unit stress given by the column formula; and thatthe expense of its manufacture is high, due to the bent batten plates. It has been used extensively with the full unit stress; however, it seems more reasonable to make some reduction. Since the battens are quite rigid the column is probably as good as a laced column, hence it can be used with a reduction of 25 per cent from the full unit stress. This column is not adapted to eccentric loads and is best suited to load conditions which would bring in equal loads to each of its four parts. This seldom occurs, the most common arrangement being two girders on opposite sides and two joists on the other sides. Thus two segments of the column are loaded much more heavily than the other two. The batten plates cannot be relied upon to equalize the load, but 'heavier angles can be used for the heavier loads. If this system of proportioning each segment to suit the loads which connect directly to it is used, the chief objection to this type of column is eliminated. When filled and encased in concrete, the Gray column is very rigid and can then be loaded to the full unit stress. It is especially suitable as the core of concrete columns, and can be used thus in 'Designed and patented by J. H. Gray, C. E., New York, N. Y. 186 STEEL CONSTRUCTION connection with reinforced concrete floor framing. When so used, the column may be rotated 45 degrees irom the axis of the girders if it is desired to pass the reinforcing rods through the column. The bearing of the beams and girders in part can be directly on the concrete core and in part on lug angles riveted to the faces of the column. The Gray column can be made any desired size using any standard angles. 'The practicable limits are ten inches square (minimum) and twenty inches square (maximum). Sectidn g. A column made olfour angles laced has little merit as compared with the plate and angle .column which is next described. Its only claim is that in some cases it may. be cheaper to use lacing than to use a web plate. This would be so if there were some special condition requiring a, deep column. As with other laced columns, it should not be allowed the full unit stress and should not be subject to any considerable eccentricity, Section h. The plate and angle column' is probably the most pop- ular shape for buildings. It does not give the most economical dis- tribution of metal, as the value of f is much greater about the axis 1-1 than about 2-2. Its advantages are economy of manufacture and ease of making connections. Advantage can be taken of the greater value of r (and therefore of /) about the axis 1-1, in providing for eccentric loads by so placing the column that the bending moment is about this axis. Sections i, j, and k. In the use of heavy forms of plate and angle columns, a considerable variation in area can be made by varying the thickness of metal, keeping the depth constant, and making only a slight change in the width. If greater area is needed, flange and web plates may be added as in i, and still greater area may be secured by using the forms ,; and k. Section k is difficult to fabricate. The flange plates must be riveted to the center web first, and after this is done it is difficult to insert the outside web. Section L Two channels laced have a large value of r in propor- tion to the area. The channels can be so spaced that the values of r for both axes are about equal. This section of column has the same disadvantage's as to unit stress and eccentric loads as other laced columns. The connections for beams and columns are more difficult to make than on plate and angle columns. STEEL CONSTRUCTION 187 Sections m, n, and o. The columns made of channels and plates have good distribution of metal. Their chief disadvantage is the difficulty of making connections. All rivets in connections, except those which go through the flanges of the channels, must be driven before the plates and channels are assembled. The section o, having three webs, has the same difficulty of fabrication as section k. Ob- jection is sometimes made to the closed box section; This is dis- cussed later. Sections p. and q. Section p is the standard Z-bar column, and section q is the Z-bar column with flange plates. The distribution of metal is not as good as in channel columns and the connections are even more difficult. These sections were formerly much used but now only rarely. Section r. The standard I-beam is not an economical column section but is used to meet special conditions. It is suitable when built into a solid masonry wall with its web perpendicular to the axis of the wall. It is thus supported sidewise continuously and can be designed in reference to its larger radius of gyration. In apartment or residence work it is sometimes so desirable to keep the column within the thickness of the partition that the lack of economy of the I-beam column is justified. Sections s, t, w, and v. The columns s, t, u, and v are not much used. There are no serious objections to any of them, and they may have advantages in special situations. Quick service from stock material may require the use of tJiese sections. Section w. The Carnegie \-\-sections are designed especially for use as columns. There are only four sizes, viz, 4, 5, 6, and 8 inches, respectively, and only one weight for each size, consequently their range of usefulness is very limited. The radius of gyration about the axis 1-1 is greater than that about 2-2, but the distribution of metal is as good as in any H-shaped column. They are economical because so little labor is required for fabricating them. Only the 6-inch and 8-inch sizes can be used where beams must be connected to the flanges. Sections x and y. The Bethlehem columns have a large range of sizes and weights. If the H-section in x is not heavy enough for the load, it can be increased by riveting on flange plates as in y. The advantage of this type of column is economy of fabrication, the only 188 STEEL CONSTRUCTION riveting required being for connections, except when flange plates are used. A part of this advantage is lost in the heavier sections because all holes must be drilled, due to thickness of metal. The thick metal is not as strong nor as reliable as the thinner metal used in built-up sections. Tables. No comprehensive set of tables giving the properties and strength of columns has been published. But there are many partial tables which are of great assistance in designing. These tables can be divided into three classes as follows: (1) tables giving the properties of the sections; (2) tables giving the values of the allowable unit stresses for different values of -;.and (3) tables giving strength of columns of various sections and lengths. Properties of Sections. The properties of sections needed are area A; radius of gyration r; moment of inertia 7; and distance to extreme fiber c. (See p. 181). If the column is a single rolled section, its properties can be taken from the tables in the handbooks. The values for standard angles and I-beams are given in all the handbooks; for the. Carnegie H-columns, in the Carnegie Pocket Companion, 1913 edition; and for the Bethlehem columns, in the Bethlehem handbook. Built-up columns may be made up in such vast numbers of combinations that no complete or very extensive tables have been published. However, the more common sizes are given in some of the handbooks. The area A and the distance to the extreme fiber c are readily computed from the sizes of material used in the column. The Cambria and Carnegie (1913) handbooks give the radii of gyration r and the moments of inertia / for laced channel columns, plate and channel columns, and plate and angle columns. The Carnegie handbook (1903) gives these properties for Z-bar columns. Similar data for about the same range of sizes are given in a number of other books on steel construction. Allowable Unit Stress. The allowable unit stress adopted for this work has been given and illustrated heretofore. Its formula is P= 16,000-70- r This is sometimes known as the American Railway Engineers' formula and is hereinafter referred to as the A. R. E. formula. STEEL CONSTRUCTION 189 In the Carnegie Pocket Companion, (1913 Edition) pp. 254-5, are shown a table and a diagram which give the values of P as determined from several other formulas. The formula recom- mended by the American Bridge Company does not differ greatly from the A. 11. E. formula and may be used (unless local building ordinances require otherwise). The formula used by the Bethlehem Steel Company is P = 10,000-55- r with a maximum value 13,000. The resulting unit stresses for values of greater than 45 are higher than given by the A. R. E. formula, and for values of - greater than G5 are higher than given by the American Bridge Company formula. It saves much time in designing to have the values of P worked out for the usual values of I and r. Table V gives the values of P for values of r ranging from 0.1 inch to 6.0 inches and for lengths ranging from 3 feet to 40 feet. Table VI gives the values of P for values of ranging from 30 to 150. Strength of Columns. As indicated above, there has not been general agreement on the formula for the allowable unit stress, consequently the tables of strength of columns- which have been published have been based on several different formulas. The Bethlehem handbook gives the strength of Bethlehem H- columns computed from their formula given above. Table VII gives the strengths of these columns based on the A. R. E. formula, f Computed by the Bethlehem Steel Company, for use in Chicago.) The Carnegie Pocket Companion (1913) gives' tables for Car- negie H-columns, I-beam columns, channel columns, and plate and angle columns, based on the American Bridge Company formula. Table VIII gives the strengths of channel columns based on the A. R. E. formula (computed by the American Bridge Company). The strengths of plate and angle columns based on the A. R. E. formula are given in a pamphlet "Specifications for Steel Structures" (Chicago Edition), published by the American Bridge Company and distributed by its Chicago office. 190 STEEL CONSTRUCTION TABLE V Unit Stress in Compression in Columns For values of r from 0.1 to 6.0 and lengths from 3 feet to 40 feet. Unit Stresses are given in Thousands of Pounds per Square Inch. Radius of Gyration LENGTH OF COLUMN 3' 4' 5' 6' 7' 8' 9' |10' I IV |12' 13' 1 14' 15' 16' 0.1 0.2 0.3 7.6 0.4 9.7 7.6 5.5 0.5 11.0 9.3 7.6 5.9 0.6 11.8 10.4 9.0 7.6 1 6.2 0.7 12.4 11.2 10.0 8.8 7.6 6.4 0.8 12.8 11.8 10.7 9.7 8.6 7.6 6.5 5.5 0.9 13.2 12.3 11.3 10.4 9.5 8.5 7.6 1 6.7 5.7 1.0 13.5 12.6 11.8 11.0 10.1 9.3 8.4 7.6 6.8 5.9 1.1 13.7 12.9 12.2 11.4 10.6 9.9 9.1 8.4 7.6 6.8 6.1 1.2 13.9 13.2 12.5 11.8 11.1 10.4 9.7 9.0 8.3 7.6 \ 6.9 6.2 5.5 1.3 14.1 13.4 12.8 12.1 11.5 10.8 10.2 9.5 8.9 8.2 7.6 6.9 6.3 5.7 1.4 14.2 13.6 13.0 12.4 11.8 11.2 10.6 10.0 9.4 8.8 8.2 7.6 7.0 | 6.4 1.5 14.3 13.8 13.2 12.6 12.1 11.5 11.0 10.4 9.8 9.3 8.7 8.2 7.6 7.0 1.6 14.4 13.9 13.4 12.8 12.3 11.8 11.3 10.7 10.2 9.7 9.2 8.6 8.1 7.6 1.7 14.5 14.0 13.5 13.0 12.5 12.0 11.5 11.1 10.6 10.1 9.6 9.1 8.6 8.1 1.8 14.6 14.1 13.7 13.2 12.7 12.3 11.8 11.3 10.9 10.4 9.9 9.5 9.0 8.5 1.9 14.7 14.2 13.8 13.3 12.9 12.5 12.0 11.6 11.1 10.7 10.2 9.8 9.4 8.9 2.0 14.7 14.3 13.9 13.5 13.1 12.6 12.2 11.8 11.4 11.0 10.5 10.1 9.7 9.3 2.1 14.8 14.4 14.0 13.6 13.2 12.8 12.4 12.0 11.6 11.2 10.8 10.4 10.0 9.6 2.2 14.8 14.5 14.1 13.7 13.3 12.9 12.6 12.2 11.8 11.4 11.0 10.6 10.3 9.9 2.3 14.9 14.5 14.2 13.8 13.4 13.1 12.7 12.3 12.0 11.6 11.2 10.9 10.5 10.2 2.4 14.9 14.6 14.2 13.9 13.5 13.2 12.8 12.5 12.1 11.8 11.4 11.1 10.7 10.4 2.5 15.0 14.7 14.3 14.0 13.6 13.3 13.0 12.6 12.3 12.0 11.6 11.3 11.0 10.6 2.6 15.0 14.7 14.4 14.1 13.7 13.4 13.1 12.8 12.4 12.1 11.8 ll.rf 11.1 10.8 2.7 15.1 [ 14.8 14.4 14.1 13.8 13.5 13.2 12.9 12.6 12.3 12.0 11.6 11.3 11.0 2.8 15.1 14.8 14.5 14.2 13.9 13.6 13.3 13.0 12.7 12.4 12,1 11.8 11.5 11.2 2.9 15.1 14.8 14.5 14.3 14.0 13.7 13.4 13.1 12.8 12.5 12.2 11.9 11.7 11.4 3.0 15.2 14.9 14.6 14.3 14.0 13.8 13.5 13.2 12.9 12.6 12.4 12.1 11.8 11.5 Sg 3' 4' 5'- 6' 7' 8' 9' 10' IV 12' 13' 14' 15' 16' STEEL CONSTRUCTION 191 TABLE V (Continued) Formula P= 16,000- 70 - in which P = unit stress in pounds per square inch r = radius of gyration in inches 1= length in inches Unit stresses above the heavy zigzag line are values of y from 125 to 150 LENGTH OF COLUMN Radius of Gyration 17' IF 19' 20' 21' 22' 23' 24' 25' 26' 27' 28' |29' 30' 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 5.8 1.4 65 5.9 1.5 7.1 6.5 6.0 5.5 1.6 7.6 7.1 6.6 6.1 5.6 1.7 8.1 7.6 7.1 6.7 6.2 5.7 1.8 8.5 8.0 7.6 7.2 6.7 6.3 5.8 1.9 8.9 8.4 8.0 7.6 7.2 6.8 6.3 5.9 5.5 2.0 9.2 8.8 8.4 8.0 7.6 7.2 6.8 6.4 6.0 5.6 2.1 9.5 9.1 8.7 8.4 8.0 7.6 7.2 6.8 6.4 6.1 5.7 2.2 9.8 9.4 9.1 8.7 8.3 8.0 7.6 7.2 6.9 6.5 6.1 5.8 2.3 10.0 9.7 9.3 9.0 8.6 8.3 7.9 7.6 7.2 6.9 6.5 6.2 5.8 5.5 2.4 10.3 9.9 9.6 9.3 8.9 8.6 8.3 7.9 7.6 7.3 6.9 6.6 6.3 5.9 2.5 10.5 10.2 9.9 9.5 9.2 8.9 8.6 8.2 7.9 7.6 7.3 6.9 6.6 6.3 2.6 10.7 10.4 10.1 9.8 9.5 9.2 8.8 8.5 8.2 7.9 7.6 7.3 7.0 6.7 2.7 10.9 10.6 10.3 10.0 9.7 9.4 9.1 8.8 8.5 8.2 7.9 7.6 7.3 7.0 2.8 11.1 10.8 10.5 10.2 9.9 9.6 9.3 9.0 8.8 8.5 8.2 7.9 7.6 7.3 2.9 11.2 11.0 10.7 10.4 10.1 9.8 9.6 9.3 9.0 8.7 8.4 8.2 7.9 7.6 3.0 17' 18' 19' 20' 2V 22' 23' 24' 25' 26' 27' 28' 29' 30' Sg 192 STEEL CONSTRUCTION TABLE V (Continued) Unit Stress in Compression in Columns For values of r from 0.1 to 6.0 and lengths from 3 feet to 40 feet. Unit Stresses are given in Thousands of Pounds per Square Inch 8g LENGTH OF COLUMN 8' 9' 10' 11' 12' 1 13' 14' 15' 16' 17' | 18' 19' 20' 21' 3.1 13.8 13.6 13.3 13.0 12.7 1 12.5 12.2 11.9 11.7 11.4 11.1 10.8 10.6 10.3 3.2 13.9 13.6 13.4 13.1 12.8 12.6 12.3 12.1 11.8 11.5 11.3 11.0 10.7 10.5 3.3 14.0 13.7 13.4 13.2 12.9 12.7 12.4 12.2 11.9 11.7 11.4 11.2 10.9 10.6 3.4 14.0 13.8 13.5 13.3 13.0 12.8 12.5 12.3 12.0 11.8 11.5 11.3 11.1 10.8 3.5 14.1 13.8 13.6 13.4 13.1 12.9 12.6 12.4 12.2 11.9 11.7 11.4 11.2 11.0 3.6 14.1 13.9 13.7 13.4 13.2 13.0 12.7 12.5 12.3 12.0 11.8 11.6 11.3 11.1 3.7 14.2 14.0 13.7 13.5 13.3 13.0 12.8 12.6 12.4 12.1 11.9 11.7 11.5 11.2 3.8 14.2 14.0 13.8 13.6 13.3 13.1 12.9 12.7 12.5 12.2 12.0 11.8 11.6 11.4 3.9 14.3 14.1 13.8 13.6 13.4 13.2 13.0 12.8 12.5 12.3 12.1 11.9 11.7 11.5 4.0 14.3 14.1 13.D 13.7 13.5 13.3 13.1 12.8 12.6 12.4 12.2 12.0 11.8 11.6 4.1 14.4 14.2 13.9 13.7 13.5 13.3 13.1 12.9 12.7 12.5 12.3 12.1 11.9 11.7 4.2 14.4 14.2 14.0 13.$ 13.6 13.4 13.2 13.0 12.8 12.6 12.4 12.2 12.0 11.8 4.3 14.4 14.2 14.0 13.8 13.6 13.5 13.3 13.1 12.9 12.7 12.5 12.3 12.1 11.9 4.4 14.5 14.3 14.1 13.9 13.7 13.5 13.3 13.1 12.9 12.8 12.6 12.4 12.2 12.0 4.5 14.5 14.3 14.1 13.9 13.8 13.6 13.4 13.2 13.0 12.8 12.6 12.4 12.3 12.1 4.6 14.5 14.4 14.2 14.0 13.8 13.G 13.4 13.3 13.1 12.9 12.7 12.5 12.3 12.2 4.7 14.6 14.4 14.2 14.0 13.8 13.7 13.5 13.3 13.1 13.0 12.8 12.6 12.4 12.2 4.8 14.6 14.4 14.2 14.1 13.9 13.7 13.5 13.4 13.2 13.0 12.8 12.7 12.5 12.3 4.9 14.6 14.5 14.3 14.1 13.9 13.8 13.6 13.4 13.3 13.1 12.9 12.7 12.6 12.4 5.0 14.7 14.5 14.3 14.1 14.0 13.8 13.6 13.5 13.3 13.1 13.0 12.8 12.6 1 12.5 5.1 14.7 14.5 14.3 14.2 14.0 13.9 13.7 13.5 13.4 13.2 13.0 12.9 12.7 1 12.5. 5.2 14.7 14.5 14.4 14.2 14.1 13.9 13.7 13.6 13.4 13.2 13.1 12.9 12.8 12.6 5.3 14.7 14.6 14.4 14.3 14.1 13.9 13.8 13.6 13.5 13.3 13.1 13.0 12.8 12.7 5.4 14.7 14.6 14.4 14.3 14.1 14.0 13.8 13.7 13.5 13.3 13.2 13.0 12.9 12.7 5.5 14.8 14.6 14.5 14.3 14.2 14.0 13.9 13.7 13.6 13.4 13.2 13.1 12.9 12.8 5.6 14.8 14.6 14.5 14.3 14.2 14.0 13.9 13.7 13.6 13.4 13.3 13.1 13.0 12.8 5.7 14.8 14.7 14.5 14.4 14.2 14.1 13.9 13.8 13.6 13.5 13.3 13.2 13.0 12.9. 5.8 14.8 14.7 14.5 14.4 14.3 14.1 14.0 13.8 13.7 13.5 13.4 13.2 13.1 13.0 5.9 14.9 14.7 14.6 14.4 14.3 14.1 14.0 13.9 13.7 13.6 13.4 13.3 13.1 13.0 6.0 14.9 14.7 14.6 1 14.5 14.3 14.2 14.0 13.9 13.8 13.6 13.5 13.3 13.2 13.1 | Radius of I Gyration 8' 9' 10' TV 12' 13' 14' 15' 16' 17; 18' 19' 20' 21' STEEL CONSTRUCTION 103 TABLE V (Continued) Formula P= 10,000-70 - in which P = unit stress in pounds per square inch r = radius of gyration in inches. 1 = length in inches. 1'nit stresses above the heavy zigzag line are values of from 125 to 150 LKNGT1I OF COLUMN 1| KO 22' 23' 24' 25' 26' 27' 28' 29' 30' 32' 34' 36' 38' 40' 1().0| 9.8 9.5 9.2 8.9 | 8.7 8.4 8.1 7.9 1 7.3 6.8 6.2 5.7 3.1 10.2 10.0 97 9.4 | 9.2 8.9 | 8.6 8.4 8.1 7.6 7.1 6.5 6.0 5.5 3,2 10.4 10. l| 9.9 9.6 9.4 | 9.1 1 8.9 8.6 8.4 7.8 7.3 6.8 | 6.3 5.8 3.3 10.6 10.3 10.1 9.8 9.6 9.3 9.1 8.8 8.6 8.1 7.6 7.1 6.6 6.1 3.4 10.7 10.5 10.2 10.0 9.8 9.5 9.3 9.0 8.8 8.3 7.8 7.4 6.9 6.4 3.5 10.9 10.6 10.4 10.2 9.9 9.7 9.5 9.2 9.0 8.5 8.1 7.6 7.1 6.7 1 3.6 11.0 10.8 1 10.5 1 10.3 10.1 9.9 9.6 9.4 9.2 8.7 8.3 7.8 7.4 6.9 3.7 11.1 |10.9 10.7 10.5 10.2 10.0 9.8 9.6 9.4 8,9 8.5 8.0 7.6 7.2 3.8 11.3|ll.O 10.8 10.6 10.4 10.2 10.0 9.7 9.5 9.1 8.7 8.2 7.8 7.4 3.9 11.4 1 11.2 11.0 10.7 10.5 10.3 10.1 9.9 9.7 9.3 8.9 8.4 8.0 7.6 4.0 11.5 1 11.3 11.1 10.9 10.7 10.5 10.3 10.1 9.8 9.4 9.0 8.6 8.2 7.8 4.1 11.6 11.4 11.2 | ll.0| 10.8 1 10.6 1 10.4 10.2 1 10.0 9.6 9.2 8.8 | 8.4 8.0 4.2 11.7 11.5 11.3|ll.l 10.9 1 10.7 1 10.5 1 10.3 1 10.1 1 9.7 | 9.4 9.0 | 8.6 8.2 4.3 11.8 J1.6 11.4 1 11.2 11.0|l0.8 10.7 1 10.5 1 10.3 | 9.9 | 9.5 9.l| 8.7 8.4 4.4 11.9 11.7 11.5 11.3 11.1 11.0 10.8 10.6 10.4 10.0 9.6 9.3 8.9 8.5 4.5 12.0 11.8 11.6 11.4 11.2 11.1 10.9 10.7 10.5 10.2 9.8 9.4 9.1 8.7 4.6 12.1 11.9 1 11.7 11.5 11.3 11.2 11.0 10.8 10.6 1 10.3 9.9 9.6 9.2 8.8 1 4.7 12.l|l20 11.8 11.6 1 11.4 11.3 1 11.1 1 10.9 10.7 1 10.4 10.0 | 9.7 9.3 9.0 4.8 12.2 12.1 11.9 11.7 1 11.5 11.4 1 11.2 11.0 1 10.9 1 10.5 10.2 | 9.8 9.5 9.1 4.9 12.3 12.1 12.0 11.8 11.6 11.5 11.3 11.1 11.0 10.6 10.3 9.9 9.6 9.3 5.0 12.4 12.2 120 11.9 11.7 11.5 11.4 11.2 11.1 10.7 10.4 10.1 9.7 9.4 5.1 12.4 12.3 12.1 12.0 11.8 11.6 11.5 11.3 11.1 10.8 10.5 10.2 | 9.9 9.5 5.2 12.5 1 12.3 12.2 12.0 |l 1.9 11.7 1 11.6 11.4 11.2 10.9 10.6 10.3 10.0 9.7 5.3 12.6 12.4 12.3 12.1 1 11.9 1 11.8 1 11.6 11.5 1 11.3 1 11.0 1 10.7 10.4 10.1 9.8 5.4 12.6 12.5 12.3 12.2 12.0 11.9 11.7 11.6 11.4 11.1 10.8 10.5 10.2 9.9 5.5 12.7 12.5 12.4 12.2 12.1 11.9 11.8 11.6 11.5 11.2 10.9 10.6 10.3 10.0 5.6 12.8 12.6 12.5 12.3 12.2 12.0 11.9 11.7 11.6 11.3 11.0 1 10.7 10.4 10.1 5.7 12.8 12.7 12.5 12.4 12.2 12.1 11.9 11.8 11.6 11.4 11. l| 10.8 10.5 10.2 5.8 12.9 12.7 12.6 12.4 12.3 12.2 1 12.0 11.9 11.7 11.4 11.2 10.9 1 10.6 10.3 5.9 12.9 12.8 12.6 12.5 12.4 12.2 12.1 11.9 11.8 11.5 11.2 11.0 10.7 10.4 6.0 22' 23' 24' 25' 26' 27' 28' 29' 30' 32' 34' 36' 38' 40' 1 Radius of Gyration 194 STEEL CONSTRUCTION TABLE VI Unit. Stress in Compression Values of P for values of - = 30 to - = 150 from the formula P= 16,000-70 - I r 16,000-70- 14.000 max. jt r 16,000-70^ 14,000 max. 30 - 13900 105 8650 35 13550 110 8300 40 13200 115 7950 45 12850 120 7600 50 12500 125 7250 55 12150 130 6900 60 11800 135 6550 65 11450 140 6200 70 11100 145 5850 75 10750 150 5500 80 10400 85 10050 90 9700 95 9350 100 9000 It must be noted that the tables of strength of columns take no account of eccentricity. If there are eccentric loads, the equivalent concentric loads must be computed by the method given on p. 178, and then these values added to the actual loads. This result gives the total load to be used in selecting the column section from the tables. Use of the Tables. The following illustrations show the manner of using the tables: (1) Assume a concentric load of 492,000 pounds on a column 12 feet long. Determine the required column sections made of plates and channels and of plates and angles. Compare the areas of the two columns. (a) From Table VIII, the channel column section required is 2 L 12"X30" Area = 36.9 sq. in. STEEL CONSTRUCTION 195 (b) From the table of plate and angle columns (see handbook), the angle column section required is 1 PI. 12" XT 4Ls6"x4"xr 2 PI. 14" Xf Area = 39.0 sq. in. In both cases other sections might be selected. (2) Assume a load of 640,000 pounds on a column 16 feet long; 80,000 pounds of the load has an eccentricity of 9 inches in the direc- tion of the greatest radius of gyration. Determine the plate and angle column required, using the A. R. E. formula. A preliminary selection from the table indicates a column whose greatest r is about 6.8 inches and whose c is about 8J inches. From these approximate values the concentric equivalent load is This added to the direct load gives a total of 739,000 pounds. The column section required is 1 PL 14" Xf" 4Ls6"X4"Xf 2 PL 14" XI A' The values of r and c for this section are 6.83 inches and 8 A inches, so the approximate values of r and c used above are accurate enough, hence no corrections need be made. (3) Assume a column which has an unsupported length of 10 feet 6 inches in its weaker direction and 18 feet in its stronger direc- tion made of 1 PL 12"X|" 4Ls 6"X4"Xf Determine the allowable unit stress. From the table the values of r are 2.69 and 4.91. The cor- responding values of / are 126 inches and 216 inches; and of are 43 and 44. The respective unit stresses are taken from Table VI by interpolating between the values for 40 and 45, giving 13,590 and 13,720. The smaller value must be used. 196 STEEL CONSTRUCTION ' * 1 , . TABLE VH Safe Loads on Bethlehem Columns 14* H -Section with Cover Plates Safe Loads are given in Thousands of Pounds Lg '1- c^ Weight Section Lb. per Ft. Dimensions, in. Ares of Section Square Inches Least Radius of Qyr.. Inch* UNSUPPORTED LENGTH c P H 10 11 11 13 14 15 284.0 16 IK 16% 83.52 3.98 1160.0 1142.4 1124.8 1107.2 1089.6 1072.0 290.8 16 lA 16^ 85.52 3.99 1188.2 1170.2 1152.2 1134.2 1116.2 1098.2 297.6 16 1H 16% 87.52 4.01 1217.0 1198.6 1180.4 1162.0 1143.6 1125.4 304.4 311.2 16 16 lA 1% 17 17% 89.52 9L52 4.02 4.04 1245.2 1274.0 1226.6 1255.0 1207.8 1236.0 1189.2 1207.0 1170.4 1198.0 1151.8 1178.8 318.0 16 lA 17% 93.52 4.05 1302.4 1283.0 1263.6 1244.2 1224.8 1205.4 324.8 16 1H 17% 95.52 4.06 1330.6 1311.0 1291.2 1271.4 1251.6 1231.8 331.6 16 1H 17% 97.52 4.08 1359.6 1339.4 1319.4 1299.4 1279.2 1259.2 338.4 16 l% 17% 99.52 4.09 1388.0 1367.4 1347.0 1326.6 1306.2 1285.8 345.2 16 itt 17H 101.52 4.10 1416.4 1395.6 1374.8 1354.0 1333.2 1312.4 350.3 17 IK 17% 103.02 4.30 1447.0 1427.0 1406.8 1388.6 1366.6 1346.4 357.5 17 iH 1754 105.15 4.31 1477.4 1457.0 1436.4 1416.0 1395.4 1375.0 364.7 17 1% 17% 107.27 4.32 1507.8 1486.0 1466.0 1445.2 1424.4 1403.4 372.0 17 iH 18 109.40 4.33 1538.2 1517.0 1495.8 1474.6 1453.2 1432.0 379.2 17 2 18% 111.52 4.35 1569.0 1547.4 1526.0 1504.4 1482.8 1461.2 386.4 17 2A 18% 113.65 4.36 1599.4 1577.6 1555.6 1533.8 1511.8 1490.0 393.6 17 2% 18% 115.72 4.37 1629.8 1607.6 1585.2 1563.0 1440.8 1518.6 400.9 17 2A 18% 117.90 4.38 1660.2 1637.6 1615.0 1592.4 1569.8 1547.2 408.1 17 2% 18% 120.02 4.39 1690.6 1667.8 1644.8 1621.8 1598.8 1575.8 415.3 17 2A 18H 122.15 4.40 1721.2 1697.8 1674.6 1651.2 1628.0 1604.6 423.4 18 2K 18% 124.52 4.62 1766.0 1743.2 1720.6 1698.0 1675.4 1652.8 431.0 18 2A 18H 126.77 4.63 1798.4 1775.4 1752.4 1729.4 1706.4 1683.4 438.7 18 2 3 / 8 18% 129.02 4.64 1830.8 1807.4 1784.0 1?60.6 1737.4 1714.0 446.3 18 2A 19 131.27 4.65 1863.2 1839.4 1814.8 1792.0 1768.4 1744.6 454.0 18 2% 19% 133.52 4.66 1895.6 1871.6 1847.6 1823.4 1799.4 1775.4 461.6 18 2A 19% 135.77 4.67 1928.2 1903.6 1879.2 1854.8 1830.4 1806.0 469.3 18 2^8 19% 138.02 4.68 1960.6 1935.8 1911.0 1886.2 1861.6 1836.8 476.9 18 2H 19% 140.27 4.69 1993.0 1968.0 1942.8 1917.8 1892.6 1867.4 484.6 18 254 19^ 142.52 4.70 2025.6 2000.2 1974.6 1949.2 1923.8 189 8.2 Columns composed of a 14'X148# Special Column Section (H14b) reenforced with cover plates of width and thickness given in table. STEEL CONSTRUCTION 197 TABLE VII (Continued) I I jj r Formula P= 16,000-70^ ' JTJJT" 1 in which P = unit stress in pounds per square inch r = radius of gyration in inches* 1 = length in inches To the left of heavy line values of - do not exceed 120 T 1* o " ' "I OF COLUMNS IN FEET We,ght 16 18 20 22 24 28 32 36 40 Section Lb. per Ft. 1054.2 1019.0 983.8 948.6 913.2 842.8 772.2 701.8 631.2 284.0 1080.2 1044.2 1008.2 972.2 936.2 864.2 792.2 720.2 648.2 290.8 1107.0 1070.4 1033.6 997.0 960.4 887.0 813.6 740.4 667.0 297.6 1133.0 1095.6 1058.2 1020.8 983.4 908,6 833.8 759.0 684.0 304.4 1159.8 1121.8 1083.8 1045.6 1007.6 931.6 855.4 779.2 703.2 311.2 1186.0 1147.2 1108.4 1069.6 1030.8 953.2 875.6 798.0 720.4 318.0 1212.2 1172.6 1133.0 1093.6 1054.0 975.0 896.0 816.8 737.8 324.8 1239.0 1199.0 1158.8 1118.6 1078.4 998.2 917.8 837.6 757.2 331.6 1265.2 1225.4 1183.6 1142.6 1101.8 1020.0 938.2 856.6 774.8 338.4 1291.6 1250.0 1208.4 1166.8 1125.2 1042.0 958.8 875.6 792.4 345.2 1326.4 1286.0 1245.8 1205.6 1165.4 1084.8 1004.4 923.8 843.4 350.3 1354.6 1313.6 1272.6 1231.6 1190.6 1 108.6 1026.6 944.6 862.6 357.5 1382.6 1340.8 1299.2 1257.4 1215.8 1132.2 1048.8 965.4 882.0 364.7 1410.8 1368.4 1326.0 1283.4 1241.0 1156.2 1071.2 986.4 901.4 372.0 1439.8 1396.6 1353.6 1310.6 1267.4 1181.4 1095.2 1009.0 923.0 379.2 1468.0 1424.2 1380.4 1336.6 1292.8 1205.4 1117.8 1030.2 942.6 386.4 1496.2 1451.8 1407.2 1362.8 1318.2 1229.2 1140.2 1051.2 962.2 393.6 1524.6 1479.4 1434.2 1389.0 1343.8 1253.2 1162.8 1072.4 982.0 400.9 1552.8 1507.0 1461.0 1415.0 1369.2 1277.2 1185.4 1093.6 1001.8 408.1 1581.2 1534.6 1488.0 1441.4 1394.8 1301.4 1208.2 1115.0 1021.6 415.3 1630.0 1584.8 1539.6 1494.2 1449.0 1358.4 1267.8 1177.2 1086.8 423.4 1660.4 1614.4 1568.4 1522.4 1476.4 1384.4 1292.4 1200.4 1108.4 431.0 1690.6 1643.8 1597.2 1550.4 1503.8 1410.4 1316.8 1223.4 1130.0 438.7 1721.0 1673.4 1626.0 1578.6 1531.2 1436.4 1341.4 1246.6 1151.8 446.3 1751.2 1703.0 1655.0 1606.8 1558.6 1462.4 1366.2 1269.8 1173.6 454.0 1781.6 1732.8 1683.8 1635.0 1586:2 1488.6 1390.8 1293.2 1195.4 461.6 1812.0 1762.4 1712.8 1663.4 1613.8 1514.6 1415.6 1316.4 1217.4 469.3 1842.4 1792.2 1741.8 1691.6 1641.4 1540.8 1440.4 1339.8 1239.4 476.9 1872.8 1821.8 1770.8 1720.0 1669.0 1567.0 1465.2 1363.4 1261.4 484.6 198 STEEL CONSTRUCTION r-. * . TABLE VII (Continued) Safe Loads on Bethlehem Columns t^ J ^ 14* H-Section Safe lo ads are given in Thousands of Pounds C *_i Section Number Weight Section Lb. per Ft. Dimensions. Inches Least Radius of Gyr.. Inches UNSUPPORTED LENGTH D T B Area of Section Sq. In. 10 11 12 13 14 83.5 13% H 13.92 24.46 3.47 332.2 326.2 320.4 314.4 308.4 91.0 13% % 13.96 26.76 3.49 363'.8 357.4 350.8 344.4 338.0 99.0 14 H 14.00 29.06 3.50 395.2 388.2 381.2 374.2 367.4 106.5 14% % 14.04 31.38 3.52 427.2 419.8 412.2 404.8 397.2 114.5 14J4 H 14.08 33.70 3.53 459.0 451.0 443.0 435.0 427.0 122.5 14% i 14.12 36.04 3.55 491.4 482.8 474.4 465.8 457.2 ; 130.5 14% io 14.16 38.38 3.56 523.6 514.4 505.4 496.4 487.2 138.0 14% 1% 14.19 40.59 3.58 554.2 544.6 535.2 525.6 516.2 . 146.0 14% 1A 14.23 42.95 3.59 586.8 576.6 566.6 556.6 546.6 154.0 14% 1% 14.27 45.33 3.61 619.8 609.2 598.8 588.2 577.6 162.0 15 l^ 14.31 47.71 3.62 652.6 641.6 630.6 619.4 608.4 170.5 15% 1% 14.35 50.11 3.64 686.2 674.6 663.0 651.4 639.8 178.5 15% 1A 14.39 52.51 3.65 719.4 707.2 695.2 683.0 671.0 H14 186.5 15% 1% 14.43 54.92 3.66 752.6 740.0 727.4 714.8 702.2 195.0 15H lA 14.47 57.35 3.68 786.6 773.6 760.6 747.4 734.4 203.5 15% 1% 14.51 59.78 3.69 820.4 806.8 793.2 779.6 766.0 211.0 15% 1H 14.54 62.07 3.70 852.2 838.2 824.0 810.0 795.8 219.5 15% 1% 14.58 64.52 3.71 886.2 871.6 857.0 842.4 827.8 227.5 16 1H 14.62 66.98 3.72 920.4 905.4 890.2 875.0 860.0 236.0 16% 1% 14.66 69.45 3.74 955.2 939.6 924.0 908.4 892.8 244.5 16% itt 14.70 71.94 3.75 989.8 973.8 957.6 941.6 925.4 253.0 16% 2 14.74 74.43 3.76 1024.6 1008.0 991.4 974.8 958.0 261.5 16% 2A 14.78 76.93 3.77 1059.4 1042.4 1025.2 1008.0 991.0 270.0 16% 2H 14.82 79.44 3.79 1095.0 1077,4 1059.8 1042.2 1024.6 278.5 16% 2A 14.86 81.97 3.80 1130.4 1112.2 1094.0 1076.0 1057.8 287.5 16% 2% 14.90 84.50 3.81 1165.8 1 147.0 1128.4 1109.8 1091.2 STEEL CONSTRUCTION 199 TABLE VII (Continued) Formula P =16,000- 70- r in which F = unit stress in pounds per square inch T = radius of gyration in inches / = length in inches To the left of heavy line values of.- do not exceed 120 1 L T 1 ( I .-. \ OF COLUMNS IN FEET Weight Section Lb. per Ft. 15 16 18 20 22 24 28 32 36 40 302.6 296.6 284.8 273.0 261.0 249.2 225.6 201.8 178.2 154.6 83.5 331.6 325.2 312.2 299.4 286.4 273.6 247.8 222.0 196.2 170.6 9J.O 380.4 353.4 339.4 325.4 311.6 297.6 269.6 241.8 213.8 186.0 99.0 389.8 382.2 367.2 352.4 337.4 322.4 292.4 262.4 232.4 202.6 106.5 419.0 410.8 394.8 378.8 362.8 346.8 314.6 282.6 250.4 218.4 114.5 448.8 440.2 423.2 406.0 389.0 372.0 337.8 303.8 269.6 235.6 122.5 478.2 469.2 451.0 433.0 414.8 396.8 360.6 324.2 288.0 251.8 130.5 506.6 497.0 478.0 459.0 440.0 420.8 382.8 344.6 306.6 268.4 138.0 536.4 567.0 526.4 556.6 506.2 535.4 486.2 514.4 466.2 493.2 446.0 472.2 405.8 430.0 365.6 387.8 325.4 285.2 303.4 146.0 154.0 345.6 597.2 586.2 564.0 542.0 519.8 497.6 453.4 409.0 364.8 320.6 162.0 628.4 616.8 593.6 570.4 547.4 524.2 478.0 431.8 385.4 339.2 170.5 658.8 646.8 622.6 598.4 574.4 550.2 501.8 453.4 405.2 356.8 178.5 689.6 677.0 651.8 626.6 601.4 576.2 525.8 475.4 425.0 374.6 186.5 721.2 708.2 682.0 655.8 62S.6 603.4 551.0 498.6 446.4 394.0 195.0 752.4 738.8 711.6 684.4 657.0 629.8 575.4 521.0 466.6 412.2 203.5 781.8 767.6 739.4 711.2 683.2 655.0 598.6 542.2 485.8 429.4 211.0 813.2 798.6 769.4 740.2 711.0 681.8 623.2 564.8 506.4 448.0 219.5 844.8 829.6 799.4 769.2 739.0 708.6 648.2 587.6 527.2 466.8 227.5 877.2 861.6 830.4 799.2 768.0 736.8 674.4 612.0 549.6 487.2 236.0 909.4 893.2 861.0 828.8 796.6 764.2 699.8 635.4 570.8 506.4 244.5 941.4 924.8 891.6 858.4 825.0 791.8 725.2 658.8 592.2 525.8 253.0 973.8 956.6 922.4 888.0 853.8 819.4 751.0 682.4 613.8 545.2 261.5 1007.0 989.4 954.2 919.0 8S3.6 848.4 778.0 707.6 637.2 566.8 270.0 1039.8 1021.6 985.4 949.2 912.8 876.6 804.2 731.6 659.2 586.8 278.5 1072.6 1054.0 1016.6 979.4 942.2 904.8 830.4 755.8 681.4 606.8 287.5 200 STEEL CONSTRUCTION a TABLE VII (Continued) Safe Loads on Bethlehem Columns 12' H-Section Safe loads are given in Thousands of Pounds 2 u* C) 1 L .-4 Section Number Weight Section Lb. per Foot Dimension. Inches Area of Section Sq.ln. Least Radius ofGyr. Inches UNSUPPORTED LENGTH D T B 10 11 12 13 14 64.5 HH H 11.92 19.00 2.98 250.4 245.0 239.8 234.4 229.0 71.5 Mi H 11.96 20.96 3.00 276.6 270.8 265.0 259.0 253.2 78.0 12 H 12.00 22.94 3.01 303.0 296.6 290.2 283.8 277.4 84.5 I2H H 12.04 24.92 3.03 329.6 322.8 315.8 309.0 302.0 91.5 12K H 12.08 26.92 3.04 356.4 348.8 341.4 334.0 326.6 98.5 12H H 12.12 28.92 3.06 383.4 375.4 367.4 359.6 351.6 105.0 12H i 12.16 30.94 3.07 410.4 402.0 393.4 385.0 376.6 H12 112.0 H lA 12.20 32.96 3.08 437.4 428.4 419.4 410.6 401.6 118.5 12H IK 12.23 34.87 3.10 463.4 454.0 444.6 435.0 425.6 125.5 12% lA 12.27 36.91 3.11 490.8 480.8 471.0 461.0 451.0 132.5 13 IK 12.31 38.97 3.13 519.0 508.4 498.0 487.6 477.2 139.5 13K ift 12.35 41.03 3.14 546.8 535.8 524.8 513.8 502.8 146.5 13K IK 12.39 43.10 3.15 574.6 563.2 551.6 540.2 528.6 153.5 13H 1A 12.43 45.19 3.16 603.0 591.0 578.8 566.8 554.8 161.0 13M IK 12.47 47.28 3.18 631.6 619.2 606.6 594.2 581.6 STEEL CONSTRUCTION 201 TABLE VII (Continued) i Formula P = 16,000-70y j k 1 in which P = unit stress in pounds p<>r square inches r = radius of gyration in inches 1 = length in inches \ - t To the left of heavy line values of - do not exceed 120 * B "* OF COLUMNS IN FEET Weight 15 16 18 20 22 24 28 32 36 Lb. per Foot 223.6 218.4 207.6 106.8 186.2 165.4 154.0 132.6 111.2 64.5 247.4 241.4 220.8 218.0 206.2 104.6 171.0 1476 124.0 7*1.5 271.0 264.6 251.S 230.0 226.2 213.4 187.8 162.2 136.6 78.0 205.0 2SS.2 274.4 260.0 246.8 233.0 205.2 177.6 150.0 84.5 310.2 311.* 206.8 282.0 267.0 <),> o 222.4 102.6 163.0 01.5 343.6 335.6 310.8 304.0 28S.O 070 o 240.4 208.6 177.0 08.5 3G8.0 350.G 342.6 325.8 308.8 291.8 258.0 224,2 100.2 105.0 302.6 3S3.6 365.6 347.6 320.6 311.6 .375.6 230.8 203.8 112.0 416.2 406.8 387. S 360.0 350.0 331.2 203.4 255.6 217.8 118.5 441.0 431.0 411.2 301.2 371.2 351.2 311.4 271.6 231.6 125.5 466.C 456.2 435.2 414.4 303.4 372.6 330.6 288.8 247.0 132.5 401.8 4SO.S 450.0 437.0 415.0 303.0 340.2 305.2 261.4 130.5 517.2 505.S 482.8 450.8 436.8 413.8 367.8 321.8 275.8 146.5 542.8 530.8 506.8 482.8 458.8 434.8 386.6 338.6 200.6 153.5 569.2 556.6 531.6 506.6 481.8 456.8 406.8 356.8 306.8 161.0 202 STEEL CONSTRUCTION i T TABLE VII (Continued) L r* 1 -1 F Safe Loads on Bethlehem Columns c 10" H-Section ( Safe loads are given in Thousands of Pounds t . | Weight Dimensions. Inches Area of Least UNSUPPORTED LENGTH Section Number Section Lb. per Ft. D T B Square Inches of Gyr. Inches 10 11 12 13 14 49.0 A 9.97 14.37 2.49 181.4 176.6 171.8 167.0 162.0 54.0 10 H 10.00 15.91 2.51 201.4 196*0 190.6 185.4 180.0 59.5 IQK H 10.04 17.57 2.53 222.8 217.0 211.2 205.2 199.4 65.5 10* H 10.08 19.23 2.54 244.0 237.8 231.4 225.0 218.6 71.0 10H H 10.12 20.91 2.56 266.0 259.0 252.2 245.4 238.6 77.0 10H K 10.16 22.59 2.57 287.6 280.2 272.8 265.4 258.0 82.5 10M H 10.20 24.29 2.58 309.6 301.6 293.8 285.8 278.0 88.5 WK i 10.24 25.99 2.60 331.8 323.4 315.0 306.6 298.2 H10 94.0 IOK IA 10.28 27.71 2.61 354.2 345.2 336.4 327.4 318.6 99.5 11 iK 10.31 29.32 2.62 375.2 365.8 356.4 347.0 337.6 105.5 UK IA 10.35 31.06 2.64 398.2 388.2 378.4 368.4 358.6 111.5 UK IK 10.39 32.80 2.65 420.8 410.4 400.0 389.6 379.2 117.5 UN lA 10.43 34.55 2.66 443.6 432.8 421.8 411.0 400.0 123.5 10.47 36.32 2.67 466.8 455.4 444.0 432.6 421.2 STEEL CONSTRUCTION 203 TABLE VII r Continued} , ,4 i * \r- f T J Formula P= 16,000-70^ \\^ in which P=unit stress in pounds per square inch <* r= radius of gyration in inches 1 = length in inches f~, ..__,,) ; To the left of heavy line values of do not exceed 120 a OF COLUMNS IN FEET Wei K ht 15 16 18 20 22 24 26 28 30 Lb. per Ft. 157.2 152.4 142.6 133.0 123.2 113.6 103.8 94 J2 84.4 49.0 174.6 169.4 158.8 148.0 137.4 126.8 116.2 105.4 94.8 54.0 103.6 187.8 176.2 164.4 152.8 141.2 129.4 117.8 106.2 59.5 212.2 206.0 193.2 180.4 167.8 155.0 142.4 129.6 116.8 65.5 231.6 224.8 211.0 197.4 183.6 169.8 156.2 142.4 128.8 71.0 250.6 243.4 228.6 213.8 199.0 184.2 169.4 154.8 140.0 77.0 270.0 262.2 246.2 230.4 214.6 198.8 183.0 167.2 151.4 82.5 289.8 281.4 264.6 248.0 231.2 214.4 197.6 180.8 164.0 88.5 309.6 300.6 282.8 265.0 247.2 229.4 211.4 193.6 175.8 94.0 328.2 318.8 300.0 281.2 262.4 243.6 224.8 206.0 187.2 99.5 348.8 338.8 319.0 299.4 279.6 269.8 240.0 220.2 200.4 105.5 368.8 358.4 337.6 316.8 296.0 275.2 254.4 233.6 212.8 111.5 389.2 378.2 356.4 334.6 312.8 291.0 269.2 247.4 225.4 117.5 409.8 398.2 375.4 352.G 329.8 306.8 284.0 261.2 238.4 123.5 204 STEEL CONSTRUCTION 1 TABLE VII (Continued) Safe Loads on Bethlehem Columns t^,. <* J k 8* H-Section Safe loads are given in Thousands of Pounds U-,_| Section Number .Weicht Section Lb. per Ft. Dimensions. Inches Section 8*. In. Least Radius of Gvr. Inches UNSUPPORTED LENGTH D T B 8 9 10 11 12 31.5 7H A 8.00 9.17 1.98 115.6 111.8 107.8 104.0 100.0 34.5 8 H 8.00 10.17 2.01 12S.S 124.4 120.2 116.0 111.8 39.0 Vi T 9 6 S.04 11.50 2.03 146.6 141.2 136.4 131.6 126.8 43.5 *K H 8.08 12.83 2.04 163.0 157.8 152.4 147.2 141.8 48.0 8N H 8.12 14.18 2.05 180.4 174.6 168.S 163.0 157.2 53.0 SM % 8.16 15.53 2.07 198.0 191.8 185.4 179.2 172.8 57.5 & H 8.20 16.90 2.08 215.8 209.0 202.2 195.4 188.4 62.0 8M K 8.24 18.27 2.09 233.6 226.2 218.8 211.6 204.2 H8 67.0 8H H 8.28 19.66 2.11 252.0 244.2 236'.2 228.4 220.6 71.5 9 i 8.32 21.05 2.12 270.0 261.8 253.4 245.0 236.8 76.5 OH I* 8.36 22.46 2.13 288.4 279.6 270.8 262.0 253.0 81.0 OK iK 8.39 23.78 2.14 305.8 296.4 287.2 277.8 268.4 85.5 OH ti 8.43 25.20 2.16 324.S 315.0 305.2 295.4 285.6 90.5 8.47 26.64 2.17 343.8 333.4 323.2 312.8 302.4 STEEL CONSTRUCTION TABLE VH (Continued) Formula P= 16,000-70^ ' j r^fH in which P = unit stress in pounds per square inch r = radius of gyration in inches ^ 1 = length in inches Jl To the left of heavy line values of do not exceed 12( > L *-H OF COLUMNS IN FEET Weight 13 14 15 16 17 18 20 22 24 Section Lb. per Foot 96.2 92.2 88.4 84.4 80.6 76.6 69.0 61.0 53.4 31.5 107. -1 103.2 99.0 94.8 90.4 86.2 77.8 69.2 60.8 34.5 122.2 117.4 112.6 107.8 103.2 98.4 88.8 79.4 69.8 39.0 136.6 131.4 126.0 120.8 115.4 110.2 99.6 89.0 78.4 43.5 151.4 145.6 139.8 134.0 128.2 122.2 1106 99.0 87.4 48.0 166.6 160.2 154.0 147.6 141.4 135.0 122.4 109.8 97.2 53.0 181.6 174.8 168.0 161.2 154.4 147.6 133.8 120.2 106.6 57.5 196.8 189.6 182.2 174.8 167.4 160.2 145.4 130.8 116.0 62.0 212.8 205.0 197.2 189.4 181.6 173.6 158.0 142.4 126.8 67.0 228.-1 220.0 211.6 203.4 195.0 186.6 170.0 153.4 136.6 71.5 244.2 235.4 226.4 217.6 208.8 200.0 182.2 164.4 146.8 76.5 259.2 249.8 240.4 231.2 221.8 212.4 193.8 175.2 156.4 81.0 266.0 256.2 246.4 236.6 226.8 207.2 187.6 168.0 85.5 292.2 281.8 271.6 261.2 251.0 240.6 220.0 199.4 178.8 90.5 206 STEEL CONSTRUCTION TABLE VII (Continued) Safe Loads on Bethlehem Columns Girder Beams Used as Columns Safe loads are given in Thousands of Pounds Section Number Depth of Beam Inches Weight per Foot Pounds Area of Section Sq. In. Least Rad. of Gyr. In. UNSUPPORTED LENGTH 8 9 10 11 12 G30a 30 200 58.71 3.28 819.0 804.0 789.0 774.0 759.0 G30 30 180 53.00 2.86 723.4 708.0 692.4 676.8 . 661.2 G28a 28 180 52.86 3.18 734.0 720.C 7C6.2 692.2 678.2 G28 28 165 48.47 2.77 658.0 643.2 628.6 613.8 599.2 G26a 26 160 46.91 3.05 647.2 634.2 621.4 608.4 595.6 G26 26 150 43.94 2.68 592.8 579.0 565.4 551.6 537.8 G24a 24 140 41.16 2.90 563.2 551.2 539.4 527.4 515.4 G24 24 120 35.38 2.66 476.6 465.6 454.4 443.2 432.0 G20a 20 140 41.19 2.91 564.0 552.0 540.2 528.2 516.4 G20 20 112 32.81 2.70 443.2 433.0 422.8 412.6 402.4 G18 18 92 27.12 2.59 363.6 354.8 346.0 337.2 328.4 G15b 15 140 41.27 2.83 562.4 550.0 537.8 525.6 513.4 G15a 15 104 30.50 2.64 410.4 400.6 391.0 381.2 371.6 G15 15 73 21.49 2.39 283.4 275.8 268.4 260.8 253.2 G12a 12 70 20.58 2.36 270.6 263.4 256.0 248.8 241.4 G12 12 55 16.18 2.24 210.4 204.2 198.2 192.2 186.0 G10 10 44 12.95 2.10 165.8 160.6 155.4 150.2 145.0 G9 9 38 11.22 1.98 141.4 136.6 132.0 127.2 122.4 G8 8 32.5 9.54 1.86 118.2 113.8 109.6 105.2 101.0 Beams not secured against yielding sideways and free to fail in direction of least radius of gyration. STEEL CONSTRUCTION 207 TABLE VII (Continued) Formula P= 16, 000-70^- in which P = unit stress in pounds per square inch r = radius of gyration in inches I = length in inches. To the left of heavy line values of - do not exceed 120 OF COLUMNS IN FEET Weight per Ft. Pounds 13 14 15 16 18 20 22 24 28 32 36 743.8 6-15.6 664.2 5S4.4 5S2.6 524.0 503.6 420.8 504.4 392.2 310.6 501.0 3G1.S 245.6 234.0 180.0 139.8 117.6 06.6 728.8 630.0 650.2 569.8 569.6 G10.2 491.6 409.6 492.6 382.0 310.8 48S.8 352.2 238.0 226.8 174.0 134.6 112.8 92.4 713.8 614.6 636.4 555.0 556.8 496.4 479.8 398.4 480.6 371.8 302.0 476.6 342.4 230.6 219.4 167.8 129.4 108.2 88.0 698.8 599.0 622.4 540.4 543.8 482.6 467.8 387.4 468.8 361.6 293.2 464.4 332.8 223.0 212.0 161.8 124.4 103.4 83.8 668.8 567.8 594.4 511.0 518.0 455.2 444.0 365.0 445.0 341.2 275.6 439.8 313.4 207.8 197.4 149.6 114.0 93.S 75.0 638.6 536.6 566.4 481.6 492.2 427.6 420.2 342.6 421.2 320.8 258.0 415.4 294.0 192.8 182.8 137.6 103.6 608.6 505.6 538.6 452.2 466.4 400.0 396.2 320.2 397.4 300.4 240.4 390.8 274.4' 177.6 168.2 125.4 578.6 474.4 510.6 422.8 440.4 372.6 372.4 518.4 412.2 454.8 364.0 388.8 45S.2 398.0 287.6 343.0 200 180 180 165 160 150 140 120 140 112 92 110 104 73 70 55 44 38 32.5 349.8 399.0 305.2 337.2 262.4 277.0 208.6 278.6 198.4 152.4 268.4 177.4 317.4 324.8 298.0 373.6 280.0 222.8 366.4 255.0 ir.2.o 253.2 326.2 239.2 187.6 317.4 216.2 132.4 124.2 89.0 153.4 113.2 82.8 93.2 74.8 57.8 84.4 66.4 208 STEEL CONSTRUCTION TABLE VII (Continued) Safe Loads on Bethlehem Columns I -Beams Used as Columns Safe Loads are given in Thousands of Pounds Sertion Number Depth of Beam Inchea Weight per Foot Pounds Area of Section Si. In. Least Had. of Gyr. In. UNSUPPORTED LENGTH 5 6 7 8 9 10 B30 30 120 35.30 2.16 496.2 482.4 4688 455.0 441.2 427.6 B28 28 105 30.88 2.06 431.2 418.6 406.0 393.4 380.8 368.2 B26 26 90 26.49 1.95 366.8 355.4 344.0 332.6 321.2 309.8 B24a 24 84 24.80 1.92 342.6 331.8 320.8 310.0 299.2 288.4 24 83 24.59 1.78 335.4 323.8 312.2 300.6 289.0 277.4 B24 24 73 21.47 1.86 295.0 285.4 275.6 266.0 256.2 246.6 B20a 20 82 24.17 1.82 331.0 319.8 308.6 297.4 286.4 275.2 20 72 21.37 1.88 294.2 284.6 275.0 265.6 256.0 246.4 20 69 20.26 1.59 270.6 260.0 249.2 238.6 227.8 217.2 B20 20 64 18.86 1.62 252.8 243.0 233.4 223.6 213.8 204.0. 20 59 17.36 1.66 233.8 225.0 216.2 207.4 198.6 190.0 18 59 17.40 1.50 229.6 220.0 210.2 200.4 190.8 181.0 B18 18 54 15.87 1.54 210.6 202.0 193.4 184.6 176.0 167.4 18 52 15.24 1.56 202.8 194.6 186.4 178.2 170.0 161.8 18 48,5 14.25 1.59 190.4 182.8 175.4 167.8 160.2 152.8 B15b 15 71 20.95 1.71 283.8 273.4 263.2 252.8 242.6 232.2 B15a 15 64 18.81 1.49 248.0 237.4 226.8 216.2 205.6 195.0 15 54 15.88 1.55 211.0 202.4 193.8 185.2 176.6 168.0 15 46 13.52 1.36 174.6 166.2 157.8 149.6 141.2 132.8 B15 15 41 12.02 1.41 156.6 149.4 142.2 135.0 127.8 120.8 15 38 11.27 1.44 147.4 140.8 134.4 127.8 121.2 114.6 B12a 12 36 10.61 1.42 138.4 132.2 125.8 119.6 113.2 107.0 12 32 9.44 1.30 120.6 114.4 108.4 102.2 96.2 90.0 B12 12 28.5 8.42 1.35 108.6 103.2 98.0 92.8 87.6 82.4 BIO 10 28.5 8.34 1.21 104.4 98.8 93.0 87.2 81.4 75.6 10 23.5 6.94 1.27 88.0 83.4 79.0 74.4 69.8 65.2 Beams not secured against yielding sideways and free to fail in direction of least radius of gyration. STEEL CONSTRUCTION 209 TABLE VII (Continued) Formula P= 16,000-70^ in which P = unit stress in pounds per square inch r= radius of gyration in inches 1 = length in inches To the left of heavy line values of do not exceed 120 OF COLUMNS IN FEET Weight per Foot Pounds 11 12 13 14 15 16 18 20 22 24 413.8 400.0 386.4 372.6 358.8 345.2 317.6 290.2 262.8 235.4 120 355.6 298.4 343.0 287.0 330.4 275.4 317.8 264.0 305.2 252.6 . 292.6 241.2 267.4 218.4 242.2 217.0 172.8 191.8 105 90 195.6 277.4 266.6 255.8 245.0 234.0 223.2 201.6 179.8 158.2 84 265.8 254.2 242.6 231.0 219.4 207.8 184.6 161.4 138.2 83 236.8 227.2 217.4 207.8 198.0 188.4 169.0 149.6 130.2 73 2(54.0 252.8 241.6 230.6 219.4 208.2 186.0 163.6 141.4 82 236.8 206.4 227.4 195.8 217.8 185.0 208.2 174.4 198.6 163.6 189.2 153.0 170.0 151.0 110.0 131.8 72 69 131.4 194.2 184.4 174.6 164.8 155.0 145.2 125.8 106.2 64 181.2 171.2 172.4 161.4 163.6 151.8 154.8 142.0 146.0 132.2 137.2 119.6 103.0 102.0 59 59 122.4 158.6 150.0 141.4 132.8 124.0 115.4 98.2 54 153.6 145.4 137.2 129.0 120.8 112.6 96.2 52 145.2 222.0 184.4 137.6 211.8 173.8 1302 201.4 163.2 122.6 191.2 152.4 115.0 180.8 141.8 107.6 92.4 150.0 110.0 48.5 71 64 170.6 131.2 159.4 124.4 113.6 150.8 116.2 106.4 142.2 107.8 99.2 133.6 125.0 116.4 82.8 77.8 99.2 54 46 41 99.4 91.0 85.0 92.0 108.0 101.4 94.8 88.2 81.8 75.2 38 100.8 84.0 94.4 77.8 88.2 71.8 81.8 75.6 59.6 69.4 36 32 65.6 77.0 69.8 71.8 64.0 66.6 61.4 52.4 56.2 28.5 28.5 58.2 60.6 56.0 51.4 46.8 23.5 210 STEEL CONSTRUCTION TABLE VIII Safe Loads on Channel Columns 6*, 7", 8*, 9', and 10' Channels Safe Loads are given in Thousands of Pounds H 2Cs 2 Pis. r Area 2 Pis Area Total UNSUPPORTED LENGTH 8' 9' 10' 11' 12' 13' 6"-8# Latt. 2 33 4.76 62 61 59 57 55 54 " 8X* 2.32 4.00 8.76 115 112 108 105 | 102 99 " 5 2.32 5 00 9.76 128 124 121 | 117 114 110 1 7"-9f# Latt. 2 72 5 70 77 75 74 | 72 70 68 " 9Xi 2.67 4.50 10.20 138 134 131 128 125 122 " A 2.67 5 63 11.33 153 149 145 142 138 135 8'-lU# Latt. 3 11 6.70 93 91 89 87 85 84 " lOXi 3 03 5.00 11 70 161 158 155 152 148 145 * A 3.02 6 25 12.95 178 175 171 168 164 160 " 1 3.01 7 50 14.20 196 192 188 184 180 176 8"-13!# Latt. 2 98 8.08 111 109 106 104 102 100 " 10XA 2 97 6.25 14 33 197 193 189 185 181 177 " 1 2.96 7.50 15.58 214 210 205 201 196 192 9"-13i# Latt. 3.49 7.78 109 107 106 104 102 100 " ux* 3 40 5 50 13.28 IS6 183 180 176 173 170 " 5 3.38 6.88 14 66 205 202 198 195 | 191 187 " t 3.36 8.25 16 03 224 220 216 212 | 208 204 1 9"-15# Latt. 3 40 8.82 124 121 119 117 115 113 " nxl 3.36 5 50 14.32 200 197 193 190 186 183 " A 3.34 6.88 15.70 220 216 212 208 204 200 " j 3.33 8.25 17 07 239 235 230 226 221 217 10"- 15# Latt. 3 87 8.92 127 125 123 121 120 118 " 12XA 3 74 7 50 16.42 233 230 226 222 218 215 " 1 3 72 9 00 17.92 254 250 246 242 238 234 " A 3 70 10 50 19 42 275 271 267 262 258 253 " I 3.68 12 00 20.92 296 292 287 282 277 272 10"-20# Latt. 3 66 11.76 167 164 161 159 156 153 " 12 X A 3.64 10 50 22.26 315 310 305 300 295 289 " I 3 63 12 00 23 76 336 331 325 320 314 309 " A 3.62 13.50 25.26 357 351 346 340 334 328 5 3.61 15 00 26.76 378 372 366 360 354 348 8' 9' 10' 1V 12' 13' STEEL CONSTRUCTION 211 TABLE VIII (Continued) Formula P = 16,000 -70 in which P = unit stress in pounds per square inch r = radius of gyration in inches I = length in inches To left of heavy line values of do not exceed 125 To right of heavy line values of do not exceed 150 OF COLUMN IN FEET 14' 15' 16' 17' 18' 19' 20' | 21' 22' 23' 24' 26' 28' 30' 52 50 49 47 45 43 41 40 38 36 35 32 28 96 93 89 86 83 80 77 74 70 67 64 58 51 107 103 100 96 93 89 86 82 78 75 71 64 57 1 67 65 63 61 | 60| 58 56| 54 53 51 49 45 42 38 118 115 112 109 106 102 99 96 93 90 86 1 80 73 67 131 128 124 121 L 117 113 110 106 103 99 96 1 89 81 74 82 80 78 76 75 73 71 69 1 67 1 66 64| 60 57 53 142 139 136 132 129 126 122 119 116 113 109 103 96 90 157 153 150 146 142 139 136 132 128 124 121 113 106 99 172 168 164 160 156 152 148 144 140 136 132 124 116 108 97 95 93 91 88 86 84 81 79 77 75 70 66 61 173 169 164 160 156 152 148 144 140 136 132 124 116 108 187 183 179 174 170 165 161 156 152 148 143 134 125 117 98 96 95 93 91 89 87 85 83 81 80 76 72 68 166 163 160 157 153 150 147 144 140 137 134 127 121 114 184 180 176 173 169 165 162 158 154 151 147 140 133 125 200 196 192 188 184 180 176 172 168 164 160 152 144 136 111 108 L 106 104 102 100 98 95 93 91 89 85 80 76 179 175 172 168 165 161 158 154 150 147 143 136 129 122 196 192 188 184 180 176 172 168 164 160 156 149 141 133 213 209 204 200 196 192 187 183 178 174 170 161 153 144 116 114 112 110 108 106 104 102 100 98 96 92 88 85 211 | 207 204 200 196 193 189 185 182 178 174 167 159 152 230 226 222 218 214 210 206 202 198 194 190 182 173 165 249 244 240 236 231 227 223 218 214 209 205 196 187 178 268 263 258 254 249 244 239 235 230 225 220 211 201 191 150 148 145 142 | 140 137 134 132| 129 126 123 118 113 107 284 279 274 269 264 2591 253 248 243 | 238 [ 233 223 212 202 303 298 292 287 281) 276 270 265 259) 254 | 248 237 226 215 322 316 310 305 299) 293 287 281 2751 269 | 263 252 240 228 341 335 329 322 3161 3101 304 297 291 | 285 279 267 | 254 241 14' 15' 16' 17' 18' 19' 20' 21' 22' 23' 24' 26' 28' 30' 212 STEEL CONSTRUCTION TABLE VIII (Continued) Safe Loads on Channel Columns 12" Channels Safe Loads are given in Thousands of Pounds 2 Us 2 Pis. r Area 2 Pis. Area Total UNSUPPORTED LENGTH 8' 9' 10' IV 12' 13' 12*-20# Latt. 4.61 12.06 .175 173 171 169 167 164 " 14XA 4.40 8.75 20.81 301 297 293 289 285 281 " i 4 38 10 50 22 56 326 322 317 313 309' 304 " A 4.35 12 25 24.31 352 346 342 337 333 328 " i 4 33 14 00 26 06 377 371 366 361 356 351 12"-25# Latt. 4.43 14; 70 213 210 207 204 202 199 " 14XA 4.30 12.25 26.95 389 384 378 373 368 363 " 1 4 29 14.00 28.70 414 409 403 397 392 386 " 5 4.27 15.75 30.45 439 433 427 421 415 409 " 4 26 17.50 32.20 464 458 452 445 439 433 " s 4 25 19.25 33.95 489 483 476 469 463 456 " i 4.24 21.00 35.70 514 507 500 493 486 479 12"-30# Latt. 4.28 17 64 255 251 247 244 241 237 " 14X& 4.23 15.75 33.39 481 474 | 468 461 455 448 " ! 4.22 17.50 35.14 506 499 492 485 478 471 " fi 4.21 19.25 36.89 531 524 517 509 502 494 " 4.20 21.00 38 64 556 549 541 533 525 518 " i 4.20 22.75 40 39 582 574 566 557 549 541 " 4 19 24.50 42.14 607 598 590 581 573 564 " -i 4.18 26.25 43.89 632 623 614 605 597 588 " i 4 18 28.00 45.64 657 648 639 630 620 611 12"-35# Latt. 4 17 20.58 296 292 288 284 280 276 " 14XH 4 17 19 25 39.83 573 565 557 549 541 533 " 4 16 21 00 41.58 598 590 581 573 565 556 " 1 4.16 22.75 43.33 623 614 606 597 588 579 " 4.15 24.50 45.08 648 639 630 621 612 603 " H 4. .15 26.25 46.83 674 664 655 645 635 626 " 4.14 28 00 48.58 699 689 679 669 659 649 " H 4.14 31 50 52.08 749 738 727 717 706 696 " H 4.13 35.00 55 58 799 787 776 765 753 742 8' 9' 10' 11' 12' 13' STEEL CONSTRUCTION 213 TABLE VIII (Continued) Formula P= 16,000-70 - in which P = unit stress in pounds per square inch r = radius of gyration in inches 1 = length in inches To left of heavy line values of do not exceed 125 To right of heavy line values of do not exceed 150 n OF COLUMN IN FEET 14' 15' 16' 17' 18' 19' 20' 21' 22' 23' 24' 26' 28' 30' 162 160 158 156 153 151 149 147 145 142 140 136 131 127 277 273 269 265 261 257 253 250 246 242 238 230 222 214 300 296 291 287 283 279 274 270 266 261 257 248 240 231 323 318 314 309 304 300 295 290 286 281 276 267 257 248 346 341 336 331 326 321 316 311 306 301 | 295 285 275 265 196 193 191 188 185 182 179 177 174 171 168 183 157 152 357 352 347 342 336 331 326 321 315 310 305 294 284 273 381 375 369 364 358 352 347 341 335 330 324 313 302 291 403 397 391 385 379 373 367 361 355 349 343 331 319 308 426 420 413 407 401 394 388 382 375 369 363 350 337 325 449 442 436 429 422 416 409 402 395 389 382 369 355 342 472 465 458 451 444 437 430 423 415 408 401 387 373 359 234 230 227 223 220 216 213 210 206 203 199 192 185 178 441 435 428 421 415 408 402 395 388 382 375 362 349 335 464 457 450 443 436 429 422 415 408 401 394 380 366 352 487 480 472 465 458 450 443 436 428 421 414 399 384 370 510 502 495 487 479 471 464 456 | 448 440 433 417 402 386 533 525 517 509 501 493 485 477 469 460 452 436 420 404 556 548 539 531 522 514 505 497 488 480 472 455 438 421 579 570 561 552 543 535 526 517 508 499 491 473 455 438 602 593 583 574 565 556 547 538 529 519 510 492 473 455 271 267 263 259 255 ^250 246 242 238 234 230 221 L213 205 525 517 509 501 493 485 477 469 461 453 445 429 413 397 548 539 531 523 514 506 497 489 480 472 464 447 430 413 571 562 553 545 536 527 518 510 501 492 483 466 448 431 594 584 575 566 557 548 539 530 520 511 502 484 466 448 617 607 597 588 579 569 559 550 541 531 522 503 484 465 639 629 619 610 600 590 580 570 560 550 541 521 501 481 685 675 664 653 643 632 622 611 601 590! 580 558 537 516 731 720 708 697 686 674 663 652 640 629 618 595 572 550 14' 15' 16' 17' 18' 19' 20' 21' 22' 23' 24' 26' 28' 30' 214 STEEL CONSTRUCTION TABLE VIII (Continued) Safe Loads on Channel Columns 12" and 15" Channels Safe Loads are given in Thousands of Pounds II =r 2 20 2 Pis. r Area 2 Pis. Area Total UNSUPPORTED &ENGTH 8' 9' 10' 11' 12' 13' 12*-40# Latt. 4.09 23.52 338 333 328 323 318 314 " 14 X'| 4.12 22.75 46.27 66-5 655 646 636 627 618 ." 4.11 24.50 48.02 690 680 670 660 651 641 a 1 4.11 26.25 49.77 715 705 695 684 674 664 " 4.11 28.00 51.52 740 730 719 708 698 687 " H 4.10 31.50 55.02 790 779 768 757 745 734 " u 4.10 35.00 58.52 840 828 816 804 | 792 780 " if 4.10 ,38.50 62.02 891 878 j 865 853 840 8!?7 4 4.09 42.00 65.52 941 927 914 900 887 873 15*-33# Latt. 4.98 19.80 290 287 283 280 277 273 " 16X I 4.84 12.00 31.80 465 459 453 448 443 437 " A 4.83 14.00 33.80 494 488 482 476 470 464 " 1 4.82 16.00 35.80 523 517 510 504 498 492 2 * 4.80 20.00 39.80 581 574 567 560 553 546 a 1 4.79 24.00 43.80 639 632 624 616 609 601 " 4.76 32.00 51.80 756 747 738 728 719 710 l5*-35# Latt. 4.94 20.58 301 298 294 291 287 284 " 16X i' 4.81 16.00 36.58 534 528 521 515 508 502 " 4.79 20.00 40.58 592 585 | 578 571 564 557 " 4.77 24.00 44.58 650 642 635 627 619 611 " 1 4.75 32 00 52 58 767 758 748 739 730 720 11 Q 4.72 48 00 68.58 1000 988 975 963 950 938 15MO# Latt. 4.84 23.52 344 340 335 331 327 323 " 16X $ 4.75 16.00 39 52 576 569 562 555 548 541 " 4 74 20.00 43.52 635 627 619 611 604 596 " 4.73 24.00 47 52 693 684 676 668 | 659 651 " 1 4.71 32 00 55.52 809 . 799 789 780 | 770 760 " o 4.69 48 00 71.52 1042 1029 1016 1003 991 978 41 2 4.68 64.00 87 52 1274 1259 1243 1227 1211 1196 15'-45# 16X 1 4.H9 20 00 46.48 677 669 660 652 644 635 " f 4 68 24.00 50.48 735 726 717 708 699 690 44 1 4 68 32.00 58.48 851 841 830 820 809 799 44 Q 4 66 48.00 74.48 1084 1071 1058 |1044 1031 1017 44 4 66 64 00 90. 48 317 1301 1285 1268 1252 1235 15'~50# 16X1 4 64 32 00 61.42 894 883 872 861 849 838 " Q 4 64 48.00 77.42 1126 1112 1098 1084 1070 1056 " 2 4.63 64.00 93 42 1359 1342 1325 1308 1291 1274 g 4 63 SO. 00 109 42 592 1572 1552 1532 1312 1492 8' 9' 10' ir 12' 13' STEEL CONSTRUCTION 215 TABLE Formula in which P = unit s1 r = radius / = length To left of heavy lin To right of heavy li] VIII (Cor itinu K)0- nds p< in in - do ido ed) 70 l ,ress in pou of gyration in inches e values of ae values of 70 r ?r square inch abet aot exceed 125 not exceed 150 P~~ OF COLUMNS IN FEET 14' 15' 16' 17' i 18' 19' 20' | 21' | 22' 23' 24' 26' 28' 30' i 1 1 309 304 299 294J 289 285 280| 275 270 265 260| 251 241 231 608 599 | 589 580 570 561 552 542 533 523 514 495 | 476 | 457 531 621 611 602 592 582 572 562 552 543 533 513 494 474 654 644 634 624J 613) 603 | 593 583 | 572 | 562 | 552 532 512 491 677 666 656 646 | 635 624 1 614| 6031_592J_582 571 551 530 509 722 711 700 689 677 666| 655 | 644) 632 621 610 1 587Lj5S5 542 768 | 756 744 732 720 | 708 696 684 672 660 648 624 600 576 814 802 789 776 763 751 738LJ726 713 700 687 662 636 611 860 846 833 820 806 793 779 766 752 739 725 698 672 645 270 267 263 260 1 257 253 250 247 243 | 240 237 230 223 217 432 | 426 420 415 | 409 404 | 398 393 387 382 376 365 354 343 458 ^53 447 441 435 429 423 417 411 406 400 388 376 364 485 479 473 467 460 454 448 442 435 429 423 411 398 386 539 532 525 518 511 | 504 j 497 490 483 476 470J 456 442 428 593 586 578 570 562 | 555 547 540 532 524 L516| 501 486 470 701 692 683 673 664 655 646 637 628 619 609 591 573 554 280 277 273 270 266 263 259 256 252 249 245 238 231 224 496 489 483 477 470 464 458 451 445 438 432 419 406 394 549 | 542 535 528 521 | 514 T 507 | 500 | 493 486 478 464 | 450| 436 603 596 588 580 572 | 564 | 556 548 | 541 533 525 509 494 478 711 702 693. 683 674 | 665 | 655 646 637 627 618 599 581 562 926 914 902 890 878 | 866 | 853 841 828 816 804 780 756 731 319 315 311 307 303 | 299 295 290 286 282) 278 270 262 254 534 527 520 513 506 | 499 492 485 478 47 1| 464 450 436 422 588 581 573 565 557 550 542 534 527 519 511 496 480| 465 642 634 625 617 608 600 | 592 583 575 566 558 541 524 507 750 740 730 720 | 710 700 | 690 680 | 67 1| 661 651 1 631 611 591 965 952 939 926 914 1 901 888 | 875 | 863 | 850 837 811 785 760 1181 1165 1149 1133 1118 1102 1086 1070 1055 1039 1023 992 | 960 929 627 | 619 610 602 594 586 577 569 561 552 544 527 510 494 681 | 672 663 654 645 636 626 617 608 599 590 572 554 536 789 ! 778 768 757 747 736 726 715 705 694 684 663 642 620 1003 990 976 963 950 | 936) 923) 909 896 883 869 | 842 816 789 1219 1 202 1186 1170 1 1 54 1137 |11 21 11 105 1088 107211056 1023 991 958 827 816 805 794 783 771 | 76QI 749 738 727 j 716 6915 671 649 1042 1028 1014 1000 986) 972| 95S| 944 930 916| 902 874 846 818 1257 [1241 1224 1206 1189 1172 1156|1139 1122 1105(1087 1054 1020 987 1473 j 1453 1433 1413 1393 1373 1354|1334|1314 1294|1274 123411195 1156 14' 15' 16' 17' | 18' 19' 20' 21' 22' 23' | 24' 26' | 28' | 30' 216 STEEL CONSTRUCTION Details of Construction. Splices. The several columns in a stack may be made in one-, two-, or three-story lengths. Two- story lengths are most commonly used. The one-story length per- mits each story of the column to be designed for the load in that story, whereas a two-story col- umn is designed for the load in the lower of the two stories, the same section being used through- out the two-story length; this gives a greater area in the upper story than is required for the stress in that story. Similarly, for the three-story column the middle and upper stories are ex- cessive; also the three-story col- rig. 145. Splice in a Channel Column umn is more difficult to erect. The saving in favor of the one-story column is offset by the expense of the splices for material, shop labor, and erection; hence the common use of the two-story lengths. The splice is placed above the floor line a sufficient distance so that the splice plates will not in- terfere with the beam connec- tions; usually 18 inches is enough space. The strength of the splice plates may vary from a nominal amount to the full strength of the column, generally the former, it being considered that the splice plates serve only to hold the col- umns rigidly in line. Even when there is bending stress due to eccentric loads, it seldom hap- pens that there is actual tension on one side of the column, hence the splice plates do not transmit Fig. 146. Splice in a Plate and Angle Column any StrCSS. STEEL CONSTRUCTION 217 As the splice plates are not designed to carry stress, the load must be transmitted by direct bearing of the upper column on the lower. This requires that the ends be milled exactly at right angles to the axis of the columns and that the end of the upper column have full bearing on the top of the lower column, or, if this cannot be had on account of change in size or shape of columns, then that a bearing plate be used between the column sections. Fig. 145 shows a column splice in which the upper section of column rests directly on the lower section. The splice is made by means of the plates m and the angles o. The plates n are fillers which make up the difference in width of the two sections of column. The angles o are used on the web of the channels because plates could not be riveted on after the columns are in place. Fig. 146 shows a column splice in which the upper section of column does not rest directly. on the lower section. In addition to Fig. 147. Types of Lacing for Columns the splice plates m, there are required the filler plates n, the bearing plate p, and the 'connection angles o. No rules can be given for the thickness of splice plates, but they should be made consistent with the column section. Riveting. The specifications for riveting, p. 365, govern the rivet spacing in columns. Refer to these specifications and note the spacing at the ends and the maximum spacing. It is interesting, as an indication of relative cost, to note the number of lines of rivets required for various styles of columns as follows: Plate and angle columns without cover plates 2 rows Plate and angle columns with cover plates . . 4 or 6 rows Channel columns 4 rows Bethlehem columns with cover plates 4 rows Zee-bar columns without cover plates 2 rows Zee* bar columns with cover plates G rows Lacing. Schneider's Specifications* contain provisions regard-' "Specifications for Structural Steel for Building", by C. C. Schneider, M. Am. Soc. C. E., Transaction American Society of Civil Engineers, Vol. LIV. p. 449. 218 STEEL CONSTRUCTION ing lattice bars, p. 365. Fig. 147 shows the style of lacing referred to. At the ends of laced columns tie plates are required. These plates should have a length not less than the width of the member. Tie plates must also be used where beams connect to the column and when the lacing must be omitted for any cause. Connections. Connections for beams and girders are described and illustrated under the discussion of beams and girders. The methods there given will enable the designer to work out any special connections required. Brackets. Brackets projecting to a considerable distance from the face of columns are used for supporting cornices, balconies, etc. If the bracket is constructed with a solid web plate and with parallel flanges, it may be designed as a cantilever girder. The bracket may Fig. 148. Bracket on Column be made up of a tie and a strut, Fig. 148, with no web plate. In this case the stresses are determined by the methods given in "Stat- ics". To illustrate, use the data given in Fig. 148-a and the stress diagram, Fig. 148-b. For a load of 18,000 pounds on the end of the bracket, the stress in the tie is 18,000 pounds and the stress in the strut is 25,200 pounds. The tie and strut can now be designed by the methods given for tension and compression members. It is very important to keep in mind that loads on all projecting brackets are eccentric loads on the columns and the columns must be designed accordingly Bases. As the allowable pressure on the masonry foundation of the column is very much less than the stress in the column, it is STEEL CONSTRUCTION 219 necessary to provide a base plate to spread the load over the required area of the masonry. Whatever the form of base used, the bottom of the column section must be milled and the top of the base must be also a flat surface. If a steel plate is used, it will be true enough without milling, but all other forms require milling to give a true top surface. Two or more angles are riveted to the bottom of the column to provide a means of bolting the column to the base, Fig. 149. This bolting is done chiefly for assistance in erection. Fig. 149. Details of Bottom of Column The bases are usually set exactly to elevation and alignment before the columns are set. This makes it easy to get the columns in their correct position. The bases are first supported on wedges and then the space under them grouted. Flat Plates. The simplest form of column base is a flat plate, which may be either steel or cast iron. Having the load on the column and the allowable unit pressure on the masonry, the area 220 STEEL CONSTRUCTION of the plate is computed therefrom. The thickness of the plate is computed in the same manner as bearing plates for beams, p. 130. The thickest steel plate ordinarily available is 1 inch and this limits the size of steel plate that can be used. However, steel slabs up to 12 inches thick can be had from the rolling mills if the quan- tity is large and considerable time can be allowed for delivery. They are designed in the same manner as plates of ordinary thickness except that the unit stress from bending should be 14,000 pounds per square inch. There is not likely to be any economy in using steel slabs when there is room for using cast-iron pedestals. Cast-iron plates can be made of any thickness, but when the thickness would be greater than 4 inches, it becomes economical to use cast-iron pedestals. Fig. 150 is a cast-iron plate. The hole in the center is for grouting. In this form of plate the bolts must be in place before the plate is set ; the bottom of the plate is recessed for the bolt heads. Cast- Iron Pedestals. When the size of the required base is so great that a flat plate is not practicable, the cast-iron pedestal is used, Fig. 151. It is impossible to compute the stresses in a cast-iron pedestal with any certainty. However, Fig. isu. Cast-iron Base. Plate it is customary to design them by the flexure formula, which seems to give results that are satisfactory. This cannot be done directly, hence the dimensions must be assumed or determined from other considerations, and the resulting section checked by computing its resisting moment. Illustrative Example. Assume that the load on a column is 600,000 pounds and the unit bearing on masonry is 500 pounds per square inch. Then the area required is 600,000 10An * =1200 sq. m. Use a plate 3'-0"X3'-0", which gives an area slightly in excess of the amount required. RECESS rox BOLT HEAD B-O TO 3-0 J J-0 TO S'OSQUAfie BASE.. S . o To 6 '. o ' S QUA* BASE. Fig. 151. Types of Cast-Iron Pedestals 222 STEEL CONSTRUCTION The size of the top plate is determined by the size of the column and its connection angles. In this case assume 20 inches. The height must be assumed. It may vary between one-third and one-half the base. Use 16 inches. The diameter of the hub is assumed. Use 8 inches inside. The thickness of metal must be assumed for trial. Use 1 J-inch for hub; 1J inches for top plate; and If inches for base plate. The shaded area in Fig. 152 Fig. 152. Be^f^Cggpj^Stoe.ttkol sh()ws the ^^ available for resisting bending. To determine its resisting moment R M it is first necessary to locate its neutral axis and then compute its moment of inertia. The center of gravity is found by the method given on p. 36. The area of the cross section is fora area = 33" X If" = 57.75 for b area= 2"X13"XH" = 32.50 ford area= 2"x6"Xli" = 15.00 105. 25 sq. in. Taking moments about the bottom line fora moment = 57. 75 X .875= 50.53 for 6 moment = 32.50X 8.25 =268.12 ford moment = 15. 00X15. 375 = 230. 62 549.27 The distance from the bottom of the plate to the neutral axis 0-0 is c _549.27_ r 105.25 ' The moment of inertia about the axis 0-0 is /from tables = \57.75X(4.33) /from tables = \32.50X (3. 04) ffrom tables fora 1 = for b 7 = ford 15 1083 458 301 2 \15X(10.16) 3 1548 3407 STEEL CONSTRUCTION 223 The allowable stress on cast iron in tension is 3000 pounds per square inch. Then the resisting moment of the section is 30 OX 3407 5.21 = 1 ,940,000 in.-lb. The bending moment M, resulting from the pressure on the bottom of the plate, is determined by treating the plate as an inverted cantilever, Fig. 152. Then M = 300, 000X9 = 2, 700,000 in.-lb. This amount is excessive because it assumes the column load applied at a point at the center of the top of the plate, whereas it occupies considerable area. As the bending moment computed for the load is 2,700,000 inch-pounds and the resisting moment is 1,940,000 inch-pounds, the trial section is not sufficient. The section can be increased in strength by increasing the height or by increasing the thickness of metal. The most effective places for additional metal are -in the top and bottom plates. PROBLEM Increase the height of the cast-iron pedestal to T-G", retaining all other dimensions. Compute the resisting moment. Number of Ribs. The number of ribs to be used can be as indicated by the bases shown in Fig. 151. Therefore, 12 ribs are used for the case illustrated above. The thickness of the rib should be not less than 1 inch and about T V the clear height be- tween the bottom and top plates. Also there must be enough section in the ribs and hub just below the top plate to take the whole load at 10,000 pounds per square inch. In this case the clear height is 13 inches, which indicates 1-inch ribs. This thickness gives ample section for compression. Shape of Pedestal. Cast-iron pedestals may be made round instead of square if so desired, Fig. 151. The round pedestal has some advantages in manufacture and is especially well suited for round piers. The bending moment on a round base is approxi- mately the total column load multiplied by 0.10 of the diameter of the plate. The resisting moment of the pedestal is computed by the method given above* 224 STEEL CONSTRUCTION When a rim is used around the edge of the bottom plate, it can be computed in the section resisting bending. This rim is desirable in large pedestals. There must always be a grout hole at or near the center of the pedestal. In large plates additional holes are used. Steel Grillage. If the masonry bearing is long and narrow, steel I-beams may be used for spreading the load. When so used, they are designed in the same manner as given for bearings for beams, p. 133. These beams rest directly on the masonry, and are filled _BOTH FL'ffS FOR GROUT 3I S -^4 'xiopx S-O. L ONG -i. s -JXJXj 'x I '-I /'ABOUT \GPIND TO FIT /O-PLTS.-6"xJ'xi ZO-BOLTS$ * XI- 6-? HEX NUTS /-PLT ZtXlkl : 4 {BOL T) Fig. 153. Steel Grillage Designed for Base of a Column ol a 16 Story Building with cement, concrete, or grout. The webs of the beams must be investigated for shearing strength and, if at all deficient, tight- fitting separators must be used. Separators should be used in any case to hold the beams in position. The flanges of I-beams are not always exactly at right angles to the webs, hence the beams may not furnish a flat surface for seating the columns. This makes it necessary to plane enough off the top of beams to provide a true surface for the bottom of the column to rest upon. In order to be effective, this must be done after the beams are assembled and rigidly held together. STEEL CONSTRUCTION 225 The load from the column must be properly distributed to the beams forming the grillage, using a steel or cast-iron plate of proper thickness. It may be necessary in some cases to use a cast-iron pedestal on the steel grillage. Fig. 153 shows a steel grillage designed for the base of a column of a 16-story building. CAST-IRON COLUMNS Cast-iron columns formerly were used extensively for building work, even for fireproof buildings ten or more stories in height. Now they are used only for small buildings of non-fireproof con- struction. The change has come about through greater demand for safety and the reduction in cost of steel columns. Characteristics. Advantages. The advantages of cast-iron col- umns are: They offer greater resistance to fire than unprotected steel columns. They generally can be more quickly obtained. They can be made of any desired shape and ornamented to suit the requirements of architectural design. They occupy a minimum of space in the building. Disadvantages. Cast-iron columns have the following disad- vantages: For supporting a given load a cast-iron column costs more than a steel column. They are subject to defects that are difficult to discover by usual methods of inspection. Cast-iron columns are made to order. As the brackets and flanges must be cast on the column shaft at the time it is made, it is not possible to have the column shafts in stock. Cast iron is subject to considerable variation in quality, depend- ing upon the materials used in the melt and the treatment in the furnace and in the molds. It may be soft and tough, or hard and brittle. It is made in 'small foundries, as compared with the rolling mills which make structural steel. Hence it is not possible to control the quality closely, as can be done with steel. Blow holes in castings are spaces which the iron does not fill, due to bubbles of air or gas becoming entrapped in the mold. Sand pockets may be formed by the dropping of sand from the molds. In both of these cases the surface of the casting may be perfect, and the defects thus difficult or impossible f to find. The most frequent fault with round columns is eccentricity, due to displacement of the core. The core may sag in the mold, due 226 STEEL CONSTRUCTION Fig. 154. An Eccentric Cast-Iron Column to its weight, or it may float in the liquid iron. The result is shown in Fig. 154. It may occur at any place in the length of the column. At the ends the fault is easily detected, but at intermediate points it is necessary to drill test holes as indicated in the figure. The test holes should be drilled in the top or in the bottom of the casting in reference to its position in the mold. An eccentricity. of inch causes appre- ciable loss of strength. A greater amount than this should cause rejection. Column Sections. Unless there is some rea- son for using a special shape, cast-iron columns are made round. The size is designated by the external diameter and the thickness of metal. The sizes commonly made for structural purposes vary from 6 inches to 15 inches in diameter and from J inch to 2| inches in thickness. Special sections sometimes used are shown in Fig. 155. The angles, U-shapes, and square sections are used chiefly for store front work. They are generally made with the exposed surfaces paneled or otherwise ornamented. H-shaped columns may be used for general purposes. They are not as economical as round columns, hence are not much used. In some respects they are better than round columns as connections Fig. 155. Typical Cast-Iron Column Sections are easily made and all surfaces are open to inspection, making it easier to find defects. Method of Design. The method of designing cast-iron columns is similar to that used in designing steel columns. The direct load and the concentric equivalent of eccentric loads, if any, are com- puted in the same manner. The allowable unit stress is computed from a formula similar to that for steel columns. The formula given under Unit Stresses, p.^ 51, is P =10,000 -GO - r STEEL CONSTRUCTION 227 Eccentric Loading. The concentric equivalent for eccentric loads is computed by the same formula as used for steel columns, For round cast-iron columns an approximate formula is in which M is the eccentric moment in inch-pounds and d is the diameter of the column in inches. Fig. 156 shows two cases of eccentric loading of a round column. For the load m, the eccentricity e m is the distance from the center of the column to the center of the web of the beam. For the load n, Fig. 156. Diagrams Showing Eccentric Loading on a Round Column the eccentricity e n is the distance from the center of the column to the center of bearing on the bracket, this center of bearing being taken at 2 inches from the face of the column, when standard brackets are used. On page 177, it was pointed out that when two eccentric loads act about the axis 1-1 and 2-2, respectively, their results must be added together. This is true also of rectangular and round cast- iron columns. But for round columns the maximum effect of two such loads is somewhat less than the sum of their separate effects. The resultant varies with the relative amounts of the eccentric moments, but the difference is not great and the sum of the separate effects can be used without much error. Factors Required. If the concentric equivalent load is used, the only properties of the section required are: area A; radius of 228 STEEL CONSTRUCTION gyration r; and distance to extreme fiber c. The values of these prop- erties can be computed for the rectangular sections by the methods given. For round columns the area is computed from the formula the radius of gyration is computed from the formula the distance c is \ d. In these formulas TT is 3.1416; d is outside diameter of column; and d v is inside diameter of column. The inside diameter equals the outside diameter less twice the thickness of metal. Thus a column 8 inches in diameter and 1 J inches thick- ness of metal has an inside diameter of 5 inches. llluslrative Example. Assume a column with the following dimensions and loads, and determine the thickness of metal required: Length of column 140" Concentric load from column above 1 60,000 # Eccentric load 40,000 #- eccentricity 7" ' Outside diameter of column (assumed) 10* Then the eccentric moment is 40,000X7 = 280,000 in.-lb. which by the rule on p. 175, is reduced to f X 280,000 = 21 0,000 in.-lb. The concentric equivalent is . _ a 10 The total load for which the column must be designed is Load from upper column 160,000 # Eccentric load 40,000 Concentric equivalent load 105,000 305,000 # It is now necessary to assume a trial thickness of metal and compute the strength. Assume 2 inches. A = (d 2 -d*) = X (100-36) =50.26 sq. in. / 140 P = 10,000-60 - = 10,000 T 60X^ = 7100# per sq. in. T 2 . y Total capacity 7 1 00 X 50. 26 = 356,800 # TABLE IX SAFE LOADS FOR ROUND CAST-IRON COLUMNS Thousand Pound Units P=10,000-60 Values to right of heavy line are beyond limit of length, 70 r. 11- I' LENGTH FEET Weight Ibs. per) ft. of length ** il" I Radius of | Gyration 6 8 10 12 14 16 18 20 22 6 1 81.7 73.7 1 65.7 57.8 ! 1 33.2 10.6 38.6 1.91 j 95.1) 85.6] 76.1 66.6 38.6) 12.4) 43.5 1.87 A 107.8} 96.8) 85.8 74.7) 1 44.0) 14.1] 47.6 1.84 1 119.4(106.8) 94.3 81.7 1 49.0) 15.7) 51.0 1.80 LI 130.2] 11 6.2) 102.2 8S.2 53.8] 17.2) 53.9)1.77 n 140.2)124.8 109.4 93.9 58.2) 18.6| 56.2 1.74 7 118.7)109.2 99.7| 90.2 80.7 46.0 1 14.7] 72.9|2.23 135.2)124.1)113.0 102.0 90.91 52.6| 16.8| 80.6|2.19 i 150.6 138.0)125.4 112.7 100.1 I 58.9 18.8) 87.212.15 3 165.1 151.0)136.8)122.6 108.4! 64.8 20.8| 92.9 2.11 Li 178.9 163.3J147.6 132.OJ116.4j 70.7) 22.6) 97.7 2.08 l j s 191.8 174.7)157.6 140.6J 123.5 76.1) 24.3) 101.8 2.05 Ej 203.8 185.3) 166.8 148.3 1129.8) 81.1 1 25.9| 105.3 [2.02 8 142.2 132.7 1123.2 113.61104.0 94.6) 53.3! 17.1 113.4 2.58 1 162.6! 151.41 140.3) 129.2) 118.1 107.0, 61.3J 19.6 126.2 2.54 181.9] 169.2 |156.6J 143.9] 131.2 118.6 68.6 22.0 137.4)2.50 li. 200.3] 186.1 1171.9,157.7) 143.4 129.2; 76.1) 24.3 147.4 2.46 218.0 202.3 186.6|170.9 1 55.2 1 139.5 82.7 26.5 156.1 2.43 i ^ 234.4j 217.2 199.9 182.7J 165.3 148.2) 89.3) 28.6 163.8 2.39 1 250.3 231.6 212.9 194.2|175.5 156.8 94.8) 30.6 170.4 2.36 9 1 156.3 146.6 137.11127.5 118.0 108.4! 60.6 19.4 166.8 2.93 j 1 178.8 167.7 156.6] 145.4) 134.3 123.2) 69.8 22.3 186.4 2.89 i 200,5 187.8 175.1 1162.4 1149.7 137.0 78.41 25.1 204.2 2.85 i j 221.3 207.0 192.8 178.51164.2 150.0) 87.0) 27.8 220.2 1 2.81 i* 241.3)225.5 209.8 1194.0] 178.2 162.5) 94.91 30.4 234.5J 2.78 q 260.1)242.8 225.6)208.3 1191.0 173.7) 103.0 32.9 247.312.74 n 278.0 259.2 240.3)221.5 202.6 183.8 110.3) 35.31 258.4 2.70 10 1 179.7)170.1 160.5)151.0 141.4 131.8 122.3 68,2) 21.8) 234.6 3.28 1 [231.81219.1)206.41193.7 181.0)168.2 155.5 88.2 28.3) 289.913.20 n 280.4 264.6|248.8|233.0 216.3|201.3 185.5 107.21 34.4| 335.6! 3. 13 n 324.9 306.0) 287.1] 268.2 249.3 1230.4 211.5) 125.0| 40.0) 373.lj3.05 )365.9 344.0)322.1)300.2 278.3 256.41234.4 141.7) 45.4) 403.212.98 11 i 263.2 250.4 1237.7) 225.0 1212.2 199,5 1186.7 174.0 98.0) 31.4) 396.7; 3.55 ii 319.4|303.6|287.7)271.8 255.9)239.9)224.0 208.1 119.5 38.3) 462.613.48 IG 371.8)352.9) 333.9) 315.0| 296.0) 277.0 258.1 1 239.1 139.7| 44.8! 517.8)3.40 jj 420.6)398.6! 376.6| 354.6! 332.6) 310.fi 288.7 1 266.7 158.7) 50.9] 563.5)3.33 2 465.6 1 440.6J415.6 j 390.6 1 365.6 1 340.7 315.71290.7 176.4) 56.5 601.0)3.26 12 1 294.7(281.9] 269.2| 256,5) 243.81 231.0 218.3! 204.7 107.5) 34.6) 527.1|3.91 n 358.7 ) 342.8 1 326.9 J 31 1 .OJ 295.2 1 279.3 263.4 1 247.6 131.4) 42.2) 618.213.83 Q 418.8)399.8)380.8) 361.8) 342.8) 323.8 304.8 285.8 154.1 49.5 696.0)3.75 1 J 475.3] 453.3 1 43 1 .2 1 409.2 1 387. 1 1 365. 1 343.0 3 I'd. 1 175.5 56,4 761.8 3.68 2 528. 1| 503.0 1478.0 452.9 1427.8! 402.8 377.7 352.fi 195.8 62.8| 817.0)3.61 13 1 326.0 1 3 1 3.3 1 300.5 1 287.8 1 275.0 1 262.3 24 192.9) 61.911002.4)4.02 2 590.4 ! 565.2 1 540.0 1 51 4.8 1 489.6 1 464.4 1 439.2 1 4 1 4.0 215.6) 69.1)1080.2)3.95 a Make allowance for eccentricity in accordance with the following formu a: W e '=5 -r FF' e '=Equivalent concentric load, Ib.; Af=Moment of eccentricity, in.-lb.;and d=Dia in. See pp. 227, 228. meter. 230 STEEL CONSTRUCTION This amount is greater than required, so the thickness may be reduced. It can be shown that the thickness required is 1 f inches. PROBLEM From the data given above, determine the thickness required for a column 12 inches in diameter. Note that eccentricity is 8 inches for this diameter Tables. The published tables of strength of cast-iron columns vary greatly, due to the variety of formulas used. Columns other than round are used so little and when used are so likely to be of special dimensions that tables of strength would be of little value. Table IX gives the strength of round columns in accordance with the formula adopted. It also gives the value of r for use in comput- ing the concentric equivalent for eccentric loads. The Chicago Building Ordinance from which this formula is taken limits the Fig 157. Splice of Cast- Fig. 158. Splices of Cast-Iron Columns by Dowel Plates Iron Column by Flanges length of cast-iron columns to 70 Xr. This limit is marked by the heavy zigzag line in the table. Illustrative Example. Determine the column required to sup- port a load of 191,000 pounds, the length being 11 feet. From Table IX either of the following sizes may be used: S"diam. X If metal 9"diam. XlJ" metal 10"diam. Xl "metal The 9-inch column is the lightest and will be used if no special con- sideration indicates the use of one of the other sizes. STEEL CONSTRUCTION 231 PROBLEM The loads and lengths of a stack of cast-iron columns are given below. Dct ermine the sections. 4th story, column load, 20,000# length 13 ft.. 3rd " " " 70,000$ length 12 ft 2nd " . " '' " 115,000# length 14ft. 1st " " , " 155,000# length 16 ft Basement " " 205,000$ length 9ft IO"& 9" All seats to slope All Webs on lugs to be f thick. The above connections have capacities corrtspondiny to those of standard connect/on angles. The distance from top of column to beam seat must be sufficient to allow a clearance of ' Between top of beam and underside of flange Or bolt head. Distance A will vary to fit position of holes when beams are adapted to multiple punch. Otherwist tht distance A will be for 24" Beams /.' l5"Beoms J/". B'Becmy jj. 6"Beoms 3" >(?" 4", if- 3j~ a" 4~. Id" ,. 4- 10" ^ 3f. 7" * J/ Holes should btj larger than corresponding rivet holes in beam- 8" 7" & 6" Fig. 159. American Bridge Company Standard Beam Connections 232 STEEL CONSTRUCTION Details of Construction. Splices. Splices in cast-iron columns are made by means of flanges as shown in Fig. 157. The load is transmitted from upper to lower column by bearing. The bearing surfaces must be milled exactly at right angles to the axis of the column. If the sections do not match, the metal must be thickened as shown at m and n to provide the bearing. Some manufacturers set the flanges back from the ends of the column to reduce the area Fig. 160. Double Beam Connections to Cast-Iron Column; of the milled surface. The flange is made wide enough to take a row of 1-inch bolts. Four or more bolts are used. The splice can be made by means of a dowel plate. It is not so satisfactory as the flange splice. It is used when there is no space avail- able for the flanges, and also for replacing broken flanges, Fig. 158. Beam Connections. Beam connections are made by mean's of brackets and lugs cast on the column. The standard connections designed a*id used by the American Bridge Company are given in Fig. 159. The entire load is supported by the bracket. The seat STEEL CONSTRUCTION 233 of the bracket slopes so that the beam will not bear on the end of the bracket when it deflects. The lug serves to tie the construc- tion together and to hold the beam upright. Bolts must be use"d for all connections to cast iron, as the casting would be broken by driving rivets. When double beams are used, the connection is modified as shown in Fig. 160. This figure also shows brackets for supporting wood beams. Fig. 161 Fig. 162. Base Plate for Cast-Iron Columns Fig. 101. Top of Cast-iron Col- umn for Supporting I-Beams shows the detail of the top of a cast-iron column which supports two steel beams. Bases. Cast-iron base plates or cast-iron pedestals are used for cast-iron columns. They are designed in the manner described for the bases of steel columns. If the plate is used, a raised cross is cast on the top to fit inside the column and hold it in place, Fig. 162. If the pedestal is used, the top of it is made to match the flange cast on the column. TENSION MEMBERS Definition and Theory. In building construction, it does not often occur that loads must be supported by tension members. Occasional special features, such as balconies or stair landings, require this form of support. The most frequent use of it occurs in trusses (which are not covered in this work). Axial Tension. A member is subjected to axial tension when the load is applied in line with the axis of the member in a way that tends to stretch or pull the member apart, Fig. 163. 234 STEEL CONSTRUCTION The strength of steel in axial tension varies directly in proportion to the net cross-section area, not being affected by the length (except as to the weight of the member) or by the shape of the section. Under Unit Stresses, the allowable value of P for axial tension is given as 16,000 pounds per square inch; then the strength ] of a section is The area used in this formula must be the net area, i. e., the smallest area at any section in the length of the member. In axial tension the stress is assumed to be distrib- uted over the entire area, as indicated in Fig. 163. This differs from the tension due to bending, which is not uniformly distributed but increases from nothing at the neutral axis to a maximum at the extreme fiber, as ex- plained on p. 78. Tension Due to Eccentricity. As in the case of com- Fif. ins. Dia- pression members, the load on a tension member may be fnTaTr^on eccentric, and thus produce both axial tension and ten- sion due to bending. The discussion of concentric and eccentric loads in compression applies to tension members. Fig. 164 illustrates the stresses from an eccentric load in tension which corresponds to Fig. 140 in compression; abed represents the total axial tension and a b the axial ten- sion per square inch due to the load W; bb' represents the tension on the extreme fiber due to the bending moment We. Then the total extreme fiber stress due to the load IF' is a b f . The concentric equivalent of an eccentric load, as for compression, is expressed by the formula If the member is not symmetrical, the value of c to be Fig 164 Di t gram used is from the neutral axis to the extreme fiber on the fUS*S3i side toward the eccentric load. Eccentricity in tension members usually results from the form of the connection, and in most cases it can be avoided by careful STEEL CONSTRUCTION 235 attention to the details. It generally will be more economical thus to avoid the eccentricity than to provide the additional section necessary to resist it. In altogether too many cases this is neglected. The importance of the effect of eccentricity is illustrated by the following computations. Assume a load of 100,000 pounds concentric, then the net area required is or 6 . 25 square inch. Now assume the same load 10,000 with an eccentricity of 1 inch, a value of c equal to 2| inches and / equal to 1.9 inches. The concentric equivalent is "p&gfc*'* The total load is 100,000+70,000 or 170,000 pounds, and the area 170 000 required is l or 10.6 square inches. In this case it requires lUjUUU ft) . (c) Fig. 105. Types of Connections for Angles an increase of 70 per cent in the section to provide for the eccentricity. Fig. 165-a shows a single angle connected by one leg. It is eccentric about both axes. Fig, 165-b shows a pair of angles each connected by one leg. This is eccentric about the axis 1-1. Fig. 105-c shows two views of the same pair of angles m, with a pair of connection angles n added, which eliminates the eccentricity. Sections. Almost any form of steel can be used as a tension member. The choice of the section is governed largely by the connections that are to be made to it. Of the structural shapes, angles, plates, and channels are best adapted for tension members in ordinary building work. Round rods are used for tie-rods, balcony hangers, temporary bracing, and other similar purposes. 236 STEEL CONSTRUCTION Eyebars are seldom used in building work, being more especially adapted to bridge trusses. They may be used where heavy loads occur and rigidity is not important. Fig. 166. Types of Connections for Hangers Net Area. Plates and shapes in tension must be connected by rivets and the rivet holes must be deducted to determine the net vSTEEL CONSTRUCTION 237 area of cross section. The number of rivet holes to be deducted in any case depends upon their arrangement as explained on p. 69. The size of the hole deducted is J inch greater than the nominal diameter of the rivet. This allowance is an arbitrary one to cover the actual size of the hole, which is about ^ inch larger than the rivet, and to compensate for injury to the metal around the hole due to punching. Care must be taken to arrange the rivet holes so as to retain the greatest possible area at the critical section. Round rods can be figured full size if the ends are upset, other- wise the net area must be taken at the root of the thread. When upset ends are used, they are made large enough so that there is an excess of strength in the threads, making the whole section of the rod available. Generally the threads on rods are cut, but they can be made by cold rolling. The latter method makes the diameter at the root of the thread somewhat less than the diameter of the body of the rod, but the treatment seems to make the steel stronger. Tests show that the rolled thread is stronger than the rod on which it is rolled, thus making the whole section of the rod available. Eyebar heads are always made of sufficient size to develop the strength of the bar, so that the whole section is available. Details of Connections. Riveted Connections. Riveted con- nections are required w r hen structural shapes or plates are used. Angles, plates, and channels are most commonly used. The top connection usually is made with a gusset plate depending from a beam or girder. Fig. 166 illustrates a number of such connections. The gusset plate may be spliced into the web of a plate girder; set in between two channels; may be an extension of the gusset at the joint of a truss; or may be connected by angles riveted to the flange of an I-beam. (See p. 64). The requirements for the top connec- tion are that the gusset plate shall be of sufficient thickness to give the required bearing for the rivets; and that the rivets connecting the plate to the beam or girder, also those connecting the hanger to the gusset, be sufficient in number and be placed symmetrically about the axis of the tensile stress. It has been noted that angles in tension must be connected by both legs to avoid eccentricity. This sort of connection is desirable for the further purpose of distributing the stress over the entire section of the hanger as evenly as possible. Angles in pairs are 238 STEEL CONSTRUCTION much preferred to single angles. They shduld be stitched together with rivets and ring fillers spaced about 2 feet apart. Fig. 107. Turnbucklc and Sleeve Nut The connections at the bottom of the hanger may be made with gusset plates in the same manner as at the top, or the connect- ing members may be attached direct to the hanger. rrh Fig. 1G8. Types of End Connections for Rods When it is necessary to splice a tension member, it is evident that the splice must transmit the entire stress in the member. The principles involved and methods to be used are fully explained under Strength of Riveted Joints, p. 67, and have been used in designing the splices in plate girders. Details of Rods. Rods are specinlly suited for adjustable members. With certain forms of Fig. 169. Det ails of End Connection of Eyebar Connections, the adjustment Can STEEL CONSTRUCTION 239 be made at the ends; with splices, the adjustment can be made at the splice. A rod is spliced by means of a turnbuckle, or sleeve nut, Fig. 1G7. The ends are threaded right and left to make the member adjustable. The threaded ends are upset to maintain the full strength of the section. The various forms of end connections are shown in Fig. 168. They need no explanation. Details of Eyebars. Eyebars must be connected at the ends with pins, Fig. 169. Refer to "Structural Drafting" for details of eyebars. WIND BRACING GENERAL CONDITIONS Horizontal Pressures. In the preceding discussion, the loads considered have been gravity loads, i. e., loads acting vertically. In addition to these gravity loads, all structures are subjected to wind loads, or pressures, which are assumed to act horizontally. Probably no locality is entirely free from wind storms, so it is always necessary to provide for wind pressures in designing the framework of buildings. It is assumed that wind pressure acts horizontally and bears uniformly over the entire windward surface of the building, and that it may occur in any direction. These assumptions are not strictly correct. The wind may be inclined, due to the contour of the ground or to obstructions. It is known that the pressure near the top of a building is greater than near the ground; that the pressure is not uniform over large areas; that the rush of air around the corners produces greater pressure near the corners; and that there is a suction on the leeward side as well as a pressure on the windward side. The wind may strike the building at any angle, but the maxi- mum effect is produced when it strikes squarely against the side (or end) of the building. While the above variations are known to be true, it is impossible to provide for them in detail, hence the assumption stated above is followed and leads to satisfactory results. Unit Pressure. Many experiments have been made to estab- lish the relation between wind velocity and wind pressure. While a large amount of data has been developed, the mathematical 240 STEEL CONSTRUCTION relations are not fully established. Furthermore, it is not certain what maximum velocity should be provided for. Hence it is the general practice to use an assumed pressure in pounds per square foot of the surface. The amount assumed varies. In some cities the building ordinances specify the amount to be used ; some specify 20 pounds per square foot; others, 30 pounds. The writer recom- mends that the framework of all buildings be designed to resist a wind pressure of 20 pounds per square foot on the surface of the building. It can reasonably be assumed that the partitions and walls will add enough to the strength so that the completed struc- ture will resist a pressure of 30 pounds per square foot. Walls should not be counted as resisting any part of the 20 pounds, unless practically solid, i. e., without openings. The above recommenda- tions should be followed with some discretion : increasing the amount carried by the framework in very high buildings, and in buildings which have few partitions or a very large percentage of openings in the walls; decreasing the amount in low buildings, and in buildings which have masonry cross walls. In buildings having outside bearing walls of masonry and a reasonable amount of cross walls, or partitions, these parts may be relied upon to resist the entire wind pressure, provided the height of the building is not more than twice its width. The maximum wind pressure occurs only at long intervals. It is, therefore, allowable to use higher unit stresses for wind stresses than for gravity stresses. Under Unit Stresses it is provided that for stresses produced by wind forces alone, or combined with those from live and dead loads, the units may be increased fifty per cent over those given for live load and dead load stresses ; but the section shall not be less than required, if wind forces be neglected. Gen- erally, the members required to support the gravity loads are utilized for the wind loads. In such cases no additional area is required on account of the wind stress unless this stress exceeds fifty per cent of the gravity load stress. Paths of Stress. Transmission of Load to Foundation. The total wind pressure on the building in the direction under considera- tion is the assumed unit pressure per square foot multiplied by the projected area exposed to the pressure. This pressure must ulti- mately be resisted by the foundations of the building. Hence, STEEL CONSTRUCTION 241 there must be paths for transmitting the pressure to the founda- tions from the area to which it is applied. The pressure is applied directly to the masonry walls and windows These are strong enough as ordinarily built to carry the load to the floors. The floor construction, whether of tile arches, concrete, or even wood con- struction, acting as a horizontal girder, transmits the load to the points selected for applying it to the steel framework. Thence the steel framework carries the load to the foundation Routing the Stress. The de- , ^_ .,_ , signer has some choice as to the steel members which he will utilize for carrying the wind load So far as the steel is concerned the shortest path is the best, but other considerations may require the use of less direct courses, most commonly through the spandrel beams around the outside of the building Thus in Fig 170 is shown a plan of the columns of a building, with the typical floor framing The heavier lines repre- sent girders and the lighter lines, /7 ' joists. Considering first the wind from either the East or the West, the direction of the load is par- allel to the narrow way of the building and in the same direc- tion as the floor girders. This ^ situation indicates that the wind load should be carried down along each E.-W row of columns, viz, 1-4, 5-8, 9-12, etc. Then each line of columns and its girders will have to support the wind pressure on one panel of the face of the building from top to bottom. It is probable that these columns and girders as designed for the gravity stresses will carry the wind stresses. (This of course is governed by the height of the building.) Now if it were decided to carry the Fig. 170. Framing Plan of Building for Study of Bracing System 242 STEEL CONSTRUCTION entire load to the two ends and carry it through the columns and girders L-4 and 25-28, the intensity of the stresses would be three times as great and probably would require extra metal in these members. Therefore, so far as economy of steel is concerned, the wind load should be carried down each row of columns. But it may happen that, in order to do this, deep brackets are required in the lower stories for connecting girders to columns, brackets of greater size than is permitted by the architectural requirements; then it becomes necessary to carry the load to the ends, where the spandrel beams and their connections can be made as large as need be A combination of the two arrangements may be made, the load above a certain floor being carried down on each row of columns, and that below being carried down the end rows. Next considering the wind from the North or the South, its direction is parallel to the joists. It is probable that these joists are not strong enough to take the wind stresses without adding metal to that required for the gravity stresses. The wind pressure can easily be carried to the two sides of the building along the lines 1-25 and 4-28, where the necessary strength in the spandrel girders can readily be obtained. The foregoing illustration is comparatively simple; most cases are not so easy to settle. In general terms, the designer should take all possible advantage of interior framing, carrying through the spandrels only that portion of the wind load which cannot be taken by the interior framing. The bracing strength of the interior framing is limited by the strength of the connections to the columns and riot by the strength of the girder and joist sections. The maximum bending moments occur at these connections, and to develop the full strength of the beams would require larger brackets than the architectural treat- ment would permit. So generally it will be that a large proportion of the wind load must go through the spandrel beams where the limitations as to depth of beams and size of brackets are not so restricted. It is sometimes possible to use diagonal members for bracing. They make the most direct and efficient form of bracing, and should be used when the conditions permit. STEEL CONSTRUCTION SYSTEMS OF FRAMEWORK 243 A horizontal load can be transmitted vertically by means of framework by two systems: (1) by triangular framework, Fig. 171, Fig. 171. Diagram of Triangular Framing. Fig. 172. Diagram of Rectangular Framing having axial stresses; and (2) by rectangular framework, Fig. 172, having bending stresses. ^ Triangular Framework. Single Panels. Fi 173 shows a single panel of triangular framing supporting the horizontal force IF. The reactions at the foundations are R, V, and V. Fig. 173. Diagram of Stresses in Triangular Framing 7=F' = L By inspection it is to be seen that the stress in a equals W; in c equals V. The stresses in b and c can be determined from that in a by resolution of forces (See Concurrent Forces in- "Statics"), as indicated in the figure. These stresses are all axial; a and c in compression ; b in tension. When the values of //, L, and W are known, the numerical values for a, 6, c, and V can be determined. Two or More Horizontal Panels. Two or more adjacent panels can be used, as shown in Fig. 174. It is first necessary to divide the load between the two panels. It is simplest to divide the load equally, irrespective of whether the panels are equal in length. 244 STEEL CONSTRUCTION On this. basis the stress in a equals W, and in d equals \W. By resolution, the stresses in 6 and c, and in e and/ can be determined. F A equals the stress in c, F 3 equals the stress in/, and F 2 is the difference in stresses c and /. If in this case L l equals L 2 , then the stress in b equals stress in e\ the stress in c equals the stress in /; Fj equals 0. equals F 3 ; and F 2 /., Fig. 174. Diagram of Two Horizontal Panels of Triangular Framing PROBLEM Assume four panels similar to those shown in Fig. 174. Let // equal 16 feet; L,, L 2 , L 3 , and L 4 equal 20 feet; and W equal 36,000 pounds. Compute the stresses in the diagonals. Two or More Vertical Plincls. Two or more panels may be placed one above the other as in Fig. 175. In this case R, = W, + TF 8 +JK 2 . The value of V l = F 2 is determined by taking moments about from which 1 Tig. 175. Diagram of Vertical Panels of Triangular Framing TF 4 (77 1 +ff 2 +77 3 ) L The stresses in the members a to k inclusive can be determined by the methods given in "Statics", when the values of IF 4 , TF S , JF 2 , H 3 , 7/ 2 , 7/j, and L are known and of 7?, and F, are computed. STEEL CONSTRUCTION 245 PROBLEM In Fig. 175 assume W 4 equals 10,000 pounds; W 3 equals 10,000 pounds; H' , equals 12,000 pounds; //, equals 18 feet; 7/ 2 equals 13 feet; H 3 equals 13 feet; L equals 16 feet. Determine the stresses in a to k inclusive. Extension of Triangular Framework. Similarly, the triangular framework can be extended indefinitely in both directions, as in Fig. 176. For convenience in solving this case the figure can be separated into horizontal tiers, or stories, and each computed. In doing this, the anti-reactions of one tier must be applied as loads / \ /v- Fig. 17G. Diagram of Triangular Framing Extending Over a Building in the next lower tier. The horizontal load to be resisted at any tier is the sum of all the horizontal loads above that tier; thus the horizontal load or shear at the top of the first story is PROBLEM Assume loads and dimensions for Fig. 176 and compute the stresses in the diagonal members. 246 STEEL CONSTRUCTION In Figs. 173 to 176 inclusive the diagonals are shown in one direction only. As the wind may come from either direction, both A A r\ Fig. 177. Diagram of Rectangular Frame with Hinged Joints Fig. 178. Diagram of Rectangular Frame with Rigid Joints diagonals will be used in all cases. In certain panels, circumstan- ces may prevent the use of any diagonal bracing, Fig. 176, in Fig. 179. Diagram of Rectangular Frame Showing Points of Contraflexure which case the stresses must be distributed among the other panels. Rectangular Framework. Single Panel. A single panel of rectangular framing is illustrated in Fig. 177. The four corners STEEL CONSTRUCTION 247 are represented as being hinged, so when the load W is applied the frame will collapse, as indicated by the dotted lines. It has no strength to resist the horizontal force. Next consider the rectangular frame as shown in Fig. 178. The corners are rigidly connected. When the load W is applied, the frame tends to take the shape indicated by the dotted lines. In doing so, each of the members must bend into reverse curves. Thus the frame offers great resistance to the horizontal force. When a member is bent into reverse curves, the point of reversal is called the "point of contraflexure" There is no bending stress in the member at this point and hinged joints might be introduced at such points without affecting the stability of the frame so far as the horizontal load is concerned. This is indicated in Fig. 179. The point of contraflexure is taken at the middle of the length of each member. This is not exactly correct, but is accurate enough for designing, in all ordinary cases. In order to more easily understand the stresses in the frame, consider the points of contraflexure e, f, and g as hinged joints.. They divide the frame into' four parts which can be considered separately in determining the stresses. Take first e af, and assume the horizontal reactions at e and / to be equal, hence each is \W. The vertical reactions at e and / must form a couple which will balance the moment of the horizontal loads, hence, taking moments about e, from which V = $W- LJ The bending moment at a in the vertical member is \\Vx\H, or JTF/7; and in the horizontal member is Vx\L which equals \ IV II. Next consider the part e c, which is subjected to the loads \W and V applied at e. The reactions at o are the same in amount but opposite in direction, To maintain equilibrium, there must be a couple to neutralize the moment of the horizontal force at e about the center c. This couple is furnished by the foundation which is 248 STEEL CONSTRUCTION assumed to be ample to resist the bending moment in the post at c, which is 1 WH In like manner the bending moments at b and d can be shown to be J WH. Note that the numerical value of the bend- ing moment is the same at the four corners of the frame. The moment diagram is given in Fig. 180. In addition to the bending stresses in the members, there are axial stresses, as indicated by the forces and reactions illus- trated: J W, compression TT V ^W t compression Lt TJ in a c V = %W , tension L PROBLEM Refer to Fig. 179. Assume W equals 10,000 pounds, H equals 16 feet, L equals 20 feet. Compute the axial stresses in the three members of the frame. Compute the bending moment at a. Construct the moment diagram. Fig. 180. Moment Diagram of Single Rec- tangular Panel in a b 'mbd /[A Fig. 181. Diagram for Two Rectangular Panels Two Horizontal Panels. Next consider a framework of two panels, i. e., made of three columns and two girders, as in Fig. 181, STEEL CONSTRUCTION 249 subjected to a load W. It is necessary to assume the division of the horizontal reactions between the foundations 1, 2, and 3. Sev- eral different: methods are used in practice. It is not of much importance which is used, if the stresses resulting from the assumed divisions are adequately provided for. In this text it is assumed that the reactions at the end columns are one-half of those at the intermediate columns. Thus the reactions at /, 2, and 8 are J W, \ H', and \ IV, respectively. By reasoning similar to that used for the single panel, the maximum bending moments are found to be: at the base and top of columns / and 3, \ Wx% II - at the base and top of column 2, and in the girders to the right of a and 61 and to the left of b and c, / In analyzing this case, the frame niay be considered as made up of two separate panels, each of which carries one-half the load W. Fig. 182. Moment Diagram for Frame of Two Rectangular Panels Then the bending moment at all maximum points is ^IV II. But column 2 is common to both, hence its total stresses are the algebraic sums .of the stresses from the two panels. As the bending stresses are of the same sign, the bending stresses in column 2 are twice those in columns 1 and 3; on the other hand the axial stresses in column 2 are opposite in sign and tend to neutralize each other. The resultant is zero if L, equals L r The moment diagram of this case is given in Fig. 182. Horizontal Row of Panels. The foregoing method now can be applied to a frame of any number of panels The total horizontal load or shear is divided by the number of panels. Give one portion 250 STEEL CONSTRUCTION to each of the intermediate columns and one-half portion to each of the outside columns. Thus in Fig. 183 there are five panels. Fig. 183. Diagram Showing Division of Shear in a Frame of Five Panels The shear is distributed thus: IF at columns / and 6, and < W at columns #j#>-4> and tl. The bending moments in columns 1 and are: WH' t in columns 2^3, 4, and 5, IF//; and in all girders,- W 11. Fig. 1S4. Stresses in a Two-Story Rectangular Framework PROBLEM Assume a frame of 7 panels, supporting a wind load of 115,000 pounds. Let H equal 14 feet. Compute the maximum bending moments and draw the moment diagram. Two^Story Framework. Next assume the case illustrated in Fig. 184. This shows the framework of a two-story building. The points of contraflexure occur at the points indicated by the black dots. The loads applied are W B at the roof and IF 2 at the second STEEL CONSTRUCTION 251 floor. The first-story frame serves as a foundation for the second- story frame. The horizontal shears which are transmitted through the points of contraflexure in the second-story columns are - W R and - W R as indicated; those transmitted through the points of o contraflexure in the first-story columns are - (W R +WJ and - ^6 3 (W R +IV 2 ) as shown. The vertical shears transmitted through points of contraflexure in the roof girders are F = -, and 6 L those transmitted through the second-floor girders are v _1 W R H 2 +(W R +W 2 )H t K ~ ~~~ (assuming panels of equal length). Then the bending moments are . at a in roof girders ~~TzW R H- 12 at b in 2nd floor girder - [W R H 2 +(W R +WJ HJ at c in columns + W R H t 12 at d in columns +W R H 2 \ at e in columns H - (Wn+W.) H. 12 at/ in columns + (W R +WJ H l An important relation to be noted is that at any joint the sum of the moments in the members equals zero, or the sum of the moments in the column equals the sum of the moment in the girders. Thus at column 1, 2nd floor t l - R at column 2, 2nd floor 1 (W R +WJ J7.-2X ^5 [W B H,+(W S +W,) H,] O 1Z 252 STEEL CONSTRUCTION Extension of System in Either Direction. The method can now be applied to a frame of any extent, vertically and horizontally. Fig. 185 shows such a frame six panels in width and six stories and basement in height. The loads applied at the several floor levels are represented by W v W 2 .... WR. The total shears in the several stories are represented by WJ, WJ, W 2 ' W 6 '. Fig. 185. Diagram of Wind Stresses in a Building Frame The total shear in any story is the sum of all the loads applied at the floors above, thus, The total shear in any story is divided between the columns in that story in accordance with the rule given. This is illustrated in the figure by the values given in the first story. STEEL CONSTRUCTION 253 The bending moments are illustrated at the third floor in the figure and the moments diagrams at the fifth floor. The procedure can now be reduced to simple rules and formulas. The bending moment in an intermediate column .in any story equals the total shear in that story multiplied by the story height, and the product divided by two times the number of panels. This is expressed by the formula * The bending moment in an outside column is one-half that in an intermediate column, or, ^f The bending moment in a girder is the mean between the bending moments in the column above and below the girder. It is expressed by the formula NOTE, a and b refer to two adjacent stories, as the third and fourth. The panel length does not affect the value of the bending moment. Illustrative Example. Compute the bending moments at the first floor in the frame in Fig. 185. Assume that the loads applied above the first story sum a total of 66,000 pounds equal WJ, those above the basement story a total of 75,000 pounds equal WB'> Let H B equal 10 feet, and H l equal 16 feet. Then the bending moment is: in an intermediate basement column 75,000X10 2X6 in the intermediate first-story columns 66,000X16 62,500 ft.-lb. 2X6 in the first-floor girders 88,000 ft-lb. Axial Stresses. The axial stresses may be disregarded in most cases. They are usually small in proportion to the sections otherwise required for the members. The girders may be considered as being 254 STEEL CONSTRUCTION relieved from this stress by the floor construction. If there be no floor construction along the girders, the axial stress should be considered. In the intermediate columns the axial stress is zero if the panel -L- Fig. 1S6. Diagram of Overturning Stresses in a Building Frame lengths are equal. In the outside columns the axial stress occurs, but here the bending moment is only one-half that in the intermedi- ate columns, so the axial stress is usually not important; however, in tall, narrow buildings it may be important and should be com- puted. When required, it can be computed thus: In Fig. 186 the arrows represent the wind pressure on the framework shown. The STEEL CONSTRUCTION 255 resultant .of this pressure is W, acting at mid-height of the exposed part of the structure. The axial stress V in the basement section of the end column is found by taking moments about the point B. The stress in the first-story section is found by taking moments about the point 1. PROBLEMS 1. Assign values to the structure illustrated in Fig. 186 and compute the axial stress in the second-story sections of the end columns. 2. In Fig. 185 assume the following values: H B = lO'-O" Hi =16'-6* // 2 ,// 3 ---ffo=12'-6* W, = 8,000# W 2 =14,500# W R = 10,000# (a) Compute W B ', W,' t ----- W u '. (b) Compute the maximum bending moment for an interior column above and below each floor line. (c) Compute the maximum bending moment in the girders at each floor. (d) What is the bending moment in the second-floor girder at a point l'-9" to the right of column 4? (e) Construct the moment diagram for column 7 from basement floor 10 roof. DESIGN OF WIND-BRACING GIRDERS In the preceding pages the method has been developed for determining the bending moments in wind-bracing girders and columns. It has been shown that the maximum bending moment occurs at the intersection of the column and the girder, and zero moment occurs at the center of the girder. Between these points the moment varies uniformly, as shown by the moment diagrams in Figs. 180, 182, and 185. By laying out the moment diagram to scale, the bending moment at any point may be measured. End Connections for Riveted Girders. Heretofore in designing beams, end connections have been required to resist only vertical shear, but in the case of wind-bracing girders it is evident that the connection of the girders to the column is chiefly to resist the bending moment. This connection requires careful designing to insure effective results. To illustrate the design, assume an example as follows: In Fig. 187 the distance center to center of columns is 20 feet; the max- cp (ASSUM \LINES IN GUSSET PLT. O (p Fig. 187. Design of a Wind Bracing Girder STEEL CONSTRUCTION 257 imum bending moment is 400,000 foot-pounds or 4,800,000 inch- pounds; the depth of girder is 3 feet \ inch back to back of angles. As stated on page 51, the unit stresses to be used are fifty per cent in excess of those allowed for gravity loads. The girder connects to the web of the column. As the end of the girder thus lacks only about an inch of reaching to the column center, the maximum bending moment must be provided for, viz, 4,800,000 inch-pounds. Rivets Connecting Girder to Column. The rivets through the end angles and column webs are field driven, | inch diameter, and on the tension side of the girder (above the neutral axis in this case) are in tension, As in a beam, the unit fiber stress varies from zero at the neutral axis to a maximum at the extreme fiber; so the unit stress' in these rivets varies from zero at the neutral axis to the max- imum allowable amount at the farthest rivet. Then, if the rivets are equally spaced, the average stress is one-half the maximum. The total resistance of the rivets is the average value of one rivet multiplied by the number of rivets in the tension (or compression) group represented by t (and c); the centers of gravity of the groups are at the points t and c. The moment arm is the distance a between t and c, and the resisting moment is aXt (or c).* The number of rivets required is determined by trial. The full value of a J-inch rivet, field driven, in tension is one and one- half times 6000 pounds or 9000 pounds. Several trials lead to the use of 28 rivets on each side of the neutral axis. The value of t is 9000 X 28 - or 126,000 pounds. The moment arm a is 42 inches and 2i the resisting moment of the joint is 126,000X42 or 5,292,000 inch- pounds, which is about ten per cent in excess of the bending moment. PROBLEM Design the above joint, using f-inch rivets spaced 2| inches. Rivets Connecting End Angles to Gusset Plate. Now consider the rivets connecting the end angles to the gusset plate. The method is the same as that for the connections of the end angles to the column, except that the rivets are shop driven in double shear. This is not exact, for the rivets on the compression side do not act, the compression being resisted by the direct bearing of the end of the girder against the column. The error is on tho safe aide 258 STEEL CONSTRUCTION The required results can easily be obtained by comparison with field-driven rivets. With one row of rivets there will be one-half as many (less one). One shop rivet in double shear is good for 21,600 pounds. This is greater than the value of two rivets in ten- sion (18,000 pounds), hence the proposed arrangement is satis- factory. It gives greater strength than is required. The thickness of gusset plate required to develop the full shearing value of the rivets is H inch. The thickness required for the actual stress is ft inch, which use. (See rivet tables in handbook.) PROBLEM What thickness of gusset plate is required for f-inch shop rivrts? Bending Stresses in Connecting Angles. No accurate determi- nation can be made of bending stresses in connecting angles, so thickness must, be adopted arbitrarily. If the gage line of the rivets is not more than 2J inches from the back of the angle, the thickness should be f inch. In many cases wide angles with large gage distance must be used in order to match the gage lines in the . column. A thickness of 1 inch seems to be safe for a gage distance of 4 inches. Intermediate values may be interpolated. Gusset Plate. The slope of the gusset plate should be about 45 degrees, but may vary to suit conditions, such as clearance from windows, etc. Stresses in the gusset plate may be imagined to act along the dotted lines shown in the figure. On the tension side of the girder the plate is in tension, and on the compression side in compression. The thickness of plate required for rivet bearing is sufficient to give the necessary strength on the tension side, but on the compression side stiffener angles may be required. These angles can be designed according to rules similar to those given for the stiffeners of plate girder webs, p. 148. They should be used when the length of the diagonal edge of the plate is more than thirty times the thickness. The leg of the angle against the plate should be of suitable width for one row of rivets, say 3 inches, 3| inches, or 4 inches. The outstanding leg may vary from 3 to 6 inches. A thickness of -J- inch is suitable usually; it may be made more or less to be consistent with size and thickness of the main members of girder. For the case illustrated use 2Ls SV'XS^'X ". Girder Section. The critical section of the main girder is at the end of the gusset plate (because there arc no gravity loads). The STEEL CONSTRUCTION 259 WEB PL A TE Of CMD ANGLES OF Gl plate being 2'-(i" wide, the bending moment at this point, as s ; ? ff rackets about 4'- O C.-C. 97-6 3*- FLOOR FRAMING PLAN. Plate E. Third Floor Framing Plan and Spandrel Sections, Fort Dearborn Hotel Courtesy, Holabird & Roche, Architects Tops of interior beams are 5$ belout finished floor-id Ft. " i 5." tG/tf. <>! Floors. 6th. Ft. Spat* ' " 4 " 3 ~ fo ps^^S j rrn^,! . j ''i*} 'Z^jfrtf !*"'* V*"/-J6*. ^_2__ S fzT / i '; - 9K ' ' '] !j ;N : ^ *> 1 (79) 3 . /*> -46* n i '/X 3 ; i r\ ' i ^ (2L _ ||i -" ^ s i ''1 /^.r- ? @/~ s '* 5 ^ i b . 1 '! '! *- ']^ ? A <-/;// A'S w, ^ 's ?'"'' % ^ Lyv* "^ / ' fi 1 1 i V ^ i S ;< t ,-^ 1 i < ^ ill H> MI [_*>'*' J L ^-^" . [ 97 :*"'.> 1 x-^ j , /J'/- J< * i il'l-S7I* TYPICAL FLOOR FRAMING PLAN-. f /A! - /* ry. _ /w/?i \lSlVK~ATH.FLndtt SIMILAR. /7 Plate. F. Typical Floor Framing Plan, Fifth to Sixteenth Floors Inclusive. Fort Dearborn Hotel Courtesy, Holabird & Roche, Architects r f ///- J J//VMF LAC> JECT/OH OF 9TH FLOOR 6 BAM OF BRACING /kT/POJJ SOUTH FfiD. M/SCCL L ANZOUS DETAILS. Plate I. Miscellaneous Details, Fort Dearborn Hotel Courtesy, Holabird a-. c PLASTER /?" 4 /t Fig. 200. Section of Reinforced Concrete and Tile Floor Tile Arch Floor. Considering first the flat tile arch, the loads per square foot of floor on joists are Tile arch set in place 14 in. deep 43 Ib. Concrete 3J in. deep 42 Ib. Steel joists 6 Ib. Plaster 5 Ib. Partitions 35 Ib. Total dead load Live load Total load on joists 131 Ib. _501b. 181 Ib. 302 STEEL CONSTRUCTION ^ /9-f. " AT--* " &' g 1 - ( ^ur). z-a\ 4S' 6 -9" 6- 6 >-jj_ 6-HS g 1 1 j i s ju *N i J a t t 7 1 ^_ - 1 - r r-ts"*4 a 'e . ..7-3" & r J ( J ., ff-Q" &* j-*" ^s'-e'i 1 .! ? S t | t l-l"x3i.5" t i t ? S _l u . !*:*, m 1 * /- /S'4 >' b i V "i 1 I-Kf'R t s M ie"* l-9"*ei Fig. 201. Diagram Showing Framing for Tile Arch Floor STEEL CONSTRUCTION 303 The loads per square foot of floor, as applied to the girder are Total dead load of floor as above 131 Ib. Steel girder 4 Ib. Fireproofing on girder 2 Ib. Total dead load 137 Ib. Live load 85% of 50 Ib. 43 Ib. Total load on girders 180 Ib. Therefore, 180 pounds per square feet may be used for both joists and girders. The allowance for partitions is determined by computing the total quantity and weight on one floor and dividing by the number of square feet of floor area. The depth of the joists is assumed for trial to be 12 inches. The joists may be spaced as far apart as 8 feet, but a closer spacing is preferred. They may be arranged in the three ways shown in Fig. 201. The beams 15-22 and 17-24 support the wall load as well as the floor load. The amount of the wall load is calculated as follows: Gross wall area 1 1'-O" X 19'-4" 212 sq. ft. Less windows 2X6'-4"X4'-0" 51 sq. ft. Net wall area 161 sq. ft. Weight of material composing wall is 4 -inch pressed brick weighing 140 Ib., per cu. ft. 47 Ib. 4-inch common brick weighing 120 Ib., per cu. ft. 40 Ib. 4J-inch hollow brick weighing 90 Ib., per cu. ft. 34 Ib. Total weight per sq. ft. of wall area 121 Ib. Using even figures, the weight of wall on the spandrel beam is 160 X 120 = 19,200 # Scheme a. In scheme a, Fig. 201, the sizes of beams required to support the loads computed above are as marked on the diagram. The lengths used in computing are the actual lengths of the beams, that is, allowance is made for the width of column. Thus the joist between columns 16 and 23 is taken at 18'-2" long, and because it is shorter than the other joists it is made lighter. Scheme b. Scheme 6, Fig. 201, is similar to scheme a, the only difference being in the spacing and, consequently, in the weight of the joists. It has the advantage of using joists all alike and equally 304 STEEL CONSTRUCTION spaced. It has -the disadvantages of greater weight (slight), greater number of pieces to be handled, and of not providing a direct brace between columns 16-23, Scheme c. In scheme c, Fig. 201, the direction of the joists differs from that in the other schemes. It has the disadvantages of a greater variety of sizes of joists and of throwing a heavy load on the spandrel girders which have eccentric connections to the columns. Its advantage (which is not apparent from the sketches but is shown on the architectural plans of the building) is that the girders do not cross the corridor which extends along the middle of the building alongside of columns 16-23. The weights of the steel in the three schemes differ so little that this feature would not govern. Scheme a seems to be the best one because it has the least number of pieces to handle, braces all col- umns in both directions, and loads the columns with the least eccen- tricity. PROBLEMS 1. Estimate the weights of steel in the panels shown in Fig. 201 for schemes a, 6, and c. 2. Check the sizes of I-beams used in schemes a, b, and c. Combination Tile and Concrete Floor. Now consider the type of floor construction shown in Fig. 200, that is, the combina- tion tile and concrete. There being no steel joists, the weight per square foot as applied to the girders is estimated as follows: Concrete slab 3J in. 42 Ib. Concrete joists 4" X 10", 40 # X f 30 Ib. TilelO"Xl2";32#Xi 24 Ib. Plaster 5 Ib. Reinforcing steel 3 Ib. Girder steel 4 Ib. Girder fireproofing 10 Ib. Partitions 35 Ib. Total dead load 153 Ib. Live load, 85% of 50 Ib. _43 Ib. Total load 196 Ib. On the narrow panels the tile fillers are 8 inches deep, the resulting saving in weight of tile and concrete and concrete joists being 9 pounds. This leaves a total weight of 187 pounds per square foot on these narrow panels. STEEL CONSTRUCTION 30r> Two schemes For the arrangement of girders are shown in Fig. 202. In both cases the spandrel beams have the same wall load as computed in connection with the tile arch type of floor, viz, 19,200 pounds. The sizes of beams required are marked on the diagrams. Note that in scheme a the lighter load applies in the narrow panel, whereas in scheme b the heavier load must be used in both panels. fr r Fig. 202. Diagram Showing Framing for Combination Tile and Concrete Floor The members marked S are struts which support only narrow strips of floor load but are required to brace the columns in the direction in which girders do not occur. For this purpose light I-beams or H-sections are commonly used, but in this case reinforced concrete is used. Neither scheme has any definite advantage in weight of steel. Scheme a is adopted because the arrangement is better suited to the plan of the floor. The girder 16-23 is alongside the corridor and is covered by the partition. No girder crosses the corridor. The use of the larger spandrel beams assists in bracing the building. A 306 STEEL CONSTRUCTION definite disadvantage is that the spandrel beams, carrying large loads, have eccentric connections to the columns. PROBLEM Check the sizes of beams given in Fig. 202. Selection of Floor Type. The selection of the type of floor con- struction is affected by a number of items in addition to the cost of the steel, which cannot be considered in detail here. Some of them are: the effect of difference in weight on the cost of the columns; the effect of the difference in weight on the cost of foundations; the relative cost of the floors; the thickness of the floor construction; and soundproofness. In this particular case the cost of the steel is the most important item. The combination type is used for this building on account of its economy, all conditions being considered, Plates J and K. FRAMING SPECIFICATIONS Arrangement of Girders. Some attention has already been given to the arrangement of the girders in the discussion of typical floor panels, but this arrangement really needs to be con- sidered in its relation to the entire building. Refer to the archi- tectural and the framing plans of the typical floors, Plates R and G. Exterior. It is necessary of course to have girders around the entire perimeter of the building to support the walls. Interior. The next thing to settle is whether the interior girders shall be parallel to or perpendicular to the outside lines of the building The former arrangement is used. It is to be noted that the girders and their covering project several inches below the ceiling line, hence it is important to place them so that they interfere as little as practicable with the interior arrangement. In the plan adopted the principal lines of girders are along the side of the corri- dors and thus can be partially or wholly concealed. They cross the corridors only at two places. The arrangement used gives practically a set of duplicate floor panels along the outside walls of the building and another along the court walls. The other plan would be nearly as good in this respect. However, columns 2 and 6 are not opposite the columns in the next row so that if girders perpendicular to the outside lines were used, they would be connected at one end to the columns mentioned but STEEL CONSTRUCTION 307 would require cross girders to support the other ends. Having main lines of girders east and west, and also north and south, is advanta- geous in bracing the building. Special Cases. On the first floor, Plate C, girders are required between columns 17-19 on account of the length of span. Along the east and south sides no wall girders are required because the basement walls can be used to support the first-story walls, hence along these two sides the girders are placed perpendicular to the side lines. Other interior girders are placed so as to give the greatest possible uniformity in the floor construction. Around openings, such framing is used as may be needed. No instruction is necessary for this, as the framing required can easily be determined from the conditions in each case. Each building has its special conditions affecting the placing of the girders. Flat ceilings, permitting no projecting beams, may compel the placing of girders on the short spans and perhaps the use of double girders. The use of reinforced concrete floors with rods in two directions requires girders on all four sides of the panels. Pipe shafts in line with the columns in one direction may require the placing of the girders in the other direction.' Columns in rows in one direction, only, limit the girders to those lines. Arrangement of Joists. Having established girder lines, the joists, if used, are spaced as uniformly as practicable. A joist should connect to each column in order to brace it, and the intervening panels should be divided into a number of equal spaces. Their spacing is governed in most cases by the type of floor construction; for the style of construction adopted no steel joists are required. Beam Elevations. The elevations of beams are given in refer- ence to the elevations of the floors. The distance from the floor lines to the top of the beams is governed by the floor construction. The items entering into this dimension are: the thickness of flooring, whether of wood, marble, tutti colori, etc.; the mortar bed for setting marble and similar floors; the thickness of the wood nailing strips for wood floors; the space for electrical and other conduits. The minimum thickness of concrete floors over beams should be 3 inches to allow space for conduits and to prevent cracks. Other floors require from 3 to 6 inches, depending upon conditions. In flat tile arch construction the total thickness is fixed by the 308 STEEL CONSTRUCTION depth of the typical joist. All beams deeper than this will be placed flush on top, and all beams shallower flush on the bottom. Thus, if the typical joist is 12 inches, the girder, which probably is deeper, will be placed flush with the top of the joist and will project below the ceiling line; other joists and framing around openings which may be 8-, 9-, or 10-inch beams will be placed flush with bottom to provide bearing for the skew back of the arch at the proper level. For combination tile and concrete, and for concrete floors, all the beams will be placed flush on top except such as may require a different elevation to suit some special condition. Spandrel beams, being embedded in the walls, are not governed by the elevation of the floor. In many cases these beams serve as the lintels over the windows and their elevations are fixed accord- ingly. This is shown in the spandrel sections, Plates L and T. For flat roofs, the beams may be set on slopes parallel to the roof surface, or may be set level, depending on whether the roof or the ceiling has the greater control. Arrangement of Columns. Location. It is desirable that the columns be arranged in rows across the building in both direc- tions, but this may be prevented by the arrangement of the rooms in the building. The column spacing is also affected by the design of the exterior; the layout determined by the architectural require- ments governs in most cases. Thus in the problem the position of column 18 is fixed by the light court wall; of columns 19 and 26 by the space required for elevators and stairs, Plate R; of column 33 in the lower part of the building, to suit the arrangement of rooms in the first story, Plate N, it being offset at the fourth floor, Plates Q and R, on account of the light court wall. The spacing of the col- umns along the west facade conforms to the architectural treatment, an odd number of panels being used to allow an entrance at the center. The spacing along the north fagade is governed chiefly by the interior divisions. Distance from Building Line. The distances of the columns from the building lines are governed by the fireproofing, as has been explained. They are l'-10" along the north and west fa9ades, l'-3" along the alley and court, and l'-0" along the south side. This latter value is used because provision is made for a building on the adjoining lot which will supply any additional protection needed. STEEL CONSTRUCTION 309 DESIGN OF STEEL MEMBERS Design of Beams. The spacing of columns, arrangement of girders, and type of construction being settled, the next step is the design of the beams. Joists. There are no joists except in a few cases and these can better be classed as special beams. Joists when used are almost invariably simple beams with uniformly distributed loads. There- fore, having computed the total load per square foot of floor, and having fixed the span and spacing, the total load on the beam is the product of these three quantities, and from it the size of beam is taken from the tables. Or, if the size has been selected, the capac- ity for the given span can be taken from the tables; and from this the floor area which it will support, and then the maximum spacing can be determined. The length of span and of load area used is the distance, center to center, of girders if the joist frames between girders, and the actual length of the joist if it connects to columns. Girders. The typical girders were designed in connection with the preliminary study of the floor construction. The special cases remain to be designed. For example take girders 8-9 and 10-11. Girder 8-9 typical floor, Plate F, span 18'-6". Load area on one side only. Total load u. d. 1 8'-6* X 1 0'-O'Xl 96 # = 36,260 # This requires a 15" I 42 # Girder 10-11 typical floor, span 15'-3". Heavier slab north side, lighter span south side. . /15'-3"X10'-0"X196# = Total load u. d. 47,000 # This requires an 18* I 46 #* On the first floor all the slabs are built with 10-inch tile and provision is made for a marble or a tutti colori floor. The live load allowance is 1QO pounds per square foot. The partition allowance can be reduced to 20 pounds per square foot because of the larger rooms. Therefore, the load per square foot carried by the girder is 'Light weight Carnegie beam. These special beams are not always available, 310 STEEL CONSTRUCTION Marble floor 10 Ib. Mortar 10 Ib. Concrete slab 3" 42 Ib. Concrete joists 4" X 10", 40 # X f 30 Ib. Tile 10" X 12", 32 #X| 24 Ib. Plaster 5 Ib. Reinforcing steel 3 Ib. Girder steel 4 Ib. Girder fireproofing 10 Ib. Partitions 20 Ib. Total dead load 158 Ib. Live load 85% of 100 Ib. j85 Ib. Total load 243 Ib. Applying this to girder 8-9, which has a span 18'-6", gives Total load u. d. 18'-6" X 19'-5" X 243 # = 87,480 # This requires a 24" I 69 J# PROBLEMS 1. Design girder 9-10, typical floor; girder 17-19, first floor; and girder 13-20, first floor, Plates F and C. 2. Compute the total load per square feet of floor in the freight room on the first floor (panel 29-30-81 '-86). Floor, a reinforced concrete slab 8 inches thick. See Plates C and N for construction of floor. No partitions. Live load 150 pounds. Design the bejim across the center of the panel. 3. Compute the load on the roof girders, und design girders 8-9, 9-10, and 10-11. (See Plates G and J.) Spandrel Girders. The spandrel girders in this design carry in most cases one-half panel of floor load and a panel of wall. The spandrel girders of the typical* panels of the typical floors were designed in the study of the floor types. The spandrel girder 1-8, typical floor, carries only the wall load; this is practically uniformly distributed. The -wall in this panel is 17 inches thick; its weight per square foot of surface is computed thus: 4 in. pressed brick, 140 Ib., per cu. ft. 47 Ib. 8i in. common brick, 120 Ib., per cu. ft. 85 Ib. 4J in. hollow brick, 90 Ib., per cu. ft. 34 Ib. 166 Ib. The wall surface is the panel area less the window area, viz, ll'-0"Xl8'-4" 201 sq.ft. Less 2 X 3'-6" X 6'-0" 42 sq. ft. Net area 159 sq. ft. STEEL CONSTRUCTION 311 Therefore the weight on the girder is 166X159 = 26,400# The span is IS'-G*. This requires a 15" I 36 #. More exact compu- tations would take into account the position of the windows, weight of . concrete around beams, and weight of girder, but would not change the result in this case. The effect of the wind stresses on the spandrel girders is con- sidered later in the text. PBOBLEMS 1. Design spandrel girder 1-2, typical floor. 2. Design spandrel girder 10-17, typical floor. 3. Design spandrel girder 18-17, typical floor. Special Beams. Special beams are required around elevators and stairs, and for the support of elevator machinery, chimney, penthouses, and tanks. Panel 80-31-88-37. The panel 1 80-31-38-87 contains several special features, viz, a stairway, an elevator shaft, a chimney and vent space, and a pipe shaft. There is only a small section of floor in the panel, adjacent to column 37 on the typical floor. In the north half of the panel the 8-inch I -beams support only partitions. None of them are fully loaded, but this size is considered the minimum for this situation. The stair load may be taken at 50 pounds per square foot for the dead load and 100 pounds per square foot for the live load. It is supported by the 8-inch I-beam near column 37, and the span- drel beam 81-38. The latter beam cannot be placed at the floor level because the windows just above the stair landing interfere, so it must be placed near the level of the stair landing. Framing around stairwells should be so designed that the weight of the stair can be supported from either the sides or the ends. In some cases the entire stair load is carried by the stringers to the beams at the ends of the well and in other cases hangers and struts transmit the loads to the side beams. Usually this cannot be determined by the structural steel designer unless he designs the stair. PROBLEM Design the cross beam near the middle of panel 30-31-38-37, typical floor. Panel 19-20-27-26. The special framing in the panel 19-20- 27-26, Fig. 197 and Plate F, provides for elevators and stair. It presents no unusual features. 312 STEEL CONSTRUCTION f oTcio oasttc ^ XeS ^ i C/2 - CQ 1 | ; ;| iO 1 | o>o : :cc a> o ' * t^- ^r g 5? iO t^ N wX-" xx (N X^ >> Hill g i co ^O 1 " 1 S iE & 2 TT i CO 1 ^HT^O m T3 ^ef^ 00 " ^ 0) V ?5 S CO to" co 1,035,300 X^XX ^X^t^- >> lilll ^ 8 1 8 -^CO"- 1 KJKS ^ocooot^ 0) s l 5 ^* c^c^ ^ 11111 s R r^ g i Tfl ^OJC^OOt^ 0) c^ CO c So CO g *x* x-^x ^x^ > lilll CO rf rf ^co 1 ^ EJS iO "* 05MOOt^ C4 -H 0) (M CO 00 5 00 f-Ct ^ >> lilii 1 8 g .a TfO^OOt^ y> a> - !* V "I 1 * x^x 2X2! > lilli 1 1 g 8 CO J] t^. t oc^ooi> <0 V (M CO 1 s 00 f>- rHTtKN | Hill I *o 8 8 ^ O50400t^ V V C^ CO 1 i 1 x2x 2X^ > QQ ^cT^foor^ 4) 0) s s" 564,200 1 1 I O S'JS 'H"* , 11 8 1 | 8 '-'CO 1 "' 1 S 1S5 35 OO CO .00 1 C5 s i-H^rtN >> III 1 8 8 8 O3 1 00 00 CO ^ III | I 8 8 XI ^ QOCOC s 1 C5 Tf X w>, III I 8 8 1 -H O I-H . SJEE O ooogic 1 ^) 1 O5 co CC ^^^ (N C^ >> III S 8 8 8 CO ^2 0000>C M *f I> iC t> iX nNI X^ X 2 X S g III s 8 8 1 *^ CD SJS 5 t 00 GO iC 1 C5 s ^^w >> HI I 8 8 | ja 00 00 CO iO s 8 CO cr 3 -^ iX*^ x-^x ^x^ >. & III I 1 | .0 E_jE ot GO 00 O ^ s C5 1 -394 = 4,990,000 in.-lb. 6 .85 The bending moment of the load is M = 1,132,000X44X^ = 4,980,000 in.-lb. Hence the assumed plate has the required resistance to bending. 9TH eeooo 8TH eeooo l_ 7TH eeooo 133/SOO OTH eeooo I45SOOO 1512500 5TH 22OOO isrjooo I63JSOO 4TH. eeooo 1734500 3RP 245OO IOI300O 2IO4OOO 2ND ISOOO 23QJOOO 1ST #500 errjooo 8377300 > I \ or eeooo 60300 X / = IS 00 Fig. 206. Diagram Showing Method of Computing Resisting Moment of Girder Connection of brackets which would project through the fireproofing. The spandrels are not so limited and brackets can be used to increase their resistance. In this manner the resistance to wind stresses can be provided down to and including the fourth floor, Fig. 192. Girder Resistance for Third Floor. At the third floor, the wall construction is such as to make desirable deep spandrel girders STEEL CONSTRUCTION 325 between columns 1-8 and 7-42. These girders with their connec- tions are shown in Plate E. The total amount to be resisted at the third floor is 2X2,104,000 or 4,208,000 foot-pounds. Of this about 1,500,000 foot-pounds are resisted by the interior beams, leaving 2,700,000 foot-pounds to be resisted by the spandrel beams. Con- sider this divided equally between the two sides, there being 10 connections on each side, so that each connection in the spandrels 1-36 and 7-42 must resist 135,000 foot-pounds. This requires brackets of the type shown in Fig. 192 for the I-beams 8-36 and the connec- tions shown for the plate girders, Plate E. The computations of the connection of the plate girders are shown in Fig. 206; a is the rivet spacing; b is a graphical diagram giving the proportions of the full rivet stress for the rivets at various distances from the center, and c is the computations. Thus item 1 is 2 field rivets, j-inch diameter, in single shear, at full unit stress, with a moment arm of 3| feet; item 3 is 2 field rivets, J-inch diam- eter, in single shear, at 0.72 of the full unit stress, with a moment arm of 2J feet. The total resistance is somewhat larger than required. The girder section is excessive, the depth being fixed by the spandrel construction, and plates and angles being the minimum sizes suitable for this situation. Girder Resistance for Second Floor. At the second floor the interior girders are arranged differently, so their resistance must be computed. The methods just given, applied here give 172,000 foot- pounds as the bending moment at each spandrel connection. The connections to the columns are designed in the manner previously illustrated, Plate D. Girder Resistance for First Floor. At the first floor there are no spandrel girders between columns 1-36. The columns in this row are bedded in the basement wall. The wall is assumed to resist one-half of the wind stress at this floor. The other half of the stress is resisted by the interior girders 20-41 and the spandrel girders 7-4#, Plate C. The mistake is sometimes made of neglecting the wind bracing at the first floor. This is the most important place where it should be given attention. It cannot be expected that the pressure will be transmitted to the earth at a higher level than the basement floor. 326 STEEL CONSTRUCTION Proof of Column Sections. It remains to be determined whether the column sections are overstressed by adding the wind stress to the gravity stresses. One case serves to illustrate the method. At the second floor, the bending moments in column 8, corre- sponding to those in the connecting spandrel girders, are 160,000 foot-pouniis and 184,000 foot-pounds above and below the floor, respectively. Consider the first-story column. This bending mo- ment is based on a moment arm of 1\ feet. The critical section is at the base of the bracket which is 3 feet below the center of the 41 girder. At this point the bending moment is 184,000 X^or 108,000 foot-pounds, or 1,296,000 inch-pounds. The column section in the first story is 1 web plate 12"X ?" 4Ls 6"X4 "Xf 6 cover plates 14" X |" The bending is about the axis which is parallel to the web, so the values of c and r must be taken in reference to this axis, c is 7 inches, one-half of the width of cover plate, and r taken from the tables for this column is 3.5. Then the concentric equivalent load is The gravity load on this column is 1,088,000 pounds, making the total for which it must be designed 1,828,000 pounds. The length may be taken at 11 feet on account of the depth of bracket. According to the column formula, this section is good for 1,196,000 pounds. For the combined stress this is increased 50 per cent and equals 1,794,000 pounds. As this is within 2 per cent of the required capacity, it is accepted. The designer is warranted in making liberal assumptions as to the lengths of columns and the allowance of excess stress when they are built into substantial masonry walls. This case illustrates the desirability of carrying as much of the wind load as practicable on the interior columns and girders, other- wise the exterior columns may need to be increased above the re- quirements of the gravity loads in order to take the heavy wind stresses. STEEL CONSTRUCTION 327 In cases like that above, it may be best to turn the columns in the other direction. It is simply a question whether the effect of the wind stress is more important than the effect of the eccentric gravity loads. Other Wind Stresses. Now, consider the wind from the East or from the West. It happens that the south wall of the building is solid, so that- diagonal bracing can be used, as shown in Plate I, and such bracing is designed to take one-half of the wind stress in this direction. At the ninth floor a strut extends across the court so that the two sets of bracing co-operate below that level. The other half of the wind stress is carried by the interior east and west girders and the spandrel girders 1-7. The problems involved do not differ from those that have been described. MISCELLANEOUS FEATURES Chimney and Its Supports. The chimney, Plates H and I, is located near column 31. It extends from the sub-basement floor to the top of the penthouse. It is made of steel plates. The thick- ness of plates is arbitrary, the chief consideration being durability. The chimney is lined inside with an insulating material which is supported by shelf angles spaced 3 feet apart. The chimney is designed to be built in sections corresponding to the two-story column lengths. The sections are joined together by means of flange angles and bolts. The entire weight of the chimney must be carried from one support, as its length varies with changes in temperature. So far as the finished structure is concerned, it could rest on the sub-base- ment floor, but for convenience in erection it is supported at the first floor. Thus it can be erected along with the structural steel, the basement and sub-basement sections being placed at any con- venient time afterward. Usually the sub-basement work is not done until after the steel framework is erected and it would then be difficult to get the chimney into place. The details of the breeching connection are given to control both the structural steel fabricator and the builder of the breeching. Masonry Supports. Along the two facades at the first floor are some granite bases which require supports. These supports, detailed in Plate C, are made independent of the sidewalk construe- 328 STEEL CONSTRUCTION tion so that the granite can be set in advance of building -the side- walk and also so it will not be affected by any possible settlement of the sidewalk. At all floor levels or other convenient points, provision must be made for supporting the masonry across the face of the columns. This can be done on this building in most cases by extending a part of the spandrel sections across the column. But in many buildings special shelves must be built. Lintels. Most of the spandrel girders are so located that they serve as lintels over the windows. Plates are riveted on the bottom flange over these openings to support the outer course of bricks or the terra cotta lintel. The edge of the plate is placed 2 inches back from the outer face of the brickwork. Some designers prefer to extend these plates the entire length of the girder to support the face brick, Plates L and T. When the windows are not high enough for the above lintel detail, detached angle lintels are used. Spandrel Sections. On burldings having elaborate facades, many special details must be designed for supporting the masonry* The spandrel sections on this building, Plates L and T, are com- paratively simple. At the second floor a projecting plate is .used along the bottom flange of the girder. At the third floor a similar plate is used and, at the top of the girder, brackets project out for supporting a belt course of terra cotta. Ornamental metal balconies at the seventh, ninth, eleventh, and thirteenth floors are supported by light angle brackets riveted to the girders. A terra cotta balcony at the fifteenth floor requires the special framing shown for it. In general, wherever terra cotta is used, anchor holes are re- quired in the structural steel. It is the duty of the designer to secure the necessary data and put it on the drawings. These holes usually are spaced about six inches apart horizontally. Only the vertical dimensions need be supplied. The cornice support is quite similar to that of the terra cotta course at the third floor. For wide cornices, brackets project from the columns, and these brackets carry beams for the support of the terra cotta. Every case requires its special design. STEEL CONSTRUCTION 329 Flag Pole Support. Near column 7 on the roof plan, Plate G, is shown a pair of channels for supporting a flag pole. A similar pair of channels occurs at the attic floor. On some buildings the flag pole can be connected directly to a column. This is the simplest and most desirable scheme. In some cases it may be set in sockets on the roof and braced with angle or other struts. No data are known to the writer regarding the load on a flag pole. A load of 20 pounds per square foot applied to the area of the flag seems sufficient to cover the actual wind pressure and vibration. Mullions. Where the space between windows is not enough to permit a substantial masonry pier, the mullion should be reinforced. I-beams, tees, or angles may be used, depending on the conditions. In this case two rods are built into the brickwork, Plate L. Anchors. The anchor rods shown extending through the span- drel girders and into the concrete slab hold the spandrel girders laterally and make a rigid connection between the framework and the floor construction, Plate L. DIMENSIONING DRAWINGS Base Lines. The base lines for horizontal dimensions are the building lines of the structure. They are shown on the first-floor plan, Plate C. The building lines nominally represent the outside lines of the building walls. In reality they are often imaginary reference lines, for, on account of the offsets, parts of the wall may extend beyond these lines and other parts be inside of them. For the class of buildings under consideration, the building lines usually coincide with the lot lines. If they do not, then the lot lines should be shown and dimensioned from the building lines. If the corners of the building are not exactly right angles, the angles must be marked on the first-floor plan. The cardinal points of the compass should be marked with approximate accuracy on the first-floor plan. One of these points is used as a reference in marking one side of columns and one end of girders for convenience in erecting; thus E on the east face of a column, or N on the north end of a girder. Column Centers. Having established the building lines, the next step is to dimension the column centers. The simplest situa- tion is had when the building is rectangular and the columns are in rows in both directions. Then two lines of dimensions will suffice 330 STEEL CONSTRUCTION to fix the location of all columns, Plate D. Any irregularity of spacing in any row requires a special line of dimensions in that row. Fig. 207. Diagram Showing Method of Dimensioning Column Centers in an Irregular Building With anr irregularly shaped building, the dimensioning becomes more complicated. One building line should be adopted as a refer- ence line, taking the one to which the greatest number of column lines are perpendicular and parallel. Then all columns should be located by dimension lines perpendicular and parallel to this refer- ence line, that is, by rectangular co-ordinates. The only diagonal dimensions needed are those along which, or parallel to which, steel members are placed. In Fig. 207, the reference line used is the south building line. The building lines in this case are probably lot lines. Their lengths and the angles are de- termined by a survey. The distance from the lot lines to the column centers is established at I'-IO* on all sides. The spacing of columns 1 to 7 and the ar- Fig. 208. Construction Diagram for J Details of Figure 207 rangement of the other columns are fixed by architectural conditions. From the foregoing data all the required dimensions can be computed by trigonometry. First, compute the distances from STEEL CONSTRUCTION 331 column 7 to the corner of the building. From Fig. 208 Jt is apparent that these distances a b and a'b are equal to each other and equal to caXcot 41 15'; then a& = a'& = 22"Xl.l40 = 25 T V The distance between columns 9 and 15 is 20'-0"Xtan 19 20" = 20'-0"X.3508 = 7'-Oft" In this manner all the dimensions can be computed. PROBLEM Compute the distances between columns which are lacking in Fig. 207. The column center dimensions should be repeated on all the floor plans. If the floor framing plan is crowded, a separate diagram at small scale may be placed on the drawing to display the column center distarces. Girders and Joists. Girders and joists are dimensioned from the column centers. The dimension lines required are illustrated in Figs. 201 and 202. Note in Fig. 201-b that there is no joist at column 23, so the space is divided and the adjacent joists tied in the column. No dimensions are required for the lengths of joists and girders other than those locating the centers of the columns and beams to which they connect. The shop detailer computes the actual lengths of beams required. But if one end of a beam rests on a wall, one face of the wall and its thickness must be given. Such details as struts, mullions, plates for supporting brick- work, etc., are also located from column centers, as illustrated on the floor plans. Vertical Dimensions. The vertical dimensions from floor to floor are given in a separate diagram or in connection with the column schedule, Plate H. At the first floor a reference is made to established sidewalk grade in terms of its elevation above datum, Plate C. The elevations of beams are given in reference to the fin- ished floor elevations, respectively. Usually the elevation of joists and girders can be covered by a note, Plate F. Special cases can be given by figures alongside the beams indicating the distance from the floor level to the top flange of the beam ; thus 5J" means that the top flange is 5| inches below the floor line. Elevations of Spandrel Beams. The elevations of spandrel beams can be shown best on the sections, where both the elevation 332 STEEL CONSTRUCTION and the horizontal position can be given in relation to the other materials of construction thereabout, Plate L. Summary. The use of unnecessary dimensions and needless repetitions may be a source of much inconvenience. It increases the probability of errors and causes extra work in checking. While structural steel drawings should be made reasonably accurate to scale, scaled dimensions must not be used in executing the work. The scales used in making drawings of structural steel should be as follows: for framing plans, J inch or \ inch; for spandrel sec- tions, % inch or f inch; and for details showing all dimensions and rivet spacing, 1 inch or 1 J inches. In each case the scale first given is preferred. The use of a number of different scales in the same set of drawings is objectionable. UNIVERSITY CLUB AND MONROE BUILDING, CHICAGO Holabird & Roche, Architects CONSTRUCTION PART V PROTECTION OF STEEL PROTECTION FROM RUST Rust. Although steel is the strongest of building materials, under unfavorable conditions it may be one of th east durable. Its great enemy is rust. The corrosion or rusting of iron and steel is familiar to every one. It is a chemical change in which the metallic iron unites with oxygen and forms oxide of iron or rust. RUST FORMATION Theory. While rust is largely or wholly oxide of iron, it is not produced directly by the contact of the iron with the oxygen of the air. The presence of moisture seems essential to its formation. Much study has been given to the process of rust formation, but the reactions have not yet been determined positively. It is quite generally believed that electrolytic action occurs. This theory is well described by Houston Lowe in "Paints for Steel Structures" as follows:* "The electrolytic theory, which no doubt has the strongest support, is based upon the recognized tendency of metals to go into solution, even in pure water. The act is accompanied by the release of hydrogen positively charged with electricity, leaving on the metal a corresponding charge of negative elec- tricity. If oxygen is at hand to combine with the hydrogen, the electrical tension is relieved in an infinitely small current and new portions of the metal pass into solution ; otherwise the action is arrested by the non-conducting quality of the thin film of hydrogen. "The presence of minute particles of suitable impurities in or on the iron, whose solution tension differs from the iron, or the presence of acids in the water, facilitates the discharge of the electric tension and, hence, the continuous re- moval of particles of iron On the other hand, the presence of alkalies, and a few other substances that decrease hydrogen ion concentration, will diminish or even stop iron solution and rusting altogether. "This, in brief, is the substance of the electrolytic theory of rusting, the *John WUey & Sons. Publishers. New York. 334 STEEL CONSTRUCTION more complete explanation of which would involve the details and language of the ionic theory of chemical action. Corrosion of iron, in the sense in which that term has been used in this section, has nothing whatever to do with elec- trolysis by stray electrical currents from outside sources. The currents involved in rusting under the theory of electrolytic action are almost infinitely short and minute, a d originate in or on the metal itself. "The theory is valuable to the extent that it suggests reasonable and practical remedy of the defects either of the metal or its proposed covering, or both. As in the treatment of diseased animal and plant tissues, so in this case, intelligent diagnosis must precede the application of prev5ntives of rust. Ex- perimental work following the lines of the electrolytic theory in seeking, first, to prevent, or 'inhibit' corrosion by a priming coat and, secondly, to diminish the penetration of water by suitable overcoats, is promising good results, and a final solution of the problem is confidently looked for. "The tendency of rust to grow and spread out from a center has an adequate explanation in the electrolytic theory. This phenomenon is especially per- nicious, as it results in pitting or, under a paint coat, in a growth which finally flakes off the paint and exposes large areas of the iron." Degrees of Exposure. A piece of steel exposed to the air will ultimately change entirely to oxide of iron (except as to the contents other than pure iron) i. e., it will be entirely destroyed by rusting. The rapidity of the change varies with the conditions of exposure. The rusting will proceed very slowly if the steel is kept in dry air; less slowly if subjected occasionally to moist air; rapidly if exposed to moisture frequently; and very rapidly if exposed to moisture in the presence of sulphur or other acid fumes. The first condition prevails when steel is enclosed in other materials of construction, as columns and beams enclosed by plaster in partitions, and in floor construction, so that the moisture condi- tions change only slightly. The second condition applies when the steel is within the building, but not encased in other materials, thus being exposed to varying degrees of moisture, as unprotected col- umns and beams in storerooms. The third degree of exposure fairly represents unprotected beams in basements, vaults under sidewalks, and steel work out of doors. And the worst possible exposure, that is, to moisture in the presence of acid fumes, is had in smelters, and in structures where the steel is subjected to the smoke from railroad locomotives. Rate of Rusting. Some studies have been made of the rate of corrosion under different conditions. It is very evident that the rate varies greatly with the conditions of exposure. Experiments along this line have not gone far enough to give conclusive results, STEEL CONSTRUCTION 335 i.e., definite figures as to the thickness of metal that will change to rust in a given time. But it is a matter of common knowledge that there is enough rusting even under the most favorable conditions to make it important that steel be protected. Effect of Composition of Metal. The composition of the metal lias some effect on the rate of corrosion. Structural steel probably rusts more rapidly than any other form or alloy of iron. Cast iron rusts slowly, probably due to the presence of graphite, which protects the iron. Wrought iron rusts more rapidly than cast iron and much less rapidly than steel. It is believed that the slag in wrought iron protects the fibers of iron from exposure to the air and moisture. The presence of manganese is supposed to accel- erate corrosion, while copper and other alloys retard it. Efforts have been made to produce rust-resisting metals by two methods; by making iron nearly pure, and by using an alloy of copper. The -resulting metals are not rustproof but show much slower rates of corrosion than ordinary steel. Both have been commercially successful as applied to sheet steel, but are not yet used for structural steel. Pure iron is not suitable for structural purposes because of its lack of strength. It is quite possible that an alloy of copper or other metal will be developed for structural steel that will be nearly rustproof. PAINT Purpose. The usual means employed to prevent corrosion is to exclude all air and moisture from contact with the metal by a covering of paint. It is desirable that the paint material be such as will inhibit the formation of rust, thus counteracting any imper- fections of the paint in excluding moisture. Qualities. ' The following qualities are desirable: (1) Adhesive, so that it will hold fast to the steel. (2) Non-porous, so that it will exclude air and moisture. (3) Elastic, so that it will not crack with changes in tempera- ture, or with the deflection of the steel. (4) Hard at all ordinary temperatures. (5) Non-volatile, so that the oils may not evaporate and leave the inert materials of the paint without a binder. (6) Not soluble in water. (7) Not soluble in oil, so that it will not soften when addi- tional coats are applied. 336 STEEL CONSTRUCTION (8) Inhibit ivc," that is, of such material as will prevent the chem- ical or electrolytic action of rusting. (9) Color may be important. Many of these qualities obviously are much more important on out-of-door work than on ordinary building work. No paint has all of these desirable qualities, but by using different paints for the several coats, the ideal conditions may be approximated. Thus the first coat should be inhibitive and adhesive; and the second (or last coat, if more than two are used) should be non-porous and should provide the required wearing properties. Composition. A paint is made of "a liquid and a solid, called, respectively, the "vehicle" and the "pigment". Vehicle. The best vehicle for paint is linseed oil. It may be had as raw oil or boiled oil. The latter is used when quick drying is desired but the raw oil is believed to give better results under most circumstances, and especially with red lead/ The drying of paint is accelerated by the use of driers in the oil. A drier may be a volatile oil, as turpentine, which effects its purpose by rapidly evaporating after the paint is applied; or it may be a japan, which hastens the hardening of the oil and pigment. Turpentine being cheaper, it is more used than japans. The drier should not exceed 8 per cent of the vehicle. Linseed oil varies greatly in quality even when pure, and is subject to adulterations which are difficult to detect. Some paint makers claim, and probably justly so, that they improve the vehicle by adding other oils to the linseed oil; but in general- any additions other than the drier must be considered adulterations. Pigments. Pigments commonly used for structural steel paints are red lead, iron oxide, graphite, and lampblack. Red lead is the red oxide of lead, Pb 3 4 , but the red lead of commerce contains a certain amount of litharge and metallic lead. These elements cannot be entirely eliminated on a commercial .basis, but it is practicable to obtain a red lead which is 95 per cent pure and it should be so specified. When mixed with linseed oil, red lead hardens, much as cement when mixed with water, and forms a strong tenacious coating. It can be made into a heavy paint, almost a paste, thus giving a heavy coat on the steel, or it can be thinned to give a light coat. On STEEL CONSTRUCTION 337 account of its weight, red lead is difficult to mix with oil. This is especially true when a large proportion of lead is used. The maxi- mum proportion is 33 pounds of red lead to one gallon of raw linseed oil. While this heavy mixture is desirable, it is expensive as to labor and materials. A more practicable proportion is 25 pounds of red lead to one gallon of oil; a still smaller weight of lead is often used and will invariably be used unless the proportions required are definitely specified, for there is no standard practice to govern it. Red lead paint with a small proportion of red lead can be mixed by hand, but if the amount of lead is as much as 25 pounds, the mixing should be done in a churn, or ground into the oil at the paint factory. On account of its weight and its settling qualities, it has not been practicable, heretofore, to keep red lead paint for any length of time, as the lead settles to the bottom and hardens. The hardening quality seems to be due largely to the litharge. Now that the lith- arge can be eliminated from the red lead, it is practicable to keep the ready-mixed paint for a much longer period. It can now be obtained from the paint manufacturers ground into the oil, forming a thick paste, which can be thinned to the proper consistency by the addition of oil when it is to be used. The thinning can be gaged by the weight of the finished paint on the following basis: A w r eight of 24.43 pounds for the finished paint corresponds to 25 pounds of lead to one gallon of oil. A weight of 25.92 pounds corresponds to 28 pounds of lead to one gallon of oil. A weight of 26.76 pounds corresponds to 30 pounds of lead to one gallon of oil. A weight of 27.10 pounds corresponds to 33 pounds of lead to one gallon of oil. (These values are taken from a circular issued by the National Lead Company.). A ready-mixed red lead paint can be made by substituting for a part of the red lead some other pigment of inert material which will retard the settling, and harden. Lampblack, asbestine, and mica are sometimes used for this purpose. Such paints usually contain less than 15 pounds of red lead per gallon of oil, and are much less satisfactory than the red lead paste. Iron oxide, commercially available, varies greatly in weight and physical characteristics. Some is taken direct from mines but most 338 STEEL CONSTRUCTION of it is manufactured. It does not have any cementing properties when mixed with linseed oil so must be held in place by the oil. The paint will last only as long as the oil binder remains intact. The iron oxide does not inhibit corrosion but under some circum- stances accelerates it, -thus leading 'to the formation of patches of rust under the paint. Under favorable conditions it makes a good protective coating. Iron oxide is mixed with boiled linseed oil, using about 8 pounds of the pigment to one gallon of oil. The carbon paints, which include lampblack and graphite, have no cementing properties when mixed with oil. The amount of pigment used is small compared with that used in red lead paint. It, therefore, has much greater spreading power and consequently makes a much thinner film. As it does not inhibit corrosion, its protective power depends, entirely on the oil, making it necessary to use several coats in order to get satisfactory results. It makes a satisfactory second coat over red lead. The carbon pigments, particularly graphite, are subject to many adulterations. There are no standard proportions. Carbon paints can be made at the factory and will keep for an indefinite period. Prepared Paints. Many proprietary paints are offered for structural steel. Some have much merit, others none. They should not be used unless there are authentic records of successful use-. Painting Required. Structural steel in buildings is protected from moisture by being enclosed by other materials. On the other hand, in most cases it cannot be repainted, so the original painting is of great importance. The writer recommends painting it two coats, first red lead, second graphite or lampblack. If the steel is to be encased in concrete, the second coat may be omitted, the con- crete furnishing as much protection as the second coat of paint. Cleaning. The paint can have no mechanical bond to the steel so must depend on adhesion to hold it in place. This makes it necessary that the surfaces be cleaned before painting, removing all rust, dirt, grease, and mill scale. The cleaning is of utmost impor- tance, for if not done thoroughly, the paint will not adhere; and, if rusting has already started, it may continue under the paint. It is not uncommon to find large patches of rust over which the paint remains unbroken. This is apt to occur when the surface is not properly cleaned before repainting. STEEL CONSTRUCTION 339 The most effective way of cleaning steel is by means of the sand blast. This method is expensive and is not much used for steel work for buildings. It is used chiefly for cleaning old steel work, especially bridges, for repainting. The usual means of cleaning is by the use of the scraper, chisel, and wire brush. This work can be well done with tto?se tools, if enough labor is expended on it. Applying the Paint. The paint is best applied with heavy round brushes. It must be spread evenly and cover the entire surface and be worked into all corners and joints. The metal surfaces should be warm and free from moisture. In cold weather the paint should be warmed. Surfaces in Contact. It is customary to specify that surfaces which will be in contact after assembling shall be painted before assembling. The desirability of this has been questioned on the basis that the paint is probably destroyed by the heat from the rivets. Nevertheless, there is no evidence that such painting does any harm and it is best to do it in accordance with usual practice. Box sections, such as channel columns, should have two coats on the inner surfaces before assembling." Cement as a Rust Preventive. Portland cement mortar and concrete are inhibitors of rust and, if dense and in actual contact with the metal, provide the necessary protection against moisture. If applied to clean steel surfaces, no other protection is required. But the steel, if not painted at the shop, usually will become badly rusted before it is enclosed in the building, making it desirable that the shop coat of paint be used. Then the concrete casing will make it unnecessary to apply the second coat of paint. PROTECTION FROM FIRE Effects of Heat on Steel. Expansion. Heat applied to steel causes it to expand. Its coefficient of expansion is 0.0000067 for one degree Fahrenheit, that is, for each increase of one degree in temperature a unit of length increases by the amount of the coeffi- cient. Thus for an increase of 100 degrees in temperature, the increase for each unit of length is 100X0.0000067 = 0.00067; for a length of 18 feet, the total increase in length is 0.00067x18 = 0.01206 feet, or .14472 inches. 340 STEEL CONSTRUCTION There is a corresponding change in the opposite direction, if the temperature decreases. From this it is clear that expansion and contraction due to changes in temperature occur in appreciable amount. The longer the member, or series of members, the greater the change in length. Within buildings, the change in temperature ordinarily is not enough to cause trouble, but if -the steel is exposed to fire, it might expand enough to push a wall out of place even though not heated enough to affect its strength. Cases have occurred where walls have been seriously displaced by ordinary changes of temperature, because the expansion of the steel pushed the wall outward, whereas the succeeding contraction did not pull it back; then the next expansion pushed it farther out, and thus by succes- sive movements the wall was pushed farther and farther out of place. Loss of Strength. Experiments indicate that steel can be heated to a temperature of about 600 degrees Fahrenheit before it begins to lose strength. At Righer temperatures, it loses strength rapidly and will fail of its own weight at a temperature of about 1500 de- grees. Steel melts at 2500 degrees (approx.). Intensity of Heat in a Fire. The intensity of heat developed in a fire varies greatly according to conditions. Many cases are recorded showing steel bent into a tangled mass from the burning of a building, indicating temperatures of 1500 degrees or more. Such temperatures can be produced by burning the wood framework of an ordinary building, or even the contents of a fireproof building. Protective Methods. Unprotected steel yields very quickly in a fire, much more quickly than wood beams of the same strength. It is dangerous and inexcusable to use structural steel in a building without providing for its safety. Steel is protected from fire by encasing it in a fireproof material. Almost any material encasing steel will protect it to some extent. Even a tight casing of wood will protect it for a little while in a fire. Ordinary plaster on wood lath will protect it only until the fire gets through the plaster, after which the burning of the lath aids in the destruction of the steel. Cement plaster on metal lath is efficient only to a limited degree, and while it is an incombustible material, it is not fireproof within the meaning of that term as used in building construction. Misuse of the Term Fireproof. Many buildings are called fire- proof when the protection of the steel is nothing more than described STEEL CONSTRUCTION 341 above. Instances can be cited of hotels advertised as fireproof with steel beams placed among wood joists with no protection whatever. Amount of Protection Depends on Conditions. A building may be made entirely of incombustible material and still not be fireproof, if the steel is not encased to protect it from the contents of the Fig. 209. Brick and Concrete Arch Construction Showing Partial Protection for I-Beams building. Fig. 209 illustrates a form of construction of this sort which was much used a number of years ago. The brick arches and the concrete filling protect the beam except on the bottom flange, which is left exposed to fire from the burning of the contents of the room below. Fig. 210 is a similar form of construction in which a corrugated-steel arch replaces the brick arch. This partial protection is of some value, but it is so easy under present methods .to get complete protection that these forms are no longer used. On the other hand, a building having no combustible material ^<^ ; *.'&t*-:<^*^*%i?s<.^. _xtt2&ff&& f^g&SS^- ==" ^^^^^gjggjglll^S COR RUG A TED IRQH APCH CO/i5TQUCT/OM Tig. 210. Corrugated Iron and Concrete Arch Construction Showing Insufficient Protection for I-Beams in its construction or contents, and having no external hazard, need not have its steel framework fireproofed. A foundry building or a machine shop may be such a case. Standard Specifications. Steel to be really fireproofed must be entirely encased in a fireproof material. The material must be such that it will conduct heat very slowly and that it will maintain its integrity when subjected to a fire of the greatest in tensity and longest duration likely to occur, and when subjected to a stream of water from a fire hose while at its maximum heat. The "Standard Test for Fireproof Floor Construction" adopted by the American Society for Testing Materials* requires: American Society for Testing Materials, Edgar Marburg. Secretary, University of Penn- sylvania, Philadelphia. 342 STEEL CONSTRUCTION "No plastering shall be applied to the underside of the floor construction under test. "The floor shall be subjected for four hours to the continuous heat of a fire of an average temperature of not less than 1700 F. , the fuel used being either wood or gas, so introduced as to cause an even distribution of heat throughout the test structure. "The heat obtained, shall be measured by means of standard pyrometers, under the direction of an experienced person. The type of pyrometer is immater- ial so long as its accuracy is secured by proper standardization. The heat should be measured at not less than two points when the main floor span is not more than 10 feet and one additional point when it exceeds 10 feet. Tempera- ture readings at each point are to be taken every three minutes. The heat determination shall be made at points directly beneath the floor so as to secure a fair average. "At the end of the heat test a stream of water shall be directed against the underside of the floor, discharged through a 1 1-inch nozzle, being held at more than 3 feet from the firing door during the application of the water." 1 Material which will withstand this test is suitable for fireproofing steel in any part of a building. Fireproof Materials. Cinder Concrete. Cinder concrete has been used extensively for fireproofing but it is not altogether satis- factory. It is difficult to get cinders free from unburned coal,, ashes, and refuse. Sulphur in the cinders causes rusting of the steel. Its use is not warranted on first-class work. Portland Cement Concrete. Portland cement concrete, made of crushed stone or gravel, is an excellent fireproofing material. It has the necessary resistance to fire and water, prevents rusting of the steel, and in many situations adds to the strength of the steel member. If its surface is left rough or is roughened after the forms are removed, plaster will stick to it. When subjected to a fire, the concrete is damaged. The depth of the injury may be as much as 1J inches, depending on the quality of the concrete and the kind of stone used in it. The better the concrete, the less it is injured by the heat. Heat calcines limestone and disintegrates granite, so that these stones are not as suitable for fireproofing purposes as hard sandstones, trap, and other stones not so easily affected -by heat. An excellent concrete for fireproofing can be made from crushed tile and brick. On buildings where tile is used for floor arches and partitions, the broken pieces can be crushed and used for fireproofing the columns and any other mem- bers not protected by the tile floor arches. STEEL CONSTRUCTION 343- Concrete which has been. damaged by fire does not lose its property of non-conductivity, consequently it is efficient as fire- proofing so long as it remains in place; although it has lost its strength, it usually will remain in place until removed by some me- chanical means, as the application of a stream of water. After a fire, the damaged concrete must be removed and replaced. Concrete is placed around steel by building forms around the members and pouring concrete into them, Fig. 211. Wire mesh or expanded metal should be attached to the bottom flanges of beams and wrapped around columns to provide a mechanical bond for the concrete so that it will not fall off during or after a fire. Fig .211. I-Beam and Coliifnn Sections Showing Concrete Fireproofing. Hollow Tile. Hollow tile is molded from clay and baked at a high temperature. The clay used must be such that it will not warp, or fuse in the kiln. It is desirable that the tile be porous and tough rather than dense and brittle. The tile is made porous by mixing sawdust with the clay. This burns out during the baking, leaving voids and producing the desired porosity. Dense tile and tile which is glazed is likely to shatter, if exposed to a stream of water when hot, thus making it useless for fire protection; further- more, plaster does not adhere to it as well as to porous tile. The tile is made hollow to save weight, and to provide air spaces which are insulators against both heat and moisture. This material is molded into a great variety of shapes to suit the various requirements of the steel members to be protected. Certain shapes are practically standard; special shapes can be had only when required in large quantity. Figs. 212, 213, 214, and 215 show a number of illustrations of tile fireproofing of joists, girders, spandrels, and columns. The 344 STEEL CONSTRUCTION joists are usually fireproofed by the skewbacks of the floor arches. On other members the tile serves only for fireproofing and for furnish- Fig. 212. Method of Fireproofiing Joists in Connection with Flat Tile Floor Arch ing a surface for plastering. It can be used for fireproofing steel members in almost any situation. Tile is set in mortar in the same manner as bricks are laid. Any space between the tile and the steel should be filled with Port- Fig. 213. Sections Showing Method of Fireproofing Beams land cement mortar. A heavy layer of mortar should be plastered on the webs of beams before setting skewbacks or other tiles against them. Fig. 214. Sections Showing Method of Fireprcofing Spandrels 346 STEEL CONSTRUCTION Fireproofing tile must be designed to be securely supported by the steel. Steel clips or wire must be used in some situations. Thus the column casing should be held in place by copper wire bands unless it is securely held by interlocking of the tile. Soffit tile on joists and girders require metal clips or woven wire fabric to hold them in place even though they appear to have support from shoe tile or other adjacent members. Tile has considerable strength in compression and may be so used, but should not be subjected to other stresses. Brick. Brick masonry is an excellent fireproofing material so far as its resistance to heat is concerned. However, it is not easily Fig. 215. Sections Showing Method of Fireproofing Columns with Tile and Concrete .supported and, therefore, is not generally available for this purpose on beams, but in some cases ^it can be used to good advantage for e.ncasing columns. Selection of Fireproofing. Portland cement concrete and hollow tile are the materials best suited for fireproofing. Both are efficient for this purpose. The choice between them is usually governed by other considerations, chief of which is the type of floor construc- tion, which in turn may be determined by cost or some other con- sideration. If the floor is to be of reinforced concrete, concrete will be used for fireproofing the steel framework. If the floor is to be of tile arch construction, that material will be used for fireproofing; but even in this case concrete can be used advantageously for the columns. Thickness of Fireproofing. The thickness of the covering required to furnish the desired protection varies with the situation and the importance of the member. Columns being vital to the support of the building are given the most protection. Lintels and spandrel girders are subject to severe exposure and are given about STEEL CONSTRUCTION 347 the same protection as columns. Joists and girders are local mem- bers and not so heavily fireproofed. The top flanges of beams and girders do not need as much protection as the bottom flanges. The requirements in Chicago are:* Columns Exterior, (a) All iron or steel used as vertical supporting members of the external construction of any building exceeding fifty feet in height shall be protected against the effects of external change of temperature and of fire by a covering of fireproof material consisting of at least four inches of brick, hollow terra cotta, concrete, burnt clay tiles, or of a combination of any two of these materials, provided that their combined thickness is not less than four inches. The distance of the extreme projection of the metal, where such metal projects beyond the face of the column, shall be not less than two inches from the face of the fireproofing; provided, that the inner side of exterior columns shall be fireproofed as hereafter required for interior columns. (b) Where stone or other incombustible material not of the type defined in this ordinance as fireproof material is used for the exterior facing of a building, the distance between the back of the facing and the extreme projection of the metal of the column proper shall be at least two inches, and the intervening space shall be filled with. one of the fireproof materials. (c) In all cases, the brick, burnt clay, tile, or terra cotta, if used as a fire- proof covering, shall be bedded in cement mortar close up to the iron or steel members, and all joints shall be made full and solid. Columns Interior, (a) Covering of interior columns shall consist of one or more of the fireproof materials herein described. (b) If such covering is of brick it shall be not less than four inches thick; if of concrete, not less than three inches thick; if of burnt clay tile, such covering shall be in two consecutive layers, each not less than two inches thick, each having one air space of not less than one-half inch, and in no such burnt clay tile shall the burnt clay be less than five-eighths of an inch thick; or if of porous clay solid tiles, it shall consist of at least two consecutive layers, each not less than two inches thick; or if constituted of a combination of any two of these materials, one-half of the total thickness required for each of the materials shall be applied, provided that if concrete is used for such layer it shall not be less than two inches thick. (c) In the case of columns having an "H" shaped cross section or ot columns having any other cross section with channels or chases open from base plates to cap plates on one or more sides of the columns, then the thickness of the fireproof covering may be reduced to two and one-half inches, measuring in the direction. in which the flange or flanges project, and provided that the thin edge in the projecting flange or arms of the cross sections does not exceed three-quarters of an inch in thickness The thickness of the fireproof covering on all surfaces measuring more than three-quarters of an inch wide and measur- ing in a direction perpendicular to such surfaces shall be not less than that specified for interior columns in the beginning of this section, and all spaces, including channels or chases between the fireproof covering and the metal of the columns, shall be filled solid with fireproof material. Lattice or other open columns shall be completely filled with approved cement concrete. 'Revised Building Ordinances of the City of Chicago as amended Feb. 20. 1911. 348 STEEL CONSTRUCTION Columns Wiring Clay Tile On. (a) Burnt clay tile -column covering shall be secured by winding wire around the columns -after the tile has all been set around such columns. The wire shall be securely wound around tile in such manner that every tile is crossed at least once by a wire. If iron or steel wire is used it shall be galvanized and no wire used shall be less than -number twelve gage. ******** Pipes Enclosed by Covering, (a) Pipes shall not be enclosed in the fire- proofing of columns or in the fireproofing of other structural members of any fireproof building; provided, however, gas or electric light conduits not exceeding one inch diameter may be inserted in the outer three-fourths inch of .the fire- proofing of such structural member, where such fireproofing is entirely composed of concrete. (b) Pipes or conduits may rest upon the tops of the steel floor beams or girders, provided they are imbedded in cinder concrete to which slaked lime equal to five per cent of the volume of concrete has been added before mixing or their being imbedded in stone concrete. Spandrel Beams, Girders, Lintels. The metal of the exterior side of the spandrel beams or spandrel girders of exterior walls, or lintels of exterior walls, which support a part of exterior walls, shall be covered in the same manner, and with the same material as specified for the exterior columns in this chapter; provided, however, that shelf angles connected to girders by brackets or pro- jections of girder flanges not figured as part of the flange section may come within two inches of the face of the brick or other covering of such spandrel beams, girders, or lintels. The covering thickness shall be measured from the extreme projection of the metal in every case. Beams, Girders and Trusses Coverings of. (a) The metal beams, girders, and trusses of the interior structural parts of a building shall be covered by one of the fireproof materials hereinbefore specified, so applied as to be sup- ported entirely by the beam or girder protected, and shall be held in place by the support of the flan eras of such beams or girders and by the cement mortar used in setting. (b) If the covering is of brick, it shall be not less than four inches thick; if of hollow tiles or if of solid porous tiles or if of terra cotta, such tiles shall be not less than two inches thick, applied to the metal in a bed of cement mortar; hollow. tiles shall be constructed in such a manner that there shall be one air .space of at least three-fourths of an inch by the width of the metal surface to be covered within such clay coverings; the minimum thickness of concrete on the bottom and sides of metal shall be two inches. (c) The top of all beams, girders, and trusses shall be protected with not less than two inches of concrete or one inch of burnt clay bedded solid on the metal in cement mortar. (d) In all cases of beams, girders, or trusses, in roofs or floors, the pro- tection of the bottom flanges of the beams and girders and as much of the web of the same as is not covered by the arches shall be made as hereinbefore specified for the covering of beams and girders. In every case the thickness of the cover- ing shall be measured from the extreme projection of the metal, and the entire space or spaces between the covering and the metal shall be filled solid with one of the fireproof materials, excepting the air spaces in hollow tile. STEEL CONSTRUCTION 349 (e) Provided, however, that all girders or trusses when supporting loads from more than one story shall be fireproofed with two thicknesses of fireproof material or a combination of two fireproof materials as required for exterior columns, and each covering of fireproof material shall be bedded solid in cement mortar. Fireproofing of Exterior Sides of M ullions. In buildings required by this chapter to be of fireproof construction on exposures where metal frames, doors, sash, and wire glass are not required, all vertical door or window mullions over eight inches wide shall be fae*ed with incombustible material, and horizontal transom bars over six inches wide shall be faced with a fireproof or with an incom- bustible material. Iron or Steel Plates for Support of Wall. Where iron orsteel plates or angles are used in each story for the support of the facings of the walls of such story, such plates or angles shall be of sufficient strength to carry the weight within the limits of fiber stress for iron and steel elsewhere specified in this chapter of the enveloping material for such story, and such plates or angles may extend to within two inches of the exterior of such covering. SPECIFICATIONS Purpose. The purpose of specifications is to give a detailed description of such features of the work as can thus be given more clearly or be more easily defined than on drawings. They must co-operate with and supplement the drawings, but should not repeat the data given on the drawings, for every repetition is an added opportunity for conflict or error. In addition to the technical requirements referred to above, the specifications usually include certain items more related to the business transaction between the purchaser and the contractor. The specifications prepared by the designer are to be used for the guidance of the contractor in estimating the value of the work, of the mill in rolling the steel, of the engineer in preparing working drawings, and of the fabricating shop in manufacturing the material. These purposes should be kept in mind in writing specifications. The relation of the specifications to the contract should be clearly understood. In all cases the specifications should be made a part of the contract and they are then just as binding as if written into the contract. This indicates the importance of having them correctly written. As far as practicable, items in the specifications should not be repeated in the contract and, on the other hand, items which belong in the contract should not be in the specifications, for such repetitions lead to conflicting or ambiguous provisions. 350 STEEL CONSTRUCTION GENERAL CHARACTERISTICS A number of proposed standard specifications for structural steel have been published. Usually their purpose is more for the guidance of the designer than of the contractor. Some of them cover both purposes quite fully. Such a one is "Revised General Specifications for Structural Work for Buildings" by C. C. Schneider, M. Am. Soc., C. E., published in the Transactions of the American Society of Civil Engineers, Vol. LIV, page 490. This is referred to as Schneider's Specifications. It can be used in whole or in part in making up specifications for a particular work. It is published and for sale by the Engineering News Publishing Company, so that copies are readily available. Consequently, in using the specifi- cations, the parts desired need not be copied but can be referred to by subject and paragraph number. Considerable portions are quoted in the specifications given later. When such general specifications are used, they must be supple- mented to provide for the special requirements of the work and for the business features before mentioned. Outline for Specifications. Complete specifications should include the following subjects: Instructions to Bidders Quality of Materials General Conditions Details of Construction Scope of Work Workmanship Loads Painting Unit Stresses Inspection Erection Instructions to Bidders. This is entirely a business feature and may be made a separate document from the specifications. But if so, it should accompany the specifications which are sent to bidders. As the instructions may contain items which might later affect the interpretation of the contract, it is best that they be included in the specifications and thus, automatically, become a part of the contract. The instructions give the time and place for submitting bids, the price basis, and any other directions pertinent to the case in hand. Bidders may be required to state the length of time required by them, if this will be a consideration in letting the contract. STEEL CONSTRUCTION 351 General Conditions. The general conditions have no very direct relation to the technical requirements but are more clearly business features. They cover such items as bonds, liability insur- ance, watchman service, etr. Scope of Work. This section of the specifications is devoted to the particular work under consideration and should be most care- fully stated, for it governs the amounts of material and service to be furnished. The paragraphs should cover the following items: (a) Describe definitely the work included. If separate draw- ings are made for the structural steel and show completely all the material to be furnished, the work may be so described. But if the structural steel is shown on drawings with other materials, particularly ornamental or miscellaneous iron, then the description must be given in sufficient detail to make it perfectly clear. .It must be understood that the term "structural steel" is not definite enough to be used without such a description as required above, for struc- tural shapes may be used in stair construction, for furring, for win- dow frames, and in other situations, when it is desirable that such items be furnished .by other contractors. Cast-iron pedestals for steel columns and cast-iron columns, if used, are usually included in the contract with the structural steel. (b) Identify the drawings involved by numbers and dates. (c) State the place of delivery if erection is not included, and specify by whom transportation charges are to be paid. (d) Give requirements as to working drawings. Loads. It is desirable that the loads used in making the design be given in the specifications or marked on the drawings. The latter method is preferable for special loads, such as machinery, tanks, storage space, etc. This information is needed in detailing connections, stiffeners, etc. It is not sufficient to say that con- nections shall develop the full strength of the member, for there may be situations when a concentrated load near the end of a beam may produce a stress at the connection greater than would be produced by a uniformly distributed load. Unit Stresses. The unit stresses concern the design of the structural steel more than they do the manufacture and construction of it. However, they are needed in making the working drawings and should be included in the specifications. Those given in Schnei- 352 STEEL CONSTRUCTION der's Specifications should be used unless local building ordinances require other values. Quality of Material. The quality -of material to be used is dis- cussed at length on p. 42. The specifications of the American Society for Testing Materials are recommended for general use. They need not be written into the specifications, it being sufficient to state that the steel shall comply with the "Standard Specifications for Structural Steel for Buildings", adopted by the American Society for Testing Materials. Similarly, the quality of cast iron may be specified. In this section the kind and quality of paint should be given. Details of Construction. This section of the specifications is concerned with such items as connections, rivet spacing, etc. It is chiefly to guide the engineers and draftsmen in making working drawings. Design drawings should be consistent with its provisions. Schneider's Specifications are recommended for this portion of the specifications. They may be used by reference, saying that the details of construction should conform to Schneider's Specifications in so far as they apply to this work; or the specific paragraphs which do apply may be referred to by number. Workmanship. The specifications for workmanship govern the operations in the shop. Schneider's Specifications are recom- mended and may be used the same as for construction details. Painting. This is well covered by Schneider's Specifications, which may be used without modification unless some special pro- vision is to be inserted. Inspection and Tests. Schneider's Specifications are used for this part of the work without change. Erection. The specifications for erection must deal with the specific job. However, some of its provisions are general. The conditions at the site, the relations to the other parts of the structure, order of procedure, storage available, etc., etc., must be written to suit each case. If the contract for erection is separate from the contract for furnishing the steel, the division between them must be clearly defined. This division is usually best made at the place where the material is delivered on board cars. Quality of workmanship of erection applies generally to all structures. STEEL CONSTRUCTION 353 EXAMPLE OF SPECIFICATIONS The following specifications accord with the preceding discus- sions and may be used as a guide in writing specifications for a par- ticular structure. SPECIFICATIONS for the Structural Steel and Iron for a (Kind of Building) for (Owner) Instructions to Bidders. Bids will be received for the struc- tural steel and iron work required for (kind of building) located at Street, in the City of for the ( wner ) in accordance with the following specifications and the plans des- cribed therein. Bids must be filed at the office of Architect, on or before noon, 19 Bidders shall state a lump sum which shall include furnishing, delivering, and erecting the structural steel and iron work and shall also include the cost pf the bond, insurance, and watch service as required under general conditions. General Conditions. Ownership. The building is known as the Build- ing and is owned by the [a partnership (or corporation) existing under the laws of the State of ] Location. It is located at , Street in the City of on lots (give legal description). Bond. The contractor shall furnish surety bond in the penal sum of one-half the contract price, guaranteeing the fulfillment of 354 STEEL CONSTRUCTION the terms of the contract. Said bond shall be in terms and with surety satisfactory to the Architect. Liability Insurance. The contractor shall protect the owner against loss due to any damage to property or injury to persons which may result from his operations. He shall provide adequate liability insurance in a company approved by the Architect. Patented Articles. The contractor shall protect the owner against any claim arising out of the use of any patented article, appliance, or method. Protection. The contractor shall provide such barricades, scaffolding, staging, and other means of protection as may be re- quired to comply with the state and municipal laws and to ade- quately safeguard property and persons. Watchmen. The contractor shall keep competent watchmen on the building day and night. Scope. [Give a general description similar to the following: The building is designed for office purposes with stores on the first and second floors. It is twenty stories high above street level with a basement and sub-basement below street level. The ground area occupied is approximately 100 feet by 162 feet.] Work Covered. The work to be done under the specifications is the furnishing and the erecting of the structural steel and iron work. The contractor shall make the working drawings, furnish and fabri- cate the material, pay all transportation charges, assemble the material in place in the building, rivet the connections, and furnish the materials and labor for shop and field painting. Materials Included. The structural steel and iron work consists of the following items: (To be changed to suit the case). Grillage Beams and Girders Cast-Iron Pedestals I-Beam Reinforcement in Retaining Walls Structural Steel Framework Cast-Iron Columns Detached Lintels Cornice Brackets Roofing Tees Steel Chimney All minor parts belonging to the above items STEEL CONSTRUCTION 355 It includes all the material of the above character shown in the structural plans of the building and, in addition, it includes the detached lintels over exterior windows which are shown on the architectural plans. Materials Not Included. The structural steel and iron work (to be changed to suit the case) does not include the angles, channels, and hangers of the suspended ceiling over the top story, the elevator sheave beams, the beams and channels for the stairs other than those shown on the framing plans, the marquise framing, the steel column guards and door guards in the shipping room, and other like items shown on the architectural plans. It does not include the rods for reinforced concrete work shown on the structural plans except cer- tain items which are definitely marked on the drawings to be fur- nished with the structural steel. Plans. The structural plans consist of drawings prepared by Structural Engineer for Architect, as follows: (Give list of drawings) The architectural plans prepared by Architect, which show structural steel and iron work not given on the structural plans are drawings Xo While making the working drawings, the contractor shall con- sult all architectural drawings which may be supplied to him, for the purpose of discovering discrepancies, making necessary allow- ances for clearance, providing connections and supports for other materials, etc. \Yhen provision must be made for attaching other materials to the structural steel work, the contractor shall furnish the holes required. If the necessary data are not given on the structural or architectural drawings, he shall apply to the Architect for the data before completing the working drawings. This applies particularly to stone, terra cotta, concrete, miscellaneous iron, ornamental iron, furring (wood and steel), pipes, and conduits. Working Drawings. The contractor is required to prepare working drawings to supplement the 'design drawings prepared by the Engineer and the Architect. Two copies of such drawings shall 356 STEEL CONSTRUCTION be submitted to the Architect for approval. After approval, three copies shall be furnished to the Architect for his files, and as many copies as may be required shall be furnished to the inspector and to other trades. Copies or prints of drawings issued before approval shall be marked "Not Approved" and those issued after approval shall be marked "Approved Drawing." During the preparation of the working drawings, the contractor shall examine the design drawings carefully for omissions and errors, and w r hen such omissions and errors are discovered, he shall submit them to the Architect for correction. Figured dimensions only shall be used. If the contractor does not have a force of engineers competent to prepare working drawings to the satisfaction of the Architect, he shall employ a consulting engineer for that purpose. Working drawings shall be accompanied by erection diagrams and a complete index giving marking numbers of the material and page or sheet numbers of the drawings. Approval of Working Drawings. If the working drawings are found to be consistent with the design drawings and these specifica- tions, and if the details shown on them are satisfactory, they will be approved. One copy so marked will be returned to the contractor. If not consistent and satisfactory as above, one copy will be marked to indicate the required changes and returned to the contractor^ who shall then make the .required changes, and if so ordered, shall submit copies of revised drawings for final approval. The Architect's approval will cover the arrangement of the principal members and auxiliary members, and the strength of con- nections. At the same time an effort \vill be made to discover any errors in sizes of material, in general dimensions, and in detail dimen- sions; but the responsibility for these items shall remain with the contractor. The manufacturing of any material or the performing of any work before approval of working drawings will be entirely at the risk of the contractor. Transportation. The contractor shall pay all costs of transpor- tation of material from his shop to the building site and shall assume all risk of loss and damage in transit. Loads. The structural steel and iron work is designed to sup- STEEL CONSTRUCTION 357 port the estimated dead loads and the assumed live loads. In making the working drawings, the contractor shall design all con- nections to carry the same loads. The dead loads are the actual weights of all materials of con- struction in the positions which they occupy, except that the effect of movable partitions may be assumed to be equivalent to a uni- formly distributed load of 25 pounds per square foot of floor on all office floors. On other floors and along corridors, the partitions shall be provided for where they occur. The live loads for which this structure is designed are: (Subject to change) Roof Office floor Second floor First floor Sidewalk Wagon space and snipping room 50 Ib. per sq. ft. 50 Ib. per sq. ft. 100 Ib. per sq. ft. 1251b. per sq. ft. 150 Ib. per sq. ft. 250 Ib. per sq. ft. The special loads from elevators, tanks, etc., are marked on the drawings. The framework is designed for a wind pressure of 20 pounds per square foot applied horizontally to the vertical projection of the building in any direction. Where stresses are marked on the drawings, they may be used as the full effect of the loads. Beams and girders shall have their connections made strong enough to develop the full capacity of the members when they are uniformly loaded, even when the live and dead loads are less than this capacity. Unit Stresses. The design is based on the unit stresses given in Schneider's Specifications, * paragraphs 19 to 34 inclusive. These unit stresses shall be used in proportioning the details. Steel 19. Permissible Strains. All parts of the structure shall be proportioned so that the sum of the dead and live loads, together with the impact, if any, shall not cause the strains to exceed those given in the following table: *"Rcvi3cd Specifications for Structural Work for Buildings" by C. C. Schneider, M. Am. Soc. C. E., Trant. Am. Sec. C. E., Vol. LIV, Page 494. 358 STEEL CONSTRUCTION Pounds per square inch Tension, net section 16,000 Direct compression 16,000 Shear, on rivets and pins 12,000 Shear, on bolts and field rivets 9,000 Shear, on ^late-girder web (gross section) 10,000 Bearing pressure, on pins and rivets 24,000 Bearing pressure, on bolts and field rivets 18,000 Fiber strain, on pins 24,000 20. Permissible Compression Strains. For compression members, the permissible strain of 16,000 Ib. per sq. in. shall be reduced by the following formula: p = 16,000-70^ Where p = permissible working strain per square inch in compression; I = length of piece, in inches, from center to center of connections; r = least radius of gyration of the section, in inches. 21 For wind bracing, and the combined strains due to wind and the other loading, the permissible working strains may be increased 25%, or to 20,000 Ib. for direct compression or tension. 22. Provision for Eccentric Loading. In proportioning columns, provision must be made for eccentric loading. 23. Expansion Rollers. The pressure per linear inch on expansion rollers shall not exceed 600 d, where d = diameter of rollers, in inches. 24. Combined Strains. Members subject to the action of both axial and bending strains shall be proportioned so that the greatest fiber strain will not exceed the allowed limits for the axial tension or compression in that member. 25. Reversal of Strains. Members subject to reversal of strains shall be proportioned for the strain giving the largest section, but their connections shall be proportioned for the sum of the strains. 26. Net Sections. Net sections must be used in calculating tension mem- bers, and in deducting the rivet holes; they must be taken | in. larger than the nominal size of the rivets. 27 Pin-connected riveted tension members shall have a net section through the pin holes 25% in excess of the net section of the body of the member. The net section back of the pin hole shall be at least 0.75 of the net section through the pin hole. 28. Compression Members Limiting Length. No compression member shall have a length exceeding 125 times its least radius of gyration, except those for wind and lateral bracing, which may have a length not exceeding 150 times the least radius of gyration. 29. Plate Girders. Plate girders shall be proportioned on the assumption that one-eighth of the gross area of the web is available 'as flange area. The compression flange shall have at least the same sectional area as the tension flange, but the unsupported length of the flange shall not exceed 16 times its width. 30. In plate girders used as crane runways, if the unsupported length of the compression flange exceeds 12 times its width, the flange shall be figured as a column between the points of support. STEEL CONSTRUCTION 359 51. Web Stiff eriers. The web shall have stiffeners at the ends and inner edges of bearing plates, and at all points of concentrated loads, and also at intermediate points, when the thickness of the web is less than one-sixtieth of the unsupported distance between flange angles, generally not farther apart than the depth of the full web plate, with a minimum limit of 5 feet. 52. Rotted Beams. I-beams, and channels used as beams or girders, shall be proportioned by their moments of inertia. 53. Limiting Depth of Beams and Girders. The depth of rolled beams in floors shall be not less than one-twentieth of the span and, if used as roof purlins, not less than one-thirtieth of the span. In case of floors subject to shocks and vibrations, the depth of beams and girders shall be limited to one-fifteenth of the span. If shallower beams are used, the sectional area shall be increased until the maximum deflection is not greater than that of a beam having a depth of one-fifteenth of the span, but the depth of such beams shall in no case be less than one-twentieth of the span. Cast Iron $4> Permissible Strains. Compression 12,000 Ib. per sq. in. Tension 2,500 " w " " Shear , 1,500 " " " " Quality of Materials. Steel. The structural steel shapes, plates, and rivets shall conform to the Standard Specifications for Structural Steel for Buildings adopted by tho American Society for Testing Materials*, as follows; SPECIFICATIONS FOR STRUCTURAL STEEL FOR BUILDINGS Structural steel may be made by either the open-hearth or Bessemer process. Rivet steel and plate or angle material over f inch thick, which is to be punched, shall be made by the open-hearth process.. The chemical and physical properties shall conform to the limits shown in the tabular matter on the following page. For the purposes of these specifications, the yield point shall be determined by the careful observation of the drop of the beam or halt in the gage of the testing machine. In order to determine if the material conforms to the chemical limitations prescribed * * * * * * * analysis shall be made by the manufacturer from a test ingot taken at the time of the pouring of each melt. or blow of steel, and a correct copy of such analysis furnished to the engineer or his inspector. Specimens for tensile and bending tests shall be made by cutting coupons from the finished product, which shall have both faces rolled and both edges milled to the form shown by Fig. 1 (see Fig. 46); or with both edges parallel; or they may be turned to a diameter of f inch for a length of at least 9 inches, with enlarged ends. (a) For material more than f inch thick the bending test specimen may be 1 inch by \ inch in section. (6) Rivet rounds and small rolled bars shall be tested as rolled. American Society for Testing Materials, Edgar Marburg, Secretary, University of Penn- ylvania, Philadelphia. 360 STEEL CONSTRUCTION Properties of Structural Steel Properties Considered Structural Steel Rivet Steel, Open Hearth Phosphorus, max., Bessemer. .....,.,.. 0.10 per cent Phosphorus, max., open hearth 0.06 per cent 06 per cent Ult. tensile strength, pounds per sq. in. . 55,000-05,000 i Ult. tens str 48,000-58,000 i Ult tens str Elongation, min. per cent in 8 in. *...... 1,400.000 1,400,000 Ult. tens. str. Silky Ult. tens. str. Silky 180 to diameter 180 flat of 1 thickness Material which is to be used without annealing or further treatment shall be tested in the condition in which it comes from the rolls. When material is to be annealed or otherwise treated before use, the specimens for tensile tests, representing such material, shall be cut from properly annealed or similarly treated short lengths of the full section of the bar. At least one tensile and one bending test shall be made from each melt or blow of steel as rolled. In case steel differing f inch and more in thickness is rolled from one melt or blow, a test shall be made from the thickest and thinnest material rolled. , Should either of these test specimens develop flaws, .or should the tensile test specimen break, outside of the middle third of its gaged length, it may be discarded and another, test specimen substituted therefor. If tensile test specimen does not meet the specification, additional tests may be made. (c) The bending test may bo made by pressure or by blows. For material less than & inch and more than f inch in thickness, the follow- ing modifications shall be made in the requirements for elongation. (d) For each increase of i inch in thickness above f inch, a deduction of 1 shall be made from the specified percentage of elongation. (e) For each decrease of ^ inch in thickness below & inch, a deduction of 1\ shall be made from the specified percentage of elongation. (/) For pins, the required percentage of elongation shall be 5 less than that specified ***** as determined on a test specimen, the center of which shall be 1 inch from the surface. Finished material must be free from injurious seams, flaws, or cracks, and have a workmanlike finish. Test specimens and every finished piece of steel shall be stamped with melt or blow number, except that small pieces may be shipped in bundles securely wired together, with the melt or blow number on a metal tag attached- A variation in cross section or weight of each piece of steel of more than 2f per cent from that specified will be sufficient cause for rejection, except in case of sheared plates, which will be covered by the following permissible variations, which are to apply to single plates. STEEL CONSTRUCTION' 361 When Ordered to Weight Plates 12\ pounds per square foot or heavier: (g) Up to 100 inches wide, 2^ per cent above or below the prescribed weight. (h) 100 inches wide and over, 5 per cent above or below. Plates under i2\ pounds per square foot: () Up to 75 inches wide, 2\ per cent above or below. 75 inches and up to 100 inches wide, 5 per cent above or 3 per cent below. 0) 100 inches wide and over, 10 per cent above or 3 per cent below. When Ordered to Gage Plates will be accepted if they measure not more than 0.01 inch below the ordered thickness. An excess over the nominal weight corresponding to the dimensions on the order will be allowed for each plate, if not more than that shown in the following tables, one cubic inch of rolled steel being assumed to weigh 0.2833 pound. Plates \ inch and over in thickness Thickness Ordered. Inches Nominal Weights Lb. per sq. ft. Width of Plate Up to 75 in. 75 in. and up to 100 in. 100 in. and up to 115 in. Over 115 in. 1-4 5-16 3-8 7-16 1-2 9-16 5-8 Over 5-8 10.20 12.75 15.30 17 85 20.40 22.95 25.50 10 per cent 8 per cent 7 per cent 6 per cent 5 per cent 4| per cent 4 per cent 3 1 per cent 14 per cent 12 per cent 10 per cent 8 per cent 7 per cent 6| per cent 6 per cent 5 per cent 18 per cent 16 per cent 13 per cent 10 per cent. 9 per cent 8| per cent . 8 per cent 6 per cent 17 per cent 13 per cent 12 per cent 1 1 per cent 10 per cent 9 per cent Plates under \ inch in thickness Thickness Ordered Inches Nominal Weights Lb. per sq. ft. Width of Plate Up to 50 in. 50 in. and up to 70 in. Over 70 in. 1-8 up to 5-32 5-32 up to 3-16 3-16 up to 1-4 5.10 to 6.37 6.37 to 7.65 7.65 to 10.20 10 per cent 8^ per cent 7 per cent 15 per cent 12| per cent 10 per cent 20 per cent 17 per cent 15 per -cent The inspector representing the purchaser shall have all reasonable facilities afforded to him by the manufacturer to safisfy him that the finished material is furnished in accordance with these specifications. All tests and inspections shall be made at the place of manufacture, prior to shipment. Cast Iron. The cast iron shall conform to the Standard Speci- fications for Gray Iron Castings adopted by the American Society for Testing Materials*, as follows: *American Society for Testing Materials, Edgar Marburg, Secretary, University of Penn- sylvania, Philadelphia. 362 STEEL CONSTRUCTION SPECIFICATIONS FOR GRAY IRON CASTINGS Unless furnace iron is specified, all gray castings are understood to be made by the cupola process. The sulphur contents to be as follows: Light castings ,....".*... .not over 0.08 per cent Medium castings not over 0.10 per cent Heavy casting not over 0.12 per cent In dividing castings into light, medium, and heavy classes, the following standards have been adopted:. Castings having any section less than Hnch thick shall be known as light castings. Castings in which no section is less than 2 inches thick shall be known as heavy castings. Medium castings are those not included in the above classification. Transverse Test. The minimum breaking strength of the "Arbitration Bar" under transverse load shall not be under: Light castings . . . . i.. ..... .2,500 lb. Medium castings 2,900 lb. Heavy castings. ................ , . .3,300 lb. In no case shall the deflection be under 0.10 inch. Tensile. Test. Where specified, this shall not run less than; Light castings , 18,000 lb. per 'sq. in. Medium castings 21,000 lb. per sq. in. Heavy castings 24,000 lb. per sq. in. The quality of the iron going into castings under specification shall be determined by means of the "Arbitration Bar". This.is a bar 1 J inches in diam- eter and 15 inches long. It shall be prepared as stated further on and tested transversely. The tensile test is not recommended, but in case it is called for, the bar as shown in Fig. 1, (figure not given) and turned up from any of the broken pieces of the transverse test shall be used. The expense of the tensile test shall fall on the purchaser. Two sets of two bars shall be cast from each heat, one set from the first and the other set from the last iron going into the castings. Where the heat exceeds twenty tons, an additional set of two bars shall be cast for each twenty tons or fraction thereof above this amount. In case of a change of mixture during the heat, one set of two bars shall also be cast for every mixture other than the regular one. Each set of two bars is to go into a single mold. The bars shall not be rumbled or otherwise treated, being simply brushed of! before testing. The transverse test shall be made on all the bars cast, with supports 12 inches apart, load applied at the middle, and the deflection at rupture noted. One bar of every two of each set made must fulfil the requirements to permit acceptance of the castings represented. The mold for the bars is shown in Fig. 2 (figure not given.). The bottom of the bar is ^ inch smaller in diameter than the top, to allow for draft and for the strain of pouring. The pattern shall not be rapped before withdrawing. The flask is to be rammed up with green molding sand, a little damper than STEEL CONSTRUCTION 363 usual, well mixed and put through a No. 8 sieve, with a mixture of one to twelve bituminous facing The mold shall be rammed evenly and fairly hard, thor- oughly dried, and not cast until it is cold. The test bar shall not be removed from the mold until cold enough to be handled. The rate of application of the load shall be from 20 to 40 seconds for a deflection of 0.10 inch. Borings from the broken pieces of the "Arbitration Bar" shall be used for the sulphur determinations. One determination for each mold made shall be required. In case of dispute, the standards of the American Foundrymen's Association shall be used for comparison. Castings shall be true to pattern, free from cracks, flaws, and excessive shrinkage. In other respects they shall conform to whatever points may be specially agreed upon. The inspector shall have reasonable facilities afforded him by the manu- facturer to satisfy him that the finished material is furnished in accordance with these specifications. All tests and inspections shall, as far as possible, be made at the place of manufacture prior to shipment. Paint. The paints used shall be red lead paint for the shop coat and graphite paint for the field coat. The red lead paint shall be made of red lead containing not less than 95 per cent Pb 3 O 4 , for the pigment and pure raw linseed oil with not more than 8 per cent of turpentine or Japan drier for the vehicle. The red lead paint shall be mixed on the premises where it is used, and each batch shall be used within twenty-four hours after being mixed. The mixing shall be done in a churn or other mechanical mixer. The material shall be used in the proportion of twenty-five pounds of red lead to one gallon of oil. The contractor shall furnish -samples of the lead and oil for testing, and if required to do so shall furnish the name of the manu- facturer of the oil and of the dealers who have handled it. The graphite shall be the brand manufactured by the Company, or any other graphite paint of equal quality, if it is approved by the Architect. The contractor shall furnish samples of the graphite paint for analysis and test. He shall guarantee that the paint will fulfill all the published claims made for it by its manufacturer. Details of Construction. The details of construction shall con- form to paragraphs 37 to 81, inclusive, of Schneider's Specifications, in so far as their provisions are applicable to this work. 364 . STEEL CONSTRUCTION 37. Minimum Thickness of Material No steel of less than \ in. thickness shall be used, except for lining or filling vacant spaces. 38. Adjustable Members. Adjustable members in any part of structures shall preferably be avoided. 39. Symmetrical Sections. Sections shall preferably be made symmetrical. 40. Connections. The strength of connections shall be sufficient to develop the full strength 'of the member: 41. No connection, except lattice bars, shall have less than two rivets. 42. Floor Beams. Floor beams "shall generally be rolled steel beams. 43. For fireproof floors, they shall generally be tied with tie-rods at inter- vals not exceeding eight times the depth of the beams. This spacing may be increased for floors which are not of the arch type of construction. Holes for tie-rods, where the construction of the floor permits, shall be spaced about 3 in. above the bottom of the beam. 44- Beam Girder.- When more than one rolled beam is used to form a girder, they shall be connected by bolts and separators at intervals of not more than 5 ft. All beams having a depth of 12 in. and more shall have at least two bolts to each separator. 45. Wall Ends of Beams and. Girders. Wall ends of a sufficient number of joists and girders shall be anchored securely to impart rigidity to the structure. 46. Wall Plates and Column Bases. Wall plates and column bases shall be constructed so that the load will be well distributed over the entire bearing. If they do not get the full bearing on the masonry, the deficiency shall be made good with.Portland cement mortar. '47. Floor Girders. The floor girders may be rolled beams or plate girders ; they shall preferably be 'riveted or bolted to columns by means of connection angles. Shelf angles or other support may be provided for convenience during erection. 48. Flange Plates. The flange plates of all girders shall be limited in width, so as not to extend, beyond the outer line of rivets connecting them to the angles, more than 6 in., or more than eight times the thickness of the thinnest plate. 49. Web Stiffeners. Web stiffeners' shall be in pairs, and shall have a close bearing against the flange angles. Those over the end bearing, or forming the connection between girder and column, shall be on fillers'. Intermediate stiff- eners may be on fillers or crimped over the flange angles. The rivet pitch in stiffeners shall not be more than 5 in. 50. Web Splices. Web plates of girders must be spliced at all points by a plate on each side of the web, capable of transmitting the full strain through splice rivets. 51. Columns. Columns shall be designed so as to provide for effective connections of floor beams, girders, or brackets. They shall preferably be continuous over several stories. 52. Column Splices. The splices shall be strong enough to resist the bending strain and make the columns practically continuous for their whole length. 53. Trusses. Trusses shall preferably be riveted structures. Heavy trusses of long span, where the riveted field connections would become un- wieldy, or for other good reasons, may be designed as pin-connected structures. 54. Intersecting Members. Main members of trusses shall be designed so that the neutral axes of intersecting members shall meet in a common point. STEEL CONSTRUCTION 365 55. Roof Trusses. Roof trusses shall be braced in pairs in the plane of the chords. Purlins shall be made of shapes, or riveted-up plate, or lattice girders- Trussed purlins will not be allowed. 66. Eyebars. The eyebars in pin-connected trusses composing a member shall be as nearly parallel to the axis of the truss as possible. 67. Spacing of Rivets. The minimum distance between centers of rivet holes shall be three diameters of the rivet; but the distance shall preferably be not less than. 3 in. for J-in. rivets. 24 in. for l-in. rivets, 2i in. for f-in. rivets, and 1J in. for $-in. rivets. 68. For angles with two gage lines, with rivets staggered, the maximum in each line shall be twice as great as given in Paragraph 57, and, where two or more plates are used in contact, rivets not more than 12 in. apart in any direc- tion shall be used to hold the plates together. 59. The pitch of the rivet, in the direction of the strain, shall not exceed 6 in., nor 16 times the thinnest outside plate connected, and not more than 50 times that thickness at right angles to the strain. 60. Edge Distance. The minimum distance from the center of any rivet hole to a sheared edge shall be 1 j in. for |-in. rivets, 1 \ in. for f-in. rivets, \\ in. for |-in. rivets, and I in. for -in. rivets; and to a rolled edge, 11, 1J, 1, and fin., respectively. 61. The maximum distance from any edge shall be eight times the thick- ness of the plate. 62. Maximum Diameter. The diameter of the rivets in any angle carrying calculated strains shall not exceed one-quarter of the width of the leg in which they are driven. In minor parts, rivets may be \ in. greater in diameter. 63. Pitch at Ends. The pitch of rivets at the ends of built compression members shall not exceed four diameters of the rivets for a length equal to one and one-half times the maximum width of the member. 64" Tie Plates. The open sides of compression members shall be provided with lattice having tie plates at each end at intermediate points where the lattice is interrupted. The tie plates shall be as near the ends as practicable. In main members, carrying calculated strains, the end tie plates shall have a length not less than the distance between the lines of rivets connecting them to the flanges, and intermediate ones not less than half this distance. Their thickness shall be not less than one-fiftieth of the same distance. 65. Lattice. The thickness of lattice bars shall be not less than one-fortieth for single lattice and one-sixtieth for double lattice, of the distance between end rivets; their minimum width shall be as follows: For 15-in. channels, or built sections \ , n . % with 3* and 4-in. angles ?* m ' (i ' ln * nvets) For 12-, 10- and 9-in. channels, or built \ 01 /, . . \ sections with 3-in. angles / 2 m " ( *-' n - nvets) For & and 7-in. channels, or built \ - , 5 : . . ^ sections with 2J-in. angles J 2 m ' ( *' m ' nvets) For 6- and 5-in. channels, or built \ ia fl , % sections with 2-in. angles I 1 * ln ' ( ^ In ' nvets) 66. Lattice bars with two rivets shall generally be used in flanges more than 5 in. wide. 366 STEEL CONSTRUCTION 67. Angle of Lattice. The inclination of lattice bars with the axis of the member, generally, shall be not less than 45, and when the distance between the rivet lines in the flange is more than 15 in., if a single rivet bar is used, the lattice shall be double and riveted at the intersection. 68. Spacing of Lattice. The pitch of lattice connections, along the flange divided by the least radius of gyration of the member between connections, shall be less than the corresponding ratio of the member as a whole. 69. Faced Joints. Abutting joints in compression members when faced for bearing shall be spliced sufficiently to hold the connecting members accur- ately in place. 70. All other joints in riveted work, whether in tension or compression, shall be fully spliced 71. Pin Plates. Pin holes shall be reinforced by plates where necessary; and at least one plate shall be as wide as the flange will allow; where angles are used, this plate shall be on the same side as the angles. The plates shall contain sufficient rivets to distribute their portion of the pin pressure to the full cross section of the member 72. Pins. Pins shall be long enough to insure a full bearing of all parts connected upon the turned-down body of the pin 73. Members packed on pins shall be held against lateral movement. 74. Bolts. Where members are connected by bolts, the body of these bolts shall be long enough to extend through the metal. A washer at least & in thick shall be used under the nut 75. Fillers. Fillers between parts carrying strain shall have a sufficient number of independent rivets to transmit the strain to the member to which the filler is attached 76. Temperature. Provision shall be made for expansion and contraction, corresponding to a variation of temperature of 150 Fahr., where necessary. 77. Rollers. Expansion rollers shall be not less than 4 in. in diameter. 78. Stone Bolts Stone bolts shall extend not less than 4 in. into granite pedestals and 8 in. into other material. 79. Anchorage. Columns which are strained in tension at their base shall be anchored to the foundations 80. Anchor bolts shall be long enough to engage a mass of masonry, the weight of which shall be one and one-half times the tension in the anchor 81. Bracing. Lateral, longitudinal, and transverse bracing in all struc- tures shall preferably be composed of rigid members. Adjacent ends of column sections, which do not have full bear- ing, shall have bearing plates not less than f inch thick. Rivets generally shall be f inch in diameter, but the diameter of the rivet shall not be less than one-fourth of its grip; |-inch rivets shall be used when the pieces connected are f inch or more in thickness. No beam connections shall be less than the standards of the American Bridge Company. The clearance from the ends of beams to columns or to girders shall not exceed \ inch. STEEL CONSTRUCTION 367 Tie-rods between floor beams shall be threaded at both ends for a length of at least 3 inches. The number of rivets furnished for field connections shall be 10 per cent in excess of the nominal number required. Chimney. The connections of the cast-iron or steel chimney to the framework shall be such as to permit expansion and contraction, due to changes in temperature. Provide flanges with holes for breeching connection. Cast-iron chimneys may have either flanged joints or hub and spigot joints. The bearing surfaces shall have contact on the entire perimeter and shall be exactly at right angles to the axis of the pipe, being turned or planed, if necessary to make them so. The calking space in hub and spigot joints shall be filled with iron fillings and sal ammoniac and calked solid. Connections for anchors shall be cast on. Steel chimneys shall have lap joints for all shop connections. They may have either lap or flange joints for the field connections, except that the lap joints generally will be required for self-support- ing chimneys exposed to wind pressure. All joints shall be prac- tically air-tight and, if not so made by the riveting, shall be calked. Cast Iron. The ends of cast-iron columns and the tops of cast- iron base plates and pedestals shall be planed. Bolt holes in cast iron shall be drilled. Holes for grout may be cored. In each cast-iron pedestal a grout hole shall be provided which shall be not less than 2| inches in diameter and placed as near the center of the base as practicable. Additional holes shall be provided in bases larger than 4 feet in diameter. The joints in cast-iron columns shall be made by means of flanges cast on the columns. Each joint shall be bolted with not less than four J-inch bolts. The metal in the flanges shall be not less than 1 inch thick. Unless otherwise designed, each beam connection shall consist of a bracket and a lug. The bracket shall sustain the entire reaction from the beam. It shall project not less than 4 inches from the column and shall slope J inch. The lug shall provide for two or more bolts connecting to the web of the beam. 368 STEEL CONSTRUCTION Workmanship. The workmanship in the fabrication of the structural steel shall conform to paragraphs 23 to 51 of Schneider's Specifications, in so far as they concern this work. 23 General. All parts forming a structure shall be built in accordance with approved drawings The workmanship and finish shall be equal to the best practice in modern bridge work. S4. Straightening Material Material shall be thoroughly straightened in the shop, by methods which will not injure it, before being laid off or worked in any way. 25. Finish. Shearing shall be done neatly and accurately, and all por- tions of the work exposed to view shall be neatly finished 26. Rivets. The size of rivets called for on the plans shall be understood to mean the actual size of the cold rivet before heating. 27. Rivet Holes. The diameter of the punch for material not more than | in. thick shall be not more than pg in., nor that of the die more than | in. larger than the diameter of the rivet. Material more than | in thick, excepting in minor details, shall be sub-punched and reamed or drilled from the solid 28. Punching. Punching shall be done accurately. Slight inaccuracy in the matching of holes may be corrected with reamers. Drifting to enlarge unfair holes will not be allowed. Poor matching of holes will be cause for rejec- tion, at the option of the inspector 29. Assembling. Riveted members shall have all parts well pinned up and firmly drawn together with bolts before riveting is commenced. Contact surfaces shall be painted (See Paragraph 52.) 30. Lattice Bars. Lattice bars shall have neatly-rounded ends, unless otherwise called for. 31. Web Stiff eners. Stiffeners shall fit neatly between the flanges of girders. Where tight fits are called for, the ends of the stiffeners shall be faced and shall be brought to a true contact bearing with the flange angles 32. Splice Plates and Fillers. Web splice plates and fillers under stiffeners shall be cut to fit within f in. of flange angles. 33 Connection Angles. Connection angles for floor girders shall be flush with each other and correct as to position and length of girder. 34' Riveting. Rivets shall be driven by pressure tools wherever possible. Pneumatic hammers shall be used in preference to hand driving 35 Rivets. Rivets shall look neat and finished, with heads of approved shape, full, and of equal size. They shall be central on the shank and shall grip the assembled pieces firmly. Re-cupping and calking will not be allowed. Loose, burned, or otherwise defective rivets shall be cut out and replaced In cutting out rivets, great care shall be taken not to injure the adjoining metal. If necessary, they shall be drilled out. 36. Field Bolts. Wherever bolts are used in place of rivets which trans- mit shear, such bolts must have a driving fit. A washer not less than J in. thick shall be used under the nut. 37. Members to be Straight. The several pieces forming one built member shall be straight and shall fit closely together, and finished members shall be free from twists, bends, or open joints. STEEL CONSTRUCTION 369 38. Finish of Joints. Abutting joints shall- be cut or dressed true and straight and fitted closely together, especially where open to view. In compres- sion joints depending on contact bearing/ the surfaces shall be truly faced, so as to have even bearings after they are riveted up complete and when perfectly aligned. 39. Eyebars. Eyebars shall be straight and true to size, and shall be free from twists, folds in the neck or head, or any other defect. Heads shall be made by upsetting, rolling, or forging. Welding will not be allowed. The form of the heads will be determined by the dies in use at the works where the eyebars are made, if satisfactory to the engineer, but the manufacturer shall guarantee the bars to break in the body with a silky fracture, when tested to rupture. The thickness of the head and neck shall not vary more tnan & in. from the thickness of the bar. 40. Boring Eyebars. Before , boring, each eyebar shall be perfectly an- nealed and carefully straightened.' Pin holes shall be in the center line of bars and in the center of heads.. Bars of the same length shall be .bored so accurately that, when placed together, pins ^? in. .smaller in diameter than the pin holes can be passed through the- holes at .both ends of the bars at the same time. 41. Pin Holes. Pin. holes shall be -bored true to 'gages, smooth and straight; at right angles to the 1 axis of the member, and parallel to each other, unless otherwise called for. Wherever possible, the boring shall be done. afteY the member is riveted up. 42. Variation in Pin. Holes, The distance from center to .center of pin holes shall be correct within ^j in., and the diameter of the hole not more than B"& in. larger than that of the pin, for pins UD to 5 in. diameter, and & in, for larger pins. 43. Pins and Rollers. - Pins and rollers shall be turned accurately .to gages, and shall be straight, smooth, and entirely free from flaws. 44- Pilot Nuts. At least one pilot and driving nut shall be furnished for each size of pin for each structure. 45. Screw Threads. Screw threads shall make tight fits in the nuts, and shall be United States standard, except for diameters greater than If in., when they shall be made. with six threads per inch. 46. Annealing. Steel, except in minor details, which has been partially heated shall be properly annealed. 47. Steel Castings. All steel castings shall be annealed. 48. Welds. Welds in steel will not be allowed. 49. Bed Plates. Expansion bed plates shall be planed true and smooth. Cast wall plates shall i>e planed at top and bottom. The cut of the planing tool shall correspond with the direction of expansion. 60. Shipping Details. Pins, nuts, bolts, rivets, and other small details shall be boxed of crated. 61. Weight. The weight of every piece and box* shall be marked on it in plain figures. Curved framing, hoppers, bins, and other complicated work shall be assembled and fitted in the shop. 370 STEEL CONSTRUCTION \ Cast Iron. The ends of cast-iron columns and the tops of base plates and pedestals must be finished exactly at right angles to the vertical axis of the column. The thickness of metal in cast-iron columns shall be not less at any point than, that marked on the design drawings. The inside must be concentric with the outside. Shifting of the core more than inch will cause rejection. At least three holes shall be drilled in each column to test the thickness of metal. Fins, chaplets, and other irregularities shall be removed by chipping, leaving neatly-finished surfaces. No holes shall be filled with cement or other substance without permission from the Archi- tect. The best practice shall be followed in reference to the quality of sand, molding, and the stripping of molds from castings. Painting* The material shall be painted one coat of red lead paint at the shop and one coat of graphite paint after erection. The painting shall be done in accordance with paragraphs 52 to 58 of Schneider's Specifications. 5%. Shop Painting. Steelwork, before leaving the shop, shall be thor- oughly cleaned and given one good coating of pure linseed oil, or such paint as may be called for, well worked into all joints and open spaces. 53. In riveted work, the surfaces coming in contact shall be painted before being riveted together. 54' Pieces and parts which are not accessible for painting after erection shall have two coats of paint before leaving the shop. 55. Steelwork to be entirely embedded in concrete shall not be painted. 56. Painting shall be done only when the surface of the metal is perfectly dry. It. shall not b done in wet or freezing weather, unless protected under cover. 57. Machine-finished surfaces shall be coated with white lead and tallow before shipment, or before being put out into the open air. 58. Field Painting. After the structure is erected, the metal work shall be painted thoroughly and evenly with an additional coat of paint, mixed wi!h pure linseed oil, of such quality and color as may be selected, The field paint shall be of different color from the shop paint. Inspection and Testing. The inspection and testing will be done by the Architect or his representative. The contractor shall furnish the facilities for inspecting and testing and be governed by all of the provisions contained in paragraphs 59 to 64 of Schneider's Specifications. 59. The manufacturer shall furnish all facilities for inspecting and testing the weight, quality of material, and workmanship. He shall furnish a suitable STEEL CONSTRUCTION 371 testing machine for testing the specimens, as well as prepare the pieces for the machine, free of cost. 00. When an inspector is furnished by the purchaser, he shall have full it all times to all parts of the works where material under his inspection is manufactured. f>'l. The purchaser* shall be furnished with complete copies of mill orders, and no material shall bo rolled and no work done before he has been notified as to where the orders have boon placed, so that he wiay arrange for the inspection. 62. The purchaser shall also be furnished with complete shop plans, and must be notified well in advance of the start of the work in the shop, in order that he may have an inspector on hand to inspect the material and workmanship. 63. Complete copies of shipping invoices shall be furnished to the pur- chaser with each shipment. 64- If the inspector, through an oversight or otherwise, has accepted material or work which is defective or contrary to the specifications, this material, no matter in what stage of completion, may be rejected by the purchaser. Erection. Conditions at the Site. (To be changed to suit the case). The site of the building cannot be given over to the con- tractor for his exclusive use. He must conduct his work as directed by the Architect, and in harmony with the other contractors working on the building at the same time. There is no storage space on or adjacent to the building site so the contractor must deliver the material as needed for erection, except arrangements may be made from time to time for the tem- porary storage of small quantities of material. He shall provide elsewhere such storage space as he may need. Construction Equipment. The contractor shall furnish all equipment required for his operations. The equipment shall be ade- quate for its purpose, and must have ample capacity to carry on the work quickly and safely. The Architect shall have authority to order changes in equipment. if, in his judgment, it is not adequate or safe. Storing. Stored materials must be placed on skids and not on the ground. They must be piled and blocked up so that they will not become bent or otherwise injured. Unpainted material shall not be so stored in the open. The materials shall be handled with cranes or derricks as far as prac- ticable. They must not be dumped off of cars or wagons nor in any other way treated in a manner likely to cause injury. Erecting Steel and Iron Work. The structural steel and iron work shall be erected as rapidly as the progress of the other work (particularly foundations and walls) will permit. 372 STEEL CONSTRUCTION Setting Plates and Grouting. Base plates, bearing plates, and ends of girders which require to be grouted, shall be supported exactly at proper level by means of steel wedges. The grout will be furnished and poured by the mason contractor. - Plumbing, Leveling, Bracing. The structural steel and iron work shall be set accurately to the lines and levels established for the building, as shown on the drawings. Particular care shall be taken to have the work plumb and level before riveting. Necessary bracing shall be provided for this purpose, and for resisting stresses due to derricks and other erection equipment and erection operations. Elevator shafts shall be plumbed from top to bottom with piano wire and must be left perfectly plumb. Temporary Bolts. The members shall be connected tempor- arily with sufficient bolts to insure the safety of the structure until it is riveted. Not less than one-third the holes shall be bolted. Riveting. All field connections shall be riveted unless other- wise ordered. The riveting shall follow as closely as practicable after erection. The connecting members shall be drawn up tight with bolts before riveting. Rivets generally shall be driven with pneumatic hammers. The rivets must be of proper length to form full heads. Rivets must be tight, with full concentric heads. Defective rivets must be cut out and re-driven. No re-cupping or calking will be allowed. Permanent Bolts. When bolts are used for permanent connec- tions, washers shall be placed under the nuts, the nuts drawn tight, and the threads checked. In such cases, bolts must be used which are provided for that purpose, and not ordinary machine bolts. Connections to cast iron shall be bolted. Removal of Equipment and Rubbish. The contractor shall remove the construction equipment as rapidly as its service is com- pleted and shall remove all rubbish from day to day. Immediately after final acceptance of the work, the contractor shall remove all his equipment and property and shall remove all rubbish resulting from his operations. INDEX INDEX Angle collections 120 Angles - 29 B Beam _ - 75 restrained 75 simple 75 Beam box girders _ ___ __. 159 Beam design _ _ _. 76 deflection . __ __77, 80 flexure 77 modulus of elasticity 80 shear 77,79 Beam? anchors .. .. 134 beam design, theory of _ __ 76 bearings 130 classification _ 75 connection of beams to beams 120 angle connections ._ 120 special connections. ._ _ 124 connections of beams to columns. __ 124 combination connections 127 seat connections _ 124 web connections _ _ 126 construction details , 120 definitions _ 75 design of, practical illustration _ 309 details of construction 120 lateral support 112 load effects, calculation of_. 80 miscellaneous details __ 134 practical applications __ 113 resistance, calculation of 97 sections 76 separators 127 strength of, tables. 100-107 tie rods 129 Bearing _ __ __ 64 Bearing plates _ 130, 165 Bending moment 76 2 INDEX PAGE Bending moment diagram _ - 262 restrained beam 262 unit bracing 263 Bessemer process ._ . 13 Bethlehem columns 189, 196-209 tables - 196 Bolts 71 bolts in tension .j 72 machine bolts _ . . 72 turned bolts 72 Breaking load 47 C Cantilevers 1 18 Cast iron 51 Cast-iron columns 225 column sections. . 226 details of 232 method of design __ 226 tables 229 Cast-iron pedestals. 220, 3 1 9 Cement as a rust preventive 339 Center of gravity (C. G.) 35 Channel columns, tables 210-215 Channels . 28 Chemical composition of steel 45 Chimney supports 327 Chord stress in girders 135 Column bases 218, 319 cast-iron plates 220 flat plates 219 steel grillage 224 Column loads and their effects _ _ 173 computation of loads 173 concentric loads 174 eccentric loads 174, 315 illustration 175 Column sections 183, 226, 318 area. 181. distance from neutral axis to extreme fiber 181 moments of inertia 182 properties of 181 radius of gyration 182 Columns 1 73 Bethlehem 189 details of ; 216 brackets 218 connections . * 218 lacing 217 INDEX 3 PAGE Columns details of riveting . 217 splices 216 location of - 308 practical illustration 313 steel _ --. -. 173 strength of 179,196-215,229 formulas. 179, 189,229 unit stress 179, 189, 190. 192, 194 tables -. 196-209 wind bracing, stresses in 266 Connections 120 beams to beams 120 beams to column 124 girders to columns 166 D Deflection 77, 80, 109 Details of construction '. 120, 134, 166, 231, 261, 263 Dimensioning drawings _ 329 E Eccentric loads on columns 174, 227, 315 Elastic limit 47 Equilibrium . 3 Erection . 371 F Factor of safety 7 Fire, protection from 339 Fireproof floor construction 301 , 306 Fireproof materials _. _. 342 Fireproofing 294, 339 requirements, Chicago Building Ordinances 347 Floor construction, fireproof 301, 306 Floor framing, panel of . 113, 303, 305, 306 Friction .. .67 G Girders (see Riveted girders) 134 H H-sections _ _ 1 33 Hangers (see Tension members) 233 4 INDEX PAGE I I-beam with flange plates _. 158 I-beams __ _ 25 Inspection .__ _ 370 Inspection and tests __ ___ ... 48 J Joist 75, 81 L Lateral support 172 Lintel.. 75, 116 Load effects, calculation of _ 137 combined loads _ 89 concentrated loads _ _ 85 cantilever beams 86 simple beam 85 simple beams on two supports and projecting at both ends 86 typical loadings 93 beam with two or more loadings __ 96 moving loads 96 simple lo'ads _ 93 tabular data__ 93 uniformly distributed loads 80 cantilever beam 81 combination simple and cantilever beam 82 joists 81 Loads. 295, 351, 356 dead.... 1 295, 303, 304, 309 live J...297, 299, 314 M Manufacture of steel _._ 9 iron ore to pig iron _ 9 pig iron 10 process of smelting. _ 9 pig iron to steel . 11 acid open-hearth process 14 basic open-hearth process 16 bessemer process. 13 rolling the ingots 18 blooming ... 19 plate rolls 22 roughing and finishing rolls... _ 19 Manufacture of steel sections 44 Masonry 52 Masonry supports _- 327 INDEX 5 PAQB Material, quality of 42 miscellaneous sections 34 plates _ 32 tees -_ _ 31 Mill and stock orders _ _. 40 Miscellaneous properties _ _ 39 Moment of inertia (I) ., ..36, 140, 182 N 7 Neutral axis 181 O Open-hearth process 14 P Paint - ......335,363 Painting _ ..335, 370 Pig iron __ 10 Plate box girders.. ._- 160 Plate girder (see Riveted girder) _ 134 Plates.... - 32 Practical design of sixteen-story fireproof hotel ; 269 column pedestals _ 319 column specifications 313 dimensioning drawings 329 fireproof specifications _ 294 floor construction, type of _ 301 framing specifications * _ 306 loads. _ _ 295 miscellaneo is features __ _. 327 wind bracing __ 322 Price basis ... 40 Protection (see Rust, Painting, and Fireproofing) 333 Punching _ __ 62 Q Quality of materials _ 352 cast-iron 361 paint. 363 steel 359 R Radius of gyration (r) 38, 182, 228 Railway bridge grade steel _ _ 46 Reaming _ 62 Reduction of area 48 Reference books 5 6 INDEX PAGE Resistance, calculation of 97 deflection 109 deflection formulas 109 safe span length 110 lateral support 112 resisting moment 97 application of tables to concentrated loads 99 section modulus 98 tabular values for 98 shearing resistance _, 108 Resisting moment 76, 77, 97, 135 determination of 135 chord stress method 135 moment of inertia method 135 Restrained beam 75 Rivet tables 67 Rivets 52 bearing 64 driving 58 hand riveting 62 pneumatic hammer 61 riveting machines in shop 60 friction 67 function of 63 investigation of riveted joints 67 length of 73 ordinary sizes 52 punching and reaming 62 rivet heads 56 button head 57 flattened and countersunk head 57 manufacture 57 shear 65 spacing 53 clearance 55 edge distance 55 gage 54 pitch 54 tension 67 Riveted girder J 134 beam box girder 159 crane girder .__ 164 design, tKeory of 135 girder supporting a column 162 I-beam with flange plates 158 plate box girder 160 plate girder .- 138 plate girder lintel 164 practical applications, .._ ^ _ - 162 INDEX 7 I'AOB Riveted girder roof girder 164 unsymmetrical sections 160 Riveted girder design 135 depth 138 economy 138 flange section 141 width of flange plates. 143 with flange plates 142 without flange plates 141 length of flange plates _ _ _ 144 graphical solution for concentrated loads 145 graphical solution for uniformly distributed loads 145 moment of inertia required ___ 140 rivets connecting flange angles to web _.. r 149 number of rivets 149 rivet spacing computed from web bearing 152 rivet spacing in flanges 150 riveting for cover plates 150 spacing when load transmitted through flange rivets into web 152 tables and diagrams 154 thickness of web 139 shearing value of web plates 140 web stiffeners 146 intermediate stiffeners 148 stiffeners at loaded points 146 Riveted girder details. 165 connections to columns 166 bracket connection _ 167 web angle connection 166 end bearings 165 lateral support 172 splices 168 Riveted joints 67 Riveters 59 Riveting in girders 149 Rolling steel 18 Rust 333 cement as a preventive 339 paint as a preventive 335 S Section modulus (QJ - 39 Section, steel adaptability and use _ 23 angles. _ 29 channels 28 H r section 33 8 INDEX PAGE Section, steel adaptability and use I-beams 25 Bethlehem sections 26 Carnegie sections 26 efficiency of minimum sections 27 special sections , 25 standard sections 25 Shear 65, 77, 79, 108 Simple beam 75, 81, 85 Smelting 9 Span 75 Spandrel = 75 Spandrel girders, practical illustration 310, 323, 328 Specifications 349 example of _ 353 general characteristics 350 purpose of 349 details of construction 363 erection 371 example of 353 general conditions 353 inspection and testing 370 loads. 356 outline 350 painting 370 quality of materials '_ 359 unit stresses 357 workmanship 368 Standard specifications 350 bending requirements 44 chemical analysis 43 elongation and fracture 44 process of manufacture 43 range of application 43 rivet steel strength 44 tensile strength 43 Strength of columns (see Tables) 189 Structural steel. _ _ 9 manufacture of _. 9 maximum allowable stresses on __ 51 procedure in furnishing 8 reliability of ___ 42 T Tables beams, strength of _ 100-107 gages for angles _ __ 54 moments of inertia of I-beams with holes in flanges _ _ 159 safe loads for round cast-iron columns 229 INDEX 9 PAOB Tables safe loads on Bethlehem columns 196-209 safe loads on channel columns 210-215 typical loadings, reactions and bending moments for 94-95 unit stress in compression 194 unit stress in compression in columns .190-193 Tables, use of - 194 Tank support 118 Tees - 31 Tension members 233 connection details 237 definition and theory 233 axial tension 233 tension due to eccentricity 234 not area 236 sections 235 Trsting . 370 U Unit stresses.. 50, 51, 351, 357 columns 179, 190, 192 tension _. 234 zees - 30 w Weights of materials 295 Weight, variation in 41 Wind ....322,329 Wind bracing 239, 322 combined wind and gravity stresses in girders 262 framework, systems of rectangular framework 246 axial stresses 253 triangular framework 243 horizontal pressures 239, 322 moment diagram for a restrained beam 262 paths of stress _ 240 wind bracing girders, design of _ .255, 323 end connections for I-beam girders .261, 323 end connections for riveted girders 255, 324 wind stresses on columns, effect of 266, 322, 326 Workmanship 368 Y Yield point 47 Yield point and factor of safety. 48 Zees 30 TIP OAN PERIOD 1 2 3 I 5 6 ALL BOOKS MAY BE RECALLED AFTER 7 DAYS DUE AS STAMPED BELOW DUE NRLF MAR 2 6 1985 -> -N j UNIVERSITY OF CALIFORNIA, BERKELEY : ORM NO. DDO, 5m, 12/80 BERKELEY, CA 94720 YB, 10863 GENERAL LIBRARY -U.C. BERKELEY TH THE UNIVERSITY OF CALIFORNIA LIBRARY