T H UC-NRLF B 3 ESS D3fl GODFREY BUILDINGS STEEL AND REINFORCED CONCRETE IN BUILDINGS -BY- EDWARD GODFREY, M. Am. Soc. C. E. STRUCTURAL ENGINEER FOR ROBERT IA. MVJNT & OO. CHICAGO NEW YORK PITTSBURG LONDON AUTHOR OF- Structural Engineering Book I, TABLES I Structural Engineering Book II, CONCRETE Structural Engineering Book III, STEEL DESIGNING (In Manuscript) A MINORITY REPORT ON THE QUEBEC "BRIDGE DISASTER (Pamphlet) SOME MOQTED QUESTIONS IN REINFORCED CONCRETE DESIGN (Paper Betore Am. Soc. C, E.) PRICE $2.00 - Copyright 191 1 by EDWARD GODFREY CONTENTS INTRODUCTION ................................ 1 CHAPTER I. FOUNDATIONS ....................... 3 CHAPTER II. FOOTINGS .......................... 7 CHAPTER III. COLUMN BASES ................... 14 CHAPTER IV. COLUMNS AND OTHER COMPRESSION MEMBERS ....................... 16 WOODEN COLUMNS ................ 17 CAST IRON COLUMNS ............... 20 STEEL COLUMNS ................... 25 REINFORCED CONCRETE COLUMNS ____ 30 COLUMN TABLES .................. 34-46 CHAPTER V. LINTELS ................. .......... 47 CHAPTER VI. BEAMS ........................... 49 WOODEN BEAMS ................... 49 CAST IRON BEAMS ................. 50 STEEL BEAMS ..................... 51 STEEL BEAM TABLES ............... 58-60 REINFORCED CONCRETE BEAMS ....... 61 REINFORCED CONCRETE BEAM TABLES.69-74 CHAPTER VII. GIRDERS .......................... 75 PLATE GIRDERS .................... 80 PLATE GIRDER TABLES .............. 81-82 Box GIRDER TABLE ................. 90 CHAPTER VIII. TRUSSES ......... .' .............. 93 TRUSS DIAGRAMS ................ 98-112 TENSION MEMBERS ................ 113 COMPRESSION MEMBERS ............ 1 16 TRUSS MEMBERS IN BENDING ....... 116 CHAPTER IX. FLOOR ARCHES AND ' SLABS .......... 121 REINFORCED CONCRETE SLABS ........ 123 CHAPTER X. STRUCTURAL DETAILS ............... 127 RIVETS ............................ 127 BOLTS ............................ 128 SPLICES ........................... 130 END CONNECTIONS OF BEAMS ....... 131 END CONNECTIONS OF GIRDERS ____ .. 132 DETAILS OF TIMBER TRUSSES ........ 134 CHAPTER XI. ESTIMATING LOADS . 140 INTRODUCJICN. The purpose of this book is to supply a want in work where designing is done on a small scale that does not justify the employment of an engineer. A large amount of this sort of designing is done, and very much of it is faulty. While it may be to the interest of the author and his class to discourage designing on the part of men whose training does not fit them to do it more intelli- gently, the fact remains that the work is done and will be done, and done very often by men who do not un- derstand much about the principles of proper design. The aim in writing this book is to lay down the princi- ples of correct and consistent design as applied to build- ings, and to give simple rules and tables to be used in designing. Architects' designs for structural work of any magni- tude should, of course, be checked by a structural en- gineer. The fee for this is less than for making an orig- inal design and may be included in the price of inspec- tion. The checking of the details is another matter that can be best handled by a structural engineer : this can also be covered in a contract for the inspection of the steel work. It is the author's intention, while indicating what may be safely done by one not thoroughly conversant with structural design, to indicate also, by the contents of the book, the line beyond which such a one ventures at his peril and to the jeopardy of life and property. Bracing of buildings, while it is a matter of utmost importance, has been omitted from this book, for the reason that it is an engineering problem and one that can scarcely be standardized. In the majority of build- ings bracing or stiffness is supplied by the walls. High or narrow buildings should be braced. The system of bracing is a ma-ter requiring special consideration, a matter for judgment and calculation and not for standards. In the actual proportioning of a building generally the smaller details are designed first, that is, the floor sys- tem is decided upon first, then the floor beams are laid out, and their sizes as well as those of the girders are determined. Then the sections of the columns are worked out, and when the load on the base of a column is known, the pedestal and foundation may be propor- tioned. In this book the reverse order will be adopted in treating these parts, beginning with the foundation and going up and out toward the smaller details. While this book is designed to be of special use to architects who have occasion to design in steel and re- inforced concrete, it is believed that it will also be found useful to students and beginners as a preliminary to the author's more complete work on Steel Designing. There is also much in it that should be found convenient to structural designers in all lines. An almost necessary accompaniment to this book is a book giving the dimensions and properties of steel sec- tions, such as the Carnegie Pocket Companion or God- frey's Tables. CHAPTER I. Foundations. The area of a foundation in contact with the soil will depend upon the bearing power of the soil. This bearing power is best determined by experience rather than ex- periment, though in some cases experiments are re- sorted to. These are in the nature of a test load applied on a certain area for a given length of time. There are many features that must be taken into consideration in designing a foundation. The bearing power of a soil depends not only upon the nature of the soil itself, but also upon the degree of confinement of the soil. The degree of confinement will be gaged largely by the depth below the surface to which the trench or excavation is made. A clay that might stand safely two tons per square foot at six feet below the surface might heave and allow the same load to sink, if the trench is made only a foot deep. Moisture in a soil during construction has been the cause of disastrous settlement. Hence drain- age at such a time is of prime importance. The base- ment floor of a building during construction is subject to repeated wetting, and may, if proper care is not taken, be the recipient of drainage from other ground. After completion of a structure the basement will be protected from moisture due to rains. If ground water is not naturally present, the soil will sustain much more load. Another feature that should, if possible, be taken into consideration in planning a foundation is the possibility of excavation in close proximity to the foundation. If excavation is made near a foundation carrying a heavy load, and if that excavation extends to or below the level of the foundation in question, the soil may flow and allow large settlement of the structure. Thus, excavating for a neighboring building or a vault or subway may ieopardize the safety of a building that otherwise is quite safe. Clay soils flow readily and are compressible. Sandy soils are not very compressible, but they will flow laterally, especially when wet, if not confined. Gravel is not com- pressible and is not so apt to flow. Mixtures of these in varying proportions combine the properties of each. Some clays, if kept perfectly dry, will bear heavy loads, but if wet, become like putty. Hence assurance that clay is dry or else confined is of great importance. A good method of confining the soil under a structure to prevent flow is to drive sheet piling around it, thus holding the soil in a sort of box. As far as practicable, where the soil is of a uniform carrying capacity, the pressure per square foot should be constant for the entire structure. Some settlement is to be expected, and it is important that this settlement be uniform over the entire foundation. When soils of dif- ferent compressibilities are met with in the same building, such as clay and sand, the more compressible soil should have the larger footings. The pressures allowed, by the New York Building Code, per square foot for various soils are as follows : Soft clay, one ton ;, ordinary clay and sand together, in layers, wet and springy, two tons; loam, clay or fine sand, firm and dry, three tons; very firm, coarse sand, stiff gravel or hard clay, four tons. In Baker's Masonry Construction the following are given as the safe bearing power of soils in tons per square foot: Quicksand, alluvial soils, etc., 0.5 to 1 ; sand, clean dry, 2 to 4 ; sand, compact and well cemented, 4 to 6; gravel and coarse sand, well cemented, 8 to 10; clay, soft, 1 to 2; clay in thick beds, moderately dry, 2 to 4; clay in thick beds, always dry, 4 to 6; rock, from 5 up. This lower value is for rock equal to poor brick masonry. In case of hard rock the area of foun- dation may sometimes be determined by the strength of the foundation rather than that of the rock. Thus, if concrete is used in a pier with a bearing power of 15 tons per sq. ft., this sets the limit, though the rock may be capable of carrying a greater load. Sometimes the compressibility of the soil is such that it is impracticable to give the footing the spread necessary for the load to be carried. Piles may then be driven and the load supported on these. Piles are sometimes driven to hard bottom and sometimes to a depth that results in a cer- tain degree of refusal, depending in such cases upon fric- tion of their sides for their supporting power. The usual loads allowed on wooden piles -are 10 to 15 tons per pile. Sometimes as much as 20 tons is allowed on a pile. Piles supported by friction alone should not be loaded so heavily as those that are driven to hard bottom. Piles are gener- ally kept 2^/2 to 3 feet apart as a minimum. Wooden piles should be used only where they will be always wet, as they will rot if alternately wet and dry or if the soil is not constantly water soaked. In this case too, neighboring excavation should be anticipated if pos- sible. Ground water level may be lowered by drainage subsequently made. Thus, in such locations as New Or- leans, ground water level has been lowered by the con- struction of a sewer system. Concrete piles, when properly made, are more reliable and durable than wooden piles and are capable of tak- ing greater loads. Fifteen to twenty tons per square foot of sectional area may safely be allowed on concrete piles. The higher unit loads are for piles of larger diameter, as slender piles would act as columns to some extent. The pressure on the footing for a wall is found by tak- ing the load per running foot carried by that wall. This includes: the weight of the wall itself, making deduc- tions for windows (say one-quarter or one-third of the area, depending on the circumstances;) the weight of the floors and roof bearing on the wall ; the live or snow loads on floors and roofs supported on the wall. From this load per running foot of the wall and the allowed pressure per square foot the width of the footing is determined. Footings under columns have the load of the column to carry and the load of the footing itself. The area is de- termined by the allowed pressure on the soil. Concrete walls and footings are very much superior to rubble, because the monolithic character enables the former to settle uniformly. Settlement in a building is not of seri- ous consequence, except when it is unequal settlement, and monolithic construction greatly reduces the possibilities of unequal settlement. To effect uniform settlement, as stated, the unit pres- sure on the entire foundation should be made as near uni- form as possible. Strictly, this cannot be done in ordi- nary cases because of the unknown and varying amount of the live load, also because of the fact that some of the walls or columns will have a greater or less proportion of their load as live load. Thus, the walls and exterior col- umns will have a more steady load because they take less of the floor load than the interior columns. One way to approximate equality of soil pressure is to make the areas of footings proportional to loads which include one-half or less of the total live load to be carried. This would necessitate somewhat greater area under the parts tak- ing the smaller percentage of live load than the allowed soil pressure for its total load would demand. When a structure rests on piles, uniformity of pressure is effected by spacing the piles to suit the intensity of the load carried. For example, if at one part of a wall the load carried is four tons per foot on piles that are good for 12 tons each, and in another part the load carried is three tons per foot, the spacing of piles should be three feet and four feet respectively. In large piers carrying unsymmetrical loads the spacing of the piles should be such that the center of gravity of the piles will coincide with the center of gravity of the load. For a fuller discussion of foundation methods and de- signing the reader is referred to the author's book, Con- crete. CHAPTER II. Footings. The footings of walls and columns must of necessity have greater area than the walls and columns themselves. This spread must be effected in ways that will preserve the structural strength and distribute the load uniformly, or that will distribute the load so that the allowed pressure on the soil is not exceeded. The simplest way to spread a wall footing is to in- crease the thickness of the wall by one or more steps at the base. In a brick or rubble wall the height of the step should be about four times the projection ; or if the sides of the wall slope, the spread on either side should not be more than about one-quarter of the vertical height. The same relation should be observed in column footings of brick or rubble. In a concrete wall or pier the projection or spread should be proportioned according to the allowed pressure on the soil by the following formula : sp*=h* (1) where J is the pressure in tons per sq. ft. allowed on the soil, p is the projection of the wall or pier and h is the height in which the step or slope p occurs. For derivation of these relations, as well as those that follow, bearing on reinforced concrete footings, see the author's book Concrete. A wall footing may be made of reinforced concrete as shown in Fig. 1, with the following relations: fc.35 p s />=50 d .r=9 d (2) (3) (4) where s is the allowed pressure on the soil in tons per sq. ft, and d is the diameter in inches of square reinforcing rods. The projection p will be found from the load per running foot on the wall and the allowed soil pressure. Then from equations (2), (3), and (4) the other dimen- sions may be found. Assuming p=4 ft. and s\ l / 2 tons, h will be 2 ft. \V 2 in. The reinforcing rods would be one inch square, spaced 9 in. apart. This sort of footing is appropriate chiefly where the soil is of low bearing power, since the height h required for shear where heavy pressures are considered will usu- ally make reinforcement uneconomical, as a somewhat greater height will make reinforcement unnecessary. Any footings in reinforced concrete must be made of sloppy concrete, as no other will grip and protect the steel. Dry or rammed concrete is quite unsuitable for reinforced work. Fig. 2. Column footings may be made in plain concrete as shown in Fig. 2 with either stepped or sloping sides. The rela- tion between p and h may be the same as given in Equa- tion (1). fig.3. A reinforced concrete footing should be made as shown in Fig. 3. All rods should pass under the upper plinth. There are designs in which the rods are space' equally out to the edges of the rectangle. This is poor jesign, as the rods near the outer edges can do little or nothing. la this footing, with s as before : h=.5 Equations (3) and (4) apply as in the wall footing. (5) When the outside line of a wall is the property line, of course ill offsets must be made on the inside. If these off- sets are not large, the pressure on the soil may be con- sidered as uniformly distributed. When the wall is not a long one, or where there are cross walls, a projection of considerable width could be made without the necessity of assuming eccentric load on the foundation. If the projection of a wall is wide as in the L-shaped wall shown in Fig. 5, unequal pressure on the soil must be considered. The resultant pressure must fall within the middle third of the base. The size and spacing of rods for this projection, as well as the width and depth of 'the pro- 9 Fig. 4. Fiq.5. Ficj.e. jection, may be of the same dimensions as those given under Fig. 1 for symmetrical footings. The rods should be given an easy curve and not a sharp bend. The radius of the curve should be about 20 times the diameter of the rod. Rods should run up into the wall as indicated for anchorage. Anchorage for a rod requires embedment in concrete for a distance equal to 50 times the diameter of the rod. The projection p in the wall, shown in Fig. 5, must be less than twice the thickness of the wall, that is, the re- sultant pressure must come under the wall itself, so as to prevent, or at least minimize, bending in the wall itself. Wall footings are sometimes made by using steel beams or rails as needle beams, as indicated in Fig. 6. Rails are not economical for this purpose, because they are much heavier for the same strength than I-beams. The size of I-beams necessary for any given case is found as follows: The upward pressure on the soil is considered as a uni- form load on the beam. The beam is a cantilever with an overhang or a span /. This distance / is a few inches more than the projection p, say 2 to 6 in., depending on the mag- nitude of the footing. The load that a beam can sustain as a cantilever of a span / is just one-quarter as much as that which it can sustain as a simple beam of the same span. Turning to Chapter VI, Table II, it is seen that the capacity of an I-beam of any span is found by divid- ing the quantity Q in the table by the length of that span in 10 feet. This capacity is in tons of total load carried by the beam as a simple span. It must be divided by four to find the safe load that the beam can take as a cantilever. If the operation be reversed, we would multiply the load on the cantilever by four and then by / to find the value of Q. For example, if / is four feet and the upward pressure of the soil is two tons per sq. ft., we find Q to be 4x2x4x4=128. This is the value per running foot of the wall. As Q, for a 10" I 25 Ib. is 130, we could use a 10" beam every foot. These needle beams must be completely surrounded with concrete. Grillages for column footings are often made as shown in Fig. 7. In this grillage the load of the soil is first taken by the lower tier of beams to the upper tier; it is then de- livered by the upper tier to the column base. The span of the lower tier is the distance from the center of outer beam of the upper tier to the edge of the footing. The span of the upper tier is the distance from the edge of the footing to a point a few inches within the column base, as indicated. Fig. 7 $-* 1 C02 *& Fi s .8. 11 As an example, suppose it is desired to proportion the beams for a column footing in which w is 10 ft., w\ is 8 ft., / is 3 ft., and /i is 4 ft, the upward pressure of the soil being 4 tons per sq. ft. The load taken by the lower tier of beams as a cantilever of span / is 10x3x4=120 tons. Multiplying this by 4 and by the span / we have for the aggregate value of Q for the set of beams 1,440. We could use 5-15" 42-lb. beams, for which Q is 1,571. For the upper tier of beams the load carried is Wix/i, as the lower beams deliver this area of load into the upper beams. Q for this set of beams is then 8x4x4x4x4=2048. We could use 4-20" 65-lb. beams, for which Q is 2,263.6. These beams would have separators with bolts' running through the set. Each would have about three lines of these separators. Very often in wall columns only one set of beams will be used under the column base. The size of these will be found in the same way as for the grillage beams. Sometimes, on account of keeping the column footing within property lines, two columns are built on the same grillage as indicated in Fig. 8. Here the four beams of the upper tier take the cantilever load on the area Wix/i, and are designed as before. The lower beams carry the up- ward pressure on the area tc^x/o, but they act as simple b^p.'ns and not as cantilevers. The spr.n is the distance center to center of columns, for there is but little balanc- ing load on the other side of the columns. If w 2 is 6 ft. and lz is 18 ft, with an upward pressure of the soil of 3 tons per sq. ft., Q=18x6x3xl8=5,832. (Note that we do not multiply by 4, as the beams act as a simple span and not a cantilever.) We could use 6-24-in. 80-lb. beams, for which Q is 5,568. This is about 5 per cent. shy. Beams weighing 90 Ibs. per foot, would meet the requirements. If either of the columns of Fig. 8 carried a heavier load than the other, the beams could be placed fan-shaped with the center of gravity of the footing corresponding with that of the combined load. 12 Fi 9 .9. Another way to take care of the footing of a wall col- umn is illustrated in Fig. 9. Here a lower tier of beams is provided for each column, but the upper beams have the added office to perform of carrying the load of the wall column back to the middle of its grillage. This load is carried on the beams as a cantilever with an overhang I 2. The load is the concentrated load of the column. A beam acting as a cantilever of a given span supporting a load at its outer end will sustain only one-eighth as much total load as the same beam acting as a simple span with the load uniformly distributed. Hence, to find Q, we would multiply the load by the span and by 8. For example, sup- pose / 2=4 ft. and the column load is 70 tons. Q=70x4x- 8=2,240. This would require 3-20 in. 80-lb. beams, for which Q is 2,347.2. Where the depth permits of a deep girder being used, a plate girder or a box girder is more economical than beams for heavy column loads. A column may be riveted between the webs of a box girder, which acts as a cantilever to carry tfie load to a grillage, located within the property line. 13 CHAPTER III. Column Bases. Usually the foot of a column rests on a separate cast base. The reason for this is because the cast base can be set up on the foundation and leveled and brought to a proper elevation much more easily than a column. It can also be more readily located, as a mark can be made at the center of the base on the planed top of the same. The cast base is invariably planed on top. Sometimes it is also planed on the bottom ; but more commonly the bottom is left as cast, and the base is set in cement mortar or is shimmed up to its proper level and grouted through holes in the bottom. In the design of a cast base the first consideration is to have area enough in contact with the masonry so that the pressure on the same will not be excessive. A pressure of 300 Ibs. per sq. in. may be allowed on concrete. This will give a basis for finding the area of the base. Thus, a load on the column of 150,000 Ibs. would require a base of 500 sq. ins. A round cast iron column could have a base 26 ins. in diameter, or a steel column could have a square base 23 ins. in diameter. 14 The usual design of a base for a cast iron column has aH upper flange to which the column is bolted and a lower plate resting on the masonry. This plate, as in all other masonry bearing plates, should have no unstiffened pro- jection greater than about twice the thickness of metal in cast iron or four times the thickness in steel. That is, p in Fig. 1, should not exceed 2 t. When there are stiffening ribs, as in Fig. 2, the spacing of ribs or the thickness of the base plate should be govern- ed by the relation of ^ to t. In cast iron s should not ex- ceed about four times t, and in steel s should not exceed about eight times /. The relation of a to b, to give the proper slope to the rib, depends upon the thickness of rib and base plate. If a be made equal to b in a cast-iron base, the stresses will generally not be excessive. In a cast-steel base a may be about 1.5 times as great as b without giving excessive stresses. Usually, however, the value of a is made rela- tively less than these ratios would show. Another feature of a cast base that should receive at- tention is the location and shape of the vertical webs under the shaft of the column. If the column is of an I shape, these webs should be approximately the esame shape, as shown in Fig. 2. A column approximately square in shape should have the webs of the base formed in a square box. It is a good plan to have a good sized hole in the bottom of this box for grouting and a number of other holes for the escape of air. In large bases holes are usually left for grouting. If, as intimated in the last paragraph, a vertical opening be left at the middle of the base, this can be filled with grout to act as a sink head to give pressure to the grout. If the grout be allowed to rise in other openings in the base, a better filling of the space is assured than if grout is poured in several holes at once. The latter method allows en- trapped air to form pockets under the base. Column bases in buildings are usually laid on the con- crete footing without being anchored or bolted thereto. 15 CHAPTER IV, Columns and Other Compression Members-. Building columns may be of wood, cast iron, steel or re- inforced concrete. After the following discussion on the method of finding the load carried by a column, the meth- ods of designing the columns of these several dasses will be taken up. The load taken by a column at any given floor or roof level would of course be the sum of the loads delivered to it by the beams, girders or trusses connecting to the column at that level. But to find the reactions of all of these would generally be very tedious work. The usual method is to find the area of floor and the length of wall tributary to the column and from suitable units for dead and live load to calculate the load delivered at each floor level. The load per square foot of the floor construction must include floor covering, sleepers, filling, arches or slabs, an allowance for beams, and an allowance for girders. The allowance for beams is a load per sq. ft. that will cver the weight of the beams. Thus, if 25-pound beams are spaced 5 ft. apart, this allowance is 5 Ibs. If girders, weighing 45 Ibs. per ft, are spaced 15 ft. apart, 3 Ibs. would be allowed for the girders. The area tributary to a column is the surface of floor that the column carries. It is usu- ally a rectangle bounded by lines midway between this column and the next in each of the four directions (or midway between the column and the wall). The area for live or superimposed load is the same as for dead load. Ordinary partitions are usually considered as covered by the live load allowance. However, it is well to make an allowance, of say 5 Ibs. per sq. ft. in the dead load, to cover the weight of partitions. Extra heavy partitions should be estimated. Any interior brick walls should be allowed for by finding the reactions of the beams supporting the same. When the walls are carried by the columns, the full weight of wall may be estimated and the windows de- ducted; or, if the window openings are fairly regular, an estimate may be made of the proportion of solid wall, the load on the column being calculated from this. Of course each column will tarry a length cvf wall equal to half the sum of the distances to the next adjacent columns, and a height equal to that to the next wall beam above or to top of wall. Ordinary brick walls weigh about 10 Ibs. per sq. ft. for each inch in thickness. Stone walls weigh about 12 or 13 Ibs. per sq. ft. for each inch in thickness. Where possible, columns should be symmetrically loaded, as unsymmetrical loads produce bending moments in the column, and these are seldom provided for in proportion- ing the section of the column. In interior columns balance of the loads is usually easily accomplished. In wall col- umns a practical balance can be effected by attaching the wall beams to the outer side of the column and the floor beams or girders to the inner side. The most economical and satisfactory method of offsetting the effect of a heavy eccentric load on a column is to make a deep riveted con- nection of the girder to the column. This puts the bend- ing stress into the girder that would otherwise have to be taken by the column, and the girder is generally amply able to carry the bending stress. The riveted connection may be for the full depth of the girder, or it may be made greater than the depth by use of gusset plates or corner brackets. In a rolled beam -top and bottom riveted flange connections aid greatly in overcoming bending due to ec- centric loads. Wooden Columns, The allowed load, in direct compres- sion on a wooden column is very simply found. It depends upon the ratio of the free height of the column to the least width "This raticT'bf free' or unsupported height to width must b^'' clearly undfe^tood, however. In a simple post without* traces from tee to top thetfree height is the full length of the post. In posts having knee braces or struts connecting to some part of the building capable of offer- ing ample resistance, the free height is the distance from the base to the point where the braces connect. If the braces hold the column, in only one direction, as in Fig. 1, there will be two ratios to consider, namely: l/d and I' /d' . The smaller of these two ratios will be the governing factor in determining the strength of the col- umn. It is to be observed that the braces must be capable of holding the column in line. Two equally strong or equally weak columns braced together by a horizontal brace would not be shortened in their effective length by such a brace. When the ratio of length to width of a wooden column is known the allowed load per square inch is as follows : For yellow pine or oak 1,00018 l/d For white pine 80015 l/d In the following table the allowed load per sq. in. is shown for three different ratios. TABLE I. STRESSES PER SQ. IN. ALLOWED ON WOODEN POSTS. Yellow,Pine or Ratio White Oak White Pine 30 460 350 20 640 500 10 820 650 18 For example, suppose an 8x8 yellow pine post is 10 feet long. The length is 15 times the width and the unit com- pression allowed is 730 Ibs. per sq. in. This post would carry safely 730x64=46,720 Ibs. A white pine post 6x8 in section and eight feet long would have a ratio of length to least width of 16. A load of 560 Ibs. per sq. in. could be allowed, or a total load of 26,880 Ibs. Generally, wooden posts should not be less in width than Ir30 of the length. The base of a wooden post or column is sometimes made of cast iron. A socket is cast in the base into which the post fits. The spread of this cast base must be such as to keep the pressure on the masonry within the allowed limits. Thus, the 8x8 post of the last paragraph with its load of 46,720 Ibs., if 250 Ibs. per sq. in. be allowed on the masonry, would require -37 sq. in. of base. A base 14 ins. sq. would do for this column. As the projection around the column is 3 ins. the thickness should be half of this or \ l /2 in. Cast-iron caps are very often used at the tops of col- umns to act as splices and as seats for girders. Steel plates or angles would be very much better, as cast iron is brittle and liable to be broken by the concentration of the beam load on the edge of the bracket. Fig. 2 shows a suggested detail. Fia. 2 19 Cast-iron Columns. The allowed load in direct com- pression on a cast-iron column is found in a similar man- ner to that on a wooden column. It is true that there are many formulas for the strength of a cast-iron column, but they are for the most part highly theoretical and their al- lowed unit loads are not borne out by tests. A few simple rules for designing and a simple formula for the allowed compression are all that a material such as cast iron de- mands. Fig. 3 shows the common sections used in cast-iron col' umns. The round and square shapes are generally used for interior or exposed columns. The oblong column may be used in a wall or between windows. The H-shaped column may also be used between windows. The thickness t should ordinarily be not less than about Y 2 in. In the H-shaped column the thickness / should not be less than about one-fifth of x. The allowed unit stress on cast-iron columns should not exceed 7,600-40 l/d where / is the unsupported length of the column and d is the least width. In Fig. 3, d is indicated. It will be the outside diameter of a round or square column. In the other shapes it will be di or d 2 , depending upon the un- supported length of the column for these two directions. If the column is supported in one direction and not sup- ported in the other, there will be two ratios to consider, namely: h/di and h/d z ; /, being the free length cor- responding to di, etc. The smaller of these two ratios will determine the unit load to use on the column. 20 From the foregoing unit stress the allowed load per sq. in. on cast-iron columns may be found for various ratios and tabulated as follows: TABLE IT. STRESSES PER SQ. IN. ALLOWED ON CAST-IRON POSTS. Ratio Allowed Stress Ratio Allowed Stress 40 30 6000 6400 20 10 6800 7200 Generally, cast-iron columns should not be less in width than 1-40 of the length. For convenience in finding the areas of hollow square and circular columns, the following table is given. The column area will of course be the difference between the inner and the outer circle or square. When the outside di- ameter and the desired area are known, the area of the inner circle or square will be the difference between that of the outer circle or square and the required area. From this the inner diameter can be found in the table. TABLE III. Areas of Squares and Circles, Area Area Area Area | Area Area _ Dia. |Ro'nd |Sq'art Dia. | Round | Square Dia. | Round Square 3 7.069| 9.000 7 38.485 49.000 11 1 95.0331121.000 8.296 10.563 41.283 52.563 11J4J 99.402J126.563 3 l /2 9.621 12.250 7 1 /* 44.179| 56.250 11/4 132.250 324 11. 045| 14. 063 734 47.1731 60.063 1134|108.434 138.063 4 12.566 16.000 8 50.2661 64.000 12 1113.097 144.000 4% 14.186 18.063 8/4 53.4561 68.063 12i4|117.859 150.063 4*/2 15.904|20.250 S l /2 56.745| 72.250 12J4 122.718 156.250 17.721|22.563 834 60.1321 76.563 1234)127.676 162.563 5 4 19.635125.000 9 63.617 81.000 13 |132. 732|169. 000 5J4i21.648i27.563 9J4 67.201 1 85.563 13J4I137.886J175.563 5^123.758 30.250 9/2 70.8821 90.250 1354 143439 182.250 524 25.967 [33.063 74.662 95.063 1334 |148.489| 189. 063 6 28.274 36.000 10 I 78.540 1 100. 000 14 153.9381 196.000 6J4i30.680i 39.063 10J4I 82.516|105.063 14/4 159.4851203.063 6^|33.183|42.250 lO^j 86.590illO.250 14J4|165. 1301210.250 634135.785145.563 10341 90.7631115.563 14341170.8731217.563 Cast-iron columns are not to be recommended for build- ings of mere than about three or four stories in height. They should not be used in any case in a building whose lateral stability depends in any wise on the columns, such as one whose exterior walls are carried by the metal frame. Cast iron lacks toughness and should be used only in simple compression in columns and in situations where there is little or no bending stress. Given an example where the wall between two buildings is to be removed and replaced by cast-iron columns. As- sume the width of each building to be 20 feet; the height of the first story 14 ft.; three stories above this of 11 ft. each;, thickness of wall 13 in.; total weight for floors 150 Ibs. per sq. ft. ; total weight for roof 120 Ibs. per sq. ft. ; spacing of columns 18 ft. Each column will carry the following load: 18 ft. of wall, 33 ft. high =18x33x130= 77,220 20x18 ft. of roof, at 120 =20x18x120= 43,200 3 floors, 360 sq. ft. each, at 150 =3x360x150=162,000 282,420 Assume a round section of column 12 ins. in outside di- ameter. The ratio l/r is 14/1 or 14. The allowed load per sq. in. is 7,040 Ibs. The area required is 40 sq. ins. A circle 12 ins. in diameter has an area of 113 sq. ins. This leaves 73 sq. ins. as the area of the inner circle, or say a 9.5-in. circle. This gives a thickness of metal of \ l /4 in. At the top of this column there will, of course, be pairs of I beams or a box girder to carry the load of the wall and the floors above. These beams would not have to be designed to carry all of this load as uniformly distributed, because the rigidity of the solid wall wo'jld allow much of it to be carried by the wall directly to the columns. Of the 141 tons on a pair of beams of a span of 18 ft, we may assume 100 tons as a uniform load on a pair of beams. The value of Q in the table of the capacity of beams is then 100x18=1,800. Two 24-in. 80-lb. beams would bo used. These have a combined value of Q equal to 1,856. The base of this column should not be made to rest di- rectly on the foundation wall, but should have distributing beams so that the pressure on the wall will not be exces- sive. If two beams be used, each 10 ft. in length, the load per foot on the pair of beams will be 141-f-10 or 14.1 tons per ft. The beams will have a cantilever span of about 4.5 ft. Each I beam will have a load on this cantilever of 7.05x4.5=31.7 tons. For the value Q of the table this is to be multiplied by 4 and by the span 4.5, or Q =3 1.7x4x4. 5- =571. There will then be required 2-15" 80-lb. beams. The area of the flanges of these beams in bearing on the wall is 2x6.4x120=1,536 sq. ins. This is a pressure on the wall of 282,420^-1,536=184 Ibs. per sq. in. The wall should have a concrete or a cement mortar finish in which to bed the beams. Fig. -4-. Splices. Cast-iron columns are generally spliced by four or more bolts through flanges. The flanges are made of about the same thickness as the shell of the column. The splice is made about at the floor level. The flanges should be about 2 l / 2 or 3 inches wide to allow space for bolt heads. The bolr. holes should be drilled and not cored. The enda of columns should, of course, be planed true. Where a change in section of cast-iron columns occurs, provision must be made for carrying the load from the up- per to the lower section. This may be done, as in Fig. 5, by making extra heavy flanges, stiffened with ribs, on the upper column. Generally, the shaft of a cast-iron colunm, should be uni- form from end to end of the column. If the column is flared out for an ornamental head or base, it should be strengthened by inside ribs to carry the column load. Ficj.8 Beams generally connect to cast-iron columns by means of brackets on which they rest and lugs for bolted con- nection to the web. The brackets are usually made as indicated in Figs. 6, 7, 8. These brackets should project about 3 or 4 ins. from the face of the column. There is no advantage in a wide shelf, but rather the reverse, as the beam is apt to bear on the outer edge and produce heavy bending stresses on the bracket. There should be a sti-ffen- ing rib under each -beam, not less than twice as deep as the width of the bracket. The shelves and ribs should have a thickness of metal about equal to that of the shell of the column, but not less, for ordinary work, than about one .inch. The shelves are not planed, but are cast smooth; the bolt holes are usually cored. Eccentric of unbalanced loads should be guarded against in cast-iron columns, because of the lack of toughness in the metal. Steel Columns. There are many forms of steel columns from the single angle up to the built column of several hundred square inches of sectional area. The selection of an appropriate style of column for any given case will depend upon the several conditions of the case. There are many column formulas that purport to give the correct load that will cause ultimate failure in a col- umn or the correct safe load; but, excepting the formulas of the form known as the Euler formula, these usually bring in empirical "constants" that are, in fact, not constant and that depend upon conditions that cannot be made uniform in commercial work. A steel column acts partly as a spring to resist bowing and partly as a shaft in compression to resist crushing. The ultimate strength of a slender column can be calcu- lated closely, but the ultimate strength of a shorter column can only be very roughly approximated. The ratio of slenderness of a column is the ratio between the length and the least radius of gyration of the cross section. The large majority of compression members have ratios of slender- ness varying between 30 and 150, and it is between these limits that the greatest uncertainty as to calculated strength exists. When a compression member is very short, its ultimate unit strength is nearly equal to the ultimate unit strength of cubical specimens; when the member has a ratio of slenderness of 150 or more, its ultimate strength is the definite value shown by the Euler formula. A few words are deemed advisable here in the way of warning to the inexperienced designer. It is often asked, "What is the factor of safety of a certain structure?" and thf answer usually given is 4 or 5, according as the de- signer thinks he has split up the ultimate strength of his members into 4 or 5 parts. The builder may say that he is satisfied with a factor of safety of 3 or less, and the de- signer is asked to cut down his sections accordingly. This 25 is a dangerous undertaking, especially when the commonly used column formulas are taken at their face value. As the author has shown in. Railway Age-Gazette, July 2, 1909, the Gordon-Rankine column formula shows apparent ulti- mate strengths of columns that are in some cases more than 100 per cent 'too great. This subject is more fully treated in the author's Structural Engineering, Book III. In some manufacturers' handbooks the supposed ultimate strength of columns is worked out on the basis of the Gordon-Rankine formula for values of the ratio Length in feet Radius of gyration in inches as high as 20 or more. This is an actual ratio of slender- ness of 240. It is entirely too slender for a practical column. Furthermore, the ultimate strength given for a pin-ended column of this ratio, is nearly 12,000 Ibs. per sq. in. The actual ultimate strength of this column is 5,000 Ibs. per sq. in., even if the column be made of the highest grade and hardest steel that it is possible to manu- facture. Designers are warned against using columns or other compression members of a ratio of slenderness greater than about T50. Some specifications and building codes do not allow a greater ratio than 120. What is known as the straight-line formula for the strength of a column is better than formulas of the Gor- don-Rankine type, because the straight-line formula shows very low strength for slender columns and because it agrees more nearly with tests. A straight-line formula in common use for building work gives a unit stress per sq. in. equal to 15,20058 l/r. where / is the length in inches and r is the least radius of gyration in inches. In a well-built and properly designed and centrally-loaded column, this formula gives the load that can safely be sustained. The factor of safety is a matter depending entirely on the perfection of the work 26 and is a value quite impossible to determine. Designers are cautioned to adhere to the -formula. The length / in the column formula is, of course, the unsupported or unbraced length of the column or other compression member. As explained heretofore in this chapter, there may be two or more ratios of slenderness to consider. A compression member may be braced in one direction and free to buckle or bow in another direc- tion. Steel compression members may be of unsym- metrical sections, as in the case of a single angle or zee bar; in such case the diagonal radius of gyration must be found, as this is less than the radii on the rectangular axes. A single angle or zee bar would fail by bowing in a diagonal direction. Single channels and single I-beams do not make good compression members, because the radius of gyration with the neutral axis parallel with the web is so small. In gen- eral, these should not be used as compression members, un- less they are braced at close intervals, or bolted to a wall, or built into a wall. Tables IV to XX give the total load allowed on com- pression members of various shapes. These tables should be used with caution and a knowledge of their limitations. Correct design and proper end details of columns are es- sential to produce a column that will have safe carry- ing capacities as shown in the tables. The heavy zig-zag lines in the several tables show the limits of safe length of columns at about 120 times the radius of gyration. Preferably the length of column should be kept within this limit. In some cases the ratio may be made as high as 150, when values to the right of the zig- zag line apply. The value of the radius of gyration of nearly all of these sections may be found in Godfrey's lables. The following rules apply approximately for some of the sections : For the star-shaped sections shown in Table IX, the value of r is about four-tenths of the width of the leg of 27 ne angle. The limit of 120 times r is then about 48 times the width of the leg of one angle. Thus, for 4 4"X4" angles this limiting length would be 16 ft. For gas pipe the radius of gyration is about .35 of the outside diameter. At 120 radii the unsupported length is then about 40 times the outside diameter., For Bethlehem H Sections the radius of gyration is about .4 of the width B of flange, hence 120 radii is about 48 times the flange width. For the sections shown in Tables XII and XIII r is about .20 to .22 times the width of flange, hence 120 radii is about 25 times the flange width. For the channel columns of Table XVI r is about .4 of the depth of channel, hence 120 radii is about 48 times the depth of channel. For the zee-bar columns r (minimum value) is about .62 times the web of one zee bar. The limit of column length, at 120 radii, is 18.5 ft. for 3-in. zees, 24.5 ft. for 4-in. zees, 31 ft. for 5-in. zees, and 37 ft. for 6-in. zees. Tables IV and V give the strength of single angles in compression, but in order to develop the strength shown in these tables the angles should preferably be milled on the ends. They need a square end bearing, so that the load will not be eccentric. Connection by means of rivets through each leg of the angle may be sufficient to balance the load, but that connection should be to rigidly held parts. Single angles should generally be avoided as members of a truss, but if used, the allowed stress should be only about half of that shown in the table, so as to allow for eccentricity. This is true, whether or not both legs of the rngle are connected with rivets at the ends. When the stress is applied to the end of an angle by a gusset plate, extra lug angles connecting to the outstanding flange do not centralize the stress from the gusset plate. When a single angle used as a post has a channel riveted to each flange, as in Fig. 10, a good rigid end connection is obtained, and, if the base of the post is milled and, has a sguare bearing, the post may be taken as -good for the 28 value in the table. If the angle is not milled on the end its value in compression may be determined by the rivets in the lugs at the end. Very frequently these angles are simply sheared off at the ends and do not bear against the base plate. Figs. 9, 10 and 11 illustrate small angle posts. When two angles are used as a post or compression member, they should be riveted together at intervals of a foot or two, so that they will act together as one member. When they are separated, as in a truss by the thickness of a gusset plate, washers are used between the angles at these rivets. Fig. 9. Bit Fig.lO. o;;;o Fig. II. Compression members are sometimes made of twd an- gles separated several inches and joined by small batten plates at intervals of three or four feet. These do not make good compression members, unless they are consid- ered as two separate angles, and the ratio of slenderness so taken. When the two angles are joined by lattice from end to end of member, they may be considered as, one member, for then the triangular system of lattice bars compels one angle to aid the other in resisting buckling from end to end of the member. Gas pipe posts usually have a threaded cast iron flange for an end connection. Beam connections to steel columns and column splices will be considered in another chapter. In selecting the sections for columns in the successive stories of a building, they should be arranged so that the metal of the upper section will bear against metal of the lower section, unless special provision is made in the splice. Frequent changes in the general outside dimensions of the columns should not be made, as these involve special splices and more irregular beam connections. In closed channel sections the thickness of cover plates and the weights of channels may be reduced, using the same depth of channel for several tiers. In I-shaped built columns cover plates may be reduced in number and thickness, in the successive tiers, then omitted ; then angles may be reduced in thickness and in length of legs, maintaining the same web plate or distance back to back of angles. (The distance back to back of angles is usually made Y-Z inch greater than the width of web plate.) Reinforced Concrete Columns. True reinforced concrete must of necessity be concrete reinforced or strengthened where the concrete is weak. Any system that combines steel and concrete where the steel is in compression is not reinforced concrete, but may be termed concrete-steel, a combination of the two ma- terials assumed to be acting together. Concrete is strong in compression (confined or in short blocks), but weak in tension and shear. If steel is to reinforce concrete, it must do it by making up the lack existing in the concrete, that is, it must take up the tensile stresses and relieve the con- crete of the same. There are tensile stresses in concrete acting as a simple post or column. This is scarcely recog- nized in books on engineering, though it is of tremendous importance, especially in reinforced concrete design. The cement mortar that is strongest in tension will make the strongest column. A bundle of thin straight wires would be useless as a column. But if the same wires were tight- ly bound about with a spiral wire, a heavy load could be borne by the same thin wires. Slender rods in a concrete shaft are very imperfectly and insecurely held together and held from buckling by the concrete. Hence a con- crete column built with slender rods in it, with the idea that these rods will reinforce it, is most absurdly de- signed. In spite of the fact that such design is standard and accepted by nearly all authorities on reinforced con- crete, it is absolutely dangerous and indefensible. It has been the cause of a large number of very disastrous wrecks. Such design and practice cannot be too severely condemned. Books on reinforced concrete are woefully lacking and inexcusably blameworthy in this respect that they encourage and hold out as standard and proper de- sign such miserably poor construction. For a full pre- sentation of this subject the reader is referred to the au- thor's book "Concrete," to his paper, read, before the American Society of Civil Engineers in March, 1910, en- titled, "Some Mooted Questions in Reinforced Concrete Design," and to files of Engineering News and Concrete Engineering, 1907 to 1910, inclusive. No valid argument has been brought forth to controvert the author's posi- tion ; tests and wrecks have amply demonstrated the sound- ness of it. In this book only one form of reinforced concrete col- umn will be considered as worthy of use, namely, the hooped column. A discussion of the proper dimensions of such a column will be found in the author's book, "Con- crete." These are as follows : Reinforced columns will be round or octagonal. They will have embedded in the concrete a coil of square steel having a diameter one-fortieth of the diameter of the col- umn and eight upright rods just inside the coil and wired to the same, so as to prevent displacement of both coil and straight rods. The coil will have a diameter seven- eighths of that of the column and a pitch one-eighth of the diameter of the column. The upright rods will be of the same section as the rod in the coil. Where a coil ends, the next coil will lap one-half of a circle. Where upright rods end there will be a lap of 50 diameters of the steel rods. 31 On a column such as that described in the last para- graph a load per square inch may be allowed on the full section of the concrete, of 550 pounds, on columns having a length not more -than ten times their diameter. Between 10 and 25 diameters the following load will be allowed : p =670 12 l/D where p =load per square inch, / =length in inches, D=diameter in inches. Reinforced concrete columns should not be of greater length than 25 times their diameter. Reinforced concrete cannot be recommended for eco- nomic construction in columns. Also the difficulties in the way of complete filling of the forms are many. Bet- ter construction is effected by the use of steel columns surrounded with concrete for fire protection or concrete columns in which are embedded stiff steel sections, which depend in a small degree only upon aid supplied by the concrete. These two classes of columns will be more fully described in what follows. When steel columns are surrounded by concrete, to a depth of say \ l /t or 2 inches over the metal, the steel columns should be designed in every respect as columns quite free of concrete, or as those protected by tile. Efficient and safe columns can be made of steel angles or other stiff steel sections held together at intervals by batten plates riveted thereto, the whole being surrounded and filled with concrete. These batten plates should be sufficiently close so that each individual angle, or other stiff section of which the steel column is composed, will act as a short column between the batten plates. Such a steel column would not make a good compression mem- ber alone, but the concrete can be relied upon to add suf- ficient stiffness to the columns, within certain limits. In- stead of battens, lattice may be used in the columns, ex- cept at girder connections, where angle shelves may b( used upon which to rest the girders. The columns maj be left open at girders for the passage of continuou; 'rods. 32 It is recommended that concrete-steel columns such as those described in the preceeding paragraph be propor- tioned on the basis of a flat unit stress of 16,000 Ibs. per sq. in., and that the width out to out of steel column be not less than one-twelfth of the unsupported height, and that concrete to a depth of 2 inches be used outside of all metal. The concrete should be considered merely as protecting the steel and carrying shear from one side to the other of the column. No compressive value should be allowed for the concrete. Pig. 1 2.. Fig.!3. Fig.14. Fig.15. Figs. 12 to 15, inclusive, show examples of these con- crete-steel columns. The dotted lines indicate batten plates or lattice bars. A good rule for the spacing of batten plates is to make them no farther apart than twelve times the width of the flange of the angle or channel. TABLE IV. Total Load in Thousands of Pounds, Allowed on Single Angles as Com- pression Members. Size of Unsupported Length of Member. Angle. | 2 ft. 3ft. 4 ft. 5 ft. 6 ft. 7 ft. 8ft. 2 x2 xy 4 2 x2 xy & 2y 2 x2y 2 xy 4 2y 2 x2y 2 xy 2 3 x3 xy 4 3 x3 xH 3y 2 x3y 2 *y& 3y 2 x3y 2 x}/ 4 2y 2 x2 xV 4 2y 2 x2 X y 2 3 x2y 2 xy 4 3 x2y 2 *y 2 3?4x2j4xj4 3y 2 x2y 2 xy 8 3y 2 x3 xfg 3^x3 xft 4 x3 xH 4 x3 xM 11 16 15 28 18 43 33 62 13 24 16 31 18 42 30 56 32 61 9 13 13 24 17 39 30 57 11 20 15 28 16 38 27 51 30 56 8 11 11 21 15 35 28 52 9 17 13 25 14 33 25 46 27 51 6 9 8 15 10 22 "20~ ii 14 27 16 31 10 18 13 31 25 47 27 23 42 7 14 10 18 11 25 '9 20 17 32 19 36 11 21 13 29 22 41 24 46 19 37 22 41 TABLE V. Total Loads in Thousands of Pounds, Allowed on Single Angles as Com- pression Members* Size of Angle. Unsupported Length of Member. 4 ft. 5 ft. | 6 ft. 7 ft. 8 ft. 9ft. | 10 ft. 4 x4 x3/ & 4 x4 x^ 6 x6 xy s b x6 x$4 8 x8 x l / 2 8 x8 x4 5 x3 xH 5 x3 x^ 5 x3y 3 xH 5 x3y 2 xM 6 x3^x^ 6 x3y 2 x& 6 x4 x^ 6 x4 x$ 8 x6 xy 2 8 x6 x^ 33 63 56 108 104 154 31 59 35 67 40 75 43 83 88 129 31 58 54 103 101 149 28 53 32 61 37 69 41 77 85 124 28 53 51 98 97 143 25 47 30 56 33 63 38 72 81 119 26 48 48 93 94 138 23 43 46 88 90 133 21 38 IS 34 43 83 87 128 41 78 84 123 22 41 19 35 24 45 27 51 21 40 24 45 26 49 66 97 27 51 30 57 35 "1 32 29 66 61 55 77 74 70 113 108 102 34 TABLE VI. Total Load in Thousands of Pounds, Allowed on Two Angles Placed Thus ip Seperated i in,, as Com pression Members, Size of Angles. j Unsupported Length of Member. 4 ft. 5 ft. 6 ft. 7 ft 8 ft. 9 ft | 10 ft. 2^x2 xy 4 \ 2y 2 x2 xy 2 \ 3 x2y 2X y 4 \ 3 x2y 2 xy 2< 3y 2 x2y 2 xy 4 3y 2 x2y 2 xy 2 3y 2 x3 x3/ 8 3 l / 2 x3 x3 /4 4 x3 x3/ 8 4 x3 x3/ 4 5 x3 x3/ 8 5 x3 x3/ 4 5 x3y 2 x3/ s 5 x3y 2 x3/ 4 6 x3y 2 x3/ 8 6 x3 l / 2 xy 4 6 x4 x3/ 8 6 x4 x3/ 4 25 46 32 61 37 70 58 108 64 121 74 143 81 156 91 175 98 189 23 42 30 57 35 66 55 102 62 116 71 138 79 151 87 169 95 183 21 39 28 53 33 63 52 97 59 111 68 132 76 145 84 163 92 178 19 35 26 50 31 59 49 91 56 105 65 126 73 140 81 157 89 172 17 31 24 46 29 56 46 85 53 100 62 121 70 135 151 86 167 15 1 44 s 1 52 43 80 51 94 59 115 67 130 74 145 83 161 21 38 "16 49 41 74 48 89 56 110 65 124 71 139 80 156 TABLE VII. Total Load in Thousands of Pounds, Allowed on Two Angles Placed Thus .^ ^ . as Compression Members, Size of Angles. Unsup ported Length of Member. 4 ft. 5 ft. 6 ft. | 7 ft 8 ft. 9 ft | 10 ft. 2^x2 xJ4 2y 2 x2 xy 2 3 x2y 2 xy 4 3 x2y 2 xy, 3y 2 x2y 2 xy 4 3y 2 x2y 2 xy 2 22 1 41 | 30 57 33 62 i 56 103 60 112 68 128 I 76 | 144 | 85 | 161 I 93 | 176 20 36 28 52 30 56 52 96 56 104 63 118 72 135 80 151 88 168 17 31 15 26 20 37 22 40 18 33 19 34 25 47 27 51 49 89 52 96 59 109 68 127 75 141 84 159 23 42 24 45 45 82 48 88 54 99 64 119 70 131 | 80 151 3y 2 x3 xY 3 l / 2 x3 x3/ 4 4 x3 x3/ s 4 x3 xy 4 5 x3 x3/ 8 5 x3 x3/ 4 5 x3y 2 x3/ s 5 x3y 2 x3/ 4 6 x3y 2 x3/ 8 6 x3y 2 x3/ 4 6 x4 xH 6 x4 x% 41 75 44 80 49 90 59 111 65 122 75 142 38 67 40 73 3* 60 36 65 40 71 44 80 55 102 61 112 71 133 51 94 56 102 67 125 TABLE VIII. Total Load in Thousands of Pounds, Allowed on Two Angles Placed Thus "ip" as Compression Members. Size of Angles. Unsup ported Length of Member. 4 ft. | 5 ft. 6 ft. 7 ft. 8 ft. 9 ft 10 ft. 2 x2 xJ4| 20 18 16 14 2 x2 xHJ 29 25 22 19 2 l / 2 x2y 2 x I A\ 28 25 23 " 21 ] 19 . . . . 2 l /2x2 l /2X l / 2 \ 51 47 43 39 1 35 3 x3 xJ4| 35 33 31 29 27 24 22 3 x3 x^| 81 76 | 70 65 60 54 49 3y 2 xZ i / 2 x^\ 62 59 56 53 50 46 43 3^x3^x341 117 111 105 98 92 86 79 4 x4 x3/ 74 71 68 64 61 58 55 4 x4 xfa 140 134 127 121 114 108 102 6 x6 x3/ & 120 116 113 110 107 104 100 6 x6 xY* 231 224 218 212 205 199 192 8 x8 x*/ 2 218 214 210 205 201 197 192 8 x8 x34 322 316 309 303 296 290 I 283 TABLE IX. Total Load in Thousands of Pounds, on Four Angles Placed Thus JL as Compression Members, Size of Angles. Unsupported Length of Member. 4 ft. 5 ft. | 6 ft. 7 ft. 8 ft. 9 ft | 10 ft. 2 x2 x l /4 45 42 39 36 33 29 26 2 x2 xy s 65 61 57 52 48 44 39 2y 2 x2 l / 2 x% 60 57 53 50 47 44 ~Ti 2y 2 x2 l / 2 x l / 2 114 108 103 97 91 86 80 3 x3 xy 4 75 72 68 65 62 59 56 3 x3 x54 176 169 162 155 148 141 133 3 l / 2 x3 I / 2 x3/& 132 127 123 118 113 109 104 3 I / 2 x3 l / 2 x3 / 4 251 243 234 226 217 209 200 4 x4 x3/ s \ 155 150 145 141 136 131 126 4 x4 xY*\ 296 287 279 270 261 252 244 6 x6 xYz 246 241 236 231 226 221 216 6 x6 -X.YA. 476 467 1 458 449 439 430 421 8 x8 xy 2 \ 445 439 j 432 426 419 413 406 8 x8 xY 4 \ 658 648 | 639 I 629 j 620 610 ! 601 ' 36 TABLE X. Total Load in Thousands of Pounds, Allowed on Standard Gas Pipe as Compression Members, Nominal External I Internal Size of Diam. in f Diam. in Pipe. In. | In. Unsup. Lgth. of Member. | 5 ft. | 6 ft. | 7 ft. | 8 ft. | 9 ft. 1 10 ft. 2.375 2.875 3.500 4.000 4.500 5.000 5.563 6.625 7.625 8.625 9.625 10.750 t"W TABLE XI. r-T . Total Load in Thousands of Pounds Allowed on Bethlehem H-Sections as Compression Members* I mn. in In. and Weight of Sec. D B T w Weight in L,bs. ! per Ft. Unsupported L,gth. of Member. 10ft|12ft|14ft|16ft|18ft 20ft. 8 8.00| y a \ .31| 34.5 119 1 12 105 98 91 84 8 l / 2 8.16| 34 .47 53.0 184 173J 163 152 142 132 854 8.24 H .55 62.0 217 205 192 180 168 156 9 8.32 i .63 71.5 251 237 j 223 209| 196 182 9 l /2 8.47 1 14 .78 90.5 320 302 285 268 251 234 10 10.00 >M$ .39 54.0 198 189 180 171 162| 153 10J4|10.08 M .47 65.5 240| 229| 219| 208| 197| 187 \Q l /2 10.16 % .55 77.0 282 270 258 246 234 221 11 10.31 1 1 A .70 99.5 368 352 3371 321 306! 290 11J4I10.47 \y^ .86 123.5 457 4381 4201 401 3811 363 1 1 54 1 1 1 . 92 $i .39 64 . 5 244J 235| 227| 2181 209| 200 12 |12.00 y* .47| 78.0 296| 285| 274| 264| 253| 243 \2 l / 2 12.16|1 .63| 105.0 400| 386| 372 358 344| 330 13 12.31|1J4 .78| 132.5 506| 4881 471 453 4361 418 143/6114 153/6114 14 .47 .96 .1211 .94| .471 .63! .94! .74|2 |1.25| .90 1 2 '/ill. 41 1 161.0 91.0 122.5 186.5 253.0 287.5 | 6151 5951 574| 5531 533 512 | 353| 343| 332| 321| 311| 300 I 477| 463| 449| 435] 421 | 407 730| 710| 6891 668J 647| 626 994| 966| 9391 911! 884| 856 1130!1099|1069|1038!1007! 976 TABLE XIII. H Total Load in Thousands of Pounds Allowed on I- Shaped Sections as Com- pression Members. Web. Angles. Unsupported l^ength of iVieiiiu> .. 10ft. 12ft. 14ft.|16ft. 18ft.|20it. 12xA 12xA 12x^ 12xA 12xA 12x^ 12xA 12x T 8 5 12x^ 12x3/6 12x3/S 12x34 I4x A 14x T 5 s 14xJ* 14xA 14xA 14xj4 14 Xl 5 g 14xA 14x^ 14x3/g 14x3/6 14x34 14x3^ 14x3^ 14x34 16 X1 S 5 16xA 16x^ 16 X1 5 S 16xA 16x^ 16x3/6 16x3/6 16x34 16x3^ 16x44 16x34 3^x3 xA 3^x3 x^ 3^x3 xy a 4 x3 xA 4 x3 xj^ 4 x3 xj4 . 5 x3 xA 5 x3 xj^ 5 x3 x l /2 6 x3 l / 2 x3/s 6 x3#x# 6 x3>ax34 3^x3 xA 3^x3 x^ 3^x3 x>S 4 x3 x* s 4 x3 xj^ 4 x3 x^a 5 x3 xA 5 x3 x^ 5 x3 x l / 2 6 x3j4x5^ 6 x3^xM 6 x3j4x^ 6 x4 x?/6 6 x4 x34 6 x4 x?4 4 x3 x, 5 c 4 x3 x^ 4 x3 x# 5 x3 xA 5 x3 xj^ 5 x3 x>i 6 x3!4x3^ 6 x3^x34 6 x3j4x# 6 x4 xJ'g 6 x4 x-)4 6 x4 x^ 115 164 186 131 186 210 158 226 252 227 391 446 120 169 194 136 192 219 165 233 262 235 399 463 244 417 481 142 198 228 171 239 272 244 408 480 252 425 498 103 149 168 120 173 194 149 214 238 217 375 428 107 153 176 125 178 202 155 220 248 225 383 444 232 400 460 129 182 210 160 226. 257 232 391 460 240 408 477 91 134 151 109 159 178 140 203 225 207 360 410 79 119 133 99 146 162 131 191 211 197 345 392 104 116 88 132 146 122 179 198 187 329 375 77 118 130 113~ 167 184 177 314 357 94 137 157 113 163 184 145 208 233 214 368 425 221 383 440 117 167 191 150 213 241 221 375 440 228 390 455 81 121 138 105 119 90 135 150 120 133 102 149 167 136 196 219 204 352 406 210 365 420 126 183 204 193 336 387 199 348 400 117 171 190 183 320 368 188 331 3PO 105 1 152 173 | 140 200 226 210 358 420 217 372 434 92 137 155 l22 137 130 187 210 j 199 342 400 205 355 413 119 175 195 188 326 380 193 337 392 38 TABLE XII. H Total Load in Thousands of Pounds Allowed on I- Shaped Sections as Com- pression Members. Web. Angles. Unsupported Length of Member. 8 ft. 10 ft. 12 ft. 14 ft. 16 ft. 18 ft. 6x I / 4 2 l / 2 x2 xJ4 56 48 41 6xy 4 2^x2 xj4 98 87 75 64 6xy 2 2 l / 2 x2 x J /2 114 101 87 74 7xy 4 2y 2 x2 x T 4 58 50 , 42 7x I / 4 2 Kx2 xJ/2 100 88 76 64 7x l / 2 2J/ax2 x}4 118 104 90 76 8xy 4 2y 2 x2 xVi 60 51 42 8x T / 4 2^x2 xj4 102 90 77 *65 8xy 2 2j^x2 x^ 122 107 92 77 8xy 4 3 x2y 2 xy 4 76 68 59 51 8x*4 3 x2j^x^ 132 119 106 94 81 8xy 2 153 138 124 109 94 9x B 3 x2l/x B - 98 87 77 66 . . . 9 X J? 3 x2pxj/ 140 126 112 99 85 9 x i| 3 x2>|x^| 158 142 126 111 95 9x 5 3*/x2y 2 x 5 113 103 93^ 84 74 65 9xi 5 ff 3y 2 yt2y 2 xy 2 160 148 136 123 111 98 9xJ^ 3y 2 x2y 2 x.y 2 179 165 151 137 123 109 9x 5 3y 2 x3 xA 118 108 97 87 76 ... 9x 5 170 156 143 129 115 101 9xV 3y 2 x3 x^z 189 174 158 143 127 112 9xT 5 s 4 x3 X T B S 132 123 113 104 94 \ 85 9xJL 4 x3 x}4 190 178 165 153 140 \ 128 f) x y 2 4 x3 x^ 210 196 182 168 154 140 9x B 5 x3 x-fg 156 148 140 132 124 116 9XT 5 ff 5 x3 xj4 227 216 205 195 184 173 5 x3 x^ 248 236 224 212 199 187 10xW 3^x3 X T B S 121 110 99 88 77 10xW 3^x3 xy 2 173 159 145 131 117 103 10x^4 3y 2 x3 x/ 2 194 178 162 146 130 114 lOx B 4 x3 xA 135 125 115 105 96 86 JQ X \ 4 x3 x^ 194 181 168 155 142 129 10xJ^ 4 x3 xj^ 215 200 186 171 156 142 lOx B 5 x 3 x i % 160 152 143 135 127 ' 118 1 0x 5 5 x3 xy 2 231 220 209 197 186 175 10xl| 5 x3 xj^ 254 241 228 216 203 191 10x3/1 6 x3^x-K 228 219 209 200 191 182 10x3^ 397 382 367 352 338 323 6 X3K.X54 446 429 412 395 379 362 39 H TABLE XIV. Total Load in Thousands of Pounds Allowed on I-Shaped Sections as Compression Members. | Cover Web. Aneles. | Plates. Area |l,.R's| Unsup. Lgth. of M'b'r. in | of | 10| 12] 14| 16 18] 20 sq.in.] Gyr. | ft. | ft. | ft. | ft. 8x 11.24| 1.68|124|115|106| 96| 87| 78 15.24 1.86|175J163il52|140|129|118 20.00J 1.78 226J210 195 179 163| 148 22.00| 1.74|246|229|211|194|176il58 9x4 11.74] 16.24] 21.00] 23.00] 14.92)" 18.29] 21.81] 23.50] 1.86|135 2.09|193 1.97|245 126|117|108| 99 | 91 182| 171 | 160| 150| 139 230|215|201 | 186| 171 1.92|266|250|233 1 2J 6j 20 1 1 8 3 1.86|l71|160|149|i37|T2fa|il5 2.01|215]202|189|177|164|151 1.94)253 |238|222| 206] 191 j 175 1.90)271 1 254 1 237 1 219] 202) 185 2.05|183|173|162|152|141|131 2.24|233|221|209|197|185|173 2.15|273|258|243|229|214|199 2. 09)291 | 274 | 258)242] 226|20 9 1.91|187|175|163|151|140|128 2.04|230j217j204|190|177(16-4 1.99|279|262|245|229|212|195 1.95 297 278 | 260 | 242 j 224 | 206 16.78] 2.08|199|188|176J165|154|143 20.53J 2.25 249] 236] 223 1210| 198] 185 24.81| 2.17|298|282|266|250|234|218 26.50] 2.13]316|299|282|264|247|230 9xA|4x3 9x^14x3 16.80] 2. 02] 198] 186] 174] 163] 15 1|14U 20.17] 2. 11|240|227|213|200|187|174 24.81| 2.10|295]279|262|246|229|213 26.50] 2.07)314)296 278) 260 |242| 225 9x T 5 8 |4x3 xftUOxft 9xA|4x3 9xA 4x3 9x^ 4x3 x 17.42| 2.17|209|198]187|175]164|153 21.17] 2.32|258|246|233|220!208|195 25.81] 2. 26] 313] 297 |281|265|249| 233 27.50] 2.22 332) 315) 297 | 280] 263] 246 10xA|4x3 10xft|4x3 10xA|4x3 17.74] 2.15)212 201 | 189) 178] 166] 155 21.49] 2.30|262|249|236|223|210|197 26.13] 2. 25 |316|300| 284 J268|252|236 28.00] 2.20I337|319|302|284|266|248 10xA|4x3 18.36] 2.33|224|213|202|191|1.80|169 22.49| 2.50|279|267|254|242|229|217 27.13] 2. 43 | 335 | 31 9)304] 288] 273) 257 29 . 00 | 2 . 37 | 356 | 339 | 322 | 305 | 287 | 270 40 TABLE XV. H Total Load in Thousands of Pounds Allowed on I- Shaped Sections as Com- pression Members. I I Cover Web. Angles. | Plates. Area |L.R's| Unsup. L,gth. of M'b'r. in of | 10| 12) 14| 16 18 sq. in. | Gyr. | ft. | ft. | ft. | ft. ft. 20 ft. 10x3^ |6x3Hx3/6 |13x3/g 10x3x3 1 6x3^x3/3-1 13x34 1 Ox ^ 16x3x^x34) 13x34 10x^|6x3Hx34|13x34 27.18 3.07|351|339|327|315|302|290 36.93 3.27|483|467|451|436|420|404 49 . 49 3 . 22 j 645 1 624 1 603 581 j 560 1 538 50.74 3. 21 |661 | 639 \617\ 595 | 573) 551 10x3/^| 6x3^x3/8 j 14x3^ 10x3/6 \6x3y 2 xy s \ 14x34 10x3,8 |6x3/^x34| 14x34 10x^)6x3x^x34)14x34 27.93 3.23|364|352|340|328|316|304 38.43] 3.47J507 492)476 461 J445J430 50.99J 3.38|670 649)628 |607|S86|56S 52.24J 3. 36 |686|664 |643 |621 |599 |578 12x^1 4x3 x T 5 s 12xf 6 12x T B 6 (4x3 xft|12x# 12x T s s |4x3 xy 2 \12xy 2 12x^14x3 xy 2 \l2xy 2 19.61| 2. 48) 243) 232) 221)210] 199) 188 24.11 | 2.69|304|292|279|267|254|242 28.75| 2.59|360|344|329]314 298)283 31.001 2.52 386)368 351 334 317|300 12xft|4x3 x T 5 s |13x T 5 s 12x^(4x3 x T 5 8 |13xK 12x&|4x3 xK(13xH 12xH|4x3 x^|13xH 20.24] 2. 67 | 255 |244| 234 |223I213| 202 25.11| 2.91|322|310|298|286|274|262 29.75] 2. 79 J378J363 (348)333 |319| 304 32.00] 2. 71 |404|388|371 | 355) 338) 322' l2x3/ 8 \bx3 l / 2 x3/ 8 \13x3/ 8 12x3^16x3^x3^113x34 12x3^ |6x3^x34| 13x34 12x^16x3x^x34)13x34 27.93 3.03)360)3481330,32213091296 37.68 3.23 492(475 459 4431427 410 50.24J 3.20 655|633|611|589 567)545 51.74) 3.18|673|651|628|605 583)560 12x3^16x3^x3^114x3^ 12xM|6x3^x^|14x34 12x3^|6x3^x34|14x34 12x^16x3^x34 |14x34 28.68) 3. 18) 373)361 |348)336| 323] 310 39.18] 3.43i516|500j484|468|453|437 51.74] 3. 36) 679] 658] 636] 615] 594] 572 53.24] 3. 33 |698|676|653 |631|609| 587 14x^(4x3 x T 5 5 |14x T 5 ff 14x^4x3 x/ g |14xH 14x? 6 |4x3 xy 2 \l4xy 2 14x^14x3 xy 2 Hx'X 21.49] 2. 84 | 274 | 263 | 253) 242] 232] 221 26.74] 3.11|347|335|323|311|299|287 31.38] 2. 97)404] 389) 374) 359] 345(330 34.00] 2. 88 (435 | 418(402(385] 369] 352 14 Xl s s !4x3 xi' 5 ISxfu 14x^5 1 4x3 xjis jlSx^ 14x T S 6 4x3 x^|15x>i 14xK 4x3 xy 2 \l5xy 2 ^2.11 3. 05 (286 (276(265 | 255) 245)235 27.74 3. 35 | 364(353) 341 ) 329(31 8) 306 32.38 3. 19 |422)407 |393|379| 365) 351 35.00 3. 09 |453|437|422 (406 (390(374 14xl/ 8 |6x3^x3,^j 14x^ 8 14x y s \6x3y 2 xi/ s |14x34 14x3^16x3^x3x4)14x34 Hx^ 16x3^x34 |14xM ^9.43| 3.14|382|369J356|343 330 39.931 3.40|525|509|493|476 460 52.49| 3.33|688|666|644|622|600 54.24) 3.30|710|687|664|641|618 317 444 578 596 14x3^16x3^x^)15x3^ 14x3^|6x3Hx3^!l5x34 14x3^|6x3Hx34|15x34 14x^1 6x3 '4x34 |15x34 30.18| 3. 31 (395 (383 (370 j 357) 345 (332 41.43 3. 61 (550 |534| 5181 502(486(470 53.99 3. 50(71 3 |692|670 |649| 627 1606 55.74! 3. 47 |735|713 1691 1668 |646| 624 41 TABLE XVI. Total Load in Thousands 9 Cof Pounds Allowed in Latticed Channel Sec- tions as Compression Members. D not less than .65 of the depth of channel. Sizeof Channels. Unsupported Length of Member. Depth Weight in Ubs. in In. per Foot. 10ft. 12ft. 14ft. 16ft. 18 ft.) 20 ft. s 6.5 45 43 40 37 34 31 5 9.0 60 56 52 48 44 40 5 11.5 76 70 65 60 54 | 49 6 8. 58 55 53 50 47 | 44 6 10.5 74 71 67 63 59 55 6 13.0 91 86 81 76 71 66 6 15.5 108 102 96 90 83 77 7 9.75 72 69 66 63 60 57 7 12.25 90 86 82 78 75 71 7 14.75 108 103 98 93 88 84 7 17.25 125 119 114 108 102 96 7 19.75 143 136 129 122 116 109 5 ? 11.25 87 84 81 78 75 72 3 13.75 104 100 96 93 89 85 16.25 122 118 113 108 104 99 8 18.75 140 135 129 124 119 113 1 3 21.25 159 152 146 140 133 127 9 13.25 103 100 97 93 ,90 87 9 15.00 116 112 109 105 102 98 9 20.00 153 148 143 138 133 128 9 25.00 190 184 177 171 164 157 10 15.00 120 116 113 110 107 103 1( ) 20.00 156 152 147 143 138 134 10 25.00 194 189 183 177 171 165 10 30.00 232 225 218 211 204 196 10 35.00 270 261 253 244 236 227 12 20.50 165 161 158 154 151 147 12 25.00 200 196 191 186 182 177 12 30.00 239 234 228 222 216 211 12 35.00 278 272 265 258 251 244 12 40.00 317 309 301 293 285 277 15 33.00 277 272 267 262 257 252 15 35.00 287 282 277 272 267 261 15 40.00 327 321 315 309 303 297 15 45.00 368 361 354 347 340 333 15 50.00 408 400 392 384 377 369 15 55.00 448 439 431 422 413 405 42 TABLE XVII. n Total Load in Thousands of Pounds Allowed on Channel and Plate Sections as Compression Members. Size of Channels Size of Unsupported Length of Member. Depth in Weight in Lbs. In. per Ft. Plates. 10 ft. 12 ft. 14 ft. 16 ft. 18 ft. 20 ft. 7 9.75 9x^4 128 123 118 112 107 102 7 9.75 9x l / 2 185 177 169 161 154 146 7 12.25 9xj 5 5 161 154 147 140 133 126 7 12.25 9x T 9 5 217 208 198 189 180 170 7 14.75 9x3/6 192 184 175 167 158 150 7 14.75 9xy s 248 238 227 216 205 194 7 17.25 9x T 7 ff 224 213 203 193 183 173 7 17.25 9xfi 280 267 255 242 230 217 7 9.75 11x54 146 141 136 131 126 122 7 9.75 Hx}/2 219 212 205 198 192 185 7 12.25 llx T 5 s 183 177 171 164 158 152 7 12.25 llxft 257 249 240 232 224 216 7 14.75 llx^ 220 212 205 197 190 182 7 14.75 llx^g" 294 284 275 265 256 246 7 17.25 llx/ff 257 248 239 230 221 213 7 17.25 Hx} 330 319 309 298 287 276 8 11.25 10x^4 151 146 140 135 129 124 8 11.25 215 207 199 192 184 176 8 13.75 10x^5 184 177 171 164 157 151 8 13.75 10x T 9 ff 248 239 230 221 212 203 8 16.25 10x3^ 219 211 202 194 186 178 8 16.25 283 272 261 251 240 230 8 18.75 lOx-fe 253 243 233 224 214 205 8 18.75 lOxji 317 305 293 281 269 257 8 11.25 12x^4 169 164 159 154 149 144 8 11.25 l2x l / 2 249 242 235 228 221 214 8 13.75 12x T 5 ff 207 201 195 189 183 177 8 13.75 12x& 287 279 271 263 255 246 8 16.25 12x3/3 246 239 232 224 217 210 8 16.25 327 317 308 298 289 280 8 18.75 12x T 7 5 285 277 268 260 252 243 8 18.75 366 355 344 334 323 313 43 TABLE XVIII. n Total Load in Thousands of Pounds Allowed on Channel and Plate Sections as Com- pression Members. Size of Channels) Unsupported Length of Member. Depth Weight Size in In. in Lbs. per Ft. OI Plates. 10ft. 12ft. 14ft.|16ft. 18ft.|20ft. 9 13.25 llxJ4 175 169 164 158 153 147 9 13.25 llxtf 246 238 231 223 215 207 9 15.00 llx T 5 ff 206 199 193 186 180 173 9 15.00 llxA 278 269 260 251 242 233 9 20.00 1 1*8 261 253 244 235 227 218 9 20.00 llxfc 333 322 311 300 289 278 9 25.00 Hxft 316 306 295 284 274 263 9 25.00 Hxli 388 375 362 349 336 322 9 13.25 13xK 192 188 183 178 173 168 9 13.25 13xH 280 273 266 259 252 245 9 15.00 13xft 229 223 217 211 205 199 9 15.00 13xA 316 308 300 292 284 275 9 20.00 13x^ 289 281 274 266 259 251 9 20.00 13x^ 377 367 357 347 338 328 9 25.00 13x* 350 340 331 322 312 303 9 25.00 Uxg 438 426 414 403 391 380 10 15 12xA 219 213 207 201 195 189 10 15 12xA 298 290 281 273 264 256 10 20 I2x 276 268 260 252 244 236 10 20 12x^ 355 345 335 324 314 304 10 25 12x^r 334 324 314 305 295 285 10 25 12xH 413 401 389 377 364 352 10 30 12x^ 392 380 368 356 345 333 10 30 12x^4 471 457 443 428 414 400 10 15 14x^ 241 236 230 225 220 214 10 15 14x T 9 ff 336 328 320 312 305 297 10 20 14xM 304 297 290 283 276 269 10 20 14x^ 398 389 379 370 " 360 351 10 25 14xft 367 358 350 341 333 324 10 25 14xjJ 461 450 439 428 417 406 10 30 14x^ 430 420 410 399 389 379 10 30 14x& 524 512 499 487 474 461 44 TABLE XIX. .. Total Load in Thousands of Pounds Allowed on Channel and Plate Sections as Com- JL | JHB pression Members. Size of Channels Size of Unsupported Length of Member. Depth in Weight in L,bs. In. per Ft. Plates. 10 ft. 12ft. 14 ft. | 16ft. | 18ft. | 20 ft. 12 20.5 14x3/3 307 300 293 286 278 271 12 20.5 14x^ 401 392 382 373 363 354 12 25 !4xA 366 357 349 340 331 323 12 25 | 14xH 460 449 438 427 416 405 12 30 | 14x}4 429 419 408 398 387 377 12 30 14x3/4 523 510 498 485- 472 459 12 35 14xA 492 480 468 456 443 431 -8- 35 Hx}2- 586 333- 572 "127" 557 543 528 514 20.5 16x3/8 320 314 307 301 12 20.5 I6x^ 443 434 425 416 407 399 12 25 16x T V 397 389 381 373 366 358 12 25 16xH 507 496 486 476 466 456 12 30 16x# 465 456 446 437 428 418 12 30 16x?4 574 563 551 539 528 516 12 35 16x& 533 522 511 500 489 479 12 35 16xif 642 629 616 602 589 576 15 33 17x T V 483 475 466 457 448 439 15 33 17xft 601 589 578 567 556 545 15 40 17x^ 564 553 543 533 522 512 15 40 17x34 681 668 656 643 630 617 15 45 17xrk 634 622 610 599 587 575 15 45 17xl| 751 737 723 709 695 680 15 50 17x54 704 690 677 664 651 637 15 50 I7x7/ s 821 805 790 774 758 743 15 15 33 33 19x& 19x 513 646 505 636 497 625 489 615 481 | 473 604 | 594 15 40 19x^ 599 589 580 570 561 551 15 40 19x54 731 719 708 696 684 672 15 45 19xft 674 663 652 641 630 619 15 45 19x|| 806 793 | 780 767 753 740 IS 50 19x5% 748 736 724 711 699 687 15 50 19x7/ & 880 866 851 837 822 808 45 TABLE XX. H Total Load in Thousands of Pounds Allowed on Zee- Bar Columns* Width of Web Plate Webof|Thick- Z-Bar | ness Unsupported Length of Column. in In. in In. of Metal 10ft. 12 ft. |14 ft. 16ft. 18 ft. | 20 ft. 6 3 54 107 100 | 93 86 79 72 6 3 I 5 e 136 128 | 119 110 102 9.-: 6 3 In 157 147 137 127 116 106 6 3 & 186 174 163 151 139 128 6 3 H 205 192 178 165 152 139 6 3 S 234 219 205 191 176 162 7 4 ft 141 134 | 128 122 115 109 7 4 v\ 178 170 162 154 146 138 7 4 y 215 206 196 187 178 168 7 4 2 239 228 217 206 195 185 7 4 S 276 263 251 239 227 215 7 4 ft 313 299 286 272 259 245 7 4 8 330 316 301 286 271 257 7 4 H 367 351 335 319 303 287 7 4 M 404 1 387 370 353 336 319 7 5 A 204 | 197 | 190 183 176 169 7 5 H 247 238 | 230 222 213 205 7 5 <& 290 280 271 261 251 241 7 5 Vz 317 306 295 284 273 262 7 s & 360 348 335 323 311 299 7 s ii 403 390 376 363 350 336 7 5 u 424 409 395 380 366 351 7 5 M 466 450 435 419 403 388 7 5 ft 509 j 492 476 459 442 425 8 6 Hi 284 276 268 260 252 244 8 6 S 334 325 315 306 297 287 8 6 s 384 373 363 352 342 331 8 6 & 416 404 392 381 369 357 8 6 465 452 439 426 413 401 8 6 Jl 515 501 486 473 458 444 8 6 ^ 540 525 510 495 479 464 8 6 11 589 572 556 540 523 507 8 6 s 636 618 601 583 565 J 547 46 CHAPTER V. Lintels. Some examples of cast iron lintels will be found in Chapter VI. This chapter will be taken up with the sub- ject of steel lintels. Lintels are often made so that only the edge of a plate or the edge of an angle will show in the face of the wall. The steel must be set back a little so as to allow pointing at the supports. (i) Fig. 1 shows a number of different styles of lintels. In a solid wall it is usual to calculate the lintels as carrying a height of wall equal to one-third of the opening. Where the 'top of a wall or a large opening occurs a short distance above the lintel, say a height equal to the span or less, the full height of wall should be borne by the lintel. If floor concentrations or wall piers occur over the opening, the effect of these loads must be considered. A lintel such as that shown at (a) Fig. 1, made up of 2 4"x3"x5-16" angles with the short legs vertical and riv- eted together, may be used in a 9-in. solid wall for spans up to 8 ft. Two 6"x3%"x^" angles may be used in like manner in a 13-in. wall for spans up to 8 ft. A standard 9-in. channel may be used as at (e) for openings up to &/ 2 ft., and a standard 12-in. channel may 47 be used for openings up to 7 1 /6 ft., 'these in 9-in. and 13-in. walls, respectively. In the following table, taken from "Steel in Construc- tion" (Pencoid Iron Works), the lintels are selected to deflect 1/360 of the span up to 10 ft, and 1/500 of the span above 15 ft. The fiber stress, assuming 'the lintel to carry a height of wall Y$ of the opening, is within 16,000 Ibs. per sq. in. TABLE I. ' SIZE OF STANDARD I-BEAMS FOR LINTELS. Span in Feet. oT h Wail 8 <> r 9 10 or 11 12 or 13 14 or 15 16 or 17 18 or 20 9-in. | 2-4-in. 2-5-in. 2-7-in. 2-8-in. 2-9-in. 2-12-in. 13-in. | 2-4-in. 2-6-in. 2-7 -m. 2-8-in. 2-9-in. 2-12-in. 18-in. | 2-5-in. 2-7 -in. 2-8-in. 2-9-in. 2-10-in. 2-12-in. 22-in. | 2-5-in. 2-7 -in. 2-8-in. 2-9-in. 2-10-in. 2-12-in. NOTE: Cast iron separators are to be used in every case. Table I can be used in selecting the sizes of beams and channels to be used in lintels, such as those shown in (c) and (d) Fig. 1, using two channels in place of a beam. The angles should be counted as simply acting as sup- ports for the first few courses of bricks. The methods given in Chapter VI may be employed to find the size of beams and channels required in any lintel. Sometimes a loose angle is used with the lintel, as at (g) Fig. 1. This is merely to carry the face brick up to the level of the top of the beams. Sometimes an I-beam, instead of the channel shown at (cl), is exposed in the face of the wall ; this allows building up of the brick work over supports, if no offset occurs in the wall at jambs. The wooden pieces shown at (g), (h) and (i) are for nailing on the wood finish. Separator bolts should be ordered long enough to include these. Separators for lintels are usually short pieces of gas pipe slipped over the bolts. 48 CHAPTER VI. Beams. Beams may be made of wood, cast iron, steel or rein- forced concrete, though cast iron is seldom used for beams, except in the case of window lintels and the like. The selection of wooden beams or joists to carry a certain load is restricted, and is also simplified by the commercial sizes. A unit stress of 800 Ibs. per sq. in. should be used for soft woods, such as white pine, and 1,000 Ibs. may be used for white oak and long-leaf yel- low pine. A simple way to find the size of wooden beam is by use of Table I. In this table the coefficient C is equal to the product of the span of the beam in feet and the total uniform load in pounds, which the beam can safely carry. If, for example, a wooden beam of a span of 10 feet is to carry a load of 150 Ibs. per lineal foot, or 1,500 Ibs., the value of 'the coefficient C for such a beam would need to be 10x1,500 or 15,000. A 2x10 beam in white pine or a 2x9 beam in oak or yellow pine would suffice. The total load, uniformly distributed, that any beam may safely carry is readily found from the table by dividing the value C by the span of the beam in feet. (Note that C is the product of one-ninth of the unit stress by the width of beam by the square of the depth.) If the load on a beam is central and concentrated, in- stead of being uniformly distributed, it should be dou- bled for finding the size required, as such a concentrated load is twice as effective in producing bending moments as the same load uniformly distributed. If, for example, a wooden girder having a span of 16 feet is to carry a center load of 3,500 Ibs., the value of C would be 2x3,500x 16=112,000. A yellow pine beam 4x16 would suffice. The depth of wooden beams should generally be be- tween one-tenth and one-twentieth of the span. Beams deeper 'than one-tenth will be overstressed in shear, when strained to their capacity in bending, with a uniform load; beams shallower than about one-twentieth will deflect too much under load. TABLE I. Size of Beam in Inches. C, for White Pine. C, for Oak or Y. P. 2x 4 2,840 3,550 2x 5 4,440 5,550 2x 5 6,400 8,000 2x 8 11,400 14,220 2x 9 14,400 18,000 2x10 17,800 22,220 2x12 25,600 32,000 3x14 52,270 65,330 3x15 60,000 75,000 4x16 91,020 113,770 Cast Iron Beams. Cast iron can only be used economically in beams in shapes that have wide or heavy tension flanges, because of -the weakness of cast iron in tension. as (c) fd) Lintels for brick walls are sometimes made in cast iron in shapes such as shown in Fig. 1. Calculating 4,000 Ibs. per sq. in. tension on the cast iron, and assuming that a height of wall one-third the height of the opening is carried by the lintel, the lintel shown in end view at (b) could be used in a 9-in. brick wall, in ^-in. metal, for openings up to about five feet. In ^-in. metal it could be used for openings up to six feet. The lintel shown in end view at (d) has just about double the strength and dou- ble the load of that shown at (b), so that the same limits 50 of spans can be used. The one shown at (c) could span larger openings, theoretically, but it is not advisable to use long beams in cast iron, because of the uncertainties in the metal. Steel beams are more reliable for large openings. Also, if the opening has a pier or a concen- trated load above it, steel lintels should be used, designed to carry that load. Steel Beams. Nearly all of the beams in a building are designed for uniform load, so that the determination of the sizes is generally a simple matter, when tables are at hand. It is a common standard in building work to allow 16,000 Ibs. per sq. in. extreme fiber stress on the steel. This is a correct unit for quiescent loads, such as those in build- ings. It would be too high for rolling loads such as bridges, so that the methods and units of this chapter cannot be employed to design bridges. It should be clear- ly understood that this chapter, and in fact this entire book, applies only to building work. Bridges are designed on quite a different standard and by different methods. Many handbooks give tables showing 'the total load which a beam will carry. The tables of this chapter give instead a quantity for the several sizes of beams, desig- nated Q, by which the capacity of a beam may readily be found. The quantity Q is equal to the product of the span of a beam in feet and the load in tons (of 2,000 Ibs.) that the beam can safely carry as a uniformly dis- tributed load. To find the size of a beam for a given case, it is only necessary to find the load in tons that the beam must carry and multiply this by the span. Then by looking in the tables l?nd a value Q that equals this product. That beam is then a proper size for the case, assuming that it is held against lateral displacement in the building. The full strength of beams, as exhibited in this chap- ter, is only realized when the beams are properly stif- fened and properly supported at the ends. For the end supports of beams see Chapter X. The matter of stiff- 51 ening of the beams or lateral support will be considered here, as this is a matter vitally connected with the general strength of the beam, and it is a matter not so generally understood nor appreciated as that of the necessity for proper support at the ends of a beam. In Engineering News, January 6, 1910, will be found the record of an experiment on small beams built of tin plate, in which the mere addition of end stiffeners to one of two beams identically made added 129 per cent to the ultimate strength of the beam thus stiffened. The purpose of adding the stiffeners was not to prevent the web from buckling, but to prevent the beam from keeling over at the support. The beam which had not the end stiffeners failed by leaning of the web in opposite directions at the ends, or by a twisting of the entire beam. This shows con- clusively, what analysis would dictate, namely, that it is necessary in all beams, in order to develop the full strength, that the beam be held against lateral tilting at the ends. In the ordinary case in buildings this is accom- plished by building the ends of beams into the wall or by the riveted end connections of the beam. The top flange of a beam should also be held laterally at intermediate points. This is usually accomplished by the arches between the beams or the floor slabs resting on top of them. Where it is not practicable to stiffen the compression flange of a beam continuously, it should be braced at intervals. The intervals should not be more than about sixteen times the width of the flange, if the full tabular value of the beam is used. If it is necessary to have the compression flange unsupported for 50 times the width, only one-half of the tabular value for the strength of the beam should be used. At 25 times the flange width, unsupported, use y% of the tabular load; at 33 times, use 54 '> at 42 times, use ^&. When there is any plastered work or concrete covering, the depth of steel beam should not be less than about one- twenty-fourth of the span, so that the deflection will not be too great. In other work a limit of one-thirtieth may tc" observed. 52 Examples. (1) Given a mill roof with channel purlins spaced 5 ft. apart, 2-inch matched tongue-and-groove board sheath- ing, tar and gravel covering, snow load 50 Ibs. per sq. ft., span between trusses 16 ft. Assume 7 Ibs. per sq. ft. for covering, 8 Ibs. per sq. ft. for sheathing, and 3 Ibs. per sq. ft. for purlins. The load per foot on purlin is (50-}-7-f- 8-f3)X5=340 Ibs. The load carried by one purlin is 340X16=5,440 Ibs., or 2.72 tons. Q is then 2.72x16=43.5. Q for a standard 8-in. 11 -/4 Ib. channel is 43.2, hence this size would be used. (2) Given floor beams supporting tile arches, span 13 ft, distance apart 6 ft., 1" floor on sleepers filled with cin- der concrete, live load 80 Ibs. per sq. ft. Assume 10-in. arches, which weigh 39 Ibs. per sq. ft. The several weights are: 15 Ibs. for cinder concrete and sleepers;, 4 Ibs. for wooden flooring; 7 Ibs. for steel, fireproofiwg and ceiling, and 80 Ibs. for live load. This is a total of 145 Ibs. per sq. ft. or 7.83 tons per beam. Q is 7.83X18=140.9. By interpolating between a 10" beam 25 Ibs. and 40 Ibs., it is found that a 10" 30 Ib. beam would suffice. If standard beams are preferred 12" 31^ Ib. beams could be used. Ten-inch arches can be used on these by offsetting the ceiling at each beam. If conditions permitted, closer spac- ing of the beams could be used, and 10-in. 25 Ib. I-beams would suffice. (3) Given floor beams spaced 9 ft. apart supporting a 4-inch reinforced concrete slab with 1-inch tile floor on the same, the span being 20 ft, and live load 100 Ibs. per sq. ft. The load per sq. ft. is as follows: Live load 100, concrete 50, tile and filling 20. This is 1,530 Ibs. per lineal foot of beam. Adding for weight of beam and surround- ing concrete 150 Ibs. per ft., the weight on the beam is 1,680X20=33,600, or 16.8 tons. Q is 336. By interpola- tion a 15" 50-lb. beam is found to be correct. (4) Given a double wall beam to be made up of an I-- beam and a channel of the same depth, the beam to carry 12 ft. of vertical height of a 13-inch wall and 4 ft. of a 53 floor load at 200 Ibs. per sq. ft. total, the span being 18 ft. The wall will weigh 130X12 or 1,560 Ibs. per lin. ft. Adding to this 800 Ibs. for the floor load and 60 Ibs. for the weight of the beam, we have 2,420 Ibs. per lineal foot. The load carried by the beam is then 21.78 tons, and Q is 392. By trial it is seen that a 12" I 40 Ibs. and a 12" chan- nel 35 Ibs. will have a combined value of Q equal to this. By using a channel and beam of different depths stand- ard sections could be employed, as a 15" beam 42 Ibs. and a 12" channel 20.5 Ibs. (5) Given a system of T bars, supporting 18-inch book tiles, carried on purlins spaced 10 ft. apart. Weight of book tile arid roofing per sq. ft. 30 Ibs., live load 50 Ibs. Total weight on T bar 80x1^X10=1,200=0.6 ton. Q=6. A 3X3X10.1 Ib. T would suffice. (6) Given a system of double angles spaced 4 ft. apart on a span of 8 ft. supporting a balcony ; live load 60 Ibs. per sq. ft. Assume a slab weight of 50 Ibs. per sq. ft. total. A pair of angles will carry 110x4x8=3,520 Ibs or 1.76 tons. Q=1.76x8=14.08. The value of Q for 2 angles 4"x3"x->, long legs vertical, is 15.6. Note that these angles would weigh more than beams or channels of the same strength, and they would hence not be the most economical section to use. However, they afford a better seat for a slab, if it is the intention to keep the supporting beam within the depth of the slab. Xote that a 4x5x1 5.7-lb. T- bar would be of sufficient strength for this case, but the 5-inch stem might be too deep. WJ M = Fig. 2. 54 M . wi In Fig. 2 are given several cases of beams and the bending moments for each. Case 1 is that of a simple beam uniformly loaded. The values of Q in Tables II to VII are for this case. They can be made to apply to any of 'the other cases as follows: For a single concentrated load at the center of a given span it is seen that the bending moment M is just double that which the same load would produce if uniformly dis- tributed over the span. Hence a single concentration at the center of a span will give the same bending as twice that load uniformly distributed. To use Tables II to VII, then, we will have to double the concentration and use that load as a uniform load. Examples : (1) Given an I-beam on a 12-ft. span supporting a concentrated load at the center of span of 24,000 Ibs. Doubling this to find the equivalent uniform load and multiplying by 12 (after reducing to tons) we have 288 as the value of Q, A 15" -I, 42 Ibs. would then be re- quired. (2) Given a pair of beams on a span of 8 ft. support- ing a column load at the center of span of 150,000 Ibs. 150,000X2=300,000 Ibs. or 150 tons. 150x8=1,200, the value of Q. Two 20" beams 65 Ibs. have a value Q=l,248. (3) Given an opening in an 18-in. wall 17 ft. wide and a floor-girder just above the middle of same with a load of 37,500 Ibs. Call the span of the lintel 18 ft. wide and as sume a wall load 6 ft. high or 180X6X18=19,440 Ibs. The equivalent uniform load is 37,500X2+19,440=94,440 Ibs. or 47.22 tons. Q is 47.22x18=850. .Two 18" beams 55 Ibs. would be somewhat stronger than necessary. When the concentrated load is not at the center of span, a special case arises, and the simplified methods of this chapter do not apply. Case 3 in Fig. 2 is for a cantilever beam uniformly loaded. It is seen that the bending moment is four times as great for the same load and span as that found in a 55 simple beam. Hence the equivalent load for a simple span to be used in tables II to VII will be four times the actual uniform load on the span. Examples : (1) Given a roof truss load of 80,000 Ibs. to be distrib- uted by means of two wall beams 5 ft. long into a brick wall. . 25' 1 2.5 mtmmt BO ooo LSV Fig .3. Here the load which is uniformly distributed is an up- ward one, being the reaction of the brick wall against the beams. The span / is 2.5 ft. and the load on each of these cantilevers is 40,000 Ibs. The equivalent load for a simple beam is 4X40,000=160,000 Ibs. or 80 tons. Q is 80x2^= 200. Two 9" beams 21 Ibs. have a value of Q equal to 201.6. (2) Given a building in which the wall is omitted at the corner for a distance of 6 feet, there being no corner post but cantilever beams at the second story meeting at the corner and supporting the wall and floors above. As- sume that the total weight of wall and floor load is 4,200 Ibs. per running foot, and that the effectual span of the cantilever is 7 ft. The load carried by the cantilever is 4,200X^=29,400 Ibs. The equivalent load for a simple span is 29,400X4=117,600 Ibs. or 58.8 tons. Q is 58.8x7= 411.6. Two 12-in. 35-lb. beams would come within a small percentage of filling the requirements. (3) Given roof rafters projecting 4 ft. beyond a wall and supporting rienforced concrete slabs, the rafters be- ing spaced 6 ft. and the total load carried being 80 Ibs. per horizontal square foot. The load on a rafter is 80X4X 6 =1,920 Ibs. The equivalent load for a simple beam is 1,920X4=7,680=3.84 tons. Q is 3.84X4=15.36. 56 The rafter could be a 4" 7,^-lb. beam, or a 5" 6^-lb. channel, or a 2-4"X3"X^s" angles, or a 4"X/4" zee-bar, or a 4"x5"Xl6.7-lb. T-bar. Case 4 in Fig. 2 is for a concentrated load at the end of a cantilever. The moment here is eight times as great for a given span and load as that for a simple beam. The equivalent load for a simple beam is then eight times the amount of the concentration. Examples. (1) Given a balcony 7 ft. wide supported on cantilever beams spaced 12 ft. apart. A facia beam supports one side of a slab and a railing. Assume the floor load on the facia beam to be 420 Ibs. per ft., and the railing to weigh 40 Ibs. per ft. The concentrated load at the end of the cantilever beam is then 460X12=5,520 Ibs. or 2.76 tons. The equivalent uniform load for a simple span is 2.76X8= 22.08. Q is 22.08X7=154.56. This could be a 10"-I 35 Ibs. or 2-10" channels 20 Ibs. (2) Given a cantilever beam supporting a column at its end, the overhang being 4 ft and the column load being 120,000 Ibs. The equivalent load for a simple beam is 120,000X8=960,000, or 480 tons. Q is 480x4=1,920. This would require 2-24" I beams 85 Ibs. (3) Given a cantilever beam supporting a uniform load of 800 Ibs. per ft. and a concentrated load at the outer end of 10,000 Ibs., 'the span being 10 ft. The equivalent uniform load for a simple beam is 8,000 (the total uniform load) x 4+10,000X8 or 112,000 lbs.=56 tons. Q is 56x10 =560. A 15" I 80 Ibs. would do, but a 20" I 65 Ibs. is much stronger and would weigh less. 57 TABLE II. Capacity of Standard I Beams and Channels Extreme fiber stress 16,000 Ibs. per sq. in. Size. Q. Size. 0- Size. Q. 24" 100 Ib. 1058.2 / 10" I 40 Ib. | 169.1 j 12" Ch. 40 Ib. 174 24" 80 Ib. 928.0 X 10" I 25 Ib. 130.1 1 12" Ch. 20>4 Ib. 114 20" 100 Ib. 883.2 j 9" I 35 Ib. 132.3 / 10" Ch. 35 Ib. 123 20" 80 Ib. 782.4 J 9" I 21 Ib. 100.8 \ 10" Ch. 15 Ib. 71 20" 75 Ib. 676.9 j 8" I 25 54 Ib. 91.2 f 9" Ch. 25 Ib. 83. 20" 65 Ib. 624.0 j 8" I 18 Ib. 75.7 1 9" Ch. 1354 Ib. 56. 18" 70 Ib. 546.1 ) 7" 20 Ib. 64.5 j 8" Ch. 2154 Ib. 63. 18" 55 Ib. 471.6 } 7" 15 Ib. 55.5 < 8" Ch. 1 1 54 Ib. 43. / 15" 100 Ib. 640.6 / 6" 1754 Ib. 46.4 ( 7" Ch. 19^4 Ib. 50 1 15" 80 Ib. 565.9 \ 6" 1*54 Ib. 38.9 1 7" Ch. 9)4 Ib. 32 / 15" 75 Ib. 491.7 / 5" 14y 4 Ib. 32.5 / 6" Ch. 1554 Ib. 34. 115" 60 Ib. 433.0 15" 9M Ib. 25.6 1 6" Ch. 8 Ib. 22. {15" 55 Ib. 363.2 J 4" 1054 Ib. 19.2 J 5" Ch. 1154 Ib. 22 115" 42 Ib. I 314. T 1 4" 754 Ib. 16.0 1 5" Ch. 654 Ib. 16. f 12" 55 Ib. 285.3 J 3" 754 Ib. 10.1 / 4" Ch. 754 Ib. 12 1 12" 40 Ib. 238.9 13" 554 Ib. 9.1 \ 4" Ch. 554 Ib. 10 M2" 35 Ib. 202.7 f 15" Ch. 55 Ib. 306.1 j 3" Ch. 6 Ib. 7 1 '2" 3154 Ib. 192.0 1 15" Ch. 33 Ib. 222.4 1 3" Ch. 4 Ib. 5 NOTE; It is preferable to use the lighter or standard weight of the several bracketed pairs. For intermediate weigkti interpolate to find the value of Q. TABLE III. Capacity of Bethlehem I Beams* Extreme fiber stress 16.000 Ibs. per sq in. Size. Q. Size. Q. Size. 1 Q. 30" 120 Ib. |1862. 9 20" I 59 lb.| 625.1 15" 1 38 Ib. 314. 28" 105 Ib. 1529.1 18" I 59 Ib. 523.2 12" I 36 Ib. 239. 26" 90 Ib. 1221.3 18" I 54 Ib. 499.2 12" I 32 Ib. 203. 24" 84 Ib. 1058.7 18" I 52 Ib. 489.1 12" I 2854 Ib. 192. 24" 83 lb.| 995.7 18" I 4854 Ib.i 473.1 10" I 2854 Ib. 143. 24" 73 lb.| 929.6 15" I 71 Ib. 566.4 10" I 2354 Ib. 131. 20" 82 li). 832. Oj 15" I 64 Ib. 472.5 9" I 24 Ib. 109. 20" 72 Ib. 782.4 15" I 54 Ib. 433.6 9" I 20 Ib. 100. 20" - 69 Ib. 676. 8 1 15" I 46 Ib. 344.5 8" I 1954 Ib. 80. 20" I 64 Ib. 651 .7 15" I 41 Ib.i 324.8 8" T WV* Ib. 76. 58 TABLE IV. Capacity of Bethlehem Girder Beams* Extreme fiber stress 16,000 Ibs. per sq. in. Size. | Q. Size. | Q. Size. | Q. 30" 200 lt>. 30" 180 Ib. 28" 180 Ib. 28" 165 Ib. 26" 160 Ib. 26" 150 Ib. 24" 140 Ib. 3253.3 2913.6 2767.5 2500.3 2306.1 2114.7 1867.2 24" 120 Ib. 20" 140 Ib. 20" 112 Ib. 18" 92 Ib. 15" 140 Ib. 15" 104 Ib. 15" 73 Ib. 1603.2 11565.3 1249.1 942.9 1132.8 867.7 628.3 12" 70 Ib. 12" 55 Ib. 10" 44 Ib. 9" 38 Ib. 8" 32 H Ib. 478.9 384.0 260.3 202.7 152.5 TABLE V. CAPACITY OF ANGLES IN BENDING. Long Leg Vertical, for Unequal Leg olngles. Extreme fiber stress 16,000 Ibs. per sq. in. Size. | Q. Size. | Q. Size. | Q. 8 x8 xl 84.3 2j4x2J4x l / 2 \ 3.9 5 x3 x ft 18.9 8 x8 x y 2 44.6 2^x2^x y 4 2.1 5 x3 x A| 10.1 6 x6 x y 4 35.5 2 x2 x ft 1.9 4 x3 x ft 12.3 6 x6 A 3/ 8 18.8 2 x2 x T 3 ff 1.0 4 x3 x ft| 6.6 5 x5 x Y 4 24.2 7 x3^x ft\ 43.8 3Hx3 x ft 9.4 5 x5 x ft 12.9 7 x3^x f e \ 26.7 3^x3 x M 5.1 4 x4 x Y 4 15.0 6 x4 x Y 4 33.3 3^x2^x y 2 7.5 4 x4 x T B 8 6.9 6 x4 x ft 17.7 3^x2^x y 4 4.0 3y 2 x3y 2 x ft 9.7 6 x3y 2 x ft 32.5 3 x2^x y a 5.6 3^x3^x A| 5.2 6 x3y 2 x ft 17.3 3 x2^x y 4 3.0 3 x3 x y 2 5.7 5 x3^x ft 22.8 2y 2 x2 x ft 2.9 3 x3 x y 4 3.1 5 x3 J / 2 x T 5 ff 10.3 2^x2 x A| 1.6 NOTE Interpolate for intermediate thicknesses. 59 TABLE VI. Capacity of Zee-Bars in Bending. Extreme fiber stress 16,000 Ibs. per sq. in. Size. Q. Size. | Q. Size. Q. 6 x3 l / 2 x Ml 45.0 5 x3J4x y 2 \ 41.0 4 x3J s x 5^ 32.3 Al 52.4 Al 46.0 H 35.5 59.9 H\ 51.0 M 38.7 6 x3j^x T 9 g 61.4 5 x3y 4 x HI 50.5 3 x2H* 54 10.2 H 68.4 ?4 55.2 A| 12.7 H 75.2 if 59.7 3 x2Hx Ml 13.7 74.9 4 x3Ax H 16.8 Al 15.9 x }i 81.2 A 20.9 3 x2}Jx y.\ 16.3 87.5 24.9 9 18.3 5 x3J^x i s g 28.5 4 xS-i^x A 25.8 H 34.1 HI 29.3 A 39.7 T 9 *l 33.0 NOTFy Web, flange and thickness increase by same amount in each group. TABLE VII. Capacity of Carnegie Tee- Bars in Bending. Extreme fiber stress 16,000 Ibs. per sq. in. Size, Flange by Stem by Wt. per Ft. Q. Size, Flange by Stem by Wt. per Ft. Q. Size, Flange by Stem by Wt. per Ft. Q- 5 x3 x!3.6| 6.3 3^x4 xlO.O 8.3 2>4x3 x 7.2 4.6 5 x2^xll.O 4.6 3^x3^x11.9 8.1 2j^x3 x 6.2 4.1 4^x3^x15.9 11.4 3Hx3^x 9.3 6.4 2^x2^x 6.8 3.9 4J/2X3 x 8.6 4.3 3^x3 xll.O 6.0 2^x2^x 5.9 3.2 4j4x3 xlO.O 5.0 3^x3 x 8.7 4.7 . 2^x2^x 6.5 3.1 4y 2 x2y 2 x 8:0 3.0 3^x3 x 7.7 3.8 2^x2^x5.6 2.7 4*/ 2 x2y 2 x 9.3 3.5 3 x4 xll.9 10.3 2^x1 J4x 3.0 0.5 4 x5 x!5.7 16.5 3 x4 xlO.6 9.5 2y 4 x2y 4 x 5.0 2.2 4 x5 x!2.3 13.0 3 x4 x 9.3 8.4 2%x2y 4 x 4.2 1.7 4 x4^x!4.8 13.6 3 x3^xll.O 7.9 2 x2 x 4.4 1.8 4 x4^xll.6 10.6 3 x3j^x 9.8 7.3 2 x2 x 3.7 1.3 4 x4 x!3.9 10.8 3 x3^x 8.6 6.5 2 xl^x 3.2 0.8 4 x4 xlO.9 8.7 3 x3 xlO.l 5.9 \Mxiy 4 x 3.2 1.0 4 x3 x 9.3 4.7 3 x3 x 9.0 5.4 l^xl^x 2.6 0.7 4 x2^x 8.7 3.3 3 x3 x 7.9 4.6 iy 2 xiy 2 x 2.0 0.6 4 x2^x 7.4 2.9 3 x3 x 6.8 3.9 i i Axiy 4 x 2.1 0.5 4 x2 x 7.9 2.1 3 x2^x 7.2 3.2 \y 4 x\y 4 x 1.7 0.4 4 x2 x 6.7 1.8 3 x2^x 6.2 2.8 1 xl x 1.3 0.3 3^x4 x!2.8 10.6 2^x2 x 7.4 4.0 1 xl x 1.0 0.2 60 Reinforced Concrete Beams. In the author's book "Concrete" a simple theoretic treat- ment of reinforced concrete beams is given; also certain rules are derived for the design of such beams. The reader is referred to that book for a discussion of the theory ; the rules will be summarized here and a brief out- line of the theory given. The generally accepted standard of reinforced concrete design in America is a hodge-podge of so-called practical mens' patented ideas, given a semblance of authority by eminent investigators and authors, who discuss designs and tests with little or no logical analysis of the stresses in the reinforcement. Sharp bends are made in rods, loose stirrups are assigned stresses that they could not possibly take, steel rods are crowded into the stem of T-beams with no regard to the ability of the concrete to transmit stress into the steel these and many other absurdities stamp present day practice in reinforced concrete as be- ing on a far lower plane than highway bridge design of 20 years ago. The light highway bridges ofc the early days of steel bridge are gradually being condemned or fail- ing, not because of wear but because of original weakness; many large reinforced concrete buildings have already failed, at the time when they were nearly completed, be- cause of weak design. Reinforced concrete is a most excellent form of con- struction, when properly designed, but American standard design, as exhibited in nearly all the books and in the greater part of the work as illustrated in engineering peri- odicals, is far from being on a sound basis. In a paper entitled, "Some Mooted Questions in Rein- forced Concrete Design," by the author, read before the American Society of Civil Engineers in March, 1910, com- mon practice in reinforced concrete design is severely criti- cised in sixteen indictments covering as many phases of that practice. The wide publicity given this paper, (it was reprinted in Engineering News and very fully reviewed in Concrete Engineering), puts it beyond peradventure that 61 all of the authors and investigators whose methods of design and analysis were attacked in that paper are aware of the attack. Very few have made any defense of any sort. The criticism which followed the reading of the paper, by its illogical analysis, dogmatic assertions and dodging arguments, as well as the strong support given by many eminent engineers, has served to strengthen the stand taken by the author; it proves the crying need of reform in reinforced concrete design. The foregoing is deemed to have proper place in this book because the book is designed for a class of men who have to deal with buildings, and because it is in building work that the greatest faults in design are exhibited ; it is in building work too that the greatest wrecks have oc- curred. The author's castigation of common practice, both in reinforced concrete and in steel design, (See "Engineer- ing News," April 11, 1907) has no other motive than a desire to do what he can to place structural design of all kinds on a sound engineering basis. Following are a number of rules of design for beams in reinforced concrete. Rule 1. Use no loose stirrups. They interfere with the pouring of the concrete ; they cannot possibly take any kind of stress commensurate with their size ; they are prac- tically useless until failure has begun in the beam and are therefore illogical as an element of design. Figs. 4 and 5 show how beams with stirrups may fail. The upper loose ends may readily pull out of the concrete. r \fL 62 Rule 2. Make no sharp bends in reinforcing rods where any considerable stress in the rods exists. At the bend there is set up a side stress in the concrete which the lat- ter is unable to resist. Rods should be given gentle curves, preferably with a radius equal to 20 times the diameter of the rod. Rule 3. Place no dependence upon hooks or sharp bends in rods as anchors. Anchorage of steel rods may be erf- fected by embedment in concrete to a depth of 50 times the diameter of the rod beyond the point where the full strength of the rod is needed;, or it may be effected in a round rod by use of an end nut and a washer or bearing plate, the latter having a bearing surface about twenty times the area of the rod. Rule 4. Reinforcing rods at the bottom of a reinforced concrete beam extending straight from end to end of span, should have a diameter not more than 1-200 of the length of span. Rule 5. Reinforcing rods, when curved up to the top of a beam, should run to the end of span and be anchored over the support or run beyond the support so as to take a hold in the concrete. The practice of bending up rods with a sarp bend and of ending them short of the sup- port, or even at the support, and not anchoring them over or beyond the support, is a poor and illogical one. Rule 6. In beams having a depth of about one-tenth of the span or more, shear reinforcement is needed. Some of the reinforcing rods should be curved up as shown in- Figs. 6, 7, 8, 9. 63 Note that 50 diameters of the rod is allowed beyond the edge of support for anchorage in Fig. 6, 7, and 8. In Fig. 9 washer plates and nuts are used. If the width of a beam resting on a wall is sufficient, the rod may be curved down, as in Fig. 7, and receive sufficient anchorage within the confines of the beam. The curve should not be sharp but with a radius of about 20 times the diameter of the rod. In a continuous line of beams the portion of the rod that extends into the next beam for anchorage may per- form the additional service of acting as upper reinforce- ment in that 'beam. Continuity of beams will of course give rise to tension over the suports at the top of the beams. Some of the rods may be bent as shown in Fig. 8 (all of these should run into the next beam for full an- chorage), but there is scarcely any need of this; they could all be bent as in Fig. 6, as any local irregularities in the shear can readily be taken care of in the concrete. Rule 7. The width of a beam should be about equal to the sum of the perimeters of all reinforcing rods that lie near the bottom of the beam from end to end of span. This rule would make the spacing of square rods four times their diameters and of round rods 3.14 times their diameters, with a side distance of 2 and 1.57 diameters respectively on each side of the outer rods. Several tiers of rods in the bottom of a beam should, in general, be avoided. In addition to the foregoing rules for the design of individual beams it is important to add these two pre- cautions : First, in the general design the entire structure should be tied together so as to preserve its integrity. Beams should be joined to one another by rods; they should be tied into the columns; slabs should be tied into the beams and girders. Second, where beams or girders frame end to end, there should be reinforcing rods near the top running across the support to prevent cracking. It is recommended that the area of this reinforcing steel across the supports be equal to one-half of that of the reinforcement of the beams at middle of span, also that 64 the rods reach from quarter-sp$ to quarter-span of the beams. The following unit stresses are recommended : Tension on steel, 14,000 Ibs. per sq. in. Compression on extereme fiber of the concrete, 600 Ibs. per sq. in. Shear on gross section of concrete about 30 Ibs. per sq. in. Tables VIII to XIII give reinforcement and sizes of rectangle of concrete, as well as a coefficient to determine the carrying capacity, of beams designed according to the foregoing rules and with the unit stresses just given. In all of these tables b is the width of concrete beam; d is the depth out to out of the concrete beam. The center of the reinforcing rods, at middle of span, is one-eighth of the depth d from the bottom of the beam. This makes the depth of concrete protecting and gripping the steel proportional to the magnitude of the rod, as it should be. The neutral axis of the beam is in all cases assumed to be at the middle of the depth of the concrete beam. Tables VIII and IX are for a single straight rod. (Of course several rods may be used by making the width in multiples of b.} In these tables as in the others, the steel area is 1.07 per cent. This governs the area of beam or the product of b and d. The minimum value of b is the perimeter of a rod. The minimum value of the span length is governed first by 200 times the diameter of the rod and second by twelve times the depth. The first is in accordance with Rule 4; the second is to keep the beam well within Rule 6, since it has no shear reinforcement. Tables X and XI are for reinforcement with three rods, two of which are straight, and the third is curved up as illustrated in Figs. 6, 7, and 9. The last mentioned rod carries the shear which the concrete is not capable of tak- ing. This rod, being curved up in an approximate para- bolic shape, will take the shear incident to its own stress, 65 or one-third of the total. The remainder of the shear is carried by the concrete. This condition governs the minimum span length. Another governing condition in the minimum span length is 200 times the diameter of rods. It is seen that the width of beam is nowhere less than the sum of the perimeters of the two straight rods. It will also be seen that the depths all lie between 23 and 36 times the diameter of the rods. This, however, has no special significance. Tables XI and XII are for reinforcement with four rods, two of which are straight and the other two are curved up as illustrated in Figs. 6, 7 and 9. The two curv- ed rods carry one-half the shear and the concrete carries the other half. This condition governs the minimum span length, which is further limited by 200 times the diameter of rods. The width of the beam is nowhere less than 2Vz times the perimeter of one rod. The depths all lie between 29 and 38 diameters. Examples. (1) Given a 9-in. wall spanning a 6-ft. opening, 5 ft. of wall above the opening. Required a reinforced concrete lintel to carry the wall and 1,000 Ibs. per ft. of floor load. The weight of the wall is 90X5X6=2,700 Ibs., and the floor load is 6,000 Ibs. C=8,700X6.5=56,600. (Note that 6.5 ft. is used as the span to allow for bearing on the wall. By reference to Table VIII it is seen that 4 beams 2^4" wide and 10^" deep, with four y 2 " square rods for reinforcement, would have a value C 69,400. This is more than necessary. The lintel would, of course, be 9" wide and W l / 2 " deep with four W square rods lying near the bottom. It is assumed that the depth of lintel is in- cluded in the height of wall, so that no extra allowance was made for the weight of the lintel. The Ikitel should rest on the wall for about 10" at each end. The rods would be about 7 l / 2 feet long. (2) It is desired to design a ribbed floor filled with 12" t'le, the reinforced concrete ribs being about 4" wide. Span, 16 ft. Over the ribs will be laid wooden sleepers, filled in between with cinder concrete ; on the sleepers will be nailed a 1" maple floor. Live load 66 Ibs. per sq, ft. Each rib supports 16" of floor. The weights per foot are: Live load, 88; tile, 44; rib (estimated), 50; cinder fill and sleepers, 30; flooring, 5. Total, 217 Ibs. per ft. Total load on one rib=21 7X16=3,472 Ibs. C=3,472X 16=55,550. By reference 'to Table VIII it is seen that a 324"X14" rib with one 24" square rod for reinforce- ment has a value C=52,100, which is sufficiently close to the requirements. (3) Required a reinforced concrete beam carrying a floor load of 800 Ibs. per ft. on a clear span of 16 ft. The assumed weight of the beam is 180 Ibs. per ft. Total load on beam 980X16=17,480 Ibs. 0=17,480X16=279,700. Ap- plying tables VIII to XIII inclusive we find the following: Table VIII. A single reinforcing rod, without end an- chorage, will not suffice, since beams with a value of C= 279,700 or more have 'too great a minimum span length. The same is true if we take C= 139,900 and use two rods. At C=93,200, using three rods, we could use a beam 16^2" wide and 16^>" deep with three I" square rods as rein- forcement (as the minimum span is here 16.5 ft.). This would not be a good beam and would not be economical. Table IX. Neither one nor two rod beams can be used here for the same reason as stated in the foregoing paragraph. It is also seen that when C=93,200 the mini- mum span is over 18 ft. The conclusion is that a beam for this case needs shear reinforcement. Table X. Here a beam 10%" wide and 20^" deep with three %" square rods has a value C=31 1,000, which is more than required. The area of steel reinforcement could be reduced by taking 280/311 of the total and mak- ing the two straight rods of smaller section, but as this gives 13/16", an odd size, for their diameter it is hardly worth while. One of these rods, the middle one, must be curved up and run beyond the edge of support 50 dia- meters, or otherwise anchored at the supports of the beam. 67 Table XI. Here we find that a beam 7" wide and 24" deep with three %" round rods comes near meeting all the requirements. One of these rods must be curved up and anchored. Table XII. In this table the beam 7^" wide and 22y 4 " deep with four 11/16" square rods meets all the require- ments. Two of these rods must be curved up and an- chored. Table XIII. In this table the beam 7" wide and 23^" deep with four y" round rods comes close to meeting all requirements. Two of these rods must be curved up and anchored. The proper beam for this case may be determined by the desired depth or by the availability of round or square rods. In the very deep beams one-eighth of 'the depth of beam may be more than necessary below the center of the rods. The standard beam of these tables has an effective depth of 17/24 of the outside depth of the con- crete rectangle. If the rods are dropped so that this effective depth (distance from centroid of compression in the concrete to the center of steel) is increased, the coefficient C of the strength of the beam is increased pro- portionally. Thus at a depth of 48" the standard beam would have the rods l /& of the depth or 6" from the bot- tom. The effective depth is 17/24 of this or 34". If it is desired to place the rods 4" above the bottom of the beam, the effective depth is increased by 2", and C is 36/34 of the tabular value. TABLE VIII. Reinforced Concrete Beams with Straight Rods Not Anchored* R'f'n't One Square Rod Diam. in In. Sec Cone Be b in In. of rete j im d in In. Min Sp'n in Ft. Prod, of Span in Ft. and Unif'm L,oad in Pounds. R'f'n't One Square Rod Diam. in In. | Sec. of Concrete Beam Min Sp'n in Ft. 1 c Prod, of Span in Ft. and Unif'm Load in Pounds. > in In. d in In. % 1 154 in 6 434 4 6 4?4 2480 1960 1650 1 4 454 454 43,4 5 554 55^ 2354 22 2034 1934 1834 1734 1654 2354 22 2034 1934 1834 1734 1654 153200 145400 137200 130500 123900 117200 106100 i 5 * 03 1/2 134 754 6 554 754 6 554 4660 3830 3390 3/8 in m 834 754 654 834 7/2 654 8130 6970 5990 15i 4^ 4J4 554 554 5?4 6 654 2654 2434 23>4 2254 2154 20/ 2 1934 1834 2654 2434 2354 2254 2154 2054 1934 1834 219600 206100 195600 188200 179900 171200 165200 155600 Is 134 254 254 1054 9 8 754 1054 9 8 754 12970 11390 10120 9170 54 2 254 2/ 2 2M im 1054 954 854 1134 1054 954 854 19420 17350 15700 14050 154 5 554 554 53,4 6 654 6y 2 634 2954 2734 2654 2554 2454 2354 22/2 2154 2034 2954 2734 2654 2554 2454 2354 22 V 3 2154 2034 302200 286400 273600 259700 249900 239300 232400 221000 213500 ft 254 254 JK 354 1354 1134 1034 934 954 1354 1134 1034 934 954 27700 24400 22500 20200 19300 M 2/2 234 3 354 354 14/ 2 1354 1254 1154 1054 14/2 1354 1254 1154 1054 37200 34200 31600 29000 27100 i$f 5/ 534 6 654 654 63/4 754 754 734 32 3034 2954 2854 2754 2654 2554 2454 2354 2234 32 3034 2954 2854 2754 2654 2554 2454 2354 2234 399000 384300 368700 353000 340500 328000 315500 302000 293400 284100 U 23/ 4 3 354 354 3?4 16 143,4 13/2 1254 1154 16 1434 1354 1254 11/2 49900 46100 41900 38700 35100 X 3 354 354 334 4 454 17/2 1654 IS 14 1354 12*4 17/2 1654 15 14 1354 1254 65100 60400 55800 52100 49300 46500 154 6 654 654 634 754 754 I* 854 854 35 3354 if* 30 29 28 27 2654 2554 2434 35 3354 3254 31 30 29 28 27 2654 25/2 2434 520600 496800 478800 459500 446200 431400 416500 400200 390500 379300 368200 H 3/2 334 454 454 434 20/2 19 18 1634 16 IS 14i4 20/2 19 18 1654 16 15 H/2 103700 95900 91100 84500 81000 75700 73400 TABLE IX. Reinforced Concrete Beams with Straight Rods Not Anchored* R'f'n't One Sec. of Concrete c Prod, of R'f'n't | Sec. of One | Concrete 1 c | Prod, of Round Beam Min Span in Round Beam Min Span in "Rnrl Sp'n Ft and Rod Diam. h d in Unif'm Diam. h d in Unif'm in in in Ft. Load in in in in Ft. (Load in In. In. In. Pounds. In. | In. In. J Pounds. 6 6 I 1910 354 225412254! 116500 54 1 454 4541 1430 354 21 21 109000 15* 4 4 | 1300 l 354 1954 1954 101000 I 5 6 I 15* 1 I// 754 Stf 754 524 3680 2920 2540 454 454 io/4 1754 1654 10/4 1754 1654 89600 84200 354(2654 35412454 2654 2454 174100 162600 154 854 854 6020 tt iv* 7 7 5110 4 ?V/f 23X4 152800 m 654 654 4560 156 454 2154 2154 142400 & 15* 154 1M 1154 954 8 H54 954 8 112CO 9090 7930 454 454 M l /2 1954 1854 2054 1954 1854 133900 127900 121200 2 7 7 6940 4 2854 2854 233300 X 154 154 2 254 1254 1054 954 8^ 1254 1054 954 854 15800 13600 12600 10700 154 454 454 4 554 27 2554 24 23 2154 27 2554 24 23 2154 219100 206900 193800 186600 175900 154 1354 1354 21800 554 2054 2054| 167700 & 254 2/2 1154 1054 954 1154 1054 954 18700 16700 15200 454 454 454 3254 3054 2954 3254 3054 2954 318000 301400 287100 H 2 254 254 254 1454 1254 1154 10 54 1454 i2y 4 1154 1054 29400 25900 23300 21300 IH 5 554 554 554 6 2/54 2654 2554 24 23 2754 2654 2554 24 23 272400 260100 247900 234600 224800 H 25* 254 254 1554 139* 1254 1154 1554 13M 1254 ll/ 2 38000 33500 30400 28100 454 5 554 5'/ ? 3454 33 3154 30 3454 33 3154 30 406000 385500 368000 350500 M 25* 254 254 3 1854 1654 15 1354 1854 1654 15 1354 531(70 48200 43800 40200 154 5* 654 654 2854 2754 2654 2554 2854 2754 2654 2554 335900 321300 309600 297700 354 12^4 1J& 37300 2ft 2054 2054 81500 3 18 1854 74700 H 354 1754 1754 68500 354 16 16 63500 354 15 15 59600 Reinforced Concrete Beams One Rod Curved Up and Anchored. R'f'n't Three Square Rods Diam. in In. Sec Cone B b in In. of rete un d in In. Min| Sp'n in Ft. | C Prod, of Span in Ft. and Unif'm Load in Pounds. R'f'n't Three Square Rods Diam. in In. Sec Con Be b in In. of :rete am ~ in In. Min Sp'n in Ft. C Prod, of Span in Ft. and Unif'm Load in [Pounds. l /4 2 254 854 5M 6.2 5.0 4.1 10900 8680 7030 1 8 8H 9 9y 2 10 wy 2 11 1154 12 35 33 31 2954 28 2654 25/2 2454 2-354 24.8 23.4 22.0 20.9 19.8 19.0 18.1 17.2 16.5 694000 654000 613000 585000 555000 531000 506000 479000 460000 & 2J4I11 3 | 954 35^1 754 7.8 6.6 5.5 21300 17900 14900 H 3 3J4 JH 13 H54 10 854 9.2 8.0 7.1 .6.2 35900 31400 27900 24400 I'tf 9 9^ 10 10J4 11 11J4 12 12J4 13 3954 3754 35 y, 3354 3254 3054 2954 2854 2754 27.8 26.4 25.1 23.9 22.8 21.8 20.9 20.0 19.3 982000 934000 891000 847000 810000 770000 740000 707000 684000 & 3/2 454 1554 13J4 12 1054 10.81 57700 9.6| 51300 8.5| 45600 7.6] 40800 54 4 454 $ l /2 6 17J/2 1554 14 1254 1154 12.4 11.0 9.9 9.0 8.3 86800 76600 69400 63200 58300 l 10 1054 11 1154 12 i2y 2 13 1354 14 1454 4354 4154 3954 38 3654 35 3354 325^ 3154 3054 31.0 29.6 28.2 26.9 25.9 24.8 23.9 23.0 22.1 21.4 1356000 129400-0 1231000 1176000 1131000 1085000 1046000 1007000 969000 937000 * 4/2 5 554 6 654 1954 1754 16 1454 1354 14.0 12.6 11.3 10.5 9.6 123900 111400 99700 92500 83900 N 5 554 6 6y 2 7 l /2 22 20 1854 1654 1554 1454 15.6 14.2 12.9 11.9 11.2 10.3 170400 154900 141600 129200 122000 111700 i 11 11J4 12 1254 13 1354 14 1454 15 1554 16 48 46 44 4254 4054 3954 3754 3654 3554 3454 33 34.0 32.6 31.2 29.9 28.9 27.8 26.7 25.9 25.0 24.3 23.4 1795000 1724000 1646000 1581000 1528000 1472000 1413000 1368000 1320000 1284000 1234000 U i>54 s 6y 2 754 8 24 22 2054 19 1754 1654 17.0 15.6 14.3 13.5 12.6 11.7 224400 205700 188800 178100 166400 154300 K 6 <* 754 8 854 9 2654 24 y 4 22y 2 21 1954 1854 1754 18.6 17.2 15.9 14.9 14.0 13.1 12.4 292900 270500 251000 234300 220300 206100 195200 IH 12 1254 13 1354 14 1454 15 1554 16 1654 ' 17 i 1754 5254 5054 4854 4654 45 435^ 42 4054 3954 3854 37 36 37.2 2343000 35.8 2254000 34.3|2164000 33.1 [2086000 31.9(2008000 30.8(1941000 29.7(1874000 28.7)1801000 28.0(1762000 27.1(1707000 26.2(1648000 25.511606000 H 7 |30^4 21. 8| 467000 754|2854|20. 2| 432000 8 |2654|19.0| 406000 854|2554|17.9| 383000 9 |2354|16. 8| 360000 95412254(15. 9( 341000 10 I21J4I15.2I 327000 1054!2054|14.5( 311000 TABLE XI. Reinforced Concrete Beams --One Rod Curved Up and Anchored. R'f'n't Three Round Rods Diam. in In. Sec. of Concrete Beam Min Sp'n in Ft. C Prod, of Span in Ft. and Unif'm Load in Pounds. R'f'n't Three Round Rods Diam. in In. Sec. of 1 Concrete 1 Beam 1 Min Sp'n in Ft. C Prod, of Span in Ft. and Unif'm Load in | Pounds. b in In. d in In. b in In. d in In. tt 154 zy* 954 554 6.6 5.0 3.9 9010 6820 5360 1 ft 5* sy 2 9 9 l /2 3334 3154 2954 27^ 26 24^ 23^ [23.9 22.3 20.7 19.5 18.4 17.4 16.5 1 524000 491000 | 455000 428000 405000 | 382000 362000 ft 1034 854 754 | 7.6 6.0 5.1 16400 12800 11000 N f% 354 12/4 1054 8*4 8.7 7.3 6.2 26600 22300 19000 13* 7 7y 2 8 sy 2 9 9K 10 IOH 3934 37 34?4 !? 2954 2734 26^ 28.2 26.2 24.6 23.2 22.0 20.7 19.7 18.8 783000 727000 684000 646000 611000 576000 545000 522000 ft 3 w 14 12 1054 9.9 8.5 7.4 41700 35700 31200 l /2 35^1534 4 |1334 454|i254 11.2 9.7 8.7 61300 53500 47700 I* 8 sy 2 9 9/2 10 ioy 2 11 11% 43 40K 3854 3654 34K 3234 3154 30 30.5 28.7 27.1 25.7 24.4 23.2 22.1 21.2 1047000 986000 931000 882000 840000 797000 761000 730000 354 ft 4 ir< 20 1754 1554 14 14.2 12.4 11.0 9.9 98600 86300 76400 69000 H r* S I A 2154 19 1754 1554 15.2 13.5 12.2 11.0 131000 115000 105000 93600 1H 9 9X 10 IQtf 11 ny 2 12 I2J4 13 46J4 4334 4154 3954 3734 36>4 3434 33/4 32 32.8 31.0 29.4 28.0 26.7 25.7 24.6 23.5 22.7, 1362000 1288000 1220000 1160000 1110000 1068000 1023000 979000 942000 ii 454 554 6 654. 23 2034 19 1754 16 16.3 14.7 13.5 12.2 11. 3j 168600 152500 139900 126400 117800 M ly, 6 r* 2434 2254 2054 19 17*4 17.5| 216900 15.9 197200 14.5) 178600 13.51 166200 12.6J 155500 iK 10 | toj* 11 ny 2 12 12J4 13 13^ 14 | 4954 47 45 43 4154 3954 38 3634 3554 35.1| 33.3 31.9 30.5 29.2 28.0 26.9 26.0 25.0 1735000 1643000 1577000 1506000 1446000 1381000 1330000 1288000 1232000 554 6 H 654| 7y 2 8 3054 28 2 /< ' 22H 21 21.6| 362000 19. 8| 333000 18.4| 310000 17. 0| 285600 15.9| 268300 14. 9 249900 TABLE XII. Reinforced Concrete Beams Two Rods Curved Up and Anchored. R'f'n't Four Square Rods Diam. in In. Sec. of Concrete Beam C ]Prod. of Min j Span in Sp'n|Ft. and in Unif'm Ft. | Load in | Pounds. R'f'n't Four Square Rods Diam. in In. Sec. of Concrete Beam Min Sp'n in Ft. C Prod, of Span in Ft. and Unif'm Load in Pounds. b in In. d in In. b in In. d in In. /4 !* 9^4 7?4 4.9 4.1 15200 12800 1 10 10H 11 ny 2 12 37J4 35^ 34 32^ 31 19.8 18.9 18.1 17.3 16.5 983000 937000 899000 860000 817000 * 3K'H^ 3541 9*4 6.0| 29100 5.2| 25200 tf 4 4H 13 J4 1134 7.01 49300 6.3J 43700 IX iiH 12 12H 13 13/ 2 41 39^ 373,4 36^4 35 21.8 21.0 20.1 19.3 18.6 1369000 1322000 1262000 1210000 1171000 & 434115 5J4J13J4 8.0| 75700 7.2J 67800 K 5H 6 18K 15# 10.0| 124000 9.0J 112400 8.2| 102100 l 12^ 13 13^ 14 14J4 15 l4l M 43^4 4134 40^ 39 24.9 23.9 23.0 22.2 21.4 20.7 1932000 1859000 1787000 1725000 1663000 1611000 ft 534|20^|10. 9| 171200 6^4119 |10.1| 159000 634|17H| 9.3J 146400 M 6H 7/2 22J4 20 M 19^ 12.0 11.0 10.4 233000 213500 202000 IH 14 14^ 15 isy 2 16 16H 50^ %* 45 H 44 4234 26.9 25.9 25.0 24.2 23.4 22.7 2525000 2438000 2347000 2273000 2194000 2136000 |i 7MI24^|12.9| 302000 7# 22# 12.1 284000 8J4|21#|11.4| 269000 1^ 15 IStf 16 16^ 17 17^ 18 56 54^4 52H 51 49H 48 46?4 29.8 28.8 27.9 27.1 26.3 25.5 24.9 3332000 3228000 3124000 3035000 2945000 2856000 2782000 4 7K 8 8fc 9 28 |14.9 26^|14.0 24^|13. 2 23^|12.4 417000 391000 368000 345000 9 9y 2 H |io \ioy 2 31^4 30 28^ 27M 16.9 16.0 15.2 14.5 643000 606000 575000 552000 ^ TABLE XIII. Reinforced Concrete Beams Two Rods Curved Up and Anchored, R'f'n't Four Round Rods Diam. in In. Sec. of Concrete Beam b d in in In. In. Min ISp'n in Ft. C Prod.- of Span in |Ft. and Unif'm Load in j Pounds. R'f'n't Sec. of Four | Concrete Round Beam RnH<- | Prod, of Min ) Span in Sp'nJFt. and in | Unif'm Ft. |Load in J j Pounds. Diam. b in in In. In. d in In. /4 2 1 9y 4 \ 4.9 2 l /2\ 754J 3.9 12000 9400 8 i 854 9 954 3634 32 J/2 19.5 763000 18.3 717000 17.3 673000 16.3 636000 2y 2 ny 2 3 9/ 2 6. If 23300 5.1| 19200 \ 9 l/s 954 10 |1054 39 37 21.9)1084000 20.7)1024000 19.7) 970000 18.7) 924000 H 3 1334 3J4 UK 7.3 6.3 40200 34200 & 3^)16 4 |14 8.5f 63500 7.5| 55500 |10 154 H 2 11J4 4534 4334 4134 40 3854 24.311483000 23.3)1420000 22.2)1355000 21.3 1298000 20.3)1241000 y* 4 18541 9.7) 94400 454 1654] 8.6J 84200 ft 454I205^|10.9[ 134000 | 5 |1854| 9.8| 121200 11 13/6 12 1 125-^ soy 2 4654 44J4 4234 26.9|1983000 25.7)1896000 24.6)1816000 23.5)1734000 22.7)1679000 5 23 6 2 19 4 12.2 11.0 10.1 186600 167700 153400 ii 6 2 |23 4 |12'.2 6y 2 21J4I11.3 248000 225000 208000 12 154 13 14 2 55 5234 5034 49 47 29.2)2570000 28.0)2464000 27.0 2372000 26.1)2290000 25.0)2191000 ,4 6 27y 2 T 2 2354 14.6 13.6 12.5 321000 298000 274000 H 7 32 7 l / 2 30 8 28 17.0 16.0 14.9 508000 477000 444000 CHAPTER VII. Girders. In building work a girder is usually understood to be a large-sized beam, whether rolled or built, particularly a beam that carries smaller floor beams. The selection of the size of a rolled beam acting as a girder may, of course, be done in the same manner as in 'the case of simple beams, if the load is uniformly distrib- uted along the beam. When the load is distributed in equal concentrations at equal intervals, the same method may be used with but small error ; that is, the total load carried by the floor area tributary to the girder may be used as a uniformly distributed load. This will need cor- rection only where there is an odd number of panels in the girder, as shown in the next paragraph. F'.^.l. Fig- 2. It will be found that the effect on the girder EF, Fig. 1, of the three beam concentrations is the same as the total floor load enclosed by the rectangle ABCD, assumed to be uniformly distributed on the girder. The effect of the two beam concentrations on girder KL, Fig. 2, is less than the load GHIJ, assumed uniformly distributed, by 'the fraction 1/72. The following rules may then be used in designing girders in such cases. 75 Rule 1. When there is an even number of equal panels (or an odd number of concentrations), assume the load tributary to a girder (the rectangle ABCD of Fig. 1, the lines AB and CD being midway between girders, etc.), as uniformly distributed on the girder. Rule 2. When there is an odd number of equal panels (or an even number of concentrations), assume the load tributary to a girder as uniformly distributed on the gir- der, but deduct 1/72 for 3 panels, 1/200 for 5 panels, 1/392 for 7 panels, etc. The denominator of the fraction is eight times the square of the number of panels. It is seen 'that the deduction is scarcely worth considering for more than three panels. In all cases where these rules apply a beam occurs at each column or each end of the girder. When the girders are not parallel, the method of as- suming the load to be uniformly distributed may still be applied with but little error, if the lines AB, DC, etc., be drawn midway between girders. The general method of finding the bending moment on a girder for any system of concentrated loads is as fol- lows: p. dz ^ Rz Pt l . d5 , L d-* rrr, [5 , ^ [ r\ i t ) X ( f x f PloM - Pzd2--F3ol3+ etc R\ M - R\ K -P\ y - 76 (0 -(2) (3) M is the bending moment in foot pounds, assuming that all loads are in pounds and all distances are in feet. The above is on the assumption that the maximum mo- ment occurs under the load P g . The maximum moment will generally occur under a load near the middle of span. In order to find definitely which load is the critical one, first find the reaction Ri, as indicated, then subtract successively Pi, P 2 , P 3 , etc., until the load is found where the "shear passes through zero," that is, where a nega- tive value is obtained in this subtracting process. As a rough check this moment should be nearly equal to half the sum of the products of each several load and the distance to the nearest support. (See Godfrey's Ta- bles, page 43.) To use this bending moment in the beam and girder tables multiply it by eight and use that product as C in the tables, or divide it by 250 and use that quotient as Q in the tables of rolled beams. Sometimes an I-beam is reinforced by the addition of top and bottom flange plates. This is not economic construc- tion, but is occasionally necessary to keep down the depth. It is also done sometimes to reinforce existing beams in place. The punching or drilling of holes in the flange of a beam diminishes the strength of that beam in the ten- sion flange, and this must be considered in calculating the reinforcement added by the flange plate. In order to minimize this deduction of area rivet holes should not be located opposite one another in the flanges, but should be alternated, except near the ends of the plate. Here, how- ever, the bending moment is less than at the middle of span. Table I gives coefficients for finding the load bearing ca- pacity of standard I-beams with flange plates, as well as the length of plate required in terms of the length of span. These tables are figured with 'two holes out of beam and plate in both top and bottom flanges. Box girders made of two channels and cover plates or two I-beams and cover plates are frequently used under 77 TABLE I. Capacity of I Beams with Flange Plates. Size of | Size of Top | and Bottom Length of Q Fl'nge Plate I Prod. of I-Beam Flange Plate Iin Inches. Portion of Span. Safe Ld. in T'ns & Sp'n in Feet. 10" 25 Ib. 7xJi .79 187. 1 10" 25 Ib. 7 X H .87 254.2 12" 31.5 Ib. 7xt/ s .74 258.3 12" 31.5 Ib. 7x5/1 .83 337.9 15" 42 Ib. 8x*/2 .77 469.4 15" 42 Ib. 8x^4 .84 588.6 18" 55 Ib. 9x*/ 2 .75 693.7 18" 55 Ib. 9xJ4 .82 859.8 20" 65 Ib. 9xy 2 .70 857.6 20" 65 Ib. 9x$4 .79 1041.0 24" 80 Ib. 10X^2 .70 1244.0 24" 80 Ib. 10x^4 .77 1 1495.0 TABLE II. Capacity of Channel Beams with Cover Plates. 2 Channels Size. Size of Top and Bottom Cover Plate in Inches. Length of Bot. Plate Portion of Span. Q Prod, of Safe Ld. in Tons & Span in Feet. 7" 9.75 Ib. 7" 9.75 Ib. 8" 11.25 Ib. 8" 11.25 Ib. 9" 13.25 Ib. 9" 13.25 Ib. 10" 15 Ib. 10" 15 Ib. 12" 20.5 Ib. 12" 20.5 Ib. 15" 33 Ib. 15" 33 Ib. 9* l /4 9xy 2 9xy 4 9xy 2 9xJ4 9x^ 12xf6 12x^ 12x^ 12x*4 18xJ^ 18x34 .83 .93 .80 .90 .78 .89 .87 .93 .86 .91 .86 .91 112.6 180.6 134.5 209.3 161.8 245.7 303.4 436.9 491.4 651.0 993.0 1310.0 78 walls and sometimes in other locations. Table II gives a number of such box girders and coefficients for finding the load bearing capacity. Generally the top plate is run the full length. The bottom plate may be made short- er, as indicated in the table. The values in the third column of Tables I and II are .06 greater than the theoretical length of cover plate re- quired. This is to allow for rivets near the ends of the plates. The rivets should be spcaed 3 inches apart for a short ditsance at the ends of the plates. Examples. (1) Given a 12-inch 31 J^-lb. I-beam in place that is to be reinforced so that on a span of 16 ft. it will carry 20 tons. The value of Q should be 20X16=320. By ref- erence to Table I it is seen that this comes between the two values of Q for a 12-inch I-beam. By interpolation it is found that 7"X9/16" flange plates will be required. Interpolating again these plates should be about .81 of the span in length, or 13 feet. (2) Given a 9-in. wall six feet high carrying a roof slab, whose total load is 900 Ibs. per foot. The span is 15 feet. The weight of the wall is 90X6X15=8,100, and the roof load is 900X15=13,500, a total of 10.8 tons. Q is 10.8X 15=162. By reference to Table II it is seen that 2 9-in. 13.25-lb. channels with 9"X^4" top and bottom cover plates will meet the requirements. The top plate may be full length and the bottom plate .78X15, or say 12 feet long. (3) Given a bay window, the walls of which are sup- ported on columns at the first floor. Find the size of box girder of channels and plates for the following data: Span, 12 ft. ; weight of wall, 72,000 Ibs. ; weight of floors, 48,000 Ibs. The total load carried is 120,000 Ibs., or 60 tons. Q is 60X12=720. In Table II it is seen that 2 15- in. channels and two 18"X/4" plates would have more strength than necessary. It is also seen that W in thick- ness of the cover plates adds or deducts about 150 in the value of Q. Hence with 18"X&$" plates Q is about 840. This size of plates could then be used. Both plates should 79 be full length ; the lower plate can act as a bearing plate on the column. PLATE GIRDERS. In a plate girder there are several points of design that must be considered. First The section of the flanges must be sufficient to take the longitudinal stresses resulting from the maximum bending moment. Second The web plate must be thick enough to take the maximum shear. Third The rivets in the flange angles connecting the same to the web must be sufficient to take the flange stress from web to flange. Fourth The web plate must be stiffened against buck- ling, if it is not of sufficient rigidity in itself to take the shear without buckling. Fifth There must be end stiffeners designed to take the full reaction of the girder and to transmit the same into the web plate. Tables III and IV give 170 girders and coefficients to determine the capacity of the same. The number may be indefinitely extended by interpolating for different thicknesses of flange plates or angles. Also by noting the increase in the value of Qi and Q 2 per inch increase in depth of web, in the various pairs of groups of girders having the same flanges, the value of these coefficients for different depths may readily be found. (These tables are based on tables in "Godfrey's Tables," pages 94 to 98 in- clusive.) The depth of girder back to back of angles is ;4 in. more than the depth of web plate. The coefficient Q 2 is to be used only when the web plate of the entire girder is in one piece or is spliced for bending with extra flange plates or extra side plates near the top and bottom of the girder to take the flange stress assumed to be carried by one-eighth of the web of the girder. The unit stress of 15,000 Ibs. per sq. in. is used here because it is be- lieved that a member made up of several pieces acting together does not have the same uniformity of distribu- 80 TABLE III. Capacity of Plate Girders* Unit stress 15,000 Ibs. per sq. in. inches. All Dimensions in Angles C'v'r | Plate Part of W'b (Inc. in Flngs. I Q, I 1 A of feb Inc. in Flngs. Angles C'v'r Plate W'b Qi 1 0. No Part H of of W'b | Web Inc. injlnc. in Flngs. Flngs. 163. 301. 262. 363. 501. 213.0 351.0 312.0 413.4 551.4 3^x3 x-fr 354x3 xft 6 WT2 2 448.2 2| 397.2 6] 520.2 2| 691.8 8xA 308 575 510 718 986 386 652 593 796 1063 2y 3 x2y 3 xy 3 201. 373. 322. 444. 616. 407 763 668 934 1291 539 894 800 1066 1423 7xy 2 \ 184. 345. 306 431 592 234.6 394.8 356.4 481.8 642.6 4 x3 xAI 4 x3 x 4 x3> x 4 x3 x 4 x3 x 4 x3 xA 4 x3 x^ 4 x3 x T s g 4 x3 xA 4 x3 x5^ 340 636 574 814 1111 418 713 651 892 1189 228. 427. 376. 527, ^26_ 207, 389. 352, 501, 683 303.6 502.8 451.8 603.0 9xA 6| 802.8 258.0" ~449 842 750| 10591 14531 581 974 882 1192 1585 439.2 402.6 552.0 733.2 5 x3 5 x3 5 x3 527] 984| 921| 1327] 1785] 622 1078 1016 1422 1879 354x254x54 354x254x54 8x54 8x54 256 481. 432 612 837. ^78" 514, 448 622 860 8] 332.4 8| 556.8 61 508.2 6] 688.2 6] 913.2 5 x3 5 x3 5 x3 5 x3 5 x3 4] 355.8 8 | 592.2 2] 526.2 8 700.8 4] 937.8 11x54 11x3/4 "679] 1271| 1177| 1687 2280] 831 1423 1329 1840 2432 3 x3 x T 5 g 3 x3 x^ 3 x3 x T 5 g 3 x3 xA 3 x3 xM -B 7x 3 x3 xA 3 x3 x^ 3 x3 3 x3 3 x3 xAI 7xA 8x34 8x34 | 369. | 684. | 588. 811. 1127. 01 500.4 S15.4 01 720.0 8| 944.4 411260.0 8x3^ 8x34 435 805 701 977 1349) 529 898 796 1070 1443 564| S 10471 x| 901| % I 1246] I 17321 716 1198 1053 1398 1883 TABLE IV. Capacity of Plate Girders* Unit stress 15,000 Ibs. per sq. in. All dimensions in inches. Q, I Q Q, No I No Angles C'v'r Plate Part | y & of W'b|ofW'b| Web Angles C'v'r Plate | W'b Part of W'bl VA [nc. in] Inc. in [nc. in Inc. in Flngs. | Flngs. Flngs. Flngs. 5 x3 y 2 x3/f, 613] 725 x6 xy 2 1753 2122 5 x3y 2 x$/i 1147] 1259 x6 x7^ 2925 3294 5 x3J^x3/6 |llx3/ * 1042 1154 x6 x l / 2 14x14 ^? 2972 3344 5 x3y 2 x}4 11x3/4 1483 1595 x6 x l / 2 114x1 X 4223 4595 5 x3^2x34 11X34 TJ- CM 2018 2130 x6 x7/J5|14xl T 5393] 5765 5 x3J/2x3/6 776I 951 6 x6 x l / 2 \ 2227] 2807 1456 1631 6 x6 x7^| 3724| 4303 . -y vj 1 1 x3/ J9 1309 1484 6 x6 xy 2 \l4x l / 2 V 3747] 4330 5 x3y 2 xy, 11x34 X 1854 2029 6 x6 x^|14xl 5298| 5881 5 x3^x34 g 2535 2711 6 x6 x%|14xl 6792] 7374 r Ti7 JJT" 790 921 6 x6 xy 2 2702 3539 6 x3>y 2 x7/% ^ to 1463 1444 1595 1576 6 x6 x7/ 8 6 x6 x l / 2 Uxj* ^ 4523 4522 5359 5362 , X T / $ 1 ? 7/ X 2121 2253 6 x6 x l / 2 14x1 6372 7212 6 x3y 2 x7^ 13x7/6 CM 2792| 2924 6 x6 x7^|14xl 8190 9030 6 3 1 / JK 982] 1180 6 x6 xy 2 3178] 4318 6 31/xP* 1825 2023 6 x6 x% 5322 6462 6 si/x 7 13x 7 e 1784 1983 6 x6 x l / 2 14x}/2 ^ 5297 6438 6 x3y 2 x% 13x11 X cq 2608], 2808 3449J 3648 6 x6 xy 2 6 x6 xj^ 14x1 14x1 O 7445 9588 8592 10730 A - A i/ 556 668 6 x6 xy 2 3652] 5145 1039 1150 6 x6 x7/$ 6120| 7614 4 x4 x3/ 4 x4 x^i 4 x4 c x?4 9x1/6 9x34 9x34 * X rj- C-J 893 1240 1724 1005 1352 1836 6 x6 x l / 2 6 x6 x l / 2 6 x6 xi/% 14x1 14x1 1 6072 7566 8520] 10020 10990] 12490 707 882 6 x6 xy 2 4127 6330 I 4 X J/ 1326 1500 6 x6 x7/& 6918 9120 4 x4 x3/jj 4 x4 xH 4 x4 x?4 9x34 9x34 g 1126] 1301 15551 1729 2174] 2348 6 x6 x l / 2 6 x6 xy 2 6 x6 x7/% 15x */ 15x1^ 15x1^ \ ^ 2 ]^ 7074] 9282 13070] 15280 15850] 18070 6 x4 xJ3 831 962 6 x6 xV 2 46021 7326 6 x4 xJ/6 1551 1682 6 x6 x7^ ^o 77161 10440 6 x4 XT^ ISxi 7 H 1485 1617 6 x6 x l / 2 i5x y t X 7872] 10600 6 x4 x-fo I3x7/ x 2162 2294 6 x6 x l /2 ISxlJ/ ; 14510| 17250 6 x4 x?^ 13x7/6 C^ 2880 3012 6 x6 x7^|15xl^| - 17630] 20360 6 x4 x-fa 1036 1234 8 x8 xy 2 6474| 9582 6 x4 x7^ 1939 2136 8 x8 xj^ Sfi 10970] 14090 6 x4 x^r 13xvk -s 1838 2037 8 x8 x l / 2 i8x y z x 10500] 13610 13x5/ 2662 2862 8 x8 xy 2 ISxlV ; s 18680] 21800 6 x4 xj/fj 13x7/6 fo 3563 3762 8 x8 x7^|18xlj^| - 1 23180| 26300 6 x6 x^ 12771 1486 8 x8 x l / 2 7824 12310 6 x6 jc7/6 2126 2334 8 x8 xj^ X? 13270 17750 6 x6 xj4 14xi/ 5H 2197 2407 8 x8 y. l /2 i8x y ; x 1265C 17140 X 3148 3359 8 x8 x^|18xiy i S 22430] 26920 6 x6 x 7^ |14xl 5 3994] 4204 |8 x8 x7^ll8xl'/| ^ 27870 1 32370 tion of stress that single pieces such as I-beams would show. By selecting the girder according to Tables III and IV, the first requisite may be fulfilled. When the load is not a uniformly distributed load or its equivalent, the maxi- mum bending moment must be found in ft.-lbs., and by dividing this by 250 Tables III and IV may be used, since 1/250 of the bending moment is equal to the value Q of these tables. The shear in the web plate should not exceed about 7,500 Ibs. per sq. in. of the gross section of the web. Hence to determine whether the second requisite is ful- filled it must be seen whether or not the area of the web agrees with this condition. The maximum shear on a girder in a simple span is the end reaction. In the case of a uniformly loaded beam this is one-half of the total load carried. In other cases, as for concentrated loads, use the methods of equations (1) and (2) to find the re> actions. The greater of these is the maximum shear. The gross area of the web is the full section of the plate, no deduction being made for rivets. Thus a 62" X 5/16" web plate will take a shear of 62X5/16X7,500=145,300 pounds. The spacing of rivets in the flange angles is a detail usually left to the bridge shop, where the girder is made or to the draftsman; but it is also very often carried out in an improper manner. Sometimes the design is such as not to allow rivets enough in the leg of angle connecting to the web. Two rows of rivets may be needed where it is only possible to use one, as when 6"X3^2" angles are used with the 3 1 /&-in. leg against the web. The de- signer must bear this in mind in selecting the section of girder. If the shear is such as to require two rows of rivets, a six-inch angle leg should be used against the web. Flange plates such as 14"Xl" or 15" 1%" may be made up of two or more plates as 2 14" XH" plates or 3 15"xV2' r plates. Usually one top flange plate is made nearly or quite the full length of the girder. The theoretical length of the other flange or cover plates may be found by the follow- ing formula: Total flange area Area of cover plate Square of span in feet Square of length of cover plate To this theoretical length of the cover plate add a foot or more. This formula applies as stated for the outside cover plate. For the second cover plate substitute for "area of cover plate" the area of the first plus the second; for the third cover plate this "area of cover plate" is the area of the first three, etc. TABLE V. RIVET PITCH IN FLANGES OF GIRDERS FOR VARIOUS UNIT SHEARS. On basis of bearing value of rivets at 18,000 Ibs. per sq. in. Unit Shear 8000 7000 6000 5000 4000 3000 2000 2 /4 Rivets Rivets ' Rivets 1.97 1.69 1.41 2 1 1 .25 .93 .61 2 2 1 .63 .25 .88 3, 2, 2 ,15 ,70 .25 3.94 3.38 2.81 5.25 4.50 3.75 7.87 6.75 5.62 The rivet spacing in the flange angles for rivets through the web may be found by Table V, by determing first the shear per sq. in. in the web. The closest spacing is re- quired near the ends of span, and near the middle of span the spacing reaches a maximum, which is generally six inches. A few different spaces will be employed, using the closest for a few feet at the ends, then stepping up at intervals to the maximum. The thickness of the web plate should not be less in any case than about 1/200 of the clear depth between the flange angles, as thin wide plates are apt to have buckles due to cooling, which are very hard to remove. 84 TABLE VI. SHEAR ON PLATE GIRDER WEBS. d [Allowed Shr. T | per Sq. In. 1 t Allowed Shr. per Sq. In. d | Allowed Shr. t~ | per Sq. In. 40 50 60 70 7830 6550 5450 4560 80 90 100 120 3830 3240 2770 2070 140 160 180 200 1590 1260 1020 840 d=either clear depth between flange angles or clear dis- tance between stiffeners. t=thickness of web. When the thickness of web plate is relatively less than that shown in Table VI, stiffeners are needed. Thus, sup- pose a H-in- girder web is 40 in. between flange angles in clear depth and is subject to 5,000 Ibs. per sq. ft. of shear. The ratio of depth to thickness is here 107. By Table VI a shear of about 2,500 Ibs. per sq. in. is allowed. Stiffeners are needed. At 5,000 Ibs. per sq. in. a ratio of depth to thickness of 65 is allowed This would require about 24 in. in the clear between stiffeners. A pair of stiffener angles should then be used about two feet from the end of girder. If the shear at this stiffener is less than at the end of girder, 'the space to the next stiffener will be more. At the section where the shear is 2,500 Ibs. per sq. in. no stiffeners are required. If this were a uniform- ly loaded girder, no stiffeners would be required in the middle half. One quarter of the girder at each end would need stiffeners varying in clear spacing from 24 in. at the ends of span to 40 inches. The end stiffeners of a girder have an office to per- form which is more than the mere stiffening of the web. They should be designed to take the full end reaction of the girder and transmit it into the web. A unit stress of about 15,000 Ibs. per sq. in. may be used in determining the area required. Thus suppose the end reaction of a girder is 240,000 Ibs. At 15,000 Ibs. per sq. in. this would require 16 sq. in. in the angles. This could be made up 85 of 4 angles 5x3^x 1 /&. These four angles must deliver the load of 240,000 Ibs. to the web of the girder. At 18,- 000 Ibs. per sq. in. the bearing value, say of a %-in. rivet in a ^-in. web. is 7880 Ibs. Thirty rivets are required, or 15 in each pair of angles. Examples : (1) Given a girder of 40 ft. span carrying a load of 3,000 Ibs. per ft. The total load on the girder is 60 tons. Q is 40X60=2,400. By Table IV a girder having a 30"x^" web, 6"x6"x^" flange angles and a 14"x%" cover plate will suffice, if the web plate is in one piece or spliced for bending. The end shear is 3,000x2060,000 Ibs. On the 30"x^" web this is 5,330 Ibs, per sq. in. By Table V the rivet spacing of 24" rivets should be about 2.5" near the ends. By Table VI the clear depth of web may be 60 times the thickness, which is 22.5" ; as the clear depth here is 30 12 or 18", no intermediate stiffeners are needed. The end stiffeners, for the reaction of 60,000 Ibs., require 60,000-1-15,000 or 4 sq. in. On account of the 6" flange angles the stiffener angles should not be less than say 2 angles 5"X3 1 /&"X D o 5 o o I 3 o 3 C Kq'o : o o o < I 0* *o oo o o o o o o o 6 ~o~~ o o o o o > 00 Fig 5. Fioj.7 End stiffeners should be turned as shown in Figs. 4 and 6 and not as in Figs. 5 and 7. In the latter case the outstanding legs of angles, which take 'the greater part of the bearing, are over ithe edge of bearing plate and end of angles, whereas they should be well back. Where there is a heavy concentrated load, such as a column, supported by a girder, the stiffener under the same must be designed to take the column load. The sec- tional area and the rivets in the web may be found as for end stiffeners, as illustrat?^ above. The bearing plate of a gt>the depth of the girder in feet. (In exact work it should be the effective depth or the dis- tance between the centers of gravity of the flanges, but the depth of web is close enough for ordinary work.) Then divide this shear per foot by the single shear value of one rivet. This quotient is the number of rivets re- quired in one foot along the flange. In the case of a box girder these rivets are in two rows. Thus, suppose a 30" girder has an end shear of 60,000 Ibs. The shear per foot is 60,000-^-2.5=24,000 Ibs. The value of a $4 -in. rivet in single shear at 9,000 Ibs. per sq. in. is 3,980 Ibs. ; 24,000-h 3,980=6 rivets per ft. In two rows this would require 4-inch spacing. TABLE VIII. Capacity of Box Girders, Unit stress 15,000 Ibs. per sq. in. All Dimensions in inches. Angles No | CVr Part | */ 8 of Plate IW'b ofW'bl Web | Inc. in I Inc. in j Flngs. | Flngs. 3 x3 3 x3 3 x3 12x34 12x34 "R I 813! 1038 4 I 1299J 1527 I 1587J 1811 3 x3 xft|12xf$| { | 1018| 1369 3 x3 x-ft 1 12x34 1 H 1620| 1974 4 x3 x^ 1 12x3/| ro | i987[ 2337 3^x3^x3/6112x3^1 , | 11951 1545 3^x3 1^x3^ 1 12x34 | x | 1799| 2150 3^x3^x14112x341 % | 2319| 2669 3^x3^x3^112x3/61 "V, | 1440] 3^x3^x1^112x14! 2159| 3j/2x3!/ 3 xi4ll2x3/,| n I 2792| 4 x4 x 3^| 12x3/61 -R | 1563| 4 x4 x 3/6 1 12x34 X | 2284| 4' x4 x 34 1 12x34 | 3035| 4 x4 x 3^ |12x^ 4 x4 xH |12x34 4 x4 x 341 12x34 3 x3 3 x3 xa^ |18x34 3 x3 1830! 2667| 3553J 1946 2666 3297 2070 2791 3541 2518 3354 4240 1437| 2382| 2679| 1788 2736 3031 3 x3 x3/6|18x^| R I 17271 2137 3 x3 x3^|18xi4| x I 28551 3366 3 x3 xH 1 18x34 1 ^ | 3214| 3723 3^x3^x3^118x3/6 | 1850) 2989! 3620| 2358 3498 4126 18x34| x | 3^x3^x34 18x34J 5? I 2162! 3484| 4227| 2850 4172 4915 4 x4 x?^ 1 18xi^ | -B | 2308| 2996 4 x4 xi^|18xi4| * I 3630| 4321 4 x4 xi4|18xi4| ^r [ 4516| 5205 4 x4 4 6 x4 x^| 18x34 4 x4 2643 4148 51691 3545 5052 6070 Angles CVr Plate Part | y 8 of W'b | of W'b | Web Inc. in Inc. in Flngs. Flngs. .. . . 122x34 3^x3^x14122x341 ^ ! 2743| 3431 x I 4390J 5080 ^ I 4870| 5560 x3/ 8 ! 22x34| 3139| 5014| 5567| 4041 5918 6470 4 x4 4 x4 x}i |22x34l 4 x4 xi4 |22x34| j. 3006| x 48811 5902[ 3908 5785 6804 4 x4 x3^| 22x3/8 1 4 x4 x 4 x4 xa <-> 3386| ^ 5489| % 6644 1 4525 6630 7782 *, 4122| K 6806| * 7454| 5261 7950 8593 3^x3Kx34|24x%| | 4583| | 75581 | 8280| 5986 8967 9685 4 x4 4 x4 4 x4 | 4867| i 78601 | 8700| 6269 9270 10110 4 x4 xy 2 24x T 7 R | 4 x4 x^ 1 24x7^| 4 x4 5357| I 8640| | 9570| 7"058 10350 11280 6 x6 6 x6 6 x6 x34|30xl 6 x6 x 6 x6 xH 30x1 6 x6 x34|30xl 6 x6 xy 2 \ 6 x6 xj^|36xl 6 x6 xi4|36xl 6 x6 6 x6 6 x6 ;^|36xl :34|36xl -0 I 8240| x I 133101 S I 14790| 10540 15600 17080 v I 9440| X I 15200 I 16910! 12430 18200 19910 sa 11990| 19840| 21770] 17050 24900 26840 13330] 19580 220401 28290 241901 30440 Examples : (1) Given a floor girder of 30 ft. span, to be limited in depth to about 24 inches, the total load being 3,600 Ibs. per ft. The load in tons is 1.8X30=54. Q is 54X30=1620. A box girder with 24"x5-16" webs, 3"x3"x^" angles and 12"xM" cover plates will suffice. The angles could be 9-16" thick, if the web plates are in one piece. (2) Given a box girder on a 60-foot span supporting a 24-inch wall, the total load per ft. being 5,000 Ibs. The load carried is 5,000X60=300,000 Ibs. or 150 tons. Q is 150X60=9,000. By Table VIII it is seen that a box girder with two 66"x5-16" webs 4"x4"x^" angles and 24"x^" cover plates would do. The web plates need not be spliced for bending, as .Qi is used, but of course they should be spliced for shear. The end shear of this girder is 150,000 Ibs. On the two 56"x5-16" webs this is 3,640 Ibs. per sq. in. The webs need stitfeners. These should be spaced, according to Table VI, about 83 times the thickness of the web in the clear or 26 inches at the end of girder. At quarter points the spacing of stiffeners is about 40 inches; etc. For flange rivets, the shear per foot at end of span is 150,OOQ-=-5. 5=27,500 Ibs. At 3,980 Ibs. per rivet 6.9 rivets are required per ft. or 3.5" spacing in each of the two rows. Box girders should have occasional inside diaphragms composed of a plate and angles riveted to the v/ebs These are quite necessary where the load is applied to one side of the girder, so as to insure the uniform distri- bution of it he load into the two sides of the girder. A diaphragm could take the place of a pair of stiffener angles in a deep girder. Box girders are sometimes used as cantilever girders in foundation work to support wall columns that must have their foundation located back from the center of the column. In such case, to use Table VIII the bending moment in the girder should be found in foot-pounds and this moment divided by 250, which will give an equivalent of Q in the table. 91 Example of cantilever girder. Given a cantilever girder supporting a column having a load of 120,000 Ibs., the overhang being 5 ft. The bend- ing moment is 120,000X5=600,000 ft.-lbs. Dividing this by 250, Q is found to be 2,400. By Table VIII, interpolat- ing, it is found that the girder could be composed of 2 webs 42"x5-16", 4 angles 4"x4"xH", and 2 plates 12"xK,,. 92 CHAPTER VIII. Trusses. The designing of a truss involves first the calculation of the stresses in the several members and the selection of suitable members to take these stresses. The bending stresses as well as the direct stress must be found for any members subject to transverse loading, and such members must be designed to resist both kinds of stress. The end connections of all members must be detailed so that they will be capable of taking the full stress of the mem- bers, and the truss must be braced against lateral dis- placement both as a whole and locally so that compres- sion members that are considered of certain free lengths in the general design will be supported at these limits of length. In general truss members should be symmetrical about the plane of the truss, and the lines through the centers of gravity of the several members meeting at a common point should intersect in a common point. Persuant of the author's intention to cover in this book only simple designing, this chapter will take up only the design of simple trusses and simple methods of finding the stresses in the same. Plates I to III, inclusive, give co-efficients on the sev- eral truss members by which the stresses in these mem- bers may be found. The condition is that of a simple truss resting on walls and not of a truss acting to brace a building through the medium of knee braces. The trusses are further symmetrically loaded and not subject to unusual loads, such as suspended galleries, etc. To find the stress in any member compute the total load that a truss must carry; then multiply this by the co-efficient on the member in which the stress is desired. The minus sign stands for compression, and the plus sign stands for tension. 93 As indicated on Plate III, these same diagrams may be used to find the stresses in a lean-to truss, that is, a truss of the shape of half of one of these. The stresses, for the same panel loads, will be the same for the half truss as for the full truss for all members except the horizontal member or the bottom chord and 'the long inclined mem- ber or the top chord. The "total load" for a lean-to truss is of course the load that the full truss would carry and not the load on the half truss. The co-efficient for each member of the bottom chord is reduced by .375, .433, etc., for the several pitches. It is seen that these are the stresses of the middle portion of this chord, which, of course, has a nominal stress when the truss is supported at the peak. (By using the term nominal it is meant to convey that there is no calculable stress in the member in question.) The top chord stress in the half trusses will be reduced throughout by the amounts given on Plate III. Plates IV to VIII, inclusive, give the stresses, in terms of the panel loads P and the lengths of members, for trusses with parallel chords. The panel load for a four- panel truss is one-quarter of the total load carried by the truss; that for a five-panel truss, one-fifth; etc. At each end there is of course a half panel load. It is seen that these stresses are worked out on the assumption that the full load is applied at the top chord. If the load or any part of it is applied at the bottom chord, the compres- sion in all vertical members will be diminished by just the amount of the panel load that is transferred to the bottom chord, (or the tension in the verticals will be increased by that amount) ; the stresses in diagonal mem- bers and chords will not be affected. The stresses in Plates IV to VIII, inclusive, are for uniform load on the trusses; that is, they are for the or- dinary case of roof trusses carrying their full load and not subject to unsymmetrical loading. These diagrams would not apply to floor trusses, where the full load may not be applied uniformly; for, while they would give the maximum chord stresses, the web stresses, particularly 94 near the middle of truss, would be quite different under partial loading with the same panel loads. Plate IX shows the method of finding graphically the stresses in a common form of roof truss, whose upper chord is sloped. In this example the stress computation L simplified by omitting in the diagram loads 3, 5, and 7 and concentrating the roof loads at 2, 4, 6, and 8. The graphic diagram is made as though the vertical members of the truss were omitted. Members 2-11, 4-13, etc., would have nominal stress. Members 3-12, 5-14, etc., would have a compression equal to the panel load at 3. Very frequently graphical computation of stresses may be greatly simplified and expedited by assuming some un- important members to be absent. The stresses in ithe main members are not greatly affected by this short-cut. The method of proceedure in finding by the graphical method the stresses in a truss is as follows: First find the panel loads, and mark the same on the 'diagram. Then find the reactions, and mark these on the diagram. In the case shown on Plate IX the panel loads are the vertical forces shown at 2, 4, 6, and 8. (Note that loads 2 and 8 are \ l / 2 single panel loads and 4 and 6 are equal to two single panel loads.) The reactions are the forces shown at 10 and 18. Or- dinarily the reactions are each equal to one-half the sum of the panel loads. The next step is to letter the diagram of the truss. This is done by placing a letter below the truss, then at the ends of truss and between the panel loads, then in each triangle making up the frame of the truss. The object in this lettering is to make it possible 'to designate any member or force by naming two letters, one on each side of that member or force. Thus, in passing from the space A to the space B the reaction at the left end of truss will be crossed; that reaction is then the force AB; in passing from space B to space C the panel load at 2 is crossed; that panel load is then BC; in passing from space M to space L, the member 12-4 is crossed; that 95 member then ML, etc. The significance of this lettering of the spaces can best be understood by a study of the subsequent processes. The next step is to make a diagram of the applied loads. These loads are the two reactions and the several panel loads. These are drawn to scale. In the example on Plate IX, BA is the left-hand reaction and AF is the right-hand reaction. FE, ED, DC, and CB are the several panel loads. The arrows indicate the direction of these forces. If the reaction AB is 25,000 Ibs., the line AB in the stress diagram will be made 25 units in length on some suitable scale. All stresses and forces will be laid out or measured on this same scale. The stress diagram is then completed in the following manner. Beginning at either end of the truss, as at the right end, a line is drawn from A parallel to the member AG (or 16-18) ; then a line is drawn from F parallel to FG (or 8-18). The intersection of these lines is marked G. The length of the line FG, measured on the chosen scale, is the stress in the member FG, and the length of AG is the stress in member AG - n the former is compression, and the latter is tension, as indicated by the minus and plus signs on the members. Lines EH and GH are drawn parallell to their respective members, locating the point H. Then HJ and AJ are drawn ; then JK and DK ; then KL and AL; then LM and CM; then MN and BN. If the final line BN is found to be parallel with member 2-10 the polygon is said to "close." This is evidence that the work is correct. The diagram could have been worked up from both right and left ends of the truss at the same time, as by drawing AN and BN, NM and CM, etc. The closing line would then be one of the short lines about L, K, and J. All of the stresses in the members arc found by scaling this diagram. In order to find the sign of a stress proceed as follows: Select a point, as 4, and trace the diagram of the forces meeting at this point. This diagram is CDKLM. If the direction of one of these forces is known, the direction or sign of the others may be found thus. In this case the direction of CD is known, that is, this force is down, or toward the point4. Following the diagram around in this direction the next force is CM, which is in the direction of the arrow, or toward point 4. The next force is ML, which is also toward point 4. The next force around the polygon is LK, which is downward to the right or away from point 4. KD is toward point 4. All the members that can be replaced by forces toward point 4 are in compression. LK or the force away from point 4, is in tension. In this manner the sign of any of the stresses can be found. It is necessary to try only a few points. The top chords will be in compression and the bottom chords will be in tension. As in the case of the previously mentioned trusses the diagram of Plate IX is for uniform loading. However the method may be applied to find the stresses for any sort of loading. If the loading is unsymmetrical, the re- actions will not be equal. These reactions may be calcu- lated by taking moments around either support. The clos- ing of the polygon of forces will check the correctness of the reactions as well as other parts of the work. Plate X shows another style of roof truss and the graphical solution of the stresses in the same. The meth- ods are the same as for Plate IX. Note that the top chord of this truss is member 3-5. Members 3-4 and 4-5 act merely as supports for the panel load at 4. The diagonals in the middle quadrilateral have nominal stress. Plate XI shows a truss similar in shape to that on Plate X and a simplified method of finding the stresses in the main members. The applied loads are here con- centrated at 2 and 3. If there are other members than these main members, they may be light enough to need no special calculation. Plates XII and XIII show a detailed and a simplified method of finding the stresses in 'the truss shown, as also Plates XIV and XV. Plate XVI shows still another common form of roof truss and the graphical solution of the stresses. 97 PLATE i STRESSED IN ROOF TRUSSES TOTAL LOAD ON TRUSS - UNITY PLATE. II 5TR.E5SE5 IN R.OOF TR.US5Ev5 SPAN PLATE III STR.E55ES IN R.OOF TRUSSED SPAN TOTAL LOAD ON TRUSS is UNITY FOR A LEAN-TO (ONE- HALT or ANY OF THESE TRUSSES) THE WEB STRESSES ARE SAME AS GIVEN IN FI6S .451 TOP CHORD STRESS is DEDUCED BY. . 500 BoTrCHof?D.433@ . . 559 STRESS BY . .673$) 100 PLATE IV TRUSSED WITH PARALLEL CHORDS PLATE V TRU55E5 WITH PARALLEL CHORDS f r ^ ^ 1^ * Lr-UirJ-r- 2" .E P P P P -7- i-g l-g 1 J} / ^4-r-ir ~f -! I L I X 101 PLATE VI TR.US5E5 WITH PARALLEL CHORDS- I ' , -4B, - 2R it . 102 PLATE Vll TRUSSED WITH PARALLEL CHORDS Up IDS PLATE. VIII TRUSSES WITH PARALLEL r r r r# r* +i $ r-^-r+-r + r- i r-r-+- PH^P^ 104 PLATE IX 10 + II + + + H + > 1C * Y + 105 PLATLX 106 PLATE. XI .7 107 108 PLATLXIJI 109 PLATE XIV 110 PLATtXY 111 112 TENSION MEMBERS. In riveted trusses light tension members are usually made of angles, single or double. Flats are sometimes used, but they are troublesome in a truss, because they are apt to be buckled when the truss is riveted up. When a single angle is used in tension, its effective area should be counted as 'the area of one leg only of the angle. Thus, a 3"x3"x^" angle would be counted/ as though it were a 3"x^$" flat, a 5"x3^z"x%" angle would be counted as a 5"x^" flat, etc. This is to compensate for the lack of symmetry, or the eccentric application of the stress, and the consequent bending stress in the member. A member composed of two angles symmetrically placed with respect to the plane of the truss does not have the bending stress mentioned in the last paragraph. How- ever such angle is not good in tension for its full sec- tional area. The available area of the angle is reduced by the punching away of metal for rivet holes. Fig. I. It is seen that at section AA, Fig. 1, the area of metal in tension is equal to the full area of the angle less the prod- uct of the thickness of metal by the diameter of the rivet hole. In practice this diameter of the rivet hole is as- sumed to be I /s" greater than the nominal diameter of the rivet. It is also seen that if the hole in the other flange of the angle is near the section AA, the net area through a zig-zag line cutting both holes may be less than through the square section cutting one hole only. In detailing tension members care must be taken to see that the minmum number of rivet holes occur at or near any given transverse section. Angles having three or four rows of rivets (as 6"x3 1 /" and 6"x6" angles) usually have two rivet holes deducted in the net section. 113 IK channel sections in tension one or more rivet holes will be deducted, depending on the deail of 'the member. If the member has lattice or batten plates, that is, if the flanges are punched, two flange holes will be deducted from the gross area and as many web holes as occur in the same transverse section. Eye-bars and rods with loops at the ends are designed for tension in the full section of the bar or rod, as the eye or loop is made capable of taking the full value of the bar or rod. Bolts or rods with either plain nuts or clevis nuts at the ends are designed for tension in the full section of the bolt or rod, provided the threaded ends are upset. I the threaded ends are not upset, the value of the bolt or rod is only that of the metal in a circle whose diameter is measured at the root of the threads. Table I gives the tensile strength of rods of various diameters, the area be- ing measured at the root of threads. The unit used in the table is 10,000 Ibs. For any other unit, as 16,000 Ibs. per sq. in. multiply the tabular value by 1.6, etc. The screw threads used are Franklin Institute Standard. (See Godfrey's Tables, page 35.) TABLE I. Tensile Strength of Rods at 10,000 Ibs. per sq. in. Area Measured at Root of Threads. Dia. of Rod in In. Tensile Strength. Dia. of Rod in In. Tensile Strength. Dia. of Rod in In. Tensile Strength. M H 1/8 1% m i% IH m .1% 3020 4200 5500 6940 8910 10570 12950 15150 17440 20480 23020 2H 2y 4 2% 2y 2 2ti 2H 2H l*A z% ty* 26500 30240 34210 37160 41550 46180 51070 54290 59570 65100 70900 3^ 3tt 324 3^ 4 4H 454 4M 4^ 4^ 4^4 75500 81700 86400 93000 99900 107100 113300 120900 127400 135500 142200 114 In building work a unit stress of 16,000 Ibs. per sq. in, is usually allowed on rods and bars. The same unit is sometimes allowed on the net section of shapes such as angles and channels, though 15,000 Ibs. is preferable, be- cause of the uncertain effect of punching, and because stress is not so uniformly distributed in shapes as in rods and bars. Examples : (1) Required the section of a tension member in a light truss to take 11,000 Ibs. of stress. Here the area, at 15,000 Ibs. is .73 sq. in. The area of one leg of a 3"x2^"x YA!' angle is .75 sq. in. This could be used. A \Y%" rod, not upset has a tensile strength, by Table I, at 16,000 Ibs. per sq. in., of 11,100 Ibs. This rod could be used, if the style of truss permit. (2) Required the section of a member to take a tensile stress of 35,000 Ibs. The net area required, at 15,000 Ibs. per sq. in., is 2.33 sq. in. If the member is composed of 2 angles, each angle will have a net area of 1.17 sq. in. or a gross area, adding .33 sq. in. for the rivet hole, of about 1.50 sq. in. A 3"x3"xj/4" angle has a net area of 1.44 .22=1.22 sq. in. (The deduction of .22 is for a H" rivet hole or %x^4.) Two such angles could be used. (3) Required the section of an upset rod to take a stress of 80,000 Ibs. The area, at 16,000 Ibs. per sq. in., is 5 sq. in. By reference to a table of the area of rounds (Godfrey's Tables, page 61, et seq.) it is found that a 2 9-16" round rod would be required. If two rods were used, each should have a diameter of 1 13-16." Tension members in timber trusses are usually made of steel or iron rods, though the bottom chords are often made of wood. The section required is usually determined by the detail at the ends or splices. Wooden members do not admit of very efficient details for tension. A large portion of a wooden tension member may be notched away for the splice or bored out for bolts. A tensile stress of 1,200 Ibs. per sq. in. for white pine and 1,600 Ibs. 115 per sq. in. for yellow pine or white oak may be allowed on ithe net section of the wood. COMPRESSION MEMBERS. The selection of the size of compression members in a truss should be carried out by the methods of Chapter IV. Tables IV and V of that chapter, as stated in the chapter, are for single angles as members having square- ended or rigid details. In an ordinary light truss, if a single angle is used in compression, only about half of the value shown in Tables IV and V should be used as safe values of the members. Tables VI ito IX, inclusive, of Chapter IV may be used for truss members without any reduction of the tabular load. In general it is best to select standard angles and a small number of different sizes for any given truss. TRUSS MEMBERS IN BENDING. Truss members are sometimes subject to transverse or bending stresses as well as direct stress ('tension or com- pression). Such members must be designed for both bend- ing and direct stress, the unit stress in the steel being kept within certain limits. When all of the load on a truss is cencentrated in beams 'that connect to the truss at the panel points only, there will be no bending in the truss members, but direct stress only. The roof load, however, is very frequently dis- tributed uniformly along the top chord of a truss or con- centrated in beams or purlins that do not connect to the truss at panel points. The top chord must then act as a beam as well as a compression member and must be de- signed accordingly. A member suitable for this condi- tion is deep vertically. Examples of such members are. two angles of unequal legs with the long legs vertical, two channels, two angles of equal legs with a deep plate riv- eted between them. In wooden trusses of course 'the mem- ber is made deeper in the vertical dimension than in the horizontal. 116 There is much variation in the practice of designing members under combined direct and bending stress. There is also very frequently little attention paid to the neces- sity for care in such designing. The rigid or correct treatment of the problem will not be given here, as it in- volves structural engineering principles outside of the scope of this book. Approximate methods only will be given here. They will be found to be safe, though not wasteful ; the results will be close to correct theoretical methods and very much superior to the guess-work so often resorted to. WOODEN TRUSS MEMBERS IN BENDING. First find the actual or equivalent uniform load on the member by the methods of Chapter VI. Then fmd the value of C, that is, the product of the uniform load by the span in feet. The span in feet is the horizontal dis- tance between the panel points or supports of the member considered. (It is not the inclined distance for inclined members.) Next find in Table I of Chapter VI a section whose value C is greater than that just computed, for a trial design. Then find by Chapter IV, using Table T, the value of 'this member in compression. Now compare the value of C required with that of the member selected 'as also the actual compression 'in the member with its allowed compression, and add these two ratios ; they should equal unity. Thus, if the member is under 7-10 of its allowed bending, it may carry at the same titre 3-10 of its allowed compression. If the sum of the ratios is greater than unity, select a heavier or deeper member ; if less than unity, select a lighter section. Examples : (1) Required the section of a rafter five feet long on the slope and four feet in the horizontal direction, carry- ing a load of 400 Ibs. per horizontal foot and subject to 10,000 Ibs. of compression. In this case C is 400X4X4= 6,400. A4"x6" in white pine has a value C= 12,800, by Table I, Chapter VI. The rafter would be stayed hori- zontally by the joists resting upon it, hence the unsup- 117 ported dimension would be six inches. The ratio of this to the length of rafter is 10. By Table I, Chapter IV, the allowed unit stress for this ratio is 820 Ibs. per sq. in. The member is then good for a compressive stress of 820X24=19,680 Ibs. The member is thus subject to .50 of its allowed bending value and .51 of its allowed com- pression. The sum of these two is 1.01, and the member is therefore correct. (2) Required the i size of a horizontal chord mem- ber 10 ft. between panel points, the roof load being 600 Ibs. per foot and the compression being 28,000 Ibs. The roof beams are five feet apart, that is, at panel points and midway between panel points. In this case C=600XlOX 10=60,000. In yellow pine a 4x16 piece has a value C=l 13,770. For compression the unsupported length is 5 ft. and the width is 4 in. The ratio for Table I, Chap- ter IV, is 15 and by interpolation the unit stress is found to be 730 Ibs. per sq. in. The allowed compression is 730X4X16=46,720 Ibs. The bending is then .53 of the capacity and the compression .60. This gives a total of 1.13 which is more than the limit. The member could be 5"xl6", or by trial it will be seen that 6"xl4" would be somewhat stronger than necessary. This could be made of three 2"xl4" pieces spiked or bolted together. STEEL, TRUSS MEMBERS IN BENDING. The same method of proceedure would be used for steel members as for wooden members except that the load is found in tons and Q instead of C thus found. Examples : (1) Required the section of a top chord member 4 ft. long, the compression being 75,000 Ibs. and the load per ft. on the chord 1,000 Ibs. Here the load per panel on the chord is 4,000 Ibs. or 2 tons and Q is 8. In Table V, Chapter VI, it is seen that Q for two angles 6"x4"xf", with the long legs vertical, is 2x17.7=35.4. In Table VI, Chapter IV, it is seen that this same section 4 ft. long has a strength in compression of 98,000 Ibs. 75,000 di- vided by 98,000=r.77, and 8 divided by 35.4 .23. The sum 118 of these two ratios is just unity; hence this section is correct. (2) Given a top chord supporting a reinforced con- crete slab. Panel length, 12 ft.; compression, 80,000 Ibs.; load per ft, 1,600 Ibs. The total load on a panel is!2X 1,600 Ibs. or 9.6 tons, and Q is 115.2. By Table II, Chap- ter VI, Q for 2-12" channels 20.5 Ibs, is 228.1. By Table XVI, Chapter IV, the same channels in compression for a length of 12 ft. will carry 161,000 Ibs. The sum of the two ratios will be found to be close to unity. It is to be noted that this channel section would not be good for 161,000 Ibs. if it were not supported continuously or at close intervals laterally, or unless the channels were sepa- rated and latticed, as indicated in Table XVI, Chapter IV. A common method of providing for bending in the top chord of a roof truss is by using a web plate between two angles, such sections as shown in Godfrey's Tables, page 122. By using the section modulus as found in that table the stress in such member due single shear would govern, at 2,760. Note that the values in the table between the heavy zig-zag lines are greater than single shear and less than double shear. I o o i Fig. I. The strength of the connection shown in Fig. 2 is the double shear value of two rivets, or four times the single shear value of one rivet, for to fail in shear eaoh of these rivets must be sheared twice. The strength of the connection is also that of two rivets in bearing against the plate or the double thickness of angles. If, for exam- ple, a 5^-in. plate be used and ^-in. angles, -the thick- ness of plate will govern so far as bearing is concerned, and in %-in. rivets the strength is 9,840X2 or 19,680 Ibs. Double shear on two rivets is good for 5,410X4, or 21,640 Ibs. The former value governs. If the plate were 11/16 in. or more in thickness, shear would govern. In ^4 -in. rivets shear would govern with the 5^-in. plate. This is indicated by the zig-zag line of Table I. The foregoing rules and principles apply for rinding the strength of the end connections of tension or compression members, or the strength of tension splices, or the strength of the end connection of beams and girders. 129 The rivets in any riveted connection should be sym- metrically disposed about the line of application of the stress, insofar as it is practicable to effect this condition. This is to avoid eccentric stress on the rivets. If it is necessary to place rivets unsymmetrical with respect to the line of stress, additional rivets must be used. No rivet connection should be made with less than two rivets, preferably not less than three. Fig. 3. Frequently, in order to cut down the size of the gusset plate, lug angles are used to take some of the rivets in the end connection of a member as shown on the diagonal members of Fig. 3. Generally the larger number of rivets should be in the member itself. Tension Splices. Splices in tension members should be made with splicing pieces having a net sectional area through any cross section (whether at right angles, dia- gonally, or zig-zag across the section) equal to the net sectional area of the piece cut. There must be rivets enough on each side of the cut to take the full stress in the member spliced. Compression Splices. Splices in compression members are generally made by planing the ends of the members square, so that they will fit exactly one on the other and providing a sufficient number of splice plates to hold these planed ends rigidly in line. In building columns made of I-shaped sections there should be a plate on the outside of each flange with about 130 six rivets above and below the cut in each plate. There should also be a plate on each side of the web of the column. In columns made of two channels and two plates it is preferable to use a horizontal plate besides the splices on the cover plates. The reason for this is that the webs of the channels may not be opposite one another, and splicing plates on these webs cannot be riveted, as the section is a closed one. Wherever there is a change in the general size of a col- umn there should be horizontal plates used in the splice, so as to distribute the load of the upper column into the lower. When only a portion of a compression member is cut and spliced, the full area and the full number of rivets should be used in the splice, even though the spliced part has the ends milled for a bearing ; for in building up such piece in the shop the milled ends may not be in contact. It is practically impossible to insure close contact. End Connections of Beams. The end connections of beams are commonly made according to the standards found in the Carnegie Pocket Companion (or Godfrey's Tables, pages 37 and 38). Channels should have the same symmetrical end con- nection as beams of the same depth. Where this is not practicable, a 6"X6" angle may be used with two rows of rivets in each leg. Beams connecting to columns are usually supported on a shelf angle riveted to the column and are riveted through the flange to the same. An upper angle, shipped loose with the column, is riveted in the field to the top flange of the beam and to the column. When more than four rivets are required to carry a beam or a girder on a shelf, stiffener angles are used to take the additional rivets. These should be placed with the outstanding legs directly under the beam. 131 End Connections of Girders. When a girder rests on a support such as the top of a column or a shelf having stiffeners under it, the metal of the column or of stiffener angles or diaphragms in the head of the column or the stiffener angles below the shelf should be directly oppo- site the metal of the end stiffeners of the girder. This is an important feature of design that is very often over- looked. It is illustrated in Fig. 4. If the end angles of this girder were turned with the outstanding legs at the end of girder, these angles would not be opposite the metal of the channel of the column. The result would be excessive bending either in the top plate of the colmun or in the flange angles of the girder. g o o o o 1 o \ o o o I I Pin 4. r in 5 J IJJ.3 When the end connection of a girder is with angles connecting to the web of the girder, there must be enough rivets through the web of the girder to take the full end reaction of the girder. These rivets are in bear- ing on the web of the girder, even though some of them pass through the flanges of the angles also. If there is not room enough for the required number of rivets, on the basis of this bearing value in the web, the fillers can be extended as in Fig. 5. The four additional rivets shown in this figure unite these fillers and the web plate so as to increase the value of the five rivets in the angles. The field rivets in the girder connection of Fig. 5 will have a strength of 14 rivets in single shear or in bear- ing either on the angles or the metal to which they con- ilCt. 132 Seven-eighth-inch rivets are used in flanges as nar- row as 3 inches;, $4-in. rivets, in flanges as narrow as 2% inches; ^-in. rivets, in flanges as narrow as 2 inches. When it is known that %-in. rivets are to be used, the design must be made with this fact in view and flanges less than 2^ in. wide must not be placed where rivets will have to be driven in them. The same must be ob- served with other sizes. It is preferable, because of econ- omy in the shop, to use only one size of rivet in a piece of work. An exception may be made in the case of chan- nel flanges, as these must often take smaller rivets than the rest of the work. They must be handled twice in any event to punch web and flange holes, as these require sepa- rate dies. Rivets should be spaced not less than three diameters apart center to center, nor generally more than six inches apart. They should not be closer to the edge of metal than about two diameters (two times the diameter of the rivet). Lattice bars for single lacing should be about 60 de- grees with the axis of the member. Lattice bars for dou- ble lacing should be about 45 degrees with the axis of the member. Some common sizes of lattice bars, with the depth of member in which they may be used are given in the following- list : Size of bar. Depth of member. Size of rivets. iy 2X y 4 mx y 4 2 x5/16 2^x & 2^x7/16 6 in. and under 7 to 8 in. 9 to 12 in. 13 to 16 in. 17 in. and upward 5 /s 5/8 tt H tt or % In general rivets should not be used in tension, that is, in stress that tends to pull the heads off. If it is neces- sary to use rivets in tension no less than four should be used in the joint, and these must be symmetrical with the application of the load. The angles used should be of thick metal, so that they will not bend under the load, pre- ferably V% in. or ^ in. thick. 133 For tension on rivet heads use no more than one half of the single shear value. Separators are made either of short pieces of gas pipe or of castings. (See Godfrey's Tables, page 33.) These are the pieces that are placed between double beams to hold them a given distance apart and to take the bolts that united the beams. Usually separators in double beam work are placed about 4 or 5 feet apart. The office of separators in some cases is to distribute load that may be applied to one beam only of a pair, so that they will deflect together. In cases where afll or nearly all of the load is delivered to one beam of a pair, as when floor- beams connect to the web of one beam of the pair, ordi- nary cast separators are not sufficient. In such cases there should be riveted diaphragms between the beams. These may be opposite the beam connections. Beams resting on walls should have anchors at the ends. The usual anchor is a plain 24-in. round rod 6 in. long .for beams up to 10 in. and 12 in. long for larger beams. A hole is punched in the web of the beam 2 in to 4 in. from the end to receive the anchor. The anchor rod is usually kinked at the middle. A pair of 6x4 angles 2 or 3 in. long, riveted to the web of the beam, may also be used as an anchor. Details in Timber Trusses. The details in timber work are very often neglected or given little consideration, or they may be left to the workmen to work out on the job. The strength of bolts and spikes can not be so definitely determined as that of rivets in steel work. Some stand- dard, however, should be used. The following table is recommended for ordinary conditions in sound wood of the hardness of yellow pine. For white pine deduct 20 per cent. 134 TABLE II. VALUE OF BOLTS OR SPIKES IN SHEAR. Diameter in ins. y 8 3/16 Y 4 5/16 3/ 8 y 2 5/ 8 ti 7 /s 1 Load in Ibs. 40 80 150 200 300 500 800 1200 1600 2000 Table. II is based primarily on the value of a spike or bolt in bending, for in the ordinary case the spike will bend in the wood before it will shear off. In using the term shear in the heading of the table it is meant to con- vey the idea that the stress on the bolt or spike is at right angles to the axis. It is assumed that the thickness of the wood will be such as to give proper bearing against the same, as, for example, not less than one-inch boards for J.^-in. bolts, and not less than 2-in. boards for one-inch bolts. If the pressure is tranverse with the grain of the wood, use one-half of the values in Table I. The distance between bolts along the grain and from a bolt to the end of a piece should not be less than about six times the diameter of the bolt. Fig. 6. Fi 9- 7 Figs. 6 and 7 illustrate two kinds of splices in wood. For full efficiency in the splice of Fig. 6 the sum of the widths of the two splicing pieces (if of wood) should be equal to the piece spliced, or 2h should equal b. However, the full tensile strength of members in wood is not often demanded. In a 4"x8" piece with one-inch bolts the net section would be 4\6=24 S q. m . At 1,600 Ibs. per sq. 135 in. this would take a tension of 38,400 Ibs. The six bolts in double shear are good for 12X2,000=24,000 Ibs. The distances a should be six inches. The splice shown in Fig. 7 is with steel or cast iron plates having gibs at the ends. Here the bolts are used to hold the plates together, cy^e measures the net area in tension. 2gXe measures the area in bearing against the gibs, which has a value of 800 and 1,000 Ibs. per sq. in. for white pine and yellow pine respectively. 2/X? mea- sures the area in shear along the grain. Wood is par- ticularly weak in this respect, so that a comparatively large area is needed here. For white pine use 80 Ibs. per sq. in., and for yellow pine use 100 Ibs. per sq. in. for this shearing value. One of the most important and difficult details to take care of in wood is this one, where the wood is in longi- tudinal shear. In many details the wood is notched, as for the inclined end post of a truss, and a tension is ap- plied at this notch. Frequently the distance from this notch to the end of the piece is not sufficient to develop the tension of the piece at a proper safe shear on the fibers of the wood. Figs. 8 to 15 inclusive show various methods of con- necting the inclined end post or rafter to the bottom chord or tie in a wooden truss. Trusses are often built up of two-inch plank as indi- cated in Fig. 8. They may be bolted or spiked together. Filling or separating blocks should be used at interme- diate points in long compression members. There are sev- eral advantages in this kind of construction. Pieces can be more easily handled, details can be more readily made, and the lighter pieces are in better condition for season- ing. The diagram in Fig. 11 indicates the method of finding the tension in the bolt. The side ba of the triangle is the stress in the rafter. On the same scale be is the tension in. the bolt. 136 Fig. \ 5 137 Fig. 1 9. If ^ Fig ZO 138 Figs. 16 to 20 inclusive show other details in wooden construction. Attention is called to the caps or corbels in Fig. 20. The one marked CD, together with the knee braces, could be counted upon to relieve the load in the timber beam above the post, if that load is a symmetrical one; but AB can- not offer such aid except by putting a bending moment in the post. It is an error to rely upon such construction as that shown to the left of Fig. 20 for any other pur- pose than to brace the building. 139 CHAPTER XI. Estimating Loads. For estimating the load carried by a beam or truss, use the following data : Wood 4 Ibs. per sq. ft. one inch thick Stone concrete 13 " " " ' Cinder concrete 9 ' Brick walls 10 Stone walls (not granite) 13 Granite 14 Lime mortar 9 Hollow brick arches weigh about 8 Ibs. per sq. ft. per inch of thickness. Ordinary tile arches weigh about 4 Ibs. per sq. ft. per inch of thickness. Tile partitions weigh as follows: WEIGHT PER SQ. FT. 2-in. 3-in. 4-in. 5-in. 6-in. Semi-porous . . . . 12 Ibs. 15 Ibs. 16 Ibs. 18 Ibs. 24 Ibs. Porous 14 Ibs. 17 Ibs. 18 Ibs. 20 Ibs. 26 Ibs. Book tile or flat tile for ceilings and roofs are made in lengths of 16, 18 and 20 inches in 2-in. tile; 16, 18, 20 and 24 inches in 3-in, tile ; and 24 inches in 4-in. tile. The 2-in. tile weigh 12 Ibs. per sq. ft. ; the 3-in. tile, 20 Ibs. per sq. ft.; the 4-in. tile, 22 Ibs. per sq. ft. For wooden shingles on a roof allow 2*4 Ibs. per sq. ft., for slate shingles allow 5 to 7 Ibs. per sq. ft. For Spanish tiles allow 7>^ to 8 Ibs. per sq. ft. For tarred felt and gravel or slag allow 2 Ibs. per sq. ft. for the felt and tar, 3 Ibs. per sq. ft. for slag, and 4 Ibs. per sq. ft. for gravel. For slate tiles allow 14 Ibs. per sq. ft. per inch of thick- ness. For solid clay tiles allow 11 Ibs. per sq. ft. per inch of thickness 140 For corrugated steel in gages of 16, 18, 20 and 22, allow 3.6, 2.7, 1.9 and 1.5 Ibs. per sq. ft. respectively. In ordinary floor work the steel beams will weigh, in pounds per sq ft of floor, about one-third of the span in ft, and the girders one-fifth of their span in feet Thus, if the span of the beams is 15 ft., use 5 Ibs. per sq. ft. for a trial weight or the beams; if the span of the girders is 20 ft., use 4 Ibs. per sq. ft. for a trial weight of the girders. For trusses carrying roof loads only use one-tenth of the span for a trial load per sq. ft. For steel columns estimate the weight per lineal foot at about four times the area of the section in square inches. Ordinary partitions in a building are usually considered as covered in the allowance for live load. When an al- lowance is made for their weight, it may be in a uniform load of say 5 or 10 Ibs. per sq. ft. Fire walls around elevator shafts and 'the like are taken at their full weight for the beam on which they are built. For exterior walls, estimate the weight per running foot for a solid wall and deduct the proportion of the wall oc- cupied by windows or other openings. The New York Building Code allows a reduction of the live load on columns carrying several floors as fol- lows : For top story use full live load. For next story use full live load. For each succeeding story deduct 5 per cent from full live load until 50 per cent of live load is reached. Use 50 per cent of live load for all remaining stories. 141 INDEX Allowed pressure on soils, Allowed stresses in rein- forced concrete beams, 65. Allowed stresses on wooden posts, 18. Allowed stress on cast iron posts, 21. Anchorage of rods, 63, 64. Anchors for beams, 134. Angles in bending, capacity of 59. Areas of squares and cir- cles, 21. Batten plates on posts, 29, Beams, 49, 74. Beam seats, 24. Bearing plates, 88. Bearing power of soils, 3. Bending moments on beams, 54. Bending moments on gird- ers, 76, 77. Bethlehem beams, 58, 59. Bethlehem columns, 28. Bolts, 128. Bolts and spikes in wood, 135 Box girders, 77, 78, 89, 90, 91. Bracing of beams. 51, 52. Bracing of buildings, 1. C, (coefficient), 49. Cantilevers, 54, 57, 91. Capacity of beams, 58-60. Capacity of box girders, 78, 90. Capacity of plate girders, 81, 82. Cast iron bases for columns, 14, 15. Cast iron beams, 50. Cast iron column details, 24 Cast iron columns, 20-24. Channel columns, 27, 28, 42- Clay, bearing power of , 3. Column bases, 14, 15. Column footings, 8, 11. 12, 13. Column formulas, 25. Column loads, 16. Columns and other com- " pression members, 16-46. Columns, loading of . 17. Compression members, 16- 46, 116. Concrete piles, 5. Concrete steel columns, 32, 33 Corbels, 139. Cover plates, 77, 78, 79, 84, 86. Depth of beams, 49, 52, 63. Details of timber trusses, 134-139. Diameter of reinforcing rods, 63. End connections of beams, 131. End connections of girders, 132. Estimating loads, 140, 141. Eye-bars, 114. Factor of safety, 25. Flange plates, 77, 78, 79, 84, 86. Floor arches and slabs, 121- 126. Footings, 7-13. Foundations, 3-6. Gas pipe columns, 28, 29, 37. Girder beams, capacity of, 59. Girders, 75-92. Graphical calculation or stresses, 95-97. Grillages, 11. Hooks in rods, 63. I-beam columns, 27. I-beams, capacity of , 58. Knee braces, 139. lattice bars, 133. Lattice in columns, 29. Lean-to trusses, 94. Limits of column lengths 27. Lintels, 47, 48. Lintels, cast iron , 50. Loop rods, 115. 142 Weedle beams, 10. Net section of members, 113, 114. Openings in floors, 125, 126. Panel loads, 95. Partitions, weight of , 16, 141. Piles, 5. Plate girders, 80-84. Pressure on footings, calcu- lation of , 5. Q, (coefficient), 61. Single angles in tension, 113. Splices, 131, 135, 136. Spreading beams, 56. Star-shaped columns, 27, 36. Steel beams, 51-60. Steel columns, 25-30. Steel truss members in bending, 118, 119. Stiffeners in girders, 85, 87, 132. Stirrups in reinforced con- crete beams, 61, 62. Straight line formula, 26. Strength of columns, 25. Structural details, 127-139. Batio of slenderness, 18, 26. Reinforced channel beams, 77, 78. Reinforced concrete beams, 61-74. Reinforced concrete beam tables. 69-74. Reinforced concrete col- umns, 30-32. Reinforced concrete slabs, 123-126. Reinforced I-beams, 77, 78. Rivets in tension, 133, 134. Rivets, 127-130, 133. Rivet spacing in girders, 84, 89. Rules for reinforced con- crete beam design, 62-64. Selecting column sections, 30. Separators, 12, 134. Settlement of buildings, 4, 6. Sharp bends in rods, 61, 63. Shear in plate girders, 83, 84, 85. Shear on wood, 136. Shear reinforcement in re- inforced concrete beams, 63, 65, 66. Sheet piling, 4. Sign of stresses, 93, 96, 97. Single angle columns, 28, 29, 34. Tee-bars in bending, capac- ity of , 60. Tensile strength of thread- ed rods, 114. Tie rods, 121, 122. Tile arches, 121, 122. Tension members, 113, 114, 115. Trusses, 93-120. Truss members in bending, 116. Unbraced beams, 52. Wall footings, 7, 10. Wall plates, 88. Walls, weight of , 17. Webs of plate girders, 85. Width of reinforced con- crete beams, 64. Wooden beams, 49, 50. Wooden columns, 17-19. Wooden piles, 5. Wooden post splice, 19. Wooden truss members in bending, 117. Zee-bar columns, 28. Zee-bars in bending, capaO ity , 60. 143 WILSON ROLLING DOORS, either steel or wood, are the most satisfactory method of clos- ing openings. They afford an absolute protection, are easy to operate, difficult to destroy, and last but not least, they cost little to erect. If you are interested write for the fine catalogue we have prepared on the subject and for full size detail sheets. Your request will bring them postpaid. J. G. WILSON MANUFACTURING CO. Bancroft Building, NEW YORK, 148 "TOCKOLITH" (Patented) A CEMENT PAINT which will render immune to corrosion, all metals to which it is applied. In setting, "Tockolith" generates Calcium Hy- droxide (Lime) in minute quantities, and, this material being the best inhibitive, prevents the metal from rusting. Tockolith should be second-coated with one of our "R. I. W." DAMP RESISTING PAINTS, as a guard against electrolysis. "DIFFERENT FROM ALL OTHER PAINTS." TOCH BROTHERS Established 1848. - Manufacturers of - TECHNICAL PAINTS, ENAMELS, VARNISHES AND DAMPPROOFING COMPOUNDS. 320 Fifth Avenue, NEW YORK, N. Y. WORKS: Long Island City, N. Y. and Toronto, Ont.. Can. Fireproof In Reality Not Only In Name. X s !? 1 ANCHOR ISO By the use of re-inforced concrete construction, the walls, floors and partitions of a building may be made fireproof. By the use of "Dahlstrom" Metal Doors and Trim the fire- proofing is completed, and protection is provided for the contents and the lives of the occupants of such a building, making it "Absolutely" fireproof in reality, as well as in name. The illustrations herewith show different methods of prop- erly installing "Dahlstrom" Doors and Trim in reinforced concrete partitions. In Section No. 1 is shown an angle iron frame connected by perforated anchor plates. The frames are shop made to proper size for the doors and are set in position before the concrete is poured. The concrete passing through the per- forations will securely anchor the frame in position and affords a good fastening for the finished Metal Trim. Section No. 2 shows perforated channel shaped clips of sizes to suit the thickness of the concrete. These are laid in the forms as the concrete is poured, leaving the 2" flanges exposed on each side of the partition after the forms are taken down. A I"xj4" channel is 'then applied by machine screws which are tapped into the flanges of the perforated clips. These channels will then serve as grounds for the plaster, and also to fasten the finished steel jambs to, which are made adjustable so as to take up any possible variation in the thickness of the partition. Another method of construction for concrete partition is shown in section No. 3. In this case the bucks are of re-in- forced concrete made up separately and erected before the partitions are placed. Provision for fastening the flanges of the steel jambs is made by sleeves or holes through the bucks, through which the fastening bolts can pass. Additional information and submis- sion drawings to meet special re- quirements will be cheerfully furn- ished by applying to Dahlstrom Metallic Door Co. Executive Offices and Factories, 3 BLACXSTONE AVENUE. JAMESTOWN, N. Y. Why Every Man Who Is Interested In Con* crete Design or Construction Should have a Copy of "CONCRETE" by Edward Godfrey BECAUSE it is not an automatic designer, but aims to show how to design by teaching the principles of design. BECAUSE There are things in this book that are not found in any other book in any language. BECAUSE the book points out many prevalent errors in current and permanent literature on the subject of con- crete construction. Some of these errors are the work and the utterances of the most eminent engineers and authorities enjoying the highest reputation. BECAUSE it contains 444 pages of live information on this live subject. BECAUSE it tells how to design concrete and reinforced concrete beams, slabs, columns, chimneys, arches, domes, conical roofs, vaults, retaining walls, dams, foundations, etc. It tells also how not to design these. BECAUSE it contains a series of articles that appeared in the Engineering News in 1906, which brought out so much discussion that, after filling 36 columns with the articles and discussion, the editor refused to print any more, un- less something very important and new should be brought out. All of these articles and the discussion are reprinted in the book. BECAUSE it contains a series of articles published in 1907 in Concrete Engineering, which also brought out much discussion. Three of these articles were very fully quoted in that excellent periodical, The Engineering Digest. BECAUSE it contains 31 pages of drawings showing standard practice in culverts, arch centering, piers, etc. These are from current periodicals and show actual struc- tures. BECAUSE it contains over 160 pages of information on the properties and use of cement, concrete, steel, etc., fin- ishing of concrete surfaces, designing forms, and other practical information. BECAUSE the theoretical portion is given in the sim- plest possible manner, at the same time being as thorough ac the materials demand. 152 BECAUSE the reader is treated as a reasoning being and not a child to accept dogma and "say so." BECAUSE "It contains a large amount of very good ma- terial" Engineering-Contracting, May 6, '08. BECAUSE "A thorough exposition of the properties of concrete and cement is given. * * To those unfamiliar with Mr. Godfrey's articles * * * this work will prove interest- ing and valuable reading. The rather novel method which he uses * * makes the book valuable * * and adds an ele- ment of interest to the reading that practicalfy all techni- cal works lack. Altogether Mr. Godfrey's work is a valu- able contribution to the literature of concrete and concrete engineering." Engineering Digest, May, '08. BECAUSE "It has a truly flexible back, is printed on good paper, and the workmanship is first class. * * The book is full of meat and good things. * * There is a lot of spice in it. * * The book has so much of good in it that every man who possesses a satisfying amount of knowledge of rein- forced concrete will enjoy reading it. The handy pocket size and good binding make it a book one can take on the cars to read." The Contractor, April, '08. BECAUSE "The text is written straight to the point, free from unnecessary technicalities and full of practical points. The tables and illustrations are of value, and the book at its price should prove an excellent investment to the worker in reinforced concrete, whether he is engin- eer, foreman or designer." Concrete, April, '08. BECAUSE "In his theory the author is sound." Engin- eering News, May 14, '08. BECAUSE the price is only $2.50 net. WHY EVERY MAN WHO IS INTERESTED IN THE DESIGN OF STEEL STRUCTURES SHOULD HAVE A COPY OF GODFREY'S TABLES. BECAUSE it is the best book of its kind in the English language. "The author of these Tables' has produced a work that is in many respects distinctly ahead of anything yet pub- lished in the English language. * * As a whole the book represents a very useful collection of structural tables, and a very compact one." Engineering News. 153 Godfrey's Tables [Structural Engineering, Book One] This book is a compilation of tables and data for use in structural designing. About one-third of it is collected from manufacturer's hand-books and includes such data as the properties of rolled sections, standards for bolts and rivets, eyebar tables, fractions to decimals, and other tables common to many books and indespen- sable to the designer. Besides the foregoing there is more new matter in the book than in any other simi- lar book published. There is scarcely a problem in struc- tural designing or detailing in which this book will not be found useful. The book contains more than 200 pages. Following is a list of the contents: Decimals of a foot and inch. Properties and useful dimensions of beams, channels, angles, zees, tees, rails. Information on eyebars, clevises, sleevenuts, separators, nuts, rivets, bolts, cir- cular and rectangular plates, corrugated and buckled plates. Standard beam connections. Bending moments on beams for concentrated and uniform loads. Deflec- tion formulas in terms of fibre stress, new. Working unit stresses on columns. Ultimate strength of tank plates, new. Weights of substances. Conversion table for French units. Moments of inertia of rectangles varying by eights, new. Weights and areas of rods, bars, and plates. Mensuration, lengths of curves and areas if segments, new. Miscellaneous formulas in usable shape (brake bands, hoops, cylinders, springs, flat plates, R. R. curves, etc.) Skewdetails, hip and val- ley details, no angles used, new. Stresses in eight styles of roof trusses, four pitches each. Moments, shears, etc., Cooper E 50 loading Tables of built girders, new. Over 2000 built sections with their properties. Functions of angles. Typical' details, 38 pages. Tables of roots and circular areas. Tables of squares of num- bers to 2736. Tables of squares of feet, inches, and fractions for finding hypothenuse, lengths to 57 feet, new. Gears, chain, rope. Electric cranes, clearances, loads, etc. All of this in a small pocktbook. Could anything be more useful to a structural designer, draftsman or stu- dent? 154 JNO. J. CONE ROBERT W. HUNT D. w. MCNAUGHER JAS. C. HALLSTED ROBERT W. HUNT 4 CO, ENGINEERS BUREAU OF INSPECTION, TESTS AND CONSULTATION Thoroughly equipped Chemical and Physical Laboratories maintained at Chicago, New York, San Francisco 4 London. Inspection and tests of Rails and Fastenings, Locomotives, Cars, Pipe, Bridges, Buildings, Machinery and 2nd hand equipment. Examination and reports on existing structures. Reviews of metal and concrete-steel construction. CHICAGO : 1121 The Rookery NEW YORK : PITTSBURG : 90 West Street Monongahela Bank Building LONDON : Norfolk House, Cannon Street, E. C. MONTREAL: SAN FRANCISCO : Board of Trade Building 425 Washington Street 155 GODFREY PATENT RETAINING WALL 6B68 See Engineering News, Oct. 18, 1906. See Engineering-Contracting, Dec. 21, 1910. See Engineering-Contracting, Jan. 18, 1911. \ A complete description of this retaining wall will be found in the above references, as well as the method of designing such walls. This is the safest design for rein- forced concrete retaining walls that is before the public. It is also economical. For further information address Edward Godfrey, Monongahela Bank Building, Pittsburg, Penn'a. 156 II 5 Q Z i o m o 1 K> CO fe ,co GENERAL LIBRARY -U.C. BERKELEY BDocmsssi 268762 UNIVERSITY OF CALIFORNIA LIBRARY